From 3d3368ed9988a2acb9d247eb120ae82c6c64f673 Mon Sep 17 00:00:00 2001 From: Jacob Gissinger Date: Fri, 9 Dec 2022 12:02:09 -0500 Subject: [PATCH 01/47] Update Packages_details.rst --- doc/src/Packages_details.rst | 10 ++++++---- 1 file changed, 6 insertions(+), 4 deletions(-) diff --git a/doc/src/Packages_details.rst b/doc/src/Packages_details.rst index ecbc54233a..4d230af51a 100644 --- a/doc/src/Packages_details.rst +++ b/doc/src/Packages_details.rst @@ -2548,11 +2548,12 @@ Topology changes are defined in pre- and post-reaction molecule templates and can include creation and deletion of bonds, angles, dihedrals, impropers, atom types, bond types, angle types, dihedral types, improper types, and/or atomic charges. Other options currently -available include reaction constraints (e.g. angle and Arrhenius +available include reaction constraints (e.g., angle and Arrhenius constraints), deletion of reaction byproducts or other small -molecules, and chiral-sensitive reactions. +molecules, creation of new atoms or molecules bonded to existing +atoms, and using LAMMPS variables for input parameters. -**Author:** Jacob R. Gissinger (CU Boulder) while at NASA Langley Research Center. +**Author:** Jacob R. Gissinger (NASA Langley Research Center). **Supporting info:** @@ -2562,7 +2563,8 @@ molecules, and chiral-sensitive reactions. * examples/PACKAGES/reaction * `2017 LAMMPS Workshop `_ * `2019 LAMMPS Workshop `_ -* reacter.org +* `2021 LAMMPS Workshop `_ +* `reacter.org `_ ---------- From 72789904c399e55f632d7fe27cc1808ea921fc57 Mon Sep 17 00:00:00 2001 From: Jacob Gissinger Date: Fri, 9 Dec 2022 15:35:14 -0500 Subject: [PATCH 02/47] Update packages_details.rst take 2 --- doc/src/Packages_details.rst | 20 ++++++++++---------- 1 file changed, 10 insertions(+), 10 deletions(-) diff --git a/doc/src/Packages_details.rst b/doc/src/Packages_details.rst index 4d230af51a..55eb918a49 100644 --- a/doc/src/Packages_details.rst +++ b/doc/src/Packages_details.rst @@ -2542,15 +2542,15 @@ REACTION package **Contents:** -This package allows for complex bond topology changes (reactions) -during a running MD simulation, when using classical force fields. -Topology changes are defined in pre- and post-reaction molecule -templates and can include creation and deletion of bonds, angles, -dihedrals, impropers, atom types, bond types, angle types, dihedral -types, improper types, and/or atomic charges. Other options currently -available include reaction constraints (e.g., angle and Arrhenius -constraints), deletion of reaction byproducts or other small -molecules, creation of new atoms or molecules bonded to existing +This package implements the REACTER protocol, which allows for complex +bond topology changes (reactions) during a running MD simulation when +using classical force fields. Topology changes are defined in pre- and +post-reaction molecule templates and can include creation and deletion +of bonds, angles, dihedrals, impropers, atom types, bond types, angle +types, dihedral types, improper types, and/or atomic charges. Other +options currently available include reaction constraints (e.g., angle +and Arrhenius constraints), deletion of reaction byproducts or other +small molecules, creation of new atoms or molecules bonded to existing atoms, and using LAMMPS variables for input parameters. **Author:** Jacob R. Gissinger (NASA Langley Research Center). @@ -2564,7 +2564,7 @@ atoms, and using LAMMPS variables for input parameters. * `2017 LAMMPS Workshop `_ * `2019 LAMMPS Workshop `_ * `2021 LAMMPS Workshop `_ -* `reacter.org `_ +* `REACTER website (reacter.org) `_ ---------- From db13738056299fca4da202ead726fe8b992b761b Mon Sep 17 00:00:00 2001 From: Jacob Gissinger Date: Fri, 9 Dec 2022 17:52:05 -0500 Subject: [PATCH 03/47] Update bond/react readme --- src/REACTION/README | 10 +++++++--- 1 file changed, 7 insertions(+), 3 deletions(-) diff --git a/src/REACTION/README b/src/REACTION/README index f5fc929c9d..99a5d604ec 100644 --- a/src/REACTION/README +++ b/src/REACTION/README @@ -13,12 +13,16 @@ crosslinked materials. Any number of competing or reversible reaction pathways can be specified, and reacting sites can be stabilized. Other advanced options currently available include reaction constraints (e.g. angle and Arrhenius constraints), deletion of reaction -byproducts or other small molecules, and chiral-sensitive reactions. +byproducts or other small molecules, creation of new atoms or +molecules bonded to existing atoms, and using LAMMPS variables for +input parameters. The REACTER methodology is detailed in: Gissinger et al., Polymer 128, 211-217 (2017) https://doi.org/10.1016/j.polymer.2017.09.038 + Gissinger et al., Macromolecules 53, 22, 9953-9961 (2020). + https://doi.org/10.1021/acs.macromol.0c02012 + This package was created by Jacob Gissinger -(jacob.r.gissinger@gmail.com), while at the NASA Langley Research -Center. +(jacob.r.gissinger@gmail.com) at the NASA Langley Research Center. From 0375a7569ecbf706f34400b34fd428a6ff933a52 Mon Sep 17 00:00:00 2001 From: Jacob Gissinger Date: Mon, 12 Dec 2022 17:08:42 -0500 Subject: [PATCH 04/47] type labels for tiny_epoxy example --- .../tiny_epoxy/in.tiny_epoxy.stabilized | 16 +- .../log.20Nov19.tiny_epoxy.stabilized.g++.1 | 172 - .../log.20Nov19.tiny_epoxy.stabilized.g++.4 | 172 - .../log.4Nov2022.tiny_epoxy.stabilized.g++.1 | 189 + .../log.4Nov2022.tiny_epoxy.stabilized.g++.4 | 190 + .../tiny_epoxy/rxn1_stp1_post.data_template | 315 -- .../rxn1_stp1_post.molecule_template | 317 ++ .../tiny_epoxy/rxn1_stp1_pre.data_template | 301 -- .../rxn1_stp1_pre.molecule_template | 307 ++ .../tiny_epoxy/rxn1_stp2_post.data_template | 307 -- .../rxn1_stp2_post.molecule_template | 313 ++ .../tiny_epoxy/rxn2_stp1_post.data_template | 424 --- .../rxn2_stp1_post.molecule_template | 425 +++ .../tiny_epoxy/rxn2_stp1_pre.data_template | 407 -- .../rxn2_stp1_pre.molecule_template | 412 +++ .../tiny_epoxy/rxn2_stp2_post.data_template | 413 --- .../rxn2_stp2_post.molecule_template | 418 +++ .../reaction/tiny_epoxy/tiny_epoxy.data | 3261 +++++++++-------- 18 files changed, 4301 insertions(+), 4058 deletions(-) delete mode 100644 examples/PACKAGES/reaction/tiny_epoxy/log.20Nov19.tiny_epoxy.stabilized.g++.1 delete mode 100644 examples/PACKAGES/reaction/tiny_epoxy/log.20Nov19.tiny_epoxy.stabilized.g++.4 create mode 100644 examples/PACKAGES/reaction/tiny_epoxy/log.4Nov2022.tiny_epoxy.stabilized.g++.1 create mode 100644 examples/PACKAGES/reaction/tiny_epoxy/log.4Nov2022.tiny_epoxy.stabilized.g++.4 delete mode 100644 examples/PACKAGES/reaction/tiny_epoxy/rxn1_stp1_post.data_template create mode 100644 examples/PACKAGES/reaction/tiny_epoxy/rxn1_stp1_post.molecule_template delete mode 100644 examples/PACKAGES/reaction/tiny_epoxy/rxn1_stp1_pre.data_template create mode 100644 examples/PACKAGES/reaction/tiny_epoxy/rxn1_stp1_pre.molecule_template delete mode 100644 examples/PACKAGES/reaction/tiny_epoxy/rxn1_stp2_post.data_template create mode 100644 examples/PACKAGES/reaction/tiny_epoxy/rxn1_stp2_post.molecule_template delete mode 100644 examples/PACKAGES/reaction/tiny_epoxy/rxn2_stp1_post.data_template create mode 100644 examples/PACKAGES/reaction/tiny_epoxy/rxn2_stp1_post.molecule_template delete mode 100644 examples/PACKAGES/reaction/tiny_epoxy/rxn2_stp1_pre.data_template create mode 100644 examples/PACKAGES/reaction/tiny_epoxy/rxn2_stp1_pre.molecule_template delete mode 100644 examples/PACKAGES/reaction/tiny_epoxy/rxn2_stp2_post.data_template create mode 100644 examples/PACKAGES/reaction/tiny_epoxy/rxn2_stp2_post.molecule_template diff --git a/examples/PACKAGES/reaction/tiny_epoxy/in.tiny_epoxy.stabilized b/examples/PACKAGES/reaction/tiny_epoxy/in.tiny_epoxy.stabilized index 0e6e97cd46..1309eff3a3 100644 --- a/examples/PACKAGES/reaction/tiny_epoxy/in.tiny_epoxy.stabilized +++ b/examples/PACKAGES/reaction/tiny_epoxy/in.tiny_epoxy.stabilized @@ -9,9 +9,9 @@ atom_style full pair_style lj/class2 8 -angle_style class2 +angle_style class2 -bond_style class2 +bond_style class2 dihedral_style class2 @@ -21,12 +21,12 @@ read_data tiny_epoxy.data velocity all create 300.0 4928459 dist gaussian -molecule mol1 rxn1_stp1_pre.data_template -molecule mol2 rxn1_stp1_post.data_template -molecule mol3 rxn1_stp2_post.data_template -molecule mol4 rxn2_stp1_pre.data_template -molecule mol5 rxn2_stp1_post.data_template -molecule mol6 rxn2_stp2_post.data_template +molecule mol1 rxn1_stp1_pre.molecule_template +molecule mol2 rxn1_stp1_post.molecule_template +molecule mol3 rxn1_stp2_post.molecule_template +molecule mol4 rxn2_stp1_pre.molecule_template +molecule mol5 rxn2_stp1_post.molecule_template +molecule mol6 rxn2_stp2_post.molecule_template thermo 50 diff --git a/examples/PACKAGES/reaction/tiny_epoxy/log.20Nov19.tiny_epoxy.stabilized.g++.1 b/examples/PACKAGES/reaction/tiny_epoxy/log.20Nov19.tiny_epoxy.stabilized.g++.1 deleted file mode 100644 index 6ca0361513..0000000000 --- a/examples/PACKAGES/reaction/tiny_epoxy/log.20Nov19.tiny_epoxy.stabilized.g++.1 +++ /dev/null @@ -1,172 +0,0 @@ -LAMMPS (20 Nov 2019) - -WARNING-WARNING-WARNING-WARNING-WARNING -This LAMMPS executable was compiled using C++98 compatibility. -Please report the compiler info below at https://github.com/lammps/lammps/issues/1659 -GNU C++ 4.8.5 -WARNING-WARNING-WARNING-WARNING-WARNING - -Reading data file ... - orthogonal box = (10 -10 -15) to (30 20 10) - 1 by 1 by 1 MPI processor grid - reading atoms ... - 118 atoms - scanning bonds ... - 4 = max bonds/atom - scanning angles ... - 6 = max angles/atom - scanning dihedrals ... - 18 = max dihedrals/atom - scanning impropers ... - 4 = max impropers/atom - reading bonds ... - 123 bonds - reading angles ... - 221 angles - reading dihedrals ... - 302 dihedrals - reading impropers ... - 115 impropers -Finding 1-2 1-3 1-4 neighbors ... - special bond factors lj: 0 0 0 - special bond factors coul: 0 0 0 - 4 = max # of 1-2 neighbors - 10 = max # of 1-3 neighbors - 19 = max # of 1-4 neighbors - 22 = max # of special neighbors - special bonds CPU = 0.000286808 secs - read_data CPU = 0.00724107 secs -Read molecule mol1: - 31 atoms with max type 10 - 30 bonds with max type 15 - 53 angles with max type 29 - 66 dihedrals with max type 39 - 31 impropers with max type 5 -Read molecule mol2: - 31 atoms with max type 10 - 30 bonds with max type 17 - 55 angles with max type 36 - 75 dihedrals with max type 51 - 34 impropers with max type 5 -Read molecule mol3: - 31 atoms with max type 11 - 30 bonds with max type 18 - 53 angles with max type 37 - 72 dihedrals with max type 53 - 31 impropers with max type 5 -Read molecule mol4: - 42 atoms with max type 11 - 41 bonds with max type 18 - 73 angles with max type 41 - 96 dihedrals with max type 54 - 43 impropers with max type 5 -Read molecule mol5: - 42 atoms with max type 11 - 41 bonds with max type 18 - 75 angles with max type 37 - 108 dihedrals with max type 53 - 46 impropers with max type 5 -Read molecule mol6: - 42 atoms with max type 11 - 41 bonds with max type 19 - 73 angles with max type 50 - 102 dihedrals with max type 66 - 43 impropers with max type 22 -dynamic group bond_react_MASTER_group defined -dynamic group statted_grp_REACT defined -Neighbor list info ... - update every 1 steps, delay 10 steps, check yes - max neighbors/atom: 2000, page size: 100000 - master list distance cutoff = 10 - ghost atom cutoff = 10 - binsize = 5, bins = 4 6 5 - 2 neighbor lists, perpetual/occasional/extra = 1 1 0 - (1) pair lj/class2, perpetual - attributes: half, newton on - pair build: half/bin/newton - stencil: half/bin/3d/newton - bin: standard - (2) fix bond/react, occasional, copy from (1) - attributes: half, newton on - pair build: copy - stencil: none - bin: none -Setting up Verlet run ... - Unit style : real - Current step : 0 - Time step : 1 -Per MPI rank memory allocation (min/avg/max) = 17.28 | 17.28 | 17.28 Mbytes -Step Temp f_rxns[1] f_rxns[2] f_rxns[3] f_rxns[4] - 0 300 0 0 0 0 - 50 391.52956 1 0 0 0 - 100 475.26826 1 1 0 0 - 150 605.26215 1 1 1 0 - 200 545.7485 1 1 1 0 - 250 461.64929 1 1 1 1 - 300 452.10611 1 1 1 1 - 350 379.61671 1 1 1 1 - 400 331.22444 1 1 1 1 - 450 275.63969 1 1 1 1 - 500 316.63407 1 1 1 1 - 550 261.39841 1 1 1 1 - 600 313.70928 1 1 1 1 - 650 294.24011 1 1 1 1 - 700 285.81736 1 1 1 1 - 750 340.37496 1 1 1 1 - 800 333.2496 1 1 1 1 - 850 307.40826 1 1 1 1 - 900 304.68718 1 1 1 1 - 950 328.0289 1 1 1 1 - 1000 290.22808 1 1 1 1 - 1050 272.78518 1 1 1 1 - 1100 291.30546 1 1 1 1 - 1150 320.33992 1 1 1 1 - 1200 330.57057 1 1 1 1 - 1250 300.51008 1 1 1 1 - 1300 293.6209 1 1 1 1 - 1350 324.36604 1 1 1 1 - 1400 331.15408 1 1 1 1 - 1450 302.23396 1 1 1 1 - 1500 297.55562 1 1 1 1 - 1550 277.3187 1 1 1 1 - 1600 289.66052 1 1 1 1 - 1650 281.85404 1 1 1 1 - 1700 293.4999 1 1 1 1 - 1750 306.21866 1 1 1 1 - 1800 283.22696 1 1 1 1 - 1850 295.10473 1 1 1 1 - 1900 317.3843 1 1 1 1 - 1950 305.14825 1 1 1 1 - 2000 289.00911 1 1 1 1 -Loop time of 1.87066 on 1 procs for 2000 steps with 118 atoms - -Performance: 92.374 ns/day, 0.260 hours/ns, 1069.141 timesteps/s -98.4% CPU use with 1 MPI tasks x no OpenMP threads - -MPI task timing breakdown: -Section | min time | avg time | max time |%varavg| %total ---------------------------------------------------------------- -Pair | 0.12832 | 0.12832 | 0.12832 | 0.0 | 6.86 -Bond | 0.77458 | 0.77458 | 0.77458 | 0.0 | 41.41 -Neigh | 0.45068 | 0.45068 | 0.45068 | 0.0 | 24.09 -Comm | 0.029785 | 0.029785 | 0.029785 | 0.0 | 1.59 -Output | 0.31635 | 0.31635 | 0.31635 | 0.0 | 16.91 -Modify | 0.16657 | 0.16657 | 0.16657 | 0.0 | 8.90 -Other | | 0.004368 | | | 0.23 - -Nlocal: 118 ave 118 max 118 min -Histogram: 1 0 0 0 0 0 0 0 0 0 -Nghost: 332 ave 332 max 332 min -Histogram: 1 0 0 0 0 0 0 0 0 0 -Neighs: 4338 ave 4338 max 4338 min -Histogram: 1 0 0 0 0 0 0 0 0 0 - -Total # of neighbors = 4338 -Ave neighs/atom = 36.7627 -Ave special neighs/atom = 10.5763 -Neighbor list builds = 2000 -Dangerous builds = 0 - -Please see the log.cite file for references relevant to this simulation - -Total wall time: 0:00:02 diff --git a/examples/PACKAGES/reaction/tiny_epoxy/log.20Nov19.tiny_epoxy.stabilized.g++.4 b/examples/PACKAGES/reaction/tiny_epoxy/log.20Nov19.tiny_epoxy.stabilized.g++.4 deleted file mode 100644 index 4673ba3980..0000000000 --- a/examples/PACKAGES/reaction/tiny_epoxy/log.20Nov19.tiny_epoxy.stabilized.g++.4 +++ /dev/null @@ -1,172 +0,0 @@ -LAMMPS (20 Nov 2019) - -WARNING-WARNING-WARNING-WARNING-WARNING -This LAMMPS executable was compiled using C++98 compatibility. -Please report the compiler info below at https://github.com/lammps/lammps/issues/1659 -GNU C++ 4.8.5 -WARNING-WARNING-WARNING-WARNING-WARNING - -Reading data file ... - orthogonal box = (10 -10 -15) to (30 20 10) - 1 by 2 by 2 MPI processor grid - reading atoms ... - 118 atoms - scanning bonds ... - 4 = max bonds/atom - scanning angles ... - 6 = max angles/atom - scanning dihedrals ... - 18 = max dihedrals/atom - scanning impropers ... - 4 = max impropers/atom - reading bonds ... - 123 bonds - reading angles ... - 221 angles - reading dihedrals ... - 302 dihedrals - reading impropers ... - 115 impropers -Finding 1-2 1-3 1-4 neighbors ... - special bond factors lj: 0 0 0 - special bond factors coul: 0 0 0 - 4 = max # of 1-2 neighbors - 10 = max # of 1-3 neighbors - 19 = max # of 1-4 neighbors - 22 = max # of special neighbors - special bonds CPU = 0.000239905 secs - read_data CPU = 0.0080783 secs -Read molecule mol1: - 31 atoms with max type 10 - 30 bonds with max type 15 - 53 angles with max type 29 - 66 dihedrals with max type 39 - 31 impropers with max type 5 -Read molecule mol2: - 31 atoms with max type 10 - 30 bonds with max type 17 - 55 angles with max type 36 - 75 dihedrals with max type 51 - 34 impropers with max type 5 -Read molecule mol3: - 31 atoms with max type 11 - 30 bonds with max type 18 - 53 angles with max type 37 - 72 dihedrals with max type 53 - 31 impropers with max type 5 -Read molecule mol4: - 42 atoms with max type 11 - 41 bonds with max type 18 - 73 angles with max type 41 - 96 dihedrals with max type 54 - 43 impropers with max type 5 -Read molecule mol5: - 42 atoms with max type 11 - 41 bonds with max type 18 - 75 angles with max type 37 - 108 dihedrals with max type 53 - 46 impropers with max type 5 -Read molecule mol6: - 42 atoms with max type 11 - 41 bonds with max type 19 - 73 angles with max type 50 - 102 dihedrals with max type 66 - 43 impropers with max type 22 -dynamic group bond_react_MASTER_group defined -dynamic group statted_grp_REACT defined -Neighbor list info ... - update every 1 steps, delay 10 steps, check yes - max neighbors/atom: 2000, page size: 100000 - master list distance cutoff = 10 - ghost atom cutoff = 10 - binsize = 5, bins = 4 6 5 - 2 neighbor lists, perpetual/occasional/extra = 1 1 0 - (1) pair lj/class2, perpetual - attributes: half, newton on - pair build: half/bin/newton - stencil: half/bin/3d/newton - bin: standard - (2) fix bond/react, occasional, copy from (1) - attributes: half, newton on - pair build: copy - stencil: none - bin: none -Setting up Verlet run ... - Unit style : real - Current step : 0 - Time step : 1 -Per MPI rank memory allocation (min/avg/max) = 16.26 | 16.45 | 16.63 Mbytes -Step Temp f_rxns[1] f_rxns[2] f_rxns[3] f_rxns[4] - 0 300 0 0 0 0 - 50 391.52956 1 0 0 0 - 100 475.26826 1 1 0 0 - 150 605.26215 1 1 1 0 - 200 545.7485 1 1 1 0 - 250 461.64929 1 1 1 1 - 300 452.10611 1 1 1 1 - 350 379.61671 1 1 1 1 - 400 331.22444 1 1 1 1 - 450 275.63969 1 1 1 1 - 500 316.63407 1 1 1 1 - 550 261.39841 1 1 1 1 - 600 313.70928 1 1 1 1 - 650 294.24011 1 1 1 1 - 700 285.81736 1 1 1 1 - 750 340.37496 1 1 1 1 - 800 333.2496 1 1 1 1 - 850 307.40826 1 1 1 1 - 900 304.68718 1 1 1 1 - 950 328.0289 1 1 1 1 - 1000 290.22808 1 1 1 1 - 1050 272.78518 1 1 1 1 - 1100 291.30546 1 1 1 1 - 1150 320.33992 1 1 1 1 - 1200 330.57057 1 1 1 1 - 1250 300.51008 1 1 1 1 - 1300 293.6209 1 1 1 1 - 1350 324.36604 1 1 1 1 - 1400 331.15408 1 1 1 1 - 1450 302.23396 1 1 1 1 - 1500 297.55562 1 1 1 1 - 1550 277.3187 1 1 1 1 - 1600 289.66052 1 1 1 1 - 1650 281.85404 1 1 1 1 - 1700 293.4999 1 1 1 1 - 1750 306.21866 1 1 1 1 - 1800 283.22695 1 1 1 1 - 1850 295.10472 1 1 1 1 - 1900 317.38431 1 1 1 1 - 1950 305.14824 1 1 1 1 - 2000 289.00909 1 1 1 1 -Loop time of 0.689125 on 4 procs for 2000 steps with 118 atoms - -Performance: 250.753 ns/day, 0.096 hours/ns, 2902.231 timesteps/s -100.0% CPU use with 4 MPI tasks x no OpenMP threads - -MPI task timing breakdown: -Section | min time | avg time | max time |%varavg| %total ---------------------------------------------------------------- -Pair | 0.02002 | 0.030617 | 0.053133 | 7.7 | 4.44 -Bond | 0.10356 | 0.18908 | 0.22691 | 11.6 | 27.44 -Neigh | 0.16721 | 0.17002 | 0.17247 | 0.5 | 24.67 -Comm | 0.057286 | 0.12002 | 0.21612 | 17.0 | 17.42 -Output | 0.00028991 | 0.00034121 | 0.00049323 | 0.0 | 0.05 -Modify | 0.17626 | 0.17675 | 0.17721 | 0.1 | 25.65 -Other | | 0.002287 | | | 0.33 - -Nlocal: 29.5 ave 41 max 18 min -Histogram: 1 0 0 1 0 0 1 0 0 1 -Nghost: 306 ave 349 max 269 min -Histogram: 1 1 0 0 0 0 1 0 0 1 -Neighs: 1084.5 ave 2154 max 397 min -Histogram: 1 0 1 1 0 0 0 0 0 1 - -Total # of neighbors = 4338 -Ave neighs/atom = 36.7627 -Ave special neighs/atom = 10.5763 -Neighbor list builds = 2000 -Dangerous builds = 0 - -Please see the log.cite file for references relevant to this simulation - -Total wall time: 0:00:01 diff --git a/examples/PACKAGES/reaction/tiny_epoxy/log.4Nov2022.tiny_epoxy.stabilized.g++.1 b/examples/PACKAGES/reaction/tiny_epoxy/log.4Nov2022.tiny_epoxy.stabilized.g++.1 new file mode 100644 index 0000000000..b5eb8c4157 --- /dev/null +++ b/examples/PACKAGES/reaction/tiny_epoxy/log.4Nov2022.tiny_epoxy.stabilized.g++.1 @@ -0,0 +1,189 @@ +LAMMPS (4 Nov 2022) +Reading data file ... + orthogonal box = (10 -10 -15) to (30 20 10) + 1 by 1 by 1 MPI processor grid + reading atom labelmap ... + reading bond labelmap ... + reading angle labelmap ... + reading dihedral labelmap ... + reading improper labelmap ... + reading atoms ... + 118 atoms + scanning bonds ... + 4 = max bonds/atom + scanning angles ... + 6 = max angles/atom + scanning dihedrals ... + 18 = max dihedrals/atom + scanning impropers ... + 4 = max impropers/atom + reading bonds ... + 123 bonds + reading angles ... + 221 angles + reading dihedrals ... + 302 dihedrals + reading impropers ... + 115 impropers +Finding 1-2 1-3 1-4 neighbors ... + special bond factors lj: 0 0 0 + special bond factors coul: 0 0 0 + 4 = max # of 1-2 neighbors + 10 = max # of 1-3 neighbors + 19 = max # of 1-4 neighbors + 22 = max # of special neighbors + special bonds CPU = 0.000 seconds + read_data CPU = 0.022 seconds +Read molecule template mol1: + 1 molecules + 0 fragments + 31 atoms with max type 10 + 30 bonds with max type 15 + 53 angles with max type 29 + 66 dihedrals with max type 39 + 3 impropers with max type 5 +Read molecule template mol2: + 1 molecules + 0 fragments + 31 atoms with max type 10 + 30 bonds with max type 17 + 55 angles with max type 36 + 75 dihedrals with max type 51 + 2 impropers with max type 5 +Read molecule template mol3: + 1 molecules + 0 fragments + 31 atoms with max type 11 + 30 bonds with max type 18 + 53 angles with max type 37 + 72 dihedrals with max type 53 + 3 impropers with max type 5 +Read molecule template mol4: + 1 molecules + 0 fragments + 42 atoms with max type 11 + 41 bonds with max type 18 + 73 angles with max type 41 + 96 dihedrals with max type 54 + 3 impropers with max type 5 +Read molecule template mol5: + 1 molecules + 0 fragments + 42 atoms with max type 11 + 41 bonds with max type 18 + 75 angles with max type 37 + 108 dihedrals with max type 53 + 2 impropers with max type 5 +Read molecule template mol6: + 1 molecules + 0 fragments + 42 atoms with max type 11 + 41 bonds with max type 19 + 73 angles with max type 50 + 102 dihedrals with max type 66 + 3 impropers with max type 22 +dynamic group bond_react_MASTER_group defined +dynamic group statted_grp_REACT defined + +CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE + +Your simulation uses code contributions which should be cited: +- fix bond/react: reacter.org doi:10.1016/j.polymer.2017.09.038, doi:10.1021/acs.macromol.0c02012 +The log file lists these citations in BibTeX format. + +CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE + +Generated 55 of 55 mixed pair_coeff terms from sixthpower/geometric mixing rule +Neighbor list info ... + update: every = 1 steps, delay = 0 steps, check = yes + max neighbors/atom: 2000, page size: 100000 + master list distance cutoff = 10 + ghost atom cutoff = 10 + binsize = 5, bins = 4 6 5 + 2 neighbor lists, perpetual/occasional/extra = 1 1 0 + (1) pair lj/class2, perpetual + attributes: half, newton on + pair build: half/bin/newton + stencil: half/bin/3d + bin: standard + (2) fix bond/react, occasional, copy from (1) + attributes: half, newton on + pair build: copy + stencil: none + bin: none +Setting up Verlet run ... + Unit style : real + Current step : 0 + Time step : 1 +Per MPI rank memory allocation (min/avg/max) = 16.64 | 16.64 | 16.64 Mbytes + Step Temp f_rxns[1] f_rxns[2] f_rxns[3] f_rxns[4] + 0 300 0 0 0 0 + 50 378.29345 1 0 0 0 + 100 471.04152 1 1 0 0 + 150 583.79755 1 1 1 0 + 200 526.00812 1 1 1 1 + 250 429.56812 1 1 1 1 + 300 512.54655 1 1 1 1 + 350 461.18357 1 1 1 1 + 400 379.38965 1 1 1 1 + 450 424.89528 1 1 1 1 + 500 324.72257 1 1 1 1 + 550 302.91042 1 1 1 1 + 600 253.80911 1 1 1 1 + 650 252.90262 1 1 1 1 + 700 270.62628 1 1 1 1 + 750 311.64391 1 1 1 1 + 800 318.9413 1 1 1 1 + 850 354.20196 1 1 1 1 + 900 302.19641 1 1 1 1 + 950 316.97905 1 1 1 1 + 1000 303.08194 1 1 1 1 + 1050 317.51619 1 1 1 1 + 1100 287.57204 1 1 1 1 + 1150 226.72101 1 1 1 1 + 1200 283.97519 1 1 1 1 + 1250 287.0607 1 1 1 1 + 1300 327.65278 1 1 1 1 + 1350 316.06809 1 1 1 1 + 1400 337.69947 1 1 1 1 + 1450 326.12278 1 1 1 1 + 1500 300.89265 1 1 1 1 + 1550 325.2415 1 1 1 1 + 1600 294.1844 1 1 1 1 + 1650 293.98596 1 1 1 1 + 1700 317.35477 1 1 1 1 + 1750 296.97768 1 1 1 1 + 1800 274.97297 1 1 1 1 + 1850 335.36697 1 1 1 1 + 1900 315.3756 1 1 1 1 + 1950 260.65335 1 1 1 1 + 2000 354.03612 1 1 1 1 +Loop time of 0.909774 on 1 procs for 2000 steps with 118 atoms + +Performance: 189.937 ns/day, 0.126 hours/ns, 2198.347 timesteps/s, 259.405 katom-step/s +100.0% CPU use with 1 MPI tasks x no OpenMP threads + +MPI task timing breakdown: +Section | min time | avg time | max time |%varavg| %total +--------------------------------------------------------------- +Pair | 0.10261 | 0.10261 | 0.10261 | 0.0 | 11.28 +Bond | 0.63695 | 0.63695 | 0.63695 | 0.0 | 70.01 +Neigh | 0.013916 | 0.013916 | 0.013916 | 0.0 | 1.53 +Comm | 0.0057214 | 0.0057214 | 0.0057214 | 0.0 | 0.63 +Output | 0.0005856 | 0.0005856 | 0.0005856 | 0.0 | 0.06 +Modify | 0.14641 | 0.14641 | 0.14641 | 0.0 | 16.09 +Other | | 0.003576 | | | 0.39 + +Nlocal: 118 ave 118 max 118 min +Histogram: 1 0 0 0 0 0 0 0 0 0 +Nghost: 372 ave 372 max 372 min +Histogram: 1 0 0 0 0 0 0 0 0 0 +Neighs: 3487 ave 3487 max 3487 min +Histogram: 1 0 0 0 0 0 0 0 0 0 + +Total # of neighbors = 3487 +Ave neighs/atom = 29.550847 +Ave special neighs/atom = 10.576271 +Neighbor list builds = 68 +Dangerous builds = 0 +Total wall time: 0:00:01 diff --git a/examples/PACKAGES/reaction/tiny_epoxy/log.4Nov2022.tiny_epoxy.stabilized.g++.4 b/examples/PACKAGES/reaction/tiny_epoxy/log.4Nov2022.tiny_epoxy.stabilized.g++.4 new file mode 100644 index 0000000000..5d6ac8ab21 --- /dev/null +++ b/examples/PACKAGES/reaction/tiny_epoxy/log.4Nov2022.tiny_epoxy.stabilized.g++.4 @@ -0,0 +1,190 @@ +LAMMPS (4 Nov 2022) +WARNING: Using I/O redirection is unreliable with parallel runs. Better use -in switch to read input file. (../lammps.cpp:529) +Reading data file ... + orthogonal box = (10 -10 -15) to (30 20 10) + 1 by 2 by 2 MPI processor grid + reading atom labelmap ... + reading bond labelmap ... + reading angle labelmap ... + reading dihedral labelmap ... + reading improper labelmap ... + reading atoms ... + 118 atoms + scanning bonds ... + 4 = max bonds/atom + scanning angles ... + 6 = max angles/atom + scanning dihedrals ... + 18 = max dihedrals/atom + scanning impropers ... + 4 = max impropers/atom + reading bonds ... + 123 bonds + reading angles ... + 221 angles + reading dihedrals ... + 302 dihedrals + reading impropers ... + 115 impropers +Finding 1-2 1-3 1-4 neighbors ... + special bond factors lj: 0 0 0 + special bond factors coul: 0 0 0 + 4 = max # of 1-2 neighbors + 10 = max # of 1-3 neighbors + 19 = max # of 1-4 neighbors + 22 = max # of special neighbors + special bonds CPU = 0.000 seconds + read_data CPU = 0.009 seconds +Read molecule template mol1: + 1 molecules + 0 fragments + 31 atoms with max type 10 + 30 bonds with max type 15 + 53 angles with max type 29 + 66 dihedrals with max type 39 + 3 impropers with max type 5 +Read molecule template mol2: + 1 molecules + 0 fragments + 31 atoms with max type 10 + 30 bonds with max type 17 + 55 angles with max type 36 + 75 dihedrals with max type 51 + 2 impropers with max type 5 +Read molecule template mol3: + 1 molecules + 0 fragments + 31 atoms with max type 11 + 30 bonds with max type 18 + 53 angles with max type 37 + 72 dihedrals with max type 53 + 3 impropers with max type 5 +Read molecule template mol4: + 1 molecules + 0 fragments + 42 atoms with max type 11 + 41 bonds with max type 18 + 73 angles with max type 41 + 96 dihedrals with max type 54 + 3 impropers with max type 5 +Read molecule template mol5: + 1 molecules + 0 fragments + 42 atoms with max type 11 + 41 bonds with max type 18 + 75 angles with max type 37 + 108 dihedrals with max type 53 + 2 impropers with max type 5 +Read molecule template mol6: + 1 molecules + 0 fragments + 42 atoms with max type 11 + 41 bonds with max type 19 + 73 angles with max type 50 + 102 dihedrals with max type 66 + 3 impropers with max type 22 +dynamic group bond_react_MASTER_group defined +dynamic group statted_grp_REACT defined + +CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE + +Your simulation uses code contributions which should be cited: +- fix bond/react: reacter.org doi:10.1016/j.polymer.2017.09.038, doi:10.1021/acs.macromol.0c02012 +The log file lists these citations in BibTeX format. + +CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE + +Generated 55 of 55 mixed pair_coeff terms from sixthpower/geometric mixing rule +Neighbor list info ... + update: every = 1 steps, delay = 0 steps, check = yes + max neighbors/atom: 2000, page size: 100000 + master list distance cutoff = 10 + ghost atom cutoff = 10 + binsize = 5, bins = 4 6 5 + 2 neighbor lists, perpetual/occasional/extra = 1 1 0 + (1) pair lj/class2, perpetual + attributes: half, newton on + pair build: half/bin/newton + stencil: half/bin/3d + bin: standard + (2) fix bond/react, occasional, copy from (1) + attributes: half, newton on + pair build: copy + stencil: none + bin: none +Setting up Verlet run ... + Unit style : real + Current step : 0 + Time step : 1 +Per MPI rank memory allocation (min/avg/max) = 16.63 | 16.63 | 16.64 Mbytes + Step Temp f_rxns[1] f_rxns[2] f_rxns[3] f_rxns[4] + 0 300 0 0 0 0 + 50 378.29345 1 0 0 0 + 100 471.04152 1 1 0 0 + 150 583.79755 1 1 1 0 + 200 526.00812 1 1 1 1 + 250 429.56812 1 1 1 1 + 300 512.54655 1 1 1 1 + 350 461.18357 1 1 1 1 + 400 379.38965 1 1 1 1 + 450 424.89528 1 1 1 1 + 500 324.72257 1 1 1 1 + 550 302.91042 1 1 1 1 + 600 253.80911 1 1 1 1 + 650 252.90262 1 1 1 1 + 700 270.62628 1 1 1 1 + 750 311.64391 1 1 1 1 + 800 318.9413 1 1 1 1 + 850 354.20196 1 1 1 1 + 900 302.19641 1 1 1 1 + 950 316.97905 1 1 1 1 + 1000 303.08194 1 1 1 1 + 1050 317.51619 1 1 1 1 + 1100 287.57204 1 1 1 1 + 1150 226.72101 1 1 1 1 + 1200 283.97519 1 1 1 1 + 1250 287.0607 1 1 1 1 + 1300 327.65278 1 1 1 1 + 1350 316.06809 1 1 1 1 + 1400 337.69947 1 1 1 1 + 1450 326.12278 1 1 1 1 + 1500 300.89265 1 1 1 1 + 1550 325.2415 1 1 1 1 + 1600 294.1844 1 1 1 1 + 1650 293.98596 1 1 1 1 + 1700 317.35477 1 1 1 1 + 1750 296.97768 1 1 1 1 + 1800 274.97297 1 1 1 1 + 1850 335.36698 1 1 1 1 + 1900 315.3756 1 1 1 1 + 1950 260.65334 1 1 1 1 + 2000 354.03612 1 1 1 1 +Loop time of 0.473184 on 4 procs for 2000 steps with 118 atoms + +Performance: 365.186 ns/day, 0.066 hours/ns, 4226.686 timesteps/s, 498.749 katom-step/s +100.0% CPU use with 4 MPI tasks x no OpenMP threads + +MPI task timing breakdown: +Section | min time | avg time | max time |%varavg| %total +--------------------------------------------------------------- +Pair | 0.01651 | 0.024868 | 0.039209 | 5.4 | 5.26 +Bond | 0.072805 | 0.16458 | 0.21783 | 13.9 | 34.78 +Neigh | 0.0056701 | 0.0057265 | 0.0057792 | 0.1 | 1.21 +Comm | 0.028105 | 0.095922 | 0.19546 | 20.3 | 20.27 +Output | 0.00034311 | 0.00041507 | 0.0006278 | 0.0 | 0.09 +Modify | 0.17725 | 0.17761 | 0.17826 | 0.1 | 37.54 +Other | | 0.004064 | | | 0.86 + +Nlocal: 29.5 ave 45 max 7 min +Histogram: 1 0 0 0 0 0 1 1 0 1 +Nghost: 315 ave 343 max 287 min +Histogram: 1 1 0 0 0 0 0 0 1 1 +Neighs: 871.75 ave 1772 max 236 min +Histogram: 1 0 1 1 0 0 0 0 0 1 + +Total # of neighbors = 3487 +Ave neighs/atom = 29.550847 +Ave special neighs/atom = 10.576271 +Neighbor list builds = 68 +Dangerous builds = 0 +Total wall time: 0:00:00 diff --git a/examples/PACKAGES/reaction/tiny_epoxy/rxn1_stp1_post.data_template b/examples/PACKAGES/reaction/tiny_epoxy/rxn1_stp1_post.data_template deleted file mode 100644 index e510883432..0000000000 --- a/examples/PACKAGES/reaction/tiny_epoxy/rxn1_stp1_post.data_template +++ /dev/null @@ -1,315 +0,0 @@ -rxn1_stp1_post - -31 atoms -30 bonds -55 angles -75 dihedrals -34 impropers - -Types - -1 1 -2 6 -3 1 -4 7 -5 4 -6 7 -7 8 -8 8 -9 8 -10 8 -11 8 -12 9 -13 1 -14 1 -15 9 -16 9 -17 1 -18 1 -19 10 -20 8 -21 8 -22 8 -23 8 -24 10 -25 10 -26 10 -27 10 -28 8 -29 8 -30 8 -31 8 - -Charges - -1 0.000000 -2 0.000000 -3 0.000000 -4 0.100000 -5 0.000000 -6 0.000000 -7 0.000000 -8 0.000000 -9 0.000000 -10 0.000000 -11 0.000000 -12 0.000000 -13 0.000000 -14 0.000000 -15 -0.025000 -16 -0.025000 -17 0.000000 -18 0.000000 -19 0.000000 -20 0.000000 -21 0.000000 -22 0.000000 -23 0.000000 -24 0.000000 -25 0.000000 -26 0.000000 -27 0.000000 -28 0.000000 -29 0.000000 -30 0.000000 -31 0.000000 - -Coords - -1 22.582573 10.988183 -5.014054 -2 23.904713 10.750493 -4.202215 -3 23.989172 9.487042 -3.323374 -4 24.067001 11.723383 -4.037435 -5 24.627851 7.325302 -3.319944 -6 24.554632 8.418972 -4.080365 -7 22.667763 11.445703 -5.999605 -8 21.787441 10.247643 -4.916974 -9 24.964962 10.712683 -4.449374 -10 24.616703 9.689913 -2.456034 -11 22.989313 9.208153 -2.991455 -12 18.808882 13.758042 -3.958724 -13 19.293213 12.549683 -3.196594 -14 20.810543 12.417832 -3.417504 -15 21.090193 12.251203 -4.891234 -16 17.657042 16.437199 -3.985224 -17 19.126713 16.210239 -4.245154 -18 19.589151 14.957593 -3.479565 -19 19.000433 13.609432 -5.041715 -20 18.761223 11.614392 -3.573184 -21 19.082903 12.688992 -2.085145 -22 21.202852 11.511562 -2.848624 -23 21.328482 13.360252 -3.038924 -24 19.949852 12.199403 -5.680355 -25 21.477343 13.247442 -5.445915 -26 17.080341 15.555528 -4.334374 -27 17.319832 17.341927 -4.532204 -28 19.720472 17.115158 -3.887564 -29 19.298622 16.058659 -5.361685 -30 19.410772 15.105113 -2.363724 -31 20.700163 14.782252 -3.666344 - -Bonds - -1 1 1 8 -2 16 1 2 -3 1 1 7 -4 13 1 15 -5 16 3 2 -6 12 2 9 -7 17 2 4 -8 3 3 6 -9 1 3 10 -10 1 3 11 -11 8 6 5 -12 13 13 12 -13 13 18 12 -14 14 12 19 -15 15 13 14 -16 1 13 20 -17 1 13 21 -18 13 14 15 -19 1 14 22 -20 1 14 23 -21 14 15 24 -22 14 15 25 -23 13 17 16 -24 14 16 26 -25 14 16 27 -26 15 17 18 -27 1 17 28 -28 1 17 29 -29 1 18 30 -30 1 18 31 - -Angles - -1 30 2 1 8 -2 2 8 1 7 -3 26 8 1 15 -4 30 2 1 7 -5 31 2 1 15 -6 26 7 1 15 -7 32 1 2 3 -8 33 1 2 9 -9 34 1 2 4 -10 33 3 2 9 -11 34 3 2 4 -12 35 4 2 9 -13 36 2 3 6 -14 30 2 3 10 -15 30 2 3 11 -16 3 6 3 10 -17 3 6 3 11 -18 2 10 3 11 -19 22 3 6 5 -20 23 13 12 18 -21 24 13 12 19 -22 24 18 12 19 -23 25 14 13 12 -24 26 20 13 12 -25 26 21 13 12 -26 27 14 13 20 -27 27 14 13 21 -28 2 20 13 21 -29 25 13 14 15 -30 27 13 14 22 -31 27 13 14 23 -32 26 22 14 15 -33 26 23 14 15 -34 2 22 14 23 -35 23 1 15 14 -36 24 1 15 24 -37 24 1 15 25 -38 24 14 15 24 -39 24 14 15 25 -40 28 24 15 25 -41 24 17 16 26 -42 24 17 16 27 -43 28 26 16 27 -44 25 18 17 16 -45 26 28 17 16 -46 26 29 17 16 -47 27 18 17 28 -48 27 18 17 29 -49 2 28 17 29 -50 25 17 18 12 -51 26 30 18 12 -52 26 31 18 12 -53 27 17 18 30 -54 27 17 18 31 -55 2 30 18 31 - -Dihedrals - -1 40 8 1 2 3 -2 41 8 1 2 9 -3 42 8 1 2 4 -4 40 7 1 2 3 -5 41 7 1 2 9 -6 42 7 1 2 4 -7 43 15 1 2 3 -8 44 15 1 2 9 -9 45 15 1 2 4 -10 28 8 1 15 14 -11 30 8 1 15 24 -12 30 8 1 15 25 -13 46 2 1 15 14 -14 47 2 1 15 24 -15 47 2 1 15 25 -16 28 7 1 15 14 -17 30 7 1 15 24 -18 30 7 1 15 25 -19 48 6 3 2 1 -20 40 10 3 2 1 -21 40 11 3 2 1 -22 49 6 3 2 9 -23 41 10 3 2 9 -24 41 11 3 2 9 -25 50 6 3 2 4 -26 42 10 3 2 4 -27 42 11 3 2 4 -28 51 2 3 6 5 -29 7 10 3 6 5 -30 7 11 3 6 5 -31 27 14 13 12 18 -32 28 20 13 12 18 -33 28 21 13 12 18 -34 29 14 13 12 19 -35 30 20 13 12 19 -36 30 21 13 12 19 -37 27 17 18 12 13 -38 28 30 18 12 13 -39 28 31 18 12 13 -40 29 17 18 12 19 -41 30 30 18 12 19 -42 30 31 18 12 19 -43 31 12 13 14 15 -44 32 22 14 13 12 -45 32 23 14 13 12 -46 32 20 13 14 15 -47 33 20 13 14 22 -48 33 20 13 14 23 -49 32 21 13 14 15 -50 33 21 13 14 22 -51 33 21 13 14 23 -52 27 13 14 15 1 -53 29 13 14 15 24 -54 29 13 14 15 25 -55 28 22 14 15 1 -56 30 22 14 15 24 -57 30 22 14 15 25 -58 28 23 14 15 1 -59 30 23 14 15 24 -60 30 23 14 15 25 -61 29 18 17 16 26 -62 30 28 17 16 26 -63 30 29 17 16 26 -64 29 18 17 16 27 -65 30 28 17 16 27 -66 30 29 17 16 27 -67 31 16 17 18 12 -68 32 30 18 17 16 -69 32 31 18 17 16 -70 32 28 17 18 12 -71 33 28 17 18 30 -72 33 28 17 18 31 -73 32 29 17 18 12 -74 33 29 17 18 30 -75 33 29 17 18 31 - -Impropers - -1 4 13 12 18 19 -2 5 17 16 26 27 -3 1 2 1 8 7 -4 1 2 1 8 15 -5 1 8 1 7 15 -6 1 2 1 7 15 -7 1 1 2 3 9 -8 1 1 2 3 4 -9 1 1 2 4 9 -10 1 3 2 4 9 -11 1 2 3 6 10 -12 1 2 3 6 11 -13 1 2 3 10 11 -14 1 6 3 10 11 -15 1 14 13 20 12 -16 1 14 13 21 12 -17 1 20 13 21 12 -18 1 14 13 20 21 -19 1 13 14 22 15 -20 1 13 14 23 15 -21 1 13 14 22 23 -22 1 22 14 23 15 -23 1 1 15 14 24 -24 1 1 15 14 25 -25 1 1 15 24 25 -26 1 14 15 24 25 -27 1 18 17 28 16 -28 1 18 17 29 16 -29 1 28 17 29 16 -30 1 18 17 28 29 -31 1 17 18 30 12 -32 1 17 18 31 12 -33 1 30 18 31 12 -34 1 17 18 30 31 diff --git a/examples/PACKAGES/reaction/tiny_epoxy/rxn1_stp1_post.molecule_template b/examples/PACKAGES/reaction/tiny_epoxy/rxn1_stp1_post.molecule_template new file mode 100644 index 0000000000..4db26814c5 --- /dev/null +++ b/examples/PACKAGES/reaction/tiny_epoxy/rxn1_stp1_post.molecule_template @@ -0,0 +1,317 @@ +rxn1_stp1_post + + 31 atoms + 30 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4 c3m-c2-hc 2 1 7 + 5 c3m-c2-na 2 1 15 + 6 hc-c2-na 7 1 15 + 7 c2-c3m-c2 1 2 3 + 8 c2-c3m-hc 1 2 9 + 9 c2-c3m-oc 1 2 4 + 10 c2-c3m-hc 3 2 9 + 11 c2-c3m-oc 3 2 4 + 12 oc-c3m-hc 4 2 9 + 13 c3m-c2-oc 2 3 6 + 14 c3m-c2-hc 2 3 10 + 15 c3m-c2-hc 2 3 11 + 16 oc-c2-hc 6 3 10 + 17 oc-c2-hc 6 3 11 + 18 hc-c2-hc 10 3 11 + 19 c3m-oc-ho 2 4 25 + 20 c2-oc-cp 3 6 5 + 21 c2-na-c2 13 12 18 + 22 c2-na-hn 13 12 19 + 23 c2-na-hn 18 12 19 + 24 c2-c2-na 14 13 12 + 25 hc-c2-na 20 13 12 + 26 hc-c2-na 21 13 12 + 27 c2-c2-hc 14 13 20 + 28 c2-c2-hc 14 13 21 + 29 hc-c2-hc 20 13 21 + 30 c2-c2-na 13 14 15 + 31 c2-c2-hc 13 14 22 + 32 c2-c2-hc 13 14 23 + 33 hc-c2-na 22 14 15 + 34 hc-c2-na 23 14 15 + 35 hc-c2-hc 22 14 23 + 36 c2-na-c2 1 15 14 + 37 c2-na-c2 1 15 32 + 38 c2-na-c2 14 15 32 + 39 c2-na-hn 17 16 26 + 40 c2-na-hn 17 16 27 + 41 hn-na-hn 26 16 27 + 42 c2-c2-na 18 17 16 + 43 hc-c2-na 28 17 16 + 44 hc-c2-na 29 17 16 + 45 c2-c2-hc 18 17 28 + 46 c2-c2-hc 18 17 29 + 47 hc-c2-hc 28 17 29 + 48 c2-c2-na 17 18 12 + 49 hc-c2-na 30 18 12 + 50 hc-c2-na 31 18 12 + 51 c2-c2-hc 17 18 30 + 52 c2-c2-hc 17 18 31 + 53 hc-c2-hc 30 18 31 + 54 hc-c2-na 39 32 15 + 55 na-c2-c3 15 32 33 + 56 hc-c2-na 38 32 15 + 57 hc-c2-c3 39 32 33 + 58 hc-c2-hc 39 32 38 + 59 hc-c2-c3 38 32 33 + 60 c2-c3-oc 32 33 35 + 61 c2-c3-c2 32 33 34 + 62 c2-c3-hc 32 33 40 + 63 c2-c3-oc 34 33 35 + 64 oc-c3-hc 35 33 40 + 65 c2-c3-hc 34 33 40 + 66 oc-c2-c3 37 34 33 + 67 hc-c2-c3 41 34 33 + 68 hc-c2-c3 42 34 33 + 69 oc-c2-hc 37 34 41 + 70 oc-c2-hc 37 34 42 + 71 hc-c2-hc 41 34 42 + 72 ho-oc-c3 24 35 33 + 73 c2-oc-cp 34 37 36 + +Dihedrals + + 1 hc-c2-c3m-c2 8 1 2 3 + 2 hc-c2-c3m-hc 8 1 2 9 + 3 hc-c2-c3m-oc 8 1 2 4 + 4 hc-c2-c3m-c2 7 1 2 3 + 5 hc-c2-c3m-hc 7 1 2 9 + 6 hc-c2-c3m-oc 7 1 2 4 + 7 na-c2-c3m-c2 15 1 2 3 + 8 na-c2-c3m-hc 15 1 2 9 + 9 na-c2-c3m-oc 15 1 2 4 + 10 hc-c2-na-c2 8 1 15 14 + 11 hc-c2-na-c2 8 1 15 32 + 12 c3m-c2-na-c2 2 1 15 14 + 13 c3m-c2-na-c2 2 1 15 32 + 14 hc-c2-na-c2 7 1 15 14 + 15 hc-c2-na-c2 7 1 15 32 + 16 oc-c2-c3m-c2 6 3 2 1 + 17 hc-c2-c3m-c2 10 3 2 1 + 18 hc-c2-c3m-c2 11 3 2 1 + 19 oc-c2-c3m-hc 6 3 2 9 + 20 hc-c2-c3m-hc 10 3 2 9 + 21 hc-c2-c3m-hc 11 3 2 9 + 22 oc-c2-c3m-oc 6 3 2 4 + 23 hc-c2-c3m-oc 10 3 2 4 + 24 hc-c2-c3m-oc 11 3 2 4 + 25 c2-c3m-oc-ho 1 2 4 25 + 26 c2-c3m-oc-ho 3 2 4 25 + 27 hc-c3m-oc-ho 9 2 4 25 + 28 c3m-c2-oc-cp 2 3 6 5 + 29 hc-c2-oc-cp 10 3 6 5 + 30 hc-c2-oc-cp 11 3 6 5 + 31 c2-c2-na-c2 14 13 12 18 + 32 hc-c2-na-c2 20 13 12 18 + 33 hc-c2-na-c2 21 13 12 18 + 34 c2-c2-na-hn 14 13 12 19 + 35 hc-c2-na-hn 20 13 12 19 + 36 hc-c2-na-hn 21 13 12 19 + 37 c2-c2-na-c2 17 18 12 13 + 38 hc-c2-na-c2 30 18 12 13 + 39 hc-c2-na-c2 31 18 12 13 + 40 c2-c2-na-hn 17 18 12 19 + 41 hc-c2-na-hn 30 18 12 19 + 42 hc-c2-na-hn 31 18 12 19 + 43 na-c2-c2-na 12 13 14 15 + 44 hc-c2-c2-na 22 14 13 12 + 45 hc-c2-c2-na 23 14 13 12 + 46 hc-c2-c2-na 20 13 14 15 + 47 hc-c2-c2-hc 20 13 14 22 + 48 hc-c2-c2-hc 20 13 14 23 + 49 hc-c2-c2-na 21 13 14 15 + 50 hc-c2-c2-hc 21 13 14 22 + 51 hc-c2-c2-hc 21 13 14 23 + 52 c2-c2-na-c2 13 14 15 1 + 53 c2-c2-na-c2 13 14 15 32 + 54 hc-c2-na-c2 22 14 15 1 + 55 hc-c2-na-c2 22 14 15 32 + 56 hc-c2-na-c2 23 14 15 1 + 57 hc-c2-na-c2 23 14 15 32 + 58 hc-c2-na-c2 39 32 15 1 + 59 c3-c2-na-c2 33 32 15 1 + 60 hc-c2-na-c2 38 32 15 1 + 61 hc-c2-na-c2 39 32 15 14 + 62 c3-c2-na-c2 33 32 15 14 + 63 hc-c2-na-c2 38 32 15 14 + 64 c2-c2-na-hn 18 17 16 26 + 65 hc-c2-na-hn 28 17 16 26 + 66 hc-c2-na-hn 29 17 16 26 + 67 c2-c2-na-hn 18 17 16 27 + 68 hc-c2-na-hn 28 17 16 27 + 69 hc-c2-na-hn 29 17 16 27 + 70 na-c2-c2-na 16 17 18 12 + 71 hc-c2-c2-na 30 18 17 16 + 72 hc-c2-c2-na 31 18 17 16 + 73 hc-c2-c2-na 28 17 18 12 + 74 hc-c2-c2-hc 28 17 18 30 + 75 hc-c2-c2-hc 28 17 18 31 + 76 hc-c2-c2-na 29 17 18 12 + 77 hc-c2-c2-hc 29 17 18 30 + 78 hc-c2-c2-hc 29 17 18 31 + 79 na-c2-c3-oc 15 32 33 35 + 80 na-c2-c3-c2 15 32 33 34 + 81 na-c2-c3-hc 15 32 33 40 + 82 hc-c2-c3-oc 39 32 33 35 + 83 hc-c2-c3-c2 39 32 33 34 + 84 hc-c2-c3-hc 39 32 33 40 + 85 hc-c2-c3-oc 38 32 33 35 + 86 hc-c2-c3-c2 38 32 33 34 + 87 hc-c2-c3-hc 38 32 33 40 + 88 ho-oc-c3-c2 24 35 33 32 + 89 ho-oc-c3-c2 24 35 33 34 + 90 ho-oc-c3-hc 24 35 33 40 + 91 oc-c2-c3-c2 37 34 33 32 + 92 hc-c2-c3-c2 41 34 33 32 + 93 hc-c2-c3-c2 42 34 33 32 + 94 oc-c2-c3-oc 37 34 33 35 + 95 hc-c2-c3-oc 41 34 33 35 + 96 hc-c2-c3-oc 42 34 33 35 + 97 oc-c2-c3-hc 37 34 33 40 + 98 hc-c2-c3-hc 41 34 33 40 + 99 hc-c2-c3-hc 42 34 33 40 + 100 c3-c2-oc-cp 33 34 37 36 + 101 hc-c2-oc-cp 41 34 37 36 + 102 hc-c2-oc-cp 42 34 37 36 + +Impropers + + 1 c2-na-c2-hn 13 12 18 19 + 2 c2-na-c2-c2 1 15 14 32 + 3 c2-na-hn-hn 17 16 26 27 diff --git a/examples/PACKAGES/reaction/tiny_epoxy/tiny_epoxy.data b/examples/PACKAGES/reaction/tiny_epoxy/tiny_epoxy.data index d98006b107..90c074fde0 100644 --- a/examples/PACKAGES/reaction/tiny_epoxy/tiny_epoxy.data +++ b/examples/PACKAGES/reaction/tiny_epoxy/tiny_epoxy.data @@ -1,1582 +1,1765 @@ # two molecules DGEBA (diepoxy) and one DETA (linker) -118 atoms -123 bonds -221 angles -302 dihedrals -115 impropers -11 atom types -19 bond types -50 angle types -66 dihedral types -22 improper types +118 atoms +123 bonds +221 angles +302 dihedrals +115 impropers +11 atom types +19 bond types +50 angle types +66 dihedral types +22 improper types 10 30 xlo xhi -10 20 ylo yhi -15 10 zlo zhi -Masses +Atom Type Labels -1 12.011150 # c2 -2 12.011150 # c3m -3 15.999400 # o3e -4 12.011150 # cp -5 12.011150 # c -6 12.011150 # c3 -7 15.999400 # oc -8 1.007970 # hc -9 14.006700 # na -10 1.007970 # hn -11 1.007970 # ho +1 c2 +2 c3m +3 o3e +4 cp +5 c +6 c3 +7 oc +8 hc +9 na +10 hn +11 ho -Pair Coeffs # lj/class2/coul/long +Bond Type Labels -1 0.0540000000 4.0100000000 # c2 -2 0.0540000000 4.0100000000 # c3m -3 0.2400000000 3.5350000000 # o3e -4 0.0640000000 4.0100000000 # cp -5 0.0540000000 4.0100000000 # c -6 0.0540000000 4.0100000000 # c3 -7 0.2400000000 3.5350000000 # oc -8 0.0200000000 2.7000000000 # hc -9 0.0650000000 4.0700000000 # na -10 0.0130000000 1.0980000000 # hn -11 0.0130000000 1.0980000000 # ho +1 c2-hc +2 c3m-c2 +3 c2-oc +4 c3m-o3e +5 c3m-c3m +6 c3m-hc +7 cp-cp +8 cp-oc +9 cp-hc +10 cp-c +11 c-c3 +12 c3-hc +13 c2-na +14 na-hn +15 c2-c2 +16 c2-c3 +17 c3-oc +18 oc-ho +19 c3m-oc -Bond Coeffs # class2 +Angle Type Labels -1 1.1010 345.0000 -691.8900 844.6000 # c2-hc -2 1.5300 299.6700 -501.7700 679.8100 # c2-c3m -3 1.4200 400.3954 -835.1951 1313.0142 # c2-oc -4 1.4200 400.3954 -835.1951 1313.0142 # c3m-o3e -5 1.5300 299.6700 -501.7700 679.8100 # c3m-c3m -6 1.1010 345.0000 -691.8900 844.6000 # c3m-hc -7 1.4170 470.8361 -627.6179 1327.6345 # cp-cp -8 1.3768 428.8798 -738.2351 1114.9655 # cp-oc -9 1.0982 372.8251 -803.4526 894.3173 # cp-hc -10 1.5010 321.9021 -521.8208 572.1628 # cp-c -11 1.5300 299.6700 -501.7700 679.8100 # c-c3 -12 1.1010 345.0000 -691.8900 844.6000 # c3-hc -13 1.4570 365.8052 -699.6368 998.4842 # c2-na -14 1.0060 466.7400 -1073.6018 1251.1056 # na-hn -15 1.5300 299.6700 -501.7700 679.8100 # c2-c2 -16 1.5300 299.6700 -501.7700 679.8100 # c2-c3 -17 1.4200 400.3954 -835.1951 1313.0142 # c3-oc -18 0.9650 532.5062 -1282.9050 2004.7658 # oc-ho -19 1.4200 400.3954 -835.1951 1313.0142 # c3m-oc +1 c3m-c2-hc +2 hc-c2-hc +3 oc-c2-hc +4 c3m-c2-oc +5 c2-c3m-o3e +6 c2-c3m-c3m +7 c2-c3m-hc +8 c3m-c3m-o3e +9 o3e-c3m-hc +10 c3m-c3m-hc +11 hc-c3m-hc +12 c3m-o3e-c3m +13 cp-cp-cp +14 cp-cp-oc +15 cp-cp-hc +16 cp-cp-c +17 cp-c-c3 +18 cp-c-cp +19 c3-c-c3 +20 c-c3-hc +21 hc-c3-hc +22 c2-oc-cp +23 c2-na-c2 +24 c2-na-hn +25 c2-c2-na +26 hc-c2-na +27 c2-c2-hc +28 hn-na-hn +29 c3m-c3m-c2 +30 c3-c2-hc +31 c3-c2-na +32 c2-c3-c2 +33 c2-c3-hc +34 c2-c3-oc +35 oc-c3-hc +36 c3-c2-oc +37 c3-oc-ho +38 hc-c3m-o3e +39 hc-c3m-c3m +40 oc-c2-c3m +41 hc-c2-c3m +42 c3m-c2-na +43 c2-c3m-c2 +44 c2-c3m-oc +45 oc-c3m-hc +46 c3m-oc-ho +47 na-c2-c3 +48 hc-c2-c3 +49 oc-c2-c3 +50 ho-oc-c3 -Angle Coeffs # class2 +Dihedral Type Labels -1 110.7700 41.4530 -10.6040 5.1290 # c3m-c2-hc -2 107.6600 39.6410 -12.9210 -2.4318 # hc-c2-hc -3 108.7280 58.5446 -10.8088 -12.4006 # oc-c2-hc -4 111.2700 54.5381 -8.3642 -13.0838 # c3m-c2-oc -5 111.2700 54.5381 -8.3642 -13.0838 # c2-c3m-o3e -6 112.6700 39.5160 -7.4430 -9.5583 # c2-c3m-c3m -7 110.7700 41.4530 -10.6040 5.1290 # c2-c3m-hc -8 111.2700 54.5381 -8.3642 -13.0838 # c3m-c3m-o3e -9 108.7280 58.5446 -10.8088 -12.4006 # o3e-c3m-hc -10 110.7700 41.4530 -10.6040 5.1290 # c3m-c3m-hc -11 107.6600 39.6410 -12.9210 -2.4318 # hc-c3m-hc -12 104.5000 35.7454 -10.0067 -6.2729 # c3m-o3e-c3m -13 118.9000 61.0226 -34.9931 0.0000 # cp-cp-cp -14 123.4200 73.6781 -21.6787 0.0000 # cp-cp-oc -15 117.9400 35.1558 -12.4682 0.0000 # cp-cp-hc -16 120.0500 44.7148 -22.7352 0.0000 # cp-cp-c -17 108.4000 43.9594 -8.3924 -9.3379 # cp-c-c3 -18 111.0000 44.3234 -9.4454 0.0000 # cp-c-cp -19 112.6700 39.5160 -7.4430 -9.5583 # c3-c-c3 -20 110.7700 41.4530 -10.6040 5.1290 # c-c3-hc -21 107.6600 39.6410 -12.9210 -2.4318 # hc-c3-hc -22 102.9695 38.9739 -6.2595 -8.1710 # c2-oc-cp -23 112.4436 47.2337 -10.6612 -10.2062 # c2-na-c2 -24 110.9538 50.8652 -4.4522 -10.0298 # c2-na-hn -25 111.9100 60.7147 -13.3366 -13.0785 # c2-c2-na -26 110.6204 51.3137 -6.7198 -2.6003 # hc-c2-na -27 110.7700 41.4530 -10.6040 5.1290 # c2-c2-hc -28 107.0671 45.2520 -7.5558 -9.5120 # hn-na-hn -29 112.6700 39.5160 -7.4430 -9.5583 # c3m-c3m-c2 -30 110.7700 41.4530 -10.6040 5.1290 # c3-c2-hc -31 111.9100 60.7147 -13.3366 -13.0785 # c3-c2-na -32 112.6700 39.5160 -7.4430 -9.5583 # c2-c3-c2 -33 110.7700 41.4530 -10.6040 5.1290 # c2-c3-hc -34 111.2700 54.5381 -8.3642 -13.0838 # c2-c3-oc -35 108.7280 58.5446 -10.8088 -12.4006 # oc-c3-hc -36 111.2700 54.5381 -8.3642 -13.0838 # c3-c2-oc -37 105.8000 52.7061 -12.1090 -9.8681 # c3-oc-ho -38 108.7280 58.5446 -10.8088 -12.4006 # hc-c3m-o3e -39 110.7700 41.4530 -10.6040 5.1290 # hc-c3m-c3m -40 111.2700 54.5381 -8.3642 -13.0838 # oc-c2-c3m -41 110.7700 41.4530 -10.6040 5.1290 # hc-c2-c3m -42 111.9100 60.7147 -13.3366 -13.0785 # c3m-c2-na -43 112.6700 39.5160 -7.4430 -9.5583 # c2-c3m-c2 -44 111.2700 54.5381 -8.3642 -13.0838 # c2-c3m-oc -45 108.7280 58.5446 -10.8088 -12.4006 # oc-c3m-hc -46 105.8000 52.7061 -12.1090 -9.8681 # c3m-oc-ho -47 111.9100 60.7147 -13.3366 -13.0785 # na-c2-c3 -48 110.7700 41.4530 -10.6040 5.1290 # hc-c2-c3 -49 111.2700 54.5381 -8.3642 -13.0838 # oc-c2-c3 -50 105.8000 52.7061 -12.1090 -9.8681 # ho-oc-c3 +1 hc-c2-c3m-o3e +2 hc-c2-c3m-c3m +3 hc-c2-c3m-hc +4 oc-c2-c3m-o3e +5 oc-c2-c3m-c3m +6 oc-c2-c3m-hc +7 hc-c2-oc-cp +8 c3m-c2-oc-cp +9 c2-c3m-o3e-c3m +10 hc-c3m-o3e-c3m +11 c2-c3m-c3m-o3e +12 c2-c3m-c3m-hc +13 o3e-c3m-c3m-hc +14 hc-c3m-c3m-hc +15 cp-cp-cp-cp +16 cp-cp-cp-hc +17 cp-cp-cp-oc +18 oc-cp-cp-hc +19 cp-cp-oc-c2 +20 hc-cp-cp-hc +21 cp-cp-cp-c +22 c-cp-cp-hc +23 cp-cp-c-c3 +24 cp-cp-c-cp +25 cp-c-c3-hc +26 c3-c-c3-hc +27 c2-c2-na-c2 +28 hc-c2-na-c2 +29 c2-c2-na-hn +30 hc-c2-na-hn +31 na-c2-c2-na +32 hc-c2-c2-na +33 hc-c2-c2-hc +34 c3m-c3m-c2-oc +35 c3m-c3m-c2-hc +36 o3e-c3m-c2-oc +37 o3e-c3m-c2-hc +38 hc-c3m-c2-oc +39 hc-c3m-c2-hc +40 hc-c2-c3-c2 +41 hc-c2-c3-hc +42 hc-c2-c3-oc +43 na-c2-c3-c2 +44 na-c2-c3-hc +45 na-c2-c3-oc +46 c3-c2-na-c2 +47 c3-c2-na-hn +48 oc-c2-c3-c2 +49 oc-c2-c3-hc +50 oc-c2-c3-oc +51 c3-c2-oc-cp +52 c2-c3-oc-ho +53 hc-c3-oc-ho +54 hc-c3m-c3m-o3e +55 hc-c2-c3m-c2 +56 hc-c2-c3m-oc +57 na-c2-c3m-c2 +58 na-c2-c3m-hc +59 na-c2-c3m-oc +60 c3m-c2-na-c2 +61 oc-c2-c3m-c2 +62 oc-c2-c3m-oc +63 c2-c3m-oc-ho +64 hc-c3m-oc-ho +65 ho-oc-c3-c2 +66 ho-oc-c3-hc -Dihedral Coeffs # class2 +Improper Type Labels -1 -0.1435 0.0000 0.2530 0.0000 -0.0905 0.0000# hc-c2-c3m-o3e -2 0.0000 0.0000 0.0316 0.0000 -0.1681 0.0000# hc-c2-c3m-c3m -3 -0.1432 0.0000 0.0617 0.0000 -0.1083 0.0000# hc-c2-c3m-hc -4 -0.1820 0.0000 -0.1084 0.0000 -0.7047 0.0000# oc-c2-c3m-o3e -5 0.7137 0.0000 0.2660 0.0000 -0.2545 0.0000# oc-c2-c3m-c3m -6 -0.1435 0.0000 0.2530 0.0000 -0.0905 0.0000# oc-c2-c3m-hc -7 0.9513 0.0000 0.1155 0.0000 0.0720 0.0000# hc-c2-oc-cp -8 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000# c3m-c2-oc-cp -9 -0.5203 0.0000 -0.3028 0.0000 -0.3450 0.0000# c2-c3m-o3e-c3m -10 0.5302 0.0000 0.0000 0.0000 -0.3966 0.0000# hc-c3m-o3e-c3m -11 0.7137 0.0000 0.2660 0.0000 -0.2545 0.0000# c2-c3m-c3m-o3e -12 0.0000 0.0000 0.0316 0.0000 -0.1681 0.0000# c2-c3m-c3m-hc -13 -0.1435 0.0000 0.2530 0.0000 -0.0905 0.0000# o3e-c3m-c3m-hc -14 -0.1432 0.0000 0.0617 0.0000 -0.1083 0.0000# hc-c3m-c3m-hc -15 8.3667 0.0000 1.1932 0.0000 0.0000 0.0000# cp-cp-cp-cp -16 0.0000 0.0000 3.9661 0.0000 0.0000 0.0000# cp-cp-cp-hc -17 0.0000 0.0000 4.8498 0.0000 0.0000 0.0000# cp-cp-cp-oc -18 0.0000 0.0000 1.7234 0.0000 0.0000 0.0000# oc-cp-cp-hc -19 0.0000 0.0000 1.5000 0.0000 0.0000 0.0000# cp-cp-oc-c2 -20 0.0000 0.0000 1.8769 0.0000 0.0000 0.0000# hc-cp-cp-hc -21 0.0000 0.0000 4.4072 0.0000 0.0000 0.0000# cp-cp-cp-c -22 0.0000 0.0000 1.5590 0.0000 0.0000 0.0000# c-cp-cp-hc -23 -0.2802 0.0000 -0.0678 0.0000 -0.0122 0.0000# cp-cp-c-c3 -24 -0.2802 0.0000 -0.0678 0.0000 -0.0122 0.0000# cp-cp-c-cp -25 -0.0228 0.0000 0.0280 0.0000 -0.1863 0.0000# cp-c-c3-hc -26 0.0000 0.0000 0.0316 0.0000 -0.1681 0.0000# c3-c-c3-hc -27 -0.1406 0.0000 0.4168 0.0000 0.0150 0.0000# c2-c2-na-c2 -28 0.1904 0.0000 -0.1342 0.0000 -0.2460 0.0000# hc-c2-na-c2 -29 -1.1506 0.0000 -0.6344 0.0000 -0.1845 0.0000# c2-c2-na-hn -30 -0.5187 0.0000 -0.4837 0.0000 -0.1692 0.0000# hc-c2-na-hn -31 0.3805 0.0000 0.3547 0.0000 -0.1102 0.0000# na-c2-c2-na -32 -0.2428 0.0000 0.4065 0.0000 -0.3079 0.0000# hc-c2-c2-na -33 -0.1432 0.0000 0.0617 0.0000 -0.1083 0.0000# hc-c2-c2-hc -34 0.7137 0.0000 0.2660 0.0000 -0.2545 0.0000# c3m-c3m-c2-oc -35 0.0000 0.0000 0.0316 0.0000 -0.1681 0.0000# c3m-c3m-c2-hc -36 -0.1820 0.0000 -0.1084 0.0000 -0.7047 0.0000# o3e-c3m-c2-oc -37 -0.1435 0.0000 0.2530 0.0000 -0.0905 0.0000# o3e-c3m-c2-hc -38 -0.1435 0.0000 0.2530 0.0000 -0.0905 0.0000# hc-c3m-c2-oc -39 -0.1432 0.0000 0.0617 0.0000 -0.1083 0.0000# hc-c3m-c2-hc -40 0.0000 0.0000 0.0316 0.0000 -0.1681 0.0000# hc-c2-c3-c2 -41 -0.1432 0.0000 0.0617 0.0000 -0.1083 0.0000# hc-c2-c3-hc -42 -0.1435 0.0000 0.2530 0.0000 -0.0905 0.0000# hc-c2-c3-oc -43 0.1764 0.0000 0.1766 0.0000 -0.5206 0.0000# na-c2-c3-c2 -44 -0.2428 0.0000 0.4065 0.0000 -0.3079 0.0000# na-c2-c3-hc -45 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000# na-c2-c3-oc -46 -0.1406 0.0000 0.4168 0.0000 0.0150 0.0000# c3-c2-na-c2 -47 -1.1506 0.0000 -0.6344 0.0000 -0.1845 0.0000# c3-c2-na-hn -48 0.7137 0.0000 0.2660 0.0000 -0.2545 0.0000# oc-c2-c3-c2 -49 -0.1435 0.0000 0.2530 0.0000 -0.0905 0.0000# oc-c2-c3-hc -50 -0.1820 0.0000 -0.1084 0.0000 -0.7047 0.0000# oc-c2-c3-oc -51 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000# c3-c2-oc-cp -52 -0.6732 0.0000 -0.4778 0.0000 -0.1670 0.0000# c2-c3-oc-ho -53 0.1863 0.0000 -0.4338 0.0000 -0.2121 0.0000# hc-c3-oc-ho -54 -0.1435 0.0000 0.2530 0.0000 -0.0905 0.0000# hc-c3m-c3m-o3e -55 0.0000 0.0000 0.0316 0.0000 -0.1681 0.0000# hc-c2-c3m-c2 -56 -0.1435 0.0000 0.2530 0.0000 -0.0905 0.0000# hc-c2-c3m-oc -57 0.1764 0.0000 0.1766 0.0000 -0.5206 0.0000# na-c2-c3m-c2 -58 -0.2428 0.0000 0.4065 0.0000 -0.3079 0.0000# na-c2-c3m-hc -59 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000# na-c2-c3m-oc -60 -0.1406 0.0000 0.4168 0.0000 0.0150 0.0000# c3m-c2-na-c2 -61 0.7137 0.0000 0.2660 0.0000 -0.2545 0.0000# oc-c2-c3m-c2 -62 -0.1820 0.0000 -0.1084 0.0000 -0.7047 0.0000# oc-c2-c3m-oc -63 -0.6732 0.0000 -0.4778 0.0000 -0.1670 0.0000# c2-c3m-oc-ho -64 0.1863 0.0000 -0.4338 0.0000 -0.2121 0.0000# hc-c3m-oc-ho -65 -0.6732 0.0000 -0.4778 0.0000 -0.1670 0.0000# ho-oc-c3-c2 -66 0.1863 0.0000 -0.4338 0.0000 -0.2121 0.0000# ho-oc-c3-hc +1 cp-cp-cp-oc +2 cp-cp-cp-hc +3 cp-cp-cp-c +4 c2-na-c2-hn +5 c2-na-hn-hn +6 zero6 +7 zero7 +8 zero8 +9 zero9 +10 zero10 +11 zero11 +12 zero12 +13 zero13 +14 zero14 +15 zero15 +16 zero16 +17 zero17 +18 zero18 +19 zero19 +20 zero20 +21 zero21 +22 c2-na-c2-c2 -Improper Coeffs # class2 +Masses -1 13.0421 0.0000 # cp-cp-cp-oc -2 4.8912 0.0000 # cp-cp-cp-hc -3 7.8153 0.0000 # cp-cp-cp-c -4 0.0000 0.0000 # c2-na-c2-hn -5 0.0000 0.0000 # c2-na-hn-hn -6 0.0000 0.0000 -7 0.0000 0.0000 -8 0.0000 0.0000 -9 0.0000 0.0000 -10 0.0000 0.0000 -11 0.0000 0.0000 -12 0.0000 0.0000 -13 0.0000 0.0000 -14 0.0000 0.0000 -15 0.0000 0.0000 -16 0.0000 0.0000 -17 0.0000 0.0000 -18 0.0000 0.0000 -19 0.0000 0.0000 -20 0.0000 0.0000 -21 0.0000 0.0000 -22 0.0000 0.0000 # c2-na-c2-c2 +1 12.011150 +2 12.011150 +3 15.999400 +4 12.011150 +5 12.011150 +6 12.011150 +7 15.999400 +8 1.007970 +9 14.006700 +10 1.007970 +11 1.007970 -BondBond Coeffs +Pair Coeffs # lj/class2/coul/long -1 3.3872 1.5300 1.1010 -2 5.3316 1.1010 1.1010 -3 23.1979 1.4200 1.1010 -4 11.4318 1.5300 1.4200 -5 11.4318 1.5300 1.4200 -6 0.0000 1.5300 1.5300 -7 3.3872 1.5300 1.1010 -8 11.4318 1.5300 1.4200 -9 23.1979 1.4200 1.1010 -10 3.3872 1.5300 1.1010 -11 5.3316 1.1010 1.1010 -12 -7.1131 1.4200 1.4200 -13 68.2856 1.4170 1.4170 -14 48.4754 1.4170 1.3768 -15 1.0795 1.4170 1.0982 -16 12.0676 1.4170 1.5010 -17 0.0000 1.5010 1.5300 -18 0.0000 1.5010 1.5010 -19 0.0000 1.5300 1.5300 -20 3.3872 1.5300 1.1010 -21 5.3316 1.1010 1.1010 -22 0.0000 1.4200 1.3768 -23 -2.1113 1.4570 1.4570 -24 -6.4168 1.4570 1.0060 -25 4.6217 1.5300 1.4570 -26 12.4260 1.1010 1.4570 -27 3.3872 1.5300 1.1010 -28 -1.8749 1.0060 1.0060 -29 0.0000 1.5300 1.5300 -30 3.3872 1.5300 1.1010 -31 4.6217 1.5300 1.4570 -32 0.0000 1.5300 1.5300 -33 3.3872 1.5300 1.1010 -34 11.4318 1.5300 1.4200 -35 23.1979 1.4200 1.1010 -36 11.4318 1.5300 1.4200 -37 -9.6879 1.4200 0.9650 -38 23.1979 1.1010 1.4200 -39 3.3872 1.1010 1.5300 -40 11.4318 1.4200 1.5300 -41 3.3872 1.1010 1.5300 -42 4.6217 1.5300 1.4570 -43 0.0000 1.5300 1.5300 -44 11.4318 1.5300 1.4200 -45 23.1979 1.4200 1.1010 -46 -9.6879 1.4200 0.9650 -47 4.6217 1.4570 1.5300 -48 3.3872 1.1010 1.5300 -49 11.4318 1.4200 1.5300 -50 -9.6879 0.9650 1.4200 +1 0.0540000000 4.0100000000 +2 0.0540000000 4.0100000000 +3 0.2400000000 3.5350000000 +4 0.0640000000 4.0100000000 +5 0.0540000000 4.0100000000 +6 0.0540000000 4.0100000000 +7 0.2400000000 3.5350000000 +8 0.0200000000 2.7000000000 +9 0.0650000000 4.0700000000 +10 0.0130000000 1.0980000000 +11 0.0130000000 1.0980000000 -BondAngle Coeffs +Bond Coeffs # class2 -1 20.7540 11.4210 1.5300 1.1010 -2 18.1030 18.1030 1.1010 1.1010 -3 55.3270 4.6189 1.4200 1.1010 -4 2.6868 20.4033 1.5300 1.4200 -5 2.6868 20.4033 1.5300 1.4200 -6 8.0160 8.0160 1.5300 1.5300 -7 20.7540 11.4210 1.5300 1.1010 -8 2.6868 20.4033 1.5300 1.4200 -9 55.3270 4.6189 1.4200 1.1010 -10 20.7540 11.4210 1.5300 1.1010 -11 18.1030 18.1030 1.1010 1.1010 -12 -2.8112 -2.8112 1.4200 1.4200 -13 28.8708 28.8708 1.4170 1.4170 -14 58.4790 107.6806 1.4170 1.3768 -15 20.0033 24.2183 1.4170 1.0982 -16 31.0771 47.0579 1.4170 1.5010 -17 0.0000 0.0000 1.5010 1.5300 -18 0.0000 0.0000 1.5010 1.5010 -19 8.0160 8.0160 1.5300 1.5300 -20 20.7540 11.4210 1.5300 1.1010 -21 18.1030 18.1030 1.1010 1.1010 -22 0.0000 0.0000 1.4200 1.3768 -23 -7.2229 -7.2229 1.4570 1.4570 -24 31.8096 20.5799 1.4570 1.0060 -25 6.0876 16.5702 1.5300 1.4570 -26 13.4582 42.4332 1.1010 1.4570 -27 20.7540 11.4210 1.5300 1.1010 -28 28.0322 28.0322 1.0060 1.0060 -29 8.0160 8.0160 1.5300 1.5300 -30 20.7540 11.4210 1.5300 1.1010 -31 6.0876 16.5702 1.5300 1.4570 -32 8.0160 8.0160 1.5300 1.5300 -33 20.7540 11.4210 1.5300 1.1010 -34 2.6868 20.4033 1.5300 1.4200 -35 55.3270 4.6189 1.4200 1.1010 -36 2.6868 20.4033 1.5300 1.4200 -37 28.5800 18.9277 1.4200 0.9650 -38 4.6189 55.3270 1.1010 1.4200 -39 11.4210 20.7540 1.1010 1.5300 -40 20.4033 2.6868 1.4200 1.5300 -41 11.4210 20.7540 1.1010 1.5300 -42 6.0876 16.5702 1.5300 1.4570 -43 8.0160 8.0160 1.5300 1.5300 -44 2.6868 20.4033 1.5300 1.4200 -45 55.3270 4.6189 1.4200 1.1010 -46 28.5800 18.9277 1.4200 0.9650 -47 16.5702 6.0876 1.4570 1.5300 -48 11.4210 20.7540 1.1010 1.5300 -49 20.4033 2.6868 1.4200 1.5300 -50 18.9277 28.5800 0.9650 1.4200 +1 1.1010 345.0000 -691.8900 844.6000 +2 1.5300 299.6700 -501.7700 679.8100 +3 1.4200 400.3954 -835.1951 1313.0142 +4 1.4200 400.3954 -835.1951 1313.0142 +5 1.5300 299.6700 -501.7700 679.8100 +6 1.1010 345.0000 -691.8900 844.6000 +7 1.4170 470.8361 -627.6179 1327.6345 +8 1.3768 428.8798 -738.2351 1114.9655 +9 1.0982 372.8251 -803.4526 894.3173 +10 1.5010 321.9021 -521.8208 572.1628 +11 1.5300 299.6700 -501.7700 679.8100 +12 1.1010 345.0000 -691.8900 844.6000 +13 1.4570 365.8052 -699.6368 998.4842 +14 1.0060 466.7400 -1073.6018 1251.1056 +15 1.5300 299.6700 -501.7700 679.8100 +16 1.5300 299.6700 -501.7700 679.8100 +17 1.4200 400.3954 -835.1951 1313.0142 +18 0.9650 532.5062 -1282.9050 2004.7658 +19 1.4200 400.3954 -835.1951 1313.0142 -AngleAngle Coeffs +Angle Coeffs # class2 -1 0.0000 0.0000 0.0000 118.9000 123.4200 123.4200 -2 0.0000 0.0000 0.0000 118.9000 117.9400 117.9400 -3 0.0000 0.0000 0.0000 118.9000 120.0500 120.0500 -4 0.0000 0.0000 0.0000 112.4436 110.9538 110.9538 -5 0.0000 0.0000 0.0000 110.9538 107.0671 110.9538 -6 0.2738 -0.4825 0.2738 110.7700 107.6600 110.7700 -7 0.1689 2.5926 3.9177 111.2700 108.7280 110.7700 -8 2.4259 2.1283 2.4259 108.7280 107.6600 108.7280 -9 -0.8330 -0.8330 -3.5744 112.6700 111.2700 111.2700 -10 0.1689 2.5926 3.9177 111.2700 108.7280 110.7700 -11 -1.3199 -1.3199 0.1184 112.6700 110.7700 110.7700 -12 0.1689 2.5926 3.9177 111.2700 108.7280 110.7700 -13 0.2738 -0.4825 0.2738 110.7700 107.6600 110.7700 -14 2.4259 2.1283 2.4259 108.7280 107.6600 108.7280 -15 0.0000 0.0000 0.0000 108.4000 112.6700 108.4000 -16 0.0000 0.0000 0.0000 111.0000 108.4000 108.4000 -17 0.2738 -0.4825 0.2738 110.7700 107.6600 110.7700 -18 -0.3157 -0.3157 -0.3157 107.6600 107.6600 107.6600 -19 2.4286 0.5381 -2.5301 110.7700 110.6204 111.9100 -20 2.4321 2.4321 -3.5496 107.6600 110.6204 110.6204 -21 0.2738 -0.4825 0.2738 110.7700 107.6600 110.7700 -22 0.0000 0.0000 0.0000 112.4436 112.4436 112.4436 +1 110.7700 41.4530 -10.6040 5.1290 +2 107.6600 39.6410 -12.9210 -2.4318 +3 108.7280 58.5446 -10.8088 -12.4006 +4 111.2700 54.5381 -8.3642 -13.0838 +5 111.2700 54.5381 -8.3642 -13.0838 +6 112.6700 39.5160 -7.4430 -9.5583 +7 110.7700 41.4530 -10.6040 5.1290 +8 111.2700 54.5381 -8.3642 -13.0838 +9 108.7280 58.5446 -10.8088 -12.4006 +10 110.7700 41.4530 -10.6040 5.1290 +11 107.6600 39.6410 -12.9210 -2.4318 +12 104.5000 35.7454 -10.0067 -6.2729 +13 118.9000 61.0226 -34.9931 0.0000 +14 123.4200 73.6781 -21.6787 0.0000 +15 117.9400 35.1558 -12.4682 0.0000 +16 120.0500 44.7148 -22.7352 0.0000 +17 108.4000 43.9594 -8.3924 -9.3379 +18 111.0000 44.3234 -9.4454 0.0000 +19 112.6700 39.5160 -7.4430 -9.5583 +20 110.7700 41.4530 -10.6040 5.1290 +21 107.6600 39.6410 -12.9210 -2.4318 +22 102.9695 38.9739 -6.2595 -8.1710 +23 112.4436 47.2337 -10.6612 -10.2062 +24 110.9538 50.8652 -4.4522 -10.0298 +25 111.9100 60.7147 -13.3366 -13.0785 +26 110.6204 51.3137 -6.7198 -2.6003 +27 110.7700 41.4530 -10.6040 5.1290 +28 107.0671 45.2520 -7.5558 -9.5120 +29 112.6700 39.5160 -7.4430 -9.5583 +30 110.7700 41.4530 -10.6040 5.1290 +31 111.9100 60.7147 -13.3366 -13.0785 +32 112.6700 39.5160 -7.4430 -9.5583 +33 110.7700 41.4530 -10.6040 5.1290 +34 111.2700 54.5381 -8.3642 -13.0838 +35 108.7280 58.5446 -10.8088 -12.4006 +36 111.2700 54.5381 -8.3642 -13.0838 +37 105.8000 52.7061 -12.1090 -9.8681 +38 108.7280 58.5446 -10.8088 -12.4006 +39 110.7700 41.4530 -10.6040 5.1290 +40 111.2700 54.5381 -8.3642 -13.0838 +41 110.7700 41.4530 -10.6040 5.1290 +42 111.9100 60.7147 -13.3366 -13.0785 +43 112.6700 39.5160 -7.4430 -9.5583 +44 111.2700 54.5381 -8.3642 -13.0838 +45 108.7280 58.5446 -10.8088 -12.4006 +46 105.8000 52.7061 -12.1090 -9.8681 +47 111.9100 60.7147 -13.3366 -13.0785 +48 110.7700 41.4530 -10.6040 5.1290 +49 111.2700 54.5381 -8.3642 -13.0838 +50 105.8000 52.7061 -12.1090 -9.8681 -AngleAngleTorsion Coeffs +Dihedral Coeffs # class2 -1 -20.2006 110.7700 111.2700 -2 -16.1640 110.7700 112.6700 -3 -12.5640 110.7700 110.7700 -4 -14.0484 111.2700 111.2700 -5 -29.0420 111.2700 112.6700 -6 -20.2006 111.2700 110.7700 -7 0.0000 108.7280 102.9695 -8 0.0000 111.2700 102.9695 -9 -19.0059 111.2700 104.5000 -10 -16.4438 108.7280 104.5000 -11 -29.0420 112.6700 111.2700 -12 -16.1640 112.6700 110.7700 -13 -20.2006 111.2700 110.7700 -14 -12.5640 110.7700 110.7700 -15 0.0000 118.9000 118.9000 -16 -4.8141 118.9000 117.9400 -17 -21.0247 118.9000 123.4200 -18 4.2296 123.4200 117.9400 -19 0.0000 123.4200 102.9695 -20 0.3598 117.9400 117.9400 -21 -14.4097 118.9000 120.0500 -22 4.4444 120.0500 117.9400 -23 0.0000 120.0500 108.4000 -24 0.0000 120.0500 111.0000 -25 0.0000 108.4000 110.7700 -26 -16.1640 112.6700 110.7700 -27 -24.3818 111.9100 112.4436 -28 -12.5567 110.6204 112.4436 -29 -7.5499 111.9100 110.9538 -30 -10.4258 110.6204 110.9538 -31 -11.2307 111.9100 111.9100 -32 -15.7572 110.7700 111.9100 -33 -12.5640 110.7700 110.7700 -34 -29.0420 112.6700 111.2700 -35 -16.1640 112.6700 110.7700 -36 -14.0484 111.2700 111.2700 -37 -20.2006 111.2700 110.7700 -38 -20.2006 110.7700 111.2700 -39 -12.5640 110.7700 110.7700 -40 -16.1640 110.7700 112.6700 -41 -12.5640 110.7700 110.7700 -42 -20.2006 110.7700 111.2700 -43 -27.3953 111.9100 112.6700 -44 -15.7572 111.9100 110.7700 -45 0.0000 111.9100 111.2700 -46 -24.3818 111.9100 112.4436 -47 -7.5499 111.9100 110.9538 -48 -29.0420 111.2700 112.6700 -49 -20.2006 111.2700 110.7700 -50 -14.0484 111.2700 111.2700 -51 0.0000 111.2700 102.9695 -52 -12.1038 111.2700 105.8000 -53 -10.5093 108.7280 105.8000 -54 -20.2006 110.7700 111.2700 -55 -16.1640 110.7700 112.6700 -56 -20.2006 110.7700 111.2700 -57 -27.3953 111.9100 112.6700 -58 -15.7572 111.9100 110.7700 -59 0.0000 111.9100 111.2700 -60 -24.3818 111.9100 112.4436 -61 -29.0420 111.2700 112.6700 -62 -14.0484 111.2700 111.2700 -63 -12.1038 111.2700 105.8000 -64 -10.5093 108.7280 105.8000 -65 -12.1038 105.8000 111.2700 -66 -10.5093 105.8000 108.7280 +1 -0.1435 0.0000 0.2530 0.0000 -0.0905 0.0000 +2 0.0000 0.0000 0.0316 0.0000 -0.1681 0.0000 +3 -0.1432 0.0000 0.0617 0.0000 -0.1083 0.0000 +4 -0.1820 0.0000 -0.1084 0.0000 -0.7047 0.0000 +5 0.7137 0.0000 0.2660 0.0000 -0.2545 0.0000 +6 -0.1435 0.0000 0.2530 0.0000 -0.0905 0.0000 +7 0.9513 0.0000 0.1155 0.0000 0.0720 0.0000 +8 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 +9 -0.5203 0.0000 -0.3028 0.0000 -0.3450 0.0000 +10 0.5302 0.0000 0.0000 0.0000 -0.3966 0.0000 +11 0.7137 0.0000 0.2660 0.0000 -0.2545 0.0000 +12 0.0000 0.0000 0.0316 0.0000 -0.1681 0.0000 +13 -0.1435 0.0000 0.2530 0.0000 -0.0905 0.0000 +14 -0.1432 0.0000 0.0617 0.0000 -0.1083 0.0000 +15 8.3667 0.0000 1.1932 0.0000 0.0000 0.0000 +16 0.0000 0.0000 3.9661 0.0000 0.0000 0.0000 +17 0.0000 0.0000 4.8498 0.0000 0.0000 0.0000 +18 0.0000 0.0000 1.7234 0.0000 0.0000 0.0000 +19 0.0000 0.0000 1.5000 0.0000 0.0000 0.0000 +20 0.0000 0.0000 1.8769 0.0000 0.0000 0.0000 +21 0.0000 0.0000 4.4072 0.0000 0.0000 0.0000 +22 0.0000 0.0000 1.5590 0.0000 0.0000 0.0000 +23 -0.2802 0.0000 -0.0678 0.0000 -0.0122 0.0000 +24 -0.2802 0.0000 -0.0678 0.0000 -0.0122 0.0000 +25 -0.0228 0.0000 0.0280 0.0000 -0.1863 0.0000 +26 0.0000 0.0000 0.0316 0.0000 -0.1681 0.0000 +27 -0.1406 0.0000 0.4168 0.0000 0.0150 0.0000 +28 0.1904 0.0000 -0.1342 0.0000 -0.2460 0.0000 +29 -1.1506 0.0000 -0.6344 0.0000 -0.1845 0.0000 +30 -0.5187 0.0000 -0.4837 0.0000 -0.1692 0.0000 +31 0.3805 0.0000 0.3547 0.0000 -0.1102 0.0000 +32 -0.2428 0.0000 0.4065 0.0000 -0.3079 0.0000 +33 -0.1432 0.0000 0.0617 0.0000 -0.1083 0.0000 +34 0.7137 0.0000 0.2660 0.0000 -0.2545 0.0000 +35 0.0000 0.0000 0.0316 0.0000 -0.1681 0.0000 +36 -0.1820 0.0000 -0.1084 0.0000 -0.7047 0.0000 +37 -0.1435 0.0000 0.2530 0.0000 -0.0905 0.0000 +38 -0.1435 0.0000 0.2530 0.0000 -0.0905 0.0000 +39 -0.1432 0.0000 0.0617 0.0000 -0.1083 0.0000 +40 0.0000 0.0000 0.0316 0.0000 -0.1681 0.0000 +41 -0.1432 0.0000 0.0617 0.0000 -0.1083 0.0000 +42 -0.1435 0.0000 0.2530 0.0000 -0.0905 0.0000 +43 0.1764 0.0000 0.1766 0.0000 -0.5206 0.0000 +44 -0.2428 0.0000 0.4065 0.0000 -0.3079 0.0000 +45 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 +46 -0.1406 0.0000 0.4168 0.0000 0.0150 0.0000 +47 -1.1506 0.0000 -0.6344 0.0000 -0.1845 0.0000 +48 0.7137 0.0000 0.2660 0.0000 -0.2545 0.0000 +49 -0.1435 0.0000 0.2530 0.0000 -0.0905 0.0000 +50 -0.1820 0.0000 -0.1084 0.0000 -0.7047 0.0000 +51 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 +52 -0.6732 0.0000 -0.4778 0.0000 -0.1670 0.0000 +53 0.1863 0.0000 -0.4338 0.0000 -0.2121 0.0000 +54 -0.1435 0.0000 0.2530 0.0000 -0.0905 0.0000 +55 0.0000 0.0000 0.0316 0.0000 -0.1681 0.0000 +56 -0.1435 0.0000 0.2530 0.0000 -0.0905 0.0000 +57 0.1764 0.0000 0.1766 0.0000 -0.5206 0.0000 +58 -0.2428 0.0000 0.4065 0.0000 -0.3079 0.0000 +59 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 +60 -0.1406 0.0000 0.4168 0.0000 0.0150 0.0000 +61 0.7137 0.0000 0.2660 0.0000 -0.2545 0.0000 +62 -0.1820 0.0000 -0.1084 0.0000 -0.7047 0.0000 +63 -0.6732 0.0000 -0.4778 0.0000 -0.1670 0.0000 +64 0.1863 0.0000 -0.4338 0.0000 -0.2121 0.0000 +65 -0.6732 0.0000 -0.4778 0.0000 -0.1670 0.0000 +66 0.1863 0.0000 -0.4338 0.0000 -0.2121 0.0000 -EndBondTorsion Coeffs +Improper Coeffs # class2 -1 0.9681 0.9551 0.0436 0.5903 0.6669 0.8584 1.1010 1.4200 -2 0.0814 0.0591 0.2219 0.2486 0.2422 -0.0925 1.1010 1.5300 -3 0.2130 0.3120 0.0777 0.2130 0.3120 0.0777 1.1010 1.1010 -4 1.0165 0.7553 -0.4609 1.0165 0.7553 -0.4609 1.4200 1.4200 -5 1.1538 0.8409 -0.9138 -0.3190 0.4411 -0.7174 1.4200 1.5300 -6 0.5903 0.6669 0.8584 0.9681 0.9551 0.0436 1.4200 1.1010 -7 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.1010 1.3768 -8 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.5300 1.3768 -9 -0.2456 1.0517 -0.7795 0.4741 1.2635 0.5576 1.5300 1.4200 -10 -0.6054 1.3339 0.9648 -0.1620 0.1564 -1.1408 1.1010 1.4200 -11 -0.3190 0.4411 -0.7174 1.1538 0.8409 -0.9138 1.5300 1.4200 -12 0.2486 0.2422 -0.0925 0.0814 0.0591 0.2219 1.5300 1.1010 -13 0.5903 0.6669 0.8584 0.9681 0.9551 0.0436 1.4200 1.1010 -14 0.2130 0.3120 0.0777 0.2130 0.3120 0.0777 1.1010 1.1010 -15 -0.1185 6.3204 0.0000 -0.1185 6.3204 0.0000 1.4170 1.4170 -16 0.0000 -6.8958 0.0000 0.0000 -0.4669 0.0000 1.4170 1.0982 -17 0.0000 0.2655 0.0000 0.0000 4.8905 0.0000 1.4170 1.3768 -18 0.0000 4.2641 0.0000 0.0000 -1.5867 0.0000 1.3768 1.0982 -19 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.4170 1.4200 -20 0.0000 -0.6890 0.0000 0.0000 -0.6890 0.0000 1.0982 1.0982 -21 0.0000 -0.6918 0.0000 0.0000 0.2421 0.0000 1.4170 1.5010 -22 0.0000 -1.7970 0.0000 0.0000 -0.4879 0.0000 1.5010 1.0982 -23 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.4170 1.5300 -24 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.4170 1.5010 -25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.5010 1.1010 -26 0.2486 0.2422 -0.0925 0.0814 0.0591 0.2219 1.5300 1.1010 -27 0.0997 -0.0046 -0.2657 -0.0128 -0.0495 -0.1079 1.5300 1.4570 -28 -0.5892 0.7140 0.3505 0.0628 0.0873 -0.0882 1.1010 1.4570 -29 -0.9466 0.9356 -0.5542 0.0570 0.0625 0.4112 1.5300 1.0060 -30 -1.1685 0.9266 -0.0993 0.0850 0.3061 0.2104 1.1010 1.0060 -31 0.0286 0.0566 -0.0493 0.0286 0.0566 -0.0493 1.4570 1.4570 -32 0.1960 0.7056 0.1120 0.1022 0.2090 0.6433 1.1010 1.4570 -33 0.2130 0.3120 0.0777 0.2130 0.3120 0.0777 1.1010 1.1010 -34 -0.3190 0.4411 -0.7174 1.1538 0.8409 -0.9138 1.5300 1.4200 -35 0.2486 0.2422 -0.0925 0.0814 0.0591 0.2219 1.5300 1.1010 -36 1.0165 0.7553 -0.4609 1.0165 0.7553 -0.4609 1.4200 1.4200 -37 0.5903 0.6669 0.8584 0.9681 0.9551 0.0436 1.4200 1.1010 -38 0.9681 0.9551 0.0436 0.5903 0.6669 0.8584 1.1010 1.4200 -39 0.2130 0.3120 0.0777 0.2130 0.3120 0.0777 1.1010 1.1010 -40 0.0814 0.0591 0.2219 0.2486 0.2422 -0.0925 1.1010 1.5300 -41 0.2130 0.3120 0.0777 0.2130 0.3120 0.0777 1.1010 1.1010 -42 0.9681 0.9551 0.0436 0.5903 0.6669 0.8584 1.1010 1.4200 -43 0.0579 -0.0043 -0.1906 0.1032 0.5896 -0.4836 1.4570 1.5300 -44 0.1022 0.2090 0.6433 0.1960 0.7056 0.1120 1.4570 1.1010 -45 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.4570 1.4200 -46 0.0997 -0.0046 -0.2657 -0.0128 -0.0495 -0.1079 1.5300 1.4570 -47 -0.9466 0.9356 -0.5542 0.0570 0.0625 0.4112 1.5300 1.0060 -48 1.1538 0.8409 -0.9138 -0.3190 0.4411 -0.7174 1.4200 1.5300 -49 0.5903 0.6669 0.8584 0.9681 0.9551 0.0436 1.4200 1.1010 -50 1.0165 0.7553 -0.4609 1.0165 0.7553 -0.4609 1.4200 1.4200 -51 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.5300 1.3768 -52 -0.5800 0.9004 0.0000 0.0000 0.5343 0.9025 1.5300 0.9650 -53 -1.7554 1.3145 0.2263 0.2493 0.6803 0.0000 1.1010 0.9650 -54 0.9681 0.9551 0.0436 0.5903 0.6669 0.8584 1.1010 1.4200 -55 0.0814 0.0591 0.2219 0.2486 0.2422 -0.0925 1.1010 1.5300 -56 0.9681 0.9551 0.0436 0.5903 0.6669 0.8584 1.1010 1.4200 -57 0.0579 -0.0043 -0.1906 0.1032 0.5896 -0.4836 1.4570 1.5300 -58 0.1022 0.2090 0.6433 0.1960 0.7056 0.1120 1.4570 1.1010 -59 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.4570 1.4200 -60 0.0997 -0.0046 -0.2657 -0.0128 -0.0495 -0.1079 1.5300 1.4570 -61 1.1538 0.8409 -0.9138 -0.3190 0.4411 -0.7174 1.4200 1.5300 -62 1.0165 0.7553 -0.4609 1.0165 0.7553 -0.4609 1.4200 1.4200 -63 -0.5800 0.9004 0.0000 0.0000 0.5343 0.9025 1.5300 0.9650 -64 -1.7554 1.3145 0.2263 0.2493 0.6803 0.0000 1.1010 0.9650 -65 0.0000 0.5343 0.9025 -0.5800 0.9004 0.0000 0.9650 1.5300 -66 0.2493 0.6803 0.0000 -1.7554 1.3145 0.2263 0.9650 1.1010 +1 13.0421 0.0000 # cp-cp-cp-oc +2 4.8912 0.0000 # cp-cp-cp-hc +3 7.8153 0.0000 # cp-cp-cp-c +4 0.0000 0.0000 # c2-na-c2-hn +5 0.0000 0.0000 # c2-na-hn-hn +6 0.0000 0.0000 +7 0.0000 0.0000 +8 0.0000 0.0000 +9 0.0000 0.0000 +10 0.0000 0.0000 +11 0.0000 0.0000 +12 0.0000 0.0000 +13 0.0000 0.0000 +14 0.0000 0.0000 +15 0.0000 0.0000 +16 0.0000 0.0000 +17 0.0000 0.0000 +18 0.0000 0.0000 +19 0.0000 0.0000 +20 0.0000 0.0000 +21 0.0000 0.0000 +22 0.0000 0.0000 # c2-na-c2-c2 -MiddleBondTorsion Coeffs +BondBond Coeffs -1 -16.7975 -1.2296 -0.2750 1.5300 -2 -14.8790 -3.6581 -0.3138 1.5300 -3 -14.2610 -0.5322 -0.4864 1.5300 -4 -17.2585 -3.6157 -0.8364 1.5300 -5 -21.8842 -7.6764 -0.6868 1.5300 -6 -16.7975 -1.2296 -0.2750 1.5300 -7 0.0000 0.0000 0.0000 1.4200 -8 0.0000 0.0000 0.0000 1.4200 -9 -5.9288 -2.7007 -0.3175 1.4200 -10 -6.8007 -4.6546 -1.4101 1.4200 -11 -21.8842 -7.6764 -0.6868 1.5300 -12 -14.8790 -3.6581 -0.3138 1.5300 -13 -16.7975 -1.2296 -0.2750 1.5300 -14 -14.2610 -0.5322 -0.4864 1.5300 -15 27.5989 -2.3120 0.0000 1.4170 -16 0.0000 -1.1521 0.0000 1.4170 -17 0.0000 4.8255 0.0000 1.4170 -18 0.0000 5.5432 0.0000 1.4170 -19 0.0000 0.0000 0.0000 1.3768 -20 0.0000 4.8228 0.0000 1.4170 -21 0.0000 9.1792 0.0000 1.4170 -22 0.0000 3.9421 0.0000 1.4170 -23 0.0000 0.0000 0.0000 1.5010 -24 0.0000 0.0000 0.0000 1.5010 -25 0.0000 0.0000 0.0000 1.5300 -26 -14.8790 -3.6581 -0.3138 1.5300 -27 -8.0036 -7.7321 -3.0640 1.4570 -28 -6.4529 -6.8122 -1.1632 1.4570 -29 -2.2208 0.5479 -0.3527 1.4570 -30 -3.4611 1.6996 -0.6007 1.4570 -31 -3.3497 1.0143 -3.0062 1.5300 -32 -10.4959 -0.7647 -0.0545 1.5300 -33 -14.2610 -0.5322 -0.4864 1.5300 -34 -21.8842 -7.6764 -0.6868 1.5300 -35 -14.8790 -3.6581 -0.3138 1.5300 -36 -17.2585 -3.6157 -0.8364 1.5300 -37 -16.7975 -1.2296 -0.2750 1.5300 -38 -16.7975 -1.2296 -0.2750 1.5300 -39 -14.2610 -0.5322 -0.4864 1.5300 -40 -14.8790 -3.6581 -0.3138 1.5300 -41 -14.2610 -0.5322 -0.4864 1.5300 -42 -16.7975 -1.2296 -0.2750 1.5300 -43 -15.4174 -7.3055 -1.0749 1.5300 -44 -10.4959 -0.7647 -0.0545 1.5300 -45 0.0000 0.0000 0.0000 1.5300 -46 -8.0036 -7.7321 -3.0640 1.4570 -47 -2.2208 0.5479 -0.3527 1.4570 -48 -21.8842 -7.6764 -0.6868 1.5300 -49 -16.7975 -1.2296 -0.2750 1.5300 -50 -17.2585 -3.6157 -0.8364 1.5300 -51 0.0000 0.0000 0.0000 1.4200 -52 1.2472 0.0000 0.7485 1.4200 -53 0.0000 0.9241 -0.5889 1.4200 -54 -16.7975 -1.2296 -0.2750 1.5300 -55 -14.8790 -3.6581 -0.3138 1.5300 -56 -16.7975 -1.2296 -0.2750 1.5300 -57 -15.4174 -7.3055 -1.0749 1.5300 -58 -10.4959 -0.7647 -0.0545 1.5300 -59 0.0000 0.0000 0.0000 1.5300 -60 -8.0036 -7.7321 -3.0640 1.4570 -61 -21.8842 -7.6764 -0.6868 1.5300 -62 -17.2585 -3.6157 -0.8364 1.5300 -63 1.2472 0.0000 0.7485 1.4200 -64 0.0000 0.9241 -0.5889 1.4200 -65 1.2472 0.0000 0.7485 1.4200 -66 0.0000 0.9241 -0.5889 1.4200 +1 3.3872 1.5300 1.1010 +2 5.3316 1.1010 1.1010 +3 23.1979 1.4200 1.1010 +4 11.4318 1.5300 1.4200 +5 11.4318 1.5300 1.4200 +6 0.0000 1.5300 1.5300 +7 3.3872 1.5300 1.1010 +8 11.4318 1.5300 1.4200 +9 23.1979 1.4200 1.1010 +10 3.3872 1.5300 1.1010 +11 5.3316 1.1010 1.1010 +12 -7.1131 1.4200 1.4200 +13 68.2856 1.4170 1.4170 +14 48.4754 1.4170 1.3768 +15 1.0795 1.4170 1.0982 +16 12.0676 1.4170 1.5010 +17 0.0000 1.5010 1.5300 +18 0.0000 1.5010 1.5010 +19 0.0000 1.5300 1.5300 +20 3.3872 1.5300 1.1010 +21 5.3316 1.1010 1.1010 +22 0.0000 1.4200 1.3768 +23 -2.1113 1.4570 1.4570 +24 -6.4168 1.4570 1.0060 +25 4.6217 1.5300 1.4570 +26 12.4260 1.1010 1.4570 +27 3.3872 1.5300 1.1010 +28 -1.8749 1.0060 1.0060 +29 0.0000 1.5300 1.5300 +30 3.3872 1.5300 1.1010 +31 4.6217 1.5300 1.4570 +32 0.0000 1.5300 1.5300 +33 3.3872 1.5300 1.1010 +34 11.4318 1.5300 1.4200 +35 23.1979 1.4200 1.1010 +36 11.4318 1.5300 1.4200 +37 -9.6879 1.4200 0.9650 +38 23.1979 1.1010 1.4200 +39 3.3872 1.1010 1.5300 +40 11.4318 1.4200 1.5300 +41 3.3872 1.1010 1.5300 +42 4.6217 1.5300 1.4570 +43 0.0000 1.5300 1.5300 +44 11.4318 1.5300 1.4200 +45 23.1979 1.4200 1.1010 +46 -9.6879 1.4200 0.9650 +47 4.6217 1.4570 1.5300 +48 3.3872 1.1010 1.5300 +49 11.4318 1.4200 1.5300 +50 -9.6879 0.9650 1.4200 -BondBond13 Coeffs +BondAngle Coeffs -1 0.0000 1.1010 1.4200 -2 0.0000 1.1010 1.5300 -3 0.0000 1.1010 1.1010 -4 0.0000 1.4200 1.4200 -5 0.0000 1.4200 1.5300 -6 0.0000 1.4200 1.1010 -7 0.0000 1.1010 1.3768 -8 0.0000 1.5300 1.3768 -9 0.0000 1.5300 1.4200 -10 0.0000 1.1010 1.4200 -11 0.0000 1.5300 1.4200 -12 0.0000 1.5300 1.1010 -13 0.0000 1.4200 1.1010 -14 0.0000 1.1010 1.1010 -15 53.0000 1.4170 1.4170 -16 -6.2741 1.4170 1.0982 -17 -2.2436 1.4170 1.3768 -18 2.0517 1.3768 1.0982 -19 0.0000 1.4170 1.4200 -20 -1.7077 1.0982 1.0982 -21 2.5085 1.4170 1.5010 -22 0.8743 1.5010 1.0982 -23 0.0000 1.4170 1.5300 -24 0.0000 1.4170 1.5010 -25 0.0000 1.5010 1.1010 -26 0.0000 1.5300 1.1010 -27 0.0000 1.5300 1.4570 -28 0.0000 1.1010 1.4570 -29 0.0000 1.5300 1.0060 -30 0.0000 1.1010 1.0060 -31 0.0000 1.4570 1.4570 -32 0.0000 1.1010 1.4570 -33 0.0000 1.1010 1.1010 -34 0.0000 1.5300 1.4200 -35 0.0000 1.5300 1.1010 -36 0.0000 1.4200 1.4200 -37 0.0000 1.4200 1.1010 -38 0.0000 1.1010 1.4200 -39 0.0000 1.1010 1.1010 -40 0.0000 1.1010 1.5300 -41 0.0000 1.1010 1.1010 -42 0.0000 1.1010 1.4200 -43 0.0000 1.4570 1.5300 -44 0.0000 1.4570 1.1010 -45 0.0000 1.4570 1.4200 -46 0.0000 1.5300 1.4570 -47 0.0000 1.5300 1.0060 -48 0.0000 1.4200 1.5300 -49 0.0000 1.4200 1.1010 -50 0.0000 1.4200 1.4200 -51 0.0000 1.5300 1.3768 -52 0.0000 1.5300 0.9650 -53 0.0000 1.1010 0.9650 -54 0.0000 1.1010 1.4200 -55 0.0000 1.1010 1.5300 -56 0.0000 1.1010 1.4200 -57 0.0000 1.4570 1.5300 -58 0.0000 1.4570 1.1010 -59 0.0000 1.4570 1.4200 -60 0.0000 1.5300 1.4570 -61 0.0000 1.4200 1.5300 -62 0.0000 1.4200 1.4200 -63 0.0000 1.5300 0.9650 -64 0.0000 1.1010 0.9650 -65 0.0000 0.9650 1.5300 -66 0.0000 0.9650 1.1010 +1 20.7540 11.4210 1.5300 1.1010 +2 18.1030 18.1030 1.1010 1.1010 +3 55.3270 4.6189 1.4200 1.1010 +4 2.6868 20.4033 1.5300 1.4200 +5 2.6868 20.4033 1.5300 1.4200 +6 8.0160 8.0160 1.5300 1.5300 +7 20.7540 11.4210 1.5300 1.1010 +8 2.6868 20.4033 1.5300 1.4200 +9 55.3270 4.6189 1.4200 1.1010 +10 20.7540 11.4210 1.5300 1.1010 +11 18.1030 18.1030 1.1010 1.1010 +12 -2.8112 -2.8112 1.4200 1.4200 +13 28.8708 28.8708 1.4170 1.4170 +14 58.4790 107.6806 1.4170 1.3768 +15 20.0033 24.2183 1.4170 1.0982 +16 31.0771 47.0579 1.4170 1.5010 +17 0.0000 0.0000 1.5010 1.5300 +18 0.0000 0.0000 1.5010 1.5010 +19 8.0160 8.0160 1.5300 1.5300 +20 20.7540 11.4210 1.5300 1.1010 +21 18.1030 18.1030 1.1010 1.1010 +22 0.0000 0.0000 1.4200 1.3768 +23 -7.2229 -7.2229 1.4570 1.4570 +24 31.8096 20.5799 1.4570 1.0060 +25 6.0876 16.5702 1.5300 1.4570 +26 13.4582 42.4332 1.1010 1.4570 +27 20.7540 11.4210 1.5300 1.1010 +28 28.0322 28.0322 1.0060 1.0060 +29 8.0160 8.0160 1.5300 1.5300 +30 20.7540 11.4210 1.5300 1.1010 +31 6.0876 16.5702 1.5300 1.4570 +32 8.0160 8.0160 1.5300 1.5300 +33 20.7540 11.4210 1.5300 1.1010 +34 2.6868 20.4033 1.5300 1.4200 +35 55.3270 4.6189 1.4200 1.1010 +36 2.6868 20.4033 1.5300 1.4200 +37 28.5800 18.9277 1.4200 0.9650 +38 4.6189 55.3270 1.1010 1.4200 +39 11.4210 20.7540 1.1010 1.5300 +40 20.4033 2.6868 1.4200 1.5300 +41 11.4210 20.7540 1.1010 1.5300 +42 6.0876 16.5702 1.5300 1.4570 +43 8.0160 8.0160 1.5300 1.5300 +44 2.6868 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33 +47 10 6 5 8 33 +48 7 5 6 24 34 +49 7 5 6 24 35 +50 6 5 6 34 35 +51 8 24 6 34 35 +52 15 12 15 16 17 +53 16 12 15 18 16 +54 16 12 15 18 17 +55 15 18 15 17 16 +56 17 15 16 40 41 +57 17 15 16 40 42 +58 17 15 16 41 42 +59 18 40 16 41 42 +60 17 15 17 43 44 +61 17 15 17 43 45 +62 17 15 17 44 45 +63 18 43 17 44 45 +64 6 51 50 75 76 +65 7 51 50 74 75 +66 8 74 50 76 75 +67 7 51 50 74 76 +68 9 50 51 52 56 +69 10 50 51 56 77 +70 11 50 51 52 77 +71 12 52 51 56 77 +72 12 51 52 56 78 +73 12 51 52 56 79 +74 13 51 52 78 79 +75 14 56 52 78 79 +76 12 54 53 57 81 +77 14 57 53 81 80 +78 13 54 53 81 80 +79 12 54 53 57 80 +80 9 55 54 53 57 +81 12 53 54 57 82 +82 11 55 54 53 82 +83 10 55 54 57 82 +84 7 54 55 73 83 +85 7 54 55 73 84 +86 6 54 55 83 84 +87 8 73 55 83 84 +88 15 61 64 65 66 +89 16 61 64 67 65 +90 16 61 64 67 66 +91 15 67 64 66 65 +92 17 64 65 89 90 +93 17 64 65 89 91 +94 17 64 65 90 91 +95 18 89 65 90 91 +96 17 64 66 92 93 +97 17 64 66 92 94 +98 17 64 66 93 94 +99 18 92 66 93 94 +100 19 101 100 107 99 +101 19 101 100 108 99 +102 20 107 100 108 99 +103 21 101 100 107 108 +104 19 100 101 109 102 +105 19 100 101 110 102 +106 21 100 101 109 110 +107 20 109 101 110 102 +108 19 105 104 115 103 +109 19 105 104 116 103 +110 20 115 104 116 103 +111 21 105 104 115 116 +112 19 104 105 117 99 +113 19 104 105 118 99 +114 20 117 105 118 99 +115 21 104 105 117 118 From 983401b015abb5447e2c790ff72db61135cb6705 Mon Sep 17 00:00:00 2001 From: Jacob Gissinger Date: Tue, 13 Dec 2022 00:37:09 -0500 Subject: [PATCH 05/47] type labels for nylon_melt example --- .../nylon,6-6_melt/in.large_nylon_melt | 15 +- .../nylon,6-6_melt/large_nylon_melt.data.gz | Bin 3745227 -> 3777723 bytes .../log.20Apr18.large_nylon_melt.g++.1 | 175 ---------------- .../log.20Apr18.large_nylon_melt.g++.4 | 175 ---------------- .../log.4Nov2022.large_nylon_melt.g++.1 | 150 ++++++++++++++ .../log.4Nov2022.large_nylon_melt.g++.4 | 151 ++++++++++++++ .../rxn1_stp1_reacted.data_template | 189 ------------------ .../rxn1_stp1_reacted.molecule_template | 187 +++++++++++++++++ .../rxn1_stp1_unreacted.data_template | 160 --------------- .../rxn1_stp1_unreacted.molecule_template | 169 ++++++++++++++++ .../rxn1_stp2_reacted.data_template | 131 ------------ .../rxn1_stp2_reacted.molecule_template | 141 +++++++++++++ .../rxn1_stp2_unreacted.data_template | 158 --------------- .../rxn1_stp2_unreacted.molecule_template | 157 +++++++++++++++ 14 files changed, 965 insertions(+), 993 deletions(-) delete mode 100644 examples/PACKAGES/reaction/nylon,6-6_melt/log.20Apr18.large_nylon_melt.g++.1 delete mode 100644 examples/PACKAGES/reaction/nylon,6-6_melt/log.20Apr18.large_nylon_melt.g++.4 create mode 100644 examples/PACKAGES/reaction/nylon,6-6_melt/log.4Nov2022.large_nylon_melt.g++.1 create mode 100644 examples/PACKAGES/reaction/nylon,6-6_melt/log.4Nov2022.large_nylon_melt.g++.4 delete mode 100644 examples/PACKAGES/reaction/nylon,6-6_melt/rxn1_stp1_reacted.data_template create mode 100644 examples/PACKAGES/reaction/nylon,6-6_melt/rxn1_stp1_reacted.molecule_template delete mode 100644 examples/PACKAGES/reaction/nylon,6-6_melt/rxn1_stp1_unreacted.data_template create mode 100644 examples/PACKAGES/reaction/nylon,6-6_melt/rxn1_stp1_unreacted.molecule_template delete mode 100644 examples/PACKAGES/reaction/nylon,6-6_melt/rxn1_stp2_reacted.data_template create mode 100644 examples/PACKAGES/reaction/nylon,6-6_melt/rxn1_stp2_reacted.molecule_template delete mode 100644 examples/PACKAGES/reaction/nylon,6-6_melt/rxn1_stp2_unreacted.data_template create mode 100644 examples/PACKAGES/reaction/nylon,6-6_melt/rxn1_stp2_unreacted.molecule_template diff --git a/examples/PACKAGES/reaction/nylon,6-6_melt/in.large_nylon_melt b/examples/PACKAGES/reaction/nylon,6-6_melt/in.large_nylon_melt index 3982da799d..6fbf46f844 100644 --- a/examples/PACKAGES/reaction/nylon,6-6_melt/in.large_nylon_melt +++ b/examples/PACKAGES/reaction/nylon,6-6_melt/in.large_nylon_melt @@ -18,14 +18,19 @@ dihedral_style class2 improper_style class2 -read_data large_nylon_melt.data.gz +read_data large_nylon_melt.data.gz & + extra/bond/per/atom 5 & + extra/angle/per/atom 15 & + extra/dihedral/per/atom 15 & + extra/improper/per/atom 25 & + extra/special/per/atom 25 velocity all create 800.0 4928459 dist gaussian -molecule mol1 rxn1_stp1_unreacted.data_template -molecule mol2 rxn1_stp1_reacted.data_template -molecule mol3 rxn1_stp2_unreacted.data_template -molecule mol4 rxn1_stp2_reacted.data_template +molecule mol1 rxn1_stp1_unreacted.molecule_template +molecule mol2 rxn1_stp1_reacted.molecule_template +molecule mol3 rxn1_stp2_unreacted.molecule_template +molecule mol4 rxn1_stp2_reacted.molecule_template thermo 50 diff --git a/examples/PACKAGES/reaction/nylon,6-6_melt/large_nylon_melt.data.gz b/examples/PACKAGES/reaction/nylon,6-6_melt/large_nylon_melt.data.gz index c620b879a883817b8eb7abe4495e585ecacfaf02..e1ec3079f7409c8256f105ad922a97a5ec4304ed 100644 GIT binary patch literal 3777723 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653c7582f8..0000000000 --- a/examples/PACKAGES/reaction/nylon,6-6_melt/log.20Apr18.large_nylon_melt.g++.1 +++ /dev/null @@ -1,175 +0,0 @@ -LAMMPS (20 Apr 2018) -OMP_NUM_THREADS environment is not set. Defaulting to 1 thread. (../comm.cpp:90) - using 1 OpenMP thread(s) per MPI task -# 35,000 atom nylon melt example - -units real - -boundary p p p - -atom_style full - -kspace_style pppm 1.0e-4 - -pair_style lj/class2/coul/long 8.5 - -angle_style class2 - -bond_style class2 - -dihedral_style class2 - -improper_style class2 - -read_data large_nylon_melt.data.gz - orthogonal box = (-2.68344 -2.06791 -2.21988) to (73.4552 73.2448 73.4065) - 1 by 1 by 1 MPI processor grid - reading atoms ... - 35200 atoms - reading velocities ... - 35200 velocities - scanning bonds ... - 9 = max bonds/atom - scanning angles ... - 21 = max angles/atom - scanning dihedrals ... - 31 = max dihedrals/atom - scanning impropers ... - 29 = max impropers/atom - reading bonds ... - 33600 bonds - reading angles ... - 59200 angles - reading dihedrals ... - 80000 dihedrals - reading impropers ... - 35200 impropers - 4 = max # of 1-2 neighbors - 6 = max # of 1-3 neighbors - 12 = max # of 1-4 neighbors - 41 = max # of special neighbors - -velocity all create 800.0 4928459 dist gaussian - -molecule mol1 rxn1_stp1_unreacted.data_template -Read molecule mol1: - 18 atoms with max type 8 - 16 bonds with max type 12 - 25 angles with max type 24 - 23 dihedrals with max type 33 - 14 impropers with max type 9 -molecule mol2 rxn1_stp1_reacted.data_template -Read molecule mol2: - 18 atoms with max type 9 - 17 bonds with max type 11 - 31 angles with max type 23 - 39 dihedrals with max type 30 - 20 impropers with max type 1 -molecule mol3 rxn1_stp2_unreacted.data_template -Read molecule mol3: - 15 atoms with max type 9 - 14 bonds with max type 11 - 25 angles with max type 23 - 30 dihedrals with max type 30 - 16 impropers with max type 1 -molecule mol4 rxn1_stp2_reacted.data_template -Read molecule mol4: - 15 atoms with max type 11 - 13 bonds with max type 13 - 19 angles with max type 25 - 16 dihedrals with max type 29 - 10 impropers with max type 11 - -thermo 50 - -# dump 1 all xyz 100 test_vis.xyz - -fix myrxns all bond/react stabilization yes statted_grp .03 react rxn1 all 1 0.0 2.9 mol1 mol2 rxn1_stp1_map react rxn2 all 1 0.0 5.0 mol3 mol4 rxn1_stp2_map -WARNING: An atom in 'react #1' changes bond connectivity but not atom type (../fix_bond_react.cpp:1489) -WARNING: An atom in 'react #2' changes bond connectivity but not atom type (../fix_bond_react.cpp:1489) -dynamic group bond_react_MASTER_group defined -dynamic group statted_grp defined -dynamic group bond_react_MASTER_group defined -dynamic group statted_grp defined - -# stable at 800K -fix 1 statted_grp nvt temp 800 800 100 - -# in order to customize behavior of reacting atoms, -# you can use the internally created 'bond_react_MASTER_group', like so: -# fix 2 bond_react_MASTER_group temp/rescale 1 800 800 10 1 - -thermo_style custom step temp press density f_myrxns[1] f_myrxns[2] # cumulative reaction counts - -# restart 100 restart1 restart2 - -run 200 -PPPM initialization ... - using 12-bit tables for long-range coulomb (../kspace.cpp:321) - G vector (1/distance) = 0.20765 - grid = 18 18 18 - stencil order = 5 - estimated absolute RMS force accuracy = 0.0333156 - estimated relative force accuracy = 0.000100329 - using double precision FFTs - 3d grid and FFT values/proc = 12167 5832 -Neighbor list info ... - update every 1 steps, delay 10 steps, check yes - max neighbors/atom: 2000, page size: 100000 - master list distance cutoff = 10.5 - ghost atom cutoff = 10.5 - binsize = 5.25, bins = 15 15 15 - 2 neighbor lists, perpetual/occasional/extra = 1 1 0 - (1) pair lj/class2/coul/long, perpetual - attributes: half, newton on - pair build: half/bin/newton - stencil: half/bin/3d/newton - bin: standard - (2) fix bond/react, occasional, copy from (1) - attributes: half, newton on - pair build: copy - stencil: none - bin: none -Per MPI rank memory allocation (min/avg/max) = 209.1 | 209.1 | 209.1 Mbytes -Step Temp Press Density f_myrxns[1] f_myrxns[2] - 0 800 3666.3948 0.80366765 0 0 - 50 673.95238 -9670.9169 0.80366765 31 0 - 100 697.22819 -4624.0512 0.80366765 57 22 - 150 723.60507 -17175.571 0.80366765 76 48 - 200 736.71277 -12961.963 0.80366765 84 64 -Loop time of 102.825 on 1 procs for 200 steps with 35200 atoms - -Performance: 0.168 ns/day, 142.812 hours/ns, 1.945 timesteps/s -99.7% CPU use with 1 MPI tasks x 1 OpenMP threads - -MPI task timing breakdown: -Section | min time | avg time | max time |%varavg| %total ---------------------------------------------------------------- -Pair | 27.193 | 27.193 | 27.193 | 0.0 | 26.45 -Bond | 11.324 | 11.324 | 11.324 | 0.0 | 11.01 -Kspace | 4.1878 | 4.1878 | 4.1878 | 0.0 | 4.07 -Neigh | 54.724 | 54.724 | 54.724 | 0.0 | 53.22 -Comm | 0.40662 | 0.40662 | 0.40662 | 0.0 | 0.40 -Output | 0.0011101 | 0.0011101 | 0.0011101 | 0.0 | 0.00 -Modify | 4.9422 | 4.9422 | 4.9422 | 0.0 | 4.81 -Other | | 0.04545 | | | 0.04 - -Nlocal: 35200 ave 35200 max 35200 min -Histogram: 1 0 0 0 0 0 0 0 0 0 -Nghost: 38403 ave 38403 max 38403 min -Histogram: 1 0 0 0 0 0 0 0 0 0 -Neighs: 6.9281e+06 ave 6.9281e+06 max 6.9281e+06 min -Histogram: 1 0 0 0 0 0 0 0 0 0 - -Total # of neighbors = 6928101 -Ave neighs/atom = 196.821 -Ave special neighs/atom = 9.83727 -Neighbor list builds = 200 -Dangerous builds = 0 - -# write_restart restart_longrun -# write_data restart_longrun.data - -Please see the log.cite file for references relevant to this simulation - -Total wall time: 0:01:43 diff --git a/examples/PACKAGES/reaction/nylon,6-6_melt/log.20Apr18.large_nylon_melt.g++.4 b/examples/PACKAGES/reaction/nylon,6-6_melt/log.20Apr18.large_nylon_melt.g++.4 deleted file mode 100644 index cc0dda60c7..0000000000 --- a/examples/PACKAGES/reaction/nylon,6-6_melt/log.20Apr18.large_nylon_melt.g++.4 +++ /dev/null @@ -1,175 +0,0 @@ -LAMMPS (20 Apr 2018) -OMP_NUM_THREADS environment is not set. Defaulting to 1 thread. (../comm.cpp:90) - using 1 OpenMP thread(s) per MPI task -# 35,000 atom nylon melt example - -units real - -boundary p p p - -atom_style full - -kspace_style pppm 1.0e-4 - -pair_style lj/class2/coul/long 8.5 - -angle_style class2 - -bond_style class2 - -dihedral_style class2 - -improper_style class2 - -read_data large_nylon_melt.data.gz - orthogonal box = (-2.68344 -2.06791 -2.21988) to (73.4552 73.2448 73.4065) - 2 by 1 by 2 MPI processor grid - reading atoms ... - 35200 atoms - reading velocities ... - 35200 velocities - scanning bonds ... - 9 = max bonds/atom - scanning angles ... - 21 = max angles/atom - scanning dihedrals ... - 31 = max dihedrals/atom - scanning impropers ... - 29 = max impropers/atom - reading bonds ... - 33600 bonds - reading angles ... - 59200 angles - reading dihedrals ... - 80000 dihedrals - reading impropers ... - 35200 impropers - 4 = max # of 1-2 neighbors - 6 = max # of 1-3 neighbors - 12 = max # of 1-4 neighbors - 41 = max # of special neighbors - -velocity all create 800.0 4928459 dist gaussian - -molecule mol1 rxn1_stp1_unreacted.data_template -Read molecule mol1: - 18 atoms with max type 8 - 16 bonds with max type 12 - 25 angles with max type 24 - 23 dihedrals with max type 33 - 14 impropers with max type 9 -molecule mol2 rxn1_stp1_reacted.data_template -Read molecule mol2: - 18 atoms with max type 9 - 17 bonds with max type 11 - 31 angles with max type 23 - 39 dihedrals with max type 30 - 20 impropers with max type 1 -molecule mol3 rxn1_stp2_unreacted.data_template -Read molecule mol3: - 15 atoms with max type 9 - 14 bonds with max type 11 - 25 angles with max type 23 - 30 dihedrals with max type 30 - 16 impropers with max type 1 -molecule mol4 rxn1_stp2_reacted.data_template -Read molecule mol4: - 15 atoms with max type 11 - 13 bonds with max type 13 - 19 angles with max type 25 - 16 dihedrals with max type 29 - 10 impropers with max type 11 - -thermo 50 - -# dump 1 all xyz 100 test_vis.xyz - -fix myrxns all bond/react stabilization yes statted_grp .03 react rxn1 all 1 0.0 2.9 mol1 mol2 rxn1_stp1_map react rxn2 all 1 0.0 5.0 mol3 mol4 rxn1_stp2_map -WARNING: An atom in 'react #1' changes bond connectivity but not atom type (../fix_bond_react.cpp:1489) -WARNING: An atom in 'react #2' changes bond connectivity but not atom type (../fix_bond_react.cpp:1489) -dynamic group bond_react_MASTER_group defined -dynamic group statted_grp defined -dynamic group bond_react_MASTER_group defined -dynamic group statted_grp defined - -# stable at 800K -fix 1 statted_grp nvt temp 800 800 100 - -# in order to customize behavior of reacting atoms, -# you can use the internally created 'bond_react_MASTER_group', like so: -# fix 2 bond_react_MASTER_group temp/rescale 1 800 800 10 1 - -thermo_style custom step temp press density f_myrxns[1] f_myrxns[2] # cumulative reaction counts - -# restart 100 restart1 restart2 - -run 200 -PPPM initialization ... - using 12-bit tables for long-range coulomb (../kspace.cpp:321) - G vector (1/distance) = 0.20765 - grid = 18 18 18 - stencil order = 5 - estimated absolute RMS force accuracy = 0.0333156 - estimated relative force accuracy = 0.000100329 - using double precision FFTs - 3d grid and FFT values/proc = 4508 1620 -Neighbor list info ... - update every 1 steps, delay 10 steps, check yes - max neighbors/atom: 2000, page size: 100000 - master list distance cutoff = 10.5 - ghost atom cutoff = 10.5 - binsize = 5.25, bins = 15 15 15 - 2 neighbor lists, perpetual/occasional/extra = 1 1 0 - (1) pair lj/class2/coul/long, perpetual - attributes: half, newton on - pair build: half/bin/newton - stencil: half/bin/3d/newton - bin: standard - (2) fix bond/react, occasional, copy from (1) - attributes: half, newton on - pair build: copy - stencil: none - bin: none -Per MPI rank memory allocation (min/avg/max) = 81.11 | 81.13 | 81.15 Mbytes -Step Temp Press Density f_myrxns[1] f_myrxns[2] - 0 800 3666.3948 0.80366765 0 0 - 50 673.95238 -9670.9169 0.80366765 31 0 - 100 697.22819 -4624.0512 0.80366765 57 22 - 150 724.40407 -17166.729 0.80366765 76 49 - 200 737.28582 -12968.224 0.80366765 84 65 -Loop time of 51.171 on 4 procs for 200 steps with 35200 atoms - -Performance: 0.338 ns/day, 71.071 hours/ns, 3.908 timesteps/s -98.4% CPU use with 4 MPI tasks x 1 OpenMP threads - -MPI task timing breakdown: -Section | min time | avg time | max time |%varavg| %total ---------------------------------------------------------------- -Pair | 12.926 | 13.247 | 13.493 | 6.7 | 25.89 -Bond | 5.2132 | 5.2733 | 5.3367 | 1.9 | 10.31 -Kspace | 2.3601 | 2.6534 | 3.0067 | 16.0 | 5.19 -Neigh | 25.93 | 25.934 | 25.937 | 0.1 | 50.68 -Comm | 0.73273 | 0.75464 | 0.78505 | 2.3 | 1.47 -Output | 0.00045228 | 0.00067407 | 0.0013323 | 0.0 | 0.00 -Modify | 3.2682 | 3.2686 | 3.2692 | 0.0 | 6.39 -Other | | 0.03995 | | | 0.08 - -Nlocal: 8800 ave 8913 max 8652 min -Histogram: 1 0 0 0 1 0 0 0 1 1 -Nghost: 18366 ave 18461 max 18190 min -Histogram: 1 0 0 0 0 0 0 1 1 1 -Neighs: 1.73203e+06 ave 1.77261e+06 max 1.68165e+06 min -Histogram: 1 0 1 0 0 0 0 0 0 2 - -Total # of neighbors = 6928132 -Ave neighs/atom = 196.822 -Ave special neighs/atom = 9.83608 -Neighbor list builds = 200 -Dangerous builds = 0 - -# write_restart restart_longrun -# write_data restart_longrun.data - -Please see the log.cite file for references relevant to this simulation - -Total wall time: 0:00:52 diff --git a/examples/PACKAGES/reaction/nylon,6-6_melt/log.4Nov2022.large_nylon_melt.g++.1 b/examples/PACKAGES/reaction/nylon,6-6_melt/log.4Nov2022.large_nylon_melt.g++.1 new file mode 100644 index 0000000000..26c11bd020 --- /dev/null +++ b/examples/PACKAGES/reaction/nylon,6-6_melt/log.4Nov2022.large_nylon_melt.g++.1 @@ -0,0 +1,150 @@ +LAMMPS (4 Nov 2022) +Reading data file ... + orthogonal box = (-2.6834403 -2.0679138 -2.2198803) to (73.455228 73.244835 73.40648) + 1 by 1 by 1 MPI processor grid + reading atom labelmap ... + reading bond labelmap ... + reading angle labelmap ... + reading dihedral labelmap ... + reading improper labelmap ... + reading atoms ... + 35200 atoms + reading velocities ... + 35200 velocities + scanning bonds ... + 9 = max bonds/atom + scanning angles ... + 21 = max angles/atom + scanning dihedrals ... + 31 = max dihedrals/atom + scanning impropers ... + 29 = max impropers/atom + reading bonds ... + 33600 bonds + reading angles ... + 59200 angles + reading dihedrals ... + 80000 dihedrals + reading impropers ... + 35200 impropers +Finding 1-2 1-3 1-4 neighbors ... + special bond factors lj: 0 0 0 + special bond factors coul: 0 0 0 + 4 = max # of 1-2 neighbors + 6 = max # of 1-3 neighbors + 12 = max # of 1-4 neighbors + 41 = max # of special neighbors + special bonds CPU = 0.026 seconds + read_data CPU = 0.937 seconds +Read molecule template mol1: + 1 molecules + 0 fragments + 18 atoms with max type 8 + 16 bonds with max type 12 + 25 angles with max type 24 + 23 dihedrals with max type 33 + 2 impropers with max type 9 +Read molecule template mol2: + 1 molecules + 0 fragments + 18 atoms with max type 9 + 17 bonds with max type 11 + 31 angles with max type 23 + 39 dihedrals with max type 30 + 0 impropers with max type 0 +Read molecule template mol3: + 1 molecules + 0 fragments + 15 atoms with max type 9 + 14 bonds with max type 11 + 25 angles with max type 23 + 30 dihedrals with max type 30 + 0 impropers with max type 0 +Read molecule template mol4: + 1 molecules + 0 fragments + 15 atoms with max type 11 + 13 bonds with max type 13 + 19 angles with max type 25 + 16 dihedrals with max type 29 + 2 impropers with max type 11 +WARNING: Fix bond/react: Atom affected by reaction rxn2 is too close to template edge (../fix_bond_react.cpp:2624) +dynamic group bond_react_MASTER_group defined +dynamic group statted_grp_REACT defined + +CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE + +Your simulation uses code contributions which should be cited: +- fix bond/react: reacter.org doi:10.1016/j.polymer.2017.09.038, doi:10.1021/acs.macromol.0c02012 +The log file lists these citations in BibTeX format. + +CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE + +PPPM initialization ... + using 12-bit tables for long-range coulomb (../kspace.cpp:342) + G vector (1/distance) = 0.20765034 + grid = 18 18 18 + stencil order = 5 + estimated absolute RMS force accuracy = 0.033315619 + estimated relative force accuracy = 0.000100329 + using double precision KISS FFT + 3d grid and FFT values/proc = 12167 5832 +Generated 55 of 55 mixed pair_coeff terms from sixthpower/geometric mixing rule +Neighbor list info ... + update: every = 1 steps, delay = 0 steps, check = yes + max neighbors/atom: 2000, page size: 100000 + master list distance cutoff = 10.5 + ghost atom cutoff = 10.5 + binsize = 5.25, bins = 15 15 15 + 2 neighbor lists, perpetual/occasional/extra = 1 1 0 + (1) pair lj/class2/coul/long, perpetual + attributes: half, newton on + pair build: half/bin/newton + stencil: half/bin/3d + bin: standard + (2) fix bond/react, occasional, copy from (1) + attributes: half, newton on + pair build: copy + stencil: none + bin: none +Setting up Verlet run ... + Unit style : real + Current step : 0 + Time step : 1 +Per MPI rank memory allocation (min/avg/max) = 209.8 | 209.8 | 209.8 Mbytes + Step Temp Press Density f_myrxns[1] f_myrxns[2] + 0 800 3666.3948 0.80366765 0 0 + 50 673.94821 -9679.5038 0.80366765 31 0 + 100 694.45718 -2104.8514 0.80366765 57 22 + 150 716.53915 -12356.83 0.80366765 77 50 + 200 723.33218 -1319.9666 0.80366765 84 67 +Loop time of 87.9809 on 1 procs for 200 steps with 35200 atoms + +Performance: 0.196 ns/day, 122.196 hours/ns, 2.273 timesteps/s, 80.017 katom-step/s +100.0% CPU use with 1 MPI tasks x no OpenMP threads + +MPI task timing breakdown: +Section | min time | avg time | max time |%varavg| %total +--------------------------------------------------------------- +Pair | 25.691 | 25.691 | 25.691 | 0.0 | 29.20 +Bond | 15.772 | 15.772 | 15.772 | 0.0 | 17.93 +Kspace | 4.611 | 4.611 | 4.611 | 0.0 | 5.24 +Neigh | 35.616 | 35.616 | 35.616 | 0.0 | 40.48 +Comm | 0.24971 | 0.24971 | 0.24971 | 0.0 | 0.28 +Output | 0.00098602 | 0.00098602 | 0.00098602 | 0.0 | 0.00 +Modify | 5.9596 | 5.9596 | 5.9596 | 0.0 | 6.77 +Other | | 0.08051 | | | 0.09 + +Nlocal: 35200 ave 35200 max 35200 min +Histogram: 1 0 0 0 0 0 0 0 0 0 +Nghost: 38403 ave 38403 max 38403 min +Histogram: 1 0 0 0 0 0 0 0 0 0 +Neighs: 6.92764e+06 ave 6.92764e+06 max 6.92764e+06 min +Histogram: 1 0 0 0 0 0 0 0 0 0 + +Total # of neighbors = 6927635 +Ave neighs/atom = 196.80781 +Ave special neighs/atom = 9.8480114 +Neighbor list builds = 128 +Dangerous builds = 0 +Total wall time: 0:01:29 diff --git a/examples/PACKAGES/reaction/nylon,6-6_melt/log.4Nov2022.large_nylon_melt.g++.4 b/examples/PACKAGES/reaction/nylon,6-6_melt/log.4Nov2022.large_nylon_melt.g++.4 new file mode 100644 index 0000000000..69a663c59c --- /dev/null +++ b/examples/PACKAGES/reaction/nylon,6-6_melt/log.4Nov2022.large_nylon_melt.g++.4 @@ -0,0 +1,151 @@ +LAMMPS (4 Nov 2022) +WARNING: Using I/O redirection is unreliable with parallel runs. Better use -in switch to read input file. (../lammps.cpp:529) +Reading data file ... + orthogonal box = (-2.6834403 -2.0679138 -2.2198803) to (73.455228 73.244835 73.40648) + 2 by 1 by 2 MPI processor grid + reading atom labelmap ... + reading bond labelmap ... + reading angle labelmap ... + reading dihedral labelmap ... + reading improper labelmap ... + reading atoms ... + 35200 atoms + reading velocities ... + 35200 velocities + scanning bonds ... + 9 = max bonds/atom + scanning angles ... + 21 = max angles/atom + scanning dihedrals ... + 31 = max dihedrals/atom + scanning impropers ... + 29 = max impropers/atom + reading bonds ... + 33600 bonds + reading angles ... + 59200 angles + reading dihedrals ... + 80000 dihedrals + reading impropers ... + 35200 impropers +Finding 1-2 1-3 1-4 neighbors ... + special bond factors lj: 0 0 0 + special bond factors coul: 0 0 0 + 4 = max # of 1-2 neighbors + 6 = max # of 1-3 neighbors + 12 = max # of 1-4 neighbors + 41 = max # of special neighbors + special bonds CPU = 0.007 seconds + read_data CPU = 0.853 seconds +Read molecule template mol1: + 1 molecules + 0 fragments + 18 atoms with max type 8 + 16 bonds with max type 12 + 25 angles with max type 24 + 23 dihedrals with max type 33 + 2 impropers with max type 9 +Read molecule template mol2: + 1 molecules + 0 fragments + 18 atoms with max type 9 + 17 bonds with max type 11 + 31 angles with max type 23 + 39 dihedrals with max type 30 + 0 impropers with max type 0 +Read molecule template mol3: + 1 molecules + 0 fragments + 15 atoms with max type 9 + 14 bonds with max type 11 + 25 angles with max type 23 + 30 dihedrals with max type 30 + 0 impropers with max type 0 +Read molecule template mol4: + 1 molecules + 0 fragments + 15 atoms with max type 11 + 13 bonds with max type 13 + 19 angles with max type 25 + 16 dihedrals with max type 29 + 2 impropers with max type 11 +WARNING: Fix bond/react: Atom affected by reaction rxn2 is too close to template edge (../fix_bond_react.cpp:2624) +dynamic group bond_react_MASTER_group defined +dynamic group statted_grp_REACT defined + +CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE + +Your simulation uses code contributions which should be cited: +- fix bond/react: reacter.org doi:10.1016/j.polymer.2017.09.038, doi:10.1021/acs.macromol.0c02012 +The log file lists these citations in BibTeX format. + +CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE + +PPPM initialization ... + using 12-bit tables for long-range coulomb (../kspace.cpp:342) + G vector (1/distance) = 0.20765034 + grid = 18 18 18 + stencil order = 5 + estimated absolute RMS force accuracy = 0.033315619 + estimated relative force accuracy = 0.000100329 + using double precision KISS FFT + 3d grid and FFT values/proc = 4508 1620 +Generated 55 of 55 mixed pair_coeff terms from sixthpower/geometric mixing rule +Neighbor list info ... + update: every = 1 steps, delay = 0 steps, check = yes + max neighbors/atom: 2000, page size: 100000 + master list distance cutoff = 10.5 + ghost atom cutoff = 10.5 + binsize = 5.25, bins = 15 15 15 + 2 neighbor lists, perpetual/occasional/extra = 1 1 0 + (1) pair lj/class2/coul/long, perpetual + attributes: half, newton on + pair build: half/bin/newton + stencil: half/bin/3d + bin: standard + (2) fix bond/react, occasional, copy from (1) + attributes: half, newton on + pair build: copy + stencil: none + bin: none +Setting up Verlet run ... + Unit style : real + Current step : 0 + Time step : 1 +Per MPI rank memory allocation (min/avg/max) = 81.39 | 81.41 | 81.43 Mbytes + Step Temp Press Density f_myrxns[1] f_myrxns[2] + 0 800 3666.3948 0.80366765 0 0 + 50 673.94821 -9679.5038 0.80366765 31 0 + 100 694.36354 -2108.4881 0.80366765 57 22 + 150 716.5075 -12356.04 0.80366765 77 50 + 200 722.97306 -1308.3439 0.80366765 84 67 +Loop time of 23.0703 on 4 procs for 200 steps with 35200 atoms + +Performance: 0.749 ns/day, 32.042 hours/ns, 8.669 timesteps/s, 305.154 katom-step/s +100.0% CPU use with 4 MPI tasks x no OpenMP threads + +MPI task timing breakdown: +Section | min time | avg time | max time |%varavg| %total +--------------------------------------------------------------- +Pair | 6.6778 | 6.8513 | 6.9896 | 5.2 | 29.70 +Bond | 3.8962 | 3.9719 | 4.0488 | 3.0 | 17.22 +Kspace | 1.1907 | 1.3846 | 1.6278 | 15.9 | 6.00 +Neigh | 8.7963 | 8.7965 | 8.7967 | 0.0 | 38.13 +Comm | 0.1468 | 0.15512 | 0.16131 | 1.6 | 0.67 +Output | 0.00035931 | 0.00037432 | 0.00041707 | 0.0 | 0.00 +Modify | 1.8808 | 1.8808 | 1.8809 | 0.0 | 8.15 +Other | | 0.02973 | | | 0.13 + +Nlocal: 8800 ave 8911 max 8662 min +Histogram: 1 0 0 1 0 0 0 0 1 1 +Nghost: 18358.5 ave 18438 max 18183 min +Histogram: 1 0 0 0 0 0 0 0 1 2 +Neighs: 1.73191e+06 ave 1.77313e+06 max 1.68375e+06 min +Histogram: 1 0 1 0 0 0 0 0 0 2 + +Total # of neighbors = 6927655 +Ave neighs/atom = 196.80838 +Ave special neighs/atom = 9.8480114 +Neighbor list builds = 128 +Dangerous builds = 0 +Total wall time: 0:00:24 diff --git a/examples/PACKAGES/reaction/nylon,6-6_melt/rxn1_stp1_reacted.data_template b/examples/PACKAGES/reaction/nylon,6-6_melt/rxn1_stp1_reacted.data_template deleted file mode 100644 index 61c0408ce3..0000000000 --- a/examples/PACKAGES/reaction/nylon,6-6_melt/rxn1_stp1_reacted.data_template +++ /dev/null @@ -1,189 +0,0 @@ -this is a molecule template for: initial nylon crosslink, post-reacting - -18 atoms -17 bonds -31 angles -39 dihedrals -20 impropers - -Types - -1 9 -2 1 -3 1 -4 4 -5 4 -6 3 -7 3 -8 1 -9 1 -10 5 -11 8 -12 6 -13 3 -14 3 -15 7 -16 1 -17 3 -18 3 - -Charges - -1 -0.300000 -2 0.000000 -3 0.000000 -4 0.000000 -5 0.000000 -6 0.000000 -7 0.000000 -8 0.000000 -9 0.000000 -10 0.300000 -11 0.000000 -12 0.000000 -13 0.000000 -14 0.000000 -15 0.000000 -16 0.000000 -17 0.000000 -18 0.000000 - -Coords - -1 -5.522237 -0.752722 1.631158 -2 -5.170398 -0.545733 0.178130 -3 -6.469695 -0.553072 -0.648889 -4 -6.052076 -1.721152 1.744648 -5 -6.183059 0.071387 1.971497 -6 -4.489340 -1.389197 -0.173156 -7 -4.637591 0.453703 0.051252 -8 -5.618658 0.138919 4.386107 -9 -4.669492 -0.989819 3.943591 -10 -4.270194 -0.766405 2.474102 -11 -3.348470 -1.875393 2.024289 -12 -3.569794 0.564183 2.345995 -13 -5.201079 -1.993301 4.044219 -14 -3.736682 -0.984819 4.598305 -15 -4.255402 1.370923 2.679069 -16 -6.136394 -0.339866 -2.136775 -17 -6.996331 -1.555519 -0.517408 -18 -7.153308 0.284949 -0.289930 - -Bonds - -1 9 1 2 -2 10 1 4 -3 10 1 5 -4 11 1 10 -5 1 2 3 -6 2 2 6 -7 2 2 7 -8 1 3 16 -9 2 3 17 -10 2 3 18 -11 1 8 9 -12 6 9 10 -13 2 9 13 -14 2 9 14 -15 7 10 11 -16 5 10 12 -17 8 12 15 - -Angles - -1 14 2 1 4 -2 14 2 1 5 -3 15 2 1 10 -4 16 4 1 5 -5 17 4 1 10 -6 17 5 1 10 -7 18 1 2 3 -8 19 1 2 6 -9 19 1 2 7 -10 1 3 2 6 -11 1 3 2 7 -12 3 6 2 7 -13 2 2 3 16 -14 1 2 3 17 -15 1 2 3 18 -16 1 16 3 17 -17 1 16 3 18 -18 3 17 3 18 -19 12 8 9 10 -20 1 8 9 13 -21 1 8 9 14 -22 13 13 9 10 -23 13 14 9 10 -24 3 13 9 14 -25 10 9 10 11 -26 8 9 10 12 -27 20 1 10 9 -28 21 11 10 12 -29 22 1 10 11 -30 23 1 10 12 -31 11 10 12 15 - -Dihedrals - -1 16 4 1 2 3 -2 17 4 1 2 6 -3 17 4 1 2 7 -4 16 5 1 2 3 -5 17 5 1 2 6 -6 17 5 1 2 7 -7 18 10 1 2 3 -8 19 10 1 2 6 -9 19 10 1 2 7 -10 20 2 1 10 9 -11 21 2 1 10 11 -12 22 2 1 10 12 -13 23 4 1 10 9 -14 24 4 1 10 11 -15 25 4 1 10 12 -16 23 5 1 10 9 -17 24 5 1 10 11 -18 25 5 1 10 12 -19 26 1 2 3 16 -20 27 1 2 3 17 -21 27 1 2 3 18 -22 4 16 3 2 6 -23 2 6 2 3 17 -24 2 6 2 3 18 -25 4 16 3 2 7 -26 2 7 2 3 17 -27 2 7 2 3 18 -28 14 8 9 10 11 -29 12 8 9 10 12 -30 28 8 9 10 1 -31 15 13 9 10 11 -32 13 13 9 10 12 -33 29 13 9 10 1 -34 15 14 9 10 11 -35 13 14 9 10 12 -36 29 14 9 10 1 -37 10 9 10 12 15 -38 11 11 10 12 15 -39 30 1 10 12 15 - -Impropers - -1 1 2 1 4 5 -2 1 2 1 4 10 -3 1 2 1 5 10 -4 1 4 1 5 10 -5 1 1 2 3 6 -6 1 1 2 3 7 -7 1 1 2 6 7 -8 1 3 2 6 7 -9 1 2 3 16 17 -10 1 2 3 16 18 -11 1 2 3 17 18 -12 1 16 3 17 18 -13 1 8 9 13 10 -14 1 8 9 14 10 -15 1 8 9 13 14 -16 1 13 9 14 10 -17 1 9 10 11 12 -18 1 1 10 9 11 -19 1 1 10 9 12 -20 1 1 10 11 12 diff --git a/examples/PACKAGES/reaction/nylon,6-6_melt/rxn1_stp1_reacted.molecule_template b/examples/PACKAGES/reaction/nylon,6-6_melt/rxn1_stp1_reacted.molecule_template new file mode 100644 index 0000000000..40f3aa8276 --- /dev/null +++ b/examples/PACKAGES/reaction/nylon,6-6_melt/rxn1_stp1_reacted.molecule_template @@ -0,0 +1,187 @@ +this is a molecule template for: initial nylon crosslink, post-reacting + + 18 atoms + 17 bonds + 31 angles + 39 dihedrals + 0 impropers + +Coords + + 1 -5.522237178 -0.752722499 1.631158408 + 2 -5.170398325 -0.545733378 0.178129978 + 3 -6.469694974 -0.553071841 -0.648889109 + 4 -6.052075697 -1.721152483 1.744647858 + 5 -6.183058842 0.071386755 1.971497329 + 6 -4.489339595 -1.389196844 -0.173156276 + 7 -4.637590712 0.453703382 0.051251954 + 8 -5.618657658 0.138918810 4.386106928 + 9 -4.669491736 -0.989818781 3.943591338 + 10 -4.270193542 -0.766405234 2.474102239 + 11 -3.348470373 -1.875393291 2.024289246 + 12 -3.569793683 0.564183226 2.345995471 + 13 -5.201078949 -1.993301389 4.044218837 + 14 -3.736681607 -0.984819193 4.598304847 + 15 -4.255401979 1.370923174 2.679069013 + 16 -6.136393628 -0.339866195 -2.136774990 + 17 -6.996331494 -1.555519161 -0.517408063 + 18 -7.153308038 0.284949373 -0.289930394 + +Types + + 1 n + 2 c2 + 3 c2 + 4 hn + 5 hn + 6 hc + 7 hc + 8 c2 + 9 c2 + 10 c_1 + 11 o_1 + 12 o + 13 hc + 14 hc + 15 ho + 16 c2 + 17 hc + 18 hc + +Charges + + 1 -0.300000 + 2 0.000000 + 3 0.000000 + 4 0.000000 + 5 0.000000 + 6 0.000000 + 7 0.000000 + 8 0.000000 + 9 0.000000 + 10 0.300000 + 11 0.000000 + 12 0.000000 + 13 0.000000 + 14 0.000000 + 15 0.000000 + 16 0.000000 + 17 0.000000 + 18 0.000000 + +Molecules + + 1 1 + 2 1 + 3 1 + 4 1 + 5 1 + 6 1 + 7 1 + 8 1 + 9 1 + 10 1 + 11 1 + 12 1 + 13 1 + 14 1 + 15 1 + 16 1 + 17 1 + 18 1 + +Bonds + + 1 n-c2 1 2 + 2 n-hn 1 4 + 3 n-hn 1 5 + 4 n-c_1 1 10 + 5 c2-c2 2 3 + 6 c2-hc 2 6 + 7 c2-hc 2 7 + 8 c2-c2 3 16 + 9 c2-hc 3 17 + 10 c2-hc 3 18 + 11 c2-c2 8 9 + 12 c2-c_1 9 10 + 13 c2-hc 9 13 + 14 c2-hc 9 14 + 15 c_1-o_1 10 11 + 16 c_1-o 10 12 + 17 o-ho 12 15 + +Angles + + 1 c2-n-hn 2 1 4 + 2 c2-n-hn 2 1 5 + 3 c2-n-c_1 2 1 10 + 4 hn-n-hn 4 1 5 + 5 hn-n-c_1 4 1 10 + 6 hn-n-c_1 5 1 10 + 7 n-c2-c2 1 2 3 + 8 n-c2-hc 1 2 6 + 9 n-c2-hc 1 2 7 + 10 c2-c2-hc 3 2 6 + 11 c2-c2-hc 3 2 7 + 12 hc-c2-hc 6 2 7 + 13 c2-c2-c2 2 3 16 + 14 c2-c2-hc 2 3 17 + 15 c2-c2-hc 2 3 18 + 16 c2-c2-hc 16 3 17 + 17 c2-c2-hc 16 3 18 + 18 hc-c2-hc 17 3 18 + 19 c2-c2-c_1 8 9 10 + 20 c2-c2-hc 8 9 13 + 21 c2-c2-hc 8 9 14 + 22 hc-c2-c_1 13 9 10 + 23 hc-c2-c_1 14 9 10 + 24 hc-c2-hc 13 9 14 + 25 c2-c_1-o_1 9 10 11 + 26 c2-c_1-o 9 10 12 + 27 n-c_1-c2 1 10 9 + 28 o_1-c_1-o 11 10 12 + 29 n-c_1-o_1 1 10 11 + 30 n-c_1-o 1 10 12 + 31 c_1-o-ho 10 12 15 + +Dihedrals + + 1 hn-n-c2-c2 4 1 2 3 + 2 hn-n-c2-hc 4 1 2 6 + 3 hn-n-c2-hc 4 1 2 7 + 4 hn-n-c2-c2 5 1 2 3 + 5 hn-n-c2-hc 5 1 2 6 + 6 hn-n-c2-hc 5 1 2 7 + 7 c_1-n-c2-c2 10 1 2 3 + 8 c_1-n-c2-hc 10 1 2 6 + 9 c_1-n-c2-hc 10 1 2 7 + 10 c2-n-c_1-c2 2 1 10 9 + 11 c2-n-c_1-o_1 2 1 10 11 + 12 c2-n-c_1-o 2 1 10 12 + 13 hn-n-c_1-c2 4 1 10 9 + 14 hn-n-c_1-o_1 4 1 10 11 + 15 hn-n-c_1-o 4 1 10 12 + 16 hn-n-c_1-c2 5 1 10 9 + 17 hn-n-c_1-o_1 5 1 10 11 + 18 hn-n-c_1-o 5 1 10 12 + 19 n-c2-c2-c2 1 2 3 16 + 20 n-c2-c2-hc 1 2 3 17 + 21 n-c2-c2-hc 1 2 3 18 + 22 c2-c2-c2-hc 16 3 2 6 + 23 hc-c2-c2-hc 6 2 3 17 + 24 hc-c2-c2-hc 6 2 3 18 + 25 c2-c2-c2-hc 16 3 2 7 + 26 hc-c2-c2-hc 7 2 3 17 + 27 hc-c2-c2-hc 7 2 3 18 + 28 c2-c2-c_1-o_1 8 9 10 11 + 29 c2-c2-c_1-o 8 9 10 12 + 30 c2-c2-c_1-n 8 9 10 1 + 31 hc-c2-c_1-o_1 13 9 10 11 + 32 hc-c2-c_1-o 13 9 10 12 + 33 hc-c2-c_1-n 13 9 10 1 + 34 hc-c2-c_1-o_1 14 9 10 11 + 35 hc-c2-c_1-o 14 9 10 12 + 36 hc-c2-c_1-n 14 9 10 1 + 37 c2-c_1-o-ho 9 10 12 15 + 38 o_1-c_1-o-ho 11 10 12 15 + 39 n-c_1-o-ho 1 10 12 15 diff --git a/examples/PACKAGES/reaction/nylon,6-6_melt/rxn1_stp1_unreacted.data_template b/examples/PACKAGES/reaction/nylon,6-6_melt/rxn1_stp1_unreacted.data_template deleted file mode 100644 index 944d6918c5..0000000000 --- a/examples/PACKAGES/reaction/nylon,6-6_melt/rxn1_stp1_unreacted.data_template +++ /dev/null @@ -1,160 +0,0 @@ -this is a molecule template for: initial nylon crosslink, pre-reacting - -18 atoms -16 bonds -25 angles -23 dihedrals -14 impropers - -Types - -1 2 -2 1 -3 1 -4 4 -5 4 -6 3 -7 3 -8 1 -9 1 -10 5 -11 8 -12 6 -13 3 -14 3 -15 7 -16 1 -17 3 -18 3 - -Charges - -1 -0.300000 -2 0.000000 -3 0.000000 -4 0.000000 -5 0.000000 -6 0.000000 -7 0.000000 -8 0.000000 -9 0.000000 -10 0.300000 -11 0.000000 -12 0.000000 -13 0.000000 -14 0.000000 -15 0.000000 -16 0.000000 -17 0.000000 -18 0.000000 - -Coords - -1 -4.922858 -0.946982 1.146055 -2 -5.047195 -0.935267 -0.358173 -3 -6.526281 -0.755366 -0.743523 -4 -5.282604 0.020447 1.552710 -5 -3.860697 -1.095850 1.428305 -6 -4.662382 -1.920900 -0.781524 -7 -4.433977 -0.072765 -0.784071 -8 -5.506279 0.202610 4.825816 -9 -4.449177 -0.844592 4.423366 -10 -4.103916 -0.749629 2.925195 -11 -3.376249 -1.886171 2.245643 -12 -4.493235 0.477214 2.137199 -13 -4.849053 -1.888877 4.663994 -14 -3.491823 -0.662913 5.018510 -15 -5.020777 1.189745 2.805427 -16 -3.964987 2.900602 -1.551341 -17 -4.460694 2.836102 0.668882 -18 -4.828494 3.219656 -0.122111 - -Bonds - -1 12 1 2 -2 4 1 4 -3 4 1 5 -4 1 2 3 -5 2 2 6 -6 2 2 7 -7 1 3 16 -8 2 3 17 -9 2 3 18 -10 1 8 9 -11 6 9 10 -12 2 9 13 -13 2 9 14 -14 7 10 11 -15 5 10 12 -16 8 12 15 - -Angles - -1 6 2 1 4 -2 6 2 1 5 -3 7 4 1 5 -4 24 1 2 3 -5 5 1 2 6 -6 5 1 2 7 -7 1 3 2 6 -8 1 3 2 7 -9 3 6 2 7 -10 2 2 3 16 -11 1 2 3 17 -12 1 2 3 18 -13 1 16 3 17 -14 1 16 3 18 -15 3 17 3 18 -16 12 8 9 10 -17 1 8 9 13 -18 1 8 9 14 -19 13 13 9 10 -20 13 14 9 10 -21 3 13 9 14 -22 10 9 10 11 -23 8 9 10 12 -24 21 11 10 12 -25 11 10 12 15 - -Dihedrals - -1 31 4 1 2 3 -2 32 4 1 2 6 -3 32 4 1 2 7 -4 31 5 1 2 3 -5 32 5 1 2 6 -6 32 5 1 2 7 -7 33 1 2 3 16 -8 1 1 2 3 17 -9 1 1 2 3 18 -10 4 16 3 2 6 -11 2 6 2 3 17 -12 2 6 2 3 18 -13 4 16 3 2 7 -14 2 7 2 3 17 -15 2 7 2 3 18 -16 14 8 9 10 11 -17 12 8 9 10 12 -18 15 13 9 10 11 -19 13 13 9 10 12 -20 15 14 9 10 11 -21 13 14 9 10 12 -22 10 9 10 12 15 -23 11 11 10 12 15 - -Impropers - -1 1 2 1 4 5 -2 9 9 10 11 12 -3 1 1 2 3 6 -4 1 1 2 3 7 -5 1 1 2 6 7 -6 1 3 2 6 7 -7 1 2 3 16 17 -8 1 2 3 16 18 -9 1 2 3 17 18 -10 1 16 3 17 18 -11 1 8 9 13 10 -12 1 8 9 14 10 -13 1 8 9 13 14 -14 1 13 9 14 10 diff --git a/examples/PACKAGES/reaction/nylon,6-6_melt/rxn1_stp1_unreacted.molecule_template b/examples/PACKAGES/reaction/nylon,6-6_melt/rxn1_stp1_unreacted.molecule_template new file mode 100644 index 0000000000..7de7512f1c --- /dev/null +++ b/examples/PACKAGES/reaction/nylon,6-6_melt/rxn1_stp1_unreacted.molecule_template @@ -0,0 +1,169 @@ +this is a molecule template for: initial nylon crosslink, pre-reacting + + 18 atoms + 16 bonds + 25 angles + 23 dihedrals + 2 impropers + +Coords + + 1 -4.922858499 -0.946981747 1.146055346 + 2 -5.047194816 -0.935266843 -0.358172771 + 3 -6.526281447 -0.755365854 -0.743523227 + 4 -5.282604074 0.020446894 1.552710361 + 5 -3.860696509 -1.095850190 1.428304925 + 6 -4.662381862 -1.920899862 -0.781524026 + 7 -4.433976540 -0.072765142 -0.784070641 + 8 -5.506279186 0.202610302 4.825815562 + 9 -4.449176624 -0.844592213 4.423366146 + 10 -4.103915981 -0.749628655 2.925195217 + 11 -3.376248536 -1.886171498 2.245643443 + 12 -4.493235430 0.477213651 2.137199034 + 13 -4.849052953 -1.888876753 4.663993750 + 14 -3.491822950 -0.662913310 5.018510248 + 15 -5.020776528 1.189745133 2.805427194 + 16 -3.964987378 2.900602044 -1.551341170 + 17 -4.460693773 2.836101897 0.668881952 + 18 -4.828494000 3.219655862 -0.122111278 + +Types + + 1 na + 2 c2 + 3 c2 + 4 hn + 5 hn + 6 hc + 7 hc + 8 c2 + 9 c2 + 10 c_1 + 11 o_1 + 12 o + 13 hc + 14 hc + 15 ho + 16 c2 + 17 hc + 18 hc + +Charges + + 1 -0.300000 + 2 0.000000 + 3 0.000000 + 4 0.000000 + 5 0.000000 + 6 0.000000 + 7 0.000000 + 8 0.000000 + 9 0.000000 + 10 0.300000 + 11 0.000000 + 12 0.000000 + 13 0.000000 + 14 0.000000 + 15 0.000000 + 16 0.000000 + 17 0.000000 + 18 0.000000 + +Molecules + + 1 1 + 2 1 + 3 1 + 4 1 + 5 1 + 6 1 + 7 1 + 8 1 + 9 1 + 10 1 + 11 1 + 12 1 + 13 1 + 14 1 + 15 1 + 16 1 + 17 1 + 18 1 + +Bonds + + 1 na-c2 1 2 + 2 na-hn 1 4 + 3 na-hn 1 5 + 4 c2-c2 2 3 + 5 c2-hc 2 6 + 6 c2-hc 2 7 + 7 c2-c2 3 16 + 8 c2-hc 3 17 + 9 c2-hc 3 18 + 10 c2-c2 8 9 + 11 c2-c_1 9 10 + 12 c2-hc 9 13 + 13 c2-hc 9 14 + 14 c_1-o_1 10 11 + 15 c_1-o 10 12 + 16 o-ho 12 15 + +Angles + + 1 c2-na-hn 2 1 4 + 2 c2-na-hn 2 1 5 + 3 hn-na-hn 4 1 5 + 4 na-c2-c2 1 2 3 + 5 na-c2-hc 1 2 6 + 6 na-c2-hc 1 2 7 + 7 c2-c2-hc 3 2 6 + 8 c2-c2-hc 3 2 7 + 9 hc-c2-hc 6 2 7 + 10 c2-c2-c2 2 3 16 + 11 c2-c2-hc 2 3 17 + 12 c2-c2-hc 2 3 18 + 13 c2-c2-hc 16 3 17 + 14 c2-c2-hc 16 3 18 + 15 hc-c2-hc 17 3 18 + 16 c2-c2-c_1 8 9 10 + 17 c2-c2-hc 8 9 13 + 18 c2-c2-hc 8 9 14 + 19 hc-c2-c_1 13 9 10 + 20 hc-c2-c_1 14 9 10 + 21 hc-c2-hc 13 9 14 + 22 c2-c_1-o_1 9 10 11 + 23 c2-c_1-o 9 10 12 + 24 o_1-c_1-o 11 10 12 + 25 c_1-o-ho 10 12 15 + +Dihedrals + + 1 hn-na-c2-c2 4 1 2 3 + 2 hn-na-c2-hc 4 1 2 6 + 3 hn-na-c2-hc 4 1 2 7 + 4 hn-na-c2-c2 5 1 2 3 + 5 hn-na-c2-hc 5 1 2 6 + 6 hn-na-c2-hc 5 1 2 7 + 7 na-c2-c2-c2 1 2 3 16 + 8 na-c2-c2-hc 1 2 3 17 + 9 na-c2-c2-hc 1 2 3 18 + 10 c2-c2-c2-hc 16 3 2 6 + 11 hc-c2-c2-hc 6 2 3 17 + 12 hc-c2-c2-hc 6 2 3 18 + 13 c2-c2-c2-hc 16 3 2 7 + 14 hc-c2-c2-hc 7 2 3 17 + 15 hc-c2-c2-hc 7 2 3 18 + 16 c2-c2-c_1-o_1 8 9 10 11 + 17 c2-c2-c_1-o 8 9 10 12 + 18 hc-c2-c_1-o_1 13 9 10 11 + 19 hc-c2-c_1-o 13 9 10 12 + 20 hc-c2-c_1-o_1 14 9 10 11 + 21 hc-c2-c_1-o 14 9 10 12 + 22 c2-c_1-o-ho 9 10 12 15 + 23 o_1-c_1-o-ho 11 10 12 15 + +Impropers + + 1 c2-na-hn-hn 2 1 4 5 + 2 c2-c_1-o_1-o 9 10 11 12 diff --git a/examples/PACKAGES/reaction/nylon,6-6_melt/rxn1_stp2_reacted.data_template b/examples/PACKAGES/reaction/nylon,6-6_melt/rxn1_stp2_reacted.data_template deleted file mode 100644 index ffd3ef733c..0000000000 --- a/examples/PACKAGES/reaction/nylon,6-6_melt/rxn1_stp2_reacted.data_template +++ /dev/null @@ -1,131 +0,0 @@ -this is a molecule template for: water condensation, post-reacting - -15 atoms -13 bonds -19 angles -16 dihedrals -10 impropers - -Types - -1 9 -2 1 -3 1 -4 10 -5 4 -6 3 -7 3 -8 1 -9 1 -10 5 -11 8 -12 11 -13 3 -14 3 -15 10 - -Charges - -1 -0.300000 -2 0.000000 -3 0.000000 -4 0.410000 -5 0.000000 -6 0.000000 -7 0.000000 -8 0.000000 -9 0.000000 -10 0.300000 -11 0.000000 -12 -0.820000 -13 0.000000 -14 0.000000 -15 0.410000 - -Coords - -1 -4.856280 -1.050468 1.432625 -2 -5.047195 -0.935267 -0.358173 -3 -6.526281 -0.755366 -0.743523 -4 -5.282604 0.020447 1.552710 -5 -3.860697 -1.095850 1.428305 -6 -4.662382 -1.920900 -0.781524 -7 -4.433977 -0.072765 -0.784071 -8 -5.506279 0.202610 4.825816 -9 -4.449177 -0.844592 4.423366 -10 -4.103916 -0.749629 2.925195 -11 -3.376249 -1.886171 2.245643 -12 -4.493235 0.477214 2.137199 -13 -4.849053 -1.888877 4.663994 -14 -3.491823 -0.662913 5.018510 -15 -5.020777 1.189745 2.805427 - -Bonds - -1 9 1 2 -2 10 1 5 -3 11 1 10 -4 1 2 3 -5 2 2 6 -6 2 2 7 -7 13 4 12 -8 1 8 9 -9 6 9 10 -10 2 9 13 -11 2 9 14 -12 7 10 11 -13 13 15 12 - -Angles - -1 14 2 1 5 -2 15 2 1 10 -3 17 5 1 10 -4 18 1 2 3 -5 19 1 2 6 -6 19 1 2 7 -7 1 3 2 6 -8 1 3 2 7 -9 3 6 2 7 -10 12 8 9 10 -11 1 8 9 13 -12 1 8 9 14 -13 13 13 9 10 -14 13 14 9 10 -15 3 13 9 14 -16 10 9 10 11 -17 20 1 10 9 -18 22 1 10 11 -19 25 15 12 4 - -Dihedrals - -1 16 5 1 2 3 -2 17 5 1 2 6 -3 17 5 1 2 7 -4 18 10 1 2 3 -5 19 10 1 2 6 -6 19 10 1 2 7 -7 20 2 1 10 9 -8 21 2 1 10 11 -9 23 5 1 10 9 -10 24 5 1 10 11 -11 14 8 9 10 11 -12 28 8 9 10 1 -13 15 13 9 10 11 -14 29 13 9 10 1 -15 15 14 9 10 11 -16 29 14 9 10 1 - -Impropers - -1 10 2 1 5 10 -2 11 1 10 9 11 -3 1 1 2 3 6 -4 1 1 2 3 7 -5 1 1 2 6 7 -6 1 3 2 6 7 -7 1 8 9 13 10 -8 1 8 9 14 10 -9 1 8 9 13 14 -10 1 13 9 14 10 diff --git a/examples/PACKAGES/reaction/nylon,6-6_melt/rxn1_stp2_reacted.molecule_template b/examples/PACKAGES/reaction/nylon,6-6_melt/rxn1_stp2_reacted.molecule_template new file mode 100644 index 0000000000..2e91261468 --- /dev/null +++ b/examples/PACKAGES/reaction/nylon,6-6_melt/rxn1_stp2_reacted.molecule_template @@ -0,0 +1,141 @@ +this is a molecule template for: water condensation, post-reacting + + 15 atoms + 13 bonds + 19 angles + 16 dihedrals + 2 impropers + +Coords + + 1 -4.856280281 -1.050467974 1.432625159 + 2 -5.047194816 -0.935266843 -0.358172771 + 3 -6.526281447 -0.755365854 -0.743523227 + 4 -5.282604074 0.020446894 1.552710361 + 5 -3.860696509 -1.095850190 1.428304925 + 6 -4.662381862 -1.920899862 -0.781524026 + 7 -4.433976540 -0.072765142 -0.784070641 + 8 -5.506279186 0.202610302 4.825815562 + 9 -4.449176624 -0.844592213 4.423366146 + 10 -4.103915981 -0.749628655 2.925195217 + 11 -3.376248536 -1.886171498 2.245643443 + 12 -4.493235430 0.477213651 2.137199034 + 13 -4.849052953 -1.888876753 4.663993750 + 14 -3.491822950 -0.662913310 5.018510248 + 15 -5.020776528 1.189745133 2.805427194 + +Types + + 1 n + 2 c2 + 3 c2 + 4 hw + 5 hn + 6 hc + 7 hc + 8 c2 + 9 c2 + 10 c_1 + 11 o_1 + 12 o* + 13 hc + 14 hc + 15 hw + +Charges + + 1 -0.300000 + 2 0.000000 + 3 0.000000 + 4 0.410000 + 5 0.000000 + 6 0.000000 + 7 0.000000 + 8 0.000000 + 9 0.000000 + 10 0.300000 + 11 0.000000 + 12 -0.820000 + 13 0.000000 + 14 0.000000 + 15 0.410000 + +Molecules + + 1 1 + 2 1 + 3 1 + 4 1 + 5 1 + 6 1 + 7 1 + 8 1 + 9 1 + 10 1 + 11 1 + 12 1 + 13 1 + 14 1 + 15 1 + +Bonds + + 1 n-c2 1 2 + 2 n-hn 1 5 + 3 n-c_1 1 10 + 4 c2-c2 2 3 + 5 c2-hc 2 6 + 6 c2-hc 2 7 + 7 hw-o* 4 12 + 8 c2-c2 8 9 + 9 c2-c_1 9 10 + 10 c2-hc 9 13 + 11 c2-hc 9 14 + 12 c_1-o_1 10 11 + 13 hw-o* 15 12 + +Angles + + 1 c2-n-hn 2 1 5 + 2 c2-n-c_1 2 1 10 + 3 hn-n-c_1 5 1 10 + 4 n-c2-c2 1 2 3 + 5 n-c2-hc 1 2 6 + 6 n-c2-hc 1 2 7 + 7 c2-c2-hc 3 2 6 + 8 c2-c2-hc 3 2 7 + 9 hc-c2-hc 6 2 7 + 10 c2-c2-c_1 8 9 10 + 11 c2-c2-hc 8 9 13 + 12 c2-c2-hc 8 9 14 + 13 hc-c2-c_1 13 9 10 + 14 hc-c2-c_1 14 9 10 + 15 hc-c2-hc 13 9 14 + 16 c2-c_1-o_1 9 10 11 + 17 n-c_1-c2 1 10 9 + 18 n-c_1-o_1 1 10 11 + 19 hw-o*-hw 15 12 4 + +Dihedrals + + 1 hn-n-c2-c2 5 1 2 3 + 2 hn-n-c2-hc 5 1 2 6 + 3 hn-n-c2-hc 5 1 2 7 + 4 c_1-n-c2-c2 10 1 2 3 + 5 c_1-n-c2-hc 10 1 2 6 + 6 c_1-n-c2-hc 10 1 2 7 + 7 c2-n-c_1-c2 2 1 10 9 + 8 c2-n-c_1-o_1 2 1 10 11 + 9 hn-n-c_1-c2 5 1 10 9 + 10 hn-n-c_1-o_1 5 1 10 11 + 11 c2-c2-c_1-o_1 8 9 10 11 + 12 c2-c2-c_1-n 8 9 10 1 + 13 hc-c2-c_1-o_1 13 9 10 11 + 14 hc-c2-c_1-n 13 9 10 1 + 15 hc-c2-c_1-o_1 14 9 10 11 + 16 hc-c2-c_1-n 14 9 10 1 + +Impropers + + 1 c2-n-hn-c_1 2 1 5 10 + 2 n-c_1-c2-o_1 1 10 9 11 diff --git a/examples/PACKAGES/reaction/nylon,6-6_melt/rxn1_stp2_unreacted.data_template b/examples/PACKAGES/reaction/nylon,6-6_melt/rxn1_stp2_unreacted.data_template deleted file mode 100644 index 7abe15ada8..0000000000 --- a/examples/PACKAGES/reaction/nylon,6-6_melt/rxn1_stp2_unreacted.data_template +++ /dev/null @@ -1,158 +0,0 @@ -this is a molecule template for: water condensation, pre-reacting - -15 atoms -14 bonds -25 angles -30 dihedrals -16 impropers - -Types - -1 9 -2 1 -3 1 -4 4 -5 4 -6 3 -7 3 -8 1 -9 1 -10 5 -11 8 -12 6 -13 3 -14 3 -15 7 - -Charges - -1 -0.300000 -2 0.000000 -3 0.000000 -4 0.000000 -5 0.000000 -6 0.000000 -7 0.000000 -8 0.000000 -9 0.000000 -10 0.300000 -11 0.000000 -12 0.000000 -13 0.000000 -14 0.000000 -15 0.000000 - -Coords - -1 -4.922858 -0.946982 1.146055 -2 -5.047195 -0.935267 -0.358173 -3 -6.526281 -0.755366 -0.743523 -4 -5.282604 0.020447 1.552710 -5 -3.860697 -1.095850 1.428305 -6 -4.662382 -1.920900 -0.781524 -7 -4.433977 -0.072765 -0.784071 -8 -5.506279 0.202610 4.825816 -9 -4.449177 -0.844592 4.423366 -10 -4.103916 -0.749629 2.925195 -11 -3.376249 -1.886171 2.245643 -12 -4.493235 0.477214 2.137199 -13 -4.849053 -1.888877 4.663994 -14 -3.491823 -0.662913 5.018510 -15 -5.020777 1.189745 2.805427 - -Bonds - -1 9 1 2 -2 10 1 4 -3 10 1 5 -4 11 1 10 -5 1 2 3 -6 2 2 6 -7 2 2 7 -8 1 8 9 -9 6 9 10 -10 2 9 13 -11 2 9 14 -12 7 10 11 -13 5 10 12 -14 8 12 15 - -Angles - -1 14 2 1 4 -2 14 2 1 5 -3 15 2 1 10 -4 16 4 1 5 -5 17 4 1 10 -6 17 5 1 10 -7 18 1 2 3 -8 19 1 2 6 -9 19 1 2 7 -10 1 3 2 6 -11 1 3 2 7 -12 3 6 2 7 -13 12 8 9 10 -14 1 8 9 13 -15 1 8 9 14 -16 13 13 9 10 -17 13 14 9 10 -18 3 13 9 14 -19 10 9 10 11 -20 8 9 10 12 -21 20 1 10 9 -22 21 11 10 12 -23 22 1 10 11 -24 23 1 10 12 -25 11 10 12 15 - -Dihedrals - -1 16 4 1 2 3 -2 17 4 1 2 6 -3 17 4 1 2 7 -4 16 5 1 2 3 -5 17 5 1 2 6 -6 17 5 1 2 7 -7 18 10 1 2 3 -8 19 10 1 2 6 -9 19 10 1 2 7 -10 20 2 1 10 9 -11 21 2 1 10 11 -12 22 2 1 10 12 -13 23 4 1 10 9 -14 24 4 1 10 11 -15 25 4 1 10 12 -16 23 5 1 10 9 -17 24 5 1 10 11 -18 25 5 1 10 12 -19 14 8 9 10 11 -20 12 8 9 10 12 -21 28 8 9 10 1 -22 15 13 9 10 11 -23 13 13 9 10 12 -24 29 13 9 10 1 -25 15 14 9 10 11 -26 13 14 9 10 12 -27 29 14 9 10 1 -28 10 9 10 12 15 -29 11 11 10 12 15 -30 30 1 10 12 15 - -Impropers - -1 1 2 1 4 5 -2 1 2 1 4 10 -3 1 2 1 5 10 -4 1 4 1 5 10 -5 1 1 2 3 6 -6 1 1 2 3 7 -7 1 1 2 6 7 -8 1 3 2 6 7 -9 1 8 9 13 10 -10 1 8 9 14 10 -11 1 8 9 13 14 -12 1 13 9 14 10 -13 1 9 10 11 12 -14 1 1 10 9 11 -15 1 1 10 9 12 -16 1 1 10 11 12 diff --git a/examples/PACKAGES/reaction/nylon,6-6_melt/rxn1_stp2_unreacted.molecule_template b/examples/PACKAGES/reaction/nylon,6-6_melt/rxn1_stp2_unreacted.molecule_template new file mode 100644 index 0000000000..86a772634d --- /dev/null +++ b/examples/PACKAGES/reaction/nylon,6-6_melt/rxn1_stp2_unreacted.molecule_template @@ -0,0 +1,157 @@ +this is a molecule template for: water condensation, pre-reacting + + 15 atoms + 14 bonds + 25 angles + 30 dihedrals + 0 impropers + +Coords + + 1 -4.922858499 -0.946981747 1.146055346 + 2 -5.047194816 -0.935266843 -0.358172771 + 3 -6.526281447 -0.755365854 -0.743523227 + 4 -5.282604074 0.020446894 1.552710361 + 5 -3.860696509 -1.095850190 1.428304925 + 6 -4.662381862 -1.920899862 -0.781524026 + 7 -4.433976540 -0.072765142 -0.784070641 + 8 -5.506279186 0.202610302 4.825815562 + 9 -4.449176624 -0.844592213 4.423366146 + 10 -4.103915981 -0.749628655 2.925195217 + 11 -3.376248536 -1.886171498 2.245643443 + 12 -4.493235430 0.477213651 2.137199034 + 13 -4.849052953 -1.888876753 4.663993750 + 14 -3.491822950 -0.662913310 5.018510248 + 15 -5.020776528 1.189745133 2.805427194 + +Types + + 1 n + 2 c2 + 3 c2 + 4 hn + 5 hn + 6 hc + 7 hc + 8 c2 + 9 c2 + 10 c_1 + 11 o_1 + 12 o + 13 hc + 14 hc + 15 ho + +Charges + + 1 -0.300000 + 2 0.000000 + 3 0.000000 + 4 0.000000 + 5 0.000000 + 6 0.000000 + 7 0.000000 + 8 0.000000 + 9 0.000000 + 10 0.300000 + 11 0.000000 + 12 0.000000 + 13 0.000000 + 14 0.000000 + 15 0.000000 + +Molecules + + 1 1 + 2 1 + 3 1 + 4 1 + 5 1 + 6 1 + 7 1 + 8 1 + 9 1 + 10 1 + 11 1 + 12 1 + 13 1 + 14 1 + 15 1 + +Bonds + + 1 n-c2 1 2 + 2 n-hn 1 4 + 3 n-hn 1 5 + 4 n-c_1 1 10 + 5 c2-c2 2 3 + 6 c2-hc 2 6 + 7 c2-hc 2 7 + 8 c2-c2 8 9 + 9 c2-c_1 9 10 + 10 c2-hc 9 13 + 11 c2-hc 9 14 + 12 c_1-o_1 10 11 + 13 c_1-o 10 12 + 14 o-ho 12 15 + +Angles + + 1 c2-n-hn 2 1 4 + 2 c2-n-hn 2 1 5 + 3 c2-n-c_1 2 1 10 + 4 hn-n-hn 4 1 5 + 5 hn-n-c_1 4 1 10 + 6 hn-n-c_1 5 1 10 + 7 n-c2-c2 1 2 3 + 8 n-c2-hc 1 2 6 + 9 n-c2-hc 1 2 7 + 10 c2-c2-hc 3 2 6 + 11 c2-c2-hc 3 2 7 + 12 hc-c2-hc 6 2 7 + 13 c2-c2-c_1 8 9 10 + 14 c2-c2-hc 8 9 13 + 15 c2-c2-hc 8 9 14 + 16 hc-c2-c_1 13 9 10 + 17 hc-c2-c_1 14 9 10 + 18 hc-c2-hc 13 9 14 + 19 c2-c_1-o_1 9 10 11 + 20 c2-c_1-o 9 10 12 + 21 n-c_1-c2 1 10 9 + 22 o_1-c_1-o 11 10 12 + 23 n-c_1-o_1 1 10 11 + 24 n-c_1-o 1 10 12 + 25 c_1-o-ho 10 12 15 + +Dihedrals + + 1 hn-n-c2-c2 4 1 2 3 + 2 hn-n-c2-hc 4 1 2 6 + 3 hn-n-c2-hc 4 1 2 7 + 4 hn-n-c2-c2 5 1 2 3 + 5 hn-n-c2-hc 5 1 2 6 + 6 hn-n-c2-hc 5 1 2 7 + 7 c_1-n-c2-c2 10 1 2 3 + 8 c_1-n-c2-hc 10 1 2 6 + 9 c_1-n-c2-hc 10 1 2 7 + 10 c2-n-c_1-c2 2 1 10 9 + 11 c2-n-c_1-o_1 2 1 10 11 + 12 c2-n-c_1-o 2 1 10 12 + 13 hn-n-c_1-c2 4 1 10 9 + 14 hn-n-c_1-o_1 4 1 10 11 + 15 hn-n-c_1-o 4 1 10 12 + 16 hn-n-c_1-c2 5 1 10 9 + 17 hn-n-c_1-o_1 5 1 10 11 + 18 hn-n-c_1-o 5 1 10 12 + 19 c2-c2-c_1-o_1 8 9 10 11 + 20 c2-c2-c_1-o 8 9 10 12 + 21 c2-c2-c_1-n 8 9 10 1 + 22 hc-c2-c_1-o_1 13 9 10 11 + 23 hc-c2-c_1-o 13 9 10 12 + 24 hc-c2-c_1-n 13 9 10 1 + 25 hc-c2-c_1-o_1 14 9 10 11 + 26 hc-c2-c_1-o 14 9 10 12 + 27 hc-c2-c_1-n 14 9 10 1 + 28 c2-c_1-o-ho 9 10 12 15 + 29 o_1-c_1-o-ho 11 10 12 15 + 30 n-c_1-o-ho 1 10 12 15 From b5eb64cc0c2ab83497cc0964a9b626b779245940 Mon Sep 17 00:00:00 2001 From: Jacob Gissinger Date: Thu, 15 Dec 2022 13:08:25 -0500 Subject: [PATCH 06/47] type labels for tiny_nylon example --- .../tiny_nylon/in.tiny_nylon.stabilized | 15 +- ...tiny_nylon.stabilized_variable_probability | 15 +- .../tiny_nylon/in.tiny_nylon.unstabilized | 16 +- ...ylon.stabilized_variable_probability.g++.1 | 201 --------- ...ylon.stabilized_variable_probability.g++.4 | 201 --------- .../log.4Nov2020.tiny_nylon.stabilized.g++.1 | 412 ++++++++++++++++++ .../log.4Nov2020.tiny_nylon.stabilized.g++.4 | 412 ++++++++++++++++++ ...ylon.stabilized_variable_probability.g++.1 | 237 ++++++++++ ...ylon.stabilized_variable_probability.g++.4 | 237 ++++++++++ ...log.4Nov2020.tiny_nylon.unstabilized.g++.1 | 228 ++++++++++ ...log.4Nov2020.tiny_nylon.unstabilized.g++.4 | 228 ++++++++++ .../log.5Jun19.tiny_nylon.stabilized.g++.1 | 148 ------- .../log.5Jun19.tiny_nylon.stabilized.g++.4 | 148 ------- .../log.5Jun19.tiny_nylon.unstabilized.g++.1 | 147 ------- .../log.5Jun19.tiny_nylon.unstabilized.g++.4 | 147 ------- .../rxn1_stp1_reacted.data_template | 189 -------- .../rxn1_stp1_reacted.molecule_template | 187 ++++++++ .../rxn1_stp1_unreacted.data_template | 160 ------- .../rxn1_stp1_unreacted.molecule_template | 169 +++++++ .../rxn1_stp2_reacted.data_template | 131 ------ .../rxn1_stp2_reacted.molecule_template | 141 ++++++ .../rxn1_stp2_unreacted.data_template | 158 ------- .../rxn1_stp2_unreacted.molecule_template | 157 +++++++ .../reaction/tiny_nylon/tiny_nylon.data | 126 +++++- 24 files changed, 2559 insertions(+), 1651 deletions(-) delete mode 100644 examples/PACKAGES/reaction/tiny_nylon/log.22Apr20.tiny_nylon.stabilized_variable_probability.g++.1 delete mode 100644 examples/PACKAGES/reaction/tiny_nylon/log.22Apr20.tiny_nylon.stabilized_variable_probability.g++.4 create mode 100644 examples/PACKAGES/reaction/tiny_nylon/log.4Nov2020.tiny_nylon.stabilized.g++.1 create mode 100644 examples/PACKAGES/reaction/tiny_nylon/log.4Nov2020.tiny_nylon.stabilized.g++.4 create mode 100644 examples/PACKAGES/reaction/tiny_nylon/log.4Nov2020.tiny_nylon.stabilized_variable_probability.g++.1 create mode 100644 examples/PACKAGES/reaction/tiny_nylon/log.4Nov2020.tiny_nylon.stabilized_variable_probability.g++.4 create mode 100644 examples/PACKAGES/reaction/tiny_nylon/log.4Nov2020.tiny_nylon.unstabilized.g++.1 create mode 100644 examples/PACKAGES/reaction/tiny_nylon/log.4Nov2020.tiny_nylon.unstabilized.g++.4 delete mode 100644 examples/PACKAGES/reaction/tiny_nylon/log.5Jun19.tiny_nylon.stabilized.g++.1 delete mode 100644 examples/PACKAGES/reaction/tiny_nylon/log.5Jun19.tiny_nylon.stabilized.g++.4 delete mode 100644 examples/PACKAGES/reaction/tiny_nylon/log.5Jun19.tiny_nylon.unstabilized.g++.1 delete mode 100644 examples/PACKAGES/reaction/tiny_nylon/log.5Jun19.tiny_nylon.unstabilized.g++.4 delete mode 100644 examples/PACKAGES/reaction/tiny_nylon/rxn1_stp1_reacted.data_template create mode 100644 examples/PACKAGES/reaction/tiny_nylon/rxn1_stp1_reacted.molecule_template delete mode 100644 examples/PACKAGES/reaction/tiny_nylon/rxn1_stp1_unreacted.data_template create mode 100644 examples/PACKAGES/reaction/tiny_nylon/rxn1_stp1_unreacted.molecule_template delete mode 100644 examples/PACKAGES/reaction/tiny_nylon/rxn1_stp2_reacted.data_template create mode 100644 examples/PACKAGES/reaction/tiny_nylon/rxn1_stp2_reacted.molecule_template delete mode 100644 examples/PACKAGES/reaction/tiny_nylon/rxn1_stp2_unreacted.data_template create mode 100644 examples/PACKAGES/reaction/tiny_nylon/rxn1_stp2_unreacted.molecule_template diff --git a/examples/PACKAGES/reaction/tiny_nylon/in.tiny_nylon.stabilized b/examples/PACKAGES/reaction/tiny_nylon/in.tiny_nylon.stabilized index b152dec00a..81a12b4ccb 100644 --- a/examples/PACKAGES/reaction/tiny_nylon/in.tiny_nylon.stabilized +++ b/examples/PACKAGES/reaction/tiny_nylon/in.tiny_nylon.stabilized @@ -19,14 +19,19 @@ dihedral_style class2 improper_style class2 -read_data tiny_nylon.data +read_data tiny_nylon.data & + extra/bond/per/atom 5 & + extra/angle/per/atom 15 & + extra/dihedral/per/atom 15 & + extra/improper/per/atom 25 & + extra/special/per/atom 25 velocity all create 300.0 4928459 dist gaussian -molecule mol1 rxn1_stp1_unreacted.data_template -molecule mol2 rxn1_stp1_reacted.data_template -molecule mol3 rxn1_stp2_unreacted.data_template -molecule mol4 rxn1_stp2_reacted.data_template +molecule mol1 rxn1_stp1_unreacted.molecule_template +molecule mol2 rxn1_stp1_reacted.molecule_template +molecule mol3 rxn1_stp2_unreacted.molecule_template +molecule mol4 rxn1_stp2_reacted.molecule_template thermo 50 diff --git a/examples/PACKAGES/reaction/tiny_nylon/in.tiny_nylon.stabilized_variable_probability b/examples/PACKAGES/reaction/tiny_nylon/in.tiny_nylon.stabilized_variable_probability index e81fedc34a..515d4cb2f8 100644 --- a/examples/PACKAGES/reaction/tiny_nylon/in.tiny_nylon.stabilized_variable_probability +++ b/examples/PACKAGES/reaction/tiny_nylon/in.tiny_nylon.stabilized_variable_probability @@ -19,7 +19,12 @@ dihedral_style class2 improper_style class2 -read_data tiny_nylon.data +read_data tiny_nylon.data & + extra/bond/per/atom 5 & + extra/angle/per/atom 15 & + extra/dihedral/per/atom 15 & + extra/improper/per/atom 25 & + extra/special/per/atom 25 variable runsteps equal 1000 variable prob1 equal step/v_runsteps*2+0.1 @@ -27,10 +32,10 @@ variable prob2 equal (step/v_runsteps)>0.5 velocity all create 300.0 4928459 dist gaussian -molecule mol1 rxn1_stp1_unreacted.data_template -molecule mol2 rxn1_stp1_reacted.data_template -molecule mol3 rxn1_stp2_unreacted.data_template -molecule mol4 rxn1_stp2_reacted.data_template +molecule mol1 rxn1_stp1_unreacted.molecule_template +molecule mol2 rxn1_stp1_reacted.molecule_template +molecule mol3 rxn1_stp2_unreacted.molecule_template +molecule mol4 rxn1_stp2_reacted.molecule_template thermo 50 diff --git a/examples/PACKAGES/reaction/tiny_nylon/in.tiny_nylon.unstabilized b/examples/PACKAGES/reaction/tiny_nylon/in.tiny_nylon.unstabilized index 1e5a493821..4891e9ebff 100644 --- a/examples/PACKAGES/reaction/tiny_nylon/in.tiny_nylon.unstabilized +++ b/examples/PACKAGES/reaction/tiny_nylon/in.tiny_nylon.unstabilized @@ -19,14 +19,20 @@ dihedral_style class2 improper_style class2 -read_data tiny_nylon.data +read_data tiny_nylon.data & + extra/bond/per/atom 5 & + extra/angle/per/atom 15 & + extra/dihedral/per/atom 15 & + extra/improper/per/atom 25 & + extra/special/per/atom 25 + velocity all create 300.0 4928459 dist gaussian -molecule mol1 rxn1_stp1_unreacted.data_template -molecule mol2 rxn1_stp1_reacted.data_template -molecule mol3 rxn1_stp2_unreacted.data_template -molecule mol4 rxn1_stp2_reacted.data_template +molecule mol1 rxn1_stp1_unreacted.molecule_template +molecule mol2 rxn1_stp1_reacted.molecule_template +molecule mol3 rxn1_stp2_unreacted.molecule_template +molecule mol4 rxn1_stp2_reacted.molecule_template thermo 50 diff --git a/examples/PACKAGES/reaction/tiny_nylon/log.22Apr20.tiny_nylon.stabilized_variable_probability.g++.1 b/examples/PACKAGES/reaction/tiny_nylon/log.22Apr20.tiny_nylon.stabilized_variable_probability.g++.1 deleted file mode 100644 index 57455b04f4..0000000000 --- a/examples/PACKAGES/reaction/tiny_nylon/log.22Apr20.tiny_nylon.stabilized_variable_probability.g++.1 +++ /dev/null @@ -1,201 +0,0 @@ -LAMMPS (15 Apr 2020) -OMP_NUM_THREADS environment is not set. Defaulting to 1 thread. (src/comm.cpp:94) - using 1 OpenMP thread(s) per MPI task -# two monomer nylon example -# reaction produces a condensed water molecule - -units real - -boundary p p p - -atom_style full - -kspace_style pppm 1.0e-4 - -pair_style lj/class2/coul/long 8.5 - -angle_style class2 - -bond_style class2 - -dihedral_style class2 - -improper_style class2 - -read_data tiny_nylon.data - orthogonal box = (-25 -25 -25) to (25 25 25) - 1 by 1 by 1 MPI processor grid - reading atoms ... - 44 atoms - reading velocities ... - 44 velocities - scanning bonds ... - 9 = max bonds/atom - scanning angles ... - 21 = max angles/atom - scanning dihedrals ... - 29 = max dihedrals/atom - scanning impropers ... - 29 = max impropers/atom - reading bonds ... - 42 bonds - reading angles ... - 74 angles - reading dihedrals ... - 100 dihedrals - reading impropers ... - 44 impropers - 4 = max # of 1-2 neighbors - 6 = max # of 1-3 neighbors - 12 = max # of 1-4 neighbors - 41 = max # of special neighbors - special bonds CPU = 0.000385045 secs - read_data CPU = 0.013443 secs - -variable runsteps equal 1000 -variable prob1 equal step/v_runsteps*2 -variable prob2 equal (step/v_runsteps)>0.5 - -velocity all create 300.0 4928459 dist gaussian - -molecule mol1 rxn1_stp1_unreacted.data_template -Read molecule template mol1: - 1 molecules - 18 atoms with max type 8 - 16 bonds with max type 14 - 25 angles with max type 28 - 23 dihedrals with max type 36 - 14 impropers with max type 11 -molecule mol2 rxn1_stp1_reacted.data_template -Read molecule template mol2: - 1 molecules - 18 atoms with max type 9 - 17 bonds with max type 13 - 31 angles with max type 27 - 39 dihedrals with max type 33 - 20 impropers with max type 1 -molecule mol3 rxn1_stp2_unreacted.data_template -Read molecule template mol3: - 1 molecules - 15 atoms with max type 9 - 14 bonds with max type 13 - 25 angles with max type 27 - 30 dihedrals with max type 33 - 16 impropers with max type 1 -molecule mol4 rxn1_stp2_reacted.data_template -Read molecule template mol4: - 1 molecules - 15 atoms with max type 11 - 13 bonds with max type 15 - 19 angles with max type 29 - 16 dihedrals with max type 32 - 10 impropers with max type 13 - -thermo 50 - -# dump 1 all xyz 1 test_vis.xyz - -fix myrxns all bond/react stabilization yes statted_grp .03 react rxn1 all 1 0.0 5.0 mol1 mol2 rxn1_stp1_map prob v_prob1 1234 react rxn2 all 1 0.0 5.0 mol3 mol4 rxn1_stp2_map prob v_prob2 1234 -WARNING: Bond/react: Atom affected by reaction rxn1 too close to template edge (src/REACTION/fix_bond_react.cpp:2051) -WARNING: Bond/react: Atom affected by reaction rxn2 too close to template edge (src/REACTION/fix_bond_react.cpp:2051) -dynamic group bond_react_MASTER_group defined -dynamic group statted_grp_REACT defined - -fix 1 statted_grp_REACT nvt temp 300 300 100 - -# optionally, you can customize behavior of reacting atoms, -# by using the internally-created 'bond_react_MASTER_group', like so: -fix 4 bond_react_MASTER_group temp/rescale 1 300 300 10 1 - -thermo_style custom step temp press density v_prob1 v_prob2 f_myrxns[1] f_myrxns[2] - -# restart 100 restart1 restart2 - -run ${runsteps} -run 1000 -PPPM initialization ... - using 12-bit tables for long-range coulomb (src/kspace.cpp:332) - G vector (1/distance) = 0.0534597 - grid = 2 2 2 - stencil order = 5 - estimated absolute RMS force accuracy = 0.0402256 - estimated relative force accuracy = 0.000121138 - using double precision FFTW3 - 3d grid and FFT values/proc = 343 8 -Neighbor list info ... - update every 1 steps, delay 10 steps, check yes - max neighbors/atom: 2000, page size: 100000 - master list distance cutoff = 10.5 - ghost atom cutoff = 10.5 - binsize = 5.25, bins = 10 10 10 - 2 neighbor lists, perpetual/occasional/extra = 1 1 0 - (1) pair lj/class2/coul/long, perpetual - attributes: half, newton on - pair build: half/bin/newton - stencil: half/bin/3d/newton - bin: standard - (2) fix bond/react, occasional, copy from (1) - attributes: half, newton on - pair build: copy - stencil: none - bin: none -WARNING: Inconsistent image flags (src/domain.cpp:812) -Per MPI rank memory allocation (min/avg/max) = 33.78 | 33.78 | 33.78 Mbytes -Step Temp Press Density v_prob1 v_prob2 f_myrxns[1] f_myrxns[2] - 0 300 346.78165 0.0034851739 0 0 0 0 - 50 262.63913 -492.10749 0.0034851739 0.1 0 1 0 - 100 766.52962 -29.714349 0.0034851739 0.2 0 1 0 - 150 503.86837 50.220304 0.0034851739 0.3 0 1 0 - 200 456.51295 12.312892 0.0034851739 0.4 0 1 0 - 250 391.54928 9.2335844 0.0034851739 0.5 0 1 0 - 300 336.6988 -47.193937 0.0034851739 0.6 0 1 0 - 350 254.06985 -9.2867898 0.0034851739 0.7 0 1 0 - 400 259.41098 -25.657321 0.0034851739 0.8 0 1 0 - 450 258.10364 22.5086 0.0034851739 0.9 0 1 0 - 500 272.13412 -6.5391448 0.0034851739 1 0 1 0 - 550 202.75504 54.658731 0.0034851739 1.1 1 1 1 - 600 344.79887 23.798478 0.0034851739 1.2 1 1 1 - 650 328.44488 -29.908484 0.0034851739 1.3 1 1 1 - 700 280.13593 -8.3223255 0.0034851739 1.4 1 1 1 - 750 300.67624 1.0632669 0.0034851739 1.5 1 1 1 - 800 376.64234 12.488392 0.0034851739 1.6 1 1 1 - 850 321.07642 19.814074 0.0034851739 1.7 1 1 1 - 900 332.23751 30.814079 0.0034851739 1.8 1 1 1 - 950 311.14029 5.7853136 0.0034851739 1.9 1 1 1 - 1000 253.14634 -37.560642 0.0034851739 2 1 1 1 -Loop time of 0.379454 on 1 procs for 1000 steps with 44 atoms - -Performance: 227.696 ns/day, 0.105 hours/ns, 2635.368 timesteps/s -99.6% CPU use with 1 MPI tasks x 1 OpenMP threads - -MPI task timing breakdown: -Section | min time | avg time | max time |%varavg| %total ---------------------------------------------------------------- -Pair | 0.069723 | 0.069723 | 0.069723 | 0.0 | 18.37 -Bond | 0.14802 | 0.14802 | 0.14802 | 0.0 | 39.01 -Kspace | 0.044252 | 0.044252 | 0.044252 | 0.0 | 11.66 -Neigh | 0.072359 | 0.072359 | 0.072359 | 0.0 | 19.07 -Comm | 0.0044748 | 0.0044748 | 0.0044748 | 0.0 | 1.18 -Output | 0.0022775 | 0.0022775 | 0.0022775 | 0.0 | 0.60 -Modify | 0.036509 | 0.036509 | 0.036509 | 0.0 | 9.62 -Other | | 0.00184 | | | 0.48 - -Nlocal: 44 ave 44 max 44 min -Histogram: 1 0 0 0 0 0 0 0 0 0 -Nghost: 3 ave 3 max 3 min -Histogram: 1 0 0 0 0 0 0 0 0 0 -Neighs: 722 ave 722 max 722 min -Histogram: 1 0 0 0 0 0 0 0 0 0 - -Total # of neighbors = 722 -Ave neighs/atom = 16.4091 -Ave special neighs/atom = 9.77273 -Neighbor list builds = 1000 -Dangerous builds = 0 - -# write_restart restart_longrun -# write_data restart_longrun.data - -Please see the log.cite file for references relevant to this simulation - -Total wall time: 0:00:00 diff --git a/examples/PACKAGES/reaction/tiny_nylon/log.22Apr20.tiny_nylon.stabilized_variable_probability.g++.4 b/examples/PACKAGES/reaction/tiny_nylon/log.22Apr20.tiny_nylon.stabilized_variable_probability.g++.4 deleted file mode 100644 index b6dcdafc54..0000000000 --- a/examples/PACKAGES/reaction/tiny_nylon/log.22Apr20.tiny_nylon.stabilized_variable_probability.g++.4 +++ /dev/null @@ -1,201 +0,0 @@ -LAMMPS (15 Apr 2020) -OMP_NUM_THREADS environment is not set. Defaulting to 1 thread. (src/comm.cpp:94) - using 1 OpenMP thread(s) per MPI task -# two monomer nylon example -# reaction produces a condensed water molecule - -units real - -boundary p p p - -atom_style full - -kspace_style pppm 1.0e-4 - -pair_style lj/class2/coul/long 8.5 - -angle_style class2 - -bond_style class2 - -dihedral_style class2 - -improper_style class2 - -read_data tiny_nylon.data - orthogonal box = (-25 -25 -25) to (25 25 25) - 1 by 2 by 2 MPI processor grid - reading atoms ... - 44 atoms - reading velocities ... - 44 velocities - scanning bonds ... - 9 = max bonds/atom - scanning angles ... - 21 = max angles/atom - scanning dihedrals ... - 29 = max dihedrals/atom - scanning impropers ... - 29 = max impropers/atom - reading bonds ... - 42 bonds - reading angles ... - 74 angles - reading dihedrals ... - 100 dihedrals - reading impropers ... - 44 impropers - 4 = max # of 1-2 neighbors - 6 = max # of 1-3 neighbors - 12 = max # of 1-4 neighbors - 41 = max # of special neighbors - special bonds CPU = 0.000431282 secs - read_data CPU = 0.0129571 secs - -variable runsteps equal 1000 -variable prob1 equal step/v_runsteps*2 -variable prob2 equal (step/v_runsteps)>0.5 - -velocity all create 300.0 4928459 dist gaussian - -molecule mol1 rxn1_stp1_unreacted.data_template -Read molecule template mol1: - 1 molecules - 18 atoms with max type 8 - 16 bonds with max type 14 - 25 angles with max type 28 - 23 dihedrals with max type 36 - 14 impropers with max type 11 -molecule mol2 rxn1_stp1_reacted.data_template -Read molecule template mol2: - 1 molecules - 18 atoms with max type 9 - 17 bonds with max type 13 - 31 angles with max type 27 - 39 dihedrals with max type 33 - 20 impropers with max type 1 -molecule mol3 rxn1_stp2_unreacted.data_template -Read molecule template mol3: - 1 molecules - 15 atoms with max type 9 - 14 bonds with max type 13 - 25 angles with max type 27 - 30 dihedrals with max type 33 - 16 impropers with max type 1 -molecule mol4 rxn1_stp2_reacted.data_template -Read molecule template mol4: - 1 molecules - 15 atoms with max type 11 - 13 bonds with max type 15 - 19 angles with max type 29 - 16 dihedrals with max type 32 - 10 impropers with max type 13 - -thermo 50 - -# dump 1 all xyz 1 test_vis.xyz - -fix myrxns all bond/react stabilization yes statted_grp .03 react rxn1 all 1 0.0 5.0 mol1 mol2 rxn1_stp1_map prob v_prob1 1234 react rxn2 all 1 0.0 5.0 mol3 mol4 rxn1_stp2_map prob v_prob2 1234 -WARNING: Bond/react: Atom affected by reaction rxn1 too close to template edge (src/REACTION/fix_bond_react.cpp:2051) -WARNING: Bond/react: Atom affected by reaction rxn2 too close to template edge (src/REACTION/fix_bond_react.cpp:2051) -dynamic group bond_react_MASTER_group defined -dynamic group statted_grp_REACT defined - -fix 1 statted_grp_REACT nvt temp 300 300 100 - -# optionally, you can customize behavior of reacting atoms, -# by using the internally-created 'bond_react_MASTER_group', like so: -fix 4 bond_react_MASTER_group temp/rescale 1 300 300 10 1 - -thermo_style custom step temp press density v_prob1 v_prob2 f_myrxns[1] f_myrxns[2] - -# restart 100 restart1 restart2 - -run ${runsteps} -run 1000 -PPPM initialization ... - using 12-bit tables for long-range coulomb (src/kspace.cpp:332) - G vector (1/distance) = 0.0534597 - grid = 2 2 2 - stencil order = 5 - estimated absolute RMS force accuracy = 0.0402256 - estimated relative force accuracy = 0.000121138 - using double precision FFTW3 - 3d grid and FFT values/proc = 252 2 -Neighbor list info ... - update every 1 steps, delay 10 steps, check yes - max neighbors/atom: 2000, page size: 100000 - master list distance cutoff = 10.5 - ghost atom cutoff = 10.5 - binsize = 5.25, bins = 10 10 10 - 2 neighbor lists, perpetual/occasional/extra = 1 1 0 - (1) pair lj/class2/coul/long, perpetual - attributes: half, newton on - pair build: half/bin/newton - stencil: half/bin/3d/newton - bin: standard - (2) fix bond/react, occasional, copy from (1) - attributes: half, newton on - pair build: copy - stencil: none - bin: none -WARNING: Inconsistent image flags (src/domain.cpp:812) -Per MPI rank memory allocation (min/avg/max) = 33.66 | 33.88 | 34.43 Mbytes -Step Temp Press Density v_prob1 v_prob2 f_myrxns[1] f_myrxns[2] - 0 300 346.78165 0.0034851739 0 0 0 0 - 50 266.5092 -90.813802 0.0034851739 0.1 0 1 0 - 100 559.41271 -53.23688 0.0034851739 0.2 0 1 0 - 150 489.90516 31.555817 0.0034851739 0.3 0 1 0 - 200 326.18391 7.7889992 0.0034851739 0.4 0 1 0 - 250 339.78203 2.3919541 0.0034851739 0.5 0 1 0 - 300 370.90263 -32.01673 0.0034851739 0.6 0 1 0 - 350 294.07547 -5.4019813 0.0034851739 0.7 0 1 0 - 400 287.76477 12.254133 0.0034851739 0.8 0 1 0 - 450 293.36482 66.372956 0.0034851739 0.9 0 1 0 - 500 246.84496 26.132317 0.0034851739 1 0 1 0 - 550 253.08778 -15.350262 0.0034851739 1.1 1 1 1 - 600 358.83641 25.007371 0.0034851739 1.2 1 1 1 - 650 320.51492 -32.34823 0.0034851739 1.3 1 1 1 - 700 310.87976 -8.2306669 0.0034851739 1.4 1 1 1 - 750 307.54142 12.025818 0.0034851739 1.5 1 1 1 - 800 272.51724 -22.92823 0.0034851739 1.6 1 1 1 - 850 268.66181 10.069534 0.0034851739 1.7 1 1 1 - 900 265.5531 -10.471377 0.0034851739 1.8 1 1 1 - 950 259.43086 9.4546712 0.0034851739 1.9 1 1 1 - 1000 247.14622 20.250308 0.0034851739 2 1 1 1 -Loop time of 0.357762 on 4 procs for 1000 steps with 44 atoms - -Performance: 241.502 ns/day, 0.099 hours/ns, 2795.157 timesteps/s -99.0% CPU use with 4 MPI tasks x 1 OpenMP threads - -MPI task timing breakdown: -Section | min time | avg time | max time |%varavg| %total ---------------------------------------------------------------- -Pair | 0.0003917 | 0.015545 | 0.033317 | 11.9 | 4.35 -Bond | 0.0010131 | 0.030153 | 0.076975 | 18.2 | 8.43 -Kspace | 0.092857 | 0.1462 | 0.18688 | 10.7 | 40.87 -Neigh | 0.043786 | 0.044014 | 0.044189 | 0.1 | 12.30 -Comm | 0.03636 | 0.038345 | 0.040538 | 0.8 | 10.72 -Output | 0.00091578 | 0.0012541 | 0.0020923 | 1.4 | 0.35 -Modify | 0.075379 | 0.080791 | 0.086052 | 1.8 | 22.58 -Other | | 0.00146 | | | 0.41 - -Nlocal: 11 ave 32 max 0 min -Histogram: 2 0 1 0 0 0 0 0 0 1 -Nghost: 40 ave 51 max 19 min -Histogram: 1 0 0 0 0 0 0 1 0 2 -Neighs: 191 ave 529 max 0 min -Histogram: 2 0 0 0 1 0 0 0 0 1 - -Total # of neighbors = 764 -Ave neighs/atom = 17.3636 -Ave special neighs/atom = 9.77273 -Neighbor list builds = 1000 -Dangerous builds = 0 - -# write_restart restart_longrun -# write_data restart_longrun.data - -Please see the log.cite file for references relevant to this simulation - -Total wall time: 0:00:00 diff --git a/examples/PACKAGES/reaction/tiny_nylon/log.4Nov2020.tiny_nylon.stabilized.g++.1 b/examples/PACKAGES/reaction/tiny_nylon/log.4Nov2020.tiny_nylon.stabilized.g++.1 new file mode 100644 index 0000000000..9a2d240ca4 --- /dev/null +++ b/examples/PACKAGES/reaction/tiny_nylon/log.4Nov2020.tiny_nylon.stabilized.g++.1 @@ -0,0 +1,412 @@ +LAMMPS (4 Nov 2022) +# two monomer nylon example +# reaction produces a condensed water molecule + +units real + +boundary p p p + +atom_style full + +kspace_style pppm 1.0e-4 + +pair_style lj/class2/coul/long 8.5 + +angle_style class2 + +bond_style class2 + +dihedral_style class2 + +improper_style class2 + +read_data tiny_nylon.data extra/bond/per/atom 5 extra/angle/per/atom 15 extra/dihedral/per/atom 15 extra/improper/per/atom 25 extra/special/per/atom 25 +Reading data file ... + orthogonal box = (-25 -25 -25) to (25 25 25) + 1 by 1 by 1 MPI processor grid + reading atom labelmap ... + reading bond labelmap ... + reading angle labelmap ... + reading dihedral labelmap ... + reading improper labelmap ... + reading atoms ... + 44 atoms + reading velocities ... + 44 velocities + scanning bonds ... + 9 = max bonds/atom + scanning angles ... + 21 = max angles/atom + scanning dihedrals ... + 29 = max dihedrals/atom + scanning impropers ... + 29 = max impropers/atom + reading bonds ... + 42 bonds + reading angles ... + 74 angles + reading dihedrals ... + 100 dihedrals + reading impropers ... + 44 impropers +Finding 1-2 1-3 1-4 neighbors ... + special bond factors lj: 0 0 0 + special bond factors coul: 0 0 0 + 4 = max # of 1-2 neighbors + 6 = max # of 1-3 neighbors + 12 = max # of 1-4 neighbors + 41 = max # of special neighbors + special bonds CPU = 0.000 seconds + read_data CPU = 0.007 seconds + +velocity all create 300.0 4928459 dist gaussian + +molecule mol1 rxn1_stp1_unreacted.molecule_template +Read molecule template mol1: + 1 molecules + 0 fragments + 18 atoms with max type 8 + 16 bonds with max type 10 + 25 angles with max type 28 + 23 dihedrals with max type 36 + 2 impropers with max type 3 +molecule mol2 rxn1_stp1_reacted.molecule_template +Read molecule template mol2: + 1 molecules + 0 fragments + 18 atoms with max type 9 + 17 bonds with max type 13 + 31 angles with max type 27 + 39 dihedrals with max type 33 + 0 impropers with max type 0 +molecule mol3 rxn1_stp2_unreacted.molecule_template +Read molecule template mol3: + 1 molecules + 0 fragments + 15 atoms with max type 9 + 14 bonds with max type 13 + 25 angles with max type 27 + 30 dihedrals with max type 33 + 0 impropers with max type 0 +molecule mol4 rxn1_stp2_reacted.molecule_template +Read molecule template mol4: + 1 molecules + 0 fragments + 15 atoms with max type 11 + 13 bonds with max type 15 + 19 angles with max type 29 + 16 dihedrals with max type 32 + 2 impropers with max type 13 + +thermo 50 + +# dump 1 all xyz 1 test_vis.xyz + +fix myrxns all bond/react stabilization yes statted_grp .03 react rxn1 all 1 0.0 2.9 mol1 mol2 rxn1_stp1_map react rxn2 all 1 0.0 5.0 mol3 mol4 rxn1_stp2_map +WARNING: Fix bond/react: Atom affected by reaction rxn2 is too close to template edge (../fix_bond_react.cpp:2624) +dynamic group bond_react_MASTER_group defined +dynamic group statted_grp_REACT defined + +fix 1 statted_grp_REACT nvt temp 300 300 100 + +# optionally, you can customize behavior of reacting atoms, +# by using the internally-created 'bond_react_MASTER_group', like so: +fix 4 bond_react_MASTER_group temp/rescale 1 300 300 10 1 + +thermo_style custom step temp press density f_myrxns[1] f_myrxns[2] + +# restart 100 restart1 restart2 + +run 10000 + +CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE + +Your simulation uses code contributions which should be cited: + +- fix bond/react: reacter.org doi:10.1016/j.polymer.2017.09.038, doi:10.1021/acs.macromol.0c02012 + +@Article{Gissinger17, + author = {J. R. Gissinger and B. D. Jensen and K. E. Wise}, + title = {Modeling Chemical Reactions in Classical Molecular Dynamics Simulations}, + journal = {Polymer}, + year = 2017, + volume = 128, + pages = {211--217} +} + +@Article{Gissinger20, + author = {J. R. Gissinger, B. D. Jensen, K. E. Wise}, + title = {{REACTER}: A Heuristic Method for Reactive Molecular Dynamics}, + journal = {Macromolecules}, + year = 2020, + volume = 53, + number = 22, + pages = {9953--9961} +} + +CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE + +PPPM initialization ... + using 12-bit tables for long-range coulomb (../kspace.cpp:342) + G vector (1/distance) = 0.05345967 + grid = 2 2 2 + stencil order = 5 + estimated absolute RMS force accuracy = 0.040225597 + estimated relative force accuracy = 0.00012113819 + using double precision KISS FFT + 3d grid and FFT values/proc = 343 8 +Generated 55 of 55 mixed pair_coeff terms from sixthpower/geometric mixing rule +Neighbor list info ... + update: every = 1 steps, delay = 0 steps, check = yes + max neighbors/atom: 2000, page size: 100000 + master list distance cutoff = 10.5 + ghost atom cutoff = 10.5 + binsize = 5.25, bins = 10 10 10 + 2 neighbor lists, perpetual/occasional/extra = 1 1 0 + (1) pair lj/class2/coul/long, perpetual + attributes: half, newton on + pair build: half/bin/newton + stencil: half/bin/3d + bin: standard + (2) fix bond/react, occasional, copy from (1) + attributes: half, newton on + pair build: copy + stencil: none + bin: none +WARNING: Inconsistent image flags (../domain.cpp:819) +Per MPI rank memory allocation (min/avg/max) = 33.78 | 33.78 | 33.78 Mbytes + Step Temp Press Density f_myrxns[1] f_myrxns[2] + 0 300 346.78165 0.0034851739 0 0 + 50 283.51963 -47.16359 0.0034851739 1 0 + 100 256.04648 21.778898 0.0034851739 1 1 + 150 450.78138 -11.7887 0.0034851739 1 1 + 200 400.15754 49.489858 0.0034851739 1 1 + 250 347.06066 68.952063 0.0034851739 1 1 + 300 291.89228 -1.5986302 0.0034851739 1 1 + 350 290.25995 17.634558 0.0034851739 1 1 + 400 234.89168 26.36452 0.0034851739 1 1 + 450 305.80709 -28.923896 0.0034851739 1 1 + 500 375.19218 -37.024375 0.0034851739 1 1 + 550 321.86944 -4.6961825 0.0034851739 1 1 + 600 307.2639 -31.393161 0.0034851739 1 1 + 650 255.95833 8.4995589 0.0034851739 1 1 + 700 294.54665 -17.06105 0.0034851739 1 1 + 750 273.08231 -10.7175 0.0034851739 1 1 + 800 249.69175 9.9777683 0.0034851739 1 1 + 850 307.71806 -6.9950048 0.0034851739 1 1 + 900 367.39855 9.9874985 0.0034851739 1 1 + 950 327.57334 -4.7029779 0.0034851739 1 1 + 1000 348.85247 15.763492 0.0034851739 1 1 + 1050 328.94435 -35.031279 0.0034851739 1 1 + 1100 283.23971 -16.937443 0.0034851739 1 1 + 1150 266.69676 42.308482 0.0034851739 1 1 + 1200 244.61493 -8.291143 0.0034851739 1 1 + 1250 206.68495 6.6280168 0.0034851739 1 1 + 1300 257.83339 -7.0826267 0.0034851739 1 1 + 1350 358.0875 -7.6024741 0.0034851739 1 1 + 1400 353.66614 18.091914 0.0034851739 1 1 + 1450 302.27969 13.828755 0.0034851739 1 1 + 1500 262.57851 9.256794 0.0034851739 1 1 + 1550 252.39493 1.2438641 0.0034851739 1 1 + 1600 247.18352 10.008173 0.0034851739 1 1 + 1650 290.30112 -2.1829035 0.0034851739 1 1 + 1700 272.78999 -57.305766 0.0034851739 1 1 + 1750 253.35258 24.729795 0.0034851739 1 1 + 1800 278.67831 -0.95016566 0.0034851739 1 1 + 1850 302.04743 16.002867 0.0034851739 1 1 + 1900 330.67188 -22.034206 0.0034851739 1 1 + 1950 342.64206 8.0076017 0.0034851739 1 1 + 2000 348.74388 -12.159887 0.0034851739 1 1 + 2050 300.48093 36.01054 0.0034851739 1 1 + 2100 275.01699 8.7612261 0.0034851739 1 1 + 2150 303.92758 10.317056 0.0034851739 1 1 + 2200 308.89457 33.245018 0.0034851739 1 1 + 2250 265.74177 35.857118 0.0034851739 1 1 + 2300 273.40088 53.001593 0.0034851739 1 1 + 2350 287.74746 -0.14590128 0.0034851739 1 1 + 2400 278.76055 -8.2080851 0.0034851739 1 1 + 2450 331.88978 39.025208 0.0034851739 1 1 + 2500 280.04045 -21.423616 0.0034851739 1 1 + 2550 388.81531 -12.350023 0.0034851739 1 1 + 2600 311.13452 -13.287102 0.0034851739 1 1 + 2650 325.07681 88.710878 0.0034851739 1 1 + 2700 319.08502 14.118057 0.0034851739 1 1 + 2750 261.72066 26.051675 0.0034851739 1 1 + 2800 281.03508 -21.200833 0.0034851739 1 1 + 2850 312.27359 4.3892078 0.0034851739 1 1 + 2900 274.81147 -12.738114 0.0034851739 1 1 + 2950 281.76969 11.198451 0.0034851739 1 1 + 3000 291.83918 48.595884 0.0034851739 1 1 + 3050 297.40189 -24.91102 0.0034851739 1 1 + 3100 341.47331 13.82699 0.0034851739 1 1 + 3150 347.51825 -10.458257 0.0034851739 1 1 + 3200 301.24666 26.550464 0.0034851739 1 1 + 3250 281.3679 -23.02985 0.0034851739 1 1 + 3300 279.8332 -53.222264 0.0034851739 1 1 + 3350 289.41496 -8.793156 0.0034851739 1 1 + 3400 288.5722 -25.441134 0.0034851739 1 1 + 3450 259.59524 77.884773 0.0034851739 1 1 + 3500 296.00389 30.3654 0.0034851739 1 1 + 3550 302.14443 -5.1101538 0.0034851739 1 1 + 3600 288.98098 -12.688781 0.0034851739 1 1 + 3650 333.83238 -33.121195 0.0034851739 1 1 + 3700 347.7556 -24.693995 0.0034851739 1 1 + 3750 354.42689 6.7030374 0.0034851739 1 1 + 3800 341.24011 -18.775449 0.0034851739 1 1 + 3850 320.50998 35.492418 0.0034851739 1 1 + 3900 326.81918 -49.073015 0.0034851739 1 1 + 3950 299.55145 -19.487946 0.0034851739 1 1 + 4000 308.81019 30.579971 0.0034851739 1 1 + 4050 251.83279 -17.500379 0.0034851739 1 1 + 4100 242.0783 21.228088 0.0034851739 1 1 + 4150 265.59921 -3.9446469 0.0034851739 1 1 + 4200 369.32464 -14.626205 0.0034851739 1 1 + 4250 346.22904 -32.749662 0.0034851739 1 1 + 4300 369.43175 11.916047 0.0034851739 1 1 + 4350 321.17007 -9.3009147 0.0034851739 1 1 + 4400 312.41821 -31.360537 0.0034851739 1 1 + 4450 281.59211 40.338618 0.0034851739 1 1 + 4500 289.10806 -4.2135222 0.0034851739 1 1 + 4550 317.55705 -4.3727576 0.0034851739 1 1 + 4600 310.64469 -14.403478 0.0034851739 1 1 + 4650 284.43433 37.416848 0.0034851739 1 1 + 4700 353.88469 7.7633789 0.0034851739 1 1 + 4750 328.48834 -60.780145 0.0034851739 1 1 + 4800 390.23986 4.2691385 0.0034851739 1 1 + 4850 364.06188 40.18245 0.0034851739 1 1 + 4900 304.64696 6.3557092 0.0034851739 1 1 + 4950 309.12139 -16.598924 0.0034851739 1 1 + 5000 311.03552 14.748037 0.0034851739 1 1 + 5050 320.97847 -26.733755 0.0034851739 1 1 + 5100 275.1237 -29.734972 0.0034851739 1 1 + 5150 287.76954 -2.5726321 0.0034851739 1 1 + 5200 267.72493 -6.6677739 0.0034851739 1 1 + 5250 290.63862 29.209807 0.0034851739 1 1 + 5300 276.51052 -19.746615 0.0034851739 1 1 + 5350 255.69196 25.130356 0.0034851739 1 1 + 5400 313.43108 -18.556701 0.0034851739 1 1 + 5450 327.91785 -16.08265 0.0034851739 1 1 + 5500 342.03301 33.271603 0.0034851739 1 1 + 5550 272.96564 -5.0247163 0.0034851739 1 1 + 5600 315.93807 -16.793394 0.0034851739 1 1 + 5650 294.66353 19.720691 0.0034851739 1 1 + 5700 283.4631 -6.5193772 0.0034851739 1 1 + 5750 261.06436 12.755679 0.0034851739 1 1 + 5800 274.15767 -9.6693117 0.0034851739 1 1 + 5850 271.1371 18.441828 0.0034851739 1 1 + 5900 283.39277 -4.6324708 0.0034851739 1 1 + 5950 326.30497 12.106133 0.0034851739 1 1 + 6000 316.91847 -32.864812 0.0034851739 1 1 + 6050 344.86369 21.226768 0.0034851739 1 1 + 6100 295.85211 -7.3603837 0.0034851739 1 1 + 6150 256.72292 4.6010174 0.0034851739 1 1 + 6200 248.33379 -20.795929 0.0034851739 1 1 + 6250 259.4054 63.590928 0.0034851739 1 1 + 6300 264.16648 2.6570242 0.0034851739 1 1 + 6350 243.22677 -18.621317 0.0034851739 1 1 + 6400 269.96092 53.832036 0.0034851739 1 1 + 6450 252.06358 -26.231052 0.0034851739 1 1 + 6500 275.4825 25.577441 0.0034851739 1 1 + 6550 298.27441 11.17373 0.0034851739 1 1 + 6600 297.29358 -21.382334 0.0034851739 1 1 + 6650 334.78542 38.892678 0.0034851739 1 1 + 6700 299.48699 -20.336163 0.0034851739 1 1 + 6750 315.01936 21.000444 0.0034851739 1 1 + 6800 244.68344 -6.3625659 0.0034851739 1 1 + 6850 251.56543 27.857872 0.0034851739 1 1 + 6900 280.81518 -12.494398 0.0034851739 1 1 + 6950 273.87437 -34.211085 0.0034851739 1 1 + 7000 274.91068 33.483158 0.0034851739 1 1 + 7050 298.56432 -61.821668 0.0034851739 1 1 + 7100 299.08395 10.365875 0.0034851739 1 1 + 7150 317.38233 29.049831 0.0034851739 1 1 + 7200 317.24932 -27.515026 0.0034851739 1 1 + 7250 305.63931 12.732123 0.0034851739 1 1 + 7300 309.44007 -53.922033 0.0034851739 1 1 + 7350 280.35029 45.495031 0.0034851739 1 1 + 7400 228.60929 1.7072084 0.0034851739 1 1 + 7450 276.206 -19.170327 0.0034851739 1 1 + 7500 257.9851 77.105642 0.0034851739 1 1 + 7550 306.46848 -29.189265 0.0034851739 1 1 + 7600 296.84522 -20.83365 0.0034851739 1 1 + 7650 296.5965 -14.890206 0.0034851739 1 1 + 7700 322.80474 44.883023 0.0034851739 1 1 + 7750 293.7355 -48.487658 0.0034851739 1 1 + 7800 358.41838 13.156339 0.0034851739 1 1 + 7850 293.81457 -19.50566 0.0034851739 1 1 + 7900 309.49618 -28.562417 0.0034851739 1 1 + 7950 285.6339 -22.488886 0.0034851739 1 1 + 8000 262.85312 57.125049 0.0034851739 1 1 + 8050 243.28673 -28.082125 0.0034851739 1 1 + 8100 279.71604 10.011975 0.0034851739 1 1 + 8150 344.77027 -56.89744 0.0034851739 1 1 + 8200 366.36063 21.02453 0.0034851739 1 1 + 8250 347.07209 2.7752885 0.0034851739 1 1 + 8300 337.74753 -10.957676 0.0034851739 1 1 + 8350 300.41188 -22.840776 0.0034851739 1 1 + 8400 282.27447 0.32063982 0.0034851739 1 1 + 8450 285.40722 -3.7167264 0.0034851739 1 1 + 8500 321.32722 -21.308158 0.0034851739 1 1 + 8550 293.65903 15.681219 0.0034851739 1 1 + 8600 293.38929 37.727045 0.0034851739 1 1 + 8650 299.55185 -15.004573 0.0034851739 1 1 + 8700 270.7608 14.615287 0.0034851739 1 1 + 8750 306.46813 67.018302 0.0034851739 1 1 + 8800 308.35025 -91.212286 0.0034851739 1 1 + 8850 349.40419 31.906004 0.0034851739 1 1 + 8900 351.32706 -24.901778 0.0034851739 1 1 + 8950 320.84369 18.380221 0.0034851739 1 1 + 9000 289.2862 9.981138 0.0034851739 1 1 + 9050 270.53883 12.028672 0.0034851739 1 1 + 9100 270.63206 -0.87842772 0.0034851739 1 1 + 9150 274.30671 -4.1228725 0.0034851739 1 1 + 9200 343.78546 20.427647 0.0034851739 1 1 + 9250 348.1019 13.339075 0.0034851739 1 1 + 9300 345.11791 -32.515359 0.0034851739 1 1 + 9350 329.8365 12.644587 0.0034851739 1 1 + 9400 286.41337 -28.79111 0.0034851739 1 1 + 9450 321.92318 32.154255 0.0034851739 1 1 + 9500 302.68527 -42.576022 0.0034851739 1 1 + 9550 335.24034 26.675219 0.0034851739 1 1 + 9600 270.62012 17.230138 0.0034851739 1 1 + 9650 273.71088 35.651219 0.0034851739 1 1 + 9700 286.2141 -26.15835 0.0034851739 1 1 + 9750 262.25352 -4.1954047 0.0034851739 1 1 + 9800 314.29455 23.252049 0.0034851739 1 1 + 9850 273.71272 -29.586039 0.0034851739 1 1 + 9900 300.63743 42.595289 0.0034851739 1 1 + 9950 367.68979 -64.582508 0.0034851739 1 1 + 10000 357.17941 31.607766 0.0034851739 1 1 +Loop time of 1.82433 on 1 procs for 10000 steps with 44 atoms + +Performance: 473.599 ns/day, 0.051 hours/ns, 5481.467 timesteps/s, 241.185 katom-step/s +99.8% CPU use with 1 MPI tasks x no OpenMP threads + +MPI task timing breakdown: +Section | min time | avg time | max time |%varavg| %total +--------------------------------------------------------------- +Pair | 0.25039 | 0.25039 | 0.25039 | 0.0 | 13.72 +Bond | 1.0461 | 1.0461 | 1.0461 | 0.0 | 57.34 +Kspace | 0.34339 | 0.34339 | 0.34339 | 0.0 | 18.82 +Neigh | 0.0097352 | 0.0097352 | 0.0097352 | 0.0 | 0.53 +Comm | 0.0047764 | 0.0047764 | 0.0047764 | 0.0 | 0.26 +Output | 0.0030537 | 0.0030537 | 0.0030537 | 0.0 | 0.17 +Modify | 0.15534 | 0.15534 | 0.15534 | 0.0 | 8.51 +Other | | 0.01155 | | | 0.63 + +Nlocal: 44 ave 44 max 44 min +Histogram: 1 0 0 0 0 0 0 0 0 0 +Nghost: 44 ave 44 max 44 min +Histogram: 1 0 0 0 0 0 0 0 0 0 +Neighs: 823 ave 823 max 823 min +Histogram: 1 0 0 0 0 0 0 0 0 0 + +Total # of neighbors = 823 +Ave neighs/atom = 18.704545 +Ave special neighs/atom = 9.9090909 +Neighbor list builds = 221 +Dangerous builds = 0 + +# write_restart restart_longrun +# write_data restart_longrun.data +Total wall time: 0:00:01 diff --git a/examples/PACKAGES/reaction/tiny_nylon/log.4Nov2020.tiny_nylon.stabilized.g++.4 b/examples/PACKAGES/reaction/tiny_nylon/log.4Nov2020.tiny_nylon.stabilized.g++.4 new file mode 100644 index 0000000000..0a30cd6984 --- /dev/null +++ b/examples/PACKAGES/reaction/tiny_nylon/log.4Nov2020.tiny_nylon.stabilized.g++.4 @@ -0,0 +1,412 @@ +LAMMPS (4 Nov 2022) +# two monomer nylon example +# reaction produces a condensed water molecule + +units real + +boundary p p p + +atom_style full + +kspace_style pppm 1.0e-4 + +pair_style lj/class2/coul/long 8.5 + +angle_style class2 + +bond_style class2 + +dihedral_style class2 + +improper_style class2 + +read_data tiny_nylon.data extra/bond/per/atom 5 extra/angle/per/atom 15 extra/dihedral/per/atom 15 extra/improper/per/atom 25 extra/special/per/atom 25 +Reading data file ... + orthogonal box = (-25 -25 -25) to (25 25 25) + 1 by 2 by 2 MPI processor grid + reading atom labelmap ... + reading bond labelmap ... + reading angle labelmap ... + reading dihedral labelmap ... + reading improper labelmap ... + reading atoms ... + 44 atoms + reading velocities ... + 44 velocities + scanning bonds ... + 9 = max bonds/atom + scanning angles ... + 21 = max angles/atom + scanning dihedrals ... + 29 = max dihedrals/atom + scanning impropers ... + 29 = max impropers/atom + reading bonds ... + 42 bonds + reading angles ... + 74 angles + reading dihedrals ... + 100 dihedrals + reading impropers ... + 44 impropers +Finding 1-2 1-3 1-4 neighbors ... + special bond factors lj: 0 0 0 + special bond factors coul: 0 0 0 + 4 = max # of 1-2 neighbors + 6 = max # of 1-3 neighbors + 12 = max # of 1-4 neighbors + 41 = max # of special neighbors + special bonds CPU = 0.000 seconds + read_data CPU = 0.008 seconds + +velocity all create 300.0 4928459 dist gaussian + +molecule mol1 rxn1_stp1_unreacted.molecule_template +Read molecule template mol1: + 1 molecules + 0 fragments + 18 atoms with max type 8 + 16 bonds with max type 10 + 25 angles with max type 28 + 23 dihedrals with max type 36 + 2 impropers with max type 3 +molecule mol2 rxn1_stp1_reacted.molecule_template +Read molecule template mol2: + 1 molecules + 0 fragments + 18 atoms with max type 9 + 17 bonds with max type 13 + 31 angles with max type 27 + 39 dihedrals with max type 33 + 0 impropers with max type 0 +molecule mol3 rxn1_stp2_unreacted.molecule_template +Read molecule template mol3: + 1 molecules + 0 fragments + 15 atoms with max type 9 + 14 bonds with max type 13 + 25 angles with max type 27 + 30 dihedrals with max type 33 + 0 impropers with max type 0 +molecule mol4 rxn1_stp2_reacted.molecule_template +Read molecule template mol4: + 1 molecules + 0 fragments + 15 atoms with max type 11 + 13 bonds with max type 15 + 19 angles with max type 29 + 16 dihedrals with max type 32 + 2 impropers with max type 13 + +thermo 50 + +# dump 1 all xyz 1 test_vis.xyz + +fix myrxns all bond/react stabilization yes statted_grp .03 react rxn1 all 1 0.0 2.9 mol1 mol2 rxn1_stp1_map react rxn2 all 1 0.0 5.0 mol3 mol4 rxn1_stp2_map +WARNING: Fix bond/react: Atom affected by reaction rxn2 is too close to template edge (../fix_bond_react.cpp:2624) +dynamic group bond_react_MASTER_group defined +dynamic group statted_grp_REACT defined + +fix 1 statted_grp_REACT nvt temp 300 300 100 + +# optionally, you can customize behavior of reacting atoms, +# by using the internally-created 'bond_react_MASTER_group', like so: +fix 4 bond_react_MASTER_group temp/rescale 1 300 300 10 1 + +thermo_style custom step temp press density f_myrxns[1] f_myrxns[2] + +# restart 100 restart1 restart2 + +run 10000 + +CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE + +Your simulation uses code contributions which should be cited: + +- fix bond/react: reacter.org doi:10.1016/j.polymer.2017.09.038, doi:10.1021/acs.macromol.0c02012 + +@Article{Gissinger17, + author = {J. R. Gissinger and B. D. Jensen and K. E. Wise}, + title = {Modeling Chemical Reactions in Classical Molecular Dynamics Simulations}, + journal = {Polymer}, + year = 2017, + volume = 128, + pages = {211--217} +} + +@Article{Gissinger20, + author = {J. R. Gissinger, B. D. Jensen, K. E. Wise}, + title = {{REACTER}: A Heuristic Method for Reactive Molecular Dynamics}, + journal = {Macromolecules}, + year = 2020, + volume = 53, + number = 22, + pages = {9953--9961} +} + +CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE + +PPPM initialization ... + using 12-bit tables for long-range coulomb (../kspace.cpp:342) + G vector (1/distance) = 0.05345967 + grid = 2 2 2 + stencil order = 5 + estimated absolute RMS force accuracy = 0.040225597 + estimated relative force accuracy = 0.00012113819 + using double precision KISS FFT + 3d grid and FFT values/proc = 252 2 +Generated 55 of 55 mixed pair_coeff terms from sixthpower/geometric mixing rule +Neighbor list info ... + update: every = 1 steps, delay = 0 steps, check = yes + max neighbors/atom: 2000, page size: 100000 + master list distance cutoff = 10.5 + ghost atom cutoff = 10.5 + binsize = 5.25, bins = 10 10 10 + 2 neighbor lists, perpetual/occasional/extra = 1 1 0 + (1) pair lj/class2/coul/long, perpetual + attributes: half, newton on + pair build: half/bin/newton + stencil: half/bin/3d + bin: standard + (2) fix bond/react, occasional, copy from (1) + attributes: half, newton on + pair build: copy + stencil: none + bin: none +WARNING: Inconsistent image flags (../domain.cpp:819) +Per MPI rank memory allocation (min/avg/max) = 33.66 | 33.88 | 34.43 Mbytes + Step Temp Press Density f_myrxns[1] f_myrxns[2] + 0 300 346.78165 0.0034851739 0 0 + 50 283.51963 -47.16359 0.0034851739 1 0 + 100 256.04648 21.778898 0.0034851739 1 1 + 150 450.78138 -11.7887 0.0034851739 1 1 + 200 400.15754 49.489858 0.0034851739 1 1 + 250 347.06066 68.952063 0.0034851739 1 1 + 300 291.89228 -1.5986302 0.0034851739 1 1 + 350 290.25995 17.634558 0.0034851739 1 1 + 400 234.89168 26.36452 0.0034851739 1 1 + 450 305.80709 -28.923896 0.0034851739 1 1 + 500 375.19218 -37.024375 0.0034851739 1 1 + 550 321.86944 -4.6961825 0.0034851739 1 1 + 600 307.2639 -31.393161 0.0034851739 1 1 + 650 255.95833 8.4995589 0.0034851739 1 1 + 700 294.54665 -17.06105 0.0034851739 1 1 + 750 273.08231 -10.7175 0.0034851739 1 1 + 800 249.69175 9.9777684 0.0034851739 1 1 + 850 307.71806 -6.9950047 0.0034851739 1 1 + 900 367.39855 9.9874984 0.0034851739 1 1 + 950 327.57334 -4.702978 0.0034851739 1 1 + 1000 348.85247 15.763492 0.0034851739 1 1 + 1050 328.94435 -35.031279 0.0034851739 1 1 + 1100 283.23971 -16.937443 0.0034851739 1 1 + 1150 266.69676 42.308482 0.0034851739 1 1 + 1200 244.61493 -8.2911432 0.0034851739 1 1 + 1250 206.68495 6.6280166 0.0034851739 1 1 + 1300 257.83339 -7.0826264 0.0034851739 1 1 + 1350 358.0875 -7.602474 0.0034851739 1 1 + 1400 353.66614 18.091914 0.0034851739 1 1 + 1450 302.27969 13.828755 0.0034851739 1 1 + 1500 262.57851 9.2567956 0.0034851739 1 1 + 1550 252.39492 1.2438631 0.0034851739 1 1 + 1600 247.18352 10.008173 0.0034851739 1 1 + 1650 290.30112 -2.1829055 0.0034851739 1 1 + 1700 272.78999 -57.305766 0.0034851739 1 1 + 1750 253.35258 24.729797 0.0034851739 1 1 + 1800 278.67832 -0.95017071 0.0034851739 1 1 + 1850 302.04743 16.002872 0.0034851739 1 1 + 1900 330.67188 -22.034206 0.0034851739 1 1 + 1950 342.64206 8.0075967 0.0034851739 1 1 + 2000 348.74388 -12.159899 0.0034851739 1 1 + 2050 300.48095 36.010534 0.0034851739 1 1 + 2100 275.017 8.7612294 0.0034851739 1 1 + 2150 303.92758 10.317032 0.0034851739 1 1 + 2200 308.89452 33.245012 0.0034851739 1 1 + 2250 265.74176 35.857111 0.0034851739 1 1 + 2300 273.40086 53.001626 0.0034851739 1 1 + 2350 287.74753 -0.14586562 0.0034851739 1 1 + 2400 278.7606 -8.20812 0.0034851739 1 1 + 2450 331.88979 39.02519 0.0034851739 1 1 + 2500 280.04041 -21.423589 0.0034851739 1 1 + 2550 388.81536 -12.350053 0.0034851739 1 1 + 2600 311.13468 -13.286785 0.0034851739 1 1 + 2650 325.07686 88.710881 0.0034851739 1 1 + 2700 319.08471 14.118288 0.0034851739 1 1 + 2750 261.72067 26.051439 0.0034851739 1 1 + 2800 281.03459 -21.201297 0.0034851739 1 1 + 2850 312.27342 4.3904047 0.0034851739 1 1 + 2900 274.81152 -12.739138 0.0034851739 1 1 + 2950 281.76873 11.199981 0.0034851739 1 1 + 3000 291.8377 48.595661 0.0034851739 1 1 + 3050 297.40212 -24.911752 0.0034851739 1 1 + 3100 341.48252 13.825136 0.0034851739 1 1 + 3150 347.5099 -10.452847 0.0034851739 1 1 + 3200 301.24901 26.553909 0.0034851739 1 1 + 3250 281.35392 -23.028031 0.0034851739 1 1 + 3300 279.82881 -53.225332 0.0034851739 1 1 + 3350 289.41016 -8.7866567 0.0034851739 1 1 + 3400 288.56923 -25.445059 0.0034851739 1 1 + 3450 259.59956 77.88466 0.0034851739 1 1 + 3500 295.99591 30.357393 0.0034851739 1 1 + 3550 302.1675 -5.103997 0.0034851739 1 1 + 3600 289.00244 -12.687621 0.0034851739 1 1 + 3650 333.89968 -33.124064 0.0034851739 1 1 + 3700 347.82328 -24.745583 0.0034851739 1 1 + 3750 354.51391 6.7131611 0.0034851739 1 1 + 3800 341.31124 -18.777474 0.0034851739 1 1 + 3850 320.48132 35.547595 0.0034851739 1 1 + 3900 326.8911 -49.153151 0.0034851739 1 1 + 3950 299.65543 -19.443322 0.0034851739 1 1 + 4000 308.97943 30.368402 0.0034851739 1 1 + 4050 251.46183 -17.518988 0.0034851739 1 1 + 4100 241.50223 22.103347 0.0034851739 1 1 + 4150 265.01178 -4.4952098 0.0034851739 1 1 + 4200 369.78569 -14.603579 0.0034851739 1 1 + 4250 348.20071 -33.060693 0.0034851739 1 1 + 4300 368.11836 11.897676 0.0034851739 1 1 + 4350 321.1145 -9.3124104 0.0034851739 1 1 + 4400 313.95395 -31.940883 0.0034851739 1 1 + 4450 280.50985 41.398853 0.0034851739 1 1 + 4500 289.36914 -2.3915112 0.0034851739 1 1 + 4550 318.52735 -5.0086703 0.0034851739 1 1 + 4600 308.68169 -13.642004 0.0034851739 1 1 + 4650 285.24153 35.314806 0.0034851739 1 1 + 4700 357.15021 8.8271927 0.0034851739 1 1 + 4750 359.11051 -59.672314 0.0034851739 1 1 + 4800 453.11584 0.54316266 0.0034851739 1 1 + 4850 392.52232 46.350736 0.0034851739 1 1 + 4900 310.42864 5.9002223 0.0034851739 1 1 + 4950 285.97355 -19.321724 0.0034851739 1 1 + 5000 309.41828 18.331381 0.0034851739 1 1 + 5050 324.96434 -27.143631 0.0034851739 1 1 + 5100 266.49422 -26.977074 0.0034851739 1 1 + 5150 295.35576 -14.271299 0.0034851739 1 1 + 5200 275.8961 14.057873 0.0034851739 1 1 + 5250 332.75955 26.04747 0.0034851739 1 1 + 5300 296.57102 -20.904181 0.0034851739 1 1 + 5350 264.68808 29.533914 0.0034851739 1 1 + 5400 293.373 -13.579532 0.0034851739 1 1 + 5450 290.55933 9.3458628 0.0034851739 1 1 + 5500 340.54834 8.8308229 0.0034851739 1 1 + 5550 336.08713 -6.9696582 0.0034851739 1 1 + 5600 331.77668 -7.9756709 0.0034851739 1 1 + 5650 307.8419 -10.263349 0.0034851739 1 1 + 5700 262.70119 78.855544 0.0034851739 1 1 + 5750 285.37985 -15.4042 0.0034851739 1 1 + 5800 267.44612 -30.053955 0.0034851739 1 1 + 5850 241.52125 3.2904907 0.0034851739 1 1 + 5900 265.13367 27.69901 0.0034851739 1 1 + 5950 277.95155 18.419031 0.0034851739 1 1 + 6000 309.62777 -20.054029 0.0034851739 1 1 + 6050 363.41588 16.435337 0.0034851739 1 1 + 6100 348.85793 -14.513241 0.0034851739 1 1 + 6150 323.73745 56.990265 0.0034851739 1 1 + 6200 338.66823 -19.93498 0.0034851739 1 1 + 6250 325.41329 -13.824943 0.0034851739 1 1 + 6300 279.82345 -9.0557197 0.0034851739 1 1 + 6350 285.90705 52.434161 0.0034851739 1 1 + 6400 260.34102 -15.766595 0.0034851739 1 1 + 6450 304.65686 7.5058044 0.0034851739 1 1 + 6500 265.02097 1.7203356 0.0034851739 1 1 + 6550 293.35057 1.8896974 0.0034851739 1 1 + 6600 284.06837 -9.3674953 0.0034851739 1 1 + 6650 307.29863 -2.3882614 0.0034851739 1 1 + 6700 336.20676 43.913926 0.0034851739 1 1 + 6750 291.53938 -16.749433 0.0034851739 1 1 + 6800 298.4418 -13.340335 0.0034851739 1 1 + 6850 264.13368 -11.219357 0.0034851739 1 1 + 6900 273.63109 -15.897238 0.0034851739 1 1 + 6950 282.64715 6.8275423 0.0034851739 1 1 + 7000 277.4091 -25.381099 0.0034851739 1 1 + 7050 278.07001 63.552969 0.0034851739 1 1 + 7100 293.33358 22.103462 0.0034851739 1 1 + 7150 308.36447 -27.212203 0.0034851739 1 1 + 7200 251.45077 -40.385347 0.0034851739 1 1 + 7250 317.57808 1.0302048 0.0034851739 1 1 + 7300 348.52627 48.392457 0.0034851739 1 1 + 7350 356.5821 27.933626 0.0034851739 1 1 + 7400 311.29835 -18.899768 0.0034851739 1 1 + 7450 274.24476 -19.41577 0.0034851739 1 1 + 7500 261.38075 1.2110527 0.0034851739 1 1 + 7550 299.78907 -17.64954 0.0034851739 1 1 + 7600 271.36191 25.99439 0.0034851739 1 1 + 7650 287.51241 1.532789 0.0034851739 1 1 + 7700 280.87778 -31.828432 0.0034851739 1 1 + 7750 312.22588 45.320976 0.0034851739 1 1 + 7800 312.73849 4.1022573 0.0034851739 1 1 + 7850 299.18742 50.272069 0.0034851739 1 1 + 7900 312.4916 -34.425195 0.0034851739 1 1 + 7950 284.5205 15.716375 0.0034851739 1 1 + 8000 248.39764 -7.1922339 0.0034851739 1 1 + 8050 242.65659 -32.701773 0.0034851739 1 1 + 8100 228.76112 54.351 0.0034851739 1 1 + 8150 308.67672 -15.835344 0.0034851739 1 1 + 8200 304.26746 -11.106867 0.0034851739 1 1 + 8250 338.67601 44.199636 0.0034851739 1 1 + 8300 308.59612 -9.6487546 0.0034851739 1 1 + 8350 287.08027 11.036122 0.0034851739 1 1 + 8400 319.79578 -78.918735 0.0034851739 1 1 + 8450 320.78978 57.275745 0.0034851739 1 1 + 8500 282.90803 33.716746 0.0034851739 1 1 + 8550 235.23686 -44.587941 0.0034851739 1 1 + 8600 265.62925 45.976855 0.0034851739 1 1 + 8650 260.35429 -9.3951434 0.0034851739 1 1 + 8700 236.16314 19.504695 0.0034851739 1 1 + 8750 291.51087 -13.996885 0.0034851739 1 1 + 8800 357.00246 -26.674845 0.0034851739 1 1 + 8850 327.72543 15.954838 0.0034851739 1 1 + 8900 321.17809 -14.794959 0.0034851739 1 1 + 8950 357.51102 39.861567 0.0034851739 1 1 + 9000 286.68385 -52.799636 0.0034851739 1 1 + 9050 283.96224 13.044025 0.0034851739 1 1 + 9100 304.04431 25.510777 0.0034851739 1 1 + 9150 261.33631 -18.611794 0.0034851739 1 1 + 9200 297.50501 25.733551 0.0034851739 1 1 + 9250 279.85018 -26.91045 0.0034851739 1 1 + 9300 336.07358 35.385228 0.0034851739 1 1 + 9350 326.27961 -36.941794 0.0034851739 1 1 + 9400 400.42857 7.5301492 0.0034851739 1 1 + 9450 296.80174 11.898673 0.0034851739 1 1 + 9500 275.98796 41.303486 0.0034851739 1 1 + 9550 278.56924 31.033397 0.0034851739 1 1 + 9600 260.24476 -11.416595 0.0034851739 1 1 + 9650 281.86065 12.60709 0.0034851739 1 1 + 9700 287.26789 -29.086626 0.0034851739 1 1 + 9750 290.82789 3.2830325 0.0034851739 1 1 + 9800 270.99421 -25.824595 0.0034851739 1 1 + 9850 385.1884 4.1048816 0.0034851739 1 1 + 9900 363.1711 18.815879 0.0034851739 1 1 + 9950 344.93572 17.375158 0.0034851739 1 1 + 10000 335.65852 -0.84087429 0.0034851739 1 1 +Loop time of 1.78856 on 4 procs for 10000 steps with 44 atoms + +Performance: 483.070 ns/day, 0.050 hours/ns, 5591.087 timesteps/s, 246.008 katom-step/s +100.0% CPU use with 4 MPI tasks x no OpenMP threads + +MPI task timing breakdown: +Section | min time | avg time | max time |%varavg| %total +--------------------------------------------------------------- +Pair | 0.0021174 | 0.066025 | 0.20024 | 31.5 | 3.69 +Bond | 0.0035593 | 0.2715 | 0.74757 | 58.6 | 15.18 +Kspace | 0.50386 | 1.0492 | 1.3455 | 33.6 | 58.66 +Neigh | 0.0079056 | 0.0079463 | 0.0079766 | 0.0 | 0.44 +Comm | 0.044284 | 0.08173 | 0.10388 | 8.1 | 4.57 +Output | 0.0021661 | 0.0024497 | 0.0031314 | 0.8 | 0.14 +Modify | 0.2648 | 0.29459 | 0.33479 | 5.5 | 16.47 +Other | | 0.01514 | | | 0.85 + +Nlocal: 11 ave 41 max 0 min +Histogram: 3 0 0 0 0 0 0 0 0 1 +Nghost: 27.5 ave 41 max 0 min +Histogram: 1 0 0 0 0 0 0 0 2 1 +Neighs: 205.75 ave 820 max 0 min +Histogram: 3 0 0 0 0 0 0 0 0 1 + +Total # of neighbors = 823 +Ave neighs/atom = 18.704545 +Ave special neighs/atom = 9.9090909 +Neighbor list builds = 225 +Dangerous builds = 0 + +# write_restart restart_longrun +# write_data restart_longrun.data +Total wall time: 0:00:01 diff --git a/examples/PACKAGES/reaction/tiny_nylon/log.4Nov2020.tiny_nylon.stabilized_variable_probability.g++.1 b/examples/PACKAGES/reaction/tiny_nylon/log.4Nov2020.tiny_nylon.stabilized_variable_probability.g++.1 new file mode 100644 index 0000000000..ec822e8b3b --- /dev/null +++ b/examples/PACKAGES/reaction/tiny_nylon/log.4Nov2020.tiny_nylon.stabilized_variable_probability.g++.1 @@ -0,0 +1,237 @@ +LAMMPS (4 Nov 2022) +# two monomer nylon example +# reaction produces a condensed water molecule + +units real + +boundary p p p + +atom_style full + +kspace_style pppm 1.0e-4 + +pair_style lj/class2/coul/long 8.5 + +angle_style class2 + +bond_style class2 + +dihedral_style class2 + +improper_style class2 + +read_data tiny_nylon.data extra/bond/per/atom 5 extra/angle/per/atom 15 extra/dihedral/per/atom 15 extra/improper/per/atom 25 extra/special/per/atom 25 +Reading data file ... + orthogonal box = (-25 -25 -25) to (25 25 25) + 1 by 1 by 1 MPI processor grid + reading atom labelmap ... + reading bond labelmap ... + reading angle labelmap ... + reading dihedral labelmap ... + reading improper labelmap ... + reading atoms ... + 44 atoms + reading velocities ... + 44 velocities + scanning bonds ... + 9 = max bonds/atom + scanning angles ... + 21 = max angles/atom + scanning dihedrals ... + 29 = max dihedrals/atom + scanning impropers ... + 29 = max impropers/atom + reading bonds ... + 42 bonds + reading angles ... + 74 angles + reading dihedrals ... + 100 dihedrals + reading impropers ... + 44 impropers +Finding 1-2 1-3 1-4 neighbors ... + special bond factors lj: 0 0 0 + special bond factors coul: 0 0 0 + 4 = max # of 1-2 neighbors + 6 = max # of 1-3 neighbors + 12 = max # of 1-4 neighbors + 41 = max # of special neighbors + special bonds CPU = 0.000 seconds + read_data CPU = 0.007 seconds + +variable runsteps equal 1000 +variable prob1 equal step/v_runsteps*2+0.1 +variable prob2 equal (step/v_runsteps)>0.5 + +velocity all create 300.0 4928459 dist gaussian + +molecule mol1 rxn1_stp1_unreacted.molecule_template +Read molecule template mol1: + 1 molecules + 0 fragments + 18 atoms with max type 8 + 16 bonds with max type 10 + 25 angles with max type 28 + 23 dihedrals with max type 36 + 2 impropers with max type 3 +molecule mol2 rxn1_stp1_reacted.molecule_template +Read molecule template mol2: + 1 molecules + 0 fragments + 18 atoms with max type 9 + 17 bonds with max type 13 + 31 angles with max type 27 + 39 dihedrals with max type 33 + 0 impropers with max type 0 +molecule mol3 rxn1_stp2_unreacted.molecule_template +Read molecule template mol3: + 1 molecules + 0 fragments + 15 atoms with max type 9 + 14 bonds with max type 13 + 25 angles with max type 27 + 30 dihedrals with max type 33 + 0 impropers with max type 0 +molecule mol4 rxn1_stp2_reacted.molecule_template +Read molecule template mol4: + 1 molecules + 0 fragments + 15 atoms with max type 11 + 13 bonds with max type 15 + 19 angles with max type 29 + 16 dihedrals with max type 32 + 2 impropers with max type 13 + +thermo 50 + +# dump 1 all xyz 1 test_vis.xyz + +fix myrxns all bond/react stabilization yes statted_grp .03 react rxn1 all 1 0.0 5.0 mol1 mol2 rxn1_stp1_map prob v_prob1 1234 react rxn2 all 1 0.0 5.0 mol3 mol4 rxn1_stp2_map prob v_prob2 1234 +WARNING: Fix bond/react: Atom affected by reaction rxn2 is too close to template edge (../fix_bond_react.cpp:2624) +dynamic group bond_react_MASTER_group defined +dynamic group statted_grp_REACT defined + +fix 1 statted_grp_REACT nvt temp 300 300 100 + +# optionally, you can customize behavior of reacting atoms, +# by using the internally-created 'bond_react_MASTER_group', like so: +fix 4 bond_react_MASTER_group temp/rescale 1 300 300 10 1 + +thermo_style custom step temp press density v_prob1 v_prob2 f_myrxns[1] f_myrxns[2] + +# restart 100 restart1 restart2 + +run ${runsteps} +run 1000 + +CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE + +Your simulation uses code contributions which should be cited: + +- fix bond/react: reacter.org doi:10.1016/j.polymer.2017.09.038, doi:10.1021/acs.macromol.0c02012 + +@Article{Gissinger17, + author = {J. R. Gissinger and B. D. Jensen and K. E. Wise}, + title = {Modeling Chemical Reactions in Classical Molecular Dynamics Simulations}, + journal = {Polymer}, + year = 2017, + volume = 128, + pages = {211--217} +} + +@Article{Gissinger20, + author = {J. R. Gissinger, B. D. Jensen, K. E. Wise}, + title = {{REACTER}: A Heuristic Method for Reactive Molecular Dynamics}, + journal = {Macromolecules}, + year = 2020, + volume = 53, + number = 22, + pages = {9953--9961} +} + +CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE + +PPPM initialization ... + using 12-bit tables for long-range coulomb (../kspace.cpp:342) + G vector (1/distance) = 0.05345967 + grid = 2 2 2 + stencil order = 5 + estimated absolute RMS force accuracy = 0.040225597 + estimated relative force accuracy = 0.00012113819 + using double precision KISS FFT + 3d grid and FFT values/proc = 343 8 +Generated 55 of 55 mixed pair_coeff terms from sixthpower/geometric mixing rule +Neighbor list info ... + update: every = 1 steps, delay = 0 steps, check = yes + max neighbors/atom: 2000, page size: 100000 + master list distance cutoff = 10.5 + ghost atom cutoff = 10.5 + binsize = 5.25, bins = 10 10 10 + 2 neighbor lists, perpetual/occasional/extra = 1 1 0 + (1) pair lj/class2/coul/long, perpetual + attributes: half, newton on + pair build: half/bin/newton + stencil: half/bin/3d + bin: standard + (2) fix bond/react, occasional, copy from (1) + attributes: half, newton on + pair build: copy + stencil: none + bin: none +WARNING: Inconsistent image flags (../domain.cpp:819) +Per MPI rank memory allocation (min/avg/max) = 33.78 | 33.78 | 33.78 Mbytes + Step Temp Press Density v_prob1 v_prob2 f_myrxns[1] f_myrxns[2] + 0 300 346.78165 0.0034851739 0.1 0 0 0 + 50 265.51039 -67.489756 0.0034851739 0.2 0 1 0 + 100 596.03388 -27.815189 0.0034851739 0.3 0 1 0 + 150 500.05269 2.9684972 0.0034851739 0.4 0 1 0 + 200 511.40295 56.791868 0.0034851739 0.5 0 1 0 + 250 375.95679 -4.0587677 0.0034851739 0.6 0 1 0 + 300 371.1629 -60.689059 0.0034851739 0.7 0 1 0 + 350 336.06545 8.6411023 0.0034851739 0.8 0 1 0 + 400 301.41962 50.628044 0.0034851739 0.9 0 1 0 + 450 281.08727 -15.590922 0.0034851739 1 0 1 0 + 500 297.35323 -9.5761786 0.0034851739 1.1 0 1 0 + 550 197.45298 3.6867353 0.0034851739 1.2 1 1 1 + 600 240.1748 -19.889198 0.0034851739 1.3 1 1 1 + 650 231.57018 -13.078808 0.0034851739 1.4 1 1 1 + 700 296.00816 -18.772183 0.0034851739 1.5 1 1 1 + 750 294.94016 15.43915 0.0034851739 1.6 1 1 1 + 800 316.51231 12.070563 0.0034851739 1.7 1 1 1 + 850 348.59373 9.0940092 0.0034851739 1.8 1 1 1 + 900 330.5264 -3.4868175 0.0034851739 1.9 1 1 1 + 950 307.02461 34.643373 0.0034851739 2 1 1 1 + 1000 250.06536 5.8440413 0.0034851739 2.1 1 1 1 +Loop time of 0.202863 on 1 procs for 1000 steps with 44 atoms + +Performance: 425.903 ns/day, 0.056 hours/ns, 4929.437 timesteps/s, 216.895 katom-step/s +100.0% CPU use with 1 MPI tasks x no OpenMP threads + +MPI task timing breakdown: +Section | min time | avg time | max time |%varavg| %total +--------------------------------------------------------------- +Pair | 0.025759 | 0.025759 | 0.025759 | 0.0 | 12.70 +Bond | 0.11024 | 0.11024 | 0.11024 | 0.0 | 54.34 +Kspace | 0.034344 | 0.034344 | 0.034344 | 0.0 | 16.93 +Neigh | 0.0015719 | 0.0015719 | 0.0015719 | 0.0 | 0.77 +Comm | 0.00045259 | 0.00045259 | 0.00045259 | 0.0 | 0.22 +Output | 0.0004759 | 0.0004759 | 0.0004759 | 0.0 | 0.23 +Modify | 0.028713 | 0.028713 | 0.028713 | 0.0 | 14.15 +Other | | 0.001307 | | | 0.64 + +Nlocal: 44 ave 44 max 44 min +Histogram: 1 0 0 0 0 0 0 0 0 0 +Nghost: 3 ave 3 max 3 min +Histogram: 1 0 0 0 0 0 0 0 0 0 +Neighs: 802 ave 802 max 802 min +Histogram: 1 0 0 0 0 0 0 0 0 0 + +Total # of neighbors = 802 +Ave neighs/atom = 18.227273 +Ave special neighs/atom = 9.9090909 +Neighbor list builds = 32 +Dangerous builds = 0 + +# write_restart restart_longrun +# write_data restart_longrun.data +Total wall time: 0:00:00 diff --git a/examples/PACKAGES/reaction/tiny_nylon/log.4Nov2020.tiny_nylon.stabilized_variable_probability.g++.4 b/examples/PACKAGES/reaction/tiny_nylon/log.4Nov2020.tiny_nylon.stabilized_variable_probability.g++.4 new file mode 100644 index 0000000000..d85e7fb474 --- /dev/null +++ b/examples/PACKAGES/reaction/tiny_nylon/log.4Nov2020.tiny_nylon.stabilized_variable_probability.g++.4 @@ -0,0 +1,237 @@ +LAMMPS (4 Nov 2022) +# two monomer nylon example +# reaction produces a condensed water molecule + +units real + +boundary p p p + +atom_style full + +kspace_style pppm 1.0e-4 + +pair_style lj/class2/coul/long 8.5 + +angle_style class2 + +bond_style class2 + +dihedral_style class2 + +improper_style class2 + +read_data tiny_nylon.data extra/bond/per/atom 5 extra/angle/per/atom 15 extra/dihedral/per/atom 15 extra/improper/per/atom 25 extra/special/per/atom 25 +Reading data file ... + orthogonal box = (-25 -25 -25) to (25 25 25) + 1 by 2 by 2 MPI processor grid + reading atom labelmap ... + reading bond labelmap ... + reading angle labelmap ... + reading dihedral labelmap ... + reading improper labelmap ... + reading atoms ... + 44 atoms + reading velocities ... + 44 velocities + scanning bonds ... + 9 = max bonds/atom + scanning angles ... + 21 = max angles/atom + scanning dihedrals ... + 29 = max dihedrals/atom + scanning impropers ... + 29 = max impropers/atom + reading bonds ... + 42 bonds + reading angles ... + 74 angles + reading dihedrals ... + 100 dihedrals + reading impropers ... + 44 impropers +Finding 1-2 1-3 1-4 neighbors ... + special bond factors lj: 0 0 0 + special bond factors coul: 0 0 0 + 4 = max # of 1-2 neighbors + 6 = max # of 1-3 neighbors + 12 = max # of 1-4 neighbors + 41 = max # of special neighbors + special bonds CPU = 0.000 seconds + read_data CPU = 0.008 seconds + +variable runsteps equal 1000 +variable prob1 equal step/v_runsteps*2+0.1 +variable prob2 equal (step/v_runsteps)>0.5 + +velocity all create 300.0 4928459 dist gaussian + +molecule mol1 rxn1_stp1_unreacted.molecule_template +Read molecule template mol1: + 1 molecules + 0 fragments + 18 atoms with max type 8 + 16 bonds with max type 10 + 25 angles with max type 28 + 23 dihedrals with max type 36 + 2 impropers with max type 3 +molecule mol2 rxn1_stp1_reacted.molecule_template +Read molecule template mol2: + 1 molecules + 0 fragments + 18 atoms with max type 9 + 17 bonds with max type 13 + 31 angles with max type 27 + 39 dihedrals with max type 33 + 0 impropers with max type 0 +molecule mol3 rxn1_stp2_unreacted.molecule_template +Read molecule template mol3: + 1 molecules + 0 fragments + 15 atoms with max type 9 + 14 bonds with max type 13 + 25 angles with max type 27 + 30 dihedrals with max type 33 + 0 impropers with max type 0 +molecule mol4 rxn1_stp2_reacted.molecule_template +Read molecule template mol4: + 1 molecules + 0 fragments + 15 atoms with max type 11 + 13 bonds with max type 15 + 19 angles with max type 29 + 16 dihedrals with max type 32 + 2 impropers with max type 13 + +thermo 50 + +# dump 1 all xyz 1 test_vis.xyz + +fix myrxns all bond/react stabilization yes statted_grp .03 react rxn1 all 1 0.0 5.0 mol1 mol2 rxn1_stp1_map prob v_prob1 1234 react rxn2 all 1 0.0 5.0 mol3 mol4 rxn1_stp2_map prob v_prob2 1234 +WARNING: Fix bond/react: Atom affected by reaction rxn2 is too close to template edge (../fix_bond_react.cpp:2624) +dynamic group bond_react_MASTER_group defined +dynamic group statted_grp_REACT defined + +fix 1 statted_grp_REACT nvt temp 300 300 100 + +# optionally, you can customize behavior of reacting atoms, +# by using the internally-created 'bond_react_MASTER_group', like so: +fix 4 bond_react_MASTER_group temp/rescale 1 300 300 10 1 + +thermo_style custom step temp press density v_prob1 v_prob2 f_myrxns[1] f_myrxns[2] + +# restart 100 restart1 restart2 + +run ${runsteps} +run 1000 + +CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE + +Your simulation uses code contributions which should be cited: + +- fix bond/react: reacter.org doi:10.1016/j.polymer.2017.09.038, doi:10.1021/acs.macromol.0c02012 + +@Article{Gissinger17, + author = {J. R. Gissinger and B. D. Jensen and K. E. Wise}, + title = {Modeling Chemical Reactions in Classical Molecular Dynamics Simulations}, + journal = {Polymer}, + year = 2017, + volume = 128, + pages = {211--217} +} + +@Article{Gissinger20, + author = {J. R. Gissinger, B. D. Jensen, K. E. Wise}, + title = {{REACTER}: A Heuristic Method for Reactive Molecular Dynamics}, + journal = {Macromolecules}, + year = 2020, + volume = 53, + number = 22, + pages = {9953--9961} +} + +CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE + +PPPM initialization ... + using 12-bit tables for long-range coulomb (../kspace.cpp:342) + G vector (1/distance) = 0.05345967 + grid = 2 2 2 + stencil order = 5 + estimated absolute RMS force accuracy = 0.040225597 + estimated relative force accuracy = 0.00012113819 + using double precision KISS FFT + 3d grid and FFT values/proc = 252 2 +Generated 55 of 55 mixed pair_coeff terms from sixthpower/geometric mixing rule +Neighbor list info ... + update: every = 1 steps, delay = 0 steps, check = yes + max neighbors/atom: 2000, page size: 100000 + master list distance cutoff = 10.5 + ghost atom cutoff = 10.5 + binsize = 5.25, bins = 10 10 10 + 2 neighbor lists, perpetual/occasional/extra = 1 1 0 + (1) pair lj/class2/coul/long, perpetual + attributes: half, newton on + pair build: half/bin/newton + stencil: half/bin/3d + bin: standard + (2) fix bond/react, occasional, copy from (1) + attributes: half, newton on + pair build: copy + stencil: none + bin: none +WARNING: Inconsistent image flags (../domain.cpp:819) +Per MPI rank memory allocation (min/avg/max) = 33.66 | 33.88 | 34.43 Mbytes + Step Temp Press Density v_prob1 v_prob2 f_myrxns[1] f_myrxns[2] + 0 300 346.78165 0.0034851739 0.1 0 0 0 + 50 275.80938 -29.158908 0.0034851739 0.2 0 1 0 + 100 751.80013 8.8967942 0.0034851739 0.3 0 1 0 + 150 412.82804 61.44542 0.0034851739 0.4 0 1 0 + 200 432.95275 81.052275 0.0034851739 0.5 0 1 0 + 250 338.65702 -39.770422 0.0034851739 0.6 0 1 0 + 300 326.15993 -46.690912 0.0034851739 0.7 0 1 0 + 350 286.66126 51.986782 0.0034851739 0.8 0 1 0 + 400 244.24575 25.460254 0.0034851739 0.9 0 1 0 + 450 294.06274 5.0448726 0.0034851739 1 0 1 0 + 500 280.71089 0.86710712 0.0034851739 1.1 0 1 0 + 550 241.94123 -5.7812057 0.0034851739 1.2 1 1 1 + 600 235.1535 61.669814 0.0034851739 1.3 1 1 1 + 650 359.33618 -22.053171 0.0034851739 1.4 1 1 1 + 700 329.37555 -4.7839581 0.0034851739 1.5 1 1 1 + 750 285.76974 11.553815 0.0034851739 1.6 1 1 1 + 800 303.29561 16.017529 0.0034851739 1.7 1 1 1 + 850 256.86479 8.7487305 0.0034851739 1.8 1 1 1 + 900 292.29316 -11.376211 0.0034851739 1.9 1 1 1 + 950 293.47531 -2.7153276 0.0034851739 2 1 1 1 + 1000 303.66454 -4.8603249 0.0034851739 2.1 1 1 1 +Loop time of 0.195512 on 4 procs for 1000 steps with 44 atoms + +Performance: 441.916 ns/day, 0.054 hours/ns, 5114.771 timesteps/s, 225.050 katom-step/s +99.9% CPU use with 4 MPI tasks x no OpenMP threads + +MPI task timing breakdown: +Section | min time | avg time | max time |%varavg| %total +--------------------------------------------------------------- +Pair | 0.000163 | 0.0068784 | 0.016583 | 8.5 | 3.52 +Bond | 0.00040383 | 0.028615 | 0.083462 | 20.0 | 14.64 +Kspace | 0.043566 | 0.10199 | 0.13314 | 11.4 | 52.16 +Neigh | 0.00096634 | 0.00097064 | 0.00097509 | 0.0 | 0.50 +Comm | 0.0052532 | 0.0093802 | 0.014076 | 3.2 | 4.80 +Output | 0.00039802 | 0.00043637 | 0.00050031 | 0.0 | 0.22 +Modify | 0.043549 | 0.045538 | 0.049781 | 1.2 | 23.29 +Other | | 0.001708 | | | 0.87 + +Nlocal: 11 ave 29 max 0 min +Histogram: 2 0 0 0 0 1 0 0 0 1 +Nghost: 32.5 ave 45 max 16 min +Histogram: 1 0 0 1 0 0 0 0 1 1 +Neighs: 196.25 ave 448 max 0 min +Histogram: 2 0 0 0 0 0 0 1 0 1 + +Total # of neighbors = 785 +Ave neighs/atom = 17.840909 +Ave special neighs/atom = 9.9090909 +Neighbor list builds = 27 +Dangerous builds = 0 + +# write_restart restart_longrun +# write_data restart_longrun.data +Total wall time: 0:00:00 diff --git a/examples/PACKAGES/reaction/tiny_nylon/log.4Nov2020.tiny_nylon.unstabilized.g++.1 b/examples/PACKAGES/reaction/tiny_nylon/log.4Nov2020.tiny_nylon.unstabilized.g++.1 new file mode 100644 index 0000000000..5d696dae45 --- /dev/null +++ b/examples/PACKAGES/reaction/tiny_nylon/log.4Nov2020.tiny_nylon.unstabilized.g++.1 @@ -0,0 +1,228 @@ +LAMMPS (4 Nov 2022) +# two monomer nylon example +# reaction produces a condensed water molecule + +units real + +boundary p p p + +atom_style full + +kspace_style pppm 1.0e-4 + +pair_style lj/class2/coul/long 8.5 + +angle_style class2 + +bond_style class2 + +dihedral_style class2 + +improper_style class2 + +read_data tiny_nylon.data extra/bond/per/atom 5 extra/angle/per/atom 15 extra/dihedral/per/atom 15 extra/improper/per/atom 25 extra/special/per/atom 25 +Reading data file ... + orthogonal box = (-25 -25 -25) to (25 25 25) + 1 by 1 by 1 MPI processor grid + reading atom labelmap ... + reading bond labelmap ... + reading angle labelmap ... + reading dihedral labelmap ... + reading improper labelmap ... + reading atoms ... + 44 atoms + reading velocities ... + 44 velocities + scanning bonds ... + 9 = max bonds/atom + scanning angles ... + 21 = max angles/atom + scanning dihedrals ... + 29 = max dihedrals/atom + scanning impropers ... + 29 = max impropers/atom + reading bonds ... + 42 bonds + reading angles ... + 74 angles + reading dihedrals ... + 100 dihedrals + reading impropers ... + 44 impropers +Finding 1-2 1-3 1-4 neighbors ... + special bond factors lj: 0 0 0 + special bond factors coul: 0 0 0 + 4 = max # of 1-2 neighbors + 6 = max # of 1-3 neighbors + 12 = max # of 1-4 neighbors + 41 = max # of special neighbors + special bonds CPU = 0.000 seconds + read_data CPU = 0.008 seconds + + +velocity all create 300.0 4928459 dist gaussian + +molecule mol1 rxn1_stp1_unreacted.molecule_template +Read molecule template mol1: + 1 molecules + 0 fragments + 18 atoms with max type 8 + 16 bonds with max type 10 + 25 angles with max type 28 + 23 dihedrals with max type 36 + 2 impropers with max type 3 +molecule mol2 rxn1_stp1_reacted.molecule_template +Read molecule template mol2: + 1 molecules + 0 fragments + 18 atoms with max type 9 + 17 bonds with max type 13 + 31 angles with max type 27 + 39 dihedrals with max type 33 + 0 impropers with max type 0 +molecule mol3 rxn1_stp2_unreacted.molecule_template +Read molecule template mol3: + 1 molecules + 0 fragments + 15 atoms with max type 9 + 14 bonds with max type 13 + 25 angles with max type 27 + 30 dihedrals with max type 33 + 0 impropers with max type 0 +molecule mol4 rxn1_stp2_reacted.molecule_template +Read molecule template mol4: + 1 molecules + 0 fragments + 15 atoms with max type 11 + 13 bonds with max type 15 + 19 angles with max type 29 + 16 dihedrals with max type 32 + 2 impropers with max type 13 + +thermo 50 + +# dump 1 all xyz 1 test_vis.xyz + +fix myrxns all bond/react stabilization no react rxn1 all 1 0.0 2.9 mol1 mol2 rxn1_stp1_map react rxn2 all 1 0.0 5.0 mol3 mol4 rxn1_stp2_map +WARNING: Fix bond/react: Atom affected by reaction rxn2 is too close to template edge (../fix_bond_react.cpp:2624) +dynamic group bond_react_MASTER_group defined + +fix 1 all nve/limit .03 + +thermo_style custom step temp press density f_myrxns[1] f_myrxns[2] + +# restart 100 restart1 restart2 + +run 1000 + +CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE + +Your simulation uses code contributions which should be cited: + +- fix bond/react: reacter.org doi:10.1016/j.polymer.2017.09.038, doi:10.1021/acs.macromol.0c02012 + +@Article{Gissinger17, + author = {J. R. Gissinger and B. D. Jensen and K. E. Wise}, + title = {Modeling Chemical Reactions in Classical Molecular Dynamics Simulations}, + journal = {Polymer}, + year = 2017, + volume = 128, + pages = {211--217} +} + +@Article{Gissinger20, + author = {J. R. Gissinger, B. D. Jensen, K. E. Wise}, + title = {{REACTER}: A Heuristic Method for Reactive Molecular Dynamics}, + journal = {Macromolecules}, + year = 2020, + volume = 53, + number = 22, + pages = {9953--9961} +} + +CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE + +PPPM initialization ... + using 12-bit tables for long-range coulomb (../kspace.cpp:342) + G vector (1/distance) = 0.05345967 + grid = 2 2 2 + stencil order = 5 + estimated absolute RMS force accuracy = 0.040225597 + estimated relative force accuracy = 0.00012113819 + using double precision KISS FFT + 3d grid and FFT values/proc = 343 8 +Generated 55 of 55 mixed pair_coeff terms from sixthpower/geometric mixing rule +Neighbor list info ... + update: every = 1 steps, delay = 0 steps, check = yes + max neighbors/atom: 2000, page size: 100000 + master list distance cutoff = 10.5 + ghost atom cutoff = 10.5 + binsize = 5.25, bins = 10 10 10 + 2 neighbor lists, perpetual/occasional/extra = 1 1 0 + (1) pair lj/class2/coul/long, perpetual + attributes: half, newton on + pair build: half/bin/newton + stencil: half/bin/3d + bin: standard + (2) fix bond/react, occasional, copy from (1) + attributes: half, newton on + pair build: copy + stencil: none + bin: none +WARNING: Inconsistent image flags (../domain.cpp:819) +Per MPI rank memory allocation (min/avg/max) = 33.72 | 33.72 | 33.72 Mbytes + Step Temp Press Density f_myrxns[1] f_myrxns[2] + 0 300 346.78165 0.0034851739 0 0 + 50 530.51001 -15.418012 0.0034851739 1 0 + 100 677.21327 16.545108 0.0034851739 1 1 + 150 386.79268 -28.445486 0.0034851739 1 1 + 200 380.29074 1.8065066 0.0034851739 1 1 + 250 353.27609 -7.3505628 0.0034851739 1 1 + 300 357.84405 -7.0569 0.0034851739 1 1 + 350 337.65224 54.441683 0.0034851739 1 1 + 400 322.54035 20.338902 0.0034851739 1 1 + 450 316.91217 44.76973 0.0034851739 1 1 + 500 345.40444 -8.2133383 0.0034851739 1 1 + 550 296.22085 -30.331582 0.0034851739 1 1 + 600 263.8024 -36.834323 0.0034851739 1 1 + 650 284.05699 1.2532577 0.0034851739 1 1 + 700 274.86269 4.6881357 0.0034851739 1 1 + 750 298.72284 -18.225831 0.0034851739 1 1 + 800 292.72143 -5.1622029 0.0034851739 1 1 + 850 279.30224 -10.72513 0.0034851739 1 1 + 900 284.97331 30.268801 0.0034851739 1 1 + 950 262.46089 16.98134 0.0034851739 1 1 + 1000 297.55359 28.583097 0.0034851739 1 1 +Loop time of 0.175951 on 1 procs for 1000 steps with 44 atoms + +Performance: 491.045 ns/day, 0.049 hours/ns, 5683.388 timesteps/s, 250.069 katom-step/s +99.6% CPU use with 1 MPI tasks x no OpenMP threads + +MPI task timing breakdown: +Section | min time | avg time | max time |%varavg| %total +--------------------------------------------------------------- +Pair | 0.022992 | 0.022992 | 0.022992 | 0.0 | 13.07 +Bond | 0.1045 | 0.1045 | 0.1045 | 0.0 | 59.39 +Kspace | 0.034057 | 0.034057 | 0.034057 | 0.0 | 19.36 +Neigh | 0.0013592 | 0.0013592 | 0.0013592 | 0.0 | 0.77 +Comm | 0.00040677 | 0.00040677 | 0.00040677 | 0.0 | 0.23 +Output | 0.00030929 | 0.00030929 | 0.00030929 | 0.0 | 0.18 +Modify | 0.01121 | 0.01121 | 0.01121 | 0.0 | 6.37 +Other | | 0.001118 | | | 0.64 + +Nlocal: 44 ave 44 max 44 min +Histogram: 1 0 0 0 0 0 0 0 0 0 +Nghost: 8 ave 8 max 8 min +Histogram: 1 0 0 0 0 0 0 0 0 0 +Neighs: 810 ave 810 max 810 min +Histogram: 1 0 0 0 0 0 0 0 0 0 + +Total # of neighbors = 810 +Ave neighs/atom = 18.409091 +Ave special neighs/atom = 9.9090909 +Neighbor list builds = 28 +Dangerous builds = 0 + +# write_restart restart_longrun +# write_data restart_longrun.data +Total wall time: 0:00:00 diff --git a/examples/PACKAGES/reaction/tiny_nylon/log.4Nov2020.tiny_nylon.unstabilized.g++.4 b/examples/PACKAGES/reaction/tiny_nylon/log.4Nov2020.tiny_nylon.unstabilized.g++.4 new file mode 100644 index 0000000000..0b022918be --- /dev/null +++ b/examples/PACKAGES/reaction/tiny_nylon/log.4Nov2020.tiny_nylon.unstabilized.g++.4 @@ -0,0 +1,228 @@ +LAMMPS (4 Nov 2022) +# two monomer nylon example +# reaction produces a condensed water molecule + +units real + +boundary p p p + +atom_style full + +kspace_style pppm 1.0e-4 + +pair_style lj/class2/coul/long 8.5 + +angle_style class2 + +bond_style class2 + +dihedral_style class2 + +improper_style class2 + +read_data tiny_nylon.data extra/bond/per/atom 5 extra/angle/per/atom 15 extra/dihedral/per/atom 15 extra/improper/per/atom 25 extra/special/per/atom 25 +Reading data file ... + orthogonal box = (-25 -25 -25) to (25 25 25) + 1 by 2 by 2 MPI processor grid + reading atom labelmap ... + reading bond labelmap ... + reading angle labelmap ... + reading dihedral labelmap ... + reading improper labelmap ... + reading atoms ... + 44 atoms + reading velocities ... + 44 velocities + scanning bonds ... + 9 = max bonds/atom + scanning angles ... + 21 = max angles/atom + scanning dihedrals ... + 29 = max dihedrals/atom + scanning impropers ... + 29 = max impropers/atom + reading bonds ... + 42 bonds + reading angles ... + 74 angles + reading dihedrals ... + 100 dihedrals + reading impropers ... + 44 impropers +Finding 1-2 1-3 1-4 neighbors ... + special bond factors lj: 0 0 0 + special bond factors coul: 0 0 0 + 4 = max # of 1-2 neighbors + 6 = max # of 1-3 neighbors + 12 = max # of 1-4 neighbors + 41 = max # of special neighbors + special bonds CPU = 0.000 seconds + read_data CPU = 0.008 seconds + + +velocity all create 300.0 4928459 dist gaussian + +molecule mol1 rxn1_stp1_unreacted.molecule_template +Read molecule template mol1: + 1 molecules + 0 fragments + 18 atoms with max type 8 + 16 bonds with max type 10 + 25 angles with max type 28 + 23 dihedrals with max type 36 + 2 impropers with max type 3 +molecule mol2 rxn1_stp1_reacted.molecule_template +Read molecule template mol2: + 1 molecules + 0 fragments + 18 atoms with max type 9 + 17 bonds with max type 13 + 31 angles with max type 27 + 39 dihedrals with max type 33 + 0 impropers with max type 0 +molecule mol3 rxn1_stp2_unreacted.molecule_template +Read molecule template mol3: + 1 molecules + 0 fragments + 15 atoms with max type 9 + 14 bonds with max type 13 + 25 angles with max type 27 + 30 dihedrals with max type 33 + 0 impropers with max type 0 +molecule mol4 rxn1_stp2_reacted.molecule_template +Read molecule template mol4: + 1 molecules + 0 fragments + 15 atoms with max type 11 + 13 bonds with max type 15 + 19 angles with max type 29 + 16 dihedrals with max type 32 + 2 impropers with max type 13 + +thermo 50 + +# dump 1 all xyz 1 test_vis.xyz + +fix myrxns all bond/react stabilization no react rxn1 all 1 0.0 2.9 mol1 mol2 rxn1_stp1_map react rxn2 all 1 0.0 5.0 mol3 mol4 rxn1_stp2_map +WARNING: Fix bond/react: Atom affected by reaction rxn2 is too close to template edge (../fix_bond_react.cpp:2624) +dynamic group bond_react_MASTER_group defined + +fix 1 all nve/limit .03 + +thermo_style custom step temp press density f_myrxns[1] f_myrxns[2] + +# restart 100 restart1 restart2 + +run 1000 + +CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE + +Your simulation uses code contributions which should be cited: + +- fix bond/react: reacter.org doi:10.1016/j.polymer.2017.09.038, doi:10.1021/acs.macromol.0c02012 + +@Article{Gissinger17, + author = {J. R. Gissinger and B. D. Jensen and K. E. Wise}, + title = {Modeling Chemical Reactions in Classical Molecular Dynamics Simulations}, + journal = {Polymer}, + year = 2017, + volume = 128, + pages = {211--217} +} + +@Article{Gissinger20, + author = {J. R. Gissinger, B. D. Jensen, K. E. Wise}, + title = {{REACTER}: A Heuristic Method for Reactive Molecular Dynamics}, + journal = {Macromolecules}, + year = 2020, + volume = 53, + number = 22, + pages = {9953--9961} +} + +CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE + +PPPM initialization ... + using 12-bit tables for long-range coulomb (../kspace.cpp:342) + G vector (1/distance) = 0.05345967 + grid = 2 2 2 + stencil order = 5 + estimated absolute RMS force accuracy = 0.040225597 + estimated relative force accuracy = 0.00012113819 + using double precision KISS FFT + 3d grid and FFT values/proc = 252 2 +Generated 55 of 55 mixed pair_coeff terms from sixthpower/geometric mixing rule +Neighbor list info ... + update: every = 1 steps, delay = 0 steps, check = yes + max neighbors/atom: 2000, page size: 100000 + master list distance cutoff = 10.5 + ghost atom cutoff = 10.5 + binsize = 5.25, bins = 10 10 10 + 2 neighbor lists, perpetual/occasional/extra = 1 1 0 + (1) pair lj/class2/coul/long, perpetual + attributes: half, newton on + pair build: half/bin/newton + stencil: half/bin/3d + bin: standard + (2) fix bond/react, occasional, copy from (1) + attributes: half, newton on + pair build: copy + stencil: none + bin: none +WARNING: Inconsistent image flags (../domain.cpp:819) +Per MPI rank memory allocation (min/avg/max) = 33.59 | 33.82 | 34.37 Mbytes + Step Temp Press Density f_myrxns[1] f_myrxns[2] + 0 300 346.78165 0.0034851739 0 0 + 50 530.51001 -15.418012 0.0034851739 1 0 + 100 677.21327 16.545108 0.0034851739 1 1 + 150 386.79268 -28.445486 0.0034851739 1 1 + 200 380.29074 1.8065066 0.0034851739 1 1 + 250 353.27609 -7.3505628 0.0034851739 1 1 + 300 357.84405 -7.0569 0.0034851739 1 1 + 350 337.65224 54.441683 0.0034851739 1 1 + 400 322.54035 20.338902 0.0034851739 1 1 + 450 316.91217 44.76973 0.0034851739 1 1 + 500 345.40444 -8.2133383 0.0034851739 1 1 + 550 296.22085 -30.331582 0.0034851739 1 1 + 600 263.8024 -36.834323 0.0034851739 1 1 + 650 284.05699 1.2532577 0.0034851739 1 1 + 700 274.86269 4.6881357 0.0034851739 1 1 + 750 298.72284 -18.225831 0.0034851739 1 1 + 800 292.72143 -5.1622029 0.0034851739 1 1 + 850 279.30224 -10.72513 0.0034851739 1 1 + 900 284.97331 30.268801 0.0034851739 1 1 + 950 262.46089 16.98134 0.0034851739 1 1 + 1000 297.55359 28.583097 0.0034851739 1 1 +Loop time of 0.179911 on 4 procs for 1000 steps with 44 atoms + +Performance: 480.238 ns/day, 0.050 hours/ns, 5558.315 timesteps/s, 244.566 katom-step/s +99.9% CPU use with 4 MPI tasks x no OpenMP threads + +MPI task timing breakdown: +Section | min time | avg time | max time |%varavg| %total +--------------------------------------------------------------- +Pair | 0.0001131 | 0.0060483 | 0.016546 | 8.7 | 3.36 +Bond | 0.00024262 | 0.027106 | 0.07455 | 18.6 | 15.07 +Kspace | 0.059795 | 0.11105 | 0.13995 | 9.9 | 61.72 +Neigh | 0.0012033 | 0.0012139 | 0.0012228 | 0.0 | 0.67 +Comm | 0.0056243 | 0.0098345 | 0.013482 | 2.9 | 5.47 +Output | 0.00025378 | 0.0002833 | 0.00034961 | 0.0 | 0.16 +Modify | 0.020145 | 0.02287 | 0.027899 | 2.1 | 12.71 +Other | | 0.001506 | | | 0.84 + +Nlocal: 11 ave 41 max 0 min +Histogram: 3 0 0 0 0 0 0 0 0 1 +Nghost: 34.5 ave 46 max 8 min +Histogram: 1 0 0 0 0 0 0 0 2 1 +Neighs: 202.5 ave 807 max 0 min +Histogram: 3 0 0 0 0 0 0 0 0 1 + +Total # of neighbors = 810 +Ave neighs/atom = 18.409091 +Ave special neighs/atom = 9.9090909 +Neighbor list builds = 28 +Dangerous builds = 0 + +# write_restart restart_longrun +# write_data restart_longrun.data +Total wall time: 0:00:00 diff --git a/examples/PACKAGES/reaction/tiny_nylon/log.5Jun19.tiny_nylon.stabilized.g++.1 b/examples/PACKAGES/reaction/tiny_nylon/log.5Jun19.tiny_nylon.stabilized.g++.1 deleted file mode 100644 index de1167c652..0000000000 --- a/examples/PACKAGES/reaction/tiny_nylon/log.5Jun19.tiny_nylon.stabilized.g++.1 +++ /dev/null @@ -1,148 +0,0 @@ -LAMMPS (5 Jun 2019) -Reading data file ... - orthogonal box = (-25 -25 -25) to (25 25 25) - 1 by 1 by 1 MPI processor grid - reading atoms ... - 44 atoms - reading velocities ... - 44 velocities - scanning bonds ... - 9 = max bonds/atom - scanning angles ... - 21 = max angles/atom - scanning dihedrals ... - 29 = max dihedrals/atom - scanning impropers ... - 29 = max impropers/atom - reading bonds ... - 42 bonds - reading angles ... - 74 angles - reading dihedrals ... - 100 dihedrals - reading impropers ... - 44 impropers -Finding 1-2 1-3 1-4 neighbors ... - special bond factors lj: 0 0 0 - special bond factors coul: 0 0 0 - 4 = max # of 1-2 neighbors - 6 = max # of 1-3 neighbors - 12 = max # of 1-4 neighbors - 41 = max # of special neighbors - special bonds CPU = 0.000181113 secs - read_data CPU = 0.0251833 secs -Read molecule mol1: - 18 atoms with max type 8 - 16 bonds with max type 14 - 25 angles with max type 28 - 23 dihedrals with max type 36 - 14 impropers with max type 11 -Read molecule mol2: - 18 atoms with max type 9 - 17 bonds with max type 13 - 31 angles with max type 27 - 39 dihedrals with max type 33 - 20 impropers with max type 1 -Read molecule mol3: - 15 atoms with max type 9 - 14 bonds with max type 13 - 25 angles with max type 27 - 30 dihedrals with max type 33 - 16 impropers with max type 1 -Read molecule mol4: - 15 atoms with max type 11 - 13 bonds with max type 15 - 19 angles with max type 29 - 16 dihedrals with max type 32 - 10 impropers with max type 13 -WARNING: Bond/react: Atom affected by reaction rxn1 too close to template edge (../fix_bond_react.cpp:1785) -WARNING: Bond/react: Atom affected by reaction rxn2 too close to template edge (../fix_bond_react.cpp:1785) -dynamic group bond_react_MASTER_group defined -dynamic group statted_grp_REACT defined -PPPM initialization ... - using 12-bit tables for long-range coulomb (../kspace.cpp:319) - G vector (1/distance) = 0.0534597 - grid = 2 2 2 - stencil order = 5 - estimated absolute RMS force accuracy = 0.0402256 - estimated relative force accuracy = 0.000121138 - using double precision FFTs - 3d grid and FFT values/proc = 343 8 -Neighbor list info ... - update every 1 steps, delay 10 steps, check yes - max neighbors/atom: 2000, page size: 100000 - master list distance cutoff = 10.5 - ghost atom cutoff = 10.5 - binsize = 5.25, bins = 10 10 10 - 2 neighbor lists, perpetual/occasional/extra = 1 1 0 - (1) pair lj/class2/coul/long, perpetual - attributes: half, newton on - pair build: half/bin/newton - stencil: half/bin/3d/newton - bin: standard - (2) fix bond/react, occasional, copy from (1) - attributes: half, newton on - pair build: copy - stencil: none - bin: none -Setting up Verlet run ... - Unit style : real - Current step : 0 - Time step : 1 -WARNING: Inconsistent image flags (../domain.cpp:784) -Per MPI rank memory allocation (min/avg/max) = 34.41 | 34.41 | 34.41 Mbytes -Step Temp Press Density f_myrxns[1] f_myrxns[2] - 0 300 346.78165 0.0034851739 0 0 - 50 293.70542 -52.547388 0.0034851739 1 0 - 100 276.36755 54.81826 0.0034851739 1 1 - 150 448.65869 16.874435 0.0034851739 1 1 - 200 379.84257 11.578545 0.0034851739 1 1 - 250 298.21983 90.656585 0.0034851739 1 1 - 300 333.3111 -30.139607 0.0034851739 1 1 - 350 266.57108 6.4505134 0.0034851739 1 1 - 400 264.05476 10.513204 0.0034851739 1 1 - 450 250.70418 -18.635379 0.0034851739 1 1 - 500 261.21632 10.231013 0.0034851739 1 1 - 550 309.89024 -8.8299506 0.0034851739 1 1 - 600 373.45851 30.368993 0.0034851739 1 1 - 650 338.26242 9.0362267 0.0034851739 1 1 - 700 295.67794 -5.6007538 0.0034851739 1 1 - 750 310.86563 -59.228181 0.0034851739 1 1 - 800 286.22678 -9.9022407 0.0034851739 1 1 - 850 218.42135 27.845352 0.0034851739 1 1 - 900 259.62551 24.216336 0.0034851739 1 1 - 950 250.21307 -14.560985 0.0034851739 1 1 - 1000 274.29245 -0.38768626 0.0034851739 1 1 -Loop time of 0.341061 on 1 procs for 1000 steps with 44 atoms - -Performance: 253.327 ns/day, 0.095 hours/ns, 2932.025 timesteps/s -87.9% CPU use with 1 MPI tasks x no OpenMP threads - -MPI task timing breakdown: -Section | min time | avg time | max time |%varavg| %total ---------------------------------------------------------------- -Pair | 0.031135 | 0.031135 | 0.031135 | 0.0 | 9.13 -Bond | 0.12623 | 0.12623 | 0.12623 | 0.0 | 37.01 -Kspace | 0.036491 | 0.036491 | 0.036491 | 0.0 | 10.70 -Neigh | 0.046395 | 0.046395 | 0.046395 | 0.0 | 13.60 -Comm | 0.0025396 | 0.0025396 | 0.0025396 | 0.0 | 0.74 -Output | 0.07775 | 0.07775 | 0.07775 | 0.0 | 22.80 -Modify | 0.019219 | 0.019219 | 0.019219 | 0.0 | 5.64 -Other | | 0.001306 | | | 0.38 - -Nlocal: 44 ave 44 max 44 min -Histogram: 1 0 0 0 0 0 0 0 0 0 -Nghost: 2 ave 2 max 2 min -Histogram: 1 0 0 0 0 0 0 0 0 0 -Neighs: 740 ave 740 max 740 min -Histogram: 1 0 0 0 0 0 0 0 0 0 - -Total # of neighbors = 740 -Ave neighs/atom = 16.8182 -Ave special neighs/atom = 9.77273 -Neighbor list builds = 1000 -Dangerous builds = 0 - -Please see the log.cite file for references relevant to this simulation - -Total wall time: 0:00:00 diff --git a/examples/PACKAGES/reaction/tiny_nylon/log.5Jun19.tiny_nylon.stabilized.g++.4 b/examples/PACKAGES/reaction/tiny_nylon/log.5Jun19.tiny_nylon.stabilized.g++.4 deleted file mode 100644 index b9c7a3ba15..0000000000 --- a/examples/PACKAGES/reaction/tiny_nylon/log.5Jun19.tiny_nylon.stabilized.g++.4 +++ /dev/null @@ -1,148 +0,0 @@ -LAMMPS (5 Jun 2019) -Reading data file ... - orthogonal box = (-25 -25 -25) to (25 25 25) - 1 by 2 by 2 MPI processor grid - reading atoms ... - 44 atoms - reading velocities ... - 44 velocities - scanning bonds ... - 9 = max bonds/atom - scanning angles ... - 21 = max angles/atom - scanning dihedrals ... - 29 = max dihedrals/atom - scanning impropers ... - 29 = max impropers/atom - reading bonds ... - 42 bonds - reading angles ... - 74 angles - reading dihedrals ... - 100 dihedrals - reading impropers ... - 44 impropers -Finding 1-2 1-3 1-4 neighbors ... - special bond factors lj: 0 0 0 - special bond factors coul: 0 0 0 - 4 = max # of 1-2 neighbors - 6 = max # of 1-3 neighbors - 12 = max # of 1-4 neighbors - 41 = max # of special neighbors - special bonds CPU = 0.000178751 secs - read_data CPU = 0.0385782 secs -Read molecule mol1: - 18 atoms with max type 8 - 16 bonds with max type 14 - 25 angles with max type 28 - 23 dihedrals with max type 36 - 14 impropers with max type 11 -Read molecule mol2: - 18 atoms with max type 9 - 17 bonds with max type 13 - 31 angles with max type 27 - 39 dihedrals with max type 33 - 20 impropers with max type 1 -Read molecule mol3: - 15 atoms with max type 9 - 14 bonds with max type 13 - 25 angles with max type 27 - 30 dihedrals with max type 33 - 16 impropers with max type 1 -Read molecule mol4: - 15 atoms with max type 11 - 13 bonds with max type 15 - 19 angles with max type 29 - 16 dihedrals with max type 32 - 10 impropers with max type 13 -WARNING: Bond/react: Atom affected by reaction rxn1 too close to template edge (../fix_bond_react.cpp:1785) -WARNING: Bond/react: Atom affected by reaction rxn2 too close to template edge (../fix_bond_react.cpp:1785) -dynamic group bond_react_MASTER_group defined -dynamic group statted_grp_REACT defined -PPPM initialization ... - using 12-bit tables for long-range coulomb (../kspace.cpp:319) - G vector (1/distance) = 0.0534597 - grid = 2 2 2 - stencil order = 5 - estimated absolute RMS force accuracy = 0.0402256 - estimated relative force accuracy = 0.000121138 - using double precision FFTs - 3d grid and FFT values/proc = 252 2 -Neighbor list info ... - update every 1 steps, delay 10 steps, check yes - max neighbors/atom: 2000, page size: 100000 - master list distance cutoff = 10.5 - ghost atom cutoff = 10.5 - binsize = 5.25, bins = 10 10 10 - 2 neighbor lists, perpetual/occasional/extra = 1 1 0 - (1) pair lj/class2/coul/long, perpetual - attributes: half, newton on - pair build: half/bin/newton - stencil: half/bin/3d/newton - bin: standard - (2) fix bond/react, occasional, copy from (1) - attributes: half, newton on - pair build: copy - stencil: none - bin: none -Setting up Verlet run ... - Unit style : real - Current step : 0 - Time step : 1 -WARNING: Inconsistent image flags (../domain.cpp:784) -Per MPI rank memory allocation (min/avg/max) = 34.42 | 34.77 | 35.45 Mbytes -Step Temp Press Density f_myrxns[1] f_myrxns[2] - 0 300 346.78165 0.0034851739 0 0 - 50 293.70542 -52.547388 0.0034851739 1 0 - 100 276.36755 54.81826 0.0034851739 1 1 - 150 448.65869 16.874435 0.0034851739 1 1 - 200 379.84257 11.578545 0.0034851739 1 1 - 250 298.21983 90.656585 0.0034851739 1 1 - 300 333.3111 -30.139607 0.0034851739 1 1 - 350 266.57108 6.4505134 0.0034851739 1 1 - 400 264.05476 10.513204 0.0034851739 1 1 - 450 250.70418 -18.635379 0.0034851739 1 1 - 500 261.21632 10.231013 0.0034851739 1 1 - 550 309.89024 -8.8299506 0.0034851739 1 1 - 600 373.45851 30.368993 0.0034851739 1 1 - 650 338.26242 9.0362267 0.0034851739 1 1 - 700 295.67794 -5.6007538 0.0034851739 1 1 - 750 310.86563 -59.228181 0.0034851739 1 1 - 800 286.22678 -9.9022407 0.0034851739 1 1 - 850 218.42135 27.845352 0.0034851739 1 1 - 900 259.62551 24.216336 0.0034851739 1 1 - 950 250.21307 -14.560985 0.0034851739 1 1 - 1000 274.29245 -0.38768626 0.0034851739 1 1 -Loop time of 0.271242 on 4 procs for 1000 steps with 44 atoms - -Performance: 318.535 ns/day, 0.075 hours/ns, 3686.747 timesteps/s -98.6% CPU use with 4 MPI tasks x no OpenMP threads - -MPI task timing breakdown: -Section | min time | avg time | max time |%varavg| %total ---------------------------------------------------------------- -Pair | 0.00023773 | 0.0077322 | 0.016042 | 8.4 | 2.85 -Bond | 0.00073385 | 0.032108 | 0.08446 | 19.4 | 11.84 -Kspace | 0.041659 | 0.098095 | 0.13373 | 12.3 | 36.16 -Neigh | 0.028894 | 0.029247 | 0.029558 | 0.1 | 10.78 -Comm | 0.012367 | 0.013642 | 0.01503 | 0.9 | 5.03 -Output | 0.032475 | 0.040504 | 0.061019 | 5.9 | 14.93 -Modify | 0.032934 | 0.049086 | 0.0577 | 4.3 | 18.10 -Other | | 0.0008281 | | | 0.31 - -Nlocal: 11 ave 21 max 0 min -Histogram: 1 1 0 0 0 0 0 0 0 2 -Nghost: 32.5 ave 43 max 23 min -Histogram: 2 0 0 0 0 0 0 0 0 2 -Neighs: 185 ave 376 max 0 min -Histogram: 2 0 0 0 0 0 0 0 0 2 - -Total # of neighbors = 740 -Ave neighs/atom = 16.8182 -Ave special neighs/atom = 9.77273 -Neighbor list builds = 1000 -Dangerous builds = 0 - -Please see the log.cite file for references relevant to this simulation - -Total wall time: 0:00:00 diff --git a/examples/PACKAGES/reaction/tiny_nylon/log.5Jun19.tiny_nylon.unstabilized.g++.1 b/examples/PACKAGES/reaction/tiny_nylon/log.5Jun19.tiny_nylon.unstabilized.g++.1 deleted file mode 100644 index 14cac1dfad..0000000000 --- a/examples/PACKAGES/reaction/tiny_nylon/log.5Jun19.tiny_nylon.unstabilized.g++.1 +++ /dev/null @@ -1,147 +0,0 @@ -LAMMPS (5 Jun 2019) -Reading data file ... - orthogonal box = (-25 -25 -25) to (25 25 25) - 1 by 1 by 1 MPI processor grid - reading atoms ... - 44 atoms - reading velocities ... - 44 velocities - scanning bonds ... - 9 = max bonds/atom - scanning angles ... - 21 = max angles/atom - scanning dihedrals ... - 29 = max dihedrals/atom - scanning impropers ... - 29 = max impropers/atom - reading bonds ... - 42 bonds - reading angles ... - 74 angles - reading dihedrals ... - 100 dihedrals - reading impropers ... - 44 impropers -Finding 1-2 1-3 1-4 neighbors ... - special bond factors lj: 0 0 0 - special bond factors coul: 0 0 0 - 4 = max # of 1-2 neighbors - 6 = max # of 1-3 neighbors - 12 = max # of 1-4 neighbors - 41 = max # of special neighbors - special bonds CPU = 0.000217102 secs - read_data CPU = 0.00630778 secs -Read molecule mol1: - 18 atoms with max type 8 - 16 bonds with max type 14 - 25 angles with max type 28 - 23 dihedrals with max type 36 - 14 impropers with max type 11 -Read molecule mol2: - 18 atoms with max type 9 - 17 bonds with max type 13 - 31 angles with max type 27 - 39 dihedrals with max type 33 - 20 impropers with max type 1 -Read molecule mol3: - 15 atoms with max type 9 - 14 bonds with max type 13 - 25 angles with max type 27 - 30 dihedrals with max type 33 - 16 impropers with max type 1 -Read molecule mol4: - 15 atoms with max type 11 - 13 bonds with max type 15 - 19 angles with max type 29 - 16 dihedrals with max type 32 - 10 impropers with max type 13 -WARNING: Bond/react: Atom affected by reaction rxn1 too close to template edge (../fix_bond_react.cpp:1785) -WARNING: Bond/react: Atom affected by reaction rxn2 too close to template edge (../fix_bond_react.cpp:1785) -dynamic group bond_react_MASTER_group defined -PPPM initialization ... - using 12-bit tables for long-range coulomb (../kspace.cpp:319) - G vector (1/distance) = 0.0534597 - grid = 2 2 2 - stencil order = 5 - estimated absolute RMS force accuracy = 0.0402256 - estimated relative force accuracy = 0.000121138 - using double precision FFTs - 3d grid and FFT values/proc = 343 8 -Neighbor list info ... - update every 1 steps, delay 10 steps, check yes - max neighbors/atom: 2000, page size: 100000 - master list distance cutoff = 10.5 - ghost atom cutoff = 10.5 - binsize = 5.25, bins = 10 10 10 - 2 neighbor lists, perpetual/occasional/extra = 1 1 0 - (1) pair lj/class2/coul/long, perpetual - attributes: half, newton on - pair build: half/bin/newton - stencil: half/bin/3d/newton - bin: standard - (2) fix bond/react, occasional, copy from (1) - attributes: half, newton on - pair build: copy - stencil: none - bin: none -Setting up Verlet run ... - Unit style : real - Current step : 0 - Time step : 1 -WARNING: Inconsistent image flags (../domain.cpp:784) -Per MPI rank memory allocation (min/avg/max) = 34.35 | 34.35 | 34.35 Mbytes -Step Temp Press Density f_myrxns[1] f_myrxns[2] - 0 300 346.78165 0.0034851739 0 0 - 50 416.49412 -20.293038 0.0034851739 1 0 - 100 746.49323 91.912227 0.0034851739 1 1 - 150 515.15907 -1.4024709 0.0034851739 1 1 - 200 441.14572 -19.333087 0.0034851739 1 1 - 250 376.40996 30.717679 0.0034851739 1 1 - 300 326.15127 -3.0433799 0.0034851739 1 1 - 350 326.21116 6.235391 0.0034851739 1 1 - 400 366.48556 3.9807338 0.0034851739 1 1 - 450 313.79097 7.6674629 0.0034851739 1 1 - 500 278.89836 14.102052 0.0034851739 1 1 - 550 267.50214 18.241417 0.0034851739 1 1 - 600 276.28064 7.4649611 0.0034851739 1 1 - 650 255.26713 -8.5258573 0.0034851739 1 1 - 700 258.59752 -5.3341215 0.0034851739 1 1 - 750 263.71264 33.369869 0.0034851739 1 1 - 800 246.22976 -15.349137 0.0034851739 1 1 - 850 255.93887 16.331669 0.0034851739 1 1 - 900 239.72525 -0.20075789 0.0034851739 1 1 - 950 213.73064 12.17619 0.0034851739 1 1 - 1000 218.25094 -9.0955642 0.0034851739 1 1 -Loop time of 0.348252 on 1 procs for 1000 steps with 44 atoms - -Performance: 248.096 ns/day, 0.097 hours/ns, 2871.483 timesteps/s -91.8% CPU use with 1 MPI tasks x no OpenMP threads - -MPI task timing breakdown: -Section | min time | avg time | max time |%varavg| %total ---------------------------------------------------------------- -Pair | 0.031941 | 0.031941 | 0.031941 | 0.0 | 9.17 -Bond | 0.13031 | 0.13031 | 0.13031 | 0.0 | 37.42 -Kspace | 0.037554 | 0.037554 | 0.037554 | 0.0 | 10.78 -Neigh | 0.047397 | 0.047397 | 0.047397 | 0.0 | 13.61 -Comm | 0.0025814 | 0.0025814 | 0.0025814 | 0.0 | 0.74 -Output | 0.083526 | 0.083526 | 0.083526 | 0.0 | 23.98 -Modify | 0.013602 | 0.013602 | 0.013602 | 0.0 | 3.91 -Other | | 0.001336 | | | 0.38 - -Nlocal: 44 ave 44 max 44 min -Histogram: 1 0 0 0 0 0 0 0 0 0 -Nghost: 3 ave 3 max 3 min -Histogram: 1 0 0 0 0 0 0 0 0 0 -Neighs: 818 ave 818 max 818 min -Histogram: 1 0 0 0 0 0 0 0 0 0 - -Total # of neighbors = 818 -Ave neighs/atom = 18.5909 -Ave special neighs/atom = 9.77273 -Neighbor list builds = 1000 -Dangerous builds = 0 - -Please see the log.cite file for references relevant to this simulation - -Total wall time: 0:00:00 diff --git a/examples/PACKAGES/reaction/tiny_nylon/log.5Jun19.tiny_nylon.unstabilized.g++.4 b/examples/PACKAGES/reaction/tiny_nylon/log.5Jun19.tiny_nylon.unstabilized.g++.4 deleted file mode 100644 index 6b13dd60d3..0000000000 --- a/examples/PACKAGES/reaction/tiny_nylon/log.5Jun19.tiny_nylon.unstabilized.g++.4 +++ /dev/null @@ -1,147 +0,0 @@ -LAMMPS (5 Jun 2019) -Reading data file ... - orthogonal box = (-25 -25 -25) to (25 25 25) - 1 by 2 by 2 MPI processor grid - reading atoms ... - 44 atoms - reading velocities ... - 44 velocities - scanning bonds ... - 9 = max bonds/atom - scanning angles ... - 21 = max angles/atom - scanning dihedrals ... - 29 = max dihedrals/atom - scanning impropers ... - 29 = max impropers/atom - reading bonds ... - 42 bonds - reading angles ... - 74 angles - reading dihedrals ... - 100 dihedrals - reading impropers ... - 44 impropers -Finding 1-2 1-3 1-4 neighbors ... - special bond factors lj: 0 0 0 - special bond factors coul: 0 0 0 - 4 = max # of 1-2 neighbors - 6 = max # of 1-3 neighbors - 12 = max # of 1-4 neighbors - 41 = max # of special neighbors - special bonds CPU = 0.000163256 secs - read_data CPU = 0.0244579 secs -Read molecule mol1: - 18 atoms with max type 8 - 16 bonds with max type 14 - 25 angles with max type 28 - 23 dihedrals with max type 36 - 14 impropers with max type 11 -Read molecule mol2: - 18 atoms with max type 9 - 17 bonds with max type 13 - 31 angles with max type 27 - 39 dihedrals with max type 33 - 20 impropers with max type 1 -Read molecule mol3: - 15 atoms with max type 9 - 14 bonds with max type 13 - 25 angles with max type 27 - 30 dihedrals with max type 33 - 16 impropers with max type 1 -Read molecule mol4: - 15 atoms with max type 11 - 13 bonds with max type 15 - 19 angles with max type 29 - 16 dihedrals with max type 32 - 10 impropers with max type 13 -WARNING: Bond/react: Atom affected by reaction rxn1 too close to template edge (../fix_bond_react.cpp:1785) -WARNING: Bond/react: Atom affected by reaction rxn2 too close to template edge (../fix_bond_react.cpp:1785) -dynamic group bond_react_MASTER_group defined -PPPM initialization ... - using 12-bit tables for long-range coulomb (../kspace.cpp:319) - G vector (1/distance) = 0.0534597 - grid = 2 2 2 - stencil order = 5 - estimated absolute RMS force accuracy = 0.0402256 - estimated relative force accuracy = 0.000121138 - using double precision FFTs - 3d grid and FFT values/proc = 252 2 -Neighbor list info ... - update every 1 steps, delay 10 steps, check yes - max neighbors/atom: 2000, page size: 100000 - master list distance cutoff = 10.5 - ghost atom cutoff = 10.5 - binsize = 5.25, bins = 10 10 10 - 2 neighbor lists, perpetual/occasional/extra = 1 1 0 - (1) pair lj/class2/coul/long, perpetual - attributes: half, newton on - pair build: half/bin/newton - stencil: half/bin/3d/newton - bin: standard - (2) fix bond/react, occasional, copy from (1) - attributes: half, newton on - pair build: copy - stencil: none - bin: none -Setting up Verlet run ... - Unit style : real - Current step : 0 - Time step : 1 -WARNING: Inconsistent image flags (../domain.cpp:784) -Per MPI rank memory allocation (min/avg/max) = 33.34 | 33.69 | 34.37 Mbytes -Step Temp Press Density f_myrxns[1] f_myrxns[2] - 0 300 346.78165 0.0034851739 0 0 - 50 416.49412 -20.293038 0.0034851739 1 0 - 100 746.49323 91.912227 0.0034851739 1 1 - 150 515.15907 -1.4024709 0.0034851739 1 1 - 200 441.14572 -19.333087 0.0034851739 1 1 - 250 376.40996 30.717679 0.0034851739 1 1 - 300 326.15127 -3.0433799 0.0034851739 1 1 - 350 326.21116 6.235391 0.0034851739 1 1 - 400 366.48556 3.9807338 0.0034851739 1 1 - 450 313.79097 7.6674629 0.0034851739 1 1 - 500 278.89836 14.102052 0.0034851739 1 1 - 550 267.50214 18.241417 0.0034851739 1 1 - 600 276.28064 7.4649611 0.0034851739 1 1 - 650 255.26713 -8.5258573 0.0034851739 1 1 - 700 258.59752 -5.3341215 0.0034851739 1 1 - 750 263.71264 33.369869 0.0034851739 1 1 - 800 246.22976 -15.349137 0.0034851739 1 1 - 850 255.93887 16.331669 0.0034851739 1 1 - 900 239.72525 -0.20075789 0.0034851739 1 1 - 950 213.73064 12.17619 0.0034851739 1 1 - 1000 218.25094 -9.0955642 0.0034851739 1 1 -Loop time of 0.254903 on 4 procs for 1000 steps with 44 atoms - -Performance: 338.952 ns/day, 0.071 hours/ns, 3923.053 timesteps/s -99.8% CPU use with 4 MPI tasks x no OpenMP threads - -MPI task timing breakdown: -Section | min time | avg time | max time |%varavg| %total ---------------------------------------------------------------- -Pair | 0.00014252 | 0.0090715 | 0.021332 | 9.6 | 3.56 -Bond | 0.00047028 | 0.037261 | 0.10789 | 22.7 | 14.62 -Kspace | 0.051006 | 0.12756 | 0.1693 | 13.6 | 50.04 -Neigh | 0.035644 | 0.036088 | 0.036523 | 0.2 | 14.16 -Comm | 0.013984 | 0.016074 | 0.018676 | 1.6 | 6.31 -Output | 0.0002816 | 0.00033726 | 0.00044251 | 0.0 | 0.13 -Modify | 0.023697 | 0.027803 | 0.033552 | 2.5 | 10.91 -Other | | 0.0007123 | | | 0.28 - -Nlocal: 11 ave 29 max 0 min -Histogram: 1 1 0 0 1 0 0 0 0 1 -Nghost: 25 ave 31 max 12 min -Histogram: 1 0 0 0 0 0 0 0 2 1 -Neighs: 204.5 ave 443 max 0 min -Histogram: 2 0 0 0 0 0 0 0 1 1 - -Total # of neighbors = 818 -Ave neighs/atom = 18.5909 -Ave special neighs/atom = 9.77273 -Neighbor list builds = 1000 -Dangerous builds = 0 - -Please see the log.cite file for references relevant to this simulation - -Total wall time: 0:00:00 diff --git a/examples/PACKAGES/reaction/tiny_nylon/rxn1_stp1_reacted.data_template b/examples/PACKAGES/reaction/tiny_nylon/rxn1_stp1_reacted.data_template deleted file mode 100644 index d7256f43d2..0000000000 --- a/examples/PACKAGES/reaction/tiny_nylon/rxn1_stp1_reacted.data_template +++ /dev/null @@ -1,189 +0,0 @@ -this is a molecule template for: initial nylon crosslink, post-reacting - -18 atoms -17 bonds -31 angles -39 dihedrals -20 impropers - -Types - -1 9 -2 1 -3 1 -4 8 -5 8 -6 4 -7 4 -8 1 -9 1 -10 2 -11 6 -12 3 -13 4 -14 4 -15 5 -16 1 -17 4 -18 4 - -Charges - -1 -0.300000 -2 0.000000 -3 0.000000 -4 0.000000 -5 0.000000 -6 0.000000 -7 0.000000 -8 0.000000 -9 0.000000 -10 0.300000 -11 0.000000 -12 0.000000 -13 0.000000 -14 0.000000 -15 0.000000 -16 0.000000 -17 0.000000 -18 0.000000 - -Coords - -1 -5.522237 -0.752722 1.631158 -2 -5.170398 -0.545733 0.178130 -3 -6.469695 -0.553072 -0.648889 -4 -6.052076 -1.721152 1.744648 -5 -6.183059 0.071387 1.971497 -6 -4.489340 -1.389197 -0.173156 -7 -4.637591 0.453703 0.051252 -8 -5.618658 0.138919 4.386107 -9 -4.669492 -0.989819 3.943591 -10 -4.270194 -0.766405 2.474102 -11 -3.348470 -1.875393 2.024289 -12 -3.569794 0.564183 2.345995 -13 -5.201079 -1.993301 4.044219 -14 -3.736682 -0.984819 4.598305 -15 -4.255402 1.370923 2.679069 -16 -6.136394 -0.339866 -2.136775 -17 -6.996331 -1.555519 -0.517408 -18 -7.153308 0.284949 -0.289930 - -Bonds - -1 11 1 2 -2 12 1 4 -3 12 1 5 -4 13 1 10 -5 2 2 3 -6 1 2 6 -7 1 2 7 -8 2 3 16 -9 1 3 17 -10 1 3 18 -11 2 8 9 -12 4 9 10 -13 1 9 13 -14 1 9 14 -15 5 10 11 -16 3 10 12 -17 6 12 15 - -Angles - -1 17 2 1 4 -2 17 2 1 5 -3 18 2 1 10 -4 19 4 1 5 -5 20 4 1 10 -6 20 5 1 10 -7 21 1 2 3 -8 22 1 2 6 -9 22 1 2 7 -10 2 3 2 6 -11 2 3 2 7 -12 1 6 2 7 -13 3 2 3 16 -14 2 2 3 17 -15 2 2 3 18 -16 2 16 3 17 -17 2 16 3 18 -18 1 17 3 18 -19 8 8 9 10 -20 2 8 9 13 -21 2 8 9 14 -22 23 13 9 10 -23 23 14 9 10 -24 1 13 9 14 -25 6 9 10 11 -26 4 9 10 12 -27 24 1 10 9 -28 25 11 10 12 -29 26 1 10 11 -30 27 1 10 12 -31 7 10 12 15 - -Dihedrals - -1 19 4 1 2 3 -2 20 4 1 2 6 -3 20 4 1 2 7 -4 19 5 1 2 3 -5 20 5 1 2 6 -6 20 5 1 2 7 -7 21 10 1 2 3 -8 22 10 1 2 6 -9 22 10 1 2 7 -10 23 2 1 10 9 -11 24 2 1 10 11 -12 25 2 1 10 12 -13 26 4 1 10 9 -14 27 4 1 10 11 -15 28 4 1 10 12 -16 26 5 1 10 9 -17 27 5 1 10 11 -18 28 5 1 10 12 -19 29 1 2 3 16 -20 30 1 2 3 17 -21 30 1 2 3 18 -22 4 16 3 2 6 -23 2 6 2 3 17 -24 2 6 2 3 18 -25 4 16 3 2 7 -26 2 7 2 3 17 -27 2 7 2 3 18 -28 10 8 9 10 11 -29 8 8 9 10 12 -30 31 8 9 10 1 -31 11 13 9 10 11 -32 9 13 9 10 12 -33 32 13 9 10 1 -34 11 14 9 10 11 -35 9 14 9 10 12 -36 32 14 9 10 1 -37 6 9 10 12 15 -38 7 11 10 12 15 -39 33 1 10 12 15 - -Impropers - -1 1 2 1 4 5 -2 1 2 1 4 10 -3 1 2 1 5 10 -4 1 4 1 5 10 -5 1 1 2 3 6 -6 1 1 2 3 7 -7 1 1 2 6 7 -8 1 3 2 6 7 -9 1 2 3 16 17 -10 1 2 3 16 18 -11 1 2 3 17 18 -12 1 16 3 17 18 -13 1 8 9 13 10 -14 1 8 9 14 10 -15 1 8 9 13 14 -16 1 13 9 14 10 -17 1 9 10 11 12 -18 1 1 10 9 11 -19 1 1 10 9 12 -20 1 1 10 11 12 diff --git a/examples/PACKAGES/reaction/tiny_nylon/rxn1_stp1_reacted.molecule_template b/examples/PACKAGES/reaction/tiny_nylon/rxn1_stp1_reacted.molecule_template new file mode 100644 index 0000000000..40f3aa8276 --- /dev/null +++ b/examples/PACKAGES/reaction/tiny_nylon/rxn1_stp1_reacted.molecule_template @@ -0,0 +1,187 @@ +this is a molecule template for: initial nylon crosslink, post-reacting + + 18 atoms + 17 bonds + 31 angles + 39 dihedrals + 0 impropers + +Coords + + 1 -5.522237178 -0.752722499 1.631158408 + 2 -5.170398325 -0.545733378 0.178129978 + 3 -6.469694974 -0.553071841 -0.648889109 + 4 -6.052075697 -1.721152483 1.744647858 + 5 -6.183058842 0.071386755 1.971497329 + 6 -4.489339595 -1.389196844 -0.173156276 + 7 -4.637590712 0.453703382 0.051251954 + 8 -5.618657658 0.138918810 4.386106928 + 9 -4.669491736 -0.989818781 3.943591338 + 10 -4.270193542 -0.766405234 2.474102239 + 11 -3.348470373 -1.875393291 2.024289246 + 12 -3.569793683 0.564183226 2.345995471 + 13 -5.201078949 -1.993301389 4.044218837 + 14 -3.736681607 -0.984819193 4.598304847 + 15 -4.255401979 1.370923174 2.679069013 + 16 -6.136393628 -0.339866195 -2.136774990 + 17 -6.996331494 -1.555519161 -0.517408063 + 18 -7.153308038 0.284949373 -0.289930394 + +Types + + 1 n + 2 c2 + 3 c2 + 4 hn + 5 hn + 6 hc + 7 hc + 8 c2 + 9 c2 + 10 c_1 + 11 o_1 + 12 o + 13 hc + 14 hc + 15 ho + 16 c2 + 17 hc + 18 hc + +Charges + + 1 -0.300000 + 2 0.000000 + 3 0.000000 + 4 0.000000 + 5 0.000000 + 6 0.000000 + 7 0.000000 + 8 0.000000 + 9 0.000000 + 10 0.300000 + 11 0.000000 + 12 0.000000 + 13 0.000000 + 14 0.000000 + 15 0.000000 + 16 0.000000 + 17 0.000000 + 18 0.000000 + +Molecules + + 1 1 + 2 1 + 3 1 + 4 1 + 5 1 + 6 1 + 7 1 + 8 1 + 9 1 + 10 1 + 11 1 + 12 1 + 13 1 + 14 1 + 15 1 + 16 1 + 17 1 + 18 1 + +Bonds + + 1 n-c2 1 2 + 2 n-hn 1 4 + 3 n-hn 1 5 + 4 n-c_1 1 10 + 5 c2-c2 2 3 + 6 c2-hc 2 6 + 7 c2-hc 2 7 + 8 c2-c2 3 16 + 9 c2-hc 3 17 + 10 c2-hc 3 18 + 11 c2-c2 8 9 + 12 c2-c_1 9 10 + 13 c2-hc 9 13 + 14 c2-hc 9 14 + 15 c_1-o_1 10 11 + 16 c_1-o 10 12 + 17 o-ho 12 15 + +Angles + + 1 c2-n-hn 2 1 4 + 2 c2-n-hn 2 1 5 + 3 c2-n-c_1 2 1 10 + 4 hn-n-hn 4 1 5 + 5 hn-n-c_1 4 1 10 + 6 hn-n-c_1 5 1 10 + 7 n-c2-c2 1 2 3 + 8 n-c2-hc 1 2 6 + 9 n-c2-hc 1 2 7 + 10 c2-c2-hc 3 2 6 + 11 c2-c2-hc 3 2 7 + 12 hc-c2-hc 6 2 7 + 13 c2-c2-c2 2 3 16 + 14 c2-c2-hc 2 3 17 + 15 c2-c2-hc 2 3 18 + 16 c2-c2-hc 16 3 17 + 17 c2-c2-hc 16 3 18 + 18 hc-c2-hc 17 3 18 + 19 c2-c2-c_1 8 9 10 + 20 c2-c2-hc 8 9 13 + 21 c2-c2-hc 8 9 14 + 22 hc-c2-c_1 13 9 10 + 23 hc-c2-c_1 14 9 10 + 24 hc-c2-hc 13 9 14 + 25 c2-c_1-o_1 9 10 11 + 26 c2-c_1-o 9 10 12 + 27 n-c_1-c2 1 10 9 + 28 o_1-c_1-o 11 10 12 + 29 n-c_1-o_1 1 10 11 + 30 n-c_1-o 1 10 12 + 31 c_1-o-ho 10 12 15 + +Dihedrals + + 1 hn-n-c2-c2 4 1 2 3 + 2 hn-n-c2-hc 4 1 2 6 + 3 hn-n-c2-hc 4 1 2 7 + 4 hn-n-c2-c2 5 1 2 3 + 5 hn-n-c2-hc 5 1 2 6 + 6 hn-n-c2-hc 5 1 2 7 + 7 c_1-n-c2-c2 10 1 2 3 + 8 c_1-n-c2-hc 10 1 2 6 + 9 c_1-n-c2-hc 10 1 2 7 + 10 c2-n-c_1-c2 2 1 10 9 + 11 c2-n-c_1-o_1 2 1 10 11 + 12 c2-n-c_1-o 2 1 10 12 + 13 hn-n-c_1-c2 4 1 10 9 + 14 hn-n-c_1-o_1 4 1 10 11 + 15 hn-n-c_1-o 4 1 10 12 + 16 hn-n-c_1-c2 5 1 10 9 + 17 hn-n-c_1-o_1 5 1 10 11 + 18 hn-n-c_1-o 5 1 10 12 + 19 n-c2-c2-c2 1 2 3 16 + 20 n-c2-c2-hc 1 2 3 17 + 21 n-c2-c2-hc 1 2 3 18 + 22 c2-c2-c2-hc 16 3 2 6 + 23 hc-c2-c2-hc 6 2 3 17 + 24 hc-c2-c2-hc 6 2 3 18 + 25 c2-c2-c2-hc 16 3 2 7 + 26 hc-c2-c2-hc 7 2 3 17 + 27 hc-c2-c2-hc 7 2 3 18 + 28 c2-c2-c_1-o_1 8 9 10 11 + 29 c2-c2-c_1-o 8 9 10 12 + 30 c2-c2-c_1-n 8 9 10 1 + 31 hc-c2-c_1-o_1 13 9 10 11 + 32 hc-c2-c_1-o 13 9 10 12 + 33 hc-c2-c_1-n 13 9 10 1 + 34 hc-c2-c_1-o_1 14 9 10 11 + 35 hc-c2-c_1-o 14 9 10 12 + 36 hc-c2-c_1-n 14 9 10 1 + 37 c2-c_1-o-ho 9 10 12 15 + 38 o_1-c_1-o-ho 11 10 12 15 + 39 n-c_1-o-ho 1 10 12 15 diff --git a/examples/PACKAGES/reaction/tiny_nylon/rxn1_stp1_unreacted.data_template b/examples/PACKAGES/reaction/tiny_nylon/rxn1_stp1_unreacted.data_template deleted file mode 100644 index ec3f109d7b..0000000000 --- a/examples/PACKAGES/reaction/tiny_nylon/rxn1_stp1_unreacted.data_template +++ /dev/null @@ -1,160 +0,0 @@ -this is a molecule template for: initial nylon crosslink, pre-reacting - -18 atoms -16 bonds -25 angles -23 dihedrals -14 impropers - -Types - -1 7 -2 1 -3 1 -4 8 -5 8 -6 4 -7 4 -8 1 -9 1 -10 2 -11 6 -12 3 -13 4 -14 4 -15 5 -16 1 -17 4 -18 4 - -Charges - -1 -0.300000 -2 0.000000 -3 0.000000 -4 0.000000 -5 0.000000 -6 0.000000 -7 0.000000 -8 0.000000 -9 0.000000 -10 0.300000 -11 0.000000 -12 0.000000 -13 0.000000 -14 0.000000 -15 0.000000 -16 0.000000 -17 0.000000 -18 0.000000 - -Coords - -1 -4.922858 -0.946982 1.146055 -2 -5.047195 -0.935267 -0.358173 -3 -6.526281 -0.755366 -0.743523 -4 -5.282604 0.020447 1.552710 -5 -3.860697 -1.095850 1.428305 -6 -4.662382 -1.920900 -0.781524 -7 -4.433977 -0.072765 -0.784071 -8 -5.506279 0.202610 4.825816 -9 -4.449177 -0.844592 4.423366 -10 -4.103916 -0.749629 2.925195 -11 -3.376249 -1.886171 2.245643 -12 -4.493235 0.477214 2.137199 -13 -4.849053 -1.888877 4.663994 -14 -3.491823 -0.662913 5.018510 -15 -5.020777 1.189745 2.805427 -16 -3.964987 2.900602 -1.551341 -17 -4.460694 2.836102 0.668882 -18 -4.828494 3.219656 -0.122111 - -Bonds - -1 14 1 2 -2 10 1 4 -3 10 1 5 -4 2 2 3 -5 1 2 6 -6 1 2 7 -7 2 3 16 -8 1 3 17 -9 1 3 18 -10 2 8 9 -11 4 9 10 -12 1 9 13 -13 1 9 14 -14 5 10 11 -15 3 10 12 -16 6 12 15 - -Angles - -1 15 2 1 4 -2 15 2 1 5 -3 16 4 1 5 -4 28 1 2 3 -5 14 1 2 6 -6 14 1 2 7 -7 2 3 2 6 -8 2 3 2 7 -9 1 6 2 7 -10 3 2 3 16 -11 2 2 3 17 -12 2 2 3 18 -13 2 16 3 17 -14 2 16 3 18 -15 1 17 3 18 -16 8 8 9 10 -17 2 8 9 13 -18 2 8 9 14 -19 23 13 9 10 -20 23 14 9 10 -21 1 13 9 14 -22 6 9 10 11 -23 4 9 10 12 -24 25 11 10 12 -25 7 10 12 15 - -Dihedrals - -1 34 4 1 2 3 -2 35 4 1 2 6 -3 35 4 1 2 7 -4 34 5 1 2 3 -5 35 5 1 2 6 -6 35 5 1 2 7 -7 36 1 2 3 16 -8 12 1 2 3 17 -9 12 1 2 3 18 -10 4 16 3 2 6 -11 2 6 2 3 17 -12 2 6 2 3 18 -13 4 16 3 2 7 -14 2 7 2 3 17 -15 2 7 2 3 18 -16 10 8 9 10 11 -17 8 8 9 10 12 -18 11 13 9 10 11 -19 9 13 9 10 12 -20 11 14 9 10 11 -21 9 14 9 10 12 -22 6 9 10 12 15 -23 7 11 10 12 15 - -Impropers - -1 6 2 1 4 5 -2 11 9 10 11 12 -3 1 1 2 3 6 -4 1 1 2 3 7 -5 1 1 2 6 7 -6 1 3 2 6 7 -7 1 2 3 16 17 -8 1 2 3 16 18 -9 1 2 3 17 18 -10 1 16 3 17 18 -11 1 8 9 13 10 -12 1 8 9 14 10 -13 1 8 9 13 14 -14 1 13 9 14 10 diff --git a/examples/PACKAGES/reaction/tiny_nylon/rxn1_stp1_unreacted.molecule_template b/examples/PACKAGES/reaction/tiny_nylon/rxn1_stp1_unreacted.molecule_template new file mode 100644 index 0000000000..7de7512f1c --- /dev/null +++ b/examples/PACKAGES/reaction/tiny_nylon/rxn1_stp1_unreacted.molecule_template @@ -0,0 +1,169 @@ +this is a molecule template for: initial nylon crosslink, pre-reacting + + 18 atoms + 16 bonds + 25 angles + 23 dihedrals + 2 impropers + +Coords + + 1 -4.922858499 -0.946981747 1.146055346 + 2 -5.047194816 -0.935266843 -0.358172771 + 3 -6.526281447 -0.755365854 -0.743523227 + 4 -5.282604074 0.020446894 1.552710361 + 5 -3.860696509 -1.095850190 1.428304925 + 6 -4.662381862 -1.920899862 -0.781524026 + 7 -4.433976540 -0.072765142 -0.784070641 + 8 -5.506279186 0.202610302 4.825815562 + 9 -4.449176624 -0.844592213 4.423366146 + 10 -4.103915981 -0.749628655 2.925195217 + 11 -3.376248536 -1.886171498 2.245643443 + 12 -4.493235430 0.477213651 2.137199034 + 13 -4.849052953 -1.888876753 4.663993750 + 14 -3.491822950 -0.662913310 5.018510248 + 15 -5.020776528 1.189745133 2.805427194 + 16 -3.964987378 2.900602044 -1.551341170 + 17 -4.460693773 2.836101897 0.668881952 + 18 -4.828494000 3.219655862 -0.122111278 + +Types + + 1 na + 2 c2 + 3 c2 + 4 hn + 5 hn + 6 hc + 7 hc + 8 c2 + 9 c2 + 10 c_1 + 11 o_1 + 12 o + 13 hc + 14 hc + 15 ho + 16 c2 + 17 hc + 18 hc + +Charges + + 1 -0.300000 + 2 0.000000 + 3 0.000000 + 4 0.000000 + 5 0.000000 + 6 0.000000 + 7 0.000000 + 8 0.000000 + 9 0.000000 + 10 0.300000 + 11 0.000000 + 12 0.000000 + 13 0.000000 + 14 0.000000 + 15 0.000000 + 16 0.000000 + 17 0.000000 + 18 0.000000 + +Molecules + + 1 1 + 2 1 + 3 1 + 4 1 + 5 1 + 6 1 + 7 1 + 8 1 + 9 1 + 10 1 + 11 1 + 12 1 + 13 1 + 14 1 + 15 1 + 16 1 + 17 1 + 18 1 + +Bonds + + 1 na-c2 1 2 + 2 na-hn 1 4 + 3 na-hn 1 5 + 4 c2-c2 2 3 + 5 c2-hc 2 6 + 6 c2-hc 2 7 + 7 c2-c2 3 16 + 8 c2-hc 3 17 + 9 c2-hc 3 18 + 10 c2-c2 8 9 + 11 c2-c_1 9 10 + 12 c2-hc 9 13 + 13 c2-hc 9 14 + 14 c_1-o_1 10 11 + 15 c_1-o 10 12 + 16 o-ho 12 15 + +Angles + + 1 c2-na-hn 2 1 4 + 2 c2-na-hn 2 1 5 + 3 hn-na-hn 4 1 5 + 4 na-c2-c2 1 2 3 + 5 na-c2-hc 1 2 6 + 6 na-c2-hc 1 2 7 + 7 c2-c2-hc 3 2 6 + 8 c2-c2-hc 3 2 7 + 9 hc-c2-hc 6 2 7 + 10 c2-c2-c2 2 3 16 + 11 c2-c2-hc 2 3 17 + 12 c2-c2-hc 2 3 18 + 13 c2-c2-hc 16 3 17 + 14 c2-c2-hc 16 3 18 + 15 hc-c2-hc 17 3 18 + 16 c2-c2-c_1 8 9 10 + 17 c2-c2-hc 8 9 13 + 18 c2-c2-hc 8 9 14 + 19 hc-c2-c_1 13 9 10 + 20 hc-c2-c_1 14 9 10 + 21 hc-c2-hc 13 9 14 + 22 c2-c_1-o_1 9 10 11 + 23 c2-c_1-o 9 10 12 + 24 o_1-c_1-o 11 10 12 + 25 c_1-o-ho 10 12 15 + +Dihedrals + + 1 hn-na-c2-c2 4 1 2 3 + 2 hn-na-c2-hc 4 1 2 6 + 3 hn-na-c2-hc 4 1 2 7 + 4 hn-na-c2-c2 5 1 2 3 + 5 hn-na-c2-hc 5 1 2 6 + 6 hn-na-c2-hc 5 1 2 7 + 7 na-c2-c2-c2 1 2 3 16 + 8 na-c2-c2-hc 1 2 3 17 + 9 na-c2-c2-hc 1 2 3 18 + 10 c2-c2-c2-hc 16 3 2 6 + 11 hc-c2-c2-hc 6 2 3 17 + 12 hc-c2-c2-hc 6 2 3 18 + 13 c2-c2-c2-hc 16 3 2 7 + 14 hc-c2-c2-hc 7 2 3 17 + 15 hc-c2-c2-hc 7 2 3 18 + 16 c2-c2-c_1-o_1 8 9 10 11 + 17 c2-c2-c_1-o 8 9 10 12 + 18 hc-c2-c_1-o_1 13 9 10 11 + 19 hc-c2-c_1-o 13 9 10 12 + 20 hc-c2-c_1-o_1 14 9 10 11 + 21 hc-c2-c_1-o 14 9 10 12 + 22 c2-c_1-o-ho 9 10 12 15 + 23 o_1-c_1-o-ho 11 10 12 15 + +Impropers + + 1 c2-na-hn-hn 2 1 4 5 + 2 c2-c_1-o_1-o 9 10 11 12 diff --git a/examples/PACKAGES/reaction/tiny_nylon/rxn1_stp2_reacted.data_template b/examples/PACKAGES/reaction/tiny_nylon/rxn1_stp2_reacted.data_template deleted file mode 100644 index 7853634646..0000000000 --- a/examples/PACKAGES/reaction/tiny_nylon/rxn1_stp2_reacted.data_template +++ /dev/null @@ -1,131 +0,0 @@ -this is a molecule template for: water condensation, post-reacting - -15 atoms -13 bonds -19 angles -16 dihedrals -10 impropers - -Types - -1 9 -2 1 -3 1 -4 10 -5 8 -6 4 -7 4 -8 1 -9 1 -10 2 -11 6 -12 11 -13 4 -14 4 -15 10 - -Charges - -1 -0.300000 -2 0.000000 -3 0.000000 -4 0.410000 -5 0.000000 -6 0.000000 -7 0.000000 -8 0.000000 -9 0.000000 -10 0.300000 -11 0.000000 -12 -0.820000 -13 0.000000 -14 0.000000 -15 0.410000 - -Coords - -1 -4.856280 -1.050468 1.432625 -2 -5.047195 -0.935267 -0.358173 -3 -6.526281 -0.755366 -0.743523 -4 -5.282604 0.020447 1.552710 -5 -3.860697 -1.095850 1.428305 -6 -4.662382 -1.920900 -0.781524 -7 -4.433977 -0.072765 -0.784071 -8 -5.506279 0.202610 4.825816 -9 -4.449177 -0.844592 4.423366 -10 -4.103916 -0.749629 2.925195 -11 -3.376249 -1.886171 2.245643 -12 -4.493235 0.477214 2.137199 -13 -4.849053 -1.888877 4.663994 -14 -3.491823 -0.662913 5.018510 -15 -5.020777 1.189745 2.805427 - -Bonds - -1 11 1 2 -2 12 1 5 -3 13 1 10 -4 2 2 3 -5 1 2 6 -6 1 2 7 -7 15 4 12 -8 2 8 9 -9 4 9 10 -10 1 9 13 -11 1 9 14 -12 5 10 11 -13 15 15 12 - -Angles - -1 17 2 1 5 -2 18 2 1 10 -3 20 5 1 10 -4 21 1 2 3 -5 22 1 2 6 -6 22 1 2 7 -7 2 3 2 6 -8 2 3 2 7 -9 1 6 2 7 -10 8 8 9 10 -11 2 8 9 13 -12 2 8 9 14 -13 23 13 9 10 -14 23 14 9 10 -15 1 13 9 14 -16 6 9 10 11 -17 24 1 10 9 -18 26 1 10 11 -19 29 15 12 4 - -Dihedrals - -1 19 5 1 2 3 -2 20 5 1 2 6 -3 20 5 1 2 7 -4 21 10 1 2 3 -5 22 10 1 2 6 -6 22 10 1 2 7 -7 23 2 1 10 9 -8 24 2 1 10 11 -9 26 5 1 10 9 -10 27 5 1 10 11 -11 10 8 9 10 11 -12 31 8 9 10 1 -13 11 13 9 10 11 -14 32 13 9 10 1 -15 11 14 9 10 11 -16 32 14 9 10 1 - -Impropers - -1 12 2 1 5 10 -2 13 1 10 9 11 -3 1 1 2 3 6 -4 1 1 2 3 7 -5 1 1 2 6 7 -6 1 3 2 6 7 -7 1 8 9 13 10 -8 1 8 9 14 10 -9 1 8 9 13 14 -10 1 13 9 14 10 diff --git a/examples/PACKAGES/reaction/tiny_nylon/rxn1_stp2_reacted.molecule_template b/examples/PACKAGES/reaction/tiny_nylon/rxn1_stp2_reacted.molecule_template new file mode 100644 index 0000000000..2e91261468 --- /dev/null +++ b/examples/PACKAGES/reaction/tiny_nylon/rxn1_stp2_reacted.molecule_template @@ -0,0 +1,141 @@ +this is a molecule template for: water condensation, post-reacting + + 15 atoms + 13 bonds + 19 angles + 16 dihedrals + 2 impropers + +Coords + + 1 -4.856280281 -1.050467974 1.432625159 + 2 -5.047194816 -0.935266843 -0.358172771 + 3 -6.526281447 -0.755365854 -0.743523227 + 4 -5.282604074 0.020446894 1.552710361 + 5 -3.860696509 -1.095850190 1.428304925 + 6 -4.662381862 -1.920899862 -0.781524026 + 7 -4.433976540 -0.072765142 -0.784070641 + 8 -5.506279186 0.202610302 4.825815562 + 9 -4.449176624 -0.844592213 4.423366146 + 10 -4.103915981 -0.749628655 2.925195217 + 11 -3.376248536 -1.886171498 2.245643443 + 12 -4.493235430 0.477213651 2.137199034 + 13 -4.849052953 -1.888876753 4.663993750 + 14 -3.491822950 -0.662913310 5.018510248 + 15 -5.020776528 1.189745133 2.805427194 + +Types + + 1 n + 2 c2 + 3 c2 + 4 hw + 5 hn + 6 hc + 7 hc + 8 c2 + 9 c2 + 10 c_1 + 11 o_1 + 12 o* + 13 hc + 14 hc + 15 hw + +Charges + + 1 -0.300000 + 2 0.000000 + 3 0.000000 + 4 0.410000 + 5 0.000000 + 6 0.000000 + 7 0.000000 + 8 0.000000 + 9 0.000000 + 10 0.300000 + 11 0.000000 + 12 -0.820000 + 13 0.000000 + 14 0.000000 + 15 0.410000 + +Molecules + + 1 1 + 2 1 + 3 1 + 4 1 + 5 1 + 6 1 + 7 1 + 8 1 + 9 1 + 10 1 + 11 1 + 12 1 + 13 1 + 14 1 + 15 1 + +Bonds + + 1 n-c2 1 2 + 2 n-hn 1 5 + 3 n-c_1 1 10 + 4 c2-c2 2 3 + 5 c2-hc 2 6 + 6 c2-hc 2 7 + 7 hw-o* 4 12 + 8 c2-c2 8 9 + 9 c2-c_1 9 10 + 10 c2-hc 9 13 + 11 c2-hc 9 14 + 12 c_1-o_1 10 11 + 13 hw-o* 15 12 + +Angles + + 1 c2-n-hn 2 1 5 + 2 c2-n-c_1 2 1 10 + 3 hn-n-c_1 5 1 10 + 4 n-c2-c2 1 2 3 + 5 n-c2-hc 1 2 6 + 6 n-c2-hc 1 2 7 + 7 c2-c2-hc 3 2 6 + 8 c2-c2-hc 3 2 7 + 9 hc-c2-hc 6 2 7 + 10 c2-c2-c_1 8 9 10 + 11 c2-c2-hc 8 9 13 + 12 c2-c2-hc 8 9 14 + 13 hc-c2-c_1 13 9 10 + 14 hc-c2-c_1 14 9 10 + 15 hc-c2-hc 13 9 14 + 16 c2-c_1-o_1 9 10 11 + 17 n-c_1-c2 1 10 9 + 18 n-c_1-o_1 1 10 11 + 19 hw-o*-hw 15 12 4 + +Dihedrals + + 1 hn-n-c2-c2 5 1 2 3 + 2 hn-n-c2-hc 5 1 2 6 + 3 hn-n-c2-hc 5 1 2 7 + 4 c_1-n-c2-c2 10 1 2 3 + 5 c_1-n-c2-hc 10 1 2 6 + 6 c_1-n-c2-hc 10 1 2 7 + 7 c2-n-c_1-c2 2 1 10 9 + 8 c2-n-c_1-o_1 2 1 10 11 + 9 hn-n-c_1-c2 5 1 10 9 + 10 hn-n-c_1-o_1 5 1 10 11 + 11 c2-c2-c_1-o_1 8 9 10 11 + 12 c2-c2-c_1-n 8 9 10 1 + 13 hc-c2-c_1-o_1 13 9 10 11 + 14 hc-c2-c_1-n 13 9 10 1 + 15 hc-c2-c_1-o_1 14 9 10 11 + 16 hc-c2-c_1-n 14 9 10 1 + +Impropers + + 1 c2-n-hn-c_1 2 1 5 10 + 2 n-c_1-c2-o_1 1 10 9 11 diff --git a/examples/PACKAGES/reaction/tiny_nylon/rxn1_stp2_unreacted.data_template b/examples/PACKAGES/reaction/tiny_nylon/rxn1_stp2_unreacted.data_template deleted file mode 100644 index 847f0622e5..0000000000 --- a/examples/PACKAGES/reaction/tiny_nylon/rxn1_stp2_unreacted.data_template +++ /dev/null @@ -1,158 +0,0 @@ -this is a molecule template for: water condensation, pre-reacting - -15 atoms -14 bonds -25 angles -30 dihedrals -16 impropers - -Types - -1 9 -2 1 -3 1 -4 8 -5 8 -6 4 -7 4 -8 1 -9 1 -10 2 -11 6 -12 3 -13 4 -14 4 -15 5 - -Charges - -1 -0.300000 -2 0.000000 -3 0.000000 -4 0.000000 -5 0.000000 -6 0.000000 -7 0.000000 -8 0.000000 -9 0.000000 -10 0.300000 -11 0.000000 -12 0.000000 -13 0.000000 -14 0.000000 -15 0.000000 - -Coords - -1 -4.922858 -0.946982 1.146055 -2 -5.047195 -0.935267 -0.358173 -3 -6.526281 -0.755366 -0.743523 -4 -5.282604 0.020447 1.552710 -5 -3.860697 -1.095850 1.428305 -6 -4.662382 -1.920900 -0.781524 -7 -4.433977 -0.072765 -0.784071 -8 -5.506279 0.202610 4.825816 -9 -4.449177 -0.844592 4.423366 -10 -4.103916 -0.749629 2.925195 -11 -3.376249 -1.886171 2.245643 -12 -4.493235 0.477214 2.137199 -13 -4.849053 -1.888877 4.663994 -14 -3.491823 -0.662913 5.018510 -15 -5.020777 1.189745 2.805427 - -Bonds - -1 11 1 2 -2 12 1 4 -3 12 1 5 -4 13 1 10 -5 2 2 3 -6 1 2 6 -7 1 2 7 -8 2 8 9 -9 4 9 10 -10 1 9 13 -11 1 9 14 -12 5 10 11 -13 3 10 12 -14 6 12 15 - -Angles - -1 17 2 1 4 -2 17 2 1 5 -3 18 2 1 10 -4 19 4 1 5 -5 20 4 1 10 -6 20 5 1 10 -7 21 1 2 3 -8 22 1 2 6 -9 22 1 2 7 -10 2 3 2 6 -11 2 3 2 7 -12 1 6 2 7 -13 8 8 9 10 -14 2 8 9 13 -15 2 8 9 14 -16 23 13 9 10 -17 23 14 9 10 -18 1 13 9 14 -19 6 9 10 11 -20 4 9 10 12 -21 24 1 10 9 -22 25 11 10 12 -23 26 1 10 11 -24 27 1 10 12 -25 7 10 12 15 - -Dihedrals - -1 19 4 1 2 3 -2 20 4 1 2 6 -3 20 4 1 2 7 -4 19 5 1 2 3 -5 20 5 1 2 6 -6 20 5 1 2 7 -7 21 10 1 2 3 -8 22 10 1 2 6 -9 22 10 1 2 7 -10 23 2 1 10 9 -11 24 2 1 10 11 -12 25 2 1 10 12 -13 26 4 1 10 9 -14 27 4 1 10 11 -15 28 4 1 10 12 -16 26 5 1 10 9 -17 27 5 1 10 11 -18 28 5 1 10 12 -19 10 8 9 10 11 -20 8 8 9 10 12 -21 31 8 9 10 1 -22 11 13 9 10 11 -23 9 13 9 10 12 -24 32 13 9 10 1 -25 11 14 9 10 11 -26 9 14 9 10 12 -27 32 14 9 10 1 -28 6 9 10 12 15 -29 7 11 10 12 15 -30 33 1 10 12 15 - -Impropers - -1 1 2 1 4 5 -2 1 2 1 4 10 -3 1 2 1 5 10 -4 1 4 1 5 10 -5 1 1 2 3 6 -6 1 1 2 3 7 -7 1 1 2 6 7 -8 1 3 2 6 7 -9 1 8 9 13 10 -10 1 8 9 14 10 -11 1 8 9 13 14 -12 1 13 9 14 10 -13 1 9 10 11 12 -14 1 1 10 9 11 -15 1 1 10 9 12 -16 1 1 10 11 12 diff --git a/examples/PACKAGES/reaction/tiny_nylon/rxn1_stp2_unreacted.molecule_template b/examples/PACKAGES/reaction/tiny_nylon/rxn1_stp2_unreacted.molecule_template new file mode 100644 index 0000000000..86a772634d --- /dev/null +++ b/examples/PACKAGES/reaction/tiny_nylon/rxn1_stp2_unreacted.molecule_template @@ -0,0 +1,157 @@ +this is a molecule template for: water condensation, pre-reacting + + 15 atoms + 14 bonds + 25 angles + 30 dihedrals + 0 impropers + +Coords + + 1 -4.922858499 -0.946981747 1.146055346 + 2 -5.047194816 -0.935266843 -0.358172771 + 3 -6.526281447 -0.755365854 -0.743523227 + 4 -5.282604074 0.020446894 1.552710361 + 5 -3.860696509 -1.095850190 1.428304925 + 6 -4.662381862 -1.920899862 -0.781524026 + 7 -4.433976540 -0.072765142 -0.784070641 + 8 -5.506279186 0.202610302 4.825815562 + 9 -4.449176624 -0.844592213 4.423366146 + 10 -4.103915981 -0.749628655 2.925195217 + 11 -3.376248536 -1.886171498 2.245643443 + 12 -4.493235430 0.477213651 2.137199034 + 13 -4.849052953 -1.888876753 4.663993750 + 14 -3.491822950 -0.662913310 5.018510248 + 15 -5.020776528 1.189745133 2.805427194 + +Types + + 1 n + 2 c2 + 3 c2 + 4 hn + 5 hn + 6 hc + 7 hc + 8 c2 + 9 c2 + 10 c_1 + 11 o_1 + 12 o + 13 hc + 14 hc + 15 ho + +Charges + + 1 -0.300000 + 2 0.000000 + 3 0.000000 + 4 0.000000 + 5 0.000000 + 6 0.000000 + 7 0.000000 + 8 0.000000 + 9 0.000000 + 10 0.300000 + 11 0.000000 + 12 0.000000 + 13 0.000000 + 14 0.000000 + 15 0.000000 + +Molecules + + 1 1 + 2 1 + 3 1 + 4 1 + 5 1 + 6 1 + 7 1 + 8 1 + 9 1 + 10 1 + 11 1 + 12 1 + 13 1 + 14 1 + 15 1 + +Bonds + + 1 n-c2 1 2 + 2 n-hn 1 4 + 3 n-hn 1 5 + 4 n-c_1 1 10 + 5 c2-c2 2 3 + 6 c2-hc 2 6 + 7 c2-hc 2 7 + 8 c2-c2 8 9 + 9 c2-c_1 9 10 + 10 c2-hc 9 13 + 11 c2-hc 9 14 + 12 c_1-o_1 10 11 + 13 c_1-o 10 12 + 14 o-ho 12 15 + +Angles + + 1 c2-n-hn 2 1 4 + 2 c2-n-hn 2 1 5 + 3 c2-n-c_1 2 1 10 + 4 hn-n-hn 4 1 5 + 5 hn-n-c_1 4 1 10 + 6 hn-n-c_1 5 1 10 + 7 n-c2-c2 1 2 3 + 8 n-c2-hc 1 2 6 + 9 n-c2-hc 1 2 7 + 10 c2-c2-hc 3 2 6 + 11 c2-c2-hc 3 2 7 + 12 hc-c2-hc 6 2 7 + 13 c2-c2-c_1 8 9 10 + 14 c2-c2-hc 8 9 13 + 15 c2-c2-hc 8 9 14 + 16 hc-c2-c_1 13 9 10 + 17 hc-c2-c_1 14 9 10 + 18 hc-c2-hc 13 9 14 + 19 c2-c_1-o_1 9 10 11 + 20 c2-c_1-o 9 10 12 + 21 n-c_1-c2 1 10 9 + 22 o_1-c_1-o 11 10 12 + 23 n-c_1-o_1 1 10 11 + 24 n-c_1-o 1 10 12 + 25 c_1-o-ho 10 12 15 + +Dihedrals + + 1 hn-n-c2-c2 4 1 2 3 + 2 hn-n-c2-hc 4 1 2 6 + 3 hn-n-c2-hc 4 1 2 7 + 4 hn-n-c2-c2 5 1 2 3 + 5 hn-n-c2-hc 5 1 2 6 + 6 hn-n-c2-hc 5 1 2 7 + 7 c_1-n-c2-c2 10 1 2 3 + 8 c_1-n-c2-hc 10 1 2 6 + 9 c_1-n-c2-hc 10 1 2 7 + 10 c2-n-c_1-c2 2 1 10 9 + 11 c2-n-c_1-o_1 2 1 10 11 + 12 c2-n-c_1-o 2 1 10 12 + 13 hn-n-c_1-c2 4 1 10 9 + 14 hn-n-c_1-o_1 4 1 10 11 + 15 hn-n-c_1-o 4 1 10 12 + 16 hn-n-c_1-c2 5 1 10 9 + 17 hn-n-c_1-o_1 5 1 10 11 + 18 hn-n-c_1-o 5 1 10 12 + 19 c2-c2-c_1-o_1 8 9 10 11 + 20 c2-c2-c_1-o 8 9 10 12 + 21 c2-c2-c_1-n 8 9 10 1 + 22 hc-c2-c_1-o_1 13 9 10 11 + 23 hc-c2-c_1-o 13 9 10 12 + 24 hc-c2-c_1-n 13 9 10 1 + 25 hc-c2-c_1-o_1 14 9 10 11 + 26 hc-c2-c_1-o 14 9 10 12 + 27 hc-c2-c_1-n 14 9 10 1 + 28 c2-c_1-o-ho 9 10 12 15 + 29 o_1-c_1-o-ho 11 10 12 15 + 30 n-c_1-o-ho 1 10 12 15 diff --git a/examples/PACKAGES/reaction/tiny_nylon/tiny_nylon.data b/examples/PACKAGES/reaction/tiny_nylon/tiny_nylon.data index 8466e68ea5..ee8e397956 100644 --- a/examples/PACKAGES/reaction/tiny_nylon/tiny_nylon.data +++ b/examples/PACKAGES/reaction/tiny_nylon/tiny_nylon.data @@ -10,16 +10,130 @@ this is LAMMPS data file containing two nylon monomers 36 dihedral types 44 impropers 13 improper types -5 extra bond per atom -15 extra angle per atom -15 extra dihedral per atom -25 extra improper per atom -25 extra special per atom -25 25 xlo xhi -25 25 ylo yhi -25 25 zlo zhi +Atom Type Labels + +1 c2 +2 c_1 +3 o +4 hc +5 ho +6 o_1 +7 na +8 hn +9 n +10 hw +11 o* + +Bond Type Labels + +1 c2-hc +2 c2-c2 +3 c_1-o +4 c2-c_1 +5 c_1-o_1 +6 o-ho +7 c2-c2-repeat +8 c2-hc-repeat +9 na-c2 +10 na-hn +11 n-c2 +12 n-hn +13 n-c_1 +14 c2-na +15 hw-o* + +Angle Type Labels + +1 hc-c2-hc +2 c2-c2-hc +3 c2-c2-c2 +4 c2-c_1-o_1 +5 o-c_1-o_1 +6 c2-c_1-o +7 c_1-o-ho +8 c2-c2-c_1 +9 c_1-c2-hc +10 c2-c2-hc-repeat +11 c2-c2-c2-repeat +12 hc-c2-hc-repeat +13 c2-c2-na +14 na-c2-hc +15 c2-na-hn +16 hn-na-hn +17 c2-n-hn +18 c2-n-c_1 +19 hn-n-hn +20 hn-n-c_1 +21 n-c2-c2 +22 n-c2-hc +23 hc-c2-c_1 +24 n-c_1-c2 +25 o_1-c_1-o +26 n-c_1-o_1 +27 n-c_1-o +28 na-c2-c2 +29 hw-o*-hw + +Dihedral Type Labels + +1 c_1-c2-c2-hc +2 hc-c2-c2-hc +3 c2-c2-c2-c_1 +4 c2-c2-c2-hc +5 c2-c2-c2-c2 +6 c2-c_1-o-ho +7 o_1-c_1-o-ho +8 c2-c2-c_1-o +9 hc-c2-c_1-o +10 c2-c2-c_1-o_1 +11 hc-c2-c_1-o_1 +12 na-c2-c2-hc +13 hc-c2-c2-hc-repeat +14 c2-c2-c2-na +15 c2-c2-c2-hc-repeat +16 c2-c2-c2-c2-repeat +17 c2-c2-na-hn +18 hn-na-c2-hc +19 hn-n-c2-c2 +20 hn-n-c2-hc +21 c_1-n-c2-c2 +22 c_1-n-c2-hc +23 c2-n-c_1-c2 +24 c2-n-c_1-o_1 +25 c2-n-c_1-o +26 hn-n-c_1-c2 +27 hn-n-c_1-o_1 +28 hn-n-c_1-o +29 n-c2-c2-c2 +30 n-c2-c2-hc +31 c2-c2-c_1-n +32 hc-c2-c_1-n +33 n-c_1-o-ho +34 hn-na-c2-c2 +35 hc-c2-na-hn +36 na-c2-c2-c2 + +Improper Type Labels + +1 c2-c_1-o-o_1 +2 c2-na-hn-hn +3 c2-c_1-o_1-o +4 c2-n-hn-c_1 +5 zero5 +6 zero6 +7 zero7 +8 zero8 +9 zero9 +10 zero10 +11 zero11 +12 zero12 +13 n-c_1-c2-o_1 + Masses 1 12.0112 @@ -94,7 +208,7 @@ Angle Coeffs # class2 24 116.926 39.4193 -10.9945 -8.7733 25 118.986 98.6813 -22.2485 10.3673 26 125.542 92.572 -34.48 -11.1871 -27 0 0 0 0 +27 125.542 92.572 -34.48 -11.1871 28 111.91 60.7147 -13.3366 -13.0785 29 103.7 49.84 -11.6 -8 From 35eff624abf2fa4f9e4ed4c62207bc11db5e4e9e Mon Sep 17 00:00:00 2001 From: Jacob Gissinger Date: Thu, 15 Dec 2022 13:16:49 -0500 Subject: [PATCH 07/47] nylon_melt: actually use log files not output file --- .../log.4Nov2022.large_nylon_melt.g++.1 | 75 +++++++++++++- .../log.4Nov2022.large_nylon_melt.g++.4 | 98 +++++++++++++++---- 2 files changed, 151 insertions(+), 22 deletions(-) diff --git a/examples/PACKAGES/reaction/nylon,6-6_melt/log.4Nov2022.large_nylon_melt.g++.1 b/examples/PACKAGES/reaction/nylon,6-6_melt/log.4Nov2022.large_nylon_melt.g++.1 index 26c11bd020..440b2e5cf0 100644 --- a/examples/PACKAGES/reaction/nylon,6-6_melt/log.4Nov2022.large_nylon_melt.g++.1 +++ b/examples/PACKAGES/reaction/nylon,6-6_melt/log.4Nov2022.large_nylon_melt.g++.1 @@ -1,4 +1,25 @@ LAMMPS (4 Nov 2022) +# 35,000 atom nylon melt example + +units real + +boundary p p p + +atom_style full + +kspace_style pppm 1.0e-4 + +pair_style lj/class2/coul/long 8.5 + +angle_style class2 + +bond_style class2 + +dihedral_style class2 + +improper_style class2 + +read_data large_nylon_melt.data.gz extra/bond/per/atom 5 extra/angle/per/atom 15 extra/dihedral/per/atom 15 extra/improper/per/atom 25 extra/special/per/atom 25 Reading data file ... orthogonal box = (-2.6834403 -2.0679138 -2.2198803) to (73.455228 73.244835 73.40648) 1 by 1 by 1 MPI processor grid @@ -36,6 +57,10 @@ Finding 1-2 1-3 1-4 neighbors ... 41 = max # of special neighbors special bonds CPU = 0.026 seconds read_data CPU = 0.937 seconds + +velocity all create 800.0 4928459 dist gaussian + +molecule mol1 rxn1_stp1_unreacted.molecule_template Read molecule template mol1: 1 molecules 0 fragments @@ -44,6 +69,7 @@ Read molecule template mol1: 25 angles with max type 24 23 dihedrals with max type 33 2 impropers with max type 9 +molecule mol2 rxn1_stp1_reacted.molecule_template Read molecule template mol2: 1 molecules 0 fragments @@ -52,6 +78,7 @@ Read molecule template mol2: 31 angles with max type 23 39 dihedrals with max type 30 0 impropers with max type 0 +molecule mol3 rxn1_stp2_unreacted.molecule_template Read molecule template mol3: 1 molecules 0 fragments @@ -60,6 +87,7 @@ Read molecule template mol3: 25 angles with max type 23 30 dihedrals with max type 30 0 impropers with max type 0 +molecule mol4 rxn1_stp2_reacted.molecule_template Read molecule template mol4: 1 molecules 0 fragments @@ -68,15 +96,53 @@ Read molecule template mol4: 19 angles with max type 25 16 dihedrals with max type 29 2 impropers with max type 11 + +thermo 50 + +# dump 1 all xyz 100 test_vis.xyz + +fix myrxns all bond/react stabilization yes statted_grp .03 react rxn1 all 1 0.0 2.9 mol1 mol2 rxn1_stp1_map react rxn2 all 1 0.0 5.0 mol3 mol4 rxn1_stp2_map WARNING: Fix bond/react: Atom affected by reaction rxn2 is too close to template edge (../fix_bond_react.cpp:2624) dynamic group bond_react_MASTER_group defined dynamic group statted_grp_REACT defined +# stable at 800K +fix 1 statted_grp_REACT nvt temp 800 800 100 + +# in order to customize behavior of reacting atoms, +# you can use the internally created 'bond_react_MASTER_group', like so: +# fix 2 bond_react_MASTER_group temp/rescale 1 800 800 10 1 + +thermo_style custom step temp press density f_myrxns[1] f_myrxns[2] # cumulative reaction counts + +# restart 100 restart1 restart2 + +run 200 + CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE Your simulation uses code contributions which should be cited: + - fix bond/react: reacter.org doi:10.1016/j.polymer.2017.09.038, doi:10.1021/acs.macromol.0c02012 -The log file lists these citations in BibTeX format. + +@Article{Gissinger17, + author = {J. R. Gissinger and B. D. Jensen and K. E. Wise}, + title = {Modeling Chemical Reactions in Classical Molecular Dynamics Simulations}, + journal = {Polymer}, + year = 2017, + volume = 128, + pages = {211--217} +} + +@Article{Gissinger20, + author = {J. R. Gissinger, B. D. Jensen, K. E. Wise}, + title = {{REACTER}: A Heuristic Method for Reactive Molecular Dynamics}, + journal = {Macromolecules}, + year = 2020, + volume = 53, + number = 22, + pages = {9953--9961} +} CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE @@ -107,10 +173,6 @@ Neighbor list info ... pair build: copy stencil: none bin: none -Setting up Verlet run ... - Unit style : real - Current step : 0 - Time step : 1 Per MPI rank memory allocation (min/avg/max) = 209.8 | 209.8 | 209.8 Mbytes Step Temp Press Density f_myrxns[1] f_myrxns[2] 0 800 3666.3948 0.80366765 0 0 @@ -147,4 +209,7 @@ Ave neighs/atom = 196.80781 Ave special neighs/atom = 9.8480114 Neighbor list builds = 128 Dangerous builds = 0 + +# write_restart restart_longrun +# write_data restart_longrun.data Total wall time: 0:01:29 diff --git a/examples/PACKAGES/reaction/nylon,6-6_melt/log.4Nov2022.large_nylon_melt.g++.4 b/examples/PACKAGES/reaction/nylon,6-6_melt/log.4Nov2022.large_nylon_melt.g++.4 index 69a663c59c..52b36325b8 100644 --- a/examples/PACKAGES/reaction/nylon,6-6_melt/log.4Nov2022.large_nylon_melt.g++.4 +++ b/examples/PACKAGES/reaction/nylon,6-6_melt/log.4Nov2022.large_nylon_melt.g++.4 @@ -1,5 +1,25 @@ LAMMPS (4 Nov 2022) -WARNING: Using I/O redirection is unreliable with parallel runs. Better use -in switch to read input file. (../lammps.cpp:529) +# 35,000 atom nylon melt example + +units real + +boundary p p p + +atom_style full + +kspace_style pppm 1.0e-4 + +pair_style lj/class2/coul/long 8.5 + +angle_style class2 + +bond_style class2 + +dihedral_style class2 + +improper_style class2 + +read_data large_nylon_melt.data.gz extra/bond/per/atom 5 extra/angle/per/atom 15 extra/dihedral/per/atom 15 extra/improper/per/atom 25 extra/special/per/atom 25 Reading data file ... orthogonal box = (-2.6834403 -2.0679138 -2.2198803) to (73.455228 73.244835 73.40648) 2 by 1 by 2 MPI processor grid @@ -36,7 +56,11 @@ Finding 1-2 1-3 1-4 neighbors ... 12 = max # of 1-4 neighbors 41 = max # of special neighbors special bonds CPU = 0.007 seconds - read_data CPU = 0.853 seconds + read_data CPU = 0.854 seconds + +velocity all create 800.0 4928459 dist gaussian + +molecule mol1 rxn1_stp1_unreacted.molecule_template Read molecule template mol1: 1 molecules 0 fragments @@ -45,6 +69,7 @@ Read molecule template mol1: 25 angles with max type 24 23 dihedrals with max type 33 2 impropers with max type 9 +molecule mol2 rxn1_stp1_reacted.molecule_template Read molecule template mol2: 1 molecules 0 fragments @@ -53,6 +78,7 @@ Read molecule template mol2: 31 angles with max type 23 39 dihedrals with max type 30 0 impropers with max type 0 +molecule mol3 rxn1_stp2_unreacted.molecule_template Read molecule template mol3: 1 molecules 0 fragments @@ -61,6 +87,7 @@ Read molecule template mol3: 25 angles with max type 23 30 dihedrals with max type 30 0 impropers with max type 0 +molecule mol4 rxn1_stp2_reacted.molecule_template Read molecule template mol4: 1 molecules 0 fragments @@ -69,15 +96,53 @@ Read molecule template mol4: 19 angles with max type 25 16 dihedrals with max type 29 2 impropers with max type 11 + +thermo 50 + +# dump 1 all xyz 100 test_vis.xyz + +fix myrxns all bond/react stabilization yes statted_grp .03 react rxn1 all 1 0.0 2.9 mol1 mol2 rxn1_stp1_map react rxn2 all 1 0.0 5.0 mol3 mol4 rxn1_stp2_map WARNING: Fix bond/react: Atom affected by reaction rxn2 is too close to template edge (../fix_bond_react.cpp:2624) dynamic group bond_react_MASTER_group defined dynamic group statted_grp_REACT defined +# stable at 800K +fix 1 statted_grp_REACT nvt temp 800 800 100 + +# in order to customize behavior of reacting atoms, +# you can use the internally created 'bond_react_MASTER_group', like so: +# fix 2 bond_react_MASTER_group temp/rescale 1 800 800 10 1 + +thermo_style custom step temp press density f_myrxns[1] f_myrxns[2] # cumulative reaction counts + +# restart 100 restart1 restart2 + +run 200 + CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE Your simulation uses code contributions which should be cited: + - fix bond/react: reacter.org doi:10.1016/j.polymer.2017.09.038, doi:10.1021/acs.macromol.0c02012 -The log file lists these citations in BibTeX format. + +@Article{Gissinger17, + author = {J. R. Gissinger and B. D. Jensen and K. E. Wise}, + title = {Modeling Chemical Reactions in Classical Molecular Dynamics Simulations}, + journal = {Polymer}, + year = 2017, + volume = 128, + pages = {211--217} +} + +@Article{Gissinger20, + author = {J. R. Gissinger, B. D. Jensen, K. E. Wise}, + title = {{REACTER}: A Heuristic Method for Reactive Molecular Dynamics}, + journal = {Macromolecules}, + year = 2020, + volume = 53, + number = 22, + pages = {9953--9961} +} CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE @@ -108,10 +173,6 @@ Neighbor list info ... pair build: copy stencil: none bin: none -Setting up Verlet run ... - Unit style : real - Current step : 0 - Time step : 1 Per MPI rank memory allocation (min/avg/max) = 81.39 | 81.41 | 81.43 Mbytes Step Temp Press Density f_myrxns[1] f_myrxns[2] 0 800 3666.3948 0.80366765 0 0 @@ -119,22 +180,22 @@ Per MPI rank memory allocation (min/avg/max) = 81.39 | 81.41 | 81.43 Mbytes 100 694.36354 -2108.4881 0.80366765 57 22 150 716.5075 -12356.04 0.80366765 77 50 200 722.97306 -1308.3439 0.80366765 84 67 -Loop time of 23.0703 on 4 procs for 200 steps with 35200 atoms +Loop time of 23.1041 on 4 procs for 200 steps with 35200 atoms -Performance: 0.749 ns/day, 32.042 hours/ns, 8.669 timesteps/s, 305.154 katom-step/s +Performance: 0.748 ns/day, 32.089 hours/ns, 8.656 timesteps/s, 304.708 katom-step/s 100.0% CPU use with 4 MPI tasks x no OpenMP threads MPI task timing breakdown: Section | min time | avg time | max time |%varavg| %total --------------------------------------------------------------- -Pair | 6.6778 | 6.8513 | 6.9896 | 5.2 | 29.70 -Bond | 3.8962 | 3.9719 | 4.0488 | 3.0 | 17.22 -Kspace | 1.1907 | 1.3846 | 1.6278 | 15.9 | 6.00 -Neigh | 8.7963 | 8.7965 | 8.7967 | 0.0 | 38.13 -Comm | 0.1468 | 0.15512 | 0.16131 | 1.6 | 0.67 -Output | 0.00035931 | 0.00037432 | 0.00041707 | 0.0 | 0.00 -Modify | 1.8808 | 1.8808 | 1.8809 | 0.0 | 8.15 -Other | | 0.02973 | | | 0.13 +Pair | 6.6935 | 6.8618 | 7.0049 | 5.1 | 29.70 +Bond | 3.8936 | 3.9807 | 4.0626 | 3.5 | 17.23 +Kspace | 1.1828 | 1.4033 | 1.6503 | 16.6 | 6.07 +Neigh | 8.7942 | 8.7945 | 8.7946 | 0.0 | 38.06 +Comm | 0.14682 | 0.15559 | 0.16441 | 1.8 | 0.67 +Output | 0.00035959 | 0.00037472 | 0.00041627 | 0.0 | 0.00 +Modify | 1.8787 | 1.8787 | 1.8788 | 0.0 | 8.13 +Other | | 0.02917 | | | 0.13 Nlocal: 8800 ave 8911 max 8662 min Histogram: 1 0 0 1 0 0 0 0 1 1 @@ -148,4 +209,7 @@ Ave neighs/atom = 196.80838 Ave special neighs/atom = 9.8480114 Neighbor list builds = 128 Dangerous builds = 0 + +# write_restart restart_longrun +# write_data restart_longrun.data Total wall time: 0:00:24 From f0af982d09c323b0d40128c83355e18ecda7fe32 Mon Sep 17 00:00:00 2001 From: Jacob Gissinger Date: Thu, 15 Dec 2022 13:22:15 -0500 Subject: [PATCH 08/47] tiny_epoxy: actually use log files --- .../log.4Nov2022.tiny_epoxy.stabilized.g++.1 | 92 ++++++++++++++---- .../log.4Nov2022.tiny_epoxy.stabilized.g++.4 | 93 +++++++++++++++---- 2 files changed, 152 insertions(+), 33 deletions(-) diff --git a/examples/PACKAGES/reaction/tiny_epoxy/log.4Nov2022.tiny_epoxy.stabilized.g++.1 b/examples/PACKAGES/reaction/tiny_epoxy/log.4Nov2022.tiny_epoxy.stabilized.g++.1 index b5eb8c4157..24b8fb0987 100644 --- a/examples/PACKAGES/reaction/tiny_epoxy/log.4Nov2022.tiny_epoxy.stabilized.g++.1 +++ b/examples/PACKAGES/reaction/tiny_epoxy/log.4Nov2022.tiny_epoxy.stabilized.g++.1 @@ -1,4 +1,24 @@ LAMMPS (4 Nov 2022) +# two molecules DGEBA (diepoxy) and one DETA (linker) +# two crosslinking reactions + +units real + +boundary p p p + +atom_style full + +pair_style lj/class2 8 + +angle_style class2 + +bond_style class2 + +dihedral_style class2 + +improper_style class2 + +read_data tiny_epoxy.data Reading data file ... orthogonal box = (10 -10 -15) to (30 20 10) 1 by 1 by 1 MPI processor grid @@ -33,7 +53,11 @@ Finding 1-2 1-3 1-4 neighbors ... 19 = max # of 1-4 neighbors 22 = max # of special neighbors special bonds CPU = 0.000 seconds - read_data CPU = 0.022 seconds + read_data CPU = 0.015 seconds + +velocity all create 300.0 4928459 dist gaussian + +molecule mol1 rxn1_stp1_pre.molecule_template Read molecule template mol1: 1 molecules 0 fragments @@ -42,6 +66,7 @@ Read molecule template mol1: 53 angles with max type 29 66 dihedrals with max type 39 3 impropers with max type 5 +molecule mol2 rxn1_stp1_post.molecule_template Read molecule template mol2: 1 molecules 0 fragments @@ -50,6 +75,7 @@ Read molecule template mol2: 55 angles with max type 36 75 dihedrals with max type 51 2 impropers with max type 5 +molecule mol3 rxn1_stp2_post.molecule_template Read molecule template mol3: 1 molecules 0 fragments @@ -58,6 +84,7 @@ Read molecule template mol3: 53 angles with max type 37 72 dihedrals with max type 53 3 impropers with max type 5 +molecule mol4 rxn2_stp1_pre.molecule_template Read molecule template mol4: 1 molecules 0 fragments @@ -66,6 +93,7 @@ Read molecule template mol4: 73 angles with max type 41 96 dihedrals with max type 54 3 impropers with max type 5 +molecule mol5 rxn2_stp1_post.molecule_template Read molecule template mol5: 1 molecules 0 fragments @@ -74,6 +102,7 @@ Read molecule template mol5: 75 angles with max type 37 108 dihedrals with max type 53 2 impropers with max type 5 +molecule mol6 rxn2_stp2_post.molecule_template Read molecule template mol6: 1 molecules 0 fragments @@ -82,14 +111,46 @@ Read molecule template mol6: 73 angles with max type 50 102 dihedrals with max type 66 3 impropers with max type 22 + +thermo 50 + +# dump 1 all xyz 1 test_vis.xyz + +fix rxns all bond/react stabilization yes statted_grp .03 react rxn1_stp1 all 1 0.0 5 mol1 mol2 rxn1_stp1.map react rxn1_stp2 all 1 0.0 5 mol2 mol3 rxn1_stp2.map react rxn2_stp1 all 1 0.0 5 mol4 mol5 rxn2_stp1.map react rxn2_stp2 all 1 0.0 5 mol5 mol6 rxn2_stp2.map dynamic group bond_react_MASTER_group defined dynamic group statted_grp_REACT defined + +fix 1 statted_grp_REACT nvt temp 300 300 100 + +thermo_style custom step temp f_rxns[1] f_rxns[2] f_rxns[3] f_rxns[4] + +run 2000 + CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE Your simulation uses code contributions which should be cited: + - fix bond/react: reacter.org doi:10.1016/j.polymer.2017.09.038, doi:10.1021/acs.macromol.0c02012 -The log file lists these citations in BibTeX format. + +@Article{Gissinger17, + author = {J. R. Gissinger and B. D. Jensen and K. E. Wise}, + title = {Modeling Chemical Reactions in Classical Molecular Dynamics Simulations}, + journal = {Polymer}, + year = 2017, + volume = 128, + pages = {211--217} +} + +@Article{Gissinger20, + author = {J. R. Gissinger, B. D. Jensen, K. E. Wise}, + title = {{REACTER}: A Heuristic Method for Reactive Molecular Dynamics}, + journal = {Macromolecules}, + year = 2020, + volume = 53, + number = 22, + pages = {9953--9961} +} CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE @@ -111,10 +172,6 @@ Neighbor list info ... pair build: copy stencil: none bin: none -Setting up Verlet run ... - Unit style : real - Current step : 0 - Time step : 1 Per MPI rank memory allocation (min/avg/max) = 16.64 | 16.64 | 16.64 Mbytes Step Temp f_rxns[1] f_rxns[2] f_rxns[3] f_rxns[4] 0 300 0 0 0 0 @@ -158,21 +215,21 @@ Per MPI rank memory allocation (min/avg/max) = 16.64 | 16.64 | 16.64 Mbytes 1900 315.3756 1 1 1 1 1950 260.65335 1 1 1 1 2000 354.03612 1 1 1 1 -Loop time of 0.909774 on 1 procs for 2000 steps with 118 atoms +Loop time of 0.910097 on 1 procs for 2000 steps with 118 atoms -Performance: 189.937 ns/day, 0.126 hours/ns, 2198.347 timesteps/s, 259.405 katom-step/s -100.0% CPU use with 1 MPI tasks x no OpenMP threads +Performance: 189.870 ns/day, 0.126 hours/ns, 2197.568 timesteps/s, 259.313 katom-step/s +99.9% CPU use with 1 MPI tasks x no OpenMP threads MPI task timing breakdown: Section | min time | avg time | max time |%varavg| %total --------------------------------------------------------------- -Pair | 0.10261 | 0.10261 | 0.10261 | 0.0 | 11.28 -Bond | 0.63695 | 0.63695 | 0.63695 | 0.0 | 70.01 -Neigh | 0.013916 | 0.013916 | 0.013916 | 0.0 | 1.53 -Comm | 0.0057214 | 0.0057214 | 0.0057214 | 0.0 | 0.63 -Output | 0.0005856 | 0.0005856 | 0.0005856 | 0.0 | 0.06 -Modify | 0.14641 | 0.14641 | 0.14641 | 0.0 | 16.09 -Other | | 0.003576 | | | 0.39 +Pair | 0.10286 | 0.10286 | 0.10286 | 0.0 | 11.30 +Bond | 0.63714 | 0.63714 | 0.63714 | 0.0 | 70.01 +Neigh | 0.013949 | 0.013949 | 0.013949 | 0.0 | 1.53 +Comm | 0.0056606 | 0.0056606 | 0.0056606 | 0.0 | 0.62 +Output | 0.00055825 | 0.00055825 | 0.00055825 | 0.0 | 0.06 +Modify | 0.14629 | 0.14629 | 0.14629 | 0.0 | 16.07 +Other | | 0.003637 | | | 0.40 Nlocal: 118 ave 118 max 118 min Histogram: 1 0 0 0 0 0 0 0 0 0 @@ -186,4 +243,7 @@ Ave neighs/atom = 29.550847 Ave special neighs/atom = 10.576271 Neighbor list builds = 68 Dangerous builds = 0 + +# write_restart restart_longrun +# write_data restart_longrun.data nofix Total wall time: 0:00:01 diff --git a/examples/PACKAGES/reaction/tiny_epoxy/log.4Nov2022.tiny_epoxy.stabilized.g++.4 b/examples/PACKAGES/reaction/tiny_epoxy/log.4Nov2022.tiny_epoxy.stabilized.g++.4 index 5d6ac8ab21..5d1a80405a 100644 --- a/examples/PACKAGES/reaction/tiny_epoxy/log.4Nov2022.tiny_epoxy.stabilized.g++.4 +++ b/examples/PACKAGES/reaction/tiny_epoxy/log.4Nov2022.tiny_epoxy.stabilized.g++.4 @@ -1,5 +1,24 @@ LAMMPS (4 Nov 2022) -WARNING: Using I/O redirection is unreliable with parallel runs. Better use -in switch to read input file. (../lammps.cpp:529) +# two molecules DGEBA (diepoxy) and one DETA (linker) +# two crosslinking reactions + +units real + +boundary p p p + +atom_style full + +pair_style lj/class2 8 + +angle_style class2 + +bond_style class2 + +dihedral_style class2 + +improper_style class2 + +read_data tiny_epoxy.data Reading data file ... orthogonal box = (10 -10 -15) to (30 20 10) 1 by 2 by 2 MPI processor grid @@ -34,7 +53,11 @@ Finding 1-2 1-3 1-4 neighbors ... 19 = max # of 1-4 neighbors 22 = max # of special neighbors special bonds CPU = 0.000 seconds - read_data CPU = 0.009 seconds + read_data CPU = 0.013 seconds + +velocity all create 300.0 4928459 dist gaussian + +molecule mol1 rxn1_stp1_pre.molecule_template Read molecule template mol1: 1 molecules 0 fragments @@ -43,6 +66,7 @@ Read molecule template mol1: 53 angles with max type 29 66 dihedrals with max type 39 3 impropers with max type 5 +molecule mol2 rxn1_stp1_post.molecule_template Read molecule template mol2: 1 molecules 0 fragments @@ -51,6 +75,7 @@ Read molecule template mol2: 55 angles with max type 36 75 dihedrals with max type 51 2 impropers with max type 5 +molecule mol3 rxn1_stp2_post.molecule_template Read molecule template mol3: 1 molecules 0 fragments @@ -59,6 +84,7 @@ Read molecule template mol3: 53 angles with max type 37 72 dihedrals with max type 53 3 impropers with max type 5 +molecule mol4 rxn2_stp1_pre.molecule_template Read molecule template mol4: 1 molecules 0 fragments @@ -67,6 +93,7 @@ Read molecule template mol4: 73 angles with max type 41 96 dihedrals with max type 54 3 impropers with max type 5 +molecule mol5 rxn2_stp1_post.molecule_template Read molecule template mol5: 1 molecules 0 fragments @@ -75,6 +102,7 @@ Read molecule template mol5: 75 angles with max type 37 108 dihedrals with max type 53 2 impropers with max type 5 +molecule mol6 rxn2_stp2_post.molecule_template Read molecule template mol6: 1 molecules 0 fragments @@ -83,14 +111,46 @@ Read molecule template mol6: 73 angles with max type 50 102 dihedrals with max type 66 3 impropers with max type 22 + +thermo 50 + +# dump 1 all xyz 1 test_vis.xyz + +fix rxns all bond/react stabilization yes statted_grp .03 react rxn1_stp1 all 1 0.0 5 mol1 mol2 rxn1_stp1.map react rxn1_stp2 all 1 0.0 5 mol2 mol3 rxn1_stp2.map react rxn2_stp1 all 1 0.0 5 mol4 mol5 rxn2_stp1.map react rxn2_stp2 all 1 0.0 5 mol5 mol6 rxn2_stp2.map dynamic group bond_react_MASTER_group defined dynamic group statted_grp_REACT defined + +fix 1 statted_grp_REACT nvt temp 300 300 100 + +thermo_style custom step temp f_rxns[1] f_rxns[2] f_rxns[3] f_rxns[4] + +run 2000 + CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE Your simulation uses code contributions which should be cited: + - fix bond/react: reacter.org doi:10.1016/j.polymer.2017.09.038, doi:10.1021/acs.macromol.0c02012 -The log file lists these citations in BibTeX format. + +@Article{Gissinger17, + author = {J. R. Gissinger and B. D. Jensen and K. E. Wise}, + title = {Modeling Chemical Reactions in Classical Molecular Dynamics Simulations}, + journal = {Polymer}, + year = 2017, + volume = 128, + pages = {211--217} +} + +@Article{Gissinger20, + author = {J. R. Gissinger, B. D. Jensen, K. E. Wise}, + title = {{REACTER}: A Heuristic Method for Reactive Molecular Dynamics}, + journal = {Macromolecules}, + year = 2020, + volume = 53, + number = 22, + pages = {9953--9961} +} CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE @@ -112,10 +172,6 @@ Neighbor list info ... pair build: copy stencil: none bin: none -Setting up Verlet run ... - Unit style : real - Current step : 0 - Time step : 1 Per MPI rank memory allocation (min/avg/max) = 16.63 | 16.63 | 16.64 Mbytes Step Temp f_rxns[1] f_rxns[2] f_rxns[3] f_rxns[4] 0 300 0 0 0 0 @@ -159,21 +215,21 @@ Per MPI rank memory allocation (min/avg/max) = 16.63 | 16.63 | 16.64 Mbytes 1900 315.3756 1 1 1 1 1950 260.65334 1 1 1 1 2000 354.03612 1 1 1 1 -Loop time of 0.473184 on 4 procs for 2000 steps with 118 atoms +Loop time of 0.47159 on 4 procs for 2000 steps with 118 atoms -Performance: 365.186 ns/day, 0.066 hours/ns, 4226.686 timesteps/s, 498.749 katom-step/s -100.0% CPU use with 4 MPI tasks x no OpenMP threads +Performance: 366.420 ns/day, 0.065 hours/ns, 4240.970 timesteps/s, 500.434 katom-step/s +99.9% CPU use with 4 MPI tasks x no OpenMP threads MPI task timing breakdown: Section | min time | avg time | max time |%varavg| %total --------------------------------------------------------------- -Pair | 0.01651 | 0.024868 | 0.039209 | 5.4 | 5.26 -Bond | 0.072805 | 0.16458 | 0.21783 | 13.9 | 34.78 -Neigh | 0.0056701 | 0.0057265 | 0.0057792 | 0.1 | 1.21 -Comm | 0.028105 | 0.095922 | 0.19546 | 20.3 | 20.27 -Output | 0.00034311 | 0.00041507 | 0.0006278 | 0.0 | 0.09 -Modify | 0.17725 | 0.17761 | 0.17826 | 0.1 | 37.54 -Other | | 0.004064 | | | 0.86 +Pair | 0.016546 | 0.024458 | 0.038858 | 5.5 | 5.19 +Bond | 0.072622 | 0.16458 | 0.21778 | 13.9 | 34.90 +Neigh | 0.0056307 | 0.0056812 | 0.0057292 | 0.1 | 1.20 +Comm | 0.028022 | 0.095922 | 0.19526 | 20.3 | 20.34 +Output | 0.00034591 | 0.00041633 | 0.00062378 | 0.0 | 0.09 +Modify | 0.17613 | 0.17649 | 0.17711 | 0.1 | 37.43 +Other | | 0.00404 | | | 0.86 Nlocal: 29.5 ave 45 max 7 min Histogram: 1 0 0 0 0 0 1 1 0 1 @@ -187,4 +243,7 @@ Ave neighs/atom = 29.550847 Ave special neighs/atom = 10.576271 Neighbor list builds = 68 Dangerous builds = 0 + +# write_restart restart_longrun +# write_data restart_longrun.data nofix Total wall time: 0:00:00 From ac20f22056520db12c273b0d76654bbc36db56de Mon Sep 17 00:00:00 2001 From: Jacob Gissinger Date: Fri, 16 Dec 2022 18:39:37 -0500 Subject: [PATCH 09/47] type-labels: polystyrene example --- .../2styrene_reacted.data_template | 312 ----------- .../2styrene_reacted.molecule_template | 339 +++++++++++ .../2styrene_unreacted.data_template | 284 ---------- .../2styrene_unreacted.molecule_template | 319 +++++++++++ .../chain_chain_reacted.data_template | 497 ----------------- .../chain_chain_reacted.molecule_template | 526 ++++++++++++++++++ .../chain_chain_unreacted.data_template | 467 ---------------- .../chain_chain_unreacted.molecule_template | 504 +++++++++++++++++ .../chain_plus_styrene_reacted.data_template | 451 --------------- ...ain_plus_styrene_reacted.molecule_template | 484 ++++++++++++++++ ...chain_plus_styrene_unreacted.data_template | 422 -------------- ...n_plus_styrene_unreacted.molecule_template | 463 +++++++++++++++ .../in.tiny_polystyrene.stabilized | 20 +- ....20Nov19.tiny_polystyrene.stabilized.g++.1 | 245 -------- ....20Nov19.tiny_polystyrene.stabilized.g++.4 | 255 --------- ...g.4Nov19.tiny_polystyrene.stabilized.g++.4 | 329 +++++++++++ ...4Nov2020.tiny_polystyrene.stabilized.g++.1 | 329 +++++++++++ .../tiny_polystyrene/tiny_polystyrene.data | 102 ++++ 18 files changed, 3405 insertions(+), 2943 deletions(-) delete mode 100644 examples/PACKAGES/reaction/tiny_polystyrene/2styrene_reacted.data_template create mode 100644 examples/PACKAGES/reaction/tiny_polystyrene/2styrene_reacted.molecule_template delete mode 100644 examples/PACKAGES/reaction/tiny_polystyrene/2styrene_unreacted.data_template create mode 100644 examples/PACKAGES/reaction/tiny_polystyrene/2styrene_unreacted.molecule_template delete mode 100644 examples/PACKAGES/reaction/tiny_polystyrene/chain_chain_reacted.data_template create mode 100644 examples/PACKAGES/reaction/tiny_polystyrene/chain_chain_reacted.molecule_template delete mode 100644 examples/PACKAGES/reaction/tiny_polystyrene/chain_chain_unreacted.data_template create mode 100644 examples/PACKAGES/reaction/tiny_polystyrene/chain_chain_unreacted.molecule_template delete mode 100644 examples/PACKAGES/reaction/tiny_polystyrene/chain_plus_styrene_reacted.data_template create mode 100644 examples/PACKAGES/reaction/tiny_polystyrene/chain_plus_styrene_reacted.molecule_template delete mode 100644 examples/PACKAGES/reaction/tiny_polystyrene/chain_plus_styrene_unreacted.data_template create mode 100644 examples/PACKAGES/reaction/tiny_polystyrene/chain_plus_styrene_unreacted.molecule_template delete mode 100644 examples/PACKAGES/reaction/tiny_polystyrene/log.20Nov19.tiny_polystyrene.stabilized.g++.1 delete mode 100644 examples/PACKAGES/reaction/tiny_polystyrene/log.20Nov19.tiny_polystyrene.stabilized.g++.4 create mode 100644 examples/PACKAGES/reaction/tiny_polystyrene/log.4Nov19.tiny_polystyrene.stabilized.g++.4 create mode 100644 examples/PACKAGES/reaction/tiny_polystyrene/log.4Nov2020.tiny_polystyrene.stabilized.g++.1 diff --git a/examples/PACKAGES/reaction/tiny_polystyrene/2styrene_reacted.data_template b/examples/PACKAGES/reaction/tiny_polystyrene/2styrene_reacted.data_template deleted file mode 100644 index c4fa646e9f..0000000000 --- a/examples/PACKAGES/reaction/tiny_polystyrene/2styrene_reacted.data_template +++ /dev/null @@ -1,312 +0,0 @@ -2styrene_reacted - -32 atoms -33 bonds -54 angles -79 dihedrals -22 impropers - -Types - -1 1 -2 2 -3 1 -4 5 -5 1 -6 2 -7 1 -8 2 -9 1 -10 2 -11 1 -12 2 -13 2 -14 6 -15 2 -16 2 -17 1 -18 2 -19 1 -20 5 -21 1 -22 2 -23 1 -24 2 -25 1 -26 2 -27 1 -28 2 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45 36 + 14 cp-cp-cp-c1 35 37 39 38 + 15 cp-cp-cp-hc 37 39 41 40 + 16 cp-cp-cp-hc 39 41 43 42 + 17 cp-cp-cp-hc 41 43 45 44 + 18 cp-cp-cp-hc 35 45 43 46 diff --git a/examples/PACKAGES/reaction/tiny_polystyrene/chain_chain_unreacted.data_template b/examples/PACKAGES/reaction/tiny_polystyrene/chain_chain_unreacted.data_template deleted file mode 100644 index d8e0d977df..0000000000 --- a/examples/PACKAGES/reaction/tiny_polystyrene/chain_chain_unreacted.data_template +++ /dev/null @@ -1,467 +0,0 @@ -chain_chain_unreacted - -50 atoms -51 bonds -84 angles -118 dihedrals -36 impropers - -Types - -1 1 -2 2 -3 1 -4 5 -5 1 -6 2 -7 1 -8 2 -9 1 -10 2 -11 1 -12 2 -13 2 -14 6 -15 2 -16 2 -17 5 -18 6 -19 2 -20 2 -21 1 -22 2 -23 1 -24 5 -25 1 -26 2 -27 1 -28 2 -29 1 -30 2 -31 1 -32 2 -33 2 -34 6 -35 1 -36 2 -37 1 -38 5 -39 1 -40 2 -41 1 -42 2 -43 1 -44 2 -45 1 -46 2 -47 2 -48 6 -49 2 -50 2 - -Charges - -1 -0.129000 -2 0.123700 -3 0.026600 -4 -0.018200 -5 -0.129000 -6 0.123700 -7 -0.173400 -8 0.140300 -9 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cp-cp-cp 3 1 11 + 4 cp-cp-c=1 1 3 4 + 5 cp-cp-cp 1 3 5 + 6 cp-cp-c=1 5 3 4 + 7 cp-c=1-hc 3 4 13 + 8 cp-c=1-c= 3 4 14 + 9 hc-c=1-c= 13 4 14 + 10 cp-cp-hc 3 5 6 + 11 cp-cp-cp 3 5 7 + 12 cp-cp-hc 7 5 6 + 13 cp-cp-hc 5 7 8 + 14 cp-cp-cp 5 7 9 + 15 cp-cp-hc 9 7 8 + 16 cp-cp-hc 7 9 10 + 17 cp-cp-cp 7 9 11 + 18 cp-cp-hc 11 9 10 + 19 cp-cp-cp 1 11 9 + 20 cp-cp-hc 1 11 12 + 21 cp-cp-hc 9 11 12 + 22 hc-c=-c=1 15 14 4 + 23 hc-c=-c=1 16 14 4 + 24 hc-c=-hc 15 14 16 + 25 cp-cp-hc 19 17 18 + 26 cp-cp-hc 27 17 18 + 27 cp-cp-cp 19 17 27 + 28 cp-cp-c1 17 19 20 + 29 cp-cp-cp 17 19 21 + 30 cp-cp-c1 21 19 20 + 31 cp-c1-hc 19 20 29 + 32 cp-c1-c2 19 20 30 + 33 cp-c1-c2 19 20 44 + 34 hc-c1-c2 29 20 30 + 35 hc-c1-c2 29 20 44 + 36 c2-c1-c2 30 20 44 + 37 cp-cp-hc 19 21 22 + 38 cp-cp-cp 19 21 23 + 39 cp-cp-hc 23 21 22 + 40 cp-cp-hc 21 23 24 + 41 cp-cp-cp 21 23 25 + 42 cp-cp-hc 25 23 24 + 43 cp-cp-hc 23 25 26 + 44 cp-cp-cp 23 25 27 + 45 cp-cp-hc 27 25 26 + 46 cp-cp-cp 17 27 25 + 47 cp-cp-hc 17 27 28 + 48 cp-cp-hc 25 27 28 + 49 cp-cp-hc 33 31 32 + 50 cp-cp-hc 41 31 32 + 51 cp-cp-cp 33 31 41 + 52 cp-cp-c1 31 33 34 + 53 cp-cp-cp 31 33 35 + 54 cp-cp-c1 35 33 34 + 55 cp-c1-hc 33 34 43 + 56 cp-c1-c2 33 34 44 + 57 hc-c1-c2 43 34 44 + 58 cp-cp-hc 33 35 36 + 59 cp-cp-cp 33 35 37 + 60 cp-cp-hc 37 35 36 + 61 cp-cp-hc 35 37 38 + 62 cp-cp-cp 35 37 39 + 63 cp-cp-hc 39 37 38 + 64 cp-cp-hc 37 39 40 + 65 cp-cp-cp 37 39 41 + 66 cp-cp-hc 41 39 40 + 67 cp-cp-cp 31 41 39 + 68 cp-cp-hc 31 41 42 + 69 cp-cp-hc 39 41 42 + 70 c1-c2-c1 20 44 34 + 71 hc-c2-c1 45 44 20 + 72 hc-c2-c1 46 44 20 + 73 hc-c2-c1 45 44 34 + 74 hc-c2-c1 46 44 34 + 75 hc-c2-hc 45 44 46 + +Dihedrals + + 1 hc-cp-cp-c=1 2 1 3 4 + 2 cp-cp-cp-hc 5 3 1 2 + 3 cp-cp-cp-c=1 11 1 3 4 + 4 cp-cp-cp-cp 11 1 3 5 + 5 cp-cp-cp-hc 9 11 1 2 + 6 hc-cp-cp-hc 2 1 11 12 + 7 cp-cp-cp-cp 3 1 11 9 + 8 cp-cp-cp-hc 3 1 11 12 + 9 cp-cp-c=1-hc 1 3 4 13 + 10 cp-cp-c=1-c= 1 3 4 14 + 11 cp-cp-c=1-hc 5 3 4 13 + 12 cp-cp-c=1-c= 5 3 4 14 + 13 cp-cp-cp-hc 1 3 5 6 + 14 cp-cp-cp-cp 1 3 5 7 + 15 hc-cp-cp-c=1 6 5 3 4 + 16 cp-cp-cp-c=1 7 5 3 4 + 17 cp-c=1-c=-hc 3 4 14 15 + 18 cp-c=1-c=-hc 3 4 14 16 + 19 hc-c=1-c=-hc 13 4 14 15 + 20 hc-c=1-c=-hc 13 4 14 16 + 21 cp-cp-cp-hc 3 5 7 8 + 22 cp-cp-cp-cp 3 5 7 9 + 23 hc-cp-cp-hc 6 5 7 8 + 24 cp-cp-cp-hc 9 7 5 6 + 25 cp-cp-cp-hc 5 7 9 10 + 26 cp-cp-cp-cp 5 7 9 11 + 27 hc-cp-cp-hc 8 7 9 10 + 28 cp-cp-cp-hc 11 9 7 8 + 29 cp-cp-cp-cp 7 9 11 1 + 30 cp-cp-cp-hc 7 9 11 12 + 31 cp-cp-cp-hc 1 11 9 10 + 32 hc-cp-cp-hc 10 9 11 12 + 33 hc-cp-cp-c1 18 17 19 20 + 34 cp-cp-cp-hc 21 19 17 18 + 35 cp-cp-cp-c1 27 17 19 20 + 36 cp-cp-cp-cp 27 17 19 21 + 37 cp-cp-cp-hc 25 27 17 18 + 38 hc-cp-cp-hc 18 17 27 28 + 39 cp-cp-cp-cp 19 17 27 25 + 40 cp-cp-cp-hc 19 17 27 28 + 41 cp-cp-c1-hc 17 19 20 29 + 42 cp-cp-c1-c2 17 19 20 30 + 43 cp-cp-c1-c2 17 19 20 44 + 44 cp-cp-c1-hc 21 19 20 29 + 45 cp-cp-c1-c2 21 19 20 30 + 46 cp-cp-c1-c2 21 19 20 44 + 47 cp-cp-cp-hc 17 19 21 22 + 48 cp-cp-cp-cp 17 19 21 23 + 49 hc-cp-cp-c1 22 21 19 20 + 50 cp-cp-cp-c1 23 21 19 20 + 51 cp-c1-c2-c1 19 20 44 34 + 52 cp-c1-c2-hc 19 20 44 45 + 53 cp-c1-c2-hc 19 20 44 46 + 54 hc-c1-c2-c1 29 20 44 34 + 55 hc-c1-c2-hc 29 20 44 45 + 56 hc-c1-c2-hc 29 20 44 46 + 57 c2-c1-c2-c1 30 20 44 34 + 58 c2-c1-c2-hc 30 20 44 45 + 59 c2-c1-c2-hc 30 20 44 46 + 60 cp-cp-cp-hc 19 21 23 24 + 61 cp-cp-cp-cp 19 21 23 25 + 62 hc-cp-cp-hc 22 21 23 24 + 63 cp-cp-cp-hc 25 23 21 22 + 64 cp-cp-cp-hc 21 23 25 26 + 65 cp-cp-cp-cp 21 23 25 27 + 66 hc-cp-cp-hc 24 23 25 26 + 67 cp-cp-cp-hc 27 25 23 24 + 68 cp-cp-cp-cp 23 25 27 17 + 69 cp-cp-cp-hc 23 25 27 28 + 70 cp-cp-cp-hc 17 27 25 26 + 71 hc-cp-cp-hc 26 25 27 28 + 72 hc-cp-cp-c1 32 31 33 34 + 73 cp-cp-cp-hc 35 33 31 32 + 74 cp-cp-cp-c1 41 31 33 34 + 75 cp-cp-cp-cp 41 31 33 35 + 76 cp-cp-cp-hc 39 41 31 32 + 77 hc-cp-cp-hc 32 31 41 42 + 78 cp-cp-cp-cp 33 31 41 39 + 79 cp-cp-cp-hc 33 31 41 42 + 80 cp-cp-c1-hc 31 33 34 43 + 81 cp-cp-c1-c2 31 33 34 44 + 82 cp-cp-c1-hc 35 33 34 43 + 83 cp-cp-c1-c2 35 33 34 44 + 84 cp-cp-cp-hc 31 33 35 36 + 85 cp-cp-cp-cp 31 33 35 37 + 86 hc-cp-cp-c1 36 35 33 34 + 87 cp-cp-cp-c1 37 35 33 34 + 88 cp-c1-c2-c1 33 34 44 20 + 89 cp-c1-c2-hc 33 34 44 45 + 90 cp-c1-c2-hc 33 34 44 46 + 91 hc-c1-c2-c1 43 34 44 20 + 92 hc-c1-c2-hc 43 34 44 45 + 93 hc-c1-c2-hc 43 34 44 46 + 94 cp-cp-cp-hc 33 35 37 38 + 95 cp-cp-cp-cp 33 35 37 39 + 96 hc-cp-cp-hc 36 35 37 38 + 97 cp-cp-cp-hc 39 37 35 36 + 98 cp-cp-cp-hc 35 37 39 40 + 99 cp-cp-cp-cp 35 37 39 41 + 100 hc-cp-cp-hc 38 37 39 40 + 101 cp-cp-cp-hc 41 39 37 38 + 102 cp-cp-cp-cp 37 39 41 31 + 103 cp-cp-cp-hc 37 39 41 42 + 104 cp-cp-cp-hc 31 41 39 40 + 105 hc-cp-cp-hc 40 39 41 42 + +Impropers + + 1 cp-cp-cp-hc 3 1 11 2 + 2 cp-cp-cp-c=1 1 3 5 4 + 3 cp-c=1-hc-c= 3 4 13 14 + 4 cp-cp-cp-hc 3 5 7 6 + 5 cp-cp-cp-hc 5 7 9 8 + 6 cp-cp-cp-hc 7 9 11 10 + 7 cp-cp-cp-hc 1 11 9 12 + 8 hc-c=-hc-c=1 15 14 16 4 + 9 cp-cp-cp-hc 19 17 27 18 + 10 cp-cp-cp-c1 17 19 21 20 + 11 cp-cp-cp-hc 19 21 23 22 + 12 cp-cp-cp-hc 21 23 25 24 + 13 cp-cp-cp-hc 23 25 27 26 + 14 cp-cp-cp-hc 17 27 25 28 + 15 cp-cp-cp-hc 33 31 41 32 + 16 cp-cp-cp-c1 31 33 35 34 + 17 cp-c1-hc-c2 33 34 43 44 + 18 cp-cp-cp-hc 33 35 37 36 + 19 cp-cp-cp-hc 35 37 39 38 + 20 cp-cp-cp-hc 37 39 41 40 + 21 cp-cp-cp-hc 31 41 39 42 diff --git a/examples/PACKAGES/reaction/tiny_polystyrene/in.tiny_polystyrene.stabilized b/examples/PACKAGES/reaction/tiny_polystyrene/in.tiny_polystyrene.stabilized index a711f3eaa9..ab9c012905 100644 --- a/examples/PACKAGES/reaction/tiny_polystyrene/in.tiny_polystyrene.stabilized +++ b/examples/PACKAGES/reaction/tiny_polystyrene/in.tiny_polystyrene.stabilized @@ -1,5 +1,5 @@ # 20 styrene molecules -# three reactions defined +# three reactions defined units real @@ -11,9 +11,9 @@ kspace_style pppm 1.0e-4 pair_style lj/class2/coul/long 8.5 -angle_style class2 +angle_style class2 -bond_style class2 +bond_style class2 dihedral_style class2 @@ -28,12 +28,12 @@ read_data tiny_polystyrene.data & extra/improper/per/atom 25 & extra/special/per/atom 25 -molecule mol1 2styrene_unreacted.data_template -molecule mol2 2styrene_reacted.data_template -molecule mol3 chain_plus_styrene_unreacted.data_template -molecule mol4 chain_plus_styrene_reacted.data_template -molecule mol5 chain_chain_unreacted.data_template -molecule mol6 chain_chain_reacted.data_template +molecule mol1 2styrene_unreacted.molecule_template +molecule mol2 2styrene_reacted.molecule_template +molecule mol3 chain_plus_styrene_unreacted.molecule_template +molecule mol4 chain_plus_styrene_reacted.molecule_template +molecule mol5 chain_chain_unreacted.molecule_template +molecule mol6 chain_chain_reacted.molecule_template thermo 100 @@ -53,4 +53,4 @@ thermo_style custom step temp press density f_rxn1[1] f_rxn1[2] f_rxn1[3] run 10000 # write_restart restart_longrun nofix -# write_data restart_longrun.data +# write_data restart_longrun.data diff --git a/examples/PACKAGES/reaction/tiny_polystyrene/log.20Nov19.tiny_polystyrene.stabilized.g++.1 b/examples/PACKAGES/reaction/tiny_polystyrene/log.20Nov19.tiny_polystyrene.stabilized.g++.1 deleted file mode 100644 index 274c72ece9..0000000000 --- a/examples/PACKAGES/reaction/tiny_polystyrene/log.20Nov19.tiny_polystyrene.stabilized.g++.1 +++ /dev/null @@ -1,245 +0,0 @@ -LAMMPS (20 Nov 2019) - -WARNING-WARNING-WARNING-WARNING-WARNING -This LAMMPS executable was compiled using C++98 compatibility. -Please report the compiler info below at https://github.com/lammps/lammps/issues/1659 -GNU C++ 4.8.5 -WARNING-WARNING-WARNING-WARNING-WARNING - -Reading data file ... - orthogonal box = (1.74267 1.74267 1.74267) to (18.2573 18.2573 18.2573) - 1 by 1 by 1 MPI processor grid - reading atoms ... - 320 atoms - reading velocities ... - 320 velocities - scanning bonds ... - 8 = max bonds/atom - scanning angles ... - 18 = max angles/atom - scanning dihedrals ... - 22 = max dihedrals/atom - scanning impropers ... - 26 = max impropers/atom - reading bonds ... - 320 bonds - reading angles ... - 480 angles - reading dihedrals ... - 640 dihedrals - reading impropers ... - 160 impropers -Finding 1-2 1-3 1-4 neighbors ... - special bond factors lj: 0 0 0 - special bond factors coul: 0 0 0 - 3 = max # of 1-2 neighbors - 6 = max # of 1-3 neighbors - 12 = max # of 1-4 neighbors - 39 = max # of special neighbors - special bonds CPU = 0.000929056 secs - read_data CPU = 0.00930568 secs -Read molecule mol1: - 32 atoms with max type 4 - 32 bonds with max type 6 - 48 angles with max type 8 - 64 dihedrals with max type 9 - 16 impropers with max type 4 -Read molecule mol2: - 32 atoms with max type 6 - 33 bonds with max type 10 - 54 angles with max type 16 - 79 dihedrals with max type 19 - 22 impropers with max type 7 -Read molecule mol3: - 46 atoms with max type 6 - 47 bonds with max type 10 - 75 angles with max type 16 - 105 dihedrals with max type 19 - 29 impropers with max type 7 -Read molecule mol4: - 46 atoms with max type 6 - 48 bonds with max type 13 - 81 angles with max type 22 - 121 dihedrals with max type 36 - 35 impropers with max type 9 -Read molecule mol5: - 50 atoms with max type 6 - 51 bonds with max type 10 - 84 angles with max type 16 - 118 dihedrals with max type 19 - 36 impropers with max type 7 -Read molecule mol6: - 50 atoms with max type 6 - 52 bonds with max type 10 - 90 angles with max type 16 - 135 dihedrals with max type 19 - 42 impropers with max type 5 -dynamic group bond_react_MASTER_group defined -dynamic group statted_grp_REACT defined -PPPM initialization ... -WARNING: System is not charge neutral, net charge = -0.004 (../kspace.cpp:304) - using 12-bit tables for long-range coulomb (../kspace.cpp:323) - G vector (1/distance) = 0.255611 - grid = 6 6 6 - stencil order = 5 - estimated absolute RMS force accuracy = 0.00974692 - estimated relative force accuracy = 2.93525e-05 - using double precision FFTs - 3d grid and FFT values/proc = 1331 216 -Neighbor list info ... - update every 1 steps, delay 10 steps, check yes - max neighbors/atom: 2000, page size: 100000 - master list distance cutoff = 10.5 - ghost atom cutoff = 10.5 - binsize = 5.25, bins = 4 4 4 - 2 neighbor lists, perpetual/occasional/extra = 1 1 0 - (1) pair lj/class2/coul/long, perpetual - attributes: half, newton on - pair build: half/bin/newton - stencil: half/bin/3d/newton - bin: standard - (2) fix bond/react, occasional, copy from (1) - attributes: half, newton on - pair build: copy - stencil: none - bin: none -Setting up Verlet run ... - Unit style : real - Current step : 0 - Time step : 1 -Per MPI rank memory allocation (min/avg/max) = 31.14 | 31.14 | 31.14 Mbytes -Step Temp Press Density f_rxn1[1] f_rxn1[2] f_rxn1[3] - 0 320.13638 -376.0844 0.76796752 0 0 0 - 100 520.00782 3952.7008 0.76796752 8 0 0 - 200 499.9174 2360.8219 0.76796752 8 3 1 - 300 583.93895 2453.7374 0.76796752 8 3 2 - 400 560.65536 -2243.3464 0.76796752 8 3 3 - 500 556.27995 3598.7044 0.76796752 8 3 3 - 600 570.8397 -3340.1826 0.76796752 8 4 4 - 700 456.89894 -1087.8081 0.76796752 8 4 4 - 800 572.91817 -776.19188 0.76796752 8 4 4 - 900 530.13621 -246734.46 0.76796752 8 4 5 - 1000 542.34698 1044.0793 0.76796752 8 4 5 - 1100 562.86339 1207.1715 0.76796752 8 4 5 - 1200 520.1559 2725.6523 0.76796752 8 4 5 - 1300 534.01667 951.0972 0.76796752 8 4 5 - 1400 478.68681 1184.9224 0.76796752 8 4 5 - 1500 509.05445 2020.5224 0.76796752 8 4 5 - 1600 549.5382 810.17577 0.76796752 8 4 5 - 1700 549.46882 -6349.7751 0.76796752 8 4 5 - 1800 496.77334 3953.1043 0.76796752 8 4 5 - 1900 522.28719 -2271.7599 0.76796752 8 4 6 - 2000 569.95975 5633.4352 0.76796752 8 4 6 - 2100 590.8418 2355.8447 0.76796752 8 4 6 - 2200 537.64787 6459.6743 0.76796752 8 4 6 - 2300 548.38487 -1566.3528 0.76796752 8 4 6 - 2400 533.50353 6755.664 0.76796752 8 4 6 - 2500 512.57053 325.30968 0.76796752 8 4 6 - 2600 498.4597 -2468.1165 0.76796752 8 4 6 - 2700 559.03937 2428.3446 0.76796752 8 4 6 - 2800 585.85721 -2896.3607 0.76796752 8 4 6 - 2900 523.18635 1391.254 0.76796752 8 4 6 - 3000 524.62076 375.02973 0.76796752 8 4 6 - 3100 534.65688 -1522.7879 0.76796752 8 4 6 - 3200 499.42665 3725.5476 0.76796752 8 4 6 - 3300 514.36972 1725.8329 0.76796752 8 4 6 - 3400 482.52662 4648.5013 0.76796752 8 4 6 - 3500 495.36836 967.3482 0.76796752 8 4 6 - 3600 583.28736 745.21794 0.76796752 8 4 6 - 3700 531.99717 -804.39572 0.76796752 8 4 6 - 3800 555.08359 -2381.363 0.76796752 8 4 6 - 3900 520.1818 -547.34169 0.76796752 8 4 6 - 4000 444.38804 -2488.7881 0.76796752 8 4 6 - 4100 518.65622 -3135.9573 0.76796752 8 4 6 - 4200 484.15227 -1040.2447 0.76796752 8 4 6 - 4300 514.58006 550.14626 0.76796752 8 4 6 - 4400 579.81405 -849.81454 0.76796752 8 4 6 - 4500 522.8698 5222.654 0.76796752 8 4 6 - 4600 490.78275 3251.2892 0.76796752 8 4 6 - 4700 492.64299 3785.3482 0.76796752 8 4 6 - 4800 500.11059 4441.8978 0.76796752 8 4 6 - 4900 536.80009 965.33724 0.76796752 8 4 6 - 5000 516.98575 -3794.4213 0.76796752 8 4 6 - 5100 516.76648 -3593.9106 0.76796752 8 4 6 - 5200 521.6379 -6532.7773 0.76796752 8 4 6 - 5300 535.64798 2931.412 0.76796752 8 4 6 - 5400 559.83266 7628.1659 0.76796752 8 4 6 - 5500 538.91756 2841.6746 0.76796752 8 4 6 - 5600 539.13999 10445.173 0.76796752 8 4 6 - 5700 501.56603 -2106.3309 0.76796752 8 4 6 - 5800 496.72952 -4831.0565 0.76796752 8 4 6 - 5900 536.12979 -3916.8197 0.76796752 8 4 6 - 6000 553.10092 3142.6871 0.76796752 8 4 6 - 6100 558.09546 3154.584 0.76796752 8 4 6 - 6200 523.48472 9807.0034 0.76796752 8 4 6 - 6300 551.80343 -3608.2078 0.76796752 8 4 6 - 6400 484.28359 2255.4675 0.76796752 8 4 6 - 6500 560.68443 -4826.4868 0.76796752 8 4 6 - 6600 604.50797 402.32183 0.76796752 8 4 6 - 6700 538.84714 -7670.3312 0.76796752 8 4 6 - 6800 528.82853 -380.32058 0.76796752 8 4 6 - 6900 579.30919 4438.4574 0.76796752 8 4 6 - 7000 540.3406 3738.0524 0.76796752 8 4 6 - 7100 519.53645 -1825.5563 0.76796752 8 4 6 - 7200 474.136 1657.3863 0.76796752 8 4 6 - 7300 485.55159 -221.84939 0.76796752 8 4 6 - 7400 527.38494 1037.1777 0.76796752 8 4 6 - 7500 517.14767 -2313.5823 0.76796752 8 4 6 - 7600 517.95967 -4763.4709 0.76796752 8 4 6 - 7700 513.63507 4819.0253 0.76796752 8 4 6 - 7800 503.56828 1295.1212 0.76796752 8 4 6 - 7900 520.87804 1506.9417 0.76796752 8 4 6 - 8000 509.46453 -5800.0971 0.76796752 8 4 6 - 8100 566.67059 6065.4607 0.76796752 8 4 6 - 8200 592.53068 1097.2277 0.76796752 8 4 6 - 8300 529.55235 -580.81757 0.76796752 8 4 6 - 8400 518.22587 560.45589 0.76796752 8 4 6 - 8500 521.94561 5325.9459 0.76796752 8 4 6 - 8600 510.54416 -1929.1967 0.76796752 8 4 6 - 8700 562.71252 -629.90392 0.76796752 8 4 6 - 8800 540.23123 -3484.3893 0.76796752 8 4 6 - 8900 513.82411 -5227.152 0.76796752 8 4 6 - 9000 534.3307 -3299.088 0.76796752 8 4 6 - 9100 509.24467 -5676.2775 0.76796752 8 4 6 - 9200 506.3216 -7043.8493 0.76796752 8 4 7 - 9300 480.37682 2380.4696 0.76796752 8 4 7 - 9400 546.15532 1831.0103 0.76796752 8 4 7 - 9500 567.18341 3839.9843 0.76796752 8 4 7 - 9600 536.14883 4258.5304 0.76796752 8 4 7 - 9700 496.04153 3321.3561 0.76796752 8 4 7 - 9800 531.78927 3124.9156 0.76796752 8 4 7 - 9900 530.91395 38.987859 0.76796752 8 4 7 - 10000 551.22761 1027.5706 0.76796752 8 4 7 -Loop time of 57.7096 on 1 procs for 10000 steps with 320 atoms - -Performance: 14.972 ns/day, 1.603 hours/ns, 173.281 timesteps/s -99.9% CPU use with 1 MPI tasks x no OpenMP threads - -MPI task timing breakdown: -Section | min time | avg time | max time |%varavg| %total ---------------------------------------------------------------- -Pair | 11.621 | 11.621 | 11.621 | 0.0 | 20.14 -Bond | 11.151 | 11.151 | 11.151 | 0.0 | 19.32 -Kspace | 2.2403 | 2.2403 | 2.2403 | 0.0 | 3.88 -Neigh | 25.467 | 25.467 | 25.467 | 0.0 | 44.13 -Comm | 0.90467 | 0.90467 | 0.90467 | 0.0 | 1.57 -Output | 0.0017984 | 0.0017984 | 0.0017984 | 0.0 | 0.00 -Modify | 6.2622 | 6.2622 | 6.2622 | 0.0 | 10.85 -Other | | 0.06192 | | | 0.11 - -Nlocal: 320 ave 320 max 320 min -Histogram: 1 0 0 0 0 0 0 0 0 0 -Nghost: 3240 ave 3240 max 3240 min -Histogram: 1 0 0 0 0 0 0 0 0 0 -Neighs: 54336 ave 54336 max 54336 min -Histogram: 1 0 0 0 0 0 0 0 0 0 - -Total # of neighbors = 54336 -Ave neighs/atom = 169.8 -Ave special neighs/atom = 11.3063 -Neighbor list builds = 10000 -Dangerous builds = 0 - -Please see the log.cite file for references relevant to this simulation - -Total wall time: 0:00:58 diff --git a/examples/PACKAGES/reaction/tiny_polystyrene/log.20Nov19.tiny_polystyrene.stabilized.g++.4 b/examples/PACKAGES/reaction/tiny_polystyrene/log.20Nov19.tiny_polystyrene.stabilized.g++.4 deleted file mode 100644 index 29aae1cd0b..0000000000 --- a/examples/PACKAGES/reaction/tiny_polystyrene/log.20Nov19.tiny_polystyrene.stabilized.g++.4 +++ /dev/null @@ -1,255 +0,0 @@ -LAMMPS (20 Nov 2019) - -WARNING-WARNING-WARNING-WARNING-WARNING -This LAMMPS executable was compiled using C++98 compatibility. -Please report the compiler info below at https://github.com/lammps/lammps/issues/1659 -GNU C++ 4.8.5 -WARNING-WARNING-WARNING-WARNING-WARNING - -Reading data file ... - orthogonal box = (1.74267 1.74267 1.74267) to (18.2573 18.2573 18.2573) - 1 by 2 by 2 MPI processor grid - reading atoms ... - 320 atoms - reading velocities ... - 320 velocities - scanning bonds ... - 8 = max bonds/atom - scanning angles ... - 18 = max angles/atom - scanning dihedrals ... - 22 = max dihedrals/atom - scanning impropers ... - 26 = max impropers/atom - reading bonds ... - 320 bonds - reading angles ... - 480 angles - reading dihedrals ... - 640 dihedrals - reading impropers ... - 160 impropers -Finding 1-2 1-3 1-4 neighbors ... - special bond factors lj: 0 0 0 - special bond factors coul: 0 0 0 - 3 = max # of 1-2 neighbors - 6 = max # of 1-3 neighbors - 12 = max # of 1-4 neighbors - 39 = max # of special neighbors - special bonds CPU = 0.000751222 secs - read_data CPU = 0.0268223 secs -Read molecule mol1: - 32 atoms with max type 4 - 32 bonds with max type 6 - 48 angles with max type 8 - 64 dihedrals with max type 9 - 16 impropers with max type 4 -Read molecule mol2: - 32 atoms with max type 6 - 33 bonds with max type 10 - 54 angles with max type 16 - 79 dihedrals with max type 19 - 22 impropers with max type 7 -Read molecule mol3: - 46 atoms with max type 6 - 47 bonds with max type 10 - 75 angles with max type 16 - 105 dihedrals with max type 19 - 29 impropers with max type 7 -Read molecule mol4: - 46 atoms with max type 6 - 48 bonds with max type 13 - 81 angles with max type 22 - 121 dihedrals with max type 36 - 35 impropers with max type 9 -Read molecule mol5: - 50 atoms with max type 6 - 51 bonds with max type 10 - 84 angles with max type 16 - 118 dihedrals with max type 19 - 36 impropers with max type 7 -Read molecule mol6: - 50 atoms with max type 6 - 52 bonds with max type 10 - 90 angles with max type 16 - 135 dihedrals with max type 19 - 42 impropers with max type 5 -dynamic group bond_react_MASTER_group defined -dynamic group statted_grp_REACT defined -PPPM initialization ... -WARNING: System is not charge neutral, net charge = -0.004 (../kspace.cpp:304) - using 12-bit tables for long-range coulomb (../kspace.cpp:323) - G vector (1/distance) = 0.255611 - grid = 6 6 6 - stencil order = 5 - estimated absolute RMS force accuracy = 0.00974692 - estimated relative force accuracy = 2.93525e-05 - using double precision FFTs - 3d grid and FFT values/proc = 704 72 -Neighbor list info ... - update every 1 steps, delay 10 steps, check yes - max neighbors/atom: 2000, page size: 100000 - master list distance cutoff = 10.5 - ghost atom cutoff = 10.5 - binsize = 5.25, bins = 4 4 4 - 2 neighbor lists, perpetual/occasional/extra = 1 1 0 - (1) pair lj/class2/coul/long, perpetual - attributes: half, newton on - pair build: half/bin/newton - stencil: half/bin/3d/newton - bin: standard - (2) fix bond/react, occasional, copy from (1) - attributes: half, newton on - pair build: copy - stencil: none - bin: none -Setting up Verlet run ... - Unit style : real - Current step : 0 - Time step : 1 -Per MPI rank memory allocation (min/avg/max) = 30.66 | 30.68 | 30.69 Mbytes -Step Temp Press Density f_rxn1[1] f_rxn1[2] f_rxn1[3] - 0 320.13638 -376.0844 0.76796752 0 0 0 - 100 522.71544 6623.0579 0.76796752 8 0 0 - 200 500.86716 -9439.5519 0.76796752 8 3 2 - 300 594.60588 6714.1323 0.76796752 8 3 3 - 400 598.68768 683.70457 0.76796752 8 3 3 - 500 563.1011 3576.6857 0.76796752 8 3 4 - 600 510.29713 -196148.37 0.76796752 8 3 5 - 700 494.14346 -118517.45 0.76796752 8 3 6 - 800 565.62849 7678.1235 0.76796752 8 3 6 - 900 515.74468 554.84571 0.76796752 8 3 6 - 1000 500.64636 450.15932 0.76796752 8 3 6 - 1100 463.34973 6023.8346 0.76796752 8 3 6 - 1200 529.88483 2748.185 0.76796752 8 3 6 - 1300 546.84049 1353.4891 0.76796752 8 3 6 - 1400 552.27356 1446.5807 0.76796752 8 3 6 - 1500 557.70874 -2745.1523 0.76796752 8 3 6 - 1600 572.0005 629.36722 0.76796752 8 3 6 - 1700 503.96569 5937.0231 0.76796752 8 3 6 - 1800 491.34262 -1175.8104 0.76796752 8 3 6 - 1900 538.24798 -81.197397 0.76796752 8 3 6 - 2000 523.89324 2857.2466 0.76796752 8 3 6 - 2100 515.1424 2288.2405 0.76796752 8 3 6 - 2200 546.80854 3807.1038 0.76796752 8 3 6 - 2300 500.31231 -135.33933 0.76796752 8 4 6 - 2400 497.16354 5516.857 0.76796752 8 4 6 - 2500 545.34187 3485.5645 0.76796752 8 4 6 - 2600 522.70122 3114.1284 0.76796752 8 4 6 - 2700 531.76604 6633.5518 0.76796752 8 4 6 - 2800 521.97643 -279.83682 0.76796752 8 4 6 - 2900 497.29575 7052.9409 0.76796752 8 4 6 - 3000 524.5942 2284.8918 0.76796752 8 4 6 - 3100 567.61329 -3667.4557 0.76796752 8 4 6 - 3200 506.82452 -2934.4936 0.76796752 8 4 6 - 3300 510.8521 313.36263 0.76796752 8 4 6 - 3400 516.70206 3671.1899 0.76796752 8 4 6 - 3500 535.12788 2645.2564 0.76796752 8 4 6 - 3600 580.14214 2604.3079 0.76796752 8 4 6 - 3700 529.77869 2684.0812 0.76796752 8 4 6 - 3800 502.93191 2838.6698 0.76796752 8 4 6 - 3900 585.91492 5308.0828 0.76796752 8 4 6 - 4000 548.89917 5262.5775 0.76796752 8 4 6 - 4100 550.7662 -1066.6807 0.76796752 8 4 6 - 4200 519.19198 2777.5276 0.76796752 8 4 6 - 4300 521.46332 -3429.7171 0.76796752 8 4 6 - 4400 532.64173 2301.3135 0.76796752 8 4 6 - 4500 528.96107 1369.0991 0.76796752 8 4 6 - 4600 564.66443 9687.2531 0.76796752 8 4 6 - 4700 558.49446 2322.6085 0.76796752 8 4 6 - 4800 497.78614 -442.45053 0.76796752 8 4 6 - 4900 511.09435 -10251.159 0.76796752 8 4 6 - 5000 525.6642 -1202.0584 0.76796752 8 4 6 - 5100 521.76974 1821.7811 0.76796752 8 4 6 - 5200 555.9859 7256.9632 0.76796752 8 4 6 - 5300 551.51971 -122893.16 0.76796752 8 4 7 - 5400 524.34705 2905.1033 0.76796752 8 4 7 - 5500 567.09396 2896.4824 0.76796752 8 4 7 - 5600 487.57746 1417.1715 0.76796752 8 4 7 - 5700 547.37304 3900.8734 0.76796752 8 4 7 - 5800 536.17647 -4048.7522 0.76796752 8 4 7 - 5900 536.85051 4497.9847 0.76796752 8 4 7 - 6000 548.58212 -4880.4979 0.76796752 8 4 7 - 6100 500.94692 6004.2105 0.76796752 8 4 7 - 6200 486.82494 402.5875 0.76796752 8 4 7 - 6300 478.09381 6600.767 0.76796752 8 4 7 - 6400 559.90398 2868.0805 0.76796752 8 4 7 - 6500 526.01866 -3398.4788 0.76796752 8 4 7 - 6600 539.68471 -1202.0012 0.76796752 8 4 7 - 6700 507.51217 -378.71164 0.76796752 8 4 7 - 6800 526.15958 -4536.9888 0.76796752 8 4 7 - 6900 511.37134 -2522.3553 0.76796752 8 4 7 - 7000 538.86918 -2028.0323 0.76796752 8 4 7 - 7100 523.25566 2911.9962 0.76796752 8 4 7 - 7200 513.28464 -1000.4758 0.76796752 8 4 7 - 7300 510.19826 5181.7976 0.76796752 8 4 7 - 7400 493.46528 -1166.3996 0.76796752 8 4 7 - 7500 491.51305 5669.2213 0.76796752 8 4 7 - 7600 506.72032 -2840.301 0.76796752 8 4 7 - 7700 513.4319 2802.1719 0.76796752 8 4 7 - 7800 543.7658 -7477.3623 0.76796752 8 4 7 - 7900 527.35619 -3182.3155 0.76796752 8 4 7 - 8000 533.50993 613.16561 0.76796752 8 4 7 - 8100 512.44958 -5037.3414 0.76796752 8 4 7 - 8200 494.88981 1799.3513 0.76796752 8 4 7 - 8300 554.81474 -2436.0507 0.76796752 8 4 7 - 8400 523.22917 364.30593 0.76796752 8 4 7 - 8500 515.12395 525.24581 0.76796752 8 4 7 - 8600 511.6321 -1679.8669 0.76796752 8 4 7 - 8700 531.6327 -1168.1215 0.76796752 8 4 7 - 8800 548.14438 -5222.7573 0.76796752 8 4 7 - 8900 517.72579 2073.9695 0.76796752 8 4 7 - 9000 543.11894 -5307.0759 0.76796752 8 4 7 - 9100 521.13747 -5546.8552 0.76796752 8 4 7 - 9200 509.66142 -1584.019 0.76796752 8 4 7 - 9300 488.73821 -277.85847 0.76796752 8 4 7 - 9400 513.67282 989.60653 0.76796752 8 4 7 - 9500 509.98833 -1754.8786 0.76796752 8 4 7 - 9600 558.72497 5616.6969 0.76796752 8 4 7 - 9700 533.74988 811.48871 0.76796752 8 4 7 - 9800 510.94641 -3136.5876 0.76796752 8 4 7 - 9900 517.80127 -1962.0837 0.76796752 8 4 7 - 10000 477.50428 -3768.1653 0.76796752 8 4 7 -Loop time of 20.9963 on 4 procs for 10000 steps with 320 atoms - -Performance: 41.150 ns/day, 0.583 hours/ns, 476.276 timesteps/s -100.0% CPU use with 4 MPI tasks x no OpenMP threads - -MPI task timing breakdown: -Section | min time | avg time | max time |%varavg| %total ---------------------------------------------------------------- -Pair | 2.4968 | 3.0329 | 3.3607 | 18.6 | 14.45 -Bond | 2.3164 | 2.8835 | 3.456 | 26.0 | 13.73 -Kspace | 1.3332 | 2.2082 | 3.285 | 48.0 | 10.52 -Neigh | 7.4831 | 7.4922 | 7.5012 | 0.3 | 35.68 -Comm | 1.2809 | 1.3121 | 1.3297 | 1.6 | 6.25 -Output | 0.0012138 | 0.0013506 | 0.0017552 | 0.6 | 0.01 -Modify | 4.0269 | 4.0301 | 4.0335 | 0.1 | 19.19 -Other | | 0.03583 | | | 0.17 - -Nlocal: 80 ave 94 max 66 min -Histogram: 2 0 0 0 0 0 0 0 0 2 -Nghost: 2243.75 ave 2260 max 2221 min -Histogram: 1 0 0 1 0 0 0 0 0 2 -Neighs: 13658.5 ave 17096 max 9421 min -Histogram: 1 0 0 0 0 1 1 0 0 1 - -Total # of neighbors = 54634 -Ave neighs/atom = 170.731 -Ave special neighs/atom = 11.3063 -Neighbor list builds = 10000 -Dangerous builds = 0 -System init for write_data ... -PPPM initialization ... - using 12-bit tables for long-range coulomb (../kspace.cpp:323) - G vector (1/distance) = 0.255611 - grid = 6 6 6 - stencil order = 5 - estimated absolute RMS force accuracy = 0.00974692 - estimated relative force accuracy = 2.93525e-05 - using double precision FFTs - 3d grid and FFT values/proc = 704 72 - -Please see the log.cite file for references relevant to this simulation - -Total wall time: 0:00:21 diff --git a/examples/PACKAGES/reaction/tiny_polystyrene/log.4Nov19.tiny_polystyrene.stabilized.g++.4 b/examples/PACKAGES/reaction/tiny_polystyrene/log.4Nov19.tiny_polystyrene.stabilized.g++.4 new file mode 100644 index 0000000000..aaa8b2f190 --- /dev/null +++ b/examples/PACKAGES/reaction/tiny_polystyrene/log.4Nov19.tiny_polystyrene.stabilized.g++.4 @@ -0,0 +1,329 @@ +LAMMPS (4 Nov 2022) +# 20 styrene molecules +# three reactions defined + +units real + +boundary p p p + +atom_style full + +kspace_style pppm 1.0e-4 + +pair_style lj/class2/coul/long 8.5 + +angle_style class2 + +bond_style class2 + +dihedral_style class2 + +improper_style class2 + +variable T equal 530 + +read_data tiny_polystyrene.data extra/bond/per/atom 5 extra/angle/per/atom 15 extra/dihedral/per/atom 15 extra/improper/per/atom 25 extra/special/per/atom 25 +Reading data file ... + orthogonal box = (1.7426663 1.7426663 1.7426663) to (18.257334 18.257334 18.257334) + 1 by 2 by 2 MPI processor grid + reading atom labelmap ... + reading bond labelmap ... + reading angle labelmap ... + reading dihedral labelmap ... + reading improper labelmap ... + reading atoms ... + 320 atoms + reading velocities ... + 320 velocities + scanning bonds ... + 8 = max bonds/atom + scanning angles ... + 18 = max angles/atom + scanning dihedrals ... + 22 = max dihedrals/atom + scanning impropers ... + 26 = max impropers/atom + reading bonds ... + 320 bonds + reading angles ... + 480 angles + reading dihedrals ... + 640 dihedrals + reading impropers ... + 160 impropers +Finding 1-2 1-3 1-4 neighbors ... + special bond factors lj: 0 0 0 + special bond factors coul: 0 0 0 + 3 = max # of 1-2 neighbors + 6 = max # of 1-3 neighbors + 12 = max # of 1-4 neighbors + 39 = max # of special neighbors + special bonds CPU = 0.001 seconds + read_data CPU = 0.018 seconds + +molecule mol1 2styrene_unreacted.molecule_template +Read molecule template mol1: + 1 molecules + 0 fragments + 32 atoms with max type 4 + 32 bonds with max type 11 + 48 angles with max type 19 + 64 dihedrals with max type 21 + 16 impropers with max type 8 +molecule mol2 2styrene_reacted.molecule_template +Read molecule template mol2: + 1 molecules + 0 fragments + 32 atoms with max type 6 + 33 bonds with max type 13 + 54 angles with max type 22 + 79 dihedrals with max type 19 + 14 impropers with max type 7 +molecule mol3 chain_plus_styrene_unreacted.molecule_template +Read molecule template mol3: + 1 molecules + 0 fragments + 46 atoms with max type 6 + 47 bonds with max type 13 + 75 angles with max type 22 + 105 dihedrals with max type 21 + 21 impropers with max type 8 +molecule mol4 chain_plus_styrene_reacted.molecule_template +Read molecule template mol4: + 1 molecules + 0 fragments + 46 atoms with max type 6 + 48 bonds with max type 13 + 81 angles with max type 22 + 121 dihedrals with max type 19 + 19 impropers with max type 7 +molecule mol5 chain_chain_unreacted.molecule_template +Read molecule template mol5: + 1 molecules + 0 fragments + 50 atoms with max type 6 + 51 bonds with max type 13 + 84 angles with max type 22 + 118 dihedrals with max type 19 + 20 impropers with max type 7 +molecule mol6 chain_chain_reacted.molecule_template +Read molecule template mol6: + 1 molecules + 0 fragments + 50 atoms with max type 6 + 52 bonds with max type 13 + 90 angles with max type 22 + 135 dihedrals with max type 19 + 18 impropers with max type 2 + +thermo 100 + +# dump 1 all xyz 5 test_vis.xyz + +fix rxn1 all bond/react stabilization yes statted_grp .03 react rxn1 all 1 0 3.0 mol1 mol2 2styrene_map stabilize_steps 100 react rxn2 all 1 0 3.0 mol3 mol4 chain_plus_styrene_map stabilize_steps 100 react rxn3 all 1 0 5.0 mol5 mol6 chain_chain_map stabilize_steps 100 +dynamic group bond_react_MASTER_group defined +dynamic group statted_grp_REACT defined + +fix 1 statted_grp_REACT nvt temp $T $T 100 +fix 1 statted_grp_REACT nvt temp 530 $T 100 +fix 1 statted_grp_REACT nvt temp 530 530 100 + +fix 4 bond_react_MASTER_group temp/rescale 1 $T $T 1 1 +fix 4 bond_react_MASTER_group temp/rescale 1 530 $T 1 1 +fix 4 bond_react_MASTER_group temp/rescale 1 530 530 1 1 + +thermo_style custom step temp press density f_rxn1[1] f_rxn1[2] f_rxn1[3] + +run 10000 + +CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE + +Your simulation uses code contributions which should be cited: + +- fix bond/react: reacter.org doi:10.1016/j.polymer.2017.09.038, doi:10.1021/acs.macromol.0c02012 + +@Article{Gissinger17, + author = {J. R. Gissinger and B. D. Jensen and K. E. Wise}, + title = {Modeling Chemical Reactions in Classical Molecular Dynamics Simulations}, + journal = {Polymer}, + year = 2017, + volume = 128, + pages = {211--217} +} + +@Article{Gissinger20, + author = {J. R. Gissinger, B. D. Jensen, K. E. Wise}, + title = {{REACTER}: A Heuristic Method for Reactive Molecular Dynamics}, + journal = {Macromolecules}, + year = 2020, + volume = 53, + number = 22, + pages = {9953--9961} +} + +CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE + +PPPM initialization ... +WARNING: System is not charge neutral, net charge = -0.004 (../kspace.cpp:327) + using 12-bit tables for long-range coulomb (../kspace.cpp:342) + G vector (1/distance) = 0.25561147 + grid = 6 6 6 + stencil order = 5 + estimated absolute RMS force accuracy = 0.0097469157 + estimated relative force accuracy = 2.9352547e-05 + using double precision KISS FFT + 3d grid and FFT values/proc = 704 72 +Generated 21 of 21 mixed pair_coeff terms from sixthpower/geometric mixing rule +Neighbor list info ... + update: every = 1 steps, delay = 0 steps, check = yes + max neighbors/atom: 2000, page size: 100000 + master list distance cutoff = 10.5 + ghost atom cutoff = 10.5 + binsize = 5.25, bins = 4 4 4 + 2 neighbor lists, perpetual/occasional/extra = 1 1 0 + (1) pair lj/class2/coul/long, perpetual + attributes: half, newton on + pair build: half/bin/newton + stencil: half/bin/3d + bin: standard + (2) fix bond/react, occasional, copy from (1) + attributes: half, newton on + pair build: copy + stencil: none + bin: none +Per MPI rank memory allocation (min/avg/max) = 31.03 | 31.05 | 31.06 Mbytes + Step Temp Press Density f_rxn1[1] f_rxn1[2] f_rxn1[3] + 0 320.13638 -376.0844 0.76796752 0 0 0 + 100 342.22237 -3489.4495 0.76796752 0 0 0 + 200 412.23828 -1367.104 0.76796752 0 0 0 + 300 467.98145 4841.002 0.76796752 0 0 0 + 400 505.39864 2213.0509 0.76796752 1 0 0 + 500 519.63371 -28223.513 0.76796752 2 0 0 + 600 526.40655 8701.2728 0.76796752 2 0 0 + 700 579.91953 2507.5868 0.76796752 2 0 0 + 800 517.29593 5558.2895 0.76796752 2 0 0 + 900 503.38392 -5027.1154 0.76796752 2 0 0 + 1000 509.30767 3979.0529 0.76796752 2 0 0 + 1100 551.34763 5119.0848 0.76796752 2 0 0 + 1200 562.5176 -2867.8688 0.76796752 2 0 0 + 1300 552.90918 2090.7508 0.76796752 2 0 0 + 1400 516.10716 3374.2169 0.76796752 2 0 0 + 1500 518.70418 471.99711 0.76796752 2 0 0 + 1600 559.49915 5450.8774 0.76796752 2 0 0 + 1700 531.50638 4525.5892 0.76796752 2 0 0 + 1800 529.18331 -3566.9245 0.76796752 2 0 0 + 1900 517.79846 -2364.8287 0.76796752 2 0 0 + 2000 495.0983 -488.99696 0.76796752 2 0 0 + 2100 567.80521 2050.9596 0.76796752 3 0 0 + 2200 553.24434 5665.0753 0.76796752 3 0 0 + 2300 561.08278 2879.1572 0.76796752 3 0 0 + 2400 461.3712 3185.6091 0.76796752 3 0 0 + 2500 500.95595 565.81792 0.76796752 4 0 0 + 2600 538.3865 463.58228 0.76796752 4 0 0 + 2700 525.95739 2011.1914 0.76796752 4 0 0 + 2800 533.4197 157.38106 0.76796752 4 0 0 + 2900 526.27036 1331.5115 0.76796752 5 1 0 + 3000 502.65015 -93.915921 0.76796752 5 1 0 + 3100 505.4224 -1314.224 0.76796752 5 1 0 + 3200 538.52692 10420.644 0.76796752 5 1 0 + 3300 518.32801 5933.553 0.76796752 5 2 0 + 3400 540.04815 741.54438 0.76796752 6 2 1 + 3500 554.07567 5778.8913 0.76796752 6 2 1 + 3600 546.90828 4751.5437 0.76796752 6 2 1 + 3700 529.75739 432.20829 0.76796752 6 2 1 + 3800 542.806 -380.00399 0.76796752 6 2 1 + 3900 521.55789 -1224.1912 0.76796752 6 2 2 + 4000 519.73935 2792.996 0.76796752 6 2 2 + 4100 535.06314 -1926.8692 0.76796752 6 2 2 + 4200 549.75482 2852.5521 0.76796752 6 2 2 + 4300 510.71949 6581.1729 0.76796752 7 2 2 + 4400 485.93403 -695.24007 0.76796752 7 2 2 + 4500 535.3677 2519.2711 0.76796752 7 2 2 + 4600 504.87216 533.16619 0.76796752 7 2 2 + 4700 495.68939 5502.1672 0.76796752 7 2 2 + 4800 534.13893 -1187.1228 0.76796752 7 2 2 + 4900 512.56394 1731.3856 0.76796752 7 2 2 + 5000 508.63054 2467.0387 0.76796752 7 2 2 + 5100 501.65027 3403.8111 0.76796752 7 2 2 + 5200 556.68281 4310.0492 0.76796752 7 2 2 + 5300 506.86652 -773630.77 0.76796752 7 2 3 + 5400 570.01783 11663.867 0.76796752 7 2 3 + 5500 538.08785 6391.6546 0.76796752 7 2 3 + 5600 502.48456 44.409604 0.76796752 7 2 3 + 5700 545.75445 1558.6373 0.76796752 7 2 3 + 5800 517.5076 -166.52488 0.76796752 7 2 3 + 5900 558.64383 1528.1198 0.76796752 7 2 3 + 6000 557.8358 442.21273 0.76796752 7 2 3 + 6100 483.13771 5201.4489 0.76796752 8 2 3 + 6200 533.42675 5112.0828 0.76796752 8 2 3 + 6300 576.32772 269.77058 0.76796752 8 2 3 + 6400 492.79331 565.35222 0.76796752 8 2 4 + 6500 514.5727 6233.7568 0.76796752 8 2 4 + 6600 509.86906 -943.58621 0.76796752 8 2 4 + 6700 546.62752 -323284.04 0.76796752 8 2 5 + 6800 541.19749 1306.3182 0.76796752 8 2 5 + 6900 497.72333 -1792.483 0.76796752 8 2 5 + 7000 516.02636 2028.3813 0.76796752 8 2 5 + 7100 486.54013 6153.9142 0.76796752 8 2 5 + 7200 553.33698 4352.3987 0.76796752 8 2 5 + 7300 519.23896 6536.766 0.76796752 8 2 5 + 7400 486.74787 -1744.8351 0.76796752 8 2 5 + 7500 516.71935 -315.43649 0.76796752 8 2 5 + 7600 513.62572 -1100.1363 0.76796752 8 2 5 + 7700 531.11296 1727.7113 0.76796752 8 2 5 + 7800 530.82809 9566.2386 0.76796752 8 2 5 + 7900 513.09884 8545.6728 0.76796752 8 2 5 + 8000 511.38714 2995.8438 0.76796752 8 2 5 + 8100 527.76731 709.63649 0.76796752 8 2 5 + 8200 514.09092 2103.8591 0.76796752 8 2 5 + 8300 534.90612 7707.3378 0.76796752 8 2 5 + 8400 547.40716 660.54641 0.76796752 8 2 5 + 8500 518.75522 -872.69754 0.76796752 8 2 5 + 8600 511.70922 6645.6264 0.76796752 8 2 5 + 8700 480.70739 -640.57939 0.76796752 8 2 5 + 8800 527.35475 6944.8472 0.76796752 8 2 5 + 8900 554.26477 -2311.6153 0.76796752 8 2 5 + 9000 520.48502 1469.4805 0.76796752 8 2 5 + 9100 522.0619 -4159.697 0.76796752 8 2 5 + 9200 501.34664 7486.8266 0.76796752 8 2 5 + 9300 524.96422 6158.2524 0.76796752 8 2 5 + 9400 564.30456 -2964.7187 0.76796752 8 2 6 + 9500 569.02736 5765.8856 0.76796752 8 2 6 + 9600 554.31532 2805.5671 0.76796752 8 2 6 + 9700 521.3957 -924.74562 0.76796752 8 2 6 + 9800 518.45356 -2440.5266 0.76796752 8 2 6 + 9900 512.03787 -834.07647 0.76796752 8 2 6 + 10000 573.10576 4372.5769 0.76796752 8 2 6 +Loop time of 11.2088 on 4 procs for 10000 steps with 320 atoms + +Performance: 77.082 ns/day, 0.311 hours/ns, 892.155 timesteps/s, 285.490 katom-step/s +100.0% CPU use with 4 MPI tasks x no OpenMP threads + +MPI task timing breakdown: +Section | min time | avg time | max time |%varavg| %total +--------------------------------------------------------------- +Pair | 2.6217 | 2.8126 | 3.0128 | 9.5 | 25.09 +Bond | 2.0439 | 2.1734 | 2.3326 | 7.0 | 19.39 +Kspace | 1.4277 | 1.7772 | 2.0148 | 17.9 | 15.86 +Neigh | 0.32002 | 0.3201 | 0.3202 | 0.0 | 2.86 +Comm | 0.42382 | 0.43347 | 0.4412 | 1.1 | 3.87 +Output | 0.0013461 | 0.0015202 | 0.0020328 | 0.8 | 0.01 +Modify | 3.6386 | 3.6396 | 3.6408 | 0.0 | 32.47 +Other | | 0.05092 | | | 0.45 + +Nlocal: 80 ave 93 max 71 min +Histogram: 1 1 0 0 1 0 0 0 0 1 +Nghost: 2184.75 ave 2276 max 2092 min +Histogram: 1 0 1 0 0 0 0 1 0 1 +Neighs: 13678.5 ave 15576 max 11682 min +Histogram: 1 0 0 1 0 0 0 1 0 1 + +Total # of neighbors = 54714 +Ave neighs/atom = 170.98125 +Ave special neighs/atom = 10.9125 +Neighbor list builds = 471 +Dangerous builds = 0 + +# write_restart restart_longrun nofix +# write_data restart_longrun.data +Total wall time: 0:00:11 diff --git a/examples/PACKAGES/reaction/tiny_polystyrene/log.4Nov2020.tiny_polystyrene.stabilized.g++.1 b/examples/PACKAGES/reaction/tiny_polystyrene/log.4Nov2020.tiny_polystyrene.stabilized.g++.1 new file mode 100644 index 0000000000..be40e6b0de --- /dev/null +++ b/examples/PACKAGES/reaction/tiny_polystyrene/log.4Nov2020.tiny_polystyrene.stabilized.g++.1 @@ -0,0 +1,329 @@ +LAMMPS (4 Nov 2022) +# 20 styrene molecules +# three reactions defined + +units real + +boundary p p p + +atom_style full + +kspace_style pppm 1.0e-4 + +pair_style lj/class2/coul/long 8.5 + +angle_style class2 + +bond_style class2 + +dihedral_style class2 + +improper_style class2 + +variable T equal 530 + +read_data tiny_polystyrene.data extra/bond/per/atom 5 extra/angle/per/atom 15 extra/dihedral/per/atom 15 extra/improper/per/atom 25 extra/special/per/atom 25 +Reading data file ... + orthogonal box = (1.7426663 1.7426663 1.7426663) to (18.257334 18.257334 18.257334) + 1 by 1 by 1 MPI processor grid + reading atom labelmap ... + reading bond labelmap ... + reading angle labelmap ... + reading dihedral labelmap ... + reading improper labelmap ... + reading atoms ... + 320 atoms + reading velocities ... + 320 velocities + scanning bonds ... + 8 = max bonds/atom + scanning angles ... + 18 = max angles/atom + scanning dihedrals ... + 22 = max dihedrals/atom + scanning impropers ... + 26 = max impropers/atom + reading bonds ... + 320 bonds + reading angles ... + 480 angles + reading dihedrals ... + 640 dihedrals + reading impropers ... + 160 impropers +Finding 1-2 1-3 1-4 neighbors ... + special bond factors lj: 0 0 0 + special bond factors coul: 0 0 0 + 3 = max # of 1-2 neighbors + 6 = max # of 1-3 neighbors + 12 = max # of 1-4 neighbors + 39 = max # of special neighbors + special bonds CPU = 0.001 seconds + read_data CPU = 0.015 seconds + +molecule mol1 2styrene_unreacted.molecule_template +Read molecule template mol1: + 1 molecules + 0 fragments + 32 atoms with max type 4 + 32 bonds with max type 11 + 48 angles with max type 19 + 64 dihedrals with max type 21 + 16 impropers with max type 8 +molecule mol2 2styrene_reacted.molecule_template +Read molecule template mol2: + 1 molecules + 0 fragments + 32 atoms with max type 6 + 33 bonds with max type 13 + 54 angles with max type 22 + 79 dihedrals with max type 19 + 14 impropers with max type 7 +molecule mol3 chain_plus_styrene_unreacted.molecule_template +Read molecule template mol3: + 1 molecules + 0 fragments + 46 atoms with max type 6 + 47 bonds with max type 13 + 75 angles with max type 22 + 105 dihedrals with max type 21 + 21 impropers with max type 8 +molecule mol4 chain_plus_styrene_reacted.molecule_template +Read molecule template mol4: + 1 molecules + 0 fragments + 46 atoms with max type 6 + 48 bonds with max type 13 + 81 angles with max type 22 + 121 dihedrals with max type 19 + 19 impropers with max type 7 +molecule mol5 chain_chain_unreacted.molecule_template +Read molecule template mol5: + 1 molecules + 0 fragments + 50 atoms with max type 6 + 51 bonds with max type 13 + 84 angles with max type 22 + 118 dihedrals with max type 19 + 20 impropers with max type 7 +molecule mol6 chain_chain_reacted.molecule_template +Read molecule template mol6: + 1 molecules + 0 fragments + 50 atoms with max type 6 + 52 bonds with max type 13 + 90 angles with max type 22 + 135 dihedrals with max type 19 + 18 impropers with max type 2 + +thermo 100 + +# dump 1 all xyz 5 test_vis.xyz + +fix rxn1 all bond/react stabilization yes statted_grp .03 react rxn1 all 1 0 3.0 mol1 mol2 2styrene_map stabilize_steps 100 react rxn2 all 1 0 3.0 mol3 mol4 chain_plus_styrene_map stabilize_steps 100 react rxn3 all 1 0 5.0 mol5 mol6 chain_chain_map stabilize_steps 100 +dynamic group bond_react_MASTER_group defined +dynamic group statted_grp_REACT defined + +fix 1 statted_grp_REACT nvt temp $T $T 100 +fix 1 statted_grp_REACT nvt temp 530 $T 100 +fix 1 statted_grp_REACT nvt temp 530 530 100 + +fix 4 bond_react_MASTER_group temp/rescale 1 $T $T 1 1 +fix 4 bond_react_MASTER_group temp/rescale 1 530 $T 1 1 +fix 4 bond_react_MASTER_group temp/rescale 1 530 530 1 1 + +thermo_style custom step temp press density f_rxn1[1] f_rxn1[2] f_rxn1[3] + +run 10000 + +CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE + +Your simulation uses code contributions which should be cited: + +- fix bond/react: reacter.org doi:10.1016/j.polymer.2017.09.038, doi:10.1021/acs.macromol.0c02012 + +@Article{Gissinger17, + author = {J. R. Gissinger and B. D. Jensen and K. E. Wise}, + title = {Modeling Chemical Reactions in Classical Molecular Dynamics Simulations}, + journal = {Polymer}, + year = 2017, + volume = 128, + pages = {211--217} +} + +@Article{Gissinger20, + author = {J. R. Gissinger, B. D. Jensen, K. E. Wise}, + title = {{REACTER}: A Heuristic Method for Reactive Molecular Dynamics}, + journal = {Macromolecules}, + year = 2020, + volume = 53, + number = 22, + pages = {9953--9961} +} + +CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE + +PPPM initialization ... +WARNING: System is not charge neutral, net charge = -0.004 (../kspace.cpp:327) + using 12-bit tables for long-range coulomb (../kspace.cpp:342) + G vector (1/distance) = 0.25561147 + grid = 6 6 6 + stencil order = 5 + estimated absolute RMS force accuracy = 0.0097469157 + estimated relative force accuracy = 2.9352547e-05 + using double precision KISS FFT + 3d grid and FFT values/proc = 1331 216 +Generated 21 of 21 mixed pair_coeff terms from sixthpower/geometric mixing rule +Neighbor list info ... + update: every = 1 steps, delay = 0 steps, check = yes + max neighbors/atom: 2000, page size: 100000 + master list distance cutoff = 10.5 + ghost atom cutoff = 10.5 + binsize = 5.25, bins = 4 4 4 + 2 neighbor lists, perpetual/occasional/extra = 1 1 0 + (1) pair lj/class2/coul/long, perpetual + attributes: half, newton on + pair build: half/bin/newton + stencil: half/bin/3d + bin: standard + (2) fix bond/react, occasional, copy from (1) + attributes: half, newton on + pair build: copy + stencil: none + bin: none +Per MPI rank memory allocation (min/avg/max) = 31.51 | 31.51 | 31.51 Mbytes + Step Temp Press Density f_rxn1[1] f_rxn1[2] f_rxn1[3] + 0 320.13638 -376.0844 0.76796752 0 0 0 + 100 342.22237 -3489.4495 0.76796752 0 0 0 + 200 412.23828 -1367.104 0.76796752 0 0 0 + 300 467.98145 4841.002 0.76796752 0 0 0 + 400 505.39864 2213.0509 0.76796752 1 0 0 + 500 519.63371 -28223.513 0.76796752 2 0 0 + 600 526.40655 8701.2728 0.76796752 2 0 0 + 700 579.91953 2507.5868 0.76796752 2 0 0 + 800 517.29593 5558.2894 0.76796752 2 0 0 + 900 503.38392 -5027.1155 0.76796752 2 0 0 + 1000 509.30766 3979.0526 0.76796752 2 0 0 + 1100 551.34763 5119.0854 0.76796752 2 0 0 + 1200 562.51766 -2867.8721 0.76796752 2 0 0 + 1300 552.90947 2090.7196 0.76796752 2 0 0 + 1400 516.10667 3374.3471 0.76796752 2 0 0 + 1500 518.70363 472.0237 0.76796752 2 0 0 + 1600 559.50145 5451.1908 0.76796752 2 0 0 + 1700 531.49515 4526.9547 0.76796752 2 0 0 + 1800 529.18545 -3566.8838 0.76796752 2 0 0 + 1900 517.52577 -2390.6662 0.76796752 2 0 0 + 2000 495.24246 -485.62368 0.76796752 2 0 0 + 2100 567.90338 2009.3507 0.76796752 3 0 0 + 2200 553.05006 5694.0307 0.76796752 3 0 0 + 2300 561.22521 2944.2766 0.76796752 3 0 0 + 2400 460.05535 3058.3944 0.76796752 3 0 0 + 2500 501.01426 365.04418 0.76796752 4 0 0 + 2600 543.94728 267.33298 0.76796752 4 0 0 + 2700 539.40536 4258.9345 0.76796752 4 0 0 + 2800 557.67853 -2732.3135 0.76796752 4 0 0 + 2900 539.85456 3987.7331 0.76796752 4 1 0 + 3000 501.3125 3280.3821 0.76796752 4 1 0 + 3100 537.77092 -5290.371 0.76796752 4 1 0 + 3200 528.20744 11690.902 0.76796752 4 1 0 + 3300 548.56721 2464.6039 0.76796752 4 1 0 + 3400 542.73725 -27951.173 0.76796752 4 1 1 + 3500 547.63988 7925.1202 0.76796752 4 1 1 + 3600 502.69726 7875.8308 0.76796752 4 1 1 + 3700 495.26614 -1907.7215 0.76796752 4 1 1 + 3800 526.91826 -4267.1784 0.76796752 4 1 1 + 3900 538.8248 6811.7446 0.76796752 4 1 1 + 4000 531.42158 5031.2992 0.76796752 4 1 1 + 4100 539.69772 6278.9861 0.76796752 4 1 1 + 4200 519.11497 9206.6513 0.76796752 4 1 1 + 4300 518.08237 -63.769046 0.76796752 4 1 1 + 4400 582.43352 4189.0234 0.76796752 4 1 1 + 4500 541.87979 -2072.4133 0.76796752 4 1 1 + 4600 514.7508 7502.1057 0.76796752 4 1 1 + 4700 530.22173 51.50674 0.76796752 4 1 1 + 4800 507.14885 5148.7797 0.76796752 4 1 1 + 4900 516.05055 9110.3072 0.76796752 4 1 1 + 5000 552.55865 7310.0399 0.76796752 4 1 1 + 5100 581.79588 3282.8939 0.76796752 4 1 1 + 5200 523.07607 -1312.6111 0.76796752 4 1 1 + 5300 528.44235 -2242.0268 0.76796752 4 1 1 + 5400 537.63408 4599.5474 0.76796752 4 1 1 + 5500 526.75093 5551.7841 0.76796752 4 1 1 + 5600 562.74766 2764.4556 0.76796752 4 1 1 + 5700 545.12259 -3139.3468 0.76796752 4 1 1 + 5800 563.77404 4261.7786 0.76796752 4 1 1 + 5900 514.07804 4057.43 0.76796752 4 1 1 + 6000 548.42605 -2814.3308 0.76796752 4 1 1 + 6100 525.16391 -2902.5409 0.76796752 4 1 1 + 6200 504.92542 -706.19923 0.76796752 4 1 2 + 6300 531.55271 1217.7795 0.76796752 4 1 2 + 6400 537.29797 264.24006 0.76796752 4 1 2 + 6500 581.8752 2228.1037 0.76796752 4 1 2 + 6600 536.95487 -10318.365 0.76796752 4 2 2 + 6700 498.26961 5005.4587 0.76796752 5 2 2 + 6800 526.00873 -2678.0327 0.76796752 5 2 2 + 6900 542.74619 -1567.8558 0.76796752 5 2 2 + 7000 549.02037 8321.4935 0.76796752 5 2 2 + 7100 542.28295 -1513.6114 0.76796752 5 2 2 + 7200 474.70347 2120.9699 0.76796752 5 2 2 + 7300 506.58637 2588.8837 0.76796752 5 2 2 + 7400 512.45393 -2101371.7 0.76796752 5 2 3 + 7500 546.20285 -2458.3002 0.76796752 5 2 3 + 7600 551.57132 3148.9131 0.76796752 5 2 3 + 7700 544.3684 -775.59686 0.76796752 5 2 3 + 7800 511.32529 2353.0343 0.76796752 5 2 3 + 7900 520.30502 10726.007 0.76796752 5 2 3 + 8000 561.81009 12476.296 0.76796752 5 2 3 + 8100 588.85859 5905.4979 0.76796752 5 2 3 + 8200 490.1071 1132.5027 0.76796752 5 2 3 + 8300 537.65085 -1445.0979 0.76796752 5 2 3 + 8400 523.60343 -589.18012 0.76796752 5 2 3 + 8500 538.90848 -300.32152 0.76796752 5 2 3 + 8600 573.63835 5912.9027 0.76796752 5 2 3 + 8700 557.82593 2585.6634 0.76796752 5 2 3 + 8800 562.5277 -1843272.8 0.76796752 5 2 4 + 8900 564.26894 -1396.8521 0.76796752 5 2 4 + 9000 576.4382 5029.6995 0.76796752 5 2 4 + 9100 514.83258 -935.9015 0.76796752 5 2 4 + 9200 536.33755 -1671.9254 0.76796752 5 2 4 + 9300 494.49553 582.08687 0.76796752 5 2 4 + 9400 532.12156 -6991.3223 0.76796752 6 2 4 + 9500 528.87489 4587.7048 0.76796752 6 2 4 + 9600 555.92299 -3688.5966 0.76796752 6 2 4 + 9700 510.09341 1545.1276 0.76796752 6 2 4 + 9800 505.94984 -4677.2879 0.76796752 6 2 4 + 9900 531.38104 4891.0352 0.76796752 6 2 4 + 10000 517.59995 4299.0553 0.76796752 6 2 4 +Loop time of 29.4182 on 1 procs for 10000 steps with 320 atoms + +Performance: 29.370 ns/day, 0.817 hours/ns, 339.926 timesteps/s, 108.776 katom-step/s +100.0% CPU use with 1 MPI tasks x no OpenMP threads + +MPI task timing breakdown: +Section | min time | avg time | max time |%varavg| %total +--------------------------------------------------------------- +Pair | 10.883 | 10.883 | 10.883 | 0.0 | 36.99 +Bond | 8.0953 | 8.0953 | 8.0953 | 0.0 | 27.52 +Kspace | 2.6136 | 2.6136 | 2.6136 | 0.0 | 8.88 +Neigh | 1.0863 | 1.0863 | 1.0863 | 0.0 | 3.69 +Comm | 0.2095 | 0.2095 | 0.2095 | 0.0 | 0.71 +Output | 0.0019263 | 0.0019263 | 0.0019263 | 0.0 | 0.01 +Modify | 6.4695 | 6.4695 | 6.4695 | 0.0 | 21.99 +Other | | 0.05924 | | | 0.20 + +Nlocal: 320 ave 320 max 320 min +Histogram: 1 0 0 0 0 0 0 0 0 0 +Nghost: 3425 ave 3425 max 3425 min +Histogram: 1 0 0 0 0 0 0 0 0 0 +Neighs: 54783 ave 54783 max 54783 min +Histogram: 1 0 0 0 0 0 0 0 0 0 + +Total # of neighbors = 54783 +Ave neighs/atom = 171.19688 +Ave special neighs/atom = 10.3375 +Neighbor list builds = 460 +Dangerous builds = 0 + +# write_restart restart_longrun nofix +# write_data restart_longrun.data +Total wall time: 0:00:29 diff --git a/examples/PACKAGES/reaction/tiny_polystyrene/tiny_polystyrene.data b/examples/PACKAGES/reaction/tiny_polystyrene/tiny_polystyrene.data index 5f0ed4cfa6..ab12e8d4b1 100644 --- a/examples/PACKAGES/reaction/tiny_polystyrene/tiny_polystyrene.data +++ b/examples/PACKAGES/reaction/tiny_polystyrene/tiny_polystyrene.data @@ -15,6 +15,108 @@ LAMMPS data file via write_data, version 20 Nov 2019, timestep = 25000 1.7426663385337786e+00 1.8257333661465619e+01 ylo yhi 1.7426663385337786e+00 1.8257333661465619e+01 zlo zhi +Atom Type Labels + +1 cp +2 hc +3 c=1 +4 c= +5 c1 +6 c2 +7 c3 + +Bond Type Labels + +1 cp-hc +2 cp-cp +3 cp-c1 +4 hc-c=1 +5 c=1-c= +6 hc-c= +7 cp-c3 +8 hc-c3 +9 c3-c2 +10 hc-c2 +11 cp-c=1 +12 hc-c1 +13 c1-c2 + +Angle Type Labels + +1 cp-cp-hc +2 cp-cp-cp +3 cp-cp-c1 +4 cp-c1-hc +5 cp-c1-c2 +6 hc-c=1-c= +7 hc-c=-c=1 +8 hc-c=-hc +9 cp-cp-c3 +10 cp-c3-hc +11 cp-c3-c2 +12 hc-c3-c2 +13 c3-c2-c1 +14 hc-c2-c3 +15 hc-c2-hc +16 c1-c2-c1 +17 cp-cp-c=1 +18 cp-c=1-hc +19 cp-c=1-c= +20 hc-c2-c1 +21 hc-c1-c2 +22 c2-c1-c2 + +Dihedral Type Labels + +1 hc-cp-cp-c1 +2 cp-cp-cp-hc +3 cp-cp-cp-c1 +4 cp-cp-cp-cp +5 hc-cp-cp-hc +6 cp-cp-c=1-hc +7 cp-cp-c=1-c= +8 cp-c=1-c=-hc +9 hc-c=1-c=-hc +10 hc-cp-cp-c3 +11 cp-cp-cp-c3 +12 cp-cp-c1-hc +13 cp-cp-c1-c2 +14 cp-c1-c2-hc +15 hc-c1-c2-hc +16 c2-c1-c2-hc +17 cp-c1-c2-c1 +18 hc-c1-c2-c1 +19 c2-c1-c2-c1 +20 hc-cp-cp-c=1 +21 cp-cp-cp-c=1 +22 cp-cp-c3-hc +23 cp-cp-c3-c2 +24 cp-c3-c2-hc +25 cp-c3-c2-c1 +26 hc-c3-c2-hc +27 hc-c3-c2-c1 +28 c3-c2-c1-cp +29 c3-c2-c1-hc +30 c3-c2-c1-c2 +31 hc-c2-c1-cp +32 hc-c2-c1-hc +33 hc-c2-c1-c2 +34 c1-c2-c1-cp +35 c1-c2-c1-hc +36 c1-c2-c1-c2 + +Improper Type Labels + +1 cp-cp-cp-hc +2 cp-cp-cp-c1 +3 cp-c=1-hc-c= +4 hc-c=-hc-c=1 +5 cp-cp-cp-c3 +6 hc-c2-hc-c1 +7 cp-c1-hc-c2 +8 cp-cp-cp-c=1 +9 cp-c3-hc-c2 + Masses 1 12.0112 From 7383a8957b55fe647c3fa799213154cb4453ba22 Mon Sep 17 00:00:00 2001 From: Jacob Gissinger Date: Tue, 20 Dec 2022 11:41:11 -0500 Subject: [PATCH 10/47] refactor atom stabilization code --- src/REACTION/fix_bond_react.cpp | 107 ++++++++------------------------ src/REACTION/fix_bond_react.h | 1 - 2 files changed, 26 insertions(+), 82 deletions(-) diff --git a/src/REACTION/fix_bond_react.cpp b/src/REACTION/fix_bond_react.cpp index b983172860..926c31a12f 100644 --- a/src/REACTION/fix_bond_react.cpp +++ b/src/REACTION/fix_bond_react.cpp @@ -1476,9 +1476,6 @@ void FixBondReact::superimpose_algorithm() // this updates topology next step next_reneighbor = update->ntimestep; - // call limit_bond in 'global_mega_glove mode.' oh, and local mode - limit_bond(LOCAL); // add reacting atoms to nve/limit - limit_bond(GLOBAL); update_everything(); // change topology } @@ -2779,80 +2776,6 @@ void FixBondReact::dedup_mega_gloves(int dedup_mode) delete [] dup_list; } -/* ---------------------------------------------------------------------- -let's limit movement of newly bonded atoms -and exclude them from other thermostats via exclude_group -------------------------------------------------------------------------- */ - -void FixBondReact::limit_bond(int limit_bond_mode) -{ - //two types of passes: 1) while superimpose algorithm is iterating (only local atoms) - // 2) once more for global_mega_glove [after de-duplicating rxn instances] - //in second case, only add local atoms to group - //as with update_everything, we can pre-prepare these arrays, then run generic limit_bond code - - //create local, generic variables for onemol->natoms and glove - //to be filled differently on respective passes - - int nlocal = atom->nlocal; - int temp_limit_num = 0; - tagint *temp_limit_glove; - if (limit_bond_mode == LOCAL) { - int max_temp = local_num_mega * (max_natoms + 1); - temp_limit_glove = new tagint[max_temp]; - for (int j = 0; j < local_num_mega; j++) { - rxnID = local_mega_glove[0][j]; - onemol = atom->molecules[unreacted_mol[rxnID]]; - for (int i = 0; i < onemol->natoms; i++) { - temp_limit_glove[temp_limit_num++] = local_mega_glove[i+1][j]; - } - } - - } else if (limit_bond_mode == GLOBAL) { - int max_temp = global_megasize * (max_natoms + 1); - temp_limit_glove = new tagint[max_temp]; - for (int j = 0; j < global_megasize; j++) { - rxnID = global_mega_glove[0][j]; - onemol = atom->molecules[unreacted_mol[rxnID]]; - for (int i = 0; i < onemol->natoms; i++) { - if (atom->map(global_mega_glove[i+1][j]) >= 0 && - atom->map(global_mega_glove[i+1][j]) < nlocal) - temp_limit_glove[temp_limit_num++] = global_mega_glove[i+1][j]; - } - } - } - - if (temp_limit_num == 0) { - delete [] temp_limit_glove; - return; - } - - // we must keep our own list of limited atoms - // this will be a new per-atom property! - - int flag,cols; - int index1 = atom->find_custom("limit_tags",flag,cols); - int *i_limit_tags = atom->ivector[index1]; - - int *i_statted_tags; - if (stabilization_flag == 1) { - int index2 = atom->find_custom(statted_id,flag,cols); - i_statted_tags = atom->ivector[index2]; - } - - int index3 = atom->find_custom("react_tags",flag,cols); - int *i_react_tags = atom->ivector[index3]; - - for (int i = 0; i < temp_limit_num; i++) { - // update->ntimestep could be 0. so add 1 throughout - i_limit_tags[atom->map(temp_limit_glove[i])] = update->ntimestep + 1; - if (stabilization_flag == 1) i_statted_tags[atom->map(temp_limit_glove[i])] = 0; - i_react_tags[atom->map(temp_limit_glove[i])] = rxnID; - } - - delete [] temp_limit_glove; -} - /* ---------------------------------------------------------------------- let's unlimit movement of newly bonded atoms after n timesteps. we give them back to the system thermostat @@ -3055,6 +2978,21 @@ void FixBondReact::update_everything() int delta_dihed = 0; int delta_imprp = 0; + // use the following per-atom arrays to keep track of reacting atoms + + int flag,cols; + int index1 = atom->find_custom("limit_tags",flag,cols); + int *i_limit_tags = atom->ivector[index1]; + + int *i_statted_tags; + if (stabilization_flag == 1) { + int index2 = atom->find_custom(statted_id,flag,cols); + i_statted_tags = atom->ivector[index2]; + } + + int index3 = atom->find_custom("react_tags",flag,cols); + int *i_react_tags = atom->ivector[index3]; + // pass through twice // redefining 'update_num_mega' and 'update_mega_glove' each time // first pass: when glove is all local atoms @@ -3175,18 +3113,25 @@ void FixBondReact::update_everything() } // update charges and types of landlocked atoms + // also keep track of 'stabilization' groups here for (int i = 0; i < update_num_mega; i++) { rxnID = update_mega_glove[0][i]; twomol = atom->molecules[reacted_mol[rxnID]]; for (int j = 0; j < twomol->natoms; j++) { int jj = equivalences[j][1][rxnID]-1; - if (atom->map(update_mega_glove[jj+1][i]) >= 0 && - atom->map(update_mega_glove[jj+1][i]) < nlocal) { + int ilocal = atom->map(update_mega_glove[jj+1][i]); + if (ilocal >= 0 && ilocal < nlocal) { + + // update->ntimestep could be 0. so add 1 throughout + i_limit_tags[ilocal] = update->ntimestep + 1; + if (stabilization_flag == 1) i_statted_tags[ilocal] = 0; + i_react_tags[ilocal] = rxnID; + if (landlocked_atoms[j][rxnID] == 1) - type[atom->map(update_mega_glove[jj+1][i])] = twomol->type[j]; + type[ilocal] = twomol->type[j]; if (twomol->qflag && atom->q_flag && custom_charges[jj][rxnID] == 1) { double *q = atom->q; - q[atom->map(update_mega_glove[jj+1][i])] = twomol->q[j]+charge_rescale_addend; + q[ilocal] = twomol->q[j]+charge_rescale_addend; } } } diff --git a/src/REACTION/fix_bond_react.h b/src/REACTION/fix_bond_react.h index 4751bc4eef..b434699ec7 100644 --- a/src/REACTION/fix_bond_react.h +++ b/src/REACTION/fix_bond_react.h @@ -209,7 +209,6 @@ class FixBondReact : public Fix { void update_everything(); int insert_atoms(tagint **, int); void unlimit_bond(); // removes atoms from stabilization, and other post-reaction every-step operations - void limit_bond(int); void dedup_mega_gloves(int); //dedup global mega_glove void write_restart(FILE *) override; void restart(char *buf) override; From 21b14cd7e4d886cfa8140dd34d85f1732aebd7f7 Mon Sep 17 00:00:00 2001 From: Jacob Gissinger Date: Tue, 20 Dec 2022 12:46:59 -0500 Subject: [PATCH 11/47] remove now-redundant code --- src/REACTION/fix_bond_react.cpp | 19 ------------------- 1 file changed, 19 deletions(-) diff --git a/src/REACTION/fix_bond_react.cpp b/src/REACTION/fix_bond_react.cpp index 926c31a12f..7d488c3592 100644 --- a/src/REACTION/fix_bond_react.cpp +++ b/src/REACTION/fix_bond_react.cpp @@ -3858,25 +3858,6 @@ int FixBondReact::insert_atoms(tagint **my_mega_glove, int iupdate) v[n][1] = v[n][1]/vnorm*vtnorm; v[n][2] = v[n][2]/vnorm*vtnorm; modify->create_attribute(n); - - // initialize group statuses - // why aren't these more global... - int flag,cols; - int index1 = atom->find_custom("limit_tags",flag,cols); - int *i_limit_tags = atom->ivector[index1]; - - int *i_statted_tags; - if (stabilization_flag == 1) { - int index2 = atom->find_custom(statted_id,flag,cols); - i_statted_tags = atom->ivector[index2]; - } - - int index3 = atom->find_custom("react_tags",flag,cols); - int *i_react_tags = atom->ivector[index3]; - - i_limit_tags[n] = update->ntimestep + 1; - if (stabilization_flag == 1) i_statted_tags[n] = 0; - i_react_tags[n] = rxnID; } // globally update mega_glove and equivalences MPI_Allreduce(MPI_IN_PLACE,&root,1,MPI_INT,MPI_SUM,world); From 84d97a9ef7b5dca4932701a028168b9a2341d15a Mon Sep 17 00:00:00 2001 From: Jacob Gissinger Date: Tue, 20 Dec 2022 13:15:59 -0500 Subject: [PATCH 12/47] type labels for create_atoms_polystyrene example --- .../grow_styrene_post.data_template | 456 ------ .../grow_styrene_post.molecule_template | 489 +++++++ .../grow_styrene_pre.data_template | 294 ---- .../grow_styrene_pre.molecule_template | 319 ++++ .../create_atoms_polystyrene/in.grow_styrene | 10 +- .../log.24Dec20.grow_styrene.g++.1 | 196 --- .../log.24Dec20.grow_styrene.g++.4 | 196 --- .../log.4Nov2022.grow_styrene.g++.1 | 256 ++++ .../log.4Nov2022.grow_styrene.g++.4 | 256 ++++ .../create_atoms_polystyrene/trimer.data | 1303 +++++++---------- 10 files changed, 1870 insertions(+), 1905 deletions(-) delete mode 100644 examples/PACKAGES/reaction/create_atoms_polystyrene/grow_styrene_post.data_template create mode 100644 examples/PACKAGES/reaction/create_atoms_polystyrene/grow_styrene_post.molecule_template delete mode 100644 examples/PACKAGES/reaction/create_atoms_polystyrene/grow_styrene_pre.data_template create mode 100644 examples/PACKAGES/reaction/create_atoms_polystyrene/grow_styrene_pre.molecule_template delete mode 100644 examples/PACKAGES/reaction/create_atoms_polystyrene/log.24Dec20.grow_styrene.g++.1 delete mode 100644 examples/PACKAGES/reaction/create_atoms_polystyrene/log.24Dec20.grow_styrene.g++.4 create mode 100644 examples/PACKAGES/reaction/create_atoms_polystyrene/log.4Nov2022.grow_styrene.g++.1 create mode 100644 examples/PACKAGES/reaction/create_atoms_polystyrene/log.4Nov2022.grow_styrene.g++.4 diff --git a/examples/PACKAGES/reaction/create_atoms_polystyrene/grow_styrene_post.data_template b/examples/PACKAGES/reaction/create_atoms_polystyrene/grow_styrene_post.data_template deleted file mode 100644 index 7269e3a269..0000000000 --- a/examples/PACKAGES/reaction/create_atoms_polystyrene/grow_styrene_post.data_template +++ /dev/null @@ -1,456 +0,0 @@ -molecule template: end of chain plus polymerized styrene - -46 atoms -48 bonds -81 angles -121 dihedrals -35 impropers -1 fragments - -Fragments - -create_fit 34 44 - -Types - -1 1 -2 2 -3 1 -4 5 -5 1 -6 2 -7 1 -8 2 -9 1 -10 2 -11 1 -12 2 -13 2 -14 6 -15 2 -16 2 -17 1 -18 2 -19 1 -20 5 -21 1 -22 2 -23 1 -24 2 -25 1 -26 2 -27 1 -28 2 -29 2 -30 6 -31 1 -32 2 -33 1 -34 5 -35 1 -36 2 -37 1 -38 2 -39 1 -40 2 -41 1 -42 2 -43 2 -44 6 -45 2 -46 2 - -Charges - -1 -0.129000 -2 0.123700 -3 0.026600 -4 -0.018200 -5 -0.129000 -6 0.123700 -7 -0.173400 -8 0.140300 -9 -0.113400 -10 0.128800 -11 -0.173400 -12 0.140300 -13 0.051600 -14 -0.069600 -15 0.035400 -16 0.035400 -17 -0.129000 -18 0.123700 -19 0.026600 -20 -0.018200 -21 -0.129000 -22 0.123700 -23 -0.173400 -24 0.140300 -25 -0.113400 -26 0.128800 -27 -0.173400 -28 0.140300 -29 0.051600 -30 -0.069600 -31 -0.129000 -32 0.123700 -33 0.026600 -34 -0.018200 -35 -0.129000 -36 0.123700 -37 -0.173400 -38 0.140300 -39 -0.113400 -40 0.128800 -41 -0.173400 -42 0.140300 -43 0.051600 -44 -0.069600 -45 0.035400 -46 0.035400 - -Coords - -1 24.130699 1.043900 -1.309300 -2 25.062700 1.582900 -1.309300 -3 22.900700 1.753900 -1.309300 -4 22.900700 3.253900 -1.309300 -5 21.670700 1.043900 -1.309300 -6 20.738701 1.582900 -1.309300 -7 21.670700 -0.376100 -1.309300 -8 20.738701 -0.915100 -1.309300 -9 22.900700 -1.086100 -1.309300 -10 22.900700 -2.163100 -1.309300 -11 24.130699 -0.376100 -1.309300 -12 25.062700 -0.915100 -1.309300 -13 23.766701 3.658900 -0.952300 -14 21.622700 3.802900 -1.871300 -15 21.672701 4.544900 -1.970300 -16 20.979700 2.979900 -2.165300 -17 13.465800 0.682500 -1.658900 -18 14.397800 1.221500 -1.658900 -19 12.235800 1.392500 -1.658900 -20 12.235800 2.892500 -1.658900 -21 11.005800 0.682500 -1.658900 -22 10.073800 1.221500 -1.658900 -23 11.005800 -0.737500 -1.658900 -24 10.073800 -1.276500 -1.658900 -25 12.235800 -1.447500 -1.658900 -26 12.235800 -2.524500 -1.658900 -27 13.465800 -0.737500 -1.658900 -28 14.397800 -1.276500 -1.658900 -29 13.101800 3.297500 -1.301900 -30 10.957800 3.441500 -2.220900 -31 18.663500 0.855500 -1.372100 -32 19.595501 1.394500 -1.372100 -33 17.433500 1.565500 -1.372100 -34 17.433500 3.065500 -1.372100 -35 16.203501 0.855500 -1.372100 -36 15.271500 1.394500 -1.372100 -37 16.203501 -0.564500 -1.372100 -38 15.271500 -1.103500 -1.372100 -39 17.433500 -1.274500 -1.372100 -40 17.433500 -2.351500 -1.372100 -41 18.663500 -0.564500 -1.372100 -42 19.595501 -1.103500 -1.372100 -43 18.299500 3.470500 -1.015100 -44 16.155500 3.614500 -1.934100 -45 16.205500 4.356500 -2.033100 -46 15.512500 2.791500 -2.228100 - -Bonds - -1 1 1 2 -2 2 1 3 -3 2 1 11 -4 11 3 4 -5 2 3 5 -6 12 13 4 -7 13 4 14 -8 1 5 6 -9 2 5 7 -10 1 7 8 -11 2 7 9 -12 1 9 10 -13 2 9 11 -14 1 11 12 -15 10 15 14 -16 10 16 14 -17 9 14 34 -18 1 17 18 -19 2 17 19 -20 2 17 27 -21 7 19 20 -22 2 19 21 -23 8 29 20 -24 9 30 20 -25 9 44 20 -26 1 21 22 -27 2 21 23 -28 1 23 24 -29 2 23 25 -30 1 25 26 -31 2 25 27 -32 1 27 28 -33 1 31 32 -34 2 31 33 -35 2 31 41 -36 7 33 34 -37 2 33 35 -38 8 43 34 -39 9 44 34 -40 1 35 36 -41 2 35 37 -42 1 37 38 -43 2 37 39 -44 1 39 40 -45 2 39 41 -46 1 41 42 -47 10 45 44 -48 10 46 44 - -Angles - -1 1 3 1 2 -2 1 11 1 2 -3 2 3 1 11 -4 17 1 3 4 -5 2 1 3 5 -6 17 5 3 4 -7 18 3 4 13 -8 19 3 4 14 -9 20 13 4 14 -10 1 3 5 6 -11 2 3 5 7 -12 1 7 5 6 -13 1 5 7 8 -14 2 5 7 9 -15 1 9 7 8 -16 1 7 9 10 -17 2 7 9 11 -18 1 11 9 10 -19 2 1 11 9 -20 1 1 11 12 -21 1 9 11 12 -22 21 15 14 4 -23 21 16 14 4 -24 22 4 14 34 -25 15 15 14 16 -26 14 15 14 34 -27 14 16 14 34 -28 1 19 17 18 -29 1 27 17 18 -30 2 19 17 27 -31 9 17 19 20 -32 2 17 19 21 -33 9 21 19 20 -34 10 19 20 29 -35 11 19 20 30 -36 11 19 20 44 -37 12 29 20 30 -38 12 29 20 44 -39 13 30 20 44 -40 1 19 21 22 -41 2 19 21 23 -42 1 23 21 22 -43 1 21 23 24 -44 2 21 23 25 -45 1 25 23 24 -46 1 23 25 26 -47 2 23 25 27 -48 1 27 25 26 -49 2 17 27 25 -50 1 17 27 28 -51 1 25 27 28 -52 1 33 31 32 -53 1 41 31 32 -54 2 33 31 41 -55 9 31 33 34 -56 2 31 33 35 -57 9 35 33 34 -58 11 33 34 14 -59 12 43 34 14 -60 13 14 34 44 -61 10 33 34 43 -62 11 33 34 44 -63 12 43 34 44 -64 1 33 35 36 -65 2 33 35 37 -66 1 37 35 36 -67 1 35 37 38 -68 2 35 37 39 -69 1 39 37 38 -70 1 37 39 40 -71 2 37 39 41 -72 1 41 39 40 -73 2 31 41 39 -74 1 31 41 42 -75 1 39 41 42 -76 16 20 44 34 -77 14 45 44 20 -78 14 46 44 20 -79 14 45 44 34 -80 14 46 44 34 -81 15 45 44 46 - -Dihedrals - -1 20 2 1 3 4 -2 2 5 3 1 2 -3 21 11 1 3 4 -4 4 11 1 3 5 -5 2 9 11 1 2 -6 5 2 1 11 12 -7 4 3 1 11 9 -8 2 3 1 11 12 -9 22 1 3 4 13 -10 23 1 3 4 14 -11 22 5 3 4 13 -12 23 5 3 4 14 -13 2 1 3 5 6 -14 4 1 3 5 7 -15 20 6 5 3 4 -16 21 7 5 3 4 -17 24 3 4 14 15 -18 24 3 4 14 16 -19 25 3 4 14 34 -20 26 13 4 14 15 -21 26 13 4 14 16 -22 27 13 4 14 34 -23 2 3 5 7 8 -24 4 3 5 7 9 -25 5 6 5 7 8 -26 2 9 7 5 6 -27 2 5 7 9 10 -28 4 5 7 9 11 -29 5 8 7 9 10 -30 2 11 9 7 8 -31 4 7 9 11 1 -32 2 7 9 11 12 -33 2 1 11 9 10 -34 5 10 9 11 12 -35 28 4 14 34 33 -36 29 4 14 34 43 -37 30 4 14 34 44 -38 31 15 14 34 33 -39 32 15 14 34 43 -40 33 15 14 34 44 -41 31 16 14 34 33 -42 32 16 14 34 43 -43 33 16 14 34 44 -44 10 18 17 19 20 -45 2 21 19 17 18 -46 11 27 17 19 20 -47 4 27 17 19 21 -48 2 25 27 17 18 -49 5 18 17 27 28 -50 4 19 17 27 25 -51 2 19 17 27 28 -52 12 17 19 20 29 -53 13 17 19 20 30 -54 13 17 19 20 44 -55 12 21 19 20 29 -56 13 21 19 20 30 -57 13 21 19 20 44 -58 2 17 19 21 22 -59 4 17 19 21 23 -60 10 22 21 19 20 -61 11 23 21 19 20 -62 34 34 44 20 19 -63 31 45 44 20 19 -64 31 46 44 20 19 -65 35 34 44 20 29 -66 32 45 44 20 29 -67 32 46 44 20 29 -68 36 34 44 20 30 -69 33 45 44 20 30 -70 33 46 44 20 30 -71 2 19 21 23 24 -72 4 19 21 23 25 -73 5 22 21 23 24 -74 2 25 23 21 22 -75 2 21 23 25 26 -76 4 21 23 25 27 -77 5 24 23 25 26 -78 2 27 25 23 24 -79 4 23 25 27 17 -80 2 23 25 27 28 -81 2 17 27 25 26 -82 5 26 25 27 28 -83 10 32 31 33 34 -84 2 35 33 31 32 -85 11 41 31 33 34 -86 4 41 31 33 35 -87 2 39 41 31 32 -88 5 32 31 41 42 -89 4 33 31 41 39 -90 2 33 31 41 42 -91 13 31 33 34 14 -92 12 31 33 34 43 -93 13 31 33 34 44 -94 13 35 33 34 14 -95 12 35 33 34 43 -96 13 35 33 34 44 -97 2 31 33 35 36 -98 4 31 33 35 37 -99 10 36 35 33 34 -100 11 37 35 33 34 -101 36 20 44 34 14 -102 33 45 44 34 14 -103 33 46 44 34 14 -104 34 20 44 34 33 -105 31 45 44 34 33 -106 31 46 44 34 33 -107 35 20 44 34 43 -108 32 45 44 34 43 -109 32 46 44 34 43 -110 2 33 35 37 38 -111 4 33 35 37 39 -112 5 36 35 37 38 -113 2 39 37 35 36 -114 2 35 37 39 40 -115 4 35 37 39 41 -116 5 38 37 39 40 -117 2 41 39 37 38 -118 4 37 39 41 31 -119 2 37 39 41 42 -120 2 31 41 39 40 -121 5 40 39 41 42 - -Impropers - -1 1 3 1 11 2 -2 8 1 3 5 4 -3 9 3 4 13 14 -4 1 3 5 7 6 -5 1 5 7 9 8 -6 1 7 9 11 10 -7 1 1 11 9 12 -8 1 19 17 27 18 -9 5 17 19 21 20 -10 1 19 21 23 22 -11 1 21 23 25 24 -12 1 23 25 27 26 -13 1 17 27 25 28 -14 1 33 31 41 32 -15 5 31 33 35 34 -16 1 33 35 37 36 -17 1 35 37 39 38 -18 1 37 39 41 40 -19 1 31 41 39 42 -20 1 15 14 16 4 -21 1 15 14 4 34 -22 1 16 14 4 34 -23 1 15 14 16 34 -24 1 19 20 29 30 -25 1 19 20 29 44 -26 1 19 20 30 44 -27 1 29 20 30 44 -28 1 33 34 43 14 -29 1 33 34 14 44 -30 1 43 34 14 44 -31 1 33 34 43 44 -32 1 45 44 34 20 -33 1 46 44 34 20 -34 1 45 44 46 20 -35 1 45 44 46 34 diff --git a/examples/PACKAGES/reaction/create_atoms_polystyrene/grow_styrene_post.molecule_template b/examples/PACKAGES/reaction/create_atoms_polystyrene/grow_styrene_post.molecule_template new file mode 100644 index 0000000000..62b42afd3e --- /dev/null +++ b/examples/PACKAGES/reaction/create_atoms_polystyrene/grow_styrene_post.molecule_template @@ -0,0 +1,489 @@ +molecule template: end of chain plus polymerized styrene + + 46 atoms + 48 bonds + 81 angles + 121 dihedrals + 19 impropers + 1 fragments + +Fragments + + create_fit 34 44 + +Coords + + 1 24.130699158 1.043900013 -1.309299946 + 2 25.062700272 1.582900047 -1.309299946 + 3 22.900699615 1.753900051 -1.309299946 + 4 22.900699615 3.253900051 -1.309299946 + 5 21.670700073 1.043900013 -1.309299946 + 6 20.738700867 1.582900047 -1.309299946 + 7 21.670700073 -0.376100004 -1.309299946 + 8 20.738700867 -0.915099978 -1.309299946 + 9 22.900699615 -1.086099982 -1.309299946 + 10 22.900699615 -2.163100004 -1.309299946 + 11 24.130699158 -0.376100004 -1.309299946 + 12 25.062700272 -0.915099978 -1.309299946 + 13 23.766700745 3.658900023 -0.952300012 + 14 21.622699738 3.802900076 -1.871299982 + 15 21.672700882 4.544899940 -1.970299959 + 16 20.979700089 2.979899883 -2.165299892 + 17 13.465800285 0.682500005 -1.658900023 + 18 14.397800446 1.221500039 -1.658900023 + 19 12.235799789 1.392500043 -1.658900023 + 20 12.235799789 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34 + 16 hc-cp-cp-cp 33 35 37 36 + 17 hc-cp-cp-cp 35 37 39 38 + 18 hc-cp-cp-cp 37 39 41 40 + 19 hc-cp-cp-cp 31 41 39 42 diff --git a/examples/PACKAGES/reaction/create_atoms_polystyrene/grow_styrene_pre.data_template b/examples/PACKAGES/reaction/create_atoms_polystyrene/grow_styrene_pre.data_template deleted file mode 100644 index d04fefccf5..0000000000 --- a/examples/PACKAGES/reaction/create_atoms_polystyrene/grow_styrene_pre.data_template +++ /dev/null @@ -1,294 +0,0 @@ -molecule template: end of styrene chain - -30 atoms -31 bonds -51 angles -73 dihedrals -21 impropers - -Types - -1 2 -2 2 -3 6 -4 2 -5 2 -6 1 -7 2 -8 1 -9 2 -10 1 -11 2 -12 1 -13 5 -14 1 -15 2 -16 1 -17 1 -18 2 -19 1 -20 5 -21 1 -22 2 -23 1 -24 2 -25 1 -26 2 -27 1 -28 2 -29 2 -30 6 - -Coords - -1 59.89981112372972 62.733697275315585 59.09884284578856 -2 61.41970248324232 63.42116581894993 59.52874545893742 -3 60.864754970096406 62.91724243011892 59.559720865992695 -4 62.139819000186826 61.41011937002877 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0.123700 + 23 -0.173400 + 24 0.140300 + 25 -0.113400 + 26 0.128800 + 27 -0.173400 + 28 0.140300 + 29 0.051600 + 30 -0.069600 + +Molecules + + 1 1 + 2 1 + 3 1 + 4 1 + 5 1 + 6 1 + 7 1 + 8 1 + 9 1 + 10 1 + 11 1 + 12 1 + 13 1 + 14 1 + 15 1 + 16 1 + 17 1 + 18 1 + 19 1 + 20 1 + 21 1 + 22 1 + 23 1 + 24 1 + 25 1 + 26 1 + 27 1 + 28 1 + 29 1 + 30 1 + +Bonds + + 1 hc-c2 1 3 + 2 hc-c2 2 3 + 3 c1-c2 3 13 + 4 c1-c2 3 20 + 5 hc-c1 4 13 + 6 hc-cp 5 6 + 7 cp-cp 6 8 + 8 cp-cp 6 16 + 9 hc-cp 7 8 + 10 cp-cp 8 10 + 11 hc-cp 9 10 + 12 cp-cp 10 12 + 13 hc-cp 11 12 + 14 cp-cp 12 14 + 15 cp-c1 14 13 + 16 cp-cp 14 16 + 17 hc-cp 15 16 + 18 hc-cp 18 17 + 19 cp-cp 17 19 + 20 cp-cp 17 27 + 21 cp-c1 19 20 + 22 cp-cp 19 21 + 23 c1-c2 30 20 + 24 hc-c1 29 20 + 25 hc-cp 22 21 + 26 cp-cp 21 23 + 27 hc-cp 24 23 + 28 cp-cp 23 25 + 29 hc-cp 26 25 + 30 cp-cp 25 27 + 31 hc-cp 28 27 + +Angles + + 1 hc-c2-hc 1 3 2 + 2 hc-c2-c1 1 3 13 + 3 hc-c2-c1 1 3 20 + 4 hc-c2-c1 2 3 13 + 5 hc-c2-c1 2 3 20 + 6 c1-c2-c1 13 3 20 + 7 hc-cp-cp 5 6 8 + 8 hc-cp-cp 5 6 16 + 9 cp-cp-cp 8 6 16 + 10 hc-cp-cp 7 8 6 + 11 cp-cp-cp 6 8 10 + 12 hc-cp-cp 7 8 10 + 13 hc-cp-cp 9 10 8 + 14 cp-cp-cp 8 10 12 + 15 hc-cp-cp 9 10 12 + 16 hc-cp-cp 11 12 10 + 17 cp-cp-cp 10 12 14 + 18 hc-cp-cp 11 12 14 + 19 hc-c1-c2 4 13 3 + 20 cp-c1-c2 3 13 14 + 21 hc-c1-cp 4 13 14 + 22 cp-cp-c1 12 14 13 + 23 cp-cp-cp 12 14 16 + 24 cp-cp-c1 16 14 13 + 25 cp-cp-cp 6 16 14 + 26 hc-cp-cp 15 16 6 + 27 hc-cp-cp 15 16 14 + 28 hc-cp-cp 18 17 19 + 29 hc-cp-cp 18 17 27 + 30 cp-cp-cp 19 17 27 + 31 cp-cp-c1 17 19 20 + 32 cp-cp-cp 17 19 21 + 33 cp-cp-c1 21 19 20 + 34 cp-c1-c2 3 20 19 + 35 c2-c1-c2 3 20 30 + 36 hc-c1-c2 29 20 3 + 37 cp-c1-c2 30 20 19 + 38 hc-c1-cp 29 20 19 + 39 hc-c1-c2 29 20 30 + 40 hc-cp-cp 22 21 19 + 41 cp-cp-cp 19 21 23 + 42 hc-cp-cp 22 21 23 + 43 hc-cp-cp 24 23 21 + 44 cp-cp-cp 21 23 25 + 45 hc-cp-cp 24 23 25 + 46 hc-cp-cp 26 25 23 + 47 cp-cp-cp 23 25 27 + 48 hc-cp-cp 26 25 27 + 49 cp-cp-cp 17 27 25 + 50 hc-cp-cp 28 27 17 + 51 hc-cp-cp 28 27 25 + +Dihedrals + + 1 hc-c1-c2-hc 1 3 13 4 + 2 cp-c1-c2-hc 1 3 13 14 + 3 hc-c1-c2-hc 2 3 13 4 + 4 cp-c1-c2-hc 2 3 13 14 + 5 hc-c1-c2-c1 20 3 13 4 + 6 cp-c1-c2-c1 20 3 13 14 + 7 cp-c1-c2-hc 1 3 20 19 + 8 c2-c1-c2-hc 1 3 20 30 + 9 hc-c1-c2-hc 1 3 20 29 + 10 cp-c1-c2-hc 2 3 20 19 + 11 c2-c1-c2-hc 2 3 20 30 + 12 hc-c1-c2-hc 2 3 20 29 + 13 cp-c1-c2-c1 13 3 20 19 + 14 c2-c1-c2-c1 13 3 20 30 + 15 hc-c1-c2-c1 13 3 20 29 + 16 hc-cp-cp-hc 5 6 8 7 + 17 hc-cp-cp-cp 5 6 8 10 + 18 hc-cp-cp-cp 7 8 6 16 + 19 cp-cp-cp-cp 16 6 8 10 + 20 hc-cp-cp-cp 5 6 16 14 + 21 hc-cp-cp-hc 5 6 16 15 + 22 cp-cp-cp-cp 8 6 16 14 + 23 hc-cp-cp-cp 15 16 6 8 + 24 hc-cp-cp-cp 9 10 8 6 + 25 cp-cp-cp-cp 6 8 10 12 + 26 hc-cp-cp-hc 7 8 10 9 + 27 hc-cp-cp-cp 7 8 10 12 + 28 hc-cp-cp-cp 11 12 10 8 + 29 cp-cp-cp-cp 8 10 12 14 + 30 hc-cp-cp-hc 9 10 12 11 + 31 hc-cp-cp-cp 9 10 12 14 + 32 cp-cp-cp-c1 10 12 14 13 + 33 cp-cp-cp-cp 10 12 14 16 + 34 hc-cp-cp-c1 11 12 14 13 + 35 hc-cp-cp-cp 11 12 14 16 + 36 cp-cp-c1-c2 12 14 13 3 + 37 cp-cp-c1-c2 16 14 13 3 + 38 cp-cp-c1-hc 12 14 13 4 + 39 cp-cp-c1-hc 16 14 13 4 + 40 cp-cp-cp-cp 12 14 16 6 + 41 hc-cp-cp-cp 15 16 14 12 + 42 cp-cp-cp-c1 6 16 14 13 + 43 hc-cp-cp-c1 15 16 14 13 + 44 hc-cp-cp-c1 18 17 19 20 + 45 hc-cp-cp-cp 18 17 19 21 + 46 cp-cp-cp-c1 27 17 19 20 + 47 cp-cp-cp-cp 27 17 19 21 + 48 hc-cp-cp-cp 18 17 27 25 + 49 hc-cp-cp-hc 18 17 27 28 + 50 cp-cp-cp-cp 19 17 27 25 + 51 hc-cp-cp-cp 28 27 17 19 + 52 cp-cp-c1-c2 17 19 20 3 + 53 cp-cp-c1-c2 17 19 20 30 + 54 cp-cp-c1-hc 17 19 20 29 + 55 cp-cp-c1-c2 21 19 20 3 + 56 cp-cp-c1-c2 21 19 20 30 + 57 cp-cp-c1-hc 21 19 20 29 + 58 hc-cp-cp-cp 22 21 19 17 + 59 cp-cp-cp-cp 17 19 21 23 + 60 hc-cp-cp-c1 22 21 19 20 + 61 cp-cp-cp-c1 23 21 19 20 + 62 hc-cp-cp-cp 24 23 21 19 + 63 cp-cp-cp-cp 19 21 23 25 + 64 hc-cp-cp-hc 22 21 23 24 + 65 hc-cp-cp-cp 22 21 23 25 + 66 hc-cp-cp-cp 26 25 23 21 + 67 cp-cp-cp-cp 21 23 25 27 + 68 hc-cp-cp-hc 24 23 25 26 + 69 hc-cp-cp-cp 24 23 25 27 + 70 cp-cp-cp-cp 23 25 27 17 + 71 hc-cp-cp-cp 28 27 25 23 + 72 hc-cp-cp-cp 26 25 27 17 + 73 hc-cp-cp-hc 26 25 27 28 + +Impropers + + 1 hc-cp-cp-cp 5 6 8 16 + 2 hc-cp-cp-cp 7 8 6 10 + 3 hc-cp-cp-cp 9 10 8 12 + 4 hc-cp-cp-cp 11 12 10 14 + 5 hc-c1-cp-c2 4 13 3 14 + 6 cp-cp-cp-c1 12 14 16 13 + 7 hc-cp-cp-cp 15 16 14 6 + 8 hc-cp-cp-cp 18 17 19 27 + 9 cp-cp-cp-c1 17 19 21 20 + 10 hc-cp-cp-cp 22 21 19 23 + 11 hc-cp-cp-cp 24 23 21 25 + 12 hc-cp-cp-cp 26 25 23 27 + 13 hc-cp-cp-cp 28 27 25 17 diff --git a/examples/PACKAGES/reaction/create_atoms_polystyrene/in.grow_styrene b/examples/PACKAGES/reaction/create_atoms_polystyrene/in.grow_styrene index 6e34fd2a67..b17b321fe5 100644 --- a/examples/PACKAGES/reaction/create_atoms_polystyrene/in.grow_styrene +++ b/examples/PACKAGES/reaction/create_atoms_polystyrene/in.grow_styrene @@ -6,9 +6,7 @@ boundary p p p atom_style full -kspace_style pppm 1.0e-4 - -pair_style lj/class2/coul/long 8.5 +pair_style lj/class2/coul/cut 8.5 angle_style class2 @@ -27,13 +25,13 @@ read_data trimer.data & extra/improper/per/atom 25 & extra/special/per/atom 25 -molecule mol1 grow_styrene_pre.data_template -molecule mol2 grow_styrene_post.data_template +molecule mol1 grow_styrene_pre.molecule_template +molecule mol2 grow_styrene_post.molecule_template fix myrxns all bond/react stabilization yes statted_grp .03 & react rxn1 all 1 0 3.0 mol1 mol2 grow_styrene.map & modify_create fit create_fit overlap 2.0 & - stabilize_steps 100 max_rxn 30 + stabilize_steps 200 max_rxn 30 fix 1 statted_grp_REACT nvt temp $T $T 100 diff --git a/examples/PACKAGES/reaction/create_atoms_polystyrene/log.24Dec20.grow_styrene.g++.1 b/examples/PACKAGES/reaction/create_atoms_polystyrene/log.24Dec20.grow_styrene.g++.1 deleted file mode 100644 index 5f1f2c6698..0000000000 --- a/examples/PACKAGES/reaction/create_atoms_polystyrene/log.24Dec20.grow_styrene.g++.1 +++ /dev/null @@ -1,196 +0,0 @@ -LAMMPS (24 Dec 2020) -Reading data file ... - orthogonal box = (50.000000 50.000000 50.000000) to (250.00000 250.00000 250.00000) - 1 by 1 by 1 MPI processor grid - reading atoms ... - 48 atoms - reading velocities ... - 48 velocities - scanning bonds ... - 8 = max bonds/atom - scanning angles ... - 21 = max angles/atom - scanning dihedrals ... - 33 = max dihedrals/atom - scanning impropers ... - 29 = max impropers/atom - reading bonds ... - 50 bonds - reading angles ... - 84 angles - reading dihedrals ... - 127 dihedrals - reading impropers ... - 36 impropers -Finding 1-2 1-3 1-4 neighbors ... - special bond factors lj: 0 0 0 - special bond factors coul: 0 0 0 - 4 = max # of 1-2 neighbors - 8 = max # of 1-3 neighbors - 17 = max # of 1-4 neighbors - 46 = max # of special neighbors - special bonds CPU = 0.000 seconds - read_data CPU = 0.077 seconds -Read molecule template mol1: - 1 molecules - 30 atoms with max type 6 - 31 bonds with max type 10 - 51 angles with max type 16 - 73 dihedrals with max type 19 - 21 impropers with max type 7 -Read molecule template mol2: - 1 molecules - 46 atoms with max type 6 - 48 bonds with max type 13 - 81 angles with max type 22 - 121 dihedrals with max type 36 - 35 impropers with max type 9 -dynamic group bond_react_MASTER_group defined -dynamic group statted_grp_REACT defined -PPPM initialization ... -WARNING: System is not charge neutral, net charge = -0.00060000000 (../kspace.cpp:324) - using 12-bit tables for long-range coulomb (../kspace.cpp:339) - G vector (1/distance) = 0.20144813 - grid = 45 45 45 - stencil order = 5 - estimated absolute RMS force accuracy = 0.00053712952 - estimated relative force accuracy = 1.6175496e-06 - using double precision KISS FFT - 3d grid and FFT values/proc = 125000 91125 -Neighbor list info ... - update every 1 steps, delay 10 steps, check yes - max neighbors/atom: 2000, page size: 100000 - master list distance cutoff = 10.5 - ghost atom cutoff = 10.5 - binsize = 5.25, bins = 39 39 39 - 2 neighbor lists, perpetual/occasional/extra = 1 1 0 - (1) pair lj/class2/coul/long, perpetual - attributes: half, newton on - pair build: half/bin/newton - stencil: half/bin/3d/newton - bin: standard - (2) fix bond/react, occasional, copy from (1) - attributes: half, newton on - pair build: copy - stencil: none - bin: none -Setting up Verlet run ... - Unit style : real - Current step : 0 - Time step : 1 -Per MPI rank memory allocation (min/avg/max) = 48.02 | 48.02 | 48.02 Mbytes -Step Temp Press Density f_myrxns[1] - 0 496.23742 0.9983211 6.4856516e-05 0 - 100 534.05394 -0.76952227 6.4856516e-05 0 - 200 552.2225 -0.55375493 6.4856516e-05 0 - 300 857.52834 -0.4272061 8.6475354e-05 1 - 400 714.10681 1.5004615 8.6475354e-05 1 - 500 678.19171 0.21965471 8.6475354e-05 1 - 600 572.3234 0.87879933 8.6475354e-05 1 - 700 996.17398 -0.24269717 0.00010809419 2 - 800 904.50395 1.3662054 0.00010809419 2 - 900 1097.1568 -2.2909907 0.00012971303 3 - 1000 954.08892 1.7705672 0.00012971303 3 - 1100 1102.0377 -1.7018446 0.00015133187 4 - 1200 1239.785 -0.30442903 0.00015133187 4 - 1300 1388.4127 1.3301175 0.00017295071 5 - 1400 1559.3853 1.6709729 0.00017295071 5 - 1500 1471.8623 0.8268427 0.00017295071 5 - 1600 1543.6793 2.1987908 0.00019456955 6 - 1700 1694.5595 0.48852817 0.00019456955 6 - 1800 1632.7737 -1.4617692 0.00021618839 7 - 1900 1922.6502 1.1664257 0.00021618839 7 - 2000 2223.503 -0.95799878 0.00023780722 8 - 2100 2142.6035 0.88444463 0.00025942606 9 - 2200 2298.8636 3.4239313 0.00025942606 9 - 2300 2252.4355 0.82167302 0.00025942606 9 - 2400 2321.0788 1.7499714 0.00025942606 9 - 2500 2095.6715 0.55288444 0.00025942606 9 - 2600 2136.0316 -3.833114 0.00025942606 9 - 2700 2466.3134 -2.2519511 0.00025942606 9 - 2800 2294.3454 1.0637304 0.00025942606 9 - 2900 2340.3891 1.3997049 0.0002810449 10 - 3000 2272.0013 -0.27591886 0.0002810449 10 - 3100 2333.9696 -0.11772138 0.0002810449 10 - 3200 2409.0946 -1.025473 0.0002810449 10 - 3300 2148.023 1.6752329 0.0002810449 10 - 3400 2267.636 -0.45297583 0.0002810449 10 - 3500 2457.622 0.35627297 0.0002810449 10 - 3600 2288.008 -15.516626 0.00030266374 11 - 3700 2458.2681 1.4571773 0.00030266374 11 - 3800 2566.7623 -29.140553 0.00032428258 12 - 3900 2839.4062 0.64583638 0.00032428258 12 - 4000 2893.9852 -52.954497 0.00034590142 13 - 4100 3021.3611 -65.03731 0.00036752025 14 - 4200 3002.7136 1.5750081 0.00036752025 14 - 4300 3218.6248 -120.74039 0.00038913909 15 - 4400 3345.1482 -0.96545269 0.00038913909 15 - 4500 3603.2429 1.2438833 0.00038913909 15 - 4600 3129.8814 -249.91806 0.00041075793 16 - 4700 3769.052 -289.24351 0.00043237677 17 - 4800 3560.4714 -3.1655406 0.00043237677 17 - 4900 3452.2717 -2.1270765 0.00043237677 17 - 5000 3594.3247 -523.48506 0.00045399561 18 - 5100 3578.4199 1.0009097 0.00045399561 18 - 5200 3822.1566 1.0526914 0.00047561445 19 - 5300 3901.8883 -0.14607602 0.00047561445 19 - 5400 4059.3644 -1.7789927 0.00049723329 20 - 5500 4163.6847 1.0240127 0.00049723329 20 - 5600 4109.1649 0.80199787 0.00049723329 20 - 5700 4391.2091 2.8730036 0.00049723329 20 - 5800 4279.6579 -0.36499822 0.00051885212 21 - 5900 4296.2695 -1.3064528 0.00051885212 21 - 6000 4065.3758 -2.0483224 0.00051885212 21 - 6100 4772.5362 -2.6814694 0.00054047096 22 - 6200 4627.029 2.999215 0.0005620898 23 - 6300 5120.7881 0.65372968 0.00058370864 24 - 6400 4588.9559 3.7570705 0.00058370864 24 - 6500 5008.7814 2.3595833 0.00060532748 25 - 6600 5195.0053 1.4641612 0.00060532748 25 - 6700 5622.293 -0.33396047 0.00062694632 26 - 6800 5515.1957 -4.234874 0.00062694632 26 - 6900 5156.7455 0.40171954 0.00064856516 27 - 7000 5120.1639 -1.6065245 0.00064856516 27 - 7100 5650.0327 0.94436323 0.00067018399 28 - 7200 5985.1115 -3.8940347 0.00069180283 29 - 7300 5983.197 0.5293568 0.00069180283 29 - 7400 6001.1559 -0.13712834 0.00071342167 30 - 7500 5889.2134 0.17230892 0.00071342167 30 - 7600 5797.31 2.0920058 0.00071342167 30 - 7700 5865.2783 -0.18556395 0.00071342167 30 - 7800 6207.0659 -5.6237083 0.00071342167 30 - 7900 5627.5108 -2.3718942 0.00071342167 30 - 8000 5823.9502 -0.85418578 0.00071342167 30 -Loop time of 184.87 on 1 procs for 8000 steps with 528 atoms - -Performance: 3.739 ns/day, 6.419 hours/ns, 43.274 timesteps/s -99.9% CPU use with 1 MPI tasks x no OpenMP threads - -MPI task timing breakdown: -Section | min time | avg time | max time |%varavg| %total ---------------------------------------------------------------- -Pair | 3.3043 | 3.3043 | 3.3043 | 0.0 | 1.79 -Bond | 8.0003 | 8.0003 | 8.0003 | 0.0 | 4.33 -Kspace | 168.33 | 168.33 | 168.33 | 0.0 | 91.05 -Neigh | 4.6322 | 4.6322 | 4.6322 | 0.0 | 2.51 -Comm | 0.077927 | 0.077927 | 0.077927 | 0.0 | 0.04 -Output | 0.0020548 | 0.0020548 | 0.0020548 | 0.0 | 0.00 -Modify | 0.5005 | 0.5005 | 0.5005 | 0.0 | 0.27 -Other | | 0.02483 | | | 0.01 - -Nlocal: 528.000 ave 528 max 528 min -Histogram: 1 0 0 0 0 0 0 0 0 0 -Nghost: 341.000 ave 341 max 341 min -Histogram: 1 0 0 0 0 0 0 0 0 0 -Neighs: 35111.0 ave 35111 max 35111 min -Histogram: 1 0 0 0 0 0 0 0 0 0 - -Total # of neighbors = 35111 -Ave neighs/atom = 66.498106 -Ave special neighs/atom = 11.409091 -Neighbor list builds = 8000 -Dangerous builds = 0 - -Please see the log.cite file for references relevant to this simulation - -Total wall time: 0:03:05 diff --git a/examples/PACKAGES/reaction/create_atoms_polystyrene/log.24Dec20.grow_styrene.g++.4 b/examples/PACKAGES/reaction/create_atoms_polystyrene/log.24Dec20.grow_styrene.g++.4 deleted file mode 100644 index 8daa6d8161..0000000000 --- a/examples/PACKAGES/reaction/create_atoms_polystyrene/log.24Dec20.grow_styrene.g++.4 +++ /dev/null @@ -1,196 +0,0 @@ -LAMMPS (24 Dec 2020) -Reading data file ... - orthogonal box = (50.000000 50.000000 50.000000) to (250.00000 250.00000 250.00000) - 1 by 2 by 2 MPI processor grid - reading atoms ... - 48 atoms - reading velocities ... - 48 velocities - scanning bonds ... - 8 = max bonds/atom - scanning angles ... - 21 = max angles/atom - scanning dihedrals ... - 33 = max dihedrals/atom - scanning impropers ... - 29 = max impropers/atom - reading bonds ... - 50 bonds - reading angles ... - 84 angles - reading dihedrals ... - 127 dihedrals - reading impropers ... - 36 impropers -Finding 1-2 1-3 1-4 neighbors ... - special bond factors lj: 0 0 0 - special bond factors coul: 0 0 0 - 4 = max # of 1-2 neighbors - 8 = max # of 1-3 neighbors - 17 = max # of 1-4 neighbors - 46 = max # of special neighbors - special bonds CPU = 0.000 seconds - read_data CPU = 0.007 seconds -Read molecule template mol1: - 1 molecules - 30 atoms with max type 6 - 31 bonds with max type 10 - 51 angles with max type 16 - 73 dihedrals with max type 19 - 21 impropers with max type 7 -Read molecule template mol2: - 1 molecules - 46 atoms with max type 6 - 48 bonds with max type 13 - 81 angles with max type 22 - 121 dihedrals with max type 36 - 35 impropers with max type 9 -dynamic group bond_react_MASTER_group defined -dynamic group statted_grp_REACT defined -PPPM initialization ... -WARNING: System is not charge neutral, net charge = -0.00060000000 (../kspace.cpp:324) - using 12-bit tables for long-range coulomb (../kspace.cpp:339) - G vector (1/distance) = 0.20144813 - grid = 45 45 45 - stencil order = 5 - estimated absolute RMS force accuracy = 0.00053712952 - estimated relative force accuracy = 1.6175496e-06 - using double precision KISS FFT - 3d grid and FFT values/proc = 39200 24300 -Neighbor list info ... - update every 1 steps, delay 10 steps, check yes - max neighbors/atom: 2000, page size: 100000 - master list distance cutoff = 10.5 - ghost atom cutoff = 10.5 - binsize = 5.25, bins = 39 39 39 - 2 neighbor lists, perpetual/occasional/extra = 1 1 0 - (1) pair lj/class2/coul/long, perpetual - attributes: half, newton on - pair build: half/bin/newton - stencil: half/bin/3d/newton - bin: standard - (2) fix bond/react, occasional, copy from (1) - attributes: half, newton on - pair build: copy - stencil: none - bin: none -Setting up Verlet run ... - Unit style : real - Current step : 0 - Time step : 1 -Per MPI rank memory allocation (min/avg/max) = 38.70 | 38.92 | 39.43 Mbytes -Step Temp Press Density f_myrxns[1] - 0 496.23742 0.9983211 6.4856516e-05 0 - 100 534.05394 -0.76952227 6.4856516e-05 0 - 200 552.2225 -0.55375493 6.4856516e-05 0 - 300 857.52834 -0.4272061 8.6475354e-05 1 - 400 714.10681 1.5004615 8.6475354e-05 1 - 500 678.19171 0.21965471 8.6475354e-05 1 - 600 572.3234 0.87879933 8.6475354e-05 1 - 700 996.17398 -0.24269717 0.00010809419 2 - 800 904.50395 1.3662054 0.00010809419 2 - 900 1097.1568 -2.2909907 0.00012971303 3 - 1000 954.08892 1.7705672 0.00012971303 3 - 1100 1102.0377 -1.7018446 0.00015133187 4 - 1200 1239.785 -0.30442903 0.00015133187 4 - 1300 1388.4127 1.3301175 0.00017295071 5 - 1400 1559.3853 1.6709729 0.00017295071 5 - 1500 1471.8623 0.8268427 0.00017295071 5 - 1600 1543.6793 2.1987908 0.00019456955 6 - 1700 1694.5595 0.48852817 0.00019456955 6 - 1800 1632.7737 -1.4617692 0.00021618839 7 - 1900 1922.6502 1.1664257 0.00021618839 7 - 2000 2223.503 -0.95799878 0.00023780722 8 - 2100 2142.6035 0.88444463 0.00025942606 9 - 2200 2298.8636 3.4239313 0.00025942606 9 - 2300 2252.4355 0.82167302 0.00025942606 9 - 2400 2321.0788 1.7499714 0.00025942606 9 - 2500 2095.6715 0.55288444 0.00025942606 9 - 2600 2136.0316 -3.833114 0.00025942606 9 - 2700 2466.3134 -2.2519511 0.00025942606 9 - 2800 2294.3454 1.0637304 0.00025942606 9 - 2900 2340.3891 1.3997049 0.0002810449 10 - 3000 2272.0013 -0.27591886 0.0002810449 10 - 3100 2333.9696 -0.11772138 0.0002810449 10 - 3200 2409.0946 -1.025473 0.0002810449 10 - 3300 2148.023 1.6752329 0.0002810449 10 - 3400 2267.636 -0.45297583 0.0002810449 10 - 3500 2457.622 0.35627297 0.0002810449 10 - 3600 2288.008 -15.516626 0.00030266374 11 - 3700 2458.2681 1.4571773 0.00030266374 11 - 3800 2566.7623 -29.140553 0.00032428258 12 - 3900 2839.4062 0.64583638 0.00032428258 12 - 4000 2893.2204 -53.187892 0.00034590142 13 - 4100 3024.6375 -65.068146 0.00036752025 14 - 4200 3004.6784 1.4155214 0.00036752025 14 - 4300 3033.1895 1.8572273 0.00036752025 14 - 4400 3157.2542 -0.92462977 0.00036752025 14 - 4500 3557.7137 -194.46498 0.00038913909 15 - 4600 3096.485 -1.830492 0.00038913909 15 - 4700 3488.088 -286.81055 0.00041075793 16 - 4800 3390.5493 -372.77818 0.00043237677 17 - 4900 3773.7226 -446.58574 0.00045399561 18 - 5000 3703.0159 -0.81188551 0.00045399561 18 - 5100 4051.3067 1.2567439 0.00045399561 18 - 5200 3813.3682 0.92945737 0.00047561445 19 - 5300 4036.0078 -2.5336258 0.00049723329 20 - 5400 4219.803 -0.96928261 0.00049723329 20 - 5500 4433.7447 -0.026762463 0.00051885212 21 - 5600 4477.4505 -1.417316 0.00054047096 22 - 5700 4500.0306 -1.0551443 0.00054047096 22 - 5800 4600.3507 -4.9580056 0.00054047096 22 - 5900 4765.4978 -2.2546941 0.0005620898 23 - 6000 5442.6193 0.91161284 0.00058370864 24 - 6100 5086.8047 -0.9875332 0.00060532748 25 - 6200 5485.3437 -2.8296626 0.00062694632 26 - 6300 4988.0396 -0.15179023 0.00064856516 27 - 6400 5597.3703 4.2941885 0.00067018399 28 - 6500 5677.0263 -2.8611595 0.00069180283 29 - 6600 6058.0009 1.4111778 0.00071342167 30 - 6700 5859.0817 -2.5782466 0.00071342167 30 - 6800 5879.3941 -4.5681807 0.00071342167 30 - 6900 6398.288 2.5259412 0.00071342167 30 - 7000 6250.1096 -2.6049627 0.00071342167 30 - 7100 5849.651 -0.44062578 0.00071342167 30 - 7200 5778.6532 -0.27299118 0.00071342167 30 - 7300 5977.6661 4.2483639 0.00071342167 30 - 7400 5862.4231 1.0289519 0.00071342167 30 - 7500 6482.376 7.5412373 0.00071342167 30 - 7600 5810.4325 1.0343075 0.00071342167 30 - 7700 5916.7304 2.304302 0.00071342167 30 - 7800 5869.9504 -0.5946555 0.00071342167 30 - 7900 5804.0522 -4.1207689 0.00071342167 30 - 8000 6077.1704 0.52211243 0.00071342167 30 -Loop time of 60.5603 on 4 procs for 8000 steps with 528 atoms - -Performance: 11.413 ns/day, 2.103 hours/ns, 132.100 timesteps/s -99.9% CPU use with 4 MPI tasks x no OpenMP threads - -MPI task timing breakdown: -Section | min time | avg time | max time |%varavg| %total ---------------------------------------------------------------- -Pair | 0.0041695 | 0.90113 | 2.3423 | 102.8 | 1.49 -Bond | 0.011606 | 2.1188 | 5.8107 | 163.9 | 3.50 -Kspace | 47.987 | 52.817 | 55.679 | 43.7 | 87.21 -Neigh | 3.5961 | 3.6262 | 3.6496 | 1.2 | 5.99 -Comm | 0.11097 | 0.16569 | 0.26369 | 15.3 | 0.27 -Output | 0.0020366 | 0.0023427 | 0.0032469 | 1.1 | 0.00 -Modify | 0.62302 | 0.91659 | 1.1227 | 21.5 | 1.51 -Other | | 0.0126 | | | 0.02 - -Nlocal: 132.000 ave 295 max 0 min -Histogram: 2 0 0 0 0 0 0 1 0 1 -Nghost: 133.000 ave 349 max 0 min -Histogram: 2 0 0 0 0 1 0 0 0 1 -Neighs: 8383.50 ave 20143 max 0 min -Histogram: 2 0 0 0 0 0 1 0 0 1 - -Total # of neighbors = 33534 -Ave neighs/atom = 63.511364 -Ave special neighs/atom = 11.409091 -Neighbor list builds = 8000 -Dangerous builds = 0 - -Please see the log.cite file for references relevant to this simulation - -Total wall time: 0:01:00 diff --git a/examples/PACKAGES/reaction/create_atoms_polystyrene/log.4Nov2022.grow_styrene.g++.1 b/examples/PACKAGES/reaction/create_atoms_polystyrene/log.4Nov2022.grow_styrene.g++.1 new file mode 100644 index 0000000000..fb9b22d134 --- /dev/null +++ b/examples/PACKAGES/reaction/create_atoms_polystyrene/log.4Nov2022.grow_styrene.g++.1 @@ -0,0 +1,256 @@ +LAMMPS (4 Nov 2022) +# use bond/react 'create atoms' feature to add 30 new styrene monomers to chain + +units real + +boundary p p p + +atom_style full + +pair_style lj/class2/coul/cut 8.5 + +angle_style class2 + +bond_style class2 + +dihedral_style class2 + +improper_style class2 + +variable T equal 530 + +read_data trimer.data extra/bond/per/atom 5 extra/angle/per/atom 15 extra/dihedral/per/atom 15 extra/improper/per/atom 25 extra/special/per/atom 25 +Reading data file ... + orthogonal box = (-200 -200 -200) to (200 200 200) + 1 by 1 by 1 MPI processor grid + reading atom labelmap ... + reading bond labelmap ... + reading angle labelmap ... + reading dihedral labelmap ... + reading improper labelmap ... + reading atoms ... + 48 atoms + scanning bonds ... + 8 = max bonds/atom + scanning angles ... + 21 = max angles/atom + scanning dihedrals ... + 33 = max dihedrals/atom + scanning impropers ... + 26 = max impropers/atom + reading bonds ... + 50 bonds + reading angles ... + 84 angles + reading dihedrals ... + 127 dihedrals + reading impropers ... + 20 impropers +Finding 1-2 1-3 1-4 neighbors ... + special bond factors lj: 0 0 0 + special bond factors coul: 0 0 0 + 4 = max # of 1-2 neighbors + 8 = max # of 1-3 neighbors + 17 = max # of 1-4 neighbors + 46 = max # of special neighbors + special bonds CPU = 0.000 seconds + read_data CPU = 0.011 seconds + +molecule mol1 grow_styrene_pre.molecule_template +Read molecule template mol1: + 1 molecules + 0 fragments + 30 atoms with max type 4 + 31 bonds with max type 6 + 51 angles with max type 10 + 73 dihedrals with max type 13 + 13 impropers with max type 3 +molecule mol2 grow_styrene_post.molecule_template +Read molecule template mol2: + 1 molecules + 1 fragments + 46 atoms with max type 4 + 48 bonds with max type 6 + 81 angles with max type 10 + 121 dihedrals with max type 13 + 19 impropers with max type 3 + +fix myrxns all bond/react stabilization yes statted_grp .03 react rxn1 all 1 0 3.0 mol1 mol2 grow_styrene.map modify_create fit create_fit overlap 2.0 stabilize_steps 200 max_rxn 30 +dynamic group bond_react_MASTER_group defined +dynamic group statted_grp_REACT defined + +fix 1 statted_grp_REACT nvt temp $T $T 100 +fix 1 statted_grp_REACT nvt temp 530 $T 100 +fix 1 statted_grp_REACT nvt temp 530 530 100 + +fix 4 bond_react_MASTER_group temp/rescale 1 $T $T 1 1 +fix 4 bond_react_MASTER_group temp/rescale 1 530 $T 1 1 +fix 4 bond_react_MASTER_group temp/rescale 1 530 530 1 1 + +thermo_style custom step temp press density f_myrxns[1] + +thermo 100 + +dump 1 all xyz 1 test_vis.xyz + +run 8000 + +CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE + +Your simulation uses code contributions which should be cited: + +- fix bond/react: reacter.org doi:10.1016/j.polymer.2017.09.038, doi:10.1021/acs.macromol.0c02012 + +@Article{Gissinger17, + author = {J. R. Gissinger and B. D. Jensen and K. E. Wise}, + title = {Modeling Chemical Reactions in Classical Molecular Dynamics Simulations}, + journal = {Polymer}, + year = 2017, + volume = 128, + pages = {211--217} +} + +@Article{Gissinger20, + author = {J. R. Gissinger, B. D. Jensen, K. E. Wise}, + title = {{REACTER}: A Heuristic Method for Reactive Molecular Dynamics}, + journal = {Macromolecules}, + year = 2020, + volume = 53, + number = 22, + pages = {9953--9961} +} + +CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE + +Generated 6 of 6 mixed pair_coeff terms from sixthpower/geometric mixing rule +Neighbor list info ... + update: every = 1 steps, delay = 0 steps, check = yes + max neighbors/atom: 2000, page size: 100000 + master list distance cutoff = 10.5 + ghost atom cutoff = 10.5 + binsize = 5.25, bins = 77 77 77 + 2 neighbor lists, perpetual/occasional/extra = 1 1 0 + (1) pair lj/class2/coul/cut, perpetual + attributes: half, newton on + pair build: half/bin/newton + stencil: half/bin/3d + bin: standard + (2) fix bond/react, occasional, copy from (1) + attributes: half, newton on + pair build: copy + stencil: none + bin: none +Per MPI rank memory allocation (min/avg/max) = 36.99 | 36.99 | 36.99 Mbytes + Step Temp Press Density f_myrxns[1] + 0 0 0.076588866 8.1070333e-06 0 + 100 598.41967 -0.1670029 1.0809378e-05 1 + 200 696.77845 0.11857422 1.0809378e-05 1 + 300 932.97222 -0.058615676 1.3511722e-05 2 + 400 1016.3732 0.062233715 1.3511722e-05 2 + 500 1006.451 -0.17987841 1.6214067e-05 3 + 600 1143.8859 0.33297898 1.6214067e-05 3 + 700 1209.6144 -0.22743773 1.8916411e-05 4 + 800 1429.1639 0.14048255 1.8916411e-05 4 + 900 1375.0968 -0.04016551 2.1618755e-05 5 + 1000 1583.6696 -0.23364852 2.1618755e-05 5 + 1100 1811.0697 -0.054436797 2.43211e-05 6 + 1200 1928.4658 0.012242837 2.43211e-05 6 + 1300 1666.6176 0.057157656 2.43211e-05 6 + 1400 1686.18 -28.442814 2.7023444e-05 7 + 1500 1704.6248 -0.16861218 2.7023444e-05 7 + 1600 2171.7628 -33.6156 2.9725789e-05 8 + 1700 1991.2922 -0.11813381 2.9725789e-05 8 + 1800 2037.4991 -40.015612 3.2428133e-05 9 + 1900 2143.9447 -0.090964375 3.2428133e-05 9 + 2000 1927.9564 0.29856007 3.2428133e-05 9 + 2100 2255.5877 -4.9166327 3.5130478e-05 10 + 2200 2512.5193 0.00044804842 3.5130478e-05 10 + 2300 2336.1503 -45.094726 3.7832822e-05 11 + 2400 2508.9655 -0.1024684 3.7832822e-05 11 + 2500 2747.7344 -53.939212 4.0535167e-05 12 + 2600 2790.5736 0.07042181 4.0535167e-05 12 + 2700 3014.7092 -0.0025387793 4.0535167e-05 12 + 2800 2745.0295 -0.099361314 4.3237511e-05 13 + 2900 2952.1281 -0.13667582 4.3237511e-05 13 + 3000 3032.5298 0.28882784 4.5939855e-05 14 + 3100 3149.992 0.55269076 4.5939855e-05 14 + 3200 3422.5233 -0.11794908 4.86422e-05 15 + 3300 3040.2691 -0.067532834 4.86422e-05 15 + 3400 3323.3263 0.049969149 5.1344544e-05 16 + 3500 3539.0877 -0.065546641 5.1344544e-05 16 + 3600 3894.6897 -0.24222461 5.4046889e-05 17 + 3700 3689.3513 0.21366533 5.4046889e-05 17 + 3800 3924.799 -0.60817646 5.6749233e-05 18 + 3900 3713.1947 -0.024834682 5.6749233e-05 18 + 4000 3887.6151 0.052787631 5.9451578e-05 19 + 4100 3868.2877 0.42532898 5.9451578e-05 19 + 4200 3784.9874 -0.12018512 5.9451578e-05 19 + 4300 4169.9997 0.19652089 6.2153922e-05 20 + 4400 4112.291 -0.084839982 6.2153922e-05 20 + 4500 3974.2226 -0.13641761 6.2153922e-05 20 + 4600 4064.3852 0.16435039 6.2153922e-05 20 + 4700 3880.0044 -0.42874552 6.2153922e-05 20 + 4800 4508.2324 0.20208091 6.2153922e-05 20 + 4900 4364.033 -0.56300441 6.2153922e-05 20 + 5000 4030.4642 -0.29006515 6.2153922e-05 20 + 5100 4010.9518 0.32060145 6.2153922e-05 20 + 5200 4058.5072 0.088924924 6.2153922e-05 20 + 5300 4529.9866 -0.38882748 6.4856266e-05 21 + 5400 4305.9161 0.24046553 6.4856266e-05 21 + 5500 4556.8628 -0.014044879 6.4856266e-05 21 + 5600 4730.2206 0.1526293 6.4856266e-05 21 + 5700 4810.9968 -17.600253 6.7558611e-05 22 + 5800 4655.651 -0.25941928 6.7558611e-05 22 + 5900 4507.1045 -0.084691005 6.7558611e-05 22 + 6000 4516.0965 0.092662842 7.0260955e-05 23 + 6100 4592.4068 0.10403004 7.0260955e-05 23 + 6200 4583.9491 0.1692786 7.29633e-05 24 + 6300 4512.226 0.32590723 7.29633e-05 24 + 6400 4885.9205 -0.24208842 7.5665644e-05 25 + 6500 5250.5008 0.4135064 7.5665644e-05 25 + 6600 5216.9452 0.00059199905 7.8367989e-05 26 + 6700 5302.2925 0.50452368 7.8367989e-05 26 + 6800 4931.7328 -0.064719953 8.1070333e-05 27 + 6900 5549.8746 0.55101191 8.1070333e-05 27 + 7000 5472.9107 0.31358281 8.3772677e-05 28 + 7100 5559.9339 0.14034743 8.3772677e-05 28 + 7200 5726.4492 -0.39732059 8.6475022e-05 29 + 7300 5869.324 0.18989804 8.6475022e-05 29 + 7400 6109.5519 0.11206572 8.9177366e-05 30 + 7500 5966.7085 0.2059557 8.9177366e-05 30 + 7600 6051.2064 0.025316679 8.9177366e-05 30 + 7700 5719.6669 0.16548544 8.9177366e-05 30 + 7800 6118.8183 -0.20036999 8.9177366e-05 30 + 7900 6477.1901 0.10308473 8.9177366e-05 30 + 8000 6241.9498 0.090165102 8.9177366e-05 30 +Loop time of 17.4848 on 1 procs for 8000 steps with 528 atoms + +Performance: 39.531 ns/day, 0.607 hours/ns, 457.540 timesteps/s, 241.581 katom-step/s +97.6% CPU use with 1 MPI tasks x no OpenMP threads + +MPI task timing breakdown: +Section | min time | avg time | max time |%varavg| %total +--------------------------------------------------------------- +Pair | 3.0991 | 3.0991 | 3.0991 | 0.0 | 17.72 +Bond | 7.6807 | 7.6807 | 7.6807 | 0.0 | 43.93 +Neigh | 1.6906 | 1.6906 | 1.6906 | 0.0 | 9.67 +Comm | 0.019091 | 0.019091 | 0.019091 | 0.0 | 0.11 +Output | 4.5095 | 4.5095 | 4.5095 | 0.0 | 25.79 +Modify | 0.46277 | 0.46277 | 0.46277 | 0.0 | 2.65 +Other | | 0.02296 | | | 0.13 + +Nlocal: 528 ave 528 max 528 min +Histogram: 1 0 0 0 0 0 0 0 0 0 +Nghost: 0 ave 0 max 0 min +Histogram: 1 0 0 0 0 0 0 0 0 0 +Neighs: 35904 ave 35904 max 35904 min +Histogram: 1 0 0 0 0 0 0 0 0 0 + +Total # of neighbors = 35904 +Ave neighs/atom = 68 +Ave special neighs/atom = 11.409091 +Neighbor list builds = 1836 +Dangerous builds = 0 + +# write_data final.data nofix +Total wall time: 0:00:17 diff --git a/examples/PACKAGES/reaction/create_atoms_polystyrene/log.4Nov2022.grow_styrene.g++.4 b/examples/PACKAGES/reaction/create_atoms_polystyrene/log.4Nov2022.grow_styrene.g++.4 new file mode 100644 index 0000000000..b14ff6c8d0 --- /dev/null +++ b/examples/PACKAGES/reaction/create_atoms_polystyrene/log.4Nov2022.grow_styrene.g++.4 @@ -0,0 +1,256 @@ +LAMMPS (4 Nov 2022) +# use bond/react 'create atoms' feature to add 30 new styrene monomers to chain + +units real + +boundary p p p + +atom_style full + +pair_style lj/class2/coul/cut 8.5 + +angle_style class2 + +bond_style class2 + +dihedral_style class2 + +improper_style class2 + +variable T equal 530 + +read_data trimer.data extra/bond/per/atom 5 extra/angle/per/atom 15 extra/dihedral/per/atom 15 extra/improper/per/atom 25 extra/special/per/atom 25 +Reading data file ... + orthogonal box = (-200 -200 -200) to (200 200 200) + 1 by 2 by 2 MPI processor grid + reading atom labelmap ... + reading bond labelmap ... + reading angle labelmap ... + reading dihedral labelmap ... + reading improper labelmap ... + reading atoms ... + 48 atoms + scanning bonds ... + 8 = max bonds/atom + scanning angles ... + 21 = max angles/atom + scanning dihedrals ... + 33 = max dihedrals/atom + scanning impropers ... + 26 = max impropers/atom + reading bonds ... + 50 bonds + reading angles ... + 84 angles + reading dihedrals ... + 127 dihedrals + reading impropers ... + 20 impropers +Finding 1-2 1-3 1-4 neighbors ... + special bond factors lj: 0 0 0 + special bond factors coul: 0 0 0 + 4 = max # of 1-2 neighbors + 8 = max # of 1-3 neighbors + 17 = max # of 1-4 neighbors + 46 = max # of special neighbors + special bonds CPU = 0.000 seconds + read_data CPU = 0.007 seconds + +molecule mol1 grow_styrene_pre.molecule_template +Read molecule template mol1: + 1 molecules + 0 fragments + 30 atoms with max type 4 + 31 bonds with max type 6 + 51 angles with max type 10 + 73 dihedrals with max type 13 + 13 impropers with max type 3 +molecule mol2 grow_styrene_post.molecule_template +Read molecule template mol2: + 1 molecules + 1 fragments + 46 atoms with max type 4 + 48 bonds with max type 6 + 81 angles with max type 10 + 121 dihedrals with max type 13 + 19 impropers with max type 3 + +fix myrxns all bond/react stabilization yes statted_grp .03 react rxn1 all 1 0 3.0 mol1 mol2 grow_styrene.map modify_create fit create_fit overlap 2.0 stabilize_steps 200 max_rxn 30 +dynamic group bond_react_MASTER_group defined +dynamic group statted_grp_REACT defined + +fix 1 statted_grp_REACT nvt temp $T $T 100 +fix 1 statted_grp_REACT nvt temp 530 $T 100 +fix 1 statted_grp_REACT nvt temp 530 530 100 + +fix 4 bond_react_MASTER_group temp/rescale 1 $T $T 1 1 +fix 4 bond_react_MASTER_group temp/rescale 1 530 $T 1 1 +fix 4 bond_react_MASTER_group temp/rescale 1 530 530 1 1 + +thermo_style custom step temp press density f_myrxns[1] + +thermo 100 + +dump 1 all xyz 1 test_vis.xyz + +run 8000 + +CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE + +Your simulation uses code contributions which should be cited: + +- fix bond/react: reacter.org doi:10.1016/j.polymer.2017.09.038, doi:10.1021/acs.macromol.0c02012 + +@Article{Gissinger17, + author = {J. R. Gissinger and B. D. Jensen and K. E. Wise}, + title = {Modeling Chemical Reactions in Classical Molecular Dynamics Simulations}, + journal = {Polymer}, + year = 2017, + volume = 128, + pages = {211--217} +} + +@Article{Gissinger20, + author = {J. R. Gissinger, B. D. Jensen, K. E. Wise}, + title = {{REACTER}: A Heuristic Method for Reactive Molecular Dynamics}, + journal = {Macromolecules}, + year = 2020, + volume = 53, + number = 22, + pages = {9953--9961} +} + +CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE + +Generated 6 of 6 mixed pair_coeff terms from sixthpower/geometric mixing rule +Neighbor list info ... + update: every = 1 steps, delay = 0 steps, check = yes + max neighbors/atom: 2000, page size: 100000 + master list distance cutoff = 10.5 + ghost atom cutoff = 10.5 + binsize = 5.25, bins = 77 77 77 + 2 neighbor lists, perpetual/occasional/extra = 1 1 0 + (1) pair lj/class2/coul/cut, perpetual + attributes: half, newton on + pair build: half/bin/newton + stencil: half/bin/3d + bin: standard + (2) fix bond/react, occasional, copy from (1) + attributes: half, newton on + pair build: copy + stencil: none + bin: none +Per MPI rank memory allocation (min/avg/max) = 35.37 | 35.56 | 36.15 Mbytes + Step Temp Press Density f_myrxns[1] + 0 0 0.076588866 8.1070333e-06 0 + 100 598.29879 -0.17888669 1.0809378e-05 1 + 200 699.08337 0.11172183 1.0809378e-05 1 + 300 931.85797 -0.13923465 1.3511722e-05 2 + 400 893.78126 0.14680427 1.3511722e-05 2 + 500 1001.0848 -0.021703999 1.6214067e-05 3 + 600 989.24943 0.04641672 1.6214067e-05 3 + 700 1244.794 -0.19464667 1.8916411e-05 4 + 800 1210.997 -0.06710628 1.8916411e-05 4 + 900 1310.0005 0.099408095 2.1618755e-05 5 + 1000 1640.5956 -0.05975911 2.1618755e-05 5 + 1100 1380.7273 -0.025206389 2.1618755e-05 5 + 1200 1637.6542 0.057149266 2.43211e-05 6 + 1300 1757.3409 0.3232123 2.43211e-05 6 + 1400 1664.5048 -0.29656858 2.7023444e-05 7 + 1500 1578.9691 0.21997047 2.7023444e-05 7 + 1600 1848.9227 -0.11783672 2.9725789e-05 8 + 1700 1981.1695 0.28374154 2.9725789e-05 8 + 1800 2330.8852 -0.082109894 3.2428133e-05 9 + 1900 2177.4096 0.23853778 3.2428133e-05 9 + 2000 2095.1618 -1.5405667 3.5130478e-05 10 + 2100 2272.2653 0.05572226 3.5130478e-05 10 + 2200 2599.5994 -2.2307507 3.7832822e-05 11 + 2300 2457.7904 0.40228312 3.7832822e-05 11 + 2400 2372.9736 -3.3415973 4.0535167e-05 12 + 2500 2427.4613 -0.16211888 4.0535167e-05 12 + 2600 3022.2608 -4.3278098 4.3237511e-05 13 + 2700 3115.6526 0.013828954 4.3237511e-05 13 + 2800 2841.7091 -6.4163443 4.5939855e-05 14 + 2900 3047.8436 0.16052429 4.5939855e-05 14 + 3000 3373.7997 -7.7904706 4.86422e-05 15 + 3100 3381.6653 0.35152687 4.86422e-05 15 + 3200 3589.5561 -10.754027 5.1344544e-05 16 + 3300 3473.4415 -0.13274479 5.1344544e-05 16 + 3400 3696.3283 -13.75504 5.4046889e-05 17 + 3500 3486.5442 -0.31091832 5.4046889e-05 17 + 3600 3647.0818 0.34662993 5.4046889e-05 17 + 3700 3636.7138 -0.041981737 5.4046889e-05 17 + 3800 3427.6532 0.42008936 5.6749233e-05 18 + 3900 3574.0094 -0.05475272 5.6749233e-05 18 + 4000 4158.9339 0.14426361 5.9451578e-05 19 + 4100 3862.5026 0.094232438 5.9451578e-05 19 + 4200 3969.4378 -0.10602108 6.2153922e-05 20 + 4300 3840.0126 0.29190336 6.2153922e-05 20 + 4400 4365.9912 -36.954812 6.4856266e-05 21 + 4500 4565.3708 0.061879092 6.4856266e-05 21 + 4600 4565.491 -70.588435 6.7558611e-05 22 + 4700 4570.2702 -0.56661378 6.7558611e-05 22 + 4800 4445.786 0.20534323 6.7558611e-05 22 + 4900 4782.6436 0.012783481 7.0260955e-05 23 + 5000 4777.2132 0.092416308 7.0260955e-05 23 + 5100 4944.0402 0.11614993 7.29633e-05 24 + 5200 5139.165 -0.23180938 7.29633e-05 24 + 5300 4647.2328 0.13570142 7.5665644e-05 25 + 5400 4982.7355 -0.25477884 7.5665644e-05 25 + 5500 5400.5924 0.19902824 7.8367989e-05 26 + 5600 5761.3552 0.083102065 7.8367989e-05 26 + 5700 5723.8581 0.039332796 8.1070333e-05 27 + 5800 5548.0789 -0.14511631 8.1070333e-05 27 + 5900 5358.5431 -0.099694264 8.3772677e-05 28 + 6000 5591.2678 9.9924655e-05 8.3772677e-05 28 + 6100 6101.8008 0.26538732 8.6475022e-05 29 + 6200 5848.9979 0.091137862 8.6475022e-05 29 + 6300 5582.1828 -0.039900602 8.9177366e-05 30 + 6400 6077.0548 0.3191104 8.9177366e-05 30 + 6500 5794.6827 0.69322336 8.9177366e-05 30 + 6600 5610.4331 0.080420058 8.9177366e-05 30 + 6700 5615.3492 0.12810868 8.9177366e-05 30 + 6800 5900.9749 -0.31704866 8.9177366e-05 30 + 6900 6233.9524 0.010288514 8.9177366e-05 30 + 7000 5972.7488 -1.0442089 8.9177366e-05 30 + 7100 6258.1332 0.56270399 8.9177366e-05 30 + 7200 6172.5919 -0.19595153 8.9177366e-05 30 + 7300 5898.7547 0.020862491 8.9177366e-05 30 + 7400 5815.1659 -0.0020680171 8.9177366e-05 30 + 7500 6003.867 -0.12288131 8.9177366e-05 30 + 7600 5966.0609 -0.1504333 8.9177366e-05 30 + 7700 6274.3331 -0.62752757 8.9177366e-05 30 + 7800 6051.0914 0.22821201 8.9177366e-05 30 + 7900 5981.5209 -0.19623554 8.9177366e-05 30 + 8000 5835.4657 0.3602475 8.9177366e-05 30 +Loop time of 13.936 on 4 procs for 8000 steps with 528 atoms + +Performance: 49.598 ns/day, 0.484 hours/ns, 574.051 timesteps/s, 303.099 katom-step/s +99.4% CPU use with 4 MPI tasks x no OpenMP threads + +MPI task timing breakdown: +Section | min time | avg time | max time |%varavg| %total +--------------------------------------------------------------- +Pair | 0.001058 | 0.78388 | 3.1317 | 153.1 | 5.62 +Bond | 0.0031874 | 2.0525 | 8.1984 | 247.7 | 14.73 +Neigh | 0.53495 | 0.53527 | 0.53551 | 0.0 | 3.84 +Comm | 0.01177 | 0.012451 | 0.013306 | 0.5 | 0.09 +Output | 1.3336 | 1.4735 | 1.7322 | 13.2 | 10.57 +Modify | 0.55142 | 9.0568 | 12.031 | 163.3 | 64.99 +Other | | 0.02159 | | | 0.15 + +Nlocal: 132 ave 528 max 0 min +Histogram: 3 0 0 0 0 0 0 0 0 1 +Nghost: 0 ave 0 max 0 min +Histogram: 4 0 0 0 0 0 0 0 0 0 +Neighs: 9115.75 ave 36463 max 0 min +Histogram: 3 0 0 0 0 0 0 0 0 1 + +Total # of neighbors = 36463 +Ave neighs/atom = 69.058712 +Ave special neighs/atom = 11.409091 +Neighbor list builds = 771 +Dangerous builds = 0 + +# write_data final.data nofix +Total wall time: 0:00:13 diff --git a/examples/PACKAGES/reaction/create_atoms_polystyrene/trimer.data b/examples/PACKAGES/reaction/create_atoms_polystyrene/trimer.data index b3ad132f03..2608a0ed10 100644 --- a/examples/PACKAGES/reaction/create_atoms_polystyrene/trimer.data +++ b/examples/PACKAGES/reaction/create_atoms_polystyrene/trimer.data @@ -1,796 +1,585 @@ polystyrene trimer -48 atoms -7 atom types -50 bonds -13 bond types -84 angles -22 angle types -127 dihedrals -36 dihedral types -36 impropers -9 improper types + 48 atoms + 50 bonds + 84 angles + 127 dihedrals + 20 impropers -50 250 xlo xhi -50 250 ylo yhi -50 250 zlo zhi + 4 atom types + 6 bond types + 10 angle types + 13 dihedral types + 4 improper types + + -200 200 xlo xhi + -200 200 ylo yhi + -200 200 zlo zhi + +Atom Type Labels + + 1 hc + 2 cp + 3 c1 + 4 c2 + +Bond Type Labels + + 1 hc-cp + 2 cp-cp + 3 hc-c2 + 4 c1-c2 + 5 cp-c1 + 6 hc-c1 + +Angle Type Labels + + 1 hc-cp-cp + 2 cp-cp-cp + 3 cp-c1-c2 + 4 hc-c1-c2 + 5 hc-c1-cp + 6 hc-c2-c1 + 7 hc-c2-hc + 8 c1-c2-c1 + 9 cp-cp-c1 + 10 c2-c1-c2 + +Dihedral Type Labels + + 1 hc-cp-cp-hc + 2 hc-cp-cp-cp + 3 cp-cp-cp-cp + 4 cp-cp-cp-c1 + 5 hc-cp-cp-c1 + 6 cp-c1-c2-hc + 7 cp-c1-c2-c1 + 8 hc-c1-c2-hc + 9 hc-c1-c2-c1 + 10 cp-cp-c1-c2 + 11 cp-cp-c1-hc + 12 c2-c1-c2-hc + 13 c2-c1-c2-c1 + +Improper Type Labels + + 1 hc-cp-cp-cp + 2 hc-c1-cp-c2 + 3 cp-cp-cp-c1 + 4 hc-c2-hc-c1 Masses -1 12.0112 -2 1.00797 -3 12.0112 -4 12.0112 -5 12.0112 -6 12.0112 -7 12.0112 + 1 1.007970 # hc + 2 12.011150 # cp + 3 12.011150 # c1 + 4 12.011150 # c2 Pair Coeffs # lj/class2/coul/long -1 0.064 4.01 -2 0.02 2.7 -3 0.064 4.01 -4 0.064 3.9 -5 0.054 4.01 -6 0.054 4.01 -7 0.054 4.01 + 1 0.0200000000 2.7000000000 + 2 0.0640000000 4.0100000000 + 3 0.0540000000 4.0100000000 + 4 0.0540000000 4.0100000000 Bond Coeffs # class2 -1 1.0982 372.825 -803.453 894.317 -2 1.417 470.836 -627.618 1327.63 -3 1.501 321.902 -521.821 572.163 -4 1.0883 365.768 -725.54 781.662 -5 1.34 543.99 -1238.2 1644.03 -6 1.0883 365.768 -725.54 781.662 -7 1.501 321.902 -521.821 572.163 -8 1.101 345 -691.89 844.6 -9 1.53 299.67 -501.77 679.81 -10 1.101 345 -691.89 844.6 -11 1.501 321.902 -521.821 572.163 -12 1.101 345 -691.89 844.6 -13 1.53 299.67 -501.77 679.81 + 1 1.0982 372.8251 -803.4526 894.3173 + 2 1.4170 470.8361 -627.6179 1327.6345 + 3 1.1010 345.0000 -691.8900 844.6000 + 4 1.5300 299.6700 -501.7700 679.8100 + 5 1.5010 321.9021 -521.8208 572.1628 + 6 1.1010 345.0000 -691.8900 844.6000 Angle Coeffs # class2 -1 117.94 35.1558 -12.4682 0 -2 118.9 61.0226 -34.9931 0 -3 120.05 44.7148 -22.7352 0 -4 111 44.3234 -9.4454 0 -5 108.4 43.9594 -8.3924 -9.3379 -6 124.88 35.2766 -17.774 -1.6215 -7 124.88 35.2766 -17.774 -1.6215 -8 115.49 29.6363 -12.4853 -6.2218 -9 120.05 44.7148 -22.7352 0 -10 111 44.3234 -9.4454 0 -11 108.4 43.9594 -8.3924 -9.3379 -12 110.77 41.453 -10.604 5.129 -13 112.67 39.516 -7.443 -9.5583 -14 110.77 41.453 -10.604 5.129 -15 107.66 39.641 -12.921 -2.4318 -16 112.67 39.516 -7.443 -9.5583 -17 120.05 44.7148 -22.7352 0 -18 111 44.3234 -9.4454 0 -19 108.4 43.9594 -8.3924 -9.3379 -20 110.77 41.453 -10.604 5.129 -21 110.77 41.453 -10.604 5.129 -22 112.67 39.516 -7.443 -9.5583 - -BondBond Coeffs - -1 1.0795 1.417 1.0982 -2 68.2856 1.417 1.417 -3 12.0676 1.417 1.501 -4 2.9168 1.501 1.0883 -5 0 1.501 1.34 -6 10.1047 1.0883 1.34 -7 10.1047 1.0883 1.34 -8 4.8506 1.0883 1.0883 -9 12.0676 1.417 1.501 -10 2.9168 1.501 1.101 -11 0 1.501 1.53 -12 3.3872 1.101 1.53 -13 0 1.53 1.53 -14 3.3872 1.101 1.53 -15 5.3316 1.101 1.101 -16 0 1.53 1.53 -17 12.0676 1.417 1.501 -18 2.9168 1.501 1.101 -19 0 1.501 1.53 -20 3.3872 1.101 1.53 -21 3.3872 1.101 1.53 -22 0 1.53 1.53 - -BondAngle Coeffs - -1 20.0033 24.2183 1.417 1.0982 -2 28.8708 28.8708 1.417 1.417 -3 31.0771 47.0579 1.417 1.501 -4 26.4608 11.7717 1.501 1.0883 -5 0 0 1.501 1.34 -6 19.0592 23.3588 1.0883 1.34 -7 19.0592 23.3588 1.0883 1.34 -8 17.9795 17.9795 1.0883 1.0883 -9 31.0771 47.0579 1.417 1.501 -10 26.4608 11.7717 1.501 1.101 -11 0 0 1.501 1.53 -12 11.421 20.754 1.101 1.53 -13 8.016 8.016 1.53 1.53 -14 11.421 20.754 1.101 1.53 -15 18.103 18.103 1.101 1.101 -16 8.016 8.016 1.53 1.53 -17 31.0771 47.0579 1.417 1.501 -18 26.4608 11.7717 1.501 1.101 -19 0 0 1.501 1.53 -20 11.421 20.754 1.101 1.53 -21 11.421 20.754 1.101 1.53 -22 8.016 8.016 1.53 1.53 + 1 117.9400 35.1558 -12.4682 0.0000 + 2 118.9000 61.0226 -34.9931 0.0000 + 3 108.4000 43.9594 -8.3924 -9.3379 + 4 110.7700 41.4530 -10.6040 5.1290 + 5 111.0000 44.3234 -9.4454 0.0000 + 6 110.7700 41.4530 -10.6040 5.1290 + 7 107.6600 39.6410 -12.9210 -2.4318 + 8 112.6700 39.5160 -7.4430 -9.5583 + 9 120.0500 44.7148 -22.7352 0.0000 + 10 112.6700 39.5160 -7.4430 -9.5583 Dihedral Coeffs # class2 -1 0 0 1.559 0 0 0 -2 0 0 3.9661 0 0 0 -3 0 0 4.4072 0 0 0 -4 8.3667 0 1.1932 0 0 0 -5 0 0 1.8769 0 0 0 -6 0 0 0 0 0 0 -7 0 0 0 0 0 0 -8 0 0 0 0 0 0 -9 0 0 4.8974 0 0 0 -10 0 0 1.559 0 0 0 -11 0 0 4.4072 0 0 0 -12 -0.2801 0 -0.0678 0 -0.0122 0 -13 -0.2802 0 -0.0678 0 -0.0122 0 -14 -0.0228 0 0.028 0 -0.1863 0 -15 -0.1432 0 0.0617 0 -0.1083 0 -16 0 0 0.0316 0 -0.1681 0 -17 0 0 0 0 0 0 -18 0 0 0.0316 0 -0.1681 0 -19 0 0 0.0514 0 -0.143 0 -20 0 0 1.559 0 0 0 -21 0 0 4.4072 0 0 0 -22 -0.2801 0 -0.0678 0 -0.0122 0 -23 -0.2802 0 -0.0678 0 -0.0122 0 -24 -0.0228 0 0.028 0 -0.1863 0 -25 0 0 0 0 0 0 -26 -0.1432 0 0.0617 0 -0.1083 0 -27 0 0 0.0316 0 -0.1681 0 -28 0 0 0 0 0 0 -29 0 0 0.0316 0 -0.1681 0 -30 0 0 0.0514 0 -0.143 0 -31 -0.0228 0 0.028 0 -0.1863 0 -32 -0.1432 0 0.0617 0 -0.1083 0 -33 0 0 0.0316 0 -0.1681 0 -34 0 0 0 0 0 0 -35 0 0 0.0316 0 -0.1681 0 -36 0 0 0.0514 0 -0.143 0 - -AngleAngleTorsion Coeffs - -1 4.4444 117.94 120.05 -2 -4.8141 118.9 117.94 -3 -14.4097 118.9 120.05 -4 0 118.9 118.9 -5 0.3598 117.94 117.94 -6 0 120.05 111 -7 0 120.05 108.4 -8 0 108.4 124.88 -9 -7.0058 124.88 124.88 -10 4.4444 117.94 120.05 -11 -14.4097 118.9 120.05 -12 -5.8888 120.05 111 -13 0 120.05 108.4 -14 0 108.4 110.77 -15 -12.564 110.77 110.77 -16 -16.164 112.67 110.77 -17 0 108.4 112.67 -18 -16.164 110.77 112.67 -19 -22.045 112.67 112.67 -20 4.4444 117.94 120.05 -21 -14.4097 118.9 120.05 -22 -5.8888 120.05 111 -23 0 120.05 108.4 -24 0 108.4 110.77 -25 0 108.4 112.67 -26 -12.564 110.77 110.77 -27 -16.164 110.77 112.67 -28 0 112.67 108.4 -29 -16.164 112.67 110.77 -30 -22.045 112.67 112.67 -31 0 110.77 108.4 -32 -12.564 110.77 110.77 -33 -16.164 110.77 112.67 -34 0 112.67 108.4 -35 -16.164 112.67 110.77 -36 -22.045 112.67 112.67 - -EndBondTorsion Coeffs - -1 0 -0.4879 0 0 -1.797 0 1.0982 1.501 -2 0 -6.8958 0 0 -0.4669 0 1.417 1.0982 -3 0 -0.6918 0 0 0.2421 0 1.417 1.501 -4 -0.1185 6.3204 0 -0.1185 6.3204 0 1.417 1.417 -5 0 -0.689 0 0 -0.689 0 1.0982 1.0982 -6 0 0 0 0 0 0 1.417 1.0883 -7 0 0 0 0 0 0 1.417 1.34 -8 0 0 0 0 0 0 1.501 1.0883 -9 0.7129 0.5161 0 0.7129 0.5161 0 1.0883 1.0883 -10 0 -0.4879 0 0 -1.797 0 1.0982 1.501 -11 0 -0.6918 0 0 0.2421 0 1.417 1.501 -12 -0.5835 1.122 0.3978 1.3997 0.7756 0 1.417 1.101 -13 0 0 0 0 0 0 1.417 1.53 -14 0 0 0 0 0 0 1.501 1.101 -15 0.213 0.312 0.0777 0.213 0.312 0.0777 1.101 1.101 -16 0.2486 0.2422 -0.0925 0.0814 0.0591 0.2219 1.53 1.101 -17 0 0 0 0 0 0 1.501 1.53 -18 0.0814 0.0591 0.2219 0.2486 0.2422 -0.0925 1.101 1.53 -19 -0.0732 0 0 -0.0732 0 0 1.53 1.53 -20 0 -0.4879 0 0 -1.797 0 1.0982 1.501 -21 0 -0.6918 0 0 0.2421 0 1.417 1.501 -22 -0.5835 1.122 0.3978 1.3997 0.7756 0 1.417 1.101 -23 0 0 0 0 0 0 1.417 1.53 -24 0 0 0 0 0 0 1.501 1.101 -25 0 0 0 0 0 0 1.501 1.53 -26 0.213 0.312 0.0777 0.213 0.312 0.0777 1.101 1.101 -27 0.0814 0.0591 0.2219 0.2486 0.2422 -0.0925 1.101 1.53 -28 0 0 0 0 0 0 1.53 1.501 -29 0.2486 0.2422 -0.0925 0.0814 0.0591 0.2219 1.53 1.101 -30 -0.0732 0 0 -0.0732 0 0 1.53 1.53 -31 0 0 0 0 0 0 1.101 1.501 -32 0.213 0.312 0.0777 0.213 0.312 0.0777 1.101 1.101 -33 0.0814 0.0591 0.2219 0.2486 0.2422 -0.0925 1.101 1.53 -34 0 0 0 0 0 0 1.53 1.501 -35 0.2486 0.2422 -0.0925 0.0814 0.0591 0.2219 1.53 1.101 -36 -0.0732 0 0 -0.0732 0 0 1.53 1.53 - -MiddleBondTorsion Coeffs - -1 0 3.9421 0 1.417 -2 0 -1.1521 0 1.417 -3 0 9.1792 0 1.417 -4 27.5989 -2.312 0 1.417 -5 0 4.8228 0 1.417 -6 0 0 0 1.501 -7 0 0 0 1.501 -8 0 0 0 1.34 -9 0.8558 6.3911 0 1.34 -10 0 3.9421 0 1.417 -11 0 9.1792 0 1.417 -12 -5.5679 1.4083 0.301 1.501 -13 0 0 0 1.501 -14 0 0 0 1.53 -15 -14.261 -0.5322 -0.4864 1.53 -16 -14.879 -3.6581 -0.3138 1.53 -17 0 0 0 1.53 -18 -14.879 -3.6581 -0.3138 1.53 -19 -17.787 -7.1877 0 1.53 -20 0 3.9421 0 1.417 -21 0 9.1792 0 1.417 -22 -5.5679 1.4083 0.301 1.501 -23 0 0 0 1.501 -24 0 0 0 1.53 -25 0 0 0 1.53 -26 -14.261 -0.5322 -0.4864 1.53 -27 -14.879 -3.6581 -0.3138 1.53 -28 0 0 0 1.53 -29 -14.879 -3.6581 -0.3138 1.53 -30 -17.787 -7.1877 0 1.53 -31 0 0 0 1.53 -32 -14.261 -0.5322 -0.4864 1.53 -33 -14.879 -3.6581 -0.3138 1.53 -34 0 0 0 1.53 -35 -14.879 -3.6581 -0.3138 1.53 -36 -17.787 -7.1877 0 1.53 - -BondBond13 Coeffs - -1 0.8743 1.0982 1.501 -2 -6.2741 1.417 1.0982 -3 2.5085 1.417 1.501 -4 53 1.417 1.417 -5 -1.7077 1.0982 1.0982 -6 0 1.417 1.0883 -7 0 1.417 1.34 -8 0 1.501 1.0883 -9 0 1.0883 1.0883 -10 0.8743 1.0982 1.501 -11 2.5085 1.417 1.501 -12 -3.4826 1.417 1.101 -13 0 1.417 1.53 -14 0 1.501 1.101 -15 0 1.101 1.101 -16 0 1.53 1.101 -17 0 1.501 1.53 -18 0 1.101 1.53 -19 0 1.53 1.53 -20 0.8743 1.0982 1.501 -21 2.5085 1.417 1.501 -22 -3.4826 1.417 1.101 -23 0 1.417 1.53 -24 0 1.501 1.101 -25 0 1.501 1.53 -26 0 1.101 1.101 -27 0 1.101 1.53 -28 0 1.53 1.501 -29 0 1.53 1.101 -30 0 1.53 1.53 -31 0 1.101 1.501 -32 0 1.101 1.101 -33 0 1.101 1.53 -34 0 1.53 1.501 -35 0 1.53 1.101 -36 0 1.53 1.53 - -AngleTorsion Coeffs - -1 0 3.4601 0 0 -0.1242 0 117.94 120.05 -2 0 2.5014 0 0 2.7147 0 118.9 117.94 -3 0 3.8987 0 0 -4.4683 0 118.9 120.05 -4 1.9767 1.0239 0 1.9767 1.0239 0 118.9 118.9 -5 0 2.4501 0 0 2.4501 0 117.94 117.94 -6 0 0 0 0 0 0 120.05 111 -7 0 0 0 0 0 0 120.05 108.4 -8 0 0 0 0 0 0 108.4 124.88 -9 -1.8911 3.254 0 -1.8911 3.254 0 124.88 124.88 -10 0 3.4601 0 0 -0.1242 0 117.94 120.05 -11 0 3.8987 0 0 -4.4683 0 118.9 120.05 -12 0.2251 0.6548 0.1237 4.6266 0.1632 0.0461 120.05 111 -13 0 0 0 0 0 0 120.05 108.4 -14 0 0 0 0 0 0 108.4 110.77 -15 -0.8085 0.5569 -0.2466 -0.8085 0.5569 -0.2466 110.77 110.77 -16 -0.2454 0 -0.1136 0.3113 0.4516 -0.1988 112.67 110.77 -17 0 0 0 0 0 0 108.4 112.67 -18 0.3113 0.4516 -0.1988 -0.2454 0 -0.1136 110.77 112.67 -19 0.3886 -0.3139 0.1389 0.3886 -0.3139 0.1389 112.67 112.67 -20 0 3.4601 0 0 -0.1242 0 117.94 120.05 -21 0 3.8987 0 0 -4.4683 0 118.9 120.05 -22 0.2251 0.6548 0.1237 4.6266 0.1632 0.0461 120.05 111 -23 0 0 0 0 0 0 120.05 108.4 -24 0 0 0 0 0 0 108.4 110.77 -25 0 0 0 0 0 0 108.4 112.67 -26 -0.8085 0.5569 -0.2466 -0.8085 0.5569 -0.2466 110.77 110.77 -27 0.3113 0.4516 -0.1988 -0.2454 0 -0.1136 110.77 112.67 -28 0 0 0 0 0 0 112.67 108.4 -29 -0.2454 0 -0.1136 0.3113 0.4516 -0.1988 112.67 110.77 -30 0.3886 -0.3139 0.1389 0.3886 -0.3139 0.1389 112.67 112.67 -31 0 0 0 0 0 0 110.77 108.4 -32 -0.8085 0.5569 -0.2466 -0.8085 0.5569 -0.2466 110.77 110.77 -33 0.3113 0.4516 -0.1988 -0.2454 0 -0.1136 110.77 112.67 -34 0 0 0 0 0 0 112.67 108.4 -35 -0.2454 0 -0.1136 0.3113 0.4516 -0.1988 112.67 110.77 -36 0.3886 -0.3139 0.1389 0.3886 -0.3139 0.1389 112.67 112.67 + 1 0.0000 0.0000 1.8769 0.0000 0.0000 0.0000 + 2 0.0000 0.0000 3.9661 0.0000 0.0000 0.0000 + 3 8.3667 0.0000 1.1932 0.0000 0.0000 0.0000 + 4 0.0000 0.0000 4.4072 0.0000 0.0000 0.0000 + 5 0.0000 0.0000 1.5590 0.0000 0.0000 0.0000 + 6 -0.0228 0.0000 0.0280 0.0000 -0.1863 0.0000 + 7 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 + 8 -0.1432 0.0000 0.0617 0.0000 -0.1083 0.0000 + 9 0.0000 0.0000 0.0316 0.0000 -0.1681 0.0000 + 10 -0.2802 0.0000 -0.0678 0.0000 -0.0122 0.0000 + 11 -0.2801 0.0000 -0.0678 0.0000 -0.0122 0.0000 + 12 0.0000 0.0000 0.0316 0.0000 -0.1681 0.0000 + 13 0.0000 0.0000 0.0514 0.0000 -0.1430 0.0000 Improper Coeffs # class2 -1 4.8912 0 -2 7.8153 0 -3 0 0 -4 2.8561 0 -5 7.8153 0 -6 0 0 -7 0 0 -8 7.8153 0 -9 0 0 + 1 4.8912 0.0000 + 2 0.0000 0.0000 + 3 7.8153 0.0000 + 4 0.0000 0.0000 + +BondBond Coeffs + + 1 1.0795 1.0982 1.4170 + 2 68.2856 1.4170 1.4170 + 3 0.0000 1.5010 1.5300 + 4 3.3872 1.1010 1.5300 + 5 2.9168 1.1010 1.5010 + 6 3.3872 1.1010 1.5300 + 7 5.3316 1.1010 1.1010 + 8 0.0000 1.5300 1.5300 + 9 12.0676 1.4170 1.5010 + 10 0.0000 1.5300 1.5300 + +BondAngle Coeffs + + 1 24.2183 20.0033 1.0982 1.4170 + 2 28.8708 28.8708 1.4170 1.4170 + 3 0.0000 0.0000 1.5010 1.5300 + 4 11.4210 20.7540 1.1010 1.5300 + 5 11.7717 26.4608 1.1010 1.5010 + 6 11.4210 20.7540 1.1010 1.5300 + 7 18.1030 18.1030 1.1010 1.1010 + 8 8.0160 8.0160 1.5300 1.5300 + 9 31.0771 47.0579 1.4170 1.5010 + 10 8.0160 8.0160 1.5300 1.5300 AngleAngle Coeffs -1 0 0 0 118.9 117.94 117.94 -2 0 0 0 118.9 120.05 120.05 -3 0 0 0 111 124.88 108.4 -4 0 0 0 115.49 124.88 124.88 -5 0 0 0 118.9 120.05 120.05 -6 0 0 0 107.66 110.77 110.77 -7 0 0 0 111 110.77 108.4 -8 0 0 0 118.9 120.05 120.05 -9 0 0 0 111 110.77 108.4 + 1 0.0000 0.0000 0.0000 117.9400 118.9000 117.9400 + 2 0.0000 0.0000 0.0000 111.0000 108.4000 110.7700 + 3 0.0000 0.0000 0.0000 118.9000 120.0500 120.0500 + 4 0.0000 0.0000 0.0000 107.6600 110.7700 110.7700 + +AngleAngleTorsion Coeffs + + 1 0.3598 117.9400 117.9400 + 2 -4.8141 117.9400 118.9000 + 3 0.0000 118.9000 118.9000 + 4 -14.4097 118.9000 120.0500 + 5 4.4444 117.9400 120.0500 + 6 0.0000 108.4000 110.7700 + 7 0.0000 108.4000 112.6700 + 8 -12.5640 110.7700 110.7700 + 9 -16.1640 110.7700 112.6700 + 10 0.0000 120.0500 108.4000 + 11 -5.8888 120.0500 111.0000 + 12 -16.1640 112.6700 110.7700 + 13 -22.0450 112.6700 112.6700 + +EndBondTorsion Coeffs + +1 0.0000 -0.6890 0.0000 0.0000 -0.6890 0.0000 1.0982 1.0982 +2 0.0000 -0.4669 0.0000 0.0000 -6.8958 0.0000 1.0982 1.4170 +3 -0.1185 6.3204 0.0000 -0.1185 6.3204 0.0000 1.4170 1.4170 +4 0.0000 -0.6918 0.0000 0.0000 0.2421 0.0000 1.4170 1.5010 +5 0.0000 -0.4879 0.0000 0.0000 -1.7970 0.0000 1.0982 1.5010 +6 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.5010 1.1010 +7 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.5010 1.5300 +8 0.2130 0.3120 0.0777 0.2130 0.3120 0.0777 1.1010 1.1010 +9 0.0814 0.0591 0.2219 0.2486 0.2422 -0.0925 1.1010 1.5300 +10 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.4170 1.5300 +11 -0.5835 1.1220 0.3978 1.3997 0.7756 0.0000 1.4170 1.1010 +12 0.2486 0.2422 -0.0925 0.0814 0.0591 0.2219 1.5300 1.1010 +13 -0.0732 0.0000 0.0000 -0.0732 0.0000 0.0000 1.5300 1.5300 + +MiddleBondTorsion Coeffs + + 1 0.0000 4.8228 0.0000 1.4170 + 2 0.0000 -1.1521 0.0000 1.4170 + 3 27.5989 -2.3120 0.0000 1.4170 + 4 0.0000 9.1792 0.0000 1.4170 + 5 0.0000 3.9421 0.0000 1.4170 + 6 0.0000 0.0000 0.0000 1.5300 + 7 0.0000 0.0000 0.0000 1.5300 + 8 -14.2610 -0.5322 -0.4864 1.5300 + 9 -14.8790 -3.6581 -0.3138 1.5300 + 10 0.0000 0.0000 0.0000 1.5010 + 11 -5.5679 1.4083 0.3010 1.5010 + 12 -14.8790 -3.6581 -0.3138 1.5300 + 13 -17.7870 -7.1877 0.0000 1.5300 + +BondBond13 Coeffs + + 1 -1.7077 1.0982 1.0982 + 2 -6.2741 1.0982 1.4170 + 3 53.0000 1.4170 1.4170 + 4 2.5085 1.4170 1.5010 + 5 0.8743 1.0982 1.5010 + 6 0.0000 1.5010 1.1010 + 7 0.0000 1.5010 1.5300 + 8 0.0000 1.1010 1.1010 + 9 0.0000 1.1010 1.5300 + 10 0.0000 1.4170 1.5300 + 11 -3.4826 1.4170 1.1010 + 12 0.0000 1.5300 1.1010 + 13 0.0000 1.5300 1.5300 + +AngleTorsion Coeffs + + 1 0.0000 2.4501 0.0000 0.0000 2.4501 0.0000 117.9400 117.9400 + 2 0.0000 2.7147 0.0000 0.0000 2.5014 0.0000 117.9400 118.9000 + 3 1.9767 1.0239 0.0000 1.9767 1.0239 0.0000 118.9000 118.9000 + 4 0.0000 3.8987 0.0000 0.0000 -4.4683 0.0000 118.9000 120.0500 + 5 0.0000 3.4601 0.0000 0.0000 -0.1242 0.0000 117.9400 120.0500 + 6 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 108.4000 110.7700 + 7 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 108.4000 112.6700 + 8 -0.8085 0.5569 -0.2466 -0.8085 0.5569 -0.2466 110.7700 110.7700 + 9 0.3113 0.4516 -0.1988 -0.2454 0.0000 -0.1136 110.7700 112.6700 + 10 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 120.0500 108.4000 + 11 0.2251 0.6548 0.1237 4.6266 0.1632 0.0461 120.0500 111.0000 + 12 -0.2454 0.0000 -0.1136 0.3113 0.4516 -0.1988 112.6700 110.7700 + 13 0.3886 -0.3139 0.1389 0.3886 -0.3139 0.1389 112.6700 112.6700 Atoms # full -44 1 2 3.5400000000000001e-02 6.1476397222913839e+01 8.2376490601205234e+01 6.0906939115836181e+01 -45 1276 2 3.5400000000000001e-02 5.8398688202244472e+01 8.0172948526664996e+01 6.2115536813582672e+01 -46 1276 6 -6.9599999999999995e-02 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38 21 39 40 + 74 2 37 39 21 22 + 75 3 22 21 39 40 + 76 5 20 24 22 18 + 77 4 41 24 22 18 + 78 2 20 24 22 21 + 79 3 21 22 24 41 + 80 2 20 24 41 40 + 81 1 20 24 41 43 + 82 3 22 24 41 40 + 83 2 43 41 24 22 + 84 12 19 28 46 45 + 85 12 19 28 46 48 + 86 8 27 28 46 45 + 87 8 27 28 46 48 + 88 6 29 28 46 45 + 89 6 29 28 46 48 + 90 10 35 29 28 19 + 91 10 32 29 28 19 + 92 11 35 29 28 27 + 93 11 32 29 28 27 + 94 10 35 29 28 46 + 95 10 32 29 28 46 + 96 5 47 35 29 28 + 97 4 36 35 29 28 + 98 2 47 35 29 32 + 99 3 32 29 35 36 + 100 5 31 32 29 28 + 101 4 33 32 29 28 + 102 2 31 32 29 35 + 103 3 35 29 32 33 + 104 2 30 33 32 29 + 105 3 29 32 33 34 + 106 1 31 32 33 30 + 107 2 31 32 33 34 + 108 1 30 33 34 9 + 109 2 30 33 34 36 + 110 2 9 34 33 32 + 111 3 32 33 34 36 + 112 1 9 34 36 10 + 113 2 9 34 36 35 + 114 2 10 36 34 33 + 115 3 33 34 36 35 + 116 2 10 36 35 29 + 117 3 29 35 36 34 + 118 1 47 35 36 10 + 119 2 47 35 36 34 + 120 2 42 40 39 21 + 121 3 21 39 40 41 + 122 1 37 39 40 42 + 123 2 37 39 40 41 + 124 3 39 40 41 24 + 125 2 43 41 40 39 + 126 2 42 40 41 24 + 127 1 42 40 41 43 Impropers -1 6 45 46 48 28 -2 1 22 18 17 13 -3 1 22 18 13 19 -4 1 17 18 13 19 -5 1 22 18 17 19 -6 1 44 19 18 28 -7 1 23 19 18 28 -8 1 44 19 23 28 -9 1 44 19 23 18 -10 1 22 21 39 38 -11 5 21 22 24 18 -12 1 29 28 27 46 -13 1 29 28 27 19 -14 1 29 28 46 19 -15 1 27 28 46 19 -16 1 22 24 41 20 -17 1 21 39 40 37 -18 1 41 40 39 42 -19 1 24 41 40 43 -20 1 32 33 34 30 -21 1 36 34 33 9 -22 1 7 6 2 5 -23 1 16 7 6 8 -24 9 16 12 26 13 -25 1 25 13 11 12 -26 1 25 13 12 18 -27 1 11 13 12 18 -28 1 25 13 11 18 -29 1 16 15 4 14 -30 8 15 16 7 12 -31 5 32 29 35 28 -32 1 29 32 33 31 -33 1 29 35 36 47 -34 1 35 36 34 10 -35 1 6 2 4 1 -36 1 15 4 2 3 + 1 1 1 2 6 4 + 2 1 3 4 2 15 + 3 1 5 6 2 7 + 4 1 8 7 6 16 + 5 2 26 12 16 13 + 6 1 14 15 4 16 + 7 3 7 16 15 12 + 8 1 38 21 22 39 + 9 3 21 22 24 18 + 10 1 20 24 22 41 + 11 3 35 29 32 28 + 12 1 31 32 29 33 + 13 1 30 33 32 34 + 14 1 9 34 33 36 + 15 1 47 35 29 36 + 16 1 10 36 34 35 + 17 1 37 39 21 40 + 18 1 42 40 39 41 + 19 1 43 41 40 24 + 20 4 45 46 48 28 From a235cd4719d53d28fbfaff61ea8c2fde76bde435 Mon Sep 17 00:00:00 2001 From: Jacob Gissinger Date: Tue, 20 Dec 2022 14:02:46 -0500 Subject: [PATCH 13/47] mention type labels in bond/react docs --- doc/src/fix_bond_react.rst | 40 +++++++++++++++++++++++++------------- 1 file changed, 27 insertions(+), 13 deletions(-) diff --git a/doc/src/fix_bond_react.rst b/doc/src/fix_bond_react.rst index 4377d9d946..d8071facd2 100644 --- a/doc/src/fix_bond_react.rst +++ b/doc/src/fix_bond_react.rst @@ -123,6 +123,17 @@ using this fix is (4) create a map that relates the template-atom-IDs of each atom between pre- and post-reaction molecule templates (5) fill a simulation box with molecules and run a simulation with fix bond/react. +.. note:: + + .. versionadded:: 15Sep2022 + + :doc:`Type labels ` allow for molecule templates + and data files to use alphanumeric atom types that match those of + a force field. Input files that use type labels are inherently + compatible with each other and portable between different + simulations. Therefore, it is highly recommended to use type labels + to specify atom, bond, etc. types when using fix bond/react. + Only one 'fix bond/react' command can be used at a time. Multiple reactions can be simultaneously applied by specifying multiple *react* arguments to a single 'fix bond/react' command. This syntax is @@ -228,18 +239,18 @@ pairs are identified within the cutoff distance: initiator partners, these two atoms are identified as the initiator atom pair of the reaction site. -Note that it can be helpful to select -unique atom types for the initiator atoms: if an initiator atom pair -is identified, as described in the previous steps, but it does not -correspond to the same pair specified in the pre-reaction template, an -otherwise eligible reaction could be prevented from occurring. Once -this unique initiator atom pair is identified for each reaction, there -could be two or more reactions that involve the same atom on the same -time step. If this is the case, only one such reaction is permitted to -occur. This reaction is chosen randomly from all potential reactions -involving the overlapping atom. This capability allows, for example, -different reaction pathways to proceed from identical reaction sites -with user-specified probabilities. +Note that it can be helpful to select unique atom types for the +initiator atoms: if an initiator atom pair is identified, as described +in the previous steps, but it does not correspond to the same pair +specified in the pre-reaction template, an otherwise eligible reaction +could be prevented from occurring. Once this unique initiator atom +pair is identified for each reaction, there could be two or more +reactions that involve the same atom on the same time step. If this is +the case, only one such reaction is permitted to occur. This reaction +is chosen randomly from all potential reactions involving the +overlapping atom. This capability allows, for example, different +reaction pathways to proceed from identical reaction sites with +user-specified probabilities. The pre-reacted molecule template is specified by a molecule command. This molecule template file contains a sample reaction site and its @@ -280,7 +291,10 @@ for a given simulation. All atom types in the pre-reacted template must be the same as those of a potential reaction site in the simulation. A detailed discussion of matching molecule template atom types with the simulation is provided on the :doc:`molecule ` -command page. +command page. It is highly recommended to use :doc:`Type labels ` +(added in version 15Sep2022) in both molecule templates and data +files, which automates the process of syncing atom types between +different input files. The post-reacted molecule template contains a sample of the reaction site and its surrounding topology after the reaction has occurred. It From da98363a25ec6cb6f18aed85fc621525fbf94fa7 Mon Sep 17 00:00:00 2001 From: Axel Kohlmeyer Date: Sat, 24 Dec 2022 22:49:42 -0500 Subject: [PATCH 14/47] implement angle_write command --- doc/src/Commands_all.rst | 1 + doc/src/angle_table.rst | 11 +- doc/src/angle_write.rst | 98 ++++++++ doc/src/bond_write.rst | 2 +- doc/src/commands_list.rst | 1 + doc/utils/sphinx-config/false_positives.txt | 1 + src/angle_write.cpp | 244 ++++++++++++++++++++ src/angle_write.h | 34 +++ 8 files changed, 387 insertions(+), 5 deletions(-) create mode 100644 doc/src/angle_write.rst create mode 100644 src/angle_write.cpp create mode 100644 src/angle_write.h diff --git a/doc/src/Commands_all.rst b/doc/src/Commands_all.rst index bd9d0ed09c..2ba5cba51d 100644 --- a/doc/src/Commands_all.rst +++ b/doc/src/Commands_all.rst @@ -24,6 +24,7 @@ table above. * :doc:`angle_coeff ` * :doc:`angle_style ` + * :doc:`angle_write ` * :doc:`atom_modify ` * :doc:`atom_style ` * :doc:`balance ` diff --git a/doc/src/angle_table.rst b/doc/src/angle_table.rst index c0faa3f046..fba41db045 100644 --- a/doc/src/angle_table.rst +++ b/doc/src/angle_table.rst @@ -59,9 +59,12 @@ format of this file is described below. ---------- -Suitable tables for use with this angle style can be created using the -Python code in the ``tools/tabulate`` folder of the LAMMPS source code -distribution. +Suitable tables for use with this angle style can be created by LAMMPS +itself from existing angle styles using the :doc:`angle_write +` command. This can be useful to have a template file for +testing the angle style settings and to build a compatible custom file. +Another option to generate tables is the Python code in the +``tools/tabulate`` folder of the LAMMPS source code distribution. The format of a tabulated file is as follows (without the parenthesized comments): @@ -154,7 +157,7 @@ for more info. Related commands """""""""""""""" -:doc:`angle_coeff ` +:doc:`angle_coeff `, :doc:`angle_write ` Default """"""" diff --git a/doc/src/angle_write.rst b/doc/src/angle_write.rst new file mode 100644 index 0000000000..16a4ee4e2c --- /dev/null +++ b/doc/src/angle_write.rst @@ -0,0 +1,98 @@ +.. index:: angle_write + +angle_write command +=================== + +Syntax +"""""" + +.. code-block:: LAMMPS + + angle_write atype N file keyword + +* atype = angle type +* N = # of values +* file = name of file to write values to +* keyword = section name in file for this set of tabulated values + +Examples +"""""""" + +.. code-block:: LAMMPS + + angle_write 1 500 table.txt Harmonic_1 + angle_write 3 1000 table.txt Harmonic_3 + +Description +""""""""""" + +Write energy and force values to a file as a function of angle for the +currently defined angle potential. Force in this context means the +angle force, not the force on individual atoms. This is useful for +plotting the potential function or otherwise debugging its values. The +resulting file can also be used as input for use with :doc:`angle style +table `. + +If the file already exists, the table of values is appended to the end +of the file to allow multiple tables of energy and force to be included +in one file. The individual sections may be identified by the *keyword*. + +The energy and force values are computed for angles ranging from 0 +degrees to 180 degrees for 3 interacting atoms forming an angle type +atype, using the appropriate :doc:`angle_coeff ` +coefficients. N evenly spaced angles are used. + +For example, for N = 6, values are computed at :math:`\theta = 0, 36, +72, 108, 144, 180`. + +The file is written in the format used as input for the +:doc:`angle_style table ` option with *keyword* as the +section name. Each line written to the file lists an index number +(1-N), an angle (in degrees), an energy (in energy units), and a force +(in force units per radians^2). In case a new file is created, the +first line will be a comment with a "DATE:" and "UNITS:" tag with the +current date and :doc:`units ` settings. For subsequent +invocations of the *angle_write* command for the same file, data will be +appended and the current units settings will be compared to the data +from the header, if present. The *angle_write* will refuse to add a +table to an existing file if the units are not the same. + +Restrictions +"""""""""""" + +All force field coefficients for angle and other kinds of interactions +must be set before this command can be invoked. + +The table of the angle energy and force data data is created by using a +separate, internally created, new LAMMPS instance with a dummy system of +3 atoms for which the angle potential energy is computed after +transferring the angle style and coefficients and arranging the 3 atoms +into the corresponding geometries. The angle force is then determined +from the potential energies through numerical differentiation. As a +consequence or this approach, not all angle styles are compatible. The +following conditions must be met: + +- The angle style must be able to write its coefficients to a data file. + This condition excludes for example :doc:`angle style hybrid ` and + :doc:`angle style table `. +- The potential function must not have any terms that depend on geometry + properties other than the angle. This condition excludes for example + all angle types for :doc:`angle style charmm ` that have + non-zero Urey-Bradley terms. Please note that the *write_angle* + command has no way of checking for this condition, so the resulting tables + may be bogus. It is strongly recommended to make careful tests for any + created tables. +- There must not be multiple angle interactions defined for the same + triple of atoms. This applies for example to :doc:`angle_style class2 + `. + +Related commands +"""""""""""""""" + +:doc:`angle_style table `, :doc:`bond_write `, +:doc:`angle_style `, :doc:`angle_coeff ` + +Default +""""""" + +none diff --git a/doc/src/bond_write.rst b/doc/src/bond_write.rst index 4170029239..51e0653f51 100644 --- a/doc/src/bond_write.rst +++ b/doc/src/bond_write.rst @@ -67,7 +67,7 @@ be specified even if the potential has a finite value at r = 0.0. Related commands """""""""""""""" -:doc:`bond_style table `, +:doc:`bond_style table `, `angle_write `, :doc:`bond_style `, :doc:`bond_coeff ` Default diff --git a/doc/src/commands_list.rst b/doc/src/commands_list.rst index ff2502189d..5731cbb755 100644 --- a/doc/src/commands_list.rst +++ b/doc/src/commands_list.rst @@ -6,6 +6,7 @@ Commands angle_coeff angle_style + angle_write atom_modify atom_style balance diff --git a/doc/utils/sphinx-config/false_positives.txt b/doc/utils/sphinx-config/false_positives.txt index 7cb409d040..13cc96f993 100644 --- a/doc/utils/sphinx-config/false_positives.txt +++ b/doc/utils/sphinx-config/false_positives.txt @@ -174,6 +174,7 @@ attrac Atw Atwater atwt +atype augt AuO automagically diff --git a/src/angle_write.cpp b/src/angle_write.cpp new file mode 100644 index 0000000000..e0d6827a66 --- /dev/null +++ b/src/angle_write.cpp @@ -0,0 +1,244 @@ +/* ---------------------------------------------------------------------- + LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator + https://www.lammps.org/, Sandia National Laboratories + LAMMPS development team: developers@lammps.org + + Copyright (2003) Sandia Corporation. Under the terms of Contract + DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains + certain rights in this software. This software is distributed under + the GNU General Public License. + + See the README file in the top-level LAMMPS directory. +------------------------------------------------------------------------- */ + +/* ---------------------------------------------------------------------- + Contributing authors: Axel Kohlmeyer (Temple U) +------------------------------------------------------------------------- */ + +#include "angle_write.h" + +#include "angle.h" +#include "atom.h" +#include "atom_vec.h" +#include "comm.h" +#include "domain.h" +#include "error.h" +#include "force.h" +#include "input.h" +#include "lammps.h" +#include "math_const.h" +#include "update.h" + +#include +using namespace LAMMPS_NS; +using MathConst::DEG2RAD; +using MathConst::RAD2DEG; + +static constexpr double epsilon = 6.5e-6; +#define MAXLINE 1024 +/* ---------------------------------------------------------------------- */ + +void AngleWrite::command(int narg, char **arg) +{ + // sanity checks + + if (domain->box_exist == 0) + error->all(FLERR, "Angle_write command before simulation box is defined"); + if (atom->avec->angles_allow == 0) + error->all(FLERR, "Angle_write command when no angles allowed"); + auto angle = force->angle; + if (angle == nullptr) error->all(FLERR, "Angle_write command before an angle_style is defined"); + if (angle && (force->angle->writedata == 0)) + error->all(FLERR, "Angle style must support writing coeffs to data file for angle_write"); + + // parse arguments + + if (narg != 4) error->all(FLERR, "Illegal angle_write command"); + + int atype = utils::inumeric(FLERR, arg[0], false, lmp); + int n = utils::inumeric(FLERR, arg[1], false, lmp); + std::string table_file = arg[2]; + std::string keyword = arg[3]; + + // make sure system is initialized before calling any functions + + lmp->init(); + + double theta0 = angle->equilibrium_angle(atype) * RAD2DEG; + + // write out all angle_coeff settings to file. use function from write_data. + // open table file in append mode if it already exists + // add line with DATE: and UNITS: tag when creating new file + // otherwise make certain that units are consistent + // print header in format used by angle_style table + + FILE *fp = nullptr; + std::string coeffs_file = table_file + ".tmp.coeffs"; + if (comm->me == 0) { + + fp = fopen(coeffs_file.c_str(), "w"); + force->angle->write_data(fp); + fclose(fp); + + // units sanity check: + // - if this is the first time we write to this potential file, + // write out a line with "DATE:" and "UNITS:" tags + // - if the file already exists, print a message about appending + // while printing the date and check that units are consistent. + if (platform::file_is_readable(table_file)) { + std::string units = utils::get_potential_units(table_file, "table"); + if (!units.empty() && (units != update->unit_style)) { + error->one(FLERR, "Trying to append to a table file with UNITS: {} while units are {}", + units, update->unit_style); + } + std::string date = utils::get_potential_date(table_file, "table"); + utils::logmesg(lmp, "Appending to table file {} with DATE: {}\n", table_file, date); + fp = fopen(table_file.c_str(), "a"); + } else { + utils::logmesg(lmp, "Creating table file {} with DATE: {}\n", table_file, + utils::current_date()); + fp = fopen(table_file.c_str(), "w"); + if (fp) + fmt::print(fp, "# DATE: {} UNITS: {} Created by angle_write\n", utils::current_date(), + update->unit_style); + } + if (fp == nullptr) + error->one(FLERR, "Cannot open angle_write file {}: {}", table_file, utils::getsyserror()); + } + + // split communicator so that we can run a new LAMMPS class instance only on comm->me == 0 + + MPI_Comm singlecomm; + int color = (comm->me == 0) ? 1 : MPI_UNDEFINED; + int key = comm->me; + MPI_Comm_split(world, color, key, &singlecomm); + + if (comm->me == 0) { + // set up new LAMMPS instance with dummy system to evaluate angle potential + const char *args[] = {"AngleWrite", "-nocite", "-echo", "none", + "-log", "none", "-screen", "none"}; + char **argv = (char **) args; + int argc = sizeof(args) / sizeof(char *); + LAMMPS *writer = new LAMMPS(argc, argv, singlecomm); + + // create dummy system replicating angle style settings + writer->input->one(fmt::format("units {}", update->unit_style)); + writer->input->one("atom_style angle"); + writer->input->one("atom_modify map array"); + writer->input->one("boundary f f f"); + writer->input->one("region box block -2 2 -2 2 -1 1"); + writer->input->one(fmt::format("create_box {} box angle/types {} " + "extra/angle/per/atom 1 " + "extra/special/per/atom 4", + atom->ntypes, atom->nangletypes)); + writer->input->one("create_atoms 1 single 0.0 0.0 0.0"); + writer->input->one("create_atoms 1 single 1.0 0.0 0.0"); + writer->input->one("create_atoms 1 single -1.0 0.0 0.0"); + writer->input->one(fmt::format("create_bonds single/angle {} 2 1 3", atype)); + + writer->input->one("pair_style zero 10.0"); + writer->input->one("pair_coeff * *"); + writer->input->one("mass * 1.0"); + writer->input->one(fmt::format("angle_style {}", force->angle_style)); + FILE *coeffs; + char line[MAXLINE]; + coeffs = fopen(coeffs_file.c_str(), "r"); + for (int i = 0; i < atom->nangletypes; ++i) { + fgets(line, MAXLINE, coeffs); + writer->input->one(fmt::format("angle_coeff {}", line)); + } + platform::unlink(coeffs_file); + + // initialize system + + writer->init(); + + // move third atom to reproduce angles + + double theta, phi, phi1, phi2, f; + angle = writer->force->angle; + int i1, i2, i3; + i1 = writer->atom->map(1); + i2 = writer->atom->map(2); + i3 = writer->atom->map(3); + auto atom3 = writer->atom->x[i3]; + + // evaluate energy and force at each of N distances + + fmt::print(fp, "# Angle potential {} for angle type {}: i,theta,energy,force\n", + force->angle_style, atype); + fmt::print(fp, "\n{}\nN {} EQ {:.15g}\n\n", keyword, n, theta0); + + const double dtheta = 180.0 / static_cast(n - 1); + + // get force for divergent 0 degree angle from interpolation to the right + theta = 0.0; + atom3[0] = cos(theta * DEG2RAD); + atom3[1] = sin(theta * DEG2RAD); + phi = angle->single(atype, i2, i1, i3); + + theta = epsilon; + atom3[0] = cos(theta * DEG2RAD); + atom3[1] = sin(theta * DEG2RAD); + phi1 = angle->single(atype, i2, i1, i3); + + theta = 2.0 * epsilon; + atom3[0] = cos(theta * DEG2RAD); + atom3[1] = sin(theta * DEG2RAD); + phi2 = angle->single(atype, i2, i1, i3); + + f = (1.5 * phi - 2.0 * phi1 + 0.5 * phi2) / epsilon; + if (!std::isfinite(f)) f = 0.0; + if (!std::isfinite(phi)) phi = 0.0; + fprintf(fp, "%8d %- 22.15g %- 22.15g %- 22.15g\n", 1, 0.0, phi, f); + + for (int i = 1; i < n - 1; i++) { + theta = dtheta * static_cast(i) - epsilon; + atom3[0] = cos(theta * DEG2RAD); + atom3[1] = sin(theta * DEG2RAD); + phi1 = angle->single(atype, i2, i1, i3); + + theta = dtheta * static_cast(i) + epsilon; + atom3[0] = cos(theta * DEG2RAD); + atom3[1] = sin(theta * DEG2RAD); + phi2 = angle->single(atype, i2, i1, i3); + + theta = dtheta * static_cast(i); + atom3[0] = cos(theta * DEG2RAD); + atom3[1] = sin(theta * DEG2RAD); + phi = angle->single(atype, i2, i1, i3); + if (!std::isfinite(phi)) phi = 0.0; + + // get force from numerical differentiation + f = -0.5 * (phi2 - phi1) / epsilon; + if (!std::isfinite(f)) f = 0.0; + fprintf(fp, "%8d %- 22.15g %- 22.15g %- 22.15g\n", i + 1, theta, phi, f); + } + + // get force for divergent 180 degree angle from interpolation to the left + theta = 180.0; + atom3[0] = cos(theta * DEG2RAD); + atom3[1] = sin(theta * DEG2RAD); + phi = angle->single(atype, i2, i1, i3); + + theta = 180.0 - epsilon; + atom3[0] = cos(theta * DEG2RAD); + atom3[1] = sin(theta * DEG2RAD); + phi1 = angle->single(atype, i2, i1, i3); + + theta = 180.0 - 2.0 * epsilon; + atom3[0] = cos(theta * DEG2RAD); + atom3[1] = sin(theta * DEG2RAD); + phi2 = angle->single(atype, i2, i1, i3); + + f = (2.0 * phi1 - 1.5 * phi - 0.5 * phi2) / epsilon; + if (!std::isfinite(f)) f = 0.0; + if (!std::isfinite(phi)) phi = 0.0; + fprintf(fp, "%8d %- 22.15g %- 22.15g %- 22.15g\n", 1, 180.0, phi, f); + + // clean up + delete writer; + fclose(fp); + } + MPI_Comm_free(&singlecomm); +} diff --git a/src/angle_write.h b/src/angle_write.h new file mode 100644 index 0000000000..5c56cd8efc --- /dev/null +++ b/src/angle_write.h @@ -0,0 +1,34 @@ +/* -*- c++ -*- ---------------------------------------------------------- + LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator + https://www.lammps.org/, Sandia National Laboratories + LAMMPS development team: developers@lammps.org + + Copyright (2003) Sandia Corporation. Under the terms of Contract + DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains + certain rights in this software. This software is distributed under + the GNU General Public License. + + See the README file in the top-level LAMMPS directory. +------------------------------------------------------------------------- */ + +#ifdef COMMAND_CLASS +// clang-format off +CommandStyle(angle_write,AngleWrite); +// clang-format on +#else + +#ifndef LMP_ANGLE_WRITE_H +#define LMP_ANGLE_WRITE_H + +#include "command.h" + +namespace LAMMPS_NS { + +class AngleWrite : public Command { + public: + AngleWrite(class LAMMPS *lmp) : Command(lmp){}; + void command(int, char **) override; +}; +} // namespace LAMMPS_NS +#endif +#endif From bbdc6fd3ab1ef7ce093fcc6337342e680d0942d5 Mon Sep 17 00:00:00 2001 From: Axel Kohlmeyer Date: Sun, 25 Dec 2022 04:35:03 -0500 Subject: [PATCH 15/47] fix file handle leak --- src/angle_write.cpp | 1 + 1 file changed, 1 insertion(+) diff --git a/src/angle_write.cpp b/src/angle_write.cpp index e0d6827a66..ca0118eda5 100644 --- a/src/angle_write.cpp +++ b/src/angle_write.cpp @@ -147,6 +147,7 @@ void AngleWrite::command(int narg, char **arg) fgets(line, MAXLINE, coeffs); writer->input->one(fmt::format("angle_coeff {}", line)); } + fclose(coeffs); platform::unlink(coeffs_file); // initialize system From ecf11f2f20d16de4a81bed70efc6e21090148dbb Mon Sep 17 00:00:00 2001 From: Axel Kohlmeyer Date: Sun, 25 Dec 2022 06:06:34 -0500 Subject: [PATCH 16/47] use macro for keeping repetitive code consistent --- src/angle_write.cpp | 55 +++++++++++++-------------------------------- 1 file changed, 15 insertions(+), 40 deletions(-) diff --git a/src/angle_write.cpp b/src/angle_write.cpp index ca0118eda5..554f03d18f 100644 --- a/src/angle_write.cpp +++ b/src/angle_write.cpp @@ -170,23 +170,19 @@ void AngleWrite::command(int narg, char **arg) force->angle_style, atype); fmt::print(fp, "\n{}\nN {} EQ {:.15g}\n\n", keyword, n, theta0); +#define GET_ENERGY(myphi, mytheta) \ + theta = mytheta; \ + atom3[0] = cos(theta * DEG2RAD); \ + atom3[1] = sin(theta * DEG2RAD); \ + myphi = angle->single(atype, i2, i1, i3) + const double dtheta = 180.0 / static_cast(n - 1); // get force for divergent 0 degree angle from interpolation to the right - theta = 0.0; - atom3[0] = cos(theta * DEG2RAD); - atom3[1] = sin(theta * DEG2RAD); - phi = angle->single(atype, i2, i1, i3); - theta = epsilon; - atom3[0] = cos(theta * DEG2RAD); - atom3[1] = sin(theta * DEG2RAD); - phi1 = angle->single(atype, i2, i1, i3); - - theta = 2.0 * epsilon; - atom3[0] = cos(theta * DEG2RAD); - atom3[1] = sin(theta * DEG2RAD); - phi2 = angle->single(atype, i2, i1, i3); + GET_ENERGY(phi, 0.0); + GET_ENERGY(phi1, epsilon); + GET_ENERGY(phi2, 2.0 * epsilon); f = (1.5 * phi - 2.0 * phi1 + 0.5 * phi2) / epsilon; if (!std::isfinite(f)) f = 0.0; @@ -194,20 +190,10 @@ void AngleWrite::command(int narg, char **arg) fprintf(fp, "%8d %- 22.15g %- 22.15g %- 22.15g\n", 1, 0.0, phi, f); for (int i = 1; i < n - 1; i++) { - theta = dtheta * static_cast(i) - epsilon; - atom3[0] = cos(theta * DEG2RAD); - atom3[1] = sin(theta * DEG2RAD); - phi1 = angle->single(atype, i2, i1, i3); + GET_ENERGY(phi1, dtheta * static_cast(i) - epsilon); + GET_ENERGY(phi2, dtheta * static_cast(i) + epsilon); + GET_ENERGY(phi, dtheta * static_cast(i)); - theta = dtheta * static_cast(i) + epsilon; - atom3[0] = cos(theta * DEG2RAD); - atom3[1] = sin(theta * DEG2RAD); - phi2 = angle->single(atype, i2, i1, i3); - - theta = dtheta * static_cast(i); - atom3[0] = cos(theta * DEG2RAD); - atom3[1] = sin(theta * DEG2RAD); - phi = angle->single(atype, i2, i1, i3); if (!std::isfinite(phi)) phi = 0.0; // get force from numerical differentiation @@ -217,20 +203,9 @@ void AngleWrite::command(int narg, char **arg) } // get force for divergent 180 degree angle from interpolation to the left - theta = 180.0; - atom3[0] = cos(theta * DEG2RAD); - atom3[1] = sin(theta * DEG2RAD); - phi = angle->single(atype, i2, i1, i3); - - theta = 180.0 - epsilon; - atom3[0] = cos(theta * DEG2RAD); - atom3[1] = sin(theta * DEG2RAD); - phi1 = angle->single(atype, i2, i1, i3); - - theta = 180.0 - 2.0 * epsilon; - atom3[0] = cos(theta * DEG2RAD); - atom3[1] = sin(theta * DEG2RAD); - phi2 = angle->single(atype, i2, i1, i3); + GET_ENERGY(phi, 180.0); + GET_ENERGY(phi1, 180.0 - epsilon); + GET_ENERGY(phi2, 180.0 - 2.0 * epsilon); f = (2.0 * phi1 - 1.5 * phi - 0.5 * phi2) / epsilon; if (!std::isfinite(f)) f = 0.0; From c4f2befb1f535daf06f42c7bebe98ee3c4ba21c9 Mon Sep 17 00:00:00 2001 From: Axel Kohlmeyer Date: Sun, 25 Dec 2022 06:25:45 -0500 Subject: [PATCH 17/47] add sanity check on valid angle type --- src/angle_write.cpp | 3 +++ 1 file changed, 3 insertions(+) diff --git a/src/angle_write.cpp b/src/angle_write.cpp index 554f03d18f..3b7c7f2e24 100644 --- a/src/angle_write.cpp +++ b/src/angle_write.cpp @@ -56,6 +56,9 @@ void AngleWrite::command(int narg, char **arg) if (narg != 4) error->all(FLERR, "Illegal angle_write command"); int atype = utils::inumeric(FLERR, arg[0], false, lmp); + if ((atype <= 0) || (atype > atom->nangletypes)) + error->all(FLERR, "Invalid angle type {} in angle_write command", atype); + int n = utils::inumeric(FLERR, arg[1], false, lmp); std::string table_file = arg[2]; std::string keyword = arg[3]; From a4f8cb9a9230566d72d579e7bdb0a260130d3ef7 Mon Sep 17 00:00:00 2001 From: Axel Kohlmeyer Date: Sun, 25 Dec 2022 06:54:40 -0500 Subject: [PATCH 18/47] explicitly disallow angle_write with angle_style class2 --- src/angle_write.cpp | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/src/angle_write.cpp b/src/angle_write.cpp index 3b7c7f2e24..e7c95be3cf 100644 --- a/src/angle_write.cpp +++ b/src/angle_write.cpp @@ -51,6 +51,10 @@ void AngleWrite::command(int narg, char **arg) if (angle && (force->angle->writedata == 0)) error->all(FLERR, "Angle style must support writing coeffs to data file for angle_write"); + if (angle && (utils::strmatch(force->angle_style, "^class2"))) + error->all(FLERR, "Angle_write command is not compatible with angle style {}", + force->angle_style); + // parse arguments if (narg != 4) error->all(FLERR, "Illegal angle_write command"); From bbfc7381fb81dca21ffc9b109e6761150cc4d63a Mon Sep 17 00:00:00 2001 From: Axel Kohlmeyer Date: Sun, 25 Dec 2022 06:54:53 -0500 Subject: [PATCH 19/47] updates and corrections for docs --- doc/src/angle_write.rst | 27 +++++++++++++-------------- 1 file changed, 13 insertions(+), 14 deletions(-) diff --git a/doc/src/angle_write.rst b/doc/src/angle_write.rst index 16a4ee4e2c..8bc94b5191 100644 --- a/doc/src/angle_write.rst +++ b/doc/src/angle_write.rst @@ -28,10 +28,10 @@ Description Write energy and force values to a file as a function of angle for the currently defined angle potential. Force in this context means the -angle force, not the force on individual atoms. This is useful for -plotting the potential function or otherwise debugging its values. The -resulting file can also be used as input for use with :doc:`angle style -table `. +force with respect to the angle, not the force on individual atoms. +This is useful for plotting the potential function or otherwise +debugging its values. The resulting file can also be used as input for +use with :doc:`angle style table `. If the file already exists, the table of values is appended to the end of the file to allow multiple tables of energy and force to be included @@ -69,7 +69,7 @@ separate, internally created, new LAMMPS instance with a dummy system of transferring the angle style and coefficients and arranging the 3 atoms into the corresponding geometries. The angle force is then determined from the potential energies through numerical differentiation. As a -consequence or this approach, not all angle styles are compatible. The +consequence of this approach, not all angle styles are compatible. The following conditions must be met: - The angle style must be able to write its coefficients to a data file. @@ -77,20 +77,19 @@ following conditions must be met: :doc:`angle style table `. - The potential function must not have any terms that depend on geometry properties other than the angle. This condition excludes for example - all angle types for :doc:`angle style charmm ` that have - non-zero Urey-Bradley terms. Please note that the *write_angle* - command has no way of checking for this condition, so the resulting tables - may be bogus. It is strongly recommended to make careful tests for any - created tables. -- There must not be multiple angle interactions defined for the same - triple of atoms. This applies for example to :doc:`angle_style class2 - `. + :doc:`angle style class2 ` all angle types for + :doc:`angle style charmm ` that have non-zero + Urey-Bradley terms. Please note that the *write_angle* command has no + way of checking for this condition, so the resulting tables may be + bogus if the requirement is not met. It is thus recommended to make + careful tests for any created tables. Related commands """""""""""""""" :doc:`angle_style table `, :doc:`bond_write `, -:doc:`angle_style `, :doc:`angle_coeff ` +:doc:`dihedral_write `, :doc:`angle_style `, +:doc:`angle_coeff ` Default """"""" From 4ac830bf73a90820070b96c54057c36a829fd3c9 Mon Sep 17 00:00:00 2001 From: Axel Kohlmeyer Date: Sun, 25 Dec 2022 06:57:38 -0500 Subject: [PATCH 20/47] add dihedral_write command --- doc/src/Commands_all.rst | 1 + doc/src/commands_list.rst | 1 + doc/src/dihedral_write.rst | 99 ++++++++++ doc/utils/sphinx-config/false_positives.txt | 1 + src/dihedral_write.cpp | 206 ++++++++++++++++++++ src/dihedral_write.h | 34 ++++ 6 files changed, 342 insertions(+) create mode 100644 doc/src/dihedral_write.rst create mode 100644 src/dihedral_write.cpp create mode 100644 src/dihedral_write.h diff --git a/doc/src/Commands_all.rst b/doc/src/Commands_all.rst index 2ba5cba51d..4a035f5b41 100644 --- a/doc/src/Commands_all.rst +++ b/doc/src/Commands_all.rst @@ -46,6 +46,7 @@ table above. * :doc:`dielectric ` * :doc:`dihedral_coeff ` * :doc:`dihedral_style ` + * :doc:`dihedral_write ` * :doc:`dimension ` * :doc:`displace_atoms ` * :doc:`dump ` diff --git a/doc/src/commands_list.rst b/doc/src/commands_list.rst index 5731cbb755..cea237f14e 100644 --- a/doc/src/commands_list.rst +++ b/doc/src/commands_list.rst @@ -28,6 +28,7 @@ Commands dielectric dihedral_coeff dihedral_style + dihedral_write dimension displace_atoms dump diff --git a/doc/src/dihedral_write.rst b/doc/src/dihedral_write.rst new file mode 100644 index 0000000000..d0deb1d2e8 --- /dev/null +++ b/doc/src/dihedral_write.rst @@ -0,0 +1,99 @@ +.. index:: dihedral_write + +dihedral_write command +====================== + +Syntax +"""""" + +.. code-block:: LAMMPS + + dihedral_write dtype N file keyword + +* dtype = dihedral type +* N = # of values +* file = name of file to write values to +* keyword = section name in file for this set of tabulated values + +Examples +"""""""" + +.. code-block:: LAMMPS + + dihedral_write 1 500 table.txt Harmonic_1 + dihedral_write 3 1000 table.txt Harmonic_3 + +Description +""""""""""" + +Write energy and force values to a file as a function of the dihedral +angle for the currently defined dihedral potential. Force in this +context means the force with respect to the dihedral angle, not the +force on individual atoms. This is useful for plotting the potential +function or otherwise debugging its values. The resulting file can also +be used as input for use with :doc:`dihedral style table +`. + +If the file already exists, the table of values is appended to the end +of the file to allow multiple tables of energy and force to be included +in one file. The individual sections may be identified by the *keyword*. + +The energy and force values are computed for dihedrals ranging from 0 +degrees to 360 degrees for 4 interacting atoms forming an dihedral type +dtype, using the appropriate :doc:`dihedral_coeff ` +coefficients. N evenly spaced dihedrals are used. Since 0 and 360 +degrees are the same dihedral angle, the latter entry is skipped. + +For example, for N = 6, values would be computed at +:math:`\phi = 0, 60, 120, 180, 240, 300`. + +The file is written in the format used as input for the +:doc:`dihedral_style table ` option with *keyword* as +the section name. Each line written to the file lists an index number +(1-N), an dihedral angle (in degrees), an energy (in energy units), and +a force (in force units per radians^2). In case a new file is created, +the first line will be a comment with a "DATE:" and "UNITS:" tag with +the current date and :doc:`units ` settings. For subsequent +invocations of the *dihedral_write* command for the same file, data will +be appended and the current units settings will be compared to the data +from the header, if present. The *dihedral_write* will refuse to add a +table to an existing file if the units are not the same. + +Restrictions +"""""""""""" + +All force field coefficients for dihedrals and other kinds of interactions +must be set before this command can be invoked. + +The table of the dihedral energy and force data data is created by using a +separate, internally created, new LAMMPS instance with a dummy system of +4 atoms for which the dihedral potential energy is computed after +transferring the dihedral style and coefficients and arranging the 4 atoms +into the corresponding geometries. The dihedral force is then determined +from the potential energies through numerical differentiation. As a +consequence of this approach, not all dihedral styles are compatible. The +following conditions must be met: + +- The dihedral style must be able to write its coefficients to a data file. + This condition excludes for example :doc:`dihedral style hybrid ` and + :doc:`dihedral style table `. +- The potential function must not have any terms that depend on geometry + properties other than the dihedral. This condition excludes for + example :doc:`dihedral style class2 `. Please note + that the *write_dihedral* command has no way of checking for this + condition. It will check the style name against an internal list of + known to be incompatible styles. The resulting tables may be bogus + for unlisted dihedral styles if the requirement is not met. It is + thus recommended to make careful tests for any created tables. + +Related commands +"""""""""""""""" + +:doc:`dihedral_style table `, :doc:`bond_write `, +:doc:`angle_write `, :doc:`dihedral_style `, +:doc:`dihedral_coeff ` + +Default +""""""" + +none diff --git a/doc/utils/sphinx-config/false_positives.txt b/doc/utils/sphinx-config/false_positives.txt index 13cc96f993..855f306f84 100644 --- a/doc/utils/sphinx-config/false_positives.txt +++ b/doc/utils/sphinx-config/false_positives.txt @@ -829,6 +829,7 @@ dtemp dtgrow dtheta dtshrink +dtype du dU Ducastelle diff --git a/src/dihedral_write.cpp b/src/dihedral_write.cpp new file mode 100644 index 0000000000..eedcde0eb8 --- /dev/null +++ b/src/dihedral_write.cpp @@ -0,0 +1,206 @@ +/* ---------------------------------------------------------------------- + LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator + https://www.lammps.org/, Sandia National Laboratories + LAMMPS development team: developers@lammps.org + + Copyright (2003) Sandia Corporation. Under the terms of Contract + DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains + certain rights in this software. This software is distributed under + the GNU General Public License. + + See the README file in the top-level LAMMPS directory. +------------------------------------------------------------------------- */ + +/* ---------------------------------------------------------------------- + Contributing authors: Axel Kohlmeyer (Temple U) +------------------------------------------------------------------------- */ + +#include "dihedral_write.h" + +#include "atom.h" +#include "atom_vec.h" +#include "comm.h" +#include "dihedral.h" +#include "domain.h" +#include "error.h" +#include "force.h" +#include "input.h" +#include "lammps.h" +#include "math_const.h" +#include "update.h" + +#include +using namespace LAMMPS_NS; +using MathConst::DEG2RAD; +using MathConst::RAD2DEG; + +static constexpr double epsilon = 6.5e-6; +#define MAXLINE 1024 +/* ---------------------------------------------------------------------- */ + +void DihedralWrite::command(int narg, char **arg) +{ + // sanity checks + + if (domain->box_exist == 0) + error->all(FLERR, "Dihedral_write command before simulation box is defined"); + if (atom->avec->dihedrals_allow == 0) + error->all(FLERR, "Dihedral_write command when no dihedrals allowed"); + auto dihedral = force->dihedral; + if (dihedral == nullptr) + error->all(FLERR, "Dihedral_write command before an dihedral_style is defined"); + if (dihedral && (force->dihedral->writedata == 0)) + error->all(FLERR, "Dihedral style must support writing coeffs to data file for dihedral_write"); + + if (dihedral && + (utils::strmatch(force->dihedral_style, "^charmm") || + utils::strmatch(force->dihedral_style, "^class2"))) + error->all(FLERR, "Dihedral_write command is not compatible with dihedral style {}", + force->dihedral_style); + + // parse arguments + + if (narg != 4) error->all(FLERR, "Illegal dihedral_write command"); + + int dtype = utils::inumeric(FLERR, arg[0], false, lmp); + if ((dtype <= 0) || (dtype > atom->ndihedraltypes)) + error->all(FLERR, "Invalid dihedral type {} in dihedral_write command", dtype); + + int n = utils::inumeric(FLERR, arg[1], false, lmp); + std::string table_file = arg[2]; + std::string keyword = arg[3]; + + // make sure system is initialized before calling any functions + + lmp->init(); + + // write out all dihedral_coeff settings to file. use function from write_data. + // open table file in append mode if it already exists + // add line with DATE: and UNITS: tag when creating new file + // otherwise make certain that units are consistent + // print header in format used by dihedral_style table + + FILE *fp = nullptr; + std::string coeffs_file = table_file + ".tmp.coeffs"; + if (comm->me == 0) { + + fp = fopen(coeffs_file.c_str(), "w"); + force->dihedral->write_data(fp); + fclose(fp); + + // units sanity check: + // - if this is the first time we write to this potential file, + // write out a line with "DATE:" and "UNITS:" tags + // - if the file already exists, print a message about appending + // while printing the date and check that units are consistent. + if (platform::file_is_readable(table_file)) { + std::string units = utils::get_potential_units(table_file, "table"); + if (!units.empty() && (units != update->unit_style)) { + error->one(FLERR, "Trying to append to a table file with UNITS: {} while units are {}", + units, update->unit_style); + } + std::string date = utils::get_potential_date(table_file, "table"); + utils::logmesg(lmp, "Appending to table file {} with DATE: {}\n", table_file, date); + fp = fopen(table_file.c_str(), "a"); + } else { + utils::logmesg(lmp, "Creating table file {} with DATE: {}\n", table_file, + utils::current_date()); + fp = fopen(table_file.c_str(), "w"); + if (fp) + fmt::print(fp, "# DATE: {} UNITS: {} Created by dihedral_write\n", utils::current_date(), + update->unit_style); + } + if (fp == nullptr) + error->one(FLERR, "Cannot open dihedral_write file {}: {}", table_file, utils::getsyserror()); + } + + // split communicator so that we can run a new LAMMPS class instance only on comm->me == 0 + + MPI_Comm singlecomm; + int color = (comm->me == 0) ? 1 : MPI_UNDEFINED; + int key = comm->me; + MPI_Comm_split(world, color, key, &singlecomm); + + if (comm->me == 0) { + // set up new LAMMPS instance with dummy system to evaluate dihedral potential + // const char *args[] = {"DihedralWrite", "-nocite", "-echo", "none", + // "-log", "none", "-screen", "none"}; + const char *args[] = {"DihedralWrite", "-nocite", "-echo", "screen", "-log", "none"}; + char **argv = (char **) args; + int argc = sizeof(args) / sizeof(char *); + LAMMPS *writer = new LAMMPS(argc, argv, singlecomm); + + // create dummy system replicating dihedral style settings + writer->input->one(fmt::format("units {}", update->unit_style)); + writer->input->one("atom_style molecular"); + writer->input->one("atom_modify map array"); + writer->input->one("boundary f f f"); + writer->input->one("region box block -2 2 -2 2 -2 2"); + writer->input->one(fmt::format("create_box {} box dihedral/types {} " + "extra/dihedral/per/atom 1 " + "extra/special/per/atom 4", + atom->ntypes, atom->ndihedraltypes)); + writer->input->one("create_atoms 1 single 1.0 0.0 -1.0"); + writer->input->one("create_atoms 1 single 0.0 0.0 -1.0"); + writer->input->one("create_atoms 1 single 0.0 0.0 1.0"); + writer->input->one("create_atoms 1 single 1.0 0.0 1.0"); + writer->input->one(fmt::format("create_bonds single/dihedral {} 1 2 3 4", dtype)); + + writer->input->one("pair_style zero 10.0"); + writer->input->one("pair_coeff * *"); + writer->input->one("mass * 1.0"); + writer->input->one(fmt::format("dihedral_style {}", force->dihedral_style)); + FILE *coeffs; + char line[MAXLINE]; + coeffs = fopen(coeffs_file.c_str(), "r"); + for (int i = 0; i < atom->ndihedraltypes; ++i) { + fgets(line, MAXLINE, coeffs); + writer->input->one(fmt::format("dihedral_coeff {}", line)); + } + fclose(coeffs); + platform::unlink(coeffs_file); + + // must complete a full setup() to initialize system including neighbor and dihedral lists. + + writer->input->one("run 0 post no"); + + // move third atom to reproduce dihedrals + + double theta, phi, phi1, phi2, f; + dihedral = writer->force->dihedral; + auto atom4 = writer->atom->x[writer->atom->map(4)]; + + // evaluate energy and force at each of N distances + + fmt::print(fp, "# Dihedral potential {} for dihedral type {}: i,theta,energy,force\n", + force->dihedral_style, dtype); + fmt::print(fp, "\n{}\nN {} DEGREES\n\n", keyword, n); + +#define GET_ENERGY(myphi, mytheta) \ + theta = mytheta; \ + atom4[0] = cos(theta * DEG2RAD); \ + atom4[1] = sin(theta * DEG2RAD); \ + dihedral->energy = 0.0; \ + dihedral->compute(ENERGY_GLOBAL, 0); \ + myphi = dihedral->energy + + const double dtheta = 360.0 / static_cast(n); + for (int i = 0; i < n; i++) { + GET_ENERGY(phi1, dtheta * static_cast(i) - epsilon); + GET_ENERGY(phi2, dtheta * static_cast(i) + epsilon); + GET_ENERGY(phi, dtheta * static_cast(i)); + + if (!std::isfinite(phi)) phi = 0.0; + + // get force from numerical differentiation + f = -0.5 * (phi2 - phi1) / epsilon; + if (!std::isfinite(f)) f = 0.0; + fprintf(fp, "%8d %- 22.15g %- 22.15g %- 22.15g\n", i + 1, theta, phi, f); + } + + // clean up + delete writer; + fclose(fp); + } + MPI_Comm_free(&singlecomm); +} diff --git a/src/dihedral_write.h b/src/dihedral_write.h new file mode 100644 index 0000000000..b17f8d19da --- /dev/null +++ b/src/dihedral_write.h @@ -0,0 +1,34 @@ +/* -*- c++ -*- ---------------------------------------------------------- + LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator + https://www.lammps.org/, Sandia National Laboratories + LAMMPS development team: developers@lammps.org + + Copyright (2003) Sandia Corporation. Under the terms of Contract + DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains + certain rights in this software. This software is distributed under + the GNU General Public License. + + See the README file in the top-level LAMMPS directory. +------------------------------------------------------------------------- */ + +#ifdef COMMAND_CLASS +// clang-format off +CommandStyle(dihedral_write,DihedralWrite); +// clang-format on +#else + +#ifndef LMP_DIHEDRAL_WRITE_H +#define LMP_DIHEDRAL_WRITE_H + +#include "command.h" + +namespace LAMMPS_NS { + +class DihedralWrite : public Command { + public: + DihedralWrite(class LAMMPS *lmp) : Command(lmp){}; + void command(int, char **) override; +}; +} // namespace LAMMPS_NS +#endif +#endif From 63ddb07c594fd7124a20df849f4e6b6ec05d2698 Mon Sep 17 00:00:00 2001 From: Axel Kohlmeyer Date: Sun, 25 Dec 2022 07:04:20 -0500 Subject: [PATCH 21/47] add versionadded tags --- doc/src/angle_write.rst | 2 ++ doc/src/dihedral_write.rst | 2 ++ 2 files changed, 4 insertions(+) diff --git a/doc/src/angle_write.rst b/doc/src/angle_write.rst index 8bc94b5191..1541a7120a 100644 --- a/doc/src/angle_write.rst +++ b/doc/src/angle_write.rst @@ -26,6 +26,8 @@ Examples Description """"""""""" +.. versionadded:: TBD + Write energy and force values to a file as a function of angle for the currently defined angle potential. Force in this context means the force with respect to the angle, not the force on individual atoms. diff --git a/doc/src/dihedral_write.rst b/doc/src/dihedral_write.rst index d0deb1d2e8..94fa3da0fa 100644 --- a/doc/src/dihedral_write.rst +++ b/doc/src/dihedral_write.rst @@ -26,6 +26,8 @@ Examples Description """"""""""" +.. versionadded:: TBD + Write energy and force values to a file as a function of the dihedral angle for the currently defined dihedral potential. Force in this context means the force with respect to the dihedral angle, not the From 7cceabe5bdc3243064c48805e2a7d760b183eac1 Mon Sep 17 00:00:00 2001 From: Axel Kohlmeyer Date: Wed, 28 Dec 2022 12:14:36 -0500 Subject: [PATCH 22/47] ILAENV function does not use IPARAM2STAGE anymore --- lib/linalg/Makefile.gfortran | 8 +- lib/linalg/Makefile.mpi | 8 +- lib/linalg/ilaenv.f | 4 +- lib/linalg/iparam2stage.F | 386 ----------------------------------- 4 files changed, 6 insertions(+), 400 deletions(-) delete mode 100644 lib/linalg/iparam2stage.F diff --git a/lib/linalg/Makefile.gfortran b/lib/linalg/Makefile.gfortran index 2a777099e9..89ac3bbe6d 100644 --- a/lib/linalg/Makefile.gfortran +++ b/lib/linalg/Makefile.gfortran @@ -7,14 +7,13 @@ SHELL = /bin/sh # ------ FILES ------ SRC = $(wildcard *.f) -SRC1 = $(wildcard *.F) -FILES = $(SRC) $(SRC1) Makefile.* README +FILES = $(SRC) Makefile.* README # ------ DEFINITIONS ------ LIB = liblinalg.a -OBJ = $(SRC:.f=.o) $(SRC1:.F=.o) +OBJ = $(SRC:.f=.o) # ------ SETTINGS ------ @@ -34,9 +33,6 @@ lib: $(OBJ) # ------ COMPILE RULES ------ -%.o:%.F - $(FC) $(FFLAGS) -c $< - %.o:%.f $(FC) $(FFLAGS) -c $< diff --git a/lib/linalg/Makefile.mpi b/lib/linalg/Makefile.mpi index 26bfab4c80..74de6cdf3d 100644 --- a/lib/linalg/Makefile.mpi +++ b/lib/linalg/Makefile.mpi @@ -7,14 +7,13 @@ SHELL = /bin/sh # ------ FILES ------ SRC = $(wildcard *.f) -SRC1 = $(wildcard *.F) -FILES = $(SRC) $(SRC1) Makefile.* README +FILES = $(SRC) Makefile.* README # ------ DEFINITIONS ------ LIB = liblinalg.a -OBJ = $(SRC:.f=.o) $(SRC1:.F=.o) +OBJ = $(SRC:.f=.o) # ------ SETTINGS ------ @@ -34,9 +33,6 @@ lib: $(OBJ) # ------ COMPILE RULES ------ -%.o:%.F - $(FC) $(FFLAGS) -c $< - %.o:%.f $(FC) $(FFLAGS) -c $< diff --git a/lib/linalg/ilaenv.f b/lib/linalg/ilaenv.f index a639e0375a..3f0800b95e 100644 --- a/lib/linalg/ilaenv.f +++ b/lib/linalg/ilaenv.f @@ -180,8 +180,8 @@ INTRINSIC CHAR, ICHAR, INT, MIN, REAL * .. * .. External Functions .. - INTEGER IEEECK, IPARMQ, IPARAM2STAGE - EXTERNAL IEEECK, IPARMQ, IPARAM2STAGE + INTEGER IEEECK, IPARMQ + EXTERNAL IEEECK, IPARMQ * .. * .. Executable Statements .. * diff --git a/lib/linalg/iparam2stage.F b/lib/linalg/iparam2stage.F deleted file mode 100644 index ecf30dbea8..0000000000 --- a/lib/linalg/iparam2stage.F +++ /dev/null @@ -1,386 +0,0 @@ -*> \brief \b IPARAM2STAGE -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download IPARAM2STAGE + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* INTEGER FUNCTION IPARAM2STAGE( ISPEC, NAME, OPTS, -* NI, NBI, IBI, NXI ) -* #if defined(_OPENMP) -* use omp_lib -* #endif -* IMPLICIT NONE -* -* .. Scalar Arguments .. -* CHARACTER*( * ) NAME, OPTS -* INTEGER ISPEC, NI, NBI, IBI, NXI -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> This program sets problem and machine dependent parameters -*> useful for xHETRD_2STAGE, xHETRD_H@2HB, xHETRD_HB2ST, -*> xGEBRD_2STAGE, xGEBRD_GE2GB, xGEBRD_GB2BD -*> and related subroutines for eigenvalue problems. -*> It is called whenever ILAENV is called with 17 <= ISPEC <= 21 -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] ISPEC -*> \verbatim -*> ISPEC is integer scalar -*> ISPEC specifies which tunable parameter IPARAM2STAGE should -*> return. -*> -*> ISPEC=17: the optimal blocksize nb for the reduction to -* BAND -*> -*> ISPEC=18: the optimal blocksize ib for the eigenvectors -*> singular vectors update routine -*> -*> ISPEC=19: The length of the array that store the Housholder -*> representation for the second stage -*> Band to Tridiagonal or Bidiagonal -*> -*> ISPEC=20: The workspace needed for the routine in input. -*> -*> ISPEC=21: For future release. -*> \endverbatim -*> -*> \param[in] NAME -*> \verbatim -*> NAME is character string -*> Name of the calling subroutine -*> \endverbatim -*> -*> \param[in] OPTS -*> \verbatim -*> OPTS is CHARACTER*(*) -*> The character options to the subroutine NAME, concatenated -*> into a single character string. For example, UPLO = 'U', -*> TRANS = 'T', and DIAG = 'N' for a triangular routine would -*> be specified as OPTS = 'UTN'. -*> \endverbatim -*> -*> \param[in] NI -*> \verbatim -*> NI is INTEGER which is the size of the matrix -*> \endverbatim -*> -*> \param[in] NBI -*> \verbatim -*> NBI is INTEGER which is the used in the reduction, -* (e.g., the size of the band), needed to compute workspace -* and LHOUS2. -*> \endverbatim -*> -*> \param[in] IBI -*> \verbatim -*> IBI is INTEGER which represent the IB of the reduction, -* needed to compute workspace and LHOUS2. -*> \endverbatim -*> -*> \param[in] NXI -*> \verbatim -*> NXI is INTEGER needed in the future release. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \date June 2016 -* -*> \ingroup auxOTHERauxiliary -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> Implemented by Azzam Haidar. -*> -*> All detail are available on technical report, SC11, SC13 papers. -*> -*> Azzam Haidar, Hatem Ltaief, and Jack Dongarra. -*> Parallel reduction to condensed forms for symmetric eigenvalue problems -*> using aggregated fine-grained and memory-aware kernels. In Proceedings -*> of 2011 International Conference for High Performance Computing, -*> Networking, Storage and Analysis (SC '11), New York, NY, USA, -*> Article 8 , 11 pages. -*> https://doi.acm.org/10.1145/2063384.2063394 -*> -*> A. Haidar, J. Kurzak, P. Luszczek, 2013. -*> An improved parallel singular value algorithm and its implementation -*> for multicore hardware, In Proceedings of 2013 International Conference -*> for High Performance Computing, Networking, Storage and Analysis (SC '13). -*> Denver, Colorado, USA, 2013. -*> Article 90, 12 pages. -*> https://doi.acm.org/10.1145/2503210.2503292 -*> -*> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra. -*> A novel hybrid CPU-GPU generalized eigensolver for electronic structure -*> calculations based on fine-grained memory aware tasks. -*> International Journal of High Performance Computing Applications. -*> Volume 28 Issue 2, Pages 196-209, May 2014. -*> http://hpc.sagepub.com/content/28/2/196 -*> -*> \endverbatim -*> -* ===================================================================== - INTEGER FUNCTION IPARAM2STAGE( ISPEC, NAME, OPTS, - $ NI, NBI, IBI, NXI ) -#if defined(_OPENMP) - use omp_lib -#endif - IMPLICIT NONE -* -* -- LAPACK auxiliary routine (version 3.7.0) -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* June 2016 -* -* .. Scalar Arguments .. - CHARACTER*( * ) NAME, OPTS - INTEGER ISPEC, NI, NBI, IBI, NXI -* -* ================================================================ -* .. -* .. Local Scalars .. - INTEGER I, IC, IZ, KD, IB, LHOUS, LWORK, NTHREADS, - $ FACTOPTNB, QROPTNB, LQOPTNB - LOGICAL RPREC, CPREC - CHARACTER PREC*1, ALGO*3, STAG*5, SUBNAM*12, VECT*1 -* .. -* .. Intrinsic Functions .. - INTRINSIC CHAR, ICHAR, MAX -* .. -* .. External Functions .. - INTEGER ILAENV - EXTERNAL ILAENV -* .. -* .. Executable Statements .. -* -* Invalid value for ISPEC -* - IF( (ISPEC.LT.17).OR.(ISPEC.GT.21) ) THEN - IPARAM2STAGE = -1 - RETURN - ENDIF -* -* Get the number of threads -* - NTHREADS = 1 -#if defined(_OPENMP) -!$OMP PARALLEL - NTHREADS = OMP_GET_NUM_THREADS() -!$OMP END PARALLEL -#endif -* WRITE(*,*) 'IPARAM VOICI NTHREADS ISPEC ',NTHREADS, ISPEC -* - IF( ISPEC .NE. 19 ) THEN -* -* Convert NAME to upper case if the first character is lower case. -* - IPARAM2STAGE = -1 - SUBNAM = NAME - IC = ICHAR( SUBNAM( 1: 1 ) ) - IZ = ICHAR( 'Z' ) - IF( IZ.EQ.90 .OR. IZ.EQ.122 ) THEN -* -* ASCII character set -* - IF( IC.GE.97 .AND. IC.LE.122 ) THEN - SUBNAM( 1: 1 ) = CHAR( IC-32 ) - DO 100 I = 2, 12 - IC = ICHAR( SUBNAM( I: I ) ) - IF( IC.GE.97 .AND. IC.LE.122 ) - $ SUBNAM( I: I ) = CHAR( IC-32 ) - 100 CONTINUE - END IF -* - ELSE IF( IZ.EQ.233 .OR. IZ.EQ.169 ) THEN -* -* EBCDIC character set -* - IF( ( IC.GE.129 .AND. IC.LE.137 ) .OR. - $ ( IC.GE.145 .AND. IC.LE.153 ) .OR. - $ ( IC.GE.162 .AND. IC.LE.169 ) ) THEN - SUBNAM( 1: 1 ) = CHAR( IC+64 ) - DO 110 I = 2, 12 - IC = ICHAR( SUBNAM( I: I ) ) - IF( ( IC.GE.129 .AND. IC.LE.137 ) .OR. - $ ( IC.GE.145 .AND. IC.LE.153 ) .OR. - $ ( IC.GE.162 .AND. IC.LE.169 ) )SUBNAM( I: - $ I ) = CHAR( IC+64 ) - 110 CONTINUE - END IF -* - ELSE IF( IZ.EQ.218 .OR. IZ.EQ.250 ) THEN -* -* Prime machines: ASCII+128 -* - IF( IC.GE.225 .AND. IC.LE.250 ) THEN - SUBNAM( 1: 1 ) = CHAR( IC-32 ) - DO 120 I = 2, 12 - IC = ICHAR( SUBNAM( I: I ) ) - IF( IC.GE.225 .AND. IC.LE.250 ) - $ SUBNAM( I: I ) = CHAR( IC-32 ) - 120 CONTINUE - END IF - END IF -* - PREC = SUBNAM( 1: 1 ) - ALGO = SUBNAM( 4: 6 ) - STAG = SUBNAM( 8:12 ) - RPREC = PREC.EQ.'S' .OR. PREC.EQ.'D' - CPREC = PREC.EQ.'C' .OR. PREC.EQ.'Z' -* -* Invalid value for PRECISION -* - IF( .NOT.( RPREC .OR. CPREC ) ) THEN - IPARAM2STAGE = -1 - RETURN - ENDIF - ENDIF -* WRITE(*,*),'RPREC,CPREC ',RPREC,CPREC, -* $ ' ALGO ',ALGO,' STAGE ',STAG -* -* - IF (( ISPEC .EQ. 17 ) .OR. ( ISPEC .EQ. 18 )) THEN -* -* ISPEC = 17, 18: block size KD, IB -* Could be also dependent from N but for now it -* depend only on sequential or parallel -* - IF( NTHREADS.GT.4 ) THEN - IF( CPREC ) THEN - KD = 128 - IB = 32 - ELSE - KD = 160 - IB = 40 - ENDIF - ELSE IF( NTHREADS.GT.1 ) THEN - IF( CPREC ) THEN - KD = 64 - IB = 32 - ELSE - KD = 64 - IB = 32 - ENDIF - ELSE - IF( CPREC ) THEN - KD = 16 - IB = 16 - ELSE - KD = 32 - IB = 16 - ENDIF - ENDIF - IF( ISPEC.EQ.17 ) IPARAM2STAGE = KD - IF( ISPEC.EQ.18 ) IPARAM2STAGE = IB -* - ELSE IF ( ISPEC .EQ. 19 ) THEN -* -* ISPEC = 19: -* LHOUS length of the Houselholder representation -* matrix (V,T) of the second stage. should be >= 1. -* -* Will add the VECT OPTION HERE next release - VECT = OPTS(1:1) - IF( VECT.EQ.'N' ) THEN - LHOUS = MAX( 1, 4*NI ) - ELSE -* This is not correct, it need to call the ALGO and the stage2 - LHOUS = MAX( 1, 4*NI ) + IBI - ENDIF - IF( LHOUS.GE.0 ) THEN - IPARAM2STAGE = LHOUS - ELSE - IPARAM2STAGE = -1 - ENDIF -* - ELSE IF ( ISPEC .EQ. 20 ) THEN -* -* ISPEC = 20: (21 for future use) -* LWORK length of the workspace for -* either or both stages for TRD and BRD. should be >= 1. -* TRD: -* TRD_stage 1: = LT + LW + LS1 + LS2 -* = LDT*KD + N*KD + N*MAX(KD,FACTOPTNB) + LDS2*KD -* where LDT=LDS2=KD -* = N*KD + N*max(KD,FACTOPTNB) + 2*KD*KD -* TRD_stage 2: = (2NB+1)*N + KD*NTHREADS -* TRD_both : = max(stage1,stage2) + AB ( AB=(KD+1)*N ) -* = N*KD + N*max(KD+1,FACTOPTNB) -* + max(2*KD*KD, KD*NTHREADS) -* + (KD+1)*N - LWORK = -1 - SUBNAM(1:1) = PREC - SUBNAM(2:6) = 'GEQRF' - QROPTNB = ILAENV( 1, SUBNAM, ' ', NI, NBI, -1, -1 ) - SUBNAM(2:6) = 'GELQF' - LQOPTNB = ILAENV( 1, SUBNAM, ' ', NBI, NI, -1, -1 ) -* Could be QR or LQ for TRD and the max for BRD - FACTOPTNB = MAX(QROPTNB, LQOPTNB) - IF( ALGO.EQ.'TRD' ) THEN - IF( STAG.EQ.'2STAG' ) THEN - LWORK = NI*NBI + NI*MAX(NBI+1,FACTOPTNB) - $ + MAX(2*NBI*NBI, NBI*NTHREADS) - $ + (NBI+1)*NI - ELSE IF( (STAG.EQ.'HE2HB').OR.(STAG.EQ.'SY2SB') ) THEN - LWORK = NI*NBI + NI*MAX(NBI,FACTOPTNB) + 2*NBI*NBI - ELSE IF( (STAG.EQ.'HB2ST').OR.(STAG.EQ.'SB2ST') ) THEN - LWORK = (2*NBI+1)*NI + NBI*NTHREADS - ENDIF - ELSE IF( ALGO.EQ.'BRD' ) THEN - IF( STAG.EQ.'2STAG' ) THEN - LWORK = 2*NI*NBI + NI*MAX(NBI+1,FACTOPTNB) - $ + MAX(2*NBI*NBI, NBI*NTHREADS) - $ + (NBI+1)*NI - ELSE IF( STAG.EQ.'GE2GB' ) THEN - LWORK = NI*NBI + NI*MAX(NBI,FACTOPTNB) + 2*NBI*NBI - ELSE IF( STAG.EQ.'GB2BD' ) THEN - LWORK = (3*NBI+1)*NI + NBI*NTHREADS - ENDIF - ENDIF - LWORK = MAX ( 1, LWORK ) - - IF( LWORK.GT.0 ) THEN - IPARAM2STAGE = LWORK - ELSE - IPARAM2STAGE = -1 - ENDIF -* - ELSE IF ( ISPEC .EQ. 21 ) THEN -* -* ISPEC = 21 for future use - IPARAM2STAGE = NXI - ENDIF -* -* ==== End of IPARAM2STAGE ==== -* - END From c5a87f75d6cfbcca5a4b6e2e2f44865c55bf6a89 Mon Sep 17 00:00:00 2001 From: Axel Kohlmeyer Date: Wed, 28 Dec 2022 13:18:38 -0500 Subject: [PATCH 23/47] convert linalg library from Fortran to C++ --- cmake/CMakeLists.txt | 9 +- .../{Makefile.gfortran => Makefile.g++} | 18 +- lib/linalg/Makefile.mpi | 18 +- lib/linalg/Makefile.serial | 2 +- lib/linalg/convert.sh | 44 + lib/linalg/dasum.cpp | 168 + lib/linalg/daxpy.cpp | 194 + lib/linalg/dbdsqr.cpp | 1053 +++++ lib/linalg/dcabs1.cpp | 92 + lib/linalg/dcopy.cpp | 187 + lib/linalg/ddot.cpp | 189 + lib/linalg/dgebd2.cpp | 393 ++ lib/linalg/dgebrd.cpp | 431 ++ lib/linalg/dgecon.cpp | 313 ++ lib/linalg/dgelq2.cpp | 245 + lib/linalg/dgelqf.cpp | 345 ++ lib/linalg/dgelsd.cpp | 816 ++++ lib/linalg/dgelss.cpp | 988 ++++ lib/linalg/dgemm.cpp | 458 ++ lib/linalg/dgemv.cpp | 385 ++ lib/linalg/dgeqr2.cpp | 250 + lib/linalg/dgeqrf.cpp | 354 ++ lib/linalg/dger.cpp | 265 ++ lib/linalg/dgesv.cpp | 217 + lib/linalg/dgesvd.cpp | 4158 +++++++++++++++++ lib/linalg/dgetf2.cpp | 266 ++ lib/linalg/dgetrf.cpp | 293 ++ lib/linalg/dgetrf2.cpp | 331 ++ lib/linalg/dgetri.cpp | 343 ++ lib/linalg/dgetrs.cpp | 272 ++ lib/linalg/disnan.cpp | 14 + lib/linalg/dlabad.cpp | 128 + lib/linalg/dlabrd.cpp | 532 +++ lib/linalg/dlacn2.cpp | 364 ++ lib/linalg/dlacpy.cpp | 200 + lib/linalg/dladiv.cpp | 277 ++ lib/linalg/dlae2.cpp | 210 + lib/linalg/dlaed0.cpp | 534 +++ lib/linalg/dlaed1.cpp | 336 ++ lib/linalg/dlaed2.cpp | 646 +++ lib/linalg/dlaed3.cpp | 437 ++ lib/linalg/dlaed4.cpp | 1036 ++++ lib/linalg/dlaed5.cpp | 219 + lib/linalg/dlaed6.cpp | 463 ++ lib/linalg/dlaed7.cpp | 483 ++ lib/linalg/dlaed8.cpp | 610 +++ lib/linalg/dlaed9.cpp | 370 ++ lib/linalg/dlaeda.cpp | 386 ++ lib/linalg/dlaev2.cpp | 263 ++ lib/linalg/dlals0.cpp | 602 +++ lib/linalg/dlalsa.cpp | 598 +++ lib/linalg/dlalsd.cpp | 632 +++ lib/linalg/dlamch.cpp | 45 + lib/linalg/dlamrg.cpp | 206 + lib/linalg/dlange.cpp | 277 ++ lib/linalg/dlanst.cpp | 239 + lib/linalg/dlansy.cpp | 317 ++ lib/linalg/dlapy2.cpp | 150 + lib/linalg/dlapy3.cpp | 149 + lib/linalg/dlarf.cpp | 275 ++ lib/linalg/dlarfb.cpp | 886 ++++ lib/linalg/dlarfg.cpp | 240 + lib/linalg/dlarft.cpp | 417 ++ lib/linalg/dlartg.cpp | 258 + lib/linalg/dlas2.cpp | 212 + lib/linalg/dlascl.cpp | 448 ++ lib/linalg/dlasd4.cpp | 1198 +++++ lib/linalg/dlasd5.cpp | 264 ++ lib/linalg/dlasd6.cpp | 514 ++ lib/linalg/dlasd7.cpp | 663 +++ lib/linalg/dlasd8.cpp | 419 ++ lib/linalg/dlasda.cpp | 624 +++ lib/linalg/dlasdq.cpp | 486 ++ lib/linalg/dlasdt.cpp | 209 + lib/linalg/dlaset.cpp | 229 + lib/linalg/dlasq1.cpp | 298 ++ lib/linalg/dlasq2.cpp | 716 +++ lib/linalg/dlasq3.cpp | 475 ++ lib/linalg/dlasq4.cpp | 501 ++ lib/linalg/dlasq5.cpp | 480 ++ lib/linalg/dlasq6.cpp | 291 ++ lib/linalg/dlasr.cpp | 536 +++ lib/linalg/dlasrt.cpp | 352 ++ lib/linalg/dlassq.cpp | 191 + lib/linalg/dlasv2.cpp | 356 ++ lib/linalg/dlaswp.cpp | 238 + lib/linalg/dlatrd.cpp | 445 ++ lib/linalg/dlatrs.cpp | 984 ++++ lib/linalg/dnrm2.cpp | 169 + lib/linalg/dorg2l.cpp | 252 + lib/linalg/dorg2r.cpp | 255 + lib/linalg/dorgbr.cpp | 404 ++ lib/linalg/dorgl2.cpp | 254 + lib/linalg/dorglq.cpp | 366 ++ lib/linalg/dorgql.cpp | 376 ++ lib/linalg/dorgqr.cpp | 367 ++ lib/linalg/dorgtr.cpp | 331 ++ lib/linalg/dorm2l.cpp | 324 ++ lib/linalg/dorm2r.cpp | 328 ++ lib/linalg/dormbr.cpp | 464 ++ lib/linalg/dorml2.cpp | 324 ++ lib/linalg/dormlq.cpp | 424 ++ lib/linalg/dormql.cpp | 416 ++ lib/linalg/dormqr.cpp | 417 ++ lib/linalg/dormtr.cpp | 396 ++ lib/linalg/dposv.cpp | 232 + lib/linalg/dpotf2.cpp | 294 ++ lib/linalg/dpotrf.cpp | 322 ++ lib/linalg/dpotrf2.cpp | 285 ++ lib/linalg/dpotrs.cpp | 248 + lib/linalg/drot.cpp | 180 + lib/linalg/drscl.cpp | 200 + lib/linalg/dscal.cpp | 173 + lib/linalg/dstedc.cpp | 576 +++ lib/linalg/dsteqr.cpp | 704 +++ lib/linalg/dsterf.cpp | 534 +++ lib/linalg/dswap.cpp | 194 + lib/linalg/dsyev.cpp | 369 ++ lib/linalg/dsyevd.cpp | 440 ++ lib/linalg/dsygs2.cpp | 381 ++ lib/linalg/dsygst.cpp | 436 ++ lib/linalg/dsygv.cpp | 384 ++ lib/linalg/dsygvd.cpp | 445 ++ lib/linalg/dsymm.cpp | 440 ++ lib/linalg/dsymv.cpp | 388 ++ lib/linalg/dsyr2.cpp | 347 ++ lib/linalg/dsyr2k.cpp | 485 ++ lib/linalg/dsyrk.cpp | 445 ++ lib/linalg/dsytd2.cpp | 389 ++ lib/linalg/dsytrd.cpp | 454 ++ lib/linalg/dtrmm.cpp | 527 +++ lib/linalg/dtrmv.cpp | 415 ++ lib/linalg/dtrsm.cpp | 565 +++ lib/linalg/dtrsv.cpp | 411 ++ lib/linalg/dtrti2.cpp | 258 + lib/linalg/dtrtri.cpp | 321 ++ lib/linalg/dznrm2.cpp | 183 + lib/linalg/{ => fortran}/dasum.f | 0 lib/linalg/{ => fortran}/daxpy.f | 0 lib/linalg/{ => fortran}/dbdsqr.f | 0 lib/linalg/{ => fortran}/dcabs1.f | 0 lib/linalg/{ => fortran}/dcopy.f | 0 lib/linalg/{ => fortran}/ddot.f | 0 lib/linalg/{ => fortran}/dgebd2.f | 0 lib/linalg/{ => fortran}/dgebrd.f | 0 lib/linalg/{ => fortran}/dgecon.f | 0 lib/linalg/{ => fortran}/dgelq2.f | 0 lib/linalg/{ => fortran}/dgelqf.f | 0 lib/linalg/{ => fortran}/dgelsd.f | 0 lib/linalg/{ => fortran}/dgelss.f | 0 lib/linalg/{ => fortran}/dgemm.f | 0 lib/linalg/{ => fortran}/dgemv.f | 0 lib/linalg/{ => fortran}/dgeqr2.f | 0 lib/linalg/{ => fortran}/dgeqrf.f | 0 lib/linalg/{ => fortran}/dger.f | 0 lib/linalg/{ => fortran}/dgesv.f | 0 lib/linalg/{ => fortran}/dgesvd.f | 0 lib/linalg/{ => fortran}/dgetf2.f | 0 lib/linalg/{ => fortran}/dgetrf.f | 0 lib/linalg/{ => fortran}/dgetrf2.f | 0 lib/linalg/{ => fortran}/dgetri.f | 0 lib/linalg/{ => fortran}/dgetrs.f | 0 lib/linalg/{ => fortran}/disnan.f | 0 lib/linalg/{ => fortran}/dlabad.f | 0 lib/linalg/{ => fortran}/dlabrd.f | 0 lib/linalg/{ => fortran}/dlacn2.f | 0 lib/linalg/{ => fortran}/dlacpy.f | 0 lib/linalg/{ => fortran}/dladiv.f | 0 lib/linalg/{ => fortran}/dlae2.f | 0 lib/linalg/{ => fortran}/dlaed0.f | 0 lib/linalg/{ => fortran}/dlaed1.f | 0 lib/linalg/{ => fortran}/dlaed2.f | 0 lib/linalg/{ => fortran}/dlaed3.f | 0 lib/linalg/{ => fortran}/dlaed4.f | 0 lib/linalg/{ => fortran}/dlaed5.f | 0 lib/linalg/{ => fortran}/dlaed6.f | 0 lib/linalg/{ => fortran}/dlaed7.f | 0 lib/linalg/{ => fortran}/dlaed8.f | 0 lib/linalg/{ => fortran}/dlaed9.f | 0 lib/linalg/{ => fortran}/dlaeda.f | 0 lib/linalg/{ => fortran}/dlaev2.f | 0 lib/linalg/{ => fortran}/dlaisnan.f | 0 lib/linalg/{ => fortran}/dlals0.f | 0 lib/linalg/{ => fortran}/dlalsa.f | 0 lib/linalg/{ => fortran}/dlalsd.f | 0 lib/linalg/{ => fortran}/dlamch.f | 0 lib/linalg/{ => fortran}/dlamrg.f | 0 lib/linalg/{ => fortran}/dlange.f | 0 lib/linalg/{ => fortran}/dlanst.f | 0 lib/linalg/{ => fortran}/dlansy.f | 0 lib/linalg/{ => fortran}/dlapy2.f | 0 lib/linalg/{ => fortran}/dlapy3.f | 0 lib/linalg/{ => fortran}/dlarf.f | 0 lib/linalg/{ => fortran}/dlarfb.f | 0 lib/linalg/{ => fortran}/dlarfg.f | 0 lib/linalg/{ => fortran}/dlarft.f | 0 lib/linalg/{ => fortran}/dlartg.f | 0 lib/linalg/{ => fortran}/dlas2.f | 0 lib/linalg/{ => fortran}/dlascl.f | 0 lib/linalg/{ => fortran}/dlasd4.f | 0 lib/linalg/{ => fortran}/dlasd5.f | 0 lib/linalg/{ => fortran}/dlasd6.f | 0 lib/linalg/{ => fortran}/dlasd7.f | 0 lib/linalg/{ => fortran}/dlasd8.f | 0 lib/linalg/{ => fortran}/dlasda.f | 0 lib/linalg/{ => fortran}/dlasdq.f | 0 lib/linalg/{ => fortran}/dlasdt.f | 0 lib/linalg/{ => fortran}/dlaset.f | 0 lib/linalg/{ => fortran}/dlasq1.f | 0 lib/linalg/{ => fortran}/dlasq2.f | 0 lib/linalg/{ => fortran}/dlasq3.f | 0 lib/linalg/{ => fortran}/dlasq4.f | 0 lib/linalg/{ => fortran}/dlasq5.f | 0 lib/linalg/{ => fortran}/dlasq6.f | 0 lib/linalg/{ => fortran}/dlasr.f | 0 lib/linalg/{ => fortran}/dlasrt.f | 0 lib/linalg/{ => fortran}/dlassq.f | 0 lib/linalg/{ => fortran}/dlasv2.f | 0 lib/linalg/{ => fortran}/dlaswp.f | 0 lib/linalg/{ => fortran}/dlatrd.f | 0 lib/linalg/{ => fortran}/dlatrs.f | 0 lib/linalg/{ => fortran}/dnrm2.f | 0 lib/linalg/{ => fortran}/dorg2l.f | 0 lib/linalg/{ => fortran}/dorg2r.f | 0 lib/linalg/{ => fortran}/dorgbr.f | 0 lib/linalg/{ => fortran}/dorgl2.f | 0 lib/linalg/{ => fortran}/dorglq.f | 0 lib/linalg/{ => fortran}/dorgql.f | 0 lib/linalg/{ => fortran}/dorgqr.f | 0 lib/linalg/{ => fortran}/dorgtr.f | 0 lib/linalg/{ => fortran}/dorm2l.f | 0 lib/linalg/{ => fortran}/dorm2r.f | 0 lib/linalg/{ => fortran}/dormbr.f | 0 lib/linalg/{ => fortran}/dorml2.f | 0 lib/linalg/{ => fortran}/dormlq.f | 0 lib/linalg/{ => fortran}/dormql.f | 0 lib/linalg/{ => fortran}/dormqr.f | 0 lib/linalg/{ => fortran}/dormtr.f | 0 lib/linalg/{ => fortran}/dposv.f | 0 lib/linalg/{ => fortran}/dpotf2.f | 0 lib/linalg/{ => fortran}/dpotrf.f | 0 lib/linalg/{ => fortran}/dpotrf2.f | 0 lib/linalg/{ => fortran}/dpotrs.f | 0 lib/linalg/{ => fortran}/drot.f | 0 lib/linalg/{ => fortran}/drscl.f | 0 lib/linalg/{ => fortran}/dscal.f | 0 lib/linalg/{ => fortran}/dstedc.f | 0 lib/linalg/{ => fortran}/dsteqr.f | 0 lib/linalg/{ => fortran}/dsterf.f | 0 lib/linalg/{ => fortran}/dswap.f | 0 lib/linalg/{ => fortran}/dsyev.f | 0 lib/linalg/{ => fortran}/dsyevd.f | 0 lib/linalg/{ => fortran}/dsygs2.f | 0 lib/linalg/{ => fortran}/dsygst.f | 0 lib/linalg/{ => fortran}/dsygv.f | 0 lib/linalg/{ => fortran}/dsygvd.f | 0 lib/linalg/{ => fortran}/dsymm.f | 0 lib/linalg/{ => fortran}/dsymv.f | 0 lib/linalg/{ => fortran}/dsyr2.f | 0 lib/linalg/{ => fortran}/dsyr2k.f | 0 lib/linalg/{ => fortran}/dsyrk.f | 0 lib/linalg/{ => fortran}/dsytd2.f | 0 lib/linalg/{ => fortran}/dsytrd.f | 0 lib/linalg/{ => fortran}/dtrmm.f | 0 lib/linalg/{ => fortran}/dtrmv.f | 0 lib/linalg/{ => fortran}/dtrsm.f | 0 lib/linalg/{ => fortran}/dtrsv.f | 0 lib/linalg/{ => fortran}/dtrti2.f | 0 lib/linalg/{ => fortran}/dtrtri.f | 0 lib/linalg/{ => fortran}/dznrm2.f | 0 lib/linalg/{ => fortran}/idamax.f | 0 lib/linalg/{ => fortran}/ieeeck.f | 0 lib/linalg/{ => fortran}/iladlc.f | 0 lib/linalg/{ => fortran}/iladlr.f | 0 lib/linalg/{ => fortran}/ilaenv.f | 0 lib/linalg/{ => fortran}/ilazlc.f | 0 lib/linalg/{ => fortran}/ilazlr.f | 0 lib/linalg/{ => fortran}/iparmq.f | 0 lib/linalg/{ => fortran}/lsame.f | 0 lib/linalg/{ => fortran}/xerbla.f | 0 lib/linalg/{ => fortran}/zaxpy.f | 0 lib/linalg/{ => fortran}/zcopy.f | 0 lib/linalg/{ => fortran}/zdotc.f | 0 lib/linalg/{ => fortran}/zdrot.f | 0 lib/linalg/{ => fortran}/zdscal.f | 0 lib/linalg/{ => fortran}/zgemm.f | 0 lib/linalg/{ => fortran}/zgemv.f | 0 lib/linalg/{ => fortran}/zgerc.f | 0 lib/linalg/{ => fortran}/zheev.f | 0 lib/linalg/{ => fortran}/zheevd.f | 0 lib/linalg/{ => fortran}/zhemv.f | 0 lib/linalg/{ => fortran}/zher2.f | 0 lib/linalg/{ => fortran}/zher2k.f | 0 lib/linalg/{ => fortran}/zhetd2.f | 0 lib/linalg/{ => fortran}/zhetrd.f | 0 lib/linalg/{ => fortran}/zhpr.f | 0 lib/linalg/{ => fortran}/zlacgv.f | 0 lib/linalg/{ => fortran}/zlacpy.f | 0 lib/linalg/{ => fortran}/zlacrm.f | 0 lib/linalg/{ => fortran}/zladiv.f | 0 lib/linalg/{ => fortran}/zlaed0.f | 0 lib/linalg/{ => fortran}/zlaed7.f | 0 lib/linalg/{ => fortran}/zlaed8.f | 0 lib/linalg/{ => fortran}/zlanhe.f | 0 lib/linalg/{ => fortran}/zlarf.f | 0 lib/linalg/{ => fortran}/zlarfb.f | 0 lib/linalg/{ => fortran}/zlarfg.f | 0 lib/linalg/{ => fortran}/zlarft.f | 0 lib/linalg/{ => fortran}/zlascl.f | 0 lib/linalg/{ => fortran}/zlaset.f | 0 lib/linalg/{ => fortran}/zlasr.f | 0 lib/linalg/{ => fortran}/zlassq.f | 0 lib/linalg/{ => fortran}/zlatrd.f | 0 lib/linalg/{ => fortran}/zpptrf.f | 0 lib/linalg/{ => fortran}/zpptri.f | 0 lib/linalg/{ => fortran}/zscal.f | 0 lib/linalg/{ => fortran}/zstedc.f | 0 lib/linalg/{ => fortran}/zsteqr.f | 0 lib/linalg/{ => fortran}/zswap.f | 0 lib/linalg/{ => fortran}/ztpmv.f | 0 lib/linalg/{ => fortran}/ztpsv.f | 0 lib/linalg/{ => fortran}/ztptri.f | 0 lib/linalg/{ => fortran}/ztrmm.f | 0 lib/linalg/{ => fortran}/ztrmv.f | 0 lib/linalg/{ => fortran}/zung2l.f | 0 lib/linalg/{ => fortran}/zung2r.f | 0 lib/linalg/{ => fortran}/zungl2.f | 0 lib/linalg/{ => fortran}/zungql.f | 0 lib/linalg/{ => fortran}/zungqr.f | 0 lib/linalg/{ => fortran}/zungtr.f | 0 lib/linalg/{ => fortran}/zunm2l.f | 0 lib/linalg/{ => fortran}/zunm2r.f | 0 lib/linalg/{ => fortran}/zunmql.f | 0 lib/linalg/{ => fortran}/zunmqr.f | 0 lib/linalg/{ => fortran}/zunmtr.f | 0 lib/linalg/idamax.cpp | 161 + lib/linalg/ieeeck.cpp | 228 + lib/linalg/iladlc.cpp | 150 + lib/linalg/iladlr.cpp | 151 + lib/linalg/ilaenv.cpp | 845 ++++ lib/linalg/ilazlc.cpp | 156 + lib/linalg/ilazlr.cpp | 159 + lib/linalg/iparmq.cpp | 449 ++ lib/linalg/lmp_f2c.h | 223 + lib/linalg/lsame.cpp | 17 + lib/linalg/static/README | 5 + lib/linalg/static/dgetrf2.f | 269 ++ lib/linalg/static/disnan.cpp | 14 + lib/linalg/static/dlamch.cpp | 45 + lib/linalg/static/dlarft.f | 327 ++ lib/linalg/static/dpotrf2.f | 234 + lib/linalg/static/lsame.cpp | 17 + lib/linalg/static/xerbla.cpp | 30 + lib/linalg/static/zlarft.f | 328 ++ lib/linalg/xerbla.cpp | 30 + lib/linalg/zaxpy.cpp | 191 + lib/linalg/zcopy.cpp | 168 + lib/linalg/zdotc.cpp | 186 + lib/linalg/zdrot.cpp | 213 + lib/linalg/zdscal.cpp | 169 + lib/linalg/zgemm.cpp | 763 +++ lib/linalg/zgemv.cpp | 477 ++ lib/linalg/zgerc.cpp | 289 ++ lib/linalg/zheev.cpp | 379 ++ lib/linalg/zheevd.cpp | 486 ++ lib/linalg/zhemv.cpp | 508 ++ lib/linalg/zher2.cpp | 519 ++ lib/linalg/zher2k.cpp | 750 +++ lib/linalg/zhetd2.cpp | 439 ++ lib/linalg/zhetrd.cpp | 463 ++ lib/linalg/zhpr.cpp | 405 ++ lib/linalg/zlacgv.cpp | 157 + lib/linalg/zlacpy.cpp | 210 + lib/linalg/zlacrm.cpp | 258 + lib/linalg/zladiv.cpp | 132 + lib/linalg/zlaed0.cpp | 458 ++ lib/linalg/zlaed7.cpp | 456 ++ lib/linalg/zlaed8.cpp | 569 +++ lib/linalg/zlanhe.cpp | 348 ++ lib/linalg/zlarf.cpp | 283 ++ lib/linalg/zlarfb.cpp | 949 ++++ lib/linalg/zlarfg.cpp | 261 ++ lib/linalg/zlarft.cpp | 465 ++ lib/linalg/zlascl.cpp | 470 ++ lib/linalg/zlaset.cpp | 240 + lib/linalg/zlasr.cpp | 694 +++ lib/linalg/zlassq.cpp | 212 + lib/linalg/zlatrd.cpp | 509 ++ lib/linalg/zpptrf.cpp | 301 ++ lib/linalg/zpptri.cpp | 248 + lib/linalg/zscal.cpp | 162 + lib/linalg/zstedc.cpp | 590 +++ lib/linalg/zsteqr.cpp | 706 +++ lib/linalg/zswap.cpp | 176 + lib/linalg/ztpmv.cpp | 639 +++ lib/linalg/ztpsv.cpp | 607 +++ lib/linalg/ztptri.cpp | 308 ++ lib/linalg/ztrmm.cpp | 762 +++ lib/linalg/ztrmv.cpp | 624 +++ lib/linalg/zung2l.cpp | 262 ++ lib/linalg/zung2r.cpp | 264 ++ lib/linalg/zungl2.cpp | 273 ++ lib/linalg/zungql.cpp | 381 ++ lib/linalg/zungqr.cpp | 372 ++ lib/linalg/zungtr.cpp | 342 ++ lib/linalg/zunm2l.cpp | 339 ++ lib/linalg/zunm2r.cpp | 343 ++ lib/linalg/zunmql.cpp | 419 ++ lib/linalg/zunmqr.cpp | 420 ++ lib/linalg/zunmtr.cpp | 397 ++ 410 files changed, 80736 insertions(+), 30 deletions(-) rename lib/linalg/{Makefile.gfortran => Makefile.g++} (65%) create mode 100755 lib/linalg/convert.sh create mode 100644 lib/linalg/dasum.cpp create mode 100644 lib/linalg/daxpy.cpp create mode 100644 lib/linalg/dbdsqr.cpp create mode 100644 lib/linalg/dcabs1.cpp create mode 100644 lib/linalg/dcopy.cpp create mode 100644 lib/linalg/ddot.cpp create mode 100644 lib/linalg/dgebd2.cpp create mode 100644 lib/linalg/dgebrd.cpp create mode 100644 lib/linalg/dgecon.cpp create mode 100644 lib/linalg/dgelq2.cpp create mode 100644 lib/linalg/dgelqf.cpp create mode 100644 lib/linalg/dgelsd.cpp create mode 100644 lib/linalg/dgelss.cpp create mode 100644 lib/linalg/dgemm.cpp create mode 100644 lib/linalg/dgemv.cpp create mode 100644 lib/linalg/dgeqr2.cpp create mode 100644 lib/linalg/dgeqrf.cpp create mode 100644 lib/linalg/dger.cpp create mode 100644 lib/linalg/dgesv.cpp create mode 100644 lib/linalg/dgesvd.cpp create mode 100644 lib/linalg/dgetf2.cpp create mode 100644 lib/linalg/dgetrf.cpp create mode 100644 lib/linalg/dgetrf2.cpp create mode 100644 lib/linalg/dgetri.cpp create mode 100644 lib/linalg/dgetrs.cpp create mode 100644 lib/linalg/disnan.cpp create mode 100644 lib/linalg/dlabad.cpp create mode 100644 lib/linalg/dlabrd.cpp create mode 100644 lib/linalg/dlacn2.cpp create mode 100644 lib/linalg/dlacpy.cpp create mode 100644 lib/linalg/dladiv.cpp create mode 100644 lib/linalg/dlae2.cpp create mode 100644 lib/linalg/dlaed0.cpp create mode 100644 lib/linalg/dlaed1.cpp create mode 100644 lib/linalg/dlaed2.cpp create mode 100644 lib/linalg/dlaed3.cpp create mode 100644 lib/linalg/dlaed4.cpp create mode 100644 lib/linalg/dlaed5.cpp create mode 100644 lib/linalg/dlaed6.cpp create mode 100644 lib/linalg/dlaed7.cpp create mode 100644 lib/linalg/dlaed8.cpp create mode 100644 lib/linalg/dlaed9.cpp create mode 100644 lib/linalg/dlaeda.cpp create mode 100644 lib/linalg/dlaev2.cpp create mode 100644 lib/linalg/dlals0.cpp create mode 100644 lib/linalg/dlalsa.cpp create mode 100644 lib/linalg/dlalsd.cpp create mode 100644 lib/linalg/dlamch.cpp create mode 100644 lib/linalg/dlamrg.cpp create mode 100644 lib/linalg/dlange.cpp create mode 100644 lib/linalg/dlanst.cpp create mode 100644 lib/linalg/dlansy.cpp create mode 100644 lib/linalg/dlapy2.cpp create mode 100644 lib/linalg/dlapy3.cpp create mode 100644 lib/linalg/dlarf.cpp create mode 100644 lib/linalg/dlarfb.cpp create mode 100644 lib/linalg/dlarfg.cpp create mode 100644 lib/linalg/dlarft.cpp create mode 100644 lib/linalg/dlartg.cpp create mode 100644 lib/linalg/dlas2.cpp create mode 100644 lib/linalg/dlascl.cpp create mode 100644 lib/linalg/dlasd4.cpp create mode 100644 lib/linalg/dlasd5.cpp create mode 100644 lib/linalg/dlasd6.cpp create mode 100644 lib/linalg/dlasd7.cpp create mode 100644 lib/linalg/dlasd8.cpp create mode 100644 lib/linalg/dlasda.cpp create mode 100644 lib/linalg/dlasdq.cpp create mode 100644 lib/linalg/dlasdt.cpp create mode 100644 lib/linalg/dlaset.cpp create mode 100644 lib/linalg/dlasq1.cpp create mode 100644 lib/linalg/dlasq2.cpp create mode 100644 lib/linalg/dlasq3.cpp create mode 100644 lib/linalg/dlasq4.cpp create mode 100644 lib/linalg/dlasq5.cpp create mode 100644 lib/linalg/dlasq6.cpp create mode 100644 lib/linalg/dlasr.cpp create mode 100644 lib/linalg/dlasrt.cpp create mode 100644 lib/linalg/dlassq.cpp create mode 100644 lib/linalg/dlasv2.cpp create mode 100644 lib/linalg/dlaswp.cpp create mode 100644 lib/linalg/dlatrd.cpp create mode 100644 lib/linalg/dlatrs.cpp create mode 100644 lib/linalg/dnrm2.cpp create mode 100644 lib/linalg/dorg2l.cpp create mode 100644 lib/linalg/dorg2r.cpp create mode 100644 lib/linalg/dorgbr.cpp create mode 100644 lib/linalg/dorgl2.cpp create mode 100644 lib/linalg/dorglq.cpp create mode 100644 lib/linalg/dorgql.cpp create mode 100644 lib/linalg/dorgqr.cpp create mode 100644 lib/linalg/dorgtr.cpp create mode 100644 lib/linalg/dorm2l.cpp create mode 100644 lib/linalg/dorm2r.cpp create mode 100644 lib/linalg/dormbr.cpp create mode 100644 lib/linalg/dorml2.cpp create mode 100644 lib/linalg/dormlq.cpp create mode 100644 lib/linalg/dormql.cpp create mode 100644 lib/linalg/dormqr.cpp create mode 100644 lib/linalg/dormtr.cpp create mode 100644 lib/linalg/dposv.cpp create mode 100644 lib/linalg/dpotf2.cpp create mode 100644 lib/linalg/dpotrf.cpp create mode 100644 lib/linalg/dpotrf2.cpp create mode 100644 lib/linalg/dpotrs.cpp create mode 100644 lib/linalg/drot.cpp create mode 100644 lib/linalg/drscl.cpp create mode 100644 lib/linalg/dscal.cpp create mode 100644 lib/linalg/dstedc.cpp create mode 100644 lib/linalg/dsteqr.cpp create mode 100644 lib/linalg/dsterf.cpp create mode 100644 lib/linalg/dswap.cpp create mode 100644 lib/linalg/dsyev.cpp create mode 100644 lib/linalg/dsyevd.cpp create mode 100644 lib/linalg/dsygs2.cpp create mode 100644 lib/linalg/dsygst.cpp create mode 100644 lib/linalg/dsygv.cpp create mode 100644 lib/linalg/dsygvd.cpp create mode 100644 lib/linalg/dsymm.cpp create mode 100644 lib/linalg/dsymv.cpp create mode 100644 lib/linalg/dsyr2.cpp create mode 100644 lib/linalg/dsyr2k.cpp create mode 100644 lib/linalg/dsyrk.cpp create mode 100644 lib/linalg/dsytd2.cpp create mode 100644 lib/linalg/dsytrd.cpp create mode 100644 lib/linalg/dtrmm.cpp create mode 100644 lib/linalg/dtrmv.cpp create mode 100644 lib/linalg/dtrsm.cpp create mode 100644 lib/linalg/dtrsv.cpp create mode 100644 lib/linalg/dtrti2.cpp create mode 100644 lib/linalg/dtrtri.cpp create mode 100644 lib/linalg/dznrm2.cpp rename lib/linalg/{ => fortran}/dasum.f (100%) rename lib/linalg/{ => fortran}/daxpy.f (100%) rename lib/linalg/{ => fortran}/dbdsqr.f (100%) rename lib/linalg/{ => fortran}/dcabs1.f (100%) rename lib/linalg/{ => fortran}/dcopy.f (100%) rename lib/linalg/{ => fortran}/ddot.f (100%) rename lib/linalg/{ => fortran}/dgebd2.f (100%) rename lib/linalg/{ => fortran}/dgebrd.f (100%) rename lib/linalg/{ => fortran}/dgecon.f (100%) rename lib/linalg/{ => fortran}/dgelq2.f (100%) rename lib/linalg/{ => fortran}/dgelqf.f (100%) rename lib/linalg/{ => fortran}/dgelsd.f (100%) rename lib/linalg/{ => fortran}/dgelss.f (100%) rename lib/linalg/{ => fortran}/dgemm.f (100%) rename lib/linalg/{ => fortran}/dgemv.f (100%) rename lib/linalg/{ => fortran}/dgeqr2.f (100%) rename lib/linalg/{ => fortran}/dgeqrf.f (100%) rename lib/linalg/{ => fortran}/dger.f (100%) rename lib/linalg/{ => fortran}/dgesv.f (100%) rename lib/linalg/{ => fortran}/dgesvd.f (100%) rename lib/linalg/{ => fortran}/dgetf2.f (100%) rename lib/linalg/{ => fortran}/dgetrf.f (100%) rename lib/linalg/{ => fortran}/dgetrf2.f (100%) rename lib/linalg/{ => fortran}/dgetri.f (100%) rename lib/linalg/{ => fortran}/dgetrs.f (100%) rename lib/linalg/{ => fortran}/disnan.f (100%) rename lib/linalg/{ => fortran}/dlabad.f (100%) rename lib/linalg/{ => fortran}/dlabrd.f (100%) rename lib/linalg/{ => fortran}/dlacn2.f (100%) rename lib/linalg/{ => fortran}/dlacpy.f (100%) rename lib/linalg/{ => fortran}/dladiv.f (100%) rename lib/linalg/{ => fortran}/dlae2.f (100%) rename lib/linalg/{ => fortran}/dlaed0.f (100%) rename lib/linalg/{ => fortran}/dlaed1.f (100%) rename lib/linalg/{ => fortran}/dlaed2.f (100%) rename lib/linalg/{ => fortran}/dlaed3.f (100%) rename lib/linalg/{ => fortran}/dlaed4.f (100%) rename lib/linalg/{ => fortran}/dlaed5.f (100%) rename lib/linalg/{ => fortran}/dlaed6.f (100%) rename lib/linalg/{ => fortran}/dlaed7.f (100%) rename lib/linalg/{ => fortran}/dlaed8.f (100%) rename lib/linalg/{ => fortran}/dlaed9.f (100%) rename lib/linalg/{ => fortran}/dlaeda.f (100%) rename lib/linalg/{ => fortran}/dlaev2.f (100%) rename lib/linalg/{ => fortran}/dlaisnan.f (100%) rename lib/linalg/{ => fortran}/dlals0.f (100%) rename lib/linalg/{ => fortran}/dlalsa.f (100%) rename lib/linalg/{ => fortran}/dlalsd.f (100%) rename lib/linalg/{ => fortran}/dlamch.f (100%) rename lib/linalg/{ => fortran}/dlamrg.f (100%) rename lib/linalg/{ => fortran}/dlange.f (100%) rename lib/linalg/{ => fortran}/dlanst.f (100%) rename lib/linalg/{ => fortran}/dlansy.f (100%) rename lib/linalg/{ => fortran}/dlapy2.f (100%) rename lib/linalg/{ => fortran}/dlapy3.f (100%) rename lib/linalg/{ => fortran}/dlarf.f (100%) rename lib/linalg/{ => fortran}/dlarfb.f (100%) rename lib/linalg/{ => fortran}/dlarfg.f (100%) rename lib/linalg/{ => fortran}/dlarft.f (100%) rename lib/linalg/{ => fortran}/dlartg.f (100%) rename lib/linalg/{ => fortran}/dlas2.f (100%) rename lib/linalg/{ => fortran}/dlascl.f (100%) rename lib/linalg/{ => fortran}/dlasd4.f (100%) rename lib/linalg/{ => fortran}/dlasd5.f (100%) rename lib/linalg/{ => fortran}/dlasd6.f (100%) rename lib/linalg/{ => fortran}/dlasd7.f (100%) rename lib/linalg/{ => fortran}/dlasd8.f (100%) rename lib/linalg/{ => fortran}/dlasda.f (100%) rename lib/linalg/{ => fortran}/dlasdq.f (100%) rename lib/linalg/{ => fortran}/dlasdt.f (100%) rename lib/linalg/{ => fortran}/dlaset.f (100%) rename lib/linalg/{ => fortran}/dlasq1.f (100%) rename lib/linalg/{ => fortran}/dlasq2.f (100%) rename lib/linalg/{ => fortran}/dlasq3.f (100%) rename lib/linalg/{ => fortran}/dlasq4.f (100%) rename lib/linalg/{ => fortran}/dlasq5.f (100%) rename lib/linalg/{ => fortran}/dlasq6.f (100%) rename lib/linalg/{ => fortran}/dlasr.f (100%) rename lib/linalg/{ => fortran}/dlasrt.f (100%) rename lib/linalg/{ => fortran}/dlassq.f (100%) rename lib/linalg/{ => fortran}/dlasv2.f (100%) rename lib/linalg/{ => fortran}/dlaswp.f (100%) rename lib/linalg/{ => fortran}/dlatrd.f (100%) rename lib/linalg/{ => fortran}/dlatrs.f (100%) rename lib/linalg/{ => fortran}/dnrm2.f (100%) rename lib/linalg/{ => fortran}/dorg2l.f (100%) rename lib/linalg/{ => fortran}/dorg2r.f (100%) rename lib/linalg/{ => fortran}/dorgbr.f (100%) rename lib/linalg/{ => fortran}/dorgl2.f (100%) rename lib/linalg/{ => fortran}/dorglq.f (100%) rename lib/linalg/{ => fortran}/dorgql.f (100%) rename lib/linalg/{ => fortran}/dorgqr.f (100%) rename lib/linalg/{ => fortran}/dorgtr.f (100%) rename lib/linalg/{ => fortran}/dorm2l.f (100%) rename lib/linalg/{ => fortran}/dorm2r.f (100%) rename lib/linalg/{ => fortran}/dormbr.f (100%) rename lib/linalg/{ => fortran}/dorml2.f (100%) rename lib/linalg/{ => fortran}/dormlq.f (100%) rename lib/linalg/{ => fortran}/dormql.f (100%) rename lib/linalg/{ => fortran}/dormqr.f (100%) rename lib/linalg/{ => fortran}/dormtr.f (100%) rename lib/linalg/{ => fortran}/dposv.f (100%) rename lib/linalg/{ => fortran}/dpotf2.f (100%) rename lib/linalg/{ => fortran}/dpotrf.f (100%) rename lib/linalg/{ => fortran}/dpotrf2.f (100%) rename lib/linalg/{ => fortran}/dpotrs.f (100%) rename lib/linalg/{ => fortran}/drot.f (100%) rename lib/linalg/{ => fortran}/drscl.f (100%) rename lib/linalg/{ => fortran}/dscal.f (100%) rename lib/linalg/{ => fortran}/dstedc.f (100%) rename lib/linalg/{ => fortran}/dsteqr.f (100%) rename lib/linalg/{ => fortran}/dsterf.f (100%) rename lib/linalg/{ => fortran}/dswap.f (100%) rename lib/linalg/{ => fortran}/dsyev.f (100%) rename lib/linalg/{ => fortran}/dsyevd.f (100%) rename lib/linalg/{ => fortran}/dsygs2.f (100%) rename lib/linalg/{ => fortran}/dsygst.f (100%) rename lib/linalg/{ => fortran}/dsygv.f (100%) rename lib/linalg/{ => fortran}/dsygvd.f (100%) rename lib/linalg/{ => fortran}/dsymm.f (100%) rename lib/linalg/{ => fortran}/dsymv.f (100%) rename lib/linalg/{ => fortran}/dsyr2.f (100%) rename lib/linalg/{ => fortran}/dsyr2k.f (100%) rename lib/linalg/{ => fortran}/dsyrk.f (100%) rename lib/linalg/{ => fortran}/dsytd2.f (100%) rename lib/linalg/{ => fortran}/dsytrd.f (100%) rename lib/linalg/{ => fortran}/dtrmm.f (100%) rename lib/linalg/{ => fortran}/dtrmv.f (100%) rename lib/linalg/{ => fortran}/dtrsm.f (100%) rename lib/linalg/{ => fortran}/dtrsv.f (100%) rename lib/linalg/{ => fortran}/dtrti2.f (100%) rename lib/linalg/{ => fortran}/dtrtri.f (100%) rename lib/linalg/{ => fortran}/dznrm2.f (100%) rename lib/linalg/{ => fortran}/idamax.f (100%) rename lib/linalg/{ => fortran}/ieeeck.f (100%) rename lib/linalg/{ => fortran}/iladlc.f (100%) rename lib/linalg/{ => fortran}/iladlr.f (100%) rename lib/linalg/{ => fortran}/ilaenv.f (100%) rename lib/linalg/{ => fortran}/ilazlc.f (100%) rename lib/linalg/{ => fortran}/ilazlr.f (100%) rename lib/linalg/{ => fortran}/iparmq.f (100%) rename lib/linalg/{ => fortran}/lsame.f (100%) rename lib/linalg/{ => fortran}/xerbla.f (100%) rename lib/linalg/{ => fortran}/zaxpy.f (100%) rename lib/linalg/{ => fortran}/zcopy.f (100%) rename lib/linalg/{ => fortran}/zdotc.f (100%) rename lib/linalg/{ => fortran}/zdrot.f (100%) rename lib/linalg/{ => fortran}/zdscal.f (100%) rename lib/linalg/{ => fortran}/zgemm.f (100%) rename lib/linalg/{ => fortran}/zgemv.f (100%) rename lib/linalg/{ => fortran}/zgerc.f (100%) rename lib/linalg/{ => fortran}/zheev.f (100%) rename lib/linalg/{ => fortran}/zheevd.f (100%) rename lib/linalg/{ => fortran}/zhemv.f (100%) rename lib/linalg/{ => fortran}/zher2.f (100%) rename lib/linalg/{ => fortran}/zher2k.f (100%) rename lib/linalg/{ => fortran}/zhetd2.f (100%) rename lib/linalg/{ => fortran}/zhetrd.f (100%) rename lib/linalg/{ => fortran}/zhpr.f (100%) rename lib/linalg/{ => fortran}/zlacgv.f (100%) rename lib/linalg/{ => fortran}/zlacpy.f (100%) rename lib/linalg/{ => fortran}/zlacrm.f (100%) rename lib/linalg/{ => fortran}/zladiv.f (100%) rename lib/linalg/{ => fortran}/zlaed0.f (100%) rename lib/linalg/{ => fortran}/zlaed7.f (100%) rename lib/linalg/{ => fortran}/zlaed8.f (100%) rename lib/linalg/{ => fortran}/zlanhe.f (100%) rename lib/linalg/{ => fortran}/zlarf.f (100%) rename lib/linalg/{ => fortran}/zlarfb.f (100%) rename lib/linalg/{ => fortran}/zlarfg.f (100%) rename lib/linalg/{ => fortran}/zlarft.f (100%) rename lib/linalg/{ => fortran}/zlascl.f (100%) rename lib/linalg/{ => fortran}/zlaset.f (100%) rename lib/linalg/{ => fortran}/zlasr.f (100%) rename lib/linalg/{ => fortran}/zlassq.f (100%) rename lib/linalg/{ => fortran}/zlatrd.f (100%) rename lib/linalg/{ => fortran}/zpptrf.f (100%) rename lib/linalg/{ => fortran}/zpptri.f (100%) rename lib/linalg/{ => fortran}/zscal.f (100%) rename lib/linalg/{ => fortran}/zstedc.f (100%) rename lib/linalg/{ => fortran}/zsteqr.f (100%) rename lib/linalg/{ => fortran}/zswap.f (100%) rename lib/linalg/{ => fortran}/ztpmv.f (100%) rename lib/linalg/{ => fortran}/ztpsv.f (100%) rename lib/linalg/{ => fortran}/ztptri.f (100%) rename lib/linalg/{ => fortran}/ztrmm.f (100%) rename lib/linalg/{ => fortran}/ztrmv.f (100%) rename lib/linalg/{ => fortran}/zung2l.f (100%) rename lib/linalg/{ => fortran}/zung2r.f (100%) rename lib/linalg/{ => fortran}/zungl2.f (100%) rename lib/linalg/{ => fortran}/zungql.f (100%) rename lib/linalg/{ => fortran}/zungqr.f (100%) rename lib/linalg/{ => fortran}/zungtr.f (100%) rename lib/linalg/{ => fortran}/zunm2l.f (100%) rename lib/linalg/{ => fortran}/zunm2r.f (100%) rename lib/linalg/{ => fortran}/zunmql.f (100%) rename lib/linalg/{ => fortran}/zunmqr.f (100%) rename lib/linalg/{ => fortran}/zunmtr.f (100%) create mode 100644 lib/linalg/idamax.cpp create mode 100644 lib/linalg/ieeeck.cpp create mode 100644 lib/linalg/iladlc.cpp create mode 100644 lib/linalg/iladlr.cpp create mode 100644 lib/linalg/ilaenv.cpp create mode 100644 lib/linalg/ilazlc.cpp create mode 100644 lib/linalg/ilazlr.cpp create mode 100644 lib/linalg/iparmq.cpp create mode 100644 lib/linalg/lmp_f2c.h create mode 100644 lib/linalg/lsame.cpp create mode 100644 lib/linalg/static/README create mode 100644 lib/linalg/static/dgetrf2.f create mode 100644 lib/linalg/static/disnan.cpp create mode 100644 lib/linalg/static/dlamch.cpp create mode 100644 lib/linalg/static/dlarft.f create mode 100644 lib/linalg/static/dpotrf2.f create mode 100644 lib/linalg/static/lsame.cpp create mode 100644 lib/linalg/static/xerbla.cpp create mode 100644 lib/linalg/static/zlarft.f create mode 100644 lib/linalg/xerbla.cpp create mode 100644 lib/linalg/zaxpy.cpp create mode 100644 lib/linalg/zcopy.cpp create mode 100644 lib/linalg/zdotc.cpp create mode 100644 lib/linalg/zdrot.cpp create mode 100644 lib/linalg/zdscal.cpp create mode 100644 lib/linalg/zgemm.cpp create mode 100644 lib/linalg/zgemv.cpp create mode 100644 lib/linalg/zgerc.cpp create mode 100644 lib/linalg/zheev.cpp create mode 100644 lib/linalg/zheevd.cpp create mode 100644 lib/linalg/zhemv.cpp create mode 100644 lib/linalg/zher2.cpp create mode 100644 lib/linalg/zher2k.cpp create mode 100644 lib/linalg/zhetd2.cpp create mode 100644 lib/linalg/zhetrd.cpp create mode 100644 lib/linalg/zhpr.cpp create mode 100644 lib/linalg/zlacgv.cpp create mode 100644 lib/linalg/zlacpy.cpp create mode 100644 lib/linalg/zlacrm.cpp create mode 100644 lib/linalg/zladiv.cpp create mode 100644 lib/linalg/zlaed0.cpp create mode 100644 lib/linalg/zlaed7.cpp create mode 100644 lib/linalg/zlaed8.cpp create mode 100644 lib/linalg/zlanhe.cpp create mode 100644 lib/linalg/zlarf.cpp create mode 100644 lib/linalg/zlarfb.cpp create mode 100644 lib/linalg/zlarfg.cpp create mode 100644 lib/linalg/zlarft.cpp create mode 100644 lib/linalg/zlascl.cpp create mode 100644 lib/linalg/zlaset.cpp create mode 100644 lib/linalg/zlasr.cpp create mode 100644 lib/linalg/zlassq.cpp create mode 100644 lib/linalg/zlatrd.cpp create mode 100644 lib/linalg/zpptrf.cpp create mode 100644 lib/linalg/zpptri.cpp create mode 100644 lib/linalg/zscal.cpp create mode 100644 lib/linalg/zstedc.cpp create mode 100644 lib/linalg/zsteqr.cpp create mode 100644 lib/linalg/zswap.cpp create mode 100644 lib/linalg/ztpmv.cpp create mode 100644 lib/linalg/ztpsv.cpp create mode 100644 lib/linalg/ztptri.cpp create mode 100644 lib/linalg/ztrmm.cpp create mode 100644 lib/linalg/ztrmv.cpp create mode 100644 lib/linalg/zung2l.cpp create mode 100644 lib/linalg/zung2r.cpp create mode 100644 lib/linalg/zungl2.cpp create mode 100644 lib/linalg/zungql.cpp create mode 100644 lib/linalg/zungqr.cpp create mode 100644 lib/linalg/zungtr.cpp create mode 100644 lib/linalg/zunm2l.cpp create mode 100644 lib/linalg/zunm2r.cpp create mode 100644 lib/linalg/zunmql.cpp create mode 100644 lib/linalg/zunmqr.cpp create mode 100644 lib/linalg/zunmtr.cpp diff --git a/cmake/CMakeLists.txt b/cmake/CMakeLists.txt index 6666636a09..4351c40d75 100644 --- a/cmake/CMakeLists.txt +++ b/cmake/CMakeLists.txt @@ -440,13 +440,8 @@ if(PKG_MSCG OR PKG_ATC OR PKG_AWPMD OR PKG_ML-QUIP OR PKG_ML-POD OR PKG_LATTE OR find_package(BLAS) endif() if(NOT LAPACK_FOUND OR NOT BLAS_FOUND OR USE_INTERNAL_LINALG) - include(CheckGeneratorSupport) - if(NOT CMAKE_GENERATOR_SUPPORT_FORTRAN) - status(FATAL_ERROR "Cannot build internal linear algebra library as CMake build tool lacks Fortran support") - endif() - enable_language(Fortran) - file(GLOB LAPACK_SOURCES ${LAMMPS_LIB_SOURCE_DIR}/linalg/[^.]*.[fF]) - add_library(linalg STATIC ${LAPACK_SOURCES}) + file(GLOB LINALG_SOURCES ${LAMMPS_LIB_SOURCE_DIR}/linalg/[^.]*.cpp) + add_library(linalg STATIC ${LINALG_SOURCES}) set_target_properties(linalg PROPERTIES OUTPUT_NAME lammps_linalg${LAMMPS_MACHINE}) set(BLAS_LIBRARIES "$") set(LAPACK_LIBRARIES "$") diff --git a/lib/linalg/Makefile.gfortran b/lib/linalg/Makefile.g++ similarity index 65% rename from lib/linalg/Makefile.gfortran rename to lib/linalg/Makefile.g++ index 89ac3bbe6d..b1e18e8fd3 100644 --- a/lib/linalg/Makefile.gfortran +++ b/lib/linalg/Makefile.g++ @@ -6,20 +6,19 @@ SHELL = /bin/sh # ------ FILES ------ -SRC = $(wildcard *.f) +SRC = $(wildcard *.cpp) FILES = $(SRC) Makefile.* README # ------ DEFINITIONS ------ LIB = liblinalg.a -OBJ = $(SRC:.f=.o) +OBJ = $(SRC:.cpp=.o) # ------ SETTINGS ------ -FC = gfortran -FFLAGS = -O3 -fPIC -ffast-math -fstrict-aliasing -fno-second-underscore -FFLAGS0 = -O0 -fPIC -fno-second-underscore +CXX = g++ -std=c++11 +CCFLAGS = -O3 -fPIC -ffast-math -fstrict-aliasing ARCHIVE = ar AR = ar ARCHFLAG = -rcs @@ -33,16 +32,13 @@ lib: $(OBJ) # ------ COMPILE RULES ------ -%.o:%.f - $(FC) $(FFLAGS) -c $< - -dlamch.o: dlamch.f - $(FC) $(FFLAGS0) -c $< +%.o:%.cpp + $(CC) $(CCFLAGS) -c $< # ------ CLEAN ------ clean: - -rm -f *.o *.mod *~ $(LIB) + -rm -f *.o *~ $(LIB) tar: -tar -czvf ../linalg.tar.gz $(FILES) diff --git a/lib/linalg/Makefile.mpi b/lib/linalg/Makefile.mpi index 74de6cdf3d..567653cebc 100644 --- a/lib/linalg/Makefile.mpi +++ b/lib/linalg/Makefile.mpi @@ -6,20 +6,19 @@ SHELL = /bin/sh # ------ FILES ------ -SRC = $(wildcard *.f) +SRC = $(wildcard *.cpp) FILES = $(SRC) Makefile.* README # ------ DEFINITIONS ------ LIB = liblinalg.a -OBJ = $(SRC:.f=.o) +OBJ = $(SRC:.cpp=.o) # ------ SETTINGS ------ -FC = mpifort -FFLAGS = -O3 -fPIC -FFLAGS0 = -O0 -fPIC +CC = mpicxx +CCFLAGS = -O3 -fPIC ARCHIVE = ar AR = ar ARCHFLAG = -rcs @@ -33,16 +32,13 @@ lib: $(OBJ) # ------ COMPILE RULES ------ -%.o:%.f - $(FC) $(FFLAGS) -c $< - -dlamch.o: dlamch.f - $(FC) $(FFLAGS0) -c $< +%.o:%.cpp + $(CC) $(CCFLAGS) -c $< # ------ CLEAN ------ clean: - -rm -f *.o *.mod *~ $(LIB) + -rm -f *.o *~ $(LIB) tar: -tar -czvf ../linalg.tar.gz $(FILES) diff --git a/lib/linalg/Makefile.serial b/lib/linalg/Makefile.serial index c52fbcb986..9d7bb000f9 120000 --- a/lib/linalg/Makefile.serial +++ b/lib/linalg/Makefile.serial @@ -1 +1 @@ -Makefile.gfortran \ No newline at end of file +Makefile.g++ \ No newline at end of file diff --git a/lib/linalg/convert.sh b/lib/linalg/convert.sh new file mode 100755 index 0000000000..c73e0d3393 --- /dev/null +++ b/lib/linalg/convert.sh @@ -0,0 +1,44 @@ +#!/bin/bash + +has_f2c=$(type f2c > /dev/null 2>&1 && echo 1 || echo 0) +if test ${has_f2c} -eq 0 +then + echo "Must have f2c installed to run this script" + exit 1 +fi + +# cleanup +rm -f *.c *.cpp *.P *~ *.orig *.bak *.rej + +# translate files directly, skip those for which we have replacements. +for f in fortran/*.f +do \ + b=$(basename $f .f) + if test $b == dgetrf2 || test $b == disnan || test $b == dlaisnan || \ + test $b == dlamch || test $b == dlarft || test $b == dpotrf2 || \ + test $b == lsame || test $b == xerbla || test $b == zlarft + then + echo Skipping $b + else + f2c -C++ -a -f $f && mv $b.c $b.cpp || exit 2 + # silence c++ compiler warnings about string constants + sed -i -e 's/\("[^"]\+"\)/(char *)\1/g' -e 's/^extern.*"C"/extern "C"/' \ + -e 's/^#include.*"f2c.h"/#include "lmp_f2c.h"/' $b.cpp + fi +done + +# translate modified versions +for f in static/*.f +do \ + b=$(basename $f .f) + f2c -C++ -a -f $f && mv $b.c $b.cpp || exit 2 + # silence c++ compiler warnings about string constants + sed -i -e 's/\("[^"]\+"\)/(char *)\1/g' -e 's/^extern.*"C"/extern "C"/' \ + -e 's/^#include.*"f2c.h"/#include "lmp_f2c.h"/' $b.cpp +done + +# copy direct C++ alternatives +for c in static/*.cpp +do \ + cp -v $c . +done diff --git a/lib/linalg/dasum.cpp b/lib/linalg/dasum.cpp new file mode 100644 index 0000000000..0119bed6fd --- /dev/null +++ b/lib/linalg/dasum.cpp @@ -0,0 +1,168 @@ +/* fortran/dasum.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DASUM */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* DOUBLE PRECISION FUNCTION DASUM(N,DX,INCX) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INCX,N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION DX(*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DASUM takes the sum of the absolute values. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > number of elements in input vector(s) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DX */ +/* > \verbatim */ +/* > DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > storage spacing between elements of DX */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup double_blas_level1 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > jack dongarra, linpack, 3/11/78. */ +/* > modified 3/93 to return if incx .le. 0. */ +/* > modified 12/3/93, array(1) declarations changed to array(*) */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +doublereal dasum_(integer *n, doublereal *dx, integer *incx) +{ + /* System generated locals */ + integer i__1, i__2; + doublereal ret_val, d__1, d__2, d__3, d__4, d__5, d__6; + + /* Local variables */ + integer i__, m, mp1; + doublereal dtemp; + integer nincx; + + +/* -- Reference BLAS level1 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ + /* Parameter adjustments */ + --dx; + + /* Function Body */ + ret_val = 0.; + dtemp = 0.; + if (*n <= 0 || *incx <= 0) { + return ret_val; + } + if (*incx == 1) { +/* code for increment equal to 1 */ + + +/* clean-up loop */ + + m = *n % 6; + if (m != 0) { + i__1 = m; + for (i__ = 1; i__ <= i__1; ++i__) { + dtemp += (d__1 = dx[i__], abs(d__1)); + } + if (*n < 6) { + ret_val = dtemp; + return ret_val; + } + } + mp1 = m + 1; + i__1 = *n; + for (i__ = mp1; i__ <= i__1; i__ += 6) { + dtemp = dtemp + (d__1 = dx[i__], abs(d__1)) + (d__2 = dx[i__ + 1], + abs(d__2)) + (d__3 = dx[i__ + 2], abs(d__3)) + (d__4 = + dx[i__ + 3], abs(d__4)) + (d__5 = dx[i__ + 4], abs(d__5)) + + (d__6 = dx[i__ + 5], abs(d__6)); + } + } else { + +/* code for increment not equal to 1 */ + + nincx = *n * *incx; + i__1 = nincx; + i__2 = *incx; + for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { + dtemp += (d__1 = dx[i__], abs(d__1)); + } + } + ret_val = dtemp; + return ret_val; + +/* End of DASUM */ + +} /* dasum_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/daxpy.cpp b/lib/linalg/daxpy.cpp new file mode 100644 index 0000000000..d89cd6e9c4 --- /dev/null +++ b/lib/linalg/daxpy.cpp @@ -0,0 +1,194 @@ +/* fortran/daxpy.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DAXPY */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DAXPY(N,DA,DX,INCX,DY,INCY) */ + +/* .. Scalar Arguments .. */ +/* DOUBLE PRECISION DA */ +/* INTEGER INCX,INCY,N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION DX(*),DY(*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DAXPY constant times a vector plus a vector. */ +/* > uses unrolled loops for increments equal to one. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > number of elements in input vector(s) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DA */ +/* > \verbatim */ +/* > DA is DOUBLE PRECISION */ +/* > On entry, DA specifies the scalar alpha. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DX */ +/* > \verbatim */ +/* > DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > storage spacing between elements of DX */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] DY */ +/* > \verbatim */ +/* > DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCY */ +/* > \verbatim */ +/* > INCY is INTEGER */ +/* > storage spacing between elements of DY */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup double_blas_level1 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > jack dongarra, linpack, 3/11/78. */ +/* > modified 12/3/93, array(1) declarations changed to array(*) */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int daxpy_(integer *n, doublereal *da, doublereal *dx, + integer *incx, doublereal *dy, integer *incy) +{ + /* System generated locals */ + integer i__1; + + /* Local variables */ + integer i__, m, ix, iy, mp1; + + +/* -- Reference BLAS level1 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ + /* Parameter adjustments */ + --dy; + --dx; + + /* Function Body */ + if (*n <= 0) { + return 0; + } + if (*da == 0.) { + return 0; + } + if (*incx == 1 && *incy == 1) { + +/* code for both increments equal to 1 */ + + +/* clean-up loop */ + + m = *n % 4; + if (m != 0) { + i__1 = m; + for (i__ = 1; i__ <= i__1; ++i__) { + dy[i__] += *da * dx[i__]; + } + } + if (*n < 4) { + return 0; + } + mp1 = m + 1; + i__1 = *n; + for (i__ = mp1; i__ <= i__1; i__ += 4) { + dy[i__] += *da * dx[i__]; + dy[i__ + 1] += *da * dx[i__ + 1]; + dy[i__ + 2] += *da * dx[i__ + 2]; + dy[i__ + 3] += *da * dx[i__ + 3]; + } + } else { + +/* code for unequal increments or equal increments */ +/* not equal to 1 */ + + ix = 1; + iy = 1; + if (*incx < 0) { + ix = (-(*n) + 1) * *incx + 1; + } + if (*incy < 0) { + iy = (-(*n) + 1) * *incy + 1; + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + dy[iy] += *da * dx[ix]; + ix += *incx; + iy += *incy; + } + } + return 0; + +/* End of DAXPY */ + +} /* daxpy_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dbdsqr.cpp b/lib/linalg/dbdsqr.cpp new file mode 100644 index 0000000000..78c996dc2b --- /dev/null +++ b/lib/linalg/dbdsqr.cpp @@ -0,0 +1,1053 @@ +/* fortran/dbdsqr.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static doublereal c_b15 = -.125; +static integer c__1 = 1; +static doublereal c_b49 = 1.; +static doublereal c_b72 = -1.; + +/* > \brief \b DBDSQR */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DBDSQR + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DBDSQR( UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, */ +/* LDU, C, LDC, WORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER UPLO */ +/* INTEGER INFO, LDC, LDU, LDVT, N, NCC, NCVT, NRU */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION C( LDC, * ), D( * ), E( * ), U( LDU, * ), */ +/* $ VT( LDVT, * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DBDSQR computes the singular values and, optionally, the right and/or */ +/* > left singular vectors from the singular value decomposition (SVD) of */ +/* > a real N-by-N (upper or lower) bidiagonal matrix B using the implicit */ +/* > zero-shift QR algorithm. The SVD of B has the form */ +/* > */ +/* > B = Q * S * P**T */ +/* > */ +/* > where S is the diagonal matrix of singular values, Q is an orthogonal */ +/* > matrix of left singular vectors, and P is an orthogonal matrix of */ +/* > right singular vectors. If left singular vectors are requested, this */ +/* > subroutine actually returns U*Q instead of Q, and, if right singular */ +/* > vectors are requested, this subroutine returns P**T*VT instead of */ +/* > P**T, for given real input matrices U and VT. When U and VT are the */ +/* > orthogonal matrices that reduce a general matrix A to bidiagonal */ +/* > form: A = U*B*VT, as computed by DGEBRD, then */ +/* > */ +/* > A = (U*Q) * S * (P**T*VT) */ +/* > */ +/* > is the SVD of A. Optionally, the subroutine may also compute Q**T*C */ +/* > for a given real input matrix C. */ +/* > */ +/* > See "Computing Small Singular Values of Bidiagonal Matrices With */ +/* > Guaranteed High Relative Accuracy," by J. Demmel and W. Kahan, */ +/* > LAPACK Working Note #3 (or SIAM J. Sci. Statist. Comput. vol. 11, */ +/* > no. 5, pp. 873-912, Sept 1990) and */ +/* > (char *)"Accurate singular values and differential qd algorithms," by */ +/* > B. Parlett and V. Fernando, Technical Report CPAM-554, Mathematics */ +/* > Department, University of California at Berkeley, July 1992 */ +/* > for a detailed description of the algorithm. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > = 'U': B is upper bidiagonal; */ +/* > = 'L': B is lower bidiagonal. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrix B. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] NCVT */ +/* > \verbatim */ +/* > NCVT is INTEGER */ +/* > The number of columns of the matrix VT. NCVT >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] NRU */ +/* > \verbatim */ +/* > NRU is INTEGER */ +/* > The number of rows of the matrix U. NRU >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] NCC */ +/* > \verbatim */ +/* > NCC is INTEGER */ +/* > The number of columns of the matrix C. NCC >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension (N) */ +/* > On entry, the n diagonal elements of the bidiagonal matrix B. */ +/* > On exit, if INFO=0, the singular values of B in decreasing */ +/* > order. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] E */ +/* > \verbatim */ +/* > E is DOUBLE PRECISION array, dimension (N-1) */ +/* > On entry, the N-1 offdiagonal elements of the bidiagonal */ +/* > matrix B. */ +/* > On exit, if INFO = 0, E is destroyed; if INFO > 0, D and E */ +/* > will contain the diagonal and superdiagonal elements of a */ +/* > bidiagonal matrix orthogonally equivalent to the one given */ +/* > as input. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] VT */ +/* > \verbatim */ +/* > VT is DOUBLE PRECISION array, dimension (LDVT, NCVT) */ +/* > On entry, an N-by-NCVT matrix VT. */ +/* > On exit, VT is overwritten by P**T * VT. */ +/* > Not referenced if NCVT = 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDVT */ +/* > \verbatim */ +/* > LDVT is INTEGER */ +/* > The leading dimension of the array VT. */ +/* > LDVT >= max(1,N) if NCVT > 0; LDVT >= 1 if NCVT = 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] U */ +/* > \verbatim */ +/* > U is DOUBLE PRECISION array, dimension (LDU, N) */ +/* > On entry, an NRU-by-N matrix U. */ +/* > On exit, U is overwritten by U * Q. */ +/* > Not referenced if NRU = 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDU */ +/* > \verbatim */ +/* > LDU is INTEGER */ +/* > The leading dimension of the array U. LDU >= max(1,NRU). */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] C */ +/* > \verbatim */ +/* > C is DOUBLE PRECISION array, dimension (LDC, NCC) */ +/* > On entry, an N-by-NCC matrix C. */ +/* > On exit, C is overwritten by Q**T * C. */ +/* > Not referenced if NCC = 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDC */ +/* > \verbatim */ +/* > LDC is INTEGER */ +/* > The leading dimension of the array C. */ +/* > LDC >= max(1,N) if NCC > 0; LDC >=1 if NCC = 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (4*(N-1)) */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: If INFO = -i, the i-th argument had an illegal value */ +/* > > 0: */ +/* > if NCVT = NRU = NCC = 0, */ +/* > = 1, a split was marked by a positive value in E */ +/* > = 2, current block of Z not diagonalized after 30*N */ +/* > iterations (in inner while loop) */ +/* > = 3, termination criterion of outer while loop not met */ +/* > (program created more than N unreduced blocks) */ +/* > else NCVT = NRU = NCC = 0, */ +/* > the algorithm did not converge; D and E contain the */ +/* > elements of a bidiagonal matrix which is orthogonally */ +/* > similar to the input matrix B; if INFO = i, i */ +/* > elements of E have not converged to zero. */ +/* > \endverbatim */ + +/* > \par Internal Parameters: */ +/* ========================= */ +/* > */ +/* > \verbatim */ +/* > TOLMUL DOUBLE PRECISION, default = max(10,min(100,EPS**(-1/8))) */ +/* > TOLMUL controls the convergence criterion of the QR loop. */ +/* > If it is positive, TOLMUL*EPS is the desired relative */ +/* > precision in the computed singular values. */ +/* > If it is negative, abs(TOLMUL*EPS*sigma_max) is the */ +/* > desired absolute accuracy in the computed singular */ +/* > values (corresponds to relative accuracy */ +/* > abs(TOLMUL*EPS) in the largest singular value. */ +/* > abs(TOLMUL) should be between 1 and 1/EPS, and preferably */ +/* > between 10 (for fast convergence) and .1/EPS */ +/* > (for there to be some accuracy in the results). */ +/* > Default is to lose at either one eighth or 2 of the */ +/* > available decimal digits in each computed singular value */ +/* > (whichever is smaller). */ +/* > */ +/* > MAXITR INTEGER, default = 6 */ +/* > MAXITR controls the maximum number of passes of the */ +/* > algorithm through its inner loop. The algorithms stops */ +/* > (and so fails to converge) if the number of passes */ +/* > through the inner loop exceeds MAXITR*N**2. */ +/* > */ +/* > \endverbatim */ + +/* > \par Note: */ +/* =========== */ +/* > */ +/* > \verbatim */ +/* > Bug report from Cezary Dendek. */ +/* > On March 23rd 2017, the INTEGER variable MAXIT = MAXITR*N**2 is */ +/* > removed since it can overflow pretty easily (for N larger or equal */ +/* > than 18,919). We instead use MAXITDIVN = MAXITR*N. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup auxOTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dbdsqr_(char *uplo, integer *n, integer *ncvt, integer * + nru, integer *ncc, doublereal *d__, doublereal *e, doublereal *vt, + integer *ldvt, doublereal *u, integer *ldu, doublereal *c__, integer * + ldc, doublereal *work, integer *info, ftnlen uplo_len) +{ + /* System generated locals */ + integer c_dim1, c_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1, + i__2; + doublereal d__1, d__2, d__3, d__4; + + /* Builtin functions */ + double pow_dd(doublereal *, doublereal *), sqrt(doublereal), d_sign( + doublereal *, doublereal *); + + /* Local variables */ + integer iterdivn; + doublereal f, g, h__; + integer i__, j, m; + doublereal r__; + integer maxitdivn; + doublereal cs; + integer ll; + doublereal sn, mu; + integer nm1, nm12, nm13, lll; + doublereal eps, sll, tol, abse; + integer idir; + doublereal abss; + integer oldm; + doublereal cosl; + integer isub, iter; + doublereal unfl, sinl, cosr, smin, smax, sinr; + extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, + doublereal *, integer *, doublereal *, doublereal *), dlas2_( + doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *), dscal_(integer *, doublereal *, doublereal *, + integer *); + extern logical lsame_(char *, char *, ftnlen, ftnlen); + doublereal oldcs; + extern /* Subroutine */ int dlasr_(char *, char *, char *, integer *, + integer *, doublereal *, doublereal *, doublereal *, integer *, + ftnlen, ftnlen, ftnlen); + integer oldll; + doublereal shift, sigmn, oldsn; + extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, + doublereal *, integer *); + doublereal sminl, sigmx; + logical lower; + extern /* Subroutine */ int dlasq1_(integer *, doublereal *, doublereal *, + doublereal *, integer *), dlasv2_(doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *); + extern doublereal dlamch_(char *, ftnlen); + extern /* Subroutine */ int dlartg_(doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *), xerbla_(char *, + integer *, ftnlen); + doublereal sminoa, thresh; + logical rotate; + doublereal tolmul; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --d__; + --e; + vt_dim1 = *ldvt; + vt_offset = 1 + vt_dim1; + vt -= vt_offset; + u_dim1 = *ldu; + u_offset = 1 + u_dim1; + u -= u_offset; + c_dim1 = *ldc; + c_offset = 1 + c_dim1; + c__ -= c_offset; + --work; + + /* Function Body */ + *info = 0; + lower = lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1); + if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lower) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } else if (*ncvt < 0) { + *info = -3; + } else if (*nru < 0) { + *info = -4; + } else if (*ncc < 0) { + *info = -5; + } else if (*ncvt == 0 && *ldvt < 1 || *ncvt > 0 && *ldvt < max(1,*n)) { + *info = -9; + } else if (*ldu < max(1,*nru)) { + *info = -11; + } else if (*ncc == 0 && *ldc < 1 || *ncc > 0 && *ldc < max(1,*n)) { + *info = -13; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DBDSQR", &i__1, (ftnlen)6); + return 0; + } + if (*n == 0) { + return 0; + } + if (*n == 1) { + goto L160; + } + +/* ROTATE is true if any singular vectors desired, false otherwise */ + + rotate = *ncvt > 0 || *nru > 0 || *ncc > 0; + +/* If no singular vectors desired, use qd algorithm */ + + if (! rotate) { + dlasq1_(n, &d__[1], &e[1], &work[1], info); + +/* If INFO equals 2, dqds didn't finish, try to finish */ + + if (*info != 2) { + return 0; + } + *info = 0; + } + + nm1 = *n - 1; + nm12 = nm1 + nm1; + nm13 = nm12 + nm1; + idir = 0; + +/* Get machine constants */ + + eps = dlamch_((char *)"Epsilon", (ftnlen)7); + unfl = dlamch_((char *)"Safe minimum", (ftnlen)12); + +/* If matrix lower bidiagonal, rotate to be upper bidiagonal */ +/* by applying Givens rotations on the left */ + + if (lower) { + i__1 = *n - 1; + for (i__ = 1; i__ <= i__1; ++i__) { + dlartg_(&d__[i__], &e[i__], &cs, &sn, &r__); + d__[i__] = r__; + e[i__] = sn * d__[i__ + 1]; + d__[i__ + 1] = cs * d__[i__ + 1]; + work[i__] = cs; + work[nm1 + i__] = sn; +/* L10: */ + } + +/* Update singular vectors if desired */ + + if (*nru > 0) { + dlasr_((char *)"R", (char *)"V", (char *)"F", nru, n, &work[1], &work[*n], &u[u_offset], + ldu, (ftnlen)1, (ftnlen)1, (ftnlen)1); + } + if (*ncc > 0) { + dlasr_((char *)"L", (char *)"V", (char *)"F", n, ncc, &work[1], &work[*n], &c__[c_offset], + ldc, (ftnlen)1, (ftnlen)1, (ftnlen)1); + } + } + +/* Compute singular values to relative accuracy TOL */ +/* (By setting TOL to be negative, algorithm will compute */ +/* singular values to absolute accuracy ABS(TOL)*norm(input matrix)) */ + +/* Computing MAX */ +/* Computing MIN */ + d__3 = 100., d__4 = pow_dd(&eps, &c_b15); + d__1 = 10., d__2 = min(d__3,d__4); + tolmul = max(d__1,d__2); + tol = tolmul * eps; + +/* Compute approximate maximum, minimum singular values */ + + smax = 0.; + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { +/* Computing MAX */ + d__2 = smax, d__3 = (d__1 = d__[i__], abs(d__1)); + smax = max(d__2,d__3); +/* L20: */ + } + i__1 = *n - 1; + for (i__ = 1; i__ <= i__1; ++i__) { +/* Computing MAX */ + d__2 = smax, d__3 = (d__1 = e[i__], abs(d__1)); + smax = max(d__2,d__3); +/* L30: */ + } + sminl = 0.; + if (tol >= 0.) { + +/* Relative accuracy desired */ + + sminoa = abs(d__[1]); + if (sminoa == 0.) { + goto L50; + } + mu = sminoa; + i__1 = *n; + for (i__ = 2; i__ <= i__1; ++i__) { + mu = (d__2 = d__[i__], abs(d__2)) * (mu / (mu + (d__1 = e[i__ - 1] + , abs(d__1)))); + sminoa = min(sminoa,mu); + if (sminoa == 0.) { + goto L50; + } +/* L40: */ + } +L50: + sminoa /= sqrt((doublereal) (*n)); +/* Computing MAX */ + d__1 = tol * sminoa, d__2 = *n * (*n * unfl) * 6; + thresh = max(d__1,d__2); + } else { + +/* Absolute accuracy desired */ + +/* Computing MAX */ + d__1 = abs(tol) * smax, d__2 = *n * (*n * unfl) * 6; + thresh = max(d__1,d__2); + } + +/* Prepare for main iteration loop for the singular values */ +/* (MAXIT is the maximum number of passes through the inner */ +/* loop permitted before nonconvergence signalled.) */ + + maxitdivn = *n * 6; + iterdivn = 0; + iter = -1; + oldll = -1; + oldm = -1; + +/* M points to last element of unconverged part of matrix */ + + m = *n; + +/* Begin main iteration loop */ + +L60: + +/* Check for convergence or exceeding iteration count */ + + if (m <= 1) { + goto L160; + } + + if (iter >= *n) { + iter -= *n; + ++iterdivn; + if (iterdivn >= maxitdivn) { + goto L200; + } + } + +/* Find diagonal block of matrix to work on */ + + if (tol < 0. && (d__1 = d__[m], abs(d__1)) <= thresh) { + d__[m] = 0.; + } + smax = (d__1 = d__[m], abs(d__1)); + smin = smax; + i__1 = m - 1; + for (lll = 1; lll <= i__1; ++lll) { + ll = m - lll; + abss = (d__1 = d__[ll], abs(d__1)); + abse = (d__1 = e[ll], abs(d__1)); + if (tol < 0. && abss <= thresh) { + d__[ll] = 0.; + } + if (abse <= thresh) { + goto L80; + } + smin = min(smin,abss); +/* Computing MAX */ + d__1 = max(smax,abss); + smax = max(d__1,abse); +/* L70: */ + } + ll = 0; + goto L90; +L80: + e[ll] = 0.; + +/* Matrix splits since E(LL) = 0 */ + + if (ll == m - 1) { + +/* Convergence of bottom singular value, return to top of loop */ + + --m; + goto L60; + } +L90: + ++ll; + +/* E(LL) through E(M-1) are nonzero, E(LL-1) is zero */ + + if (ll == m - 1) { + +/* 2 by 2 block, handle separately */ + + dlasv2_(&d__[m - 1], &e[m - 1], &d__[m], &sigmn, &sigmx, &sinr, &cosr, + &sinl, &cosl); + d__[m - 1] = sigmx; + e[m - 1] = 0.; + d__[m] = sigmn; + +/* Compute singular vectors, if desired */ + + if (*ncvt > 0) { + drot_(ncvt, &vt[m - 1 + vt_dim1], ldvt, &vt[m + vt_dim1], ldvt, & + cosr, &sinr); + } + if (*nru > 0) { + drot_(nru, &u[(m - 1) * u_dim1 + 1], &c__1, &u[m * u_dim1 + 1], & + c__1, &cosl, &sinl); + } + if (*ncc > 0) { + drot_(ncc, &c__[m - 1 + c_dim1], ldc, &c__[m + c_dim1], ldc, & + cosl, &sinl); + } + m += -2; + goto L60; + } + +/* If working on new submatrix, choose shift direction */ +/* (from larger end diagonal element towards smaller) */ + + if (ll > oldm || m < oldll) { + if ((d__1 = d__[ll], abs(d__1)) >= (d__2 = d__[m], abs(d__2))) { + +/* Chase bulge from top (big end) to bottom (small end) */ + + idir = 1; + } else { + +/* Chase bulge from bottom (big end) to top (small end) */ + + idir = 2; + } + } + +/* Apply convergence tests */ + + if (idir == 1) { + +/* Run convergence test in forward direction */ +/* First apply standard test to bottom of matrix */ + + if ((d__2 = e[m - 1], abs(d__2)) <= abs(tol) * (d__1 = d__[m], abs( + d__1)) || tol < 0. && (d__3 = e[m - 1], abs(d__3)) <= thresh) + { + e[m - 1] = 0.; + goto L60; + } + + if (tol >= 0.) { + +/* If relative accuracy desired, */ +/* apply convergence criterion forward */ + + mu = (d__1 = d__[ll], abs(d__1)); + sminl = mu; + i__1 = m - 1; + for (lll = ll; lll <= i__1; ++lll) { + if ((d__1 = e[lll], abs(d__1)) <= tol * mu) { + e[lll] = 0.; + goto L60; + } + mu = (d__2 = d__[lll + 1], abs(d__2)) * (mu / (mu + (d__1 = e[ + lll], abs(d__1)))); + sminl = min(sminl,mu); +/* L100: */ + } + } + + } else { + +/* Run convergence test in backward direction */ +/* First apply standard test to top of matrix */ + + if ((d__2 = e[ll], abs(d__2)) <= abs(tol) * (d__1 = d__[ll], abs(d__1) + ) || tol < 0. && (d__3 = e[ll], abs(d__3)) <= thresh) { + e[ll] = 0.; + goto L60; + } + + if (tol >= 0.) { + +/* If relative accuracy desired, */ +/* apply convergence criterion backward */ + + mu = (d__1 = d__[m], abs(d__1)); + sminl = mu; + i__1 = ll; + for (lll = m - 1; lll >= i__1; --lll) { + if ((d__1 = e[lll], abs(d__1)) <= tol * mu) { + e[lll] = 0.; + goto L60; + } + mu = (d__2 = d__[lll], abs(d__2)) * (mu / (mu + (d__1 = e[lll] + , abs(d__1)))); + sminl = min(sminl,mu); +/* L110: */ + } + } + } + oldll = ll; + oldm = m; + +/* Compute shift. First, test if shifting would ruin relative */ +/* accuracy, and if so set the shift to zero. */ + +/* Computing MAX */ + d__1 = eps, d__2 = tol * .01; + if (tol >= 0. && *n * tol * (sminl / smax) <= max(d__1,d__2)) { + +/* Use a zero shift to avoid loss of relative accuracy */ + + shift = 0.; + } else { + +/* Compute the shift from 2-by-2 block at end of matrix */ + + if (idir == 1) { + sll = (d__1 = d__[ll], abs(d__1)); + dlas2_(&d__[m - 1], &e[m - 1], &d__[m], &shift, &r__); + } else { + sll = (d__1 = d__[m], abs(d__1)); + dlas2_(&d__[ll], &e[ll], &d__[ll + 1], &shift, &r__); + } + +/* Test if shift negligible, and if so set to zero */ + + if (sll > 0.) { +/* Computing 2nd power */ + d__1 = shift / sll; + if (d__1 * d__1 < eps) { + shift = 0.; + } + } + } + +/* Increment iteration count */ + + iter = iter + m - ll; + +/* If SHIFT = 0, do simplified QR iteration */ + + if (shift == 0.) { + if (idir == 1) { + +/* Chase bulge from top to bottom */ +/* Save cosines and sines for later singular vector updates */ + + cs = 1.; + oldcs = 1.; + i__1 = m - 1; + for (i__ = ll; i__ <= i__1; ++i__) { + d__1 = d__[i__] * cs; + dlartg_(&d__1, &e[i__], &cs, &sn, &r__); + if (i__ > ll) { + e[i__ - 1] = oldsn * r__; + } + d__1 = oldcs * r__; + d__2 = d__[i__ + 1] * sn; + dlartg_(&d__1, &d__2, &oldcs, &oldsn, &d__[i__]); + work[i__ - ll + 1] = cs; + work[i__ - ll + 1 + nm1] = sn; + work[i__ - ll + 1 + nm12] = oldcs; + work[i__ - ll + 1 + nm13] = oldsn; +/* L120: */ + } + h__ = d__[m] * cs; + d__[m] = h__ * oldcs; + e[m - 1] = h__ * oldsn; + +/* Update singular vectors */ + + if (*ncvt > 0) { + i__1 = m - ll + 1; + dlasr_((char *)"L", (char *)"V", (char *)"F", &i__1, ncvt, &work[1], &work[*n], &vt[ + ll + vt_dim1], ldvt, (ftnlen)1, (ftnlen)1, (ftnlen)1); + } + if (*nru > 0) { + i__1 = m - ll + 1; + dlasr_((char *)"R", (char *)"V", (char *)"F", nru, &i__1, &work[nm12 + 1], &work[nm13 + + 1], &u[ll * u_dim1 + 1], ldu, (ftnlen)1, (ftnlen)1, + (ftnlen)1); + } + if (*ncc > 0) { + i__1 = m - ll + 1; + dlasr_((char *)"L", (char *)"V", (char *)"F", &i__1, ncc, &work[nm12 + 1], &work[nm13 + + 1], &c__[ll + c_dim1], ldc, (ftnlen)1, (ftnlen)1, ( + ftnlen)1); + } + +/* Test convergence */ + + if ((d__1 = e[m - 1], abs(d__1)) <= thresh) { + e[m - 1] = 0.; + } + + } else { + +/* Chase bulge from bottom to top */ +/* Save cosines and sines for later singular vector updates */ + + cs = 1.; + oldcs = 1.; + i__1 = ll + 1; + for (i__ = m; i__ >= i__1; --i__) { + d__1 = d__[i__] * cs; + dlartg_(&d__1, &e[i__ - 1], &cs, &sn, &r__); + if (i__ < m) { + e[i__] = oldsn * r__; + } + d__1 = oldcs * r__; + d__2 = d__[i__ - 1] * sn; + dlartg_(&d__1, &d__2, &oldcs, &oldsn, &d__[i__]); + work[i__ - ll] = cs; + work[i__ - ll + nm1] = -sn; + work[i__ - ll + nm12] = oldcs; + work[i__ - ll + nm13] = -oldsn; +/* L130: */ + } + h__ = d__[ll] * cs; + d__[ll] = h__ * oldcs; + e[ll] = h__ * oldsn; + +/* Update singular vectors */ + + if (*ncvt > 0) { + i__1 = m - ll + 1; + dlasr_((char *)"L", (char *)"V", (char *)"B", &i__1, ncvt, &work[nm12 + 1], &work[ + nm13 + 1], &vt[ll + vt_dim1], ldvt, (ftnlen)1, ( + ftnlen)1, (ftnlen)1); + } + if (*nru > 0) { + i__1 = m - ll + 1; + dlasr_((char *)"R", (char *)"V", (char *)"B", nru, &i__1, &work[1], &work[*n], &u[ll * + u_dim1 + 1], ldu, (ftnlen)1, (ftnlen)1, (ftnlen)1); + } + if (*ncc > 0) { + i__1 = m - ll + 1; + dlasr_((char *)"L", (char *)"V", (char *)"B", &i__1, ncc, &work[1], &work[*n], &c__[ + ll + c_dim1], ldc, (ftnlen)1, (ftnlen)1, (ftnlen)1); + } + +/* Test convergence */ + + if ((d__1 = e[ll], abs(d__1)) <= thresh) { + e[ll] = 0.; + } + } + } else { + +/* Use nonzero shift */ + + if (idir == 1) { + +/* Chase bulge from top to bottom */ +/* Save cosines and sines for later singular vector updates */ + + f = ((d__1 = d__[ll], abs(d__1)) - shift) * (d_sign(&c_b49, &d__[ + ll]) + shift / d__[ll]); + g = e[ll]; + i__1 = m - 1; + for (i__ = ll; i__ <= i__1; ++i__) { + dlartg_(&f, &g, &cosr, &sinr, &r__); + if (i__ > ll) { + e[i__ - 1] = r__; + } + f = cosr * d__[i__] + sinr * e[i__]; + e[i__] = cosr * e[i__] - sinr * d__[i__]; + g = sinr * d__[i__ + 1]; + d__[i__ + 1] = cosr * d__[i__ + 1]; + dlartg_(&f, &g, &cosl, &sinl, &r__); + d__[i__] = r__; + f = cosl * e[i__] + sinl * d__[i__ + 1]; + d__[i__ + 1] = cosl * d__[i__ + 1] - sinl * e[i__]; + if (i__ < m - 1) { + g = sinl * e[i__ + 1]; + e[i__ + 1] = cosl * e[i__ + 1]; + } + work[i__ - ll + 1] = cosr; + work[i__ - ll + 1 + nm1] = sinr; + work[i__ - ll + 1 + nm12] = cosl; + work[i__ - ll + 1 + nm13] = sinl; +/* L140: */ + } + e[m - 1] = f; + +/* Update singular vectors */ + + if (*ncvt > 0) { + i__1 = m - ll + 1; + dlasr_((char *)"L", (char *)"V", (char *)"F", &i__1, ncvt, &work[1], &work[*n], &vt[ + ll + vt_dim1], ldvt, (ftnlen)1, (ftnlen)1, (ftnlen)1); + } + if (*nru > 0) { + i__1 = m - ll + 1; + dlasr_((char *)"R", (char *)"V", (char *)"F", nru, &i__1, &work[nm12 + 1], &work[nm13 + + 1], &u[ll * u_dim1 + 1], ldu, (ftnlen)1, (ftnlen)1, + (ftnlen)1); + } + if (*ncc > 0) { + i__1 = m - ll + 1; + dlasr_((char *)"L", (char *)"V", (char *)"F", &i__1, ncc, &work[nm12 + 1], &work[nm13 + + 1], &c__[ll + c_dim1], ldc, (ftnlen)1, (ftnlen)1, ( + ftnlen)1); + } + +/* Test convergence */ + + if ((d__1 = e[m - 1], abs(d__1)) <= thresh) { + e[m - 1] = 0.; + } + + } else { + +/* Chase bulge from bottom to top */ +/* Save cosines and sines for later singular vector updates */ + + f = ((d__1 = d__[m], abs(d__1)) - shift) * (d_sign(&c_b49, &d__[m] + ) + shift / d__[m]); + g = e[m - 1]; + i__1 = ll + 1; + for (i__ = m; i__ >= i__1; --i__) { + dlartg_(&f, &g, &cosr, &sinr, &r__); + if (i__ < m) { + e[i__] = r__; + } + f = cosr * d__[i__] + sinr * e[i__ - 1]; + e[i__ - 1] = cosr * e[i__ - 1] - sinr * d__[i__]; + g = sinr * d__[i__ - 1]; + d__[i__ - 1] = cosr * d__[i__ - 1]; + dlartg_(&f, &g, &cosl, &sinl, &r__); + d__[i__] = r__; + f = cosl * e[i__ - 1] + sinl * d__[i__ - 1]; + d__[i__ - 1] = cosl * d__[i__ - 1] - sinl * e[i__ - 1]; + if (i__ > ll + 1) { + g = sinl * e[i__ - 2]; + e[i__ - 2] = cosl * e[i__ - 2]; + } + work[i__ - ll] = cosr; + work[i__ - ll + nm1] = -sinr; + work[i__ - ll + nm12] = cosl; + work[i__ - ll + nm13] = -sinl; +/* L150: */ + } + e[ll] = f; + +/* Test convergence */ + + if ((d__1 = e[ll], abs(d__1)) <= thresh) { + e[ll] = 0.; + } + +/* Update singular vectors if desired */ + + if (*ncvt > 0) { + i__1 = m - ll + 1; + dlasr_((char *)"L", (char *)"V", (char *)"B", &i__1, ncvt, &work[nm12 + 1], &work[ + nm13 + 1], &vt[ll + vt_dim1], ldvt, (ftnlen)1, ( + ftnlen)1, (ftnlen)1); + } + if (*nru > 0) { + i__1 = m - ll + 1; + dlasr_((char *)"R", (char *)"V", (char *)"B", nru, &i__1, &work[1], &work[*n], &u[ll * + u_dim1 + 1], ldu, (ftnlen)1, (ftnlen)1, (ftnlen)1); + } + if (*ncc > 0) { + i__1 = m - ll + 1; + dlasr_((char *)"L", (char *)"V", (char *)"B", &i__1, ncc, &work[1], &work[*n], &c__[ + ll + c_dim1], ldc, (ftnlen)1, (ftnlen)1, (ftnlen)1); + } + } + } + +/* QR iteration finished, go back and check convergence */ + + goto L60; + +/* All singular values converged, so make them positive */ + +L160: + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + if (d__[i__] < 0.) { + d__[i__] = -d__[i__]; + +/* Change sign of singular vectors, if desired */ + + if (*ncvt > 0) { + dscal_(ncvt, &c_b72, &vt[i__ + vt_dim1], ldvt); + } + } +/* L170: */ + } + +/* Sort the singular values into decreasing order (insertion sort on */ +/* singular values, but only one transposition per singular vector) */ + + i__1 = *n - 1; + for (i__ = 1; i__ <= i__1; ++i__) { + +/* Scan for smallest D(I) */ + + isub = 1; + smin = d__[1]; + i__2 = *n + 1 - i__; + for (j = 2; j <= i__2; ++j) { + if (d__[j] <= smin) { + isub = j; + smin = d__[j]; + } +/* L180: */ + } + if (isub != *n + 1 - i__) { + +/* Swap singular values and vectors */ + + d__[isub] = d__[*n + 1 - i__]; + d__[*n + 1 - i__] = smin; + if (*ncvt > 0) { + dswap_(ncvt, &vt[isub + vt_dim1], ldvt, &vt[*n + 1 - i__ + + vt_dim1], ldvt); + } + if (*nru > 0) { + dswap_(nru, &u[isub * u_dim1 + 1], &c__1, &u[(*n + 1 - i__) * + u_dim1 + 1], &c__1); + } + if (*ncc > 0) { + dswap_(ncc, &c__[isub + c_dim1], ldc, &c__[*n + 1 - i__ + + c_dim1], ldc); + } + } +/* L190: */ + } + goto L220; + +/* Maximum number of iterations exceeded, failure to converge */ + +L200: + *info = 0; + i__1 = *n - 1; + for (i__ = 1; i__ <= i__1; ++i__) { + if (e[i__] != 0.) { + ++(*info); + } +/* L210: */ + } +L220: + return 0; + +/* End of DBDSQR */ + +} /* dbdsqr_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dcabs1.cpp b/lib/linalg/dcabs1.cpp new file mode 100644 index 0000000000..2733be3c74 --- /dev/null +++ b/lib/linalg/dcabs1.cpp @@ -0,0 +1,92 @@ +/* fortran/dcabs1.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DCABS1 */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* DOUBLE PRECISION FUNCTION DCABS1(Z) */ + +/* .. Scalar Arguments .. */ +/* COMPLEX*16 Z */ +/* .. */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DCABS1 computes |Re(.)| + |Im(.)| of a double complex number */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] Z */ +/* > \verbatim */ +/* > Z is COMPLEX*16 */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup double_blas_level1 */ + +/* ===================================================================== */ +doublereal dcabs1_(doublecomplex *z__) +{ + /* System generated locals */ + doublereal ret_val, d__1, d__2; + + /* Builtin functions */ + double d_imag(doublecomplex *); + + +/* -- Reference BLAS level1 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. */ +/* ===================================================================== */ + +/* .. Intrinsic Functions .. */ + + ret_val = (d__1 = z__->r, abs(d__1)) + (d__2 = d_imag(z__), abs(d__2)); + return ret_val; + +/* End of DCABS1 */ + +} /* dcabs1_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dcopy.cpp b/lib/linalg/dcopy.cpp new file mode 100644 index 0000000000..52fe214e90 --- /dev/null +++ b/lib/linalg/dcopy.cpp @@ -0,0 +1,187 @@ +/* fortran/dcopy.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DCOPY */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DCOPY(N,DX,INCX,DY,INCY) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INCX,INCY,N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION DX(*),DY(*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DCOPY copies a vector, x, to a vector, y. */ +/* > uses unrolled loops for increments equal to 1. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > number of elements in input vector(s) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DX */ +/* > \verbatim */ +/* > DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > storage spacing between elements of DX */ +/* > \endverbatim */ +/* > */ +/* > \param[out] DY */ +/* > \verbatim */ +/* > DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCY */ +/* > \verbatim */ +/* > INCY is INTEGER */ +/* > storage spacing between elements of DY */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup double_blas_level1 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > jack dongarra, linpack, 3/11/78. */ +/* > modified 12/3/93, array(1) declarations changed to array(*) */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dcopy_(integer *n, doublereal *dx, integer *incx, + doublereal *dy, integer *incy) +{ + /* System generated locals */ + integer i__1; + + /* Local variables */ + integer i__, m, ix, iy, mp1; + + +/* -- Reference BLAS level1 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ + /* Parameter adjustments */ + --dy; + --dx; + + /* Function Body */ + if (*n <= 0) { + return 0; + } + if (*incx == 1 && *incy == 1) { + +/* code for both increments equal to 1 */ + + +/* clean-up loop */ + + m = *n % 7; + if (m != 0) { + i__1 = m; + for (i__ = 1; i__ <= i__1; ++i__) { + dy[i__] = dx[i__]; + } + if (*n < 7) { + return 0; + } + } + mp1 = m + 1; + i__1 = *n; + for (i__ = mp1; i__ <= i__1; i__ += 7) { + dy[i__] = dx[i__]; + dy[i__ + 1] = dx[i__ + 1]; + dy[i__ + 2] = dx[i__ + 2]; + dy[i__ + 3] = dx[i__ + 3]; + dy[i__ + 4] = dx[i__ + 4]; + dy[i__ + 5] = dx[i__ + 5]; + dy[i__ + 6] = dx[i__ + 6]; + } + } else { + +/* code for unequal increments or equal increments */ +/* not equal to 1 */ + + ix = 1; + iy = 1; + if (*incx < 0) { + ix = (-(*n) + 1) * *incx + 1; + } + if (*incy < 0) { + iy = (-(*n) + 1) * *incy + 1; + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + dy[iy] = dx[ix]; + ix += *incx; + iy += *incy; + } + } + return 0; + +/* End of DCOPY */ + +} /* dcopy_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/ddot.cpp b/lib/linalg/ddot.cpp new file mode 100644 index 0000000000..3f57f45459 --- /dev/null +++ b/lib/linalg/ddot.cpp @@ -0,0 +1,189 @@ +/* fortran/ddot.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DDOT */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* DOUBLE PRECISION FUNCTION DDOT(N,DX,INCX,DY,INCY) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INCX,INCY,N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION DX(*),DY(*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DDOT forms the dot product of two vectors. */ +/* > uses unrolled loops for increments equal to one. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > number of elements in input vector(s) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DX */ +/* > \verbatim */ +/* > DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > storage spacing between elements of DX */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DY */ +/* > \verbatim */ +/* > DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCY */ +/* > \verbatim */ +/* > INCY is INTEGER */ +/* > storage spacing between elements of DY */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup double_blas_level1 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > jack dongarra, linpack, 3/11/78. */ +/* > modified 12/3/93, array(1) declarations changed to array(*) */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +doublereal ddot_(integer *n, doublereal *dx, integer *incx, doublereal *dy, + integer *incy) +{ + /* System generated locals */ + integer i__1; + doublereal ret_val; + + /* Local variables */ + integer i__, m, ix, iy, mp1; + doublereal dtemp; + + +/* -- Reference BLAS level1 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ + /* Parameter adjustments */ + --dy; + --dx; + + /* Function Body */ + ret_val = 0.; + dtemp = 0.; + if (*n <= 0) { + return ret_val; + } + if (*incx == 1 && *incy == 1) { + +/* code for both increments equal to 1 */ + + +/* clean-up loop */ + + m = *n % 5; + if (m != 0) { + i__1 = m; + for (i__ = 1; i__ <= i__1; ++i__) { + dtemp += dx[i__] * dy[i__]; + } + if (*n < 5) { + ret_val = dtemp; + return ret_val; + } + } + mp1 = m + 1; + i__1 = *n; + for (i__ = mp1; i__ <= i__1; i__ += 5) { + dtemp = dtemp + dx[i__] * dy[i__] + dx[i__ + 1] * dy[i__ + 1] + + dx[i__ + 2] * dy[i__ + 2] + dx[i__ + 3] * dy[i__ + 3] + + dx[i__ + 4] * dy[i__ + 4]; + } + } else { + +/* code for unequal increments or equal increments */ +/* not equal to 1 */ + + ix = 1; + iy = 1; + if (*incx < 0) { + ix = (-(*n) + 1) * *incx + 1; + } + if (*incy < 0) { + iy = (-(*n) + 1) * *incy + 1; + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + dtemp += dx[ix] * dy[iy]; + ix += *incx; + iy += *incy; + } + } + ret_val = dtemp; + return ret_val; + +/* End of DDOT */ + +} /* ddot_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dgebd2.cpp b/lib/linalg/dgebd2.cpp new file mode 100644 index 0000000000..399cd3ca6e --- /dev/null +++ b/lib/linalg/dgebd2.cpp @@ -0,0 +1,393 @@ +/* fortran/dgebd2.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; + +/* > \brief \b DGEBD2 reduces a general matrix to bidiagonal form using an unblocked algorithm. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DGEBD2 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DGEBD2( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INFO, LDA, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), TAUP( * ), */ +/* $ TAUQ( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DGEBD2 reduces a real general m by n matrix A to upper or lower */ +/* > bidiagonal form B by an orthogonal transformation: Q**T * A * P = B. */ +/* > */ +/* > If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows in the matrix A. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns in the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On entry, the m by n general matrix to be reduced. */ +/* > On exit, */ +/* > if m >= n, the diagonal and the first superdiagonal are */ +/* > overwritten with the upper bidiagonal matrix B; the */ +/* > elements below the diagonal, with the array TAUQ, represent */ +/* > the orthogonal matrix Q as a product of elementary */ +/* > reflectors, and the elements above the first superdiagonal, */ +/* > with the array TAUP, represent the orthogonal matrix P as */ +/* > a product of elementary reflectors; */ +/* > if m < n, the diagonal and the first subdiagonal are */ +/* > overwritten with the lower bidiagonal matrix B; the */ +/* > elements below the first subdiagonal, with the array TAUQ, */ +/* > represent the orthogonal matrix Q as a product of */ +/* > elementary reflectors, and the elements above the diagonal, */ +/* > with the array TAUP, represent the orthogonal matrix P as */ +/* > a product of elementary reflectors. */ +/* > See Further Details. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension (min(M,N)) */ +/* > The diagonal elements of the bidiagonal matrix B: */ +/* > D(i) = A(i,i). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] E */ +/* > \verbatim */ +/* > E is DOUBLE PRECISION array, dimension (min(M,N)-1) */ +/* > The off-diagonal elements of the bidiagonal matrix B: */ +/* > if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1; */ +/* > if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] TAUQ */ +/* > \verbatim */ +/* > TAUQ is DOUBLE PRECISION array, dimension (min(M,N)) */ +/* > The scalar factors of the elementary reflectors which */ +/* > represent the orthogonal matrix Q. See Further Details. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] TAUP */ +/* > \verbatim */ +/* > TAUP is DOUBLE PRECISION array, dimension (min(M,N)) */ +/* > The scalar factors of the elementary reflectors which */ +/* > represent the orthogonal matrix P. See Further Details. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (max(M,N)) */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit. */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleGEcomputational */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > The matrices Q and P are represented as products of elementary */ +/* > reflectors: */ +/* > */ +/* > If m >= n, */ +/* > */ +/* > Q = H(1) H(2) . . . H(n) and P = G(1) G(2) . . . G(n-1) */ +/* > */ +/* > Each H(i) and G(i) has the form: */ +/* > */ +/* > H(i) = I - tauq * v * v**T and G(i) = I - taup * u * u**T */ +/* > */ +/* > where tauq and taup are real scalars, and v and u are real vectors; */ +/* > v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in A(i+1:m,i); */ +/* > u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in A(i,i+2:n); */ +/* > tauq is stored in TAUQ(i) and taup in TAUP(i). */ +/* > */ +/* > If m < n, */ +/* > */ +/* > Q = H(1) H(2) . . . H(m-1) and P = G(1) G(2) . . . G(m) */ +/* > */ +/* > Each H(i) and G(i) has the form: */ +/* > */ +/* > H(i) = I - tauq * v * v**T and G(i) = I - taup * u * u**T */ +/* > */ +/* > where tauq and taup are real scalars, and v and u are real vectors; */ +/* > v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i); */ +/* > u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n); */ +/* > tauq is stored in TAUQ(i) and taup in TAUP(i). */ +/* > */ +/* > The contents of A on exit are illustrated by the following examples: */ +/* > */ +/* > m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n): */ +/* > */ +/* > ( d e u1 u1 u1 ) ( d u1 u1 u1 u1 u1 ) */ +/* > ( v1 d e u2 u2 ) ( e d u2 u2 u2 u2 ) */ +/* > ( v1 v2 d e u3 ) ( v1 e d u3 u3 u3 ) */ +/* > ( v1 v2 v3 d e ) ( v1 v2 e d u4 u4 ) */ +/* > ( v1 v2 v3 v4 d ) ( v1 v2 v3 e d u5 ) */ +/* > ( v1 v2 v3 v4 v5 ) */ +/* > */ +/* > where d and e denote diagonal and off-diagonal elements of B, vi */ +/* > denotes an element of the vector defining H(i), and ui an element of */ +/* > the vector defining G(i). */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dgebd2_(integer *m, integer *n, doublereal *a, integer * + lda, doublereal *d__, doublereal *e, doublereal *tauq, doublereal * + taup, doublereal *work, integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3; + + /* Local variables */ + integer i__; + extern /* Subroutine */ int dlarf_(char *, integer *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, + doublereal *, ftnlen), dlarfg_(integer *, doublereal *, + doublereal *, integer *, doublereal *), xerbla_(char *, integer *, + ftnlen); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --d__; + --e; + --tauq; + --taup; + --work; + + /* Function Body */ + *info = 0; + if (*m < 0) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } else if (*lda < max(1,*m)) { + *info = -4; + } + if (*info < 0) { + i__1 = -(*info); + xerbla_((char *)"DGEBD2", &i__1, (ftnlen)6); + return 0; + } + + if (*m >= *n) { + +/* Reduce to upper bidiagonal form */ + + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + +/* Generate elementary reflector H(i) to annihilate A(i+1:m,i) */ + + i__2 = *m - i__ + 1; +/* Computing MIN */ + i__3 = i__ + 1; + dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[min(i__3,*m) + i__ * + a_dim1], &c__1, &tauq[i__]); + d__[i__] = a[i__ + i__ * a_dim1]; + a[i__ + i__ * a_dim1] = 1.; + +/* Apply H(i) to A(i:m,i+1:n) from the left */ + + if (i__ < *n) { + i__2 = *m - i__ + 1; + i__3 = *n - i__; + dlarf_((char *)"Left", &i__2, &i__3, &a[i__ + i__ * a_dim1], &c__1, & + tauq[i__], &a[i__ + (i__ + 1) * a_dim1], lda, &work[1] + , (ftnlen)4); + } + a[i__ + i__ * a_dim1] = d__[i__]; + + if (i__ < *n) { + +/* Generate elementary reflector G(i) to annihilate */ +/* A(i,i+2:n) */ + + i__2 = *n - i__; +/* Computing MIN */ + i__3 = i__ + 2; + dlarfg_(&i__2, &a[i__ + (i__ + 1) * a_dim1], &a[i__ + min( + i__3,*n) * a_dim1], lda, &taup[i__]); + e[i__] = a[i__ + (i__ + 1) * a_dim1]; + a[i__ + (i__ + 1) * a_dim1] = 1.; + +/* Apply G(i) to A(i+1:m,i+1:n) from the right */ + + i__2 = *m - i__; + i__3 = *n - i__; + dlarf_((char *)"Right", &i__2, &i__3, &a[i__ + (i__ + 1) * a_dim1], + lda, &taup[i__], &a[i__ + 1 + (i__ + 1) * a_dim1], + lda, &work[1], (ftnlen)5); + a[i__ + (i__ + 1) * a_dim1] = e[i__]; + } else { + taup[i__] = 0.; + } +/* L10: */ + } + } else { + +/* Reduce to lower bidiagonal form */ + + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + +/* Generate elementary reflector G(i) to annihilate A(i,i+1:n) */ + + i__2 = *n - i__ + 1; +/* Computing MIN */ + i__3 = i__ + 1; + dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[i__ + min(i__3,*n) * + a_dim1], lda, &taup[i__]); + d__[i__] = a[i__ + i__ * a_dim1]; + a[i__ + i__ * a_dim1] = 1.; + +/* Apply G(i) to A(i+1:m,i:n) from the right */ + + if (i__ < *m) { + i__2 = *m - i__; + i__3 = *n - i__ + 1; + dlarf_((char *)"Right", &i__2, &i__3, &a[i__ + i__ * a_dim1], lda, & + taup[i__], &a[i__ + 1 + i__ * a_dim1], lda, &work[1], + (ftnlen)5); + } + a[i__ + i__ * a_dim1] = d__[i__]; + + if (i__ < *m) { + +/* Generate elementary reflector H(i) to annihilate */ +/* A(i+2:m,i) */ + + i__2 = *m - i__; +/* Computing MIN */ + i__3 = i__ + 2; + dlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3,*m) + + i__ * a_dim1], &c__1, &tauq[i__]); + e[i__] = a[i__ + 1 + i__ * a_dim1]; + a[i__ + 1 + i__ * a_dim1] = 1.; + +/* Apply H(i) to A(i+1:m,i+1:n) from the left */ + + i__2 = *m - i__; + i__3 = *n - i__; + dlarf_((char *)"Left", &i__2, &i__3, &a[i__ + 1 + i__ * a_dim1], & + c__1, &tauq[i__], &a[i__ + 1 + (i__ + 1) * a_dim1], + lda, &work[1], (ftnlen)4); + a[i__ + 1 + i__ * a_dim1] = e[i__]; + } else { + tauq[i__] = 0.; + } +/* L20: */ + } + } + return 0; + +/* End of DGEBD2 */ + +} /* dgebd2_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dgebrd.cpp b/lib/linalg/dgebrd.cpp new file mode 100644 index 0000000000..84827afcfd --- /dev/null +++ b/lib/linalg/dgebrd.cpp @@ -0,0 +1,431 @@ +/* fortran/dgebrd.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c_n1 = -1; +static integer c__3 = 3; +static integer c__2 = 2; +static doublereal c_b21 = -1.; +static doublereal c_b22 = 1.; + +/* > \brief \b DGEBRD */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DGEBRD + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DGEBRD( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK, */ +/* INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INFO, LDA, LWORK, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), TAUP( * ), */ +/* $ TAUQ( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DGEBRD reduces a general real M-by-N matrix A to upper or lower */ +/* > bidiagonal form B by an orthogonal transformation: Q**T * A * P = B. */ +/* > */ +/* > If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows in the matrix A. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns in the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On entry, the M-by-N general matrix to be reduced. */ +/* > On exit, */ +/* > if m >= n, the diagonal and the first superdiagonal are */ +/* > overwritten with the upper bidiagonal matrix B; the */ +/* > elements below the diagonal, with the array TAUQ, represent */ +/* > the orthogonal matrix Q as a product of elementary */ +/* > reflectors, and the elements above the first superdiagonal, */ +/* > with the array TAUP, represent the orthogonal matrix P as */ +/* > a product of elementary reflectors; */ +/* > if m < n, the diagonal and the first subdiagonal are */ +/* > overwritten with the lower bidiagonal matrix B; the */ +/* > elements below the first subdiagonal, with the array TAUQ, */ +/* > represent the orthogonal matrix Q as a product of */ +/* > elementary reflectors, and the elements above the diagonal, */ +/* > with the array TAUP, represent the orthogonal matrix P as */ +/* > a product of elementary reflectors. */ +/* > See Further Details. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension (min(M,N)) */ +/* > The diagonal elements of the bidiagonal matrix B: */ +/* > D(i) = A(i,i). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] E */ +/* > \verbatim */ +/* > E is DOUBLE PRECISION array, dimension (min(M,N)-1) */ +/* > The off-diagonal elements of the bidiagonal matrix B: */ +/* > if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1; */ +/* > if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] TAUQ */ +/* > \verbatim */ +/* > TAUQ is DOUBLE PRECISION array, dimension (min(M,N)) */ +/* > The scalar factors of the elementary reflectors which */ +/* > represent the orthogonal matrix Q. See Further Details. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] TAUP */ +/* > \verbatim */ +/* > TAUP is DOUBLE PRECISION array, dimension (min(M,N)) */ +/* > The scalar factors of the elementary reflectors which */ +/* > represent the orthogonal matrix P. See Further Details. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ +/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LWORK */ +/* > \verbatim */ +/* > LWORK is INTEGER */ +/* > The length of the array WORK. LWORK >= max(1,M,N). */ +/* > For optimum performance LWORK >= (M+N)*NB, where NB */ +/* > is the optimal blocksize. */ +/* > */ +/* > If LWORK = -1, then a workspace query is assumed; the routine */ +/* > only calculates the optimal size of the WORK array, returns */ +/* > this value as the first entry of the WORK array, and no error */ +/* > message related to LWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleGEcomputational */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > The matrices Q and P are represented as products of elementary */ +/* > reflectors: */ +/* > */ +/* > If m >= n, */ +/* > */ +/* > Q = H(1) H(2) . . . H(n) and P = G(1) G(2) . . . G(n-1) */ +/* > */ +/* > Each H(i) and G(i) has the form: */ +/* > */ +/* > H(i) = I - tauq * v * v**T and G(i) = I - taup * u * u**T */ +/* > */ +/* > where tauq and taup are real scalars, and v and u are real vectors; */ +/* > v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in A(i+1:m,i); */ +/* > u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in A(i,i+2:n); */ +/* > tauq is stored in TAUQ(i) and taup in TAUP(i). */ +/* > */ +/* > If m < n, */ +/* > */ +/* > Q = H(1) H(2) . . . H(m-1) and P = G(1) G(2) . . . G(m) */ +/* > */ +/* > Each H(i) and G(i) has the form: */ +/* > */ +/* > H(i) = I - tauq * v * v**T and G(i) = I - taup * u * u**T */ +/* > */ +/* > where tauq and taup are real scalars, and v and u are real vectors; */ +/* > v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i); */ +/* > u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n); */ +/* > tauq is stored in TAUQ(i) and taup in TAUP(i). */ +/* > */ +/* > The contents of A on exit are illustrated by the following examples: */ +/* > */ +/* > m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n): */ +/* > */ +/* > ( d e u1 u1 u1 ) ( d u1 u1 u1 u1 u1 ) */ +/* > ( v1 d e u2 u2 ) ( e d u2 u2 u2 u2 ) */ +/* > ( v1 v2 d e u3 ) ( v1 e d u3 u3 u3 ) */ +/* > ( v1 v2 v3 d e ) ( v1 v2 e d u4 u4 ) */ +/* > ( v1 v2 v3 v4 d ) ( v1 v2 v3 e d u5 ) */ +/* > ( v1 v2 v3 v4 v5 ) */ +/* > */ +/* > where d and e denote diagonal and off-diagonal elements of B, vi */ +/* > denotes an element of the vector defining H(i), and ui an element of */ +/* > the vector defining G(i). */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dgebrd_(integer *m, integer *n, doublereal *a, integer * + lda, doublereal *d__, doublereal *e, doublereal *tauq, doublereal * + taup, doublereal *work, integer *lwork, integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3, i__4; + + /* Local variables */ + integer i__, j, nb, nx, ws; + extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); + integer nbmin, iinfo, minmn; + extern /* Subroutine */ int dgebd2_(integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, integer *), dlabrd_(integer *, integer *, integer * + , doublereal *, integer *, doublereal *, doublereal *, doublereal + *, doublereal *, doublereal *, integer *, doublereal *, integer *) + , xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + integer ldwrkx, ldwrky, lwkopt; + logical lquery; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --d__; + --e; + --tauq; + --taup; + --work; + + /* Function Body */ + *info = 0; +/* Computing MAX */ + i__1 = 1, i__2 = ilaenv_(&c__1, (char *)"DGEBRD", (char *)" ", m, n, &c_n1, &c_n1, ( + ftnlen)6, (ftnlen)1); + nb = max(i__1,i__2); + lwkopt = (*m + *n) * nb; + work[1] = (doublereal) lwkopt; + lquery = *lwork == -1; + if (*m < 0) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } else if (*lda < max(1,*m)) { + *info = -4; + } else /* if(complicated condition) */ { +/* Computing MAX */ + i__1 = max(1,*m); + if (*lwork < max(i__1,*n) && ! lquery) { + *info = -10; + } + } + if (*info < 0) { + i__1 = -(*info); + xerbla_((char *)"DGEBRD", &i__1, (ftnlen)6); + return 0; + } else if (lquery) { + return 0; + } + +/* Quick return if possible */ + + minmn = min(*m,*n); + if (minmn == 0) { + work[1] = 1.; + return 0; + } + + ws = max(*m,*n); + ldwrkx = *m; + ldwrky = *n; + + if (nb > 1 && nb < minmn) { + +/* Set the crossover point NX. */ + +/* Computing MAX */ + i__1 = nb, i__2 = ilaenv_(&c__3, (char *)"DGEBRD", (char *)" ", m, n, &c_n1, &c_n1, ( + ftnlen)6, (ftnlen)1); + nx = max(i__1,i__2); + +/* Determine when to switch from blocked to unblocked code. */ + + if (nx < minmn) { + ws = (*m + *n) * nb; + if (*lwork < ws) { + +/* Not enough work space for the optimal NB, consider using */ +/* a smaller block size. */ + + nbmin = ilaenv_(&c__2, (char *)"DGEBRD", (char *)" ", m, n, &c_n1, &c_n1, ( + ftnlen)6, (ftnlen)1); + if (*lwork >= (*m + *n) * nbmin) { + nb = *lwork / (*m + *n); + } else { + nb = 1; + nx = minmn; + } + } + } + } else { + nx = minmn; + } + + i__1 = minmn - nx; + i__2 = nb; + for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { + +/* Reduce rows and columns i:i+nb-1 to bidiagonal form and return */ +/* the matrices X and Y which are needed to update the unreduced */ +/* part of the matrix */ + + i__3 = *m - i__ + 1; + i__4 = *n - i__ + 1; + dlabrd_(&i__3, &i__4, &nb, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[ + i__], &tauq[i__], &taup[i__], &work[1], &ldwrkx, &work[ldwrkx + * nb + 1], &ldwrky); + +/* Update the trailing submatrix A(i+nb:m,i+nb:n), using an update */ +/* of the form A := A - V*Y**T - X*U**T */ + + i__3 = *m - i__ - nb + 1; + i__4 = *n - i__ - nb + 1; + dgemm_((char *)"No transpose", (char *)"Transpose", &i__3, &i__4, &nb, &c_b21, &a[i__ + + nb + i__ * a_dim1], lda, &work[ldwrkx * nb + nb + 1], & + ldwrky, &c_b22, &a[i__ + nb + (i__ + nb) * a_dim1], lda, ( + ftnlen)12, (ftnlen)9); + i__3 = *m - i__ - nb + 1; + i__4 = *n - i__ - nb + 1; + dgemm_((char *)"No transpose", (char *)"No transpose", &i__3, &i__4, &nb, &c_b21, & + work[nb + 1], &ldwrkx, &a[i__ + (i__ + nb) * a_dim1], lda, & + c_b22, &a[i__ + nb + (i__ + nb) * a_dim1], lda, (ftnlen)12, ( + ftnlen)12); + +/* Copy diagonal and off-diagonal elements of B back into A */ + + if (*m >= *n) { + i__3 = i__ + nb - 1; + for (j = i__; j <= i__3; ++j) { + a[j + j * a_dim1] = d__[j]; + a[j + (j + 1) * a_dim1] = e[j]; +/* L10: */ + } + } else { + i__3 = i__ + nb - 1; + for (j = i__; j <= i__3; ++j) { + a[j + j * a_dim1] = d__[j]; + a[j + 1 + j * a_dim1] = e[j]; +/* L20: */ + } + } +/* L30: */ + } + +/* Use unblocked code to reduce the remainder of the matrix */ + + i__2 = *m - i__ + 1; + i__1 = *n - i__ + 1; + dgebd2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[i__], & + tauq[i__], &taup[i__], &work[1], &iinfo); + work[1] = (doublereal) ws; + return 0; + +/* End of DGEBRD */ + +} /* dgebrd_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dgecon.cpp b/lib/linalg/dgecon.cpp new file mode 100644 index 0000000000..07a305d74f --- /dev/null +++ b/lib/linalg/dgecon.cpp @@ -0,0 +1,313 @@ +/* fortran/dgecon.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; + +/* > \brief \b DGECON */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DGECON + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DGECON( NORM, N, A, LDA, ANORM, RCOND, WORK, IWORK, */ +/* INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER NORM */ +/* INTEGER INFO, LDA, N */ +/* DOUBLE PRECISION ANORM, RCOND */ +/* .. */ +/* .. Array Arguments .. */ +/* INTEGER IWORK( * ) */ +/* DOUBLE PRECISION A( LDA, * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DGECON estimates the reciprocal of the condition number of a general */ +/* > real matrix A, in either the 1-norm or the infinity-norm, using */ +/* > the LU factorization computed by DGETRF. */ +/* > */ +/* > An estimate is obtained for norm(inv(A)), and the reciprocal of the */ +/* > condition number is computed as */ +/* > RCOND = 1 / ( norm(A) * norm(inv(A)) ). */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] NORM */ +/* > \verbatim */ +/* > NORM is CHARACTER*1 */ +/* > Specifies whether the 1-norm condition number or the */ +/* > infinity-norm condition number is required: */ +/* > = '1' or 'O': 1-norm; */ +/* > = 'I': Infinity-norm. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > The factors L and U from the factorization A = P*L*U */ +/* > as computed by DGETRF. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] ANORM */ +/* > \verbatim */ +/* > ANORM is DOUBLE PRECISION */ +/* > If NORM = '1' or 'O', the 1-norm of the original matrix A. */ +/* > If NORM = 'I', the infinity-norm of the original matrix A. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] RCOND */ +/* > \verbatim */ +/* > RCOND is DOUBLE PRECISION */ +/* > The reciprocal of the condition number of the matrix A, */ +/* > computed as RCOND = 1/(norm(A) * norm(inv(A))). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (4*N) */ +/* > \endverbatim */ +/* > */ +/* > \param[out] IWORK */ +/* > \verbatim */ +/* > IWORK is INTEGER array, dimension (N) */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleGEcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dgecon_(char *norm, integer *n, doublereal *a, integer * + lda, doublereal *anorm, doublereal *rcond, doublereal *work, integer * + iwork, integer *info, ftnlen norm_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1; + doublereal d__1; + + /* Local variables */ + doublereal sl; + integer ix; + doublereal su; + integer kase, kase1; + doublereal scale; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + integer isave[3]; + extern /* Subroutine */ int drscl_(integer *, doublereal *, doublereal *, + integer *), dlacn2_(integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, integer *); + extern doublereal dlamch_(char *, ftnlen); + extern integer idamax_(integer *, doublereal *, integer *); + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + doublereal ainvnm; + extern /* Subroutine */ int dlatrs_(char *, char *, char *, char *, + integer *, doublereal *, integer *, doublereal *, doublereal *, + doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + logical onenrm; + char normin[1]; + doublereal smlnum; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Local Arrays .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --work; + --iwork; + + /* Function Body */ + *info = 0; + onenrm = *(unsigned char *)norm == '1' || lsame_(norm, (char *)"O", (ftnlen)1, ( + ftnlen)1); + if (! onenrm && ! lsame_(norm, (char *)"I", (ftnlen)1, (ftnlen)1)) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } else if (*lda < max(1,*n)) { + *info = -4; + } else if (*anorm < 0.) { + *info = -5; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DGECON", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + *rcond = 0.; + if (*n == 0) { + *rcond = 1.; + return 0; + } else if (*anorm == 0.) { + return 0; + } + + smlnum = dlamch_((char *)"Safe minimum", (ftnlen)12); + +/* Estimate the norm of inv(A). */ + + ainvnm = 0.; + *(unsigned char *)normin = 'N'; + if (onenrm) { + kase1 = 1; + } else { + kase1 = 2; + } + kase = 0; +L10: + dlacn2_(n, &work[*n + 1], &work[1], &iwork[1], &ainvnm, &kase, isave); + if (kase != 0) { + if (kase == kase1) { + +/* Multiply by inv(L). */ + + dlatrs_((char *)"Lower", (char *)"No transpose", (char *)"Unit", normin, n, &a[a_offset], + lda, &work[1], &sl, &work[(*n << 1) + 1], info, (ftnlen)5, + (ftnlen)12, (ftnlen)4, (ftnlen)1); + +/* Multiply by inv(U). */ + + dlatrs_((char *)"Upper", (char *)"No transpose", (char *)"Non-unit", normin, n, &a[ + a_offset], lda, &work[1], &su, &work[*n * 3 + 1], info, ( + ftnlen)5, (ftnlen)12, (ftnlen)8, (ftnlen)1); + } else { + +/* Multiply by inv(U**T). */ + + dlatrs_((char *)"Upper", (char *)"Transpose", (char *)"Non-unit", normin, n, &a[a_offset], + lda, &work[1], &su, &work[*n * 3 + 1], info, (ftnlen)5, ( + ftnlen)9, (ftnlen)8, (ftnlen)1); + +/* Multiply by inv(L**T). */ + + dlatrs_((char *)"Lower", (char *)"Transpose", (char *)"Unit", normin, n, &a[a_offset], + lda, &work[1], &sl, &work[(*n << 1) + 1], info, (ftnlen)5, + (ftnlen)9, (ftnlen)4, (ftnlen)1); + } + +/* Divide X by 1/(SL*SU) if doing so will not cause overflow. */ + + scale = sl * su; + *(unsigned char *)normin = 'Y'; + if (scale != 1.) { + ix = idamax_(n, &work[1], &c__1); + if (scale < (d__1 = work[ix], abs(d__1)) * smlnum || scale == 0.) + { + goto L20; + } + drscl_(n, &scale, &work[1], &c__1); + } + goto L10; + } + +/* Compute the estimate of the reciprocal condition number. */ + + if (ainvnm != 0.) { + *rcond = 1. / ainvnm / *anorm; + } + +L20: + return 0; + +/* End of DGECON */ + +} /* dgecon_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dgelq2.cpp b/lib/linalg/dgelq2.cpp new file mode 100644 index 0000000000..6000253184 --- /dev/null +++ b/lib/linalg/dgelq2.cpp @@ -0,0 +1,245 @@ +/* fortran/dgelq2.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorit +hm. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DGELQ2 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DGELQ2( M, N, A, LDA, TAU, WORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INFO, LDA, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DGELQ2 computes an LQ factorization of a real m-by-n matrix A: */ +/* > */ +/* > A = ( L 0 ) * Q */ +/* > */ +/* > where: */ +/* > */ +/* > Q is a n-by-n orthogonal matrix; */ +/* > L is a lower-triangular m-by-m matrix; */ +/* > 0 is a m-by-(n-m) zero matrix, if m < n. */ +/* > */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix A. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On entry, the m by n matrix A. */ +/* > On exit, the elements on and below the diagonal of the array */ +/* > contain the m by min(m,n) lower trapezoidal matrix L (L is */ +/* > lower triangular if m <= n); the elements above the diagonal, */ +/* > with the array TAU, represent the orthogonal matrix Q as a */ +/* > product of elementary reflectors (see Further Details). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] TAU */ +/* > \verbatim */ +/* > TAU is DOUBLE PRECISION array, dimension (min(M,N)) */ +/* > The scalar factors of the elementary reflectors (see Further */ +/* > Details). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (M) */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleGEcomputational */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > The matrix Q is represented as a product of elementary reflectors */ +/* > */ +/* > Q = H(k) . . . H(2) H(1), where k = min(m,n). */ +/* > */ +/* > Each H(i) has the form */ +/* > */ +/* > H(i) = I - tau * v * v**T */ +/* > */ +/* > where tau is a real scalar, and v is a real vector with */ +/* > v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n), */ +/* > and tau in TAU(i). */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dgelq2_(integer *m, integer *n, doublereal *a, integer * + lda, doublereal *tau, doublereal *work, integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3; + + /* Local variables */ + integer i__, k; + doublereal aii; + extern /* Subroutine */ int dlarf_(char *, integer *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, + doublereal *, ftnlen), dlarfg_(integer *, doublereal *, + doublereal *, integer *, doublereal *), xerbla_(char *, integer *, + ftnlen); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --tau; + --work; + + /* Function Body */ + *info = 0; + if (*m < 0) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } else if (*lda < max(1,*m)) { + *info = -4; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DGELQ2", &i__1, (ftnlen)6); + return 0; + } + + k = min(*m,*n); + + i__1 = k; + for (i__ = 1; i__ <= i__1; ++i__) { + +/* Generate elementary reflector H(i) to annihilate A(i,i+1:n) */ + + i__2 = *n - i__ + 1; +/* Computing MIN */ + i__3 = i__ + 1; + dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[i__ + min(i__3,*n) * a_dim1] + , lda, &tau[i__]); + if (i__ < *m) { + +/* Apply H(i) to A(i+1:m,i:n) from the right */ + + aii = a[i__ + i__ * a_dim1]; + a[i__ + i__ * a_dim1] = 1.; + i__2 = *m - i__; + i__3 = *n - i__ + 1; + dlarf_((char *)"Right", &i__2, &i__3, &a[i__ + i__ * a_dim1], lda, &tau[ + i__], &a[i__ + 1 + i__ * a_dim1], lda, &work[1], (ftnlen) + 5); + a[i__ + i__ * a_dim1] = aii; + } +/* L10: */ + } + return 0; + +/* End of DGELQ2 */ + +} /* dgelq2_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dgelqf.cpp b/lib/linalg/dgelqf.cpp new file mode 100644 index 0000000000..ede5b8198b --- /dev/null +++ b/lib/linalg/dgelqf.cpp @@ -0,0 +1,345 @@ +/* fortran/dgelqf.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c_n1 = -1; +static integer c__3 = 3; +static integer c__2 = 2; + +/* > \brief \b DGELQF */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DGELQF + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INFO, LDA, LWORK, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DGELQF computes an LQ factorization of a real M-by-N matrix A: */ +/* > */ +/* > A = ( L 0 ) * Q */ +/* > */ +/* > where: */ +/* > */ +/* > Q is a N-by-N orthogonal matrix; */ +/* > L is a lower-triangular M-by-M matrix; */ +/* > 0 is a M-by-(N-M) zero matrix, if M < N. */ +/* > */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix A. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On entry, the M-by-N matrix A. */ +/* > On exit, the elements on and below the diagonal of the array */ +/* > contain the m-by-min(m,n) lower trapezoidal matrix L (L is */ +/* > lower triangular if m <= n); the elements above the diagonal, */ +/* > with the array TAU, represent the orthogonal matrix Q as a */ +/* > product of elementary reflectors (see Further Details). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] TAU */ +/* > \verbatim */ +/* > TAU is DOUBLE PRECISION array, dimension (min(M,N)) */ +/* > The scalar factors of the elementary reflectors (see Further */ +/* > Details). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ +/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LWORK */ +/* > \verbatim */ +/* > LWORK is INTEGER */ +/* > The dimension of the array WORK. LWORK >= max(1,M). */ +/* > For optimum performance LWORK >= M*NB, where NB is the */ +/* > optimal blocksize. */ +/* > */ +/* > If LWORK = -1, then a workspace query is assumed; the routine */ +/* > only calculates the optimal size of the WORK array, returns */ +/* > this value as the first entry of the WORK array, and no error */ +/* > message related to LWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleGEcomputational */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > The matrix Q is represented as a product of elementary reflectors */ +/* > */ +/* > Q = H(k) . . . H(2) H(1), where k = min(m,n). */ +/* > */ +/* > Each H(i) has the form */ +/* > */ +/* > H(i) = I - tau * v * v**T */ +/* > */ +/* > where tau is a real scalar, and v is a real vector with */ +/* > v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n), */ +/* > and tau in TAU(i). */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dgelqf_(integer *m, integer *n, doublereal *a, integer * + lda, doublereal *tau, doublereal *work, integer *lwork, integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3, i__4; + + /* Local variables */ + integer i__, k, ib, nb, nx, iws, nbmin, iinfo; + extern /* Subroutine */ int dgelq2_(integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *), dlarfb_(char *, + char *, char *, char *, integer *, integer *, integer *, + doublereal *, integer *, doublereal *, integer *, doublereal *, + integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, + ftnlen), dlarft_(char *, char *, integer *, integer *, doublereal + *, integer *, doublereal *, doublereal *, integer *, ftnlen, + ftnlen), xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + integer ldwork, lwkopt; + logical lquery; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --tau; + --work; + + /* Function Body */ + *info = 0; + nb = ilaenv_(&c__1, (char *)"DGELQF", (char *)" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen) + 1); + lwkopt = *m * nb; + work[1] = (doublereal) lwkopt; + lquery = *lwork == -1; + if (*m < 0) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } else if (*lda < max(1,*m)) { + *info = -4; + } else if (*lwork < max(1,*m) && ! lquery) { + *info = -7; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DGELQF", &i__1, (ftnlen)6); + return 0; + } else if (lquery) { + return 0; + } + +/* Quick return if possible */ + + k = min(*m,*n); + if (k == 0) { + work[1] = 1.; + return 0; + } + + nbmin = 2; + nx = 0; + iws = *m; + if (nb > 1 && nb < k) { + +/* Determine when to cross over from blocked to unblocked code. */ + +/* Computing MAX */ + i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"DGELQF", (char *)" ", m, n, &c_n1, &c_n1, ( + ftnlen)6, (ftnlen)1); + nx = max(i__1,i__2); + if (nx < k) { + +/* Determine if workspace is large enough for blocked code. */ + + ldwork = *m; + iws = ldwork * nb; + if (*lwork < iws) { + +/* Not enough workspace to use optimal NB: reduce NB and */ +/* determine the minimum value of NB. */ + + nb = *lwork / ldwork; +/* Computing MAX */ + i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DGELQF", (char *)" ", m, n, &c_n1, & + c_n1, (ftnlen)6, (ftnlen)1); + nbmin = max(i__1,i__2); + } + } + } + + if (nb >= nbmin && nb < k && nx < k) { + +/* Use blocked code initially */ + + i__1 = k - nx; + i__2 = nb; + for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { +/* Computing MIN */ + i__3 = k - i__ + 1; + ib = min(i__3,nb); + +/* Compute the LQ factorization of the current block */ +/* A(i:i+ib-1,i:n) */ + + i__3 = *n - i__ + 1; + dgelq2_(&ib, &i__3, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[ + 1], &iinfo); + if (i__ + ib <= *m) { + +/* Form the triangular factor of the block reflector */ +/* H = H(i) H(i+1) . . . H(i+ib-1) */ + + i__3 = *n - i__ + 1; + dlarft_((char *)"Forward", (char *)"Rowwise", &i__3, &ib, &a[i__ + i__ * + a_dim1], lda, &tau[i__], &work[1], &ldwork, (ftnlen)7, + (ftnlen)7); + +/* Apply H to A(i+ib:m,i:n) from the right */ + + i__3 = *m - i__ - ib + 1; + i__4 = *n - i__ + 1; + dlarfb_((char *)"Right", (char *)"No transpose", (char *)"Forward", (char *)"Rowwise", &i__3, + &i__4, &ib, &a[i__ + i__ * a_dim1], lda, &work[1], & + ldwork, &a[i__ + ib + i__ * a_dim1], lda, &work[ib + + 1], &ldwork, (ftnlen)5, (ftnlen)12, (ftnlen)7, ( + ftnlen)7); + } +/* L10: */ + } + } else { + i__ = 1; + } + +/* Use unblocked code to factor the last or only block. */ + + if (i__ <= k) { + i__2 = *m - i__ + 1; + i__1 = *n - i__ + 1; + dgelq2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[1] + , &iinfo); + } + + work[1] = (doublereal) iws; + return 0; + +/* End of DGELQF */ + +} /* dgelqf_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dgelsd.cpp b/lib/linalg/dgelsd.cpp new file mode 100644 index 0000000000..7a74d30ef2 --- /dev/null +++ b/lib/linalg/dgelsd.cpp @@ -0,0 +1,816 @@ +/* fortran/dgelsd.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__6 = 6; +static integer c_n1 = -1; +static integer c__9 = 9; +static integer c__0 = 0; +static integer c__1 = 1; +static doublereal c_b82 = 0.; + +/* > \brief DGELSD computes the minimum-norm solution to a linear least squares problem for GE matrices */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DGELSD + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DGELSD( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, */ +/* WORK, LWORK, IWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS, RANK */ +/* DOUBLE PRECISION RCOND */ +/* .. */ +/* .. Array Arguments .. */ +/* INTEGER IWORK( * ) */ +/* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), S( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DGELSD computes the minimum-norm solution to a real linear least */ +/* > squares problem: */ +/* > minimize 2-norm(| b - A*x |) */ +/* > using the singular value decomposition (SVD) of A. A is an M-by-N */ +/* > matrix which may be rank-deficient. */ +/* > */ +/* > Several right hand side vectors b and solution vectors x can be */ +/* > handled in a single call; they are stored as the columns of the */ +/* > M-by-NRHS right hand side matrix B and the N-by-NRHS solution */ +/* > matrix X. */ +/* > */ +/* > The problem is solved in three steps: */ +/* > (1) Reduce the coefficient matrix A to bidiagonal form with */ +/* > Householder transformations, reducing the original problem */ +/* > into a (char *)"bidiagonal least squares problem" (BLS) */ +/* > (2) Solve the BLS using a divide and conquer approach. */ +/* > (3) Apply back all the Householder transformations to solve */ +/* > the original least squares problem. */ +/* > */ +/* > The effective rank of A is determined by treating as zero those */ +/* > singular values which are less than RCOND times the largest singular */ +/* > value. */ +/* > */ +/* > The divide and conquer algorithm makes very mild assumptions about */ +/* > floating point arithmetic. It will work on machines with a guard */ +/* > digit in add/subtract, or on those binary machines without guard */ +/* > digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */ +/* > Cray-2. It could conceivably fail on hexadecimal or decimal machines */ +/* > without guard digits, but we know of none. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of A. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] NRHS */ +/* > \verbatim */ +/* > NRHS is INTEGER */ +/* > The number of right hand sides, i.e., the number of columns */ +/* > of the matrices B and X. NRHS >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On entry, the M-by-N matrix A. */ +/* > On exit, A has been destroyed. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] B */ +/* > \verbatim */ +/* > B is DOUBLE PRECISION array, dimension (LDB,NRHS) */ +/* > On entry, the M-by-NRHS right hand side matrix B. */ +/* > On exit, B is overwritten by the N-by-NRHS solution */ +/* > matrix X. If m >= n and RANK = n, the residual */ +/* > sum-of-squares for the solution in the i-th column is given */ +/* > by the sum of squares of elements n+1:m in that column. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDB */ +/* > \verbatim */ +/* > LDB is INTEGER */ +/* > The leading dimension of the array B. LDB >= max(1,max(M,N)). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] S */ +/* > \verbatim */ +/* > S is DOUBLE PRECISION array, dimension (min(M,N)) */ +/* > The singular values of A in decreasing order. */ +/* > The condition number of A in the 2-norm = S(1)/S(min(m,n)). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] RCOND */ +/* > \verbatim */ +/* > RCOND is DOUBLE PRECISION */ +/* > RCOND is used to determine the effective rank of A. */ +/* > Singular values S(i) <= RCOND*S(1) are treated as zero. */ +/* > If RCOND < 0, machine precision is used instead. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] RANK */ +/* > \verbatim */ +/* > RANK is INTEGER */ +/* > The effective rank of A, i.e., the number of singular values */ +/* > which are greater than RCOND*S(1). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ +/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LWORK */ +/* > \verbatim */ +/* > LWORK is INTEGER */ +/* > The dimension of the array WORK. LWORK must be at least 1. */ +/* > The exact minimum amount of workspace needed depends on M, */ +/* > N and NRHS. As long as LWORK is at least */ +/* > 12*N + 2*N*SMLSIZ + 8*N*NLVL + N*NRHS + (SMLSIZ+1)**2, */ +/* > if M is greater than or equal to N or */ +/* > 12*M + 2*M*SMLSIZ + 8*M*NLVL + M*NRHS + (SMLSIZ+1)**2, */ +/* > if M is less than N, the code will execute correctly. */ +/* > SMLSIZ is returned by ILAENV and is equal to the maximum */ +/* > size of the subproblems at the bottom of the computation */ +/* > tree (usually about 25), and */ +/* > NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 ) */ +/* > For good performance, LWORK should generally be larger. */ +/* > */ +/* > If LWORK = -1, then a workspace query is assumed; the routine */ +/* > only calculates the optimal size of the WORK array, returns */ +/* > this value as the first entry of the WORK array, and no error */ +/* > message related to LWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] IWORK */ +/* > \verbatim */ +/* > IWORK is INTEGER array, dimension (MAX(1,LIWORK)) */ +/* > LIWORK >= max(1, 3 * MINMN * NLVL + 11 * MINMN), */ +/* > where MINMN = MIN( M,N ). */ +/* > On exit, if INFO = 0, IWORK(1) returns the minimum LIWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ +/* > > 0: the algorithm for computing the SVD failed to converge; */ +/* > if INFO = i, i off-diagonal elements of an intermediate */ +/* > bidiagonal form did not converge to zero. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleGEsolve */ + +/* > \par Contributors: */ +/* ================== */ +/* > */ +/* > Ming Gu and Ren-Cang Li, Computer Science Division, University of */ +/* > California at Berkeley, USA \n */ +/* > Osni Marques, LBNL/NERSC, USA \n */ + +/* ===================================================================== */ +/* Subroutine */ int dgelsd_(integer *m, integer *n, integer *nrhs, + doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal * + s, doublereal *rcond, integer *rank, doublereal *work, integer *lwork, + integer *iwork, integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4; + + /* Builtin functions */ + double log(doublereal); + + /* Local variables */ + integer ie, il, mm; + doublereal eps, anrm, bnrm; + integer itau, nlvl, iascl, ibscl; + doublereal sfmin; + integer minmn, maxmn, itaup, itauq, mnthr, nwork; + extern /* Subroutine */ int dlabad_(doublereal *, doublereal *), dgebrd_( + integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, doublereal *, doublereal *, doublereal *, integer *, + integer *); + extern doublereal dlamch_(char *, ftnlen), dlange_(char *, integer *, + integer *, doublereal *, integer *, doublereal *, ftnlen); + extern /* Subroutine */ int dgelqf_(integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, integer *), + dlalsd_(char *, integer *, integer *, integer *, doublereal *, + doublereal *, doublereal *, integer *, doublereal *, integer *, + doublereal *, integer *, integer *, ftnlen), dlascl_(char *, + integer *, integer *, doublereal *, doublereal *, integer *, + integer *, doublereal *, integer *, integer *, ftnlen), dgeqrf_( + integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, integer *), dlacpy_(char *, integer *, + integer *, doublereal *, integer *, doublereal *, integer *, + ftnlen), dlaset_(char *, integer *, integer *, doublereal *, + doublereal *, doublereal *, integer *, ftnlen), xerbla_(char *, + integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + doublereal bignum; + extern /* Subroutine */ int dormbr_(char *, char *, char *, integer *, + integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, doublereal *, integer *, integer *, + ftnlen, ftnlen, ftnlen); + integer wlalsd; + extern /* Subroutine */ int dormlq_(char *, char *, integer *, integer *, + integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, integer *, ftnlen, ftnlen); + integer ldwork; + extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *, + integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, integer *, ftnlen, ftnlen); + integer liwork, minwrk, maxwrk; + doublereal smlnum; + logical lquery; + integer smlsiz; + + +/* -- LAPACK driver routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + b_dim1 = *ldb; + b_offset = 1 + b_dim1; + b -= b_offset; + --s; + --work; + --iwork; + + /* Function Body */ + *info = 0; + minmn = min(*m,*n); + maxmn = max(*m,*n); + mnthr = ilaenv_(&c__6, (char *)"DGELSD", (char *)" ", m, n, nrhs, &c_n1, (ftnlen)6, ( + ftnlen)1); + lquery = *lwork == -1; + if (*m < 0) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } else if (*nrhs < 0) { + *info = -3; + } else if (*lda < max(1,*m)) { + *info = -5; + } else if (*ldb < max(1,maxmn)) { + *info = -7; + } + + smlsiz = ilaenv_(&c__9, (char *)"DGELSD", (char *)" ", &c__0, &c__0, &c__0, &c__0, ( + ftnlen)6, (ftnlen)1); + +/* Compute workspace. */ +/* (Note: Comments in the code beginning (char *)"Workspace:" describe the */ +/* minimal amount of workspace needed at that point in the code, */ +/* as well as the preferred amount for good performance. */ +/* NB refers to the optimal block size for the immediately */ +/* following subroutine, as returned by ILAENV.) */ + + minwrk = 1; + liwork = 1; + minmn = max(1,minmn); +/* Computing MAX */ + i__1 = (integer) (log((doublereal) minmn / (doublereal) (smlsiz + 1)) / + log(2.)) + 1; + nlvl = max(i__1,0); + + if (*info == 0) { + maxwrk = 0; + liwork = minmn * 3 * nlvl + minmn * 11; + mm = *m; + if (*m >= *n && *m >= mnthr) { + +/* Path 1a - overdetermined, with many more rows than columns. */ + + mm = *n; +/* Computing MAX */ + i__1 = maxwrk, i__2 = *n + *n * ilaenv_(&c__1, (char *)"DGEQRF", (char *)" ", m, + n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); + maxwrk = max(i__1,i__2); +/* Computing MAX */ + i__1 = maxwrk, i__2 = *n + *nrhs * ilaenv_(&c__1, (char *)"DORMQR", (char *)"LT", + m, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)2); + maxwrk = max(i__1,i__2); + } + if (*m >= *n) { + +/* Path 1 - overdetermined or exactly determined. */ + +/* Computing MAX */ + i__1 = maxwrk, i__2 = *n * 3 + (mm + *n) * ilaenv_(&c__1, (char *)"DGEBRD" + , (char *)" ", &mm, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); + maxwrk = max(i__1,i__2); +/* Computing MAX */ + i__1 = maxwrk, i__2 = *n * 3 + *nrhs * ilaenv_(&c__1, (char *)"DORMBR", + (char *)"QLT", &mm, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)3); + maxwrk = max(i__1,i__2); +/* Computing MAX */ + i__1 = maxwrk, i__2 = *n * 3 + (*n - 1) * ilaenv_(&c__1, (char *)"DORMBR", + (char *)"PLN", n, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)3); + maxwrk = max(i__1,i__2); +/* Computing 2nd power */ + i__1 = smlsiz + 1; + wlalsd = *n * 9 + (*n << 1) * smlsiz + (*n << 3) * nlvl + *n * * + nrhs + i__1 * i__1; +/* Computing MAX */ + i__1 = maxwrk, i__2 = *n * 3 + wlalsd; + maxwrk = max(i__1,i__2); +/* Computing MAX */ + i__1 = *n * 3 + mm, i__2 = *n * 3 + *nrhs, i__1 = max(i__1,i__2), + i__2 = *n * 3 + wlalsd; + minwrk = max(i__1,i__2); + } + if (*n > *m) { +/* Computing 2nd power */ + i__1 = smlsiz + 1; + wlalsd = *m * 9 + (*m << 1) * smlsiz + (*m << 3) * nlvl + *m * * + nrhs + i__1 * i__1; + if (*n >= mnthr) { + +/* Path 2a - underdetermined, with many more columns */ +/* than rows. */ + + maxwrk = *m + *m * ilaenv_(&c__1, (char *)"DGELQF", (char *)" ", m, n, &c_n1, + &c_n1, (ftnlen)6, (ftnlen)1); +/* Computing MAX */ + i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m << 1) * + ilaenv_(&c__1, (char *)"DGEBRD", (char *)" ", m, m, &c_n1, &c_n1, ( + ftnlen)6, (ftnlen)1); + maxwrk = max(i__1,i__2); +/* Computing MAX */ + i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + *nrhs * ilaenv_(& + c__1, (char *)"DORMBR", (char *)"QLT", m, nrhs, m, &c_n1, (ftnlen)6, ( + ftnlen)3); + maxwrk = max(i__1,i__2); +/* Computing MAX */ + i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m - 1) * + ilaenv_(&c__1, (char *)"DORMBR", (char *)"PLN", m, nrhs, m, &c_n1, ( + ftnlen)6, (ftnlen)3); + maxwrk = max(i__1,i__2); + if (*nrhs > 1) { +/* Computing MAX */ + i__1 = maxwrk, i__2 = *m * *m + *m + *m * *nrhs; + maxwrk = max(i__1,i__2); + } else { +/* Computing MAX */ + i__1 = maxwrk, i__2 = *m * *m + (*m << 1); + maxwrk = max(i__1,i__2); + } +/* Computing MAX */ + i__1 = maxwrk, i__2 = *m + *nrhs * ilaenv_(&c__1, (char *)"DORMLQ", + (char *)"LT", n, nrhs, m, &c_n1, (ftnlen)6, (ftnlen)2); + maxwrk = max(i__1,i__2); +/* Computing MAX */ + i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + wlalsd; + maxwrk = max(i__1,i__2); +/* XXX: Ensure the Path 2a case below is triggered. The workspace */ +/* calculation should use queries for all routines eventually. */ +/* Computing MAX */ +/* Computing MAX */ + i__3 = *m, i__4 = (*m << 1) - 4, i__3 = max(i__3,i__4), i__3 = + max(i__3,*nrhs), i__4 = *n - *m * 3; + i__1 = maxwrk, i__2 = (*m << 2) + *m * *m + max(i__3,i__4); + maxwrk = max(i__1,i__2); + } else { + +/* Path 2 - remaining underdetermined cases. */ + + maxwrk = *m * 3 + (*n + *m) * ilaenv_(&c__1, (char *)"DGEBRD", (char *)" ", m, + n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); +/* Computing MAX */ + i__1 = maxwrk, i__2 = *m * 3 + *nrhs * ilaenv_(&c__1, (char *)"DORMBR" + , (char *)"QLT", m, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)3); + maxwrk = max(i__1,i__2); +/* Computing MAX */ + i__1 = maxwrk, i__2 = *m * 3 + *m * ilaenv_(&c__1, (char *)"DORMBR", + (char *)"PLN", n, nrhs, m, &c_n1, (ftnlen)6, (ftnlen)3); + maxwrk = max(i__1,i__2); +/* Computing MAX */ + i__1 = maxwrk, i__2 = *m * 3 + wlalsd; + maxwrk = max(i__1,i__2); + } +/* Computing MAX */ + i__1 = *m * 3 + *nrhs, i__2 = *m * 3 + *m, i__1 = max(i__1,i__2), + i__2 = *m * 3 + wlalsd; + minwrk = max(i__1,i__2); + } + minwrk = min(minwrk,maxwrk); + work[1] = (doublereal) maxwrk; + iwork[1] = liwork; + if (*lwork < minwrk && ! lquery) { + *info = -12; + } + } + + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DGELSD", &i__1, (ftnlen)6); + return 0; + } else if (lquery) { + goto L10; + } + +/* Quick return if possible. */ + + if (*m == 0 || *n == 0) { + *rank = 0; + return 0; + } + +/* Get machine parameters. */ + + eps = dlamch_((char *)"P", (ftnlen)1); + sfmin = dlamch_((char *)"S", (ftnlen)1); + smlnum = sfmin / eps; + bignum = 1. / smlnum; + dlabad_(&smlnum, &bignum); + +/* Scale A if max entry outside range [SMLNUM,BIGNUM]. */ + + anrm = dlange_((char *)"M", m, n, &a[a_offset], lda, &work[1], (ftnlen)1); + iascl = 0; + if (anrm > 0. && anrm < smlnum) { + +/* Scale matrix norm up to SMLNUM. */ + + dlascl_((char *)"G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, + info, (ftnlen)1); + iascl = 1; + } else if (anrm > bignum) { + +/* Scale matrix norm down to BIGNUM. */ + + dlascl_((char *)"G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, + info, (ftnlen)1); + iascl = 2; + } else if (anrm == 0.) { + +/* Matrix all zero. Return zero solution. */ + + i__1 = max(*m,*n); + dlaset_((char *)"F", &i__1, nrhs, &c_b82, &c_b82, &b[b_offset], ldb, (ftnlen) + 1); + dlaset_((char *)"F", &minmn, &c__1, &c_b82, &c_b82, &s[1], &c__1, (ftnlen)1); + *rank = 0; + goto L10; + } + +/* Scale B if max entry outside range [SMLNUM,BIGNUM]. */ + + bnrm = dlange_((char *)"M", m, nrhs, &b[b_offset], ldb, &work[1], (ftnlen)1); + ibscl = 0; + if (bnrm > 0. && bnrm < smlnum) { + +/* Scale matrix norm up to SMLNUM. */ + + dlascl_((char *)"G", &c__0, &c__0, &bnrm, &smlnum, m, nrhs, &b[b_offset], ldb, + info, (ftnlen)1); + ibscl = 1; + } else if (bnrm > bignum) { + +/* Scale matrix norm down to BIGNUM. */ + + dlascl_((char *)"G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb, + info, (ftnlen)1); + ibscl = 2; + } + +/* If M < N make sure certain entries of B are zero. */ + + if (*m < *n) { + i__1 = *n - *m; + dlaset_((char *)"F", &i__1, nrhs, &c_b82, &c_b82, &b[*m + 1 + b_dim1], ldb, ( + ftnlen)1); + } + +/* Overdetermined case. */ + + if (*m >= *n) { + +/* Path 1 - overdetermined or exactly determined. */ + + mm = *m; + if (*m >= mnthr) { + +/* Path 1a - overdetermined, with many more rows than columns. */ + + mm = *n; + itau = 1; + nwork = itau + *n; + +/* Compute A=Q*R. */ +/* (Workspace: need 2*N, prefer N+N*NB) */ + + i__1 = *lwork - nwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__1, + info); + +/* Multiply B by transpose(Q). */ +/* (Workspace: need N+NRHS, prefer N+NRHS*NB) */ + + i__1 = *lwork - nwork + 1; + dormqr_((char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, &work[itau], &b[ + b_offset], ldb, &work[nwork], &i__1, info, (ftnlen)1, ( + ftnlen)1); + +/* Zero out below R. */ + + if (*n > 1) { + i__1 = *n - 1; + i__2 = *n - 1; + dlaset_((char *)"L", &i__1, &i__2, &c_b82, &c_b82, &a[a_dim1 + 2], + lda, (ftnlen)1); + } + } + + ie = 1; + itauq = ie + *n; + itaup = itauq + *n; + nwork = itaup + *n; + +/* Bidiagonalize R in A. */ +/* (Workspace: need 3*N+MM, prefer 3*N+(MM+N)*NB) */ + + i__1 = *lwork - nwork + 1; + dgebrd_(&mm, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], & + work[itaup], &work[nwork], &i__1, info); + +/* Multiply B by transpose of left bidiagonalizing vectors of R. */ +/* (Workspace: need 3*N+NRHS, prefer 3*N+NRHS*NB) */ + + i__1 = *lwork - nwork + 1; + dormbr_((char *)"Q", (char *)"L", (char *)"T", &mm, nrhs, n, &a[a_offset], lda, &work[itauq], + &b[b_offset], ldb, &work[nwork], &i__1, info, (ftnlen)1, ( + ftnlen)1, (ftnlen)1); + +/* Solve the bidiagonal least squares problem. */ + + dlalsd_((char *)"U", &smlsiz, n, nrhs, &s[1], &work[ie], &b[b_offset], ldb, + rcond, rank, &work[nwork], &iwork[1], info, (ftnlen)1); + if (*info != 0) { + goto L10; + } + +/* Multiply B by right bidiagonalizing vectors of R. */ + + i__1 = *lwork - nwork + 1; + dormbr_((char *)"P", (char *)"L", (char *)"N", n, nrhs, n, &a[a_offset], lda, &work[itaup], & + b[b_offset], ldb, &work[nwork], &i__1, info, (ftnlen)1, ( + ftnlen)1, (ftnlen)1); + + } else /* if(complicated condition) */ { +/* Computing MAX */ + i__1 = *m, i__2 = (*m << 1) - 4, i__1 = max(i__1,i__2), i__1 = max( + i__1,*nrhs), i__2 = *n - *m * 3, i__1 = max(i__1,i__2); + if (*n >= mnthr && *lwork >= (*m << 2) + *m * *m + max(i__1,wlalsd)) { + +/* Path 2a - underdetermined, with many more columns than rows */ +/* and sufficient workspace for an efficient algorithm. */ + + ldwork = *m; +/* Computing MAX */ +/* Computing MAX */ + i__3 = *m, i__4 = (*m << 1) - 4, i__3 = max(i__3,i__4), i__3 = + max(i__3,*nrhs), i__4 = *n - *m * 3; + i__1 = (*m << 2) + *m * *lda + max(i__3,i__4), i__2 = *m * *lda + + *m + *m * *nrhs, i__1 = max(i__1,i__2), i__2 = (*m << 2) + + *m * *lda + wlalsd; + if (*lwork >= max(i__1,i__2)) { + ldwork = *lda; + } + itau = 1; + nwork = *m + 1; + +/* Compute A=L*Q. */ +/* (Workspace: need 2*M, prefer M+M*NB) */ + + i__1 = *lwork - nwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__1, + info); + il = nwork; + +/* Copy L to WORK(IL), zeroing out above its diagonal. */ + + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[il], &ldwork, (ftnlen) + 1); + i__1 = *m - 1; + i__2 = *m - 1; + dlaset_((char *)"U", &i__1, &i__2, &c_b82, &c_b82, &work[il + ldwork], & + ldwork, (ftnlen)1); + ie = il + ldwork * *m; + itauq = ie + *m; + itaup = itauq + *m; + nwork = itaup + *m; + +/* Bidiagonalize L in WORK(IL). */ +/* (Workspace: need M*M+5*M, prefer M*M+4*M+2*M*NB) */ + + i__1 = *lwork - nwork + 1; + dgebrd_(m, m, &work[il], &ldwork, &s[1], &work[ie], &work[itauq], + &work[itaup], &work[nwork], &i__1, info); + +/* Multiply B by transpose of left bidiagonalizing vectors of L. */ +/* (Workspace: need M*M+4*M+NRHS, prefer M*M+4*M+NRHS*NB) */ + + i__1 = *lwork - nwork + 1; + dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, m, &work[il], &ldwork, &work[ + itauq], &b[b_offset], ldb, &work[nwork], &i__1, info, ( + ftnlen)1, (ftnlen)1, (ftnlen)1); + +/* Solve the bidiagonal least squares problem. */ + + dlalsd_((char *)"U", &smlsiz, m, nrhs, &s[1], &work[ie], &b[b_offset], + ldb, rcond, rank, &work[nwork], &iwork[1], info, (ftnlen) + 1); + if (*info != 0) { + goto L10; + } + +/* Multiply B by right bidiagonalizing vectors of L. */ + + i__1 = *lwork - nwork + 1; + dormbr_((char *)"P", (char *)"L", (char *)"N", m, nrhs, m, &work[il], &ldwork, &work[ + itaup], &b[b_offset], ldb, &work[nwork], &i__1, info, ( + ftnlen)1, (ftnlen)1, (ftnlen)1); + +/* Zero out below first M rows of B. */ + + i__1 = *n - *m; + dlaset_((char *)"F", &i__1, nrhs, &c_b82, &c_b82, &b[*m + 1 + b_dim1], + ldb, (ftnlen)1); + nwork = itau + *m; + +/* Multiply transpose(Q) by B. */ +/* (Workspace: need M+NRHS, prefer M+NRHS*NB) */ + + i__1 = *lwork - nwork + 1; + dormlq_((char *)"L", (char *)"T", n, nrhs, m, &a[a_offset], lda, &work[itau], &b[ + b_offset], ldb, &work[nwork], &i__1, info, (ftnlen)1, ( + ftnlen)1); + + } else { + +/* Path 2 - remaining underdetermined cases. */ + + ie = 1; + itauq = ie + *m; + itaup = itauq + *m; + nwork = itaup + *m; + +/* Bidiagonalize A. */ +/* (Workspace: need 3*M+N, prefer 3*M+(M+N)*NB) */ + + i__1 = *lwork - nwork + 1; + dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], & + work[itaup], &work[nwork], &i__1, info); + +/* Multiply B by transpose of left bidiagonalizing vectors. */ +/* (Workspace: need 3*M+NRHS, prefer 3*M+NRHS*NB) */ + + i__1 = *lwork - nwork + 1; + dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, &work[itauq] + , &b[b_offset], ldb, &work[nwork], &i__1, info, (ftnlen)1, + (ftnlen)1, (ftnlen)1); + +/* Solve the bidiagonal least squares problem. */ + + dlalsd_((char *)"L", &smlsiz, m, nrhs, &s[1], &work[ie], &b[b_offset], + ldb, rcond, rank, &work[nwork], &iwork[1], info, (ftnlen) + 1); + if (*info != 0) { + goto L10; + } + +/* Multiply B by right bidiagonalizing vectors of A. */ + + i__1 = *lwork - nwork + 1; + dormbr_((char *)"P", (char *)"L", (char *)"N", n, nrhs, m, &a[a_offset], lda, &work[itaup] + , &b[b_offset], ldb, &work[nwork], &i__1, info, (ftnlen)1, + (ftnlen)1, (ftnlen)1); + + } + } + +/* Undo scaling. */ + + if (iascl == 1) { + dlascl_((char *)"G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb, + info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], & + minmn, info, (ftnlen)1); + } else if (iascl == 2) { + dlascl_((char *)"G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb, + info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], & + minmn, info, (ftnlen)1); + } + if (ibscl == 1) { + dlascl_((char *)"G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb, + info, (ftnlen)1); + } else if (ibscl == 2) { + dlascl_((char *)"G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb, + info, (ftnlen)1); + } + +L10: + work[1] = (doublereal) maxwrk; + iwork[1] = liwork; + return 0; + +/* End of DGELSD */ + +} /* dgelsd_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dgelss.cpp b/lib/linalg/dgelss.cpp new file mode 100644 index 0000000000..6377208923 --- /dev/null +++ b/lib/linalg/dgelss.cpp @@ -0,0 +1,988 @@ +/* fortran/dgelss.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__6 = 6; +static integer c_n1 = -1; +static integer c__0 = 0; +static doublereal c_b46 = 0.; +static integer c__1 = 1; +static doublereal c_b79 = 1.; + +/* > \brief DGELSS solves overdetermined or underdetermined systems for GE matrices */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DGELSS + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DGELSS( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, */ +/* WORK, LWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS, RANK */ +/* DOUBLE PRECISION RCOND */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), S( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DGELSS computes the minimum norm solution to a real linear least */ +/* > squares problem: */ +/* > */ +/* > Minimize 2-norm(| b - A*x |). */ +/* > */ +/* > using the singular value decomposition (SVD) of A. A is an M-by-N */ +/* > matrix which may be rank-deficient. */ +/* > */ +/* > Several right hand side vectors b and solution vectors x can be */ +/* > handled in a single call; they are stored as the columns of the */ +/* > M-by-NRHS right hand side matrix B and the N-by-NRHS solution matrix */ +/* > X. */ +/* > */ +/* > The effective rank of A is determined by treating as zero those */ +/* > singular values which are less than RCOND times the largest singular */ +/* > value. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix A. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] NRHS */ +/* > \verbatim */ +/* > NRHS is INTEGER */ +/* > The number of right hand sides, i.e., the number of columns */ +/* > of the matrices B and X. NRHS >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On entry, the M-by-N matrix A. */ +/* > On exit, the first min(m,n) rows of A are overwritten with */ +/* > its right singular vectors, stored rowwise. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] B */ +/* > \verbatim */ +/* > B is DOUBLE PRECISION array, dimension (LDB,NRHS) */ +/* > On entry, the M-by-NRHS right hand side matrix B. */ +/* > On exit, B is overwritten by the N-by-NRHS solution */ +/* > matrix X. If m >= n and RANK = n, the residual */ +/* > sum-of-squares for the solution in the i-th column is given */ +/* > by the sum of squares of elements n+1:m in that column. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDB */ +/* > \verbatim */ +/* > LDB is INTEGER */ +/* > The leading dimension of the array B. LDB >= max(1,max(M,N)). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] S */ +/* > \verbatim */ +/* > S is DOUBLE PRECISION array, dimension (min(M,N)) */ +/* > The singular values of A in decreasing order. */ +/* > The condition number of A in the 2-norm = S(1)/S(min(m,n)). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] RCOND */ +/* > \verbatim */ +/* > RCOND is DOUBLE PRECISION */ +/* > RCOND is used to determine the effective rank of A. */ +/* > Singular values S(i) <= RCOND*S(1) are treated as zero. */ +/* > If RCOND < 0, machine precision is used instead. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] RANK */ +/* > \verbatim */ +/* > RANK is INTEGER */ +/* > The effective rank of A, i.e., the number of singular values */ +/* > which are greater than RCOND*S(1). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ +/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LWORK */ +/* > \verbatim */ +/* > LWORK is INTEGER */ +/* > The dimension of the array WORK. LWORK >= 1, and also: */ +/* > LWORK >= 3*min(M,N) + max( 2*min(M,N), max(M,N), NRHS ) */ +/* > For good performance, LWORK should generally be larger. */ +/* > */ +/* > If LWORK = -1, then a workspace query is assumed; the routine */ +/* > only calculates the optimal size of the WORK array, returns */ +/* > this value as the first entry of the WORK array, and no error */ +/* > message related to LWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ +/* > > 0: the algorithm for computing the SVD failed to converge; */ +/* > if INFO = i, i off-diagonal elements of an intermediate */ +/* > bidiagonal form did not converge to zero. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleGEsolve */ + +/* ===================================================================== */ +/* Subroutine */ int dgelss_(integer *m, integer *n, integer *nrhs, + doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal * + s, doublereal *rcond, integer *rank, doublereal *work, integer *lwork, + integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4; + doublereal d__1; + + /* Local variables */ + integer i__, bl, ie, il, mm; + doublereal dum[1], eps, thr, anrm, bnrm; + integer itau, lwork_dgebrd__, lwork_dgelqf__, lwork_dgeqrf__, + lwork_dorgbr__, lwork_dormbr__, lwork_dormlq__, lwork_dormqr__; + extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); + integer iascl, ibscl; + extern /* Subroutine */ int dgemv_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, ftnlen), drscl_(integer *, + doublereal *, doublereal *, integer *); + integer chunk; + doublereal sfmin; + integer minmn; + extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, + doublereal *, integer *); + integer maxmn, itaup, itauq, mnthr, iwork; + extern /* Subroutine */ int dlabad_(doublereal *, doublereal *), dgebrd_( + integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, doublereal *, doublereal *, doublereal *, integer *, + integer *); + extern doublereal dlamch_(char *, ftnlen), dlange_(char *, integer *, + integer *, doublereal *, integer *, doublereal *, ftnlen); + integer bdspac; + extern /* Subroutine */ int dgelqf_(integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, integer *), + dlascl_(char *, integer *, integer *, doublereal *, doublereal *, + integer *, integer *, doublereal *, integer *, integer *, ftnlen), + dgeqrf_(integer *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, integer *), dlacpy_(char *, + integer *, integer *, doublereal *, integer *, doublereal *, + integer *, ftnlen), dlaset_(char *, integer *, integer *, + doublereal *, doublereal *, doublereal *, integer *, ftnlen), + xerbla_(char *, integer *, ftnlen), dbdsqr_(char *, integer *, + integer *, integer *, integer *, doublereal *, doublereal *, + doublereal *, integer *, doublereal *, integer *, doublereal *, + integer *, doublereal *, integer *, ftnlen), dorgbr_(char *, + integer *, integer *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, integer *, ftnlen); + doublereal bignum; + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dormbr_(char *, char *, char *, integer *, + integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, doublereal *, integer *, integer *, + ftnlen, ftnlen, ftnlen), dormlq_(char *, char *, integer *, + integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, doublereal *, integer *, integer *, + ftnlen, ftnlen); + integer ldwork; + extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *, + integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, integer *, ftnlen, ftnlen); + integer minwrk, maxwrk; + doublereal smlnum; + logical lquery; + + +/* -- LAPACK driver routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Local Arrays .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + b_dim1 = *ldb; + b_offset = 1 + b_dim1; + b -= b_offset; + --s; + --work; + + /* Function Body */ + *info = 0; + minmn = min(*m,*n); + maxmn = max(*m,*n); + lquery = *lwork == -1; + if (*m < 0) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } else if (*nrhs < 0) { + *info = -3; + } else if (*lda < max(1,*m)) { + *info = -5; + } else if (*ldb < max(1,maxmn)) { + *info = -7; + } + +/* Compute workspace */ +/* (Note: Comments in the code beginning (char *)"Workspace:" describe the */ +/* minimal amount of workspace needed at that point in the code, */ +/* as well as the preferred amount for good performance. */ +/* NB refers to the optimal block size for the immediately */ +/* following subroutine, as returned by ILAENV.) */ + + if (*info == 0) { + minwrk = 1; + maxwrk = 1; + if (minmn > 0) { + mm = *m; + mnthr = ilaenv_(&c__6, (char *)"DGELSS", (char *)" ", m, n, nrhs, &c_n1, (ftnlen) + 6, (ftnlen)1); + if (*m >= *n && *m >= mnthr) { + +/* Path 1a - overdetermined, with many more rows than */ +/* columns */ + +/* Compute space needed for DGEQRF */ + dgeqrf_(m, n, &a[a_offset], lda, dum, dum, &c_n1, info); + lwork_dgeqrf__ = (integer) dum[0]; +/* Compute space needed for DORMQR */ + dormqr_((char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, dum, &b[ + b_offset], ldb, dum, &c_n1, info, (ftnlen)1, (ftnlen) + 1); + lwork_dormqr__ = (integer) dum[0]; + mm = *n; +/* Computing MAX */ + i__1 = maxwrk, i__2 = *n + lwork_dgeqrf__; + maxwrk = max(i__1,i__2); +/* Computing MAX */ + i__1 = maxwrk, i__2 = *n + lwork_dormqr__; + maxwrk = max(i__1,i__2); + } + if (*m >= *n) { + +/* Path 1 - overdetermined or exactly determined */ + +/* Compute workspace needed for DBDSQR */ + +/* Computing MAX */ + i__1 = 1, i__2 = *n * 5; + bdspac = max(i__1,i__2); +/* Compute space needed for DGEBRD */ + dgebrd_(&mm, n, &a[a_offset], lda, &s[1], dum, dum, dum, dum, + &c_n1, info); + lwork_dgebrd__ = (integer) dum[0]; +/* Compute space needed for DORMBR */ + dormbr_((char *)"Q", (char *)"L", (char *)"T", &mm, nrhs, n, &a[a_offset], lda, dum, & + b[b_offset], ldb, dum, &c_n1, info, (ftnlen)1, ( + ftnlen)1, (ftnlen)1); + lwork_dormbr__ = (integer) dum[0]; +/* Compute space needed for DORGBR */ + dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, dum, dum, &c_n1, + info, (ftnlen)1); + lwork_dorgbr__ = (integer) dum[0]; +/* Compute total workspace needed */ +/* Computing MAX */ + i__1 = maxwrk, i__2 = *n * 3 + lwork_dgebrd__; + maxwrk = max(i__1,i__2); +/* Computing MAX */ + i__1 = maxwrk, i__2 = *n * 3 + lwork_dormbr__; + maxwrk = max(i__1,i__2); +/* Computing MAX */ + i__1 = maxwrk, i__2 = *n * 3 + lwork_dorgbr__; + maxwrk = max(i__1,i__2); + maxwrk = max(maxwrk,bdspac); +/* Computing MAX */ + i__1 = maxwrk, i__2 = *n * *nrhs; + maxwrk = max(i__1,i__2); +/* Computing MAX */ + i__1 = *n * 3 + mm, i__2 = *n * 3 + *nrhs, i__1 = max(i__1, + i__2); + minwrk = max(i__1,bdspac); + maxwrk = max(minwrk,maxwrk); + } + if (*n > *m) { + +/* Compute workspace needed for DBDSQR */ + +/* Computing MAX */ + i__1 = 1, i__2 = *m * 5; + bdspac = max(i__1,i__2); +/* Computing MAX */ + i__1 = *m * 3 + *nrhs, i__2 = *m * 3 + *n, i__1 = max(i__1, + i__2); + minwrk = max(i__1,bdspac); + if (*n >= mnthr) { + +/* Path 2a - underdetermined, with many more columns */ +/* than rows */ + +/* Compute space needed for DGELQF */ + dgelqf_(m, n, &a[a_offset], lda, dum, dum, &c_n1, info); + lwork_dgelqf__ = (integer) dum[0]; +/* Compute space needed for DGEBRD */ + dgebrd_(m, m, &a[a_offset], lda, &s[1], dum, dum, dum, + dum, &c_n1, info); + lwork_dgebrd__ = (integer) dum[0]; +/* Compute space needed for DORMBR */ + dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, dum, + &b[b_offset], ldb, dum, &c_n1, info, (ftnlen)1, ( + ftnlen)1, (ftnlen)1); + lwork_dormbr__ = (integer) dum[0]; +/* Compute space needed for DORGBR */ + dorgbr_((char *)"P", m, m, m, &a[a_offset], lda, dum, dum, &c_n1, + info, (ftnlen)1); + lwork_dorgbr__ = (integer) dum[0]; +/* Compute space needed for DORMLQ */ + dormlq_((char *)"L", (char *)"T", n, nrhs, m, &a[a_offset], lda, dum, &b[ + b_offset], ldb, dum, &c_n1, info, (ftnlen)1, ( + ftnlen)1); + lwork_dormlq__ = (integer) dum[0]; +/* Compute total workspace needed */ + maxwrk = *m + lwork_dgelqf__; +/* Computing MAX */ + i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + + lwork_dgebrd__; + maxwrk = max(i__1,i__2); +/* Computing MAX */ + i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + + lwork_dormbr__; + maxwrk = max(i__1,i__2); +/* Computing MAX */ + i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + + lwork_dorgbr__; + maxwrk = max(i__1,i__2); +/* Computing MAX */ + i__1 = maxwrk, i__2 = *m * *m + *m + bdspac; + maxwrk = max(i__1,i__2); + if (*nrhs > 1) { +/* Computing MAX */ + i__1 = maxwrk, i__2 = *m * *m + *m + *m * *nrhs; + maxwrk = max(i__1,i__2); + } else { +/* Computing MAX */ + i__1 = maxwrk, i__2 = *m * *m + (*m << 1); + maxwrk = max(i__1,i__2); + } +/* Computing MAX */ + i__1 = maxwrk, i__2 = *m + lwork_dormlq__; + maxwrk = max(i__1,i__2); + } else { + +/* Path 2 - underdetermined */ + +/* Compute space needed for DGEBRD */ + dgebrd_(m, n, &a[a_offset], lda, &s[1], dum, dum, dum, + dum, &c_n1, info); + lwork_dgebrd__ = (integer) dum[0]; +/* Compute space needed for DORMBR */ + dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, m, &a[a_offset], lda, dum, + &b[b_offset], ldb, dum, &c_n1, info, (ftnlen)1, ( + ftnlen)1, (ftnlen)1); + lwork_dormbr__ = (integer) dum[0]; +/* Compute space needed for DORGBR */ + dorgbr_((char *)"P", m, n, m, &a[a_offset], lda, dum, dum, &c_n1, + info, (ftnlen)1); + lwork_dorgbr__ = (integer) dum[0]; + maxwrk = *m * 3 + lwork_dgebrd__; +/* Computing MAX */ + i__1 = maxwrk, i__2 = *m * 3 + lwork_dormbr__; + maxwrk = max(i__1,i__2); +/* Computing MAX */ + i__1 = maxwrk, i__2 = *m * 3 + lwork_dorgbr__; + maxwrk = max(i__1,i__2); + maxwrk = max(maxwrk,bdspac); +/* Computing MAX */ + i__1 = maxwrk, i__2 = *n * *nrhs; + maxwrk = max(i__1,i__2); + } + } + maxwrk = max(minwrk,maxwrk); + } + work[1] = (doublereal) maxwrk; + + if (*lwork < minwrk && ! lquery) { + *info = -12; + } + } + + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DGELSS", &i__1, (ftnlen)6); + return 0; + } else if (lquery) { + return 0; + } + +/* Quick return if possible */ + + if (*m == 0 || *n == 0) { + *rank = 0; + return 0; + } + +/* Get machine parameters */ + + eps = dlamch_((char *)"P", (ftnlen)1); + sfmin = dlamch_((char *)"S", (ftnlen)1); + smlnum = sfmin / eps; + bignum = 1. / smlnum; + dlabad_(&smlnum, &bignum); + +/* Scale A if max element outside range [SMLNUM,BIGNUM] */ + + anrm = dlange_((char *)"M", m, n, &a[a_offset], lda, &work[1], (ftnlen)1); + iascl = 0; + if (anrm > 0. && anrm < smlnum) { + +/* Scale matrix norm up to SMLNUM */ + + dlascl_((char *)"G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, + info, (ftnlen)1); + iascl = 1; + } else if (anrm > bignum) { + +/* Scale matrix norm down to BIGNUM */ + + dlascl_((char *)"G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, + info, (ftnlen)1); + iascl = 2; + } else if (anrm == 0.) { + +/* Matrix all zero. Return zero solution. */ + + i__1 = max(*m,*n); + dlaset_((char *)"F", &i__1, nrhs, &c_b46, &c_b46, &b[b_offset], ldb, (ftnlen) + 1); + dlaset_((char *)"F", &minmn, &c__1, &c_b46, &c_b46, &s[1], &minmn, (ftnlen)1); + *rank = 0; + goto L70; + } + +/* Scale B if max element outside range [SMLNUM,BIGNUM] */ + + bnrm = dlange_((char *)"M", m, nrhs, &b[b_offset], ldb, &work[1], (ftnlen)1); + ibscl = 0; + if (bnrm > 0. && bnrm < smlnum) { + +/* Scale matrix norm up to SMLNUM */ + + dlascl_((char *)"G", &c__0, &c__0, &bnrm, &smlnum, m, nrhs, &b[b_offset], ldb, + info, (ftnlen)1); + ibscl = 1; + } else if (bnrm > bignum) { + +/* Scale matrix norm down to BIGNUM */ + + dlascl_((char *)"G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb, + info, (ftnlen)1); + ibscl = 2; + } + +/* Overdetermined case */ + + if (*m >= *n) { + +/* Path 1 - overdetermined or exactly determined */ + + mm = *m; + if (*m >= mnthr) { + +/* Path 1a - overdetermined, with many more rows than columns */ + + mm = *n; + itau = 1; + iwork = itau + *n; + +/* Compute A=Q*R */ +/* (Workspace: need 2*N, prefer N+N*NB) */ + + i__1 = *lwork - iwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__1, + info); + +/* Multiply B by transpose(Q) */ +/* (Workspace: need N+NRHS, prefer N+NRHS*NB) */ + + i__1 = *lwork - iwork + 1; + dormqr_((char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, &work[itau], &b[ + b_offset], ldb, &work[iwork], &i__1, info, (ftnlen)1, ( + ftnlen)1); + +/* Zero out below R */ + + if (*n > 1) { + i__1 = *n - 1; + i__2 = *n - 1; + dlaset_((char *)"L", &i__1, &i__2, &c_b46, &c_b46, &a[a_dim1 + 2], + lda, (ftnlen)1); + } + } + + ie = 1; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; + +/* Bidiagonalize R in A */ +/* (Workspace: need 3*N+MM, prefer 3*N+(MM+N)*NB) */ + + i__1 = *lwork - iwork + 1; + dgebrd_(&mm, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], & + work[itaup], &work[iwork], &i__1, info); + +/* Multiply B by transpose of left bidiagonalizing vectors of R */ +/* (Workspace: need 3*N+NRHS, prefer 3*N+NRHS*NB) */ + + i__1 = *lwork - iwork + 1; + dormbr_((char *)"Q", (char *)"L", (char *)"T", &mm, nrhs, n, &a[a_offset], lda, &work[itauq], + &b[b_offset], ldb, &work[iwork], &i__1, info, (ftnlen)1, ( + ftnlen)1, (ftnlen)1); + +/* Generate right bidiagonalizing vectors of R in A */ +/* (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB) */ + + i__1 = *lwork - iwork + 1; + dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, &work[itaup], &work[iwork], & + i__1, info, (ftnlen)1); + iwork = ie + *n; + +/* Perform bidiagonal QR iteration */ +/* multiply B by transpose of left singular vectors */ +/* compute right singular vectors in A */ +/* (Workspace: need BDSPAC) */ + + dbdsqr_((char *)"U", n, n, &c__0, nrhs, &s[1], &work[ie], &a[a_offset], lda, + dum, &c__1, &b[b_offset], ldb, &work[iwork], info, (ftnlen)1); + if (*info != 0) { + goto L70; + } + +/* Multiply B by reciprocals of singular values */ + +/* Computing MAX */ + d__1 = *rcond * s[1]; + thr = max(d__1,sfmin); + if (*rcond < 0.) { +/* Computing MAX */ + d__1 = eps * s[1]; + thr = max(d__1,sfmin); + } + *rank = 0; + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + if (s[i__] > thr) { + drscl_(nrhs, &s[i__], &b[i__ + b_dim1], ldb); + ++(*rank); + } else { + dlaset_((char *)"F", &c__1, nrhs, &c_b46, &c_b46, &b[i__ + b_dim1], + ldb, (ftnlen)1); + } +/* L10: */ + } + +/* Multiply B by right singular vectors */ +/* (Workspace: need N, prefer N*NRHS) */ + + if (*lwork >= *ldb * *nrhs && *nrhs > 1) { + dgemm_((char *)"T", (char *)"N", n, nrhs, n, &c_b79, &a[a_offset], lda, &b[ + b_offset], ldb, &c_b46, &work[1], ldb, (ftnlen)1, (ftnlen) + 1); + dlacpy_((char *)"G", n, nrhs, &work[1], ldb, &b[b_offset], ldb, (ftnlen)1) + ; + } else if (*nrhs > 1) { + chunk = *lwork / *n; + i__1 = *nrhs; + i__2 = chunk; + for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { +/* Computing MIN */ + i__3 = *nrhs - i__ + 1; + bl = min(i__3,chunk); + dgemm_((char *)"T", (char *)"N", n, &bl, n, &c_b79, &a[a_offset], lda, &b[i__ + * b_dim1 + 1], ldb, &c_b46, &work[1], n, (ftnlen)1, ( + ftnlen)1); + dlacpy_((char *)"G", n, &bl, &work[1], n, &b[i__ * b_dim1 + 1], ldb, ( + ftnlen)1); +/* L20: */ + } + } else { + dgemv_((char *)"T", n, n, &c_b79, &a[a_offset], lda, &b[b_offset], &c__1, + &c_b46, &work[1], &c__1, (ftnlen)1); + dcopy_(n, &work[1], &c__1, &b[b_offset], &c__1); + } + + } else /* if(complicated condition) */ { +/* Computing MAX */ + i__2 = *m, i__1 = (*m << 1) - 4, i__2 = max(i__2,i__1), i__2 = max( + i__2,*nrhs), i__1 = *n - *m * 3; + if (*n >= mnthr && *lwork >= (*m << 2) + *m * *m + max(i__2,i__1)) { + +/* Path 2a - underdetermined, with many more columns than rows */ +/* and sufficient workspace for an efficient algorithm */ + + ldwork = *m; +/* Computing MAX */ +/* Computing MAX */ + i__3 = *m, i__4 = (*m << 1) - 4, i__3 = max(i__3,i__4), i__3 = + max(i__3,*nrhs), i__4 = *n - *m * 3; + i__2 = (*m << 2) + *m * *lda + max(i__3,i__4), i__1 = *m * *lda + + *m + *m * *nrhs; + if (*lwork >= max(i__2,i__1)) { + ldwork = *lda; + } + itau = 1; + iwork = *m + 1; + +/* Compute A=L*Q */ +/* (Workspace: need 2*M, prefer M+M*NB) */ + + i__2 = *lwork - iwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, + info); + il = iwork; + +/* Copy L to WORK(IL), zeroing out above it */ + + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[il], &ldwork, (ftnlen) + 1); + i__2 = *m - 1; + i__1 = *m - 1; + dlaset_((char *)"U", &i__2, &i__1, &c_b46, &c_b46, &work[il + ldwork], & + ldwork, (ftnlen)1); + ie = il + ldwork * *m; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; + +/* Bidiagonalize L in WORK(IL) */ +/* (Workspace: need M*M+5*M, prefer M*M+4*M+2*M*NB) */ + + i__2 = *lwork - iwork + 1; + dgebrd_(m, m, &work[il], &ldwork, &s[1], &work[ie], &work[itauq], + &work[itaup], &work[iwork], &i__2, info); + +/* Multiply B by transpose of left bidiagonalizing vectors of L */ +/* (Workspace: need M*M+4*M+NRHS, prefer M*M+4*M+NRHS*NB) */ + + i__2 = *lwork - iwork + 1; + dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, m, &work[il], &ldwork, &work[ + itauq], &b[b_offset], ldb, &work[iwork], &i__2, info, ( + ftnlen)1, (ftnlen)1, (ftnlen)1); + +/* Generate right bidiagonalizing vectors of R in WORK(IL) */ +/* (Workspace: need M*M+5*M-1, prefer M*M+4*M+(M-1)*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", m, m, m, &work[il], &ldwork, &work[itaup], &work[ + iwork], &i__2, info, (ftnlen)1); + iwork = ie + *m; + +/* Perform bidiagonal QR iteration, */ +/* computing right singular vectors of L in WORK(IL) and */ +/* multiplying B by transpose of left singular vectors */ +/* (Workspace: need M*M+M+BDSPAC) */ + + dbdsqr_((char *)"U", m, m, &c__0, nrhs, &s[1], &work[ie], &work[il], & + ldwork, &a[a_offset], lda, &b[b_offset], ldb, &work[iwork] + , info, (ftnlen)1); + if (*info != 0) { + goto L70; + } + +/* Multiply B by reciprocals of singular values */ + +/* Computing MAX */ + d__1 = *rcond * s[1]; + thr = max(d__1,sfmin); + if (*rcond < 0.) { +/* Computing MAX */ + d__1 = eps * s[1]; + thr = max(d__1,sfmin); + } + *rank = 0; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + if (s[i__] > thr) { + drscl_(nrhs, &s[i__], &b[i__ + b_dim1], ldb); + ++(*rank); + } else { + dlaset_((char *)"F", &c__1, nrhs, &c_b46, &c_b46, &b[i__ + b_dim1] + , ldb, (ftnlen)1); + } +/* L30: */ + } + iwork = ie; + +/* Multiply B by right singular vectors of L in WORK(IL) */ +/* (Workspace: need M*M+2*M, prefer M*M+M+M*NRHS) */ + + if (*lwork >= *ldb * *nrhs + iwork - 1 && *nrhs > 1) { + dgemm_((char *)"T", (char *)"N", m, nrhs, m, &c_b79, &work[il], &ldwork, &b[ + b_offset], ldb, &c_b46, &work[iwork], ldb, (ftnlen)1, + (ftnlen)1); + dlacpy_((char *)"G", m, nrhs, &work[iwork], ldb, &b[b_offset], ldb, ( + ftnlen)1); + } else if (*nrhs > 1) { + chunk = (*lwork - iwork + 1) / *m; + i__2 = *nrhs; + i__1 = chunk; + for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += + i__1) { +/* Computing MIN */ + i__3 = *nrhs - i__ + 1; + bl = min(i__3,chunk); + dgemm_((char *)"T", (char *)"N", m, &bl, m, &c_b79, &work[il], &ldwork, & + b[i__ * b_dim1 + 1], ldb, &c_b46, &work[iwork], m, + (ftnlen)1, (ftnlen)1); + dlacpy_((char *)"G", m, &bl, &work[iwork], m, &b[i__ * b_dim1 + 1] + , ldb, (ftnlen)1); +/* L40: */ + } + } else { + dgemv_((char *)"T", m, m, &c_b79, &work[il], &ldwork, &b[b_dim1 + 1], + &c__1, &c_b46, &work[iwork], &c__1, (ftnlen)1); + dcopy_(m, &work[iwork], &c__1, &b[b_dim1 + 1], &c__1); + } + +/* Zero out below first M rows of B */ + + i__1 = *n - *m; + dlaset_((char *)"F", &i__1, nrhs, &c_b46, &c_b46, &b[*m + 1 + b_dim1], + ldb, (ftnlen)1); + iwork = itau + *m; + +/* Multiply transpose(Q) by B */ +/* (Workspace: need M+NRHS, prefer M+NRHS*NB) */ + + i__1 = *lwork - iwork + 1; + dormlq_((char *)"L", (char *)"T", n, nrhs, m, &a[a_offset], lda, &work[itau], &b[ + b_offset], ldb, &work[iwork], &i__1, info, (ftnlen)1, ( + ftnlen)1); + + } else { + +/* Path 2 - remaining underdetermined cases */ + + ie = 1; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; + +/* Bidiagonalize A */ +/* (Workspace: need 3*M+N, prefer 3*M+(M+N)*NB) */ + + i__1 = *lwork - iwork + 1; + dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], & + work[itaup], &work[iwork], &i__1, info); + +/* Multiply B by transpose of left bidiagonalizing vectors */ +/* (Workspace: need 3*M+NRHS, prefer 3*M+NRHS*NB) */ + + i__1 = *lwork - iwork + 1; + dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, &work[itauq] + , &b[b_offset], ldb, &work[iwork], &i__1, info, (ftnlen)1, + (ftnlen)1, (ftnlen)1); + +/* Generate right bidiagonalizing vectors in A */ +/* (Workspace: need 4*M, prefer 3*M+M*NB) */ + + i__1 = *lwork - iwork + 1; + dorgbr_((char *)"P", m, n, m, &a[a_offset], lda, &work[itaup], &work[ + iwork], &i__1, info, (ftnlen)1); + iwork = ie + *m; + +/* Perform bidiagonal QR iteration, */ +/* computing right singular vectors of A in A and */ +/* multiplying B by transpose of left singular vectors */ +/* (Workspace: need BDSPAC) */ + + dbdsqr_((char *)"L", m, n, &c__0, nrhs, &s[1], &work[ie], &a[a_offset], + lda, dum, &c__1, &b[b_offset], ldb, &work[iwork], info, ( + ftnlen)1); + if (*info != 0) { + goto L70; + } + +/* Multiply B by reciprocals of singular values */ + +/* Computing MAX */ + d__1 = *rcond * s[1]; + thr = max(d__1,sfmin); + if (*rcond < 0.) { +/* Computing MAX */ + d__1 = eps * s[1]; + thr = max(d__1,sfmin); + } + *rank = 0; + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + if (s[i__] > thr) { + drscl_(nrhs, &s[i__], &b[i__ + b_dim1], ldb); + ++(*rank); + } else { + dlaset_((char *)"F", &c__1, nrhs, &c_b46, &c_b46, &b[i__ + b_dim1] + , ldb, (ftnlen)1); + } +/* L50: */ + } + +/* Multiply B by right singular vectors of A */ +/* (Workspace: need N, prefer N*NRHS) */ + + if (*lwork >= *ldb * *nrhs && *nrhs > 1) { + dgemm_((char *)"T", (char *)"N", n, nrhs, m, &c_b79, &a[a_offset], lda, &b[ + b_offset], ldb, &c_b46, &work[1], ldb, (ftnlen)1, ( + ftnlen)1); + dlacpy_((char *)"F", n, nrhs, &work[1], ldb, &b[b_offset], ldb, ( + ftnlen)1); + } else if (*nrhs > 1) { + chunk = *lwork / *n; + i__1 = *nrhs; + i__2 = chunk; + for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += + i__2) { +/* Computing MIN */ + i__3 = *nrhs - i__ + 1; + bl = min(i__3,chunk); + dgemm_((char *)"T", (char *)"N", n, &bl, m, &c_b79, &a[a_offset], lda, &b[ + i__ * b_dim1 + 1], ldb, &c_b46, &work[1], n, ( + ftnlen)1, (ftnlen)1); + dlacpy_((char *)"F", n, &bl, &work[1], n, &b[i__ * b_dim1 + 1], + ldb, (ftnlen)1); +/* L60: */ + } + } else { + dgemv_((char *)"T", m, n, &c_b79, &a[a_offset], lda, &b[b_offset], & + c__1, &c_b46, &work[1], &c__1, (ftnlen)1); + dcopy_(n, &work[1], &c__1, &b[b_offset], &c__1); + } + } + } + +/* Undo scaling */ + + if (iascl == 1) { + dlascl_((char *)"G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb, + info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], & + minmn, info, (ftnlen)1); + } else if (iascl == 2) { + dlascl_((char *)"G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb, + info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], & + minmn, info, (ftnlen)1); + } + if (ibscl == 1) { + dlascl_((char *)"G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb, + info, (ftnlen)1); + } else if (ibscl == 2) { + dlascl_((char *)"G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb, + info, (ftnlen)1); + } + +L70: + work[1] = (doublereal) maxwrk; + return 0; + +/* End of DGELSS */ + +} /* dgelss_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dgemm.cpp b/lib/linalg/dgemm.cpp new file mode 100644 index 0000000000..2f59801245 --- /dev/null +++ b/lib/linalg/dgemm.cpp @@ -0,0 +1,458 @@ +/* fortran/dgemm.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DGEMM */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) */ + +/* .. Scalar Arguments .. */ +/* DOUBLE PRECISION ALPHA,BETA */ +/* INTEGER K,LDA,LDB,LDC,M,N */ +/* CHARACTER TRANSA,TRANSB */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DGEMM performs one of the matrix-matrix operations */ +/* > */ +/* > C := alpha*op( A )*op( B ) + beta*C, */ +/* > */ +/* > where op( X ) is one of */ +/* > */ +/* > op( X ) = X or op( X ) = X**T, */ +/* > */ +/* > alpha and beta are scalars, and A, B and C are matrices, with op( A ) */ +/* > an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] TRANSA */ +/* > \verbatim */ +/* > TRANSA is CHARACTER*1 */ +/* > On entry, TRANSA specifies the form of op( A ) to be used in */ +/* > the matrix multiplication as follows: */ +/* > */ +/* > TRANSA = 'N' or 'n', op( A ) = A. */ +/* > */ +/* > TRANSA = 'T' or 't', op( A ) = A**T. */ +/* > */ +/* > TRANSA = 'C' or 'c', op( A ) = A**T. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TRANSB */ +/* > \verbatim */ +/* > TRANSB is CHARACTER*1 */ +/* > On entry, TRANSB specifies the form of op( B ) to be used in */ +/* > the matrix multiplication as follows: */ +/* > */ +/* > TRANSB = 'N' or 'n', op( B ) = B. */ +/* > */ +/* > TRANSB = 'T' or 't', op( B ) = B**T. */ +/* > */ +/* > TRANSB = 'C' or 'c', op( B ) = B**T. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > On entry, M specifies the number of rows of the matrix */ +/* > op( A ) and of the matrix C. M must be at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > On entry, N specifies the number of columns of the matrix */ +/* > op( B ) and the number of columns of the matrix C. N must be */ +/* > at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > On entry, K specifies the number of columns of the matrix */ +/* > op( A ) and the number of rows of the matrix op( B ). K must */ +/* > be at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] ALPHA */ +/* > \verbatim */ +/* > ALPHA is DOUBLE PRECISION. */ +/* > On entry, ALPHA specifies the scalar alpha. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is */ +/* > k when TRANSA = 'N' or 'n', and is m otherwise. */ +/* > Before entry with TRANSA = 'N' or 'n', the leading m by k */ +/* > part of the array A must contain the matrix A, otherwise */ +/* > the leading k by m part of the array A must contain the */ +/* > matrix A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > On entry, LDA specifies the first dimension of A as declared */ +/* > in the calling (sub) program. When TRANSA = 'N' or 'n' then */ +/* > LDA must be at least max( 1, m ), otherwise LDA must be at */ +/* > least max( 1, k ). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] B */ +/* > \verbatim */ +/* > B is DOUBLE PRECISION array, dimension ( LDB, kb ), where kb is */ +/* > n when TRANSB = 'N' or 'n', and is k otherwise. */ +/* > Before entry with TRANSB = 'N' or 'n', the leading k by n */ +/* > part of the array B must contain the matrix B, otherwise */ +/* > the leading n by k part of the array B must contain the */ +/* > matrix B. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDB */ +/* > \verbatim */ +/* > LDB is INTEGER */ +/* > On entry, LDB specifies the first dimension of B as declared */ +/* > in the calling (sub) program. When TRANSB = 'N' or 'n' then */ +/* > LDB must be at least max( 1, k ), otherwise LDB must be at */ +/* > least max( 1, n ). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] BETA */ +/* > \verbatim */ +/* > BETA is DOUBLE PRECISION. */ +/* > On entry, BETA specifies the scalar beta. When BETA is */ +/* > supplied as zero then C need not be set on input. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] C */ +/* > \verbatim */ +/* > C is DOUBLE PRECISION array, dimension ( LDC, N ) */ +/* > Before entry, the leading m by n part of the array C must */ +/* > contain the matrix C, except when beta is zero, in which */ +/* > case C need not be set on entry. */ +/* > On exit, the array C is overwritten by the m by n matrix */ +/* > ( alpha*op( A )*op( B ) + beta*C ). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDC */ +/* > \verbatim */ +/* > LDC is INTEGER */ +/* > On entry, LDC specifies the first dimension of C as declared */ +/* > in the calling (sub) program. LDC must be at least */ +/* > max( 1, m ). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup double_blas_level3 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > Level 3 Blas routine. */ +/* > */ +/* > -- Written on 8-February-1989. */ +/* > Jack Dongarra, Argonne National Laboratory. */ +/* > Iain Duff, AERE Harwell. */ +/* > Jeremy Du Croz, Numerical Algorithms Group Ltd. */ +/* > Sven Hammarling, Numerical Algorithms Group Ltd. */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dgemm_(char *transa, char *transb, integer *m, integer * + n, integer *k, doublereal *alpha, doublereal *a, integer *lda, + doublereal *b, integer *ldb, doublereal *beta, doublereal *c__, + integer *ldc, ftnlen transa_len, ftnlen transb_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, + i__3; + + /* Local variables */ + integer i__, j, l, info; + logical nota, notb; + doublereal temp; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + integer nrowa, nrowb; + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + + +/* -- Reference BLAS level3 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Parameters .. */ +/* .. */ + +/* Set NOTA and NOTB as true if A and B respectively are not */ +/* transposed and set NROWA and NROWB as the number of rows of A */ +/* and B respectively. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + b_dim1 = *ldb; + b_offset = 1 + b_dim1; + b -= b_offset; + c_dim1 = *ldc; + c_offset = 1 + c_dim1; + c__ -= c_offset; + + /* Function Body */ + nota = lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1); + notb = lsame_(transb, (char *)"N", (ftnlen)1, (ftnlen)1); + if (nota) { + nrowa = *m; + } else { + nrowa = *k; + } + if (notb) { + nrowb = *k; + } else { + nrowb = *n; + } + +/* Test the input parameters. */ + + info = 0; + if (! nota && ! lsame_(transa, (char *)"C", (ftnlen)1, (ftnlen)1) && ! lsame_( + transa, (char *)"T", (ftnlen)1, (ftnlen)1)) { + info = 1; + } else if (! notb && ! lsame_(transb, (char *)"C", (ftnlen)1, (ftnlen)1) && ! + lsame_(transb, (char *)"T", (ftnlen)1, (ftnlen)1)) { + info = 2; + } else if (*m < 0) { + info = 3; + } else if (*n < 0) { + info = 4; + } else if (*k < 0) { + info = 5; + } else if (*lda < max(1,nrowa)) { + info = 8; + } else if (*ldb < max(1,nrowb)) { + info = 10; + } else if (*ldc < max(1,*m)) { + info = 13; + } + if (info != 0) { + xerbla_((char *)"DGEMM ", &info, (ftnlen)6); + return 0; + } + +/* Quick return if possible. */ + + if (*m == 0 || *n == 0 || (*alpha == 0. || *k == 0) && *beta == 1.) { + return 0; + } + +/* And if alpha.eq.zero. */ + + if (*alpha == 0.) { + if (*beta == 0.) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = 0.; +/* L10: */ + } +/* L20: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; +/* L30: */ + } +/* L40: */ + } + } + return 0; + } + +/* Start the operations. */ + + if (notb) { + if (nota) { + +/* Form C := alpha*A*B + beta*C. */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (*beta == 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = 0.; +/* L50: */ + } + } else if (*beta != 1.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; +/* L60: */ + } + } + i__2 = *k; + for (l = 1; l <= i__2; ++l) { + temp = *alpha * b[l + j * b_dim1]; + i__3 = *m; + for (i__ = 1; i__ <= i__3; ++i__) { + c__[i__ + j * c_dim1] += temp * a[i__ + l * a_dim1]; +/* L70: */ + } +/* L80: */ + } +/* L90: */ + } + } else { + +/* Form C := alpha*A**T*B + beta*C */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp = 0.; + i__3 = *k; + for (l = 1; l <= i__3; ++l) { + temp += a[l + i__ * a_dim1] * b[l + j * b_dim1]; +/* L100: */ + } + if (*beta == 0.) { + c__[i__ + j * c_dim1] = *alpha * temp; + } else { + c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[ + i__ + j * c_dim1]; + } +/* L110: */ + } +/* L120: */ + } + } + } else { + if (nota) { + +/* Form C := alpha*A*B**T + beta*C */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (*beta == 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = 0.; +/* L130: */ + } + } else if (*beta != 1.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; +/* L140: */ + } + } + i__2 = *k; + for (l = 1; l <= i__2; ++l) { + temp = *alpha * b[j + l * b_dim1]; + i__3 = *m; + for (i__ = 1; i__ <= i__3; ++i__) { + c__[i__ + j * c_dim1] += temp * a[i__ + l * a_dim1]; +/* L150: */ + } +/* L160: */ + } +/* L170: */ + } + } else { + +/* Form C := alpha*A**T*B**T + beta*C */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp = 0.; + i__3 = *k; + for (l = 1; l <= i__3; ++l) { + temp += a[l + i__ * a_dim1] * b[j + l * b_dim1]; +/* L180: */ + } + if (*beta == 0.) { + c__[i__ + j * c_dim1] = *alpha * temp; + } else { + c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[ + i__ + j * c_dim1]; + } +/* L190: */ + } +/* L200: */ + } + } + } + + return 0; + +/* End of DGEMM */ + +} /* dgemm_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dgemv.cpp b/lib/linalg/dgemv.cpp new file mode 100644 index 0000000000..1d121c33c0 --- /dev/null +++ b/lib/linalg/dgemv.cpp @@ -0,0 +1,385 @@ +/* fortran/dgemv.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DGEMV */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) */ + +/* .. Scalar Arguments .. */ +/* DOUBLE PRECISION ALPHA,BETA */ +/* INTEGER INCX,INCY,LDA,M,N */ +/* CHARACTER TRANS */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A(LDA,*),X(*),Y(*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DGEMV performs one of the matrix-vector operations */ +/* > */ +/* > y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, */ +/* > */ +/* > where alpha and beta are scalars, x and y are vectors and A is an */ +/* > m by n matrix. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] TRANS */ +/* > \verbatim */ +/* > TRANS is CHARACTER*1 */ +/* > On entry, TRANS specifies the operation to be performed as */ +/* > follows: */ +/* > */ +/* > TRANS = 'N' or 'n' y := alpha*A*x + beta*y. */ +/* > */ +/* > TRANS = 'T' or 't' y := alpha*A**T*x + beta*y. */ +/* > */ +/* > TRANS = 'C' or 'c' y := alpha*A**T*x + beta*y. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > On entry, M specifies the number of rows of the matrix A. */ +/* > M must be at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > On entry, N specifies the number of columns of the matrix A. */ +/* > N must be at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] ALPHA */ +/* > \verbatim */ +/* > ALPHA is DOUBLE PRECISION. */ +/* > On entry, ALPHA specifies the scalar alpha. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension ( LDA, N ) */ +/* > Before entry, the leading m by n part of the array A must */ +/* > contain the matrix of coefficients. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > On entry, LDA specifies the first dimension of A as declared */ +/* > in the calling (sub) program. LDA must be at least */ +/* > max( 1, m ). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] X */ +/* > \verbatim */ +/* > X is DOUBLE PRECISION array, dimension at least */ +/* > ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' */ +/* > and at least */ +/* > ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. */ +/* > Before entry, the incremented array X must contain the */ +/* > vector x. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > On entry, INCX specifies the increment for the elements of */ +/* > X. INCX must not be zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] BETA */ +/* > \verbatim */ +/* > BETA is DOUBLE PRECISION. */ +/* > On entry, BETA specifies the scalar beta. When BETA is */ +/* > supplied as zero then Y need not be set on input. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] Y */ +/* > \verbatim */ +/* > Y is DOUBLE PRECISION array, dimension at least */ +/* > ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' */ +/* > and at least */ +/* > ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. */ +/* > Before entry with BETA non-zero, the incremented array Y */ +/* > must contain the vector y. On exit, Y is overwritten by the */ +/* > updated vector y. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCY */ +/* > \verbatim */ +/* > INCY is INTEGER */ +/* > On entry, INCY specifies the increment for the elements of */ +/* > Y. INCY must not be zero. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup double_blas_level2 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > Level 2 Blas routine. */ +/* > The vector and matrix arguments are not referenced when N = 0, or M = 0 */ +/* > */ +/* > -- Written on 22-October-1986. */ +/* > Jack Dongarra, Argonne National Lab. */ +/* > Jeremy Du Croz, Nag Central Office. */ +/* > Sven Hammarling, Nag Central Office. */ +/* > Richard Hanson, Sandia National Labs. */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dgemv_(char *trans, integer *m, integer *n, doublereal * + alpha, doublereal *a, integer *lda, doublereal *x, integer *incx, + doublereal *beta, doublereal *y, integer *incy, ftnlen trans_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2; + + /* Local variables */ + integer i__, j, ix, iy, jx, jy, kx, ky, info; + doublereal temp; + integer lenx, leny; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + + +/* -- Reference BLAS level2 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --x; + --y; + + /* Function Body */ + info = 0; + if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"T", ( + ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1) + ) { + info = 1; + } else if (*m < 0) { + info = 2; + } else if (*n < 0) { + info = 3; + } else if (*lda < max(1,*m)) { + info = 6; + } else if (*incx == 0) { + info = 8; + } else if (*incy == 0) { + info = 11; + } + if (info != 0) { + xerbla_((char *)"DGEMV ", &info, (ftnlen)6); + return 0; + } + +/* Quick return if possible. */ + + if (*m == 0 || *n == 0 || *alpha == 0. && *beta == 1.) { + return 0; + } + +/* Set LENX and LENY, the lengths of the vectors x and y, and set */ +/* up the start points in X and Y. */ + + if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { + lenx = *n; + leny = *m; + } else { + lenx = *m; + leny = *n; + } + if (*incx > 0) { + kx = 1; + } else { + kx = 1 - (lenx - 1) * *incx; + } + if (*incy > 0) { + ky = 1; + } else { + ky = 1 - (leny - 1) * *incy; + } + +/* Start the operations. In this version the elements of A are */ +/* accessed sequentially with one pass through A. */ + +/* First form y := beta*y. */ + + if (*beta != 1.) { + if (*incy == 1) { + if (*beta == 0.) { + i__1 = leny; + for (i__ = 1; i__ <= i__1; ++i__) { + y[i__] = 0.; +/* L10: */ + } + } else { + i__1 = leny; + for (i__ = 1; i__ <= i__1; ++i__) { + y[i__] = *beta * y[i__]; +/* L20: */ + } + } + } else { + iy = ky; + if (*beta == 0.) { + i__1 = leny; + for (i__ = 1; i__ <= i__1; ++i__) { + y[iy] = 0.; + iy += *incy; +/* L30: */ + } + } else { + i__1 = leny; + for (i__ = 1; i__ <= i__1; ++i__) { + y[iy] = *beta * y[iy]; + iy += *incy; +/* L40: */ + } + } + } + } + if (*alpha == 0.) { + return 0; + } + if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { + +/* Form y := alpha*A*x + y. */ + + jx = kx; + if (*incy == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp = *alpha * x[jx]; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + y[i__] += temp * a[i__ + j * a_dim1]; +/* L50: */ + } + jx += *incx; +/* L60: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp = *alpha * x[jx]; + iy = ky; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + y[iy] += temp * a[i__ + j * a_dim1]; + iy += *incy; +/* L70: */ + } + jx += *incx; +/* L80: */ + } + } + } else { + +/* Form y := alpha*A**T*x + y. */ + + jy = ky; + if (*incx == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp = 0.; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp += a[i__ + j * a_dim1] * x[i__]; +/* L90: */ + } + y[jy] += *alpha * temp; + jy += *incy; +/* L100: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp = 0.; + ix = kx; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp += a[i__ + j * a_dim1] * x[ix]; + ix += *incx; +/* L110: */ + } + y[jy] += *alpha * temp; + jy += *incy; +/* L120: */ + } + } + } + + return 0; + +/* End of DGEMV */ + +} /* dgemv_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dgeqr2.cpp b/lib/linalg/dgeqr2.cpp new file mode 100644 index 0000000000..635e360bc7 --- /dev/null +++ b/lib/linalg/dgeqr2.cpp @@ -0,0 +1,250 @@ +/* fortran/dgeqr2.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; + +/* > \brief \b DGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorit +hm. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DGEQR2 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DGEQR2( M, N, A, LDA, TAU, WORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INFO, LDA, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DGEQR2 computes a QR factorization of a real m-by-n matrix A: */ +/* > */ +/* > A = Q * ( R ), */ +/* > ( 0 ) */ +/* > */ +/* > where: */ +/* > */ +/* > Q is a m-by-m orthogonal matrix; */ +/* > R is an upper-triangular n-by-n matrix; */ +/* > 0 is a (m-n)-by-n zero matrix, if m > n. */ +/* > */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix A. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On entry, the m by n matrix A. */ +/* > On exit, the elements on and above the diagonal of the array */ +/* > contain the min(m,n) by n upper trapezoidal matrix R (R is */ +/* > upper triangular if m >= n); the elements below the diagonal, */ +/* > with the array TAU, represent the orthogonal matrix Q as a */ +/* > product of elementary reflectors (see Further Details). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] TAU */ +/* > \verbatim */ +/* > TAU is DOUBLE PRECISION array, dimension (min(M,N)) */ +/* > The scalar factors of the elementary reflectors (see Further */ +/* > Details). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (N) */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleGEcomputational */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > The matrix Q is represented as a product of elementary reflectors */ +/* > */ +/* > Q = H(1) H(2) . . . H(k), where k = min(m,n). */ +/* > */ +/* > Each H(i) has the form */ +/* > */ +/* > H(i) = I - tau * v * v**T */ +/* > */ +/* > where tau is a real scalar, and v is a real vector with */ +/* > v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), */ +/* > and tau in TAU(i). */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dgeqr2_(integer *m, integer *n, doublereal *a, integer * + lda, doublereal *tau, doublereal *work, integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3; + + /* Local variables */ + integer i__, k; + doublereal aii; + extern /* Subroutine */ int dlarf_(char *, integer *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, + doublereal *, ftnlen), dlarfg_(integer *, doublereal *, + doublereal *, integer *, doublereal *), xerbla_(char *, integer *, + ftnlen); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --tau; + --work; + + /* Function Body */ + *info = 0; + if (*m < 0) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } else if (*lda < max(1,*m)) { + *info = -4; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DGEQR2", &i__1, (ftnlen)6); + return 0; + } + + k = min(*m,*n); + + i__1 = k; + for (i__ = 1; i__ <= i__1; ++i__) { + +/* Generate elementary reflector H(i) to annihilate A(i+1:m,i) */ + + i__2 = *m - i__ + 1; +/* Computing MIN */ + i__3 = i__ + 1; + dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[min(i__3,*m) + i__ * a_dim1] + , &c__1, &tau[i__]); + if (i__ < *n) { + +/* Apply H(i) to A(i:m,i+1:n) from the left */ + + aii = a[i__ + i__ * a_dim1]; + a[i__ + i__ * a_dim1] = 1.; + i__2 = *m - i__ + 1; + i__3 = *n - i__; + dlarf_((char *)"Left", &i__2, &i__3, &a[i__ + i__ * a_dim1], &c__1, &tau[ + i__], &a[i__ + (i__ + 1) * a_dim1], lda, &work[1], ( + ftnlen)4); + a[i__ + i__ * a_dim1] = aii; + } +/* L10: */ + } + return 0; + +/* End of DGEQR2 */ + +} /* dgeqr2_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dgeqrf.cpp b/lib/linalg/dgeqrf.cpp new file mode 100644 index 0000000000..fa0aca3f47 --- /dev/null +++ b/lib/linalg/dgeqrf.cpp @@ -0,0 +1,354 @@ +/* fortran/dgeqrf.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c_n1 = -1; +static integer c__3 = 3; +static integer c__2 = 2; + +/* > \brief \b DGEQRF */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DGEQRF + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DGEQRF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INFO, LDA, LWORK, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DGEQRF computes a QR factorization of a real M-by-N matrix A: */ +/* > */ +/* > A = Q * ( R ), */ +/* > ( 0 ) */ +/* > */ +/* > where: */ +/* > */ +/* > Q is a M-by-M orthogonal matrix; */ +/* > R is an upper-triangular N-by-N matrix; */ +/* > 0 is a (M-N)-by-N zero matrix, if M > N. */ +/* > */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix A. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On entry, the M-by-N matrix A. */ +/* > On exit, the elements on and above the diagonal of the array */ +/* > contain the min(M,N)-by-N upper trapezoidal matrix R (R is */ +/* > upper triangular if m >= n); the elements below the diagonal, */ +/* > with the array TAU, represent the orthogonal matrix Q as a */ +/* > product of min(m,n) elementary reflectors (see Further */ +/* > Details). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] TAU */ +/* > \verbatim */ +/* > TAU is DOUBLE PRECISION array, dimension (min(M,N)) */ +/* > The scalar factors of the elementary reflectors (see Further */ +/* > Details). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ +/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LWORK */ +/* > \verbatim */ +/* > LWORK is INTEGER */ +/* > The dimension of the array WORK. */ +/* > LWORK >= 1, if MIN(M,N) = 0, and LWORK >= N, otherwise. */ +/* > For optimum performance LWORK >= N*NB, where NB is */ +/* > the optimal blocksize. */ +/* > */ +/* > If LWORK = -1, then a workspace query is assumed; the routine */ +/* > only calculates the optimal size of the WORK array, returns */ +/* > this value as the first entry of the WORK array, and no error */ +/* > message related to LWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleGEcomputational */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > The matrix Q is represented as a product of elementary reflectors */ +/* > */ +/* > Q = H(1) H(2) . . . H(k), where k = min(m,n). */ +/* > */ +/* > Each H(i) has the form */ +/* > */ +/* > H(i) = I - tau * v * v**T */ +/* > */ +/* > where tau is a real scalar, and v is a real vector with */ +/* > v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), */ +/* > and tau in TAU(i). */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dgeqrf_(integer *m, integer *n, doublereal *a, integer * + lda, doublereal *tau, doublereal *work, integer *lwork, integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3, i__4; + + /* Local variables */ + integer i__, k, ib, nb, nx, iws, nbmin, iinfo; + extern /* Subroutine */ int dgeqr2_(integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *), dlarfb_(char *, + char *, char *, char *, integer *, integer *, integer *, + doublereal *, integer *, doublereal *, integer *, doublereal *, + integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, + ftnlen), dlarft_(char *, char *, integer *, integer *, doublereal + *, integer *, doublereal *, doublereal *, integer *, ftnlen, + ftnlen), xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + integer ldwork, lwkopt; + logical lquery; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --tau; + --work; + + /* Function Body */ + k = min(*m,*n); + *info = 0; + nb = ilaenv_(&c__1, (char *)"DGEQRF", (char *)" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen) + 1); + lquery = *lwork == -1; + if (*m < 0) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } else if (*lda < max(1,*m)) { + *info = -4; + } else if (! lquery) { + if (*lwork <= 0 || *m > 0 && *lwork < max(1,*n)) { + *info = -7; + } + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DGEQRF", &i__1, (ftnlen)6); + return 0; + } else if (lquery) { + if (k == 0) { + lwkopt = 1; + } else { + lwkopt = *n * nb; + } + work[1] = (doublereal) lwkopt; + return 0; + } + +/* Quick return if possible */ + + if (k == 0) { + work[1] = 1.; + return 0; + } + + nbmin = 2; + nx = 0; + iws = *n; + if (nb > 1 && nb < k) { + +/* Determine when to cross over from blocked to unblocked code. */ + +/* Computing MAX */ + i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"DGEQRF", (char *)" ", m, n, &c_n1, &c_n1, ( + ftnlen)6, (ftnlen)1); + nx = max(i__1,i__2); + if (nx < k) { + +/* Determine if workspace is large enough for blocked code. */ + + ldwork = *n; + iws = ldwork * nb; + if (*lwork < iws) { + +/* Not enough workspace to use optimal NB: reduce NB and */ +/* determine the minimum value of NB. */ + + nb = *lwork / ldwork; +/* Computing MAX */ + i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DGEQRF", (char *)" ", m, n, &c_n1, & + c_n1, (ftnlen)6, (ftnlen)1); + nbmin = max(i__1,i__2); + } + } + } + + if (nb >= nbmin && nb < k && nx < k) { + +/* Use blocked code initially */ + + i__1 = k - nx; + i__2 = nb; + for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { +/* Computing MIN */ + i__3 = k - i__ + 1; + ib = min(i__3,nb); + +/* Compute the QR factorization of the current block */ +/* A(i:m,i:i+ib-1) */ + + i__3 = *m - i__ + 1; + dgeqr2_(&i__3, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[ + 1], &iinfo); + if (i__ + ib <= *n) { + +/* Form the triangular factor of the block reflector */ +/* H = H(i) H(i+1) . . . H(i+ib-1) */ + + i__3 = *m - i__ + 1; + dlarft_((char *)"Forward", (char *)"Columnwise", &i__3, &ib, &a[i__ + i__ * + a_dim1], lda, &tau[i__], &work[1], &ldwork, (ftnlen)7, + (ftnlen)10); + +/* Apply H**T to A(i:m,i+ib:n) from the left */ + + i__3 = *m - i__ + 1; + i__4 = *n - i__ - ib + 1; + dlarfb_((char *)"Left", (char *)"Transpose", (char *)"Forward", (char *)"Columnwise", &i__3, & + i__4, &ib, &a[i__ + i__ * a_dim1], lda, &work[1], & + ldwork, &a[i__ + (i__ + ib) * a_dim1], lda, &work[ib + + 1], &ldwork, (ftnlen)4, (ftnlen)9, (ftnlen)7, ( + ftnlen)10); + } +/* L10: */ + } + } else { + i__ = 1; + } + +/* Use unblocked code to factor the last or only block. */ + + if (i__ <= k) { + i__2 = *m - i__ + 1; + i__1 = *n - i__ + 1; + dgeqr2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[1] + , &iinfo); + } + + work[1] = (doublereal) iws; + return 0; + +/* End of DGEQRF */ + +} /* dgeqrf_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dger.cpp b/lib/linalg/dger.cpp new file mode 100644 index 0000000000..fd5c4940bf --- /dev/null +++ b/lib/linalg/dger.cpp @@ -0,0 +1,265 @@ +/* fortran/dger.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DGER */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DGER(M,N,ALPHA,X,INCX,Y,INCY,A,LDA) */ + +/* .. Scalar Arguments .. */ +/* DOUBLE PRECISION ALPHA */ +/* INTEGER INCX,INCY,LDA,M,N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A(LDA,*),X(*),Y(*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DGER performs the rank 1 operation */ +/* > */ +/* > A := alpha*x*y**T + A, */ +/* > */ +/* > where alpha is a scalar, x is an m element vector, y is an n element */ +/* > vector and A is an m by n matrix. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > On entry, M specifies the number of rows of the matrix A. */ +/* > M must be at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > On entry, N specifies the number of columns of the matrix A. */ +/* > N must be at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] ALPHA */ +/* > \verbatim */ +/* > ALPHA is DOUBLE PRECISION. */ +/* > On entry, ALPHA specifies the scalar alpha. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] X */ +/* > \verbatim */ +/* > X is DOUBLE PRECISION array, dimension at least */ +/* > ( 1 + ( m - 1 )*abs( INCX ) ). */ +/* > Before entry, the incremented array X must contain the m */ +/* > element vector x. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > On entry, INCX specifies the increment for the elements of */ +/* > X. INCX must not be zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] Y */ +/* > \verbatim */ +/* > Y is DOUBLE PRECISION array, dimension at least */ +/* > ( 1 + ( n - 1 )*abs( INCY ) ). */ +/* > Before entry, the incremented array Y must contain the n */ +/* > element vector y. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCY */ +/* > \verbatim */ +/* > INCY is INTEGER */ +/* > On entry, INCY specifies the increment for the elements of */ +/* > Y. INCY must not be zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension ( LDA, N ) */ +/* > Before entry, the leading m by n part of the array A must */ +/* > contain the matrix of coefficients. On exit, A is */ +/* > overwritten by the updated matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > On entry, LDA specifies the first dimension of A as declared */ +/* > in the calling (sub) program. LDA must be at least */ +/* > max( 1, m ). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup double_blas_level2 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > Level 2 Blas routine. */ +/* > */ +/* > -- Written on 22-October-1986. */ +/* > Jack Dongarra, Argonne National Lab. */ +/* > Jeremy Du Croz, Nag Central Office. */ +/* > Sven Hammarling, Nag Central Office. */ +/* > Richard Hanson, Sandia National Labs. */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dger_(integer *m, integer *n, doublereal *alpha, + doublereal *x, integer *incx, doublereal *y, integer *incy, + doublereal *a, integer *lda) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2; + + /* Local variables */ + integer i__, j, ix, jy, kx, info; + doublereal temp; + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + + +/* -- Reference BLAS level2 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --x; + --y; + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + + /* Function Body */ + info = 0; + if (*m < 0) { + info = 1; + } else if (*n < 0) { + info = 2; + } else if (*incx == 0) { + info = 5; + } else if (*incy == 0) { + info = 7; + } else if (*lda < max(1,*m)) { + info = 9; + } + if (info != 0) { + xerbla_((char *)"DGER ", &info, (ftnlen)6); + return 0; + } + +/* Quick return if possible. */ + + if (*m == 0 || *n == 0 || *alpha == 0.) { + return 0; + } + +/* Start the operations. In this version the elements of A are */ +/* accessed sequentially with one pass through A. */ + + if (*incy > 0) { + jy = 1; + } else { + jy = 1 - (*n - 1) * *incy; + } + if (*incx == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (y[jy] != 0.) { + temp = *alpha * y[jy]; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] += x[i__] * temp; +/* L10: */ + } + } + jy += *incy; +/* L20: */ + } + } else { + if (*incx > 0) { + kx = 1; + } else { + kx = 1 - (*m - 1) * *incx; + } + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (y[jy] != 0.) { + temp = *alpha * y[jy]; + ix = kx; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] += x[ix] * temp; + ix += *incx; +/* L30: */ + } + } + jy += *incy; +/* L40: */ + } + } + + return 0; + +/* End of DGER */ + +} /* dger_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dgesv.cpp b/lib/linalg/dgesv.cpp new file mode 100644 index 0000000000..a71b2caa68 --- /dev/null +++ b/lib/linalg/dgesv.cpp @@ -0,0 +1,217 @@ +/* fortran/dgesv.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief DGESV computes the solution to system of linear equations A * X = B for GE matrices */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DGESV + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DGESV( N, NRHS, A, LDA, IPIV, B, LDB, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INFO, LDA, LDB, N, NRHS */ +/* .. */ +/* .. Array Arguments .. */ +/* INTEGER IPIV( * ) */ +/* DOUBLE PRECISION A( LDA, * ), B( LDB, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DGESV computes the solution to a real system of linear equations */ +/* > A * X = B, */ +/* > where A is an N-by-N matrix and X and B are N-by-NRHS matrices. */ +/* > */ +/* > The LU decomposition with partial pivoting and row interchanges is */ +/* > used to factor A as */ +/* > A = P * L * U, */ +/* > where P is a permutation matrix, L is unit lower triangular, and U is */ +/* > upper triangular. The factored form of A is then used to solve the */ +/* > system of equations A * X = B. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of linear equations, i.e., the order of the */ +/* > matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] NRHS */ +/* > \verbatim */ +/* > NRHS is INTEGER */ +/* > The number of right hand sides, i.e., the number of columns */ +/* > of the matrix B. NRHS >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On entry, the N-by-N coefficient matrix A. */ +/* > On exit, the factors L and U from the factorization */ +/* > A = P*L*U; the unit diagonal elements of L are not stored. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] IPIV */ +/* > \verbatim */ +/* > IPIV is INTEGER array, dimension (N) */ +/* > The pivot indices that define the permutation matrix P; */ +/* > row i of the matrix was interchanged with row IPIV(i). */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] B */ +/* > \verbatim */ +/* > B is DOUBLE PRECISION array, dimension (LDB,NRHS) */ +/* > On entry, the N-by-NRHS matrix of right hand side matrix B. */ +/* > On exit, if INFO = 0, the N-by-NRHS solution matrix X. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDB */ +/* > \verbatim */ +/* > LDB is INTEGER */ +/* > The leading dimension of the array B. LDB >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > > 0: if INFO = i, U(i,i) is exactly zero. The factorization */ +/* > has been completed, but the factor U is exactly */ +/* > singular, so the solution could not be computed. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleGEsolve */ + +/* ===================================================================== */ +/* Subroutine */ int dgesv_(integer *n, integer *nrhs, doublereal *a, integer + *lda, integer *ipiv, doublereal *b, integer *ldb, integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, b_dim1, b_offset, i__1; + + /* Local variables */ + extern /* Subroutine */ int dgetrf_(integer *, integer *, doublereal *, + integer *, integer *, integer *), xerbla_(char *, integer *, + ftnlen), dgetrs_(char *, integer *, integer *, doublereal *, + integer *, integer *, doublereal *, integer *, integer *, ftnlen); + + +/* -- LAPACK driver routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --ipiv; + b_dim1 = *ldb; + b_offset = 1 + b_dim1; + b -= b_offset; + + /* Function Body */ + *info = 0; + if (*n < 0) { + *info = -1; + } else if (*nrhs < 0) { + *info = -2; + } else if (*lda < max(1,*n)) { + *info = -4; + } else if (*ldb < max(1,*n)) { + *info = -7; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DGESV ", &i__1, (ftnlen)6); + return 0; + } + +/* Compute the LU factorization of A. */ + + dgetrf_(n, n, &a[a_offset], lda, &ipiv[1], info); + if (*info == 0) { + +/* Solve the system A*X = B, overwriting B with X. */ + + dgetrs_((char *)"No transpose", n, nrhs, &a[a_offset], lda, &ipiv[1], &b[ + b_offset], ldb, info, (ftnlen)12); + } + return 0; + +/* End of DGESV */ + +} /* dgesv_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dgesvd.cpp b/lib/linalg/dgesvd.cpp new file mode 100644 index 0000000000..96fd8735b0 --- /dev/null +++ b/lib/linalg/dgesvd.cpp @@ -0,0 +1,4158 @@ +/* fortran/dgesvd.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__6 = 6; +static integer c__0 = 0; +static integer c__2 = 2; +static integer c_n1 = -1; +static doublereal c_b57 = 0.; +static integer c__1 = 1; +static doublereal c_b79 = 1.; + +/* > \brief DGESVD computes the singular value decomposition (SVD) for GE matrices */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DGESVD + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, */ +/* WORK, LWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER JOBU, JOBVT */ +/* INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), S( * ), U( LDU, * ), */ +/* $ VT( LDVT, * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DGESVD computes the singular value decomposition (SVD) of a real */ +/* > M-by-N matrix A, optionally computing the left and/or right singular */ +/* > vectors. The SVD is written */ +/* > */ +/* > A = U * SIGMA * transpose(V) */ +/* > */ +/* > where SIGMA is an M-by-N matrix which is zero except for its */ +/* > min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and */ +/* > V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA */ +/* > are the singular values of A; they are real and non-negative, and */ +/* > are returned in descending order. The first min(m,n) columns of */ +/* > U and V are the left and right singular vectors of A. */ +/* > */ +/* > Note that the routine returns V**T, not V. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] JOBU */ +/* > \verbatim */ +/* > JOBU is CHARACTER*1 */ +/* > Specifies options for computing all or part of the matrix U: */ +/* > = 'A': all M columns of U are returned in array U: */ +/* > = 'S': the first min(m,n) columns of U (the left singular */ +/* > vectors) are returned in the array U; */ +/* > = 'O': the first min(m,n) columns of U (the left singular */ +/* > vectors) are overwritten on the array A; */ +/* > = 'N': no columns of U (no left singular vectors) are */ +/* > computed. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] JOBVT */ +/* > \verbatim */ +/* > JOBVT is CHARACTER*1 */ +/* > Specifies options for computing all or part of the matrix */ +/* > V**T: */ +/* > = 'A': all N rows of V**T are returned in the array VT; */ +/* > = 'S': the first min(m,n) rows of V**T (the right singular */ +/* > vectors) are returned in the array VT; */ +/* > = 'O': the first min(m,n) rows of V**T (the right singular */ +/* > vectors) are overwritten on the array A; */ +/* > = 'N': no rows of V**T (no right singular vectors) are */ +/* > computed. */ +/* > */ +/* > JOBVT and JOBU cannot both be 'O'. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the input matrix A. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the input matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On entry, the M-by-N matrix A. */ +/* > On exit, */ +/* > if JOBU = 'O', A is overwritten with the first min(m,n) */ +/* > columns of U (the left singular vectors, */ +/* > stored columnwise); */ +/* > if JOBVT = 'O', A is overwritten with the first min(m,n) */ +/* > rows of V**T (the right singular vectors, */ +/* > stored rowwise); */ +/* > if JOBU .ne. 'O' and JOBVT .ne. 'O', the contents of A */ +/* > are destroyed. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] S */ +/* > \verbatim */ +/* > S is DOUBLE PRECISION array, dimension (min(M,N)) */ +/* > The singular values of A, sorted so that S(i) >= S(i+1). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] U */ +/* > \verbatim */ +/* > U is DOUBLE PRECISION array, dimension (LDU,UCOL) */ +/* > (LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'S'. */ +/* > If JOBU = 'A', U contains the M-by-M orthogonal matrix U; */ +/* > if JOBU = 'S', U contains the first min(m,n) columns of U */ +/* > (the left singular vectors, stored columnwise); */ +/* > if JOBU = 'N' or 'O', U is not referenced. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDU */ +/* > \verbatim */ +/* > LDU is INTEGER */ +/* > The leading dimension of the array U. LDU >= 1; if */ +/* > JOBU = 'S' or 'A', LDU >= M. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] VT */ +/* > \verbatim */ +/* > VT is DOUBLE PRECISION array, dimension (LDVT,N) */ +/* > If JOBVT = 'A', VT contains the N-by-N orthogonal matrix */ +/* > V**T; */ +/* > if JOBVT = 'S', VT contains the first min(m,n) rows of */ +/* > V**T (the right singular vectors, stored rowwise); */ +/* > if JOBVT = 'N' or 'O', VT is not referenced. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDVT */ +/* > \verbatim */ +/* > LDVT is INTEGER */ +/* > The leading dimension of the array VT. LDVT >= 1; if */ +/* > JOBVT = 'A', LDVT >= N; if JOBVT = 'S', LDVT >= min(M,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ +/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK; */ +/* > if INFO > 0, WORK(2:MIN(M,N)) contains the unconverged */ +/* > superdiagonal elements of an upper bidiagonal matrix B */ +/* > whose diagonal is in S (not necessarily sorted). B */ +/* > satisfies A = U * B * VT, so it has the same singular values */ +/* > as A, and singular vectors related by U and VT. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LWORK */ +/* > \verbatim */ +/* > LWORK is INTEGER */ +/* > The dimension of the array WORK. */ +/* > LWORK >= MAX(1,5*MIN(M,N)) for the paths (see comments inside code): */ +/* > - PATH 1 (M much larger than N, JOBU='N') */ +/* > - PATH 1t (N much larger than M, JOBVT='N') */ +/* > LWORK >= MAX(1,3*MIN(M,N) + MAX(M,N),5*MIN(M,N)) for the other paths */ +/* > For good performance, LWORK should generally be larger. */ +/* > */ +/* > If LWORK = -1, then a workspace query is assumed; the routine */ +/* > only calculates the optimal size of the WORK array, returns */ +/* > this value as the first entry of the WORK array, and no error */ +/* > message related to LWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit. */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ +/* > > 0: if DBDSQR did not converge, INFO specifies how many */ +/* > superdiagonals of an intermediate bidiagonal form B */ +/* > did not converge to zero. See the description of WORK */ +/* > above for details. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleGEsing */ + +/* ===================================================================== */ +/* Subroutine */ int dgesvd_(char *jobu, char *jobvt, integer *m, integer *n, + doublereal *a, integer *lda, doublereal *s, doublereal *u, integer * + ldu, doublereal *vt, integer *ldvt, doublereal *work, integer *lwork, + integer *info, ftnlen jobu_len, ftnlen jobvt_len) +{ + /* System generated locals */ + address a__1[2]; + integer a_dim1, a_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1[2], + i__2, i__3, i__4; + char ch__1[2]; + + /* Builtin functions */ + /* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen); + double sqrt(doublereal); + + /* Local variables */ + integer i__, ie, ir, iu, blk, ncu; + doublereal dum[1], eps; + integer nru, iscl; + doublereal anrm; + integer ierr, itau, ncvt, nrvt, lwork_dgebrd__, lwork_dgelqf__, + lwork_dgeqrf__; + extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); + extern logical lsame_(char *, char *, ftnlen, ftnlen); + integer chunk, minmn, wrkbl, itaup, itauq, mnthr, iwork; + logical wntua, wntva, wntun, wntuo, wntvn, wntvo, wntus, wntvs; + extern /* Subroutine */ int dgebrd_(integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, integer *, integer *); + extern doublereal dlamch_(char *, ftnlen), dlange_(char *, integer *, + integer *, doublereal *, integer *, doublereal *, ftnlen); + integer bdspac; + extern /* Subroutine */ int dgelqf_(integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, integer *), + dlascl_(char *, integer *, integer *, doublereal *, doublereal *, + integer *, integer *, doublereal *, integer *, integer *, ftnlen), + dgeqrf_(integer *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, integer *), dlacpy_(char *, + integer *, integer *, doublereal *, integer *, doublereal *, + integer *, ftnlen), dlaset_(char *, integer *, integer *, + doublereal *, doublereal *, doublereal *, integer *, ftnlen), + dbdsqr_(char *, integer *, integer *, integer *, integer *, + doublereal *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, integer *, doublereal *, integer *, + ftnlen), dorgbr_(char *, integer *, integer *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, + integer *, ftnlen); + doublereal bignum; + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dormbr_(char *, char *, char *, integer *, + integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, doublereal *, integer *, integer *, + ftnlen, ftnlen, ftnlen), dorglq_(integer *, integer *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, + integer *), dorgqr_(integer *, integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, integer *); + integer ldwrkr, minwrk, ldwrku, maxwrk; + doublereal smlnum; + logical lquery, wntuas, wntvas; + integer lwork_dorgbr_p__, lwork_dorgbr_q__, lwork_dorglq_m__, + lwork_dorglq_n__, lwork_dorgqr_m__, lwork_dorgqr_n__; + + +/* -- LAPACK driver routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Local Arrays .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --s; + u_dim1 = *ldu; + u_offset = 1 + u_dim1; + u -= u_offset; + vt_dim1 = *ldvt; + vt_offset = 1 + vt_dim1; + vt -= vt_offset; + --work; + + /* Function Body */ + *info = 0; + minmn = min(*m,*n); + wntua = lsame_(jobu, (char *)"A", (ftnlen)1, (ftnlen)1); + wntus = lsame_(jobu, (char *)"S", (ftnlen)1, (ftnlen)1); + wntuas = wntua || wntus; + wntuo = lsame_(jobu, (char *)"O", (ftnlen)1, (ftnlen)1); + wntun = lsame_(jobu, (char *)"N", (ftnlen)1, (ftnlen)1); + wntva = lsame_(jobvt, (char *)"A", (ftnlen)1, (ftnlen)1); + wntvs = lsame_(jobvt, (char *)"S", (ftnlen)1, (ftnlen)1); + wntvas = wntva || wntvs; + wntvo = lsame_(jobvt, (char *)"O", (ftnlen)1, (ftnlen)1); + wntvn = lsame_(jobvt, (char *)"N", (ftnlen)1, (ftnlen)1); + lquery = *lwork == -1; + + if (! (wntua || wntus || wntuo || wntun)) { + *info = -1; + } else if (! (wntva || wntvs || wntvo || wntvn) || wntvo && wntuo) { + *info = -2; + } else if (*m < 0) { + *info = -3; + } else if (*n < 0) { + *info = -4; + } else if (*lda < max(1,*m)) { + *info = -6; + } else if (*ldu < 1 || wntuas && *ldu < *m) { + *info = -9; + } else if (*ldvt < 1 || wntva && *ldvt < *n || wntvs && *ldvt < minmn) { + *info = -11; + } + +/* Compute workspace */ +/* (Note: Comments in the code beginning (char *)"Workspace:" describe the */ +/* minimal amount of workspace needed at that point in the code, */ +/* as well as the preferred amount for good performance. */ +/* NB refers to the optimal block size for the immediately */ +/* following subroutine, as returned by ILAENV.) */ + + if (*info == 0) { + minwrk = 1; + maxwrk = 1; + if (*m >= *n && minmn > 0) { + +/* Compute space needed for DBDSQR */ + +/* Writing concatenation */ + i__1[0] = 1, a__1[0] = jobu; + i__1[1] = 1, a__1[1] = jobvt; + s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); + mnthr = ilaenv_(&c__6, (char *)"DGESVD", ch__1, m, n, &c__0, &c__0, ( + ftnlen)6, (ftnlen)2); + bdspac = *n * 5; +/* Compute space needed for DGEQRF */ + dgeqrf_(m, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr); + lwork_dgeqrf__ = (integer) dum[0]; +/* Compute space needed for DORGQR */ + dorgqr_(m, n, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr); + lwork_dorgqr_n__ = (integer) dum[0]; + dorgqr_(m, m, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr); + lwork_dorgqr_m__ = (integer) dum[0]; +/* Compute space needed for DGEBRD */ + dgebrd_(n, n, &a[a_offset], lda, &s[1], dum, dum, dum, dum, &c_n1, + &ierr); + lwork_dgebrd__ = (integer) dum[0]; +/* Compute space needed for DORGBR P */ + dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr, ( + ftnlen)1); + lwork_dorgbr_p__ = (integer) dum[0]; +/* Compute space needed for DORGBR Q */ + dorgbr_((char *)"Q", n, n, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr, ( + ftnlen)1); + lwork_dorgbr_q__ = (integer) dum[0]; + + if (*m >= mnthr) { + if (wntun) { + +/* Path 1 (M much larger than N, JOBU='N') */ + + maxwrk = *n + lwork_dgeqrf__; +/* Computing MAX */ + i__2 = maxwrk, i__3 = *n * 3 + lwork_dgebrd__; + maxwrk = max(i__2,i__3); + if (wntvo || wntvas) { +/* Computing MAX */ + i__2 = maxwrk, i__3 = *n * 3 + lwork_dorgbr_p__; + maxwrk = max(i__2,i__3); + } + maxwrk = max(maxwrk,bdspac); +/* Computing MAX */ + i__2 = *n << 2; + minwrk = max(i__2,bdspac); + } else if (wntuo && wntvn) { + +/* Path 2 (M much larger than N, JOBU='O', JOBVT='N') */ + + wrkbl = *n + lwork_dgeqrf__; +/* Computing MAX */ + i__2 = wrkbl, i__3 = *n + lwork_dorgqr_n__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__; + wrkbl = max(i__2,i__3); + wrkbl = max(wrkbl,bdspac); +/* Computing MAX */ + i__2 = *n * *n + wrkbl, i__3 = *n * *n + *m * *n + *n; + maxwrk = max(i__2,i__3); +/* Computing MAX */ + i__2 = *n * 3 + *m; + minwrk = max(i__2,bdspac); + } else if (wntuo && wntvas) { + +/* Path 3 (M much larger than N, JOBU='O', JOBVT='S' or */ +/* 'A') */ + + wrkbl = *n + lwork_dgeqrf__; +/* Computing MAX */ + i__2 = wrkbl, i__3 = *n + lwork_dorgqr_n__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_p__; + wrkbl = max(i__2,i__3); + wrkbl = max(wrkbl,bdspac); +/* Computing MAX */ + i__2 = *n * *n + wrkbl, i__3 = *n * *n + *m * *n + *n; + maxwrk = max(i__2,i__3); +/* Computing MAX */ + i__2 = *n * 3 + *m; + minwrk = max(i__2,bdspac); + } else if (wntus && wntvn) { + +/* Path 4 (M much larger than N, JOBU='S', JOBVT='N') */ + + wrkbl = *n + lwork_dgeqrf__; +/* Computing MAX */ + i__2 = wrkbl, i__3 = *n + lwork_dorgqr_n__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__; + wrkbl = max(i__2,i__3); + wrkbl = max(wrkbl,bdspac); + maxwrk = *n * *n + wrkbl; +/* Computing MAX */ + i__2 = *n * 3 + *m; + minwrk = max(i__2,bdspac); + } else if (wntus && wntvo) { + +/* Path 5 (M much larger than N, JOBU='S', JOBVT='O') */ + + wrkbl = *n + lwork_dgeqrf__; +/* Computing MAX */ + i__2 = wrkbl, i__3 = *n + lwork_dorgqr_n__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_p__; + wrkbl = max(i__2,i__3); + wrkbl = max(wrkbl,bdspac); + maxwrk = (*n << 1) * *n + wrkbl; +/* Computing MAX */ + i__2 = *n * 3 + *m; + minwrk = max(i__2,bdspac); + } else if (wntus && wntvas) { + +/* Path 6 (M much larger than N, JOBU='S', JOBVT='S' or */ +/* 'A') */ + + wrkbl = *n + lwork_dgeqrf__; +/* Computing MAX */ + i__2 = wrkbl, i__3 = *n + lwork_dorgqr_n__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_p__; + wrkbl = max(i__2,i__3); + wrkbl = max(wrkbl,bdspac); + maxwrk = *n * *n + wrkbl; +/* Computing MAX */ + i__2 = *n * 3 + *m; + minwrk = max(i__2,bdspac); + } else if (wntua && wntvn) { + +/* Path 7 (M much larger than N, JOBU='A', JOBVT='N') */ + + wrkbl = *n + lwork_dgeqrf__; +/* Computing MAX */ + i__2 = wrkbl, i__3 = *n + lwork_dorgqr_m__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__; + wrkbl = max(i__2,i__3); + wrkbl = max(wrkbl,bdspac); + maxwrk = *n * *n + wrkbl; +/* Computing MAX */ + i__2 = *n * 3 + *m; + minwrk = max(i__2,bdspac); + } else if (wntua && wntvo) { + +/* Path 8 (M much larger than N, JOBU='A', JOBVT='O') */ + + wrkbl = *n + lwork_dgeqrf__; +/* Computing MAX */ + i__2 = wrkbl, i__3 = *n + lwork_dorgqr_m__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_p__; + wrkbl = max(i__2,i__3); + wrkbl = max(wrkbl,bdspac); + maxwrk = (*n << 1) * *n + wrkbl; +/* Computing MAX */ + i__2 = *n * 3 + *m; + minwrk = max(i__2,bdspac); + } else if (wntua && wntvas) { + +/* Path 9 (M much larger than N, JOBU='A', JOBVT='S' or */ +/* 'A') */ + + wrkbl = *n + lwork_dgeqrf__; +/* Computing MAX */ + i__2 = wrkbl, i__3 = *n + lwork_dorgqr_m__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_p__; + wrkbl = max(i__2,i__3); + wrkbl = max(wrkbl,bdspac); + maxwrk = *n * *n + wrkbl; +/* Computing MAX */ + i__2 = *n * 3 + *m; + minwrk = max(i__2,bdspac); + } + } else { + +/* Path 10 (M at least N, but not much larger) */ + + dgebrd_(m, n, &a[a_offset], lda, &s[1], dum, dum, dum, dum, & + c_n1, &ierr); + lwork_dgebrd__ = (integer) dum[0]; + maxwrk = *n * 3 + lwork_dgebrd__; + if (wntus || wntuo) { + dorgbr_((char *)"Q", m, n, n, &a[a_offset], lda, dum, dum, &c_n1, + &ierr, (ftnlen)1); + lwork_dorgbr_q__ = (integer) dum[0]; +/* Computing MAX */ + i__2 = maxwrk, i__3 = *n * 3 + lwork_dorgbr_q__; + maxwrk = max(i__2,i__3); + } + if (wntua) { + dorgbr_((char *)"Q", m, m, n, &a[a_offset], lda, dum, dum, &c_n1, + &ierr, (ftnlen)1); + lwork_dorgbr_q__ = (integer) dum[0]; +/* Computing MAX */ + i__2 = maxwrk, i__3 = *n * 3 + lwork_dorgbr_q__; + maxwrk = max(i__2,i__3); + } + if (! wntvn) { +/* Computing MAX */ + i__2 = maxwrk, i__3 = *n * 3 + lwork_dorgbr_p__; + maxwrk = max(i__2,i__3); + } + maxwrk = max(maxwrk,bdspac); +/* Computing MAX */ + i__2 = *n * 3 + *m; + minwrk = max(i__2,bdspac); + } + } else if (minmn > 0) { + +/* Compute space needed for DBDSQR */ + +/* Writing concatenation */ + i__1[0] = 1, a__1[0] = jobu; + i__1[1] = 1, a__1[1] = jobvt; + s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); + mnthr = ilaenv_(&c__6, (char *)"DGESVD", ch__1, m, n, &c__0, &c__0, ( + ftnlen)6, (ftnlen)2); + bdspac = *m * 5; +/* Compute space needed for DGELQF */ + dgelqf_(m, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr); + lwork_dgelqf__ = (integer) dum[0]; +/* Compute space needed for DORGLQ */ + dorglq_(n, n, m, dum, n, dum, dum, &c_n1, &ierr); + lwork_dorglq_n__ = (integer) dum[0]; + dorglq_(m, n, m, &a[a_offset], lda, dum, dum, &c_n1, &ierr); + lwork_dorglq_m__ = (integer) dum[0]; +/* Compute space needed for DGEBRD */ + dgebrd_(m, m, &a[a_offset], lda, &s[1], dum, dum, dum, dum, &c_n1, + &ierr); + lwork_dgebrd__ = (integer) dum[0]; +/* Compute space needed for DORGBR P */ + dorgbr_((char *)"P", m, m, m, &a[a_offset], n, dum, dum, &c_n1, &ierr, ( + ftnlen)1); + lwork_dorgbr_p__ = (integer) dum[0]; +/* Compute space needed for DORGBR Q */ + dorgbr_((char *)"Q", m, m, m, &a[a_offset], n, dum, dum, &c_n1, &ierr, ( + ftnlen)1); + lwork_dorgbr_q__ = (integer) dum[0]; + if (*n >= mnthr) { + if (wntvn) { + +/* Path 1t(N much larger than M, JOBVT='N') */ + + maxwrk = *m + lwork_dgelqf__; +/* Computing MAX */ + i__2 = maxwrk, i__3 = *m * 3 + lwork_dgebrd__; + maxwrk = max(i__2,i__3); + if (wntuo || wntuas) { +/* Computing MAX */ + i__2 = maxwrk, i__3 = *m * 3 + lwork_dorgbr_q__; + maxwrk = max(i__2,i__3); + } + maxwrk = max(maxwrk,bdspac); +/* Computing MAX */ + i__2 = *m << 2; + minwrk = max(i__2,bdspac); + } else if (wntvo && wntun) { + +/* Path 2t(N much larger than M, JOBU='N', JOBVT='O') */ + + wrkbl = *m + lwork_dgelqf__; +/* Computing MAX */ + i__2 = wrkbl, i__3 = *m + lwork_dorglq_m__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__; + wrkbl = max(i__2,i__3); + wrkbl = max(wrkbl,bdspac); +/* Computing MAX */ + i__2 = *m * *m + wrkbl, i__3 = *m * *m + *m * *n + *m; + maxwrk = max(i__2,i__3); +/* Computing MAX */ + i__2 = *m * 3 + *n; + minwrk = max(i__2,bdspac); + } else if (wntvo && wntuas) { + +/* Path 3t(N much larger than M, JOBU='S' or 'A', */ +/* JOBVT='O') */ + + wrkbl = *m + lwork_dgelqf__; +/* Computing MAX */ + i__2 = wrkbl, i__3 = *m + lwork_dorglq_m__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_q__; + wrkbl = max(i__2,i__3); + wrkbl = max(wrkbl,bdspac); +/* Computing MAX */ + i__2 = *m * *m + wrkbl, i__3 = *m * *m + *m * *n + *m; + maxwrk = max(i__2,i__3); +/* Computing MAX */ + i__2 = *m * 3 + *n; + minwrk = max(i__2,bdspac); + } else if (wntvs && wntun) { + +/* Path 4t(N much larger than M, JOBU='N', JOBVT='S') */ + + wrkbl = *m + lwork_dgelqf__; +/* Computing MAX */ + i__2 = wrkbl, i__3 = *m + lwork_dorglq_m__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__; + wrkbl = max(i__2,i__3); + wrkbl = max(wrkbl,bdspac); + maxwrk = *m * *m + wrkbl; +/* Computing MAX */ + i__2 = *m * 3 + *n; + minwrk = max(i__2,bdspac); + } else if (wntvs && wntuo) { + +/* Path 5t(N much larger than M, JOBU='O', JOBVT='S') */ + + wrkbl = *m + lwork_dgelqf__; +/* Computing MAX */ + i__2 = wrkbl, i__3 = *m + lwork_dorglq_m__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_q__; + wrkbl = max(i__2,i__3); + wrkbl = max(wrkbl,bdspac); + maxwrk = (*m << 1) * *m + wrkbl; +/* Computing MAX */ + i__2 = *m * 3 + *n; + minwrk = max(i__2,bdspac); + } else if (wntvs && wntuas) { + +/* Path 6t(N much larger than M, JOBU='S' or 'A', */ +/* JOBVT='S') */ + + wrkbl = *m + lwork_dgelqf__; +/* Computing MAX */ + i__2 = wrkbl, i__3 = *m + lwork_dorglq_m__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_q__; + wrkbl = max(i__2,i__3); + wrkbl = max(wrkbl,bdspac); + maxwrk = *m * *m + wrkbl; +/* Computing MAX */ + i__2 = *m * 3 + *n; + minwrk = max(i__2,bdspac); + } else if (wntva && wntun) { + +/* Path 7t(N much larger than M, JOBU='N', JOBVT='A') */ + + wrkbl = *m + lwork_dgelqf__; +/* Computing MAX */ + i__2 = wrkbl, i__3 = *m + lwork_dorglq_n__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__; + wrkbl = max(i__2,i__3); + wrkbl = max(wrkbl,bdspac); + maxwrk = *m * *m + wrkbl; +/* Computing MAX */ + i__2 = *m * 3 + *n; + minwrk = max(i__2,bdspac); + } else if (wntva && wntuo) { + +/* Path 8t(N much larger than M, JOBU='O', JOBVT='A') */ + + wrkbl = *m + lwork_dgelqf__; +/* Computing MAX */ + i__2 = wrkbl, i__3 = *m + lwork_dorglq_n__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_q__; + wrkbl = max(i__2,i__3); + wrkbl = max(wrkbl,bdspac); + maxwrk = (*m << 1) * *m + wrkbl; +/* Computing MAX */ + i__2 = *m * 3 + *n; + minwrk = max(i__2,bdspac); + } else if (wntva && wntuas) { + +/* Path 9t(N much larger than M, JOBU='S' or 'A', */ +/* JOBVT='A') */ + + wrkbl = *m + lwork_dgelqf__; +/* Computing MAX */ + i__2 = wrkbl, i__3 = *m + lwork_dorglq_n__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__; + wrkbl = max(i__2,i__3); +/* Computing MAX */ + i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_q__; + wrkbl = max(i__2,i__3); + wrkbl = max(wrkbl,bdspac); + maxwrk = *m * *m + wrkbl; +/* Computing MAX */ + i__2 = *m * 3 + *n; + minwrk = max(i__2,bdspac); + } + } else { + +/* Path 10t(N greater than M, but not much larger) */ + + dgebrd_(m, n, &a[a_offset], lda, &s[1], dum, dum, dum, dum, & + c_n1, &ierr); + lwork_dgebrd__ = (integer) dum[0]; + maxwrk = *m * 3 + lwork_dgebrd__; + if (wntvs || wntvo) { +/* Compute space needed for DORGBR P */ + dorgbr_((char *)"P", m, n, m, &a[a_offset], n, dum, dum, &c_n1, & + ierr, (ftnlen)1); + lwork_dorgbr_p__ = (integer) dum[0]; +/* Computing MAX */ + i__2 = maxwrk, i__3 = *m * 3 + lwork_dorgbr_p__; + maxwrk = max(i__2,i__3); + } + if (wntva) { + dorgbr_((char *)"P", n, n, m, &a[a_offset], n, dum, dum, &c_n1, & + ierr, (ftnlen)1); + lwork_dorgbr_p__ = (integer) dum[0]; +/* Computing MAX */ + i__2 = maxwrk, i__3 = *m * 3 + lwork_dorgbr_p__; + maxwrk = max(i__2,i__3); + } + if (! wntun) { +/* Computing MAX */ + i__2 = maxwrk, i__3 = *m * 3 + lwork_dorgbr_q__; + maxwrk = max(i__2,i__3); + } + maxwrk = max(maxwrk,bdspac); +/* Computing MAX */ + i__2 = *m * 3 + *n; + minwrk = max(i__2,bdspac); + } + } + maxwrk = max(maxwrk,minwrk); + work[1] = (doublereal) maxwrk; + + if (*lwork < minwrk && ! lquery) { + *info = -13; + } + } + + if (*info != 0) { + i__2 = -(*info); + xerbla_((char *)"DGESVD", &i__2, (ftnlen)6); + return 0; + } else if (lquery) { + return 0; + } + +/* Quick return if possible */ + + if (*m == 0 || *n == 0) { + return 0; + } + +/* Get machine constants */ + + eps = dlamch_((char *)"P", (ftnlen)1); + smlnum = sqrt(dlamch_((char *)"S", (ftnlen)1)) / eps; + bignum = 1. / smlnum; + +/* Scale A if max element outside range [SMLNUM,BIGNUM] */ + + anrm = dlange_((char *)"M", m, n, &a[a_offset], lda, dum, (ftnlen)1); + iscl = 0; + if (anrm > 0. && anrm < smlnum) { + iscl = 1; + dlascl_((char *)"G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, & + ierr, (ftnlen)1); + } else if (anrm > bignum) { + iscl = 1; + dlascl_((char *)"G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, & + ierr, (ftnlen)1); + } + + if (*m >= *n) { + +/* A has at least as many rows as columns. If A has sufficiently */ +/* more rows than columns, first reduce using the QR */ +/* decomposition (if sufficient workspace available) */ + + if (*m >= mnthr) { + + if (wntun) { + +/* Path 1 (M much larger than N, JOBU='N') */ +/* No left singular vectors to be computed */ + + itau = 1; + iwork = itau + *n; + +/* Compute A=Q*R */ +/* (Workspace: need 2*N, prefer N + N*NB) */ + + i__2 = *lwork - iwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], & + i__2, &ierr); + +/* Zero out below R */ + + if (*n > 1) { + i__2 = *n - 1; + i__3 = *n - 1; + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &a[a_dim1 + 2], + lda, (ftnlen)1); + } + ie = 1; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; + +/* Bidiagonalize R in A */ +/* (Workspace: need 4*N, prefer 3*N + 2*N*NB) */ + + i__2 = *lwork - iwork + 1; + dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &work[ + itauq], &work[itaup], &work[iwork], &i__2, &ierr); + ncvt = 0; + if (wntvo || wntvas) { + +/* If right singular vectors desired, generate P'. */ +/* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, &work[itaup], & + work[iwork], &i__2, &ierr, (ftnlen)1); + ncvt = *n; + } + iwork = ie + *n; + +/* Perform bidiagonal QR iteration, computing right */ +/* singular vectors of A in A if desired */ +/* (Workspace: need BDSPAC) */ + + dbdsqr_((char *)"U", n, &ncvt, &c__0, &c__0, &s[1], &work[ie], &a[ + a_offset], lda, dum, &c__1, dum, &c__1, &work[iwork], + info, (ftnlen)1); + +/* If right singular vectors desired in VT, copy them there */ + + if (wntvas) { + dlacpy_((char *)"F", n, n, &a[a_offset], lda, &vt[vt_offset], + ldvt, (ftnlen)1); + } + + } else if (wntuo && wntvn) { + +/* Path 2 (M much larger than N, JOBU='O', JOBVT='N') */ +/* N left singular vectors to be overwritten on A and */ +/* no right singular vectors to be computed */ + +/* Computing MAX */ + i__2 = *n << 2; + if (*lwork >= *n * *n + max(i__2,bdspac)) { + +/* Sufficient workspace for a fast algorithm */ + + ir = 1; +/* Computing MAX */ + i__2 = wrkbl, i__3 = *lda * *n + *n; + if (*lwork >= max(i__2,i__3) + *lda * *n) { + +/* WORK(IU) is LDA by N, WORK(IR) is LDA by N */ + + ldwrku = *lda; + ldwrkr = *lda; + } else /* if(complicated condition) */ { +/* Computing MAX */ + i__2 = wrkbl, i__3 = *lda * *n + *n; + if (*lwork >= max(i__2,i__3) + *n * *n) { + +/* WORK(IU) is LDA by N, WORK(IR) is N by N */ + + ldwrku = *lda; + ldwrkr = *n; + } else { + +/* WORK(IU) is LDWRKU by N, WORK(IR) is N by N */ + + ldwrku = (*lwork - *n * *n - *n) / *n; + ldwrkr = *n; + } + } + itau = ir + ldwrkr * *n; + iwork = itau + *n; + +/* Compute A=Q*R */ +/* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */ + + i__2 = *lwork - iwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork] + , &i__2, &ierr); + +/* Copy R to WORK(IR) and zero out below it */ + + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr, + (ftnlen)1); + i__2 = *n - 1; + i__3 = *n - 1; + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[ir + 1], + &ldwrkr, (ftnlen)1); + +/* Generate Q in A */ +/* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */ + + i__2 = *lwork - iwork + 1; + dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; + +/* Bidiagonalize R in WORK(IR) */ +/* (Workspace: need N*N + 4*N, prefer N*N + 3*N + 2*N*NB) */ + + i__2 = *lwork - iwork + 1; + dgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], &work[ + itauq], &work[itaup], &work[iwork], &i__2, &ierr); + +/* Generate left vectors bidiagonalizing R */ +/* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", n, n, n, &work[ir], &ldwrkr, &work[itauq], & + work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *n; + +/* Perform bidiagonal QR iteration, computing left */ +/* singular vectors of R in WORK(IR) */ +/* (Workspace: need N*N + BDSPAC) */ + + dbdsqr_((char *)"U", n, &c__0, n, &c__0, &s[1], &work[ie], dum, & + c__1, &work[ir], &ldwrkr, dum, &c__1, &work[iwork] + , info, (ftnlen)1); + iu = ie + *n; + +/* Multiply Q in A by left singular vectors of R in */ +/* WORK(IR), storing result in WORK(IU) and copying to A */ +/* (Workspace: need N*N + 2*N, prefer N*N + M*N + N) */ + + i__2 = *m; + i__3 = ldwrku; + for (i__ = 1; i__3 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += + i__3) { +/* Computing MIN */ + i__4 = *m - i__ + 1; + chunk = min(i__4,ldwrku); + dgemm_((char *)"N", (char *)"N", &chunk, n, n, &c_b79, &a[i__ + + a_dim1], lda, &work[ir], &ldwrkr, &c_b57, & + work[iu], &ldwrku, (ftnlen)1, (ftnlen)1); + dlacpy_((char *)"F", &chunk, n, &work[iu], &ldwrku, &a[i__ + + a_dim1], lda, (ftnlen)1); +/* L10: */ + } + + } else { + +/* Insufficient workspace for a fast algorithm */ + + ie = 1; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; + +/* Bidiagonalize A */ +/* (Workspace: need 3*N + M, prefer 3*N + (M + N)*NB) */ + + i__3 = *lwork - iwork + 1; + dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[ + itauq], &work[itaup], &work[iwork], &i__3, &ierr); + +/* Generate left vectors bidiagonalizing A */ +/* (Workspace: need 4*N, prefer 3*N + N*NB) */ + + i__3 = *lwork - iwork + 1; + dorgbr_((char *)"Q", m, n, n, &a[a_offset], lda, &work[itauq], & + work[iwork], &i__3, &ierr, (ftnlen)1); + iwork = ie + *n; + +/* Perform bidiagonal QR iteration, computing left */ +/* singular vectors of A in A */ +/* (Workspace: need BDSPAC) */ + + dbdsqr_((char *)"U", n, &c__0, m, &c__0, &s[1], &work[ie], dum, & + c__1, &a[a_offset], lda, dum, &c__1, &work[iwork], + info, (ftnlen)1); + + } + + } else if (wntuo && wntvas) { + +/* Path 3 (M much larger than N, JOBU='O', JOBVT='S' or 'A') */ +/* N left singular vectors to be overwritten on A and */ +/* N right singular vectors to be computed in VT */ + +/* Computing MAX */ + i__3 = *n << 2; + if (*lwork >= *n * *n + max(i__3,bdspac)) { + +/* Sufficient workspace for a fast algorithm */ + + ir = 1; +/* Computing MAX */ + i__3 = wrkbl, i__2 = *lda * *n + *n; + if (*lwork >= max(i__3,i__2) + *lda * *n) { + +/* WORK(IU) is LDA by N and WORK(IR) is LDA by N */ + + ldwrku = *lda; + ldwrkr = *lda; + } else /* if(complicated condition) */ { +/* Computing MAX */ + i__3 = wrkbl, i__2 = *lda * *n + *n; + if (*lwork >= max(i__3,i__2) + *n * *n) { + +/* WORK(IU) is LDA by N and WORK(IR) is N by N */ + + ldwrku = *lda; + ldwrkr = *n; + } else { + +/* WORK(IU) is LDWRKU by N and WORK(IR) is N by N */ + + ldwrku = (*lwork - *n * *n - *n) / *n; + ldwrkr = *n; + } + } + itau = ir + ldwrkr * *n; + iwork = itau + *n; + +/* Compute A=Q*R */ +/* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */ + + i__3 = *lwork - iwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork] + , &i__3, &ierr); + +/* Copy R to VT, zeroing out below it */ + + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &vt[vt_offset], + ldvt, (ftnlen)1); + if (*n > 1) { + i__3 = *n - 1; + i__2 = *n - 1; + dlaset_((char *)"L", &i__3, &i__2, &c_b57, &c_b57, &vt[ + vt_dim1 + 2], ldvt, (ftnlen)1); + } + +/* Generate Q in A */ +/* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */ + + i__3 = *lwork - iwork + 1; + dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__3, &ierr); + ie = itau; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; + +/* Bidiagonalize R in VT, copying result to WORK(IR) */ +/* (Workspace: need N*N + 4*N, prefer N*N + 3*N + 2*N*NB) */ + + i__3 = *lwork - iwork + 1; + dgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], &i__3, & + ierr); + dlacpy_((char *)"L", n, n, &vt[vt_offset], ldvt, &work[ir], & + ldwrkr, (ftnlen)1); + +/* Generate left vectors bidiagonalizing R in WORK(IR) */ +/* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB) */ + + i__3 = *lwork - iwork + 1; + dorgbr_((char *)"Q", n, n, n, &work[ir], &ldwrkr, &work[itauq], & + work[iwork], &i__3, &ierr, (ftnlen)1); + +/* Generate right vectors bidiagonalizing R in VT */ +/* (Workspace: need N*N + 4*N-1, prefer N*N + 3*N + (N-1)*NB) */ + + i__3 = *lwork - iwork + 1; + dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], + &work[iwork], &i__3, &ierr, (ftnlen)1); + iwork = ie + *n; + +/* Perform bidiagonal QR iteration, computing left */ +/* singular vectors of R in WORK(IR) and computing right */ +/* singular vectors of R in VT */ +/* (Workspace: need N*N + BDSPAC) */ + + dbdsqr_((char *)"U", n, n, n, &c__0, &s[1], &work[ie], &vt[ + vt_offset], ldvt, &work[ir], &ldwrkr, dum, &c__1, + &work[iwork], info, (ftnlen)1); + iu = ie + *n; + +/* Multiply Q in A by left singular vectors of R in */ +/* WORK(IR), storing result in WORK(IU) and copying to A */ +/* (Workspace: need N*N + 2*N, prefer N*N + M*N + N) */ + + i__3 = *m; + i__2 = ldwrku; + for (i__ = 1; i__2 < 0 ? i__ >= i__3 : i__ <= i__3; i__ += + i__2) { +/* Computing MIN */ + i__4 = *m - i__ + 1; + chunk = min(i__4,ldwrku); + dgemm_((char *)"N", (char *)"N", &chunk, n, n, &c_b79, &a[i__ + + a_dim1], lda, &work[ir], &ldwrkr, &c_b57, & + work[iu], &ldwrku, (ftnlen)1, (ftnlen)1); + dlacpy_((char *)"F", &chunk, n, &work[iu], &ldwrku, &a[i__ + + a_dim1], lda, (ftnlen)1); +/* L20: */ + } + + } else { + +/* Insufficient workspace for a fast algorithm */ + + itau = 1; + iwork = itau + *n; + +/* Compute A=Q*R */ +/* (Workspace: need 2*N, prefer N + N*NB) */ + + i__2 = *lwork - iwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork] + , &i__2, &ierr); + +/* Copy R to VT, zeroing out below it */ + + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &vt[vt_offset], + ldvt, (ftnlen)1); + if (*n > 1) { + i__2 = *n - 1; + i__3 = *n - 1; + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &vt[ + vt_dim1 + 2], ldvt, (ftnlen)1); + } + +/* Generate Q in A */ +/* (Workspace: need 2*N, prefer N + N*NB) */ + + i__2 = *lwork - iwork + 1; + dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; + +/* Bidiagonalize R in VT */ +/* (Workspace: need 4*N, prefer 3*N + 2*N*NB) */ + + i__2 = *lwork - iwork + 1; + dgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], &i__2, & + ierr); + +/* Multiply Q in A by left vectors bidiagonalizing R */ +/* (Workspace: need 3*N + M, prefer 3*N + M*NB) */ + + i__2 = *lwork - iwork + 1; + dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &vt[vt_offset], ldvt, & + work[itauq], &a[a_offset], lda, &work[iwork], & + i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen)1); + +/* Generate right vectors bidiagonalizing R in VT */ +/* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], + &work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *n; + +/* Perform bidiagonal QR iteration, computing left */ +/* singular vectors of A in A and computing right */ +/* singular vectors of A in VT */ +/* (Workspace: need BDSPAC) */ + + dbdsqr_((char *)"U", n, n, m, &c__0, &s[1], &work[ie], &vt[ + vt_offset], ldvt, &a[a_offset], lda, dum, &c__1, & + work[iwork], info, (ftnlen)1); + + } + + } else if (wntus) { + + if (wntvn) { + +/* Path 4 (M much larger than N, JOBU='S', JOBVT='N') */ +/* N left singular vectors to be computed in U and */ +/* no right singular vectors to be computed */ + +/* Computing MAX */ + i__2 = *n << 2; + if (*lwork >= *n * *n + max(i__2,bdspac)) { + +/* Sufficient workspace for a fast algorithm */ + + ir = 1; + if (*lwork >= wrkbl + *lda * *n) { + +/* WORK(IR) is LDA by N */ + + ldwrkr = *lda; + } else { + +/* WORK(IR) is N by N */ + + ldwrkr = *n; + } + itau = ir + ldwrkr * *n; + iwork = itau + *n; + +/* Compute A=Q*R */ +/* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */ + + i__2 = *lwork - iwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + +/* Copy R to WORK(IR), zeroing out below it */ + + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[ir], & + ldwrkr, (ftnlen)1); + i__2 = *n - 1; + i__3 = *n - 1; + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[ir + + 1], &ldwrkr, (ftnlen)1); + +/* Generate Q in A */ +/* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */ + + i__2 = *lwork - iwork + 1; + dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], & + work[iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; + +/* Bidiagonalize R in WORK(IR) */ +/* (Workspace: need N*N + 4*N, prefer N*N + 3*N + 2*N*NB) */ + + i__2 = *lwork - iwork + 1; + dgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); + +/* Generate left vectors bidiagonalizing R in WORK(IR) */ +/* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", n, n, n, &work[ir], &ldwrkr, &work[itauq] + , &work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *n; + +/* Perform bidiagonal QR iteration, computing left */ +/* singular vectors of R in WORK(IR) */ +/* (Workspace: need N*N + BDSPAC) */ + + dbdsqr_((char *)"U", n, &c__0, n, &c__0, &s[1], &work[ie], + dum, &c__1, &work[ir], &ldwrkr, dum, &c__1, & + work[iwork], info, (ftnlen)1); + +/* Multiply Q in A by left singular vectors of R in */ +/* WORK(IR), storing result in U */ +/* (Workspace: need N*N) */ + + dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &a[a_offset], lda, & + work[ir], &ldwrkr, &c_b57, &u[u_offset], ldu, + (ftnlen)1, (ftnlen)1); + + } else { + +/* Insufficient workspace for a fast algorithm */ + + itau = 1; + iwork = itau + *n; + +/* Compute A=Q*R, copying result to U */ +/* (Workspace: need 2*N, prefer N + N*NB) */ + + i__2 = *lwork - iwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], + ldu, (ftnlen)1); + +/* Generate Q in U */ +/* (Workspace: need 2*N, prefer N + N*NB) */ + + i__2 = *lwork - iwork + 1; + dorgqr_(m, n, n, &u[u_offset], ldu, &work[itau], & + work[iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; + +/* Zero out below R in A */ + + if (*n > 1) { + i__2 = *n - 1; + i__3 = *n - 1; + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &a[ + a_dim1 + 2], lda, (ftnlen)1); + } + +/* Bidiagonalize R in A */ +/* (Workspace: need 4*N, prefer 3*N + 2*N*NB) */ + + i__2 = *lwork - iwork + 1; + dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); + +/* Multiply Q in U by left vectors bidiagonalizing R */ +/* (Workspace: need 3*N + M, prefer 3*N + M*NB) */ + + i__2 = *lwork - iwork + 1; + dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &a[a_offset], lda, & + work[itauq], &u[u_offset], ldu, &work[iwork], + &i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen)1) + ; + iwork = ie + *n; + +/* Perform bidiagonal QR iteration, computing left */ +/* singular vectors of A in U */ +/* (Workspace: need BDSPAC) */ + + dbdsqr_((char *)"U", n, &c__0, m, &c__0, &s[1], &work[ie], + dum, &c__1, &u[u_offset], ldu, dum, &c__1, & + work[iwork], info, (ftnlen)1); + + } + + } else if (wntvo) { + +/* Path 5 (M much larger than N, JOBU='S', JOBVT='O') */ +/* N left singular vectors to be computed in U and */ +/* N right singular vectors to be overwritten on A */ + +/* Computing MAX */ + i__2 = *n << 2; + if (*lwork >= (*n << 1) * *n + max(i__2,bdspac)) { + +/* Sufficient workspace for a fast algorithm */ + + iu = 1; + if (*lwork >= wrkbl + (*lda << 1) * *n) { + +/* WORK(IU) is LDA by N and WORK(IR) is LDA by N */ + + ldwrku = *lda; + ir = iu + ldwrku * *n; + ldwrkr = *lda; + } else if (*lwork >= wrkbl + (*lda + *n) * *n) { + +/* WORK(IU) is LDA by N and WORK(IR) is N by N */ + + ldwrku = *lda; + ir = iu + ldwrku * *n; + ldwrkr = *n; + } else { + +/* WORK(IU) is N by N and WORK(IR) is N by N */ + + ldwrku = *n; + ir = iu + ldwrku * *n; + ldwrkr = *n; + } + itau = ir + ldwrkr * *n; + iwork = itau + *n; + +/* Compute A=Q*R */ +/* (Workspace: need 2*N*N + 2*N, prefer 2*N*N + N + N*NB) */ + + i__2 = *lwork - iwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + +/* Copy R to WORK(IU), zeroing out below it */ + + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[iu], & + ldwrku, (ftnlen)1); + i__2 = *n - 1; + i__3 = *n - 1; + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[iu + + 1], &ldwrku, (ftnlen)1); + +/* Generate Q in A */ +/* (Workspace: need 2*N*N + 2*N, prefer 2*N*N + N + N*NB) */ + + i__2 = *lwork - iwork + 1; + dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], & + work[iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; + +/* Bidiagonalize R in WORK(IU), copying result to */ +/* WORK(IR) */ +/* (Workspace: need 2*N*N + 4*N, */ +/* prefer 2*N*N+3*N+2*N*NB) */ + + i__2 = *lwork - iwork + 1; + dgebrd_(n, n, &work[iu], &ldwrku, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); + dlacpy_((char *)"U", n, n, &work[iu], &ldwrku, &work[ir], & + ldwrkr, (ftnlen)1); + +/* Generate left bidiagonalizing vectors in WORK(IU) */ +/* (Workspace: need 2*N*N + 4*N, prefer 2*N*N + 3*N + N*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", n, n, n, &work[iu], &ldwrku, &work[itauq] + , &work[iwork], &i__2, &ierr, (ftnlen)1); + +/* Generate right bidiagonalizing vectors in WORK(IR) */ +/* (Workspace: need 2*N*N + 4*N-1, */ +/* prefer 2*N*N+3*N+(N-1)*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", n, n, n, &work[ir], &ldwrkr, &work[itaup] + , &work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *n; + +/* Perform bidiagonal QR iteration, computing left */ +/* singular vectors of R in WORK(IU) and computing */ +/* right singular vectors of R in WORK(IR) */ +/* (Workspace: need 2*N*N + BDSPAC) */ + + dbdsqr_((char *)"U", n, n, n, &c__0, &s[1], &work[ie], &work[ + ir], &ldwrkr, &work[iu], &ldwrku, dum, &c__1, + &work[iwork], info, (ftnlen)1); + +/* Multiply Q in A by left singular vectors of R in */ +/* WORK(IU), storing result in U */ +/* (Workspace: need N*N) */ + + dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &a[a_offset], lda, & + work[iu], &ldwrku, &c_b57, &u[u_offset], ldu, + (ftnlen)1, (ftnlen)1); + +/* Copy right singular vectors of R to A */ +/* (Workspace: need N*N) */ + + dlacpy_((char *)"F", n, n, &work[ir], &ldwrkr, &a[a_offset], + lda, (ftnlen)1); + + } else { + +/* Insufficient workspace for a fast algorithm */ + + itau = 1; + iwork = itau + *n; + +/* Compute A=Q*R, copying result to U */ +/* (Workspace: need 2*N, prefer N + N*NB) */ + + i__2 = *lwork - iwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], + ldu, (ftnlen)1); + +/* Generate Q in U */ +/* (Workspace: need 2*N, prefer N + N*NB) */ + + i__2 = *lwork - iwork + 1; + dorgqr_(m, n, n, &u[u_offset], ldu, &work[itau], & + work[iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; + +/* Zero out below R in A */ + + if (*n > 1) { + i__2 = *n - 1; + i__3 = *n - 1; + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &a[ + a_dim1 + 2], lda, (ftnlen)1); + } + +/* Bidiagonalize R in A */ +/* (Workspace: need 4*N, prefer 3*N + 2*N*NB) */ + + i__2 = *lwork - iwork + 1; + dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); + +/* Multiply Q in U by left vectors bidiagonalizing R */ +/* (Workspace: need 3*N + M, prefer 3*N + M*NB) */ + + i__2 = *lwork - iwork + 1; + dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &a[a_offset], lda, & + work[itauq], &u[u_offset], ldu, &work[iwork], + &i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen)1) + ; + +/* Generate right vectors bidiagonalizing R in A */ +/* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, &work[itaup], + &work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *n; + +/* Perform bidiagonal QR iteration, computing left */ +/* singular vectors of A in U and computing right */ +/* singular vectors of A in A */ +/* (Workspace: need BDSPAC) */ + + dbdsqr_((char *)"U", n, n, m, &c__0, &s[1], &work[ie], &a[ + a_offset], lda, &u[u_offset], ldu, dum, &c__1, + &work[iwork], info, (ftnlen)1); + + } + + } else if (wntvas) { + +/* Path 6 (M much larger than N, JOBU='S', JOBVT='S' */ +/* or 'A') */ +/* N left singular vectors to be computed in U and */ +/* N right singular vectors to be computed in VT */ + +/* Computing MAX */ + i__2 = *n << 2; + if (*lwork >= *n * *n + max(i__2,bdspac)) { + +/* Sufficient workspace for a fast algorithm */ + + iu = 1; + if (*lwork >= wrkbl + *lda * *n) { + +/* WORK(IU) is LDA by N */ + + ldwrku = *lda; + } else { + +/* WORK(IU) is N by N */ + + ldwrku = *n; + } + itau = iu + ldwrku * *n; + iwork = itau + *n; + +/* Compute A=Q*R */ +/* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */ + + i__2 = *lwork - iwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + +/* Copy R to WORK(IU), zeroing out below it */ + + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[iu], & + ldwrku, (ftnlen)1); + i__2 = *n - 1; + i__3 = *n - 1; + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[iu + + 1], &ldwrku, (ftnlen)1); + +/* Generate Q in A */ +/* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */ + + i__2 = *lwork - iwork + 1; + dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], & + work[iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; + +/* Bidiagonalize R in WORK(IU), copying result to VT */ +/* (Workspace: need N*N + 4*N, prefer N*N + 3*N + 2*N*NB) */ + + i__2 = *lwork - iwork + 1; + dgebrd_(n, n, &work[iu], &ldwrku, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); + dlacpy_((char *)"U", n, n, &work[iu], &ldwrku, &vt[vt_offset], + ldvt, (ftnlen)1); + +/* Generate left bidiagonalizing vectors in WORK(IU) */ +/* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", n, n, n, &work[iu], &ldwrku, &work[itauq] + , &work[iwork], &i__2, &ierr, (ftnlen)1); + +/* Generate right bidiagonalizing vectors in VT */ +/* (Workspace: need N*N + 4*N-1, */ +/* prefer N*N+3*N+(N-1)*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[ + itaup], &work[iwork], &i__2, &ierr, (ftnlen)1) + ; + iwork = ie + *n; + +/* Perform bidiagonal QR iteration, computing left */ +/* singular vectors of R in WORK(IU) and computing */ +/* right singular vectors of R in VT */ +/* (Workspace: need N*N + BDSPAC) */ + + dbdsqr_((char *)"U", n, n, n, &c__0, &s[1], &work[ie], &vt[ + vt_offset], ldvt, &work[iu], &ldwrku, dum, & + c__1, &work[iwork], info, (ftnlen)1); + +/* Multiply Q in A by left singular vectors of R in */ +/* WORK(IU), storing result in U */ +/* (Workspace: need N*N) */ + + dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &a[a_offset], lda, & + work[iu], &ldwrku, &c_b57, &u[u_offset], ldu, + (ftnlen)1, (ftnlen)1); + + } else { + +/* Insufficient workspace for a fast algorithm */ + + itau = 1; + iwork = itau + *n; + +/* Compute A=Q*R, copying result to U */ +/* (Workspace: need 2*N, prefer N + N*NB) */ + + i__2 = *lwork - iwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], + ldu, (ftnlen)1); + +/* Generate Q in U */ +/* (Workspace: need 2*N, prefer N + N*NB) */ + + i__2 = *lwork - iwork + 1; + dorgqr_(m, n, n, &u[u_offset], ldu, &work[itau], & + work[iwork], &i__2, &ierr); + +/* Copy R to VT, zeroing out below it */ + + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &vt[vt_offset], + ldvt, (ftnlen)1); + if (*n > 1) { + i__2 = *n - 1; + i__3 = *n - 1; + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &vt[ + vt_dim1 + 2], ldvt, (ftnlen)1); + } + ie = itau; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; + +/* Bidiagonalize R in VT */ +/* (Workspace: need 4*N, prefer 3*N + 2*N*NB) */ + + i__2 = *lwork - iwork + 1; + dgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &work[ie], + &work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); + +/* Multiply Q in U by left bidiagonalizing vectors */ +/* in VT */ +/* (Workspace: need 3*N + M, prefer 3*N + M*NB) */ + + i__2 = *lwork - iwork + 1; + dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &vt[vt_offset], ldvt, + &work[itauq], &u[u_offset], ldu, &work[iwork], + &i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen) + 1); + +/* Generate right bidiagonalizing vectors in VT */ +/* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[ + itaup], &work[iwork], &i__2, &ierr, (ftnlen)1) + ; + iwork = ie + *n; + +/* Perform bidiagonal QR iteration, computing left */ +/* singular vectors of A in U and computing right */ +/* singular vectors of A in VT */ +/* (Workspace: need BDSPAC) */ + + dbdsqr_((char *)"U", n, n, m, &c__0, &s[1], &work[ie], &vt[ + vt_offset], ldvt, &u[u_offset], ldu, dum, & + c__1, &work[iwork], info, (ftnlen)1); + + } + + } + + } else if (wntua) { + + if (wntvn) { + +/* Path 7 (M much larger than N, JOBU='A', JOBVT='N') */ +/* M left singular vectors to be computed in U and */ +/* no right singular vectors to be computed */ + +/* Computing MAX */ + i__2 = *n + *m, i__3 = *n << 2, i__2 = max(i__2,i__3); + if (*lwork >= *n * *n + max(i__2,bdspac)) { + +/* Sufficient workspace for a fast algorithm */ + + ir = 1; + if (*lwork >= wrkbl + *lda * *n) { + +/* WORK(IR) is LDA by N */ + + ldwrkr = *lda; + } else { + +/* WORK(IR) is N by N */ + + ldwrkr = *n; + } + itau = ir + ldwrkr * *n; + iwork = itau + *n; + +/* Compute A=Q*R, copying result to U */ +/* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */ + + i__2 = *lwork - iwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], + ldu, (ftnlen)1); + +/* Copy R to WORK(IR), zeroing out below it */ + + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[ir], & + ldwrkr, (ftnlen)1); + i__2 = *n - 1; + i__3 = *n - 1; + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[ir + + 1], &ldwrkr, (ftnlen)1); + +/* Generate Q in U */ +/* (Workspace: need N*N + N + M, prefer N*N + N + M*NB) */ + + i__2 = *lwork - iwork + 1; + dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], & + work[iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; + +/* Bidiagonalize R in WORK(IR) */ +/* (Workspace: need N*N + 4*N, prefer N*N + 3*N + 2*N*NB) */ + + i__2 = *lwork - iwork + 1; + dgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); + +/* Generate left bidiagonalizing vectors in WORK(IR) */ +/* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", n, n, n, &work[ir], &ldwrkr, &work[itauq] + , &work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *n; + +/* Perform bidiagonal QR iteration, computing left */ +/* singular vectors of R in WORK(IR) */ +/* (Workspace: need N*N + BDSPAC) */ + + dbdsqr_((char *)"U", n, &c__0, n, &c__0, &s[1], &work[ie], + dum, &c__1, &work[ir], &ldwrkr, dum, &c__1, & + work[iwork], info, (ftnlen)1); + +/* Multiply Q in U by left singular vectors of R in */ +/* WORK(IR), storing result in A */ +/* (Workspace: need N*N) */ + + dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &u[u_offset], ldu, & + work[ir], &ldwrkr, &c_b57, &a[a_offset], lda, + (ftnlen)1, (ftnlen)1); + +/* Copy left singular vectors of A from A to U */ + + dlacpy_((char *)"F", m, n, &a[a_offset], lda, &u[u_offset], + ldu, (ftnlen)1); + + } else { + +/* Insufficient workspace for a fast algorithm */ + + itau = 1; + iwork = itau + *n; + +/* Compute A=Q*R, copying result to U */ +/* (Workspace: need 2*N, prefer N + N*NB) */ + + i__2 = *lwork - iwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], + ldu, (ftnlen)1); + +/* Generate Q in U */ +/* (Workspace: need N + M, prefer N + M*NB) */ + + i__2 = *lwork - iwork + 1; + dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], & + work[iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; + +/* Zero out below R in A */ + + if (*n > 1) { + i__2 = *n - 1; + i__3 = *n - 1; + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &a[ + a_dim1 + 2], lda, (ftnlen)1); + } + +/* Bidiagonalize R in A */ +/* (Workspace: need 4*N, prefer 3*N + 2*N*NB) */ + + i__2 = *lwork - iwork + 1; + dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); + +/* Multiply Q in U by left bidiagonalizing vectors */ +/* in A */ +/* (Workspace: need 3*N + M, prefer 3*N + M*NB) */ + + i__2 = *lwork - iwork + 1; + dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &a[a_offset], lda, & + work[itauq], &u[u_offset], ldu, &work[iwork], + &i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen)1) + ; + iwork = ie + *n; + +/* Perform bidiagonal QR iteration, computing left */ +/* singular vectors of A in U */ +/* (Workspace: need BDSPAC) */ + + dbdsqr_((char *)"U", n, &c__0, m, &c__0, &s[1], &work[ie], + dum, &c__1, &u[u_offset], ldu, dum, &c__1, & + work[iwork], info, (ftnlen)1); + + } + + } else if (wntvo) { + +/* Path 8 (M much larger than N, JOBU='A', JOBVT='O') */ +/* M left singular vectors to be computed in U and */ +/* N right singular vectors to be overwritten on A */ + +/* Computing MAX */ + i__2 = *n + *m, i__3 = *n << 2, i__2 = max(i__2,i__3); + if (*lwork >= (*n << 1) * *n + max(i__2,bdspac)) { + +/* Sufficient workspace for a fast algorithm */ + + iu = 1; + if (*lwork >= wrkbl + (*lda << 1) * *n) { + +/* WORK(IU) is LDA by N and WORK(IR) is LDA by N */ + + ldwrku = *lda; + ir = iu + ldwrku * *n; + ldwrkr = *lda; + } else if (*lwork >= wrkbl + (*lda + *n) * *n) { + +/* WORK(IU) is LDA by N and WORK(IR) is N by N */ + + ldwrku = *lda; + ir = iu + ldwrku * *n; + ldwrkr = *n; + } else { + +/* WORK(IU) is N by N and WORK(IR) is N by N */ + + ldwrku = *n; + ir = iu + ldwrku * *n; + ldwrkr = *n; + } + itau = ir + ldwrkr * *n; + iwork = itau + *n; + +/* Compute A=Q*R, copying result to U */ +/* (Workspace: need 2*N*N + 2*N, prefer 2*N*N + N + N*NB) */ + + i__2 = *lwork - iwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], + ldu, (ftnlen)1); + +/* Generate Q in U */ +/* (Workspace: need 2*N*N + N + M, prefer 2*N*N + N + M*NB) */ + + i__2 = *lwork - iwork + 1; + dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], & + work[iwork], &i__2, &ierr); + +/* Copy R to WORK(IU), zeroing out below it */ + + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[iu], & + ldwrku, (ftnlen)1); + i__2 = *n - 1; + i__3 = *n - 1; + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[iu + + 1], &ldwrku, (ftnlen)1); + ie = itau; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; + +/* Bidiagonalize R in WORK(IU), copying result to */ +/* WORK(IR) */ +/* (Workspace: need 2*N*N + 4*N, */ +/* prefer 2*N*N+3*N+2*N*NB) */ + + i__2 = *lwork - iwork + 1; + dgebrd_(n, n, &work[iu], &ldwrku, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); + dlacpy_((char *)"U", n, n, &work[iu], &ldwrku, &work[ir], & + ldwrkr, (ftnlen)1); + +/* Generate left bidiagonalizing vectors in WORK(IU) */ +/* (Workspace: need 2*N*N + 4*N, prefer 2*N*N + 3*N + N*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", n, n, n, &work[iu], &ldwrku, &work[itauq] + , &work[iwork], &i__2, &ierr, (ftnlen)1); + +/* Generate right bidiagonalizing vectors in WORK(IR) */ +/* (Workspace: need 2*N*N + 4*N-1, */ +/* prefer 2*N*N+3*N+(N-1)*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", n, n, n, &work[ir], &ldwrkr, &work[itaup] + , &work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *n; + +/* Perform bidiagonal QR iteration, computing left */ +/* singular vectors of R in WORK(IU) and computing */ +/* right singular vectors of R in WORK(IR) */ +/* (Workspace: need 2*N*N + BDSPAC) */ + + dbdsqr_((char *)"U", n, n, n, &c__0, &s[1], &work[ie], &work[ + ir], &ldwrkr, &work[iu], &ldwrku, dum, &c__1, + &work[iwork], info, (ftnlen)1); + +/* Multiply Q in U by left singular vectors of R in */ +/* WORK(IU), storing result in A */ +/* (Workspace: need N*N) */ + + dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &u[u_offset], ldu, & + work[iu], &ldwrku, &c_b57, &a[a_offset], lda, + (ftnlen)1, (ftnlen)1); + +/* Copy left singular vectors of A from A to U */ + + dlacpy_((char *)"F", m, n, &a[a_offset], lda, &u[u_offset], + ldu, (ftnlen)1); + +/* Copy right singular vectors of R from WORK(IR) to A */ + + dlacpy_((char *)"F", n, n, &work[ir], &ldwrkr, &a[a_offset], + lda, (ftnlen)1); + + } else { + +/* Insufficient workspace for a fast algorithm */ + + itau = 1; + iwork = itau + *n; + +/* Compute A=Q*R, copying result to U */ +/* (Workspace: need 2*N, prefer N + N*NB) */ + + i__2 = *lwork - iwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], + ldu, (ftnlen)1); + +/* Generate Q in U */ +/* (Workspace: need N + M, prefer N + M*NB) */ + + i__2 = *lwork - iwork + 1; + dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], & + work[iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; + +/* Zero out below R in A */ + + if (*n > 1) { + i__2 = *n - 1; + i__3 = *n - 1; + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &a[ + a_dim1 + 2], lda, (ftnlen)1); + } + +/* Bidiagonalize R in A */ +/* (Workspace: need 4*N, prefer 3*N + 2*N*NB) */ + + i__2 = *lwork - iwork + 1; + dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); + +/* Multiply Q in U by left bidiagonalizing vectors */ +/* in A */ +/* (Workspace: need 3*N + M, prefer 3*N + M*NB) */ + + i__2 = *lwork - iwork + 1; + dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &a[a_offset], lda, & + work[itauq], &u[u_offset], ldu, &work[iwork], + &i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen)1) + ; + +/* Generate right bidiagonalizing vectors in A */ +/* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, &work[itaup], + &work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *n; + +/* Perform bidiagonal QR iteration, computing left */ +/* singular vectors of A in U and computing right */ +/* singular vectors of A in A */ +/* (Workspace: need BDSPAC) */ + + dbdsqr_((char *)"U", n, n, m, &c__0, &s[1], &work[ie], &a[ + a_offset], lda, &u[u_offset], ldu, dum, &c__1, + &work[iwork], info, (ftnlen)1); + + } + + } else if (wntvas) { + +/* Path 9 (M much larger than N, JOBU='A', JOBVT='S' */ +/* or 'A') */ +/* M left singular vectors to be computed in U and */ +/* N right singular vectors to be computed in VT */ + +/* Computing MAX */ + i__2 = *n + *m, i__3 = *n << 2, i__2 = max(i__2,i__3); + if (*lwork >= *n * *n + max(i__2,bdspac)) { + +/* Sufficient workspace for a fast algorithm */ + + iu = 1; + if (*lwork >= wrkbl + *lda * *n) { + +/* WORK(IU) is LDA by N */ + + ldwrku = *lda; + } else { + +/* WORK(IU) is N by N */ + + ldwrku = *n; + } + itau = iu + ldwrku * *n; + iwork = itau + *n; + +/* Compute A=Q*R, copying result to U */ +/* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */ + + i__2 = *lwork - iwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], + ldu, (ftnlen)1); + +/* Generate Q in U */ +/* (Workspace: need N*N + N + M, prefer N*N + N + M*NB) */ + + i__2 = *lwork - iwork + 1; + dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], & + work[iwork], &i__2, &ierr); + +/* Copy R to WORK(IU), zeroing out below it */ + + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[iu], & + ldwrku, (ftnlen)1); + i__2 = *n - 1; + i__3 = *n - 1; + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[iu + + 1], &ldwrku, (ftnlen)1); + ie = itau; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; + +/* Bidiagonalize R in WORK(IU), copying result to VT */ +/* (Workspace: need N*N + 4*N, prefer N*N + 3*N + 2*N*NB) */ + + i__2 = *lwork - iwork + 1; + dgebrd_(n, n, &work[iu], &ldwrku, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); + dlacpy_((char *)"U", n, n, &work[iu], &ldwrku, &vt[vt_offset], + ldvt, (ftnlen)1); + +/* Generate left bidiagonalizing vectors in WORK(IU) */ +/* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", n, n, n, &work[iu], &ldwrku, &work[itauq] + , &work[iwork], &i__2, &ierr, (ftnlen)1); + +/* Generate right bidiagonalizing vectors in VT */ +/* (Workspace: need N*N + 4*N-1, */ +/* prefer N*N+3*N+(N-1)*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[ + itaup], &work[iwork], &i__2, &ierr, (ftnlen)1) + ; + iwork = ie + *n; + +/* Perform bidiagonal QR iteration, computing left */ +/* singular vectors of R in WORK(IU) and computing */ +/* right singular vectors of R in VT */ +/* (Workspace: need N*N + BDSPAC) */ + + dbdsqr_((char *)"U", n, n, n, &c__0, &s[1], &work[ie], &vt[ + vt_offset], ldvt, &work[iu], &ldwrku, dum, & + c__1, &work[iwork], info, (ftnlen)1); + +/* Multiply Q in U by left singular vectors of R in */ +/* WORK(IU), storing result in A */ +/* (Workspace: need N*N) */ + + dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &u[u_offset], ldu, & + work[iu], &ldwrku, &c_b57, &a[a_offset], lda, + (ftnlen)1, (ftnlen)1); + +/* Copy left singular vectors of A from A to U */ + + dlacpy_((char *)"F", m, n, &a[a_offset], lda, &u[u_offset], + ldu, (ftnlen)1); + + } else { + +/* Insufficient workspace for a fast algorithm */ + + itau = 1; + iwork = itau + *n; + +/* Compute A=Q*R, copying result to U */ +/* (Workspace: need 2*N, prefer N + N*NB) */ + + i__2 = *lwork - iwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], + ldu, (ftnlen)1); + +/* Generate Q in U */ +/* (Workspace: need N + M, prefer N + M*NB) */ + + i__2 = *lwork - iwork + 1; + dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], & + work[iwork], &i__2, &ierr); + +/* Copy R from A to VT, zeroing out below it */ + + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &vt[vt_offset], + ldvt, (ftnlen)1); + if (*n > 1) { + i__2 = *n - 1; + i__3 = *n - 1; + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &vt[ + vt_dim1 + 2], ldvt, (ftnlen)1); + } + ie = itau; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; + +/* Bidiagonalize R in VT */ +/* (Workspace: need 4*N, prefer 3*N + 2*N*NB) */ + + i__2 = *lwork - iwork + 1; + dgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &work[ie], + &work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); + +/* Multiply Q in U by left bidiagonalizing vectors */ +/* in VT */ +/* (Workspace: need 3*N + M, prefer 3*N + M*NB) */ + + i__2 = *lwork - iwork + 1; + dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &vt[vt_offset], ldvt, + &work[itauq], &u[u_offset], ldu, &work[iwork], + &i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen) + 1); + +/* Generate right bidiagonalizing vectors in VT */ +/* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[ + itaup], &work[iwork], &i__2, &ierr, (ftnlen)1) + ; + iwork = ie + *n; + +/* Perform bidiagonal QR iteration, computing left */ +/* singular vectors of A in U and computing right */ +/* singular vectors of A in VT */ +/* (Workspace: need BDSPAC) */ + + dbdsqr_((char *)"U", n, n, m, &c__0, &s[1], &work[ie], &vt[ + vt_offset], ldvt, &u[u_offset], ldu, dum, & + c__1, &work[iwork], info, (ftnlen)1); + + } + + } + + } + + } else { + +/* M .LT. MNTHR */ + +/* Path 10 (M at least N, but not much larger) */ +/* Reduce to bidiagonal form without QR decomposition */ + + ie = 1; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; + +/* Bidiagonalize A */ +/* (Workspace: need 3*N + M, prefer 3*N + (M + N)*NB) */ + + i__2 = *lwork - iwork + 1; + dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], & + work[itaup], &work[iwork], &i__2, &ierr); + if (wntuas) { + +/* If left singular vectors desired in U, copy result to U */ +/* and generate left bidiagonalizing vectors in U */ +/* (Workspace: need 3*N + NCU, prefer 3*N + NCU*NB) */ + + dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], ldu, ( + ftnlen)1); + if (wntus) { + ncu = *n; + } + if (wntua) { + ncu = *m; + } + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", m, &ncu, n, &u[u_offset], ldu, &work[itauq], & + work[iwork], &i__2, &ierr, (ftnlen)1); + } + if (wntvas) { + +/* If right singular vectors desired in VT, copy result to */ +/* VT and generate right bidiagonalizing vectors in VT */ +/* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) */ + + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt, ( + ftnlen)1); + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], & + work[iwork], &i__2, &ierr, (ftnlen)1); + } + if (wntuo) { + +/* If left singular vectors desired in A, generate left */ +/* bidiagonalizing vectors in A */ +/* (Workspace: need 4*N, prefer 3*N + N*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", m, n, n, &a[a_offset], lda, &work[itauq], &work[ + iwork], &i__2, &ierr, (ftnlen)1); + } + if (wntvo) { + +/* If right singular vectors desired in A, generate right */ +/* bidiagonalizing vectors in A */ +/* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, &work[itaup], &work[ + iwork], &i__2, &ierr, (ftnlen)1); + } + iwork = ie + *n; + if (wntuas || wntuo) { + nru = *m; + } + if (wntun) { + nru = 0; + } + if (wntvas || wntvo) { + ncvt = *n; + } + if (wntvn) { + ncvt = 0; + } + if (! wntuo && ! wntvo) { + +/* Perform bidiagonal QR iteration, if desired, computing */ +/* left singular vectors in U and computing right singular */ +/* vectors in VT */ +/* (Workspace: need BDSPAC) */ + + dbdsqr_((char *)"U", n, &ncvt, &nru, &c__0, &s[1], &work[ie], &vt[ + vt_offset], ldvt, &u[u_offset], ldu, dum, &c__1, & + work[iwork], info, (ftnlen)1); + } else if (! wntuo && wntvo) { + +/* Perform bidiagonal QR iteration, if desired, computing */ +/* left singular vectors in U and computing right singular */ +/* vectors in A */ +/* (Workspace: need BDSPAC) */ + + dbdsqr_((char *)"U", n, &ncvt, &nru, &c__0, &s[1], &work[ie], &a[ + a_offset], lda, &u[u_offset], ldu, dum, &c__1, &work[ + iwork], info, (ftnlen)1); + } else { + +/* Perform bidiagonal QR iteration, if desired, computing */ +/* left singular vectors in A and computing right singular */ +/* vectors in VT */ +/* (Workspace: need BDSPAC) */ + + dbdsqr_((char *)"U", n, &ncvt, &nru, &c__0, &s[1], &work[ie], &vt[ + vt_offset], ldvt, &a[a_offset], lda, dum, &c__1, & + work[iwork], info, (ftnlen)1); + } + + } + + } else { + +/* A has more columns than rows. If A has sufficiently more */ +/* columns than rows, first reduce using the LQ decomposition (if */ +/* sufficient workspace available) */ + + if (*n >= mnthr) { + + if (wntvn) { + +/* Path 1t(N much larger than M, JOBVT='N') */ +/* No right singular vectors to be computed */ + + itau = 1; + iwork = itau + *m; + +/* Compute A=L*Q */ +/* (Workspace: need 2*M, prefer M + M*NB) */ + + i__2 = *lwork - iwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], & + i__2, &ierr); + +/* Zero out above L */ + + i__2 = *m - 1; + i__3 = *m - 1; + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &a[(a_dim1 << 1) + + 1], lda, (ftnlen)1); + ie = 1; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; + +/* Bidiagonalize L in A */ +/* (Workspace: need 4*M, prefer 3*M + 2*M*NB) */ + + i__2 = *lwork - iwork + 1; + dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &work[ + itauq], &work[itaup], &work[iwork], &i__2, &ierr); + if (wntuo || wntuas) { + +/* If left singular vectors desired, generate Q */ +/* (Workspace: need 4*M, prefer 3*M + M*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", m, m, m, &a[a_offset], lda, &work[itauq], & + work[iwork], &i__2, &ierr, (ftnlen)1); + } + iwork = ie + *m; + nru = 0; + if (wntuo || wntuas) { + nru = *m; + } + +/* Perform bidiagonal QR iteration, computing left singular */ +/* vectors of A in A if desired */ +/* (Workspace: need BDSPAC) */ + + dbdsqr_((char *)"U", m, &c__0, &nru, &c__0, &s[1], &work[ie], dum, & + c__1, &a[a_offset], lda, dum, &c__1, &work[iwork], + info, (ftnlen)1); + +/* If left singular vectors desired in U, copy them there */ + + if (wntuas) { + dlacpy_((char *)"F", m, m, &a[a_offset], lda, &u[u_offset], ldu, ( + ftnlen)1); + } + + } else if (wntvo && wntun) { + +/* Path 2t(N much larger than M, JOBU='N', JOBVT='O') */ +/* M right singular vectors to be overwritten on A and */ +/* no left singular vectors to be computed */ + +/* Computing MAX */ + i__2 = *m << 2; + if (*lwork >= *m * *m + max(i__2,bdspac)) { + +/* Sufficient workspace for a fast algorithm */ + + ir = 1; +/* Computing MAX */ + i__2 = wrkbl, i__3 = *lda * *n + *m; + if (*lwork >= max(i__2,i__3) + *lda * *m) { + +/* WORK(IU) is LDA by N and WORK(IR) is LDA by M */ + + ldwrku = *lda; + chunk = *n; + ldwrkr = *lda; + } else /* if(complicated condition) */ { +/* Computing MAX */ + i__2 = wrkbl, i__3 = *lda * *n + *m; + if (*lwork >= max(i__2,i__3) + *m * *m) { + +/* WORK(IU) is LDA by N and WORK(IR) is M by M */ + + ldwrku = *lda; + chunk = *n; + ldwrkr = *m; + } else { + +/* WORK(IU) is M by CHUNK and WORK(IR) is M by M */ + + ldwrku = *m; + chunk = (*lwork - *m * *m - *m) / *m; + ldwrkr = *m; + } + } + itau = ir + ldwrkr * *m; + iwork = itau + *m; + +/* Compute A=L*Q */ +/* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */ + + i__2 = *lwork - iwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork] + , &i__2, &ierr); + +/* Copy L to WORK(IR) and zero out above it */ + + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[ir], &ldwrkr, + (ftnlen)1); + i__2 = *m - 1; + i__3 = *m - 1; + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[ir + + ldwrkr], &ldwrkr, (ftnlen)1); + +/* Generate Q in A */ +/* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */ + + i__2 = *lwork - iwork + 1; + dorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; + +/* Bidiagonalize L in WORK(IR) */ +/* (Workspace: need M*M + 4*M, prefer M*M + 3*M + 2*M*NB) */ + + i__2 = *lwork - iwork + 1; + dgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &work[ie], &work[ + itauq], &work[itaup], &work[iwork], &i__2, &ierr); + +/* Generate right vectors bidiagonalizing L */ +/* (Workspace: need M*M + 4*M-1, prefer M*M + 3*M + (M-1)*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", m, m, m, &work[ir], &ldwrkr, &work[itaup], & + work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *m; + +/* Perform bidiagonal QR iteration, computing right */ +/* singular vectors of L in WORK(IR) */ +/* (Workspace: need M*M + BDSPAC) */ + + dbdsqr_((char *)"U", m, m, &c__0, &c__0, &s[1], &work[ie], &work[ + ir], &ldwrkr, dum, &c__1, dum, &c__1, &work[iwork] + , info, (ftnlen)1); + iu = ie + *m; + +/* Multiply right singular vectors of L in WORK(IR) by Q */ +/* in A, storing result in WORK(IU) and copying to A */ +/* (Workspace: need M*M + 2*M, prefer M*M + M*N + M) */ + + i__2 = *n; + i__3 = chunk; + for (i__ = 1; i__3 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += + i__3) { +/* Computing MIN */ + i__4 = *n - i__ + 1; + blk = min(i__4,chunk); + dgemm_((char *)"N", (char *)"N", m, &blk, m, &c_b79, &work[ir], & + ldwrkr, &a[i__ * a_dim1 + 1], lda, &c_b57, & + work[iu], &ldwrku, (ftnlen)1, (ftnlen)1); + dlacpy_((char *)"F", m, &blk, &work[iu], &ldwrku, &a[i__ * + a_dim1 + 1], lda, (ftnlen)1); +/* L30: */ + } + + } else { + +/* Insufficient workspace for a fast algorithm */ + + ie = 1; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; + +/* Bidiagonalize A */ +/* (Workspace: need 3*M + N, prefer 3*M + (M + N)*NB) */ + + i__3 = *lwork - iwork + 1; + dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[ + itauq], &work[itaup], &work[iwork], &i__3, &ierr); + +/* Generate right vectors bidiagonalizing A */ +/* (Workspace: need 4*M, prefer 3*M + M*NB) */ + + i__3 = *lwork - iwork + 1; + dorgbr_((char *)"P", m, n, m, &a[a_offset], lda, &work[itaup], & + work[iwork], &i__3, &ierr, (ftnlen)1); + iwork = ie + *m; + +/* Perform bidiagonal QR iteration, computing right */ +/* singular vectors of A in A */ +/* (Workspace: need BDSPAC) */ + + dbdsqr_((char *)"L", m, n, &c__0, &c__0, &s[1], &work[ie], &a[ + a_offset], lda, dum, &c__1, dum, &c__1, &work[ + iwork], info, (ftnlen)1); + + } + + } else if (wntvo && wntuas) { + +/* Path 3t(N much larger than M, JOBU='S' or 'A', JOBVT='O') */ +/* M right singular vectors to be overwritten on A and */ +/* M left singular vectors to be computed in U */ + +/* Computing MAX */ + i__3 = *m << 2; + if (*lwork >= *m * *m + max(i__3,bdspac)) { + +/* Sufficient workspace for a fast algorithm */ + + ir = 1; +/* Computing MAX */ + i__3 = wrkbl, i__2 = *lda * *n + *m; + if (*lwork >= max(i__3,i__2) + *lda * *m) { + +/* WORK(IU) is LDA by N and WORK(IR) is LDA by M */ + + ldwrku = *lda; + chunk = *n; + ldwrkr = *lda; + } else /* if(complicated condition) */ { +/* Computing MAX */ + i__3 = wrkbl, i__2 = *lda * *n + *m; + if (*lwork >= max(i__3,i__2) + *m * *m) { + +/* WORK(IU) is LDA by N and WORK(IR) is M by M */ + + ldwrku = *lda; + chunk = *n; + ldwrkr = *m; + } else { + +/* WORK(IU) is M by CHUNK and WORK(IR) is M by M */ + + ldwrku = *m; + chunk = (*lwork - *m * *m - *m) / *m; + ldwrkr = *m; + } + } + itau = ir + ldwrkr * *m; + iwork = itau + *m; + +/* Compute A=L*Q */ +/* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */ + + i__3 = *lwork - iwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork] + , &i__3, &ierr); + +/* Copy L to U, zeroing about above it */ + + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &u[u_offset], ldu, ( + ftnlen)1); + i__3 = *m - 1; + i__2 = *m - 1; + dlaset_((char *)"U", &i__3, &i__2, &c_b57, &c_b57, &u[(u_dim1 << + 1) + 1], ldu, (ftnlen)1); + +/* Generate Q in A */ +/* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */ + + i__3 = *lwork - iwork + 1; + dorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__3, &ierr); + ie = itau; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; + +/* Bidiagonalize L in U, copying result to WORK(IR) */ +/* (Workspace: need M*M + 4*M, prefer M*M + 3*M + 2*M*NB) */ + + i__3 = *lwork - iwork + 1; + dgebrd_(m, m, &u[u_offset], ldu, &s[1], &work[ie], &work[ + itauq], &work[itaup], &work[iwork], &i__3, &ierr); + dlacpy_((char *)"U", m, m, &u[u_offset], ldu, &work[ir], &ldwrkr, + (ftnlen)1); + +/* Generate right vectors bidiagonalizing L in WORK(IR) */ +/* (Workspace: need M*M + 4*M-1, prefer M*M + 3*M + (M-1)*NB) */ + + i__3 = *lwork - iwork + 1; + dorgbr_((char *)"P", m, m, m, &work[ir], &ldwrkr, &work[itaup], & + work[iwork], &i__3, &ierr, (ftnlen)1); + +/* Generate left vectors bidiagonalizing L in U */ +/* (Workspace: need M*M + 4*M, prefer M*M + 3*M + M*NB) */ + + i__3 = *lwork - iwork + 1; + dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq], & + work[iwork], &i__3, &ierr, (ftnlen)1); + iwork = ie + *m; + +/* Perform bidiagonal QR iteration, computing left */ +/* singular vectors of L in U, and computing right */ +/* singular vectors of L in WORK(IR) */ +/* (Workspace: need M*M + BDSPAC) */ + + dbdsqr_((char *)"U", m, m, m, &c__0, &s[1], &work[ie], &work[ir], + &ldwrkr, &u[u_offset], ldu, dum, &c__1, &work[ + iwork], info, (ftnlen)1); + iu = ie + *m; + +/* Multiply right singular vectors of L in WORK(IR) by Q */ +/* in A, storing result in WORK(IU) and copying to A */ +/* (Workspace: need M*M + 2*M, prefer M*M + M*N + M)) */ + + i__3 = *n; + i__2 = chunk; + for (i__ = 1; i__2 < 0 ? i__ >= i__3 : i__ <= i__3; i__ += + i__2) { +/* Computing MIN */ + i__4 = *n - i__ + 1; + blk = min(i__4,chunk); + dgemm_((char *)"N", (char *)"N", m, &blk, m, &c_b79, &work[ir], & + ldwrkr, &a[i__ * a_dim1 + 1], lda, &c_b57, & + work[iu], &ldwrku, (ftnlen)1, (ftnlen)1); + dlacpy_((char *)"F", m, &blk, &work[iu], &ldwrku, &a[i__ * + a_dim1 + 1], lda, (ftnlen)1); +/* L40: */ + } + + } else { + +/* Insufficient workspace for a fast algorithm */ + + itau = 1; + iwork = itau + *m; + +/* Compute A=L*Q */ +/* (Workspace: need 2*M, prefer M + M*NB) */ + + i__2 = *lwork - iwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork] + , &i__2, &ierr); + +/* Copy L to U, zeroing out above it */ + + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &u[u_offset], ldu, ( + ftnlen)1); + i__2 = *m - 1; + i__3 = *m - 1; + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &u[(u_dim1 << + 1) + 1], ldu, (ftnlen)1); + +/* Generate Q in A */ +/* (Workspace: need 2*M, prefer M + M*NB) */ + + i__2 = *lwork - iwork + 1; + dorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; + +/* Bidiagonalize L in U */ +/* (Workspace: need 4*M, prefer 3*M + 2*M*NB) */ + + i__2 = *lwork - iwork + 1; + dgebrd_(m, m, &u[u_offset], ldu, &s[1], &work[ie], &work[ + itauq], &work[itaup], &work[iwork], &i__2, &ierr); + +/* Multiply right vectors bidiagonalizing L by Q in A */ +/* (Workspace: need 3*M + N, prefer 3*M + N*NB) */ + + i__2 = *lwork - iwork + 1; + dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &u[u_offset], ldu, &work[ + itaup], &a[a_offset], lda, &work[iwork], &i__2, & + ierr, (ftnlen)1, (ftnlen)1, (ftnlen)1); + +/* Generate left vectors bidiagonalizing L in U */ +/* (Workspace: need 4*M, prefer 3*M + M*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq], & + work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *m; + +/* Perform bidiagonal QR iteration, computing left */ +/* singular vectors of A in U and computing right */ +/* singular vectors of A in A */ +/* (Workspace: need BDSPAC) */ + + dbdsqr_((char *)"U", m, n, m, &c__0, &s[1], &work[ie], &a[ + a_offset], lda, &u[u_offset], ldu, dum, &c__1, & + work[iwork], info, (ftnlen)1); + + } + + } else if (wntvs) { + + if (wntun) { + +/* Path 4t(N much larger than M, JOBU='N', JOBVT='S') */ +/* M right singular vectors to be computed in VT and */ +/* no left singular vectors to be computed */ + +/* Computing MAX */ + i__2 = *m << 2; + if (*lwork >= *m * *m + max(i__2,bdspac)) { + +/* Sufficient workspace for a fast algorithm */ + + ir = 1; + if (*lwork >= wrkbl + *lda * *m) { + +/* WORK(IR) is LDA by M */ + + ldwrkr = *lda; + } else { + +/* WORK(IR) is M by M */ + + ldwrkr = *m; + } + itau = ir + ldwrkr * *m; + iwork = itau + *m; + +/* Compute A=L*Q */ +/* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */ + + i__2 = *lwork - iwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + +/* Copy L to WORK(IR), zeroing out above it */ + + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[ir], & + ldwrkr, (ftnlen)1); + i__2 = *m - 1; + i__3 = *m - 1; + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[ir + + ldwrkr], &ldwrkr, (ftnlen)1); + +/* Generate Q in A */ +/* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */ + + i__2 = *lwork - iwork + 1; + dorglq_(m, n, m, &a[a_offset], lda, &work[itau], & + work[iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; + +/* Bidiagonalize L in WORK(IR) */ +/* (Workspace: need M*M + 4*M, prefer M*M + 3*M + 2*M*NB) */ + + i__2 = *lwork - iwork + 1; + dgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); + +/* Generate right vectors bidiagonalizing L in */ +/* WORK(IR) */ +/* (Workspace: need M*M + 4*M, prefer M*M + 3*M + (M-1)*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", m, m, m, &work[ir], &ldwrkr, &work[itaup] + , &work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *m; + +/* Perform bidiagonal QR iteration, computing right */ +/* singular vectors of L in WORK(IR) */ +/* (Workspace: need M*M + BDSPAC) */ + + dbdsqr_((char *)"U", m, m, &c__0, &c__0, &s[1], &work[ie], & + work[ir], &ldwrkr, dum, &c__1, dum, &c__1, & + work[iwork], info, (ftnlen)1); + +/* Multiply right singular vectors of L in WORK(IR) by */ +/* Q in A, storing result in VT */ +/* (Workspace: need M*M) */ + + dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[ir], &ldwrkr, + &a[a_offset], lda, &c_b57, &vt[vt_offset], + ldvt, (ftnlen)1, (ftnlen)1); + + } else { + +/* Insufficient workspace for a fast algorithm */ + + itau = 1; + iwork = itau + *m; + +/* Compute A=L*Q */ +/* (Workspace: need 2*M, prefer M + M*NB) */ + + i__2 = *lwork - iwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + +/* Copy result to VT */ + + dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], + ldvt, (ftnlen)1); + +/* Generate Q in VT */ +/* (Workspace: need 2*M, prefer M + M*NB) */ + + i__2 = *lwork - iwork + 1; + dorglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], & + work[iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; + +/* Zero out above L in A */ + + i__2 = *m - 1; + i__3 = *m - 1; + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &a[(a_dim1 + << 1) + 1], lda, (ftnlen)1); + +/* Bidiagonalize L in A */ +/* (Workspace: need 4*M, prefer 3*M + 2*M*NB) */ + + i__2 = *lwork - iwork + 1; + dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); + +/* Multiply right vectors bidiagonalizing L by Q in VT */ +/* (Workspace: need 3*M + N, prefer 3*M + N*NB) */ + + i__2 = *lwork - iwork + 1; + dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &a[a_offset], lda, & + work[itaup], &vt[vt_offset], ldvt, &work[ + iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, ( + ftnlen)1); + iwork = ie + *m; + +/* Perform bidiagonal QR iteration, computing right */ +/* singular vectors of A in VT */ +/* (Workspace: need BDSPAC) */ + + dbdsqr_((char *)"U", m, n, &c__0, &c__0, &s[1], &work[ie], & + vt[vt_offset], ldvt, dum, &c__1, dum, &c__1, & + work[iwork], info, (ftnlen)1); + + } + + } else if (wntuo) { + +/* Path 5t(N much larger than M, JOBU='O', JOBVT='S') */ +/* M right singular vectors to be computed in VT and */ +/* M left singular vectors to be overwritten on A */ + +/* Computing MAX */ + i__2 = *m << 2; + if (*lwork >= (*m << 1) * *m + max(i__2,bdspac)) { + +/* Sufficient workspace for a fast algorithm */ + + iu = 1; + if (*lwork >= wrkbl + (*lda << 1) * *m) { + +/* WORK(IU) is LDA by M and WORK(IR) is LDA by M */ + + ldwrku = *lda; + ir = iu + ldwrku * *m; + ldwrkr = *lda; + } else if (*lwork >= wrkbl + (*lda + *m) * *m) { + +/* WORK(IU) is LDA by M and WORK(IR) is M by M */ + + ldwrku = *lda; + ir = iu + ldwrku * *m; + ldwrkr = *m; + } else { + +/* WORK(IU) is M by M and WORK(IR) is M by M */ + + ldwrku = *m; + ir = iu + ldwrku * *m; + ldwrkr = *m; + } + itau = ir + ldwrkr * *m; + iwork = itau + *m; + +/* Compute A=L*Q */ +/* (Workspace: need 2*M*M + 2*M, prefer 2*M*M + M + M*NB) */ + + i__2 = *lwork - iwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + +/* Copy L to WORK(IU), zeroing out below it */ + + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[iu], & + ldwrku, (ftnlen)1); + i__2 = *m - 1; + i__3 = *m - 1; + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[iu + + ldwrku], &ldwrku, (ftnlen)1); + +/* Generate Q in A */ +/* (Workspace: need 2*M*M + 2*M, prefer 2*M*M + M + M*NB) */ + + i__2 = *lwork - iwork + 1; + dorglq_(m, n, m, &a[a_offset], lda, &work[itau], & + work[iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; + +/* Bidiagonalize L in WORK(IU), copying result to */ +/* WORK(IR) */ +/* (Workspace: need 2*M*M + 4*M, */ +/* prefer 2*M*M+3*M+2*M*NB) */ + + i__2 = *lwork - iwork + 1; + dgebrd_(m, m, &work[iu], &ldwrku, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); + dlacpy_((char *)"L", m, m, &work[iu], &ldwrku, &work[ir], & + ldwrkr, (ftnlen)1); + +/* Generate right bidiagonalizing vectors in WORK(IU) */ +/* (Workspace: need 2*M*M + 4*M-1, */ +/* prefer 2*M*M+3*M+(M-1)*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", m, m, m, &work[iu], &ldwrku, &work[itaup] + , &work[iwork], &i__2, &ierr, (ftnlen)1); + +/* Generate left bidiagonalizing vectors in WORK(IR) */ +/* (Workspace: need 2*M*M + 4*M, prefer 2*M*M + 3*M + M*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", m, m, m, &work[ir], &ldwrkr, &work[itauq] + , &work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *m; + +/* Perform bidiagonal QR iteration, computing left */ +/* singular vectors of L in WORK(IR) and computing */ +/* right singular vectors of L in WORK(IU) */ +/* (Workspace: need 2*M*M + BDSPAC) */ + + dbdsqr_((char *)"U", m, m, m, &c__0, &s[1], &work[ie], &work[ + iu], &ldwrku, &work[ir], &ldwrkr, dum, &c__1, + &work[iwork], info, (ftnlen)1); + +/* Multiply right singular vectors of L in WORK(IU) by */ +/* Q in A, storing result in VT */ +/* (Workspace: need M*M) */ + + dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[iu], &ldwrku, + &a[a_offset], lda, &c_b57, &vt[vt_offset], + ldvt, (ftnlen)1, (ftnlen)1); + +/* Copy left singular vectors of L to A */ +/* (Workspace: need M*M) */ + + dlacpy_((char *)"F", m, m, &work[ir], &ldwrkr, &a[a_offset], + lda, (ftnlen)1); + + } else { + +/* Insufficient workspace for a fast algorithm */ + + itau = 1; + iwork = itau + *m; + +/* Compute A=L*Q, copying result to VT */ +/* (Workspace: need 2*M, prefer M + M*NB) */ + + i__2 = *lwork - iwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], + ldvt, (ftnlen)1); + +/* Generate Q in VT */ +/* (Workspace: need 2*M, prefer M + M*NB) */ + + i__2 = *lwork - iwork + 1; + dorglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], & + work[iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; + +/* Zero out above L in A */ + + i__2 = *m - 1; + i__3 = *m - 1; + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &a[(a_dim1 + << 1) + 1], lda, (ftnlen)1); + +/* Bidiagonalize L in A */ +/* (Workspace: need 4*M, prefer 3*M + 2*M*NB) */ + + i__2 = *lwork - iwork + 1; + dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); + +/* Multiply right vectors bidiagonalizing L by Q in VT */ +/* (Workspace: need 3*M + N, prefer 3*M + N*NB) */ + + i__2 = *lwork - iwork + 1; + dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &a[a_offset], lda, & + work[itaup], &vt[vt_offset], ldvt, &work[ + iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, ( + ftnlen)1); + +/* Generate left bidiagonalizing vectors of L in A */ +/* (Workspace: need 4*M, prefer 3*M + M*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", m, m, m, &a[a_offset], lda, &work[itauq], + &work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *m; + +/* Perform bidiagonal QR iteration, compute left */ +/* singular vectors of A in A and compute right */ +/* singular vectors of A in VT */ +/* (Workspace: need BDSPAC) */ + + dbdsqr_((char *)"U", m, n, m, &c__0, &s[1], &work[ie], &vt[ + vt_offset], ldvt, &a[a_offset], lda, dum, & + c__1, &work[iwork], info, (ftnlen)1); + + } + + } else if (wntuas) { + +/* Path 6t(N much larger than M, JOBU='S' or 'A', */ +/* JOBVT='S') */ +/* M right singular vectors to be computed in VT and */ +/* M left singular vectors to be computed in U */ + +/* Computing MAX */ + i__2 = *m << 2; + if (*lwork >= *m * *m + max(i__2,bdspac)) { + +/* Sufficient workspace for a fast algorithm */ + + iu = 1; + if (*lwork >= wrkbl + *lda * *m) { + +/* WORK(IU) is LDA by N */ + + ldwrku = *lda; + } else { + +/* WORK(IU) is LDA by M */ + + ldwrku = *m; + } + itau = iu + ldwrku * *m; + iwork = itau + *m; + +/* Compute A=L*Q */ +/* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */ + + i__2 = *lwork - iwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + +/* Copy L to WORK(IU), zeroing out above it */ + + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[iu], & + ldwrku, (ftnlen)1); + i__2 = *m - 1; + i__3 = *m - 1; + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[iu + + ldwrku], &ldwrku, (ftnlen)1); + +/* Generate Q in A */ +/* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */ + + i__2 = *lwork - iwork + 1; + dorglq_(m, n, m, &a[a_offset], lda, &work[itau], & + work[iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; + +/* Bidiagonalize L in WORK(IU), copying result to U */ +/* (Workspace: need M*M + 4*M, prefer M*M + 3*M + 2*M*NB) */ + + i__2 = *lwork - iwork + 1; + dgebrd_(m, m, &work[iu], &ldwrku, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); + dlacpy_((char *)"L", m, m, &work[iu], &ldwrku, &u[u_offset], + ldu, (ftnlen)1); + +/* Generate right bidiagonalizing vectors in WORK(IU) */ +/* (Workspace: need M*M + 4*M-1, */ +/* prefer M*M+3*M+(M-1)*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", m, m, m, &work[iu], &ldwrku, &work[itaup] + , &work[iwork], &i__2, &ierr, (ftnlen)1); + +/* Generate left bidiagonalizing vectors in U */ +/* (Workspace: need M*M + 4*M, prefer M*M + 3*M + M*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq], + &work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *m; + +/* Perform bidiagonal QR iteration, computing left */ +/* singular vectors of L in U and computing right */ +/* singular vectors of L in WORK(IU) */ +/* (Workspace: need M*M + BDSPAC) */ + + dbdsqr_((char *)"U", m, m, m, &c__0, &s[1], &work[ie], &work[ + iu], &ldwrku, &u[u_offset], ldu, dum, &c__1, & + work[iwork], info, (ftnlen)1); + +/* Multiply right singular vectors of L in WORK(IU) by */ +/* Q in A, storing result in VT */ +/* (Workspace: need M*M) */ + + dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[iu], &ldwrku, + &a[a_offset], lda, &c_b57, &vt[vt_offset], + ldvt, (ftnlen)1, (ftnlen)1); + + } else { + +/* Insufficient workspace for a fast algorithm */ + + itau = 1; + iwork = itau + *m; + +/* Compute A=L*Q, copying result to VT */ +/* (Workspace: need 2*M, prefer M + M*NB) */ + + i__2 = *lwork - iwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], + ldvt, (ftnlen)1); + +/* Generate Q in VT */ +/* (Workspace: need 2*M, prefer M + M*NB) */ + + i__2 = *lwork - iwork + 1; + dorglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], & + work[iwork], &i__2, &ierr); + +/* Copy L to U, zeroing out above it */ + + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &u[u_offset], + ldu, (ftnlen)1); + i__2 = *m - 1; + i__3 = *m - 1; + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &u[(u_dim1 + << 1) + 1], ldu, (ftnlen)1); + ie = itau; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; + +/* Bidiagonalize L in U */ +/* (Workspace: need 4*M, prefer 3*M + 2*M*NB) */ + + i__2 = *lwork - iwork + 1; + dgebrd_(m, m, &u[u_offset], ldu, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); + +/* Multiply right bidiagonalizing vectors in U by Q */ +/* in VT */ +/* (Workspace: need 3*M + N, prefer 3*M + N*NB) */ + + i__2 = *lwork - iwork + 1; + dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &u[u_offset], ldu, & + work[itaup], &vt[vt_offset], ldvt, &work[ + iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, ( + ftnlen)1); + +/* Generate left bidiagonalizing vectors in U */ +/* (Workspace: need 4*M, prefer 3*M + M*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq], + &work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *m; + +/* Perform bidiagonal QR iteration, computing left */ +/* singular vectors of A in U and computing right */ +/* singular vectors of A in VT */ +/* (Workspace: need BDSPAC) */ + + dbdsqr_((char *)"U", m, n, m, &c__0, &s[1], &work[ie], &vt[ + vt_offset], ldvt, &u[u_offset], ldu, dum, & + c__1, &work[iwork], info, (ftnlen)1); + + } + + } + + } else if (wntva) { + + if (wntun) { + +/* Path 7t(N much larger than M, JOBU='N', JOBVT='A') */ +/* N right singular vectors to be computed in VT and */ +/* no left singular vectors to be computed */ + +/* Computing MAX */ + i__2 = *n + *m, i__3 = *m << 2, i__2 = max(i__2,i__3); + if (*lwork >= *m * *m + max(i__2,bdspac)) { + +/* Sufficient workspace for a fast algorithm */ + + ir = 1; + if (*lwork >= wrkbl + *lda * *m) { + +/* WORK(IR) is LDA by M */ + + ldwrkr = *lda; + } else { + +/* WORK(IR) is M by M */ + + ldwrkr = *m; + } + itau = ir + ldwrkr * *m; + iwork = itau + *m; + +/* Compute A=L*Q, copying result to VT */ +/* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */ + + i__2 = *lwork - iwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], + ldvt, (ftnlen)1); + +/* Copy L to WORK(IR), zeroing out above it */ + + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[ir], & + ldwrkr, (ftnlen)1); + i__2 = *m - 1; + i__3 = *m - 1; + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[ir + + ldwrkr], &ldwrkr, (ftnlen)1); + +/* Generate Q in VT */ +/* (Workspace: need M*M + M + N, prefer M*M + M + N*NB) */ + + i__2 = *lwork - iwork + 1; + dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], & + work[iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; + +/* Bidiagonalize L in WORK(IR) */ +/* (Workspace: need M*M + 4*M, prefer M*M + 3*M + 2*M*NB) */ + + i__2 = *lwork - iwork + 1; + dgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); + +/* Generate right bidiagonalizing vectors in WORK(IR) */ +/* (Workspace: need M*M + 4*M-1, */ +/* prefer M*M+3*M+(M-1)*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", m, m, m, &work[ir], &ldwrkr, &work[itaup] + , &work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *m; + +/* Perform bidiagonal QR iteration, computing right */ +/* singular vectors of L in WORK(IR) */ +/* (Workspace: need M*M + BDSPAC) */ + + dbdsqr_((char *)"U", m, m, &c__0, &c__0, &s[1], &work[ie], & + work[ir], &ldwrkr, dum, &c__1, dum, &c__1, & + work[iwork], info, (ftnlen)1); + +/* Multiply right singular vectors of L in WORK(IR) by */ +/* Q in VT, storing result in A */ +/* (Workspace: need M*M) */ + + dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[ir], &ldwrkr, + &vt[vt_offset], ldvt, &c_b57, &a[a_offset], + lda, (ftnlen)1, (ftnlen)1); + +/* Copy right singular vectors of A from A to VT */ + + dlacpy_((char *)"F", m, n, &a[a_offset], lda, &vt[vt_offset], + ldvt, (ftnlen)1); + + } else { + +/* Insufficient workspace for a fast algorithm */ + + itau = 1; + iwork = itau + *m; + +/* Compute A=L*Q, copying result to VT */ +/* (Workspace: need 2*M, prefer M + M*NB) */ + + i__2 = *lwork - iwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], + ldvt, (ftnlen)1); + +/* Generate Q in VT */ +/* (Workspace: need M + N, prefer M + N*NB) */ + + i__2 = *lwork - iwork + 1; + dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], & + work[iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; + +/* Zero out above L in A */ + + i__2 = *m - 1; + i__3 = *m - 1; + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &a[(a_dim1 + << 1) + 1], lda, (ftnlen)1); + +/* Bidiagonalize L in A */ +/* (Workspace: need 4*M, prefer 3*M + 2*M*NB) */ + + i__2 = *lwork - iwork + 1; + dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); + +/* Multiply right bidiagonalizing vectors in A by Q */ +/* in VT */ +/* (Workspace: need 3*M + N, prefer 3*M + N*NB) */ + + i__2 = *lwork - iwork + 1; + dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &a[a_offset], lda, & + work[itaup], &vt[vt_offset], ldvt, &work[ + iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, ( + ftnlen)1); + iwork = ie + *m; + +/* Perform bidiagonal QR iteration, computing right */ +/* singular vectors of A in VT */ +/* (Workspace: need BDSPAC) */ + + dbdsqr_((char *)"U", m, n, &c__0, &c__0, &s[1], &work[ie], & + vt[vt_offset], ldvt, dum, &c__1, dum, &c__1, & + work[iwork], info, (ftnlen)1); + + } + + } else if (wntuo) { + +/* Path 8t(N much larger than M, JOBU='O', JOBVT='A') */ +/* N right singular vectors to be computed in VT and */ +/* M left singular vectors to be overwritten on A */ + +/* Computing MAX */ + i__2 = *n + *m, i__3 = *m << 2, i__2 = max(i__2,i__3); + if (*lwork >= (*m << 1) * *m + max(i__2,bdspac)) { + +/* Sufficient workspace for a fast algorithm */ + + iu = 1; + if (*lwork >= wrkbl + (*lda << 1) * *m) { + +/* WORK(IU) is LDA by M and WORK(IR) is LDA by M */ + + ldwrku = *lda; + ir = iu + ldwrku * *m; + ldwrkr = *lda; + } else if (*lwork >= wrkbl + (*lda + *m) * *m) { + +/* WORK(IU) is LDA by M and WORK(IR) is M by M */ + + ldwrku = *lda; + ir = iu + ldwrku * *m; + ldwrkr = *m; + } else { + +/* WORK(IU) is M by M and WORK(IR) is M by M */ + + ldwrku = *m; + ir = iu + ldwrku * *m; + ldwrkr = *m; + } + itau = ir + ldwrkr * *m; + iwork = itau + *m; + +/* Compute A=L*Q, copying result to VT */ +/* (Workspace: need 2*M*M + 2*M, prefer 2*M*M + M + M*NB) */ + + i__2 = *lwork - iwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], + ldvt, (ftnlen)1); + +/* Generate Q in VT */ +/* (Workspace: need 2*M*M + M + N, prefer 2*M*M + M + N*NB) */ + + i__2 = *lwork - iwork + 1; + dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], & + work[iwork], &i__2, &ierr); + +/* Copy L to WORK(IU), zeroing out above it */ + + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[iu], & + ldwrku, (ftnlen)1); + i__2 = *m - 1; + i__3 = *m - 1; + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[iu + + ldwrku], &ldwrku, (ftnlen)1); + ie = itau; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; + +/* Bidiagonalize L in WORK(IU), copying result to */ +/* WORK(IR) */ +/* (Workspace: need 2*M*M + 4*M, */ +/* prefer 2*M*M+3*M+2*M*NB) */ + + i__2 = *lwork - iwork + 1; + dgebrd_(m, m, &work[iu], &ldwrku, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); + dlacpy_((char *)"L", m, m, &work[iu], &ldwrku, &work[ir], & + ldwrkr, (ftnlen)1); + +/* Generate right bidiagonalizing vectors in WORK(IU) */ +/* (Workspace: need 2*M*M + 4*M-1, */ +/* prefer 2*M*M+3*M+(M-1)*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", m, m, m, &work[iu], &ldwrku, &work[itaup] + , &work[iwork], &i__2, &ierr, (ftnlen)1); + +/* Generate left bidiagonalizing vectors in WORK(IR) */ +/* (Workspace: need 2*M*M + 4*M, prefer 2*M*M + 3*M + M*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", m, m, m, &work[ir], &ldwrkr, &work[itauq] + , &work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *m; + +/* Perform bidiagonal QR iteration, computing left */ +/* singular vectors of L in WORK(IR) and computing */ +/* right singular vectors of L in WORK(IU) */ +/* (Workspace: need 2*M*M + BDSPAC) */ + + dbdsqr_((char *)"U", m, m, m, &c__0, &s[1], &work[ie], &work[ + iu], &ldwrku, &work[ir], &ldwrkr, dum, &c__1, + &work[iwork], info, (ftnlen)1); + +/* Multiply right singular vectors of L in WORK(IU) by */ +/* Q in VT, storing result in A */ +/* (Workspace: need M*M) */ + + dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[iu], &ldwrku, + &vt[vt_offset], ldvt, &c_b57, &a[a_offset], + lda, (ftnlen)1, (ftnlen)1); + +/* Copy right singular vectors of A from A to VT */ + + dlacpy_((char *)"F", m, n, &a[a_offset], lda, &vt[vt_offset], + ldvt, (ftnlen)1); + +/* Copy left singular vectors of A from WORK(IR) to A */ + + dlacpy_((char *)"F", m, m, &work[ir], &ldwrkr, &a[a_offset], + lda, (ftnlen)1); + + } else { + +/* Insufficient workspace for a fast algorithm */ + + itau = 1; + iwork = itau + *m; + +/* Compute A=L*Q, copying result to VT */ +/* (Workspace: need 2*M, prefer M + M*NB) */ + + i__2 = *lwork - iwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], + ldvt, (ftnlen)1); + +/* Generate Q in VT */ +/* (Workspace: need M + N, prefer M + N*NB) */ + + i__2 = *lwork - iwork + 1; + dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], & + work[iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; + +/* Zero out above L in A */ + + i__2 = *m - 1; + i__3 = *m - 1; + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &a[(a_dim1 + << 1) + 1], lda, (ftnlen)1); + +/* Bidiagonalize L in A */ +/* (Workspace: need 4*M, prefer 3*M + 2*M*NB) */ + + i__2 = *lwork - iwork + 1; + dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); + +/* Multiply right bidiagonalizing vectors in A by Q */ +/* in VT */ +/* (Workspace: need 3*M + N, prefer 3*M + N*NB) */ + + i__2 = *lwork - iwork + 1; + dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &a[a_offset], lda, & + work[itaup], &vt[vt_offset], ldvt, &work[ + iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, ( + ftnlen)1); + +/* Generate left bidiagonalizing vectors in A */ +/* (Workspace: need 4*M, prefer 3*M + M*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", m, m, m, &a[a_offset], lda, &work[itauq], + &work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *m; + +/* Perform bidiagonal QR iteration, computing left */ +/* singular vectors of A in A and computing right */ +/* singular vectors of A in VT */ +/* (Workspace: need BDSPAC) */ + + dbdsqr_((char *)"U", m, n, m, &c__0, &s[1], &work[ie], &vt[ + vt_offset], ldvt, &a[a_offset], lda, dum, & + c__1, &work[iwork], info, (ftnlen)1); + + } + + } else if (wntuas) { + +/* Path 9t(N much larger than M, JOBU='S' or 'A', */ +/* JOBVT='A') */ +/* N right singular vectors to be computed in VT and */ +/* M left singular vectors to be computed in U */ + +/* Computing MAX */ + i__2 = *n + *m, i__3 = *m << 2, i__2 = max(i__2,i__3); + if (*lwork >= *m * *m + max(i__2,bdspac)) { + +/* Sufficient workspace for a fast algorithm */ + + iu = 1; + if (*lwork >= wrkbl + *lda * *m) { + +/* WORK(IU) is LDA by M */ + + ldwrku = *lda; + } else { + +/* WORK(IU) is M by M */ + + ldwrku = *m; + } + itau = iu + ldwrku * *m; + iwork = itau + *m; + +/* Compute A=L*Q, copying result to VT */ +/* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */ + + i__2 = *lwork - iwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], + ldvt, (ftnlen)1); + +/* Generate Q in VT */ +/* (Workspace: need M*M + M + N, prefer M*M + M + N*NB) */ + + i__2 = *lwork - iwork + 1; + dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], & + work[iwork], &i__2, &ierr); + +/* Copy L to WORK(IU), zeroing out above it */ + + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[iu], & + ldwrku, (ftnlen)1); + i__2 = *m - 1; + i__3 = *m - 1; + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[iu + + ldwrku], &ldwrku, (ftnlen)1); + ie = itau; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; + +/* Bidiagonalize L in WORK(IU), copying result to U */ +/* (Workspace: need M*M + 4*M, prefer M*M + 3*M + 2*M*NB) */ + + i__2 = *lwork - iwork + 1; + dgebrd_(m, m, &work[iu], &ldwrku, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); + dlacpy_((char *)"L", m, m, &work[iu], &ldwrku, &u[u_offset], + ldu, (ftnlen)1); + +/* Generate right bidiagonalizing vectors in WORK(IU) */ +/* (Workspace: need M*M + 4*M, prefer M*M + 3*M + (M-1)*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", m, m, m, &work[iu], &ldwrku, &work[itaup] + , &work[iwork], &i__2, &ierr, (ftnlen)1); + +/* Generate left bidiagonalizing vectors in U */ +/* (Workspace: need M*M + 4*M, prefer M*M + 3*M + M*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq], + &work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *m; + +/* Perform bidiagonal QR iteration, computing left */ +/* singular vectors of L in U and computing right */ +/* singular vectors of L in WORK(IU) */ +/* (Workspace: need M*M + BDSPAC) */ + + dbdsqr_((char *)"U", m, m, m, &c__0, &s[1], &work[ie], &work[ + iu], &ldwrku, &u[u_offset], ldu, dum, &c__1, & + work[iwork], info, (ftnlen)1); + +/* Multiply right singular vectors of L in WORK(IU) by */ +/* Q in VT, storing result in A */ +/* (Workspace: need M*M) */ + + dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[iu], &ldwrku, + &vt[vt_offset], ldvt, &c_b57, &a[a_offset], + lda, (ftnlen)1, (ftnlen)1); + +/* Copy right singular vectors of A from A to VT */ + + dlacpy_((char *)"F", m, n, &a[a_offset], lda, &vt[vt_offset], + ldvt, (ftnlen)1); + + } else { + +/* Insufficient workspace for a fast algorithm */ + + itau = 1; + iwork = itau + *m; + +/* Compute A=L*Q, copying result to VT */ +/* (Workspace: need 2*M, prefer M + M*NB) */ + + i__2 = *lwork - iwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], + ldvt, (ftnlen)1); + +/* Generate Q in VT */ +/* (Workspace: need M + N, prefer M + N*NB) */ + + i__2 = *lwork - iwork + 1; + dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], & + work[iwork], &i__2, &ierr); + +/* Copy L to U, zeroing out above it */ + + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &u[u_offset], + ldu, (ftnlen)1); + i__2 = *m - 1; + i__3 = *m - 1; + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &u[(u_dim1 + << 1) + 1], ldu, (ftnlen)1); + ie = itau; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; + +/* Bidiagonalize L in U */ +/* (Workspace: need 4*M, prefer 3*M + 2*M*NB) */ + + i__2 = *lwork - iwork + 1; + dgebrd_(m, m, &u[u_offset], ldu, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); + +/* Multiply right bidiagonalizing vectors in U by Q */ +/* in VT */ +/* (Workspace: need 3*M + N, prefer 3*M + N*NB) */ + + i__2 = *lwork - iwork + 1; + dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &u[u_offset], ldu, & + work[itaup], &vt[vt_offset], ldvt, &work[ + iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, ( + ftnlen)1); + +/* Generate left bidiagonalizing vectors in U */ +/* (Workspace: need 4*M, prefer 3*M + M*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq], + &work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *m; + +/* Perform bidiagonal QR iteration, computing left */ +/* singular vectors of A in U and computing right */ +/* singular vectors of A in VT */ +/* (Workspace: need BDSPAC) */ + + dbdsqr_((char *)"U", m, n, m, &c__0, &s[1], &work[ie], &vt[ + vt_offset], ldvt, &u[u_offset], ldu, dum, & + c__1, &work[iwork], info, (ftnlen)1); + + } + + } + + } + + } else { + +/* N .LT. MNTHR */ + +/* Path 10t(N greater than M, but not much larger) */ +/* Reduce to bidiagonal form without LQ decomposition */ + + ie = 1; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; + +/* Bidiagonalize A */ +/* (Workspace: need 3*M + N, prefer 3*M + (M + N)*NB) */ + + i__2 = *lwork - iwork + 1; + dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], & + work[itaup], &work[iwork], &i__2, &ierr); + if (wntuas) { + +/* If left singular vectors desired in U, copy result to U */ +/* and generate left bidiagonalizing vectors in U */ +/* (Workspace: need 4*M-1, prefer 3*M + (M-1)*NB) */ + + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &u[u_offset], ldu, ( + ftnlen)1); + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[ + iwork], &i__2, &ierr, (ftnlen)1); + } + if (wntvas) { + +/* If right singular vectors desired in VT, copy result to */ +/* VT and generate right bidiagonalizing vectors in VT */ +/* (Workspace: need 3*M + NRVT, prefer 3*M + NRVT*NB) */ + + dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt, ( + ftnlen)1); + if (wntva) { + nrvt = *n; + } + if (wntvs) { + nrvt = *m; + } + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", &nrvt, n, m, &vt[vt_offset], ldvt, &work[itaup], + &work[iwork], &i__2, &ierr, (ftnlen)1); + } + if (wntuo) { + +/* If left singular vectors desired in A, generate left */ +/* bidiagonalizing vectors in A */ +/* (Workspace: need 4*M-1, prefer 3*M + (M-1)*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", m, m, n, &a[a_offset], lda, &work[itauq], &work[ + iwork], &i__2, &ierr, (ftnlen)1); + } + if (wntvo) { + +/* If right singular vectors desired in A, generate right */ +/* bidiagonalizing vectors in A */ +/* (Workspace: need 4*M, prefer 3*M + M*NB) */ + + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", m, n, m, &a[a_offset], lda, &work[itaup], &work[ + iwork], &i__2, &ierr, (ftnlen)1); + } + iwork = ie + *m; + if (wntuas || wntuo) { + nru = *m; + } + if (wntun) { + nru = 0; + } + if (wntvas || wntvo) { + ncvt = *n; + } + if (wntvn) { + ncvt = 0; + } + if (! wntuo && ! wntvo) { + +/* Perform bidiagonal QR iteration, if desired, computing */ +/* left singular vectors in U and computing right singular */ +/* vectors in VT */ +/* (Workspace: need BDSPAC) */ + + dbdsqr_((char *)"L", m, &ncvt, &nru, &c__0, &s[1], &work[ie], &vt[ + vt_offset], ldvt, &u[u_offset], ldu, dum, &c__1, & + work[iwork], info, (ftnlen)1); + } else if (! wntuo && wntvo) { + +/* Perform bidiagonal QR iteration, if desired, computing */ +/* left singular vectors in U and computing right singular */ +/* vectors in A */ +/* (Workspace: need BDSPAC) */ + + dbdsqr_((char *)"L", m, &ncvt, &nru, &c__0, &s[1], &work[ie], &a[ + a_offset], lda, &u[u_offset], ldu, dum, &c__1, &work[ + iwork], info, (ftnlen)1); + } else { + +/* Perform bidiagonal QR iteration, if desired, computing */ +/* left singular vectors in A and computing right singular */ +/* vectors in VT */ +/* (Workspace: need BDSPAC) */ + + dbdsqr_((char *)"L", m, &ncvt, &nru, &c__0, &s[1], &work[ie], &vt[ + vt_offset], ldvt, &a[a_offset], lda, dum, &c__1, & + work[iwork], info, (ftnlen)1); + } + + } + + } + +/* If DBDSQR failed to converge, copy unconverged superdiagonals */ +/* to WORK( 2:MINMN ) */ + + if (*info != 0) { + if (ie > 2) { + i__2 = minmn - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + work[i__ + 1] = work[i__ + ie - 1]; +/* L50: */ + } + } + if (ie < 2) { + for (i__ = minmn - 1; i__ >= 1; --i__) { + work[i__ + 1] = work[i__ + ie - 1]; +/* L60: */ + } + } + } + +/* Undo scaling if necessary */ + + if (iscl == 1) { + if (anrm > bignum) { + dlascl_((char *)"G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], & + minmn, &ierr, (ftnlen)1); + } + if (*info != 0 && anrm > bignum) { + i__2 = minmn - 1; + dlascl_((char *)"G", &c__0, &c__0, &bignum, &anrm, &i__2, &c__1, &work[2], + &minmn, &ierr, (ftnlen)1); + } + if (anrm < smlnum) { + dlascl_((char *)"G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], & + minmn, &ierr, (ftnlen)1); + } + if (*info != 0 && anrm < smlnum) { + i__2 = minmn - 1; + dlascl_((char *)"G", &c__0, &c__0, &smlnum, &anrm, &i__2, &c__1, &work[2], + &minmn, &ierr, (ftnlen)1); + } + } + +/* Return optimal workspace in WORK(1) */ + + work[1] = (doublereal) maxwrk; + + return 0; + +/* End of DGESVD */ + +} /* dgesvd_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dgetf2.cpp b/lib/linalg/dgetf2.cpp new file mode 100644 index 0000000000..0cb6b57a2f --- /dev/null +++ b/lib/linalg/dgetf2.cpp @@ -0,0 +1,266 @@ +/* fortran/dgetf2.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static doublereal c_b8 = -1.; + +/* > \brief \b DGETF2 computes the LU factorization of a general m-by-n matrix using partial pivoting with row + interchanges (unblocked algorithm). */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DGETF2 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DGETF2( M, N, A, LDA, IPIV, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INFO, LDA, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* INTEGER IPIV( * ) */ +/* DOUBLE PRECISION A( LDA, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DGETF2 computes an LU factorization of a general m-by-n matrix A */ +/* > using partial pivoting with row interchanges. */ +/* > */ +/* > The factorization has the form */ +/* > A = P * L * U */ +/* > where P is a permutation matrix, L is lower triangular with unit */ +/* > diagonal elements (lower trapezoidal if m > n), and U is upper */ +/* > triangular (upper trapezoidal if m < n). */ +/* > */ +/* > This is the right-looking Level 2 BLAS version of the algorithm. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix A. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On entry, the m by n matrix to be factored. */ +/* > On exit, the factors L and U from the factorization */ +/* > A = P*L*U; the unit diagonal elements of L are not stored. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] IPIV */ +/* > \verbatim */ +/* > IPIV is INTEGER array, dimension (min(M,N)) */ +/* > The pivot indices; for 1 <= i <= min(M,N), row i of the */ +/* > matrix was interchanged with row IPIV(i). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -k, the k-th argument had an illegal value */ +/* > > 0: if INFO = k, U(k,k) is exactly zero. The factorization */ +/* > has been completed, but the factor U is exactly */ +/* > singular, and division by zero will occur if it is used */ +/* > to solve a system of equations. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleGEcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dgetf2_(integer *m, integer *n, doublereal *a, integer * + lda, integer *ipiv, integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3; + doublereal d__1; + + /* Local variables */ + integer i__, j, jp; + extern /* Subroutine */ int dger_(integer *, integer *, doublereal *, + doublereal *, integer *, doublereal *, integer *, doublereal *, + integer *), dscal_(integer *, doublereal *, doublereal *, integer + *); + doublereal sfmin; + extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, + doublereal *, integer *); + extern doublereal dlamch_(char *, ftnlen); + extern integer idamax_(integer *, doublereal *, integer *); + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --ipiv; + + /* Function Body */ + *info = 0; + if (*m < 0) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } else if (*lda < max(1,*m)) { + *info = -4; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DGETF2", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*m == 0 || *n == 0) { + return 0; + } + +/* Compute machine safe minimum */ + + sfmin = dlamch_((char *)"S", (ftnlen)1); + + i__1 = min(*m,*n); + for (j = 1; j <= i__1; ++j) { + +/* Find pivot and test for singularity. */ + + i__2 = *m - j + 1; + jp = j - 1 + idamax_(&i__2, &a[j + j * a_dim1], &c__1); + ipiv[j] = jp; + if (a[jp + j * a_dim1] != 0.) { + +/* Apply the interchange to columns 1:N. */ + + if (jp != j) { + dswap_(n, &a[j + a_dim1], lda, &a[jp + a_dim1], lda); + } + +/* Compute elements J+1:M of J-th column. */ + + if (j < *m) { + if ((d__1 = a[j + j * a_dim1], abs(d__1)) >= sfmin) { + i__2 = *m - j; + d__1 = 1. / a[j + j * a_dim1]; + dscal_(&i__2, &d__1, &a[j + 1 + j * a_dim1], &c__1); + } else { + i__2 = *m - j; + for (i__ = 1; i__ <= i__2; ++i__) { + a[j + i__ + j * a_dim1] /= a[j + j * a_dim1]; +/* L20: */ + } + } + } + + } else if (*info == 0) { + + *info = j; + } + + if (j < min(*m,*n)) { + +/* Update trailing submatrix. */ + + i__2 = *m - j; + i__3 = *n - j; + dger_(&i__2, &i__3, &c_b8, &a[j + 1 + j * a_dim1], &c__1, &a[j + ( + j + 1) * a_dim1], lda, &a[j + 1 + (j + 1) * a_dim1], lda); + } +/* L10: */ + } + return 0; + +/* End of DGETF2 */ + +} /* dgetf2_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dgetrf.cpp b/lib/linalg/dgetrf.cpp new file mode 100644 index 0000000000..eca7500a03 --- /dev/null +++ b/lib/linalg/dgetrf.cpp @@ -0,0 +1,293 @@ +/* fortran/dgetrf.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c_n1 = -1; +static doublereal c_b16 = 1.; +static doublereal c_b19 = -1.; + +/* > \brief \b DGETRF */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DGETRF + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DGETRF( M, N, A, LDA, IPIV, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INFO, LDA, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* INTEGER IPIV( * ) */ +/* DOUBLE PRECISION A( LDA, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DGETRF computes an LU factorization of a general M-by-N matrix A */ +/* > using partial pivoting with row interchanges. */ +/* > */ +/* > The factorization has the form */ +/* > A = P * L * U */ +/* > where P is a permutation matrix, L is lower triangular with unit */ +/* > diagonal elements (lower trapezoidal if m > n), and U is upper */ +/* > triangular (upper trapezoidal if m < n). */ +/* > */ +/* > This is the right-looking Level 3 BLAS version of the algorithm. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix A. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On entry, the M-by-N matrix to be factored. */ +/* > On exit, the factors L and U from the factorization */ +/* > A = P*L*U; the unit diagonal elements of L are not stored. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] IPIV */ +/* > \verbatim */ +/* > IPIV is INTEGER array, dimension (min(M,N)) */ +/* > The pivot indices; for 1 <= i <= min(M,N), row i of the */ +/* > matrix was interchanged with row IPIV(i). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > > 0: if INFO = i, U(i,i) is exactly zero. The factorization */ +/* > has been completed, but the factor U is exactly */ +/* > singular, and division by zero will occur if it is used */ +/* > to solve a system of equations. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleGEcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dgetrf_(integer *m, integer *n, doublereal *a, integer * + lda, integer *ipiv, integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; + + /* Local variables */ + integer i__, j, jb, nb; + extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); + integer iinfo; + extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, + integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen), xerbla_( + char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dlaswp_(integer *, doublereal *, integer *, + integer *, integer *, integer *, integer *), dgetrf2_(integer *, + integer *, doublereal *, integer *, integer *, integer *); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --ipiv; + + /* Function Body */ + *info = 0; + if (*m < 0) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } else if (*lda < max(1,*m)) { + *info = -4; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DGETRF", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*m == 0 || *n == 0) { + return 0; + } + +/* Determine the block size for this environment. */ + + nb = ilaenv_(&c__1, (char *)"DGETRF", (char *)" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen) + 1); + if (nb <= 1 || nb >= min(*m,*n)) { + +/* Use unblocked code. */ + + dgetrf2_(m, n, &a[a_offset], lda, &ipiv[1], info); + } else { + +/* Use blocked code. */ + + i__1 = min(*m,*n); + i__2 = nb; + for (j = 1; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) { +/* Computing MIN */ + i__3 = min(*m,*n) - j + 1; + jb = min(i__3,nb); + +/* Factor diagonal and subdiagonal blocks and test for exact */ +/* singularity. */ + + i__3 = *m - j + 1; + dgetrf2_(&i__3, &jb, &a[j + j * a_dim1], lda, &ipiv[j], &iinfo); + +/* Adjust INFO and the pivot indices. */ + + if (*info == 0 && iinfo > 0) { + *info = iinfo + j - 1; + } +/* Computing MIN */ + i__4 = *m, i__5 = j + jb - 1; + i__3 = min(i__4,i__5); + for (i__ = j; i__ <= i__3; ++i__) { + ipiv[i__] = j - 1 + ipiv[i__]; +/* L10: */ + } + +/* Apply interchanges to columns 1:J-1. */ + + i__3 = j - 1; + i__4 = j + jb - 1; + dlaswp_(&i__3, &a[a_offset], lda, &j, &i__4, &ipiv[1], &c__1); + + if (j + jb <= *n) { + +/* Apply interchanges to columns J+JB:N. */ + + i__3 = *n - j - jb + 1; + i__4 = j + jb - 1; + dlaswp_(&i__3, &a[(j + jb) * a_dim1 + 1], lda, &j, &i__4, & + ipiv[1], &c__1); + +/* Compute block row of U. */ + + i__3 = *n - j - jb + 1; + dtrsm_((char *)"Left", (char *)"Lower", (char *)"No transpose", (char *)"Unit", &jb, &i__3, & + c_b16, &a[j + j * a_dim1], lda, &a[j + (j + jb) * + a_dim1], lda, (ftnlen)4, (ftnlen)5, (ftnlen)12, ( + ftnlen)4); + if (j + jb <= *m) { + +/* Update trailing submatrix. */ + + i__3 = *m - j - jb + 1; + i__4 = *n - j - jb + 1; + dgemm_((char *)"No transpose", (char *)"No transpose", &i__3, &i__4, &jb, + &c_b19, &a[j + jb + j * a_dim1], lda, &a[j + (j + + jb) * a_dim1], lda, &c_b16, &a[j + jb + (j + jb) * + a_dim1], lda, (ftnlen)12, (ftnlen)12); + } + } +/* L20: */ + } + } + return 0; + +/* End of DGETRF */ + +} /* dgetrf_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dgetrf2.cpp b/lib/linalg/dgetrf2.cpp new file mode 100644 index 0000000000..94162fdca8 --- /dev/null +++ b/lib/linalg/dgetrf2.cpp @@ -0,0 +1,331 @@ +/* static/dgetrf2.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static doublereal c_b13 = 1.; +static doublereal c_b16 = -1.; + +/* > \brief \b DGETRF2 */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* RECURSIVE SUBROUTINE DGETRF2( M, N, A, LDA, IPIV, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INFO, LDA, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* INTEGER IPIV( * ) */ +/* DOUBLE PRECISION A( LDA, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DGETRF2 computes an LU factorization of a general M-by-N matrix A */ +/* > using partial pivoting with row interchanges. */ +/* > */ +/* > The factorization has the form */ +/* > A = P * L * U */ +/* > where P is a permutation matrix, L is lower triangular with unit */ +/* > diagonal elements (lower trapezoidal if m > n), and U is upper */ +/* > triangular (upper trapezoidal if m < n). */ +/* > */ +/* > This is the recursive version of the algorithm. It divides */ +/* > the matrix into four submatrices: */ +/* > */ +/* > [ A11 | A12 ] where A11 is n1 by n1 and A22 is n2 by n2 */ +/* > A = [ -----|----- ] with n1 = min(m,n)/2 */ +/* > [ A21 | A22 ] n2 = n-n1 */ +/* > */ +/* > [ A11 ] */ +/* > The subroutine calls itself to factor [ --- ], */ +/* > [ A12 ] */ +/* > [ A12 ] */ +/* > do the swaps on [ --- ], solve A12, update A22, */ +/* > [ A22 ] */ +/* > */ +/* > then calls itself to factor A22 and do the swaps on A21. */ +/* > */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix A. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On entry, the M-by-N matrix to be factored. */ +/* > On exit, the factors L and U from the factorization */ +/* > A = P*L*U; the unit diagonal elements of L are not stored. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] IPIV */ +/* > \verbatim */ +/* > IPIV is INTEGER array, dimension (min(M,N)) */ +/* > The pivot indices; for 1 <= i <= min(M,N), row i of the */ +/* > matrix was interchanged with row IPIV(i). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > > 0: if INFO = i, U(i,i) is exactly zero. The factorization */ +/* > has been completed, but the factor U is exactly */ +/* > singular, and division by zero will occur if it is used */ +/* > to solve a system of equations. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleGEcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dgetrf2_(integer *m, integer *n, doublereal *a, integer * + lda, integer *ipiv, integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2; + doublereal d__1; + + /* Local variables */ + integer i__, n1, n2; + doublereal temp; + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *), dgemm_(char *, char *, integer *, integer *, integer * + , doublereal *, doublereal *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, ftnlen, ftnlen); + integer iinfo; + doublereal sfmin; + extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, + integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + extern doublereal dlamch_(char *, ftnlen); + extern integer idamax_(integer *, doublereal *, integer *); + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), dlaswp_( + integer *, doublereal *, integer *, integer *, integer *, integer + *, integer *); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --ipiv; + + /* Function Body */ + *info = 0; + if (*m < 0) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } else if (*lda < max(1,*m)) { + *info = -4; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DGETRF2", &i__1, (ftnlen)7); + return 0; + } + +/* Quick return if possible */ + + if (*m == 0 || *n == 0) { + return 0; + } + if (*m == 1) { + +/* Use unblocked code for one row case */ +/* Just need to handle IPIV and INFO */ + + ipiv[1] = 1; + if (a[a_dim1 + 1] == 0.) { + *info = 1; + } + + } else if (*n == 1) { + +/* Use unblocked code for one column case */ + + +/* Compute machine safe minimum */ + + sfmin = dlamch_((char *)"S", (ftnlen)1); + +/* Find pivot and test for singularity */ + + i__ = idamax_(m, &a[a_dim1 + 1], &c__1); + ipiv[1] = i__; + if (a[i__ + a_dim1] != 0.) { + +/* Apply the interchange */ + + if (i__ != 1) { + temp = a[a_dim1 + 1]; + a[a_dim1 + 1] = a[i__ + a_dim1]; + a[i__ + a_dim1] = temp; + } + +/* Compute elements 2:M of the column */ + + if ((d__1 = a[a_dim1 + 1], abs(d__1)) >= sfmin) { + i__1 = *m - 1; + d__1 = 1. / a[a_dim1 + 1]; + dscal_(&i__1, &d__1, &a[a_dim1 + 2], &c__1); + } else { + i__1 = *m - 1; + for (i__ = 1; i__ <= i__1; ++i__) { + a[i__ + 1 + a_dim1] /= a[a_dim1 + 1]; +/* L10: */ + } + } + + } else { + *info = 1; + } + + } else { + +/* Use recursive code */ + + n1 = min(*m,*n) / 2; + n2 = *n - n1; + +/* [ A11 ] */ +/* Factor [ --- ] */ +/* [ A21 ] */ + + dgetrf2_(m, &n1, &a[a_offset], lda, &ipiv[1], &iinfo); + if (*info == 0 && iinfo > 0) { + *info = iinfo; + } + +/* [ A12 ] */ +/* Apply interchanges to [ --- ] */ +/* [ A22 ] */ + + dlaswp_(&n2, &a[(n1 + 1) * a_dim1 + 1], lda, &c__1, &n1, &ipiv[1], & + c__1); + +/* Solve A12 */ + + dtrsm_((char *)"L", (char *)"L", (char *)"N", (char *)"U", &n1, &n2, &c_b13, &a[a_offset], lda, &a[( + n1 + 1) * a_dim1 + 1], lda, (ftnlen)1, (ftnlen)1, (ftnlen)1, ( + ftnlen)1); + +/* Update A22 */ + + i__1 = *m - n1; + dgemm_((char *)"N", (char *)"N", &i__1, &n2, &n1, &c_b16, &a[n1 + 1 + a_dim1], lda, & + a[(n1 + 1) * a_dim1 + 1], lda, &c_b13, &a[n1 + 1 + (n1 + 1) * + a_dim1], lda, (ftnlen)1, (ftnlen)1); + +/* Factor A22 */ + + i__1 = *m - n1; + dgetrf2_(&i__1, &n2, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, &ipiv[n1 + + 1], &iinfo); + +/* Adjust INFO and the pivot indices */ + + if (*info == 0 && iinfo > 0) { + *info = iinfo + n1; + } + i__1 = min(*m,*n); + for (i__ = n1 + 1; i__ <= i__1; ++i__) { + ipiv[i__] += n1; +/* L20: */ + } + +/* Apply interchanges to A21 */ + + i__1 = n1 + 1; + i__2 = min(*m,*n); + dlaswp_(&n1, &a[a_dim1 + 1], lda, &i__1, &i__2, &ipiv[1], &c__1); + + } + return 0; + +/* End of DGETRF2 */ + +} /* dgetrf2_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dgetri.cpp b/lib/linalg/dgetri.cpp new file mode 100644 index 0000000000..23178071b6 --- /dev/null +++ b/lib/linalg/dgetri.cpp @@ -0,0 +1,343 @@ +/* fortran/dgetri.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c_n1 = -1; +static integer c__2 = 2; +static doublereal c_b20 = -1.; +static doublereal c_b22 = 1.; + +/* > \brief \b DGETRI */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DGETRI + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INFO, LDA, LWORK, N */ +/* .. */ +/* .. Array Arguments .. */ +/* INTEGER IPIV( * ) */ +/* DOUBLE PRECISION A( LDA, * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DGETRI computes the inverse of a matrix using the LU factorization */ +/* > computed by DGETRF. */ +/* > */ +/* > This method inverts U and then computes inv(A) by solving the system */ +/* > inv(A)*L = inv(U) for inv(A). */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On entry, the factors L and U from the factorization */ +/* > A = P*L*U as computed by DGETRF. */ +/* > On exit, if INFO = 0, the inverse of the original matrix A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] IPIV */ +/* > \verbatim */ +/* > IPIV is INTEGER array, dimension (N) */ +/* > The pivot indices from DGETRF; for 1<=i<=N, row i of the */ +/* > matrix was interchanged with row IPIV(i). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ +/* > On exit, if INFO=0, then WORK(1) returns the optimal LWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LWORK */ +/* > \verbatim */ +/* > LWORK is INTEGER */ +/* > The dimension of the array WORK. LWORK >= max(1,N). */ +/* > For optimal performance LWORK >= N*NB, where NB is */ +/* > the optimal blocksize returned by ILAENV. */ +/* > */ +/* > If LWORK = -1, then a workspace query is assumed; the routine */ +/* > only calculates the optimal size of the WORK array, returns */ +/* > this value as the first entry of the WORK array, and no error */ +/* > message related to LWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > > 0: if INFO = i, U(i,i) is exactly zero; the matrix is */ +/* > singular and its inverse could not be computed. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleGEcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dgetri_(integer *n, doublereal *a, integer *lda, integer + *ipiv, doublereal *work, integer *lwork, integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3; + + /* Local variables */ + integer i__, j, jb, nb, jj, jp, nn, iws; + extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen), + dgemv_(char *, integer *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, ftnlen); + integer nbmin; + extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, + doublereal *, integer *), dtrsm_(char *, char *, char *, char *, + integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen), xerbla_( + char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + integer ldwork; + extern /* Subroutine */ int dtrtri_(char *, char *, integer *, doublereal + *, integer *, integer *, ftnlen, ftnlen); + integer lwkopt; + logical lquery; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --ipiv; + --work; + + /* Function Body */ + *info = 0; + nb = ilaenv_(&c__1, (char *)"DGETRI", (char *)" ", n, &c_n1, &c_n1, &c_n1, (ftnlen)6, ( + ftnlen)1); + lwkopt = *n * nb; + work[1] = (doublereal) lwkopt; + lquery = *lwork == -1; + if (*n < 0) { + *info = -1; + } else if (*lda < max(1,*n)) { + *info = -3; + } else if (*lwork < max(1,*n) && ! lquery) { + *info = -6; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DGETRI", &i__1, (ftnlen)6); + return 0; + } else if (lquery) { + return 0; + } + +/* Quick return if possible */ + + if (*n == 0) { + return 0; + } + +/* Form inv(U). If INFO > 0 from DTRTRI, then U is singular, */ +/* and the inverse is not computed. */ + + dtrtri_((char *)"Upper", (char *)"Non-unit", n, &a[a_offset], lda, info, (ftnlen)5, ( + ftnlen)8); + if (*info > 0) { + return 0; + } + + nbmin = 2; + ldwork = *n; + if (nb > 1 && nb < *n) { +/* Computing MAX */ + i__1 = ldwork * nb; + iws = max(i__1,1); + if (*lwork < iws) { + nb = *lwork / ldwork; +/* Computing MAX */ + i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DGETRI", (char *)" ", n, &c_n1, &c_n1, & + c_n1, (ftnlen)6, (ftnlen)1); + nbmin = max(i__1,i__2); + } + } else { + iws = *n; + } + +/* Solve the equation inv(A)*L = inv(U) for inv(A). */ + + if (nb < nbmin || nb >= *n) { + +/* Use unblocked code. */ + + for (j = *n; j >= 1; --j) { + +/* Copy current column of L to WORK and replace with zeros. */ + + i__1 = *n; + for (i__ = j + 1; i__ <= i__1; ++i__) { + work[i__] = a[i__ + j * a_dim1]; + a[i__ + j * a_dim1] = 0.; +/* L10: */ + } + +/* Compute current column of inv(A). */ + + if (j < *n) { + i__1 = *n - j; + dgemv_((char *)"No transpose", n, &i__1, &c_b20, &a[(j + 1) * a_dim1 + + 1], lda, &work[j + 1], &c__1, &c_b22, &a[j * a_dim1 + + 1], &c__1, (ftnlen)12); + } +/* L20: */ + } + } else { + +/* Use blocked code. */ + + nn = (*n - 1) / nb * nb + 1; + i__1 = -nb; + for (j = nn; i__1 < 0 ? j >= 1 : j <= 1; j += i__1) { +/* Computing MIN */ + i__2 = nb, i__3 = *n - j + 1; + jb = min(i__2,i__3); + +/* Copy current block column of L to WORK and replace with */ +/* zeros. */ + + i__2 = j + jb - 1; + for (jj = j; jj <= i__2; ++jj) { + i__3 = *n; + for (i__ = jj + 1; i__ <= i__3; ++i__) { + work[i__ + (jj - j) * ldwork] = a[i__ + jj * a_dim1]; + a[i__ + jj * a_dim1] = 0.; +/* L30: */ + } +/* L40: */ + } + +/* Compute current block column of inv(A). */ + + if (j + jb <= *n) { + i__2 = *n - j - jb + 1; + dgemm_((char *)"No transpose", (char *)"No transpose", n, &jb, &i__2, &c_b20, + &a[(j + jb) * a_dim1 + 1], lda, &work[j + jb], & + ldwork, &c_b22, &a[j * a_dim1 + 1], lda, (ftnlen)12, ( + ftnlen)12); + } + dtrsm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", n, &jb, &c_b22, & + work[j], &ldwork, &a[j * a_dim1 + 1], lda, (ftnlen)5, ( + ftnlen)5, (ftnlen)12, (ftnlen)4); +/* L50: */ + } + } + +/* Apply column interchanges. */ + + for (j = *n - 1; j >= 1; --j) { + jp = ipiv[j]; + if (jp != j) { + dswap_(n, &a[j * a_dim1 + 1], &c__1, &a[jp * a_dim1 + 1], &c__1); + } +/* L60: */ + } + + work[1] = (doublereal) iws; + return 0; + +/* End of DGETRI */ + +} /* dgetri_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dgetrs.cpp b/lib/linalg/dgetrs.cpp new file mode 100644 index 0000000000..4df18e8650 --- /dev/null +++ b/lib/linalg/dgetrs.cpp @@ -0,0 +1,272 @@ +/* fortran/dgetrs.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static doublereal c_b12 = 1.; +static integer c_n1 = -1; + +/* > \brief \b DGETRS */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DGETRS + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DGETRS( TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER TRANS */ +/* INTEGER INFO, LDA, LDB, N, NRHS */ +/* .. */ +/* .. Array Arguments .. */ +/* INTEGER IPIV( * ) */ +/* DOUBLE PRECISION A( LDA, * ), B( LDB, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DGETRS solves a system of linear equations */ +/* > A * X = B or A**T * X = B */ +/* > with a general N-by-N matrix A using the LU factorization computed */ +/* > by DGETRF. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] TRANS */ +/* > \verbatim */ +/* > TRANS is CHARACTER*1 */ +/* > Specifies the form of the system of equations: */ +/* > = 'N': A * X = B (No transpose) */ +/* > = 'T': A**T* X = B (Transpose) */ +/* > = 'C': A**T* X = B (Conjugate transpose = Transpose) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] NRHS */ +/* > \verbatim */ +/* > NRHS is INTEGER */ +/* > The number of right hand sides, i.e., the number of columns */ +/* > of the matrix B. NRHS >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > The factors L and U from the factorization A = P*L*U */ +/* > as computed by DGETRF. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] IPIV */ +/* > \verbatim */ +/* > IPIV is INTEGER array, dimension (N) */ +/* > The pivot indices from DGETRF; for 1<=i<=N, row i of the */ +/* > matrix was interchanged with row IPIV(i). */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] B */ +/* > \verbatim */ +/* > B is DOUBLE PRECISION array, dimension (LDB,NRHS) */ +/* > On entry, the right hand side matrix B. */ +/* > On exit, the solution matrix X. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDB */ +/* > \verbatim */ +/* > LDB is INTEGER */ +/* > The leading dimension of the array B. LDB >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleGEcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dgetrs_(char *trans, integer *n, integer *nrhs, + doublereal *a, integer *lda, integer *ipiv, doublereal *b, integer * + ldb, integer *info, ftnlen trans_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, b_dim1, b_offset, i__1; + + /* Local variables */ + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, + integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen), xerbla_( + char *, integer *, ftnlen), dlaswp_(integer *, doublereal *, + integer *, integer *, integer *, integer *, integer *); + logical notran; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --ipiv; + b_dim1 = *ldb; + b_offset = 1 + b_dim1; + b -= b_offset; + + /* Function Body */ + *info = 0; + notran = lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1); + if (! notran && ! lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_( + trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } else if (*nrhs < 0) { + *info = -3; + } else if (*lda < max(1,*n)) { + *info = -5; + } else if (*ldb < max(1,*n)) { + *info = -8; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DGETRS", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*n == 0 || *nrhs == 0) { + return 0; + } + + if (notran) { + +/* Solve A * X = B. */ + +/* Apply row interchanges to the right hand sides. */ + + dlaswp_(nrhs, &b[b_offset], ldb, &c__1, n, &ipiv[1], &c__1); + +/* Solve L*X = B, overwriting B with X. */ + + dtrsm_((char *)"Left", (char *)"Lower", (char *)"No transpose", (char *)"Unit", n, nrhs, &c_b12, &a[ + a_offset], lda, &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, ( + ftnlen)12, (ftnlen)4); + +/* Solve U*X = B, overwriting B with X. */ + + dtrsm_((char *)"Left", (char *)"Upper", (char *)"No transpose", (char *)"Non-unit", n, nrhs, &c_b12, & + a[a_offset], lda, &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, ( + ftnlen)12, (ftnlen)8); + } else { + +/* Solve A**T * X = B. */ + +/* Solve U**T *X = B, overwriting B with X. */ + + dtrsm_((char *)"Left", (char *)"Upper", (char *)"Transpose", (char *)"Non-unit", n, nrhs, &c_b12, &a[ + a_offset], lda, &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, ( + ftnlen)9, (ftnlen)8); + +/* Solve L**T *X = B, overwriting B with X. */ + + dtrsm_((char *)"Left", (char *)"Lower", (char *)"Transpose", (char *)"Unit", n, nrhs, &c_b12, &a[ + a_offset], lda, &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, ( + ftnlen)9, (ftnlen)4); + +/* Apply row interchanges to the solution vectors. */ + + dlaswp_(nrhs, &b[b_offset], ldb, &c__1, n, &ipiv[1], &c_n1); + } + + return 0; + +/* End of DGETRS */ + +} /* dgetrs_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/disnan.cpp b/lib/linalg/disnan.cpp new file mode 100644 index 0000000000..9e5bc1094e --- /dev/null +++ b/lib/linalg/disnan.cpp @@ -0,0 +1,14 @@ + +#include + +extern "C" { + +#include "lmp_f2c.h" + +logical disnan_(const doublereal *din) +{ + if (!din) return TRUE_; + + return std::isnan(*din) ? TRUE_ : FALSE_; +} +} diff --git a/lib/linalg/dlabad.cpp b/lib/linalg/dlabad.cpp new file mode 100644 index 0000000000..96eb6efcca --- /dev/null +++ b/lib/linalg/dlabad.cpp @@ -0,0 +1,128 @@ +/* fortran/dlabad.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DLABAD */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLABAD + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLABAD( SMALL, LARGE ) */ + +/* .. Scalar Arguments .. */ +/* DOUBLE PRECISION LARGE, SMALL */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLABAD takes as input the values computed by DLAMCH for underflow and */ +/* > overflow, and returns the square root of each of these values if the */ +/* > log of LARGE is sufficiently large. This subroutine is intended to */ +/* > identify machines with a large exponent range, such as the Crays, and */ +/* > redefine the underflow and overflow limits to be the square roots of */ +/* > the values computed by DLAMCH. This subroutine is needed because */ +/* > DLAMCH does not compensate for poor arithmetic in the upper half of */ +/* > the exponent range, as is found on a Cray. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in,out] SMALL */ +/* > \verbatim */ +/* > SMALL is DOUBLE PRECISION */ +/* > On entry, the underflow threshold as computed by DLAMCH. */ +/* > On exit, if LOG10(LARGE) is sufficiently large, the square */ +/* > root of SMALL, otherwise unchanged. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] LARGE */ +/* > \verbatim */ +/* > LARGE is DOUBLE PRECISION */ +/* > On entry, the overflow threshold as computed by DLAMCH. */ +/* > On exit, if LOG10(LARGE) is sufficiently large, the square */ +/* > root of LARGE, otherwise unchanged. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup OTHERauxiliary */ + +/* ===================================================================== */ +/* Subroutine */ int dlabad_(doublereal *small, doublereal *large) +{ + /* Builtin functions */ + double d_lg10(doublereal *), sqrt(doublereal); + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* If it looks like we're on a Cray, take the square root of */ +/* SMALL and LARGE to avoid overflow and underflow problems. */ + + if (d_lg10(large) > 2e3) { + *small = sqrt(*small); + *large = sqrt(*large); + } + + return 0; + +/* End of DLABAD */ + +} /* dlabad_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlabrd.cpp b/lib/linalg/dlabrd.cpp new file mode 100644 index 0000000000..5775cc7bc1 --- /dev/null +++ b/lib/linalg/dlabrd.cpp @@ -0,0 +1,532 @@ +/* fortran/dlabrd.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static doublereal c_b4 = -1.; +static doublereal c_b5 = 1.; +static integer c__1 = 1; +static doublereal c_b16 = 0.; + +/* > \brief \b DLABRD reduces the first nb rows and columns of a general matrix to a bidiagonal form. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLABRD + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLABRD( M, N, NB, A, LDA, D, E, TAUQ, TAUP, X, LDX, Y, */ +/* LDY ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER LDA, LDX, LDY, M, N, NB */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), TAUP( * ), */ +/* $ TAUQ( * ), X( LDX, * ), Y( LDY, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLABRD reduces the first NB rows and columns of a real general */ +/* > m by n matrix A to upper or lower bidiagonal form by an orthogonal */ +/* > transformation Q**T * A * P, and returns the matrices X and Y which */ +/* > are needed to apply the transformation to the unreduced part of A. */ +/* > */ +/* > If m >= n, A is reduced to upper bidiagonal form; if m < n, to lower */ +/* > bidiagonal form. */ +/* > */ +/* > This is an auxiliary routine called by DGEBRD */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows in the matrix A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns in the matrix A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] NB */ +/* > \verbatim */ +/* > NB is INTEGER */ +/* > The number of leading rows and columns of A to be reduced. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On entry, the m by n general matrix to be reduced. */ +/* > On exit, the first NB rows and columns of the matrix are */ +/* > overwritten; the rest of the array is unchanged. */ +/* > If m >= n, elements on and below the diagonal in the first NB */ +/* > columns, with the array TAUQ, represent the orthogonal */ +/* > matrix Q as a product of elementary reflectors; and */ +/* > elements above the diagonal in the first NB rows, with the */ +/* > array TAUP, represent the orthogonal matrix P as a product */ +/* > of elementary reflectors. */ +/* > If m < n, elements below the diagonal in the first NB */ +/* > columns, with the array TAUQ, represent the orthogonal */ +/* > matrix Q as a product of elementary reflectors, and */ +/* > elements on and above the diagonal in the first NB rows, */ +/* > with the array TAUP, represent the orthogonal matrix P as */ +/* > a product of elementary reflectors. */ +/* > See Further Details. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension (NB) */ +/* > The diagonal elements of the first NB rows and columns of */ +/* > the reduced matrix. D(i) = A(i,i). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] E */ +/* > \verbatim */ +/* > E is DOUBLE PRECISION array, dimension (NB) */ +/* > The off-diagonal elements of the first NB rows and columns of */ +/* > the reduced matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] TAUQ */ +/* > \verbatim */ +/* > TAUQ is DOUBLE PRECISION array, dimension (NB) */ +/* > The scalar factors of the elementary reflectors which */ +/* > represent the orthogonal matrix Q. See Further Details. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] TAUP */ +/* > \verbatim */ +/* > TAUP is DOUBLE PRECISION array, dimension (NB) */ +/* > The scalar factors of the elementary reflectors which */ +/* > represent the orthogonal matrix P. See Further Details. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] X */ +/* > \verbatim */ +/* > X is DOUBLE PRECISION array, dimension (LDX,NB) */ +/* > The m-by-nb matrix X required to update the unreduced part */ +/* > of A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDX */ +/* > \verbatim */ +/* > LDX is INTEGER */ +/* > The leading dimension of the array X. LDX >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] Y */ +/* > \verbatim */ +/* > Y is DOUBLE PRECISION array, dimension (LDY,NB) */ +/* > The n-by-nb matrix Y required to update the unreduced part */ +/* > of A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDY */ +/* > \verbatim */ +/* > LDY is INTEGER */ +/* > The leading dimension of the array Y. LDY >= max(1,N). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleOTHERauxiliary */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > The matrices Q and P are represented as products of elementary */ +/* > reflectors: */ +/* > */ +/* > Q = H(1) H(2) . . . H(nb) and P = G(1) G(2) . . . G(nb) */ +/* > */ +/* > Each H(i) and G(i) has the form: */ +/* > */ +/* > H(i) = I - tauq * v * v**T and G(i) = I - taup * u * u**T */ +/* > */ +/* > where tauq and taup are real scalars, and v and u are real vectors. */ +/* > */ +/* > If m >= n, v(1:i-1) = 0, v(i) = 1, and v(i:m) is stored on exit in */ +/* > A(i:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+1:n) is stored on exit in */ +/* > A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i). */ +/* > */ +/* > If m < n, v(1:i) = 0, v(i+1) = 1, and v(i+1:m) is stored on exit in */ +/* > A(i+2:m,i); u(1:i-1) = 0, u(i) = 1, and u(i:n) is stored on exit in */ +/* > A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i). */ +/* > */ +/* > The elements of the vectors v and u together form the m-by-nb matrix */ +/* > V and the nb-by-n matrix U**T which are needed, with X and Y, to apply */ +/* > the transformation to the unreduced part of the matrix, using a block */ +/* > update of the form: A := A - V*Y**T - X*U**T. */ +/* > */ +/* > The contents of A on exit are illustrated by the following examples */ +/* > with nb = 2: */ +/* > */ +/* > m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n): */ +/* > */ +/* > ( 1 1 u1 u1 u1 ) ( 1 u1 u1 u1 u1 u1 ) */ +/* > ( v1 1 1 u2 u2 ) ( 1 1 u2 u2 u2 u2 ) */ +/* > ( v1 v2 a a a ) ( v1 1 a a a a ) */ +/* > ( v1 v2 a a a ) ( v1 v2 a a a a ) */ +/* > ( v1 v2 a a a ) ( v1 v2 a a a a ) */ +/* > ( v1 v2 a a a ) */ +/* > */ +/* > where a denotes an element of the original matrix which is unchanged, */ +/* > vi denotes an element of the vector defining H(i), and ui an element */ +/* > of the vector defining G(i). */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dlabrd_(integer *m, integer *n, integer *nb, doublereal * + a, integer *lda, doublereal *d__, doublereal *e, doublereal *tauq, + doublereal *taup, doublereal *x, integer *ldx, doublereal *y, integer + *ldy) +{ + /* System generated locals */ + integer a_dim1, a_offset, x_dim1, x_offset, y_dim1, y_offset, i__1, i__2, + i__3; + + /* Local variables */ + integer i__; + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *), dgemv_(char *, integer *, integer *, doublereal *, + doublereal *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, ftnlen), dlarfg_(integer *, doublereal *, + doublereal *, integer *, doublereal *); + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Quick return if possible */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --d__; + --e; + --tauq; + --taup; + x_dim1 = *ldx; + x_offset = 1 + x_dim1; + x -= x_offset; + y_dim1 = *ldy; + y_offset = 1 + y_dim1; + y -= y_offset; + + /* Function Body */ + if (*m <= 0 || *n <= 0) { + return 0; + } + + if (*m >= *n) { + +/* Reduce to upper bidiagonal form */ + + i__1 = *nb; + for (i__ = 1; i__ <= i__1; ++i__) { + +/* Update A(i:m,i) */ + + i__2 = *m - i__ + 1; + i__3 = i__ - 1; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &a[i__ + a_dim1], lda, + &y[i__ + y_dim1], ldy, &c_b5, &a[i__ + i__ * a_dim1], & + c__1, (ftnlen)12); + i__2 = *m - i__ + 1; + i__3 = i__ - 1; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &x[i__ + x_dim1], ldx, + &a[i__ * a_dim1 + 1], &c__1, &c_b5, &a[i__ + i__ * + a_dim1], &c__1, (ftnlen)12); + +/* Generate reflection Q(i) to annihilate A(i+1:m,i) */ + + i__2 = *m - i__ + 1; +/* Computing MIN */ + i__3 = i__ + 1; + dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[min(i__3,*m) + i__ * + a_dim1], &c__1, &tauq[i__]); + d__[i__] = a[i__ + i__ * a_dim1]; + if (i__ < *n) { + a[i__ + i__ * a_dim1] = 1.; + +/* Compute Y(i+1:n,i) */ + + i__2 = *m - i__ + 1; + i__3 = *n - i__; + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b5, &a[i__ + (i__ + 1) * + a_dim1], lda, &a[i__ + i__ * a_dim1], &c__1, &c_b16, & + y[i__ + 1 + i__ * y_dim1], &c__1, (ftnlen)9); + i__2 = *m - i__ + 1; + i__3 = i__ - 1; + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b5, &a[i__ + a_dim1], + lda, &a[i__ + i__ * a_dim1], &c__1, &c_b16, &y[i__ * + y_dim1 + 1], &c__1, (ftnlen)9); + i__2 = *n - i__; + i__3 = i__ - 1; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &y[i__ + 1 + + y_dim1], ldy, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[ + i__ + 1 + i__ * y_dim1], &c__1, (ftnlen)12); + i__2 = *m - i__ + 1; + i__3 = i__ - 1; + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b5, &x[i__ + x_dim1], + ldx, &a[i__ + i__ * a_dim1], &c__1, &c_b16, &y[i__ * + y_dim1 + 1], &c__1, (ftnlen)9); + i__2 = i__ - 1; + i__3 = *n - i__; + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b4, &a[(i__ + 1) * + a_dim1 + 1], lda, &y[i__ * y_dim1 + 1], &c__1, &c_b5, + &y[i__ + 1 + i__ * y_dim1], &c__1, (ftnlen)9); + i__2 = *n - i__; + dscal_(&i__2, &tauq[i__], &y[i__ + 1 + i__ * y_dim1], &c__1); + +/* Update A(i,i+1:n) */ + + i__2 = *n - i__; + dgemv_((char *)"No transpose", &i__2, &i__, &c_b4, &y[i__ + 1 + + y_dim1], ldy, &a[i__ + a_dim1], lda, &c_b5, &a[i__ + ( + i__ + 1) * a_dim1], lda, (ftnlen)12); + i__2 = i__ - 1; + i__3 = *n - i__; + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b4, &a[(i__ + 1) * + a_dim1 + 1], lda, &x[i__ + x_dim1], ldx, &c_b5, &a[ + i__ + (i__ + 1) * a_dim1], lda, (ftnlen)9); + +/* Generate reflection P(i) to annihilate A(i,i+2:n) */ + + i__2 = *n - i__; +/* Computing MIN */ + i__3 = i__ + 2; + dlarfg_(&i__2, &a[i__ + (i__ + 1) * a_dim1], &a[i__ + min( + i__3,*n) * a_dim1], lda, &taup[i__]); + e[i__] = a[i__ + (i__ + 1) * a_dim1]; + a[i__ + (i__ + 1) * a_dim1] = 1.; + +/* Compute X(i+1:m,i) */ + + i__2 = *m - i__; + i__3 = *n - i__; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + (i__ + + 1) * a_dim1], lda, &a[i__ + (i__ + 1) * a_dim1], + lda, &c_b16, &x[i__ + 1 + i__ * x_dim1], &c__1, ( + ftnlen)12); + i__2 = *n - i__; + dgemv_((char *)"Transpose", &i__2, &i__, &c_b5, &y[i__ + 1 + y_dim1], + ldy, &a[i__ + (i__ + 1) * a_dim1], lda, &c_b16, &x[ + i__ * x_dim1 + 1], &c__1, (ftnlen)9); + i__2 = *m - i__; + dgemv_((char *)"No transpose", &i__2, &i__, &c_b4, &a[i__ + 1 + + a_dim1], lda, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[ + i__ + 1 + i__ * x_dim1], &c__1, (ftnlen)12); + i__2 = i__ - 1; + i__3 = *n - i__; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[(i__ + 1) * + a_dim1 + 1], lda, &a[i__ + (i__ + 1) * a_dim1], lda, & + c_b16, &x[i__ * x_dim1 + 1], &c__1, (ftnlen)12); + i__2 = *m - i__; + i__3 = i__ - 1; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &x[i__ + 1 + + x_dim1], ldx, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[ + i__ + 1 + i__ * x_dim1], &c__1, (ftnlen)12); + i__2 = *m - i__; + dscal_(&i__2, &taup[i__], &x[i__ + 1 + i__ * x_dim1], &c__1); + } +/* L10: */ + } + } else { + +/* Reduce to lower bidiagonal form */ + + i__1 = *nb; + for (i__ = 1; i__ <= i__1; ++i__) { + +/* Update A(i,i:n) */ + + i__2 = *n - i__ + 1; + i__3 = i__ - 1; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &y[i__ + y_dim1], ldy, + &a[i__ + a_dim1], lda, &c_b5, &a[i__ + i__ * a_dim1], + lda, (ftnlen)12); + i__2 = i__ - 1; + i__3 = *n - i__ + 1; + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b4, &a[i__ * a_dim1 + 1], + lda, &x[i__ + x_dim1], ldx, &c_b5, &a[i__ + i__ * a_dim1], + lda, (ftnlen)9); + +/* Generate reflection P(i) to annihilate A(i,i+1:n) */ + + i__2 = *n - i__ + 1; +/* Computing MIN */ + i__3 = i__ + 1; + dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[i__ + min(i__3,*n) * + a_dim1], lda, &taup[i__]); + d__[i__] = a[i__ + i__ * a_dim1]; + if (i__ < *m) { + a[i__ + i__ * a_dim1] = 1.; + +/* Compute X(i+1:m,i) */ + + i__2 = *m - i__; + i__3 = *n - i__ + 1; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + i__ * + a_dim1], lda, &a[i__ + i__ * a_dim1], lda, &c_b16, & + x[i__ + 1 + i__ * x_dim1], &c__1, (ftnlen)12); + i__2 = *n - i__ + 1; + i__3 = i__ - 1; + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b5, &y[i__ + y_dim1], + ldy, &a[i__ + i__ * a_dim1], lda, &c_b16, &x[i__ * + x_dim1 + 1], &c__1, (ftnlen)9); + i__2 = *m - i__; + i__3 = i__ - 1; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &a[i__ + 1 + + a_dim1], lda, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[ + i__ + 1 + i__ * x_dim1], &c__1, (ftnlen)12); + i__2 = i__ - 1; + i__3 = *n - i__ + 1; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[i__ * a_dim1 + + 1], lda, &a[i__ + i__ * a_dim1], lda, &c_b16, &x[i__ * + x_dim1 + 1], &c__1, (ftnlen)12); + i__2 = *m - i__; + i__3 = i__ - 1; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &x[i__ + 1 + + x_dim1], ldx, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[ + i__ + 1 + i__ * x_dim1], &c__1, (ftnlen)12); + i__2 = *m - i__; + dscal_(&i__2, &taup[i__], &x[i__ + 1 + i__ * x_dim1], &c__1); + +/* Update A(i+1:m,i) */ + + i__2 = *m - i__; + i__3 = i__ - 1; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &a[i__ + 1 + + a_dim1], lda, &y[i__ + y_dim1], ldy, &c_b5, &a[i__ + + 1 + i__ * a_dim1], &c__1, (ftnlen)12); + i__2 = *m - i__; + dgemv_((char *)"No transpose", &i__2, &i__, &c_b4, &x[i__ + 1 + + x_dim1], ldx, &a[i__ * a_dim1 + 1], &c__1, &c_b5, &a[ + i__ + 1 + i__ * a_dim1], &c__1, (ftnlen)12); + +/* Generate reflection Q(i) to annihilate A(i+2:m,i) */ + + i__2 = *m - i__; +/* Computing MIN */ + i__3 = i__ + 2; + dlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3,*m) + + i__ * a_dim1], &c__1, &tauq[i__]); + e[i__] = a[i__ + 1 + i__ * a_dim1]; + a[i__ + 1 + i__ * a_dim1] = 1.; + +/* Compute Y(i+1:n,i) */ + + i__2 = *m - i__; + i__3 = *n - i__; + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + (i__ + + 1) * a_dim1], lda, &a[i__ + 1 + i__ * a_dim1], &c__1, + &c_b16, &y[i__ + 1 + i__ * y_dim1], &c__1, (ftnlen)9); + i__2 = *m - i__; + i__3 = i__ - 1; + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + a_dim1], + lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &y[ + i__ * y_dim1 + 1], &c__1, (ftnlen)9); + i__2 = *n - i__; + i__3 = i__ - 1; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &y[i__ + 1 + + y_dim1], ldy, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[ + i__ + 1 + i__ * y_dim1], &c__1, (ftnlen)12); + i__2 = *m - i__; + dgemv_((char *)"Transpose", &i__2, &i__, &c_b5, &x[i__ + 1 + x_dim1], + ldx, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &y[ + i__ * y_dim1 + 1], &c__1, (ftnlen)9); + i__2 = *n - i__; + dgemv_((char *)"Transpose", &i__, &i__2, &c_b4, &a[(i__ + 1) * a_dim1 + + 1], lda, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[i__ + + 1 + i__ * y_dim1], &c__1, (ftnlen)9); + i__2 = *n - i__; + dscal_(&i__2, &tauq[i__], &y[i__ + 1 + i__ * y_dim1], &c__1); + } +/* L20: */ + } + } + return 0; + +/* End of DLABRD */ + +} /* dlabrd_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlacn2.cpp b/lib/linalg/dlacn2.cpp new file mode 100644 index 0000000000..befb0b4e52 --- /dev/null +++ b/lib/linalg/dlacn2.cpp @@ -0,0 +1,364 @@ +/* fortran/dlacn2.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; + +/* > \brief \b DLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matr +ix-vector products. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLACN2 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLACN2( N, V, X, ISGN, EST, KASE, ISAVE ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER KASE, N */ +/* DOUBLE PRECISION EST */ +/* .. */ +/* .. Array Arguments .. */ +/* INTEGER ISGN( * ), ISAVE( 3 ) */ +/* DOUBLE PRECISION V( * ), X( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLACN2 estimates the 1-norm of a square, real matrix A. */ +/* > Reverse communication is used for evaluating matrix-vector products. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrix. N >= 1. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] V */ +/* > \verbatim */ +/* > V is DOUBLE PRECISION array, dimension (N) */ +/* > On the final return, V = A*W, where EST = norm(V)/norm(W) */ +/* > (W is not returned). */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] X */ +/* > \verbatim */ +/* > X is DOUBLE PRECISION array, dimension (N) */ +/* > On an intermediate return, X should be overwritten by */ +/* > A * X, if KASE=1, */ +/* > A**T * X, if KASE=2, */ +/* > and DLACN2 must be re-called with all the other parameters */ +/* > unchanged. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] ISGN */ +/* > \verbatim */ +/* > ISGN is INTEGER array, dimension (N) */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] EST */ +/* > \verbatim */ +/* > EST is DOUBLE PRECISION */ +/* > On entry with KASE = 1 or 2 and ISAVE(1) = 3, EST should be */ +/* > unchanged from the previous call to DLACN2. */ +/* > On exit, EST is an estimate (a lower bound) for norm(A). */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] KASE */ +/* > \verbatim */ +/* > KASE is INTEGER */ +/* > On the initial call to DLACN2, KASE should be 0. */ +/* > On an intermediate return, KASE will be 1 or 2, indicating */ +/* > whether X should be overwritten by A * X or A**T * X. */ +/* > On the final return from DLACN2, KASE will again be 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] ISAVE */ +/* > \verbatim */ +/* > ISAVE is INTEGER array, dimension (3) */ +/* > ISAVE is used to save variables between calls to DLACN2 */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleOTHERauxiliary */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > Originally named SONEST, dated March 16, 1988. */ +/* > */ +/* > This is a thread safe version of DLACON, which uses the array ISAVE */ +/* > in place of a SAVE statement, as follows: */ +/* > */ +/* > DLACON DLACN2 */ +/* > JUMP ISAVE(1) */ +/* > J ISAVE(2) */ +/* > ITER ISAVE(3) */ +/* > \endverbatim */ + +/* > \par Contributors: */ +/* ================== */ +/* > */ +/* > Nick Higham, University of Manchester */ + +/* > \par References: */ +/* ================ */ +/* > */ +/* > N.J. Higham, "FORTRAN codes for estimating the one-norm of */ +/* > a real or complex matrix, with applications to condition estimation", */ +/* > ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988. */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dlacn2_(integer *n, doublereal *v, doublereal *x, + integer *isgn, doublereal *est, integer *kase, integer *isave) +{ + /* System generated locals */ + integer i__1; + doublereal d__1; + + /* Builtin functions */ + integer i_dnnt(doublereal *); + + /* Local variables */ + integer i__; + doublereal xs, temp; + extern doublereal dasum_(integer *, doublereal *, integer *); + integer jlast; + extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, + doublereal *, integer *); + extern integer idamax_(integer *, doublereal *, integer *); + doublereal altsgn, estold; + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + + /* Parameter adjustments */ + --isave; + --isgn; + --x; + --v; + + /* Function Body */ + if (*kase == 0) { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + x[i__] = 1. / (doublereal) (*n); +/* L10: */ + } + *kase = 1; + isave[1] = 1; + return 0; + } + + switch (isave[1]) { + case 1: goto L20; + case 2: goto L40; + case 3: goto L70; + case 4: goto L110; + case 5: goto L140; + } + +/* ................ ENTRY (ISAVE( 1 ) = 1) */ +/* FIRST ITERATION. X HAS BEEN OVERWRITTEN BY A*X. */ + +L20: + if (*n == 1) { + v[1] = x[1]; + *est = abs(v[1]); +/* ... QUIT */ + goto L150; + } + *est = dasum_(n, &x[1], &c__1); + + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + if (x[i__] >= 0.) { + x[i__] = 1.; + } else { + x[i__] = -1.; + } + isgn[i__] = i_dnnt(&x[i__]); +/* L30: */ + } + *kase = 2; + isave[1] = 2; + return 0; + +/* ................ ENTRY (ISAVE( 1 ) = 2) */ +/* FIRST ITERATION. X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X. */ + +L40: + isave[2] = idamax_(n, &x[1], &c__1); + isave[3] = 2; + +/* MAIN LOOP - ITERATIONS 2,3,...,ITMAX. */ + +L50: + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + x[i__] = 0.; +/* L60: */ + } + x[isave[2]] = 1.; + *kase = 1; + isave[1] = 3; + return 0; + +/* ................ ENTRY (ISAVE( 1 ) = 3) */ +/* X HAS BEEN OVERWRITTEN BY A*X. */ + +L70: + dcopy_(n, &x[1], &c__1, &v[1], &c__1); + estold = *est; + *est = dasum_(n, &v[1], &c__1); + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + if (x[i__] >= 0.) { + xs = 1.; + } else { + xs = -1.; + } + if (i_dnnt(&xs) != isgn[i__]) { + goto L90; + } +/* L80: */ + } +/* REPEATED SIGN VECTOR DETECTED, HENCE ALGORITHM HAS CONVERGED. */ + goto L120; + +L90: +/* TEST FOR CYCLING. */ + if (*est <= estold) { + goto L120; + } + + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + if (x[i__] >= 0.) { + x[i__] = 1.; + } else { + x[i__] = -1.; + } + isgn[i__] = i_dnnt(&x[i__]); +/* L100: */ + } + *kase = 2; + isave[1] = 4; + return 0; + +/* ................ ENTRY (ISAVE( 1 ) = 4) */ +/* X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X. */ + +L110: + jlast = isave[2]; + isave[2] = idamax_(n, &x[1], &c__1); + if (x[jlast] != (d__1 = x[isave[2]], abs(d__1)) && isave[3] < 5) { + ++isave[3]; + goto L50; + } + +/* ITERATION COMPLETE. FINAL STAGE. */ + +L120: + altsgn = 1.; + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + x[i__] = altsgn * ((doublereal) (i__ - 1) / (doublereal) (*n - 1) + + 1.); + altsgn = -altsgn; +/* L130: */ + } + *kase = 1; + isave[1] = 5; + return 0; + +/* ................ ENTRY (ISAVE( 1 ) = 5) */ +/* X HAS BEEN OVERWRITTEN BY A*X. */ + +L140: + temp = dasum_(n, &x[1], &c__1) / (doublereal) (*n * 3) * 2.; + if (temp > *est) { + dcopy_(n, &x[1], &c__1, &v[1], &c__1); + *est = temp; + } + +L150: + *kase = 0; + return 0; + +/* End of DLACN2 */ + +} /* dlacn2_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlacpy.cpp b/lib/linalg/dlacpy.cpp new file mode 100644 index 0000000000..b1e62a5336 --- /dev/null +++ b/lib/linalg/dlacpy.cpp @@ -0,0 +1,200 @@ +/* fortran/dlacpy.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DLACPY copies all or part of one two-dimensional array to another. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLACPY + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLACPY( UPLO, M, N, A, LDA, B, LDB ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER UPLO */ +/* INTEGER LDA, LDB, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), B( LDB, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLACPY copies all or part of a two-dimensional matrix A to another */ +/* > matrix B. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > Specifies the part of the matrix A to be copied to B. */ +/* > = 'U': Upper triangular part */ +/* > = 'L': Lower triangular part */ +/* > Otherwise: All of the matrix A */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix A. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > The m by n matrix A. If UPLO = 'U', only the upper triangle */ +/* > or trapezoid is accessed; if UPLO = 'L', only the lower */ +/* > triangle or trapezoid is accessed. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] B */ +/* > \verbatim */ +/* > B is DOUBLE PRECISION array, dimension (LDB,N) */ +/* > On exit, B = A in the locations specified by UPLO. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDB */ +/* > \verbatim */ +/* > LDB is INTEGER */ +/* > The leading dimension of the array B. LDB >= max(1,M). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup OTHERauxiliary */ + +/* ===================================================================== */ +/* Subroutine */ int dlacpy_(char *uplo, integer *m, integer *n, doublereal * + a, integer *lda, doublereal *b, integer *ldb, ftnlen uplo_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2; + + /* Local variables */ + integer i__, j; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + b_dim1 = *ldb; + b_offset = 1 + b_dim1; + b -= b_offset; + + /* Function Body */ + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = min(j,*m); + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] = a[i__ + j * a_dim1]; +/* L10: */ + } +/* L20: */ + } + } else if (lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = j; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] = a[i__ + j * a_dim1]; +/* L30: */ + } +/* L40: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] = a[i__ + j * a_dim1]; +/* L50: */ + } +/* L60: */ + } + } + return 0; + +/* End of DLACPY */ + +} /* dlacpy_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dladiv.cpp b/lib/linalg/dladiv.cpp new file mode 100644 index 0000000000..7ffd5485cc --- /dev/null +++ b/lib/linalg/dladiv.cpp @@ -0,0 +1,277 @@ +/* fortran/dladiv.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DLADIV performs complex division in real arithmetic, avoiding unnecessary overflow. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLADIV + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLADIV( A, B, C, D, P, Q ) */ + +/* .. Scalar Arguments .. */ +/* DOUBLE PRECISION A, B, C, D, P, Q */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLADIV performs complex division in real arithmetic */ +/* > */ +/* > a + i*b */ +/* > p + i*q = --------- */ +/* > c + i*d */ +/* > */ +/* > The algorithm is due to Michael Baudin and Robert L. Smith */ +/* > and can be found in the paper */ +/* > (char *)"A Robust Complex Division in Scilab" */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION */ +/* > \endverbatim */ +/* > */ +/* > \param[in] B */ +/* > \verbatim */ +/* > B is DOUBLE PRECISION */ +/* > \endverbatim */ +/* > */ +/* > \param[in] C */ +/* > \verbatim */ +/* > C is DOUBLE PRECISION */ +/* > \endverbatim */ +/* > */ +/* > \param[in] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION */ +/* > The scalars a, b, c, and d in the above expression. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] P */ +/* > \verbatim */ +/* > P is DOUBLE PRECISION */ +/* > \endverbatim */ +/* > */ +/* > \param[out] Q */ +/* > \verbatim */ +/* > Q is DOUBLE PRECISION */ +/* > The scalars p and q in the above expression. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleOTHERauxiliary */ + +/* ===================================================================== */ +/* Subroutine */ int dladiv_(doublereal *a, doublereal *b, doublereal *c__, + doublereal *d__, doublereal *p, doublereal *q) +{ + /* System generated locals */ + doublereal d__1, d__2; + + /* Local variables */ + doublereal s, aa, ab, bb, cc, cd, dd, be, un, ov, eps; + extern doublereal dlamch_(char *, ftnlen); + extern /* Subroutine */ int dladiv1_(doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *, doublereal *); + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + + aa = *a; + bb = *b; + cc = *c__; + dd = *d__; +/* Computing MAX */ + d__1 = abs(*a), d__2 = abs(*b); + ab = max(d__1,d__2); +/* Computing MAX */ + d__1 = abs(*c__), d__2 = abs(*d__); + cd = max(d__1,d__2); + s = 1.; + ov = dlamch_((char *)"Overflow threshold", (ftnlen)18); + un = dlamch_((char *)"Safe minimum", (ftnlen)12); + eps = dlamch_((char *)"Epsilon", (ftnlen)7); + be = 2. / (eps * eps); + if (ab >= ov * .5) { + aa *= .5; + bb *= .5; + s *= 2.; + } + if (cd >= ov * .5) { + cc *= .5; + dd *= .5; + s *= .5; + } + if (ab <= un * 2. / eps) { + aa *= be; + bb *= be; + s /= be; + } + if (cd <= un * 2. / eps) { + cc *= be; + dd *= be; + s *= be; + } + if (abs(*d__) <= abs(*c__)) { + dladiv1_(&aa, &bb, &cc, &dd, p, q); + } else { + dladiv1_(&bb, &aa, &dd, &cc, p, q); + *q = -(*q); + } + *p *= s; + *q *= s; + + return 0; + +/* End of DLADIV */ + +} /* dladiv_ */ + +/* > \ingroup doubleOTHERauxiliary */ +/* Subroutine */ int dladiv1_(doublereal *a, doublereal *b, doublereal *c__, + doublereal *d__, doublereal *p, doublereal *q) +{ + doublereal r__, t; + extern doublereal dladiv2_(doublereal *, doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *); + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + + r__ = *d__ / *c__; + t = 1. / (*c__ + *d__ * r__); + *p = dladiv2_(a, b, c__, d__, &r__, &t); + *a = -(*a); + *q = dladiv2_(b, a, c__, d__, &r__, &t); + + return 0; + +/* End of DLADIV1 */ + +} /* dladiv1_ */ + +/* > \ingroup doubleOTHERauxiliary */ +doublereal dladiv2_(doublereal *a, doublereal *b, doublereal *c__, doublereal + *d__, doublereal *r__, doublereal *t) +{ + /* System generated locals */ + doublereal ret_val; + + /* Local variables */ + doublereal br; + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. Executable Statements .. */ + + if (*r__ != 0.) { + br = *b * *r__; + if (br != 0.) { + ret_val = (*a + br) * *t; + } else { + ret_val = *a * *t + *b * *t * *r__; + } + } else { + ret_val = (*a + *d__ * (*b / *c__)) * *t; + } + + return ret_val; + +/* End of DLADIV2 */ + +} /* dladiv2_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlae2.cpp b/lib/linalg/dlae2.cpp new file mode 100644 index 0000000000..2a1be2816d --- /dev/null +++ b/lib/linalg/dlae2.cpp @@ -0,0 +1,210 @@ +/* fortran/dlae2.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLAE2 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLAE2( A, B, C, RT1, RT2 ) */ + +/* .. Scalar Arguments .. */ +/* DOUBLE PRECISION A, B, C, RT1, RT2 */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix */ +/* > [ A B ] */ +/* > [ B C ]. */ +/* > On return, RT1 is the eigenvalue of larger absolute value, and RT2 */ +/* > is the eigenvalue of smaller absolute value. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION */ +/* > The (1,1) element of the 2-by-2 matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] B */ +/* > \verbatim */ +/* > B is DOUBLE PRECISION */ +/* > The (1,2) and (2,1) elements of the 2-by-2 matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] C */ +/* > \verbatim */ +/* > C is DOUBLE PRECISION */ +/* > The (2,2) element of the 2-by-2 matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] RT1 */ +/* > \verbatim */ +/* > RT1 is DOUBLE PRECISION */ +/* > The eigenvalue of larger absolute value. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] RT2 */ +/* > \verbatim */ +/* > RT2 is DOUBLE PRECISION */ +/* > The eigenvalue of smaller absolute value. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup OTHERauxiliary */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > RT1 is accurate to a few ulps barring over/underflow. */ +/* > */ +/* > RT2 may be inaccurate if there is massive cancellation in the */ +/* > determinant A*C-B*B; higher precision or correctly rounded or */ +/* > correctly truncated arithmetic would be needed to compute RT2 */ +/* > accurately in all cases. */ +/* > */ +/* > Overflow is possible only if RT1 is within a factor of 5 of overflow. */ +/* > Underflow is harmless if the input data is 0 or exceeds */ +/* > underflow_threshold / macheps. */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dlae2_(doublereal *a, doublereal *b, doublereal *c__, + doublereal *rt1, doublereal *rt2) +{ + /* System generated locals */ + doublereal d__1; + + /* Builtin functions */ + double sqrt(doublereal); + + /* Local variables */ + doublereal ab, df, tb, sm, rt, adf, acmn, acmx; + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Compute the eigenvalues */ + + sm = *a + *c__; + df = *a - *c__; + adf = abs(df); + tb = *b + *b; + ab = abs(tb); + if (abs(*a) > abs(*c__)) { + acmx = *a; + acmn = *c__; + } else { + acmx = *c__; + acmn = *a; + } + if (adf > ab) { +/* Computing 2nd power */ + d__1 = ab / adf; + rt = adf * sqrt(d__1 * d__1 + 1.); + } else if (adf < ab) { +/* Computing 2nd power */ + d__1 = adf / ab; + rt = ab * sqrt(d__1 * d__1 + 1.); + } else { + +/* Includes case AB=ADF=0 */ + + rt = ab * sqrt(2.); + } + if (sm < 0.) { + *rt1 = (sm - rt) * .5; + +/* Order of execution important. */ +/* To get fully accurate smaller eigenvalue, */ +/* next line needs to be executed in higher precision. */ + + *rt2 = acmx / *rt1 * acmn - *b / *rt1 * *b; + } else if (sm > 0.) { + *rt1 = (sm + rt) * .5; + +/* Order of execution important. */ +/* To get fully accurate smaller eigenvalue, */ +/* next line needs to be executed in higher precision. */ + + *rt2 = acmx / *rt1 * acmn - *b / *rt1 * *b; + } else { + +/* Includes case RT1 = RT2 = 0 */ + + *rt1 = rt * .5; + *rt2 = rt * -.5; + } + return 0; + +/* End of DLAE2 */ + +} /* dlae2_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlaed0.cpp b/lib/linalg/dlaed0.cpp new file mode 100644 index 0000000000..41b13a3cac --- /dev/null +++ b/lib/linalg/dlaed0.cpp @@ -0,0 +1,534 @@ +/* fortran/dlaed0.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__9 = 9; +static integer c__0 = 0; +static integer c__2 = 2; +static doublereal c_b23 = 1.; +static doublereal c_b24 = 0.; +static integer c__1 = 1; + +/* > \brief \b DLAED0 used by DSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced +symmetric tridiagonal matrix using the divide and conquer method. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLAED0 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, */ +/* WORK, IWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER ICOMPQ, INFO, LDQ, LDQS, N, QSIZ */ +/* .. */ +/* .. Array Arguments .. */ +/* INTEGER IWORK( * ) */ +/* DOUBLE PRECISION D( * ), E( * ), Q( LDQ, * ), QSTORE( LDQS, * ), */ +/* $ WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLAED0 computes all eigenvalues and corresponding eigenvectors of a */ +/* > symmetric tridiagonal matrix using the divide and conquer method. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] ICOMPQ */ +/* > \verbatim */ +/* > ICOMPQ is INTEGER */ +/* > = 0: Compute eigenvalues only. */ +/* > = 1: Compute eigenvectors of original dense symmetric matrix */ +/* > also. On entry, Q contains the orthogonal matrix used */ +/* > to reduce the original matrix to tridiagonal form. */ +/* > = 2: Compute eigenvalues and eigenvectors of tridiagonal */ +/* > matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] QSIZ */ +/* > \verbatim */ +/* > QSIZ is INTEGER */ +/* > The dimension of the orthogonal matrix used to reduce */ +/* > the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The dimension of the symmetric tridiagonal matrix. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension (N) */ +/* > On entry, the main diagonal of the tridiagonal matrix. */ +/* > On exit, its eigenvalues. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] E */ +/* > \verbatim */ +/* > E is DOUBLE PRECISION array, dimension (N-1) */ +/* > The off-diagonal elements of the tridiagonal matrix. */ +/* > On exit, E has been destroyed. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] Q */ +/* > \verbatim */ +/* > Q is DOUBLE PRECISION array, dimension (LDQ, N) */ +/* > On entry, Q must contain an N-by-N orthogonal matrix. */ +/* > If ICOMPQ = 0 Q is not referenced. */ +/* > If ICOMPQ = 1 On entry, Q is a subset of the columns of the */ +/* > orthogonal matrix used to reduce the full */ +/* > matrix to tridiagonal form corresponding to */ +/* > the subset of the full matrix which is being */ +/* > decomposed at this time. */ +/* > If ICOMPQ = 2 On entry, Q will be the identity matrix. */ +/* > On exit, Q contains the eigenvectors of the */ +/* > tridiagonal matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDQ */ +/* > \verbatim */ +/* > LDQ is INTEGER */ +/* > The leading dimension of the array Q. If eigenvectors are */ +/* > desired, then LDQ >= max(1,N). In any case, LDQ >= 1. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] QSTORE */ +/* > \verbatim */ +/* > QSTORE is DOUBLE PRECISION array, dimension (LDQS, N) */ +/* > Referenced only when ICOMPQ = 1. Used to store parts of */ +/* > the eigenvector matrix when the updating matrix multiplies */ +/* > take place. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDQS */ +/* > \verbatim */ +/* > LDQS is INTEGER */ +/* > The leading dimension of the array QSTORE. If ICOMPQ = 1, */ +/* > then LDQS >= max(1,N). In any case, LDQS >= 1. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, */ +/* > If ICOMPQ = 0 or 1, the dimension of WORK must be at least */ +/* > 1 + 3*N + 2*N*lg N + 3*N**2 */ +/* > ( lg( N ) = smallest integer k */ +/* > such that 2^k >= N ) */ +/* > If ICOMPQ = 2, the dimension of WORK must be at least */ +/* > 4*N + N**2. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] IWORK */ +/* > \verbatim */ +/* > IWORK is INTEGER array, */ +/* > If ICOMPQ = 0 or 1, the dimension of IWORK must be at least */ +/* > 6 + 6*N + 5*N*lg N. */ +/* > ( lg( N ) = smallest integer k */ +/* > such that 2^k >= N ) */ +/* > If ICOMPQ = 2, the dimension of IWORK must be at least */ +/* > 3 + 5*N. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit. */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ +/* > > 0: The algorithm failed to compute an eigenvalue while */ +/* > working on the submatrix lying in rows and columns */ +/* > INFO/(N+1) through mod(INFO,N+1). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup auxOTHERcomputational */ + +/* > \par Contributors: */ +/* ================== */ +/* > */ +/* > Jeff Rutter, Computer Science Division, University of California */ +/* > at Berkeley, USA */ + +/* ===================================================================== */ +/* Subroutine */ int dlaed0_(integer *icompq, integer *qsiz, integer *n, + doublereal *d__, doublereal *e, doublereal *q, integer *ldq, + doublereal *qstore, integer *ldqs, doublereal *work, integer *iwork, + integer *info) +{ + /* System generated locals */ + integer q_dim1, q_offset, qstore_dim1, qstore_offset, i__1, i__2; + doublereal d__1; + + /* Builtin functions */ + double log(doublereal); + integer pow_ii(integer *, integer *); + + /* Local variables */ + integer i__, j, k, iq, lgn, msd2, smm1, spm1, spm2; + doublereal temp; + integer curr; + extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); + integer iperm; + extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, + doublereal *, integer *); + integer indxq, iwrem; + extern /* Subroutine */ int dlaed1_(integer *, doublereal *, doublereal *, + integer *, integer *, doublereal *, integer *, doublereal *, + integer *, integer *); + integer iqptr; + extern /* Subroutine */ int dlaed7_(integer *, integer *, integer *, + integer *, integer *, integer *, doublereal *, doublereal *, + integer *, integer *, doublereal *, integer *, doublereal *, + integer *, integer *, integer *, integer *, integer *, doublereal + *, doublereal *, integer *, integer *); + integer tlvls; + extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, + doublereal *, integer *, doublereal *, integer *, ftnlen); + integer igivcl; + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + integer igivnm, submat, curprb, subpbs, igivpt; + extern /* Subroutine */ int dsteqr_(char *, integer *, doublereal *, + doublereal *, doublereal *, integer *, doublereal *, integer *, + ftnlen); + integer curlvl, matsiz, iprmpt, smlsiz; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --d__; + --e; + q_dim1 = *ldq; + q_offset = 1 + q_dim1; + q -= q_offset; + qstore_dim1 = *ldqs; + qstore_offset = 1 + qstore_dim1; + qstore -= qstore_offset; + --work; + --iwork; + + /* Function Body */ + *info = 0; + + if (*icompq < 0 || *icompq > 2) { + *info = -1; + } else if (*icompq == 1 && *qsiz < max(0,*n)) { + *info = -2; + } else if (*n < 0) { + *info = -3; + } else if (*ldq < max(1,*n)) { + *info = -7; + } else if (*ldqs < max(1,*n)) { + *info = -9; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DLAED0", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*n == 0) { + return 0; + } + + smlsiz = ilaenv_(&c__9, (char *)"DLAED0", (char *)" ", &c__0, &c__0, &c__0, &c__0, ( + ftnlen)6, (ftnlen)1); + +/* Determine the size and placement of the submatrices, and save in */ +/* the leading elements of IWORK. */ + + iwork[1] = *n; + subpbs = 1; + tlvls = 0; +L10: + if (iwork[subpbs] > smlsiz) { + for (j = subpbs; j >= 1; --j) { + iwork[j * 2] = (iwork[j] + 1) / 2; + iwork[(j << 1) - 1] = iwork[j] / 2; +/* L20: */ + } + ++tlvls; + subpbs <<= 1; + goto L10; + } + i__1 = subpbs; + for (j = 2; j <= i__1; ++j) { + iwork[j] += iwork[j - 1]; +/* L30: */ + } + +/* Divide the matrix into SUBPBS submatrices of size at most SMLSIZ+1 */ +/* using rank-1 modifications (cuts). */ + + spm1 = subpbs - 1; + i__1 = spm1; + for (i__ = 1; i__ <= i__1; ++i__) { + submat = iwork[i__] + 1; + smm1 = submat - 1; + d__[smm1] -= (d__1 = e[smm1], abs(d__1)); + d__[submat] -= (d__1 = e[smm1], abs(d__1)); +/* L40: */ + } + + indxq = (*n << 2) + 3; + if (*icompq != 2) { + +/* Set up workspaces for eigenvalues only/accumulate new vectors */ +/* routine */ + + temp = log((doublereal) (*n)) / log(2.); + lgn = (integer) temp; + if (pow_ii(&c__2, &lgn) < *n) { + ++lgn; + } + if (pow_ii(&c__2, &lgn) < *n) { + ++lgn; + } + iprmpt = indxq + *n + 1; + iperm = iprmpt + *n * lgn; + iqptr = iperm + *n * lgn; + igivpt = iqptr + *n + 2; + igivcl = igivpt + *n * lgn; + + igivnm = 1; + iq = igivnm + (*n << 1) * lgn; +/* Computing 2nd power */ + i__1 = *n; + iwrem = iq + i__1 * i__1 + 1; + +/* Initialize pointers */ + + i__1 = subpbs; + for (i__ = 0; i__ <= i__1; ++i__) { + iwork[iprmpt + i__] = 1; + iwork[igivpt + i__] = 1; +/* L50: */ + } + iwork[iqptr] = 1; + } + +/* Solve each submatrix eigenproblem at the bottom of the divide and */ +/* conquer tree. */ + + curr = 0; + i__1 = spm1; + for (i__ = 0; i__ <= i__1; ++i__) { + if (i__ == 0) { + submat = 1; + matsiz = iwork[1]; + } else { + submat = iwork[i__] + 1; + matsiz = iwork[i__ + 1] - iwork[i__]; + } + if (*icompq == 2) { + dsteqr_((char *)"I", &matsiz, &d__[submat], &e[submat], &q[submat + + submat * q_dim1], ldq, &work[1], info, (ftnlen)1); + if (*info != 0) { + goto L130; + } + } else { + dsteqr_((char *)"I", &matsiz, &d__[submat], &e[submat], &work[iq - 1 + + iwork[iqptr + curr]], &matsiz, &work[1], info, (ftnlen)1); + if (*info != 0) { + goto L130; + } + if (*icompq == 1) { + dgemm_((char *)"N", (char *)"N", qsiz, &matsiz, &matsiz, &c_b23, &q[submat * + q_dim1 + 1], ldq, &work[iq - 1 + iwork[iqptr + curr]], + &matsiz, &c_b24, &qstore[submat * qstore_dim1 + 1], + ldqs, (ftnlen)1, (ftnlen)1); + } +/* Computing 2nd power */ + i__2 = matsiz; + iwork[iqptr + curr + 1] = iwork[iqptr + curr] + i__2 * i__2; + ++curr; + } + k = 1; + i__2 = iwork[i__ + 1]; + for (j = submat; j <= i__2; ++j) { + iwork[indxq + j] = k; + ++k; +/* L60: */ + } +/* L70: */ + } + +/* Successively merge eigensystems of adjacent submatrices */ +/* into eigensystem for the corresponding larger matrix. */ + +/* while ( SUBPBS > 1 ) */ + + curlvl = 1; +L80: + if (subpbs > 1) { + spm2 = subpbs - 2; + i__1 = spm2; + for (i__ = 0; i__ <= i__1; i__ += 2) { + if (i__ == 0) { + submat = 1; + matsiz = iwork[2]; + msd2 = iwork[1]; + curprb = 0; + } else { + submat = iwork[i__] + 1; + matsiz = iwork[i__ + 2] - iwork[i__]; + msd2 = matsiz / 2; + ++curprb; + } + +/* Merge lower order eigensystems (of size MSD2 and MATSIZ - MSD2) */ +/* into an eigensystem of size MATSIZ. */ +/* DLAED1 is used only for the full eigensystem of a tridiagonal */ +/* matrix. */ +/* DLAED7 handles the cases in which eigenvalues only or eigenvalues */ +/* and eigenvectors of a full symmetric matrix (which was reduced to */ +/* tridiagonal form) are desired. */ + + if (*icompq == 2) { + dlaed1_(&matsiz, &d__[submat], &q[submat + submat * q_dim1], + ldq, &iwork[indxq + submat], &e[submat + msd2 - 1], & + msd2, &work[1], &iwork[subpbs + 1], info); + } else { + dlaed7_(icompq, &matsiz, qsiz, &tlvls, &curlvl, &curprb, &d__[ + submat], &qstore[submat * qstore_dim1 + 1], ldqs, & + iwork[indxq + submat], &e[submat + msd2 - 1], &msd2, & + work[iq], &iwork[iqptr], &iwork[iprmpt], &iwork[iperm] + , &iwork[igivpt], &iwork[igivcl], &work[igivnm], & + work[iwrem], &iwork[subpbs + 1], info); + } + if (*info != 0) { + goto L130; + } + iwork[i__ / 2 + 1] = iwork[i__ + 2]; +/* L90: */ + } + subpbs /= 2; + ++curlvl; + goto L80; + } + +/* end while */ + +/* Re-merge the eigenvalues/vectors which were deflated at the final */ +/* merge step. */ + + if (*icompq == 1) { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + j = iwork[indxq + i__]; + work[i__] = d__[j]; + dcopy_(qsiz, &qstore[j * qstore_dim1 + 1], &c__1, &q[i__ * q_dim1 + + 1], &c__1); +/* L100: */ + } + dcopy_(n, &work[1], &c__1, &d__[1], &c__1); + } else if (*icompq == 2) { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + j = iwork[indxq + i__]; + work[i__] = d__[j]; + dcopy_(n, &q[j * q_dim1 + 1], &c__1, &work[*n * i__ + 1], &c__1); +/* L110: */ + } + dcopy_(n, &work[1], &c__1, &d__[1], &c__1); + dlacpy_((char *)"A", n, n, &work[*n + 1], n, &q[q_offset], ldq, (ftnlen)1); + } else { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + j = iwork[indxq + i__]; + work[i__] = d__[j]; +/* L120: */ + } + dcopy_(n, &work[1], &c__1, &d__[1], &c__1); + } + goto L140; + +L130: + *info = submat * (*n + 1) + submat + matsiz - 1; + +L140: + return 0; + +/* End of DLAED0 */ + +} /* dlaed0_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlaed1.cpp b/lib/linalg/dlaed1.cpp new file mode 100644 index 0000000000..a448e3363e --- /dev/null +++ b/lib/linalg/dlaed1.cpp @@ -0,0 +1,336 @@ +/* fortran/dlaed1.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c_n1 = -1; + +/* > \brief \b DLAED1 used by DSTEDC. Computes the updated eigensystem of a diagonal matrix after modification + by a rank-one symmetric matrix. Used when the original matrix is tridiagonal. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLAED1 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLAED1( N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK, */ +/* INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER CUTPNT, INFO, LDQ, N */ +/* DOUBLE PRECISION RHO */ +/* .. */ +/* .. Array Arguments .. */ +/* INTEGER INDXQ( * ), IWORK( * ) */ +/* DOUBLE PRECISION D( * ), Q( LDQ, * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLAED1 computes the updated eigensystem of a diagonal */ +/* > matrix after modification by a rank-one symmetric matrix. This */ +/* > routine is used only for the eigenproblem which requires all */ +/* > eigenvalues and eigenvectors of a tridiagonal matrix. DLAED7 handles */ +/* > the case in which eigenvalues only or eigenvalues and eigenvectors */ +/* > of a full symmetric matrix (which was reduced to tridiagonal form) */ +/* > are desired. */ +/* > */ +/* > T = Q(in) ( D(in) + RHO * Z*Z**T ) Q**T(in) = Q(out) * D(out) * Q**T(out) */ +/* > */ +/* > where Z = Q**T*u, u is a vector of length N with ones in the */ +/* > CUTPNT and CUTPNT + 1 th elements and zeros elsewhere. */ +/* > */ +/* > The eigenvectors of the original matrix are stored in Q, and the */ +/* > eigenvalues are in D. The algorithm consists of three stages: */ +/* > */ +/* > The first stage consists of deflating the size of the problem */ +/* > when there are multiple eigenvalues or if there is a zero in */ +/* > the Z vector. For each such occurrence the dimension of the */ +/* > secular equation problem is reduced by one. This stage is */ +/* > performed by the routine DLAED2. */ +/* > */ +/* > The second stage consists of calculating the updated */ +/* > eigenvalues. This is done by finding the roots of the secular */ +/* > equation via the routine DLAED4 (as called by DLAED3). */ +/* > This routine also calculates the eigenvectors of the current */ +/* > problem. */ +/* > */ +/* > The final stage consists of computing the updated eigenvectors */ +/* > directly using the updated eigenvalues. The eigenvectors for */ +/* > the current problem are multiplied with the eigenvectors from */ +/* > the overall problem. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The dimension of the symmetric tridiagonal matrix. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension (N) */ +/* > On entry, the eigenvalues of the rank-1-perturbed matrix. */ +/* > On exit, the eigenvalues of the repaired matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] Q */ +/* > \verbatim */ +/* > Q is DOUBLE PRECISION array, dimension (LDQ,N) */ +/* > On entry, the eigenvectors of the rank-1-perturbed matrix. */ +/* > On exit, the eigenvectors of the repaired tridiagonal matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDQ */ +/* > \verbatim */ +/* > LDQ is INTEGER */ +/* > The leading dimension of the array Q. LDQ >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] INDXQ */ +/* > \verbatim */ +/* > INDXQ is INTEGER array, dimension (N) */ +/* > On entry, the permutation which separately sorts the two */ +/* > subproblems in D into ascending order. */ +/* > On exit, the permutation which will reintegrate the */ +/* > subproblems back into sorted order, */ +/* > i.e. D( INDXQ( I = 1, N ) ) will be in ascending order. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] RHO */ +/* > \verbatim */ +/* > RHO is DOUBLE PRECISION */ +/* > The subdiagonal entry used to create the rank-1 modification. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] CUTPNT */ +/* > \verbatim */ +/* > CUTPNT is INTEGER */ +/* > The location of the last eigenvalue in the leading sub-matrix. */ +/* > min(1,N) <= CUTPNT <= N/2. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (4*N + N**2) */ +/* > \endverbatim */ +/* > */ +/* > \param[out] IWORK */ +/* > \verbatim */ +/* > IWORK is INTEGER array, dimension (4*N) */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit. */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ +/* > > 0: if INFO = 1, an eigenvalue did not converge */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup auxOTHERcomputational */ + +/* > \par Contributors: */ +/* ================== */ +/* > */ +/* > Jeff Rutter, Computer Science Division, University of California */ +/* > at Berkeley, USA \n */ +/* > Modified by Francoise Tisseur, University of Tennessee */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dlaed1_(integer *n, doublereal *d__, doublereal *q, + integer *ldq, integer *indxq, doublereal *rho, integer *cutpnt, + doublereal *work, integer *iwork, integer *info) +{ + /* System generated locals */ + integer q_dim1, q_offset, i__1, i__2; + + /* Local variables */ + integer i__, k, n1, n2, is, iw, iz, iq2, zpp1, indx, indxc; + extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, + doublereal *, integer *); + integer indxp; + extern /* Subroutine */ int dlaed2_(integer *, integer *, integer *, + doublereal *, doublereal *, integer *, integer *, doublereal *, + doublereal *, doublereal *, doublereal *, doublereal *, integer *, + integer *, integer *, integer *, integer *), dlaed3_(integer *, + integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, doublereal *, doublereal *, integer *, integer *, + doublereal *, doublereal *, integer *); + integer idlmda; + extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *, + integer *, integer *, integer *), xerbla_(char *, integer *, + ftnlen); + integer coltyp; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --d__; + q_dim1 = *ldq; + q_offset = 1 + q_dim1; + q -= q_offset; + --indxq; + --work; + --iwork; + + /* Function Body */ + *info = 0; + + if (*n < 0) { + *info = -1; + } else if (*ldq < max(1,*n)) { + *info = -4; + } else /* if(complicated condition) */ { +/* Computing MIN */ + i__1 = 1, i__2 = *n / 2; + if (min(i__1,i__2) > *cutpnt || *n / 2 < *cutpnt) { + *info = -7; + } + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DLAED1", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*n == 0) { + return 0; + } + +/* The following values are integer pointers which indicate */ +/* the portion of the workspace */ +/* used by a particular array in DLAED2 and DLAED3. */ + + iz = 1; + idlmda = iz + *n; + iw = idlmda + *n; + iq2 = iw + *n; + + indx = 1; + indxc = indx + *n; + coltyp = indxc + *n; + indxp = coltyp + *n; + + +/* Form the z-vector which consists of the last row of Q_1 and the */ +/* first row of Q_2. */ + + dcopy_(cutpnt, &q[*cutpnt + q_dim1], ldq, &work[iz], &c__1); + zpp1 = *cutpnt + 1; + i__1 = *n - *cutpnt; + dcopy_(&i__1, &q[zpp1 + zpp1 * q_dim1], ldq, &work[iz + *cutpnt], &c__1); + +/* Deflate eigenvalues. */ + + dlaed2_(&k, n, cutpnt, &d__[1], &q[q_offset], ldq, &indxq[1], rho, &work[ + iz], &work[idlmda], &work[iw], &work[iq2], &iwork[indx], &iwork[ + indxc], &iwork[indxp], &iwork[coltyp], info); + + if (*info != 0) { + goto L20; + } + +/* Solve Secular Equation. */ + + if (k != 0) { + is = (iwork[coltyp] + iwork[coltyp + 1]) * *cutpnt + (iwork[coltyp + + 1] + iwork[coltyp + 2]) * (*n - *cutpnt) + iq2; + dlaed3_(&k, n, cutpnt, &d__[1], &q[q_offset], ldq, rho, &work[idlmda], + &work[iq2], &iwork[indxc], &iwork[coltyp], &work[iw], &work[ + is], info); + if (*info != 0) { + goto L20; + } + +/* Prepare the INDXQ sorting permutation. */ + + n1 = k; + n2 = *n - k; + dlamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &indxq[1]); + } else { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + indxq[i__] = i__; +/* L10: */ + } + } + +L20: + return 0; + +/* End of DLAED1 */ + +} /* dlaed1_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlaed2.cpp b/lib/linalg/dlaed2.cpp new file mode 100644 index 0000000000..746c07ba33 --- /dev/null +++ b/lib/linalg/dlaed2.cpp @@ -0,0 +1,646 @@ +/* fortran/dlaed2.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static doublereal c_b3 = -1.; +static integer c__1 = 1; + +/* > \brief \b DLAED2 used by DSTEDC. Merges eigenvalues and deflates secular equation. Used when the original + matrix is tridiagonal. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLAED2 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLAED2( K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W, */ +/* Q2, INDX, INDXC, INDXP, COLTYP, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INFO, K, LDQ, N, N1 */ +/* DOUBLE PRECISION RHO */ +/* .. */ +/* .. Array Arguments .. */ +/* INTEGER COLTYP( * ), INDX( * ), INDXC( * ), INDXP( * ), */ +/* $ INDXQ( * ) */ +/* DOUBLE PRECISION D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( * ), */ +/* $ W( * ), Z( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLAED2 merges the two sets of eigenvalues together into a single */ +/* > sorted set. Then it tries to deflate the size of the problem. */ +/* > There are two ways in which deflation can occur: when two or more */ +/* > eigenvalues are close together or if there is a tiny entry in the */ +/* > Z vector. For each such occurrence the order of the related secular */ +/* > equation problem is reduced by one. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[out] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > The number of non-deflated eigenvalues, and the order of the */ +/* > related secular equation. 0 <= K <=N. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The dimension of the symmetric tridiagonal matrix. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N1 */ +/* > \verbatim */ +/* > N1 is INTEGER */ +/* > The location of the last eigenvalue in the leading sub-matrix. */ +/* > min(1,N) <= N1 <= N/2. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension (N) */ +/* > On entry, D contains the eigenvalues of the two submatrices to */ +/* > be combined. */ +/* > On exit, D contains the trailing (N-K) updated eigenvalues */ +/* > (those which were deflated) sorted into increasing order. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] Q */ +/* > \verbatim */ +/* > Q is DOUBLE PRECISION array, dimension (LDQ, N) */ +/* > On entry, Q contains the eigenvectors of two submatrices in */ +/* > the two square blocks with corners at (1,1), (N1,N1) */ +/* > and (N1+1, N1+1), (N,N). */ +/* > On exit, Q contains the trailing (N-K) updated eigenvectors */ +/* > (those which were deflated) in its last N-K columns. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDQ */ +/* > \verbatim */ +/* > LDQ is INTEGER */ +/* > The leading dimension of the array Q. LDQ >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] INDXQ */ +/* > \verbatim */ +/* > INDXQ is INTEGER array, dimension (N) */ +/* > The permutation which separately sorts the two sub-problems */ +/* > in D into ascending order. Note that elements in the second */ +/* > half of this permutation must first have N1 added to their */ +/* > values. Destroyed on exit. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] RHO */ +/* > \verbatim */ +/* > RHO is DOUBLE PRECISION */ +/* > On entry, the off-diagonal element associated with the rank-1 */ +/* > cut which originally split the two submatrices which are now */ +/* > being recombined. */ +/* > On exit, RHO has been modified to the value required by */ +/* > DLAED3. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] Z */ +/* > \verbatim */ +/* > Z is DOUBLE PRECISION array, dimension (N) */ +/* > On entry, Z contains the updating vector (the last */ +/* > row of the first sub-eigenvector matrix and the first row of */ +/* > the second sub-eigenvector matrix). */ +/* > On exit, the contents of Z have been destroyed by the updating */ +/* > process. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] DLAMDA */ +/* > \verbatim */ +/* > DLAMDA is DOUBLE PRECISION array, dimension (N) */ +/* > A copy of the first K eigenvalues which will be used by */ +/* > DLAED3 to form the secular equation. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] W */ +/* > \verbatim */ +/* > W is DOUBLE PRECISION array, dimension (N) */ +/* > The first k values of the final deflation-altered z-vector */ +/* > which will be passed to DLAED3. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] Q2 */ +/* > \verbatim */ +/* > Q2 is DOUBLE PRECISION array, dimension (N1**2+(N-N1)**2) */ +/* > A copy of the first K eigenvectors which will be used by */ +/* > DLAED3 in a matrix multiply (DGEMM) to solve for the new */ +/* > eigenvectors. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INDX */ +/* > \verbatim */ +/* > INDX is INTEGER array, dimension (N) */ +/* > The permutation used to sort the contents of DLAMDA into */ +/* > ascending order. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INDXC */ +/* > \verbatim */ +/* > INDXC is INTEGER array, dimension (N) */ +/* > The permutation used to arrange the columns of the deflated */ +/* > Q matrix into three groups: the first group contains non-zero */ +/* > elements only at and above N1, the second contains */ +/* > non-zero elements only below N1, and the third is dense. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INDXP */ +/* > \verbatim */ +/* > INDXP is INTEGER array, dimension (N) */ +/* > The permutation used to place deflated values of D at the end */ +/* > of the array. INDXP(1:K) points to the nondeflated D-values */ +/* > and INDXP(K+1:N) points to the deflated eigenvalues. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] COLTYP */ +/* > \verbatim */ +/* > COLTYP is INTEGER array, dimension (N) */ +/* > During execution, a label which will indicate which of the */ +/* > following types a column in the Q2 matrix is: */ +/* > 1 : non-zero in the upper half only; */ +/* > 2 : dense; */ +/* > 3 : non-zero in the lower half only; */ +/* > 4 : deflated. */ +/* > On exit, COLTYP(i) is the number of columns of type i, */ +/* > for i=1 to 4 only. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit. */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup auxOTHERcomputational */ + +/* > \par Contributors: */ +/* ================== */ +/* > */ +/* > Jeff Rutter, Computer Science Division, University of California */ +/* > at Berkeley, USA \n */ +/* > Modified by Francoise Tisseur, University of Tennessee */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dlaed2_(integer *k, integer *n, integer *n1, doublereal * + d__, doublereal *q, integer *ldq, integer *indxq, doublereal *rho, + doublereal *z__, doublereal *dlamda, doublereal *w, doublereal *q2, + integer *indx, integer *indxc, integer *indxp, integer *coltyp, + integer *info) +{ + /* System generated locals */ + integer q_dim1, q_offset, i__1, i__2; + doublereal d__1, d__2, d__3, d__4; + + /* Builtin functions */ + double sqrt(doublereal); + + /* Local variables */ + doublereal c__; + integer i__, j; + doublereal s, t; + integer k2, n2, ct, nj, pj, js, iq1, iq2, n1p1; + doublereal eps, tau, tol; + integer psm[4], imax, jmax; + extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, + doublereal *, integer *, doublereal *, doublereal *); + integer ctot[4]; + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *), dcopy_(integer *, doublereal *, integer *, doublereal + *, integer *); + extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, + ftnlen); + extern integer idamax_(integer *, doublereal *, integer *); + extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *, + integer *, integer *, integer *), dlacpy_(char *, integer *, + integer *, doublereal *, integer *, doublereal *, integer *, + ftnlen), xerbla_(char *, integer *, ftnlen); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Arrays .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --d__; + q_dim1 = *ldq; + q_offset = 1 + q_dim1; + q -= q_offset; + --indxq; + --z__; + --dlamda; + --w; + --q2; + --indx; + --indxc; + --indxp; + --coltyp; + + /* Function Body */ + *info = 0; + + if (*n < 0) { + *info = -2; + } else if (*ldq < max(1,*n)) { + *info = -6; + } else /* if(complicated condition) */ { +/* Computing MIN */ + i__1 = 1, i__2 = *n / 2; + if (min(i__1,i__2) > *n1 || *n / 2 < *n1) { + *info = -3; + } + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DLAED2", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*n == 0) { + return 0; + } + + n2 = *n - *n1; + n1p1 = *n1 + 1; + + if (*rho < 0.) { + dscal_(&n2, &c_b3, &z__[n1p1], &c__1); + } + +/* Normalize z so that norm(z) = 1. Since z is the concatenation of */ +/* two normalized vectors, norm2(z) = sqrt(2). */ + + t = 1. / sqrt(2.); + dscal_(n, &t, &z__[1], &c__1); + +/* RHO = ABS( norm(z)**2 * RHO ) */ + + *rho = (d__1 = *rho * 2., abs(d__1)); + +/* Sort the eigenvalues into increasing order */ + + i__1 = *n; + for (i__ = n1p1; i__ <= i__1; ++i__) { + indxq[i__] += *n1; +/* L10: */ + } + +/* re-integrate the deflated parts from the last pass */ + + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + dlamda[i__] = d__[indxq[i__]]; +/* L20: */ + } + dlamrg_(n1, &n2, &dlamda[1], &c__1, &c__1, &indxc[1]); + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + indx[i__] = indxq[indxc[i__]]; +/* L30: */ + } + +/* Calculate the allowable deflation tolerance */ + + imax = idamax_(n, &z__[1], &c__1); + jmax = idamax_(n, &d__[1], &c__1); + eps = dlamch_((char *)"Epsilon", (ftnlen)7); +/* Computing MAX */ + d__3 = (d__1 = d__[jmax], abs(d__1)), d__4 = (d__2 = z__[imax], abs(d__2)) + ; + tol = eps * 8. * max(d__3,d__4); + +/* If the rank-1 modifier is small enough, no more needs to be done */ +/* except to reorganize Q so that its columns correspond with the */ +/* elements in D. */ + + if (*rho * (d__1 = z__[imax], abs(d__1)) <= tol) { + *k = 0; + iq2 = 1; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__ = indx[j]; + dcopy_(n, &q[i__ * q_dim1 + 1], &c__1, &q2[iq2], &c__1); + dlamda[j] = d__[i__]; + iq2 += *n; +/* L40: */ + } + dlacpy_((char *)"A", n, n, &q2[1], n, &q[q_offset], ldq, (ftnlen)1); + dcopy_(n, &dlamda[1], &c__1, &d__[1], &c__1); + goto L190; + } + +/* If there are multiple eigenvalues then the problem deflates. Here */ +/* the number of equal eigenvalues are found. As each equal */ +/* eigenvalue is found, an elementary reflector is computed to rotate */ +/* the corresponding eigensubspace so that the corresponding */ +/* components of Z are zero in this new basis. */ + + i__1 = *n1; + for (i__ = 1; i__ <= i__1; ++i__) { + coltyp[i__] = 1; +/* L50: */ + } + i__1 = *n; + for (i__ = n1p1; i__ <= i__1; ++i__) { + coltyp[i__] = 3; +/* L60: */ + } + + + *k = 0; + k2 = *n + 1; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + nj = indx[j]; + if (*rho * (d__1 = z__[nj], abs(d__1)) <= tol) { + +/* Deflate due to small z component. */ + + --k2; + coltyp[nj] = 4; + indxp[k2] = nj; + if (j == *n) { + goto L100; + } + } else { + pj = nj; + goto L80; + } +/* L70: */ + } +L80: + ++j; + nj = indx[j]; + if (j > *n) { + goto L100; + } + if (*rho * (d__1 = z__[nj], abs(d__1)) <= tol) { + +/* Deflate due to small z component. */ + + --k2; + coltyp[nj] = 4; + indxp[k2] = nj; + } else { + +/* Check if eigenvalues are close enough to allow deflation. */ + + s = z__[pj]; + c__ = z__[nj]; + +/* Find sqrt(a**2+b**2) without overflow or */ +/* destructive underflow. */ + + tau = dlapy2_(&c__, &s); + t = d__[nj] - d__[pj]; + c__ /= tau; + s = -s / tau; + if ((d__1 = t * c__ * s, abs(d__1)) <= tol) { + +/* Deflation is possible. */ + + z__[nj] = tau; + z__[pj] = 0.; + if (coltyp[nj] != coltyp[pj]) { + coltyp[nj] = 2; + } + coltyp[pj] = 4; + drot_(n, &q[pj * q_dim1 + 1], &c__1, &q[nj * q_dim1 + 1], &c__1, & + c__, &s); +/* Computing 2nd power */ + d__1 = c__; +/* Computing 2nd power */ + d__2 = s; + t = d__[pj] * (d__1 * d__1) + d__[nj] * (d__2 * d__2); +/* Computing 2nd power */ + d__1 = s; +/* Computing 2nd power */ + d__2 = c__; + d__[nj] = d__[pj] * (d__1 * d__1) + d__[nj] * (d__2 * d__2); + d__[pj] = t; + --k2; + i__ = 1; +L90: + if (k2 + i__ <= *n) { + if (d__[pj] < d__[indxp[k2 + i__]]) { + indxp[k2 + i__ - 1] = indxp[k2 + i__]; + indxp[k2 + i__] = pj; + ++i__; + goto L90; + } else { + indxp[k2 + i__ - 1] = pj; + } + } else { + indxp[k2 + i__ - 1] = pj; + } + pj = nj; + } else { + ++(*k); + dlamda[*k] = d__[pj]; + w[*k] = z__[pj]; + indxp[*k] = pj; + pj = nj; + } + } + goto L80; +L100: + +/* Record the last eigenvalue. */ + + ++(*k); + dlamda[*k] = d__[pj]; + w[*k] = z__[pj]; + indxp[*k] = pj; + +/* Count up the total number of the various types of columns, then */ +/* form a permutation which positions the four column types into */ +/* four uniform groups (although one or more of these groups may be */ +/* empty). */ + + for (j = 1; j <= 4; ++j) { + ctot[j - 1] = 0; +/* L110: */ + } + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + ct = coltyp[j]; + ++ctot[ct - 1]; +/* L120: */ + } + +/* PSM(*) = Position in SubMatrix (of types 1 through 4) */ + + psm[0] = 1; + psm[1] = ctot[0] + 1; + psm[2] = psm[1] + ctot[1]; + psm[3] = psm[2] + ctot[2]; + *k = *n - ctot[3]; + +/* Fill out the INDXC array so that the permutation which it induces */ +/* will place all type-1 columns first, all type-2 columns next, */ +/* then all type-3's, and finally all type-4's. */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + js = indxp[j]; + ct = coltyp[js]; + indx[psm[ct - 1]] = js; + indxc[psm[ct - 1]] = j; + ++psm[ct - 1]; +/* L130: */ + } + +/* Sort the eigenvalues and corresponding eigenvectors into DLAMDA */ +/* and Q2 respectively. The eigenvalues/vectors which were not */ +/* deflated go into the first K slots of DLAMDA and Q2 respectively, */ +/* while those which were deflated go into the last N - K slots. */ + + i__ = 1; + iq1 = 1; + iq2 = (ctot[0] + ctot[1]) * *n1 + 1; + i__1 = ctot[0]; + for (j = 1; j <= i__1; ++j) { + js = indx[i__]; + dcopy_(n1, &q[js * q_dim1 + 1], &c__1, &q2[iq1], &c__1); + z__[i__] = d__[js]; + ++i__; + iq1 += *n1; +/* L140: */ + } + + i__1 = ctot[1]; + for (j = 1; j <= i__1; ++j) { + js = indx[i__]; + dcopy_(n1, &q[js * q_dim1 + 1], &c__1, &q2[iq1], &c__1); + dcopy_(&n2, &q[*n1 + 1 + js * q_dim1], &c__1, &q2[iq2], &c__1); + z__[i__] = d__[js]; + ++i__; + iq1 += *n1; + iq2 += n2; +/* L150: */ + } + + i__1 = ctot[2]; + for (j = 1; j <= i__1; ++j) { + js = indx[i__]; + dcopy_(&n2, &q[*n1 + 1 + js * q_dim1], &c__1, &q2[iq2], &c__1); + z__[i__] = d__[js]; + ++i__; + iq2 += n2; +/* L160: */ + } + + iq1 = iq2; + i__1 = ctot[3]; + for (j = 1; j <= i__1; ++j) { + js = indx[i__]; + dcopy_(n, &q[js * q_dim1 + 1], &c__1, &q2[iq2], &c__1); + iq2 += *n; + z__[i__] = d__[js]; + ++i__; +/* L170: */ + } + +/* The deflated eigenvalues and their corresponding vectors go back */ +/* into the last N - K slots of D and Q respectively. */ + + if (*k < *n) { + dlacpy_((char *)"A", n, &ctot[3], &q2[iq1], n, &q[(*k + 1) * q_dim1 + 1], ldq, + (ftnlen)1); + i__1 = *n - *k; + dcopy_(&i__1, &z__[*k + 1], &c__1, &d__[*k + 1], &c__1); + } + +/* Copy CTOT into COLTYP for referencing in DLAED3. */ + + for (j = 1; j <= 4; ++j) { + coltyp[j] = ctot[j - 1]; +/* L180: */ + } + +L190: + return 0; + +/* End of DLAED2 */ + +} /* dlaed2_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlaed3.cpp b/lib/linalg/dlaed3.cpp new file mode 100644 index 0000000000..e56c3fb41b --- /dev/null +++ b/lib/linalg/dlaed3.cpp @@ -0,0 +1,437 @@ +/* fortran/dlaed3.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static doublereal c_b22 = 1.; +static doublereal c_b23 = 0.; + +/* > \brief \b DLAED3 used by DSTEDC. Finds the roots of the secular equation and updates the eigenvectors. Us +ed when the original matrix is tridiagonal. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLAED3 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLAED3( K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX, */ +/* CTOT, W, S, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INFO, K, LDQ, N, N1 */ +/* DOUBLE PRECISION RHO */ +/* .. */ +/* .. Array Arguments .. */ +/* INTEGER CTOT( * ), INDX( * ) */ +/* DOUBLE PRECISION D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( * ), */ +/* $ S( * ), W( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLAED3 finds the roots of the secular equation, as defined by the */ +/* > values in D, W, and RHO, between 1 and K. It makes the */ +/* > appropriate calls to DLAED4 and then updates the eigenvectors by */ +/* > multiplying the matrix of eigenvectors of the pair of eigensystems */ +/* > being combined by the matrix of eigenvectors of the K-by-K system */ +/* > which is solved here. */ +/* > */ +/* > This code makes very mild assumptions about floating point */ +/* > arithmetic. It will work on machines with a guard digit in */ +/* > add/subtract, or on those binary machines without guard digits */ +/* > which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. */ +/* > It could conceivably fail on hexadecimal or decimal machines */ +/* > without guard digits, but we know of none. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > The number of terms in the rational function to be solved by */ +/* > DLAED4. K >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of rows and columns in the Q matrix. */ +/* > N >= K (deflation may result in N>K). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N1 */ +/* > \verbatim */ +/* > N1 is INTEGER */ +/* > The location of the last eigenvalue in the leading submatrix. */ +/* > min(1,N) <= N1 <= N/2. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension (N) */ +/* > D(I) contains the updated eigenvalues for */ +/* > 1 <= I <= K. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] Q */ +/* > \verbatim */ +/* > Q is DOUBLE PRECISION array, dimension (LDQ,N) */ +/* > Initially the first K columns are used as workspace. */ +/* > On output the columns 1 to K contain */ +/* > the updated eigenvectors. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDQ */ +/* > \verbatim */ +/* > LDQ is INTEGER */ +/* > The leading dimension of the array Q. LDQ >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] RHO */ +/* > \verbatim */ +/* > RHO is DOUBLE PRECISION */ +/* > The value of the parameter in the rank one update equation. */ +/* > RHO >= 0 required. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] DLAMDA */ +/* > \verbatim */ +/* > DLAMDA is DOUBLE PRECISION array, dimension (K) */ +/* > The first K elements of this array contain the old roots */ +/* > of the deflated updating problem. These are the poles */ +/* > of the secular equation. May be changed on output by */ +/* > having lowest order bit set to zero on Cray X-MP, Cray Y-MP, */ +/* > Cray-2, or Cray C-90, as described above. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] Q2 */ +/* > \verbatim */ +/* > Q2 is DOUBLE PRECISION array, dimension (LDQ2*N) */ +/* > The first K columns of this matrix contain the non-deflated */ +/* > eigenvectors for the split problem. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INDX */ +/* > \verbatim */ +/* > INDX is INTEGER array, dimension (N) */ +/* > The permutation used to arrange the columns of the deflated */ +/* > Q matrix into three groups (see DLAED2). */ +/* > The rows of the eigenvectors found by DLAED4 must be likewise */ +/* > permuted before the matrix multiply can take place. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] CTOT */ +/* > \verbatim */ +/* > CTOT is INTEGER array, dimension (4) */ +/* > A count of the total number of the various types of columns */ +/* > in Q, as described in INDX. The fourth column type is any */ +/* > column which has been deflated. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] W */ +/* > \verbatim */ +/* > W is DOUBLE PRECISION array, dimension (K) */ +/* > The first K elements of this array contain the components */ +/* > of the deflation-adjusted updating vector. Destroyed on */ +/* > output. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] S */ +/* > \verbatim */ +/* > S is DOUBLE PRECISION array, dimension (N1 + 1)*K */ +/* > Will contain the eigenvectors of the repaired matrix which */ +/* > will be multiplied by the previously accumulated eigenvectors */ +/* > to update the system. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit. */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ +/* > > 0: if INFO = 1, an eigenvalue did not converge */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup auxOTHERcomputational */ + +/* > \par Contributors: */ +/* ================== */ +/* > */ +/* > Jeff Rutter, Computer Science Division, University of California */ +/* > at Berkeley, USA \n */ +/* > Modified by Francoise Tisseur, University of Tennessee */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dlaed3_(integer *k, integer *n, integer *n1, doublereal * + d__, doublereal *q, integer *ldq, doublereal *rho, doublereal *dlamda, + doublereal *q2, integer *indx, integer *ctot, doublereal *w, + doublereal *s, integer *info) +{ + /* System generated locals */ + integer q_dim1, q_offset, i__1, i__2; + doublereal d__1; + + /* Builtin functions */ + double sqrt(doublereal), d_sign(doublereal *, doublereal *); + + /* Local variables */ + integer i__, j, n2, n12, ii, n23, iq2; + doublereal temp; + extern doublereal dnrm2_(integer *, doublereal *, integer *); + extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen), + dcopy_(integer *, doublereal *, integer *, doublereal *, integer + *), dlaed4_(integer *, integer *, doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *, integer *); + extern doublereal dlamc3_(doublereal *, doublereal *); + extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, + doublereal *, integer *, doublereal *, integer *, ftnlen), + dlaset_(char *, integer *, integer *, doublereal *, doublereal *, + doublereal *, integer *, ftnlen), xerbla_(char *, integer *, + ftnlen); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --d__; + q_dim1 = *ldq; + q_offset = 1 + q_dim1; + q -= q_offset; + --dlamda; + --q2; + --indx; + --ctot; + --w; + --s; + + /* Function Body */ + *info = 0; + + if (*k < 0) { + *info = -1; + } else if (*n < *k) { + *info = -2; + } else if (*ldq < max(1,*n)) { + *info = -6; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DLAED3", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*k == 0) { + return 0; + } + +/* Modify values DLAMDA(i) to make sure all DLAMDA(i)-DLAMDA(j) can */ +/* be computed with high relative accuracy (barring over/underflow). */ +/* This is a problem on machines without a guard digit in */ +/* add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2). */ +/* The following code replaces DLAMDA(I) by 2*DLAMDA(I)-DLAMDA(I), */ +/* which on any of these machines zeros out the bottommost */ +/* bit of DLAMDA(I) if it is 1; this makes the subsequent */ +/* subtractions DLAMDA(I)-DLAMDA(J) unproblematic when cancellation */ +/* occurs. On binary machines with a guard digit (almost all */ +/* machines) it does not change DLAMDA(I) at all. On hexadecimal */ +/* and decimal machines with a guard digit, it slightly */ +/* changes the bottommost bits of DLAMDA(I). It does not account */ +/* for hexadecimal or decimal machines without guard digits */ +/* (we know of none). We use a subroutine call to compute */ +/* 2*DLAMBDA(I) to prevent optimizing compilers from eliminating */ +/* this code. */ + + i__1 = *k; + for (i__ = 1; i__ <= i__1; ++i__) { + dlamda[i__] = dlamc3_(&dlamda[i__], &dlamda[i__]) - dlamda[i__]; +/* L10: */ + } + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + dlaed4_(k, &j, &dlamda[1], &w[1], &q[j * q_dim1 + 1], rho, &d__[j], + info); + +/* If the zero finder fails, the computation is terminated. */ + + if (*info != 0) { + goto L120; + } +/* L20: */ + } + + if (*k == 1) { + goto L110; + } + if (*k == 2) { + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + w[1] = q[j * q_dim1 + 1]; + w[2] = q[j * q_dim1 + 2]; + ii = indx[1]; + q[j * q_dim1 + 1] = w[ii]; + ii = indx[2]; + q[j * q_dim1 + 2] = w[ii]; +/* L30: */ + } + goto L110; + } + +/* Compute updated W. */ + + dcopy_(k, &w[1], &c__1, &s[1], &c__1); + +/* Initialize W(I) = Q(I,I) */ + + i__1 = *ldq + 1; + dcopy_(k, &q[q_offset], &i__1, &w[1], &c__1); + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]); +/* L40: */ + } + i__2 = *k; + for (i__ = j + 1; i__ <= i__2; ++i__) { + w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]); +/* L50: */ + } +/* L60: */ + } + i__1 = *k; + for (i__ = 1; i__ <= i__1; ++i__) { + d__1 = sqrt(-w[i__]); + w[i__] = d_sign(&d__1, &s[i__]); +/* L70: */ + } + +/* Compute eigenvectors of the modified rank-1 modification. */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *k; + for (i__ = 1; i__ <= i__2; ++i__) { + s[i__] = w[i__] / q[i__ + j * q_dim1]; +/* L80: */ + } + temp = dnrm2_(k, &s[1], &c__1); + i__2 = *k; + for (i__ = 1; i__ <= i__2; ++i__) { + ii = indx[i__]; + q[i__ + j * q_dim1] = s[ii] / temp; +/* L90: */ + } +/* L100: */ + } + +/* Compute the updated eigenvectors. */ + +L110: + + n2 = *n - *n1; + n12 = ctot[1] + ctot[2]; + n23 = ctot[2] + ctot[3]; + + dlacpy_((char *)"A", &n23, k, &q[ctot[1] + 1 + q_dim1], ldq, &s[1], &n23, (ftnlen) + 1); + iq2 = *n1 * n12 + 1; + if (n23 != 0) { + dgemm_((char *)"N", (char *)"N", &n2, k, &n23, &c_b22, &q2[iq2], &n2, &s[1], &n23, & + c_b23, &q[*n1 + 1 + q_dim1], ldq, (ftnlen)1, (ftnlen)1); + } else { + dlaset_((char *)"A", &n2, k, &c_b23, &c_b23, &q[*n1 + 1 + q_dim1], ldq, ( + ftnlen)1); + } + + dlacpy_((char *)"A", &n12, k, &q[q_offset], ldq, &s[1], &n12, (ftnlen)1); + if (n12 != 0) { + dgemm_((char *)"N", (char *)"N", n1, k, &n12, &c_b22, &q2[1], n1, &s[1], &n12, &c_b23, + &q[q_offset], ldq, (ftnlen)1, (ftnlen)1); + } else { + dlaset_((char *)"A", n1, k, &c_b23, &c_b23, &q[q_dim1 + 1], ldq, (ftnlen)1); + } + + +L120: + return 0; + +/* End of DLAED3 */ + +} /* dlaed3_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlaed4.cpp b/lib/linalg/dlaed4.cpp new file mode 100644 index 0000000000..5cc622887d --- /dev/null +++ b/lib/linalg/dlaed4.cpp @@ -0,0 +1,1036 @@ +/* fortran/dlaed4.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DLAED4 used by DSTEDC. Finds a single root of the secular equation. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLAED4 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLAED4( N, I, D, Z, DELTA, RHO, DLAM, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER I, INFO, N */ +/* DOUBLE PRECISION DLAM, RHO */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION D( * ), DELTA( * ), Z( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > This subroutine computes the I-th updated eigenvalue of a symmetric */ +/* > rank-one modification to a diagonal matrix whose elements are */ +/* > given in the array d, and that */ +/* > */ +/* > D(i) < D(j) for i < j */ +/* > */ +/* > and that RHO > 0. This is arranged by the calling routine, and is */ +/* > no loss in generality. The rank-one modified system is thus */ +/* > */ +/* > diag( D ) + RHO * Z * Z_transpose. */ +/* > */ +/* > where we assume the Euclidean norm of Z is 1. */ +/* > */ +/* > The method consists of approximating the rational functions in the */ +/* > secular equation by simpler interpolating rational functions. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The length of all arrays. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] I */ +/* > \verbatim */ +/* > I is INTEGER */ +/* > The index of the eigenvalue to be computed. 1 <= I <= N. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension (N) */ +/* > The original eigenvalues. It is assumed that they are in */ +/* > order, D(I) < D(J) for I < J. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] Z */ +/* > \verbatim */ +/* > Z is DOUBLE PRECISION array, dimension (N) */ +/* > The components of the updating vector. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] DELTA */ +/* > \verbatim */ +/* > DELTA is DOUBLE PRECISION array, dimension (N) */ +/* > If N > 2, DELTA contains (D(j) - lambda_I) in its j-th */ +/* > component. If N = 1, then DELTA(1) = 1. If N = 2, see DLAED5 */ +/* > for detail. The vector DELTA contains the information necessary */ +/* > to construct the eigenvectors by DLAED3 and DLAED9. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] RHO */ +/* > \verbatim */ +/* > RHO is DOUBLE PRECISION */ +/* > The scalar in the symmetric updating formula. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] DLAM */ +/* > \verbatim */ +/* > DLAM is DOUBLE PRECISION */ +/* > The computed lambda_I, the I-th updated eigenvalue. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > > 0: if INFO = 1, the updating process failed. */ +/* > \endverbatim */ + +/* > \par Internal Parameters: */ +/* ========================= */ +/* > */ +/* > \verbatim */ +/* > Logical variable ORGATI (origin-at-i?) is used for distinguishing */ +/* > whether D(i) or D(i+1) is treated as the origin. */ +/* > */ +/* > ORGATI = .true. origin at i */ +/* > ORGATI = .false. origin at i+1 */ +/* > */ +/* > Logical variable SWTCH3 (switch-for-3-poles?) is for noting */ +/* > if we are working with THREE poles! */ +/* > */ +/* > MAXIT is the maximum number of iterations allowed for each */ +/* > eigenvalue. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup auxOTHERcomputational */ + +/* > \par Contributors: */ +/* ================== */ +/* > */ +/* > Ren-Cang Li, Computer Science Division, University of California */ +/* > at Berkeley, USA */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dlaed4_(integer *n, integer *i__, doublereal *d__, + doublereal *z__, doublereal *delta, doublereal *rho, doublereal *dlam, + integer *info) +{ + /* System generated locals */ + integer i__1; + doublereal d__1; + + /* Builtin functions */ + double sqrt(doublereal); + + /* Local variables */ + doublereal a, b, c__; + integer j; + doublereal w; + integer ii; + doublereal dw, zz[3]; + integer ip1; + doublereal del, eta, phi, eps, tau, psi; + integer iim1, iip1; + doublereal dphi, dpsi; + integer iter; + doublereal temp, prew, temp1, dltlb, dltub, midpt; + integer niter; + logical swtch; + extern /* Subroutine */ int dlaed5_(integer *, doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *), dlaed6_(integer *, + logical *, doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, integer *); + logical swtch3; + extern doublereal dlamch_(char *, ftnlen); + logical orgati; + doublereal erretm, rhoinv; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Local Arrays .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Since this routine is called in an inner loop, we do no argument */ +/* checking. */ + +/* Quick return for N=1 and 2. */ + + /* Parameter adjustments */ + --delta; + --z__; + --d__; + + /* Function Body */ + *info = 0; + if (*n == 1) { + +/* Presumably, I=1 upon entry */ + + *dlam = d__[1] + *rho * z__[1] * z__[1]; + delta[1] = 1.; + return 0; + } + if (*n == 2) { + dlaed5_(i__, &d__[1], &z__[1], &delta[1], rho, dlam); + return 0; + } + +/* Compute machine epsilon */ + + eps = dlamch_((char *)"Epsilon", (ftnlen)7); + rhoinv = 1. / *rho; + +/* The case I = N */ + + if (*i__ == *n) { + +/* Initialize some basic variables */ + + ii = *n - 1; + niter = 1; + +/* Calculate initial guess */ + + midpt = *rho / 2.; + +/* If ||Z||_2 is not one, then TEMP should be set to */ +/* RHO * ||Z||_2^2 / TWO */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + delta[j] = d__[j] - d__[*i__] - midpt; +/* L10: */ + } + + psi = 0.; + i__1 = *n - 2; + for (j = 1; j <= i__1; ++j) { + psi += z__[j] * z__[j] / delta[j]; +/* L20: */ + } + + c__ = rhoinv + psi; + w = c__ + z__[ii] * z__[ii] / delta[ii] + z__[*n] * z__[*n] / delta[* + n]; + + if (w <= 0.) { + temp = z__[*n - 1] * z__[*n - 1] / (d__[*n] - d__[*n - 1] + *rho) + + z__[*n] * z__[*n] / *rho; + if (c__ <= temp) { + tau = *rho; + } else { + del = d__[*n] - d__[*n - 1]; + a = -c__ * del + z__[*n - 1] * z__[*n - 1] + z__[*n] * z__[*n] + ; + b = z__[*n] * z__[*n] * del; + if (a < 0.) { + tau = b * 2. / (sqrt(a * a + b * 4. * c__) - a); + } else { + tau = (a + sqrt(a * a + b * 4. * c__)) / (c__ * 2.); + } + } + +/* It can be proved that */ +/* D(N)+RHO/2 <= LAMBDA(N) < D(N)+TAU <= D(N)+RHO */ + + dltlb = midpt; + dltub = *rho; + } else { + del = d__[*n] - d__[*n - 1]; + a = -c__ * del + z__[*n - 1] * z__[*n - 1] + z__[*n] * z__[*n]; + b = z__[*n] * z__[*n] * del; + if (a < 0.) { + tau = b * 2. / (sqrt(a * a + b * 4. * c__) - a); + } else { + tau = (a + sqrt(a * a + b * 4. * c__)) / (c__ * 2.); + } + +/* It can be proved that */ +/* D(N) < D(N)+TAU < LAMBDA(N) < D(N)+RHO/2 */ + + dltlb = 0.; + dltub = midpt; + } + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + delta[j] = d__[j] - d__[*i__] - tau; +/* L30: */ + } + +/* Evaluate PSI and the derivative DPSI */ + + dpsi = 0.; + psi = 0.; + erretm = 0.; + i__1 = ii; + for (j = 1; j <= i__1; ++j) { + temp = z__[j] / delta[j]; + psi += z__[j] * temp; + dpsi += temp * temp; + erretm += psi; +/* L40: */ + } + erretm = abs(erretm); + +/* Evaluate PHI and the derivative DPHI */ + + temp = z__[*n] / delta[*n]; + phi = z__[*n] * temp; + dphi = temp * temp; + erretm = (-phi - psi) * 8. + erretm - phi + rhoinv + abs(tau) * (dpsi + + dphi); + + w = rhoinv + phi + psi; + +/* Test for convergence */ + + if (abs(w) <= eps * erretm) { + *dlam = d__[*i__] + tau; + goto L250; + } + + if (w <= 0.) { + dltlb = max(dltlb,tau); + } else { + dltub = min(dltub,tau); + } + +/* Calculate the new step */ + + ++niter; + c__ = w - delta[*n - 1] * dpsi - delta[*n] * dphi; + a = (delta[*n - 1] + delta[*n]) * w - delta[*n - 1] * delta[*n] * ( + dpsi + dphi); + b = delta[*n - 1] * delta[*n] * w; + if (c__ < 0.) { + c__ = abs(c__); + } + if (c__ == 0.) { +/* ETA = B/A */ +/* ETA = RHO - TAU */ +/* ETA = DLTUB - TAU */ + +/* Update proposed by Li, Ren-Cang: */ + eta = -w / (dpsi + dphi); + } else if (a >= 0.) { + eta = (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (c__ + * 2.); + } else { + eta = b * 2. / (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1))) + ); + } + +/* Note, eta should be positive if w is negative, and */ +/* eta should be negative otherwise. However, */ +/* if for some reason caused by roundoff, eta*w > 0, */ +/* we simply use one Newton step instead. This way */ +/* will guarantee eta*w < 0. */ + + if (w * eta > 0.) { + eta = -w / (dpsi + dphi); + } + temp = tau + eta; + if (temp > dltub || temp < dltlb) { + if (w < 0.) { + eta = (dltub - tau) / 2.; + } else { + eta = (dltlb - tau) / 2.; + } + } + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + delta[j] -= eta; +/* L50: */ + } + + tau += eta; + +/* Evaluate PSI and the derivative DPSI */ + + dpsi = 0.; + psi = 0.; + erretm = 0.; + i__1 = ii; + for (j = 1; j <= i__1; ++j) { + temp = z__[j] / delta[j]; + psi += z__[j] * temp; + dpsi += temp * temp; + erretm += psi; +/* L60: */ + } + erretm = abs(erretm); + +/* Evaluate PHI and the derivative DPHI */ + + temp = z__[*n] / delta[*n]; + phi = z__[*n] * temp; + dphi = temp * temp; + erretm = (-phi - psi) * 8. + erretm - phi + rhoinv + abs(tau) * (dpsi + + dphi); + + w = rhoinv + phi + psi; + +/* Main loop to update the values of the array DELTA */ + + iter = niter + 1; + + for (niter = iter; niter <= 30; ++niter) { + +/* Test for convergence */ + + if (abs(w) <= eps * erretm) { + *dlam = d__[*i__] + tau; + goto L250; + } + + if (w <= 0.) { + dltlb = max(dltlb,tau); + } else { + dltub = min(dltub,tau); + } + +/* Calculate the new step */ + + c__ = w - delta[*n - 1] * dpsi - delta[*n] * dphi; + a = (delta[*n - 1] + delta[*n]) * w - delta[*n - 1] * delta[*n] * + (dpsi + dphi); + b = delta[*n - 1] * delta[*n] * w; + if (a >= 0.) { + eta = (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / ( + c__ * 2.); + } else { + eta = b * 2. / (a - sqrt((d__1 = a * a - b * 4. * c__, abs( + d__1)))); + } + +/* Note, eta should be positive if w is negative, and */ +/* eta should be negative otherwise. However, */ +/* if for some reason caused by roundoff, eta*w > 0, */ +/* we simply use one Newton step instead. This way */ +/* will guarantee eta*w < 0. */ + + if (w * eta > 0.) { + eta = -w / (dpsi + dphi); + } + temp = tau + eta; + if (temp > dltub || temp < dltlb) { + if (w < 0.) { + eta = (dltub - tau) / 2.; + } else { + eta = (dltlb - tau) / 2.; + } + } + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + delta[j] -= eta; +/* L70: */ + } + + tau += eta; + +/* Evaluate PSI and the derivative DPSI */ + + dpsi = 0.; + psi = 0.; + erretm = 0.; + i__1 = ii; + for (j = 1; j <= i__1; ++j) { + temp = z__[j] / delta[j]; + psi += z__[j] * temp; + dpsi += temp * temp; + erretm += psi; +/* L80: */ + } + erretm = abs(erretm); + +/* Evaluate PHI and the derivative DPHI */ + + temp = z__[*n] / delta[*n]; + phi = z__[*n] * temp; + dphi = temp * temp; + erretm = (-phi - psi) * 8. + erretm - phi + rhoinv + abs(tau) * ( + dpsi + dphi); + + w = rhoinv + phi + psi; +/* L90: */ + } + +/* Return with INFO = 1, NITER = MAXIT and not converged */ + + *info = 1; + *dlam = d__[*i__] + tau; + goto L250; + +/* End for the case I = N */ + + } else { + +/* The case for I < N */ + + niter = 1; + ip1 = *i__ + 1; + +/* Calculate initial guess */ + + del = d__[ip1] - d__[*i__]; + midpt = del / 2.; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + delta[j] = d__[j] - d__[*i__] - midpt; +/* L100: */ + } + + psi = 0.; + i__1 = *i__ - 1; + for (j = 1; j <= i__1; ++j) { + psi += z__[j] * z__[j] / delta[j]; +/* L110: */ + } + + phi = 0.; + i__1 = *i__ + 2; + for (j = *n; j >= i__1; --j) { + phi += z__[j] * z__[j] / delta[j]; +/* L120: */ + } + c__ = rhoinv + psi + phi; + w = c__ + z__[*i__] * z__[*i__] / delta[*i__] + z__[ip1] * z__[ip1] / + delta[ip1]; + + if (w > 0.) { + +/* d(i)< the ith eigenvalue < (d(i)+d(i+1))/2 */ + +/* We choose d(i) as origin. */ + + orgati = TRUE_; + a = c__ * del + z__[*i__] * z__[*i__] + z__[ip1] * z__[ip1]; + b = z__[*i__] * z__[*i__] * del; + if (a > 0.) { + tau = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs( + d__1)))); + } else { + tau = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / ( + c__ * 2.); + } + dltlb = 0.; + dltub = midpt; + } else { + +/* (d(i)+d(i+1))/2 <= the ith eigenvalue < d(i+1) */ + +/* We choose d(i+1) as origin. */ + + orgati = FALSE_; + a = c__ * del - z__[*i__] * z__[*i__] - z__[ip1] * z__[ip1]; + b = z__[ip1] * z__[ip1] * del; + if (a < 0.) { + tau = b * 2. / (a - sqrt((d__1 = a * a + b * 4. * c__, abs( + d__1)))); + } else { + tau = -(a + sqrt((d__1 = a * a + b * 4. * c__, abs(d__1)))) / + (c__ * 2.); + } + dltlb = -midpt; + dltub = 0.; + } + + if (orgati) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + delta[j] = d__[j] - d__[*i__] - tau; +/* L130: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + delta[j] = d__[j] - d__[ip1] - tau; +/* L140: */ + } + } + if (orgati) { + ii = *i__; + } else { + ii = *i__ + 1; + } + iim1 = ii - 1; + iip1 = ii + 1; + +/* Evaluate PSI and the derivative DPSI */ + + dpsi = 0.; + psi = 0.; + erretm = 0.; + i__1 = iim1; + for (j = 1; j <= i__1; ++j) { + temp = z__[j] / delta[j]; + psi += z__[j] * temp; + dpsi += temp * temp; + erretm += psi; +/* L150: */ + } + erretm = abs(erretm); + +/* Evaluate PHI and the derivative DPHI */ + + dphi = 0.; + phi = 0.; + i__1 = iip1; + for (j = *n; j >= i__1; --j) { + temp = z__[j] / delta[j]; + phi += z__[j] * temp; + dphi += temp * temp; + erretm += phi; +/* L160: */ + } + + w = rhoinv + phi + psi; + +/* W is the value of the secular function with */ +/* its ii-th element removed. */ + + swtch3 = FALSE_; + if (orgati) { + if (w < 0.) { + swtch3 = TRUE_; + } + } else { + if (w > 0.) { + swtch3 = TRUE_; + } + } + if (ii == 1 || ii == *n) { + swtch3 = FALSE_; + } + + temp = z__[ii] / delta[ii]; + dw = dpsi + dphi + temp * temp; + temp = z__[ii] * temp; + w += temp; + erretm = (phi - psi) * 8. + erretm + rhoinv * 2. + abs(temp) * 3. + + abs(tau) * dw; + +/* Test for convergence */ + + if (abs(w) <= eps * erretm) { + if (orgati) { + *dlam = d__[*i__] + tau; + } else { + *dlam = d__[ip1] + tau; + } + goto L250; + } + + if (w <= 0.) { + dltlb = max(dltlb,tau); + } else { + dltub = min(dltub,tau); + } + +/* Calculate the new step */ + + ++niter; + if (! swtch3) { + if (orgati) { +/* Computing 2nd power */ + d__1 = z__[*i__] / delta[*i__]; + c__ = w - delta[ip1] * dw - (d__[*i__] - d__[ip1]) * (d__1 * + d__1); + } else { +/* Computing 2nd power */ + d__1 = z__[ip1] / delta[ip1]; + c__ = w - delta[*i__] * dw - (d__[ip1] - d__[*i__]) * (d__1 * + d__1); + } + a = (delta[*i__] + delta[ip1]) * w - delta[*i__] * delta[ip1] * + dw; + b = delta[*i__] * delta[ip1] * w; + if (c__ == 0.) { + if (a == 0.) { + if (orgati) { + a = z__[*i__] * z__[*i__] + delta[ip1] * delta[ip1] * + (dpsi + dphi); + } else { + a = z__[ip1] * z__[ip1] + delta[*i__] * delta[*i__] * + (dpsi + dphi); + } + } + eta = b / a; + } else if (a <= 0.) { + eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / ( + c__ * 2.); + } else { + eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs( + d__1)))); + } + } else { + +/* Interpolation using THREE most relevant poles */ + + temp = rhoinv + psi + phi; + if (orgati) { + temp1 = z__[iim1] / delta[iim1]; + temp1 *= temp1; + c__ = temp - delta[iip1] * (dpsi + dphi) - (d__[iim1] - d__[ + iip1]) * temp1; + zz[0] = z__[iim1] * z__[iim1]; + zz[2] = delta[iip1] * delta[iip1] * (dpsi - temp1 + dphi); + } else { + temp1 = z__[iip1] / delta[iip1]; + temp1 *= temp1; + c__ = temp - delta[iim1] * (dpsi + dphi) - (d__[iip1] - d__[ + iim1]) * temp1; + zz[0] = delta[iim1] * delta[iim1] * (dpsi + (dphi - temp1)); + zz[2] = z__[iip1] * z__[iip1]; + } + zz[1] = z__[ii] * z__[ii]; + dlaed6_(&niter, &orgati, &c__, &delta[iim1], zz, &w, &eta, info); + if (*info != 0) { + goto L250; + } + } + +/* Note, eta should be positive if w is negative, and */ +/* eta should be negative otherwise. However, */ +/* if for some reason caused by roundoff, eta*w > 0, */ +/* we simply use one Newton step instead. This way */ +/* will guarantee eta*w < 0. */ + + if (w * eta >= 0.) { + eta = -w / dw; + } + temp = tau + eta; + if (temp > dltub || temp < dltlb) { + if (w < 0.) { + eta = (dltub - tau) / 2.; + } else { + eta = (dltlb - tau) / 2.; + } + } + + prew = w; + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + delta[j] -= eta; +/* L180: */ + } + +/* Evaluate PSI and the derivative DPSI */ + + dpsi = 0.; + psi = 0.; + erretm = 0.; + i__1 = iim1; + for (j = 1; j <= i__1; ++j) { + temp = z__[j] / delta[j]; + psi += z__[j] * temp; + dpsi += temp * temp; + erretm += psi; +/* L190: */ + } + erretm = abs(erretm); + +/* Evaluate PHI and the derivative DPHI */ + + dphi = 0.; + phi = 0.; + i__1 = iip1; + for (j = *n; j >= i__1; --j) { + temp = z__[j] / delta[j]; + phi += z__[j] * temp; + dphi += temp * temp; + erretm += phi; +/* L200: */ + } + + temp = z__[ii] / delta[ii]; + dw = dpsi + dphi + temp * temp; + temp = z__[ii] * temp; + w = rhoinv + phi + psi + temp; + erretm = (phi - psi) * 8. + erretm + rhoinv * 2. + abs(temp) * 3. + ( + d__1 = tau + eta, abs(d__1)) * dw; + + swtch = FALSE_; + if (orgati) { + if (-w > abs(prew) / 10.) { + swtch = TRUE_; + } + } else { + if (w > abs(prew) / 10.) { + swtch = TRUE_; + } + } + + tau += eta; + +/* Main loop to update the values of the array DELTA */ + + iter = niter + 1; + + for (niter = iter; niter <= 30; ++niter) { + +/* Test for convergence */ + + if (abs(w) <= eps * erretm) { + if (orgati) { + *dlam = d__[*i__] + tau; + } else { + *dlam = d__[ip1] + tau; + } + goto L250; + } + + if (w <= 0.) { + dltlb = max(dltlb,tau); + } else { + dltub = min(dltub,tau); + } + +/* Calculate the new step */ + + if (! swtch3) { + if (! swtch) { + if (orgati) { +/* Computing 2nd power */ + d__1 = z__[*i__] / delta[*i__]; + c__ = w - delta[ip1] * dw - (d__[*i__] - d__[ip1]) * ( + d__1 * d__1); + } else { +/* Computing 2nd power */ + d__1 = z__[ip1] / delta[ip1]; + c__ = w - delta[*i__] * dw - (d__[ip1] - d__[*i__]) * + (d__1 * d__1); + } + } else { + temp = z__[ii] / delta[ii]; + if (orgati) { + dpsi += temp * temp; + } else { + dphi += temp * temp; + } + c__ = w - delta[*i__] * dpsi - delta[ip1] * dphi; + } + a = (delta[*i__] + delta[ip1]) * w - delta[*i__] * delta[ip1] + * dw; + b = delta[*i__] * delta[ip1] * w; + if (c__ == 0.) { + if (a == 0.) { + if (! swtch) { + if (orgati) { + a = z__[*i__] * z__[*i__] + delta[ip1] * + delta[ip1] * (dpsi + dphi); + } else { + a = z__[ip1] * z__[ip1] + delta[*i__] * delta[ + *i__] * (dpsi + dphi); + } + } else { + a = delta[*i__] * delta[*i__] * dpsi + delta[ip1] + * delta[ip1] * dphi; + } + } + eta = b / a; + } else if (a <= 0.) { + eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) + / (c__ * 2.); + } else { + eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, + abs(d__1)))); + } + } else { + +/* Interpolation using THREE most relevant poles */ + + temp = rhoinv + psi + phi; + if (swtch) { + c__ = temp - delta[iim1] * dpsi - delta[iip1] * dphi; + zz[0] = delta[iim1] * delta[iim1] * dpsi; + zz[2] = delta[iip1] * delta[iip1] * dphi; + } else { + if (orgati) { + temp1 = z__[iim1] / delta[iim1]; + temp1 *= temp1; + c__ = temp - delta[iip1] * (dpsi + dphi) - (d__[iim1] + - d__[iip1]) * temp1; + zz[0] = z__[iim1] * z__[iim1]; + zz[2] = delta[iip1] * delta[iip1] * (dpsi - temp1 + + dphi); + } else { + temp1 = z__[iip1] / delta[iip1]; + temp1 *= temp1; + c__ = temp - delta[iim1] * (dpsi + dphi) - (d__[iip1] + - d__[iim1]) * temp1; + zz[0] = delta[iim1] * delta[iim1] * (dpsi + (dphi - + temp1)); + zz[2] = z__[iip1] * z__[iip1]; + } + } + dlaed6_(&niter, &orgati, &c__, &delta[iim1], zz, &w, &eta, + info); + if (*info != 0) { + goto L250; + } + } + +/* Note, eta should be positive if w is negative, and */ +/* eta should be negative otherwise. However, */ +/* if for some reason caused by roundoff, eta*w > 0, */ +/* we simply use one Newton step instead. This way */ +/* will guarantee eta*w < 0. */ + + if (w * eta >= 0.) { + eta = -w / dw; + } + temp = tau + eta; + if (temp > dltub || temp < dltlb) { + if (w < 0.) { + eta = (dltub - tau) / 2.; + } else { + eta = (dltlb - tau) / 2.; + } + } + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + delta[j] -= eta; +/* L210: */ + } + + tau += eta; + prew = w; + +/* Evaluate PSI and the derivative DPSI */ + + dpsi = 0.; + psi = 0.; + erretm = 0.; + i__1 = iim1; + for (j = 1; j <= i__1; ++j) { + temp = z__[j] / delta[j]; + psi += z__[j] * temp; + dpsi += temp * temp; + erretm += psi; +/* L220: */ + } + erretm = abs(erretm); + +/* Evaluate PHI and the derivative DPHI */ + + dphi = 0.; + phi = 0.; + i__1 = iip1; + for (j = *n; j >= i__1; --j) { + temp = z__[j] / delta[j]; + phi += z__[j] * temp; + dphi += temp * temp; + erretm += phi; +/* L230: */ + } + + temp = z__[ii] / delta[ii]; + dw = dpsi + dphi + temp * temp; + temp = z__[ii] * temp; + w = rhoinv + phi + psi + temp; + erretm = (phi - psi) * 8. + erretm + rhoinv * 2. + abs(temp) * 3. + + abs(tau) * dw; + if (w * prew > 0. && abs(w) > abs(prew) / 10.) { + swtch = ! swtch; + } + +/* L240: */ + } + +/* Return with INFO = 1, NITER = MAXIT and not converged */ + + *info = 1; + if (orgati) { + *dlam = d__[*i__] + tau; + } else { + *dlam = d__[ip1] + tau; + } + + } + +L250: + + return 0; + +/* End of DLAED4 */ + +} /* dlaed4_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlaed5.cpp b/lib/linalg/dlaed5.cpp new file mode 100644 index 0000000000..14e8a429ee --- /dev/null +++ b/lib/linalg/dlaed5.cpp @@ -0,0 +1,219 @@ +/* fortran/dlaed5.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DLAED5 used by DSTEDC. Solves the 2-by-2 secular equation. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLAED5 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLAED5( I, D, Z, DELTA, RHO, DLAM ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER I */ +/* DOUBLE PRECISION DLAM, RHO */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION D( 2 ), DELTA( 2 ), Z( 2 ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > This subroutine computes the I-th eigenvalue of a symmetric rank-one */ +/* > modification of a 2-by-2 diagonal matrix */ +/* > */ +/* > diag( D ) + RHO * Z * transpose(Z) . */ +/* > */ +/* > The diagonal elements in the array D are assumed to satisfy */ +/* > */ +/* > D(i) < D(j) for i < j . */ +/* > */ +/* > We also assume RHO > 0 and that the Euclidean norm of the vector */ +/* > Z is one. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] I */ +/* > \verbatim */ +/* > I is INTEGER */ +/* > The index of the eigenvalue to be computed. I = 1 or I = 2. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension (2) */ +/* > The original eigenvalues. We assume D(1) < D(2). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] Z */ +/* > \verbatim */ +/* > Z is DOUBLE PRECISION array, dimension (2) */ +/* > The components of the updating vector. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] DELTA */ +/* > \verbatim */ +/* > DELTA is DOUBLE PRECISION array, dimension (2) */ +/* > The vector DELTA contains the information necessary */ +/* > to construct the eigenvectors. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] RHO */ +/* > \verbatim */ +/* > RHO is DOUBLE PRECISION */ +/* > The scalar in the symmetric updating formula. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] DLAM */ +/* > \verbatim */ +/* > DLAM is DOUBLE PRECISION */ +/* > The computed lambda_I, the I-th updated eigenvalue. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup auxOTHERcomputational */ + +/* > \par Contributors: */ +/* ================== */ +/* > */ +/* > Ren-Cang Li, Computer Science Division, University of California */ +/* > at Berkeley, USA */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dlaed5_(integer *i__, doublereal *d__, doublereal *z__, + doublereal *delta, doublereal *rho, doublereal *dlam) +{ + /* System generated locals */ + doublereal d__1; + + /* Builtin functions */ + double sqrt(doublereal); + + /* Local variables */ + doublereal b, c__, w, del, tau, temp; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + + /* Parameter adjustments */ + --delta; + --z__; + --d__; + + /* Function Body */ + del = d__[2] - d__[1]; + if (*i__ == 1) { + w = *rho * 2. * (z__[2] * z__[2] - z__[1] * z__[1]) / del + 1.; + if (w > 0.) { + b = del + *rho * (z__[1] * z__[1] + z__[2] * z__[2]); + c__ = *rho * z__[1] * z__[1] * del; + +/* B > ZERO, always */ + + tau = c__ * 2. / (b + sqrt((d__1 = b * b - c__ * 4., abs(d__1)))); + *dlam = d__[1] + tau; + delta[1] = -z__[1] / tau; + delta[2] = z__[2] / (del - tau); + } else { + b = -del + *rho * (z__[1] * z__[1] + z__[2] * z__[2]); + c__ = *rho * z__[2] * z__[2] * del; + if (b > 0.) { + tau = c__ * -2. / (b + sqrt(b * b + c__ * 4.)); + } else { + tau = (b - sqrt(b * b + c__ * 4.)) / 2.; + } + *dlam = d__[2] + tau; + delta[1] = -z__[1] / (del + tau); + delta[2] = -z__[2] / tau; + } + temp = sqrt(delta[1] * delta[1] + delta[2] * delta[2]); + delta[1] /= temp; + delta[2] /= temp; + } else { + +/* Now I=2 */ + + b = -del + *rho * (z__[1] * z__[1] + z__[2] * z__[2]); + c__ = *rho * z__[2] * z__[2] * del; + if (b > 0.) { + tau = (b + sqrt(b * b + c__ * 4.)) / 2.; + } else { + tau = c__ * 2. / (-b + sqrt(b * b + c__ * 4.)); + } + *dlam = d__[2] + tau; + delta[1] = -z__[1] / (del + tau); + delta[2] = -z__[2] / tau; + temp = sqrt(delta[1] * delta[1] + delta[2] * delta[2]); + delta[1] /= temp; + delta[2] /= temp; + } + return 0; + +/* End of DLAED5 */ + +} /* dlaed5_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlaed6.cpp b/lib/linalg/dlaed6.cpp new file mode 100644 index 0000000000..7a855780f0 --- /dev/null +++ b/lib/linalg/dlaed6.cpp @@ -0,0 +1,463 @@ +/* fortran/dlaed6.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DLAED6 used by DSTEDC. Computes one Newton step in solution of the secular equation. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLAED6 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLAED6( KNITER, ORGATI, RHO, D, Z, FINIT, TAU, INFO ) */ + +/* .. Scalar Arguments .. */ +/* LOGICAL ORGATI */ +/* INTEGER INFO, KNITER */ +/* DOUBLE PRECISION FINIT, RHO, TAU */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION D( 3 ), Z( 3 ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLAED6 computes the positive or negative root (closest to the origin) */ +/* > of */ +/* > z(1) z(2) z(3) */ +/* > f(x) = rho + --------- + ---------- + --------- */ +/* > d(1)-x d(2)-x d(3)-x */ +/* > */ +/* > It is assumed that */ +/* > */ +/* > if ORGATI = .true. the root is between d(2) and d(3); */ +/* > otherwise it is between d(1) and d(2) */ +/* > */ +/* > This routine will be called by DLAED4 when necessary. In most cases, */ +/* > the root sought is the smallest in magnitude, though it might not be */ +/* > in some extremely rare situations. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] KNITER */ +/* > \verbatim */ +/* > KNITER is INTEGER */ +/* > Refer to DLAED4 for its significance. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] ORGATI */ +/* > \verbatim */ +/* > ORGATI is LOGICAL */ +/* > If ORGATI is true, the needed root is between d(2) and */ +/* > d(3); otherwise it is between d(1) and d(2). See */ +/* > DLAED4 for further details. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] RHO */ +/* > \verbatim */ +/* > RHO is DOUBLE PRECISION */ +/* > Refer to the equation f(x) above. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension (3) */ +/* > D satisfies d(1) < d(2) < d(3). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] Z */ +/* > \verbatim */ +/* > Z is DOUBLE PRECISION array, dimension (3) */ +/* > Each of the elements in z must be positive. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] FINIT */ +/* > \verbatim */ +/* > FINIT is DOUBLE PRECISION */ +/* > The value of f at 0. It is more accurate than the one */ +/* > evaluated inside this routine (if someone wants to do */ +/* > so). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] TAU */ +/* > \verbatim */ +/* > TAU is DOUBLE PRECISION */ +/* > The root of the equation f(x). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > > 0: if INFO = 1, failure to converge */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup auxOTHERcomputational */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > 10/02/03: This version has a few statements commented out for thread */ +/* > safety (machine parameters are computed on each entry). SJH. */ +/* > */ +/* > 05/10/06: Modified from a new version of Ren-Cang Li, use */ +/* > Gragg-Thornton-Warner cubic convergent scheme for better stability. */ +/* > \endverbatim */ + +/* > \par Contributors: */ +/* ================== */ +/* > */ +/* > Ren-Cang Li, Computer Science Division, University of California */ +/* > at Berkeley, USA */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dlaed6_(integer *kniter, logical *orgati, doublereal * + rho, doublereal *d__, doublereal *z__, doublereal *finit, doublereal * + tau, integer *info) +{ + /* System generated locals */ + integer i__1; + doublereal d__1, d__2, d__3, d__4; + + /* Builtin functions */ + double sqrt(doublereal), log(doublereal), pow_di(doublereal *, integer *); + + /* Local variables */ + doublereal a, b, c__, f; + integer i__; + doublereal fc, df, ddf, lbd, eta, ubd, eps, base; + integer iter; + doublereal temp, temp1, temp2, temp3, temp4; + logical scale; + integer niter; + doublereal small1, small2, sminv1, sminv2; + extern doublereal dlamch_(char *, ftnlen); + doublereal dscale[3], sclfac, zscale[3], erretm, sclinv; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Local Arrays .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + + /* Parameter adjustments */ + --z__; + --d__; + + /* Function Body */ + *info = 0; + + if (*orgati) { + lbd = d__[2]; + ubd = d__[3]; + } else { + lbd = d__[1]; + ubd = d__[2]; + } + if (*finit < 0.) { + lbd = 0.; + } else { + ubd = 0.; + } + + niter = 1; + *tau = 0.; + if (*kniter == 2) { + if (*orgati) { + temp = (d__[3] - d__[2]) / 2.; + c__ = *rho + z__[1] / (d__[1] - d__[2] - temp); + a = c__ * (d__[2] + d__[3]) + z__[2] + z__[3]; + b = c__ * d__[2] * d__[3] + z__[2] * d__[3] + z__[3] * d__[2]; + } else { + temp = (d__[1] - d__[2]) / 2.; + c__ = *rho + z__[3] / (d__[3] - d__[2] - temp); + a = c__ * (d__[1] + d__[2]) + z__[1] + z__[2]; + b = c__ * d__[1] * d__[2] + z__[1] * d__[2] + z__[2] * d__[1]; + } +/* Computing MAX */ + d__1 = abs(a), d__2 = abs(b), d__1 = max(d__1,d__2), d__2 = abs(c__); + temp = max(d__1,d__2); + a /= temp; + b /= temp; + c__ /= temp; + if (c__ == 0.) { + *tau = b / a; + } else if (a <= 0.) { + *tau = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / ( + c__ * 2.); + } else { + *tau = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)) + )); + } + if (*tau < lbd || *tau > ubd) { + *tau = (lbd + ubd) / 2.; + } + if (d__[1] == *tau || d__[2] == *tau || d__[3] == *tau) { + *tau = 0.; + } else { + temp = *finit + *tau * z__[1] / (d__[1] * (d__[1] - *tau)) + *tau + * z__[2] / (d__[2] * (d__[2] - *tau)) + *tau * z__[3] / ( + d__[3] * (d__[3] - *tau)); + if (temp <= 0.) { + lbd = *tau; + } else { + ubd = *tau; + } + if (abs(*finit) <= abs(temp)) { + *tau = 0.; + } + } + } + +/* get machine parameters for possible scaling to avoid overflow */ + +/* modified by Sven: parameters SMALL1, SMINV1, SMALL2, */ +/* SMINV2, EPS are not SAVEd anymore between one call to the */ +/* others but recomputed at each call */ + + eps = dlamch_((char *)"Epsilon", (ftnlen)7); + base = dlamch_((char *)"Base", (ftnlen)4); + i__1 = (integer) (log(dlamch_((char *)"SafMin", (ftnlen)6)) / log(base) / 3.); + small1 = pow_di(&base, &i__1); + sminv1 = 1. / small1; + small2 = small1 * small1; + sminv2 = sminv1 * sminv1; + +/* Determine if scaling of inputs necessary to avoid overflow */ +/* when computing 1/TEMP**3 */ + + if (*orgati) { +/* Computing MIN */ + d__3 = (d__1 = d__[2] - *tau, abs(d__1)), d__4 = (d__2 = d__[3] - * + tau, abs(d__2)); + temp = min(d__3,d__4); + } else { +/* Computing MIN */ + d__3 = (d__1 = d__[1] - *tau, abs(d__1)), d__4 = (d__2 = d__[2] - * + tau, abs(d__2)); + temp = min(d__3,d__4); + } + scale = FALSE_; + if (temp <= small1) { + scale = TRUE_; + if (temp <= small2) { + +/* Scale up by power of radix nearest 1/SAFMIN**(2/3) */ + + sclfac = sminv2; + sclinv = small2; + } else { + +/* Scale up by power of radix nearest 1/SAFMIN**(1/3) */ + + sclfac = sminv1; + sclinv = small1; + } + +/* Scaling up safe because D, Z, TAU scaled elsewhere to be O(1) */ + + for (i__ = 1; i__ <= 3; ++i__) { + dscale[i__ - 1] = d__[i__] * sclfac; + zscale[i__ - 1] = z__[i__] * sclfac; +/* L10: */ + } + *tau *= sclfac; + lbd *= sclfac; + ubd *= sclfac; + } else { + +/* Copy D and Z to DSCALE and ZSCALE */ + + for (i__ = 1; i__ <= 3; ++i__) { + dscale[i__ - 1] = d__[i__]; + zscale[i__ - 1] = z__[i__]; +/* L20: */ + } + } + + fc = 0.; + df = 0.; + ddf = 0.; + for (i__ = 1; i__ <= 3; ++i__) { + temp = 1. / (dscale[i__ - 1] - *tau); + temp1 = zscale[i__ - 1] * temp; + temp2 = temp1 * temp; + temp3 = temp2 * temp; + fc += temp1 / dscale[i__ - 1]; + df += temp2; + ddf += temp3; +/* L30: */ + } + f = *finit + *tau * fc; + + if (abs(f) <= 0.) { + goto L60; + } + if (f <= 0.) { + lbd = *tau; + } else { + ubd = *tau; + } + +/* Iteration begins -- Use Gragg-Thornton-Warner cubic convergent */ +/* scheme */ + +/* It is not hard to see that */ + +/* 1) Iterations will go up monotonically */ +/* if FINIT < 0; */ + +/* 2) Iterations will go down monotonically */ +/* if FINIT > 0. */ + + iter = niter + 1; + + for (niter = iter; niter <= 40; ++niter) { + + if (*orgati) { + temp1 = dscale[1] - *tau; + temp2 = dscale[2] - *tau; + } else { + temp1 = dscale[0] - *tau; + temp2 = dscale[1] - *tau; + } + a = (temp1 + temp2) * f - temp1 * temp2 * df; + b = temp1 * temp2 * f; + c__ = f - (temp1 + temp2) * df + temp1 * temp2 * ddf; +/* Computing MAX */ + d__1 = abs(a), d__2 = abs(b), d__1 = max(d__1,d__2), d__2 = abs(c__); + temp = max(d__1,d__2); + a /= temp; + b /= temp; + c__ /= temp; + if (c__ == 0.) { + eta = b / a; + } else if (a <= 0.) { + eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (c__ + * 2.); + } else { + eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1))) + ); + } + if (f * eta >= 0.) { + eta = -f / df; + } + + *tau += eta; + if (*tau < lbd || *tau > ubd) { + *tau = (lbd + ubd) / 2.; + } + + fc = 0.; + erretm = 0.; + df = 0.; + ddf = 0.; + for (i__ = 1; i__ <= 3; ++i__) { + if (dscale[i__ - 1] - *tau != 0.) { + temp = 1. / (dscale[i__ - 1] - *tau); + temp1 = zscale[i__ - 1] * temp; + temp2 = temp1 * temp; + temp3 = temp2 * temp; + temp4 = temp1 / dscale[i__ - 1]; + fc += temp4; + erretm += abs(temp4); + df += temp2; + ddf += temp3; + } else { + goto L60; + } +/* L40: */ + } + f = *finit + *tau * fc; + erretm = (abs(*finit) + abs(*tau) * erretm) * 8. + abs(*tau) * df; + if (abs(f) <= eps * 4. * erretm || ubd - lbd <= eps * 4. * abs(*tau)) + { + goto L60; + } + if (f <= 0.) { + lbd = *tau; + } else { + ubd = *tau; + } +/* L50: */ + } + *info = 1; +L60: + +/* Undo scaling */ + + if (scale) { + *tau *= sclinv; + } + return 0; + +/* End of DLAED6 */ + +} /* dlaed6_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlaed7.cpp b/lib/linalg/dlaed7.cpp new file mode 100644 index 0000000000..367bf37a46 --- /dev/null +++ b/lib/linalg/dlaed7.cpp @@ -0,0 +1,483 @@ +/* fortran/dlaed7.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__2 = 2; +static integer c__1 = 1; +static doublereal c_b10 = 1.; +static doublereal c_b11 = 0.; +static integer c_n1 = -1; + +/* > \brief \b DLAED7 used by DSTEDC. Computes the updated eigensystem of a diagonal matrix after modification + by a rank-one symmetric matrix. Used when the original matrix is dense. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLAED7 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLAED7( ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, */ +/* LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR, */ +/* PERM, GIVPTR, GIVCOL, GIVNUM, WORK, IWORK, */ +/* INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER CURLVL, CURPBM, CUTPNT, ICOMPQ, INFO, LDQ, N, */ +/* $ QSIZ, TLVLS */ +/* DOUBLE PRECISION RHO */ +/* .. */ +/* .. Array Arguments .. */ +/* INTEGER GIVCOL( 2, * ), GIVPTR( * ), INDXQ( * ), */ +/* $ IWORK( * ), PERM( * ), PRMPTR( * ), QPTR( * ) */ +/* DOUBLE PRECISION D( * ), GIVNUM( 2, * ), Q( LDQ, * ), */ +/* $ QSTORE( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLAED7 computes the updated eigensystem of a diagonal */ +/* > matrix after modification by a rank-one symmetric matrix. This */ +/* > routine is used only for the eigenproblem which requires all */ +/* > eigenvalues and optionally eigenvectors of a dense symmetric matrix */ +/* > that has been reduced to tridiagonal form. DLAED1 handles */ +/* > the case in which all eigenvalues and eigenvectors of a symmetric */ +/* > tridiagonal matrix are desired. */ +/* > */ +/* > T = Q(in) ( D(in) + RHO * Z*Z**T ) Q**T(in) = Q(out) * D(out) * Q**T(out) */ +/* > */ +/* > where Z = Q**Tu, u is a vector of length N with ones in the */ +/* > CUTPNT and CUTPNT + 1 th elements and zeros elsewhere. */ +/* > */ +/* > The eigenvectors of the original matrix are stored in Q, and the */ +/* > eigenvalues are in D. The algorithm consists of three stages: */ +/* > */ +/* > The first stage consists of deflating the size of the problem */ +/* > when there are multiple eigenvalues or if there is a zero in */ +/* > the Z vector. For each such occurrence the dimension of the */ +/* > secular equation problem is reduced by one. This stage is */ +/* > performed by the routine DLAED8. */ +/* > */ +/* > The second stage consists of calculating the updated */ +/* > eigenvalues. This is done by finding the roots of the secular */ +/* > equation via the routine DLAED4 (as called by DLAED9). */ +/* > This routine also calculates the eigenvectors of the current */ +/* > problem. */ +/* > */ +/* > The final stage consists of computing the updated eigenvectors */ +/* > directly using the updated eigenvalues. The eigenvectors for */ +/* > the current problem are multiplied with the eigenvectors from */ +/* > the overall problem. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] ICOMPQ */ +/* > \verbatim */ +/* > ICOMPQ is INTEGER */ +/* > = 0: Compute eigenvalues only. */ +/* > = 1: Compute eigenvectors of original dense symmetric matrix */ +/* > also. On entry, Q contains the orthogonal matrix used */ +/* > to reduce the original matrix to tridiagonal form. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The dimension of the symmetric tridiagonal matrix. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] QSIZ */ +/* > \verbatim */ +/* > QSIZ is INTEGER */ +/* > The dimension of the orthogonal matrix used to reduce */ +/* > the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TLVLS */ +/* > \verbatim */ +/* > TLVLS is INTEGER */ +/* > The total number of merging levels in the overall divide and */ +/* > conquer tree. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] CURLVL */ +/* > \verbatim */ +/* > CURLVL is INTEGER */ +/* > The current level in the overall merge routine, */ +/* > 0 <= CURLVL <= TLVLS. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] CURPBM */ +/* > \verbatim */ +/* > CURPBM is INTEGER */ +/* > The current problem in the current level in the overall */ +/* > merge routine (counting from upper left to lower right). */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension (N) */ +/* > On entry, the eigenvalues of the rank-1-perturbed matrix. */ +/* > On exit, the eigenvalues of the repaired matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] Q */ +/* > \verbatim */ +/* > Q is DOUBLE PRECISION array, dimension (LDQ, N) */ +/* > On entry, the eigenvectors of the rank-1-perturbed matrix. */ +/* > On exit, the eigenvectors of the repaired tridiagonal matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDQ */ +/* > \verbatim */ +/* > LDQ is INTEGER */ +/* > The leading dimension of the array Q. LDQ >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INDXQ */ +/* > \verbatim */ +/* > INDXQ is INTEGER array, dimension (N) */ +/* > The permutation which will reintegrate the subproblem just */ +/* > solved back into sorted order, i.e., D( INDXQ( I = 1, N ) ) */ +/* > will be in ascending order. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] RHO */ +/* > \verbatim */ +/* > RHO is DOUBLE PRECISION */ +/* > The subdiagonal element used to create the rank-1 */ +/* > modification. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] CUTPNT */ +/* > \verbatim */ +/* > CUTPNT is INTEGER */ +/* > Contains the location of the last eigenvalue in the leading */ +/* > sub-matrix. min(1,N) <= CUTPNT <= N. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] QSTORE */ +/* > \verbatim */ +/* > QSTORE is DOUBLE PRECISION array, dimension (N**2+1) */ +/* > Stores eigenvectors of submatrices encountered during */ +/* > divide and conquer, packed together. QPTR points to */ +/* > beginning of the submatrices. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] QPTR */ +/* > \verbatim */ +/* > QPTR is INTEGER array, dimension (N+2) */ +/* > List of indices pointing to beginning of submatrices stored */ +/* > in QSTORE. The submatrices are numbered starting at the */ +/* > bottom left of the divide and conquer tree, from left to */ +/* > right and bottom to top. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] PRMPTR */ +/* > \verbatim */ +/* > PRMPTR is INTEGER array, dimension (N lg N) */ +/* > Contains a list of pointers which indicate where in PERM a */ +/* > level's permutation is stored. PRMPTR(i+1) - PRMPTR(i) */ +/* > indicates the size of the permutation and also the size of */ +/* > the full, non-deflated problem. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] PERM */ +/* > \verbatim */ +/* > PERM is INTEGER array, dimension (N lg N) */ +/* > Contains the permutations (from deflation and sorting) to be */ +/* > applied to each eigenblock. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] GIVPTR */ +/* > \verbatim */ +/* > GIVPTR is INTEGER array, dimension (N lg N) */ +/* > Contains a list of pointers which indicate where in GIVCOL a */ +/* > level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i) */ +/* > indicates the number of Givens rotations. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] GIVCOL */ +/* > \verbatim */ +/* > GIVCOL is INTEGER array, dimension (2, N lg N) */ +/* > Each pair of numbers indicates a pair of columns to take place */ +/* > in a Givens rotation. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] GIVNUM */ +/* > \verbatim */ +/* > GIVNUM is DOUBLE PRECISION array, dimension (2, N lg N) */ +/* > Each number indicates the S value to be used in the */ +/* > corresponding Givens rotation. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (3*N+2*QSIZ*N) */ +/* > \endverbatim */ +/* > */ +/* > \param[out] IWORK */ +/* > \verbatim */ +/* > IWORK is INTEGER array, dimension (4*N) */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit. */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ +/* > > 0: if INFO = 1, an eigenvalue did not converge */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup auxOTHERcomputational */ + +/* > \par Contributors: */ +/* ================== */ +/* > */ +/* > Jeff Rutter, Computer Science Division, University of California */ +/* > at Berkeley, USA */ + +/* ===================================================================== */ +/* Subroutine */ int dlaed7_(integer *icompq, integer *n, integer *qsiz, + integer *tlvls, integer *curlvl, integer *curpbm, doublereal *d__, + doublereal *q, integer *ldq, integer *indxq, doublereal *rho, integer + *cutpnt, doublereal *qstore, integer *qptr, integer *prmptr, integer * + perm, integer *givptr, integer *givcol, doublereal *givnum, + doublereal *work, integer *iwork, integer *info) +{ + /* System generated locals */ + integer q_dim1, q_offset, i__1, i__2; + + /* Builtin functions */ + integer pow_ii(integer *, integer *); + + /* Local variables */ + integer i__, k, n1, n2, is, iw, iz, iq2, ptr, ldq2, indx, curr; + extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); + integer indxc, indxp; + extern /* Subroutine */ int dlaed8_(integer *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, integer *, + doublereal *, integer *, doublereal *, doublereal *, doublereal *, + integer *, doublereal *, integer *, integer *, integer *, + doublereal *, integer *, integer *, integer *), dlaed9_(integer *, + integer *, integer *, integer *, doublereal *, doublereal *, + integer *, doublereal *, doublereal *, doublereal *, doublereal *, + integer *, integer *), dlaeda_(integer *, integer *, integer *, + integer *, integer *, integer *, integer *, integer *, doublereal + *, doublereal *, integer *, doublereal *, doublereal *, integer *) + ; + integer idlmda; + extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *, + integer *, integer *, integer *), xerbla_(char *, integer *, + ftnlen); + integer coltyp; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --d__; + q_dim1 = *ldq; + q_offset = 1 + q_dim1; + q -= q_offset; + --indxq; + --qstore; + --qptr; + --prmptr; + --perm; + --givptr; + givcol -= 3; + givnum -= 3; + --work; + --iwork; + + /* Function Body */ + *info = 0; + + if (*icompq < 0 || *icompq > 1) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } else if (*icompq == 1 && *qsiz < *n) { + *info = -3; + } else if (*ldq < max(1,*n)) { + *info = -9; + } else if (min(1,*n) > *cutpnt || *n < *cutpnt) { + *info = -12; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DLAED7", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*n == 0) { + return 0; + } + +/* The following values are for bookkeeping purposes only. They are */ +/* integer pointers which indicate the portion of the workspace */ +/* used by a particular array in DLAED8 and DLAED9. */ + + if (*icompq == 1) { + ldq2 = *qsiz; + } else { + ldq2 = *n; + } + + iz = 1; + idlmda = iz + *n; + iw = idlmda + *n; + iq2 = iw + *n; + is = iq2 + *n * ldq2; + + indx = 1; + indxc = indx + *n; + coltyp = indxc + *n; + indxp = coltyp + *n; + +/* Form the z-vector which consists of the last row of Q_1 and the */ +/* first row of Q_2. */ + + ptr = pow_ii(&c__2, tlvls) + 1; + i__1 = *curlvl - 1; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = *tlvls - i__; + ptr += pow_ii(&c__2, &i__2); +/* L10: */ + } + curr = ptr + *curpbm; + dlaeda_(n, tlvls, curlvl, curpbm, &prmptr[1], &perm[1], &givptr[1], & + givcol[3], &givnum[3], &qstore[1], &qptr[1], &work[iz], &work[iz + + *n], info); + +/* When solving the final problem, we no longer need the stored data, */ +/* so we will overwrite the data from this level onto the previously */ +/* used storage space. */ + + if (*curlvl == *tlvls) { + qptr[curr] = 1; + prmptr[curr] = 1; + givptr[curr] = 1; + } + +/* Sort and Deflate eigenvalues. */ + + dlaed8_(icompq, &k, n, qsiz, &d__[1], &q[q_offset], ldq, &indxq[1], rho, + cutpnt, &work[iz], &work[idlmda], &work[iq2], &ldq2, &work[iw], & + perm[prmptr[curr]], &givptr[curr + 1], &givcol[(givptr[curr] << 1) + + 1], &givnum[(givptr[curr] << 1) + 1], &iwork[indxp], &iwork[ + indx], info); + prmptr[curr + 1] = prmptr[curr] + *n; + givptr[curr + 1] += givptr[curr]; + +/* Solve Secular Equation. */ + + if (k != 0) { + dlaed9_(&k, &c__1, &k, n, &d__[1], &work[is], &k, rho, &work[idlmda], + &work[iw], &qstore[qptr[curr]], &k, info); + if (*info != 0) { + goto L30; + } + if (*icompq == 1) { + dgemm_((char *)"N", (char *)"N", qsiz, &k, &k, &c_b10, &work[iq2], &ldq2, &qstore[ + qptr[curr]], &k, &c_b11, &q[q_offset], ldq, (ftnlen)1, ( + ftnlen)1); + } +/* Computing 2nd power */ + i__1 = k; + qptr[curr + 1] = qptr[curr] + i__1 * i__1; + +/* Prepare the INDXQ sorting permutation. */ + + n1 = k; + n2 = *n - k; + dlamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &indxq[1]); + } else { + qptr[curr + 1] = qptr[curr]; + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + indxq[i__] = i__; +/* L20: */ + } + } + +L30: + return 0; + +/* End of DLAED7 */ + +} /* dlaed7_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlaed8.cpp b/lib/linalg/dlaed8.cpp new file mode 100644 index 0000000000..263bea75d5 --- /dev/null +++ b/lib/linalg/dlaed8.cpp @@ -0,0 +1,610 @@ +/* fortran/dlaed8.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static doublereal c_b3 = -1.; +static integer c__1 = 1; + +/* > \brief \b DLAED8 used by DSTEDC. Merges eigenvalues and deflates secular equation. Used when the original + matrix is dense. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLAED8 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLAED8( ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, */ +/* CUTPNT, Z, DLAMDA, Q2, LDQ2, W, PERM, GIVPTR, */ +/* GIVCOL, GIVNUM, INDXP, INDX, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER CUTPNT, GIVPTR, ICOMPQ, INFO, K, LDQ, LDQ2, N, */ +/* $ QSIZ */ +/* DOUBLE PRECISION RHO */ +/* .. */ +/* .. Array Arguments .. */ +/* INTEGER GIVCOL( 2, * ), INDX( * ), INDXP( * ), */ +/* $ INDXQ( * ), PERM( * ) */ +/* DOUBLE PRECISION D( * ), DLAMDA( * ), GIVNUM( 2, * ), */ +/* $ Q( LDQ, * ), Q2( LDQ2, * ), W( * ), Z( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLAED8 merges the two sets of eigenvalues together into a single */ +/* > sorted set. Then it tries to deflate the size of the problem. */ +/* > There are two ways in which deflation can occur: when two or more */ +/* > eigenvalues are close together or if there is a tiny element in the */ +/* > Z vector. For each such occurrence the order of the related secular */ +/* > equation problem is reduced by one. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] ICOMPQ */ +/* > \verbatim */ +/* > ICOMPQ is INTEGER */ +/* > = 0: Compute eigenvalues only. */ +/* > = 1: Compute eigenvectors of original dense symmetric matrix */ +/* > also. On entry, Q contains the orthogonal matrix used */ +/* > to reduce the original matrix to tridiagonal form. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > The number of non-deflated eigenvalues, and the order of the */ +/* > related secular equation. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The dimension of the symmetric tridiagonal matrix. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] QSIZ */ +/* > \verbatim */ +/* > QSIZ is INTEGER */ +/* > The dimension of the orthogonal matrix used to reduce */ +/* > the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension (N) */ +/* > On entry, the eigenvalues of the two submatrices to be */ +/* > combined. On exit, the trailing (N-K) updated eigenvalues */ +/* > (those which were deflated) sorted into increasing order. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] Q */ +/* > \verbatim */ +/* > Q is DOUBLE PRECISION array, dimension (LDQ,N) */ +/* > If ICOMPQ = 0, Q is not referenced. Otherwise, */ +/* > on entry, Q contains the eigenvectors of the partially solved */ +/* > system which has been previously updated in matrix */ +/* > multiplies with other partially solved eigensystems. */ +/* > On exit, Q contains the trailing (N-K) updated eigenvectors */ +/* > (those which were deflated) in its last N-K columns. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDQ */ +/* > \verbatim */ +/* > LDQ is INTEGER */ +/* > The leading dimension of the array Q. LDQ >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INDXQ */ +/* > \verbatim */ +/* > INDXQ is INTEGER array, dimension (N) */ +/* > The permutation which separately sorts the two sub-problems */ +/* > in D into ascending order. Note that elements in the second */ +/* > half of this permutation must first have CUTPNT added to */ +/* > their values in order to be accurate. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] RHO */ +/* > \verbatim */ +/* > RHO is DOUBLE PRECISION */ +/* > On entry, the off-diagonal element associated with the rank-1 */ +/* > cut which originally split the two submatrices which are now */ +/* > being recombined. */ +/* > On exit, RHO has been modified to the value required by */ +/* > DLAED3. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] CUTPNT */ +/* > \verbatim */ +/* > CUTPNT is INTEGER */ +/* > The location of the last eigenvalue in the leading */ +/* > sub-matrix. min(1,N) <= CUTPNT <= N. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] Z */ +/* > \verbatim */ +/* > Z is DOUBLE PRECISION array, dimension (N) */ +/* > On entry, Z contains the updating vector (the last row of */ +/* > the first sub-eigenvector matrix and the first row of the */ +/* > second sub-eigenvector matrix). */ +/* > On exit, the contents of Z are destroyed by the updating */ +/* > process. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] DLAMDA */ +/* > \verbatim */ +/* > DLAMDA is DOUBLE PRECISION array, dimension (N) */ +/* > A copy of the first K eigenvalues which will be used by */ +/* > DLAED3 to form the secular equation. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] Q2 */ +/* > \verbatim */ +/* > Q2 is DOUBLE PRECISION array, dimension (LDQ2,N) */ +/* > If ICOMPQ = 0, Q2 is not referenced. Otherwise, */ +/* > a copy of the first K eigenvectors which will be used by */ +/* > DLAED7 in a matrix multiply (DGEMM) to update the new */ +/* > eigenvectors. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDQ2 */ +/* > \verbatim */ +/* > LDQ2 is INTEGER */ +/* > The leading dimension of the array Q2. LDQ2 >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] W */ +/* > \verbatim */ +/* > W is DOUBLE PRECISION array, dimension (N) */ +/* > The first k values of the final deflation-altered z-vector and */ +/* > will be passed to DLAED3. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] PERM */ +/* > \verbatim */ +/* > PERM is INTEGER array, dimension (N) */ +/* > The permutations (from deflation and sorting) to be applied */ +/* > to each eigenblock. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] GIVPTR */ +/* > \verbatim */ +/* > GIVPTR is INTEGER */ +/* > The number of Givens rotations which took place in this */ +/* > subproblem. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] GIVCOL */ +/* > \verbatim */ +/* > GIVCOL is INTEGER array, dimension (2, N) */ +/* > Each pair of numbers indicates a pair of columns to take place */ +/* > in a Givens rotation. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] GIVNUM */ +/* > \verbatim */ +/* > GIVNUM is DOUBLE PRECISION array, dimension (2, N) */ +/* > Each number indicates the S value to be used in the */ +/* > corresponding Givens rotation. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INDXP */ +/* > \verbatim */ +/* > INDXP is INTEGER array, dimension (N) */ +/* > The permutation used to place deflated values of D at the end */ +/* > of the array. INDXP(1:K) points to the nondeflated D-values */ +/* > and INDXP(K+1:N) points to the deflated eigenvalues. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INDX */ +/* > \verbatim */ +/* > INDX is INTEGER array, dimension (N) */ +/* > The permutation used to sort the contents of D into ascending */ +/* > order. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit. */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup auxOTHERcomputational */ + +/* > \par Contributors: */ +/* ================== */ +/* > */ +/* > Jeff Rutter, Computer Science Division, University of California */ +/* > at Berkeley, USA */ + +/* ===================================================================== */ +/* Subroutine */ int dlaed8_(integer *icompq, integer *k, integer *n, integer + *qsiz, doublereal *d__, doublereal *q, integer *ldq, integer *indxq, + doublereal *rho, integer *cutpnt, doublereal *z__, doublereal *dlamda, + doublereal *q2, integer *ldq2, doublereal *w, integer *perm, integer + *givptr, integer *givcol, doublereal *givnum, integer *indxp, integer + *indx, integer *info) +{ + /* System generated locals */ + integer q_dim1, q_offset, q2_dim1, q2_offset, i__1; + doublereal d__1; + + /* Builtin functions */ + double sqrt(doublereal); + + /* Local variables */ + doublereal c__; + integer i__, j; + doublereal s, t; + integer k2, n1, n2, jp, n1p1; + doublereal eps, tau, tol; + integer jlam, imax, jmax; + extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, + doublereal *, integer *, doublereal *, doublereal *), dscal_( + integer *, doublereal *, doublereal *, integer *), dcopy_(integer + *, doublereal *, integer *, doublereal *, integer *); + extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, + ftnlen); + extern integer idamax_(integer *, doublereal *, integer *); + extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *, + integer *, integer *, integer *), dlacpy_(char *, integer *, + integer *, doublereal *, integer *, doublereal *, integer *, + ftnlen), xerbla_(char *, integer *, ftnlen); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ + +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --d__; + q_dim1 = *ldq; + q_offset = 1 + q_dim1; + q -= q_offset; + --indxq; + --z__; + --dlamda; + q2_dim1 = *ldq2; + q2_offset = 1 + q2_dim1; + q2 -= q2_offset; + --w; + --perm; + givcol -= 3; + givnum -= 3; + --indxp; + --indx; + + /* Function Body */ + *info = 0; + + if (*icompq < 0 || *icompq > 1) { + *info = -1; + } else if (*n < 0) { + *info = -3; + } else if (*icompq == 1 && *qsiz < *n) { + *info = -4; + } else if (*ldq < max(1,*n)) { + *info = -7; + } else if (*cutpnt < min(1,*n) || *cutpnt > *n) { + *info = -10; + } else if (*ldq2 < max(1,*n)) { + *info = -14; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DLAED8", &i__1, (ftnlen)6); + return 0; + } + +/* Need to initialize GIVPTR to O here in case of quick exit */ +/* to prevent an unspecified code behavior (usually sigfault) */ +/* when IWORK array on entry to *stedc is not zeroed */ +/* (or at least some IWORK entries which used in *laed7 for GIVPTR). */ + + *givptr = 0; + +/* Quick return if possible */ + + if (*n == 0) { + return 0; + } + + n1 = *cutpnt; + n2 = *n - n1; + n1p1 = n1 + 1; + + if (*rho < 0.) { + dscal_(&n2, &c_b3, &z__[n1p1], &c__1); + } + +/* Normalize z so that norm(z) = 1 */ + + t = 1. / sqrt(2.); + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + indx[j] = j; +/* L10: */ + } + dscal_(n, &t, &z__[1], &c__1); + *rho = (d__1 = *rho * 2., abs(d__1)); + +/* Sort the eigenvalues into increasing order */ + + i__1 = *n; + for (i__ = *cutpnt + 1; i__ <= i__1; ++i__) { + indxq[i__] += *cutpnt; +/* L20: */ + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + dlamda[i__] = d__[indxq[i__]]; + w[i__] = z__[indxq[i__]]; +/* L30: */ + } + i__ = 1; + j = *cutpnt + 1; + dlamrg_(&n1, &n2, &dlamda[1], &c__1, &c__1, &indx[1]); + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + d__[i__] = dlamda[indx[i__]]; + z__[i__] = w[indx[i__]]; +/* L40: */ + } + +/* Calculate the allowable deflation tolerance */ + + imax = idamax_(n, &z__[1], &c__1); + jmax = idamax_(n, &d__[1], &c__1); + eps = dlamch_((char *)"Epsilon", (ftnlen)7); + tol = eps * 8. * (d__1 = d__[jmax], abs(d__1)); + +/* If the rank-1 modifier is small enough, no more needs to be done */ +/* except to reorganize Q so that its columns correspond with the */ +/* elements in D. */ + + if (*rho * (d__1 = z__[imax], abs(d__1)) <= tol) { + *k = 0; + if (*icompq == 0) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + perm[j] = indxq[indx[j]]; +/* L50: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + perm[j] = indxq[indx[j]]; + dcopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 + + 1], &c__1); +/* L60: */ + } + dlacpy_((char *)"A", qsiz, n, &q2[q2_dim1 + 1], ldq2, &q[q_dim1 + 1], ldq, + (ftnlen)1); + } + return 0; + } + +/* If there are multiple eigenvalues then the problem deflates. Here */ +/* the number of equal eigenvalues are found. As each equal */ +/* eigenvalue is found, an elementary reflector is computed to rotate */ +/* the corresponding eigensubspace so that the corresponding */ +/* components of Z are zero in this new basis. */ + + *k = 0; + k2 = *n + 1; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (*rho * (d__1 = z__[j], abs(d__1)) <= tol) { + +/* Deflate due to small z component. */ + + --k2; + indxp[k2] = j; + if (j == *n) { + goto L110; + } + } else { + jlam = j; + goto L80; + } +/* L70: */ + } +L80: + ++j; + if (j > *n) { + goto L100; + } + if (*rho * (d__1 = z__[j], abs(d__1)) <= tol) { + +/* Deflate due to small z component. */ + + --k2; + indxp[k2] = j; + } else { + +/* Check if eigenvalues are close enough to allow deflation. */ + + s = z__[jlam]; + c__ = z__[j]; + +/* Find sqrt(a**2+b**2) without overflow or */ +/* destructive underflow. */ + + tau = dlapy2_(&c__, &s); + t = d__[j] - d__[jlam]; + c__ /= tau; + s = -s / tau; + if ((d__1 = t * c__ * s, abs(d__1)) <= tol) { + +/* Deflation is possible. */ + + z__[j] = tau; + z__[jlam] = 0.; + +/* Record the appropriate Givens rotation */ + + ++(*givptr); + givcol[(*givptr << 1) + 1] = indxq[indx[jlam]]; + givcol[(*givptr << 1) + 2] = indxq[indx[j]]; + givnum[(*givptr << 1) + 1] = c__; + givnum[(*givptr << 1) + 2] = s; + if (*icompq == 1) { + drot_(qsiz, &q[indxq[indx[jlam]] * q_dim1 + 1], &c__1, &q[ + indxq[indx[j]] * q_dim1 + 1], &c__1, &c__, &s); + } + t = d__[jlam] * c__ * c__ + d__[j] * s * s; + d__[j] = d__[jlam] * s * s + d__[j] * c__ * c__; + d__[jlam] = t; + --k2; + i__ = 1; +L90: + if (k2 + i__ <= *n) { + if (d__[jlam] < d__[indxp[k2 + i__]]) { + indxp[k2 + i__ - 1] = indxp[k2 + i__]; + indxp[k2 + i__] = jlam; + ++i__; + goto L90; + } else { + indxp[k2 + i__ - 1] = jlam; + } + } else { + indxp[k2 + i__ - 1] = jlam; + } + jlam = j; + } else { + ++(*k); + w[*k] = z__[jlam]; + dlamda[*k] = d__[jlam]; + indxp[*k] = jlam; + jlam = j; + } + } + goto L80; +L100: + +/* Record the last eigenvalue. */ + + ++(*k); + w[*k] = z__[jlam]; + dlamda[*k] = d__[jlam]; + indxp[*k] = jlam; + +L110: + +/* Sort the eigenvalues and corresponding eigenvectors into DLAMDA */ +/* and Q2 respectively. The eigenvalues/vectors which were not */ +/* deflated go into the first K slots of DLAMDA and Q2 respectively, */ +/* while those which were deflated go into the last N - K slots. */ + + if (*icompq == 0) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + jp = indxp[j]; + dlamda[j] = d__[jp]; + perm[j] = indxq[indx[jp]]; +/* L120: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + jp = indxp[j]; + dlamda[j] = d__[jp]; + perm[j] = indxq[indx[jp]]; + dcopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 + 1] + , &c__1); +/* L130: */ + } + } + +/* The deflated eigenvalues and their corresponding vectors go back */ +/* into the last N - K slots of D and Q respectively. */ + + if (*k < *n) { + if (*icompq == 0) { + i__1 = *n - *k; + dcopy_(&i__1, &dlamda[*k + 1], &c__1, &d__[*k + 1], &c__1); + } else { + i__1 = *n - *k; + dcopy_(&i__1, &dlamda[*k + 1], &c__1, &d__[*k + 1], &c__1); + i__1 = *n - *k; + dlacpy_((char *)"A", qsiz, &i__1, &q2[(*k + 1) * q2_dim1 + 1], ldq2, &q[(* + k + 1) * q_dim1 + 1], ldq, (ftnlen)1); + } + } + + return 0; + +/* End of DLAED8 */ + +} /* dlaed8_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlaed9.cpp b/lib/linalg/dlaed9.cpp new file mode 100644 index 0000000000..f74b8f5bc0 --- /dev/null +++ b/lib/linalg/dlaed9.cpp @@ -0,0 +1,370 @@ +/* fortran/dlaed9.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; + +/* > \brief \b DLAED9 used by DSTEDC. Finds the roots of the secular equation and updates the eigenvectors. Us +ed when the original matrix is dense. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLAED9 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLAED9( K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA, W, */ +/* S, LDS, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INFO, K, KSTART, KSTOP, LDQ, LDS, N */ +/* DOUBLE PRECISION RHO */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION D( * ), DLAMDA( * ), Q( LDQ, * ), S( LDS, * ), */ +/* $ W( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLAED9 finds the roots of the secular equation, as defined by the */ +/* > values in D, Z, and RHO, between KSTART and KSTOP. It makes the */ +/* > appropriate calls to DLAED4 and then stores the new matrix of */ +/* > eigenvectors for use in calculating the next level of Z vectors. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > The number of terms in the rational function to be solved by */ +/* > DLAED4. K >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] KSTART */ +/* > \verbatim */ +/* > KSTART is INTEGER */ +/* > \endverbatim */ +/* > */ +/* > \param[in] KSTOP */ +/* > \verbatim */ +/* > KSTOP is INTEGER */ +/* > The updated eigenvalues Lambda(I), KSTART <= I <= KSTOP */ +/* > are to be computed. 1 <= KSTART <= KSTOP <= K. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of rows and columns in the Q matrix. */ +/* > N >= K (delation may result in N > K). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension (N) */ +/* > D(I) contains the updated eigenvalues */ +/* > for KSTART <= I <= KSTOP. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] Q */ +/* > \verbatim */ +/* > Q is DOUBLE PRECISION array, dimension (LDQ,N) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDQ */ +/* > \verbatim */ +/* > LDQ is INTEGER */ +/* > The leading dimension of the array Q. LDQ >= max( 1, N ). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] RHO */ +/* > \verbatim */ +/* > RHO is DOUBLE PRECISION */ +/* > The value of the parameter in the rank one update equation. */ +/* > RHO >= 0 required. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DLAMDA */ +/* > \verbatim */ +/* > DLAMDA is DOUBLE PRECISION array, dimension (K) */ +/* > The first K elements of this array contain the old roots */ +/* > of the deflated updating problem. These are the poles */ +/* > of the secular equation. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] W */ +/* > \verbatim */ +/* > W is DOUBLE PRECISION array, dimension (K) */ +/* > The first K elements of this array contain the components */ +/* > of the deflation-adjusted updating vector. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] S */ +/* > \verbatim */ +/* > S is DOUBLE PRECISION array, dimension (LDS, K) */ +/* > Will contain the eigenvectors of the repaired matrix which */ +/* > will be stored for subsequent Z vector calculation and */ +/* > multiplied by the previously accumulated eigenvectors */ +/* > to update the system. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDS */ +/* > \verbatim */ +/* > LDS is INTEGER */ +/* > The leading dimension of S. LDS >= max( 1, K ). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit. */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ +/* > > 0: if INFO = 1, an eigenvalue did not converge */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup auxOTHERcomputational */ + +/* > \par Contributors: */ +/* ================== */ +/* > */ +/* > Jeff Rutter, Computer Science Division, University of California */ +/* > at Berkeley, USA */ + +/* ===================================================================== */ +/* Subroutine */ int dlaed9_(integer *k, integer *kstart, integer *kstop, + integer *n, doublereal *d__, doublereal *q, integer *ldq, doublereal * + rho, doublereal *dlamda, doublereal *w, doublereal *s, integer *lds, + integer *info) +{ + /* System generated locals */ + integer q_dim1, q_offset, s_dim1, s_offset, i__1, i__2; + doublereal d__1; + + /* Builtin functions */ + double sqrt(doublereal), d_sign(doublereal *, doublereal *); + + /* Local variables */ + integer i__, j; + doublereal temp; + extern doublereal dnrm2_(integer *, doublereal *, integer *); + extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, + doublereal *, integer *), dlaed4_(integer *, integer *, + doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, integer *); + extern doublereal dlamc3_(doublereal *, doublereal *); + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --d__; + q_dim1 = *ldq; + q_offset = 1 + q_dim1; + q -= q_offset; + --dlamda; + --w; + s_dim1 = *lds; + s_offset = 1 + s_dim1; + s -= s_offset; + + /* Function Body */ + *info = 0; + + if (*k < 0) { + *info = -1; + } else if (*kstart < 1 || *kstart > max(1,*k)) { + *info = -2; + } else if (max(1,*kstop) < *kstart || *kstop > max(1,*k)) { + *info = -3; + } else if (*n < *k) { + *info = -4; + } else if (*ldq < max(1,*k)) { + *info = -7; + } else if (*lds < max(1,*k)) { + *info = -12; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DLAED9", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*k == 0) { + return 0; + } + +/* Modify values DLAMDA(i) to make sure all DLAMDA(i)-DLAMDA(j) can */ +/* be computed with high relative accuracy (barring over/underflow). */ +/* This is a problem on machines without a guard digit in */ +/* add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2). */ +/* The following code replaces DLAMDA(I) by 2*DLAMDA(I)-DLAMDA(I), */ +/* which on any of these machines zeros out the bottommost */ +/* bit of DLAMDA(I) if it is 1; this makes the subsequent */ +/* subtractions DLAMDA(I)-DLAMDA(J) unproblematic when cancellation */ +/* occurs. On binary machines with a guard digit (almost all */ +/* machines) it does not change DLAMDA(I) at all. On hexadecimal */ +/* and decimal machines with a guard digit, it slightly */ +/* changes the bottommost bits of DLAMDA(I). It does not account */ +/* for hexadecimal or decimal machines without guard digits */ +/* (we know of none). We use a subroutine call to compute */ +/* 2*DLAMBDA(I) to prevent optimizing compilers from eliminating */ +/* this code. */ + + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + dlamda[i__] = dlamc3_(&dlamda[i__], &dlamda[i__]) - dlamda[i__]; +/* L10: */ + } + + i__1 = *kstop; + for (j = *kstart; j <= i__1; ++j) { + dlaed4_(k, &j, &dlamda[1], &w[1], &q[j * q_dim1 + 1], rho, &d__[j], + info); + +/* If the zero finder fails, the computation is terminated. */ + + if (*info != 0) { + goto L120; + } +/* L20: */ + } + + if (*k == 1 || *k == 2) { + i__1 = *k; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = *k; + for (j = 1; j <= i__2; ++j) { + s[j + i__ * s_dim1] = q[j + i__ * q_dim1]; +/* L30: */ + } +/* L40: */ + } + goto L120; + } + +/* Compute updated W. */ + + dcopy_(k, &w[1], &c__1, &s[s_offset], &c__1); + +/* Initialize W(I) = Q(I,I) */ + + i__1 = *ldq + 1; + dcopy_(k, &q[q_offset], &i__1, &w[1], &c__1); + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]); +/* L50: */ + } + i__2 = *k; + for (i__ = j + 1; i__ <= i__2; ++i__) { + w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]); +/* L60: */ + } +/* L70: */ + } + i__1 = *k; + for (i__ = 1; i__ <= i__1; ++i__) { + d__1 = sqrt(-w[i__]); + w[i__] = d_sign(&d__1, &s[i__ + s_dim1]); +/* L80: */ + } + +/* Compute eigenvectors of the modified rank-1 modification. */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *k; + for (i__ = 1; i__ <= i__2; ++i__) { + q[i__ + j * q_dim1] = w[i__] / q[i__ + j * q_dim1]; +/* L90: */ + } + temp = dnrm2_(k, &q[j * q_dim1 + 1], &c__1); + i__2 = *k; + for (i__ = 1; i__ <= i__2; ++i__) { + s[i__ + j * s_dim1] = q[i__ + j * q_dim1] / temp; +/* L100: */ + } +/* L110: */ + } + +L120: + return 0; + +/* End of DLAED9 */ + +} /* dlaed9_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlaeda.cpp b/lib/linalg/dlaeda.cpp new file mode 100644 index 0000000000..f487609f82 --- /dev/null +++ b/lib/linalg/dlaeda.cpp @@ -0,0 +1,386 @@ +/* fortran/dlaeda.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__2 = 2; +static integer c__1 = 1; +static doublereal c_b24 = 1.; +static doublereal c_b26 = 0.; + +/* > \brief \b DLAEDA used by DSTEDC. Computes the Z vector determining the rank-one modification of the diago +nal matrix. Used when the original matrix is dense. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLAEDA + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLAEDA( N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR, */ +/* GIVCOL, GIVNUM, Q, QPTR, Z, ZTEMP, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER CURLVL, CURPBM, INFO, N, TLVLS */ +/* .. */ +/* .. Array Arguments .. */ +/* INTEGER GIVCOL( 2, * ), GIVPTR( * ), PERM( * ), */ +/* $ PRMPTR( * ), QPTR( * ) */ +/* DOUBLE PRECISION GIVNUM( 2, * ), Q( * ), Z( * ), ZTEMP( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLAEDA computes the Z vector corresponding to the merge step in the */ +/* > CURLVLth step of the merge process with TLVLS steps for the CURPBMth */ +/* > problem. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The dimension of the symmetric tridiagonal matrix. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TLVLS */ +/* > \verbatim */ +/* > TLVLS is INTEGER */ +/* > The total number of merging levels in the overall divide and */ +/* > conquer tree. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] CURLVL */ +/* > \verbatim */ +/* > CURLVL is INTEGER */ +/* > The current level in the overall merge routine, */ +/* > 0 <= curlvl <= tlvls. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] CURPBM */ +/* > \verbatim */ +/* > CURPBM is INTEGER */ +/* > The current problem in the current level in the overall */ +/* > merge routine (counting from upper left to lower right). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] PRMPTR */ +/* > \verbatim */ +/* > PRMPTR is INTEGER array, dimension (N lg N) */ +/* > Contains a list of pointers which indicate where in PERM a */ +/* > level's permutation is stored. PRMPTR(i+1) - PRMPTR(i) */ +/* > indicates the size of the permutation and incidentally the */ +/* > size of the full, non-deflated problem. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] PERM */ +/* > \verbatim */ +/* > PERM is INTEGER array, dimension (N lg N) */ +/* > Contains the permutations (from deflation and sorting) to be */ +/* > applied to each eigenblock. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] GIVPTR */ +/* > \verbatim */ +/* > GIVPTR is INTEGER array, dimension (N lg N) */ +/* > Contains a list of pointers which indicate where in GIVCOL a */ +/* > level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i) */ +/* > indicates the number of Givens rotations. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] GIVCOL */ +/* > \verbatim */ +/* > GIVCOL is INTEGER array, dimension (2, N lg N) */ +/* > Each pair of numbers indicates a pair of columns to take place */ +/* > in a Givens rotation. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] GIVNUM */ +/* > \verbatim */ +/* > GIVNUM is DOUBLE PRECISION array, dimension (2, N lg N) */ +/* > Each number indicates the S value to be used in the */ +/* > corresponding Givens rotation. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] Q */ +/* > \verbatim */ +/* > Q is DOUBLE PRECISION array, dimension (N**2) */ +/* > Contains the square eigenblocks from previous levels, the */ +/* > starting positions for blocks are given by QPTR. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] QPTR */ +/* > \verbatim */ +/* > QPTR is INTEGER array, dimension (N+2) */ +/* > Contains a list of pointers which indicate where in Q an */ +/* > eigenblock is stored. SQRT( QPTR(i+1) - QPTR(i) ) indicates */ +/* > the size of the block. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] Z */ +/* > \verbatim */ +/* > Z is DOUBLE PRECISION array, dimension (N) */ +/* > On output this vector contains the updating vector (the last */ +/* > row of the first sub-eigenvector matrix and the first row of */ +/* > the second sub-eigenvector matrix). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] ZTEMP */ +/* > \verbatim */ +/* > ZTEMP is DOUBLE PRECISION array, dimension (N) */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit. */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup auxOTHERcomputational */ + +/* > \par Contributors: */ +/* ================== */ +/* > */ +/* > Jeff Rutter, Computer Science Division, University of California */ +/* > at Berkeley, USA */ + +/* ===================================================================== */ +/* Subroutine */ int dlaeda_(integer *n, integer *tlvls, integer *curlvl, + integer *curpbm, integer *prmptr, integer *perm, integer *givptr, + integer *givcol, doublereal *givnum, doublereal *q, integer *qptr, + doublereal *z__, doublereal *ztemp, integer *info) +{ + /* System generated locals */ + integer i__1, i__2, i__3; + + /* Builtin functions */ + integer pow_ii(integer *, integer *); + double sqrt(doublereal); + + /* Local variables */ + integer i__, k, mid, ptr; + extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, + doublereal *, integer *, doublereal *, doublereal *); + integer curr, bsiz1, bsiz2, psiz1, psiz2, zptr1; + extern /* Subroutine */ int dgemv_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, ftnlen), dcopy_(integer *, + doublereal *, integer *, doublereal *, integer *), xerbla_(char *, + integer *, ftnlen); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --ztemp; + --z__; + --qptr; + --q; + givnum -= 3; + givcol -= 3; + --givptr; + --perm; + --prmptr; + + /* Function Body */ + *info = 0; + + if (*n < 0) { + *info = -1; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DLAEDA", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*n == 0) { + return 0; + } + +/* Determine location of first number in second half. */ + + mid = *n / 2 + 1; + +/* Gather last/first rows of appropriate eigenblocks into center of Z */ + + ptr = 1; + +/* Determine location of lowest level subproblem in the full storage */ +/* scheme */ + + i__1 = *curlvl - 1; + curr = ptr + *curpbm * pow_ii(&c__2, curlvl) + pow_ii(&c__2, &i__1) - 1; + +/* Determine size of these matrices. We add HALF to the value of */ +/* the SQRT in case the machine underestimates one of these square */ +/* roots. */ + + bsiz1 = (integer) (sqrt((doublereal) (qptr[curr + 1] - qptr[curr])) + .5); + bsiz2 = (integer) (sqrt((doublereal) (qptr[curr + 2] - qptr[curr + 1])) + + .5); + i__1 = mid - bsiz1 - 1; + for (k = 1; k <= i__1; ++k) { + z__[k] = 0.; +/* L10: */ + } + dcopy_(&bsiz1, &q[qptr[curr] + bsiz1 - 1], &bsiz1, &z__[mid - bsiz1], & + c__1); + dcopy_(&bsiz2, &q[qptr[curr + 1]], &bsiz2, &z__[mid], &c__1); + i__1 = *n; + for (k = mid + bsiz2; k <= i__1; ++k) { + z__[k] = 0.; +/* L20: */ + } + +/* Loop through remaining levels 1 -> CURLVL applying the Givens */ +/* rotations and permutation and then multiplying the center matrices */ +/* against the current Z. */ + + ptr = pow_ii(&c__2, tlvls) + 1; + i__1 = *curlvl - 1; + for (k = 1; k <= i__1; ++k) { + i__2 = *curlvl - k; + i__3 = *curlvl - k - 1; + curr = ptr + *curpbm * pow_ii(&c__2, &i__2) + pow_ii(&c__2, &i__3) - + 1; + psiz1 = prmptr[curr + 1] - prmptr[curr]; + psiz2 = prmptr[curr + 2] - prmptr[curr + 1]; + zptr1 = mid - psiz1; + +/* Apply Givens at CURR and CURR+1 */ + + i__2 = givptr[curr + 1] - 1; + for (i__ = givptr[curr]; i__ <= i__2; ++i__) { + drot_(&c__1, &z__[zptr1 + givcol[(i__ << 1) + 1] - 1], &c__1, & + z__[zptr1 + givcol[(i__ << 1) + 2] - 1], &c__1, &givnum[( + i__ << 1) + 1], &givnum[(i__ << 1) + 2]); +/* L30: */ + } + i__2 = givptr[curr + 2] - 1; + for (i__ = givptr[curr + 1]; i__ <= i__2; ++i__) { + drot_(&c__1, &z__[mid - 1 + givcol[(i__ << 1) + 1]], &c__1, &z__[ + mid - 1 + givcol[(i__ << 1) + 2]], &c__1, &givnum[(i__ << + 1) + 1], &givnum[(i__ << 1) + 2]); +/* L40: */ + } + psiz1 = prmptr[curr + 1] - prmptr[curr]; + psiz2 = prmptr[curr + 2] - prmptr[curr + 1]; + i__2 = psiz1 - 1; + for (i__ = 0; i__ <= i__2; ++i__) { + ztemp[i__ + 1] = z__[zptr1 + perm[prmptr[curr] + i__] - 1]; +/* L50: */ + } + i__2 = psiz2 - 1; + for (i__ = 0; i__ <= i__2; ++i__) { + ztemp[psiz1 + i__ + 1] = z__[mid + perm[prmptr[curr + 1] + i__] - + 1]; +/* L60: */ + } + +/* Multiply Blocks at CURR and CURR+1 */ + +/* Determine size of these matrices. We add HALF to the value of */ +/* the SQRT in case the machine underestimates one of these */ +/* square roots. */ + + bsiz1 = (integer) (sqrt((doublereal) (qptr[curr + 1] - qptr[curr])) + + .5); + bsiz2 = (integer) (sqrt((doublereal) (qptr[curr + 2] - qptr[curr + 1]) + ) + .5); + if (bsiz1 > 0) { + dgemv_((char *)"T", &bsiz1, &bsiz1, &c_b24, &q[qptr[curr]], &bsiz1, & + ztemp[1], &c__1, &c_b26, &z__[zptr1], &c__1, (ftnlen)1); + } + i__2 = psiz1 - bsiz1; + dcopy_(&i__2, &ztemp[bsiz1 + 1], &c__1, &z__[zptr1 + bsiz1], &c__1); + if (bsiz2 > 0) { + dgemv_((char *)"T", &bsiz2, &bsiz2, &c_b24, &q[qptr[curr + 1]], &bsiz2, & + ztemp[psiz1 + 1], &c__1, &c_b26, &z__[mid], &c__1, ( + ftnlen)1); + } + i__2 = psiz2 - bsiz2; + dcopy_(&i__2, &ztemp[psiz1 + bsiz2 + 1], &c__1, &z__[mid + bsiz2], & + c__1); + + i__2 = *tlvls - k; + ptr += pow_ii(&c__2, &i__2); +/* L70: */ + } + + return 0; + +/* End of DLAEDA */ + +} /* dlaeda_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlaev2.cpp b/lib/linalg/dlaev2.cpp new file mode 100644 index 0000000000..32f4eb5424 --- /dev/null +++ b/lib/linalg/dlaev2.cpp @@ -0,0 +1,263 @@ +/* fortran/dlaev2.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLAEV2 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLAEV2( A, B, C, RT1, RT2, CS1, SN1 ) */ + +/* .. Scalar Arguments .. */ +/* DOUBLE PRECISION A, B, C, CS1, RT1, RT2, SN1 */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix */ +/* > [ A B ] */ +/* > [ B C ]. */ +/* > On return, RT1 is the eigenvalue of larger absolute value, RT2 is the */ +/* > eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right */ +/* > eigenvector for RT1, giving the decomposition */ +/* > */ +/* > [ CS1 SN1 ] [ A B ] [ CS1 -SN1 ] = [ RT1 0 ] */ +/* > [-SN1 CS1 ] [ B C ] [ SN1 CS1 ] [ 0 RT2 ]. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION */ +/* > The (1,1) element of the 2-by-2 matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] B */ +/* > \verbatim */ +/* > B is DOUBLE PRECISION */ +/* > The (1,2) element and the conjugate of the (2,1) element of */ +/* > the 2-by-2 matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] C */ +/* > \verbatim */ +/* > C is DOUBLE PRECISION */ +/* > The (2,2) element of the 2-by-2 matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] RT1 */ +/* > \verbatim */ +/* > RT1 is DOUBLE PRECISION */ +/* > The eigenvalue of larger absolute value. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] RT2 */ +/* > \verbatim */ +/* > RT2 is DOUBLE PRECISION */ +/* > The eigenvalue of smaller absolute value. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] CS1 */ +/* > \verbatim */ +/* > CS1 is DOUBLE PRECISION */ +/* > \endverbatim */ +/* > */ +/* > \param[out] SN1 */ +/* > \verbatim */ +/* > SN1 is DOUBLE PRECISION */ +/* > The vector (CS1, SN1) is a unit right eigenvector for RT1. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup OTHERauxiliary */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > RT1 is accurate to a few ulps barring over/underflow. */ +/* > */ +/* > RT2 may be inaccurate if there is massive cancellation in the */ +/* > determinant A*C-B*B; higher precision or correctly rounded or */ +/* > correctly truncated arithmetic would be needed to compute RT2 */ +/* > accurately in all cases. */ +/* > */ +/* > CS1 and SN1 are accurate to a few ulps barring over/underflow. */ +/* > */ +/* > Overflow is possible only if RT1 is within a factor of 5 of overflow. */ +/* > Underflow is harmless if the input data is 0 or exceeds */ +/* > underflow_threshold / macheps. */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dlaev2_(doublereal *a, doublereal *b, doublereal *c__, + doublereal *rt1, doublereal *rt2, doublereal *cs1, doublereal *sn1) +{ + /* System generated locals */ + doublereal d__1; + + /* Builtin functions */ + double sqrt(doublereal); + + /* Local variables */ + doublereal ab, df, cs, ct, tb, sm, tn, rt, adf, acs; + integer sgn1, sgn2; + doublereal acmn, acmx; + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Compute the eigenvalues */ + + sm = *a + *c__; + df = *a - *c__; + adf = abs(df); + tb = *b + *b; + ab = abs(tb); + if (abs(*a) > abs(*c__)) { + acmx = *a; + acmn = *c__; + } else { + acmx = *c__; + acmn = *a; + } + if (adf > ab) { +/* Computing 2nd power */ + d__1 = ab / adf; + rt = adf * sqrt(d__1 * d__1 + 1.); + } else if (adf < ab) { +/* Computing 2nd power */ + d__1 = adf / ab; + rt = ab * sqrt(d__1 * d__1 + 1.); + } else { + +/* Includes case AB=ADF=0 */ + + rt = ab * sqrt(2.); + } + if (sm < 0.) { + *rt1 = (sm - rt) * .5; + sgn1 = -1; + +/* Order of execution important. */ +/* To get fully accurate smaller eigenvalue, */ +/* next line needs to be executed in higher precision. */ + + *rt2 = acmx / *rt1 * acmn - *b / *rt1 * *b; + } else if (sm > 0.) { + *rt1 = (sm + rt) * .5; + sgn1 = 1; + +/* Order of execution important. */ +/* To get fully accurate smaller eigenvalue, */ +/* next line needs to be executed in higher precision. */ + + *rt2 = acmx / *rt1 * acmn - *b / *rt1 * *b; + } else { + +/* Includes case RT1 = RT2 = 0 */ + + *rt1 = rt * .5; + *rt2 = rt * -.5; + sgn1 = 1; + } + +/* Compute the eigenvector */ + + if (df >= 0.) { + cs = df + rt; + sgn2 = 1; + } else { + cs = df - rt; + sgn2 = -1; + } + acs = abs(cs); + if (acs > ab) { + ct = -tb / cs; + *sn1 = 1. / sqrt(ct * ct + 1.); + *cs1 = ct * *sn1; + } else { + if (ab == 0.) { + *cs1 = 1.; + *sn1 = 0.; + } else { + tn = -cs / tb; + *cs1 = 1. / sqrt(tn * tn + 1.); + *sn1 = tn * *cs1; + } + } + if (sgn1 == sgn2) { + tn = *cs1; + *cs1 = -(*sn1); + *sn1 = tn; + } + return 0; + +/* End of DLAEV2 */ + +} /* dlaev2_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlals0.cpp b/lib/linalg/dlals0.cpp new file mode 100644 index 0000000000..ce36d7d553 --- /dev/null +++ b/lib/linalg/dlals0.cpp @@ -0,0 +1,602 @@ +/* fortran/dlals0.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static doublereal c_b5 = -1.; +static integer c__1 = 1; +static doublereal c_b11 = 1.; +static doublereal c_b13 = 0.; +static integer c__0 = 0; + +/* > \brief \b DLALS0 applies back multiplying factors in solving the least squares problem using divide and c +onquer SVD approach. Used by sgelsd. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLALS0 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLALS0( ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX, */ +/* PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, */ +/* POLES, DIFL, DIFR, Z, K, C, S, WORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER GIVPTR, ICOMPQ, INFO, K, LDB, LDBX, LDGCOL, */ +/* $ LDGNUM, NL, NR, NRHS, SQRE */ +/* DOUBLE PRECISION C, S */ +/* .. */ +/* .. Array Arguments .. */ +/* INTEGER GIVCOL( LDGCOL, * ), PERM( * ) */ +/* DOUBLE PRECISION B( LDB, * ), BX( LDBX, * ), DIFL( * ), */ +/* $ DIFR( LDGNUM, * ), GIVNUM( LDGNUM, * ), */ +/* $ POLES( LDGNUM, * ), WORK( * ), Z( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLALS0 applies back the multiplying factors of either the left or the */ +/* > right singular vector matrix of a diagonal matrix appended by a row */ +/* > to the right hand side matrix B in solving the least squares problem */ +/* > using the divide-and-conquer SVD approach. */ +/* > */ +/* > For the left singular vector matrix, three types of orthogonal */ +/* > matrices are involved: */ +/* > */ +/* > (1L) Givens rotations: the number of such rotations is GIVPTR; the */ +/* > pairs of columns/rows they were applied to are stored in GIVCOL; */ +/* > and the C- and S-values of these rotations are stored in GIVNUM. */ +/* > */ +/* > (2L) Permutation. The (NL+1)-st row of B is to be moved to the first */ +/* > row, and for J=2:N, PERM(J)-th row of B is to be moved to the */ +/* > J-th row. */ +/* > */ +/* > (3L) The left singular vector matrix of the remaining matrix. */ +/* > */ +/* > For the right singular vector matrix, four types of orthogonal */ +/* > matrices are involved: */ +/* > */ +/* > (1R) The right singular vector matrix of the remaining matrix. */ +/* > */ +/* > (2R) If SQRE = 1, one extra Givens rotation to generate the right */ +/* > null space. */ +/* > */ +/* > (3R) The inverse transformation of (2L). */ +/* > */ +/* > (4R) The inverse transformation of (1L). */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] ICOMPQ */ +/* > \verbatim */ +/* > ICOMPQ is INTEGER */ +/* > Specifies whether singular vectors are to be computed in */ +/* > factored form: */ +/* > = 0: Left singular vector matrix. */ +/* > = 1: Right singular vector matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] NL */ +/* > \verbatim */ +/* > NL is INTEGER */ +/* > The row dimension of the upper block. NL >= 1. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] NR */ +/* > \verbatim */ +/* > NR is INTEGER */ +/* > The row dimension of the lower block. NR >= 1. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] SQRE */ +/* > \verbatim */ +/* > SQRE is INTEGER */ +/* > = 0: the lower block is an NR-by-NR square matrix. */ +/* > = 1: the lower block is an NR-by-(NR+1) rectangular matrix. */ +/* > */ +/* > The bidiagonal matrix has row dimension N = NL + NR + 1, */ +/* > and column dimension M = N + SQRE. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] NRHS */ +/* > \verbatim */ +/* > NRHS is INTEGER */ +/* > The number of columns of B and BX. NRHS must be at least 1. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] B */ +/* > \verbatim */ +/* > B is DOUBLE PRECISION array, dimension ( LDB, NRHS ) */ +/* > On input, B contains the right hand sides of the least */ +/* > squares problem in rows 1 through M. On output, B contains */ +/* > the solution X in rows 1 through N. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDB */ +/* > \verbatim */ +/* > LDB is INTEGER */ +/* > The leading dimension of B. LDB must be at least */ +/* > max(1,MAX( M, N ) ). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] BX */ +/* > \verbatim */ +/* > BX is DOUBLE PRECISION array, dimension ( LDBX, NRHS ) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDBX */ +/* > \verbatim */ +/* > LDBX is INTEGER */ +/* > The leading dimension of BX. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] PERM */ +/* > \verbatim */ +/* > PERM is INTEGER array, dimension ( N ) */ +/* > The permutations (from deflation and sorting) applied */ +/* > to the two blocks. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] GIVPTR */ +/* > \verbatim */ +/* > GIVPTR is INTEGER */ +/* > The number of Givens rotations which took place in this */ +/* > subproblem. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] GIVCOL */ +/* > \verbatim */ +/* > GIVCOL is INTEGER array, dimension ( LDGCOL, 2 ) */ +/* > Each pair of numbers indicates a pair of rows/columns */ +/* > involved in a Givens rotation. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDGCOL */ +/* > \verbatim */ +/* > LDGCOL is INTEGER */ +/* > The leading dimension of GIVCOL, must be at least N. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] GIVNUM */ +/* > \verbatim */ +/* > GIVNUM is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) */ +/* > Each number indicates the C or S value used in the */ +/* > corresponding Givens rotation. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDGNUM */ +/* > \verbatim */ +/* > LDGNUM is INTEGER */ +/* > The leading dimension of arrays DIFR, POLES and */ +/* > GIVNUM, must be at least K. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] POLES */ +/* > \verbatim */ +/* > POLES is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) */ +/* > On entry, POLES(1:K, 1) contains the new singular */ +/* > values obtained from solving the secular equation, and */ +/* > POLES(1:K, 2) is an array containing the poles in the secular */ +/* > equation. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DIFL */ +/* > \verbatim */ +/* > DIFL is DOUBLE PRECISION array, dimension ( K ). */ +/* > On entry, DIFL(I) is the distance between I-th updated */ +/* > (undeflated) singular value and the I-th (undeflated) old */ +/* > singular value. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DIFR */ +/* > \verbatim */ +/* > DIFR is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ). */ +/* > On entry, DIFR(I, 1) contains the distances between I-th */ +/* > updated (undeflated) singular value and the I+1-th */ +/* > (undeflated) old singular value. And DIFR(I, 2) is the */ +/* > normalizing factor for the I-th right singular vector. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] Z */ +/* > \verbatim */ +/* > Z is DOUBLE PRECISION array, dimension ( K ) */ +/* > Contain the components of the deflation-adjusted updating row */ +/* > vector. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > Contains the dimension of the non-deflated matrix, */ +/* > This is the order of the related secular equation. 1 <= K <=N. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] C */ +/* > \verbatim */ +/* > C is DOUBLE PRECISION */ +/* > C contains garbage if SQRE =0 and the C-value of a Givens */ +/* > rotation related to the right null space if SQRE = 1. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] S */ +/* > \verbatim */ +/* > S is DOUBLE PRECISION */ +/* > S contains garbage if SQRE =0 and the S-value of a Givens */ +/* > rotation related to the right null space if SQRE = 1. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension ( K ) */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit. */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleOTHERcomputational */ + +/* > \par Contributors: */ +/* ================== */ +/* > */ +/* > Ming Gu and Ren-Cang Li, Computer Science Division, University of */ +/* > California at Berkeley, USA \n */ +/* > Osni Marques, LBNL/NERSC, USA \n */ + +/* ===================================================================== */ +/* Subroutine */ int dlals0_(integer *icompq, integer *nl, integer *nr, + integer *sqre, integer *nrhs, doublereal *b, integer *ldb, doublereal + *bx, integer *ldbx, integer *perm, integer *givptr, integer *givcol, + integer *ldgcol, doublereal *givnum, integer *ldgnum, doublereal * + poles, doublereal *difl, doublereal *difr, doublereal *z__, integer * + k, doublereal *c__, doublereal *s, doublereal *work, integer *info) +{ + /* System generated locals */ + integer givcol_dim1, givcol_offset, b_dim1, b_offset, bx_dim1, bx_offset, + difr_dim1, difr_offset, givnum_dim1, givnum_offset, poles_dim1, + poles_offset, i__1, i__2; + doublereal d__1; + + /* Local variables */ + integer i__, j, m, n; + doublereal dj; + integer nlp1; + doublereal temp; + extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, + doublereal *, integer *, doublereal *, doublereal *); + extern doublereal dnrm2_(integer *, doublereal *, integer *); + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *); + doublereal diflj, difrj, dsigj; + extern /* Subroutine */ int dgemv_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, ftnlen), dcopy_(integer *, + doublereal *, integer *, doublereal *, integer *); + extern doublereal dlamc3_(doublereal *, doublereal *); + extern /* Subroutine */ int dlascl_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, integer *, doublereal *, + integer *, integer *, ftnlen), dlacpy_(char *, integer *, integer + *, doublereal *, integer *, doublereal *, integer *, ftnlen), + xerbla_(char *, integer *, ftnlen); + doublereal dsigjp; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + b_dim1 = *ldb; + b_offset = 1 + b_dim1; + b -= b_offset; + bx_dim1 = *ldbx; + bx_offset = 1 + bx_dim1; + bx -= bx_offset; + --perm; + givcol_dim1 = *ldgcol; + givcol_offset = 1 + givcol_dim1; + givcol -= givcol_offset; + difr_dim1 = *ldgnum; + difr_offset = 1 + difr_dim1; + difr -= difr_offset; + poles_dim1 = *ldgnum; + poles_offset = 1 + poles_dim1; + poles -= poles_offset; + givnum_dim1 = *ldgnum; + givnum_offset = 1 + givnum_dim1; + givnum -= givnum_offset; + --difl; + --z__; + --work; + + /* Function Body */ + *info = 0; + n = *nl + *nr + 1; + + if (*icompq < 0 || *icompq > 1) { + *info = -1; + } else if (*nl < 1) { + *info = -2; + } else if (*nr < 1) { + *info = -3; + } else if (*sqre < 0 || *sqre > 1) { + *info = -4; + } else if (*nrhs < 1) { + *info = -5; + } else if (*ldb < n) { + *info = -7; + } else if (*ldbx < n) { + *info = -9; + } else if (*givptr < 0) { + *info = -11; + } else if (*ldgcol < n) { + *info = -13; + } else if (*ldgnum < n) { + *info = -15; + } else if (*k < 1) { + *info = -20; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DLALS0", &i__1, (ftnlen)6); + return 0; + } + + m = n + *sqre; + nlp1 = *nl + 1; + + if (*icompq == 0) { + +/* Apply back orthogonal transformations from the left. */ + +/* Step (1L): apply back the Givens rotations performed. */ + + i__1 = *givptr; + for (i__ = 1; i__ <= i__1; ++i__) { + drot_(nrhs, &b[givcol[i__ + (givcol_dim1 << 1)] + b_dim1], ldb, & + b[givcol[i__ + givcol_dim1] + b_dim1], ldb, &givnum[i__ + + (givnum_dim1 << 1)], &givnum[i__ + givnum_dim1]); +/* L10: */ + } + +/* Step (2L): permute rows of B. */ + + dcopy_(nrhs, &b[nlp1 + b_dim1], ldb, &bx[bx_dim1 + 1], ldbx); + i__1 = n; + for (i__ = 2; i__ <= i__1; ++i__) { + dcopy_(nrhs, &b[perm[i__] + b_dim1], ldb, &bx[i__ + bx_dim1], + ldbx); +/* L20: */ + } + +/* Step (3L): apply the inverse of the left singular vector */ +/* matrix to BX. */ + + if (*k == 1) { + dcopy_(nrhs, &bx[bx_offset], ldbx, &b[b_offset], ldb); + if (z__[1] < 0.) { + dscal_(nrhs, &c_b5, &b[b_offset], ldb); + } + } else { + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + diflj = difl[j]; + dj = poles[j + poles_dim1]; + dsigj = -poles[j + (poles_dim1 << 1)]; + if (j < *k) { + difrj = -difr[j + difr_dim1]; + dsigjp = -poles[j + 1 + (poles_dim1 << 1)]; + } + if (z__[j] == 0. || poles[j + (poles_dim1 << 1)] == 0.) { + work[j] = 0.; + } else { + work[j] = -poles[j + (poles_dim1 << 1)] * z__[j] / diflj / + (poles[j + (poles_dim1 << 1)] + dj); + } + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + if (z__[i__] == 0. || poles[i__ + (poles_dim1 << 1)] == + 0.) { + work[i__] = 0.; + } else { + work[i__] = poles[i__ + (poles_dim1 << 1)] * z__[i__] + / (dlamc3_(&poles[i__ + (poles_dim1 << 1)], & + dsigj) - diflj) / (poles[i__ + (poles_dim1 << + 1)] + dj); + } +/* L30: */ + } + i__2 = *k; + for (i__ = j + 1; i__ <= i__2; ++i__) { + if (z__[i__] == 0. || poles[i__ + (poles_dim1 << 1)] == + 0.) { + work[i__] = 0.; + } else { + work[i__] = poles[i__ + (poles_dim1 << 1)] * z__[i__] + / (dlamc3_(&poles[i__ + (poles_dim1 << 1)], & + dsigjp) + difrj) / (poles[i__ + (poles_dim1 << + 1)] + dj); + } +/* L40: */ + } + work[1] = -1.; + temp = dnrm2_(k, &work[1], &c__1); + dgemv_((char *)"T", k, nrhs, &c_b11, &bx[bx_offset], ldbx, &work[1], & + c__1, &c_b13, &b[j + b_dim1], ldb, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &temp, &c_b11, &c__1, nrhs, &b[j + + b_dim1], ldb, info, (ftnlen)1); +/* L50: */ + } + } + +/* Move the deflated rows of BX to B also. */ + + if (*k < max(m,n)) { + i__1 = n - *k; + dlacpy_((char *)"A", &i__1, nrhs, &bx[*k + 1 + bx_dim1], ldbx, &b[*k + 1 + + b_dim1], ldb, (ftnlen)1); + } + } else { + +/* Apply back the right orthogonal transformations. */ + +/* Step (1R): apply back the new right singular vector matrix */ +/* to B. */ + + if (*k == 1) { + dcopy_(nrhs, &b[b_offset], ldb, &bx[bx_offset], ldbx); + } else { + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + dsigj = poles[j + (poles_dim1 << 1)]; + if (z__[j] == 0.) { + work[j] = 0.; + } else { + work[j] = -z__[j] / difl[j] / (dsigj + poles[j + + poles_dim1]) / difr[j + (difr_dim1 << 1)]; + } + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + if (z__[j] == 0.) { + work[i__] = 0.; + } else { + d__1 = -poles[i__ + 1 + (poles_dim1 << 1)]; + work[i__] = z__[j] / (dlamc3_(&dsigj, &d__1) - difr[ + i__ + difr_dim1]) / (dsigj + poles[i__ + + poles_dim1]) / difr[i__ + (difr_dim1 << 1)]; + } +/* L60: */ + } + i__2 = *k; + for (i__ = j + 1; i__ <= i__2; ++i__) { + if (z__[j] == 0.) { + work[i__] = 0.; + } else { + d__1 = -poles[i__ + (poles_dim1 << 1)]; + work[i__] = z__[j] / (dlamc3_(&dsigj, &d__1) - difl[ + i__]) / (dsigj + poles[i__ + poles_dim1]) / + difr[i__ + (difr_dim1 << 1)]; + } +/* L70: */ + } + dgemv_((char *)"T", k, nrhs, &c_b11, &b[b_offset], ldb, &work[1], & + c__1, &c_b13, &bx[j + bx_dim1], ldbx, (ftnlen)1); +/* L80: */ + } + } + +/* Step (2R): if SQRE = 1, apply back the rotation that is */ +/* related to the right null space of the subproblem. */ + + if (*sqre == 1) { + dcopy_(nrhs, &b[m + b_dim1], ldb, &bx[m + bx_dim1], ldbx); + drot_(nrhs, &bx[bx_dim1 + 1], ldbx, &bx[m + bx_dim1], ldbx, c__, + s); + } + if (*k < max(m,n)) { + i__1 = n - *k; + dlacpy_((char *)"A", &i__1, nrhs, &b[*k + 1 + b_dim1], ldb, &bx[*k + 1 + + bx_dim1], ldbx, (ftnlen)1); + } + +/* Step (3R): permute rows of B. */ + + dcopy_(nrhs, &bx[bx_dim1 + 1], ldbx, &b[nlp1 + b_dim1], ldb); + if (*sqre == 1) { + dcopy_(nrhs, &bx[m + bx_dim1], ldbx, &b[m + b_dim1], ldb); + } + i__1 = n; + for (i__ = 2; i__ <= i__1; ++i__) { + dcopy_(nrhs, &bx[i__ + bx_dim1], ldbx, &b[perm[i__] + b_dim1], + ldb); +/* L90: */ + } + +/* Step (4R): apply back the Givens rotations performed. */ + + for (i__ = *givptr; i__ >= 1; --i__) { + d__1 = -givnum[i__ + givnum_dim1]; + drot_(nrhs, &b[givcol[i__ + (givcol_dim1 << 1)] + b_dim1], ldb, & + b[givcol[i__ + givcol_dim1] + b_dim1], ldb, &givnum[i__ + + (givnum_dim1 << 1)], &d__1); +/* L100: */ + } + } + + return 0; + +/* End of DLALS0 */ + +} /* dlals0_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlalsa.cpp b/lib/linalg/dlalsa.cpp new file mode 100644 index 0000000000..7c09a46de3 --- /dev/null +++ b/lib/linalg/dlalsa.cpp @@ -0,0 +1,598 @@ +/* fortran/dlalsa.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static doublereal c_b7 = 1.; +static doublereal c_b8 = 0.; +static integer c__2 = 2; + +/* > \brief \b DLALSA computes the SVD of the coefficient matrix in compact form. Used by sgelsd. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLALSA + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLALSA( ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U, */ +/* LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR, */ +/* GIVCOL, LDGCOL, PERM, GIVNUM, C, S, WORK, */ +/* IWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER ICOMPQ, INFO, LDB, LDBX, LDGCOL, LDU, N, NRHS, */ +/* $ SMLSIZ */ +/* .. */ +/* .. Array Arguments .. */ +/* INTEGER GIVCOL( LDGCOL, * ), GIVPTR( * ), IWORK( * ), */ +/* $ K( * ), PERM( LDGCOL, * ) */ +/* DOUBLE PRECISION B( LDB, * ), BX( LDBX, * ), C( * ), */ +/* $ DIFL( LDU, * ), DIFR( LDU, * ), */ +/* $ GIVNUM( LDU, * ), POLES( LDU, * ), S( * ), */ +/* $ U( LDU, * ), VT( LDU, * ), WORK( * ), */ +/* $ Z( LDU, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLALSA is an itermediate step in solving the least squares problem */ +/* > by computing the SVD of the coefficient matrix in compact form (The */ +/* > singular vectors are computed as products of simple orthorgonal */ +/* > matrices.). */ +/* > */ +/* > If ICOMPQ = 0, DLALSA applies the inverse of the left singular vector */ +/* > matrix of an upper bidiagonal matrix to the right hand side; and if */ +/* > ICOMPQ = 1, DLALSA applies the right singular vector matrix to the */ +/* > right hand side. The singular vector matrices were generated in */ +/* > compact form by DLALSA. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] ICOMPQ */ +/* > \verbatim */ +/* > ICOMPQ is INTEGER */ +/* > Specifies whether the left or the right singular vector */ +/* > matrix is involved. */ +/* > = 0: Left singular vector matrix */ +/* > = 1: Right singular vector matrix */ +/* > \endverbatim */ +/* > */ +/* > \param[in] SMLSIZ */ +/* > \verbatim */ +/* > SMLSIZ is INTEGER */ +/* > The maximum size of the subproblems at the bottom of the */ +/* > computation tree. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The row and column dimensions of the upper bidiagonal matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] NRHS */ +/* > \verbatim */ +/* > NRHS is INTEGER */ +/* > The number of columns of B and BX. NRHS must be at least 1. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] B */ +/* > \verbatim */ +/* > B is DOUBLE PRECISION array, dimension ( LDB, NRHS ) */ +/* > On input, B contains the right hand sides of the least */ +/* > squares problem in rows 1 through M. */ +/* > On output, B contains the solution X in rows 1 through N. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDB */ +/* > \verbatim */ +/* > LDB is INTEGER */ +/* > The leading dimension of B in the calling subprogram. */ +/* > LDB must be at least max(1,MAX( M, N ) ). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] BX */ +/* > \verbatim */ +/* > BX is DOUBLE PRECISION array, dimension ( LDBX, NRHS ) */ +/* > On exit, the result of applying the left or right singular */ +/* > vector matrix to B. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDBX */ +/* > \verbatim */ +/* > LDBX is INTEGER */ +/* > The leading dimension of BX. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] U */ +/* > \verbatim */ +/* > U is DOUBLE PRECISION array, dimension ( LDU, SMLSIZ ). */ +/* > On entry, U contains the left singular vector matrices of all */ +/* > subproblems at the bottom level. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDU */ +/* > \verbatim */ +/* > LDU is INTEGER, LDU = > N. */ +/* > The leading dimension of arrays U, VT, DIFL, DIFR, */ +/* > POLES, GIVNUM, and Z. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] VT */ +/* > \verbatim */ +/* > VT is DOUBLE PRECISION array, dimension ( LDU, SMLSIZ+1 ). */ +/* > On entry, VT**T contains the right singular vector matrices of */ +/* > all subproblems at the bottom level. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER array, dimension ( N ). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DIFL */ +/* > \verbatim */ +/* > DIFL is DOUBLE PRECISION array, dimension ( LDU, NLVL ). */ +/* > where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DIFR */ +/* > \verbatim */ +/* > DIFR is DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ). */ +/* > On entry, DIFL(*, I) and DIFR(*, 2 * I -1) record */ +/* > distances between singular values on the I-th level and */ +/* > singular values on the (I -1)-th level, and DIFR(*, 2 * I) */ +/* > record the normalizing factors of the right singular vectors */ +/* > matrices of subproblems on I-th level. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] Z */ +/* > \verbatim */ +/* > Z is DOUBLE PRECISION array, dimension ( LDU, NLVL ). */ +/* > On entry, Z(1, I) contains the components of the deflation- */ +/* > adjusted updating row vector for subproblems on the I-th */ +/* > level. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] POLES */ +/* > \verbatim */ +/* > POLES is DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ). */ +/* > On entry, POLES(*, 2 * I -1: 2 * I) contains the new and old */ +/* > singular values involved in the secular equations on the I-th */ +/* > level. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] GIVPTR */ +/* > \verbatim */ +/* > GIVPTR is INTEGER array, dimension ( N ). */ +/* > On entry, GIVPTR( I ) records the number of Givens */ +/* > rotations performed on the I-th problem on the computation */ +/* > tree. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] GIVCOL */ +/* > \verbatim */ +/* > GIVCOL is INTEGER array, dimension ( LDGCOL, 2 * NLVL ). */ +/* > On entry, for each I, GIVCOL(*, 2 * I - 1: 2 * I) records the */ +/* > locations of Givens rotations performed on the I-th level on */ +/* > the computation tree. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDGCOL */ +/* > \verbatim */ +/* > LDGCOL is INTEGER, LDGCOL = > N. */ +/* > The leading dimension of arrays GIVCOL and PERM. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] PERM */ +/* > \verbatim */ +/* > PERM is INTEGER array, dimension ( LDGCOL, NLVL ). */ +/* > On entry, PERM(*, I) records permutations done on the I-th */ +/* > level of the computation tree. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] GIVNUM */ +/* > \verbatim */ +/* > GIVNUM is DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ). */ +/* > On entry, GIVNUM(*, 2 *I -1 : 2 * I) records the C- and S- */ +/* > values of Givens rotations performed on the I-th level on the */ +/* > computation tree. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] C */ +/* > \verbatim */ +/* > C is DOUBLE PRECISION array, dimension ( N ). */ +/* > On entry, if the I-th subproblem is not square, */ +/* > C( I ) contains the C-value of a Givens rotation related to */ +/* > the right null space of the I-th subproblem. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] S */ +/* > \verbatim */ +/* > S is DOUBLE PRECISION array, dimension ( N ). */ +/* > On entry, if the I-th subproblem is not square, */ +/* > S( I ) contains the S-value of a Givens rotation related to */ +/* > the right null space of the I-th subproblem. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (N) */ +/* > \endverbatim */ +/* > */ +/* > \param[out] IWORK */ +/* > \verbatim */ +/* > IWORK is INTEGER array, dimension (3*N) */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit. */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleOTHERcomputational */ + +/* > \par Contributors: */ +/* ================== */ +/* > */ +/* > Ming Gu and Ren-Cang Li, Computer Science Division, University of */ +/* > California at Berkeley, USA \n */ +/* > Osni Marques, LBNL/NERSC, USA \n */ + +/* ===================================================================== */ +/* Subroutine */ int dlalsa_(integer *icompq, integer *smlsiz, integer *n, + integer *nrhs, doublereal *b, integer *ldb, doublereal *bx, integer * + ldbx, doublereal *u, integer *ldu, doublereal *vt, integer *k, + doublereal *difl, doublereal *difr, doublereal *z__, doublereal * + poles, integer *givptr, integer *givcol, integer *ldgcol, integer * + perm, doublereal *givnum, doublereal *c__, doublereal *s, doublereal * + work, integer *iwork, integer *info) +{ + /* System generated locals */ + integer givcol_dim1, givcol_offset, perm_dim1, perm_offset, b_dim1, + b_offset, bx_dim1, bx_offset, difl_dim1, difl_offset, difr_dim1, + difr_offset, givnum_dim1, givnum_offset, poles_dim1, poles_offset, + u_dim1, u_offset, vt_dim1, vt_offset, z_dim1, z_offset, i__1, + i__2; + + /* Builtin functions */ + integer pow_ii(integer *, integer *); + + /* Local variables */ + integer i__, j, i1, ic, lf, nd, ll, nl, nr, im1, nlf, nrf, lvl, ndb1, + nlp1, lvl2, nrp1, nlvl, sqre; + extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); + integer inode, ndiml, ndimr; + extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, + doublereal *, integer *), dlals0_(integer *, integer *, integer *, + integer *, integer *, doublereal *, integer *, doublereal *, + integer *, integer *, integer *, integer *, integer *, doublereal + *, integer *, doublereal *, doublereal *, doublereal *, + doublereal *, integer *, doublereal *, doublereal *, doublereal *, + integer *), dlasdt_(integer *, integer *, integer *, integer *, + integer *, integer *, integer *), xerbla_(char *, integer *, + ftnlen); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + b_dim1 = *ldb; + b_offset = 1 + b_dim1; + b -= b_offset; + bx_dim1 = *ldbx; + bx_offset = 1 + bx_dim1; + bx -= bx_offset; + givnum_dim1 = *ldu; + givnum_offset = 1 + givnum_dim1; + givnum -= givnum_offset; + poles_dim1 = *ldu; + poles_offset = 1 + poles_dim1; + poles -= poles_offset; + z_dim1 = *ldu; + z_offset = 1 + z_dim1; + z__ -= z_offset; + difr_dim1 = *ldu; + difr_offset = 1 + difr_dim1; + difr -= difr_offset; + difl_dim1 = *ldu; + difl_offset = 1 + difl_dim1; + difl -= difl_offset; + vt_dim1 = *ldu; + vt_offset = 1 + vt_dim1; + vt -= vt_offset; + u_dim1 = *ldu; + u_offset = 1 + u_dim1; + u -= u_offset; + --k; + --givptr; + perm_dim1 = *ldgcol; + perm_offset = 1 + perm_dim1; + perm -= perm_offset; + givcol_dim1 = *ldgcol; + givcol_offset = 1 + givcol_dim1; + givcol -= givcol_offset; + --c__; + --s; + --work; + --iwork; + + /* Function Body */ + *info = 0; + + if (*icompq < 0 || *icompq > 1) { + *info = -1; + } else if (*smlsiz < 3) { + *info = -2; + } else if (*n < *smlsiz) { + *info = -3; + } else if (*nrhs < 1) { + *info = -4; + } else if (*ldb < *n) { + *info = -6; + } else if (*ldbx < *n) { + *info = -8; + } else if (*ldu < *n) { + *info = -10; + } else if (*ldgcol < *n) { + *info = -19; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DLALSA", &i__1, (ftnlen)6); + return 0; + } + +/* Book-keeping and setting up the computation tree. */ + + inode = 1; + ndiml = inode + *n; + ndimr = ndiml + *n; + + dlasdt_(n, &nlvl, &nd, &iwork[inode], &iwork[ndiml], &iwork[ndimr], + smlsiz); + +/* The following code applies back the left singular vector factors. */ +/* For applying back the right singular vector factors, go to 50. */ + + if (*icompq == 1) { + goto L50; + } + +/* The nodes on the bottom level of the tree were solved */ +/* by DLASDQ. The corresponding left and right singular vector */ +/* matrices are in explicit form. First apply back the left */ +/* singular vector matrices. */ + + ndb1 = (nd + 1) / 2; + i__1 = nd; + for (i__ = ndb1; i__ <= i__1; ++i__) { + +/* IC : center row of each node */ +/* NL : number of rows of left subproblem */ +/* NR : number of rows of right subproblem */ +/* NLF: starting row of the left subproblem */ +/* NRF: starting row of the right subproblem */ + + i1 = i__ - 1; + ic = iwork[inode + i1]; + nl = iwork[ndiml + i1]; + nr = iwork[ndimr + i1]; + nlf = ic - nl; + nrf = ic + 1; + dgemm_((char *)"T", (char *)"N", &nl, nrhs, &nl, &c_b7, &u[nlf + u_dim1], ldu, &b[nlf + + b_dim1], ldb, &c_b8, &bx[nlf + bx_dim1], ldbx, (ftnlen)1, ( + ftnlen)1); + dgemm_((char *)"T", (char *)"N", &nr, nrhs, &nr, &c_b7, &u[nrf + u_dim1], ldu, &b[nrf + + b_dim1], ldb, &c_b8, &bx[nrf + bx_dim1], ldbx, (ftnlen)1, ( + ftnlen)1); +/* L10: */ + } + +/* Next copy the rows of B that correspond to unchanged rows */ +/* in the bidiagonal matrix to BX. */ + + i__1 = nd; + for (i__ = 1; i__ <= i__1; ++i__) { + ic = iwork[inode + i__ - 1]; + dcopy_(nrhs, &b[ic + b_dim1], ldb, &bx[ic + bx_dim1], ldbx); +/* L20: */ + } + +/* Finally go through the left singular vector matrices of all */ +/* the other subproblems bottom-up on the tree. */ + + j = pow_ii(&c__2, &nlvl); + sqre = 0; + + for (lvl = nlvl; lvl >= 1; --lvl) { + lvl2 = (lvl << 1) - 1; + +/* find the first node LF and last node LL on */ +/* the current level LVL */ + + if (lvl == 1) { + lf = 1; + ll = 1; + } else { + i__1 = lvl - 1; + lf = pow_ii(&c__2, &i__1); + ll = (lf << 1) - 1; + } + i__1 = ll; + for (i__ = lf; i__ <= i__1; ++i__) { + im1 = i__ - 1; + ic = iwork[inode + im1]; + nl = iwork[ndiml + im1]; + nr = iwork[ndimr + im1]; + nlf = ic - nl; + nrf = ic + 1; + --j; + dlals0_(icompq, &nl, &nr, &sqre, nrhs, &bx[nlf + bx_dim1], ldbx, & + b[nlf + b_dim1], ldb, &perm[nlf + lvl * perm_dim1], & + givptr[j], &givcol[nlf + lvl2 * givcol_dim1], ldgcol, & + givnum[nlf + lvl2 * givnum_dim1], ldu, &poles[nlf + lvl2 * + poles_dim1], &difl[nlf + lvl * difl_dim1], &difr[nlf + + lvl2 * difr_dim1], &z__[nlf + lvl * z_dim1], &k[j], &c__[ + j], &s[j], &work[1], info); +/* L30: */ + } +/* L40: */ + } + goto L90; + +/* ICOMPQ = 1: applying back the right singular vector factors. */ + +L50: + +/* First now go through the right singular vector matrices of all */ +/* the tree nodes top-down. */ + + j = 0; + i__1 = nlvl; + for (lvl = 1; lvl <= i__1; ++lvl) { + lvl2 = (lvl << 1) - 1; + +/* Find the first node LF and last node LL on */ +/* the current level LVL. */ + + if (lvl == 1) { + lf = 1; + ll = 1; + } else { + i__2 = lvl - 1; + lf = pow_ii(&c__2, &i__2); + ll = (lf << 1) - 1; + } + i__2 = lf; + for (i__ = ll; i__ >= i__2; --i__) { + im1 = i__ - 1; + ic = iwork[inode + im1]; + nl = iwork[ndiml + im1]; + nr = iwork[ndimr + im1]; + nlf = ic - nl; + nrf = ic + 1; + if (i__ == ll) { + sqre = 0; + } else { + sqre = 1; + } + ++j; + dlals0_(icompq, &nl, &nr, &sqre, nrhs, &b[nlf + b_dim1], ldb, &bx[ + nlf + bx_dim1], ldbx, &perm[nlf + lvl * perm_dim1], & + givptr[j], &givcol[nlf + lvl2 * givcol_dim1], ldgcol, & + givnum[nlf + lvl2 * givnum_dim1], ldu, &poles[nlf + lvl2 * + poles_dim1], &difl[nlf + lvl * difl_dim1], &difr[nlf + + lvl2 * difr_dim1], &z__[nlf + lvl * z_dim1], &k[j], &c__[ + j], &s[j], &work[1], info); +/* L60: */ + } +/* L70: */ + } + +/* The nodes on the bottom level of the tree were solved */ +/* by DLASDQ. The corresponding right singular vector */ +/* matrices are in explicit form. Apply them back. */ + + ndb1 = (nd + 1) / 2; + i__1 = nd; + for (i__ = ndb1; i__ <= i__1; ++i__) { + i1 = i__ - 1; + ic = iwork[inode + i1]; + nl = iwork[ndiml + i1]; + nr = iwork[ndimr + i1]; + nlp1 = nl + 1; + if (i__ == nd) { + nrp1 = nr; + } else { + nrp1 = nr + 1; + } + nlf = ic - nl; + nrf = ic + 1; + dgemm_((char *)"T", (char *)"N", &nlp1, nrhs, &nlp1, &c_b7, &vt[nlf + vt_dim1], ldu, & + b[nlf + b_dim1], ldb, &c_b8, &bx[nlf + bx_dim1], ldbx, ( + ftnlen)1, (ftnlen)1); + dgemm_((char *)"T", (char *)"N", &nrp1, nrhs, &nrp1, &c_b7, &vt[nrf + vt_dim1], ldu, & + b[nrf + b_dim1], ldb, &c_b8, &bx[nrf + bx_dim1], ldbx, ( + ftnlen)1, (ftnlen)1); +/* L80: */ + } + +L90: + + return 0; + +/* End of DLALSA */ + +} /* dlalsa_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlalsd.cpp b/lib/linalg/dlalsd.cpp new file mode 100644 index 0000000000..07c3ca57f0 --- /dev/null +++ b/lib/linalg/dlalsd.cpp @@ -0,0 +1,632 @@ +/* fortran/dlalsd.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static doublereal c_b6 = 0.; +static integer c__0 = 0; +static doublereal c_b11 = 1.; + +/* > \brief \b DLALSD uses the singular value decomposition of A to solve the least squares problem. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLALSD + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND, */ +/* RANK, WORK, IWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER UPLO */ +/* INTEGER INFO, LDB, N, NRHS, RANK, SMLSIZ */ +/* DOUBLE PRECISION RCOND */ +/* .. */ +/* .. Array Arguments .. */ +/* INTEGER IWORK( * ) */ +/* DOUBLE PRECISION B( LDB, * ), D( * ), E( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLALSD uses the singular value decomposition of A to solve the least */ +/* > squares problem of finding X to minimize the Euclidean norm of each */ +/* > column of A*X-B, where A is N-by-N upper bidiagonal, and X and B */ +/* > are N-by-NRHS. The solution X overwrites B. */ +/* > */ +/* > The singular values of A smaller than RCOND times the largest */ +/* > singular value are treated as zero in solving the least squares */ +/* > problem; in this case a minimum norm solution is returned. */ +/* > The actual singular values are returned in D in ascending order. */ +/* > */ +/* > This code makes very mild assumptions about floating point */ +/* > arithmetic. It will work on machines with a guard digit in */ +/* > add/subtract, or on those binary machines without guard digits */ +/* > which subtract like the Cray XMP, Cray YMP, Cray C 90, or Cray 2. */ +/* > It could conceivably fail on hexadecimal or decimal machines */ +/* > without guard digits, but we know of none. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > = 'U': D and E define an upper bidiagonal matrix. */ +/* > = 'L': D and E define a lower bidiagonal matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] SMLSIZ */ +/* > \verbatim */ +/* > SMLSIZ is INTEGER */ +/* > The maximum size of the subproblems at the bottom of the */ +/* > computation tree. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The dimension of the bidiagonal matrix. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] NRHS */ +/* > \verbatim */ +/* > NRHS is INTEGER */ +/* > The number of columns of B. NRHS must be at least 1. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension (N) */ +/* > On entry D contains the main diagonal of the bidiagonal */ +/* > matrix. On exit, if INFO = 0, D contains its singular values. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] E */ +/* > \verbatim */ +/* > E is DOUBLE PRECISION array, dimension (N-1) */ +/* > Contains the super-diagonal entries of the bidiagonal matrix. */ +/* > On exit, E has been destroyed. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] B */ +/* > \verbatim */ +/* > B is DOUBLE PRECISION array, dimension (LDB,NRHS) */ +/* > On input, B contains the right hand sides of the least */ +/* > squares problem. On output, B contains the solution X. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDB */ +/* > \verbatim */ +/* > LDB is INTEGER */ +/* > The leading dimension of B in the calling subprogram. */ +/* > LDB must be at least max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] RCOND */ +/* > \verbatim */ +/* > RCOND is DOUBLE PRECISION */ +/* > The singular values of A less than or equal to RCOND times */ +/* > the largest singular value are treated as zero in solving */ +/* > the least squares problem. If RCOND is negative, */ +/* > machine precision is used instead. */ +/* > For example, if diag(S)*X=B were the least squares problem, */ +/* > where diag(S) is a diagonal matrix of singular values, the */ +/* > solution would be X(i) = B(i) / S(i) if S(i) is greater than */ +/* > RCOND*max(S), and X(i) = 0 if S(i) is less than or equal to */ +/* > RCOND*max(S). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] RANK */ +/* > \verbatim */ +/* > RANK is INTEGER */ +/* > The number of singular values of A greater than RCOND times */ +/* > the largest singular value. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension at least */ +/* > (9*N + 2*N*SMLSIZ + 8*N*NLVL + N*NRHS + (SMLSIZ+1)**2), */ +/* > where NLVL = max(0, INT(log_2 (N/(SMLSIZ+1))) + 1). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] IWORK */ +/* > \verbatim */ +/* > IWORK is INTEGER array, dimension at least */ +/* > (3*N*NLVL + 11*N) */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit. */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ +/* > > 0: The algorithm failed to compute a singular value while */ +/* > working on the submatrix lying in rows and columns */ +/* > INFO/(N+1) through MOD(INFO,N+1). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleOTHERcomputational */ + +/* > \par Contributors: */ +/* ================== */ +/* > */ +/* > Ming Gu and Ren-Cang Li, Computer Science Division, University of */ +/* > California at Berkeley, USA \n */ +/* > Osni Marques, LBNL/NERSC, USA \n */ + +/* ===================================================================== */ +/* Subroutine */ int dlalsd_(char *uplo, integer *smlsiz, integer *n, integer + *nrhs, doublereal *d__, doublereal *e, doublereal *b, integer *ldb, + doublereal *rcond, integer *rank, doublereal *work, integer *iwork, + integer *info, ftnlen uplo_len) +{ + /* System generated locals */ + integer b_dim1, b_offset, i__1, i__2; + doublereal d__1; + + /* Builtin functions */ + double log(doublereal), d_sign(doublereal *, doublereal *); + + /* Local variables */ + integer c__, i__, j, k; + doublereal r__; + integer s, u, z__; + doublereal cs; + integer bx; + doublereal sn; + integer st, vt, nm1, st1; + doublereal eps; + integer iwk; + doublereal tol; + integer difl, difr; + doublereal rcnd; + integer perm, nsub; + extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, + doublereal *, integer *, doublereal *, doublereal *); + integer nlvl, sqre, bxst; + extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen), + dcopy_(integer *, doublereal *, integer *, doublereal *, integer + *); + integer poles, sizei, nsize, nwork, icmpq1, icmpq2; + extern doublereal dlamch_(char *, ftnlen); + extern /* Subroutine */ int dlasda_(integer *, integer *, integer *, + integer *, doublereal *, doublereal *, doublereal *, integer *, + doublereal *, integer *, doublereal *, doublereal *, doublereal *, + doublereal *, integer *, integer *, integer *, integer *, + doublereal *, doublereal *, doublereal *, doublereal *, integer *, + integer *), dlalsa_(integer *, integer *, integer *, integer *, + doublereal *, integer *, doublereal *, integer *, doublereal *, + integer *, doublereal *, integer *, doublereal *, doublereal *, + doublereal *, doublereal *, integer *, integer *, integer *, + integer *, doublereal *, doublereal *, doublereal *, doublereal *, + integer *, integer *), dlascl_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, integer *, doublereal *, + integer *, integer *, ftnlen); + extern integer idamax_(integer *, doublereal *, integer *); + extern /* Subroutine */ int dlasdq_(char *, integer *, integer *, integer + *, integer *, integer *, doublereal *, doublereal *, doublereal *, + integer *, doublereal *, integer *, doublereal *, integer *, + doublereal *, integer *, ftnlen), dlacpy_(char *, integer *, + integer *, doublereal *, integer *, doublereal *, integer *, + ftnlen), dlartg_(doublereal *, doublereal *, doublereal *, + doublereal *, doublereal *), dlaset_(char *, integer *, integer *, + doublereal *, doublereal *, doublereal *, integer *, ftnlen), + xerbla_(char *, integer *, ftnlen); + integer givcol; + extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *, + ftnlen); + extern /* Subroutine */ int dlasrt_(char *, integer *, doublereal *, + integer *, ftnlen); + doublereal orgnrm; + integer givnum, givptr, smlszp; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --d__; + --e; + b_dim1 = *ldb; + b_offset = 1 + b_dim1; + b -= b_offset; + --work; + --iwork; + + /* Function Body */ + *info = 0; + + if (*n < 0) { + *info = -3; + } else if (*nrhs < 1) { + *info = -4; + } else if (*ldb < 1 || *ldb < *n) { + *info = -8; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DLALSD", &i__1, (ftnlen)6); + return 0; + } + + eps = dlamch_((char *)"Epsilon", (ftnlen)7); + +/* Set up the tolerance. */ + + if (*rcond <= 0. || *rcond >= 1.) { + rcnd = eps; + } else { + rcnd = *rcond; + } + + *rank = 0; + +/* Quick return if possible. */ + + if (*n == 0) { + return 0; + } else if (*n == 1) { + if (d__[1] == 0.) { + dlaset_((char *)"A", &c__1, nrhs, &c_b6, &c_b6, &b[b_offset], ldb, ( + ftnlen)1); + } else { + *rank = 1; + dlascl_((char *)"G", &c__0, &c__0, &d__[1], &c_b11, &c__1, nrhs, &b[ + b_offset], ldb, info, (ftnlen)1); + d__[1] = abs(d__[1]); + } + return 0; + } + +/* Rotate the matrix if it is lower bidiagonal. */ + + if (*(unsigned char *)uplo == 'L') { + i__1 = *n - 1; + for (i__ = 1; i__ <= i__1; ++i__) { + dlartg_(&d__[i__], &e[i__], &cs, &sn, &r__); + d__[i__] = r__; + e[i__] = sn * d__[i__ + 1]; + d__[i__ + 1] = cs * d__[i__ + 1]; + if (*nrhs == 1) { + drot_(&c__1, &b[i__ + b_dim1], &c__1, &b[i__ + 1 + b_dim1], & + c__1, &cs, &sn); + } else { + work[(i__ << 1) - 1] = cs; + work[i__ * 2] = sn; + } +/* L10: */ + } + if (*nrhs > 1) { + i__1 = *nrhs; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = *n - 1; + for (j = 1; j <= i__2; ++j) { + cs = work[(j << 1) - 1]; + sn = work[j * 2]; + drot_(&c__1, &b[j + i__ * b_dim1], &c__1, &b[j + 1 + i__ * + b_dim1], &c__1, &cs, &sn); +/* L20: */ + } +/* L30: */ + } + } + } + +/* Scale. */ + + nm1 = *n - 1; + orgnrm = dlanst_((char *)"M", n, &d__[1], &e[1], (ftnlen)1); + if (orgnrm == 0.) { + dlaset_((char *)"A", n, nrhs, &c_b6, &c_b6, &b[b_offset], ldb, (ftnlen)1); + return 0; + } + + dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b11, n, &c__1, &d__[1], n, info, ( + ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b11, &nm1, &c__1, &e[1], &nm1, + info, (ftnlen)1); + +/* If N is smaller than the minimum divide size SMLSIZ, then solve */ +/* the problem with another solver. */ + + if (*n <= *smlsiz) { + nwork = *n * *n + 1; + dlaset_((char *)"A", n, n, &c_b6, &c_b11, &work[1], n, (ftnlen)1); + dlasdq_((char *)"U", &c__0, n, n, &c__0, nrhs, &d__[1], &e[1], &work[1], n, & + work[1], n, &b[b_offset], ldb, &work[nwork], info, (ftnlen)1); + if (*info != 0) { + return 0; + } + tol = rcnd * (d__1 = d__[idamax_(n, &d__[1], &c__1)], abs(d__1)); + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + if (d__[i__] <= tol) { + dlaset_((char *)"A", &c__1, nrhs, &c_b6, &c_b6, &b[i__ + b_dim1], ldb, + (ftnlen)1); + } else { + dlascl_((char *)"G", &c__0, &c__0, &d__[i__], &c_b11, &c__1, nrhs, &b[ + i__ + b_dim1], ldb, info, (ftnlen)1); + ++(*rank); + } +/* L40: */ + } + dgemm_((char *)"T", (char *)"N", n, nrhs, n, &c_b11, &work[1], n, &b[b_offset], ldb, & + c_b6, &work[nwork], n, (ftnlen)1, (ftnlen)1); + dlacpy_((char *)"A", n, nrhs, &work[nwork], n, &b[b_offset], ldb, (ftnlen)1); + +/* Unscale. */ + + dlascl_((char *)"G", &c__0, &c__0, &c_b11, &orgnrm, n, &c__1, &d__[1], n, + info, (ftnlen)1); + dlasrt_((char *)"D", n, &d__[1], info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b11, n, nrhs, &b[b_offset], + ldb, info, (ftnlen)1); + + return 0; + } + +/* Book-keeping and setting up some constants. */ + + nlvl = (integer) (log((doublereal) (*n) / (doublereal) (*smlsiz + 1)) / + log(2.)) + 1; + + smlszp = *smlsiz + 1; + + u = 1; + vt = *smlsiz * *n + 1; + difl = vt + smlszp * *n; + difr = difl + nlvl * *n; + z__ = difr + (nlvl * *n << 1); + c__ = z__ + nlvl * *n; + s = c__ + *n; + poles = s + *n; + givnum = poles + (nlvl << 1) * *n; + bx = givnum + (nlvl << 1) * *n; + nwork = bx + *n * *nrhs; + + sizei = *n + 1; + k = sizei + *n; + givptr = k + *n; + perm = givptr + *n; + givcol = perm + nlvl * *n; + iwk = givcol + (nlvl * *n << 1); + + st = 1; + sqre = 0; + icmpq1 = 1; + icmpq2 = 0; + nsub = 0; + + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + if ((d__1 = d__[i__], abs(d__1)) < eps) { + d__[i__] = d_sign(&eps, &d__[i__]); + } +/* L50: */ + } + + i__1 = nm1; + for (i__ = 1; i__ <= i__1; ++i__) { + if ((d__1 = e[i__], abs(d__1)) < eps || i__ == nm1) { + ++nsub; + iwork[nsub] = st; + +/* Subproblem found. First determine its size and then */ +/* apply divide and conquer on it. */ + + if (i__ < nm1) { + +/* A subproblem with E(I) small for I < NM1. */ + + nsize = i__ - st + 1; + iwork[sizei + nsub - 1] = nsize; + } else if ((d__1 = e[i__], abs(d__1)) >= eps) { + +/* A subproblem with E(NM1) not too small but I = NM1. */ + + nsize = *n - st + 1; + iwork[sizei + nsub - 1] = nsize; + } else { + +/* A subproblem with E(NM1) small. This implies an */ +/* 1-by-1 subproblem at D(N), which is not solved */ +/* explicitly. */ + + nsize = i__ - st + 1; + iwork[sizei + nsub - 1] = nsize; + ++nsub; + iwork[nsub] = *n; + iwork[sizei + nsub - 1] = 1; + dcopy_(nrhs, &b[*n + b_dim1], ldb, &work[bx + nm1], n); + } + st1 = st - 1; + if (nsize == 1) { + +/* This is a 1-by-1 subproblem and is not solved */ +/* explicitly. */ + + dcopy_(nrhs, &b[st + b_dim1], ldb, &work[bx + st1], n); + } else if (nsize <= *smlsiz) { + +/* This is a small subproblem and is solved by DLASDQ. */ + + dlaset_((char *)"A", &nsize, &nsize, &c_b6, &c_b11, &work[vt + st1], + n, (ftnlen)1); + dlasdq_((char *)"U", &c__0, &nsize, &nsize, &c__0, nrhs, &d__[st], &e[ + st], &work[vt + st1], n, &work[nwork], n, &b[st + + b_dim1], ldb, &work[nwork], info, (ftnlen)1); + if (*info != 0) { + return 0; + } + dlacpy_((char *)"A", &nsize, nrhs, &b[st + b_dim1], ldb, &work[bx + + st1], n, (ftnlen)1); + } else { + +/* A large problem. Solve it using divide and conquer. */ + + dlasda_(&icmpq1, smlsiz, &nsize, &sqre, &d__[st], &e[st], & + work[u + st1], n, &work[vt + st1], &iwork[k + st1], & + work[difl + st1], &work[difr + st1], &work[z__ + st1], + &work[poles + st1], &iwork[givptr + st1], &iwork[ + givcol + st1], n, &iwork[perm + st1], &work[givnum + + st1], &work[c__ + st1], &work[s + st1], &work[nwork], + &iwork[iwk], info); + if (*info != 0) { + return 0; + } + bxst = bx + st1; + dlalsa_(&icmpq2, smlsiz, &nsize, nrhs, &b[st + b_dim1], ldb, & + work[bxst], n, &work[u + st1], n, &work[vt + st1], & + iwork[k + st1], &work[difl + st1], &work[difr + st1], + &work[z__ + st1], &work[poles + st1], &iwork[givptr + + st1], &iwork[givcol + st1], n, &iwork[perm + st1], & + work[givnum + st1], &work[c__ + st1], &work[s + st1], + &work[nwork], &iwork[iwk], info); + if (*info != 0) { + return 0; + } + } + st = i__ + 1; + } +/* L60: */ + } + +/* Apply the singular values and treat the tiny ones as zero. */ + + tol = rcnd * (d__1 = d__[idamax_(n, &d__[1], &c__1)], abs(d__1)); + + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + +/* Some of the elements in D can be negative because 1-by-1 */ +/* subproblems were not solved explicitly. */ + + if ((d__1 = d__[i__], abs(d__1)) <= tol) { + dlaset_((char *)"A", &c__1, nrhs, &c_b6, &c_b6, &work[bx + i__ - 1], n, ( + ftnlen)1); + } else { + ++(*rank); + dlascl_((char *)"G", &c__0, &c__0, &d__[i__], &c_b11, &c__1, nrhs, &work[ + bx + i__ - 1], n, info, (ftnlen)1); + } + d__[i__] = (d__1 = d__[i__], abs(d__1)); +/* L70: */ + } + +/* Now apply back the right singular vectors. */ + + icmpq2 = 1; + i__1 = nsub; + for (i__ = 1; i__ <= i__1; ++i__) { + st = iwork[i__]; + st1 = st - 1; + nsize = iwork[sizei + i__ - 1]; + bxst = bx + st1; + if (nsize == 1) { + dcopy_(nrhs, &work[bxst], n, &b[st + b_dim1], ldb); + } else if (nsize <= *smlsiz) { + dgemm_((char *)"T", (char *)"N", &nsize, nrhs, &nsize, &c_b11, &work[vt + st1], n, + &work[bxst], n, &c_b6, &b[st + b_dim1], ldb, (ftnlen)1, ( + ftnlen)1); + } else { + dlalsa_(&icmpq2, smlsiz, &nsize, nrhs, &work[bxst], n, &b[st + + b_dim1], ldb, &work[u + st1], n, &work[vt + st1], &iwork[ + k + st1], &work[difl + st1], &work[difr + st1], &work[z__ + + st1], &work[poles + st1], &iwork[givptr + st1], &iwork[ + givcol + st1], n, &iwork[perm + st1], &work[givnum + st1], + &work[c__ + st1], &work[s + st1], &work[nwork], &iwork[ + iwk], info); + if (*info != 0) { + return 0; + } + } +/* L80: */ + } + +/* Unscale and sort the singular values. */ + + dlascl_((char *)"G", &c__0, &c__0, &c_b11, &orgnrm, n, &c__1, &d__[1], n, info, ( + ftnlen)1); + dlasrt_((char *)"D", n, &d__[1], info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b11, n, nrhs, &b[b_offset], ldb, + info, (ftnlen)1); + + return 0; + +/* End of DLALSD */ + +} /* dlalsd_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlamch.cpp b/lib/linalg/dlamch.cpp new file mode 100644 index 0000000000..3d616d95d2 --- /dev/null +++ b/lib/linalg/dlamch.cpp @@ -0,0 +1,45 @@ + +#include +#include + +extern "C" { + +#include "lmp_f2c.h" + +// undefine conflicting f2c macros +#undef min +#undef max + +doublereal dlamch_(const char *cmach) +{ + if (!cmach) return 0.0; + char select = toupper(*cmach); + + // BLAS assumes rounding not truncation => epsilon is half + const double eps = 0.5 * std::numeric_limits::epsilon(); + if (select == 'E') return eps; + + double min = std::numeric_limits::min(); + const double max = std::numeric_limits::max(); + double small = 1.0 / max; + if (small >= min) min = small * (1.0 + eps); + if (select == 'S') return min; + + const double radix = std::numeric_limits::radix; + if (select == 'B') return radix; + + if (select == 'P') return eps * radix; + + if (select == 'N') return std::numeric_limits::digits; + + if (select == 'M') return std::numeric_limits::min_exponent; + + if (select == 'U') return min; + + if (select == 'L') return std::numeric_limits::max_exponent; + + if (select == 'O') return max; + + return 0.0; +} +} diff --git a/lib/linalg/dlamrg.cpp b/lib/linalg/dlamrg.cpp new file mode 100644 index 0000000000..581a64fba7 --- /dev/null +++ b/lib/linalg/dlamrg.cpp @@ -0,0 +1,206 @@ +/* fortran/dlamrg.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DLAMRG creates a permutation list to merge the entries of two independently sorted sets into a +single set sorted in ascending order. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLAMRG + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLAMRG( N1, N2, A, DTRD1, DTRD2, INDEX ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER DTRD1, DTRD2, N1, N2 */ +/* .. */ +/* .. Array Arguments .. */ +/* INTEGER INDEX( * ) */ +/* DOUBLE PRECISION A( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLAMRG will create a permutation list which will merge the elements */ +/* > of A (which is composed of two independently sorted sets) into a */ +/* > single set which is sorted in ascending order. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N1 */ +/* > \verbatim */ +/* > N1 is INTEGER */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N2 */ +/* > \verbatim */ +/* > N2 is INTEGER */ +/* > These arguments contain the respective lengths of the two */ +/* > sorted lists to be merged. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (N1+N2) */ +/* > The first N1 elements of A contain a list of numbers which */ +/* > are sorted in either ascending or descending order. Likewise */ +/* > for the final N2 elements. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DTRD1 */ +/* > \verbatim */ +/* > DTRD1 is INTEGER */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DTRD2 */ +/* > \verbatim */ +/* > DTRD2 is INTEGER */ +/* > These are the strides to be taken through the array A. */ +/* > Allowable strides are 1 and -1. They indicate whether a */ +/* > subset of A is sorted in ascending (DTRDx = 1) or descending */ +/* > (DTRDx = -1) order. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INDEX */ +/* > \verbatim */ +/* > INDEX is INTEGER array, dimension (N1+N2) */ +/* > On exit this array will contain a permutation such that */ +/* > if B( I ) = A( INDEX( I ) ) for I=1,N1+N2, then B will be */ +/* > sorted in ascending order. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup auxOTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dlamrg_(integer *n1, integer *n2, doublereal *a, integer + *dtrd1, integer *dtrd2, integer *index) +{ + /* System generated locals */ + integer i__1; + + /* Local variables */ + integer i__, ind1, ind2, n1sv, n2sv; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. Executable Statements .. */ + + /* Parameter adjustments */ + --index; + --a; + + /* Function Body */ + n1sv = *n1; + n2sv = *n2; + if (*dtrd1 > 0) { + ind1 = 1; + } else { + ind1 = *n1; + } + if (*dtrd2 > 0) { + ind2 = *n1 + 1; + } else { + ind2 = *n1 + *n2; + } + i__ = 1; +/* while ( (N1SV > 0) & (N2SV > 0) ) */ +L10: + if (n1sv > 0 && n2sv > 0) { + if (a[ind1] <= a[ind2]) { + index[i__] = ind1; + ++i__; + ind1 += *dtrd1; + --n1sv; + } else { + index[i__] = ind2; + ++i__; + ind2 += *dtrd2; + --n2sv; + } + goto L10; + } +/* end while */ + if (n1sv == 0) { + i__1 = n2sv; + for (n1sv = 1; n1sv <= i__1; ++n1sv) { + index[i__] = ind2; + ++i__; + ind2 += *dtrd2; +/* L20: */ + } + } else { +/* N2SV .EQ. 0 */ + i__1 = n1sv; + for (n2sv = 1; n2sv <= i__1; ++n2sv) { + index[i__] = ind1; + ++i__; + ind1 += *dtrd1; +/* L30: */ + } + } + + return 0; + +/* End of DLAMRG */ + +} /* dlamrg_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlange.cpp b/lib/linalg/dlange.cpp new file mode 100644 index 0000000000..1ccc6fae2b --- /dev/null +++ b/lib/linalg/dlange.cpp @@ -0,0 +1,277 @@ +/* fortran/dlange.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; + +/* > \brief \b DLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute +value of any element of a general rectangular matrix. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLANGE + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* DOUBLE PRECISION FUNCTION DLANGE( NORM, M, N, A, LDA, WORK ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER NORM */ +/* INTEGER LDA, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLANGE returns the value of the one norm, or the Frobenius norm, or */ +/* > the infinity norm, or the element of largest absolute value of a */ +/* > real matrix A. */ +/* > \endverbatim */ +/* > */ +/* > \return DLANGE */ +/* > \verbatim */ +/* > */ +/* > DLANGE = ( max(abs(A(i,j))), NORM = 'M' or 'm' */ +/* > ( */ +/* > ( norm1(A), NORM = '1', 'O' or 'o' */ +/* > ( */ +/* > ( normI(A), NORM = 'I' or 'i' */ +/* > ( */ +/* > ( normF(A), NORM = 'F', 'f', 'E' or 'e' */ +/* > */ +/* > where norm1 denotes the one norm of a matrix (maximum column sum), */ +/* > normI denotes the infinity norm of a matrix (maximum row sum) and */ +/* > normF denotes the Frobenius norm of a matrix (square root of sum of */ +/* > squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] NORM */ +/* > \verbatim */ +/* > NORM is CHARACTER*1 */ +/* > Specifies the value to be returned in DLANGE as described */ +/* > above. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix A. M >= 0. When M = 0, */ +/* > DLANGE is set to zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix A. N >= 0. When N = 0, */ +/* > DLANGE is set to zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > The m by n matrix A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(M,1). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), */ +/* > where LWORK >= M when NORM = 'I'; otherwise, WORK is not */ +/* > referenced. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleGEauxiliary */ + +/* ===================================================================== */ +doublereal dlange_(char *norm, integer *m, integer *n, doublereal *a, integer + *lda, doublereal *work, ftnlen norm_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2; + doublereal ret_val, d__1; + + /* Builtin functions */ + double sqrt(doublereal); + + /* Local variables */ + integer i__, j; + doublereal sum, temp, scale; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + doublereal value; + extern logical disnan_(doublereal *); + extern /* Subroutine */ int dlassq_(integer *, doublereal *, integer *, + doublereal *, doublereal *); + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --work; + + /* Function Body */ + if (min(*m,*n) == 0) { + value = 0.; + } else if (lsame_(norm, (char *)"M", (ftnlen)1, (ftnlen)1)) { + +/* Find max(abs(A(i,j))). */ + + value = 0.; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp = (d__1 = a[i__ + j * a_dim1], abs(d__1)); + if (value < temp || disnan_(&temp)) { + value = temp; + } +/* L10: */ + } +/* L20: */ + } + } else if (lsame_(norm, (char *)"O", (ftnlen)1, (ftnlen)1) || *(unsigned char *) + norm == '1') { + +/* Find norm1(A). */ + + value = 0.; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + sum = 0.; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + sum += (d__1 = a[i__ + j * a_dim1], abs(d__1)); +/* L30: */ + } + if (value < sum || disnan_(&sum)) { + value = sum; + } +/* L40: */ + } + } else if (lsame_(norm, (char *)"I", (ftnlen)1, (ftnlen)1)) { + +/* Find normI(A). */ + + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + work[i__] = 0.; +/* L50: */ + } + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + work[i__] += (d__1 = a[i__ + j * a_dim1], abs(d__1)); +/* L60: */ + } +/* L70: */ + } + value = 0.; + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + temp = work[i__]; + if (value < temp || disnan_(&temp)) { + value = temp; + } +/* L80: */ + } + } else if (lsame_(norm, (char *)"F", (ftnlen)1, (ftnlen)1) || lsame_(norm, (char *)"E", ( + ftnlen)1, (ftnlen)1)) { + +/* Find normF(A). */ + + scale = 0.; + sum = 1.; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + dlassq_(m, &a[j * a_dim1 + 1], &c__1, &scale, &sum); +/* L90: */ + } + value = scale * sqrt(sum); + } + + ret_val = value; + return ret_val; + +/* End of DLANGE */ + +} /* dlange_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlanst.cpp b/lib/linalg/dlanst.cpp new file mode 100644 index 0000000000..8a71bcd12d --- /dev/null +++ b/lib/linalg/dlanst.cpp @@ -0,0 +1,239 @@ +/* fortran/dlanst.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; + +/* > \brief \b DLANST returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the ele +ment of largest absolute value of a real symmetric tridiagonal matrix. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLANST + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* DOUBLE PRECISION FUNCTION DLANST( NORM, N, D, E ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER NORM */ +/* INTEGER N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION D( * ), E( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLANST returns the value of the one norm, or the Frobenius norm, or */ +/* > the infinity norm, or the element of largest absolute value of a */ +/* > real symmetric tridiagonal matrix A. */ +/* > \endverbatim */ +/* > */ +/* > \return DLANST */ +/* > \verbatim */ +/* > */ +/* > DLANST = ( max(abs(A(i,j))), NORM = 'M' or 'm' */ +/* > ( */ +/* > ( norm1(A), NORM = '1', 'O' or 'o' */ +/* > ( */ +/* > ( normI(A), NORM = 'I' or 'i' */ +/* > ( */ +/* > ( normF(A), NORM = 'F', 'f', 'E' or 'e' */ +/* > */ +/* > where norm1 denotes the one norm of a matrix (maximum column sum), */ +/* > normI denotes the infinity norm of a matrix (maximum row sum) and */ +/* > normF denotes the Frobenius norm of a matrix (square root of sum of */ +/* > squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] NORM */ +/* > \verbatim */ +/* > NORM is CHARACTER*1 */ +/* > Specifies the value to be returned in DLANST as described */ +/* > above. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrix A. N >= 0. When N = 0, DLANST is */ +/* > set to zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension (N) */ +/* > The diagonal elements of A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] E */ +/* > \verbatim */ +/* > E is DOUBLE PRECISION array, dimension (N-1) */ +/* > The (n-1) sub-diagonal or super-diagonal elements of A. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup OTHERauxiliary */ + +/* ===================================================================== */ +doublereal dlanst_(char *norm, integer *n, doublereal *d__, doublereal *e, + ftnlen norm_len) +{ + /* System generated locals */ + integer i__1; + doublereal ret_val, d__1, d__2, d__3; + + /* Builtin functions */ + double sqrt(doublereal); + + /* Local variables */ + integer i__; + doublereal sum, scale; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + doublereal anorm; + extern logical disnan_(doublereal *); + extern /* Subroutine */ int dlassq_(integer *, doublereal *, integer *, + doublereal *, doublereal *); + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + + /* Parameter adjustments */ + --e; + --d__; + + /* Function Body */ + if (*n <= 0) { + anorm = 0.; + } else if (lsame_(norm, (char *)"M", (ftnlen)1, (ftnlen)1)) { + +/* Find max(abs(A(i,j))). */ + + anorm = (d__1 = d__[*n], abs(d__1)); + i__1 = *n - 1; + for (i__ = 1; i__ <= i__1; ++i__) { + sum = (d__1 = d__[i__], abs(d__1)); + if (anorm < sum || disnan_(&sum)) { + anorm = sum; + } + sum = (d__1 = e[i__], abs(d__1)); + if (anorm < sum || disnan_(&sum)) { + anorm = sum; + } +/* L10: */ + } + } else if (lsame_(norm, (char *)"O", (ftnlen)1, (ftnlen)1) || *(unsigned char *) + norm == '1' || lsame_(norm, (char *)"I", (ftnlen)1, (ftnlen)1)) { + +/* Find norm1(A). */ + + if (*n == 1) { + anorm = abs(d__[1]); + } else { + anorm = abs(d__[1]) + abs(e[1]); + sum = (d__1 = e[*n - 1], abs(d__1)) + (d__2 = d__[*n], abs(d__2)); + if (anorm < sum || disnan_(&sum)) { + anorm = sum; + } + i__1 = *n - 1; + for (i__ = 2; i__ <= i__1; ++i__) { + sum = (d__1 = d__[i__], abs(d__1)) + (d__2 = e[i__], abs(d__2) + ) + (d__3 = e[i__ - 1], abs(d__3)); + if (anorm < sum || disnan_(&sum)) { + anorm = sum; + } +/* L20: */ + } + } + } else if (lsame_(norm, (char *)"F", (ftnlen)1, (ftnlen)1) || lsame_(norm, (char *)"E", ( + ftnlen)1, (ftnlen)1)) { + +/* Find normF(A). */ + + scale = 0.; + sum = 1.; + if (*n > 1) { + i__1 = *n - 1; + dlassq_(&i__1, &e[1], &c__1, &scale, &sum); + sum *= 2; + } + dlassq_(n, &d__[1], &c__1, &scale, &sum); + anorm = scale * sqrt(sum); + } + + ret_val = anorm; + return ret_val; + +/* End of DLANST */ + +} /* dlanst_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlansy.cpp b/lib/linalg/dlansy.cpp new file mode 100644 index 0000000000..1c5a1fa24c --- /dev/null +++ b/lib/linalg/dlansy.cpp @@ -0,0 +1,317 @@ +/* fortran/dlansy.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; + +/* > \brief \b DLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the ele +ment of largest absolute value of a real symmetric matrix. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLANSY + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* DOUBLE PRECISION FUNCTION DLANSY( NORM, UPLO, N, A, LDA, WORK ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER NORM, UPLO */ +/* INTEGER LDA, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLANSY returns the value of the one norm, or the Frobenius norm, or */ +/* > the infinity norm, or the element of largest absolute value of a */ +/* > real symmetric matrix A. */ +/* > \endverbatim */ +/* > */ +/* > \return DLANSY */ +/* > \verbatim */ +/* > */ +/* > DLANSY = ( max(abs(A(i,j))), NORM = 'M' or 'm' */ +/* > ( */ +/* > ( norm1(A), NORM = '1', 'O' or 'o' */ +/* > ( */ +/* > ( normI(A), NORM = 'I' or 'i' */ +/* > ( */ +/* > ( normF(A), NORM = 'F', 'f', 'E' or 'e' */ +/* > */ +/* > where norm1 denotes the one norm of a matrix (maximum column sum), */ +/* > normI denotes the infinity norm of a matrix (maximum row sum) and */ +/* > normF denotes the Frobenius norm of a matrix (square root of sum of */ +/* > squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] NORM */ +/* > \verbatim */ +/* > NORM is CHARACTER*1 */ +/* > Specifies the value to be returned in DLANSY as described */ +/* > above. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > Specifies whether the upper or lower triangular part of the */ +/* > symmetric matrix A is to be referenced. */ +/* > = 'U': Upper triangular part of A is referenced */ +/* > = 'L': Lower triangular part of A is referenced */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrix A. N >= 0. When N = 0, DLANSY is */ +/* > set to zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > The symmetric matrix A. If UPLO = 'U', the leading n by n */ +/* > upper triangular part of A contains the upper triangular part */ +/* > of the matrix A, and the strictly lower triangular part of A */ +/* > is not referenced. If UPLO = 'L', the leading n by n lower */ +/* > triangular part of A contains the lower triangular part of */ +/* > the matrix A, and the strictly upper triangular part of A is */ +/* > not referenced. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(N,1). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), */ +/* > where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, */ +/* > WORK is not referenced. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleSYauxiliary */ + +/* ===================================================================== */ +doublereal dlansy_(char *norm, char *uplo, integer *n, doublereal *a, integer + *lda, doublereal *work, ftnlen norm_len, ftnlen uplo_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2; + doublereal ret_val, d__1; + + /* Builtin functions */ + double sqrt(doublereal); + + /* Local variables */ + integer i__, j; + doublereal sum, absa, scale; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + doublereal value; + extern logical disnan_(doublereal *); + extern /* Subroutine */ int dlassq_(integer *, doublereal *, integer *, + doublereal *, doublereal *); + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --work; + + /* Function Body */ + if (*n == 0) { + value = 0.; + } else if (lsame_(norm, (char *)"M", (ftnlen)1, (ftnlen)1)) { + +/* Find max(abs(A(i,j))). */ + + value = 0.; + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + for (i__ = 1; i__ <= i__2; ++i__) { + sum = (d__1 = a[i__ + j * a_dim1], abs(d__1)); + if (value < sum || disnan_(&sum)) { + value = sum; + } +/* L10: */ + } +/* L20: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = j; i__ <= i__2; ++i__) { + sum = (d__1 = a[i__ + j * a_dim1], abs(d__1)); + if (value < sum || disnan_(&sum)) { + value = sum; + } +/* L30: */ + } +/* L40: */ + } + } + } else if (lsame_(norm, (char *)"I", (ftnlen)1, (ftnlen)1) || lsame_(norm, (char *)"O", ( + ftnlen)1, (ftnlen)1) || *(unsigned char *)norm == '1') { + +/* Find normI(A) ( = norm1(A), since A is symmetric). */ + + value = 0.; + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + sum = 0.; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + absa = (d__1 = a[i__ + j * a_dim1], abs(d__1)); + sum += absa; + work[i__] += absa; +/* L50: */ + } + work[j] = sum + (d__1 = a[j + j * a_dim1], abs(d__1)); +/* L60: */ + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + sum = work[i__]; + if (value < sum || disnan_(&sum)) { + value = sum; + } +/* L70: */ + } + } else { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + work[i__] = 0.; +/* L80: */ + } + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + sum = work[j] + (d__1 = a[j + j * a_dim1], abs(d__1)); + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + absa = (d__1 = a[i__ + j * a_dim1], abs(d__1)); + sum += absa; + work[i__] += absa; +/* L90: */ + } + if (value < sum || disnan_(&sum)) { + value = sum; + } +/* L100: */ + } + } + } else if (lsame_(norm, (char *)"F", (ftnlen)1, (ftnlen)1) || lsame_(norm, (char *)"E", ( + ftnlen)1, (ftnlen)1)) { + +/* Find normF(A). */ + + scale = 0.; + sum = 1.; + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + i__1 = *n; + for (j = 2; j <= i__1; ++j) { + i__2 = j - 1; + dlassq_(&i__2, &a[j * a_dim1 + 1], &c__1, &scale, &sum); +/* L110: */ + } + } else { + i__1 = *n - 1; + for (j = 1; j <= i__1; ++j) { + i__2 = *n - j; + dlassq_(&i__2, &a[j + 1 + j * a_dim1], &c__1, &scale, &sum); +/* L120: */ + } + } + sum *= 2; + i__1 = *lda + 1; + dlassq_(n, &a[a_offset], &i__1, &scale, &sum); + value = scale * sqrt(sum); + } + + ret_val = value; + return ret_val; + +/* End of DLANSY */ + +} /* dlansy_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlapy2.cpp b/lib/linalg/dlapy2.cpp new file mode 100644 index 0000000000..6a5443d8df --- /dev/null +++ b/lib/linalg/dlapy2.cpp @@ -0,0 +1,150 @@ +/* fortran/dlapy2.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DLAPY2 returns sqrt(x2+y2). */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLAPY2 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* DOUBLE PRECISION FUNCTION DLAPY2( X, Y ) */ + +/* .. Scalar Arguments .. */ +/* DOUBLE PRECISION X, Y */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLAPY2 returns sqrt(x**2+y**2), taking care not to cause unnecessary */ +/* > overflow and unnecessary underflow. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] X */ +/* > \verbatim */ +/* > X is DOUBLE PRECISION */ +/* > \endverbatim */ +/* > */ +/* > \param[in] Y */ +/* > \verbatim */ +/* > Y is DOUBLE PRECISION */ +/* > X and Y specify the values x and y. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup OTHERauxiliary */ + +/* ===================================================================== */ +doublereal dlapy2_(doublereal *x, doublereal *y) +{ + /* System generated locals */ + doublereal ret_val, d__1; + + /* Builtin functions */ + double sqrt(doublereal); + + /* Local variables */ + logical x_is_nan__, y_is_nan__; + doublereal w, z__, xabs, yabs; + extern doublereal dlamch_(char *, ftnlen); + extern logical disnan_(doublereal *); + doublereal hugeval; + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + + x_is_nan__ = disnan_(x); + y_is_nan__ = disnan_(y); + if (x_is_nan__) { + ret_val = *x; + } + if (y_is_nan__) { + ret_val = *y; + } + hugeval = dlamch_((char *)"Overflow", (ftnlen)8); + + if (! (x_is_nan__ || y_is_nan__)) { + xabs = abs(*x); + yabs = abs(*y); + w = max(xabs,yabs); + z__ = min(xabs,yabs); + if (z__ == 0. || w > hugeval) { + ret_val = w; + } else { +/* Computing 2nd power */ + d__1 = z__ / w; + ret_val = w * sqrt(d__1 * d__1 + 1.); + } + } + return ret_val; + +/* End of DLAPY2 */ + +} /* dlapy2_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlapy3.cpp b/lib/linalg/dlapy3.cpp new file mode 100644 index 0000000000..528afbf3d8 --- /dev/null +++ b/lib/linalg/dlapy3.cpp @@ -0,0 +1,149 @@ +/* fortran/dlapy3.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DLAPY3 returns sqrt(x2+y2+z2). */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLAPY3 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* DOUBLE PRECISION FUNCTION DLAPY3( X, Y, Z ) */ + +/* .. Scalar Arguments .. */ +/* DOUBLE PRECISION X, Y, Z */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLAPY3 returns sqrt(x**2+y**2+z**2), taking care not to cause */ +/* > unnecessary overflow and unnecessary underflow. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] X */ +/* > \verbatim */ +/* > X is DOUBLE PRECISION */ +/* > \endverbatim */ +/* > */ +/* > \param[in] Y */ +/* > \verbatim */ +/* > Y is DOUBLE PRECISION */ +/* > \endverbatim */ +/* > */ +/* > \param[in] Z */ +/* > \verbatim */ +/* > Z is DOUBLE PRECISION */ +/* > X, Y and Z specify the values x, y and z. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup OTHERauxiliary */ + +/* ===================================================================== */ +doublereal dlapy3_(doublereal *x, doublereal *y, doublereal *z__) +{ + /* System generated locals */ + doublereal ret_val, d__1, d__2, d__3; + + /* Builtin functions */ + double sqrt(doublereal); + + /* Local variables */ + doublereal w, xabs, yabs, zabs; + extern doublereal dlamch_(char *, ftnlen); + doublereal hugeval; + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + + hugeval = dlamch_((char *)"Overflow", (ftnlen)8); + xabs = abs(*x); + yabs = abs(*y); + zabs = abs(*z__); +/* Computing MAX */ + d__1 = max(xabs,yabs); + w = max(d__1,zabs); + if (w == 0. || w > hugeval) { +/* W can be zero for max(0,nan,0) */ +/* adding all three entries together will make sure */ +/* NaN will not disappear. */ + ret_val = xabs + yabs + zabs; + } else { +/* Computing 2nd power */ + d__1 = xabs / w; +/* Computing 2nd power */ + d__2 = yabs / w; +/* Computing 2nd power */ + d__3 = zabs / w; + ret_val = w * sqrt(d__1 * d__1 + d__2 * d__2 + d__3 * d__3); + } + return ret_val; + +/* End of DLAPY3 */ + +} /* dlapy3_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlarf.cpp b/lib/linalg/dlarf.cpp new file mode 100644 index 0000000000..5534559e63 --- /dev/null +++ b/lib/linalg/dlarf.cpp @@ -0,0 +1,275 @@ +/* fortran/dlarf.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static doublereal c_b4 = 1.; +static doublereal c_b5 = 0.; +static integer c__1 = 1; + +/* > \brief \b DLARF applies an elementary reflector to a general rectangular matrix. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLARF + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER SIDE */ +/* INTEGER INCV, LDC, M, N */ +/* DOUBLE PRECISION TAU */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION C( LDC, * ), V( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLARF applies a real elementary reflector H to a real m by n matrix */ +/* > C, from either the left or the right. H is represented in the form */ +/* > */ +/* > H = I - tau * v * v**T */ +/* > */ +/* > where tau is a real scalar and v is a real vector. */ +/* > */ +/* > If tau = 0, then H is taken to be the unit matrix. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] SIDE */ +/* > \verbatim */ +/* > SIDE is CHARACTER*1 */ +/* > = 'L': form H * C */ +/* > = 'R': form C * H */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix C. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix C. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] V */ +/* > \verbatim */ +/* > V is DOUBLE PRECISION array, dimension */ +/* > (1 + (M-1)*abs(INCV)) if SIDE = 'L' */ +/* > or (1 + (N-1)*abs(INCV)) if SIDE = 'R' */ +/* > The vector v in the representation of H. V is not used if */ +/* > TAU = 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCV */ +/* > \verbatim */ +/* > INCV is INTEGER */ +/* > The increment between elements of v. INCV <> 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TAU */ +/* > \verbatim */ +/* > TAU is DOUBLE PRECISION */ +/* > The value tau in the representation of H. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] C */ +/* > \verbatim */ +/* > C is DOUBLE PRECISION array, dimension (LDC,N) */ +/* > On entry, the m by n matrix C. */ +/* > On exit, C is overwritten by the matrix H * C if SIDE = 'L', */ +/* > or C * H if SIDE = 'R'. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDC */ +/* > \verbatim */ +/* > LDC is INTEGER */ +/* > The leading dimension of the array C. LDC >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension */ +/* > (N) if SIDE = 'L' */ +/* > or (M) if SIDE = 'R' */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleOTHERauxiliary */ + +/* ===================================================================== */ +/* Subroutine */ int dlarf_(char *side, integer *m, integer *n, doublereal *v, + integer *incv, doublereal *tau, doublereal *c__, integer *ldc, + doublereal *work, ftnlen side_len) +{ + /* System generated locals */ + integer c_dim1, c_offset; + doublereal d__1; + + /* Local variables */ + integer i__; + logical applyleft; + extern /* Subroutine */ int dger_(integer *, integer *, doublereal *, + doublereal *, integer *, doublereal *, integer *, doublereal *, + integer *); + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int dgemv_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, ftnlen); + integer lastc, lastv; + extern integer iladlc_(integer *, integer *, doublereal *, integer *), + iladlr_(integer *, integer *, doublereal *, integer *); + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + + /* Parameter adjustments */ + --v; + c_dim1 = *ldc; + c_offset = 1 + c_dim1; + c__ -= c_offset; + --work; + + /* Function Body */ + applyleft = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); + lastv = 0; + lastc = 0; + if (*tau != 0.) { +/* Set up variables for scanning V. LASTV begins pointing to the end */ +/* of V. */ + if (applyleft) { + lastv = *m; + } else { + lastv = *n; + } + if (*incv > 0) { + i__ = (lastv - 1) * *incv + 1; + } else { + i__ = 1; + } +/* Look for the last non-zero row in V. */ + while(lastv > 0 && v[i__] == 0.) { + --lastv; + i__ -= *incv; + } + if (applyleft) { +/* Scan for the last non-zero column in C(1:lastv,:). */ + lastc = iladlc_(&lastv, n, &c__[c_offset], ldc); + } else { +/* Scan for the last non-zero row in C(:,1:lastv). */ + lastc = iladlr_(m, &lastv, &c__[c_offset], ldc); + } + } +/* Note that lastc.eq.0 renders the BLAS operations null; no special */ +/* case is needed at this level. */ + if (applyleft) { + +/* Form H * C */ + + if (lastv > 0) { + +/* w(1:lastc,1) := C(1:lastv,1:lastc)**T * v(1:lastv,1) */ + + dgemv_((char *)"Transpose", &lastv, &lastc, &c_b4, &c__[c_offset], ldc, & + v[1], incv, &c_b5, &work[1], &c__1, (ftnlen)9); + +/* C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**T */ + + d__1 = -(*tau); + dger_(&lastv, &lastc, &d__1, &v[1], incv, &work[1], &c__1, &c__[ + c_offset], ldc); + } + } else { + +/* Form C * H */ + + if (lastv > 0) { + +/* w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1) */ + + dgemv_((char *)"No transpose", &lastc, &lastv, &c_b4, &c__[c_offset], ldc, + &v[1], incv, &c_b5, &work[1], &c__1, (ftnlen)12); + +/* C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**T */ + + d__1 = -(*tau); + dger_(&lastc, &lastv, &d__1, &work[1], &c__1, &v[1], incv, &c__[ + c_offset], ldc); + } + } + return 0; + +/* End of DLARF */ + +} /* dlarf_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlarfb.cpp b/lib/linalg/dlarfb.cpp new file mode 100644 index 0000000000..df15d11900 --- /dev/null +++ b/lib/linalg/dlarfb.cpp @@ -0,0 +1,886 @@ +/* fortran/dlarfb.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static doublereal c_b14 = 1.; +static doublereal c_b25 = -1.; + +/* > \brief \b DLARFB applies a block reflector or its transpose to a general rectangular matrix. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLARFB + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, */ +/* T, LDT, C, LDC, WORK, LDWORK ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER DIRECT, SIDE, STOREV, TRANS */ +/* INTEGER K, LDC, LDT, LDV, LDWORK, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION C( LDC, * ), T( LDT, * ), V( LDV, * ), */ +/* $ WORK( LDWORK, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLARFB applies a real block reflector H or its transpose H**T to a */ +/* > real m by n matrix C, from either the left or the right. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] SIDE */ +/* > \verbatim */ +/* > SIDE is CHARACTER*1 */ +/* > = 'L': apply H or H**T from the Left */ +/* > = 'R': apply H or H**T from the Right */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TRANS */ +/* > \verbatim */ +/* > TRANS is CHARACTER*1 */ +/* > = 'N': apply H (No transpose) */ +/* > = 'T': apply H**T (Transpose) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DIRECT */ +/* > \verbatim */ +/* > DIRECT is CHARACTER*1 */ +/* > Indicates how H is formed from a product of elementary */ +/* > reflectors */ +/* > = 'F': H = H(1) H(2) . . . H(k) (Forward) */ +/* > = 'B': H = H(k) . . . H(2) H(1) (Backward) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] STOREV */ +/* > \verbatim */ +/* > STOREV is CHARACTER*1 */ +/* > Indicates how the vectors which define the elementary */ +/* > reflectors are stored: */ +/* > = 'C': Columnwise */ +/* > = 'R': Rowwise */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix C. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix C. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > The order of the matrix T (= the number of elementary */ +/* > reflectors whose product defines the block reflector). */ +/* > If SIDE = 'L', M >= K >= 0; */ +/* > if SIDE = 'R', N >= K >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] V */ +/* > \verbatim */ +/* > V is DOUBLE PRECISION array, dimension */ +/* > (LDV,K) if STOREV = 'C' */ +/* > (LDV,M) if STOREV = 'R' and SIDE = 'L' */ +/* > (LDV,N) if STOREV = 'R' and SIDE = 'R' */ +/* > The matrix V. See Further Details. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDV */ +/* > \verbatim */ +/* > LDV is INTEGER */ +/* > The leading dimension of the array V. */ +/* > If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M); */ +/* > if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N); */ +/* > if STOREV = 'R', LDV >= K. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] T */ +/* > \verbatim */ +/* > T is DOUBLE PRECISION array, dimension (LDT,K) */ +/* > The triangular k by k matrix T in the representation of the */ +/* > block reflector. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDT */ +/* > \verbatim */ +/* > LDT is INTEGER */ +/* > The leading dimension of the array T. LDT >= K. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] C */ +/* > \verbatim */ +/* > C is DOUBLE PRECISION array, dimension (LDC,N) */ +/* > On entry, the m by n matrix C. */ +/* > On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDC */ +/* > \verbatim */ +/* > LDC is INTEGER */ +/* > The leading dimension of the array C. LDC >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (LDWORK,K) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDWORK */ +/* > \verbatim */ +/* > LDWORK is INTEGER */ +/* > The leading dimension of the array WORK. */ +/* > If SIDE = 'L', LDWORK >= max(1,N); */ +/* > if SIDE = 'R', LDWORK >= max(1,M). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleOTHERauxiliary */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > The shape of the matrix V and the storage of the vectors which define */ +/* > the H(i) is best illustrated by the following example with n = 5 and */ +/* > k = 3. The elements equal to 1 are not stored; the corresponding */ +/* > array elements are modified but restored on exit. The rest of the */ +/* > array is not used. */ +/* > */ +/* > DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': */ +/* > */ +/* > V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) */ +/* > ( v1 1 ) ( 1 v2 v2 v2 ) */ +/* > ( v1 v2 1 ) ( 1 v3 v3 ) */ +/* > ( v1 v2 v3 ) */ +/* > ( v1 v2 v3 ) */ +/* > */ +/* > DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': */ +/* > */ +/* > V = ( v1 v2 v3 ) V = ( v1 v1 1 ) */ +/* > ( v1 v2 v3 ) ( v2 v2 v2 1 ) */ +/* > ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) */ +/* > ( 1 v3 ) */ +/* > ( 1 ) */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dlarfb_(char *side, char *trans, char *direct, char * + storev, integer *m, integer *n, integer *k, doublereal *v, integer * + ldv, doublereal *t, integer *ldt, doublereal *c__, integer *ldc, + doublereal *work, integer *ldwork, ftnlen side_len, ftnlen trans_len, + ftnlen direct_len, ftnlen storev_len) +{ + /* System generated locals */ + integer c_dim1, c_offset, t_dim1, t_offset, v_dim1, v_offset, work_dim1, + work_offset, i__1, i__2; + + /* Local variables */ + integer i__, j; + extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, + doublereal *, integer *), dtrmm_(char *, char *, char *, char *, + integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + char transt[1]; + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Quick return if possible */ + + /* Parameter adjustments */ + v_dim1 = *ldv; + v_offset = 1 + v_dim1; + v -= v_offset; + t_dim1 = *ldt; + t_offset = 1 + t_dim1; + t -= t_offset; + c_dim1 = *ldc; + c_offset = 1 + c_dim1; + c__ -= c_offset; + work_dim1 = *ldwork; + work_offset = 1 + work_dim1; + work -= work_offset; + + /* Function Body */ + if (*m <= 0 || *n <= 0) { + return 0; + } + + if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { + *(unsigned char *)transt = 'T'; + } else { + *(unsigned char *)transt = 'N'; + } + + if (lsame_(storev, (char *)"C", (ftnlen)1, (ftnlen)1)) { + + if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { + +/* Let V = ( V1 ) (first K rows) */ +/* ( V2 ) */ +/* where V1 is unit lower triangular. */ + + if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { + +/* Form H * C or H**T * C where C = ( C1 ) */ +/* ( C2 ) */ + +/* W := C**T * V = (C1**T * V1 + C2**T * V2) (stored in WORK) */ + +/* W := C1**T */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + dcopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1], + &c__1); +/* L10: */ + } + +/* W := W * V1 */ + + dtrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", n, k, &c_b14, + &v[v_offset], ldv, &work[work_offset], ldwork, ( + ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); + if (*m > *k) { + +/* W := W + C2**T * V2 */ + + i__1 = *m - *k; + dgemm_((char *)"Transpose", (char *)"No transpose", n, k, &i__1, &c_b14, & + c__[*k + 1 + c_dim1], ldc, &v[*k + 1 + v_dim1], + ldv, &c_b14, &work[work_offset], ldwork, (ftnlen) + 9, (ftnlen)12); + } + +/* W := W * T**T or W * T */ + + dtrmm_((char *)"Right", (char *)"Upper", transt, (char *)"Non-unit", n, k, &c_b14, &t[ + t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)1, (ftnlen)8); + +/* C := C - V * W**T */ + + if (*m > *k) { + +/* C2 := C2 - V2 * W**T */ + + i__1 = *m - *k; + dgemm_((char *)"No transpose", (char *)"Transpose", &i__1, n, k, &c_b25, & + v[*k + 1 + v_dim1], ldv, &work[work_offset], + ldwork, &c_b14, &c__[*k + 1 + c_dim1], ldc, ( + ftnlen)12, (ftnlen)9); + } + +/* W := W * V1**T */ + + dtrmm_((char *)"Right", (char *)"Lower", (char *)"Transpose", (char *)"Unit", n, k, &c_b14, & + v[v_offset], ldv, &work[work_offset], ldwork, (ftnlen) + 5, (ftnlen)5, (ftnlen)9, (ftnlen)4); + +/* C1 := C1 - W**T */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[j + i__ * c_dim1] -= work[i__ + j * work_dim1]; +/* L20: */ + } +/* L30: */ + } + + } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + +/* Form C * H or C * H**T where C = ( C1 C2 ) */ + +/* W := C * V = (C1*V1 + C2*V2) (stored in WORK) */ + +/* W := C1 */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + dcopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j * + work_dim1 + 1], &c__1); +/* L40: */ + } + +/* W := W * V1 */ + + dtrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", m, k, &c_b14, + &v[v_offset], ldv, &work[work_offset], ldwork, ( + ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); + if (*n > *k) { + +/* W := W + C2 * V2 */ + + i__1 = *n - *k; + dgemm_((char *)"No transpose", (char *)"No transpose", m, k, &i__1, & + c_b14, &c__[(*k + 1) * c_dim1 + 1], ldc, &v[*k + + 1 + v_dim1], ldv, &c_b14, &work[work_offset], + ldwork, (ftnlen)12, (ftnlen)12); + } + +/* W := W * T or W * T**T */ + + dtrmm_((char *)"Right", (char *)"Upper", trans, (char *)"Non-unit", m, k, &c_b14, &t[ + t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)1, (ftnlen)8); + +/* C := C - W * V**T */ + + if (*n > *k) { + +/* C2 := C2 - W * V2**T */ + + i__1 = *n - *k; + dgemm_((char *)"No transpose", (char *)"Transpose", m, &i__1, k, &c_b25, & + work[work_offset], ldwork, &v[*k + 1 + v_dim1], + ldv, &c_b14, &c__[(*k + 1) * c_dim1 + 1], ldc, ( + ftnlen)12, (ftnlen)9); + } + +/* W := W * V1**T */ + + dtrmm_((char *)"Right", (char *)"Lower", (char *)"Transpose", (char *)"Unit", m, k, &c_b14, & + v[v_offset], ldv, &work[work_offset], ldwork, (ftnlen) + 5, (ftnlen)5, (ftnlen)9, (ftnlen)4); + +/* C1 := C1 - W */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] -= work[i__ + j * work_dim1]; +/* L50: */ + } +/* L60: */ + } + } + + } else { + +/* Let V = ( V1 ) */ +/* ( V2 ) (last K rows) */ +/* where V2 is unit upper triangular. */ + + if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { + +/* Form H * C or H**T * C where C = ( C1 ) */ +/* ( C2 ) */ + +/* W := C**T * V = (C1**T * V1 + C2**T * V2) (stored in WORK) */ + +/* W := C2**T */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + dcopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j * + work_dim1 + 1], &c__1); +/* L70: */ + } + +/* W := W * V2 */ + + dtrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", n, k, &c_b14, + &v[*m - *k + 1 + v_dim1], ldv, &work[work_offset], + ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); + if (*m > *k) { + +/* W := W + C1**T * V1 */ + + i__1 = *m - *k; + dgemm_((char *)"Transpose", (char *)"No transpose", n, k, &i__1, &c_b14, & + c__[c_offset], ldc, &v[v_offset], ldv, &c_b14, & + work[work_offset], ldwork, (ftnlen)9, (ftnlen)12); + } + +/* W := W * T**T or W * T */ + + dtrmm_((char *)"Right", (char *)"Lower", transt, (char *)"Non-unit", n, k, &c_b14, &t[ + t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)1, (ftnlen)8); + +/* C := C - V * W**T */ + + if (*m > *k) { + +/* C1 := C1 - V1 * W**T */ + + i__1 = *m - *k; + dgemm_((char *)"No transpose", (char *)"Transpose", &i__1, n, k, &c_b25, & + v[v_offset], ldv, &work[work_offset], ldwork, & + c_b14, &c__[c_offset], ldc, (ftnlen)12, (ftnlen)9) + ; + } + +/* W := W * V2**T */ + + dtrmm_((char *)"Right", (char *)"Upper", (char *)"Transpose", (char *)"Unit", n, k, &c_b14, & + v[*m - *k + 1 + v_dim1], ldv, &work[work_offset], + ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)9, (ftnlen)4); + +/* C2 := C2 - W**T */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[*m - *k + j + i__ * c_dim1] -= work[i__ + j * + work_dim1]; +/* L80: */ + } +/* L90: */ + } + + } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + +/* Form C * H or C * H**T where C = ( C1 C2 ) */ + +/* W := C * V = (C1*V1 + C2*V2) (stored in WORK) */ + +/* W := C2 */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + dcopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[ + j * work_dim1 + 1], &c__1); +/* L100: */ + } + +/* W := W * V2 */ + + dtrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", m, k, &c_b14, + &v[*n - *k + 1 + v_dim1], ldv, &work[work_offset], + ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); + if (*n > *k) { + +/* W := W + C1 * V1 */ + + i__1 = *n - *k; + dgemm_((char *)"No transpose", (char *)"No transpose", m, k, &i__1, & + c_b14, &c__[c_offset], ldc, &v[v_offset], ldv, & + c_b14, &work[work_offset], ldwork, (ftnlen)12, ( + ftnlen)12); + } + +/* W := W * T or W * T**T */ + + dtrmm_((char *)"Right", (char *)"Lower", trans, (char *)"Non-unit", m, k, &c_b14, &t[ + t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)1, (ftnlen)8); + +/* C := C - W * V**T */ + + if (*n > *k) { + +/* C1 := C1 - W * V1**T */ + + i__1 = *n - *k; + dgemm_((char *)"No transpose", (char *)"Transpose", m, &i__1, k, &c_b25, & + work[work_offset], ldwork, &v[v_offset], ldv, & + c_b14, &c__[c_offset], ldc, (ftnlen)12, (ftnlen)9) + ; + } + +/* W := W * V2**T */ + + dtrmm_((char *)"Right", (char *)"Upper", (char *)"Transpose", (char *)"Unit", m, k, &c_b14, & + v[*n - *k + 1 + v_dim1], ldv, &work[work_offset], + ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)9, (ftnlen)4); + +/* C2 := C2 - W */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + (*n - *k + j) * c_dim1] -= work[i__ + j * + work_dim1]; +/* L110: */ + } +/* L120: */ + } + } + } + + } else if (lsame_(storev, (char *)"R", (ftnlen)1, (ftnlen)1)) { + + if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { + +/* Let V = ( V1 V2 ) (V1: first K columns) */ +/* where V1 is unit upper triangular. */ + + if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { + +/* Form H * C or H**T * C where C = ( C1 ) */ +/* ( C2 ) */ + +/* W := C**T * V**T = (C1**T * V1**T + C2**T * V2**T) (stored in WORK) */ + +/* W := C1**T */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + dcopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1], + &c__1); +/* L130: */ + } + +/* W := W * V1**T */ + + dtrmm_((char *)"Right", (char *)"Upper", (char *)"Transpose", (char *)"Unit", n, k, &c_b14, & + v[v_offset], ldv, &work[work_offset], ldwork, (ftnlen) + 5, (ftnlen)5, (ftnlen)9, (ftnlen)4); + if (*m > *k) { + +/* W := W + C2**T * V2**T */ + + i__1 = *m - *k; + dgemm_((char *)"Transpose", (char *)"Transpose", n, k, &i__1, &c_b14, & + c__[*k + 1 + c_dim1], ldc, &v[(*k + 1) * v_dim1 + + 1], ldv, &c_b14, &work[work_offset], ldwork, ( + ftnlen)9, (ftnlen)9); + } + +/* W := W * T**T or W * T */ + + dtrmm_((char *)"Right", (char *)"Upper", transt, (char *)"Non-unit", n, k, &c_b14, &t[ + t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)1, (ftnlen)8); + +/* C := C - V**T * W**T */ + + if (*m > *k) { + +/* C2 := C2 - V2**T * W**T */ + + i__1 = *m - *k; + dgemm_((char *)"Transpose", (char *)"Transpose", &i__1, n, k, &c_b25, &v[( + *k + 1) * v_dim1 + 1], ldv, &work[work_offset], + ldwork, &c_b14, &c__[*k + 1 + c_dim1], ldc, ( + ftnlen)9, (ftnlen)9); + } + +/* W := W * V1 */ + + dtrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", n, k, &c_b14, + &v[v_offset], ldv, &work[work_offset], ldwork, ( + ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); + +/* C1 := C1 - W**T */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[j + i__ * c_dim1] -= work[i__ + j * work_dim1]; +/* L140: */ + } +/* L150: */ + } + + } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + +/* Form C * H or C * H**T where C = ( C1 C2 ) */ + +/* W := C * V**T = (C1*V1**T + C2*V2**T) (stored in WORK) */ + +/* W := C1 */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + dcopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j * + work_dim1 + 1], &c__1); +/* L160: */ + } + +/* W := W * V1**T */ + + dtrmm_((char *)"Right", (char *)"Upper", (char *)"Transpose", (char *)"Unit", m, k, &c_b14, & + v[v_offset], ldv, &work[work_offset], ldwork, (ftnlen) + 5, (ftnlen)5, (ftnlen)9, (ftnlen)4); + if (*n > *k) { + +/* W := W + C2 * V2**T */ + + i__1 = *n - *k; + dgemm_((char *)"No transpose", (char *)"Transpose", m, k, &i__1, &c_b14, & + c__[(*k + 1) * c_dim1 + 1], ldc, &v[(*k + 1) * + v_dim1 + 1], ldv, &c_b14, &work[work_offset], + ldwork, (ftnlen)12, (ftnlen)9); + } + +/* W := W * T or W * T**T */ + + dtrmm_((char *)"Right", (char *)"Upper", trans, (char *)"Non-unit", m, k, &c_b14, &t[ + t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)1, (ftnlen)8); + +/* C := C - W * V */ + + if (*n > *k) { + +/* C2 := C2 - W * V2 */ + + i__1 = *n - *k; + dgemm_((char *)"No transpose", (char *)"No transpose", m, &i__1, k, & + c_b25, &work[work_offset], ldwork, &v[(*k + 1) * + v_dim1 + 1], ldv, &c_b14, &c__[(*k + 1) * c_dim1 + + 1], ldc, (ftnlen)12, (ftnlen)12); + } + +/* W := W * V1 */ + + dtrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", m, k, &c_b14, + &v[v_offset], ldv, &work[work_offset], ldwork, ( + ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); + +/* C1 := C1 - W */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] -= work[i__ + j * work_dim1]; +/* L170: */ + } +/* L180: */ + } + + } + + } else { + +/* Let V = ( V1 V2 ) (V2: last K columns) */ +/* where V2 is unit lower triangular. */ + + if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { + +/* Form H * C or H**T * C where C = ( C1 ) */ +/* ( C2 ) */ + +/* W := C**T * V**T = (C1**T * V1**T + C2**T * V2**T) (stored in WORK) */ + +/* W := C2**T */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + dcopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j * + work_dim1 + 1], &c__1); +/* L190: */ + } + +/* W := W * V2**T */ + + dtrmm_((char *)"Right", (char *)"Lower", (char *)"Transpose", (char *)"Unit", n, k, &c_b14, & + v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[work_offset] + , ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)9, (ftnlen)4); + if (*m > *k) { + +/* W := W + C1**T * V1**T */ + + i__1 = *m - *k; + dgemm_((char *)"Transpose", (char *)"Transpose", n, k, &i__1, &c_b14, & + c__[c_offset], ldc, &v[v_offset], ldv, &c_b14, & + work[work_offset], ldwork, (ftnlen)9, (ftnlen)9); + } + +/* W := W * T**T or W * T */ + + dtrmm_((char *)"Right", (char *)"Lower", transt, (char *)"Non-unit", n, k, &c_b14, &t[ + t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)1, (ftnlen)8); + +/* C := C - V**T * W**T */ + + if (*m > *k) { + +/* C1 := C1 - V1**T * W**T */ + + i__1 = *m - *k; + dgemm_((char *)"Transpose", (char *)"Transpose", &i__1, n, k, &c_b25, &v[ + v_offset], ldv, &work[work_offset], ldwork, & + c_b14, &c__[c_offset], ldc, (ftnlen)9, (ftnlen)9); + } + +/* W := W * V2 */ + + dtrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", n, k, &c_b14, + &v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[ + work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen) + 12, (ftnlen)4); + +/* C2 := C2 - W**T */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[*m - *k + j + i__ * c_dim1] -= work[i__ + j * + work_dim1]; +/* L200: */ + } +/* L210: */ + } + + } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + +/* Form C * H or C * H' where C = ( C1 C2 ) */ + +/* W := C * V**T = (C1*V1**T + C2*V2**T) (stored in WORK) */ + +/* W := C2 */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + dcopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[ + j * work_dim1 + 1], &c__1); +/* L220: */ + } + +/* W := W * V2**T */ + + dtrmm_((char *)"Right", (char *)"Lower", (char *)"Transpose", (char *)"Unit", m, k, &c_b14, & + v[(*n - *k + 1) * v_dim1 + 1], ldv, &work[work_offset] + , ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)9, (ftnlen)4); + if (*n > *k) { + +/* W := W + C1 * V1**T */ + + i__1 = *n - *k; + dgemm_((char *)"No transpose", (char *)"Transpose", m, k, &i__1, &c_b14, & + c__[c_offset], ldc, &v[v_offset], ldv, &c_b14, & + work[work_offset], ldwork, (ftnlen)12, (ftnlen)9); + } + +/* W := W * T or W * T**T */ + + dtrmm_((char *)"Right", (char *)"Lower", trans, (char *)"Non-unit", m, k, &c_b14, &t[ + t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)1, (ftnlen)8); + +/* C := C - W * V */ + + if (*n > *k) { + +/* C1 := C1 - W * V1 */ + + i__1 = *n - *k; + dgemm_((char *)"No transpose", (char *)"No transpose", m, &i__1, k, & + c_b25, &work[work_offset], ldwork, &v[v_offset], + ldv, &c_b14, &c__[c_offset], ldc, (ftnlen)12, ( + ftnlen)12); + } + +/* W := W * V2 */ + + dtrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", m, k, &c_b14, + &v[(*n - *k + 1) * v_dim1 + 1], ldv, &work[ + work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen) + 12, (ftnlen)4); + +/* C1 := C1 - W */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + (*n - *k + j) * c_dim1] -= work[i__ + j * + work_dim1]; +/* L230: */ + } +/* L240: */ + } + + } + + } + } + + return 0; + +/* End of DLARFB */ + +} /* dlarfb_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlarfg.cpp b/lib/linalg/dlarfg.cpp new file mode 100644 index 0000000000..cb544ccf18 --- /dev/null +++ b/lib/linalg/dlarfg.cpp @@ -0,0 +1,240 @@ +/* fortran/dlarfg.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DLARFG generates an elementary reflector (Householder matrix). */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLARFG + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INCX, N */ +/* DOUBLE PRECISION ALPHA, TAU */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION X( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLARFG generates a real elementary reflector H of order n, such */ +/* > that */ +/* > */ +/* > H * ( alpha ) = ( beta ), H**T * H = I. */ +/* > ( x ) ( 0 ) */ +/* > */ +/* > where alpha and beta are scalars, and x is an (n-1)-element real */ +/* > vector. H is represented in the form */ +/* > */ +/* > H = I - tau * ( 1 ) * ( 1 v**T ) , */ +/* > ( v ) */ +/* > */ +/* > where tau is a real scalar and v is a real (n-1)-element */ +/* > vector. */ +/* > */ +/* > If the elements of x are all zero, then tau = 0 and H is taken to be */ +/* > the unit matrix. */ +/* > */ +/* > Otherwise 1 <= tau <= 2. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the elementary reflector. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] ALPHA */ +/* > \verbatim */ +/* > ALPHA is DOUBLE PRECISION */ +/* > On entry, the value alpha. */ +/* > On exit, it is overwritten with the value beta. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] X */ +/* > \verbatim */ +/* > X is DOUBLE PRECISION array, dimension */ +/* > (1+(N-2)*abs(INCX)) */ +/* > On entry, the vector x. */ +/* > On exit, it is overwritten with the vector v. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > The increment between elements of X. INCX > 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] TAU */ +/* > \verbatim */ +/* > TAU is DOUBLE PRECISION */ +/* > The value tau. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleOTHERauxiliary */ + +/* ===================================================================== */ +/* Subroutine */ int dlarfg_(integer *n, doublereal *alpha, doublereal *x, + integer *incx, doublereal *tau) +{ + /* System generated locals */ + integer i__1; + doublereal d__1; + + /* Builtin functions */ + double d_sign(doublereal *, doublereal *); + + /* Local variables */ + integer j, knt; + doublereal beta; + extern doublereal dnrm2_(integer *, doublereal *, integer *); + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *); + doublereal xnorm; + extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, + ftnlen); + doublereal safmin, rsafmn; + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Executable Statements .. */ + + /* Parameter adjustments */ + --x; + + /* Function Body */ + if (*n <= 1) { + *tau = 0.; + return 0; + } + + i__1 = *n - 1; + xnorm = dnrm2_(&i__1, &x[1], incx); + + if (xnorm == 0.) { + +/* H = I */ + + *tau = 0.; + } else { + +/* general case */ + + d__1 = dlapy2_(alpha, &xnorm); + beta = -d_sign(&d__1, alpha); + safmin = dlamch_((char *)"S", (ftnlen)1) / dlamch_((char *)"E", (ftnlen)1); + knt = 0; + if (abs(beta) < safmin) { + +/* XNORM, BETA may be inaccurate; scale X and recompute them */ + + rsafmn = 1. / safmin; +L10: + ++knt; + i__1 = *n - 1; + dscal_(&i__1, &rsafmn, &x[1], incx); + beta *= rsafmn; + *alpha *= rsafmn; + if (abs(beta) < safmin && knt < 20) { + goto L10; + } + +/* New BETA is at most 1, at least SAFMIN */ + + i__1 = *n - 1; + xnorm = dnrm2_(&i__1, &x[1], incx); + d__1 = dlapy2_(alpha, &xnorm); + beta = -d_sign(&d__1, alpha); + } + *tau = (beta - *alpha) / beta; + i__1 = *n - 1; + d__1 = 1. / (*alpha - beta); + dscal_(&i__1, &d__1, &x[1], incx); + +/* If ALPHA is subnormal, it may lose relative accuracy */ + + i__1 = knt; + for (j = 1; j <= i__1; ++j) { + beta *= safmin; +/* L20: */ + } + *alpha = beta; + } + + return 0; + +/* End of DLARFG */ + +} /* dlarfg_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlarft.cpp b/lib/linalg/dlarft.cpp new file mode 100644 index 0000000000..220c9f0082 --- /dev/null +++ b/lib/linalg/dlarft.cpp @@ -0,0 +1,417 @@ +/* static/dlarft.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static doublereal c_b7 = 1.; + +/* > \brief \b DLARFT forms the triangular factor T of a block reflector H = I - vtvH */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLARFT + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER DIRECT, STOREV */ +/* INTEGER K, LDT, LDV, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLARFT forms the triangular factor T of a real block reflector H */ +/* > of order n, which is defined as a product of k elementary reflectors. */ +/* > */ +/* > If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; */ +/* > */ +/* > If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. */ +/* > */ +/* > If STOREV = 'C', the vector which defines the elementary reflector */ +/* > H(i) is stored in the i-th column of the array V, and */ +/* > */ +/* > H = I - V * T * V**T */ +/* > */ +/* > If STOREV = 'R', the vector which defines the elementary reflector */ +/* > H(i) is stored in the i-th row of the array V, and */ +/* > */ +/* > H = I - V**T * T * V */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] DIRECT */ +/* > \verbatim */ +/* > DIRECT is CHARACTER*1 */ +/* > Specifies the order in which the elementary reflectors are */ +/* > multiplied to form the block reflector: */ +/* > = 'F': H = H(1) H(2) . . . H(k) (Forward) */ +/* > = 'B': H = H(k) . . . H(2) H(1) (Backward) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] STOREV */ +/* > \verbatim */ +/* > STOREV is CHARACTER*1 */ +/* > Specifies how the vectors which define the elementary */ +/* > reflectors are stored (see also Further Details): */ +/* > = 'C': columnwise */ +/* > = 'R': rowwise */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the block reflector H. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > The order of the triangular factor T (= the number of */ +/* > elementary reflectors). K >= 1. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] V */ +/* > \verbatim */ +/* > V is DOUBLE PRECISION array, dimension */ +/* > (LDV,K) if STOREV = 'C' */ +/* > (LDV,N) if STOREV = 'R' */ +/* > The matrix V. See further details. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDV */ +/* > \verbatim */ +/* > LDV is INTEGER */ +/* > The leading dimension of the array V. */ +/* > If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TAU */ +/* > \verbatim */ +/* > TAU is DOUBLE PRECISION array, dimension (K) */ +/* > TAU(i) must contain the scalar factor of the elementary */ +/* > reflector H(i). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] T */ +/* > \verbatim */ +/* > T is DOUBLE PRECISION array, dimension (LDT,K) */ +/* > The k by k triangular factor T of the block reflector. */ +/* > If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is */ +/* > lower triangular. The rest of the array is not used. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDT */ +/* > \verbatim */ +/* > LDT is INTEGER */ +/* > The leading dimension of the array T. LDT >= K. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleOTHERauxiliary */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > The shape of the matrix V and the storage of the vectors which define */ +/* > the H(i) is best illustrated by the following example with n = 5 and */ +/* > k = 3. The elements equal to 1 are not stored. */ +/* > */ +/* > DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': */ +/* > */ +/* > V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) */ +/* > ( v1 1 ) ( 1 v2 v2 v2 ) */ +/* > ( v1 v2 1 ) ( 1 v3 v3 ) */ +/* > ( v1 v2 v3 ) */ +/* > ( v1 v2 v3 ) */ +/* > */ +/* > DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': */ +/* > */ +/* > V = ( v1 v2 v3 ) V = ( v1 v1 1 ) */ +/* > ( v1 v2 v3 ) ( v2 v2 v2 1 ) */ +/* > ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) */ +/* > ( 1 v3 ) */ +/* > ( 1 ) */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dlarft_(char *direct, char *storev, integer *n, integer * + k, doublereal *v, integer *ldv, doublereal *tau, doublereal *t, + integer *ldt, ftnlen direct_len, ftnlen storev_len) +{ + /* System generated locals */ + integer t_dim1, t_offset, v_dim1, v_offset, i__1, i__2, i__3; + doublereal d__1; + + /* Local variables */ + integer i__, j, prevlastv; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int dgemv_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, ftnlen); + integer lastv; + extern /* Subroutine */ int dtrmv_(char *, char *, char *, integer *, + doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, + ftnlen); + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Quick return if possible */ + + /* Parameter adjustments */ + v_dim1 = *ldv; + v_offset = 1 + v_dim1; + v -= v_offset; + --tau; + t_dim1 = *ldt; + t_offset = 1 + t_dim1; + t -= t_offset; + + /* Function Body */ + if (*n == 0) { + return 0; + } + + if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { + prevlastv = *n; + i__1 = *k; + for (i__ = 1; i__ <= i__1; ++i__) { + prevlastv = max(i__,prevlastv); + if (tau[i__] == 0.) { + +/* H(i) = I */ + + i__2 = i__; + for (j = 1; j <= i__2; ++j) { + t[j + i__ * t_dim1] = 0.; + } + } else { + +/* general case */ + + if (lsame_(storev, (char *)"C", (ftnlen)1, (ftnlen)1)) { +/* Skip any trailing zeros. */ + i__2 = i__ + 1; + for (lastv = *n; lastv >= i__2; --lastv) { + if (v[lastv + i__ * v_dim1] != 0.) { + goto L219; + } + } +L219: + i__2 = i__ - 1; + for (j = 1; j <= i__2; ++j) { + t[j + i__ * t_dim1] = -tau[i__] * v[i__ + j * v_dim1]; + } + j = min(lastv,prevlastv); + +/* T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**T * V(i:j,i) */ + + i__2 = j - i__; + i__3 = i__ - 1; + d__1 = -tau[i__]; + dgemv_((char *)"Transpose", &i__2, &i__3, &d__1, &v[i__ + 1 + + v_dim1], ldv, &v[i__ + 1 + i__ * v_dim1], &c__1, & + c_b7, &t[i__ * t_dim1 + 1], &c__1, (ftnlen)9); + } else { +/* Skip any trailing zeros. */ + i__2 = i__ + 1; + for (lastv = *n; lastv >= i__2; --lastv) { + if (v[i__ + lastv * v_dim1] != 0.) { + goto L235; + } + } +L235: + i__2 = i__ - 1; + for (j = 1; j <= i__2; ++j) { + t[j + i__ * t_dim1] = -tau[i__] * v[j + i__ * v_dim1]; + } + j = min(lastv,prevlastv); + +/* T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**T */ + + i__2 = i__ - 1; + i__3 = j - i__; + d__1 = -tau[i__]; + dgemv_((char *)"No transpose", &i__2, &i__3, &d__1, &v[(i__ + 1) * + v_dim1 + 1], ldv, &v[i__ + (i__ + 1) * v_dim1], + ldv, &c_b7, &t[i__ * t_dim1 + 1], &c__1, (ftnlen) + 12); + } + +/* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) */ + + i__2 = i__ - 1; + dtrmv_((char *)"Upper", (char *)"No transpose", (char *)"Non-unit", &i__2, &t[ + t_offset], ldt, &t[i__ * t_dim1 + 1], &c__1, (ftnlen) + 5, (ftnlen)12, (ftnlen)8); + t[i__ + i__ * t_dim1] = tau[i__]; + if (i__ > 1) { + prevlastv = max(prevlastv,lastv); + } else { + prevlastv = lastv; + } + } + } + } else { + prevlastv = 1; + for (i__ = *k; i__ >= 1; --i__) { + if (tau[i__] == 0.) { + +/* H(i) = I */ + + i__1 = *k; + for (j = i__; j <= i__1; ++j) { + t[j + i__ * t_dim1] = 0.; + } + } else { + +/* general case */ + + if (i__ < *k) { + if (lsame_(storev, (char *)"C", (ftnlen)1, (ftnlen)1)) { +/* Skip any leading zeros. */ + i__1 = i__ - 1; + for (lastv = 1; lastv <= i__1; ++lastv) { + if (v[lastv + i__ * v_dim1] != 0.) { + goto L280; + } + } +L280: + i__1 = *k; + for (j = i__ + 1; j <= i__1; ++j) { + t[j + i__ * t_dim1] = -tau[i__] * v[*n - *k + i__ + + j * v_dim1]; + } + j = max(lastv,prevlastv); + +/* T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**T * V(j:n-k+i,i) */ + + i__1 = *n - *k + i__ - j; + i__2 = *k - i__; + d__1 = -tau[i__]; + dgemv_((char *)"Transpose", &i__1, &i__2, &d__1, &v[j + (i__ + + 1) * v_dim1], ldv, &v[j + i__ * v_dim1], & + c__1, &c_b7, &t[i__ + 1 + i__ * t_dim1], & + c__1, (ftnlen)9); + } else { +/* Skip any leading zeros. */ + i__1 = i__ - 1; + for (lastv = 1; lastv <= i__1; ++lastv) { + if (v[i__ + lastv * v_dim1] != 0.) { + goto L296; + } + } +L296: + i__1 = *k; + for (j = i__ + 1; j <= i__1; ++j) { + t[j + i__ * t_dim1] = -tau[i__] * v[j + (*n - *k + + i__) * v_dim1]; + } + j = max(lastv,prevlastv); + +/* T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**T */ + + i__1 = *k - i__; + i__2 = *n - *k + i__ - j; + d__1 = -tau[i__]; + dgemv_((char *)"No transpose", &i__1, &i__2, &d__1, &v[i__ + + 1 + j * v_dim1], ldv, &v[i__ + j * v_dim1], + ldv, &c_b7, &t[i__ + 1 + i__ * t_dim1], &c__1, + (ftnlen)12); + } + +/* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) */ + + i__1 = *k - i__; + dtrmv_((char *)"Lower", (char *)"No transpose", (char *)"Non-unit", &i__1, &t[i__ + + 1 + (i__ + 1) * t_dim1], ldt, &t[i__ + 1 + i__ * + t_dim1], &c__1, (ftnlen)5, (ftnlen)12, (ftnlen)8) + ; + if (i__ > 1) { + prevlastv = min(prevlastv,lastv); + } else { + prevlastv = lastv; + } + } + t[i__ + i__ * t_dim1] = tau[i__]; + } + } + } + return 0; + +/* End of DLARFT */ + +} /* dlarft_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlartg.cpp b/lib/linalg/dlartg.cpp new file mode 100644 index 0000000000..118d7865f6 --- /dev/null +++ b/lib/linalg/dlartg.cpp @@ -0,0 +1,258 @@ +/* fortran/dlartg.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DLARTG generates a plane rotation with real cosine and real sine. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLARTG + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLARTG( F, G, CS, SN, R ) */ + +/* .. Scalar Arguments .. */ +/* DOUBLE PRECISION CS, F, G, R, SN */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLARTG generate a plane rotation so that */ +/* > */ +/* > [ CS SN ] . [ F ] = [ R ] where CS**2 + SN**2 = 1. */ +/* > [ -SN CS ] [ G ] [ 0 ] */ +/* > */ +/* > This is a slower, more accurate version of the BLAS1 routine DROTG, */ +/* > with the following other differences: */ +/* > F and G are unchanged on return. */ +/* > If G=0, then CS=1 and SN=0. */ +/* > If F=0 and (G .ne. 0), then CS=0 and SN=1 without doing any */ +/* > floating point operations (saves work in DBDSQR when */ +/* > there are zeros on the diagonal). */ +/* > */ +/* > If F exceeds G in magnitude, CS will be positive. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] F */ +/* > \verbatim */ +/* > F is DOUBLE PRECISION */ +/* > The first component of vector to be rotated. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] G */ +/* > \verbatim */ +/* > G is DOUBLE PRECISION */ +/* > The second component of vector to be rotated. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] CS */ +/* > \verbatim */ +/* > CS is DOUBLE PRECISION */ +/* > The cosine of the rotation. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] SN */ +/* > \verbatim */ +/* > SN is DOUBLE PRECISION */ +/* > The sine of the rotation. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] R */ +/* > \verbatim */ +/* > R is DOUBLE PRECISION */ +/* > The nonzero component of the rotated vector. */ +/* > */ +/* > This version has a few statements commented out for thread safety */ +/* > (machine parameters are computed on each entry). 10 feb 03, SJH. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \date December 2016 */ + +/* > \ingroup OTHERauxiliary */ + +/* ===================================================================== */ +/* Subroutine */ int dlartg_(doublereal *f, doublereal *g, doublereal *cs, + doublereal *sn, doublereal *r__) +{ + /* System generated locals */ + integer i__1; + doublereal d__1, d__2; + + /* Builtin functions */ + double log(doublereal), pow_di(doublereal *, integer *), sqrt(doublereal); + + /* Local variables */ + integer i__; + doublereal f1, g1, eps, scale; + integer count; + doublereal safmn2, safmx2; + extern doublereal dlamch_(char *, ftnlen); + doublereal safmin; + + +/* -- LAPACK auxiliary routine (version 3.7.0) -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ +/* December 2016 */ + +/* .. Scalar Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* LOGICAL FIRST */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Save statement .. */ +/* SAVE FIRST, SAFMX2, SAFMIN, SAFMN2 */ +/* .. */ +/* .. Data statements .. */ +/* DATA FIRST / .TRUE. / */ +/* .. */ +/* .. Executable Statements .. */ + +/* IF( FIRST ) THEN */ + safmin = dlamch_((char *)"S", (ftnlen)1); + eps = dlamch_((char *)"E", (ftnlen)1); + d__1 = dlamch_((char *)"B", (ftnlen)1); + i__1 = (integer) (log(safmin / eps) / log(dlamch_((char *)"B", (ftnlen)1)) / 2.); + safmn2 = pow_di(&d__1, &i__1); + safmx2 = 1. / safmn2; +/* FIRST = .FALSE. */ +/* END IF */ + if (*g == 0.) { + *cs = 1.; + *sn = 0.; + *r__ = *f; + } else if (*f == 0.) { + *cs = 0.; + *sn = 1.; + *r__ = *g; + } else { + f1 = *f; + g1 = *g; +/* Computing MAX */ + d__1 = abs(f1), d__2 = abs(g1); + scale = max(d__1,d__2); + if (scale >= safmx2) { + count = 0; +L10: + ++count; + f1 *= safmn2; + g1 *= safmn2; +/* Computing MAX */ + d__1 = abs(f1), d__2 = abs(g1); + scale = max(d__1,d__2); + if (scale >= safmx2) { + goto L10; + } +/* Computing 2nd power */ + d__1 = f1; +/* Computing 2nd power */ + d__2 = g1; + *r__ = sqrt(d__1 * d__1 + d__2 * d__2); + *cs = f1 / *r__; + *sn = g1 / *r__; + i__1 = count; + for (i__ = 1; i__ <= i__1; ++i__) { + *r__ *= safmx2; +/* L20: */ + } + } else if (scale <= safmn2) { + count = 0; +L30: + ++count; + f1 *= safmx2; + g1 *= safmx2; +/* Computing MAX */ + d__1 = abs(f1), d__2 = abs(g1); + scale = max(d__1,d__2); + if (scale <= safmn2) { + goto L30; + } +/* Computing 2nd power */ + d__1 = f1; +/* Computing 2nd power */ + d__2 = g1; + *r__ = sqrt(d__1 * d__1 + d__2 * d__2); + *cs = f1 / *r__; + *sn = g1 / *r__; + i__1 = count; + for (i__ = 1; i__ <= i__1; ++i__) { + *r__ *= safmn2; +/* L40: */ + } + } else { +/* Computing 2nd power */ + d__1 = f1; +/* Computing 2nd power */ + d__2 = g1; + *r__ = sqrt(d__1 * d__1 + d__2 * d__2); + *cs = f1 / *r__; + *sn = g1 / *r__; + } + if (abs(*f) > abs(*g) && *cs < 0.) { + *cs = -(*cs); + *sn = -(*sn); + *r__ = -(*r__); + } + } + return 0; + +/* End of DLARTG */ + +} /* dlartg_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlas2.cpp b/lib/linalg/dlas2.cpp new file mode 100644 index 0000000000..e3a53a9bac --- /dev/null +++ b/lib/linalg/dlas2.cpp @@ -0,0 +1,212 @@ +/* fortran/dlas2.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DLAS2 computes singular values of a 2-by-2 triangular matrix. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLAS2 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLAS2( F, G, H, SSMIN, SSMAX ) */ + +/* .. Scalar Arguments .. */ +/* DOUBLE PRECISION F, G, H, SSMAX, SSMIN */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLAS2 computes the singular values of the 2-by-2 matrix */ +/* > [ F G ] */ +/* > [ 0 H ]. */ +/* > On return, SSMIN is the smaller singular value and SSMAX is the */ +/* > larger singular value. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] F */ +/* > \verbatim */ +/* > F is DOUBLE PRECISION */ +/* > The (1,1) element of the 2-by-2 matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] G */ +/* > \verbatim */ +/* > G is DOUBLE PRECISION */ +/* > The (1,2) element of the 2-by-2 matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] H */ +/* > \verbatim */ +/* > H is DOUBLE PRECISION */ +/* > The (2,2) element of the 2-by-2 matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] SSMIN */ +/* > \verbatim */ +/* > SSMIN is DOUBLE PRECISION */ +/* > The smaller singular value. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] SSMAX */ +/* > \verbatim */ +/* > SSMAX is DOUBLE PRECISION */ +/* > The larger singular value. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup OTHERauxiliary */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > Barring over/underflow, all output quantities are correct to within */ +/* > a few units in the last place (ulps), even in the absence of a guard */ +/* > digit in addition/subtraction. */ +/* > */ +/* > In IEEE arithmetic, the code works correctly if one matrix element is */ +/* > infinite. */ +/* > */ +/* > Overflow will not occur unless the largest singular value itself */ +/* > overflows, or is within a few ulps of overflow. (On machines with */ +/* > partial overflow, like the Cray, overflow may occur if the largest */ +/* > singular value is within a factor of 2 of overflow.) */ +/* > */ +/* > Underflow is harmless if underflow is gradual. Otherwise, results */ +/* > may correspond to a matrix modified by perturbations of size near */ +/* > the underflow threshold. */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dlas2_(doublereal *f, doublereal *g, doublereal *h__, + doublereal *ssmin, doublereal *ssmax) +{ + /* System generated locals */ + doublereal d__1, d__2; + + /* Builtin functions */ + double sqrt(doublereal); + + /* Local variables */ + doublereal c__, fa, ga, ha, as, at, au, fhmn, fhmx; + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ + +/* ==================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + + fa = abs(*f); + ga = abs(*g); + ha = abs(*h__); + fhmn = min(fa,ha); + fhmx = max(fa,ha); + if (fhmn == 0.) { + *ssmin = 0.; + if (fhmx == 0.) { + *ssmax = ga; + } else { +/* Computing 2nd power */ + d__1 = min(fhmx,ga) / max(fhmx,ga); + *ssmax = max(fhmx,ga) * sqrt(d__1 * d__1 + 1.); + } + } else { + if (ga < fhmx) { + as = fhmn / fhmx + 1.; + at = (fhmx - fhmn) / fhmx; +/* Computing 2nd power */ + d__1 = ga / fhmx; + au = d__1 * d__1; + c__ = 2. / (sqrt(as * as + au) + sqrt(at * at + au)); + *ssmin = fhmn * c__; + *ssmax = fhmx / c__; + } else { + au = fhmx / ga; + if (au == 0.) { + +/* Avoid possible harmful underflow if exponent range */ +/* asymmetric (true SSMIN may not underflow even if */ +/* AU underflows) */ + + *ssmin = fhmn * fhmx / ga; + *ssmax = ga; + } else { + as = fhmn / fhmx + 1.; + at = (fhmx - fhmn) / fhmx; +/* Computing 2nd power */ + d__1 = as * au; +/* Computing 2nd power */ + d__2 = at * au; + c__ = 1. / (sqrt(d__1 * d__1 + 1.) + sqrt(d__2 * d__2 + 1.)); + *ssmin = fhmn * c__ * au; + *ssmin += *ssmin; + *ssmax = ga / (c__ + c__); + } + } + } + return 0; + +/* End of DLAS2 */ + +} /* dlas2_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlascl.cpp b/lib/linalg/dlascl.cpp new file mode 100644 index 0000000000..932e1c63cb --- /dev/null +++ b/lib/linalg/dlascl.cpp @@ -0,0 +1,448 @@ +/* fortran/dlascl.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLASCL + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLASCL( TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER TYPE */ +/* INTEGER INFO, KL, KU, LDA, M, N */ +/* DOUBLE PRECISION CFROM, CTO */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLASCL multiplies the M by N real matrix A by the real scalar */ +/* > CTO/CFROM. This is done without over/underflow as long as the final */ +/* > result CTO*A(I,J)/CFROM does not over/underflow. TYPE specifies that */ +/* > A may be full, upper triangular, lower triangular, upper Hessenberg, */ +/* > or banded. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] TYPE */ +/* > \verbatim */ +/* > TYPE is CHARACTER*1 */ +/* > TYPE indices the storage type of the input matrix. */ +/* > = 'G': A is a full matrix. */ +/* > = 'L': A is a lower triangular matrix. */ +/* > = 'U': A is an upper triangular matrix. */ +/* > = 'H': A is an upper Hessenberg matrix. */ +/* > = 'B': A is a symmetric band matrix with lower bandwidth KL */ +/* > and upper bandwidth KU and with the only the lower */ +/* > half stored. */ +/* > = 'Q': A is a symmetric band matrix with lower bandwidth KL */ +/* > and upper bandwidth KU and with the only the upper */ +/* > half stored. */ +/* > = 'Z': A is a band matrix with lower bandwidth KL and upper */ +/* > bandwidth KU. See DGBTRF for storage details. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] KL */ +/* > \verbatim */ +/* > KL is INTEGER */ +/* > The lower bandwidth of A. Referenced only if TYPE = 'B', */ +/* > 'Q' or 'Z'. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] KU */ +/* > \verbatim */ +/* > KU is INTEGER */ +/* > The upper bandwidth of A. Referenced only if TYPE = 'B', */ +/* > 'Q' or 'Z'. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] CFROM */ +/* > \verbatim */ +/* > CFROM is DOUBLE PRECISION */ +/* > \endverbatim */ +/* > */ +/* > \param[in] CTO */ +/* > \verbatim */ +/* > CTO is DOUBLE PRECISION */ +/* > */ +/* > The matrix A is multiplied by CTO/CFROM. A(I,J) is computed */ +/* > without over/underflow if the final result CTO*A(I,J)/CFROM */ +/* > can be represented without over/underflow. CFROM must be */ +/* > nonzero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix A. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > The matrix to be multiplied by CTO/CFROM. See TYPE for the */ +/* > storage type. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. */ +/* > If TYPE = 'G', 'L', 'U', 'H', LDA >= max(1,M); */ +/* > TYPE = 'B', LDA >= KL+1; */ +/* > TYPE = 'Q', LDA >= KU+1; */ +/* > TYPE = 'Z', LDA >= 2*KL+KU+1. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > 0 - successful exit */ +/* > <0 - if INFO = -i, the i-th argument had an illegal value. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup OTHERauxiliary */ + +/* ===================================================================== */ +/* Subroutine */ int dlascl_(char *type__, integer *kl, integer *ku, + doublereal *cfrom, doublereal *cto, integer *m, integer *n, + doublereal *a, integer *lda, integer *info, ftnlen type_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; + + /* Local variables */ + integer i__, j, k1, k2, k3, k4; + doublereal mul, cto1; + logical done; + doublereal ctoc; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + integer itype; + doublereal cfrom1; + extern doublereal dlamch_(char *, ftnlen); + doublereal cfromc; + extern logical disnan_(doublereal *); + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + doublereal bignum, smlnum; + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + + /* Function Body */ + *info = 0; + + if (lsame_(type__, (char *)"G", (ftnlen)1, (ftnlen)1)) { + itype = 0; + } else if (lsame_(type__, (char *)"L", (ftnlen)1, (ftnlen)1)) { + itype = 1; + } else if (lsame_(type__, (char *)"U", (ftnlen)1, (ftnlen)1)) { + itype = 2; + } else if (lsame_(type__, (char *)"H", (ftnlen)1, (ftnlen)1)) { + itype = 3; + } else if (lsame_(type__, (char *)"B", (ftnlen)1, (ftnlen)1)) { + itype = 4; + } else if (lsame_(type__, (char *)"Q", (ftnlen)1, (ftnlen)1)) { + itype = 5; + } else if (lsame_(type__, (char *)"Z", (ftnlen)1, (ftnlen)1)) { + itype = 6; + } else { + itype = -1; + } + + if (itype == -1) { + *info = -1; + } else if (*cfrom == 0. || disnan_(cfrom)) { + *info = -4; + } else if (disnan_(cto)) { + *info = -5; + } else if (*m < 0) { + *info = -6; + } else if (*n < 0 || itype == 4 && *n != *m || itype == 5 && *n != *m) { + *info = -7; + } else if (itype <= 3 && *lda < max(1,*m)) { + *info = -9; + } else if (itype >= 4) { +/* Computing MAX */ + i__1 = *m - 1; + if (*kl < 0 || *kl > max(i__1,0)) { + *info = -2; + } else /* if(complicated condition) */ { +/* Computing MAX */ + i__1 = *n - 1; + if (*ku < 0 || *ku > max(i__1,0) || (itype == 4 || itype == 5) && + *kl != *ku) { + *info = -3; + } else if (itype == 4 && *lda < *kl + 1 || itype == 5 && *lda < * + ku + 1 || itype == 6 && *lda < (*kl << 1) + *ku + 1) { + *info = -9; + } + } + } + + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DLASCL", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*n == 0 || *m == 0) { + return 0; + } + +/* Get machine parameters */ + + smlnum = dlamch_((char *)"S", (ftnlen)1); + bignum = 1. / smlnum; + + cfromc = *cfrom; + ctoc = *cto; + +L10: + cfrom1 = cfromc * smlnum; + if (cfrom1 == cfromc) { +/* CFROMC is an inf. Multiply by a correctly signed zero for */ +/* finite CTOC, or a NaN if CTOC is infinite. */ + mul = ctoc / cfromc; + done = TRUE_; + cto1 = ctoc; + } else { + cto1 = ctoc / bignum; + if (cto1 == ctoc) { +/* CTOC is either 0 or an inf. In both cases, CTOC itself */ +/* serves as the correct multiplication factor. */ + mul = ctoc; + done = TRUE_; + cfromc = 1.; + } else if (abs(cfrom1) > abs(ctoc) && ctoc != 0.) { + mul = smlnum; + done = FALSE_; + cfromc = cfrom1; + } else if (abs(cto1) > abs(cfromc)) { + mul = bignum; + done = FALSE_; + ctoc = cto1; + } else { + mul = ctoc / cfromc; + done = TRUE_; + if (mul == 1.) { + return 0; + } + } + } + + if (itype == 0) { + +/* Full matrix */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] *= mul; +/* L20: */ + } +/* L30: */ + } + + } else if (itype == 1) { + +/* Lower triangular matrix */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = j; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] *= mul; +/* L40: */ + } +/* L50: */ + } + + } else if (itype == 2) { + +/* Upper triangular matrix */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = min(j,*m); + for (i__ = 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] *= mul; +/* L60: */ + } +/* L70: */ + } + + } else if (itype == 3) { + +/* Upper Hessenberg matrix */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { +/* Computing MIN */ + i__3 = j + 1; + i__2 = min(i__3,*m); + for (i__ = 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] *= mul; +/* L80: */ + } +/* L90: */ + } + + } else if (itype == 4) { + +/* Lower half of a symmetric band matrix */ + + k3 = *kl + 1; + k4 = *n + 1; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { +/* Computing MIN */ + i__3 = k3, i__4 = k4 - j; + i__2 = min(i__3,i__4); + for (i__ = 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] *= mul; +/* L100: */ + } +/* L110: */ + } + + } else if (itype == 5) { + +/* Upper half of a symmetric band matrix */ + + k1 = *ku + 2; + k3 = *ku + 1; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { +/* Computing MAX */ + i__2 = k1 - j; + i__3 = k3; + for (i__ = max(i__2,1); i__ <= i__3; ++i__) { + a[i__ + j * a_dim1] *= mul; +/* L120: */ + } +/* L130: */ + } + + } else if (itype == 6) { + +/* Band matrix */ + + k1 = *kl + *ku + 2; + k2 = *kl + 1; + k3 = (*kl << 1) + *ku + 1; + k4 = *kl + *ku + 1 + *m; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { +/* Computing MAX */ + i__3 = k1 - j; +/* Computing MIN */ + i__4 = k3, i__5 = k4 - j; + i__2 = min(i__4,i__5); + for (i__ = max(i__3,k2); i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] *= mul; +/* L140: */ + } +/* L150: */ + } + + } + + if (! done) { + goto L10; + } + + return 0; + +/* End of DLASCL */ + +} /* dlascl_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlasd4.cpp b/lib/linalg/dlasd4.cpp new file mode 100644 index 0000000000..b0d8d1f7fe --- /dev/null +++ b/lib/linalg/dlasd4.cpp @@ -0,0 +1,1198 @@ +/* fortran/dlasd4.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DLASD4 computes the square root of the i-th updated eigenvalue of a positive symmetric rank-one + modification to a positive diagonal matrix. Used by dbdsdc. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLASD4 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLASD4( N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER I, INFO, N */ +/* DOUBLE PRECISION RHO, SIGMA */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION D( * ), DELTA( * ), WORK( * ), Z( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > This subroutine computes the square root of the I-th updated */ +/* > eigenvalue of a positive symmetric rank-one modification to */ +/* > a positive diagonal matrix whose entries are given as the squares */ +/* > of the corresponding entries in the array d, and that */ +/* > */ +/* > 0 <= D(i) < D(j) for i < j */ +/* > */ +/* > and that RHO > 0. This is arranged by the calling routine, and is */ +/* > no loss in generality. The rank-one modified system is thus */ +/* > */ +/* > diag( D ) * diag( D ) + RHO * Z * Z_transpose. */ +/* > */ +/* > where we assume the Euclidean norm of Z is 1. */ +/* > */ +/* > The method consists of approximating the rational functions in the */ +/* > secular equation by simpler interpolating rational functions. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The length of all arrays. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] I */ +/* > \verbatim */ +/* > I is INTEGER */ +/* > The index of the eigenvalue to be computed. 1 <= I <= N. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension ( N ) */ +/* > The original eigenvalues. It is assumed that they are in */ +/* > order, 0 <= D(I) < D(J) for I < J. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] Z */ +/* > \verbatim */ +/* > Z is DOUBLE PRECISION array, dimension ( N ) */ +/* > The components of the updating vector. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] DELTA */ +/* > \verbatim */ +/* > DELTA is DOUBLE PRECISION array, dimension ( N ) */ +/* > If N .ne. 1, DELTA contains (D(j) - sigma_I) in its j-th */ +/* > component. If N = 1, then DELTA(1) = 1. The vector DELTA */ +/* > contains the information necessary to construct the */ +/* > (singular) eigenvectors. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] RHO */ +/* > \verbatim */ +/* > RHO is DOUBLE PRECISION */ +/* > The scalar in the symmetric updating formula. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] SIGMA */ +/* > \verbatim */ +/* > SIGMA is DOUBLE PRECISION */ +/* > The computed sigma_I, the I-th updated eigenvalue. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension ( N ) */ +/* > If N .ne. 1, WORK contains (D(j) + sigma_I) in its j-th */ +/* > component. If N = 1, then WORK( 1 ) = 1. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > > 0: if INFO = 1, the updating process failed. */ +/* > \endverbatim */ + +/* > \par Internal Parameters: */ +/* ========================= */ +/* > */ +/* > \verbatim */ +/* > Logical variable ORGATI (origin-at-i?) is used for distinguishing */ +/* > whether D(i) or D(i+1) is treated as the origin. */ +/* > */ +/* > ORGATI = .true. origin at i */ +/* > ORGATI = .false. origin at i+1 */ +/* > */ +/* > Logical variable SWTCH3 (switch-for-3-poles?) is for noting */ +/* > if we are working with THREE poles! */ +/* > */ +/* > MAXIT is the maximum number of iterations allowed for each */ +/* > eigenvalue. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup OTHERauxiliary */ + +/* > \par Contributors: */ +/* ================== */ +/* > */ +/* > Ren-Cang Li, Computer Science Division, University of California */ +/* > at Berkeley, USA */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dlasd4_(integer *n, integer *i__, doublereal *d__, + doublereal *z__, doublereal *delta, doublereal *rho, doublereal * + sigma, doublereal *work, integer *info) +{ + /* System generated locals */ + integer i__1; + doublereal d__1; + + /* Builtin functions */ + double sqrt(doublereal); + + /* Local variables */ + doublereal a, b, c__; + integer j; + doublereal w, dd[3]; + integer ii; + doublereal dw, zz[3]; + integer ip1; + doublereal sq2, eta, phi, eps, tau, psi; + integer iim1, iip1; + doublereal tau2, dphi, sglb, dpsi, sgub; + integer iter; + doublereal temp, prew, temp1, temp2, dtiim, delsq, dtiip; + integer niter; + doublereal dtisq; + logical swtch; + doublereal dtnsq; + extern /* Subroutine */ int dlaed6_(integer *, logical *, doublereal *, + doublereal *, doublereal *, doublereal *, doublereal *, integer *) + , dlasd5_(integer *, doublereal *, doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *); + doublereal delsq2, dtnsq1; + logical swtch3; + extern doublereal dlamch_(char *, ftnlen); + logical orgati; + doublereal erretm, dtipsq, rhoinv; + logical geomavg; + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Local Arrays .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Since this routine is called in an inner loop, we do no argument */ +/* checking. */ + +/* Quick return for N=1 and 2. */ + + /* Parameter adjustments */ + --work; + --delta; + --z__; + --d__; + + /* Function Body */ + *info = 0; + if (*n == 1) { + +/* Presumably, I=1 upon entry */ + + *sigma = sqrt(d__[1] * d__[1] + *rho * z__[1] * z__[1]); + delta[1] = 1.; + work[1] = 1.; + return 0; + } + if (*n == 2) { + dlasd5_(i__, &d__[1], &z__[1], &delta[1], rho, sigma, &work[1]); + return 0; + } + +/* Compute machine epsilon */ + + eps = dlamch_((char *)"Epsilon", (ftnlen)7); + rhoinv = 1. / *rho; + tau2 = 0.; + +/* The case I = N */ + + if (*i__ == *n) { + +/* Initialize some basic variables */ + + ii = *n - 1; + niter = 1; + +/* Calculate initial guess */ + + temp = *rho / 2.; + +/* If ||Z||_2 is not one, then TEMP should be set to */ +/* RHO * ||Z||_2^2 / TWO */ + + temp1 = temp / (d__[*n] + sqrt(d__[*n] * d__[*n] + temp)); + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + work[j] = d__[j] + d__[*n] + temp1; + delta[j] = d__[j] - d__[*n] - temp1; +/* L10: */ + } + + psi = 0.; + i__1 = *n - 2; + for (j = 1; j <= i__1; ++j) { + psi += z__[j] * z__[j] / (delta[j] * work[j]); +/* L20: */ + } + + c__ = rhoinv + psi; + w = c__ + z__[ii] * z__[ii] / (delta[ii] * work[ii]) + z__[*n] * z__[* + n] / (delta[*n] * work[*n]); + + if (w <= 0.) { + temp1 = sqrt(d__[*n] * d__[*n] + *rho); + temp = z__[*n - 1] * z__[*n - 1] / ((d__[*n - 1] + temp1) * (d__[* + n] - d__[*n - 1] + *rho / (d__[*n] + temp1))) + z__[*n] * + z__[*n] / *rho; + +/* The following TAU2 is to approximate */ +/* SIGMA_n^2 - D( N )*D( N ) */ + + if (c__ <= temp) { + tau = *rho; + } else { + delsq = (d__[*n] - d__[*n - 1]) * (d__[*n] + d__[*n - 1]); + a = -c__ * delsq + z__[*n - 1] * z__[*n - 1] + z__[*n] * z__[* + n]; + b = z__[*n] * z__[*n] * delsq; + if (a < 0.) { + tau2 = b * 2. / (sqrt(a * a + b * 4. * c__) - a); + } else { + tau2 = (a + sqrt(a * a + b * 4. * c__)) / (c__ * 2.); + } + tau = tau2 / (d__[*n] + sqrt(d__[*n] * d__[*n] + tau2)); + } + +/* It can be proved that */ +/* D(N)^2+RHO/2 <= SIGMA_n^2 < D(N)^2+TAU2 <= D(N)^2+RHO */ + + } else { + delsq = (d__[*n] - d__[*n - 1]) * (d__[*n] + d__[*n - 1]); + a = -c__ * delsq + z__[*n - 1] * z__[*n - 1] + z__[*n] * z__[*n]; + b = z__[*n] * z__[*n] * delsq; + +/* The following TAU2 is to approximate */ +/* SIGMA_n^2 - D( N )*D( N ) */ + + if (a < 0.) { + tau2 = b * 2. / (sqrt(a * a + b * 4. * c__) - a); + } else { + tau2 = (a + sqrt(a * a + b * 4. * c__)) / (c__ * 2.); + } + tau = tau2 / (d__[*n] + sqrt(d__[*n] * d__[*n] + tau2)); + +/* It can be proved that */ +/* D(N)^2 < D(N)^2+TAU2 < SIGMA(N)^2 < D(N)^2+RHO/2 */ + + } + +/* The following TAU is to approximate SIGMA_n - D( N ) */ + +/* TAU = TAU2 / ( D( N )+SQRT( D( N )*D( N )+TAU2 ) ) */ + + *sigma = d__[*n] + tau; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + delta[j] = d__[j] - d__[*n] - tau; + work[j] = d__[j] + d__[*n] + tau; +/* L30: */ + } + +/* Evaluate PSI and the derivative DPSI */ + + dpsi = 0.; + psi = 0.; + erretm = 0.; + i__1 = ii; + for (j = 1; j <= i__1; ++j) { + temp = z__[j] / (delta[j] * work[j]); + psi += z__[j] * temp; + dpsi += temp * temp; + erretm += psi; +/* L40: */ + } + erretm = abs(erretm); + +/* Evaluate PHI and the derivative DPHI */ + + temp = z__[*n] / (delta[*n] * work[*n]); + phi = z__[*n] * temp; + dphi = temp * temp; + erretm = (-phi - psi) * 8. + erretm - phi + rhoinv; +/* $ + ABS( TAU2 )*( DPSI+DPHI ) */ + + w = rhoinv + phi + psi; + +/* Test for convergence */ + + if (abs(w) <= eps * erretm) { + goto L240; + } + +/* Calculate the new step */ + + ++niter; + dtnsq1 = work[*n - 1] * delta[*n - 1]; + dtnsq = work[*n] * delta[*n]; + c__ = w - dtnsq1 * dpsi - dtnsq * dphi; + a = (dtnsq + dtnsq1) * w - dtnsq * dtnsq1 * (dpsi + dphi); + b = dtnsq * dtnsq1 * w; + if (c__ < 0.) { + c__ = abs(c__); + } + if (c__ == 0.) { + eta = *rho - *sigma * *sigma; + } else if (a >= 0.) { + eta = (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (c__ + * 2.); + } else { + eta = b * 2. / (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1))) + ); + } + +/* Note, eta should be positive if w is negative, and */ +/* eta should be negative otherwise. However, */ +/* if for some reason caused by roundoff, eta*w > 0, */ +/* we simply use one Newton step instead. This way */ +/* will guarantee eta*w < 0. */ + + if (w * eta > 0.) { + eta = -w / (dpsi + dphi); + } + temp = eta - dtnsq; + if (temp > *rho) { + eta = *rho + dtnsq; + } + + eta /= *sigma + sqrt(eta + *sigma * *sigma); + tau += eta; + *sigma += eta; + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + delta[j] -= eta; + work[j] += eta; +/* L50: */ + } + +/* Evaluate PSI and the derivative DPSI */ + + dpsi = 0.; + psi = 0.; + erretm = 0.; + i__1 = ii; + for (j = 1; j <= i__1; ++j) { + temp = z__[j] / (work[j] * delta[j]); + psi += z__[j] * temp; + dpsi += temp * temp; + erretm += psi; +/* L60: */ + } + erretm = abs(erretm); + +/* Evaluate PHI and the derivative DPHI */ + + tau2 = work[*n] * delta[*n]; + temp = z__[*n] / tau2; + phi = z__[*n] * temp; + dphi = temp * temp; + erretm = (-phi - psi) * 8. + erretm - phi + rhoinv; +/* $ + ABS( TAU2 )*( DPSI+DPHI ) */ + + w = rhoinv + phi + psi; + +/* Main loop to update the values of the array DELTA */ + + iter = niter + 1; + + for (niter = iter; niter <= 400; ++niter) { + +/* Test for convergence */ + + if (abs(w) <= eps * erretm) { + goto L240; + } + +/* Calculate the new step */ + + dtnsq1 = work[*n - 1] * delta[*n - 1]; + dtnsq = work[*n] * delta[*n]; + c__ = w - dtnsq1 * dpsi - dtnsq * dphi; + a = (dtnsq + dtnsq1) * w - dtnsq1 * dtnsq * (dpsi + dphi); + b = dtnsq1 * dtnsq * w; + if (a >= 0.) { + eta = (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / ( + c__ * 2.); + } else { + eta = b * 2. / (a - sqrt((d__1 = a * a - b * 4. * c__, abs( + d__1)))); + } + +/* Note, eta should be positive if w is negative, and */ +/* eta should be negative otherwise. However, */ +/* if for some reason caused by roundoff, eta*w > 0, */ +/* we simply use one Newton step instead. This way */ +/* will guarantee eta*w < 0. */ + + if (w * eta > 0.) { + eta = -w / (dpsi + dphi); + } + temp = eta - dtnsq; + if (temp <= 0.) { + eta /= 2.; + } + + eta /= *sigma + sqrt(eta + *sigma * *sigma); + tau += eta; + *sigma += eta; + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + delta[j] -= eta; + work[j] += eta; +/* L70: */ + } + +/* Evaluate PSI and the derivative DPSI */ + + dpsi = 0.; + psi = 0.; + erretm = 0.; + i__1 = ii; + for (j = 1; j <= i__1; ++j) { + temp = z__[j] / (work[j] * delta[j]); + psi += z__[j] * temp; + dpsi += temp * temp; + erretm += psi; +/* L80: */ + } + erretm = abs(erretm); + +/* Evaluate PHI and the derivative DPHI */ + + tau2 = work[*n] * delta[*n]; + temp = z__[*n] / tau2; + phi = z__[*n] * temp; + dphi = temp * temp; + erretm = (-phi - psi) * 8. + erretm - phi + rhoinv; +/* $ + ABS( TAU2 )*( DPSI+DPHI ) */ + + w = rhoinv + phi + psi; +/* L90: */ + } + +/* Return with INFO = 1, NITER = MAXIT and not converged */ + + *info = 1; + goto L240; + +/* End for the case I = N */ + + } else { + +/* The case for I < N */ + + niter = 1; + ip1 = *i__ + 1; + +/* Calculate initial guess */ + + delsq = (d__[ip1] - d__[*i__]) * (d__[ip1] + d__[*i__]); + delsq2 = delsq / 2.; + sq2 = sqrt((d__[*i__] * d__[*i__] + d__[ip1] * d__[ip1]) / 2.); + temp = delsq2 / (d__[*i__] + sq2); + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + work[j] = d__[j] + d__[*i__] + temp; + delta[j] = d__[j] - d__[*i__] - temp; +/* L100: */ + } + + psi = 0.; + i__1 = *i__ - 1; + for (j = 1; j <= i__1; ++j) { + psi += z__[j] * z__[j] / (work[j] * delta[j]); +/* L110: */ + } + + phi = 0.; + i__1 = *i__ + 2; + for (j = *n; j >= i__1; --j) { + phi += z__[j] * z__[j] / (work[j] * delta[j]); +/* L120: */ + } + c__ = rhoinv + psi + phi; + w = c__ + z__[*i__] * z__[*i__] / (work[*i__] * delta[*i__]) + z__[ + ip1] * z__[ip1] / (work[ip1] * delta[ip1]); + + geomavg = FALSE_; + if (w > 0.) { + +/* d(i)^2 < the ith sigma^2 < (d(i)^2+d(i+1)^2)/2 */ + +/* We choose d(i) as origin. */ + + orgati = TRUE_; + ii = *i__; + sglb = 0.; + sgub = delsq2 / (d__[*i__] + sq2); + a = c__ * delsq + z__[*i__] * z__[*i__] + z__[ip1] * z__[ip1]; + b = z__[*i__] * z__[*i__] * delsq; + if (a > 0.) { + tau2 = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs( + d__1)))); + } else { + tau2 = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / + (c__ * 2.); + } + +/* TAU2 now is an estimation of SIGMA^2 - D( I )^2. The */ +/* following, however, is the corresponding estimation of */ +/* SIGMA - D( I ). */ + + tau = tau2 / (d__[*i__] + sqrt(d__[*i__] * d__[*i__] + tau2)); + temp = sqrt(eps); + if (d__[*i__] <= temp * d__[ip1] && (d__1 = z__[*i__], abs(d__1)) + <= temp && d__[*i__] > 0.) { +/* Computing MIN */ + d__1 = d__[*i__] * 10.; + tau = min(d__1,sgub); + geomavg = TRUE_; + } + } else { + +/* (d(i)^2+d(i+1)^2)/2 <= the ith sigma^2 < d(i+1)^2/2 */ + +/* We choose d(i+1) as origin. */ + + orgati = FALSE_; + ii = ip1; + sglb = -delsq2 / (d__[ii] + sq2); + sgub = 0.; + a = c__ * delsq - z__[*i__] * z__[*i__] - z__[ip1] * z__[ip1]; + b = z__[ip1] * z__[ip1] * delsq; + if (a < 0.) { + tau2 = b * 2. / (a - sqrt((d__1 = a * a + b * 4. * c__, abs( + d__1)))); + } else { + tau2 = -(a + sqrt((d__1 = a * a + b * 4. * c__, abs(d__1)))) / + (c__ * 2.); + } + +/* TAU2 now is an estimation of SIGMA^2 - D( IP1 )^2. The */ +/* following, however, is the corresponding estimation of */ +/* SIGMA - D( IP1 ). */ + + tau = tau2 / (d__[ip1] + sqrt((d__1 = d__[ip1] * d__[ip1] + tau2, + abs(d__1)))); + } + + *sigma = d__[ii] + tau; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + work[j] = d__[j] + d__[ii] + tau; + delta[j] = d__[j] - d__[ii] - tau; +/* L130: */ + } + iim1 = ii - 1; + iip1 = ii + 1; + +/* Evaluate PSI and the derivative DPSI */ + + dpsi = 0.; + psi = 0.; + erretm = 0.; + i__1 = iim1; + for (j = 1; j <= i__1; ++j) { + temp = z__[j] / (work[j] * delta[j]); + psi += z__[j] * temp; + dpsi += temp * temp; + erretm += psi; +/* L150: */ + } + erretm = abs(erretm); + +/* Evaluate PHI and the derivative DPHI */ + + dphi = 0.; + phi = 0.; + i__1 = iip1; + for (j = *n; j >= i__1; --j) { + temp = z__[j] / (work[j] * delta[j]); + phi += z__[j] * temp; + dphi += temp * temp; + erretm += phi; +/* L160: */ + } + + w = rhoinv + phi + psi; + +/* W is the value of the secular function with */ +/* its ii-th element removed. */ + + swtch3 = FALSE_; + if (orgati) { + if (w < 0.) { + swtch3 = TRUE_; + } + } else { + if (w > 0.) { + swtch3 = TRUE_; + } + } + if (ii == 1 || ii == *n) { + swtch3 = FALSE_; + } + + temp = z__[ii] / (work[ii] * delta[ii]); + dw = dpsi + dphi + temp * temp; + temp = z__[ii] * temp; + w += temp; + erretm = (phi - psi) * 8. + erretm + rhoinv * 2. + abs(temp) * 3.; +/* $ + ABS( TAU2 )*DW */ + +/* Test for convergence */ + + if (abs(w) <= eps * erretm) { + goto L240; + } + + if (w <= 0.) { + sglb = max(sglb,tau); + } else { + sgub = min(sgub,tau); + } + +/* Calculate the new step */ + + ++niter; + if (! swtch3) { + dtipsq = work[ip1] * delta[ip1]; + dtisq = work[*i__] * delta[*i__]; + if (orgati) { +/* Computing 2nd power */ + d__1 = z__[*i__] / dtisq; + c__ = w - dtipsq * dw + delsq * (d__1 * d__1); + } else { +/* Computing 2nd power */ + d__1 = z__[ip1] / dtipsq; + c__ = w - dtisq * dw - delsq * (d__1 * d__1); + } + a = (dtipsq + dtisq) * w - dtipsq * dtisq * dw; + b = dtipsq * dtisq * w; + if (c__ == 0.) { + if (a == 0.) { + if (orgati) { + a = z__[*i__] * z__[*i__] + dtipsq * dtipsq * (dpsi + + dphi); + } else { + a = z__[ip1] * z__[ip1] + dtisq * dtisq * (dpsi + + dphi); + } + } + eta = b / a; + } else if (a <= 0.) { + eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / ( + c__ * 2.); + } else { + eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs( + d__1)))); + } + } else { + +/* Interpolation using THREE most relevant poles */ + + dtiim = work[iim1] * delta[iim1]; + dtiip = work[iip1] * delta[iip1]; + temp = rhoinv + psi + phi; + if (orgati) { + temp1 = z__[iim1] / dtiim; + temp1 *= temp1; + c__ = temp - dtiip * (dpsi + dphi) - (d__[iim1] - d__[iip1]) * + (d__[iim1] + d__[iip1]) * temp1; + zz[0] = z__[iim1] * z__[iim1]; + if (dpsi < temp1) { + zz[2] = dtiip * dtiip * dphi; + } else { + zz[2] = dtiip * dtiip * (dpsi - temp1 + dphi); + } + } else { + temp1 = z__[iip1] / dtiip; + temp1 *= temp1; + c__ = temp - dtiim * (dpsi + dphi) - (d__[iip1] - d__[iim1]) * + (d__[iim1] + d__[iip1]) * temp1; + if (dphi < temp1) { + zz[0] = dtiim * dtiim * dpsi; + } else { + zz[0] = dtiim * dtiim * (dpsi + (dphi - temp1)); + } + zz[2] = z__[iip1] * z__[iip1]; + } + zz[1] = z__[ii] * z__[ii]; + dd[0] = dtiim; + dd[1] = delta[ii] * work[ii]; + dd[2] = dtiip; + dlaed6_(&niter, &orgati, &c__, dd, zz, &w, &eta, info); + + if (*info != 0) { + +/* If INFO is not 0, i.e., DLAED6 failed, switch back */ +/* to 2 pole interpolation. */ + + swtch3 = FALSE_; + *info = 0; + dtipsq = work[ip1] * delta[ip1]; + dtisq = work[*i__] * delta[*i__]; + if (orgati) { +/* Computing 2nd power */ + d__1 = z__[*i__] / dtisq; + c__ = w - dtipsq * dw + delsq * (d__1 * d__1); + } else { +/* Computing 2nd power */ + d__1 = z__[ip1] / dtipsq; + c__ = w - dtisq * dw - delsq * (d__1 * d__1); + } + a = (dtipsq + dtisq) * w - dtipsq * dtisq * dw; + b = dtipsq * dtisq * w; + if (c__ == 0.) { + if (a == 0.) { + if (orgati) { + a = z__[*i__] * z__[*i__] + dtipsq * dtipsq * ( + dpsi + dphi); + } else { + a = z__[ip1] * z__[ip1] + dtisq * dtisq * (dpsi + + dphi); + } + } + eta = b / a; + } else if (a <= 0.) { + eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) + / (c__ * 2.); + } else { + eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, + abs(d__1)))); + } + } + } + +/* Note, eta should be positive if w is negative, and */ +/* eta should be negative otherwise. However, */ +/* if for some reason caused by roundoff, eta*w > 0, */ +/* we simply use one Newton step instead. This way */ +/* will guarantee eta*w < 0. */ + + if (w * eta >= 0.) { + eta = -w / dw; + } + + eta /= *sigma + sqrt(*sigma * *sigma + eta); + temp = tau + eta; + if (temp > sgub || temp < sglb) { + if (w < 0.) { + eta = (sgub - tau) / 2.; + } else { + eta = (sglb - tau) / 2.; + } + if (geomavg) { + if (w < 0.) { + if (tau > 0.) { + eta = sqrt(sgub * tau) - tau; + } + } else { + if (sglb > 0.) { + eta = sqrt(sglb * tau) - tau; + } + } + } + } + + prew = w; + + tau += eta; + *sigma += eta; + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + work[j] += eta; + delta[j] -= eta; +/* L170: */ + } + +/* Evaluate PSI and the derivative DPSI */ + + dpsi = 0.; + psi = 0.; + erretm = 0.; + i__1 = iim1; + for (j = 1; j <= i__1; ++j) { + temp = z__[j] / (work[j] * delta[j]); + psi += z__[j] * temp; + dpsi += temp * temp; + erretm += psi; +/* L180: */ + } + erretm = abs(erretm); + +/* Evaluate PHI and the derivative DPHI */ + + dphi = 0.; + phi = 0.; + i__1 = iip1; + for (j = *n; j >= i__1; --j) { + temp = z__[j] / (work[j] * delta[j]); + phi += z__[j] * temp; + dphi += temp * temp; + erretm += phi; +/* L190: */ + } + + tau2 = work[ii] * delta[ii]; + temp = z__[ii] / tau2; + dw = dpsi + dphi + temp * temp; + temp = z__[ii] * temp; + w = rhoinv + phi + psi + temp; + erretm = (phi - psi) * 8. + erretm + rhoinv * 2. + abs(temp) * 3.; +/* $ + ABS( TAU2 )*DW */ + + swtch = FALSE_; + if (orgati) { + if (-w > abs(prew) / 10.) { + swtch = TRUE_; + } + } else { + if (w > abs(prew) / 10.) { + swtch = TRUE_; + } + } + +/* Main loop to update the values of the array DELTA and WORK */ + + iter = niter + 1; + + for (niter = iter; niter <= 400; ++niter) { + +/* Test for convergence */ + + if (abs(w) <= eps * erretm) { +/* $ .OR. (SGUB-SGLB).LE.EIGHT*ABS(SGUB+SGLB) ) THEN */ + goto L240; + } + + if (w <= 0.) { + sglb = max(sglb,tau); + } else { + sgub = min(sgub,tau); + } + +/* Calculate the new step */ + + if (! swtch3) { + dtipsq = work[ip1] * delta[ip1]; + dtisq = work[*i__] * delta[*i__]; + if (! swtch) { + if (orgati) { +/* Computing 2nd power */ + d__1 = z__[*i__] / dtisq; + c__ = w - dtipsq * dw + delsq * (d__1 * d__1); + } else { +/* Computing 2nd power */ + d__1 = z__[ip1] / dtipsq; + c__ = w - dtisq * dw - delsq * (d__1 * d__1); + } + } else { + temp = z__[ii] / (work[ii] * delta[ii]); + if (orgati) { + dpsi += temp * temp; + } else { + dphi += temp * temp; + } + c__ = w - dtisq * dpsi - dtipsq * dphi; + } + a = (dtipsq + dtisq) * w - dtipsq * dtisq * dw; + b = dtipsq * dtisq * w; + if (c__ == 0.) { + if (a == 0.) { + if (! swtch) { + if (orgati) { + a = z__[*i__] * z__[*i__] + dtipsq * dtipsq * + (dpsi + dphi); + } else { + a = z__[ip1] * z__[ip1] + dtisq * dtisq * ( + dpsi + dphi); + } + } else { + a = dtisq * dtisq * dpsi + dtipsq * dtipsq * dphi; + } + } + eta = b / a; + } else if (a <= 0.) { + eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) + / (c__ * 2.); + } else { + eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, + abs(d__1)))); + } + } else { + +/* Interpolation using THREE most relevant poles */ + + dtiim = work[iim1] * delta[iim1]; + dtiip = work[iip1] * delta[iip1]; + temp = rhoinv + psi + phi; + if (swtch) { + c__ = temp - dtiim * dpsi - dtiip * dphi; + zz[0] = dtiim * dtiim * dpsi; + zz[2] = dtiip * dtiip * dphi; + } else { + if (orgati) { + temp1 = z__[iim1] / dtiim; + temp1 *= temp1; + temp2 = (d__[iim1] - d__[iip1]) * (d__[iim1] + d__[ + iip1]) * temp1; + c__ = temp - dtiip * (dpsi + dphi) - temp2; + zz[0] = z__[iim1] * z__[iim1]; + if (dpsi < temp1) { + zz[2] = dtiip * dtiip * dphi; + } else { + zz[2] = dtiip * dtiip * (dpsi - temp1 + dphi); + } + } else { + temp1 = z__[iip1] / dtiip; + temp1 *= temp1; + temp2 = (d__[iip1] - d__[iim1]) * (d__[iim1] + d__[ + iip1]) * temp1; + c__ = temp - dtiim * (dpsi + dphi) - temp2; + if (dphi < temp1) { + zz[0] = dtiim * dtiim * dpsi; + } else { + zz[0] = dtiim * dtiim * (dpsi + (dphi - temp1)); + } + zz[2] = z__[iip1] * z__[iip1]; + } + } + dd[0] = dtiim; + dd[1] = delta[ii] * work[ii]; + dd[2] = dtiip; + dlaed6_(&niter, &orgati, &c__, dd, zz, &w, &eta, info); + + if (*info != 0) { + +/* If INFO is not 0, i.e., DLAED6 failed, switch */ +/* back to two pole interpolation */ + + swtch3 = FALSE_; + *info = 0; + dtipsq = work[ip1] * delta[ip1]; + dtisq = work[*i__] * delta[*i__]; + if (! swtch) { + if (orgati) { +/* Computing 2nd power */ + d__1 = z__[*i__] / dtisq; + c__ = w - dtipsq * dw + delsq * (d__1 * d__1); + } else { +/* Computing 2nd power */ + d__1 = z__[ip1] / dtipsq; + c__ = w - dtisq * dw - delsq * (d__1 * d__1); + } + } else { + temp = z__[ii] / (work[ii] * delta[ii]); + if (orgati) { + dpsi += temp * temp; + } else { + dphi += temp * temp; + } + c__ = w - dtisq * dpsi - dtipsq * dphi; + } + a = (dtipsq + dtisq) * w - dtipsq * dtisq * dw; + b = dtipsq * dtisq * w; + if (c__ == 0.) { + if (a == 0.) { + if (! swtch) { + if (orgati) { + a = z__[*i__] * z__[*i__] + dtipsq * + dtipsq * (dpsi + dphi); + } else { + a = z__[ip1] * z__[ip1] + dtisq * dtisq * + (dpsi + dphi); + } + } else { + a = dtisq * dtisq * dpsi + dtipsq * dtipsq * + dphi; + } + } + eta = b / a; + } else if (a <= 0.) { + eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs( + d__1)))) / (c__ * 2.); + } else { + eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, + abs(d__1)))); + } + } + } + +/* Note, eta should be positive if w is negative, and */ +/* eta should be negative otherwise. However, */ +/* if for some reason caused by roundoff, eta*w > 0, */ +/* we simply use one Newton step instead. This way */ +/* will guarantee eta*w < 0. */ + + if (w * eta >= 0.) { + eta = -w / dw; + } + + eta /= *sigma + sqrt(*sigma * *sigma + eta); + temp = tau + eta; + if (temp > sgub || temp < sglb) { + if (w < 0.) { + eta = (sgub - tau) / 2.; + } else { + eta = (sglb - tau) / 2.; + } + if (geomavg) { + if (w < 0.) { + if (tau > 0.) { + eta = sqrt(sgub * tau) - tau; + } + } else { + if (sglb > 0.) { + eta = sqrt(sglb * tau) - tau; + } + } + } + } + + prew = w; + + tau += eta; + *sigma += eta; + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + work[j] += eta; + delta[j] -= eta; +/* L200: */ + } + +/* Evaluate PSI and the derivative DPSI */ + + dpsi = 0.; + psi = 0.; + erretm = 0.; + i__1 = iim1; + for (j = 1; j <= i__1; ++j) { + temp = z__[j] / (work[j] * delta[j]); + psi += z__[j] * temp; + dpsi += temp * temp; + erretm += psi; +/* L210: */ + } + erretm = abs(erretm); + +/* Evaluate PHI and the derivative DPHI */ + + dphi = 0.; + phi = 0.; + i__1 = iip1; + for (j = *n; j >= i__1; --j) { + temp = z__[j] / (work[j] * delta[j]); + phi += z__[j] * temp; + dphi += temp * temp; + erretm += phi; +/* L220: */ + } + + tau2 = work[ii] * delta[ii]; + temp = z__[ii] / tau2; + dw = dpsi + dphi + temp * temp; + temp = z__[ii] * temp; + w = rhoinv + phi + psi + temp; + erretm = (phi - psi) * 8. + erretm + rhoinv * 2. + abs(temp) * 3.; +/* $ + ABS( TAU2 )*DW */ + + if (w * prew > 0. && abs(w) > abs(prew) / 10.) { + swtch = ! swtch; + } + +/* L230: */ + } + +/* Return with INFO = 1, NITER = MAXIT and not converged */ + + *info = 1; + + } + +L240: + return 0; + +/* End of DLASD4 */ + +} /* dlasd4_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlasd5.cpp b/lib/linalg/dlasd5.cpp new file mode 100644 index 0000000000..a789475cad --- /dev/null +++ b/lib/linalg/dlasd5.cpp @@ -0,0 +1,264 @@ +/* fortran/dlasd5.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DLASD5 computes the square root of the i-th eigenvalue of a positive symmetric rank-one modific +ation of a 2-by-2 diagonal matrix. Used by sbdsdc. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLASD5 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLASD5( I, D, Z, DELTA, RHO, DSIGMA, WORK ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER I */ +/* DOUBLE PRECISION DSIGMA, RHO */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION D( 2 ), DELTA( 2 ), WORK( 2 ), Z( 2 ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > This subroutine computes the square root of the I-th eigenvalue */ +/* > of a positive symmetric rank-one modification of a 2-by-2 diagonal */ +/* > matrix */ +/* > */ +/* > diag( D ) * diag( D ) + RHO * Z * transpose(Z) . */ +/* > */ +/* > The diagonal entries in the array D are assumed to satisfy */ +/* > */ +/* > 0 <= D(i) < D(j) for i < j . */ +/* > */ +/* > We also assume RHO > 0 and that the Euclidean norm of the vector */ +/* > Z is one. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] I */ +/* > \verbatim */ +/* > I is INTEGER */ +/* > The index of the eigenvalue to be computed. I = 1 or I = 2. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension ( 2 ) */ +/* > The original eigenvalues. We assume 0 <= D(1) < D(2). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] Z */ +/* > \verbatim */ +/* > Z is DOUBLE PRECISION array, dimension ( 2 ) */ +/* > The components of the updating vector. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] DELTA */ +/* > \verbatim */ +/* > DELTA is DOUBLE PRECISION array, dimension ( 2 ) */ +/* > Contains (D(j) - sigma_I) in its j-th component. */ +/* > The vector DELTA contains the information necessary */ +/* > to construct the eigenvectors. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] RHO */ +/* > \verbatim */ +/* > RHO is DOUBLE PRECISION */ +/* > The scalar in the symmetric updating formula. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] DSIGMA */ +/* > \verbatim */ +/* > DSIGMA is DOUBLE PRECISION */ +/* > The computed sigma_I, the I-th updated eigenvalue. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension ( 2 ) */ +/* > WORK contains (D(j) + sigma_I) in its j-th component. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup OTHERauxiliary */ + +/* > \par Contributors: */ +/* ================== */ +/* > */ +/* > Ren-Cang Li, Computer Science Division, University of California */ +/* > at Berkeley, USA */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dlasd5_(integer *i__, doublereal *d__, doublereal *z__, + doublereal *delta, doublereal *rho, doublereal *dsigma, doublereal * + work) +{ + /* System generated locals */ + doublereal d__1; + + /* Builtin functions */ + double sqrt(doublereal); + + /* Local variables */ + doublereal b, c__, w, del, tau, delsq; + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + + /* Parameter adjustments */ + --work; + --delta; + --z__; + --d__; + + /* Function Body */ + del = d__[2] - d__[1]; + delsq = del * (d__[2] + d__[1]); + if (*i__ == 1) { + w = *rho * 4. * (z__[2] * z__[2] / (d__[1] + d__[2] * 3.) - z__[1] * + z__[1] / (d__[1] * 3. + d__[2])) / del + 1.; + if (w > 0.) { + b = delsq + *rho * (z__[1] * z__[1] + z__[2] * z__[2]); + c__ = *rho * z__[1] * z__[1] * delsq; + +/* B > ZERO, always */ + +/* The following TAU is DSIGMA * DSIGMA - D( 1 ) * D( 1 ) */ + + tau = c__ * 2. / (b + sqrt((d__1 = b * b - c__ * 4., abs(d__1)))); + +/* The following TAU is DSIGMA - D( 1 ) */ + + tau /= d__[1] + sqrt(d__[1] * d__[1] + tau); + *dsigma = d__[1] + tau; + delta[1] = -tau; + delta[2] = del - tau; + work[1] = d__[1] * 2. + tau; + work[2] = d__[1] + tau + d__[2]; +/* DELTA( 1 ) = -Z( 1 ) / TAU */ +/* DELTA( 2 ) = Z( 2 ) / ( DEL-TAU ) */ + } else { + b = -delsq + *rho * (z__[1] * z__[1] + z__[2] * z__[2]); + c__ = *rho * z__[2] * z__[2] * delsq; + +/* The following TAU is DSIGMA * DSIGMA - D( 2 ) * D( 2 ) */ + + if (b > 0.) { + tau = c__ * -2. / (b + sqrt(b * b + c__ * 4.)); + } else { + tau = (b - sqrt(b * b + c__ * 4.)) / 2.; + } + +/* The following TAU is DSIGMA - D( 2 ) */ + + tau /= d__[2] + sqrt((d__1 = d__[2] * d__[2] + tau, abs(d__1))); + *dsigma = d__[2] + tau; + delta[1] = -(del + tau); + delta[2] = -tau; + work[1] = d__[1] + tau + d__[2]; + work[2] = d__[2] * 2. + tau; +/* DELTA( 1 ) = -Z( 1 ) / ( DEL+TAU ) */ +/* DELTA( 2 ) = -Z( 2 ) / TAU */ + } +/* TEMP = SQRT( DELTA( 1 )*DELTA( 1 )+DELTA( 2 )*DELTA( 2 ) ) */ +/* DELTA( 1 ) = DELTA( 1 ) / TEMP */ +/* DELTA( 2 ) = DELTA( 2 ) / TEMP */ + } else { + +/* Now I=2 */ + + b = -delsq + *rho * (z__[1] * z__[1] + z__[2] * z__[2]); + c__ = *rho * z__[2] * z__[2] * delsq; + +/* The following TAU is DSIGMA * DSIGMA - D( 2 ) * D( 2 ) */ + + if (b > 0.) { + tau = (b + sqrt(b * b + c__ * 4.)) / 2.; + } else { + tau = c__ * 2. / (-b + sqrt(b * b + c__ * 4.)); + } + +/* The following TAU is DSIGMA - D( 2 ) */ + + tau /= d__[2] + sqrt(d__[2] * d__[2] + tau); + *dsigma = d__[2] + tau; + delta[1] = -(del + tau); + delta[2] = -tau; + work[1] = d__[1] + tau + d__[2]; + work[2] = d__[2] * 2. + tau; +/* DELTA( 1 ) = -Z( 1 ) / ( DEL+TAU ) */ +/* DELTA( 2 ) = -Z( 2 ) / TAU */ +/* TEMP = SQRT( DELTA( 1 )*DELTA( 1 )+DELTA( 2 )*DELTA( 2 ) ) */ +/* DELTA( 1 ) = DELTA( 1 ) / TEMP */ +/* DELTA( 2 ) = DELTA( 2 ) / TEMP */ + } + return 0; + +/* End of DLASD5 */ + +} /* dlasd5_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlasd6.cpp b/lib/linalg/dlasd6.cpp new file mode 100644 index 0000000000..d3b6cddd86 --- /dev/null +++ b/lib/linalg/dlasd6.cpp @@ -0,0 +1,514 @@ +/* fortran/dlasd6.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__0 = 0; +static doublereal c_b7 = 1.; +static integer c__1 = 1; +static integer c_n1 = -1; + +/* > \brief \b DLASD6 computes the SVD of an updated upper bidiagonal matrix obtained by merging two smaller o +nes by appending a row. Used by sbdsdc. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLASD6 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLASD6( ICOMPQ, NL, NR, SQRE, D, VF, VL, ALPHA, BETA, */ +/* IDXQ, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, */ +/* LDGNUM, POLES, DIFL, DIFR, Z, K, C, S, WORK, */ +/* IWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER GIVPTR, ICOMPQ, INFO, K, LDGCOL, LDGNUM, NL, */ +/* $ NR, SQRE */ +/* DOUBLE PRECISION ALPHA, BETA, C, S */ +/* .. */ +/* .. Array Arguments .. */ +/* INTEGER GIVCOL( LDGCOL, * ), IDXQ( * ), IWORK( * ), */ +/* $ PERM( * ) */ +/* DOUBLE PRECISION D( * ), DIFL( * ), DIFR( * ), */ +/* $ GIVNUM( LDGNUM, * ), POLES( LDGNUM, * ), */ +/* $ VF( * ), VL( * ), WORK( * ), Z( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLASD6 computes the SVD of an updated upper bidiagonal matrix B */ +/* > obtained by merging two smaller ones by appending a row. This */ +/* > routine is used only for the problem which requires all singular */ +/* > values and optionally singular vector matrices in factored form. */ +/* > B is an N-by-M matrix with N = NL + NR + 1 and M = N + SQRE. */ +/* > A related subroutine, DLASD1, handles the case in which all singular */ +/* > values and singular vectors of the bidiagonal matrix are desired. */ +/* > */ +/* > DLASD6 computes the SVD as follows: */ +/* > */ +/* > ( D1(in) 0 0 0 ) */ +/* > B = U(in) * ( Z1**T a Z2**T b ) * VT(in) */ +/* > ( 0 0 D2(in) 0 ) */ +/* > */ +/* > = U(out) * ( D(out) 0) * VT(out) */ +/* > */ +/* > where Z**T = (Z1**T a Z2**T b) = u**T VT**T, and u is a vector of dimension M */ +/* > with ALPHA and BETA in the NL+1 and NL+2 th entries and zeros */ +/* > elsewhere; and the entry b is empty if SQRE = 0. */ +/* > */ +/* > The singular values of B can be computed using D1, D2, the first */ +/* > components of all the right singular vectors of the lower block, and */ +/* > the last components of all the right singular vectors of the upper */ +/* > block. These components are stored and updated in VF and VL, */ +/* > respectively, in DLASD6. Hence U and VT are not explicitly */ +/* > referenced. */ +/* > */ +/* > The singular values are stored in D. The algorithm consists of two */ +/* > stages: */ +/* > */ +/* > The first stage consists of deflating the size of the problem */ +/* > when there are multiple singular values or if there is a zero */ +/* > in the Z vector. For each such occurrence the dimension of the */ +/* > secular equation problem is reduced by one. This stage is */ +/* > performed by the routine DLASD7. */ +/* > */ +/* > The second stage consists of calculating the updated */ +/* > singular values. This is done by finding the roots of the */ +/* > secular equation via the routine DLASD4 (as called by DLASD8). */ +/* > This routine also updates VF and VL and computes the distances */ +/* > between the updated singular values and the old singular */ +/* > values. */ +/* > */ +/* > DLASD6 is called from DLASDA. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] ICOMPQ */ +/* > \verbatim */ +/* > ICOMPQ is INTEGER */ +/* > Specifies whether singular vectors are to be computed in */ +/* > factored form: */ +/* > = 0: Compute singular values only. */ +/* > = 1: Compute singular vectors in factored form as well. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] NL */ +/* > \verbatim */ +/* > NL is INTEGER */ +/* > The row dimension of the upper block. NL >= 1. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] NR */ +/* > \verbatim */ +/* > NR is INTEGER */ +/* > The row dimension of the lower block. NR >= 1. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] SQRE */ +/* > \verbatim */ +/* > SQRE is INTEGER */ +/* > = 0: the lower block is an NR-by-NR square matrix. */ +/* > = 1: the lower block is an NR-by-(NR+1) rectangular matrix. */ +/* > */ +/* > The bidiagonal matrix has row dimension N = NL + NR + 1, */ +/* > and column dimension M = N + SQRE. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension ( NL+NR+1 ). */ +/* > On entry D(1:NL,1:NL) contains the singular values of the */ +/* > upper block, and D(NL+2:N) contains the singular values */ +/* > of the lower block. On exit D(1:N) contains the singular */ +/* > values of the modified matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] VF */ +/* > \verbatim */ +/* > VF is DOUBLE PRECISION array, dimension ( M ) */ +/* > On entry, VF(1:NL+1) contains the first components of all */ +/* > right singular vectors of the upper block; and VF(NL+2:M) */ +/* > contains the first components of all right singular vectors */ +/* > of the lower block. On exit, VF contains the first components */ +/* > of all right singular vectors of the bidiagonal matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] VL */ +/* > \verbatim */ +/* > VL is DOUBLE PRECISION array, dimension ( M ) */ +/* > On entry, VL(1:NL+1) contains the last components of all */ +/* > right singular vectors of the upper block; and VL(NL+2:M) */ +/* > contains the last components of all right singular vectors of */ +/* > the lower block. On exit, VL contains the last components of */ +/* > all right singular vectors of the bidiagonal matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] ALPHA */ +/* > \verbatim */ +/* > ALPHA is DOUBLE PRECISION */ +/* > Contains the diagonal element associated with the added row. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] BETA */ +/* > \verbatim */ +/* > BETA is DOUBLE PRECISION */ +/* > Contains the off-diagonal element associated with the added */ +/* > row. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] IDXQ */ +/* > \verbatim */ +/* > IDXQ is INTEGER array, dimension ( N ) */ +/* > This contains the permutation which will reintegrate the */ +/* > subproblem just solved back into sorted order, i.e. */ +/* > D( IDXQ( I = 1, N ) ) will be in ascending order. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] PERM */ +/* > \verbatim */ +/* > PERM is INTEGER array, dimension ( N ) */ +/* > The permutations (from deflation and sorting) to be applied */ +/* > to each block. Not referenced if ICOMPQ = 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] GIVPTR */ +/* > \verbatim */ +/* > GIVPTR is INTEGER */ +/* > The number of Givens rotations which took place in this */ +/* > subproblem. Not referenced if ICOMPQ = 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] GIVCOL */ +/* > \verbatim */ +/* > GIVCOL is INTEGER array, dimension ( LDGCOL, 2 ) */ +/* > Each pair of numbers indicates a pair of columns to take place */ +/* > in a Givens rotation. Not referenced if ICOMPQ = 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDGCOL */ +/* > \verbatim */ +/* > LDGCOL is INTEGER */ +/* > leading dimension of GIVCOL, must be at least N. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] GIVNUM */ +/* > \verbatim */ +/* > GIVNUM is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) */ +/* > Each number indicates the C or S value to be used in the */ +/* > corresponding Givens rotation. Not referenced if ICOMPQ = 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDGNUM */ +/* > \verbatim */ +/* > LDGNUM is INTEGER */ +/* > The leading dimension of GIVNUM and POLES, must be at least N. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] POLES */ +/* > \verbatim */ +/* > POLES is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) */ +/* > On exit, POLES(1,*) is an array containing the new singular */ +/* > values obtained from solving the secular equation, and */ +/* > POLES(2,*) is an array containing the poles in the secular */ +/* > equation. Not referenced if ICOMPQ = 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] DIFL */ +/* > \verbatim */ +/* > DIFL is DOUBLE PRECISION array, dimension ( N ) */ +/* > On exit, DIFL(I) is the distance between I-th updated */ +/* > (undeflated) singular value and the I-th (undeflated) old */ +/* > singular value. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] DIFR */ +/* > \verbatim */ +/* > DIFR is DOUBLE PRECISION array, */ +/* > dimension ( LDDIFR, 2 ) if ICOMPQ = 1 and */ +/* > dimension ( K ) if ICOMPQ = 0. */ +/* > On exit, DIFR(I,1) = D(I) - DSIGMA(I+1), DIFR(K,1) is not */ +/* > defined and will not be referenced. */ +/* > */ +/* > If ICOMPQ = 1, DIFR(1:K,2) is an array containing the */ +/* > normalizing factors for the right singular vector matrix. */ +/* > */ +/* > See DLASD8 for details on DIFL and DIFR. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] Z */ +/* > \verbatim */ +/* > Z is DOUBLE PRECISION array, dimension ( M ) */ +/* > The first elements of this array contain the components */ +/* > of the deflation-adjusted updating row vector. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > Contains the dimension of the non-deflated matrix, */ +/* > This is the order of the related secular equation. 1 <= K <=N. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] C */ +/* > \verbatim */ +/* > C is DOUBLE PRECISION */ +/* > C contains garbage if SQRE =0 and the C-value of a Givens */ +/* > rotation related to the right null space if SQRE = 1. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] S */ +/* > \verbatim */ +/* > S is DOUBLE PRECISION */ +/* > S contains garbage if SQRE =0 and the S-value of a Givens */ +/* > rotation related to the right null space if SQRE = 1. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension ( 4 * M ) */ +/* > \endverbatim */ +/* > */ +/* > \param[out] IWORK */ +/* > \verbatim */ +/* > IWORK is INTEGER array, dimension ( 3 * N ) */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit. */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ +/* > > 0: if INFO = 1, a singular value did not converge */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup OTHERauxiliary */ + +/* > \par Contributors: */ +/* ================== */ +/* > */ +/* > Ming Gu and Huan Ren, Computer Science Division, University of */ +/* > California at Berkeley, USA */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dlasd6_(integer *icompq, integer *nl, integer *nr, + integer *sqre, doublereal *d__, doublereal *vf, doublereal *vl, + doublereal *alpha, doublereal *beta, integer *idxq, integer *perm, + integer *givptr, integer *givcol, integer *ldgcol, doublereal *givnum, + integer *ldgnum, doublereal *poles, doublereal *difl, doublereal * + difr, doublereal *z__, integer *k, doublereal *c__, doublereal *s, + doublereal *work, integer *iwork, integer *info) +{ + /* System generated locals */ + integer givcol_dim1, givcol_offset, givnum_dim1, givnum_offset, + poles_dim1, poles_offset, i__1; + doublereal d__1, d__2; + + /* Local variables */ + integer i__, m, n, n1, n2, iw, idx, idxc, idxp, ivfw, ivlw; + extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, + doublereal *, integer *), dlasd7_(integer *, integer *, integer *, + integer *, integer *, doublereal *, doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *, integer *, integer *, + integer *, integer *, integer *, integer *, integer *, doublereal + *, integer *, doublereal *, doublereal *, integer *), dlasd8_( + integer *, integer *, doublereal *, doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *, integer *, doublereal *, + doublereal *, integer *), dlascl_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, integer *, doublereal *, + integer *, integer *, ftnlen), dlamrg_(integer *, integer *, + doublereal *, integer *, integer *, integer *); + integer isigma; + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + doublereal orgnrm; + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --d__; + --vf; + --vl; + --idxq; + --perm; + givcol_dim1 = *ldgcol; + givcol_offset = 1 + givcol_dim1; + givcol -= givcol_offset; + poles_dim1 = *ldgnum; + poles_offset = 1 + poles_dim1; + poles -= poles_offset; + givnum_dim1 = *ldgnum; + givnum_offset = 1 + givnum_dim1; + givnum -= givnum_offset; + --difl; + --difr; + --z__; + --work; + --iwork; + + /* Function Body */ + *info = 0; + n = *nl + *nr + 1; + m = n + *sqre; + + if (*icompq < 0 || *icompq > 1) { + *info = -1; + } else if (*nl < 1) { + *info = -2; + } else if (*nr < 1) { + *info = -3; + } else if (*sqre < 0 || *sqre > 1) { + *info = -4; + } else if (*ldgcol < n) { + *info = -14; + } else if (*ldgnum < n) { + *info = -16; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DLASD6", &i__1, (ftnlen)6); + return 0; + } + +/* The following values are for bookkeeping purposes only. They are */ +/* integer pointers which indicate the portion of the workspace */ +/* used by a particular array in DLASD7 and DLASD8. */ + + isigma = 1; + iw = isigma + n; + ivfw = iw + m; + ivlw = ivfw + m; + + idx = 1; + idxc = idx + n; + idxp = idxc + n; + +/* Scale. */ + +/* Computing MAX */ + d__1 = abs(*alpha), d__2 = abs(*beta); + orgnrm = max(d__1,d__2); + d__[*nl + 1] = 0.; + i__1 = n; + for (i__ = 1; i__ <= i__1; ++i__) { + if ((d__1 = d__[i__], abs(d__1)) > orgnrm) { + orgnrm = (d__1 = d__[i__], abs(d__1)); + } +/* L10: */ + } + dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b7, &n, &c__1, &d__[1], &n, info, ( + ftnlen)1); + *alpha /= orgnrm; + *beta /= orgnrm; + +/* Sort and Deflate singular values. */ + + dlasd7_(icompq, nl, nr, sqre, k, &d__[1], &z__[1], &work[iw], &vf[1], & + work[ivfw], &vl[1], &work[ivlw], alpha, beta, &work[isigma], & + iwork[idx], &iwork[idxp], &idxq[1], &perm[1], givptr, &givcol[ + givcol_offset], ldgcol, &givnum[givnum_offset], ldgnum, c__, s, + info); + +/* Solve Secular Equation, compute DIFL, DIFR, and update VF, VL. */ + + dlasd8_(icompq, k, &d__[1], &z__[1], &vf[1], &vl[1], &difl[1], &difr[1], + ldgnum, &work[isigma], &work[iw], info); + +/* Report the possible convergence failure. */ + + if (*info != 0) { + return 0; + } + +/* Save the poles if ICOMPQ = 1. */ + + if (*icompq == 1) { + dcopy_(k, &d__[1], &c__1, &poles[poles_dim1 + 1], &c__1); + dcopy_(k, &work[isigma], &c__1, &poles[(poles_dim1 << 1) + 1], &c__1); + } + +/* Unscale. */ + + dlascl_((char *)"G", &c__0, &c__0, &c_b7, &orgnrm, &n, &c__1, &d__[1], &n, info, ( + ftnlen)1); + +/* Prepare the IDXQ sorting permutation. */ + + n1 = *k; + n2 = n - *k; + dlamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &idxq[1]); + + return 0; + +/* End of DLASD6 */ + +} /* dlasd6_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlasd7.cpp b/lib/linalg/dlasd7.cpp new file mode 100644 index 0000000000..29169c7a84 --- /dev/null +++ b/lib/linalg/dlasd7.cpp @@ -0,0 +1,663 @@ +/* fortran/dlasd7.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; + +/* > \brief \b DLASD7 merges the two sets of singular values together into a single sorted set. Then it tries +to deflate the size of the problem. Used by sbdsdc. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLASD7 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLASD7( ICOMPQ, NL, NR, SQRE, K, D, Z, ZW, VF, VFW, VL, */ +/* VLW, ALPHA, BETA, DSIGMA, IDX, IDXP, IDXQ, */ +/* PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, */ +/* C, S, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER GIVPTR, ICOMPQ, INFO, K, LDGCOL, LDGNUM, NL, */ +/* $ NR, SQRE */ +/* DOUBLE PRECISION ALPHA, BETA, C, S */ +/* .. */ +/* .. Array Arguments .. */ +/* INTEGER GIVCOL( LDGCOL, * ), IDX( * ), IDXP( * ), */ +/* $ IDXQ( * ), PERM( * ) */ +/* DOUBLE PRECISION D( * ), DSIGMA( * ), GIVNUM( LDGNUM, * ), */ +/* $ VF( * ), VFW( * ), VL( * ), VLW( * ), Z( * ), */ +/* $ ZW( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLASD7 merges the two sets of singular values together into a single */ +/* > sorted set. Then it tries to deflate the size of the problem. There */ +/* > are two ways in which deflation can occur: when two or more singular */ +/* > values are close together or if there is a tiny entry in the Z */ +/* > vector. For each such occurrence the order of the related */ +/* > secular equation problem is reduced by one. */ +/* > */ +/* > DLASD7 is called from DLASD6. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] ICOMPQ */ +/* > \verbatim */ +/* > ICOMPQ is INTEGER */ +/* > Specifies whether singular vectors are to be computed */ +/* > in compact form, as follows: */ +/* > = 0: Compute singular values only. */ +/* > = 1: Compute singular vectors of upper */ +/* > bidiagonal matrix in compact form. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] NL */ +/* > \verbatim */ +/* > NL is INTEGER */ +/* > The row dimension of the upper block. NL >= 1. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] NR */ +/* > \verbatim */ +/* > NR is INTEGER */ +/* > The row dimension of the lower block. NR >= 1. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] SQRE */ +/* > \verbatim */ +/* > SQRE is INTEGER */ +/* > = 0: the lower block is an NR-by-NR square matrix. */ +/* > = 1: the lower block is an NR-by-(NR+1) rectangular matrix. */ +/* > */ +/* > The bidiagonal matrix has */ +/* > N = NL + NR + 1 rows and */ +/* > M = N + SQRE >= N columns. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > Contains the dimension of the non-deflated matrix, this is */ +/* > the order of the related secular equation. 1 <= K <=N. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension ( N ) */ +/* > On entry D contains the singular values of the two submatrices */ +/* > to be combined. On exit D contains the trailing (N-K) updated */ +/* > singular values (those which were deflated) sorted into */ +/* > increasing order. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] Z */ +/* > \verbatim */ +/* > Z is DOUBLE PRECISION array, dimension ( M ) */ +/* > On exit Z contains the updating row vector in the secular */ +/* > equation. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] ZW */ +/* > \verbatim */ +/* > ZW is DOUBLE PRECISION array, dimension ( M ) */ +/* > Workspace for Z. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] VF */ +/* > \verbatim */ +/* > VF is DOUBLE PRECISION array, dimension ( M ) */ +/* > On entry, VF(1:NL+1) contains the first components of all */ +/* > right singular vectors of the upper block; and VF(NL+2:M) */ +/* > contains the first components of all right singular vectors */ +/* > of the lower block. On exit, VF contains the first components */ +/* > of all right singular vectors of the bidiagonal matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] VFW */ +/* > \verbatim */ +/* > VFW is DOUBLE PRECISION array, dimension ( M ) */ +/* > Workspace for VF. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] VL */ +/* > \verbatim */ +/* > VL is DOUBLE PRECISION array, dimension ( M ) */ +/* > On entry, VL(1:NL+1) contains the last components of all */ +/* > right singular vectors of the upper block; and VL(NL+2:M) */ +/* > contains the last components of all right singular vectors */ +/* > of the lower block. On exit, VL contains the last components */ +/* > of all right singular vectors of the bidiagonal matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] VLW */ +/* > \verbatim */ +/* > VLW is DOUBLE PRECISION array, dimension ( M ) */ +/* > Workspace for VL. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] ALPHA */ +/* > \verbatim */ +/* > ALPHA is DOUBLE PRECISION */ +/* > Contains the diagonal element associated with the added row. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] BETA */ +/* > \verbatim */ +/* > BETA is DOUBLE PRECISION */ +/* > Contains the off-diagonal element associated with the added */ +/* > row. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] DSIGMA */ +/* > \verbatim */ +/* > DSIGMA is DOUBLE PRECISION array, dimension ( N ) */ +/* > Contains a copy of the diagonal elements (K-1 singular values */ +/* > and one zero) in the secular equation. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] IDX */ +/* > \verbatim */ +/* > IDX is INTEGER array, dimension ( N ) */ +/* > This will contain the permutation used to sort the contents of */ +/* > D into ascending order. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] IDXP */ +/* > \verbatim */ +/* > IDXP is INTEGER array, dimension ( N ) */ +/* > This will contain the permutation used to place deflated */ +/* > values of D at the end of the array. On output IDXP(2:K) */ +/* > points to the nondeflated D-values and IDXP(K+1:N) */ +/* > points to the deflated singular values. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] IDXQ */ +/* > \verbatim */ +/* > IDXQ is INTEGER array, dimension ( N ) */ +/* > This contains the permutation which separately sorts the two */ +/* > sub-problems in D into ascending order. Note that entries in */ +/* > the first half of this permutation must first be moved one */ +/* > position backward; and entries in the second half */ +/* > must first have NL+1 added to their values. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] PERM */ +/* > \verbatim */ +/* > PERM is INTEGER array, dimension ( N ) */ +/* > The permutations (from deflation and sorting) to be applied */ +/* > to each singular block. Not referenced if ICOMPQ = 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] GIVPTR */ +/* > \verbatim */ +/* > GIVPTR is INTEGER */ +/* > The number of Givens rotations which took place in this */ +/* > subproblem. Not referenced if ICOMPQ = 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] GIVCOL */ +/* > \verbatim */ +/* > GIVCOL is INTEGER array, dimension ( LDGCOL, 2 ) */ +/* > Each pair of numbers indicates a pair of columns to take place */ +/* > in a Givens rotation. Not referenced if ICOMPQ = 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDGCOL */ +/* > \verbatim */ +/* > LDGCOL is INTEGER */ +/* > The leading dimension of GIVCOL, must be at least N. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] GIVNUM */ +/* > \verbatim */ +/* > GIVNUM is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) */ +/* > Each number indicates the C or S value to be used in the */ +/* > corresponding Givens rotation. Not referenced if ICOMPQ = 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDGNUM */ +/* > \verbatim */ +/* > LDGNUM is INTEGER */ +/* > The leading dimension of GIVNUM, must be at least N. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] C */ +/* > \verbatim */ +/* > C is DOUBLE PRECISION */ +/* > C contains garbage if SQRE =0 and the C-value of a Givens */ +/* > rotation related to the right null space if SQRE = 1. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] S */ +/* > \verbatim */ +/* > S is DOUBLE PRECISION */ +/* > S contains garbage if SQRE =0 and the S-value of a Givens */ +/* > rotation related to the right null space if SQRE = 1. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit. */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup OTHERauxiliary */ + +/* > \par Contributors: */ +/* ================== */ +/* > */ +/* > Ming Gu and Huan Ren, Computer Science Division, University of */ +/* > California at Berkeley, USA */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dlasd7_(integer *icompq, integer *nl, integer *nr, + integer *sqre, integer *k, doublereal *d__, doublereal *z__, + doublereal *zw, doublereal *vf, doublereal *vfw, doublereal *vl, + doublereal *vlw, doublereal *alpha, doublereal *beta, doublereal * + dsigma, integer *idx, integer *idxp, integer *idxq, integer *perm, + integer *givptr, integer *givcol, integer *ldgcol, doublereal *givnum, + integer *ldgnum, doublereal *c__, doublereal *s, integer *info) +{ + /* System generated locals */ + integer givcol_dim1, givcol_offset, givnum_dim1, givnum_offset, i__1; + doublereal d__1, d__2; + + /* Local variables */ + integer i__, j, m, n, k2; + doublereal z1; + integer jp; + doublereal eps, tau, tol; + integer nlp1, nlp2, idxi, idxj; + extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, + doublereal *, integer *, doublereal *, doublereal *); + integer idxjp; + extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, + doublereal *, integer *); + integer jprev; + extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, + ftnlen); + extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *, + integer *, integer *, integer *), xerbla_(char *, integer *, + ftnlen); + doublereal hlftol; + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ + +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --d__; + --z__; + --zw; + --vf; + --vfw; + --vl; + --vlw; + --dsigma; + --idx; + --idxp; + --idxq; + --perm; + givcol_dim1 = *ldgcol; + givcol_offset = 1 + givcol_dim1; + givcol -= givcol_offset; + givnum_dim1 = *ldgnum; + givnum_offset = 1 + givnum_dim1; + givnum -= givnum_offset; + + /* Function Body */ + *info = 0; + n = *nl + *nr + 1; + m = n + *sqre; + + if (*icompq < 0 || *icompq > 1) { + *info = -1; + } else if (*nl < 1) { + *info = -2; + } else if (*nr < 1) { + *info = -3; + } else if (*sqre < 0 || *sqre > 1) { + *info = -4; + } else if (*ldgcol < n) { + *info = -22; + } else if (*ldgnum < n) { + *info = -24; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DLASD7", &i__1, (ftnlen)6); + return 0; + } + + nlp1 = *nl + 1; + nlp2 = *nl + 2; + if (*icompq == 1) { + *givptr = 0; + } + +/* Generate the first part of the vector Z and move the singular */ +/* values in the first part of D one position backward. */ + + z1 = *alpha * vl[nlp1]; + vl[nlp1] = 0.; + tau = vf[nlp1]; + for (i__ = *nl; i__ >= 1; --i__) { + z__[i__ + 1] = *alpha * vl[i__]; + vl[i__] = 0.; + vf[i__ + 1] = vf[i__]; + d__[i__ + 1] = d__[i__]; + idxq[i__ + 1] = idxq[i__] + 1; +/* L10: */ + } + vf[1] = tau; + +/* Generate the second part of the vector Z. */ + + i__1 = m; + for (i__ = nlp2; i__ <= i__1; ++i__) { + z__[i__] = *beta * vf[i__]; + vf[i__] = 0.; +/* L20: */ + } + +/* Sort the singular values into increasing order */ + + i__1 = n; + for (i__ = nlp2; i__ <= i__1; ++i__) { + idxq[i__] += nlp1; +/* L30: */ + } + +/* DSIGMA, IDXC, IDXC, and ZW are used as storage space. */ + + i__1 = n; + for (i__ = 2; i__ <= i__1; ++i__) { + dsigma[i__] = d__[idxq[i__]]; + zw[i__] = z__[idxq[i__]]; + vfw[i__] = vf[idxq[i__]]; + vlw[i__] = vl[idxq[i__]]; +/* L40: */ + } + + dlamrg_(nl, nr, &dsigma[2], &c__1, &c__1, &idx[2]); + + i__1 = n; + for (i__ = 2; i__ <= i__1; ++i__) { + idxi = idx[i__] + 1; + d__[i__] = dsigma[idxi]; + z__[i__] = zw[idxi]; + vf[i__] = vfw[idxi]; + vl[i__] = vlw[idxi]; +/* L50: */ + } + +/* Calculate the allowable deflation tolerance */ + + eps = dlamch_((char *)"Epsilon", (ftnlen)7); +/* Computing MAX */ + d__1 = abs(*alpha), d__2 = abs(*beta); + tol = max(d__1,d__2); +/* Computing MAX */ + d__2 = (d__1 = d__[n], abs(d__1)); + tol = eps * 64. * max(d__2,tol); + +/* There are 2 kinds of deflation -- first a value in the z-vector */ +/* is small, second two (or more) singular values are very close */ +/* together (their difference is small). */ + +/* If the value in the z-vector is small, we simply permute the */ +/* array so that the corresponding singular value is moved to the */ +/* end. */ + +/* If two values in the D-vector are close, we perform a two-sided */ +/* rotation designed to make one of the corresponding z-vector */ +/* entries zero, and then permute the array so that the deflated */ +/* singular value is moved to the end. */ + +/* If there are multiple singular values then the problem deflates. */ +/* Here the number of equal singular values are found. As each equal */ +/* singular value is found, an elementary reflector is computed to */ +/* rotate the corresponding singular subspace so that the */ +/* corresponding components of Z are zero in this new basis. */ + + *k = 1; + k2 = n + 1; + i__1 = n; + for (j = 2; j <= i__1; ++j) { + if ((d__1 = z__[j], abs(d__1)) <= tol) { + +/* Deflate due to small z component. */ + + --k2; + idxp[k2] = j; + if (j == n) { + goto L100; + } + } else { + jprev = j; + goto L70; + } +/* L60: */ + } +L70: + j = jprev; +L80: + ++j; + if (j > n) { + goto L90; + } + if ((d__1 = z__[j], abs(d__1)) <= tol) { + +/* Deflate due to small z component. */ + + --k2; + idxp[k2] = j; + } else { + +/* Check if singular values are close enough to allow deflation. */ + + if ((d__1 = d__[j] - d__[jprev], abs(d__1)) <= tol) { + +/* Deflation is possible. */ + + *s = z__[jprev]; + *c__ = z__[j]; + +/* Find sqrt(a**2+b**2) without overflow or */ +/* destructive underflow. */ + + tau = dlapy2_(c__, s); + z__[j] = tau; + z__[jprev] = 0.; + *c__ /= tau; + *s = -(*s) / tau; + +/* Record the appropriate Givens rotation */ + + if (*icompq == 1) { + ++(*givptr); + idxjp = idxq[idx[jprev] + 1]; + idxj = idxq[idx[j] + 1]; + if (idxjp <= nlp1) { + --idxjp; + } + if (idxj <= nlp1) { + --idxj; + } + givcol[*givptr + (givcol_dim1 << 1)] = idxjp; + givcol[*givptr + givcol_dim1] = idxj; + givnum[*givptr + (givnum_dim1 << 1)] = *c__; + givnum[*givptr + givnum_dim1] = *s; + } + drot_(&c__1, &vf[jprev], &c__1, &vf[j], &c__1, c__, s); + drot_(&c__1, &vl[jprev], &c__1, &vl[j], &c__1, c__, s); + --k2; + idxp[k2] = jprev; + jprev = j; + } else { + ++(*k); + zw[*k] = z__[jprev]; + dsigma[*k] = d__[jprev]; + idxp[*k] = jprev; + jprev = j; + } + } + goto L80; +L90: + +/* Record the last singular value. */ + + ++(*k); + zw[*k] = z__[jprev]; + dsigma[*k] = d__[jprev]; + idxp[*k] = jprev; + +L100: + +/* Sort the singular values into DSIGMA. The singular values which */ +/* were not deflated go into the first K slots of DSIGMA, except */ +/* that DSIGMA(1) is treated separately. */ + + i__1 = n; + for (j = 2; j <= i__1; ++j) { + jp = idxp[j]; + dsigma[j] = d__[jp]; + vfw[j] = vf[jp]; + vlw[j] = vl[jp]; +/* L110: */ + } + if (*icompq == 1) { + i__1 = n; + for (j = 2; j <= i__1; ++j) { + jp = idxp[j]; + perm[j] = idxq[idx[jp] + 1]; + if (perm[j] <= nlp1) { + --perm[j]; + } +/* L120: */ + } + } + +/* The deflated singular values go back into the last N - K slots of */ +/* D. */ + + i__1 = n - *k; + dcopy_(&i__1, &dsigma[*k + 1], &c__1, &d__[*k + 1], &c__1); + +/* Determine DSIGMA(1), DSIGMA(2), Z(1), VF(1), VL(1), VF(M), and */ +/* VL(M). */ + + dsigma[1] = 0.; + hlftol = tol / 2.; + if (abs(dsigma[2]) <= hlftol) { + dsigma[2] = hlftol; + } + if (m > n) { + z__[1] = dlapy2_(&z1, &z__[m]); + if (z__[1] <= tol) { + *c__ = 1.; + *s = 0.; + z__[1] = tol; + } else { + *c__ = z1 / z__[1]; + *s = -z__[m] / z__[1]; + } + drot_(&c__1, &vf[m], &c__1, &vf[1], &c__1, c__, s); + drot_(&c__1, &vl[m], &c__1, &vl[1], &c__1, c__, s); + } else { + if (abs(z1) <= tol) { + z__[1] = tol; + } else { + z__[1] = z1; + } + } + +/* Restore Z, VF, and VL. */ + + i__1 = *k - 1; + dcopy_(&i__1, &zw[2], &c__1, &z__[2], &c__1); + i__1 = n - 1; + dcopy_(&i__1, &vfw[2], &c__1, &vf[2], &c__1); + i__1 = n - 1; + dcopy_(&i__1, &vlw[2], &c__1, &vl[2], &c__1); + + return 0; + +/* End of DLASD7 */ + +} /* dlasd7_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlasd8.cpp b/lib/linalg/dlasd8.cpp new file mode 100644 index 0000000000..b95d5b11cc --- /dev/null +++ b/lib/linalg/dlasd8.cpp @@ -0,0 +1,419 @@ +/* fortran/dlasd8.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c__0 = 0; +static doublereal c_b8 = 1.; + +/* > \brief \b DLASD8 finds the square roots of the roots of the secular equation, and stores, for each elemen +t in D, the distance to its two nearest poles. Used by sbdsdc. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLASD8 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLASD8( ICOMPQ, K, D, Z, VF, VL, DIFL, DIFR, LDDIFR, */ +/* DSIGMA, WORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER ICOMPQ, INFO, K, LDDIFR */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION D( * ), DIFL( * ), DIFR( LDDIFR, * ), */ +/* $ DSIGMA( * ), VF( * ), VL( * ), WORK( * ), */ +/* $ Z( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLASD8 finds the square roots of the roots of the secular equation, */ +/* > as defined by the values in DSIGMA and Z. It makes the appropriate */ +/* > calls to DLASD4, and stores, for each element in D, the distance */ +/* > to its two nearest poles (elements in DSIGMA). It also updates */ +/* > the arrays VF and VL, the first and last components of all the */ +/* > right singular vectors of the original bidiagonal matrix. */ +/* > */ +/* > DLASD8 is called from DLASD6. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] ICOMPQ */ +/* > \verbatim */ +/* > ICOMPQ is INTEGER */ +/* > Specifies whether singular vectors are to be computed in */ +/* > factored form in the calling routine: */ +/* > = 0: Compute singular values only. */ +/* > = 1: Compute singular vectors in factored form as well. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > The number of terms in the rational function to be solved */ +/* > by DLASD4. K >= 1. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension ( K ) */ +/* > On output, D contains the updated singular values. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] Z */ +/* > \verbatim */ +/* > Z is DOUBLE PRECISION array, dimension ( K ) */ +/* > On entry, the first K elements of this array contain the */ +/* > components of the deflation-adjusted updating row vector. */ +/* > On exit, Z is updated. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] VF */ +/* > \verbatim */ +/* > VF is DOUBLE PRECISION array, dimension ( K ) */ +/* > On entry, VF contains information passed through DBEDE8. */ +/* > On exit, VF contains the first K components of the first */ +/* > components of all right singular vectors of the bidiagonal */ +/* > matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] VL */ +/* > \verbatim */ +/* > VL is DOUBLE PRECISION array, dimension ( K ) */ +/* > On entry, VL contains information passed through DBEDE8. */ +/* > On exit, VL contains the first K components of the last */ +/* > components of all right singular vectors of the bidiagonal */ +/* > matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] DIFL */ +/* > \verbatim */ +/* > DIFL is DOUBLE PRECISION array, dimension ( K ) */ +/* > On exit, DIFL(I) = D(I) - DSIGMA(I). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] DIFR */ +/* > \verbatim */ +/* > DIFR is DOUBLE PRECISION array, */ +/* > dimension ( LDDIFR, 2 ) if ICOMPQ = 1 and */ +/* > dimension ( K ) if ICOMPQ = 0. */ +/* > On exit, DIFR(I,1) = D(I) - DSIGMA(I+1), DIFR(K,1) is not */ +/* > defined and will not be referenced. */ +/* > */ +/* > If ICOMPQ = 1, DIFR(1:K,2) is an array containing the */ +/* > normalizing factors for the right singular vector matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDDIFR */ +/* > \verbatim */ +/* > LDDIFR is INTEGER */ +/* > The leading dimension of DIFR, must be at least K. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] DSIGMA */ +/* > \verbatim */ +/* > DSIGMA is DOUBLE PRECISION array, dimension ( K ) */ +/* > On entry, the first K elements of this array contain the old */ +/* > roots of the deflated updating problem. These are the poles */ +/* > of the secular equation. */ +/* > On exit, the elements of DSIGMA may be very slightly altered */ +/* > in value. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (3*K) */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit. */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ +/* > > 0: if INFO = 1, a singular value did not converge */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup OTHERauxiliary */ + +/* > \par Contributors: */ +/* ================== */ +/* > */ +/* > Ming Gu and Huan Ren, Computer Science Division, University of */ +/* > California at Berkeley, USA */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dlasd8_(integer *icompq, integer *k, doublereal *d__, + doublereal *z__, doublereal *vf, doublereal *vl, doublereal *difl, + doublereal *difr, integer *lddifr, doublereal *dsigma, doublereal * + work, integer *info) +{ + /* System generated locals */ + integer difr_dim1, difr_offset, i__1, i__2; + doublereal d__1, d__2; + + /* Builtin functions */ + double sqrt(doublereal), d_sign(doublereal *, doublereal *); + + /* Local variables */ + integer i__, j; + doublereal dj, rho; + integer iwk1, iwk2, iwk3; + extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, + integer *); + doublereal temp; + extern doublereal dnrm2_(integer *, doublereal *, integer *); + integer iwk2i, iwk3i; + doublereal diflj, difrj, dsigj; + extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, + doublereal *, integer *); + extern doublereal dlamc3_(doublereal *, doublereal *); + extern /* Subroutine */ int dlasd4_(integer *, integer *, doublereal *, + doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, integer *), dlascl_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, integer *, doublereal *, + integer *, integer *, ftnlen), dlaset_(char *, integer *, integer + *, doublereal *, doublereal *, doublereal *, integer *, ftnlen), + xerbla_(char *, integer *, ftnlen); + doublereal dsigjp; + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --d__; + --z__; + --vf; + --vl; + --difl; + difr_dim1 = *lddifr; + difr_offset = 1 + difr_dim1; + difr -= difr_offset; + --dsigma; + --work; + + /* Function Body */ + *info = 0; + + if (*icompq < 0 || *icompq > 1) { + *info = -1; + } else if (*k < 1) { + *info = -2; + } else if (*lddifr < *k) { + *info = -9; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DLASD8", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*k == 1) { + d__[1] = abs(z__[1]); + difl[1] = d__[1]; + if (*icompq == 1) { + difl[2] = 1.; + difr[(difr_dim1 << 1) + 1] = 1.; + } + return 0; + } + +/* Modify values DSIGMA(i) to make sure all DSIGMA(i)-DSIGMA(j) can */ +/* be computed with high relative accuracy (barring over/underflow). */ +/* This is a problem on machines without a guard digit in */ +/* add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2). */ +/* The following code replaces DSIGMA(I) by 2*DSIGMA(I)-DSIGMA(I), */ +/* which on any of these machines zeros out the bottommost */ +/* bit of DSIGMA(I) if it is 1; this makes the subsequent */ +/* subtractions DSIGMA(I)-DSIGMA(J) unproblematic when cancellation */ +/* occurs. On binary machines with a guard digit (almost all */ +/* machines) it does not change DSIGMA(I) at all. On hexadecimal */ +/* and decimal machines with a guard digit, it slightly */ +/* changes the bottommost bits of DSIGMA(I). It does not account */ +/* for hexadecimal or decimal machines without guard digits */ +/* (we know of none). We use a subroutine call to compute */ +/* 2*DLAMBDA(I) to prevent optimizing compilers from eliminating */ +/* this code. */ + + i__1 = *k; + for (i__ = 1; i__ <= i__1; ++i__) { + dsigma[i__] = dlamc3_(&dsigma[i__], &dsigma[i__]) - dsigma[i__]; +/* L10: */ + } + +/* Book keeping. */ + + iwk1 = 1; + iwk2 = iwk1 + *k; + iwk3 = iwk2 + *k; + iwk2i = iwk2 - 1; + iwk3i = iwk3 - 1; + +/* Normalize Z. */ + + rho = dnrm2_(k, &z__[1], &c__1); + dlascl_((char *)"G", &c__0, &c__0, &rho, &c_b8, k, &c__1, &z__[1], k, info, ( + ftnlen)1); + rho *= rho; + +/* Initialize WORK(IWK3). */ + + dlaset_((char *)"A", k, &c__1, &c_b8, &c_b8, &work[iwk3], k, (ftnlen)1); + +/* Compute the updated singular values, the arrays DIFL, DIFR, */ +/* and the updated Z. */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + dlasd4_(k, &j, &dsigma[1], &z__[1], &work[iwk1], &rho, &d__[j], &work[ + iwk2], info); + +/* If the root finder fails, report the convergence failure. */ + + if (*info != 0) { + return 0; + } + work[iwk3i + j] = work[iwk3i + j] * work[j] * work[iwk2i + j]; + difl[j] = -work[j]; + difr[j + difr_dim1] = -work[j + 1]; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + work[iwk3i + i__] = work[iwk3i + i__] * work[i__] * work[iwk2i + + i__] / (dsigma[i__] - dsigma[j]) / (dsigma[i__] + dsigma[ + j]); +/* L20: */ + } + i__2 = *k; + for (i__ = j + 1; i__ <= i__2; ++i__) { + work[iwk3i + i__] = work[iwk3i + i__] * work[i__] * work[iwk2i + + i__] / (dsigma[i__] - dsigma[j]) / (dsigma[i__] + dsigma[ + j]); +/* L30: */ + } +/* L40: */ + } + +/* Compute updated Z. */ + + i__1 = *k; + for (i__ = 1; i__ <= i__1; ++i__) { + d__2 = sqrt((d__1 = work[iwk3i + i__], abs(d__1))); + z__[i__] = d_sign(&d__2, &z__[i__]); +/* L50: */ + } + +/* Update VF and VL. */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + diflj = difl[j]; + dj = d__[j]; + dsigj = -dsigma[j]; + if (j < *k) { + difrj = -difr[j + difr_dim1]; + dsigjp = -dsigma[j + 1]; + } + work[j] = -z__[j] / diflj / (dsigma[j] + dj); + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + work[i__] = z__[i__] / (dlamc3_(&dsigma[i__], &dsigj) - diflj) / ( + dsigma[i__] + dj); +/* L60: */ + } + i__2 = *k; + for (i__ = j + 1; i__ <= i__2; ++i__) { + work[i__] = z__[i__] / (dlamc3_(&dsigma[i__], &dsigjp) + difrj) / + (dsigma[i__] + dj); +/* L70: */ + } + temp = dnrm2_(k, &work[1], &c__1); + work[iwk2i + j] = ddot_(k, &work[1], &c__1, &vf[1], &c__1) / temp; + work[iwk3i + j] = ddot_(k, &work[1], &c__1, &vl[1], &c__1) / temp; + if (*icompq == 1) { + difr[j + (difr_dim1 << 1)] = temp; + } +/* L80: */ + } + + dcopy_(k, &work[iwk2], &c__1, &vf[1], &c__1); + dcopy_(k, &work[iwk3], &c__1, &vl[1], &c__1); + + return 0; + +/* End of DLASD8 */ + +} /* dlasd8_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlasda.cpp b/lib/linalg/dlasda.cpp new file mode 100644 index 0000000000..a63dc14dec --- /dev/null +++ b/lib/linalg/dlasda.cpp @@ -0,0 +1,624 @@ +/* fortran/dlasda.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__0 = 0; +static doublereal c_b11 = 0.; +static doublereal c_b12 = 1.; +static integer c__1 = 1; +static integer c__2 = 2; + +/* > \brief \b DLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal matrix with d +iagonal d and off-diagonal e. Used by sbdsdc. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLASDA + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLASDA( ICOMPQ, SMLSIZ, N, SQRE, D, E, U, LDU, VT, K, */ +/* DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, */ +/* PERM, GIVNUM, C, S, WORK, IWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER ICOMPQ, INFO, LDGCOL, LDU, N, SMLSIZ, SQRE */ +/* .. */ +/* .. Array Arguments .. */ +/* INTEGER GIVCOL( LDGCOL, * ), GIVPTR( * ), IWORK( * ), */ +/* $ K( * ), PERM( LDGCOL, * ) */ +/* DOUBLE PRECISION C( * ), D( * ), DIFL( LDU, * ), DIFR( LDU, * ), */ +/* $ E( * ), GIVNUM( LDU, * ), POLES( LDU, * ), */ +/* $ S( * ), U( LDU, * ), VT( LDU, * ), WORK( * ), */ +/* $ Z( LDU, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > Using a divide and conquer approach, DLASDA computes the singular */ +/* > value decomposition (SVD) of a real upper bidiagonal N-by-M matrix */ +/* > B with diagonal D and offdiagonal E, where M = N + SQRE. The */ +/* > algorithm computes the singular values in the SVD B = U * S * VT. */ +/* > The orthogonal matrices U and VT are optionally computed in */ +/* > compact form. */ +/* > */ +/* > A related subroutine, DLASD0, computes the singular values and */ +/* > the singular vectors in explicit form. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] ICOMPQ */ +/* > \verbatim */ +/* > ICOMPQ is INTEGER */ +/* > Specifies whether singular vectors are to be computed */ +/* > in compact form, as follows */ +/* > = 0: Compute singular values only. */ +/* > = 1: Compute singular vectors of upper bidiagonal */ +/* > matrix in compact form. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] SMLSIZ */ +/* > \verbatim */ +/* > SMLSIZ is INTEGER */ +/* > The maximum size of the subproblems at the bottom of the */ +/* > computation tree. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The row dimension of the upper bidiagonal matrix. This is */ +/* > also the dimension of the main diagonal array D. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] SQRE */ +/* > \verbatim */ +/* > SQRE is INTEGER */ +/* > Specifies the column dimension of the bidiagonal matrix. */ +/* > = 0: The bidiagonal matrix has column dimension M = N; */ +/* > = 1: The bidiagonal matrix has column dimension M = N + 1. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension ( N ) */ +/* > On entry D contains the main diagonal of the bidiagonal */ +/* > matrix. On exit D, if INFO = 0, contains its singular values. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] E */ +/* > \verbatim */ +/* > E is DOUBLE PRECISION array, dimension ( M-1 ) */ +/* > Contains the subdiagonal entries of the bidiagonal matrix. */ +/* > On exit, E has been destroyed. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] U */ +/* > \verbatim */ +/* > U is DOUBLE PRECISION array, */ +/* > dimension ( LDU, SMLSIZ ) if ICOMPQ = 1, and not referenced */ +/* > if ICOMPQ = 0. If ICOMPQ = 1, on exit, U contains the left */ +/* > singular vector matrices of all subproblems at the bottom */ +/* > level. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDU */ +/* > \verbatim */ +/* > LDU is INTEGER, LDU = > N. */ +/* > The leading dimension of arrays U, VT, DIFL, DIFR, POLES, */ +/* > GIVNUM, and Z. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] VT */ +/* > \verbatim */ +/* > VT is DOUBLE PRECISION array, */ +/* > dimension ( LDU, SMLSIZ+1 ) if ICOMPQ = 1, and not referenced */ +/* > if ICOMPQ = 0. If ICOMPQ = 1, on exit, VT**T contains the right */ +/* > singular vector matrices of all subproblems at the bottom */ +/* > level. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] K */ +/* > \verbatim */ +/* > K is INTEGER array, */ +/* > dimension ( N ) if ICOMPQ = 1 and dimension 1 if ICOMPQ = 0. */ +/* > If ICOMPQ = 1, on exit, K(I) is the dimension of the I-th */ +/* > secular equation on the computation tree. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] DIFL */ +/* > \verbatim */ +/* > DIFL is DOUBLE PRECISION array, dimension ( LDU, NLVL ), */ +/* > where NLVL = floor(log_2 (N/SMLSIZ))). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] DIFR */ +/* > \verbatim */ +/* > DIFR is DOUBLE PRECISION array, */ +/* > dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1 and */ +/* > dimension ( N ) if ICOMPQ = 0. */ +/* > If ICOMPQ = 1, on exit, DIFL(1:N, I) and DIFR(1:N, 2 * I - 1) */ +/* > record distances between singular values on the I-th */ +/* > level and singular values on the (I -1)-th level, and */ +/* > DIFR(1:N, 2 * I ) contains the normalizing factors for */ +/* > the right singular vector matrix. See DLASD8 for details. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] Z */ +/* > \verbatim */ +/* > Z is DOUBLE PRECISION array, */ +/* > dimension ( LDU, NLVL ) if ICOMPQ = 1 and */ +/* > dimension ( N ) if ICOMPQ = 0. */ +/* > The first K elements of Z(1, I) contain the components of */ +/* > the deflation-adjusted updating row vector for subproblems */ +/* > on the I-th level. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] POLES */ +/* > \verbatim */ +/* > POLES is DOUBLE PRECISION array, */ +/* > dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not referenced */ +/* > if ICOMPQ = 0. If ICOMPQ = 1, on exit, POLES(1, 2*I - 1) and */ +/* > POLES(1, 2*I) contain the new and old singular values */ +/* > involved in the secular equations on the I-th level. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] GIVPTR */ +/* > \verbatim */ +/* > GIVPTR is INTEGER array, */ +/* > dimension ( N ) if ICOMPQ = 1, and not referenced if */ +/* > ICOMPQ = 0. If ICOMPQ = 1, on exit, GIVPTR( I ) records */ +/* > the number of Givens rotations performed on the I-th */ +/* > problem on the computation tree. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] GIVCOL */ +/* > \verbatim */ +/* > GIVCOL is INTEGER array, */ +/* > dimension ( LDGCOL, 2 * NLVL ) if ICOMPQ = 1, and not */ +/* > referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, */ +/* > GIVCOL(1, 2 *I - 1) and GIVCOL(1, 2 *I) record the locations */ +/* > of Givens rotations performed on the I-th level on the */ +/* > computation tree. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDGCOL */ +/* > \verbatim */ +/* > LDGCOL is INTEGER, LDGCOL = > N. */ +/* > The leading dimension of arrays GIVCOL and PERM. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] PERM */ +/* > \verbatim */ +/* > PERM is INTEGER array, */ +/* > dimension ( LDGCOL, NLVL ) if ICOMPQ = 1, and not referenced */ +/* > if ICOMPQ = 0. If ICOMPQ = 1, on exit, PERM(1, I) records */ +/* > permutations done on the I-th level of the computation tree. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] GIVNUM */ +/* > \verbatim */ +/* > GIVNUM is DOUBLE PRECISION array, */ +/* > dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not */ +/* > referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, */ +/* > GIVNUM(1, 2 *I - 1) and GIVNUM(1, 2 *I) record the C- and S- */ +/* > values of Givens rotations performed on the I-th level on */ +/* > the computation tree. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] C */ +/* > \verbatim */ +/* > C is DOUBLE PRECISION array, */ +/* > dimension ( N ) if ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. */ +/* > If ICOMPQ = 1 and the I-th subproblem is not square, on exit, */ +/* > C( I ) contains the C-value of a Givens rotation related to */ +/* > the right null space of the I-th subproblem. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] S */ +/* > \verbatim */ +/* > S is DOUBLE PRECISION array, dimension ( N ) if */ +/* > ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1 */ +/* > and the I-th subproblem is not square, on exit, S( I ) */ +/* > contains the S-value of a Givens rotation related to */ +/* > the right null space of the I-th subproblem. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension */ +/* > (6 * N + (SMLSIZ + 1)*(SMLSIZ + 1)). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] IWORK */ +/* > \verbatim */ +/* > IWORK is INTEGER array, dimension (7*N) */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit. */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ +/* > > 0: if INFO = 1, a singular value did not converge */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup OTHERauxiliary */ + +/* > \par Contributors: */ +/* ================== */ +/* > */ +/* > Ming Gu and Huan Ren, Computer Science Division, University of */ +/* > California at Berkeley, USA */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dlasda_(integer *icompq, integer *smlsiz, integer *n, + integer *sqre, doublereal *d__, doublereal *e, doublereal *u, integer + *ldu, doublereal *vt, integer *k, doublereal *difl, doublereal *difr, + doublereal *z__, doublereal *poles, integer *givptr, integer *givcol, + integer *ldgcol, integer *perm, doublereal *givnum, doublereal *c__, + doublereal *s, doublereal *work, integer *iwork, integer *info) +{ + /* System generated locals */ + integer givcol_dim1, givcol_offset, perm_dim1, perm_offset, difl_dim1, + difl_offset, difr_dim1, difr_offset, givnum_dim1, givnum_offset, + poles_dim1, poles_offset, u_dim1, u_offset, vt_dim1, vt_offset, + z_dim1, z_offset, i__1, i__2; + + /* Builtin functions */ + integer pow_ii(integer *, integer *); + + /* Local variables */ + integer i__, j, m, i1, ic, lf, nd, ll, nl, vf, nr, vl, im1, ncc, nlf, nrf, + vfi, iwk, vli, lvl, nru, ndb1, nlp1, lvl2, nrp1; + doublereal beta; + integer idxq, nlvl; + doublereal alpha; + integer inode, ndiml, ndimr, idxqi, itemp; + extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, + doublereal *, integer *); + integer sqrei; + extern /* Subroutine */ int dlasd6_(integer *, integer *, integer *, + integer *, doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, integer *, integer *, integer *, integer *, + integer *, doublereal *, integer *, doublereal *, doublereal *, + doublereal *, doublereal *, integer *, doublereal *, doublereal *, + doublereal *, integer *, integer *); + integer nwork1, nwork2; + extern /* Subroutine */ int dlasdq_(char *, integer *, integer *, integer + *, integer *, integer *, doublereal *, doublereal *, doublereal *, + integer *, doublereal *, integer *, doublereal *, integer *, + doublereal *, integer *, ftnlen), dlasdt_(integer *, integer *, + integer *, integer *, integer *, integer *, integer *), dlaset_( + char *, integer *, integer *, doublereal *, doublereal *, + doublereal *, integer *, ftnlen), xerbla_(char *, integer *, + ftnlen); + integer smlszp; + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --d__; + --e; + givnum_dim1 = *ldu; + givnum_offset = 1 + givnum_dim1; + givnum -= givnum_offset; + poles_dim1 = *ldu; + poles_offset = 1 + poles_dim1; + poles -= poles_offset; + z_dim1 = *ldu; + z_offset = 1 + z_dim1; + z__ -= z_offset; + difr_dim1 = *ldu; + difr_offset = 1 + difr_dim1; + difr -= difr_offset; + difl_dim1 = *ldu; + difl_offset = 1 + difl_dim1; + difl -= difl_offset; + vt_dim1 = *ldu; + vt_offset = 1 + vt_dim1; + vt -= vt_offset; + u_dim1 = *ldu; + u_offset = 1 + u_dim1; + u -= u_offset; + --k; + --givptr; + perm_dim1 = *ldgcol; + perm_offset = 1 + perm_dim1; + perm -= perm_offset; + givcol_dim1 = *ldgcol; + givcol_offset = 1 + givcol_dim1; + givcol -= givcol_offset; + --c__; + --s; + --work; + --iwork; + + /* Function Body */ + *info = 0; + + if (*icompq < 0 || *icompq > 1) { + *info = -1; + } else if (*smlsiz < 3) { + *info = -2; + } else if (*n < 0) { + *info = -3; + } else if (*sqre < 0 || *sqre > 1) { + *info = -4; + } else if (*ldu < *n + *sqre) { + *info = -8; + } else if (*ldgcol < *n) { + *info = -17; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DLASDA", &i__1, (ftnlen)6); + return 0; + } + + m = *n + *sqre; + +/* If the input matrix is too small, call DLASDQ to find the SVD. */ + + if (*n <= *smlsiz) { + if (*icompq == 0) { + dlasdq_((char *)"U", sqre, n, &c__0, &c__0, &c__0, &d__[1], &e[1], &vt[ + vt_offset], ldu, &u[u_offset], ldu, &u[u_offset], ldu, & + work[1], info, (ftnlen)1); + } else { + dlasdq_((char *)"U", sqre, n, &m, n, &c__0, &d__[1], &e[1], &vt[vt_offset] + , ldu, &u[u_offset], ldu, &u[u_offset], ldu, &work[1], + info, (ftnlen)1); + } + return 0; + } + +/* Book-keeping and set up the computation tree. */ + + inode = 1; + ndiml = inode + *n; + ndimr = ndiml + *n; + idxq = ndimr + *n; + iwk = idxq + *n; + + ncc = 0; + nru = 0; + + smlszp = *smlsiz + 1; + vf = 1; + vl = vf + m; + nwork1 = vl + m; + nwork2 = nwork1 + smlszp * smlszp; + + dlasdt_(n, &nlvl, &nd, &iwork[inode], &iwork[ndiml], &iwork[ndimr], + smlsiz); + +/* for the nodes on bottom level of the tree, solve */ +/* their subproblems by DLASDQ. */ + + ndb1 = (nd + 1) / 2; + i__1 = nd; + for (i__ = ndb1; i__ <= i__1; ++i__) { + +/* IC : center row of each node */ +/* NL : number of rows of left subproblem */ +/* NR : number of rows of right subproblem */ +/* NLF: starting row of the left subproblem */ +/* NRF: starting row of the right subproblem */ + + i1 = i__ - 1; + ic = iwork[inode + i1]; + nl = iwork[ndiml + i1]; + nlp1 = nl + 1; + nr = iwork[ndimr + i1]; + nlf = ic - nl; + nrf = ic + 1; + idxqi = idxq + nlf - 2; + vfi = vf + nlf - 1; + vli = vl + nlf - 1; + sqrei = 1; + if (*icompq == 0) { + dlaset_((char *)"A", &nlp1, &nlp1, &c_b11, &c_b12, &work[nwork1], &smlszp, + (ftnlen)1); + dlasdq_((char *)"U", &sqrei, &nl, &nlp1, &nru, &ncc, &d__[nlf], &e[nlf], & + work[nwork1], &smlszp, &work[nwork2], &nl, &work[nwork2], + &nl, &work[nwork2], info, (ftnlen)1); + itemp = nwork1 + nl * smlszp; + dcopy_(&nlp1, &work[nwork1], &c__1, &work[vfi], &c__1); + dcopy_(&nlp1, &work[itemp], &c__1, &work[vli], &c__1); + } else { + dlaset_((char *)"A", &nl, &nl, &c_b11, &c_b12, &u[nlf + u_dim1], ldu, ( + ftnlen)1); + dlaset_((char *)"A", &nlp1, &nlp1, &c_b11, &c_b12, &vt[nlf + vt_dim1], + ldu, (ftnlen)1); + dlasdq_((char *)"U", &sqrei, &nl, &nlp1, &nl, &ncc, &d__[nlf], &e[nlf], & + vt[nlf + vt_dim1], ldu, &u[nlf + u_dim1], ldu, &u[nlf + + u_dim1], ldu, &work[nwork1], info, (ftnlen)1); + dcopy_(&nlp1, &vt[nlf + vt_dim1], &c__1, &work[vfi], &c__1); + dcopy_(&nlp1, &vt[nlf + nlp1 * vt_dim1], &c__1, &work[vli], &c__1) + ; + } + if (*info != 0) { + return 0; + } + i__2 = nl; + for (j = 1; j <= i__2; ++j) { + iwork[idxqi + j] = j; +/* L10: */ + } + if (i__ == nd && *sqre == 0) { + sqrei = 0; + } else { + sqrei = 1; + } + idxqi += nlp1; + vfi += nlp1; + vli += nlp1; + nrp1 = nr + sqrei; + if (*icompq == 0) { + dlaset_((char *)"A", &nrp1, &nrp1, &c_b11, &c_b12, &work[nwork1], &smlszp, + (ftnlen)1); + dlasdq_((char *)"U", &sqrei, &nr, &nrp1, &nru, &ncc, &d__[nrf], &e[nrf], & + work[nwork1], &smlszp, &work[nwork2], &nr, &work[nwork2], + &nr, &work[nwork2], info, (ftnlen)1); + itemp = nwork1 + (nrp1 - 1) * smlszp; + dcopy_(&nrp1, &work[nwork1], &c__1, &work[vfi], &c__1); + dcopy_(&nrp1, &work[itemp], &c__1, &work[vli], &c__1); + } else { + dlaset_((char *)"A", &nr, &nr, &c_b11, &c_b12, &u[nrf + u_dim1], ldu, ( + ftnlen)1); + dlaset_((char *)"A", &nrp1, &nrp1, &c_b11, &c_b12, &vt[nrf + vt_dim1], + ldu, (ftnlen)1); + dlasdq_((char *)"U", &sqrei, &nr, &nrp1, &nr, &ncc, &d__[nrf], &e[nrf], & + vt[nrf + vt_dim1], ldu, &u[nrf + u_dim1], ldu, &u[nrf + + u_dim1], ldu, &work[nwork1], info, (ftnlen)1); + dcopy_(&nrp1, &vt[nrf + vt_dim1], &c__1, &work[vfi], &c__1); + dcopy_(&nrp1, &vt[nrf + nrp1 * vt_dim1], &c__1, &work[vli], &c__1) + ; + } + if (*info != 0) { + return 0; + } + i__2 = nr; + for (j = 1; j <= i__2; ++j) { + iwork[idxqi + j] = j; +/* L20: */ + } +/* L30: */ + } + +/* Now conquer each subproblem bottom-up. */ + + j = pow_ii(&c__2, &nlvl); + for (lvl = nlvl; lvl >= 1; --lvl) { + lvl2 = (lvl << 1) - 1; + +/* Find the first node LF and last node LL on */ +/* the current level LVL. */ + + if (lvl == 1) { + lf = 1; + ll = 1; + } else { + i__1 = lvl - 1; + lf = pow_ii(&c__2, &i__1); + ll = (lf << 1) - 1; + } + i__1 = ll; + for (i__ = lf; i__ <= i__1; ++i__) { + im1 = i__ - 1; + ic = iwork[inode + im1]; + nl = iwork[ndiml + im1]; + nr = iwork[ndimr + im1]; + nlf = ic - nl; + nrf = ic + 1; + if (i__ == ll) { + sqrei = *sqre; + } else { + sqrei = 1; + } + vfi = vf + nlf - 1; + vli = vl + nlf - 1; + idxqi = idxq + nlf - 1; + alpha = d__[ic]; + beta = e[ic]; + if (*icompq == 0) { + dlasd6_(icompq, &nl, &nr, &sqrei, &d__[nlf], &work[vfi], & + work[vli], &alpha, &beta, &iwork[idxqi], &perm[ + perm_offset], &givptr[1], &givcol[givcol_offset], + ldgcol, &givnum[givnum_offset], ldu, &poles[ + poles_offset], &difl[difl_offset], &difr[difr_offset], + &z__[z_offset], &k[1], &c__[1], &s[1], &work[nwork1], + &iwork[iwk], info); + } else { + --j; + dlasd6_(icompq, &nl, &nr, &sqrei, &d__[nlf], &work[vfi], & + work[vli], &alpha, &beta, &iwork[idxqi], &perm[nlf + + lvl * perm_dim1], &givptr[j], &givcol[nlf + lvl2 * + givcol_dim1], ldgcol, &givnum[nlf + lvl2 * + givnum_dim1], ldu, &poles[nlf + lvl2 * poles_dim1], & + difl[nlf + lvl * difl_dim1], &difr[nlf + lvl2 * + difr_dim1], &z__[nlf + lvl * z_dim1], &k[j], &c__[j], + &s[j], &work[nwork1], &iwork[iwk], info); + } + if (*info != 0) { + return 0; + } +/* L40: */ + } +/* L50: */ + } + + return 0; + +/* End of DLASDA */ + +} /* dlasda_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlasdq.cpp b/lib/linalg/dlasdq.cpp new file mode 100644 index 0000000000..efb468cef4 --- /dev/null +++ b/lib/linalg/dlasdq.cpp @@ -0,0 +1,486 @@ +/* fortran/dlasdq.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; + +/* > \brief \b DLASDQ computes the SVD of a real bidiagonal matrix with diagonal d and off-diagonal e. Used by + sbdsdc. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLASDQ + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLASDQ( UPLO, SQRE, N, NCVT, NRU, NCC, D, E, VT, LDVT, */ +/* U, LDU, C, LDC, WORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER UPLO */ +/* INTEGER INFO, LDC, LDU, LDVT, N, NCC, NCVT, NRU, SQRE */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION C( LDC, * ), D( * ), E( * ), U( LDU, * ), */ +/* $ VT( LDVT, * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLASDQ computes the singular value decomposition (SVD) of a real */ +/* > (upper or lower) bidiagonal matrix with diagonal D and offdiagonal */ +/* > E, accumulating the transformations if desired. Letting B denote */ +/* > the input bidiagonal matrix, the algorithm computes orthogonal */ +/* > matrices Q and P such that B = Q * S * P**T (P**T denotes the transpose */ +/* > of P). The singular values S are overwritten on D. */ +/* > */ +/* > The input matrix U is changed to U * Q if desired. */ +/* > The input matrix VT is changed to P**T * VT if desired. */ +/* > The input matrix C is changed to Q**T * C if desired. */ +/* > */ +/* > See "Computing Small Singular Values of Bidiagonal Matrices With */ +/* > Guaranteed High Relative Accuracy," by J. Demmel and W. Kahan, */ +/* > LAPACK Working Note #3, for a detailed description of the algorithm. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > On entry, UPLO specifies whether the input bidiagonal matrix */ +/* > is upper or lower bidiagonal, and whether it is square are */ +/* > not. */ +/* > UPLO = 'U' or 'u' B is upper bidiagonal. */ +/* > UPLO = 'L' or 'l' B is lower bidiagonal. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] SQRE */ +/* > \verbatim */ +/* > SQRE is INTEGER */ +/* > = 0: then the input matrix is N-by-N. */ +/* > = 1: then the input matrix is N-by-(N+1) if UPLU = 'U' and */ +/* > (N+1)-by-N if UPLU = 'L'. */ +/* > */ +/* > The bidiagonal matrix has */ +/* > N = NL + NR + 1 rows and */ +/* > M = N + SQRE >= N columns. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > On entry, N specifies the number of rows and columns */ +/* > in the matrix. N must be at least 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] NCVT */ +/* > \verbatim */ +/* > NCVT is INTEGER */ +/* > On entry, NCVT specifies the number of columns of */ +/* > the matrix VT. NCVT must be at least 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] NRU */ +/* > \verbatim */ +/* > NRU is INTEGER */ +/* > On entry, NRU specifies the number of rows of */ +/* > the matrix U. NRU must be at least 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] NCC */ +/* > \verbatim */ +/* > NCC is INTEGER */ +/* > On entry, NCC specifies the number of columns of */ +/* > the matrix C. NCC must be at least 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension (N) */ +/* > On entry, D contains the diagonal entries of the */ +/* > bidiagonal matrix whose SVD is desired. On normal exit, */ +/* > D contains the singular values in ascending order. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] E */ +/* > \verbatim */ +/* > E is DOUBLE PRECISION array. */ +/* > dimension is (N-1) if SQRE = 0 and N if SQRE = 1. */ +/* > On entry, the entries of E contain the offdiagonal entries */ +/* > of the bidiagonal matrix whose SVD is desired. On normal */ +/* > exit, E will contain 0. If the algorithm does not converge, */ +/* > D and E will contain the diagonal and superdiagonal entries */ +/* > of a bidiagonal matrix orthogonally equivalent to the one */ +/* > given as input. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] VT */ +/* > \verbatim */ +/* > VT is DOUBLE PRECISION array, dimension (LDVT, NCVT) */ +/* > On entry, contains a matrix which on exit has been */ +/* > premultiplied by P**T, dimension N-by-NCVT if SQRE = 0 */ +/* > and (N+1)-by-NCVT if SQRE = 1 (not referenced if NCVT=0). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDVT */ +/* > \verbatim */ +/* > LDVT is INTEGER */ +/* > On entry, LDVT specifies the leading dimension of VT as */ +/* > declared in the calling (sub) program. LDVT must be at */ +/* > least 1. If NCVT is nonzero LDVT must also be at least N. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] U */ +/* > \verbatim */ +/* > U is DOUBLE PRECISION array, dimension (LDU, N) */ +/* > On entry, contains a matrix which on exit has been */ +/* > postmultiplied by Q, dimension NRU-by-N if SQRE = 0 */ +/* > and NRU-by-(N+1) if SQRE = 1 (not referenced if NRU=0). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDU */ +/* > \verbatim */ +/* > LDU is INTEGER */ +/* > On entry, LDU specifies the leading dimension of U as */ +/* > declared in the calling (sub) program. LDU must be at */ +/* > least max( 1, NRU ) . */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] C */ +/* > \verbatim */ +/* > C is DOUBLE PRECISION array, dimension (LDC, NCC) */ +/* > On entry, contains an N-by-NCC matrix which on exit */ +/* > has been premultiplied by Q**T dimension N-by-NCC if SQRE = 0 */ +/* > and (N+1)-by-NCC if SQRE = 1 (not referenced if NCC=0). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDC */ +/* > \verbatim */ +/* > LDC is INTEGER */ +/* > On entry, LDC specifies the leading dimension of C as */ +/* > declared in the calling (sub) program. LDC must be at */ +/* > least 1. If NCC is nonzero, LDC must also be at least N. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (4*N) */ +/* > Workspace. Only referenced if one of NCVT, NRU, or NCC is */ +/* > nonzero, and if N is at least 2. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > On exit, a value of 0 indicates a successful exit. */ +/* > If INFO < 0, argument number -INFO is illegal. */ +/* > If INFO > 0, the algorithm did not converge, and INFO */ +/* > specifies how many superdiagonals did not converge. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup OTHERauxiliary */ + +/* > \par Contributors: */ +/* ================== */ +/* > */ +/* > Ming Gu and Huan Ren, Computer Science Division, University of */ +/* > California at Berkeley, USA */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dlasdq_(char *uplo, integer *sqre, integer *n, integer * + ncvt, integer *nru, integer *ncc, doublereal *d__, doublereal *e, + doublereal *vt, integer *ldvt, doublereal *u, integer *ldu, + doublereal *c__, integer *ldc, doublereal *work, integer *info, + ftnlen uplo_len) +{ + /* System generated locals */ + integer c_dim1, c_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1, + i__2; + + /* Local variables */ + integer i__, j; + doublereal r__, cs, sn; + integer np1, isub; + doublereal smin; + integer sqre1; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int dlasr_(char *, char *, char *, integer *, + integer *, doublereal *, doublereal *, doublereal *, integer *, + ftnlen, ftnlen, ftnlen), dswap_(integer *, doublereal *, integer * + , doublereal *, integer *); + integer iuplo; + extern /* Subroutine */ int dlartg_(doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *), xerbla_(char *, + integer *, ftnlen), dbdsqr_(char *, integer *, integer *, integer + *, integer *, doublereal *, doublereal *, doublereal *, integer *, + doublereal *, integer *, doublereal *, integer *, doublereal *, + integer *, ftnlen); + logical rotate; + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --d__; + --e; + vt_dim1 = *ldvt; + vt_offset = 1 + vt_dim1; + vt -= vt_offset; + u_dim1 = *ldu; + u_offset = 1 + u_dim1; + u -= u_offset; + c_dim1 = *ldc; + c_offset = 1 + c_dim1; + c__ -= c_offset; + --work; + + /* Function Body */ + *info = 0; + iuplo = 0; + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + iuplo = 1; + } + if (lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + iuplo = 2; + } + if (iuplo == 0) { + *info = -1; + } else if (*sqre < 0 || *sqre > 1) { + *info = -2; + } else if (*n < 0) { + *info = -3; + } else if (*ncvt < 0) { + *info = -4; + } else if (*nru < 0) { + *info = -5; + } else if (*ncc < 0) { + *info = -6; + } else if (*ncvt == 0 && *ldvt < 1 || *ncvt > 0 && *ldvt < max(1,*n)) { + *info = -10; + } else if (*ldu < max(1,*nru)) { + *info = -12; + } else if (*ncc == 0 && *ldc < 1 || *ncc > 0 && *ldc < max(1,*n)) { + *info = -14; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DLASDQ", &i__1, (ftnlen)6); + return 0; + } + if (*n == 0) { + return 0; + } + +/* ROTATE is true if any singular vectors desired, false otherwise */ + + rotate = *ncvt > 0 || *nru > 0 || *ncc > 0; + np1 = *n + 1; + sqre1 = *sqre; + +/* If matrix non-square upper bidiagonal, rotate to be lower */ +/* bidiagonal. The rotations are on the right. */ + + if (iuplo == 1 && sqre1 == 1) { + i__1 = *n - 1; + for (i__ = 1; i__ <= i__1; ++i__) { + dlartg_(&d__[i__], &e[i__], &cs, &sn, &r__); + d__[i__] = r__; + e[i__] = sn * d__[i__ + 1]; + d__[i__ + 1] = cs * d__[i__ + 1]; + if (rotate) { + work[i__] = cs; + work[*n + i__] = sn; + } +/* L10: */ + } + dlartg_(&d__[*n], &e[*n], &cs, &sn, &r__); + d__[*n] = r__; + e[*n] = 0.; + if (rotate) { + work[*n] = cs; + work[*n + *n] = sn; + } + iuplo = 2; + sqre1 = 0; + +/* Update singular vectors if desired. */ + + if (*ncvt > 0) { + dlasr_((char *)"L", (char *)"V", (char *)"F", &np1, ncvt, &work[1], &work[np1], &vt[ + vt_offset], ldvt, (ftnlen)1, (ftnlen)1, (ftnlen)1); + } + } + +/* If matrix lower bidiagonal, rotate to be upper bidiagonal */ +/* by applying Givens rotations on the left. */ + + if (iuplo == 2) { + i__1 = *n - 1; + for (i__ = 1; i__ <= i__1; ++i__) { + dlartg_(&d__[i__], &e[i__], &cs, &sn, &r__); + d__[i__] = r__; + e[i__] = sn * d__[i__ + 1]; + d__[i__ + 1] = cs * d__[i__ + 1]; + if (rotate) { + work[i__] = cs; + work[*n + i__] = sn; + } +/* L20: */ + } + +/* If matrix (N+1)-by-N lower bidiagonal, one additional */ +/* rotation is needed. */ + + if (sqre1 == 1) { + dlartg_(&d__[*n], &e[*n], &cs, &sn, &r__); + d__[*n] = r__; + if (rotate) { + work[*n] = cs; + work[*n + *n] = sn; + } + } + +/* Update singular vectors if desired. */ + + if (*nru > 0) { + if (sqre1 == 0) { + dlasr_((char *)"R", (char *)"V", (char *)"F", nru, n, &work[1], &work[np1], &u[ + u_offset], ldu, (ftnlen)1, (ftnlen)1, (ftnlen)1); + } else { + dlasr_((char *)"R", (char *)"V", (char *)"F", nru, &np1, &work[1], &work[np1], &u[ + u_offset], ldu, (ftnlen)1, (ftnlen)1, (ftnlen)1); + } + } + if (*ncc > 0) { + if (sqre1 == 0) { + dlasr_((char *)"L", (char *)"V", (char *)"F", n, ncc, &work[1], &work[np1], &c__[ + c_offset], ldc, (ftnlen)1, (ftnlen)1, (ftnlen)1); + } else { + dlasr_((char *)"L", (char *)"V", (char *)"F", &np1, ncc, &work[1], &work[np1], &c__[ + c_offset], ldc, (ftnlen)1, (ftnlen)1, (ftnlen)1); + } + } + } + +/* Call DBDSQR to compute the SVD of the reduced real */ +/* N-by-N upper bidiagonal matrix. */ + + dbdsqr_((char *)"U", n, ncvt, nru, ncc, &d__[1], &e[1], &vt[vt_offset], ldvt, &u[ + u_offset], ldu, &c__[c_offset], ldc, &work[1], info, (ftnlen)1); + +/* Sort the singular values into ascending order (insertion sort on */ +/* singular values, but only one transposition per singular vector) */ + + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + +/* Scan for smallest D(I). */ + + isub = i__; + smin = d__[i__]; + i__2 = *n; + for (j = i__ + 1; j <= i__2; ++j) { + if (d__[j] < smin) { + isub = j; + smin = d__[j]; + } +/* L30: */ + } + if (isub != i__) { + +/* Swap singular values and vectors. */ + + d__[isub] = d__[i__]; + d__[i__] = smin; + if (*ncvt > 0) { + dswap_(ncvt, &vt[isub + vt_dim1], ldvt, &vt[i__ + vt_dim1], + ldvt); + } + if (*nru > 0) { + dswap_(nru, &u[isub * u_dim1 + 1], &c__1, &u[i__ * u_dim1 + 1] + , &c__1); + } + if (*ncc > 0) { + dswap_(ncc, &c__[isub + c_dim1], ldc, &c__[i__ + c_dim1], ldc) + ; + } + } +/* L40: */ + } + + return 0; + +/* End of DLASDQ */ + +} /* dlasdq_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlasdt.cpp b/lib/linalg/dlasdt.cpp new file mode 100644 index 0000000000..0e507af8f2 --- /dev/null +++ b/lib/linalg/dlasdt.cpp @@ -0,0 +1,209 @@ +/* fortran/dlasdt.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DLASDT creates a tree of subproblems for bidiagonal divide and conquer. Used by sbdsdc. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLASDT + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLASDT( N, LVL, ND, INODE, NDIML, NDIMR, MSUB ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER LVL, MSUB, N, ND */ +/* .. */ +/* .. Array Arguments .. */ +/* INTEGER INODE( * ), NDIML( * ), NDIMR( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLASDT creates a tree of subproblems for bidiagonal divide and */ +/* > conquer. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > On entry, the number of diagonal elements of the */ +/* > bidiagonal matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] LVL */ +/* > \verbatim */ +/* > LVL is INTEGER */ +/* > On exit, the number of levels on the computation tree. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] ND */ +/* > \verbatim */ +/* > ND is INTEGER */ +/* > On exit, the number of nodes on the tree. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INODE */ +/* > \verbatim */ +/* > INODE is INTEGER array, dimension ( N ) */ +/* > On exit, centers of subproblems. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] NDIML */ +/* > \verbatim */ +/* > NDIML is INTEGER array, dimension ( N ) */ +/* > On exit, row dimensions of left children. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] NDIMR */ +/* > \verbatim */ +/* > NDIMR is INTEGER array, dimension ( N ) */ +/* > On exit, row dimensions of right children. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] MSUB */ +/* > \verbatim */ +/* > MSUB is INTEGER */ +/* > On entry, the maximum row dimension each subproblem at the */ +/* > bottom of the tree can be of. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup OTHERauxiliary */ + +/* > \par Contributors: */ +/* ================== */ +/* > */ +/* > Ming Gu and Huan Ren, Computer Science Division, University of */ +/* > California at Berkeley, USA */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dlasdt_(integer *n, integer *lvl, integer *nd, integer * + inode, integer *ndiml, integer *ndimr, integer *msub) +{ + /* System generated locals */ + integer i__1, i__2; + + /* Builtin functions */ + double log(doublereal); + + /* Local variables */ + integer i__, il, ir, maxn; + doublereal temp; + integer nlvl, llst, ncrnt; + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Find the number of levels on the tree. */ + + /* Parameter adjustments */ + --ndimr; + --ndiml; + --inode; + + /* Function Body */ + maxn = max(1,*n); + temp = log((doublereal) maxn / (doublereal) (*msub + 1)) / log(2.); + *lvl = (integer) temp + 1; + + i__ = *n / 2; + inode[1] = i__ + 1; + ndiml[1] = i__; + ndimr[1] = *n - i__ - 1; + il = 0; + ir = 1; + llst = 1; + i__1 = *lvl - 1; + for (nlvl = 1; nlvl <= i__1; ++nlvl) { + +/* Constructing the tree at (NLVL+1)-st level. The number of */ +/* nodes created on this level is LLST * 2. */ + + i__2 = llst - 1; + for (i__ = 0; i__ <= i__2; ++i__) { + il += 2; + ir += 2; + ncrnt = llst + i__; + ndiml[il] = ndiml[ncrnt] / 2; + ndimr[il] = ndiml[ncrnt] - ndiml[il] - 1; + inode[il] = inode[ncrnt] - ndimr[il] - 1; + ndiml[ir] = ndimr[ncrnt] / 2; + ndimr[ir] = ndimr[ncrnt] - ndiml[ir] - 1; + inode[ir] = inode[ncrnt] + ndiml[ir] + 1; +/* L10: */ + } + llst <<= 1; +/* L20: */ + } + *nd = (llst << 1) - 1; + + return 0; + +/* End of DLASDT */ + +} /* dlasdt_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlaset.cpp b/lib/linalg/dlaset.cpp new file mode 100644 index 0000000000..072bbf1500 --- /dev/null +++ b/lib/linalg/dlaset.cpp @@ -0,0 +1,229 @@ +/* fortran/dlaset.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given val +ues. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLASET + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLASET( UPLO, M, N, ALPHA, BETA, A, LDA ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER UPLO */ +/* INTEGER LDA, M, N */ +/* DOUBLE PRECISION ALPHA, BETA */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLASET initializes an m-by-n matrix A to BETA on the diagonal and */ +/* > ALPHA on the offdiagonals. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > Specifies the part of the matrix A to be set. */ +/* > = 'U': Upper triangular part is set; the strictly lower */ +/* > triangular part of A is not changed. */ +/* > = 'L': Lower triangular part is set; the strictly upper */ +/* > triangular part of A is not changed. */ +/* > Otherwise: All of the matrix A is set. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix A. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] ALPHA */ +/* > \verbatim */ +/* > ALPHA is DOUBLE PRECISION */ +/* > The constant to which the offdiagonal elements are to be set. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] BETA */ +/* > \verbatim */ +/* > BETA is DOUBLE PRECISION */ +/* > The constant to which the diagonal elements are to be set. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On exit, the leading m-by-n submatrix of A is set as follows: */ +/* > */ +/* > if UPLO = 'U', A(i,j) = ALPHA, 1<=i<=j-1, 1<=j<=n, */ +/* > if UPLO = 'L', A(i,j) = ALPHA, j+1<=i<=m, 1<=j<=n, */ +/* > otherwise, A(i,j) = ALPHA, 1<=i<=m, 1<=j<=n, i.ne.j, */ +/* > */ +/* > and, for all UPLO, A(i,i) = BETA, 1<=i<=min(m,n). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,M). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup OTHERauxiliary */ + +/* ===================================================================== */ +/* Subroutine */ int dlaset_(char *uplo, integer *m, integer *n, doublereal * + alpha, doublereal *beta, doublereal *a, integer *lda, ftnlen uplo_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3; + + /* Local variables */ + integer i__, j; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + + /* Function Body */ + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + +/* Set the strictly upper triangular or trapezoidal part of the */ +/* array to ALPHA. */ + + i__1 = *n; + for (j = 2; j <= i__1; ++j) { +/* Computing MIN */ + i__3 = j - 1; + i__2 = min(i__3,*m); + for (i__ = 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] = *alpha; +/* L10: */ + } +/* L20: */ + } + + } else if (lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + +/* Set the strictly lower triangular or trapezoidal part of the */ +/* array to ALPHA. */ + + i__1 = min(*m,*n); + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = j + 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] = *alpha; +/* L30: */ + } +/* L40: */ + } + + } else { + +/* Set the leading m-by-n submatrix to ALPHA. */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] = *alpha; +/* L50: */ + } +/* L60: */ + } + } + +/* Set the first min(M,N) diagonal elements to BETA. */ + + i__1 = min(*m,*n); + for (i__ = 1; i__ <= i__1; ++i__) { + a[i__ + i__ * a_dim1] = *beta; +/* L70: */ + } + + return 0; + +/* End of DLASET */ + +} /* dlaset_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlasq1.cpp b/lib/linalg/dlasq1.cpp new file mode 100644 index 0000000000..090f680525 --- /dev/null +++ b/lib/linalg/dlasq1.cpp @@ -0,0 +1,298 @@ +/* fortran/dlasq1.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c__2 = 2; +static integer c__0 = 0; + +/* > \brief \b DLASQ1 computes the singular values of a real square bidiagonal matrix. Used by sbdsqr. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLASQ1 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLASQ1( N, D, E, WORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INFO, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION D( * ), E( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLASQ1 computes the singular values of a real N-by-N bidiagonal */ +/* > matrix with diagonal D and off-diagonal E. The singular values */ +/* > are computed to high relative accuracy, in the absence of */ +/* > denormalization, underflow and overflow. The algorithm was first */ +/* > presented in */ +/* > */ +/* > (char *)"Accurate singular values and differential qd algorithms" by K. V. */ +/* > Fernando and B. N. Parlett, Numer. Math., Vol-67, No. 2, pp. 191-230, */ +/* > 1994, */ +/* > */ +/* > and the present implementation is described in "An implementation of */ +/* > the dqds Algorithm (Positive Case)", LAPACK Working Note. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of rows and columns in the matrix. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension (N) */ +/* > On entry, D contains the diagonal elements of the */ +/* > bidiagonal matrix whose SVD is desired. On normal exit, */ +/* > D contains the singular values in decreasing order. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] E */ +/* > \verbatim */ +/* > E is DOUBLE PRECISION array, dimension (N) */ +/* > On entry, elements E(1:N-1) contain the off-diagonal elements */ +/* > of the bidiagonal matrix whose SVD is desired. */ +/* > On exit, E is overwritten. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (4*N) */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > > 0: the algorithm failed */ +/* > = 1, a split was marked by a positive value in E */ +/* > = 2, current block of Z not diagonalized after 100*N */ +/* > iterations (in inner while loop) On exit D and E */ +/* > represent a matrix with the same singular values */ +/* > which the calling subroutine could use to finish the */ +/* > computation, or even feed back into DLASQ1 */ +/* > = 3, termination criterion of outer while loop not met */ +/* > (program created more than N unreduced blocks) */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup auxOTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dlasq1_(integer *n, doublereal *d__, doublereal *e, + doublereal *work, integer *info) +{ + /* System generated locals */ + integer i__1, i__2; + doublereal d__1, d__2, d__3; + + /* Builtin functions */ + double sqrt(doublereal); + + /* Local variables */ + integer i__; + doublereal eps; + extern /* Subroutine */ int dlas2_(doublereal *, doublereal *, doublereal + *, doublereal *, doublereal *); + doublereal scale; + integer iinfo; + doublereal sigmn; + extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, + doublereal *, integer *); + doublereal sigmx; + extern /* Subroutine */ int dlasq2_(integer *, doublereal *, integer *); + extern doublereal dlamch_(char *, ftnlen); + extern /* Subroutine */ int dlascl_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, integer *, doublereal *, + integer *, integer *, ftnlen); + doublereal safmin; + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), dlasrt_( + char *, integer *, doublereal *, integer *, ftnlen); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + + /* Parameter adjustments */ + --work; + --e; + --d__; + + /* Function Body */ + *info = 0; + if (*n < 0) { + *info = -1; + i__1 = -(*info); + xerbla_((char *)"DLASQ1", &i__1, (ftnlen)6); + return 0; + } else if (*n == 0) { + return 0; + } else if (*n == 1) { + d__[1] = abs(d__[1]); + return 0; + } else if (*n == 2) { + dlas2_(&d__[1], &e[1], &d__[2], &sigmn, &sigmx); + d__[1] = sigmx; + d__[2] = sigmn; + return 0; + } + +/* Estimate the largest singular value. */ + + sigmx = 0.; + i__1 = *n - 1; + for (i__ = 1; i__ <= i__1; ++i__) { + d__[i__] = (d__1 = d__[i__], abs(d__1)); +/* Computing MAX */ + d__2 = sigmx, d__3 = (d__1 = e[i__], abs(d__1)); + sigmx = max(d__2,d__3); +/* L10: */ + } + d__[*n] = (d__1 = d__[*n], abs(d__1)); + +/* Early return if SIGMX is zero (matrix is already diagonal). */ + + if (sigmx == 0.) { + dlasrt_((char *)"D", n, &d__[1], &iinfo, (ftnlen)1); + return 0; + } + + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { +/* Computing MAX */ + d__1 = sigmx, d__2 = d__[i__]; + sigmx = max(d__1,d__2); +/* L20: */ + } + +/* Copy D and E into WORK (in the Z format) and scale (squaring the */ +/* input data makes scaling by a power of the radix pointless). */ + + eps = dlamch_((char *)"Precision", (ftnlen)9); + safmin = dlamch_((char *)"Safe minimum", (ftnlen)12); + scale = sqrt(eps / safmin); + dcopy_(n, &d__[1], &c__1, &work[1], &c__2); + i__1 = *n - 1; + dcopy_(&i__1, &e[1], &c__1, &work[2], &c__2); + i__1 = (*n << 1) - 1; + i__2 = (*n << 1) - 1; + dlascl_((char *)"G", &c__0, &c__0, &sigmx, &scale, &i__1, &c__1, &work[1], &i__2, + &iinfo, (ftnlen)1); + +/* Compute the q's and e's. */ + + i__1 = (*n << 1) - 1; + for (i__ = 1; i__ <= i__1; ++i__) { +/* Computing 2nd power */ + d__1 = work[i__]; + work[i__] = d__1 * d__1; +/* L30: */ + } + work[*n * 2] = 0.; + + dlasq2_(n, &work[1], info); + + if (*info == 0) { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + d__[i__] = sqrt(work[i__]); +/* L40: */ + } + dlascl_((char *)"G", &c__0, &c__0, &scale, &sigmx, n, &c__1, &d__[1], n, & + iinfo, (ftnlen)1); + } else if (*info == 2) { + +/* Maximum number of iterations exceeded. Move data from WORK */ +/* into D and E so the calling subroutine can try to finish */ + + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + d__[i__] = sqrt(work[(i__ << 1) - 1]); + e[i__] = sqrt(work[i__ * 2]); + } + dlascl_((char *)"G", &c__0, &c__0, &scale, &sigmx, n, &c__1, &d__[1], n, & + iinfo, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &scale, &sigmx, n, &c__1, &e[1], n, &iinfo, + (ftnlen)1); + } + + return 0; + +/* End of DLASQ1 */ + +} /* dlasq1_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlasq2.cpp b/lib/linalg/dlasq2.cpp new file mode 100644 index 0000000000..a6362ecfdf --- /dev/null +++ b/lib/linalg/dlasq2.cpp @@ -0,0 +1,716 @@ +/* fortran/dlasq2.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c__2 = 2; +static integer c__10 = 10; +static integer c__3 = 3; +static integer c__4 = 4; + +/* > \brief \b DLASQ2 computes all the eigenvalues of the symmetric positive definite tridiagonal matrix assoc +iated with the qd Array Z to high relative accuracy. Used by sbdsqr and sstegr. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLASQ2 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLASQ2( N, Z, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INFO, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION Z( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLASQ2 computes all the eigenvalues of the symmetric positive */ +/* > definite tridiagonal matrix associated with the qd array Z to high */ +/* > relative accuracy are computed to high relative accuracy, in the */ +/* > absence of denormalization, underflow and overflow. */ +/* > */ +/* > To see the relation of Z to the tridiagonal matrix, let L be a */ +/* > unit lower bidiagonal matrix with subdiagonals Z(2,4,6,,..) and */ +/* > let U be an upper bidiagonal matrix with 1's above and diagonal */ +/* > Z(1,3,5,,..). The tridiagonal is L*U or, if you prefer, the */ +/* > symmetric tridiagonal to which it is similar. */ +/* > */ +/* > Note : DLASQ2 defines a logical variable, IEEE, which is true */ +/* > on machines which follow ieee-754 floating-point standard in their */ +/* > handling of infinities and NaNs, and false otherwise. This variable */ +/* > is passed to DLASQ3. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of rows and columns in the matrix. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] Z */ +/* > \verbatim */ +/* > Z is DOUBLE PRECISION array, dimension ( 4*N ) */ +/* > On entry Z holds the qd array. On exit, entries 1 to N hold */ +/* > the eigenvalues in decreasing order, Z( 2*N+1 ) holds the */ +/* > trace, and Z( 2*N+2 ) holds the sum of the eigenvalues. If */ +/* > N > 2, then Z( 2*N+3 ) holds the iteration count, Z( 2*N+4 ) */ +/* > holds NDIVS/NIN^2, and Z( 2*N+5 ) holds the percentage of */ +/* > shifts that failed. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if the i-th argument is a scalar and had an illegal */ +/* > value, then INFO = -i, if the i-th argument is an */ +/* > array and the j-entry had an illegal value, then */ +/* > INFO = -(i*100+j) */ +/* > > 0: the algorithm failed */ +/* > = 1, a split was marked by a positive value in E */ +/* > = 2, current block of Z not diagonalized after 100*N */ +/* > iterations (in inner while loop). On exit Z holds */ +/* > a qd array with the same eigenvalues as the given Z. */ +/* > = 3, termination criterion of outer while loop not met */ +/* > (program created more than N unreduced blocks) */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup auxOTHERcomputational */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > Local Variables: I0:N0 defines a current unreduced segment of Z. */ +/* > The shifts are accumulated in SIGMA. Iteration count is in ITER. */ +/* > Ping-pong is controlled by PP (alternates between 0 and 1). */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dlasq2_(integer *n, doublereal *z__, integer *info) +{ + /* System generated locals */ + integer i__1, i__2, i__3; + doublereal d__1, d__2; + + /* Builtin functions */ + double sqrt(doublereal); + + /* Local variables */ + doublereal d__, e, g; + integer k; + doublereal s, t; + integer i0, i1, i4, n0, n1; + doublereal dn; + integer pp; + doublereal dn1, dn2, dee, eps, tau, tol; + integer ipn4; + doublereal tol2; + logical ieee; + integer nbig; + doublereal dmin__, emin, emax; + integer kmin, ndiv, iter; + doublereal qmin, temp, qmax, zmax; + integer splt; + doublereal dmin1, dmin2; + integer nfail; + doublereal desig, trace, sigma; + integer iinfo; + doublereal tempe, tempq; + integer ttype; + extern /* Subroutine */ int dlasq3_(integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, doublereal *, doublereal *, + integer *, integer *, integer *, logical *, integer *, + doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *); + extern doublereal dlamch_(char *, ftnlen); + doublereal deemin; + integer iwhila, iwhilb; + doublereal oldemn, safmin; + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dlasrt_(char *, integer *, doublereal *, + integer *, ftnlen); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments. */ +/* (in case DLASQ2 is not called by DLASQ1) */ + + /* Parameter adjustments */ + --z__; + + /* Function Body */ + *info = 0; + eps = dlamch_((char *)"Precision", (ftnlen)9); + safmin = dlamch_((char *)"Safe minimum", (ftnlen)12); + tol = eps * 100.; +/* Computing 2nd power */ + d__1 = tol; + tol2 = d__1 * d__1; + + if (*n < 0) { + *info = -1; + xerbla_((char *)"DLASQ2", &c__1, (ftnlen)6); + return 0; + } else if (*n == 0) { + return 0; + } else if (*n == 1) { + +/* 1-by-1 case. */ + + if (z__[1] < 0.) { + *info = -201; + xerbla_((char *)"DLASQ2", &c__2, (ftnlen)6); + } + return 0; + } else if (*n == 2) { + +/* 2-by-2 case. */ + + if (z__[1] < 0.) { + *info = -201; + xerbla_((char *)"DLASQ2", &c__2, (ftnlen)6); + return 0; + } else if (z__[2] < 0.) { + *info = -202; + xerbla_((char *)"DLASQ2", &c__2, (ftnlen)6); + return 0; + } else if (z__[3] < 0.) { + *info = -203; + xerbla_((char *)"DLASQ2", &c__2, (ftnlen)6); + return 0; + } else if (z__[3] > z__[1]) { + d__ = z__[3]; + z__[3] = z__[1]; + z__[1] = d__; + } + z__[5] = z__[1] + z__[2] + z__[3]; + if (z__[2] > z__[3] * tol2) { + t = (z__[1] - z__[3] + z__[2]) * .5; + s = z__[3] * (z__[2] / t); + if (s <= t) { + s = z__[3] * (z__[2] / (t * (sqrt(s / t + 1.) + 1.))); + } else { + s = z__[3] * (z__[2] / (t + sqrt(t) * sqrt(t + s))); + } + t = z__[1] + (s + z__[2]); + z__[3] *= z__[1] / t; + z__[1] = t; + } + z__[2] = z__[3]; + z__[6] = z__[2] + z__[1]; + return 0; + } + +/* Check for negative data and compute sums of q's and e's. */ + + z__[*n * 2] = 0.; + emin = z__[2]; + qmax = 0.; + zmax = 0.; + d__ = 0.; + e = 0.; + + i__1 = *n - 1 << 1; + for (k = 1; k <= i__1; k += 2) { + if (z__[k] < 0.) { + *info = -(k + 200); + xerbla_((char *)"DLASQ2", &c__2, (ftnlen)6); + return 0; + } else if (z__[k + 1] < 0.) { + *info = -(k + 201); + xerbla_((char *)"DLASQ2", &c__2, (ftnlen)6); + return 0; + } + d__ += z__[k]; + e += z__[k + 1]; +/* Computing MAX */ + d__1 = qmax, d__2 = z__[k]; + qmax = max(d__1,d__2); +/* Computing MIN */ + d__1 = emin, d__2 = z__[k + 1]; + emin = min(d__1,d__2); +/* Computing MAX */ + d__1 = max(qmax,zmax), d__2 = z__[k + 1]; + zmax = max(d__1,d__2); +/* L10: */ + } + if (z__[(*n << 1) - 1] < 0.) { + *info = -((*n << 1) + 199); + xerbla_((char *)"DLASQ2", &c__2, (ftnlen)6); + return 0; + } + d__ += z__[(*n << 1) - 1]; +/* Computing MAX */ + d__1 = qmax, d__2 = z__[(*n << 1) - 1]; + qmax = max(d__1,d__2); + zmax = max(qmax,zmax); + +/* Check for diagonality. */ + + if (e == 0.) { + i__1 = *n; + for (k = 2; k <= i__1; ++k) { + z__[k] = z__[(k << 1) - 1]; +/* L20: */ + } + dlasrt_((char *)"D", n, &z__[1], &iinfo, (ftnlen)1); + z__[(*n << 1) - 1] = d__; + return 0; + } + + trace = d__ + e; + +/* Check for zero data. */ + + if (trace == 0.) { + z__[(*n << 1) - 1] = 0.; + return 0; + } + +/* Check whether the machine is IEEE conformable. */ + + ieee = ilaenv_(&c__10, (char *)"DLASQ2", (char *)"N", &c__1, &c__2, &c__3, &c__4, (ftnlen) + 6, (ftnlen)1) == 1; + +/* Rearrange data for locality: Z=(q1,qq1,e1,ee1,q2,qq2,e2,ee2,...). */ + + for (k = *n << 1; k >= 2; k += -2) { + z__[k * 2] = 0.; + z__[(k << 1) - 1] = z__[k]; + z__[(k << 1) - 2] = 0.; + z__[(k << 1) - 3] = z__[k - 1]; +/* L30: */ + } + + i0 = 1; + n0 = *n; + +/* Reverse the qd-array, if warranted. */ + + if (z__[(i0 << 2) - 3] * 1.5 < z__[(n0 << 2) - 3]) { + ipn4 = i0 + n0 << 2; + i__1 = i0 + n0 - 1 << 1; + for (i4 = i0 << 2; i4 <= i__1; i4 += 4) { + temp = z__[i4 - 3]; + z__[i4 - 3] = z__[ipn4 - i4 - 3]; + z__[ipn4 - i4 - 3] = temp; + temp = z__[i4 - 1]; + z__[i4 - 1] = z__[ipn4 - i4 - 5]; + z__[ipn4 - i4 - 5] = temp; +/* L40: */ + } + } + +/* Initial split checking via dqd and Li's test. */ + + pp = 0; + + for (k = 1; k <= 2; ++k) { + + d__ = z__[(n0 << 2) + pp - 3]; + i__1 = (i0 << 2) + pp; + for (i4 = (n0 - 1 << 2) + pp; i4 >= i__1; i4 += -4) { + if (z__[i4 - 1] <= tol2 * d__) { + z__[i4 - 1] = -0.; + d__ = z__[i4 - 3]; + } else { + d__ = z__[i4 - 3] * (d__ / (d__ + z__[i4 - 1])); + } +/* L50: */ + } + +/* dqd maps Z to ZZ plus Li's test. */ + + emin = z__[(i0 << 2) + pp + 1]; + d__ = z__[(i0 << 2) + pp - 3]; + i__1 = (n0 - 1 << 2) + pp; + for (i4 = (i0 << 2) + pp; i4 <= i__1; i4 += 4) { + z__[i4 - (pp << 1) - 2] = d__ + z__[i4 - 1]; + if (z__[i4 - 1] <= tol2 * d__) { + z__[i4 - 1] = -0.; + z__[i4 - (pp << 1) - 2] = d__; + z__[i4 - (pp << 1)] = 0.; + d__ = z__[i4 + 1]; + } else if (safmin * z__[i4 + 1] < z__[i4 - (pp << 1) - 2] && + safmin * z__[i4 - (pp << 1) - 2] < z__[i4 + 1]) { + temp = z__[i4 + 1] / z__[i4 - (pp << 1) - 2]; + z__[i4 - (pp << 1)] = z__[i4 - 1] * temp; + d__ *= temp; + } else { + z__[i4 - (pp << 1)] = z__[i4 + 1] * (z__[i4 - 1] / z__[i4 - ( + pp << 1) - 2]); + d__ = z__[i4 + 1] * (d__ / z__[i4 - (pp << 1) - 2]); + } +/* Computing MIN */ + d__1 = emin, d__2 = z__[i4 - (pp << 1)]; + emin = min(d__1,d__2); +/* L60: */ + } + z__[(n0 << 2) - pp - 2] = d__; + +/* Now find qmax. */ + + qmax = z__[(i0 << 2) - pp - 2]; + i__1 = (n0 << 2) - pp - 2; + for (i4 = (i0 << 2) - pp + 2; i4 <= i__1; i4 += 4) { +/* Computing MAX */ + d__1 = qmax, d__2 = z__[i4]; + qmax = max(d__1,d__2); +/* L70: */ + } + +/* Prepare for the next iteration on K. */ + + pp = 1 - pp; +/* L80: */ + } + +/* Initialise variables to pass to DLASQ3. */ + + ttype = 0; + dmin1 = 0.; + dmin2 = 0.; + dn = 0.; + dn1 = 0.; + dn2 = 0.; + g = 0.; + tau = 0.; + + iter = 2; + nfail = 0; + ndiv = n0 - i0 << 1; + + i__1 = *n + 1; + for (iwhila = 1; iwhila <= i__1; ++iwhila) { + if (n0 < 1) { + goto L170; + } + +/* While array unfinished do */ + +/* E(N0) holds the value of SIGMA when submatrix in I0:N0 */ +/* splits from the rest of the array, but is negated. */ + + desig = 0.; + if (n0 == *n) { + sigma = 0.; + } else { + sigma = -z__[(n0 << 2) - 1]; + } + if (sigma < 0.) { + *info = 1; + return 0; + } + +/* Find last unreduced submatrix's top index I0, find QMAX and */ +/* EMIN. Find Gershgorin-type bound if Q's much greater than E's. */ + + emax = 0.; + if (n0 > i0) { + emin = (d__1 = z__[(n0 << 2) - 5], abs(d__1)); + } else { + emin = 0.; + } + qmin = z__[(n0 << 2) - 3]; + qmax = qmin; + for (i4 = n0 << 2; i4 >= 8; i4 += -4) { + if (z__[i4 - 5] <= 0.) { + goto L100; + } + if (qmin >= emax * 4.) { +/* Computing MIN */ + d__1 = qmin, d__2 = z__[i4 - 3]; + qmin = min(d__1,d__2); +/* Computing MAX */ + d__1 = emax, d__2 = z__[i4 - 5]; + emax = max(d__1,d__2); + } +/* Computing MAX */ + d__1 = qmax, d__2 = z__[i4 - 7] + z__[i4 - 5]; + qmax = max(d__1,d__2); +/* Computing MIN */ + d__1 = emin, d__2 = z__[i4 - 5]; + emin = min(d__1,d__2); +/* L90: */ + } + i4 = 4; + +L100: + i0 = i4 / 4; + pp = 0; + + if (n0 - i0 > 1) { + dee = z__[(i0 << 2) - 3]; + deemin = dee; + kmin = i0; + i__2 = (n0 << 2) - 3; + for (i4 = (i0 << 2) + 1; i4 <= i__2; i4 += 4) { + dee = z__[i4] * (dee / (dee + z__[i4 - 2])); + if (dee <= deemin) { + deemin = dee; + kmin = (i4 + 3) / 4; + } +/* L110: */ + } + if (kmin - i0 << 1 < n0 - kmin && deemin <= z__[(n0 << 2) - 3] * + .5) { + ipn4 = i0 + n0 << 2; + pp = 2; + i__2 = i0 + n0 - 1 << 1; + for (i4 = i0 << 2; i4 <= i__2; i4 += 4) { + temp = z__[i4 - 3]; + z__[i4 - 3] = z__[ipn4 - i4 - 3]; + z__[ipn4 - i4 - 3] = temp; + temp = z__[i4 - 2]; + z__[i4 - 2] = z__[ipn4 - i4 - 2]; + z__[ipn4 - i4 - 2] = temp; + temp = z__[i4 - 1]; + z__[i4 - 1] = z__[ipn4 - i4 - 5]; + z__[ipn4 - i4 - 5] = temp; + temp = z__[i4]; + z__[i4] = z__[ipn4 - i4 - 4]; + z__[ipn4 - i4 - 4] = temp; +/* L120: */ + } + } + } + +/* Put -(initial shift) into DMIN. */ + +/* Computing MAX */ + d__1 = 0., d__2 = qmin - sqrt(qmin) * 2. * sqrt(emax); + dmin__ = -max(d__1,d__2); + +/* Now I0:N0 is unreduced. */ +/* PP = 0 for ping, PP = 1 for pong. */ +/* PP = 2 indicates that flipping was applied to the Z array and */ +/* and that the tests for deflation upon entry in DLASQ3 */ +/* should not be performed. */ + + nbig = (n0 - i0 + 1) * 100; + i__2 = nbig; + for (iwhilb = 1; iwhilb <= i__2; ++iwhilb) { + if (i0 > n0) { + goto L150; + } + +/* While submatrix unfinished take a good dqds step. */ + + dlasq3_(&i0, &n0, &z__[1], &pp, &dmin__, &sigma, &desig, &qmax, & + nfail, &iter, &ndiv, &ieee, &ttype, &dmin1, &dmin2, &dn, & + dn1, &dn2, &g, &tau); + + pp = 1 - pp; + +/* When EMIN is very small check for splits. */ + + if (pp == 0 && n0 - i0 >= 3) { + if (z__[n0 * 4] <= tol2 * qmax || z__[(n0 << 2) - 1] <= tol2 * + sigma) { + splt = i0 - 1; + qmax = z__[(i0 << 2) - 3]; + emin = z__[(i0 << 2) - 1]; + oldemn = z__[i0 * 4]; + i__3 = n0 - 3 << 2; + for (i4 = i0 << 2; i4 <= i__3; i4 += 4) { + if (z__[i4] <= tol2 * z__[i4 - 3] || z__[i4 - 1] <= + tol2 * sigma) { + z__[i4 - 1] = -sigma; + splt = i4 / 4; + qmax = 0.; + emin = z__[i4 + 3]; + oldemn = z__[i4 + 4]; + } else { +/* Computing MAX */ + d__1 = qmax, d__2 = z__[i4 + 1]; + qmax = max(d__1,d__2); +/* Computing MIN */ + d__1 = emin, d__2 = z__[i4 - 1]; + emin = min(d__1,d__2); +/* Computing MIN */ + d__1 = oldemn, d__2 = z__[i4]; + oldemn = min(d__1,d__2); + } +/* L130: */ + } + z__[(n0 << 2) - 1] = emin; + z__[n0 * 4] = oldemn; + i0 = splt + 1; + } + } + +/* L140: */ + } + + *info = 2; + +/* Maximum number of iterations exceeded, restore the shift */ +/* SIGMA and place the new d's and e's in a qd array. */ +/* This might need to be done for several blocks */ + + i1 = i0; + n1 = n0; +L145: + tempq = z__[(i0 << 2) - 3]; + z__[(i0 << 2) - 3] += sigma; + i__2 = n0; + for (k = i0 + 1; k <= i__2; ++k) { + tempe = z__[(k << 2) - 5]; + z__[(k << 2) - 5] *= tempq / z__[(k << 2) - 7]; + tempq = z__[(k << 2) - 3]; + z__[(k << 2) - 3] = z__[(k << 2) - 3] + sigma + tempe - z__[(k << + 2) - 5]; + } + +/* Prepare to do this on the previous block if there is one */ + + if (i1 > 1) { + n1 = i1 - 1; + while(i1 >= 2 && z__[(i1 << 2) - 5] >= 0.) { + --i1; + } + sigma = -z__[(n1 << 2) - 1]; + goto L145; + } + i__2 = *n; + for (k = 1; k <= i__2; ++k) { + z__[(k << 1) - 1] = z__[(k << 2) - 3]; + +/* Only the block 1..N0 is unfinished. The rest of the e's */ +/* must be essentially zero, although sometimes other data */ +/* has been stored in them. */ + + if (k < n0) { + z__[k * 2] = z__[(k << 2) - 1]; + } else { + z__[k * 2] = 0.; + } + } + return 0; + +/* end IWHILB */ + +L150: + +/* L160: */ + ; + } + + *info = 3; + return 0; + +/* end IWHILA */ + +L170: + +/* Move q's to the front. */ + + i__1 = *n; + for (k = 2; k <= i__1; ++k) { + z__[k] = z__[(k << 2) - 3]; +/* L180: */ + } + +/* Sort and compute sum of eigenvalues. */ + + dlasrt_((char *)"D", n, &z__[1], &iinfo, (ftnlen)1); + + e = 0.; + for (k = *n; k >= 1; --k) { + e += z__[k]; +/* L190: */ + } + +/* Store trace, sum(eigenvalues) and information on performance. */ + + z__[(*n << 1) + 1] = trace; + z__[(*n << 1) + 2] = e; + z__[(*n << 1) + 3] = (doublereal) iter; +/* Computing 2nd power */ + i__1 = *n; + z__[(*n << 1) + 4] = (doublereal) ndiv / (doublereal) (i__1 * i__1); + z__[(*n << 1) + 5] = nfail * 100. / (doublereal) iter; + return 0; + +/* End of DLASQ2 */ + +} /* dlasq2_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlasq3.cpp b/lib/linalg/dlasq3.cpp new file mode 100644 index 0000000000..e5974545a6 --- /dev/null +++ b/lib/linalg/dlasq3.cpp @@ -0,0 +1,475 @@ +/* fortran/dlasq3.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DLASQ3 checks for deflation, computes a shift and calls dqds. Used by sbdsqr. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLASQ3 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLASQ3( I0, N0, Z, PP, DMIN, SIGMA, DESIG, QMAX, NFAIL, */ +/* ITER, NDIV, IEEE, TTYPE, DMIN1, DMIN2, DN, DN1, */ +/* DN2, G, TAU ) */ + +/* .. Scalar Arguments .. */ +/* LOGICAL IEEE */ +/* INTEGER I0, ITER, N0, NDIV, NFAIL, PP */ +/* DOUBLE PRECISION DESIG, DMIN, DMIN1, DMIN2, DN, DN1, DN2, G, */ +/* $ QMAX, SIGMA, TAU */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION Z( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLASQ3 checks for deflation, computes a shift (TAU) and calls dqds. */ +/* > In case of failure it changes shifts, and tries again until output */ +/* > is positive. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] I0 */ +/* > \verbatim */ +/* > I0 is INTEGER */ +/* > First index. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] N0 */ +/* > \verbatim */ +/* > N0 is INTEGER */ +/* > Last index. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] Z */ +/* > \verbatim */ +/* > Z is DOUBLE PRECISION array, dimension ( 4*N0 ) */ +/* > Z holds the qd array. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] PP */ +/* > \verbatim */ +/* > PP is INTEGER */ +/* > PP=0 for ping, PP=1 for pong. */ +/* > PP=2 indicates that flipping was applied to the Z array */ +/* > and that the initial tests for deflation should not be */ +/* > performed. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] DMIN */ +/* > \verbatim */ +/* > DMIN is DOUBLE PRECISION */ +/* > Minimum value of d. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] SIGMA */ +/* > \verbatim */ +/* > SIGMA is DOUBLE PRECISION */ +/* > Sum of shifts used in current segment. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] DESIG */ +/* > \verbatim */ +/* > DESIG is DOUBLE PRECISION */ +/* > Lower order part of SIGMA */ +/* > \endverbatim */ +/* > */ +/* > \param[in] QMAX */ +/* > \verbatim */ +/* > QMAX is DOUBLE PRECISION */ +/* > Maximum value of q. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] NFAIL */ +/* > \verbatim */ +/* > NFAIL is INTEGER */ +/* > Increment NFAIL by 1 each time the shift was too big. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] ITER */ +/* > \verbatim */ +/* > ITER is INTEGER */ +/* > Increment ITER by 1 for each iteration. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] NDIV */ +/* > \verbatim */ +/* > NDIV is INTEGER */ +/* > Increment NDIV by 1 for each division. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] IEEE */ +/* > \verbatim */ +/* > IEEE is LOGICAL */ +/* > Flag for IEEE or non IEEE arithmetic (passed to DLASQ5). */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] TTYPE */ +/* > \verbatim */ +/* > TTYPE is INTEGER */ +/* > Shift type. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] DMIN1 */ +/* > \verbatim */ +/* > DMIN1 is DOUBLE PRECISION */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] DMIN2 */ +/* > \verbatim */ +/* > DMIN2 is DOUBLE PRECISION */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] DN */ +/* > \verbatim */ +/* > DN is DOUBLE PRECISION */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] DN1 */ +/* > \verbatim */ +/* > DN1 is DOUBLE PRECISION */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] DN2 */ +/* > \verbatim */ +/* > DN2 is DOUBLE PRECISION */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] G */ +/* > \verbatim */ +/* > G is DOUBLE PRECISION */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] TAU */ +/* > \verbatim */ +/* > TAU is DOUBLE PRECISION */ +/* > */ +/* > These are passed as arguments in order to save their values */ +/* > between calls to DLASQ3. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup auxOTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dlasq3_(integer *i0, integer *n0, doublereal *z__, + integer *pp, doublereal *dmin__, doublereal *sigma, doublereal *desig, + doublereal *qmax, integer *nfail, integer *iter, integer *ndiv, + logical *ieee, integer *ttype, doublereal *dmin1, doublereal *dmin2, + doublereal *dn, doublereal *dn1, doublereal *dn2, doublereal *g, + doublereal *tau) +{ + /* System generated locals */ + integer i__1; + doublereal d__1, d__2; + + /* Builtin functions */ + double sqrt(doublereal); + + /* Local variables */ + doublereal s, t; + integer j4, nn; + doublereal eps, tol; + integer n0in, ipn4; + doublereal tol2, temp; + extern /* Subroutine */ int dlasq4_(integer *, integer *, doublereal *, + integer *, integer *, doublereal *, doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *, doublereal *, integer *, + doublereal *), dlasq5_(integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *, doublereal *, logical * + , doublereal *), dlasq6_(integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, doublereal *); + extern doublereal dlamch_(char *, ftnlen); + extern logical disnan_(doublereal *); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. External Function .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + + /* Parameter adjustments */ + --z__; + + /* Function Body */ + n0in = *n0; + eps = dlamch_((char *)"Precision", (ftnlen)9); + tol = eps * 100.; +/* Computing 2nd power */ + d__1 = tol; + tol2 = d__1 * d__1; + +/* Check for deflation. */ + +L10: + + if (*n0 < *i0) { + return 0; + } + if (*n0 == *i0) { + goto L20; + } + nn = (*n0 << 2) + *pp; + if (*n0 == *i0 + 1) { + goto L40; + } + +/* Check whether E(N0-1) is negligible, 1 eigenvalue. */ + + if (z__[nn - 5] > tol2 * (*sigma + z__[nn - 3]) && z__[nn - (*pp << 1) - + 4] > tol2 * z__[nn - 7]) { + goto L30; + } + +L20: + + z__[(*n0 << 2) - 3] = z__[(*n0 << 2) + *pp - 3] + *sigma; + --(*n0); + goto L10; + +/* Check whether E(N0-2) is negligible, 2 eigenvalues. */ + +L30: + + if (z__[nn - 9] > tol2 * *sigma && z__[nn - (*pp << 1) - 8] > tol2 * z__[ + nn - 11]) { + goto L50; + } + +L40: + + if (z__[nn - 3] > z__[nn - 7]) { + s = z__[nn - 3]; + z__[nn - 3] = z__[nn - 7]; + z__[nn - 7] = s; + } + t = (z__[nn - 7] - z__[nn - 3] + z__[nn - 5]) * .5; + if (z__[nn - 5] > z__[nn - 3] * tol2 && t != 0.) { + s = z__[nn - 3] * (z__[nn - 5] / t); + if (s <= t) { + s = z__[nn - 3] * (z__[nn - 5] / (t * (sqrt(s / t + 1.) + 1.))); + } else { + s = z__[nn - 3] * (z__[nn - 5] / (t + sqrt(t) * sqrt(t + s))); + } + t = z__[nn - 7] + (s + z__[nn - 5]); + z__[nn - 3] *= z__[nn - 7] / t; + z__[nn - 7] = t; + } + z__[(*n0 << 2) - 7] = z__[nn - 7] + *sigma; + z__[(*n0 << 2) - 3] = z__[nn - 3] + *sigma; + *n0 += -2; + goto L10; + +L50: + if (*pp == 2) { + *pp = 0; + } + +/* Reverse the qd-array, if warranted. */ + + if (*dmin__ <= 0. || *n0 < n0in) { + if (z__[(*i0 << 2) + *pp - 3] * 1.5 < z__[(*n0 << 2) + *pp - 3]) { + ipn4 = *i0 + *n0 << 2; + i__1 = *i0 + *n0 - 1 << 1; + for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { + temp = z__[j4 - 3]; + z__[j4 - 3] = z__[ipn4 - j4 - 3]; + z__[ipn4 - j4 - 3] = temp; + temp = z__[j4 - 2]; + z__[j4 - 2] = z__[ipn4 - j4 - 2]; + z__[ipn4 - j4 - 2] = temp; + temp = z__[j4 - 1]; + z__[j4 - 1] = z__[ipn4 - j4 - 5]; + z__[ipn4 - j4 - 5] = temp; + temp = z__[j4]; + z__[j4] = z__[ipn4 - j4 - 4]; + z__[ipn4 - j4 - 4] = temp; +/* L60: */ + } + if (*n0 - *i0 <= 4) { + z__[(*n0 << 2) + *pp - 1] = z__[(*i0 << 2) + *pp - 1]; + z__[(*n0 << 2) - *pp] = z__[(*i0 << 2) - *pp]; + } +/* Computing MIN */ + d__1 = *dmin2, d__2 = z__[(*n0 << 2) + *pp - 1]; + *dmin2 = min(d__1,d__2); +/* Computing MIN */ + d__1 = z__[(*n0 << 2) + *pp - 1], d__2 = z__[(*i0 << 2) + *pp - 1] + , d__1 = min(d__1,d__2), d__2 = z__[(*i0 << 2) + *pp + 3]; + z__[(*n0 << 2) + *pp - 1] = min(d__1,d__2); +/* Computing MIN */ + d__1 = z__[(*n0 << 2) - *pp], d__2 = z__[(*i0 << 2) - *pp], d__1 = + min(d__1,d__2), d__2 = z__[(*i0 << 2) - *pp + 4]; + z__[(*n0 << 2) - *pp] = min(d__1,d__2); +/* Computing MAX */ + d__1 = *qmax, d__2 = z__[(*i0 << 2) + *pp - 3], d__1 = max(d__1, + d__2), d__2 = z__[(*i0 << 2) + *pp + 1]; + *qmax = max(d__1,d__2); + *dmin__ = -0.; + } + } + +/* Choose a shift. */ + + dlasq4_(i0, n0, &z__[1], pp, &n0in, dmin__, dmin1, dmin2, dn, dn1, dn2, + tau, ttype, g); + +/* Call dqds until DMIN > 0. */ + +L70: + + dlasq5_(i0, n0, &z__[1], pp, tau, sigma, dmin__, dmin1, dmin2, dn, dn1, + dn2, ieee, &eps); + + *ndiv += *n0 - *i0 + 2; + ++(*iter); + +/* Check status. */ + + if (*dmin__ >= 0. && *dmin1 >= 0.) { + +/* Success. */ + + goto L90; + + } else if (*dmin__ < 0. && *dmin1 > 0. && z__[(*n0 - 1 << 2) - *pp] < tol + * (*sigma + *dn1) && abs(*dn) < tol * *sigma) { + +/* Convergence hidden by negative DN. */ + + z__[(*n0 - 1 << 2) - *pp + 2] = 0.; + *dmin__ = 0.; + goto L90; + } else if (*dmin__ < 0.) { + +/* TAU too big. Select new TAU and try again. */ + + ++(*nfail); + if (*ttype < -22) { + +/* Failed twice. Play it safe. */ + + *tau = 0.; + } else if (*dmin1 > 0.) { + +/* Late failure. Gives excellent shift. */ + + *tau = (*tau + *dmin__) * (1. - eps * 2.); + *ttype += -11; + } else { + +/* Early failure. Divide by 4. */ + + *tau *= .25; + *ttype += -12; + } + goto L70; + } else if (disnan_(dmin__)) { + +/* NaN. */ + + if (*tau == 0.) { + goto L80; + } else { + *tau = 0.; + goto L70; + } + } else { + +/* Possible underflow. Play it safe. */ + + goto L80; + } + +/* Risk of underflow. */ + +L80: + dlasq6_(i0, n0, &z__[1], pp, dmin__, dmin1, dmin2, dn, dn1, dn2); + *ndiv += *n0 - *i0 + 2; + ++(*iter); + *tau = 0.; + +L90: + if (*tau < *sigma) { + *desig += *tau; + t = *sigma + *desig; + *desig -= t - *sigma; + } else { + t = *sigma + *tau; + *desig = *sigma - (t - *tau) + *desig; + } + *sigma = t; + + return 0; + +/* End of DLASQ3 */ + +} /* dlasq3_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlasq4.cpp b/lib/linalg/dlasq4.cpp new file mode 100644 index 0000000000..4841ada1d2 --- /dev/null +++ b/lib/linalg/dlasq4.cpp @@ -0,0 +1,501 @@ +/* fortran/dlasq4.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DLASQ4 computes an approximation to the smallest eigenvalue using values of d from the previous + transform. Used by sbdsqr. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLASQ4 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLASQ4( I0, N0, Z, PP, N0IN, DMIN, DMIN1, DMIN2, DN, */ +/* DN1, DN2, TAU, TTYPE, G ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER I0, N0, N0IN, PP, TTYPE */ +/* DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DN1, DN2, G, TAU */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION Z( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLASQ4 computes an approximation TAU to the smallest eigenvalue */ +/* > using values of d from the previous transform. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] I0 */ +/* > \verbatim */ +/* > I0 is INTEGER */ +/* > First index. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N0 */ +/* > \verbatim */ +/* > N0 is INTEGER */ +/* > Last index. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] Z */ +/* > \verbatim */ +/* > Z is DOUBLE PRECISION array, dimension ( 4*N0 ) */ +/* > Z holds the qd array. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] PP */ +/* > \verbatim */ +/* > PP is INTEGER */ +/* > PP=0 for ping, PP=1 for pong. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N0IN */ +/* > \verbatim */ +/* > N0IN is INTEGER */ +/* > The value of N0 at start of EIGTEST. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DMIN */ +/* > \verbatim */ +/* > DMIN is DOUBLE PRECISION */ +/* > Minimum value of d. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DMIN1 */ +/* > \verbatim */ +/* > DMIN1 is DOUBLE PRECISION */ +/* > Minimum value of d, excluding D( N0 ). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DMIN2 */ +/* > \verbatim */ +/* > DMIN2 is DOUBLE PRECISION */ +/* > Minimum value of d, excluding D( N0 ) and D( N0-1 ). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DN */ +/* > \verbatim */ +/* > DN is DOUBLE PRECISION */ +/* > d(N) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DN1 */ +/* > \verbatim */ +/* > DN1 is DOUBLE PRECISION */ +/* > d(N-1) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DN2 */ +/* > \verbatim */ +/* > DN2 is DOUBLE PRECISION */ +/* > d(N-2) */ +/* > \endverbatim */ +/* > */ +/* > \param[out] TAU */ +/* > \verbatim */ +/* > TAU is DOUBLE PRECISION */ +/* > This is the shift. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] TTYPE */ +/* > \verbatim */ +/* > TTYPE is INTEGER */ +/* > Shift type. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] G */ +/* > \verbatim */ +/* > G is DOUBLE PRECISION */ +/* > G is passed as an argument in order to save its value between */ +/* > calls to DLASQ4. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup auxOTHERcomputational */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > CNST1 = 9/16 */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dlasq4_(integer *i0, integer *n0, doublereal *z__, + integer *pp, integer *n0in, doublereal *dmin__, doublereal *dmin1, + doublereal *dmin2, doublereal *dn, doublereal *dn1, doublereal *dn2, + doublereal *tau, integer *ttype, doublereal *g) +{ + /* System generated locals */ + integer i__1; + doublereal d__1, d__2; + + /* Builtin functions */ + double sqrt(doublereal); + + /* Local variables */ + doublereal s, a2, b1, b2; + integer i4, nn, np; + doublereal gam, gap1, gap2; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* A negative DMIN forces the shift to take that absolute value */ +/* TTYPE records the type of shift. */ + + /* Parameter adjustments */ + --z__; + + /* Function Body */ + if (*dmin__ <= 0.) { + *tau = -(*dmin__); + *ttype = -1; + return 0; + } + + nn = (*n0 << 2) + *pp; + if (*n0in == *n0) { + +/* No eigenvalues deflated. */ + + if (*dmin__ == *dn || *dmin__ == *dn1) { + + b1 = sqrt(z__[nn - 3]) * sqrt(z__[nn - 5]); + b2 = sqrt(z__[nn - 7]) * sqrt(z__[nn - 9]); + a2 = z__[nn - 7] + z__[nn - 5]; + +/* Cases 2 and 3. */ + + if (*dmin__ == *dn && *dmin1 == *dn1) { + gap2 = *dmin2 - a2 - *dmin2 * .25; + if (gap2 > 0. && gap2 > b2) { + gap1 = a2 - *dn - b2 / gap2 * b2; + } else { + gap1 = a2 - *dn - (b1 + b2); + } + if (gap1 > 0. && gap1 > b1) { +/* Computing MAX */ + d__1 = *dn - b1 / gap1 * b1, d__2 = *dmin__ * .5; + s = max(d__1,d__2); + *ttype = -2; + } else { + s = 0.; + if (*dn > b1) { + s = *dn - b1; + } + if (a2 > b1 + b2) { +/* Computing MIN */ + d__1 = s, d__2 = a2 - (b1 + b2); + s = min(d__1,d__2); + } +/* Computing MAX */ + d__1 = s, d__2 = *dmin__ * .333; + s = max(d__1,d__2); + *ttype = -3; + } + } else { + +/* Case 4. */ + + *ttype = -4; + s = *dmin__ * .25; + if (*dmin__ == *dn) { + gam = *dn; + a2 = 0.; + if (z__[nn - 5] > z__[nn - 7]) { + return 0; + } + b2 = z__[nn - 5] / z__[nn - 7]; + np = nn - 9; + } else { + np = nn - (*pp << 1); + gam = *dn1; + if (z__[np - 4] > z__[np - 2]) { + return 0; + } + a2 = z__[np - 4] / z__[np - 2]; + if (z__[nn - 9] > z__[nn - 11]) { + return 0; + } + b2 = z__[nn - 9] / z__[nn - 11]; + np = nn - 13; + } + +/* Approximate contribution to norm squared from I < NN-1. */ + + a2 += b2; + i__1 = (*i0 << 2) - 1 + *pp; + for (i4 = np; i4 >= i__1; i4 += -4) { + if (b2 == 0.) { + goto L20; + } + b1 = b2; + if (z__[i4] > z__[i4 - 2]) { + return 0; + } + b2 *= z__[i4] / z__[i4 - 2]; + a2 += b2; + if (max(b2,b1) * 100. < a2 || .563 < a2) { + goto L20; + } +/* L10: */ + } +L20: + a2 *= 1.05; + +/* Rayleigh quotient residual bound. */ + + if (a2 < .563) { + s = gam * (1. - sqrt(a2)) / (a2 + 1.); + } + } + } else if (*dmin__ == *dn2) { + +/* Case 5. */ + + *ttype = -5; + s = *dmin__ * .25; + +/* Compute contribution to norm squared from I > NN-2. */ + + np = nn - (*pp << 1); + b1 = z__[np - 2]; + b2 = z__[np - 6]; + gam = *dn2; + if (z__[np - 8] > b2 || z__[np - 4] > b1) { + return 0; + } + a2 = z__[np - 8] / b2 * (z__[np - 4] / b1 + 1.); + +/* Approximate contribution to norm squared from I < NN-2. */ + + if (*n0 - *i0 > 2) { + b2 = z__[nn - 13] / z__[nn - 15]; + a2 += b2; + i__1 = (*i0 << 2) - 1 + *pp; + for (i4 = nn - 17; i4 >= i__1; i4 += -4) { + if (b2 == 0.) { + goto L40; + } + b1 = b2; + if (z__[i4] > z__[i4 - 2]) { + return 0; + } + b2 *= z__[i4] / z__[i4 - 2]; + a2 += b2; + if (max(b2,b1) * 100. < a2 || .563 < a2) { + goto L40; + } +/* L30: */ + } +L40: + a2 *= 1.05; + } + + if (a2 < .563) { + s = gam * (1. - sqrt(a2)) / (a2 + 1.); + } + } else { + +/* Case 6, no information to guide us. */ + + if (*ttype == -6) { + *g += (1. - *g) * .333; + } else if (*ttype == -18) { + *g = .083250000000000005; + } else { + *g = .25; + } + s = *g * *dmin__; + *ttype = -6; + } + + } else if (*n0in == *n0 + 1) { + +/* One eigenvalue just deflated. Use DMIN1, DN1 for DMIN and DN. */ + + if (*dmin1 == *dn1 && *dmin2 == *dn2) { + +/* Cases 7 and 8. */ + + *ttype = -7; + s = *dmin1 * .333; + if (z__[nn - 5] > z__[nn - 7]) { + return 0; + } + b1 = z__[nn - 5] / z__[nn - 7]; + b2 = b1; + if (b2 == 0.) { + goto L60; + } + i__1 = (*i0 << 2) - 1 + *pp; + for (i4 = (*n0 << 2) - 9 + *pp; i4 >= i__1; i4 += -4) { + a2 = b1; + if (z__[i4] > z__[i4 - 2]) { + return 0; + } + b1 *= z__[i4] / z__[i4 - 2]; + b2 += b1; + if (max(b1,a2) * 100. < b2) { + goto L60; + } +/* L50: */ + } +L60: + b2 = sqrt(b2 * 1.05); +/* Computing 2nd power */ + d__1 = b2; + a2 = *dmin1 / (d__1 * d__1 + 1.); + gap2 = *dmin2 * .5 - a2; + if (gap2 > 0. && gap2 > b2 * a2) { +/* Computing MAX */ + d__1 = s, d__2 = a2 * (1. - a2 * 1.01 * (b2 / gap2) * b2); + s = max(d__1,d__2); + } else { +/* Computing MAX */ + d__1 = s, d__2 = a2 * (1. - b2 * 1.01); + s = max(d__1,d__2); + *ttype = -8; + } + } else { + +/* Case 9. */ + + s = *dmin1 * .25; + if (*dmin1 == *dn1) { + s = *dmin1 * .5; + } + *ttype = -9; + } + + } else if (*n0in == *n0 + 2) { + +/* Two eigenvalues deflated. Use DMIN2, DN2 for DMIN and DN. */ + +/* Cases 10 and 11. */ + + if (*dmin2 == *dn2 && z__[nn - 5] * 2. < z__[nn - 7]) { + *ttype = -10; + s = *dmin2 * .333; + if (z__[nn - 5] > z__[nn - 7]) { + return 0; + } + b1 = z__[nn - 5] / z__[nn - 7]; + b2 = b1; + if (b2 == 0.) { + goto L80; + } + i__1 = (*i0 << 2) - 1 + *pp; + for (i4 = (*n0 << 2) - 9 + *pp; i4 >= i__1; i4 += -4) { + if (z__[i4] > z__[i4 - 2]) { + return 0; + } + b1 *= z__[i4] / z__[i4 - 2]; + b2 += b1; + if (b1 * 100. < b2) { + goto L80; + } +/* L70: */ + } +L80: + b2 = sqrt(b2 * 1.05); +/* Computing 2nd power */ + d__1 = b2; + a2 = *dmin2 / (d__1 * d__1 + 1.); + gap2 = z__[nn - 7] + z__[nn - 9] - sqrt(z__[nn - 11]) * sqrt(z__[ + nn - 9]) - a2; + if (gap2 > 0. && gap2 > b2 * a2) { +/* Computing MAX */ + d__1 = s, d__2 = a2 * (1. - a2 * 1.01 * (b2 / gap2) * b2); + s = max(d__1,d__2); + } else { +/* Computing MAX */ + d__1 = s, d__2 = a2 * (1. - b2 * 1.01); + s = max(d__1,d__2); + } + } else { + s = *dmin2 * .25; + *ttype = -11; + } + } else if (*n0in > *n0 + 2) { + +/* Case 12, more than two eigenvalues deflated. No information. */ + + s = 0.; + *ttype = -12; + } + + *tau = s; + return 0; + +/* End of DLASQ4 */ + +} /* dlasq4_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlasq5.cpp b/lib/linalg/dlasq5.cpp new file mode 100644 index 0000000000..13ae0ed20c --- /dev/null +++ b/lib/linalg/dlasq5.cpp @@ -0,0 +1,480 @@ +/* fortran/dlasq5.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DLASQ5 computes one dqds transform in ping-pong form. Used by sbdsqr and sstegr. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLASQ5 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLASQ5( I0, N0, Z, PP, TAU, SIGMA, DMIN, DMIN1, DMIN2, DN, */ +/* DNM1, DNM2, IEEE, EPS ) */ + +/* .. Scalar Arguments .. */ +/* LOGICAL IEEE */ +/* INTEGER I0, N0, PP */ +/* DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DNM1, DNM2, TAU, SIGMA, EPS */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION Z( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLASQ5 computes one dqds transform in ping-pong form, one */ +/* > version for IEEE machines another for non IEEE machines. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] I0 */ +/* > \verbatim */ +/* > I0 is INTEGER */ +/* > First index. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N0 */ +/* > \verbatim */ +/* > N0 is INTEGER */ +/* > Last index. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] Z */ +/* > \verbatim */ +/* > Z is DOUBLE PRECISION array, dimension ( 4*N ) */ +/* > Z holds the qd array. EMIN is stored in Z(4*N0) to avoid */ +/* > an extra argument. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] PP */ +/* > \verbatim */ +/* > PP is INTEGER */ +/* > PP=0 for ping, PP=1 for pong. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TAU */ +/* > \verbatim */ +/* > TAU is DOUBLE PRECISION */ +/* > This is the shift. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] SIGMA */ +/* > \verbatim */ +/* > SIGMA is DOUBLE PRECISION */ +/* > This is the accumulated shift up to this step. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] DMIN */ +/* > \verbatim */ +/* > DMIN is DOUBLE PRECISION */ +/* > Minimum value of d. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] DMIN1 */ +/* > \verbatim */ +/* > DMIN1 is DOUBLE PRECISION */ +/* > Minimum value of d, excluding D( N0 ). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] DMIN2 */ +/* > \verbatim */ +/* > DMIN2 is DOUBLE PRECISION */ +/* > Minimum value of d, excluding D( N0 ) and D( N0-1 ). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] DN */ +/* > \verbatim */ +/* > DN is DOUBLE PRECISION */ +/* > d(N0), the last value of d. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] DNM1 */ +/* > \verbatim */ +/* > DNM1 is DOUBLE PRECISION */ +/* > d(N0-1). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] DNM2 */ +/* > \verbatim */ +/* > DNM2 is DOUBLE PRECISION */ +/* > d(N0-2). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] IEEE */ +/* > \verbatim */ +/* > IEEE is LOGICAL */ +/* > Flag for IEEE or non IEEE arithmetic. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] EPS */ +/* > \verbatim */ +/* > EPS is DOUBLE PRECISION */ +/* > This is the value of epsilon used. */ +/* > \endverbatim */ +/* > */ +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup auxOTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dlasq5_(integer *i0, integer *n0, doublereal *z__, + integer *pp, doublereal *tau, doublereal *sigma, doublereal *dmin__, + doublereal *dmin1, doublereal *dmin2, doublereal *dn, doublereal * + dnm1, doublereal *dnm2, logical *ieee, doublereal *eps) +{ + /* System generated locals */ + integer i__1; + doublereal d__1, d__2; + + /* Local variables */ + doublereal d__; + integer j4, j4p2; + doublereal emin, temp, dthresh; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameter .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + + /* Parameter adjustments */ + --z__; + + /* Function Body */ + if (*n0 - *i0 - 1 <= 0) { + return 0; + } + + dthresh = *eps * (*sigma + *tau); + if (*tau < dthresh * .5) { + *tau = 0.; + } + if (*tau != 0.) { + j4 = (*i0 << 2) + *pp - 3; + emin = z__[j4 + 4]; + d__ = z__[j4] - *tau; + *dmin__ = d__; + *dmin1 = -z__[j4]; + + if (*ieee) { + +/* Code for IEEE arithmetic. */ + + if (*pp == 0) { + i__1 = *n0 - 3 << 2; + for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { + z__[j4 - 2] = d__ + z__[j4 - 1]; + temp = z__[j4 + 1] / z__[j4 - 2]; + d__ = d__ * temp - *tau; + *dmin__ = min(*dmin__,d__); + z__[j4] = z__[j4 - 1] * temp; +/* Computing MIN */ + d__1 = z__[j4]; + emin = min(d__1,emin); +/* L10: */ + } + } else { + i__1 = *n0 - 3 << 2; + for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { + z__[j4 - 3] = d__ + z__[j4]; + temp = z__[j4 + 2] / z__[j4 - 3]; + d__ = d__ * temp - *tau; + *dmin__ = min(*dmin__,d__); + z__[j4 - 1] = z__[j4] * temp; +/* Computing MIN */ + d__1 = z__[j4 - 1]; + emin = min(d__1,emin); +/* L20: */ + } + } + +/* Unroll last two steps. */ + + *dnm2 = d__; + *dmin2 = *dmin__; + j4 = (*n0 - 2 << 2) - *pp; + j4p2 = j4 + (*pp << 1) - 1; + z__[j4 - 2] = *dnm2 + z__[j4p2]; + z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); + *dnm1 = z__[j4p2 + 2] * (*dnm2 / z__[j4 - 2]) - *tau; + *dmin__ = min(*dmin__,*dnm1); + + *dmin1 = *dmin__; + j4 += 4; + j4p2 = j4 + (*pp << 1) - 1; + z__[j4 - 2] = *dnm1 + z__[j4p2]; + z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); + *dn = z__[j4p2 + 2] * (*dnm1 / z__[j4 - 2]) - *tau; + *dmin__ = min(*dmin__,*dn); + + } else { + +/* Code for non IEEE arithmetic. */ + + if (*pp == 0) { + i__1 = *n0 - 3 << 2; + for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { + z__[j4 - 2] = d__ + z__[j4 - 1]; + if (d__ < 0.) { + return 0; + } else { + z__[j4] = z__[j4 + 1] * (z__[j4 - 1] / z__[j4 - 2]); + d__ = z__[j4 + 1] * (d__ / z__[j4 - 2]) - *tau; + } + *dmin__ = min(*dmin__,d__); +/* Computing MIN */ + d__1 = emin, d__2 = z__[j4]; + emin = min(d__1,d__2); +/* L30: */ + } + } else { + i__1 = *n0 - 3 << 2; + for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { + z__[j4 - 3] = d__ + z__[j4]; + if (d__ < 0.) { + return 0; + } else { + z__[j4 - 1] = z__[j4 + 2] * (z__[j4] / z__[j4 - 3]); + d__ = z__[j4 + 2] * (d__ / z__[j4 - 3]) - *tau; + } + *dmin__ = min(*dmin__,d__); +/* Computing MIN */ + d__1 = emin, d__2 = z__[j4 - 1]; + emin = min(d__1,d__2); +/* L40: */ + } + } + +/* Unroll last two steps. */ + + *dnm2 = d__; + *dmin2 = *dmin__; + j4 = (*n0 - 2 << 2) - *pp; + j4p2 = j4 + (*pp << 1) - 1; + z__[j4 - 2] = *dnm2 + z__[j4p2]; + if (*dnm2 < 0.) { + return 0; + } else { + z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); + *dnm1 = z__[j4p2 + 2] * (*dnm2 / z__[j4 - 2]) - *tau; + } + *dmin__ = min(*dmin__,*dnm1); + + *dmin1 = *dmin__; + j4 += 4; + j4p2 = j4 + (*pp << 1) - 1; + z__[j4 - 2] = *dnm1 + z__[j4p2]; + if (*dnm1 < 0.) { + return 0; + } else { + z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); + *dn = z__[j4p2 + 2] * (*dnm1 / z__[j4 - 2]) - *tau; + } + *dmin__ = min(*dmin__,*dn); + + } + } else { +/* This is the version that sets d's to zero if they are small enough */ + j4 = (*i0 << 2) + *pp - 3; + emin = z__[j4 + 4]; + d__ = z__[j4] - *tau; + *dmin__ = d__; + *dmin1 = -z__[j4]; + if (*ieee) { + +/* Code for IEEE arithmetic. */ + + if (*pp == 0) { + i__1 = *n0 - 3 << 2; + for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { + z__[j4 - 2] = d__ + z__[j4 - 1]; + temp = z__[j4 + 1] / z__[j4 - 2]; + d__ = d__ * temp - *tau; + if (d__ < dthresh) { + d__ = 0.; + } + *dmin__ = min(*dmin__,d__); + z__[j4] = z__[j4 - 1] * temp; +/* Computing MIN */ + d__1 = z__[j4]; + emin = min(d__1,emin); +/* L50: */ + } + } else { + i__1 = *n0 - 3 << 2; + for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { + z__[j4 - 3] = d__ + z__[j4]; + temp = z__[j4 + 2] / z__[j4 - 3]; + d__ = d__ * temp - *tau; + if (d__ < dthresh) { + d__ = 0.; + } + *dmin__ = min(*dmin__,d__); + z__[j4 - 1] = z__[j4] * temp; +/* Computing MIN */ + d__1 = z__[j4 - 1]; + emin = min(d__1,emin); +/* L60: */ + } + } + +/* Unroll last two steps. */ + + *dnm2 = d__; + *dmin2 = *dmin__; + j4 = (*n0 - 2 << 2) - *pp; + j4p2 = j4 + (*pp << 1) - 1; + z__[j4 - 2] = *dnm2 + z__[j4p2]; + z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); + *dnm1 = z__[j4p2 + 2] * (*dnm2 / z__[j4 - 2]) - *tau; + *dmin__ = min(*dmin__,*dnm1); + + *dmin1 = *dmin__; + j4 += 4; + j4p2 = j4 + (*pp << 1) - 1; + z__[j4 - 2] = *dnm1 + z__[j4p2]; + z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); + *dn = z__[j4p2 + 2] * (*dnm1 / z__[j4 - 2]) - *tau; + *dmin__ = min(*dmin__,*dn); + + } else { + +/* Code for non IEEE arithmetic. */ + + if (*pp == 0) { + i__1 = *n0 - 3 << 2; + for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { + z__[j4 - 2] = d__ + z__[j4 - 1]; + if (d__ < 0.) { + return 0; + } else { + z__[j4] = z__[j4 + 1] * (z__[j4 - 1] / z__[j4 - 2]); + d__ = z__[j4 + 1] * (d__ / z__[j4 - 2]) - *tau; + } + if (d__ < dthresh) { + d__ = 0.; + } + *dmin__ = min(*dmin__,d__); +/* Computing MIN */ + d__1 = emin, d__2 = z__[j4]; + emin = min(d__1,d__2); +/* L70: */ + } + } else { + i__1 = *n0 - 3 << 2; + for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { + z__[j4 - 3] = d__ + z__[j4]; + if (d__ < 0.) { + return 0; + } else { + z__[j4 - 1] = z__[j4 + 2] * (z__[j4] / z__[j4 - 3]); + d__ = z__[j4 + 2] * (d__ / z__[j4 - 3]) - *tau; + } + if (d__ < dthresh) { + d__ = 0.; + } + *dmin__ = min(*dmin__,d__); +/* Computing MIN */ + d__1 = emin, d__2 = z__[j4 - 1]; + emin = min(d__1,d__2); +/* L80: */ + } + } + +/* Unroll last two steps. */ + + *dnm2 = d__; + *dmin2 = *dmin__; + j4 = (*n0 - 2 << 2) - *pp; + j4p2 = j4 + (*pp << 1) - 1; + z__[j4 - 2] = *dnm2 + z__[j4p2]; + if (*dnm2 < 0.) { + return 0; + } else { + z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); + *dnm1 = z__[j4p2 + 2] * (*dnm2 / z__[j4 - 2]) - *tau; + } + *dmin__ = min(*dmin__,*dnm1); + + *dmin1 = *dmin__; + j4 += 4; + j4p2 = j4 + (*pp << 1) - 1; + z__[j4 - 2] = *dnm1 + z__[j4p2]; + if (*dnm1 < 0.) { + return 0; + } else { + z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); + *dn = z__[j4p2 + 2] * (*dnm1 / z__[j4 - 2]) - *tau; + } + *dmin__ = min(*dmin__,*dn); + + } + } + + z__[j4 + 2] = *dn; + z__[(*n0 << 2) - *pp] = emin; + return 0; + +/* End of DLASQ5 */ + +} /* dlasq5_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlasq6.cpp b/lib/linalg/dlasq6.cpp new file mode 100644 index 0000000000..b06e9ad028 --- /dev/null +++ b/lib/linalg/dlasq6.cpp @@ -0,0 +1,291 @@ +/* fortran/dlasq6.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DLASQ6 computes one dqd transform in ping-pong form. Used by sbdsqr and sstegr. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLASQ6 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLASQ6( I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN, */ +/* DNM1, DNM2 ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER I0, N0, PP */ +/* DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DNM1, DNM2 */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION Z( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLASQ6 computes one dqd (shift equal to zero) transform in */ +/* > ping-pong form, with protection against underflow and overflow. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] I0 */ +/* > \verbatim */ +/* > I0 is INTEGER */ +/* > First index. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N0 */ +/* > \verbatim */ +/* > N0 is INTEGER */ +/* > Last index. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] Z */ +/* > \verbatim */ +/* > Z is DOUBLE PRECISION array, dimension ( 4*N ) */ +/* > Z holds the qd array. EMIN is stored in Z(4*N0) to avoid */ +/* > an extra argument. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] PP */ +/* > \verbatim */ +/* > PP is INTEGER */ +/* > PP=0 for ping, PP=1 for pong. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] DMIN */ +/* > \verbatim */ +/* > DMIN is DOUBLE PRECISION */ +/* > Minimum value of d. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] DMIN1 */ +/* > \verbatim */ +/* > DMIN1 is DOUBLE PRECISION */ +/* > Minimum value of d, excluding D( N0 ). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] DMIN2 */ +/* > \verbatim */ +/* > DMIN2 is DOUBLE PRECISION */ +/* > Minimum value of d, excluding D( N0 ) and D( N0-1 ). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] DN */ +/* > \verbatim */ +/* > DN is DOUBLE PRECISION */ +/* > d(N0), the last value of d. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] DNM1 */ +/* > \verbatim */ +/* > DNM1 is DOUBLE PRECISION */ +/* > d(N0-1). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] DNM2 */ +/* > \verbatim */ +/* > DNM2 is DOUBLE PRECISION */ +/* > d(N0-2). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup auxOTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dlasq6_(integer *i0, integer *n0, doublereal *z__, + integer *pp, doublereal *dmin__, doublereal *dmin1, doublereal *dmin2, + doublereal *dn, doublereal *dnm1, doublereal *dnm2) +{ + /* System generated locals */ + integer i__1; + doublereal d__1, d__2; + + /* Local variables */ + doublereal d__; + integer j4, j4p2; + doublereal emin, temp; + extern doublereal dlamch_(char *, ftnlen); + doublereal safmin; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameter .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Function .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + + /* Parameter adjustments */ + --z__; + + /* Function Body */ + if (*n0 - *i0 - 1 <= 0) { + return 0; + } + + safmin = dlamch_((char *)"Safe minimum", (ftnlen)12); + j4 = (*i0 << 2) + *pp - 3; + emin = z__[j4 + 4]; + d__ = z__[j4]; + *dmin__ = d__; + + if (*pp == 0) { + i__1 = *n0 - 3 << 2; + for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { + z__[j4 - 2] = d__ + z__[j4 - 1]; + if (z__[j4 - 2] == 0.) { + z__[j4] = 0.; + d__ = z__[j4 + 1]; + *dmin__ = d__; + emin = 0.; + } else if (safmin * z__[j4 + 1] < z__[j4 - 2] && safmin * z__[j4 + - 2] < z__[j4 + 1]) { + temp = z__[j4 + 1] / z__[j4 - 2]; + z__[j4] = z__[j4 - 1] * temp; + d__ *= temp; + } else { + z__[j4] = z__[j4 + 1] * (z__[j4 - 1] / z__[j4 - 2]); + d__ = z__[j4 + 1] * (d__ / z__[j4 - 2]); + } + *dmin__ = min(*dmin__,d__); +/* Computing MIN */ + d__1 = emin, d__2 = z__[j4]; + emin = min(d__1,d__2); +/* L10: */ + } + } else { + i__1 = *n0 - 3 << 2; + for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { + z__[j4 - 3] = d__ + z__[j4]; + if (z__[j4 - 3] == 0.) { + z__[j4 - 1] = 0.; + d__ = z__[j4 + 2]; + *dmin__ = d__; + emin = 0.; + } else if (safmin * z__[j4 + 2] < z__[j4 - 3] && safmin * z__[j4 + - 3] < z__[j4 + 2]) { + temp = z__[j4 + 2] / z__[j4 - 3]; + z__[j4 - 1] = z__[j4] * temp; + d__ *= temp; + } else { + z__[j4 - 1] = z__[j4 + 2] * (z__[j4] / z__[j4 - 3]); + d__ = z__[j4 + 2] * (d__ / z__[j4 - 3]); + } + *dmin__ = min(*dmin__,d__); +/* Computing MIN */ + d__1 = emin, d__2 = z__[j4 - 1]; + emin = min(d__1,d__2); +/* L20: */ + } + } + +/* Unroll last two steps. */ + + *dnm2 = d__; + *dmin2 = *dmin__; + j4 = (*n0 - 2 << 2) - *pp; + j4p2 = j4 + (*pp << 1) - 1; + z__[j4 - 2] = *dnm2 + z__[j4p2]; + if (z__[j4 - 2] == 0.) { + z__[j4] = 0.; + *dnm1 = z__[j4p2 + 2]; + *dmin__ = *dnm1; + emin = 0.; + } else if (safmin * z__[j4p2 + 2] < z__[j4 - 2] && safmin * z__[j4 - 2] < + z__[j4p2 + 2]) { + temp = z__[j4p2 + 2] / z__[j4 - 2]; + z__[j4] = z__[j4p2] * temp; + *dnm1 = *dnm2 * temp; + } else { + z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); + *dnm1 = z__[j4p2 + 2] * (*dnm2 / z__[j4 - 2]); + } + *dmin__ = min(*dmin__,*dnm1); + + *dmin1 = *dmin__; + j4 += 4; + j4p2 = j4 + (*pp << 1) - 1; + z__[j4 - 2] = *dnm1 + z__[j4p2]; + if (z__[j4 - 2] == 0.) { + z__[j4] = 0.; + *dn = z__[j4p2 + 2]; + *dmin__ = *dn; + emin = 0.; + } else if (safmin * z__[j4p2 + 2] < z__[j4 - 2] && safmin * z__[j4 - 2] < + z__[j4p2 + 2]) { + temp = z__[j4p2 + 2] / z__[j4 - 2]; + z__[j4] = z__[j4p2] * temp; + *dn = *dnm1 * temp; + } else { + z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); + *dn = z__[j4p2 + 2] * (*dnm1 / z__[j4 - 2]); + } + *dmin__ = min(*dmin__,*dn); + + z__[j4 + 2] = *dn; + z__[(*n0 << 2) - *pp] = emin; + return 0; + +/* End of DLASQ6 */ + +} /* dlasq6_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlasr.cpp b/lib/linalg/dlasr.cpp new file mode 100644 index 0000000000..c4de2f85a9 --- /dev/null +++ b/lib/linalg/dlasr.cpp @@ -0,0 +1,536 @@ +/* fortran/dlasr.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DLASR applies a sequence of plane rotations to a general rectangular matrix. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLASR + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER DIRECT, PIVOT, SIDE */ +/* INTEGER LDA, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), C( * ), S( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLASR applies a sequence of plane rotations to a real matrix A, */ +/* > from either the left or the right. */ +/* > */ +/* > When SIDE = 'L', the transformation takes the form */ +/* > */ +/* > A := P*A */ +/* > */ +/* > and when SIDE = 'R', the transformation takes the form */ +/* > */ +/* > A := A*P**T */ +/* > */ +/* > where P is an orthogonal matrix consisting of a sequence of z plane */ +/* > rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R', */ +/* > and P**T is the transpose of P. */ +/* > */ +/* > When DIRECT = 'F' (Forward sequence), then */ +/* > */ +/* > P = P(z-1) * ... * P(2) * P(1) */ +/* > */ +/* > and when DIRECT = 'B' (Backward sequence), then */ +/* > */ +/* > P = P(1) * P(2) * ... * P(z-1) */ +/* > */ +/* > where P(k) is a plane rotation matrix defined by the 2-by-2 rotation */ +/* > */ +/* > R(k) = ( c(k) s(k) ) */ +/* > = ( -s(k) c(k) ). */ +/* > */ +/* > When PIVOT = 'V' (Variable pivot), the rotation is performed */ +/* > for the plane (k,k+1), i.e., P(k) has the form */ +/* > */ +/* > P(k) = ( 1 ) */ +/* > ( ... ) */ +/* > ( 1 ) */ +/* > ( c(k) s(k) ) */ +/* > ( -s(k) c(k) ) */ +/* > ( 1 ) */ +/* > ( ... ) */ +/* > ( 1 ) */ +/* > */ +/* > where R(k) appears as a rank-2 modification to the identity matrix in */ +/* > rows and columns k and k+1. */ +/* > */ +/* > When PIVOT = 'T' (Top pivot), the rotation is performed for the */ +/* > plane (1,k+1), so P(k) has the form */ +/* > */ +/* > P(k) = ( c(k) s(k) ) */ +/* > ( 1 ) */ +/* > ( ... ) */ +/* > ( 1 ) */ +/* > ( -s(k) c(k) ) */ +/* > ( 1 ) */ +/* > ( ... ) */ +/* > ( 1 ) */ +/* > */ +/* > where R(k) appears in rows and columns 1 and k+1. */ +/* > */ +/* > Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is */ +/* > performed for the plane (k,z), giving P(k) the form */ +/* > */ +/* > P(k) = ( 1 ) */ +/* > ( ... ) */ +/* > ( 1 ) */ +/* > ( c(k) s(k) ) */ +/* > ( 1 ) */ +/* > ( ... ) */ +/* > ( 1 ) */ +/* > ( -s(k) c(k) ) */ +/* > */ +/* > where R(k) appears in rows and columns k and z. The rotations are */ +/* > performed without ever forming P(k) explicitly. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] SIDE */ +/* > \verbatim */ +/* > SIDE is CHARACTER*1 */ +/* > Specifies whether the plane rotation matrix P is applied to */ +/* > A on the left or the right. */ +/* > = 'L': Left, compute A := P*A */ +/* > = 'R': Right, compute A:= A*P**T */ +/* > \endverbatim */ +/* > */ +/* > \param[in] PIVOT */ +/* > \verbatim */ +/* > PIVOT is CHARACTER*1 */ +/* > Specifies the plane for which P(k) is a plane rotation */ +/* > matrix. */ +/* > = 'V': Variable pivot, the plane (k,k+1) */ +/* > = 'T': Top pivot, the plane (1,k+1) */ +/* > = 'B': Bottom pivot, the plane (k,z) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DIRECT */ +/* > \verbatim */ +/* > DIRECT is CHARACTER*1 */ +/* > Specifies whether P is a forward or backward sequence of */ +/* > plane rotations. */ +/* > = 'F': Forward, P = P(z-1)*...*P(2)*P(1) */ +/* > = 'B': Backward, P = P(1)*P(2)*...*P(z-1) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix A. If m <= 1, an immediate */ +/* > return is effected. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix A. If n <= 1, an */ +/* > immediate return is effected. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] C */ +/* > \verbatim */ +/* > C is DOUBLE PRECISION array, dimension */ +/* > (M-1) if SIDE = 'L' */ +/* > (N-1) if SIDE = 'R' */ +/* > The cosines c(k) of the plane rotations. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] S */ +/* > \verbatim */ +/* > S is DOUBLE PRECISION array, dimension */ +/* > (M-1) if SIDE = 'L' */ +/* > (N-1) if SIDE = 'R' */ +/* > The sines s(k) of the plane rotations. The 2-by-2 plane */ +/* > rotation part of the matrix P(k), R(k), has the form */ +/* > R(k) = ( c(k) s(k) ) */ +/* > ( -s(k) c(k) ). */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > The M-by-N matrix A. On exit, A is overwritten by P*A if */ +/* > SIDE = 'L' or by A*P**T if SIDE = 'R'. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,M). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup OTHERauxiliary */ + +/* ===================================================================== */ +/* Subroutine */ int dlasr_(char *side, char *pivot, char *direct, integer *m, + integer *n, doublereal *c__, doublereal *s, doublereal *a, integer * + lda, ftnlen side_len, ftnlen pivot_len, ftnlen direct_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2; + + /* Local variables */ + integer i__, j, info; + doublereal temp; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + doublereal ctemp, stemp; + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters */ + + /* Parameter adjustments */ + --c__; + --s; + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + + /* Function Body */ + info = 0; + if (! (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1) || lsame_(side, (char *)"R", ( + ftnlen)1, (ftnlen)1))) { + info = 1; + } else if (! (lsame_(pivot, (char *)"V", (ftnlen)1, (ftnlen)1) || lsame_(pivot, + (char *)"T", (ftnlen)1, (ftnlen)1) || lsame_(pivot, (char *)"B", (ftnlen)1, ( + ftnlen)1))) { + info = 2; + } else if (! (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1) || lsame_(direct, + (char *)"B", (ftnlen)1, (ftnlen)1))) { + info = 3; + } else if (*m < 0) { + info = 4; + } else if (*n < 0) { + info = 5; + } else if (*lda < max(1,*m)) { + info = 9; + } + if (info != 0) { + xerbla_((char *)"DLASR ", &info, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*m == 0 || *n == 0) { + return 0; + } + if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { + +/* Form P * A */ + + if (lsame_(pivot, (char *)"V", (ftnlen)1, (ftnlen)1)) { + if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { + i__1 = *m - 1; + for (j = 1; j <= i__1; ++j) { + ctemp = c__[j]; + stemp = s[j]; + if (ctemp != 1. || stemp != 0.) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + temp = a[j + 1 + i__ * a_dim1]; + a[j + 1 + i__ * a_dim1] = ctemp * temp - stemp * + a[j + i__ * a_dim1]; + a[j + i__ * a_dim1] = stemp * temp + ctemp * a[j + + i__ * a_dim1]; +/* L10: */ + } + } +/* L20: */ + } + } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { + for (j = *m - 1; j >= 1; --j) { + ctemp = c__[j]; + stemp = s[j]; + if (ctemp != 1. || stemp != 0.) { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + temp = a[j + 1 + i__ * a_dim1]; + a[j + 1 + i__ * a_dim1] = ctemp * temp - stemp * + a[j + i__ * a_dim1]; + a[j + i__ * a_dim1] = stemp * temp + ctemp * a[j + + i__ * a_dim1]; +/* L30: */ + } + } +/* L40: */ + } + } + } else if (lsame_(pivot, (char *)"T", (ftnlen)1, (ftnlen)1)) { + if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { + i__1 = *m; + for (j = 2; j <= i__1; ++j) { + ctemp = c__[j - 1]; + stemp = s[j - 1]; + if (ctemp != 1. || stemp != 0.) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + temp = a[j + i__ * a_dim1]; + a[j + i__ * a_dim1] = ctemp * temp - stemp * a[ + i__ * a_dim1 + 1]; + a[i__ * a_dim1 + 1] = stemp * temp + ctemp * a[ + i__ * a_dim1 + 1]; +/* L50: */ + } + } +/* L60: */ + } + } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { + for (j = *m; j >= 2; --j) { + ctemp = c__[j - 1]; + stemp = s[j - 1]; + if (ctemp != 1. || stemp != 0.) { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + temp = a[j + i__ * a_dim1]; + a[j + i__ * a_dim1] = ctemp * temp - stemp * a[ + i__ * a_dim1 + 1]; + a[i__ * a_dim1 + 1] = stemp * temp + ctemp * a[ + i__ * a_dim1 + 1]; +/* L70: */ + } + } +/* L80: */ + } + } + } else if (lsame_(pivot, (char *)"B", (ftnlen)1, (ftnlen)1)) { + if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { + i__1 = *m - 1; + for (j = 1; j <= i__1; ++j) { + ctemp = c__[j]; + stemp = s[j]; + if (ctemp != 1. || stemp != 0.) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + temp = a[j + i__ * a_dim1]; + a[j + i__ * a_dim1] = stemp * a[*m + i__ * a_dim1] + + ctemp * temp; + a[*m + i__ * a_dim1] = ctemp * a[*m + i__ * + a_dim1] - stemp * temp; +/* L90: */ + } + } +/* L100: */ + } + } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { + for (j = *m - 1; j >= 1; --j) { + ctemp = c__[j]; + stemp = s[j]; + if (ctemp != 1. || stemp != 0.) { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + temp = a[j + i__ * a_dim1]; + a[j + i__ * a_dim1] = stemp * a[*m + i__ * a_dim1] + + ctemp * temp; + a[*m + i__ * a_dim1] = ctemp * a[*m + i__ * + a_dim1] - stemp * temp; +/* L110: */ + } + } +/* L120: */ + } + } + } + } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + +/* Form A * P**T */ + + if (lsame_(pivot, (char *)"V", (ftnlen)1, (ftnlen)1)) { + if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { + i__1 = *n - 1; + for (j = 1; j <= i__1; ++j) { + ctemp = c__[j]; + stemp = s[j]; + if (ctemp != 1. || stemp != 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp = a[i__ + (j + 1) * a_dim1]; + a[i__ + (j + 1) * a_dim1] = ctemp * temp - stemp * + a[i__ + j * a_dim1]; + a[i__ + j * a_dim1] = stemp * temp + ctemp * a[ + i__ + j * a_dim1]; +/* L130: */ + } + } +/* L140: */ + } + } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { + for (j = *n - 1; j >= 1; --j) { + ctemp = c__[j]; + stemp = s[j]; + if (ctemp != 1. || stemp != 0.) { + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + temp = a[i__ + (j + 1) * a_dim1]; + a[i__ + (j + 1) * a_dim1] = ctemp * temp - stemp * + a[i__ + j * a_dim1]; + a[i__ + j * a_dim1] = stemp * temp + ctemp * a[ + i__ + j * a_dim1]; +/* L150: */ + } + } +/* L160: */ + } + } + } else if (lsame_(pivot, (char *)"T", (ftnlen)1, (ftnlen)1)) { + if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { + i__1 = *n; + for (j = 2; j <= i__1; ++j) { + ctemp = c__[j - 1]; + stemp = s[j - 1]; + if (ctemp != 1. || stemp != 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp = a[i__ + j * a_dim1]; + a[i__ + j * a_dim1] = ctemp * temp - stemp * a[ + i__ + a_dim1]; + a[i__ + a_dim1] = stemp * temp + ctemp * a[i__ + + a_dim1]; +/* L170: */ + } + } +/* L180: */ + } + } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { + for (j = *n; j >= 2; --j) { + ctemp = c__[j - 1]; + stemp = s[j - 1]; + if (ctemp != 1. || stemp != 0.) { + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + temp = a[i__ + j * a_dim1]; + a[i__ + j * a_dim1] = ctemp * temp - stemp * a[ + i__ + a_dim1]; + a[i__ + a_dim1] = stemp * temp + ctemp * a[i__ + + a_dim1]; +/* L190: */ + } + } +/* L200: */ + } + } + } else if (lsame_(pivot, (char *)"B", (ftnlen)1, (ftnlen)1)) { + if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { + i__1 = *n - 1; + for (j = 1; j <= i__1; ++j) { + ctemp = c__[j]; + stemp = s[j]; + if (ctemp != 1. || stemp != 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp = a[i__ + j * a_dim1]; + a[i__ + j * a_dim1] = stemp * a[i__ + *n * a_dim1] + + ctemp * temp; + a[i__ + *n * a_dim1] = ctemp * a[i__ + *n * + a_dim1] - stemp * temp; +/* L210: */ + } + } +/* L220: */ + } + } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { + for (j = *n - 1; j >= 1; --j) { + ctemp = c__[j]; + stemp = s[j]; + if (ctemp != 1. || stemp != 0.) { + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + temp = a[i__ + j * a_dim1]; + a[i__ + j * a_dim1] = stemp * a[i__ + *n * a_dim1] + + ctemp * temp; + a[i__ + *n * a_dim1] = ctemp * a[i__ + *n * + a_dim1] - stemp * temp; +/* L230: */ + } + } +/* L240: */ + } + } + } + } + + return 0; + +/* End of DLASR */ + +} /* dlasr_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlasrt.cpp b/lib/linalg/dlasrt.cpp new file mode 100644 index 0000000000..8c0eec5f2e --- /dev/null +++ b/lib/linalg/dlasrt.cpp @@ -0,0 +1,352 @@ +/* fortran/dlasrt.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DLASRT sorts numbers in increasing or decreasing order. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLASRT + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLASRT( ID, N, D, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER ID */ +/* INTEGER INFO, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION D( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > Sort the numbers in D in increasing order (if ID = 'I') or */ +/* > in decreasing order (if ID = 'D' ). */ +/* > */ +/* > Use Quick Sort, reverting to Insertion sort on arrays of */ +/* > size <= 20. Dimension of STACK limits N to about 2**32. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] ID */ +/* > \verbatim */ +/* > ID is CHARACTER*1 */ +/* > = 'I': sort D in increasing order; */ +/* > = 'D': sort D in decreasing order. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The length of the array D. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension (N) */ +/* > On entry, the array to be sorted. */ +/* > On exit, D has been sorted into increasing order */ +/* > (D(1) <= ... <= D(N) ) or into decreasing order */ +/* > (D(1) >= ... >= D(N) ), depending on ID. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup auxOTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dlasrt_(char *id, integer *n, doublereal *d__, integer * + info, ftnlen id_len) +{ + /* System generated locals */ + integer i__1, i__2; + + /* Local variables */ + integer i__, j; + doublereal d1, d2, d3; + integer dir; + doublereal tmp; + integer endd; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + integer stack[64] /* was [2][32] */; + doublereal dmnmx; + integer start; + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + integer stkpnt; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Local Arrays .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --d__; + + /* Function Body */ + *info = 0; + dir = -1; + if (lsame_(id, (char *)"D", (ftnlen)1, (ftnlen)1)) { + dir = 0; + } else if (lsame_(id, (char *)"I", (ftnlen)1, (ftnlen)1)) { + dir = 1; + } + if (dir == -1) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DLASRT", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*n <= 1) { + return 0; + } + + stkpnt = 1; + stack[0] = 1; + stack[1] = *n; +L10: + start = stack[(stkpnt << 1) - 2]; + endd = stack[(stkpnt << 1) - 1]; + --stkpnt; + if (endd - start <= 20 && endd - start > 0) { + +/* Do Insertion sort on D( START:ENDD ) */ + + if (dir == 0) { + +/* Sort into decreasing order */ + + i__1 = endd; + for (i__ = start + 1; i__ <= i__1; ++i__) { + i__2 = start + 1; + for (j = i__; j >= i__2; --j) { + if (d__[j] > d__[j - 1]) { + dmnmx = d__[j]; + d__[j] = d__[j - 1]; + d__[j - 1] = dmnmx; + } else { + goto L30; + } +/* L20: */ + } +L30: + ; + } + + } else { + +/* Sort into increasing order */ + + i__1 = endd; + for (i__ = start + 1; i__ <= i__1; ++i__) { + i__2 = start + 1; + for (j = i__; j >= i__2; --j) { + if (d__[j] < d__[j - 1]) { + dmnmx = d__[j]; + d__[j] = d__[j - 1]; + d__[j - 1] = dmnmx; + } else { + goto L50; + } +/* L40: */ + } +L50: + ; + } + + } + + } else if (endd - start > 20) { + +/* Partition D( START:ENDD ) and stack parts, largest one first */ + +/* Choose partition entry as median of 3 */ + + d1 = d__[start]; + d2 = d__[endd]; + i__ = (start + endd) / 2; + d3 = d__[i__]; + if (d1 < d2) { + if (d3 < d1) { + dmnmx = d1; + } else if (d3 < d2) { + dmnmx = d3; + } else { + dmnmx = d2; + } + } else { + if (d3 < d2) { + dmnmx = d2; + } else if (d3 < d1) { + dmnmx = d3; + } else { + dmnmx = d1; + } + } + + if (dir == 0) { + +/* Sort into decreasing order */ + + i__ = start - 1; + j = endd + 1; +L60: +L70: + --j; + if (d__[j] < dmnmx) { + goto L70; + } +L80: + ++i__; + if (d__[i__] > dmnmx) { + goto L80; + } + if (i__ < j) { + tmp = d__[i__]; + d__[i__] = d__[j]; + d__[j] = tmp; + goto L60; + } + if (j - start > endd - j - 1) { + ++stkpnt; + stack[(stkpnt << 1) - 2] = start; + stack[(stkpnt << 1) - 1] = j; + ++stkpnt; + stack[(stkpnt << 1) - 2] = j + 1; + stack[(stkpnt << 1) - 1] = endd; + } else { + ++stkpnt; + stack[(stkpnt << 1) - 2] = j + 1; + stack[(stkpnt << 1) - 1] = endd; + ++stkpnt; + stack[(stkpnt << 1) - 2] = start; + stack[(stkpnt << 1) - 1] = j; + } + } else { + +/* Sort into increasing order */ + + i__ = start - 1; + j = endd + 1; +L90: +L100: + --j; + if (d__[j] > dmnmx) { + goto L100; + } +L110: + ++i__; + if (d__[i__] < dmnmx) { + goto L110; + } + if (i__ < j) { + tmp = d__[i__]; + d__[i__] = d__[j]; + d__[j] = tmp; + goto L90; + } + if (j - start > endd - j - 1) { + ++stkpnt; + stack[(stkpnt << 1) - 2] = start; + stack[(stkpnt << 1) - 1] = j; + ++stkpnt; + stack[(stkpnt << 1) - 2] = j + 1; + stack[(stkpnt << 1) - 1] = endd; + } else { + ++stkpnt; + stack[(stkpnt << 1) - 2] = j + 1; + stack[(stkpnt << 1) - 1] = endd; + ++stkpnt; + stack[(stkpnt << 1) - 2] = start; + stack[(stkpnt << 1) - 1] = j; + } + } + } + if (stkpnt > 0) { + goto L10; + } + return 0; + +/* End of DLASRT */ + +} /* dlasrt_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlassq.cpp b/lib/linalg/dlassq.cpp new file mode 100644 index 0000000000..fe346d2247 --- /dev/null +++ b/lib/linalg/dlassq.cpp @@ -0,0 +1,191 @@ +/* fortran/dlassq.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DLASSQ updates a sum of squares represented in scaled form. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLASSQ + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLASSQ( N, X, INCX, SCALE, SUMSQ ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INCX, N */ +/* DOUBLE PRECISION SCALE, SUMSQ */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION X( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLASSQ returns the values scl and smsq such that */ +/* > */ +/* > ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq, */ +/* > */ +/* > where x( i ) = X( 1 + ( i - 1 )*INCX ). The value of sumsq is */ +/* > assumed to be non-negative and scl returns the value */ +/* > */ +/* > scl = max( scale, abs( x( i ) ) ). */ +/* > */ +/* > scale and sumsq must be supplied in SCALE and SUMSQ and */ +/* > scl and smsq are overwritten on SCALE and SUMSQ respectively. */ +/* > */ +/* > The routine makes only one pass through the vector x. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of elements to be used from the vector X. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] X */ +/* > \verbatim */ +/* > X is DOUBLE PRECISION array, dimension (N) */ +/* > The vector for which a scaled sum of squares is computed. */ +/* > x( i ) = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > The increment between successive values of the vector X. */ +/* > INCX > 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] SCALE */ +/* > \verbatim */ +/* > SCALE is DOUBLE PRECISION */ +/* > On entry, the value scale in the equation above. */ +/* > On exit, SCALE is overwritten with scl , the scaling factor */ +/* > for the sum of squares. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] SUMSQ */ +/* > \verbatim */ +/* > SUMSQ is DOUBLE PRECISION */ +/* > On entry, the value sumsq in the equation above. */ +/* > On exit, SUMSQ is overwritten with smsq , the basic sum of */ +/* > squares from which scl has been factored out. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \date December 2016 */ + +/* > \ingroup OTHERauxiliary */ + +/* ===================================================================== */ +/* Subroutine */ int dlassq_(integer *n, doublereal *x, integer *incx, + doublereal *scale, doublereal *sumsq) +{ + /* System generated locals */ + integer i__1, i__2; + doublereal d__1; + + /* Local variables */ + integer ix; + doublereal absxi; + extern logical disnan_(doublereal *); + + +/* -- LAPACK auxiliary routine (version 3.7.0) -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ +/* December 2016 */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + + /* Parameter adjustments */ + --x; + + /* Function Body */ + if (*n > 0) { + i__1 = (*n - 1) * *incx + 1; + i__2 = *incx; + for (ix = 1; i__2 < 0 ? ix >= i__1 : ix <= i__1; ix += i__2) { + absxi = (d__1 = x[ix], abs(d__1)); + if (absxi > 0. || disnan_(&absxi)) { + if (*scale < absxi) { +/* Computing 2nd power */ + d__1 = *scale / absxi; + *sumsq = *sumsq * (d__1 * d__1) + 1; + *scale = absxi; + } else { +/* Computing 2nd power */ + d__1 = absxi / *scale; + *sumsq += d__1 * d__1; + } + } +/* L10: */ + } + } + return 0; + +/* End of DLASSQ */ + +} /* dlassq_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlasv2.cpp b/lib/linalg/dlasv2.cpp new file mode 100644 index 0000000000..4667b941d4 --- /dev/null +++ b/lib/linalg/dlasv2.cpp @@ -0,0 +1,356 @@ +/* fortran/dlasv2.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static doublereal c_b3 = 2.; +static doublereal c_b4 = 1.; + +/* > \brief \b DLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLASV2 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLASV2( F, G, H, SSMIN, SSMAX, SNR, CSR, SNL, CSL ) */ + +/* .. Scalar Arguments .. */ +/* DOUBLE PRECISION CSL, CSR, F, G, H, SNL, SNR, SSMAX, SSMIN */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLASV2 computes the singular value decomposition of a 2-by-2 */ +/* > triangular matrix */ +/* > [ F G ] */ +/* > [ 0 H ]. */ +/* > On return, abs(SSMAX) is the larger singular value, abs(SSMIN) is the */ +/* > smaller singular value, and (CSL,SNL) and (CSR,SNR) are the left and */ +/* > right singular vectors for abs(SSMAX), giving the decomposition */ +/* > */ +/* > [ CSL SNL ] [ F G ] [ CSR -SNR ] = [ SSMAX 0 ] */ +/* > [-SNL CSL ] [ 0 H ] [ SNR CSR ] [ 0 SSMIN ]. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] F */ +/* > \verbatim */ +/* > F is DOUBLE PRECISION */ +/* > The (1,1) element of the 2-by-2 matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] G */ +/* > \verbatim */ +/* > G is DOUBLE PRECISION */ +/* > The (1,2) element of the 2-by-2 matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] H */ +/* > \verbatim */ +/* > H is DOUBLE PRECISION */ +/* > The (2,2) element of the 2-by-2 matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] SSMIN */ +/* > \verbatim */ +/* > SSMIN is DOUBLE PRECISION */ +/* > abs(SSMIN) is the smaller singular value. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] SSMAX */ +/* > \verbatim */ +/* > SSMAX is DOUBLE PRECISION */ +/* > abs(SSMAX) is the larger singular value. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] SNL */ +/* > \verbatim */ +/* > SNL is DOUBLE PRECISION */ +/* > \endverbatim */ +/* > */ +/* > \param[out] CSL */ +/* > \verbatim */ +/* > CSL is DOUBLE PRECISION */ +/* > The vector (CSL, SNL) is a unit left singular vector for the */ +/* > singular value abs(SSMAX). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] SNR */ +/* > \verbatim */ +/* > SNR is DOUBLE PRECISION */ +/* > \endverbatim */ +/* > */ +/* > \param[out] CSR */ +/* > \verbatim */ +/* > CSR is DOUBLE PRECISION */ +/* > The vector (CSR, SNR) is a unit right singular vector for the */ +/* > singular value abs(SSMAX). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup OTHERauxiliary */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > Any input parameter may be aliased with any output parameter. */ +/* > */ +/* > Barring over/underflow and assuming a guard digit in subtraction, all */ +/* > output quantities are correct to within a few units in the last */ +/* > place (ulps). */ +/* > */ +/* > In IEEE arithmetic, the code works correctly if one matrix element is */ +/* > infinite. */ +/* > */ +/* > Overflow will not occur unless the largest singular value itself */ +/* > overflows or is within a few ulps of overflow. (On machines with */ +/* > partial overflow, like the Cray, overflow may occur if the largest */ +/* > singular value is within a factor of 2 of overflow.) */ +/* > */ +/* > Underflow is harmless if underflow is gradual. Otherwise, results */ +/* > may correspond to a matrix modified by perturbations of size near */ +/* > the underflow threshold. */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dlasv2_(doublereal *f, doublereal *g, doublereal *h__, + doublereal *ssmin, doublereal *ssmax, doublereal *snr, doublereal * + csr, doublereal *snl, doublereal *csl) +{ + /* System generated locals */ + doublereal d__1; + + /* Builtin functions */ + double sqrt(doublereal), d_sign(doublereal *, doublereal *); + + /* Local variables */ + doublereal a, d__, l, m, r__, s, t, fa, ga, ha, ft, gt, ht, mm, tt, clt, + crt, slt, srt; + integer pmax; + doublereal temp; + logical swap; + doublereal tsign; + extern doublereal dlamch_(char *, ftnlen); + logical gasmal; + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + + ft = *f; + fa = abs(ft); + ht = *h__; + ha = abs(*h__); + +/* PMAX points to the maximum absolute element of matrix */ +/* PMAX = 1 if F largest in absolute values */ +/* PMAX = 2 if G largest in absolute values */ +/* PMAX = 3 if H largest in absolute values */ + + pmax = 1; + swap = ha > fa; + if (swap) { + pmax = 3; + temp = ft; + ft = ht; + ht = temp; + temp = fa; + fa = ha; + ha = temp; + +/* Now FA .ge. HA */ + + } + gt = *g; + ga = abs(gt); + if (ga == 0.) { + +/* Diagonal matrix */ + + *ssmin = ha; + *ssmax = fa; + clt = 1.; + crt = 1.; + slt = 0.; + srt = 0.; + } else { + gasmal = TRUE_; + if (ga > fa) { + pmax = 2; + if (fa / ga < dlamch_((char *)"EPS", (ftnlen)3)) { + +/* Case of very large GA */ + + gasmal = FALSE_; + *ssmax = ga; + if (ha > 1.) { + *ssmin = fa / (ga / ha); + } else { + *ssmin = fa / ga * ha; + } + clt = 1.; + slt = ht / gt; + srt = 1.; + crt = ft / gt; + } + } + if (gasmal) { + +/* Normal case */ + + d__ = fa - ha; + if (d__ == fa) { + +/* Copes with infinite F or H */ + + l = 1.; + } else { + l = d__ / fa; + } + +/* Note that 0 .le. L .le. 1 */ + + m = gt / ft; + +/* Note that abs(M) .le. 1/macheps */ + + t = 2. - l; + +/* Note that T .ge. 1 */ + + mm = m * m; + tt = t * t; + s = sqrt(tt + mm); + +/* Note that 1 .le. S .le. 1 + 1/macheps */ + + if (l == 0.) { + r__ = abs(m); + } else { + r__ = sqrt(l * l + mm); + } + +/* Note that 0 .le. R .le. 1 + 1/macheps */ + + a = (s + r__) * .5; + +/* Note that 1 .le. A .le. 1 + abs(M) */ + + *ssmin = ha / a; + *ssmax = fa * a; + if (mm == 0.) { + +/* Note that M is very tiny */ + + if (l == 0.) { + t = d_sign(&c_b3, &ft) * d_sign(&c_b4, >); + } else { + t = gt / d_sign(&d__, &ft) + m / t; + } + } else { + t = (m / (s + t) + m / (r__ + l)) * (a + 1.); + } + l = sqrt(t * t + 4.); + crt = 2. / l; + srt = t / l; + clt = (crt + srt * m) / a; + slt = ht / ft * srt / a; + } + } + if (swap) { + *csl = srt; + *snl = crt; + *csr = slt; + *snr = clt; + } else { + *csl = clt; + *snl = slt; + *csr = crt; + *snr = srt; + } + +/* Correct signs of SSMAX and SSMIN */ + + if (pmax == 1) { + tsign = d_sign(&c_b4, csr) * d_sign(&c_b4, csl) * d_sign(&c_b4, f); + } + if (pmax == 2) { + tsign = d_sign(&c_b4, snr) * d_sign(&c_b4, csl) * d_sign(&c_b4, g); + } + if (pmax == 3) { + tsign = d_sign(&c_b4, snr) * d_sign(&c_b4, snl) * d_sign(&c_b4, h__); + } + *ssmax = d_sign(ssmax, &tsign); + d__1 = tsign * d_sign(&c_b4, f) * d_sign(&c_b4, h__); + *ssmin = d_sign(ssmin, &d__1); + return 0; + +/* End of DLASV2 */ + +} /* dlasv2_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlaswp.cpp b/lib/linalg/dlaswp.cpp new file mode 100644 index 0000000000..db83b75947 --- /dev/null +++ b/lib/linalg/dlaswp.cpp @@ -0,0 +1,238 @@ +/* fortran/dlaswp.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DLASWP performs a series of row interchanges on a general rectangular matrix. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLASWP + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLASWP( N, A, LDA, K1, K2, IPIV, INCX ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INCX, K1, K2, LDA, N */ +/* .. */ +/* .. Array Arguments .. */ +/* INTEGER IPIV( * ) */ +/* DOUBLE PRECISION A( LDA, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLASWP performs a series of row interchanges on the matrix A. */ +/* > One row interchange is initiated for each of rows K1 through K2 of A. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On entry, the matrix of column dimension N to which the row */ +/* > interchanges will be applied. */ +/* > On exit, the permuted matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K1 */ +/* > \verbatim */ +/* > K1 is INTEGER */ +/* > The first element of IPIV for which a row interchange will */ +/* > be done. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K2 */ +/* > \verbatim */ +/* > K2 is INTEGER */ +/* > (K2-K1+1) is the number of elements of IPIV for which a row */ +/* > interchange will be done. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] IPIV */ +/* > \verbatim */ +/* > IPIV is INTEGER array, dimension (K1+(K2-K1)*abs(INCX)) */ +/* > The vector of pivot indices. Only the elements in positions */ +/* > K1 through K1+(K2-K1)*abs(INCX) of IPIV are accessed. */ +/* > IPIV(K1+(K-K1)*abs(INCX)) = L implies rows K and L are to be */ +/* > interchanged. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > The increment between successive values of IPIV. If INCX */ +/* > is negative, the pivots are applied in reverse order. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleOTHERauxiliary */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > Modified by */ +/* > R. C. Whaley, Computer Science Dept., Univ. of Tenn., Knoxville, USA */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dlaswp_(integer *n, doublereal *a, integer *lda, integer + *k1, integer *k2, integer *ipiv, integer *incx) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3, i__4; + + /* Local variables */ + integer i__, j, k, i1, i2, n32, ip, ix, ix0, inc; + doublereal temp; + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Interchange row I with row IPIV(K1+(I-K1)*abs(INCX)) for each of rows */ +/* K1 through K2. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --ipiv; + + /* Function Body */ + if (*incx > 0) { + ix0 = *k1; + i1 = *k1; + i2 = *k2; + inc = 1; + } else if (*incx < 0) { + ix0 = *k1 + (*k1 - *k2) * *incx; + i1 = *k2; + i2 = *k1; + inc = -1; + } else { + return 0; + } + + n32 = *n / 32 << 5; + if (n32 != 0) { + i__1 = n32; + for (j = 1; j <= i__1; j += 32) { + ix = ix0; + i__2 = i2; + i__3 = inc; + for (i__ = i1; i__3 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__3) + { + ip = ipiv[ix]; + if (ip != i__) { + i__4 = j + 31; + for (k = j; k <= i__4; ++k) { + temp = a[i__ + k * a_dim1]; + a[i__ + k * a_dim1] = a[ip + k * a_dim1]; + a[ip + k * a_dim1] = temp; +/* L10: */ + } + } + ix += *incx; +/* L20: */ + } +/* L30: */ + } + } + if (n32 != *n) { + ++n32; + ix = ix0; + i__1 = i2; + i__3 = inc; + for (i__ = i1; i__3 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__3) { + ip = ipiv[ix]; + if (ip != i__) { + i__2 = *n; + for (k = n32; k <= i__2; ++k) { + temp = a[i__ + k * a_dim1]; + a[i__ + k * a_dim1] = a[ip + k * a_dim1]; + a[ip + k * a_dim1] = temp; +/* L40: */ + } + } + ix += *incx; +/* L50: */ + } + } + + return 0; + +/* End of DLASWP */ + +} /* dlaswp_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlatrd.cpp b/lib/linalg/dlatrd.cpp new file mode 100644 index 0000000000..b291e1adbf --- /dev/null +++ b/lib/linalg/dlatrd.cpp @@ -0,0 +1,445 @@ +/* fortran/dlatrd.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static doublereal c_b5 = -1.; +static doublereal c_b6 = 1.; +static integer c__1 = 1; +static doublereal c_b16 = 0.; + +/* > \brief \b DLATRD reduces the first nb rows and columns of a symmetric/Hermitian matrix A to real tridiago +nal form by an orthogonal similarity transformation. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLATRD + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLATRD( UPLO, N, NB, A, LDA, E, TAU, W, LDW ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER UPLO */ +/* INTEGER LDA, LDW, N, NB */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), E( * ), TAU( * ), W( LDW, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLATRD reduces NB rows and columns of a real symmetric matrix A to */ +/* > symmetric tridiagonal form by an orthogonal similarity */ +/* > transformation Q**T * A * Q, and returns the matrices V and W which are */ +/* > needed to apply the transformation to the unreduced part of A. */ +/* > */ +/* > If UPLO = 'U', DLATRD reduces the last NB rows and columns of a */ +/* > matrix, of which the upper triangle is supplied; */ +/* > if UPLO = 'L', DLATRD reduces the first NB rows and columns of a */ +/* > matrix, of which the lower triangle is supplied. */ +/* > */ +/* > This is an auxiliary routine called by DSYTRD. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > Specifies whether the upper or lower triangular part of the */ +/* > symmetric matrix A is stored: */ +/* > = 'U': Upper triangular */ +/* > = 'L': Lower triangular */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrix A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] NB */ +/* > \verbatim */ +/* > NB is INTEGER */ +/* > The number of rows and columns to be reduced. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On entry, the symmetric matrix A. If UPLO = 'U', the leading */ +/* > n-by-n upper triangular part of A contains the upper */ +/* > triangular part of the matrix A, and the strictly lower */ +/* > triangular part of A is not referenced. If UPLO = 'L', the */ +/* > leading n-by-n lower triangular part of A contains the lower */ +/* > triangular part of the matrix A, and the strictly upper */ +/* > triangular part of A is not referenced. */ +/* > On exit: */ +/* > if UPLO = 'U', the last NB columns have been reduced to */ +/* > tridiagonal form, with the diagonal elements overwriting */ +/* > the diagonal elements of A; the elements above the diagonal */ +/* > with the array TAU, represent the orthogonal matrix Q as a */ +/* > product of elementary reflectors; */ +/* > if UPLO = 'L', the first NB columns have been reduced to */ +/* > tridiagonal form, with the diagonal elements overwriting */ +/* > the diagonal elements of A; the elements below the diagonal */ +/* > with the array TAU, represent the orthogonal matrix Q as a */ +/* > product of elementary reflectors. */ +/* > See Further Details. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= (1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] E */ +/* > \verbatim */ +/* > E is DOUBLE PRECISION array, dimension (N-1) */ +/* > If UPLO = 'U', E(n-nb:n-1) contains the superdiagonal */ +/* > elements of the last NB columns of the reduced matrix; */ +/* > if UPLO = 'L', E(1:nb) contains the subdiagonal elements of */ +/* > the first NB columns of the reduced matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] TAU */ +/* > \verbatim */ +/* > TAU is DOUBLE PRECISION array, dimension (N-1) */ +/* > The scalar factors of the elementary reflectors, stored in */ +/* > TAU(n-nb:n-1) if UPLO = 'U', and in TAU(1:nb) if UPLO = 'L'. */ +/* > See Further Details. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] W */ +/* > \verbatim */ +/* > W is DOUBLE PRECISION array, dimension (LDW,NB) */ +/* > The n-by-nb matrix W required to update the unreduced part */ +/* > of A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDW */ +/* > \verbatim */ +/* > LDW is INTEGER */ +/* > The leading dimension of the array W. LDW >= max(1,N). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleOTHERauxiliary */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > If UPLO = 'U', the matrix Q is represented as a product of elementary */ +/* > reflectors */ +/* > */ +/* > Q = H(n) H(n-1) . . . H(n-nb+1). */ +/* > */ +/* > Each H(i) has the form */ +/* > */ +/* > H(i) = I - tau * v * v**T */ +/* > */ +/* > where tau is a real scalar, and v is a real vector with */ +/* > v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i), */ +/* > and tau in TAU(i-1). */ +/* > */ +/* > If UPLO = 'L', the matrix Q is represented as a product of elementary */ +/* > reflectors */ +/* > */ +/* > Q = H(1) H(2) . . . H(nb). */ +/* > */ +/* > Each H(i) has the form */ +/* > */ +/* > H(i) = I - tau * v * v**T */ +/* > */ +/* > where tau is a real scalar, and v is a real vector with */ +/* > v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i), */ +/* > and tau in TAU(i). */ +/* > */ +/* > The elements of the vectors v together form the n-by-nb matrix V */ +/* > which is needed, with W, to apply the transformation to the unreduced */ +/* > part of the matrix, using a symmetric rank-2k update of the form: */ +/* > A := A - V*W**T - W*V**T. */ +/* > */ +/* > The contents of A on exit are illustrated by the following examples */ +/* > with n = 5 and nb = 2: */ +/* > */ +/* > if UPLO = 'U': if UPLO = 'L': */ +/* > */ +/* > ( a a a v4 v5 ) ( d ) */ +/* > ( a a v4 v5 ) ( 1 d ) */ +/* > ( a 1 v5 ) ( v1 1 a ) */ +/* > ( d 1 ) ( v1 v2 a a ) */ +/* > ( d ) ( v1 v2 a a a ) */ +/* > */ +/* > where d denotes a diagonal element of the reduced matrix, a denotes */ +/* > an element of the original matrix that is unchanged, and vi denotes */ +/* > an element of the vector defining H(i). */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dlatrd_(char *uplo, integer *n, integer *nb, doublereal * + a, integer *lda, doublereal *e, doublereal *tau, doublereal *w, + integer *ldw, ftnlen uplo_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, w_dim1, w_offset, i__1, i__2, i__3; + + /* Local variables */ + integer i__, iw; + extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, + integer *); + doublereal alpha; + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *); + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int dgemv_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, ftnlen), daxpy_(integer *, + doublereal *, doublereal *, integer *, doublereal *, integer *), + dsymv_(char *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, + ftnlen), dlarfg_(integer *, doublereal *, doublereal *, integer *, + doublereal *); + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Quick return if possible */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --e; + --tau; + w_dim1 = *ldw; + w_offset = 1 + w_dim1; + w -= w_offset; + + /* Function Body */ + if (*n <= 0) { + return 0; + } + + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + +/* Reduce last NB columns of upper triangle */ + + i__1 = *n - *nb + 1; + for (i__ = *n; i__ >= i__1; --i__) { + iw = i__ - *n + *nb; + if (i__ < *n) { + +/* Update A(1:i,i) */ + + i__2 = *n - i__; + dgemv_((char *)"No transpose", &i__, &i__2, &c_b5, &a[(i__ + 1) * + a_dim1 + 1], lda, &w[i__ + (iw + 1) * w_dim1], ldw, & + c_b6, &a[i__ * a_dim1 + 1], &c__1, (ftnlen)12); + i__2 = *n - i__; + dgemv_((char *)"No transpose", &i__, &i__2, &c_b5, &w[(iw + 1) * + w_dim1 + 1], ldw, &a[i__ + (i__ + 1) * a_dim1], lda, & + c_b6, &a[i__ * a_dim1 + 1], &c__1, (ftnlen)12); + } + if (i__ > 1) { + +/* Generate elementary reflector H(i) to annihilate */ +/* A(1:i-2,i) */ + + i__2 = i__ - 1; + dlarfg_(&i__2, &a[i__ - 1 + i__ * a_dim1], &a[i__ * a_dim1 + + 1], &c__1, &tau[i__ - 1]); + e[i__ - 1] = a[i__ - 1 + i__ * a_dim1]; + a[i__ - 1 + i__ * a_dim1] = 1.; + +/* Compute W(1:i-1,i) */ + + i__2 = i__ - 1; + dsymv_((char *)"Upper", &i__2, &c_b6, &a[a_offset], lda, &a[i__ * + a_dim1 + 1], &c__1, &c_b16, &w[iw * w_dim1 + 1], & + c__1, (ftnlen)5); + if (i__ < *n) { + i__2 = i__ - 1; + i__3 = *n - i__; + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b6, &w[(iw + 1) * + w_dim1 + 1], ldw, &a[i__ * a_dim1 + 1], &c__1, & + c_b16, &w[i__ + 1 + iw * w_dim1], &c__1, (ftnlen) + 9); + i__2 = i__ - 1; + i__3 = *n - i__; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[(i__ + 1) * + a_dim1 + 1], lda, &w[i__ + 1 + iw * w_dim1], & + c__1, &c_b6, &w[iw * w_dim1 + 1], &c__1, (ftnlen) + 12); + i__2 = i__ - 1; + i__3 = *n - i__; + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b6, &a[(i__ + 1) * + a_dim1 + 1], lda, &a[i__ * a_dim1 + 1], &c__1, & + c_b16, &w[i__ + 1 + iw * w_dim1], &c__1, (ftnlen) + 9); + i__2 = i__ - 1; + i__3 = *n - i__; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &w[(iw + 1) * + w_dim1 + 1], ldw, &w[i__ + 1 + iw * w_dim1], & + c__1, &c_b6, &w[iw * w_dim1 + 1], &c__1, (ftnlen) + 12); + } + i__2 = i__ - 1; + dscal_(&i__2, &tau[i__ - 1], &w[iw * w_dim1 + 1], &c__1); + i__2 = i__ - 1; + alpha = tau[i__ - 1] * -.5 * ddot_(&i__2, &w[iw * w_dim1 + 1], + &c__1, &a[i__ * a_dim1 + 1], &c__1); + i__2 = i__ - 1; + daxpy_(&i__2, &alpha, &a[i__ * a_dim1 + 1], &c__1, &w[iw * + w_dim1 + 1], &c__1); + } + +/* L10: */ + } + } else { + +/* Reduce first NB columns of lower triangle */ + + i__1 = *nb; + for (i__ = 1; i__ <= i__1; ++i__) { + +/* Update A(i:n,i) */ + + i__2 = *n - i__ + 1; + i__3 = i__ - 1; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[i__ + a_dim1], lda, + &w[i__ + w_dim1], ldw, &c_b6, &a[i__ + i__ * a_dim1], & + c__1, (ftnlen)12); + i__2 = *n - i__ + 1; + i__3 = i__ - 1; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &w[i__ + w_dim1], ldw, + &a[i__ + a_dim1], lda, &c_b6, &a[i__ + i__ * a_dim1], & + c__1, (ftnlen)12); + if (i__ < *n) { + +/* Generate elementary reflector H(i) to annihilate */ +/* A(i+2:n,i) */ + + i__2 = *n - i__; +/* Computing MIN */ + i__3 = i__ + 2; + dlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3,*n) + + i__ * a_dim1], &c__1, &tau[i__]); + e[i__] = a[i__ + 1 + i__ * a_dim1]; + a[i__ + 1 + i__ * a_dim1] = 1.; + +/* Compute W(i+1:n,i) */ + + i__2 = *n - i__; + dsymv_((char *)"Lower", &i__2, &c_b6, &a[i__ + 1 + (i__ + 1) * a_dim1] + , lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[ + i__ + 1 + i__ * w_dim1], &c__1, (ftnlen)5); + i__2 = *n - i__; + i__3 = i__ - 1; + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b6, &w[i__ + 1 + w_dim1], + ldw, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[ + i__ * w_dim1 + 1], &c__1, (ftnlen)9); + i__2 = *n - i__; + i__3 = i__ - 1; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + + a_dim1], lda, &w[i__ * w_dim1 + 1], &c__1, &c_b6, &w[ + i__ + 1 + i__ * w_dim1], &c__1, (ftnlen)12); + i__2 = *n - i__; + i__3 = i__ - 1; + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b6, &a[i__ + 1 + a_dim1], + lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[ + i__ * w_dim1 + 1], &c__1, (ftnlen)9); + i__2 = *n - i__; + i__3 = i__ - 1; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &w[i__ + 1 + + w_dim1], ldw, &w[i__ * w_dim1 + 1], &c__1, &c_b6, &w[ + i__ + 1 + i__ * w_dim1], &c__1, (ftnlen)12); + i__2 = *n - i__; + dscal_(&i__2, &tau[i__], &w[i__ + 1 + i__ * w_dim1], &c__1); + i__2 = *n - i__; + alpha = tau[i__] * -.5 * ddot_(&i__2, &w[i__ + 1 + i__ * + w_dim1], &c__1, &a[i__ + 1 + i__ * a_dim1], &c__1); + i__2 = *n - i__; + daxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &w[ + i__ + 1 + i__ * w_dim1], &c__1); + } + +/* L20: */ + } + } + + return 0; + +/* End of DLATRD */ + +} /* dlatrd_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlatrs.cpp b/lib/linalg/dlatrs.cpp new file mode 100644 index 0000000000..0b68eac917 --- /dev/null +++ b/lib/linalg/dlatrs.cpp @@ -0,0 +1,984 @@ +/* fortran/dlatrs.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static doublereal c_b46 = .5; + +/* > \brief \b DLATRS solves a triangular system of equations with the scale factor set to prevent overflow. +*/ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DLATRS + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DLATRS( UPLO, TRANS, DIAG, NORMIN, N, A, LDA, X, SCALE, */ +/* CNORM, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER DIAG, NORMIN, TRANS, UPLO */ +/* INTEGER INFO, LDA, N */ +/* DOUBLE PRECISION SCALE */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), CNORM( * ), X( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DLATRS solves one of the triangular systems */ +/* > */ +/* > A *x = s*b or A**T *x = s*b */ +/* > */ +/* > with scaling to prevent overflow. Here A is an upper or lower */ +/* > triangular matrix, A**T denotes the transpose of A, x and b are */ +/* > n-element vectors, and s is a scaling factor, usually less than */ +/* > or equal to 1, chosen so that the components of x will be less than */ +/* > the overflow threshold. If the unscaled problem will not cause */ +/* > overflow, the Level 2 BLAS routine DTRSV is called. If the matrix A */ +/* > is singular (A(j,j) = 0 for some j), then s is set to 0 and a */ +/* > non-trivial solution to A*x = 0 is returned. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > Specifies whether the matrix A is upper or lower triangular. */ +/* > = 'U': Upper triangular */ +/* > = 'L': Lower triangular */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TRANS */ +/* > \verbatim */ +/* > TRANS is CHARACTER*1 */ +/* > Specifies the operation applied to A. */ +/* > = 'N': Solve A * x = s*b (No transpose) */ +/* > = 'T': Solve A**T* x = s*b (Transpose) */ +/* > = 'C': Solve A**T* x = s*b (Conjugate transpose = Transpose) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DIAG */ +/* > \verbatim */ +/* > DIAG is CHARACTER*1 */ +/* > Specifies whether or not the matrix A is unit triangular. */ +/* > = 'N': Non-unit triangular */ +/* > = 'U': Unit triangular */ +/* > \endverbatim */ +/* > */ +/* > \param[in] NORMIN */ +/* > \verbatim */ +/* > NORMIN is CHARACTER*1 */ +/* > Specifies whether CNORM has been set or not. */ +/* > = 'Y': CNORM contains the column norms on entry */ +/* > = 'N': CNORM is not set on entry. On exit, the norms will */ +/* > be computed and stored in CNORM. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > The triangular matrix A. If UPLO = 'U', the leading n by n */ +/* > upper triangular part of the array A contains the upper */ +/* > triangular matrix, and the strictly lower triangular part of */ +/* > A is not referenced. If UPLO = 'L', the leading n by n lower */ +/* > triangular part of the array A contains the lower triangular */ +/* > matrix, and the strictly upper triangular part of A is not */ +/* > referenced. If DIAG = 'U', the diagonal elements of A are */ +/* > also not referenced and are assumed to be 1. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max (1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] X */ +/* > \verbatim */ +/* > X is DOUBLE PRECISION array, dimension (N) */ +/* > On entry, the right hand side b of the triangular system. */ +/* > On exit, X is overwritten by the solution vector x. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] SCALE */ +/* > \verbatim */ +/* > SCALE is DOUBLE PRECISION */ +/* > The scaling factor s for the triangular system */ +/* > A * x = s*b or A**T* x = s*b. */ +/* > If SCALE = 0, the matrix A is singular or badly scaled, and */ +/* > the vector x is an exact or approximate solution to A*x = 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] CNORM */ +/* > \verbatim */ +/* > CNORM is DOUBLE PRECISION array, dimension (N) */ +/* > */ +/* > If NORMIN = 'Y', CNORM is an input argument and CNORM(j) */ +/* > contains the norm of the off-diagonal part of the j-th column */ +/* > of A. If TRANS = 'N', CNORM(j) must be greater than or equal */ +/* > to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j) */ +/* > must be greater than or equal to the 1-norm. */ +/* > */ +/* > If NORMIN = 'N', CNORM is an output argument and CNORM(j) */ +/* > returns the 1-norm of the offdiagonal part of the j-th column */ +/* > of A. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -k, the k-th argument had an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleOTHERauxiliary */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > A rough bound on x is computed; if that is less than overflow, DTRSV */ +/* > is called, otherwise, specific code is used which checks for possible */ +/* > overflow or divide-by-zero at every operation. */ +/* > */ +/* > A columnwise scheme is used for solving A*x = b. The basic algorithm */ +/* > if A is lower triangular is */ +/* > */ +/* > x[1:n] := b[1:n] */ +/* > for j = 1, ..., n */ +/* > x(j) := x(j) / A(j,j) */ +/* > x[j+1:n] := x[j+1:n] - x(j) * A[j+1:n,j] */ +/* > end */ +/* > */ +/* > Define bounds on the components of x after j iterations of the loop: */ +/* > M(j) = bound on x[1:j] */ +/* > G(j) = bound on x[j+1:n] */ +/* > Initially, let M(0) = 0 and G(0) = max{x(i), i=1,...,n}. */ +/* > */ +/* > Then for iteration j+1 we have */ +/* > M(j+1) <= G(j) / | A(j+1,j+1) | */ +/* > G(j+1) <= G(j) + M(j+1) * | A[j+2:n,j+1] | */ +/* > <= G(j) ( 1 + CNORM(j+1) / | A(j+1,j+1) | ) */ +/* > */ +/* > where CNORM(j+1) is greater than or equal to the infinity-norm of */ +/* > column j+1 of A, not counting the diagonal. Hence */ +/* > */ +/* > G(j) <= G(0) product ( 1 + CNORM(i) / | A(i,i) | ) */ +/* > 1<=i<=j */ +/* > and */ +/* > */ +/* > |x(j)| <= ( G(0) / |A(j,j)| ) product ( 1 + CNORM(i) / |A(i,i)| ) */ +/* > 1<=i< j */ +/* > */ +/* > Since |x(j)| <= M(j), we use the Level 2 BLAS routine DTRSV if the */ +/* > reciprocal of the largest M(j), j=1,..,n, is larger than */ +/* > max(underflow, 1/overflow). */ +/* > */ +/* > The bound on x(j) is also used to determine when a step in the */ +/* > columnwise method can be performed without fear of overflow. If */ +/* > the computed bound is greater than a large constant, x is scaled to */ +/* > prevent overflow, but if the bound overflows, x is set to 0, x(j) to */ +/* > 1, and scale to 0, and a non-trivial solution to A*x = 0 is found. */ +/* > */ +/* > Similarly, a row-wise scheme is used to solve A**T*x = b. The basic */ +/* > algorithm for A upper triangular is */ +/* > */ +/* > for j = 1, ..., n */ +/* > x(j) := ( b(j) - A[1:j-1,j]**T * x[1:j-1] ) / A(j,j) */ +/* > end */ +/* > */ +/* > We simultaneously compute two bounds */ +/* > G(j) = bound on ( b(i) - A[1:i-1,i]**T * x[1:i-1] ), 1<=i<=j */ +/* > M(j) = bound on x(i), 1<=i<=j */ +/* > */ +/* > The initial values are G(0) = 0, M(0) = max{b(i), i=1,..,n}, and we */ +/* > add the constraint G(j) >= G(j-1) and M(j) >= M(j-1) for j >= 1. */ +/* > Then the bound on x(j) is */ +/* > */ +/* > M(j) <= M(j-1) * ( 1 + CNORM(j) ) / | A(j,j) | */ +/* > */ +/* > <= M(0) * product ( ( 1 + CNORM(i) ) / |A(i,i)| ) */ +/* > 1<=i<=j */ +/* > */ +/* > and we can safely call DTRSV if 1/M(n) and 1/G(n) are both greater */ +/* > than max(underflow, 1/overflow). */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dlatrs_(char *uplo, char *trans, char *diag, char * + normin, integer *n, doublereal *a, integer *lda, doublereal *x, + doublereal *scale, doublereal *cnorm, integer *info, ftnlen uplo_len, + ftnlen trans_len, ftnlen diag_len, ftnlen normin_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3; + doublereal d__1, d__2, d__3; + + /* Local variables */ + integer i__, j; + doublereal xj, rec, tjj; + integer jinc; + extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, + integer *); + doublereal xbnd; + integer imax; + doublereal tmax, tjjs, xmax, grow, sumj; + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *); + extern logical lsame_(char *, char *, ftnlen, ftnlen); + doublereal tscal, uscal; + extern doublereal dasum_(integer *, doublereal *, integer *); + integer jlast; + extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *); + logical upper; + extern /* Subroutine */ int dtrsv_(char *, char *, char *, integer *, + doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, + ftnlen); + extern doublereal dlamch_(char *, ftnlen), dlange_(char *, integer *, + integer *, doublereal *, integer *, doublereal *, ftnlen); + extern integer idamax_(integer *, doublereal *, integer *); + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + doublereal bignum; + logical notran; + integer jfirst; + doublereal smlnum; + logical nounit; + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --x; + --cnorm; + + /* Function Body */ + *info = 0; + upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); + notran = lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1); + nounit = lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1); + +/* Test the input parameters. */ + + if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + *info = -1; + } else if (! notran && ! lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1) && ! + lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { + *info = -2; + } else if (! nounit && ! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1)) { + *info = -3; + } else if (! lsame_(normin, (char *)"Y", (ftnlen)1, (ftnlen)1) && ! lsame_(normin, + (char *)"N", (ftnlen)1, (ftnlen)1)) { + *info = -4; + } else if (*n < 0) { + *info = -5; + } else if (*lda < max(1,*n)) { + *info = -7; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DLATRS", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + *scale = 1.; + if (*n == 0) { + return 0; + } + +/* Determine machine dependent parameters to control overflow. */ + + smlnum = dlamch_((char *)"Safe minimum", (ftnlen)12) / dlamch_((char *)"Precision", ( + ftnlen)9); + bignum = 1. / smlnum; + + if (lsame_(normin, (char *)"N", (ftnlen)1, (ftnlen)1)) { + +/* Compute the 1-norm of each column, not including the diagonal. */ + + if (upper) { + +/* A is upper triangular. */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j - 1; + cnorm[j] = dasum_(&i__2, &a[j * a_dim1 + 1], &c__1); +/* L10: */ + } + } else { + +/* A is lower triangular. */ + + i__1 = *n - 1; + for (j = 1; j <= i__1; ++j) { + i__2 = *n - j; + cnorm[j] = dasum_(&i__2, &a[j + 1 + j * a_dim1], &c__1); +/* L20: */ + } + cnorm[*n] = 0.; + } + } + +/* Scale the column norms by TSCAL if the maximum element in CNORM is */ +/* greater than BIGNUM. */ + + imax = idamax_(n, &cnorm[1], &c__1); + tmax = cnorm[imax]; + if (tmax <= bignum) { + tscal = 1.; + } else { + +/* Avoid NaN generation if entries in CNORM exceed the */ +/* overflow threshold */ + + if (tmax <= dlamch_((char *)"Overflow", (ftnlen)8)) { +/* Case 1: All entries in CNORM are valid floating-point numbers */ + tscal = 1. / (smlnum * tmax); + dscal_(n, &tscal, &cnorm[1], &c__1); + } else { +/* Case 2: At least one column norm of A cannot be represented */ +/* as floating-point number. Find the offdiagonal entry A( I, J ) */ +/* with the largest absolute value. If this entry is not +/- Infinity, */ +/* use this value as TSCAL. */ + tmax = 0.; + if (upper) { + +/* A is upper triangular. */ + + i__1 = *n; + for (j = 2; j <= i__1; ++j) { +/* Computing MAX */ + i__2 = j - 1; + d__1 = dlange_((char *)"M", &i__2, &c__1, &a[j * a_dim1 + 1], & + c__1, &sumj, (ftnlen)1); + tmax = max(d__1,tmax); + } + } else { + +/* A is lower triangular. */ + + i__1 = *n - 1; + for (j = 1; j <= i__1; ++j) { +/* Computing MAX */ + i__2 = *n - j; + d__1 = dlange_((char *)"M", &i__2, &c__1, &a[j + 1 + j * a_dim1], + &c__1, &sumj, (ftnlen)1); + tmax = max(d__1,tmax); + } + } + + if (tmax <= dlamch_((char *)"Overflow", (ftnlen)8)) { + tscal = 1. / (smlnum * tmax); + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (cnorm[j] <= dlamch_((char *)"Overflow", (ftnlen)8)) { + cnorm[j] *= tscal; + } else { +/* Recompute the 1-norm without introducing Infinity */ +/* in the summation */ + cnorm[j] = 0.; + if (upper) { + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + cnorm[j] += tscal * (d__1 = a[i__ + j * + a_dim1], abs(d__1)); + } + } else { + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + cnorm[j] += tscal * (d__1 = a[i__ + j * + a_dim1], abs(d__1)); + } + } + } + } + } else { +/* At least one entry of A is not a valid floating-point entry. */ +/* Rely on TRSV to propagate Inf and NaN. */ + dtrsv_(uplo, trans, diag, n, &a[a_offset], lda, &x[1], &c__1, + (ftnlen)1, (ftnlen)1, (ftnlen)1); + return 0; + } + } + } + +/* Compute a bound on the computed solution vector to see if the */ +/* Level 2 BLAS routine DTRSV can be used. */ + + j = idamax_(n, &x[1], &c__1); + xmax = (d__1 = x[j], abs(d__1)); + xbnd = xmax; + if (notran) { + +/* Compute the growth in A * x = b. */ + + if (upper) { + jfirst = *n; + jlast = 1; + jinc = -1; + } else { + jfirst = 1; + jlast = *n; + jinc = 1; + } + + if (tscal != 1.) { + grow = 0.; + goto L50; + } + + if (nounit) { + +/* A is non-unit triangular. */ + +/* Compute GROW = 1/G(j) and XBND = 1/M(j). */ +/* Initially, G(0) = max{x(i), i=1,...,n}. */ + + grow = 1. / max(xbnd,smlnum); + xbnd = grow; + i__1 = jlast; + i__2 = jinc; + for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) { + +/* Exit the loop if the growth factor is too small. */ + + if (grow <= smlnum) { + goto L50; + } + +/* M(j) = G(j-1) / abs(A(j,j)) */ + + tjj = (d__1 = a[j + j * a_dim1], abs(d__1)); +/* Computing MIN */ + d__1 = xbnd, d__2 = min(1.,tjj) * grow; + xbnd = min(d__1,d__2); + if (tjj + cnorm[j] >= smlnum) { + +/* G(j) = G(j-1)*( 1 + CNORM(j) / abs(A(j,j)) ) */ + + grow *= tjj / (tjj + cnorm[j]); + } else { + +/* G(j) could overflow, set GROW to 0. */ + + grow = 0.; + } +/* L30: */ + } + grow = xbnd; + } else { + +/* A is unit triangular. */ + +/* Compute GROW = 1/G(j), where G(0) = max{x(i), i=1,...,n}. */ + +/* Computing MIN */ + d__1 = 1., d__2 = 1. / max(xbnd,smlnum); + grow = min(d__1,d__2); + i__2 = jlast; + i__1 = jinc; + for (j = jfirst; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) { + +/* Exit the loop if the growth factor is too small. */ + + if (grow <= smlnum) { + goto L50; + } + +/* G(j) = G(j-1)*( 1 + CNORM(j) ) */ + + grow *= 1. / (cnorm[j] + 1.); +/* L40: */ + } + } +L50: + + ; + } else { + +/* Compute the growth in A**T * x = b. */ + + if (upper) { + jfirst = 1; + jlast = *n; + jinc = 1; + } else { + jfirst = *n; + jlast = 1; + jinc = -1; + } + + if (tscal != 1.) { + grow = 0.; + goto L80; + } + + if (nounit) { + +/* A is non-unit triangular. */ + +/* Compute GROW = 1/G(j) and XBND = 1/M(j). */ +/* Initially, M(0) = max{x(i), i=1,...,n}. */ + + grow = 1. / max(xbnd,smlnum); + xbnd = grow; + i__1 = jlast; + i__2 = jinc; + for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) { + +/* Exit the loop if the growth factor is too small. */ + + if (grow <= smlnum) { + goto L80; + } + +/* G(j) = max( G(j-1), M(j-1)*( 1 + CNORM(j) ) ) */ + + xj = cnorm[j] + 1.; +/* Computing MIN */ + d__1 = grow, d__2 = xbnd / xj; + grow = min(d__1,d__2); + +/* M(j) = M(j-1)*( 1 + CNORM(j) ) / abs(A(j,j)) */ + + tjj = (d__1 = a[j + j * a_dim1], abs(d__1)); + if (xj > tjj) { + xbnd *= tjj / xj; + } +/* L60: */ + } + grow = min(grow,xbnd); + } else { + +/* A is unit triangular. */ + +/* Compute GROW = 1/G(j), where G(0) = max{x(i), i=1,...,n}. */ + +/* Computing MIN */ + d__1 = 1., d__2 = 1. / max(xbnd,smlnum); + grow = min(d__1,d__2); + i__2 = jlast; + i__1 = jinc; + for (j = jfirst; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) { + +/* Exit the loop if the growth factor is too small. */ + + if (grow <= smlnum) { + goto L80; + } + +/* G(j) = ( 1 + CNORM(j) )*G(j-1) */ + + xj = cnorm[j] + 1.; + grow /= xj; +/* L70: */ + } + } +L80: + ; + } + + if (grow * tscal > smlnum) { + +/* Use the Level 2 BLAS solve if the reciprocal of the bound on */ +/* elements of X is not too small. */ + + dtrsv_(uplo, trans, diag, n, &a[a_offset], lda, &x[1], &c__1, (ftnlen) + 1, (ftnlen)1, (ftnlen)1); + } else { + +/* Use a Level 1 BLAS solve, scaling intermediate results. */ + + if (xmax > bignum) { + +/* Scale X so that its components are less than or equal to */ +/* BIGNUM in absolute value. */ + + *scale = bignum / xmax; + dscal_(n, scale, &x[1], &c__1); + xmax = bignum; + } + + if (notran) { + +/* Solve A * x = b */ + + i__1 = jlast; + i__2 = jinc; + for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) { + +/* Compute x(j) = b(j) / A(j,j), scaling x if necessary. */ + + xj = (d__1 = x[j], abs(d__1)); + if (nounit) { + tjjs = a[j + j * a_dim1] * tscal; + } else { + tjjs = tscal; + if (tscal == 1.) { + goto L100; + } + } + tjj = abs(tjjs); + if (tjj > smlnum) { + +/* abs(A(j,j)) > SMLNUM: */ + + if (tjj < 1.) { + if (xj > tjj * bignum) { + +/* Scale x by 1/b(j). */ + + rec = 1. / xj; + dscal_(n, &rec, &x[1], &c__1); + *scale *= rec; + xmax *= rec; + } + } + x[j] /= tjjs; + xj = (d__1 = x[j], abs(d__1)); + } else if (tjj > 0.) { + +/* 0 < abs(A(j,j)) <= SMLNUM: */ + + if (xj > tjj * bignum) { + +/* Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM */ +/* to avoid overflow when dividing by A(j,j). */ + + rec = tjj * bignum / xj; + if (cnorm[j] > 1.) { + +/* Scale by 1/CNORM(j) to avoid overflow when */ +/* multiplying x(j) times column j. */ + + rec /= cnorm[j]; + } + dscal_(n, &rec, &x[1], &c__1); + *scale *= rec; + xmax *= rec; + } + x[j] /= tjjs; + xj = (d__1 = x[j], abs(d__1)); + } else { + +/* A(j,j) = 0: Set x(1:n) = 0, x(j) = 1, and */ +/* scale = 0, and compute a solution to A*x = 0. */ + + i__3 = *n; + for (i__ = 1; i__ <= i__3; ++i__) { + x[i__] = 0.; +/* L90: */ + } + x[j] = 1.; + xj = 1.; + *scale = 0.; + xmax = 0.; + } +L100: + +/* Scale x if necessary to avoid overflow when adding a */ +/* multiple of column j of A. */ + + if (xj > 1.) { + rec = 1. / xj; + if (cnorm[j] > (bignum - xmax) * rec) { + +/* Scale x by 1/(2*abs(x(j))). */ + + rec *= .5; + dscal_(n, &rec, &x[1], &c__1); + *scale *= rec; + } + } else if (xj * cnorm[j] > bignum - xmax) { + +/* Scale x by 1/2. */ + + dscal_(n, &c_b46, &x[1], &c__1); + *scale *= .5; + } + + if (upper) { + if (j > 1) { + +/* Compute the update */ +/* x(1:j-1) := x(1:j-1) - x(j) * A(1:j-1,j) */ + + i__3 = j - 1; + d__1 = -x[j] * tscal; + daxpy_(&i__3, &d__1, &a[j * a_dim1 + 1], &c__1, &x[1], + &c__1); + i__3 = j - 1; + i__ = idamax_(&i__3, &x[1], &c__1); + xmax = (d__1 = x[i__], abs(d__1)); + } + } else { + if (j < *n) { + +/* Compute the update */ +/* x(j+1:n) := x(j+1:n) - x(j) * A(j+1:n,j) */ + + i__3 = *n - j; + d__1 = -x[j] * tscal; + daxpy_(&i__3, &d__1, &a[j + 1 + j * a_dim1], &c__1, & + x[j + 1], &c__1); + i__3 = *n - j; + i__ = j + idamax_(&i__3, &x[j + 1], &c__1); + xmax = (d__1 = x[i__], abs(d__1)); + } + } +/* L110: */ + } + + } else { + +/* Solve A**T * x = b */ + + i__2 = jlast; + i__1 = jinc; + for (j = jfirst; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) { + +/* Compute x(j) = b(j) - sum A(k,j)*x(k). */ +/* k<>j */ + + xj = (d__1 = x[j], abs(d__1)); + uscal = tscal; + rec = 1. / max(xmax,1.); + if (cnorm[j] > (bignum - xj) * rec) { + +/* If x(j) could overflow, scale x by 1/(2*XMAX). */ + + rec *= .5; + if (nounit) { + tjjs = a[j + j * a_dim1] * tscal; + } else { + tjjs = tscal; + } + tjj = abs(tjjs); + if (tjj > 1.) { + +/* Divide by A(j,j) when scaling x if A(j,j) > 1. */ + +/* Computing MIN */ + d__1 = 1., d__2 = rec * tjj; + rec = min(d__1,d__2); + uscal /= tjjs; + } + if (rec < 1.) { + dscal_(n, &rec, &x[1], &c__1); + *scale *= rec; + xmax *= rec; + } + } + + sumj = 0.; + if (uscal == 1.) { + +/* If the scaling needed for A in the dot product is 1, */ +/* call DDOT to perform the dot product. */ + + if (upper) { + i__3 = j - 1; + sumj = ddot_(&i__3, &a[j * a_dim1 + 1], &c__1, &x[1], + &c__1); + } else if (j < *n) { + i__3 = *n - j; + sumj = ddot_(&i__3, &a[j + 1 + j * a_dim1], &c__1, &x[ + j + 1], &c__1); + } + } else { + +/* Otherwise, use in-line code for the dot product. */ + + if (upper) { + i__3 = j - 1; + for (i__ = 1; i__ <= i__3; ++i__) { + sumj += a[i__ + j * a_dim1] * uscal * x[i__]; +/* L120: */ + } + } else if (j < *n) { + i__3 = *n; + for (i__ = j + 1; i__ <= i__3; ++i__) { + sumj += a[i__ + j * a_dim1] * uscal * x[i__]; +/* L130: */ + } + } + } + + if (uscal == tscal) { + +/* Compute x(j) := ( x(j) - sumj ) / A(j,j) if 1/A(j,j) */ +/* was not used to scale the dotproduct. */ + + x[j] -= sumj; + xj = (d__1 = x[j], abs(d__1)); + if (nounit) { + tjjs = a[j + j * a_dim1] * tscal; + } else { + tjjs = tscal; + if (tscal == 1.) { + goto L150; + } + } + +/* Compute x(j) = x(j) / A(j,j), scaling if necessary. */ + + tjj = abs(tjjs); + if (tjj > smlnum) { + +/* abs(A(j,j)) > SMLNUM: */ + + if (tjj < 1.) { + if (xj > tjj * bignum) { + +/* Scale X by 1/abs(x(j)). */ + + rec = 1. / xj; + dscal_(n, &rec, &x[1], &c__1); + *scale *= rec; + xmax *= rec; + } + } + x[j] /= tjjs; + } else if (tjj > 0.) { + +/* 0 < abs(A(j,j)) <= SMLNUM: */ + + if (xj > tjj * bignum) { + +/* Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM. */ + + rec = tjj * bignum / xj; + dscal_(n, &rec, &x[1], &c__1); + *scale *= rec; + xmax *= rec; + } + x[j] /= tjjs; + } else { + +/* A(j,j) = 0: Set x(1:n) = 0, x(j) = 1, and */ +/* scale = 0, and compute a solution to A**T*x = 0. */ + + i__3 = *n; + for (i__ = 1; i__ <= i__3; ++i__) { + x[i__] = 0.; +/* L140: */ + } + x[j] = 1.; + *scale = 0.; + xmax = 0.; + } +L150: + ; + } else { + +/* Compute x(j) := x(j) / A(j,j) - sumj if the dot */ +/* product has already been divided by 1/A(j,j). */ + + x[j] = x[j] / tjjs - sumj; + } +/* Computing MAX */ + d__2 = xmax, d__3 = (d__1 = x[j], abs(d__1)); + xmax = max(d__2,d__3); +/* L160: */ + } + } + *scale /= tscal; + } + +/* Scale the column norms by 1/TSCAL for return. */ + + if (tscal != 1.) { + d__1 = 1. / tscal; + dscal_(n, &d__1, &cnorm[1], &c__1); + } + + return 0; + +/* End of DLATRS */ + +} /* dlatrs_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dnrm2.cpp b/lib/linalg/dnrm2.cpp new file mode 100644 index 0000000000..6ebf2d935e --- /dev/null +++ b/lib/linalg/dnrm2.cpp @@ -0,0 +1,169 @@ +/* fortran/dnrm2.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DNRM2 */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* DOUBLE PRECISION FUNCTION DNRM2(N,X,INCX) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INCX,N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION X(*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DNRM2 returns the euclidean norm of a vector via the function */ +/* > name, so that */ +/* > */ +/* > DNRM2 := sqrt( x'*x ) */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > number of elements in input vector(s) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] X */ +/* > \verbatim */ +/* > X is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > storage spacing between elements of DX */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \date December 2016 */ + +/* > \ingroup double_blas_level1 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > -- This version written on 25-October-1982. */ +/* > Modified on 14-October-1993 to inline the call to DLASSQ. */ +/* > Sven Hammarling, Nag Ltd. */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +doublereal dnrm2_(integer *n, doublereal *x, integer *incx) +{ + /* System generated locals */ + integer i__1, i__2; + doublereal ret_val, d__1; + + /* Builtin functions */ + double sqrt(doublereal); + + /* Local variables */ + integer ix; + doublereal ssq, norm, scale, absxi; + + +/* -- Reference BLAS level1 routine (version 3.7.0) -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ +/* December 2016 */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ + /* Parameter adjustments */ + --x; + + /* Function Body */ + if (*n < 1 || *incx < 1) { + norm = 0.; + } else if (*n == 1) { + norm = abs(x[1]); + } else { + scale = 0.; + ssq = 1.; +/* The following loop is equivalent to this call to the LAPACK */ +/* auxiliary routine: */ +/* CALL DLASSQ( N, X, INCX, SCALE, SSQ ) */ + + i__1 = (*n - 1) * *incx + 1; + i__2 = *incx; + for (ix = 1; i__2 < 0 ? ix >= i__1 : ix <= i__1; ix += i__2) { + if (x[ix] != 0.) { + absxi = (d__1 = x[ix], abs(d__1)); + if (scale < absxi) { +/* Computing 2nd power */ + d__1 = scale / absxi; + ssq = ssq * (d__1 * d__1) + 1.; + scale = absxi; + } else { +/* Computing 2nd power */ + d__1 = absxi / scale; + ssq += d__1 * d__1; + } + } +/* L10: */ + } + norm = scale * sqrt(ssq); + } + + ret_val = norm; + return ret_val; + +/* End of DNRM2. */ + +} /* dnrm2_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dorg2l.cpp b/lib/linalg/dorg2l.cpp new file mode 100644 index 0000000000..5705f3b630 --- /dev/null +++ b/lib/linalg/dorg2l.cpp @@ -0,0 +1,252 @@ +/* fortran/dorg2l.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; + +/* > \brief \b DORG2L generates all or part of the orthogonal matrix Q from a QL factorization determined by s +geqlf (unblocked algorithm). */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DORG2L + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DORG2L( M, N, K, A, LDA, TAU, WORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INFO, K, LDA, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DORG2L generates an m by n real matrix Q with orthonormal columns, */ +/* > which is defined as the last n columns of a product of k elementary */ +/* > reflectors of order m */ +/* > */ +/* > Q = H(k) . . . H(2) H(1) */ +/* > */ +/* > as returned by DGEQLF. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix Q. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix Q. M >= N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > The number of elementary reflectors whose product defines the */ +/* > matrix Q. N >= K >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On entry, the (n-k+i)-th column must contain the vector which */ +/* > defines the elementary reflector H(i), for i = 1,2,...,k, as */ +/* > returned by DGEQLF in the last k columns of its array */ +/* > argument A. */ +/* > On exit, the m by n matrix Q. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The first dimension of the array A. LDA >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TAU */ +/* > \verbatim */ +/* > TAU is DOUBLE PRECISION array, dimension (K) */ +/* > TAU(i) must contain the scalar factor of the elementary */ +/* > reflector H(i), as returned by DGEQLF. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (N) */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument has an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleOTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dorg2l_(integer *m, integer *n, integer *k, doublereal * + a, integer *lda, doublereal *tau, doublereal *work, integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3; + doublereal d__1; + + /* Local variables */ + integer i__, j, l, ii; + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *), dlarf_(char *, integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + ftnlen), xerbla_(char *, integer *, ftnlen); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --tau; + --work; + + /* Function Body */ + *info = 0; + if (*m < 0) { + *info = -1; + } else if (*n < 0 || *n > *m) { + *info = -2; + } else if (*k < 0 || *k > *n) { + *info = -3; + } else if (*lda < max(1,*m)) { + *info = -5; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DORG2L", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*n <= 0) { + return 0; + } + +/* Initialise columns 1:n-k to columns of the unit matrix */ + + i__1 = *n - *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (l = 1; l <= i__2; ++l) { + a[l + j * a_dim1] = 0.; +/* L10: */ + } + a[*m - *n + j + j * a_dim1] = 1.; +/* L20: */ + } + + i__1 = *k; + for (i__ = 1; i__ <= i__1; ++i__) { + ii = *n - *k + i__; + +/* Apply H(i) to A(1:m-k+i,1:n-k+i) from the left */ + + a[*m - *n + ii + ii * a_dim1] = 1.; + i__2 = *m - *n + ii; + i__3 = ii - 1; + dlarf_((char *)"Left", &i__2, &i__3, &a[ii * a_dim1 + 1], &c__1, &tau[i__], & + a[a_offset], lda, &work[1], (ftnlen)4); + i__2 = *m - *n + ii - 1; + d__1 = -tau[i__]; + dscal_(&i__2, &d__1, &a[ii * a_dim1 + 1], &c__1); + a[*m - *n + ii + ii * a_dim1] = 1. - tau[i__]; + +/* Set A(m-k+i+1:m,n-k+i) to zero */ + + i__2 = *m; + for (l = *m - *n + ii + 1; l <= i__2; ++l) { + a[l + ii * a_dim1] = 0.; +/* L30: */ + } +/* L40: */ + } + return 0; + +/* End of DORG2L */ + +} /* dorg2l_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dorg2r.cpp b/lib/linalg/dorg2r.cpp new file mode 100644 index 0000000000..90ebed3963 --- /dev/null +++ b/lib/linalg/dorg2r.cpp @@ -0,0 +1,255 @@ +/* fortran/dorg2r.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; + +/* > \brief \b DORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by s +geqrf (unblocked algorithm). */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DORG2R + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DORG2R( M, N, K, A, LDA, TAU, WORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INFO, K, LDA, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DORG2R generates an m by n real matrix Q with orthonormal columns, */ +/* > which is defined as the first n columns of a product of k elementary */ +/* > reflectors of order m */ +/* > */ +/* > Q = H(1) H(2) . . . H(k) */ +/* > */ +/* > as returned by DGEQRF. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix Q. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix Q. M >= N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > The number of elementary reflectors whose product defines the */ +/* > matrix Q. N >= K >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On entry, the i-th column must contain the vector which */ +/* > defines the elementary reflector H(i), for i = 1,2,...,k, as */ +/* > returned by DGEQRF in the first k columns of its array */ +/* > argument A. */ +/* > On exit, the m-by-n matrix Q. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The first dimension of the array A. LDA >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TAU */ +/* > \verbatim */ +/* > TAU is DOUBLE PRECISION array, dimension (K) */ +/* > TAU(i) must contain the scalar factor of the elementary */ +/* > reflector H(i), as returned by DGEQRF. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (N) */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument has an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleOTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dorg2r_(integer *m, integer *n, integer *k, doublereal * + a, integer *lda, doublereal *tau, doublereal *work, integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2; + doublereal d__1; + + /* Local variables */ + integer i__, j, l; + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *), dlarf_(char *, integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + ftnlen), xerbla_(char *, integer *, ftnlen); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --tau; + --work; + + /* Function Body */ + *info = 0; + if (*m < 0) { + *info = -1; + } else if (*n < 0 || *n > *m) { + *info = -2; + } else if (*k < 0 || *k > *n) { + *info = -3; + } else if (*lda < max(1,*m)) { + *info = -5; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DORG2R", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*n <= 0) { + return 0; + } + +/* Initialise columns k+1:n to columns of the unit matrix */ + + i__1 = *n; + for (j = *k + 1; j <= i__1; ++j) { + i__2 = *m; + for (l = 1; l <= i__2; ++l) { + a[l + j * a_dim1] = 0.; +/* L10: */ + } + a[j + j * a_dim1] = 1.; +/* L20: */ + } + + for (i__ = *k; i__ >= 1; --i__) { + +/* Apply H(i) to A(i:m,i:n) from the left */ + + if (i__ < *n) { + a[i__ + i__ * a_dim1] = 1.; + i__1 = *m - i__ + 1; + i__2 = *n - i__; + dlarf_((char *)"Left", &i__1, &i__2, &a[i__ + i__ * a_dim1], &c__1, &tau[ + i__], &a[i__ + (i__ + 1) * a_dim1], lda, &work[1], ( + ftnlen)4); + } + if (i__ < *m) { + i__1 = *m - i__; + d__1 = -tau[i__]; + dscal_(&i__1, &d__1, &a[i__ + 1 + i__ * a_dim1], &c__1); + } + a[i__ + i__ * a_dim1] = 1. - tau[i__]; + +/* Set A(1:i-1,i) to zero */ + + i__1 = i__ - 1; + for (l = 1; l <= i__1; ++l) { + a[l + i__ * a_dim1] = 0.; +/* L30: */ + } +/* L40: */ + } + return 0; + +/* End of DORG2R */ + +} /* dorg2r_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dorgbr.cpp b/lib/linalg/dorgbr.cpp new file mode 100644 index 0000000000..4991344c01 --- /dev/null +++ b/lib/linalg/dorgbr.cpp @@ -0,0 +1,404 @@ +/* fortran/dorgbr.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c_n1 = -1; + +/* > \brief \b DORGBR */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DORGBR + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER VECT */ +/* INTEGER INFO, K, LDA, LWORK, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DORGBR generates one of the real orthogonal matrices Q or P**T */ +/* > determined by DGEBRD when reducing a real matrix A to bidiagonal */ +/* > form: A = Q * B * P**T. Q and P**T are defined as products of */ +/* > elementary reflectors H(i) or G(i) respectively. */ +/* > */ +/* > If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q */ +/* > is of order M: */ +/* > if m >= k, Q = H(1) H(2) . . . H(k) and DORGBR returns the first n */ +/* > columns of Q, where m >= n >= k; */ +/* > if m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR returns Q as an */ +/* > M-by-M matrix. */ +/* > */ +/* > If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T */ +/* > is of order N: */ +/* > if k < n, P**T = G(k) . . . G(2) G(1) and DORGBR returns the first m */ +/* > rows of P**T, where n >= m >= k; */ +/* > if k >= n, P**T = G(n-1) . . . G(2) G(1) and DORGBR returns P**T as */ +/* > an N-by-N matrix. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] VECT */ +/* > \verbatim */ +/* > VECT is CHARACTER*1 */ +/* > Specifies whether the matrix Q or the matrix P**T is */ +/* > required, as defined in the transformation applied by DGEBRD: */ +/* > = 'Q': generate Q; */ +/* > = 'P': generate P**T. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix Q or P**T to be returned. */ +/* > M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix Q or P**T to be returned. */ +/* > N >= 0. */ +/* > If VECT = 'Q', M >= N >= min(M,K); */ +/* > if VECT = 'P', N >= M >= min(N,K). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > If VECT = 'Q', the number of columns in the original M-by-K */ +/* > matrix reduced by DGEBRD. */ +/* > If VECT = 'P', the number of rows in the original K-by-N */ +/* > matrix reduced by DGEBRD. */ +/* > K >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On entry, the vectors which define the elementary reflectors, */ +/* > as returned by DGEBRD. */ +/* > On exit, the M-by-N matrix Q or P**T. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TAU */ +/* > \verbatim */ +/* > TAU is DOUBLE PRECISION array, dimension */ +/* > (min(M,K)) if VECT = 'Q' */ +/* > (min(N,K)) if VECT = 'P' */ +/* > TAU(i) must contain the scalar factor of the elementary */ +/* > reflector H(i) or G(i), which determines Q or P**T, as */ +/* > returned by DGEBRD in its array argument TAUQ or TAUP. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ +/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LWORK */ +/* > \verbatim */ +/* > LWORK is INTEGER */ +/* > The dimension of the array WORK. LWORK >= max(1,min(M,N)). */ +/* > For optimum performance LWORK >= min(M,N)*NB, where NB */ +/* > is the optimal blocksize. */ +/* > */ +/* > If LWORK = -1, then a workspace query is assumed; the routine */ +/* > only calculates the optimal size of the WORK array, returns */ +/* > this value as the first entry of the WORK array, and no error */ +/* > message related to LWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleGBcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dorgbr_(char *vect, integer *m, integer *n, integer *k, + doublereal *a, integer *lda, doublereal *tau, doublereal *work, + integer *lwork, integer *info, ftnlen vect_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3; + + /* Local variables */ + integer i__, j, mn; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + integer iinfo; + logical wantq; + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), dorglq_( + integer *, integer *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, integer *), dorgqr_( + integer *, integer *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, integer *); + integer lwkopt; + logical lquery; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --tau; + --work; + + /* Function Body */ + *info = 0; + wantq = lsame_(vect, (char *)"Q", (ftnlen)1, (ftnlen)1); + mn = min(*m,*n); + lquery = *lwork == -1; + if (! wantq && ! lsame_(vect, (char *)"P", (ftnlen)1, (ftnlen)1)) { + *info = -1; + } else if (*m < 0) { + *info = -2; + } else if (*n < 0 || wantq && (*n > *m || *n < min(*m,*k)) || ! wantq && ( + *m > *n || *m < min(*n,*k))) { + *info = -3; + } else if (*k < 0) { + *info = -4; + } else if (*lda < max(1,*m)) { + *info = -6; + } else if (*lwork < max(1,mn) && ! lquery) { + *info = -9; + } + + if (*info == 0) { + work[1] = 1.; + if (wantq) { + if (*m >= *k) { + dorgqr_(m, n, k, &a[a_offset], lda, &tau[1], &work[1], &c_n1, + &iinfo); + } else { + if (*m > 1) { + i__1 = *m - 1; + i__2 = *m - 1; + i__3 = *m - 1; + dorgqr_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], & + work[1], &c_n1, &iinfo); + } + } + } else { + if (*k < *n) { + dorglq_(m, n, k, &a[a_offset], lda, &tau[1], &work[1], &c_n1, + &iinfo); + } else { + if (*n > 1) { + i__1 = *n - 1; + i__2 = *n - 1; + i__3 = *n - 1; + dorglq_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], & + work[1], &c_n1, &iinfo); + } + } + } + lwkopt = (integer) work[1]; + lwkopt = max(lwkopt,mn); + } + + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DORGBR", &i__1, (ftnlen)6); + return 0; + } else if (lquery) { + work[1] = (doublereal) lwkopt; + return 0; + } + +/* Quick return if possible */ + + if (*m == 0 || *n == 0) { + work[1] = 1.; + return 0; + } + + if (wantq) { + +/* Form Q, determined by a call to DGEBRD to reduce an m-by-k */ +/* matrix */ + + if (*m >= *k) { + +/* If m >= k, assume m >= n >= k */ + + dorgqr_(m, n, k, &a[a_offset], lda, &tau[1], &work[1], lwork, & + iinfo); + + } else { + +/* If m < k, assume m = n */ + +/* Shift the vectors which define the elementary reflectors one */ +/* column to the right, and set the first row and column of Q */ +/* to those of the unit matrix */ + + for (j = *m; j >= 2; --j) { + a[j * a_dim1 + 1] = 0.; + i__1 = *m; + for (i__ = j + 1; i__ <= i__1; ++i__) { + a[i__ + j * a_dim1] = a[i__ + (j - 1) * a_dim1]; +/* L10: */ + } +/* L20: */ + } + a[a_dim1 + 1] = 1.; + i__1 = *m; + for (i__ = 2; i__ <= i__1; ++i__) { + a[i__ + a_dim1] = 0.; +/* L30: */ + } + if (*m > 1) { + +/* Form Q(2:m,2:m) */ + + i__1 = *m - 1; + i__2 = *m - 1; + i__3 = *m - 1; + dorgqr_(&i__1, &i__2, &i__3, &a[(a_dim1 << 1) + 2], lda, &tau[ + 1], &work[1], lwork, &iinfo); + } + } + } else { + +/* Form P**T, determined by a call to DGEBRD to reduce a k-by-n */ +/* matrix */ + + if (*k < *n) { + +/* If k < n, assume k <= m <= n */ + + dorglq_(m, n, k, &a[a_offset], lda, &tau[1], &work[1], lwork, & + iinfo); + + } else { + +/* If k >= n, assume m = n */ + +/* Shift the vectors which define the elementary reflectors one */ +/* row downward, and set the first row and column of P**T to */ +/* those of the unit matrix */ + + a[a_dim1 + 1] = 1.; + i__1 = *n; + for (i__ = 2; i__ <= i__1; ++i__) { + a[i__ + a_dim1] = 0.; +/* L40: */ + } + i__1 = *n; + for (j = 2; j <= i__1; ++j) { + for (i__ = j - 1; i__ >= 2; --i__) { + a[i__ + j * a_dim1] = a[i__ - 1 + j * a_dim1]; +/* L50: */ + } + a[j * a_dim1 + 1] = 0.; +/* L60: */ + } + if (*n > 1) { + +/* Form P**T(2:n,2:n) */ + + i__1 = *n - 1; + i__2 = *n - 1; + i__3 = *n - 1; + dorglq_(&i__1, &i__2, &i__3, &a[(a_dim1 << 1) + 2], lda, &tau[ + 1], &work[1], lwork, &iinfo); + } + } + } + work[1] = (doublereal) lwkopt; + return 0; + +/* End of DORGBR */ + +} /* dorgbr_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dorgl2.cpp b/lib/linalg/dorgl2.cpp new file mode 100644 index 0000000000..a2cce985f3 --- /dev/null +++ b/lib/linalg/dorgl2.cpp @@ -0,0 +1,254 @@ +/* fortran/dorgl2.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DORGL2 */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DORGL2 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DORGL2( M, N, K, A, LDA, TAU, WORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INFO, K, LDA, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DORGL2 generates an m by n real matrix Q with orthonormal rows, */ +/* > which is defined as the first m rows of a product of k elementary */ +/* > reflectors of order n */ +/* > */ +/* > Q = H(k) . . . H(2) H(1) */ +/* > */ +/* > as returned by DGELQF. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix Q. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix Q. N >= M. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > The number of elementary reflectors whose product defines the */ +/* > matrix Q. M >= K >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On entry, the i-th row must contain the vector which defines */ +/* > the elementary reflector H(i), for i = 1,2,...,k, as returned */ +/* > by DGELQF in the first k rows of its array argument A. */ +/* > On exit, the m-by-n matrix Q. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The first dimension of the array A. LDA >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TAU */ +/* > \verbatim */ +/* > TAU is DOUBLE PRECISION array, dimension (K) */ +/* > TAU(i) must contain the scalar factor of the elementary */ +/* > reflector H(i), as returned by DGELQF. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (M) */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument has an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleOTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dorgl2_(integer *m, integer *n, integer *k, doublereal * + a, integer *lda, doublereal *tau, doublereal *work, integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2; + doublereal d__1; + + /* Local variables */ + integer i__, j, l; + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *), dlarf_(char *, integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + ftnlen), xerbla_(char *, integer *, ftnlen); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --tau; + --work; + + /* Function Body */ + *info = 0; + if (*m < 0) { + *info = -1; + } else if (*n < *m) { + *info = -2; + } else if (*k < 0 || *k > *m) { + *info = -3; + } else if (*lda < max(1,*m)) { + *info = -5; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DORGL2", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*m <= 0) { + return 0; + } + + if (*k < *m) { + +/* Initialise rows k+1:m to rows of the unit matrix */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (l = *k + 1; l <= i__2; ++l) { + a[l + j * a_dim1] = 0.; +/* L10: */ + } + if (j > *k && j <= *m) { + a[j + j * a_dim1] = 1.; + } +/* L20: */ + } + } + + for (i__ = *k; i__ >= 1; --i__) { + +/* Apply H(i) to A(i:m,i:n) from the right */ + + if (i__ < *n) { + if (i__ < *m) { + a[i__ + i__ * a_dim1] = 1.; + i__1 = *m - i__; + i__2 = *n - i__ + 1; + dlarf_((char *)"Right", &i__1, &i__2, &a[i__ + i__ * a_dim1], lda, & + tau[i__], &a[i__ + 1 + i__ * a_dim1], lda, &work[1], ( + ftnlen)5); + } + i__1 = *n - i__; + d__1 = -tau[i__]; + dscal_(&i__1, &d__1, &a[i__ + (i__ + 1) * a_dim1], lda); + } + a[i__ + i__ * a_dim1] = 1. - tau[i__]; + +/* Set A(i,1:i-1) to zero */ + + i__1 = i__ - 1; + for (l = 1; l <= i__1; ++l) { + a[i__ + l * a_dim1] = 0.; +/* L30: */ + } +/* L40: */ + } + return 0; + +/* End of DORGL2 */ + +} /* dorgl2_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dorglq.cpp b/lib/linalg/dorglq.cpp new file mode 100644 index 0000000000..3dc2d1986c --- /dev/null +++ b/lib/linalg/dorglq.cpp @@ -0,0 +1,366 @@ +/* fortran/dorglq.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c_n1 = -1; +static integer c__3 = 3; +static integer c__2 = 2; + +/* > \brief \b DORGLQ */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DORGLQ + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DORGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INFO, K, LDA, LWORK, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DORGLQ generates an M-by-N real matrix Q with orthonormal rows, */ +/* > which is defined as the first M rows of a product of K elementary */ +/* > reflectors of order N */ +/* > */ +/* > Q = H(k) . . . H(2) H(1) */ +/* > */ +/* > as returned by DGELQF. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix Q. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix Q. N >= M. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > The number of elementary reflectors whose product defines the */ +/* > matrix Q. M >= K >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On entry, the i-th row must contain the vector which defines */ +/* > the elementary reflector H(i), for i = 1,2,...,k, as returned */ +/* > by DGELQF in the first k rows of its array argument A. */ +/* > On exit, the M-by-N matrix Q. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The first dimension of the array A. LDA >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TAU */ +/* > \verbatim */ +/* > TAU is DOUBLE PRECISION array, dimension (K) */ +/* > TAU(i) must contain the scalar factor of the elementary */ +/* > reflector H(i), as returned by DGELQF. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ +/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LWORK */ +/* > \verbatim */ +/* > LWORK is INTEGER */ +/* > The dimension of the array WORK. LWORK >= max(1,M). */ +/* > For optimum performance LWORK >= M*NB, where NB is */ +/* > the optimal blocksize. */ +/* > */ +/* > If LWORK = -1, then a workspace query is assumed; the routine */ +/* > only calculates the optimal size of the WORK array, returns */ +/* > this value as the first entry of the WORK array, and no error */ +/* > message related to LWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument has an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleOTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dorglq_(integer *m, integer *n, integer *k, doublereal * + a, integer *lda, doublereal *tau, doublereal *work, integer *lwork, + integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3; + + /* Local variables */ + integer i__, j, l, ib, nb, ki, kk, nx, iws, nbmin, iinfo; + extern /* Subroutine */ int dorgl2_(integer *, integer *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *), + dlarfb_(char *, char *, char *, char *, integer *, integer *, + integer *, doublereal *, integer *, doublereal *, integer *, + doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, + ftnlen, ftnlen), dlarft_(char *, char *, integer *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, + ftnlen, ftnlen), xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + integer ldwork, lwkopt; + logical lquery; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --tau; + --work; + + /* Function Body */ + *info = 0; + nb = ilaenv_(&c__1, (char *)"DORGLQ", (char *)" ", m, n, k, &c_n1, (ftnlen)6, (ftnlen)1); + lwkopt = max(1,*m) * nb; + work[1] = (doublereal) lwkopt; + lquery = *lwork == -1; + if (*m < 0) { + *info = -1; + } else if (*n < *m) { + *info = -2; + } else if (*k < 0 || *k > *m) { + *info = -3; + } else if (*lda < max(1,*m)) { + *info = -5; + } else if (*lwork < max(1,*m) && ! lquery) { + *info = -8; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DORGLQ", &i__1, (ftnlen)6); + return 0; + } else if (lquery) { + return 0; + } + +/* Quick return if possible */ + + if (*m <= 0) { + work[1] = 1.; + return 0; + } + + nbmin = 2; + nx = 0; + iws = *m; + if (nb > 1 && nb < *k) { + +/* Determine when to cross over from blocked to unblocked code. */ + +/* Computing MAX */ + i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"DORGLQ", (char *)" ", m, n, k, &c_n1, ( + ftnlen)6, (ftnlen)1); + nx = max(i__1,i__2); + if (nx < *k) { + +/* Determine if workspace is large enough for blocked code. */ + + ldwork = *m; + iws = ldwork * nb; + if (*lwork < iws) { + +/* Not enough workspace to use optimal NB: reduce NB and */ +/* determine the minimum value of NB. */ + + nb = *lwork / ldwork; +/* Computing MAX */ + i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DORGLQ", (char *)" ", m, n, k, &c_n1, + (ftnlen)6, (ftnlen)1); + nbmin = max(i__1,i__2); + } + } + } + + if (nb >= nbmin && nb < *k && nx < *k) { + +/* Use blocked code after the last block. */ +/* The first kk rows are handled by the block method. */ + + ki = (*k - nx - 1) / nb * nb; +/* Computing MIN */ + i__1 = *k, i__2 = ki + nb; + kk = min(i__1,i__2); + +/* Set A(kk+1:m,1:kk) to zero. */ + + i__1 = kk; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = kk + 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] = 0.; +/* L10: */ + } +/* L20: */ + } + } else { + kk = 0; + } + +/* Use unblocked code for the last or only block. */ + + if (kk < *m) { + i__1 = *m - kk; + i__2 = *n - kk; + i__3 = *k - kk; + dorgl2_(&i__1, &i__2, &i__3, &a[kk + 1 + (kk + 1) * a_dim1], lda, & + tau[kk + 1], &work[1], &iinfo); + } + + if (kk > 0) { + +/* Use blocked code */ + + i__1 = -nb; + for (i__ = ki + 1; i__1 < 0 ? i__ >= 1 : i__ <= 1; i__ += i__1) { +/* Computing MIN */ + i__2 = nb, i__3 = *k - i__ + 1; + ib = min(i__2,i__3); + if (i__ + ib <= *m) { + +/* Form the triangular factor of the block reflector */ +/* H = H(i) H(i+1) . . . H(i+ib-1) */ + + i__2 = *n - i__ + 1; + dlarft_((char *)"Forward", (char *)"Rowwise", &i__2, &ib, &a[i__ + i__ * + a_dim1], lda, &tau[i__], &work[1], &ldwork, (ftnlen)7, + (ftnlen)7); + +/* Apply H**T to A(i+ib:m,i:n) from the right */ + + i__2 = *m - i__ - ib + 1; + i__3 = *n - i__ + 1; + dlarfb_((char *)"Right", (char *)"Transpose", (char *)"Forward", (char *)"Rowwise", &i__2, & + i__3, &ib, &a[i__ + i__ * a_dim1], lda, &work[1], & + ldwork, &a[i__ + ib + i__ * a_dim1], lda, &work[ib + + 1], &ldwork, (ftnlen)5, (ftnlen)9, (ftnlen)7, (ftnlen) + 7); + } + +/* Apply H**T to columns i:n of current block */ + + i__2 = *n - i__ + 1; + dorgl2_(&ib, &i__2, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], & + work[1], &iinfo); + +/* Set columns 1:i-1 of current block to zero */ + + i__2 = i__ - 1; + for (j = 1; j <= i__2; ++j) { + i__3 = i__ + ib - 1; + for (l = i__; l <= i__3; ++l) { + a[l + j * a_dim1] = 0.; +/* L30: */ + } +/* L40: */ + } +/* L50: */ + } + } + + work[1] = (doublereal) iws; + return 0; + +/* End of DORGLQ */ + +} /* dorglq_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dorgql.cpp b/lib/linalg/dorgql.cpp new file mode 100644 index 0000000000..22a9b05b4b --- /dev/null +++ b/lib/linalg/dorgql.cpp @@ -0,0 +1,376 @@ +/* fortran/dorgql.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c_n1 = -1; +static integer c__3 = 3; +static integer c__2 = 2; + +/* > \brief \b DORGQL */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DORGQL + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DORGQL( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INFO, K, LDA, LWORK, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DORGQL generates an M-by-N real matrix Q with orthonormal columns, */ +/* > which is defined as the last N columns of a product of K elementary */ +/* > reflectors of order M */ +/* > */ +/* > Q = H(k) . . . H(2) H(1) */ +/* > */ +/* > as returned by DGEQLF. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix Q. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix Q. M >= N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > The number of elementary reflectors whose product defines the */ +/* > matrix Q. N >= K >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On entry, the (n-k+i)-th column must contain the vector which */ +/* > defines the elementary reflector H(i), for i = 1,2,...,k, as */ +/* > returned by DGEQLF in the last k columns of its array */ +/* > argument A. */ +/* > On exit, the M-by-N matrix Q. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The first dimension of the array A. LDA >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TAU */ +/* > \verbatim */ +/* > TAU is DOUBLE PRECISION array, dimension (K) */ +/* > TAU(i) must contain the scalar factor of the elementary */ +/* > reflector H(i), as returned by DGEQLF. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ +/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LWORK */ +/* > \verbatim */ +/* > LWORK is INTEGER */ +/* > The dimension of the array WORK. LWORK >= max(1,N). */ +/* > For optimum performance LWORK >= N*NB, where NB is the */ +/* > optimal blocksize. */ +/* > */ +/* > If LWORK = -1, then a workspace query is assumed; the routine */ +/* > only calculates the optimal size of the WORK array, returns */ +/* > this value as the first entry of the WORK array, and no error */ +/* > message related to LWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument has an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleOTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dorgql_(integer *m, integer *n, integer *k, doublereal * + a, integer *lda, doublereal *tau, doublereal *work, integer *lwork, + integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3, i__4; + + /* Local variables */ + integer i__, j, l, ib, nb, kk, nx, iws, nbmin, iinfo; + extern /* Subroutine */ int dorg2l_(integer *, integer *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *), + dlarfb_(char *, char *, char *, char *, integer *, integer *, + integer *, doublereal *, integer *, doublereal *, integer *, + doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, + ftnlen, ftnlen), dlarft_(char *, char *, integer *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, + ftnlen, ftnlen), xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + integer ldwork, lwkopt; + logical lquery; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --tau; + --work; + + /* Function Body */ + *info = 0; + lquery = *lwork == -1; + if (*m < 0) { + *info = -1; + } else if (*n < 0 || *n > *m) { + *info = -2; + } else if (*k < 0 || *k > *n) { + *info = -3; + } else if (*lda < max(1,*m)) { + *info = -5; + } + + if (*info == 0) { + if (*n == 0) { + lwkopt = 1; + } else { + nb = ilaenv_(&c__1, (char *)"DORGQL", (char *)" ", m, n, k, &c_n1, (ftnlen)6, ( + ftnlen)1); + lwkopt = *n * nb; + } + work[1] = (doublereal) lwkopt; + + if (*lwork < max(1,*n) && ! lquery) { + *info = -8; + } + } + + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DORGQL", &i__1, (ftnlen)6); + return 0; + } else if (lquery) { + return 0; + } + +/* Quick return if possible */ + + if (*n <= 0) { + return 0; + } + + nbmin = 2; + nx = 0; + iws = *n; + if (nb > 1 && nb < *k) { + +/* Determine when to cross over from blocked to unblocked code. */ + +/* Computing MAX */ + i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"DORGQL", (char *)" ", m, n, k, &c_n1, ( + ftnlen)6, (ftnlen)1); + nx = max(i__1,i__2); + if (nx < *k) { + +/* Determine if workspace is large enough for blocked code. */ + + ldwork = *n; + iws = ldwork * nb; + if (*lwork < iws) { + +/* Not enough workspace to use optimal NB: reduce NB and */ +/* determine the minimum value of NB. */ + + nb = *lwork / ldwork; +/* Computing MAX */ + i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DORGQL", (char *)" ", m, n, k, &c_n1, + (ftnlen)6, (ftnlen)1); + nbmin = max(i__1,i__2); + } + } + } + + if (nb >= nbmin && nb < *k && nx < *k) { + +/* Use blocked code after the first block. */ +/* The last kk columns are handled by the block method. */ + +/* Computing MIN */ + i__1 = *k, i__2 = (*k - nx + nb - 1) / nb * nb; + kk = min(i__1,i__2); + +/* Set A(m-kk+1:m,1:n-kk) to zero. */ + + i__1 = *n - kk; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = *m - kk + 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] = 0.; +/* L10: */ + } +/* L20: */ + } + } else { + kk = 0; + } + +/* Use unblocked code for the first or only block. */ + + i__1 = *m - kk; + i__2 = *n - kk; + i__3 = *k - kk; + dorg2l_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], &work[1], &iinfo) + ; + + if (kk > 0) { + +/* Use blocked code */ + + i__1 = *k; + i__2 = nb; + for (i__ = *k - kk + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += + i__2) { +/* Computing MIN */ + i__3 = nb, i__4 = *k - i__ + 1; + ib = min(i__3,i__4); + if (*n - *k + i__ > 1) { + +/* Form the triangular factor of the block reflector */ +/* H = H(i+ib-1) . . . H(i+1) H(i) */ + + i__3 = *m - *k + i__ + ib - 1; + dlarft_((char *)"Backward", (char *)"Columnwise", &i__3, &ib, &a[(*n - *k + + i__) * a_dim1 + 1], lda, &tau[i__], &work[1], &ldwork, + (ftnlen)8, (ftnlen)10); + +/* Apply H to A(1:m-k+i+ib-1,1:n-k+i-1) from the left */ + + i__3 = *m - *k + i__ + ib - 1; + i__4 = *n - *k + i__ - 1; + dlarfb_((char *)"Left", (char *)"No transpose", (char *)"Backward", (char *)"Columnwise", & + i__3, &i__4, &ib, &a[(*n - *k + i__) * a_dim1 + 1], + lda, &work[1], &ldwork, &a[a_offset], lda, &work[ib + + 1], &ldwork, (ftnlen)4, (ftnlen)12, (ftnlen)8, ( + ftnlen)10); + } + +/* Apply H to rows 1:m-k+i+ib-1 of current block */ + + i__3 = *m - *k + i__ + ib - 1; + dorg2l_(&i__3, &ib, &ib, &a[(*n - *k + i__) * a_dim1 + 1], lda, & + tau[i__], &work[1], &iinfo); + +/* Set rows m-k+i+ib:m of current block to zero */ + + i__3 = *n - *k + i__ + ib - 1; + for (j = *n - *k + i__; j <= i__3; ++j) { + i__4 = *m; + for (l = *m - *k + i__ + ib; l <= i__4; ++l) { + a[l + j * a_dim1] = 0.; +/* L30: */ + } +/* L40: */ + } +/* L50: */ + } + } + + work[1] = (doublereal) iws; + return 0; + +/* End of DORGQL */ + +} /* dorgql_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dorgqr.cpp b/lib/linalg/dorgqr.cpp new file mode 100644 index 0000000000..30f175f707 --- /dev/null +++ b/lib/linalg/dorgqr.cpp @@ -0,0 +1,367 @@ +/* fortran/dorgqr.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c_n1 = -1; +static integer c__3 = 3; +static integer c__2 = 2; + +/* > \brief \b DORGQR */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DORGQR + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INFO, K, LDA, LWORK, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DORGQR generates an M-by-N real matrix Q with orthonormal columns, */ +/* > which is defined as the first N columns of a product of K elementary */ +/* > reflectors of order M */ +/* > */ +/* > Q = H(1) H(2) . . . H(k) */ +/* > */ +/* > as returned by DGEQRF. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix Q. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix Q. M >= N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > The number of elementary reflectors whose product defines the */ +/* > matrix Q. N >= K >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On entry, the i-th column must contain the vector which */ +/* > defines the elementary reflector H(i), for i = 1,2,...,k, as */ +/* > returned by DGEQRF in the first k columns of its array */ +/* > argument A. */ +/* > On exit, the M-by-N matrix Q. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The first dimension of the array A. LDA >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TAU */ +/* > \verbatim */ +/* > TAU is DOUBLE PRECISION array, dimension (K) */ +/* > TAU(i) must contain the scalar factor of the elementary */ +/* > reflector H(i), as returned by DGEQRF. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ +/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LWORK */ +/* > \verbatim */ +/* > LWORK is INTEGER */ +/* > The dimension of the array WORK. LWORK >= max(1,N). */ +/* > For optimum performance LWORK >= N*NB, where NB is the */ +/* > optimal blocksize. */ +/* > */ +/* > If LWORK = -1, then a workspace query is assumed; the routine */ +/* > only calculates the optimal size of the WORK array, returns */ +/* > this value as the first entry of the WORK array, and no error */ +/* > message related to LWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument has an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleOTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dorgqr_(integer *m, integer *n, integer *k, doublereal * + a, integer *lda, doublereal *tau, doublereal *work, integer *lwork, + integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3; + + /* Local variables */ + integer i__, j, l, ib, nb, ki, kk, nx, iws, nbmin, iinfo; + extern /* Subroutine */ int dorg2r_(integer *, integer *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *), + dlarfb_(char *, char *, char *, char *, integer *, integer *, + integer *, doublereal *, integer *, doublereal *, integer *, + doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, + ftnlen, ftnlen), dlarft_(char *, char *, integer *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, + ftnlen, ftnlen), xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + integer ldwork, lwkopt; + logical lquery; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --tau; + --work; + + /* Function Body */ + *info = 0; + nb = ilaenv_(&c__1, (char *)"DORGQR", (char *)" ", m, n, k, &c_n1, (ftnlen)6, (ftnlen)1); + lwkopt = max(1,*n) * nb; + work[1] = (doublereal) lwkopt; + lquery = *lwork == -1; + if (*m < 0) { + *info = -1; + } else if (*n < 0 || *n > *m) { + *info = -2; + } else if (*k < 0 || *k > *n) { + *info = -3; + } else if (*lda < max(1,*m)) { + *info = -5; + } else if (*lwork < max(1,*n) && ! lquery) { + *info = -8; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DORGQR", &i__1, (ftnlen)6); + return 0; + } else if (lquery) { + return 0; + } + +/* Quick return if possible */ + + if (*n <= 0) { + work[1] = 1.; + return 0; + } + + nbmin = 2; + nx = 0; + iws = *n; + if (nb > 1 && nb < *k) { + +/* Determine when to cross over from blocked to unblocked code. */ + +/* Computing MAX */ + i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"DORGQR", (char *)" ", m, n, k, &c_n1, ( + ftnlen)6, (ftnlen)1); + nx = max(i__1,i__2); + if (nx < *k) { + +/* Determine if workspace is large enough for blocked code. */ + + ldwork = *n; + iws = ldwork * nb; + if (*lwork < iws) { + +/* Not enough workspace to use optimal NB: reduce NB and */ +/* determine the minimum value of NB. */ + + nb = *lwork / ldwork; +/* Computing MAX */ + i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DORGQR", (char *)" ", m, n, k, &c_n1, + (ftnlen)6, (ftnlen)1); + nbmin = max(i__1,i__2); + } + } + } + + if (nb >= nbmin && nb < *k && nx < *k) { + +/* Use blocked code after the last block. */ +/* The first kk columns are handled by the block method. */ + + ki = (*k - nx - 1) / nb * nb; +/* Computing MIN */ + i__1 = *k, i__2 = ki + nb; + kk = min(i__1,i__2); + +/* Set A(1:kk,kk+1:n) to zero. */ + + i__1 = *n; + for (j = kk + 1; j <= i__1; ++j) { + i__2 = kk; + for (i__ = 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] = 0.; +/* L10: */ + } +/* L20: */ + } + } else { + kk = 0; + } + +/* Use unblocked code for the last or only block. */ + + if (kk < *n) { + i__1 = *m - kk; + i__2 = *n - kk; + i__3 = *k - kk; + dorg2r_(&i__1, &i__2, &i__3, &a[kk + 1 + (kk + 1) * a_dim1], lda, & + tau[kk + 1], &work[1], &iinfo); + } + + if (kk > 0) { + +/* Use blocked code */ + + i__1 = -nb; + for (i__ = ki + 1; i__1 < 0 ? i__ >= 1 : i__ <= 1; i__ += i__1) { +/* Computing MIN */ + i__2 = nb, i__3 = *k - i__ + 1; + ib = min(i__2,i__3); + if (i__ + ib <= *n) { + +/* Form the triangular factor of the block reflector */ +/* H = H(i) H(i+1) . . . H(i+ib-1) */ + + i__2 = *m - i__ + 1; + dlarft_((char *)"Forward", (char *)"Columnwise", &i__2, &ib, &a[i__ + i__ * + a_dim1], lda, &tau[i__], &work[1], &ldwork, (ftnlen)7, + (ftnlen)10); + +/* Apply H to A(i:m,i+ib:n) from the left */ + + i__2 = *m - i__ + 1; + i__3 = *n - i__ - ib + 1; + dlarfb_((char *)"Left", (char *)"No transpose", (char *)"Forward", (char *)"Columnwise", & + i__2, &i__3, &ib, &a[i__ + i__ * a_dim1], lda, &work[ + 1], &ldwork, &a[i__ + (i__ + ib) * a_dim1], lda, & + work[ib + 1], &ldwork, (ftnlen)4, (ftnlen)12, (ftnlen) + 7, (ftnlen)10); + } + +/* Apply H to rows i:m of current block */ + + i__2 = *m - i__ + 1; + dorg2r_(&i__2, &ib, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], & + work[1], &iinfo); + +/* Set rows 1:i-1 of current block to zero */ + + i__2 = i__ + ib - 1; + for (j = i__; j <= i__2; ++j) { + i__3 = i__ - 1; + for (l = 1; l <= i__3; ++l) { + a[l + j * a_dim1] = 0.; +/* L30: */ + } +/* L40: */ + } +/* L50: */ + } + } + + work[1] = (doublereal) iws; + return 0; + +/* End of DORGQR */ + +} /* dorgqr_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dorgtr.cpp b/lib/linalg/dorgtr.cpp new file mode 100644 index 0000000000..7686c56d19 --- /dev/null +++ b/lib/linalg/dorgtr.cpp @@ -0,0 +1,331 @@ +/* fortran/dorgtr.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c_n1 = -1; + +/* > \brief \b DORGTR */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DORGTR + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DORGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER UPLO */ +/* INTEGER INFO, LDA, LWORK, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DORGTR generates a real orthogonal matrix Q which is defined as the */ +/* > product of n-1 elementary reflectors of order N, as returned by */ +/* > DSYTRD: */ +/* > */ +/* > if UPLO = 'U', Q = H(n-1) . . . H(2) H(1), */ +/* > */ +/* > if UPLO = 'L', Q = H(1) H(2) . . . H(n-1). */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > = 'U': Upper triangle of A contains elementary reflectors */ +/* > from DSYTRD; */ +/* > = 'L': Lower triangle of A contains elementary reflectors */ +/* > from DSYTRD. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrix Q. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On entry, the vectors which define the elementary reflectors, */ +/* > as returned by DSYTRD. */ +/* > On exit, the N-by-N orthogonal matrix Q. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TAU */ +/* > \verbatim */ +/* > TAU is DOUBLE PRECISION array, dimension (N-1) */ +/* > TAU(i) must contain the scalar factor of the elementary */ +/* > reflector H(i), as returned by DSYTRD. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ +/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LWORK */ +/* > \verbatim */ +/* > LWORK is INTEGER */ +/* > The dimension of the array WORK. LWORK >= max(1,N-1). */ +/* > For optimum performance LWORK >= (N-1)*NB, where NB is */ +/* > the optimal blocksize. */ +/* > */ +/* > If LWORK = -1, then a workspace query is assumed; the routine */ +/* > only calculates the optimal size of the WORK array, returns */ +/* > this value as the first entry of the WORK array, and no error */ +/* > message related to LWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleOTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dorgtr_(char *uplo, integer *n, doublereal *a, integer * + lda, doublereal *tau, doublereal *work, integer *lwork, integer *info, + ftnlen uplo_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3; + + /* Local variables */ + integer i__, j, nb; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + integer iinfo; + logical upper; + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dorgql_(integer *, integer *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, + integer *), dorgqr_(integer *, integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, integer *); + integer lwkopt; + logical lquery; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --tau; + --work; + + /* Function Body */ + *info = 0; + lquery = *lwork == -1; + upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); + if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } else if (*lda < max(1,*n)) { + *info = -4; + } else /* if(complicated condition) */ { +/* Computing MAX */ + i__1 = 1, i__2 = *n - 1; + if (*lwork < max(i__1,i__2) && ! lquery) { + *info = -7; + } + } + + if (*info == 0) { + if (upper) { + i__1 = *n - 1; + i__2 = *n - 1; + i__3 = *n - 1; + nb = ilaenv_(&c__1, (char *)"DORGQL", (char *)" ", &i__1, &i__2, &i__3, &c_n1, ( + ftnlen)6, (ftnlen)1); + } else { + i__1 = *n - 1; + i__2 = *n - 1; + i__3 = *n - 1; + nb = ilaenv_(&c__1, (char *)"DORGQR", (char *)" ", &i__1, &i__2, &i__3, &c_n1, ( + ftnlen)6, (ftnlen)1); + } +/* Computing MAX */ + i__1 = 1, i__2 = *n - 1; + lwkopt = max(i__1,i__2) * nb; + work[1] = (doublereal) lwkopt; + } + + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DORGTR", &i__1, (ftnlen)6); + return 0; + } else if (lquery) { + return 0; + } + +/* Quick return if possible */ + + if (*n == 0) { + work[1] = 1.; + return 0; + } + + if (upper) { + +/* Q was determined by a call to DSYTRD with UPLO = 'U' */ + +/* Shift the vectors which define the elementary reflectors one */ +/* column to the left, and set the last row and column of Q to */ +/* those of the unit matrix */ + + i__1 = *n - 1; + for (j = 1; j <= i__1; ++j) { + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] = a[i__ + (j + 1) * a_dim1]; +/* L10: */ + } + a[*n + j * a_dim1] = 0.; +/* L20: */ + } + i__1 = *n - 1; + for (i__ = 1; i__ <= i__1; ++i__) { + a[i__ + *n * a_dim1] = 0.; +/* L30: */ + } + a[*n + *n * a_dim1] = 1.; + +/* Generate Q(1:n-1,1:n-1) */ + + i__1 = *n - 1; + i__2 = *n - 1; + i__3 = *n - 1; + dorgql_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], &work[1], + lwork, &iinfo); + + } else { + +/* Q was determined by a call to DSYTRD with UPLO = 'L'. */ + +/* Shift the vectors which define the elementary reflectors one */ +/* column to the right, and set the first row and column of Q to */ +/* those of the unit matrix */ + + for (j = *n; j >= 2; --j) { + a[j * a_dim1 + 1] = 0.; + i__1 = *n; + for (i__ = j + 1; i__ <= i__1; ++i__) { + a[i__ + j * a_dim1] = a[i__ + (j - 1) * a_dim1]; +/* L40: */ + } +/* L50: */ + } + a[a_dim1 + 1] = 1.; + i__1 = *n; + for (i__ = 2; i__ <= i__1; ++i__) { + a[i__ + a_dim1] = 0.; +/* L60: */ + } + if (*n > 1) { + +/* Generate Q(2:n,2:n) */ + + i__1 = *n - 1; + i__2 = *n - 1; + i__3 = *n - 1; + dorgqr_(&i__1, &i__2, &i__3, &a[(a_dim1 << 1) + 2], lda, &tau[1], + &work[1], lwork, &iinfo); + } + } + work[1] = (doublereal) lwkopt; + return 0; + +/* End of DORGTR */ + +} /* dorgtr_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dorm2l.cpp b/lib/linalg/dorm2l.cpp new file mode 100644 index 0000000000..6669a81614 --- /dev/null +++ b/lib/linalg/dorm2l.cpp @@ -0,0 +1,324 @@ +/* fortran/dorm2l.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; + +/* > \brief \b DORM2L multiplies a general matrix by the orthogonal matrix from a QL factorization determined +by sgeqlf (unblocked algorithm). */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DORM2L + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DORM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, */ +/* WORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER SIDE, TRANS */ +/* INTEGER INFO, K, LDA, LDC, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DORM2L overwrites the general real m by n matrix C with */ +/* > */ +/* > Q * C if SIDE = 'L' and TRANS = 'N', or */ +/* > */ +/* > Q**T * C if SIDE = 'L' and TRANS = 'T', or */ +/* > */ +/* > C * Q if SIDE = 'R' and TRANS = 'N', or */ +/* > */ +/* > C * Q**T if SIDE = 'R' and TRANS = 'T', */ +/* > */ +/* > where Q is a real orthogonal matrix defined as the product of k */ +/* > elementary reflectors */ +/* > */ +/* > Q = H(k) . . . H(2) H(1) */ +/* > */ +/* > as returned by DGEQLF. Q is of order m if SIDE = 'L' and of order n */ +/* > if SIDE = 'R'. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] SIDE */ +/* > \verbatim */ +/* > SIDE is CHARACTER*1 */ +/* > = 'L': apply Q or Q**T from the Left */ +/* > = 'R': apply Q or Q**T from the Right */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TRANS */ +/* > \verbatim */ +/* > TRANS is CHARACTER*1 */ +/* > = 'N': apply Q (No transpose) */ +/* > = 'T': apply Q**T (Transpose) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix C. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix C. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > The number of elementary reflectors whose product defines */ +/* > the matrix Q. */ +/* > If SIDE = 'L', M >= K >= 0; */ +/* > if SIDE = 'R', N >= K >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,K) */ +/* > The i-th column must contain the vector which defines the */ +/* > elementary reflector H(i), for i = 1,2,...,k, as returned by */ +/* > DGEQLF in the last k columns of its array argument A. */ +/* > A is modified by the routine but restored on exit. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. */ +/* > If SIDE = 'L', LDA >= max(1,M); */ +/* > if SIDE = 'R', LDA >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TAU */ +/* > \verbatim */ +/* > TAU is DOUBLE PRECISION array, dimension (K) */ +/* > TAU(i) must contain the scalar factor of the elementary */ +/* > reflector H(i), as returned by DGEQLF. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] C */ +/* > \verbatim */ +/* > C is DOUBLE PRECISION array, dimension (LDC,N) */ +/* > On entry, the m by n matrix C. */ +/* > On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDC */ +/* > \verbatim */ +/* > LDC is INTEGER */ +/* > The leading dimension of the array C. LDC >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension */ +/* > (N) if SIDE = 'L', */ +/* > (M) if SIDE = 'R' */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleOTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dorm2l_(char *side, char *trans, integer *m, integer *n, + integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal * + c__, integer *ldc, doublereal *work, integer *info, ftnlen side_len, + ftnlen trans_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2; + + /* Local variables */ + integer i__, i1, i2, i3, mi, ni, nq; + doublereal aii; + logical left; + extern /* Subroutine */ int dlarf_(char *, integer *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, + doublereal *, ftnlen); + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + logical notran; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --tau; + c_dim1 = *ldc; + c_offset = 1 + c_dim1; + c__ -= c_offset; + --work; + + /* Function Body */ + *info = 0; + left = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); + notran = lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1); + +/* NQ is the order of Q */ + + if (left) { + nq = *m; + } else { + nq = *n; + } + if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + *info = -1; + } else if (! notran && ! lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1)) { + *info = -2; + } else if (*m < 0) { + *info = -3; + } else if (*n < 0) { + *info = -4; + } else if (*k < 0 || *k > nq) { + *info = -5; + } else if (*lda < max(1,nq)) { + *info = -7; + } else if (*ldc < max(1,*m)) { + *info = -10; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DORM2L", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*m == 0 || *n == 0 || *k == 0) { + return 0; + } + + if (left && notran || ! left && ! notran) { + i1 = 1; + i2 = *k; + i3 = 1; + } else { + i1 = *k; + i2 = 1; + i3 = -1; + } + + if (left) { + ni = *n; + } else { + mi = *m; + } + + i__1 = i2; + i__2 = i3; + for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { + if (left) { + +/* H(i) is applied to C(1:m-k+i,1:n) */ + + mi = *m - *k + i__; + } else { + +/* H(i) is applied to C(1:m,1:n-k+i) */ + + ni = *n - *k + i__; + } + +/* Apply H(i) */ + + aii = a[nq - *k + i__ + i__ * a_dim1]; + a[nq - *k + i__ + i__ * a_dim1] = 1.; + dlarf_(side, &mi, &ni, &a[i__ * a_dim1 + 1], &c__1, &tau[i__], &c__[ + c_offset], ldc, &work[1], (ftnlen)1); + a[nq - *k + i__ + i__ * a_dim1] = aii; +/* L10: */ + } + return 0; + +/* End of DORM2L */ + +} /* dorm2l_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dorm2r.cpp b/lib/linalg/dorm2r.cpp new file mode 100644 index 0000000000..13a74e8fe1 --- /dev/null +++ b/lib/linalg/dorm2r.cpp @@ -0,0 +1,328 @@ +/* fortran/dorm2r.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; + +/* > \brief \b DORM2R multiplies a general matrix by the orthogonal matrix from a QR factorization determined +by sgeqrf (unblocked algorithm). */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DORM2R + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DORM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, */ +/* WORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER SIDE, TRANS */ +/* INTEGER INFO, K, LDA, LDC, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DORM2R overwrites the general real m by n matrix C with */ +/* > */ +/* > Q * C if SIDE = 'L' and TRANS = 'N', or */ +/* > */ +/* > Q**T* C if SIDE = 'L' and TRANS = 'T', or */ +/* > */ +/* > C * Q if SIDE = 'R' and TRANS = 'N', or */ +/* > */ +/* > C * Q**T if SIDE = 'R' and TRANS = 'T', */ +/* > */ +/* > where Q is a real orthogonal matrix defined as the product of k */ +/* > elementary reflectors */ +/* > */ +/* > Q = H(1) H(2) . . . H(k) */ +/* > */ +/* > as returned by DGEQRF. Q is of order m if SIDE = 'L' and of order n */ +/* > if SIDE = 'R'. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] SIDE */ +/* > \verbatim */ +/* > SIDE is CHARACTER*1 */ +/* > = 'L': apply Q or Q**T from the Left */ +/* > = 'R': apply Q or Q**T from the Right */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TRANS */ +/* > \verbatim */ +/* > TRANS is CHARACTER*1 */ +/* > = 'N': apply Q (No transpose) */ +/* > = 'T': apply Q**T (Transpose) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix C. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix C. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > The number of elementary reflectors whose product defines */ +/* > the matrix Q. */ +/* > If SIDE = 'L', M >= K >= 0; */ +/* > if SIDE = 'R', N >= K >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,K) */ +/* > The i-th column must contain the vector which defines the */ +/* > elementary reflector H(i), for i = 1,2,...,k, as returned by */ +/* > DGEQRF in the first k columns of its array argument A. */ +/* > A is modified by the routine but restored on exit. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. */ +/* > If SIDE = 'L', LDA >= max(1,M); */ +/* > if SIDE = 'R', LDA >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TAU */ +/* > \verbatim */ +/* > TAU is DOUBLE PRECISION array, dimension (K) */ +/* > TAU(i) must contain the scalar factor of the elementary */ +/* > reflector H(i), as returned by DGEQRF. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] C */ +/* > \verbatim */ +/* > C is DOUBLE PRECISION array, dimension (LDC,N) */ +/* > On entry, the m by n matrix C. */ +/* > On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDC */ +/* > \verbatim */ +/* > LDC is INTEGER */ +/* > The leading dimension of the array C. LDC >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension */ +/* > (N) if SIDE = 'L', */ +/* > (M) if SIDE = 'R' */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleOTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dorm2r_(char *side, char *trans, integer *m, integer *n, + integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal * + c__, integer *ldc, doublereal *work, integer *info, ftnlen side_len, + ftnlen trans_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2; + + /* Local variables */ + integer i__, i1, i2, i3, ic, jc, mi, ni, nq; + doublereal aii; + logical left; + extern /* Subroutine */ int dlarf_(char *, integer *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, + doublereal *, ftnlen); + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + logical notran; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --tau; + c_dim1 = *ldc; + c_offset = 1 + c_dim1; + c__ -= c_offset; + --work; + + /* Function Body */ + *info = 0; + left = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); + notran = lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1); + +/* NQ is the order of Q */ + + if (left) { + nq = *m; + } else { + nq = *n; + } + if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + *info = -1; + } else if (! notran && ! lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1)) { + *info = -2; + } else if (*m < 0) { + *info = -3; + } else if (*n < 0) { + *info = -4; + } else if (*k < 0 || *k > nq) { + *info = -5; + } else if (*lda < max(1,nq)) { + *info = -7; + } else if (*ldc < max(1,*m)) { + *info = -10; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DORM2R", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*m == 0 || *n == 0 || *k == 0) { + return 0; + } + + if (left && ! notran || ! left && notran) { + i1 = 1; + i2 = *k; + i3 = 1; + } else { + i1 = *k; + i2 = 1; + i3 = -1; + } + + if (left) { + ni = *n; + jc = 1; + } else { + mi = *m; + ic = 1; + } + + i__1 = i2; + i__2 = i3; + for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { + if (left) { + +/* H(i) is applied to C(i:m,1:n) */ + + mi = *m - i__ + 1; + ic = i__; + } else { + +/* H(i) is applied to C(1:m,i:n) */ + + ni = *n - i__ + 1; + jc = i__; + } + +/* Apply H(i) */ + + aii = a[i__ + i__ * a_dim1]; + a[i__ + i__ * a_dim1] = 1.; + dlarf_(side, &mi, &ni, &a[i__ + i__ * a_dim1], &c__1, &tau[i__], &c__[ + ic + jc * c_dim1], ldc, &work[1], (ftnlen)1); + a[i__ + i__ * a_dim1] = aii; +/* L10: */ + } + return 0; + +/* End of DORM2R */ + +} /* dorm2r_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dormbr.cpp b/lib/linalg/dormbr.cpp new file mode 100644 index 0000000000..e00ec3ecb0 --- /dev/null +++ b/lib/linalg/dormbr.cpp @@ -0,0 +1,464 @@ +/* fortran/dormbr.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c_n1 = -1; +static integer c__2 = 2; + +/* > \brief \b DORMBR */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DORMBR + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, */ +/* LDC, WORK, LWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER SIDE, TRANS, VECT */ +/* INTEGER INFO, K, LDA, LDC, LWORK, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > If VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C */ +/* > with */ +/* > SIDE = 'L' SIDE = 'R' */ +/* > TRANS = 'N': Q * C C * Q */ +/* > TRANS = 'T': Q**T * C C * Q**T */ +/* > */ +/* > If VECT = 'P', DORMBR overwrites the general real M-by-N matrix C */ +/* > with */ +/* > SIDE = 'L' SIDE = 'R' */ +/* > TRANS = 'N': P * C C * P */ +/* > TRANS = 'T': P**T * C C * P**T */ +/* > */ +/* > Here Q and P**T are the orthogonal matrices determined by DGEBRD when */ +/* > reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and */ +/* > P**T are defined as products of elementary reflectors H(i) and G(i) */ +/* > respectively. */ +/* > */ +/* > Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the */ +/* > order of the orthogonal matrix Q or P**T that is applied. */ +/* > */ +/* > If VECT = 'Q', A is assumed to have been an NQ-by-K matrix: */ +/* > if nq >= k, Q = H(1) H(2) . . . H(k); */ +/* > if nq < k, Q = H(1) H(2) . . . H(nq-1). */ +/* > */ +/* > If VECT = 'P', A is assumed to have been a K-by-NQ matrix: */ +/* > if k < nq, P = G(1) G(2) . . . G(k); */ +/* > if k >= nq, P = G(1) G(2) . . . G(nq-1). */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] VECT */ +/* > \verbatim */ +/* > VECT is CHARACTER*1 */ +/* > = 'Q': apply Q or Q**T; */ +/* > = 'P': apply P or P**T. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] SIDE */ +/* > \verbatim */ +/* > SIDE is CHARACTER*1 */ +/* > = 'L': apply Q, Q**T, P or P**T from the Left; */ +/* > = 'R': apply Q, Q**T, P or P**T from the Right. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TRANS */ +/* > \verbatim */ +/* > TRANS is CHARACTER*1 */ +/* > = 'N': No transpose, apply Q or P; */ +/* > = 'T': Transpose, apply Q**T or P**T. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix C. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix C. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > If VECT = 'Q', the number of columns in the original */ +/* > matrix reduced by DGEBRD. */ +/* > If VECT = 'P', the number of rows in the original */ +/* > matrix reduced by DGEBRD. */ +/* > K >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension */ +/* > (LDA,min(nq,K)) if VECT = 'Q' */ +/* > (LDA,nq) if VECT = 'P' */ +/* > The vectors which define the elementary reflectors H(i) and */ +/* > G(i), whose products determine the matrices Q and P, as */ +/* > returned by DGEBRD. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. */ +/* > If VECT = 'Q', LDA >= max(1,nq); */ +/* > if VECT = 'P', LDA >= max(1,min(nq,K)). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TAU */ +/* > \verbatim */ +/* > TAU is DOUBLE PRECISION array, dimension (min(nq,K)) */ +/* > TAU(i) must contain the scalar factor of the elementary */ +/* > reflector H(i) or G(i) which determines Q or P, as returned */ +/* > by DGEBRD in the array argument TAUQ or TAUP. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] C */ +/* > \verbatim */ +/* > C is DOUBLE PRECISION array, dimension (LDC,N) */ +/* > On entry, the M-by-N matrix C. */ +/* > On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q */ +/* > or P*C or P**T*C or C*P or C*P**T. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDC */ +/* > \verbatim */ +/* > LDC is INTEGER */ +/* > The leading dimension of the array C. LDC >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ +/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LWORK */ +/* > \verbatim */ +/* > LWORK is INTEGER */ +/* > The dimension of the array WORK. */ +/* > If SIDE = 'L', LWORK >= max(1,N); */ +/* > if SIDE = 'R', LWORK >= max(1,M). */ +/* > For optimum performance LWORK >= N*NB if SIDE = 'L', and */ +/* > LWORK >= M*NB if SIDE = 'R', where NB is the optimal */ +/* > blocksize. */ +/* > */ +/* > If LWORK = -1, then a workspace query is assumed; the routine */ +/* > only calculates the optimal size of the WORK array, returns */ +/* > this value as the first entry of the WORK array, and no error */ +/* > message related to LWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleOTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dormbr_(char *vect, char *side, char *trans, integer *m, + integer *n, integer *k, doublereal *a, integer *lda, doublereal *tau, + doublereal *c__, integer *ldc, doublereal *work, integer *lwork, + integer *info, ftnlen vect_len, ftnlen side_len, ftnlen trans_len) +{ + /* System generated locals */ + address a__1[2]; + integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2]; + char ch__1[2]; + + /* Builtin functions */ + /* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen); + + /* Local variables */ + integer i1, i2, nb, mi, ni, nq, nw; + logical left; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + integer iinfo; + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dormlq_(char *, char *, integer *, integer *, + integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, integer *, ftnlen, ftnlen); + logical notran; + extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *, + integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, integer *, ftnlen, ftnlen); + logical applyq; + char transt[1]; + integer lwkopt; + logical lquery; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --tau; + c_dim1 = *ldc; + c_offset = 1 + c_dim1; + c__ -= c_offset; + --work; + + /* Function Body */ + *info = 0; + applyq = lsame_(vect, (char *)"Q", (ftnlen)1, (ftnlen)1); + left = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); + notran = lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1); + lquery = *lwork == -1; + +/* NQ is the order of Q or P and NW is the minimum dimension of WORK */ + + if (left) { + nq = *m; + nw = max(1,*n); + } else { + nq = *n; + nw = max(1,*m); + } + if (! applyq && ! lsame_(vect, (char *)"P", (ftnlen)1, (ftnlen)1)) { + *info = -1; + } else if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + *info = -2; + } else if (! notran && ! lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1)) { + *info = -3; + } else if (*m < 0) { + *info = -4; + } else if (*n < 0) { + *info = -5; + } else if (*k < 0) { + *info = -6; + } else /* if(complicated condition) */ { +/* Computing MAX */ + i__1 = 1, i__2 = min(nq,*k); + if (applyq && *lda < max(1,nq) || ! applyq && *lda < max(i__1,i__2)) { + *info = -8; + } else if (*ldc < max(1,*m)) { + *info = -11; + } else if (*lwork < nw && ! lquery) { + *info = -13; + } + } + + if (*info == 0) { + if (applyq) { + if (left) { +/* Writing concatenation */ + i__3[0] = 1, a__1[0] = side; + i__3[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + i__1 = *m - 1; + i__2 = *m - 1; + nb = ilaenv_(&c__1, (char *)"DORMQR", ch__1, &i__1, n, &i__2, &c_n1, ( + ftnlen)6, (ftnlen)2); + } else { +/* Writing concatenation */ + i__3[0] = 1, a__1[0] = side; + i__3[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + i__1 = *n - 1; + i__2 = *n - 1; + nb = ilaenv_(&c__1, (char *)"DORMQR", ch__1, m, &i__1, &i__2, &c_n1, ( + ftnlen)6, (ftnlen)2); + } + } else { + if (left) { +/* Writing concatenation */ + i__3[0] = 1, a__1[0] = side; + i__3[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + i__1 = *m - 1; + i__2 = *m - 1; + nb = ilaenv_(&c__1, (char *)"DORMLQ", ch__1, &i__1, n, &i__2, &c_n1, ( + ftnlen)6, (ftnlen)2); + } else { +/* Writing concatenation */ + i__3[0] = 1, a__1[0] = side; + i__3[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + i__1 = *n - 1; + i__2 = *n - 1; + nb = ilaenv_(&c__1, (char *)"DORMLQ", ch__1, m, &i__1, &i__2, &c_n1, ( + ftnlen)6, (ftnlen)2); + } + } + lwkopt = nw * nb; + work[1] = (doublereal) lwkopt; + } + + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DORMBR", &i__1, (ftnlen)6); + return 0; + } else if (lquery) { + return 0; + } + +/* Quick return if possible */ + + work[1] = 1.; + if (*m == 0 || *n == 0) { + return 0; + } + + if (applyq) { + +/* Apply Q */ + + if (nq >= *k) { + +/* Q was determined by a call to DGEBRD with nq >= k */ + + dormqr_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[ + c_offset], ldc, &work[1], lwork, &iinfo, (ftnlen)1, ( + ftnlen)1); + } else if (nq > 1) { + +/* Q was determined by a call to DGEBRD with nq < k */ + + if (left) { + mi = *m - 1; + ni = *n; + i1 = 2; + i2 = 1; + } else { + mi = *m; + ni = *n - 1; + i1 = 1; + i2 = 2; + } + i__1 = nq - 1; + dormqr_(side, trans, &mi, &ni, &i__1, &a[a_dim1 + 2], lda, &tau[1] + , &c__[i1 + i2 * c_dim1], ldc, &work[1], lwork, &iinfo, ( + ftnlen)1, (ftnlen)1); + } + } else { + +/* Apply P */ + + if (notran) { + *(unsigned char *)transt = 'T'; + } else { + *(unsigned char *)transt = 'N'; + } + if (nq > *k) { + +/* P was determined by a call to DGEBRD with nq > k */ + + dormlq_(side, transt, m, n, k, &a[a_offset], lda, &tau[1], &c__[ + c_offset], ldc, &work[1], lwork, &iinfo, (ftnlen)1, ( + ftnlen)1); + } else if (nq > 1) { + +/* P was determined by a call to DGEBRD with nq <= k */ + + if (left) { + mi = *m - 1; + ni = *n; + i1 = 2; + i2 = 1; + } else { + mi = *m; + ni = *n - 1; + i1 = 1; + i2 = 2; + } + i__1 = nq - 1; + dormlq_(side, transt, &mi, &ni, &i__1, &a[(a_dim1 << 1) + 1], lda, + &tau[1], &c__[i1 + i2 * c_dim1], ldc, &work[1], lwork, & + iinfo, (ftnlen)1, (ftnlen)1); + } + } + work[1] = (doublereal) lwkopt; + return 0; + +/* End of DORMBR */ + +} /* dormbr_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dorml2.cpp b/lib/linalg/dorml2.cpp new file mode 100644 index 0000000000..9085a5a0ce --- /dev/null +++ b/lib/linalg/dorml2.cpp @@ -0,0 +1,324 @@ +/* fortran/dorml2.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DORML2 multiplies a general matrix by the orthogonal matrix from a LQ factorization determined +by sgelqf (unblocked algorithm). */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DORML2 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DORML2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, */ +/* WORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER SIDE, TRANS */ +/* INTEGER INFO, K, LDA, LDC, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DORML2 overwrites the general real m by n matrix C with */ +/* > */ +/* > Q * C if SIDE = 'L' and TRANS = 'N', or */ +/* > */ +/* > Q**T* C if SIDE = 'L' and TRANS = 'T', or */ +/* > */ +/* > C * Q if SIDE = 'R' and TRANS = 'N', or */ +/* > */ +/* > C * Q**T if SIDE = 'R' and TRANS = 'T', */ +/* > */ +/* > where Q is a real orthogonal matrix defined as the product of k */ +/* > elementary reflectors */ +/* > */ +/* > Q = H(k) . . . H(2) H(1) */ +/* > */ +/* > as returned by DGELQF. Q is of order m if SIDE = 'L' and of order n */ +/* > if SIDE = 'R'. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] SIDE */ +/* > \verbatim */ +/* > SIDE is CHARACTER*1 */ +/* > = 'L': apply Q or Q**T from the Left */ +/* > = 'R': apply Q or Q**T from the Right */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TRANS */ +/* > \verbatim */ +/* > TRANS is CHARACTER*1 */ +/* > = 'N': apply Q (No transpose) */ +/* > = 'T': apply Q**T (Transpose) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix C. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix C. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > The number of elementary reflectors whose product defines */ +/* > the matrix Q. */ +/* > If SIDE = 'L', M >= K >= 0; */ +/* > if SIDE = 'R', N >= K >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension */ +/* > (LDA,M) if SIDE = 'L', */ +/* > (LDA,N) if SIDE = 'R' */ +/* > The i-th row must contain the vector which defines the */ +/* > elementary reflector H(i), for i = 1,2,...,k, as returned by */ +/* > DGELQF in the first k rows of its array argument A. */ +/* > A is modified by the routine but restored on exit. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,K). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TAU */ +/* > \verbatim */ +/* > TAU is DOUBLE PRECISION array, dimension (K) */ +/* > TAU(i) must contain the scalar factor of the elementary */ +/* > reflector H(i), as returned by DGELQF. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] C */ +/* > \verbatim */ +/* > C is DOUBLE PRECISION array, dimension (LDC,N) */ +/* > On entry, the m by n matrix C. */ +/* > On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDC */ +/* > \verbatim */ +/* > LDC is INTEGER */ +/* > The leading dimension of the array C. LDC >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension */ +/* > (N) if SIDE = 'L', */ +/* > (M) if SIDE = 'R' */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleOTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dorml2_(char *side, char *trans, integer *m, integer *n, + integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal * + c__, integer *ldc, doublereal *work, integer *info, ftnlen side_len, + ftnlen trans_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2; + + /* Local variables */ + integer i__, i1, i2, i3, ic, jc, mi, ni, nq; + doublereal aii; + logical left; + extern /* Subroutine */ int dlarf_(char *, integer *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, + doublereal *, ftnlen); + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + logical notran; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --tau; + c_dim1 = *ldc; + c_offset = 1 + c_dim1; + c__ -= c_offset; + --work; + + /* Function Body */ + *info = 0; + left = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); + notran = lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1); + +/* NQ is the order of Q */ + + if (left) { + nq = *m; + } else { + nq = *n; + } + if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + *info = -1; + } else if (! notran && ! lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1)) { + *info = -2; + } else if (*m < 0) { + *info = -3; + } else if (*n < 0) { + *info = -4; + } else if (*k < 0 || *k > nq) { + *info = -5; + } else if (*lda < max(1,*k)) { + *info = -7; + } else if (*ldc < max(1,*m)) { + *info = -10; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DORML2", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*m == 0 || *n == 0 || *k == 0) { + return 0; + } + + if (left && notran || ! left && ! notran) { + i1 = 1; + i2 = *k; + i3 = 1; + } else { + i1 = *k; + i2 = 1; + i3 = -1; + } + + if (left) { + ni = *n; + jc = 1; + } else { + mi = *m; + ic = 1; + } + + i__1 = i2; + i__2 = i3; + for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { + if (left) { + +/* H(i) is applied to C(i:m,1:n) */ + + mi = *m - i__ + 1; + ic = i__; + } else { + +/* H(i) is applied to C(1:m,i:n) */ + + ni = *n - i__ + 1; + jc = i__; + } + +/* Apply H(i) */ + + aii = a[i__ + i__ * a_dim1]; + a[i__ + i__ * a_dim1] = 1.; + dlarf_(side, &mi, &ni, &a[i__ + i__ * a_dim1], lda, &tau[i__], &c__[ + ic + jc * c_dim1], ldc, &work[1], (ftnlen)1); + a[i__ + i__ * a_dim1] = aii; +/* L10: */ + } + return 0; + +/* End of DORML2 */ + +} /* dorml2_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dormlq.cpp b/lib/linalg/dormlq.cpp new file mode 100644 index 0000000000..e5ed90a9fa --- /dev/null +++ b/lib/linalg/dormlq.cpp @@ -0,0 +1,424 @@ +/* fortran/dormlq.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c_n1 = -1; +static integer c__2 = 2; +static integer c__65 = 65; + +/* > \brief \b DORMLQ */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DORMLQ + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DORMLQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, */ +/* WORK, LWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER SIDE, TRANS */ +/* INTEGER INFO, K, LDA, LDC, LWORK, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DORMLQ overwrites the general real M-by-N matrix C with */ +/* > */ +/* > SIDE = 'L' SIDE = 'R' */ +/* > TRANS = 'N': Q * C C * Q */ +/* > TRANS = 'T': Q**T * C C * Q**T */ +/* > */ +/* > where Q is a real orthogonal matrix defined as the product of k */ +/* > elementary reflectors */ +/* > */ +/* > Q = H(k) . . . H(2) H(1) */ +/* > */ +/* > as returned by DGELQF. Q is of order M if SIDE = 'L' and of order N */ +/* > if SIDE = 'R'. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] SIDE */ +/* > \verbatim */ +/* > SIDE is CHARACTER*1 */ +/* > = 'L': apply Q or Q**T from the Left; */ +/* > = 'R': apply Q or Q**T from the Right. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TRANS */ +/* > \verbatim */ +/* > TRANS is CHARACTER*1 */ +/* > = 'N': No transpose, apply Q; */ +/* > = 'T': Transpose, apply Q**T. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix C. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix C. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > The number of elementary reflectors whose product defines */ +/* > the matrix Q. */ +/* > If SIDE = 'L', M >= K >= 0; */ +/* > if SIDE = 'R', N >= K >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension */ +/* > (LDA,M) if SIDE = 'L', */ +/* > (LDA,N) if SIDE = 'R' */ +/* > The i-th row must contain the vector which defines the */ +/* > elementary reflector H(i), for i = 1,2,...,k, as returned by */ +/* > DGELQF in the first k rows of its array argument A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,K). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TAU */ +/* > \verbatim */ +/* > TAU is DOUBLE PRECISION array, dimension (K) */ +/* > TAU(i) must contain the scalar factor of the elementary */ +/* > reflector H(i), as returned by DGELQF. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] C */ +/* > \verbatim */ +/* > C is DOUBLE PRECISION array, dimension (LDC,N) */ +/* > On entry, the M-by-N matrix C. */ +/* > On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDC */ +/* > \verbatim */ +/* > LDC is INTEGER */ +/* > The leading dimension of the array C. LDC >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ +/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LWORK */ +/* > \verbatim */ +/* > LWORK is INTEGER */ +/* > The dimension of the array WORK. */ +/* > If SIDE = 'L', LWORK >= max(1,N); */ +/* > if SIDE = 'R', LWORK >= max(1,M). */ +/* > For good performance, LWORK should generally be larger. */ +/* > */ +/* > If LWORK = -1, then a workspace query is assumed; the routine */ +/* > only calculates the optimal size of the WORK array, returns */ +/* > this value as the first entry of the WORK array, and no error */ +/* > message related to LWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleOTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dormlq_(char *side, char *trans, integer *m, integer *n, + integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal * + c__, integer *ldc, doublereal *work, integer *lwork, integer *info, + ftnlen side_len, ftnlen trans_len) +{ + /* System generated locals */ + address a__1[2]; + integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4, + i__5; + char ch__1[2]; + + /* Builtin functions */ + /* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen); + + /* Local variables */ + integer i__, i1, i2, i3, ib, ic, jc, nb, mi, ni, nq, nw, iwt; + logical left; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + integer nbmin, iinfo; + extern /* Subroutine */ int dorml2_(char *, char *, integer *, integer *, + integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, ftnlen, ftnlen), dlarfb_(char + *, char *, char *, char *, integer *, integer *, integer *, + doublereal *, integer *, doublereal *, integer *, doublereal *, + integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, + ftnlen), dlarft_(char *, char *, integer *, integer *, doublereal + *, integer *, doublereal *, doublereal *, integer *, ftnlen, + ftnlen), xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + logical notran; + integer ldwork; + char transt[1]; + integer lwkopt; + logical lquery; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --tau; + c_dim1 = *ldc; + c_offset = 1 + c_dim1; + c__ -= c_offset; + --work; + + /* Function Body */ + *info = 0; + left = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); + notran = lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1); + lquery = *lwork == -1; + +/* NQ is the order of Q and NW is the minimum dimension of WORK */ + + if (left) { + nq = *m; + nw = max(1,*n); + } else { + nq = *n; + nw = max(1,*m); + } + if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + *info = -1; + } else if (! notran && ! lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1)) { + *info = -2; + } else if (*m < 0) { + *info = -3; + } else if (*n < 0) { + *info = -4; + } else if (*k < 0 || *k > nq) { + *info = -5; + } else if (*lda < max(1,*k)) { + *info = -7; + } else if (*ldc < max(1,*m)) { + *info = -10; + } else if (*lwork < nw && ! lquery) { + *info = -12; + } + + if (*info == 0) { + +/* Compute the workspace requirements */ + +/* Computing MIN */ +/* Writing concatenation */ + i__3[0] = 1, a__1[0] = side; + i__3[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + i__1 = 64, i__2 = ilaenv_(&c__1, (char *)"DORMLQ", ch__1, m, n, k, &c_n1, ( + ftnlen)6, (ftnlen)2); + nb = min(i__1,i__2); + lwkopt = nw * nb + 4160; + work[1] = (doublereal) lwkopt; + } + + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DORMLQ", &i__1, (ftnlen)6); + return 0; + } else if (lquery) { + return 0; + } + +/* Quick return if possible */ + + if (*m == 0 || *n == 0 || *k == 0) { + work[1] = 1.; + return 0; + } + + nbmin = 2; + ldwork = nw; + if (nb > 1 && nb < *k) { + if (*lwork < lwkopt) { + nb = (*lwork - 4160) / ldwork; +/* Computing MAX */ +/* Writing concatenation */ + i__3[0] = 1, a__1[0] = side; + i__3[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DORMLQ", ch__1, m, n, k, &c_n1, ( + ftnlen)6, (ftnlen)2); + nbmin = max(i__1,i__2); + } + } + + if (nb < nbmin || nb >= *k) { + +/* Use unblocked code */ + + dorml2_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[ + c_offset], ldc, &work[1], &iinfo, (ftnlen)1, (ftnlen)1); + } else { + +/* Use blocked code */ + + iwt = nw * nb + 1; + if (left && notran || ! left && ! notran) { + i1 = 1; + i2 = *k; + i3 = nb; + } else { + i1 = (*k - 1) / nb * nb + 1; + i2 = 1; + i3 = -nb; + } + + if (left) { + ni = *n; + jc = 1; + } else { + mi = *m; + ic = 1; + } + + if (notran) { + *(unsigned char *)transt = 'T'; + } else { + *(unsigned char *)transt = 'N'; + } + + i__1 = i2; + i__2 = i3; + for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { +/* Computing MIN */ + i__4 = nb, i__5 = *k - i__ + 1; + ib = min(i__4,i__5); + +/* Form the triangular factor of the block reflector */ +/* H = H(i) H(i+1) . . . H(i+ib-1) */ + + i__4 = nq - i__ + 1; + dlarft_((char *)"Forward", (char *)"Rowwise", &i__4, &ib, &a[i__ + i__ * a_dim1], + lda, &tau[i__], &work[iwt], &c__65, (ftnlen)7, (ftnlen)7); + if (left) { + +/* H or H**T is applied to C(i:m,1:n) */ + + mi = *m - i__ + 1; + ic = i__; + } else { + +/* H or H**T is applied to C(1:m,i:n) */ + + ni = *n - i__ + 1; + jc = i__; + } + +/* Apply H or H**T */ + + dlarfb_(side, transt, (char *)"Forward", (char *)"Rowwise", &mi, &ni, &ib, &a[i__ + + i__ * a_dim1], lda, &work[iwt], &c__65, &c__[ic + jc * + c_dim1], ldc, &work[1], &ldwork, (ftnlen)1, (ftnlen)1, ( + ftnlen)7, (ftnlen)7); +/* L10: */ + } + } + work[1] = (doublereal) lwkopt; + return 0; + +/* End of DORMLQ */ + +} /* dormlq_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dormql.cpp b/lib/linalg/dormql.cpp new file mode 100644 index 0000000000..735f9e3d2b --- /dev/null +++ b/lib/linalg/dormql.cpp @@ -0,0 +1,416 @@ +/* fortran/dormql.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c_n1 = -1; +static integer c__2 = 2; +static integer c__65 = 65; + +/* > \brief \b DORMQL */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DORMQL + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DORMQL( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, */ +/* WORK, LWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER SIDE, TRANS */ +/* INTEGER INFO, K, LDA, LDC, LWORK, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DORMQL overwrites the general real M-by-N matrix C with */ +/* > */ +/* > SIDE = 'L' SIDE = 'R' */ +/* > TRANS = 'N': Q * C C * Q */ +/* > TRANS = 'T': Q**T * C C * Q**T */ +/* > */ +/* > where Q is a real orthogonal matrix defined as the product of k */ +/* > elementary reflectors */ +/* > */ +/* > Q = H(k) . . . H(2) H(1) */ +/* > */ +/* > as returned by DGEQLF. Q is of order M if SIDE = 'L' and of order N */ +/* > if SIDE = 'R'. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] SIDE */ +/* > \verbatim */ +/* > SIDE is CHARACTER*1 */ +/* > = 'L': apply Q or Q**T from the Left; */ +/* > = 'R': apply Q or Q**T from the Right. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TRANS */ +/* > \verbatim */ +/* > TRANS is CHARACTER*1 */ +/* > = 'N': No transpose, apply Q; */ +/* > = 'T': Transpose, apply Q**T. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix C. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix C. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > The number of elementary reflectors whose product defines */ +/* > the matrix Q. */ +/* > If SIDE = 'L', M >= K >= 0; */ +/* > if SIDE = 'R', N >= K >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,K) */ +/* > The i-th column must contain the vector which defines the */ +/* > elementary reflector H(i), for i = 1,2,...,k, as returned by */ +/* > DGEQLF in the last k columns of its array argument A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. */ +/* > If SIDE = 'L', LDA >= max(1,M); */ +/* > if SIDE = 'R', LDA >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TAU */ +/* > \verbatim */ +/* > TAU is DOUBLE PRECISION array, dimension (K) */ +/* > TAU(i) must contain the scalar factor of the elementary */ +/* > reflector H(i), as returned by DGEQLF. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] C */ +/* > \verbatim */ +/* > C is DOUBLE PRECISION array, dimension (LDC,N) */ +/* > On entry, the M-by-N matrix C. */ +/* > On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDC */ +/* > \verbatim */ +/* > LDC is INTEGER */ +/* > The leading dimension of the array C. LDC >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ +/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LWORK */ +/* > \verbatim */ +/* > LWORK is INTEGER */ +/* > The dimension of the array WORK. */ +/* > If SIDE = 'L', LWORK >= max(1,N); */ +/* > if SIDE = 'R', LWORK >= max(1,M). */ +/* > For good performance, LWORK should generally be larger. */ +/* > */ +/* > If LWORK = -1, then a workspace query is assumed; the routine */ +/* > only calculates the optimal size of the WORK array, returns */ +/* > this value as the first entry of the WORK array, and no error */ +/* > message related to LWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleOTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dormql_(char *side, char *trans, integer *m, integer *n, + integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal * + c__, integer *ldc, doublereal *work, integer *lwork, integer *info, + ftnlen side_len, ftnlen trans_len) +{ + /* System generated locals */ + address a__1[2]; + integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4, + i__5; + char ch__1[2]; + + /* Builtin functions */ + /* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen); + + /* Local variables */ + integer i__, i1, i2, i3, ib, nb, mi, ni, nq, nw, iwt; + logical left; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + integer nbmin, iinfo; + extern /* Subroutine */ int dorm2l_(char *, char *, integer *, integer *, + integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, ftnlen, ftnlen), dlarfb_(char + *, char *, char *, char *, integer *, integer *, integer *, + doublereal *, integer *, doublereal *, integer *, doublereal *, + integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, + ftnlen), dlarft_(char *, char *, integer *, integer *, doublereal + *, integer *, doublereal *, doublereal *, integer *, ftnlen, + ftnlen), xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + logical notran; + integer ldwork, lwkopt; + logical lquery; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --tau; + c_dim1 = *ldc; + c_offset = 1 + c_dim1; + c__ -= c_offset; + --work; + + /* Function Body */ + *info = 0; + left = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); + notran = lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1); + lquery = *lwork == -1; + +/* NQ is the order of Q and NW is the minimum dimension of WORK */ + + if (left) { + nq = *m; + nw = max(1,*n); + } else { + nq = *n; + nw = max(1,*m); + } + if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + *info = -1; + } else if (! notran && ! lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1)) { + *info = -2; + } else if (*m < 0) { + *info = -3; + } else if (*n < 0) { + *info = -4; + } else if (*k < 0 || *k > nq) { + *info = -5; + } else if (*lda < max(1,nq)) { + *info = -7; + } else if (*ldc < max(1,*m)) { + *info = -10; + } else if (*lwork < nw && ! lquery) { + *info = -12; + } + + if (*info == 0) { + +/* Compute the workspace requirements */ + + if (*m == 0 || *n == 0) { + lwkopt = 1; + } else { +/* Computing MIN */ +/* Writing concatenation */ + i__3[0] = 1, a__1[0] = side; + i__3[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + i__1 = 64, i__2 = ilaenv_(&c__1, (char *)"DORMQL", ch__1, m, n, k, &c_n1, + (ftnlen)6, (ftnlen)2); + nb = min(i__1,i__2); + lwkopt = nw * nb + 4160; + } + work[1] = (doublereal) lwkopt; + } + + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DORMQL", &i__1, (ftnlen)6); + return 0; + } else if (lquery) { + return 0; + } + +/* Quick return if possible */ + + if (*m == 0 || *n == 0) { + return 0; + } + + nbmin = 2; + ldwork = nw; + if (nb > 1 && nb < *k) { + if (*lwork < lwkopt) { + nb = (*lwork - 4160) / ldwork; +/* Computing MAX */ +/* Writing concatenation */ + i__3[0] = 1, a__1[0] = side; + i__3[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DORMQL", ch__1, m, n, k, &c_n1, ( + ftnlen)6, (ftnlen)2); + nbmin = max(i__1,i__2); + } + } + + if (nb < nbmin || nb >= *k) { + +/* Use unblocked code */ + + dorm2l_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[ + c_offset], ldc, &work[1], &iinfo, (ftnlen)1, (ftnlen)1); + } else { + +/* Use blocked code */ + + iwt = nw * nb + 1; + if (left && notran || ! left && ! notran) { + i1 = 1; + i2 = *k; + i3 = nb; + } else { + i1 = (*k - 1) / nb * nb + 1; + i2 = 1; + i3 = -nb; + } + + if (left) { + ni = *n; + } else { + mi = *m; + } + + i__1 = i2; + i__2 = i3; + for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { +/* Computing MIN */ + i__4 = nb, i__5 = *k - i__ + 1; + ib = min(i__4,i__5); + +/* Form the triangular factor of the block reflector */ +/* H = H(i+ib-1) . . . H(i+1) H(i) */ + + i__4 = nq - *k + i__ + ib - 1; + dlarft_((char *)"Backward", (char *)"Columnwise", &i__4, &ib, &a[i__ * a_dim1 + 1] + , lda, &tau[i__], &work[iwt], &c__65, (ftnlen)8, (ftnlen) + 10); + if (left) { + +/* H or H**T is applied to C(1:m-k+i+ib-1,1:n) */ + + mi = *m - *k + i__ + ib - 1; + } else { + +/* H or H**T is applied to C(1:m,1:n-k+i+ib-1) */ + + ni = *n - *k + i__ + ib - 1; + } + +/* Apply H or H**T */ + + dlarfb_(side, trans, (char *)"Backward", (char *)"Columnwise", &mi, &ni, &ib, &a[ + i__ * a_dim1 + 1], lda, &work[iwt], &c__65, &c__[c_offset] + , ldc, &work[1], &ldwork, (ftnlen)1, (ftnlen)1, (ftnlen)8, + (ftnlen)10); +/* L10: */ + } + } + work[1] = (doublereal) lwkopt; + return 0; + +/* End of DORMQL */ + +} /* dormql_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dormqr.cpp b/lib/linalg/dormqr.cpp new file mode 100644 index 0000000000..7fce43b587 --- /dev/null +++ b/lib/linalg/dormqr.cpp @@ -0,0 +1,417 @@ +/* fortran/dormqr.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c_n1 = -1; +static integer c__2 = 2; +static integer c__65 = 65; + +/* > \brief \b DORMQR */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DORMQR + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DORMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, */ +/* WORK, LWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER SIDE, TRANS */ +/* INTEGER INFO, K, LDA, LDC, LWORK, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DORMQR overwrites the general real M-by-N matrix C with */ +/* > */ +/* > SIDE = 'L' SIDE = 'R' */ +/* > TRANS = 'N': Q * C C * Q */ +/* > TRANS = 'T': Q**T * C C * Q**T */ +/* > */ +/* > where Q is a real orthogonal matrix defined as the product of k */ +/* > elementary reflectors */ +/* > */ +/* > Q = H(1) H(2) . . . H(k) */ +/* > */ +/* > as returned by DGEQRF. Q is of order M if SIDE = 'L' and of order N */ +/* > if SIDE = 'R'. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] SIDE */ +/* > \verbatim */ +/* > SIDE is CHARACTER*1 */ +/* > = 'L': apply Q or Q**T from the Left; */ +/* > = 'R': apply Q or Q**T from the Right. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TRANS */ +/* > \verbatim */ +/* > TRANS is CHARACTER*1 */ +/* > = 'N': No transpose, apply Q; */ +/* > = 'T': Transpose, apply Q**T. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix C. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix C. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > The number of elementary reflectors whose product defines */ +/* > the matrix Q. */ +/* > If SIDE = 'L', M >= K >= 0; */ +/* > if SIDE = 'R', N >= K >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,K) */ +/* > The i-th column must contain the vector which defines the */ +/* > elementary reflector H(i), for i = 1,2,...,k, as returned by */ +/* > DGEQRF in the first k columns of its array argument A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. */ +/* > If SIDE = 'L', LDA >= max(1,M); */ +/* > if SIDE = 'R', LDA >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TAU */ +/* > \verbatim */ +/* > TAU is DOUBLE PRECISION array, dimension (K) */ +/* > TAU(i) must contain the scalar factor of the elementary */ +/* > reflector H(i), as returned by DGEQRF. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] C */ +/* > \verbatim */ +/* > C is DOUBLE PRECISION array, dimension (LDC,N) */ +/* > On entry, the M-by-N matrix C. */ +/* > On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDC */ +/* > \verbatim */ +/* > LDC is INTEGER */ +/* > The leading dimension of the array C. LDC >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ +/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LWORK */ +/* > \verbatim */ +/* > LWORK is INTEGER */ +/* > The dimension of the array WORK. */ +/* > If SIDE = 'L', LWORK >= max(1,N); */ +/* > if SIDE = 'R', LWORK >= max(1,M). */ +/* > For good performance, LWORK should generally be larger. */ +/* > */ +/* > If LWORK = -1, then a workspace query is assumed; the routine */ +/* > only calculates the optimal size of the WORK array, returns */ +/* > this value as the first entry of the WORK array, and no error */ +/* > message related to LWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleOTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dormqr_(char *side, char *trans, integer *m, integer *n, + integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal * + c__, integer *ldc, doublereal *work, integer *lwork, integer *info, + ftnlen side_len, ftnlen trans_len) +{ + /* System generated locals */ + address a__1[2]; + integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4, + i__5; + char ch__1[2]; + + /* Builtin functions */ + /* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen); + + /* Local variables */ + integer i__, i1, i2, i3, ib, ic, jc, nb, mi, ni, nq, nw, iwt; + logical left; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + integer nbmin, iinfo; + extern /* Subroutine */ int dorm2r_(char *, char *, integer *, integer *, + integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, ftnlen, ftnlen), dlarfb_(char + *, char *, char *, char *, integer *, integer *, integer *, + doublereal *, integer *, doublereal *, integer *, doublereal *, + integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, + ftnlen), dlarft_(char *, char *, integer *, integer *, doublereal + *, integer *, doublereal *, doublereal *, integer *, ftnlen, + ftnlen), xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + logical notran; + integer ldwork, lwkopt; + logical lquery; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --tau; + c_dim1 = *ldc; + c_offset = 1 + c_dim1; + c__ -= c_offset; + --work; + + /* Function Body */ + *info = 0; + left = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); + notran = lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1); + lquery = *lwork == -1; + +/* NQ is the order of Q and NW is the minimum dimension of WORK */ + + if (left) { + nq = *m; + nw = max(1,*n); + } else { + nq = *n; + nw = max(1,*m); + } + if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + *info = -1; + } else if (! notran && ! lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1)) { + *info = -2; + } else if (*m < 0) { + *info = -3; + } else if (*n < 0) { + *info = -4; + } else if (*k < 0 || *k > nq) { + *info = -5; + } else if (*lda < max(1,nq)) { + *info = -7; + } else if (*ldc < max(1,*m)) { + *info = -10; + } else if (*lwork < nw && ! lquery) { + *info = -12; + } + + if (*info == 0) { + +/* Compute the workspace requirements */ + +/* Computing MIN */ +/* Writing concatenation */ + i__3[0] = 1, a__1[0] = side; + i__3[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + i__1 = 64, i__2 = ilaenv_(&c__1, (char *)"DORMQR", ch__1, m, n, k, &c_n1, ( + ftnlen)6, (ftnlen)2); + nb = min(i__1,i__2); + lwkopt = nw * nb + 4160; + work[1] = (doublereal) lwkopt; + } + + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DORMQR", &i__1, (ftnlen)6); + return 0; + } else if (lquery) { + return 0; + } + +/* Quick return if possible */ + + if (*m == 0 || *n == 0 || *k == 0) { + work[1] = 1.; + return 0; + } + + nbmin = 2; + ldwork = nw; + if (nb > 1 && nb < *k) { + if (*lwork < lwkopt) { + nb = (*lwork - 4160) / ldwork; +/* Computing MAX */ +/* Writing concatenation */ + i__3[0] = 1, a__1[0] = side; + i__3[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DORMQR", ch__1, m, n, k, &c_n1, ( + ftnlen)6, (ftnlen)2); + nbmin = max(i__1,i__2); + } + } + + if (nb < nbmin || nb >= *k) { + +/* Use unblocked code */ + + dorm2r_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[ + c_offset], ldc, &work[1], &iinfo, (ftnlen)1, (ftnlen)1); + } else { + +/* Use blocked code */ + + iwt = nw * nb + 1; + if (left && ! notran || ! left && notran) { + i1 = 1; + i2 = *k; + i3 = nb; + } else { + i1 = (*k - 1) / nb * nb + 1; + i2 = 1; + i3 = -nb; + } + + if (left) { + ni = *n; + jc = 1; + } else { + mi = *m; + ic = 1; + } + + i__1 = i2; + i__2 = i3; + for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { +/* Computing MIN */ + i__4 = nb, i__5 = *k - i__ + 1; + ib = min(i__4,i__5); + +/* Form the triangular factor of the block reflector */ +/* H = H(i) H(i+1) . . . H(i+ib-1) */ + + i__4 = nq - i__ + 1; + dlarft_((char *)"Forward", (char *)"Columnwise", &i__4, &ib, &a[i__ + i__ * + a_dim1], lda, &tau[i__], &work[iwt], &c__65, (ftnlen)7, ( + ftnlen)10); + if (left) { + +/* H or H**T is applied to C(i:m,1:n) */ + + mi = *m - i__ + 1; + ic = i__; + } else { + +/* H or H**T is applied to C(1:m,i:n) */ + + ni = *n - i__ + 1; + jc = i__; + } + +/* Apply H or H**T */ + + dlarfb_(side, trans, (char *)"Forward", (char *)"Columnwise", &mi, &ni, &ib, &a[ + i__ + i__ * a_dim1], lda, &work[iwt], &c__65, &c__[ic + + jc * c_dim1], ldc, &work[1], &ldwork, (ftnlen)1, (ftnlen) + 1, (ftnlen)7, (ftnlen)10); +/* L10: */ + } + } + work[1] = (doublereal) lwkopt; + return 0; + +/* End of DORMQR */ + +} /* dormqr_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dormtr.cpp b/lib/linalg/dormtr.cpp new file mode 100644 index 0000000000..d917e95b06 --- /dev/null +++ b/lib/linalg/dormtr.cpp @@ -0,0 +1,396 @@ +/* fortran/dormtr.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c_n1 = -1; +static integer c__2 = 2; + +/* > \brief \b DORMTR */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DORMTR + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DORMTR( SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC, */ +/* WORK, LWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER SIDE, TRANS, UPLO */ +/* INTEGER INFO, LDA, LDC, LWORK, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DORMTR overwrites the general real M-by-N matrix C with */ +/* > */ +/* > SIDE = 'L' SIDE = 'R' */ +/* > TRANS = 'N': Q * C C * Q */ +/* > TRANS = 'T': Q**T * C C * Q**T */ +/* > */ +/* > where Q is a real orthogonal matrix of order nq, with nq = m if */ +/* > SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of */ +/* > nq-1 elementary reflectors, as returned by DSYTRD: */ +/* > */ +/* > if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1); */ +/* > */ +/* > if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1). */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] SIDE */ +/* > \verbatim */ +/* > SIDE is CHARACTER*1 */ +/* > = 'L': apply Q or Q**T from the Left; */ +/* > = 'R': apply Q or Q**T from the Right. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > = 'U': Upper triangle of A contains elementary reflectors */ +/* > from DSYTRD; */ +/* > = 'L': Lower triangle of A contains elementary reflectors */ +/* > from DSYTRD. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TRANS */ +/* > \verbatim */ +/* > TRANS is CHARACTER*1 */ +/* > = 'N': No transpose, apply Q; */ +/* > = 'T': Transpose, apply Q**T. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix C. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix C. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension */ +/* > (LDA,M) if SIDE = 'L' */ +/* > (LDA,N) if SIDE = 'R' */ +/* > The vectors which define the elementary reflectors, as */ +/* > returned by DSYTRD. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. */ +/* > LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TAU */ +/* > \verbatim */ +/* > TAU is DOUBLE PRECISION array, dimension */ +/* > (M-1) if SIDE = 'L' */ +/* > (N-1) if SIDE = 'R' */ +/* > TAU(i) must contain the scalar factor of the elementary */ +/* > reflector H(i), as returned by DSYTRD. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] C */ +/* > \verbatim */ +/* > C is DOUBLE PRECISION array, dimension (LDC,N) */ +/* > On entry, the M-by-N matrix C. */ +/* > On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDC */ +/* > \verbatim */ +/* > LDC is INTEGER */ +/* > The leading dimension of the array C. LDC >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ +/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LWORK */ +/* > \verbatim */ +/* > LWORK is INTEGER */ +/* > The dimension of the array WORK. */ +/* > If SIDE = 'L', LWORK >= max(1,N); */ +/* > if SIDE = 'R', LWORK >= max(1,M). */ +/* > For optimum performance LWORK >= N*NB if SIDE = 'L', and */ +/* > LWORK >= M*NB if SIDE = 'R', where NB is the optimal */ +/* > blocksize. */ +/* > */ +/* > If LWORK = -1, then a workspace query is assumed; the routine */ +/* > only calculates the optimal size of the WORK array, returns */ +/* > this value as the first entry of the WORK array, and no error */ +/* > message related to LWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleOTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dormtr_(char *side, char *uplo, char *trans, integer *m, + integer *n, doublereal *a, integer *lda, doublereal *tau, doublereal * + c__, integer *ldc, doublereal *work, integer *lwork, integer *info, + ftnlen side_len, ftnlen uplo_len, ftnlen trans_len) +{ + /* System generated locals */ + address a__1[2]; + integer a_dim1, a_offset, c_dim1, c_offset, i__1[2], i__2, i__3; + char ch__1[2]; + + /* Builtin functions */ + /* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen); + + /* Local variables */ + integer i1, i2, nb, mi, ni, nq, nw; + logical left; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + integer iinfo; + logical upper; + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dormql_(char *, char *, integer *, integer *, + integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, integer *, ftnlen, ftnlen), + dormqr_(char *, char *, integer *, integer *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, integer *, ftnlen, ftnlen); + integer lwkopt; + logical lquery; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --tau; + c_dim1 = *ldc; + c_offset = 1 + c_dim1; + c__ -= c_offset; + --work; + + /* Function Body */ + *info = 0; + left = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); + upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); + lquery = *lwork == -1; + +/* NQ is the order of Q and NW is the minimum dimension of WORK */ + + if (left) { + nq = *m; + nw = max(1,*n); + } else { + nq = *n; + nw = max(1,*m); + } + if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + *info = -1; + } else if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + *info = -2; + } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, + (char *)"T", (ftnlen)1, (ftnlen)1)) { + *info = -3; + } else if (*m < 0) { + *info = -4; + } else if (*n < 0) { + *info = -5; + } else if (*lda < max(1,nq)) { + *info = -7; + } else if (*ldc < max(1,*m)) { + *info = -10; + } else if (*lwork < nw && ! lquery) { + *info = -12; + } + + if (*info == 0) { + if (upper) { + if (left) { +/* Writing concatenation */ + i__1[0] = 1, a__1[0] = side; + i__1[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); + i__2 = *m - 1; + i__3 = *m - 1; + nb = ilaenv_(&c__1, (char *)"DORMQL", ch__1, &i__2, n, &i__3, &c_n1, ( + ftnlen)6, (ftnlen)2); + } else { +/* Writing concatenation */ + i__1[0] = 1, a__1[0] = side; + i__1[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); + i__2 = *n - 1; + i__3 = *n - 1; + nb = ilaenv_(&c__1, (char *)"DORMQL", ch__1, m, &i__2, &i__3, &c_n1, ( + ftnlen)6, (ftnlen)2); + } + } else { + if (left) { +/* Writing concatenation */ + i__1[0] = 1, a__1[0] = side; + i__1[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); + i__2 = *m - 1; + i__3 = *m - 1; + nb = ilaenv_(&c__1, (char *)"DORMQR", ch__1, &i__2, n, &i__3, &c_n1, ( + ftnlen)6, (ftnlen)2); + } else { +/* Writing concatenation */ + i__1[0] = 1, a__1[0] = side; + i__1[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); + i__2 = *n - 1; + i__3 = *n - 1; + nb = ilaenv_(&c__1, (char *)"DORMQR", ch__1, m, &i__2, &i__3, &c_n1, ( + ftnlen)6, (ftnlen)2); + } + } + lwkopt = nw * nb; + work[1] = (doublereal) lwkopt; + } + + if (*info != 0) { + i__2 = -(*info); + xerbla_((char *)"DORMTR", &i__2, (ftnlen)6); + return 0; + } else if (lquery) { + return 0; + } + +/* Quick return if possible */ + + if (*m == 0 || *n == 0 || nq == 1) { + work[1] = 1.; + return 0; + } + + if (left) { + mi = *m - 1; + ni = *n; + } else { + mi = *m; + ni = *n - 1; + } + + if (upper) { + +/* Q was determined by a call to DSYTRD with UPLO = 'U' */ + + i__2 = nq - 1; + dormql_(side, trans, &mi, &ni, &i__2, &a[(a_dim1 << 1) + 1], lda, & + tau[1], &c__[c_offset], ldc, &work[1], lwork, &iinfo, (ftnlen) + 1, (ftnlen)1); + } else { + +/* Q was determined by a call to DSYTRD with UPLO = 'L' */ + + if (left) { + i1 = 2; + i2 = 1; + } else { + i1 = 1; + i2 = 2; + } + i__2 = nq - 1; + dormqr_(side, trans, &mi, &ni, &i__2, &a[a_dim1 + 2], lda, &tau[1], & + c__[i1 + i2 * c_dim1], ldc, &work[1], lwork, &iinfo, (ftnlen) + 1, (ftnlen)1); + } + work[1] = (doublereal) lwkopt; + return 0; + +/* End of DORMTR */ + +} /* dormtr_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dposv.cpp b/lib/linalg/dposv.cpp new file mode 100644 index 0000000000..6981ea843d --- /dev/null +++ b/lib/linalg/dposv.cpp @@ -0,0 +1,232 @@ +/* fortran/dposv.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief DPOSV computes the solution to system of linear equations A * X = B for PO matrices */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DPOSV + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DPOSV( UPLO, N, NRHS, A, LDA, B, LDB, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER UPLO */ +/* INTEGER INFO, LDA, LDB, N, NRHS */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), B( LDB, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DPOSV computes the solution to a real system of linear equations */ +/* > A * X = B, */ +/* > where A is an N-by-N symmetric positive definite matrix and X and B */ +/* > are N-by-NRHS matrices. */ +/* > */ +/* > The Cholesky decomposition is used to factor A as */ +/* > A = U**T* U, if UPLO = 'U', or */ +/* > A = L * L**T, if UPLO = 'L', */ +/* > where U is an upper triangular matrix and L is a lower triangular */ +/* > matrix. The factored form of A is then used to solve the system of */ +/* > equations A * X = B. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > = 'U': Upper triangle of A is stored; */ +/* > = 'L': Lower triangle of A is stored. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of linear equations, i.e., the order of the */ +/* > matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] NRHS */ +/* > \verbatim */ +/* > NRHS is INTEGER */ +/* > The number of right hand sides, i.e., the number of columns */ +/* > of the matrix B. NRHS >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On entry, the symmetric matrix A. If UPLO = 'U', the leading */ +/* > N-by-N upper triangular part of A contains the upper */ +/* > triangular part of the matrix A, and the strictly lower */ +/* > triangular part of A is not referenced. If UPLO = 'L', the */ +/* > leading N-by-N lower triangular part of A contains the lower */ +/* > triangular part of the matrix A, and the strictly upper */ +/* > triangular part of A is not referenced. */ +/* > */ +/* > On exit, if INFO = 0, the factor U or L from the Cholesky */ +/* > factorization A = U**T*U or A = L*L**T. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] B */ +/* > \verbatim */ +/* > B is DOUBLE PRECISION array, dimension (LDB,NRHS) */ +/* > On entry, the N-by-NRHS right hand side matrix B. */ +/* > On exit, if INFO = 0, the N-by-NRHS solution matrix X. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDB */ +/* > \verbatim */ +/* > LDB is INTEGER */ +/* > The leading dimension of the array B. LDB >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > > 0: if INFO = i, the leading minor of order i of A is not */ +/* > positive definite, so the factorization could not be */ +/* > completed, and the solution has not been computed. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doublePOsolve */ + +/* ===================================================================== */ +/* Subroutine */ int dposv_(char *uplo, integer *n, integer *nrhs, doublereal + *a, integer *lda, doublereal *b, integer *ldb, integer *info, ftnlen + uplo_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, b_dim1, b_offset, i__1; + + /* Local variables */ + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), dpotrf_( + char *, integer *, doublereal *, integer *, integer *, ftnlen), + dpotrs_(char *, integer *, integer *, doublereal *, integer *, + doublereal *, integer *, integer *, ftnlen); + + +/* -- LAPACK driver routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + b_dim1 = *ldb; + b_offset = 1 + b_dim1; + b -= b_offset; + + /* Function Body */ + *info = 0; + if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", ( + ftnlen)1, (ftnlen)1)) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } else if (*nrhs < 0) { + *info = -3; + } else if (*lda < max(1,*n)) { + *info = -5; + } else if (*ldb < max(1,*n)) { + *info = -7; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DPOSV ", &i__1, (ftnlen)6); + return 0; + } + +/* Compute the Cholesky factorization A = U**T*U or A = L*L**T. */ + + dpotrf_(uplo, n, &a[a_offset], lda, info, (ftnlen)1); + if (*info == 0) { + +/* Solve the system A*X = B, overwriting B with X. */ + + dpotrs_(uplo, n, nrhs, &a[a_offset], lda, &b[b_offset], ldb, info, ( + ftnlen)1); + + } + return 0; + +/* End of DPOSV */ + +} /* dposv_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dpotf2.cpp b/lib/linalg/dpotf2.cpp new file mode 100644 index 0000000000..e32a52c97c --- /dev/null +++ b/lib/linalg/dpotf2.cpp @@ -0,0 +1,294 @@ +/* fortran/dpotf2.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static doublereal c_b10 = -1.; +static doublereal c_b12 = 1.; + +/* > \brief \b DPOTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix (u +nblocked algorithm). */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DPOTF2 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DPOTF2( UPLO, N, A, LDA, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER UPLO */ +/* INTEGER INFO, LDA, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DPOTF2 computes the Cholesky factorization of a real symmetric */ +/* > positive definite matrix A. */ +/* > */ +/* > The factorization has the form */ +/* > A = U**T * U , if UPLO = 'U', or */ +/* > A = L * L**T, if UPLO = 'L', */ +/* > where U is an upper triangular matrix and L is lower triangular. */ +/* > */ +/* > This is the unblocked version of the algorithm, calling Level 2 BLAS. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > Specifies whether the upper or lower triangular part of the */ +/* > symmetric matrix A is stored. */ +/* > = 'U': Upper triangular */ +/* > = 'L': Lower triangular */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On entry, the symmetric matrix A. If UPLO = 'U', the leading */ +/* > n by n upper triangular part of A contains the upper */ +/* > triangular part of the matrix A, and the strictly lower */ +/* > triangular part of A is not referenced. If UPLO = 'L', the */ +/* > leading n by n lower triangular part of A contains the lower */ +/* > triangular part of the matrix A, and the strictly upper */ +/* > triangular part of A is not referenced. */ +/* > */ +/* > On exit, if INFO = 0, the factor U or L from the Cholesky */ +/* > factorization A = U**T *U or A = L*L**T. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -k, the k-th argument had an illegal value */ +/* > > 0: if INFO = k, the leading minor of order k is not */ +/* > positive definite, and the factorization could not be */ +/* > completed. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doublePOcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dpotf2_(char *uplo, integer *n, doublereal *a, integer * + lda, integer *info, ftnlen uplo_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3; + doublereal d__1; + + /* Builtin functions */ + double sqrt(doublereal); + + /* Local variables */ + integer j; + doublereal ajj; + extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, + integer *); + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *); + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int dgemv_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, ftnlen); + logical upper; + extern logical disnan_(doublereal *); + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + + /* Function Body */ + *info = 0; + upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); + if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } else if (*lda < max(1,*n)) { + *info = -4; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DPOTF2", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*n == 0) { + return 0; + } + + if (upper) { + +/* Compute the Cholesky factorization A = U**T *U. */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + +/* Compute U(J,J) and test for non-positive-definiteness. */ + + i__2 = j - 1; + ajj = a[j + j * a_dim1] - ddot_(&i__2, &a[j * a_dim1 + 1], &c__1, + &a[j * a_dim1 + 1], &c__1); + if (ajj <= 0. || disnan_(&ajj)) { + a[j + j * a_dim1] = ajj; + goto L30; + } + ajj = sqrt(ajj); + a[j + j * a_dim1] = ajj; + +/* Compute elements J+1:N of row J. */ + + if (j < *n) { + i__2 = j - 1; + i__3 = *n - j; + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b10, &a[(j + 1) * a_dim1 + + 1], lda, &a[j * a_dim1 + 1], &c__1, &c_b12, &a[j + ( + j + 1) * a_dim1], lda, (ftnlen)9); + i__2 = *n - j; + d__1 = 1. / ajj; + dscal_(&i__2, &d__1, &a[j + (j + 1) * a_dim1], lda); + } +/* L10: */ + } + } else { + +/* Compute the Cholesky factorization A = L*L**T. */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + +/* Compute L(J,J) and test for non-positive-definiteness. */ + + i__2 = j - 1; + ajj = a[j + j * a_dim1] - ddot_(&i__2, &a[j + a_dim1], lda, &a[j + + a_dim1], lda); + if (ajj <= 0. || disnan_(&ajj)) { + a[j + j * a_dim1] = ajj; + goto L30; + } + ajj = sqrt(ajj); + a[j + j * a_dim1] = ajj; + +/* Compute elements J+1:N of column J. */ + + if (j < *n) { + i__2 = *n - j; + i__3 = j - 1; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b10, &a[j + 1 + + a_dim1], lda, &a[j + a_dim1], lda, &c_b12, &a[j + 1 + + j * a_dim1], &c__1, (ftnlen)12); + i__2 = *n - j; + d__1 = 1. / ajj; + dscal_(&i__2, &d__1, &a[j + 1 + j * a_dim1], &c__1); + } +/* L20: */ + } + } + goto L40; + +L30: + *info = j; + +L40: + return 0; + +/* End of DPOTF2 */ + +} /* dpotf2_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dpotrf.cpp b/lib/linalg/dpotrf.cpp new file mode 100644 index 0000000000..cd343efd77 --- /dev/null +++ b/lib/linalg/dpotrf.cpp @@ -0,0 +1,322 @@ +/* fortran/dpotrf.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c_n1 = -1; +static doublereal c_b13 = -1.; +static doublereal c_b14 = 1.; + +/* > \brief \b DPOTRF */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DPOTRF + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DPOTRF( UPLO, N, A, LDA, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER UPLO */ +/* INTEGER INFO, LDA, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DPOTRF computes the Cholesky factorization of a real symmetric */ +/* > positive definite matrix A. */ +/* > */ +/* > The factorization has the form */ +/* > A = U**T * U, if UPLO = 'U', or */ +/* > A = L * L**T, if UPLO = 'L', */ +/* > where U is an upper triangular matrix and L is lower triangular. */ +/* > */ +/* > This is the block version of the algorithm, calling Level 3 BLAS. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > = 'U': Upper triangle of A is stored; */ +/* > = 'L': Lower triangle of A is stored. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On entry, the symmetric matrix A. If UPLO = 'U', the leading */ +/* > N-by-N upper triangular part of A contains the upper */ +/* > triangular part of the matrix A, and the strictly lower */ +/* > triangular part of A is not referenced. If UPLO = 'L', the */ +/* > leading N-by-N lower triangular part of A contains the lower */ +/* > triangular part of the matrix A, and the strictly upper */ +/* > triangular part of A is not referenced. */ +/* > */ +/* > On exit, if INFO = 0, the factor U or L from the Cholesky */ +/* > factorization A = U**T*U or A = L*L**T. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > > 0: if INFO = i, the leading minor of order i is not */ +/* > positive definite, and the factorization could not be */ +/* > completed. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doublePOcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dpotrf_(char *uplo, integer *n, doublereal *a, integer * + lda, integer *info, ftnlen uplo_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3, i__4; + + /* Local variables */ + integer j, jb, nb; + extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, + integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + logical upper; + extern /* Subroutine */ int dsyrk_(char *, char *, integer *, integer *, + doublereal *, doublereal *, integer *, doublereal *, doublereal *, + integer *, ftnlen, ftnlen), xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dpotrf2_(char *, integer *, doublereal *, + integer *, integer *, ftnlen); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + + /* Function Body */ + *info = 0; + upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); + if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } else if (*lda < max(1,*n)) { + *info = -4; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DPOTRF", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*n == 0) { + return 0; + } + +/* Determine the block size for this environment. */ + + nb = ilaenv_(&c__1, (char *)"DPOTRF", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, ( + ftnlen)1); + if (nb <= 1 || nb >= *n) { + +/* Use unblocked code. */ + + dpotrf2_(uplo, n, &a[a_offset], lda, info, (ftnlen)1); + } else { + +/* Use blocked code. */ + + if (upper) { + +/* Compute the Cholesky factorization A = U**T*U. */ + + i__1 = *n; + i__2 = nb; + for (j = 1; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) { + +/* Update and factorize the current diagonal block and test */ +/* for non-positive-definiteness. */ + +/* Computing MIN */ + i__3 = nb, i__4 = *n - j + 1; + jb = min(i__3,i__4); + i__3 = j - 1; + dsyrk_((char *)"Upper", (char *)"Transpose", &jb, &i__3, &c_b13, &a[j * + a_dim1 + 1], lda, &c_b14, &a[j + j * a_dim1], lda, ( + ftnlen)5, (ftnlen)9); + dpotrf2_((char *)"Upper", &jb, &a[j + j * a_dim1], lda, info, (ftnlen) + 5); + if (*info != 0) { + goto L30; + } + if (j + jb <= *n) { + +/* Compute the current block row. */ + + i__3 = *n - j - jb + 1; + i__4 = j - 1; + dgemm_((char *)"Transpose", (char *)"No transpose", &jb, &i__3, &i__4, & + c_b13, &a[j * a_dim1 + 1], lda, &a[(j + jb) * + a_dim1 + 1], lda, &c_b14, &a[j + (j + jb) * + a_dim1], lda, (ftnlen)9, (ftnlen)12); + i__3 = *n - j - jb + 1; + dtrsm_((char *)"Left", (char *)"Upper", (char *)"Transpose", (char *)"Non-unit", &jb, & + i__3, &c_b14, &a[j + j * a_dim1], lda, &a[j + (j + + jb) * a_dim1], lda, (ftnlen)4, (ftnlen)5, ( + ftnlen)9, (ftnlen)8); + } +/* L10: */ + } + + } else { + +/* Compute the Cholesky factorization A = L*L**T. */ + + i__2 = *n; + i__1 = nb; + for (j = 1; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) { + +/* Update and factorize the current diagonal block and test */ +/* for non-positive-definiteness. */ + +/* Computing MIN */ + i__3 = nb, i__4 = *n - j + 1; + jb = min(i__3,i__4); + i__3 = j - 1; + dsyrk_((char *)"Lower", (char *)"No transpose", &jb, &i__3, &c_b13, &a[j + + a_dim1], lda, &c_b14, &a[j + j * a_dim1], lda, ( + ftnlen)5, (ftnlen)12); + dpotrf2_((char *)"Lower", &jb, &a[j + j * a_dim1], lda, info, (ftnlen) + 5); + if (*info != 0) { + goto L30; + } + if (j + jb <= *n) { + +/* Compute the current block column. */ + + i__3 = *n - j - jb + 1; + i__4 = j - 1; + dgemm_((char *)"No transpose", (char *)"Transpose", &i__3, &jb, &i__4, & + c_b13, &a[j + jb + a_dim1], lda, &a[j + a_dim1], + lda, &c_b14, &a[j + jb + j * a_dim1], lda, ( + ftnlen)12, (ftnlen)9); + i__3 = *n - j - jb + 1; + dtrsm_((char *)"Right", (char *)"Lower", (char *)"Transpose", (char *)"Non-unit", &i__3, & + jb, &c_b14, &a[j + j * a_dim1], lda, &a[j + jb + + j * a_dim1], lda, (ftnlen)5, (ftnlen)5, (ftnlen)9, + (ftnlen)8); + } +/* L20: */ + } + } + } + goto L40; + +L30: + *info = *info + j - 1; + +L40: + return 0; + +/* End of DPOTRF */ + +} /* dpotrf_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dpotrf2.cpp b/lib/linalg/dpotrf2.cpp new file mode 100644 index 0000000000..9b882bb9e0 --- /dev/null +++ b/lib/linalg/dpotrf2.cpp @@ -0,0 +1,285 @@ +/* static/dpotrf2.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static doublereal c_b9 = 1.; +static doublereal c_b11 = -1.; + +/* > \brief \b DPOTRF2 */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* RECURSIVE SUBROUTINE DPOTRF2( UPLO, N, A, LDA, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER UPLO */ +/* INTEGER INFO, LDA, N */ +/* .. */ +/* .. Array Arguments .. */ +/* REAL A( LDA, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DPOTRF2 computes the Cholesky factorization of a real symmetric */ +/* > positive definite matrix A using the recursive algorithm. */ +/* > */ +/* > The factorization has the form */ +/* > A = U**T * U, if UPLO = 'U', or */ +/* > A = L * L**T, if UPLO = 'L', */ +/* > where U is an upper triangular matrix and L is lower triangular. */ +/* > */ +/* > This is the recursive version of the algorithm. It divides */ +/* > the matrix into four submatrices: */ +/* > */ +/* > [ A11 | A12 ] where A11 is n1 by n1 and A22 is n2 by n2 */ +/* > A = [ -----|----- ] with n1 = n/2 */ +/* > [ A21 | A22 ] n2 = n-n1 */ +/* > */ +/* > The subroutine calls itself to factor A11. Update and scale A21 */ +/* > or A12, update A22 then calls itself to factor A22. */ +/* > */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > = 'U': Upper triangle of A is stored; */ +/* > = 'L': Lower triangle of A is stored. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On entry, the symmetric matrix A. If UPLO = 'U', the leading */ +/* > N-by-N upper triangular part of A contains the upper */ +/* > triangular part of the matrix A, and the strictly lower */ +/* > triangular part of A is not referenced. If UPLO = 'L', the */ +/* > leading N-by-N lower triangular part of A contains the lower */ +/* > triangular part of the matrix A, and the strictly upper */ +/* > triangular part of A is not referenced. */ +/* > */ +/* > On exit, if INFO = 0, the factor U or L from the Cholesky */ +/* > factorization A = U**T*U or A = L*L**T. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > > 0: if INFO = i, the leading minor of order i is not */ +/* > positive definite, and the factorization could not be */ +/* > completed. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doublePOcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dpotrf2_(char *uplo, integer *n, doublereal *a, integer * + lda, integer *info, ftnlen uplo_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1; + + /* Builtin functions */ + double sqrt(doublereal); + + /* Local variables */ + integer n1, n2; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + integer iinfo; + extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, + integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + logical upper; + extern /* Subroutine */ int dsyrk_(char *, char *, integer *, integer *, + doublereal *, doublereal *, integer *, doublereal *, doublereal *, + integer *, ftnlen, ftnlen); + extern logical disnan_(doublereal *); + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + + /* Function Body */ + *info = 0; + upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); + if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } else if (*lda < max(1,*n)) { + *info = -4; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DPOTRF2", &i__1, (ftnlen)7); + return 0; + } + +/* Quick return if possible */ + + if (*n == 0) { + return 0; + } + +/* N=1 case */ + + if (*n == 1) { + +/* Test for non-positive-definiteness */ + + if (a[a_dim1 + 1] <= 0. || disnan_(&a[a_dim1 + 1])) { + *info = 1; + return 0; + } + +/* Factor */ + + a[a_dim1 + 1] = sqrt(a[a_dim1 + 1]); + +/* Use recursive code */ + + } else { + n1 = *n / 2; + n2 = *n - n1; + +/* Factor A11 */ + + dpotrf2_(uplo, &n1, &a[a_dim1 + 1], lda, &iinfo, (ftnlen)1); + if (iinfo != 0) { + *info = iinfo; + return 0; + } + +/* Compute the Cholesky factorization A = U**T*U */ + + if (upper) { + +/* Update and scale A12 */ + + dtrsm_((char *)"L", (char *)"U", (char *)"T", (char *)"N", &n1, &n2, &c_b9, &a[a_dim1 + 1], lda, & + a[(n1 + 1) * a_dim1 + 1], lda, (ftnlen)1, (ftnlen)1, ( + ftnlen)1, (ftnlen)1); + +/* Update and factor A22 */ + + dsyrk_(uplo, (char *)"T", &n2, &n1, &c_b11, &a[(n1 + 1) * a_dim1 + 1], + lda, &c_b9, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, (ftnlen) + 1, (ftnlen)1); + dpotrf2_(uplo, &n2, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, &iinfo, ( + ftnlen)1); + if (iinfo != 0) { + *info = iinfo + n1; + return 0; + } + +/* Compute the Cholesky factorization A = L*L**T */ + + } else { + +/* Update and scale A21 */ + + dtrsm_((char *)"R", (char *)"L", (char *)"T", (char *)"N", &n2, &n1, &c_b9, &a[a_dim1 + 1], lda, & + a[n1 + 1 + a_dim1], lda, (ftnlen)1, (ftnlen)1, (ftnlen)1, + (ftnlen)1); + +/* Update and factor A22 */ + + dsyrk_(uplo, (char *)"N", &n2, &n1, &c_b11, &a[n1 + 1 + a_dim1], lda, & + c_b9, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, (ftnlen)1, ( + ftnlen)1); + dpotrf2_(uplo, &n2, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, &iinfo, ( + ftnlen)1); + if (iinfo != 0) { + *info = iinfo + n1; + return 0; + } + } + } + return 0; + +/* End of DPOTRF2 */ + +} /* dpotrf2_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dpotrs.cpp b/lib/linalg/dpotrs.cpp new file mode 100644 index 0000000000..169f851130 --- /dev/null +++ b/lib/linalg/dpotrs.cpp @@ -0,0 +1,248 @@ +/* fortran/dpotrs.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static doublereal c_b9 = 1.; + +/* > \brief \b DPOTRS */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DPOTRS + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DPOTRS( UPLO, N, NRHS, A, LDA, B, LDB, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER UPLO */ +/* INTEGER INFO, LDA, LDB, N, NRHS */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), B( LDB, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DPOTRS solves a system of linear equations A*X = B with a symmetric */ +/* > positive definite matrix A using the Cholesky factorization */ +/* > A = U**T*U or A = L*L**T computed by DPOTRF. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > = 'U': Upper triangle of A is stored; */ +/* > = 'L': Lower triangle of A is stored. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] NRHS */ +/* > \verbatim */ +/* > NRHS is INTEGER */ +/* > The number of right hand sides, i.e., the number of columns */ +/* > of the matrix B. NRHS >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > The triangular factor U or L from the Cholesky factorization */ +/* > A = U**T*U or A = L*L**T, as computed by DPOTRF. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] B */ +/* > \verbatim */ +/* > B is DOUBLE PRECISION array, dimension (LDB,NRHS) */ +/* > On entry, the right hand side matrix B. */ +/* > On exit, the solution matrix X. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDB */ +/* > \verbatim */ +/* > LDB is INTEGER */ +/* > The leading dimension of the array B. LDB >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doublePOcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dpotrs_(char *uplo, integer *n, integer *nrhs, + doublereal *a, integer *lda, doublereal *b, integer *ldb, integer * + info, ftnlen uplo_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, b_dim1, b_offset, i__1; + + /* Local variables */ + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, + integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + logical upper; + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + b_dim1 = *ldb; + b_offset = 1 + b_dim1; + b -= b_offset; + + /* Function Body */ + *info = 0; + upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); + if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } else if (*nrhs < 0) { + *info = -3; + } else if (*lda < max(1,*n)) { + *info = -5; + } else if (*ldb < max(1,*n)) { + *info = -7; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DPOTRS", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*n == 0 || *nrhs == 0) { + return 0; + } + + if (upper) { + +/* Solve A*X = B where A = U**T *U. */ + +/* Solve U**T *X = B, overwriting B with X. */ + + dtrsm_((char *)"Left", (char *)"Upper", (char *)"Transpose", (char *)"Non-unit", n, nrhs, &c_b9, &a[ + a_offset], lda, &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, ( + ftnlen)9, (ftnlen)8); + +/* Solve U*X = B, overwriting B with X. */ + + dtrsm_((char *)"Left", (char *)"Upper", (char *)"No transpose", (char *)"Non-unit", n, nrhs, &c_b9, & + a[a_offset], lda, &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, ( + ftnlen)12, (ftnlen)8); + } else { + +/* Solve A*X = B where A = L*L**T. */ + +/* Solve L*X = B, overwriting B with X. */ + + dtrsm_((char *)"Left", (char *)"Lower", (char *)"No transpose", (char *)"Non-unit", n, nrhs, &c_b9, & + a[a_offset], lda, &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, ( + ftnlen)12, (ftnlen)8); + +/* Solve L**T *X = B, overwriting B with X. */ + + dtrsm_((char *)"Left", (char *)"Lower", (char *)"Transpose", (char *)"Non-unit", n, nrhs, &c_b9, &a[ + a_offset], lda, &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, ( + ftnlen)9, (ftnlen)8); + } + + return 0; + +/* End of DPOTRS */ + +} /* dpotrs_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/drot.cpp b/lib/linalg/drot.cpp new file mode 100644 index 0000000000..efd339cdf0 --- /dev/null +++ b/lib/linalg/drot.cpp @@ -0,0 +1,180 @@ +/* fortran/drot.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DROT */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DROT(N,DX,INCX,DY,INCY,C,S) */ + +/* .. Scalar Arguments .. */ +/* DOUBLE PRECISION C,S */ +/* INTEGER INCX,INCY,N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION DX(*),DY(*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DROT applies a plane rotation. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > number of elements in input vector(s) */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] DX */ +/* > \verbatim */ +/* > DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > storage spacing between elements of DX */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] DY */ +/* > \verbatim */ +/* > DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCY */ +/* > \verbatim */ +/* > INCY is INTEGER */ +/* > storage spacing between elements of DY */ +/* > \endverbatim */ +/* > */ +/* > \param[in] C */ +/* > \verbatim */ +/* > C is DOUBLE PRECISION */ +/* > \endverbatim */ +/* > */ +/* > \param[in] S */ +/* > \verbatim */ +/* > S is DOUBLE PRECISION */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup double_blas_level1 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > jack dongarra, linpack, 3/11/78. */ +/* > modified 12/3/93, array(1) declarations changed to array(*) */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int drot_(integer *n, doublereal *dx, integer *incx, + doublereal *dy, integer *incy, doublereal *c__, doublereal *s) +{ + /* System generated locals */ + integer i__1; + + /* Local variables */ + integer i__, ix, iy; + doublereal dtemp; + + +/* -- Reference BLAS level1 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ + /* Parameter adjustments */ + --dy; + --dx; + + /* Function Body */ + if (*n <= 0) { + return 0; + } + if (*incx == 1 && *incy == 1) { + +/* code for both increments equal to 1 */ + + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + dtemp = *c__ * dx[i__] + *s * dy[i__]; + dy[i__] = *c__ * dy[i__] - *s * dx[i__]; + dx[i__] = dtemp; + } + } else { + +/* code for unequal increments or equal increments not equal */ +/* to 1 */ + + ix = 1; + iy = 1; + if (*incx < 0) { + ix = (-(*n) + 1) * *incx + 1; + } + if (*incy < 0) { + iy = (-(*n) + 1) * *incy + 1; + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + dtemp = *c__ * dx[ix] + *s * dy[iy]; + dy[iy] = *c__ * dy[iy] - *s * dx[ix]; + dx[ix] = dtemp; + ix += *incx; + iy += *incy; + } + } + return 0; + +/* End of DROT */ + +} /* drot_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/drscl.cpp b/lib/linalg/drscl.cpp new file mode 100644 index 0000000000..041c7fbba3 --- /dev/null +++ b/lib/linalg/drscl.cpp @@ -0,0 +1,200 @@ +/* fortran/drscl.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DRSCL multiplies a vector by the reciprocal of a real scalar. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DRSCL + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DRSCL( N, SA, SX, INCX ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INCX, N */ +/* DOUBLE PRECISION SA */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION SX( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DRSCL multiplies an n-element real vector x by the real scalar 1/a. */ +/* > This is done without overflow or underflow as long as */ +/* > the final result x/a does not overflow or underflow. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of components of the vector x. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] SA */ +/* > \verbatim */ +/* > SA is DOUBLE PRECISION */ +/* > The scalar a which is used to divide each component of x. */ +/* > SA must be >= 0, or the subroutine will divide by zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] SX */ +/* > \verbatim */ +/* > SX is DOUBLE PRECISION array, dimension */ +/* > (1+(N-1)*abs(INCX)) */ +/* > The n-element vector x. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > The increment between successive values of the vector SX. */ +/* > > 0: SX(1) = X(1) and SX(1+(i-1)*INCX) = x(i), 1< i<= n */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleOTHERauxiliary */ + +/* ===================================================================== */ +/* Subroutine */ int drscl_(integer *n, doublereal *sa, doublereal *sx, + integer *incx) +{ + doublereal mul, cden; + logical done; + doublereal cnum, cden1, cnum1; + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *), dlabad_(doublereal *, doublereal *); + extern doublereal dlamch_(char *, ftnlen); + doublereal bignum, smlnum; + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Quick return if possible */ + + /* Parameter adjustments */ + --sx; + + /* Function Body */ + if (*n <= 0) { + return 0; + } + +/* Get machine parameters */ + + smlnum = dlamch_((char *)"S", (ftnlen)1); + bignum = 1. / smlnum; + dlabad_(&smlnum, &bignum); + +/* Initialize the denominator to SA and the numerator to 1. */ + + cden = *sa; + cnum = 1.; + +L10: + cden1 = cden * smlnum; + cnum1 = cnum / bignum; + if (abs(cden1) > abs(cnum) && cnum != 0.) { + +/* Pre-multiply X by SMLNUM if CDEN is large compared to CNUM. */ + + mul = smlnum; + done = FALSE_; + cden = cden1; + } else if (abs(cnum1) > abs(cden)) { + +/* Pre-multiply X by BIGNUM if CDEN is small compared to CNUM. */ + + mul = bignum; + done = FALSE_; + cnum = cnum1; + } else { + +/* Multiply X by CNUM / CDEN and return. */ + + mul = cnum / cden; + done = TRUE_; + } + +/* Scale the vector X by MUL */ + + dscal_(n, &mul, &sx[1], incx); + + if (! done) { + goto L10; + } + + return 0; + +/* End of DRSCL */ + +} /* drscl_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dscal.cpp b/lib/linalg/dscal.cpp new file mode 100644 index 0000000000..d1fc1d43ee --- /dev/null +++ b/lib/linalg/dscal.cpp @@ -0,0 +1,173 @@ +/* fortran/dscal.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DSCAL */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DSCAL(N,DA,DX,INCX) */ + +/* .. Scalar Arguments .. */ +/* DOUBLE PRECISION DA */ +/* INTEGER INCX,N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION DX(*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DSCAL scales a vector by a constant. */ +/* > uses unrolled loops for increment equal to 1. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > number of elements in input vector(s) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DA */ +/* > \verbatim */ +/* > DA is DOUBLE PRECISION */ +/* > On entry, DA specifies the scalar alpha. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] DX */ +/* > \verbatim */ +/* > DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > storage spacing between elements of DX */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup double_blas_level1 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > jack dongarra, linpack, 3/11/78. */ +/* > modified 3/93 to return if incx .le. 0. */ +/* > modified 12/3/93, array(1) declarations changed to array(*) */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dscal_(integer *n, doublereal *da, doublereal *dx, + integer *incx) +{ + /* System generated locals */ + integer i__1, i__2; + + /* Local variables */ + integer i__, m, mp1, nincx; + + +/* -- Reference BLAS level1 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. Parameters .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ + /* Parameter adjustments */ + --dx; + + /* Function Body */ + if (*n <= 0 || *incx <= 0 || *da == 1.) { + return 0; + } + if (*incx == 1) { + +/* code for increment equal to 1 */ + + +/* clean-up loop */ + + m = *n % 5; + if (m != 0) { + i__1 = m; + for (i__ = 1; i__ <= i__1; ++i__) { + dx[i__] = *da * dx[i__]; + } + if (*n < 5) { + return 0; + } + } + mp1 = m + 1; + i__1 = *n; + for (i__ = mp1; i__ <= i__1; i__ += 5) { + dx[i__] = *da * dx[i__]; + dx[i__ + 1] = *da * dx[i__ + 1]; + dx[i__ + 2] = *da * dx[i__ + 2]; + dx[i__ + 3] = *da * dx[i__ + 3]; + dx[i__ + 4] = *da * dx[i__ + 4]; + } + } else { + +/* code for increment not equal to 1 */ + + nincx = *n * *incx; + i__1 = nincx; + i__2 = *incx; + for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { + dx[i__] = *da * dx[i__]; + } + } + return 0; + +/* End of DSCAL */ + +} /* dscal_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dstedc.cpp b/lib/linalg/dstedc.cpp new file mode 100644 index 0000000000..e71b373994 --- /dev/null +++ b/lib/linalg/dstedc.cpp @@ -0,0 +1,576 @@ +/* fortran/dstedc.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__9 = 9; +static integer c__0 = 0; +static integer c__2 = 2; +static doublereal c_b17 = 0.; +static doublereal c_b18 = 1.; +static integer c__1 = 1; + +/* > \brief \b DSTEDC */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DSTEDC + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, */ +/* LIWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER COMPZ */ +/* INTEGER INFO, LDZ, LIWORK, LWORK, N */ +/* .. */ +/* .. Array Arguments .. */ +/* INTEGER IWORK( * ) */ +/* DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DSTEDC computes all eigenvalues and, optionally, eigenvectors of a */ +/* > symmetric tridiagonal matrix using the divide and conquer method. */ +/* > The eigenvectors of a full or band real symmetric matrix can also be */ +/* > found if DSYTRD or DSPTRD or DSBTRD has been used to reduce this */ +/* > matrix to tridiagonal form. */ +/* > */ +/* > This code makes very mild assumptions about floating point */ +/* > arithmetic. It will work on machines with a guard digit in */ +/* > add/subtract, or on those binary machines without guard digits */ +/* > which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. */ +/* > It could conceivably fail on hexadecimal or decimal machines */ +/* > without guard digits, but we know of none. See DLAED3 for details. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] COMPZ */ +/* > \verbatim */ +/* > COMPZ is CHARACTER*1 */ +/* > = 'N': Compute eigenvalues only. */ +/* > = 'I': Compute eigenvectors of tridiagonal matrix also. */ +/* > = 'V': Compute eigenvectors of original dense symmetric */ +/* > matrix also. On entry, Z contains the orthogonal */ +/* > matrix used to reduce the original matrix to */ +/* > tridiagonal form. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The dimension of the symmetric tridiagonal matrix. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension (N) */ +/* > On entry, the diagonal elements of the tridiagonal matrix. */ +/* > On exit, if INFO = 0, the eigenvalues in ascending order. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] E */ +/* > \verbatim */ +/* > E is DOUBLE PRECISION array, dimension (N-1) */ +/* > On entry, the subdiagonal elements of the tridiagonal matrix. */ +/* > On exit, E has been destroyed. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] Z */ +/* > \verbatim */ +/* > Z is DOUBLE PRECISION array, dimension (LDZ,N) */ +/* > On entry, if COMPZ = 'V', then Z contains the orthogonal */ +/* > matrix used in the reduction to tridiagonal form. */ +/* > On exit, if INFO = 0, then if COMPZ = 'V', Z contains the */ +/* > orthonormal eigenvectors of the original symmetric matrix, */ +/* > and if COMPZ = 'I', Z contains the orthonormal eigenvectors */ +/* > of the symmetric tridiagonal matrix. */ +/* > If COMPZ = 'N', then Z is not referenced. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDZ */ +/* > \verbatim */ +/* > LDZ is INTEGER */ +/* > The leading dimension of the array Z. LDZ >= 1. */ +/* > If eigenvectors are desired, then LDZ >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ +/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LWORK */ +/* > \verbatim */ +/* > LWORK is INTEGER */ +/* > The dimension of the array WORK. */ +/* > If COMPZ = 'N' or N <= 1 then LWORK must be at least 1. */ +/* > If COMPZ = 'V' and N > 1 then LWORK must be at least */ +/* > ( 1 + 3*N + 2*N*lg N + 4*N**2 ), */ +/* > where lg( N ) = smallest integer k such */ +/* > that 2**k >= N. */ +/* > If COMPZ = 'I' and N > 1 then LWORK must be at least */ +/* > ( 1 + 4*N + N**2 ). */ +/* > Note that for COMPZ = 'I' or 'V', then if N is less than or */ +/* > equal to the minimum divide size, usually 25, then LWORK need */ +/* > only be max(1,2*(N-1)). */ +/* > */ +/* > If LWORK = -1, then a workspace query is assumed; the routine */ +/* > only calculates the optimal size of the WORK array, returns */ +/* > this value as the first entry of the WORK array, and no error */ +/* > message related to LWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] IWORK */ +/* > \verbatim */ +/* > IWORK is INTEGER array, dimension (MAX(1,LIWORK)) */ +/* > On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LIWORK */ +/* > \verbatim */ +/* > LIWORK is INTEGER */ +/* > The dimension of the array IWORK. */ +/* > If COMPZ = 'N' or N <= 1 then LIWORK must be at least 1. */ +/* > If COMPZ = 'V' and N > 1 then LIWORK must be at least */ +/* > ( 6 + 6*N + 5*N*lg N ). */ +/* > If COMPZ = 'I' and N > 1 then LIWORK must be at least */ +/* > ( 3 + 5*N ). */ +/* > Note that for COMPZ = 'I' or 'V', then if N is less than or */ +/* > equal to the minimum divide size, usually 25, then LIWORK */ +/* > need only be 1. */ +/* > */ +/* > If LIWORK = -1, then a workspace query is assumed; the */ +/* > routine only calculates the optimal size of the IWORK array, */ +/* > returns this value as the first entry of the IWORK array, and */ +/* > no error message related to LIWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit. */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ +/* > > 0: The algorithm failed to compute an eigenvalue while */ +/* > working on the submatrix lying in rows and columns */ +/* > INFO/(N+1) through mod(INFO,N+1). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup auxOTHERcomputational */ + +/* > \par Contributors: */ +/* ================== */ +/* > */ +/* > Jeff Rutter, Computer Science Division, University of California */ +/* > at Berkeley, USA \n */ +/* > Modified by Francoise Tisseur, University of Tennessee */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dstedc_(char *compz, integer *n, doublereal *d__, + doublereal *e, doublereal *z__, integer *ldz, doublereal *work, + integer *lwork, integer *iwork, integer *liwork, integer *info, + ftnlen compz_len) +{ + /* System generated locals */ + integer z_dim1, z_offset, i__1, i__2; + doublereal d__1, d__2; + + /* Builtin functions */ + double log(doublereal); + integer pow_ii(integer *, integer *); + double sqrt(doublereal); + + /* Local variables */ + integer i__, j, k, m; + doublereal p; + integer ii, lgn; + doublereal eps, tiny; + extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, + doublereal *, integer *); + integer lwmin; + extern /* Subroutine */ int dlaed0_(integer *, integer *, integer *, + doublereal *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, integer *, integer *); + integer start; + extern doublereal dlamch_(char *, ftnlen); + extern /* Subroutine */ int dlascl_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, integer *, doublereal *, + integer *, integer *, ftnlen), dlacpy_(char *, integer *, integer + *, doublereal *, integer *, doublereal *, integer *, ftnlen), + dlaset_(char *, integer *, integer *, doublereal *, doublereal *, + doublereal *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + integer finish; + extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *, + ftnlen); + extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *, + integer *), dlasrt_(char *, integer *, doublereal *, integer *, + ftnlen); + integer liwmin, icompz; + extern /* Subroutine */ int dsteqr_(char *, integer *, doublereal *, + doublereal *, doublereal *, integer *, doublereal *, integer *, + ftnlen); + doublereal orgnrm; + logical lquery; + integer smlsiz, storez, strtrw; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --d__; + --e; + z_dim1 = *ldz; + z_offset = 1 + z_dim1; + z__ -= z_offset; + --work; + --iwork; + + /* Function Body */ + *info = 0; + lquery = *lwork == -1 || *liwork == -1; + + if (lsame_(compz, (char *)"N", (ftnlen)1, (ftnlen)1)) { + icompz = 0; + } else if (lsame_(compz, (char *)"V", (ftnlen)1, (ftnlen)1)) { + icompz = 1; + } else if (lsame_(compz, (char *)"I", (ftnlen)1, (ftnlen)1)) { + icompz = 2; + } else { + icompz = -1; + } + if (icompz < 0) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } else if (*ldz < 1 || icompz > 0 && *ldz < max(1,*n)) { + *info = -6; + } + + if (*info == 0) { + +/* Compute the workspace requirements */ + + smlsiz = ilaenv_(&c__9, (char *)"DSTEDC", (char *)" ", &c__0, &c__0, &c__0, &c__0, ( + ftnlen)6, (ftnlen)1); + if (*n <= 1 || icompz == 0) { + liwmin = 1; + lwmin = 1; + } else if (*n <= smlsiz) { + liwmin = 1; + lwmin = *n - 1 << 1; + } else { + lgn = (integer) (log((doublereal) (*n)) / log(2.)); + if (pow_ii(&c__2, &lgn) < *n) { + ++lgn; + } + if (pow_ii(&c__2, &lgn) < *n) { + ++lgn; + } + if (icompz == 1) { +/* Computing 2nd power */ + i__1 = *n; + lwmin = *n * 3 + 1 + (*n << 1) * lgn + (i__1 * i__1 << 2); + liwmin = *n * 6 + 6 + *n * 5 * lgn; + } else if (icompz == 2) { +/* Computing 2nd power */ + i__1 = *n; + lwmin = (*n << 2) + 1 + i__1 * i__1; + liwmin = *n * 5 + 3; + } + } + work[1] = (doublereal) lwmin; + iwork[1] = liwmin; + + if (*lwork < lwmin && ! lquery) { + *info = -8; + } else if (*liwork < liwmin && ! lquery) { + *info = -10; + } + } + + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DSTEDC", &i__1, (ftnlen)6); + return 0; + } else if (lquery) { + return 0; + } + +/* Quick return if possible */ + + if (*n == 0) { + return 0; + } + if (*n == 1) { + if (icompz != 0) { + z__[z_dim1 + 1] = 1.; + } + return 0; + } + +/* If the following conditional clause is removed, then the routine */ +/* will use the Divide and Conquer routine to compute only the */ +/* eigenvalues, which requires (3N + 3N**2) real workspace and */ +/* (2 + 5N + 2N lg(N)) integer workspace. */ +/* Since on many architectures DSTERF is much faster than any other */ +/* algorithm for finding eigenvalues only, it is used here */ +/* as the default. If the conditional clause is removed, then */ +/* information on the size of workspace needs to be changed. */ + +/* If COMPZ = 'N', use DSTERF to compute the eigenvalues. */ + + if (icompz == 0) { + dsterf_(n, &d__[1], &e[1], info); + goto L50; + } + +/* If N is smaller than the minimum divide size (SMLSIZ+1), then */ +/* solve the problem with another solver. */ + + if (*n <= smlsiz) { + + dsteqr_(compz, n, &d__[1], &e[1], &z__[z_offset], ldz, &work[1], info, + (ftnlen)1); + + } else { + +/* If COMPZ = 'V', the Z matrix must be stored elsewhere for later */ +/* use. */ + + if (icompz == 1) { + storez = *n * *n + 1; + } else { + storez = 1; + } + + if (icompz == 2) { + dlaset_((char *)"Full", n, n, &c_b17, &c_b18, &z__[z_offset], ldz, ( + ftnlen)4); + } + +/* Scale. */ + + orgnrm = dlanst_((char *)"M", n, &d__[1], &e[1], (ftnlen)1); + if (orgnrm == 0.) { + goto L50; + } + + eps = dlamch_((char *)"Epsilon", (ftnlen)7); + + start = 1; + +/* while ( START <= N ) */ + +L10: + if (start <= *n) { + +/* Let FINISH be the position of the next subdiagonal entry */ +/* such that E( FINISH ) <= TINY or FINISH = N if no such */ +/* subdiagonal exists. The matrix identified by the elements */ +/* between START and FINISH constitutes an independent */ +/* sub-problem. */ + + finish = start; +L20: + if (finish < *n) { + tiny = eps * sqrt((d__1 = d__[finish], abs(d__1))) * sqrt(( + d__2 = d__[finish + 1], abs(d__2))); + if ((d__1 = e[finish], abs(d__1)) > tiny) { + ++finish; + goto L20; + } + } + +/* (Sub) Problem determined. Compute its size and solve it. */ + + m = finish - start + 1; + if (m == 1) { + start = finish + 1; + goto L10; + } + if (m > smlsiz) { + +/* Scale. */ + + orgnrm = dlanst_((char *)"M", &m, &d__[start], &e[start], (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b18, &m, &c__1, &d__[ + start], &m, info, (ftnlen)1); + i__1 = m - 1; + i__2 = m - 1; + dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b18, &i__1, &c__1, &e[ + start], &i__2, info, (ftnlen)1); + + if (icompz == 1) { + strtrw = 1; + } else { + strtrw = start; + } + dlaed0_(&icompz, n, &m, &d__[start], &e[start], &z__[strtrw + + start * z_dim1], ldz, &work[1], n, &work[storez], & + iwork[1], info); + if (*info != 0) { + *info = (*info / (m + 1) + start - 1) * (*n + 1) + *info % + (m + 1) + start - 1; + goto L50; + } + +/* Scale back. */ + + dlascl_((char *)"G", &c__0, &c__0, &c_b18, &orgnrm, &m, &c__1, &d__[ + start], &m, info, (ftnlen)1); + + } else { + if (icompz == 1) { + +/* Since QR won't update a Z matrix which is larger than */ +/* the length of D, we must solve the sub-problem in a */ +/* workspace and then multiply back into Z. */ + + dsteqr_((char *)"I", &m, &d__[start], &e[start], &work[1], &m, & + work[m * m + 1], info, (ftnlen)1); + dlacpy_((char *)"A", n, &m, &z__[start * z_dim1 + 1], ldz, &work[ + storez], n, (ftnlen)1); + dgemm_((char *)"N", (char *)"N", n, &m, &m, &c_b18, &work[storez], n, & + work[1], &m, &c_b17, &z__[start * z_dim1 + 1], + ldz, (ftnlen)1, (ftnlen)1); + } else if (icompz == 2) { + dsteqr_((char *)"I", &m, &d__[start], &e[start], &z__[start + + start * z_dim1], ldz, &work[1], info, (ftnlen)1); + } else { + dsterf_(&m, &d__[start], &e[start], info); + } + if (*info != 0) { + *info = start * (*n + 1) + finish; + goto L50; + } + } + + start = finish + 1; + goto L10; + } + +/* endwhile */ + + if (icompz == 0) { + +/* Use Quick Sort */ + + dlasrt_((char *)"I", n, &d__[1], info, (ftnlen)1); + + } else { + +/* Use Selection Sort to minimize swaps of eigenvectors */ + + i__1 = *n; + for (ii = 2; ii <= i__1; ++ii) { + i__ = ii - 1; + k = i__; + p = d__[i__]; + i__2 = *n; + for (j = ii; j <= i__2; ++j) { + if (d__[j] < p) { + k = j; + p = d__[j]; + } +/* L30: */ + } + if (k != i__) { + d__[k] = d__[i__]; + d__[i__] = p; + dswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1 + + 1], &c__1); + } +/* L40: */ + } + } + } + +L50: + work[1] = (doublereal) lwmin; + iwork[1] = liwmin; + + return 0; + +/* End of DSTEDC */ + +} /* dstedc_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dsteqr.cpp b/lib/linalg/dsteqr.cpp new file mode 100644 index 0000000000..65209d15d3 --- /dev/null +++ b/lib/linalg/dsteqr.cpp @@ -0,0 +1,704 @@ +/* fortran/dsteqr.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static doublereal c_b9 = 0.; +static doublereal c_b10 = 1.; +static integer c__0 = 0; +static integer c__1 = 1; +static integer c__2 = 2; + +/* > \brief \b DSTEQR */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DSTEQR + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER COMPZ */ +/* INTEGER INFO, LDZ, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DSTEQR computes all eigenvalues and, optionally, eigenvectors of a */ +/* > symmetric tridiagonal matrix using the implicit QL or QR method. */ +/* > The eigenvectors of a full or band symmetric matrix can also be found */ +/* > if DSYTRD or DSPTRD or DSBTRD has been used to reduce this matrix to */ +/* > tridiagonal form. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] COMPZ */ +/* > \verbatim */ +/* > COMPZ is CHARACTER*1 */ +/* > = 'N': Compute eigenvalues only. */ +/* > = 'V': Compute eigenvalues and eigenvectors of the original */ +/* > symmetric matrix. On entry, Z must contain the */ +/* > orthogonal matrix used to reduce the original matrix */ +/* > to tridiagonal form. */ +/* > = 'I': Compute eigenvalues and eigenvectors of the */ +/* > tridiagonal matrix. Z is initialized to the identity */ +/* > matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrix. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension (N) */ +/* > On entry, the diagonal elements of the tridiagonal matrix. */ +/* > On exit, if INFO = 0, the eigenvalues in ascending order. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] E */ +/* > \verbatim */ +/* > E is DOUBLE PRECISION array, dimension (N-1) */ +/* > On entry, the (n-1) subdiagonal elements of the tridiagonal */ +/* > matrix. */ +/* > On exit, E has been destroyed. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] Z */ +/* > \verbatim */ +/* > Z is DOUBLE PRECISION array, dimension (LDZ, N) */ +/* > On entry, if COMPZ = 'V', then Z contains the orthogonal */ +/* > matrix used in the reduction to tridiagonal form. */ +/* > On exit, if INFO = 0, then if COMPZ = 'V', Z contains the */ +/* > orthonormal eigenvectors of the original symmetric matrix, */ +/* > and if COMPZ = 'I', Z contains the orthonormal eigenvectors */ +/* > of the symmetric tridiagonal matrix. */ +/* > If COMPZ = 'N', then Z is not referenced. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDZ */ +/* > \verbatim */ +/* > LDZ is INTEGER */ +/* > The leading dimension of the array Z. LDZ >= 1, and if */ +/* > eigenvectors are desired, then LDZ >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (max(1,2*N-2)) */ +/* > If COMPZ = 'N', then WORK is not referenced. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > > 0: the algorithm has failed to find all the eigenvalues in */ +/* > a total of 30*N iterations; if INFO = i, then i */ +/* > elements of E have not converged to zero; on exit, D */ +/* > and E contain the elements of a symmetric tridiagonal */ +/* > matrix which is orthogonally similar to the original */ +/* > matrix. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup auxOTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dsteqr_(char *compz, integer *n, doublereal *d__, + doublereal *e, doublereal *z__, integer *ldz, doublereal *work, + integer *info, ftnlen compz_len) +{ + /* System generated locals */ + integer z_dim1, z_offset, i__1, i__2; + doublereal d__1, d__2; + + /* Builtin functions */ + double sqrt(doublereal), d_sign(doublereal *, doublereal *); + + /* Local variables */ + doublereal b, c__, f, g; + integer i__, j, k, l, m; + doublereal p, r__, s; + integer l1, ii, mm, lm1, mm1, nm1; + doublereal rt1, rt2, eps; + integer lsv; + doublereal tst, eps2; + integer lend, jtot; + extern /* Subroutine */ int dlae2_(doublereal *, doublereal *, doublereal + *, doublereal *, doublereal *); + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int dlasr_(char *, char *, char *, integer *, + integer *, doublereal *, doublereal *, doublereal *, integer *, + ftnlen, ftnlen, ftnlen); + doublereal anorm; + extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, + doublereal *, integer *), dlaev2_(doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *); + integer lendm1, lendp1; + extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, + ftnlen); + integer iscale; + extern /* Subroutine */ int dlascl_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, integer *, doublereal *, + integer *, integer *, ftnlen), dlaset_(char *, integer *, integer + *, doublereal *, doublereal *, doublereal *, integer *, ftnlen); + doublereal safmin; + extern /* Subroutine */ int dlartg_(doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *); + doublereal safmax; + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *, + ftnlen); + extern /* Subroutine */ int dlasrt_(char *, integer *, doublereal *, + integer *, ftnlen); + integer lendsv; + doublereal ssfmin; + integer nmaxit, icompz; + doublereal ssfmax; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --d__; + --e; + z_dim1 = *ldz; + z_offset = 1 + z_dim1; + z__ -= z_offset; + --work; + + /* Function Body */ + *info = 0; + + if (lsame_(compz, (char *)"N", (ftnlen)1, (ftnlen)1)) { + icompz = 0; + } else if (lsame_(compz, (char *)"V", (ftnlen)1, (ftnlen)1)) { + icompz = 1; + } else if (lsame_(compz, (char *)"I", (ftnlen)1, (ftnlen)1)) { + icompz = 2; + } else { + icompz = -1; + } + if (icompz < 0) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } else if (*ldz < 1 || icompz > 0 && *ldz < max(1,*n)) { + *info = -6; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DSTEQR", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*n == 0) { + return 0; + } + + if (*n == 1) { + if (icompz == 2) { + z__[z_dim1 + 1] = 1.; + } + return 0; + } + +/* Determine the unit roundoff and over/underflow thresholds. */ + + eps = dlamch_((char *)"E", (ftnlen)1); +/* Computing 2nd power */ + d__1 = eps; + eps2 = d__1 * d__1; + safmin = dlamch_((char *)"S", (ftnlen)1); + safmax = 1. / safmin; + ssfmax = sqrt(safmax) / 3.; + ssfmin = sqrt(safmin) / eps2; + +/* Compute the eigenvalues and eigenvectors of the tridiagonal */ +/* matrix. */ + + if (icompz == 2) { + dlaset_((char *)"Full", n, n, &c_b9, &c_b10, &z__[z_offset], ldz, (ftnlen)4); + } + + nmaxit = *n * 30; + jtot = 0; + +/* Determine where the matrix splits and choose QL or QR iteration */ +/* for each block, according to whether top or bottom diagonal */ +/* element is smaller. */ + + l1 = 1; + nm1 = *n - 1; + +L10: + if (l1 > *n) { + goto L160; + } + if (l1 > 1) { + e[l1 - 1] = 0.; + } + if (l1 <= nm1) { + i__1 = nm1; + for (m = l1; m <= i__1; ++m) { + tst = (d__1 = e[m], abs(d__1)); + if (tst == 0.) { + goto L30; + } + if (tst <= sqrt((d__1 = d__[m], abs(d__1))) * sqrt((d__2 = d__[m + + 1], abs(d__2))) * eps) { + e[m] = 0.; + goto L30; + } +/* L20: */ + } + } + m = *n; + +L30: + l = l1; + lsv = l; + lend = m; + lendsv = lend; + l1 = m + 1; + if (lend == l) { + goto L10; + } + +/* Scale submatrix in rows and columns L to LEND */ + + i__1 = lend - l + 1; + anorm = dlanst_((char *)"M", &i__1, &d__[l], &e[l], (ftnlen)1); + iscale = 0; + if (anorm == 0.) { + goto L10; + } + if (anorm > ssfmax) { + iscale = 1; + i__1 = lend - l + 1; + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n, + info, (ftnlen)1); + i__1 = lend - l; + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &e[l], n, + info, (ftnlen)1); + } else if (anorm < ssfmin) { + iscale = 2; + i__1 = lend - l + 1; + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n, + info, (ftnlen)1); + i__1 = lend - l; + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n, + info, (ftnlen)1); + } + +/* Choose between QL and QR iteration */ + + if ((d__1 = d__[lend], abs(d__1)) < (d__2 = d__[l], abs(d__2))) { + lend = lsv; + l = lendsv; + } + + if (lend > l) { + +/* QL Iteration */ + +/* Look for small subdiagonal element. */ + +L40: + if (l != lend) { + lendm1 = lend - 1; + i__1 = lendm1; + for (m = l; m <= i__1; ++m) { +/* Computing 2nd power */ + d__2 = (d__1 = e[m], abs(d__1)); + tst = d__2 * d__2; + if (tst <= eps2 * (d__1 = d__[m], abs(d__1)) * (d__2 = d__[m + + 1], abs(d__2)) + safmin) { + goto L60; + } +/* L50: */ + } + } + + m = lend; + +L60: + if (m < lend) { + e[m] = 0.; + } + p = d__[l]; + if (m == l) { + goto L80; + } + +/* If remaining matrix is 2-by-2, use DLAE2 or SLAEV2 */ +/* to compute its eigensystem. */ + + if (m == l + 1) { + if (icompz > 0) { + dlaev2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2, &c__, &s); + work[l] = c__; + work[*n - 1 + l] = s; + dlasr_((char *)"R", (char *)"V", (char *)"B", n, &c__2, &work[l], &work[*n - 1 + l], & + z__[l * z_dim1 + 1], ldz, (ftnlen)1, (ftnlen)1, ( + ftnlen)1); + } else { + dlae2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2); + } + d__[l] = rt1; + d__[l + 1] = rt2; + e[l] = 0.; + l += 2; + if (l <= lend) { + goto L40; + } + goto L140; + } + + if (jtot == nmaxit) { + goto L140; + } + ++jtot; + +/* Form shift. */ + + g = (d__[l + 1] - p) / (e[l] * 2.); + r__ = dlapy2_(&g, &c_b10); + g = d__[m] - p + e[l] / (g + d_sign(&r__, &g)); + + s = 1.; + c__ = 1.; + p = 0.; + +/* Inner loop */ + + mm1 = m - 1; + i__1 = l; + for (i__ = mm1; i__ >= i__1; --i__) { + f = s * e[i__]; + b = c__ * e[i__]; + dlartg_(&g, &f, &c__, &s, &r__); + if (i__ != m - 1) { + e[i__ + 1] = r__; + } + g = d__[i__ + 1] - p; + r__ = (d__[i__] - g) * s + c__ * 2. * b; + p = s * r__; + d__[i__ + 1] = g + p; + g = c__ * r__ - b; + +/* If eigenvectors are desired, then save rotations. */ + + if (icompz > 0) { + work[i__] = c__; + work[*n - 1 + i__] = -s; + } + +/* L70: */ + } + +/* If eigenvectors are desired, then apply saved rotations. */ + + if (icompz > 0) { + mm = m - l + 1; + dlasr_((char *)"R", (char *)"V", (char *)"B", n, &mm, &work[l], &work[*n - 1 + l], &z__[l + * z_dim1 + 1], ldz, (ftnlen)1, (ftnlen)1, (ftnlen)1); + } + + d__[l] -= p; + e[l] = g; + goto L40; + +/* Eigenvalue found. */ + +L80: + d__[l] = p; + + ++l; + if (l <= lend) { + goto L40; + } + goto L140; + + } else { + +/* QR Iteration */ + +/* Look for small superdiagonal element. */ + +L90: + if (l != lend) { + lendp1 = lend + 1; + i__1 = lendp1; + for (m = l; m >= i__1; --m) { +/* Computing 2nd power */ + d__2 = (d__1 = e[m - 1], abs(d__1)); + tst = d__2 * d__2; + if (tst <= eps2 * (d__1 = d__[m], abs(d__1)) * (d__2 = d__[m + - 1], abs(d__2)) + safmin) { + goto L110; + } +/* L100: */ + } + } + + m = lend; + +L110: + if (m > lend) { + e[m - 1] = 0.; + } + p = d__[l]; + if (m == l) { + goto L130; + } + +/* If remaining matrix is 2-by-2, use DLAE2 or SLAEV2 */ +/* to compute its eigensystem. */ + + if (m == l - 1) { + if (icompz > 0) { + dlaev2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2, &c__, &s) + ; + work[m] = c__; + work[*n - 1 + m] = s; + dlasr_((char *)"R", (char *)"V", (char *)"F", n, &c__2, &work[m], &work[*n - 1 + m], & + z__[(l - 1) * z_dim1 + 1], ldz, (ftnlen)1, (ftnlen)1, + (ftnlen)1); + } else { + dlae2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2); + } + d__[l - 1] = rt1; + d__[l] = rt2; + e[l - 1] = 0.; + l += -2; + if (l >= lend) { + goto L90; + } + goto L140; + } + + if (jtot == nmaxit) { + goto L140; + } + ++jtot; + +/* Form shift. */ + + g = (d__[l - 1] - p) / (e[l - 1] * 2.); + r__ = dlapy2_(&g, &c_b10); + g = d__[m] - p + e[l - 1] / (g + d_sign(&r__, &g)); + + s = 1.; + c__ = 1.; + p = 0.; + +/* Inner loop */ + + lm1 = l - 1; + i__1 = lm1; + for (i__ = m; i__ <= i__1; ++i__) { + f = s * e[i__]; + b = c__ * e[i__]; + dlartg_(&g, &f, &c__, &s, &r__); + if (i__ != m) { + e[i__ - 1] = r__; + } + g = d__[i__] - p; + r__ = (d__[i__ + 1] - g) * s + c__ * 2. * b; + p = s * r__; + d__[i__] = g + p; + g = c__ * r__ - b; + +/* If eigenvectors are desired, then save rotations. */ + + if (icompz > 0) { + work[i__] = c__; + work[*n - 1 + i__] = s; + } + +/* L120: */ + } + +/* If eigenvectors are desired, then apply saved rotations. */ + + if (icompz > 0) { + mm = l - m + 1; + dlasr_((char *)"R", (char *)"V", (char *)"F", n, &mm, &work[m], &work[*n - 1 + m], &z__[m + * z_dim1 + 1], ldz, (ftnlen)1, (ftnlen)1, (ftnlen)1); + } + + d__[l] -= p; + e[lm1] = g; + goto L90; + +/* Eigenvalue found. */ + +L130: + d__[l] = p; + + --l; + if (l >= lend) { + goto L90; + } + goto L140; + + } + +/* Undo scaling if necessary */ + +L140: + if (iscale == 1) { + i__1 = lendsv - lsv + 1; + dlascl_((char *)"G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv], + n, info, (ftnlen)1); + i__1 = lendsv - lsv; + dlascl_((char *)"G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &e[lsv], n, + info, (ftnlen)1); + } else if (iscale == 2) { + i__1 = lendsv - lsv + 1; + dlascl_((char *)"G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[lsv], + n, info, (ftnlen)1); + i__1 = lendsv - lsv; + dlascl_((char *)"G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &e[lsv], n, + info, (ftnlen)1); + } + +/* Check for no convergence to an eigenvalue after a total */ +/* of N*MAXIT iterations. */ + + if (jtot < nmaxit) { + goto L10; + } + i__1 = *n - 1; + for (i__ = 1; i__ <= i__1; ++i__) { + if (e[i__] != 0.) { + ++(*info); + } +/* L150: */ + } + goto L190; + +/* Order eigenvalues and eigenvectors. */ + +L160: + if (icompz == 0) { + +/* Use Quick Sort */ + + dlasrt_((char *)"I", n, &d__[1], info, (ftnlen)1); + + } else { + +/* Use Selection Sort to minimize swaps of eigenvectors */ + + i__1 = *n; + for (ii = 2; ii <= i__1; ++ii) { + i__ = ii - 1; + k = i__; + p = d__[i__]; + i__2 = *n; + for (j = ii; j <= i__2; ++j) { + if (d__[j] < p) { + k = j; + p = d__[j]; + } +/* L170: */ + } + if (k != i__) { + d__[k] = d__[i__]; + d__[i__] = p; + dswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1 + 1], + &c__1); + } +/* L180: */ + } + } + +L190: + return 0; + +/* End of DSTEQR */ + +} /* dsteqr_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dsterf.cpp b/lib/linalg/dsterf.cpp new file mode 100644 index 0000000000..03172b87f3 --- /dev/null +++ b/lib/linalg/dsterf.cpp @@ -0,0 +1,534 @@ +/* fortran/dsterf.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__0 = 0; +static integer c__1 = 1; +static doublereal c_b33 = 1.; + +/* > \brief \b DSTERF */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DSTERF + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DSTERF( N, D, E, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INFO, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION D( * ), E( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DSTERF computes all eigenvalues of a symmetric tridiagonal matrix */ +/* > using the Pal-Walker-Kahan variant of the QL or QR algorithm. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrix. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension (N) */ +/* > On entry, the n diagonal elements of the tridiagonal matrix. */ +/* > On exit, if INFO = 0, the eigenvalues in ascending order. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] E */ +/* > \verbatim */ +/* > E is DOUBLE PRECISION array, dimension (N-1) */ +/* > On entry, the (n-1) subdiagonal elements of the tridiagonal */ +/* > matrix. */ +/* > On exit, E has been destroyed. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > > 0: the algorithm failed to find all of the eigenvalues in */ +/* > a total of 30*N iterations; if INFO = i, then i */ +/* > elements of E have not converged to zero. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup auxOTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dsterf_(integer *n, doublereal *d__, doublereal *e, + integer *info) +{ + /* System generated locals */ + integer i__1; + doublereal d__1, d__2, d__3; + + /* Builtin functions */ + double sqrt(doublereal), d_sign(doublereal *, doublereal *); + + /* Local variables */ + doublereal c__; + integer i__, l, m; + doublereal p, r__, s; + integer l1; + doublereal bb, rt1, rt2, eps, rte; + integer lsv; + doublereal eps2, oldc; + integer lend; + doublereal rmax; + integer jtot; + extern /* Subroutine */ int dlae2_(doublereal *, doublereal *, doublereal + *, doublereal *, doublereal *); + doublereal gamma, alpha, sigma, anorm; + extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, + ftnlen); + integer iscale; + extern /* Subroutine */ int dlascl_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, integer *, doublereal *, + integer *, integer *, ftnlen); + doublereal oldgam, safmin; + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + doublereal safmax; + extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *, + ftnlen); + extern /* Subroutine */ int dlasrt_(char *, integer *, doublereal *, + integer *, ftnlen); + integer lendsv; + doublereal ssfmin; + integer nmaxit; + doublereal ssfmax; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --e; + --d__; + + /* Function Body */ + *info = 0; + +/* Quick return if possible */ + + if (*n < 0) { + *info = -1; + i__1 = -(*info); + xerbla_((char *)"DSTERF", &i__1, (ftnlen)6); + return 0; + } + if (*n <= 1) { + return 0; + } + +/* Determine the unit roundoff for this environment. */ + + eps = dlamch_((char *)"E", (ftnlen)1); +/* Computing 2nd power */ + d__1 = eps; + eps2 = d__1 * d__1; + safmin = dlamch_((char *)"S", (ftnlen)1); + safmax = 1. / safmin; + ssfmax = sqrt(safmax) / 3.; + ssfmin = sqrt(safmin) / eps2; + rmax = dlamch_((char *)"O", (ftnlen)1); + +/* Compute the eigenvalues of the tridiagonal matrix. */ + + nmaxit = *n * 30; + sigma = 0.; + jtot = 0; + +/* Determine where the matrix splits and choose QL or QR iteration */ +/* for each block, according to whether top or bottom diagonal */ +/* element is smaller. */ + + l1 = 1; + +L10: + if (l1 > *n) { + goto L170; + } + if (l1 > 1) { + e[l1 - 1] = 0.; + } + i__1 = *n - 1; + for (m = l1; m <= i__1; ++m) { + if ((d__3 = e[m], abs(d__3)) <= sqrt((d__1 = d__[m], abs(d__1))) * + sqrt((d__2 = d__[m + 1], abs(d__2))) * eps) { + e[m] = 0.; + goto L30; + } +/* L20: */ + } + m = *n; + +L30: + l = l1; + lsv = l; + lend = m; + lendsv = lend; + l1 = m + 1; + if (lend == l) { + goto L10; + } + +/* Scale submatrix in rows and columns L to LEND */ + + i__1 = lend - l + 1; + anorm = dlanst_((char *)"M", &i__1, &d__[l], &e[l], (ftnlen)1); + iscale = 0; + if (anorm == 0.) { + goto L10; + } + if (anorm > ssfmax) { + iscale = 1; + i__1 = lend - l + 1; + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n, + info, (ftnlen)1); + i__1 = lend - l; + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &e[l], n, + info, (ftnlen)1); + } else if (anorm < ssfmin) { + iscale = 2; + i__1 = lend - l + 1; + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n, + info, (ftnlen)1); + i__1 = lend - l; + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n, + info, (ftnlen)1); + } + + i__1 = lend - 1; + for (i__ = l; i__ <= i__1; ++i__) { +/* Computing 2nd power */ + d__1 = e[i__]; + e[i__] = d__1 * d__1; +/* L40: */ + } + +/* Choose between QL and QR iteration */ + + if ((d__1 = d__[lend], abs(d__1)) < (d__2 = d__[l], abs(d__2))) { + lend = lsv; + l = lendsv; + } + + if (lend >= l) { + +/* QL Iteration */ + +/* Look for small subdiagonal element. */ + +L50: + if (l != lend) { + i__1 = lend - 1; + for (m = l; m <= i__1; ++m) { + if ((d__2 = e[m], abs(d__2)) <= eps2 * (d__1 = d__[m] * d__[m + + 1], abs(d__1))) { + goto L70; + } +/* L60: */ + } + } + m = lend; + +L70: + if (m < lend) { + e[m] = 0.; + } + p = d__[l]; + if (m == l) { + goto L90; + } + +/* If remaining matrix is 2 by 2, use DLAE2 to compute its */ +/* eigenvalues. */ + + if (m == l + 1) { + rte = sqrt(e[l]); + dlae2_(&d__[l], &rte, &d__[l + 1], &rt1, &rt2); + d__[l] = rt1; + d__[l + 1] = rt2; + e[l] = 0.; + l += 2; + if (l <= lend) { + goto L50; + } + goto L150; + } + + if (jtot == nmaxit) { + goto L150; + } + ++jtot; + +/* Form shift. */ + + rte = sqrt(e[l]); + sigma = (d__[l + 1] - p) / (rte * 2.); + r__ = dlapy2_(&sigma, &c_b33); + sigma = p - rte / (sigma + d_sign(&r__, &sigma)); + + c__ = 1.; + s = 0.; + gamma = d__[m] - sigma; + p = gamma * gamma; + +/* Inner loop */ + + i__1 = l; + for (i__ = m - 1; i__ >= i__1; --i__) { + bb = e[i__]; + r__ = p + bb; + if (i__ != m - 1) { + e[i__ + 1] = s * r__; + } + oldc = c__; + c__ = p / r__; + s = bb / r__; + oldgam = gamma; + alpha = d__[i__]; + gamma = c__ * (alpha - sigma) - s * oldgam; + d__[i__ + 1] = oldgam + (alpha - gamma); + if (c__ != 0.) { + p = gamma * gamma / c__; + } else { + p = oldc * bb; + } +/* L80: */ + } + + e[l] = s * p; + d__[l] = sigma + gamma; + goto L50; + +/* Eigenvalue found. */ + +L90: + d__[l] = p; + + ++l; + if (l <= lend) { + goto L50; + } + goto L150; + + } else { + +/* QR Iteration */ + +/* Look for small superdiagonal element. */ + +L100: + i__1 = lend + 1; + for (m = l; m >= i__1; --m) { + if ((d__2 = e[m - 1], abs(d__2)) <= eps2 * (d__1 = d__[m] * d__[m + - 1], abs(d__1))) { + goto L120; + } +/* L110: */ + } + m = lend; + +L120: + if (m > lend) { + e[m - 1] = 0.; + } + p = d__[l]; + if (m == l) { + goto L140; + } + +/* If remaining matrix is 2 by 2, use DLAE2 to compute its */ +/* eigenvalues. */ + + if (m == l - 1) { + rte = sqrt(e[l - 1]); + dlae2_(&d__[l], &rte, &d__[l - 1], &rt1, &rt2); + d__[l] = rt1; + d__[l - 1] = rt2; + e[l - 1] = 0.; + l += -2; + if (l >= lend) { + goto L100; + } + goto L150; + } + + if (jtot == nmaxit) { + goto L150; + } + ++jtot; + +/* Form shift. */ + + rte = sqrt(e[l - 1]); + sigma = (d__[l - 1] - p) / (rte * 2.); + r__ = dlapy2_(&sigma, &c_b33); + sigma = p - rte / (sigma + d_sign(&r__, &sigma)); + + c__ = 1.; + s = 0.; + gamma = d__[m] - sigma; + p = gamma * gamma; + +/* Inner loop */ + + i__1 = l - 1; + for (i__ = m; i__ <= i__1; ++i__) { + bb = e[i__]; + r__ = p + bb; + if (i__ != m) { + e[i__ - 1] = s * r__; + } + oldc = c__; + c__ = p / r__; + s = bb / r__; + oldgam = gamma; + alpha = d__[i__ + 1]; + gamma = c__ * (alpha - sigma) - s * oldgam; + d__[i__] = oldgam + (alpha - gamma); + if (c__ != 0.) { + p = gamma * gamma / c__; + } else { + p = oldc * bb; + } +/* L130: */ + } + + e[l - 1] = s * p; + d__[l] = sigma + gamma; + goto L100; + +/* Eigenvalue found. */ + +L140: + d__[l] = p; + + --l; + if (l >= lend) { + goto L100; + } + goto L150; + + } + +/* Undo scaling if necessary */ + +L150: + if (iscale == 1) { + i__1 = lendsv - lsv + 1; + dlascl_((char *)"G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv], + n, info, (ftnlen)1); + } + if (iscale == 2) { + i__1 = lendsv - lsv + 1; + dlascl_((char *)"G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[lsv], + n, info, (ftnlen)1); + } + +/* Check for no convergence to an eigenvalue after a total */ +/* of N*MAXIT iterations. */ + + if (jtot < nmaxit) { + goto L10; + } + i__1 = *n - 1; + for (i__ = 1; i__ <= i__1; ++i__) { + if (e[i__] != 0.) { + ++(*info); + } +/* L160: */ + } + goto L180; + +/* Sort eigenvalues in increasing order. */ + +L170: + dlasrt_((char *)"I", n, &d__[1], info, (ftnlen)1); + +L180: + return 0; + +/* End of DSTERF */ + +} /* dsterf_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dswap.cpp b/lib/linalg/dswap.cpp new file mode 100644 index 0000000000..a1eca4fc06 --- /dev/null +++ b/lib/linalg/dswap.cpp @@ -0,0 +1,194 @@ +/* fortran/dswap.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DSWAP */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DSWAP(N,DX,INCX,DY,INCY) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INCX,INCY,N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION DX(*),DY(*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DSWAP interchanges two vectors. */ +/* > uses unrolled loops for increments equal to 1. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > number of elements in input vector(s) */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] DX */ +/* > \verbatim */ +/* > DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > storage spacing between elements of DX */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] DY */ +/* > \verbatim */ +/* > DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCY */ +/* > \verbatim */ +/* > INCY is INTEGER */ +/* > storage spacing between elements of DY */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup double_blas_level1 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > jack dongarra, linpack, 3/11/78. */ +/* > modified 12/3/93, array(1) declarations changed to array(*) */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dswap_(integer *n, doublereal *dx, integer *incx, + doublereal *dy, integer *incy) +{ + /* System generated locals */ + integer i__1; + + /* Local variables */ + integer i__, m, ix, iy, mp1; + doublereal dtemp; + + +/* -- Reference BLAS level1 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ + /* Parameter adjustments */ + --dy; + --dx; + + /* Function Body */ + if (*n <= 0) { + return 0; + } + if (*incx == 1 && *incy == 1) { + +/* code for both increments equal to 1 */ + + +/* clean-up loop */ + + m = *n % 3; + if (m != 0) { + i__1 = m; + for (i__ = 1; i__ <= i__1; ++i__) { + dtemp = dx[i__]; + dx[i__] = dy[i__]; + dy[i__] = dtemp; + } + if (*n < 3) { + return 0; + } + } + mp1 = m + 1; + i__1 = *n; + for (i__ = mp1; i__ <= i__1; i__ += 3) { + dtemp = dx[i__]; + dx[i__] = dy[i__]; + dy[i__] = dtemp; + dtemp = dx[i__ + 1]; + dx[i__ + 1] = dy[i__ + 1]; + dy[i__ + 1] = dtemp; + dtemp = dx[i__ + 2]; + dx[i__ + 2] = dy[i__ + 2]; + dy[i__ + 2] = dtemp; + } + } else { + +/* code for unequal increments or equal increments not equal */ +/* to 1 */ + + ix = 1; + iy = 1; + if (*incx < 0) { + ix = (-(*n) + 1) * *incx + 1; + } + if (*incy < 0) { + iy = (-(*n) + 1) * *incy + 1; + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + dtemp = dx[ix]; + dx[ix] = dy[iy]; + dy[iy] = dtemp; + ix += *incx; + iy += *incy; + } + } + return 0; + +/* End of DSWAP */ + +} /* dswap_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dsyev.cpp b/lib/linalg/dsyev.cpp new file mode 100644 index 0000000000..603b633195 --- /dev/null +++ b/lib/linalg/dsyev.cpp @@ -0,0 +1,369 @@ +/* fortran/dsyev.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c_n1 = -1; +static integer c__0 = 0; +static doublereal c_b17 = 1.; + +/* > \brief DSYEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matr +ices */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DSYEV + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DSYEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER JOBZ, UPLO */ +/* INTEGER INFO, LDA, LWORK, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DSYEV computes all eigenvalues and, optionally, eigenvectors of a */ +/* > real symmetric matrix A. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] JOBZ */ +/* > \verbatim */ +/* > JOBZ is CHARACTER*1 */ +/* > = 'N': Compute eigenvalues only; */ +/* > = 'V': Compute eigenvalues and eigenvectors. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > = 'U': Upper triangle of A is stored; */ +/* > = 'L': Lower triangle of A is stored. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA, N) */ +/* > On entry, the symmetric matrix A. If UPLO = 'U', the */ +/* > leading N-by-N upper triangular part of A contains the */ +/* > upper triangular part of the matrix A. If UPLO = 'L', */ +/* > the leading N-by-N lower triangular part of A contains */ +/* > the lower triangular part of the matrix A. */ +/* > On exit, if JOBZ = 'V', then if INFO = 0, A contains the */ +/* > orthonormal eigenvectors of the matrix A. */ +/* > If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') */ +/* > or the upper triangle (if UPLO='U') of A, including the */ +/* > diagonal, is destroyed. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] W */ +/* > \verbatim */ +/* > W is DOUBLE PRECISION array, dimension (N) */ +/* > If INFO = 0, the eigenvalues in ascending order. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ +/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LWORK */ +/* > \verbatim */ +/* > LWORK is INTEGER */ +/* > The length of the array WORK. LWORK >= max(1,3*N-1). */ +/* > For optimal efficiency, LWORK >= (NB+2)*N, */ +/* > where NB is the blocksize for DSYTRD returned by ILAENV. */ +/* > */ +/* > If LWORK = -1, then a workspace query is assumed; the routine */ +/* > only calculates the optimal size of the WORK array, returns */ +/* > this value as the first entry of the WORK array, and no error */ +/* > message related to LWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > > 0: if INFO = i, the algorithm failed to converge; i */ +/* > off-diagonal elements of an intermediate tridiagonal */ +/* > form did not converge to zero. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleSYeigen */ + +/* ===================================================================== */ +/* Subroutine */ int dsyev_(char *jobz, char *uplo, integer *n, doublereal *a, + integer *lda, doublereal *w, doublereal *work, integer *lwork, + integer *info, ftnlen jobz_len, ftnlen uplo_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2; + doublereal d__1; + + /* Builtin functions */ + double sqrt(doublereal); + + /* Local variables */ + integer nb; + doublereal eps; + integer inde; + doublereal anrm; + integer imax; + doublereal rmin, rmax; + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *); + doublereal sigma; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + integer iinfo; + logical lower, wantz; + extern doublereal dlamch_(char *, ftnlen); + integer iscale; + extern /* Subroutine */ int dlascl_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, integer *, doublereal *, + integer *, integer *, ftnlen); + doublereal safmin; + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + doublereal bignum; + integer indtau; + extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *, + integer *); + extern doublereal dlansy_(char *, char *, integer *, doublereal *, + integer *, doublereal *, ftnlen, ftnlen); + integer indwrk; + extern /* Subroutine */ int dorgtr_(char *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, integer *, + ftnlen), dsteqr_(char *, integer *, doublereal *, doublereal *, + doublereal *, integer *, doublereal *, integer *, ftnlen), + dsytrd_(char *, integer *, doublereal *, integer *, doublereal *, + doublereal *, doublereal *, doublereal *, integer *, integer *, + ftnlen); + integer llwork; + doublereal smlnum; + integer lwkopt; + logical lquery; + + +/* -- LAPACK driver routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --w; + --work; + + /* Function Body */ + wantz = lsame_(jobz, (char *)"V", (ftnlen)1, (ftnlen)1); + lower = lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1); + lquery = *lwork == -1; + + *info = 0; + if (! (wantz || lsame_(jobz, (char *)"N", (ftnlen)1, (ftnlen)1))) { + *info = -1; + } else if (! (lower || lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1))) { + *info = -2; + } else if (*n < 0) { + *info = -3; + } else if (*lda < max(1,*n)) { + *info = -5; + } + + if (*info == 0) { + nb = ilaenv_(&c__1, (char *)"DSYTRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, + (ftnlen)1); +/* Computing MAX */ + i__1 = 1, i__2 = (nb + 2) * *n; + lwkopt = max(i__1,i__2); + work[1] = (doublereal) lwkopt; + +/* Computing MAX */ + i__1 = 1, i__2 = *n * 3 - 1; + if (*lwork < max(i__1,i__2) && ! lquery) { + *info = -8; + } + } + + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DSYEV ", &i__1, (ftnlen)6); + return 0; + } else if (lquery) { + return 0; + } + +/* Quick return if possible */ + + if (*n == 0) { + return 0; + } + + if (*n == 1) { + w[1] = a[a_dim1 + 1]; + work[1] = 2.; + if (wantz) { + a[a_dim1 + 1] = 1.; + } + return 0; + } + +/* Get machine constants. */ + + safmin = dlamch_((char *)"Safe minimum", (ftnlen)12); + eps = dlamch_((char *)"Precision", (ftnlen)9); + smlnum = safmin / eps; + bignum = 1. / smlnum; + rmin = sqrt(smlnum); + rmax = sqrt(bignum); + +/* Scale matrix to allowable range, if necessary. */ + + anrm = dlansy_((char *)"M", uplo, n, &a[a_offset], lda, &work[1], (ftnlen)1, ( + ftnlen)1); + iscale = 0; + if (anrm > 0. && anrm < rmin) { + iscale = 1; + sigma = rmin / anrm; + } else if (anrm > rmax) { + iscale = 1; + sigma = rmax / anrm; + } + if (iscale == 1) { + dlascl_(uplo, &c__0, &c__0, &c_b17, &sigma, n, n, &a[a_offset], lda, + info, (ftnlen)1); + } + +/* Call DSYTRD to reduce symmetric matrix to tridiagonal form. */ + + inde = 1; + indtau = inde + *n; + indwrk = indtau + *n; + llwork = *lwork - indwrk + 1; + dsytrd_(uplo, n, &a[a_offset], lda, &w[1], &work[inde], &work[indtau], & + work[indwrk], &llwork, &iinfo, (ftnlen)1); + +/* For eigenvalues only, call DSTERF. For eigenvectors, first call */ +/* DORGTR to generate the orthogonal matrix, then call DSTEQR. */ + + if (! wantz) { + dsterf_(n, &w[1], &work[inde], info); + } else { + dorgtr_(uplo, n, &a[a_offset], lda, &work[indtau], &work[indwrk], & + llwork, &iinfo, (ftnlen)1); + dsteqr_(jobz, n, &w[1], &work[inde], &a[a_offset], lda, &work[indtau], + info, (ftnlen)1); + } + +/* If matrix was scaled, then rescale eigenvalues appropriately. */ + + if (iscale == 1) { + if (*info == 0) { + imax = *n; + } else { + imax = *info - 1; + } + d__1 = 1. / sigma; + dscal_(&imax, &d__1, &w[1], &c__1); + } + +/* Set WORK(1) to optimal workspace size. */ + + work[1] = (doublereal) lwkopt; + + return 0; + +/* End of DSYEV */ + +} /* dsyev_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dsyevd.cpp b/lib/linalg/dsyevd.cpp new file mode 100644 index 0000000000..a0e0084884 --- /dev/null +++ b/lib/linalg/dsyevd.cpp @@ -0,0 +1,440 @@ +/* fortran/dsyevd.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c_n1 = -1; +static integer c__0 = 0; +static doublereal c_b17 = 1.; + +/* > \brief DSYEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY mat +rices */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DSYEVD + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK, */ +/* LIWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER JOBZ, UPLO */ +/* INTEGER INFO, LDA, LIWORK, LWORK, N */ +/* .. */ +/* .. Array Arguments .. */ +/* INTEGER IWORK( * ) */ +/* DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DSYEVD computes all eigenvalues and, optionally, eigenvectors of a */ +/* > real symmetric matrix A. If eigenvectors are desired, it uses a */ +/* > divide and conquer algorithm. */ +/* > */ +/* > The divide and conquer algorithm makes very mild assumptions about */ +/* > floating point arithmetic. It will work on machines with a guard */ +/* > digit in add/subtract, or on those binary machines without guard */ +/* > digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */ +/* > Cray-2. It could conceivably fail on hexadecimal or decimal machines */ +/* > without guard digits, but we know of none. */ +/* > */ +/* > Because of large use of BLAS of level 3, DSYEVD needs N**2 more */ +/* > workspace than DSYEVX. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] JOBZ */ +/* > \verbatim */ +/* > JOBZ is CHARACTER*1 */ +/* > = 'N': Compute eigenvalues only; */ +/* > = 'V': Compute eigenvalues and eigenvectors. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > = 'U': Upper triangle of A is stored; */ +/* > = 'L': Lower triangle of A is stored. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA, N) */ +/* > On entry, the symmetric matrix A. If UPLO = 'U', the */ +/* > leading N-by-N upper triangular part of A contains the */ +/* > upper triangular part of the matrix A. If UPLO = 'L', */ +/* > the leading N-by-N lower triangular part of A contains */ +/* > the lower triangular part of the matrix A. */ +/* > On exit, if JOBZ = 'V', then if INFO = 0, A contains the */ +/* > orthonormal eigenvectors of the matrix A. */ +/* > If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') */ +/* > or the upper triangle (if UPLO='U') of A, including the */ +/* > diagonal, is destroyed. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] W */ +/* > \verbatim */ +/* > W is DOUBLE PRECISION array, dimension (N) */ +/* > If INFO = 0, the eigenvalues in ascending order. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, */ +/* > dimension (LWORK) */ +/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LWORK */ +/* > \verbatim */ +/* > LWORK is INTEGER */ +/* > The dimension of the array WORK. */ +/* > If N <= 1, LWORK must be at least 1. */ +/* > If JOBZ = 'N' and N > 1, LWORK must be at least 2*N+1. */ +/* > If JOBZ = 'V' and N > 1, LWORK must be at least */ +/* > 1 + 6*N + 2*N**2. */ +/* > */ +/* > If LWORK = -1, then a workspace query is assumed; the routine */ +/* > only calculates the optimal sizes of the WORK and IWORK */ +/* > arrays, returns these values as the first entries of the WORK */ +/* > and IWORK arrays, and no error message related to LWORK or */ +/* > LIWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] IWORK */ +/* > \verbatim */ +/* > IWORK is INTEGER array, dimension (MAX(1,LIWORK)) */ +/* > On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LIWORK */ +/* > \verbatim */ +/* > LIWORK is INTEGER */ +/* > The dimension of the array IWORK. */ +/* > If N <= 1, LIWORK must be at least 1. */ +/* > If JOBZ = 'N' and N > 1, LIWORK must be at least 1. */ +/* > If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N. */ +/* > */ +/* > If LIWORK = -1, then a workspace query is assumed; the */ +/* > routine only calculates the optimal sizes of the WORK and */ +/* > IWORK arrays, returns these values as the first entries of */ +/* > the WORK and IWORK arrays, and no error message related to */ +/* > LWORK or LIWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > > 0: if INFO = i and JOBZ = 'N', then the algorithm failed */ +/* > to converge; i off-diagonal elements of an intermediate */ +/* > tridiagonal form did not converge to zero; */ +/* > if INFO = i and JOBZ = 'V', then the algorithm failed */ +/* > to compute an eigenvalue while working on the submatrix */ +/* > lying in rows and columns INFO/(N+1) through */ +/* > mod(INFO,N+1). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleSYeigen */ + +/* > \par Contributors: */ +/* ================== */ +/* > */ +/* > Jeff Rutter, Computer Science Division, University of California */ +/* > at Berkeley, USA \n */ +/* > Modified by Francoise Tisseur, University of Tennessee \n */ +/* > Modified description of INFO. Sven, 16 Feb 05. \n */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dsyevd_(char *jobz, char *uplo, integer *n, doublereal * + a, integer *lda, doublereal *w, doublereal *work, integer *lwork, + integer *iwork, integer *liwork, integer *info, ftnlen jobz_len, + ftnlen uplo_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2; + doublereal d__1; + + /* Builtin functions */ + double sqrt(doublereal); + + /* Local variables */ + doublereal eps; + integer inde; + doublereal anrm, rmin, rmax; + integer lopt; + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *); + doublereal sigma; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + integer iinfo, lwmin, liopt; + logical lower, wantz; + integer indwk2, llwrk2; + extern doublereal dlamch_(char *, ftnlen); + integer iscale; + extern /* Subroutine */ int dlascl_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, integer *, doublereal *, + integer *, integer *, ftnlen), dstedc_(char *, integer *, + doublereal *, doublereal *, doublereal *, integer *, doublereal *, + integer *, integer *, integer *, integer *, ftnlen), dlacpy_( + char *, integer *, integer *, doublereal *, integer *, doublereal + *, integer *, ftnlen); + doublereal safmin; + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + doublereal bignum; + integer indtau; + extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *, + integer *); + extern doublereal dlansy_(char *, char *, integer *, doublereal *, + integer *, doublereal *, ftnlen, ftnlen); + integer indwrk, liwmin; + extern /* Subroutine */ int dormtr_(char *, char *, char *, integer *, + integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, integer *, ftnlen, ftnlen, + ftnlen), dsytrd_(char *, integer *, doublereal *, integer *, + doublereal *, doublereal *, doublereal *, doublereal *, integer *, + integer *, ftnlen); + integer llwork; + doublereal smlnum; + logical lquery; + + +/* -- LAPACK driver routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ + +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --w; + --work; + --iwork; + + /* Function Body */ + wantz = lsame_(jobz, (char *)"V", (ftnlen)1, (ftnlen)1); + lower = lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1); + lquery = *lwork == -1 || *liwork == -1; + + *info = 0; + if (! (wantz || lsame_(jobz, (char *)"N", (ftnlen)1, (ftnlen)1))) { + *info = -1; + } else if (! (lower || lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1))) { + *info = -2; + } else if (*n < 0) { + *info = -3; + } else if (*lda < max(1,*n)) { + *info = -5; + } + + if (*info == 0) { + if (*n <= 1) { + liwmin = 1; + lwmin = 1; + lopt = lwmin; + liopt = liwmin; + } else { + if (wantz) { + liwmin = *n * 5 + 3; +/* Computing 2nd power */ + i__1 = *n; + lwmin = *n * 6 + 1 + (i__1 * i__1 << 1); + } else { + liwmin = 1; + lwmin = (*n << 1) + 1; + } +/* Computing MAX */ + i__1 = lwmin, i__2 = (*n << 1) + *n * ilaenv_(&c__1, (char *)"DSYTRD", + uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); + lopt = max(i__1,i__2); + liopt = liwmin; + } + work[1] = (doublereal) lopt; + iwork[1] = liopt; + + if (*lwork < lwmin && ! lquery) { + *info = -8; + } else if (*liwork < liwmin && ! lquery) { + *info = -10; + } + } + + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DSYEVD", &i__1, (ftnlen)6); + return 0; + } else if (lquery) { + return 0; + } + +/* Quick return if possible */ + + if (*n == 0) { + return 0; + } + + if (*n == 1) { + w[1] = a[a_dim1 + 1]; + if (wantz) { + a[a_dim1 + 1] = 1.; + } + return 0; + } + +/* Get machine constants. */ + + safmin = dlamch_((char *)"Safe minimum", (ftnlen)12); + eps = dlamch_((char *)"Precision", (ftnlen)9); + smlnum = safmin / eps; + bignum = 1. / smlnum; + rmin = sqrt(smlnum); + rmax = sqrt(bignum); + +/* Scale matrix to allowable range, if necessary. */ + + anrm = dlansy_((char *)"M", uplo, n, &a[a_offset], lda, &work[1], (ftnlen)1, ( + ftnlen)1); + iscale = 0; + if (anrm > 0. && anrm < rmin) { + iscale = 1; + sigma = rmin / anrm; + } else if (anrm > rmax) { + iscale = 1; + sigma = rmax / anrm; + } + if (iscale == 1) { + dlascl_(uplo, &c__0, &c__0, &c_b17, &sigma, n, n, &a[a_offset], lda, + info, (ftnlen)1); + } + +/* Call DSYTRD to reduce symmetric matrix to tridiagonal form. */ + + inde = 1; + indtau = inde + *n; + indwrk = indtau + *n; + llwork = *lwork - indwrk + 1; + indwk2 = indwrk + *n * *n; + llwrk2 = *lwork - indwk2 + 1; + + dsytrd_(uplo, n, &a[a_offset], lda, &w[1], &work[inde], &work[indtau], & + work[indwrk], &llwork, &iinfo, (ftnlen)1); + +/* For eigenvalues only, call DSTERF. For eigenvectors, first call */ +/* DSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the */ +/* tridiagonal matrix, then call DORMTR to multiply it by the */ +/* Householder transformations stored in A. */ + + if (! wantz) { + dsterf_(n, &w[1], &work[inde], info); + } else { + dstedc_((char *)"I", n, &w[1], &work[inde], &work[indwrk], n, &work[indwk2], & + llwrk2, &iwork[1], liwork, info, (ftnlen)1); + dormtr_((char *)"L", uplo, (char *)"N", n, n, &a[a_offset], lda, &work[indtau], &work[ + indwrk], n, &work[indwk2], &llwrk2, &iinfo, (ftnlen)1, ( + ftnlen)1, (ftnlen)1); + dlacpy_((char *)"A", n, n, &work[indwrk], n, &a[a_offset], lda, (ftnlen)1); + } + +/* If matrix was scaled, then rescale eigenvalues appropriately. */ + + if (iscale == 1) { + d__1 = 1. / sigma; + dscal_(n, &d__1, &w[1], &c__1); + } + + work[1] = (doublereal) lopt; + iwork[1] = liopt; + + return 0; + +/* End of DSYEVD */ + +} /* dsyevd_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dsygs2.cpp b/lib/linalg/dsygs2.cpp new file mode 100644 index 0000000000..8b0089be28 --- /dev/null +++ b/lib/linalg/dsygs2.cpp @@ -0,0 +1,381 @@ +/* fortran/dsygs2.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static doublereal c_b6 = -1.; +static integer c__1 = 1; +static doublereal c_b27 = 1.; + +/* > \brief \b DSYGS2 reduces a symmetric definite generalized eigenproblem to standard form, using the factor +ization results obtained from spotrf (unblocked algorithm). */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DSYGS2 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DSYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER UPLO */ +/* INTEGER INFO, ITYPE, LDA, LDB, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), B( LDB, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DSYGS2 reduces a real symmetric-definite generalized eigenproblem */ +/* > to standard form. */ +/* > */ +/* > If ITYPE = 1, the problem is A*x = lambda*B*x, */ +/* > and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T) */ +/* > */ +/* > If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or */ +/* > B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T *A*L. */ +/* > */ +/* > B must have been previously factorized as U**T *U or L*L**T by DPOTRF. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] ITYPE */ +/* > \verbatim */ +/* > ITYPE is INTEGER */ +/* > = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T); */ +/* > = 2 or 3: compute U*A*U**T or L**T *A*L. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > Specifies whether the upper or lower triangular part of the */ +/* > symmetric matrix A is stored, and how B has been factorized. */ +/* > = 'U': Upper triangular */ +/* > = 'L': Lower triangular */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrices A and B. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On entry, the symmetric matrix A. If UPLO = 'U', the leading */ +/* > n by n upper triangular part of A contains the upper */ +/* > triangular part of the matrix A, and the strictly lower */ +/* > triangular part of A is not referenced. If UPLO = 'L', the */ +/* > leading n by n lower triangular part of A contains the lower */ +/* > triangular part of the matrix A, and the strictly upper */ +/* > triangular part of A is not referenced. */ +/* > */ +/* > On exit, if INFO = 0, the transformed matrix, stored in the */ +/* > same format as A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] B */ +/* > \verbatim */ +/* > B is DOUBLE PRECISION array, dimension (LDB,N) */ +/* > The triangular factor from the Cholesky factorization of B, */ +/* > as returned by DPOTRF. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDB */ +/* > \verbatim */ +/* > LDB is INTEGER */ +/* > The leading dimension of the array B. LDB >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit. */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleSYcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dsygs2_(integer *itype, char *uplo, integer *n, + doublereal *a, integer *lda, doublereal *b, integer *ldb, integer * + info, ftnlen uplo_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2; + doublereal d__1; + + /* Local variables */ + integer k; + doublereal ct, akk, bkk; + extern /* Subroutine */ int dsyr2_(char *, integer *, doublereal *, + doublereal *, integer *, doublereal *, integer *, doublereal *, + integer *, ftnlen), dscal_(integer *, doublereal *, doublereal *, + integer *); + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *); + logical upper; + extern /* Subroutine */ int dtrmv_(char *, char *, char *, integer *, + doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, + ftnlen), dtrsv_(char *, char *, char *, integer *, doublereal *, + integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen), + xerbla_(char *, integer *, ftnlen); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + b_dim1 = *ldb; + b_offset = 1 + b_dim1; + b -= b_offset; + + /* Function Body */ + *info = 0; + upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); + if (*itype < 1 || *itype > 3) { + *info = -1; + } else if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + *info = -2; + } else if (*n < 0) { + *info = -3; + } else if (*lda < max(1,*n)) { + *info = -5; + } else if (*ldb < max(1,*n)) { + *info = -7; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DSYGS2", &i__1, (ftnlen)6); + return 0; + } + + if (*itype == 1) { + if (upper) { + +/* Compute inv(U**T)*A*inv(U) */ + + i__1 = *n; + for (k = 1; k <= i__1; ++k) { + +/* Update the upper triangle of A(k:n,k:n) */ + + akk = a[k + k * a_dim1]; + bkk = b[k + k * b_dim1]; +/* Computing 2nd power */ + d__1 = bkk; + akk /= d__1 * d__1; + a[k + k * a_dim1] = akk; + if (k < *n) { + i__2 = *n - k; + d__1 = 1. / bkk; + dscal_(&i__2, &d__1, &a[k + (k + 1) * a_dim1], lda); + ct = akk * -.5; + i__2 = *n - k; + daxpy_(&i__2, &ct, &b[k + (k + 1) * b_dim1], ldb, &a[k + ( + k + 1) * a_dim1], lda); + i__2 = *n - k; + dsyr2_(uplo, &i__2, &c_b6, &a[k + (k + 1) * a_dim1], lda, + &b[k + (k + 1) * b_dim1], ldb, &a[k + 1 + (k + 1) + * a_dim1], lda, (ftnlen)1); + i__2 = *n - k; + daxpy_(&i__2, &ct, &b[k + (k + 1) * b_dim1], ldb, &a[k + ( + k + 1) * a_dim1], lda); + i__2 = *n - k; + dtrsv_(uplo, (char *)"Transpose", (char *)"Non-unit", &i__2, &b[k + 1 + ( + k + 1) * b_dim1], ldb, &a[k + (k + 1) * a_dim1], + lda, (ftnlen)1, (ftnlen)9, (ftnlen)8); + } +/* L10: */ + } + } else { + +/* Compute inv(L)*A*inv(L**T) */ + + i__1 = *n; + for (k = 1; k <= i__1; ++k) { + +/* Update the lower triangle of A(k:n,k:n) */ + + akk = a[k + k * a_dim1]; + bkk = b[k + k * b_dim1]; +/* Computing 2nd power */ + d__1 = bkk; + akk /= d__1 * d__1; + a[k + k * a_dim1] = akk; + if (k < *n) { + i__2 = *n - k; + d__1 = 1. / bkk; + dscal_(&i__2, &d__1, &a[k + 1 + k * a_dim1], &c__1); + ct = akk * -.5; + i__2 = *n - k; + daxpy_(&i__2, &ct, &b[k + 1 + k * b_dim1], &c__1, &a[k + + 1 + k * a_dim1], &c__1); + i__2 = *n - k; + dsyr2_(uplo, &i__2, &c_b6, &a[k + 1 + k * a_dim1], &c__1, + &b[k + 1 + k * b_dim1], &c__1, &a[k + 1 + (k + 1) + * a_dim1], lda, (ftnlen)1); + i__2 = *n - k; + daxpy_(&i__2, &ct, &b[k + 1 + k * b_dim1], &c__1, &a[k + + 1 + k * a_dim1], &c__1); + i__2 = *n - k; + dtrsv_(uplo, (char *)"No transpose", (char *)"Non-unit", &i__2, &b[k + 1 + + (k + 1) * b_dim1], ldb, &a[k + 1 + k * a_dim1], + &c__1, (ftnlen)1, (ftnlen)12, (ftnlen)8); + } +/* L20: */ + } + } + } else { + if (upper) { + +/* Compute U*A*U**T */ + + i__1 = *n; + for (k = 1; k <= i__1; ++k) { + +/* Update the upper triangle of A(1:k,1:k) */ + + akk = a[k + k * a_dim1]; + bkk = b[k + k * b_dim1]; + i__2 = k - 1; + dtrmv_(uplo, (char *)"No transpose", (char *)"Non-unit", &i__2, &b[b_offset], + ldb, &a[k * a_dim1 + 1], &c__1, (ftnlen)1, (ftnlen)12, + (ftnlen)8); + ct = akk * .5; + i__2 = k - 1; + daxpy_(&i__2, &ct, &b[k * b_dim1 + 1], &c__1, &a[k * a_dim1 + + 1], &c__1); + i__2 = k - 1; + dsyr2_(uplo, &i__2, &c_b27, &a[k * a_dim1 + 1], &c__1, &b[k * + b_dim1 + 1], &c__1, &a[a_offset], lda, (ftnlen)1); + i__2 = k - 1; + daxpy_(&i__2, &ct, &b[k * b_dim1 + 1], &c__1, &a[k * a_dim1 + + 1], &c__1); + i__2 = k - 1; + dscal_(&i__2, &bkk, &a[k * a_dim1 + 1], &c__1); +/* Computing 2nd power */ + d__1 = bkk; + a[k + k * a_dim1] = akk * (d__1 * d__1); +/* L30: */ + } + } else { + +/* Compute L**T *A*L */ + + i__1 = *n; + for (k = 1; k <= i__1; ++k) { + +/* Update the lower triangle of A(1:k,1:k) */ + + akk = a[k + k * a_dim1]; + bkk = b[k + k * b_dim1]; + i__2 = k - 1; + dtrmv_(uplo, (char *)"Transpose", (char *)"Non-unit", &i__2, &b[b_offset], + ldb, &a[k + a_dim1], lda, (ftnlen)1, (ftnlen)9, ( + ftnlen)8); + ct = akk * .5; + i__2 = k - 1; + daxpy_(&i__2, &ct, &b[k + b_dim1], ldb, &a[k + a_dim1], lda); + i__2 = k - 1; + dsyr2_(uplo, &i__2, &c_b27, &a[k + a_dim1], lda, &b[k + + b_dim1], ldb, &a[a_offset], lda, (ftnlen)1); + i__2 = k - 1; + daxpy_(&i__2, &ct, &b[k + b_dim1], ldb, &a[k + a_dim1], lda); + i__2 = k - 1; + dscal_(&i__2, &bkk, &a[k + a_dim1], lda); +/* Computing 2nd power */ + d__1 = bkk; + a[k + k * a_dim1] = akk * (d__1 * d__1); +/* L40: */ + } + } + } + return 0; + +/* End of DSYGS2 */ + +} /* dsygs2_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dsygst.cpp b/lib/linalg/dsygst.cpp new file mode 100644 index 0000000000..2f5189a6f1 --- /dev/null +++ b/lib/linalg/dsygst.cpp @@ -0,0 +1,436 @@ +/* fortran/dsygst.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c_n1 = -1; +static doublereal c_b14 = 1.; +static doublereal c_b16 = -.5; +static doublereal c_b19 = -1.; +static doublereal c_b52 = .5; + +/* > \brief \b DSYGST */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DSYGST + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER UPLO */ +/* INTEGER INFO, ITYPE, LDA, LDB, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), B( LDB, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DSYGST reduces a real symmetric-definite generalized eigenproblem */ +/* > to standard form. */ +/* > */ +/* > If ITYPE = 1, the problem is A*x = lambda*B*x, */ +/* > and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T) */ +/* > */ +/* > If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or */ +/* > B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T*A*L. */ +/* > */ +/* > B must have been previously factorized as U**T*U or L*L**T by DPOTRF. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] ITYPE */ +/* > \verbatim */ +/* > ITYPE is INTEGER */ +/* > = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T); */ +/* > = 2 or 3: compute U*A*U**T or L**T*A*L. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > = 'U': Upper triangle of A is stored and B is factored as */ +/* > U**T*U; */ +/* > = 'L': Lower triangle of A is stored and B is factored as */ +/* > L*L**T. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrices A and B. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On entry, the symmetric matrix A. If UPLO = 'U', the leading */ +/* > N-by-N upper triangular part of A contains the upper */ +/* > triangular part of the matrix A, and the strictly lower */ +/* > triangular part of A is not referenced. If UPLO = 'L', the */ +/* > leading N-by-N lower triangular part of A contains the lower */ +/* > triangular part of the matrix A, and the strictly upper */ +/* > triangular part of A is not referenced. */ +/* > */ +/* > On exit, if INFO = 0, the transformed matrix, stored in the */ +/* > same format as A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] B */ +/* > \verbatim */ +/* > B is DOUBLE PRECISION array, dimension (LDB,N) */ +/* > The triangular factor from the Cholesky factorization of B, */ +/* > as returned by DPOTRF. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDB */ +/* > \verbatim */ +/* > LDB is INTEGER */ +/* > The leading dimension of the array B. LDB >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleSYcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dsygst_(integer *itype, char *uplo, integer *n, + doublereal *a, integer *lda, doublereal *b, integer *ldb, integer * + info, ftnlen uplo_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3; + + /* Local variables */ + integer k, kb, nb; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int dtrmm_(char *, char *, char *, char *, + integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen), dsymm_( + char *, char *, integer *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, ftnlen, ftnlen); + logical upper; + extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, + integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen), dsygs2_( + integer *, char *, integer *, doublereal *, integer *, doublereal + *, integer *, integer *, ftnlen), dsyr2k_(char *, char *, integer + *, integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen) + , xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + b_dim1 = *ldb; + b_offset = 1 + b_dim1; + b -= b_offset; + + /* Function Body */ + *info = 0; + upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); + if (*itype < 1 || *itype > 3) { + *info = -1; + } else if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + *info = -2; + } else if (*n < 0) { + *info = -3; + } else if (*lda < max(1,*n)) { + *info = -5; + } else if (*ldb < max(1,*n)) { + *info = -7; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DSYGST", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*n == 0) { + return 0; + } + +/* Determine the block size for this environment. */ + + nb = ilaenv_(&c__1, (char *)"DSYGST", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, ( + ftnlen)1); + + if (nb <= 1 || nb >= *n) { + +/* Use unblocked code */ + + dsygs2_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info, ( + ftnlen)1); + } else { + +/* Use blocked code */ + + if (*itype == 1) { + if (upper) { + +/* Compute inv(U**T)*A*inv(U) */ + + i__1 = *n; + i__2 = nb; + for (k = 1; i__2 < 0 ? k >= i__1 : k <= i__1; k += i__2) { +/* Computing MIN */ + i__3 = *n - k + 1; + kb = min(i__3,nb); + +/* Update the upper triangle of A(k:n,k:n) */ + + dsygs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k + + k * b_dim1], ldb, info, (ftnlen)1); + if (k + kb <= *n) { + i__3 = *n - k - kb + 1; + dtrsm_((char *)"Left", uplo, (char *)"Transpose", (char *)"Non-unit", &kb, & + i__3, &c_b14, &b[k + k * b_dim1], ldb, &a[k + + (k + kb) * a_dim1], lda, (ftnlen)4, (ftnlen)1, + (ftnlen)9, (ftnlen)8); + i__3 = *n - k - kb + 1; + dsymm_((char *)"Left", uplo, &kb, &i__3, &c_b16, &a[k + k * + a_dim1], lda, &b[k + (k + kb) * b_dim1], ldb, + &c_b14, &a[k + (k + kb) * a_dim1], lda, ( + ftnlen)4, (ftnlen)1); + i__3 = *n - k - kb + 1; + dsyr2k_(uplo, (char *)"Transpose", &i__3, &kb, &c_b19, &a[k + + (k + kb) * a_dim1], lda, &b[k + (k + kb) * + b_dim1], ldb, &c_b14, &a[k + kb + (k + kb) * + a_dim1], lda, (ftnlen)1, (ftnlen)9); + i__3 = *n - k - kb + 1; + dsymm_((char *)"Left", uplo, &kb, &i__3, &c_b16, &a[k + k * + a_dim1], lda, &b[k + (k + kb) * b_dim1], ldb, + &c_b14, &a[k + (k + kb) * a_dim1], lda, ( + ftnlen)4, (ftnlen)1); + i__3 = *n - k - kb + 1; + dtrsm_((char *)"Right", uplo, (char *)"No transpose", (char *)"Non-unit", &kb, + &i__3, &c_b14, &b[k + kb + (k + kb) * b_dim1] + , ldb, &a[k + (k + kb) * a_dim1], lda, ( + ftnlen)5, (ftnlen)1, (ftnlen)12, (ftnlen)8); + } +/* L10: */ + } + } else { + +/* Compute inv(L)*A*inv(L**T) */ + + i__2 = *n; + i__1 = nb; + for (k = 1; i__1 < 0 ? k >= i__2 : k <= i__2; k += i__1) { +/* Computing MIN */ + i__3 = *n - k + 1; + kb = min(i__3,nb); + +/* Update the lower triangle of A(k:n,k:n) */ + + dsygs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k + + k * b_dim1], ldb, info, (ftnlen)1); + if (k + kb <= *n) { + i__3 = *n - k - kb + 1; + dtrsm_((char *)"Right", uplo, (char *)"Transpose", (char *)"Non-unit", &i__3, + &kb, &c_b14, &b[k + k * b_dim1], ldb, &a[k + + kb + k * a_dim1], lda, (ftnlen)5, (ftnlen)1, ( + ftnlen)9, (ftnlen)8); + i__3 = *n - k - kb + 1; + dsymm_((char *)"Right", uplo, &i__3, &kb, &c_b16, &a[k + k * + a_dim1], lda, &b[k + kb + k * b_dim1], ldb, & + c_b14, &a[k + kb + k * a_dim1], lda, (ftnlen) + 5, (ftnlen)1); + i__3 = *n - k - kb + 1; + dsyr2k_(uplo, (char *)"No transpose", &i__3, &kb, &c_b19, &a[ + k + kb + k * a_dim1], lda, &b[k + kb + k * + b_dim1], ldb, &c_b14, &a[k + kb + (k + kb) * + a_dim1], lda, (ftnlen)1, (ftnlen)12); + i__3 = *n - k - kb + 1; + dsymm_((char *)"Right", uplo, &i__3, &kb, &c_b16, &a[k + k * + a_dim1], lda, &b[k + kb + k * b_dim1], ldb, & + c_b14, &a[k + kb + k * a_dim1], lda, (ftnlen) + 5, (ftnlen)1); + i__3 = *n - k - kb + 1; + dtrsm_((char *)"Left", uplo, (char *)"No transpose", (char *)"Non-unit", & + i__3, &kb, &c_b14, &b[k + kb + (k + kb) * + b_dim1], ldb, &a[k + kb + k * a_dim1], lda, ( + ftnlen)4, (ftnlen)1, (ftnlen)12, (ftnlen)8); + } +/* L20: */ + } + } + } else { + if (upper) { + +/* Compute U*A*U**T */ + + i__1 = *n; + i__2 = nb; + for (k = 1; i__2 < 0 ? k >= i__1 : k <= i__1; k += i__2) { +/* Computing MIN */ + i__3 = *n - k + 1; + kb = min(i__3,nb); + +/* Update the upper triangle of A(1:k+kb-1,1:k+kb-1) */ + + i__3 = k - 1; + dtrmm_((char *)"Left", uplo, (char *)"No transpose", (char *)"Non-unit", &i__3, & + kb, &c_b14, &b[b_offset], ldb, &a[k * a_dim1 + 1], + lda, (ftnlen)4, (ftnlen)1, (ftnlen)12, (ftnlen)8) + ; + i__3 = k - 1; + dsymm_((char *)"Right", uplo, &i__3, &kb, &c_b52, &a[k + k * + a_dim1], lda, &b[k * b_dim1 + 1], ldb, &c_b14, &a[ + k * a_dim1 + 1], lda, (ftnlen)5, (ftnlen)1); + i__3 = k - 1; + dsyr2k_(uplo, (char *)"No transpose", &i__3, &kb, &c_b14, &a[k * + a_dim1 + 1], lda, &b[k * b_dim1 + 1], ldb, &c_b14, + &a[a_offset], lda, (ftnlen)1, (ftnlen)12); + i__3 = k - 1; + dsymm_((char *)"Right", uplo, &i__3, &kb, &c_b52, &a[k + k * + a_dim1], lda, &b[k * b_dim1 + 1], ldb, &c_b14, &a[ + k * a_dim1 + 1], lda, (ftnlen)5, (ftnlen)1); + i__3 = k - 1; + dtrmm_((char *)"Right", uplo, (char *)"Transpose", (char *)"Non-unit", &i__3, &kb, + &c_b14, &b[k + k * b_dim1], ldb, &a[k * a_dim1 + + 1], lda, (ftnlen)5, (ftnlen)1, (ftnlen)9, (ftnlen) + 8); + dsygs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k + + k * b_dim1], ldb, info, (ftnlen)1); +/* L30: */ + } + } else { + +/* Compute L**T*A*L */ + + i__2 = *n; + i__1 = nb; + for (k = 1; i__1 < 0 ? k >= i__2 : k <= i__2; k += i__1) { +/* Computing MIN */ + i__3 = *n - k + 1; + kb = min(i__3,nb); + +/* Update the lower triangle of A(1:k+kb-1,1:k+kb-1) */ + + i__3 = k - 1; + dtrmm_((char *)"Right", uplo, (char *)"No transpose", (char *)"Non-unit", &kb, & + i__3, &c_b14, &b[b_offset], ldb, &a[k + a_dim1], + lda, (ftnlen)5, (ftnlen)1, (ftnlen)12, (ftnlen)8); + i__3 = k - 1; + dsymm_((char *)"Left", uplo, &kb, &i__3, &c_b52, &a[k + k * + a_dim1], lda, &b[k + b_dim1], ldb, &c_b14, &a[k + + a_dim1], lda, (ftnlen)4, (ftnlen)1); + i__3 = k - 1; + dsyr2k_(uplo, (char *)"Transpose", &i__3, &kb, &c_b14, &a[k + + a_dim1], lda, &b[k + b_dim1], ldb, &c_b14, &a[ + a_offset], lda, (ftnlen)1, (ftnlen)9); + i__3 = k - 1; + dsymm_((char *)"Left", uplo, &kb, &i__3, &c_b52, &a[k + k * + a_dim1], lda, &b[k + b_dim1], ldb, &c_b14, &a[k + + a_dim1], lda, (ftnlen)4, (ftnlen)1); + i__3 = k - 1; + dtrmm_((char *)"Left", uplo, (char *)"Transpose", (char *)"Non-unit", &kb, &i__3, + &c_b14, &b[k + k * b_dim1], ldb, &a[k + a_dim1], + lda, (ftnlen)4, (ftnlen)1, (ftnlen)9, (ftnlen)8); + dsygs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k + + k * b_dim1], ldb, info, (ftnlen)1); +/* L40: */ + } + } + } + } + return 0; + +/* End of DSYGST */ + +} /* dsygst_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dsygv.cpp b/lib/linalg/dsygv.cpp new file mode 100644 index 0000000000..e7078e8006 --- /dev/null +++ b/lib/linalg/dsygv.cpp @@ -0,0 +1,384 @@ +/* fortran/dsygv.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c_n1 = -1; +static doublereal c_b16 = 1.; + +/* > \brief \b DSYGV */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DSYGV + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DSYGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, */ +/* LWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER JOBZ, UPLO */ +/* INTEGER INFO, ITYPE, LDA, LDB, LWORK, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DSYGV computes all the eigenvalues, and optionally, the eigenvectors */ +/* > of a real generalized symmetric-definite eigenproblem, of the form */ +/* > A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. */ +/* > Here A and B are assumed to be symmetric and B is also */ +/* > positive definite. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] ITYPE */ +/* > \verbatim */ +/* > ITYPE is INTEGER */ +/* > Specifies the problem type to be solved: */ +/* > = 1: A*x = (lambda)*B*x */ +/* > = 2: A*B*x = (lambda)*x */ +/* > = 3: B*A*x = (lambda)*x */ +/* > \endverbatim */ +/* > */ +/* > \param[in] JOBZ */ +/* > \verbatim */ +/* > JOBZ is CHARACTER*1 */ +/* > = 'N': Compute eigenvalues only; */ +/* > = 'V': Compute eigenvalues and eigenvectors. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > = 'U': Upper triangles of A and B are stored; */ +/* > = 'L': Lower triangles of A and B are stored. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrices A and B. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA, N) */ +/* > On entry, the symmetric matrix A. If UPLO = 'U', the */ +/* > leading N-by-N upper triangular part of A contains the */ +/* > upper triangular part of the matrix A. If UPLO = 'L', */ +/* > the leading N-by-N lower triangular part of A contains */ +/* > the lower triangular part of the matrix A. */ +/* > */ +/* > On exit, if JOBZ = 'V', then if INFO = 0, A contains the */ +/* > matrix Z of eigenvectors. The eigenvectors are normalized */ +/* > as follows: */ +/* > if ITYPE = 1 or 2, Z**T*B*Z = I; */ +/* > if ITYPE = 3, Z**T*inv(B)*Z = I. */ +/* > If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') */ +/* > or the lower triangle (if UPLO='L') of A, including the */ +/* > diagonal, is destroyed. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] B */ +/* > \verbatim */ +/* > B is DOUBLE PRECISION array, dimension (LDB, N) */ +/* > On entry, the symmetric positive definite matrix B. */ +/* > If UPLO = 'U', the leading N-by-N upper triangular part of B */ +/* > contains the upper triangular part of the matrix B. */ +/* > If UPLO = 'L', the leading N-by-N lower triangular part of B */ +/* > contains the lower triangular part of the matrix B. */ +/* > */ +/* > On exit, if INFO <= N, the part of B containing the matrix is */ +/* > overwritten by the triangular factor U or L from the Cholesky */ +/* > factorization B = U**T*U or B = L*L**T. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDB */ +/* > \verbatim */ +/* > LDB is INTEGER */ +/* > The leading dimension of the array B. LDB >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] W */ +/* > \verbatim */ +/* > W is DOUBLE PRECISION array, dimension (N) */ +/* > If INFO = 0, the eigenvalues in ascending order. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ +/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LWORK */ +/* > \verbatim */ +/* > LWORK is INTEGER */ +/* > The length of the array WORK. LWORK >= max(1,3*N-1). */ +/* > For optimal efficiency, LWORK >= (NB+2)*N, */ +/* > where NB is the blocksize for DSYTRD returned by ILAENV. */ +/* > */ +/* > If LWORK = -1, then a workspace query is assumed; the routine */ +/* > only calculates the optimal size of the WORK array, returns */ +/* > this value as the first entry of the WORK array, and no error */ +/* > message related to LWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > > 0: DPOTRF or DSYEV returned an error code: */ +/* > <= N: if INFO = i, DSYEV failed to converge; */ +/* > i off-diagonal elements of an intermediate */ +/* > tridiagonal form did not converge to zero; */ +/* > > N: if INFO = N + i, for 1 <= i <= N, then the leading */ +/* > minor of order i of B is not positive definite. */ +/* > The factorization of B could not be completed and */ +/* > no eigenvalues or eigenvectors were computed. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleSYeigen */ + +/* ===================================================================== */ +/* Subroutine */ int dsygv_(integer *itype, char *jobz, char *uplo, integer * + n, doublereal *a, integer *lda, doublereal *b, integer *ldb, + doublereal *w, doublereal *work, integer *lwork, integer *info, + ftnlen jobz_len, ftnlen uplo_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2; + + /* Local variables */ + integer nb, neig; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int dtrmm_(char *, char *, char *, char *, + integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + char trans[1]; + extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, + integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + logical upper; + extern /* Subroutine */ int dsyev_(char *, char *, integer *, doublereal * + , integer *, doublereal *, doublereal *, integer *, integer *, + ftnlen, ftnlen); + logical wantz; + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dpotrf_(char *, integer *, doublereal *, + integer *, integer *, ftnlen); + integer lwkmin; + extern /* Subroutine */ int dsygst_(integer *, char *, integer *, + doublereal *, integer *, doublereal *, integer *, integer *, + ftnlen); + integer lwkopt; + logical lquery; + + +/* -- LAPACK driver routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + b_dim1 = *ldb; + b_offset = 1 + b_dim1; + b -= b_offset; + --w; + --work; + + /* Function Body */ + wantz = lsame_(jobz, (char *)"V", (ftnlen)1, (ftnlen)1); + upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); + lquery = *lwork == -1; + + *info = 0; + if (*itype < 1 || *itype > 3) { + *info = -1; + } else if (! (wantz || lsame_(jobz, (char *)"N", (ftnlen)1, (ftnlen)1))) { + *info = -2; + } else if (! (upper || lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1))) { + *info = -3; + } else if (*n < 0) { + *info = -4; + } else if (*lda < max(1,*n)) { + *info = -6; + } else if (*ldb < max(1,*n)) { + *info = -8; + } + + if (*info == 0) { +/* Computing MAX */ + i__1 = 1, i__2 = *n * 3 - 1; + lwkmin = max(i__1,i__2); + nb = ilaenv_(&c__1, (char *)"DSYTRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, + (ftnlen)1); +/* Computing MAX */ + i__1 = lwkmin, i__2 = (nb + 2) * *n; + lwkopt = max(i__1,i__2); + work[1] = (doublereal) lwkopt; + + if (*lwork < lwkmin && ! lquery) { + *info = -11; + } + } + + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DSYGV ", &i__1, (ftnlen)6); + return 0; + } else if (lquery) { + return 0; + } + +/* Quick return if possible */ + + if (*n == 0) { + return 0; + } + +/* Form a Cholesky factorization of B. */ + + dpotrf_(uplo, n, &b[b_offset], ldb, info, (ftnlen)1); + if (*info != 0) { + *info = *n + *info; + return 0; + } + +/* Transform problem to standard eigenvalue problem and solve. */ + + dsygst_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info, ( + ftnlen)1); + dsyev_(jobz, uplo, n, &a[a_offset], lda, &w[1], &work[1], lwork, info, ( + ftnlen)1, (ftnlen)1); + + if (wantz) { + +/* Backtransform eigenvectors to the original problem. */ + + neig = *n; + if (*info > 0) { + neig = *info - 1; + } + if (*itype == 1 || *itype == 2) { + +/* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; */ +/* backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y */ + + if (upper) { + *(unsigned char *)trans = 'N'; + } else { + *(unsigned char *)trans = 'T'; + } + + dtrsm_((char *)"Left", uplo, trans, (char *)"Non-unit", n, &neig, &c_b16, &b[ + b_offset], ldb, &a[a_offset], lda, (ftnlen)4, (ftnlen)1, ( + ftnlen)1, (ftnlen)8); + + } else if (*itype == 3) { + +/* For B*A*x=(lambda)*x; */ +/* backtransform eigenvectors: x = L*y or U**T*y */ + + if (upper) { + *(unsigned char *)trans = 'T'; + } else { + *(unsigned char *)trans = 'N'; + } + + dtrmm_((char *)"Left", uplo, trans, (char *)"Non-unit", n, &neig, &c_b16, &b[ + b_offset], ldb, &a[a_offset], lda, (ftnlen)4, (ftnlen)1, ( + ftnlen)1, (ftnlen)8); + } + } + + work[1] = (doublereal) lwkopt; + return 0; + +/* End of DSYGV */ + +} /* dsygv_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dsygvd.cpp b/lib/linalg/dsygvd.cpp new file mode 100644 index 0000000000..80513dfdcc --- /dev/null +++ b/lib/linalg/dsygvd.cpp @@ -0,0 +1,445 @@ +/* fortran/dsygvd.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static doublereal c_b11 = 1.; + +/* > \brief \b DSYGVD */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DSYGVD + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DSYGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, */ +/* LWORK, IWORK, LIWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER JOBZ, UPLO */ +/* INTEGER INFO, ITYPE, LDA, LDB, LIWORK, LWORK, N */ +/* .. */ +/* .. Array Arguments .. */ +/* INTEGER IWORK( * ) */ +/* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DSYGVD computes all the eigenvalues, and optionally, the eigenvectors */ +/* > of a real generalized symmetric-definite eigenproblem, of the form */ +/* > A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and */ +/* > B are assumed to be symmetric and B is also positive definite. */ +/* > If eigenvectors are desired, it uses a divide and conquer algorithm. */ +/* > */ +/* > The divide and conquer algorithm makes very mild assumptions about */ +/* > floating point arithmetic. It will work on machines with a guard */ +/* > digit in add/subtract, or on those binary machines without guard */ +/* > digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */ +/* > Cray-2. It could conceivably fail on hexadecimal or decimal machines */ +/* > without guard digits, but we know of none. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] ITYPE */ +/* > \verbatim */ +/* > ITYPE is INTEGER */ +/* > Specifies the problem type to be solved: */ +/* > = 1: A*x = (lambda)*B*x */ +/* > = 2: A*B*x = (lambda)*x */ +/* > = 3: B*A*x = (lambda)*x */ +/* > \endverbatim */ +/* > */ +/* > \param[in] JOBZ */ +/* > \verbatim */ +/* > JOBZ is CHARACTER*1 */ +/* > = 'N': Compute eigenvalues only; */ +/* > = 'V': Compute eigenvalues and eigenvectors. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > = 'U': Upper triangles of A and B are stored; */ +/* > = 'L': Lower triangles of A and B are stored. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrices A and B. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA, N) */ +/* > On entry, the symmetric matrix A. If UPLO = 'U', the */ +/* > leading N-by-N upper triangular part of A contains the */ +/* > upper triangular part of the matrix A. If UPLO = 'L', */ +/* > the leading N-by-N lower triangular part of A contains */ +/* > the lower triangular part of the matrix A. */ +/* > */ +/* > On exit, if JOBZ = 'V', then if INFO = 0, A contains the */ +/* > matrix Z of eigenvectors. The eigenvectors are normalized */ +/* > as follows: */ +/* > if ITYPE = 1 or 2, Z**T*B*Z = I; */ +/* > if ITYPE = 3, Z**T*inv(B)*Z = I. */ +/* > If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') */ +/* > or the lower triangle (if UPLO='L') of A, including the */ +/* > diagonal, is destroyed. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] B */ +/* > \verbatim */ +/* > B is DOUBLE PRECISION array, dimension (LDB, N) */ +/* > On entry, the symmetric matrix B. If UPLO = 'U', the */ +/* > leading N-by-N upper triangular part of B contains the */ +/* > upper triangular part of the matrix B. If UPLO = 'L', */ +/* > the leading N-by-N lower triangular part of B contains */ +/* > the lower triangular part of the matrix B. */ +/* > */ +/* > On exit, if INFO <= N, the part of B containing the matrix is */ +/* > overwritten by the triangular factor U or L from the Cholesky */ +/* > factorization B = U**T*U or B = L*L**T. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDB */ +/* > \verbatim */ +/* > LDB is INTEGER */ +/* > The leading dimension of the array B. LDB >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] W */ +/* > \verbatim */ +/* > W is DOUBLE PRECISION array, dimension (N) */ +/* > If INFO = 0, the eigenvalues in ascending order. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ +/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LWORK */ +/* > \verbatim */ +/* > LWORK is INTEGER */ +/* > The dimension of the array WORK. */ +/* > If N <= 1, LWORK >= 1. */ +/* > If JOBZ = 'N' and N > 1, LWORK >= 2*N+1. */ +/* > If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2. */ +/* > */ +/* > If LWORK = -1, then a workspace query is assumed; the routine */ +/* > only calculates the optimal sizes of the WORK and IWORK */ +/* > arrays, returns these values as the first entries of the WORK */ +/* > and IWORK arrays, and no error message related to LWORK or */ +/* > LIWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] IWORK */ +/* > \verbatim */ +/* > IWORK is INTEGER array, dimension (MAX(1,LIWORK)) */ +/* > On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LIWORK */ +/* > \verbatim */ +/* > LIWORK is INTEGER */ +/* > The dimension of the array IWORK. */ +/* > If N <= 1, LIWORK >= 1. */ +/* > If JOBZ = 'N' and N > 1, LIWORK >= 1. */ +/* > If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. */ +/* > */ +/* > If LIWORK = -1, then a workspace query is assumed; the */ +/* > routine only calculates the optimal sizes of the WORK and */ +/* > IWORK arrays, returns these values as the first entries of */ +/* > the WORK and IWORK arrays, and no error message related to */ +/* > LWORK or LIWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > > 0: DPOTRF or DSYEVD returned an error code: */ +/* > <= N: if INFO = i and JOBZ = 'N', then the algorithm */ +/* > failed to converge; i off-diagonal elements of an */ +/* > intermediate tridiagonal form did not converge to */ +/* > zero; */ +/* > if INFO = i and JOBZ = 'V', then the algorithm */ +/* > failed to compute an eigenvalue while working on */ +/* > the submatrix lying in rows and columns INFO/(N+1) */ +/* > through mod(INFO,N+1); */ +/* > > N: if INFO = N + i, for 1 <= i <= N, then the leading */ +/* > minor of order i of B is not positive definite. */ +/* > The factorization of B could not be completed and */ +/* > no eigenvalues or eigenvectors were computed. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleSYeigen */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > Modified so that no backsubstitution is performed if DSYEVD fails to */ +/* > converge (NEIG in old code could be greater than N causing out of */ +/* > bounds reference to A - reported by Ralf Meyer). Also corrected the */ +/* > description of INFO and the test on ITYPE. Sven, 16 Feb 05. */ +/* > \endverbatim */ + +/* > \par Contributors: */ +/* ================== */ +/* > */ +/* > Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dsygvd_(integer *itype, char *jobz, char *uplo, integer * + n, doublereal *a, integer *lda, doublereal *b, integer *ldb, + doublereal *w, doublereal *work, integer *lwork, integer *iwork, + integer *liwork, integer *info, ftnlen jobz_len, ftnlen uplo_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, b_dim1, b_offset, i__1; + doublereal d__1, d__2; + + /* Local variables */ + integer lopt; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int dtrmm_(char *, char *, char *, char *, + integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + integer lwmin; + char trans[1]; + integer liopt; + extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, + integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + logical upper, wantz; + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), dpotrf_( + char *, integer *, doublereal *, integer *, integer *, ftnlen); + integer liwmin; + extern /* Subroutine */ int dsyevd_(char *, char *, integer *, doublereal + *, integer *, doublereal *, doublereal *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen), dsygst_(integer *, char *, + integer *, doublereal *, integer *, doublereal *, integer *, + integer *, ftnlen); + logical lquery; + + +/* -- LAPACK driver routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + b_dim1 = *ldb; + b_offset = 1 + b_dim1; + b -= b_offset; + --w; + --work; + --iwork; + + /* Function Body */ + wantz = lsame_(jobz, (char *)"V", (ftnlen)1, (ftnlen)1); + upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); + lquery = *lwork == -1 || *liwork == -1; + + *info = 0; + if (*n <= 1) { + liwmin = 1; + lwmin = 1; + } else if (wantz) { + liwmin = *n * 5 + 3; +/* Computing 2nd power */ + i__1 = *n; + lwmin = *n * 6 + 1 + (i__1 * i__1 << 1); + } else { + liwmin = 1; + lwmin = (*n << 1) + 1; + } + lopt = lwmin; + liopt = liwmin; + if (*itype < 1 || *itype > 3) { + *info = -1; + } else if (! (wantz || lsame_(jobz, (char *)"N", (ftnlen)1, (ftnlen)1))) { + *info = -2; + } else if (! (upper || lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1))) { + *info = -3; + } else if (*n < 0) { + *info = -4; + } else if (*lda < max(1,*n)) { + *info = -6; + } else if (*ldb < max(1,*n)) { + *info = -8; + } + + if (*info == 0) { + work[1] = (doublereal) lopt; + iwork[1] = liopt; + + if (*lwork < lwmin && ! lquery) { + *info = -11; + } else if (*liwork < liwmin && ! lquery) { + *info = -13; + } + } + + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DSYGVD", &i__1, (ftnlen)6); + return 0; + } else if (lquery) { + return 0; + } + +/* Quick return if possible */ + + if (*n == 0) { + return 0; + } + +/* Form a Cholesky factorization of B. */ + + dpotrf_(uplo, n, &b[b_offset], ldb, info, (ftnlen)1); + if (*info != 0) { + *info = *n + *info; + return 0; + } + +/* Transform problem to standard eigenvalue problem and solve. */ + + dsygst_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info, ( + ftnlen)1); + dsyevd_(jobz, uplo, n, &a[a_offset], lda, &w[1], &work[1], lwork, &iwork[ + 1], liwork, info, (ftnlen)1, (ftnlen)1); +/* Computing MAX */ + d__1 = (doublereal) lopt; + lopt = (integer) max(d__1,work[1]); +/* Computing MAX */ + d__1 = (doublereal) liopt, d__2 = (doublereal) iwork[1]; + liopt = (integer) max(d__1,d__2); + + if (wantz && *info == 0) { + +/* Backtransform eigenvectors to the original problem. */ + + if (*itype == 1 || *itype == 2) { + +/* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; */ +/* backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y */ + + if (upper) { + *(unsigned char *)trans = 'N'; + } else { + *(unsigned char *)trans = 'T'; + } + + dtrsm_((char *)"Left", uplo, trans, (char *)"Non-unit", n, n, &c_b11, &b[b_offset] + , ldb, &a[a_offset], lda, (ftnlen)4, (ftnlen)1, (ftnlen)1, + (ftnlen)8); + + } else if (*itype == 3) { + +/* For B*A*x=(lambda)*x; */ +/* backtransform eigenvectors: x = L*y or U**T*y */ + + if (upper) { + *(unsigned char *)trans = 'T'; + } else { + *(unsigned char *)trans = 'N'; + } + + dtrmm_((char *)"Left", uplo, trans, (char *)"Non-unit", n, n, &c_b11, &b[b_offset] + , ldb, &a[a_offset], lda, (ftnlen)4, (ftnlen)1, (ftnlen)1, + (ftnlen)8); + } + } + + work[1] = (doublereal) lopt; + iwork[1] = liopt; + + return 0; + +/* End of DSYGVD */ + +} /* dsygvd_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dsymm.cpp b/lib/linalg/dsymm.cpp new file mode 100644 index 0000000000..223551570d --- /dev/null +++ b/lib/linalg/dsymm.cpp @@ -0,0 +1,440 @@ +/* fortran/dsymm.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DSYMM */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC) */ + +/* .. Scalar Arguments .. */ +/* DOUBLE PRECISION ALPHA,BETA */ +/* INTEGER LDA,LDB,LDC,M,N */ +/* CHARACTER SIDE,UPLO */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DSYMM performs one of the matrix-matrix operations */ +/* > */ +/* > C := alpha*A*B + beta*C, */ +/* > */ +/* > or */ +/* > */ +/* > C := alpha*B*A + beta*C, */ +/* > */ +/* > where alpha and beta are scalars, A is a symmetric matrix and B and */ +/* > C are m by n matrices. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] SIDE */ +/* > \verbatim */ +/* > SIDE is CHARACTER*1 */ +/* > On entry, SIDE specifies whether the symmetric matrix A */ +/* > appears on the left or right in the operation as follows: */ +/* > */ +/* > SIDE = 'L' or 'l' C := alpha*A*B + beta*C, */ +/* > */ +/* > SIDE = 'R' or 'r' C := alpha*B*A + beta*C, */ +/* > \endverbatim */ +/* > */ +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > On entry, UPLO specifies whether the upper or lower */ +/* > triangular part of the symmetric matrix A is to be */ +/* > referenced as follows: */ +/* > */ +/* > UPLO = 'U' or 'u' Only the upper triangular part of the */ +/* > symmetric matrix is to be referenced. */ +/* > */ +/* > UPLO = 'L' or 'l' Only the lower triangular part of the */ +/* > symmetric matrix is to be referenced. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > On entry, M specifies the number of rows of the matrix C. */ +/* > M must be at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > On entry, N specifies the number of columns of the matrix C. */ +/* > N must be at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] ALPHA */ +/* > \verbatim */ +/* > ALPHA is DOUBLE PRECISION. */ +/* > On entry, ALPHA specifies the scalar alpha. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is */ +/* > m when SIDE = 'L' or 'l' and is n otherwise. */ +/* > Before entry with SIDE = 'L' or 'l', the m by m part of */ +/* > the array A must contain the symmetric matrix, such that */ +/* > when UPLO = 'U' or 'u', the leading m by m upper triangular */ +/* > part of the array A must contain the upper triangular part */ +/* > of the symmetric matrix and the strictly lower triangular */ +/* > part of A is not referenced, and when UPLO = 'L' or 'l', */ +/* > the leading m by m lower triangular part of the array A */ +/* > must contain the lower triangular part of the symmetric */ +/* > matrix and the strictly upper triangular part of A is not */ +/* > referenced. */ +/* > Before entry with SIDE = 'R' or 'r', the n by n part of */ +/* > the array A must contain the symmetric matrix, such that */ +/* > when UPLO = 'U' or 'u', the leading n by n upper triangular */ +/* > part of the array A must contain the upper triangular part */ +/* > of the symmetric matrix and the strictly lower triangular */ +/* > part of A is not referenced, and when UPLO = 'L' or 'l', */ +/* > the leading n by n lower triangular part of the array A */ +/* > must contain the lower triangular part of the symmetric */ +/* > matrix and the strictly upper triangular part of A is not */ +/* > referenced. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > On entry, LDA specifies the first dimension of A as declared */ +/* > in the calling (sub) program. When SIDE = 'L' or 'l' then */ +/* > LDA must be at least max( 1, m ), otherwise LDA must be at */ +/* > least max( 1, n ). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] B */ +/* > \verbatim */ +/* > B is DOUBLE PRECISION array, dimension ( LDB, N ) */ +/* > Before entry, the leading m by n part of the array B must */ +/* > contain the matrix B. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDB */ +/* > \verbatim */ +/* > LDB is INTEGER */ +/* > On entry, LDB specifies the first dimension of B as declared */ +/* > in the calling (sub) program. LDB must be at least */ +/* > max( 1, m ). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] BETA */ +/* > \verbatim */ +/* > BETA is DOUBLE PRECISION. */ +/* > On entry, BETA specifies the scalar beta. When BETA is */ +/* > supplied as zero then C need not be set on input. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] C */ +/* > \verbatim */ +/* > C is DOUBLE PRECISION array, dimension ( LDC, N ) */ +/* > Before entry, the leading m by n part of the array C must */ +/* > contain the matrix C, except when beta is zero, in which */ +/* > case C need not be set on entry. */ +/* > On exit, the array C is overwritten by the m by n updated */ +/* > matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDC */ +/* > \verbatim */ +/* > LDC is INTEGER */ +/* > On entry, LDC specifies the first dimension of C as declared */ +/* > in the calling (sub) program. LDC must be at least */ +/* > max( 1, m ). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup double_blas_level3 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > Level 3 Blas routine. */ +/* > */ +/* > -- Written on 8-February-1989. */ +/* > Jack Dongarra, Argonne National Laboratory. */ +/* > Iain Duff, AERE Harwell. */ +/* > Jeremy Du Croz, Numerical Algorithms Group Ltd. */ +/* > Sven Hammarling, Numerical Algorithms Group Ltd. */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dsymm_(char *side, char *uplo, integer *m, integer *n, + doublereal *alpha, doublereal *a, integer *lda, doublereal *b, + integer *ldb, doublereal *beta, doublereal *c__, integer *ldc, ftnlen + side_len, ftnlen uplo_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, + i__3; + + /* Local variables */ + integer i__, j, k, info; + doublereal temp1, temp2; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + integer nrowa; + logical upper; + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + + +/* -- Reference BLAS level3 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Parameters .. */ +/* .. */ + +/* Set NROWA as the number of rows of A. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + b_dim1 = *ldb; + b_offset = 1 + b_dim1; + b -= b_offset; + c_dim1 = *ldc; + c_offset = 1 + c_dim1; + c__ -= c_offset; + + /* Function Body */ + if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { + nrowa = *m; + } else { + nrowa = *n; + } + upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); + +/* Test the input parameters. */ + + info = 0; + if (! lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1) && ! lsame_(side, (char *)"R", ( + ftnlen)1, (ftnlen)1)) { + info = 1; + } else if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + info = 2; + } else if (*m < 0) { + info = 3; + } else if (*n < 0) { + info = 4; + } else if (*lda < max(1,nrowa)) { + info = 7; + } else if (*ldb < max(1,*m)) { + info = 9; + } else if (*ldc < max(1,*m)) { + info = 12; + } + if (info != 0) { + xerbla_((char *)"DSYMM ", &info, (ftnlen)6); + return 0; + } + +/* Quick return if possible. */ + + if (*m == 0 || *n == 0 || *alpha == 0. && *beta == 1.) { + return 0; + } + +/* And when alpha.eq.zero. */ + + if (*alpha == 0.) { + if (*beta == 0.) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = 0.; +/* L10: */ + } +/* L20: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; +/* L30: */ + } +/* L40: */ + } + } + return 0; + } + +/* Start the operations. */ + + if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { + +/* Form C := alpha*A*B + beta*C. */ + + if (upper) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp1 = *alpha * b[i__ + j * b_dim1]; + temp2 = 0.; + i__3 = i__ - 1; + for (k = 1; k <= i__3; ++k) { + c__[k + j * c_dim1] += temp1 * a[k + i__ * a_dim1]; + temp2 += b[k + j * b_dim1] * a[k + i__ * a_dim1]; +/* L50: */ + } + if (*beta == 0.) { + c__[i__ + j * c_dim1] = temp1 * a[i__ + i__ * a_dim1] + + *alpha * temp2; + } else { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1] + + temp1 * a[i__ + i__ * a_dim1] + *alpha * + temp2; + } +/* L60: */ + } +/* L70: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + for (i__ = *m; i__ >= 1; --i__) { + temp1 = *alpha * b[i__ + j * b_dim1]; + temp2 = 0.; + i__2 = *m; + for (k = i__ + 1; k <= i__2; ++k) { + c__[k + j * c_dim1] += temp1 * a[k + i__ * a_dim1]; + temp2 += b[k + j * b_dim1] * a[k + i__ * a_dim1]; +/* L80: */ + } + if (*beta == 0.) { + c__[i__ + j * c_dim1] = temp1 * a[i__ + i__ * a_dim1] + + *alpha * temp2; + } else { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1] + + temp1 * a[i__ + i__ * a_dim1] + *alpha * + temp2; + } +/* L90: */ + } +/* L100: */ + } + } + } else { + +/* Form C := alpha*B*A + beta*C. */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp1 = *alpha * a[j + j * a_dim1]; + if (*beta == 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = temp1 * b[i__ + j * b_dim1]; +/* L110: */ + } + } else { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1] + + temp1 * b[i__ + j * b_dim1]; +/* L120: */ + } + } + i__2 = j - 1; + for (k = 1; k <= i__2; ++k) { + if (upper) { + temp1 = *alpha * a[k + j * a_dim1]; + } else { + temp1 = *alpha * a[j + k * a_dim1]; + } + i__3 = *m; + for (i__ = 1; i__ <= i__3; ++i__) { + c__[i__ + j * c_dim1] += temp1 * b[i__ + k * b_dim1]; +/* L130: */ + } +/* L140: */ + } + i__2 = *n; + for (k = j + 1; k <= i__2; ++k) { + if (upper) { + temp1 = *alpha * a[j + k * a_dim1]; + } else { + temp1 = *alpha * a[k + j * a_dim1]; + } + i__3 = *m; + for (i__ = 1; i__ <= i__3; ++i__) { + c__[i__ + j * c_dim1] += temp1 * b[i__ + k * b_dim1]; +/* L150: */ + } +/* L160: */ + } +/* L170: */ + } + } + + return 0; + +/* End of DSYMM */ + +} /* dsymm_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dsymv.cpp b/lib/linalg/dsymv.cpp new file mode 100644 index 0000000000..4dc77ad743 --- /dev/null +++ b/lib/linalg/dsymv.cpp @@ -0,0 +1,388 @@ +/* fortran/dsymv.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DSYMV */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DSYMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) */ + +/* .. Scalar Arguments .. */ +/* DOUBLE PRECISION ALPHA,BETA */ +/* INTEGER INCX,INCY,LDA,N */ +/* CHARACTER UPLO */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A(LDA,*),X(*),Y(*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DSYMV performs the matrix-vector operation */ +/* > */ +/* > y := alpha*A*x + beta*y, */ +/* > */ +/* > where alpha and beta are scalars, x and y are n element vectors and */ +/* > A is an n by n symmetric matrix. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > On entry, UPLO specifies whether the upper or lower */ +/* > triangular part of the array A is to be referenced as */ +/* > follows: */ +/* > */ +/* > UPLO = 'U' or 'u' Only the upper triangular part of A */ +/* > is to be referenced. */ +/* > */ +/* > UPLO = 'L' or 'l' Only the lower triangular part of A */ +/* > is to be referenced. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > On entry, N specifies the order of the matrix A. */ +/* > N must be at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] ALPHA */ +/* > \verbatim */ +/* > ALPHA is DOUBLE PRECISION. */ +/* > On entry, ALPHA specifies the scalar alpha. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension ( LDA, N ) */ +/* > Before entry with UPLO = 'U' or 'u', the leading n by n */ +/* > upper triangular part of the array A must contain the upper */ +/* > triangular part of the symmetric matrix and the strictly */ +/* > lower triangular part of A is not referenced. */ +/* > Before entry with UPLO = 'L' or 'l', the leading n by n */ +/* > lower triangular part of the array A must contain the lower */ +/* > triangular part of the symmetric matrix and the strictly */ +/* > upper triangular part of A is not referenced. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > On entry, LDA specifies the first dimension of A as declared */ +/* > in the calling (sub) program. LDA must be at least */ +/* > max( 1, n ). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] X */ +/* > \verbatim */ +/* > X is DOUBLE PRECISION array, dimension at least */ +/* > ( 1 + ( n - 1 )*abs( INCX ) ). */ +/* > Before entry, the incremented array X must contain the n */ +/* > element vector x. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > On entry, INCX specifies the increment for the elements of */ +/* > X. INCX must not be zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] BETA */ +/* > \verbatim */ +/* > BETA is DOUBLE PRECISION. */ +/* > On entry, BETA specifies the scalar beta. When BETA is */ +/* > supplied as zero then Y need not be set on input. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] Y */ +/* > \verbatim */ +/* > Y is DOUBLE PRECISION array, dimension at least */ +/* > ( 1 + ( n - 1 )*abs( INCY ) ). */ +/* > Before entry, the incremented array Y must contain the n */ +/* > element vector y. On exit, Y is overwritten by the updated */ +/* > vector y. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCY */ +/* > \verbatim */ +/* > INCY is INTEGER */ +/* > On entry, INCY specifies the increment for the elements of */ +/* > Y. INCY must not be zero. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup double_blas_level2 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > Level 2 Blas routine. */ +/* > The vector and matrix arguments are not referenced when N = 0, or M = 0 */ +/* > */ +/* > -- Written on 22-October-1986. */ +/* > Jack Dongarra, Argonne National Lab. */ +/* > Jeremy Du Croz, Nag Central Office. */ +/* > Sven Hammarling, Nag Central Office. */ +/* > Richard Hanson, Sandia National Labs. */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dsymv_(char *uplo, integer *n, doublereal *alpha, + doublereal *a, integer *lda, doublereal *x, integer *incx, doublereal + *beta, doublereal *y, integer *incy, ftnlen uplo_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2; + + /* Local variables */ + integer i__, j, ix, iy, jx, jy, kx, ky, info; + doublereal temp1, temp2; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + + +/* -- Reference BLAS level2 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --x; + --y; + + /* Function Body */ + info = 0; + if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", ( + ftnlen)1, (ftnlen)1)) { + info = 1; + } else if (*n < 0) { + info = 2; + } else if (*lda < max(1,*n)) { + info = 5; + } else if (*incx == 0) { + info = 7; + } else if (*incy == 0) { + info = 10; + } + if (info != 0) { + xerbla_((char *)"DSYMV ", &info, (ftnlen)6); + return 0; + } + +/* Quick return if possible. */ + + if (*n == 0 || *alpha == 0. && *beta == 1.) { + return 0; + } + +/* Set up the start points in X and Y. */ + + if (*incx > 0) { + kx = 1; + } else { + kx = 1 - (*n - 1) * *incx; + } + if (*incy > 0) { + ky = 1; + } else { + ky = 1 - (*n - 1) * *incy; + } + +/* Start the operations. In this version the elements of A are */ +/* accessed sequentially with one pass through the triangular part */ +/* of A. */ + +/* First form y := beta*y. */ + + if (*beta != 1.) { + if (*incy == 1) { + if (*beta == 0.) { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + y[i__] = 0.; +/* L10: */ + } + } else { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + y[i__] = *beta * y[i__]; +/* L20: */ + } + } + } else { + iy = ky; + if (*beta == 0.) { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + y[iy] = 0.; + iy += *incy; +/* L30: */ + } + } else { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + y[iy] = *beta * y[iy]; + iy += *incy; +/* L40: */ + } + } + } + } + if (*alpha == 0.) { + return 0; + } + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + +/* Form y when A is stored in upper triangle. */ + + if (*incx == 1 && *incy == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp1 = *alpha * x[j]; + temp2 = 0.; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + y[i__] += temp1 * a[i__ + j * a_dim1]; + temp2 += a[i__ + j * a_dim1] * x[i__]; +/* L50: */ + } + y[j] = y[j] + temp1 * a[j + j * a_dim1] + *alpha * temp2; +/* L60: */ + } + } else { + jx = kx; + jy = ky; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp1 = *alpha * x[jx]; + temp2 = 0.; + ix = kx; + iy = ky; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + y[iy] += temp1 * a[i__ + j * a_dim1]; + temp2 += a[i__ + j * a_dim1] * x[ix]; + ix += *incx; + iy += *incy; +/* L70: */ + } + y[jy] = y[jy] + temp1 * a[j + j * a_dim1] + *alpha * temp2; + jx += *incx; + jy += *incy; +/* L80: */ + } + } + } else { + +/* Form y when A is stored in lower triangle. */ + + if (*incx == 1 && *incy == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp1 = *alpha * x[j]; + temp2 = 0.; + y[j] += temp1 * a[j + j * a_dim1]; + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + y[i__] += temp1 * a[i__ + j * a_dim1]; + temp2 += a[i__ + j * a_dim1] * x[i__]; +/* L90: */ + } + y[j] += *alpha * temp2; +/* L100: */ + } + } else { + jx = kx; + jy = ky; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp1 = *alpha * x[jx]; + temp2 = 0.; + y[jy] += temp1 * a[j + j * a_dim1]; + ix = jx; + iy = jy; + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + ix += *incx; + iy += *incy; + y[iy] += temp1 * a[i__ + j * a_dim1]; + temp2 += a[i__ + j * a_dim1] * x[ix]; +/* L110: */ + } + y[jy] += *alpha * temp2; + jx += *incx; + jy += *incy; +/* L120: */ + } + } + } + + return 0; + +/* End of DSYMV */ + +} /* dsymv_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dsyr2.cpp b/lib/linalg/dsyr2.cpp new file mode 100644 index 0000000000..f017821e1d --- /dev/null +++ b/lib/linalg/dsyr2.cpp @@ -0,0 +1,347 @@ +/* fortran/dsyr2.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DSYR2 */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DSYR2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA) */ + +/* .. Scalar Arguments .. */ +/* DOUBLE PRECISION ALPHA */ +/* INTEGER INCX,INCY,LDA,N */ +/* CHARACTER UPLO */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A(LDA,*),X(*),Y(*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DSYR2 performs the symmetric rank 2 operation */ +/* > */ +/* > A := alpha*x*y**T + alpha*y*x**T + A, */ +/* > */ +/* > where alpha is a scalar, x and y are n element vectors and A is an n */ +/* > by n symmetric matrix. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > On entry, UPLO specifies whether the upper or lower */ +/* > triangular part of the array A is to be referenced as */ +/* > follows: */ +/* > */ +/* > UPLO = 'U' or 'u' Only the upper triangular part of A */ +/* > is to be referenced. */ +/* > */ +/* > UPLO = 'L' or 'l' Only the lower triangular part of A */ +/* > is to be referenced. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > On entry, N specifies the order of the matrix A. */ +/* > N must be at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] ALPHA */ +/* > \verbatim */ +/* > ALPHA is DOUBLE PRECISION. */ +/* > On entry, ALPHA specifies the scalar alpha. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] X */ +/* > \verbatim */ +/* > X is DOUBLE PRECISION array, dimension at least */ +/* > ( 1 + ( n - 1 )*abs( INCX ) ). */ +/* > Before entry, the incremented array X must contain the n */ +/* > element vector x. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > On entry, INCX specifies the increment for the elements of */ +/* > X. INCX must not be zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] Y */ +/* > \verbatim */ +/* > Y is DOUBLE PRECISION array, dimension at least */ +/* > ( 1 + ( n - 1 )*abs( INCY ) ). */ +/* > Before entry, the incremented array Y must contain the n */ +/* > element vector y. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCY */ +/* > \verbatim */ +/* > INCY is INTEGER */ +/* > On entry, INCY specifies the increment for the elements of */ +/* > Y. INCY must not be zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension ( LDA, N ) */ +/* > Before entry with UPLO = 'U' or 'u', the leading n by n */ +/* > upper triangular part of the array A must contain the upper */ +/* > triangular part of the symmetric matrix and the strictly */ +/* > lower triangular part of A is not referenced. On exit, the */ +/* > upper triangular part of the array A is overwritten by the */ +/* > upper triangular part of the updated matrix. */ +/* > Before entry with UPLO = 'L' or 'l', the leading n by n */ +/* > lower triangular part of the array A must contain the lower */ +/* > triangular part of the symmetric matrix and the strictly */ +/* > upper triangular part of A is not referenced. On exit, the */ +/* > lower triangular part of the array A is overwritten by the */ +/* > lower triangular part of the updated matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > On entry, LDA specifies the first dimension of A as declared */ +/* > in the calling (sub) program. LDA must be at least */ +/* > max( 1, n ). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup double_blas_level2 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > Level 2 Blas routine. */ +/* > */ +/* > -- Written on 22-October-1986. */ +/* > Jack Dongarra, Argonne National Lab. */ +/* > Jeremy Du Croz, Nag Central Office. */ +/* > Sven Hammarling, Nag Central Office. */ +/* > Richard Hanson, Sandia National Labs. */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dsyr2_(char *uplo, integer *n, doublereal *alpha, + doublereal *x, integer *incx, doublereal *y, integer *incy, + doublereal *a, integer *lda, ftnlen uplo_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2; + + /* Local variables */ + integer i__, j, ix, iy, jx, jy, kx, ky, info; + doublereal temp1, temp2; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + + +/* -- Reference BLAS level2 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --x; + --y; + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + + /* Function Body */ + info = 0; + if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", ( + ftnlen)1, (ftnlen)1)) { + info = 1; + } else if (*n < 0) { + info = 2; + } else if (*incx == 0) { + info = 5; + } else if (*incy == 0) { + info = 7; + } else if (*lda < max(1,*n)) { + info = 9; + } + if (info != 0) { + xerbla_((char *)"DSYR2 ", &info, (ftnlen)6); + return 0; + } + +/* Quick return if possible. */ + + if (*n == 0 || *alpha == 0.) { + return 0; + } + +/* Set up the start points in X and Y if the increments are not both */ +/* unity. */ + + if (*incx != 1 || *incy != 1) { + if (*incx > 0) { + kx = 1; + } else { + kx = 1 - (*n - 1) * *incx; + } + if (*incy > 0) { + ky = 1; + } else { + ky = 1 - (*n - 1) * *incy; + } + jx = kx; + jy = ky; + } + +/* Start the operations. In this version the elements of A are */ +/* accessed sequentially with one pass through the triangular part */ +/* of A. */ + + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + +/* Form A when A is stored in the upper triangle. */ + + if (*incx == 1 && *incy == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (x[j] != 0. || y[j] != 0.) { + temp1 = *alpha * y[j]; + temp2 = *alpha * x[j]; + i__2 = j; + for (i__ = 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] = a[i__ + j * a_dim1] + x[i__] * + temp1 + y[i__] * temp2; +/* L10: */ + } + } +/* L20: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (x[jx] != 0. || y[jy] != 0.) { + temp1 = *alpha * y[jy]; + temp2 = *alpha * x[jx]; + ix = kx; + iy = ky; + i__2 = j; + for (i__ = 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] = a[i__ + j * a_dim1] + x[ix] * + temp1 + y[iy] * temp2; + ix += *incx; + iy += *incy; +/* L30: */ + } + } + jx += *incx; + jy += *incy; +/* L40: */ + } + } + } else { + +/* Form A when A is stored in the lower triangle. */ + + if (*incx == 1 && *incy == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (x[j] != 0. || y[j] != 0.) { + temp1 = *alpha * y[j]; + temp2 = *alpha * x[j]; + i__2 = *n; + for (i__ = j; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] = a[i__ + j * a_dim1] + x[i__] * + temp1 + y[i__] * temp2; +/* L50: */ + } + } +/* L60: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (x[jx] != 0. || y[jy] != 0.) { + temp1 = *alpha * y[jy]; + temp2 = *alpha * x[jx]; + ix = jx; + iy = jy; + i__2 = *n; + for (i__ = j; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] = a[i__ + j * a_dim1] + x[ix] * + temp1 + y[iy] * temp2; + ix += *incx; + iy += *incy; +/* L70: */ + } + } + jx += *incx; + jy += *incy; +/* L80: */ + } + } + } + + return 0; + +/* End of DSYR2 */ + +} /* dsyr2_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dsyr2k.cpp b/lib/linalg/dsyr2k.cpp new file mode 100644 index 0000000000..33d32b3440 --- /dev/null +++ b/lib/linalg/dsyr2k.cpp @@ -0,0 +1,485 @@ +/* fortran/dsyr2k.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DSYR2K */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) */ + +/* .. Scalar Arguments .. */ +/* DOUBLE PRECISION ALPHA,BETA */ +/* INTEGER K,LDA,LDB,LDC,N */ +/* CHARACTER TRANS,UPLO */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DSYR2K performs one of the symmetric rank 2k operations */ +/* > */ +/* > C := alpha*A*B**T + alpha*B*A**T + beta*C, */ +/* > */ +/* > or */ +/* > */ +/* > C := alpha*A**T*B + alpha*B**T*A + beta*C, */ +/* > */ +/* > where alpha and beta are scalars, C is an n by n symmetric matrix */ +/* > and A and B are n by k matrices in the first case and k by n */ +/* > matrices in the second case. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > On entry, UPLO specifies whether the upper or lower */ +/* > triangular part of the array C is to be referenced as */ +/* > follows: */ +/* > */ +/* > UPLO = 'U' or 'u' Only the upper triangular part of C */ +/* > is to be referenced. */ +/* > */ +/* > UPLO = 'L' or 'l' Only the lower triangular part of C */ +/* > is to be referenced. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TRANS */ +/* > \verbatim */ +/* > TRANS is CHARACTER*1 */ +/* > On entry, TRANS specifies the operation to be performed as */ +/* > follows: */ +/* > */ +/* > TRANS = 'N' or 'n' C := alpha*A*B**T + alpha*B*A**T + */ +/* > beta*C. */ +/* > */ +/* > TRANS = 'T' or 't' C := alpha*A**T*B + alpha*B**T*A + */ +/* > beta*C. */ +/* > */ +/* > TRANS = 'C' or 'c' C := alpha*A**T*B + alpha*B**T*A + */ +/* > beta*C. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > On entry, N specifies the order of the matrix C. N must be */ +/* > at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > On entry with TRANS = 'N' or 'n', K specifies the number */ +/* > of columns of the matrices A and B, and on entry with */ +/* > TRANS = 'T' or 't' or 'C' or 'c', K specifies the number */ +/* > of rows of the matrices A and B. K must be at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] ALPHA */ +/* > \verbatim */ +/* > ALPHA is DOUBLE PRECISION. */ +/* > On entry, ALPHA specifies the scalar alpha. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is */ +/* > k when TRANS = 'N' or 'n', and is n otherwise. */ +/* > Before entry with TRANS = 'N' or 'n', the leading n by k */ +/* > part of the array A must contain the matrix A, otherwise */ +/* > the leading k by n part of the array A must contain the */ +/* > matrix A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > On entry, LDA specifies the first dimension of A as declared */ +/* > in the calling (sub) program. When TRANS = 'N' or 'n' */ +/* > then LDA must be at least max( 1, n ), otherwise LDA must */ +/* > be at least max( 1, k ). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] B */ +/* > \verbatim */ +/* > B is DOUBLE PRECISION array, dimension ( LDB, kb ), where kb is */ +/* > k when TRANS = 'N' or 'n', and is n otherwise. */ +/* > Before entry with TRANS = 'N' or 'n', the leading n by k */ +/* > part of the array B must contain the matrix B, otherwise */ +/* > the leading k by n part of the array B must contain the */ +/* > matrix B. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDB */ +/* > \verbatim */ +/* > LDB is INTEGER */ +/* > On entry, LDB specifies the first dimension of B as declared */ +/* > in the calling (sub) program. When TRANS = 'N' or 'n' */ +/* > then LDB must be at least max( 1, n ), otherwise LDB must */ +/* > be at least max( 1, k ). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] BETA */ +/* > \verbatim */ +/* > BETA is DOUBLE PRECISION. */ +/* > On entry, BETA specifies the scalar beta. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] C */ +/* > \verbatim */ +/* > C is DOUBLE PRECISION array, dimension ( LDC, N ) */ +/* > Before entry with UPLO = 'U' or 'u', the leading n by n */ +/* > upper triangular part of the array C must contain the upper */ +/* > triangular part of the symmetric matrix and the strictly */ +/* > lower triangular part of C is not referenced. On exit, the */ +/* > upper triangular part of the array C is overwritten by the */ +/* > upper triangular part of the updated matrix. */ +/* > Before entry with UPLO = 'L' or 'l', the leading n by n */ +/* > lower triangular part of the array C must contain the lower */ +/* > triangular part of the symmetric matrix and the strictly */ +/* > upper triangular part of C is not referenced. On exit, the */ +/* > lower triangular part of the array C is overwritten by the */ +/* > lower triangular part of the updated matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDC */ +/* > \verbatim */ +/* > LDC is INTEGER */ +/* > On entry, LDC specifies the first dimension of C as declared */ +/* > in the calling (sub) program. LDC must be at least */ +/* > max( 1, n ). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup double_blas_level3 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > Level 3 Blas routine. */ +/* > */ +/* > */ +/* > -- Written on 8-February-1989. */ +/* > Jack Dongarra, Argonne National Laboratory. */ +/* > Iain Duff, AERE Harwell. */ +/* > Jeremy Du Croz, Numerical Algorithms Group Ltd. */ +/* > Sven Hammarling, Numerical Algorithms Group Ltd. */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dsyr2k_(char *uplo, char *trans, integer *n, integer *k, + doublereal *alpha, doublereal *a, integer *lda, doublereal *b, + integer *ldb, doublereal *beta, doublereal *c__, integer *ldc, ftnlen + uplo_len, ftnlen trans_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, + i__3; + + /* Local variables */ + integer i__, j, l, info; + doublereal temp1, temp2; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + integer nrowa; + logical upper; + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + + +/* -- Reference BLAS level3 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Parameters .. */ +/* .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + b_dim1 = *ldb; + b_offset = 1 + b_dim1; + b -= b_offset; + c_dim1 = *ldc; + c_offset = 1 + c_dim1; + c__ -= c_offset; + + /* Function Body */ + if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { + nrowa = *n; + } else { + nrowa = *k; + } + upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); + + info = 0; + if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + info = 1; + } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, + (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, ( + ftnlen)1)) { + info = 2; + } else if (*n < 0) { + info = 3; + } else if (*k < 0) { + info = 4; + } else if (*lda < max(1,nrowa)) { + info = 7; + } else if (*ldb < max(1,nrowa)) { + info = 9; + } else if (*ldc < max(1,*n)) { + info = 12; + } + if (info != 0) { + xerbla_((char *)"DSYR2K", &info, (ftnlen)6); + return 0; + } + +/* Quick return if possible. */ + + if (*n == 0 || (*alpha == 0. || *k == 0) && *beta == 1.) { + return 0; + } + +/* And when alpha.eq.zero. */ + + if (*alpha == 0.) { + if (upper) { + if (*beta == 0.) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = 0.; +/* L10: */ + } +/* L20: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; +/* L30: */ + } +/* L40: */ + } + } + } else { + if (*beta == 0.) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = j; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = 0.; +/* L50: */ + } +/* L60: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = j; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; +/* L70: */ + } +/* L80: */ + } + } + } + return 0; + } + +/* Start the operations. */ + + if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { + +/* Form C := alpha*A*B**T + alpha*B*A**T + C. */ + + if (upper) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (*beta == 0.) { + i__2 = j; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = 0.; +/* L90: */ + } + } else if (*beta != 1.) { + i__2 = j; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; +/* L100: */ + } + } + i__2 = *k; + for (l = 1; l <= i__2; ++l) { + if (a[j + l * a_dim1] != 0. || b[j + l * b_dim1] != 0.) { + temp1 = *alpha * b[j + l * b_dim1]; + temp2 = *alpha * a[j + l * a_dim1]; + i__3 = j; + for (i__ = 1; i__ <= i__3; ++i__) { + c__[i__ + j * c_dim1] = c__[i__ + j * c_dim1] + a[ + i__ + l * a_dim1] * temp1 + b[i__ + l * + b_dim1] * temp2; +/* L110: */ + } + } +/* L120: */ + } +/* L130: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (*beta == 0.) { + i__2 = *n; + for (i__ = j; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = 0.; +/* L140: */ + } + } else if (*beta != 1.) { + i__2 = *n; + for (i__ = j; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; +/* L150: */ + } + } + i__2 = *k; + for (l = 1; l <= i__2; ++l) { + if (a[j + l * a_dim1] != 0. || b[j + l * b_dim1] != 0.) { + temp1 = *alpha * b[j + l * b_dim1]; + temp2 = *alpha * a[j + l * a_dim1]; + i__3 = *n; + for (i__ = j; i__ <= i__3; ++i__) { + c__[i__ + j * c_dim1] = c__[i__ + j * c_dim1] + a[ + i__ + l * a_dim1] * temp1 + b[i__ + l * + b_dim1] * temp2; +/* L160: */ + } + } +/* L170: */ + } +/* L180: */ + } + } + } else { + +/* Form C := alpha*A**T*B + alpha*B**T*A + C. */ + + if (upper) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + for (i__ = 1; i__ <= i__2; ++i__) { + temp1 = 0.; + temp2 = 0.; + i__3 = *k; + for (l = 1; l <= i__3; ++l) { + temp1 += a[l + i__ * a_dim1] * b[l + j * b_dim1]; + temp2 += b[l + i__ * b_dim1] * a[l + j * a_dim1]; +/* L190: */ + } + if (*beta == 0.) { + c__[i__ + j * c_dim1] = *alpha * temp1 + *alpha * + temp2; + } else { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1] + + *alpha * temp1 + *alpha * temp2; + } +/* L200: */ + } +/* L210: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = j; i__ <= i__2; ++i__) { + temp1 = 0.; + temp2 = 0.; + i__3 = *k; + for (l = 1; l <= i__3; ++l) { + temp1 += a[l + i__ * a_dim1] * b[l + j * b_dim1]; + temp2 += b[l + i__ * b_dim1] * a[l + j * a_dim1]; +/* L220: */ + } + if (*beta == 0.) { + c__[i__ + j * c_dim1] = *alpha * temp1 + *alpha * + temp2; + } else { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1] + + *alpha * temp1 + *alpha * temp2; + } +/* L230: */ + } +/* L240: */ + } + } + } + + return 0; + +/* End of DSYR2K */ + +} /* dsyr2k_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dsyrk.cpp b/lib/linalg/dsyrk.cpp new file mode 100644 index 0000000000..28dc601121 --- /dev/null +++ b/lib/linalg/dsyrk.cpp @@ -0,0 +1,445 @@ +/* fortran/dsyrk.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DSYRK */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC) */ + +/* .. Scalar Arguments .. */ +/* DOUBLE PRECISION ALPHA,BETA */ +/* INTEGER K,LDA,LDC,N */ +/* CHARACTER TRANS,UPLO */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A(LDA,*),C(LDC,*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DSYRK performs one of the symmetric rank k operations */ +/* > */ +/* > C := alpha*A*A**T + beta*C, */ +/* > */ +/* > or */ +/* > */ +/* > C := alpha*A**T*A + beta*C, */ +/* > */ +/* > where alpha and beta are scalars, C is an n by n symmetric matrix */ +/* > and A is an n by k matrix in the first case and a k by n matrix */ +/* > in the second case. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > On entry, UPLO specifies whether the upper or lower */ +/* > triangular part of the array C is to be referenced as */ +/* > follows: */ +/* > */ +/* > UPLO = 'U' or 'u' Only the upper triangular part of C */ +/* > is to be referenced. */ +/* > */ +/* > UPLO = 'L' or 'l' Only the lower triangular part of C */ +/* > is to be referenced. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TRANS */ +/* > \verbatim */ +/* > TRANS is CHARACTER*1 */ +/* > On entry, TRANS specifies the operation to be performed as */ +/* > follows: */ +/* > */ +/* > TRANS = 'N' or 'n' C := alpha*A*A**T + beta*C. */ +/* > */ +/* > TRANS = 'T' or 't' C := alpha*A**T*A + beta*C. */ +/* > */ +/* > TRANS = 'C' or 'c' C := alpha*A**T*A + beta*C. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > On entry, N specifies the order of the matrix C. N must be */ +/* > at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > On entry with TRANS = 'N' or 'n', K specifies the number */ +/* > of columns of the matrix A, and on entry with */ +/* > TRANS = 'T' or 't' or 'C' or 'c', K specifies the number */ +/* > of rows of the matrix A. K must be at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] ALPHA */ +/* > \verbatim */ +/* > ALPHA is DOUBLE PRECISION. */ +/* > On entry, ALPHA specifies the scalar alpha. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is */ +/* > k when TRANS = 'N' or 'n', and is n otherwise. */ +/* > Before entry with TRANS = 'N' or 'n', the leading n by k */ +/* > part of the array A must contain the matrix A, otherwise */ +/* > the leading k by n part of the array A must contain the */ +/* > matrix A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > On entry, LDA specifies the first dimension of A as declared */ +/* > in the calling (sub) program. When TRANS = 'N' or 'n' */ +/* > then LDA must be at least max( 1, n ), otherwise LDA must */ +/* > be at least max( 1, k ). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] BETA */ +/* > \verbatim */ +/* > BETA is DOUBLE PRECISION. */ +/* > On entry, BETA specifies the scalar beta. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] C */ +/* > \verbatim */ +/* > C is DOUBLE PRECISION array, dimension ( LDC, N ) */ +/* > Before entry with UPLO = 'U' or 'u', the leading n by n */ +/* > upper triangular part of the array C must contain the upper */ +/* > triangular part of the symmetric matrix and the strictly */ +/* > lower triangular part of C is not referenced. On exit, the */ +/* > upper triangular part of the array C is overwritten by the */ +/* > upper triangular part of the updated matrix. */ +/* > Before entry with UPLO = 'L' or 'l', the leading n by n */ +/* > lower triangular part of the array C must contain the lower */ +/* > triangular part of the symmetric matrix and the strictly */ +/* > upper triangular part of C is not referenced. On exit, the */ +/* > lower triangular part of the array C is overwritten by the */ +/* > lower triangular part of the updated matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDC */ +/* > \verbatim */ +/* > LDC is INTEGER */ +/* > On entry, LDC specifies the first dimension of C as declared */ +/* > in the calling (sub) program. LDC must be at least */ +/* > max( 1, n ). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup double_blas_level3 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > Level 3 Blas routine. */ +/* > */ +/* > -- Written on 8-February-1989. */ +/* > Jack Dongarra, Argonne National Laboratory. */ +/* > Iain Duff, AERE Harwell. */ +/* > Jeremy Du Croz, Numerical Algorithms Group Ltd. */ +/* > Sven Hammarling, Numerical Algorithms Group Ltd. */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dsyrk_(char *uplo, char *trans, integer *n, integer *k, + doublereal *alpha, doublereal *a, integer *lda, doublereal *beta, + doublereal *c__, integer *ldc, ftnlen uplo_len, ftnlen trans_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3; + + /* Local variables */ + integer i__, j, l, info; + doublereal temp; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + integer nrowa; + logical upper; + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + + +/* -- Reference BLAS level3 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Parameters .. */ +/* .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + c_dim1 = *ldc; + c_offset = 1 + c_dim1; + c__ -= c_offset; + + /* Function Body */ + if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { + nrowa = *n; + } else { + nrowa = *k; + } + upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); + + info = 0; + if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + info = 1; + } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, + (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, ( + ftnlen)1)) { + info = 2; + } else if (*n < 0) { + info = 3; + } else if (*k < 0) { + info = 4; + } else if (*lda < max(1,nrowa)) { + info = 7; + } else if (*ldc < max(1,*n)) { + info = 10; + } + if (info != 0) { + xerbla_((char *)"DSYRK ", &info, (ftnlen)6); + return 0; + } + +/* Quick return if possible. */ + + if (*n == 0 || (*alpha == 0. || *k == 0) && *beta == 1.) { + return 0; + } + +/* And when alpha.eq.zero. */ + + if (*alpha == 0.) { + if (upper) { + if (*beta == 0.) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = 0.; +/* L10: */ + } +/* L20: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; +/* L30: */ + } +/* L40: */ + } + } + } else { + if (*beta == 0.) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = j; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = 0.; +/* L50: */ + } +/* L60: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = j; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; +/* L70: */ + } +/* L80: */ + } + } + } + return 0; + } + +/* Start the operations. */ + + if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { + +/* Form C := alpha*A*A**T + beta*C. */ + + if (upper) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (*beta == 0.) { + i__2 = j; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = 0.; +/* L90: */ + } + } else if (*beta != 1.) { + i__2 = j; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; +/* L100: */ + } + } + i__2 = *k; + for (l = 1; l <= i__2; ++l) { + if (a[j + l * a_dim1] != 0.) { + temp = *alpha * a[j + l * a_dim1]; + i__3 = j; + for (i__ = 1; i__ <= i__3; ++i__) { + c__[i__ + j * c_dim1] += temp * a[i__ + l * + a_dim1]; +/* L110: */ + } + } +/* L120: */ + } +/* L130: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (*beta == 0.) { + i__2 = *n; + for (i__ = j; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = 0.; +/* L140: */ + } + } else if (*beta != 1.) { + i__2 = *n; + for (i__ = j; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; +/* L150: */ + } + } + i__2 = *k; + for (l = 1; l <= i__2; ++l) { + if (a[j + l * a_dim1] != 0.) { + temp = *alpha * a[j + l * a_dim1]; + i__3 = *n; + for (i__ = j; i__ <= i__3; ++i__) { + c__[i__ + j * c_dim1] += temp * a[i__ + l * + a_dim1]; +/* L160: */ + } + } +/* L170: */ + } +/* L180: */ + } + } + } else { + +/* Form C := alpha*A**T*A + beta*C. */ + + if (upper) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + for (i__ = 1; i__ <= i__2; ++i__) { + temp = 0.; + i__3 = *k; + for (l = 1; l <= i__3; ++l) { + temp += a[l + i__ * a_dim1] * a[l + j * a_dim1]; +/* L190: */ + } + if (*beta == 0.) { + c__[i__ + j * c_dim1] = *alpha * temp; + } else { + c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[ + i__ + j * c_dim1]; + } +/* L200: */ + } +/* L210: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = j; i__ <= i__2; ++i__) { + temp = 0.; + i__3 = *k; + for (l = 1; l <= i__3; ++l) { + temp += a[l + i__ * a_dim1] * a[l + j * a_dim1]; +/* L220: */ + } + if (*beta == 0.) { + c__[i__ + j * c_dim1] = *alpha * temp; + } else { + c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[ + i__ + j * c_dim1]; + } +/* L230: */ + } +/* L240: */ + } + } + } + + return 0; + +/* End of DSYRK */ + +} /* dsyrk_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dsytd2.cpp b/lib/linalg/dsytd2.cpp new file mode 100644 index 0000000000..4035fd0d58 --- /dev/null +++ b/lib/linalg/dsytd2.cpp @@ -0,0 +1,389 @@ +/* fortran/dsytd2.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static doublereal c_b8 = 0.; +static doublereal c_b14 = -1.; + +/* > \brief \b DSYTD2 reduces a symmetric matrix to real symmetric tridiagonal form by an orthogonal similarit +y transformation (unblocked algorithm). */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DSYTD2 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DSYTD2( UPLO, N, A, LDA, D, E, TAU, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER UPLO */ +/* INTEGER INFO, LDA, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), TAU( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DSYTD2 reduces a real symmetric matrix A to symmetric tridiagonal */ +/* > form T by an orthogonal similarity transformation: Q**T * A * Q = T. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > Specifies whether the upper or lower triangular part of the */ +/* > symmetric matrix A is stored: */ +/* > = 'U': Upper triangular */ +/* > = 'L': Lower triangular */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On entry, the symmetric matrix A. If UPLO = 'U', the leading */ +/* > n-by-n upper triangular part of A contains the upper */ +/* > triangular part of the matrix A, and the strictly lower */ +/* > triangular part of A is not referenced. If UPLO = 'L', the */ +/* > leading n-by-n lower triangular part of A contains the lower */ +/* > triangular part of the matrix A, and the strictly upper */ +/* > triangular part of A is not referenced. */ +/* > On exit, if UPLO = 'U', the diagonal and first superdiagonal */ +/* > of A are overwritten by the corresponding elements of the */ +/* > tridiagonal matrix T, and the elements above the first */ +/* > superdiagonal, with the array TAU, represent the orthogonal */ +/* > matrix Q as a product of elementary reflectors; if UPLO */ +/* > = 'L', the diagonal and first subdiagonal of A are over- */ +/* > written by the corresponding elements of the tridiagonal */ +/* > matrix T, and the elements below the first subdiagonal, with */ +/* > the array TAU, represent the orthogonal matrix Q as a product */ +/* > of elementary reflectors. See Further Details. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension (N) */ +/* > The diagonal elements of the tridiagonal matrix T: */ +/* > D(i) = A(i,i). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] E */ +/* > \verbatim */ +/* > E is DOUBLE PRECISION array, dimension (N-1) */ +/* > The off-diagonal elements of the tridiagonal matrix T: */ +/* > E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] TAU */ +/* > \verbatim */ +/* > TAU is DOUBLE PRECISION array, dimension (N-1) */ +/* > The scalar factors of the elementary reflectors (see Further */ +/* > Details). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleSYcomputational */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > If UPLO = 'U', the matrix Q is represented as a product of elementary */ +/* > reflectors */ +/* > */ +/* > Q = H(n-1) . . . H(2) H(1). */ +/* > */ +/* > Each H(i) has the form */ +/* > */ +/* > H(i) = I - tau * v * v**T */ +/* > */ +/* > where tau is a real scalar, and v is a real vector with */ +/* > v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in */ +/* > A(1:i-1,i+1), and tau in TAU(i). */ +/* > */ +/* > If UPLO = 'L', the matrix Q is represented as a product of elementary */ +/* > reflectors */ +/* > */ +/* > Q = H(1) H(2) . . . H(n-1). */ +/* > */ +/* > Each H(i) has the form */ +/* > */ +/* > H(i) = I - tau * v * v**T */ +/* > */ +/* > where tau is a real scalar, and v is a real vector with */ +/* > v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), */ +/* > and tau in TAU(i). */ +/* > */ +/* > The contents of A on exit are illustrated by the following examples */ +/* > with n = 5: */ +/* > */ +/* > if UPLO = 'U': if UPLO = 'L': */ +/* > */ +/* > ( d e v2 v3 v4 ) ( d ) */ +/* > ( d e v3 v4 ) ( e d ) */ +/* > ( d e v4 ) ( v1 e d ) */ +/* > ( d e ) ( v1 v2 e d ) */ +/* > ( d ) ( v1 v2 v3 e d ) */ +/* > */ +/* > where d and e denote diagonal and off-diagonal elements of T, and vi */ +/* > denotes an element of the vector defining H(i). */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dsytd2_(char *uplo, integer *n, doublereal *a, integer * + lda, doublereal *d__, doublereal *e, doublereal *tau, integer *info, + ftnlen uplo_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3; + + /* Local variables */ + integer i__; + extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, + integer *); + doublereal taui; + extern /* Subroutine */ int dsyr2_(char *, integer *, doublereal *, + doublereal *, integer *, doublereal *, integer *, doublereal *, + integer *, ftnlen); + doublereal alpha; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *); + logical upper; + extern /* Subroutine */ int dsymv_(char *, integer *, doublereal *, + doublereal *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, ftnlen), dlarfg_(integer *, doublereal *, + doublereal *, integer *, doublereal *), xerbla_(char *, integer * + , ftnlen); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --d__; + --e; + --tau; + + /* Function Body */ + *info = 0; + upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); + if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } else if (*lda < max(1,*n)) { + *info = -4; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DSYTD2", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*n <= 0) { + return 0; + } + + if (upper) { + +/* Reduce the upper triangle of A */ + + for (i__ = *n - 1; i__ >= 1; --i__) { + +/* Generate elementary reflector H(i) = I - tau * v * v**T */ +/* to annihilate A(1:i-1,i+1) */ + + dlarfg_(&i__, &a[i__ + (i__ + 1) * a_dim1], &a[(i__ + 1) * a_dim1 + + 1], &c__1, &taui); + e[i__] = a[i__ + (i__ + 1) * a_dim1]; + + if (taui != 0.) { + +/* Apply H(i) from both sides to A(1:i,1:i) */ + + a[i__ + (i__ + 1) * a_dim1] = 1.; + +/* Compute x := tau * A * v storing x in TAU(1:i) */ + + dsymv_(uplo, &i__, &taui, &a[a_offset], lda, &a[(i__ + 1) * + a_dim1 + 1], &c__1, &c_b8, &tau[1], &c__1, (ftnlen)1); + +/* Compute w := x - 1/2 * tau * (x**T * v) * v */ + + alpha = taui * -.5 * ddot_(&i__, &tau[1], &c__1, &a[(i__ + 1) + * a_dim1 + 1], &c__1); + daxpy_(&i__, &alpha, &a[(i__ + 1) * a_dim1 + 1], &c__1, &tau[ + 1], &c__1); + +/* Apply the transformation as a rank-2 update: */ +/* A := A - v * w**T - w * v**T */ + + dsyr2_(uplo, &i__, &c_b14, &a[(i__ + 1) * a_dim1 + 1], &c__1, + &tau[1], &c__1, &a[a_offset], lda, (ftnlen)1); + + a[i__ + (i__ + 1) * a_dim1] = e[i__]; + } + d__[i__ + 1] = a[i__ + 1 + (i__ + 1) * a_dim1]; + tau[i__] = taui; +/* L10: */ + } + d__[1] = a[a_dim1 + 1]; + } else { + +/* Reduce the lower triangle of A */ + + i__1 = *n - 1; + for (i__ = 1; i__ <= i__1; ++i__) { + +/* Generate elementary reflector H(i) = I - tau * v * v**T */ +/* to annihilate A(i+2:n,i) */ + + i__2 = *n - i__; +/* Computing MIN */ + i__3 = i__ + 2; + dlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3,*n) + i__ * + a_dim1], &c__1, &taui); + e[i__] = a[i__ + 1 + i__ * a_dim1]; + + if (taui != 0.) { + +/* Apply H(i) from both sides to A(i+1:n,i+1:n) */ + + a[i__ + 1 + i__ * a_dim1] = 1.; + +/* Compute x := tau * A * v storing y in TAU(i:n-1) */ + + i__2 = *n - i__; + dsymv_(uplo, &i__2, &taui, &a[i__ + 1 + (i__ + 1) * a_dim1], + lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b8, &tau[ + i__], &c__1, (ftnlen)1); + +/* Compute w := x - 1/2 * tau * (x**T * v) * v */ + + i__2 = *n - i__; + alpha = taui * -.5 * ddot_(&i__2, &tau[i__], &c__1, &a[i__ + + 1 + i__ * a_dim1], &c__1); + i__2 = *n - i__; + daxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &tau[ + i__], &c__1); + +/* Apply the transformation as a rank-2 update: */ +/* A := A - v * w**T - w * v**T */ + + i__2 = *n - i__; + dsyr2_(uplo, &i__2, &c_b14, &a[i__ + 1 + i__ * a_dim1], &c__1, + &tau[i__], &c__1, &a[i__ + 1 + (i__ + 1) * a_dim1], + lda, (ftnlen)1); + + a[i__ + 1 + i__ * a_dim1] = e[i__]; + } + d__[i__] = a[i__ + i__ * a_dim1]; + tau[i__] = taui; +/* L20: */ + } + d__[*n] = a[*n + *n * a_dim1]; + } + + return 0; + +/* End of DSYTD2 */ + +} /* dsytd2_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dsytrd.cpp b/lib/linalg/dsytrd.cpp new file mode 100644 index 0000000000..190dd8b1ac --- /dev/null +++ b/lib/linalg/dsytrd.cpp @@ -0,0 +1,454 @@ +/* fortran/dsytrd.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c_n1 = -1; +static integer c__3 = 3; +static integer c__2 = 2; +static doublereal c_b22 = -1.; +static doublereal c_b23 = 1.; + +/* > \brief \b DSYTRD */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DSYTRD + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DSYTRD( UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER UPLO */ +/* INTEGER INFO, LDA, LWORK, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), TAU( * ), */ +/* $ WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DSYTRD reduces a real symmetric matrix A to real symmetric */ +/* > tridiagonal form T by an orthogonal similarity transformation: */ +/* > Q**T * A * Q = T. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > = 'U': Upper triangle of A is stored; */ +/* > = 'L': Lower triangle of A is stored. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On entry, the symmetric matrix A. If UPLO = 'U', the leading */ +/* > N-by-N upper triangular part of A contains the upper */ +/* > triangular part of the matrix A, and the strictly lower */ +/* > triangular part of A is not referenced. If UPLO = 'L', the */ +/* > leading N-by-N lower triangular part of A contains the lower */ +/* > triangular part of the matrix A, and the strictly upper */ +/* > triangular part of A is not referenced. */ +/* > On exit, if UPLO = 'U', the diagonal and first superdiagonal */ +/* > of A are overwritten by the corresponding elements of the */ +/* > tridiagonal matrix T, and the elements above the first */ +/* > superdiagonal, with the array TAU, represent the orthogonal */ +/* > matrix Q as a product of elementary reflectors; if UPLO */ +/* > = 'L', the diagonal and first subdiagonal of A are over- */ +/* > written by the corresponding elements of the tridiagonal */ +/* > matrix T, and the elements below the first subdiagonal, with */ +/* > the array TAU, represent the orthogonal matrix Q as a product */ +/* > of elementary reflectors. See Further Details. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension (N) */ +/* > The diagonal elements of the tridiagonal matrix T: */ +/* > D(i) = A(i,i). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] E */ +/* > \verbatim */ +/* > E is DOUBLE PRECISION array, dimension (N-1) */ +/* > The off-diagonal elements of the tridiagonal matrix T: */ +/* > E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] TAU */ +/* > \verbatim */ +/* > TAU is DOUBLE PRECISION array, dimension (N-1) */ +/* > The scalar factors of the elementary reflectors (see Further */ +/* > Details). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ +/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LWORK */ +/* > \verbatim */ +/* > LWORK is INTEGER */ +/* > The dimension of the array WORK. LWORK >= 1. */ +/* > For optimum performance LWORK >= N*NB, where NB is the */ +/* > optimal blocksize. */ +/* > */ +/* > If LWORK = -1, then a workspace query is assumed; the routine */ +/* > only calculates the optimal size of the WORK array, returns */ +/* > this value as the first entry of the WORK array, and no error */ +/* > message related to LWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleSYcomputational */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > If UPLO = 'U', the matrix Q is represented as a product of elementary */ +/* > reflectors */ +/* > */ +/* > Q = H(n-1) . . . H(2) H(1). */ +/* > */ +/* > Each H(i) has the form */ +/* > */ +/* > H(i) = I - tau * v * v**T */ +/* > */ +/* > where tau is a real scalar, and v is a real vector with */ +/* > v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in */ +/* > A(1:i-1,i+1), and tau in TAU(i). */ +/* > */ +/* > If UPLO = 'L', the matrix Q is represented as a product of elementary */ +/* > reflectors */ +/* > */ +/* > Q = H(1) H(2) . . . H(n-1). */ +/* > */ +/* > Each H(i) has the form */ +/* > */ +/* > H(i) = I - tau * v * v**T */ +/* > */ +/* > where tau is a real scalar, and v is a real vector with */ +/* > v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), */ +/* > and tau in TAU(i). */ +/* > */ +/* > The contents of A on exit are illustrated by the following examples */ +/* > with n = 5: */ +/* > */ +/* > if UPLO = 'U': if UPLO = 'L': */ +/* > */ +/* > ( d e v2 v3 v4 ) ( d ) */ +/* > ( d e v3 v4 ) ( e d ) */ +/* > ( d e v4 ) ( v1 e d ) */ +/* > ( d e ) ( v1 v2 e d ) */ +/* > ( d ) ( v1 v2 v3 e d ) */ +/* > */ +/* > where d and e denote diagonal and off-diagonal elements of T, and vi */ +/* > denotes an element of the vector defining H(i). */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dsytrd_(char *uplo, integer *n, doublereal *a, integer * + lda, doublereal *d__, doublereal *e, doublereal *tau, doublereal * + work, integer *lwork, integer *info, ftnlen uplo_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3; + + /* Local variables */ + integer i__, j, nb, kk, nx, iws; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + integer nbmin, iinfo; + logical upper; + extern /* Subroutine */ int dsytd2_(char *, integer *, doublereal *, + integer *, doublereal *, doublereal *, doublereal *, integer *, + ftnlen), dsyr2k_(char *, char *, integer *, integer *, doublereal + *, doublereal *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, ftnlen, ftnlen), dlatrd_(char *, + integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, doublereal *, integer *, ftnlen), xerbla_(char *, + integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + integer ldwork, lwkopt; + logical lquery; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --d__; + --e; + --tau; + --work; + + /* Function Body */ + *info = 0; + upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); + lquery = *lwork == -1; + if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } else if (*lda < max(1,*n)) { + *info = -4; + } else if (*lwork < 1 && ! lquery) { + *info = -9; + } + + if (*info == 0) { + +/* Determine the block size. */ + + nb = ilaenv_(&c__1, (char *)"DSYTRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, + (ftnlen)1); + lwkopt = *n * nb; + work[1] = (doublereal) lwkopt; + } + + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DSYTRD", &i__1, (ftnlen)6); + return 0; + } else if (lquery) { + return 0; + } + +/* Quick return if possible */ + + if (*n == 0) { + work[1] = 1.; + return 0; + } + + nx = *n; + iws = 1; + if (nb > 1 && nb < *n) { + +/* Determine when to cross over from blocked to unblocked code */ +/* (last block is always handled by unblocked code). */ + +/* Computing MAX */ + i__1 = nb, i__2 = ilaenv_(&c__3, (char *)"DSYTRD", uplo, n, &c_n1, &c_n1, & + c_n1, (ftnlen)6, (ftnlen)1); + nx = max(i__1,i__2); + if (nx < *n) { + +/* Determine if workspace is large enough for blocked code. */ + + ldwork = *n; + iws = ldwork * nb; + if (*lwork < iws) { + +/* Not enough workspace to use optimal NB: determine the */ +/* minimum value of NB, and reduce NB or force use of */ +/* unblocked code by setting NX = N. */ + +/* Computing MAX */ + i__1 = *lwork / ldwork; + nb = max(i__1,1); + nbmin = ilaenv_(&c__2, (char *)"DSYTRD", uplo, n, &c_n1, &c_n1, &c_n1, + (ftnlen)6, (ftnlen)1); + if (nb < nbmin) { + nx = *n; + } + } + } else { + nx = *n; + } + } else { + nb = 1; + } + + if (upper) { + +/* Reduce the upper triangle of A. */ +/* Columns 1:kk are handled by the unblocked method. */ + + kk = *n - (*n - nx + nb - 1) / nb * nb; + i__1 = kk + 1; + i__2 = -nb; + for (i__ = *n - nb + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += + i__2) { + +/* Reduce columns i:i+nb-1 to tridiagonal form and form the */ +/* matrix W which is needed to update the unreduced part of */ +/* the matrix */ + + i__3 = i__ + nb - 1; + dlatrd_(uplo, &i__3, &nb, &a[a_offset], lda, &e[1], &tau[1], & + work[1], &ldwork, (ftnlen)1); + +/* Update the unreduced submatrix A(1:i-1,1:i-1), using an */ +/* update of the form: A := A - V*W**T - W*V**T */ + + i__3 = i__ - 1; + dsyr2k_(uplo, (char *)"No transpose", &i__3, &nb, &c_b22, &a[i__ * a_dim1 + + 1], lda, &work[1], &ldwork, &c_b23, &a[a_offset], lda, ( + ftnlen)1, (ftnlen)12); + +/* Copy superdiagonal elements back into A, and diagonal */ +/* elements into D */ + + i__3 = i__ + nb - 1; + for (j = i__; j <= i__3; ++j) { + a[j - 1 + j * a_dim1] = e[j - 1]; + d__[j] = a[j + j * a_dim1]; +/* L10: */ + } +/* L20: */ + } + +/* Use unblocked code to reduce the last or only block */ + + dsytd2_(uplo, &kk, &a[a_offset], lda, &d__[1], &e[1], &tau[1], &iinfo, + (ftnlen)1); + } else { + +/* Reduce the lower triangle of A */ + + i__2 = *n - nx; + i__1 = nb; + for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) { + +/* Reduce columns i:i+nb-1 to tridiagonal form and form the */ +/* matrix W which is needed to update the unreduced part of */ +/* the matrix */ + + i__3 = *n - i__ + 1; + dlatrd_(uplo, &i__3, &nb, &a[i__ + i__ * a_dim1], lda, &e[i__], & + tau[i__], &work[1], &ldwork, (ftnlen)1); + +/* Update the unreduced submatrix A(i+ib:n,i+ib:n), using */ +/* an update of the form: A := A - V*W**T - W*V**T */ + + i__3 = *n - i__ - nb + 1; + dsyr2k_(uplo, (char *)"No transpose", &i__3, &nb, &c_b22, &a[i__ + nb + + i__ * a_dim1], lda, &work[nb + 1], &ldwork, &c_b23, &a[ + i__ + nb + (i__ + nb) * a_dim1], lda, (ftnlen)1, (ftnlen) + 12); + +/* Copy subdiagonal elements back into A, and diagonal */ +/* elements into D */ + + i__3 = i__ + nb - 1; + for (j = i__; j <= i__3; ++j) { + a[j + 1 + j * a_dim1] = e[j]; + d__[j] = a[j + j * a_dim1]; +/* L30: */ + } +/* L40: */ + } + +/* Use unblocked code to reduce the last or only block */ + + i__1 = *n - i__ + 1; + dsytd2_(uplo, &i__1, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[i__], + &tau[i__], &iinfo, (ftnlen)1); + } + + work[1] = (doublereal) lwkopt; + return 0; + +/* End of DSYTRD */ + +} /* dsytrd_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dtrmm.cpp b/lib/linalg/dtrmm.cpp new file mode 100644 index 0000000000..ffb6a1ad6b --- /dev/null +++ b/lib/linalg/dtrmm.cpp @@ -0,0 +1,527 @@ +/* fortran/dtrmm.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DTRMM */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) */ + +/* .. Scalar Arguments .. */ +/* DOUBLE PRECISION ALPHA */ +/* INTEGER LDA,LDB,M,N */ +/* CHARACTER DIAG,SIDE,TRANSA,UPLO */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A(LDA,*),B(LDB,*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DTRMM performs one of the matrix-matrix operations */ +/* > */ +/* > B := alpha*op( A )*B, or B := alpha*B*op( A ), */ +/* > */ +/* > where alpha is a scalar, B is an m by n matrix, A is a unit, or */ +/* > non-unit, upper or lower triangular matrix and op( A ) is one of */ +/* > */ +/* > op( A ) = A or op( A ) = A**T. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] SIDE */ +/* > \verbatim */ +/* > SIDE is CHARACTER*1 */ +/* > On entry, SIDE specifies whether op( A ) multiplies B from */ +/* > the left or right as follows: */ +/* > */ +/* > SIDE = 'L' or 'l' B := alpha*op( A )*B. */ +/* > */ +/* > SIDE = 'R' or 'r' B := alpha*B*op( A ). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > On entry, UPLO specifies whether the matrix A is an upper or */ +/* > lower triangular matrix as follows: */ +/* > */ +/* > UPLO = 'U' or 'u' A is an upper triangular matrix. */ +/* > */ +/* > UPLO = 'L' or 'l' A is a lower triangular matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TRANSA */ +/* > \verbatim */ +/* > TRANSA is CHARACTER*1 */ +/* > On entry, TRANSA specifies the form of op( A ) to be used in */ +/* > the matrix multiplication as follows: */ +/* > */ +/* > TRANSA = 'N' or 'n' op( A ) = A. */ +/* > */ +/* > TRANSA = 'T' or 't' op( A ) = A**T. */ +/* > */ +/* > TRANSA = 'C' or 'c' op( A ) = A**T. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DIAG */ +/* > \verbatim */ +/* > DIAG is CHARACTER*1 */ +/* > On entry, DIAG specifies whether or not A is unit triangular */ +/* > as follows: */ +/* > */ +/* > DIAG = 'U' or 'u' A is assumed to be unit triangular. */ +/* > */ +/* > DIAG = 'N' or 'n' A is not assumed to be unit */ +/* > triangular. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > On entry, M specifies the number of rows of B. M must be at */ +/* > least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > On entry, N specifies the number of columns of B. N must be */ +/* > at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] ALPHA */ +/* > \verbatim */ +/* > ALPHA is DOUBLE PRECISION. */ +/* > On entry, ALPHA specifies the scalar alpha. When alpha is */ +/* > zero then A is not referenced and B need not be set before */ +/* > entry. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension ( LDA, k ), where k is m */ +/* > when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. */ +/* > Before entry with UPLO = 'U' or 'u', the leading k by k */ +/* > upper triangular part of the array A must contain the upper */ +/* > triangular matrix and the strictly lower triangular part of */ +/* > A is not referenced. */ +/* > Before entry with UPLO = 'L' or 'l', the leading k by k */ +/* > lower triangular part of the array A must contain the lower */ +/* > triangular matrix and the strictly upper triangular part of */ +/* > A is not referenced. */ +/* > Note that when DIAG = 'U' or 'u', the diagonal elements of */ +/* > A are not referenced either, but are assumed to be unity. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > On entry, LDA specifies the first dimension of A as declared */ +/* > in the calling (sub) program. When SIDE = 'L' or 'l' then */ +/* > LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' */ +/* > then LDA must be at least max( 1, n ). */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] B */ +/* > \verbatim */ +/* > B is DOUBLE PRECISION array, dimension ( LDB, N ) */ +/* > Before entry, the leading m by n part of the array B must */ +/* > contain the matrix B, and on exit is overwritten by the */ +/* > transformed matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDB */ +/* > \verbatim */ +/* > LDB is INTEGER */ +/* > On entry, LDB specifies the first dimension of B as declared */ +/* > in the calling (sub) program. LDB must be at least */ +/* > max( 1, m ). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup double_blas_level3 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > Level 3 Blas routine. */ +/* > */ +/* > -- Written on 8-February-1989. */ +/* > Jack Dongarra, Argonne National Laboratory. */ +/* > Iain Duff, AERE Harwell. */ +/* > Jeremy Du Croz, Numerical Algorithms Group Ltd. */ +/* > Sven Hammarling, Numerical Algorithms Group Ltd. */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dtrmm_(char *side, char *uplo, char *transa, char *diag, + integer *m, integer *n, doublereal *alpha, doublereal *a, integer * + lda, doublereal *b, integer *ldb, ftnlen side_len, ftnlen uplo_len, + ftnlen transa_len, ftnlen diag_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3; + + /* Local variables */ + integer i__, j, k, info; + doublereal temp; + logical lside; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + integer nrowa; + logical upper; + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + logical nounit; + + +/* -- Reference BLAS level3 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Parameters .. */ +/* .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + b_dim1 = *ldb; + b_offset = 1 + b_dim1; + b -= b_offset; + + /* Function Body */ + lside = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); + if (lside) { + nrowa = *m; + } else { + nrowa = *n; + } + nounit = lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1); + upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); + + info = 0; + if (! lside && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + info = 1; + } else if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + info = 2; + } else if (! lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(transa, + (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(transa, (char *)"C", (ftnlen)1, ( + ftnlen)1)) { + info = 3; + } else if (! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, + (char *)"N", (ftnlen)1, (ftnlen)1)) { + info = 4; + } else if (*m < 0) { + info = 5; + } else if (*n < 0) { + info = 6; + } else if (*lda < max(1,nrowa)) { + info = 9; + } else if (*ldb < max(1,*m)) { + info = 11; + } + if (info != 0) { + xerbla_((char *)"DTRMM ", &info, (ftnlen)6); + return 0; + } + +/* Quick return if possible. */ + + if (*m == 0 || *n == 0) { + return 0; + } + +/* And when alpha.eq.zero. */ + + if (*alpha == 0.) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] = 0.; +/* L10: */ + } +/* L20: */ + } + return 0; + } + +/* Start the operations. */ + + if (lside) { + if (lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1)) { + +/* Form B := alpha*A*B. */ + + if (upper) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (k = 1; k <= i__2; ++k) { + if (b[k + j * b_dim1] != 0.) { + temp = *alpha * b[k + j * b_dim1]; + i__3 = k - 1; + for (i__ = 1; i__ <= i__3; ++i__) { + b[i__ + j * b_dim1] += temp * a[i__ + k * + a_dim1]; +/* L30: */ + } + if (nounit) { + temp *= a[k + k * a_dim1]; + } + b[k + j * b_dim1] = temp; + } +/* L40: */ + } +/* L50: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + for (k = *m; k >= 1; --k) { + if (b[k + j * b_dim1] != 0.) { + temp = *alpha * b[k + j * b_dim1]; + b[k + j * b_dim1] = temp; + if (nounit) { + b[k + j * b_dim1] *= a[k + k * a_dim1]; + } + i__2 = *m; + for (i__ = k + 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] += temp * a[i__ + k * + a_dim1]; +/* L60: */ + } + } +/* L70: */ + } +/* L80: */ + } + } + } else { + +/* Form B := alpha*A**T*B. */ + + if (upper) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + for (i__ = *m; i__ >= 1; --i__) { + temp = b[i__ + j * b_dim1]; + if (nounit) { + temp *= a[i__ + i__ * a_dim1]; + } + i__2 = i__ - 1; + for (k = 1; k <= i__2; ++k) { + temp += a[k + i__ * a_dim1] * b[k + j * b_dim1]; +/* L90: */ + } + b[i__ + j * b_dim1] = *alpha * temp; +/* L100: */ + } +/* L110: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp = b[i__ + j * b_dim1]; + if (nounit) { + temp *= a[i__ + i__ * a_dim1]; + } + i__3 = *m; + for (k = i__ + 1; k <= i__3; ++k) { + temp += a[k + i__ * a_dim1] * b[k + j * b_dim1]; +/* L120: */ + } + b[i__ + j * b_dim1] = *alpha * temp; +/* L130: */ + } +/* L140: */ + } + } + } + } else { + if (lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1)) { + +/* Form B := alpha*B*A. */ + + if (upper) { + for (j = *n; j >= 1; --j) { + temp = *alpha; + if (nounit) { + temp *= a[j + j * a_dim1]; + } + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1]; +/* L150: */ + } + i__1 = j - 1; + for (k = 1; k <= i__1; ++k) { + if (a[k + j * a_dim1] != 0.) { + temp = *alpha * a[k + j * a_dim1]; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] += temp * b[i__ + k * + b_dim1]; +/* L160: */ + } + } +/* L170: */ + } +/* L180: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp = *alpha; + if (nounit) { + temp *= a[j + j * a_dim1]; + } + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1]; +/* L190: */ + } + i__2 = *n; + for (k = j + 1; k <= i__2; ++k) { + if (a[k + j * a_dim1] != 0.) { + temp = *alpha * a[k + j * a_dim1]; + i__3 = *m; + for (i__ = 1; i__ <= i__3; ++i__) { + b[i__ + j * b_dim1] += temp * b[i__ + k * + b_dim1]; +/* L200: */ + } + } +/* L210: */ + } +/* L220: */ + } + } + } else { + +/* Form B := alpha*B*A**T. */ + + if (upper) { + i__1 = *n; + for (k = 1; k <= i__1; ++k) { + i__2 = k - 1; + for (j = 1; j <= i__2; ++j) { + if (a[j + k * a_dim1] != 0.) { + temp = *alpha * a[j + k * a_dim1]; + i__3 = *m; + for (i__ = 1; i__ <= i__3; ++i__) { + b[i__ + j * b_dim1] += temp * b[i__ + k * + b_dim1]; +/* L230: */ + } + } +/* L240: */ + } + temp = *alpha; + if (nounit) { + temp *= a[k + k * a_dim1]; + } + if (temp != 1.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1]; +/* L250: */ + } + } +/* L260: */ + } + } else { + for (k = *n; k >= 1; --k) { + i__1 = *n; + for (j = k + 1; j <= i__1; ++j) { + if (a[j + k * a_dim1] != 0.) { + temp = *alpha * a[j + k * a_dim1]; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] += temp * b[i__ + k * + b_dim1]; +/* L270: */ + } + } +/* L280: */ + } + temp = *alpha; + if (nounit) { + temp *= a[k + k * a_dim1]; + } + if (temp != 1.) { + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1]; +/* L290: */ + } + } +/* L300: */ + } + } + } + } + + return 0; + +/* End of DTRMM */ + +} /* dtrmm_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dtrmv.cpp b/lib/linalg/dtrmv.cpp new file mode 100644 index 0000000000..77dbf2f66f --- /dev/null +++ b/lib/linalg/dtrmv.cpp @@ -0,0 +1,415 @@ +/* fortran/dtrmv.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DTRMV */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INCX,LDA,N */ +/* CHARACTER DIAG,TRANS,UPLO */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A(LDA,*),X(*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DTRMV performs one of the matrix-vector operations */ +/* > */ +/* > x := A*x, or x := A**T*x, */ +/* > */ +/* > where x is an n element vector and A is an n by n unit, or non-unit, */ +/* > upper or lower triangular matrix. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > On entry, UPLO specifies whether the matrix is an upper or */ +/* > lower triangular matrix as follows: */ +/* > */ +/* > UPLO = 'U' or 'u' A is an upper triangular matrix. */ +/* > */ +/* > UPLO = 'L' or 'l' A is a lower triangular matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TRANS */ +/* > \verbatim */ +/* > TRANS is CHARACTER*1 */ +/* > On entry, TRANS specifies the operation to be performed as */ +/* > follows: */ +/* > */ +/* > TRANS = 'N' or 'n' x := A*x. */ +/* > */ +/* > TRANS = 'T' or 't' x := A**T*x. */ +/* > */ +/* > TRANS = 'C' or 'c' x := A**T*x. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DIAG */ +/* > \verbatim */ +/* > DIAG is CHARACTER*1 */ +/* > On entry, DIAG specifies whether or not A is unit */ +/* > triangular as follows: */ +/* > */ +/* > DIAG = 'U' or 'u' A is assumed to be unit triangular. */ +/* > */ +/* > DIAG = 'N' or 'n' A is not assumed to be unit */ +/* > triangular. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > On entry, N specifies the order of the matrix A. */ +/* > N must be at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension ( LDA, N ) */ +/* > Before entry with UPLO = 'U' or 'u', the leading n by n */ +/* > upper triangular part of the array A must contain the upper */ +/* > triangular matrix and the strictly lower triangular part of */ +/* > A is not referenced. */ +/* > Before entry with UPLO = 'L' or 'l', the leading n by n */ +/* > lower triangular part of the array A must contain the lower */ +/* > triangular matrix and the strictly upper triangular part of */ +/* > A is not referenced. */ +/* > Note that when DIAG = 'U' or 'u', the diagonal elements of */ +/* > A are not referenced either, but are assumed to be unity. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > On entry, LDA specifies the first dimension of A as declared */ +/* > in the calling (sub) program. LDA must be at least */ +/* > max( 1, n ). */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] X */ +/* > \verbatim */ +/* > X is DOUBLE PRECISION array, dimension at least */ +/* > ( 1 + ( n - 1 )*abs( INCX ) ). */ +/* > Before entry, the incremented array X must contain the n */ +/* > element vector x. On exit, X is overwritten with the */ +/* > transformed vector x. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > On entry, INCX specifies the increment for the elements of */ +/* > X. INCX must not be zero. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup double_blas_level2 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > Level 2 Blas routine. */ +/* > The vector and matrix arguments are not referenced when N = 0, or M = 0 */ +/* > */ +/* > -- Written on 22-October-1986. */ +/* > Jack Dongarra, Argonne National Lab. */ +/* > Jeremy Du Croz, Nag Central Office. */ +/* > Sven Hammarling, Nag Central Office. */ +/* > Richard Hanson, Sandia National Labs. */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dtrmv_(char *uplo, char *trans, char *diag, integer *n, + doublereal *a, integer *lda, doublereal *x, integer *incx, ftnlen + uplo_len, ftnlen trans_len, ftnlen diag_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2; + + /* Local variables */ + integer i__, j, ix, jx, kx, info; + doublereal temp; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + logical nounit; + + +/* -- Reference BLAS level2 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --x; + + /* Function Body */ + info = 0; + if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", ( + ftnlen)1, (ftnlen)1)) { + info = 1; + } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, + (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, ( + ftnlen)1)) { + info = 2; + } else if (! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, + (char *)"N", (ftnlen)1, (ftnlen)1)) { + info = 3; + } else if (*n < 0) { + info = 4; + } else if (*lda < max(1,*n)) { + info = 6; + } else if (*incx == 0) { + info = 8; + } + if (info != 0) { + xerbla_((char *)"DTRMV ", &info, (ftnlen)6); + return 0; + } + +/* Quick return if possible. */ + + if (*n == 0) { + return 0; + } + + nounit = lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1); + +/* Set up the start point in X if the increment is not unity. This */ +/* will be ( N - 1 )*INCX too small for descending loops. */ + + if (*incx <= 0) { + kx = 1 - (*n - 1) * *incx; + } else if (*incx != 1) { + kx = 1; + } + +/* Start the operations. In this version the elements of A are */ +/* accessed sequentially with one pass through A. */ + + if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { + +/* Form x := A*x. */ + + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + if (*incx == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (x[j] != 0.) { + temp = x[j]; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + x[i__] += temp * a[i__ + j * a_dim1]; +/* L10: */ + } + if (nounit) { + x[j] *= a[j + j * a_dim1]; + } + } +/* L20: */ + } + } else { + jx = kx; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (x[jx] != 0.) { + temp = x[jx]; + ix = kx; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + x[ix] += temp * a[i__ + j * a_dim1]; + ix += *incx; +/* L30: */ + } + if (nounit) { + x[jx] *= a[j + j * a_dim1]; + } + } + jx += *incx; +/* L40: */ + } + } + } else { + if (*incx == 1) { + for (j = *n; j >= 1; --j) { + if (x[j] != 0.) { + temp = x[j]; + i__1 = j + 1; + for (i__ = *n; i__ >= i__1; --i__) { + x[i__] += temp * a[i__ + j * a_dim1]; +/* L50: */ + } + if (nounit) { + x[j] *= a[j + j * a_dim1]; + } + } +/* L60: */ + } + } else { + kx += (*n - 1) * *incx; + jx = kx; + for (j = *n; j >= 1; --j) { + if (x[jx] != 0.) { + temp = x[jx]; + ix = kx; + i__1 = j + 1; + for (i__ = *n; i__ >= i__1; --i__) { + x[ix] += temp * a[i__ + j * a_dim1]; + ix -= *incx; +/* L70: */ + } + if (nounit) { + x[jx] *= a[j + j * a_dim1]; + } + } + jx -= *incx; +/* L80: */ + } + } + } + } else { + +/* Form x := A**T*x. */ + + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + if (*incx == 1) { + for (j = *n; j >= 1; --j) { + temp = x[j]; + if (nounit) { + temp *= a[j + j * a_dim1]; + } + for (i__ = j - 1; i__ >= 1; --i__) { + temp += a[i__ + j * a_dim1] * x[i__]; +/* L90: */ + } + x[j] = temp; +/* L100: */ + } + } else { + jx = kx + (*n - 1) * *incx; + for (j = *n; j >= 1; --j) { + temp = x[jx]; + ix = jx; + if (nounit) { + temp *= a[j + j * a_dim1]; + } + for (i__ = j - 1; i__ >= 1; --i__) { + ix -= *incx; + temp += a[i__ + j * a_dim1] * x[ix]; +/* L110: */ + } + x[jx] = temp; + jx -= *incx; +/* L120: */ + } + } + } else { + if (*incx == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp = x[j]; + if (nounit) { + temp *= a[j + j * a_dim1]; + } + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + temp += a[i__ + j * a_dim1] * x[i__]; +/* L130: */ + } + x[j] = temp; +/* L140: */ + } + } else { + jx = kx; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp = x[jx]; + ix = jx; + if (nounit) { + temp *= a[j + j * a_dim1]; + } + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + ix += *incx; + temp += a[i__ + j * a_dim1] * x[ix]; +/* L150: */ + } + x[jx] = temp; + jx += *incx; +/* L160: */ + } + } + } + } + + return 0; + +/* End of DTRMV */ + +} /* dtrmv_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dtrsm.cpp b/lib/linalg/dtrsm.cpp new file mode 100644 index 0000000000..488da4ecdc --- /dev/null +++ b/lib/linalg/dtrsm.cpp @@ -0,0 +1,565 @@ +/* fortran/dtrsm.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DTRSM */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) */ + +/* .. Scalar Arguments .. */ +/* DOUBLE PRECISION ALPHA */ +/* INTEGER LDA,LDB,M,N */ +/* CHARACTER DIAG,SIDE,TRANSA,UPLO */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A(LDA,*),B(LDB,*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DTRSM solves one of the matrix equations */ +/* > */ +/* > op( A )*X = alpha*B, or X*op( A ) = alpha*B, */ +/* > */ +/* > where alpha is a scalar, X and B are m by n matrices, A is a unit, or */ +/* > non-unit, upper or lower triangular matrix and op( A ) is one of */ +/* > */ +/* > op( A ) = A or op( A ) = A**T. */ +/* > */ +/* > The matrix X is overwritten on B. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] SIDE */ +/* > \verbatim */ +/* > SIDE is CHARACTER*1 */ +/* > On entry, SIDE specifies whether op( A ) appears on the left */ +/* > or right of X as follows: */ +/* > */ +/* > SIDE = 'L' or 'l' op( A )*X = alpha*B. */ +/* > */ +/* > SIDE = 'R' or 'r' X*op( A ) = alpha*B. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > On entry, UPLO specifies whether the matrix A is an upper or */ +/* > lower triangular matrix as follows: */ +/* > */ +/* > UPLO = 'U' or 'u' A is an upper triangular matrix. */ +/* > */ +/* > UPLO = 'L' or 'l' A is a lower triangular matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TRANSA */ +/* > \verbatim */ +/* > TRANSA is CHARACTER*1 */ +/* > On entry, TRANSA specifies the form of op( A ) to be used in */ +/* > the matrix multiplication as follows: */ +/* > */ +/* > TRANSA = 'N' or 'n' op( A ) = A. */ +/* > */ +/* > TRANSA = 'T' or 't' op( A ) = A**T. */ +/* > */ +/* > TRANSA = 'C' or 'c' op( A ) = A**T. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DIAG */ +/* > \verbatim */ +/* > DIAG is CHARACTER*1 */ +/* > On entry, DIAG specifies whether or not A is unit triangular */ +/* > as follows: */ +/* > */ +/* > DIAG = 'U' or 'u' A is assumed to be unit triangular. */ +/* > */ +/* > DIAG = 'N' or 'n' A is not assumed to be unit */ +/* > triangular. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > On entry, M specifies the number of rows of B. M must be at */ +/* > least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > On entry, N specifies the number of columns of B. N must be */ +/* > at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] ALPHA */ +/* > \verbatim */ +/* > ALPHA is DOUBLE PRECISION. */ +/* > On entry, ALPHA specifies the scalar alpha. When alpha is */ +/* > zero then A is not referenced and B need not be set before */ +/* > entry. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension ( LDA, k ), */ +/* > where k is m when SIDE = 'L' or 'l' */ +/* > and k is n when SIDE = 'R' or 'r'. */ +/* > Before entry with UPLO = 'U' or 'u', the leading k by k */ +/* > upper triangular part of the array A must contain the upper */ +/* > triangular matrix and the strictly lower triangular part of */ +/* > A is not referenced. */ +/* > Before entry with UPLO = 'L' or 'l', the leading k by k */ +/* > lower triangular part of the array A must contain the lower */ +/* > triangular matrix and the strictly upper triangular part of */ +/* > A is not referenced. */ +/* > Note that when DIAG = 'U' or 'u', the diagonal elements of */ +/* > A are not referenced either, but are assumed to be unity. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > On entry, LDA specifies the first dimension of A as declared */ +/* > in the calling (sub) program. When SIDE = 'L' or 'l' then */ +/* > LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' */ +/* > then LDA must be at least max( 1, n ). */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] B */ +/* > \verbatim */ +/* > B is DOUBLE PRECISION array, dimension ( LDB, N ) */ +/* > Before entry, the leading m by n part of the array B must */ +/* > contain the right-hand side matrix B, and on exit is */ +/* > overwritten by the solution matrix X. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDB */ +/* > \verbatim */ +/* > LDB is INTEGER */ +/* > On entry, LDB specifies the first dimension of B as declared */ +/* > in the calling (sub) program. LDB must be at least */ +/* > max( 1, m ). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup double_blas_level3 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > Level 3 Blas routine. */ +/* > */ +/* > */ +/* > -- Written on 8-February-1989. */ +/* > Jack Dongarra, Argonne National Laboratory. */ +/* > Iain Duff, AERE Harwell. */ +/* > Jeremy Du Croz, Numerical Algorithms Group Ltd. */ +/* > Sven Hammarling, Numerical Algorithms Group Ltd. */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int dtrsm_(char *side, char *uplo, char *transa, char *diag, + integer *m, integer *n, doublereal *alpha, doublereal *a, integer * + lda, doublereal *b, integer *ldb, ftnlen side_len, ftnlen uplo_len, + ftnlen transa_len, ftnlen diag_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3; + + /* Local variables */ + integer i__, j, k, info; + doublereal temp; + logical lside; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + integer nrowa; + logical upper; + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + logical nounit; + + +/* -- Reference BLAS level3 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Parameters .. */ +/* .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + b_dim1 = *ldb; + b_offset = 1 + b_dim1; + b -= b_offset; + + /* Function Body */ + lside = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); + if (lside) { + nrowa = *m; + } else { + nrowa = *n; + } + nounit = lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1); + upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); + + info = 0; + if (! lside && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + info = 1; + } else if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + info = 2; + } else if (! lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(transa, + (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(transa, (char *)"C", (ftnlen)1, ( + ftnlen)1)) { + info = 3; + } else if (! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, + (char *)"N", (ftnlen)1, (ftnlen)1)) { + info = 4; + } else if (*m < 0) { + info = 5; + } else if (*n < 0) { + info = 6; + } else if (*lda < max(1,nrowa)) { + info = 9; + } else if (*ldb < max(1,*m)) { + info = 11; + } + if (info != 0) { + xerbla_((char *)"DTRSM ", &info, (ftnlen)6); + return 0; + } + +/* Quick return if possible. */ + + if (*m == 0 || *n == 0) { + return 0; + } + +/* And when alpha.eq.zero. */ + + if (*alpha == 0.) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] = 0.; +/* L10: */ + } +/* L20: */ + } + return 0; + } + +/* Start the operations. */ + + if (lside) { + if (lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1)) { + +/* Form B := alpha*inv( A )*B. */ + + if (upper) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (*alpha != 1.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1] + ; +/* L30: */ + } + } + for (k = *m; k >= 1; --k) { + if (b[k + j * b_dim1] != 0.) { + if (nounit) { + b[k + j * b_dim1] /= a[k + k * a_dim1]; + } + i__2 = k - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] -= b[k + j * b_dim1] * a[ + i__ + k * a_dim1]; +/* L40: */ + } + } +/* L50: */ + } +/* L60: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (*alpha != 1.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1] + ; +/* L70: */ + } + } + i__2 = *m; + for (k = 1; k <= i__2; ++k) { + if (b[k + j * b_dim1] != 0.) { + if (nounit) { + b[k + j * b_dim1] /= a[k + k * a_dim1]; + } + i__3 = *m; + for (i__ = k + 1; i__ <= i__3; ++i__) { + b[i__ + j * b_dim1] -= b[k + j * b_dim1] * a[ + i__ + k * a_dim1]; +/* L80: */ + } + } +/* L90: */ + } +/* L100: */ + } + } + } else { + +/* Form B := alpha*inv( A**T )*B. */ + + if (upper) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp = *alpha * b[i__ + j * b_dim1]; + i__3 = i__ - 1; + for (k = 1; k <= i__3; ++k) { + temp -= a[k + i__ * a_dim1] * b[k + j * b_dim1]; +/* L110: */ + } + if (nounit) { + temp /= a[i__ + i__ * a_dim1]; + } + b[i__ + j * b_dim1] = temp; +/* L120: */ + } +/* L130: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + for (i__ = *m; i__ >= 1; --i__) { + temp = *alpha * b[i__ + j * b_dim1]; + i__2 = *m; + for (k = i__ + 1; k <= i__2; ++k) { + temp -= a[k + i__ * a_dim1] * b[k + j * b_dim1]; +/* L140: */ + } + if (nounit) { + temp /= a[i__ + i__ * a_dim1]; + } + b[i__ + j * b_dim1] = temp; +/* L150: */ + } +/* L160: */ + } + } + } + } else { + if (lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1)) { + +/* Form B := alpha*B*inv( A ). */ + + if (upper) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (*alpha != 1.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1] + ; +/* L170: */ + } + } + i__2 = j - 1; + for (k = 1; k <= i__2; ++k) { + if (a[k + j * a_dim1] != 0.) { + i__3 = *m; + for (i__ = 1; i__ <= i__3; ++i__) { + b[i__ + j * b_dim1] -= a[k + j * a_dim1] * b[ + i__ + k * b_dim1]; +/* L180: */ + } + } +/* L190: */ + } + if (nounit) { + temp = 1. / a[j + j * a_dim1]; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1]; +/* L200: */ + } + } +/* L210: */ + } + } else { + for (j = *n; j >= 1; --j) { + if (*alpha != 1.) { + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1] + ; +/* L220: */ + } + } + i__1 = *n; + for (k = j + 1; k <= i__1; ++k) { + if (a[k + j * a_dim1] != 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] -= a[k + j * a_dim1] * b[ + i__ + k * b_dim1]; +/* L230: */ + } + } +/* L240: */ + } + if (nounit) { + temp = 1. / a[j + j * a_dim1]; + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1]; +/* L250: */ + } + } +/* L260: */ + } + } + } else { + +/* Form B := alpha*B*inv( A**T ). */ + + if (upper) { + for (k = *n; k >= 1; --k) { + if (nounit) { + temp = 1. / a[k + k * a_dim1]; + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1]; +/* L270: */ + } + } + i__1 = k - 1; + for (j = 1; j <= i__1; ++j) { + if (a[j + k * a_dim1] != 0.) { + temp = a[j + k * a_dim1]; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] -= temp * b[i__ + k * + b_dim1]; +/* L280: */ + } + } +/* L290: */ + } + if (*alpha != 1.) { + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + b[i__ + k * b_dim1] = *alpha * b[i__ + k * b_dim1] + ; +/* L300: */ + } + } +/* L310: */ + } + } else { + i__1 = *n; + for (k = 1; k <= i__1; ++k) { + if (nounit) { + temp = 1. / a[k + k * a_dim1]; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1]; +/* L320: */ + } + } + i__2 = *n; + for (j = k + 1; j <= i__2; ++j) { + if (a[j + k * a_dim1] != 0.) { + temp = a[j + k * a_dim1]; + i__3 = *m; + for (i__ = 1; i__ <= i__3; ++i__) { + b[i__ + j * b_dim1] -= temp * b[i__ + k * + b_dim1]; +/* L330: */ + } + } +/* L340: */ + } + if (*alpha != 1.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + k * b_dim1] = *alpha * b[i__ + k * b_dim1] + ; +/* L350: */ + } + } +/* L360: */ + } + } + } + } + + return 0; + +/* End of DTRSM */ + +} /* dtrsm_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dtrsv.cpp b/lib/linalg/dtrsv.cpp new file mode 100644 index 0000000000..58b85f9206 --- /dev/null +++ b/lib/linalg/dtrsv.cpp @@ -0,0 +1,411 @@ +/* fortran/dtrsv.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DTRSV */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INCX,LDA,N */ +/* CHARACTER DIAG,TRANS,UPLO */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A(LDA,*),X(*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DTRSV solves one of the systems of equations */ +/* > */ +/* > A*x = b, or A**T*x = b, */ +/* > */ +/* > where b and x are n element vectors and A is an n by n unit, or */ +/* > non-unit, upper or lower triangular matrix. */ +/* > */ +/* > No test for singularity or near-singularity is included in this */ +/* > routine. Such tests must be performed before calling this routine. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > On entry, UPLO specifies whether the matrix is an upper or */ +/* > lower triangular matrix as follows: */ +/* > */ +/* > UPLO = 'U' or 'u' A is an upper triangular matrix. */ +/* > */ +/* > UPLO = 'L' or 'l' A is a lower triangular matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TRANS */ +/* > \verbatim */ +/* > TRANS is CHARACTER*1 */ +/* > On entry, TRANS specifies the equations to be solved as */ +/* > follows: */ +/* > */ +/* > TRANS = 'N' or 'n' A*x = b. */ +/* > */ +/* > TRANS = 'T' or 't' A**T*x = b. */ +/* > */ +/* > TRANS = 'C' or 'c' A**T*x = b. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DIAG */ +/* > \verbatim */ +/* > DIAG is CHARACTER*1 */ +/* > On entry, DIAG specifies whether or not A is unit */ +/* > triangular as follows: */ +/* > */ +/* > DIAG = 'U' or 'u' A is assumed to be unit triangular. */ +/* > */ +/* > DIAG = 'N' or 'n' A is not assumed to be unit */ +/* > triangular. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > On entry, N specifies the order of the matrix A. */ +/* > N must be at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension ( LDA, N ) */ +/* > Before entry with UPLO = 'U' or 'u', the leading n by n */ +/* > upper triangular part of the array A must contain the upper */ +/* > triangular matrix and the strictly lower triangular part of */ +/* > A is not referenced. */ +/* > Before entry with UPLO = 'L' or 'l', the leading n by n */ +/* > lower triangular part of the array A must contain the lower */ +/* > triangular matrix and the strictly upper triangular part of */ +/* > A is not referenced. */ +/* > Note that when DIAG = 'U' or 'u', the diagonal elements of */ +/* > A are not referenced either, but are assumed to be unity. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > On entry, LDA specifies the first dimension of A as declared */ +/* > in the calling (sub) program. LDA must be at least */ +/* > max( 1, n ). */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] X */ +/* > \verbatim */ +/* > X is DOUBLE PRECISION array, dimension at least */ +/* > ( 1 + ( n - 1 )*abs( INCX ) ). */ +/* > Before entry, the incremented array X must contain the n */ +/* > element right-hand side vector b. On exit, X is overwritten */ +/* > with the solution vector x. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > On entry, INCX specifies the increment for the elements of */ +/* > X. INCX must not be zero. */ +/* > */ +/* > Level 2 Blas routine. */ +/* > */ +/* > -- Written on 22-October-1986. */ +/* > Jack Dongarra, Argonne National Lab. */ +/* > Jeremy Du Croz, Nag Central Office. */ +/* > Sven Hammarling, Nag Central Office. */ +/* > Richard Hanson, Sandia National Labs. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup double_blas_level1 */ + +/* ===================================================================== */ +/* Subroutine */ int dtrsv_(char *uplo, char *trans, char *diag, integer *n, + doublereal *a, integer *lda, doublereal *x, integer *incx, ftnlen + uplo_len, ftnlen trans_len, ftnlen diag_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2; + + /* Local variables */ + integer i__, j, ix, jx, kx, info; + doublereal temp; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + logical nounit; + + +/* -- Reference BLAS level1 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --x; + + /* Function Body */ + info = 0; + if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", ( + ftnlen)1, (ftnlen)1)) { + info = 1; + } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, + (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, ( + ftnlen)1)) { + info = 2; + } else if (! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, + (char *)"N", (ftnlen)1, (ftnlen)1)) { + info = 3; + } else if (*n < 0) { + info = 4; + } else if (*lda < max(1,*n)) { + info = 6; + } else if (*incx == 0) { + info = 8; + } + if (info != 0) { + xerbla_((char *)"DTRSV ", &info, (ftnlen)6); + return 0; + } + +/* Quick return if possible. */ + + if (*n == 0) { + return 0; + } + + nounit = lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1); + +/* Set up the start point in X if the increment is not unity. This */ +/* will be ( N - 1 )*INCX too small for descending loops. */ + + if (*incx <= 0) { + kx = 1 - (*n - 1) * *incx; + } else if (*incx != 1) { + kx = 1; + } + +/* Start the operations. In this version the elements of A are */ +/* accessed sequentially with one pass through A. */ + + if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { + +/* Form x := inv( A )*x. */ + + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + if (*incx == 1) { + for (j = *n; j >= 1; --j) { + if (x[j] != 0.) { + if (nounit) { + x[j] /= a[j + j * a_dim1]; + } + temp = x[j]; + for (i__ = j - 1; i__ >= 1; --i__) { + x[i__] -= temp * a[i__ + j * a_dim1]; +/* L10: */ + } + } +/* L20: */ + } + } else { + jx = kx + (*n - 1) * *incx; + for (j = *n; j >= 1; --j) { + if (x[jx] != 0.) { + if (nounit) { + x[jx] /= a[j + j * a_dim1]; + } + temp = x[jx]; + ix = jx; + for (i__ = j - 1; i__ >= 1; --i__) { + ix -= *incx; + x[ix] -= temp * a[i__ + j * a_dim1]; +/* L30: */ + } + } + jx -= *incx; +/* L40: */ + } + } + } else { + if (*incx == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (x[j] != 0.) { + if (nounit) { + x[j] /= a[j + j * a_dim1]; + } + temp = x[j]; + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + x[i__] -= temp * a[i__ + j * a_dim1]; +/* L50: */ + } + } +/* L60: */ + } + } else { + jx = kx; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (x[jx] != 0.) { + if (nounit) { + x[jx] /= a[j + j * a_dim1]; + } + temp = x[jx]; + ix = jx; + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + ix += *incx; + x[ix] -= temp * a[i__ + j * a_dim1]; +/* L70: */ + } + } + jx += *incx; +/* L80: */ + } + } + } + } else { + +/* Form x := inv( A**T )*x. */ + + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + if (*incx == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp = x[j]; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + temp -= a[i__ + j * a_dim1] * x[i__]; +/* L90: */ + } + if (nounit) { + temp /= a[j + j * a_dim1]; + } + x[j] = temp; +/* L100: */ + } + } else { + jx = kx; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp = x[jx]; + ix = kx; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + temp -= a[i__ + j * a_dim1] * x[ix]; + ix += *incx; +/* L110: */ + } + if (nounit) { + temp /= a[j + j * a_dim1]; + } + x[jx] = temp; + jx += *incx; +/* L120: */ + } + } + } else { + if (*incx == 1) { + for (j = *n; j >= 1; --j) { + temp = x[j]; + i__1 = j + 1; + for (i__ = *n; i__ >= i__1; --i__) { + temp -= a[i__ + j * a_dim1] * x[i__]; +/* L130: */ + } + if (nounit) { + temp /= a[j + j * a_dim1]; + } + x[j] = temp; +/* L140: */ + } + } else { + kx += (*n - 1) * *incx; + jx = kx; + for (j = *n; j >= 1; --j) { + temp = x[jx]; + ix = kx; + i__1 = j + 1; + for (i__ = *n; i__ >= i__1; --i__) { + temp -= a[i__ + j * a_dim1] * x[ix]; + ix -= *incx; +/* L150: */ + } + if (nounit) { + temp /= a[j + j * a_dim1]; + } + x[jx] = temp; + jx -= *incx; +/* L160: */ + } + } + } + } + + return 0; + +/* End of DTRSV */ + +} /* dtrsv_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dtrti2.cpp b/lib/linalg/dtrti2.cpp new file mode 100644 index 0000000000..f159e31b0d --- /dev/null +++ b/lib/linalg/dtrti2.cpp @@ -0,0 +1,258 @@ +/* fortran/dtrti2.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; + +/* > \brief \b DTRTI2 computes the inverse of a triangular matrix (unblocked algorithm). */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DTRTI2 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DTRTI2( UPLO, DIAG, N, A, LDA, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER DIAG, UPLO */ +/* INTEGER INFO, LDA, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DTRTI2 computes the inverse of a real upper or lower triangular */ +/* > matrix. */ +/* > */ +/* > This is the Level 2 BLAS version of the algorithm. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > Specifies whether the matrix A is upper or lower triangular. */ +/* > = 'U': Upper triangular */ +/* > = 'L': Lower triangular */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DIAG */ +/* > \verbatim */ +/* > DIAG is CHARACTER*1 */ +/* > Specifies whether or not the matrix A is unit triangular. */ +/* > = 'N': Non-unit triangular */ +/* > = 'U': Unit triangular */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On entry, the triangular matrix A. If UPLO = 'U', the */ +/* > leading n by n upper triangular part of the array A contains */ +/* > the upper triangular matrix, and the strictly lower */ +/* > triangular part of A is not referenced. If UPLO = 'L', the */ +/* > leading n by n lower triangular part of the array A contains */ +/* > the lower triangular matrix, and the strictly upper */ +/* > triangular part of A is not referenced. If DIAG = 'U', the */ +/* > diagonal elements of A are also not referenced and are */ +/* > assumed to be 1. */ +/* > */ +/* > On exit, the (triangular) inverse of the original matrix, in */ +/* > the same storage format. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -k, the k-th argument had an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleOTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dtrti2_(char *uplo, char *diag, integer *n, doublereal * + a, integer *lda, integer *info, ftnlen uplo_len, ftnlen diag_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2; + + /* Local variables */ + integer j; + doublereal ajj; + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *); + extern logical lsame_(char *, char *, ftnlen, ftnlen); + logical upper; + extern /* Subroutine */ int dtrmv_(char *, char *, char *, integer *, + doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, + ftnlen), xerbla_(char *, integer *, ftnlen); + logical nounit; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + + /* Function Body */ + *info = 0; + upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); + nounit = lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1); + if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + *info = -1; + } else if (! nounit && ! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1)) { + *info = -2; + } else if (*n < 0) { + *info = -3; + } else if (*lda < max(1,*n)) { + *info = -5; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DTRTI2", &i__1, (ftnlen)6); + return 0; + } + + if (upper) { + +/* Compute inverse of upper triangular matrix. */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (nounit) { + a[j + j * a_dim1] = 1. / a[j + j * a_dim1]; + ajj = -a[j + j * a_dim1]; + } else { + ajj = -1.; + } + +/* Compute elements 1:j-1 of j-th column. */ + + i__2 = j - 1; + dtrmv_((char *)"Upper", (char *)"No transpose", diag, &i__2, &a[a_offset], lda, & + a[j * a_dim1 + 1], &c__1, (ftnlen)5, (ftnlen)12, (ftnlen) + 1); + i__2 = j - 1; + dscal_(&i__2, &ajj, &a[j * a_dim1 + 1], &c__1); +/* L10: */ + } + } else { + +/* Compute inverse of lower triangular matrix. */ + + for (j = *n; j >= 1; --j) { + if (nounit) { + a[j + j * a_dim1] = 1. / a[j + j * a_dim1]; + ajj = -a[j + j * a_dim1]; + } else { + ajj = -1.; + } + if (j < *n) { + +/* Compute elements j+1:n of j-th column. */ + + i__1 = *n - j; + dtrmv_((char *)"Lower", (char *)"No transpose", diag, &i__1, &a[j + 1 + (j + + 1) * a_dim1], lda, &a[j + 1 + j * a_dim1], &c__1, ( + ftnlen)5, (ftnlen)12, (ftnlen)1); + i__1 = *n - j; + dscal_(&i__1, &ajj, &a[j + 1 + j * a_dim1], &c__1); + } +/* L20: */ + } + } + + return 0; + +/* End of DTRTI2 */ + +} /* dtrti2_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dtrtri.cpp b/lib/linalg/dtrtri.cpp new file mode 100644 index 0000000000..faecb3dd69 --- /dev/null +++ b/lib/linalg/dtrtri.cpp @@ -0,0 +1,321 @@ +/* fortran/dtrtri.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c_n1 = -1; +static integer c__2 = 2; +static doublereal c_b18 = 1.; +static doublereal c_b22 = -1.; + +/* > \brief \b DTRTRI */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download DTRTRI + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE DTRTRI( UPLO, DIAG, N, A, LDA, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER DIAG, UPLO */ +/* INTEGER INFO, LDA, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DTRTRI computes the inverse of a real upper or lower triangular */ +/* > matrix A. */ +/* > */ +/* > This is the Level 3 BLAS version of the algorithm. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > = 'U': A is upper triangular; */ +/* > = 'L': A is lower triangular. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DIAG */ +/* > \verbatim */ +/* > DIAG is CHARACTER*1 */ +/* > = 'N': A is non-unit triangular; */ +/* > = 'U': A is unit triangular. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > On entry, the triangular matrix A. If UPLO = 'U', the */ +/* > leading N-by-N upper triangular part of the array A contains */ +/* > the upper triangular matrix, and the strictly lower */ +/* > triangular part of A is not referenced. If UPLO = 'L', the */ +/* > leading N-by-N lower triangular part of the array A contains */ +/* > the lower triangular matrix, and the strictly upper */ +/* > triangular part of A is not referenced. If DIAG = 'U', the */ +/* > diagonal elements of A are also not referenced and are */ +/* > assumed to be 1. */ +/* > On exit, the (triangular) inverse of the original matrix, in */ +/* > the same storage format. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > > 0: if INFO = i, A(i,i) is exactly zero. The triangular */ +/* > matrix is singular and its inverse can not be computed. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup doubleOTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int dtrtri_(char *uplo, char *diag, integer *n, doublereal * + a, integer *lda, integer *info, ftnlen uplo_len, ftnlen diag_len) +{ + /* System generated locals */ + address a__1[2]; + integer a_dim1, a_offset, i__1, i__2[2], i__3, i__4, i__5; + char ch__1[2]; + + /* Builtin functions */ + /* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen); + + /* Local variables */ + integer j, jb, nb, nn; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int dtrmm_(char *, char *, char *, char *, + integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen), dtrsm_( + char *, char *, char *, char *, integer *, integer *, doublereal * + , doublereal *, integer *, doublereal *, integer *, ftnlen, + ftnlen, ftnlen, ftnlen); + logical upper; + extern /* Subroutine */ int dtrti2_(char *, char *, integer *, doublereal + *, integer *, integer *, ftnlen, ftnlen), xerbla_(char *, integer + *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + logical nounit; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + + /* Function Body */ + *info = 0; + upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); + nounit = lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1); + if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + *info = -1; + } else if (! nounit && ! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1)) { + *info = -2; + } else if (*n < 0) { + *info = -3; + } else if (*lda < max(1,*n)) { + *info = -5; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"DTRTRI", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*n == 0) { + return 0; + } + +/* Check for singularity if non-unit. */ + + if (nounit) { + i__1 = *n; + for (*info = 1; *info <= i__1; ++(*info)) { + if (a[*info + *info * a_dim1] == 0.) { + return 0; + } +/* L10: */ + } + *info = 0; + } + +/* Determine the block size for this environment. */ + +/* Writing concatenation */ + i__2[0] = 1, a__1[0] = uplo; + i__2[1] = 1, a__1[1] = diag; + s_cat(ch__1, a__1, i__2, &c__2, (ftnlen)2); + nb = ilaenv_(&c__1, (char *)"DTRTRI", ch__1, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, ( + ftnlen)2); + if (nb <= 1 || nb >= *n) { + +/* Use unblocked code */ + + dtrti2_(uplo, diag, n, &a[a_offset], lda, info, (ftnlen)1, (ftnlen)1); + } else { + +/* Use blocked code */ + + if (upper) { + +/* Compute inverse of upper triangular matrix */ + + i__1 = *n; + i__3 = nb; + for (j = 1; i__3 < 0 ? j >= i__1 : j <= i__1; j += i__3) { +/* Computing MIN */ + i__4 = nb, i__5 = *n - j + 1; + jb = min(i__4,i__5); + +/* Compute rows 1:j-1 of current block column */ + + i__4 = j - 1; + dtrmm_((char *)"Left", (char *)"Upper", (char *)"No transpose", diag, &i__4, &jb, & + c_b18, &a[a_offset], lda, &a[j * a_dim1 + 1], lda, ( + ftnlen)4, (ftnlen)5, (ftnlen)12, (ftnlen)1); + i__4 = j - 1; + dtrsm_((char *)"Right", (char *)"Upper", (char *)"No transpose", diag, &i__4, &jb, & + c_b22, &a[j + j * a_dim1], lda, &a[j * a_dim1 + 1], + lda, (ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)1); + +/* Compute inverse of current diagonal block */ + + dtrti2_((char *)"Upper", diag, &jb, &a[j + j * a_dim1], lda, info, ( + ftnlen)5, (ftnlen)1); +/* L20: */ + } + } else { + +/* Compute inverse of lower triangular matrix */ + + nn = (*n - 1) / nb * nb + 1; + i__3 = -nb; + for (j = nn; i__3 < 0 ? j >= 1 : j <= 1; j += i__3) { +/* Computing MIN */ + i__1 = nb, i__4 = *n - j + 1; + jb = min(i__1,i__4); + if (j + jb <= *n) { + +/* Compute rows j+jb:n of current block column */ + + i__1 = *n - j - jb + 1; + dtrmm_((char *)"Left", (char *)"Lower", (char *)"No transpose", diag, &i__1, &jb, + &c_b18, &a[j + jb + (j + jb) * a_dim1], lda, &a[j + + jb + j * a_dim1], lda, (ftnlen)4, (ftnlen)5, ( + ftnlen)12, (ftnlen)1); + i__1 = *n - j - jb + 1; + dtrsm_((char *)"Right", (char *)"Lower", (char *)"No transpose", diag, &i__1, &jb, + &c_b22, &a[j + j * a_dim1], lda, &a[j + jb + j * + a_dim1], lda, (ftnlen)5, (ftnlen)5, (ftnlen)12, ( + ftnlen)1); + } + +/* Compute inverse of current diagonal block */ + + dtrti2_((char *)"Lower", diag, &jb, &a[j + j * a_dim1], lda, info, ( + ftnlen)5, (ftnlen)1); +/* L30: */ + } + } + } + + return 0; + +/* End of DTRTRI */ + +} /* dtrtri_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dznrm2.cpp b/lib/linalg/dznrm2.cpp new file mode 100644 index 0000000000..ec71aa201b --- /dev/null +++ b/lib/linalg/dznrm2.cpp @@ -0,0 +1,183 @@ +/* fortran/dznrm2.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DZNRM2 */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* DOUBLE PRECISION FUNCTION DZNRM2(N,X,INCX) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INCX,N */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 X(*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > DZNRM2 returns the euclidean norm of a vector via the function */ +/* > name, so that */ +/* > */ +/* > DZNRM2 := sqrt( x**H*x ) */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > number of elements in input vector(s) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] X */ +/* > \verbatim */ +/* > X is COMPLEX*16 array, dimension (N) */ +/* > complex vector with N elements */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > storage spacing between elements of X */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \date December 2016 */ + +/* > \ingroup double_blas_level1 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > -- This version written on 25-October-1982. */ +/* > Modified on 14-October-1993 to inline the call to ZLASSQ. */ +/* > Sven Hammarling, Nag Ltd. */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +doublereal dznrm2_(integer *n, doublecomplex *x, integer *incx) +{ + /* System generated locals */ + integer i__1, i__2, i__3; + doublereal ret_val, d__1; + + /* Builtin functions */ + double d_imag(doublecomplex *), sqrt(doublereal); + + /* Local variables */ + integer ix; + doublereal ssq, temp, norm, scale; + + +/* -- Reference BLAS level1 routine (version 3.7.0) -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ +/* December 2016 */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ + /* Parameter adjustments */ + --x; + + /* Function Body */ + if (*n < 1 || *incx < 1) { + norm = 0.; + } else { + scale = 0.; + ssq = 1.; +/* The following loop is equivalent to this call to the LAPACK */ +/* auxiliary routine: */ +/* CALL ZLASSQ( N, X, INCX, SCALE, SSQ ) */ + + i__1 = (*n - 1) * *incx + 1; + i__2 = *incx; + for (ix = 1; i__2 < 0 ? ix >= i__1 : ix <= i__1; ix += i__2) { + i__3 = ix; + if (x[i__3].r != 0.) { + i__3 = ix; + temp = (d__1 = x[i__3].r, abs(d__1)); + if (scale < temp) { +/* Computing 2nd power */ + d__1 = scale / temp; + ssq = ssq * (d__1 * d__1) + 1.; + scale = temp; + } else { +/* Computing 2nd power */ + d__1 = temp / scale; + ssq += d__1 * d__1; + } + } + if (d_imag(&x[ix]) != 0.) { + temp = (d__1 = d_imag(&x[ix]), abs(d__1)); + if (scale < temp) { +/* Computing 2nd power */ + d__1 = scale / temp; + ssq = ssq * (d__1 * d__1) + 1.; + scale = temp; + } else { +/* Computing 2nd power */ + d__1 = temp / scale; + ssq += d__1 * d__1; + } + } +/* L10: */ + } + norm = scale * sqrt(ssq); + } + + ret_val = norm; + return ret_val; + +/* End of DZNRM2. */ + +} /* dznrm2_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dasum.f b/lib/linalg/fortran/dasum.f similarity index 100% rename from lib/linalg/dasum.f rename to lib/linalg/fortran/dasum.f diff --git a/lib/linalg/daxpy.f b/lib/linalg/fortran/daxpy.f similarity index 100% rename from lib/linalg/daxpy.f rename to lib/linalg/fortran/daxpy.f diff --git a/lib/linalg/dbdsqr.f b/lib/linalg/fortran/dbdsqr.f similarity index 100% rename from lib/linalg/dbdsqr.f rename to lib/linalg/fortran/dbdsqr.f diff --git a/lib/linalg/dcabs1.f b/lib/linalg/fortran/dcabs1.f similarity index 100% rename from lib/linalg/dcabs1.f rename to lib/linalg/fortran/dcabs1.f diff --git a/lib/linalg/dcopy.f b/lib/linalg/fortran/dcopy.f similarity index 100% rename from lib/linalg/dcopy.f rename to lib/linalg/fortran/dcopy.f diff --git a/lib/linalg/ddot.f 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rename from lib/linalg/dsyevd.f rename to lib/linalg/fortran/dsyevd.f diff --git a/lib/linalg/dsygs2.f b/lib/linalg/fortran/dsygs2.f similarity index 100% rename from lib/linalg/dsygs2.f rename to lib/linalg/fortran/dsygs2.f diff --git a/lib/linalg/dsygst.f b/lib/linalg/fortran/dsygst.f similarity index 100% rename from lib/linalg/dsygst.f rename to lib/linalg/fortran/dsygst.f diff --git a/lib/linalg/dsygv.f b/lib/linalg/fortran/dsygv.f similarity index 100% rename from lib/linalg/dsygv.f rename to lib/linalg/fortran/dsygv.f diff --git a/lib/linalg/dsygvd.f b/lib/linalg/fortran/dsygvd.f similarity index 100% rename from lib/linalg/dsygvd.f rename to lib/linalg/fortran/dsygvd.f diff --git a/lib/linalg/dsymm.f b/lib/linalg/fortran/dsymm.f similarity index 100% rename from lib/linalg/dsymm.f rename to lib/linalg/fortran/dsymm.f diff --git a/lib/linalg/dsymv.f b/lib/linalg/fortran/dsymv.f similarity index 100% rename from lib/linalg/dsymv.f rename to lib/linalg/fortran/dsymv.f diff --git 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from lib/linalg/dtrmv.f rename to lib/linalg/fortran/dtrmv.f diff --git a/lib/linalg/dtrsm.f b/lib/linalg/fortran/dtrsm.f similarity index 100% rename from lib/linalg/dtrsm.f rename to lib/linalg/fortran/dtrsm.f diff --git a/lib/linalg/dtrsv.f b/lib/linalg/fortran/dtrsv.f similarity index 100% rename from lib/linalg/dtrsv.f rename to lib/linalg/fortran/dtrsv.f diff --git a/lib/linalg/dtrti2.f b/lib/linalg/fortran/dtrti2.f similarity index 100% rename from lib/linalg/dtrti2.f rename to lib/linalg/fortran/dtrti2.f diff --git a/lib/linalg/dtrtri.f b/lib/linalg/fortran/dtrtri.f similarity index 100% rename from lib/linalg/dtrtri.f rename to lib/linalg/fortran/dtrtri.f diff --git a/lib/linalg/dznrm2.f b/lib/linalg/fortran/dznrm2.f similarity index 100% rename from lib/linalg/dznrm2.f rename to lib/linalg/fortran/dznrm2.f diff --git a/lib/linalg/idamax.f b/lib/linalg/fortran/idamax.f similarity index 100% rename from lib/linalg/idamax.f rename to lib/linalg/fortran/idamax.f diff --git a/lib/linalg/ieeeck.f b/lib/linalg/fortran/ieeeck.f similarity index 100% rename from lib/linalg/ieeeck.f rename to lib/linalg/fortran/ieeeck.f diff --git a/lib/linalg/iladlc.f b/lib/linalg/fortran/iladlc.f similarity index 100% rename from lib/linalg/iladlc.f rename to lib/linalg/fortran/iladlc.f diff --git a/lib/linalg/iladlr.f b/lib/linalg/fortran/iladlr.f similarity index 100% rename from lib/linalg/iladlr.f rename to lib/linalg/fortran/iladlr.f diff --git a/lib/linalg/ilaenv.f b/lib/linalg/fortran/ilaenv.f similarity index 100% rename from lib/linalg/ilaenv.f rename to lib/linalg/fortran/ilaenv.f diff --git a/lib/linalg/ilazlc.f b/lib/linalg/fortran/ilazlc.f similarity index 100% rename from lib/linalg/ilazlc.f rename to lib/linalg/fortran/ilazlc.f diff --git a/lib/linalg/ilazlr.f b/lib/linalg/fortran/ilazlr.f similarity index 100% rename from lib/linalg/ilazlr.f rename to lib/linalg/fortran/ilazlr.f diff --git a/lib/linalg/iparmq.f b/lib/linalg/fortran/iparmq.f similarity index 100% rename from lib/linalg/iparmq.f rename to lib/linalg/fortran/iparmq.f diff --git a/lib/linalg/lsame.f b/lib/linalg/fortran/lsame.f similarity index 100% rename from lib/linalg/lsame.f rename to lib/linalg/fortran/lsame.f diff --git a/lib/linalg/xerbla.f b/lib/linalg/fortran/xerbla.f similarity index 100% rename from lib/linalg/xerbla.f rename to lib/linalg/fortran/xerbla.f diff --git a/lib/linalg/zaxpy.f b/lib/linalg/fortran/zaxpy.f similarity index 100% rename from lib/linalg/zaxpy.f rename to lib/linalg/fortran/zaxpy.f diff --git a/lib/linalg/zcopy.f b/lib/linalg/fortran/zcopy.f similarity index 100% rename from lib/linalg/zcopy.f rename to lib/linalg/fortran/zcopy.f diff --git a/lib/linalg/zdotc.f b/lib/linalg/fortran/zdotc.f similarity index 100% rename from lib/linalg/zdotc.f rename to lib/linalg/fortran/zdotc.f diff --git a/lib/linalg/zdrot.f b/lib/linalg/fortran/zdrot.f similarity index 100% rename from lib/linalg/zdrot.f rename to lib/linalg/fortran/zdrot.f diff --git a/lib/linalg/zdscal.f b/lib/linalg/fortran/zdscal.f similarity index 100% rename from lib/linalg/zdscal.f rename to lib/linalg/fortran/zdscal.f diff --git a/lib/linalg/zgemm.f b/lib/linalg/fortran/zgemm.f similarity index 100% rename from lib/linalg/zgemm.f rename to lib/linalg/fortran/zgemm.f diff --git a/lib/linalg/zgemv.f b/lib/linalg/fortran/zgemv.f similarity index 100% rename from lib/linalg/zgemv.f rename to lib/linalg/fortran/zgemv.f diff --git a/lib/linalg/zgerc.f b/lib/linalg/fortran/zgerc.f similarity index 100% rename from lib/linalg/zgerc.f rename to lib/linalg/fortran/zgerc.f diff --git a/lib/linalg/zheev.f b/lib/linalg/fortran/zheev.f similarity index 100% rename from lib/linalg/zheev.f rename to lib/linalg/fortran/zheev.f diff --git a/lib/linalg/zheevd.f b/lib/linalg/fortran/zheevd.f similarity index 100% rename from lib/linalg/zheevd.f rename to lib/linalg/fortran/zheevd.f diff --git a/lib/linalg/zhemv.f b/lib/linalg/fortran/zhemv.f similarity index 100% rename from lib/linalg/zhemv.f rename to lib/linalg/fortran/zhemv.f diff --git a/lib/linalg/zher2.f b/lib/linalg/fortran/zher2.f similarity index 100% rename from lib/linalg/zher2.f rename to lib/linalg/fortran/zher2.f diff --git a/lib/linalg/zher2k.f b/lib/linalg/fortran/zher2k.f similarity index 100% rename from lib/linalg/zher2k.f rename to lib/linalg/fortran/zher2k.f diff --git a/lib/linalg/zhetd2.f b/lib/linalg/fortran/zhetd2.f similarity index 100% rename from lib/linalg/zhetd2.f rename to lib/linalg/fortran/zhetd2.f diff --git a/lib/linalg/zhetrd.f b/lib/linalg/fortran/zhetrd.f similarity index 100% rename from lib/linalg/zhetrd.f rename to lib/linalg/fortran/zhetrd.f diff --git a/lib/linalg/zhpr.f b/lib/linalg/fortran/zhpr.f similarity index 100% rename from lib/linalg/zhpr.f rename to lib/linalg/fortran/zhpr.f diff --git a/lib/linalg/zlacgv.f b/lib/linalg/fortran/zlacgv.f similarity index 100% rename from lib/linalg/zlacgv.f rename to lib/linalg/fortran/zlacgv.f diff --git a/lib/linalg/zlacpy.f b/lib/linalg/fortran/zlacpy.f similarity index 100% rename from lib/linalg/zlacpy.f rename to lib/linalg/fortran/zlacpy.f diff --git a/lib/linalg/zlacrm.f b/lib/linalg/fortran/zlacrm.f similarity index 100% rename from lib/linalg/zlacrm.f rename to lib/linalg/fortran/zlacrm.f diff --git a/lib/linalg/zladiv.f b/lib/linalg/fortran/zladiv.f similarity index 100% rename from lib/linalg/zladiv.f rename to lib/linalg/fortran/zladiv.f diff --git a/lib/linalg/zlaed0.f b/lib/linalg/fortran/zlaed0.f similarity index 100% rename from lib/linalg/zlaed0.f rename to lib/linalg/fortran/zlaed0.f diff --git a/lib/linalg/zlaed7.f b/lib/linalg/fortran/zlaed7.f similarity index 100% rename from lib/linalg/zlaed7.f rename to lib/linalg/fortran/zlaed7.f diff --git a/lib/linalg/zlaed8.f b/lib/linalg/fortran/zlaed8.f similarity index 100% rename from lib/linalg/zlaed8.f rename to lib/linalg/fortran/zlaed8.f diff --git a/lib/linalg/zlanhe.f b/lib/linalg/fortran/zlanhe.f similarity index 100% rename from lib/linalg/zlanhe.f rename to lib/linalg/fortran/zlanhe.f diff --git a/lib/linalg/zlarf.f b/lib/linalg/fortran/zlarf.f similarity index 100% rename from lib/linalg/zlarf.f rename to lib/linalg/fortran/zlarf.f diff --git a/lib/linalg/zlarfb.f b/lib/linalg/fortran/zlarfb.f similarity index 100% rename from lib/linalg/zlarfb.f rename to lib/linalg/fortran/zlarfb.f diff --git a/lib/linalg/zlarfg.f b/lib/linalg/fortran/zlarfg.f similarity index 100% rename from lib/linalg/zlarfg.f rename to lib/linalg/fortran/zlarfg.f diff --git a/lib/linalg/zlarft.f b/lib/linalg/fortran/zlarft.f similarity index 100% rename from lib/linalg/zlarft.f rename to lib/linalg/fortran/zlarft.f diff --git a/lib/linalg/zlascl.f b/lib/linalg/fortran/zlascl.f similarity index 100% rename from lib/linalg/zlascl.f rename to lib/linalg/fortran/zlascl.f diff --git a/lib/linalg/zlaset.f b/lib/linalg/fortran/zlaset.f similarity index 100% rename from lib/linalg/zlaset.f rename to lib/linalg/fortran/zlaset.f diff --git a/lib/linalg/zlasr.f b/lib/linalg/fortran/zlasr.f similarity index 100% rename from lib/linalg/zlasr.f rename to lib/linalg/fortran/zlasr.f diff --git a/lib/linalg/zlassq.f b/lib/linalg/fortran/zlassq.f similarity index 100% rename from lib/linalg/zlassq.f rename to lib/linalg/fortran/zlassq.f diff --git a/lib/linalg/zlatrd.f b/lib/linalg/fortran/zlatrd.f similarity index 100% rename from lib/linalg/zlatrd.f rename to lib/linalg/fortran/zlatrd.f diff --git a/lib/linalg/zpptrf.f b/lib/linalg/fortran/zpptrf.f similarity index 100% rename from lib/linalg/zpptrf.f rename to lib/linalg/fortran/zpptrf.f diff --git a/lib/linalg/zpptri.f b/lib/linalg/fortran/zpptri.f similarity index 100% rename from lib/linalg/zpptri.f rename to lib/linalg/fortran/zpptri.f diff --git a/lib/linalg/zscal.f b/lib/linalg/fortran/zscal.f similarity index 100% rename from lib/linalg/zscal.f rename to lib/linalg/fortran/zscal.f diff --git a/lib/linalg/zstedc.f b/lib/linalg/fortran/zstedc.f similarity index 100% rename from lib/linalg/zstedc.f rename to lib/linalg/fortran/zstedc.f diff --git a/lib/linalg/zsteqr.f b/lib/linalg/fortran/zsteqr.f similarity index 100% rename from lib/linalg/zsteqr.f rename to lib/linalg/fortran/zsteqr.f diff --git a/lib/linalg/zswap.f b/lib/linalg/fortran/zswap.f similarity index 100% rename from lib/linalg/zswap.f rename to lib/linalg/fortran/zswap.f diff --git a/lib/linalg/ztpmv.f b/lib/linalg/fortran/ztpmv.f similarity index 100% rename from lib/linalg/ztpmv.f rename to lib/linalg/fortran/ztpmv.f diff --git a/lib/linalg/ztpsv.f b/lib/linalg/fortran/ztpsv.f similarity index 100% rename from lib/linalg/ztpsv.f rename to lib/linalg/fortran/ztpsv.f diff --git a/lib/linalg/ztptri.f b/lib/linalg/fortran/ztptri.f similarity index 100% rename from lib/linalg/ztptri.f rename to lib/linalg/fortran/ztptri.f diff --git a/lib/linalg/ztrmm.f b/lib/linalg/fortran/ztrmm.f similarity index 100% rename from lib/linalg/ztrmm.f rename to lib/linalg/fortran/ztrmm.f diff --git a/lib/linalg/ztrmv.f b/lib/linalg/fortran/ztrmv.f similarity index 100% rename from lib/linalg/ztrmv.f rename to lib/linalg/fortran/ztrmv.f diff --git a/lib/linalg/zung2l.f b/lib/linalg/fortran/zung2l.f similarity index 100% rename from lib/linalg/zung2l.f rename to lib/linalg/fortran/zung2l.f diff --git a/lib/linalg/zung2r.f b/lib/linalg/fortran/zung2r.f similarity index 100% rename from lib/linalg/zung2r.f rename to lib/linalg/fortran/zung2r.f diff --git a/lib/linalg/zungl2.f b/lib/linalg/fortran/zungl2.f similarity index 100% rename from lib/linalg/zungl2.f rename to lib/linalg/fortran/zungl2.f diff --git a/lib/linalg/zungql.f b/lib/linalg/fortran/zungql.f similarity index 100% rename from lib/linalg/zungql.f rename to lib/linalg/fortran/zungql.f diff --git a/lib/linalg/zungqr.f b/lib/linalg/fortran/zungqr.f similarity index 100% rename from lib/linalg/zungqr.f rename to lib/linalg/fortran/zungqr.f diff --git a/lib/linalg/zungtr.f b/lib/linalg/fortran/zungtr.f similarity index 100% rename from lib/linalg/zungtr.f rename to lib/linalg/fortran/zungtr.f diff --git a/lib/linalg/zunm2l.f b/lib/linalg/fortran/zunm2l.f similarity index 100% rename from lib/linalg/zunm2l.f rename to lib/linalg/fortran/zunm2l.f diff --git a/lib/linalg/zunm2r.f b/lib/linalg/fortran/zunm2r.f similarity index 100% rename from lib/linalg/zunm2r.f rename to lib/linalg/fortran/zunm2r.f diff --git a/lib/linalg/zunmql.f b/lib/linalg/fortran/zunmql.f similarity index 100% rename from lib/linalg/zunmql.f rename to lib/linalg/fortran/zunmql.f diff --git a/lib/linalg/zunmqr.f b/lib/linalg/fortran/zunmqr.f similarity index 100% rename from lib/linalg/zunmqr.f rename to lib/linalg/fortran/zunmqr.f diff --git a/lib/linalg/zunmtr.f b/lib/linalg/fortran/zunmtr.f similarity index 100% rename from lib/linalg/zunmtr.f rename to lib/linalg/fortran/zunmtr.f diff --git a/lib/linalg/idamax.cpp b/lib/linalg/idamax.cpp new file mode 100644 index 0000000000..edcf861435 --- /dev/null +++ b/lib/linalg/idamax.cpp @@ -0,0 +1,161 @@ +/* fortran/idamax.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b IDAMAX */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* INTEGER FUNCTION IDAMAX(N,DX,INCX) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INCX,N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION DX(*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > IDAMAX finds the index of the first element having maximum absolute value. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > number of elements in input vector(s) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DX */ +/* > \verbatim */ +/* > DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > storage spacing between elements of DX */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup aux_blas */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > jack dongarra, linpack, 3/11/78. */ +/* > modified 3/93 to return if incx .le. 0. */ +/* > modified 12/3/93, array(1) declarations changed to array(*) */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +integer idamax_(integer *n, doublereal *dx, integer *incx) +{ + /* System generated locals */ + integer ret_val, i__1; + doublereal d__1; + + /* Local variables */ + integer i__, ix; + doublereal dmax__; + + +/* -- Reference BLAS level1 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ + /* Parameter adjustments */ + --dx; + + /* Function Body */ + ret_val = 0; + if (*n < 1 || *incx <= 0) { + return ret_val; + } + ret_val = 1; + if (*n == 1) { + return ret_val; + } + if (*incx == 1) { + +/* code for increment equal to 1 */ + + dmax__ = abs(dx[1]); + i__1 = *n; + for (i__ = 2; i__ <= i__1; ++i__) { + if ((d__1 = dx[i__], abs(d__1)) > dmax__) { + ret_val = i__; + dmax__ = (d__1 = dx[i__], abs(d__1)); + } + } + } else { + +/* code for increment not equal to 1 */ + + ix = 1; + dmax__ = abs(dx[1]); + ix += *incx; + i__1 = *n; + for (i__ = 2; i__ <= i__1; ++i__) { + if ((d__1 = dx[ix], abs(d__1)) > dmax__) { + ret_val = i__; + dmax__ = (d__1 = dx[ix], abs(d__1)); + } + ix += *incx; + } + } + return ret_val; + +/* End of IDAMAX */ + +} /* idamax_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/ieeeck.cpp b/lib/linalg/ieeeck.cpp new file mode 100644 index 0000000000..16626acf9d --- /dev/null +++ b/lib/linalg/ieeeck.cpp @@ -0,0 +1,228 @@ +/* fortran/ieeeck.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b IEEECK */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download IEEECK + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* INTEGER FUNCTION IEEECK( ISPEC, ZERO, ONE ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER ISPEC */ +/* REAL ONE, ZERO */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > IEEECK is called from the ILAENV to verify that Infinity and */ +/* > possibly NaN arithmetic is safe (i.e. will not trap). */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] ISPEC */ +/* > \verbatim */ +/* > ISPEC is INTEGER */ +/* > Specifies whether to test just for infinity arithmetic */ +/* > or whether to test for infinity and NaN arithmetic. */ +/* > = 0: Verify infinity arithmetic only. */ +/* > = 1: Verify infinity and NaN arithmetic. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] ZERO */ +/* > \verbatim */ +/* > ZERO is REAL */ +/* > Must contain the value 0.0 */ +/* > This is passed to prevent the compiler from optimizing */ +/* > away this code. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] ONE */ +/* > \verbatim */ +/* > ONE is REAL */ +/* > Must contain the value 1.0 */ +/* > This is passed to prevent the compiler from optimizing */ +/* > away this code. */ +/* > */ +/* > RETURN VALUE: INTEGER */ +/* > = 0: Arithmetic failed to produce the correct answers */ +/* > = 1: Arithmetic produced the correct answers */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup OTHERauxiliary */ + +/* ===================================================================== */ +integer ieeeck_(integer *ispec, real *zero, real *one) +{ + /* System generated locals */ + integer ret_val; + + /* Local variables */ + real nan1, nan2, nan3, nan4, nan5, nan6, neginf, posinf, negzro, newzro; + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. Executable Statements .. */ + ret_val = 1; + + posinf = *one / *zero; + if (posinf <= *one) { + ret_val = 0; + return ret_val; + } + + neginf = -(*one) / *zero; + if (neginf >= *zero) { + ret_val = 0; + return ret_val; + } + + negzro = *one / (neginf + *one); + if (negzro != *zero) { + ret_val = 0; + return ret_val; + } + + neginf = *one / negzro; + if (neginf >= *zero) { + ret_val = 0; + return ret_val; + } + + newzro = negzro + *zero; + if (newzro != *zero) { + ret_val = 0; + return ret_val; + } + + posinf = *one / newzro; + if (posinf <= *one) { + ret_val = 0; + return ret_val; + } + + neginf *= posinf; + if (neginf >= *zero) { + ret_val = 0; + return ret_val; + } + + posinf *= posinf; + if (posinf <= *one) { + ret_val = 0; + return ret_val; + } + + + + +/* Return if we were only asked to check infinity arithmetic */ + + if (*ispec == 0) { + return ret_val; + } + + nan1 = posinf + neginf; + + nan2 = posinf / neginf; + + nan3 = posinf / posinf; + + nan4 = posinf * *zero; + + nan5 = neginf * negzro; + + nan6 = nan5 * *zero; + + if (nan1 == nan1) { + ret_val = 0; + return ret_val; + } + + if (nan2 == nan2) { + ret_val = 0; + return ret_val; + } + + if (nan3 == nan3) { + ret_val = 0; + return ret_val; + } + + if (nan4 == nan4) { + ret_val = 0; + return ret_val; + } + + if (nan5 == nan5) { + ret_val = 0; + return ret_val; + } + + if (nan6 == nan6) { + ret_val = 0; + return ret_val; + } + + return ret_val; +} /* ieeeck_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/iladlc.cpp b/lib/linalg/iladlc.cpp new file mode 100644 index 0000000000..21b05e970a --- /dev/null +++ b/lib/linalg/iladlc.cpp @@ -0,0 +1,150 @@ +/* fortran/iladlc.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b ILADLC scans a matrix for its last non-zero column. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ILADLC + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* INTEGER FUNCTION ILADLC( M, N, A, LDA ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER M, N, LDA */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ILADLC scans A for its last non-zero column. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > The m by n matrix A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,M). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup OTHERauxiliary */ + +/* ===================================================================== */ +integer iladlc_(integer *m, integer *n, doublereal *a, integer *lda) +{ + /* System generated locals */ + integer a_dim1, a_offset, ret_val, i__1; + + /* Local variables */ + integer i__; + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Quick test for the common case where one corner is non-zero. */ + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + + /* Function Body */ + if (*n == 0) { + ret_val = *n; + } else if (a[*n * a_dim1 + 1] != 0. || a[*m + *n * a_dim1] != 0.) { + ret_val = *n; + } else { +/* Now scan each column from the end, returning with the first non-zero. */ + for (ret_val = *n; ret_val >= 1; --ret_val) { + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + if (a[i__ + ret_val * a_dim1] != 0.) { + return ret_val; + } + } + } + } + return ret_val; +} /* iladlc_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/iladlr.cpp b/lib/linalg/iladlr.cpp new file mode 100644 index 0000000000..a301b66170 --- /dev/null +++ b/lib/linalg/iladlr.cpp @@ -0,0 +1,151 @@ +/* fortran/iladlr.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b ILADLR scans a matrix for its last non-zero row. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ILADLR + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* INTEGER FUNCTION ILADLR( M, N, A, LDA ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER M, N, LDA */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION A( LDA, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ILADLR scans A for its last non-zero row. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ +/* > The m by n matrix A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,M). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup OTHERauxiliary */ + +/* ===================================================================== */ +integer iladlr_(integer *m, integer *n, doublereal *a, integer *lda) +{ + /* System generated locals */ + integer a_dim1, a_offset, ret_val, i__1; + + /* Local variables */ + integer i__, j; + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Quick test for the common case where one corner is non-zero. */ + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + + /* Function Body */ + if (*m == 0) { + ret_val = *m; + } else if (a[*m + a_dim1] != 0. || a[*m + *n * a_dim1] != 0.) { + ret_val = *m; + } else { +/* Scan up each column tracking the last zero row seen. */ + ret_val = 0; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__ = *m; + while(a[max(i__,1) + j * a_dim1] == 0. && i__ >= 1) { + --i__; + } + ret_val = max(ret_val,i__); + } + } + return ret_val; +} /* iladlr_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/ilaenv.cpp b/lib/linalg/ilaenv.cpp new file mode 100644 index 0000000000..0e9a051222 --- /dev/null +++ b/lib/linalg/ilaenv.cpp @@ -0,0 +1,845 @@ +/* fortran/ilaenv.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static real c_b176 = (float)0.; +static real c_b177 = (float)1.; +static integer c__0 = 0; + +/* > \brief \b ILAENV */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ILAENV + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* INTEGER FUNCTION ILAENV( ISPEC, NAME, OPTS, N1, N2, N3, N4 ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER*( * ) NAME, OPTS */ +/* INTEGER ISPEC, N1, N2, N3, N4 */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ILAENV is called from the LAPACK routines to choose problem-dependent */ +/* > parameters for the local environment. See ISPEC for a description of */ +/* > the parameters. */ +/* > */ +/* > ILAENV returns an INTEGER */ +/* > if ILAENV >= 0: ILAENV returns the value of the parameter specified by ISPEC */ +/* > if ILAENV < 0: if ILAENV = -k, the k-th argument had an illegal value. */ +/* > */ +/* > This version provides a set of parameters which should give good, */ +/* > but not optimal, performance on many of the currently available */ +/* > computers. Users are encouraged to modify this subroutine to set */ +/* > the tuning parameters for their particular machine using the option */ +/* > and problem size information in the arguments. */ +/* > */ +/* > This routine will not function correctly if it is converted to all */ +/* > lower case. Converting it to all upper case is allowed. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] ISPEC */ +/* > \verbatim */ +/* > ISPEC is INTEGER */ +/* > Specifies the parameter to be returned as the value of */ +/* > ILAENV. */ +/* > = 1: the optimal blocksize; if this value is 1, an unblocked */ +/* > algorithm will give the best performance. */ +/* > = 2: the minimum block size for which the block routine */ +/* > should be used; if the usable block size is less than */ +/* > this value, an unblocked routine should be used. */ +/* > = 3: the crossover point (in a block routine, for N less */ +/* > than this value, an unblocked routine should be used) */ +/* > = 4: the number of shifts, used in the nonsymmetric */ +/* > eigenvalue routines (DEPRECATED) */ +/* > = 5: the minimum column dimension for blocking to be used; */ +/* > rectangular blocks must have dimension at least k by m, */ +/* > where k is given by ILAENV(2,...) and m by ILAENV(5,...) */ +/* > = 6: the crossover point for the SVD (when reducing an m by n */ +/* > matrix to bidiagonal form, if max(m,n)/min(m,n) exceeds */ +/* > this value, a QR factorization is used first to reduce */ +/* > the matrix to a triangular form.) */ +/* > = 7: the number of processors */ +/* > = 8: the crossover point for the multishift QR method */ +/* > for nonsymmetric eigenvalue problems (DEPRECATED) */ +/* > = 9: maximum size of the subproblems at the bottom of the */ +/* > computation tree in the divide-and-conquer algorithm */ +/* > (used by xGELSD and xGESDD) */ +/* > =10: ieee infinity and NaN arithmetic can be trusted not to trap */ +/* > =11: infinity arithmetic can be trusted not to trap */ +/* > 12 <= ISPEC <= 17: */ +/* > xHSEQR or related subroutines, */ +/* > see IPARMQ for detailed explanation */ +/* > \endverbatim */ +/* > */ +/* > \param[in] NAME */ +/* > \verbatim */ +/* > NAME is CHARACTER*(*) */ +/* > The name of the calling subroutine, in either upper case or */ +/* > lower case. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] OPTS */ +/* > \verbatim */ +/* > OPTS is CHARACTER*(*) */ +/* > The character options to the subroutine NAME, concatenated */ +/* > into a single character string. For example, UPLO = 'U', */ +/* > TRANS = 'T', and DIAG = 'N' for a triangular routine would */ +/* > be specified as OPTS = 'UTN'. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N1 */ +/* > \verbatim */ +/* > N1 is INTEGER */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N2 */ +/* > \verbatim */ +/* > N2 is INTEGER */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N3 */ +/* > \verbatim */ +/* > N3 is INTEGER */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N4 */ +/* > \verbatim */ +/* > N4 is INTEGER */ +/* > Problem dimensions for the subroutine NAME; these may not all */ +/* > be required. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup OTHERauxiliary */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > The following conventions have been used when calling ILAENV from the */ +/* > LAPACK routines: */ +/* > 1) OPTS is a concatenation of all of the character options to */ +/* > subroutine NAME, in the same order that they appear in the */ +/* > argument list for NAME, even if they are not used in determining */ +/* > the value of the parameter specified by ISPEC. */ +/* > 2) The problem dimensions N1, N2, N3, N4 are specified in the order */ +/* > that they appear in the argument list for NAME. N1 is used */ +/* > first, N2 second, and so on, and unused problem dimensions are */ +/* > passed a value of -1. */ +/* > 3) The parameter value returned by ILAENV is checked for validity in */ +/* > the calling subroutine. For example, ILAENV is used to retrieve */ +/* > the optimal blocksize for STRTRI as follows: */ +/* > */ +/* > NB = ILAENV( 1, 'STRTRI', UPLO // DIAG, N, -1, -1, -1 ) */ +/* > IF( NB.LE.1 ) NB = MAX( 1, N ) */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +integer ilaenv_(integer *ispec, char *name__, char *opts, integer *n1, + integer *n2, integer *n3, integer *n4, ftnlen name_len, ftnlen + opts_len) +{ + /* System generated locals */ + integer ret_val, i__1, i__2, i__3; + + /* Builtin functions */ + /* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen); + integer i_len(char *, ftnlen), s_cmp(char *, char *, ftnlen, ftnlen); + + /* Local variables */ + logical twostage; + integer i__; + char c1[1], c2[2], c3[3], c4[2]; + integer ic, nb, iz, nx; + logical cname; + integer nbmin; + logical sname; + extern integer ieeeck_(integer *, real *, real *); + char subnam[16]; + extern integer iparmq_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + + switch (*ispec) { + case 1: goto L10; + case 2: goto L10; + case 3: goto L10; + case 4: goto L80; + case 5: goto L90; + case 6: goto L100; + case 7: goto L110; + case 8: goto L120; + case 9: goto L130; + case 10: goto L140; + case 11: goto L150; + case 12: goto L160; + case 13: goto L160; + case 14: goto L160; + case 15: goto L160; + case 16: goto L160; + case 17: goto L160; + } + +/* Invalid value for ISPEC */ + + ret_val = -1; + return ret_val; + +L10: + +/* Convert NAME to upper case if the first character is lower case. */ + + ret_val = 1; + s_copy(subnam, name__, (ftnlen)16, name_len); + ic = *(unsigned char *)subnam; + iz = 'Z'; + if (iz == 90 || iz == 122) { + +/* ASCII character set */ + + if (ic >= 97 && ic <= 122) { + *(unsigned char *)subnam = (char) (ic - 32); + for (i__ = 2; i__ <= 6; ++i__) { + ic = *(unsigned char *)&subnam[i__ - 1]; + if (ic >= 97 && ic <= 122) { + *(unsigned char *)&subnam[i__ - 1] = (char) (ic - 32); + } +/* L20: */ + } + } + + } else if (iz == 233 || iz == 169) { + +/* EBCDIC character set */ + + if (ic >= 129 && ic <= 137 || ic >= 145 && ic <= 153 || ic >= 162 && + ic <= 169) { + *(unsigned char *)subnam = (char) (ic + 64); + for (i__ = 2; i__ <= 6; ++i__) { + ic = *(unsigned char *)&subnam[i__ - 1]; + if (ic >= 129 && ic <= 137 || ic >= 145 && ic <= 153 || ic >= + 162 && ic <= 169) { + *(unsigned char *)&subnam[i__ - 1] = (char) (ic + 64); + } +/* L30: */ + } + } + + } else if (iz == 218 || iz == 250) { + +/* Prime machines: ASCII+128 */ + + if (ic >= 225 && ic <= 250) { + *(unsigned char *)subnam = (char) (ic - 32); + for (i__ = 2; i__ <= 6; ++i__) { + ic = *(unsigned char *)&subnam[i__ - 1]; + if (ic >= 225 && ic <= 250) { + *(unsigned char *)&subnam[i__ - 1] = (char) (ic - 32); + } +/* L40: */ + } + } + } + + *(unsigned char *)c1 = *(unsigned char *)subnam; + sname = *(unsigned char *)c1 == 'S' || *(unsigned char *)c1 == 'D'; + cname = *(unsigned char *)c1 == 'C' || *(unsigned char *)c1 == 'Z'; + if (! (cname || sname)) { + return ret_val; + } + s_copy(c2, subnam + 1, (ftnlen)2, (ftnlen)2); + s_copy(c3, subnam + 3, (ftnlen)3, (ftnlen)3); + s_copy(c4, c3 + 1, (ftnlen)2, (ftnlen)2); + twostage = i_len(subnam, (ftnlen)16) >= 11 && *(unsigned char *)&subnam[ + 10] == '2'; + + switch (*ispec) { + case 1: goto L50; + case 2: goto L60; + case 3: goto L70; + } + +L50: + +/* ISPEC = 1: block size */ + +/* In these examples, separate code is provided for setting NB for */ +/* real and complex. We assume that NB will take the same value in */ +/* single or double precision. */ + + nb = 1; + + if (s_cmp(subnam + 1, (char *)"LAORH", (ftnlen)5, (ftnlen)5) == 0) { + +/* This is for *LAORHR_GETRFNP routine */ + + if (sname) { + nb = 32; + } else { + nb = 32; + } + } else if (s_cmp(c2, (char *)"GE", (ftnlen)2, (ftnlen)2) == 0) { + if (s_cmp(c3, (char *)"TRF", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nb = 64; + } else { + nb = 64; + } + } else if (s_cmp(c3, (char *)"QRF", (ftnlen)3, (ftnlen)3) == 0 || s_cmp(c3, + (char *)"RQF", (ftnlen)3, (ftnlen)3) == 0 || s_cmp(c3, (char *)"LQF", (ftnlen) + 3, (ftnlen)3) == 0 || s_cmp(c3, (char *)"QLF", (ftnlen)3, (ftnlen)3) + == 0) { + if (sname) { + nb = 32; + } else { + nb = 32; + } + } else if (s_cmp(c3, (char *)"QR ", (ftnlen)3, (ftnlen)3) == 0) { + if (*n3 == 1) { + if (sname) { +/* M*N */ + if (*n1 * *n2 <= 131072 || *n1 <= 8192) { + nb = *n1; + } else { + nb = 32768 / *n2; + } + } else { + if (*n1 * *n2 <= 131072 || *n1 <= 8192) { + nb = *n1; + } else { + nb = 32768 / *n2; + } + } + } else { + if (sname) { + nb = 1; + } else { + nb = 1; + } + } + } else if (s_cmp(c3, (char *)"LQ ", (ftnlen)3, (ftnlen)3) == 0) { + if (*n3 == 2) { + if (sname) { +/* M*N */ + if (*n1 * *n2 <= 131072 || *n1 <= 8192) { + nb = *n1; + } else { + nb = 32768 / *n2; + } + } else { + if (*n1 * *n2 <= 131072 || *n1 <= 8192) { + nb = *n1; + } else { + nb = 32768 / *n2; + } + } + } else { + if (sname) { + nb = 1; + } else { + nb = 1; + } + } + } else if (s_cmp(c3, (char *)"HRD", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nb = 32; + } else { + nb = 32; + } + } else if (s_cmp(c3, (char *)"BRD", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nb = 32; + } else { + nb = 32; + } + } else if (s_cmp(c3, (char *)"TRI", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nb = 64; + } else { + nb = 64; + } + } + } else if (s_cmp(c2, (char *)"PO", (ftnlen)2, (ftnlen)2) == 0) { + if (s_cmp(c3, (char *)"TRF", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nb = 64; + } else { + nb = 64; + } + } + } else if (s_cmp(c2, (char *)"SY", (ftnlen)2, (ftnlen)2) == 0) { + if (s_cmp(c3, (char *)"TRF", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + if (twostage) { + nb = 192; + } else { + nb = 64; + } + } else { + if (twostage) { + nb = 192; + } else { + nb = 64; + } + } + } else if (sname && s_cmp(c3, (char *)"TRD", (ftnlen)3, (ftnlen)3) == 0) { + nb = 32; + } else if (sname && s_cmp(c3, (char *)"GST", (ftnlen)3, (ftnlen)3) == 0) { + nb = 64; + } + } else if (cname && s_cmp(c2, (char *)"HE", (ftnlen)2, (ftnlen)2) == 0) { + if (s_cmp(c3, (char *)"TRF", (ftnlen)3, (ftnlen)3) == 0) { + if (twostage) { + nb = 192; + } else { + nb = 64; + } + } else if (s_cmp(c3, (char *)"TRD", (ftnlen)3, (ftnlen)3) == 0) { + nb = 32; + } else if (s_cmp(c3, (char *)"GST", (ftnlen)3, (ftnlen)3) == 0) { + nb = 64; + } + } else if (sname && s_cmp(c2, (char *)"OR", (ftnlen)2, (ftnlen)2) == 0) { + if (*(unsigned char *)c3 == 'G') { + if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == + 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( + c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( + ftnlen)2, (ftnlen)2) == 0) { + nb = 32; + } + } else if (*(unsigned char *)c3 == 'M') { + if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == + 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( + c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( + ftnlen)2, (ftnlen)2) == 0) { + nb = 32; + } + } + } else if (cname && s_cmp(c2, (char *)"UN", (ftnlen)2, (ftnlen)2) == 0) { + if (*(unsigned char *)c3 == 'G') { + if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == + 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( + c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( + ftnlen)2, (ftnlen)2) == 0) { + nb = 32; + } + } else if (*(unsigned char *)c3 == 'M') { + if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == + 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( + c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( + ftnlen)2, (ftnlen)2) == 0) { + nb = 32; + } + } + } else if (s_cmp(c2, (char *)"GB", (ftnlen)2, (ftnlen)2) == 0) { + if (s_cmp(c3, (char *)"TRF", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + if (*n4 <= 64) { + nb = 1; + } else { + nb = 32; + } + } else { + if (*n4 <= 64) { + nb = 1; + } else { + nb = 32; + } + } + } + } else if (s_cmp(c2, (char *)"PB", (ftnlen)2, (ftnlen)2) == 0) { + if (s_cmp(c3, (char *)"TRF", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + if (*n2 <= 64) { + nb = 1; + } else { + nb = 32; + } + } else { + if (*n2 <= 64) { + nb = 1; + } else { + nb = 32; + } + } + } + } else if (s_cmp(c2, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0) { + if (s_cmp(c3, (char *)"TRI", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nb = 64; + } else { + nb = 64; + } + } else if (s_cmp(c3, (char *)"EVC", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nb = 64; + } else { + nb = 64; + } + } else if (s_cmp(c3, (char *)"SYL", (ftnlen)3, (ftnlen)3) == 0) { +/* The upper bound is to prevent overly aggressive scaling. */ + if (sname) { +/* Computing MIN */ +/* Computing MAX */ + i__2 = 48, i__3 = (min(*n1,*n2) << 4) / 100; + i__1 = max(i__2,i__3); + nb = min(i__1,240); + } else { +/* Computing MIN */ +/* Computing MAX */ + i__2 = 24, i__3 = (min(*n1,*n2) << 3) / 100; + i__1 = max(i__2,i__3); + nb = min(i__1,80); + } + } + } else if (s_cmp(c2, (char *)"LA", (ftnlen)2, (ftnlen)2) == 0) { + if (s_cmp(c3, (char *)"UUM", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nb = 64; + } else { + nb = 64; + } + } else if (s_cmp(c3, (char *)"TRS", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nb = 32; + } else { + nb = 32; + } + } + } else if (sname && s_cmp(c2, (char *)"ST", (ftnlen)2, (ftnlen)2) == 0) { + if (s_cmp(c3, (char *)"EBZ", (ftnlen)3, (ftnlen)3) == 0) { + nb = 1; + } + } else if (s_cmp(c2, (char *)"GG", (ftnlen)2, (ftnlen)2) == 0) { + nb = 32; + if (s_cmp(c3, (char *)"HD3", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nb = 32; + } else { + nb = 32; + } + } + } + ret_val = nb; + return ret_val; + +L60: + +/* ISPEC = 2: minimum block size */ + + nbmin = 2; + if (s_cmp(c2, (char *)"GE", (ftnlen)2, (ftnlen)2) == 0) { + if (s_cmp(c3, (char *)"QRF", (ftnlen)3, (ftnlen)3) == 0 || s_cmp(c3, (char *)"RQF", ( + ftnlen)3, (ftnlen)3) == 0 || s_cmp(c3, (char *)"LQF", (ftnlen)3, ( + ftnlen)3) == 0 || s_cmp(c3, (char *)"QLF", (ftnlen)3, (ftnlen)3) == 0) + { + if (sname) { + nbmin = 2; + } else { + nbmin = 2; + } + } else if (s_cmp(c3, (char *)"HRD", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nbmin = 2; + } else { + nbmin = 2; + } + } else if (s_cmp(c3, (char *)"BRD", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nbmin = 2; + } else { + nbmin = 2; + } + } else if (s_cmp(c3, (char *)"TRI", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nbmin = 2; + } else { + nbmin = 2; + } + } + } else if (s_cmp(c2, (char *)"SY", (ftnlen)2, (ftnlen)2) == 0) { + if (s_cmp(c3, (char *)"TRF", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nbmin = 8; + } else { + nbmin = 8; + } + } else if (sname && s_cmp(c3, (char *)"TRD", (ftnlen)3, (ftnlen)3) == 0) { + nbmin = 2; + } + } else if (cname && s_cmp(c2, (char *)"HE", (ftnlen)2, (ftnlen)2) == 0) { + if (s_cmp(c3, (char *)"TRD", (ftnlen)3, (ftnlen)3) == 0) { + nbmin = 2; + } + } else if (sname && s_cmp(c2, (char *)"OR", (ftnlen)2, (ftnlen)2) == 0) { + if (*(unsigned char *)c3 == 'G') { + if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == + 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( + c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( + ftnlen)2, (ftnlen)2) == 0) { + nbmin = 2; + } + } else if (*(unsigned char *)c3 == 'M') { + if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == + 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( + c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( + ftnlen)2, (ftnlen)2) == 0) { + nbmin = 2; + } + } + } else if (cname && s_cmp(c2, (char *)"UN", (ftnlen)2, (ftnlen)2) == 0) { + if (*(unsigned char *)c3 == 'G') { + if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == + 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( + c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( + ftnlen)2, (ftnlen)2) == 0) { + nbmin = 2; + } + } else if (*(unsigned char *)c3 == 'M') { + if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == + 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( + c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( + ftnlen)2, (ftnlen)2) == 0) { + nbmin = 2; + } + } + } else if (s_cmp(c2, (char *)"GG", (ftnlen)2, (ftnlen)2) == 0) { + nbmin = 2; + if (s_cmp(c3, (char *)"HD3", (ftnlen)3, (ftnlen)3) == 0) { + nbmin = 2; + } + } + ret_val = nbmin; + return ret_val; + +L70: + +/* ISPEC = 3: crossover point */ + + nx = 0; + if (s_cmp(c2, (char *)"GE", (ftnlen)2, (ftnlen)2) == 0) { + if (s_cmp(c3, (char *)"QRF", (ftnlen)3, (ftnlen)3) == 0 || s_cmp(c3, (char *)"RQF", ( + ftnlen)3, (ftnlen)3) == 0 || s_cmp(c3, (char *)"LQF", (ftnlen)3, ( + ftnlen)3) == 0 || s_cmp(c3, (char *)"QLF", (ftnlen)3, (ftnlen)3) == 0) + { + if (sname) { + nx = 128; + } else { + nx = 128; + } + } else if (s_cmp(c3, (char *)"HRD", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nx = 128; + } else { + nx = 128; + } + } else if (s_cmp(c3, (char *)"BRD", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nx = 128; + } else { + nx = 128; + } + } + } else if (s_cmp(c2, (char *)"SY", (ftnlen)2, (ftnlen)2) == 0) { + if (sname && s_cmp(c3, (char *)"TRD", (ftnlen)3, (ftnlen)3) == 0) { + nx = 32; + } + } else if (cname && s_cmp(c2, (char *)"HE", (ftnlen)2, (ftnlen)2) == 0) { + if (s_cmp(c3, (char *)"TRD", (ftnlen)3, (ftnlen)3) == 0) { + nx = 32; + } + } else if (sname && s_cmp(c2, (char *)"OR", (ftnlen)2, (ftnlen)2) == 0) { + if (*(unsigned char *)c3 == 'G') { + if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == + 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( + c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( + ftnlen)2, (ftnlen)2) == 0) { + nx = 128; + } + } + } else if (cname && s_cmp(c2, (char *)"UN", (ftnlen)2, (ftnlen)2) == 0) { + if (*(unsigned char *)c3 == 'G') { + if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == + 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( + c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( + ftnlen)2, (ftnlen)2) == 0) { + nx = 128; + } + } + } else if (s_cmp(c2, (char *)"GG", (ftnlen)2, (ftnlen)2) == 0) { + nx = 128; + if (s_cmp(c3, (char *)"HD3", (ftnlen)3, (ftnlen)3) == 0) { + nx = 128; + } + } + ret_val = nx; + return ret_val; + +L80: + +/* ISPEC = 4: number of shifts (used by xHSEQR) */ + + ret_val = 6; + return ret_val; + +L90: + +/* ISPEC = 5: minimum column dimension (not used) */ + + ret_val = 2; + return ret_val; + +L100: + +/* ISPEC = 6: crossover point for SVD (used by xGELSS and xGESVD) */ + + ret_val = (integer) ((real) min(*n1,*n2) * (float)1.6); + return ret_val; + +L110: + +/* ISPEC = 7: number of processors (not used) */ + + ret_val = 1; + return ret_val; + +L120: + +/* ISPEC = 8: crossover point for multishift (used by xHSEQR) */ + + ret_val = 50; + return ret_val; + +L130: + +/* ISPEC = 9: maximum size of the subproblems at the bottom of the */ +/* computation tree in the divide-and-conquer algorithm */ +/* (used by xGELSD and xGESDD) */ + + ret_val = 25; + return ret_val; + +L140: + +/* ISPEC = 10: ieee and infinity NaN arithmetic can be trusted not to trap */ + +/* ILAENV = 0 */ + ret_val = 1; + if (ret_val == 1) { + ret_val = ieeeck_(&c__1, &c_b176, &c_b177); + } + return ret_val; + +L150: + +/* ISPEC = 11: ieee infinity arithmetic can be trusted not to trap */ + +/* ILAENV = 0 */ + ret_val = 1; + if (ret_val == 1) { + ret_val = ieeeck_(&c__0, &c_b176, &c_b177); + } + return ret_val; + +L160: + +/* 12 <= ISPEC <= 17: xHSEQR or related subroutines. */ + + ret_val = iparmq_(ispec, name__, opts, n1, n2, n3, n4, name_len, opts_len) + ; + return ret_val; + +/* End of ILAENV */ + +} /* ilaenv_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/ilazlc.cpp b/lib/linalg/ilazlc.cpp new file mode 100644 index 0000000000..309c9e5edb --- /dev/null +++ b/lib/linalg/ilazlc.cpp @@ -0,0 +1,156 @@ +/* fortran/ilazlc.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b ILAZLC scans a matrix for its last non-zero column. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ILAZLC + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* INTEGER FUNCTION ILAZLC( M, N, A, LDA ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER M, N, LDA */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 A( LDA, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ILAZLC scans A for its last non-zero column. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is COMPLEX*16 array, dimension (LDA,N) */ +/* > The m by n matrix A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,M). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16OTHERauxiliary */ + +/* ===================================================================== */ +integer ilazlc_(integer *m, integer *n, doublecomplex *a, integer *lda) +{ + /* System generated locals */ + integer a_dim1, a_offset, ret_val, i__1, i__2; + + /* Local variables */ + integer i__; + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Quick test for the common case where one corner is non-zero. */ + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + + /* Function Body */ + if (*n == 0) { + ret_val = *n; + } else /* if(complicated condition) */ { + i__1 = *n * a_dim1 + 1; + i__2 = *m + *n * a_dim1; + if (a[i__1].r != 0. || a[i__1].i != 0. || (a[i__2].r != 0. || a[i__2] + .i != 0.)) { + ret_val = *n; + } else { +/* Now scan each column from the end, returning with the first non-zero. */ + for (ret_val = *n; ret_val >= 1; --ret_val) { + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__ + ret_val * a_dim1; + if (a[i__2].r != 0. || a[i__2].i != 0.) { + return ret_val; + } + } + } + } + } + return ret_val; +} /* ilazlc_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/ilazlr.cpp b/lib/linalg/ilazlr.cpp new file mode 100644 index 0000000000..8ca4fd8029 --- /dev/null +++ b/lib/linalg/ilazlr.cpp @@ -0,0 +1,159 @@ +/* fortran/ilazlr.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b ILAZLR scans a matrix for its last non-zero row. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ILAZLR + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* INTEGER FUNCTION ILAZLR( M, N, A, LDA ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER M, N, LDA */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 A( LDA, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ILAZLR scans A for its last non-zero row. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is COMPLEX*16 array, dimension (LDA,N) */ +/* > The m by n matrix A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,M). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16OTHERauxiliary */ + +/* ===================================================================== */ +integer ilazlr_(integer *m, integer *n, doublecomplex *a, integer *lda) +{ + /* System generated locals */ + integer a_dim1, a_offset, ret_val, i__1, i__2; + + /* Local variables */ + integer i__, j; + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Quick test for the common case where one corner is non-zero. */ + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + + /* Function Body */ + if (*m == 0) { + ret_val = *m; + } else /* if(complicated condition) */ { + i__1 = *m + a_dim1; + i__2 = *m + *n * a_dim1; + if (a[i__1].r != 0. || a[i__1].i != 0. || (a[i__2].r != 0. || a[i__2] + .i != 0.)) { + ret_val = *m; + } else { +/* Scan up each column tracking the last zero row seen. */ + ret_val = 0; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__ = *m; + for(;;) { /* while(complicated condition) */ + i__2 = max(i__,1) + j * a_dim1; + if (!(a[i__2].r == 0. && a[i__2].i == 0. && i__ >= 1)) + break; + --i__; + } + ret_val = max(ret_val,i__); + } + } + } + return ret_val; +} /* ilazlr_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/iparmq.cpp b/lib/linalg/iparmq.cpp new file mode 100644 index 0000000000..12f3b7f7f6 --- /dev/null +++ b/lib/linalg/iparmq.cpp @@ -0,0 +1,449 @@ +/* fortran/iparmq.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b IPARMQ */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download IPARMQ + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* INTEGER FUNCTION IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER IHI, ILO, ISPEC, LWORK, N */ +/* CHARACTER NAME*( * ), OPTS*( * ) */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > This program sets problem and machine dependent parameters */ +/* > useful for xHSEQR and related subroutines for eigenvalue */ +/* > problems. It is called whenever */ +/* > IPARMQ is called with 12 <= ISPEC <= 16 */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] ISPEC */ +/* > \verbatim */ +/* > ISPEC is INTEGER */ +/* > ISPEC specifies which tunable parameter IPARMQ should */ +/* > return. */ +/* > */ +/* > ISPEC=12: (INMIN) Matrices of order nmin or less */ +/* > are sent directly to xLAHQR, the implicit */ +/* > double shift QR algorithm. NMIN must be */ +/* > at least 11. */ +/* > */ +/* > ISPEC=13: (INWIN) Size of the deflation window. */ +/* > This is best set greater than or equal to */ +/* > the number of simultaneous shifts NS. */ +/* > Larger matrices benefit from larger deflation */ +/* > windows. */ +/* > */ +/* > ISPEC=14: (INIBL) Determines when to stop nibbling and */ +/* > invest in an (expensive) multi-shift QR sweep. */ +/* > If the aggressive early deflation subroutine */ +/* > finds LD converged eigenvalues from an order */ +/* > NW deflation window and LD > (NW*NIBBLE)/100, */ +/* > then the next QR sweep is skipped and early */ +/* > deflation is applied immediately to the */ +/* > remaining active diagonal block. Setting */ +/* > IPARMQ(ISPEC=14) = 0 causes TTQRE to skip a */ +/* > multi-shift QR sweep whenever early deflation */ +/* > finds a converged eigenvalue. Setting */ +/* > IPARMQ(ISPEC=14) greater than or equal to 100 */ +/* > prevents TTQRE from skipping a multi-shift */ +/* > QR sweep. */ +/* > */ +/* > ISPEC=15: (NSHFTS) The number of simultaneous shifts in */ +/* > a multi-shift QR iteration. */ +/* > */ +/* > ISPEC=16: (IACC22) IPARMQ is set to 0, 1 or 2 with the */ +/* > following meanings. */ +/* > 0: During the multi-shift QR/QZ sweep, */ +/* > blocked eigenvalue reordering, blocked */ +/* > Hessenberg-triangular reduction, */ +/* > reflections and/or rotations are not */ +/* > accumulated when updating the */ +/* > far-from-diagonal matrix entries. */ +/* > 1: During the multi-shift QR/QZ sweep, */ +/* > blocked eigenvalue reordering, blocked */ +/* > Hessenberg-triangular reduction, */ +/* > reflections and/or rotations are */ +/* > accumulated, and matrix-matrix */ +/* > multiplication is used to update the */ +/* > far-from-diagonal matrix entries. */ +/* > 2: During the multi-shift QR/QZ sweep, */ +/* > blocked eigenvalue reordering, blocked */ +/* > Hessenberg-triangular reduction, */ +/* > reflections and/or rotations are */ +/* > accumulated, and 2-by-2 block structure */ +/* > is exploited during matrix-matrix */ +/* > multiplies. */ +/* > (If xTRMM is slower than xGEMM, then */ +/* > IPARMQ(ISPEC=16)=1 may be more efficient than */ +/* > IPARMQ(ISPEC=16)=2 despite the greater level of */ +/* > arithmetic work implied by the latter choice.) */ +/* > */ +/* > ISPEC=17: (ICOST) An estimate of the relative cost of flops */ +/* > within the near-the-diagonal shift chase compared */ +/* > to flops within the BLAS calls of a QZ sweep. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] NAME */ +/* > \verbatim */ +/* > NAME is CHARACTER string */ +/* > Name of the calling subroutine */ +/* > \endverbatim */ +/* > */ +/* > \param[in] OPTS */ +/* > \verbatim */ +/* > OPTS is CHARACTER string */ +/* > This is a concatenation of the string arguments to */ +/* > TTQRE. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > N is the order of the Hessenberg matrix H. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] ILO */ +/* > \verbatim */ +/* > ILO is INTEGER */ +/* > \endverbatim */ +/* > */ +/* > \param[in] IHI */ +/* > \verbatim */ +/* > IHI is INTEGER */ +/* > It is assumed that H is already upper triangular */ +/* > in rows and columns 1:ILO-1 and IHI+1:N. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LWORK */ +/* > \verbatim */ +/* > LWORK is INTEGER */ +/* > The amount of workspace available. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup OTHERauxiliary */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > Little is known about how best to choose these parameters. */ +/* > It is possible to use different values of the parameters */ +/* > for each of CHSEQR, DHSEQR, SHSEQR and ZHSEQR. */ +/* > */ +/* > It is probably best to choose different parameters for */ +/* > different matrices and different parameters at different */ +/* > times during the iteration, but this has not been */ +/* > implemented --- yet. */ +/* > */ +/* > */ +/* > The best choices of most of the parameters depend */ +/* > in an ill-understood way on the relative execution */ +/* > rate of xLAQR3 and xLAQR5 and on the nature of each */ +/* > particular eigenvalue problem. Experiment may be the */ +/* > only practical way to determine which choices are most */ +/* > effective. */ +/* > */ +/* > Following is a list of default values supplied by IPARMQ. */ +/* > These defaults may be adjusted in order to attain better */ +/* > performance in any particular computational environment. */ +/* > */ +/* > IPARMQ(ISPEC=12) The xLAHQR vs xLAQR0 crossover point. */ +/* > Default: 75. (Must be at least 11.) */ +/* > */ +/* > IPARMQ(ISPEC=13) Recommended deflation window size. */ +/* > This depends on ILO, IHI and NS, the */ +/* > number of simultaneous shifts returned */ +/* > by IPARMQ(ISPEC=15). The default for */ +/* > (IHI-ILO+1) <= 500 is NS. The default */ +/* > for (IHI-ILO+1) > 500 is 3*NS/2. */ +/* > */ +/* > IPARMQ(ISPEC=14) Nibble crossover point. Default: 14. */ +/* > */ +/* > IPARMQ(ISPEC=15) Number of simultaneous shifts, NS. */ +/* > a multi-shift QR iteration. */ +/* > */ +/* > If IHI-ILO+1 is ... */ +/* > */ +/* > greater than ...but less ... the */ +/* > or equal to ... than default is */ +/* > */ +/* > 0 30 NS = 2+ */ +/* > 30 60 NS = 4+ */ +/* > 60 150 NS = 10 */ +/* > 150 590 NS = ** */ +/* > 590 3000 NS = 64 */ +/* > 3000 6000 NS = 128 */ +/* > 6000 infinity NS = 256 */ +/* > */ +/* > (+) By default matrices of this order are */ +/* > passed to the implicit double shift routine */ +/* > xLAHQR. See IPARMQ(ISPEC=12) above. These */ +/* > values of NS are used only in case of a rare */ +/* > xLAHQR failure. */ +/* > */ +/* > (**) The asterisks (**) indicate an ad-hoc */ +/* > function increasing from 10 to 64. */ +/* > */ +/* > IPARMQ(ISPEC=16) Select structured matrix multiply. */ +/* > (See ISPEC=16 above for details.) */ +/* > Default: 3. */ +/* > */ +/* > IPARMQ(ISPEC=17) Relative cost heuristic for blocksize selection. */ +/* > Expressed as a percentage. */ +/* > Default: 10. */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +integer iparmq_(integer *ispec, char *name__, char *opts, integer *n, integer + *ilo, integer *ihi, integer *lwork, ftnlen name_len, ftnlen opts_len) +{ + /* System generated locals */ + integer ret_val, i__1, i__2; + real r__1; + + /* Builtin functions */ + double log(doublereal); + integer i_nint(real *); + /* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen); + integer s_cmp(char *, char *, ftnlen, ftnlen); + + /* Local variables */ + integer i__, ic, nh, ns, iz; + char subnam[6]; + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ + +/* ================================================================ */ +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + if (*ispec == 15 || *ispec == 13 || *ispec == 16) { + +/* ==== Set the number simultaneous shifts ==== */ + + nh = *ihi - *ilo + 1; + ns = 2; + if (nh >= 30) { + ns = 4; + } + if (nh >= 60) { + ns = 10; + } + if (nh >= 150) { +/* Computing MAX */ + r__1 = log((real) nh) / log((float)2.); + i__1 = 10, i__2 = nh / i_nint(&r__1); + ns = max(i__1,i__2); + } + if (nh >= 590) { + ns = 64; + } + if (nh >= 3000) { + ns = 128; + } + if (nh >= 6000) { + ns = 256; + } +/* Computing MAX */ + i__1 = 2, i__2 = ns - ns % 2; + ns = max(i__1,i__2); + } + + if (*ispec == 12) { + + +/* ===== Matrices of order smaller than NMIN get sent */ +/* . to xLAHQR, the classic double shift algorithm. */ +/* . This must be at least 11. ==== */ + + ret_val = 75; + + } else if (*ispec == 14) { + +/* ==== INIBL: skip a multi-shift qr iteration and */ +/* . whenever aggressive early deflation finds */ +/* . at least (NIBBLE*(window size)/100) deflations. ==== */ + + ret_val = 14; + + } else if (*ispec == 15) { + +/* ==== NSHFTS: The number of simultaneous shifts ===== */ + + ret_val = ns; + + } else if (*ispec == 13) { + +/* ==== NW: deflation window size. ==== */ + + if (nh <= 500) { + ret_val = ns; + } else { + ret_val = ns * 3 / 2; + } + + } else if (*ispec == 16) { + +/* ==== IACC22: Whether to accumulate reflections */ +/* . before updating the far-from-diagonal elements */ +/* . and whether to use 2-by-2 block structure while */ +/* . doing it. A small amount of work could be saved */ +/* . by making this choice dependent also upon the */ +/* . NH=IHI-ILO+1. */ + + +/* Convert NAME to upper case if the first character is lower case. */ + + ret_val = 0; + s_copy(subnam, name__, (ftnlen)6, name_len); + ic = *(unsigned char *)subnam; + iz = 'Z'; + if (iz == 90 || iz == 122) { + +/* ASCII character set */ + + if (ic >= 97 && ic <= 122) { + *(unsigned char *)subnam = (char) (ic - 32); + for (i__ = 2; i__ <= 6; ++i__) { + ic = *(unsigned char *)&subnam[i__ - 1]; + if (ic >= 97 && ic <= 122) { + *(unsigned char *)&subnam[i__ - 1] = (char) (ic - 32); + } + } + } + + } else if (iz == 233 || iz == 169) { + +/* EBCDIC character set */ + + if (ic >= 129 && ic <= 137 || ic >= 145 && ic <= 153 || ic >= 162 + && ic <= 169) { + *(unsigned char *)subnam = (char) (ic + 64); + for (i__ = 2; i__ <= 6; ++i__) { + ic = *(unsigned char *)&subnam[i__ - 1]; + if (ic >= 129 && ic <= 137 || ic >= 145 && ic <= 153 || + ic >= 162 && ic <= 169) { + *(unsigned char *)&subnam[i__ - 1] = (char) (ic + 64); + } + } + } + + } else if (iz == 218 || iz == 250) { + +/* Prime machines: ASCII+128 */ + + if (ic >= 225 && ic <= 250) { + *(unsigned char *)subnam = (char) (ic - 32); + for (i__ = 2; i__ <= 6; ++i__) { + ic = *(unsigned char *)&subnam[i__ - 1]; + if (ic >= 225 && ic <= 250) { + *(unsigned char *)&subnam[i__ - 1] = (char) (ic - 32); + } + } + } + } + + if (s_cmp(subnam + 1, (char *)"GGHRD", (ftnlen)5, (ftnlen)5) == 0 || s_cmp( + subnam + 1, (char *)"GGHD3", (ftnlen)5, (ftnlen)5) == 0) { + ret_val = 1; + if (nh >= 14) { + ret_val = 2; + } + } else if (s_cmp(subnam + 3, (char *)"EXC", (ftnlen)3, (ftnlen)3) == 0) { + if (nh >= 14) { + ret_val = 1; + } + if (nh >= 14) { + ret_val = 2; + } + } else if (s_cmp(subnam + 1, (char *)"HSEQR", (ftnlen)5, (ftnlen)5) == 0 || + s_cmp(subnam + 1, (char *)"LAQR", (ftnlen)4, (ftnlen)4) == 0) { + if (ns >= 14) { + ret_val = 1; + } + if (ns >= 14) { + ret_val = 2; + } + } + + } else if (*ispec == 17) { + +/* === Relative cost of near-the-diagonal chase vs */ +/* BLAS updates === */ + + ret_val = 10; + } else { +/* ===== invalid value of ispec ===== */ + ret_val = -1; + + } + +/* ==== End of IPARMQ ==== */ + + return ret_val; +} /* iparmq_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/lmp_f2c.h b/lib/linalg/lmp_f2c.h new file mode 100644 index 0000000000..0b1ebac99c --- /dev/null +++ b/lib/linalg/lmp_f2c.h @@ -0,0 +1,223 @@ +/* f2c.h -- Standard Fortran to C header file */ + +/** barf [ba:rf] 2. "He suggested using FORTRAN, and everybody barfed." + + - From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */ + +#ifndef F2C_INCLUDE +#define F2C_INCLUDE + +typedef int integer; +typedef unsigned int uinteger; +typedef char *address; +typedef short int shortint; +typedef float real; +typedef double doublereal; +typedef struct { real r, i; } complex; +typedef struct { doublereal r, i; } doublecomplex; +typedef long int logical; +typedef short int shortlogical; +typedef char logical1; +typedef char integer1; +#ifdef INTEGER_STAR_8 /* Adjust for integer*8. */ +typedef long long longint; /* system-dependent */ +typedef unsigned long long ulongint; /* system-dependent */ +#define qbit_clear(a,b) ((a) & ~((ulongint)1 << (b))) +#define qbit_set(a,b) ((a) | ((ulongint)1 << (b))) +#endif + +#define TRUE_ (1) +#define FALSE_ (0) + +/* Extern is for use with -E */ +#ifndef Extern +#define Extern extern +#endif + +/* I/O stuff */ + +#ifdef f2c_i2 +/* for -i2 */ +typedef short flag; +typedef short ftnlen; +typedef short ftnint; +#else +typedef long int flag; +typedef long int ftnlen; +typedef long int ftnint; +#endif + +/*external read, write*/ +typedef struct +{ flag cierr; + ftnint ciunit; + flag ciend; + char *cifmt; + ftnint cirec; +} cilist; + +/*internal read, write*/ +typedef struct +{ flag icierr; + char *iciunit; + flag iciend; + char *icifmt; + ftnint icirlen; + ftnint icirnum; +} icilist; + +/*open*/ +typedef struct +{ flag oerr; + ftnint ounit; + char *ofnm; + ftnlen ofnmlen; + char *osta; + char *oacc; + char *ofm; + ftnint orl; + char *oblnk; +} olist; + +/*close*/ +typedef struct +{ flag cerr; + ftnint cunit; + char *csta; +} cllist; + +/*rewind, backspace, endfile*/ +typedef struct +{ flag aerr; + ftnint aunit; +} alist; + +/* inquire */ +typedef struct +{ flag inerr; + ftnint inunit; + char *infile; + ftnlen infilen; + ftnint *inex; /*parameters in standard's order*/ + ftnint *inopen; + ftnint *innum; + ftnint *innamed; + char *inname; + ftnlen innamlen; + char *inacc; + ftnlen inacclen; + char *inseq; + ftnlen inseqlen; + char *indir; + ftnlen indirlen; + char *infmt; + ftnlen infmtlen; + char *inform; + ftnint informlen; + char *inunf; + ftnlen inunflen; + ftnint *inrecl; + ftnint *innrec; + char *inblank; + ftnlen inblanklen; +} inlist; + +#define VOID void + +union Multitype { /* for multiple entry points */ + integer1 g; + shortint h; + integer i; + /* longint j; */ + real r; + doublereal d; + complex c; + doublecomplex z; + }; + +typedef union Multitype Multitype; + +/*typedef long int Long;*/ /* No longer used; formerly in Namelist */ + +struct Vardesc { /* for Namelist */ + char *name; + char *addr; + ftnlen *dims; + int type; + }; +typedef struct Vardesc Vardesc; + +struct Namelist { + char *name; + Vardesc **vars; + int nvars; + }; +typedef struct Namelist Namelist; + +#define abs(x) ((x) >= 0 ? (x) : -(x)) +#define dabs(x) (doublereal)abs(x) +#define min(a,b) ((a) <= (b) ? (a) : (b)) +#define max(a,b) ((a) >= (b) ? (a) : (b)) +#define dmin(a,b) (doublereal)min(a,b) +#define dmax(a,b) (doublereal)max(a,b) +#define bit_test(a,b) ((a) >> (b) & 1) +#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b))) +#define bit_set(a,b) ((a) | ((uinteger)1 << (b))) + +/* procedure parameter types for -A and -C++ */ + +#define F2C_proc_par_types 1 +#ifdef __cplusplus +typedef int /* Unknown procedure type */ (*U_fp)(...); +typedef shortint (*J_fp)(...); +typedef integer (*I_fp)(...); +typedef real (*R_fp)(...); +typedef doublereal (*D_fp)(...), (*E_fp)(...); +typedef /* Complex */ VOID (*C_fp)(...); +typedef /* Double Complex */ VOID (*Z_fp)(...); +typedef logical (*L_fp)(...); +typedef shortlogical (*K_fp)(...); +typedef /* Character */ VOID (*H_fp)(...); +typedef /* Subroutine */ int (*S_fp)(...); +#else +typedef int /* Unknown procedure type */ (*U_fp)(); +typedef shortint (*J_fp)(); +typedef integer (*I_fp)(); +typedef real (*R_fp)(); +typedef doublereal (*D_fp)(), (*E_fp)(); +typedef /* Complex */ VOID (*C_fp)(); +typedef /* Double Complex */ VOID (*Z_fp)(); +typedef logical (*L_fp)(); +typedef shortlogical (*K_fp)(); +typedef /* Character */ VOID (*H_fp)(); +typedef /* Subroutine */ int (*S_fp)(); +#endif +/* E_fp is for real functions when -R is not specified */ +typedef VOID C_f; /* complex function */ +typedef VOID H_f; /* character function */ +typedef VOID Z_f; /* double complex function */ +typedef doublereal E_f; /* real function with -R not specified */ + +/* undef any lower-case symbols that your C compiler predefines, e.g.: */ + +#ifndef Skip_f2c_Undefs +#undef cray +#undef gcos +#undef mc68010 +#undef mc68020 +#undef mips +#undef pdp11 +#undef sgi +#undef sparc +#undef sun +#undef sun2 +#undef sun3 +#undef sun4 +#undef u370 +#undef u3b +#undef u3b2 +#undef u3b5 +#undef unix +#undef vax +#endif +#endif diff --git a/lib/linalg/lsame.cpp b/lib/linalg/lsame.cpp new file mode 100644 index 0000000000..dcb89e3d00 --- /dev/null +++ b/lib/linalg/lsame.cpp @@ -0,0 +1,17 @@ + +#include + +extern "C" { + +#include "lmp_f2c.h" + +logical lsame_(const char *a, const char *b) +{ + char ua, ub; + if (!a || !b) return FALSE_; + + ua = toupper(*a); + ub = toupper(*b); + return (ua == ub) ? TRUE_ : FALSE_; +} +} diff --git a/lib/linalg/static/README b/lib/linalg/static/README new file mode 100644 index 0000000000..c06337c2dd --- /dev/null +++ b/lib/linalg/static/README @@ -0,0 +1,5 @@ +The C++ files in this folder are direct C++ implementations of their +Fortran equivalents using the C++ runtime. +. +The Fortran files in this folder are modified from their +original versions, so that f2c can correctly translate them. diff --git a/lib/linalg/static/dgetrf2.f b/lib/linalg/static/dgetrf2.f new file mode 100644 index 0000000000..e3d2aac299 --- /dev/null +++ b/lib/linalg/static/dgetrf2.f @@ -0,0 +1,269 @@ +*> \brief \b DGETRF2 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition: +* =========== +* +* RECURSIVE SUBROUTINE DGETRF2( M, N, A, LDA, IPIV, INFO ) +* +* .. Scalar Arguments .. +* INTEGER INFO, LDA, M, N +* .. +* .. Array Arguments .. +* INTEGER IPIV( * ) +* DOUBLE PRECISION A( LDA, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DGETRF2 computes an LU factorization of a general M-by-N matrix A +*> using partial pivoting with row interchanges. +*> +*> The factorization has the form +*> A = P * L * U +*> where P is a permutation matrix, L is lower triangular with unit +*> diagonal elements (lower trapezoidal if m > n), and U is upper +*> triangular (upper trapezoidal if m < n). +*> +*> This is the recursive version of the algorithm. It divides +*> the matrix into four submatrices: +*> +*> [ A11 | A12 ] where A11 is n1 by n1 and A22 is n2 by n2 +*> A = [ -----|----- ] with n1 = min(m,n)/2 +*> [ A21 | A22 ] n2 = n-n1 +*> +*> [ A11 ] +*> The subroutine calls itself to factor [ --- ], +*> [ A12 ] +*> [ A12 ] +*> do the swaps on [ --- ], solve A12, update A22, +*> [ A22 ] +*> +*> then calls itself to factor A22 and do the swaps on A21. +*> +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix A. M >= 0. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is DOUBLE PRECISION array, dimension (LDA,N) +*> On entry, the M-by-N matrix to be factored. +*> On exit, the factors L and U from the factorization +*> A = P*L*U; the unit diagonal elements of L are not stored. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,M). +*> \endverbatim +*> +*> \param[out] IPIV +*> \verbatim +*> IPIV is INTEGER array, dimension (min(M,N)) +*> The pivot indices; for 1 <= i <= min(M,N), row i of the +*> matrix was interchanged with row IPIV(i). +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> > 0: if INFO = i, U(i,i) is exactly zero. The factorization +*> has been completed, but the factor U is exactly +*> singular, and division by zero will occur if it is used +*> to solve a system of equations. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \ingroup doubleGEcomputational +* +* ===================================================================== + SUBROUTINE DGETRF2( M, N, A, LDA, IPIV, INFO ) +* +* -- LAPACK computational routine -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* +* .. Scalar Arguments .. + INTEGER INFO, LDA, M, N +* .. +* .. Array Arguments .. + INTEGER IPIV( * ) + DOUBLE PRECISION A( LDA, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE, ZERO + PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) +* .. +* .. Local Scalars .. + DOUBLE PRECISION SFMIN, TEMP + INTEGER I, IINFO, N1, N2 +* .. +* .. External Functions .. + DOUBLE PRECISION DLAMCH + INTEGER IDAMAX + EXTERNAL DLAMCH, IDAMAX +* .. +* .. External Subroutines .. + EXTERNAL DGEMM, DSCAL, DLASWP, DTRSM, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX, MIN +* .. +* .. Executable Statements .. +* +* Test the input parameters +* + INFO = 0 + IF( M.LT.0 ) THEN + INFO = -1 + ELSE IF( N.LT.0 ) THEN + INFO = -2 + ELSE IF( LDA.LT.MAX( 1, M ) ) THEN + INFO = -4 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'DGETRF2', -INFO ) + RETURN + END IF +* +* Quick return if possible +* + IF( M.EQ.0 .OR. N.EQ.0 ) + $ RETURN + + IF ( M.EQ.1 ) THEN +* +* Use unblocked code for one row case +* Just need to handle IPIV and INFO +* + IPIV( 1 ) = 1 + IF ( A(1,1).EQ.ZERO ) + $ INFO = 1 +* + ELSE IF( N.EQ.1 ) THEN +* +* Use unblocked code for one column case +* +* +* Compute machine safe minimum +* + SFMIN = DLAMCH('S') +* +* Find pivot and test for singularity +* + I = IDAMAX( M, A( 1, 1 ), 1 ) + IPIV( 1 ) = I + IF( A( I, 1 ).NE.ZERO ) THEN +* +* Apply the interchange +* + IF( I.NE.1 ) THEN + TEMP = A( 1, 1 ) + A( 1, 1 ) = A( I, 1 ) + A( I, 1 ) = TEMP + END IF +* +* Compute elements 2:M of the column +* + IF( ABS(A( 1, 1 )) .GE. SFMIN ) THEN + CALL DSCAL( M-1, ONE / A( 1, 1 ), A( 2, 1 ), 1 ) + ELSE + DO 10 I = 1, M-1 + A( 1+I, 1 ) = A( 1+I, 1 ) / A( 1, 1 ) + 10 CONTINUE + END IF +* + ELSE + INFO = 1 + END IF +* + ELSE +* +* Use recursive code +* + N1 = MIN( M, N ) / 2 + N2 = N-N1 +* +* [ A11 ] +* Factor [ --- ] +* [ A21 ] +* + CALL DGETRF2( M, N1, A, LDA, IPIV, IINFO ) + + IF ( INFO.EQ.0 .AND. IINFO.GT.0 ) + $ INFO = IINFO +* +* [ A12 ] +* Apply interchanges to [ --- ] +* [ A22 ] +* + CALL DLASWP( N2, A( 1, N1+1 ), LDA, 1, N1, IPIV, 1 ) +* +* Solve A12 +* + CALL DTRSM( 'L', 'L', 'N', 'U', N1, N2, ONE, A, LDA, + $ A( 1, N1+1 ), LDA ) +* +* Update A22 +* + CALL DGEMM( 'N', 'N', M-N1, N2, N1, -ONE, A( N1+1, 1 ), LDA, + $ A( 1, N1+1 ), LDA, ONE, A( N1+1, N1+1 ), LDA ) +* +* Factor A22 +* + CALL DGETRF2( M-N1, N2, A( N1+1, N1+1 ), LDA, IPIV( N1+1 ), + $ IINFO ) +* +* Adjust INFO and the pivot indices +* + IF ( INFO.EQ.0 .AND. IINFO.GT.0 ) + $ INFO = IINFO + N1 + DO 20 I = N1+1, MIN( M, N ) + IPIV( I ) = IPIV( I ) + N1 + 20 CONTINUE +* +* Apply interchanges to A21 +* + CALL DLASWP( N1, A( 1, 1 ), LDA, N1+1, MIN( M, N), IPIV, 1 ) +* + END IF + RETURN +* +* End of DGETRF2 +* + END diff --git a/lib/linalg/static/disnan.cpp b/lib/linalg/static/disnan.cpp new file mode 100644 index 0000000000..9e5bc1094e --- /dev/null +++ b/lib/linalg/static/disnan.cpp @@ -0,0 +1,14 @@ + +#include + +extern "C" { + +#include "lmp_f2c.h" + +logical disnan_(const doublereal *din) +{ + if (!din) return TRUE_; + + return std::isnan(*din) ? TRUE_ : FALSE_; +} +} diff --git a/lib/linalg/static/dlamch.cpp b/lib/linalg/static/dlamch.cpp new file mode 100644 index 0000000000..3d616d95d2 --- /dev/null +++ b/lib/linalg/static/dlamch.cpp @@ -0,0 +1,45 @@ + +#include +#include + +extern "C" { + +#include "lmp_f2c.h" + +// undefine conflicting f2c macros +#undef min +#undef max + +doublereal dlamch_(const char *cmach) +{ + if (!cmach) return 0.0; + char select = toupper(*cmach); + + // BLAS assumes rounding not truncation => epsilon is half + const double eps = 0.5 * std::numeric_limits::epsilon(); + if (select == 'E') return eps; + + double min = std::numeric_limits::min(); + const double max = std::numeric_limits::max(); + double small = 1.0 / max; + if (small >= min) min = small * (1.0 + eps); + if (select == 'S') return min; + + const double radix = std::numeric_limits::radix; + if (select == 'B') return radix; + + if (select == 'P') return eps * radix; + + if (select == 'N') return std::numeric_limits::digits; + + if (select == 'M') return std::numeric_limits::min_exponent; + + if (select == 'U') return min; + + if (select == 'L') return std::numeric_limits::max_exponent; + + if (select == 'O') return max; + + return 0.0; +} +} diff --git a/lib/linalg/static/dlarft.f b/lib/linalg/static/dlarft.f new file mode 100644 index 0000000000..e92c927971 --- /dev/null +++ b/lib/linalg/static/dlarft.f @@ -0,0 +1,327 @@ +*> \brief \b DLARFT forms the triangular factor T of a block reflector H = I - vtvH +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLARFT + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) +* +* .. Scalar Arguments .. +* CHARACTER DIRECT, STOREV +* INTEGER K, LDT, LDV, N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLARFT forms the triangular factor T of a real block reflector H +*> of order n, which is defined as a product of k elementary reflectors. +*> +*> If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; +*> +*> If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. +*> +*> If STOREV = 'C', the vector which defines the elementary reflector +*> H(i) is stored in the i-th column of the array V, and +*> +*> H = I - V * T * V**T +*> +*> If STOREV = 'R', the vector which defines the elementary reflector +*> H(i) is stored in the i-th row of the array V, and +*> +*> H = I - V**T * T * V +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] DIRECT +*> \verbatim +*> DIRECT is CHARACTER*1 +*> Specifies the order in which the elementary reflectors are +*> multiplied to form the block reflector: +*> = 'F': H = H(1) H(2) . . . H(k) (Forward) +*> = 'B': H = H(k) . . . H(2) H(1) (Backward) +*> \endverbatim +*> +*> \param[in] STOREV +*> \verbatim +*> STOREV is CHARACTER*1 +*> Specifies how the vectors which define the elementary +*> reflectors are stored (see also Further Details): +*> = 'C': columnwise +*> = 'R': rowwise +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the block reflector H. N >= 0. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> The order of the triangular factor T (= the number of +*> elementary reflectors). K >= 1. +*> \endverbatim +*> +*> \param[in] V +*> \verbatim +*> V is DOUBLE PRECISION array, dimension +*> (LDV,K) if STOREV = 'C' +*> (LDV,N) if STOREV = 'R' +*> The matrix V. See further details. +*> \endverbatim +*> +*> \param[in] LDV +*> \verbatim +*> LDV is INTEGER +*> The leading dimension of the array V. +*> If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. +*> \endverbatim +*> +*> \param[in] TAU +*> \verbatim +*> TAU is DOUBLE PRECISION array, dimension (K) +*> TAU(i) must contain the scalar factor of the elementary +*> reflector H(i). +*> \endverbatim +*> +*> \param[out] T +*> \verbatim +*> T is DOUBLE PRECISION array, dimension (LDT,K) +*> The k by k triangular factor T of the block reflector. +*> If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is +*> lower triangular. The rest of the array is not used. +*> \endverbatim +*> +*> \param[in] LDT +*> \verbatim +*> LDT is INTEGER +*> The leading dimension of the array T. LDT >= K. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \ingroup doubleOTHERauxiliary +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> The shape of the matrix V and the storage of the vectors which define +*> the H(i) is best illustrated by the following example with n = 5 and +*> k = 3. The elements equal to 1 are not stored. +*> +*> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': +*> +*> V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) +*> ( v1 1 ) ( 1 v2 v2 v2 ) +*> ( v1 v2 1 ) ( 1 v3 v3 ) +*> ( v1 v2 v3 ) +*> ( v1 v2 v3 ) +*> +*> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': +*> +*> V = ( v1 v2 v3 ) V = ( v1 v1 1 ) +*> ( v1 v2 v3 ) ( v2 v2 v2 1 ) +*> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) +*> ( 1 v3 ) +*> ( 1 ) +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) +* +* -- LAPACK auxiliary routine -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* +* .. Scalar Arguments .. + CHARACTER DIRECT, STOREV + INTEGER K, LDT, LDV, N +* .. +* .. Array Arguments .. + DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE, ZERO + PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) +* .. +* .. Local Scalars .. + INTEGER I, J, PREVLASTV, LASTV +* .. +* .. External Subroutines .. + EXTERNAL DGEMV, DTRMV +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. Executable Statements .. +* +* Quick return if possible +* + IF( N.EQ.0 ) + $ RETURN +* + IF( LSAME( DIRECT, 'F' ) ) THEN + PREVLASTV = N + DO I = 1, K + PREVLASTV = MAX( I, PREVLASTV ) + IF( TAU( I ).EQ.ZERO ) THEN +* +* H(i) = I +* + DO J = 1, I + T( J, I ) = ZERO + END DO + ELSE +* +* general case +* + IF( LSAME( STOREV, 'C' ) ) THEN +* Skip any trailing zeros. + DO LASTV = N, I+1, -1 + IF( V( LASTV, I ).NE.ZERO ) GOTO 219 + END DO + 219 CONTINUE + DO J = 1, I-1 + T( J, I ) = -TAU( I ) * V( I , J ) + END DO + J = MIN( LASTV, PREVLASTV ) +* +* T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**T * V(i:j,i) +* + CALL DGEMV( 'Transpose', J-I, I-1, -TAU( I ), + $ V( I+1, 1 ), LDV, V( I+1, I ), 1, ONE, + $ T( 1, I ), 1 ) + ELSE +* Skip any trailing zeros. + DO LASTV = N, I+1, -1 + IF( V( I, LASTV ).NE.ZERO ) GOTO 235 + END DO + 235 CONTINUE + DO J = 1, I-1 + T( J, I ) = -TAU( I ) * V( J , I ) + END DO + J = MIN( LASTV, PREVLASTV ) +* +* T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**T +* + CALL DGEMV( 'No transpose', I-1, J-I, -TAU( I ), + $ V( 1, I+1 ), LDV, V( I, I+1 ), LDV, ONE, + $ T( 1, I ), 1 ) + END IF +* +* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) +* + CALL DTRMV( 'Upper', 'No transpose', 'Non-unit', I-1, T, + $ LDT, T( 1, I ), 1 ) + T( I, I ) = TAU( I ) + IF( I.GT.1 ) THEN + PREVLASTV = MAX( PREVLASTV, LASTV ) + ELSE + PREVLASTV = LASTV + END IF + END IF + END DO + ELSE + PREVLASTV = 1 + DO I = K, 1, -1 + IF( TAU( I ).EQ.ZERO ) THEN +* +* H(i) = I +* + DO J = I, K + T( J, I ) = ZERO + END DO + ELSE +* +* general case +* + IF( I.LT.K ) THEN + IF( LSAME( STOREV, 'C' ) ) THEN +* Skip any leading zeros. + DO LASTV = 1, I-1 + IF( V( LASTV, I ).NE.ZERO ) GOTO 280 + END DO + 280 CONTINUE + DO J = I+1, K + T( J, I ) = -TAU( I ) * V( N-K+I , J ) + END DO + J = MAX( LASTV, PREVLASTV ) +* +* T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**T * V(j:n-k+i,i) +* + CALL DGEMV( 'Transpose', N-K+I-J, K-I, -TAU( I ), + $ V( J, I+1 ), LDV, V( J, I ), 1, ONE, + $ T( I+1, I ), 1 ) + ELSE +* Skip any leading zeros. + DO LASTV = 1, I-1 + IF( V( I, LASTV ).NE.ZERO ) GOTO 296 + END DO + 296 CONTINUE + DO J = I+1, K + T( J, I ) = -TAU( I ) * V( J, N-K+I ) + END DO + J = MAX( LASTV, PREVLASTV ) +* +* T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**T +* + CALL DGEMV( 'No transpose', K-I, N-K+I-J, + $ -TAU( I ), V( I+1, J ), LDV, V( I, J ), LDV, + $ ONE, T( I+1, I ), 1 ) + END IF +* +* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) +* + CALL DTRMV( 'Lower', 'No transpose', 'Non-unit', K-I, + $ T( I+1, I+1 ), LDT, T( I+1, I ), 1 ) + IF( I.GT.1 ) THEN + PREVLASTV = MIN( PREVLASTV, LASTV ) + ELSE + PREVLASTV = LASTV + END IF + END IF + T( I, I ) = TAU( I ) + END IF + END DO + END IF + RETURN +* +* End of DLARFT +* + END diff --git a/lib/linalg/static/dpotrf2.f b/lib/linalg/static/dpotrf2.f new file mode 100644 index 0000000000..ba827635a8 --- /dev/null +++ b/lib/linalg/static/dpotrf2.f @@ -0,0 +1,234 @@ +*> \brief \b DPOTRF2 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition: +* =========== +* +* RECURSIVE SUBROUTINE DPOTRF2( UPLO, N, A, LDA, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER UPLO +* INTEGER INFO, LDA, N +* .. +* .. Array Arguments .. +* REAL A( LDA, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DPOTRF2 computes the Cholesky factorization of a real symmetric +*> positive definite matrix A using the recursive algorithm. +*> +*> The factorization has the form +*> A = U**T * U, if UPLO = 'U', or +*> A = L * L**T, if UPLO = 'L', +*> where U is an upper triangular matrix and L is lower triangular. +*> +*> This is the recursive version of the algorithm. It divides +*> the matrix into four submatrices: +*> +*> [ A11 | A12 ] where A11 is n1 by n1 and A22 is n2 by n2 +*> A = [ -----|----- ] with n1 = n/2 +*> [ A21 | A22 ] n2 = n-n1 +*> +*> The subroutine calls itself to factor A11. Update and scale A21 +*> or A12, update A22 then calls itself to factor A22. +*> +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> = 'U': Upper triangle of A is stored; +*> = 'L': Lower triangle of A is stored. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is DOUBLE PRECISION array, dimension (LDA,N) +*> On entry, the symmetric matrix A. If UPLO = 'U', the leading +*> N-by-N upper triangular part of A contains the upper +*> triangular part of the matrix A, and the strictly lower +*> triangular part of A is not referenced. If UPLO = 'L', the +*> leading N-by-N lower triangular part of A contains the lower +*> triangular part of the matrix A, and the strictly upper +*> triangular part of A is not referenced. +*> +*> On exit, if INFO = 0, the factor U or L from the Cholesky +*> factorization A = U**T*U or A = L*L**T. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,N). +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> > 0: if INFO = i, the leading minor of order i is not +*> positive definite, and the factorization could not be +*> completed. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \ingroup doublePOcomputational +* +* ===================================================================== + SUBROUTINE DPOTRF2( UPLO, N, A, LDA, INFO ) +* +* -- LAPACK computational routine -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* +* .. Scalar Arguments .. + CHARACTER UPLO + INTEGER INFO, LDA, N +* .. +* .. Array Arguments .. + DOUBLE PRECISION A( LDA, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE, ZERO + PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) +* .. +* .. Local Scalars .. + LOGICAL UPPER + INTEGER N1, N2, IINFO +* .. +* .. External Functions .. + LOGICAL LSAME, DISNAN + EXTERNAL LSAME, DISNAN +* .. +* .. External Subroutines .. + EXTERNAL DSYRK, DTRSM, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX, SQRT +* .. +* .. Executable Statements .. +* +* Test the input parameters +* + INFO = 0 + UPPER = LSAME( UPLO, 'U' ) + IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN + INFO = -1 + ELSE IF( N.LT.0 ) THEN + INFO = -2 + ELSE IF( LDA.LT.MAX( 1, N ) ) THEN + INFO = -4 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'DPOTRF2', -INFO ) + RETURN + END IF +* +* Quick return if possible +* + IF( N.EQ.0 ) + $ RETURN +* +* N=1 case +* + IF( N.EQ.1 ) THEN +* +* Test for non-positive-definiteness +* + IF( A( 1, 1 ).LE.ZERO.OR.DISNAN( A( 1, 1 ) ) ) THEN + INFO = 1 + RETURN + END IF +* +* Factor +* + A( 1, 1 ) = SQRT( A( 1, 1 ) ) +* +* Use recursive code +* + ELSE + N1 = N/2 + N2 = N-N1 +* +* Factor A11 +* + CALL DPOTRF2( UPLO, N1, A( 1, 1 ), LDA, IINFO ) + IF ( IINFO.NE.0 ) THEN + INFO = IINFO + RETURN + END IF +* +* Compute the Cholesky factorization A = U**T*U +* + IF( UPPER ) THEN +* +* Update and scale A12 +* + CALL DTRSM( 'L', 'U', 'T', 'N', N1, N2, ONE, + $ A( 1, 1 ), LDA, A( 1, N1+1 ), LDA ) +* +* Update and factor A22 +* + CALL DSYRK( UPLO, 'T', N2, N1, -ONE, A( 1, N1+1 ), LDA, + $ ONE, A( N1+1, N1+1 ), LDA ) + CALL DPOTRF2( UPLO, N2, A( N1+1, N1+1 ), LDA, IINFO ) + IF ( IINFO.NE.0 ) THEN + INFO = IINFO + N1 + RETURN + END IF +* +* Compute the Cholesky factorization A = L*L**T +* + ELSE +* +* Update and scale A21 +* + CALL DTRSM( 'R', 'L', 'T', 'N', N2, N1, ONE, + $ A( 1, 1 ), LDA, A( N1+1, 1 ), LDA ) +* +* Update and factor A22 +* + CALL DSYRK( UPLO, 'N', N2, N1, -ONE, A( N1+1, 1 ), LDA, + $ ONE, A( N1+1, N1+1 ), LDA ) + CALL DPOTRF2( UPLO, N2, A( N1+1, N1+1 ), LDA, IINFO ) + IF ( IINFO.NE.0 ) THEN + INFO = IINFO + N1 + RETURN + END IF + END IF + END IF + RETURN +* +* End of DPOTRF2 +* + END diff --git a/lib/linalg/static/lsame.cpp b/lib/linalg/static/lsame.cpp new file mode 100644 index 0000000000..dcb89e3d00 --- /dev/null +++ b/lib/linalg/static/lsame.cpp @@ -0,0 +1,17 @@ + +#include + +extern "C" { + +#include "lmp_f2c.h" + +logical lsame_(const char *a, const char *b) +{ + char ua, ub; + if (!a || !b) return FALSE_; + + ua = toupper(*a); + ub = toupper(*b); + return (ua == ub) ? TRUE_ : FALSE_; +} +} diff --git a/lib/linalg/static/xerbla.cpp b/lib/linalg/static/xerbla.cpp new file mode 100644 index 0000000000..cf2f7b1c69 --- /dev/null +++ b/lib/linalg/static/xerbla.cpp @@ -0,0 +1,30 @@ + +#include +#include + +class LinalgException : public std::exception { + std::string message; + + public: + LinalgException() = delete; + + explicit LinalgException(const std::string &msg) { message = msg; } + const char *what() const noexcept override { return message.c_str(); } +}; + +extern "C" { + +#include "lmp_f2c.h" + +integer xerbla_(const char *srname, integer *info) +{ + std::string mesg = " ** On entry to "; + for (int i = 0; i < 1024; ++i) { + if ((srname[i] == '\0') || (srname[i] == ' ')) break; + mesg.push_back(srname[i]); + } + mesg += " parameter number " + std::to_string(*info) + " had an illegal value\n"; + throw LinalgException(mesg); + return 0; +} +} diff --git a/lib/linalg/static/zlarft.f b/lib/linalg/static/zlarft.f new file mode 100644 index 0000000000..b59ba93213 --- /dev/null +++ b/lib/linalg/static/zlarft.f @@ -0,0 +1,328 @@ +*> \brief \b ZLARFT forms the triangular factor T of a block reflector H = I - vtvH +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ZLARFT + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE ZLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) +* +* .. Scalar Arguments .. +* CHARACTER DIRECT, STOREV +* INTEGER K, LDT, LDV, N +* .. +* .. Array Arguments .. +* COMPLEX*16 T( LDT, * ), TAU( * ), V( LDV, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ZLARFT forms the triangular factor T of a complex block reflector H +*> of order n, which is defined as a product of k elementary reflectors. +*> +*> If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; +*> +*> If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. +*> +*> If STOREV = 'C', the vector which defines the elementary reflector +*> H(i) is stored in the i-th column of the array V, and +*> +*> H = I - V * T * V**H +*> +*> If STOREV = 'R', the vector which defines the elementary reflector +*> H(i) is stored in the i-th row of the array V, and +*> +*> H = I - V**H * T * V +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] DIRECT +*> \verbatim +*> DIRECT is CHARACTER*1 +*> Specifies the order in which the elementary reflectors are +*> multiplied to form the block reflector: +*> = 'F': H = H(1) H(2) . . . H(k) (Forward) +*> = 'B': H = H(k) . . . H(2) H(1) (Backward) +*> \endverbatim +*> +*> \param[in] STOREV +*> \verbatim +*> STOREV is CHARACTER*1 +*> Specifies how the vectors which define the elementary +*> reflectors are stored (see also Further Details): +*> = 'C': columnwise +*> = 'R': rowwise +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the block reflector H. N >= 0. +*> \endverbatim +*> +*> \param[in] K +*> \verbatim +*> K is INTEGER +*> The order of the triangular factor T (= the number of +*> elementary reflectors). K >= 1. +*> \endverbatim +*> +*> \param[in] V +*> \verbatim +*> V is COMPLEX*16 array, dimension +*> (LDV,K) if STOREV = 'C' +*> (LDV,N) if STOREV = 'R' +*> The matrix V. See further details. +*> \endverbatim +*> +*> \param[in] LDV +*> \verbatim +*> LDV is INTEGER +*> The leading dimension of the array V. +*> If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. +*> \endverbatim +*> +*> \param[in] TAU +*> \verbatim +*> TAU is COMPLEX*16 array, dimension (K) +*> TAU(i) must contain the scalar factor of the elementary +*> reflector H(i). +*> \endverbatim +*> +*> \param[out] T +*> \verbatim +*> T is COMPLEX*16 array, dimension (LDT,K) +*> The k by k triangular factor T of the block reflector. +*> If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is +*> lower triangular. The rest of the array is not used. +*> \endverbatim +*> +*> \param[in] LDT +*> \verbatim +*> LDT is INTEGER +*> The leading dimension of the array T. LDT >= K. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \ingroup complex16OTHERauxiliary +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> The shape of the matrix V and the storage of the vectors which define +*> the H(i) is best illustrated by the following example with n = 5 and +*> k = 3. The elements equal to 1 are not stored. +*> +*> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': +*> +*> V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) +*> ( v1 1 ) ( 1 v2 v2 v2 ) +*> ( v1 v2 1 ) ( 1 v3 v3 ) +*> ( v1 v2 v3 ) +*> ( v1 v2 v3 ) +*> +*> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': +*> +*> V = ( v1 v2 v3 ) V = ( v1 v1 1 ) +*> ( v1 v2 v3 ) ( v2 v2 v2 1 ) +*> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) +*> ( 1 v3 ) +*> ( 1 ) +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE ZLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) +* +* -- LAPACK auxiliary routine -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* +* .. Scalar Arguments .. + CHARACTER DIRECT, STOREV + INTEGER K, LDT, LDV, N +* .. +* .. Array Arguments .. + COMPLEX*16 T( LDT, * ), TAU( * ), V( LDV, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX*16 ONE, ZERO + PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ), + $ ZERO = ( 0.0D+0, 0.0D+0 ) ) +* .. +* .. Local Scalars .. + INTEGER I, J, PREVLASTV, LASTV +* .. +* .. External Subroutines .. + EXTERNAL ZGEMV, ZTRMV, ZGEMM +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. Executable Statements .. +* +* Quick return if possible +* + IF( N.EQ.0 ) + $ RETURN +* + IF( LSAME( DIRECT, 'F' ) ) THEN + PREVLASTV = N + DO I = 1, K + PREVLASTV = MAX( PREVLASTV, I ) + IF( TAU( I ).EQ.ZERO ) THEN +* +* H(i) = I +* + DO J = 1, I + T( J, I ) = ZERO + END DO + ELSE +* +* general case +* + IF( LSAME( STOREV, 'C' ) ) THEN +* Skip any trailing zeros. + DO LASTV = N, I+1, -1 + IF( V( LASTV, I ).NE.ZERO ) GOTO 220 + END DO + 220 CONTINUE + DO J = 1, I-1 + T( J, I ) = -TAU( I ) * CONJG( V( I , J ) ) + END DO + J = MIN( LASTV, PREVLASTV ) +* +* T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**H * V(i:j,i) +* + CALL ZGEMV( 'Conjugate transpose', J-I, I-1, + $ -TAU( I ), V( I+1, 1 ), LDV, + $ V( I+1, I ), 1, ONE, T( 1, I ), 1 ) + ELSE +* Skip any trailing zeros. + DO LASTV = N, I+1, -1 + IF( V( I, LASTV ).NE.ZERO ) GOTO 236 + END DO + 236 CONTINUE + DO J = 1, I-1 + T( J, I ) = -TAU( I ) * V( J , I ) + END DO + J = MIN( LASTV, PREVLASTV ) +* +* T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**H +* + CALL ZGEMM( 'N', 'C', I-1, 1, J-I, -TAU( I ), + $ V( 1, I+1 ), LDV, V( I, I+1 ), LDV, + $ ONE, T( 1, I ), LDT ) + END IF +* +* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) +* + CALL ZTRMV( 'Upper', 'No transpose', 'Non-unit', I-1, T, + $ LDT, T( 1, I ), 1 ) + T( I, I ) = TAU( I ) + IF( I.GT.1 ) THEN + PREVLASTV = MAX( PREVLASTV, LASTV ) + ELSE + PREVLASTV = LASTV + END IF + END IF + END DO + ELSE + PREVLASTV = 1 + DO I = K, 1, -1 + IF( TAU( I ).EQ.ZERO ) THEN +* +* H(i) = I +* + DO J = I, K + T( J, I ) = ZERO + END DO + ELSE +* +* general case +* + IF( I.LT.K ) THEN + IF( LSAME( STOREV, 'C' ) ) THEN +* Skip any leading zeros. + DO LASTV = 1, I-1 + IF( V( LASTV, I ).NE.ZERO ) GOTO 281 + END DO + 281 CONTINUE + DO J = I+1, K + T( J, I ) = -TAU( I ) * CONJG( V( N-K+I , J ) ) + END DO + J = MAX( LASTV, PREVLASTV ) +* +* T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**H * V(j:n-k+i,i) +* + CALL ZGEMV( 'Conjugate transpose', N-K+I-J, K-I, + $ -TAU( I ), V( J, I+1 ), LDV, V( J, I ), + $ 1, ONE, T( I+1, I ), 1 ) + ELSE +* Skip any leading zeros. + DO LASTV = 1, I-1 + IF( V( I, LASTV ).NE.ZERO ) GOTO 297 + END DO + 297 CONTINUE + DO J = I+1, K + T( J, I ) = -TAU( I ) * V( J, N-K+I ) + END DO + J = MAX( LASTV, PREVLASTV ) +* +* T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**H +* + CALL ZGEMM( 'N', 'C', K-I, 1, N-K+I-J, -TAU( I ), + $ V( I+1, J ), LDV, V( I, J ), LDV, + $ ONE, T( I+1, I ), LDT ) + END IF +* +* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) +* + CALL ZTRMV( 'Lower', 'No transpose', 'Non-unit', K-I, + $ T( I+1, I+1 ), LDT, T( I+1, I ), 1 ) + IF( I.GT.1 ) THEN + PREVLASTV = MIN( PREVLASTV, LASTV ) + ELSE + PREVLASTV = LASTV + END IF + END IF + T( I, I ) = TAU( I ) + END IF + END DO + END IF + RETURN +* +* End of ZLARFT +* + END diff --git a/lib/linalg/xerbla.cpp b/lib/linalg/xerbla.cpp new file mode 100644 index 0000000000..cf2f7b1c69 --- /dev/null +++ b/lib/linalg/xerbla.cpp @@ -0,0 +1,30 @@ + +#include +#include + +class LinalgException : public std::exception { + std::string message; + + public: + LinalgException() = delete; + + explicit LinalgException(const std::string &msg) { message = msg; } + const char *what() const noexcept override { return message.c_str(); } +}; + +extern "C" { + +#include "lmp_f2c.h" + +integer xerbla_(const char *srname, integer *info) +{ + std::string mesg = " ** On entry to "; + for (int i = 0; i < 1024; ++i) { + if ((srname[i] == '\0') || (srname[i] == ' ')) break; + mesg.push_back(srname[i]); + } + mesg += " parameter number " + std::to_string(*info) + " had an illegal value\n"; + throw LinalgException(mesg); + return 0; +} +} diff --git a/lib/linalg/zaxpy.cpp b/lib/linalg/zaxpy.cpp new file mode 100644 index 0000000000..2788743a40 --- /dev/null +++ b/lib/linalg/zaxpy.cpp @@ -0,0 +1,191 @@ +/* fortran/zaxpy.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b ZAXPY */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZAXPY(N,ZA,ZX,INCX,ZY,INCY) */ + +/* .. Scalar Arguments .. */ +/* COMPLEX*16 ZA */ +/* INTEGER INCX,INCY,N */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 ZX(*),ZY(*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZAXPY constant times a vector plus a vector. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > number of elements in input vector(s) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] ZA */ +/* > \verbatim */ +/* > ZA is COMPLEX*16 */ +/* > On entry, ZA specifies the scalar alpha. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] ZX */ +/* > \verbatim */ +/* > ZX is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > storage spacing between elements of ZX */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] ZY */ +/* > \verbatim */ +/* > ZY is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCY */ +/* > \verbatim */ +/* > INCY is INTEGER */ +/* > storage spacing between elements of ZY */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16_blas_level1 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > jack dongarra, 3/11/78. */ +/* > modified 12/3/93, array(1) declarations changed to array(*) */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int zaxpy_(integer *n, doublecomplex *za, doublecomplex *zx, + integer *incx, doublecomplex *zy, integer *incy) +{ + /* System generated locals */ + integer i__1, i__2, i__3, i__4; + doublecomplex z__1, z__2; + + /* Local variables */ + integer i__, ix, iy; + extern doublereal dcabs1_(doublecomplex *); + + +/* -- Reference BLAS level1 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ + /* Parameter adjustments */ + --zy; + --zx; + + /* Function Body */ + if (*n <= 0) { + return 0; + } + if (dcabs1_(za) == 0.) { + return 0; + } + if (*incx == 1 && *incy == 1) { + +/* code for both increments equal to 1 */ + + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__; + i__3 = i__; + i__4 = i__; + z__2.r = za->r * zx[i__4].r - za->i * zx[i__4].i, z__2.i = za->r * + zx[i__4].i + za->i * zx[i__4].r; + z__1.r = zy[i__3].r + z__2.r, z__1.i = zy[i__3].i + z__2.i; + zy[i__2].r = z__1.r, zy[i__2].i = z__1.i; + } + } else { + +/* code for unequal increments or equal increments */ +/* not equal to 1 */ + + ix = 1; + iy = 1; + if (*incx < 0) { + ix = (-(*n) + 1) * *incx + 1; + } + if (*incy < 0) { + iy = (-(*n) + 1) * *incy + 1; + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = iy; + i__3 = iy; + i__4 = ix; + z__2.r = za->r * zx[i__4].r - za->i * zx[i__4].i, z__2.i = za->r * + zx[i__4].i + za->i * zx[i__4].r; + z__1.r = zy[i__3].r + z__2.r, z__1.i = zy[i__3].i + z__2.i; + zy[i__2].r = z__1.r, zy[i__2].i = z__1.i; + ix += *incx; + iy += *incy; + } + } + + return 0; + +/* End of ZAXPY */ + +} /* zaxpy_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zcopy.cpp b/lib/linalg/zcopy.cpp new file mode 100644 index 0000000000..357bd961a0 --- /dev/null +++ b/lib/linalg/zcopy.cpp @@ -0,0 +1,168 @@ +/* fortran/zcopy.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b ZCOPY */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZCOPY(N,ZX,INCX,ZY,INCY) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INCX,INCY,N */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 ZX(*),ZY(*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZCOPY copies a vector, x, to a vector, y. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > number of elements in input vector(s) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] ZX */ +/* > \verbatim */ +/* > ZX is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > storage spacing between elements of ZX */ +/* > \endverbatim */ +/* > */ +/* > \param[out] ZY */ +/* > \verbatim */ +/* > ZY is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCY */ +/* > \verbatim */ +/* > INCY is INTEGER */ +/* > storage spacing between elements of ZY */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16_blas_level1 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > jack dongarra, linpack, 4/11/78. */ +/* > modified 12/3/93, array(1) declarations changed to array(*) */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int zcopy_(integer *n, doublecomplex *zx, integer *incx, + doublecomplex *zy, integer *incy) +{ + /* System generated locals */ + integer i__1, i__2, i__3; + + /* Local variables */ + integer i__, ix, iy; + + +/* -- Reference BLAS level1 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ + /* Parameter adjustments */ + --zy; + --zx; + + /* Function Body */ + if (*n <= 0) { + return 0; + } + if (*incx == 1 && *incy == 1) { + +/* code for both increments equal to 1 */ + + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__; + i__3 = i__; + zy[i__2].r = zx[i__3].r, zy[i__2].i = zx[i__3].i; + } + } else { + +/* code for unequal increments or equal increments */ +/* not equal to 1 */ + + ix = 1; + iy = 1; + if (*incx < 0) { + ix = (-(*n) + 1) * *incx + 1; + } + if (*incy < 0) { + iy = (-(*n) + 1) * *incy + 1; + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = iy; + i__3 = ix; + zy[i__2].r = zx[i__3].r, zy[i__2].i = zx[i__3].i; + ix += *incx; + iy += *incy; + } + } + return 0; + +/* End of ZCOPY */ + +} /* zcopy_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zdotc.cpp b/lib/linalg/zdotc.cpp new file mode 100644 index 0000000000..943f923bea --- /dev/null +++ b/lib/linalg/zdotc.cpp @@ -0,0 +1,186 @@ +/* fortran/zdotc.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b ZDOTC */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* COMPLEX*16 FUNCTION ZDOTC(N,ZX,INCX,ZY,INCY) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INCX,INCY,N */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 ZX(*),ZY(*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZDOTC forms the dot product of two complex vectors */ +/* > ZDOTC = X^H * Y */ +/* > */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > number of elements in input vector(s) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] ZX */ +/* > \verbatim */ +/* > ZX is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > storage spacing between elements of ZX */ +/* > \endverbatim */ +/* > */ +/* > \param[in] ZY */ +/* > \verbatim */ +/* > ZY is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCY */ +/* > \verbatim */ +/* > INCY is INTEGER */ +/* > storage spacing between elements of ZY */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16_blas_level1 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > jack dongarra, 3/11/78. */ +/* > modified 12/3/93, array(1) declarations changed to array(*) */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Double Complex */ VOID zdotc_(doublecomplex * ret_val, integer *n, + doublecomplex *zx, integer *incx, doublecomplex *zy, integer *incy) +{ + /* System generated locals */ + integer i__1, i__2; + doublecomplex z__1, z__2, z__3; + + /* Builtin functions */ + void d_cnjg(doublecomplex *, doublecomplex *); + + /* Local variables */ + integer i__, ix, iy; + doublecomplex ztemp; + + +/* -- Reference BLAS level1 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ + /* Parameter adjustments */ + --zy; + --zx; + + /* Function Body */ + ztemp.r = 0., ztemp.i = 0.; + ret_val->r = 0., ret_val->i = 0.; + if (*n <= 0) { + return ; + } + if (*incx == 1 && *incy == 1) { + +/* code for both increments equal to 1 */ + + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + d_cnjg(&z__3, &zx[i__]); + i__2 = i__; + z__2.r = z__3.r * zy[i__2].r - z__3.i * zy[i__2].i, z__2.i = + z__3.r * zy[i__2].i + z__3.i * zy[i__2].r; + z__1.r = ztemp.r + z__2.r, z__1.i = ztemp.i + z__2.i; + ztemp.r = z__1.r, ztemp.i = z__1.i; + } + } else { + +/* code for unequal increments or equal increments */ +/* not equal to 1 */ + + ix = 1; + iy = 1; + if (*incx < 0) { + ix = (-(*n) + 1) * *incx + 1; + } + if (*incy < 0) { + iy = (-(*n) + 1) * *incy + 1; + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + d_cnjg(&z__3, &zx[ix]); + i__2 = iy; + z__2.r = z__3.r * zy[i__2].r - z__3.i * zy[i__2].i, z__2.i = + z__3.r * zy[i__2].i + z__3.i * zy[i__2].r; + z__1.r = ztemp.r + z__2.r, z__1.i = ztemp.i + z__2.i; + ztemp.r = z__1.r, ztemp.i = z__1.i; + ix += *incx; + iy += *incy; + } + } + ret_val->r = ztemp.r, ret_val->i = ztemp.i; + return ; + +/* End of ZDOTC */ + +} /* zdotc_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zdrot.cpp b/lib/linalg/zdrot.cpp new file mode 100644 index 0000000000..c6ec16b053 --- /dev/null +++ b/lib/linalg/zdrot.cpp @@ -0,0 +1,213 @@ +/* fortran/zdrot.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b ZDROT */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZDROT( N, ZX, INCX, ZY, INCY, C, S ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INCX, INCY, N */ +/* DOUBLE PRECISION C, S */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 ZX( * ), ZY( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > Applies a plane rotation, where the cos and sin (c and s) are real */ +/* > and the vectors cx and cy are complex. */ +/* > jack dongarra, linpack, 3/11/78. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > On entry, N specifies the order of the vectors cx and cy. */ +/* > N must be at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] ZX */ +/* > \verbatim */ +/* > ZX is COMPLEX*16 array, dimension at least */ +/* > ( 1 + ( N - 1 )*abs( INCX ) ). */ +/* > Before entry, the incremented array ZX must contain the n */ +/* > element vector cx. On exit, ZX is overwritten by the updated */ +/* > vector cx. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > On entry, INCX specifies the increment for the elements of */ +/* > ZX. INCX must not be zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] ZY */ +/* > \verbatim */ +/* > ZY is COMPLEX*16 array, dimension at least */ +/* > ( 1 + ( N - 1 )*abs( INCY ) ). */ +/* > Before entry, the incremented array ZY must contain the n */ +/* > element vector cy. On exit, ZY is overwritten by the updated */ +/* > vector cy. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCY */ +/* > \verbatim */ +/* > INCY is INTEGER */ +/* > On entry, INCY specifies the increment for the elements of */ +/* > ZY. INCY must not be zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] C */ +/* > \verbatim */ +/* > C is DOUBLE PRECISION */ +/* > On entry, C specifies the cosine, cos. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] S */ +/* > \verbatim */ +/* > S is DOUBLE PRECISION */ +/* > On entry, S specifies the sine, sin. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16_blas_level1 */ + +/* ===================================================================== */ +/* Subroutine */ int zdrot_(integer *n, doublecomplex *zx, integer *incx, + doublecomplex *zy, integer *incy, doublereal *c__, doublereal *s) +{ + /* System generated locals */ + integer i__1, i__2, i__3, i__4; + doublecomplex z__1, z__2, z__3; + + /* Local variables */ + integer i__, ix, iy; + doublecomplex ctemp; + + +/* -- Reference BLAS level1 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. Executable Statements .. */ + + /* Parameter adjustments */ + --zy; + --zx; + + /* Function Body */ + if (*n <= 0) { + return 0; + } + if (*incx == 1 && *incy == 1) { + +/* code for both increments equal to 1 */ + + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__; + z__2.r = *c__ * zx[i__2].r, z__2.i = *c__ * zx[i__2].i; + i__3 = i__; + z__3.r = *s * zy[i__3].r, z__3.i = *s * zy[i__3].i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; + ctemp.r = z__1.r, ctemp.i = z__1.i; + i__2 = i__; + i__3 = i__; + z__2.r = *c__ * zy[i__3].r, z__2.i = *c__ * zy[i__3].i; + i__4 = i__; + z__3.r = *s * zx[i__4].r, z__3.i = *s * zx[i__4].i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i; + zy[i__2].r = z__1.r, zy[i__2].i = z__1.i; + i__2 = i__; + zx[i__2].r = ctemp.r, zx[i__2].i = ctemp.i; + } + } else { + +/* code for unequal increments or equal increments not equal */ +/* to 1 */ + + ix = 1; + iy = 1; + if (*incx < 0) { + ix = (-(*n) + 1) * *incx + 1; + } + if (*incy < 0) { + iy = (-(*n) + 1) * *incy + 1; + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = ix; + z__2.r = *c__ * zx[i__2].r, z__2.i = *c__ * zx[i__2].i; + i__3 = iy; + z__3.r = *s * zy[i__3].r, z__3.i = *s * zy[i__3].i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; + ctemp.r = z__1.r, ctemp.i = z__1.i; + i__2 = iy; + i__3 = iy; + z__2.r = *c__ * zy[i__3].r, z__2.i = *c__ * zy[i__3].i; + i__4 = ix; + z__3.r = *s * zx[i__4].r, z__3.i = *s * zx[i__4].i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i; + zy[i__2].r = z__1.r, zy[i__2].i = z__1.i; + i__2 = ix; + zx[i__2].r = ctemp.r, zx[i__2].i = ctemp.i; + ix += *incx; + iy += *incy; + } + } + return 0; + +/* End of ZDROT */ + +} /* zdrot_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zdscal.cpp b/lib/linalg/zdscal.cpp new file mode 100644 index 0000000000..c7c6406782 --- /dev/null +++ b/lib/linalg/zdscal.cpp @@ -0,0 +1,169 @@ +/* fortran/zdscal.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b ZDSCAL */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZDSCAL(N,DA,ZX,INCX) */ + +/* .. Scalar Arguments .. */ +/* DOUBLE PRECISION DA */ +/* INTEGER INCX,N */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 ZX(*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZDSCAL scales a vector by a constant. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > number of elements in input vector(s) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DA */ +/* > \verbatim */ +/* > DA is DOUBLE PRECISION */ +/* > On entry, DA specifies the scalar alpha. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] ZX */ +/* > \verbatim */ +/* > ZX is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > storage spacing between elements of ZX */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16_blas_level1 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > jack dongarra, 3/11/78. */ +/* > modified 3/93 to return if incx .le. 0. */ +/* > modified 12/3/93, array(1) declarations changed to array(*) */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int zdscal_(integer *n, doublereal *da, doublecomplex *zx, + integer *incx) +{ + /* System generated locals */ + integer i__1, i__2, i__3, i__4; + doublereal d__1, d__2; + doublecomplex z__1; + + /* Builtin functions */ + double d_imag(doublecomplex *); + + /* Local variables */ + integer i__, nincx; + + +/* -- Reference BLAS level1 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. Parameters .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ + /* Parameter adjustments */ + --zx; + + /* Function Body */ + if (*n <= 0 || *incx <= 0 || *da == 1.) { + return 0; + } + if (*incx == 1) { + +/* code for increment equal to 1 */ + + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__; + i__3 = i__; + d__1 = *da * zx[i__3].r; + d__2 = *da * d_imag(&zx[i__]); + z__1.r = d__1, z__1.i = d__2; + zx[i__2].r = z__1.r, zx[i__2].i = z__1.i; + } + } else { + +/* code for increment not equal to 1 */ + + nincx = *n * *incx; + i__1 = nincx; + i__2 = *incx; + for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { + i__3 = i__; + i__4 = i__; + d__1 = *da * zx[i__4].r; + d__2 = *da * d_imag(&zx[i__]); + z__1.r = d__1, z__1.i = d__2; + zx[i__3].r = z__1.r, zx[i__3].i = z__1.i; + } + } + return 0; + +/* End of ZDSCAL */ + +} /* zdscal_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zgemm.cpp b/lib/linalg/zgemm.cpp new file mode 100644 index 0000000000..92434e720f --- /dev/null +++ b/lib/linalg/zgemm.cpp @@ -0,0 +1,763 @@ +/* fortran/zgemm.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b ZGEMM */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) */ + +/* .. Scalar Arguments .. */ +/* COMPLEX*16 ALPHA,BETA */ +/* INTEGER K,LDA,LDB,LDC,M,N */ +/* CHARACTER TRANSA,TRANSB */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZGEMM performs one of the matrix-matrix operations */ +/* > */ +/* > C := alpha*op( A )*op( B ) + beta*C, */ +/* > */ +/* > where op( X ) is one of */ +/* > */ +/* > op( X ) = X or op( X ) = X**T or op( X ) = X**H, */ +/* > */ +/* > alpha and beta are scalars, and A, B and C are matrices, with op( A ) */ +/* > an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] TRANSA */ +/* > \verbatim */ +/* > TRANSA is CHARACTER*1 */ +/* > On entry, TRANSA specifies the form of op( A ) to be used in */ +/* > the matrix multiplication as follows: */ +/* > */ +/* > TRANSA = 'N' or 'n', op( A ) = A. */ +/* > */ +/* > TRANSA = 'T' or 't', op( A ) = A**T. */ +/* > */ +/* > TRANSA = 'C' or 'c', op( A ) = A**H. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TRANSB */ +/* > \verbatim */ +/* > TRANSB is CHARACTER*1 */ +/* > On entry, TRANSB specifies the form of op( B ) to be used in */ +/* > the matrix multiplication as follows: */ +/* > */ +/* > TRANSB = 'N' or 'n', op( B ) = B. */ +/* > */ +/* > TRANSB = 'T' or 't', op( B ) = B**T. */ +/* > */ +/* > TRANSB = 'C' or 'c', op( B ) = B**H. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > On entry, M specifies the number of rows of the matrix */ +/* > op( A ) and of the matrix C. M must be at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > On entry, N specifies the number of columns of the matrix */ +/* > op( B ) and the number of columns of the matrix C. N must be */ +/* > at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > On entry, K specifies the number of columns of the matrix */ +/* > op( A ) and the number of rows of the matrix op( B ). K must */ +/* > be at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] ALPHA */ +/* > \verbatim */ +/* > ALPHA is COMPLEX*16 */ +/* > On entry, ALPHA specifies the scalar alpha. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is COMPLEX*16 array, dimension ( LDA, ka ), where ka is */ +/* > k when TRANSA = 'N' or 'n', and is m otherwise. */ +/* > Before entry with TRANSA = 'N' or 'n', the leading m by k */ +/* > part of the array A must contain the matrix A, otherwise */ +/* > the leading k by m part of the array A must contain the */ +/* > matrix A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > On entry, LDA specifies the first dimension of A as declared */ +/* > in the calling (sub) program. When TRANSA = 'N' or 'n' then */ +/* > LDA must be at least max( 1, m ), otherwise LDA must be at */ +/* > least max( 1, k ). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] B */ +/* > \verbatim */ +/* > B is COMPLEX*16 array, dimension ( LDB, kb ), where kb is */ +/* > n when TRANSB = 'N' or 'n', and is k otherwise. */ +/* > Before entry with TRANSB = 'N' or 'n', the leading k by n */ +/* > part of the array B must contain the matrix B, otherwise */ +/* > the leading n by k part of the array B must contain the */ +/* > matrix B. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDB */ +/* > \verbatim */ +/* > LDB is INTEGER */ +/* > On entry, LDB specifies the first dimension of B as declared */ +/* > in the calling (sub) program. When TRANSB = 'N' or 'n' then */ +/* > LDB must be at least max( 1, k ), otherwise LDB must be at */ +/* > least max( 1, n ). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] BETA */ +/* > \verbatim */ +/* > BETA is COMPLEX*16 */ +/* > On entry, BETA specifies the scalar beta. When BETA is */ +/* > supplied as zero then C need not be set on input. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] C */ +/* > \verbatim */ +/* > C is COMPLEX*16 array, dimension ( LDC, N ) */ +/* > Before entry, the leading m by n part of the array C must */ +/* > contain the matrix C, except when beta is zero, in which */ +/* > case C need not be set on entry. */ +/* > On exit, the array C is overwritten by the m by n matrix */ +/* > ( alpha*op( A )*op( B ) + beta*C ). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDC */ +/* > \verbatim */ +/* > LDC is INTEGER */ +/* > On entry, LDC specifies the first dimension of C as declared */ +/* > in the calling (sub) program. LDC must be at least */ +/* > max( 1, m ). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16_blas_level3 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > Level 3 Blas routine. */ +/* > */ +/* > -- Written on 8-February-1989. */ +/* > Jack Dongarra, Argonne National Laboratory. */ +/* > Iain Duff, AERE Harwell. */ +/* > Jeremy Du Croz, Numerical Algorithms Group Ltd. */ +/* > Sven Hammarling, Numerical Algorithms Group Ltd. */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int zgemm_(char *transa, char *transb, integer *m, integer * + n, integer *k, doublecomplex *alpha, doublecomplex *a, integer *lda, + doublecomplex *b, integer *ldb, doublecomplex *beta, doublecomplex * + c__, integer *ldc, ftnlen transa_len, ftnlen transb_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, + i__3, i__4, i__5, i__6; + doublecomplex z__1, z__2, z__3, z__4; + + /* Builtin functions */ + void d_cnjg(doublecomplex *, doublecomplex *); + + /* Local variables */ + integer i__, j, l, info; + logical nota, notb; + doublecomplex temp; + logical conja, conjb; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + integer nrowa, nrowb; + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + + +/* -- Reference BLAS level3 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Parameters .. */ +/* .. */ + +/* Set NOTA and NOTB as true if A and B respectively are not */ +/* conjugated or transposed, set CONJA and CONJB as true if A and */ +/* B respectively are to be transposed but not conjugated and set */ +/* NROWA and NROWB as the number of rows of A and B respectively. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + b_dim1 = *ldb; + b_offset = 1 + b_dim1; + b -= b_offset; + c_dim1 = *ldc; + c_offset = 1 + c_dim1; + c__ -= c_offset; + + /* Function Body */ + nota = lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1); + notb = lsame_(transb, (char *)"N", (ftnlen)1, (ftnlen)1); + conja = lsame_(transa, (char *)"C", (ftnlen)1, (ftnlen)1); + conjb = lsame_(transb, (char *)"C", (ftnlen)1, (ftnlen)1); + if (nota) { + nrowa = *m; + } else { + nrowa = *k; + } + if (notb) { + nrowb = *k; + } else { + nrowb = *n; + } + +/* Test the input parameters. */ + + info = 0; + if (! nota && ! conja && ! lsame_(transa, (char *)"T", (ftnlen)1, (ftnlen)1)) { + info = 1; + } else if (! notb && ! conjb && ! lsame_(transb, (char *)"T", (ftnlen)1, (ftnlen) + 1)) { + info = 2; + } else if (*m < 0) { + info = 3; + } else if (*n < 0) { + info = 4; + } else if (*k < 0) { + info = 5; + } else if (*lda < max(1,nrowa)) { + info = 8; + } else if (*ldb < max(1,nrowb)) { + info = 10; + } else if (*ldc < max(1,*m)) { + info = 13; + } + if (info != 0) { + xerbla_((char *)"ZGEMM ", &info, (ftnlen)6); + return 0; + } + +/* Quick return if possible. */ + + if (*m == 0 || *n == 0 || (alpha->r == 0. && alpha->i == 0. || *k == 0) && + (beta->r == 1. && beta->i == 0.)) { + return 0; + } + +/* And when alpha.eq.zero. */ + + if (alpha->r == 0. && alpha->i == 0.) { + if (beta->r == 0. && beta->i == 0.) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + c__[i__3].r = 0., c__[i__3].i = 0.; +/* L10: */ + } +/* L20: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + i__4 = i__ + j * c_dim1; + z__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4].i, + z__1.i = beta->r * c__[i__4].i + beta->i * c__[ + i__4].r; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; +/* L30: */ + } +/* L40: */ + } + } + return 0; + } + +/* Start the operations. */ + + if (notb) { + if (nota) { + +/* Form C := alpha*A*B + beta*C. */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (beta->r == 0. && beta->i == 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + c__[i__3].r = 0., c__[i__3].i = 0.; +/* L50: */ + } + } else if (beta->r != 1. || beta->i != 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + i__4 = i__ + j * c_dim1; + z__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4] + .i, z__1.i = beta->r * c__[i__4].i + beta->i * + c__[i__4].r; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; +/* L60: */ + } + } + i__2 = *k; + for (l = 1; l <= i__2; ++l) { + i__3 = l + j * b_dim1; + z__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3].i, + z__1.i = alpha->r * b[i__3].i + alpha->i * b[i__3] + .r; + temp.r = z__1.r, temp.i = z__1.i; + i__3 = *m; + for (i__ = 1; i__ <= i__3; ++i__) { + i__4 = i__ + j * c_dim1; + i__5 = i__ + j * c_dim1; + i__6 = i__ + l * a_dim1; + z__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i, + z__2.i = temp.r * a[i__6].i + temp.i * a[i__6] + .r; + z__1.r = c__[i__5].r + z__2.r, z__1.i = c__[i__5].i + + z__2.i; + c__[i__4].r = z__1.r, c__[i__4].i = z__1.i; +/* L70: */ + } +/* L80: */ + } +/* L90: */ + } + } else if (conja) { + +/* Form C := alpha*A**H*B + beta*C. */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp.r = 0., temp.i = 0.; + i__3 = *k; + for (l = 1; l <= i__3; ++l) { + d_cnjg(&z__3, &a[l + i__ * a_dim1]); + i__4 = l + j * b_dim1; + z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4].i, + z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4] + .r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; +/* L100: */ + } + if (beta->r == 0. && beta->i == 0.) { + i__3 = i__ + j * c_dim1; + z__1.r = alpha->r * temp.r - alpha->i * temp.i, + z__1.i = alpha->r * temp.i + alpha->i * + temp.r; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } else { + i__3 = i__ + j * c_dim1; + z__2.r = alpha->r * temp.r - alpha->i * temp.i, + z__2.i = alpha->r * temp.i + alpha->i * + temp.r; + i__4 = i__ + j * c_dim1; + z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4] + .i, z__3.i = beta->r * c__[i__4].i + beta->i * + c__[i__4].r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } +/* L110: */ + } +/* L120: */ + } + } else { + +/* Form C := alpha*A**T*B + beta*C */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp.r = 0., temp.i = 0.; + i__3 = *k; + for (l = 1; l <= i__3; ++l) { + i__4 = l + i__ * a_dim1; + i__5 = l + j * b_dim1; + z__2.r = a[i__4].r * b[i__5].r - a[i__4].i * b[i__5] + .i, z__2.i = a[i__4].r * b[i__5].i + a[i__4] + .i * b[i__5].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; +/* L130: */ + } + if (beta->r == 0. && beta->i == 0.) { + i__3 = i__ + j * c_dim1; + z__1.r = alpha->r * temp.r - alpha->i * temp.i, + z__1.i = alpha->r * temp.i + alpha->i * + temp.r; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } else { + i__3 = i__ + j * c_dim1; + z__2.r = alpha->r * temp.r - alpha->i * temp.i, + z__2.i = alpha->r * temp.i + alpha->i * + temp.r; + i__4 = i__ + j * c_dim1; + z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4] + .i, z__3.i = beta->r * c__[i__4].i + beta->i * + c__[i__4].r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } +/* L140: */ + } +/* L150: */ + } + } + } else if (nota) { + if (conjb) { + +/* Form C := alpha*A*B**H + beta*C. */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (beta->r == 0. && beta->i == 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + c__[i__3].r = 0., c__[i__3].i = 0.; +/* L160: */ + } + } else if (beta->r != 1. || beta->i != 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + i__4 = i__ + j * c_dim1; + z__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4] + .i, z__1.i = beta->r * c__[i__4].i + beta->i * + c__[i__4].r; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; +/* L170: */ + } + } + i__2 = *k; + for (l = 1; l <= i__2; ++l) { + d_cnjg(&z__2, &b[j + l * b_dim1]); + z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = + alpha->r * z__2.i + alpha->i * z__2.r; + temp.r = z__1.r, temp.i = z__1.i; + i__3 = *m; + for (i__ = 1; i__ <= i__3; ++i__) { + i__4 = i__ + j * c_dim1; + i__5 = i__ + j * c_dim1; + i__6 = i__ + l * a_dim1; + z__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i, + z__2.i = temp.r * a[i__6].i + temp.i * a[i__6] + .r; + z__1.r = c__[i__5].r + z__2.r, z__1.i = c__[i__5].i + + z__2.i; + c__[i__4].r = z__1.r, c__[i__4].i = z__1.i; +/* L180: */ + } +/* L190: */ + } +/* L200: */ + } + } else { + +/* Form C := alpha*A*B**T + beta*C */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (beta->r == 0. && beta->i == 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + c__[i__3].r = 0., c__[i__3].i = 0.; +/* L210: */ + } + } else if (beta->r != 1. || beta->i != 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + i__4 = i__ + j * c_dim1; + z__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4] + .i, z__1.i = beta->r * c__[i__4].i + beta->i * + c__[i__4].r; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; +/* L220: */ + } + } + i__2 = *k; + for (l = 1; l <= i__2; ++l) { + i__3 = j + l * b_dim1; + z__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3].i, + z__1.i = alpha->r * b[i__3].i + alpha->i * b[i__3] + .r; + temp.r = z__1.r, temp.i = z__1.i; + i__3 = *m; + for (i__ = 1; i__ <= i__3; ++i__) { + i__4 = i__ + j * c_dim1; + i__5 = i__ + j * c_dim1; + i__6 = i__ + l * a_dim1; + z__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i, + z__2.i = temp.r * a[i__6].i + temp.i * a[i__6] + .r; + z__1.r = c__[i__5].r + z__2.r, z__1.i = c__[i__5].i + + z__2.i; + c__[i__4].r = z__1.r, c__[i__4].i = z__1.i; +/* L230: */ + } +/* L240: */ + } +/* L250: */ + } + } + } else if (conja) { + if (conjb) { + +/* Form C := alpha*A**H*B**H + beta*C. */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp.r = 0., temp.i = 0.; + i__3 = *k; + for (l = 1; l <= i__3; ++l) { + d_cnjg(&z__3, &a[l + i__ * a_dim1]); + d_cnjg(&z__4, &b[j + l * b_dim1]); + z__2.r = z__3.r * z__4.r - z__3.i * z__4.i, z__2.i = + z__3.r * z__4.i + z__3.i * z__4.r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; +/* L260: */ + } + if (beta->r == 0. && beta->i == 0.) { + i__3 = i__ + j * c_dim1; + z__1.r = alpha->r * temp.r - alpha->i * temp.i, + z__1.i = alpha->r * temp.i + alpha->i * + temp.r; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } else { + i__3 = i__ + j * c_dim1; + z__2.r = alpha->r * temp.r - alpha->i * temp.i, + z__2.i = alpha->r * temp.i + alpha->i * + temp.r; + i__4 = i__ + j * c_dim1; + z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4] + .i, z__3.i = beta->r * c__[i__4].i + beta->i * + c__[i__4].r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } +/* L270: */ + } +/* L280: */ + } + } else { + +/* Form C := alpha*A**H*B**T + beta*C */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp.r = 0., temp.i = 0.; + i__3 = *k; + for (l = 1; l <= i__3; ++l) { + d_cnjg(&z__3, &a[l + i__ * a_dim1]); + i__4 = j + l * b_dim1; + z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4].i, + z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4] + .r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; +/* L290: */ + } + if (beta->r == 0. && beta->i == 0.) { + i__3 = i__ + j * c_dim1; + z__1.r = alpha->r * temp.r - alpha->i * temp.i, + z__1.i = alpha->r * temp.i + alpha->i * + temp.r; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } else { + i__3 = i__ + j * c_dim1; + z__2.r = alpha->r * temp.r - alpha->i * temp.i, + z__2.i = alpha->r * temp.i + alpha->i * + temp.r; + i__4 = i__ + j * c_dim1; + z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4] + .i, z__3.i = beta->r * c__[i__4].i + beta->i * + c__[i__4].r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } +/* L300: */ + } +/* L310: */ + } + } + } else { + if (conjb) { + +/* Form C := alpha*A**T*B**H + beta*C */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp.r = 0., temp.i = 0.; + i__3 = *k; + for (l = 1; l <= i__3; ++l) { + i__4 = l + i__ * a_dim1; + d_cnjg(&z__3, &b[j + l * b_dim1]); + z__2.r = a[i__4].r * z__3.r - a[i__4].i * z__3.i, + z__2.i = a[i__4].r * z__3.i + a[i__4].i * + z__3.r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; +/* L320: */ + } + if (beta->r == 0. && beta->i == 0.) { + i__3 = i__ + j * c_dim1; + z__1.r = alpha->r * temp.r - alpha->i * temp.i, + z__1.i = alpha->r * temp.i + alpha->i * + temp.r; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } else { + i__3 = i__ + j * c_dim1; + z__2.r = alpha->r * temp.r - alpha->i * temp.i, + z__2.i = alpha->r * temp.i + alpha->i * + temp.r; + i__4 = i__ + j * c_dim1; + z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4] + .i, z__3.i = beta->r * c__[i__4].i + beta->i * + c__[i__4].r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } +/* L330: */ + } +/* L340: */ + } + } else { + +/* Form C := alpha*A**T*B**T + beta*C */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp.r = 0., temp.i = 0.; + i__3 = *k; + for (l = 1; l <= i__3; ++l) { + i__4 = l + i__ * a_dim1; + i__5 = j + l * b_dim1; + z__2.r = a[i__4].r * b[i__5].r - a[i__4].i * b[i__5] + .i, z__2.i = a[i__4].r * b[i__5].i + a[i__4] + .i * b[i__5].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; +/* L350: */ + } + if (beta->r == 0. && beta->i == 0.) { + i__3 = i__ + j * c_dim1; + z__1.r = alpha->r * temp.r - alpha->i * temp.i, + z__1.i = alpha->r * temp.i + alpha->i * + temp.r; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } else { + i__3 = i__ + j * c_dim1; + z__2.r = alpha->r * temp.r - alpha->i * temp.i, + z__2.i = alpha->r * temp.i + alpha->i * + temp.r; + i__4 = i__ + j * c_dim1; + z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4] + .i, z__3.i = beta->r * c__[i__4].i + beta->i * + c__[i__4].r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } +/* L360: */ + } +/* L370: */ + } + } + } + + return 0; + +/* End of ZGEMM */ + +} /* zgemm_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zgemv.cpp b/lib/linalg/zgemv.cpp new file mode 100644 index 0000000000..9524445dba --- /dev/null +++ b/lib/linalg/zgemv.cpp @@ -0,0 +1,477 @@ +/* fortran/zgemv.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b ZGEMV */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) */ + +/* .. Scalar Arguments .. */ +/* COMPLEX*16 ALPHA,BETA */ +/* INTEGER INCX,INCY,LDA,M,N */ +/* CHARACTER TRANS */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 A(LDA,*),X(*),Y(*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZGEMV performs one of the matrix-vector operations */ +/* > */ +/* > y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, or */ +/* > */ +/* > y := alpha*A**H*x + beta*y, */ +/* > */ +/* > where alpha and beta are scalars, x and y are vectors and A is an */ +/* > m by n matrix. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] TRANS */ +/* > \verbatim */ +/* > TRANS is CHARACTER*1 */ +/* > On entry, TRANS specifies the operation to be performed as */ +/* > follows: */ +/* > */ +/* > TRANS = 'N' or 'n' y := alpha*A*x + beta*y. */ +/* > */ +/* > TRANS = 'T' or 't' y := alpha*A**T*x + beta*y. */ +/* > */ +/* > TRANS = 'C' or 'c' y := alpha*A**H*x + beta*y. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > On entry, M specifies the number of rows of the matrix A. */ +/* > M must be at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > On entry, N specifies the number of columns of the matrix A. */ +/* > N must be at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] ALPHA */ +/* > \verbatim */ +/* > ALPHA is COMPLEX*16 */ +/* > On entry, ALPHA specifies the scalar alpha. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is COMPLEX*16 array, dimension ( LDA, N ) */ +/* > Before entry, the leading m by n part of the array A must */ +/* > contain the matrix of coefficients. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > On entry, LDA specifies the first dimension of A as declared */ +/* > in the calling (sub) program. LDA must be at least */ +/* > max( 1, m ). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] X */ +/* > \verbatim */ +/* > X is COMPLEX*16 array, dimension at least */ +/* > ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' */ +/* > and at least */ +/* > ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. */ +/* > Before entry, the incremented array X must contain the */ +/* > vector x. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > On entry, INCX specifies the increment for the elements of */ +/* > X. INCX must not be zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] BETA */ +/* > \verbatim */ +/* > BETA is COMPLEX*16 */ +/* > On entry, BETA specifies the scalar beta. When BETA is */ +/* > supplied as zero then Y need not be set on input. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] Y */ +/* > \verbatim */ +/* > Y is COMPLEX*16 array, dimension at least */ +/* > ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' */ +/* > and at least */ +/* > ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. */ +/* > Before entry with BETA non-zero, the incremented array Y */ +/* > must contain the vector y. On exit, Y is overwritten by the */ +/* > updated vector y. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCY */ +/* > \verbatim */ +/* > INCY is INTEGER */ +/* > On entry, INCY specifies the increment for the elements of */ +/* > Y. INCY must not be zero. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16_blas_level2 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > Level 2 Blas routine. */ +/* > The vector and matrix arguments are not referenced when N = 0, or M = 0 */ +/* > */ +/* > -- Written on 22-October-1986. */ +/* > Jack Dongarra, Argonne National Lab. */ +/* > Jeremy Du Croz, Nag Central Office. */ +/* > Sven Hammarling, Nag Central Office. */ +/* > Richard Hanson, Sandia National Labs. */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int zgemv_(char *trans, integer *m, integer *n, + doublecomplex *alpha, doublecomplex *a, integer *lda, doublecomplex * + x, integer *incx, doublecomplex *beta, doublecomplex *y, integer * + incy, ftnlen trans_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; + doublecomplex z__1, z__2, z__3; + + /* Builtin functions */ + void d_cnjg(doublecomplex *, doublecomplex *); + + /* Local variables */ + integer i__, j, ix, iy, jx, jy, kx, ky, info; + doublecomplex temp; + integer lenx, leny; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + logical noconj; + + +/* -- Reference BLAS level2 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --x; + --y; + + /* Function Body */ + info = 0; + if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"T", ( + ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1) + ) { + info = 1; + } else if (*m < 0) { + info = 2; + } else if (*n < 0) { + info = 3; + } else if (*lda < max(1,*m)) { + info = 6; + } else if (*incx == 0) { + info = 8; + } else if (*incy == 0) { + info = 11; + } + if (info != 0) { + xerbla_((char *)"ZGEMV ", &info, (ftnlen)6); + return 0; + } + +/* Quick return if possible. */ + + if (*m == 0 || *n == 0 || alpha->r == 0. && alpha->i == 0. && (beta->r == + 1. && beta->i == 0.)) { + return 0; + } + + noconj = lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1); + +/* Set LENX and LENY, the lengths of the vectors x and y, and set */ +/* up the start points in X and Y. */ + + if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { + lenx = *n; + leny = *m; + } else { + lenx = *m; + leny = *n; + } + if (*incx > 0) { + kx = 1; + } else { + kx = 1 - (lenx - 1) * *incx; + } + if (*incy > 0) { + ky = 1; + } else { + ky = 1 - (leny - 1) * *incy; + } + +/* Start the operations. In this version the elements of A are */ +/* accessed sequentially with one pass through A. */ + +/* First form y := beta*y. */ + + if (beta->r != 1. || beta->i != 0.) { + if (*incy == 1) { + if (beta->r == 0. && beta->i == 0.) { + i__1 = leny; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__; + y[i__2].r = 0., y[i__2].i = 0.; +/* L10: */ + } + } else { + i__1 = leny; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__; + i__3 = i__; + z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i, + z__1.i = beta->r * y[i__3].i + beta->i * y[i__3] + .r; + y[i__2].r = z__1.r, y[i__2].i = z__1.i; +/* L20: */ + } + } + } else { + iy = ky; + if (beta->r == 0. && beta->i == 0.) { + i__1 = leny; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = iy; + y[i__2].r = 0., y[i__2].i = 0.; + iy += *incy; +/* L30: */ + } + } else { + i__1 = leny; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = iy; + i__3 = iy; + z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i, + z__1.i = beta->r * y[i__3].i + beta->i * y[i__3] + .r; + y[i__2].r = z__1.r, y[i__2].i = z__1.i; + iy += *incy; +/* L40: */ + } + } + } + } + if (alpha->r == 0. && alpha->i == 0.) { + return 0; + } + if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { + +/* Form y := alpha*A*x + y. */ + + jx = kx; + if (*incy == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = jx; + z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i = + alpha->r * x[i__2].i + alpha->i * x[i__2].r; + temp.r = z__1.r, temp.i = z__1.i; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__; + i__4 = i__; + i__5 = i__ + j * a_dim1; + z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, z__2.i = + temp.r * a[i__5].i + temp.i * a[i__5].r; + z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; + y[i__3].r = z__1.r, y[i__3].i = z__1.i; +/* L50: */ + } + jx += *incx; +/* L60: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = jx; + z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i = + alpha->r * x[i__2].i + alpha->i * x[i__2].r; + temp.r = z__1.r, temp.i = z__1.i; + iy = ky; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = iy; + i__4 = iy; + i__5 = i__ + j * a_dim1; + z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, z__2.i = + temp.r * a[i__5].i + temp.i * a[i__5].r; + z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; + y[i__3].r = z__1.r, y[i__3].i = z__1.i; + iy += *incy; +/* L70: */ + } + jx += *incx; +/* L80: */ + } + } + } else { + +/* Form y := alpha*A**T*x + y or y := alpha*A**H*x + y. */ + + jy = ky; + if (*incx == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp.r = 0., temp.i = 0.; + if (noconj) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + i__4 = i__; + z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[i__4] + .i, z__2.i = a[i__3].r * x[i__4].i + a[i__3] + .i * x[i__4].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; +/* L90: */ + } + } else { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + d_cnjg(&z__3, &a[i__ + j * a_dim1]); + i__3 = i__; + z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, + z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3] + .r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; +/* L100: */ + } + } + i__2 = jy; + i__3 = jy; + z__2.r = alpha->r * temp.r - alpha->i * temp.i, z__2.i = + alpha->r * temp.i + alpha->i * temp.r; + z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i; + y[i__2].r = z__1.r, y[i__2].i = z__1.i; + jy += *incy; +/* L110: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp.r = 0., temp.i = 0.; + ix = kx; + if (noconj) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + i__4 = ix; + z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[i__4] + .i, z__2.i = a[i__3].r * x[i__4].i + a[i__3] + .i * x[i__4].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + ix += *incx; +/* L120: */ + } + } else { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + d_cnjg(&z__3, &a[i__ + j * a_dim1]); + i__3 = ix; + z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, + z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3] + .r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + ix += *incx; +/* L130: */ + } + } + i__2 = jy; + i__3 = jy; + z__2.r = alpha->r * temp.r - alpha->i * temp.i, z__2.i = + alpha->r * temp.i + alpha->i * temp.r; + z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i; + y[i__2].r = z__1.r, y[i__2].i = z__1.i; + jy += *incy; +/* L140: */ + } + } + } + + return 0; + +/* End of ZGEMV */ + +} /* zgemv_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zgerc.cpp b/lib/linalg/zgerc.cpp new file mode 100644 index 0000000000..db1e60a2eb --- /dev/null +++ b/lib/linalg/zgerc.cpp @@ -0,0 +1,289 @@ +/* fortran/zgerc.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b ZGERC */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZGERC(M,N,ALPHA,X,INCX,Y,INCY,A,LDA) */ + +/* .. Scalar Arguments .. */ +/* COMPLEX*16 ALPHA */ +/* INTEGER INCX,INCY,LDA,M,N */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 A(LDA,*),X(*),Y(*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZGERC performs the rank 1 operation */ +/* > */ +/* > A := alpha*x*y**H + A, */ +/* > */ +/* > where alpha is a scalar, x is an m element vector, y is an n element */ +/* > vector and A is an m by n matrix. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > On entry, M specifies the number of rows of the matrix A. */ +/* > M must be at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > On entry, N specifies the number of columns of the matrix A. */ +/* > N must be at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] ALPHA */ +/* > \verbatim */ +/* > ALPHA is COMPLEX*16 */ +/* > On entry, ALPHA specifies the scalar alpha. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] X */ +/* > \verbatim */ +/* > X is COMPLEX*16 array, dimension at least */ +/* > ( 1 + ( m - 1 )*abs( INCX ) ). */ +/* > Before entry, the incremented array X must contain the m */ +/* > element vector x. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > On entry, INCX specifies the increment for the elements of */ +/* > X. INCX must not be zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] Y */ +/* > \verbatim */ +/* > Y is COMPLEX*16 array, dimension at least */ +/* > ( 1 + ( n - 1 )*abs( INCY ) ). */ +/* > Before entry, the incremented array Y must contain the n */ +/* > element vector y. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCY */ +/* > \verbatim */ +/* > INCY is INTEGER */ +/* > On entry, INCY specifies the increment for the elements of */ +/* > Y. INCY must not be zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is COMPLEX*16 array, dimension ( LDA, N ) */ +/* > Before entry, the leading m by n part of the array A must */ +/* > contain the matrix of coefficients. On exit, A is */ +/* > overwritten by the updated matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > On entry, LDA specifies the first dimension of A as declared */ +/* > in the calling (sub) program. LDA must be at least */ +/* > max( 1, m ). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16_blas_level2 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > Level 2 Blas routine. */ +/* > */ +/* > -- Written on 22-October-1986. */ +/* > Jack Dongarra, Argonne National Lab. */ +/* > Jeremy Du Croz, Nag Central Office. */ +/* > Sven Hammarling, Nag Central Office. */ +/* > Richard Hanson, Sandia National Labs. */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int zgerc_(integer *m, integer *n, doublecomplex *alpha, + doublecomplex *x, integer *incx, doublecomplex *y, integer *incy, + doublecomplex *a, integer *lda) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; + doublecomplex z__1, z__2; + + /* Builtin functions */ + void d_cnjg(doublecomplex *, doublecomplex *); + + /* Local variables */ + integer i__, j, ix, jy, kx, info; + doublecomplex temp; + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + + +/* -- Reference BLAS level2 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --x; + --y; + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + + /* Function Body */ + info = 0; + if (*m < 0) { + info = 1; + } else if (*n < 0) { + info = 2; + } else if (*incx == 0) { + info = 5; + } else if (*incy == 0) { + info = 7; + } else if (*lda < max(1,*m)) { + info = 9; + } + if (info != 0) { + xerbla_((char *)"ZGERC ", &info, (ftnlen)6); + return 0; + } + +/* Quick return if possible. */ + + if (*m == 0 || *n == 0 || alpha->r == 0. && alpha->i == 0.) { + return 0; + } + +/* Start the operations. In this version the elements of A are */ +/* accessed sequentially with one pass through A. */ + + if (*incy > 0) { + jy = 1; + } else { + jy = 1 - (*n - 1) * *incy; + } + if (*incx == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = jy; + if (y[i__2].r != 0. || y[i__2].i != 0.) { + d_cnjg(&z__2, &y[jy]); + z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = + alpha->r * z__2.i + alpha->i * z__2.r; + temp.r = z__1.r, temp.i = z__1.i; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + i__4 = i__ + j * a_dim1; + i__5 = i__; + z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, z__2.i = + x[i__5].r * temp.i + x[i__5].i * temp.r; + z__1.r = a[i__4].r + z__2.r, z__1.i = a[i__4].i + z__2.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; +/* L10: */ + } + } + jy += *incy; +/* L20: */ + } + } else { + if (*incx > 0) { + kx = 1; + } else { + kx = 1 - (*m - 1) * *incx; + } + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = jy; + if (y[i__2].r != 0. || y[i__2].i != 0.) { + d_cnjg(&z__2, &y[jy]); + z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = + alpha->r * z__2.i + alpha->i * z__2.r; + temp.r = z__1.r, temp.i = z__1.i; + ix = kx; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + i__4 = i__ + j * a_dim1; + i__5 = ix; + z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, z__2.i = + x[i__5].r * temp.i + x[i__5].i * temp.r; + z__1.r = a[i__4].r + z__2.r, z__1.i = a[i__4].i + z__2.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; + ix += *incx; +/* L30: */ + } + } + jy += *incy; +/* L40: */ + } + } + + return 0; + +/* End of ZGERC */ + +} /* zgerc_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zheev.cpp b/lib/linalg/zheev.cpp new file mode 100644 index 0000000000..f421e49090 --- /dev/null +++ b/lib/linalg/zheev.cpp @@ -0,0 +1,379 @@ +/* fortran/zheev.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c_n1 = -1; +static integer c__0 = 0; +static doublereal c_b18 = 1.; + +/* > \brief ZHEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matr +ices */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZHEEV + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZHEEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, */ +/* INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER JOBZ, UPLO */ +/* INTEGER INFO, LDA, LWORK, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION RWORK( * ), W( * ) */ +/* COMPLEX*16 A( LDA, * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZHEEV computes all eigenvalues and, optionally, eigenvectors of a */ +/* > complex Hermitian matrix A. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] JOBZ */ +/* > \verbatim */ +/* > JOBZ is CHARACTER*1 */ +/* > = 'N': Compute eigenvalues only; */ +/* > = 'V': Compute eigenvalues and eigenvectors. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > = 'U': Upper triangle of A is stored; */ +/* > = 'L': Lower triangle of A is stored. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is COMPLEX*16 array, dimension (LDA, N) */ +/* > On entry, the Hermitian matrix A. If UPLO = 'U', the */ +/* > leading N-by-N upper triangular part of A contains the */ +/* > upper triangular part of the matrix A. If UPLO = 'L', */ +/* > the leading N-by-N lower triangular part of A contains */ +/* > the lower triangular part of the matrix A. */ +/* > On exit, if JOBZ = 'V', then if INFO = 0, A contains the */ +/* > orthonormal eigenvectors of the matrix A. */ +/* > If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') */ +/* > or the upper triangle (if UPLO='U') of A, including the */ +/* > diagonal, is destroyed. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] W */ +/* > \verbatim */ +/* > W is DOUBLE PRECISION array, dimension (N) */ +/* > If INFO = 0, the eigenvalues in ascending order. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) */ +/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LWORK */ +/* > \verbatim */ +/* > LWORK is INTEGER */ +/* > The length of the array WORK. LWORK >= max(1,2*N-1). */ +/* > For optimal efficiency, LWORK >= (NB+1)*N, */ +/* > where NB is the blocksize for ZHETRD returned by ILAENV. */ +/* > */ +/* > If LWORK = -1, then a workspace query is assumed; the routine */ +/* > only calculates the optimal size of the WORK array, returns */ +/* > this value as the first entry of the WORK array, and no error */ +/* > message related to LWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] RWORK */ +/* > \verbatim */ +/* > RWORK is DOUBLE PRECISION array, dimension (max(1, 3*N-2)) */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > > 0: if INFO = i, the algorithm failed to converge; i */ +/* > off-diagonal elements of an intermediate tridiagonal */ +/* > form did not converge to zero. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16HEeigen */ + +/* ===================================================================== */ +/* Subroutine */ int zheev_(char *jobz, char *uplo, integer *n, doublecomplex + *a, integer *lda, doublereal *w, doublecomplex *work, integer *lwork, + doublereal *rwork, integer *info, ftnlen jobz_len, ftnlen uplo_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2; + doublereal d__1; + + /* Builtin functions */ + double sqrt(doublereal); + + /* Local variables */ + integer nb; + doublereal eps; + integer inde; + doublereal anrm; + integer imax; + doublereal rmin, rmax; + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *); + doublereal sigma; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + integer iinfo; + logical lower, wantz; + extern doublereal dlamch_(char *, ftnlen); + integer iscale; + doublereal safmin; + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + doublereal bignum; + extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *, + integer *, doublereal *, ftnlen, ftnlen); + integer indtau; + extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *, + integer *), zlascl_(char *, integer *, integer *, doublereal *, + doublereal *, integer *, integer *, doublecomplex *, integer *, + integer *, ftnlen); + integer indwrk; + extern /* Subroutine */ int zhetrd_(char *, integer *, doublecomplex *, + integer *, doublereal *, doublereal *, doublecomplex *, + doublecomplex *, integer *, integer *, ftnlen); + integer llwork; + doublereal smlnum; + integer lwkopt; + logical lquery; + extern /* Subroutine */ int zsteqr_(char *, integer *, doublereal *, + doublereal *, doublecomplex *, integer *, doublereal *, integer *, + ftnlen), zungtr_(char *, integer *, doublecomplex *, integer *, + doublecomplex *, doublecomplex *, integer *, integer *, ftnlen); + + +/* -- LAPACK driver routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --w; + --work; + --rwork; + + /* Function Body */ + wantz = lsame_(jobz, (char *)"V", (ftnlen)1, (ftnlen)1); + lower = lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1); + lquery = *lwork == -1; + + *info = 0; + if (! (wantz || lsame_(jobz, (char *)"N", (ftnlen)1, (ftnlen)1))) { + *info = -1; + } else if (! (lower || lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1))) { + *info = -2; + } else if (*n < 0) { + *info = -3; + } else if (*lda < max(1,*n)) { + *info = -5; + } + + if (*info == 0) { + nb = ilaenv_(&c__1, (char *)"ZHETRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, + (ftnlen)1); +/* Computing MAX */ + i__1 = 1, i__2 = (nb + 1) * *n; + lwkopt = max(i__1,i__2); + work[1].r = (doublereal) lwkopt, work[1].i = 0.; + +/* Computing MAX */ + i__1 = 1, i__2 = (*n << 1) - 1; + if (*lwork < max(i__1,i__2) && ! lquery) { + *info = -8; + } + } + + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"ZHEEV ", &i__1, (ftnlen)6); + return 0; + } else if (lquery) { + return 0; + } + +/* Quick return if possible */ + + if (*n == 0) { + return 0; + } + + if (*n == 1) { + i__1 = a_dim1 + 1; + w[1] = a[i__1].r; + work[1].r = 1., work[1].i = 0.; + if (wantz) { + i__1 = a_dim1 + 1; + a[i__1].r = 1., a[i__1].i = 0.; + } + return 0; + } + +/* Get machine constants. */ + + safmin = dlamch_((char *)"Safe minimum", (ftnlen)12); + eps = dlamch_((char *)"Precision", (ftnlen)9); + smlnum = safmin / eps; + bignum = 1. / smlnum; + rmin = sqrt(smlnum); + rmax = sqrt(bignum); + +/* Scale matrix to allowable range, if necessary. */ + + anrm = zlanhe_((char *)"M", uplo, n, &a[a_offset], lda, &rwork[1], (ftnlen)1, ( + ftnlen)1); + iscale = 0; + if (anrm > 0. && anrm < rmin) { + iscale = 1; + sigma = rmin / anrm; + } else if (anrm > rmax) { + iscale = 1; + sigma = rmax / anrm; + } + if (iscale == 1) { + zlascl_(uplo, &c__0, &c__0, &c_b18, &sigma, n, n, &a[a_offset], lda, + info, (ftnlen)1); + } + +/* Call ZHETRD to reduce Hermitian matrix to tridiagonal form. */ + + inde = 1; + indtau = 1; + indwrk = indtau + *n; + llwork = *lwork - indwrk + 1; + zhetrd_(uplo, n, &a[a_offset], lda, &w[1], &rwork[inde], &work[indtau], & + work[indwrk], &llwork, &iinfo, (ftnlen)1); + +/* For eigenvalues only, call DSTERF. For eigenvectors, first call */ +/* ZUNGTR to generate the unitary matrix, then call ZSTEQR. */ + + if (! wantz) { + dsterf_(n, &w[1], &rwork[inde], info); + } else { + zungtr_(uplo, n, &a[a_offset], lda, &work[indtau], &work[indwrk], & + llwork, &iinfo, (ftnlen)1); + indwrk = inde + *n; + zsteqr_(jobz, n, &w[1], &rwork[inde], &a[a_offset], lda, &rwork[ + indwrk], info, (ftnlen)1); + } + +/* If matrix was scaled, then rescale eigenvalues appropriately. */ + + if (iscale == 1) { + if (*info == 0) { + imax = *n; + } else { + imax = *info - 1; + } + d__1 = 1. / sigma; + dscal_(&imax, &d__1, &w[1], &c__1); + } + +/* Set WORK(1) to optimal complex workspace size. */ + + work[1].r = (doublereal) lwkopt, work[1].i = 0.; + + return 0; + +/* End of ZHEEV */ + +} /* zheev_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zheevd.cpp b/lib/linalg/zheevd.cpp new file mode 100644 index 0000000000..c340c17718 --- /dev/null +++ b/lib/linalg/zheevd.cpp @@ -0,0 +1,486 @@ +/* fortran/zheevd.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c_n1 = -1; +static integer c__0 = 0; +static doublereal c_b18 = 1.; + +/* > \brief ZHEEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE mat +rices */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZHEEVD + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, */ +/* LRWORK, IWORK, LIWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER JOBZ, UPLO */ +/* INTEGER INFO, LDA, LIWORK, LRWORK, LWORK, N */ +/* .. */ +/* .. Array Arguments .. */ +/* INTEGER IWORK( * ) */ +/* DOUBLE PRECISION RWORK( * ), W( * ) */ +/* COMPLEX*16 A( LDA, * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZHEEVD computes all eigenvalues and, optionally, eigenvectors of a */ +/* > complex Hermitian matrix A. If eigenvectors are desired, it uses a */ +/* > divide and conquer algorithm. */ +/* > */ +/* > The divide and conquer algorithm makes very mild assumptions about */ +/* > floating point arithmetic. It will work on machines with a guard */ +/* > digit in add/subtract, or on those binary machines without guard */ +/* > digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */ +/* > Cray-2. It could conceivably fail on hexadecimal or decimal machines */ +/* > without guard digits, but we know of none. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] JOBZ */ +/* > \verbatim */ +/* > JOBZ is CHARACTER*1 */ +/* > = 'N': Compute eigenvalues only; */ +/* > = 'V': Compute eigenvalues and eigenvectors. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > = 'U': Upper triangle of A is stored; */ +/* > = 'L': Lower triangle of A is stored. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is COMPLEX*16 array, dimension (LDA, N) */ +/* > On entry, the Hermitian matrix A. If UPLO = 'U', the */ +/* > leading N-by-N upper triangular part of A contains the */ +/* > upper triangular part of the matrix A. If UPLO = 'L', */ +/* > the leading N-by-N lower triangular part of A contains */ +/* > the lower triangular part of the matrix A. */ +/* > On exit, if JOBZ = 'V', then if INFO = 0, A contains the */ +/* > orthonormal eigenvectors of the matrix A. */ +/* > If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') */ +/* > or the upper triangle (if UPLO='U') of A, including the */ +/* > diagonal, is destroyed. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] W */ +/* > \verbatim */ +/* > W is DOUBLE PRECISION array, dimension (N) */ +/* > If INFO = 0, the eigenvalues in ascending order. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) */ +/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LWORK */ +/* > \verbatim */ +/* > LWORK is INTEGER */ +/* > The length of the array WORK. */ +/* > If N <= 1, LWORK must be at least 1. */ +/* > If JOBZ = 'N' and N > 1, LWORK must be at least N + 1. */ +/* > If JOBZ = 'V' and N > 1, LWORK must be at least 2*N + N**2. */ +/* > */ +/* > If LWORK = -1, then a workspace query is assumed; the routine */ +/* > only calculates the optimal sizes of the WORK, RWORK and */ +/* > IWORK arrays, returns these values as the first entries of */ +/* > the WORK, RWORK and IWORK arrays, and no error message */ +/* > related to LWORK or LRWORK or LIWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] RWORK */ +/* > \verbatim */ +/* > RWORK is DOUBLE PRECISION array, */ +/* > dimension (LRWORK) */ +/* > On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LRWORK */ +/* > \verbatim */ +/* > LRWORK is INTEGER */ +/* > The dimension of the array RWORK. */ +/* > If N <= 1, LRWORK must be at least 1. */ +/* > If JOBZ = 'N' and N > 1, LRWORK must be at least N. */ +/* > If JOBZ = 'V' and N > 1, LRWORK must be at least */ +/* > 1 + 5*N + 2*N**2. */ +/* > */ +/* > If LRWORK = -1, then a workspace query is assumed; the */ +/* > routine only calculates the optimal sizes of the WORK, RWORK */ +/* > and IWORK arrays, returns these values as the first entries */ +/* > of the WORK, RWORK and IWORK arrays, and no error message */ +/* > related to LWORK or LRWORK or LIWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] IWORK */ +/* > \verbatim */ +/* > IWORK is INTEGER array, dimension (MAX(1,LIWORK)) */ +/* > On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LIWORK */ +/* > \verbatim */ +/* > LIWORK is INTEGER */ +/* > The dimension of the array IWORK. */ +/* > If N <= 1, LIWORK must be at least 1. */ +/* > If JOBZ = 'N' and N > 1, LIWORK must be at least 1. */ +/* > If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N. */ +/* > */ +/* > If LIWORK = -1, then a workspace query is assumed; the */ +/* > routine only calculates the optimal sizes of the WORK, RWORK */ +/* > and IWORK arrays, returns these values as the first entries */ +/* > of the WORK, RWORK and IWORK arrays, and no error message */ +/* > related to LWORK or LRWORK or LIWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > > 0: if INFO = i and JOBZ = 'N', then the algorithm failed */ +/* > to converge; i off-diagonal elements of an intermediate */ +/* > tridiagonal form did not converge to zero; */ +/* > if INFO = i and JOBZ = 'V', then the algorithm failed */ +/* > to compute an eigenvalue while working on the submatrix */ +/* > lying in rows and columns INFO/(N+1) through */ +/* > mod(INFO,N+1). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16HEeigen */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > Modified description of INFO. Sven, 16 Feb 05. */ + +/* > \par Contributors: */ +/* ================== */ +/* > */ +/* > Jeff Rutter, Computer Science Division, University of California */ +/* > at Berkeley, USA */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int zheevd_(char *jobz, char *uplo, integer *n, + doublecomplex *a, integer *lda, doublereal *w, doublecomplex *work, + integer *lwork, doublereal *rwork, integer *lrwork, integer *iwork, + integer *liwork, integer *info, ftnlen jobz_len, ftnlen uplo_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2; + doublereal d__1; + + /* Builtin functions */ + double sqrt(doublereal); + + /* Local variables */ + doublereal eps; + integer inde; + doublereal anrm; + integer imax; + doublereal rmin, rmax; + integer lopt; + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *); + doublereal sigma; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + integer iinfo, lwmin, liopt; + logical lower; + integer llrwk, lropt; + logical wantz; + integer indwk2, llwrk2; + extern doublereal dlamch_(char *, ftnlen); + integer iscale; + doublereal safmin; + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + doublereal bignum; + extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *, + integer *, doublereal *, ftnlen, ftnlen); + integer indtau; + extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *, + integer *), zlascl_(char *, integer *, integer *, doublereal *, + doublereal *, integer *, integer *, doublecomplex *, integer *, + integer *, ftnlen), zstedc_(char *, integer *, doublereal *, + doublereal *, doublecomplex *, integer *, doublecomplex *, + integer *, doublereal *, integer *, integer *, integer *, integer + *, ftnlen); + integer indrwk, indwrk, liwmin; + extern /* Subroutine */ int zhetrd_(char *, integer *, doublecomplex *, + integer *, doublereal *, doublereal *, doublecomplex *, + doublecomplex *, integer *, integer *, ftnlen), zlacpy_(char *, + integer *, integer *, doublecomplex *, integer *, doublecomplex *, + integer *, ftnlen); + integer lrwmin, llwork; + doublereal smlnum; + logical lquery; + extern /* Subroutine */ int zunmtr_(char *, char *, char *, integer *, + integer *, doublecomplex *, integer *, doublecomplex *, + doublecomplex *, integer *, doublecomplex *, integer *, integer *, + ftnlen, ftnlen, ftnlen); + + +/* -- LAPACK driver routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --w; + --work; + --rwork; + --iwork; + + /* Function Body */ + wantz = lsame_(jobz, (char *)"V", (ftnlen)1, (ftnlen)1); + lower = lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1); + lquery = *lwork == -1 || *lrwork == -1 || *liwork == -1; + + *info = 0; + if (! (wantz || lsame_(jobz, (char *)"N", (ftnlen)1, (ftnlen)1))) { + *info = -1; + } else if (! (lower || lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1))) { + *info = -2; + } else if (*n < 0) { + *info = -3; + } else if (*lda < max(1,*n)) { + *info = -5; + } + + if (*info == 0) { + if (*n <= 1) { + lwmin = 1; + lrwmin = 1; + liwmin = 1; + lopt = lwmin; + lropt = lrwmin; + liopt = liwmin; + } else { + if (wantz) { + lwmin = (*n << 1) + *n * *n; +/* Computing 2nd power */ + i__1 = *n; + lrwmin = *n * 5 + 1 + (i__1 * i__1 << 1); + liwmin = *n * 5 + 3; + } else { + lwmin = *n + 1; + lrwmin = *n; + liwmin = 1; + } +/* Computing MAX */ + i__1 = lwmin, i__2 = *n + *n * ilaenv_(&c__1, (char *)"ZHETRD", uplo, n, & + c_n1, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); + lopt = max(i__1,i__2); + lropt = lrwmin; + liopt = liwmin; + } + work[1].r = (doublereal) lopt, work[1].i = 0.; + rwork[1] = (doublereal) lropt; + iwork[1] = liopt; + + if (*lwork < lwmin && ! lquery) { + *info = -8; + } else if (*lrwork < lrwmin && ! lquery) { + *info = -10; + } else if (*liwork < liwmin && ! lquery) { + *info = -12; + } + } + + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"ZHEEVD", &i__1, (ftnlen)6); + return 0; + } else if (lquery) { + return 0; + } + +/* Quick return if possible */ + + if (*n == 0) { + return 0; + } + + if (*n == 1) { + i__1 = a_dim1 + 1; + w[1] = a[i__1].r; + if (wantz) { + i__1 = a_dim1 + 1; + a[i__1].r = 1., a[i__1].i = 0.; + } + return 0; + } + +/* Get machine constants. */ + + safmin = dlamch_((char *)"Safe minimum", (ftnlen)12); + eps = dlamch_((char *)"Precision", (ftnlen)9); + smlnum = safmin / eps; + bignum = 1. / smlnum; + rmin = sqrt(smlnum); + rmax = sqrt(bignum); + +/* Scale matrix to allowable range, if necessary. */ + + anrm = zlanhe_((char *)"M", uplo, n, &a[a_offset], lda, &rwork[1], (ftnlen)1, ( + ftnlen)1); + iscale = 0; + if (anrm > 0. && anrm < rmin) { + iscale = 1; + sigma = rmin / anrm; + } else if (anrm > rmax) { + iscale = 1; + sigma = rmax / anrm; + } + if (iscale == 1) { + zlascl_(uplo, &c__0, &c__0, &c_b18, &sigma, n, n, &a[a_offset], lda, + info, (ftnlen)1); + } + +/* Call ZHETRD to reduce Hermitian matrix to tridiagonal form. */ + + inde = 1; + indtau = 1; + indwrk = indtau + *n; + indrwk = inde + *n; + indwk2 = indwrk + *n * *n; + llwork = *lwork - indwrk + 1; + llwrk2 = *lwork - indwk2 + 1; + llrwk = *lrwork - indrwk + 1; + zhetrd_(uplo, n, &a[a_offset], lda, &w[1], &rwork[inde], &work[indtau], & + work[indwrk], &llwork, &iinfo, (ftnlen)1); + +/* For eigenvalues only, call DSTERF. For eigenvectors, first call */ +/* ZSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the */ +/* tridiagonal matrix, then call ZUNMTR to multiply it to the */ +/* Householder transformations represented as Householder vectors in */ +/* A. */ + + if (! wantz) { + dsterf_(n, &w[1], &rwork[inde], info); + } else { + zstedc_((char *)"I", n, &w[1], &rwork[inde], &work[indwrk], n, &work[indwk2], + &llwrk2, &rwork[indrwk], &llrwk, &iwork[1], liwork, info, ( + ftnlen)1); + zunmtr_((char *)"L", uplo, (char *)"N", n, n, &a[a_offset], lda, &work[indtau], &work[ + indwrk], n, &work[indwk2], &llwrk2, &iinfo, (ftnlen)1, ( + ftnlen)1, (ftnlen)1); + zlacpy_((char *)"A", n, n, &work[indwrk], n, &a[a_offset], lda, (ftnlen)1); + } + +/* If matrix was scaled, then rescale eigenvalues appropriately. */ + + if (iscale == 1) { + if (*info == 0) { + imax = *n; + } else { + imax = *info - 1; + } + d__1 = 1. / sigma; + dscal_(&imax, &d__1, &w[1], &c__1); + } + + work[1].r = (doublereal) lopt, work[1].i = 0.; + rwork[1] = (doublereal) lropt; + iwork[1] = liopt; + + return 0; + +/* End of ZHEEVD */ + +} /* zheevd_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zhemv.cpp b/lib/linalg/zhemv.cpp new file mode 100644 index 0000000000..f965dcfcdf --- /dev/null +++ b/lib/linalg/zhemv.cpp @@ -0,0 +1,508 @@ +/* fortran/zhemv.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b ZHEMV */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZHEMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) */ + +/* .. Scalar Arguments .. */ +/* COMPLEX*16 ALPHA,BETA */ +/* INTEGER INCX,INCY,LDA,N */ +/* CHARACTER UPLO */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 A(LDA,*),X(*),Y(*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZHEMV performs the matrix-vector operation */ +/* > */ +/* > y := alpha*A*x + beta*y, */ +/* > */ +/* > where alpha and beta are scalars, x and y are n element vectors and */ +/* > A is an n by n hermitian matrix. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > On entry, UPLO specifies whether the upper or lower */ +/* > triangular part of the array A is to be referenced as */ +/* > follows: */ +/* > */ +/* > UPLO = 'U' or 'u' Only the upper triangular part of A */ +/* > is to be referenced. */ +/* > */ +/* > UPLO = 'L' or 'l' Only the lower triangular part of A */ +/* > is to be referenced. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > On entry, N specifies the order of the matrix A. */ +/* > N must be at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] ALPHA */ +/* > \verbatim */ +/* > ALPHA is COMPLEX*16 */ +/* > On entry, ALPHA specifies the scalar alpha. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is COMPLEX*16 array, dimension ( LDA, N ) */ +/* > Before entry with UPLO = 'U' or 'u', the leading n by n */ +/* > upper triangular part of the array A must contain the upper */ +/* > triangular part of the hermitian matrix and the strictly */ +/* > lower triangular part of A is not referenced. */ +/* > Before entry with UPLO = 'L' or 'l', the leading n by n */ +/* > lower triangular part of the array A must contain the lower */ +/* > triangular part of the hermitian matrix and the strictly */ +/* > upper triangular part of A is not referenced. */ +/* > Note that the imaginary parts of the diagonal elements need */ +/* > not be set and are assumed to be zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > On entry, LDA specifies the first dimension of A as declared */ +/* > in the calling (sub) program. LDA must be at least */ +/* > max( 1, n ). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] X */ +/* > \verbatim */ +/* > X is COMPLEX*16 array, dimension at least */ +/* > ( 1 + ( n - 1 )*abs( INCX ) ). */ +/* > Before entry, the incremented array X must contain the n */ +/* > element vector x. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > On entry, INCX specifies the increment for the elements of */ +/* > X. INCX must not be zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] BETA */ +/* > \verbatim */ +/* > BETA is COMPLEX*16 */ +/* > On entry, BETA specifies the scalar beta. When BETA is */ +/* > supplied as zero then Y need not be set on input. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] Y */ +/* > \verbatim */ +/* > Y is COMPLEX*16 array, dimension at least */ +/* > ( 1 + ( n - 1 )*abs( INCY ) ). */ +/* > Before entry, the incremented array Y must contain the n */ +/* > element vector y. On exit, Y is overwritten by the updated */ +/* > vector y. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCY */ +/* > \verbatim */ +/* > INCY is INTEGER */ +/* > On entry, INCY specifies the increment for the elements of */ +/* > Y. INCY must not be zero. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16_blas_level2 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > Level 2 Blas routine. */ +/* > The vector and matrix arguments are not referenced when N = 0, or M = 0 */ +/* > */ +/* > -- Written on 22-October-1986. */ +/* > Jack Dongarra, Argonne National Lab. */ +/* > Jeremy Du Croz, Nag Central Office. */ +/* > Sven Hammarling, Nag Central Office. */ +/* > Richard Hanson, Sandia National Labs. */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int zhemv_(char *uplo, integer *n, doublecomplex *alpha, + doublecomplex *a, integer *lda, doublecomplex *x, integer *incx, + doublecomplex *beta, doublecomplex *y, integer *incy, ftnlen uplo_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; + doublereal d__1; + doublecomplex z__1, z__2, z__3, z__4; + + /* Builtin functions */ + void d_cnjg(doublecomplex *, doublecomplex *); + + /* Local variables */ + integer i__, j, ix, iy, jx, jy, kx, ky, info; + doublecomplex temp1, temp2; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + + +/* -- Reference BLAS level2 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --x; + --y; + + /* Function Body */ + info = 0; + if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", ( + ftnlen)1, (ftnlen)1)) { + info = 1; + } else if (*n < 0) { + info = 2; + } else if (*lda < max(1,*n)) { + info = 5; + } else if (*incx == 0) { + info = 7; + } else if (*incy == 0) { + info = 10; + } + if (info != 0) { + xerbla_((char *)"ZHEMV ", &info, (ftnlen)6); + return 0; + } + +/* Quick return if possible. */ + + if (*n == 0 || alpha->r == 0. && alpha->i == 0. && (beta->r == 1. && + beta->i == 0.)) { + return 0; + } + +/* Set up the start points in X and Y. */ + + if (*incx > 0) { + kx = 1; + } else { + kx = 1 - (*n - 1) * *incx; + } + if (*incy > 0) { + ky = 1; + } else { + ky = 1 - (*n - 1) * *incy; + } + +/* Start the operations. In this version the elements of A are */ +/* accessed sequentially with one pass through the triangular part */ +/* of A. */ + +/* First form y := beta*y. */ + + if (beta->r != 1. || beta->i != 0.) { + if (*incy == 1) { + if (beta->r == 0. && beta->i == 0.) { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__; + y[i__2].r = 0., y[i__2].i = 0.; +/* L10: */ + } + } else { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__; + i__3 = i__; + z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i, + z__1.i = beta->r * y[i__3].i + beta->i * y[i__3] + .r; + y[i__2].r = z__1.r, y[i__2].i = z__1.i; +/* L20: */ + } + } + } else { + iy = ky; + if (beta->r == 0. && beta->i == 0.) { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = iy; + y[i__2].r = 0., y[i__2].i = 0.; + iy += *incy; +/* L30: */ + } + } else { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = iy; + i__3 = iy; + z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i, + z__1.i = beta->r * y[i__3].i + beta->i * y[i__3] + .r; + y[i__2].r = z__1.r, y[i__2].i = z__1.i; + iy += *incy; +/* L40: */ + } + } + } + } + if (alpha->r == 0. && alpha->i == 0.) { + return 0; + } + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + +/* Form y when A is stored in upper triangle. */ + + if (*incx == 1 && *incy == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i = + alpha->r * x[i__2].i + alpha->i * x[i__2].r; + temp1.r = z__1.r, temp1.i = z__1.i; + temp2.r = 0., temp2.i = 0.; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__; + i__4 = i__; + i__5 = i__ + j * a_dim1; + z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, + z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5] + .r; + z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; + y[i__3].r = z__1.r, y[i__3].i = z__1.i; + d_cnjg(&z__3, &a[i__ + j * a_dim1]); + i__3 = i__; + z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = + z__3.r * x[i__3].i + z__3.i * x[i__3].r; + z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; + temp2.r = z__1.r, temp2.i = z__1.i; +/* L50: */ + } + i__2 = j; + i__3 = j; + i__4 = j + j * a_dim1; + d__1 = a[i__4].r; + z__3.r = d__1 * temp1.r, z__3.i = d__1 * temp1.i; + z__2.r = y[i__3].r + z__3.r, z__2.i = y[i__3].i + z__3.i; + z__4.r = alpha->r * temp2.r - alpha->i * temp2.i, z__4.i = + alpha->r * temp2.i + alpha->i * temp2.r; + z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; + y[i__2].r = z__1.r, y[i__2].i = z__1.i; +/* L60: */ + } + } else { + jx = kx; + jy = ky; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = jx; + z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i = + alpha->r * x[i__2].i + alpha->i * x[i__2].r; + temp1.r = z__1.r, temp1.i = z__1.i; + temp2.r = 0., temp2.i = 0.; + ix = kx; + iy = ky; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = iy; + i__4 = iy; + i__5 = i__ + j * a_dim1; + z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, + z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5] + .r; + z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; + y[i__3].r = z__1.r, y[i__3].i = z__1.i; + d_cnjg(&z__3, &a[i__ + j * a_dim1]); + i__3 = ix; + z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = + z__3.r * x[i__3].i + z__3.i * x[i__3].r; + z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; + temp2.r = z__1.r, temp2.i = z__1.i; + ix += *incx; + iy += *incy; +/* L70: */ + } + i__2 = jy; + i__3 = jy; + i__4 = j + j * a_dim1; + d__1 = a[i__4].r; + z__3.r = d__1 * temp1.r, z__3.i = d__1 * temp1.i; + z__2.r = y[i__3].r + z__3.r, z__2.i = y[i__3].i + z__3.i; + z__4.r = alpha->r * temp2.r - alpha->i * temp2.i, z__4.i = + alpha->r * temp2.i + alpha->i * temp2.r; + z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; + y[i__2].r = z__1.r, y[i__2].i = z__1.i; + jx += *incx; + jy += *incy; +/* L80: */ + } + } + } else { + +/* Form y when A is stored in lower triangle. */ + + if (*incx == 1 && *incy == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i = + alpha->r * x[i__2].i + alpha->i * x[i__2].r; + temp1.r = z__1.r, temp1.i = z__1.i; + temp2.r = 0., temp2.i = 0.; + i__2 = j; + i__3 = j; + i__4 = j + j * a_dim1; + d__1 = a[i__4].r; + z__2.r = d__1 * temp1.r, z__2.i = d__1 * temp1.i; + z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i; + y[i__2].r = z__1.r, y[i__2].i = z__1.i; + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + i__3 = i__; + i__4 = i__; + i__5 = i__ + j * a_dim1; + z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, + z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5] + .r; + z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; + y[i__3].r = z__1.r, y[i__3].i = z__1.i; + d_cnjg(&z__3, &a[i__ + j * a_dim1]); + i__3 = i__; + z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = + z__3.r * x[i__3].i + z__3.i * x[i__3].r; + z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; + temp2.r = z__1.r, temp2.i = z__1.i; +/* L90: */ + } + i__2 = j; + i__3 = j; + z__2.r = alpha->r * temp2.r - alpha->i * temp2.i, z__2.i = + alpha->r * temp2.i + alpha->i * temp2.r; + z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i; + y[i__2].r = z__1.r, y[i__2].i = z__1.i; +/* L100: */ + } + } else { + jx = kx; + jy = ky; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = jx; + z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i = + alpha->r * x[i__2].i + alpha->i * x[i__2].r; + temp1.r = z__1.r, temp1.i = z__1.i; + temp2.r = 0., temp2.i = 0.; + i__2 = jy; + i__3 = jy; + i__4 = j + j * a_dim1; + d__1 = a[i__4].r; + z__2.r = d__1 * temp1.r, z__2.i = d__1 * temp1.i; + z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i; + y[i__2].r = z__1.r, y[i__2].i = z__1.i; + ix = jx; + iy = jy; + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + ix += *incx; + iy += *incy; + i__3 = iy; + i__4 = iy; + i__5 = i__ + j * a_dim1; + z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, + z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5] + .r; + z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; + y[i__3].r = z__1.r, y[i__3].i = z__1.i; + d_cnjg(&z__3, &a[i__ + j * a_dim1]); + i__3 = ix; + z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = + z__3.r * x[i__3].i + z__3.i * x[i__3].r; + z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; + temp2.r = z__1.r, temp2.i = z__1.i; +/* L110: */ + } + i__2 = jy; + i__3 = jy; + z__2.r = alpha->r * temp2.r - alpha->i * temp2.i, z__2.i = + alpha->r * temp2.i + alpha->i * temp2.r; + z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i; + y[i__2].r = z__1.r, y[i__2].i = z__1.i; + jx += *incx; + jy += *incy; +/* L120: */ + } + } + } + + return 0; + +/* End of ZHEMV */ + +} /* zhemv_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zher2.cpp b/lib/linalg/zher2.cpp new file mode 100644 index 0000000000..2f77acd257 --- /dev/null +++ b/lib/linalg/zher2.cpp @@ -0,0 +1,519 @@ +/* fortran/zher2.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b ZHER2 */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZHER2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA) */ + +/* .. Scalar Arguments .. */ +/* COMPLEX*16 ALPHA */ +/* INTEGER INCX,INCY,LDA,N */ +/* CHARACTER UPLO */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 A(LDA,*),X(*),Y(*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZHER2 performs the hermitian rank 2 operation */ +/* > */ +/* > A := alpha*x*y**H + conjg( alpha )*y*x**H + A, */ +/* > */ +/* > where alpha is a scalar, x and y are n element vectors and A is an n */ +/* > by n hermitian matrix. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > On entry, UPLO specifies whether the upper or lower */ +/* > triangular part of the array A is to be referenced as */ +/* > follows: */ +/* > */ +/* > UPLO = 'U' or 'u' Only the upper triangular part of A */ +/* > is to be referenced. */ +/* > */ +/* > UPLO = 'L' or 'l' Only the lower triangular part of A */ +/* > is to be referenced. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > On entry, N specifies the order of the matrix A. */ +/* > N must be at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] ALPHA */ +/* > \verbatim */ +/* > ALPHA is COMPLEX*16 */ +/* > On entry, ALPHA specifies the scalar alpha. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] X */ +/* > \verbatim */ +/* > X is COMPLEX*16 array, dimension at least */ +/* > ( 1 + ( n - 1 )*abs( INCX ) ). */ +/* > Before entry, the incremented array X must contain the n */ +/* > element vector x. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > On entry, INCX specifies the increment for the elements of */ +/* > X. INCX must not be zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] Y */ +/* > \verbatim */ +/* > Y is COMPLEX*16 array, dimension at least */ +/* > ( 1 + ( n - 1 )*abs( INCY ) ). */ +/* > Before entry, the incremented array Y must contain the n */ +/* > element vector y. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCY */ +/* > \verbatim */ +/* > INCY is INTEGER */ +/* > On entry, INCY specifies the increment for the elements of */ +/* > Y. INCY must not be zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is COMPLEX*16 array, dimension ( LDA, N ) */ +/* > Before entry with UPLO = 'U' or 'u', the leading n by n */ +/* > upper triangular part of the array A must contain the upper */ +/* > triangular part of the hermitian matrix and the strictly */ +/* > lower triangular part of A is not referenced. On exit, the */ +/* > upper triangular part of the array A is overwritten by the */ +/* > upper triangular part of the updated matrix. */ +/* > Before entry with UPLO = 'L' or 'l', the leading n by n */ +/* > lower triangular part of the array A must contain the lower */ +/* > triangular part of the hermitian matrix and the strictly */ +/* > upper triangular part of A is not referenced. On exit, the */ +/* > lower triangular part of the array A is overwritten by the */ +/* > lower triangular part of the updated matrix. */ +/* > Note that the imaginary parts of the diagonal elements need */ +/* > not be set, they are assumed to be zero, and on exit they */ +/* > are set to zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > On entry, LDA specifies the first dimension of A as declared */ +/* > in the calling (sub) program. LDA must be at least */ +/* > max( 1, n ). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16_blas_level2 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > Level 2 Blas routine. */ +/* > */ +/* > -- Written on 22-October-1986. */ +/* > Jack Dongarra, Argonne National Lab. */ +/* > Jeremy Du Croz, Nag Central Office. */ +/* > Sven Hammarling, Nag Central Office. */ +/* > Richard Hanson, Sandia National Labs. */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int zher2_(char *uplo, integer *n, doublecomplex *alpha, + doublecomplex *x, integer *incx, doublecomplex *y, integer *incy, + doublecomplex *a, integer *lda, ftnlen uplo_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6; + doublereal d__1; + doublecomplex z__1, z__2, z__3, z__4; + + /* Builtin functions */ + void d_cnjg(doublecomplex *, doublecomplex *); + + /* Local variables */ + integer i__, j, ix, iy, jx, jy, kx, ky, info; + doublecomplex temp1, temp2; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + + +/* -- Reference BLAS level2 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --x; + --y; + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + + /* Function Body */ + info = 0; + if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", ( + ftnlen)1, (ftnlen)1)) { + info = 1; + } else if (*n < 0) { + info = 2; + } else if (*incx == 0) { + info = 5; + } else if (*incy == 0) { + info = 7; + } else if (*lda < max(1,*n)) { + info = 9; + } + if (info != 0) { + xerbla_((char *)"ZHER2 ", &info, (ftnlen)6); + return 0; + } + +/* Quick return if possible. */ + + if (*n == 0 || alpha->r == 0. && alpha->i == 0.) { + return 0; + } + +/* Set up the start points in X and Y if the increments are not both */ +/* unity. */ + + if (*incx != 1 || *incy != 1) { + if (*incx > 0) { + kx = 1; + } else { + kx = 1 - (*n - 1) * *incx; + } + if (*incy > 0) { + ky = 1; + } else { + ky = 1 - (*n - 1) * *incy; + } + jx = kx; + jy = ky; + } + +/* Start the operations. In this version the elements of A are */ +/* accessed sequentially with one pass through the triangular part */ +/* of A. */ + + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + +/* Form A when A is stored in the upper triangle. */ + + if (*incx == 1 && *incy == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + i__3 = j; + if (x[i__2].r != 0. || x[i__2].i != 0. || (y[i__3].r != 0. || + y[i__3].i != 0.)) { + d_cnjg(&z__2, &y[j]); + z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = + alpha->r * z__2.i + alpha->i * z__2.r; + temp1.r = z__1.r, temp1.i = z__1.i; + i__2 = j; + z__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, + z__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2] + .r; + d_cnjg(&z__1, &z__2); + temp2.r = z__1.r, temp2.i = z__1.i; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + i__4 = i__ + j * a_dim1; + i__5 = i__; + z__3.r = x[i__5].r * temp1.r - x[i__5].i * temp1.i, + z__3.i = x[i__5].r * temp1.i + x[i__5].i * + temp1.r; + z__2.r = a[i__4].r + z__3.r, z__2.i = a[i__4].i + + z__3.i; + i__6 = i__; + z__4.r = y[i__6].r * temp2.r - y[i__6].i * temp2.i, + z__4.i = y[i__6].r * temp2.i + y[i__6].i * + temp2.r; + z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; +/* L10: */ + } + i__2 = j + j * a_dim1; + i__3 = j + j * a_dim1; + i__4 = j; + z__2.r = x[i__4].r * temp1.r - x[i__4].i * temp1.i, + z__2.i = x[i__4].r * temp1.i + x[i__4].i * + temp1.r; + i__5 = j; + z__3.r = y[i__5].r * temp2.r - y[i__5].i * temp2.i, + z__3.i = y[i__5].r * temp2.i + y[i__5].i * + temp2.r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; + d__1 = a[i__3].r + z__1.r; + a[i__2].r = d__1, a[i__2].i = 0.; + } else { + i__2 = j + j * a_dim1; + i__3 = j + j * a_dim1; + d__1 = a[i__3].r; + a[i__2].r = d__1, a[i__2].i = 0.; + } +/* L20: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = jx; + i__3 = jy; + if (x[i__2].r != 0. || x[i__2].i != 0. || (y[i__3].r != 0. || + y[i__3].i != 0.)) { + d_cnjg(&z__2, &y[jy]); + z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = + alpha->r * z__2.i + alpha->i * z__2.r; + temp1.r = z__1.r, temp1.i = z__1.i; + i__2 = jx; + z__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, + z__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2] + .r; + d_cnjg(&z__1, &z__2); + temp2.r = z__1.r, temp2.i = z__1.i; + ix = kx; + iy = ky; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + i__4 = i__ + j * a_dim1; + i__5 = ix; + z__3.r = x[i__5].r * temp1.r - x[i__5].i * temp1.i, + z__3.i = x[i__5].r * temp1.i + x[i__5].i * + temp1.r; + z__2.r = a[i__4].r + z__3.r, z__2.i = a[i__4].i + + z__3.i; + i__6 = iy; + z__4.r = y[i__6].r * temp2.r - y[i__6].i * temp2.i, + z__4.i = y[i__6].r * temp2.i + y[i__6].i * + temp2.r; + z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; + ix += *incx; + iy += *incy; +/* L30: */ + } + i__2 = j + j * a_dim1; + i__3 = j + j * a_dim1; + i__4 = jx; + z__2.r = x[i__4].r * temp1.r - x[i__4].i * temp1.i, + z__2.i = x[i__4].r * temp1.i + x[i__4].i * + temp1.r; + i__5 = jy; + z__3.r = y[i__5].r * temp2.r - y[i__5].i * temp2.i, + z__3.i = y[i__5].r * temp2.i + y[i__5].i * + temp2.r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; + d__1 = a[i__3].r + z__1.r; + a[i__2].r = d__1, a[i__2].i = 0.; + } else { + i__2 = j + j * a_dim1; + i__3 = j + j * a_dim1; + d__1 = a[i__3].r; + a[i__2].r = d__1, a[i__2].i = 0.; + } + jx += *incx; + jy += *incy; +/* L40: */ + } + } + } else { + +/* Form A when A is stored in the lower triangle. */ + + if (*incx == 1 && *incy == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + i__3 = j; + if (x[i__2].r != 0. || x[i__2].i != 0. || (y[i__3].r != 0. || + y[i__3].i != 0.)) { + d_cnjg(&z__2, &y[j]); + z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = + alpha->r * z__2.i + alpha->i * z__2.r; + temp1.r = z__1.r, temp1.i = z__1.i; + i__2 = j; + z__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, + z__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2] + .r; + d_cnjg(&z__1, &z__2); + temp2.r = z__1.r, temp2.i = z__1.i; + i__2 = j + j * a_dim1; + i__3 = j + j * a_dim1; + i__4 = j; + z__2.r = x[i__4].r * temp1.r - x[i__4].i * temp1.i, + z__2.i = x[i__4].r * temp1.i + x[i__4].i * + temp1.r; + i__5 = j; + z__3.r = y[i__5].r * temp2.r - y[i__5].i * temp2.i, + z__3.i = y[i__5].r * temp2.i + y[i__5].i * + temp2.r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; + d__1 = a[i__3].r + z__1.r; + a[i__2].r = d__1, a[i__2].i = 0.; + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + i__4 = i__ + j * a_dim1; + i__5 = i__; + z__3.r = x[i__5].r * temp1.r - x[i__5].i * temp1.i, + z__3.i = x[i__5].r * temp1.i + x[i__5].i * + temp1.r; + z__2.r = a[i__4].r + z__3.r, z__2.i = a[i__4].i + + z__3.i; + i__6 = i__; + z__4.r = y[i__6].r * temp2.r - y[i__6].i * temp2.i, + z__4.i = y[i__6].r * temp2.i + y[i__6].i * + temp2.r; + z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; +/* L50: */ + } + } else { + i__2 = j + j * a_dim1; + i__3 = j + j * a_dim1; + d__1 = a[i__3].r; + a[i__2].r = d__1, a[i__2].i = 0.; + } +/* L60: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = jx; + i__3 = jy; + if (x[i__2].r != 0. || x[i__2].i != 0. || (y[i__3].r != 0. || + y[i__3].i != 0.)) { + d_cnjg(&z__2, &y[jy]); + z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = + alpha->r * z__2.i + alpha->i * z__2.r; + temp1.r = z__1.r, temp1.i = z__1.i; + i__2 = jx; + z__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, + z__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2] + .r; + d_cnjg(&z__1, &z__2); + temp2.r = z__1.r, temp2.i = z__1.i; + i__2 = j + j * a_dim1; + i__3 = j + j * a_dim1; + i__4 = jx; + z__2.r = x[i__4].r * temp1.r - x[i__4].i * temp1.i, + z__2.i = x[i__4].r * temp1.i + x[i__4].i * + temp1.r; + i__5 = jy; + z__3.r = y[i__5].r * temp2.r - y[i__5].i * temp2.i, + z__3.i = y[i__5].r * temp2.i + y[i__5].i * + temp2.r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; + d__1 = a[i__3].r + z__1.r; + a[i__2].r = d__1, a[i__2].i = 0.; + ix = jx; + iy = jy; + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + ix += *incx; + iy += *incy; + i__3 = i__ + j * a_dim1; + i__4 = i__ + j * a_dim1; + i__5 = ix; + z__3.r = x[i__5].r * temp1.r - x[i__5].i * temp1.i, + z__3.i = x[i__5].r * temp1.i + x[i__5].i * + temp1.r; + z__2.r = a[i__4].r + z__3.r, z__2.i = a[i__4].i + + z__3.i; + i__6 = iy; + z__4.r = y[i__6].r * temp2.r - y[i__6].i * temp2.i, + z__4.i = y[i__6].r * temp2.i + y[i__6].i * + temp2.r; + z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; +/* L70: */ + } + } else { + i__2 = j + j * a_dim1; + i__3 = j + j * a_dim1; + d__1 = a[i__3].r; + a[i__2].r = d__1, a[i__2].i = 0.; + } + jx += *incx; + jy += *incy; +/* L80: */ + } + } + } + + return 0; + +/* End of ZHER2 */ + +} /* zher2_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zher2k.cpp b/lib/linalg/zher2k.cpp new file mode 100644 index 0000000000..1b94010d33 --- /dev/null +++ b/lib/linalg/zher2k.cpp @@ -0,0 +1,750 @@ +/* fortran/zher2k.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b ZHER2K */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZHER2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) */ + +/* .. Scalar Arguments .. */ +/* COMPLEX*16 ALPHA */ +/* DOUBLE PRECISION BETA */ +/* INTEGER K,LDA,LDB,LDC,N */ +/* CHARACTER TRANS,UPLO */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZHER2K performs one of the hermitian rank 2k operations */ +/* > */ +/* > C := alpha*A*B**H + conjg( alpha )*B*A**H + beta*C, */ +/* > */ +/* > or */ +/* > */ +/* > C := alpha*A**H*B + conjg( alpha )*B**H*A + beta*C, */ +/* > */ +/* > where alpha and beta are scalars with beta real, C is an n by n */ +/* > hermitian matrix and A and B are n by k matrices in the first case */ +/* > and k by n matrices in the second case. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > On entry, UPLO specifies whether the upper or lower */ +/* > triangular part of the array C is to be referenced as */ +/* > follows: */ +/* > */ +/* > UPLO = 'U' or 'u' Only the upper triangular part of C */ +/* > is to be referenced. */ +/* > */ +/* > UPLO = 'L' or 'l' Only the lower triangular part of C */ +/* > is to be referenced. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TRANS */ +/* > \verbatim */ +/* > TRANS is CHARACTER*1 */ +/* > On entry, TRANS specifies the operation to be performed as */ +/* > follows: */ +/* > */ +/* > TRANS = 'N' or 'n' C := alpha*A*B**H + */ +/* > conjg( alpha )*B*A**H + */ +/* > beta*C. */ +/* > */ +/* > TRANS = 'C' or 'c' C := alpha*A**H*B + */ +/* > conjg( alpha )*B**H*A + */ +/* > beta*C. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > On entry, N specifies the order of the matrix C. N must be */ +/* > at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > On entry with TRANS = 'N' or 'n', K specifies the number */ +/* > of columns of the matrices A and B, and on entry with */ +/* > TRANS = 'C' or 'c', K specifies the number of rows of the */ +/* > matrices A and B. K must be at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] ALPHA */ +/* > \verbatim */ +/* > ALPHA is COMPLEX*16 . */ +/* > On entry, ALPHA specifies the scalar alpha. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is COMPLEX*16 array, dimension ( LDA, ka ), where ka is */ +/* > k when TRANS = 'N' or 'n', and is n otherwise. */ +/* > Before entry with TRANS = 'N' or 'n', the leading n by k */ +/* > part of the array A must contain the matrix A, otherwise */ +/* > the leading k by n part of the array A must contain the */ +/* > matrix A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > On entry, LDA specifies the first dimension of A as declared */ +/* > in the calling (sub) program. When TRANS = 'N' or 'n' */ +/* > then LDA must be at least max( 1, n ), otherwise LDA must */ +/* > be at least max( 1, k ). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] B */ +/* > \verbatim */ +/* > B is COMPLEX*16 array, dimension ( LDB, kb ), where kb is */ +/* > k when TRANS = 'N' or 'n', and is n otherwise. */ +/* > Before entry with TRANS = 'N' or 'n', the leading n by k */ +/* > part of the array B must contain the matrix B, otherwise */ +/* > the leading k by n part of the array B must contain the */ +/* > matrix B. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDB */ +/* > \verbatim */ +/* > LDB is INTEGER */ +/* > On entry, LDB specifies the first dimension of B as declared */ +/* > in the calling (sub) program. When TRANS = 'N' or 'n' */ +/* > then LDB must be at least max( 1, n ), otherwise LDB must */ +/* > be at least max( 1, k ). */ +/* > Unchanged on exit. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] BETA */ +/* > \verbatim */ +/* > BETA is DOUBLE PRECISION . */ +/* > On entry, BETA specifies the scalar beta. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] C */ +/* > \verbatim */ +/* > C is COMPLEX*16 array, dimension ( LDC, N ) */ +/* > Before entry with UPLO = 'U' or 'u', the leading n by n */ +/* > upper triangular part of the array C must contain the upper */ +/* > triangular part of the hermitian matrix and the strictly */ +/* > lower triangular part of C is not referenced. On exit, the */ +/* > upper triangular part of the array C is overwritten by the */ +/* > upper triangular part of the updated matrix. */ +/* > Before entry with UPLO = 'L' or 'l', the leading n by n */ +/* > lower triangular part of the array C must contain the lower */ +/* > triangular part of the hermitian matrix and the strictly */ +/* > upper triangular part of C is not referenced. On exit, the */ +/* > lower triangular part of the array C is overwritten by the */ +/* > lower triangular part of the updated matrix. */ +/* > Note that the imaginary parts of the diagonal elements need */ +/* > not be set, they are assumed to be zero, and on exit they */ +/* > are set to zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDC */ +/* > \verbatim */ +/* > LDC is INTEGER */ +/* > On entry, LDC specifies the first dimension of C as declared */ +/* > in the calling (sub) program. LDC must be at least */ +/* > max( 1, n ). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16_blas_level3 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > Level 3 Blas routine. */ +/* > */ +/* > -- Written on 8-February-1989. */ +/* > Jack Dongarra, Argonne National Laboratory. */ +/* > Iain Duff, AERE Harwell. */ +/* > Jeremy Du Croz, Numerical Algorithms Group Ltd. */ +/* > Sven Hammarling, Numerical Algorithms Group Ltd. */ +/* > */ +/* > -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1. */ +/* > Ed Anderson, Cray Research Inc. */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int zher2k_(char *uplo, char *trans, integer *n, integer *k, + doublecomplex *alpha, doublecomplex *a, integer *lda, doublecomplex * + b, integer *ldb, doublereal *beta, doublecomplex *c__, integer *ldc, + ftnlen uplo_len, ftnlen trans_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, + i__3, i__4, i__5, i__6, i__7; + doublereal d__1; + doublecomplex z__1, z__2, z__3, z__4, z__5, z__6; + + /* Builtin functions */ + void d_cnjg(doublecomplex *, doublecomplex *); + + /* Local variables */ + integer i__, j, l, info; + doublecomplex temp1, temp2; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + integer nrowa; + logical upper; + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + + +/* -- Reference BLAS level3 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Parameters .. */ +/* .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + b_dim1 = *ldb; + b_offset = 1 + b_dim1; + b -= b_offset; + c_dim1 = *ldc; + c_offset = 1 + c_dim1; + c__ -= c_offset; + + /* Function Body */ + if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { + nrowa = *n; + } else { + nrowa = *k; + } + upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); + + info = 0; + if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + info = 1; + } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, + (char *)"C", (ftnlen)1, (ftnlen)1)) { + info = 2; + } else if (*n < 0) { + info = 3; + } else if (*k < 0) { + info = 4; + } else if (*lda < max(1,nrowa)) { + info = 7; + } else if (*ldb < max(1,nrowa)) { + info = 9; + } else if (*ldc < max(1,*n)) { + info = 12; + } + if (info != 0) { + xerbla_((char *)"ZHER2K", &info, (ftnlen)6); + return 0; + } + +/* Quick return if possible. */ + + if (*n == 0 || (alpha->r == 0. && alpha->i == 0. || *k == 0) && *beta == + 1.) { + return 0; + } + +/* And when alpha.eq.zero. */ + + if (alpha->r == 0. && alpha->i == 0.) { + if (upper) { + if (*beta == 0.) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + c__[i__3].r = 0., c__[i__3].i = 0.; +/* L10: */ + } +/* L20: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + i__4 = i__ + j * c_dim1; + z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[ + i__4].i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; +/* L30: */ + } + i__2 = j + j * c_dim1; + i__3 = j + j * c_dim1; + d__1 = *beta * c__[i__3].r; + c__[i__2].r = d__1, c__[i__2].i = 0.; +/* L40: */ + } + } + } else { + if (*beta == 0.) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = j; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + c__[i__3].r = 0., c__[i__3].i = 0.; +/* L50: */ + } +/* L60: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j + j * c_dim1; + i__3 = j + j * c_dim1; + d__1 = *beta * c__[i__3].r; + c__[i__2].r = d__1, c__[i__2].i = 0.; + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + i__4 = i__ + j * c_dim1; + z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[ + i__4].i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; +/* L70: */ + } +/* L80: */ + } + } + } + return 0; + } + +/* Start the operations. */ + + if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { + +/* Form C := alpha*A*B**H + conjg( alpha )*B*A**H + */ +/* C. */ + + if (upper) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (*beta == 0.) { + i__2 = j; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + c__[i__3].r = 0., c__[i__3].i = 0.; +/* L90: */ + } + } else if (*beta != 1.) { + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + i__4 = i__ + j * c_dim1; + z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[ + i__4].i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; +/* L100: */ + } + i__2 = j + j * c_dim1; + i__3 = j + j * c_dim1; + d__1 = *beta * c__[i__3].r; + c__[i__2].r = d__1, c__[i__2].i = 0.; + } else { + i__2 = j + j * c_dim1; + i__3 = j + j * c_dim1; + d__1 = c__[i__3].r; + c__[i__2].r = d__1, c__[i__2].i = 0.; + } + i__2 = *k; + for (l = 1; l <= i__2; ++l) { + i__3 = j + l * a_dim1; + i__4 = j + l * b_dim1; + if (a[i__3].r != 0. || a[i__3].i != 0. || (b[i__4].r != + 0. || b[i__4].i != 0.)) { + d_cnjg(&z__2, &b[j + l * b_dim1]); + z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, + z__1.i = alpha->r * z__2.i + alpha->i * + z__2.r; + temp1.r = z__1.r, temp1.i = z__1.i; + i__3 = j + l * a_dim1; + z__2.r = alpha->r * a[i__3].r - alpha->i * a[i__3].i, + z__2.i = alpha->r * a[i__3].i + alpha->i * a[ + i__3].r; + d_cnjg(&z__1, &z__2); + temp2.r = z__1.r, temp2.i = z__1.i; + i__3 = j - 1; + for (i__ = 1; i__ <= i__3; ++i__) { + i__4 = i__ + j * c_dim1; + i__5 = i__ + j * c_dim1; + i__6 = i__ + l * a_dim1; + z__3.r = a[i__6].r * temp1.r - a[i__6].i * + temp1.i, z__3.i = a[i__6].r * temp1.i + a[ + i__6].i * temp1.r; + z__2.r = c__[i__5].r + z__3.r, z__2.i = c__[i__5] + .i + z__3.i; + i__7 = i__ + l * b_dim1; + z__4.r = b[i__7].r * temp2.r - b[i__7].i * + temp2.i, z__4.i = b[i__7].r * temp2.i + b[ + i__7].i * temp2.r; + z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + + z__4.i; + c__[i__4].r = z__1.r, c__[i__4].i = z__1.i; +/* L110: */ + } + i__3 = j + j * c_dim1; + i__4 = j + j * c_dim1; + i__5 = j + l * a_dim1; + z__2.r = a[i__5].r * temp1.r - a[i__5].i * temp1.i, + z__2.i = a[i__5].r * temp1.i + a[i__5].i * + temp1.r; + i__6 = j + l * b_dim1; + z__3.r = b[i__6].r * temp2.r - b[i__6].i * temp2.i, + z__3.i = b[i__6].r * temp2.i + b[i__6].i * + temp2.r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; + d__1 = c__[i__4].r + z__1.r; + c__[i__3].r = d__1, c__[i__3].i = 0.; + } +/* L120: */ + } +/* L130: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (*beta == 0.) { + i__2 = *n; + for (i__ = j; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + c__[i__3].r = 0., c__[i__3].i = 0.; +/* L140: */ + } + } else if (*beta != 1.) { + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + i__4 = i__ + j * c_dim1; + z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[ + i__4].i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; +/* L150: */ + } + i__2 = j + j * c_dim1; + i__3 = j + j * c_dim1; + d__1 = *beta * c__[i__3].r; + c__[i__2].r = d__1, c__[i__2].i = 0.; + } else { + i__2 = j + j * c_dim1; + i__3 = j + j * c_dim1; + d__1 = c__[i__3].r; + c__[i__2].r = d__1, c__[i__2].i = 0.; + } + i__2 = *k; + for (l = 1; l <= i__2; ++l) { + i__3 = j + l * a_dim1; + i__4 = j + l * b_dim1; + if (a[i__3].r != 0. || a[i__3].i != 0. || (b[i__4].r != + 0. || b[i__4].i != 0.)) { + d_cnjg(&z__2, &b[j + l * b_dim1]); + z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, + z__1.i = alpha->r * z__2.i + alpha->i * + z__2.r; + temp1.r = z__1.r, temp1.i = z__1.i; + i__3 = j + l * a_dim1; + z__2.r = alpha->r * a[i__3].r - alpha->i * a[i__3].i, + z__2.i = alpha->r * a[i__3].i + alpha->i * a[ + i__3].r; + d_cnjg(&z__1, &z__2); + temp2.r = z__1.r, temp2.i = z__1.i; + i__3 = *n; + for (i__ = j + 1; i__ <= i__3; ++i__) { + i__4 = i__ + j * c_dim1; + i__5 = i__ + j * c_dim1; + i__6 = i__ + l * a_dim1; + z__3.r = a[i__6].r * temp1.r - a[i__6].i * + temp1.i, z__3.i = a[i__6].r * temp1.i + a[ + i__6].i * temp1.r; + z__2.r = c__[i__5].r + z__3.r, z__2.i = c__[i__5] + .i + z__3.i; + i__7 = i__ + l * b_dim1; + z__4.r = b[i__7].r * temp2.r - b[i__7].i * + temp2.i, z__4.i = b[i__7].r * temp2.i + b[ + i__7].i * temp2.r; + z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + + z__4.i; + c__[i__4].r = z__1.r, c__[i__4].i = z__1.i; +/* L160: */ + } + i__3 = j + j * c_dim1; + i__4 = j + j * c_dim1; + i__5 = j + l * a_dim1; + z__2.r = a[i__5].r * temp1.r - a[i__5].i * temp1.i, + z__2.i = a[i__5].r * temp1.i + a[i__5].i * + temp1.r; + i__6 = j + l * b_dim1; + z__3.r = b[i__6].r * temp2.r - b[i__6].i * temp2.i, + z__3.i = b[i__6].r * temp2.i + b[i__6].i * + temp2.r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; + d__1 = c__[i__4].r + z__1.r; + c__[i__3].r = d__1, c__[i__3].i = 0.; + } +/* L170: */ + } +/* L180: */ + } + } + } else { + +/* Form C := alpha*A**H*B + conjg( alpha )*B**H*A + */ +/* C. */ + + if (upper) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + for (i__ = 1; i__ <= i__2; ++i__) { + temp1.r = 0., temp1.i = 0.; + temp2.r = 0., temp2.i = 0.; + i__3 = *k; + for (l = 1; l <= i__3; ++l) { + d_cnjg(&z__3, &a[l + i__ * a_dim1]); + i__4 = l + j * b_dim1; + z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4].i, + z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4] + .r; + z__1.r = temp1.r + z__2.r, z__1.i = temp1.i + z__2.i; + temp1.r = z__1.r, temp1.i = z__1.i; + d_cnjg(&z__3, &b[l + i__ * b_dim1]); + i__4 = l + j * a_dim1; + z__2.r = z__3.r * a[i__4].r - z__3.i * a[i__4].i, + z__2.i = z__3.r * a[i__4].i + z__3.i * a[i__4] + .r; + z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; + temp2.r = z__1.r, temp2.i = z__1.i; +/* L190: */ + } + if (i__ == j) { + if (*beta == 0.) { + i__3 = j + j * c_dim1; + z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, + z__2.i = alpha->r * temp1.i + alpha->i * + temp1.r; + d_cnjg(&z__4, alpha); + z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, + z__3.i = z__4.r * temp2.i + z__4.i * + temp2.r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + d__1 = z__1.r; + c__[i__3].r = d__1, c__[i__3].i = 0.; + } else { + i__3 = j + j * c_dim1; + i__4 = j + j * c_dim1; + z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, + z__2.i = alpha->r * temp1.i + alpha->i * + temp1.r; + d_cnjg(&z__4, alpha); + z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, + z__3.i = z__4.r * temp2.i + z__4.i * + temp2.r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + d__1 = *beta * c__[i__4].r + z__1.r; + c__[i__3].r = d__1, c__[i__3].i = 0.; + } + } else { + if (*beta == 0.) { + i__3 = i__ + j * c_dim1; + z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, + z__2.i = alpha->r * temp1.i + alpha->i * + temp1.r; + d_cnjg(&z__4, alpha); + z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, + z__3.i = z__4.r * temp2.i + z__4.i * + temp2.r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } else { + i__3 = i__ + j * c_dim1; + i__4 = i__ + j * c_dim1; + z__3.r = *beta * c__[i__4].r, z__3.i = *beta * + c__[i__4].i; + z__4.r = alpha->r * temp1.r - alpha->i * temp1.i, + z__4.i = alpha->r * temp1.i + alpha->i * + temp1.r; + z__2.r = z__3.r + z__4.r, z__2.i = z__3.i + + z__4.i; + d_cnjg(&z__6, alpha); + z__5.r = z__6.r * temp2.r - z__6.i * temp2.i, + z__5.i = z__6.r * temp2.i + z__6.i * + temp2.r; + z__1.r = z__2.r + z__5.r, z__1.i = z__2.i + + z__5.i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } + } +/* L200: */ + } +/* L210: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = j; i__ <= i__2; ++i__) { + temp1.r = 0., temp1.i = 0.; + temp2.r = 0., temp2.i = 0.; + i__3 = *k; + for (l = 1; l <= i__3; ++l) { + d_cnjg(&z__3, &a[l + i__ * a_dim1]); + i__4 = l + j * b_dim1; + z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4].i, + z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4] + .r; + z__1.r = temp1.r + z__2.r, z__1.i = temp1.i + z__2.i; + temp1.r = z__1.r, temp1.i = z__1.i; + d_cnjg(&z__3, &b[l + i__ * b_dim1]); + i__4 = l + j * a_dim1; + z__2.r = z__3.r * a[i__4].r - z__3.i * a[i__4].i, + z__2.i = z__3.r * a[i__4].i + z__3.i * a[i__4] + .r; + z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; + temp2.r = z__1.r, temp2.i = z__1.i; +/* L220: */ + } + if (i__ == j) { + if (*beta == 0.) { + i__3 = j + j * c_dim1; + z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, + z__2.i = alpha->r * temp1.i + alpha->i * + temp1.r; + d_cnjg(&z__4, alpha); + z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, + z__3.i = z__4.r * temp2.i + z__4.i * + temp2.r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + d__1 = z__1.r; + c__[i__3].r = d__1, c__[i__3].i = 0.; + } else { + i__3 = j + j * c_dim1; + i__4 = j + j * c_dim1; + z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, + z__2.i = alpha->r * temp1.i + alpha->i * + temp1.r; + d_cnjg(&z__4, alpha); + z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, + z__3.i = z__4.r * temp2.i + z__4.i * + temp2.r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + d__1 = *beta * c__[i__4].r + z__1.r; + c__[i__3].r = d__1, c__[i__3].i = 0.; + } + } else { + if (*beta == 0.) { + i__3 = i__ + j * c_dim1; + z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, + z__2.i = alpha->r * temp1.i + alpha->i * + temp1.r; + d_cnjg(&z__4, alpha); + z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, + z__3.i = z__4.r * temp2.i + z__4.i * + temp2.r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } else { + i__3 = i__ + j * c_dim1; + i__4 = i__ + j * c_dim1; + z__3.r = *beta * c__[i__4].r, z__3.i = *beta * + c__[i__4].i; + z__4.r = alpha->r * temp1.r - alpha->i * temp1.i, + z__4.i = alpha->r * temp1.i + alpha->i * + temp1.r; + z__2.r = z__3.r + z__4.r, z__2.i = z__3.i + + z__4.i; + d_cnjg(&z__6, alpha); + z__5.r = z__6.r * temp2.r - z__6.i * temp2.i, + z__5.i = z__6.r * temp2.i + z__6.i * + temp2.r; + z__1.r = z__2.r + z__5.r, z__1.i = z__2.i + + z__5.i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } + } +/* L230: */ + } +/* L240: */ + } + } + } + + return 0; + +/* End of ZHER2K */ + +} /* zher2k_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zhetd2.cpp b/lib/linalg/zhetd2.cpp new file mode 100644 index 0000000000..c6c59ad6d5 --- /dev/null +++ b/lib/linalg/zhetd2.cpp @@ -0,0 +1,439 @@ +/* fortran/zhetd2.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static doublecomplex c_b2 = {0.,0.}; +static integer c__1 = 1; + +/* > \brief \b ZHETD2 reduces a Hermitian matrix to real symmetric tridiagonal form by an unitary similarity t +ransformation (unblocked algorithm). */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZHETD2 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZHETD2( UPLO, N, A, LDA, D, E, TAU, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER UPLO */ +/* INTEGER INFO, LDA, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION D( * ), E( * ) */ +/* COMPLEX*16 A( LDA, * ), TAU( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZHETD2 reduces a complex Hermitian matrix A to real symmetric */ +/* > tridiagonal form T by a unitary similarity transformation: */ +/* > Q**H * A * Q = T. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > Specifies whether the upper or lower triangular part of the */ +/* > Hermitian matrix A is stored: */ +/* > = 'U': Upper triangular */ +/* > = 'L': Lower triangular */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is COMPLEX*16 array, dimension (LDA,N) */ +/* > On entry, the Hermitian matrix A. If UPLO = 'U', the leading */ +/* > n-by-n upper triangular part of A contains the upper */ +/* > triangular part of the matrix A, and the strictly lower */ +/* > triangular part of A is not referenced. If UPLO = 'L', the */ +/* > leading n-by-n lower triangular part of A contains the lower */ +/* > triangular part of the matrix A, and the strictly upper */ +/* > triangular part of A is not referenced. */ +/* > On exit, if UPLO = 'U', the diagonal and first superdiagonal */ +/* > of A are overwritten by the corresponding elements of the */ +/* > tridiagonal matrix T, and the elements above the first */ +/* > superdiagonal, with the array TAU, represent the unitary */ +/* > matrix Q as a product of elementary reflectors; if UPLO */ +/* > = 'L', the diagonal and first subdiagonal of A are over- */ +/* > written by the corresponding elements of the tridiagonal */ +/* > matrix T, and the elements below the first subdiagonal, with */ +/* > the array TAU, represent the unitary matrix Q as a product */ +/* > of elementary reflectors. See Further Details. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension (N) */ +/* > The diagonal elements of the tridiagonal matrix T: */ +/* > D(i) = A(i,i). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] E */ +/* > \verbatim */ +/* > E is DOUBLE PRECISION array, dimension (N-1) */ +/* > The off-diagonal elements of the tridiagonal matrix T: */ +/* > E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] TAU */ +/* > \verbatim */ +/* > TAU is COMPLEX*16 array, dimension (N-1) */ +/* > The scalar factors of the elementary reflectors (see Further */ +/* > Details). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16HEcomputational */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > If UPLO = 'U', the matrix Q is represented as a product of elementary */ +/* > reflectors */ +/* > */ +/* > Q = H(n-1) . . . H(2) H(1). */ +/* > */ +/* > Each H(i) has the form */ +/* > */ +/* > H(i) = I - tau * v * v**H */ +/* > */ +/* > where tau is a complex scalar, and v is a complex vector with */ +/* > v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in */ +/* > A(1:i-1,i+1), and tau in TAU(i). */ +/* > */ +/* > If UPLO = 'L', the matrix Q is represented as a product of elementary */ +/* > reflectors */ +/* > */ +/* > Q = H(1) H(2) . . . H(n-1). */ +/* > */ +/* > Each H(i) has the form */ +/* > */ +/* > H(i) = I - tau * v * v**H */ +/* > */ +/* > where tau is a complex scalar, and v is a complex vector with */ +/* > v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), */ +/* > and tau in TAU(i). */ +/* > */ +/* > The contents of A on exit are illustrated by the following examples */ +/* > with n = 5: */ +/* > */ +/* > if UPLO = 'U': if UPLO = 'L': */ +/* > */ +/* > ( d e v2 v3 v4 ) ( d ) */ +/* > ( d e v3 v4 ) ( e d ) */ +/* > ( d e v4 ) ( v1 e d ) */ +/* > ( d e ) ( v1 v2 e d ) */ +/* > ( d ) ( v1 v2 v3 e d ) */ +/* > */ +/* > where d and e denote diagonal and off-diagonal elements of T, and vi */ +/* > denotes an element of the vector defining H(i). */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int zhetd2_(char *uplo, integer *n, doublecomplex *a, + integer *lda, doublereal *d__, doublereal *e, doublecomplex *tau, + integer *info, ftnlen uplo_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3; + doublereal d__1; + doublecomplex z__1, z__2, z__3, z__4; + + /* Local variables */ + integer i__; + doublecomplex taui; + extern /* Subroutine */ int zher2_(char *, integer *, doublecomplex *, + doublecomplex *, integer *, doublecomplex *, integer *, + doublecomplex *, integer *, ftnlen); + doublecomplex alpha; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *, + doublecomplex *, integer *, doublecomplex *, integer *); + extern /* Subroutine */ int zhemv_(char *, integer *, doublecomplex *, + doublecomplex *, integer *, doublecomplex *, integer *, + doublecomplex *, doublecomplex *, integer *, ftnlen); + logical upper; + extern /* Subroutine */ int zaxpy_(integer *, doublecomplex *, + doublecomplex *, integer *, doublecomplex *, integer *), xerbla_( + char *, integer *, ftnlen), zlarfg_(integer *, doublecomplex *, + doublecomplex *, integer *, doublecomplex *); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --d__; + --e; + --tau; + + /* Function Body */ + *info = 0; + upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); + if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } else if (*lda < max(1,*n)) { + *info = -4; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"ZHETD2", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*n <= 0) { + return 0; + } + + if (upper) { + +/* Reduce the upper triangle of A */ + + i__1 = *n + *n * a_dim1; + i__2 = *n + *n * a_dim1; + d__1 = a[i__2].r; + a[i__1].r = d__1, a[i__1].i = 0.; + for (i__ = *n - 1; i__ >= 1; --i__) { + +/* Generate elementary reflector H(i) = I - tau * v * v**H */ +/* to annihilate A(1:i-1,i+1) */ + + i__1 = i__ + (i__ + 1) * a_dim1; + alpha.r = a[i__1].r, alpha.i = a[i__1].i; + zlarfg_(&i__, &alpha, &a[(i__ + 1) * a_dim1 + 1], &c__1, &taui); + e[i__] = alpha.r; + + if (taui.r != 0. || taui.i != 0.) { + +/* Apply H(i) from both sides to A(1:i,1:i) */ + + i__1 = i__ + (i__ + 1) * a_dim1; + a[i__1].r = 1., a[i__1].i = 0.; + +/* Compute x := tau * A * v storing x in TAU(1:i) */ + + zhemv_(uplo, &i__, &taui, &a[a_offset], lda, &a[(i__ + 1) * + a_dim1 + 1], &c__1, &c_b2, &tau[1], &c__1, (ftnlen)1); + +/* Compute w := x - 1/2 * tau * (x**H * v) * v */ + + z__3.r = -.5, z__3.i = -0.; + z__2.r = z__3.r * taui.r - z__3.i * taui.i, z__2.i = z__3.r * + taui.i + z__3.i * taui.r; + zdotc_(&z__4, &i__, &tau[1], &c__1, &a[(i__ + 1) * a_dim1 + 1] + , &c__1); + z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, z__1.i = z__2.r * + z__4.i + z__2.i * z__4.r; + alpha.r = z__1.r, alpha.i = z__1.i; + zaxpy_(&i__, &alpha, &a[(i__ + 1) * a_dim1 + 1], &c__1, &tau[ + 1], &c__1); + +/* Apply the transformation as a rank-2 update: */ +/* A := A - v * w**H - w * v**H */ + + z__1.r = -1., z__1.i = -0.; + zher2_(uplo, &i__, &z__1, &a[(i__ + 1) * a_dim1 + 1], &c__1, & + tau[1], &c__1, &a[a_offset], lda, (ftnlen)1); + + } else { + i__1 = i__ + i__ * a_dim1; + i__2 = i__ + i__ * a_dim1; + d__1 = a[i__2].r; + a[i__1].r = d__1, a[i__1].i = 0.; + } + i__1 = i__ + (i__ + 1) * a_dim1; + i__2 = i__; + a[i__1].r = e[i__2], a[i__1].i = 0.; + i__1 = i__ + 1 + (i__ + 1) * a_dim1; + d__[i__ + 1] = a[i__1].r; + i__1 = i__; + tau[i__1].r = taui.r, tau[i__1].i = taui.i; +/* L10: */ + } + i__1 = a_dim1 + 1; + d__[1] = a[i__1].r; + } else { + +/* Reduce the lower triangle of A */ + + i__1 = a_dim1 + 1; + i__2 = a_dim1 + 1; + d__1 = a[i__2].r; + a[i__1].r = d__1, a[i__1].i = 0.; + i__1 = *n - 1; + for (i__ = 1; i__ <= i__1; ++i__) { + +/* Generate elementary reflector H(i) = I - tau * v * v**H */ +/* to annihilate A(i+2:n,i) */ + + i__2 = i__ + 1 + i__ * a_dim1; + alpha.r = a[i__2].r, alpha.i = a[i__2].i; + i__2 = *n - i__; +/* Computing MIN */ + i__3 = i__ + 2; + zlarfg_(&i__2, &alpha, &a[min(i__3,*n) + i__ * a_dim1], &c__1, & + taui); + e[i__] = alpha.r; + + if (taui.r != 0. || taui.i != 0.) { + +/* Apply H(i) from both sides to A(i+1:n,i+1:n) */ + + i__2 = i__ + 1 + i__ * a_dim1; + a[i__2].r = 1., a[i__2].i = 0.; + +/* Compute x := tau * A * v storing y in TAU(i:n-1) */ + + i__2 = *n - i__; + zhemv_(uplo, &i__2, &taui, &a[i__ + 1 + (i__ + 1) * a_dim1], + lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b2, &tau[ + i__], &c__1, (ftnlen)1); + +/* Compute w := x - 1/2 * tau * (x**H * v) * v */ + + z__3.r = -.5, z__3.i = -0.; + z__2.r = z__3.r * taui.r - z__3.i * taui.i, z__2.i = z__3.r * + taui.i + z__3.i * taui.r; + i__2 = *n - i__; + zdotc_(&z__4, &i__2, &tau[i__], &c__1, &a[i__ + 1 + i__ * + a_dim1], &c__1); + z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, z__1.i = z__2.r * + z__4.i + z__2.i * z__4.r; + alpha.r = z__1.r, alpha.i = z__1.i; + i__2 = *n - i__; + zaxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &tau[ + i__], &c__1); + +/* Apply the transformation as a rank-2 update: */ +/* A := A - v * w**H - w * v**H */ + + i__2 = *n - i__; + z__1.r = -1., z__1.i = -0.; + zher2_(uplo, &i__2, &z__1, &a[i__ + 1 + i__ * a_dim1], &c__1, + &tau[i__], &c__1, &a[i__ + 1 + (i__ + 1) * a_dim1], + lda, (ftnlen)1); + + } else { + i__2 = i__ + 1 + (i__ + 1) * a_dim1; + i__3 = i__ + 1 + (i__ + 1) * a_dim1; + d__1 = a[i__3].r; + a[i__2].r = d__1, a[i__2].i = 0.; + } + i__2 = i__ + 1 + i__ * a_dim1; + i__3 = i__; + a[i__2].r = e[i__3], a[i__2].i = 0.; + i__2 = i__ + i__ * a_dim1; + d__[i__] = a[i__2].r; + i__2 = i__; + tau[i__2].r = taui.r, tau[i__2].i = taui.i; +/* L20: */ + } + i__1 = *n + *n * a_dim1; + d__[*n] = a[i__1].r; + } + + return 0; + +/* End of ZHETD2 */ + +} /* zhetd2_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zhetrd.cpp b/lib/linalg/zhetrd.cpp new file mode 100644 index 0000000000..e1c8481bbb --- /dev/null +++ b/lib/linalg/zhetrd.cpp @@ -0,0 +1,463 @@ +/* fortran/zhetrd.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c_n1 = -1; +static integer c__3 = 3; +static integer c__2 = 2; +static doublereal c_b23 = 1.; + +/* > \brief \b ZHETRD */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZHETRD + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZHETRD( UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER UPLO */ +/* INTEGER INFO, LDA, LWORK, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION D( * ), E( * ) */ +/* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZHETRD reduces a complex Hermitian matrix A to real symmetric */ +/* > tridiagonal form T by a unitary similarity transformation: */ +/* > Q**H * A * Q = T. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > = 'U': Upper triangle of A is stored; */ +/* > = 'L': Lower triangle of A is stored. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is COMPLEX*16 array, dimension (LDA,N) */ +/* > On entry, the Hermitian matrix A. If UPLO = 'U', the leading */ +/* > N-by-N upper triangular part of A contains the upper */ +/* > triangular part of the matrix A, and the strictly lower */ +/* > triangular part of A is not referenced. If UPLO = 'L', the */ +/* > leading N-by-N lower triangular part of A contains the lower */ +/* > triangular part of the matrix A, and the strictly upper */ +/* > triangular part of A is not referenced. */ +/* > On exit, if UPLO = 'U', the diagonal and first superdiagonal */ +/* > of A are overwritten by the corresponding elements of the */ +/* > tridiagonal matrix T, and the elements above the first */ +/* > superdiagonal, with the array TAU, represent the unitary */ +/* > matrix Q as a product of elementary reflectors; if UPLO */ +/* > = 'L', the diagonal and first subdiagonal of A are over- */ +/* > written by the corresponding elements of the tridiagonal */ +/* > matrix T, and the elements below the first subdiagonal, with */ +/* > the array TAU, represent the unitary matrix Q as a product */ +/* > of elementary reflectors. See Further Details. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension (N) */ +/* > The diagonal elements of the tridiagonal matrix T: */ +/* > D(i) = A(i,i). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] E */ +/* > \verbatim */ +/* > E is DOUBLE PRECISION array, dimension (N-1) */ +/* > The off-diagonal elements of the tridiagonal matrix T: */ +/* > E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] TAU */ +/* > \verbatim */ +/* > TAU is COMPLEX*16 array, dimension (N-1) */ +/* > The scalar factors of the elementary reflectors (see Further */ +/* > Details). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) */ +/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LWORK */ +/* > \verbatim */ +/* > LWORK is INTEGER */ +/* > The dimension of the array WORK. LWORK >= 1. */ +/* > For optimum performance LWORK >= N*NB, where NB is the */ +/* > optimal blocksize. */ +/* > */ +/* > If LWORK = -1, then a workspace query is assumed; the routine */ +/* > only calculates the optimal size of the WORK array, returns */ +/* > this value as the first entry of the WORK array, and no error */ +/* > message related to LWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16HEcomputational */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > If UPLO = 'U', the matrix Q is represented as a product of elementary */ +/* > reflectors */ +/* > */ +/* > Q = H(n-1) . . . H(2) H(1). */ +/* > */ +/* > Each H(i) has the form */ +/* > */ +/* > H(i) = I - tau * v * v**H */ +/* > */ +/* > where tau is a complex scalar, and v is a complex vector with */ +/* > v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in */ +/* > A(1:i-1,i+1), and tau in TAU(i). */ +/* > */ +/* > If UPLO = 'L', the matrix Q is represented as a product of elementary */ +/* > reflectors */ +/* > */ +/* > Q = H(1) H(2) . . . H(n-1). */ +/* > */ +/* > Each H(i) has the form */ +/* > */ +/* > H(i) = I - tau * v * v**H */ +/* > */ +/* > where tau is a complex scalar, and v is a complex vector with */ +/* > v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), */ +/* > and tau in TAU(i). */ +/* > */ +/* > The contents of A on exit are illustrated by the following examples */ +/* > with n = 5: */ +/* > */ +/* > if UPLO = 'U': if UPLO = 'L': */ +/* > */ +/* > ( d e v2 v3 v4 ) ( d ) */ +/* > ( d e v3 v4 ) ( e d ) */ +/* > ( d e v4 ) ( v1 e d ) */ +/* > ( d e ) ( v1 v2 e d ) */ +/* > ( d ) ( v1 v2 v3 e d ) */ +/* > */ +/* > where d and e denote diagonal and off-diagonal elements of T, and vi */ +/* > denotes an element of the vector defining H(i). */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int zhetrd_(char *uplo, integer *n, doublecomplex *a, + integer *lda, doublereal *d__, doublereal *e, doublecomplex *tau, + doublecomplex *work, integer *lwork, integer *info, ftnlen uplo_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; + doublecomplex z__1; + + /* Local variables */ + integer i__, j, nb, kk, nx, iws; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + integer nbmin, iinfo; + logical upper; + extern /* Subroutine */ int zhetd2_(char *, integer *, doublecomplex *, + integer *, doublereal *, doublereal *, doublecomplex *, integer *, + ftnlen), zher2k_(char *, char *, integer *, integer *, + doublecomplex *, doublecomplex *, integer *, doublecomplex *, + integer *, doublereal *, doublecomplex *, integer *, ftnlen, + ftnlen), xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int zlatrd_(char *, integer *, integer *, + doublecomplex *, integer *, doublereal *, doublecomplex *, + doublecomplex *, integer *, ftnlen); + integer ldwork, lwkopt; + logical lquery; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --d__; + --e; + --tau; + --work; + + /* Function Body */ + *info = 0; + upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); + lquery = *lwork == -1; + if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } else if (*lda < max(1,*n)) { + *info = -4; + } else if (*lwork < 1 && ! lquery) { + *info = -9; + } + + if (*info == 0) { + +/* Determine the block size. */ + + nb = ilaenv_(&c__1, (char *)"ZHETRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, + (ftnlen)1); + lwkopt = *n * nb; + work[1].r = (doublereal) lwkopt, work[1].i = 0.; + } + + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"ZHETRD", &i__1, (ftnlen)6); + return 0; + } else if (lquery) { + return 0; + } + +/* Quick return if possible */ + + if (*n == 0) { + work[1].r = 1., work[1].i = 0.; + return 0; + } + + nx = *n; + iws = 1; + if (nb > 1 && nb < *n) { + +/* Determine when to cross over from blocked to unblocked code */ +/* (last block is always handled by unblocked code). */ + +/* Computing MAX */ + i__1 = nb, i__2 = ilaenv_(&c__3, (char *)"ZHETRD", uplo, n, &c_n1, &c_n1, & + c_n1, (ftnlen)6, (ftnlen)1); + nx = max(i__1,i__2); + if (nx < *n) { + +/* Determine if workspace is large enough for blocked code. */ + + ldwork = *n; + iws = ldwork * nb; + if (*lwork < iws) { + +/* Not enough workspace to use optimal NB: determine the */ +/* minimum value of NB, and reduce NB or force use of */ +/* unblocked code by setting NX = N. */ + +/* Computing MAX */ + i__1 = *lwork / ldwork; + nb = max(i__1,1); + nbmin = ilaenv_(&c__2, (char *)"ZHETRD", uplo, n, &c_n1, &c_n1, &c_n1, + (ftnlen)6, (ftnlen)1); + if (nb < nbmin) { + nx = *n; + } + } + } else { + nx = *n; + } + } else { + nb = 1; + } + + if (upper) { + +/* Reduce the upper triangle of A. */ +/* Columns 1:kk are handled by the unblocked method. */ + + kk = *n - (*n - nx + nb - 1) / nb * nb; + i__1 = kk + 1; + i__2 = -nb; + for (i__ = *n - nb + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += + i__2) { + +/* Reduce columns i:i+nb-1 to tridiagonal form and form the */ +/* matrix W which is needed to update the unreduced part of */ +/* the matrix */ + + i__3 = i__ + nb - 1; + zlatrd_(uplo, &i__3, &nb, &a[a_offset], lda, &e[1], &tau[1], & + work[1], &ldwork, (ftnlen)1); + +/* Update the unreduced submatrix A(1:i-1,1:i-1), using an */ +/* update of the form: A := A - V*W**H - W*V**H */ + + i__3 = i__ - 1; + z__1.r = -1., z__1.i = -0.; + zher2k_(uplo, (char *)"No transpose", &i__3, &nb, &z__1, &a[i__ * a_dim1 + + 1], lda, &work[1], &ldwork, &c_b23, &a[a_offset], lda, ( + ftnlen)1, (ftnlen)12); + +/* Copy superdiagonal elements back into A, and diagonal */ +/* elements into D */ + + i__3 = i__ + nb - 1; + for (j = i__; j <= i__3; ++j) { + i__4 = j - 1 + j * a_dim1; + i__5 = j - 1; + a[i__4].r = e[i__5], a[i__4].i = 0.; + i__4 = j + j * a_dim1; + d__[j] = a[i__4].r; +/* L10: */ + } +/* L20: */ + } + +/* Use unblocked code to reduce the last or only block */ + + zhetd2_(uplo, &kk, &a[a_offset], lda, &d__[1], &e[1], &tau[1], &iinfo, + (ftnlen)1); + } else { + +/* Reduce the lower triangle of A */ + + i__2 = *n - nx; + i__1 = nb; + for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) { + +/* Reduce columns i:i+nb-1 to tridiagonal form and form the */ +/* matrix W which is needed to update the unreduced part of */ +/* the matrix */ + + i__3 = *n - i__ + 1; + zlatrd_(uplo, &i__3, &nb, &a[i__ + i__ * a_dim1], lda, &e[i__], & + tau[i__], &work[1], &ldwork, (ftnlen)1); + +/* Update the unreduced submatrix A(i+nb:n,i+nb:n), using */ +/* an update of the form: A := A - V*W**H - W*V**H */ + + i__3 = *n - i__ - nb + 1; + z__1.r = -1., z__1.i = -0.; + zher2k_(uplo, (char *)"No transpose", &i__3, &nb, &z__1, &a[i__ + nb + + i__ * a_dim1], lda, &work[nb + 1], &ldwork, &c_b23, &a[ + i__ + nb + (i__ + nb) * a_dim1], lda, (ftnlen)1, (ftnlen) + 12); + +/* Copy subdiagonal elements back into A, and diagonal */ +/* elements into D */ + + i__3 = i__ + nb - 1; + for (j = i__; j <= i__3; ++j) { + i__4 = j + 1 + j * a_dim1; + i__5 = j; + a[i__4].r = e[i__5], a[i__4].i = 0.; + i__4 = j + j * a_dim1; + d__[j] = a[i__4].r; +/* L30: */ + } +/* L40: */ + } + +/* Use unblocked code to reduce the last or only block */ + + i__1 = *n - i__ + 1; + zhetd2_(uplo, &i__1, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[i__], + &tau[i__], &iinfo, (ftnlen)1); + } + + work[1].r = (doublereal) lwkopt, work[1].i = 0.; + return 0; + +/* End of ZHETRD */ + +} /* zhetrd_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zhpr.cpp b/lib/linalg/zhpr.cpp new file mode 100644 index 0000000000..f3c36d5826 --- /dev/null +++ b/lib/linalg/zhpr.cpp @@ -0,0 +1,405 @@ +/* fortran/zhpr.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b ZHPR */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZHPR(UPLO,N,ALPHA,X,INCX,AP) */ + +/* .. Scalar Arguments .. */ +/* DOUBLE PRECISION ALPHA */ +/* INTEGER INCX,N */ +/* CHARACTER UPLO */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 AP(*),X(*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZHPR performs the hermitian rank 1 operation */ +/* > */ +/* > A := alpha*x*x**H + A, */ +/* > */ +/* > where alpha is a real scalar, x is an n element vector and A is an */ +/* > n by n hermitian matrix, supplied in packed form. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > On entry, UPLO specifies whether the upper or lower */ +/* > triangular part of the matrix A is supplied in the packed */ +/* > array AP as follows: */ +/* > */ +/* > UPLO = 'U' or 'u' The upper triangular part of A is */ +/* > supplied in AP. */ +/* > */ +/* > UPLO = 'L' or 'l' The lower triangular part of A is */ +/* > supplied in AP. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > On entry, N specifies the order of the matrix A. */ +/* > N must be at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] ALPHA */ +/* > \verbatim */ +/* > ALPHA is DOUBLE PRECISION. */ +/* > On entry, ALPHA specifies the scalar alpha. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] X */ +/* > \verbatim */ +/* > X is COMPLEX*16 array, dimension at least */ +/* > ( 1 + ( n - 1 )*abs( INCX ) ). */ +/* > Before entry, the incremented array X must contain the n */ +/* > element vector x. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > On entry, INCX specifies the increment for the elements of */ +/* > X. INCX must not be zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] AP */ +/* > \verbatim */ +/* > AP is COMPLEX*16 array, dimension at least */ +/* > ( ( n*( n + 1 ) )/2 ). */ +/* > Before entry with UPLO = 'U' or 'u', the array AP must */ +/* > contain the upper triangular part of the hermitian matrix */ +/* > packed sequentially, column by column, so that AP( 1 ) */ +/* > contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) */ +/* > and a( 2, 2 ) respectively, and so on. On exit, the array */ +/* > AP is overwritten by the upper triangular part of the */ +/* > updated matrix. */ +/* > Before entry with UPLO = 'L' or 'l', the array AP must */ +/* > contain the lower triangular part of the hermitian matrix */ +/* > packed sequentially, column by column, so that AP( 1 ) */ +/* > contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) */ +/* > and a( 3, 1 ) respectively, and so on. On exit, the array */ +/* > AP is overwritten by the lower triangular part of the */ +/* > updated matrix. */ +/* > Note that the imaginary parts of the diagonal elements need */ +/* > not be set, they are assumed to be zero, and on exit they */ +/* > are set to zero. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16_blas_level2 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > Level 2 Blas routine. */ +/* > */ +/* > -- Written on 22-October-1986. */ +/* > Jack Dongarra, Argonne National Lab. */ +/* > Jeremy Du Croz, Nag Central Office. */ +/* > Sven Hammarling, Nag Central Office. */ +/* > Richard Hanson, Sandia National Labs. */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int zhpr_(char *uplo, integer *n, doublereal *alpha, + doublecomplex *x, integer *incx, doublecomplex *ap, ftnlen uplo_len) +{ + /* System generated locals */ + integer i__1, i__2, i__3, i__4, i__5; + doublereal d__1; + doublecomplex z__1, z__2; + + /* Builtin functions */ + void d_cnjg(doublecomplex *, doublecomplex *); + + /* Local variables */ + integer i__, j, k, kk, ix, jx, kx, info; + doublecomplex temp; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + + +/* -- Reference BLAS level2 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --ap; + --x; + + /* Function Body */ + info = 0; + if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", ( + ftnlen)1, (ftnlen)1)) { + info = 1; + } else if (*n < 0) { + info = 2; + } else if (*incx == 0) { + info = 5; + } + if (info != 0) { + xerbla_((char *)"ZHPR ", &info, (ftnlen)6); + return 0; + } + +/* Quick return if possible. */ + + if (*n == 0 || *alpha == 0.) { + return 0; + } + +/* Set the start point in X if the increment is not unity. */ + + if (*incx <= 0) { + kx = 1 - (*n - 1) * *incx; + } else if (*incx != 1) { + kx = 1; + } + +/* Start the operations. In this version the elements of the array AP */ +/* are accessed sequentially with one pass through AP. */ + + kk = 1; + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + +/* Form A when upper triangle is stored in AP. */ + + if (*incx == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + if (x[i__2].r != 0. || x[i__2].i != 0.) { + d_cnjg(&z__2, &x[j]); + z__1.r = *alpha * z__2.r, z__1.i = *alpha * z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + k = kk; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = k; + i__4 = k; + i__5 = i__; + z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, + z__2.i = x[i__5].r * temp.i + x[i__5].i * + temp.r; + z__1.r = ap[i__4].r + z__2.r, z__1.i = ap[i__4].i + + z__2.i; + ap[i__3].r = z__1.r, ap[i__3].i = z__1.i; + ++k; +/* L10: */ + } + i__2 = kk + j - 1; + i__3 = kk + j - 1; + i__4 = j; + z__1.r = x[i__4].r * temp.r - x[i__4].i * temp.i, z__1.i = + x[i__4].r * temp.i + x[i__4].i * temp.r; + d__1 = ap[i__3].r + z__1.r; + ap[i__2].r = d__1, ap[i__2].i = 0.; + } else { + i__2 = kk + j - 1; + i__3 = kk + j - 1; + d__1 = ap[i__3].r; + ap[i__2].r = d__1, ap[i__2].i = 0.; + } + kk += j; +/* L20: */ + } + } else { + jx = kx; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = jx; + if (x[i__2].r != 0. || x[i__2].i != 0.) { + d_cnjg(&z__2, &x[jx]); + z__1.r = *alpha * z__2.r, z__1.i = *alpha * z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + ix = kx; + i__2 = kk + j - 2; + for (k = kk; k <= i__2; ++k) { + i__3 = k; + i__4 = k; + i__5 = ix; + z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, + z__2.i = x[i__5].r * temp.i + x[i__5].i * + temp.r; + z__1.r = ap[i__4].r + z__2.r, z__1.i = ap[i__4].i + + z__2.i; + ap[i__3].r = z__1.r, ap[i__3].i = z__1.i; + ix += *incx; +/* L30: */ + } + i__2 = kk + j - 1; + i__3 = kk + j - 1; + i__4 = jx; + z__1.r = x[i__4].r * temp.r - x[i__4].i * temp.i, z__1.i = + x[i__4].r * temp.i + x[i__4].i * temp.r; + d__1 = ap[i__3].r + z__1.r; + ap[i__2].r = d__1, ap[i__2].i = 0.; + } else { + i__2 = kk + j - 1; + i__3 = kk + j - 1; + d__1 = ap[i__3].r; + ap[i__2].r = d__1, ap[i__2].i = 0.; + } + jx += *incx; + kk += j; +/* L40: */ + } + } + } else { + +/* Form A when lower triangle is stored in AP. */ + + if (*incx == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + if (x[i__2].r != 0. || x[i__2].i != 0.) { + d_cnjg(&z__2, &x[j]); + z__1.r = *alpha * z__2.r, z__1.i = *alpha * z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + i__2 = kk; + i__3 = kk; + i__4 = j; + z__1.r = temp.r * x[i__4].r - temp.i * x[i__4].i, z__1.i = + temp.r * x[i__4].i + temp.i * x[i__4].r; + d__1 = ap[i__3].r + z__1.r; + ap[i__2].r = d__1, ap[i__2].i = 0.; + k = kk + 1; + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + i__3 = k; + i__4 = k; + i__5 = i__; + z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, + z__2.i = x[i__5].r * temp.i + x[i__5].i * + temp.r; + z__1.r = ap[i__4].r + z__2.r, z__1.i = ap[i__4].i + + z__2.i; + ap[i__3].r = z__1.r, ap[i__3].i = z__1.i; + ++k; +/* L50: */ + } + } else { + i__2 = kk; + i__3 = kk; + d__1 = ap[i__3].r; + ap[i__2].r = d__1, ap[i__2].i = 0.; + } + kk = kk + *n - j + 1; +/* L60: */ + } + } else { + jx = kx; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = jx; + if (x[i__2].r != 0. || x[i__2].i != 0.) { + d_cnjg(&z__2, &x[jx]); + z__1.r = *alpha * z__2.r, z__1.i = *alpha * z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + i__2 = kk; + i__3 = kk; + i__4 = jx; + z__1.r = temp.r * x[i__4].r - temp.i * x[i__4].i, z__1.i = + temp.r * x[i__4].i + temp.i * x[i__4].r; + d__1 = ap[i__3].r + z__1.r; + ap[i__2].r = d__1, ap[i__2].i = 0.; + ix = jx; + i__2 = kk + *n - j; + for (k = kk + 1; k <= i__2; ++k) { + ix += *incx; + i__3 = k; + i__4 = k; + i__5 = ix; + z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, + z__2.i = x[i__5].r * temp.i + x[i__5].i * + temp.r; + z__1.r = ap[i__4].r + z__2.r, z__1.i = ap[i__4].i + + z__2.i; + ap[i__3].r = z__1.r, ap[i__3].i = z__1.i; +/* L70: */ + } + } else { + i__2 = kk; + i__3 = kk; + d__1 = ap[i__3].r; + ap[i__2].r = d__1, ap[i__2].i = 0.; + } + jx += *incx; + kk = kk + *n - j + 1; +/* L80: */ + } + } + } + + return 0; + +/* End of ZHPR */ + +} /* zhpr_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zlacgv.cpp b/lib/linalg/zlacgv.cpp new file mode 100644 index 0000000000..46c1c5c0ce --- /dev/null +++ b/lib/linalg/zlacgv.cpp @@ -0,0 +1,157 @@ +/* fortran/zlacgv.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b ZLACGV conjugates a complex vector. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZLACGV + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZLACGV( N, X, INCX ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INCX, N */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 X( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZLACGV conjugates a complex vector of length N. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The length of the vector X. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] X */ +/* > \verbatim */ +/* > X is COMPLEX*16 array, dimension */ +/* > (1+(N-1)*abs(INCX)) */ +/* > On entry, the vector of length N to be conjugated. */ +/* > On exit, X is overwritten with conjg(X). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > The spacing between successive elements of X. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16OTHERauxiliary */ + +/* ===================================================================== */ +/* Subroutine */ int zlacgv_(integer *n, doublecomplex *x, integer *incx) +{ + /* System generated locals */ + integer i__1, i__2; + doublecomplex z__1; + + /* Builtin functions */ + void d_cnjg(doublecomplex *, doublecomplex *); + + /* Local variables */ + integer i__, ioff; + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + + /* Parameter adjustments */ + --x; + + /* Function Body */ + if (*incx == 1) { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__; + d_cnjg(&z__1, &x[i__]); + x[i__2].r = z__1.r, x[i__2].i = z__1.i; +/* L10: */ + } + } else { + ioff = 1; + if (*incx < 0) { + ioff = 1 - (*n - 1) * *incx; + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = ioff; + d_cnjg(&z__1, &x[ioff]); + x[i__2].r = z__1.r, x[i__2].i = z__1.i; + ioff += *incx; +/* L20: */ + } + } + return 0; + +/* End of ZLACGV */ + +} /* zlacgv_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zlacpy.cpp b/lib/linalg/zlacpy.cpp new file mode 100644 index 0000000000..1cb52d4c0a --- /dev/null +++ b/lib/linalg/zlacpy.cpp @@ -0,0 +1,210 @@ +/* fortran/zlacpy.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b ZLACPY copies all or part of one two-dimensional array to another. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZLACPY + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZLACPY( UPLO, M, N, A, LDA, B, LDB ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER UPLO */ +/* INTEGER LDA, LDB, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 A( LDA, * ), B( LDB, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZLACPY copies all or part of a two-dimensional matrix A to another */ +/* > matrix B. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > Specifies the part of the matrix A to be copied to B. */ +/* > = 'U': Upper triangular part */ +/* > = 'L': Lower triangular part */ +/* > Otherwise: All of the matrix A */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix A. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is COMPLEX*16 array, dimension (LDA,N) */ +/* > The m by n matrix A. If UPLO = 'U', only the upper trapezium */ +/* > is accessed; if UPLO = 'L', only the lower trapezium is */ +/* > accessed. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] B */ +/* > \verbatim */ +/* > B is COMPLEX*16 array, dimension (LDB,N) */ +/* > On exit, B = A in the locations specified by UPLO. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDB */ +/* > \verbatim */ +/* > LDB is INTEGER */ +/* > The leading dimension of the array B. LDB >= max(1,M). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16OTHERauxiliary */ + +/* ===================================================================== */ +/* Subroutine */ int zlacpy_(char *uplo, integer *m, integer *n, + doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, + ftnlen uplo_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4; + + /* Local variables */ + integer i__, j; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + b_dim1 = *ldb; + b_offset = 1 + b_dim1; + b -= b_offset; + + /* Function Body */ + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = min(j,*m); + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * b_dim1; + i__4 = i__ + j * a_dim1; + b[i__3].r = a[i__4].r, b[i__3].i = a[i__4].i; +/* L10: */ + } +/* L20: */ + } + + } else if (lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = j; i__ <= i__2; ++i__) { + i__3 = i__ + j * b_dim1; + i__4 = i__ + j * a_dim1; + b[i__3].r = a[i__4].r, b[i__3].i = a[i__4].i; +/* L30: */ + } +/* L40: */ + } + + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * b_dim1; + i__4 = i__ + j * a_dim1; + b[i__3].r = a[i__4].r, b[i__3].i = a[i__4].i; +/* L50: */ + } +/* L60: */ + } + } + + return 0; + +/* End of ZLACPY */ + +} /* zlacpy_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zlacrm.cpp b/lib/linalg/zlacrm.cpp new file mode 100644 index 0000000000..e993f79aa5 --- /dev/null +++ b/lib/linalg/zlacrm.cpp @@ -0,0 +1,258 @@ +/* fortran/zlacrm.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static doublereal c_b6 = 1.; +static doublereal c_b7 = 0.; + +/* > \brief \b ZLACRM multiplies a complex matrix by a square real matrix. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZLACRM + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZLACRM( M, N, A, LDA, B, LDB, C, LDC, RWORK ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER LDA, LDB, LDC, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION B( LDB, * ), RWORK( * ) */ +/* COMPLEX*16 A( LDA, * ), C( LDC, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZLACRM performs a very simple matrix-matrix multiplication: */ +/* > C := A * B, */ +/* > where A is M by N and complex; B is N by N and real; */ +/* > C is M by N and complex. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix A and of the matrix C. */ +/* > M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns and rows of the matrix B and */ +/* > the number of columns of the matrix C. */ +/* > N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is COMPLEX*16 array, dimension (LDA, N) */ +/* > On entry, A contains the M by N matrix A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >=max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] B */ +/* > \verbatim */ +/* > B is DOUBLE PRECISION array, dimension (LDB, N) */ +/* > On entry, B contains the N by N matrix B. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDB */ +/* > \verbatim */ +/* > LDB is INTEGER */ +/* > The leading dimension of the array B. LDB >=max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] C */ +/* > \verbatim */ +/* > C is COMPLEX*16 array, dimension (LDC, N) */ +/* > On exit, C contains the M by N matrix C. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDC */ +/* > \verbatim */ +/* > LDC is INTEGER */ +/* > The leading dimension of the array C. LDC >=max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] RWORK */ +/* > \verbatim */ +/* > RWORK is DOUBLE PRECISION array, dimension (2*M*N) */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16OTHERauxiliary */ + +/* ===================================================================== */ +/* Subroutine */ int zlacrm_(integer *m, integer *n, doublecomplex *a, + integer *lda, doublereal *b, integer *ldb, doublecomplex *c__, + integer *ldc, doublereal *rwork) +{ + /* System generated locals */ + integer b_dim1, b_offset, a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, + i__3, i__4, i__5; + doublereal d__1; + doublecomplex z__1; + + /* Builtin functions */ + double d_imag(doublecomplex *); + + /* Local variables */ + integer i__, j, l; + extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Quick return if possible. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + b_dim1 = *ldb; + b_offset = 1 + b_dim1; + b -= b_offset; + c_dim1 = *ldc; + c_offset = 1 + c_dim1; + c__ -= c_offset; + --rwork; + + /* Function Body */ + if (*m == 0 || *n == 0) { + return 0; + } + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + rwork[(j - 1) * *m + i__] = a[i__3].r; +/* L10: */ + } +/* L20: */ + } + + l = *m * *n + 1; + dgemm_((char *)"N", (char *)"N", m, n, n, &c_b6, &rwork[1], m, &b[b_offset], ldb, &c_b7, & + rwork[l], m, (ftnlen)1, (ftnlen)1); + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + i__4 = l + (j - 1) * *m + i__ - 1; + c__[i__3].r = rwork[i__4], c__[i__3].i = 0.; +/* L30: */ + } +/* L40: */ + } + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + rwork[(j - 1) * *m + i__] = d_imag(&a[i__ + j * a_dim1]); +/* L50: */ + } +/* L60: */ + } + dgemm_((char *)"N", (char *)"N", m, n, n, &c_b6, &rwork[1], m, &b[b_offset], ldb, &c_b7, & + rwork[l], m, (ftnlen)1, (ftnlen)1); + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + i__4 = i__ + j * c_dim1; + d__1 = c__[i__4].r; + i__5 = l + (j - 1) * *m + i__ - 1; + z__1.r = d__1, z__1.i = rwork[i__5]; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; +/* L70: */ + } +/* L80: */ + } + + return 0; + +/* End of ZLACRM */ + +} /* zlacrm_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zladiv.cpp b/lib/linalg/zladiv.cpp new file mode 100644 index 0000000000..6e80b3371a --- /dev/null +++ b/lib/linalg/zladiv.cpp @@ -0,0 +1,132 @@ +/* fortran/zladiv.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b ZLADIV performs complex division in real arithmetic, avoiding unnecessary overflow. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZLADIV + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* COMPLEX*16 FUNCTION ZLADIV( X, Y ) */ + +/* .. Scalar Arguments .. */ +/* COMPLEX*16 X, Y */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZLADIV := X / Y, where X and Y are complex. The computation of X / Y */ +/* > will not overflow on an intermediary step unless the results */ +/* > overflows. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] X */ +/* > \verbatim */ +/* > X is COMPLEX*16 */ +/* > \endverbatim */ +/* > */ +/* > \param[in] Y */ +/* > \verbatim */ +/* > Y is COMPLEX*16 */ +/* > The complex scalars X and Y. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16OTHERauxiliary */ + +/* ===================================================================== */ +/* Double Complex */ VOID zladiv_(doublecomplex * ret_val, doublecomplex *x, + doublecomplex *y) +{ + /* System generated locals */ + doublereal d__1, d__2, d__3, d__4; + doublecomplex z__1; + + /* Builtin functions */ + double d_imag(doublecomplex *); + + /* Local variables */ + doublereal zi, zr; + extern /* Subroutine */ int dladiv_(doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *, doublereal *); + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + + d__1 = x->r; + d__2 = d_imag(x); + d__3 = y->r; + d__4 = d_imag(y); + dladiv_(&d__1, &d__2, &d__3, &d__4, &zr, &zi); + z__1.r = zr, z__1.i = zi; + ret_val->r = z__1.r, ret_val->i = z__1.i; + + return ; + +/* End of ZLADIV */ + +} /* zladiv_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zlaed0.cpp b/lib/linalg/zlaed0.cpp new file mode 100644 index 0000000000..680dd85054 --- /dev/null +++ b/lib/linalg/zlaed0.cpp @@ -0,0 +1,458 @@ +/* fortran/zlaed0.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__9 = 9; +static integer c__0 = 0; +static integer c__2 = 2; +static integer c__1 = 1; + +/* > \brief \b ZLAED0 used by ZSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced +symmetric tridiagonal matrix using the divide and conquer method. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZLAED0 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZLAED0( QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, RWORK, */ +/* IWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INFO, LDQ, LDQS, N, QSIZ */ +/* .. */ +/* .. Array Arguments .. */ +/* INTEGER IWORK( * ) */ +/* DOUBLE PRECISION D( * ), E( * ), RWORK( * ) */ +/* COMPLEX*16 Q( LDQ, * ), QSTORE( LDQS, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > Using the divide and conquer method, ZLAED0 computes all eigenvalues */ +/* > of a symmetric tridiagonal matrix which is one diagonal block of */ +/* > those from reducing a dense or band Hermitian matrix and */ +/* > corresponding eigenvectors of the dense or band matrix. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] QSIZ */ +/* > \verbatim */ +/* > QSIZ is INTEGER */ +/* > The dimension of the unitary matrix used to reduce */ +/* > the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The dimension of the symmetric tridiagonal matrix. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension (N) */ +/* > On entry, the diagonal elements of the tridiagonal matrix. */ +/* > On exit, the eigenvalues in ascending order. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] E */ +/* > \verbatim */ +/* > E is DOUBLE PRECISION array, dimension (N-1) */ +/* > On entry, the off-diagonal elements of the tridiagonal matrix. */ +/* > On exit, E has been destroyed. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] Q */ +/* > \verbatim */ +/* > Q is COMPLEX*16 array, dimension (LDQ,N) */ +/* > On entry, Q must contain an QSIZ x N matrix whose columns */ +/* > unitarily orthonormal. It is a part of the unitary matrix */ +/* > that reduces the full dense Hermitian matrix to a */ +/* > (reducible) symmetric tridiagonal matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDQ */ +/* > \verbatim */ +/* > LDQ is INTEGER */ +/* > The leading dimension of the array Q. LDQ >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] IWORK */ +/* > \verbatim */ +/* > IWORK is INTEGER array, */ +/* > the dimension of IWORK must be at least */ +/* > 6 + 6*N + 5*N*lg N */ +/* > ( lg( N ) = smallest integer k */ +/* > such that 2^k >= N ) */ +/* > \endverbatim */ +/* > */ +/* > \param[out] RWORK */ +/* > \verbatim */ +/* > RWORK is DOUBLE PRECISION array, */ +/* > dimension (1 + 3*N + 2*N*lg N + 3*N**2) */ +/* > ( lg( N ) = smallest integer k */ +/* > such that 2^k >= N ) */ +/* > \endverbatim */ +/* > */ +/* > \param[out] QSTORE */ +/* > \verbatim */ +/* > QSTORE is COMPLEX*16 array, dimension (LDQS, N) */ +/* > Used to store parts of */ +/* > the eigenvector matrix when the updating matrix multiplies */ +/* > take place. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDQS */ +/* > \verbatim */ +/* > LDQS is INTEGER */ +/* > The leading dimension of the array QSTORE. */ +/* > LDQS >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit. */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ +/* > > 0: The algorithm failed to compute an eigenvalue while */ +/* > working on the submatrix lying in rows and columns */ +/* > INFO/(N+1) through mod(INFO,N+1). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16OTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int zlaed0_(integer *qsiz, integer *n, doublereal *d__, + doublereal *e, doublecomplex *q, integer *ldq, doublecomplex *qstore, + integer *ldqs, doublereal *rwork, integer *iwork, integer *info) +{ + /* System generated locals */ + integer q_dim1, q_offset, qstore_dim1, qstore_offset, i__1, i__2; + doublereal d__1; + + /* Builtin functions */ + double log(doublereal); + integer pow_ii(integer *, integer *); + + /* Local variables */ + integer i__, j, k, ll, iq, lgn, msd2, smm1, spm1, spm2; + doublereal temp; + integer curr, iperm; + extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, + doublereal *, integer *); + integer indxq, iwrem, iqptr, tlvls; + extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, + doublecomplex *, integer *), zlaed7_(integer *, integer *, + integer *, integer *, integer *, integer *, doublereal *, + doublecomplex *, integer *, doublereal *, integer *, doublereal *, + integer *, integer *, integer *, integer *, integer *, + doublereal *, doublecomplex *, doublereal *, integer *, integer *) + ; + integer igivcl; + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int zlacrm_(integer *, integer *, doublecomplex *, + integer *, doublereal *, integer *, doublecomplex *, integer *, + doublereal *); + integer igivnm, submat, curprb, subpbs, igivpt; + extern /* Subroutine */ int dsteqr_(char *, integer *, doublereal *, + doublereal *, doublereal *, integer *, doublereal *, integer *, + ftnlen); + integer curlvl, matsiz, iprmpt, smlsiz; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* Warning: N could be as big as QSIZ! */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --d__; + --e; + q_dim1 = *ldq; + q_offset = 1 + q_dim1; + q -= q_offset; + qstore_dim1 = *ldqs; + qstore_offset = 1 + qstore_dim1; + qstore -= qstore_offset; + --rwork; + --iwork; + + /* Function Body */ + *info = 0; + +/* IF( ICOMPQ .LT. 0 .OR. ICOMPQ .GT. 2 ) THEN */ +/* INFO = -1 */ +/* ELSE IF( ( ICOMPQ .EQ. 1 ) .AND. ( QSIZ .LT. MAX( 0, N ) ) ) */ +/* $ THEN */ + if (*qsiz < max(0,*n)) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } else if (*ldq < max(1,*n)) { + *info = -6; + } else if (*ldqs < max(1,*n)) { + *info = -8; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"ZLAED0", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*n == 0) { + return 0; + } + + smlsiz = ilaenv_(&c__9, (char *)"ZLAED0", (char *)" ", &c__0, &c__0, &c__0, &c__0, ( + ftnlen)6, (ftnlen)1); + +/* Determine the size and placement of the submatrices, and save in */ +/* the leading elements of IWORK. */ + + iwork[1] = *n; + subpbs = 1; + tlvls = 0; +L10: + if (iwork[subpbs] > smlsiz) { + for (j = subpbs; j >= 1; --j) { + iwork[j * 2] = (iwork[j] + 1) / 2; + iwork[(j << 1) - 1] = iwork[j] / 2; +/* L20: */ + } + ++tlvls; + subpbs <<= 1; + goto L10; + } + i__1 = subpbs; + for (j = 2; j <= i__1; ++j) { + iwork[j] += iwork[j - 1]; +/* L30: */ + } + +/* Divide the matrix into SUBPBS submatrices of size at most SMLSIZ+1 */ +/* using rank-1 modifications (cuts). */ + + spm1 = subpbs - 1; + i__1 = spm1; + for (i__ = 1; i__ <= i__1; ++i__) { + submat = iwork[i__] + 1; + smm1 = submat - 1; + d__[smm1] -= (d__1 = e[smm1], abs(d__1)); + d__[submat] -= (d__1 = e[smm1], abs(d__1)); +/* L40: */ + } + + indxq = (*n << 2) + 3; + +/* Set up workspaces for eigenvalues only/accumulate new vectors */ +/* routine */ + + temp = log((doublereal) (*n)) / log(2.); + lgn = (integer) temp; + if (pow_ii(&c__2, &lgn) < *n) { + ++lgn; + } + if (pow_ii(&c__2, &lgn) < *n) { + ++lgn; + } + iprmpt = indxq + *n + 1; + iperm = iprmpt + *n * lgn; + iqptr = iperm + *n * lgn; + igivpt = iqptr + *n + 2; + igivcl = igivpt + *n * lgn; + + igivnm = 1; + iq = igivnm + (*n << 1) * lgn; +/* Computing 2nd power */ + i__1 = *n; + iwrem = iq + i__1 * i__1 + 1; +/* Initialize pointers */ + i__1 = subpbs; + for (i__ = 0; i__ <= i__1; ++i__) { + iwork[iprmpt + i__] = 1; + iwork[igivpt + i__] = 1; +/* L50: */ + } + iwork[iqptr] = 1; + +/* Solve each submatrix eigenproblem at the bottom of the divide and */ +/* conquer tree. */ + + curr = 0; + i__1 = spm1; + for (i__ = 0; i__ <= i__1; ++i__) { + if (i__ == 0) { + submat = 1; + matsiz = iwork[1]; + } else { + submat = iwork[i__] + 1; + matsiz = iwork[i__ + 1] - iwork[i__]; + } + ll = iq - 1 + iwork[iqptr + curr]; + dsteqr_((char *)"I", &matsiz, &d__[submat], &e[submat], &rwork[ll], &matsiz, & + rwork[1], info, (ftnlen)1); + zlacrm_(qsiz, &matsiz, &q[submat * q_dim1 + 1], ldq, &rwork[ll], & + matsiz, &qstore[submat * qstore_dim1 + 1], ldqs, &rwork[iwrem] + ); +/* Computing 2nd power */ + i__2 = matsiz; + iwork[iqptr + curr + 1] = iwork[iqptr + curr] + i__2 * i__2; + ++curr; + if (*info > 0) { + *info = submat * (*n + 1) + submat + matsiz - 1; + return 0; + } + k = 1; + i__2 = iwork[i__ + 1]; + for (j = submat; j <= i__2; ++j) { + iwork[indxq + j] = k; + ++k; +/* L60: */ + } +/* L70: */ + } + +/* Successively merge eigensystems of adjacent submatrices */ +/* into eigensystem for the corresponding larger matrix. */ + +/* while ( SUBPBS > 1 ) */ + + curlvl = 1; +L80: + if (subpbs > 1) { + spm2 = subpbs - 2; + i__1 = spm2; + for (i__ = 0; i__ <= i__1; i__ += 2) { + if (i__ == 0) { + submat = 1; + matsiz = iwork[2]; + msd2 = iwork[1]; + curprb = 0; + } else { + submat = iwork[i__] + 1; + matsiz = iwork[i__ + 2] - iwork[i__]; + msd2 = matsiz / 2; + ++curprb; + } + +/* Merge lower order eigensystems (of size MSD2 and MATSIZ - MSD2) */ +/* into an eigensystem of size MATSIZ. ZLAED7 handles the case */ +/* when the eigenvectors of a full or band Hermitian matrix (which */ +/* was reduced to tridiagonal form) are desired. */ + +/* I am free to use Q as a valuable working space until Loop 150. */ + + zlaed7_(&matsiz, &msd2, qsiz, &tlvls, &curlvl, &curprb, &d__[ + submat], &qstore[submat * qstore_dim1 + 1], ldqs, &e[ + submat + msd2 - 1], &iwork[indxq + submat], &rwork[iq], & + iwork[iqptr], &iwork[iprmpt], &iwork[iperm], &iwork[ + igivpt], &iwork[igivcl], &rwork[igivnm], &q[submat * + q_dim1 + 1], &rwork[iwrem], &iwork[subpbs + 1], info); + if (*info > 0) { + *info = submat * (*n + 1) + submat + matsiz - 1; + return 0; + } + iwork[i__ / 2 + 1] = iwork[i__ + 2]; +/* L90: */ + } + subpbs /= 2; + ++curlvl; + goto L80; + } + +/* end while */ + +/* Re-merge the eigenvalues/vectors which were deflated at the final */ +/* merge step. */ + + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + j = iwork[indxq + i__]; + rwork[i__] = d__[j]; + zcopy_(qsiz, &qstore[j * qstore_dim1 + 1], &c__1, &q[i__ * q_dim1 + 1] + , &c__1); +/* L100: */ + } + dcopy_(n, &rwork[1], &c__1, &d__[1], &c__1); + + return 0; + +/* End of ZLAED0 */ + +} /* zlaed0_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zlaed7.cpp b/lib/linalg/zlaed7.cpp new file mode 100644 index 0000000000..9c06a0c334 --- /dev/null +++ b/lib/linalg/zlaed7.cpp @@ -0,0 +1,456 @@ +/* fortran/zlaed7.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__2 = 2; +static integer c__1 = 1; +static integer c_n1 = -1; + +/* > \brief \b ZLAED7 used by ZSTEDC. Computes the updated eigensystem of a diagonal matrix after modification + by a rank-one symmetric matrix. Used when the original matrix is dense. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZLAED7 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZLAED7( N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, */ +/* LDQ, RHO, INDXQ, QSTORE, QPTR, PRMPTR, PERM, */ +/* GIVPTR, GIVCOL, GIVNUM, WORK, RWORK, IWORK, */ +/* INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER CURLVL, CURPBM, CUTPNT, INFO, LDQ, N, QSIZ, */ +/* $ TLVLS */ +/* DOUBLE PRECISION RHO */ +/* .. */ +/* .. Array Arguments .. */ +/* INTEGER GIVCOL( 2, * ), GIVPTR( * ), INDXQ( * ), */ +/* $ IWORK( * ), PERM( * ), PRMPTR( * ), QPTR( * ) */ +/* DOUBLE PRECISION D( * ), GIVNUM( 2, * ), QSTORE( * ), RWORK( * ) */ +/* COMPLEX*16 Q( LDQ, * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZLAED7 computes the updated eigensystem of a diagonal */ +/* > matrix after modification by a rank-one symmetric matrix. This */ +/* > routine is used only for the eigenproblem which requires all */ +/* > eigenvalues and optionally eigenvectors of a dense or banded */ +/* > Hermitian matrix that has been reduced to tridiagonal form. */ +/* > */ +/* > T = Q(in) ( D(in) + RHO * Z*Z**H ) Q**H(in) = Q(out) * D(out) * Q**H(out) */ +/* > */ +/* > where Z = Q**Hu, u is a vector of length N with ones in the */ +/* > CUTPNT and CUTPNT + 1 th elements and zeros elsewhere. */ +/* > */ +/* > The eigenvectors of the original matrix are stored in Q, and the */ +/* > eigenvalues are in D. The algorithm consists of three stages: */ +/* > */ +/* > The first stage consists of deflating the size of the problem */ +/* > when there are multiple eigenvalues or if there is a zero in */ +/* > the Z vector. For each such occurrence the dimension of the */ +/* > secular equation problem is reduced by one. This stage is */ +/* > performed by the routine DLAED2. */ +/* > */ +/* > The second stage consists of calculating the updated */ +/* > eigenvalues. This is done by finding the roots of the secular */ +/* > equation via the routine DLAED4 (as called by SLAED3). */ +/* > This routine also calculates the eigenvectors of the current */ +/* > problem. */ +/* > */ +/* > The final stage consists of computing the updated eigenvectors */ +/* > directly using the updated eigenvalues. The eigenvectors for */ +/* > the current problem are multiplied with the eigenvectors from */ +/* > the overall problem. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The dimension of the symmetric tridiagonal matrix. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] CUTPNT */ +/* > \verbatim */ +/* > CUTPNT is INTEGER */ +/* > Contains the location of the last eigenvalue in the leading */ +/* > sub-matrix. min(1,N) <= CUTPNT <= N. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] QSIZ */ +/* > \verbatim */ +/* > QSIZ is INTEGER */ +/* > The dimension of the unitary matrix used to reduce */ +/* > the full matrix to tridiagonal form. QSIZ >= N. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TLVLS */ +/* > \verbatim */ +/* > TLVLS is INTEGER */ +/* > The total number of merging levels in the overall divide and */ +/* > conquer tree. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] CURLVL */ +/* > \verbatim */ +/* > CURLVL is INTEGER */ +/* > The current level in the overall merge routine, */ +/* > 0 <= curlvl <= tlvls. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] CURPBM */ +/* > \verbatim */ +/* > CURPBM is INTEGER */ +/* > The current problem in the current level in the overall */ +/* > merge routine (counting from upper left to lower right). */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension (N) */ +/* > On entry, the eigenvalues of the rank-1-perturbed matrix. */ +/* > On exit, the eigenvalues of the repaired matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] Q */ +/* > \verbatim */ +/* > Q is COMPLEX*16 array, dimension (LDQ,N) */ +/* > On entry, the eigenvectors of the rank-1-perturbed matrix. */ +/* > On exit, the eigenvectors of the repaired tridiagonal matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDQ */ +/* > \verbatim */ +/* > LDQ is INTEGER */ +/* > The leading dimension of the array Q. LDQ >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] RHO */ +/* > \verbatim */ +/* > RHO is DOUBLE PRECISION */ +/* > Contains the subdiagonal element used to create the rank-1 */ +/* > modification. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INDXQ */ +/* > \verbatim */ +/* > INDXQ is INTEGER array, dimension (N) */ +/* > This contains the permutation which will reintegrate the */ +/* > subproblem just solved back into sorted order, */ +/* > ie. D( INDXQ( I = 1, N ) ) will be in ascending order. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] IWORK */ +/* > \verbatim */ +/* > IWORK is INTEGER array, dimension (4*N) */ +/* > \endverbatim */ +/* > */ +/* > \param[out] RWORK */ +/* > \verbatim */ +/* > RWORK is DOUBLE PRECISION array, */ +/* > dimension (3*N+2*QSIZ*N) */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is COMPLEX*16 array, dimension (QSIZ*N) */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] QSTORE */ +/* > \verbatim */ +/* > QSTORE is DOUBLE PRECISION array, dimension (N**2+1) */ +/* > Stores eigenvectors of submatrices encountered during */ +/* > divide and conquer, packed together. QPTR points to */ +/* > beginning of the submatrices. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] QPTR */ +/* > \verbatim */ +/* > QPTR is INTEGER array, dimension (N+2) */ +/* > List of indices pointing to beginning of submatrices stored */ +/* > in QSTORE. The submatrices are numbered starting at the */ +/* > bottom left of the divide and conquer tree, from left to */ +/* > right and bottom to top. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] PRMPTR */ +/* > \verbatim */ +/* > PRMPTR is INTEGER array, dimension (N lg N) */ +/* > Contains a list of pointers which indicate where in PERM a */ +/* > level's permutation is stored. PRMPTR(i+1) - PRMPTR(i) */ +/* > indicates the size of the permutation and also the size of */ +/* > the full, non-deflated problem. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] PERM */ +/* > \verbatim */ +/* > PERM is INTEGER array, dimension (N lg N) */ +/* > Contains the permutations (from deflation and sorting) to be */ +/* > applied to each eigenblock. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] GIVPTR */ +/* > \verbatim */ +/* > GIVPTR is INTEGER array, dimension (N lg N) */ +/* > Contains a list of pointers which indicate where in GIVCOL a */ +/* > level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i) */ +/* > indicates the number of Givens rotations. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] GIVCOL */ +/* > \verbatim */ +/* > GIVCOL is INTEGER array, dimension (2, N lg N) */ +/* > Each pair of numbers indicates a pair of columns to take place */ +/* > in a Givens rotation. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] GIVNUM */ +/* > \verbatim */ +/* > GIVNUM is DOUBLE PRECISION array, dimension (2, N lg N) */ +/* > Each number indicates the S value to be used in the */ +/* > corresponding Givens rotation. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit. */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ +/* > > 0: if INFO = 1, an eigenvalue did not converge */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16OTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int zlaed7_(integer *n, integer *cutpnt, integer *qsiz, + integer *tlvls, integer *curlvl, integer *curpbm, doublereal *d__, + doublecomplex *q, integer *ldq, doublereal *rho, integer *indxq, + doublereal *qstore, integer *qptr, integer *prmptr, integer *perm, + integer *givptr, integer *givcol, doublereal *givnum, doublecomplex * + work, doublereal *rwork, integer *iwork, integer *info) +{ + /* System generated locals */ + integer q_dim1, q_offset, i__1, i__2; + + /* Builtin functions */ + integer pow_ii(integer *, integer *); + + /* Local variables */ + integer i__, k, n1, n2, iq, iw, iz, ptr, indx, curr, indxc, indxp; + extern /* Subroutine */ int dlaed9_(integer *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + doublereal *, doublereal *, doublereal *, integer *, integer *), + zlaed8_(integer *, integer *, integer *, doublecomplex *, integer + *, doublereal *, doublereal *, integer *, doublereal *, + doublereal *, doublecomplex *, integer *, doublereal *, integer *, + integer *, integer *, integer *, integer *, integer *, + doublereal *, integer *), dlaeda_(integer *, integer *, integer *, + integer *, integer *, integer *, integer *, integer *, + doublereal *, doublereal *, integer *, doublereal *, doublereal *, + integer *); + integer idlmda; + extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *, + integer *, integer *, integer *), xerbla_(char *, integer *, + ftnlen), zlacrm_(integer *, integer *, doublecomplex *, integer *, + doublereal *, integer *, doublecomplex *, integer *, doublereal * + ); + integer coltyp; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --d__; + q_dim1 = *ldq; + q_offset = 1 + q_dim1; + q -= q_offset; + --indxq; + --qstore; + --qptr; + --prmptr; + --perm; + --givptr; + givcol -= 3; + givnum -= 3; + --work; + --rwork; + --iwork; + + /* Function Body */ + *info = 0; + +/* IF( ICOMPQ.LT.0 .OR. ICOMPQ.GT.1 ) THEN */ +/* INFO = -1 */ +/* ELSE IF( N.LT.0 ) THEN */ + if (*n < 0) { + *info = -1; + } else if (min(1,*n) > *cutpnt || *n < *cutpnt) { + *info = -2; + } else if (*qsiz < *n) { + *info = -3; + } else if (*ldq < max(1,*n)) { + *info = -9; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"ZLAED7", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*n == 0) { + return 0; + } + +/* The following values are for bookkeeping purposes only. They are */ +/* integer pointers which indicate the portion of the workspace */ +/* used by a particular array in DLAED2 and SLAED3. */ + + iz = 1; + idlmda = iz + *n; + iw = idlmda + *n; + iq = iw + *n; + + indx = 1; + indxc = indx + *n; + coltyp = indxc + *n; + indxp = coltyp + *n; + +/* Form the z-vector which consists of the last row of Q_1 and the */ +/* first row of Q_2. */ + + ptr = pow_ii(&c__2, tlvls) + 1; + i__1 = *curlvl - 1; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = *tlvls - i__; + ptr += pow_ii(&c__2, &i__2); +/* L10: */ + } + curr = ptr + *curpbm; + dlaeda_(n, tlvls, curlvl, curpbm, &prmptr[1], &perm[1], &givptr[1], & + givcol[3], &givnum[3], &qstore[1], &qptr[1], &rwork[iz], &rwork[ + iz + *n], info); + +/* When solving the final problem, we no longer need the stored data, */ +/* so we will overwrite the data from this level onto the previously */ +/* used storage space. */ + + if (*curlvl == *tlvls) { + qptr[curr] = 1; + prmptr[curr] = 1; + givptr[curr] = 1; + } + +/* Sort and Deflate eigenvalues. */ + + zlaed8_(&k, n, qsiz, &q[q_offset], ldq, &d__[1], rho, cutpnt, &rwork[iz], + &rwork[idlmda], &work[1], qsiz, &rwork[iw], &iwork[indxp], &iwork[ + indx], &indxq[1], &perm[prmptr[curr]], &givptr[curr + 1], &givcol[ + (givptr[curr] << 1) + 1], &givnum[(givptr[curr] << 1) + 1], info); + prmptr[curr + 1] = prmptr[curr] + *n; + givptr[curr + 1] += givptr[curr]; + +/* Solve Secular Equation. */ + + if (k != 0) { + dlaed9_(&k, &c__1, &k, n, &d__[1], &rwork[iq], &k, rho, &rwork[idlmda] + , &rwork[iw], &qstore[qptr[curr]], &k, info); + zlacrm_(qsiz, &k, &work[1], qsiz, &qstore[qptr[curr]], &k, &q[ + q_offset], ldq, &rwork[iq]); +/* Computing 2nd power */ + i__1 = k; + qptr[curr + 1] = qptr[curr] + i__1 * i__1; + if (*info != 0) { + return 0; + } + +/* Prepare the INDXQ sorting premutation. */ + + n1 = k; + n2 = *n - k; + dlamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &indxq[1]); + } else { + qptr[curr + 1] = qptr[curr]; + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + indxq[i__] = i__; +/* L20: */ + } + } + + return 0; + +/* End of ZLAED7 */ + +} /* zlaed7_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zlaed8.cpp b/lib/linalg/zlaed8.cpp new file mode 100644 index 0000000000..00f4db857b --- /dev/null +++ b/lib/linalg/zlaed8.cpp @@ -0,0 +1,569 @@ +/* fortran/zlaed8.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static doublereal c_b3 = -1.; +static integer c__1 = 1; + +/* > \brief \b ZLAED8 used by ZSTEDC. Merges eigenvalues and deflates secular equation. Used when the original + matrix is dense. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZLAED8 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZLAED8( K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA, */ +/* Q2, LDQ2, W, INDXP, INDX, INDXQ, PERM, GIVPTR, */ +/* GIVCOL, GIVNUM, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER CUTPNT, GIVPTR, INFO, K, LDQ, LDQ2, N, QSIZ */ +/* DOUBLE PRECISION RHO */ +/* .. */ +/* .. Array Arguments .. */ +/* INTEGER GIVCOL( 2, * ), INDX( * ), INDXP( * ), */ +/* $ INDXQ( * ), PERM( * ) */ +/* DOUBLE PRECISION D( * ), DLAMDA( * ), GIVNUM( 2, * ), W( * ), */ +/* $ Z( * ) */ +/* COMPLEX*16 Q( LDQ, * ), Q2( LDQ2, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZLAED8 merges the two sets of eigenvalues together into a single */ +/* > sorted set. Then it tries to deflate the size of the problem. */ +/* > There are two ways in which deflation can occur: when two or more */ +/* > eigenvalues are close together or if there is a tiny element in the */ +/* > Z vector. For each such occurrence the order of the related secular */ +/* > equation problem is reduced by one. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[out] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > Contains the number of non-deflated eigenvalues. */ +/* > This is the order of the related secular equation. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The dimension of the symmetric tridiagonal matrix. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] QSIZ */ +/* > \verbatim */ +/* > QSIZ is INTEGER */ +/* > The dimension of the unitary matrix used to reduce */ +/* > the dense or band matrix to tridiagonal form. */ +/* > QSIZ >= N if ICOMPQ = 1. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] Q */ +/* > \verbatim */ +/* > Q is COMPLEX*16 array, dimension (LDQ,N) */ +/* > On entry, Q contains the eigenvectors of the partially solved */ +/* > system which has been previously updated in matrix */ +/* > multiplies with other partially solved eigensystems. */ +/* > On exit, Q contains the trailing (N-K) updated eigenvectors */ +/* > (those which were deflated) in its last N-K columns. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDQ */ +/* > \verbatim */ +/* > LDQ is INTEGER */ +/* > The leading dimension of the array Q. LDQ >= max( 1, N ). */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension (N) */ +/* > On entry, D contains the eigenvalues of the two submatrices to */ +/* > be combined. On exit, D contains the trailing (N-K) updated */ +/* > eigenvalues (those which were deflated) sorted into increasing */ +/* > order. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] RHO */ +/* > \verbatim */ +/* > RHO is DOUBLE PRECISION */ +/* > Contains the off diagonal element associated with the rank-1 */ +/* > cut which originally split the two submatrices which are now */ +/* > being recombined. RHO is modified during the computation to */ +/* > the value required by DLAED3. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] CUTPNT */ +/* > \verbatim */ +/* > CUTPNT is INTEGER */ +/* > Contains the location of the last eigenvalue in the leading */ +/* > sub-matrix. MIN(1,N) <= CUTPNT <= N. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] Z */ +/* > \verbatim */ +/* > Z is DOUBLE PRECISION array, dimension (N) */ +/* > On input this vector contains the updating vector (the last */ +/* > row of the first sub-eigenvector matrix and the first row of */ +/* > the second sub-eigenvector matrix). The contents of Z are */ +/* > destroyed during the updating process. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] DLAMDA */ +/* > \verbatim */ +/* > DLAMDA is DOUBLE PRECISION array, dimension (N) */ +/* > Contains a copy of the first K eigenvalues which will be used */ +/* > by DLAED3 to form the secular equation. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] Q2 */ +/* > \verbatim */ +/* > Q2 is COMPLEX*16 array, dimension (LDQ2,N) */ +/* > If ICOMPQ = 0, Q2 is not referenced. Otherwise, */ +/* > Contains a copy of the first K eigenvectors which will be used */ +/* > by DLAED7 in a matrix multiply (DGEMM) to update the new */ +/* > eigenvectors. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDQ2 */ +/* > \verbatim */ +/* > LDQ2 is INTEGER */ +/* > The leading dimension of the array Q2. LDQ2 >= max( 1, N ). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] W */ +/* > \verbatim */ +/* > W is DOUBLE PRECISION array, dimension (N) */ +/* > This will hold the first k values of the final */ +/* > deflation-altered z-vector and will be passed to DLAED3. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INDXP */ +/* > \verbatim */ +/* > INDXP is INTEGER array, dimension (N) */ +/* > This will contain the permutation used to place deflated */ +/* > values of D at the end of the array. On output INDXP(1:K) */ +/* > points to the nondeflated D-values and INDXP(K+1:N) */ +/* > points to the deflated eigenvalues. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INDX */ +/* > \verbatim */ +/* > INDX is INTEGER array, dimension (N) */ +/* > This will contain the permutation used to sort the contents of */ +/* > D into ascending order. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INDXQ */ +/* > \verbatim */ +/* > INDXQ is INTEGER array, dimension (N) */ +/* > This contains the permutation which separately sorts the two */ +/* > sub-problems in D into ascending order. Note that elements in */ +/* > the second half of this permutation must first have CUTPNT */ +/* > added to their values in order to be accurate. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] PERM */ +/* > \verbatim */ +/* > PERM is INTEGER array, dimension (N) */ +/* > Contains the permutations (from deflation and sorting) to be */ +/* > applied to each eigenblock. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] GIVPTR */ +/* > \verbatim */ +/* > GIVPTR is INTEGER */ +/* > Contains the number of Givens rotations which took place in */ +/* > this subproblem. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] GIVCOL */ +/* > \verbatim */ +/* > GIVCOL is INTEGER array, dimension (2, N) */ +/* > Each pair of numbers indicates a pair of columns to take place */ +/* > in a Givens rotation. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] GIVNUM */ +/* > \verbatim */ +/* > GIVNUM is DOUBLE PRECISION array, dimension (2, N) */ +/* > Each number indicates the S value to be used in the */ +/* > corresponding Givens rotation. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit. */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16OTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int zlaed8_(integer *k, integer *n, integer *qsiz, + doublecomplex *q, integer *ldq, doublereal *d__, doublereal *rho, + integer *cutpnt, doublereal *z__, doublereal *dlamda, doublecomplex * + q2, integer *ldq2, doublereal *w, integer *indxp, integer *indx, + integer *indxq, integer *perm, integer *givptr, integer *givcol, + doublereal *givnum, integer *info) +{ + /* System generated locals */ + integer q_dim1, q_offset, q2_dim1, q2_offset, i__1; + doublereal d__1; + + /* Builtin functions */ + double sqrt(doublereal); + + /* Local variables */ + doublereal c__; + integer i__, j; + doublereal s, t; + integer k2, n1, n2, jp, n1p1; + doublereal eps, tau, tol; + integer jlam, imax, jmax; + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *), dcopy_(integer *, doublereal *, integer *, doublereal + *, integer *), zdrot_(integer *, doublecomplex *, integer *, + doublecomplex *, integer *, doublereal *, doublereal *), zcopy_( + integer *, doublecomplex *, integer *, doublecomplex *, integer *) + ; + extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, + ftnlen); + extern integer idamax_(integer *, doublereal *, integer *); + extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *, + integer *, integer *, integer *), xerbla_(char *, integer *, + ftnlen), zlacpy_(char *, integer *, integer *, doublecomplex *, + integer *, doublecomplex *, integer *, ftnlen); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + q_dim1 = *ldq; + q_offset = 1 + q_dim1; + q -= q_offset; + --d__; + --z__; + --dlamda; + q2_dim1 = *ldq2; + q2_offset = 1 + q2_dim1; + q2 -= q2_offset; + --w; + --indxp; + --indx; + --indxq; + --perm; + givcol -= 3; + givnum -= 3; + + /* Function Body */ + *info = 0; + + if (*n < 0) { + *info = -2; + } else if (*qsiz < *n) { + *info = -3; + } else if (*ldq < max(1,*n)) { + *info = -5; + } else if (*cutpnt < min(1,*n) || *cutpnt > *n) { + *info = -8; + } else if (*ldq2 < max(1,*n)) { + *info = -12; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"ZLAED8", &i__1, (ftnlen)6); + return 0; + } + +/* Need to initialize GIVPTR to O here in case of quick exit */ +/* to prevent an unspecified code behavior (usually sigfault) */ +/* when IWORK array on entry to *stedc is not zeroed */ +/* (or at least some IWORK entries which used in *laed7 for GIVPTR). */ + + *givptr = 0; + +/* Quick return if possible */ + + if (*n == 0) { + return 0; + } + + n1 = *cutpnt; + n2 = *n - n1; + n1p1 = n1 + 1; + + if (*rho < 0.) { + dscal_(&n2, &c_b3, &z__[n1p1], &c__1); + } + +/* Normalize z so that norm(z) = 1 */ + + t = 1. / sqrt(2.); + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + indx[j] = j; +/* L10: */ + } + dscal_(n, &t, &z__[1], &c__1); + *rho = (d__1 = *rho * 2., abs(d__1)); + +/* Sort the eigenvalues into increasing order */ + + i__1 = *n; + for (i__ = *cutpnt + 1; i__ <= i__1; ++i__) { + indxq[i__] += *cutpnt; +/* L20: */ + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + dlamda[i__] = d__[indxq[i__]]; + w[i__] = z__[indxq[i__]]; +/* L30: */ + } + i__ = 1; + j = *cutpnt + 1; + dlamrg_(&n1, &n2, &dlamda[1], &c__1, &c__1, &indx[1]); + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + d__[i__] = dlamda[indx[i__]]; + z__[i__] = w[indx[i__]]; +/* L40: */ + } + +/* Calculate the allowable deflation tolerance */ + + imax = idamax_(n, &z__[1], &c__1); + jmax = idamax_(n, &d__[1], &c__1); + eps = dlamch_((char *)"Epsilon", (ftnlen)7); + tol = eps * 8. * (d__1 = d__[jmax], abs(d__1)); + +/* If the rank-1 modifier is small enough, no more needs to be done */ +/* -- except to reorganize Q so that its columns correspond with the */ +/* elements in D. */ + + if (*rho * (d__1 = z__[imax], abs(d__1)) <= tol) { + *k = 0; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + perm[j] = indxq[indx[j]]; + zcopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 + 1] + , &c__1); +/* L50: */ + } + zlacpy_((char *)"A", qsiz, n, &q2[q2_dim1 + 1], ldq2, &q[q_dim1 + 1], ldq, ( + ftnlen)1); + return 0; + } + +/* If there are multiple eigenvalues then the problem deflates. Here */ +/* the number of equal eigenvalues are found. As each equal */ +/* eigenvalue is found, an elementary reflector is computed to rotate */ +/* the corresponding eigensubspace so that the corresponding */ +/* components of Z are zero in this new basis. */ + + *k = 0; + k2 = *n + 1; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (*rho * (d__1 = z__[j], abs(d__1)) <= tol) { + +/* Deflate due to small z component. */ + + --k2; + indxp[k2] = j; + if (j == *n) { + goto L100; + } + } else { + jlam = j; + goto L70; + } +/* L60: */ + } +L70: + ++j; + if (j > *n) { + goto L90; + } + if (*rho * (d__1 = z__[j], abs(d__1)) <= tol) { + +/* Deflate due to small z component. */ + + --k2; + indxp[k2] = j; + } else { + +/* Check if eigenvalues are close enough to allow deflation. */ + + s = z__[jlam]; + c__ = z__[j]; + +/* Find sqrt(a**2+b**2) without overflow or */ +/* destructive underflow. */ + + tau = dlapy2_(&c__, &s); + t = d__[j] - d__[jlam]; + c__ /= tau; + s = -s / tau; + if ((d__1 = t * c__ * s, abs(d__1)) <= tol) { + +/* Deflation is possible. */ + + z__[j] = tau; + z__[jlam] = 0.; + +/* Record the appropriate Givens rotation */ + + ++(*givptr); + givcol[(*givptr << 1) + 1] = indxq[indx[jlam]]; + givcol[(*givptr << 1) + 2] = indxq[indx[j]]; + givnum[(*givptr << 1) + 1] = c__; + givnum[(*givptr << 1) + 2] = s; + zdrot_(qsiz, &q[indxq[indx[jlam]] * q_dim1 + 1], &c__1, &q[indxq[ + indx[j]] * q_dim1 + 1], &c__1, &c__, &s); + t = d__[jlam] * c__ * c__ + d__[j] * s * s; + d__[j] = d__[jlam] * s * s + d__[j] * c__ * c__; + d__[jlam] = t; + --k2; + i__ = 1; +L80: + if (k2 + i__ <= *n) { + if (d__[jlam] < d__[indxp[k2 + i__]]) { + indxp[k2 + i__ - 1] = indxp[k2 + i__]; + indxp[k2 + i__] = jlam; + ++i__; + goto L80; + } else { + indxp[k2 + i__ - 1] = jlam; + } + } else { + indxp[k2 + i__ - 1] = jlam; + } + jlam = j; + } else { + ++(*k); + w[*k] = z__[jlam]; + dlamda[*k] = d__[jlam]; + indxp[*k] = jlam; + jlam = j; + } + } + goto L70; +L90: + +/* Record the last eigenvalue. */ + + ++(*k); + w[*k] = z__[jlam]; + dlamda[*k] = d__[jlam]; + indxp[*k] = jlam; + +L100: + +/* Sort the eigenvalues and corresponding eigenvectors into DLAMDA */ +/* and Q2 respectively. The eigenvalues/vectors which were not */ +/* deflated go into the first K slots of DLAMDA and Q2 respectively, */ +/* while those which were deflated go into the last N - K slots. */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + jp = indxp[j]; + dlamda[j] = d__[jp]; + perm[j] = indxq[indx[jp]]; + zcopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 + 1], & + c__1); +/* L110: */ + } + +/* The deflated eigenvalues and their corresponding vectors go back */ +/* into the last N - K slots of D and Q respectively. */ + + if (*k < *n) { + i__1 = *n - *k; + dcopy_(&i__1, &dlamda[*k + 1], &c__1, &d__[*k + 1], &c__1); + i__1 = *n - *k; + zlacpy_((char *)"A", qsiz, &i__1, &q2[(*k + 1) * q2_dim1 + 1], ldq2, &q[(*k + + 1) * q_dim1 + 1], ldq, (ftnlen)1); + } + + return 0; + +/* End of ZLAED8 */ + +} /* zlaed8_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zlanhe.cpp b/lib/linalg/zlanhe.cpp new file mode 100644 index 0000000000..2522e8d500 --- /dev/null +++ b/lib/linalg/zlanhe.cpp @@ -0,0 +1,348 @@ +/* fortran/zlanhe.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; + +/* > \brief \b ZLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the ele +ment of largest absolute value of a complex Hermitian matrix. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZLANHE + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* DOUBLE PRECISION FUNCTION ZLANHE( NORM, UPLO, N, A, LDA, WORK ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER NORM, UPLO */ +/* INTEGER LDA, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION WORK( * ) */ +/* COMPLEX*16 A( LDA, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZLANHE returns the value of the one norm, or the Frobenius norm, or */ +/* > the infinity norm, or the element of largest absolute value of a */ +/* > complex hermitian matrix A. */ +/* > \endverbatim */ +/* > */ +/* > \return ZLANHE */ +/* > \verbatim */ +/* > */ +/* > ZLANHE = ( max(abs(A(i,j))), NORM = 'M' or 'm' */ +/* > ( */ +/* > ( norm1(A), NORM = '1', 'O' or 'o' */ +/* > ( */ +/* > ( normI(A), NORM = 'I' or 'i' */ +/* > ( */ +/* > ( normF(A), NORM = 'F', 'f', 'E' or 'e' */ +/* > */ +/* > where norm1 denotes the one norm of a matrix (maximum column sum), */ +/* > normI denotes the infinity norm of a matrix (maximum row sum) and */ +/* > normF denotes the Frobenius norm of a matrix (square root of sum of */ +/* > squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] NORM */ +/* > \verbatim */ +/* > NORM is CHARACTER*1 */ +/* > Specifies the value to be returned in ZLANHE as described */ +/* > above. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > Specifies whether the upper or lower triangular part of the */ +/* > hermitian matrix A is to be referenced. */ +/* > = 'U': Upper triangular part of A is referenced */ +/* > = 'L': Lower triangular part of A is referenced */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrix A. N >= 0. When N = 0, ZLANHE is */ +/* > set to zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is COMPLEX*16 array, dimension (LDA,N) */ +/* > The hermitian matrix A. If UPLO = 'U', the leading n by n */ +/* > upper triangular part of A contains the upper triangular part */ +/* > of the matrix A, and the strictly lower triangular part of A */ +/* > is not referenced. If UPLO = 'L', the leading n by n lower */ +/* > triangular part of A contains the lower triangular part of */ +/* > the matrix A, and the strictly upper triangular part of A is */ +/* > not referenced. Note that the imaginary parts of the diagonal */ +/* > elements need not be set and are assumed to be zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(N,1). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), */ +/* > where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, */ +/* > WORK is not referenced. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16HEauxiliary */ + +/* ===================================================================== */ +doublereal zlanhe_(char *norm, char *uplo, integer *n, doublecomplex *a, + integer *lda, doublereal *work, ftnlen norm_len, ftnlen uplo_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2; + doublereal ret_val, d__1; + + /* Builtin functions */ + double z_abs(doublecomplex *), sqrt(doublereal); + + /* Local variables */ + integer i__, j; + doublereal sum, absa, scale; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + doublereal value; + extern logical disnan_(doublereal *); + extern /* Subroutine */ int zlassq_(integer *, doublecomplex *, integer *, + doublereal *, doublereal *); + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --work; + + /* Function Body */ + if (*n == 0) { + value = 0.; + } else if (lsame_(norm, (char *)"M", (ftnlen)1, (ftnlen)1)) { + +/* Find max(abs(A(i,j))). */ + + value = 0.; + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + sum = z_abs(&a[i__ + j * a_dim1]); + if (value < sum || disnan_(&sum)) { + value = sum; + } +/* L10: */ + } + i__2 = j + j * a_dim1; + sum = (d__1 = a[i__2].r, abs(d__1)); + if (value < sum || disnan_(&sum)) { + value = sum; + } +/* L20: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j + j * a_dim1; + sum = (d__1 = a[i__2].r, abs(d__1)); + if (value < sum || disnan_(&sum)) { + value = sum; + } + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + sum = z_abs(&a[i__ + j * a_dim1]); + if (value < sum || disnan_(&sum)) { + value = sum; + } +/* L30: */ + } +/* L40: */ + } + } + } else if (lsame_(norm, (char *)"I", (ftnlen)1, (ftnlen)1) || lsame_(norm, (char *)"O", ( + ftnlen)1, (ftnlen)1) || *(unsigned char *)norm == '1') { + +/* Find normI(A) ( = norm1(A), since A is hermitian). */ + + value = 0.; + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + sum = 0.; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + absa = z_abs(&a[i__ + j * a_dim1]); + sum += absa; + work[i__] += absa; +/* L50: */ + } + i__2 = j + j * a_dim1; + work[j] = sum + (d__1 = a[i__2].r, abs(d__1)); +/* L60: */ + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + sum = work[i__]; + if (value < sum || disnan_(&sum)) { + value = sum; + } +/* L70: */ + } + } else { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + work[i__] = 0.; +/* L80: */ + } + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j + j * a_dim1; + sum = work[j] + (d__1 = a[i__2].r, abs(d__1)); + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + absa = z_abs(&a[i__ + j * a_dim1]); + sum += absa; + work[i__] += absa; +/* L90: */ + } + if (value < sum || disnan_(&sum)) { + value = sum; + } +/* L100: */ + } + } + } else if (lsame_(norm, (char *)"F", (ftnlen)1, (ftnlen)1) || lsame_(norm, (char *)"E", ( + ftnlen)1, (ftnlen)1)) { + +/* Find normF(A). */ + + scale = 0.; + sum = 1.; + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + i__1 = *n; + for (j = 2; j <= i__1; ++j) { + i__2 = j - 1; + zlassq_(&i__2, &a[j * a_dim1 + 1], &c__1, &scale, &sum); +/* L110: */ + } + } else { + i__1 = *n - 1; + for (j = 1; j <= i__1; ++j) { + i__2 = *n - j; + zlassq_(&i__2, &a[j + 1 + j * a_dim1], &c__1, &scale, &sum); +/* L120: */ + } + } + sum *= 2; + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__ + i__ * a_dim1; + if (a[i__2].r != 0.) { + i__2 = i__ + i__ * a_dim1; + absa = (d__1 = a[i__2].r, abs(d__1)); + if (scale < absa) { +/* Computing 2nd power */ + d__1 = scale / absa; + sum = sum * (d__1 * d__1) + 1.; + scale = absa; + } else { +/* Computing 2nd power */ + d__1 = absa / scale; + sum += d__1 * d__1; + } + } +/* L130: */ + } + value = scale * sqrt(sum); + } + + ret_val = value; + return ret_val; + +/* End of ZLANHE */ + +} /* zlanhe_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zlarf.cpp b/lib/linalg/zlarf.cpp new file mode 100644 index 0000000000..453644e7d9 --- /dev/null +++ b/lib/linalg/zlarf.cpp @@ -0,0 +1,283 @@ +/* fortran/zlarf.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static doublecomplex c_b1 = {1.,0.}; +static doublecomplex c_b2 = {0.,0.}; +static integer c__1 = 1; + +/* > \brief \b ZLARF applies an elementary reflector to a general rectangular matrix. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZLARF + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER SIDE */ +/* INTEGER INCV, LDC, M, N */ +/* COMPLEX*16 TAU */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 C( LDC, * ), V( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZLARF applies a complex elementary reflector H to a complex M-by-N */ +/* > matrix C, from either the left or the right. H is represented in the */ +/* > form */ +/* > */ +/* > H = I - tau * v * v**H */ +/* > */ +/* > where tau is a complex scalar and v is a complex vector. */ +/* > */ +/* > If tau = 0, then H is taken to be the unit matrix. */ +/* > */ +/* > To apply H**H, supply conjg(tau) instead */ +/* > tau. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] SIDE */ +/* > \verbatim */ +/* > SIDE is CHARACTER*1 */ +/* > = 'L': form H * C */ +/* > = 'R': form C * H */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix C. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix C. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] V */ +/* > \verbatim */ +/* > V is COMPLEX*16 array, dimension */ +/* > (1 + (M-1)*abs(INCV)) if SIDE = 'L' */ +/* > or (1 + (N-1)*abs(INCV)) if SIDE = 'R' */ +/* > The vector v in the representation of H. V is not used if */ +/* > TAU = 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCV */ +/* > \verbatim */ +/* > INCV is INTEGER */ +/* > The increment between elements of v. INCV <> 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TAU */ +/* > \verbatim */ +/* > TAU is COMPLEX*16 */ +/* > The value tau in the representation of H. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] C */ +/* > \verbatim */ +/* > C is COMPLEX*16 array, dimension (LDC,N) */ +/* > On entry, the M-by-N matrix C. */ +/* > On exit, C is overwritten by the matrix H * C if SIDE = 'L', */ +/* > or C * H if SIDE = 'R'. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDC */ +/* > \verbatim */ +/* > LDC is INTEGER */ +/* > The leading dimension of the array C. LDC >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is COMPLEX*16 array, dimension */ +/* > (N) if SIDE = 'L' */ +/* > or (M) if SIDE = 'R' */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16OTHERauxiliary */ + +/* ===================================================================== */ +/* Subroutine */ int zlarf_(char *side, integer *m, integer *n, doublecomplex + *v, integer *incv, doublecomplex *tau, doublecomplex *c__, integer * + ldc, doublecomplex *work, ftnlen side_len) +{ + /* System generated locals */ + integer c_dim1, c_offset, i__1; + doublecomplex z__1; + + /* Local variables */ + integer i__; + logical applyleft; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + integer lastc; + extern /* Subroutine */ int zgerc_(integer *, integer *, doublecomplex *, + doublecomplex *, integer *, doublecomplex *, integer *, + doublecomplex *, integer *), zgemv_(char *, integer *, integer *, + doublecomplex *, doublecomplex *, integer *, doublecomplex *, + integer *, doublecomplex *, doublecomplex *, integer *, ftnlen); + integer lastv; + extern integer ilazlc_(integer *, integer *, doublecomplex *, integer *), + ilazlr_(integer *, integer *, doublecomplex *, integer *); + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + + /* Parameter adjustments */ + --v; + c_dim1 = *ldc; + c_offset = 1 + c_dim1; + c__ -= c_offset; + --work; + + /* Function Body */ + applyleft = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); + lastv = 0; + lastc = 0; + if (tau->r != 0. || tau->i != 0.) { +/* Set up variables for scanning V. LASTV begins pointing to the end */ +/* of V. */ + if (applyleft) { + lastv = *m; + } else { + lastv = *n; + } + if (*incv > 0) { + i__ = (lastv - 1) * *incv + 1; + } else { + i__ = 1; + } +/* Look for the last non-zero row in V. */ + for(;;) { /* while(complicated condition) */ + i__1 = i__; + if (!(lastv > 0 && (v[i__1].r == 0. && v[i__1].i == 0.))) + break; + --lastv; + i__ -= *incv; + } + if (applyleft) { +/* Scan for the last non-zero column in C(1:lastv,:). */ + lastc = ilazlc_(&lastv, n, &c__[c_offset], ldc); + } else { +/* Scan for the last non-zero row in C(:,1:lastv). */ + lastc = ilazlr_(m, &lastv, &c__[c_offset], ldc); + } + } +/* Note that lastc.eq.0 renders the BLAS operations null; no special */ +/* case is needed at this level. */ + if (applyleft) { + +/* Form H * C */ + + if (lastv > 0) { + +/* w(1:lastc,1) := C(1:lastv,1:lastc)**H * v(1:lastv,1) */ + + zgemv_((char *)"Conjugate transpose", &lastv, &lastc, &c_b1, &c__[ + c_offset], ldc, &v[1], incv, &c_b2, &work[1], &c__1, ( + ftnlen)19); + +/* C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**H */ + + z__1.r = -tau->r, z__1.i = -tau->i; + zgerc_(&lastv, &lastc, &z__1, &v[1], incv, &work[1], &c__1, &c__[ + c_offset], ldc); + } + } else { + +/* Form C * H */ + + if (lastv > 0) { + +/* w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1) */ + + zgemv_((char *)"No transpose", &lastc, &lastv, &c_b1, &c__[c_offset], ldc, + &v[1], incv, &c_b2, &work[1], &c__1, (ftnlen)12); + +/* C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**H */ + + z__1.r = -tau->r, z__1.i = -tau->i; + zgerc_(&lastc, &lastv, &z__1, &work[1], &c__1, &v[1], incv, &c__[ + c_offset], ldc); + } + } + return 0; + +/* End of ZLARF */ + +} /* zlarf_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zlarfb.cpp b/lib/linalg/zlarfb.cpp new file mode 100644 index 0000000000..0ea0c17bd4 --- /dev/null +++ b/lib/linalg/zlarfb.cpp @@ -0,0 +1,949 @@ +/* fortran/zlarfb.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static doublecomplex c_b1 = {1.,0.}; +static integer c__1 = 1; + +/* > \brief \b ZLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZLARFB + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, */ +/* T, LDT, C, LDC, WORK, LDWORK ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER DIRECT, SIDE, STOREV, TRANS */ +/* INTEGER K, LDC, LDT, LDV, LDWORK, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 C( LDC, * ), T( LDT, * ), V( LDV, * ), */ +/* $ WORK( LDWORK, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZLARFB applies a complex block reflector H or its transpose H**H to a */ +/* > complex M-by-N matrix C, from either the left or the right. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] SIDE */ +/* > \verbatim */ +/* > SIDE is CHARACTER*1 */ +/* > = 'L': apply H or H**H from the Left */ +/* > = 'R': apply H or H**H from the Right */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TRANS */ +/* > \verbatim */ +/* > TRANS is CHARACTER*1 */ +/* > = 'N': apply H (No transpose) */ +/* > = 'C': apply H**H (Conjugate transpose) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DIRECT */ +/* > \verbatim */ +/* > DIRECT is CHARACTER*1 */ +/* > Indicates how H is formed from a product of elementary */ +/* > reflectors */ +/* > = 'F': H = H(1) H(2) . . . H(k) (Forward) */ +/* > = 'B': H = H(k) . . . H(2) H(1) (Backward) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] STOREV */ +/* > \verbatim */ +/* > STOREV is CHARACTER*1 */ +/* > Indicates how the vectors which define the elementary */ +/* > reflectors are stored: */ +/* > = 'C': Columnwise */ +/* > = 'R': Rowwise */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix C. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix C. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > The order of the matrix T (= the number of elementary */ +/* > reflectors whose product defines the block reflector). */ +/* > If SIDE = 'L', M >= K >= 0; */ +/* > if SIDE = 'R', N >= K >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] V */ +/* > \verbatim */ +/* > V is COMPLEX*16 array, dimension */ +/* > (LDV,K) if STOREV = 'C' */ +/* > (LDV,M) if STOREV = 'R' and SIDE = 'L' */ +/* > (LDV,N) if STOREV = 'R' and SIDE = 'R' */ +/* > See Further Details. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDV */ +/* > \verbatim */ +/* > LDV is INTEGER */ +/* > The leading dimension of the array V. */ +/* > If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M); */ +/* > if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N); */ +/* > if STOREV = 'R', LDV >= K. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] T */ +/* > \verbatim */ +/* > T is COMPLEX*16 array, dimension (LDT,K) */ +/* > The triangular K-by-K matrix T in the representation of the */ +/* > block reflector. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDT */ +/* > \verbatim */ +/* > LDT is INTEGER */ +/* > The leading dimension of the array T. LDT >= K. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] C */ +/* > \verbatim */ +/* > C is COMPLEX*16 array, dimension (LDC,N) */ +/* > On entry, the M-by-N matrix C. */ +/* > On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDC */ +/* > \verbatim */ +/* > LDC is INTEGER */ +/* > The leading dimension of the array C. LDC >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is COMPLEX*16 array, dimension (LDWORK,K) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDWORK */ +/* > \verbatim */ +/* > LDWORK is INTEGER */ +/* > The leading dimension of the array WORK. */ +/* > If SIDE = 'L', LDWORK >= max(1,N); */ +/* > if SIDE = 'R', LDWORK >= max(1,M). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16OTHERauxiliary */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > The shape of the matrix V and the storage of the vectors which define */ +/* > the H(i) is best illustrated by the following example with n = 5 and */ +/* > k = 3. The elements equal to 1 are not stored; the corresponding */ +/* > array elements are modified but restored on exit. The rest of the */ +/* > array is not used. */ +/* > */ +/* > DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': */ +/* > */ +/* > V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) */ +/* > ( v1 1 ) ( 1 v2 v2 v2 ) */ +/* > ( v1 v2 1 ) ( 1 v3 v3 ) */ +/* > ( v1 v2 v3 ) */ +/* > ( v1 v2 v3 ) */ +/* > */ +/* > DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': */ +/* > */ +/* > V = ( v1 v2 v3 ) V = ( v1 v1 1 ) */ +/* > ( v1 v2 v3 ) ( v2 v2 v2 1 ) */ +/* > ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) */ +/* > ( 1 v3 ) */ +/* > ( 1 ) */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int zlarfb_(char *side, char *trans, char *direct, char * + storev, integer *m, integer *n, integer *k, doublecomplex *v, integer + *ldv, doublecomplex *t, integer *ldt, doublecomplex *c__, integer * + ldc, doublecomplex *work, integer *ldwork, ftnlen side_len, ftnlen + trans_len, ftnlen direct_len, ftnlen storev_len) +{ + /* System generated locals */ + integer c_dim1, c_offset, t_dim1, t_offset, v_dim1, v_offset, work_dim1, + work_offset, i__1, i__2, i__3, i__4, i__5; + doublecomplex z__1, z__2; + + /* Builtin functions */ + void d_cnjg(doublecomplex *, doublecomplex *); + + /* Local variables */ + integer i__, j; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *, + integer *, doublecomplex *, doublecomplex *, integer *, + doublecomplex *, integer *, doublecomplex *, doublecomplex *, + integer *, ftnlen, ftnlen), zcopy_(integer *, doublecomplex *, + integer *, doublecomplex *, integer *), ztrmm_(char *, char *, + char *, char *, integer *, integer *, doublecomplex *, + doublecomplex *, integer *, doublecomplex *, integer *, ftnlen, + ftnlen, ftnlen, ftnlen), zlacgv_(integer *, doublecomplex *, + integer *); + char transt[1]; + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Quick return if possible */ + + /* Parameter adjustments */ + v_dim1 = *ldv; + v_offset = 1 + v_dim1; + v -= v_offset; + t_dim1 = *ldt; + t_offset = 1 + t_dim1; + t -= t_offset; + c_dim1 = *ldc; + c_offset = 1 + c_dim1; + c__ -= c_offset; + work_dim1 = *ldwork; + work_offset = 1 + work_dim1; + work -= work_offset; + + /* Function Body */ + if (*m <= 0 || *n <= 0) { + return 0; + } + + if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { + *(unsigned char *)transt = 'C'; + } else { + *(unsigned char *)transt = 'N'; + } + + if (lsame_(storev, (char *)"C", (ftnlen)1, (ftnlen)1)) { + + if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { + +/* Let V = ( V1 ) (first K rows) */ +/* ( V2 ) */ +/* where V1 is unit lower triangular. */ + + if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { + +/* Form H * C or H**H * C where C = ( C1 ) */ +/* ( C2 ) */ + +/* W := C**H * V = (C1**H * V1 + C2**H * V2) (stored in WORK) */ + +/* W := C1**H */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + zcopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1], + &c__1); + zlacgv_(n, &work[j * work_dim1 + 1], &c__1); +/* L10: */ + } + +/* W := W * V1 */ + + ztrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", n, k, &c_b1, + &v[v_offset], ldv, &work[work_offset], ldwork, ( + ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); + if (*m > *k) { + +/* W := W + C2**H * V2 */ + + i__1 = *m - *k; + zgemm_((char *)"Conjugate transpose", (char *)"No transpose", n, k, &i__1, + &c_b1, &c__[*k + 1 + c_dim1], ldc, &v[*k + 1 + + v_dim1], ldv, &c_b1, &work[work_offset], ldwork, ( + ftnlen)19, (ftnlen)12); + } + +/* W := W * T**H or W * T */ + + ztrmm_((char *)"Right", (char *)"Upper", transt, (char *)"Non-unit", n, k, &c_b1, &t[ + t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)1, (ftnlen)8); + +/* C := C - V * W**H */ + + if (*m > *k) { + +/* C2 := C2 - V2 * W**H */ + + i__1 = *m - *k; + z__1.r = -1., z__1.i = -0.; + zgemm_((char *)"No transpose", (char *)"Conjugate transpose", &i__1, n, k, + &z__1, &v[*k + 1 + v_dim1], ldv, &work[ + work_offset], ldwork, &c_b1, &c__[*k + 1 + c_dim1] + , ldc, (ftnlen)12, (ftnlen)19); + } + +/* W := W * V1**H */ + + ztrmm_((char *)"Right", (char *)"Lower", (char *)"Conjugate transpose", (char *)"Unit", n, k, + &c_b1, &v[v_offset], ldv, &work[work_offset], ldwork, + (ftnlen)5, (ftnlen)5, (ftnlen)19, (ftnlen)4); + +/* C1 := C1 - W**H */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = j + i__ * c_dim1; + i__4 = j + i__ * c_dim1; + d_cnjg(&z__2, &work[i__ + j * work_dim1]); + z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i - + z__2.i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; +/* L20: */ + } +/* L30: */ + } + + } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + +/* Form C * H or C * H**H where C = ( C1 C2 ) */ + +/* W := C * V = (C1*V1 + C2*V2) (stored in WORK) */ + +/* W := C1 */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + zcopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j * + work_dim1 + 1], &c__1); +/* L40: */ + } + +/* W := W * V1 */ + + ztrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", m, k, &c_b1, + &v[v_offset], ldv, &work[work_offset], ldwork, ( + ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); + if (*n > *k) { + +/* W := W + C2 * V2 */ + + i__1 = *n - *k; + zgemm_((char *)"No transpose", (char *)"No transpose", m, k, &i__1, &c_b1, + &c__[(*k + 1) * c_dim1 + 1], ldc, &v[*k + 1 + + v_dim1], ldv, &c_b1, &work[work_offset], ldwork, ( + ftnlen)12, (ftnlen)12); + } + +/* W := W * T or W * T**H */ + + ztrmm_((char *)"Right", (char *)"Upper", trans, (char *)"Non-unit", m, k, &c_b1, &t[ + t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)1, (ftnlen)8); + +/* C := C - W * V**H */ + + if (*n > *k) { + +/* C2 := C2 - W * V2**H */ + + i__1 = *n - *k; + z__1.r = -1., z__1.i = -0.; + zgemm_((char *)"No transpose", (char *)"Conjugate transpose", m, &i__1, k, + &z__1, &work[work_offset], ldwork, &v[*k + 1 + + v_dim1], ldv, &c_b1, &c__[(*k + 1) * c_dim1 + 1], + ldc, (ftnlen)12, (ftnlen)19); + } + +/* W := W * V1**H */ + + ztrmm_((char *)"Right", (char *)"Lower", (char *)"Conjugate transpose", (char *)"Unit", m, k, + &c_b1, &v[v_offset], ldv, &work[work_offset], ldwork, + (ftnlen)5, (ftnlen)5, (ftnlen)19, (ftnlen)4); + +/* C1 := C1 - W */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + i__4 = i__ + j * c_dim1; + i__5 = i__ + j * work_dim1; + z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[ + i__4].i - work[i__5].i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; +/* L50: */ + } +/* L60: */ + } + } + + } else { + +/* Let V = ( V1 ) */ +/* ( V2 ) (last K rows) */ +/* where V2 is unit upper triangular. */ + + if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { + +/* Form H * C or H**H * C where C = ( C1 ) */ +/* ( C2 ) */ + +/* W := C**H * V = (C1**H * V1 + C2**H * V2) (stored in WORK) */ + +/* W := C2**H */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + zcopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j * + work_dim1 + 1], &c__1); + zlacgv_(n, &work[j * work_dim1 + 1], &c__1); +/* L70: */ + } + +/* W := W * V2 */ + + ztrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", n, k, &c_b1, + &v[*m - *k + 1 + v_dim1], ldv, &work[work_offset], + ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); + if (*m > *k) { + +/* W := W + C1**H * V1 */ + + i__1 = *m - *k; + zgemm_((char *)"Conjugate transpose", (char *)"No transpose", n, k, &i__1, + &c_b1, &c__[c_offset], ldc, &v[v_offset], ldv, & + c_b1, &work[work_offset], ldwork, (ftnlen)19, ( + ftnlen)12); + } + +/* W := W * T**H or W * T */ + + ztrmm_((char *)"Right", (char *)"Lower", transt, (char *)"Non-unit", n, k, &c_b1, &t[ + t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)1, (ftnlen)8); + +/* C := C - V * W**H */ + + if (*m > *k) { + +/* C1 := C1 - V1 * W**H */ + + i__1 = *m - *k; + z__1.r = -1., z__1.i = -0.; + zgemm_((char *)"No transpose", (char *)"Conjugate transpose", &i__1, n, k, + &z__1, &v[v_offset], ldv, &work[work_offset], + ldwork, &c_b1, &c__[c_offset], ldc, (ftnlen)12, ( + ftnlen)19); + } + +/* W := W * V2**H */ + + ztrmm_((char *)"Right", (char *)"Upper", (char *)"Conjugate transpose", (char *)"Unit", n, k, + &c_b1, &v[*m - *k + 1 + v_dim1], ldv, &work[ + work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen) + 19, (ftnlen)4); + +/* C2 := C2 - W**H */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = *m - *k + j + i__ * c_dim1; + i__4 = *m - *k + j + i__ * c_dim1; + d_cnjg(&z__2, &work[i__ + j * work_dim1]); + z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i - + z__2.i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; +/* L80: */ + } +/* L90: */ + } + + } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + +/* Form C * H or C * H**H where C = ( C1 C2 ) */ + +/* W := C * V = (C1*V1 + C2*V2) (stored in WORK) */ + +/* W := C2 */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + zcopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[ + j * work_dim1 + 1], &c__1); +/* L100: */ + } + +/* W := W * V2 */ + + ztrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", m, k, &c_b1, + &v[*n - *k + 1 + v_dim1], ldv, &work[work_offset], + ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); + if (*n > *k) { + +/* W := W + C1 * V1 */ + + i__1 = *n - *k; + zgemm_((char *)"No transpose", (char *)"No transpose", m, k, &i__1, &c_b1, + &c__[c_offset], ldc, &v[v_offset], ldv, &c_b1, & + work[work_offset], ldwork, (ftnlen)12, (ftnlen)12) + ; + } + +/* W := W * T or W * T**H */ + + ztrmm_((char *)"Right", (char *)"Lower", trans, (char *)"Non-unit", m, k, &c_b1, &t[ + t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)1, (ftnlen)8); + +/* C := C - W * V**H */ + + if (*n > *k) { + +/* C1 := C1 - W * V1**H */ + + i__1 = *n - *k; + z__1.r = -1., z__1.i = -0.; + zgemm_((char *)"No transpose", (char *)"Conjugate transpose", m, &i__1, k, + &z__1, &work[work_offset], ldwork, &v[v_offset], + ldv, &c_b1, &c__[c_offset], ldc, (ftnlen)12, ( + ftnlen)19); + } + +/* W := W * V2**H */ + + ztrmm_((char *)"Right", (char *)"Upper", (char *)"Conjugate transpose", (char *)"Unit", m, k, + &c_b1, &v[*n - *k + 1 + v_dim1], ldv, &work[ + work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen) + 19, (ftnlen)4); + +/* C2 := C2 - W */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + (*n - *k + j) * c_dim1; + i__4 = i__ + (*n - *k + j) * c_dim1; + i__5 = i__ + j * work_dim1; + z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[ + i__4].i - work[i__5].i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; +/* L110: */ + } +/* L120: */ + } + } + } + + } else if (lsame_(storev, (char *)"R", (ftnlen)1, (ftnlen)1)) { + + if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { + +/* Let V = ( V1 V2 ) (V1: first K columns) */ +/* where V1 is unit upper triangular. */ + + if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { + +/* Form H * C or H**H * C where C = ( C1 ) */ +/* ( C2 ) */ + +/* W := C**H * V**H = (C1**H * V1**H + C2**H * V2**H) (stored in WORK) */ + +/* W := C1**H */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + zcopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1], + &c__1); + zlacgv_(n, &work[j * work_dim1 + 1], &c__1); +/* L130: */ + } + +/* W := W * V1**H */ + + ztrmm_((char *)"Right", (char *)"Upper", (char *)"Conjugate transpose", (char *)"Unit", n, k, + &c_b1, &v[v_offset], ldv, &work[work_offset], ldwork, + (ftnlen)5, (ftnlen)5, (ftnlen)19, (ftnlen)4); + if (*m > *k) { + +/* W := W + C2**H * V2**H */ + + i__1 = *m - *k; + zgemm_((char *)"Conjugate transpose", (char *)"Conjugate transpose", n, k, + &i__1, &c_b1, &c__[*k + 1 + c_dim1], ldc, &v[(*k + + 1) * v_dim1 + 1], ldv, &c_b1, &work[work_offset] + , ldwork, (ftnlen)19, (ftnlen)19); + } + +/* W := W * T**H or W * T */ + + ztrmm_((char *)"Right", (char *)"Upper", transt, (char *)"Non-unit", n, k, &c_b1, &t[ + t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)1, (ftnlen)8); + +/* C := C - V**H * W**H */ + + if (*m > *k) { + +/* C2 := C2 - V2**H * W**H */ + + i__1 = *m - *k; + z__1.r = -1., z__1.i = -0.; + zgemm_((char *)"Conjugate transpose", (char *)"Conjugate transpose", & + i__1, n, k, &z__1, &v[(*k + 1) * v_dim1 + 1], ldv, + &work[work_offset], ldwork, &c_b1, &c__[*k + 1 + + c_dim1], ldc, (ftnlen)19, (ftnlen)19); + } + +/* W := W * V1 */ + + ztrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", n, k, &c_b1, + &v[v_offset], ldv, &work[work_offset], ldwork, ( + ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); + +/* C1 := C1 - W**H */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = j + i__ * c_dim1; + i__4 = j + i__ * c_dim1; + d_cnjg(&z__2, &work[i__ + j * work_dim1]); + z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i - + z__2.i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; +/* L140: */ + } +/* L150: */ + } + + } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + +/* Form C * H or C * H**H where C = ( C1 C2 ) */ + +/* W := C * V**H = (C1*V1**H + C2*V2**H) (stored in WORK) */ + +/* W := C1 */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + zcopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j * + work_dim1 + 1], &c__1); +/* L160: */ + } + +/* W := W * V1**H */ + + ztrmm_((char *)"Right", (char *)"Upper", (char *)"Conjugate transpose", (char *)"Unit", m, k, + &c_b1, &v[v_offset], ldv, &work[work_offset], ldwork, + (ftnlen)5, (ftnlen)5, (ftnlen)19, (ftnlen)4); + if (*n > *k) { + +/* W := W + C2 * V2**H */ + + i__1 = *n - *k; + zgemm_((char *)"No transpose", (char *)"Conjugate transpose", m, k, &i__1, + &c_b1, &c__[(*k + 1) * c_dim1 + 1], ldc, &v[(*k + + 1) * v_dim1 + 1], ldv, &c_b1, &work[work_offset] + , ldwork, (ftnlen)12, (ftnlen)19); + } + +/* W := W * T or W * T**H */ + + ztrmm_((char *)"Right", (char *)"Upper", trans, (char *)"Non-unit", m, k, &c_b1, &t[ + t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)1, (ftnlen)8); + +/* C := C - W * V */ + + if (*n > *k) { + +/* C2 := C2 - W * V2 */ + + i__1 = *n - *k; + z__1.r = -1., z__1.i = -0.; + zgemm_((char *)"No transpose", (char *)"No transpose", m, &i__1, k, &z__1, + &work[work_offset], ldwork, &v[(*k + 1) * v_dim1 + + 1], ldv, &c_b1, &c__[(*k + 1) * c_dim1 + 1], + ldc, (ftnlen)12, (ftnlen)12); + } + +/* W := W * V1 */ + + ztrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", m, k, &c_b1, + &v[v_offset], ldv, &work[work_offset], ldwork, ( + ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); + +/* C1 := C1 - W */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + i__4 = i__ + j * c_dim1; + i__5 = i__ + j * work_dim1; + z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[ + i__4].i - work[i__5].i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; +/* L170: */ + } +/* L180: */ + } + + } + + } else { + +/* Let V = ( V1 V2 ) (V2: last K columns) */ +/* where V2 is unit lower triangular. */ + + if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { + +/* Form H * C or H**H * C where C = ( C1 ) */ +/* ( C2 ) */ + +/* W := C**H * V**H = (C1**H * V1**H + C2**H * V2**H) (stored in WORK) */ + +/* W := C2**H */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + zcopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j * + work_dim1 + 1], &c__1); + zlacgv_(n, &work[j * work_dim1 + 1], &c__1); +/* L190: */ + } + +/* W := W * V2**H */ + + ztrmm_((char *)"Right", (char *)"Lower", (char *)"Conjugate transpose", (char *)"Unit", n, k, + &c_b1, &v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[ + work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen) + 19, (ftnlen)4); + if (*m > *k) { + +/* W := W + C1**H * V1**H */ + + i__1 = *m - *k; + zgemm_((char *)"Conjugate transpose", (char *)"Conjugate transpose", n, k, + &i__1, &c_b1, &c__[c_offset], ldc, &v[v_offset], + ldv, &c_b1, &work[work_offset], ldwork, (ftnlen) + 19, (ftnlen)19); + } + +/* W := W * T**H or W * T */ + + ztrmm_((char *)"Right", (char *)"Lower", transt, (char *)"Non-unit", n, k, &c_b1, &t[ + t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)1, (ftnlen)8); + +/* C := C - V**H * W**H */ + + if (*m > *k) { + +/* C1 := C1 - V1**H * W**H */ + + i__1 = *m - *k; + z__1.r = -1., z__1.i = -0.; + zgemm_((char *)"Conjugate transpose", (char *)"Conjugate transpose", & + i__1, n, k, &z__1, &v[v_offset], ldv, &work[ + work_offset], ldwork, &c_b1, &c__[c_offset], ldc, + (ftnlen)19, (ftnlen)19); + } + +/* W := W * V2 */ + + ztrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", n, k, &c_b1, + &v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[ + work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen) + 12, (ftnlen)4); + +/* C2 := C2 - W**H */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = *m - *k + j + i__ * c_dim1; + i__4 = *m - *k + j + i__ * c_dim1; + d_cnjg(&z__2, &work[i__ + j * work_dim1]); + z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i - + z__2.i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; +/* L200: */ + } +/* L210: */ + } + + } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + +/* Form C * H or C * H**H where C = ( C1 C2 ) */ + +/* W := C * V**H = (C1*V1**H + C2*V2**H) (stored in WORK) */ + +/* W := C2 */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + zcopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[ + j * work_dim1 + 1], &c__1); +/* L220: */ + } + +/* W := W * V2**H */ + + ztrmm_((char *)"Right", (char *)"Lower", (char *)"Conjugate transpose", (char *)"Unit", m, k, + &c_b1, &v[(*n - *k + 1) * v_dim1 + 1], ldv, &work[ + work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen) + 19, (ftnlen)4); + if (*n > *k) { + +/* W := W + C1 * V1**H */ + + i__1 = *n - *k; + zgemm_((char *)"No transpose", (char *)"Conjugate transpose", m, k, &i__1, + &c_b1, &c__[c_offset], ldc, &v[v_offset], ldv, & + c_b1, &work[work_offset], ldwork, (ftnlen)12, ( + ftnlen)19); + } + +/* W := W * T or W * T**H */ + + ztrmm_((char *)"Right", (char *)"Lower", trans, (char *)"Non-unit", m, k, &c_b1, &t[ + t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)1, (ftnlen)8); + +/* C := C - W * V */ + + if (*n > *k) { + +/* C1 := C1 - W * V1 */ + + i__1 = *n - *k; + z__1.r = -1., z__1.i = -0.; + zgemm_((char *)"No transpose", (char *)"No transpose", m, &i__1, k, &z__1, + &work[work_offset], ldwork, &v[v_offset], ldv, & + c_b1, &c__[c_offset], ldc, (ftnlen)12, (ftnlen)12) + ; + } + +/* W := W * V2 */ + + ztrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", m, k, &c_b1, + &v[(*n - *k + 1) * v_dim1 + 1], ldv, &work[ + work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen) + 12, (ftnlen)4); + +/* C1 := C1 - W */ + + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + (*n - *k + j) * c_dim1; + i__4 = i__ + (*n - *k + j) * c_dim1; + i__5 = i__ + j * work_dim1; + z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[ + i__4].i - work[i__5].i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; +/* L230: */ + } +/* L240: */ + } + + } + + } + } + + return 0; + +/* End of ZLARFB */ + +} /* zlarfb_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zlarfg.cpp b/lib/linalg/zlarfg.cpp new file mode 100644 index 0000000000..e3d58be892 --- /dev/null +++ b/lib/linalg/zlarfg.cpp @@ -0,0 +1,261 @@ +/* fortran/zlarfg.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static doublecomplex c_b5 = {1.,0.}; + +/* > \brief \b ZLARFG generates an elementary reflector (Householder matrix). */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZLARFG + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZLARFG( N, ALPHA, X, INCX, TAU ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INCX, N */ +/* COMPLEX*16 ALPHA, TAU */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 X( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZLARFG generates a complex elementary reflector H of order n, such */ +/* > that */ +/* > */ +/* > H**H * ( alpha ) = ( beta ), H**H * H = I. */ +/* > ( x ) ( 0 ) */ +/* > */ +/* > where alpha and beta are scalars, with beta real, and x is an */ +/* > (n-1)-element complex vector. H is represented in the form */ +/* > */ +/* > H = I - tau * ( 1 ) * ( 1 v**H ) , */ +/* > ( v ) */ +/* > */ +/* > where tau is a complex scalar and v is a complex (n-1)-element */ +/* > vector. Note that H is not hermitian. */ +/* > */ +/* > If the elements of x are all zero and alpha is real, then tau = 0 */ +/* > and H is taken to be the unit matrix. */ +/* > */ +/* > Otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1 . */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the elementary reflector. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] ALPHA */ +/* > \verbatim */ +/* > ALPHA is COMPLEX*16 */ +/* > On entry, the value alpha. */ +/* > On exit, it is overwritten with the value beta. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] X */ +/* > \verbatim */ +/* > X is COMPLEX*16 array, dimension */ +/* > (1+(N-2)*abs(INCX)) */ +/* > On entry, the vector x. */ +/* > On exit, it is overwritten with the vector v. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > The increment between elements of X. INCX > 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] TAU */ +/* > \verbatim */ +/* > TAU is COMPLEX*16 */ +/* > The value tau. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16OTHERauxiliary */ + +/* ===================================================================== */ +/* Subroutine */ int zlarfg_(integer *n, doublecomplex *alpha, doublecomplex * + x, integer *incx, doublecomplex *tau) +{ + /* System generated locals */ + integer i__1; + doublereal d__1, d__2; + doublecomplex z__1, z__2; + + /* Builtin functions */ + double d_imag(doublecomplex *), d_sign(doublereal *, doublereal *); + + /* Local variables */ + integer j, knt; + doublereal beta, alphi, alphr; + extern /* Subroutine */ int zscal_(integer *, doublecomplex *, + doublecomplex *, integer *); + doublereal xnorm; + extern doublereal dlapy3_(doublereal *, doublereal *, doublereal *), + dznrm2_(integer *, doublecomplex *, integer *), dlamch_(char *, + ftnlen); + doublereal safmin; + extern /* Subroutine */ int zdscal_(integer *, doublereal *, + doublecomplex *, integer *); + doublereal rsafmn; + extern /* Double Complex */ VOID zladiv_(doublecomplex *, doublecomplex *, + doublecomplex *); + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Executable Statements .. */ + + /* Parameter adjustments */ + --x; + + /* Function Body */ + if (*n <= 0) { + tau->r = 0., tau->i = 0.; + return 0; + } + + i__1 = *n - 1; + xnorm = dznrm2_(&i__1, &x[1], incx); + alphr = alpha->r; + alphi = d_imag(alpha); + + if (xnorm == 0. && alphi == 0.) { + +/* H = I */ + + tau->r = 0., tau->i = 0.; + } else { + +/* general case */ + + d__1 = dlapy3_(&alphr, &alphi, &xnorm); + beta = -d_sign(&d__1, &alphr); + safmin = dlamch_((char *)"S", (ftnlen)1) / dlamch_((char *)"E", (ftnlen)1); + rsafmn = 1. / safmin; + + knt = 0; + if (abs(beta) < safmin) { + +/* XNORM, BETA may be inaccurate; scale X and recompute them */ + +L10: + ++knt; + i__1 = *n - 1; + zdscal_(&i__1, &rsafmn, &x[1], incx); + beta *= rsafmn; + alphi *= rsafmn; + alphr *= rsafmn; + if (abs(beta) < safmin && knt < 20) { + goto L10; + } + +/* New BETA is at most 1, at least SAFMIN */ + + i__1 = *n - 1; + xnorm = dznrm2_(&i__1, &x[1], incx); + z__1.r = alphr, z__1.i = alphi; + alpha->r = z__1.r, alpha->i = z__1.i; + d__1 = dlapy3_(&alphr, &alphi, &xnorm); + beta = -d_sign(&d__1, &alphr); + } + d__1 = (beta - alphr) / beta; + d__2 = -alphi / beta; + z__1.r = d__1, z__1.i = d__2; + tau->r = z__1.r, tau->i = z__1.i; + z__2.r = alpha->r - beta, z__2.i = alpha->i; + zladiv_(&z__1, &c_b5, &z__2); + alpha->r = z__1.r, alpha->i = z__1.i; + i__1 = *n - 1; + zscal_(&i__1, alpha, &x[1], incx); + +/* If ALPHA is subnormal, it may lose relative accuracy */ + + i__1 = knt; + for (j = 1; j <= i__1; ++j) { + beta *= safmin; +/* L20: */ + } + alpha->r = beta, alpha->i = 0.; + } + + return 0; + +/* End of ZLARFG */ + +} /* zlarfg_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zlarft.cpp b/lib/linalg/zlarft.cpp new file mode 100644 index 0000000000..d907f6792d --- /dev/null +++ b/lib/linalg/zlarft.cpp @@ -0,0 +1,465 @@ +/* static/zlarft.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static doublecomplex c_b1 = {1.,0.}; +static integer c__1 = 1; + +/* > \brief \b ZLARFT forms the triangular factor T of a block reflector H = I - vtvH */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZLARFT + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER DIRECT, STOREV */ +/* INTEGER K, LDT, LDV, N */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 T( LDT, * ), TAU( * ), V( LDV, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZLARFT forms the triangular factor T of a complex block reflector H */ +/* > of order n, which is defined as a product of k elementary reflectors. */ +/* > */ +/* > If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; */ +/* > */ +/* > If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. */ +/* > */ +/* > If STOREV = 'C', the vector which defines the elementary reflector */ +/* > H(i) is stored in the i-th column of the array V, and */ +/* > */ +/* > H = I - V * T * V**H */ +/* > */ +/* > If STOREV = 'R', the vector which defines the elementary reflector */ +/* > H(i) is stored in the i-th row of the array V, and */ +/* > */ +/* > H = I - V**H * T * V */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] DIRECT */ +/* > \verbatim */ +/* > DIRECT is CHARACTER*1 */ +/* > Specifies the order in which the elementary reflectors are */ +/* > multiplied to form the block reflector: */ +/* > = 'F': H = H(1) H(2) . . . H(k) (Forward) */ +/* > = 'B': H = H(k) . . . H(2) H(1) (Backward) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] STOREV */ +/* > \verbatim */ +/* > STOREV is CHARACTER*1 */ +/* > Specifies how the vectors which define the elementary */ +/* > reflectors are stored (see also Further Details): */ +/* > = 'C': columnwise */ +/* > = 'R': rowwise */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the block reflector H. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > The order of the triangular factor T (= the number of */ +/* > elementary reflectors). K >= 1. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] V */ +/* > \verbatim */ +/* > V is COMPLEX*16 array, dimension */ +/* > (LDV,K) if STOREV = 'C' */ +/* > (LDV,N) if STOREV = 'R' */ +/* > The matrix V. See further details. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDV */ +/* > \verbatim */ +/* > LDV is INTEGER */ +/* > The leading dimension of the array V. */ +/* > If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TAU */ +/* > \verbatim */ +/* > TAU is COMPLEX*16 array, dimension (K) */ +/* > TAU(i) must contain the scalar factor of the elementary */ +/* > reflector H(i). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] T */ +/* > \verbatim */ +/* > T is COMPLEX*16 array, dimension (LDT,K) */ +/* > The k by k triangular factor T of the block reflector. */ +/* > If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is */ +/* > lower triangular. The rest of the array is not used. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDT */ +/* > \verbatim */ +/* > LDT is INTEGER */ +/* > The leading dimension of the array T. LDT >= K. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16OTHERauxiliary */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > The shape of the matrix V and the storage of the vectors which define */ +/* > the H(i) is best illustrated by the following example with n = 5 and */ +/* > k = 3. The elements equal to 1 are not stored. */ +/* > */ +/* > DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': */ +/* > */ +/* > V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) */ +/* > ( v1 1 ) ( 1 v2 v2 v2 ) */ +/* > ( v1 v2 1 ) ( 1 v3 v3 ) */ +/* > ( v1 v2 v3 ) */ +/* > ( v1 v2 v3 ) */ +/* > */ +/* > DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': */ +/* > */ +/* > V = ( v1 v2 v3 ) V = ( v1 v1 1 ) */ +/* > ( v1 v2 v3 ) ( v2 v2 v2 1 ) */ +/* > ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) */ +/* > ( 1 v3 ) */ +/* > ( 1 ) */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int zlarft_(char *direct, char *storev, integer *n, integer * + k, doublecomplex *v, integer *ldv, doublecomplex *tau, doublecomplex * + t, integer *ldt, ftnlen direct_len, ftnlen storev_len) +{ + /* System generated locals */ + integer t_dim1, t_offset, v_dim1, v_offset, i__1, i__2, i__3, i__4, i__5; + doublecomplex z__1, z__2, z__3; + + /* Builtin functions */ + void d_cnjg(doublecomplex *, doublecomplex *); + + /* Local variables */ + integer i__, j, prevlastv; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *, + integer *, doublecomplex *, doublecomplex *, integer *, + doublecomplex *, integer *, doublecomplex *, doublecomplex *, + integer *, ftnlen, ftnlen), zgemv_(char *, integer *, integer *, + doublecomplex *, doublecomplex *, integer *, doublecomplex *, + integer *, doublecomplex *, doublecomplex *, integer *, ftnlen); + integer lastv; + extern /* Subroutine */ int ztrmv_(char *, char *, char *, integer *, + doublecomplex *, integer *, doublecomplex *, integer *, ftnlen, + ftnlen, ftnlen); + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Quick return if possible */ + + /* Parameter adjustments */ + v_dim1 = *ldv; + v_offset = 1 + v_dim1; + v -= v_offset; + --tau; + t_dim1 = *ldt; + t_offset = 1 + t_dim1; + t -= t_offset; + + /* Function Body */ + if (*n == 0) { + return 0; + } + + if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { + prevlastv = *n; + i__1 = *k; + for (i__ = 1; i__ <= i__1; ++i__) { + prevlastv = max(prevlastv,i__); + i__2 = i__; + if (tau[i__2].r == 0. && tau[i__2].i == 0.) { + +/* H(i) = I */ + + i__2 = i__; + for (j = 1; j <= i__2; ++j) { + i__3 = j + i__ * t_dim1; + t[i__3].r = 0., t[i__3].i = 0.; + } + } else { + +/* general case */ + + if (lsame_(storev, (char *)"C", (ftnlen)1, (ftnlen)1)) { +/* Skip any trailing zeros. */ + i__2 = i__ + 1; + for (lastv = *n; lastv >= i__2; --lastv) { + i__3 = lastv + i__ * v_dim1; + if (v[i__3].r != 0. || v[i__3].i != 0.) { + goto L220; + } + } +L220: + i__2 = i__ - 1; + for (j = 1; j <= i__2; ++j) { + i__3 = j + i__ * t_dim1; + i__4 = i__; + z__2.r = -tau[i__4].r, z__2.i = -tau[i__4].i; + d_cnjg(&z__3, &v[i__ + j * v_dim1]); + z__1.r = z__2.r * z__3.r - z__2.i * z__3.i, z__1.i = + z__2.r * z__3.i + z__2.i * z__3.r; + t[i__3].r = z__1.r, t[i__3].i = z__1.i; + } + j = min(lastv,prevlastv); + +/* T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**H * V(i:j,i) */ + + i__2 = j - i__; + i__3 = i__ - 1; + i__4 = i__; + z__1.r = -tau[i__4].r, z__1.i = -tau[i__4].i; + zgemv_((char *)"Conjugate transpose", &i__2, &i__3, &z__1, &v[i__ + + 1 + v_dim1], ldv, &v[i__ + 1 + i__ * v_dim1], & + c__1, &c_b1, &t[i__ * t_dim1 + 1], &c__1, (ftnlen) + 19); + } else { +/* Skip any trailing zeros. */ + i__2 = i__ + 1; + for (lastv = *n; lastv >= i__2; --lastv) { + i__3 = i__ + lastv * v_dim1; + if (v[i__3].r != 0. || v[i__3].i != 0.) { + goto L236; + } + } +L236: + i__2 = i__ - 1; + for (j = 1; j <= i__2; ++j) { + i__3 = j + i__ * t_dim1; + i__4 = i__; + z__2.r = -tau[i__4].r, z__2.i = -tau[i__4].i; + i__5 = j + i__ * v_dim1; + z__1.r = z__2.r * v[i__5].r - z__2.i * v[i__5].i, + z__1.i = z__2.r * v[i__5].i + z__2.i * v[i__5] + .r; + t[i__3].r = z__1.r, t[i__3].i = z__1.i; + } + j = min(lastv,prevlastv); + +/* T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**H */ + + i__2 = i__ - 1; + i__3 = j - i__; + i__4 = i__; + z__1.r = -tau[i__4].r, z__1.i = -tau[i__4].i; + zgemm_((char *)"N", (char *)"C", &i__2, &c__1, &i__3, &z__1, &v[(i__ + 1) + * v_dim1 + 1], ldv, &v[i__ + (i__ + 1) * v_dim1], + ldv, &c_b1, &t[i__ * t_dim1 + 1], ldt, (ftnlen)1, + (ftnlen)1); + } + +/* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) */ + + i__2 = i__ - 1; + ztrmv_((char *)"Upper", (char *)"No transpose", (char *)"Non-unit", &i__2, &t[ + t_offset], ldt, &t[i__ * t_dim1 + 1], &c__1, (ftnlen) + 5, (ftnlen)12, (ftnlen)8); + i__2 = i__ + i__ * t_dim1; + i__3 = i__; + t[i__2].r = tau[i__3].r, t[i__2].i = tau[i__3].i; + if (i__ > 1) { + prevlastv = max(prevlastv,lastv); + } else { + prevlastv = lastv; + } + } + } + } else { + prevlastv = 1; + for (i__ = *k; i__ >= 1; --i__) { + i__1 = i__; + if (tau[i__1].r == 0. && tau[i__1].i == 0.) { + +/* H(i) = I */ + + i__1 = *k; + for (j = i__; j <= i__1; ++j) { + i__2 = j + i__ * t_dim1; + t[i__2].r = 0., t[i__2].i = 0.; + } + } else { + +/* general case */ + + if (i__ < *k) { + if (lsame_(storev, (char *)"C", (ftnlen)1, (ftnlen)1)) { +/* Skip any leading zeros. */ + i__1 = i__ - 1; + for (lastv = 1; lastv <= i__1; ++lastv) { + i__2 = lastv + i__ * v_dim1; + if (v[i__2].r != 0. || v[i__2].i != 0.) { + goto L281; + } + } +L281: + i__1 = *k; + for (j = i__ + 1; j <= i__1; ++j) { + i__2 = j + i__ * t_dim1; + i__3 = i__; + z__2.r = -tau[i__3].r, z__2.i = -tau[i__3].i; + d_cnjg(&z__3, &v[*n - *k + i__ + j * v_dim1]); + z__1.r = z__2.r * z__3.r - z__2.i * z__3.i, + z__1.i = z__2.r * z__3.i + z__2.i * + z__3.r; + t[i__2].r = z__1.r, t[i__2].i = z__1.i; + } + j = max(lastv,prevlastv); + +/* T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**H * V(j:n-k+i,i) */ + + i__1 = *n - *k + i__ - j; + i__2 = *k - i__; + i__3 = i__; + z__1.r = -tau[i__3].r, z__1.i = -tau[i__3].i; + zgemv_((char *)"Conjugate transpose", &i__1, &i__2, &z__1, &v[ + j + (i__ + 1) * v_dim1], ldv, &v[j + i__ * + v_dim1], &c__1, &c_b1, &t[i__ + 1 + i__ * + t_dim1], &c__1, (ftnlen)19); + } else { +/* Skip any leading zeros. */ + i__1 = i__ - 1; + for (lastv = 1; lastv <= i__1; ++lastv) { + i__2 = i__ + lastv * v_dim1; + if (v[i__2].r != 0. || v[i__2].i != 0.) { + goto L297; + } + } +L297: + i__1 = *k; + for (j = i__ + 1; j <= i__1; ++j) { + i__2 = j + i__ * t_dim1; + i__3 = i__; + z__2.r = -tau[i__3].r, z__2.i = -tau[i__3].i; + i__4 = j + (*n - *k + i__) * v_dim1; + z__1.r = z__2.r * v[i__4].r - z__2.i * v[i__4].i, + z__1.i = z__2.r * v[i__4].i + z__2.i * v[ + i__4].r; + t[i__2].r = z__1.r, t[i__2].i = z__1.i; + } + j = max(lastv,prevlastv); + +/* T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**H */ + + i__1 = *k - i__; + i__2 = *n - *k + i__ - j; + i__3 = i__; + z__1.r = -tau[i__3].r, z__1.i = -tau[i__3].i; + zgemm_((char *)"N", (char *)"C", &i__1, &c__1, &i__2, &z__1, &v[i__ + + 1 + j * v_dim1], ldv, &v[i__ + j * v_dim1], + ldv, &c_b1, &t[i__ + 1 + i__ * t_dim1], ldt, ( + ftnlen)1, (ftnlen)1); + } + +/* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) */ + + i__1 = *k - i__; + ztrmv_((char *)"Lower", (char *)"No transpose", (char *)"Non-unit", &i__1, &t[i__ + + 1 + (i__ + 1) * t_dim1], ldt, &t[i__ + 1 + i__ * + t_dim1], &c__1, (ftnlen)5, (ftnlen)12, (ftnlen)8) + ; + if (i__ > 1) { + prevlastv = min(prevlastv,lastv); + } else { + prevlastv = lastv; + } + } + i__1 = i__ + i__ * t_dim1; + i__2 = i__; + t[i__1].r = tau[i__2].r, t[i__1].i = tau[i__2].i; + } + } + } + return 0; + +/* End of ZLARFT */ + +} /* zlarft_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zlascl.cpp b/lib/linalg/zlascl.cpp new file mode 100644 index 0000000000..337dd64793 --- /dev/null +++ b/lib/linalg/zlascl.cpp @@ -0,0 +1,470 @@ +/* fortran/zlascl.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b ZLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZLASCL + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZLASCL( TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER TYPE */ +/* INTEGER INFO, KL, KU, LDA, M, N */ +/* DOUBLE PRECISION CFROM, CTO */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 A( LDA, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZLASCL multiplies the M by N complex matrix A by the real scalar */ +/* > CTO/CFROM. This is done without over/underflow as long as the final */ +/* > result CTO*A(I,J)/CFROM does not over/underflow. TYPE specifies that */ +/* > A may be full, upper triangular, lower triangular, upper Hessenberg, */ +/* > or banded. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] TYPE */ +/* > \verbatim */ +/* > TYPE is CHARACTER*1 */ +/* > TYPE indices the storage type of the input matrix. */ +/* > = 'G': A is a full matrix. */ +/* > = 'L': A is a lower triangular matrix. */ +/* > = 'U': A is an upper triangular matrix. */ +/* > = 'H': A is an upper Hessenberg matrix. */ +/* > = 'B': A is a symmetric band matrix with lower bandwidth KL */ +/* > and upper bandwidth KU and with the only the lower */ +/* > half stored. */ +/* > = 'Q': A is a symmetric band matrix with lower bandwidth KL */ +/* > and upper bandwidth KU and with the only the upper */ +/* > half stored. */ +/* > = 'Z': A is a band matrix with lower bandwidth KL and upper */ +/* > bandwidth KU. See ZGBTRF for storage details. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] KL */ +/* > \verbatim */ +/* > KL is INTEGER */ +/* > The lower bandwidth of A. Referenced only if TYPE = 'B', */ +/* > 'Q' or 'Z'. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] KU */ +/* > \verbatim */ +/* > KU is INTEGER */ +/* > The upper bandwidth of A. Referenced only if TYPE = 'B', */ +/* > 'Q' or 'Z'. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] CFROM */ +/* > \verbatim */ +/* > CFROM is DOUBLE PRECISION */ +/* > \endverbatim */ +/* > */ +/* > \param[in] CTO */ +/* > \verbatim */ +/* > CTO is DOUBLE PRECISION */ +/* > */ +/* > The matrix A is multiplied by CTO/CFROM. A(I,J) is computed */ +/* > without over/underflow if the final result CTO*A(I,J)/CFROM */ +/* > can be represented without over/underflow. CFROM must be */ +/* > nonzero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix A. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is COMPLEX*16 array, dimension (LDA,N) */ +/* > The matrix to be multiplied by CTO/CFROM. See TYPE for the */ +/* > storage type. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. */ +/* > If TYPE = 'G', 'L', 'U', 'H', LDA >= max(1,M); */ +/* > TYPE = 'B', LDA >= KL+1; */ +/* > TYPE = 'Q', LDA >= KU+1; */ +/* > TYPE = 'Z', LDA >= 2*KL+KU+1. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > 0 - successful exit */ +/* > <0 - if INFO = -i, the i-th argument had an illegal value. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16OTHERauxiliary */ + +/* ===================================================================== */ +/* Subroutine */ int zlascl_(char *type__, integer *kl, integer *ku, + doublereal *cfrom, doublereal *cto, integer *m, integer *n, + doublecomplex *a, integer *lda, integer *info, ftnlen type_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; + doublecomplex z__1; + + /* Local variables */ + integer i__, j, k1, k2, k3, k4; + doublereal mul, cto1; + logical done; + doublereal ctoc; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + integer itype; + doublereal cfrom1; + extern doublereal dlamch_(char *, ftnlen); + doublereal cfromc; + extern logical disnan_(doublereal *); + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + doublereal bignum, smlnum; + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + + /* Function Body */ + *info = 0; + + if (lsame_(type__, (char *)"G", (ftnlen)1, (ftnlen)1)) { + itype = 0; + } else if (lsame_(type__, (char *)"L", (ftnlen)1, (ftnlen)1)) { + itype = 1; + } else if (lsame_(type__, (char *)"U", (ftnlen)1, (ftnlen)1)) { + itype = 2; + } else if (lsame_(type__, (char *)"H", (ftnlen)1, (ftnlen)1)) { + itype = 3; + } else if (lsame_(type__, (char *)"B", (ftnlen)1, (ftnlen)1)) { + itype = 4; + } else if (lsame_(type__, (char *)"Q", (ftnlen)1, (ftnlen)1)) { + itype = 5; + } else if (lsame_(type__, (char *)"Z", (ftnlen)1, (ftnlen)1)) { + itype = 6; + } else { + itype = -1; + } + + if (itype == -1) { + *info = -1; + } else if (*cfrom == 0. || disnan_(cfrom)) { + *info = -4; + } else if (disnan_(cto)) { + *info = -5; + } else if (*m < 0) { + *info = -6; + } else if (*n < 0 || itype == 4 && *n != *m || itype == 5 && *n != *m) { + *info = -7; + } else if (itype <= 3 && *lda < max(1,*m)) { + *info = -9; + } else if (itype >= 4) { +/* Computing MAX */ + i__1 = *m - 1; + if (*kl < 0 || *kl > max(i__1,0)) { + *info = -2; + } else /* if(complicated condition) */ { +/* Computing MAX */ + i__1 = *n - 1; + if (*ku < 0 || *ku > max(i__1,0) || (itype == 4 || itype == 5) && + *kl != *ku) { + *info = -3; + } else if (itype == 4 && *lda < *kl + 1 || itype == 5 && *lda < * + ku + 1 || itype == 6 && *lda < (*kl << 1) + *ku + 1) { + *info = -9; + } + } + } + + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"ZLASCL", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*n == 0 || *m == 0) { + return 0; + } + +/* Get machine parameters */ + + smlnum = dlamch_((char *)"S", (ftnlen)1); + bignum = 1. / smlnum; + + cfromc = *cfrom; + ctoc = *cto; + +L10: + cfrom1 = cfromc * smlnum; + if (cfrom1 == cfromc) { +/* CFROMC is an inf. Multiply by a correctly signed zero for */ +/* finite CTOC, or a NaN if CTOC is infinite. */ + mul = ctoc / cfromc; + done = TRUE_; + cto1 = ctoc; + } else { + cto1 = ctoc / bignum; + if (cto1 == ctoc) { +/* CTOC is either 0 or an inf. In both cases, CTOC itself */ +/* serves as the correct multiplication factor. */ + mul = ctoc; + done = TRUE_; + cfromc = 1.; + } else if (abs(cfrom1) > abs(ctoc) && ctoc != 0.) { + mul = smlnum; + done = FALSE_; + cfromc = cfrom1; + } else if (abs(cto1) > abs(cfromc)) { + mul = bignum; + done = FALSE_; + ctoc = cto1; + } else { + mul = ctoc / cfromc; + done = TRUE_; + if (mul == 1.) { + return 0; + } + } + } + + if (itype == 0) { + +/* Full matrix */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + i__4 = i__ + j * a_dim1; + z__1.r = mul * a[i__4].r, z__1.i = mul * a[i__4].i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; +/* L20: */ + } +/* L30: */ + } + + } else if (itype == 1) { + +/* Lower triangular matrix */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = j; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + i__4 = i__ + j * a_dim1; + z__1.r = mul * a[i__4].r, z__1.i = mul * a[i__4].i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; +/* L40: */ + } +/* L50: */ + } + + } else if (itype == 2) { + +/* Upper triangular matrix */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = min(j,*m); + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + i__4 = i__ + j * a_dim1; + z__1.r = mul * a[i__4].r, z__1.i = mul * a[i__4].i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; +/* L60: */ + } +/* L70: */ + } + + } else if (itype == 3) { + +/* Upper Hessenberg matrix */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { +/* Computing MIN */ + i__3 = j + 1; + i__2 = min(i__3,*m); + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + i__4 = i__ + j * a_dim1; + z__1.r = mul * a[i__4].r, z__1.i = mul * a[i__4].i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; +/* L80: */ + } +/* L90: */ + } + + } else if (itype == 4) { + +/* Lower half of a symmetric band matrix */ + + k3 = *kl + 1; + k4 = *n + 1; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { +/* Computing MIN */ + i__3 = k3, i__4 = k4 - j; + i__2 = min(i__3,i__4); + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + i__4 = i__ + j * a_dim1; + z__1.r = mul * a[i__4].r, z__1.i = mul * a[i__4].i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; +/* L100: */ + } +/* L110: */ + } + + } else if (itype == 5) { + +/* Upper half of a symmetric band matrix */ + + k1 = *ku + 2; + k3 = *ku + 1; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { +/* Computing MAX */ + i__2 = k1 - j; + i__3 = k3; + for (i__ = max(i__2,1); i__ <= i__3; ++i__) { + i__2 = i__ + j * a_dim1; + i__4 = i__ + j * a_dim1; + z__1.r = mul * a[i__4].r, z__1.i = mul * a[i__4].i; + a[i__2].r = z__1.r, a[i__2].i = z__1.i; +/* L120: */ + } +/* L130: */ + } + + } else if (itype == 6) { + +/* Band matrix */ + + k1 = *kl + *ku + 2; + k2 = *kl + 1; + k3 = (*kl << 1) + *ku + 1; + k4 = *kl + *ku + 1 + *m; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { +/* Computing MAX */ + i__3 = k1 - j; +/* Computing MIN */ + i__4 = k3, i__5 = k4 - j; + i__2 = min(i__4,i__5); + for (i__ = max(i__3,k2); i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + i__4 = i__ + j * a_dim1; + z__1.r = mul * a[i__4].r, z__1.i = mul * a[i__4].i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; +/* L140: */ + } +/* L150: */ + } + + } + + if (! done) { + goto L10; + } + + return 0; + +/* End of ZLASCL */ + +} /* zlascl_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zlaset.cpp b/lib/linalg/zlaset.cpp new file mode 100644 index 0000000000..e402ea02fe --- /dev/null +++ b/lib/linalg/zlaset.cpp @@ -0,0 +1,240 @@ +/* fortran/zlaset.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given val +ues. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZLASET + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZLASET( UPLO, M, N, ALPHA, BETA, A, LDA ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER UPLO */ +/* INTEGER LDA, M, N */ +/* COMPLEX*16 ALPHA, BETA */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 A( LDA, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZLASET initializes a 2-D array A to BETA on the diagonal and */ +/* > ALPHA on the offdiagonals. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > Specifies the part of the matrix A to be set. */ +/* > = 'U': Upper triangular part is set. The lower triangle */ +/* > is unchanged. */ +/* > = 'L': Lower triangular part is set. The upper triangle */ +/* > is unchanged. */ +/* > Otherwise: All of the matrix A is set. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > On entry, M specifies the number of rows of A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > On entry, N specifies the number of columns of A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] ALPHA */ +/* > \verbatim */ +/* > ALPHA is COMPLEX*16 */ +/* > All the offdiagonal array elements are set to ALPHA. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] BETA */ +/* > \verbatim */ +/* > BETA is COMPLEX*16 */ +/* > All the diagonal array elements are set to BETA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] A */ +/* > \verbatim */ +/* > A is COMPLEX*16 array, dimension (LDA,N) */ +/* > On entry, the m by n matrix A. */ +/* > On exit, A(i,j) = ALPHA, 1 <= i <= m, 1 <= j <= n, i.ne.j; */ +/* > A(i,i) = BETA , 1 <= i <= min(m,n) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,M). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16OTHERauxiliary */ + +/* ===================================================================== */ +/* Subroutine */ int zlaset_(char *uplo, integer *m, integer *n, + doublecomplex *alpha, doublecomplex *beta, doublecomplex *a, integer * + lda, ftnlen uplo_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3; + + /* Local variables */ + integer i__, j; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + + /* Function Body */ + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + +/* Set the diagonal to BETA and the strictly upper triangular */ +/* part of the array to ALPHA. */ + + i__1 = *n; + for (j = 2; j <= i__1; ++j) { +/* Computing MIN */ + i__3 = j - 1; + i__2 = min(i__3,*m); + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + a[i__3].r = alpha->r, a[i__3].i = alpha->i; +/* L10: */ + } +/* L20: */ + } + i__1 = min(*n,*m); + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__ + i__ * a_dim1; + a[i__2].r = beta->r, a[i__2].i = beta->i; +/* L30: */ + } + + } else if (lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + +/* Set the diagonal to BETA and the strictly lower triangular */ +/* part of the array to ALPHA. */ + + i__1 = min(*m,*n); + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = j + 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + a[i__3].r = alpha->r, a[i__3].i = alpha->i; +/* L40: */ + } +/* L50: */ + } + i__1 = min(*n,*m); + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__ + i__ * a_dim1; + a[i__2].r = beta->r, a[i__2].i = beta->i; +/* L60: */ + } + + } else { + +/* Set the array to BETA on the diagonal and ALPHA on the */ +/* offdiagonal. */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + a[i__3].r = alpha->r, a[i__3].i = alpha->i; +/* L70: */ + } +/* L80: */ + } + i__1 = min(*m,*n); + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__ + i__ * a_dim1; + a[i__2].r = beta->r, a[i__2].i = beta->i; +/* L90: */ + } + } + + return 0; + +/* End of ZLASET */ + +} /* zlaset_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zlasr.cpp b/lib/linalg/zlasr.cpp new file mode 100644 index 0000000000..23d68bf82f --- /dev/null +++ b/lib/linalg/zlasr.cpp @@ -0,0 +1,694 @@ +/* fortran/zlasr.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b ZLASR applies a sequence of plane rotations to a general rectangular matrix. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZLASR + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER DIRECT, PIVOT, SIDE */ +/* INTEGER LDA, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION C( * ), S( * ) */ +/* COMPLEX*16 A( LDA, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZLASR applies a sequence of real plane rotations to a complex matrix */ +/* > A, from either the left or the right. */ +/* > */ +/* > When SIDE = 'L', the transformation takes the form */ +/* > */ +/* > A := P*A */ +/* > */ +/* > and when SIDE = 'R', the transformation takes the form */ +/* > */ +/* > A := A*P**T */ +/* > */ +/* > where P is an orthogonal matrix consisting of a sequence of z plane */ +/* > rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R', */ +/* > and P**T is the transpose of P. */ +/* > */ +/* > When DIRECT = 'F' (Forward sequence), then */ +/* > */ +/* > P = P(z-1) * ... * P(2) * P(1) */ +/* > */ +/* > and when DIRECT = 'B' (Backward sequence), then */ +/* > */ +/* > P = P(1) * P(2) * ... * P(z-1) */ +/* > */ +/* > where P(k) is a plane rotation matrix defined by the 2-by-2 rotation */ +/* > */ +/* > R(k) = ( c(k) s(k) ) */ +/* > = ( -s(k) c(k) ). */ +/* > */ +/* > When PIVOT = 'V' (Variable pivot), the rotation is performed */ +/* > for the plane (k,k+1), i.e., P(k) has the form */ +/* > */ +/* > P(k) = ( 1 ) */ +/* > ( ... ) */ +/* > ( 1 ) */ +/* > ( c(k) s(k) ) */ +/* > ( -s(k) c(k) ) */ +/* > ( 1 ) */ +/* > ( ... ) */ +/* > ( 1 ) */ +/* > */ +/* > where R(k) appears as a rank-2 modification to the identity matrix in */ +/* > rows and columns k and k+1. */ +/* > */ +/* > When PIVOT = 'T' (Top pivot), the rotation is performed for the */ +/* > plane (1,k+1), so P(k) has the form */ +/* > */ +/* > P(k) = ( c(k) s(k) ) */ +/* > ( 1 ) */ +/* > ( ... ) */ +/* > ( 1 ) */ +/* > ( -s(k) c(k) ) */ +/* > ( 1 ) */ +/* > ( ... ) */ +/* > ( 1 ) */ +/* > */ +/* > where R(k) appears in rows and columns 1 and k+1. */ +/* > */ +/* > Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is */ +/* > performed for the plane (k,z), giving P(k) the form */ +/* > */ +/* > P(k) = ( 1 ) */ +/* > ( ... ) */ +/* > ( 1 ) */ +/* > ( c(k) s(k) ) */ +/* > ( 1 ) */ +/* > ( ... ) */ +/* > ( 1 ) */ +/* > ( -s(k) c(k) ) */ +/* > */ +/* > where R(k) appears in rows and columns k and z. The rotations are */ +/* > performed without ever forming P(k) explicitly. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] SIDE */ +/* > \verbatim */ +/* > SIDE is CHARACTER*1 */ +/* > Specifies whether the plane rotation matrix P is applied to */ +/* > A on the left or the right. */ +/* > = 'L': Left, compute A := P*A */ +/* > = 'R': Right, compute A:= A*P**T */ +/* > \endverbatim */ +/* > */ +/* > \param[in] PIVOT */ +/* > \verbatim */ +/* > PIVOT is CHARACTER*1 */ +/* > Specifies the plane for which P(k) is a plane rotation */ +/* > matrix. */ +/* > = 'V': Variable pivot, the plane (k,k+1) */ +/* > = 'T': Top pivot, the plane (1,k+1) */ +/* > = 'B': Bottom pivot, the plane (k,z) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DIRECT */ +/* > \verbatim */ +/* > DIRECT is CHARACTER*1 */ +/* > Specifies whether P is a forward or backward sequence of */ +/* > plane rotations. */ +/* > = 'F': Forward, P = P(z-1)*...*P(2)*P(1) */ +/* > = 'B': Backward, P = P(1)*P(2)*...*P(z-1) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix A. If m <= 1, an immediate */ +/* > return is effected. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix A. If n <= 1, an */ +/* > immediate return is effected. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] C */ +/* > \verbatim */ +/* > C is DOUBLE PRECISION array, dimension */ +/* > (M-1) if SIDE = 'L' */ +/* > (N-1) if SIDE = 'R' */ +/* > The cosines c(k) of the plane rotations. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] S */ +/* > \verbatim */ +/* > S is DOUBLE PRECISION array, dimension */ +/* > (M-1) if SIDE = 'L' */ +/* > (N-1) if SIDE = 'R' */ +/* > The sines s(k) of the plane rotations. The 2-by-2 plane */ +/* > rotation part of the matrix P(k), R(k), has the form */ +/* > R(k) = ( c(k) s(k) ) */ +/* > ( -s(k) c(k) ). */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is COMPLEX*16 array, dimension (LDA,N) */ +/* > The M-by-N matrix A. On exit, A is overwritten by P*A if */ +/* > SIDE = 'R' or by A*P**T if SIDE = 'L'. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,M). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16OTHERauxiliary */ + +/* ===================================================================== */ +/* Subroutine */ int zlasr_(char *side, char *pivot, char *direct, integer *m, + integer *n, doublereal *c__, doublereal *s, doublecomplex *a, + integer *lda, ftnlen side_len, ftnlen pivot_len, ftnlen direct_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3, i__4; + doublecomplex z__1, z__2, z__3; + + /* Local variables */ + integer i__, j, info; + doublecomplex temp; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + doublereal ctemp, stemp; + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters */ + + /* Parameter adjustments */ + --c__; + --s; + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + + /* Function Body */ + info = 0; + if (! (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1) || lsame_(side, (char *)"R", ( + ftnlen)1, (ftnlen)1))) { + info = 1; + } else if (! (lsame_(pivot, (char *)"V", (ftnlen)1, (ftnlen)1) || lsame_(pivot, + (char *)"T", (ftnlen)1, (ftnlen)1) || lsame_(pivot, (char *)"B", (ftnlen)1, ( + ftnlen)1))) { + info = 2; + } else if (! (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1) || lsame_(direct, + (char *)"B", (ftnlen)1, (ftnlen)1))) { + info = 3; + } else if (*m < 0) { + info = 4; + } else if (*n < 0) { + info = 5; + } else if (*lda < max(1,*m)) { + info = 9; + } + if (info != 0) { + xerbla_((char *)"ZLASR ", &info, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*m == 0 || *n == 0) { + return 0; + } + if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { + +/* Form P * A */ + + if (lsame_(pivot, (char *)"V", (ftnlen)1, (ftnlen)1)) { + if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { + i__1 = *m - 1; + for (j = 1; j <= i__1; ++j) { + ctemp = c__[j]; + stemp = s[j]; + if (ctemp != 1. || stemp != 0.) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = j + 1 + i__ * a_dim1; + temp.r = a[i__3].r, temp.i = a[i__3].i; + i__3 = j + 1 + i__ * a_dim1; + z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i; + i__4 = j + i__ * a_dim1; + z__3.r = stemp * a[i__4].r, z__3.i = stemp * a[ + i__4].i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - + z__3.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; + i__3 = j + i__ * a_dim1; + z__2.r = stemp * temp.r, z__2.i = stemp * temp.i; + i__4 = j + i__ * a_dim1; + z__3.r = ctemp * a[i__4].r, z__3.i = ctemp * a[ + i__4].i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; +/* L10: */ + } + } +/* L20: */ + } + } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { + for (j = *m - 1; j >= 1; --j) { + ctemp = c__[j]; + stemp = s[j]; + if (ctemp != 1. || stemp != 0.) { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = j + 1 + i__ * a_dim1; + temp.r = a[i__2].r, temp.i = a[i__2].i; + i__2 = j + 1 + i__ * a_dim1; + z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i; + i__3 = j + i__ * a_dim1; + z__3.r = stemp * a[i__3].r, z__3.i = stemp * a[ + i__3].i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - + z__3.i; + a[i__2].r = z__1.r, a[i__2].i = z__1.i; + i__2 = j + i__ * a_dim1; + z__2.r = stemp * temp.r, z__2.i = stemp * temp.i; + i__3 = j + i__ * a_dim1; + z__3.r = ctemp * a[i__3].r, z__3.i = ctemp * a[ + i__3].i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + a[i__2].r = z__1.r, a[i__2].i = z__1.i; +/* L30: */ + } + } +/* L40: */ + } + } + } else if (lsame_(pivot, (char *)"T", (ftnlen)1, (ftnlen)1)) { + if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { + i__1 = *m; + for (j = 2; j <= i__1; ++j) { + ctemp = c__[j - 1]; + stemp = s[j - 1]; + if (ctemp != 1. || stemp != 0.) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = j + i__ * a_dim1; + temp.r = a[i__3].r, temp.i = a[i__3].i; + i__3 = j + i__ * a_dim1; + z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i; + i__4 = i__ * a_dim1 + 1; + z__3.r = stemp * a[i__4].r, z__3.i = stemp * a[ + i__4].i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - + z__3.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; + i__3 = i__ * a_dim1 + 1; + z__2.r = stemp * temp.r, z__2.i = stemp * temp.i; + i__4 = i__ * a_dim1 + 1; + z__3.r = ctemp * a[i__4].r, z__3.i = ctemp * a[ + i__4].i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; +/* L50: */ + } + } +/* L60: */ + } + } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { + for (j = *m; j >= 2; --j) { + ctemp = c__[j - 1]; + stemp = s[j - 1]; + if (ctemp != 1. || stemp != 0.) { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = j + i__ * a_dim1; + temp.r = a[i__2].r, temp.i = a[i__2].i; + i__2 = j + i__ * a_dim1; + z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i; + i__3 = i__ * a_dim1 + 1; + z__3.r = stemp * a[i__3].r, z__3.i = stemp * a[ + i__3].i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - + z__3.i; + a[i__2].r = z__1.r, a[i__2].i = z__1.i; + i__2 = i__ * a_dim1 + 1; + z__2.r = stemp * temp.r, z__2.i = stemp * temp.i; + i__3 = i__ * a_dim1 + 1; + z__3.r = ctemp * a[i__3].r, z__3.i = ctemp * a[ + i__3].i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + a[i__2].r = z__1.r, a[i__2].i = z__1.i; +/* L70: */ + } + } +/* L80: */ + } + } + } else if (lsame_(pivot, (char *)"B", (ftnlen)1, (ftnlen)1)) { + if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { + i__1 = *m - 1; + for (j = 1; j <= i__1; ++j) { + ctemp = c__[j]; + stemp = s[j]; + if (ctemp != 1. || stemp != 0.) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = j + i__ * a_dim1; + temp.r = a[i__3].r, temp.i = a[i__3].i; + i__3 = j + i__ * a_dim1; + i__4 = *m + i__ * a_dim1; + z__2.r = stemp * a[i__4].r, z__2.i = stemp * a[ + i__4].i; + z__3.r = ctemp * temp.r, z__3.i = ctemp * temp.i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; + i__3 = *m + i__ * a_dim1; + i__4 = *m + i__ * a_dim1; + z__2.r = ctemp * a[i__4].r, z__2.i = ctemp * a[ + i__4].i; + z__3.r = stemp * temp.r, z__3.i = stemp * temp.i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - + z__3.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; +/* L90: */ + } + } +/* L100: */ + } + } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { + for (j = *m - 1; j >= 1; --j) { + ctemp = c__[j]; + stemp = s[j]; + if (ctemp != 1. || stemp != 0.) { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = j + i__ * a_dim1; + temp.r = a[i__2].r, temp.i = a[i__2].i; + i__2 = j + i__ * a_dim1; + i__3 = *m + i__ * a_dim1; + z__2.r = stemp * a[i__3].r, z__2.i = stemp * a[ + i__3].i; + z__3.r = ctemp * temp.r, z__3.i = ctemp * temp.i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + a[i__2].r = z__1.r, a[i__2].i = z__1.i; + i__2 = *m + i__ * a_dim1; + i__3 = *m + i__ * a_dim1; + z__2.r = ctemp * a[i__3].r, z__2.i = ctemp * a[ + i__3].i; + z__3.r = stemp * temp.r, z__3.i = stemp * temp.i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - + z__3.i; + a[i__2].r = z__1.r, a[i__2].i = z__1.i; +/* L110: */ + } + } +/* L120: */ + } + } + } + } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + +/* Form A * P**T */ + + if (lsame_(pivot, (char *)"V", (ftnlen)1, (ftnlen)1)) { + if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { + i__1 = *n - 1; + for (j = 1; j <= i__1; ++j) { + ctemp = c__[j]; + stemp = s[j]; + if (ctemp != 1. || stemp != 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + (j + 1) * a_dim1; + temp.r = a[i__3].r, temp.i = a[i__3].i; + i__3 = i__ + (j + 1) * a_dim1; + z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i; + i__4 = i__ + j * a_dim1; + z__3.r = stemp * a[i__4].r, z__3.i = stemp * a[ + i__4].i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - + z__3.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; + i__3 = i__ + j * a_dim1; + z__2.r = stemp * temp.r, z__2.i = stemp * temp.i; + i__4 = i__ + j * a_dim1; + z__3.r = ctemp * a[i__4].r, z__3.i = ctemp * a[ + i__4].i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; +/* L130: */ + } + } +/* L140: */ + } + } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { + for (j = *n - 1; j >= 1; --j) { + ctemp = c__[j]; + stemp = s[j]; + if (ctemp != 1. || stemp != 0.) { + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__ + (j + 1) * a_dim1; + temp.r = a[i__2].r, temp.i = a[i__2].i; + i__2 = i__ + (j + 1) * a_dim1; + z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i; + i__3 = i__ + j * a_dim1; + z__3.r = stemp * a[i__3].r, z__3.i = stemp * a[ + i__3].i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - + z__3.i; + a[i__2].r = z__1.r, a[i__2].i = z__1.i; + i__2 = i__ + j * a_dim1; + z__2.r = stemp * temp.r, z__2.i = stemp * temp.i; + i__3 = i__ + j * a_dim1; + z__3.r = ctemp * a[i__3].r, z__3.i = ctemp * a[ + i__3].i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + a[i__2].r = z__1.r, a[i__2].i = z__1.i; +/* L150: */ + } + } +/* L160: */ + } + } + } else if (lsame_(pivot, (char *)"T", (ftnlen)1, (ftnlen)1)) { + if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { + i__1 = *n; + for (j = 2; j <= i__1; ++j) { + ctemp = c__[j - 1]; + stemp = s[j - 1]; + if (ctemp != 1. || stemp != 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + temp.r = a[i__3].r, temp.i = a[i__3].i; + i__3 = i__ + j * a_dim1; + z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i; + i__4 = i__ + a_dim1; + z__3.r = stemp * a[i__4].r, z__3.i = stemp * a[ + i__4].i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - + z__3.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; + i__3 = i__ + a_dim1; + z__2.r = stemp * temp.r, z__2.i = stemp * temp.i; + i__4 = i__ + a_dim1; + z__3.r = ctemp * a[i__4].r, z__3.i = ctemp * a[ + i__4].i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; +/* L170: */ + } + } +/* L180: */ + } + } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { + for (j = *n; j >= 2; --j) { + ctemp = c__[j - 1]; + stemp = s[j - 1]; + if (ctemp != 1. || stemp != 0.) { + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__ + j * a_dim1; + temp.r = a[i__2].r, temp.i = a[i__2].i; + i__2 = i__ + j * a_dim1; + z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i; + i__3 = i__ + a_dim1; + z__3.r = stemp * a[i__3].r, z__3.i = stemp * a[ + i__3].i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - + z__3.i; + a[i__2].r = z__1.r, a[i__2].i = z__1.i; + i__2 = i__ + a_dim1; + z__2.r = stemp * temp.r, z__2.i = stemp * temp.i; + i__3 = i__ + a_dim1; + z__3.r = ctemp * a[i__3].r, z__3.i = ctemp * a[ + i__3].i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + a[i__2].r = z__1.r, a[i__2].i = z__1.i; +/* L190: */ + } + } +/* L200: */ + } + } + } else if (lsame_(pivot, (char *)"B", (ftnlen)1, (ftnlen)1)) { + if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { + i__1 = *n - 1; + for (j = 1; j <= i__1; ++j) { + ctemp = c__[j]; + stemp = s[j]; + if (ctemp != 1. || stemp != 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + temp.r = a[i__3].r, temp.i = a[i__3].i; + i__3 = i__ + j * a_dim1; + i__4 = i__ + *n * a_dim1; + z__2.r = stemp * a[i__4].r, z__2.i = stemp * a[ + i__4].i; + z__3.r = ctemp * temp.r, z__3.i = ctemp * temp.i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; + i__3 = i__ + *n * a_dim1; + i__4 = i__ + *n * a_dim1; + z__2.r = ctemp * a[i__4].r, z__2.i = ctemp * a[ + i__4].i; + z__3.r = stemp * temp.r, z__3.i = stemp * temp.i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - + z__3.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; +/* L210: */ + } + } +/* L220: */ + } + } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { + for (j = *n - 1; j >= 1; --j) { + ctemp = c__[j]; + stemp = s[j]; + if (ctemp != 1. || stemp != 0.) { + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__ + j * a_dim1; + temp.r = a[i__2].r, temp.i = a[i__2].i; + i__2 = i__ + j * a_dim1; + i__3 = i__ + *n * a_dim1; + z__2.r = stemp * a[i__3].r, z__2.i = stemp * a[ + i__3].i; + z__3.r = ctemp * temp.r, z__3.i = ctemp * temp.i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + a[i__2].r = z__1.r, a[i__2].i = z__1.i; + i__2 = i__ + *n * a_dim1; + i__3 = i__ + *n * a_dim1; + z__2.r = ctemp * a[i__3].r, z__2.i = ctemp * a[ + i__3].i; + z__3.r = stemp * temp.r, z__3.i = stemp * temp.i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - + z__3.i; + a[i__2].r = z__1.r, a[i__2].i = z__1.i; +/* L230: */ + } + } +/* L240: */ + } + } + } + } + + return 0; + +/* End of ZLASR */ + +} /* zlasr_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zlassq.cpp b/lib/linalg/zlassq.cpp new file mode 100644 index 0000000000..1fa44450fe --- /dev/null +++ b/lib/linalg/zlassq.cpp @@ -0,0 +1,212 @@ +/* fortran/zlassq.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b ZLASSQ updates a sum of squares represented in scaled form. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZLASSQ + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZLASSQ( N, X, INCX, SCALE, SUMSQ ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INCX, N */ +/* DOUBLE PRECISION SCALE, SUMSQ */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 X( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZLASSQ returns the values scl and ssq such that */ +/* > */ +/* > ( scl**2 )*ssq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq, */ +/* > */ +/* > where x( i ) = abs( X( 1 + ( i - 1 )*INCX ) ). The value of sumsq is */ +/* > assumed to be at least unity and the value of ssq will then satisfy */ +/* > */ +/* > 1.0 .le. ssq .le. ( sumsq + 2*n ). */ +/* > */ +/* > scale is assumed to be non-negative and scl returns the value */ +/* > */ +/* > scl = max( scale, abs( real( x( i ) ) ), abs( aimag( x( i ) ) ) ), */ +/* > i */ +/* > */ +/* > scale and sumsq must be supplied in SCALE and SUMSQ respectively. */ +/* > SCALE and SUMSQ are overwritten by scl and ssq respectively. */ +/* > */ +/* > The routine makes only one pass through the vector X. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of elements to be used from the vector X. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] X */ +/* > \verbatim */ +/* > X is COMPLEX*16 array, dimension (N) */ +/* > The vector x as described above. */ +/* > x( i ) = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > The increment between successive values of the vector X. */ +/* > INCX > 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] SCALE */ +/* > \verbatim */ +/* > SCALE is DOUBLE PRECISION */ +/* > On entry, the value scale in the equation above. */ +/* > On exit, SCALE is overwritten with the value scl . */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] SUMSQ */ +/* > \verbatim */ +/* > SUMSQ is DOUBLE PRECISION */ +/* > On entry, the value sumsq in the equation above. */ +/* > On exit, SUMSQ is overwritten with the value ssq . */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \date December 2016 */ + +/* > \ingroup complex16OTHERauxiliary */ + +/* ===================================================================== */ +/* Subroutine */ int zlassq_(integer *n, doublecomplex *x, integer *incx, + doublereal *scale, doublereal *sumsq) +{ + /* System generated locals */ + integer i__1, i__2, i__3; + doublereal d__1; + + /* Builtin functions */ + double d_imag(doublecomplex *); + + /* Local variables */ + integer ix; + doublereal temp1; + extern logical disnan_(doublereal *); + + +/* -- LAPACK auxiliary routine (version 3.7.0) -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ +/* December 2016 */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + + /* Parameter adjustments */ + --x; + + /* Function Body */ + if (*n > 0) { + i__1 = (*n - 1) * *incx + 1; + i__2 = *incx; + for (ix = 1; i__2 < 0 ? ix >= i__1 : ix <= i__1; ix += i__2) { + i__3 = ix; + temp1 = (d__1 = x[i__3].r, abs(d__1)); + if (temp1 > 0. || disnan_(&temp1)) { + if (*scale < temp1) { +/* Computing 2nd power */ + d__1 = *scale / temp1; + *sumsq = *sumsq * (d__1 * d__1) + 1; + *scale = temp1; + } else { +/* Computing 2nd power */ + d__1 = temp1 / *scale; + *sumsq += d__1 * d__1; + } + } + temp1 = (d__1 = d_imag(&x[ix]), abs(d__1)); + if (temp1 > 0. || disnan_(&temp1)) { + if (*scale < temp1) { +/* Computing 2nd power */ + d__1 = *scale / temp1; + *sumsq = *sumsq * (d__1 * d__1) + 1; + *scale = temp1; + } else { +/* Computing 2nd power */ + d__1 = temp1 / *scale; + *sumsq += d__1 * d__1; + } + } +/* L10: */ + } + } + + return 0; + +/* End of ZLASSQ */ + +} /* zlassq_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zlatrd.cpp b/lib/linalg/zlatrd.cpp new file mode 100644 index 0000000000..eaa0fc1826 --- /dev/null +++ b/lib/linalg/zlatrd.cpp @@ -0,0 +1,509 @@ +/* fortran/zlatrd.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static doublecomplex c_b1 = {0.,0.}; +static doublecomplex c_b2 = {1.,0.}; +static integer c__1 = 1; + +/* > \brief \b ZLATRD reduces the first nb rows and columns of a symmetric/Hermitian matrix A to real tridiago +nal form by an unitary similarity transformation. */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZLATRD + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZLATRD( UPLO, N, NB, A, LDA, E, TAU, W, LDW ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER UPLO */ +/* INTEGER LDA, LDW, N, NB */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION E( * ) */ +/* COMPLEX*16 A( LDA, * ), TAU( * ), W( LDW, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZLATRD reduces NB rows and columns of a complex Hermitian matrix A to */ +/* > Hermitian tridiagonal form by a unitary similarity */ +/* > transformation Q**H * A * Q, and returns the matrices V and W which are */ +/* > needed to apply the transformation to the unreduced part of A. */ +/* > */ +/* > If UPLO = 'U', ZLATRD reduces the last NB rows and columns of a */ +/* > matrix, of which the upper triangle is supplied; */ +/* > if UPLO = 'L', ZLATRD reduces the first NB rows and columns of a */ +/* > matrix, of which the lower triangle is supplied. */ +/* > */ +/* > This is an auxiliary routine called by ZHETRD. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > Specifies whether the upper or lower triangular part of the */ +/* > Hermitian matrix A is stored: */ +/* > = 'U': Upper triangular */ +/* > = 'L': Lower triangular */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrix A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] NB */ +/* > \verbatim */ +/* > NB is INTEGER */ +/* > The number of rows and columns to be reduced. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is COMPLEX*16 array, dimension (LDA,N) */ +/* > On entry, the Hermitian matrix A. If UPLO = 'U', the leading */ +/* > n-by-n upper triangular part of A contains the upper */ +/* > triangular part of the matrix A, and the strictly lower */ +/* > triangular part of A is not referenced. If UPLO = 'L', the */ +/* > leading n-by-n lower triangular part of A contains the lower */ +/* > triangular part of the matrix A, and the strictly upper */ +/* > triangular part of A is not referenced. */ +/* > On exit: */ +/* > if UPLO = 'U', the last NB columns have been reduced to */ +/* > tridiagonal form, with the diagonal elements overwriting */ +/* > the diagonal elements of A; the elements above the diagonal */ +/* > with the array TAU, represent the unitary matrix Q as a */ +/* > product of elementary reflectors; */ +/* > if UPLO = 'L', the first NB columns have been reduced to */ +/* > tridiagonal form, with the diagonal elements overwriting */ +/* > the diagonal elements of A; the elements below the diagonal */ +/* > with the array TAU, represent the unitary matrix Q as a */ +/* > product of elementary reflectors. */ +/* > See Further Details. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] E */ +/* > \verbatim */ +/* > E is DOUBLE PRECISION array, dimension (N-1) */ +/* > If UPLO = 'U', E(n-nb:n-1) contains the superdiagonal */ +/* > elements of the last NB columns of the reduced matrix; */ +/* > if UPLO = 'L', E(1:nb) contains the subdiagonal elements of */ +/* > the first NB columns of the reduced matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] TAU */ +/* > \verbatim */ +/* > TAU is COMPLEX*16 array, dimension (N-1) */ +/* > The scalar factors of the elementary reflectors, stored in */ +/* > TAU(n-nb:n-1) if UPLO = 'U', and in TAU(1:nb) if UPLO = 'L'. */ +/* > See Further Details. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] W */ +/* > \verbatim */ +/* > W is COMPLEX*16 array, dimension (LDW,NB) */ +/* > The n-by-nb matrix W required to update the unreduced part */ +/* > of A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDW */ +/* > \verbatim */ +/* > LDW is INTEGER */ +/* > The leading dimension of the array W. LDW >= max(1,N). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16OTHERauxiliary */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > If UPLO = 'U', the matrix Q is represented as a product of elementary */ +/* > reflectors */ +/* > */ +/* > Q = H(n) H(n-1) . . . H(n-nb+1). */ +/* > */ +/* > Each H(i) has the form */ +/* > */ +/* > H(i) = I - tau * v * v**H */ +/* > */ +/* > where tau is a complex scalar, and v is a complex vector with */ +/* > v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i), */ +/* > and tau in TAU(i-1). */ +/* > */ +/* > If UPLO = 'L', the matrix Q is represented as a product of elementary */ +/* > reflectors */ +/* > */ +/* > Q = H(1) H(2) . . . H(nb). */ +/* > */ +/* > Each H(i) has the form */ +/* > */ +/* > H(i) = I - tau * v * v**H */ +/* > */ +/* > where tau is a complex scalar, and v is a complex vector with */ +/* > v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i), */ +/* > and tau in TAU(i). */ +/* > */ +/* > The elements of the vectors v together form the n-by-nb matrix V */ +/* > which is needed, with W, to apply the transformation to the unreduced */ +/* > part of the matrix, using a Hermitian rank-2k update of the form: */ +/* > A := A - V*W**H - W*V**H. */ +/* > */ +/* > The contents of A on exit are illustrated by the following examples */ +/* > with n = 5 and nb = 2: */ +/* > */ +/* > if UPLO = 'U': if UPLO = 'L': */ +/* > */ +/* > ( a a a v4 v5 ) ( d ) */ +/* > ( a a v4 v5 ) ( 1 d ) */ +/* > ( a 1 v5 ) ( v1 1 a ) */ +/* > ( d 1 ) ( v1 v2 a a ) */ +/* > ( d ) ( v1 v2 a a a ) */ +/* > */ +/* > where d denotes a diagonal element of the reduced matrix, a denotes */ +/* > an element of the original matrix that is unchanged, and vi denotes */ +/* > an element of the vector defining H(i). */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int zlatrd_(char *uplo, integer *n, integer *nb, + doublecomplex *a, integer *lda, doublereal *e, doublecomplex *tau, + doublecomplex *w, integer *ldw, ftnlen uplo_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, w_dim1, w_offset, i__1, i__2, i__3; + doublereal d__1; + doublecomplex z__1, z__2, z__3, z__4; + + /* Local variables */ + integer i__, iw; + doublecomplex alpha; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int zscal_(integer *, doublecomplex *, + doublecomplex *, integer *); + extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *, + doublecomplex *, integer *, doublecomplex *, integer *); + extern /* Subroutine */ int zgemv_(char *, integer *, integer *, + doublecomplex *, doublecomplex *, integer *, doublecomplex *, + integer *, doublecomplex *, doublecomplex *, integer *, ftnlen), + zhemv_(char *, integer *, doublecomplex *, doublecomplex *, + integer *, doublecomplex *, integer *, doublecomplex *, + doublecomplex *, integer *, ftnlen), zaxpy_(integer *, + doublecomplex *, doublecomplex *, integer *, doublecomplex *, + integer *), zlarfg_(integer *, doublecomplex *, doublecomplex *, + integer *, doublecomplex *), zlacgv_(integer *, doublecomplex *, + integer *); + + +/* -- LAPACK auxiliary routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Quick return if possible */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --e; + --tau; + w_dim1 = *ldw; + w_offset = 1 + w_dim1; + w -= w_offset; + + /* Function Body */ + if (*n <= 0) { + return 0; + } + + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + +/* Reduce last NB columns of upper triangle */ + + i__1 = *n - *nb + 1; + for (i__ = *n; i__ >= i__1; --i__) { + iw = i__ - *n + *nb; + if (i__ < *n) { + +/* Update A(1:i,i) */ + + i__2 = i__ + i__ * a_dim1; + i__3 = i__ + i__ * a_dim1; + d__1 = a[i__3].r; + a[i__2].r = d__1, a[i__2].i = 0.; + i__2 = *n - i__; + zlacgv_(&i__2, &w[i__ + (iw + 1) * w_dim1], ldw); + i__2 = *n - i__; + z__1.r = -1., z__1.i = -0.; + zgemv_((char *)"No transpose", &i__, &i__2, &z__1, &a[(i__ + 1) * + a_dim1 + 1], lda, &w[i__ + (iw + 1) * w_dim1], ldw, & + c_b2, &a[i__ * a_dim1 + 1], &c__1, (ftnlen)12); + i__2 = *n - i__; + zlacgv_(&i__2, &w[i__ + (iw + 1) * w_dim1], ldw); + i__2 = *n - i__; + zlacgv_(&i__2, &a[i__ + (i__ + 1) * a_dim1], lda); + i__2 = *n - i__; + z__1.r = -1., z__1.i = -0.; + zgemv_((char *)"No transpose", &i__, &i__2, &z__1, &w[(iw + 1) * + w_dim1 + 1], ldw, &a[i__ + (i__ + 1) * a_dim1], lda, & + c_b2, &a[i__ * a_dim1 + 1], &c__1, (ftnlen)12); + i__2 = *n - i__; + zlacgv_(&i__2, &a[i__ + (i__ + 1) * a_dim1], lda); + i__2 = i__ + i__ * a_dim1; + i__3 = i__ + i__ * a_dim1; + d__1 = a[i__3].r; + a[i__2].r = d__1, a[i__2].i = 0.; + } + if (i__ > 1) { + +/* Generate elementary reflector H(i) to annihilate */ +/* A(1:i-2,i) */ + + i__2 = i__ - 1 + i__ * a_dim1; + alpha.r = a[i__2].r, alpha.i = a[i__2].i; + i__2 = i__ - 1; + zlarfg_(&i__2, &alpha, &a[i__ * a_dim1 + 1], &c__1, &tau[i__ + - 1]); + e[i__ - 1] = alpha.r; + i__2 = i__ - 1 + i__ * a_dim1; + a[i__2].r = 1., a[i__2].i = 0.; + +/* Compute W(1:i-1,i) */ + + i__2 = i__ - 1; + zhemv_((char *)"Upper", &i__2, &c_b2, &a[a_offset], lda, &a[i__ * + a_dim1 + 1], &c__1, &c_b1, &w[iw * w_dim1 + 1], &c__1, + (ftnlen)5); + if (i__ < *n) { + i__2 = i__ - 1; + i__3 = *n - i__; + zgemv_((char *)"Conjugate transpose", &i__2, &i__3, &c_b2, &w[(iw + + 1) * w_dim1 + 1], ldw, &a[i__ * a_dim1 + 1], & + c__1, &c_b1, &w[i__ + 1 + iw * w_dim1], &c__1, ( + ftnlen)19); + i__2 = i__ - 1; + i__3 = *n - i__; + z__1.r = -1., z__1.i = -0.; + zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &a[(i__ + 1) * + a_dim1 + 1], lda, &w[i__ + 1 + iw * w_dim1], & + c__1, &c_b2, &w[iw * w_dim1 + 1], &c__1, (ftnlen) + 12); + i__2 = i__ - 1; + i__3 = *n - i__; + zgemv_((char *)"Conjugate transpose", &i__2, &i__3, &c_b2, &a[( + i__ + 1) * a_dim1 + 1], lda, &a[i__ * a_dim1 + 1], + &c__1, &c_b1, &w[i__ + 1 + iw * w_dim1], &c__1, ( + ftnlen)19); + i__2 = i__ - 1; + i__3 = *n - i__; + z__1.r = -1., z__1.i = -0.; + zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &w[(iw + 1) * + w_dim1 + 1], ldw, &w[i__ + 1 + iw * w_dim1], & + c__1, &c_b2, &w[iw * w_dim1 + 1], &c__1, (ftnlen) + 12); + } + i__2 = i__ - 1; + zscal_(&i__2, &tau[i__ - 1], &w[iw * w_dim1 + 1], &c__1); + z__3.r = -.5, z__3.i = -0.; + i__2 = i__ - 1; + z__2.r = z__3.r * tau[i__2].r - z__3.i * tau[i__2].i, z__2.i = + z__3.r * tau[i__2].i + z__3.i * tau[i__2].r; + i__3 = i__ - 1; + zdotc_(&z__4, &i__3, &w[iw * w_dim1 + 1], &c__1, &a[i__ * + a_dim1 + 1], &c__1); + z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, z__1.i = z__2.r * + z__4.i + z__2.i * z__4.r; + alpha.r = z__1.r, alpha.i = z__1.i; + i__2 = i__ - 1; + zaxpy_(&i__2, &alpha, &a[i__ * a_dim1 + 1], &c__1, &w[iw * + w_dim1 + 1], &c__1); + } + +/* L10: */ + } + } else { + +/* Reduce first NB columns of lower triangle */ + + i__1 = *nb; + for (i__ = 1; i__ <= i__1; ++i__) { + +/* Update A(i:n,i) */ + + i__2 = i__ + i__ * a_dim1; + i__3 = i__ + i__ * a_dim1; + d__1 = a[i__3].r; + a[i__2].r = d__1, a[i__2].i = 0.; + i__2 = i__ - 1; + zlacgv_(&i__2, &w[i__ + w_dim1], ldw); + i__2 = *n - i__ + 1; + i__3 = i__ - 1; + z__1.r = -1., z__1.i = -0.; + zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &a[i__ + a_dim1], lda, + &w[i__ + w_dim1], ldw, &c_b2, &a[i__ + i__ * a_dim1], & + c__1, (ftnlen)12); + i__2 = i__ - 1; + zlacgv_(&i__2, &w[i__ + w_dim1], ldw); + i__2 = i__ - 1; + zlacgv_(&i__2, &a[i__ + a_dim1], lda); + i__2 = *n - i__ + 1; + i__3 = i__ - 1; + z__1.r = -1., z__1.i = -0.; + zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &w[i__ + w_dim1], ldw, + &a[i__ + a_dim1], lda, &c_b2, &a[i__ + i__ * a_dim1], & + c__1, (ftnlen)12); + i__2 = i__ - 1; + zlacgv_(&i__2, &a[i__ + a_dim1], lda); + i__2 = i__ + i__ * a_dim1; + i__3 = i__ + i__ * a_dim1; + d__1 = a[i__3].r; + a[i__2].r = d__1, a[i__2].i = 0.; + if (i__ < *n) { + +/* Generate elementary reflector H(i) to annihilate */ +/* A(i+2:n,i) */ + + i__2 = i__ + 1 + i__ * a_dim1; + alpha.r = a[i__2].r, alpha.i = a[i__2].i; + i__2 = *n - i__; +/* Computing MIN */ + i__3 = i__ + 2; + zlarfg_(&i__2, &alpha, &a[min(i__3,*n) + i__ * a_dim1], &c__1, + &tau[i__]); + e[i__] = alpha.r; + i__2 = i__ + 1 + i__ * a_dim1; + a[i__2].r = 1., a[i__2].i = 0.; + +/* Compute W(i+1:n,i) */ + + i__2 = *n - i__; + zhemv_((char *)"Lower", &i__2, &c_b2, &a[i__ + 1 + (i__ + 1) * a_dim1] + , lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b1, &w[ + i__ + 1 + i__ * w_dim1], &c__1, (ftnlen)5); + i__2 = *n - i__; + i__3 = i__ - 1; + zgemv_((char *)"Conjugate transpose", &i__2, &i__3, &c_b2, &w[i__ + 1 + + w_dim1], ldw, &a[i__ + 1 + i__ * a_dim1], &c__1, & + c_b1, &w[i__ * w_dim1 + 1], &c__1, (ftnlen)19); + i__2 = *n - i__; + i__3 = i__ - 1; + z__1.r = -1., z__1.i = -0.; + zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &a[i__ + 1 + + a_dim1], lda, &w[i__ * w_dim1 + 1], &c__1, &c_b2, &w[ + i__ + 1 + i__ * w_dim1], &c__1, (ftnlen)12); + i__2 = *n - i__; + i__3 = i__ - 1; + zgemv_((char *)"Conjugate transpose", &i__2, &i__3, &c_b2, &a[i__ + 1 + + a_dim1], lda, &a[i__ + 1 + i__ * a_dim1], &c__1, & + c_b1, &w[i__ * w_dim1 + 1], &c__1, (ftnlen)19); + i__2 = *n - i__; + i__3 = i__ - 1; + z__1.r = -1., z__1.i = -0.; + zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &w[i__ + 1 + + w_dim1], ldw, &w[i__ * w_dim1 + 1], &c__1, &c_b2, &w[ + i__ + 1 + i__ * w_dim1], &c__1, (ftnlen)12); + i__2 = *n - i__; + zscal_(&i__2, &tau[i__], &w[i__ + 1 + i__ * w_dim1], &c__1); + z__3.r = -.5, z__3.i = -0.; + i__2 = i__; + z__2.r = z__3.r * tau[i__2].r - z__3.i * tau[i__2].i, z__2.i = + z__3.r * tau[i__2].i + z__3.i * tau[i__2].r; + i__3 = *n - i__; + zdotc_(&z__4, &i__3, &w[i__ + 1 + i__ * w_dim1], &c__1, &a[ + i__ + 1 + i__ * a_dim1], &c__1); + z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, z__1.i = z__2.r * + z__4.i + z__2.i * z__4.r; + alpha.r = z__1.r, alpha.i = z__1.i; + i__2 = *n - i__; + zaxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &w[ + i__ + 1 + i__ * w_dim1], &c__1); + } + +/* L20: */ + } + } + + return 0; + +/* End of ZLATRD */ + +} /* zlatrd_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zpptrf.cpp b/lib/linalg/zpptrf.cpp new file mode 100644 index 0000000000..ebf3b7df9a --- /dev/null +++ b/lib/linalg/zpptrf.cpp @@ -0,0 +1,301 @@ +/* fortran/zpptrf.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static doublereal c_b16 = -1.; + +/* > \brief \b ZPPTRF */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZPPTRF + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZPPTRF( UPLO, N, AP, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER UPLO */ +/* INTEGER INFO, N */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 AP( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZPPTRF computes the Cholesky factorization of a complex Hermitian */ +/* > positive definite matrix A stored in packed format. */ +/* > */ +/* > The factorization has the form */ +/* > A = U**H * U, if UPLO = 'U', or */ +/* > A = L * L**H, if UPLO = 'L', */ +/* > where U is an upper triangular matrix and L is lower triangular. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > = 'U': Upper triangle of A is stored; */ +/* > = 'L': Lower triangle of A is stored. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] AP */ +/* > \verbatim */ +/* > AP is COMPLEX*16 array, dimension (N*(N+1)/2) */ +/* > On entry, the upper or lower triangle of the Hermitian matrix */ +/* > A, packed columnwise in a linear array. The j-th column of A */ +/* > is stored in the array AP as follows: */ +/* > if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */ +/* > if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. */ +/* > See below for further details. */ +/* > */ +/* > On exit, if INFO = 0, the triangular factor U or L from the */ +/* > Cholesky factorization A = U**H*U or A = L*L**H, in the same */ +/* > storage format as A. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > > 0: if INFO = i, the leading minor of order i is not */ +/* > positive definite, and the factorization could not be */ +/* > completed. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16OTHERcomputational */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > The packed storage scheme is illustrated by the following example */ +/* > when N = 4, UPLO = 'U': */ +/* > */ +/* > Two-dimensional storage of the Hermitian matrix A: */ +/* > */ +/* > a11 a12 a13 a14 */ +/* > a22 a23 a24 */ +/* > a33 a34 (aij = conjg(aji)) */ +/* > a44 */ +/* > */ +/* > Packed storage of the upper triangle of A: */ +/* > */ +/* > AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ] */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int zpptrf_(char *uplo, integer *n, doublecomplex *ap, + integer *info, ftnlen uplo_len) +{ + /* System generated locals */ + integer i__1, i__2, i__3; + doublereal d__1; + doublecomplex z__1; + + /* Builtin functions */ + double sqrt(doublereal); + + /* Local variables */ + integer j, jc, jj; + doublereal ajj; + extern /* Subroutine */ int zhpr_(char *, integer *, doublereal *, + doublecomplex *, integer *, doublecomplex *, ftnlen); + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *, + doublecomplex *, integer *, doublecomplex *, integer *); + logical upper; + extern /* Subroutine */ int ztpsv_(char *, char *, char *, integer *, + doublecomplex *, doublecomplex *, integer *, ftnlen, ftnlen, + ftnlen), xerbla_(char *, integer *, ftnlen), zdscal_(integer *, + doublereal *, doublecomplex *, integer *); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --ap; + + /* Function Body */ + *info = 0; + upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); + if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"ZPPTRF", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*n == 0) { + return 0; + } + + if (upper) { + +/* Compute the Cholesky factorization A = U**H * U. */ + + jj = 0; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + jc = jj + 1; + jj += j; + +/* Compute elements 1:J-1 of column J. */ + + if (j > 1) { + i__2 = j - 1; + ztpsv_((char *)"Upper", (char *)"Conjugate transpose", (char *)"Non-unit", &i__2, &ap[ + 1], &ap[jc], &c__1, (ftnlen)5, (ftnlen)19, (ftnlen)8); + } + +/* Compute U(J,J) and test for non-positive-definiteness. */ + + i__2 = jj; + i__3 = j - 1; + zdotc_(&z__1, &i__3, &ap[jc], &c__1, &ap[jc], &c__1); + ajj = ap[i__2].r - z__1.r; + if (ajj <= 0.) { + i__2 = jj; + ap[i__2].r = ajj, ap[i__2].i = 0.; + goto L30; + } + i__2 = jj; + d__1 = sqrt(ajj); + ap[i__2].r = d__1, ap[i__2].i = 0.; +/* L10: */ + } + } else { + +/* Compute the Cholesky factorization A = L * L**H. */ + + jj = 1; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + +/* Compute L(J,J) and test for non-positive-definiteness. */ + + i__2 = jj; + ajj = ap[i__2].r; + if (ajj <= 0.) { + i__2 = jj; + ap[i__2].r = ajj, ap[i__2].i = 0.; + goto L30; + } + ajj = sqrt(ajj); + i__2 = jj; + ap[i__2].r = ajj, ap[i__2].i = 0.; + +/* Compute elements J+1:N of column J and update the trailing */ +/* submatrix. */ + + if (j < *n) { + i__2 = *n - j; + d__1 = 1. / ajj; + zdscal_(&i__2, &d__1, &ap[jj + 1], &c__1); + i__2 = *n - j; + zhpr_((char *)"Lower", &i__2, &c_b16, &ap[jj + 1], &c__1, &ap[jj + *n + - j + 1], (ftnlen)5); + jj = jj + *n - j + 1; + } +/* L20: */ + } + } + goto L40; + +L30: + *info = j; + +L40: + return 0; + +/* End of ZPPTRF */ + +} /* zpptrf_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zpptri.cpp b/lib/linalg/zpptri.cpp new file mode 100644 index 0000000000..fc11e435b1 --- /dev/null +++ b/lib/linalg/zpptri.cpp @@ -0,0 +1,248 @@ +/* fortran/zpptri.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static doublereal c_b8 = 1.; +static integer c__1 = 1; + +/* > \brief \b ZPPTRI */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZPPTRI + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZPPTRI( UPLO, N, AP, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER UPLO */ +/* INTEGER INFO, N */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 AP( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZPPTRI computes the inverse of a complex Hermitian positive definite */ +/* > matrix A using the Cholesky factorization A = U**H*U or A = L*L**H */ +/* > computed by ZPPTRF. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > = 'U': Upper triangular factor is stored in AP; */ +/* > = 'L': Lower triangular factor is stored in AP. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] AP */ +/* > \verbatim */ +/* > AP is COMPLEX*16 array, dimension (N*(N+1)/2) */ +/* > On entry, the triangular factor U or L from the Cholesky */ +/* > factorization A = U**H*U or A = L*L**H, packed columnwise as */ +/* > a linear array. The j-th column of U or L is stored in the */ +/* > array AP as follows: */ +/* > if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j; */ +/* > if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n. */ +/* > */ +/* > On exit, the upper or lower triangle of the (Hermitian) */ +/* > inverse of A, overwriting the input factor U or L. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > > 0: if INFO = i, the (i,i) element of the factor U or L is */ +/* > zero, and the inverse could not be computed. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16OTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int zpptri_(char *uplo, integer *n, doublecomplex *ap, + integer *info, ftnlen uplo_len) +{ + /* System generated locals */ + integer i__1, i__2, i__3; + doublereal d__1; + doublecomplex z__1; + + /* Local variables */ + integer j, jc, jj; + doublereal ajj; + integer jjn; + extern /* Subroutine */ int zhpr_(char *, integer *, doublereal *, + doublecomplex *, integer *, doublecomplex *, ftnlen); + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *, + doublecomplex *, integer *, doublecomplex *, integer *); + logical upper; + extern /* Subroutine */ int ztpmv_(char *, char *, char *, integer *, + doublecomplex *, doublecomplex *, integer *, ftnlen, ftnlen, + ftnlen), xerbla_(char *, integer *, ftnlen), zdscal_(integer *, + doublereal *, doublecomplex *, integer *), ztptri_(char *, char *, + integer *, doublecomplex *, integer *, ftnlen, ftnlen); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --ap; + + /* Function Body */ + *info = 0; + upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); + if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"ZPPTRI", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*n == 0) { + return 0; + } + +/* Invert the triangular Cholesky factor U or L. */ + + ztptri_(uplo, (char *)"Non-unit", n, &ap[1], info, (ftnlen)1, (ftnlen)8); + if (*info > 0) { + return 0; + } + if (upper) { + +/* Compute the product inv(U) * inv(U)**H. */ + + jj = 0; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + jc = jj + 1; + jj += j; + if (j > 1) { + i__2 = j - 1; + zhpr_((char *)"Upper", &i__2, &c_b8, &ap[jc], &c__1, &ap[1], (ftnlen) + 5); + } + i__2 = jj; + ajj = ap[i__2].r; + zdscal_(&j, &ajj, &ap[jc], &c__1); +/* L10: */ + } + + } else { + +/* Compute the product inv(L)**H * inv(L). */ + + jj = 1; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + jjn = jj + *n - j + 1; + i__2 = jj; + i__3 = *n - j + 1; + zdotc_(&z__1, &i__3, &ap[jj], &c__1, &ap[jj], &c__1); + d__1 = z__1.r; + ap[i__2].r = d__1, ap[i__2].i = 0.; + if (j < *n) { + i__2 = *n - j; + ztpmv_((char *)"Lower", (char *)"Conjugate transpose", (char *)"Non-unit", &i__2, &ap[ + jjn], &ap[jj + 1], &c__1, (ftnlen)5, (ftnlen)19, ( + ftnlen)8); + } + jj = jjn; +/* L20: */ + } + } + + return 0; + +/* End of ZPPTRI */ + +} /* zpptri_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zscal.cpp b/lib/linalg/zscal.cpp new file mode 100644 index 0000000000..5985adebaf --- /dev/null +++ b/lib/linalg/zscal.cpp @@ -0,0 +1,162 @@ +/* fortran/zscal.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b ZSCAL */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZSCAL(N,ZA,ZX,INCX) */ + +/* .. Scalar Arguments .. */ +/* COMPLEX*16 ZA */ +/* INTEGER INCX,N */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 ZX(*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZSCAL scales a vector by a constant. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > number of elements in input vector(s) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] ZA */ +/* > \verbatim */ +/* > ZA is COMPLEX*16 */ +/* > On entry, ZA specifies the scalar alpha. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] ZX */ +/* > \verbatim */ +/* > ZX is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > storage spacing between elements of ZX */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16_blas_level1 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > jack dongarra, 3/11/78. */ +/* > modified 3/93 to return if incx .le. 0. */ +/* > modified 12/3/93, array(1) declarations changed to array(*) */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int zscal_(integer *n, doublecomplex *za, doublecomplex *zx, + integer *incx) +{ + /* System generated locals */ + integer i__1, i__2, i__3, i__4; + doublecomplex z__1; + + /* Local variables */ + integer i__, nincx; + + +/* -- Reference BLAS level1 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. Parameters .. */ +/* .. */ + /* Parameter adjustments */ + --zx; + + /* Function Body */ + if (*n <= 0 || *incx <= 0 || za->r == 1. && za->i == 0.) { + return 0; + } + if (*incx == 1) { + +/* code for increment equal to 1 */ + + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__; + i__3 = i__; + z__1.r = za->r * zx[i__3].r - za->i * zx[i__3].i, z__1.i = za->r * + zx[i__3].i + za->i * zx[i__3].r; + zx[i__2].r = z__1.r, zx[i__2].i = z__1.i; + } + } else { + +/* code for increment not equal to 1 */ + + nincx = *n * *incx; + i__1 = nincx; + i__2 = *incx; + for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { + i__3 = i__; + i__4 = i__; + z__1.r = za->r * zx[i__4].r - za->i * zx[i__4].i, z__1.i = za->r * + zx[i__4].i + za->i * zx[i__4].r; + zx[i__3].r = z__1.r, zx[i__3].i = z__1.i; + } + } + return 0; + +/* End of ZSCAL */ + +} /* zscal_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zstedc.cpp b/lib/linalg/zstedc.cpp new file mode 100644 index 0000000000..fb52b344b1 --- /dev/null +++ b/lib/linalg/zstedc.cpp @@ -0,0 +1,590 @@ +/* fortran/zstedc.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__9 = 9; +static integer c__0 = 0; +static integer c__2 = 2; +static doublereal c_b17 = 0.; +static doublereal c_b18 = 1.; +static integer c__1 = 1; + +/* > \brief \b ZSTEDC */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZSTEDC + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, RWORK, */ +/* LRWORK, IWORK, LIWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER COMPZ */ +/* INTEGER INFO, LDZ, LIWORK, LRWORK, LWORK, N */ +/* .. */ +/* .. Array Arguments .. */ +/* INTEGER IWORK( * ) */ +/* DOUBLE PRECISION D( * ), E( * ), RWORK( * ) */ +/* COMPLEX*16 WORK( * ), Z( LDZ, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZSTEDC computes all eigenvalues and, optionally, eigenvectors of a */ +/* > symmetric tridiagonal matrix using the divide and conquer method. */ +/* > The eigenvectors of a full or band complex Hermitian matrix can also */ +/* > be found if ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this */ +/* > matrix to tridiagonal form. */ +/* > */ +/* > This code makes very mild assumptions about floating point */ +/* > arithmetic. It will work on machines with a guard digit in */ +/* > add/subtract, or on those binary machines without guard digits */ +/* > which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. */ +/* > It could conceivably fail on hexadecimal or decimal machines */ +/* > without guard digits, but we know of none. See DLAED3 for details. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] COMPZ */ +/* > \verbatim */ +/* > COMPZ is CHARACTER*1 */ +/* > = 'N': Compute eigenvalues only. */ +/* > = 'I': Compute eigenvectors of tridiagonal matrix also. */ +/* > = 'V': Compute eigenvectors of original Hermitian matrix */ +/* > also. On entry, Z contains the unitary matrix used */ +/* > to reduce the original matrix to tridiagonal form. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The dimension of the symmetric tridiagonal matrix. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension (N) */ +/* > On entry, the diagonal elements of the tridiagonal matrix. */ +/* > On exit, if INFO = 0, the eigenvalues in ascending order. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] E */ +/* > \verbatim */ +/* > E is DOUBLE PRECISION array, dimension (N-1) */ +/* > On entry, the subdiagonal elements of the tridiagonal matrix. */ +/* > On exit, E has been destroyed. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] Z */ +/* > \verbatim */ +/* > Z is COMPLEX*16 array, dimension (LDZ,N) */ +/* > On entry, if COMPZ = 'V', then Z contains the unitary */ +/* > matrix used in the reduction to tridiagonal form. */ +/* > On exit, if INFO = 0, then if COMPZ = 'V', Z contains the */ +/* > orthonormal eigenvectors of the original Hermitian matrix, */ +/* > and if COMPZ = 'I', Z contains the orthonormal eigenvectors */ +/* > of the symmetric tridiagonal matrix. */ +/* > If COMPZ = 'N', then Z is not referenced. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDZ */ +/* > \verbatim */ +/* > LDZ is INTEGER */ +/* > The leading dimension of the array Z. LDZ >= 1. */ +/* > If eigenvectors are desired, then LDZ >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) */ +/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LWORK */ +/* > \verbatim */ +/* > LWORK is INTEGER */ +/* > The dimension of the array WORK. */ +/* > If COMPZ = 'N' or 'I', or N <= 1, LWORK must be at least 1. */ +/* > If COMPZ = 'V' and N > 1, LWORK must be at least N*N. */ +/* > Note that for COMPZ = 'V', then if N is less than or */ +/* > equal to the minimum divide size, usually 25, then LWORK need */ +/* > only be 1. */ +/* > */ +/* > If LWORK = -1, then a workspace query is assumed; the routine */ +/* > only calculates the optimal sizes of the WORK, RWORK and */ +/* > IWORK arrays, returns these values as the first entries of */ +/* > the WORK, RWORK and IWORK arrays, and no error message */ +/* > related to LWORK or LRWORK or LIWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] RWORK */ +/* > \verbatim */ +/* > RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) */ +/* > On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LRWORK */ +/* > \verbatim */ +/* > LRWORK is INTEGER */ +/* > The dimension of the array RWORK. */ +/* > If COMPZ = 'N' or N <= 1, LRWORK must be at least 1. */ +/* > If COMPZ = 'V' and N > 1, LRWORK must be at least */ +/* > 1 + 3*N + 2*N*lg N + 4*N**2 , */ +/* > where lg( N ) = smallest integer k such */ +/* > that 2**k >= N. */ +/* > If COMPZ = 'I' and N > 1, LRWORK must be at least */ +/* > 1 + 4*N + 2*N**2 . */ +/* > Note that for COMPZ = 'I' or 'V', then if N is less than or */ +/* > equal to the minimum divide size, usually 25, then LRWORK */ +/* > need only be max(1,2*(N-1)). */ +/* > */ +/* > If LRWORK = -1, then a workspace query is assumed; the */ +/* > routine only calculates the optimal sizes of the WORK, RWORK */ +/* > and IWORK arrays, returns these values as the first entries */ +/* > of the WORK, RWORK and IWORK arrays, and no error message */ +/* > related to LWORK or LRWORK or LIWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] IWORK */ +/* > \verbatim */ +/* > IWORK is INTEGER array, dimension (MAX(1,LIWORK)) */ +/* > On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LIWORK */ +/* > \verbatim */ +/* > LIWORK is INTEGER */ +/* > The dimension of the array IWORK. */ +/* > If COMPZ = 'N' or N <= 1, LIWORK must be at least 1. */ +/* > If COMPZ = 'V' or N > 1, LIWORK must be at least */ +/* > 6 + 6*N + 5*N*lg N. */ +/* > If COMPZ = 'I' or N > 1, LIWORK must be at least */ +/* > 3 + 5*N . */ +/* > Note that for COMPZ = 'I' or 'V', then if N is less than or */ +/* > equal to the minimum divide size, usually 25, then LIWORK */ +/* > need only be 1. */ +/* > */ +/* > If LIWORK = -1, then a workspace query is assumed; the */ +/* > routine only calculates the optimal sizes of the WORK, RWORK */ +/* > and IWORK arrays, returns these values as the first entries */ +/* > of the WORK, RWORK and IWORK arrays, and no error message */ +/* > related to LWORK or LRWORK or LIWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit. */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ +/* > > 0: The algorithm failed to compute an eigenvalue while */ +/* > working on the submatrix lying in rows and columns */ +/* > INFO/(N+1) through mod(INFO,N+1). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16OTHERcomputational */ + +/* > \par Contributors: */ +/* ================== */ +/* > */ +/* > Jeff Rutter, Computer Science Division, University of California */ +/* > at Berkeley, USA */ + +/* ===================================================================== */ +/* Subroutine */ int zstedc_(char *compz, integer *n, doublereal *d__, + doublereal *e, doublecomplex *z__, integer *ldz, doublecomplex *work, + integer *lwork, doublereal *rwork, integer *lrwork, integer *iwork, + integer *liwork, integer *info, ftnlen compz_len) +{ + /* System generated locals */ + integer z_dim1, z_offset, i__1, i__2, i__3, i__4; + doublereal d__1, d__2; + + /* Builtin functions */ + double log(doublereal); + integer pow_ii(integer *, integer *); + double sqrt(doublereal); + + /* Local variables */ + integer i__, j, k, m; + doublereal p; + integer ii, ll, lgn; + doublereal eps, tiny; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + integer lwmin, start; + extern /* Subroutine */ int zswap_(integer *, doublecomplex *, integer *, + doublecomplex *, integer *), zlaed0_(integer *, integer *, + doublereal *, doublereal *, doublecomplex *, integer *, + doublecomplex *, integer *, doublereal *, integer *, integer *); + extern doublereal dlamch_(char *, ftnlen); + extern /* Subroutine */ int dlascl_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, integer *, doublereal *, + integer *, integer *, ftnlen), dstedc_(char *, integer *, + doublereal *, doublereal *, doublereal *, integer *, doublereal *, + integer *, integer *, integer *, integer *, ftnlen), dlaset_( + char *, integer *, integer *, doublereal *, doublereal *, + doublereal *, integer *, ftnlen), xerbla_(char *, integer *, + ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + integer finish; + extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *, + ftnlen); + extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *, + integer *), zlacrm_(integer *, integer *, doublecomplex *, + integer *, doublereal *, integer *, doublecomplex *, integer *, + doublereal *); + integer liwmin, icompz; + extern /* Subroutine */ int dsteqr_(char *, integer *, doublereal *, + doublereal *, doublereal *, integer *, doublereal *, integer *, + ftnlen), zlacpy_(char *, integer *, integer *, doublecomplex *, + integer *, doublecomplex *, integer *, ftnlen); + doublereal orgnrm; + integer lrwmin; + logical lquery; + integer smlsiz; + extern /* Subroutine */ int zsteqr_(char *, integer *, doublereal *, + doublereal *, doublecomplex *, integer *, doublereal *, integer *, + ftnlen); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --d__; + --e; + z_dim1 = *ldz; + z_offset = 1 + z_dim1; + z__ -= z_offset; + --work; + --rwork; + --iwork; + + /* Function Body */ + *info = 0; + lquery = *lwork == -1 || *lrwork == -1 || *liwork == -1; + + if (lsame_(compz, (char *)"N", (ftnlen)1, (ftnlen)1)) { + icompz = 0; + } else if (lsame_(compz, (char *)"V", (ftnlen)1, (ftnlen)1)) { + icompz = 1; + } else if (lsame_(compz, (char *)"I", (ftnlen)1, (ftnlen)1)) { + icompz = 2; + } else { + icompz = -1; + } + if (icompz < 0) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } else if (*ldz < 1 || icompz > 0 && *ldz < max(1,*n)) { + *info = -6; + } + + if (*info == 0) { + +/* Compute the workspace requirements */ + + smlsiz = ilaenv_(&c__9, (char *)"ZSTEDC", (char *)" ", &c__0, &c__0, &c__0, &c__0, ( + ftnlen)6, (ftnlen)1); + if (*n <= 1 || icompz == 0) { + lwmin = 1; + liwmin = 1; + lrwmin = 1; + } else if (*n <= smlsiz) { + lwmin = 1; + liwmin = 1; + lrwmin = *n - 1 << 1; + } else if (icompz == 1) { + lgn = (integer) (log((doublereal) (*n)) / log(2.)); + if (pow_ii(&c__2, &lgn) < *n) { + ++lgn; + } + if (pow_ii(&c__2, &lgn) < *n) { + ++lgn; + } + lwmin = *n * *n; +/* Computing 2nd power */ + i__1 = *n; + lrwmin = *n * 3 + 1 + (*n << 1) * lgn + (i__1 * i__1 << 2); + liwmin = *n * 6 + 6 + *n * 5 * lgn; + } else if (icompz == 2) { + lwmin = 1; +/* Computing 2nd power */ + i__1 = *n; + lrwmin = (*n << 2) + 1 + (i__1 * i__1 << 1); + liwmin = *n * 5 + 3; + } + work[1].r = (doublereal) lwmin, work[1].i = 0.; + rwork[1] = (doublereal) lrwmin; + iwork[1] = liwmin; + + if (*lwork < lwmin && ! lquery) { + *info = -8; + } else if (*lrwork < lrwmin && ! lquery) { + *info = -10; + } else if (*liwork < liwmin && ! lquery) { + *info = -12; + } + } + + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"ZSTEDC", &i__1, (ftnlen)6); + return 0; + } else if (lquery) { + return 0; + } + +/* Quick return if possible */ + + if (*n == 0) { + return 0; + } + if (*n == 1) { + if (icompz != 0) { + i__1 = z_dim1 + 1; + z__[i__1].r = 1., z__[i__1].i = 0.; + } + return 0; + } + +/* If the following conditional clause is removed, then the routine */ +/* will use the Divide and Conquer routine to compute only the */ +/* eigenvalues, which requires (3N + 3N**2) real workspace and */ +/* (2 + 5N + 2N lg(N)) integer workspace. */ +/* Since on many architectures DSTERF is much faster than any other */ +/* algorithm for finding eigenvalues only, it is used here */ +/* as the default. If the conditional clause is removed, then */ +/* information on the size of workspace needs to be changed. */ + +/* If COMPZ = 'N', use DSTERF to compute the eigenvalues. */ + + if (icompz == 0) { + dsterf_(n, &d__[1], &e[1], info); + goto L70; + } + +/* If N is smaller than the minimum divide size (SMLSIZ+1), then */ +/* solve the problem with another solver. */ + + if (*n <= smlsiz) { + + zsteqr_(compz, n, &d__[1], &e[1], &z__[z_offset], ldz, &rwork[1], + info, (ftnlen)1); + + } else { + +/* If COMPZ = 'I', we simply call DSTEDC instead. */ + + if (icompz == 2) { + dlaset_((char *)"Full", n, n, &c_b17, &c_b18, &rwork[1], n, (ftnlen)4); + ll = *n * *n + 1; + i__1 = *lrwork - ll + 1; + dstedc_((char *)"I", n, &d__[1], &e[1], &rwork[1], n, &rwork[ll], &i__1, & + iwork[1], liwork, info, (ftnlen)1); + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * z_dim1; + i__4 = (j - 1) * *n + i__; + z__[i__3].r = rwork[i__4], z__[i__3].i = 0.; +/* L10: */ + } +/* L20: */ + } + goto L70; + } + +/* From now on, only option left to be handled is COMPZ = 'V', */ +/* i.e. ICOMPZ = 1. */ + +/* Scale. */ + + orgnrm = dlanst_((char *)"M", n, &d__[1], &e[1], (ftnlen)1); + if (orgnrm == 0.) { + goto L70; + } + + eps = dlamch_((char *)"Epsilon", (ftnlen)7); + + start = 1; + +/* while ( START <= N ) */ + +L30: + if (start <= *n) { + +/* Let FINISH be the position of the next subdiagonal entry */ +/* such that E( FINISH ) <= TINY or FINISH = N if no such */ +/* subdiagonal exists. The matrix identified by the elements */ +/* between START and FINISH constitutes an independent */ +/* sub-problem. */ + + finish = start; +L40: + if (finish < *n) { + tiny = eps * sqrt((d__1 = d__[finish], abs(d__1))) * sqrt(( + d__2 = d__[finish + 1], abs(d__2))); + if ((d__1 = e[finish], abs(d__1)) > tiny) { + ++finish; + goto L40; + } + } + +/* (Sub) Problem determined. Compute its size and solve it. */ + + m = finish - start + 1; + if (m > smlsiz) { + +/* Scale. */ + + orgnrm = dlanst_((char *)"M", &m, &d__[start], &e[start], (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b18, &m, &c__1, &d__[ + start], &m, info, (ftnlen)1); + i__1 = m - 1; + i__2 = m - 1; + dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b18, &i__1, &c__1, &e[ + start], &i__2, info, (ftnlen)1); + + zlaed0_(n, &m, &d__[start], &e[start], &z__[start * z_dim1 + + 1], ldz, &work[1], n, &rwork[1], &iwork[1], info); + if (*info > 0) { + *info = (*info / (m + 1) + start - 1) * (*n + 1) + *info % + (m + 1) + start - 1; + goto L70; + } + +/* Scale back. */ + + dlascl_((char *)"G", &c__0, &c__0, &c_b18, &orgnrm, &m, &c__1, &d__[ + start], &m, info, (ftnlen)1); + + } else { + dsteqr_((char *)"I", &m, &d__[start], &e[start], &rwork[1], &m, & + rwork[m * m + 1], info, (ftnlen)1); + zlacrm_(n, &m, &z__[start * z_dim1 + 1], ldz, &rwork[1], &m, & + work[1], n, &rwork[m * m + 1]); + zlacpy_((char *)"A", n, &m, &work[1], n, &z__[start * z_dim1 + 1], + ldz, (ftnlen)1); + if (*info > 0) { + *info = start * (*n + 1) + finish; + goto L70; + } + } + + start = finish + 1; + goto L30; + } + +/* endwhile */ + + +/* Use Selection Sort to minimize swaps of eigenvectors */ + + i__1 = *n; + for (ii = 2; ii <= i__1; ++ii) { + i__ = ii - 1; + k = i__; + p = d__[i__]; + i__2 = *n; + for (j = ii; j <= i__2; ++j) { + if (d__[j] < p) { + k = j; + p = d__[j]; + } +/* L50: */ + } + if (k != i__) { + d__[k] = d__[i__]; + d__[i__] = p; + zswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1 + 1], + &c__1); + } +/* L60: */ + } + } + +L70: + work[1].r = (doublereal) lwmin, work[1].i = 0.; + rwork[1] = (doublereal) lrwmin; + iwork[1] = liwmin; + + return 0; + +/* End of ZSTEDC */ + +} /* zstedc_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zsteqr.cpp b/lib/linalg/zsteqr.cpp new file mode 100644 index 0000000000..21cb31cc10 --- /dev/null +++ b/lib/linalg/zsteqr.cpp @@ -0,0 +1,706 @@ +/* fortran/zsteqr.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static doublecomplex c_b1 = {0.,0.}; +static doublecomplex c_b2 = {1.,0.}; +static integer c__0 = 0; +static integer c__1 = 1; +static integer c__2 = 2; +static doublereal c_b41 = 1.; + +/* > \brief \b ZSTEQR */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZSTEQR + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER COMPZ */ +/* INTEGER INFO, LDZ, N */ +/* .. */ +/* .. Array Arguments .. */ +/* DOUBLE PRECISION D( * ), E( * ), WORK( * ) */ +/* COMPLEX*16 Z( LDZ, * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZSTEQR computes all eigenvalues and, optionally, eigenvectors of a */ +/* > symmetric tridiagonal matrix using the implicit QL or QR method. */ +/* > The eigenvectors of a full or band complex Hermitian matrix can also */ +/* > be found if ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this */ +/* > matrix to tridiagonal form. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] COMPZ */ +/* > \verbatim */ +/* > COMPZ is CHARACTER*1 */ +/* > = 'N': Compute eigenvalues only. */ +/* > = 'V': Compute eigenvalues and eigenvectors of the original */ +/* > Hermitian matrix. On entry, Z must contain the */ +/* > unitary matrix used to reduce the original matrix */ +/* > to tridiagonal form. */ +/* > = 'I': Compute eigenvalues and eigenvectors of the */ +/* > tridiagonal matrix. Z is initialized to the identity */ +/* > matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrix. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] D */ +/* > \verbatim */ +/* > D is DOUBLE PRECISION array, dimension (N) */ +/* > On entry, the diagonal elements of the tridiagonal matrix. */ +/* > On exit, if INFO = 0, the eigenvalues in ascending order. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] E */ +/* > \verbatim */ +/* > E is DOUBLE PRECISION array, dimension (N-1) */ +/* > On entry, the (n-1) subdiagonal elements of the tridiagonal */ +/* > matrix. */ +/* > On exit, E has been destroyed. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] Z */ +/* > \verbatim */ +/* > Z is COMPLEX*16 array, dimension (LDZ, N) */ +/* > On entry, if COMPZ = 'V', then Z contains the unitary */ +/* > matrix used in the reduction to tridiagonal form. */ +/* > On exit, if INFO = 0, then if COMPZ = 'V', Z contains the */ +/* > orthonormal eigenvectors of the original Hermitian matrix, */ +/* > and if COMPZ = 'I', Z contains the orthonormal eigenvectors */ +/* > of the symmetric tridiagonal matrix. */ +/* > If COMPZ = 'N', then Z is not referenced. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDZ */ +/* > \verbatim */ +/* > LDZ is INTEGER */ +/* > The leading dimension of the array Z. LDZ >= 1, and if */ +/* > eigenvectors are desired, then LDZ >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is DOUBLE PRECISION array, dimension (max(1,2*N-2)) */ +/* > If COMPZ = 'N', then WORK is not referenced. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > > 0: the algorithm has failed to find all the eigenvalues in */ +/* > a total of 30*N iterations; if INFO = i, then i */ +/* > elements of E have not converged to zero; on exit, D */ +/* > and E contain the elements of a symmetric tridiagonal */ +/* > matrix which is unitarily similar to the original */ +/* > matrix. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16OTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int zsteqr_(char *compz, integer *n, doublereal *d__, + doublereal *e, doublecomplex *z__, integer *ldz, doublereal *work, + integer *info, ftnlen compz_len) +{ + /* System generated locals */ + integer z_dim1, z_offset, i__1, i__2; + doublereal d__1, d__2; + + /* Builtin functions */ + double sqrt(doublereal), d_sign(doublereal *, doublereal *); + + /* Local variables */ + doublereal b, c__, f, g; + integer i__, j, k, l, m; + doublereal p, r__, s; + integer l1, ii, mm, lm1, mm1, nm1; + doublereal rt1, rt2, eps; + integer lsv; + doublereal tst, eps2; + integer lend, jtot; + extern /* Subroutine */ int dlae2_(doublereal *, doublereal *, doublereal + *, doublereal *, doublereal *); + extern logical lsame_(char *, char *, ftnlen, ftnlen); + doublereal anorm; + extern /* Subroutine */ int zlasr_(char *, char *, char *, integer *, + integer *, doublereal *, doublereal *, doublecomplex *, integer *, + ftnlen, ftnlen, ftnlen), zswap_(integer *, doublecomplex *, + integer *, doublecomplex *, integer *), dlaev2_(doublereal *, + doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, doublereal *); + integer lendm1, lendp1; + extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, + ftnlen); + integer iscale; + extern /* Subroutine */ int dlascl_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, integer *, doublereal *, + integer *, integer *, ftnlen); + doublereal safmin; + extern /* Subroutine */ int dlartg_(doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *); + doublereal safmax; + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *, + ftnlen); + extern /* Subroutine */ int dlasrt_(char *, integer *, doublereal *, + integer *, ftnlen); + integer lendsv; + doublereal ssfmin; + integer nmaxit, icompz; + doublereal ssfmax; + extern /* Subroutine */ int zlaset_(char *, integer *, integer *, + doublecomplex *, doublecomplex *, doublecomplex *, integer *, + ftnlen); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --d__; + --e; + z_dim1 = *ldz; + z_offset = 1 + z_dim1; + z__ -= z_offset; + --work; + + /* Function Body */ + *info = 0; + + if (lsame_(compz, (char *)"N", (ftnlen)1, (ftnlen)1)) { + icompz = 0; + } else if (lsame_(compz, (char *)"V", (ftnlen)1, (ftnlen)1)) { + icompz = 1; + } else if (lsame_(compz, (char *)"I", (ftnlen)1, (ftnlen)1)) { + icompz = 2; + } else { + icompz = -1; + } + if (icompz < 0) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } else if (*ldz < 1 || icompz > 0 && *ldz < max(1,*n)) { + *info = -6; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"ZSTEQR", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*n == 0) { + return 0; + } + + if (*n == 1) { + if (icompz == 2) { + i__1 = z_dim1 + 1; + z__[i__1].r = 1., z__[i__1].i = 0.; + } + return 0; + } + +/* Determine the unit roundoff and over/underflow thresholds. */ + + eps = dlamch_((char *)"E", (ftnlen)1); +/* Computing 2nd power */ + d__1 = eps; + eps2 = d__1 * d__1; + safmin = dlamch_((char *)"S", (ftnlen)1); + safmax = 1. / safmin; + ssfmax = sqrt(safmax) / 3.; + ssfmin = sqrt(safmin) / eps2; + +/* Compute the eigenvalues and eigenvectors of the tridiagonal */ +/* matrix. */ + + if (icompz == 2) { + zlaset_((char *)"Full", n, n, &c_b1, &c_b2, &z__[z_offset], ldz, (ftnlen)4); + } + + nmaxit = *n * 30; + jtot = 0; + +/* Determine where the matrix splits and choose QL or QR iteration */ +/* for each block, according to whether top or bottom diagonal */ +/* element is smaller. */ + + l1 = 1; + nm1 = *n - 1; + +L10: + if (l1 > *n) { + goto L160; + } + if (l1 > 1) { + e[l1 - 1] = 0.; + } + if (l1 <= nm1) { + i__1 = nm1; + for (m = l1; m <= i__1; ++m) { + tst = (d__1 = e[m], abs(d__1)); + if (tst == 0.) { + goto L30; + } + if (tst <= sqrt((d__1 = d__[m], abs(d__1))) * sqrt((d__2 = d__[m + + 1], abs(d__2))) * eps) { + e[m] = 0.; + goto L30; + } +/* L20: */ + } + } + m = *n; + +L30: + l = l1; + lsv = l; + lend = m; + lendsv = lend; + l1 = m + 1; + if (lend == l) { + goto L10; + } + +/* Scale submatrix in rows and columns L to LEND */ + + i__1 = lend - l + 1; + anorm = dlanst_((char *)"I", &i__1, &d__[l], &e[l], (ftnlen)1); + iscale = 0; + if (anorm == 0.) { + goto L10; + } + if (anorm > ssfmax) { + iscale = 1; + i__1 = lend - l + 1; + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n, + info, (ftnlen)1); + i__1 = lend - l; + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &e[l], n, + info, (ftnlen)1); + } else if (anorm < ssfmin) { + iscale = 2; + i__1 = lend - l + 1; + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n, + info, (ftnlen)1); + i__1 = lend - l; + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n, + info, (ftnlen)1); + } + +/* Choose between QL and QR iteration */ + + if ((d__1 = d__[lend], abs(d__1)) < (d__2 = d__[l], abs(d__2))) { + lend = lsv; + l = lendsv; + } + + if (lend > l) { + +/* QL Iteration */ + +/* Look for small subdiagonal element. */ + +L40: + if (l != lend) { + lendm1 = lend - 1; + i__1 = lendm1; + for (m = l; m <= i__1; ++m) { +/* Computing 2nd power */ + d__2 = (d__1 = e[m], abs(d__1)); + tst = d__2 * d__2; + if (tst <= eps2 * (d__1 = d__[m], abs(d__1)) * (d__2 = d__[m + + 1], abs(d__2)) + safmin) { + goto L60; + } +/* L50: */ + } + } + + m = lend; + +L60: + if (m < lend) { + e[m] = 0.; + } + p = d__[l]; + if (m == l) { + goto L80; + } + +/* If remaining matrix is 2-by-2, use DLAE2 or SLAEV2 */ +/* to compute its eigensystem. */ + + if (m == l + 1) { + if (icompz > 0) { + dlaev2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2, &c__, &s); + work[l] = c__; + work[*n - 1 + l] = s; + zlasr_((char *)"R", (char *)"V", (char *)"B", n, &c__2, &work[l], &work[*n - 1 + l], & + z__[l * z_dim1 + 1], ldz, (ftnlen)1, (ftnlen)1, ( + ftnlen)1); + } else { + dlae2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2); + } + d__[l] = rt1; + d__[l + 1] = rt2; + e[l] = 0.; + l += 2; + if (l <= lend) { + goto L40; + } + goto L140; + } + + if (jtot == nmaxit) { + goto L140; + } + ++jtot; + +/* Form shift. */ + + g = (d__[l + 1] - p) / (e[l] * 2.); + r__ = dlapy2_(&g, &c_b41); + g = d__[m] - p + e[l] / (g + d_sign(&r__, &g)); + + s = 1.; + c__ = 1.; + p = 0.; + +/* Inner loop */ + + mm1 = m - 1; + i__1 = l; + for (i__ = mm1; i__ >= i__1; --i__) { + f = s * e[i__]; + b = c__ * e[i__]; + dlartg_(&g, &f, &c__, &s, &r__); + if (i__ != m - 1) { + e[i__ + 1] = r__; + } + g = d__[i__ + 1] - p; + r__ = (d__[i__] - g) * s + c__ * 2. * b; + p = s * r__; + d__[i__ + 1] = g + p; + g = c__ * r__ - b; + +/* If eigenvectors are desired, then save rotations. */ + + if (icompz > 0) { + work[i__] = c__; + work[*n - 1 + i__] = -s; + } + +/* L70: */ + } + +/* If eigenvectors are desired, then apply saved rotations. */ + + if (icompz > 0) { + mm = m - l + 1; + zlasr_((char *)"R", (char *)"V", (char *)"B", n, &mm, &work[l], &work[*n - 1 + l], &z__[l + * z_dim1 + 1], ldz, (ftnlen)1, (ftnlen)1, (ftnlen)1); + } + + d__[l] -= p; + e[l] = g; + goto L40; + +/* Eigenvalue found. */ + +L80: + d__[l] = p; + + ++l; + if (l <= lend) { + goto L40; + } + goto L140; + + } else { + +/* QR Iteration */ + +/* Look for small superdiagonal element. */ + +L90: + if (l != lend) { + lendp1 = lend + 1; + i__1 = lendp1; + for (m = l; m >= i__1; --m) { +/* Computing 2nd power */ + d__2 = (d__1 = e[m - 1], abs(d__1)); + tst = d__2 * d__2; + if (tst <= eps2 * (d__1 = d__[m], abs(d__1)) * (d__2 = d__[m + - 1], abs(d__2)) + safmin) { + goto L110; + } +/* L100: */ + } + } + + m = lend; + +L110: + if (m > lend) { + e[m - 1] = 0.; + } + p = d__[l]; + if (m == l) { + goto L130; + } + +/* If remaining matrix is 2-by-2, use DLAE2 or SLAEV2 */ +/* to compute its eigensystem. */ + + if (m == l - 1) { + if (icompz > 0) { + dlaev2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2, &c__, &s) + ; + work[m] = c__; + work[*n - 1 + m] = s; + zlasr_((char *)"R", (char *)"V", (char *)"F", n, &c__2, &work[m], &work[*n - 1 + m], & + z__[(l - 1) * z_dim1 + 1], ldz, (ftnlen)1, (ftnlen)1, + (ftnlen)1); + } else { + dlae2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2); + } + d__[l - 1] = rt1; + d__[l] = rt2; + e[l - 1] = 0.; + l += -2; + if (l >= lend) { + goto L90; + } + goto L140; + } + + if (jtot == nmaxit) { + goto L140; + } + ++jtot; + +/* Form shift. */ + + g = (d__[l - 1] - p) / (e[l - 1] * 2.); + r__ = dlapy2_(&g, &c_b41); + g = d__[m] - p + e[l - 1] / (g + d_sign(&r__, &g)); + + s = 1.; + c__ = 1.; + p = 0.; + +/* Inner loop */ + + lm1 = l - 1; + i__1 = lm1; + for (i__ = m; i__ <= i__1; ++i__) { + f = s * e[i__]; + b = c__ * e[i__]; + dlartg_(&g, &f, &c__, &s, &r__); + if (i__ != m) { + e[i__ - 1] = r__; + } + g = d__[i__] - p; + r__ = (d__[i__ + 1] - g) * s + c__ * 2. * b; + p = s * r__; + d__[i__] = g + p; + g = c__ * r__ - b; + +/* If eigenvectors are desired, then save rotations. */ + + if (icompz > 0) { + work[i__] = c__; + work[*n - 1 + i__] = s; + } + +/* L120: */ + } + +/* If eigenvectors are desired, then apply saved rotations. */ + + if (icompz > 0) { + mm = l - m + 1; + zlasr_((char *)"R", (char *)"V", (char *)"F", n, &mm, &work[m], &work[*n - 1 + m], &z__[m + * z_dim1 + 1], ldz, (ftnlen)1, (ftnlen)1, (ftnlen)1); + } + + d__[l] -= p; + e[lm1] = g; + goto L90; + +/* Eigenvalue found. */ + +L130: + d__[l] = p; + + --l; + if (l >= lend) { + goto L90; + } + goto L140; + + } + +/* Undo scaling if necessary */ + +L140: + if (iscale == 1) { + i__1 = lendsv - lsv + 1; + dlascl_((char *)"G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv], + n, info, (ftnlen)1); + i__1 = lendsv - lsv; + dlascl_((char *)"G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &e[lsv], n, + info, (ftnlen)1); + } else if (iscale == 2) { + i__1 = lendsv - lsv + 1; + dlascl_((char *)"G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[lsv], + n, info, (ftnlen)1); + i__1 = lendsv - lsv; + dlascl_((char *)"G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &e[lsv], n, + info, (ftnlen)1); + } + +/* Check for no convergence to an eigenvalue after a total */ +/* of N*MAXIT iterations. */ + + if (jtot == nmaxit) { + i__1 = *n - 1; + for (i__ = 1; i__ <= i__1; ++i__) { + if (e[i__] != 0.) { + ++(*info); + } +/* L150: */ + } + return 0; + } + goto L10; + +/* Order eigenvalues and eigenvectors. */ + +L160: + if (icompz == 0) { + +/* Use Quick Sort */ + + dlasrt_((char *)"I", n, &d__[1], info, (ftnlen)1); + + } else { + +/* Use Selection Sort to minimize swaps of eigenvectors */ + + i__1 = *n; + for (ii = 2; ii <= i__1; ++ii) { + i__ = ii - 1; + k = i__; + p = d__[i__]; + i__2 = *n; + for (j = ii; j <= i__2; ++j) { + if (d__[j] < p) { + k = j; + p = d__[j]; + } +/* L170: */ + } + if (k != i__) { + d__[k] = d__[i__]; + d__[i__] = p; + zswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1 + 1], + &c__1); + } +/* L180: */ + } + } + return 0; + +/* End of ZSTEQR */ + +} /* zsteqr_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zswap.cpp b/lib/linalg/zswap.cpp new file mode 100644 index 0000000000..d00bb044fd --- /dev/null +++ b/lib/linalg/zswap.cpp @@ -0,0 +1,176 @@ +/* fortran/zswap.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b ZSWAP */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZSWAP(N,ZX,INCX,ZY,INCY) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INCX,INCY,N */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 ZX(*),ZY(*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZSWAP interchanges two vectors. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > number of elements in input vector(s) */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] ZX */ +/* > \verbatim */ +/* > ZX is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > storage spacing between elements of ZX */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] ZY */ +/* > \verbatim */ +/* > ZY is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCY */ +/* > \verbatim */ +/* > INCY is INTEGER */ +/* > storage spacing between elements of ZY */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16_blas_level1 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > jack dongarra, 3/11/78. */ +/* > modified 12/3/93, array(1) declarations changed to array(*) */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int zswap_(integer *n, doublecomplex *zx, integer *incx, + doublecomplex *zy, integer *incy) +{ + /* System generated locals */ + integer i__1, i__2, i__3; + + /* Local variables */ + integer i__, ix, iy; + doublecomplex ztemp; + + +/* -- Reference BLAS level1 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ + /* Parameter adjustments */ + --zy; + --zx; + + /* Function Body */ + if (*n <= 0) { + return 0; + } + if (*incx == 1 && *incy == 1) { + +/* code for both increments equal to 1 */ + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__; + ztemp.r = zx[i__2].r, ztemp.i = zx[i__2].i; + i__2 = i__; + i__3 = i__; + zx[i__2].r = zy[i__3].r, zx[i__2].i = zy[i__3].i; + i__2 = i__; + zy[i__2].r = ztemp.r, zy[i__2].i = ztemp.i; + } + } else { + +/* code for unequal increments or equal increments not equal */ +/* to 1 */ + + ix = 1; + iy = 1; + if (*incx < 0) { + ix = (-(*n) + 1) * *incx + 1; + } + if (*incy < 0) { + iy = (-(*n) + 1) * *incy + 1; + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = ix; + ztemp.r = zx[i__2].r, ztemp.i = zx[i__2].i; + i__2 = ix; + i__3 = iy; + zx[i__2].r = zy[i__3].r, zx[i__2].i = zy[i__3].i; + i__2 = iy; + zy[i__2].r = ztemp.r, zy[i__2].i = ztemp.i; + ix += *incx; + iy += *incy; + } + } + return 0; + +/* End of ZSWAP */ + +} /* zswap_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/ztpmv.cpp b/lib/linalg/ztpmv.cpp new file mode 100644 index 0000000000..a29145d6bd --- /dev/null +++ b/lib/linalg/ztpmv.cpp @@ -0,0 +1,639 @@ +/* fortran/ztpmv.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b ZTPMV */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INCX,N */ +/* CHARACTER DIAG,TRANS,UPLO */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 AP(*),X(*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZTPMV performs one of the matrix-vector operations */ +/* > */ +/* > x := A*x, or x := A**T*x, or x := A**H*x, */ +/* > */ +/* > where x is an n element vector and A is an n by n unit, or non-unit, */ +/* > upper or lower triangular matrix, supplied in packed form. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > On entry, UPLO specifies whether the matrix is an upper or */ +/* > lower triangular matrix as follows: */ +/* > */ +/* > UPLO = 'U' or 'u' A is an upper triangular matrix. */ +/* > */ +/* > UPLO = 'L' or 'l' A is a lower triangular matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TRANS */ +/* > \verbatim */ +/* > TRANS is CHARACTER*1 */ +/* > On entry, TRANS specifies the operation to be performed as */ +/* > follows: */ +/* > */ +/* > TRANS = 'N' or 'n' x := A*x. */ +/* > */ +/* > TRANS = 'T' or 't' x := A**T*x. */ +/* > */ +/* > TRANS = 'C' or 'c' x := A**H*x. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DIAG */ +/* > \verbatim */ +/* > DIAG is CHARACTER*1 */ +/* > On entry, DIAG specifies whether or not A is unit */ +/* > triangular as follows: */ +/* > */ +/* > DIAG = 'U' or 'u' A is assumed to be unit triangular. */ +/* > */ +/* > DIAG = 'N' or 'n' A is not assumed to be unit */ +/* > triangular. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > On entry, N specifies the order of the matrix A. */ +/* > N must be at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] AP */ +/* > \verbatim */ +/* > AP is COMPLEX*16 array, dimension at least */ +/* > ( ( n*( n + 1 ) )/2 ). */ +/* > Before entry with UPLO = 'U' or 'u', the array AP must */ +/* > contain the upper triangular matrix packed sequentially, */ +/* > column by column, so that AP( 1 ) contains a( 1, 1 ), */ +/* > AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) */ +/* > respectively, and so on. */ +/* > Before entry with UPLO = 'L' or 'l', the array AP must */ +/* > contain the lower triangular matrix packed sequentially, */ +/* > column by column, so that AP( 1 ) contains a( 1, 1 ), */ +/* > AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) */ +/* > respectively, and so on. */ +/* > Note that when DIAG = 'U' or 'u', the diagonal elements of */ +/* > A are not referenced, but are assumed to be unity. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] X */ +/* > \verbatim */ +/* > X is COMPLEX*16 array, dimension at least */ +/* > ( 1 + ( n - 1 )*abs( INCX ) ). */ +/* > Before entry, the incremented array X must contain the n */ +/* > element vector x. On exit, X is overwritten with the */ +/* > transformed vector x. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > On entry, INCX specifies the increment for the elements of */ +/* > X. INCX must not be zero. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16_blas_level2 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > Level 2 Blas routine. */ +/* > The vector and matrix arguments are not referenced when N = 0, or M = 0 */ +/* > */ +/* > -- Written on 22-October-1986. */ +/* > Jack Dongarra, Argonne National Lab. */ +/* > Jeremy Du Croz, Nag Central Office. */ +/* > Sven Hammarling, Nag Central Office. */ +/* > Richard Hanson, Sandia National Labs. */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int ztpmv_(char *uplo, char *trans, char *diag, integer *n, + doublecomplex *ap, doublecomplex *x, integer *incx, ftnlen uplo_len, + ftnlen trans_len, ftnlen diag_len) +{ + /* System generated locals */ + integer i__1, i__2, i__3, i__4, i__5; + doublecomplex z__1, z__2, z__3; + + /* Builtin functions */ + void d_cnjg(doublecomplex *, doublecomplex *); + + /* Local variables */ + integer i__, j, k, kk, ix, jx, kx, info; + doublecomplex temp; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + logical noconj, nounit; + + +/* -- Reference BLAS level2 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --x; + --ap; + + /* Function Body */ + info = 0; + if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", ( + ftnlen)1, (ftnlen)1)) { + info = 1; + } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, + (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, ( + ftnlen)1)) { + info = 2; + } else if (! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, + (char *)"N", (ftnlen)1, (ftnlen)1)) { + info = 3; + } else if (*n < 0) { + info = 4; + } else if (*incx == 0) { + info = 7; + } + if (info != 0) { + xerbla_((char *)"ZTPMV ", &info, (ftnlen)6); + return 0; + } + +/* Quick return if possible. */ + + if (*n == 0) { + return 0; + } + + noconj = lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1); + nounit = lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1); + +/* Set up the start point in X if the increment is not unity. This */ +/* will be ( N - 1 )*INCX too small for descending loops. */ + + if (*incx <= 0) { + kx = 1 - (*n - 1) * *incx; + } else if (*incx != 1) { + kx = 1; + } + +/* Start the operations. In this version the elements of AP are */ +/* accessed sequentially with one pass through AP. */ + + if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { + +/* Form x:= A*x. */ + + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + kk = 1; + if (*incx == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + if (x[i__2].r != 0. || x[i__2].i != 0.) { + i__2 = j; + temp.r = x[i__2].r, temp.i = x[i__2].i; + k = kk; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__; + i__4 = i__; + i__5 = k; + z__2.r = temp.r * ap[i__5].r - temp.i * ap[i__5] + .i, z__2.i = temp.r * ap[i__5].i + temp.i + * ap[i__5].r; + z__1.r = x[i__4].r + z__2.r, z__1.i = x[i__4].i + + z__2.i; + x[i__3].r = z__1.r, x[i__3].i = z__1.i; + ++k; +/* L10: */ + } + if (nounit) { + i__2 = j; + i__3 = j; + i__4 = kk + j - 1; + z__1.r = x[i__3].r * ap[i__4].r - x[i__3].i * ap[ + i__4].i, z__1.i = x[i__3].r * ap[i__4].i + + x[i__3].i * ap[i__4].r; + x[i__2].r = z__1.r, x[i__2].i = z__1.i; + } + } + kk += j; +/* L20: */ + } + } else { + jx = kx; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = jx; + if (x[i__2].r != 0. || x[i__2].i != 0.) { + i__2 = jx; + temp.r = x[i__2].r, temp.i = x[i__2].i; + ix = kx; + i__2 = kk + j - 2; + for (k = kk; k <= i__2; ++k) { + i__3 = ix; + i__4 = ix; + i__5 = k; + z__2.r = temp.r * ap[i__5].r - temp.i * ap[i__5] + .i, z__2.i = temp.r * ap[i__5].i + temp.i + * ap[i__5].r; + z__1.r = x[i__4].r + z__2.r, z__1.i = x[i__4].i + + z__2.i; + x[i__3].r = z__1.r, x[i__3].i = z__1.i; + ix += *incx; +/* L30: */ + } + if (nounit) { + i__2 = jx; + i__3 = jx; + i__4 = kk + j - 1; + z__1.r = x[i__3].r * ap[i__4].r - x[i__3].i * ap[ + i__4].i, z__1.i = x[i__3].r * ap[i__4].i + + x[i__3].i * ap[i__4].r; + x[i__2].r = z__1.r, x[i__2].i = z__1.i; + } + } + jx += *incx; + kk += j; +/* L40: */ + } + } + } else { + kk = *n * (*n + 1) / 2; + if (*incx == 1) { + for (j = *n; j >= 1; --j) { + i__1 = j; + if (x[i__1].r != 0. || x[i__1].i != 0.) { + i__1 = j; + temp.r = x[i__1].r, temp.i = x[i__1].i; + k = kk; + i__1 = j + 1; + for (i__ = *n; i__ >= i__1; --i__) { + i__2 = i__; + i__3 = i__; + i__4 = k; + z__2.r = temp.r * ap[i__4].r - temp.i * ap[i__4] + .i, z__2.i = temp.r * ap[i__4].i + temp.i + * ap[i__4].r; + z__1.r = x[i__3].r + z__2.r, z__1.i = x[i__3].i + + z__2.i; + x[i__2].r = z__1.r, x[i__2].i = z__1.i; + --k; +/* L50: */ + } + if (nounit) { + i__1 = j; + i__2 = j; + i__3 = kk - *n + j; + z__1.r = x[i__2].r * ap[i__3].r - x[i__2].i * ap[ + i__3].i, z__1.i = x[i__2].r * ap[i__3].i + + x[i__2].i * ap[i__3].r; + x[i__1].r = z__1.r, x[i__1].i = z__1.i; + } + } + kk -= *n - j + 1; +/* L60: */ + } + } else { + kx += (*n - 1) * *incx; + jx = kx; + for (j = *n; j >= 1; --j) { + i__1 = jx; + if (x[i__1].r != 0. || x[i__1].i != 0.) { + i__1 = jx; + temp.r = x[i__1].r, temp.i = x[i__1].i; + ix = kx; + i__1 = kk - (*n - (j + 1)); + for (k = kk; k >= i__1; --k) { + i__2 = ix; + i__3 = ix; + i__4 = k; + z__2.r = temp.r * ap[i__4].r - temp.i * ap[i__4] + .i, z__2.i = temp.r * ap[i__4].i + temp.i + * ap[i__4].r; + z__1.r = x[i__3].r + z__2.r, z__1.i = x[i__3].i + + z__2.i; + x[i__2].r = z__1.r, x[i__2].i = z__1.i; + ix -= *incx; +/* L70: */ + } + if (nounit) { + i__1 = jx; + i__2 = jx; + i__3 = kk - *n + j; + z__1.r = x[i__2].r * ap[i__3].r - x[i__2].i * ap[ + i__3].i, z__1.i = x[i__2].r * ap[i__3].i + + x[i__2].i * ap[i__3].r; + x[i__1].r = z__1.r, x[i__1].i = z__1.i; + } + } + jx -= *incx; + kk -= *n - j + 1; +/* L80: */ + } + } + } + } else { + +/* Form x := A**T*x or x := A**H*x. */ + + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + kk = *n * (*n + 1) / 2; + if (*incx == 1) { + for (j = *n; j >= 1; --j) { + i__1 = j; + temp.r = x[i__1].r, temp.i = x[i__1].i; + k = kk - 1; + if (noconj) { + if (nounit) { + i__1 = kk; + z__1.r = temp.r * ap[i__1].r - temp.i * ap[i__1] + .i, z__1.i = temp.r * ap[i__1].i + temp.i + * ap[i__1].r; + temp.r = z__1.r, temp.i = z__1.i; + } + for (i__ = j - 1; i__ >= 1; --i__) { + i__1 = k; + i__2 = i__; + z__2.r = ap[i__1].r * x[i__2].r - ap[i__1].i * x[ + i__2].i, z__2.i = ap[i__1].r * x[i__2].i + + ap[i__1].i * x[i__2].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + --k; +/* L90: */ + } + } else { + if (nounit) { + d_cnjg(&z__2, &ap[kk]); + z__1.r = temp.r * z__2.r - temp.i * z__2.i, + z__1.i = temp.r * z__2.i + temp.i * + z__2.r; + temp.r = z__1.r, temp.i = z__1.i; + } + for (i__ = j - 1; i__ >= 1; --i__) { + d_cnjg(&z__3, &ap[k]); + i__1 = i__; + z__2.r = z__3.r * x[i__1].r - z__3.i * x[i__1].i, + z__2.i = z__3.r * x[i__1].i + z__3.i * x[ + i__1].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + --k; +/* L100: */ + } + } + i__1 = j; + x[i__1].r = temp.r, x[i__1].i = temp.i; + kk -= j; +/* L110: */ + } + } else { + jx = kx + (*n - 1) * *incx; + for (j = *n; j >= 1; --j) { + i__1 = jx; + temp.r = x[i__1].r, temp.i = x[i__1].i; + ix = jx; + if (noconj) { + if (nounit) { + i__1 = kk; + z__1.r = temp.r * ap[i__1].r - temp.i * ap[i__1] + .i, z__1.i = temp.r * ap[i__1].i + temp.i + * ap[i__1].r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__1 = kk - j + 1; + for (k = kk - 1; k >= i__1; --k) { + ix -= *incx; + i__2 = k; + i__3 = ix; + z__2.r = ap[i__2].r * x[i__3].r - ap[i__2].i * x[ + i__3].i, z__2.i = ap[i__2].r * x[i__3].i + + ap[i__2].i * x[i__3].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; +/* L120: */ + } + } else { + if (nounit) { + d_cnjg(&z__2, &ap[kk]); + z__1.r = temp.r * z__2.r - temp.i * z__2.i, + z__1.i = temp.r * z__2.i + temp.i * + z__2.r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__1 = kk - j + 1; + for (k = kk - 1; k >= i__1; --k) { + ix -= *incx; + d_cnjg(&z__3, &ap[k]); + i__2 = ix; + z__2.r = z__3.r * x[i__2].r - z__3.i * x[i__2].i, + z__2.i = z__3.r * x[i__2].i + z__3.i * x[ + i__2].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; +/* L130: */ + } + } + i__1 = jx; + x[i__1].r = temp.r, x[i__1].i = temp.i; + jx -= *incx; + kk -= j; +/* L140: */ + } + } + } else { + kk = 1; + if (*incx == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + temp.r = x[i__2].r, temp.i = x[i__2].i; + k = kk + 1; + if (noconj) { + if (nounit) { + i__2 = kk; + z__1.r = temp.r * ap[i__2].r - temp.i * ap[i__2] + .i, z__1.i = temp.r * ap[i__2].i + temp.i + * ap[i__2].r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + i__3 = k; + i__4 = i__; + z__2.r = ap[i__3].r * x[i__4].r - ap[i__3].i * x[ + i__4].i, z__2.i = ap[i__3].r * x[i__4].i + + ap[i__3].i * x[i__4].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + ++k; +/* L150: */ + } + } else { + if (nounit) { + d_cnjg(&z__2, &ap[kk]); + z__1.r = temp.r * z__2.r - temp.i * z__2.i, + z__1.i = temp.r * z__2.i + temp.i * + z__2.r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + d_cnjg(&z__3, &ap[k]); + i__3 = i__; + z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, + z__2.i = z__3.r * x[i__3].i + z__3.i * x[ + i__3].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + ++k; +/* L160: */ + } + } + i__2 = j; + x[i__2].r = temp.r, x[i__2].i = temp.i; + kk += *n - j + 1; +/* L170: */ + } + } else { + jx = kx; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = jx; + temp.r = x[i__2].r, temp.i = x[i__2].i; + ix = jx; + if (noconj) { + if (nounit) { + i__2 = kk; + z__1.r = temp.r * ap[i__2].r - temp.i * ap[i__2] + .i, z__1.i = temp.r * ap[i__2].i + temp.i + * ap[i__2].r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__2 = kk + *n - j; + for (k = kk + 1; k <= i__2; ++k) { + ix += *incx; + i__3 = k; + i__4 = ix; + z__2.r = ap[i__3].r * x[i__4].r - ap[i__3].i * x[ + i__4].i, z__2.i = ap[i__3].r * x[i__4].i + + ap[i__3].i * x[i__4].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; +/* L180: */ + } + } else { + if (nounit) { + d_cnjg(&z__2, &ap[kk]); + z__1.r = temp.r * z__2.r - temp.i * z__2.i, + z__1.i = temp.r * z__2.i + temp.i * + z__2.r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__2 = kk + *n - j; + for (k = kk + 1; k <= i__2; ++k) { + ix += *incx; + d_cnjg(&z__3, &ap[k]); + i__3 = ix; + z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, + z__2.i = z__3.r * x[i__3].i + z__3.i * x[ + i__3].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; +/* L190: */ + } + } + i__2 = jx; + x[i__2].r = temp.r, x[i__2].i = temp.i; + jx += *incx; + kk += *n - j + 1; +/* L200: */ + } + } + } + } + + return 0; + +/* End of ZTPMV */ + +} /* ztpmv_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/ztpsv.cpp b/lib/linalg/ztpsv.cpp new file mode 100644 index 0000000000..7e7e64d721 --- /dev/null +++ b/lib/linalg/ztpsv.cpp @@ -0,0 +1,607 @@ +/* fortran/ztpsv.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b ZTPSV */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INCX,N */ +/* CHARACTER DIAG,TRANS,UPLO */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 AP(*),X(*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZTPSV solves one of the systems of equations */ +/* > */ +/* > A*x = b, or A**T*x = b, or A**H*x = b, */ +/* > */ +/* > where b and x are n element vectors and A is an n by n unit, or */ +/* > non-unit, upper or lower triangular matrix, supplied in packed form. */ +/* > */ +/* > No test for singularity or near-singularity is included in this */ +/* > routine. Such tests must be performed before calling this routine. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > On entry, UPLO specifies whether the matrix is an upper or */ +/* > lower triangular matrix as follows: */ +/* > */ +/* > UPLO = 'U' or 'u' A is an upper triangular matrix. */ +/* > */ +/* > UPLO = 'L' or 'l' A is a lower triangular matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TRANS */ +/* > \verbatim */ +/* > TRANS is CHARACTER*1 */ +/* > On entry, TRANS specifies the equations to be solved as */ +/* > follows: */ +/* > */ +/* > TRANS = 'N' or 'n' A*x = b. */ +/* > */ +/* > TRANS = 'T' or 't' A**T*x = b. */ +/* > */ +/* > TRANS = 'C' or 'c' A**H*x = b. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DIAG */ +/* > \verbatim */ +/* > DIAG is CHARACTER*1 */ +/* > On entry, DIAG specifies whether or not A is unit */ +/* > triangular as follows: */ +/* > */ +/* > DIAG = 'U' or 'u' A is assumed to be unit triangular. */ +/* > */ +/* > DIAG = 'N' or 'n' A is not assumed to be unit */ +/* > triangular. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > On entry, N specifies the order of the matrix A. */ +/* > N must be at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] AP */ +/* > \verbatim */ +/* > AP is COMPLEX*16 array, dimension at least */ +/* > ( ( n*( n + 1 ) )/2 ). */ +/* > Before entry with UPLO = 'U' or 'u', the array AP must */ +/* > contain the upper triangular matrix packed sequentially, */ +/* > column by column, so that AP( 1 ) contains a( 1, 1 ), */ +/* > AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) */ +/* > respectively, and so on. */ +/* > Before entry with UPLO = 'L' or 'l', the array AP must */ +/* > contain the lower triangular matrix packed sequentially, */ +/* > column by column, so that AP( 1 ) contains a( 1, 1 ), */ +/* > AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) */ +/* > respectively, and so on. */ +/* > Note that when DIAG = 'U' or 'u', the diagonal elements of */ +/* > A are not referenced, but are assumed to be unity. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] X */ +/* > \verbatim */ +/* > X is COMPLEX*16 array, dimension at least */ +/* > ( 1 + ( n - 1 )*abs( INCX ) ). */ +/* > Before entry, the incremented array X must contain the n */ +/* > element right-hand side vector b. On exit, X is overwritten */ +/* > with the solution vector x. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > On entry, INCX specifies the increment for the elements of */ +/* > X. INCX must not be zero. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16_blas_level2 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > Level 2 Blas routine. */ +/* > */ +/* > -- Written on 22-October-1986. */ +/* > Jack Dongarra, Argonne National Lab. */ +/* > Jeremy Du Croz, Nag Central Office. */ +/* > Sven Hammarling, Nag Central Office. */ +/* > Richard Hanson, Sandia National Labs. */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int ztpsv_(char *uplo, char *trans, char *diag, integer *n, + doublecomplex *ap, doublecomplex *x, integer *incx, ftnlen uplo_len, + ftnlen trans_len, ftnlen diag_len) +{ + /* System generated locals */ + integer i__1, i__2, i__3, i__4, i__5; + doublecomplex z__1, z__2, z__3; + + /* Builtin functions */ + void z_div(doublecomplex *, doublecomplex *, doublecomplex *), d_cnjg( + doublecomplex *, doublecomplex *); + + /* Local variables */ + integer i__, j, k, kk, ix, jx, kx, info; + doublecomplex temp; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + logical noconj, nounit; + + +/* -- Reference BLAS level2 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --x; + --ap; + + /* Function Body */ + info = 0; + if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", ( + ftnlen)1, (ftnlen)1)) { + info = 1; + } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, + (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, ( + ftnlen)1)) { + info = 2; + } else if (! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, + (char *)"N", (ftnlen)1, (ftnlen)1)) { + info = 3; + } else if (*n < 0) { + info = 4; + } else if (*incx == 0) { + info = 7; + } + if (info != 0) { + xerbla_((char *)"ZTPSV ", &info, (ftnlen)6); + return 0; + } + +/* Quick return if possible. */ + + if (*n == 0) { + return 0; + } + + noconj = lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1); + nounit = lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1); + +/* Set up the start point in X if the increment is not unity. This */ +/* will be ( N - 1 )*INCX too small for descending loops. */ + + if (*incx <= 0) { + kx = 1 - (*n - 1) * *incx; + } else if (*incx != 1) { + kx = 1; + } + +/* Start the operations. In this version the elements of AP are */ +/* accessed sequentially with one pass through AP. */ + + if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { + +/* Form x := inv( A )*x. */ + + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + kk = *n * (*n + 1) / 2; + if (*incx == 1) { + for (j = *n; j >= 1; --j) { + i__1 = j; + if (x[i__1].r != 0. || x[i__1].i != 0.) { + if (nounit) { + i__1 = j; + z_div(&z__1, &x[j], &ap[kk]); + x[i__1].r = z__1.r, x[i__1].i = z__1.i; + } + i__1 = j; + temp.r = x[i__1].r, temp.i = x[i__1].i; + k = kk - 1; + for (i__ = j - 1; i__ >= 1; --i__) { + i__1 = i__; + i__2 = i__; + i__3 = k; + z__2.r = temp.r * ap[i__3].r - temp.i * ap[i__3] + .i, z__2.i = temp.r * ap[i__3].i + temp.i + * ap[i__3].r; + z__1.r = x[i__2].r - z__2.r, z__1.i = x[i__2].i - + z__2.i; + x[i__1].r = z__1.r, x[i__1].i = z__1.i; + --k; +/* L10: */ + } + } + kk -= j; +/* L20: */ + } + } else { + jx = kx + (*n - 1) * *incx; + for (j = *n; j >= 1; --j) { + i__1 = jx; + if (x[i__1].r != 0. || x[i__1].i != 0.) { + if (nounit) { + i__1 = jx; + z_div(&z__1, &x[jx], &ap[kk]); + x[i__1].r = z__1.r, x[i__1].i = z__1.i; + } + i__1 = jx; + temp.r = x[i__1].r, temp.i = x[i__1].i; + ix = jx; + i__1 = kk - j + 1; + for (k = kk - 1; k >= i__1; --k) { + ix -= *incx; + i__2 = ix; + i__3 = ix; + i__4 = k; + z__2.r = temp.r * ap[i__4].r - temp.i * ap[i__4] + .i, z__2.i = temp.r * ap[i__4].i + temp.i + * ap[i__4].r; + z__1.r = x[i__3].r - z__2.r, z__1.i = x[i__3].i - + z__2.i; + x[i__2].r = z__1.r, x[i__2].i = z__1.i; +/* L30: */ + } + } + jx -= *incx; + kk -= j; +/* L40: */ + } + } + } else { + kk = 1; + if (*incx == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + if (x[i__2].r != 0. || x[i__2].i != 0.) { + if (nounit) { + i__2 = j; + z_div(&z__1, &x[j], &ap[kk]); + x[i__2].r = z__1.r, x[i__2].i = z__1.i; + } + i__2 = j; + temp.r = x[i__2].r, temp.i = x[i__2].i; + k = kk + 1; + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + i__3 = i__; + i__4 = i__; + i__5 = k; + z__2.r = temp.r * ap[i__5].r - temp.i * ap[i__5] + .i, z__2.i = temp.r * ap[i__5].i + temp.i + * ap[i__5].r; + z__1.r = x[i__4].r - z__2.r, z__1.i = x[i__4].i - + z__2.i; + x[i__3].r = z__1.r, x[i__3].i = z__1.i; + ++k; +/* L50: */ + } + } + kk += *n - j + 1; +/* L60: */ + } + } else { + jx = kx; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = jx; + if (x[i__2].r != 0. || x[i__2].i != 0.) { + if (nounit) { + i__2 = jx; + z_div(&z__1, &x[jx], &ap[kk]); + x[i__2].r = z__1.r, x[i__2].i = z__1.i; + } + i__2 = jx; + temp.r = x[i__2].r, temp.i = x[i__2].i; + ix = jx; + i__2 = kk + *n - j; + for (k = kk + 1; k <= i__2; ++k) { + ix += *incx; + i__3 = ix; + i__4 = ix; + i__5 = k; + z__2.r = temp.r * ap[i__5].r - temp.i * ap[i__5] + .i, z__2.i = temp.r * ap[i__5].i + temp.i + * ap[i__5].r; + z__1.r = x[i__4].r - z__2.r, z__1.i = x[i__4].i - + z__2.i; + x[i__3].r = z__1.r, x[i__3].i = z__1.i; +/* L70: */ + } + } + jx += *incx; + kk += *n - j + 1; +/* L80: */ + } + } + } + } else { + +/* Form x := inv( A**T )*x or x := inv( A**H )*x. */ + + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + kk = 1; + if (*incx == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + temp.r = x[i__2].r, temp.i = x[i__2].i; + k = kk; + if (noconj) { + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = k; + i__4 = i__; + z__2.r = ap[i__3].r * x[i__4].r - ap[i__3].i * x[ + i__4].i, z__2.i = ap[i__3].r * x[i__4].i + + ap[i__3].i * x[i__4].r; + z__1.r = temp.r - z__2.r, z__1.i = temp.i - + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + ++k; +/* L90: */ + } + if (nounit) { + z_div(&z__1, &temp, &ap[kk + j - 1]); + temp.r = z__1.r, temp.i = z__1.i; + } + } else { + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + d_cnjg(&z__3, &ap[k]); + i__3 = i__; + z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, + z__2.i = z__3.r * x[i__3].i + z__3.i * x[ + i__3].r; + z__1.r = temp.r - z__2.r, z__1.i = temp.i - + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + ++k; +/* L100: */ + } + if (nounit) { + d_cnjg(&z__2, &ap[kk + j - 1]); + z_div(&z__1, &temp, &z__2); + temp.r = z__1.r, temp.i = z__1.i; + } + } + i__2 = j; + x[i__2].r = temp.r, x[i__2].i = temp.i; + kk += j; +/* L110: */ + } + } else { + jx = kx; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = jx; + temp.r = x[i__2].r, temp.i = x[i__2].i; + ix = kx; + if (noconj) { + i__2 = kk + j - 2; + for (k = kk; k <= i__2; ++k) { + i__3 = k; + i__4 = ix; + z__2.r = ap[i__3].r * x[i__4].r - ap[i__3].i * x[ + i__4].i, z__2.i = ap[i__3].r * x[i__4].i + + ap[i__3].i * x[i__4].r; + z__1.r = temp.r - z__2.r, z__1.i = temp.i - + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + ix += *incx; +/* L120: */ + } + if (nounit) { + z_div(&z__1, &temp, &ap[kk + j - 1]); + temp.r = z__1.r, temp.i = z__1.i; + } + } else { + i__2 = kk + j - 2; + for (k = kk; k <= i__2; ++k) { + d_cnjg(&z__3, &ap[k]); + i__3 = ix; + z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, + z__2.i = z__3.r * x[i__3].i + z__3.i * x[ + i__3].r; + z__1.r = temp.r - z__2.r, z__1.i = temp.i - + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + ix += *incx; +/* L130: */ + } + if (nounit) { + d_cnjg(&z__2, &ap[kk + j - 1]); + z_div(&z__1, &temp, &z__2); + temp.r = z__1.r, temp.i = z__1.i; + } + } + i__2 = jx; + x[i__2].r = temp.r, x[i__2].i = temp.i; + jx += *incx; + kk += j; +/* L140: */ + } + } + } else { + kk = *n * (*n + 1) / 2; + if (*incx == 1) { + for (j = *n; j >= 1; --j) { + i__1 = j; + temp.r = x[i__1].r, temp.i = x[i__1].i; + k = kk; + if (noconj) { + i__1 = j + 1; + for (i__ = *n; i__ >= i__1; --i__) { + i__2 = k; + i__3 = i__; + z__2.r = ap[i__2].r * x[i__3].r - ap[i__2].i * x[ + i__3].i, z__2.i = ap[i__2].r * x[i__3].i + + ap[i__2].i * x[i__3].r; + z__1.r = temp.r - z__2.r, z__1.i = temp.i - + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + --k; +/* L150: */ + } + if (nounit) { + z_div(&z__1, &temp, &ap[kk - *n + j]); + temp.r = z__1.r, temp.i = z__1.i; + } + } else { + i__1 = j + 1; + for (i__ = *n; i__ >= i__1; --i__) { + d_cnjg(&z__3, &ap[k]); + i__2 = i__; + z__2.r = z__3.r * x[i__2].r - z__3.i * x[i__2].i, + z__2.i = z__3.r * x[i__2].i + z__3.i * x[ + i__2].r; + z__1.r = temp.r - z__2.r, z__1.i = temp.i - + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + --k; +/* L160: */ + } + if (nounit) { + d_cnjg(&z__2, &ap[kk - *n + j]); + z_div(&z__1, &temp, &z__2); + temp.r = z__1.r, temp.i = z__1.i; + } + } + i__1 = j; + x[i__1].r = temp.r, x[i__1].i = temp.i; + kk -= *n - j + 1; +/* L170: */ + } + } else { + kx += (*n - 1) * *incx; + jx = kx; + for (j = *n; j >= 1; --j) { + i__1 = jx; + temp.r = x[i__1].r, temp.i = x[i__1].i; + ix = kx; + if (noconj) { + i__1 = kk - (*n - (j + 1)); + for (k = kk; k >= i__1; --k) { + i__2 = k; + i__3 = ix; + z__2.r = ap[i__2].r * x[i__3].r - ap[i__2].i * x[ + i__3].i, z__2.i = ap[i__2].r * x[i__3].i + + ap[i__2].i * x[i__3].r; + z__1.r = temp.r - z__2.r, z__1.i = temp.i - + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + ix -= *incx; +/* L180: */ + } + if (nounit) { + z_div(&z__1, &temp, &ap[kk - *n + j]); + temp.r = z__1.r, temp.i = z__1.i; + } + } else { + i__1 = kk - (*n - (j + 1)); + for (k = kk; k >= i__1; --k) { + d_cnjg(&z__3, &ap[k]); + i__2 = ix; + z__2.r = z__3.r * x[i__2].r - z__3.i * x[i__2].i, + z__2.i = z__3.r * x[i__2].i + z__3.i * x[ + i__2].r; + z__1.r = temp.r - z__2.r, z__1.i = temp.i - + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + ix -= *incx; +/* L190: */ + } + if (nounit) { + d_cnjg(&z__2, &ap[kk - *n + j]); + z_div(&z__1, &temp, &z__2); + temp.r = z__1.r, temp.i = z__1.i; + } + } + i__1 = jx; + x[i__1].r = temp.r, x[i__1].i = temp.i; + jx -= *incx; + kk -= *n - j + 1; +/* L200: */ + } + } + } + } + + return 0; + +/* End of ZTPSV */ + +} /* ztpsv_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/ztptri.cpp b/lib/linalg/ztptri.cpp new file mode 100644 index 0000000000..c781cb964f --- /dev/null +++ b/lib/linalg/ztptri.cpp @@ -0,0 +1,308 @@ +/* fortran/ztptri.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static doublecomplex c_b1 = {1.,0.}; +static integer c__1 = 1; + +/* > \brief \b ZTPTRI */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZTPTRI + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZTPTRI( UPLO, DIAG, N, AP, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER DIAG, UPLO */ +/* INTEGER INFO, N */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 AP( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZTPTRI computes the inverse of a complex upper or lower triangular */ +/* > matrix A stored in packed format. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > = 'U': A is upper triangular; */ +/* > = 'L': A is lower triangular. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DIAG */ +/* > \verbatim */ +/* > DIAG is CHARACTER*1 */ +/* > = 'N': A is non-unit triangular; */ +/* > = 'U': A is unit triangular. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrix A. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] AP */ +/* > \verbatim */ +/* > AP is COMPLEX*16 array, dimension (N*(N+1)/2) */ +/* > On entry, the upper or lower triangular matrix A, stored */ +/* > columnwise in a linear array. The j-th column of A is stored */ +/* > in the array AP as follows: */ +/* > if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */ +/* > if UPLO = 'L', AP(i + (j-1)*((2*n-j)/2) = A(i,j) for j<=i<=n. */ +/* > See below for further details. */ +/* > On exit, the (triangular) inverse of the original matrix, in */ +/* > the same packed storage format. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > > 0: if INFO = i, A(i,i) is exactly zero. The triangular */ +/* > matrix is singular and its inverse can not be computed. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16OTHERcomputational */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > A triangular matrix A can be transferred to packed storage using one */ +/* > of the following program segments: */ +/* > */ +/* > UPLO = 'U': UPLO = 'L': */ +/* > */ +/* > JC = 1 JC = 1 */ +/* > DO 2 J = 1, N DO 2 J = 1, N */ +/* > DO 1 I = 1, J DO 1 I = J, N */ +/* > AP(JC+I-1) = A(I,J) AP(JC+I-J) = A(I,J) */ +/* > 1 CONTINUE 1 CONTINUE */ +/* > JC = JC + J JC = JC + N - J + 1 */ +/* > 2 CONTINUE 2 CONTINUE */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int ztptri_(char *uplo, char *diag, integer *n, + doublecomplex *ap, integer *info, ftnlen uplo_len, ftnlen diag_len) +{ + /* System generated locals */ + integer i__1, i__2; + doublecomplex z__1; + + /* Builtin functions */ + void z_div(doublecomplex *, doublecomplex *, doublecomplex *); + + /* Local variables */ + integer j, jc, jj; + doublecomplex ajj; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int zscal_(integer *, doublecomplex *, + doublecomplex *, integer *); + logical upper; + extern /* Subroutine */ int ztpmv_(char *, char *, char *, integer *, + doublecomplex *, doublecomplex *, integer *, ftnlen, ftnlen, + ftnlen), xerbla_(char *, integer *, ftnlen); + integer jclast; + logical nounit; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + --ap; + + /* Function Body */ + *info = 0; + upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); + nounit = lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1); + if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + *info = -1; + } else if (! nounit && ! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1)) { + *info = -2; + } else if (*n < 0) { + *info = -3; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"ZTPTRI", &i__1, (ftnlen)6); + return 0; + } + +/* Check for singularity if non-unit. */ + + if (nounit) { + if (upper) { + jj = 0; + i__1 = *n; + for (*info = 1; *info <= i__1; ++(*info)) { + jj += *info; + i__2 = jj; + if (ap[i__2].r == 0. && ap[i__2].i == 0.) { + return 0; + } +/* L10: */ + } + } else { + jj = 1; + i__1 = *n; + for (*info = 1; *info <= i__1; ++(*info)) { + i__2 = jj; + if (ap[i__2].r == 0. && ap[i__2].i == 0.) { + return 0; + } + jj = jj + *n - *info + 1; +/* L20: */ + } + } + *info = 0; + } + + if (upper) { + +/* Compute inverse of upper triangular matrix. */ + + jc = 1; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (nounit) { + i__2 = jc + j - 1; + z_div(&z__1, &c_b1, &ap[jc + j - 1]); + ap[i__2].r = z__1.r, ap[i__2].i = z__1.i; + i__2 = jc + j - 1; + z__1.r = -ap[i__2].r, z__1.i = -ap[i__2].i; + ajj.r = z__1.r, ajj.i = z__1.i; + } else { + z__1.r = -1., z__1.i = -0.; + ajj.r = z__1.r, ajj.i = z__1.i; + } + +/* Compute elements 1:j-1 of j-th column. */ + + i__2 = j - 1; + ztpmv_((char *)"Upper", (char *)"No transpose", diag, &i__2, &ap[1], &ap[jc], & + c__1, (ftnlen)5, (ftnlen)12, (ftnlen)1); + i__2 = j - 1; + zscal_(&i__2, &ajj, &ap[jc], &c__1); + jc += j; +/* L30: */ + } + + } else { + +/* Compute inverse of lower triangular matrix. */ + + jc = *n * (*n + 1) / 2; + for (j = *n; j >= 1; --j) { + if (nounit) { + i__1 = jc; + z_div(&z__1, &c_b1, &ap[jc]); + ap[i__1].r = z__1.r, ap[i__1].i = z__1.i; + i__1 = jc; + z__1.r = -ap[i__1].r, z__1.i = -ap[i__1].i; + ajj.r = z__1.r, ajj.i = z__1.i; + } else { + z__1.r = -1., z__1.i = -0.; + ajj.r = z__1.r, ajj.i = z__1.i; + } + if (j < *n) { + +/* Compute elements j+1:n of j-th column. */ + + i__1 = *n - j; + ztpmv_((char *)"Lower", (char *)"No transpose", diag, &i__1, &ap[jclast], &ap[ + jc + 1], &c__1, (ftnlen)5, (ftnlen)12, (ftnlen)1); + i__1 = *n - j; + zscal_(&i__1, &ajj, &ap[jc + 1], &c__1); + } + jclast = jc; + jc = jc - *n + j - 2; +/* L40: */ + } + } + + return 0; + +/* End of ZTPTRI */ + +} /* ztptri_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/ztrmm.cpp b/lib/linalg/ztrmm.cpp new file mode 100644 index 0000000000..cd71371d5b --- /dev/null +++ b/lib/linalg/ztrmm.cpp @@ -0,0 +1,762 @@ +/* fortran/ztrmm.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b ZTRMM */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) */ + +/* .. Scalar Arguments .. */ +/* COMPLEX*16 ALPHA */ +/* INTEGER LDA,LDB,M,N */ +/* CHARACTER DIAG,SIDE,TRANSA,UPLO */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 A(LDA,*),B(LDB,*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZTRMM performs one of the matrix-matrix operations */ +/* > */ +/* > B := alpha*op( A )*B, or B := alpha*B*op( A ) */ +/* > */ +/* > where alpha is a scalar, B is an m by n matrix, A is a unit, or */ +/* > non-unit, upper or lower triangular matrix and op( A ) is one of */ +/* > */ +/* > op( A ) = A or op( A ) = A**T or op( A ) = A**H. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] SIDE */ +/* > \verbatim */ +/* > SIDE is CHARACTER*1 */ +/* > On entry, SIDE specifies whether op( A ) multiplies B from */ +/* > the left or right as follows: */ +/* > */ +/* > SIDE = 'L' or 'l' B := alpha*op( A )*B. */ +/* > */ +/* > SIDE = 'R' or 'r' B := alpha*B*op( A ). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > On entry, UPLO specifies whether the matrix A is an upper or */ +/* > lower triangular matrix as follows: */ +/* > */ +/* > UPLO = 'U' or 'u' A is an upper triangular matrix. */ +/* > */ +/* > UPLO = 'L' or 'l' A is a lower triangular matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TRANSA */ +/* > \verbatim */ +/* > TRANSA is CHARACTER*1 */ +/* > On entry, TRANSA specifies the form of op( A ) to be used in */ +/* > the matrix multiplication as follows: */ +/* > */ +/* > TRANSA = 'N' or 'n' op( A ) = A. */ +/* > */ +/* > TRANSA = 'T' or 't' op( A ) = A**T. */ +/* > */ +/* > TRANSA = 'C' or 'c' op( A ) = A**H. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DIAG */ +/* > \verbatim */ +/* > DIAG is CHARACTER*1 */ +/* > On entry, DIAG specifies whether or not A is unit triangular */ +/* > as follows: */ +/* > */ +/* > DIAG = 'U' or 'u' A is assumed to be unit triangular. */ +/* > */ +/* > DIAG = 'N' or 'n' A is not assumed to be unit */ +/* > triangular. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > On entry, M specifies the number of rows of B. M must be at */ +/* > least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > On entry, N specifies the number of columns of B. N must be */ +/* > at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] ALPHA */ +/* > \verbatim */ +/* > ALPHA is COMPLEX*16 */ +/* > On entry, ALPHA specifies the scalar alpha. When alpha is */ +/* > zero then A is not referenced and B need not be set before */ +/* > entry. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is COMPLEX*16 array, dimension ( LDA, k ), where k is m */ +/* > when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. */ +/* > Before entry with UPLO = 'U' or 'u', the leading k by k */ +/* > upper triangular part of the array A must contain the upper */ +/* > triangular matrix and the strictly lower triangular part of */ +/* > A is not referenced. */ +/* > Before entry with UPLO = 'L' or 'l', the leading k by k */ +/* > lower triangular part of the array A must contain the lower */ +/* > triangular matrix and the strictly upper triangular part of */ +/* > A is not referenced. */ +/* > Note that when DIAG = 'U' or 'u', the diagonal elements of */ +/* > A are not referenced either, but are assumed to be unity. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > On entry, LDA specifies the first dimension of A as declared */ +/* > in the calling (sub) program. When SIDE = 'L' or 'l' then */ +/* > LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' */ +/* > then LDA must be at least max( 1, n ). */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] B */ +/* > \verbatim */ +/* > B is COMPLEX*16 array, dimension ( LDB, N ). */ +/* > Before entry, the leading m by n part of the array B must */ +/* > contain the matrix B, and on exit is overwritten by the */ +/* > transformed matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDB */ +/* > \verbatim */ +/* > LDB is INTEGER */ +/* > On entry, LDB specifies the first dimension of B as declared */ +/* > in the calling (sub) program. LDB must be at least */ +/* > max( 1, m ). */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16_blas_level3 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > Level 3 Blas routine. */ +/* > */ +/* > -- Written on 8-February-1989. */ +/* > Jack Dongarra, Argonne National Laboratory. */ +/* > Iain Duff, AERE Harwell. */ +/* > Jeremy Du Croz, Numerical Algorithms Group Ltd. */ +/* > Sven Hammarling, Numerical Algorithms Group Ltd. */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int ztrmm_(char *side, char *uplo, char *transa, char *diag, + integer *m, integer *n, doublecomplex *alpha, doublecomplex *a, + integer *lda, doublecomplex *b, integer *ldb, ftnlen side_len, ftnlen + uplo_len, ftnlen transa_len, ftnlen diag_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4, i__5, + i__6; + doublecomplex z__1, z__2, z__3; + + /* Builtin functions */ + void d_cnjg(doublecomplex *, doublecomplex *); + + /* Local variables */ + integer i__, j, k, info; + doublecomplex temp; + logical lside; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + integer nrowa; + logical upper; + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + logical noconj, nounit; + + +/* -- Reference BLAS level3 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. Parameters .. */ +/* .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + b_dim1 = *ldb; + b_offset = 1 + b_dim1; + b -= b_offset; + + /* Function Body */ + lside = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); + if (lside) { + nrowa = *m; + } else { + nrowa = *n; + } + noconj = lsame_(transa, (char *)"T", (ftnlen)1, (ftnlen)1); + nounit = lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1); + upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); + + info = 0; + if (! lside && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + info = 1; + } else if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + info = 2; + } else if (! lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(transa, + (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(transa, (char *)"C", (ftnlen)1, ( + ftnlen)1)) { + info = 3; + } else if (! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, + (char *)"N", (ftnlen)1, (ftnlen)1)) { + info = 4; + } else if (*m < 0) { + info = 5; + } else if (*n < 0) { + info = 6; + } else if (*lda < max(1,nrowa)) { + info = 9; + } else if (*ldb < max(1,*m)) { + info = 11; + } + if (info != 0) { + xerbla_((char *)"ZTRMM ", &info, (ftnlen)6); + return 0; + } + +/* Quick return if possible. */ + + if (*m == 0 || *n == 0) { + return 0; + } + +/* And when alpha.eq.zero. */ + + if (alpha->r == 0. && alpha->i == 0.) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * b_dim1; + b[i__3].r = 0., b[i__3].i = 0.; +/* L10: */ + } +/* L20: */ + } + return 0; + } + +/* Start the operations. */ + + if (lside) { + if (lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1)) { + +/* Form B := alpha*A*B. */ + + if (upper) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (k = 1; k <= i__2; ++k) { + i__3 = k + j * b_dim1; + if (b[i__3].r != 0. || b[i__3].i != 0.) { + i__3 = k + j * b_dim1; + z__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3] + .i, z__1.i = alpha->r * b[i__3].i + + alpha->i * b[i__3].r; + temp.r = z__1.r, temp.i = z__1.i; + i__3 = k - 1; + for (i__ = 1; i__ <= i__3; ++i__) { + i__4 = i__ + j * b_dim1; + i__5 = i__ + j * b_dim1; + i__6 = i__ + k * a_dim1; + z__2.r = temp.r * a[i__6].r - temp.i * a[i__6] + .i, z__2.i = temp.r * a[i__6].i + + temp.i * a[i__6].r; + z__1.r = b[i__5].r + z__2.r, z__1.i = b[i__5] + .i + z__2.i; + b[i__4].r = z__1.r, b[i__4].i = z__1.i; +/* L30: */ + } + if (nounit) { + i__3 = k + k * a_dim1; + z__1.r = temp.r * a[i__3].r - temp.i * a[i__3] + .i, z__1.i = temp.r * a[i__3].i + + temp.i * a[i__3].r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__3 = k + j * b_dim1; + b[i__3].r = temp.r, b[i__3].i = temp.i; + } +/* L40: */ + } +/* L50: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + for (k = *m; k >= 1; --k) { + i__2 = k + j * b_dim1; + if (b[i__2].r != 0. || b[i__2].i != 0.) { + i__2 = k + j * b_dim1; + z__1.r = alpha->r * b[i__2].r - alpha->i * b[i__2] + .i, z__1.i = alpha->r * b[i__2].i + + alpha->i * b[i__2].r; + temp.r = z__1.r, temp.i = z__1.i; + i__2 = k + j * b_dim1; + b[i__2].r = temp.r, b[i__2].i = temp.i; + if (nounit) { + i__2 = k + j * b_dim1; + i__3 = k + j * b_dim1; + i__4 = k + k * a_dim1; + z__1.r = b[i__3].r * a[i__4].r - b[i__3].i * + a[i__4].i, z__1.i = b[i__3].r * a[ + i__4].i + b[i__3].i * a[i__4].r; + b[i__2].r = z__1.r, b[i__2].i = z__1.i; + } + i__2 = *m; + for (i__ = k + 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * b_dim1; + i__4 = i__ + j * b_dim1; + i__5 = i__ + k * a_dim1; + z__2.r = temp.r * a[i__5].r - temp.i * a[i__5] + .i, z__2.i = temp.r * a[i__5].i + + temp.i * a[i__5].r; + z__1.r = b[i__4].r + z__2.r, z__1.i = b[i__4] + .i + z__2.i; + b[i__3].r = z__1.r, b[i__3].i = z__1.i; +/* L60: */ + } + } +/* L70: */ + } +/* L80: */ + } + } + } else { + +/* Form B := alpha*A**T*B or B := alpha*A**H*B. */ + + if (upper) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + for (i__ = *m; i__ >= 1; --i__) { + i__2 = i__ + j * b_dim1; + temp.r = b[i__2].r, temp.i = b[i__2].i; + if (noconj) { + if (nounit) { + i__2 = i__ + i__ * a_dim1; + z__1.r = temp.r * a[i__2].r - temp.i * a[i__2] + .i, z__1.i = temp.r * a[i__2].i + + temp.i * a[i__2].r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__2 = i__ - 1; + for (k = 1; k <= i__2; ++k) { + i__3 = k + i__ * a_dim1; + i__4 = k + j * b_dim1; + z__2.r = a[i__3].r * b[i__4].r - a[i__3].i * + b[i__4].i, z__2.i = a[i__3].r * b[ + i__4].i + a[i__3].i * b[i__4].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; +/* L90: */ + } + } else { + if (nounit) { + d_cnjg(&z__2, &a[i__ + i__ * a_dim1]); + z__1.r = temp.r * z__2.r - temp.i * z__2.i, + z__1.i = temp.r * z__2.i + temp.i * + z__2.r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__2 = i__ - 1; + for (k = 1; k <= i__2; ++k) { + d_cnjg(&z__3, &a[k + i__ * a_dim1]); + i__3 = k + j * b_dim1; + z__2.r = z__3.r * b[i__3].r - z__3.i * b[i__3] + .i, z__2.i = z__3.r * b[i__3].i + + z__3.i * b[i__3].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; +/* L100: */ + } + } + i__2 = i__ + j * b_dim1; + z__1.r = alpha->r * temp.r - alpha->i * temp.i, + z__1.i = alpha->r * temp.i + alpha->i * + temp.r; + b[i__2].r = z__1.r, b[i__2].i = z__1.i; +/* L110: */ + } +/* L120: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * b_dim1; + temp.r = b[i__3].r, temp.i = b[i__3].i; + if (noconj) { + if (nounit) { + i__3 = i__ + i__ * a_dim1; + z__1.r = temp.r * a[i__3].r - temp.i * a[i__3] + .i, z__1.i = temp.r * a[i__3].i + + temp.i * a[i__3].r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__3 = *m; + for (k = i__ + 1; k <= i__3; ++k) { + i__4 = k + i__ * a_dim1; + i__5 = k + j * b_dim1; + z__2.r = a[i__4].r * b[i__5].r - a[i__4].i * + b[i__5].i, z__2.i = a[i__4].r * b[ + i__5].i + a[i__4].i * b[i__5].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; +/* L130: */ + } + } else { + if (nounit) { + d_cnjg(&z__2, &a[i__ + i__ * a_dim1]); + z__1.r = temp.r * z__2.r - temp.i * z__2.i, + z__1.i = temp.r * z__2.i + temp.i * + z__2.r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__3 = *m; + for (k = i__ + 1; k <= i__3; ++k) { + d_cnjg(&z__3, &a[k + i__ * a_dim1]); + i__4 = k + j * b_dim1; + z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4] + .i, z__2.i = z__3.r * b[i__4].i + + z__3.i * b[i__4].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; +/* L140: */ + } + } + i__3 = i__ + j * b_dim1; + z__1.r = alpha->r * temp.r - alpha->i * temp.i, + z__1.i = alpha->r * temp.i + alpha->i * + temp.r; + b[i__3].r = z__1.r, b[i__3].i = z__1.i; +/* L150: */ + } +/* L160: */ + } + } + } + } else { + if (lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1)) { + +/* Form B := alpha*B*A. */ + + if (upper) { + for (j = *n; j >= 1; --j) { + temp.r = alpha->r, temp.i = alpha->i; + if (nounit) { + i__1 = j + j * a_dim1; + z__1.r = temp.r * a[i__1].r - temp.i * a[i__1].i, + z__1.i = temp.r * a[i__1].i + temp.i * a[i__1] + .r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__ + j * b_dim1; + i__3 = i__ + j * b_dim1; + z__1.r = temp.r * b[i__3].r - temp.i * b[i__3].i, + z__1.i = temp.r * b[i__3].i + temp.i * b[i__3] + .r; + b[i__2].r = z__1.r, b[i__2].i = z__1.i; +/* L170: */ + } + i__1 = j - 1; + for (k = 1; k <= i__1; ++k) { + i__2 = k + j * a_dim1; + if (a[i__2].r != 0. || a[i__2].i != 0.) { + i__2 = k + j * a_dim1; + z__1.r = alpha->r * a[i__2].r - alpha->i * a[i__2] + .i, z__1.i = alpha->r * a[i__2].i + + alpha->i * a[i__2].r; + temp.r = z__1.r, temp.i = z__1.i; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * b_dim1; + i__4 = i__ + j * b_dim1; + i__5 = i__ + k * b_dim1; + z__2.r = temp.r * b[i__5].r - temp.i * b[i__5] + .i, z__2.i = temp.r * b[i__5].i + + temp.i * b[i__5].r; + z__1.r = b[i__4].r + z__2.r, z__1.i = b[i__4] + .i + z__2.i; + b[i__3].r = z__1.r, b[i__3].i = z__1.i; +/* L180: */ + } + } +/* L190: */ + } +/* L200: */ + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp.r = alpha->r, temp.i = alpha->i; + if (nounit) { + i__2 = j + j * a_dim1; + z__1.r = temp.r * a[i__2].r - temp.i * a[i__2].i, + z__1.i = temp.r * a[i__2].i + temp.i * a[i__2] + .r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * b_dim1; + i__4 = i__ + j * b_dim1; + z__1.r = temp.r * b[i__4].r - temp.i * b[i__4].i, + z__1.i = temp.r * b[i__4].i + temp.i * b[i__4] + .r; + b[i__3].r = z__1.r, b[i__3].i = z__1.i; +/* L210: */ + } + i__2 = *n; + for (k = j + 1; k <= i__2; ++k) { + i__3 = k + j * a_dim1; + if (a[i__3].r != 0. || a[i__3].i != 0.) { + i__3 = k + j * a_dim1; + z__1.r = alpha->r * a[i__3].r - alpha->i * a[i__3] + .i, z__1.i = alpha->r * a[i__3].i + + alpha->i * a[i__3].r; + temp.r = z__1.r, temp.i = z__1.i; + i__3 = *m; + for (i__ = 1; i__ <= i__3; ++i__) { + i__4 = i__ + j * b_dim1; + i__5 = i__ + j * b_dim1; + i__6 = i__ + k * b_dim1; + z__2.r = temp.r * b[i__6].r - temp.i * b[i__6] + .i, z__2.i = temp.r * b[i__6].i + + temp.i * b[i__6].r; + z__1.r = b[i__5].r + z__2.r, z__1.i = b[i__5] + .i + z__2.i; + b[i__4].r = z__1.r, b[i__4].i = z__1.i; +/* L220: */ + } + } +/* L230: */ + } +/* L240: */ + } + } + } else { + +/* Form B := alpha*B*A**T or B := alpha*B*A**H. */ + + if (upper) { + i__1 = *n; + for (k = 1; k <= i__1; ++k) { + i__2 = k - 1; + for (j = 1; j <= i__2; ++j) { + i__3 = j + k * a_dim1; + if (a[i__3].r != 0. || a[i__3].i != 0.) { + if (noconj) { + i__3 = j + k * a_dim1; + z__1.r = alpha->r * a[i__3].r - alpha->i * a[ + i__3].i, z__1.i = alpha->r * a[i__3] + .i + alpha->i * a[i__3].r; + temp.r = z__1.r, temp.i = z__1.i; + } else { + d_cnjg(&z__2, &a[j + k * a_dim1]); + z__1.r = alpha->r * z__2.r - alpha->i * + z__2.i, z__1.i = alpha->r * z__2.i + + alpha->i * z__2.r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__3 = *m; + for (i__ = 1; i__ <= i__3; ++i__) { + i__4 = i__ + j * b_dim1; + i__5 = i__ + j * b_dim1; + i__6 = i__ + k * b_dim1; + z__2.r = temp.r * b[i__6].r - temp.i * b[i__6] + .i, z__2.i = temp.r * b[i__6].i + + temp.i * b[i__6].r; + z__1.r = b[i__5].r + z__2.r, z__1.i = b[i__5] + .i + z__2.i; + b[i__4].r = z__1.r, b[i__4].i = z__1.i; +/* L250: */ + } + } +/* L260: */ + } + temp.r = alpha->r, temp.i = alpha->i; + if (nounit) { + if (noconj) { + i__2 = k + k * a_dim1; + z__1.r = temp.r * a[i__2].r - temp.i * a[i__2].i, + z__1.i = temp.r * a[i__2].i + temp.i * a[ + i__2].r; + temp.r = z__1.r, temp.i = z__1.i; + } else { + d_cnjg(&z__2, &a[k + k * a_dim1]); + z__1.r = temp.r * z__2.r - temp.i * z__2.i, + z__1.i = temp.r * z__2.i + temp.i * + z__2.r; + temp.r = z__1.r, temp.i = z__1.i; + } + } + if (temp.r != 1. || temp.i != 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + k * b_dim1; + i__4 = i__ + k * b_dim1; + z__1.r = temp.r * b[i__4].r - temp.i * b[i__4].i, + z__1.i = temp.r * b[i__4].i + temp.i * b[ + i__4].r; + b[i__3].r = z__1.r, b[i__3].i = z__1.i; +/* L270: */ + } + } +/* L280: */ + } + } else { + for (k = *n; k >= 1; --k) { + i__1 = *n; + for (j = k + 1; j <= i__1; ++j) { + i__2 = j + k * a_dim1; + if (a[i__2].r != 0. || a[i__2].i != 0.) { + if (noconj) { + i__2 = j + k * a_dim1; + z__1.r = alpha->r * a[i__2].r - alpha->i * a[ + i__2].i, z__1.i = alpha->r * a[i__2] + .i + alpha->i * a[i__2].r; + temp.r = z__1.r, temp.i = z__1.i; + } else { + d_cnjg(&z__2, &a[j + k * a_dim1]); + z__1.r = alpha->r * z__2.r - alpha->i * + z__2.i, z__1.i = alpha->r * z__2.i + + alpha->i * z__2.r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * b_dim1; + i__4 = i__ + j * b_dim1; + i__5 = i__ + k * b_dim1; + z__2.r = temp.r * b[i__5].r - temp.i * b[i__5] + .i, z__2.i = temp.r * b[i__5].i + + temp.i * b[i__5].r; + z__1.r = b[i__4].r + z__2.r, z__1.i = b[i__4] + .i + z__2.i; + b[i__3].r = z__1.r, b[i__3].i = z__1.i; +/* L290: */ + } + } +/* L300: */ + } + temp.r = alpha->r, temp.i = alpha->i; + if (nounit) { + if (noconj) { + i__1 = k + k * a_dim1; + z__1.r = temp.r * a[i__1].r - temp.i * a[i__1].i, + z__1.i = temp.r * a[i__1].i + temp.i * a[ + i__1].r; + temp.r = z__1.r, temp.i = z__1.i; + } else { + d_cnjg(&z__2, &a[k + k * a_dim1]); + z__1.r = temp.r * z__2.r - temp.i * z__2.i, + z__1.i = temp.r * z__2.i + temp.i * + z__2.r; + temp.r = z__1.r, temp.i = z__1.i; + } + } + if (temp.r != 1. || temp.i != 0.) { + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__ + k * b_dim1; + i__3 = i__ + k * b_dim1; + z__1.r = temp.r * b[i__3].r - temp.i * b[i__3].i, + z__1.i = temp.r * b[i__3].i + temp.i * b[ + i__3].r; + b[i__2].r = z__1.r, b[i__2].i = z__1.i; +/* L310: */ + } + } +/* L320: */ + } + } + } + } + + return 0; + +/* End of ZTRMM */ + +} /* ztrmm_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/ztrmv.cpp b/lib/linalg/ztrmv.cpp new file mode 100644 index 0000000000..ffc55b16fe --- /dev/null +++ b/lib/linalg/ztrmv.cpp @@ -0,0 +1,624 @@ +/* fortran/ztrmv.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b ZTRMV */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INCX,LDA,N */ +/* CHARACTER DIAG,TRANS,UPLO */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 A(LDA,*),X(*) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZTRMV performs one of the matrix-vector operations */ +/* > */ +/* > x := A*x, or x := A**T*x, or x := A**H*x, */ +/* > */ +/* > where x is an n element vector and A is an n by n unit, or non-unit, */ +/* > upper or lower triangular matrix. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > On entry, UPLO specifies whether the matrix is an upper or */ +/* > lower triangular matrix as follows: */ +/* > */ +/* > UPLO = 'U' or 'u' A is an upper triangular matrix. */ +/* > */ +/* > UPLO = 'L' or 'l' A is a lower triangular matrix. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TRANS */ +/* > \verbatim */ +/* > TRANS is CHARACTER*1 */ +/* > On entry, TRANS specifies the operation to be performed as */ +/* > follows: */ +/* > */ +/* > TRANS = 'N' or 'n' x := A*x. */ +/* > */ +/* > TRANS = 'T' or 't' x := A**T*x. */ +/* > */ +/* > TRANS = 'C' or 'c' x := A**H*x. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] DIAG */ +/* > \verbatim */ +/* > DIAG is CHARACTER*1 */ +/* > On entry, DIAG specifies whether or not A is unit */ +/* > triangular as follows: */ +/* > */ +/* > DIAG = 'U' or 'u' A is assumed to be unit triangular. */ +/* > */ +/* > DIAG = 'N' or 'n' A is not assumed to be unit */ +/* > triangular. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > On entry, N specifies the order of the matrix A. */ +/* > N must be at least zero. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is COMPLEX*16 array, dimension ( LDA, N ). */ +/* > Before entry with UPLO = 'U' or 'u', the leading n by n */ +/* > upper triangular part of the array A must contain the upper */ +/* > triangular matrix and the strictly lower triangular part of */ +/* > A is not referenced. */ +/* > Before entry with UPLO = 'L' or 'l', the leading n by n */ +/* > lower triangular part of the array A must contain the lower */ +/* > triangular matrix and the strictly upper triangular part of */ +/* > A is not referenced. */ +/* > Note that when DIAG = 'U' or 'u', the diagonal elements of */ +/* > A are not referenced either, but are assumed to be unity. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > On entry, LDA specifies the first dimension of A as declared */ +/* > in the calling (sub) program. LDA must be at least */ +/* > max( 1, n ). */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] X */ +/* > \verbatim */ +/* > X is COMPLEX*16 array, dimension at least */ +/* > ( 1 + ( n - 1 )*abs( INCX ) ). */ +/* > Before entry, the incremented array X must contain the n */ +/* > element vector x. On exit, X is overwritten with the */ +/* > transformed vector x. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] INCX */ +/* > \verbatim */ +/* > INCX is INTEGER */ +/* > On entry, INCX specifies the increment for the elements of */ +/* > X. INCX must not be zero. */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16_blas_level2 */ + +/* > \par Further Details: */ +/* ===================== */ +/* > */ +/* > \verbatim */ +/* > */ +/* > Level 2 Blas routine. */ +/* > The vector and matrix arguments are not referenced when N = 0, or M = 0 */ +/* > */ +/* > -- Written on 22-October-1986. */ +/* > Jack Dongarra, Argonne National Lab. */ +/* > Jeremy Du Croz, Nag Central Office. */ +/* > Sven Hammarling, Nag Central Office. */ +/* > Richard Hanson, Sandia National Labs. */ +/* > \endverbatim */ +/* > */ +/* ===================================================================== */ +/* Subroutine */ int ztrmv_(char *uplo, char *trans, char *diag, integer *n, + doublecomplex *a, integer *lda, doublecomplex *x, integer *incx, + ftnlen uplo_len, ftnlen trans_len, ftnlen diag_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; + doublecomplex z__1, z__2, z__3; + + /* Builtin functions */ + void d_cnjg(doublecomplex *, doublecomplex *); + + /* Local variables */ + integer i__, j, ix, jx, kx, info; + doublecomplex temp; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + logical noconj, nounit; + + +/* -- Reference BLAS level2 routine -- */ +/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ + +/* Test the input parameters. */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --x; + + /* Function Body */ + info = 0; + if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", ( + ftnlen)1, (ftnlen)1)) { + info = 1; + } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, + (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, ( + ftnlen)1)) { + info = 2; + } else if (! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, + (char *)"N", (ftnlen)1, (ftnlen)1)) { + info = 3; + } else if (*n < 0) { + info = 4; + } else if (*lda < max(1,*n)) { + info = 6; + } else if (*incx == 0) { + info = 8; + } + if (info != 0) { + xerbla_((char *)"ZTRMV ", &info, (ftnlen)6); + return 0; + } + +/* Quick return if possible. */ + + if (*n == 0) { + return 0; + } + + noconj = lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1); + nounit = lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1); + +/* Set up the start point in X if the increment is not unity. This */ +/* will be ( N - 1 )*INCX too small for descending loops. */ + + if (*incx <= 0) { + kx = 1 - (*n - 1) * *incx; + } else if (*incx != 1) { + kx = 1; + } + +/* Start the operations. In this version the elements of A are */ +/* accessed sequentially with one pass through A. */ + + if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { + +/* Form x := A*x. */ + + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + if (*incx == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + if (x[i__2].r != 0. || x[i__2].i != 0.) { + i__2 = j; + temp.r = x[i__2].r, temp.i = x[i__2].i; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__; + i__4 = i__; + i__5 = i__ + j * a_dim1; + z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, + z__2.i = temp.r * a[i__5].i + temp.i * a[ + i__5].r; + z__1.r = x[i__4].r + z__2.r, z__1.i = x[i__4].i + + z__2.i; + x[i__3].r = z__1.r, x[i__3].i = z__1.i; +/* L10: */ + } + if (nounit) { + i__2 = j; + i__3 = j; + i__4 = j + j * a_dim1; + z__1.r = x[i__3].r * a[i__4].r - x[i__3].i * a[ + i__4].i, z__1.i = x[i__3].r * a[i__4].i + + x[i__3].i * a[i__4].r; + x[i__2].r = z__1.r, x[i__2].i = z__1.i; + } + } +/* L20: */ + } + } else { + jx = kx; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = jx; + if (x[i__2].r != 0. || x[i__2].i != 0.) { + i__2 = jx; + temp.r = x[i__2].r, temp.i = x[i__2].i; + ix = kx; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = ix; + i__4 = ix; + i__5 = i__ + j * a_dim1; + z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, + z__2.i = temp.r * a[i__5].i + temp.i * a[ + i__5].r; + z__1.r = x[i__4].r + z__2.r, z__1.i = x[i__4].i + + z__2.i; + x[i__3].r = z__1.r, x[i__3].i = z__1.i; + ix += *incx; +/* L30: */ + } + if (nounit) { + i__2 = jx; + i__3 = jx; + i__4 = j + j * a_dim1; + z__1.r = x[i__3].r * a[i__4].r - x[i__3].i * a[ + i__4].i, z__1.i = x[i__3].r * a[i__4].i + + x[i__3].i * a[i__4].r; + x[i__2].r = z__1.r, x[i__2].i = z__1.i; + } + } + jx += *incx; +/* L40: */ + } + } + } else { + if (*incx == 1) { + for (j = *n; j >= 1; --j) { + i__1 = j; + if (x[i__1].r != 0. || x[i__1].i != 0.) { + i__1 = j; + temp.r = x[i__1].r, temp.i = x[i__1].i; + i__1 = j + 1; + for (i__ = *n; i__ >= i__1; --i__) { + i__2 = i__; + i__3 = i__; + i__4 = i__ + j * a_dim1; + z__2.r = temp.r * a[i__4].r - temp.i * a[i__4].i, + z__2.i = temp.r * a[i__4].i + temp.i * a[ + i__4].r; + z__1.r = x[i__3].r + z__2.r, z__1.i = x[i__3].i + + z__2.i; + x[i__2].r = z__1.r, x[i__2].i = z__1.i; +/* L50: */ + } + if (nounit) { + i__1 = j; + i__2 = j; + i__3 = j + j * a_dim1; + z__1.r = x[i__2].r * a[i__3].r - x[i__2].i * a[ + i__3].i, z__1.i = x[i__2].r * a[i__3].i + + x[i__2].i * a[i__3].r; + x[i__1].r = z__1.r, x[i__1].i = z__1.i; + } + } +/* L60: */ + } + } else { + kx += (*n - 1) * *incx; + jx = kx; + for (j = *n; j >= 1; --j) { + i__1 = jx; + if (x[i__1].r != 0. || x[i__1].i != 0.) { + i__1 = jx; + temp.r = x[i__1].r, temp.i = x[i__1].i; + ix = kx; + i__1 = j + 1; + for (i__ = *n; i__ >= i__1; --i__) { + i__2 = ix; + i__3 = ix; + i__4 = i__ + j * a_dim1; + z__2.r = temp.r * a[i__4].r - temp.i * a[i__4].i, + z__2.i = temp.r * a[i__4].i + temp.i * a[ + i__4].r; + z__1.r = x[i__3].r + z__2.r, z__1.i = x[i__3].i + + z__2.i; + x[i__2].r = z__1.r, x[i__2].i = z__1.i; + ix -= *incx; +/* L70: */ + } + if (nounit) { + i__1 = jx; + i__2 = jx; + i__3 = j + j * a_dim1; + z__1.r = x[i__2].r * a[i__3].r - x[i__2].i * a[ + i__3].i, z__1.i = x[i__2].r * a[i__3].i + + x[i__2].i * a[i__3].r; + x[i__1].r = z__1.r, x[i__1].i = z__1.i; + } + } + jx -= *incx; +/* L80: */ + } + } + } + } else { + +/* Form x := A**T*x or x := A**H*x. */ + + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + if (*incx == 1) { + for (j = *n; j >= 1; --j) { + i__1 = j; + temp.r = x[i__1].r, temp.i = x[i__1].i; + if (noconj) { + if (nounit) { + i__1 = j + j * a_dim1; + z__1.r = temp.r * a[i__1].r - temp.i * a[i__1].i, + z__1.i = temp.r * a[i__1].i + temp.i * a[ + i__1].r; + temp.r = z__1.r, temp.i = z__1.i; + } + for (i__ = j - 1; i__ >= 1; --i__) { + i__1 = i__ + j * a_dim1; + i__2 = i__; + z__2.r = a[i__1].r * x[i__2].r - a[i__1].i * x[ + i__2].i, z__2.i = a[i__1].r * x[i__2].i + + a[i__1].i * x[i__2].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; +/* L90: */ + } + } else { + if (nounit) { + d_cnjg(&z__2, &a[j + j * a_dim1]); + z__1.r = temp.r * z__2.r - temp.i * z__2.i, + z__1.i = temp.r * z__2.i + temp.i * + z__2.r; + temp.r = z__1.r, temp.i = z__1.i; + } + for (i__ = j - 1; i__ >= 1; --i__) { + d_cnjg(&z__3, &a[i__ + j * a_dim1]); + i__1 = i__; + z__2.r = z__3.r * x[i__1].r - z__3.i * x[i__1].i, + z__2.i = z__3.r * x[i__1].i + z__3.i * x[ + i__1].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; +/* L100: */ + } + } + i__1 = j; + x[i__1].r = temp.r, x[i__1].i = temp.i; +/* L110: */ + } + } else { + jx = kx + (*n - 1) * *incx; + for (j = *n; j >= 1; --j) { + i__1 = jx; + temp.r = x[i__1].r, temp.i = x[i__1].i; + ix = jx; + if (noconj) { + if (nounit) { + i__1 = j + j * a_dim1; + z__1.r = temp.r * a[i__1].r - temp.i * a[i__1].i, + z__1.i = temp.r * a[i__1].i + temp.i * a[ + i__1].r; + temp.r = z__1.r, temp.i = z__1.i; + } + for (i__ = j - 1; i__ >= 1; --i__) { + ix -= *incx; + i__1 = i__ + j * a_dim1; + i__2 = ix; + z__2.r = a[i__1].r * x[i__2].r - a[i__1].i * x[ + i__2].i, z__2.i = a[i__1].r * x[i__2].i + + a[i__1].i * x[i__2].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; +/* L120: */ + } + } else { + if (nounit) { + d_cnjg(&z__2, &a[j + j * a_dim1]); + z__1.r = temp.r * z__2.r - temp.i * z__2.i, + z__1.i = temp.r * z__2.i + temp.i * + z__2.r; + temp.r = z__1.r, temp.i = z__1.i; + } + for (i__ = j - 1; i__ >= 1; --i__) { + ix -= *incx; + d_cnjg(&z__3, &a[i__ + j * a_dim1]); + i__1 = ix; + z__2.r = z__3.r * x[i__1].r - z__3.i * x[i__1].i, + z__2.i = z__3.r * x[i__1].i + z__3.i * x[ + i__1].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; +/* L130: */ + } + } + i__1 = jx; + x[i__1].r = temp.r, x[i__1].i = temp.i; + jx -= *incx; +/* L140: */ + } + } + } else { + if (*incx == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + temp.r = x[i__2].r, temp.i = x[i__2].i; + if (noconj) { + if (nounit) { + i__2 = j + j * a_dim1; + z__1.r = temp.r * a[i__2].r - temp.i * a[i__2].i, + z__1.i = temp.r * a[i__2].i + temp.i * a[ + i__2].r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + i__4 = i__; + z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[ + i__4].i, z__2.i = a[i__3].r * x[i__4].i + + a[i__3].i * x[i__4].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; +/* L150: */ + } + } else { + if (nounit) { + d_cnjg(&z__2, &a[j + j * a_dim1]); + z__1.r = temp.r * z__2.r - temp.i * z__2.i, + z__1.i = temp.r * z__2.i + temp.i * + z__2.r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + d_cnjg(&z__3, &a[i__ + j * a_dim1]); + i__3 = i__; + z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, + z__2.i = z__3.r * x[i__3].i + z__3.i * x[ + i__3].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; +/* L160: */ + } + } + i__2 = j; + x[i__2].r = temp.r, x[i__2].i = temp.i; +/* L170: */ + } + } else { + jx = kx; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = jx; + temp.r = x[i__2].r, temp.i = x[i__2].i; + ix = jx; + if (noconj) { + if (nounit) { + i__2 = j + j * a_dim1; + z__1.r = temp.r * a[i__2].r - temp.i * a[i__2].i, + z__1.i = temp.r * a[i__2].i + temp.i * a[ + i__2].r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + ix += *incx; + i__3 = i__ + j * a_dim1; + i__4 = ix; + z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[ + i__4].i, z__2.i = a[i__3].r * x[i__4].i + + a[i__3].i * x[i__4].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; +/* L180: */ + } + } else { + if (nounit) { + d_cnjg(&z__2, &a[j + j * a_dim1]); + z__1.r = temp.r * z__2.r - temp.i * z__2.i, + z__1.i = temp.r * z__2.i + temp.i * + z__2.r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + ix += *incx; + d_cnjg(&z__3, &a[i__ + j * a_dim1]); + i__3 = ix; + z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, + z__2.i = z__3.r * x[i__3].i + z__3.i * x[ + i__3].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; +/* L190: */ + } + } + i__2 = jx; + x[i__2].r = temp.r, x[i__2].i = temp.i; + jx += *incx; +/* L200: */ + } + } + } + } + + return 0; + +/* End of ZTRMV */ + +} /* ztrmv_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zung2l.cpp b/lib/linalg/zung2l.cpp new file mode 100644 index 0000000000..45c03e5c78 --- /dev/null +++ b/lib/linalg/zung2l.cpp @@ -0,0 +1,262 @@ +/* fortran/zung2l.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; + +/* > \brief \b ZUNG2L generates all or part of the unitary matrix Q from a QL factorization determined by cgeq +lf (unblocked algorithm). */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZUNG2L + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZUNG2L( M, N, K, A, LDA, TAU, WORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INFO, K, LDA, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZUNG2L generates an m by n complex matrix Q with orthonormal columns, */ +/* > which is defined as the last n columns of a product of k elementary */ +/* > reflectors of order m */ +/* > */ +/* > Q = H(k) . . . H(2) H(1) */ +/* > */ +/* > as returned by ZGEQLF. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix Q. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix Q. M >= N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > The number of elementary reflectors whose product defines the */ +/* > matrix Q. N >= K >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is COMPLEX*16 array, dimension (LDA,N) */ +/* > On entry, the (n-k+i)-th column must contain the vector which */ +/* > defines the elementary reflector H(i), for i = 1,2,...,k, as */ +/* > returned by ZGEQLF in the last k columns of its array */ +/* > argument A. */ +/* > On exit, the m-by-n matrix Q. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The first dimension of the array A. LDA >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TAU */ +/* > \verbatim */ +/* > TAU is COMPLEX*16 array, dimension (K) */ +/* > TAU(i) must contain the scalar factor of the elementary */ +/* > reflector H(i), as returned by ZGEQLF. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is COMPLEX*16 array, dimension (N) */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument has an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16OTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int zung2l_(integer *m, integer *n, integer *k, + doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex * + work, integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3; + doublecomplex z__1; + + /* Local variables */ + integer i__, j, l, ii; + extern /* Subroutine */ int zscal_(integer *, doublecomplex *, + doublecomplex *, integer *), zlarf_(char *, integer *, integer *, + doublecomplex *, integer *, doublecomplex *, doublecomplex *, + integer *, doublecomplex *, ftnlen), xerbla_(char *, integer *, + ftnlen); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --tau; + --work; + + /* Function Body */ + *info = 0; + if (*m < 0) { + *info = -1; + } else if (*n < 0 || *n > *m) { + *info = -2; + } else if (*k < 0 || *k > *n) { + *info = -3; + } else if (*lda < max(1,*m)) { + *info = -5; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"ZUNG2L", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*n <= 0) { + return 0; + } + +/* Initialise columns 1:n-k to columns of the unit matrix */ + + i__1 = *n - *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (l = 1; l <= i__2; ++l) { + i__3 = l + j * a_dim1; + a[i__3].r = 0., a[i__3].i = 0.; +/* L10: */ + } + i__2 = *m - *n + j + j * a_dim1; + a[i__2].r = 1., a[i__2].i = 0.; +/* L20: */ + } + + i__1 = *k; + for (i__ = 1; i__ <= i__1; ++i__) { + ii = *n - *k + i__; + +/* Apply H(i) to A(1:m-k+i,1:n-k+i) from the left */ + + i__2 = *m - *n + ii + ii * a_dim1; + a[i__2].r = 1., a[i__2].i = 0.; + i__2 = *m - *n + ii; + i__3 = ii - 1; + zlarf_((char *)"Left", &i__2, &i__3, &a[ii * a_dim1 + 1], &c__1, &tau[i__], & + a[a_offset], lda, &work[1], (ftnlen)4); + i__2 = *m - *n + ii - 1; + i__3 = i__; + z__1.r = -tau[i__3].r, z__1.i = -tau[i__3].i; + zscal_(&i__2, &z__1, &a[ii * a_dim1 + 1], &c__1); + i__2 = *m - *n + ii + ii * a_dim1; + i__3 = i__; + z__1.r = 1. - tau[i__3].r, z__1.i = 0. - tau[i__3].i; + a[i__2].r = z__1.r, a[i__2].i = z__1.i; + +/* Set A(m-k+i+1:m,n-k+i) to zero */ + + i__2 = *m; + for (l = *m - *n + ii + 1; l <= i__2; ++l) { + i__3 = l + ii * a_dim1; + a[i__3].r = 0., a[i__3].i = 0.; +/* L30: */ + } +/* L40: */ + } + return 0; + +/* End of ZUNG2L */ + +} /* zung2l_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zung2r.cpp b/lib/linalg/zung2r.cpp new file mode 100644 index 0000000000..4bd9202caa --- /dev/null +++ b/lib/linalg/zung2r.cpp @@ -0,0 +1,264 @@ +/* fortran/zung2r.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; + +/* > \brief \b ZUNG2R */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZUNG2R + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZUNG2R( M, N, K, A, LDA, TAU, WORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INFO, K, LDA, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZUNG2R generates an m by n complex matrix Q with orthonormal columns, */ +/* > which is defined as the first n columns of a product of k elementary */ +/* > reflectors of order m */ +/* > */ +/* > Q = H(1) H(2) . . . H(k) */ +/* > */ +/* > as returned by ZGEQRF. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix Q. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix Q. M >= N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > The number of elementary reflectors whose product defines the */ +/* > matrix Q. N >= K >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is COMPLEX*16 array, dimension (LDA,N) */ +/* > On entry, the i-th column must contain the vector which */ +/* > defines the elementary reflector H(i), for i = 1,2,...,k, as */ +/* > returned by ZGEQRF in the first k columns of its array */ +/* > argument A. */ +/* > On exit, the m by n matrix Q. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The first dimension of the array A. LDA >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TAU */ +/* > \verbatim */ +/* > TAU is COMPLEX*16 array, dimension (K) */ +/* > TAU(i) must contain the scalar factor of the elementary */ +/* > reflector H(i), as returned by ZGEQRF. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is COMPLEX*16 array, dimension (N) */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument has an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16OTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int zung2r_(integer *m, integer *n, integer *k, + doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex * + work, integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3; + doublecomplex z__1; + + /* Local variables */ + integer i__, j, l; + extern /* Subroutine */ int zscal_(integer *, doublecomplex *, + doublecomplex *, integer *), zlarf_(char *, integer *, integer *, + doublecomplex *, integer *, doublecomplex *, doublecomplex *, + integer *, doublecomplex *, ftnlen), xerbla_(char *, integer *, + ftnlen); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --tau; + --work; + + /* Function Body */ + *info = 0; + if (*m < 0) { + *info = -1; + } else if (*n < 0 || *n > *m) { + *info = -2; + } else if (*k < 0 || *k > *n) { + *info = -3; + } else if (*lda < max(1,*m)) { + *info = -5; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"ZUNG2R", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*n <= 0) { + return 0; + } + +/* Initialise columns k+1:n to columns of the unit matrix */ + + i__1 = *n; + for (j = *k + 1; j <= i__1; ++j) { + i__2 = *m; + for (l = 1; l <= i__2; ++l) { + i__3 = l + j * a_dim1; + a[i__3].r = 0., a[i__3].i = 0.; +/* L10: */ + } + i__2 = j + j * a_dim1; + a[i__2].r = 1., a[i__2].i = 0.; +/* L20: */ + } + + for (i__ = *k; i__ >= 1; --i__) { + +/* Apply H(i) to A(i:m,i:n) from the left */ + + if (i__ < *n) { + i__1 = i__ + i__ * a_dim1; + a[i__1].r = 1., a[i__1].i = 0.; + i__1 = *m - i__ + 1; + i__2 = *n - i__; + zlarf_((char *)"Left", &i__1, &i__2, &a[i__ + i__ * a_dim1], &c__1, &tau[ + i__], &a[i__ + (i__ + 1) * a_dim1], lda, &work[1], ( + ftnlen)4); + } + if (i__ < *m) { + i__1 = *m - i__; + i__2 = i__; + z__1.r = -tau[i__2].r, z__1.i = -tau[i__2].i; + zscal_(&i__1, &z__1, &a[i__ + 1 + i__ * a_dim1], &c__1); + } + i__1 = i__ + i__ * a_dim1; + i__2 = i__; + z__1.r = 1. - tau[i__2].r, z__1.i = 0. - tau[i__2].i; + a[i__1].r = z__1.r, a[i__1].i = z__1.i; + +/* Set A(1:i-1,i) to zero */ + + i__1 = i__ - 1; + for (l = 1; l <= i__1; ++l) { + i__2 = l + i__ * a_dim1; + a[i__2].r = 0., a[i__2].i = 0.; +/* L30: */ + } +/* L40: */ + } + return 0; + +/* End of ZUNG2R */ + +} /* zung2r_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zungl2.cpp b/lib/linalg/zungl2.cpp new file mode 100644 index 0000000000..bd40069fd6 --- /dev/null +++ b/lib/linalg/zungl2.cpp @@ -0,0 +1,273 @@ +/* fortran/zungl2.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b ZUNGL2 generates all or part of the unitary matrix Q from an LQ factorization determined by cge +lqf (unblocked algorithm). */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZUNGL2 + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZUNGL2( M, N, K, A, LDA, TAU, WORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INFO, K, LDA, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZUNGL2 generates an m-by-n complex matrix Q with orthonormal rows, */ +/* > which is defined as the first m rows of a product of k elementary */ +/* > reflectors of order n */ +/* > */ +/* > Q = H(k)**H . . . H(2)**H H(1)**H */ +/* > */ +/* > as returned by ZGELQF. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix Q. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix Q. N >= M. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > The number of elementary reflectors whose product defines the */ +/* > matrix Q. M >= K >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is COMPLEX*16 array, dimension (LDA,N) */ +/* > On entry, the i-th row must contain the vector which defines */ +/* > the elementary reflector H(i), for i = 1,2,...,k, as returned */ +/* > by ZGELQF in the first k rows of its array argument A. */ +/* > On exit, the m by n matrix Q. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The first dimension of the array A. LDA >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TAU */ +/* > \verbatim */ +/* > TAU is COMPLEX*16 array, dimension (K) */ +/* > TAU(i) must contain the scalar factor of the elementary */ +/* > reflector H(i), as returned by ZGELQF. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is COMPLEX*16 array, dimension (M) */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument has an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16OTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int zungl2_(integer *m, integer *n, integer *k, + doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex * + work, integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3; + doublecomplex z__1, z__2; + + /* Builtin functions */ + void d_cnjg(doublecomplex *, doublecomplex *); + + /* Local variables */ + integer i__, j, l; + extern /* Subroutine */ int zscal_(integer *, doublecomplex *, + doublecomplex *, integer *), zlarf_(char *, integer *, integer *, + doublecomplex *, integer *, doublecomplex *, doublecomplex *, + integer *, doublecomplex *, ftnlen), xerbla_(char *, integer *, + ftnlen), zlacgv_(integer *, doublecomplex *, integer *); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --tau; + --work; + + /* Function Body */ + *info = 0; + if (*m < 0) { + *info = -1; + } else if (*n < *m) { + *info = -2; + } else if (*k < 0 || *k > *m) { + *info = -3; + } else if (*lda < max(1,*m)) { + *info = -5; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"ZUNGL2", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*m <= 0) { + return 0; + } + + if (*k < *m) { + +/* Initialise rows k+1:m to rows of the unit matrix */ + + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (l = *k + 1; l <= i__2; ++l) { + i__3 = l + j * a_dim1; + a[i__3].r = 0., a[i__3].i = 0.; +/* L10: */ + } + if (j > *k && j <= *m) { + i__2 = j + j * a_dim1; + a[i__2].r = 1., a[i__2].i = 0.; + } +/* L20: */ + } + } + + for (i__ = *k; i__ >= 1; --i__) { + +/* Apply H(i)**H to A(i:m,i:n) from the right */ + + if (i__ < *n) { + i__1 = *n - i__; + zlacgv_(&i__1, &a[i__ + (i__ + 1) * a_dim1], lda); + if (i__ < *m) { + i__1 = i__ + i__ * a_dim1; + a[i__1].r = 1., a[i__1].i = 0.; + i__1 = *m - i__; + i__2 = *n - i__ + 1; + d_cnjg(&z__1, &tau[i__]); + zlarf_((char *)"Right", &i__1, &i__2, &a[i__ + i__ * a_dim1], lda, & + z__1, &a[i__ + 1 + i__ * a_dim1], lda, &work[1], ( + ftnlen)5); + } + i__1 = *n - i__; + i__2 = i__; + z__1.r = -tau[i__2].r, z__1.i = -tau[i__2].i; + zscal_(&i__1, &z__1, &a[i__ + (i__ + 1) * a_dim1], lda); + i__1 = *n - i__; + zlacgv_(&i__1, &a[i__ + (i__ + 1) * a_dim1], lda); + } + i__1 = i__ + i__ * a_dim1; + d_cnjg(&z__2, &tau[i__]); + z__1.r = 1. - z__2.r, z__1.i = 0. - z__2.i; + a[i__1].r = z__1.r, a[i__1].i = z__1.i; + +/* Set A(i,1:i-1) to zero */ + + i__1 = i__ - 1; + for (l = 1; l <= i__1; ++l) { + i__2 = i__ + l * a_dim1; + a[i__2].r = 0., a[i__2].i = 0.; +/* L30: */ + } +/* L40: */ + } + return 0; + +/* End of ZUNGL2 */ + +} /* zungl2_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zungql.cpp b/lib/linalg/zungql.cpp new file mode 100644 index 0000000000..006c4859eb --- /dev/null +++ b/lib/linalg/zungql.cpp @@ -0,0 +1,381 @@ +/* fortran/zungql.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c_n1 = -1; +static integer c__3 = 3; +static integer c__2 = 2; + +/* > \brief \b ZUNGQL */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZUNGQL + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZUNGQL( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INFO, K, LDA, LWORK, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZUNGQL generates an M-by-N complex matrix Q with orthonormal columns, */ +/* > which is defined as the last N columns of a product of K elementary */ +/* > reflectors of order M */ +/* > */ +/* > Q = H(k) . . . H(2) H(1) */ +/* > */ +/* > as returned by ZGEQLF. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix Q. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix Q. M >= N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > The number of elementary reflectors whose product defines the */ +/* > matrix Q. N >= K >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is COMPLEX*16 array, dimension (LDA,N) */ +/* > On entry, the (n-k+i)-th column must contain the vector which */ +/* > defines the elementary reflector H(i), for i = 1,2,...,k, as */ +/* > returned by ZGEQLF in the last k columns of its array */ +/* > argument A. */ +/* > On exit, the M-by-N matrix Q. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The first dimension of the array A. LDA >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TAU */ +/* > \verbatim */ +/* > TAU is COMPLEX*16 array, dimension (K) */ +/* > TAU(i) must contain the scalar factor of the elementary */ +/* > reflector H(i), as returned by ZGEQLF. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) */ +/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LWORK */ +/* > \verbatim */ +/* > LWORK is INTEGER */ +/* > The dimension of the array WORK. LWORK >= max(1,N). */ +/* > For optimum performance LWORK >= N*NB, where NB is the */ +/* > optimal blocksize. */ +/* > */ +/* > If LWORK = -1, then a workspace query is assumed; the routine */ +/* > only calculates the optimal size of the WORK array, returns */ +/* > this value as the first entry of the WORK array, and no error */ +/* > message related to LWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument has an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16OTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int zungql_(integer *m, integer *n, integer *k, + doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex * + work, integer *lwork, integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; + + /* Local variables */ + integer i__, j, l, ib, nb, kk, nx, iws, nbmin, iinfo; + extern /* Subroutine */ int zung2l_(integer *, integer *, integer *, + doublecomplex *, integer *, doublecomplex *, doublecomplex *, + integer *), xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *, + integer *, integer *, integer *, doublecomplex *, integer *, + doublecomplex *, integer *, doublecomplex *, integer *, + doublecomplex *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + integer ldwork; + extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *, + doublecomplex *, integer *, doublecomplex *, doublecomplex *, + integer *, ftnlen, ftnlen); + logical lquery; + integer lwkopt; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --tau; + --work; + + /* Function Body */ + *info = 0; + lquery = *lwork == -1; + if (*m < 0) { + *info = -1; + } else if (*n < 0 || *n > *m) { + *info = -2; + } else if (*k < 0 || *k > *n) { + *info = -3; + } else if (*lda < max(1,*m)) { + *info = -5; + } + + if (*info == 0) { + if (*n == 0) { + lwkopt = 1; + } else { + nb = ilaenv_(&c__1, (char *)"ZUNGQL", (char *)" ", m, n, k, &c_n1, (ftnlen)6, ( + ftnlen)1); + lwkopt = *n * nb; + } + work[1].r = (doublereal) lwkopt, work[1].i = 0.; + + if (*lwork < max(1,*n) && ! lquery) { + *info = -8; + } + } + + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"ZUNGQL", &i__1, (ftnlen)6); + return 0; + } else if (lquery) { + return 0; + } + +/* Quick return if possible */ + + if (*n <= 0) { + return 0; + } + + nbmin = 2; + nx = 0; + iws = *n; + if (nb > 1 && nb < *k) { + +/* Determine when to cross over from blocked to unblocked code. */ + +/* Computing MAX */ + i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"ZUNGQL", (char *)" ", m, n, k, &c_n1, ( + ftnlen)6, (ftnlen)1); + nx = max(i__1,i__2); + if (nx < *k) { + +/* Determine if workspace is large enough for blocked code. */ + + ldwork = *n; + iws = ldwork * nb; + if (*lwork < iws) { + +/* Not enough workspace to use optimal NB: reduce NB and */ +/* determine the minimum value of NB. */ + + nb = *lwork / ldwork; +/* Computing MAX */ + i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"ZUNGQL", (char *)" ", m, n, k, &c_n1, + (ftnlen)6, (ftnlen)1); + nbmin = max(i__1,i__2); + } + } + } + + if (nb >= nbmin && nb < *k && nx < *k) { + +/* Use blocked code after the first block. */ +/* The last kk columns are handled by the block method. */ + +/* Computing MIN */ + i__1 = *k, i__2 = (*k - nx + nb - 1) / nb * nb; + kk = min(i__1,i__2); + +/* Set A(m-kk+1:m,1:n-kk) to zero. */ + + i__1 = *n - kk; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = *m - kk + 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + a[i__3].r = 0., a[i__3].i = 0.; +/* L10: */ + } +/* L20: */ + } + } else { + kk = 0; + } + +/* Use unblocked code for the first or only block. */ + + i__1 = *m - kk; + i__2 = *n - kk; + i__3 = *k - kk; + zung2l_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], &work[1], &iinfo) + ; + + if (kk > 0) { + +/* Use blocked code */ + + i__1 = *k; + i__2 = nb; + for (i__ = *k - kk + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += + i__2) { +/* Computing MIN */ + i__3 = nb, i__4 = *k - i__ + 1; + ib = min(i__3,i__4); + if (*n - *k + i__ > 1) { + +/* Form the triangular factor of the block reflector */ +/* H = H(i+ib-1) . . . H(i+1) H(i) */ + + i__3 = *m - *k + i__ + ib - 1; + zlarft_((char *)"Backward", (char *)"Columnwise", &i__3, &ib, &a[(*n - *k + + i__) * a_dim1 + 1], lda, &tau[i__], &work[1], &ldwork, + (ftnlen)8, (ftnlen)10); + +/* Apply H to A(1:m-k+i+ib-1,1:n-k+i-1) from the left */ + + i__3 = *m - *k + i__ + ib - 1; + i__4 = *n - *k + i__ - 1; + zlarfb_((char *)"Left", (char *)"No transpose", (char *)"Backward", (char *)"Columnwise", & + i__3, &i__4, &ib, &a[(*n - *k + i__) * a_dim1 + 1], + lda, &work[1], &ldwork, &a[a_offset], lda, &work[ib + + 1], &ldwork, (ftnlen)4, (ftnlen)12, (ftnlen)8, ( + ftnlen)10); + } + +/* Apply H to rows 1:m-k+i+ib-1 of current block */ + + i__3 = *m - *k + i__ + ib - 1; + zung2l_(&i__3, &ib, &ib, &a[(*n - *k + i__) * a_dim1 + 1], lda, & + tau[i__], &work[1], &iinfo); + +/* Set rows m-k+i+ib:m of current block to zero */ + + i__3 = *n - *k + i__ + ib - 1; + for (j = *n - *k + i__; j <= i__3; ++j) { + i__4 = *m; + for (l = *m - *k + i__ + ib; l <= i__4; ++l) { + i__5 = l + j * a_dim1; + a[i__5].r = 0., a[i__5].i = 0.; +/* L30: */ + } +/* L40: */ + } +/* L50: */ + } + } + + work[1].r = (doublereal) iws, work[1].i = 0.; + return 0; + +/* End of ZUNGQL */ + +} /* zungql_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zungqr.cpp b/lib/linalg/zungqr.cpp new file mode 100644 index 0000000000..7ce6a2a40d --- /dev/null +++ b/lib/linalg/zungqr.cpp @@ -0,0 +1,372 @@ +/* fortran/zungqr.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c_n1 = -1; +static integer c__3 = 3; +static integer c__2 = 2; + +/* > \brief \b ZUNGQR */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZUNGQR + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZUNGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* INTEGER INFO, K, LDA, LWORK, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZUNGQR generates an M-by-N complex matrix Q with orthonormal columns, */ +/* > which is defined as the first N columns of a product of K elementary */ +/* > reflectors of order M */ +/* > */ +/* > Q = H(1) H(2) . . . H(k) */ +/* > */ +/* > as returned by ZGEQRF. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix Q. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix Q. M >= N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > The number of elementary reflectors whose product defines the */ +/* > matrix Q. N >= K >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is COMPLEX*16 array, dimension (LDA,N) */ +/* > On entry, the i-th column must contain the vector which */ +/* > defines the elementary reflector H(i), for i = 1,2,...,k, as */ +/* > returned by ZGEQRF in the first k columns of its array */ +/* > argument A. */ +/* > On exit, the M-by-N matrix Q. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The first dimension of the array A. LDA >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TAU */ +/* > \verbatim */ +/* > TAU is COMPLEX*16 array, dimension (K) */ +/* > TAU(i) must contain the scalar factor of the elementary */ +/* > reflector H(i), as returned by ZGEQRF. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) */ +/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LWORK */ +/* > \verbatim */ +/* > LWORK is INTEGER */ +/* > The dimension of the array WORK. LWORK >= max(1,N). */ +/* > For optimum performance LWORK >= N*NB, where NB is the */ +/* > optimal blocksize. */ +/* > */ +/* > If LWORK = -1, then a workspace query is assumed; the routine */ +/* > only calculates the optimal size of the WORK array, returns */ +/* > this value as the first entry of the WORK array, and no error */ +/* > message related to LWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument has an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16OTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int zungqr_(integer *m, integer *n, integer *k, + doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex * + work, integer *lwork, integer *info) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3, i__4; + + /* Local variables */ + integer i__, j, l, ib, nb, ki, kk, nx, iws, nbmin, iinfo; + extern /* Subroutine */ int zung2r_(integer *, integer *, integer *, + doublecomplex *, integer *, doublecomplex *, doublecomplex *, + integer *), xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *, + integer *, integer *, integer *, doublecomplex *, integer *, + doublecomplex *, integer *, doublecomplex *, integer *, + doublecomplex *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + integer ldwork; + extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *, + doublecomplex *, integer *, doublecomplex *, doublecomplex *, + integer *, ftnlen, ftnlen); + integer lwkopt; + logical lquery; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --tau; + --work; + + /* Function Body */ + *info = 0; + nb = ilaenv_(&c__1, (char *)"ZUNGQR", (char *)" ", m, n, k, &c_n1, (ftnlen)6, (ftnlen)1); + lwkopt = max(1,*n) * nb; + work[1].r = (doublereal) lwkopt, work[1].i = 0.; + lquery = *lwork == -1; + if (*m < 0) { + *info = -1; + } else if (*n < 0 || *n > *m) { + *info = -2; + } else if (*k < 0 || *k > *n) { + *info = -3; + } else if (*lda < max(1,*m)) { + *info = -5; + } else if (*lwork < max(1,*n) && ! lquery) { + *info = -8; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"ZUNGQR", &i__1, (ftnlen)6); + return 0; + } else if (lquery) { + return 0; + } + +/* Quick return if possible */ + + if (*n <= 0) { + work[1].r = 1., work[1].i = 0.; + return 0; + } + + nbmin = 2; + nx = 0; + iws = *n; + if (nb > 1 && nb < *k) { + +/* Determine when to cross over from blocked to unblocked code. */ + +/* Computing MAX */ + i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"ZUNGQR", (char *)" ", m, n, k, &c_n1, ( + ftnlen)6, (ftnlen)1); + nx = max(i__1,i__2); + if (nx < *k) { + +/* Determine if workspace is large enough for blocked code. */ + + ldwork = *n; + iws = ldwork * nb; + if (*lwork < iws) { + +/* Not enough workspace to use optimal NB: reduce NB and */ +/* determine the minimum value of NB. */ + + nb = *lwork / ldwork; +/* Computing MAX */ + i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"ZUNGQR", (char *)" ", m, n, k, &c_n1, + (ftnlen)6, (ftnlen)1); + nbmin = max(i__1,i__2); + } + } + } + + if (nb >= nbmin && nb < *k && nx < *k) { + +/* Use blocked code after the last block. */ +/* The first kk columns are handled by the block method. */ + + ki = (*k - nx - 1) / nb * nb; +/* Computing MIN */ + i__1 = *k, i__2 = ki + nb; + kk = min(i__1,i__2); + +/* Set A(1:kk,kk+1:n) to zero. */ + + i__1 = *n; + for (j = kk + 1; j <= i__1; ++j) { + i__2 = kk; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + a[i__3].r = 0., a[i__3].i = 0.; +/* L10: */ + } +/* L20: */ + } + } else { + kk = 0; + } + +/* Use unblocked code for the last or only block. */ + + if (kk < *n) { + i__1 = *m - kk; + i__2 = *n - kk; + i__3 = *k - kk; + zung2r_(&i__1, &i__2, &i__3, &a[kk + 1 + (kk + 1) * a_dim1], lda, & + tau[kk + 1], &work[1], &iinfo); + } + + if (kk > 0) { + +/* Use blocked code */ + + i__1 = -nb; + for (i__ = ki + 1; i__1 < 0 ? i__ >= 1 : i__ <= 1; i__ += i__1) { +/* Computing MIN */ + i__2 = nb, i__3 = *k - i__ + 1; + ib = min(i__2,i__3); + if (i__ + ib <= *n) { + +/* Form the triangular factor of the block reflector */ +/* H = H(i) H(i+1) . . . H(i+ib-1) */ + + i__2 = *m - i__ + 1; + zlarft_((char *)"Forward", (char *)"Columnwise", &i__2, &ib, &a[i__ + i__ * + a_dim1], lda, &tau[i__], &work[1], &ldwork, (ftnlen)7, + (ftnlen)10); + +/* Apply H to A(i:m,i+ib:n) from the left */ + + i__2 = *m - i__ + 1; + i__3 = *n - i__ - ib + 1; + zlarfb_((char *)"Left", (char *)"No transpose", (char *)"Forward", (char *)"Columnwise", & + i__2, &i__3, &ib, &a[i__ + i__ * a_dim1], lda, &work[ + 1], &ldwork, &a[i__ + (i__ + ib) * a_dim1], lda, & + work[ib + 1], &ldwork, (ftnlen)4, (ftnlen)12, (ftnlen) + 7, (ftnlen)10); + } + +/* Apply H to rows i:m of current block */ + + i__2 = *m - i__ + 1; + zung2r_(&i__2, &ib, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], & + work[1], &iinfo); + +/* Set rows 1:i-1 of current block to zero */ + + i__2 = i__ + ib - 1; + for (j = i__; j <= i__2; ++j) { + i__3 = i__ - 1; + for (l = 1; l <= i__3; ++l) { + i__4 = l + j * a_dim1; + a[i__4].r = 0., a[i__4].i = 0.; +/* L30: */ + } +/* L40: */ + } +/* L50: */ + } + } + + work[1].r = (doublereal) iws, work[1].i = 0.; + return 0; + +/* End of ZUNGQR */ + +} /* zungqr_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zungtr.cpp b/lib/linalg/zungtr.cpp new file mode 100644 index 0000000000..c8f42b6e21 --- /dev/null +++ b/lib/linalg/zungtr.cpp @@ -0,0 +1,342 @@ +/* fortran/zungtr.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c_n1 = -1; + +/* > \brief \b ZUNGTR */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZUNGTR + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZUNGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER UPLO */ +/* INTEGER INFO, LDA, LWORK, N */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZUNGTR generates a complex unitary matrix Q which is defined as the */ +/* > product of n-1 elementary reflectors of order N, as returned by */ +/* > ZHETRD: */ +/* > */ +/* > if UPLO = 'U', Q = H(n-1) . . . H(2) H(1), */ +/* > */ +/* > if UPLO = 'L', Q = H(1) H(2) . . . H(n-1). */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > = 'U': Upper triangle of A contains elementary reflectors */ +/* > from ZHETRD; */ +/* > = 'L': Lower triangle of A contains elementary reflectors */ +/* > from ZHETRD. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The order of the matrix Q. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] A */ +/* > \verbatim */ +/* > A is COMPLEX*16 array, dimension (LDA,N) */ +/* > On entry, the vectors which define the elementary reflectors, */ +/* > as returned by ZHETRD. */ +/* > On exit, the N-by-N unitary matrix Q. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. LDA >= N. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TAU */ +/* > \verbatim */ +/* > TAU is COMPLEX*16 array, dimension (N-1) */ +/* > TAU(i) must contain the scalar factor of the elementary */ +/* > reflector H(i), as returned by ZHETRD. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) */ +/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LWORK */ +/* > \verbatim */ +/* > LWORK is INTEGER */ +/* > The dimension of the array WORK. LWORK >= N-1. */ +/* > For optimum performance LWORK >= (N-1)*NB, where NB is */ +/* > the optimal blocksize. */ +/* > */ +/* > If LWORK = -1, then a workspace query is assumed; the routine */ +/* > only calculates the optimal size of the WORK array, returns */ +/* > this value as the first entry of the WORK array, and no error */ +/* > message related to LWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16OTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int zungtr_(char *uplo, integer *n, doublecomplex *a, + integer *lda, doublecomplex *tau, doublecomplex *work, integer *lwork, + integer *info, ftnlen uplo_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, i__1, i__2, i__3, i__4; + + /* Local variables */ + integer i__, j, nb; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + integer iinfo; + logical upper; + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + integer lwkopt; + logical lquery; + extern /* Subroutine */ int zungql_(integer *, integer *, integer *, + doublecomplex *, integer *, doublecomplex *, doublecomplex *, + integer *, integer *), zungqr_(integer *, integer *, integer *, + doublecomplex *, integer *, doublecomplex *, doublecomplex *, + integer *, integer *); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --tau; + --work; + + /* Function Body */ + *info = 0; + lquery = *lwork == -1; + upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); + if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + *info = -1; + } else if (*n < 0) { + *info = -2; + } else if (*lda < max(1,*n)) { + *info = -4; + } else /* if(complicated condition) */ { +/* Computing MAX */ + i__1 = 1, i__2 = *n - 1; + if (*lwork < max(i__1,i__2) && ! lquery) { + *info = -7; + } + } + + if (*info == 0) { + if (upper) { + i__1 = *n - 1; + i__2 = *n - 1; + i__3 = *n - 1; + nb = ilaenv_(&c__1, (char *)"ZUNGQL", (char *)" ", &i__1, &i__2, &i__3, &c_n1, ( + ftnlen)6, (ftnlen)1); + } else { + i__1 = *n - 1; + i__2 = *n - 1; + i__3 = *n - 1; + nb = ilaenv_(&c__1, (char *)"ZUNGQR", (char *)" ", &i__1, &i__2, &i__3, &c_n1, ( + ftnlen)6, (ftnlen)1); + } +/* Computing MAX */ + i__1 = 1, i__2 = *n - 1; + lwkopt = max(i__1,i__2) * nb; + work[1].r = (doublereal) lwkopt, work[1].i = 0.; + } + + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"ZUNGTR", &i__1, (ftnlen)6); + return 0; + } else if (lquery) { + return 0; + } + +/* Quick return if possible */ + + if (*n == 0) { + work[1].r = 1., work[1].i = 0.; + return 0; + } + + if (upper) { + +/* Q was determined by a call to ZHETRD with UPLO = 'U' */ + +/* Shift the vectors which define the elementary reflectors one */ +/* column to the left, and set the last row and column of Q to */ +/* those of the unit matrix */ + + i__1 = *n - 1; + for (j = 1; j <= i__1; ++j) { + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + i__4 = i__ + (j + 1) * a_dim1; + a[i__3].r = a[i__4].r, a[i__3].i = a[i__4].i; +/* L10: */ + } + i__2 = *n + j * a_dim1; + a[i__2].r = 0., a[i__2].i = 0.; +/* L20: */ + } + i__1 = *n - 1; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__ + *n * a_dim1; + a[i__2].r = 0., a[i__2].i = 0.; +/* L30: */ + } + i__1 = *n + *n * a_dim1; + a[i__1].r = 1., a[i__1].i = 0.; + +/* Generate Q(1:n-1,1:n-1) */ + + i__1 = *n - 1; + i__2 = *n - 1; + i__3 = *n - 1; + zungql_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], &work[1], + lwork, &iinfo); + + } else { + +/* Q was determined by a call to ZHETRD with UPLO = 'L'. */ + +/* Shift the vectors which define the elementary reflectors one */ +/* column to the right, and set the first row and column of Q to */ +/* those of the unit matrix */ + + for (j = *n; j >= 2; --j) { + i__1 = j * a_dim1 + 1; + a[i__1].r = 0., a[i__1].i = 0.; + i__1 = *n; + for (i__ = j + 1; i__ <= i__1; ++i__) { + i__2 = i__ + j * a_dim1; + i__3 = i__ + (j - 1) * a_dim1; + a[i__2].r = a[i__3].r, a[i__2].i = a[i__3].i; +/* L40: */ + } +/* L50: */ + } + i__1 = a_dim1 + 1; + a[i__1].r = 1., a[i__1].i = 0.; + i__1 = *n; + for (i__ = 2; i__ <= i__1; ++i__) { + i__2 = i__ + a_dim1; + a[i__2].r = 0., a[i__2].i = 0.; +/* L60: */ + } + if (*n > 1) { + +/* Generate Q(2:n,2:n) */ + + i__1 = *n - 1; + i__2 = *n - 1; + i__3 = *n - 1; + zungqr_(&i__1, &i__2, &i__3, &a[(a_dim1 << 1) + 2], lda, &tau[1], + &work[1], lwork, &iinfo); + } + } + work[1].r = (doublereal) lwkopt, work[1].i = 0.; + return 0; + +/* End of ZUNGTR */ + +} /* zungtr_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zunm2l.cpp b/lib/linalg/zunm2l.cpp new file mode 100644 index 0000000000..d7fc940517 --- /dev/null +++ b/lib/linalg/zunm2l.cpp @@ -0,0 +1,339 @@ +/* fortran/zunm2l.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; + +/* > \brief \b ZUNM2L multiplies a general matrix by the unitary matrix from a QL factorization determined by +cgeqlf (unblocked algorithm). */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZUNM2L + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZUNM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, */ +/* WORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER SIDE, TRANS */ +/* INTEGER INFO, K, LDA, LDC, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZUNM2L overwrites the general complex m-by-n matrix C with */ +/* > */ +/* > Q * C if SIDE = 'L' and TRANS = 'N', or */ +/* > */ +/* > Q**H* C if SIDE = 'L' and TRANS = 'C', or */ +/* > */ +/* > C * Q if SIDE = 'R' and TRANS = 'N', or */ +/* > */ +/* > C * Q**H if SIDE = 'R' and TRANS = 'C', */ +/* > */ +/* > where Q is a complex unitary matrix defined as the product of k */ +/* > elementary reflectors */ +/* > */ +/* > Q = H(k) . . . H(2) H(1) */ +/* > */ +/* > as returned by ZGEQLF. Q is of order m if SIDE = 'L' and of order n */ +/* > if SIDE = 'R'. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] SIDE */ +/* > \verbatim */ +/* > SIDE is CHARACTER*1 */ +/* > = 'L': apply Q or Q**H from the Left */ +/* > = 'R': apply Q or Q**H from the Right */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TRANS */ +/* > \verbatim */ +/* > TRANS is CHARACTER*1 */ +/* > = 'N': apply Q (No transpose) */ +/* > = 'C': apply Q**H (Conjugate transpose) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix C. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix C. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > The number of elementary reflectors whose product defines */ +/* > the matrix Q. */ +/* > If SIDE = 'L', M >= K >= 0; */ +/* > if SIDE = 'R', N >= K >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is COMPLEX*16 array, dimension (LDA,K) */ +/* > The i-th column must contain the vector which defines the */ +/* > elementary reflector H(i), for i = 1,2,...,k, as returned by */ +/* > ZGEQLF in the last k columns of its array argument A. */ +/* > A is modified by the routine but restored on exit. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. */ +/* > If SIDE = 'L', LDA >= max(1,M); */ +/* > if SIDE = 'R', LDA >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TAU */ +/* > \verbatim */ +/* > TAU is COMPLEX*16 array, dimension (K) */ +/* > TAU(i) must contain the scalar factor of the elementary */ +/* > reflector H(i), as returned by ZGEQLF. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] C */ +/* > \verbatim */ +/* > C is COMPLEX*16 array, dimension (LDC,N) */ +/* > On entry, the m-by-n matrix C. */ +/* > On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDC */ +/* > \verbatim */ +/* > LDC is INTEGER */ +/* > The leading dimension of the array C. LDC >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is COMPLEX*16 array, dimension */ +/* > (N) if SIDE = 'L', */ +/* > (M) if SIDE = 'R' */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16OTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int zunm2l_(char *side, char *trans, integer *m, integer *n, + integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, + doublecomplex *c__, integer *ldc, doublecomplex *work, integer *info, + ftnlen side_len, ftnlen trans_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3; + doublecomplex z__1; + + /* Builtin functions */ + void d_cnjg(doublecomplex *, doublecomplex *); + + /* Local variables */ + integer i__, i1, i2, i3, mi, ni, nq; + doublecomplex aii; + logical left; + doublecomplex taui; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int zlarf_(char *, integer *, integer *, + doublecomplex *, integer *, doublecomplex *, doublecomplex *, + integer *, doublecomplex *, ftnlen), xerbla_(char *, integer *, + ftnlen); + logical notran; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --tau; + c_dim1 = *ldc; + c_offset = 1 + c_dim1; + c__ -= c_offset; + --work; + + /* Function Body */ + *info = 0; + left = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); + notran = lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1); + +/* NQ is the order of Q */ + + if (left) { + nq = *m; + } else { + nq = *n; + } + if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + *info = -1; + } else if (! notran && ! lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { + *info = -2; + } else if (*m < 0) { + *info = -3; + } else if (*n < 0) { + *info = -4; + } else if (*k < 0 || *k > nq) { + *info = -5; + } else if (*lda < max(1,nq)) { + *info = -7; + } else if (*ldc < max(1,*m)) { + *info = -10; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"ZUNM2L", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*m == 0 || *n == 0 || *k == 0) { + return 0; + } + + if (left && notran || ! left && ! notran) { + i1 = 1; + i2 = *k; + i3 = 1; + } else { + i1 = *k; + i2 = 1; + i3 = -1; + } + + if (left) { + ni = *n; + } else { + mi = *m; + } + + i__1 = i2; + i__2 = i3; + for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { + if (left) { + +/* H(i) or H(i)**H is applied to C(1:m-k+i,1:n) */ + + mi = *m - *k + i__; + } else { + +/* H(i) or H(i)**H is applied to C(1:m,1:n-k+i) */ + + ni = *n - *k + i__; + } + +/* Apply H(i) or H(i)**H */ + + if (notran) { + i__3 = i__; + taui.r = tau[i__3].r, taui.i = tau[i__3].i; + } else { + d_cnjg(&z__1, &tau[i__]); + taui.r = z__1.r, taui.i = z__1.i; + } + i__3 = nq - *k + i__ + i__ * a_dim1; + aii.r = a[i__3].r, aii.i = a[i__3].i; + i__3 = nq - *k + i__ + i__ * a_dim1; + a[i__3].r = 1., a[i__3].i = 0.; + zlarf_(side, &mi, &ni, &a[i__ * a_dim1 + 1], &c__1, &taui, &c__[ + c_offset], ldc, &work[1], (ftnlen)1); + i__3 = nq - *k + i__ + i__ * a_dim1; + a[i__3].r = aii.r, a[i__3].i = aii.i; +/* L10: */ + } + return 0; + +/* End of ZUNM2L */ + +} /* zunm2l_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zunm2r.cpp b/lib/linalg/zunm2r.cpp new file mode 100644 index 0000000000..56ad0d944a --- /dev/null +++ b/lib/linalg/zunm2r.cpp @@ -0,0 +1,343 @@ +/* fortran/zunm2r.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; + +/* > \brief \b ZUNM2R multiplies a general matrix by the unitary matrix from a QR factorization determined by +cgeqrf (unblocked algorithm). */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZUNM2R + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZUNM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, */ +/* WORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER SIDE, TRANS */ +/* INTEGER INFO, K, LDA, LDC, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZUNM2R overwrites the general complex m-by-n matrix C with */ +/* > */ +/* > Q * C if SIDE = 'L' and TRANS = 'N', or */ +/* > */ +/* > Q**H* C if SIDE = 'L' and TRANS = 'C', or */ +/* > */ +/* > C * Q if SIDE = 'R' and TRANS = 'N', or */ +/* > */ +/* > C * Q**H if SIDE = 'R' and TRANS = 'C', */ +/* > */ +/* > where Q is a complex unitary matrix defined as the product of k */ +/* > elementary reflectors */ +/* > */ +/* > Q = H(1) H(2) . . . H(k) */ +/* > */ +/* > as returned by ZGEQRF. Q is of order m if SIDE = 'L' and of order n */ +/* > if SIDE = 'R'. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] SIDE */ +/* > \verbatim */ +/* > SIDE is CHARACTER*1 */ +/* > = 'L': apply Q or Q**H from the Left */ +/* > = 'R': apply Q or Q**H from the Right */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TRANS */ +/* > \verbatim */ +/* > TRANS is CHARACTER*1 */ +/* > = 'N': apply Q (No transpose) */ +/* > = 'C': apply Q**H (Conjugate transpose) */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix C. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix C. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > The number of elementary reflectors whose product defines */ +/* > the matrix Q. */ +/* > If SIDE = 'L', M >= K >= 0; */ +/* > if SIDE = 'R', N >= K >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is COMPLEX*16 array, dimension (LDA,K) */ +/* > The i-th column must contain the vector which defines the */ +/* > elementary reflector H(i), for i = 1,2,...,k, as returned by */ +/* > ZGEQRF in the first k columns of its array argument A. */ +/* > A is modified by the routine but restored on exit. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. */ +/* > If SIDE = 'L', LDA >= max(1,M); */ +/* > if SIDE = 'R', LDA >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TAU */ +/* > \verbatim */ +/* > TAU is COMPLEX*16 array, dimension (K) */ +/* > TAU(i) must contain the scalar factor of the elementary */ +/* > reflector H(i), as returned by ZGEQRF. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] C */ +/* > \verbatim */ +/* > C is COMPLEX*16 array, dimension (LDC,N) */ +/* > On entry, the m-by-n matrix C. */ +/* > On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDC */ +/* > \verbatim */ +/* > LDC is INTEGER */ +/* > The leading dimension of the array C. LDC >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is COMPLEX*16 array, dimension */ +/* > (N) if SIDE = 'L', */ +/* > (M) if SIDE = 'R' */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16OTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int zunm2r_(char *side, char *trans, integer *m, integer *n, + integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, + doublecomplex *c__, integer *ldc, doublecomplex *work, integer *info, + ftnlen side_len, ftnlen trans_len) +{ + /* System generated locals */ + integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3; + doublecomplex z__1; + + /* Builtin functions */ + void d_cnjg(doublecomplex *, doublecomplex *); + + /* Local variables */ + integer i__, i1, i2, i3, ic, jc, mi, ni, nq; + doublecomplex aii; + logical left; + doublecomplex taui; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + extern /* Subroutine */ int zlarf_(char *, integer *, integer *, + doublecomplex *, integer *, doublecomplex *, doublecomplex *, + integer *, doublecomplex *, ftnlen), xerbla_(char *, integer *, + ftnlen); + logical notran; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --tau; + c_dim1 = *ldc; + c_offset = 1 + c_dim1; + c__ -= c_offset; + --work; + + /* Function Body */ + *info = 0; + left = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); + notran = lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1); + +/* NQ is the order of Q */ + + if (left) { + nq = *m; + } else { + nq = *n; + } + if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + *info = -1; + } else if (! notran && ! lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { + *info = -2; + } else if (*m < 0) { + *info = -3; + } else if (*n < 0) { + *info = -4; + } else if (*k < 0 || *k > nq) { + *info = -5; + } else if (*lda < max(1,nq)) { + *info = -7; + } else if (*ldc < max(1,*m)) { + *info = -10; + } + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"ZUNM2R", &i__1, (ftnlen)6); + return 0; + } + +/* Quick return if possible */ + + if (*m == 0 || *n == 0 || *k == 0) { + return 0; + } + + if (left && ! notran || ! left && notran) { + i1 = 1; + i2 = *k; + i3 = 1; + } else { + i1 = *k; + i2 = 1; + i3 = -1; + } + + if (left) { + ni = *n; + jc = 1; + } else { + mi = *m; + ic = 1; + } + + i__1 = i2; + i__2 = i3; + for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { + if (left) { + +/* H(i) or H(i)**H is applied to C(i:m,1:n) */ + + mi = *m - i__ + 1; + ic = i__; + } else { + +/* H(i) or H(i)**H is applied to C(1:m,i:n) */ + + ni = *n - i__ + 1; + jc = i__; + } + +/* Apply H(i) or H(i)**H */ + + if (notran) { + i__3 = i__; + taui.r = tau[i__3].r, taui.i = tau[i__3].i; + } else { + d_cnjg(&z__1, &tau[i__]); + taui.r = z__1.r, taui.i = z__1.i; + } + i__3 = i__ + i__ * a_dim1; + aii.r = a[i__3].r, aii.i = a[i__3].i; + i__3 = i__ + i__ * a_dim1; + a[i__3].r = 1., a[i__3].i = 0.; + zlarf_(side, &mi, &ni, &a[i__ + i__ * a_dim1], &c__1, &taui, &c__[ic + + jc * c_dim1], ldc, &work[1], (ftnlen)1); + i__3 = i__ + i__ * a_dim1; + a[i__3].r = aii.r, a[i__3].i = aii.i; +/* L10: */ + } + return 0; + +/* End of ZUNM2R */ + +} /* zunm2r_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zunmql.cpp b/lib/linalg/zunmql.cpp new file mode 100644 index 0000000000..c7e6134831 --- /dev/null +++ b/lib/linalg/zunmql.cpp @@ -0,0 +1,419 @@ +/* fortran/zunmql.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c_n1 = -1; +static integer c__2 = 2; +static integer c__65 = 65; + +/* > \brief \b ZUNMQL */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZUNMQL + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZUNMQL( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, */ +/* WORK, LWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER SIDE, TRANS */ +/* INTEGER INFO, K, LDA, LDC, LWORK, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZUNMQL overwrites the general complex M-by-N matrix C with */ +/* > */ +/* > SIDE = 'L' SIDE = 'R' */ +/* > TRANS = 'N': Q * C C * Q */ +/* > TRANS = 'C': Q**H * C C * Q**H */ +/* > */ +/* > where Q is a complex unitary matrix defined as the product of k */ +/* > elementary reflectors */ +/* > */ +/* > Q = H(k) . . . H(2) H(1) */ +/* > */ +/* > as returned by ZGEQLF. Q is of order M if SIDE = 'L' and of order N */ +/* > if SIDE = 'R'. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] SIDE */ +/* > \verbatim */ +/* > SIDE is CHARACTER*1 */ +/* > = 'L': apply Q or Q**H from the Left; */ +/* > = 'R': apply Q or Q**H from the Right. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TRANS */ +/* > \verbatim */ +/* > TRANS is CHARACTER*1 */ +/* > = 'N': No transpose, apply Q; */ +/* > = 'C': Conjugate transpose, apply Q**H. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix C. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix C. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > The number of elementary reflectors whose product defines */ +/* > the matrix Q. */ +/* > If SIDE = 'L', M >= K >= 0; */ +/* > if SIDE = 'R', N >= K >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is COMPLEX*16 array, dimension (LDA,K) */ +/* > The i-th column must contain the vector which defines the */ +/* > elementary reflector H(i), for i = 1,2,...,k, as returned by */ +/* > ZGEQLF in the last k columns of its array argument A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. */ +/* > If SIDE = 'L', LDA >= max(1,M); */ +/* > if SIDE = 'R', LDA >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TAU */ +/* > \verbatim */ +/* > TAU is COMPLEX*16 array, dimension (K) */ +/* > TAU(i) must contain the scalar factor of the elementary */ +/* > reflector H(i), as returned by ZGEQLF. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] C */ +/* > \verbatim */ +/* > C is COMPLEX*16 array, dimension (LDC,N) */ +/* > On entry, the M-by-N matrix C. */ +/* > On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDC */ +/* > \verbatim */ +/* > LDC is INTEGER */ +/* > The leading dimension of the array C. LDC >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) */ +/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LWORK */ +/* > \verbatim */ +/* > LWORK is INTEGER */ +/* > The dimension of the array WORK. */ +/* > If SIDE = 'L', LWORK >= max(1,N); */ +/* > if SIDE = 'R', LWORK >= max(1,M). */ +/* > For good performance, LWORK should generally be larger. */ +/* > */ +/* > If LWORK = -1, then a workspace query is assumed; the routine */ +/* > only calculates the optimal size of the WORK array, returns */ +/* > this value as the first entry of the WORK array, and no error */ +/* > message related to LWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16OTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int zunmql_(char *side, char *trans, integer *m, integer *n, + integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, + doublecomplex *c__, integer *ldc, doublecomplex *work, integer *lwork, + integer *info, ftnlen side_len, ftnlen trans_len) +{ + /* System generated locals */ + address a__1[2]; + integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4, + i__5; + char ch__1[2]; + + /* Builtin functions */ + /* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen); + + /* Local variables */ + integer i__, i1, i2, i3, ib, nb, mi, ni, nq, nw, iwt; + logical left; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + integer nbmin, iinfo; + extern /* Subroutine */ int zunm2l_(char *, char *, integer *, integer *, + integer *, doublecomplex *, integer *, doublecomplex *, + doublecomplex *, integer *, doublecomplex *, integer *, ftnlen, + ftnlen), xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *, + integer *, integer *, integer *, doublecomplex *, integer *, + doublecomplex *, integer *, doublecomplex *, integer *, + doublecomplex *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + logical notran; + integer ldwork; + extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *, + doublecomplex *, integer *, doublecomplex *, doublecomplex *, + integer *, ftnlen, ftnlen); + integer lwkopt; + logical lquery; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --tau; + c_dim1 = *ldc; + c_offset = 1 + c_dim1; + c__ -= c_offset; + --work; + + /* Function Body */ + *info = 0; + left = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); + notran = lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1); + lquery = *lwork == -1; + +/* NQ is the order of Q and NW is the minimum dimension of WORK */ + + if (left) { + nq = *m; + nw = max(1,*n); + } else { + nq = *n; + nw = max(1,*m); + } + if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + *info = -1; + } else if (! notran && ! lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { + *info = -2; + } else if (*m < 0) { + *info = -3; + } else if (*n < 0) { + *info = -4; + } else if (*k < 0 || *k > nq) { + *info = -5; + } else if (*lda < max(1,nq)) { + *info = -7; + } else if (*ldc < max(1,*m)) { + *info = -10; + } else if (*lwork < nw && ! lquery) { + *info = -12; + } + + if (*info == 0) { + +/* Compute the workspace requirements */ + + if (*m == 0 || *n == 0) { + lwkopt = 1; + } else { +/* Computing MIN */ +/* Writing concatenation */ + i__3[0] = 1, a__1[0] = side; + i__3[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + i__1 = 64, i__2 = ilaenv_(&c__1, (char *)"ZUNMQL", ch__1, m, n, k, &c_n1, + (ftnlen)6, (ftnlen)2); + nb = min(i__1,i__2); + lwkopt = nw * nb + 4160; + } + work[1].r = (doublereal) lwkopt, work[1].i = 0.; + } + + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"ZUNMQL", &i__1, (ftnlen)6); + return 0; + } else if (lquery) { + return 0; + } + +/* Quick return if possible */ + + if (*m == 0 || *n == 0) { + return 0; + } + + nbmin = 2; + ldwork = nw; + if (nb > 1 && nb < *k) { + if (*lwork < lwkopt) { + nb = (*lwork - 4160) / ldwork; +/* Computing MAX */ +/* Writing concatenation */ + i__3[0] = 1, a__1[0] = side; + i__3[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"ZUNMQL", ch__1, m, n, k, &c_n1, ( + ftnlen)6, (ftnlen)2); + nbmin = max(i__1,i__2); + } + } + + if (nb < nbmin || nb >= *k) { + +/* Use unblocked code */ + + zunm2l_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[ + c_offset], ldc, &work[1], &iinfo, (ftnlen)1, (ftnlen)1); + } else { + +/* Use blocked code */ + + iwt = nw * nb + 1; + if (left && notran || ! left && ! notran) { + i1 = 1; + i2 = *k; + i3 = nb; + } else { + i1 = (*k - 1) / nb * nb + 1; + i2 = 1; + i3 = -nb; + } + + if (left) { + ni = *n; + } else { + mi = *m; + } + + i__1 = i2; + i__2 = i3; + for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { +/* Computing MIN */ + i__4 = nb, i__5 = *k - i__ + 1; + ib = min(i__4,i__5); + +/* Form the triangular factor of the block reflector */ +/* H = H(i+ib-1) . . . H(i+1) H(i) */ + + i__4 = nq - *k + i__ + ib - 1; + zlarft_((char *)"Backward", (char *)"Columnwise", &i__4, &ib, &a[i__ * a_dim1 + 1] + , lda, &tau[i__], &work[iwt], &c__65, (ftnlen)8, (ftnlen) + 10); + if (left) { + +/* H or H**H is applied to C(1:m-k+i+ib-1,1:n) */ + + mi = *m - *k + i__ + ib - 1; + } else { + +/* H or H**H is applied to C(1:m,1:n-k+i+ib-1) */ + + ni = *n - *k + i__ + ib - 1; + } + +/* Apply H or H**H */ + + zlarfb_(side, trans, (char *)"Backward", (char *)"Columnwise", &mi, &ni, &ib, &a[ + i__ * a_dim1 + 1], lda, &work[iwt], &c__65, &c__[c_offset] + , ldc, &work[1], &ldwork, (ftnlen)1, (ftnlen)1, (ftnlen)8, + (ftnlen)10); +/* L10: */ + } + } + work[1].r = (doublereal) lwkopt, work[1].i = 0.; + return 0; + +/* End of ZUNMQL */ + +} /* zunmql_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zunmqr.cpp b/lib/linalg/zunmqr.cpp new file mode 100644 index 0000000000..dc127fe1aa --- /dev/null +++ b/lib/linalg/zunmqr.cpp @@ -0,0 +1,420 @@ +/* fortran/zunmqr.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c_n1 = -1; +static integer c__2 = 2; +static integer c__65 = 65; + +/* > \brief \b ZUNMQR */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZUNMQR + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZUNMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, */ +/* WORK, LWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER SIDE, TRANS */ +/* INTEGER INFO, K, LDA, LDC, LWORK, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZUNMQR overwrites the general complex M-by-N matrix C with */ +/* > */ +/* > SIDE = 'L' SIDE = 'R' */ +/* > TRANS = 'N': Q * C C * Q */ +/* > TRANS = 'C': Q**H * C C * Q**H */ +/* > */ +/* > where Q is a complex unitary matrix defined as the product of k */ +/* > elementary reflectors */ +/* > */ +/* > Q = H(1) H(2) . . . H(k) */ +/* > */ +/* > as returned by ZGEQRF. Q is of order M if SIDE = 'L' and of order N */ +/* > if SIDE = 'R'. */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] SIDE */ +/* > \verbatim */ +/* > SIDE is CHARACTER*1 */ +/* > = 'L': apply Q or Q**H from the Left; */ +/* > = 'R': apply Q or Q**H from the Right. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TRANS */ +/* > \verbatim */ +/* > TRANS is CHARACTER*1 */ +/* > = 'N': No transpose, apply Q; */ +/* > = 'C': Conjugate transpose, apply Q**H. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix C. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix C. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] K */ +/* > \verbatim */ +/* > K is INTEGER */ +/* > The number of elementary reflectors whose product defines */ +/* > the matrix Q. */ +/* > If SIDE = 'L', M >= K >= 0; */ +/* > if SIDE = 'R', N >= K >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is COMPLEX*16 array, dimension (LDA,K) */ +/* > The i-th column must contain the vector which defines the */ +/* > elementary reflector H(i), for i = 1,2,...,k, as returned by */ +/* > ZGEQRF in the first k columns of its array argument A. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. */ +/* > If SIDE = 'L', LDA >= max(1,M); */ +/* > if SIDE = 'R', LDA >= max(1,N). */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TAU */ +/* > \verbatim */ +/* > TAU is COMPLEX*16 array, dimension (K) */ +/* > TAU(i) must contain the scalar factor of the elementary */ +/* > reflector H(i), as returned by ZGEQRF. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] C */ +/* > \verbatim */ +/* > C is COMPLEX*16 array, dimension (LDC,N) */ +/* > On entry, the M-by-N matrix C. */ +/* > On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDC */ +/* > \verbatim */ +/* > LDC is INTEGER */ +/* > The leading dimension of the array C. LDC >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) */ +/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LWORK */ +/* > \verbatim */ +/* > LWORK is INTEGER */ +/* > The dimension of the array WORK. */ +/* > If SIDE = 'L', LWORK >= max(1,N); */ +/* > if SIDE = 'R', LWORK >= max(1,M). */ +/* > For good performance, LWORK should generally be larger. */ +/* > */ +/* > If LWORK = -1, then a workspace query is assumed; the routine */ +/* > only calculates the optimal size of the WORK array, returns */ +/* > this value as the first entry of the WORK array, and no error */ +/* > message related to LWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16OTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int zunmqr_(char *side, char *trans, integer *m, integer *n, + integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, + doublecomplex *c__, integer *ldc, doublecomplex *work, integer *lwork, + integer *info, ftnlen side_len, ftnlen trans_len) +{ + /* System generated locals */ + address a__1[2]; + integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4, + i__5; + char ch__1[2]; + + /* Builtin functions */ + /* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen); + + /* Local variables */ + integer i__, i1, i2, i3, ib, ic, jc, nb, mi, ni, nq, nw, iwt; + logical left; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + integer nbmin, iinfo; + extern /* Subroutine */ int zunm2r_(char *, char *, integer *, integer *, + integer *, doublecomplex *, integer *, doublecomplex *, + doublecomplex *, integer *, doublecomplex *, integer *, ftnlen, + ftnlen), xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *, + integer *, integer *, integer *, doublecomplex *, integer *, + doublecomplex *, integer *, doublecomplex *, integer *, + doublecomplex *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + logical notran; + integer ldwork; + extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *, + doublecomplex *, integer *, doublecomplex *, doublecomplex *, + integer *, ftnlen, ftnlen); + integer lwkopt; + logical lquery; + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Parameters .. */ +/* .. */ +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --tau; + c_dim1 = *ldc; + c_offset = 1 + c_dim1; + c__ -= c_offset; + --work; + + /* Function Body */ + *info = 0; + left = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); + notran = lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1); + lquery = *lwork == -1; + +/* NQ is the order of Q and NW is the minimum dimension of WORK */ + + if (left) { + nq = *m; + nw = max(1,*n); + } else { + nq = *n; + nw = max(1,*m); + } + if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + *info = -1; + } else if (! notran && ! lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { + *info = -2; + } else if (*m < 0) { + *info = -3; + } else if (*n < 0) { + *info = -4; + } else if (*k < 0 || *k > nq) { + *info = -5; + } else if (*lda < max(1,nq)) { + *info = -7; + } else if (*ldc < max(1,*m)) { + *info = -10; + } else if (*lwork < nw && ! lquery) { + *info = -12; + } + + if (*info == 0) { + +/* Compute the workspace requirements */ + +/* Computing MIN */ +/* Writing concatenation */ + i__3[0] = 1, a__1[0] = side; + i__3[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + i__1 = 64, i__2 = ilaenv_(&c__1, (char *)"ZUNMQR", ch__1, m, n, k, &c_n1, ( + ftnlen)6, (ftnlen)2); + nb = min(i__1,i__2); + lwkopt = nw * nb + 4160; + work[1].r = (doublereal) lwkopt, work[1].i = 0.; + } + + if (*info != 0) { + i__1 = -(*info); + xerbla_((char *)"ZUNMQR", &i__1, (ftnlen)6); + return 0; + } else if (lquery) { + return 0; + } + +/* Quick return if possible */ + + if (*m == 0 || *n == 0 || *k == 0) { + work[1].r = 1., work[1].i = 0.; + return 0; + } + + nbmin = 2; + ldwork = nw; + if (nb > 1 && nb < *k) { + if (*lwork < lwkopt) { + nb = (*lwork - 4160) / ldwork; +/* Computing MAX */ +/* Writing concatenation */ + i__3[0] = 1, a__1[0] = side; + i__3[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"ZUNMQR", ch__1, m, n, k, &c_n1, ( + ftnlen)6, (ftnlen)2); + nbmin = max(i__1,i__2); + } + } + + if (nb < nbmin || nb >= *k) { + +/* Use unblocked code */ + + zunm2r_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[ + c_offset], ldc, &work[1], &iinfo, (ftnlen)1, (ftnlen)1); + } else { + +/* Use blocked code */ + + iwt = nw * nb + 1; + if (left && ! notran || ! left && notran) { + i1 = 1; + i2 = *k; + i3 = nb; + } else { + i1 = (*k - 1) / nb * nb + 1; + i2 = 1; + i3 = -nb; + } + + if (left) { + ni = *n; + jc = 1; + } else { + mi = *m; + ic = 1; + } + + i__1 = i2; + i__2 = i3; + for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { +/* Computing MIN */ + i__4 = nb, i__5 = *k - i__ + 1; + ib = min(i__4,i__5); + +/* Form the triangular factor of the block reflector */ +/* H = H(i) H(i+1) . . . H(i+ib-1) */ + + i__4 = nq - i__ + 1; + zlarft_((char *)"Forward", (char *)"Columnwise", &i__4, &ib, &a[i__ + i__ * + a_dim1], lda, &tau[i__], &work[iwt], &c__65, (ftnlen)7, ( + ftnlen)10); + if (left) { + +/* H or H**H is applied to C(i:m,1:n) */ + + mi = *m - i__ + 1; + ic = i__; + } else { + +/* H or H**H is applied to C(1:m,i:n) */ + + ni = *n - i__ + 1; + jc = i__; + } + +/* Apply H or H**H */ + + zlarfb_(side, trans, (char *)"Forward", (char *)"Columnwise", &mi, &ni, &ib, &a[ + i__ + i__ * a_dim1], lda, &work[iwt], &c__65, &c__[ic + + jc * c_dim1], ldc, &work[1], &ldwork, (ftnlen)1, (ftnlen) + 1, (ftnlen)7, (ftnlen)10); +/* L10: */ + } + } + work[1].r = (doublereal) lwkopt, work[1].i = 0.; + return 0; + +/* End of ZUNMQR */ + +} /* zunmqr_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/zunmtr.cpp b/lib/linalg/zunmtr.cpp new file mode 100644 index 0000000000..ab5e7eacb8 --- /dev/null +++ b/lib/linalg/zunmtr.cpp @@ -0,0 +1,397 @@ +/* fortran/zunmtr.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* Table of constant values */ + +static integer c__1 = 1; +static integer c_n1 = -1; +static integer c__2 = 2; + +/* > \brief \b ZUNMTR */ + +/* =========== DOCUMENTATION =========== */ + +/* Online html documentation available at */ +/* http://www.netlib.org/lapack/explore-html/ */ + +/* > \htmlonly */ +/* > Download ZUNMTR + dependencies */ +/* > */ +/* > [TGZ] */ +/* > */ +/* > [ZIP] */ +/* > */ +/* > [TXT] */ +/* > \endhtmlonly */ + +/* Definition: */ +/* =========== */ + +/* SUBROUTINE ZUNMTR( SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC, */ +/* WORK, LWORK, INFO ) */ + +/* .. Scalar Arguments .. */ +/* CHARACTER SIDE, TRANS, UPLO */ +/* INTEGER INFO, LDA, LDC, LWORK, M, N */ +/* .. */ +/* .. Array Arguments .. */ +/* COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) */ +/* .. */ + + +/* > \par Purpose: */ +/* ============= */ +/* > */ +/* > \verbatim */ +/* > */ +/* > ZUNMTR overwrites the general complex M-by-N matrix C with */ +/* > */ +/* > SIDE = 'L' SIDE = 'R' */ +/* > TRANS = 'N': Q * C C * Q */ +/* > TRANS = 'C': Q**H * C C * Q**H */ +/* > */ +/* > where Q is a complex unitary matrix of order nq, with nq = m if */ +/* > SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of */ +/* > nq-1 elementary reflectors, as returned by ZHETRD: */ +/* > */ +/* > if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1); */ +/* > */ +/* > if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1). */ +/* > \endverbatim */ + +/* Arguments: */ +/* ========== */ + +/* > \param[in] SIDE */ +/* > \verbatim */ +/* > SIDE is CHARACTER*1 */ +/* > = 'L': apply Q or Q**H from the Left; */ +/* > = 'R': apply Q or Q**H from the Right. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] UPLO */ +/* > \verbatim */ +/* > UPLO is CHARACTER*1 */ +/* > = 'U': Upper triangle of A contains elementary reflectors */ +/* > from ZHETRD; */ +/* > = 'L': Lower triangle of A contains elementary reflectors */ +/* > from ZHETRD. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TRANS */ +/* > \verbatim */ +/* > TRANS is CHARACTER*1 */ +/* > = 'N': No transpose, apply Q; */ +/* > = 'C': Conjugate transpose, apply Q**H. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] M */ +/* > \verbatim */ +/* > M is INTEGER */ +/* > The number of rows of the matrix C. M >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] N */ +/* > \verbatim */ +/* > N is INTEGER */ +/* > The number of columns of the matrix C. N >= 0. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is COMPLEX*16 array, dimension */ +/* > (LDA,M) if SIDE = 'L' */ +/* > (LDA,N) if SIDE = 'R' */ +/* > The vectors which define the elementary reflectors, as */ +/* > returned by ZHETRD. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDA */ +/* > \verbatim */ +/* > LDA is INTEGER */ +/* > The leading dimension of the array A. */ +/* > LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] TAU */ +/* > \verbatim */ +/* > TAU is COMPLEX*16 array, dimension */ +/* > (M-1) if SIDE = 'L' */ +/* > (N-1) if SIDE = 'R' */ +/* > TAU(i) must contain the scalar factor of the elementary */ +/* > reflector H(i), as returned by ZHETRD. */ +/* > \endverbatim */ +/* > */ +/* > \param[in,out] C */ +/* > \verbatim */ +/* > C is COMPLEX*16 array, dimension (LDC,N) */ +/* > On entry, the M-by-N matrix C. */ +/* > On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LDC */ +/* > \verbatim */ +/* > LDC is INTEGER */ +/* > The leading dimension of the array C. LDC >= max(1,M). */ +/* > \endverbatim */ +/* > */ +/* > \param[out] WORK */ +/* > \verbatim */ +/* > WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) */ +/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ +/* > \endverbatim */ +/* > */ +/* > \param[in] LWORK */ +/* > \verbatim */ +/* > LWORK is INTEGER */ +/* > The dimension of the array WORK. */ +/* > If SIDE = 'L', LWORK >= max(1,N); */ +/* > if SIDE = 'R', LWORK >= max(1,M). */ +/* > For optimum performance LWORK >= N*NB if SIDE = 'L', and */ +/* > LWORK >=M*NB if SIDE = 'R', where NB is the optimal */ +/* > blocksize. */ +/* > */ +/* > If LWORK = -1, then a workspace query is assumed; the routine */ +/* > only calculates the optimal size of the WORK array, returns */ +/* > this value as the first entry of the WORK array, and no error */ +/* > message related to LWORK is issued by XERBLA. */ +/* > \endverbatim */ +/* > */ +/* > \param[out] INFO */ +/* > \verbatim */ +/* > INFO is INTEGER */ +/* > = 0: successful exit */ +/* > < 0: if INFO = -i, the i-th argument had an illegal value */ +/* > \endverbatim */ + +/* Authors: */ +/* ======== */ + +/* > \author Univ. of Tennessee */ +/* > \author Univ. of California Berkeley */ +/* > \author Univ. of Colorado Denver */ +/* > \author NAG Ltd. */ + +/* > \ingroup complex16OTHERcomputational */ + +/* ===================================================================== */ +/* Subroutine */ int zunmtr_(char *side, char *uplo, char *trans, integer *m, + integer *n, doublecomplex *a, integer *lda, doublecomplex *tau, + doublecomplex *c__, integer *ldc, doublecomplex *work, integer *lwork, + integer *info, ftnlen side_len, ftnlen uplo_len, ftnlen trans_len) +{ + /* System generated locals */ + address a__1[2]; + integer a_dim1, a_offset, c_dim1, c_offset, i__1[2], i__2, i__3; + char ch__1[2]; + + /* Builtin functions */ + /* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen); + + /* Local variables */ + integer i1, i2, nb, mi, ni, nq, nw; + logical left; + extern logical lsame_(char *, char *, ftnlen, ftnlen); + integer iinfo; + logical upper; + extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + integer lwkopt; + logical lquery; + extern /* Subroutine */ int zunmql_(char *, char *, integer *, integer *, + integer *, doublecomplex *, integer *, doublecomplex *, + doublecomplex *, integer *, doublecomplex *, integer *, integer *, + ftnlen, ftnlen), zunmqr_(char *, char *, integer *, integer *, + integer *, doublecomplex *, integer *, doublecomplex *, + doublecomplex *, integer *, doublecomplex *, integer *, integer *, + ftnlen, ftnlen); + + +/* -- LAPACK computational routine -- */ +/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ +/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* .. Array Arguments .. */ +/* .. */ + +/* ===================================================================== */ + +/* .. Local Scalars .. */ +/* .. */ +/* .. External Functions .. */ +/* .. */ +/* .. External Subroutines .. */ +/* .. */ +/* .. Intrinsic Functions .. */ +/* .. */ +/* .. Executable Statements .. */ + +/* Test the input arguments */ + + /* Parameter adjustments */ + a_dim1 = *lda; + a_offset = 1 + a_dim1; + a -= a_offset; + --tau; + c_dim1 = *ldc; + c_offset = 1 + c_dim1; + c__ -= c_offset; + --work; + + /* Function Body */ + *info = 0; + left = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); + upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); + lquery = *lwork == -1; + +/* NQ is the order of Q and NW is the minimum dimension of WORK */ + + if (left) { + nq = *m; + nw = max(1,*n); + } else { + nq = *n; + nw = max(1,*m); + } + if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + *info = -1; + } else if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + *info = -2; + } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, + (char *)"C", (ftnlen)1, (ftnlen)1)) { + *info = -3; + } else if (*m < 0) { + *info = -4; + } else if (*n < 0) { + *info = -5; + } else if (*lda < max(1,nq)) { + *info = -7; + } else if (*ldc < max(1,*m)) { + *info = -10; + } else if (*lwork < nw && ! lquery) { + *info = -12; + } + + if (*info == 0) { + if (upper) { + if (left) { +/* Writing concatenation */ + i__1[0] = 1, a__1[0] = side; + i__1[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); + i__2 = *m - 1; + i__3 = *m - 1; + nb = ilaenv_(&c__1, (char *)"ZUNMQL", ch__1, &i__2, n, &i__3, &c_n1, ( + ftnlen)6, (ftnlen)2); + } else { +/* Writing concatenation */ + i__1[0] = 1, a__1[0] = side; + i__1[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); + i__2 = *n - 1; + i__3 = *n - 1; + nb = ilaenv_(&c__1, (char *)"ZUNMQL", ch__1, m, &i__2, &i__3, &c_n1, ( + ftnlen)6, (ftnlen)2); + } + } else { + if (left) { +/* Writing concatenation */ + i__1[0] = 1, a__1[0] = side; + i__1[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); + i__2 = *m - 1; + i__3 = *m - 1; + nb = ilaenv_(&c__1, (char *)"ZUNMQR", ch__1, &i__2, n, &i__3, &c_n1, ( + ftnlen)6, (ftnlen)2); + } else { +/* Writing concatenation */ + i__1[0] = 1, a__1[0] = side; + i__1[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); + i__2 = *n - 1; + i__3 = *n - 1; + nb = ilaenv_(&c__1, (char *)"ZUNMQR", ch__1, m, &i__2, &i__3, &c_n1, ( + ftnlen)6, (ftnlen)2); + } + } + lwkopt = nw * nb; + work[1].r = (doublereal) lwkopt, work[1].i = 0.; + } + + if (*info != 0) { + i__2 = -(*info); + xerbla_((char *)"ZUNMTR", &i__2, (ftnlen)6); + return 0; + } else if (lquery) { + return 0; + } + +/* Quick return if possible */ + + if (*m == 0 || *n == 0 || nq == 1) { + work[1].r = 1., work[1].i = 0.; + return 0; + } + + if (left) { + mi = *m - 1; + ni = *n; + } else { + mi = *m; + ni = *n - 1; + } + + if (upper) { + +/* Q was determined by a call to ZHETRD with UPLO = 'U' */ + + i__2 = nq - 1; + zunmql_(side, trans, &mi, &ni, &i__2, &a[(a_dim1 << 1) + 1], lda, & + tau[1], &c__[c_offset], ldc, &work[1], lwork, &iinfo, (ftnlen) + 1, (ftnlen)1); + } else { + +/* Q was determined by a call to ZHETRD with UPLO = 'L' */ + + if (left) { + i1 = 2; + i2 = 1; + } else { + i1 = 1; + i2 = 2; + } + i__2 = nq - 1; + zunmqr_(side, trans, &mi, &ni, &i__2, &a[a_dim1 + 2], lda, &tau[1], & + c__[i1 + i2 * c_dim1], ldc, &work[1], lwork, &iinfo, (ftnlen) + 1, (ftnlen)1); + } + work[1].r = (doublereal) lwkopt, work[1].i = 0.; + return 0; + +/* End of ZUNMTR */ + +} /* zunmtr_ */ + +#ifdef __cplusplus + } +#endif From b0e8ec47da492c031a61c8024bc4496e3a60ff3c Mon Sep 17 00:00:00 2001 From: Axel Kohlmeyer Date: Wed, 28 Dec 2022 13:45:13 -0500 Subject: [PATCH 24/47] update manual for linalg being C++ now. --- doc/src/Build_extras.rst | 42 ++++++++++++++++++++-------------------- 1 file changed, 21 insertions(+), 21 deletions(-) diff --git a/doc/src/Build_extras.rst b/doc/src/Build_extras.rst index 910dccbb8a..8f400519f1 100644 --- a/doc/src/Build_extras.rst +++ b/doc/src/Build_extras.rst @@ -858,11 +858,11 @@ library. .. code-block:: bash - $ make lib-latte # print help message - $ make lib-latte args="-b" # download and build in lib/latte/LATTE-master - $ make lib-latte args="-p $HOME/latte" # use existing LATTE installation in $HOME/latte - $ make lib-latte args="-b -m gfortran" # download and build in lib/latte and - # copy Makefile.lammps.gfortran to Makefile.lammps + $ make lib-latte # print help message + $ make lib-latte args="-b" # download and build in lib/latte/LATTE-master + $ make lib-latte args="-p $HOME/latte" # use existing LATTE installation in $HOME/latte + $ make lib-latte args="-b -m gfortran" # download and build in lib/latte and + # copy Makefile.lammps.gfortran to Makefile.lammps Note that 3 symbolic (soft) links, ``includelink`` and ``liblink`` and ``filelink.o``, are created in ``lib/latte`` to point to @@ -1208,10 +1208,10 @@ The ATC package requires the MANYBODY package also be installed. .. code-block:: bash - $ make lib-linalg # print help message - $ make lib-linalg args="-m serial" # build with GNU Fortran compiler (settings as with "make serial") - $ make lib-linalg args="-m mpi" # build with default MPI Fortran compiler (settings as with "make mpi") - $ make lib-linalg args="-m gfortran" # build with GNU Fortran compiler + $ make lib-linalg # print help message + $ make lib-linalg args="-m serial" # build with GNU C++ compiler (settings as with "make serial") + $ make lib-linalg args="-m mpi" # build with default MPI C++ compiler (settings as with "make mpi") + $ make lib-linalg args="-m g++" # build with GNU C++ compiler ---------- @@ -1259,10 +1259,10 @@ AWPMD package .. code-block:: bash - $ make lib-linalg # print help message - $ make lib-linalg args="-m serial" # build with GNU Fortran compiler (settings as with "make serial") - $ make lib-linalg args="-m mpi" # build with default MPI Fortran compiler (settings as with "make mpi") - $ make lib-linalg args="-m gfortran" # build with GNU Fortran compiler + $ make lib-linalg # print help message + $ make lib-linalg args="-m serial" # build with GNU C++ compiler (settings as with "make serial") + $ make lib-linalg args="-m mpi" # build with default MPI C++ compiler (settings as with "make mpi") + $ make lib-linalg args="-m g++" # build with GNU C++ compiler ---------- @@ -1363,10 +1363,10 @@ This package depends on the KSPACE package. .. code-block:: bash - $ make lib-linalg # print help message - $ make lib-linalg args="-m serial" # build with GNU Fortran compiler (settings as with "make serial") - $ make lib-linalg args="-m mpi" # build with default MPI Fortran compiler (settings as with "make mpi") - $ make lib-linalg args="-m gfortran" # build with GNU Fortran compiler + $ make lib-linalg # print help message + $ make lib-linalg args="-m serial" # build with GNU C++ compiler (settings as with "make serial") + $ make lib-linalg args="-m mpi" # build with default MPI C++ compiler (settings as with "make mpi") + $ make lib-linalg args="-m g++" # build with GNU C++ compiler The package itself is activated with ``make yes-KSPACE`` and ``make yes-ELECTRODE`` @@ -1447,10 +1447,10 @@ ML-POD package .. code-block:: bash - $ make lib-linalg # print help message - $ make lib-linalg args="-m serial" # build with GNU Fortran compiler (settings as with "make serial") - $ make lib-linalg args="-m mpi" # build with default MPI Fortran compiler (settings as with "make mpi") - $ make lib-linalg args="-m gfortran" # build with GNU Fortran compiler + $ make lib-linalg # print help message + $ make lib-linalg args="-m serial" # build with GNU C++ compiler (settings as with "make serial") + $ make lib-linalg args="-m mpi" # build with default MPI C++ compiler (settings as with "make mpi") + $ make lib-linalg args="-m g++" # build with GNU C++ compiler The package itself is activated with ``make yes-ML-POD``. From 52fb2e8156da0583d83cfc0e896bb361b11a51bb Mon Sep 17 00:00:00 2001 From: Axel Kohlmeyer Date: Wed, 28 Dec 2022 13:45:40 -0500 Subject: [PATCH 25/47] don't need to link to Fortran runtime with linalg anymore --- lib/atc/Makefile.lammps.linalg | 2 +- lib/awpmd/Makefile.lammps.linalg | 2 +- lib/electrode/Makefile.lammps.linalg | 2 +- lib/mlpod/Makefile.lammps.linalg | 2 +- 4 files changed, 4 insertions(+), 4 deletions(-) diff --git a/lib/atc/Makefile.lammps.linalg b/lib/atc/Makefile.lammps.linalg index 930ee6357b..ddbab36648 100644 --- a/lib/atc/Makefile.lammps.linalg +++ b/lib/atc/Makefile.lammps.linalg @@ -1,6 +1,6 @@ # Settings that the LAMMPS build will import when this package library is used atc_SYSINC = -atc_SYSLIB = -llinalg -lgfortran +atc_SYSLIB = -llinalg atc_SYSPATH = -L../../lib/linalg$(LIBOBJDIR) diff --git a/lib/awpmd/Makefile.lammps.linalg b/lib/awpmd/Makefile.lammps.linalg index 1d986da5d7..ce10c3ffa0 100644 --- a/lib/awpmd/Makefile.lammps.linalg +++ b/lib/awpmd/Makefile.lammps.linalg @@ -1,5 +1,5 @@ # Settings that the LAMMPS build will import when this package library is used awpmd_SYSINC = -awpmd_SYSLIB = -llinalg -lgfortran +awpmd_SYSLIB = -llinalg awpmd_SYSPATH = -L../../lib/linalg$(LIBOBJDIR) diff --git a/lib/electrode/Makefile.lammps.linalg b/lib/electrode/Makefile.lammps.linalg index e82066110e..0e03dd9bd7 100644 --- a/lib/electrode/Makefile.lammps.linalg +++ b/lib/electrode/Makefile.lammps.linalg @@ -1,5 +1,5 @@ # Settings that the LAMMPS build will import when this package library is used electrode_SYSINC = -electrode_SYSLIB = -llinalg -lgfortran +electrode_SYSLIB = -llinalg electrode_SYSPATH = -L../../lib/linalg$(LIBOBJDIR) diff --git a/lib/mlpod/Makefile.lammps.linalg b/lib/mlpod/Makefile.lammps.linalg index cb4d78df99..f37381464d 100644 --- a/lib/mlpod/Makefile.lammps.linalg +++ b/lib/mlpod/Makefile.lammps.linalg @@ -1,5 +1,5 @@ # Settings that the LAMMPS build will import when this package library is used mlpod_SYSINC = -mlpod_SYSLIB = -llinalg -lgfortran +mlpod_SYSLIB = -llinalg mlpod_SYSPATH = -L../../lib/linalg$(LIBOBJDIR) From 119fae3b8cc03989f2f15b332545359d07012244 Mon Sep 17 00:00:00 2001 From: Axel Kohlmeyer Date: Wed, 28 Dec 2022 13:45:58 -0500 Subject: [PATCH 26/47] remove unused code --- lib/linalg/Makefile.g++ | 5 ----- lib/linalg/Makefile.mpi | 5 ----- 2 files changed, 10 deletions(-) diff --git a/lib/linalg/Makefile.g++ b/lib/linalg/Makefile.g++ index b1e18e8fd3..eb482b11b8 100644 --- a/lib/linalg/Makefile.g++ +++ b/lib/linalg/Makefile.g++ @@ -8,8 +8,6 @@ SHELL = /bin/sh SRC = $(wildcard *.cpp) -FILES = $(SRC) Makefile.* README - # ------ DEFINITIONS ------ LIB = liblinalg.a @@ -40,6 +38,3 @@ lib: $(OBJ) clean: -rm -f *.o *~ $(LIB) -tar: - -tar -czvf ../linalg.tar.gz $(FILES) - diff --git a/lib/linalg/Makefile.mpi b/lib/linalg/Makefile.mpi index 567653cebc..d0542d73fb 100644 --- a/lib/linalg/Makefile.mpi +++ b/lib/linalg/Makefile.mpi @@ -8,8 +8,6 @@ SHELL = /bin/sh SRC = $(wildcard *.cpp) -FILES = $(SRC) Makefile.* README - # ------ DEFINITIONS ------ LIB = liblinalg.a @@ -40,6 +38,3 @@ lib: $(OBJ) clean: -rm -f *.o *~ $(LIB) -tar: - -tar -czvf ../linalg.tar.gz $(FILES) - From a894cbfbb7006fd54af5b74b52dbfbec35fa464e Mon Sep 17 00:00:00 2001 From: Axel Kohlmeyer Date: Wed, 28 Dec 2022 13:46:08 -0500 Subject: [PATCH 27/47] update linalg README --- lib/linalg/README | 7 +++++-- 1 file changed, 5 insertions(+), 2 deletions(-) diff --git a/lib/linalg/README b/lib/linalg/README index e3b817cacc..68f17d9986 100644 --- a/lib/linalg/README +++ b/lib/linalg/README @@ -1,7 +1,10 @@ This directory has generic BLAS and LAPACK source files needed by the ATC, AWPMD, ELECTRODE, LATTE, and ML-POD packages (and possibly by other packages) in the future that can be used instead of platform or vendor -optimized BLAS/LAPACK library. +optimized BLAS/LAPACK library. For increased portability, the +BLAS/LAPACK source files have been translated to C++ with f2c. A few +subroutines using Fortran runtime functions have been re-implemented +in C++. Please see the convert.sh script for how the conversion was done. Note that this is an *incomplete* subset of full BLAS/LAPACK. @@ -20,7 +23,7 @@ can do it manually by following the instructions below. Build the library using one of the provided Makefile.* files or create your own, specific to your compiler and system. For example: -make -f Makefile.gfortran +make -f Makefile.g++ When you are done building this library, one file should exist in this directory: From 1e8b2ad5a07fd32e63b55d7d52e1264829b96bb4 Mon Sep 17 00:00:00 2001 From: Axel Kohlmeyer Date: Wed, 28 Dec 2022 13:47:11 -0500 Subject: [PATCH 28/47] whitespace fixes --- lib/linalg/dasum.cpp | 68 +- lib/linalg/daxpy.cpp | 88 +- lib/linalg/dbdsqr.cpp | 796 ++++---- lib/linalg/dcabs1.cpp | 16 +- lib/linalg/dcopy.cpp | 92 +- lib/linalg/ddot.cpp | 86 +- lib/linalg/dgebd2.cpp | 174 +- lib/linalg/dgebrd.cpp | 166 +- lib/linalg/dgecon.cpp | 112 +- lib/linalg/dgelq2.cpp | 68 +- lib/linalg/dgelqf.cpp | 140 +- lib/linalg/dgelsd.cpp | 586 +++--- lib/linalg/dgelss.cpp | 906 ++++----- lib/linalg/dgemm.cpp | 266 +-- lib/linalg/dgemv.cpp | 216 +-- lib/linalg/dgeqr2.cpp | 68 +- lib/linalg/dgeqrf.cpp | 156 +- lib/linalg/dger.cpp | 100 +- lib/linalg/dgesv.cpp | 46 +- lib/linalg/dgesvd.cpp | 4106 ++++++++++++++++++++-------------------- lib/linalg/dgetf2.cpp | 100 +- lib/linalg/dgetrf.cpp | 136 +- lib/linalg/dgetrf2.cpp | 158 +- lib/linalg/dgetri.cpp | 172 +- lib/linalg/dgetrs.cpp | 80 +- lib/linalg/dlabad.cpp | 20 +- lib/linalg/dlabrd.cpp | 392 ++-- lib/linalg/dlacn2.cpp | 112 +- lib/linalg/dlacpy.cpp | 60 +- lib/linalg/dladiv.cpp | 80 +- lib/linalg/dlae2.cpp | 50 +- lib/linalg/dlaed0.cpp | 336 ++-- lib/linalg/dlaed1.cpp | 102 +- lib/linalg/dlaed2.cpp | 294 +-- lib/linalg/dlaed3.cpp | 148 +- lib/linalg/dlaed4.cpp | 1150 +++++------ lib/linalg/dlaed5.cpp | 92 +- lib/linalg/dlaed6.cpp | 312 +-- lib/linalg/dlaed7.cpp | 148 +- lib/linalg/dlaed8.cpp | 276 +-- lib/linalg/dlaed9.cpp | 118 +- lib/linalg/dlaeda.cpp | 158 +- lib/linalg/dlaev2.cpp | 92 +- lib/linalg/dlals0.cpp | 354 ++-- lib/linalg/dlalsa.cpp | 274 +-- lib/linalg/dlalsd.cpp | 436 ++--- lib/linalg/dlamrg.cpp | 78 +- lib/linalg/dlange.cpp | 130 +- lib/linalg/dlanst.cpp | 106 +- lib/linalg/dlansy.cpp | 194 +- lib/linalg/dlapy2.cpp | 40 +- lib/linalg/dlapy3.cpp | 26 +- lib/linalg/dlarf.cpp | 102 +- lib/linalg/dlarfb.cpp | 648 +++---- lib/linalg/dlarfg.cpp | 90 +- lib/linalg/dlarft.cpp | 282 +-- lib/linalg/dlartg.cpp | 140 +- lib/linalg/dlas2.cpp | 82 +- lib/linalg/dlascl.cpp | 256 +-- lib/linalg/dlasd4.cpp | 1364 ++++++------- lib/linalg/dlasd5.cpp | 102 +- lib/linalg/dlasd6.cpp | 106 +- lib/linalg/dlasd7.cpp | 258 +-- lib/linalg/dlasd8.cpp | 168 +- lib/linalg/dlasda.cpp | 364 ++-- lib/linalg/dlasdq.cpp | 252 +-- lib/linalg/dlasdt.cpp | 44 +- lib/linalg/dlaset.cpp | 64 +- lib/linalg/dlasq1.cpp | 110 +- lib/linalg/dlasq2.cpp | 586 +++--- lib/linalg/dlasq3.cpp | 222 +-- lib/linalg/dlasq4.cpp | 430 ++--- lib/linalg/dlasq5.cpp | 444 ++--- lib/linalg/dlasq6.cpp | 152 +- lib/linalg/dlasr.cpp | 450 ++--- lib/linalg/dlasrt.cpp | 272 +-- lib/linalg/dlassq.cpp | 50 +- lib/linalg/dlasv2.cpp | 178 +- lib/linalg/dlaswp.cpp | 108 +- lib/linalg/dlatrd.cpp | 270 +-- lib/linalg/dlatrs.cpp | 760 ++++---- lib/linalg/dnrm2.cpp | 56 +- lib/linalg/dorg2l.cpp | 80 +- lib/linalg/dorg2r.cpp | 88 +- lib/linalg/dorgbr.cpp | 214 +-- lib/linalg/dorgl2.cpp | 98 +- lib/linalg/dorglq.cpp | 176 +- lib/linalg/dorgql.cpp | 188 +- lib/linalg/dorgqr.cpp | 176 +- lib/linalg/dorgtr.cpp | 164 +- lib/linalg/dorm2l.cpp | 94 +- lib/linalg/dorm2r.cpp | 102 +- lib/linalg/dormbr.cpp | 258 +-- lib/linalg/dorml2.cpp | 102 +- lib/linalg/dormlq.cpp | 208 +- lib/linalg/dormql.cpp | 198 +- lib/linalg/dormqr.cpp | 200 +- lib/linalg/dormtr.cpp | 196 +- lib/linalg/dposv.cpp | 50 +- lib/linalg/dpotf2.cpp | 134 +- lib/linalg/dpotrf.cpp | 180 +- lib/linalg/dpotrf2.cpp | 122 +- lib/linalg/dpotrs.cpp | 70 +- lib/linalg/drot.cpp | 66 +- lib/linalg/drscl.cpp | 44 +- lib/linalg/dscal.cpp | 72 +- lib/linalg/dstedc.cpp | 374 ++-- lib/linalg/dsteqr.cpp | 566 +++--- lib/linalg/dsterf.cpp | 402 ++-- lib/linalg/dswap.cpp | 104 +- lib/linalg/dsyev.cpp | 142 +- lib/linalg/dsyevd.cpp | 176 +- lib/linalg/dsygs2.cpp | 272 +-- lib/linalg/dsygst.cpp | 352 ++-- lib/linalg/dsygv.cpp | 148 +- lib/linalg/dsygvd.cpp | 142 +- lib/linalg/dsymm.cpp | 258 +-- lib/linalg/dsymv.cpp | 242 +-- lib/linalg/dsyr2.cpp | 196 +- lib/linalg/dsyr2k.cpp | 334 ++-- lib/linalg/dsyrk.cpp | 306 +-- lib/linalg/dsytd2.cpp | 156 +- lib/linalg/dsytrd.cpp | 186 +- lib/linalg/dtrmm.cpp | 418 ++-- lib/linalg/dtrmv.cpp | 314 +-- lib/linalg/dtrsm.cpp | 474 ++--- lib/linalg/dtrsv.cpp | 314 +-- lib/linalg/dtrti2.cpp | 104 +- lib/linalg/dtrtri.cpp | 152 +- lib/linalg/dznrm2.cpp | 80 +- lib/linalg/idamax.cpp | 58 +- lib/linalg/ieeeck.cpp | 74 +- lib/linalg/iladlc.cpp | 36 +- lib/linalg/iladlr.cpp | 38 +- lib/linalg/ilaenv.cpp | 872 ++++----- lib/linalg/ilazlc.cpp | 50 +- lib/linalg/ilazlr.cpp | 56 +- lib/linalg/iparmq.cpp | 206 +- lib/linalg/lmp_f2c.h | 170 +- lib/linalg/zaxpy.cpp | 84 +- lib/linalg/zcopy.cpp | 66 +- lib/linalg/zdotc.cpp | 78 +- lib/linalg/zdrot.cpp | 114 +- lib/linalg/zdscal.cpp | 62 +- lib/linalg/zgemm.cpp | 790 ++++---- lib/linalg/zgemv.cpp | 382 ++-- lib/linalg/zgerc.cpp | 140 +- lib/linalg/zheev.cpp | 148 +- lib/linalg/zheevd.cpp | 212 +-- lib/linalg/zhemv.cpp | 470 ++--- lib/linalg/zher2.cpp | 524 ++--- lib/linalg/zher2k.cpp | 840 ++++---- lib/linalg/zhetd2.cpp | 252 +-- lib/linalg/zhetrd.cpp | 206 +- lib/linalg/zhpr.cpp | 346 ++-- lib/linalg/zlacgv.cpp | 50 +- lib/linalg/zlacpy.cpp | 76 +- lib/linalg/zlacrm.cpp | 86 +- lib/linalg/zladiv.cpp | 24 +- lib/linalg/zlaed0.cpp | 224 +-- lib/linalg/zlaed7.cpp | 132 +- lib/linalg/zlaed8.cpp | 232 +-- lib/linalg/zlanhe.cpp | 244 +-- lib/linalg/zlarf.cpp | 110 +- lib/linalg/zlarfb.cpp | 764 ++++---- lib/linalg/zlarfg.cpp | 112 +- lib/linalg/zlarft.cpp | 372 ++-- lib/linalg/zlascl.cpp | 298 +-- lib/linalg/zlaset.cpp | 102 +- lib/linalg/zlasr.cpp | 762 ++++---- lib/linalg/zlassq.cpp | 74 +- lib/linalg/zlatrd.cpp | 396 ++-- lib/linalg/zpptrf.cpp | 140 +- lib/linalg/zpptri.cpp | 114 +- lib/linalg/zscal.cpp | 58 +- lib/linalg/zstedc.cpp | 364 ++-- lib/linalg/zsteqr.cpp | 576 +++--- lib/linalg/zswap.cpp | 82 +- lib/linalg/ztpmv.cpp | 760 ++++---- lib/linalg/ztpsv.cpp | 692 +++---- lib/linalg/ztptri.cpp | 174 +- lib/linalg/ztrmm.cpp | 876 ++++----- lib/linalg/ztrmv.cpp | 714 +++---- lib/linalg/zung2l.cpp | 102 +- lib/linalg/zung2r.cpp | 110 +- lib/linalg/zungl2.cpp | 130 +- lib/linalg/zungql.cpp | 198 +- lib/linalg/zungqr.cpp | 186 +- lib/linalg/zungtr.cpp | 188 +- lib/linalg/zunm2l.cpp | 116 +- lib/linalg/zunm2r.cpp | 124 +- lib/linalg/zunmql.cpp | 202 +- lib/linalg/zunmqr.cpp | 204 +- lib/linalg/zunmtr.cpp | 198 +- 194 files changed, 24511 insertions(+), 24511 deletions(-) diff --git a/lib/linalg/dasum.cpp b/lib/linalg/dasum.cpp index 0119bed6fd..93e40126c0 100644 --- a/lib/linalg/dasum.cpp +++ b/lib/linalg/dasum.cpp @@ -1,13 +1,13 @@ /* fortran/dasum.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -118,7 +118,7 @@ doublereal dasum_(integer *n, doublereal *dx, integer *incx) ret_val = 0.; dtemp = 0.; if (*n <= 0 || *incx <= 0) { - return ret_val; + return ret_val; } if (*incx == 1) { /* code for increment equal to 1 */ @@ -126,35 +126,35 @@ doublereal dasum_(integer *n, doublereal *dx, integer *incx) /* clean-up loop */ - m = *n % 6; - if (m != 0) { - i__1 = m; - for (i__ = 1; i__ <= i__1; ++i__) { - dtemp += (d__1 = dx[i__], abs(d__1)); - } - if (*n < 6) { - ret_val = dtemp; - return ret_val; - } - } - mp1 = m + 1; - i__1 = *n; - for (i__ = mp1; i__ <= i__1; i__ += 6) { - dtemp = dtemp + (d__1 = dx[i__], abs(d__1)) + (d__2 = dx[i__ + 1], - abs(d__2)) + (d__3 = dx[i__ + 2], abs(d__3)) + (d__4 = - dx[i__ + 3], abs(d__4)) + (d__5 = dx[i__ + 4], abs(d__5)) - + (d__6 = dx[i__ + 5], abs(d__6)); - } + m = *n % 6; + if (m != 0) { + i__1 = m; + for (i__ = 1; i__ <= i__1; ++i__) { + dtemp += (d__1 = dx[i__], abs(d__1)); + } + if (*n < 6) { + ret_val = dtemp; + return ret_val; + } + } + mp1 = m + 1; + i__1 = *n; + for (i__ = mp1; i__ <= i__1; i__ += 6) { + dtemp = dtemp + (d__1 = dx[i__], abs(d__1)) + (d__2 = dx[i__ + 1], + abs(d__2)) + (d__3 = dx[i__ + 2], abs(d__3)) + (d__4 = + dx[i__ + 3], abs(d__4)) + (d__5 = dx[i__ + 4], abs(d__5)) + + (d__6 = dx[i__ + 5], abs(d__6)); + } } else { /* code for increment not equal to 1 */ - nincx = *n * *incx; - i__1 = nincx; - i__2 = *incx; - for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { - dtemp += (d__1 = dx[i__], abs(d__1)); - } + nincx = *n * *incx; + i__1 = nincx; + i__2 = *incx; + for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { + dtemp += (d__1 = dx[i__], abs(d__1)); + } } ret_val = dtemp; return ret_val; @@ -164,5 +164,5 @@ doublereal dasum_(integer *n, doublereal *dx, integer *incx) } /* dasum_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/daxpy.cpp b/lib/linalg/daxpy.cpp index d89cd6e9c4..54105d1426 100644 --- a/lib/linalg/daxpy.cpp +++ b/lib/linalg/daxpy.cpp @@ -1,13 +1,13 @@ /* fortran/daxpy.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -102,8 +102,8 @@ extern "C" { /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int daxpy_(integer *n, doublereal *da, doublereal *dx, - integer *incx, doublereal *dy, integer *incy) +/* Subroutine */ int daxpy_(integer *n, doublereal *da, doublereal *dx, + integer *incx, doublereal *dy, integer *incy) { /* System generated locals */ integer i__1; @@ -133,10 +133,10 @@ extern "C" { /* Function Body */ if (*n <= 0) { - return 0; + return 0; } if (*da == 0.) { - return 0; + return 0; } if (*incx == 1 && *incy == 1) { @@ -145,43 +145,43 @@ extern "C" { /* clean-up loop */ - m = *n % 4; - if (m != 0) { - i__1 = m; - for (i__ = 1; i__ <= i__1; ++i__) { - dy[i__] += *da * dx[i__]; - } - } - if (*n < 4) { - return 0; - } - mp1 = m + 1; - i__1 = *n; - for (i__ = mp1; i__ <= i__1; i__ += 4) { - dy[i__] += *da * dx[i__]; - dy[i__ + 1] += *da * dx[i__ + 1]; - dy[i__ + 2] += *da * dx[i__ + 2]; - dy[i__ + 3] += *da * dx[i__ + 3]; - } + m = *n % 4; + if (m != 0) { + i__1 = m; + for (i__ = 1; i__ <= i__1; ++i__) { + dy[i__] += *da * dx[i__]; + } + } + if (*n < 4) { + return 0; + } + mp1 = m + 1; + i__1 = *n; + for (i__ = mp1; i__ <= i__1; i__ += 4) { + dy[i__] += *da * dx[i__]; + dy[i__ + 1] += *da * dx[i__ + 1]; + dy[i__ + 2] += *da * dx[i__ + 2]; + dy[i__ + 3] += *da * dx[i__ + 3]; + } } else { /* code for unequal increments or equal increments */ /* not equal to 1 */ - ix = 1; - iy = 1; - if (*incx < 0) { - ix = (-(*n) + 1) * *incx + 1; - } - if (*incy < 0) { - iy = (-(*n) + 1) * *incy + 1; - } - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - dy[iy] += *da * dx[ix]; - ix += *incx; - iy += *incy; - } + ix = 1; + iy = 1; + if (*incx < 0) { + ix = (-(*n) + 1) * *incx + 1; + } + if (*incy < 0) { + iy = (-(*n) + 1) * *incy + 1; + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + dy[iy] += *da * dx[ix]; + ix += *incx; + iy += *incy; + } } return 0; @@ -190,5 +190,5 @@ extern "C" { } /* daxpy_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dbdsqr.cpp b/lib/linalg/dbdsqr.cpp index 78c996dc2b..5f5c1b1d6f 100644 --- a/lib/linalg/dbdsqr.cpp +++ b/lib/linalg/dbdsqr.cpp @@ -1,13 +1,13 @@ /* fortran/dbdsqr.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -264,18 +264,18 @@ f"> */ /* ===================================================================== */ /* Subroutine */ int dbdsqr_(char *uplo, integer *n, integer *ncvt, integer * - nru, integer *ncc, doublereal *d__, doublereal *e, doublereal *vt, - integer *ldvt, doublereal *u, integer *ldu, doublereal *c__, integer * - ldc, doublereal *work, integer *info, ftnlen uplo_len) + nru, integer *ncc, doublereal *d__, doublereal *e, doublereal *vt, + integer *ldvt, doublereal *u, integer *ldu, doublereal *c__, integer * + ldc, doublereal *work, integer *info, ftnlen uplo_len) { /* System generated locals */ - integer c_dim1, c_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1, - i__2; + integer c_dim1, c_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1, + i__2; doublereal d__1, d__2, d__3, d__4; /* Builtin functions */ double pow_dd(doublereal *, doublereal *), sqrt(doublereal), d_sign( - doublereal *, doublereal *); + doublereal *, doublereal *); /* Local variables */ integer iterdivn; @@ -294,30 +294,30 @@ f"> */ doublereal cosl; integer isub, iter; doublereal unfl, sinl, cosr, smin, smax, sinr; - extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, - doublereal *, integer *, doublereal *, doublereal *), dlas2_( - doublereal *, doublereal *, doublereal *, doublereal *, - doublereal *), dscal_(integer *, doublereal *, doublereal *, - integer *); + extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, + doublereal *, integer *, doublereal *, doublereal *), dlas2_( + doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *), dscal_(integer *, doublereal *, doublereal *, + integer *); extern logical lsame_(char *, char *, ftnlen, ftnlen); doublereal oldcs; - extern /* Subroutine */ int dlasr_(char *, char *, char *, integer *, - integer *, doublereal *, doublereal *, doublereal *, integer *, - ftnlen, ftnlen, ftnlen); + extern /* Subroutine */ int dlasr_(char *, char *, char *, integer *, + integer *, doublereal *, doublereal *, doublereal *, integer *, + ftnlen, ftnlen, ftnlen); integer oldll; doublereal shift, sigmn, oldsn; - extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, - doublereal *, integer *); + extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, + doublereal *, integer *); doublereal sminl, sigmx; logical lower; extern /* Subroutine */ int dlasq1_(integer *, doublereal *, doublereal *, - doublereal *, integer *), dlasv2_(doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *); + doublereal *, integer *), dlasv2_(doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *); extern doublereal dlamch_(char *, ftnlen); - extern /* Subroutine */ int dlartg_(doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *), xerbla_(char *, - integer *, ftnlen); + extern /* Subroutine */ int dlartg_(doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *), xerbla_(char *, + integer *, ftnlen); doublereal sminoa, thresh; logical rotate; doublereal tolmul; @@ -366,32 +366,32 @@ f"> */ *info = 0; lower = lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1); if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lower) { - *info = -1; + *info = -1; } else if (*n < 0) { - *info = -2; + *info = -2; } else if (*ncvt < 0) { - *info = -3; + *info = -3; } else if (*nru < 0) { - *info = -4; + *info = -4; } else if (*ncc < 0) { - *info = -5; + *info = -5; } else if (*ncvt == 0 && *ldvt < 1 || *ncvt > 0 && *ldvt < max(1,*n)) { - *info = -9; + *info = -9; } else if (*ldu < max(1,*nru)) { - *info = -11; + *info = -11; } else if (*ncc == 0 && *ldc < 1 || *ncc > 0 && *ldc < max(1,*n)) { - *info = -13; + *info = -13; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DBDSQR", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DBDSQR", &i__1, (ftnlen)6); + return 0; } if (*n == 0) { - return 0; + return 0; } if (*n == 1) { - goto L160; + goto L160; } /* ROTATE is true if any singular vectors desired, false otherwise */ @@ -401,14 +401,14 @@ f"> */ /* If no singular vectors desired, use qd algorithm */ if (! rotate) { - dlasq1_(n, &d__[1], &e[1], &work[1], info); + dlasq1_(n, &d__[1], &e[1], &work[1], info); /* If INFO equals 2, dqds didn't finish, try to finish */ - if (*info != 2) { - return 0; - } - *info = 0; + if (*info != 2) { + return 0; + } + *info = 0; } nm1 = *n - 1; @@ -425,27 +425,27 @@ f"> */ /* by applying Givens rotations on the left */ if (lower) { - i__1 = *n - 1; - for (i__ = 1; i__ <= i__1; ++i__) { - dlartg_(&d__[i__], &e[i__], &cs, &sn, &r__); - d__[i__] = r__; - e[i__] = sn * d__[i__ + 1]; - d__[i__ + 1] = cs * d__[i__ + 1]; - work[i__] = cs; - work[nm1 + i__] = sn; + i__1 = *n - 1; + for (i__ = 1; i__ <= i__1; ++i__) { + dlartg_(&d__[i__], &e[i__], &cs, &sn, &r__); + d__[i__] = r__; + e[i__] = sn * d__[i__ + 1]; + d__[i__ + 1] = cs * d__[i__ + 1]; + work[i__] = cs; + work[nm1 + i__] = sn; /* L10: */ - } + } /* Update singular vectors if desired */ - if (*nru > 0) { - dlasr_((char *)"R", (char *)"V", (char *)"F", nru, n, &work[1], &work[*n], &u[u_offset], - ldu, (ftnlen)1, (ftnlen)1, (ftnlen)1); - } - if (*ncc > 0) { - dlasr_((char *)"L", (char *)"V", (char *)"F", n, ncc, &work[1], &work[*n], &c__[c_offset], - ldc, (ftnlen)1, (ftnlen)1, (ftnlen)1); - } + if (*nru > 0) { + dlasr_((char *)"R", (char *)"V", (char *)"F", nru, n, &work[1], &work[*n], &u[u_offset], + ldu, (ftnlen)1, (ftnlen)1, (ftnlen)1); + } + if (*ncc > 0) { + dlasr_((char *)"L", (char *)"V", (char *)"F", n, ncc, &work[1], &work[*n], &c__[c_offset], + ldc, (ftnlen)1, (ftnlen)1, (ftnlen)1); + } } /* Compute singular values to relative accuracy TOL */ @@ -465,15 +465,15 @@ f"> */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { /* Computing MAX */ - d__2 = smax, d__3 = (d__1 = d__[i__], abs(d__1)); - smax = max(d__2,d__3); + d__2 = smax, d__3 = (d__1 = d__[i__], abs(d__1)); + smax = max(d__2,d__3); /* L20: */ } i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { /* Computing MAX */ - d__2 = smax, d__3 = (d__1 = e[i__], abs(d__1)); - smax = max(d__2,d__3); + d__2 = smax, d__3 = (d__1 = e[i__], abs(d__1)); + smax = max(d__2,d__3); /* L30: */ } sminl = 0.; @@ -481,33 +481,33 @@ f"> */ /* Relative accuracy desired */ - sminoa = abs(d__[1]); - if (sminoa == 0.) { - goto L50; - } - mu = sminoa; - i__1 = *n; - for (i__ = 2; i__ <= i__1; ++i__) { - mu = (d__2 = d__[i__], abs(d__2)) * (mu / (mu + (d__1 = e[i__ - 1] - , abs(d__1)))); - sminoa = min(sminoa,mu); - if (sminoa == 0.) { - goto L50; - } + sminoa = abs(d__[1]); + if (sminoa == 0.) { + goto L50; + } + mu = sminoa; + i__1 = *n; + for (i__ = 2; i__ <= i__1; ++i__) { + mu = (d__2 = d__[i__], abs(d__2)) * (mu / (mu + (d__1 = e[i__ - 1] + , abs(d__1)))); + sminoa = min(sminoa,mu); + if (sminoa == 0.) { + goto L50; + } /* L40: */ - } + } L50: - sminoa /= sqrt((doublereal) (*n)); + sminoa /= sqrt((doublereal) (*n)); /* Computing MAX */ - d__1 = tol * sminoa, d__2 = *n * (*n * unfl) * 6; - thresh = max(d__1,d__2); + d__1 = tol * sminoa, d__2 = *n * (*n * unfl) * 6; + thresh = max(d__1,d__2); } else { /* Absolute accuracy desired */ /* Computing MAX */ - d__1 = abs(tol) * smax, d__2 = *n * (*n * unfl) * 6; - thresh = max(d__1,d__2); + d__1 = abs(tol) * smax, d__2 = *n * (*n * unfl) * 6; + thresh = max(d__1,d__2); } /* Prepare for main iteration loop for the singular values */ @@ -531,39 +531,39 @@ L60: /* Check for convergence or exceeding iteration count */ if (m <= 1) { - goto L160; + goto L160; } if (iter >= *n) { - iter -= *n; - ++iterdivn; - if (iterdivn >= maxitdivn) { - goto L200; - } + iter -= *n; + ++iterdivn; + if (iterdivn >= maxitdivn) { + goto L200; + } } /* Find diagonal block of matrix to work on */ if (tol < 0. && (d__1 = d__[m], abs(d__1)) <= thresh) { - d__[m] = 0.; + d__[m] = 0.; } smax = (d__1 = d__[m], abs(d__1)); smin = smax; i__1 = m - 1; for (lll = 1; lll <= i__1; ++lll) { - ll = m - lll; - abss = (d__1 = d__[ll], abs(d__1)); - abse = (d__1 = e[ll], abs(d__1)); - if (tol < 0. && abss <= thresh) { - d__[ll] = 0.; - } - if (abse <= thresh) { - goto L80; - } - smin = min(smin,abss); + ll = m - lll; + abss = (d__1 = d__[ll], abs(d__1)); + abse = (d__1 = e[ll], abs(d__1)); + if (tol < 0. && abss <= thresh) { + d__[ll] = 0.; + } + if (abse <= thresh) { + goto L80; + } + smin = min(smin,abss); /* Computing MAX */ - d__1 = max(smax,abss); - smax = max(d__1,abse); + d__1 = max(smax,abss); + smax = max(d__1,abse); /* L70: */ } ll = 0; @@ -577,8 +577,8 @@ L80: /* Convergence of bottom singular value, return to top of loop */ - --m; - goto L60; + --m; + goto L60; } L90: ++ll; @@ -589,45 +589,45 @@ L90: /* 2 by 2 block, handle separately */ - dlasv2_(&d__[m - 1], &e[m - 1], &d__[m], &sigmn, &sigmx, &sinr, &cosr, - &sinl, &cosl); - d__[m - 1] = sigmx; - e[m - 1] = 0.; - d__[m] = sigmn; + dlasv2_(&d__[m - 1], &e[m - 1], &d__[m], &sigmn, &sigmx, &sinr, &cosr, + &sinl, &cosl); + d__[m - 1] = sigmx; + e[m - 1] = 0.; + d__[m] = sigmn; /* Compute singular vectors, if desired */ - if (*ncvt > 0) { - drot_(ncvt, &vt[m - 1 + vt_dim1], ldvt, &vt[m + vt_dim1], ldvt, & - cosr, &sinr); - } - if (*nru > 0) { - drot_(nru, &u[(m - 1) * u_dim1 + 1], &c__1, &u[m * u_dim1 + 1], & - c__1, &cosl, &sinl); - } - if (*ncc > 0) { - drot_(ncc, &c__[m - 1 + c_dim1], ldc, &c__[m + c_dim1], ldc, & - cosl, &sinl); - } - m += -2; - goto L60; + if (*ncvt > 0) { + drot_(ncvt, &vt[m - 1 + vt_dim1], ldvt, &vt[m + vt_dim1], ldvt, & + cosr, &sinr); + } + if (*nru > 0) { + drot_(nru, &u[(m - 1) * u_dim1 + 1], &c__1, &u[m * u_dim1 + 1], & + c__1, &cosl, &sinl); + } + if (*ncc > 0) { + drot_(ncc, &c__[m - 1 + c_dim1], ldc, &c__[m + c_dim1], ldc, & + cosl, &sinl); + } + m += -2; + goto L60; } /* If working on new submatrix, choose shift direction */ /* (from larger end diagonal element towards smaller) */ if (ll > oldm || m < oldll) { - if ((d__1 = d__[ll], abs(d__1)) >= (d__2 = d__[m], abs(d__2))) { + if ((d__1 = d__[ll], abs(d__1)) >= (d__2 = d__[m], abs(d__2))) { /* Chase bulge from top (big end) to bottom (small end) */ - idir = 1; - } else { + idir = 1; + } else { /* Chase bulge from bottom (big end) to top (small end) */ - idir = 2; - } + idir = 2; + } } /* Apply convergence tests */ @@ -637,63 +637,63 @@ L90: /* Run convergence test in forward direction */ /* First apply standard test to bottom of matrix */ - if ((d__2 = e[m - 1], abs(d__2)) <= abs(tol) * (d__1 = d__[m], abs( - d__1)) || tol < 0. && (d__3 = e[m - 1], abs(d__3)) <= thresh) - { - e[m - 1] = 0.; - goto L60; - } + if ((d__2 = e[m - 1], abs(d__2)) <= abs(tol) * (d__1 = d__[m], abs( + d__1)) || tol < 0. && (d__3 = e[m - 1], abs(d__3)) <= thresh) + { + e[m - 1] = 0.; + goto L60; + } - if (tol >= 0.) { + if (tol >= 0.) { /* If relative accuracy desired, */ /* apply convergence criterion forward */ - mu = (d__1 = d__[ll], abs(d__1)); - sminl = mu; - i__1 = m - 1; - for (lll = ll; lll <= i__1; ++lll) { - if ((d__1 = e[lll], abs(d__1)) <= tol * mu) { - e[lll] = 0.; - goto L60; - } - mu = (d__2 = d__[lll + 1], abs(d__2)) * (mu / (mu + (d__1 = e[ - lll], abs(d__1)))); - sminl = min(sminl,mu); + mu = (d__1 = d__[ll], abs(d__1)); + sminl = mu; + i__1 = m - 1; + for (lll = ll; lll <= i__1; ++lll) { + if ((d__1 = e[lll], abs(d__1)) <= tol * mu) { + e[lll] = 0.; + goto L60; + } + mu = (d__2 = d__[lll + 1], abs(d__2)) * (mu / (mu + (d__1 = e[ + lll], abs(d__1)))); + sminl = min(sminl,mu); /* L100: */ - } - } + } + } } else { /* Run convergence test in backward direction */ /* First apply standard test to top of matrix */ - if ((d__2 = e[ll], abs(d__2)) <= abs(tol) * (d__1 = d__[ll], abs(d__1) - ) || tol < 0. && (d__3 = e[ll], abs(d__3)) <= thresh) { - e[ll] = 0.; - goto L60; - } + if ((d__2 = e[ll], abs(d__2)) <= abs(tol) * (d__1 = d__[ll], abs(d__1) + ) || tol < 0. && (d__3 = e[ll], abs(d__3)) <= thresh) { + e[ll] = 0.; + goto L60; + } - if (tol >= 0.) { + if (tol >= 0.) { /* If relative accuracy desired, */ /* apply convergence criterion backward */ - mu = (d__1 = d__[m], abs(d__1)); - sminl = mu; - i__1 = ll; - for (lll = m - 1; lll >= i__1; --lll) { - if ((d__1 = e[lll], abs(d__1)) <= tol * mu) { - e[lll] = 0.; - goto L60; - } - mu = (d__2 = d__[lll], abs(d__2)) * (mu / (mu + (d__1 = e[lll] - , abs(d__1)))); - sminl = min(sminl,mu); + mu = (d__1 = d__[m], abs(d__1)); + sminl = mu; + i__1 = ll; + for (lll = m - 1; lll >= i__1; --lll) { + if ((d__1 = e[lll], abs(d__1)) <= tol * mu) { + e[lll] = 0.; + goto L60; + } + mu = (d__2 = d__[lll], abs(d__2)) * (mu / (mu + (d__1 = e[lll] + , abs(d__1)))); + sminl = min(sminl,mu); /* L110: */ - } - } + } + } } oldll = ll; oldm = m; @@ -707,28 +707,28 @@ L90: /* Use a zero shift to avoid loss of relative accuracy */ - shift = 0.; + shift = 0.; } else { /* Compute the shift from 2-by-2 block at end of matrix */ - if (idir == 1) { - sll = (d__1 = d__[ll], abs(d__1)); - dlas2_(&d__[m - 1], &e[m - 1], &d__[m], &shift, &r__); - } else { - sll = (d__1 = d__[m], abs(d__1)); - dlas2_(&d__[ll], &e[ll], &d__[ll + 1], &shift, &r__); - } + if (idir == 1) { + sll = (d__1 = d__[ll], abs(d__1)); + dlas2_(&d__[m - 1], &e[m - 1], &d__[m], &shift, &r__); + } else { + sll = (d__1 = d__[m], abs(d__1)); + dlas2_(&d__[ll], &e[ll], &d__[ll + 1], &shift, &r__); + } /* Test if shift negligible, and if so set to zero */ - if (sll > 0.) { + if (sll > 0.) { /* Computing 2nd power */ - d__1 = shift / sll; - if (d__1 * d__1 < eps) { - shift = 0.; - } - } + d__1 = shift / sll; + if (d__1 * d__1 < eps) { + shift = 0.; + } + } } /* Increment iteration count */ @@ -738,234 +738,234 @@ L90: /* If SHIFT = 0, do simplified QR iteration */ if (shift == 0.) { - if (idir == 1) { + if (idir == 1) { /* Chase bulge from top to bottom */ /* Save cosines and sines for later singular vector updates */ - cs = 1.; - oldcs = 1.; - i__1 = m - 1; - for (i__ = ll; i__ <= i__1; ++i__) { - d__1 = d__[i__] * cs; - dlartg_(&d__1, &e[i__], &cs, &sn, &r__); - if (i__ > ll) { - e[i__ - 1] = oldsn * r__; - } - d__1 = oldcs * r__; - d__2 = d__[i__ + 1] * sn; - dlartg_(&d__1, &d__2, &oldcs, &oldsn, &d__[i__]); - work[i__ - ll + 1] = cs; - work[i__ - ll + 1 + nm1] = sn; - work[i__ - ll + 1 + nm12] = oldcs; - work[i__ - ll + 1 + nm13] = oldsn; + cs = 1.; + oldcs = 1.; + i__1 = m - 1; + for (i__ = ll; i__ <= i__1; ++i__) { + d__1 = d__[i__] * cs; + dlartg_(&d__1, &e[i__], &cs, &sn, &r__); + if (i__ > ll) { + e[i__ - 1] = oldsn * r__; + } + d__1 = oldcs * r__; + d__2 = d__[i__ + 1] * sn; + dlartg_(&d__1, &d__2, &oldcs, &oldsn, &d__[i__]); + work[i__ - ll + 1] = cs; + work[i__ - ll + 1 + nm1] = sn; + work[i__ - ll + 1 + nm12] = oldcs; + work[i__ - ll + 1 + nm13] = oldsn; /* L120: */ - } - h__ = d__[m] * cs; - d__[m] = h__ * oldcs; - e[m - 1] = h__ * oldsn; + } + h__ = d__[m] * cs; + d__[m] = h__ * oldcs; + e[m - 1] = h__ * oldsn; /* Update singular vectors */ - if (*ncvt > 0) { - i__1 = m - ll + 1; - dlasr_((char *)"L", (char *)"V", (char *)"F", &i__1, ncvt, &work[1], &work[*n], &vt[ - ll + vt_dim1], ldvt, (ftnlen)1, (ftnlen)1, (ftnlen)1); - } - if (*nru > 0) { - i__1 = m - ll + 1; - dlasr_((char *)"R", (char *)"V", (char *)"F", nru, &i__1, &work[nm12 + 1], &work[nm13 - + 1], &u[ll * u_dim1 + 1], ldu, (ftnlen)1, (ftnlen)1, - (ftnlen)1); - } - if (*ncc > 0) { - i__1 = m - ll + 1; - dlasr_((char *)"L", (char *)"V", (char *)"F", &i__1, ncc, &work[nm12 + 1], &work[nm13 - + 1], &c__[ll + c_dim1], ldc, (ftnlen)1, (ftnlen)1, ( - ftnlen)1); - } + if (*ncvt > 0) { + i__1 = m - ll + 1; + dlasr_((char *)"L", (char *)"V", (char *)"F", &i__1, ncvt, &work[1], &work[*n], &vt[ + ll + vt_dim1], ldvt, (ftnlen)1, (ftnlen)1, (ftnlen)1); + } + if (*nru > 0) { + i__1 = m - ll + 1; + dlasr_((char *)"R", (char *)"V", (char *)"F", nru, &i__1, &work[nm12 + 1], &work[nm13 + + 1], &u[ll * u_dim1 + 1], ldu, (ftnlen)1, (ftnlen)1, + (ftnlen)1); + } + if (*ncc > 0) { + i__1 = m - ll + 1; + dlasr_((char *)"L", (char *)"V", (char *)"F", &i__1, ncc, &work[nm12 + 1], &work[nm13 + + 1], &c__[ll + c_dim1], ldc, (ftnlen)1, (ftnlen)1, ( + ftnlen)1); + } /* Test convergence */ - if ((d__1 = e[m - 1], abs(d__1)) <= thresh) { - e[m - 1] = 0.; - } + if ((d__1 = e[m - 1], abs(d__1)) <= thresh) { + e[m - 1] = 0.; + } - } else { + } else { /* Chase bulge from bottom to top */ /* Save cosines and sines for later singular vector updates */ - cs = 1.; - oldcs = 1.; - i__1 = ll + 1; - for (i__ = m; i__ >= i__1; --i__) { - d__1 = d__[i__] * cs; - dlartg_(&d__1, &e[i__ - 1], &cs, &sn, &r__); - if (i__ < m) { - e[i__] = oldsn * r__; - } - d__1 = oldcs * r__; - d__2 = d__[i__ - 1] * sn; - dlartg_(&d__1, &d__2, &oldcs, &oldsn, &d__[i__]); - work[i__ - ll] = cs; - work[i__ - ll + nm1] = -sn; - work[i__ - ll + nm12] = oldcs; - work[i__ - ll + nm13] = -oldsn; + cs = 1.; + oldcs = 1.; + i__1 = ll + 1; + for (i__ = m; i__ >= i__1; --i__) { + d__1 = d__[i__] * cs; + dlartg_(&d__1, &e[i__ - 1], &cs, &sn, &r__); + if (i__ < m) { + e[i__] = oldsn * r__; + } + d__1 = oldcs * r__; + d__2 = d__[i__ - 1] * sn; + dlartg_(&d__1, &d__2, &oldcs, &oldsn, &d__[i__]); + work[i__ - ll] = cs; + work[i__ - ll + nm1] = -sn; + work[i__ - ll + nm12] = oldcs; + work[i__ - ll + nm13] = -oldsn; /* L130: */ - } - h__ = d__[ll] * cs; - d__[ll] = h__ * oldcs; - e[ll] = h__ * oldsn; + } + h__ = d__[ll] * cs; + d__[ll] = h__ * oldcs; + e[ll] = h__ * oldsn; /* Update singular vectors */ - if (*ncvt > 0) { - i__1 = m - ll + 1; - dlasr_((char *)"L", (char *)"V", (char *)"B", &i__1, ncvt, &work[nm12 + 1], &work[ - nm13 + 1], &vt[ll + vt_dim1], ldvt, (ftnlen)1, ( - ftnlen)1, (ftnlen)1); - } - if (*nru > 0) { - i__1 = m - ll + 1; - dlasr_((char *)"R", (char *)"V", (char *)"B", nru, &i__1, &work[1], &work[*n], &u[ll * - u_dim1 + 1], ldu, (ftnlen)1, (ftnlen)1, (ftnlen)1); - } - if (*ncc > 0) { - i__1 = m - ll + 1; - dlasr_((char *)"L", (char *)"V", (char *)"B", &i__1, ncc, &work[1], &work[*n], &c__[ - ll + c_dim1], ldc, (ftnlen)1, (ftnlen)1, (ftnlen)1); - } + if (*ncvt > 0) { + i__1 = m - ll + 1; + dlasr_((char *)"L", (char *)"V", (char *)"B", &i__1, ncvt, &work[nm12 + 1], &work[ + nm13 + 1], &vt[ll + vt_dim1], ldvt, (ftnlen)1, ( + ftnlen)1, (ftnlen)1); + } + if (*nru > 0) { + i__1 = m - ll + 1; + dlasr_((char *)"R", (char *)"V", (char *)"B", nru, &i__1, &work[1], &work[*n], &u[ll * + u_dim1 + 1], ldu, (ftnlen)1, (ftnlen)1, (ftnlen)1); + } + if (*ncc > 0) { + i__1 = m - ll + 1; + dlasr_((char *)"L", (char *)"V", (char *)"B", &i__1, ncc, &work[1], &work[*n], &c__[ + ll + c_dim1], ldc, (ftnlen)1, (ftnlen)1, (ftnlen)1); + } /* Test convergence */ - if ((d__1 = e[ll], abs(d__1)) <= thresh) { - e[ll] = 0.; - } - } + if ((d__1 = e[ll], abs(d__1)) <= thresh) { + e[ll] = 0.; + } + } } else { /* Use nonzero shift */ - if (idir == 1) { + if (idir == 1) { /* Chase bulge from top to bottom */ /* Save cosines and sines for later singular vector updates */ - f = ((d__1 = d__[ll], abs(d__1)) - shift) * (d_sign(&c_b49, &d__[ - ll]) + shift / d__[ll]); - g = e[ll]; - i__1 = m - 1; - for (i__ = ll; i__ <= i__1; ++i__) { - dlartg_(&f, &g, &cosr, &sinr, &r__); - if (i__ > ll) { - e[i__ - 1] = r__; - } - f = cosr * d__[i__] + sinr * e[i__]; - e[i__] = cosr * e[i__] - sinr * d__[i__]; - g = sinr * d__[i__ + 1]; - d__[i__ + 1] = cosr * d__[i__ + 1]; - dlartg_(&f, &g, &cosl, &sinl, &r__); - d__[i__] = r__; - f = cosl * e[i__] + sinl * d__[i__ + 1]; - d__[i__ + 1] = cosl * d__[i__ + 1] - sinl * e[i__]; - if (i__ < m - 1) { - g = sinl * e[i__ + 1]; - e[i__ + 1] = cosl * e[i__ + 1]; - } - work[i__ - ll + 1] = cosr; - work[i__ - ll + 1 + nm1] = sinr; - work[i__ - ll + 1 + nm12] = cosl; - work[i__ - ll + 1 + nm13] = sinl; + f = ((d__1 = d__[ll], abs(d__1)) - shift) * (d_sign(&c_b49, &d__[ + ll]) + shift / d__[ll]); + g = e[ll]; + i__1 = m - 1; + for (i__ = ll; i__ <= i__1; ++i__) { + dlartg_(&f, &g, &cosr, &sinr, &r__); + if (i__ > ll) { + e[i__ - 1] = r__; + } + f = cosr * d__[i__] + sinr * e[i__]; + e[i__] = cosr * e[i__] - sinr * d__[i__]; + g = sinr * d__[i__ + 1]; + d__[i__ + 1] = cosr * d__[i__ + 1]; + dlartg_(&f, &g, &cosl, &sinl, &r__); + d__[i__] = r__; + f = cosl * e[i__] + sinl * d__[i__ + 1]; + d__[i__ + 1] = cosl * d__[i__ + 1] - sinl * e[i__]; + if (i__ < m - 1) { + g = sinl * e[i__ + 1]; + e[i__ + 1] = cosl * e[i__ + 1]; + } + work[i__ - ll + 1] = cosr; + work[i__ - ll + 1 + nm1] = sinr; + work[i__ - ll + 1 + nm12] = cosl; + work[i__ - ll + 1 + nm13] = sinl; /* L140: */ - } - e[m - 1] = f; + } + e[m - 1] = f; /* Update singular vectors */ - if (*ncvt > 0) { - i__1 = m - ll + 1; - dlasr_((char *)"L", (char *)"V", (char *)"F", &i__1, ncvt, &work[1], &work[*n], &vt[ - ll + vt_dim1], ldvt, (ftnlen)1, (ftnlen)1, (ftnlen)1); - } - if (*nru > 0) { - i__1 = m - ll + 1; - dlasr_((char *)"R", (char *)"V", (char *)"F", nru, &i__1, &work[nm12 + 1], &work[nm13 - + 1], &u[ll * u_dim1 + 1], ldu, (ftnlen)1, (ftnlen)1, - (ftnlen)1); - } - if (*ncc > 0) { - i__1 = m - ll + 1; - dlasr_((char *)"L", (char *)"V", (char *)"F", &i__1, ncc, &work[nm12 + 1], &work[nm13 - + 1], &c__[ll + c_dim1], ldc, (ftnlen)1, (ftnlen)1, ( - ftnlen)1); - } + if (*ncvt > 0) { + i__1 = m - ll + 1; + dlasr_((char *)"L", (char *)"V", (char *)"F", &i__1, ncvt, &work[1], &work[*n], &vt[ + ll + vt_dim1], ldvt, (ftnlen)1, (ftnlen)1, (ftnlen)1); + } + if (*nru > 0) { + i__1 = m - ll + 1; + dlasr_((char *)"R", (char *)"V", (char *)"F", nru, &i__1, &work[nm12 + 1], &work[nm13 + + 1], &u[ll * u_dim1 + 1], ldu, (ftnlen)1, (ftnlen)1, + (ftnlen)1); + } + if (*ncc > 0) { + i__1 = m - ll + 1; + dlasr_((char *)"L", (char *)"V", (char *)"F", &i__1, ncc, &work[nm12 + 1], &work[nm13 + + 1], &c__[ll + c_dim1], ldc, (ftnlen)1, (ftnlen)1, ( + ftnlen)1); + } /* Test convergence */ - if ((d__1 = e[m - 1], abs(d__1)) <= thresh) { - e[m - 1] = 0.; - } + if ((d__1 = e[m - 1], abs(d__1)) <= thresh) { + e[m - 1] = 0.; + } - } else { + } else { /* Chase bulge from bottom to top */ /* Save cosines and sines for later singular vector updates */ - f = ((d__1 = d__[m], abs(d__1)) - shift) * (d_sign(&c_b49, &d__[m] - ) + shift / d__[m]); - g = e[m - 1]; - i__1 = ll + 1; - for (i__ = m; i__ >= i__1; --i__) { - dlartg_(&f, &g, &cosr, &sinr, &r__); - if (i__ < m) { - e[i__] = r__; - } - f = cosr * d__[i__] + sinr * e[i__ - 1]; - e[i__ - 1] = cosr * e[i__ - 1] - sinr * d__[i__]; - g = sinr * d__[i__ - 1]; - d__[i__ - 1] = cosr * d__[i__ - 1]; - dlartg_(&f, &g, &cosl, &sinl, &r__); - d__[i__] = r__; - f = cosl * e[i__ - 1] + sinl * d__[i__ - 1]; - d__[i__ - 1] = cosl * d__[i__ - 1] - sinl * e[i__ - 1]; - if (i__ > ll + 1) { - g = sinl * e[i__ - 2]; - e[i__ - 2] = cosl * e[i__ - 2]; - } - work[i__ - ll] = cosr; - work[i__ - ll + nm1] = -sinr; - work[i__ - ll + nm12] = cosl; - work[i__ - ll + nm13] = -sinl; + f = ((d__1 = d__[m], abs(d__1)) - shift) * (d_sign(&c_b49, &d__[m] + ) + shift / d__[m]); + g = e[m - 1]; + i__1 = ll + 1; + for (i__ = m; i__ >= i__1; --i__) { + dlartg_(&f, &g, &cosr, &sinr, &r__); + if (i__ < m) { + e[i__] = r__; + } + f = cosr * d__[i__] + sinr * e[i__ - 1]; + e[i__ - 1] = cosr * e[i__ - 1] - sinr * d__[i__]; + g = sinr * d__[i__ - 1]; + d__[i__ - 1] = cosr * d__[i__ - 1]; + dlartg_(&f, &g, &cosl, &sinl, &r__); + d__[i__] = r__; + f = cosl * e[i__ - 1] + sinl * d__[i__ - 1]; + d__[i__ - 1] = cosl * d__[i__ - 1] - sinl * e[i__ - 1]; + if (i__ > ll + 1) { + g = sinl * e[i__ - 2]; + e[i__ - 2] = cosl * e[i__ - 2]; + } + work[i__ - ll] = cosr; + work[i__ - ll + nm1] = -sinr; + work[i__ - ll + nm12] = cosl; + work[i__ - ll + nm13] = -sinl; /* L150: */ - } - e[ll] = f; + } + e[ll] = f; /* Test convergence */ - if ((d__1 = e[ll], abs(d__1)) <= thresh) { - e[ll] = 0.; - } + if ((d__1 = e[ll], abs(d__1)) <= thresh) { + e[ll] = 0.; + } /* Update singular vectors if desired */ - if (*ncvt > 0) { - i__1 = m - ll + 1; - dlasr_((char *)"L", (char *)"V", (char *)"B", &i__1, ncvt, &work[nm12 + 1], &work[ - nm13 + 1], &vt[ll + vt_dim1], ldvt, (ftnlen)1, ( - ftnlen)1, (ftnlen)1); - } - if (*nru > 0) { - i__1 = m - ll + 1; - dlasr_((char *)"R", (char *)"V", (char *)"B", nru, &i__1, &work[1], &work[*n], &u[ll * - u_dim1 + 1], ldu, (ftnlen)1, (ftnlen)1, (ftnlen)1); - } - if (*ncc > 0) { - i__1 = m - ll + 1; - dlasr_((char *)"L", (char *)"V", (char *)"B", &i__1, ncc, &work[1], &work[*n], &c__[ - ll + c_dim1], ldc, (ftnlen)1, (ftnlen)1, (ftnlen)1); - } - } + if (*ncvt > 0) { + i__1 = m - ll + 1; + dlasr_((char *)"L", (char *)"V", (char *)"B", &i__1, ncvt, &work[nm12 + 1], &work[ + nm13 + 1], &vt[ll + vt_dim1], ldvt, (ftnlen)1, ( + ftnlen)1, (ftnlen)1); + } + if (*nru > 0) { + i__1 = m - ll + 1; + dlasr_((char *)"R", (char *)"V", (char *)"B", nru, &i__1, &work[1], &work[*n], &u[ll * + u_dim1 + 1], ldu, (ftnlen)1, (ftnlen)1, (ftnlen)1); + } + if (*ncc > 0) { + i__1 = m - ll + 1; + dlasr_((char *)"L", (char *)"V", (char *)"B", &i__1, ncc, &work[1], &work[*n], &c__[ + ll + c_dim1], ldc, (ftnlen)1, (ftnlen)1, (ftnlen)1); + } + } } /* QR iteration finished, go back and check convergence */ @@ -977,15 +977,15 @@ L90: L160: i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { - if (d__[i__] < 0.) { - d__[i__] = -d__[i__]; + if (d__[i__] < 0.) { + d__[i__] = -d__[i__]; /* Change sign of singular vectors, if desired */ - if (*ncvt > 0) { - dscal_(ncvt, &c_b72, &vt[i__ + vt_dim1], ldvt); - } - } + if (*ncvt > 0) { + dscal_(ncvt, &c_b72, &vt[i__ + vt_dim1], ldvt); + } + } /* L170: */ } @@ -997,35 +997,35 @@ L160: /* Scan for smallest D(I) */ - isub = 1; - smin = d__[1]; - i__2 = *n + 1 - i__; - for (j = 2; j <= i__2; ++j) { - if (d__[j] <= smin) { - isub = j; - smin = d__[j]; - } + isub = 1; + smin = d__[1]; + i__2 = *n + 1 - i__; + for (j = 2; j <= i__2; ++j) { + if (d__[j] <= smin) { + isub = j; + smin = d__[j]; + } /* L180: */ - } - if (isub != *n + 1 - i__) { + } + if (isub != *n + 1 - i__) { /* Swap singular values and vectors */ - d__[isub] = d__[*n + 1 - i__]; - d__[*n + 1 - i__] = smin; - if (*ncvt > 0) { - dswap_(ncvt, &vt[isub + vt_dim1], ldvt, &vt[*n + 1 - i__ + - vt_dim1], ldvt); - } - if (*nru > 0) { - dswap_(nru, &u[isub * u_dim1 + 1], &c__1, &u[(*n + 1 - i__) * - u_dim1 + 1], &c__1); - } - if (*ncc > 0) { - dswap_(ncc, &c__[isub + c_dim1], ldc, &c__[*n + 1 - i__ + - c_dim1], ldc); - } - } + d__[isub] = d__[*n + 1 - i__]; + d__[*n + 1 - i__] = smin; + if (*ncvt > 0) { + dswap_(ncvt, &vt[isub + vt_dim1], ldvt, &vt[*n + 1 - i__ + + vt_dim1], ldvt); + } + if (*nru > 0) { + dswap_(nru, &u[isub * u_dim1 + 1], &c__1, &u[(*n + 1 - i__) * + u_dim1 + 1], &c__1); + } + if (*ncc > 0) { + dswap_(ncc, &c__[isub + c_dim1], ldc, &c__[*n + 1 - i__ + + c_dim1], ldc); + } + } /* L190: */ } goto L220; @@ -1036,9 +1036,9 @@ L200: *info = 0; i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { - if (e[i__] != 0.) { - ++(*info); - } + if (e[i__] != 0.) { + ++(*info); + } /* L210: */ } L220: @@ -1049,5 +1049,5 @@ L220: } /* dbdsqr_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dcabs1.cpp b/lib/linalg/dcabs1.cpp index 2733be3c74..bdaf645a57 100644 --- a/lib/linalg/dcabs1.cpp +++ b/lib/linalg/dcabs1.cpp @@ -1,13 +1,13 @@ /* fortran/dcabs1.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -88,5 +88,5 @@ doublereal dcabs1_(doublecomplex *z__) } /* dcabs1_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dcopy.cpp b/lib/linalg/dcopy.cpp index 52fe214e90..dceb6ad727 100644 --- a/lib/linalg/dcopy.cpp +++ b/lib/linalg/dcopy.cpp @@ -1,13 +1,13 @@ /* fortran/dcopy.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -95,8 +95,8 @@ extern "C" { /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int dcopy_(integer *n, doublereal *dx, integer *incx, - doublereal *dy, integer *incy) +/* Subroutine */ int dcopy_(integer *n, doublereal *dx, integer *incx, + doublereal *dy, integer *incy) { /* System generated locals */ integer i__1; @@ -126,7 +126,7 @@ extern "C" { /* Function Body */ if (*n <= 0) { - return 0; + return 0; } if (*incx == 1 && *incy == 1) { @@ -135,46 +135,46 @@ extern "C" { /* clean-up loop */ - m = *n % 7; - if (m != 0) { - i__1 = m; - for (i__ = 1; i__ <= i__1; ++i__) { - dy[i__] = dx[i__]; - } - if (*n < 7) { - return 0; - } - } - mp1 = m + 1; - i__1 = *n; - for (i__ = mp1; i__ <= i__1; i__ += 7) { - dy[i__] = dx[i__]; - dy[i__ + 1] = dx[i__ + 1]; - dy[i__ + 2] = dx[i__ + 2]; - dy[i__ + 3] = dx[i__ + 3]; - dy[i__ + 4] = dx[i__ + 4]; - dy[i__ + 5] = dx[i__ + 5]; - dy[i__ + 6] = dx[i__ + 6]; - } + m = *n % 7; + if (m != 0) { + i__1 = m; + for (i__ = 1; i__ <= i__1; ++i__) { + dy[i__] = dx[i__]; + } + if (*n < 7) { + return 0; + } + } + mp1 = m + 1; + i__1 = *n; + for (i__ = mp1; i__ <= i__1; i__ += 7) { + dy[i__] = dx[i__]; + dy[i__ + 1] = dx[i__ + 1]; + dy[i__ + 2] = dx[i__ + 2]; + dy[i__ + 3] = dx[i__ + 3]; + dy[i__ + 4] = dx[i__ + 4]; + dy[i__ + 5] = dx[i__ + 5]; + dy[i__ + 6] = dx[i__ + 6]; + } } else { /* code for unequal increments or equal increments */ /* not equal to 1 */ - ix = 1; - iy = 1; - if (*incx < 0) { - ix = (-(*n) + 1) * *incx + 1; - } - if (*incy < 0) { - iy = (-(*n) + 1) * *incy + 1; - } - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - dy[iy] = dx[ix]; - ix += *incx; - iy += *incy; - } + ix = 1; + iy = 1; + if (*incx < 0) { + ix = (-(*n) + 1) * *incx + 1; + } + if (*incy < 0) { + iy = (-(*n) + 1) * *incy + 1; + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + dy[iy] = dx[ix]; + ix += *incx; + iy += *incy; + } } return 0; @@ -183,5 +183,5 @@ extern "C" { } /* dcopy_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/ddot.cpp b/lib/linalg/ddot.cpp index 3f57f45459..e2319f6803 100644 --- a/lib/linalg/ddot.cpp +++ b/lib/linalg/ddot.cpp @@ -1,13 +1,13 @@ /* fortran/ddot.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -95,8 +95,8 @@ extern "C" { /* > \endverbatim */ /* > */ /* ===================================================================== */ -doublereal ddot_(integer *n, doublereal *dx, integer *incx, doublereal *dy, - integer *incy) +doublereal ddot_(integer *n, doublereal *dx, integer *incx, doublereal *dy, + integer *incy) { /* System generated locals */ integer i__1; @@ -130,7 +130,7 @@ doublereal ddot_(integer *n, doublereal *dx, integer *incx, doublereal *dy, ret_val = 0.; dtemp = 0.; if (*n <= 0) { - return ret_val; + return ret_val; } if (*incx == 1 && *incy == 1) { @@ -139,43 +139,43 @@ doublereal ddot_(integer *n, doublereal *dx, integer *incx, doublereal *dy, /* clean-up loop */ - m = *n % 5; - if (m != 0) { - i__1 = m; - for (i__ = 1; i__ <= i__1; ++i__) { - dtemp += dx[i__] * dy[i__]; - } - if (*n < 5) { - ret_val = dtemp; - return ret_val; - } - } - mp1 = m + 1; - i__1 = *n; - for (i__ = mp1; i__ <= i__1; i__ += 5) { - dtemp = dtemp + dx[i__] * dy[i__] + dx[i__ + 1] * dy[i__ + 1] + - dx[i__ + 2] * dy[i__ + 2] + dx[i__ + 3] * dy[i__ + 3] + - dx[i__ + 4] * dy[i__ + 4]; - } + m = *n % 5; + if (m != 0) { + i__1 = m; + for (i__ = 1; i__ <= i__1; ++i__) { + dtemp += dx[i__] * dy[i__]; + } + if (*n < 5) { + ret_val = dtemp; + return ret_val; + } + } + mp1 = m + 1; + i__1 = *n; + for (i__ = mp1; i__ <= i__1; i__ += 5) { + dtemp = dtemp + dx[i__] * dy[i__] + dx[i__ + 1] * dy[i__ + 1] + + dx[i__ + 2] * dy[i__ + 2] + dx[i__ + 3] * dy[i__ + 3] + + dx[i__ + 4] * dy[i__ + 4]; + } } else { /* code for unequal increments or equal increments */ /* not equal to 1 */ - ix = 1; - iy = 1; - if (*incx < 0) { - ix = (-(*n) + 1) * *incx + 1; - } - if (*incy < 0) { - iy = (-(*n) + 1) * *incy + 1; - } - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - dtemp += dx[ix] * dy[iy]; - ix += *incx; - iy += *incy; - } + ix = 1; + iy = 1; + if (*incx < 0) { + ix = (-(*n) + 1) * *incx + 1; + } + if (*incy < 0) { + iy = (-(*n) + 1) * *incy + 1; + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + dtemp += dx[ix] * dy[iy]; + ix += *incx; + iy += *incy; + } } ret_val = dtemp; return ret_val; @@ -185,5 +185,5 @@ doublereal ddot_(integer *n, doublereal *dx, integer *incx, doublereal *dy, } /* ddot_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dgebd2.cpp b/lib/linalg/dgebd2.cpp index 399cd3ca6e..8c95869e21 100644 --- a/lib/linalg/dgebd2.cpp +++ b/lib/linalg/dgebd2.cpp @@ -1,13 +1,13 @@ /* fortran/dgebd2.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -210,19 +210,19 @@ f"> */ /* > */ /* ===================================================================== */ /* Subroutine */ int dgebd2_(integer *m, integer *n, doublereal *a, integer * - lda, doublereal *d__, doublereal *e, doublereal *tauq, doublereal * - taup, doublereal *work, integer *info) + lda, doublereal *d__, doublereal *e, doublereal *tauq, doublereal * + taup, doublereal *work, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; /* Local variables */ integer i__; - extern /* Subroutine */ int dlarf_(char *, integer *, integer *, - doublereal *, integer *, doublereal *, doublereal *, integer *, - doublereal *, ftnlen), dlarfg_(integer *, doublereal *, - doublereal *, integer *, doublereal *), xerbla_(char *, integer *, - ftnlen); + extern /* Subroutine */ int dlarf_(char *, integer *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, + doublereal *, ftnlen), dlarfg_(integer *, doublereal *, + doublereal *, integer *, doublereal *), xerbla_(char *, integer *, + ftnlen); /* -- LAPACK computational routine -- */ @@ -261,126 +261,126 @@ f"> */ /* Function Body */ *info = 0; if (*m < 0) { - *info = -1; + *info = -1; } else if (*n < 0) { - *info = -2; + *info = -2; } else if (*lda < max(1,*m)) { - *info = -4; + *info = -4; } if (*info < 0) { - i__1 = -(*info); - xerbla_((char *)"DGEBD2", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DGEBD2", &i__1, (ftnlen)6); + return 0; } if (*m >= *n) { /* Reduce to upper bidiagonal form */ - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { /* Generate elementary reflector H(i) to annihilate A(i+1:m,i) */ - i__2 = *m - i__ + 1; + i__2 = *m - i__ + 1; /* Computing MIN */ - i__3 = i__ + 1; - dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[min(i__3,*m) + i__ * - a_dim1], &c__1, &tauq[i__]); - d__[i__] = a[i__ + i__ * a_dim1]; - a[i__ + i__ * a_dim1] = 1.; + i__3 = i__ + 1; + dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[min(i__3,*m) + i__ * + a_dim1], &c__1, &tauq[i__]); + d__[i__] = a[i__ + i__ * a_dim1]; + a[i__ + i__ * a_dim1] = 1.; /* Apply H(i) to A(i:m,i+1:n) from the left */ - if (i__ < *n) { - i__2 = *m - i__ + 1; - i__3 = *n - i__; - dlarf_((char *)"Left", &i__2, &i__3, &a[i__ + i__ * a_dim1], &c__1, & - tauq[i__], &a[i__ + (i__ + 1) * a_dim1], lda, &work[1] - , (ftnlen)4); - } - a[i__ + i__ * a_dim1] = d__[i__]; + if (i__ < *n) { + i__2 = *m - i__ + 1; + i__3 = *n - i__; + dlarf_((char *)"Left", &i__2, &i__3, &a[i__ + i__ * a_dim1], &c__1, & + tauq[i__], &a[i__ + (i__ + 1) * a_dim1], lda, &work[1] + , (ftnlen)4); + } + a[i__ + i__ * a_dim1] = d__[i__]; - if (i__ < *n) { + if (i__ < *n) { /* Generate elementary reflector G(i) to annihilate */ /* A(i,i+2:n) */ - i__2 = *n - i__; + i__2 = *n - i__; /* Computing MIN */ - i__3 = i__ + 2; - dlarfg_(&i__2, &a[i__ + (i__ + 1) * a_dim1], &a[i__ + min( - i__3,*n) * a_dim1], lda, &taup[i__]); - e[i__] = a[i__ + (i__ + 1) * a_dim1]; - a[i__ + (i__ + 1) * a_dim1] = 1.; + i__3 = i__ + 2; + dlarfg_(&i__2, &a[i__ + (i__ + 1) * a_dim1], &a[i__ + min( + i__3,*n) * a_dim1], lda, &taup[i__]); + e[i__] = a[i__ + (i__ + 1) * a_dim1]; + a[i__ + (i__ + 1) * a_dim1] = 1.; /* Apply G(i) to A(i+1:m,i+1:n) from the right */ - i__2 = *m - i__; - i__3 = *n - i__; - dlarf_((char *)"Right", &i__2, &i__3, &a[i__ + (i__ + 1) * a_dim1], - lda, &taup[i__], &a[i__ + 1 + (i__ + 1) * a_dim1], - lda, &work[1], (ftnlen)5); - a[i__ + (i__ + 1) * a_dim1] = e[i__]; - } else { - taup[i__] = 0.; - } + i__2 = *m - i__; + i__3 = *n - i__; + dlarf_((char *)"Right", &i__2, &i__3, &a[i__ + (i__ + 1) * a_dim1], + lda, &taup[i__], &a[i__ + 1 + (i__ + 1) * a_dim1], + lda, &work[1], (ftnlen)5); + a[i__ + (i__ + 1) * a_dim1] = e[i__]; + } else { + taup[i__] = 0.; + } /* L10: */ - } + } } else { /* Reduce to lower bidiagonal form */ - i__1 = *m; - for (i__ = 1; i__ <= i__1; ++i__) { + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { /* Generate elementary reflector G(i) to annihilate A(i,i+1:n) */ - i__2 = *n - i__ + 1; + i__2 = *n - i__ + 1; /* Computing MIN */ - i__3 = i__ + 1; - dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[i__ + min(i__3,*n) * - a_dim1], lda, &taup[i__]); - d__[i__] = a[i__ + i__ * a_dim1]; - a[i__ + i__ * a_dim1] = 1.; + i__3 = i__ + 1; + dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[i__ + min(i__3,*n) * + a_dim1], lda, &taup[i__]); + d__[i__] = a[i__ + i__ * a_dim1]; + a[i__ + i__ * a_dim1] = 1.; /* Apply G(i) to A(i+1:m,i:n) from the right */ - if (i__ < *m) { - i__2 = *m - i__; - i__3 = *n - i__ + 1; - dlarf_((char *)"Right", &i__2, &i__3, &a[i__ + i__ * a_dim1], lda, & - taup[i__], &a[i__ + 1 + i__ * a_dim1], lda, &work[1], - (ftnlen)5); - } - a[i__ + i__ * a_dim1] = d__[i__]; + if (i__ < *m) { + i__2 = *m - i__; + i__3 = *n - i__ + 1; + dlarf_((char *)"Right", &i__2, &i__3, &a[i__ + i__ * a_dim1], lda, & + taup[i__], &a[i__ + 1 + i__ * a_dim1], lda, &work[1], + (ftnlen)5); + } + a[i__ + i__ * a_dim1] = d__[i__]; - if (i__ < *m) { + if (i__ < *m) { /* Generate elementary reflector H(i) to annihilate */ /* A(i+2:m,i) */ - i__2 = *m - i__; + i__2 = *m - i__; /* Computing MIN */ - i__3 = i__ + 2; - dlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3,*m) + - i__ * a_dim1], &c__1, &tauq[i__]); - e[i__] = a[i__ + 1 + i__ * a_dim1]; - a[i__ + 1 + i__ * a_dim1] = 1.; + i__3 = i__ + 2; + dlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3,*m) + + i__ * a_dim1], &c__1, &tauq[i__]); + e[i__] = a[i__ + 1 + i__ * a_dim1]; + a[i__ + 1 + i__ * a_dim1] = 1.; /* Apply H(i) to A(i+1:m,i+1:n) from the left */ - i__2 = *m - i__; - i__3 = *n - i__; - dlarf_((char *)"Left", &i__2, &i__3, &a[i__ + 1 + i__ * a_dim1], & - c__1, &tauq[i__], &a[i__ + 1 + (i__ + 1) * a_dim1], - lda, &work[1], (ftnlen)4); - a[i__ + 1 + i__ * a_dim1] = e[i__]; - } else { - tauq[i__] = 0.; - } + i__2 = *m - i__; + i__3 = *n - i__; + dlarf_((char *)"Left", &i__2, &i__3, &a[i__ + 1 + i__ * a_dim1], & + c__1, &tauq[i__], &a[i__ + 1 + (i__ + 1) * a_dim1], + lda, &work[1], (ftnlen)4); + a[i__ + 1 + i__ * a_dim1] = e[i__]; + } else { + tauq[i__] = 0.; + } /* L20: */ - } + } } return 0; @@ -389,5 +389,5 @@ f"> */ } /* dgebd2_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dgebrd.cpp b/lib/linalg/dgebrd.cpp index 84827afcfd..0be33bde5c 100644 --- a/lib/linalg/dgebrd.cpp +++ b/lib/linalg/dgebrd.cpp @@ -1,13 +1,13 @@ /* fortran/dgebrd.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -230,26 +230,26 @@ f"> */ /* > */ /* ===================================================================== */ /* Subroutine */ int dgebrd_(integer *m, integer *n, doublereal *a, integer * - lda, doublereal *d__, doublereal *e, doublereal *tauq, doublereal * - taup, doublereal *work, integer *lwork, integer *info) + lda, doublereal *d__, doublereal *e, doublereal *tauq, doublereal * + taup, doublereal *work, integer *lwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4; /* Local variables */ integer i__, j, nb, nx, ws; - extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); integer nbmin, iinfo, minmn; - extern /* Subroutine */ int dgebd2_(integer *, integer *, doublereal *, - integer *, doublereal *, doublereal *, doublereal *, doublereal *, - doublereal *, integer *), dlabrd_(integer *, integer *, integer * - , doublereal *, integer *, doublereal *, doublereal *, doublereal - *, doublereal *, doublereal *, integer *, doublereal *, integer *) - , xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dgebd2_(integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, integer *), dlabrd_(integer *, integer *, integer * + , doublereal *, integer *, doublereal *, doublereal *, doublereal + *, doublereal *, doublereal *, integer *, doublereal *, integer *) + , xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); integer ldwrkx, ldwrky, lwkopt; logical lquery; @@ -293,38 +293,38 @@ f"> */ *info = 0; /* Computing MAX */ i__1 = 1, i__2 = ilaenv_(&c__1, (char *)"DGEBRD", (char *)" ", m, n, &c_n1, &c_n1, ( - ftnlen)6, (ftnlen)1); + ftnlen)6, (ftnlen)1); nb = max(i__1,i__2); lwkopt = (*m + *n) * nb; work[1] = (doublereal) lwkopt; lquery = *lwork == -1; if (*m < 0) { - *info = -1; + *info = -1; } else if (*n < 0) { - *info = -2; + *info = -2; } else if (*lda < max(1,*m)) { - *info = -4; + *info = -4; } else /* if(complicated condition) */ { /* Computing MAX */ - i__1 = max(1,*m); - if (*lwork < max(i__1,*n) && ! lquery) { - *info = -10; - } + i__1 = max(1,*m); + if (*lwork < max(i__1,*n) && ! lquery) { + *info = -10; + } } if (*info < 0) { - i__1 = -(*info); - xerbla_((char *)"DGEBRD", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DGEBRD", &i__1, (ftnlen)6); + return 0; } else if (lquery) { - return 0; + return 0; } /* Quick return if possible */ minmn = min(*m,*n); if (minmn == 0) { - work[1] = 1.; - return 0; + work[1] = 1.; + return 0; } ws = max(*m,*n); @@ -336,31 +336,31 @@ f"> */ /* Set the crossover point NX. */ /* Computing MAX */ - i__1 = nb, i__2 = ilaenv_(&c__3, (char *)"DGEBRD", (char *)" ", m, n, &c_n1, &c_n1, ( - ftnlen)6, (ftnlen)1); - nx = max(i__1,i__2); + i__1 = nb, i__2 = ilaenv_(&c__3, (char *)"DGEBRD", (char *)" ", m, n, &c_n1, &c_n1, ( + ftnlen)6, (ftnlen)1); + nx = max(i__1,i__2); /* Determine when to switch from blocked to unblocked code. */ - if (nx < minmn) { - ws = (*m + *n) * nb; - if (*lwork < ws) { + if (nx < minmn) { + ws = (*m + *n) * nb; + if (*lwork < ws) { /* Not enough work space for the optimal NB, consider using */ /* a smaller block size. */ - nbmin = ilaenv_(&c__2, (char *)"DGEBRD", (char *)" ", m, n, &c_n1, &c_n1, ( - ftnlen)6, (ftnlen)1); - if (*lwork >= (*m + *n) * nbmin) { - nb = *lwork / (*m + *n); - } else { - nb = 1; - nx = minmn; - } - } - } + nbmin = ilaenv_(&c__2, (char *)"DGEBRD", (char *)" ", m, n, &c_n1, &c_n1, ( + ftnlen)6, (ftnlen)1); + if (*lwork >= (*m + *n) * nbmin) { + nb = *lwork / (*m + *n); + } else { + nb = 1; + nx = minmn; + } + } + } } else { - nx = minmn; + nx = minmn; } i__1 = minmn - nx; @@ -371,45 +371,45 @@ f"> */ /* the matrices X and Y which are needed to update the unreduced */ /* part of the matrix */ - i__3 = *m - i__ + 1; - i__4 = *n - i__ + 1; - dlabrd_(&i__3, &i__4, &nb, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[ - i__], &tauq[i__], &taup[i__], &work[1], &ldwrkx, &work[ldwrkx - * nb + 1], &ldwrky); + i__3 = *m - i__ + 1; + i__4 = *n - i__ + 1; + dlabrd_(&i__3, &i__4, &nb, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[ + i__], &tauq[i__], &taup[i__], &work[1], &ldwrkx, &work[ldwrkx + * nb + 1], &ldwrky); /* Update the trailing submatrix A(i+nb:m,i+nb:n), using an update */ /* of the form A := A - V*Y**T - X*U**T */ - i__3 = *m - i__ - nb + 1; - i__4 = *n - i__ - nb + 1; - dgemm_((char *)"No transpose", (char *)"Transpose", &i__3, &i__4, &nb, &c_b21, &a[i__ - + nb + i__ * a_dim1], lda, &work[ldwrkx * nb + nb + 1], & - ldwrky, &c_b22, &a[i__ + nb + (i__ + nb) * a_dim1], lda, ( - ftnlen)12, (ftnlen)9); - i__3 = *m - i__ - nb + 1; - i__4 = *n - i__ - nb + 1; - dgemm_((char *)"No transpose", (char *)"No transpose", &i__3, &i__4, &nb, &c_b21, & - work[nb + 1], &ldwrkx, &a[i__ + (i__ + nb) * a_dim1], lda, & - c_b22, &a[i__ + nb + (i__ + nb) * a_dim1], lda, (ftnlen)12, ( - ftnlen)12); + i__3 = *m - i__ - nb + 1; + i__4 = *n - i__ - nb + 1; + dgemm_((char *)"No transpose", (char *)"Transpose", &i__3, &i__4, &nb, &c_b21, &a[i__ + + nb + i__ * a_dim1], lda, &work[ldwrkx * nb + nb + 1], & + ldwrky, &c_b22, &a[i__ + nb + (i__ + nb) * a_dim1], lda, ( + ftnlen)12, (ftnlen)9); + i__3 = *m - i__ - nb + 1; + i__4 = *n - i__ - nb + 1; + dgemm_((char *)"No transpose", (char *)"No transpose", &i__3, &i__4, &nb, &c_b21, & + work[nb + 1], &ldwrkx, &a[i__ + (i__ + nb) * a_dim1], lda, & + c_b22, &a[i__ + nb + (i__ + nb) * a_dim1], lda, (ftnlen)12, ( + ftnlen)12); /* Copy diagonal and off-diagonal elements of B back into A */ - if (*m >= *n) { - i__3 = i__ + nb - 1; - for (j = i__; j <= i__3; ++j) { - a[j + j * a_dim1] = d__[j]; - a[j + (j + 1) * a_dim1] = e[j]; + if (*m >= *n) { + i__3 = i__ + nb - 1; + for (j = i__; j <= i__3; ++j) { + a[j + j * a_dim1] = d__[j]; + a[j + (j + 1) * a_dim1] = e[j]; /* L10: */ - } - } else { - i__3 = i__ + nb - 1; - for (j = i__; j <= i__3; ++j) { - a[j + j * a_dim1] = d__[j]; - a[j + 1 + j * a_dim1] = e[j]; + } + } else { + i__3 = i__ + nb - 1; + for (j = i__; j <= i__3; ++j) { + a[j + j * a_dim1] = d__[j]; + a[j + 1 + j * a_dim1] = e[j]; /* L20: */ - } - } + } + } /* L30: */ } @@ -418,7 +418,7 @@ f"> */ i__2 = *m - i__ + 1; i__1 = *n - i__ + 1; dgebd2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[i__], & - tauq[i__], &taup[i__], &work[1], &iinfo); + tauq[i__], &taup[i__], &work[1], &iinfo); work[1] = (doublereal) ws; return 0; @@ -427,5 +427,5 @@ f"> */ } /* dgebrd_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dgecon.cpp b/lib/linalg/dgecon.cpp index 07a305d74f..76a0186cc8 100644 --- a/lib/linalg/dgecon.cpp +++ b/lib/linalg/dgecon.cpp @@ -1,13 +1,13 @@ /* fortran/dgecon.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -144,8 +144,8 @@ f"> */ /* ===================================================================== */ /* Subroutine */ int dgecon_(char *norm, integer *n, doublereal *a, integer * - lda, doublereal *anorm, doublereal *rcond, doublereal *work, integer * - iwork, integer *info, ftnlen norm_len) + lda, doublereal *anorm, doublereal *rcond, doublereal *work, integer * + iwork, integer *info, ftnlen norm_len) { /* System generated locals */ integer a_dim1, a_offset, i__1; @@ -159,16 +159,16 @@ f"> */ doublereal scale; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer isave[3]; - extern /* Subroutine */ int drscl_(integer *, doublereal *, doublereal *, - integer *), dlacn2_(integer *, doublereal *, doublereal *, - integer *, doublereal *, integer *, integer *); + extern /* Subroutine */ int drscl_(integer *, doublereal *, doublereal *, + integer *), dlacn2_(integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, integer *); extern doublereal dlamch_(char *, ftnlen); extern integer idamax_(integer *, doublereal *, integer *); extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); doublereal ainvnm; - extern /* Subroutine */ int dlatrs_(char *, char *, char *, char *, - integer *, doublereal *, integer *, doublereal *, doublereal *, - doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + extern /* Subroutine */ int dlatrs_(char *, char *, char *, char *, + integer *, doublereal *, integer *, doublereal *, doublereal *, + doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); logical onenrm; char normin[1]; doublereal smlnum; @@ -211,30 +211,30 @@ f"> */ /* Function Body */ *info = 0; onenrm = *(unsigned char *)norm == '1' || lsame_(norm, (char *)"O", (ftnlen)1, ( - ftnlen)1); + ftnlen)1); if (! onenrm && ! lsame_(norm, (char *)"I", (ftnlen)1, (ftnlen)1)) { - *info = -1; + *info = -1; } else if (*n < 0) { - *info = -2; + *info = -2; } else if (*lda < max(1,*n)) { - *info = -4; + *info = -4; } else if (*anorm < 0.) { - *info = -5; + *info = -5; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DGECON", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DGECON", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ *rcond = 0.; if (*n == 0) { - *rcond = 1.; - return 0; + *rcond = 1.; + return 0; } else if (*anorm == 0.) { - return 0; + return 0; } smlnum = dlamch_((char *)"Safe minimum", (ftnlen)12); @@ -244,61 +244,61 @@ f"> */ ainvnm = 0.; *(unsigned char *)normin = 'N'; if (onenrm) { - kase1 = 1; + kase1 = 1; } else { - kase1 = 2; + kase1 = 2; } kase = 0; L10: dlacn2_(n, &work[*n + 1], &work[1], &iwork[1], &ainvnm, &kase, isave); if (kase != 0) { - if (kase == kase1) { + if (kase == kase1) { /* Multiply by inv(L). */ - dlatrs_((char *)"Lower", (char *)"No transpose", (char *)"Unit", normin, n, &a[a_offset], - lda, &work[1], &sl, &work[(*n << 1) + 1], info, (ftnlen)5, - (ftnlen)12, (ftnlen)4, (ftnlen)1); + dlatrs_((char *)"Lower", (char *)"No transpose", (char *)"Unit", normin, n, &a[a_offset], + lda, &work[1], &sl, &work[(*n << 1) + 1], info, (ftnlen)5, + (ftnlen)12, (ftnlen)4, (ftnlen)1); /* Multiply by inv(U). */ - dlatrs_((char *)"Upper", (char *)"No transpose", (char *)"Non-unit", normin, n, &a[ - a_offset], lda, &work[1], &su, &work[*n * 3 + 1], info, ( - ftnlen)5, (ftnlen)12, (ftnlen)8, (ftnlen)1); - } else { + dlatrs_((char *)"Upper", (char *)"No transpose", (char *)"Non-unit", normin, n, &a[ + a_offset], lda, &work[1], &su, &work[*n * 3 + 1], info, ( + ftnlen)5, (ftnlen)12, (ftnlen)8, (ftnlen)1); + } else { /* Multiply by inv(U**T). */ - dlatrs_((char *)"Upper", (char *)"Transpose", (char *)"Non-unit", normin, n, &a[a_offset], - lda, &work[1], &su, &work[*n * 3 + 1], info, (ftnlen)5, ( - ftnlen)9, (ftnlen)8, (ftnlen)1); + dlatrs_((char *)"Upper", (char *)"Transpose", (char *)"Non-unit", normin, n, &a[a_offset], + lda, &work[1], &su, &work[*n * 3 + 1], info, (ftnlen)5, ( + ftnlen)9, (ftnlen)8, (ftnlen)1); /* Multiply by inv(L**T). */ - dlatrs_((char *)"Lower", (char *)"Transpose", (char *)"Unit", normin, n, &a[a_offset], - lda, &work[1], &sl, &work[(*n << 1) + 1], info, (ftnlen)5, - (ftnlen)9, (ftnlen)4, (ftnlen)1); - } + dlatrs_((char *)"Lower", (char *)"Transpose", (char *)"Unit", normin, n, &a[a_offset], + lda, &work[1], &sl, &work[(*n << 1) + 1], info, (ftnlen)5, + (ftnlen)9, (ftnlen)4, (ftnlen)1); + } /* Divide X by 1/(SL*SU) if doing so will not cause overflow. */ - scale = sl * su; - *(unsigned char *)normin = 'Y'; - if (scale != 1.) { - ix = idamax_(n, &work[1], &c__1); - if (scale < (d__1 = work[ix], abs(d__1)) * smlnum || scale == 0.) - { - goto L20; - } - drscl_(n, &scale, &work[1], &c__1); - } - goto L10; + scale = sl * su; + *(unsigned char *)normin = 'Y'; + if (scale != 1.) { + ix = idamax_(n, &work[1], &c__1); + if (scale < (d__1 = work[ix], abs(d__1)) * smlnum || scale == 0.) + { + goto L20; + } + drscl_(n, &scale, &work[1], &c__1); + } + goto L10; } /* Compute the estimate of the reciprocal condition number. */ if (ainvnm != 0.) { - *rcond = 1. / ainvnm / *anorm; + *rcond = 1. / ainvnm / *anorm; } L20: @@ -309,5 +309,5 @@ L20: } /* dgecon_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dgelq2.cpp b/lib/linalg/dgelq2.cpp index 6000253184..fec5ae2c50 100644 --- a/lib/linalg/dgelq2.cpp +++ b/lib/linalg/dgelq2.cpp @@ -1,13 +1,13 @@ /* fortran/dgelq2.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -147,7 +147,7 @@ f"> */ /* > */ /* ===================================================================== */ /* Subroutine */ int dgelq2_(integer *m, integer *n, doublereal *a, integer * - lda, doublereal *tau, doublereal *work, integer *info) + lda, doublereal *tau, doublereal *work, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; @@ -155,11 +155,11 @@ f"> */ /* Local variables */ integer i__, k; doublereal aii; - extern /* Subroutine */ int dlarf_(char *, integer *, integer *, - doublereal *, integer *, doublereal *, doublereal *, integer *, - doublereal *, ftnlen), dlarfg_(integer *, doublereal *, - doublereal *, integer *, doublereal *), xerbla_(char *, integer *, - ftnlen); + extern /* Subroutine */ int dlarf_(char *, integer *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, + doublereal *, ftnlen), dlarfg_(integer *, doublereal *, + doublereal *, integer *, doublereal *), xerbla_(char *, integer *, + ftnlen); /* -- LAPACK computational routine -- */ @@ -195,16 +195,16 @@ f"> */ /* Function Body */ *info = 0; if (*m < 0) { - *info = -1; + *info = -1; } else if (*n < 0) { - *info = -2; + *info = -2; } else if (*lda < max(1,*m)) { - *info = -4; + *info = -4; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DGELQ2", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DGELQ2", &i__1, (ftnlen)6); + return 0; } k = min(*m,*n); @@ -214,24 +214,24 @@ f"> */ /* Generate elementary reflector H(i) to annihilate A(i,i+1:n) */ - i__2 = *n - i__ + 1; + i__2 = *n - i__ + 1; /* Computing MIN */ - i__3 = i__ + 1; - dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[i__ + min(i__3,*n) * a_dim1] - , lda, &tau[i__]); - if (i__ < *m) { + i__3 = i__ + 1; + dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[i__ + min(i__3,*n) * a_dim1] + , lda, &tau[i__]); + if (i__ < *m) { /* Apply H(i) to A(i+1:m,i:n) from the right */ - aii = a[i__ + i__ * a_dim1]; - a[i__ + i__ * a_dim1] = 1.; - i__2 = *m - i__; - i__3 = *n - i__ + 1; - dlarf_((char *)"Right", &i__2, &i__3, &a[i__ + i__ * a_dim1], lda, &tau[ - i__], &a[i__ + 1 + i__ * a_dim1], lda, &work[1], (ftnlen) - 5); - a[i__ + i__ * a_dim1] = aii; - } + aii = a[i__ + i__ * a_dim1]; + a[i__ + i__ * a_dim1] = 1.; + i__2 = *m - i__; + i__3 = *n - i__ + 1; + dlarf_((char *)"Right", &i__2, &i__3, &a[i__ + i__ * a_dim1], lda, &tau[ + i__], &a[i__ + 1 + i__ * a_dim1], lda, &work[1], (ftnlen) + 5); + a[i__ + i__ * a_dim1] = aii; + } /* L10: */ } return 0; @@ -241,5 +241,5 @@ f"> */ } /* dgelq2_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dgelqf.cpp b/lib/linalg/dgelqf.cpp index ede5b8198b..f6e60e5bcf 100644 --- a/lib/linalg/dgelqf.cpp +++ b/lib/linalg/dgelqf.cpp @@ -1,13 +1,13 @@ /* fortran/dgelqf.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -167,23 +167,23 @@ f"> */ /* > */ /* ===================================================================== */ /* Subroutine */ int dgelqf_(integer *m, integer *n, doublereal *a, integer * - lda, doublereal *tau, doublereal *work, integer *lwork, integer *info) + lda, doublereal *tau, doublereal *work, integer *lwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4; /* Local variables */ integer i__, k, ib, nb, nx, iws, nbmin, iinfo; - extern /* Subroutine */ int dgelq2_(integer *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *), dlarfb_(char *, - char *, char *, char *, integer *, integer *, integer *, - doublereal *, integer *, doublereal *, integer *, doublereal *, - integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, - ftnlen), dlarft_(char *, char *, integer *, integer *, doublereal - *, integer *, doublereal *, doublereal *, integer *, ftnlen, - ftnlen), xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dgelq2_(integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *), dlarfb_(char *, + char *, char *, char *, integer *, integer *, integer *, + doublereal *, integer *, doublereal *, integer *, doublereal *, + integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, + ftnlen), dlarft_(char *, char *, integer *, integer *, doublereal + *, integer *, doublereal *, doublereal *, integer *, ftnlen, + ftnlen), xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); integer ldwork, lwkopt; logical lquery; @@ -221,33 +221,33 @@ f"> */ /* Function Body */ *info = 0; nb = ilaenv_(&c__1, (char *)"DGELQF", (char *)" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen) - 1); + 1); lwkopt = *m * nb; work[1] = (doublereal) lwkopt; lquery = *lwork == -1; if (*m < 0) { - *info = -1; + *info = -1; } else if (*n < 0) { - *info = -2; + *info = -2; } else if (*lda < max(1,*m)) { - *info = -4; + *info = -4; } else if (*lwork < max(1,*m) && ! lquery) { - *info = -7; + *info = -7; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DGELQF", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DGELQF", &i__1, (ftnlen)6); + return 0; } else if (lquery) { - return 0; + return 0; } /* Quick return if possible */ k = min(*m,*n); if (k == 0) { - work[1] = 1.; - return 0; + work[1] = 1.; + return 0; } nbmin = 2; @@ -258,79 +258,79 @@ f"> */ /* Determine when to cross over from blocked to unblocked code. */ /* Computing MAX */ - i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"DGELQF", (char *)" ", m, n, &c_n1, &c_n1, ( - ftnlen)6, (ftnlen)1); - nx = max(i__1,i__2); - if (nx < k) { + i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"DGELQF", (char *)" ", m, n, &c_n1, &c_n1, ( + ftnlen)6, (ftnlen)1); + nx = max(i__1,i__2); + if (nx < k) { /* Determine if workspace is large enough for blocked code. */ - ldwork = *m; - iws = ldwork * nb; - if (*lwork < iws) { + ldwork = *m; + iws = ldwork * nb; + if (*lwork < iws) { /* Not enough workspace to use optimal NB: reduce NB and */ /* determine the minimum value of NB. */ - nb = *lwork / ldwork; + nb = *lwork / ldwork; /* Computing MAX */ - i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DGELQF", (char *)" ", m, n, &c_n1, & - c_n1, (ftnlen)6, (ftnlen)1); - nbmin = max(i__1,i__2); - } - } + i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DGELQF", (char *)" ", m, n, &c_n1, & + c_n1, (ftnlen)6, (ftnlen)1); + nbmin = max(i__1,i__2); + } + } } if (nb >= nbmin && nb < k && nx < k) { /* Use blocked code initially */ - i__1 = k - nx; - i__2 = nb; - for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { + i__1 = k - nx; + i__2 = nb; + for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { /* Computing MIN */ - i__3 = k - i__ + 1; - ib = min(i__3,nb); + i__3 = k - i__ + 1; + ib = min(i__3,nb); /* Compute the LQ factorization of the current block */ /* A(i:i+ib-1,i:n) */ - i__3 = *n - i__ + 1; - dgelq2_(&ib, &i__3, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[ - 1], &iinfo); - if (i__ + ib <= *m) { + i__3 = *n - i__ + 1; + dgelq2_(&ib, &i__3, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[ + 1], &iinfo); + if (i__ + ib <= *m) { /* Form the triangular factor of the block reflector */ /* H = H(i) H(i+1) . . . H(i+ib-1) */ - i__3 = *n - i__ + 1; - dlarft_((char *)"Forward", (char *)"Rowwise", &i__3, &ib, &a[i__ + i__ * - a_dim1], lda, &tau[i__], &work[1], &ldwork, (ftnlen)7, - (ftnlen)7); + i__3 = *n - i__ + 1; + dlarft_((char *)"Forward", (char *)"Rowwise", &i__3, &ib, &a[i__ + i__ * + a_dim1], lda, &tau[i__], &work[1], &ldwork, (ftnlen)7, + (ftnlen)7); /* Apply H to A(i+ib:m,i:n) from the right */ - i__3 = *m - i__ - ib + 1; - i__4 = *n - i__ + 1; - dlarfb_((char *)"Right", (char *)"No transpose", (char *)"Forward", (char *)"Rowwise", &i__3, - &i__4, &ib, &a[i__ + i__ * a_dim1], lda, &work[1], & - ldwork, &a[i__ + ib + i__ * a_dim1], lda, &work[ib + - 1], &ldwork, (ftnlen)5, (ftnlen)12, (ftnlen)7, ( - ftnlen)7); - } + i__3 = *m - i__ - ib + 1; + i__4 = *n - i__ + 1; + dlarfb_((char *)"Right", (char *)"No transpose", (char *)"Forward", (char *)"Rowwise", &i__3, + &i__4, &ib, &a[i__ + i__ * a_dim1], lda, &work[1], & + ldwork, &a[i__ + ib + i__ * a_dim1], lda, &work[ib + + 1], &ldwork, (ftnlen)5, (ftnlen)12, (ftnlen)7, ( + ftnlen)7); + } /* L10: */ - } + } } else { - i__ = 1; + i__ = 1; } /* Use unblocked code to factor the last or only block. */ if (i__ <= k) { - i__2 = *m - i__ + 1; - i__1 = *n - i__ + 1; - dgelq2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[1] - , &iinfo); + i__2 = *m - i__ + 1; + i__1 = *n - i__ + 1; + dgelq2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[1] + , &iinfo); } work[1] = (doublereal) iws; @@ -341,5 +341,5 @@ f"> */ } /* dgelqf_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dgelsd.cpp b/lib/linalg/dgelsd.cpp index 7a74d30ef2..ffe7446f85 100644 --- a/lib/linalg/dgelsd.cpp +++ b/lib/linalg/dgelsd.cpp @@ -1,13 +1,13 @@ /* fortran/dgelsd.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -234,10 +234,10 @@ f"> */ /* > Osni Marques, LBNL/NERSC, USA \n */ /* ===================================================================== */ -/* Subroutine */ int dgelsd_(integer *m, integer *n, integer *nrhs, - doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal * - s, doublereal *rcond, integer *rank, doublereal *work, integer *lwork, - integer *iwork, integer *info) +/* Subroutine */ int dgelsd_(integer *m, integer *n, integer *nrhs, + doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal * + s, doublereal *rcond, integer *rank, doublereal *work, integer *lwork, + integer *iwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4; @@ -252,39 +252,39 @@ f"> */ doublereal sfmin; integer minmn, maxmn, itaup, itauq, mnthr, nwork; extern /* Subroutine */ int dlabad_(doublereal *, doublereal *), dgebrd_( - integer *, integer *, doublereal *, integer *, doublereal *, - doublereal *, doublereal *, doublereal *, doublereal *, integer *, - integer *); - extern doublereal dlamch_(char *, ftnlen), dlange_(char *, integer *, - integer *, doublereal *, integer *, doublereal *, ftnlen); - extern /* Subroutine */ int dgelqf_(integer *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, integer *), - dlalsd_(char *, integer *, integer *, integer *, doublereal *, - doublereal *, doublereal *, integer *, doublereal *, integer *, - doublereal *, integer *, integer *, ftnlen), dlascl_(char *, - integer *, integer *, doublereal *, doublereal *, integer *, - integer *, doublereal *, integer *, integer *, ftnlen), dgeqrf_( - integer *, integer *, doublereal *, integer *, doublereal *, - doublereal *, integer *, integer *), dlacpy_(char *, integer *, - integer *, doublereal *, integer *, doublereal *, integer *, - ftnlen), dlaset_(char *, integer *, integer *, doublereal *, - doublereal *, doublereal *, integer *, ftnlen), xerbla_(char *, - integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, doublereal *, doublereal *, doublereal *, integer *, + integer *); + extern doublereal dlamch_(char *, ftnlen), dlange_(char *, integer *, + integer *, doublereal *, integer *, doublereal *, ftnlen); + extern /* Subroutine */ int dgelqf_(integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, integer *), + dlalsd_(char *, integer *, integer *, integer *, doublereal *, + doublereal *, doublereal *, integer *, doublereal *, integer *, + doublereal *, integer *, integer *, ftnlen), dlascl_(char *, + integer *, integer *, doublereal *, doublereal *, integer *, + integer *, doublereal *, integer *, integer *, ftnlen), dgeqrf_( + integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, integer *), dlacpy_(char *, integer *, + integer *, doublereal *, integer *, doublereal *, integer *, + ftnlen), dlaset_(char *, integer *, integer *, doublereal *, + doublereal *, doublereal *, integer *, ftnlen), xerbla_(char *, + integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); doublereal bignum; - extern /* Subroutine */ int dormbr_(char *, char *, char *, integer *, - integer *, integer *, doublereal *, integer *, doublereal *, - doublereal *, integer *, doublereal *, integer *, integer *, - ftnlen, ftnlen, ftnlen); + extern /* Subroutine */ int dormbr_(char *, char *, char *, integer *, + integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, doublereal *, integer *, integer *, + ftnlen, ftnlen, ftnlen); integer wlalsd; - extern /* Subroutine */ int dormlq_(char *, char *, integer *, integer *, - integer *, doublereal *, integer *, doublereal *, doublereal *, - integer *, doublereal *, integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dormlq_(char *, char *, integer *, integer *, + integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, integer *, ftnlen, ftnlen); integer ldwork; - extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *, - integer *, doublereal *, integer *, doublereal *, doublereal *, - integer *, doublereal *, integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *, + integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, integer *, ftnlen, ftnlen); integer liwork, minwrk, maxwrk; doublereal smlnum; logical lquery; @@ -332,22 +332,22 @@ f"> */ minmn = min(*m,*n); maxmn = max(*m,*n); mnthr = ilaenv_(&c__6, (char *)"DGELSD", (char *)" ", m, n, nrhs, &c_n1, (ftnlen)6, ( - ftnlen)1); + ftnlen)1); lquery = *lwork == -1; if (*m < 0) { - *info = -1; + *info = -1; } else if (*n < 0) { - *info = -2; + *info = -2; } else if (*nrhs < 0) { - *info = -3; + *info = -3; } else if (*lda < max(1,*m)) { - *info = -5; + *info = -5; } else if (*ldb < max(1,maxmn)) { - *info = -7; + *info = -7; } smlsiz = ilaenv_(&c__9, (char *)"DGELSD", (char *)" ", &c__0, &c__0, &c__0, &c__0, ( - ftnlen)6, (ftnlen)1); + ftnlen)6, (ftnlen)1); /* Compute workspace. */ /* (Note: Comments in the code beginning (char *)"Workspace:" describe the */ @@ -360,151 +360,151 @@ f"> */ liwork = 1; minmn = max(1,minmn); /* Computing MAX */ - i__1 = (integer) (log((doublereal) minmn / (doublereal) (smlsiz + 1)) / - log(2.)) + 1; + i__1 = (integer) (log((doublereal) minmn / (doublereal) (smlsiz + 1)) / + log(2.)) + 1; nlvl = max(i__1,0); if (*info == 0) { - maxwrk = 0; - liwork = minmn * 3 * nlvl + minmn * 11; - mm = *m; - if (*m >= *n && *m >= mnthr) { + maxwrk = 0; + liwork = minmn * 3 * nlvl + minmn * 11; + mm = *m; + if (*m >= *n && *m >= mnthr) { /* Path 1a - overdetermined, with many more rows than columns. */ - mm = *n; + mm = *n; /* Computing MAX */ - i__1 = maxwrk, i__2 = *n + *n * ilaenv_(&c__1, (char *)"DGEQRF", (char *)" ", m, - n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); - maxwrk = max(i__1,i__2); + i__1 = maxwrk, i__2 = *n + *n * ilaenv_(&c__1, (char *)"DGEQRF", (char *)" ", m, + n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); + maxwrk = max(i__1,i__2); /* Computing MAX */ - i__1 = maxwrk, i__2 = *n + *nrhs * ilaenv_(&c__1, (char *)"DORMQR", (char *)"LT", - m, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)2); - maxwrk = max(i__1,i__2); - } - if (*m >= *n) { + i__1 = maxwrk, i__2 = *n + *nrhs * ilaenv_(&c__1, (char *)"DORMQR", (char *)"LT", + m, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)2); + maxwrk = max(i__1,i__2); + } + if (*m >= *n) { /* Path 1 - overdetermined or exactly determined. */ /* Computing MAX */ - i__1 = maxwrk, i__2 = *n * 3 + (mm + *n) * ilaenv_(&c__1, (char *)"DGEBRD" - , (char *)" ", &mm, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); - maxwrk = max(i__1,i__2); + i__1 = maxwrk, i__2 = *n * 3 + (mm + *n) * ilaenv_(&c__1, (char *)"DGEBRD" + , (char *)" ", &mm, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); + maxwrk = max(i__1,i__2); /* Computing MAX */ - i__1 = maxwrk, i__2 = *n * 3 + *nrhs * ilaenv_(&c__1, (char *)"DORMBR", - (char *)"QLT", &mm, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)3); - maxwrk = max(i__1,i__2); + i__1 = maxwrk, i__2 = *n * 3 + *nrhs * ilaenv_(&c__1, (char *)"DORMBR", + (char *)"QLT", &mm, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)3); + maxwrk = max(i__1,i__2); /* Computing MAX */ - i__1 = maxwrk, i__2 = *n * 3 + (*n - 1) * ilaenv_(&c__1, (char *)"DORMBR", - (char *)"PLN", n, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)3); - maxwrk = max(i__1,i__2); + i__1 = maxwrk, i__2 = *n * 3 + (*n - 1) * ilaenv_(&c__1, (char *)"DORMBR", + (char *)"PLN", n, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)3); + maxwrk = max(i__1,i__2); /* Computing 2nd power */ - i__1 = smlsiz + 1; - wlalsd = *n * 9 + (*n << 1) * smlsiz + (*n << 3) * nlvl + *n * * - nrhs + i__1 * i__1; + i__1 = smlsiz + 1; + wlalsd = *n * 9 + (*n << 1) * smlsiz + (*n << 3) * nlvl + *n * * + nrhs + i__1 * i__1; /* Computing MAX */ - i__1 = maxwrk, i__2 = *n * 3 + wlalsd; - maxwrk = max(i__1,i__2); + i__1 = maxwrk, i__2 = *n * 3 + wlalsd; + maxwrk = max(i__1,i__2); /* Computing MAX */ - i__1 = *n * 3 + mm, i__2 = *n * 3 + *nrhs, i__1 = max(i__1,i__2), - i__2 = *n * 3 + wlalsd; - minwrk = max(i__1,i__2); - } - if (*n > *m) { + i__1 = *n * 3 + mm, i__2 = *n * 3 + *nrhs, i__1 = max(i__1,i__2), + i__2 = *n * 3 + wlalsd; + minwrk = max(i__1,i__2); + } + if (*n > *m) { /* Computing 2nd power */ - i__1 = smlsiz + 1; - wlalsd = *m * 9 + (*m << 1) * smlsiz + (*m << 3) * nlvl + *m * * - nrhs + i__1 * i__1; - if (*n >= mnthr) { + i__1 = smlsiz + 1; + wlalsd = *m * 9 + (*m << 1) * smlsiz + (*m << 3) * nlvl + *m * * + nrhs + i__1 * i__1; + if (*n >= mnthr) { /* Path 2a - underdetermined, with many more columns */ /* than rows. */ - maxwrk = *m + *m * ilaenv_(&c__1, (char *)"DGELQF", (char *)" ", m, n, &c_n1, - &c_n1, (ftnlen)6, (ftnlen)1); + maxwrk = *m + *m * ilaenv_(&c__1, (char *)"DGELQF", (char *)" ", m, n, &c_n1, + &c_n1, (ftnlen)6, (ftnlen)1); /* Computing MAX */ - i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m << 1) * - ilaenv_(&c__1, (char *)"DGEBRD", (char *)" ", m, m, &c_n1, &c_n1, ( - ftnlen)6, (ftnlen)1); - maxwrk = max(i__1,i__2); + i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m << 1) * + ilaenv_(&c__1, (char *)"DGEBRD", (char *)" ", m, m, &c_n1, &c_n1, ( + ftnlen)6, (ftnlen)1); + maxwrk = max(i__1,i__2); /* Computing MAX */ - i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + *nrhs * ilaenv_(& - c__1, (char *)"DORMBR", (char *)"QLT", m, nrhs, m, &c_n1, (ftnlen)6, ( - ftnlen)3); - maxwrk = max(i__1,i__2); + i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + *nrhs * ilaenv_(& + c__1, (char *)"DORMBR", (char *)"QLT", m, nrhs, m, &c_n1, (ftnlen)6, ( + ftnlen)3); + maxwrk = max(i__1,i__2); /* Computing MAX */ - i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m - 1) * - ilaenv_(&c__1, (char *)"DORMBR", (char *)"PLN", m, nrhs, m, &c_n1, ( - ftnlen)6, (ftnlen)3); - maxwrk = max(i__1,i__2); - if (*nrhs > 1) { + i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m - 1) * + ilaenv_(&c__1, (char *)"DORMBR", (char *)"PLN", m, nrhs, m, &c_n1, ( + ftnlen)6, (ftnlen)3); + maxwrk = max(i__1,i__2); + if (*nrhs > 1) { /* Computing MAX */ - i__1 = maxwrk, i__2 = *m * *m + *m + *m * *nrhs; - maxwrk = max(i__1,i__2); - } else { + i__1 = maxwrk, i__2 = *m * *m + *m + *m * *nrhs; + maxwrk = max(i__1,i__2); + } else { /* Computing MAX */ - i__1 = maxwrk, i__2 = *m * *m + (*m << 1); - maxwrk = max(i__1,i__2); - } + i__1 = maxwrk, i__2 = *m * *m + (*m << 1); + maxwrk = max(i__1,i__2); + } /* Computing MAX */ - i__1 = maxwrk, i__2 = *m + *nrhs * ilaenv_(&c__1, (char *)"DORMLQ", - (char *)"LT", n, nrhs, m, &c_n1, (ftnlen)6, (ftnlen)2); - maxwrk = max(i__1,i__2); + i__1 = maxwrk, i__2 = *m + *nrhs * ilaenv_(&c__1, (char *)"DORMLQ", + (char *)"LT", n, nrhs, m, &c_n1, (ftnlen)6, (ftnlen)2); + maxwrk = max(i__1,i__2); /* Computing MAX */ - i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + wlalsd; - maxwrk = max(i__1,i__2); + i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + wlalsd; + maxwrk = max(i__1,i__2); /* XXX: Ensure the Path 2a case below is triggered. The workspace */ /* calculation should use queries for all routines eventually. */ /* Computing MAX */ /* Computing MAX */ - i__3 = *m, i__4 = (*m << 1) - 4, i__3 = max(i__3,i__4), i__3 = - max(i__3,*nrhs), i__4 = *n - *m * 3; - i__1 = maxwrk, i__2 = (*m << 2) + *m * *m + max(i__3,i__4); - maxwrk = max(i__1,i__2); - } else { + i__3 = *m, i__4 = (*m << 1) - 4, i__3 = max(i__3,i__4), i__3 = + max(i__3,*nrhs), i__4 = *n - *m * 3; + i__1 = maxwrk, i__2 = (*m << 2) + *m * *m + max(i__3,i__4); + maxwrk = max(i__1,i__2); + } else { /* Path 2 - remaining underdetermined cases. */ - maxwrk = *m * 3 + (*n + *m) * ilaenv_(&c__1, (char *)"DGEBRD", (char *)" ", m, - n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); + maxwrk = *m * 3 + (*n + *m) * ilaenv_(&c__1, (char *)"DGEBRD", (char *)" ", m, + n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); /* Computing MAX */ - i__1 = maxwrk, i__2 = *m * 3 + *nrhs * ilaenv_(&c__1, (char *)"DORMBR" - , (char *)"QLT", m, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)3); - maxwrk = max(i__1,i__2); + i__1 = maxwrk, i__2 = *m * 3 + *nrhs * ilaenv_(&c__1, (char *)"DORMBR" + , (char *)"QLT", m, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)3); + maxwrk = max(i__1,i__2); /* Computing MAX */ - i__1 = maxwrk, i__2 = *m * 3 + *m * ilaenv_(&c__1, (char *)"DORMBR", - (char *)"PLN", n, nrhs, m, &c_n1, (ftnlen)6, (ftnlen)3); - maxwrk = max(i__1,i__2); + i__1 = maxwrk, i__2 = *m * 3 + *m * ilaenv_(&c__1, (char *)"DORMBR", + (char *)"PLN", n, nrhs, m, &c_n1, (ftnlen)6, (ftnlen)3); + maxwrk = max(i__1,i__2); /* Computing MAX */ - i__1 = maxwrk, i__2 = *m * 3 + wlalsd; - maxwrk = max(i__1,i__2); - } + i__1 = maxwrk, i__2 = *m * 3 + wlalsd; + maxwrk = max(i__1,i__2); + } /* Computing MAX */ - i__1 = *m * 3 + *nrhs, i__2 = *m * 3 + *m, i__1 = max(i__1,i__2), - i__2 = *m * 3 + wlalsd; - minwrk = max(i__1,i__2); - } - minwrk = min(minwrk,maxwrk); - work[1] = (doublereal) maxwrk; - iwork[1] = liwork; - if (*lwork < minwrk && ! lquery) { - *info = -12; - } + i__1 = *m * 3 + *nrhs, i__2 = *m * 3 + *m, i__1 = max(i__1,i__2), + i__2 = *m * 3 + wlalsd; + minwrk = max(i__1,i__2); + } + minwrk = min(minwrk,maxwrk); + work[1] = (doublereal) maxwrk; + iwork[1] = liwork; + if (*lwork < minwrk && ! lquery) { + *info = -12; + } } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DGELSD", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DGELSD", &i__1, (ftnlen)6); + return 0; } else if (lquery) { - goto L10; + goto L10; } /* Quick return if possible. */ if (*m == 0 || *n == 0) { - *rank = 0; - return 0; + *rank = 0; + return 0; } /* Get machine parameters. */ @@ -523,26 +523,26 @@ f"> */ /* Scale matrix norm up to SMLNUM. */ - dlascl_((char *)"G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, - info, (ftnlen)1); - iascl = 1; + dlascl_((char *)"G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, + info, (ftnlen)1); + iascl = 1; } else if (anrm > bignum) { /* Scale matrix norm down to BIGNUM. */ - dlascl_((char *)"G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, - info, (ftnlen)1); - iascl = 2; + dlascl_((char *)"G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, + info, (ftnlen)1); + iascl = 2; } else if (anrm == 0.) { /* Matrix all zero. Return zero solution. */ - i__1 = max(*m,*n); - dlaset_((char *)"F", &i__1, nrhs, &c_b82, &c_b82, &b[b_offset], ldb, (ftnlen) - 1); - dlaset_((char *)"F", &minmn, &c__1, &c_b82, &c_b82, &s[1], &c__1, (ftnlen)1); - *rank = 0; - goto L10; + i__1 = max(*m,*n); + dlaset_((char *)"F", &i__1, nrhs, &c_b82, &c_b82, &b[b_offset], ldb, (ftnlen) + 1); + dlaset_((char *)"F", &minmn, &c__1, &c_b82, &c_b82, &s[1], &c__1, (ftnlen)1); + *rank = 0; + goto L10; } /* Scale B if max entry outside range [SMLNUM,BIGNUM]. */ @@ -553,24 +553,24 @@ f"> */ /* Scale matrix norm up to SMLNUM. */ - dlascl_((char *)"G", &c__0, &c__0, &bnrm, &smlnum, m, nrhs, &b[b_offset], ldb, - info, (ftnlen)1); - ibscl = 1; + dlascl_((char *)"G", &c__0, &c__0, &bnrm, &smlnum, m, nrhs, &b[b_offset], ldb, + info, (ftnlen)1); + ibscl = 1; } else if (bnrm > bignum) { /* Scale matrix norm down to BIGNUM. */ - dlascl_((char *)"G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb, - info, (ftnlen)1); - ibscl = 2; + dlascl_((char *)"G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb, + info, (ftnlen)1); + ibscl = 2; } /* If M < N make sure certain entries of B are zero. */ if (*m < *n) { - i__1 = *n - *m; - dlaset_((char *)"F", &i__1, nrhs, &c_b82, &c_b82, &b[*m + 1 + b_dim1], ldb, ( - ftnlen)1); + i__1 = *n - *m; + dlaset_((char *)"F", &i__1, nrhs, &c_b82, &c_b82, &b[*m + 1 + b_dim1], ldb, ( + ftnlen)1); } /* Overdetermined case. */ @@ -579,227 +579,227 @@ f"> */ /* Path 1 - overdetermined or exactly determined. */ - mm = *m; - if (*m >= mnthr) { + mm = *m; + if (*m >= mnthr) { /* Path 1a - overdetermined, with many more rows than columns. */ - mm = *n; - itau = 1; - nwork = itau + *n; + mm = *n; + itau = 1; + nwork = itau + *n; /* Compute A=Q*R. */ /* (Workspace: need 2*N, prefer N+N*NB) */ - i__1 = *lwork - nwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__1, - info); + i__1 = *lwork - nwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__1, + info); /* Multiply B by transpose(Q). */ /* (Workspace: need N+NRHS, prefer N+NRHS*NB) */ - i__1 = *lwork - nwork + 1; - dormqr_((char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, &work[itau], &b[ - b_offset], ldb, &work[nwork], &i__1, info, (ftnlen)1, ( - ftnlen)1); + i__1 = *lwork - nwork + 1; + dormqr_((char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, &work[itau], &b[ + b_offset], ldb, &work[nwork], &i__1, info, (ftnlen)1, ( + ftnlen)1); /* Zero out below R. */ - if (*n > 1) { - i__1 = *n - 1; - i__2 = *n - 1; - dlaset_((char *)"L", &i__1, &i__2, &c_b82, &c_b82, &a[a_dim1 + 2], - lda, (ftnlen)1); - } - } + if (*n > 1) { + i__1 = *n - 1; + i__2 = *n - 1; + dlaset_((char *)"L", &i__1, &i__2, &c_b82, &c_b82, &a[a_dim1 + 2], + lda, (ftnlen)1); + } + } - ie = 1; - itauq = ie + *n; - itaup = itauq + *n; - nwork = itaup + *n; + ie = 1; + itauq = ie + *n; + itaup = itauq + *n; + nwork = itaup + *n; /* Bidiagonalize R in A. */ /* (Workspace: need 3*N+MM, prefer 3*N+(MM+N)*NB) */ - i__1 = *lwork - nwork + 1; - dgebrd_(&mm, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], & - work[itaup], &work[nwork], &i__1, info); + i__1 = *lwork - nwork + 1; + dgebrd_(&mm, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], & + work[itaup], &work[nwork], &i__1, info); /* Multiply B by transpose of left bidiagonalizing vectors of R. */ /* (Workspace: need 3*N+NRHS, prefer 3*N+NRHS*NB) */ - i__1 = *lwork - nwork + 1; - dormbr_((char *)"Q", (char *)"L", (char *)"T", &mm, nrhs, n, &a[a_offset], lda, &work[itauq], - &b[b_offset], ldb, &work[nwork], &i__1, info, (ftnlen)1, ( - ftnlen)1, (ftnlen)1); + i__1 = *lwork - nwork + 1; + dormbr_((char *)"Q", (char *)"L", (char *)"T", &mm, nrhs, n, &a[a_offset], lda, &work[itauq], + &b[b_offset], ldb, &work[nwork], &i__1, info, (ftnlen)1, ( + ftnlen)1, (ftnlen)1); /* Solve the bidiagonal least squares problem. */ - dlalsd_((char *)"U", &smlsiz, n, nrhs, &s[1], &work[ie], &b[b_offset], ldb, - rcond, rank, &work[nwork], &iwork[1], info, (ftnlen)1); - if (*info != 0) { - goto L10; - } + dlalsd_((char *)"U", &smlsiz, n, nrhs, &s[1], &work[ie], &b[b_offset], ldb, + rcond, rank, &work[nwork], &iwork[1], info, (ftnlen)1); + if (*info != 0) { + goto L10; + } /* Multiply B by right bidiagonalizing vectors of R. */ - i__1 = *lwork - nwork + 1; - dormbr_((char *)"P", (char *)"L", (char *)"N", n, nrhs, n, &a[a_offset], lda, &work[itaup], & - b[b_offset], ldb, &work[nwork], &i__1, info, (ftnlen)1, ( - ftnlen)1, (ftnlen)1); + i__1 = *lwork - nwork + 1; + dormbr_((char *)"P", (char *)"L", (char *)"N", n, nrhs, n, &a[a_offset], lda, &work[itaup], & + b[b_offset], ldb, &work[nwork], &i__1, info, (ftnlen)1, ( + ftnlen)1, (ftnlen)1); } else /* if(complicated condition) */ { /* Computing MAX */ - i__1 = *m, i__2 = (*m << 1) - 4, i__1 = max(i__1,i__2), i__1 = max( - i__1,*nrhs), i__2 = *n - *m * 3, i__1 = max(i__1,i__2); - if (*n >= mnthr && *lwork >= (*m << 2) + *m * *m + max(i__1,wlalsd)) { + i__1 = *m, i__2 = (*m << 1) - 4, i__1 = max(i__1,i__2), i__1 = max( + i__1,*nrhs), i__2 = *n - *m * 3, i__1 = max(i__1,i__2); + if (*n >= mnthr && *lwork >= (*m << 2) + *m * *m + max(i__1,wlalsd)) { /* Path 2a - underdetermined, with many more columns than rows */ /* and sufficient workspace for an efficient algorithm. */ - ldwork = *m; + ldwork = *m; /* Computing MAX */ /* Computing MAX */ - i__3 = *m, i__4 = (*m << 1) - 4, i__3 = max(i__3,i__4), i__3 = - max(i__3,*nrhs), i__4 = *n - *m * 3; - i__1 = (*m << 2) + *m * *lda + max(i__3,i__4), i__2 = *m * *lda + - *m + *m * *nrhs, i__1 = max(i__1,i__2), i__2 = (*m << 2) - + *m * *lda + wlalsd; - if (*lwork >= max(i__1,i__2)) { - ldwork = *lda; - } - itau = 1; - nwork = *m + 1; + i__3 = *m, i__4 = (*m << 1) - 4, i__3 = max(i__3,i__4), i__3 = + max(i__3,*nrhs), i__4 = *n - *m * 3; + i__1 = (*m << 2) + *m * *lda + max(i__3,i__4), i__2 = *m * *lda + + *m + *m * *nrhs, i__1 = max(i__1,i__2), i__2 = (*m << 2) + + *m * *lda + wlalsd; + if (*lwork >= max(i__1,i__2)) { + ldwork = *lda; + } + itau = 1; + nwork = *m + 1; /* Compute A=L*Q. */ /* (Workspace: need 2*M, prefer M+M*NB) */ - i__1 = *lwork - nwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__1, - info); - il = nwork; + i__1 = *lwork - nwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__1, + info); + il = nwork; /* Copy L to WORK(IL), zeroing out above its diagonal. */ - dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[il], &ldwork, (ftnlen) - 1); - i__1 = *m - 1; - i__2 = *m - 1; - dlaset_((char *)"U", &i__1, &i__2, &c_b82, &c_b82, &work[il + ldwork], & - ldwork, (ftnlen)1); - ie = il + ldwork * *m; - itauq = ie + *m; - itaup = itauq + *m; - nwork = itaup + *m; + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[il], &ldwork, (ftnlen) + 1); + i__1 = *m - 1; + i__2 = *m - 1; + dlaset_((char *)"U", &i__1, &i__2, &c_b82, &c_b82, &work[il + ldwork], & + ldwork, (ftnlen)1); + ie = il + ldwork * *m; + itauq = ie + *m; + itaup = itauq + *m; + nwork = itaup + *m; /* Bidiagonalize L in WORK(IL). */ /* (Workspace: need M*M+5*M, prefer M*M+4*M+2*M*NB) */ - i__1 = *lwork - nwork + 1; - dgebrd_(m, m, &work[il], &ldwork, &s[1], &work[ie], &work[itauq], - &work[itaup], &work[nwork], &i__1, info); + i__1 = *lwork - nwork + 1; + dgebrd_(m, m, &work[il], &ldwork, &s[1], &work[ie], &work[itauq], + &work[itaup], &work[nwork], &i__1, info); /* Multiply B by transpose of left bidiagonalizing vectors of L. */ /* (Workspace: need M*M+4*M+NRHS, prefer M*M+4*M+NRHS*NB) */ - i__1 = *lwork - nwork + 1; - dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, m, &work[il], &ldwork, &work[ - itauq], &b[b_offset], ldb, &work[nwork], &i__1, info, ( - ftnlen)1, (ftnlen)1, (ftnlen)1); + i__1 = *lwork - nwork + 1; + dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, m, &work[il], &ldwork, &work[ + itauq], &b[b_offset], ldb, &work[nwork], &i__1, info, ( + ftnlen)1, (ftnlen)1, (ftnlen)1); /* Solve the bidiagonal least squares problem. */ - dlalsd_((char *)"U", &smlsiz, m, nrhs, &s[1], &work[ie], &b[b_offset], - ldb, rcond, rank, &work[nwork], &iwork[1], info, (ftnlen) - 1); - if (*info != 0) { - goto L10; - } + dlalsd_((char *)"U", &smlsiz, m, nrhs, &s[1], &work[ie], &b[b_offset], + ldb, rcond, rank, &work[nwork], &iwork[1], info, (ftnlen) + 1); + if (*info != 0) { + goto L10; + } /* Multiply B by right bidiagonalizing vectors of L. */ - i__1 = *lwork - nwork + 1; - dormbr_((char *)"P", (char *)"L", (char *)"N", m, nrhs, m, &work[il], &ldwork, &work[ - itaup], &b[b_offset], ldb, &work[nwork], &i__1, info, ( - ftnlen)1, (ftnlen)1, (ftnlen)1); + i__1 = *lwork - nwork + 1; + dormbr_((char *)"P", (char *)"L", (char *)"N", m, nrhs, m, &work[il], &ldwork, &work[ + itaup], &b[b_offset], ldb, &work[nwork], &i__1, info, ( + ftnlen)1, (ftnlen)1, (ftnlen)1); /* Zero out below first M rows of B. */ - i__1 = *n - *m; - dlaset_((char *)"F", &i__1, nrhs, &c_b82, &c_b82, &b[*m + 1 + b_dim1], - ldb, (ftnlen)1); - nwork = itau + *m; + i__1 = *n - *m; + dlaset_((char *)"F", &i__1, nrhs, &c_b82, &c_b82, &b[*m + 1 + b_dim1], + ldb, (ftnlen)1); + nwork = itau + *m; /* Multiply transpose(Q) by B. */ /* (Workspace: need M+NRHS, prefer M+NRHS*NB) */ - i__1 = *lwork - nwork + 1; - dormlq_((char *)"L", (char *)"T", n, nrhs, m, &a[a_offset], lda, &work[itau], &b[ - b_offset], ldb, &work[nwork], &i__1, info, (ftnlen)1, ( - ftnlen)1); + i__1 = *lwork - nwork + 1; + dormlq_((char *)"L", (char *)"T", n, nrhs, m, &a[a_offset], lda, &work[itau], &b[ + b_offset], ldb, &work[nwork], &i__1, info, (ftnlen)1, ( + ftnlen)1); - } else { + } else { /* Path 2 - remaining underdetermined cases. */ - ie = 1; - itauq = ie + *m; - itaup = itauq + *m; - nwork = itaup + *m; + ie = 1; + itauq = ie + *m; + itaup = itauq + *m; + nwork = itaup + *m; /* Bidiagonalize A. */ /* (Workspace: need 3*M+N, prefer 3*M+(M+N)*NB) */ - i__1 = *lwork - nwork + 1; - dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], & - work[itaup], &work[nwork], &i__1, info); + i__1 = *lwork - nwork + 1; + dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], & + work[itaup], &work[nwork], &i__1, info); /* Multiply B by transpose of left bidiagonalizing vectors. */ /* (Workspace: need 3*M+NRHS, prefer 3*M+NRHS*NB) */ - i__1 = *lwork - nwork + 1; - dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, &work[itauq] - , &b[b_offset], ldb, &work[nwork], &i__1, info, (ftnlen)1, - (ftnlen)1, (ftnlen)1); + i__1 = *lwork - nwork + 1; + dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, &work[itauq] + , &b[b_offset], ldb, &work[nwork], &i__1, info, (ftnlen)1, + (ftnlen)1, (ftnlen)1); /* Solve the bidiagonal least squares problem. */ - dlalsd_((char *)"L", &smlsiz, m, nrhs, &s[1], &work[ie], &b[b_offset], - ldb, rcond, rank, &work[nwork], &iwork[1], info, (ftnlen) - 1); - if (*info != 0) { - goto L10; - } + dlalsd_((char *)"L", &smlsiz, m, nrhs, &s[1], &work[ie], &b[b_offset], + ldb, rcond, rank, &work[nwork], &iwork[1], info, (ftnlen) + 1); + if (*info != 0) { + goto L10; + } /* Multiply B by right bidiagonalizing vectors of A. */ - i__1 = *lwork - nwork + 1; - dormbr_((char *)"P", (char *)"L", (char *)"N", n, nrhs, m, &a[a_offset], lda, &work[itaup] - , &b[b_offset], ldb, &work[nwork], &i__1, info, (ftnlen)1, - (ftnlen)1, (ftnlen)1); + i__1 = *lwork - nwork + 1; + dormbr_((char *)"P", (char *)"L", (char *)"N", n, nrhs, m, &a[a_offset], lda, &work[itaup] + , &b[b_offset], ldb, &work[nwork], &i__1, info, (ftnlen)1, + (ftnlen)1, (ftnlen)1); - } + } } /* Undo scaling. */ if (iascl == 1) { - dlascl_((char *)"G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb, - info, (ftnlen)1); - dlascl_((char *)"G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], & - minmn, info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb, + info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], & + minmn, info, (ftnlen)1); } else if (iascl == 2) { - dlascl_((char *)"G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb, - info, (ftnlen)1); - dlascl_((char *)"G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], & - minmn, info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb, + info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], & + minmn, info, (ftnlen)1); } if (ibscl == 1) { - dlascl_((char *)"G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb, - info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb, + info, (ftnlen)1); } else if (ibscl == 2) { - dlascl_((char *)"G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb, - info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb, + info, (ftnlen)1); } L10: @@ -812,5 +812,5 @@ L10: } /* dgelsd_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dgelss.cpp b/lib/linalg/dgelss.cpp index 6377208923..86036f9179 100644 --- a/lib/linalg/dgelss.cpp +++ b/lib/linalg/dgelss.cpp @@ -1,13 +1,13 @@ /* fortran/dgelss.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -196,10 +196,10 @@ f"> */ /* > \ingroup doubleGEsolve */ /* ===================================================================== */ -/* Subroutine */ int dgelss_(integer *m, integer *n, integer *nrhs, - doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal * - s, doublereal *rcond, integer *rank, doublereal *work, integer *lwork, - integer *info) +/* Subroutine */ int dgelss_(integer *m, integer *n, integer *nrhs, + doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal * + s, doublereal *rcond, integer *rank, doublereal *work, integer *lwork, + integer *info) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4; @@ -208,58 +208,58 @@ f"> */ /* Local variables */ integer i__, bl, ie, il, mm; doublereal dum[1], eps, thr, anrm, bnrm; - integer itau, lwork_dgebrd__, lwork_dgelqf__, lwork_dgeqrf__, - lwork_dorgbr__, lwork_dormbr__, lwork_dormlq__, lwork_dormqr__; - extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); + integer itau, lwork_dgebrd__, lwork_dgelqf__, lwork_dgeqrf__, + lwork_dorgbr__, lwork_dormbr__, lwork_dormlq__, lwork_dormqr__; + extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); integer iascl, ibscl; - extern /* Subroutine */ int dgemv_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, doublereal *, integer *, - doublereal *, doublereal *, integer *, ftnlen), drscl_(integer *, - doublereal *, doublereal *, integer *); + extern /* Subroutine */ int dgemv_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, ftnlen), drscl_(integer *, + doublereal *, doublereal *, integer *); integer chunk; doublereal sfmin; integer minmn; - extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, - doublereal *, integer *); + extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, + doublereal *, integer *); integer maxmn, itaup, itauq, mnthr, iwork; extern /* Subroutine */ int dlabad_(doublereal *, doublereal *), dgebrd_( - integer *, integer *, doublereal *, integer *, doublereal *, - doublereal *, doublereal *, doublereal *, doublereal *, integer *, - integer *); - extern doublereal dlamch_(char *, ftnlen), dlange_(char *, integer *, - integer *, doublereal *, integer *, doublereal *, ftnlen); + integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, doublereal *, doublereal *, doublereal *, integer *, + integer *); + extern doublereal dlamch_(char *, ftnlen), dlange_(char *, integer *, + integer *, doublereal *, integer *, doublereal *, ftnlen); integer bdspac; - extern /* Subroutine */ int dgelqf_(integer *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, integer *), - dlascl_(char *, integer *, integer *, doublereal *, doublereal *, - integer *, integer *, doublereal *, integer *, integer *, ftnlen), - dgeqrf_(integer *, integer *, doublereal *, integer *, - doublereal *, doublereal *, integer *, integer *), dlacpy_(char *, - integer *, integer *, doublereal *, integer *, doublereal *, - integer *, ftnlen), dlaset_(char *, integer *, integer *, - doublereal *, doublereal *, doublereal *, integer *, ftnlen), - xerbla_(char *, integer *, ftnlen), dbdsqr_(char *, integer *, - integer *, integer *, integer *, doublereal *, doublereal *, - doublereal *, integer *, doublereal *, integer *, doublereal *, - integer *, doublereal *, integer *, ftnlen), dorgbr_(char *, - integer *, integer *, integer *, doublereal *, integer *, - doublereal *, doublereal *, integer *, integer *, ftnlen); + extern /* Subroutine */ int dgelqf_(integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, integer *), + dlascl_(char *, integer *, integer *, doublereal *, doublereal *, + integer *, integer *, doublereal *, integer *, integer *, ftnlen), + dgeqrf_(integer *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, integer *), dlacpy_(char *, + integer *, integer *, doublereal *, integer *, doublereal *, + integer *, ftnlen), dlaset_(char *, integer *, integer *, + doublereal *, doublereal *, doublereal *, integer *, ftnlen), + xerbla_(char *, integer *, ftnlen), dbdsqr_(char *, integer *, + integer *, integer *, integer *, doublereal *, doublereal *, + doublereal *, integer *, doublereal *, integer *, doublereal *, + integer *, doublereal *, integer *, ftnlen), dorgbr_(char *, + integer *, integer *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, integer *, ftnlen); doublereal bignum; - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - extern /* Subroutine */ int dormbr_(char *, char *, char *, integer *, - integer *, integer *, doublereal *, integer *, doublereal *, - doublereal *, integer *, doublereal *, integer *, integer *, - ftnlen, ftnlen, ftnlen), dormlq_(char *, char *, integer *, - integer *, integer *, doublereal *, integer *, doublereal *, - doublereal *, integer *, doublereal *, integer *, integer *, - ftnlen, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dormbr_(char *, char *, char *, integer *, + integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, doublereal *, integer *, integer *, + ftnlen, ftnlen, ftnlen), dormlq_(char *, char *, integer *, + integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, doublereal *, integer *, integer *, + ftnlen, ftnlen); integer ldwork; - extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *, - integer *, doublereal *, integer *, doublereal *, doublereal *, - integer *, doublereal *, integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *, + integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, integer *, ftnlen, ftnlen); integer minwrk, maxwrk; doublereal smlnum; logical lquery; @@ -308,15 +308,15 @@ f"> */ maxmn = max(*m,*n); lquery = *lwork == -1; if (*m < 0) { - *info = -1; + *info = -1; } else if (*n < 0) { - *info = -2; + *info = -2; } else if (*nrhs < 0) { - *info = -3; + *info = -3; } else if (*lda < max(1,*m)) { - *info = -5; + *info = -5; } else if (*ldb < max(1,maxmn)) { - *info = -7; + *info = -7; } /* Compute workspace */ @@ -327,193 +327,193 @@ f"> */ /* following subroutine, as returned by ILAENV.) */ if (*info == 0) { - minwrk = 1; - maxwrk = 1; - if (minmn > 0) { - mm = *m; - mnthr = ilaenv_(&c__6, (char *)"DGELSS", (char *)" ", m, n, nrhs, &c_n1, (ftnlen) - 6, (ftnlen)1); - if (*m >= *n && *m >= mnthr) { + minwrk = 1; + maxwrk = 1; + if (minmn > 0) { + mm = *m; + mnthr = ilaenv_(&c__6, (char *)"DGELSS", (char *)" ", m, n, nrhs, &c_n1, (ftnlen) + 6, (ftnlen)1); + if (*m >= *n && *m >= mnthr) { /* Path 1a - overdetermined, with many more rows than */ /* columns */ /* Compute space needed for DGEQRF */ - dgeqrf_(m, n, &a[a_offset], lda, dum, dum, &c_n1, info); - lwork_dgeqrf__ = (integer) dum[0]; + dgeqrf_(m, n, &a[a_offset], lda, dum, dum, &c_n1, info); + lwork_dgeqrf__ = (integer) dum[0]; /* Compute space needed for DORMQR */ - dormqr_((char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, dum, &b[ - b_offset], ldb, dum, &c_n1, info, (ftnlen)1, (ftnlen) - 1); - lwork_dormqr__ = (integer) dum[0]; - mm = *n; + dormqr_((char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, dum, &b[ + b_offset], ldb, dum, &c_n1, info, (ftnlen)1, (ftnlen) + 1); + lwork_dormqr__ = (integer) dum[0]; + mm = *n; /* Computing MAX */ - i__1 = maxwrk, i__2 = *n + lwork_dgeqrf__; - maxwrk = max(i__1,i__2); + i__1 = maxwrk, i__2 = *n + lwork_dgeqrf__; + maxwrk = max(i__1,i__2); /* Computing MAX */ - i__1 = maxwrk, i__2 = *n + lwork_dormqr__; - maxwrk = max(i__1,i__2); - } - if (*m >= *n) { + i__1 = maxwrk, i__2 = *n + lwork_dormqr__; + maxwrk = max(i__1,i__2); + } + if (*m >= *n) { /* Path 1 - overdetermined or exactly determined */ /* Compute workspace needed for DBDSQR */ /* Computing MAX */ - i__1 = 1, i__2 = *n * 5; - bdspac = max(i__1,i__2); + i__1 = 1, i__2 = *n * 5; + bdspac = max(i__1,i__2); /* Compute space needed for DGEBRD */ - dgebrd_(&mm, n, &a[a_offset], lda, &s[1], dum, dum, dum, dum, - &c_n1, info); - lwork_dgebrd__ = (integer) dum[0]; + dgebrd_(&mm, n, &a[a_offset], lda, &s[1], dum, dum, dum, dum, + &c_n1, info); + lwork_dgebrd__ = (integer) dum[0]; /* Compute space needed for DORMBR */ - dormbr_((char *)"Q", (char *)"L", (char *)"T", &mm, nrhs, n, &a[a_offset], lda, dum, & - b[b_offset], ldb, dum, &c_n1, info, (ftnlen)1, ( - ftnlen)1, (ftnlen)1); - lwork_dormbr__ = (integer) dum[0]; + dormbr_((char *)"Q", (char *)"L", (char *)"T", &mm, nrhs, n, &a[a_offset], lda, dum, & + b[b_offset], ldb, dum, &c_n1, info, (ftnlen)1, ( + ftnlen)1, (ftnlen)1); + lwork_dormbr__ = (integer) dum[0]; /* Compute space needed for DORGBR */ - dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, dum, dum, &c_n1, - info, (ftnlen)1); - lwork_dorgbr__ = (integer) dum[0]; + dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, dum, dum, &c_n1, + info, (ftnlen)1); + lwork_dorgbr__ = (integer) dum[0]; /* Compute total workspace needed */ /* Computing MAX */ - i__1 = maxwrk, i__2 = *n * 3 + lwork_dgebrd__; - maxwrk = max(i__1,i__2); + i__1 = maxwrk, i__2 = *n * 3 + lwork_dgebrd__; + maxwrk = max(i__1,i__2); /* Computing MAX */ - i__1 = maxwrk, i__2 = *n * 3 + lwork_dormbr__; - maxwrk = max(i__1,i__2); + i__1 = maxwrk, i__2 = *n * 3 + lwork_dormbr__; + maxwrk = max(i__1,i__2); /* Computing MAX */ - i__1 = maxwrk, i__2 = *n * 3 + lwork_dorgbr__; - maxwrk = max(i__1,i__2); - maxwrk = max(maxwrk,bdspac); + i__1 = maxwrk, i__2 = *n * 3 + lwork_dorgbr__; + maxwrk = max(i__1,i__2); + maxwrk = max(maxwrk,bdspac); /* Computing MAX */ - i__1 = maxwrk, i__2 = *n * *nrhs; - maxwrk = max(i__1,i__2); + i__1 = maxwrk, i__2 = *n * *nrhs; + maxwrk = max(i__1,i__2); /* Computing MAX */ - i__1 = *n * 3 + mm, i__2 = *n * 3 + *nrhs, i__1 = max(i__1, - i__2); - minwrk = max(i__1,bdspac); - maxwrk = max(minwrk,maxwrk); - } - if (*n > *m) { + i__1 = *n * 3 + mm, i__2 = *n * 3 + *nrhs, i__1 = max(i__1, + i__2); + minwrk = max(i__1,bdspac); + maxwrk = max(minwrk,maxwrk); + } + if (*n > *m) { /* Compute workspace needed for DBDSQR */ /* Computing MAX */ - i__1 = 1, i__2 = *m * 5; - bdspac = max(i__1,i__2); + i__1 = 1, i__2 = *m * 5; + bdspac = max(i__1,i__2); /* Computing MAX */ - i__1 = *m * 3 + *nrhs, i__2 = *m * 3 + *n, i__1 = max(i__1, - i__2); - minwrk = max(i__1,bdspac); - if (*n >= mnthr) { + i__1 = *m * 3 + *nrhs, i__2 = *m * 3 + *n, i__1 = max(i__1, + i__2); + minwrk = max(i__1,bdspac); + if (*n >= mnthr) { /* Path 2a - underdetermined, with many more columns */ /* than rows */ /* Compute space needed for DGELQF */ - dgelqf_(m, n, &a[a_offset], lda, dum, dum, &c_n1, info); - lwork_dgelqf__ = (integer) dum[0]; + dgelqf_(m, n, &a[a_offset], lda, dum, dum, &c_n1, info); + lwork_dgelqf__ = (integer) dum[0]; /* Compute space needed for DGEBRD */ - dgebrd_(m, m, &a[a_offset], lda, &s[1], dum, dum, dum, - dum, &c_n1, info); - lwork_dgebrd__ = (integer) dum[0]; + dgebrd_(m, m, &a[a_offset], lda, &s[1], dum, dum, dum, + dum, &c_n1, info); + lwork_dgebrd__ = (integer) dum[0]; /* Compute space needed for DORMBR */ - dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, dum, - &b[b_offset], ldb, dum, &c_n1, info, (ftnlen)1, ( - ftnlen)1, (ftnlen)1); - lwork_dormbr__ = (integer) dum[0]; + dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, dum, + &b[b_offset], ldb, dum, &c_n1, info, (ftnlen)1, ( + ftnlen)1, (ftnlen)1); + lwork_dormbr__ = (integer) dum[0]; /* Compute space needed for DORGBR */ - dorgbr_((char *)"P", m, m, m, &a[a_offset], lda, dum, dum, &c_n1, - info, (ftnlen)1); - lwork_dorgbr__ = (integer) dum[0]; + dorgbr_((char *)"P", m, m, m, &a[a_offset], lda, dum, dum, &c_n1, + info, (ftnlen)1); + lwork_dorgbr__ = (integer) dum[0]; /* Compute space needed for DORMLQ */ - dormlq_((char *)"L", (char *)"T", n, nrhs, m, &a[a_offset], lda, dum, &b[ - b_offset], ldb, dum, &c_n1, info, (ftnlen)1, ( - ftnlen)1); - lwork_dormlq__ = (integer) dum[0]; + dormlq_((char *)"L", (char *)"T", n, nrhs, m, &a[a_offset], lda, dum, &b[ + b_offset], ldb, dum, &c_n1, info, (ftnlen)1, ( + ftnlen)1); + lwork_dormlq__ = (integer) dum[0]; /* Compute total workspace needed */ - maxwrk = *m + lwork_dgelqf__; + maxwrk = *m + lwork_dgelqf__; /* Computing MAX */ - i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + - lwork_dgebrd__; - maxwrk = max(i__1,i__2); + i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + + lwork_dgebrd__; + maxwrk = max(i__1,i__2); /* Computing MAX */ - i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + - lwork_dormbr__; - maxwrk = max(i__1,i__2); + i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + + lwork_dormbr__; + maxwrk = max(i__1,i__2); /* Computing MAX */ - i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + - lwork_dorgbr__; - maxwrk = max(i__1,i__2); + i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + + lwork_dorgbr__; + maxwrk = max(i__1,i__2); /* Computing MAX */ - i__1 = maxwrk, i__2 = *m * *m + *m + bdspac; - maxwrk = max(i__1,i__2); - if (*nrhs > 1) { + i__1 = maxwrk, i__2 = *m * *m + *m + bdspac; + maxwrk = max(i__1,i__2); + if (*nrhs > 1) { /* Computing MAX */ - i__1 = maxwrk, i__2 = *m * *m + *m + *m * *nrhs; - maxwrk = max(i__1,i__2); - } else { + i__1 = maxwrk, i__2 = *m * *m + *m + *m * *nrhs; + maxwrk = max(i__1,i__2); + } else { /* Computing MAX */ - i__1 = maxwrk, i__2 = *m * *m + (*m << 1); - maxwrk = max(i__1,i__2); - } + i__1 = maxwrk, i__2 = *m * *m + (*m << 1); + maxwrk = max(i__1,i__2); + } /* Computing MAX */ - i__1 = maxwrk, i__2 = *m + lwork_dormlq__; - maxwrk = max(i__1,i__2); - } else { + i__1 = maxwrk, i__2 = *m + lwork_dormlq__; + maxwrk = max(i__1,i__2); + } else { /* Path 2 - underdetermined */ /* Compute space needed for DGEBRD */ - dgebrd_(m, n, &a[a_offset], lda, &s[1], dum, dum, dum, - dum, &c_n1, info); - lwork_dgebrd__ = (integer) dum[0]; + dgebrd_(m, n, &a[a_offset], lda, &s[1], dum, dum, dum, + dum, &c_n1, info); + lwork_dgebrd__ = (integer) dum[0]; /* Compute space needed for DORMBR */ - dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, m, &a[a_offset], lda, dum, - &b[b_offset], ldb, dum, &c_n1, info, (ftnlen)1, ( - ftnlen)1, (ftnlen)1); - lwork_dormbr__ = (integer) dum[0]; + dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, m, &a[a_offset], lda, dum, + &b[b_offset], ldb, dum, &c_n1, info, (ftnlen)1, ( + ftnlen)1, (ftnlen)1); + lwork_dormbr__ = (integer) dum[0]; /* Compute space needed for DORGBR */ - dorgbr_((char *)"P", m, n, m, &a[a_offset], lda, dum, dum, &c_n1, - info, (ftnlen)1); - lwork_dorgbr__ = (integer) dum[0]; - maxwrk = *m * 3 + lwork_dgebrd__; + dorgbr_((char *)"P", m, n, m, &a[a_offset], lda, dum, dum, &c_n1, + info, (ftnlen)1); + lwork_dorgbr__ = (integer) dum[0]; + maxwrk = *m * 3 + lwork_dgebrd__; /* Computing MAX */ - i__1 = maxwrk, i__2 = *m * 3 + lwork_dormbr__; - maxwrk = max(i__1,i__2); + i__1 = maxwrk, i__2 = *m * 3 + lwork_dormbr__; + maxwrk = max(i__1,i__2); /* Computing MAX */ - i__1 = maxwrk, i__2 = *m * 3 + lwork_dorgbr__; - maxwrk = max(i__1,i__2); - maxwrk = max(maxwrk,bdspac); + i__1 = maxwrk, i__2 = *m * 3 + lwork_dorgbr__; + maxwrk = max(i__1,i__2); + maxwrk = max(maxwrk,bdspac); /* Computing MAX */ - i__1 = maxwrk, i__2 = *n * *nrhs; - maxwrk = max(i__1,i__2); - } - } - maxwrk = max(minwrk,maxwrk); - } - work[1] = (doublereal) maxwrk; + i__1 = maxwrk, i__2 = *n * *nrhs; + maxwrk = max(i__1,i__2); + } + } + maxwrk = max(minwrk,maxwrk); + } + work[1] = (doublereal) maxwrk; - if (*lwork < minwrk && ! lquery) { - *info = -12; - } + if (*lwork < minwrk && ! lquery) { + *info = -12; + } } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DGELSS", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DGELSS", &i__1, (ftnlen)6); + return 0; } else if (lquery) { - return 0; + return 0; } /* Quick return if possible */ if (*m == 0 || *n == 0) { - *rank = 0; - return 0; + *rank = 0; + return 0; } /* Get machine parameters */ @@ -532,26 +532,26 @@ f"> */ /* Scale matrix norm up to SMLNUM */ - dlascl_((char *)"G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, - info, (ftnlen)1); - iascl = 1; + dlascl_((char *)"G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, + info, (ftnlen)1); + iascl = 1; } else if (anrm > bignum) { /* Scale matrix norm down to BIGNUM */ - dlascl_((char *)"G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, - info, (ftnlen)1); - iascl = 2; + dlascl_((char *)"G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, + info, (ftnlen)1); + iascl = 2; } else if (anrm == 0.) { /* Matrix all zero. Return zero solution. */ - i__1 = max(*m,*n); - dlaset_((char *)"F", &i__1, nrhs, &c_b46, &c_b46, &b[b_offset], ldb, (ftnlen) - 1); - dlaset_((char *)"F", &minmn, &c__1, &c_b46, &c_b46, &s[1], &minmn, (ftnlen)1); - *rank = 0; - goto L70; + i__1 = max(*m,*n); + dlaset_((char *)"F", &i__1, nrhs, &c_b46, &c_b46, &b[b_offset], ldb, (ftnlen) + 1); + dlaset_((char *)"F", &minmn, &c__1, &c_b46, &c_b46, &s[1], &minmn, (ftnlen)1); + *rank = 0; + goto L70; } /* Scale B if max element outside range [SMLNUM,BIGNUM] */ @@ -562,16 +562,16 @@ f"> */ /* Scale matrix norm up to SMLNUM */ - dlascl_((char *)"G", &c__0, &c__0, &bnrm, &smlnum, m, nrhs, &b[b_offset], ldb, - info, (ftnlen)1); - ibscl = 1; + dlascl_((char *)"G", &c__0, &c__0, &bnrm, &smlnum, m, nrhs, &b[b_offset], ldb, + info, (ftnlen)1); + ibscl = 1; } else if (bnrm > bignum) { /* Scale matrix norm down to BIGNUM */ - dlascl_((char *)"G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb, - info, (ftnlen)1); - ibscl = 2; + dlascl_((char *)"G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb, + info, (ftnlen)1); + ibscl = 2; } /* Overdetermined case */ @@ -580,399 +580,399 @@ f"> */ /* Path 1 - overdetermined or exactly determined */ - mm = *m; - if (*m >= mnthr) { + mm = *m; + if (*m >= mnthr) { /* Path 1a - overdetermined, with many more rows than columns */ - mm = *n; - itau = 1; - iwork = itau + *n; + mm = *n; + itau = 1; + iwork = itau + *n; /* Compute A=Q*R */ /* (Workspace: need 2*N, prefer N+N*NB) */ - i__1 = *lwork - iwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__1, - info); + i__1 = *lwork - iwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__1, + info); /* Multiply B by transpose(Q) */ /* (Workspace: need N+NRHS, prefer N+NRHS*NB) */ - i__1 = *lwork - iwork + 1; - dormqr_((char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, &work[itau], &b[ - b_offset], ldb, &work[iwork], &i__1, info, (ftnlen)1, ( - ftnlen)1); + i__1 = *lwork - iwork + 1; + dormqr_((char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, &work[itau], &b[ + b_offset], ldb, &work[iwork], &i__1, info, (ftnlen)1, ( + ftnlen)1); /* Zero out below R */ - if (*n > 1) { - i__1 = *n - 1; - i__2 = *n - 1; - dlaset_((char *)"L", &i__1, &i__2, &c_b46, &c_b46, &a[a_dim1 + 2], - lda, (ftnlen)1); - } - } + if (*n > 1) { + i__1 = *n - 1; + i__2 = *n - 1; + dlaset_((char *)"L", &i__1, &i__2, &c_b46, &c_b46, &a[a_dim1 + 2], + lda, (ftnlen)1); + } + } - ie = 1; - itauq = ie + *n; - itaup = itauq + *n; - iwork = itaup + *n; + ie = 1; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; /* Bidiagonalize R in A */ /* (Workspace: need 3*N+MM, prefer 3*N+(MM+N)*NB) */ - i__1 = *lwork - iwork + 1; - dgebrd_(&mm, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], & - work[itaup], &work[iwork], &i__1, info); + i__1 = *lwork - iwork + 1; + dgebrd_(&mm, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], & + work[itaup], &work[iwork], &i__1, info); /* Multiply B by transpose of left bidiagonalizing vectors of R */ /* (Workspace: need 3*N+NRHS, prefer 3*N+NRHS*NB) */ - i__1 = *lwork - iwork + 1; - dormbr_((char *)"Q", (char *)"L", (char *)"T", &mm, nrhs, n, &a[a_offset], lda, &work[itauq], - &b[b_offset], ldb, &work[iwork], &i__1, info, (ftnlen)1, ( - ftnlen)1, (ftnlen)1); + i__1 = *lwork - iwork + 1; + dormbr_((char *)"Q", (char *)"L", (char *)"T", &mm, nrhs, n, &a[a_offset], lda, &work[itauq], + &b[b_offset], ldb, &work[iwork], &i__1, info, (ftnlen)1, ( + ftnlen)1, (ftnlen)1); /* Generate right bidiagonalizing vectors of R in A */ /* (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB) */ - i__1 = *lwork - iwork + 1; - dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, &work[itaup], &work[iwork], & - i__1, info, (ftnlen)1); - iwork = ie + *n; + i__1 = *lwork - iwork + 1; + dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, &work[itaup], &work[iwork], & + i__1, info, (ftnlen)1); + iwork = ie + *n; /* Perform bidiagonal QR iteration */ /* multiply B by transpose of left singular vectors */ /* compute right singular vectors in A */ /* (Workspace: need BDSPAC) */ - dbdsqr_((char *)"U", n, n, &c__0, nrhs, &s[1], &work[ie], &a[a_offset], lda, - dum, &c__1, &b[b_offset], ldb, &work[iwork], info, (ftnlen)1); - if (*info != 0) { - goto L70; - } + dbdsqr_((char *)"U", n, n, &c__0, nrhs, &s[1], &work[ie], &a[a_offset], lda, + dum, &c__1, &b[b_offset], ldb, &work[iwork], info, (ftnlen)1); + if (*info != 0) { + goto L70; + } /* Multiply B by reciprocals of singular values */ /* Computing MAX */ - d__1 = *rcond * s[1]; - thr = max(d__1,sfmin); - if (*rcond < 0.) { + d__1 = *rcond * s[1]; + thr = max(d__1,sfmin); + if (*rcond < 0.) { /* Computing MAX */ - d__1 = eps * s[1]; - thr = max(d__1,sfmin); - } - *rank = 0; - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - if (s[i__] > thr) { - drscl_(nrhs, &s[i__], &b[i__ + b_dim1], ldb); - ++(*rank); - } else { - dlaset_((char *)"F", &c__1, nrhs, &c_b46, &c_b46, &b[i__ + b_dim1], - ldb, (ftnlen)1); - } + d__1 = eps * s[1]; + thr = max(d__1,sfmin); + } + *rank = 0; + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + if (s[i__] > thr) { + drscl_(nrhs, &s[i__], &b[i__ + b_dim1], ldb); + ++(*rank); + } else { + dlaset_((char *)"F", &c__1, nrhs, &c_b46, &c_b46, &b[i__ + b_dim1], + ldb, (ftnlen)1); + } /* L10: */ - } + } /* Multiply B by right singular vectors */ /* (Workspace: need N, prefer N*NRHS) */ - if (*lwork >= *ldb * *nrhs && *nrhs > 1) { - dgemm_((char *)"T", (char *)"N", n, nrhs, n, &c_b79, &a[a_offset], lda, &b[ - b_offset], ldb, &c_b46, &work[1], ldb, (ftnlen)1, (ftnlen) - 1); - dlacpy_((char *)"G", n, nrhs, &work[1], ldb, &b[b_offset], ldb, (ftnlen)1) - ; - } else if (*nrhs > 1) { - chunk = *lwork / *n; - i__1 = *nrhs; - i__2 = chunk; - for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { + if (*lwork >= *ldb * *nrhs && *nrhs > 1) { + dgemm_((char *)"T", (char *)"N", n, nrhs, n, &c_b79, &a[a_offset], lda, &b[ + b_offset], ldb, &c_b46, &work[1], ldb, (ftnlen)1, (ftnlen) + 1); + dlacpy_((char *)"G", n, nrhs, &work[1], ldb, &b[b_offset], ldb, (ftnlen)1) + ; + } else if (*nrhs > 1) { + chunk = *lwork / *n; + i__1 = *nrhs; + i__2 = chunk; + for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { /* Computing MIN */ - i__3 = *nrhs - i__ + 1; - bl = min(i__3,chunk); - dgemm_((char *)"T", (char *)"N", n, &bl, n, &c_b79, &a[a_offset], lda, &b[i__ - * b_dim1 + 1], ldb, &c_b46, &work[1], n, (ftnlen)1, ( - ftnlen)1); - dlacpy_((char *)"G", n, &bl, &work[1], n, &b[i__ * b_dim1 + 1], ldb, ( - ftnlen)1); + i__3 = *nrhs - i__ + 1; + bl = min(i__3,chunk); + dgemm_((char *)"T", (char *)"N", n, &bl, n, &c_b79, &a[a_offset], lda, &b[i__ + * b_dim1 + 1], ldb, &c_b46, &work[1], n, (ftnlen)1, ( + ftnlen)1); + dlacpy_((char *)"G", n, &bl, &work[1], n, &b[i__ * b_dim1 + 1], ldb, ( + ftnlen)1); /* L20: */ - } - } else { - dgemv_((char *)"T", n, n, &c_b79, &a[a_offset], lda, &b[b_offset], &c__1, - &c_b46, &work[1], &c__1, (ftnlen)1); - dcopy_(n, &work[1], &c__1, &b[b_offset], &c__1); - } + } + } else { + dgemv_((char *)"T", n, n, &c_b79, &a[a_offset], lda, &b[b_offset], &c__1, + &c_b46, &work[1], &c__1, (ftnlen)1); + dcopy_(n, &work[1], &c__1, &b[b_offset], &c__1); + } } else /* if(complicated condition) */ { /* Computing MAX */ - i__2 = *m, i__1 = (*m << 1) - 4, i__2 = max(i__2,i__1), i__2 = max( - i__2,*nrhs), i__1 = *n - *m * 3; - if (*n >= mnthr && *lwork >= (*m << 2) + *m * *m + max(i__2,i__1)) { + i__2 = *m, i__1 = (*m << 1) - 4, i__2 = max(i__2,i__1), i__2 = max( + i__2,*nrhs), i__1 = *n - *m * 3; + if (*n >= mnthr && *lwork >= (*m << 2) + *m * *m + max(i__2,i__1)) { /* Path 2a - underdetermined, with many more columns than rows */ /* and sufficient workspace for an efficient algorithm */ - ldwork = *m; + ldwork = *m; /* Computing MAX */ /* Computing MAX */ - i__3 = *m, i__4 = (*m << 1) - 4, i__3 = max(i__3,i__4), i__3 = - max(i__3,*nrhs), i__4 = *n - *m * 3; - i__2 = (*m << 2) + *m * *lda + max(i__3,i__4), i__1 = *m * *lda + - *m + *m * *nrhs; - if (*lwork >= max(i__2,i__1)) { - ldwork = *lda; - } - itau = 1; - iwork = *m + 1; + i__3 = *m, i__4 = (*m << 1) - 4, i__3 = max(i__3,i__4), i__3 = + max(i__3,*nrhs), i__4 = *n - *m * 3; + i__2 = (*m << 2) + *m * *lda + max(i__3,i__4), i__1 = *m * *lda + + *m + *m * *nrhs; + if (*lwork >= max(i__2,i__1)) { + ldwork = *lda; + } + itau = 1; + iwork = *m + 1; /* Compute A=L*Q */ /* (Workspace: need 2*M, prefer M+M*NB) */ - i__2 = *lwork - iwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, - info); - il = iwork; + i__2 = *lwork - iwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, + info); + il = iwork; /* Copy L to WORK(IL), zeroing out above it */ - dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[il], &ldwork, (ftnlen) - 1); - i__2 = *m - 1; - i__1 = *m - 1; - dlaset_((char *)"U", &i__2, &i__1, &c_b46, &c_b46, &work[il + ldwork], & - ldwork, (ftnlen)1); - ie = il + ldwork * *m; - itauq = ie + *m; - itaup = itauq + *m; - iwork = itaup + *m; + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[il], &ldwork, (ftnlen) + 1); + i__2 = *m - 1; + i__1 = *m - 1; + dlaset_((char *)"U", &i__2, &i__1, &c_b46, &c_b46, &work[il + ldwork], & + ldwork, (ftnlen)1); + ie = il + ldwork * *m; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; /* Bidiagonalize L in WORK(IL) */ /* (Workspace: need M*M+5*M, prefer M*M+4*M+2*M*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(m, m, &work[il], &ldwork, &s[1], &work[ie], &work[itauq], - &work[itaup], &work[iwork], &i__2, info); + i__2 = *lwork - iwork + 1; + dgebrd_(m, m, &work[il], &ldwork, &s[1], &work[ie], &work[itauq], + &work[itaup], &work[iwork], &i__2, info); /* Multiply B by transpose of left bidiagonalizing vectors of L */ /* (Workspace: need M*M+4*M+NRHS, prefer M*M+4*M+NRHS*NB) */ - i__2 = *lwork - iwork + 1; - dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, m, &work[il], &ldwork, &work[ - itauq], &b[b_offset], ldb, &work[iwork], &i__2, info, ( - ftnlen)1, (ftnlen)1, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, m, &work[il], &ldwork, &work[ + itauq], &b[b_offset], ldb, &work[iwork], &i__2, info, ( + ftnlen)1, (ftnlen)1, (ftnlen)1); /* Generate right bidiagonalizing vectors of R in WORK(IL) */ /* (Workspace: need M*M+5*M-1, prefer M*M+4*M+(M-1)*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", m, m, m, &work[il], &ldwork, &work[itaup], &work[ - iwork], &i__2, info, (ftnlen)1); - iwork = ie + *m; + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", m, m, m, &work[il], &ldwork, &work[itaup], &work[ + iwork], &i__2, info, (ftnlen)1); + iwork = ie + *m; /* Perform bidiagonal QR iteration, */ /* computing right singular vectors of L in WORK(IL) and */ /* multiplying B by transpose of left singular vectors */ /* (Workspace: need M*M+M+BDSPAC) */ - dbdsqr_((char *)"U", m, m, &c__0, nrhs, &s[1], &work[ie], &work[il], & - ldwork, &a[a_offset], lda, &b[b_offset], ldb, &work[iwork] - , info, (ftnlen)1); - if (*info != 0) { - goto L70; - } + dbdsqr_((char *)"U", m, m, &c__0, nrhs, &s[1], &work[ie], &work[il], & + ldwork, &a[a_offset], lda, &b[b_offset], ldb, &work[iwork] + , info, (ftnlen)1); + if (*info != 0) { + goto L70; + } /* Multiply B by reciprocals of singular values */ /* Computing MAX */ - d__1 = *rcond * s[1]; - thr = max(d__1,sfmin); - if (*rcond < 0.) { + d__1 = *rcond * s[1]; + thr = max(d__1,sfmin); + if (*rcond < 0.) { /* Computing MAX */ - d__1 = eps * s[1]; - thr = max(d__1,sfmin); - } - *rank = 0; - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - if (s[i__] > thr) { - drscl_(nrhs, &s[i__], &b[i__ + b_dim1], ldb); - ++(*rank); - } else { - dlaset_((char *)"F", &c__1, nrhs, &c_b46, &c_b46, &b[i__ + b_dim1] - , ldb, (ftnlen)1); - } + d__1 = eps * s[1]; + thr = max(d__1,sfmin); + } + *rank = 0; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + if (s[i__] > thr) { + drscl_(nrhs, &s[i__], &b[i__ + b_dim1], ldb); + ++(*rank); + } else { + dlaset_((char *)"F", &c__1, nrhs, &c_b46, &c_b46, &b[i__ + b_dim1] + , ldb, (ftnlen)1); + } /* L30: */ - } - iwork = ie; + } + iwork = ie; /* Multiply B by right singular vectors of L in WORK(IL) */ /* (Workspace: need M*M+2*M, prefer M*M+M+M*NRHS) */ - if (*lwork >= *ldb * *nrhs + iwork - 1 && *nrhs > 1) { - dgemm_((char *)"T", (char *)"N", m, nrhs, m, &c_b79, &work[il], &ldwork, &b[ - b_offset], ldb, &c_b46, &work[iwork], ldb, (ftnlen)1, - (ftnlen)1); - dlacpy_((char *)"G", m, nrhs, &work[iwork], ldb, &b[b_offset], ldb, ( - ftnlen)1); - } else if (*nrhs > 1) { - chunk = (*lwork - iwork + 1) / *m; - i__2 = *nrhs; - i__1 = chunk; - for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += - i__1) { + if (*lwork >= *ldb * *nrhs + iwork - 1 && *nrhs > 1) { + dgemm_((char *)"T", (char *)"N", m, nrhs, m, &c_b79, &work[il], &ldwork, &b[ + b_offset], ldb, &c_b46, &work[iwork], ldb, (ftnlen)1, + (ftnlen)1); + dlacpy_((char *)"G", m, nrhs, &work[iwork], ldb, &b[b_offset], ldb, ( + ftnlen)1); + } else if (*nrhs > 1) { + chunk = (*lwork - iwork + 1) / *m; + i__2 = *nrhs; + i__1 = chunk; + for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += + i__1) { /* Computing MIN */ - i__3 = *nrhs - i__ + 1; - bl = min(i__3,chunk); - dgemm_((char *)"T", (char *)"N", m, &bl, m, &c_b79, &work[il], &ldwork, & - b[i__ * b_dim1 + 1], ldb, &c_b46, &work[iwork], m, - (ftnlen)1, (ftnlen)1); - dlacpy_((char *)"G", m, &bl, &work[iwork], m, &b[i__ * b_dim1 + 1] - , ldb, (ftnlen)1); + i__3 = *nrhs - i__ + 1; + bl = min(i__3,chunk); + dgemm_((char *)"T", (char *)"N", m, &bl, m, &c_b79, &work[il], &ldwork, & + b[i__ * b_dim1 + 1], ldb, &c_b46, &work[iwork], m, + (ftnlen)1, (ftnlen)1); + dlacpy_((char *)"G", m, &bl, &work[iwork], m, &b[i__ * b_dim1 + 1] + , ldb, (ftnlen)1); /* L40: */ - } - } else { - dgemv_((char *)"T", m, m, &c_b79, &work[il], &ldwork, &b[b_dim1 + 1], - &c__1, &c_b46, &work[iwork], &c__1, (ftnlen)1); - dcopy_(m, &work[iwork], &c__1, &b[b_dim1 + 1], &c__1); - } + } + } else { + dgemv_((char *)"T", m, m, &c_b79, &work[il], &ldwork, &b[b_dim1 + 1], + &c__1, &c_b46, &work[iwork], &c__1, (ftnlen)1); + dcopy_(m, &work[iwork], &c__1, &b[b_dim1 + 1], &c__1); + } /* Zero out below first M rows of B */ - i__1 = *n - *m; - dlaset_((char *)"F", &i__1, nrhs, &c_b46, &c_b46, &b[*m + 1 + b_dim1], - ldb, (ftnlen)1); - iwork = itau + *m; + i__1 = *n - *m; + dlaset_((char *)"F", &i__1, nrhs, &c_b46, &c_b46, &b[*m + 1 + b_dim1], + ldb, (ftnlen)1); + iwork = itau + *m; /* Multiply transpose(Q) by B */ /* (Workspace: need M+NRHS, prefer M+NRHS*NB) */ - i__1 = *lwork - iwork + 1; - dormlq_((char *)"L", (char *)"T", n, nrhs, m, &a[a_offset], lda, &work[itau], &b[ - b_offset], ldb, &work[iwork], &i__1, info, (ftnlen)1, ( - ftnlen)1); + i__1 = *lwork - iwork + 1; + dormlq_((char *)"L", (char *)"T", n, nrhs, m, &a[a_offset], lda, &work[itau], &b[ + b_offset], ldb, &work[iwork], &i__1, info, (ftnlen)1, ( + ftnlen)1); - } else { + } else { /* Path 2 - remaining underdetermined cases */ - ie = 1; - itauq = ie + *m; - itaup = itauq + *m; - iwork = itaup + *m; + ie = 1; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; /* Bidiagonalize A */ /* (Workspace: need 3*M+N, prefer 3*M+(M+N)*NB) */ - i__1 = *lwork - iwork + 1; - dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], & - work[itaup], &work[iwork], &i__1, info); + i__1 = *lwork - iwork + 1; + dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], & + work[itaup], &work[iwork], &i__1, info); /* Multiply B by transpose of left bidiagonalizing vectors */ /* (Workspace: need 3*M+NRHS, prefer 3*M+NRHS*NB) */ - i__1 = *lwork - iwork + 1; - dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, &work[itauq] - , &b[b_offset], ldb, &work[iwork], &i__1, info, (ftnlen)1, - (ftnlen)1, (ftnlen)1); + i__1 = *lwork - iwork + 1; + dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, &work[itauq] + , &b[b_offset], ldb, &work[iwork], &i__1, info, (ftnlen)1, + (ftnlen)1, (ftnlen)1); /* Generate right bidiagonalizing vectors in A */ /* (Workspace: need 4*M, prefer 3*M+M*NB) */ - i__1 = *lwork - iwork + 1; - dorgbr_((char *)"P", m, n, m, &a[a_offset], lda, &work[itaup], &work[ - iwork], &i__1, info, (ftnlen)1); - iwork = ie + *m; + i__1 = *lwork - iwork + 1; + dorgbr_((char *)"P", m, n, m, &a[a_offset], lda, &work[itaup], &work[ + iwork], &i__1, info, (ftnlen)1); + iwork = ie + *m; /* Perform bidiagonal QR iteration, */ /* computing right singular vectors of A in A and */ /* multiplying B by transpose of left singular vectors */ /* (Workspace: need BDSPAC) */ - dbdsqr_((char *)"L", m, n, &c__0, nrhs, &s[1], &work[ie], &a[a_offset], - lda, dum, &c__1, &b[b_offset], ldb, &work[iwork], info, ( - ftnlen)1); - if (*info != 0) { - goto L70; - } + dbdsqr_((char *)"L", m, n, &c__0, nrhs, &s[1], &work[ie], &a[a_offset], + lda, dum, &c__1, &b[b_offset], ldb, &work[iwork], info, ( + ftnlen)1); + if (*info != 0) { + goto L70; + } /* Multiply B by reciprocals of singular values */ /* Computing MAX */ - d__1 = *rcond * s[1]; - thr = max(d__1,sfmin); - if (*rcond < 0.) { + d__1 = *rcond * s[1]; + thr = max(d__1,sfmin); + if (*rcond < 0.) { /* Computing MAX */ - d__1 = eps * s[1]; - thr = max(d__1,sfmin); - } - *rank = 0; - i__1 = *m; - for (i__ = 1; i__ <= i__1; ++i__) { - if (s[i__] > thr) { - drscl_(nrhs, &s[i__], &b[i__ + b_dim1], ldb); - ++(*rank); - } else { - dlaset_((char *)"F", &c__1, nrhs, &c_b46, &c_b46, &b[i__ + b_dim1] - , ldb, (ftnlen)1); - } + d__1 = eps * s[1]; + thr = max(d__1,sfmin); + } + *rank = 0; + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + if (s[i__] > thr) { + drscl_(nrhs, &s[i__], &b[i__ + b_dim1], ldb); + ++(*rank); + } else { + dlaset_((char *)"F", &c__1, nrhs, &c_b46, &c_b46, &b[i__ + b_dim1] + , ldb, (ftnlen)1); + } /* L50: */ - } + } /* Multiply B by right singular vectors of A */ /* (Workspace: need N, prefer N*NRHS) */ - if (*lwork >= *ldb * *nrhs && *nrhs > 1) { - dgemm_((char *)"T", (char *)"N", n, nrhs, m, &c_b79, &a[a_offset], lda, &b[ - b_offset], ldb, &c_b46, &work[1], ldb, (ftnlen)1, ( - ftnlen)1); - dlacpy_((char *)"F", n, nrhs, &work[1], ldb, &b[b_offset], ldb, ( - ftnlen)1); - } else if (*nrhs > 1) { - chunk = *lwork / *n; - i__1 = *nrhs; - i__2 = chunk; - for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += - i__2) { + if (*lwork >= *ldb * *nrhs && *nrhs > 1) { + dgemm_((char *)"T", (char *)"N", n, nrhs, m, &c_b79, &a[a_offset], lda, &b[ + b_offset], ldb, &c_b46, &work[1], ldb, (ftnlen)1, ( + ftnlen)1); + dlacpy_((char *)"F", n, nrhs, &work[1], ldb, &b[b_offset], ldb, ( + ftnlen)1); + } else if (*nrhs > 1) { + chunk = *lwork / *n; + i__1 = *nrhs; + i__2 = chunk; + for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += + i__2) { /* Computing MIN */ - i__3 = *nrhs - i__ + 1; - bl = min(i__3,chunk); - dgemm_((char *)"T", (char *)"N", n, &bl, m, &c_b79, &a[a_offset], lda, &b[ - i__ * b_dim1 + 1], ldb, &c_b46, &work[1], n, ( - ftnlen)1, (ftnlen)1); - dlacpy_((char *)"F", n, &bl, &work[1], n, &b[i__ * b_dim1 + 1], - ldb, (ftnlen)1); + i__3 = *nrhs - i__ + 1; + bl = min(i__3,chunk); + dgemm_((char *)"T", (char *)"N", n, &bl, m, &c_b79, &a[a_offset], lda, &b[ + i__ * b_dim1 + 1], ldb, &c_b46, &work[1], n, ( + ftnlen)1, (ftnlen)1); + dlacpy_((char *)"F", n, &bl, &work[1], n, &b[i__ * b_dim1 + 1], + ldb, (ftnlen)1); /* L60: */ - } - } else { - dgemv_((char *)"T", m, n, &c_b79, &a[a_offset], lda, &b[b_offset], & - c__1, &c_b46, &work[1], &c__1, (ftnlen)1); - dcopy_(n, &work[1], &c__1, &b[b_offset], &c__1); - } - } + } + } else { + dgemv_((char *)"T", m, n, &c_b79, &a[a_offset], lda, &b[b_offset], & + c__1, &c_b46, &work[1], &c__1, (ftnlen)1); + dcopy_(n, &work[1], &c__1, &b[b_offset], &c__1); + } + } } /* Undo scaling */ if (iascl == 1) { - dlascl_((char *)"G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb, - info, (ftnlen)1); - dlascl_((char *)"G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], & - minmn, info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb, + info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], & + minmn, info, (ftnlen)1); } else if (iascl == 2) { - dlascl_((char *)"G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb, - info, (ftnlen)1); - dlascl_((char *)"G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], & - minmn, info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb, + info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], & + minmn, info, (ftnlen)1); } if (ibscl == 1) { - dlascl_((char *)"G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb, - info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb, + info, (ftnlen)1); } else if (ibscl == 2) { - dlascl_((char *)"G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb, - info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb, + info, (ftnlen)1); } L70: @@ -984,5 +984,5 @@ L70: } /* dgelss_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dgemm.cpp b/lib/linalg/dgemm.cpp index 2f59801245..360584e254 100644 --- a/lib/linalg/dgemm.cpp +++ b/lib/linalg/dgemm.cpp @@ -1,13 +1,13 @@ /* fortran/dgemm.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -201,13 +201,13 @@ extern "C" { /* > */ /* ===================================================================== */ /* Subroutine */ int dgemm_(char *transa, char *transb, integer *m, integer * - n, integer *k, doublereal *alpha, doublereal *a, integer *lda, - doublereal *b, integer *ldb, doublereal *beta, doublereal *c__, - integer *ldc, ftnlen transa_len, ftnlen transb_len) + n, integer *k, doublereal *alpha, doublereal *a, integer *lda, + doublereal *b, integer *ldb, doublereal *beta, doublereal *c__, + integer *ldc, ftnlen transa_len, ftnlen transb_len) { /* System generated locals */ - integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, - i__3; + integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, + i__3; /* Local variables */ integer i__, j, l, info; @@ -259,192 +259,192 @@ extern "C" { nota = lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1); notb = lsame_(transb, (char *)"N", (ftnlen)1, (ftnlen)1); if (nota) { - nrowa = *m; + nrowa = *m; } else { - nrowa = *k; + nrowa = *k; } if (notb) { - nrowb = *k; + nrowb = *k; } else { - nrowb = *n; + nrowb = *n; } /* Test the input parameters. */ info = 0; if (! nota && ! lsame_(transa, (char *)"C", (ftnlen)1, (ftnlen)1) && ! lsame_( - transa, (char *)"T", (ftnlen)1, (ftnlen)1)) { - info = 1; - } else if (! notb && ! lsame_(transb, (char *)"C", (ftnlen)1, (ftnlen)1) && ! - lsame_(transb, (char *)"T", (ftnlen)1, (ftnlen)1)) { - info = 2; + transa, (char *)"T", (ftnlen)1, (ftnlen)1)) { + info = 1; + } else if (! notb && ! lsame_(transb, (char *)"C", (ftnlen)1, (ftnlen)1) && ! + lsame_(transb, (char *)"T", (ftnlen)1, (ftnlen)1)) { + info = 2; } else if (*m < 0) { - info = 3; + info = 3; } else if (*n < 0) { - info = 4; + info = 4; } else if (*k < 0) { - info = 5; + info = 5; } else if (*lda < max(1,nrowa)) { - info = 8; + info = 8; } else if (*ldb < max(1,nrowb)) { - info = 10; + info = 10; } else if (*ldc < max(1,*m)) { - info = 13; + info = 13; } if (info != 0) { - xerbla_((char *)"DGEMM ", &info, (ftnlen)6); - return 0; + xerbla_((char *)"DGEMM ", &info, (ftnlen)6); + return 0; } /* Quick return if possible. */ if (*m == 0 || *n == 0 || (*alpha == 0. || *k == 0) && *beta == 1.) { - return 0; + return 0; } /* And if alpha.eq.zero. */ if (*alpha == 0.) { - if (*beta == 0.) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - c__[i__ + j * c_dim1] = 0.; + if (*beta == 0.) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = 0.; /* L10: */ - } + } /* L20: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; /* L30: */ - } + } /* L40: */ - } - } - return 0; + } + } + return 0; } /* Start the operations. */ if (notb) { - if (nota) { + if (nota) { /* Form C := alpha*A*B + beta*C. */ - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - if (*beta == 0.) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - c__[i__ + j * c_dim1] = 0.; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (*beta == 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = 0.; /* L50: */ - } - } else if (*beta != 1.) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; + } + } else if (*beta != 1.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; /* L60: */ - } - } - i__2 = *k; - for (l = 1; l <= i__2; ++l) { - temp = *alpha * b[l + j * b_dim1]; - i__3 = *m; - for (i__ = 1; i__ <= i__3; ++i__) { - c__[i__ + j * c_dim1] += temp * a[i__ + l * a_dim1]; + } + } + i__2 = *k; + for (l = 1; l <= i__2; ++l) { + temp = *alpha * b[l + j * b_dim1]; + i__3 = *m; + for (i__ = 1; i__ <= i__3; ++i__) { + c__[i__ + j * c_dim1] += temp * a[i__ + l * a_dim1]; /* L70: */ - } + } /* L80: */ - } + } /* L90: */ - } - } else { + } + } else { /* Form C := alpha*A**T*B + beta*C */ - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - temp = 0.; - i__3 = *k; - for (l = 1; l <= i__3; ++l) { - temp += a[l + i__ * a_dim1] * b[l + j * b_dim1]; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp = 0.; + i__3 = *k; + for (l = 1; l <= i__3; ++l) { + temp += a[l + i__ * a_dim1] * b[l + j * b_dim1]; /* L100: */ - } - if (*beta == 0.) { - c__[i__ + j * c_dim1] = *alpha * temp; - } else { - c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[ - i__ + j * c_dim1]; - } + } + if (*beta == 0.) { + c__[i__ + j * c_dim1] = *alpha * temp; + } else { + c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[ + i__ + j * c_dim1]; + } /* L110: */ - } + } /* L120: */ - } - } + } + } } else { - if (nota) { + if (nota) { /* Form C := alpha*A*B**T + beta*C */ - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - if (*beta == 0.) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - c__[i__ + j * c_dim1] = 0.; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (*beta == 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = 0.; /* L130: */ - } - } else if (*beta != 1.) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; + } + } else if (*beta != 1.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; /* L140: */ - } - } - i__2 = *k; - for (l = 1; l <= i__2; ++l) { - temp = *alpha * b[j + l * b_dim1]; - i__3 = *m; - for (i__ = 1; i__ <= i__3; ++i__) { - c__[i__ + j * c_dim1] += temp * a[i__ + l * a_dim1]; + } + } + i__2 = *k; + for (l = 1; l <= i__2; ++l) { + temp = *alpha * b[j + l * b_dim1]; + i__3 = *m; + for (i__ = 1; i__ <= i__3; ++i__) { + c__[i__ + j * c_dim1] += temp * a[i__ + l * a_dim1]; /* L150: */ - } + } /* L160: */ - } + } /* L170: */ - } - } else { + } + } else { /* Form C := alpha*A**T*B**T + beta*C */ - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - temp = 0.; - i__3 = *k; - for (l = 1; l <= i__3; ++l) { - temp += a[l + i__ * a_dim1] * b[j + l * b_dim1]; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp = 0.; + i__3 = *k; + for (l = 1; l <= i__3; ++l) { + temp += a[l + i__ * a_dim1] * b[j + l * b_dim1]; /* L180: */ - } - if (*beta == 0.) { - c__[i__ + j * c_dim1] = *alpha * temp; - } else { - c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[ - i__ + j * c_dim1]; - } + } + if (*beta == 0.) { + c__[i__ + j * c_dim1] = *alpha * temp; + } else { + c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[ + i__ + j * c_dim1]; + } /* L190: */ - } + } /* L200: */ - } - } + } + } } return 0; @@ -454,5 +454,5 @@ extern "C" { } /* dgemm_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dgemv.cpp b/lib/linalg/dgemv.cpp index 1d121c33c0..5e82c1144c 100644 --- a/lib/linalg/dgemv.cpp +++ b/lib/linalg/dgemv.cpp @@ -1,13 +1,13 @@ /* fortran/dgemv.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -170,8 +170,8 @@ extern "C" { /* > */ /* ===================================================================== */ /* Subroutine */ int dgemv_(char *trans, integer *m, integer *n, doublereal * - alpha, doublereal *a, integer *lda, doublereal *x, integer *incx, - doublereal *beta, doublereal *y, integer *incy, ftnlen trans_len) + alpha, doublereal *a, integer *lda, doublereal *x, integer *incx, + doublereal *beta, doublereal *y, integer *incy, ftnlen trans_len) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; @@ -218,50 +218,50 @@ extern "C" { /* Function Body */ info = 0; if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"T", ( - ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1) - ) { - info = 1; + ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1) + ) { + info = 1; } else if (*m < 0) { - info = 2; + info = 2; } else if (*n < 0) { - info = 3; + info = 3; } else if (*lda < max(1,*m)) { - info = 6; + info = 6; } else if (*incx == 0) { - info = 8; + info = 8; } else if (*incy == 0) { - info = 11; + info = 11; } if (info != 0) { - xerbla_((char *)"DGEMV ", &info, (ftnlen)6); - return 0; + xerbla_((char *)"DGEMV ", &info, (ftnlen)6); + return 0; } /* Quick return if possible. */ if (*m == 0 || *n == 0 || *alpha == 0. && *beta == 1.) { - return 0; + return 0; } /* Set LENX and LENY, the lengths of the vectors x and y, and set */ /* up the start points in X and Y. */ if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { - lenx = *n; - leny = *m; + lenx = *n; + leny = *m; } else { - lenx = *m; - leny = *n; + lenx = *m; + leny = *n; } if (*incx > 0) { - kx = 1; + kx = 1; } else { - kx = 1 - (lenx - 1) * *incx; + kx = 1 - (lenx - 1) * *incx; } if (*incy > 0) { - ky = 1; + ky = 1; } else { - ky = 1 - (leny - 1) * *incy; + ky = 1 - (leny - 1) * *incy; } /* Start the operations. In this version the elements of A are */ @@ -270,108 +270,108 @@ extern "C" { /* First form y := beta*y. */ if (*beta != 1.) { - if (*incy == 1) { - if (*beta == 0.) { - i__1 = leny; - for (i__ = 1; i__ <= i__1; ++i__) { - y[i__] = 0.; + if (*incy == 1) { + if (*beta == 0.) { + i__1 = leny; + for (i__ = 1; i__ <= i__1; ++i__) { + y[i__] = 0.; /* L10: */ - } - } else { - i__1 = leny; - for (i__ = 1; i__ <= i__1; ++i__) { - y[i__] = *beta * y[i__]; + } + } else { + i__1 = leny; + for (i__ = 1; i__ <= i__1; ++i__) { + y[i__] = *beta * y[i__]; /* L20: */ - } - } - } else { - iy = ky; - if (*beta == 0.) { - i__1 = leny; - for (i__ = 1; i__ <= i__1; ++i__) { - y[iy] = 0.; - iy += *incy; + } + } + } else { + iy = ky; + if (*beta == 0.) { + i__1 = leny; + for (i__ = 1; i__ <= i__1; ++i__) { + y[iy] = 0.; + iy += *incy; /* L30: */ - } - } else { - i__1 = leny; - for (i__ = 1; i__ <= i__1; ++i__) { - y[iy] = *beta * y[iy]; - iy += *incy; + } + } else { + i__1 = leny; + for (i__ = 1; i__ <= i__1; ++i__) { + y[iy] = *beta * y[iy]; + iy += *incy; /* L40: */ - } - } - } + } + } + } } if (*alpha == 0.) { - return 0; + return 0; } if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { /* Form y := alpha*A*x + y. */ - jx = kx; - if (*incy == 1) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - temp = *alpha * x[jx]; - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - y[i__] += temp * a[i__ + j * a_dim1]; + jx = kx; + if (*incy == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp = *alpha * x[jx]; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + y[i__] += temp * a[i__ + j * a_dim1]; /* L50: */ - } - jx += *incx; + } + jx += *incx; /* L60: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - temp = *alpha * x[jx]; - iy = ky; - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - y[iy] += temp * a[i__ + j * a_dim1]; - iy += *incy; + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp = *alpha * x[jx]; + iy = ky; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + y[iy] += temp * a[i__ + j * a_dim1]; + iy += *incy; /* L70: */ - } - jx += *incx; + } + jx += *incx; /* L80: */ - } - } + } + } } else { /* Form y := alpha*A**T*x + y. */ - jy = ky; - if (*incx == 1) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - temp = 0.; - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - temp += a[i__ + j * a_dim1] * x[i__]; + jy = ky; + if (*incx == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp = 0.; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp += a[i__ + j * a_dim1] * x[i__]; /* L90: */ - } - y[jy] += *alpha * temp; - jy += *incy; + } + y[jy] += *alpha * temp; + jy += *incy; /* L100: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - temp = 0.; - ix = kx; - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - temp += a[i__ + j * a_dim1] * x[ix]; - ix += *incx; + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp = 0.; + ix = kx; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp += a[i__ + j * a_dim1] * x[ix]; + ix += *incx; /* L110: */ - } - y[jy] += *alpha * temp; - jy += *incy; + } + y[jy] += *alpha * temp; + jy += *incy; /* L120: */ - } - } + } + } } return 0; @@ -381,5 +381,5 @@ extern "C" { } /* dgemv_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dgeqr2.cpp b/lib/linalg/dgeqr2.cpp index 635e360bc7..6cc1bc8400 100644 --- a/lib/linalg/dgeqr2.cpp +++ b/lib/linalg/dgeqr2.cpp @@ -1,13 +1,13 @@ /* fortran/dgeqr2.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -152,7 +152,7 @@ f"> */ /* > */ /* ===================================================================== */ /* Subroutine */ int dgeqr2_(integer *m, integer *n, doublereal *a, integer * - lda, doublereal *tau, doublereal *work, integer *info) + lda, doublereal *tau, doublereal *work, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; @@ -160,11 +160,11 @@ f"> */ /* Local variables */ integer i__, k; doublereal aii; - extern /* Subroutine */ int dlarf_(char *, integer *, integer *, - doublereal *, integer *, doublereal *, doublereal *, integer *, - doublereal *, ftnlen), dlarfg_(integer *, doublereal *, - doublereal *, integer *, doublereal *), xerbla_(char *, integer *, - ftnlen); + extern /* Subroutine */ int dlarf_(char *, integer *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, + doublereal *, ftnlen), dlarfg_(integer *, doublereal *, + doublereal *, integer *, doublereal *), xerbla_(char *, integer *, + ftnlen); /* -- LAPACK computational routine -- */ @@ -200,16 +200,16 @@ f"> */ /* Function Body */ *info = 0; if (*m < 0) { - *info = -1; + *info = -1; } else if (*n < 0) { - *info = -2; + *info = -2; } else if (*lda < max(1,*m)) { - *info = -4; + *info = -4; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DGEQR2", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DGEQR2", &i__1, (ftnlen)6); + return 0; } k = min(*m,*n); @@ -219,24 +219,24 @@ f"> */ /* Generate elementary reflector H(i) to annihilate A(i+1:m,i) */ - i__2 = *m - i__ + 1; + i__2 = *m - i__ + 1; /* Computing MIN */ - i__3 = i__ + 1; - dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[min(i__3,*m) + i__ * a_dim1] - , &c__1, &tau[i__]); - if (i__ < *n) { + i__3 = i__ + 1; + dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[min(i__3,*m) + i__ * a_dim1] + , &c__1, &tau[i__]); + if (i__ < *n) { /* Apply H(i) to A(i:m,i+1:n) from the left */ - aii = a[i__ + i__ * a_dim1]; - a[i__ + i__ * a_dim1] = 1.; - i__2 = *m - i__ + 1; - i__3 = *n - i__; - dlarf_((char *)"Left", &i__2, &i__3, &a[i__ + i__ * a_dim1], &c__1, &tau[ - i__], &a[i__ + (i__ + 1) * a_dim1], lda, &work[1], ( - ftnlen)4); - a[i__ + i__ * a_dim1] = aii; - } + aii = a[i__ + i__ * a_dim1]; + a[i__ + i__ * a_dim1] = 1.; + i__2 = *m - i__ + 1; + i__3 = *n - i__; + dlarf_((char *)"Left", &i__2, &i__3, &a[i__ + i__ * a_dim1], &c__1, &tau[ + i__], &a[i__ + (i__ + 1) * a_dim1], lda, &work[1], ( + ftnlen)4); + a[i__ + i__ * a_dim1] = aii; + } /* L10: */ } return 0; @@ -246,5 +246,5 @@ f"> */ } /* dgeqr2_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dgeqrf.cpp b/lib/linalg/dgeqrf.cpp index fa0aca3f47..57b92689b9 100644 --- a/lib/linalg/dgeqrf.cpp +++ b/lib/linalg/dgeqrf.cpp @@ -1,13 +1,13 @@ /* fortran/dgeqrf.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -170,23 +170,23 @@ f"> */ /* > */ /* ===================================================================== */ /* Subroutine */ int dgeqrf_(integer *m, integer *n, doublereal *a, integer * - lda, doublereal *tau, doublereal *work, integer *lwork, integer *info) + lda, doublereal *tau, doublereal *work, integer *lwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4; /* Local variables */ integer i__, k, ib, nb, nx, iws, nbmin, iinfo; - extern /* Subroutine */ int dgeqr2_(integer *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *), dlarfb_(char *, - char *, char *, char *, integer *, integer *, integer *, - doublereal *, integer *, doublereal *, integer *, doublereal *, - integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, - ftnlen), dlarft_(char *, char *, integer *, integer *, doublereal - *, integer *, doublereal *, doublereal *, integer *, ftnlen, - ftnlen), xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dgeqr2_(integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *), dlarfb_(char *, + char *, char *, char *, integer *, integer *, integer *, + doublereal *, integer *, doublereal *, integer *, doublereal *, + integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, + ftnlen), dlarft_(char *, char *, integer *, integer *, doublereal + *, integer *, doublereal *, doublereal *, integer *, ftnlen, + ftnlen), xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); integer ldwork, lwkopt; logical lquery; @@ -225,38 +225,38 @@ f"> */ k = min(*m,*n); *info = 0; nb = ilaenv_(&c__1, (char *)"DGEQRF", (char *)" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen) - 1); + 1); lquery = *lwork == -1; if (*m < 0) { - *info = -1; + *info = -1; } else if (*n < 0) { - *info = -2; + *info = -2; } else if (*lda < max(1,*m)) { - *info = -4; + *info = -4; } else if (! lquery) { - if (*lwork <= 0 || *m > 0 && *lwork < max(1,*n)) { - *info = -7; - } + if (*lwork <= 0 || *m > 0 && *lwork < max(1,*n)) { + *info = -7; + } } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DGEQRF", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DGEQRF", &i__1, (ftnlen)6); + return 0; } else if (lquery) { - if (k == 0) { - lwkopt = 1; - } else { - lwkopt = *n * nb; - } - work[1] = (doublereal) lwkopt; - return 0; + if (k == 0) { + lwkopt = 1; + } else { + lwkopt = *n * nb; + } + work[1] = (doublereal) lwkopt; + return 0; } /* Quick return if possible */ if (k == 0) { - work[1] = 1.; - return 0; + work[1] = 1.; + return 0; } nbmin = 2; @@ -267,79 +267,79 @@ f"> */ /* Determine when to cross over from blocked to unblocked code. */ /* Computing MAX */ - i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"DGEQRF", (char *)" ", m, n, &c_n1, &c_n1, ( - ftnlen)6, (ftnlen)1); - nx = max(i__1,i__2); - if (nx < k) { + i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"DGEQRF", (char *)" ", m, n, &c_n1, &c_n1, ( + ftnlen)6, (ftnlen)1); + nx = max(i__1,i__2); + if (nx < k) { /* Determine if workspace is large enough for blocked code. */ - ldwork = *n; - iws = ldwork * nb; - if (*lwork < iws) { + ldwork = *n; + iws = ldwork * nb; + if (*lwork < iws) { /* Not enough workspace to use optimal NB: reduce NB and */ /* determine the minimum value of NB. */ - nb = *lwork / ldwork; + nb = *lwork / ldwork; /* Computing MAX */ - i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DGEQRF", (char *)" ", m, n, &c_n1, & - c_n1, (ftnlen)6, (ftnlen)1); - nbmin = max(i__1,i__2); - } - } + i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DGEQRF", (char *)" ", m, n, &c_n1, & + c_n1, (ftnlen)6, (ftnlen)1); + nbmin = max(i__1,i__2); + } + } } if (nb >= nbmin && nb < k && nx < k) { /* Use blocked code initially */ - i__1 = k - nx; - i__2 = nb; - for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { + i__1 = k - nx; + i__2 = nb; + for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { /* Computing MIN */ - i__3 = k - i__ + 1; - ib = min(i__3,nb); + i__3 = k - i__ + 1; + ib = min(i__3,nb); /* Compute the QR factorization of the current block */ /* A(i:m,i:i+ib-1) */ - i__3 = *m - i__ + 1; - dgeqr2_(&i__3, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[ - 1], &iinfo); - if (i__ + ib <= *n) { + i__3 = *m - i__ + 1; + dgeqr2_(&i__3, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[ + 1], &iinfo); + if (i__ + ib <= *n) { /* Form the triangular factor of the block reflector */ /* H = H(i) H(i+1) . . . H(i+ib-1) */ - i__3 = *m - i__ + 1; - dlarft_((char *)"Forward", (char *)"Columnwise", &i__3, &ib, &a[i__ + i__ * - a_dim1], lda, &tau[i__], &work[1], &ldwork, (ftnlen)7, - (ftnlen)10); + i__3 = *m - i__ + 1; + dlarft_((char *)"Forward", (char *)"Columnwise", &i__3, &ib, &a[i__ + i__ * + a_dim1], lda, &tau[i__], &work[1], &ldwork, (ftnlen)7, + (ftnlen)10); /* Apply H**T to A(i:m,i+ib:n) from the left */ - i__3 = *m - i__ + 1; - i__4 = *n - i__ - ib + 1; - dlarfb_((char *)"Left", (char *)"Transpose", (char *)"Forward", (char *)"Columnwise", &i__3, & - i__4, &ib, &a[i__ + i__ * a_dim1], lda, &work[1], & - ldwork, &a[i__ + (i__ + ib) * a_dim1], lda, &work[ib - + 1], &ldwork, (ftnlen)4, (ftnlen)9, (ftnlen)7, ( - ftnlen)10); - } + i__3 = *m - i__ + 1; + i__4 = *n - i__ - ib + 1; + dlarfb_((char *)"Left", (char *)"Transpose", (char *)"Forward", (char *)"Columnwise", &i__3, & + i__4, &ib, &a[i__ + i__ * a_dim1], lda, &work[1], & + ldwork, &a[i__ + (i__ + ib) * a_dim1], lda, &work[ib + + 1], &ldwork, (ftnlen)4, (ftnlen)9, (ftnlen)7, ( + ftnlen)10); + } /* L10: */ - } + } } else { - i__ = 1; + i__ = 1; } /* Use unblocked code to factor the last or only block. */ if (i__ <= k) { - i__2 = *m - i__ + 1; - i__1 = *n - i__ + 1; - dgeqr2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[1] - , &iinfo); + i__2 = *m - i__ + 1; + i__1 = *n - i__ + 1; + dgeqr2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[1] + , &iinfo); } work[1] = (doublereal) iws; @@ -350,5 +350,5 @@ f"> */ } /* dgeqrf_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dger.cpp b/lib/linalg/dger.cpp index fd5c4940bf..9bb0d19982 100644 --- a/lib/linalg/dger.cpp +++ b/lib/linalg/dger.cpp @@ -1,13 +1,13 @@ /* fortran/dger.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -143,9 +143,9 @@ extern "C" { /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int dger_(integer *m, integer *n, doublereal *alpha, - doublereal *x, integer *incx, doublereal *y, integer *incy, - doublereal *a, integer *lda) +/* Subroutine */ int dger_(integer *m, integer *n, doublereal *alpha, + doublereal *x, integer *incx, doublereal *y, integer *incy, + doublereal *a, integer *lda) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; @@ -188,70 +188,70 @@ extern "C" { /* Function Body */ info = 0; if (*m < 0) { - info = 1; + info = 1; } else if (*n < 0) { - info = 2; + info = 2; } else if (*incx == 0) { - info = 5; + info = 5; } else if (*incy == 0) { - info = 7; + info = 7; } else if (*lda < max(1,*m)) { - info = 9; + info = 9; } if (info != 0) { - xerbla_((char *)"DGER ", &info, (ftnlen)6); - return 0; + xerbla_((char *)"DGER ", &info, (ftnlen)6); + return 0; } /* Quick return if possible. */ if (*m == 0 || *n == 0 || *alpha == 0.) { - return 0; + return 0; } /* Start the operations. In this version the elements of A are */ /* accessed sequentially with one pass through A. */ if (*incy > 0) { - jy = 1; + jy = 1; } else { - jy = 1 - (*n - 1) * *incy; + jy = 1 - (*n - 1) * *incy; } if (*incx == 1) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - if (y[jy] != 0.) { - temp = *alpha * y[jy]; - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - a[i__ + j * a_dim1] += x[i__] * temp; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (y[jy] != 0.) { + temp = *alpha * y[jy]; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] += x[i__] * temp; /* L10: */ - } - } - jy += *incy; + } + } + jy += *incy; /* L20: */ - } + } } else { - if (*incx > 0) { - kx = 1; - } else { - kx = 1 - (*m - 1) * *incx; - } - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - if (y[jy] != 0.) { - temp = *alpha * y[jy]; - ix = kx; - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - a[i__ + j * a_dim1] += x[ix] * temp; - ix += *incx; + if (*incx > 0) { + kx = 1; + } else { + kx = 1 - (*m - 1) * *incx; + } + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (y[jy] != 0.) { + temp = *alpha * y[jy]; + ix = kx; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] += x[ix] * temp; + ix += *incx; /* L30: */ - } - } - jy += *incy; + } + } + jy += *incy; /* L40: */ - } + } } return 0; @@ -261,5 +261,5 @@ extern "C" { } /* dger_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dgesv.cpp b/lib/linalg/dgesv.cpp index a71b2caa68..c2e0232c37 100644 --- a/lib/linalg/dgesv.cpp +++ b/lib/linalg/dgesv.cpp @@ -1,13 +1,13 @@ /* fortran/dgesv.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -138,17 +138,17 @@ extern "C" { /* > \ingroup doubleGEsolve */ /* ===================================================================== */ -/* Subroutine */ int dgesv_(integer *n, integer *nrhs, doublereal *a, integer - *lda, integer *ipiv, doublereal *b, integer *ldb, integer *info) +/* Subroutine */ int dgesv_(integer *n, integer *nrhs, doublereal *a, integer + *lda, integer *ipiv, doublereal *b, integer *ldb, integer *info) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1; /* Local variables */ - extern /* Subroutine */ int dgetrf_(integer *, integer *, doublereal *, - integer *, integer *, integer *), xerbla_(char *, integer *, - ftnlen), dgetrs_(char *, integer *, integer *, doublereal *, - integer *, integer *, doublereal *, integer *, integer *, ftnlen); + extern /* Subroutine */ int dgetrf_(integer *, integer *, doublereal *, + integer *, integer *, integer *), xerbla_(char *, integer *, + ftnlen), dgetrs_(char *, integer *, integer *, doublereal *, + integer *, integer *, doublereal *, integer *, integer *, ftnlen); /* -- LAPACK driver routine -- */ @@ -182,18 +182,18 @@ extern "C" { /* Function Body */ *info = 0; if (*n < 0) { - *info = -1; + *info = -1; } else if (*nrhs < 0) { - *info = -2; + *info = -2; } else if (*lda < max(1,*n)) { - *info = -4; + *info = -4; } else if (*ldb < max(1,*n)) { - *info = -7; + *info = -7; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DGESV ", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DGESV ", &i__1, (ftnlen)6); + return 0; } /* Compute the LU factorization of A. */ @@ -203,8 +203,8 @@ extern "C" { /* Solve the system A*X = B, overwriting B with X. */ - dgetrs_((char *)"No transpose", n, nrhs, &a[a_offset], lda, &ipiv[1], &b[ - b_offset], ldb, info, (ftnlen)12); + dgetrs_((char *)"No transpose", n, nrhs, &a[a_offset], lda, &ipiv[1], &b[ + b_offset], ldb, info, (ftnlen)12); } return 0; @@ -213,5 +213,5 @@ extern "C" { } /* dgesv_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dgesvd.cpp b/lib/linalg/dgesvd.cpp index 96fd8735b0..6a2e70640f 100644 --- a/lib/linalg/dgesvd.cpp +++ b/lib/linalg/dgesvd.cpp @@ -1,13 +1,13 @@ /* fortran/dgesvd.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -236,15 +236,15 @@ f"> */ /* > \ingroup doubleGEsing */ /* ===================================================================== */ -/* Subroutine */ int dgesvd_(char *jobu, char *jobvt, integer *m, integer *n, - doublereal *a, integer *lda, doublereal *s, doublereal *u, integer * - ldu, doublereal *vt, integer *ldvt, doublereal *work, integer *lwork, - integer *info, ftnlen jobu_len, ftnlen jobvt_len) +/* Subroutine */ int dgesvd_(char *jobu, char *jobvt, integer *m, integer *n, + doublereal *a, integer *lda, doublereal *s, doublereal *u, integer * + ldu, doublereal *vt, integer *ldvt, doublereal *work, integer *lwork, + integer *info, ftnlen jobu_len, ftnlen jobvt_len) { /* System generated locals */ address a__1[2]; - integer a_dim1, a_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1[2], - i__2, i__3, i__4; + integer a_dim1, a_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1[2], + i__2, i__3, i__4; char ch__1[2]; /* Builtin functions */ @@ -256,51 +256,51 @@ f"> */ doublereal dum[1], eps; integer nru, iscl; doublereal anrm; - integer ierr, itau, ncvt, nrvt, lwork_dgebrd__, lwork_dgelqf__, - lwork_dgeqrf__; - extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); + integer ierr, itau, ncvt, nrvt, lwork_dgebrd__, lwork_dgelqf__, + lwork_dgeqrf__; + extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); extern logical lsame_(char *, char *, ftnlen, ftnlen); integer chunk, minmn, wrkbl, itaup, itauq, mnthr, iwork; logical wntua, wntva, wntun, wntuo, wntvn, wntvo, wntus, wntvs; - extern /* Subroutine */ int dgebrd_(integer *, integer *, doublereal *, - integer *, doublereal *, doublereal *, doublereal *, doublereal *, - doublereal *, integer *, integer *); - extern doublereal dlamch_(char *, ftnlen), dlange_(char *, integer *, - integer *, doublereal *, integer *, doublereal *, ftnlen); + extern /* Subroutine */ int dgebrd_(integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, integer *, integer *); + extern doublereal dlamch_(char *, ftnlen), dlange_(char *, integer *, + integer *, doublereal *, integer *, doublereal *, ftnlen); integer bdspac; - extern /* Subroutine */ int dgelqf_(integer *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, integer *), - dlascl_(char *, integer *, integer *, doublereal *, doublereal *, - integer *, integer *, doublereal *, integer *, integer *, ftnlen), - dgeqrf_(integer *, integer *, doublereal *, integer *, - doublereal *, doublereal *, integer *, integer *), dlacpy_(char *, - integer *, integer *, doublereal *, integer *, doublereal *, - integer *, ftnlen), dlaset_(char *, integer *, integer *, - doublereal *, doublereal *, doublereal *, integer *, ftnlen), - dbdsqr_(char *, integer *, integer *, integer *, integer *, - doublereal *, doublereal *, doublereal *, integer *, doublereal *, - integer *, doublereal *, integer *, doublereal *, integer *, - ftnlen), dorgbr_(char *, integer *, integer *, integer *, - doublereal *, integer *, doublereal *, doublereal *, integer *, - integer *, ftnlen); + extern /* Subroutine */ int dgelqf_(integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, integer *), + dlascl_(char *, integer *, integer *, doublereal *, doublereal *, + integer *, integer *, doublereal *, integer *, integer *, ftnlen), + dgeqrf_(integer *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, integer *), dlacpy_(char *, + integer *, integer *, doublereal *, integer *, doublereal *, + integer *, ftnlen), dlaset_(char *, integer *, integer *, + doublereal *, doublereal *, doublereal *, integer *, ftnlen), + dbdsqr_(char *, integer *, integer *, integer *, integer *, + doublereal *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, integer *, doublereal *, integer *, + ftnlen), dorgbr_(char *, integer *, integer *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, + integer *, ftnlen); doublereal bignum; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - extern /* Subroutine */ int dormbr_(char *, char *, char *, integer *, - integer *, integer *, doublereal *, integer *, doublereal *, - doublereal *, integer *, doublereal *, integer *, integer *, - ftnlen, ftnlen, ftnlen), dorglq_(integer *, integer *, integer *, - doublereal *, integer *, doublereal *, doublereal *, integer *, - integer *), dorgqr_(integer *, integer *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, integer *); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dormbr_(char *, char *, char *, integer *, + integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, doublereal *, integer *, integer *, + ftnlen, ftnlen, ftnlen), dorglq_(integer *, integer *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, + integer *), dorgqr_(integer *, integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, integer *); integer ldwrkr, minwrk, ldwrku, maxwrk; doublereal smlnum; logical lquery, wntuas, wntvas; - integer lwork_dorgbr_p__, lwork_dorgbr_q__, lwork_dorglq_m__, - lwork_dorglq_n__, lwork_dorgqr_m__, lwork_dorgqr_n__; + integer lwork_dorgbr_p__, lwork_dorgbr_q__, lwork_dorglq_m__, + lwork_dorglq_n__, lwork_dorgqr_m__, lwork_dorgqr_n__; /* -- LAPACK driver routine -- */ @@ -359,19 +359,19 @@ f"> */ lquery = *lwork == -1; if (! (wntua || wntus || wntuo || wntun)) { - *info = -1; + *info = -1; } else if (! (wntva || wntvs || wntvo || wntvn) || wntvo && wntuo) { - *info = -2; + *info = -2; } else if (*m < 0) { - *info = -3; + *info = -3; } else if (*n < 0) { - *info = -4; + *info = -4; } else if (*lda < max(1,*m)) { - *info = -6; + *info = -6; } else if (*ldu < 1 || wntuas && *ldu < *m) { - *info = -9; + *info = -9; } else if (*ldvt < 1 || wntva && *ldvt < *n || wntvs && *ldvt < minmn) { - *info = -11; + *info = -11; } /* Compute workspace */ @@ -382,547 +382,547 @@ f"> */ /* following subroutine, as returned by ILAENV.) */ if (*info == 0) { - minwrk = 1; - maxwrk = 1; - if (*m >= *n && minmn > 0) { + minwrk = 1; + maxwrk = 1; + if (*m >= *n && minmn > 0) { /* Compute space needed for DBDSQR */ /* Writing concatenation */ - i__1[0] = 1, a__1[0] = jobu; - i__1[1] = 1, a__1[1] = jobvt; - s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); - mnthr = ilaenv_(&c__6, (char *)"DGESVD", ch__1, m, n, &c__0, &c__0, ( - ftnlen)6, (ftnlen)2); - bdspac = *n * 5; + i__1[0] = 1, a__1[0] = jobu; + i__1[1] = 1, a__1[1] = jobvt; + s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); + mnthr = ilaenv_(&c__6, (char *)"DGESVD", ch__1, m, n, &c__0, &c__0, ( + ftnlen)6, (ftnlen)2); + bdspac = *n * 5; /* Compute space needed for DGEQRF */ - dgeqrf_(m, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr); - lwork_dgeqrf__ = (integer) dum[0]; + dgeqrf_(m, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr); + lwork_dgeqrf__ = (integer) dum[0]; /* Compute space needed for DORGQR */ - dorgqr_(m, n, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr); - lwork_dorgqr_n__ = (integer) dum[0]; - dorgqr_(m, m, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr); - lwork_dorgqr_m__ = (integer) dum[0]; + dorgqr_(m, n, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr); + lwork_dorgqr_n__ = (integer) dum[0]; + dorgqr_(m, m, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr); + lwork_dorgqr_m__ = (integer) dum[0]; /* Compute space needed for DGEBRD */ - dgebrd_(n, n, &a[a_offset], lda, &s[1], dum, dum, dum, dum, &c_n1, - &ierr); - lwork_dgebrd__ = (integer) dum[0]; + dgebrd_(n, n, &a[a_offset], lda, &s[1], dum, dum, dum, dum, &c_n1, + &ierr); + lwork_dgebrd__ = (integer) dum[0]; /* Compute space needed for DORGBR P */ - dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr, ( - ftnlen)1); - lwork_dorgbr_p__ = (integer) dum[0]; + dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr, ( + ftnlen)1); + lwork_dorgbr_p__ = (integer) dum[0]; /* Compute space needed for DORGBR Q */ - dorgbr_((char *)"Q", n, n, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr, ( - ftnlen)1); - lwork_dorgbr_q__ = (integer) dum[0]; + dorgbr_((char *)"Q", n, n, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr, ( + ftnlen)1); + lwork_dorgbr_q__ = (integer) dum[0]; - if (*m >= mnthr) { - if (wntun) { + if (*m >= mnthr) { + if (wntun) { /* Path 1 (M much larger than N, JOBU='N') */ - maxwrk = *n + lwork_dgeqrf__; + maxwrk = *n + lwork_dgeqrf__; /* Computing MAX */ - i__2 = maxwrk, i__3 = *n * 3 + lwork_dgebrd__; - maxwrk = max(i__2,i__3); - if (wntvo || wntvas) { + i__2 = maxwrk, i__3 = *n * 3 + lwork_dgebrd__; + maxwrk = max(i__2,i__3); + if (wntvo || wntvas) { /* Computing MAX */ - i__2 = maxwrk, i__3 = *n * 3 + lwork_dorgbr_p__; - maxwrk = max(i__2,i__3); - } - maxwrk = max(maxwrk,bdspac); + i__2 = maxwrk, i__3 = *n * 3 + lwork_dorgbr_p__; + maxwrk = max(i__2,i__3); + } + maxwrk = max(maxwrk,bdspac); /* Computing MAX */ - i__2 = *n << 2; - minwrk = max(i__2,bdspac); - } else if (wntuo && wntvn) { + i__2 = *n << 2; + minwrk = max(i__2,bdspac); + } else if (wntuo && wntvn) { /* Path 2 (M much larger than N, JOBU='O', JOBVT='N') */ - wrkbl = *n + lwork_dgeqrf__; + wrkbl = *n + lwork_dgeqrf__; /* Computing MAX */ - i__2 = wrkbl, i__3 = *n + lwork_dorgqr_n__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *n + lwork_dorgqr_n__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__; - wrkbl = max(i__2,i__3); - wrkbl = max(wrkbl,bdspac); + i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__; + wrkbl = max(i__2,i__3); + wrkbl = max(wrkbl,bdspac); /* Computing MAX */ - i__2 = *n * *n + wrkbl, i__3 = *n * *n + *m * *n + *n; - maxwrk = max(i__2,i__3); + i__2 = *n * *n + wrkbl, i__3 = *n * *n + *m * *n + *n; + maxwrk = max(i__2,i__3); /* Computing MAX */ - i__2 = *n * 3 + *m; - minwrk = max(i__2,bdspac); - } else if (wntuo && wntvas) { + i__2 = *n * 3 + *m; + minwrk = max(i__2,bdspac); + } else if (wntuo && wntvas) { /* Path 3 (M much larger than N, JOBU='O', JOBVT='S' or */ /* 'A') */ - wrkbl = *n + lwork_dgeqrf__; + wrkbl = *n + lwork_dgeqrf__; /* Computing MAX */ - i__2 = wrkbl, i__3 = *n + lwork_dorgqr_n__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *n + lwork_dorgqr_n__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_p__; - wrkbl = max(i__2,i__3); - wrkbl = max(wrkbl,bdspac); + i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_p__; + wrkbl = max(i__2,i__3); + wrkbl = max(wrkbl,bdspac); /* Computing MAX */ - i__2 = *n * *n + wrkbl, i__3 = *n * *n + *m * *n + *n; - maxwrk = max(i__2,i__3); + i__2 = *n * *n + wrkbl, i__3 = *n * *n + *m * *n + *n; + maxwrk = max(i__2,i__3); /* Computing MAX */ - i__2 = *n * 3 + *m; - minwrk = max(i__2,bdspac); - } else if (wntus && wntvn) { + i__2 = *n * 3 + *m; + minwrk = max(i__2,bdspac); + } else if (wntus && wntvn) { /* Path 4 (M much larger than N, JOBU='S', JOBVT='N') */ - wrkbl = *n + lwork_dgeqrf__; + wrkbl = *n + lwork_dgeqrf__; /* Computing MAX */ - i__2 = wrkbl, i__3 = *n + lwork_dorgqr_n__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *n + lwork_dorgqr_n__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__; - wrkbl = max(i__2,i__3); - wrkbl = max(wrkbl,bdspac); - maxwrk = *n * *n + wrkbl; + i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__; + wrkbl = max(i__2,i__3); + wrkbl = max(wrkbl,bdspac); + maxwrk = *n * *n + wrkbl; /* Computing MAX */ - i__2 = *n * 3 + *m; - minwrk = max(i__2,bdspac); - } else if (wntus && wntvo) { + i__2 = *n * 3 + *m; + minwrk = max(i__2,bdspac); + } else if (wntus && wntvo) { /* Path 5 (M much larger than N, JOBU='S', JOBVT='O') */ - wrkbl = *n + lwork_dgeqrf__; + wrkbl = *n + lwork_dgeqrf__; /* Computing MAX */ - i__2 = wrkbl, i__3 = *n + lwork_dorgqr_n__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *n + lwork_dorgqr_n__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_p__; - wrkbl = max(i__2,i__3); - wrkbl = max(wrkbl,bdspac); - maxwrk = (*n << 1) * *n + wrkbl; + i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_p__; + wrkbl = max(i__2,i__3); + wrkbl = max(wrkbl,bdspac); + maxwrk = (*n << 1) * *n + wrkbl; /* Computing MAX */ - i__2 = *n * 3 + *m; - minwrk = max(i__2,bdspac); - } else if (wntus && wntvas) { + i__2 = *n * 3 + *m; + minwrk = max(i__2,bdspac); + } else if (wntus && wntvas) { /* Path 6 (M much larger than N, JOBU='S', JOBVT='S' or */ /* 'A') */ - wrkbl = *n + lwork_dgeqrf__; + wrkbl = *n + lwork_dgeqrf__; /* Computing MAX */ - i__2 = wrkbl, i__3 = *n + lwork_dorgqr_n__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *n + lwork_dorgqr_n__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_p__; - wrkbl = max(i__2,i__3); - wrkbl = max(wrkbl,bdspac); - maxwrk = *n * *n + wrkbl; + i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_p__; + wrkbl = max(i__2,i__3); + wrkbl = max(wrkbl,bdspac); + maxwrk = *n * *n + wrkbl; /* Computing MAX */ - i__2 = *n * 3 + *m; - minwrk = max(i__2,bdspac); - } else if (wntua && wntvn) { + i__2 = *n * 3 + *m; + minwrk = max(i__2,bdspac); + } else if (wntua && wntvn) { /* Path 7 (M much larger than N, JOBU='A', JOBVT='N') */ - wrkbl = *n + lwork_dgeqrf__; + wrkbl = *n + lwork_dgeqrf__; /* Computing MAX */ - i__2 = wrkbl, i__3 = *n + lwork_dorgqr_m__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *n + lwork_dorgqr_m__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__; - wrkbl = max(i__2,i__3); - wrkbl = max(wrkbl,bdspac); - maxwrk = *n * *n + wrkbl; + i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__; + wrkbl = max(i__2,i__3); + wrkbl = max(wrkbl,bdspac); + maxwrk = *n * *n + wrkbl; /* Computing MAX */ - i__2 = *n * 3 + *m; - minwrk = max(i__2,bdspac); - } else if (wntua && wntvo) { + i__2 = *n * 3 + *m; + minwrk = max(i__2,bdspac); + } else if (wntua && wntvo) { /* Path 8 (M much larger than N, JOBU='A', JOBVT='O') */ - wrkbl = *n + lwork_dgeqrf__; + wrkbl = *n + lwork_dgeqrf__; /* Computing MAX */ - i__2 = wrkbl, i__3 = *n + lwork_dorgqr_m__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *n + lwork_dorgqr_m__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_p__; - wrkbl = max(i__2,i__3); - wrkbl = max(wrkbl,bdspac); - maxwrk = (*n << 1) * *n + wrkbl; + i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_p__; + wrkbl = max(i__2,i__3); + wrkbl = max(wrkbl,bdspac); + maxwrk = (*n << 1) * *n + wrkbl; /* Computing MAX */ - i__2 = *n * 3 + *m; - minwrk = max(i__2,bdspac); - } else if (wntua && wntvas) { + i__2 = *n * 3 + *m; + minwrk = max(i__2,bdspac); + } else if (wntua && wntvas) { /* Path 9 (M much larger than N, JOBU='A', JOBVT='S' or */ /* 'A') */ - wrkbl = *n + lwork_dgeqrf__; + wrkbl = *n + lwork_dgeqrf__; /* Computing MAX */ - i__2 = wrkbl, i__3 = *n + lwork_dorgqr_m__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *n + lwork_dorgqr_m__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_p__; - wrkbl = max(i__2,i__3); - wrkbl = max(wrkbl,bdspac); - maxwrk = *n * *n + wrkbl; + i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_p__; + wrkbl = max(i__2,i__3); + wrkbl = max(wrkbl,bdspac); + maxwrk = *n * *n + wrkbl; /* Computing MAX */ - i__2 = *n * 3 + *m; - minwrk = max(i__2,bdspac); - } - } else { + i__2 = *n * 3 + *m; + minwrk = max(i__2,bdspac); + } + } else { /* Path 10 (M at least N, but not much larger) */ - dgebrd_(m, n, &a[a_offset], lda, &s[1], dum, dum, dum, dum, & - c_n1, &ierr); - lwork_dgebrd__ = (integer) dum[0]; - maxwrk = *n * 3 + lwork_dgebrd__; - if (wntus || wntuo) { - dorgbr_((char *)"Q", m, n, n, &a[a_offset], lda, dum, dum, &c_n1, - &ierr, (ftnlen)1); - lwork_dorgbr_q__ = (integer) dum[0]; + dgebrd_(m, n, &a[a_offset], lda, &s[1], dum, dum, dum, dum, & + c_n1, &ierr); + lwork_dgebrd__ = (integer) dum[0]; + maxwrk = *n * 3 + lwork_dgebrd__; + if (wntus || wntuo) { + dorgbr_((char *)"Q", m, n, n, &a[a_offset], lda, dum, dum, &c_n1, + &ierr, (ftnlen)1); + lwork_dorgbr_q__ = (integer) dum[0]; /* Computing MAX */ - i__2 = maxwrk, i__3 = *n * 3 + lwork_dorgbr_q__; - maxwrk = max(i__2,i__3); - } - if (wntua) { - dorgbr_((char *)"Q", m, m, n, &a[a_offset], lda, dum, dum, &c_n1, - &ierr, (ftnlen)1); - lwork_dorgbr_q__ = (integer) dum[0]; + i__2 = maxwrk, i__3 = *n * 3 + lwork_dorgbr_q__; + maxwrk = max(i__2,i__3); + } + if (wntua) { + dorgbr_((char *)"Q", m, m, n, &a[a_offset], lda, dum, dum, &c_n1, + &ierr, (ftnlen)1); + lwork_dorgbr_q__ = (integer) dum[0]; /* Computing MAX */ - i__2 = maxwrk, i__3 = *n * 3 + lwork_dorgbr_q__; - maxwrk = max(i__2,i__3); - } - if (! wntvn) { + i__2 = maxwrk, i__3 = *n * 3 + lwork_dorgbr_q__; + maxwrk = max(i__2,i__3); + } + if (! wntvn) { /* Computing MAX */ - i__2 = maxwrk, i__3 = *n * 3 + lwork_dorgbr_p__; - maxwrk = max(i__2,i__3); - } - maxwrk = max(maxwrk,bdspac); + i__2 = maxwrk, i__3 = *n * 3 + lwork_dorgbr_p__; + maxwrk = max(i__2,i__3); + } + maxwrk = max(maxwrk,bdspac); /* Computing MAX */ - i__2 = *n * 3 + *m; - minwrk = max(i__2,bdspac); - } - } else if (minmn > 0) { + i__2 = *n * 3 + *m; + minwrk = max(i__2,bdspac); + } + } else if (minmn > 0) { /* Compute space needed for DBDSQR */ /* Writing concatenation */ - i__1[0] = 1, a__1[0] = jobu; - i__1[1] = 1, a__1[1] = jobvt; - s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); - mnthr = ilaenv_(&c__6, (char *)"DGESVD", ch__1, m, n, &c__0, &c__0, ( - ftnlen)6, (ftnlen)2); - bdspac = *m * 5; + i__1[0] = 1, a__1[0] = jobu; + i__1[1] = 1, a__1[1] = jobvt; + s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); + mnthr = ilaenv_(&c__6, (char *)"DGESVD", ch__1, m, n, &c__0, &c__0, ( + ftnlen)6, (ftnlen)2); + bdspac = *m * 5; /* Compute space needed for DGELQF */ - dgelqf_(m, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr); - lwork_dgelqf__ = (integer) dum[0]; + dgelqf_(m, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr); + lwork_dgelqf__ = (integer) dum[0]; /* Compute space needed for DORGLQ */ - dorglq_(n, n, m, dum, n, dum, dum, &c_n1, &ierr); - lwork_dorglq_n__ = (integer) dum[0]; - dorglq_(m, n, m, &a[a_offset], lda, dum, dum, &c_n1, &ierr); - lwork_dorglq_m__ = (integer) dum[0]; + dorglq_(n, n, m, dum, n, dum, dum, &c_n1, &ierr); + lwork_dorglq_n__ = (integer) dum[0]; + dorglq_(m, n, m, &a[a_offset], lda, dum, dum, &c_n1, &ierr); + lwork_dorglq_m__ = (integer) dum[0]; /* Compute space needed for DGEBRD */ - dgebrd_(m, m, &a[a_offset], lda, &s[1], dum, dum, dum, dum, &c_n1, - &ierr); - lwork_dgebrd__ = (integer) dum[0]; + dgebrd_(m, m, &a[a_offset], lda, &s[1], dum, dum, dum, dum, &c_n1, + &ierr); + lwork_dgebrd__ = (integer) dum[0]; /* Compute space needed for DORGBR P */ - dorgbr_((char *)"P", m, m, m, &a[a_offset], n, dum, dum, &c_n1, &ierr, ( - ftnlen)1); - lwork_dorgbr_p__ = (integer) dum[0]; + dorgbr_((char *)"P", m, m, m, &a[a_offset], n, dum, dum, &c_n1, &ierr, ( + ftnlen)1); + lwork_dorgbr_p__ = (integer) dum[0]; /* Compute space needed for DORGBR Q */ - dorgbr_((char *)"Q", m, m, m, &a[a_offset], n, dum, dum, &c_n1, &ierr, ( - ftnlen)1); - lwork_dorgbr_q__ = (integer) dum[0]; - if (*n >= mnthr) { - if (wntvn) { + dorgbr_((char *)"Q", m, m, m, &a[a_offset], n, dum, dum, &c_n1, &ierr, ( + ftnlen)1); + lwork_dorgbr_q__ = (integer) dum[0]; + if (*n >= mnthr) { + if (wntvn) { /* Path 1t(N much larger than M, JOBVT='N') */ - maxwrk = *m + lwork_dgelqf__; + maxwrk = *m + lwork_dgelqf__; /* Computing MAX */ - i__2 = maxwrk, i__3 = *m * 3 + lwork_dgebrd__; - maxwrk = max(i__2,i__3); - if (wntuo || wntuas) { + i__2 = maxwrk, i__3 = *m * 3 + lwork_dgebrd__; + maxwrk = max(i__2,i__3); + if (wntuo || wntuas) { /* Computing MAX */ - i__2 = maxwrk, i__3 = *m * 3 + lwork_dorgbr_q__; - maxwrk = max(i__2,i__3); - } - maxwrk = max(maxwrk,bdspac); + i__2 = maxwrk, i__3 = *m * 3 + lwork_dorgbr_q__; + maxwrk = max(i__2,i__3); + } + maxwrk = max(maxwrk,bdspac); /* Computing MAX */ - i__2 = *m << 2; - minwrk = max(i__2,bdspac); - } else if (wntvo && wntun) { + i__2 = *m << 2; + minwrk = max(i__2,bdspac); + } else if (wntvo && wntun) { /* Path 2t(N much larger than M, JOBU='N', JOBVT='O') */ - wrkbl = *m + lwork_dgelqf__; + wrkbl = *m + lwork_dgelqf__; /* Computing MAX */ - i__2 = wrkbl, i__3 = *m + lwork_dorglq_m__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *m + lwork_dorglq_m__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__; - wrkbl = max(i__2,i__3); - wrkbl = max(wrkbl,bdspac); + i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__; + wrkbl = max(i__2,i__3); + wrkbl = max(wrkbl,bdspac); /* Computing MAX */ - i__2 = *m * *m + wrkbl, i__3 = *m * *m + *m * *n + *m; - maxwrk = max(i__2,i__3); + i__2 = *m * *m + wrkbl, i__3 = *m * *m + *m * *n + *m; + maxwrk = max(i__2,i__3); /* Computing MAX */ - i__2 = *m * 3 + *n; - minwrk = max(i__2,bdspac); - } else if (wntvo && wntuas) { + i__2 = *m * 3 + *n; + minwrk = max(i__2,bdspac); + } else if (wntvo && wntuas) { /* Path 3t(N much larger than M, JOBU='S' or 'A', */ /* JOBVT='O') */ - wrkbl = *m + lwork_dgelqf__; + wrkbl = *m + lwork_dgelqf__; /* Computing MAX */ - i__2 = wrkbl, i__3 = *m + lwork_dorglq_m__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *m + lwork_dorglq_m__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_q__; - wrkbl = max(i__2,i__3); - wrkbl = max(wrkbl,bdspac); + i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_q__; + wrkbl = max(i__2,i__3); + wrkbl = max(wrkbl,bdspac); /* Computing MAX */ - i__2 = *m * *m + wrkbl, i__3 = *m * *m + *m * *n + *m; - maxwrk = max(i__2,i__3); + i__2 = *m * *m + wrkbl, i__3 = *m * *m + *m * *n + *m; + maxwrk = max(i__2,i__3); /* Computing MAX */ - i__2 = *m * 3 + *n; - minwrk = max(i__2,bdspac); - } else if (wntvs && wntun) { + i__2 = *m * 3 + *n; + minwrk = max(i__2,bdspac); + } else if (wntvs && wntun) { /* Path 4t(N much larger than M, JOBU='N', JOBVT='S') */ - wrkbl = *m + lwork_dgelqf__; + wrkbl = *m + lwork_dgelqf__; /* Computing MAX */ - i__2 = wrkbl, i__3 = *m + lwork_dorglq_m__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *m + lwork_dorglq_m__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__; - wrkbl = max(i__2,i__3); - wrkbl = max(wrkbl,bdspac); - maxwrk = *m * *m + wrkbl; + i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__; + wrkbl = max(i__2,i__3); + wrkbl = max(wrkbl,bdspac); + maxwrk = *m * *m + wrkbl; /* Computing MAX */ - i__2 = *m * 3 + *n; - minwrk = max(i__2,bdspac); - } else if (wntvs && wntuo) { + i__2 = *m * 3 + *n; + minwrk = max(i__2,bdspac); + } else if (wntvs && wntuo) { /* Path 5t(N much larger than M, JOBU='O', JOBVT='S') */ - wrkbl = *m + lwork_dgelqf__; + wrkbl = *m + lwork_dgelqf__; /* Computing MAX */ - i__2 = wrkbl, i__3 = *m + lwork_dorglq_m__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *m + lwork_dorglq_m__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_q__; - wrkbl = max(i__2,i__3); - wrkbl = max(wrkbl,bdspac); - maxwrk = (*m << 1) * *m + wrkbl; + i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_q__; + wrkbl = max(i__2,i__3); + wrkbl = max(wrkbl,bdspac); + maxwrk = (*m << 1) * *m + wrkbl; /* Computing MAX */ - i__2 = *m * 3 + *n; - minwrk = max(i__2,bdspac); - } else if (wntvs && wntuas) { + i__2 = *m * 3 + *n; + minwrk = max(i__2,bdspac); + } else if (wntvs && wntuas) { /* Path 6t(N much larger than M, JOBU='S' or 'A', */ /* JOBVT='S') */ - wrkbl = *m + lwork_dgelqf__; + wrkbl = *m + lwork_dgelqf__; /* Computing MAX */ - i__2 = wrkbl, i__3 = *m + lwork_dorglq_m__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *m + lwork_dorglq_m__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_q__; - wrkbl = max(i__2,i__3); - wrkbl = max(wrkbl,bdspac); - maxwrk = *m * *m + wrkbl; + i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_q__; + wrkbl = max(i__2,i__3); + wrkbl = max(wrkbl,bdspac); + maxwrk = *m * *m + wrkbl; /* Computing MAX */ - i__2 = *m * 3 + *n; - minwrk = max(i__2,bdspac); - } else if (wntva && wntun) { + i__2 = *m * 3 + *n; + minwrk = max(i__2,bdspac); + } else if (wntva && wntun) { /* Path 7t(N much larger than M, JOBU='N', JOBVT='A') */ - wrkbl = *m + lwork_dgelqf__; + wrkbl = *m + lwork_dgelqf__; /* Computing MAX */ - i__2 = wrkbl, i__3 = *m + lwork_dorglq_n__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *m + lwork_dorglq_n__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__; - wrkbl = max(i__2,i__3); - wrkbl = max(wrkbl,bdspac); - maxwrk = *m * *m + wrkbl; + i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__; + wrkbl = max(i__2,i__3); + wrkbl = max(wrkbl,bdspac); + maxwrk = *m * *m + wrkbl; /* Computing MAX */ - i__2 = *m * 3 + *n; - minwrk = max(i__2,bdspac); - } else if (wntva && wntuo) { + i__2 = *m * 3 + *n; + minwrk = max(i__2,bdspac); + } else if (wntva && wntuo) { /* Path 8t(N much larger than M, JOBU='O', JOBVT='A') */ - wrkbl = *m + lwork_dgelqf__; + wrkbl = *m + lwork_dgelqf__; /* Computing MAX */ - i__2 = wrkbl, i__3 = *m + lwork_dorglq_n__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *m + lwork_dorglq_n__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_q__; - wrkbl = max(i__2,i__3); - wrkbl = max(wrkbl,bdspac); - maxwrk = (*m << 1) * *m + wrkbl; + i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_q__; + wrkbl = max(i__2,i__3); + wrkbl = max(wrkbl,bdspac); + maxwrk = (*m << 1) * *m + wrkbl; /* Computing MAX */ - i__2 = *m * 3 + *n; - minwrk = max(i__2,bdspac); - } else if (wntva && wntuas) { + i__2 = *m * 3 + *n; + minwrk = max(i__2,bdspac); + } else if (wntva && wntuas) { /* Path 9t(N much larger than M, JOBU='S' or 'A', */ /* JOBVT='A') */ - wrkbl = *m + lwork_dgelqf__; + wrkbl = *m + lwork_dgelqf__; /* Computing MAX */ - i__2 = wrkbl, i__3 = *m + lwork_dorglq_n__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *m + lwork_dorglq_n__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__; - wrkbl = max(i__2,i__3); + i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__; + wrkbl = max(i__2,i__3); /* Computing MAX */ - i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_q__; - wrkbl = max(i__2,i__3); - wrkbl = max(wrkbl,bdspac); - maxwrk = *m * *m + wrkbl; + i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_q__; + wrkbl = max(i__2,i__3); + wrkbl = max(wrkbl,bdspac); + maxwrk = *m * *m + wrkbl; /* Computing MAX */ - i__2 = *m * 3 + *n; - minwrk = max(i__2,bdspac); - } - } else { + i__2 = *m * 3 + *n; + minwrk = max(i__2,bdspac); + } + } else { /* Path 10t(N greater than M, but not much larger) */ - dgebrd_(m, n, &a[a_offset], lda, &s[1], dum, dum, dum, dum, & - c_n1, &ierr); - lwork_dgebrd__ = (integer) dum[0]; - maxwrk = *m * 3 + lwork_dgebrd__; - if (wntvs || wntvo) { + dgebrd_(m, n, &a[a_offset], lda, &s[1], dum, dum, dum, dum, & + c_n1, &ierr); + lwork_dgebrd__ = (integer) dum[0]; + maxwrk = *m * 3 + lwork_dgebrd__; + if (wntvs || wntvo) { /* Compute space needed for DORGBR P */ - dorgbr_((char *)"P", m, n, m, &a[a_offset], n, dum, dum, &c_n1, & - ierr, (ftnlen)1); - lwork_dorgbr_p__ = (integer) dum[0]; + dorgbr_((char *)"P", m, n, m, &a[a_offset], n, dum, dum, &c_n1, & + ierr, (ftnlen)1); + lwork_dorgbr_p__ = (integer) dum[0]; /* Computing MAX */ - i__2 = maxwrk, i__3 = *m * 3 + lwork_dorgbr_p__; - maxwrk = max(i__2,i__3); - } - if (wntva) { - dorgbr_((char *)"P", n, n, m, &a[a_offset], n, dum, dum, &c_n1, & - ierr, (ftnlen)1); - lwork_dorgbr_p__ = (integer) dum[0]; + i__2 = maxwrk, i__3 = *m * 3 + lwork_dorgbr_p__; + maxwrk = max(i__2,i__3); + } + if (wntva) { + dorgbr_((char *)"P", n, n, m, &a[a_offset], n, dum, dum, &c_n1, & + ierr, (ftnlen)1); + lwork_dorgbr_p__ = (integer) dum[0]; /* Computing MAX */ - i__2 = maxwrk, i__3 = *m * 3 + lwork_dorgbr_p__; - maxwrk = max(i__2,i__3); - } - if (! wntun) { + i__2 = maxwrk, i__3 = *m * 3 + lwork_dorgbr_p__; + maxwrk = max(i__2,i__3); + } + if (! wntun) { /* Computing MAX */ - i__2 = maxwrk, i__3 = *m * 3 + lwork_dorgbr_q__; - maxwrk = max(i__2,i__3); - } - maxwrk = max(maxwrk,bdspac); + i__2 = maxwrk, i__3 = *m * 3 + lwork_dorgbr_q__; + maxwrk = max(i__2,i__3); + } + maxwrk = max(maxwrk,bdspac); /* Computing MAX */ - i__2 = *m * 3 + *n; - minwrk = max(i__2,bdspac); - } - } - maxwrk = max(maxwrk,minwrk); - work[1] = (doublereal) maxwrk; + i__2 = *m * 3 + *n; + minwrk = max(i__2,bdspac); + } + } + maxwrk = max(maxwrk,minwrk); + work[1] = (doublereal) maxwrk; - if (*lwork < minwrk && ! lquery) { - *info = -13; - } + if (*lwork < minwrk && ! lquery) { + *info = -13; + } } if (*info != 0) { - i__2 = -(*info); - xerbla_((char *)"DGESVD", &i__2, (ftnlen)6); - return 0; + i__2 = -(*info); + xerbla_((char *)"DGESVD", &i__2, (ftnlen)6); + return 0; } else if (lquery) { - return 0; + return 0; } /* Quick return if possible */ if (*m == 0 || *n == 0) { - return 0; + return 0; } /* Get machine constants */ @@ -936,13 +936,13 @@ f"> */ anrm = dlange_((char *)"M", m, n, &a[a_offset], lda, dum, (ftnlen)1); iscl = 0; if (anrm > 0. && anrm < smlnum) { - iscl = 1; - dlascl_((char *)"G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, & - ierr, (ftnlen)1); + iscl = 1; + dlascl_((char *)"G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, & + ierr, (ftnlen)1); } else if (anrm > bignum) { - iscl = 1; - dlascl_((char *)"G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, & - ierr, (ftnlen)1); + iscl = 1; + dlascl_((char *)"G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, & + ierr, (ftnlen)1); } if (*m >= *n) { @@ -951,751 +951,751 @@ f"> */ /* more rows than columns, first reduce using the QR */ /* decomposition (if sufficient workspace available) */ - if (*m >= mnthr) { + if (*m >= mnthr) { - if (wntun) { + if (wntun) { /* Path 1 (M much larger than N, JOBU='N') */ /* No left singular vectors to be computed */ - itau = 1; - iwork = itau + *n; + itau = 1; + iwork = itau + *n; /* Compute A=Q*R */ /* (Workspace: need 2*N, prefer N + N*NB) */ - i__2 = *lwork - iwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], & - i__2, &ierr); + i__2 = *lwork - iwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], & + i__2, &ierr); /* Zero out below R */ - if (*n > 1) { - i__2 = *n - 1; - i__3 = *n - 1; - dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &a[a_dim1 + 2], - lda, (ftnlen)1); - } - ie = 1; - itauq = ie + *n; - itaup = itauq + *n; - iwork = itaup + *n; + if (*n > 1) { + i__2 = *n - 1; + i__3 = *n - 1; + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &a[a_dim1 + 2], + lda, (ftnlen)1); + } + ie = 1; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; /* Bidiagonalize R in A */ /* (Workspace: need 4*N, prefer 3*N + 2*N*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &work[ - itauq], &work[itaup], &work[iwork], &i__2, &ierr); - ncvt = 0; - if (wntvo || wntvas) { + i__2 = *lwork - iwork + 1; + dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &work[ + itauq], &work[itaup], &work[iwork], &i__2, &ierr); + ncvt = 0; + if (wntvo || wntvas) { /* If right singular vectors desired, generate P'. */ /* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, &work[itaup], & - work[iwork], &i__2, &ierr, (ftnlen)1); - ncvt = *n; - } - iwork = ie + *n; + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, &work[itaup], & + work[iwork], &i__2, &ierr, (ftnlen)1); + ncvt = *n; + } + iwork = ie + *n; /* Perform bidiagonal QR iteration, computing right */ /* singular vectors of A in A if desired */ /* (Workspace: need BDSPAC) */ - dbdsqr_((char *)"U", n, &ncvt, &c__0, &c__0, &s[1], &work[ie], &a[ - a_offset], lda, dum, &c__1, dum, &c__1, &work[iwork], - info, (ftnlen)1); + dbdsqr_((char *)"U", n, &ncvt, &c__0, &c__0, &s[1], &work[ie], &a[ + a_offset], lda, dum, &c__1, dum, &c__1, &work[iwork], + info, (ftnlen)1); /* If right singular vectors desired in VT, copy them there */ - if (wntvas) { - dlacpy_((char *)"F", n, n, &a[a_offset], lda, &vt[vt_offset], - ldvt, (ftnlen)1); - } + if (wntvas) { + dlacpy_((char *)"F", n, n, &a[a_offset], lda, &vt[vt_offset], + ldvt, (ftnlen)1); + } - } else if (wntuo && wntvn) { + } else if (wntuo && wntvn) { /* Path 2 (M much larger than N, JOBU='O', JOBVT='N') */ /* N left singular vectors to be overwritten on A and */ /* no right singular vectors to be computed */ /* Computing MAX */ - i__2 = *n << 2; - if (*lwork >= *n * *n + max(i__2,bdspac)) { + i__2 = *n << 2; + if (*lwork >= *n * *n + max(i__2,bdspac)) { /* Sufficient workspace for a fast algorithm */ - ir = 1; + ir = 1; /* Computing MAX */ - i__2 = wrkbl, i__3 = *lda * *n + *n; - if (*lwork >= max(i__2,i__3) + *lda * *n) { + i__2 = wrkbl, i__3 = *lda * *n + *n; + if (*lwork >= max(i__2,i__3) + *lda * *n) { /* WORK(IU) is LDA by N, WORK(IR) is LDA by N */ - ldwrku = *lda; - ldwrkr = *lda; - } else /* if(complicated condition) */ { + ldwrku = *lda; + ldwrkr = *lda; + } else /* if(complicated condition) */ { /* Computing MAX */ - i__2 = wrkbl, i__3 = *lda * *n + *n; - if (*lwork >= max(i__2,i__3) + *n * *n) { + i__2 = wrkbl, i__3 = *lda * *n + *n; + if (*lwork >= max(i__2,i__3) + *n * *n) { /* WORK(IU) is LDA by N, WORK(IR) is N by N */ - ldwrku = *lda; - ldwrkr = *n; - } else { + ldwrku = *lda; + ldwrkr = *n; + } else { /* WORK(IU) is LDWRKU by N, WORK(IR) is N by N */ - ldwrku = (*lwork - *n * *n - *n) / *n; - ldwrkr = *n; - } - } - itau = ir + ldwrkr * *n; - iwork = itau + *n; + ldwrku = (*lwork - *n * *n - *n) / *n; + ldwrkr = *n; + } + } + itau = ir + ldwrkr * *n; + iwork = itau + *n; /* Compute A=Q*R */ /* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */ - i__2 = *lwork - iwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork] - , &i__2, &ierr); + i__2 = *lwork - iwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork] + , &i__2, &ierr); /* Copy R to WORK(IR) and zero out below it */ - dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr, - (ftnlen)1); - i__2 = *n - 1; - i__3 = *n - 1; - dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[ir + 1], - &ldwrkr, (ftnlen)1); + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr, + (ftnlen)1); + i__2 = *n - 1; + i__3 = *n - 1; + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[ir + 1], + &ldwrkr, (ftnlen)1); /* Generate Q in A */ /* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */ - i__2 = *lwork - iwork + 1; - dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - ie = itau; - itauq = ie + *n; - itaup = itauq + *n; - iwork = itaup + *n; + i__2 = *lwork - iwork + 1; + dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; /* Bidiagonalize R in WORK(IR) */ /* (Workspace: need N*N + 4*N, prefer N*N + 3*N + 2*N*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], &work[ - itauq], &work[itaup], &work[iwork], &i__2, &ierr); + i__2 = *lwork - iwork + 1; + dgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], &work[ + itauq], &work[itaup], &work[iwork], &i__2, &ierr); /* Generate left vectors bidiagonalizing R */ /* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", n, n, n, &work[ir], &ldwrkr, &work[itauq], & - work[iwork], &i__2, &ierr, (ftnlen)1); - iwork = ie + *n; + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", n, n, n, &work[ir], &ldwrkr, &work[itauq], & + work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *n; /* Perform bidiagonal QR iteration, computing left */ /* singular vectors of R in WORK(IR) */ /* (Workspace: need N*N + BDSPAC) */ - dbdsqr_((char *)"U", n, &c__0, n, &c__0, &s[1], &work[ie], dum, & - c__1, &work[ir], &ldwrkr, dum, &c__1, &work[iwork] - , info, (ftnlen)1); - iu = ie + *n; + dbdsqr_((char *)"U", n, &c__0, n, &c__0, &s[1], &work[ie], dum, & + c__1, &work[ir], &ldwrkr, dum, &c__1, &work[iwork] + , info, (ftnlen)1); + iu = ie + *n; /* Multiply Q in A by left singular vectors of R in */ /* WORK(IR), storing result in WORK(IU) and copying to A */ /* (Workspace: need N*N + 2*N, prefer N*N + M*N + N) */ - i__2 = *m; - i__3 = ldwrku; - for (i__ = 1; i__3 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += - i__3) { + i__2 = *m; + i__3 = ldwrku; + for (i__ = 1; i__3 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += + i__3) { /* Computing MIN */ - i__4 = *m - i__ + 1; - chunk = min(i__4,ldwrku); - dgemm_((char *)"N", (char *)"N", &chunk, n, n, &c_b79, &a[i__ + - a_dim1], lda, &work[ir], &ldwrkr, &c_b57, & - work[iu], &ldwrku, (ftnlen)1, (ftnlen)1); - dlacpy_((char *)"F", &chunk, n, &work[iu], &ldwrku, &a[i__ + - a_dim1], lda, (ftnlen)1); + i__4 = *m - i__ + 1; + chunk = min(i__4,ldwrku); + dgemm_((char *)"N", (char *)"N", &chunk, n, n, &c_b79, &a[i__ + + a_dim1], lda, &work[ir], &ldwrkr, &c_b57, & + work[iu], &ldwrku, (ftnlen)1, (ftnlen)1); + dlacpy_((char *)"F", &chunk, n, &work[iu], &ldwrku, &a[i__ + + a_dim1], lda, (ftnlen)1); /* L10: */ - } + } - } else { + } else { /* Insufficient workspace for a fast algorithm */ - ie = 1; - itauq = ie + *n; - itaup = itauq + *n; - iwork = itaup + *n; + ie = 1; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; /* Bidiagonalize A */ /* (Workspace: need 3*N + M, prefer 3*N + (M + N)*NB) */ - i__3 = *lwork - iwork + 1; - dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[ - itauq], &work[itaup], &work[iwork], &i__3, &ierr); + i__3 = *lwork - iwork + 1; + dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[ + itauq], &work[itaup], &work[iwork], &i__3, &ierr); /* Generate left vectors bidiagonalizing A */ /* (Workspace: need 4*N, prefer 3*N + N*NB) */ - i__3 = *lwork - iwork + 1; - dorgbr_((char *)"Q", m, n, n, &a[a_offset], lda, &work[itauq], & - work[iwork], &i__3, &ierr, (ftnlen)1); - iwork = ie + *n; + i__3 = *lwork - iwork + 1; + dorgbr_((char *)"Q", m, n, n, &a[a_offset], lda, &work[itauq], & + work[iwork], &i__3, &ierr, (ftnlen)1); + iwork = ie + *n; /* Perform bidiagonal QR iteration, computing left */ /* singular vectors of A in A */ /* (Workspace: need BDSPAC) */ - dbdsqr_((char *)"U", n, &c__0, m, &c__0, &s[1], &work[ie], dum, & - c__1, &a[a_offset], lda, dum, &c__1, &work[iwork], - info, (ftnlen)1); + dbdsqr_((char *)"U", n, &c__0, m, &c__0, &s[1], &work[ie], dum, & + c__1, &a[a_offset], lda, dum, &c__1, &work[iwork], + info, (ftnlen)1); - } + } - } else if (wntuo && wntvas) { + } else if (wntuo && wntvas) { /* Path 3 (M much larger than N, JOBU='O', JOBVT='S' or 'A') */ /* N left singular vectors to be overwritten on A and */ /* N right singular vectors to be computed in VT */ /* Computing MAX */ - i__3 = *n << 2; - if (*lwork >= *n * *n + max(i__3,bdspac)) { + i__3 = *n << 2; + if (*lwork >= *n * *n + max(i__3,bdspac)) { /* Sufficient workspace for a fast algorithm */ - ir = 1; + ir = 1; /* Computing MAX */ - i__3 = wrkbl, i__2 = *lda * *n + *n; - if (*lwork >= max(i__3,i__2) + *lda * *n) { + i__3 = wrkbl, i__2 = *lda * *n + *n; + if (*lwork >= max(i__3,i__2) + *lda * *n) { /* WORK(IU) is LDA by N and WORK(IR) is LDA by N */ - ldwrku = *lda; - ldwrkr = *lda; - } else /* if(complicated condition) */ { + ldwrku = *lda; + ldwrkr = *lda; + } else /* if(complicated condition) */ { /* Computing MAX */ - i__3 = wrkbl, i__2 = *lda * *n + *n; - if (*lwork >= max(i__3,i__2) + *n * *n) { + i__3 = wrkbl, i__2 = *lda * *n + *n; + if (*lwork >= max(i__3,i__2) + *n * *n) { /* WORK(IU) is LDA by N and WORK(IR) is N by N */ - ldwrku = *lda; - ldwrkr = *n; - } else { + ldwrku = *lda; + ldwrkr = *n; + } else { /* WORK(IU) is LDWRKU by N and WORK(IR) is N by N */ - ldwrku = (*lwork - *n * *n - *n) / *n; - ldwrkr = *n; - } - } - itau = ir + ldwrkr * *n; - iwork = itau + *n; + ldwrku = (*lwork - *n * *n - *n) / *n; + ldwrkr = *n; + } + } + itau = ir + ldwrkr * *n; + iwork = itau + *n; /* Compute A=Q*R */ /* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */ - i__3 = *lwork - iwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork] - , &i__3, &ierr); + i__3 = *lwork - iwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork] + , &i__3, &ierr); /* Copy R to VT, zeroing out below it */ - dlacpy_((char *)"U", n, n, &a[a_offset], lda, &vt[vt_offset], - ldvt, (ftnlen)1); - if (*n > 1) { - i__3 = *n - 1; - i__2 = *n - 1; - dlaset_((char *)"L", &i__3, &i__2, &c_b57, &c_b57, &vt[ - vt_dim1 + 2], ldvt, (ftnlen)1); - } + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &vt[vt_offset], + ldvt, (ftnlen)1); + if (*n > 1) { + i__3 = *n - 1; + i__2 = *n - 1; + dlaset_((char *)"L", &i__3, &i__2, &c_b57, &c_b57, &vt[ + vt_dim1 + 2], ldvt, (ftnlen)1); + } /* Generate Q in A */ /* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */ - i__3 = *lwork - iwork + 1; - dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__3, &ierr); - ie = itau; - itauq = ie + *n; - itaup = itauq + *n; - iwork = itaup + *n; + i__3 = *lwork - iwork + 1; + dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__3, &ierr); + ie = itau; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; /* Bidiagonalize R in VT, copying result to WORK(IR) */ /* (Workspace: need N*N + 4*N, prefer N*N + 3*N + 2*N*NB) */ - i__3 = *lwork - iwork + 1; - dgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], &i__3, & - ierr); - dlacpy_((char *)"L", n, n, &vt[vt_offset], ldvt, &work[ir], & - ldwrkr, (ftnlen)1); + i__3 = *lwork - iwork + 1; + dgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], &i__3, & + ierr); + dlacpy_((char *)"L", n, n, &vt[vt_offset], ldvt, &work[ir], & + ldwrkr, (ftnlen)1); /* Generate left vectors bidiagonalizing R in WORK(IR) */ /* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB) */ - i__3 = *lwork - iwork + 1; - dorgbr_((char *)"Q", n, n, n, &work[ir], &ldwrkr, &work[itauq], & - work[iwork], &i__3, &ierr, (ftnlen)1); + i__3 = *lwork - iwork + 1; + dorgbr_((char *)"Q", n, n, n, &work[ir], &ldwrkr, &work[itauq], & + work[iwork], &i__3, &ierr, (ftnlen)1); /* Generate right vectors bidiagonalizing R in VT */ /* (Workspace: need N*N + 4*N-1, prefer N*N + 3*N + (N-1)*NB) */ - i__3 = *lwork - iwork + 1; - dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], - &work[iwork], &i__3, &ierr, (ftnlen)1); - iwork = ie + *n; + i__3 = *lwork - iwork + 1; + dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], + &work[iwork], &i__3, &ierr, (ftnlen)1); + iwork = ie + *n; /* Perform bidiagonal QR iteration, computing left */ /* singular vectors of R in WORK(IR) and computing right */ /* singular vectors of R in VT */ /* (Workspace: need N*N + BDSPAC) */ - dbdsqr_((char *)"U", n, n, n, &c__0, &s[1], &work[ie], &vt[ - vt_offset], ldvt, &work[ir], &ldwrkr, dum, &c__1, - &work[iwork], info, (ftnlen)1); - iu = ie + *n; + dbdsqr_((char *)"U", n, n, n, &c__0, &s[1], &work[ie], &vt[ + vt_offset], ldvt, &work[ir], &ldwrkr, dum, &c__1, + &work[iwork], info, (ftnlen)1); + iu = ie + *n; /* Multiply Q in A by left singular vectors of R in */ /* WORK(IR), storing result in WORK(IU) and copying to A */ /* (Workspace: need N*N + 2*N, prefer N*N + M*N + N) */ - i__3 = *m; - i__2 = ldwrku; - for (i__ = 1; i__2 < 0 ? i__ >= i__3 : i__ <= i__3; i__ += - i__2) { + i__3 = *m; + i__2 = ldwrku; + for (i__ = 1; i__2 < 0 ? i__ >= i__3 : i__ <= i__3; i__ += + i__2) { /* Computing MIN */ - i__4 = *m - i__ + 1; - chunk = min(i__4,ldwrku); - dgemm_((char *)"N", (char *)"N", &chunk, n, n, &c_b79, &a[i__ + - a_dim1], lda, &work[ir], &ldwrkr, &c_b57, & - work[iu], &ldwrku, (ftnlen)1, (ftnlen)1); - dlacpy_((char *)"F", &chunk, n, &work[iu], &ldwrku, &a[i__ + - a_dim1], lda, (ftnlen)1); + i__4 = *m - i__ + 1; + chunk = min(i__4,ldwrku); + dgemm_((char *)"N", (char *)"N", &chunk, n, n, &c_b79, &a[i__ + + a_dim1], lda, &work[ir], &ldwrkr, &c_b57, & + work[iu], &ldwrku, (ftnlen)1, (ftnlen)1); + dlacpy_((char *)"F", &chunk, n, &work[iu], &ldwrku, &a[i__ + + a_dim1], lda, (ftnlen)1); /* L20: */ - } + } - } else { + } else { /* Insufficient workspace for a fast algorithm */ - itau = 1; - iwork = itau + *n; + itau = 1; + iwork = itau + *n; /* Compute A=Q*R */ /* (Workspace: need 2*N, prefer N + N*NB) */ - i__2 = *lwork - iwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork] - , &i__2, &ierr); + i__2 = *lwork - iwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork] + , &i__2, &ierr); /* Copy R to VT, zeroing out below it */ - dlacpy_((char *)"U", n, n, &a[a_offset], lda, &vt[vt_offset], - ldvt, (ftnlen)1); - if (*n > 1) { - i__2 = *n - 1; - i__3 = *n - 1; - dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &vt[ - vt_dim1 + 2], ldvt, (ftnlen)1); - } + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &vt[vt_offset], + ldvt, (ftnlen)1); + if (*n > 1) { + i__2 = *n - 1; + i__3 = *n - 1; + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &vt[ + vt_dim1 + 2], ldvt, (ftnlen)1); + } /* Generate Q in A */ /* (Workspace: need 2*N, prefer N + N*NB) */ - i__2 = *lwork - iwork + 1; - dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - ie = itau; - itauq = ie + *n; - itaup = itauq + *n; - iwork = itaup + *n; + i__2 = *lwork - iwork + 1; + dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; /* Bidiagonalize R in VT */ /* (Workspace: need 4*N, prefer 3*N + 2*N*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], &i__2, & - ierr); + i__2 = *lwork - iwork + 1; + dgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], &i__2, & + ierr); /* Multiply Q in A by left vectors bidiagonalizing R */ /* (Workspace: need 3*N + M, prefer 3*N + M*NB) */ - i__2 = *lwork - iwork + 1; - dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &vt[vt_offset], ldvt, & - work[itauq], &a[a_offset], lda, &work[iwork], & - i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &vt[vt_offset], ldvt, & + work[itauq], &a[a_offset], lda, &work[iwork], & + i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen)1); /* Generate right vectors bidiagonalizing R in VT */ /* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], - &work[iwork], &i__2, &ierr, (ftnlen)1); - iwork = ie + *n; + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], + &work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *n; /* Perform bidiagonal QR iteration, computing left */ /* singular vectors of A in A and computing right */ /* singular vectors of A in VT */ /* (Workspace: need BDSPAC) */ - dbdsqr_((char *)"U", n, n, m, &c__0, &s[1], &work[ie], &vt[ - vt_offset], ldvt, &a[a_offset], lda, dum, &c__1, & - work[iwork], info, (ftnlen)1); + dbdsqr_((char *)"U", n, n, m, &c__0, &s[1], &work[ie], &vt[ + vt_offset], ldvt, &a[a_offset], lda, dum, &c__1, & + work[iwork], info, (ftnlen)1); - } + } - } else if (wntus) { + } else if (wntus) { - if (wntvn) { + if (wntvn) { /* Path 4 (M much larger than N, JOBU='S', JOBVT='N') */ /* N left singular vectors to be computed in U and */ /* no right singular vectors to be computed */ /* Computing MAX */ - i__2 = *n << 2; - if (*lwork >= *n * *n + max(i__2,bdspac)) { + i__2 = *n << 2; + if (*lwork >= *n * *n + max(i__2,bdspac)) { /* Sufficient workspace for a fast algorithm */ - ir = 1; - if (*lwork >= wrkbl + *lda * *n) { + ir = 1; + if (*lwork >= wrkbl + *lda * *n) { /* WORK(IR) is LDA by N */ - ldwrkr = *lda; - } else { + ldwrkr = *lda; + } else { /* WORK(IR) is N by N */ - ldwrkr = *n; - } - itau = ir + ldwrkr * *n; - iwork = itau + *n; + ldwrkr = *n; + } + itau = ir + ldwrkr * *n; + iwork = itau + *n; /* Compute A=Q*R */ /* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */ - i__2 = *lwork - iwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); + i__2 = *lwork - iwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); /* Copy R to WORK(IR), zeroing out below it */ - dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[ir], & - ldwrkr, (ftnlen)1); - i__2 = *n - 1; - i__3 = *n - 1; - dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[ir + - 1], &ldwrkr, (ftnlen)1); + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[ir], & + ldwrkr, (ftnlen)1); + i__2 = *n - 1; + i__3 = *n - 1; + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[ir + + 1], &ldwrkr, (ftnlen)1); /* Generate Q in A */ /* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */ - i__2 = *lwork - iwork + 1; - dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], & - work[iwork], &i__2, &ierr); - ie = itau; - itauq = ie + *n; - itaup = itauq + *n; - iwork = itaup + *n; + i__2 = *lwork - iwork + 1; + dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], & + work[iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; /* Bidiagonalize R in WORK(IR) */ /* (Workspace: need N*N + 4*N, prefer N*N + 3*N + 2*N*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); + i__2 = *lwork - iwork + 1; + dgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); /* Generate left vectors bidiagonalizing R in WORK(IR) */ /* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", n, n, n, &work[ir], &ldwrkr, &work[itauq] - , &work[iwork], &i__2, &ierr, (ftnlen)1); - iwork = ie + *n; + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", n, n, n, &work[ir], &ldwrkr, &work[itauq] + , &work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *n; /* Perform bidiagonal QR iteration, computing left */ /* singular vectors of R in WORK(IR) */ /* (Workspace: need N*N + BDSPAC) */ - dbdsqr_((char *)"U", n, &c__0, n, &c__0, &s[1], &work[ie], - dum, &c__1, &work[ir], &ldwrkr, dum, &c__1, & - work[iwork], info, (ftnlen)1); + dbdsqr_((char *)"U", n, &c__0, n, &c__0, &s[1], &work[ie], + dum, &c__1, &work[ir], &ldwrkr, dum, &c__1, & + work[iwork], info, (ftnlen)1); /* Multiply Q in A by left singular vectors of R in */ /* WORK(IR), storing result in U */ /* (Workspace: need N*N) */ - dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &a[a_offset], lda, & - work[ir], &ldwrkr, &c_b57, &u[u_offset], ldu, - (ftnlen)1, (ftnlen)1); + dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &a[a_offset], lda, & + work[ir], &ldwrkr, &c_b57, &u[u_offset], ldu, + (ftnlen)1, (ftnlen)1); - } else { + } else { /* Insufficient workspace for a fast algorithm */ - itau = 1; - iwork = itau + *n; + itau = 1; + iwork = itau + *n; /* Compute A=Q*R, copying result to U */ /* (Workspace: need 2*N, prefer N + N*NB) */ - i__2 = *lwork - iwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], - ldu, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], + ldu, (ftnlen)1); /* Generate Q in U */ /* (Workspace: need 2*N, prefer N + N*NB) */ - i__2 = *lwork - iwork + 1; - dorgqr_(m, n, n, &u[u_offset], ldu, &work[itau], & - work[iwork], &i__2, &ierr); - ie = itau; - itauq = ie + *n; - itaup = itauq + *n; - iwork = itaup + *n; + i__2 = *lwork - iwork + 1; + dorgqr_(m, n, n, &u[u_offset], ldu, &work[itau], & + work[iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; /* Zero out below R in A */ - if (*n > 1) { - i__2 = *n - 1; - i__3 = *n - 1; - dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &a[ - a_dim1 + 2], lda, (ftnlen)1); - } + if (*n > 1) { + i__2 = *n - 1; + i__3 = *n - 1; + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &a[ + a_dim1 + 2], lda, (ftnlen)1); + } /* Bidiagonalize R in A */ /* (Workspace: need 4*N, prefer 3*N + 2*N*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); + i__2 = *lwork - iwork + 1; + dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); /* Multiply Q in U by left vectors bidiagonalizing R */ /* (Workspace: need 3*N + M, prefer 3*N + M*NB) */ - i__2 = *lwork - iwork + 1; - dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &a[a_offset], lda, & - work[itauq], &u[u_offset], ldu, &work[iwork], - &i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen)1) - ; - iwork = ie + *n; + i__2 = *lwork - iwork + 1; + dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &a[a_offset], lda, & + work[itauq], &u[u_offset], ldu, &work[iwork], + &i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen)1) + ; + iwork = ie + *n; /* Perform bidiagonal QR iteration, computing left */ /* singular vectors of A in U */ /* (Workspace: need BDSPAC) */ - dbdsqr_((char *)"U", n, &c__0, m, &c__0, &s[1], &work[ie], - dum, &c__1, &u[u_offset], ldu, dum, &c__1, & - work[iwork], info, (ftnlen)1); + dbdsqr_((char *)"U", n, &c__0, m, &c__0, &s[1], &work[ie], + dum, &c__1, &u[u_offset], ldu, dum, &c__1, & + work[iwork], info, (ftnlen)1); - } + } - } else if (wntvo) { + } else if (wntvo) { /* Path 5 (M much larger than N, JOBU='S', JOBVT='O') */ /* N left singular vectors to be computed in U and */ /* N right singular vectors to be overwritten on A */ /* Computing MAX */ - i__2 = *n << 2; - if (*lwork >= (*n << 1) * *n + max(i__2,bdspac)) { + i__2 = *n << 2; + if (*lwork >= (*n << 1) * *n + max(i__2,bdspac)) { /* Sufficient workspace for a fast algorithm */ - iu = 1; - if (*lwork >= wrkbl + (*lda << 1) * *n) { + iu = 1; + if (*lwork >= wrkbl + (*lda << 1) * *n) { /* WORK(IU) is LDA by N and WORK(IR) is LDA by N */ - ldwrku = *lda; - ir = iu + ldwrku * *n; - ldwrkr = *lda; - } else if (*lwork >= wrkbl + (*lda + *n) * *n) { + ldwrku = *lda; + ir = iu + ldwrku * *n; + ldwrkr = *lda; + } else if (*lwork >= wrkbl + (*lda + *n) * *n) { /* WORK(IU) is LDA by N and WORK(IR) is N by N */ - ldwrku = *lda; - ir = iu + ldwrku * *n; - ldwrkr = *n; - } else { + ldwrku = *lda; + ir = iu + ldwrku * *n; + ldwrkr = *n; + } else { /* WORK(IU) is N by N and WORK(IR) is N by N */ - ldwrku = *n; - ir = iu + ldwrku * *n; - ldwrkr = *n; - } - itau = ir + ldwrkr * *n; - iwork = itau + *n; + ldwrku = *n; + ir = iu + ldwrku * *n; + ldwrkr = *n; + } + itau = ir + ldwrkr * *n; + iwork = itau + *n; /* Compute A=Q*R */ /* (Workspace: need 2*N*N + 2*N, prefer 2*N*N + N + N*NB) */ - i__2 = *lwork - iwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); + i__2 = *lwork - iwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); /* Copy R to WORK(IU), zeroing out below it */ - dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[iu], & - ldwrku, (ftnlen)1); - i__2 = *n - 1; - i__3 = *n - 1; - dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[iu + - 1], &ldwrku, (ftnlen)1); + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[iu], & + ldwrku, (ftnlen)1); + i__2 = *n - 1; + i__3 = *n - 1; + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[iu + + 1], &ldwrku, (ftnlen)1); /* Generate Q in A */ /* (Workspace: need 2*N*N + 2*N, prefer 2*N*N + N + N*NB) */ - i__2 = *lwork - iwork + 1; - dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], & - work[iwork], &i__2, &ierr); - ie = itau; - itauq = ie + *n; - itaup = itauq + *n; - iwork = itaup + *n; + i__2 = *lwork - iwork + 1; + dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], & + work[iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; /* Bidiagonalize R in WORK(IU), copying result to */ /* WORK(IR) */ /* (Workspace: need 2*N*N + 4*N, */ /* prefer 2*N*N+3*N+2*N*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(n, n, &work[iu], &ldwrku, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); - dlacpy_((char *)"U", n, n, &work[iu], &ldwrku, &work[ir], & - ldwrkr, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dgebrd_(n, n, &work[iu], &ldwrku, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); + dlacpy_((char *)"U", n, n, &work[iu], &ldwrku, &work[ir], & + ldwrkr, (ftnlen)1); /* Generate left bidiagonalizing vectors in WORK(IU) */ /* (Workspace: need 2*N*N + 4*N, prefer 2*N*N + 3*N + N*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", n, n, n, &work[iu], &ldwrku, &work[itauq] - , &work[iwork], &i__2, &ierr, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", n, n, n, &work[iu], &ldwrku, &work[itauq] + , &work[iwork], &i__2, &ierr, (ftnlen)1); /* Generate right bidiagonalizing vectors in WORK(IR) */ /* (Workspace: need 2*N*N + 4*N-1, */ /* prefer 2*N*N+3*N+(N-1)*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", n, n, n, &work[ir], &ldwrkr, &work[itaup] - , &work[iwork], &i__2, &ierr, (ftnlen)1); - iwork = ie + *n; + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", n, n, n, &work[ir], &ldwrkr, &work[itaup] + , &work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *n; /* Perform bidiagonal QR iteration, computing left */ /* singular vectors of R in WORK(IU) and computing */ /* right singular vectors of R in WORK(IR) */ /* (Workspace: need 2*N*N + BDSPAC) */ - dbdsqr_((char *)"U", n, n, n, &c__0, &s[1], &work[ie], &work[ - ir], &ldwrkr, &work[iu], &ldwrku, dum, &c__1, - &work[iwork], info, (ftnlen)1); + dbdsqr_((char *)"U", n, n, n, &c__0, &s[1], &work[ie], &work[ + ir], &ldwrkr, &work[iu], &ldwrku, dum, &c__1, + &work[iwork], info, (ftnlen)1); /* Multiply Q in A by left singular vectors of R in */ /* WORK(IU), storing result in U */ /* (Workspace: need N*N) */ - dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &a[a_offset], lda, & - work[iu], &ldwrku, &c_b57, &u[u_offset], ldu, - (ftnlen)1, (ftnlen)1); + dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &a[a_offset], lda, & + work[iu], &ldwrku, &c_b57, &u[u_offset], ldu, + (ftnlen)1, (ftnlen)1); /* Copy right singular vectors of R to A */ /* (Workspace: need N*N) */ - dlacpy_((char *)"F", n, n, &work[ir], &ldwrkr, &a[a_offset], - lda, (ftnlen)1); + dlacpy_((char *)"F", n, n, &work[ir], &ldwrkr, &a[a_offset], + lda, (ftnlen)1); - } else { + } else { /* Insufficient workspace for a fast algorithm */ - itau = 1; - iwork = itau + *n; + itau = 1; + iwork = itau + *n; /* Compute A=Q*R, copying result to U */ /* (Workspace: need 2*N, prefer N + N*NB) */ - i__2 = *lwork - iwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], - ldu, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], + ldu, (ftnlen)1); /* Generate Q in U */ /* (Workspace: need 2*N, prefer N + N*NB) */ - i__2 = *lwork - iwork + 1; - dorgqr_(m, n, n, &u[u_offset], ldu, &work[itau], & - work[iwork], &i__2, &ierr); - ie = itau; - itauq = ie + *n; - itaup = itauq + *n; - iwork = itaup + *n; + i__2 = *lwork - iwork + 1; + dorgqr_(m, n, n, &u[u_offset], ldu, &work[itau], & + work[iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; /* Zero out below R in A */ - if (*n > 1) { - i__2 = *n - 1; - i__3 = *n - 1; - dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &a[ - a_dim1 + 2], lda, (ftnlen)1); - } + if (*n > 1) { + i__2 = *n - 1; + i__3 = *n - 1; + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &a[ + a_dim1 + 2], lda, (ftnlen)1); + } /* Bidiagonalize R in A */ /* (Workspace: need 4*N, prefer 3*N + 2*N*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); + i__2 = *lwork - iwork + 1; + dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); /* Multiply Q in U by left vectors bidiagonalizing R */ /* (Workspace: need 3*N + M, prefer 3*N + M*NB) */ - i__2 = *lwork - iwork + 1; - dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &a[a_offset], lda, & - work[itauq], &u[u_offset], ldu, &work[iwork], - &i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen)1) - ; + i__2 = *lwork - iwork + 1; + dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &a[a_offset], lda, & + work[itauq], &u[u_offset], ldu, &work[iwork], + &i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen)1) + ; /* Generate right vectors bidiagonalizing R in A */ /* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, &work[itaup], - &work[iwork], &i__2, &ierr, (ftnlen)1); - iwork = ie + *n; + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, &work[itaup], + &work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *n; /* Perform bidiagonal QR iteration, computing left */ /* singular vectors of A in U and computing right */ /* singular vectors of A in A */ /* (Workspace: need BDSPAC) */ - dbdsqr_((char *)"U", n, n, m, &c__0, &s[1], &work[ie], &a[ - a_offset], lda, &u[u_offset], ldu, dum, &c__1, - &work[iwork], info, (ftnlen)1); + dbdsqr_((char *)"U", n, n, m, &c__0, &s[1], &work[ie], &a[ + a_offset], lda, &u[u_offset], ldu, dum, &c__1, + &work[iwork], info, (ftnlen)1); - } + } - } else if (wntvas) { + } else if (wntvas) { /* Path 6 (M much larger than N, JOBU='S', JOBVT='S' */ /* or 'A') */ @@ -1703,531 +1703,531 @@ f"> */ /* N right singular vectors to be computed in VT */ /* Computing MAX */ - i__2 = *n << 2; - if (*lwork >= *n * *n + max(i__2,bdspac)) { + i__2 = *n << 2; + if (*lwork >= *n * *n + max(i__2,bdspac)) { /* Sufficient workspace for a fast algorithm */ - iu = 1; - if (*lwork >= wrkbl + *lda * *n) { + iu = 1; + if (*lwork >= wrkbl + *lda * *n) { /* WORK(IU) is LDA by N */ - ldwrku = *lda; - } else { + ldwrku = *lda; + } else { /* WORK(IU) is N by N */ - ldwrku = *n; - } - itau = iu + ldwrku * *n; - iwork = itau + *n; + ldwrku = *n; + } + itau = iu + ldwrku * *n; + iwork = itau + *n; /* Compute A=Q*R */ /* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */ - i__2 = *lwork - iwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); + i__2 = *lwork - iwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); /* Copy R to WORK(IU), zeroing out below it */ - dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[iu], & - ldwrku, (ftnlen)1); - i__2 = *n - 1; - i__3 = *n - 1; - dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[iu + - 1], &ldwrku, (ftnlen)1); + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[iu], & + ldwrku, (ftnlen)1); + i__2 = *n - 1; + i__3 = *n - 1; + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[iu + + 1], &ldwrku, (ftnlen)1); /* Generate Q in A */ /* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */ - i__2 = *lwork - iwork + 1; - dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], & - work[iwork], &i__2, &ierr); - ie = itau; - itauq = ie + *n; - itaup = itauq + *n; - iwork = itaup + *n; + i__2 = *lwork - iwork + 1; + dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], & + work[iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; /* Bidiagonalize R in WORK(IU), copying result to VT */ /* (Workspace: need N*N + 4*N, prefer N*N + 3*N + 2*N*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(n, n, &work[iu], &ldwrku, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); - dlacpy_((char *)"U", n, n, &work[iu], &ldwrku, &vt[vt_offset], - ldvt, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dgebrd_(n, n, &work[iu], &ldwrku, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); + dlacpy_((char *)"U", n, n, &work[iu], &ldwrku, &vt[vt_offset], + ldvt, (ftnlen)1); /* Generate left bidiagonalizing vectors in WORK(IU) */ /* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", n, n, n, &work[iu], &ldwrku, &work[itauq] - , &work[iwork], &i__2, &ierr, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", n, n, n, &work[iu], &ldwrku, &work[itauq] + , &work[iwork], &i__2, &ierr, (ftnlen)1); /* Generate right bidiagonalizing vectors in VT */ /* (Workspace: need N*N + 4*N-1, */ /* prefer N*N+3*N+(N-1)*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[ - itaup], &work[iwork], &i__2, &ierr, (ftnlen)1) - ; - iwork = ie + *n; + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[ + itaup], &work[iwork], &i__2, &ierr, (ftnlen)1) + ; + iwork = ie + *n; /* Perform bidiagonal QR iteration, computing left */ /* singular vectors of R in WORK(IU) and computing */ /* right singular vectors of R in VT */ /* (Workspace: need N*N + BDSPAC) */ - dbdsqr_((char *)"U", n, n, n, &c__0, &s[1], &work[ie], &vt[ - vt_offset], ldvt, &work[iu], &ldwrku, dum, & - c__1, &work[iwork], info, (ftnlen)1); + dbdsqr_((char *)"U", n, n, n, &c__0, &s[1], &work[ie], &vt[ + vt_offset], ldvt, &work[iu], &ldwrku, dum, & + c__1, &work[iwork], info, (ftnlen)1); /* Multiply Q in A by left singular vectors of R in */ /* WORK(IU), storing result in U */ /* (Workspace: need N*N) */ - dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &a[a_offset], lda, & - work[iu], &ldwrku, &c_b57, &u[u_offset], ldu, - (ftnlen)1, (ftnlen)1); + dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &a[a_offset], lda, & + work[iu], &ldwrku, &c_b57, &u[u_offset], ldu, + (ftnlen)1, (ftnlen)1); - } else { + } else { /* Insufficient workspace for a fast algorithm */ - itau = 1; - iwork = itau + *n; + itau = 1; + iwork = itau + *n; /* Compute A=Q*R, copying result to U */ /* (Workspace: need 2*N, prefer N + N*NB) */ - i__2 = *lwork - iwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], - ldu, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], + ldu, (ftnlen)1); /* Generate Q in U */ /* (Workspace: need 2*N, prefer N + N*NB) */ - i__2 = *lwork - iwork + 1; - dorgqr_(m, n, n, &u[u_offset], ldu, &work[itau], & - work[iwork], &i__2, &ierr); + i__2 = *lwork - iwork + 1; + dorgqr_(m, n, n, &u[u_offset], ldu, &work[itau], & + work[iwork], &i__2, &ierr); /* Copy R to VT, zeroing out below it */ - dlacpy_((char *)"U", n, n, &a[a_offset], lda, &vt[vt_offset], - ldvt, (ftnlen)1); - if (*n > 1) { - i__2 = *n - 1; - i__3 = *n - 1; - dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &vt[ - vt_dim1 + 2], ldvt, (ftnlen)1); - } - ie = itau; - itauq = ie + *n; - itaup = itauq + *n; - iwork = itaup + *n; + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &vt[vt_offset], + ldvt, (ftnlen)1); + if (*n > 1) { + i__2 = *n - 1; + i__3 = *n - 1; + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &vt[ + vt_dim1 + 2], ldvt, (ftnlen)1); + } + ie = itau; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; /* Bidiagonalize R in VT */ /* (Workspace: need 4*N, prefer 3*N + 2*N*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &work[ie], - &work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); + i__2 = *lwork - iwork + 1; + dgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &work[ie], + &work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); /* Multiply Q in U by left bidiagonalizing vectors */ /* in VT */ /* (Workspace: need 3*N + M, prefer 3*N + M*NB) */ - i__2 = *lwork - iwork + 1; - dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &vt[vt_offset], ldvt, - &work[itauq], &u[u_offset], ldu, &work[iwork], - &i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen) - 1); + i__2 = *lwork - iwork + 1; + dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &vt[vt_offset], ldvt, + &work[itauq], &u[u_offset], ldu, &work[iwork], + &i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen) + 1); /* Generate right bidiagonalizing vectors in VT */ /* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[ - itaup], &work[iwork], &i__2, &ierr, (ftnlen)1) - ; - iwork = ie + *n; + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[ + itaup], &work[iwork], &i__2, &ierr, (ftnlen)1) + ; + iwork = ie + *n; /* Perform bidiagonal QR iteration, computing left */ /* singular vectors of A in U and computing right */ /* singular vectors of A in VT */ /* (Workspace: need BDSPAC) */ - dbdsqr_((char *)"U", n, n, m, &c__0, &s[1], &work[ie], &vt[ - vt_offset], ldvt, &u[u_offset], ldu, dum, & - c__1, &work[iwork], info, (ftnlen)1); + dbdsqr_((char *)"U", n, n, m, &c__0, &s[1], &work[ie], &vt[ + vt_offset], ldvt, &u[u_offset], ldu, dum, & + c__1, &work[iwork], info, (ftnlen)1); - } + } - } + } - } else if (wntua) { + } else if (wntua) { - if (wntvn) { + if (wntvn) { /* Path 7 (M much larger than N, JOBU='A', JOBVT='N') */ /* M left singular vectors to be computed in U and */ /* no right singular vectors to be computed */ /* Computing MAX */ - i__2 = *n + *m, i__3 = *n << 2, i__2 = max(i__2,i__3); - if (*lwork >= *n * *n + max(i__2,bdspac)) { + i__2 = *n + *m, i__3 = *n << 2, i__2 = max(i__2,i__3); + if (*lwork >= *n * *n + max(i__2,bdspac)) { /* Sufficient workspace for a fast algorithm */ - ir = 1; - if (*lwork >= wrkbl + *lda * *n) { + ir = 1; + if (*lwork >= wrkbl + *lda * *n) { /* WORK(IR) is LDA by N */ - ldwrkr = *lda; - } else { + ldwrkr = *lda; + } else { /* WORK(IR) is N by N */ - ldwrkr = *n; - } - itau = ir + ldwrkr * *n; - iwork = itau + *n; + ldwrkr = *n; + } + itau = ir + ldwrkr * *n; + iwork = itau + *n; /* Compute A=Q*R, copying result to U */ /* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */ - i__2 = *lwork - iwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], - ldu, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], + ldu, (ftnlen)1); /* Copy R to WORK(IR), zeroing out below it */ - dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[ir], & - ldwrkr, (ftnlen)1); - i__2 = *n - 1; - i__3 = *n - 1; - dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[ir + - 1], &ldwrkr, (ftnlen)1); + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[ir], & + ldwrkr, (ftnlen)1); + i__2 = *n - 1; + i__3 = *n - 1; + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[ir + + 1], &ldwrkr, (ftnlen)1); /* Generate Q in U */ /* (Workspace: need N*N + N + M, prefer N*N + N + M*NB) */ - i__2 = *lwork - iwork + 1; - dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], & - work[iwork], &i__2, &ierr); - ie = itau; - itauq = ie + *n; - itaup = itauq + *n; - iwork = itaup + *n; + i__2 = *lwork - iwork + 1; + dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], & + work[iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; /* Bidiagonalize R in WORK(IR) */ /* (Workspace: need N*N + 4*N, prefer N*N + 3*N + 2*N*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); + i__2 = *lwork - iwork + 1; + dgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); /* Generate left bidiagonalizing vectors in WORK(IR) */ /* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", n, n, n, &work[ir], &ldwrkr, &work[itauq] - , &work[iwork], &i__2, &ierr, (ftnlen)1); - iwork = ie + *n; + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", n, n, n, &work[ir], &ldwrkr, &work[itauq] + , &work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *n; /* Perform bidiagonal QR iteration, computing left */ /* singular vectors of R in WORK(IR) */ /* (Workspace: need N*N + BDSPAC) */ - dbdsqr_((char *)"U", n, &c__0, n, &c__0, &s[1], &work[ie], - dum, &c__1, &work[ir], &ldwrkr, dum, &c__1, & - work[iwork], info, (ftnlen)1); + dbdsqr_((char *)"U", n, &c__0, n, &c__0, &s[1], &work[ie], + dum, &c__1, &work[ir], &ldwrkr, dum, &c__1, & + work[iwork], info, (ftnlen)1); /* Multiply Q in U by left singular vectors of R in */ /* WORK(IR), storing result in A */ /* (Workspace: need N*N) */ - dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &u[u_offset], ldu, & - work[ir], &ldwrkr, &c_b57, &a[a_offset], lda, - (ftnlen)1, (ftnlen)1); + dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &u[u_offset], ldu, & + work[ir], &ldwrkr, &c_b57, &a[a_offset], lda, + (ftnlen)1, (ftnlen)1); /* Copy left singular vectors of A from A to U */ - dlacpy_((char *)"F", m, n, &a[a_offset], lda, &u[u_offset], - ldu, (ftnlen)1); + dlacpy_((char *)"F", m, n, &a[a_offset], lda, &u[u_offset], + ldu, (ftnlen)1); - } else { + } else { /* Insufficient workspace for a fast algorithm */ - itau = 1; - iwork = itau + *n; + itau = 1; + iwork = itau + *n; /* Compute A=Q*R, copying result to U */ /* (Workspace: need 2*N, prefer N + N*NB) */ - i__2 = *lwork - iwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], - ldu, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], + ldu, (ftnlen)1); /* Generate Q in U */ /* (Workspace: need N + M, prefer N + M*NB) */ - i__2 = *lwork - iwork + 1; - dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], & - work[iwork], &i__2, &ierr); - ie = itau; - itauq = ie + *n; - itaup = itauq + *n; - iwork = itaup + *n; + i__2 = *lwork - iwork + 1; + dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], & + work[iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; /* Zero out below R in A */ - if (*n > 1) { - i__2 = *n - 1; - i__3 = *n - 1; - dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &a[ - a_dim1 + 2], lda, (ftnlen)1); - } + if (*n > 1) { + i__2 = *n - 1; + i__3 = *n - 1; + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &a[ + a_dim1 + 2], lda, (ftnlen)1); + } /* Bidiagonalize R in A */ /* (Workspace: need 4*N, prefer 3*N + 2*N*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); + i__2 = *lwork - iwork + 1; + dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); /* Multiply Q in U by left bidiagonalizing vectors */ /* in A */ /* (Workspace: need 3*N + M, prefer 3*N + M*NB) */ - i__2 = *lwork - iwork + 1; - dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &a[a_offset], lda, & - work[itauq], &u[u_offset], ldu, &work[iwork], - &i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen)1) - ; - iwork = ie + *n; + i__2 = *lwork - iwork + 1; + dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &a[a_offset], lda, & + work[itauq], &u[u_offset], ldu, &work[iwork], + &i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen)1) + ; + iwork = ie + *n; /* Perform bidiagonal QR iteration, computing left */ /* singular vectors of A in U */ /* (Workspace: need BDSPAC) */ - dbdsqr_((char *)"U", n, &c__0, m, &c__0, &s[1], &work[ie], - dum, &c__1, &u[u_offset], ldu, dum, &c__1, & - work[iwork], info, (ftnlen)1); + dbdsqr_((char *)"U", n, &c__0, m, &c__0, &s[1], &work[ie], + dum, &c__1, &u[u_offset], ldu, dum, &c__1, & + work[iwork], info, (ftnlen)1); - } + } - } else if (wntvo) { + } else if (wntvo) { /* Path 8 (M much larger than N, JOBU='A', JOBVT='O') */ /* M left singular vectors to be computed in U and */ /* N right singular vectors to be overwritten on A */ /* Computing MAX */ - i__2 = *n + *m, i__3 = *n << 2, i__2 = max(i__2,i__3); - if (*lwork >= (*n << 1) * *n + max(i__2,bdspac)) { + i__2 = *n + *m, i__3 = *n << 2, i__2 = max(i__2,i__3); + if (*lwork >= (*n << 1) * *n + max(i__2,bdspac)) { /* Sufficient workspace for a fast algorithm */ - iu = 1; - if (*lwork >= wrkbl + (*lda << 1) * *n) { + iu = 1; + if (*lwork >= wrkbl + (*lda << 1) * *n) { /* WORK(IU) is LDA by N and WORK(IR) is LDA by N */ - ldwrku = *lda; - ir = iu + ldwrku * *n; - ldwrkr = *lda; - } else if (*lwork >= wrkbl + (*lda + *n) * *n) { + ldwrku = *lda; + ir = iu + ldwrku * *n; + ldwrkr = *lda; + } else if (*lwork >= wrkbl + (*lda + *n) * *n) { /* WORK(IU) is LDA by N and WORK(IR) is N by N */ - ldwrku = *lda; - ir = iu + ldwrku * *n; - ldwrkr = *n; - } else { + ldwrku = *lda; + ir = iu + ldwrku * *n; + ldwrkr = *n; + } else { /* WORK(IU) is N by N and WORK(IR) is N by N */ - ldwrku = *n; - ir = iu + ldwrku * *n; - ldwrkr = *n; - } - itau = ir + ldwrkr * *n; - iwork = itau + *n; + ldwrku = *n; + ir = iu + ldwrku * *n; + ldwrkr = *n; + } + itau = ir + ldwrkr * *n; + iwork = itau + *n; /* Compute A=Q*R, copying result to U */ /* (Workspace: need 2*N*N + 2*N, prefer 2*N*N + N + N*NB) */ - i__2 = *lwork - iwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], - ldu, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], + ldu, (ftnlen)1); /* Generate Q in U */ /* (Workspace: need 2*N*N + N + M, prefer 2*N*N + N + M*NB) */ - i__2 = *lwork - iwork + 1; - dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], & - work[iwork], &i__2, &ierr); + i__2 = *lwork - iwork + 1; + dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], & + work[iwork], &i__2, &ierr); /* Copy R to WORK(IU), zeroing out below it */ - dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[iu], & - ldwrku, (ftnlen)1); - i__2 = *n - 1; - i__3 = *n - 1; - dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[iu + - 1], &ldwrku, (ftnlen)1); - ie = itau; - itauq = ie + *n; - itaup = itauq + *n; - iwork = itaup + *n; + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[iu], & + ldwrku, (ftnlen)1); + i__2 = *n - 1; + i__3 = *n - 1; + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[iu + + 1], &ldwrku, (ftnlen)1); + ie = itau; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; /* Bidiagonalize R in WORK(IU), copying result to */ /* WORK(IR) */ /* (Workspace: need 2*N*N + 4*N, */ /* prefer 2*N*N+3*N+2*N*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(n, n, &work[iu], &ldwrku, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); - dlacpy_((char *)"U", n, n, &work[iu], &ldwrku, &work[ir], & - ldwrkr, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dgebrd_(n, n, &work[iu], &ldwrku, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); + dlacpy_((char *)"U", n, n, &work[iu], &ldwrku, &work[ir], & + ldwrkr, (ftnlen)1); /* Generate left bidiagonalizing vectors in WORK(IU) */ /* (Workspace: need 2*N*N + 4*N, prefer 2*N*N + 3*N + N*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", n, n, n, &work[iu], &ldwrku, &work[itauq] - , &work[iwork], &i__2, &ierr, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", n, n, n, &work[iu], &ldwrku, &work[itauq] + , &work[iwork], &i__2, &ierr, (ftnlen)1); /* Generate right bidiagonalizing vectors in WORK(IR) */ /* (Workspace: need 2*N*N + 4*N-1, */ /* prefer 2*N*N+3*N+(N-1)*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", n, n, n, &work[ir], &ldwrkr, &work[itaup] - , &work[iwork], &i__2, &ierr, (ftnlen)1); - iwork = ie + *n; + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", n, n, n, &work[ir], &ldwrkr, &work[itaup] + , &work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *n; /* Perform bidiagonal QR iteration, computing left */ /* singular vectors of R in WORK(IU) and computing */ /* right singular vectors of R in WORK(IR) */ /* (Workspace: need 2*N*N + BDSPAC) */ - dbdsqr_((char *)"U", n, n, n, &c__0, &s[1], &work[ie], &work[ - ir], &ldwrkr, &work[iu], &ldwrku, dum, &c__1, - &work[iwork], info, (ftnlen)1); + dbdsqr_((char *)"U", n, n, n, &c__0, &s[1], &work[ie], &work[ + ir], &ldwrkr, &work[iu], &ldwrku, dum, &c__1, + &work[iwork], info, (ftnlen)1); /* Multiply Q in U by left singular vectors of R in */ /* WORK(IU), storing result in A */ /* (Workspace: need N*N) */ - dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &u[u_offset], ldu, & - work[iu], &ldwrku, &c_b57, &a[a_offset], lda, - (ftnlen)1, (ftnlen)1); + dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &u[u_offset], ldu, & + work[iu], &ldwrku, &c_b57, &a[a_offset], lda, + (ftnlen)1, (ftnlen)1); /* Copy left singular vectors of A from A to U */ - dlacpy_((char *)"F", m, n, &a[a_offset], lda, &u[u_offset], - ldu, (ftnlen)1); + dlacpy_((char *)"F", m, n, &a[a_offset], lda, &u[u_offset], + ldu, (ftnlen)1); /* Copy right singular vectors of R from WORK(IR) to A */ - dlacpy_((char *)"F", n, n, &work[ir], &ldwrkr, &a[a_offset], - lda, (ftnlen)1); + dlacpy_((char *)"F", n, n, &work[ir], &ldwrkr, &a[a_offset], + lda, (ftnlen)1); - } else { + } else { /* Insufficient workspace for a fast algorithm */ - itau = 1; - iwork = itau + *n; + itau = 1; + iwork = itau + *n; /* Compute A=Q*R, copying result to U */ /* (Workspace: need 2*N, prefer N + N*NB) */ - i__2 = *lwork - iwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], - ldu, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], + ldu, (ftnlen)1); /* Generate Q in U */ /* (Workspace: need N + M, prefer N + M*NB) */ - i__2 = *lwork - iwork + 1; - dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], & - work[iwork], &i__2, &ierr); - ie = itau; - itauq = ie + *n; - itaup = itauq + *n; - iwork = itaup + *n; + i__2 = *lwork - iwork + 1; + dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], & + work[iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; /* Zero out below R in A */ - if (*n > 1) { - i__2 = *n - 1; - i__3 = *n - 1; - dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &a[ - a_dim1 + 2], lda, (ftnlen)1); - } + if (*n > 1) { + i__2 = *n - 1; + i__3 = *n - 1; + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &a[ + a_dim1 + 2], lda, (ftnlen)1); + } /* Bidiagonalize R in A */ /* (Workspace: need 4*N, prefer 3*N + 2*N*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); + i__2 = *lwork - iwork + 1; + dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); /* Multiply Q in U by left bidiagonalizing vectors */ /* in A */ /* (Workspace: need 3*N + M, prefer 3*N + M*NB) */ - i__2 = *lwork - iwork + 1; - dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &a[a_offset], lda, & - work[itauq], &u[u_offset], ldu, &work[iwork], - &i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen)1) - ; + i__2 = *lwork - iwork + 1; + dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &a[a_offset], lda, & + work[itauq], &u[u_offset], ldu, &work[iwork], + &i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen)1) + ; /* Generate right bidiagonalizing vectors in A */ /* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, &work[itaup], - &work[iwork], &i__2, &ierr, (ftnlen)1); - iwork = ie + *n; + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, &work[itaup], + &work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *n; /* Perform bidiagonal QR iteration, computing left */ /* singular vectors of A in U and computing right */ /* singular vectors of A in A */ /* (Workspace: need BDSPAC) */ - dbdsqr_((char *)"U", n, n, m, &c__0, &s[1], &work[ie], &a[ - a_offset], lda, &u[u_offset], ldu, dum, &c__1, - &work[iwork], info, (ftnlen)1); + dbdsqr_((char *)"U", n, n, m, &c__0, &s[1], &work[ie], &a[ + a_offset], lda, &u[u_offset], ldu, dum, &c__1, + &work[iwork], info, (ftnlen)1); - } + } - } else if (wntvas) { + } else if (wntvas) { /* Path 9 (M much larger than N, JOBU='A', JOBVT='S' */ /* or 'A') */ @@ -2235,298 +2235,298 @@ f"> */ /* N right singular vectors to be computed in VT */ /* Computing MAX */ - i__2 = *n + *m, i__3 = *n << 2, i__2 = max(i__2,i__3); - if (*lwork >= *n * *n + max(i__2,bdspac)) { + i__2 = *n + *m, i__3 = *n << 2, i__2 = max(i__2,i__3); + if (*lwork >= *n * *n + max(i__2,bdspac)) { /* Sufficient workspace for a fast algorithm */ - iu = 1; - if (*lwork >= wrkbl + *lda * *n) { + iu = 1; + if (*lwork >= wrkbl + *lda * *n) { /* WORK(IU) is LDA by N */ - ldwrku = *lda; - } else { + ldwrku = *lda; + } else { /* WORK(IU) is N by N */ - ldwrku = *n; - } - itau = iu + ldwrku * *n; - iwork = itau + *n; + ldwrku = *n; + } + itau = iu + ldwrku * *n; + iwork = itau + *n; /* Compute A=Q*R, copying result to U */ /* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */ - i__2 = *lwork - iwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], - ldu, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], + ldu, (ftnlen)1); /* Generate Q in U */ /* (Workspace: need N*N + N + M, prefer N*N + N + M*NB) */ - i__2 = *lwork - iwork + 1; - dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], & - work[iwork], &i__2, &ierr); + i__2 = *lwork - iwork + 1; + dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], & + work[iwork], &i__2, &ierr); /* Copy R to WORK(IU), zeroing out below it */ - dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[iu], & - ldwrku, (ftnlen)1); - i__2 = *n - 1; - i__3 = *n - 1; - dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[iu + - 1], &ldwrku, (ftnlen)1); - ie = itau; - itauq = ie + *n; - itaup = itauq + *n; - iwork = itaup + *n; + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[iu], & + ldwrku, (ftnlen)1); + i__2 = *n - 1; + i__3 = *n - 1; + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[iu + + 1], &ldwrku, (ftnlen)1); + ie = itau; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; /* Bidiagonalize R in WORK(IU), copying result to VT */ /* (Workspace: need N*N + 4*N, prefer N*N + 3*N + 2*N*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(n, n, &work[iu], &ldwrku, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); - dlacpy_((char *)"U", n, n, &work[iu], &ldwrku, &vt[vt_offset], - ldvt, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dgebrd_(n, n, &work[iu], &ldwrku, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); + dlacpy_((char *)"U", n, n, &work[iu], &ldwrku, &vt[vt_offset], + ldvt, (ftnlen)1); /* Generate left bidiagonalizing vectors in WORK(IU) */ /* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", n, n, n, &work[iu], &ldwrku, &work[itauq] - , &work[iwork], &i__2, &ierr, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", n, n, n, &work[iu], &ldwrku, &work[itauq] + , &work[iwork], &i__2, &ierr, (ftnlen)1); /* Generate right bidiagonalizing vectors in VT */ /* (Workspace: need N*N + 4*N-1, */ /* prefer N*N+3*N+(N-1)*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[ - itaup], &work[iwork], &i__2, &ierr, (ftnlen)1) - ; - iwork = ie + *n; + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[ + itaup], &work[iwork], &i__2, &ierr, (ftnlen)1) + ; + iwork = ie + *n; /* Perform bidiagonal QR iteration, computing left */ /* singular vectors of R in WORK(IU) and computing */ /* right singular vectors of R in VT */ /* (Workspace: need N*N + BDSPAC) */ - dbdsqr_((char *)"U", n, n, n, &c__0, &s[1], &work[ie], &vt[ - vt_offset], ldvt, &work[iu], &ldwrku, dum, & - c__1, &work[iwork], info, (ftnlen)1); + dbdsqr_((char *)"U", n, n, n, &c__0, &s[1], &work[ie], &vt[ + vt_offset], ldvt, &work[iu], &ldwrku, dum, & + c__1, &work[iwork], info, (ftnlen)1); /* Multiply Q in U by left singular vectors of R in */ /* WORK(IU), storing result in A */ /* (Workspace: need N*N) */ - dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &u[u_offset], ldu, & - work[iu], &ldwrku, &c_b57, &a[a_offset], lda, - (ftnlen)1, (ftnlen)1); + dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &u[u_offset], ldu, & + work[iu], &ldwrku, &c_b57, &a[a_offset], lda, + (ftnlen)1, (ftnlen)1); /* Copy left singular vectors of A from A to U */ - dlacpy_((char *)"F", m, n, &a[a_offset], lda, &u[u_offset], - ldu, (ftnlen)1); + dlacpy_((char *)"F", m, n, &a[a_offset], lda, &u[u_offset], + ldu, (ftnlen)1); - } else { + } else { /* Insufficient workspace for a fast algorithm */ - itau = 1; - iwork = itau + *n; + itau = 1; + iwork = itau + *n; /* Compute A=Q*R, copying result to U */ /* (Workspace: need 2*N, prefer N + N*NB) */ - i__2 = *lwork - iwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], - ldu, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], + ldu, (ftnlen)1); /* Generate Q in U */ /* (Workspace: need N + M, prefer N + M*NB) */ - i__2 = *lwork - iwork + 1; - dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], & - work[iwork], &i__2, &ierr); + i__2 = *lwork - iwork + 1; + dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], & + work[iwork], &i__2, &ierr); /* Copy R from A to VT, zeroing out below it */ - dlacpy_((char *)"U", n, n, &a[a_offset], lda, &vt[vt_offset], - ldvt, (ftnlen)1); - if (*n > 1) { - i__2 = *n - 1; - i__3 = *n - 1; - dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &vt[ - vt_dim1 + 2], ldvt, (ftnlen)1); - } - ie = itau; - itauq = ie + *n; - itaup = itauq + *n; - iwork = itaup + *n; + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &vt[vt_offset], + ldvt, (ftnlen)1); + if (*n > 1) { + i__2 = *n - 1; + i__3 = *n - 1; + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &vt[ + vt_dim1 + 2], ldvt, (ftnlen)1); + } + ie = itau; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; /* Bidiagonalize R in VT */ /* (Workspace: need 4*N, prefer 3*N + 2*N*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &work[ie], - &work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); + i__2 = *lwork - iwork + 1; + dgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &work[ie], + &work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); /* Multiply Q in U by left bidiagonalizing vectors */ /* in VT */ /* (Workspace: need 3*N + M, prefer 3*N + M*NB) */ - i__2 = *lwork - iwork + 1; - dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &vt[vt_offset], ldvt, - &work[itauq], &u[u_offset], ldu, &work[iwork], - &i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen) - 1); + i__2 = *lwork - iwork + 1; + dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &vt[vt_offset], ldvt, + &work[itauq], &u[u_offset], ldu, &work[iwork], + &i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen) + 1); /* Generate right bidiagonalizing vectors in VT */ /* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[ - itaup], &work[iwork], &i__2, &ierr, (ftnlen)1) - ; - iwork = ie + *n; + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[ + itaup], &work[iwork], &i__2, &ierr, (ftnlen)1) + ; + iwork = ie + *n; /* Perform bidiagonal QR iteration, computing left */ /* singular vectors of A in U and computing right */ /* singular vectors of A in VT */ /* (Workspace: need BDSPAC) */ - dbdsqr_((char *)"U", n, n, m, &c__0, &s[1], &work[ie], &vt[ - vt_offset], ldvt, &u[u_offset], ldu, dum, & - c__1, &work[iwork], info, (ftnlen)1); + dbdsqr_((char *)"U", n, n, m, &c__0, &s[1], &work[ie], &vt[ + vt_offset], ldvt, &u[u_offset], ldu, dum, & + c__1, &work[iwork], info, (ftnlen)1); - } + } - } + } - } + } - } else { + } else { /* M .LT. MNTHR */ /* Path 10 (M at least N, but not much larger) */ /* Reduce to bidiagonal form without QR decomposition */ - ie = 1; - itauq = ie + *n; - itaup = itauq + *n; - iwork = itaup + *n; + ie = 1; + itauq = ie + *n; + itaup = itauq + *n; + iwork = itaup + *n; /* Bidiagonalize A */ /* (Workspace: need 3*N + M, prefer 3*N + (M + N)*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], & - work[itaup], &work[iwork], &i__2, &ierr); - if (wntuas) { + i__2 = *lwork - iwork + 1; + dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], & + work[itaup], &work[iwork], &i__2, &ierr); + if (wntuas) { /* If left singular vectors desired in U, copy result to U */ /* and generate left bidiagonalizing vectors in U */ /* (Workspace: need 3*N + NCU, prefer 3*N + NCU*NB) */ - dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], ldu, ( - ftnlen)1); - if (wntus) { - ncu = *n; - } - if (wntua) { - ncu = *m; - } - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", m, &ncu, n, &u[u_offset], ldu, &work[itauq], & - work[iwork], &i__2, &ierr, (ftnlen)1); - } - if (wntvas) { + dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], ldu, ( + ftnlen)1); + if (wntus) { + ncu = *n; + } + if (wntua) { + ncu = *m; + } + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", m, &ncu, n, &u[u_offset], ldu, &work[itauq], & + work[iwork], &i__2, &ierr, (ftnlen)1); + } + if (wntvas) { /* If right singular vectors desired in VT, copy result to */ /* VT and generate right bidiagonalizing vectors in VT */ /* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) */ - dlacpy_((char *)"U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt, ( - ftnlen)1); - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], & - work[iwork], &i__2, &ierr, (ftnlen)1); - } - if (wntuo) { + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt, ( + ftnlen)1); + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], & + work[iwork], &i__2, &ierr, (ftnlen)1); + } + if (wntuo) { /* If left singular vectors desired in A, generate left */ /* bidiagonalizing vectors in A */ /* (Workspace: need 4*N, prefer 3*N + N*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", m, n, n, &a[a_offset], lda, &work[itauq], &work[ - iwork], &i__2, &ierr, (ftnlen)1); - } - if (wntvo) { + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", m, n, n, &a[a_offset], lda, &work[itauq], &work[ + iwork], &i__2, &ierr, (ftnlen)1); + } + if (wntvo) { /* If right singular vectors desired in A, generate right */ /* bidiagonalizing vectors in A */ /* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, &work[itaup], &work[ - iwork], &i__2, &ierr, (ftnlen)1); - } - iwork = ie + *n; - if (wntuas || wntuo) { - nru = *m; - } - if (wntun) { - nru = 0; - } - if (wntvas || wntvo) { - ncvt = *n; - } - if (wntvn) { - ncvt = 0; - } - if (! wntuo && ! wntvo) { + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, &work[itaup], &work[ + iwork], &i__2, &ierr, (ftnlen)1); + } + iwork = ie + *n; + if (wntuas || wntuo) { + nru = *m; + } + if (wntun) { + nru = 0; + } + if (wntvas || wntvo) { + ncvt = *n; + } + if (wntvn) { + ncvt = 0; + } + if (! wntuo && ! wntvo) { /* Perform bidiagonal QR iteration, if desired, computing */ /* left singular vectors in U and computing right singular */ /* vectors in VT */ /* (Workspace: need BDSPAC) */ - dbdsqr_((char *)"U", n, &ncvt, &nru, &c__0, &s[1], &work[ie], &vt[ - vt_offset], ldvt, &u[u_offset], ldu, dum, &c__1, & - work[iwork], info, (ftnlen)1); - } else if (! wntuo && wntvo) { + dbdsqr_((char *)"U", n, &ncvt, &nru, &c__0, &s[1], &work[ie], &vt[ + vt_offset], ldvt, &u[u_offset], ldu, dum, &c__1, & + work[iwork], info, (ftnlen)1); + } else if (! wntuo && wntvo) { /* Perform bidiagonal QR iteration, if desired, computing */ /* left singular vectors in U and computing right singular */ /* vectors in A */ /* (Workspace: need BDSPAC) */ - dbdsqr_((char *)"U", n, &ncvt, &nru, &c__0, &s[1], &work[ie], &a[ - a_offset], lda, &u[u_offset], ldu, dum, &c__1, &work[ - iwork], info, (ftnlen)1); - } else { + dbdsqr_((char *)"U", n, &ncvt, &nru, &c__0, &s[1], &work[ie], &a[ + a_offset], lda, &u[u_offset], ldu, dum, &c__1, &work[ + iwork], info, (ftnlen)1); + } else { /* Perform bidiagonal QR iteration, if desired, computing */ /* left singular vectors in A and computing right singular */ /* vectors in VT */ /* (Workspace: need BDSPAC) */ - dbdsqr_((char *)"U", n, &ncvt, &nru, &c__0, &s[1], &work[ie], &vt[ - vt_offset], ldvt, &a[a_offset], lda, dum, &c__1, & - work[iwork], info, (ftnlen)1); - } + dbdsqr_((char *)"U", n, &ncvt, &nru, &c__0, &s[1], &work[ie], &vt[ + vt_offset], ldvt, &a[a_offset], lda, dum, &c__1, & + work[iwork], info, (ftnlen)1); + } - } + } } else { @@ -2534,751 +2534,751 @@ f"> */ /* columns than rows, first reduce using the LQ decomposition (if */ /* sufficient workspace available) */ - if (*n >= mnthr) { + if (*n >= mnthr) { - if (wntvn) { + if (wntvn) { /* Path 1t(N much larger than M, JOBVT='N') */ /* No right singular vectors to be computed */ - itau = 1; - iwork = itau + *m; + itau = 1; + iwork = itau + *m; /* Compute A=L*Q */ /* (Workspace: need 2*M, prefer M + M*NB) */ - i__2 = *lwork - iwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], & - i__2, &ierr); + i__2 = *lwork - iwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], & + i__2, &ierr); /* Zero out above L */ - i__2 = *m - 1; - i__3 = *m - 1; - dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &a[(a_dim1 << 1) + - 1], lda, (ftnlen)1); - ie = 1; - itauq = ie + *m; - itaup = itauq + *m; - iwork = itaup + *m; + i__2 = *m - 1; + i__3 = *m - 1; + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &a[(a_dim1 << 1) + + 1], lda, (ftnlen)1); + ie = 1; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; /* Bidiagonalize L in A */ /* (Workspace: need 4*M, prefer 3*M + 2*M*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &work[ - itauq], &work[itaup], &work[iwork], &i__2, &ierr); - if (wntuo || wntuas) { + i__2 = *lwork - iwork + 1; + dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &work[ + itauq], &work[itaup], &work[iwork], &i__2, &ierr); + if (wntuo || wntuas) { /* If left singular vectors desired, generate Q */ /* (Workspace: need 4*M, prefer 3*M + M*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", m, m, m, &a[a_offset], lda, &work[itauq], & - work[iwork], &i__2, &ierr, (ftnlen)1); - } - iwork = ie + *m; - nru = 0; - if (wntuo || wntuas) { - nru = *m; - } + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", m, m, m, &a[a_offset], lda, &work[itauq], & + work[iwork], &i__2, &ierr, (ftnlen)1); + } + iwork = ie + *m; + nru = 0; + if (wntuo || wntuas) { + nru = *m; + } /* Perform bidiagonal QR iteration, computing left singular */ /* vectors of A in A if desired */ /* (Workspace: need BDSPAC) */ - dbdsqr_((char *)"U", m, &c__0, &nru, &c__0, &s[1], &work[ie], dum, & - c__1, &a[a_offset], lda, dum, &c__1, &work[iwork], - info, (ftnlen)1); + dbdsqr_((char *)"U", m, &c__0, &nru, &c__0, &s[1], &work[ie], dum, & + c__1, &a[a_offset], lda, dum, &c__1, &work[iwork], + info, (ftnlen)1); /* If left singular vectors desired in U, copy them there */ - if (wntuas) { - dlacpy_((char *)"F", m, m, &a[a_offset], lda, &u[u_offset], ldu, ( - ftnlen)1); - } + if (wntuas) { + dlacpy_((char *)"F", m, m, &a[a_offset], lda, &u[u_offset], ldu, ( + ftnlen)1); + } - } else if (wntvo && wntun) { + } else if (wntvo && wntun) { /* Path 2t(N much larger than M, JOBU='N', JOBVT='O') */ /* M right singular vectors to be overwritten on A and */ /* no left singular vectors to be computed */ /* Computing MAX */ - i__2 = *m << 2; - if (*lwork >= *m * *m + max(i__2,bdspac)) { + i__2 = *m << 2; + if (*lwork >= *m * *m + max(i__2,bdspac)) { /* Sufficient workspace for a fast algorithm */ - ir = 1; + ir = 1; /* Computing MAX */ - i__2 = wrkbl, i__3 = *lda * *n + *m; - if (*lwork >= max(i__2,i__3) + *lda * *m) { + i__2 = wrkbl, i__3 = *lda * *n + *m; + if (*lwork >= max(i__2,i__3) + *lda * *m) { /* WORK(IU) is LDA by N and WORK(IR) is LDA by M */ - ldwrku = *lda; - chunk = *n; - ldwrkr = *lda; - } else /* if(complicated condition) */ { + ldwrku = *lda; + chunk = *n; + ldwrkr = *lda; + } else /* if(complicated condition) */ { /* Computing MAX */ - i__2 = wrkbl, i__3 = *lda * *n + *m; - if (*lwork >= max(i__2,i__3) + *m * *m) { + i__2 = wrkbl, i__3 = *lda * *n + *m; + if (*lwork >= max(i__2,i__3) + *m * *m) { /* WORK(IU) is LDA by N and WORK(IR) is M by M */ - ldwrku = *lda; - chunk = *n; - ldwrkr = *m; - } else { + ldwrku = *lda; + chunk = *n; + ldwrkr = *m; + } else { /* WORK(IU) is M by CHUNK and WORK(IR) is M by M */ - ldwrku = *m; - chunk = (*lwork - *m * *m - *m) / *m; - ldwrkr = *m; - } - } - itau = ir + ldwrkr * *m; - iwork = itau + *m; + ldwrku = *m; + chunk = (*lwork - *m * *m - *m) / *m; + ldwrkr = *m; + } + } + itau = ir + ldwrkr * *m; + iwork = itau + *m; /* Compute A=L*Q */ /* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */ - i__2 = *lwork - iwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork] - , &i__2, &ierr); + i__2 = *lwork - iwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork] + , &i__2, &ierr); /* Copy L to WORK(IR) and zero out above it */ - dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[ir], &ldwrkr, - (ftnlen)1); - i__2 = *m - 1; - i__3 = *m - 1; - dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[ir + - ldwrkr], &ldwrkr, (ftnlen)1); + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[ir], &ldwrkr, + (ftnlen)1); + i__2 = *m - 1; + i__3 = *m - 1; + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[ir + + ldwrkr], &ldwrkr, (ftnlen)1); /* Generate Q in A */ /* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */ - i__2 = *lwork - iwork + 1; - dorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - ie = itau; - itauq = ie + *m; - itaup = itauq + *m; - iwork = itaup + *m; + i__2 = *lwork - iwork + 1; + dorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; /* Bidiagonalize L in WORK(IR) */ /* (Workspace: need M*M + 4*M, prefer M*M + 3*M + 2*M*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &work[ie], &work[ - itauq], &work[itaup], &work[iwork], &i__2, &ierr); + i__2 = *lwork - iwork + 1; + dgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &work[ie], &work[ + itauq], &work[itaup], &work[iwork], &i__2, &ierr); /* Generate right vectors bidiagonalizing L */ /* (Workspace: need M*M + 4*M-1, prefer M*M + 3*M + (M-1)*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", m, m, m, &work[ir], &ldwrkr, &work[itaup], & - work[iwork], &i__2, &ierr, (ftnlen)1); - iwork = ie + *m; + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", m, m, m, &work[ir], &ldwrkr, &work[itaup], & + work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *m; /* Perform bidiagonal QR iteration, computing right */ /* singular vectors of L in WORK(IR) */ /* (Workspace: need M*M + BDSPAC) */ - dbdsqr_((char *)"U", m, m, &c__0, &c__0, &s[1], &work[ie], &work[ - ir], &ldwrkr, dum, &c__1, dum, &c__1, &work[iwork] - , info, (ftnlen)1); - iu = ie + *m; + dbdsqr_((char *)"U", m, m, &c__0, &c__0, &s[1], &work[ie], &work[ + ir], &ldwrkr, dum, &c__1, dum, &c__1, &work[iwork] + , info, (ftnlen)1); + iu = ie + *m; /* Multiply right singular vectors of L in WORK(IR) by Q */ /* in A, storing result in WORK(IU) and copying to A */ /* (Workspace: need M*M + 2*M, prefer M*M + M*N + M) */ - i__2 = *n; - i__3 = chunk; - for (i__ = 1; i__3 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += - i__3) { + i__2 = *n; + i__3 = chunk; + for (i__ = 1; i__3 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += + i__3) { /* Computing MIN */ - i__4 = *n - i__ + 1; - blk = min(i__4,chunk); - dgemm_((char *)"N", (char *)"N", m, &blk, m, &c_b79, &work[ir], & - ldwrkr, &a[i__ * a_dim1 + 1], lda, &c_b57, & - work[iu], &ldwrku, (ftnlen)1, (ftnlen)1); - dlacpy_((char *)"F", m, &blk, &work[iu], &ldwrku, &a[i__ * - a_dim1 + 1], lda, (ftnlen)1); + i__4 = *n - i__ + 1; + blk = min(i__4,chunk); + dgemm_((char *)"N", (char *)"N", m, &blk, m, &c_b79, &work[ir], & + ldwrkr, &a[i__ * a_dim1 + 1], lda, &c_b57, & + work[iu], &ldwrku, (ftnlen)1, (ftnlen)1); + dlacpy_((char *)"F", m, &blk, &work[iu], &ldwrku, &a[i__ * + a_dim1 + 1], lda, (ftnlen)1); /* L30: */ - } + } - } else { + } else { /* Insufficient workspace for a fast algorithm */ - ie = 1; - itauq = ie + *m; - itaup = itauq + *m; - iwork = itaup + *m; + ie = 1; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; /* Bidiagonalize A */ /* (Workspace: need 3*M + N, prefer 3*M + (M + N)*NB) */ - i__3 = *lwork - iwork + 1; - dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[ - itauq], &work[itaup], &work[iwork], &i__3, &ierr); + i__3 = *lwork - iwork + 1; + dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[ + itauq], &work[itaup], &work[iwork], &i__3, &ierr); /* Generate right vectors bidiagonalizing A */ /* (Workspace: need 4*M, prefer 3*M + M*NB) */ - i__3 = *lwork - iwork + 1; - dorgbr_((char *)"P", m, n, m, &a[a_offset], lda, &work[itaup], & - work[iwork], &i__3, &ierr, (ftnlen)1); - iwork = ie + *m; + i__3 = *lwork - iwork + 1; + dorgbr_((char *)"P", m, n, m, &a[a_offset], lda, &work[itaup], & + work[iwork], &i__3, &ierr, (ftnlen)1); + iwork = ie + *m; /* Perform bidiagonal QR iteration, computing right */ /* singular vectors of A in A */ /* (Workspace: need BDSPAC) */ - dbdsqr_((char *)"L", m, n, &c__0, &c__0, &s[1], &work[ie], &a[ - a_offset], lda, dum, &c__1, dum, &c__1, &work[ - iwork], info, (ftnlen)1); + dbdsqr_((char *)"L", m, n, &c__0, &c__0, &s[1], &work[ie], &a[ + a_offset], lda, dum, &c__1, dum, &c__1, &work[ + iwork], info, (ftnlen)1); - } + } - } else if (wntvo && wntuas) { + } else if (wntvo && wntuas) { /* Path 3t(N much larger than M, JOBU='S' or 'A', JOBVT='O') */ /* M right singular vectors to be overwritten on A and */ /* M left singular vectors to be computed in U */ /* Computing MAX */ - i__3 = *m << 2; - if (*lwork >= *m * *m + max(i__3,bdspac)) { + i__3 = *m << 2; + if (*lwork >= *m * *m + max(i__3,bdspac)) { /* Sufficient workspace for a fast algorithm */ - ir = 1; + ir = 1; /* Computing MAX */ - i__3 = wrkbl, i__2 = *lda * *n + *m; - if (*lwork >= max(i__3,i__2) + *lda * *m) { + i__3 = wrkbl, i__2 = *lda * *n + *m; + if (*lwork >= max(i__3,i__2) + *lda * *m) { /* WORK(IU) is LDA by N and WORK(IR) is LDA by M */ - ldwrku = *lda; - chunk = *n; - ldwrkr = *lda; - } else /* if(complicated condition) */ { + ldwrku = *lda; + chunk = *n; + ldwrkr = *lda; + } else /* if(complicated condition) */ { /* Computing MAX */ - i__3 = wrkbl, i__2 = *lda * *n + *m; - if (*lwork >= max(i__3,i__2) + *m * *m) { + i__3 = wrkbl, i__2 = *lda * *n + *m; + if (*lwork >= max(i__3,i__2) + *m * *m) { /* WORK(IU) is LDA by N and WORK(IR) is M by M */ - ldwrku = *lda; - chunk = *n; - ldwrkr = *m; - } else { + ldwrku = *lda; + chunk = *n; + ldwrkr = *m; + } else { /* WORK(IU) is M by CHUNK and WORK(IR) is M by M */ - ldwrku = *m; - chunk = (*lwork - *m * *m - *m) / *m; - ldwrkr = *m; - } - } - itau = ir + ldwrkr * *m; - iwork = itau + *m; + ldwrku = *m; + chunk = (*lwork - *m * *m - *m) / *m; + ldwrkr = *m; + } + } + itau = ir + ldwrkr * *m; + iwork = itau + *m; /* Compute A=L*Q */ /* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */ - i__3 = *lwork - iwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork] - , &i__3, &ierr); + i__3 = *lwork - iwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork] + , &i__3, &ierr); /* Copy L to U, zeroing about above it */ - dlacpy_((char *)"L", m, m, &a[a_offset], lda, &u[u_offset], ldu, ( - ftnlen)1); - i__3 = *m - 1; - i__2 = *m - 1; - dlaset_((char *)"U", &i__3, &i__2, &c_b57, &c_b57, &u[(u_dim1 << - 1) + 1], ldu, (ftnlen)1); + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &u[u_offset], ldu, ( + ftnlen)1); + i__3 = *m - 1; + i__2 = *m - 1; + dlaset_((char *)"U", &i__3, &i__2, &c_b57, &c_b57, &u[(u_dim1 << + 1) + 1], ldu, (ftnlen)1); /* Generate Q in A */ /* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */ - i__3 = *lwork - iwork + 1; - dorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__3, &ierr); - ie = itau; - itauq = ie + *m; - itaup = itauq + *m; - iwork = itaup + *m; + i__3 = *lwork - iwork + 1; + dorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__3, &ierr); + ie = itau; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; /* Bidiagonalize L in U, copying result to WORK(IR) */ /* (Workspace: need M*M + 4*M, prefer M*M + 3*M + 2*M*NB) */ - i__3 = *lwork - iwork + 1; - dgebrd_(m, m, &u[u_offset], ldu, &s[1], &work[ie], &work[ - itauq], &work[itaup], &work[iwork], &i__3, &ierr); - dlacpy_((char *)"U", m, m, &u[u_offset], ldu, &work[ir], &ldwrkr, - (ftnlen)1); + i__3 = *lwork - iwork + 1; + dgebrd_(m, m, &u[u_offset], ldu, &s[1], &work[ie], &work[ + itauq], &work[itaup], &work[iwork], &i__3, &ierr); + dlacpy_((char *)"U", m, m, &u[u_offset], ldu, &work[ir], &ldwrkr, + (ftnlen)1); /* Generate right vectors bidiagonalizing L in WORK(IR) */ /* (Workspace: need M*M + 4*M-1, prefer M*M + 3*M + (M-1)*NB) */ - i__3 = *lwork - iwork + 1; - dorgbr_((char *)"P", m, m, m, &work[ir], &ldwrkr, &work[itaup], & - work[iwork], &i__3, &ierr, (ftnlen)1); + i__3 = *lwork - iwork + 1; + dorgbr_((char *)"P", m, m, m, &work[ir], &ldwrkr, &work[itaup], & + work[iwork], &i__3, &ierr, (ftnlen)1); /* Generate left vectors bidiagonalizing L in U */ /* (Workspace: need M*M + 4*M, prefer M*M + 3*M + M*NB) */ - i__3 = *lwork - iwork + 1; - dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq], & - work[iwork], &i__3, &ierr, (ftnlen)1); - iwork = ie + *m; + i__3 = *lwork - iwork + 1; + dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq], & + work[iwork], &i__3, &ierr, (ftnlen)1); + iwork = ie + *m; /* Perform bidiagonal QR iteration, computing left */ /* singular vectors of L in U, and computing right */ /* singular vectors of L in WORK(IR) */ /* (Workspace: need M*M + BDSPAC) */ - dbdsqr_((char *)"U", m, m, m, &c__0, &s[1], &work[ie], &work[ir], - &ldwrkr, &u[u_offset], ldu, dum, &c__1, &work[ - iwork], info, (ftnlen)1); - iu = ie + *m; + dbdsqr_((char *)"U", m, m, m, &c__0, &s[1], &work[ie], &work[ir], + &ldwrkr, &u[u_offset], ldu, dum, &c__1, &work[ + iwork], info, (ftnlen)1); + iu = ie + *m; /* Multiply right singular vectors of L in WORK(IR) by Q */ /* in A, storing result in WORK(IU) and copying to A */ /* (Workspace: need M*M + 2*M, prefer M*M + M*N + M)) */ - i__3 = *n; - i__2 = chunk; - for (i__ = 1; i__2 < 0 ? i__ >= i__3 : i__ <= i__3; i__ += - i__2) { + i__3 = *n; + i__2 = chunk; + for (i__ = 1; i__2 < 0 ? i__ >= i__3 : i__ <= i__3; i__ += + i__2) { /* Computing MIN */ - i__4 = *n - i__ + 1; - blk = min(i__4,chunk); - dgemm_((char *)"N", (char *)"N", m, &blk, m, &c_b79, &work[ir], & - ldwrkr, &a[i__ * a_dim1 + 1], lda, &c_b57, & - work[iu], &ldwrku, (ftnlen)1, (ftnlen)1); - dlacpy_((char *)"F", m, &blk, &work[iu], &ldwrku, &a[i__ * - a_dim1 + 1], lda, (ftnlen)1); + i__4 = *n - i__ + 1; + blk = min(i__4,chunk); + dgemm_((char *)"N", (char *)"N", m, &blk, m, &c_b79, &work[ir], & + ldwrkr, &a[i__ * a_dim1 + 1], lda, &c_b57, & + work[iu], &ldwrku, (ftnlen)1, (ftnlen)1); + dlacpy_((char *)"F", m, &blk, &work[iu], &ldwrku, &a[i__ * + a_dim1 + 1], lda, (ftnlen)1); /* L40: */ - } + } - } else { + } else { /* Insufficient workspace for a fast algorithm */ - itau = 1; - iwork = itau + *m; + itau = 1; + iwork = itau + *m; /* Compute A=L*Q */ /* (Workspace: need 2*M, prefer M + M*NB) */ - i__2 = *lwork - iwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork] - , &i__2, &ierr); + i__2 = *lwork - iwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork] + , &i__2, &ierr); /* Copy L to U, zeroing out above it */ - dlacpy_((char *)"L", m, m, &a[a_offset], lda, &u[u_offset], ldu, ( - ftnlen)1); - i__2 = *m - 1; - i__3 = *m - 1; - dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &u[(u_dim1 << - 1) + 1], ldu, (ftnlen)1); + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &u[u_offset], ldu, ( + ftnlen)1); + i__2 = *m - 1; + i__3 = *m - 1; + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &u[(u_dim1 << + 1) + 1], ldu, (ftnlen)1); /* Generate Q in A */ /* (Workspace: need 2*M, prefer M + M*NB) */ - i__2 = *lwork - iwork + 1; - dorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - ie = itau; - itauq = ie + *m; - itaup = itauq + *m; - iwork = itaup + *m; + i__2 = *lwork - iwork + 1; + dorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; /* Bidiagonalize L in U */ /* (Workspace: need 4*M, prefer 3*M + 2*M*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(m, m, &u[u_offset], ldu, &s[1], &work[ie], &work[ - itauq], &work[itaup], &work[iwork], &i__2, &ierr); + i__2 = *lwork - iwork + 1; + dgebrd_(m, m, &u[u_offset], ldu, &s[1], &work[ie], &work[ + itauq], &work[itaup], &work[iwork], &i__2, &ierr); /* Multiply right vectors bidiagonalizing L by Q in A */ /* (Workspace: need 3*M + N, prefer 3*M + N*NB) */ - i__2 = *lwork - iwork + 1; - dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &u[u_offset], ldu, &work[ - itaup], &a[a_offset], lda, &work[iwork], &i__2, & - ierr, (ftnlen)1, (ftnlen)1, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &u[u_offset], ldu, &work[ + itaup], &a[a_offset], lda, &work[iwork], &i__2, & + ierr, (ftnlen)1, (ftnlen)1, (ftnlen)1); /* Generate left vectors bidiagonalizing L in U */ /* (Workspace: need 4*M, prefer 3*M + M*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq], & - work[iwork], &i__2, &ierr, (ftnlen)1); - iwork = ie + *m; + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq], & + work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *m; /* Perform bidiagonal QR iteration, computing left */ /* singular vectors of A in U and computing right */ /* singular vectors of A in A */ /* (Workspace: need BDSPAC) */ - dbdsqr_((char *)"U", m, n, m, &c__0, &s[1], &work[ie], &a[ - a_offset], lda, &u[u_offset], ldu, dum, &c__1, & - work[iwork], info, (ftnlen)1); + dbdsqr_((char *)"U", m, n, m, &c__0, &s[1], &work[ie], &a[ + a_offset], lda, &u[u_offset], ldu, dum, &c__1, & + work[iwork], info, (ftnlen)1); - } + } - } else if (wntvs) { + } else if (wntvs) { - if (wntun) { + if (wntun) { /* Path 4t(N much larger than M, JOBU='N', JOBVT='S') */ /* M right singular vectors to be computed in VT and */ /* no left singular vectors to be computed */ /* Computing MAX */ - i__2 = *m << 2; - if (*lwork >= *m * *m + max(i__2,bdspac)) { + i__2 = *m << 2; + if (*lwork >= *m * *m + max(i__2,bdspac)) { /* Sufficient workspace for a fast algorithm */ - ir = 1; - if (*lwork >= wrkbl + *lda * *m) { + ir = 1; + if (*lwork >= wrkbl + *lda * *m) { /* WORK(IR) is LDA by M */ - ldwrkr = *lda; - } else { + ldwrkr = *lda; + } else { /* WORK(IR) is M by M */ - ldwrkr = *m; - } - itau = ir + ldwrkr * *m; - iwork = itau + *m; + ldwrkr = *m; + } + itau = ir + ldwrkr * *m; + iwork = itau + *m; /* Compute A=L*Q */ /* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */ - i__2 = *lwork - iwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); + i__2 = *lwork - iwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); /* Copy L to WORK(IR), zeroing out above it */ - dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[ir], & - ldwrkr, (ftnlen)1); - i__2 = *m - 1; - i__3 = *m - 1; - dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[ir + - ldwrkr], &ldwrkr, (ftnlen)1); + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[ir], & + ldwrkr, (ftnlen)1); + i__2 = *m - 1; + i__3 = *m - 1; + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[ir + + ldwrkr], &ldwrkr, (ftnlen)1); /* Generate Q in A */ /* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */ - i__2 = *lwork - iwork + 1; - dorglq_(m, n, m, &a[a_offset], lda, &work[itau], & - work[iwork], &i__2, &ierr); - ie = itau; - itauq = ie + *m; - itaup = itauq + *m; - iwork = itaup + *m; + i__2 = *lwork - iwork + 1; + dorglq_(m, n, m, &a[a_offset], lda, &work[itau], & + work[iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; /* Bidiagonalize L in WORK(IR) */ /* (Workspace: need M*M + 4*M, prefer M*M + 3*M + 2*M*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); + i__2 = *lwork - iwork + 1; + dgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); /* Generate right vectors bidiagonalizing L in */ /* WORK(IR) */ /* (Workspace: need M*M + 4*M, prefer M*M + 3*M + (M-1)*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", m, m, m, &work[ir], &ldwrkr, &work[itaup] - , &work[iwork], &i__2, &ierr, (ftnlen)1); - iwork = ie + *m; + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", m, m, m, &work[ir], &ldwrkr, &work[itaup] + , &work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *m; /* Perform bidiagonal QR iteration, computing right */ /* singular vectors of L in WORK(IR) */ /* (Workspace: need M*M + BDSPAC) */ - dbdsqr_((char *)"U", m, m, &c__0, &c__0, &s[1], &work[ie], & - work[ir], &ldwrkr, dum, &c__1, dum, &c__1, & - work[iwork], info, (ftnlen)1); + dbdsqr_((char *)"U", m, m, &c__0, &c__0, &s[1], &work[ie], & + work[ir], &ldwrkr, dum, &c__1, dum, &c__1, & + work[iwork], info, (ftnlen)1); /* Multiply right singular vectors of L in WORK(IR) by */ /* Q in A, storing result in VT */ /* (Workspace: need M*M) */ - dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[ir], &ldwrkr, - &a[a_offset], lda, &c_b57, &vt[vt_offset], - ldvt, (ftnlen)1, (ftnlen)1); + dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[ir], &ldwrkr, + &a[a_offset], lda, &c_b57, &vt[vt_offset], + ldvt, (ftnlen)1, (ftnlen)1); - } else { + } else { /* Insufficient workspace for a fast algorithm */ - itau = 1; - iwork = itau + *m; + itau = 1; + iwork = itau + *m; /* Compute A=L*Q */ /* (Workspace: need 2*M, prefer M + M*NB) */ - i__2 = *lwork - iwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); + i__2 = *lwork - iwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); /* Copy result to VT */ - dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], - ldvt, (ftnlen)1); + dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], + ldvt, (ftnlen)1); /* Generate Q in VT */ /* (Workspace: need 2*M, prefer M + M*NB) */ - i__2 = *lwork - iwork + 1; - dorglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], & - work[iwork], &i__2, &ierr); - ie = itau; - itauq = ie + *m; - itaup = itauq + *m; - iwork = itaup + *m; + i__2 = *lwork - iwork + 1; + dorglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], & + work[iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; /* Zero out above L in A */ - i__2 = *m - 1; - i__3 = *m - 1; - dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &a[(a_dim1 - << 1) + 1], lda, (ftnlen)1); + i__2 = *m - 1; + i__3 = *m - 1; + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &a[(a_dim1 + << 1) + 1], lda, (ftnlen)1); /* Bidiagonalize L in A */ /* (Workspace: need 4*M, prefer 3*M + 2*M*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); + i__2 = *lwork - iwork + 1; + dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); /* Multiply right vectors bidiagonalizing L by Q in VT */ /* (Workspace: need 3*M + N, prefer 3*M + N*NB) */ - i__2 = *lwork - iwork + 1; - dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &a[a_offset], lda, & - work[itaup], &vt[vt_offset], ldvt, &work[ - iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, ( - ftnlen)1); - iwork = ie + *m; + i__2 = *lwork - iwork + 1; + dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &a[a_offset], lda, & + work[itaup], &vt[vt_offset], ldvt, &work[ + iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, ( + ftnlen)1); + iwork = ie + *m; /* Perform bidiagonal QR iteration, computing right */ /* singular vectors of A in VT */ /* (Workspace: need BDSPAC) */ - dbdsqr_((char *)"U", m, n, &c__0, &c__0, &s[1], &work[ie], & - vt[vt_offset], ldvt, dum, &c__1, dum, &c__1, & - work[iwork], info, (ftnlen)1); + dbdsqr_((char *)"U", m, n, &c__0, &c__0, &s[1], &work[ie], & + vt[vt_offset], ldvt, dum, &c__1, dum, &c__1, & + work[iwork], info, (ftnlen)1); - } + } - } else if (wntuo) { + } else if (wntuo) { /* Path 5t(N much larger than M, JOBU='O', JOBVT='S') */ /* M right singular vectors to be computed in VT and */ /* M left singular vectors to be overwritten on A */ /* Computing MAX */ - i__2 = *m << 2; - if (*lwork >= (*m << 1) * *m + max(i__2,bdspac)) { + i__2 = *m << 2; + if (*lwork >= (*m << 1) * *m + max(i__2,bdspac)) { /* Sufficient workspace for a fast algorithm */ - iu = 1; - if (*lwork >= wrkbl + (*lda << 1) * *m) { + iu = 1; + if (*lwork >= wrkbl + (*lda << 1) * *m) { /* WORK(IU) is LDA by M and WORK(IR) is LDA by M */ - ldwrku = *lda; - ir = iu + ldwrku * *m; - ldwrkr = *lda; - } else if (*lwork >= wrkbl + (*lda + *m) * *m) { + ldwrku = *lda; + ir = iu + ldwrku * *m; + ldwrkr = *lda; + } else if (*lwork >= wrkbl + (*lda + *m) * *m) { /* WORK(IU) is LDA by M and WORK(IR) is M by M */ - ldwrku = *lda; - ir = iu + ldwrku * *m; - ldwrkr = *m; - } else { + ldwrku = *lda; + ir = iu + ldwrku * *m; + ldwrkr = *m; + } else { /* WORK(IU) is M by M and WORK(IR) is M by M */ - ldwrku = *m; - ir = iu + ldwrku * *m; - ldwrkr = *m; - } - itau = ir + ldwrkr * *m; - iwork = itau + *m; + ldwrku = *m; + ir = iu + ldwrku * *m; + ldwrkr = *m; + } + itau = ir + ldwrkr * *m; + iwork = itau + *m; /* Compute A=L*Q */ /* (Workspace: need 2*M*M + 2*M, prefer 2*M*M + M + M*NB) */ - i__2 = *lwork - iwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); + i__2 = *lwork - iwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); /* Copy L to WORK(IU), zeroing out below it */ - dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[iu], & - ldwrku, (ftnlen)1); - i__2 = *m - 1; - i__3 = *m - 1; - dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[iu + - ldwrku], &ldwrku, (ftnlen)1); + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[iu], & + ldwrku, (ftnlen)1); + i__2 = *m - 1; + i__3 = *m - 1; + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[iu + + ldwrku], &ldwrku, (ftnlen)1); /* Generate Q in A */ /* (Workspace: need 2*M*M + 2*M, prefer 2*M*M + M + M*NB) */ - i__2 = *lwork - iwork + 1; - dorglq_(m, n, m, &a[a_offset], lda, &work[itau], & - work[iwork], &i__2, &ierr); - ie = itau; - itauq = ie + *m; - itaup = itauq + *m; - iwork = itaup + *m; + i__2 = *lwork - iwork + 1; + dorglq_(m, n, m, &a[a_offset], lda, &work[itau], & + work[iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; /* Bidiagonalize L in WORK(IU), copying result to */ /* WORK(IR) */ /* (Workspace: need 2*M*M + 4*M, */ /* prefer 2*M*M+3*M+2*M*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(m, m, &work[iu], &ldwrku, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); - dlacpy_((char *)"L", m, m, &work[iu], &ldwrku, &work[ir], & - ldwrkr, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dgebrd_(m, m, &work[iu], &ldwrku, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); + dlacpy_((char *)"L", m, m, &work[iu], &ldwrku, &work[ir], & + ldwrkr, (ftnlen)1); /* Generate right bidiagonalizing vectors in WORK(IU) */ /* (Workspace: need 2*M*M + 4*M-1, */ /* prefer 2*M*M+3*M+(M-1)*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", m, m, m, &work[iu], &ldwrku, &work[itaup] - , &work[iwork], &i__2, &ierr, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", m, m, m, &work[iu], &ldwrku, &work[itaup] + , &work[iwork], &i__2, &ierr, (ftnlen)1); /* Generate left bidiagonalizing vectors in WORK(IR) */ /* (Workspace: need 2*M*M + 4*M, prefer 2*M*M + 3*M + M*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", m, m, m, &work[ir], &ldwrkr, &work[itauq] - , &work[iwork], &i__2, &ierr, (ftnlen)1); - iwork = ie + *m; + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", m, m, m, &work[ir], &ldwrkr, &work[itauq] + , &work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *m; /* Perform bidiagonal QR iteration, computing left */ /* singular vectors of L in WORK(IR) and computing */ /* right singular vectors of L in WORK(IU) */ /* (Workspace: need 2*M*M + BDSPAC) */ - dbdsqr_((char *)"U", m, m, m, &c__0, &s[1], &work[ie], &work[ - iu], &ldwrku, &work[ir], &ldwrkr, dum, &c__1, - &work[iwork], info, (ftnlen)1); + dbdsqr_((char *)"U", m, m, m, &c__0, &s[1], &work[ie], &work[ + iu], &ldwrku, &work[ir], &ldwrkr, dum, &c__1, + &work[iwork], info, (ftnlen)1); /* Multiply right singular vectors of L in WORK(IU) by */ /* Q in A, storing result in VT */ /* (Workspace: need M*M) */ - dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[iu], &ldwrku, - &a[a_offset], lda, &c_b57, &vt[vt_offset], - ldvt, (ftnlen)1, (ftnlen)1); + dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[iu], &ldwrku, + &a[a_offset], lda, &c_b57, &vt[vt_offset], + ldvt, (ftnlen)1, (ftnlen)1); /* Copy left singular vectors of L to A */ /* (Workspace: need M*M) */ - dlacpy_((char *)"F", m, m, &work[ir], &ldwrkr, &a[a_offset], - lda, (ftnlen)1); + dlacpy_((char *)"F", m, m, &work[ir], &ldwrkr, &a[a_offset], + lda, (ftnlen)1); - } else { + } else { /* Insufficient workspace for a fast algorithm */ - itau = 1; - iwork = itau + *m; + itau = 1; + iwork = itau + *m; /* Compute A=L*Q, copying result to VT */ /* (Workspace: need 2*M, prefer M + M*NB) */ - i__2 = *lwork - iwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], - ldvt, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], + ldvt, (ftnlen)1); /* Generate Q in VT */ /* (Workspace: need 2*M, prefer M + M*NB) */ - i__2 = *lwork - iwork + 1; - dorglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], & - work[iwork], &i__2, &ierr); - ie = itau; - itauq = ie + *m; - itaup = itauq + *m; - iwork = itaup + *m; + i__2 = *lwork - iwork + 1; + dorglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], & + work[iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; /* Zero out above L in A */ - i__2 = *m - 1; - i__3 = *m - 1; - dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &a[(a_dim1 - << 1) + 1], lda, (ftnlen)1); + i__2 = *m - 1; + i__3 = *m - 1; + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &a[(a_dim1 + << 1) + 1], lda, (ftnlen)1); /* Bidiagonalize L in A */ /* (Workspace: need 4*M, prefer 3*M + 2*M*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); + i__2 = *lwork - iwork + 1; + dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); /* Multiply right vectors bidiagonalizing L by Q in VT */ /* (Workspace: need 3*M + N, prefer 3*M + N*NB) */ - i__2 = *lwork - iwork + 1; - dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &a[a_offset], lda, & - work[itaup], &vt[vt_offset], ldvt, &work[ - iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, ( - ftnlen)1); + i__2 = *lwork - iwork + 1; + dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &a[a_offset], lda, & + work[itaup], &vt[vt_offset], ldvt, &work[ + iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, ( + ftnlen)1); /* Generate left bidiagonalizing vectors of L in A */ /* (Workspace: need 4*M, prefer 3*M + M*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", m, m, m, &a[a_offset], lda, &work[itauq], - &work[iwork], &i__2, &ierr, (ftnlen)1); - iwork = ie + *m; + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", m, m, m, &a[a_offset], lda, &work[itauq], + &work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *m; /* Perform bidiagonal QR iteration, compute left */ /* singular vectors of A in A and compute right */ /* singular vectors of A in VT */ /* (Workspace: need BDSPAC) */ - dbdsqr_((char *)"U", m, n, m, &c__0, &s[1], &work[ie], &vt[ - vt_offset], ldvt, &a[a_offset], lda, dum, & - c__1, &work[iwork], info, (ftnlen)1); + dbdsqr_((char *)"U", m, n, m, &c__0, &s[1], &work[ie], &vt[ + vt_offset], ldvt, &a[a_offset], lda, dum, & + c__1, &work[iwork], info, (ftnlen)1); - } + } - } else if (wntuas) { + } else if (wntuas) { /* Path 6t(N much larger than M, JOBU='S' or 'A', */ /* JOBVT='S') */ @@ -3286,524 +3286,524 @@ f"> */ /* M left singular vectors to be computed in U */ /* Computing MAX */ - i__2 = *m << 2; - if (*lwork >= *m * *m + max(i__2,bdspac)) { + i__2 = *m << 2; + if (*lwork >= *m * *m + max(i__2,bdspac)) { /* Sufficient workspace for a fast algorithm */ - iu = 1; - if (*lwork >= wrkbl + *lda * *m) { + iu = 1; + if (*lwork >= wrkbl + *lda * *m) { /* WORK(IU) is LDA by N */ - ldwrku = *lda; - } else { + ldwrku = *lda; + } else { /* WORK(IU) is LDA by M */ - ldwrku = *m; - } - itau = iu + ldwrku * *m; - iwork = itau + *m; + ldwrku = *m; + } + itau = iu + ldwrku * *m; + iwork = itau + *m; /* Compute A=L*Q */ /* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */ - i__2 = *lwork - iwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); + i__2 = *lwork - iwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); /* Copy L to WORK(IU), zeroing out above it */ - dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[iu], & - ldwrku, (ftnlen)1); - i__2 = *m - 1; - i__3 = *m - 1; - dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[iu + - ldwrku], &ldwrku, (ftnlen)1); + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[iu], & + ldwrku, (ftnlen)1); + i__2 = *m - 1; + i__3 = *m - 1; + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[iu + + ldwrku], &ldwrku, (ftnlen)1); /* Generate Q in A */ /* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */ - i__2 = *lwork - iwork + 1; - dorglq_(m, n, m, &a[a_offset], lda, &work[itau], & - work[iwork], &i__2, &ierr); - ie = itau; - itauq = ie + *m; - itaup = itauq + *m; - iwork = itaup + *m; + i__2 = *lwork - iwork + 1; + dorglq_(m, n, m, &a[a_offset], lda, &work[itau], & + work[iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; /* Bidiagonalize L in WORK(IU), copying result to U */ /* (Workspace: need M*M + 4*M, prefer M*M + 3*M + 2*M*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(m, m, &work[iu], &ldwrku, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); - dlacpy_((char *)"L", m, m, &work[iu], &ldwrku, &u[u_offset], - ldu, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dgebrd_(m, m, &work[iu], &ldwrku, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); + dlacpy_((char *)"L", m, m, &work[iu], &ldwrku, &u[u_offset], + ldu, (ftnlen)1); /* Generate right bidiagonalizing vectors in WORK(IU) */ /* (Workspace: need M*M + 4*M-1, */ /* prefer M*M+3*M+(M-1)*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", m, m, m, &work[iu], &ldwrku, &work[itaup] - , &work[iwork], &i__2, &ierr, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", m, m, m, &work[iu], &ldwrku, &work[itaup] + , &work[iwork], &i__2, &ierr, (ftnlen)1); /* Generate left bidiagonalizing vectors in U */ /* (Workspace: need M*M + 4*M, prefer M*M + 3*M + M*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq], - &work[iwork], &i__2, &ierr, (ftnlen)1); - iwork = ie + *m; + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq], + &work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *m; /* Perform bidiagonal QR iteration, computing left */ /* singular vectors of L in U and computing right */ /* singular vectors of L in WORK(IU) */ /* (Workspace: need M*M + BDSPAC) */ - dbdsqr_((char *)"U", m, m, m, &c__0, &s[1], &work[ie], &work[ - iu], &ldwrku, &u[u_offset], ldu, dum, &c__1, & - work[iwork], info, (ftnlen)1); + dbdsqr_((char *)"U", m, m, m, &c__0, &s[1], &work[ie], &work[ + iu], &ldwrku, &u[u_offset], ldu, dum, &c__1, & + work[iwork], info, (ftnlen)1); /* Multiply right singular vectors of L in WORK(IU) by */ /* Q in A, storing result in VT */ /* (Workspace: need M*M) */ - dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[iu], &ldwrku, - &a[a_offset], lda, &c_b57, &vt[vt_offset], - ldvt, (ftnlen)1, (ftnlen)1); + dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[iu], &ldwrku, + &a[a_offset], lda, &c_b57, &vt[vt_offset], + ldvt, (ftnlen)1, (ftnlen)1); - } else { + } else { /* Insufficient workspace for a fast algorithm */ - itau = 1; - iwork = itau + *m; + itau = 1; + iwork = itau + *m; /* Compute A=L*Q, copying result to VT */ /* (Workspace: need 2*M, prefer M + M*NB) */ - i__2 = *lwork - iwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], - ldvt, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], + ldvt, (ftnlen)1); /* Generate Q in VT */ /* (Workspace: need 2*M, prefer M + M*NB) */ - i__2 = *lwork - iwork + 1; - dorglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], & - work[iwork], &i__2, &ierr); + i__2 = *lwork - iwork + 1; + dorglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], & + work[iwork], &i__2, &ierr); /* Copy L to U, zeroing out above it */ - dlacpy_((char *)"L", m, m, &a[a_offset], lda, &u[u_offset], - ldu, (ftnlen)1); - i__2 = *m - 1; - i__3 = *m - 1; - dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &u[(u_dim1 - << 1) + 1], ldu, (ftnlen)1); - ie = itau; - itauq = ie + *m; - itaup = itauq + *m; - iwork = itaup + *m; + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &u[u_offset], + ldu, (ftnlen)1); + i__2 = *m - 1; + i__3 = *m - 1; + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &u[(u_dim1 + << 1) + 1], ldu, (ftnlen)1); + ie = itau; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; /* Bidiagonalize L in U */ /* (Workspace: need 4*M, prefer 3*M + 2*M*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(m, m, &u[u_offset], ldu, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); + i__2 = *lwork - iwork + 1; + dgebrd_(m, m, &u[u_offset], ldu, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); /* Multiply right bidiagonalizing vectors in U by Q */ /* in VT */ /* (Workspace: need 3*M + N, prefer 3*M + N*NB) */ - i__2 = *lwork - iwork + 1; - dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &u[u_offset], ldu, & - work[itaup], &vt[vt_offset], ldvt, &work[ - iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, ( - ftnlen)1); + i__2 = *lwork - iwork + 1; + dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &u[u_offset], ldu, & + work[itaup], &vt[vt_offset], ldvt, &work[ + iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, ( + ftnlen)1); /* Generate left bidiagonalizing vectors in U */ /* (Workspace: need 4*M, prefer 3*M + M*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq], - &work[iwork], &i__2, &ierr, (ftnlen)1); - iwork = ie + *m; + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq], + &work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *m; /* Perform bidiagonal QR iteration, computing left */ /* singular vectors of A in U and computing right */ /* singular vectors of A in VT */ /* (Workspace: need BDSPAC) */ - dbdsqr_((char *)"U", m, n, m, &c__0, &s[1], &work[ie], &vt[ - vt_offset], ldvt, &u[u_offset], ldu, dum, & - c__1, &work[iwork], info, (ftnlen)1); + dbdsqr_((char *)"U", m, n, m, &c__0, &s[1], &work[ie], &vt[ + vt_offset], ldvt, &u[u_offset], ldu, dum, & + c__1, &work[iwork], info, (ftnlen)1); - } + } - } + } - } else if (wntva) { + } else if (wntva) { - if (wntun) { + if (wntun) { /* Path 7t(N much larger than M, JOBU='N', JOBVT='A') */ /* N right singular vectors to be computed in VT and */ /* no left singular vectors to be computed */ /* Computing MAX */ - i__2 = *n + *m, i__3 = *m << 2, i__2 = max(i__2,i__3); - if (*lwork >= *m * *m + max(i__2,bdspac)) { + i__2 = *n + *m, i__3 = *m << 2, i__2 = max(i__2,i__3); + if (*lwork >= *m * *m + max(i__2,bdspac)) { /* Sufficient workspace for a fast algorithm */ - ir = 1; - if (*lwork >= wrkbl + *lda * *m) { + ir = 1; + if (*lwork >= wrkbl + *lda * *m) { /* WORK(IR) is LDA by M */ - ldwrkr = *lda; - } else { + ldwrkr = *lda; + } else { /* WORK(IR) is M by M */ - ldwrkr = *m; - } - itau = ir + ldwrkr * *m; - iwork = itau + *m; + ldwrkr = *m; + } + itau = ir + ldwrkr * *m; + iwork = itau + *m; /* Compute A=L*Q, copying result to VT */ /* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */ - i__2 = *lwork - iwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], - ldvt, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], + ldvt, (ftnlen)1); /* Copy L to WORK(IR), zeroing out above it */ - dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[ir], & - ldwrkr, (ftnlen)1); - i__2 = *m - 1; - i__3 = *m - 1; - dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[ir + - ldwrkr], &ldwrkr, (ftnlen)1); + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[ir], & + ldwrkr, (ftnlen)1); + i__2 = *m - 1; + i__3 = *m - 1; + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[ir + + ldwrkr], &ldwrkr, (ftnlen)1); /* Generate Q in VT */ /* (Workspace: need M*M + M + N, prefer M*M + M + N*NB) */ - i__2 = *lwork - iwork + 1; - dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], & - work[iwork], &i__2, &ierr); - ie = itau; - itauq = ie + *m; - itaup = itauq + *m; - iwork = itaup + *m; + i__2 = *lwork - iwork + 1; + dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], & + work[iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; /* Bidiagonalize L in WORK(IR) */ /* (Workspace: need M*M + 4*M, prefer M*M + 3*M + 2*M*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); + i__2 = *lwork - iwork + 1; + dgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); /* Generate right bidiagonalizing vectors in WORK(IR) */ /* (Workspace: need M*M + 4*M-1, */ /* prefer M*M+3*M+(M-1)*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", m, m, m, &work[ir], &ldwrkr, &work[itaup] - , &work[iwork], &i__2, &ierr, (ftnlen)1); - iwork = ie + *m; + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", m, m, m, &work[ir], &ldwrkr, &work[itaup] + , &work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *m; /* Perform bidiagonal QR iteration, computing right */ /* singular vectors of L in WORK(IR) */ /* (Workspace: need M*M + BDSPAC) */ - dbdsqr_((char *)"U", m, m, &c__0, &c__0, &s[1], &work[ie], & - work[ir], &ldwrkr, dum, &c__1, dum, &c__1, & - work[iwork], info, (ftnlen)1); + dbdsqr_((char *)"U", m, m, &c__0, &c__0, &s[1], &work[ie], & + work[ir], &ldwrkr, dum, &c__1, dum, &c__1, & + work[iwork], info, (ftnlen)1); /* Multiply right singular vectors of L in WORK(IR) by */ /* Q in VT, storing result in A */ /* (Workspace: need M*M) */ - dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[ir], &ldwrkr, - &vt[vt_offset], ldvt, &c_b57, &a[a_offset], - lda, (ftnlen)1, (ftnlen)1); + dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[ir], &ldwrkr, + &vt[vt_offset], ldvt, &c_b57, &a[a_offset], + lda, (ftnlen)1, (ftnlen)1); /* Copy right singular vectors of A from A to VT */ - dlacpy_((char *)"F", m, n, &a[a_offset], lda, &vt[vt_offset], - ldvt, (ftnlen)1); + dlacpy_((char *)"F", m, n, &a[a_offset], lda, &vt[vt_offset], + ldvt, (ftnlen)1); - } else { + } else { /* Insufficient workspace for a fast algorithm */ - itau = 1; - iwork = itau + *m; + itau = 1; + iwork = itau + *m; /* Compute A=L*Q, copying result to VT */ /* (Workspace: need 2*M, prefer M + M*NB) */ - i__2 = *lwork - iwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], - ldvt, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], + ldvt, (ftnlen)1); /* Generate Q in VT */ /* (Workspace: need M + N, prefer M + N*NB) */ - i__2 = *lwork - iwork + 1; - dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], & - work[iwork], &i__2, &ierr); - ie = itau; - itauq = ie + *m; - itaup = itauq + *m; - iwork = itaup + *m; + i__2 = *lwork - iwork + 1; + dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], & + work[iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; /* Zero out above L in A */ - i__2 = *m - 1; - i__3 = *m - 1; - dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &a[(a_dim1 - << 1) + 1], lda, (ftnlen)1); + i__2 = *m - 1; + i__3 = *m - 1; + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &a[(a_dim1 + << 1) + 1], lda, (ftnlen)1); /* Bidiagonalize L in A */ /* (Workspace: need 4*M, prefer 3*M + 2*M*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); + i__2 = *lwork - iwork + 1; + dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); /* Multiply right bidiagonalizing vectors in A by Q */ /* in VT */ /* (Workspace: need 3*M + N, prefer 3*M + N*NB) */ - i__2 = *lwork - iwork + 1; - dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &a[a_offset], lda, & - work[itaup], &vt[vt_offset], ldvt, &work[ - iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, ( - ftnlen)1); - iwork = ie + *m; + i__2 = *lwork - iwork + 1; + dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &a[a_offset], lda, & + work[itaup], &vt[vt_offset], ldvt, &work[ + iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, ( + ftnlen)1); + iwork = ie + *m; /* Perform bidiagonal QR iteration, computing right */ /* singular vectors of A in VT */ /* (Workspace: need BDSPAC) */ - dbdsqr_((char *)"U", m, n, &c__0, &c__0, &s[1], &work[ie], & - vt[vt_offset], ldvt, dum, &c__1, dum, &c__1, & - work[iwork], info, (ftnlen)1); + dbdsqr_((char *)"U", m, n, &c__0, &c__0, &s[1], &work[ie], & + vt[vt_offset], ldvt, dum, &c__1, dum, &c__1, & + work[iwork], info, (ftnlen)1); - } + } - } else if (wntuo) { + } else if (wntuo) { /* Path 8t(N much larger than M, JOBU='O', JOBVT='A') */ /* N right singular vectors to be computed in VT and */ /* M left singular vectors to be overwritten on A */ /* Computing MAX */ - i__2 = *n + *m, i__3 = *m << 2, i__2 = max(i__2,i__3); - if (*lwork >= (*m << 1) * *m + max(i__2,bdspac)) { + i__2 = *n + *m, i__3 = *m << 2, i__2 = max(i__2,i__3); + if (*lwork >= (*m << 1) * *m + max(i__2,bdspac)) { /* Sufficient workspace for a fast algorithm */ - iu = 1; - if (*lwork >= wrkbl + (*lda << 1) * *m) { + iu = 1; + if (*lwork >= wrkbl + (*lda << 1) * *m) { /* WORK(IU) is LDA by M and WORK(IR) is LDA by M */ - ldwrku = *lda; - ir = iu + ldwrku * *m; - ldwrkr = *lda; - } else if (*lwork >= wrkbl + (*lda + *m) * *m) { + ldwrku = *lda; + ir = iu + ldwrku * *m; + ldwrkr = *lda; + } else if (*lwork >= wrkbl + (*lda + *m) * *m) { /* WORK(IU) is LDA by M and WORK(IR) is M by M */ - ldwrku = *lda; - ir = iu + ldwrku * *m; - ldwrkr = *m; - } else { + ldwrku = *lda; + ir = iu + ldwrku * *m; + ldwrkr = *m; + } else { /* WORK(IU) is M by M and WORK(IR) is M by M */ - ldwrku = *m; - ir = iu + ldwrku * *m; - ldwrkr = *m; - } - itau = ir + ldwrkr * *m; - iwork = itau + *m; + ldwrku = *m; + ir = iu + ldwrku * *m; + ldwrkr = *m; + } + itau = ir + ldwrkr * *m; + iwork = itau + *m; /* Compute A=L*Q, copying result to VT */ /* (Workspace: need 2*M*M + 2*M, prefer 2*M*M + M + M*NB) */ - i__2 = *lwork - iwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], - ldvt, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], + ldvt, (ftnlen)1); /* Generate Q in VT */ /* (Workspace: need 2*M*M + M + N, prefer 2*M*M + M + N*NB) */ - i__2 = *lwork - iwork + 1; - dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], & - work[iwork], &i__2, &ierr); + i__2 = *lwork - iwork + 1; + dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], & + work[iwork], &i__2, &ierr); /* Copy L to WORK(IU), zeroing out above it */ - dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[iu], & - ldwrku, (ftnlen)1); - i__2 = *m - 1; - i__3 = *m - 1; - dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[iu + - ldwrku], &ldwrku, (ftnlen)1); - ie = itau; - itauq = ie + *m; - itaup = itauq + *m; - iwork = itaup + *m; + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[iu], & + ldwrku, (ftnlen)1); + i__2 = *m - 1; + i__3 = *m - 1; + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[iu + + ldwrku], &ldwrku, (ftnlen)1); + ie = itau; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; /* Bidiagonalize L in WORK(IU), copying result to */ /* WORK(IR) */ /* (Workspace: need 2*M*M + 4*M, */ /* prefer 2*M*M+3*M+2*M*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(m, m, &work[iu], &ldwrku, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); - dlacpy_((char *)"L", m, m, &work[iu], &ldwrku, &work[ir], & - ldwrkr, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dgebrd_(m, m, &work[iu], &ldwrku, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); + dlacpy_((char *)"L", m, m, &work[iu], &ldwrku, &work[ir], & + ldwrkr, (ftnlen)1); /* Generate right bidiagonalizing vectors in WORK(IU) */ /* (Workspace: need 2*M*M + 4*M-1, */ /* prefer 2*M*M+3*M+(M-1)*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", m, m, m, &work[iu], &ldwrku, &work[itaup] - , &work[iwork], &i__2, &ierr, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", m, m, m, &work[iu], &ldwrku, &work[itaup] + , &work[iwork], &i__2, &ierr, (ftnlen)1); /* Generate left bidiagonalizing vectors in WORK(IR) */ /* (Workspace: need 2*M*M + 4*M, prefer 2*M*M + 3*M + M*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", m, m, m, &work[ir], &ldwrkr, &work[itauq] - , &work[iwork], &i__2, &ierr, (ftnlen)1); - iwork = ie + *m; + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", m, m, m, &work[ir], &ldwrkr, &work[itauq] + , &work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *m; /* Perform bidiagonal QR iteration, computing left */ /* singular vectors of L in WORK(IR) and computing */ /* right singular vectors of L in WORK(IU) */ /* (Workspace: need 2*M*M + BDSPAC) */ - dbdsqr_((char *)"U", m, m, m, &c__0, &s[1], &work[ie], &work[ - iu], &ldwrku, &work[ir], &ldwrkr, dum, &c__1, - &work[iwork], info, (ftnlen)1); + dbdsqr_((char *)"U", m, m, m, &c__0, &s[1], &work[ie], &work[ + iu], &ldwrku, &work[ir], &ldwrkr, dum, &c__1, + &work[iwork], info, (ftnlen)1); /* Multiply right singular vectors of L in WORK(IU) by */ /* Q in VT, storing result in A */ /* (Workspace: need M*M) */ - dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[iu], &ldwrku, - &vt[vt_offset], ldvt, &c_b57, &a[a_offset], - lda, (ftnlen)1, (ftnlen)1); + dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[iu], &ldwrku, + &vt[vt_offset], ldvt, &c_b57, &a[a_offset], + lda, (ftnlen)1, (ftnlen)1); /* Copy right singular vectors of A from A to VT */ - dlacpy_((char *)"F", m, n, &a[a_offset], lda, &vt[vt_offset], - ldvt, (ftnlen)1); + dlacpy_((char *)"F", m, n, &a[a_offset], lda, &vt[vt_offset], + ldvt, (ftnlen)1); /* Copy left singular vectors of A from WORK(IR) to A */ - dlacpy_((char *)"F", m, m, &work[ir], &ldwrkr, &a[a_offset], - lda, (ftnlen)1); + dlacpy_((char *)"F", m, m, &work[ir], &ldwrkr, &a[a_offset], + lda, (ftnlen)1); - } else { + } else { /* Insufficient workspace for a fast algorithm */ - itau = 1; - iwork = itau + *m; + itau = 1; + iwork = itau + *m; /* Compute A=L*Q, copying result to VT */ /* (Workspace: need 2*M, prefer M + M*NB) */ - i__2 = *lwork - iwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], - ldvt, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], + ldvt, (ftnlen)1); /* Generate Q in VT */ /* (Workspace: need M + N, prefer M + N*NB) */ - i__2 = *lwork - iwork + 1; - dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], & - work[iwork], &i__2, &ierr); - ie = itau; - itauq = ie + *m; - itaup = itauq + *m; - iwork = itaup + *m; + i__2 = *lwork - iwork + 1; + dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], & + work[iwork], &i__2, &ierr); + ie = itau; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; /* Zero out above L in A */ - i__2 = *m - 1; - i__3 = *m - 1; - dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &a[(a_dim1 - << 1) + 1], lda, (ftnlen)1); + i__2 = *m - 1; + i__3 = *m - 1; + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &a[(a_dim1 + << 1) + 1], lda, (ftnlen)1); /* Bidiagonalize L in A */ /* (Workspace: need 4*M, prefer 3*M + 2*M*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); + i__2 = *lwork - iwork + 1; + dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); /* Multiply right bidiagonalizing vectors in A by Q */ /* in VT */ /* (Workspace: need 3*M + N, prefer 3*M + N*NB) */ - i__2 = *lwork - iwork + 1; - dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &a[a_offset], lda, & - work[itaup], &vt[vt_offset], ldvt, &work[ - iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, ( - ftnlen)1); + i__2 = *lwork - iwork + 1; + dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &a[a_offset], lda, & + work[itaup], &vt[vt_offset], ldvt, &work[ + iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, ( + ftnlen)1); /* Generate left bidiagonalizing vectors in A */ /* (Workspace: need 4*M, prefer 3*M + M*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", m, m, m, &a[a_offset], lda, &work[itauq], - &work[iwork], &i__2, &ierr, (ftnlen)1); - iwork = ie + *m; + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", m, m, m, &a[a_offset], lda, &work[itauq], + &work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *m; /* Perform bidiagonal QR iteration, computing left */ /* singular vectors of A in A and computing right */ /* singular vectors of A in VT */ /* (Workspace: need BDSPAC) */ - dbdsqr_((char *)"U", m, n, m, &c__0, &s[1], &work[ie], &vt[ - vt_offset], ldvt, &a[a_offset], lda, dum, & - c__1, &work[iwork], info, (ftnlen)1); + dbdsqr_((char *)"U", m, n, m, &c__0, &s[1], &work[ie], &vt[ + vt_offset], ldvt, &a[a_offset], lda, dum, & + c__1, &work[iwork], info, (ftnlen)1); - } + } - } else if (wntuas) { + } else if (wntuas) { /* Path 9t(N much larger than M, JOBU='S' or 'A', */ /* JOBVT='A') */ @@ -3811,293 +3811,293 @@ f"> */ /* M left singular vectors to be computed in U */ /* Computing MAX */ - i__2 = *n + *m, i__3 = *m << 2, i__2 = max(i__2,i__3); - if (*lwork >= *m * *m + max(i__2,bdspac)) { + i__2 = *n + *m, i__3 = *m << 2, i__2 = max(i__2,i__3); + if (*lwork >= *m * *m + max(i__2,bdspac)) { /* Sufficient workspace for a fast algorithm */ - iu = 1; - if (*lwork >= wrkbl + *lda * *m) { + iu = 1; + if (*lwork >= wrkbl + *lda * *m) { /* WORK(IU) is LDA by M */ - ldwrku = *lda; - } else { + ldwrku = *lda; + } else { /* WORK(IU) is M by M */ - ldwrku = *m; - } - itau = iu + ldwrku * *m; - iwork = itau + *m; + ldwrku = *m; + } + itau = iu + ldwrku * *m; + iwork = itau + *m; /* Compute A=L*Q, copying result to VT */ /* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */ - i__2 = *lwork - iwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], - ldvt, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], + ldvt, (ftnlen)1); /* Generate Q in VT */ /* (Workspace: need M*M + M + N, prefer M*M + M + N*NB) */ - i__2 = *lwork - iwork + 1; - dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], & - work[iwork], &i__2, &ierr); + i__2 = *lwork - iwork + 1; + dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], & + work[iwork], &i__2, &ierr); /* Copy L to WORK(IU), zeroing out above it */ - dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[iu], & - ldwrku, (ftnlen)1); - i__2 = *m - 1; - i__3 = *m - 1; - dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[iu + - ldwrku], &ldwrku, (ftnlen)1); - ie = itau; - itauq = ie + *m; - itaup = itauq + *m; - iwork = itaup + *m; + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[iu], & + ldwrku, (ftnlen)1); + i__2 = *m - 1; + i__3 = *m - 1; + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[iu + + ldwrku], &ldwrku, (ftnlen)1); + ie = itau; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; /* Bidiagonalize L in WORK(IU), copying result to U */ /* (Workspace: need M*M + 4*M, prefer M*M + 3*M + 2*M*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(m, m, &work[iu], &ldwrku, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); - dlacpy_((char *)"L", m, m, &work[iu], &ldwrku, &u[u_offset], - ldu, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dgebrd_(m, m, &work[iu], &ldwrku, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); + dlacpy_((char *)"L", m, m, &work[iu], &ldwrku, &u[u_offset], + ldu, (ftnlen)1); /* Generate right bidiagonalizing vectors in WORK(IU) */ /* (Workspace: need M*M + 4*M, prefer M*M + 3*M + (M-1)*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", m, m, m, &work[iu], &ldwrku, &work[itaup] - , &work[iwork], &i__2, &ierr, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", m, m, m, &work[iu], &ldwrku, &work[itaup] + , &work[iwork], &i__2, &ierr, (ftnlen)1); /* Generate left bidiagonalizing vectors in U */ /* (Workspace: need M*M + 4*M, prefer M*M + 3*M + M*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq], - &work[iwork], &i__2, &ierr, (ftnlen)1); - iwork = ie + *m; + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq], + &work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *m; /* Perform bidiagonal QR iteration, computing left */ /* singular vectors of L in U and computing right */ /* singular vectors of L in WORK(IU) */ /* (Workspace: need M*M + BDSPAC) */ - dbdsqr_((char *)"U", m, m, m, &c__0, &s[1], &work[ie], &work[ - iu], &ldwrku, &u[u_offset], ldu, dum, &c__1, & - work[iwork], info, (ftnlen)1); + dbdsqr_((char *)"U", m, m, m, &c__0, &s[1], &work[ie], &work[ + iu], &ldwrku, &u[u_offset], ldu, dum, &c__1, & + work[iwork], info, (ftnlen)1); /* Multiply right singular vectors of L in WORK(IU) by */ /* Q in VT, storing result in A */ /* (Workspace: need M*M) */ - dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[iu], &ldwrku, - &vt[vt_offset], ldvt, &c_b57, &a[a_offset], - lda, (ftnlen)1, (ftnlen)1); + dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[iu], &ldwrku, + &vt[vt_offset], ldvt, &c_b57, &a[a_offset], + lda, (ftnlen)1, (ftnlen)1); /* Copy right singular vectors of A from A to VT */ - dlacpy_((char *)"F", m, n, &a[a_offset], lda, &vt[vt_offset], - ldvt, (ftnlen)1); + dlacpy_((char *)"F", m, n, &a[a_offset], lda, &vt[vt_offset], + ldvt, (ftnlen)1); - } else { + } else { /* Insufficient workspace for a fast algorithm */ - itau = 1; - iwork = itau + *m; + itau = 1; + iwork = itau + *m; /* Compute A=L*Q, copying result to VT */ /* (Workspace: need 2*M, prefer M + M*NB) */ - i__2 = *lwork - iwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], - ldvt, (ftnlen)1); + i__2 = *lwork - iwork + 1; + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ + iwork], &i__2, &ierr); + dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], + ldvt, (ftnlen)1); /* Generate Q in VT */ /* (Workspace: need M + N, prefer M + N*NB) */ - i__2 = *lwork - iwork + 1; - dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], & - work[iwork], &i__2, &ierr); + i__2 = *lwork - iwork + 1; + dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], & + work[iwork], &i__2, &ierr); /* Copy L to U, zeroing out above it */ - dlacpy_((char *)"L", m, m, &a[a_offset], lda, &u[u_offset], - ldu, (ftnlen)1); - i__2 = *m - 1; - i__3 = *m - 1; - dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &u[(u_dim1 - << 1) + 1], ldu, (ftnlen)1); - ie = itau; - itauq = ie + *m; - itaup = itauq + *m; - iwork = itaup + *m; + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &u[u_offset], + ldu, (ftnlen)1); + i__2 = *m - 1; + i__3 = *m - 1; + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &u[(u_dim1 + << 1) + 1], ldu, (ftnlen)1); + ie = itau; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; /* Bidiagonalize L in U */ /* (Workspace: need 4*M, prefer 3*M + 2*M*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(m, m, &u[u_offset], ldu, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); + i__2 = *lwork - iwork + 1; + dgebrd_(m, m, &u[u_offset], ldu, &s[1], &work[ie], & + work[itauq], &work[itaup], &work[iwork], & + i__2, &ierr); /* Multiply right bidiagonalizing vectors in U by Q */ /* in VT */ /* (Workspace: need 3*M + N, prefer 3*M + N*NB) */ - i__2 = *lwork - iwork + 1; - dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &u[u_offset], ldu, & - work[itaup], &vt[vt_offset], ldvt, &work[ - iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, ( - ftnlen)1); + i__2 = *lwork - iwork + 1; + dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &u[u_offset], ldu, & + work[itaup], &vt[vt_offset], ldvt, &work[ + iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, ( + ftnlen)1); /* Generate left bidiagonalizing vectors in U */ /* (Workspace: need 4*M, prefer 3*M + M*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq], - &work[iwork], &i__2, &ierr, (ftnlen)1); - iwork = ie + *m; + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq], + &work[iwork], &i__2, &ierr, (ftnlen)1); + iwork = ie + *m; /* Perform bidiagonal QR iteration, computing left */ /* singular vectors of A in U and computing right */ /* singular vectors of A in VT */ /* (Workspace: need BDSPAC) */ - dbdsqr_((char *)"U", m, n, m, &c__0, &s[1], &work[ie], &vt[ - vt_offset], ldvt, &u[u_offset], ldu, dum, & - c__1, &work[iwork], info, (ftnlen)1); + dbdsqr_((char *)"U", m, n, m, &c__0, &s[1], &work[ie], &vt[ + vt_offset], ldvt, &u[u_offset], ldu, dum, & + c__1, &work[iwork], info, (ftnlen)1); - } + } - } + } - } + } - } else { + } else { /* N .LT. MNTHR */ /* Path 10t(N greater than M, but not much larger) */ /* Reduce to bidiagonal form without LQ decomposition */ - ie = 1; - itauq = ie + *m; - itaup = itauq + *m; - iwork = itaup + *m; + ie = 1; + itauq = ie + *m; + itaup = itauq + *m; + iwork = itaup + *m; /* Bidiagonalize A */ /* (Workspace: need 3*M + N, prefer 3*M + (M + N)*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], & - work[itaup], &work[iwork], &i__2, &ierr); - if (wntuas) { + i__2 = *lwork - iwork + 1; + dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], & + work[itaup], &work[iwork], &i__2, &ierr); + if (wntuas) { /* If left singular vectors desired in U, copy result to U */ /* and generate left bidiagonalizing vectors in U */ /* (Workspace: need 4*M-1, prefer 3*M + (M-1)*NB) */ - dlacpy_((char *)"L", m, m, &a[a_offset], lda, &u[u_offset], ldu, ( - ftnlen)1); - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[ - iwork], &i__2, &ierr, (ftnlen)1); - } - if (wntvas) { + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &u[u_offset], ldu, ( + ftnlen)1); + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[ + iwork], &i__2, &ierr, (ftnlen)1); + } + if (wntvas) { /* If right singular vectors desired in VT, copy result to */ /* VT and generate right bidiagonalizing vectors in VT */ /* (Workspace: need 3*M + NRVT, prefer 3*M + NRVT*NB) */ - dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt, ( - ftnlen)1); - if (wntva) { - nrvt = *n; - } - if (wntvs) { - nrvt = *m; - } - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", &nrvt, n, m, &vt[vt_offset], ldvt, &work[itaup], - &work[iwork], &i__2, &ierr, (ftnlen)1); - } - if (wntuo) { + dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt, ( + ftnlen)1); + if (wntva) { + nrvt = *n; + } + if (wntvs) { + nrvt = *m; + } + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", &nrvt, n, m, &vt[vt_offset], ldvt, &work[itaup], + &work[iwork], &i__2, &ierr, (ftnlen)1); + } + if (wntuo) { /* If left singular vectors desired in A, generate left */ /* bidiagonalizing vectors in A */ /* (Workspace: need 4*M-1, prefer 3*M + (M-1)*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", m, m, n, &a[a_offset], lda, &work[itauq], &work[ - iwork], &i__2, &ierr, (ftnlen)1); - } - if (wntvo) { + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"Q", m, m, n, &a[a_offset], lda, &work[itauq], &work[ + iwork], &i__2, &ierr, (ftnlen)1); + } + if (wntvo) { /* If right singular vectors desired in A, generate right */ /* bidiagonalizing vectors in A */ /* (Workspace: need 4*M, prefer 3*M + M*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", m, n, m, &a[a_offset], lda, &work[itaup], &work[ - iwork], &i__2, &ierr, (ftnlen)1); - } - iwork = ie + *m; - if (wntuas || wntuo) { - nru = *m; - } - if (wntun) { - nru = 0; - } - if (wntvas || wntvo) { - ncvt = *n; - } - if (wntvn) { - ncvt = 0; - } - if (! wntuo && ! wntvo) { + i__2 = *lwork - iwork + 1; + dorgbr_((char *)"P", m, n, m, &a[a_offset], lda, &work[itaup], &work[ + iwork], &i__2, &ierr, (ftnlen)1); + } + iwork = ie + *m; + if (wntuas || wntuo) { + nru = *m; + } + if (wntun) { + nru = 0; + } + if (wntvas || wntvo) { + ncvt = *n; + } + if (wntvn) { + ncvt = 0; + } + if (! wntuo && ! wntvo) { /* Perform bidiagonal QR iteration, if desired, computing */ /* left singular vectors in U and computing right singular */ /* vectors in VT */ /* (Workspace: need BDSPAC) */ - dbdsqr_((char *)"L", m, &ncvt, &nru, &c__0, &s[1], &work[ie], &vt[ - vt_offset], ldvt, &u[u_offset], ldu, dum, &c__1, & - work[iwork], info, (ftnlen)1); - } else if (! wntuo && wntvo) { + dbdsqr_((char *)"L", m, &ncvt, &nru, &c__0, &s[1], &work[ie], &vt[ + vt_offset], ldvt, &u[u_offset], ldu, dum, &c__1, & + work[iwork], info, (ftnlen)1); + } else if (! wntuo && wntvo) { /* Perform bidiagonal QR iteration, if desired, computing */ /* left singular vectors in U and computing right singular */ /* vectors in A */ /* (Workspace: need BDSPAC) */ - dbdsqr_((char *)"L", m, &ncvt, &nru, &c__0, &s[1], &work[ie], &a[ - a_offset], lda, &u[u_offset], ldu, dum, &c__1, &work[ - iwork], info, (ftnlen)1); - } else { + dbdsqr_((char *)"L", m, &ncvt, &nru, &c__0, &s[1], &work[ie], &a[ + a_offset], lda, &u[u_offset], ldu, dum, &c__1, &work[ + iwork], info, (ftnlen)1); + } else { /* Perform bidiagonal QR iteration, if desired, computing */ /* left singular vectors in A and computing right singular */ /* vectors in VT */ /* (Workspace: need BDSPAC) */ - dbdsqr_((char *)"L", m, &ncvt, &nru, &c__0, &s[1], &work[ie], &vt[ - vt_offset], ldvt, &a[a_offset], lda, dum, &c__1, & - work[iwork], info, (ftnlen)1); - } + dbdsqr_((char *)"L", m, &ncvt, &nru, &c__0, &s[1], &work[ie], &vt[ + vt_offset], ldvt, &a[a_offset], lda, dum, &c__1, & + work[iwork], info, (ftnlen)1); + } - } + } } @@ -4105,42 +4105,42 @@ f"> */ /* to WORK( 2:MINMN ) */ if (*info != 0) { - if (ie > 2) { - i__2 = minmn - 1; - for (i__ = 1; i__ <= i__2; ++i__) { - work[i__ + 1] = work[i__ + ie - 1]; + if (ie > 2) { + i__2 = minmn - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + work[i__ + 1] = work[i__ + ie - 1]; /* L50: */ - } - } - if (ie < 2) { - for (i__ = minmn - 1; i__ >= 1; --i__) { - work[i__ + 1] = work[i__ + ie - 1]; + } + } + if (ie < 2) { + for (i__ = minmn - 1; i__ >= 1; --i__) { + work[i__ + 1] = work[i__ + ie - 1]; /* L60: */ - } - } + } + } } /* Undo scaling if necessary */ if (iscl == 1) { - if (anrm > bignum) { - dlascl_((char *)"G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], & - minmn, &ierr, (ftnlen)1); - } - if (*info != 0 && anrm > bignum) { - i__2 = minmn - 1; - dlascl_((char *)"G", &c__0, &c__0, &bignum, &anrm, &i__2, &c__1, &work[2], - &minmn, &ierr, (ftnlen)1); - } - if (anrm < smlnum) { - dlascl_((char *)"G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], & - minmn, &ierr, (ftnlen)1); - } - if (*info != 0 && anrm < smlnum) { - i__2 = minmn - 1; - dlascl_((char *)"G", &c__0, &c__0, &smlnum, &anrm, &i__2, &c__1, &work[2], - &minmn, &ierr, (ftnlen)1); - } + if (anrm > bignum) { + dlascl_((char *)"G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], & + minmn, &ierr, (ftnlen)1); + } + if (*info != 0 && anrm > bignum) { + i__2 = minmn - 1; + dlascl_((char *)"G", &c__0, &c__0, &bignum, &anrm, &i__2, &c__1, &work[2], + &minmn, &ierr, (ftnlen)1); + } + if (anrm < smlnum) { + dlascl_((char *)"G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], & + minmn, &ierr, (ftnlen)1); + } + if (*info != 0 && anrm < smlnum) { + i__2 = minmn - 1; + dlascl_((char *)"G", &c__0, &c__0, &smlnum, &anrm, &i__2, &c__1, &work[2], + &minmn, &ierr, (ftnlen)1); + } } /* Return optimal workspace in WORK(1) */ @@ -4154,5 +4154,5 @@ f"> */ } /* dgesvd_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dgetf2.cpp b/lib/linalg/dgetf2.cpp index 0cb6b57a2f..c5951c8703 100644 --- a/lib/linalg/dgetf2.cpp +++ b/lib/linalg/dgetf2.cpp @@ -1,13 +1,13 @@ /* fortran/dgetf2.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -131,7 +131,7 @@ f"> */ /* ===================================================================== */ /* Subroutine */ int dgetf2_(integer *m, integer *n, doublereal *a, integer * - lda, integer *ipiv, integer *info) + lda, integer *ipiv, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; @@ -139,13 +139,13 @@ f"> */ /* Local variables */ integer i__, j, jp; - extern /* Subroutine */ int dger_(integer *, integer *, doublereal *, - doublereal *, integer *, doublereal *, integer *, doublereal *, - integer *), dscal_(integer *, doublereal *, doublereal *, integer - *); + extern /* Subroutine */ int dger_(integer *, integer *, doublereal *, + doublereal *, integer *, doublereal *, integer *, doublereal *, + integer *), dscal_(integer *, doublereal *, doublereal *, integer + *); doublereal sfmin; - extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, - doublereal *, integer *); + extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, + doublereal *, integer *); extern doublereal dlamch_(char *, ftnlen); extern integer idamax_(integer *, doublereal *, integer *); extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); @@ -185,22 +185,22 @@ f"> */ /* Function Body */ *info = 0; if (*m < 0) { - *info = -1; + *info = -1; } else if (*n < 0) { - *info = -2; + *info = -2; } else if (*lda < max(1,*m)) { - *info = -4; + *info = -4; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DGETF2", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DGETF2", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*m == 0 || *n == 0) { - return 0; + return 0; } /* Compute machine safe minimum */ @@ -212,47 +212,47 @@ f"> */ /* Find pivot and test for singularity. */ - i__2 = *m - j + 1; - jp = j - 1 + idamax_(&i__2, &a[j + j * a_dim1], &c__1); - ipiv[j] = jp; - if (a[jp + j * a_dim1] != 0.) { + i__2 = *m - j + 1; + jp = j - 1 + idamax_(&i__2, &a[j + j * a_dim1], &c__1); + ipiv[j] = jp; + if (a[jp + j * a_dim1] != 0.) { /* Apply the interchange to columns 1:N. */ - if (jp != j) { - dswap_(n, &a[j + a_dim1], lda, &a[jp + a_dim1], lda); - } + if (jp != j) { + dswap_(n, &a[j + a_dim1], lda, &a[jp + a_dim1], lda); + } /* Compute elements J+1:M of J-th column. */ - if (j < *m) { - if ((d__1 = a[j + j * a_dim1], abs(d__1)) >= sfmin) { - i__2 = *m - j; - d__1 = 1. / a[j + j * a_dim1]; - dscal_(&i__2, &d__1, &a[j + 1 + j * a_dim1], &c__1); - } else { - i__2 = *m - j; - for (i__ = 1; i__ <= i__2; ++i__) { - a[j + i__ + j * a_dim1] /= a[j + j * a_dim1]; + if (j < *m) { + if ((d__1 = a[j + j * a_dim1], abs(d__1)) >= sfmin) { + i__2 = *m - j; + d__1 = 1. / a[j + j * a_dim1]; + dscal_(&i__2, &d__1, &a[j + 1 + j * a_dim1], &c__1); + } else { + i__2 = *m - j; + for (i__ = 1; i__ <= i__2; ++i__) { + a[j + i__ + j * a_dim1] /= a[j + j * a_dim1]; /* L20: */ - } - } - } + } + } + } - } else if (*info == 0) { + } else if (*info == 0) { - *info = j; - } + *info = j; + } - if (j < min(*m,*n)) { + if (j < min(*m,*n)) { /* Update trailing submatrix. */ - i__2 = *m - j; - i__3 = *n - j; - dger_(&i__2, &i__3, &c_b8, &a[j + 1 + j * a_dim1], &c__1, &a[j + ( - j + 1) * a_dim1], lda, &a[j + 1 + (j + 1) * a_dim1], lda); - } + i__2 = *m - j; + i__3 = *n - j; + dger_(&i__2, &i__3, &c_b8, &a[j + 1 + j * a_dim1], &c__1, &a[j + ( + j + 1) * a_dim1], lda, &a[j + 1 + (j + 1) * a_dim1], lda); + } /* L10: */ } return 0; @@ -262,5 +262,5 @@ f"> */ } /* dgetf2_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dgetrf.cpp b/lib/linalg/dgetrf.cpp index eca7500a03..cd1e8b50fe 100644 --- a/lib/linalg/dgetrf.cpp +++ b/lib/linalg/dgetrf.cpp @@ -1,13 +1,13 @@ /* fortran/dgetrf.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -132,26 +132,26 @@ f"> */ /* ===================================================================== */ /* Subroutine */ int dgetrf_(integer *m, integer *n, doublereal *a, integer * - lda, integer *ipiv, integer *info) + lda, integer *ipiv, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; /* Local variables */ integer i__, j, jb, nb; - extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); integer iinfo; - extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, - integer *, integer *, doublereal *, doublereal *, integer *, - doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen), xerbla_( - char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - extern /* Subroutine */ int dlaswp_(integer *, doublereal *, integer *, - integer *, integer *, integer *, integer *), dgetrf2_(integer *, - integer *, doublereal *, integer *, integer *, integer *); + extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, + integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen), xerbla_( + char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dlaswp_(integer *, doublereal *, integer *, + integer *, integer *, integer *, integer *), dgetrf2_(integer *, + integer *, doublereal *, integer *, integer *, integer *); /* -- LAPACK computational routine -- */ @@ -188,99 +188,99 @@ f"> */ /* Function Body */ *info = 0; if (*m < 0) { - *info = -1; + *info = -1; } else if (*n < 0) { - *info = -2; + *info = -2; } else if (*lda < max(1,*m)) { - *info = -4; + *info = -4; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DGETRF", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DGETRF", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*m == 0 || *n == 0) { - return 0; + return 0; } /* Determine the block size for this environment. */ nb = ilaenv_(&c__1, (char *)"DGETRF", (char *)" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen) - 1); + 1); if (nb <= 1 || nb >= min(*m,*n)) { /* Use unblocked code. */ - dgetrf2_(m, n, &a[a_offset], lda, &ipiv[1], info); + dgetrf2_(m, n, &a[a_offset], lda, &ipiv[1], info); } else { /* Use blocked code. */ - i__1 = min(*m,*n); - i__2 = nb; - for (j = 1; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) { + i__1 = min(*m,*n); + i__2 = nb; + for (j = 1; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) { /* Computing MIN */ - i__3 = min(*m,*n) - j + 1; - jb = min(i__3,nb); + i__3 = min(*m,*n) - j + 1; + jb = min(i__3,nb); /* Factor diagonal and subdiagonal blocks and test for exact */ /* singularity. */ - i__3 = *m - j + 1; - dgetrf2_(&i__3, &jb, &a[j + j * a_dim1], lda, &ipiv[j], &iinfo); + i__3 = *m - j + 1; + dgetrf2_(&i__3, &jb, &a[j + j * a_dim1], lda, &ipiv[j], &iinfo); /* Adjust INFO and the pivot indices. */ - if (*info == 0 && iinfo > 0) { - *info = iinfo + j - 1; - } + if (*info == 0 && iinfo > 0) { + *info = iinfo + j - 1; + } /* Computing MIN */ - i__4 = *m, i__5 = j + jb - 1; - i__3 = min(i__4,i__5); - for (i__ = j; i__ <= i__3; ++i__) { - ipiv[i__] = j - 1 + ipiv[i__]; + i__4 = *m, i__5 = j + jb - 1; + i__3 = min(i__4,i__5); + for (i__ = j; i__ <= i__3; ++i__) { + ipiv[i__] = j - 1 + ipiv[i__]; /* L10: */ - } + } /* Apply interchanges to columns 1:J-1. */ - i__3 = j - 1; - i__4 = j + jb - 1; - dlaswp_(&i__3, &a[a_offset], lda, &j, &i__4, &ipiv[1], &c__1); + i__3 = j - 1; + i__4 = j + jb - 1; + dlaswp_(&i__3, &a[a_offset], lda, &j, &i__4, &ipiv[1], &c__1); - if (j + jb <= *n) { + if (j + jb <= *n) { /* Apply interchanges to columns J+JB:N. */ - i__3 = *n - j - jb + 1; - i__4 = j + jb - 1; - dlaswp_(&i__3, &a[(j + jb) * a_dim1 + 1], lda, &j, &i__4, & - ipiv[1], &c__1); + i__3 = *n - j - jb + 1; + i__4 = j + jb - 1; + dlaswp_(&i__3, &a[(j + jb) * a_dim1 + 1], lda, &j, &i__4, & + ipiv[1], &c__1); /* Compute block row of U. */ - i__3 = *n - j - jb + 1; - dtrsm_((char *)"Left", (char *)"Lower", (char *)"No transpose", (char *)"Unit", &jb, &i__3, & - c_b16, &a[j + j * a_dim1], lda, &a[j + (j + jb) * - a_dim1], lda, (ftnlen)4, (ftnlen)5, (ftnlen)12, ( - ftnlen)4); - if (j + jb <= *m) { + i__3 = *n - j - jb + 1; + dtrsm_((char *)"Left", (char *)"Lower", (char *)"No transpose", (char *)"Unit", &jb, &i__3, & + c_b16, &a[j + j * a_dim1], lda, &a[j + (j + jb) * + a_dim1], lda, (ftnlen)4, (ftnlen)5, (ftnlen)12, ( + ftnlen)4); + if (j + jb <= *m) { /* Update trailing submatrix. */ - i__3 = *m - j - jb + 1; - i__4 = *n - j - jb + 1; - dgemm_((char *)"No transpose", (char *)"No transpose", &i__3, &i__4, &jb, - &c_b19, &a[j + jb + j * a_dim1], lda, &a[j + (j + - jb) * a_dim1], lda, &c_b16, &a[j + jb + (j + jb) * - a_dim1], lda, (ftnlen)12, (ftnlen)12); - } - } + i__3 = *m - j - jb + 1; + i__4 = *n - j - jb + 1; + dgemm_((char *)"No transpose", (char *)"No transpose", &i__3, &i__4, &jb, + &c_b19, &a[j + jb + j * a_dim1], lda, &a[j + (j + + jb) * a_dim1], lda, &c_b16, &a[j + jb + (j + jb) * + a_dim1], lda, (ftnlen)12, (ftnlen)12); + } + } /* L20: */ - } + } } return 0; @@ -289,5 +289,5 @@ f"> */ } /* dgetrf_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dgetrf2.cpp b/lib/linalg/dgetrf2.cpp index 94162fdca8..c7097bbfed 100644 --- a/lib/linalg/dgetrf2.cpp +++ b/lib/linalg/dgetrf2.cpp @@ -1,13 +1,13 @@ /* static/dgetrf2.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -133,7 +133,7 @@ static doublereal c_b16 = -1.; /* ===================================================================== */ /* Subroutine */ int dgetrf2_(integer *m, integer *n, doublereal *a, integer * - lda, integer *ipiv, integer *info) + lda, integer *ipiv, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; @@ -142,20 +142,20 @@ static doublereal c_b16 = -1.; /* Local variables */ integer i__, n1, n2; doublereal temp; - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *), dgemm_(char *, char *, integer *, integer *, integer * - , doublereal *, doublereal *, integer *, doublereal *, integer *, - doublereal *, doublereal *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *), dgemm_(char *, char *, integer *, integer *, integer * + , doublereal *, doublereal *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, ftnlen, ftnlen); integer iinfo; doublereal sfmin; - extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, - integer *, integer *, doublereal *, doublereal *, integer *, - doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, + integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); extern doublereal dlamch_(char *, ftnlen); extern integer idamax_(integer *, doublereal *, integer *); extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), dlaswp_( - integer *, doublereal *, integer *, integer *, integer *, integer - *, integer *); + integer *, doublereal *, integer *, integer *, integer *, integer + *, integer *); /* -- LAPACK computational routine -- */ @@ -192,32 +192,32 @@ static doublereal c_b16 = -1.; /* Function Body */ *info = 0; if (*m < 0) { - *info = -1; + *info = -1; } else if (*n < 0) { - *info = -2; + *info = -2; } else if (*lda < max(1,*m)) { - *info = -4; + *info = -4; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DGETRF2", &i__1, (ftnlen)7); - return 0; + i__1 = -(*info); + xerbla_((char *)"DGETRF2", &i__1, (ftnlen)7); + return 0; } /* Quick return if possible */ if (*m == 0 || *n == 0) { - return 0; + return 0; } if (*m == 1) { /* Use unblocked code for one row case */ /* Just need to handle IPIV and INFO */ - ipiv[1] = 1; - if (a[a_dim1 + 1] == 0.) { - *info = 1; - } + ipiv[1] = 1; + if (a[a_dim1 + 1] == 0.) { + *info = 1; + } } else if (*n == 1) { @@ -226,98 +226,98 @@ static doublereal c_b16 = -1.; /* Compute machine safe minimum */ - sfmin = dlamch_((char *)"S", (ftnlen)1); + sfmin = dlamch_((char *)"S", (ftnlen)1); /* Find pivot and test for singularity */ - i__ = idamax_(m, &a[a_dim1 + 1], &c__1); - ipiv[1] = i__; - if (a[i__ + a_dim1] != 0.) { + i__ = idamax_(m, &a[a_dim1 + 1], &c__1); + ipiv[1] = i__; + if (a[i__ + a_dim1] != 0.) { /* Apply the interchange */ - if (i__ != 1) { - temp = a[a_dim1 + 1]; - a[a_dim1 + 1] = a[i__ + a_dim1]; - a[i__ + a_dim1] = temp; - } + if (i__ != 1) { + temp = a[a_dim1 + 1]; + a[a_dim1 + 1] = a[i__ + a_dim1]; + a[i__ + a_dim1] = temp; + } /* Compute elements 2:M of the column */ - if ((d__1 = a[a_dim1 + 1], abs(d__1)) >= sfmin) { - i__1 = *m - 1; - d__1 = 1. / a[a_dim1 + 1]; - dscal_(&i__1, &d__1, &a[a_dim1 + 2], &c__1); - } else { - i__1 = *m - 1; - for (i__ = 1; i__ <= i__1; ++i__) { - a[i__ + 1 + a_dim1] /= a[a_dim1 + 1]; + if ((d__1 = a[a_dim1 + 1], abs(d__1)) >= sfmin) { + i__1 = *m - 1; + d__1 = 1. / a[a_dim1 + 1]; + dscal_(&i__1, &d__1, &a[a_dim1 + 2], &c__1); + } else { + i__1 = *m - 1; + for (i__ = 1; i__ <= i__1; ++i__) { + a[i__ + 1 + a_dim1] /= a[a_dim1 + 1]; /* L10: */ - } - } + } + } - } else { - *info = 1; - } + } else { + *info = 1; + } } else { /* Use recursive code */ - n1 = min(*m,*n) / 2; - n2 = *n - n1; + n1 = min(*m,*n) / 2; + n2 = *n - n1; /* [ A11 ] */ /* Factor [ --- ] */ /* [ A21 ] */ - dgetrf2_(m, &n1, &a[a_offset], lda, &ipiv[1], &iinfo); - if (*info == 0 && iinfo > 0) { - *info = iinfo; - } + dgetrf2_(m, &n1, &a[a_offset], lda, &ipiv[1], &iinfo); + if (*info == 0 && iinfo > 0) { + *info = iinfo; + } /* [ A12 ] */ /* Apply interchanges to [ --- ] */ /* [ A22 ] */ - dlaswp_(&n2, &a[(n1 + 1) * a_dim1 + 1], lda, &c__1, &n1, &ipiv[1], & - c__1); + dlaswp_(&n2, &a[(n1 + 1) * a_dim1 + 1], lda, &c__1, &n1, &ipiv[1], & + c__1); /* Solve A12 */ - dtrsm_((char *)"L", (char *)"L", (char *)"N", (char *)"U", &n1, &n2, &c_b13, &a[a_offset], lda, &a[( - n1 + 1) * a_dim1 + 1], lda, (ftnlen)1, (ftnlen)1, (ftnlen)1, ( - ftnlen)1); + dtrsm_((char *)"L", (char *)"L", (char *)"N", (char *)"U", &n1, &n2, &c_b13, &a[a_offset], lda, &a[( + n1 + 1) * a_dim1 + 1], lda, (ftnlen)1, (ftnlen)1, (ftnlen)1, ( + ftnlen)1); /* Update A22 */ - i__1 = *m - n1; - dgemm_((char *)"N", (char *)"N", &i__1, &n2, &n1, &c_b16, &a[n1 + 1 + a_dim1], lda, & - a[(n1 + 1) * a_dim1 + 1], lda, &c_b13, &a[n1 + 1 + (n1 + 1) * - a_dim1], lda, (ftnlen)1, (ftnlen)1); + i__1 = *m - n1; + dgemm_((char *)"N", (char *)"N", &i__1, &n2, &n1, &c_b16, &a[n1 + 1 + a_dim1], lda, & + a[(n1 + 1) * a_dim1 + 1], lda, &c_b13, &a[n1 + 1 + (n1 + 1) * + a_dim1], lda, (ftnlen)1, (ftnlen)1); /* Factor A22 */ - i__1 = *m - n1; - dgetrf2_(&i__1, &n2, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, &ipiv[n1 + - 1], &iinfo); + i__1 = *m - n1; + dgetrf2_(&i__1, &n2, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, &ipiv[n1 + + 1], &iinfo); /* Adjust INFO and the pivot indices */ - if (*info == 0 && iinfo > 0) { - *info = iinfo + n1; - } - i__1 = min(*m,*n); - for (i__ = n1 + 1; i__ <= i__1; ++i__) { - ipiv[i__] += n1; + if (*info == 0 && iinfo > 0) { + *info = iinfo + n1; + } + i__1 = min(*m,*n); + for (i__ = n1 + 1; i__ <= i__1; ++i__) { + ipiv[i__] += n1; /* L20: */ - } + } /* Apply interchanges to A21 */ - i__1 = n1 + 1; - i__2 = min(*m,*n); - dlaswp_(&n1, &a[a_dim1 + 1], lda, &i__1, &i__2, &ipiv[1], &c__1); + i__1 = n1 + 1; + i__2 = min(*m,*n); + dlaswp_(&n1, &a[a_dim1 + 1], lda, &i__1, &i__2, &ipiv[1], &c__1); } return 0; @@ -327,5 +327,5 @@ static doublereal c_b16 = -1.; } /* dgetrf2_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dgetri.cpp b/lib/linalg/dgetri.cpp index 23178071b6..368c6701ac 100644 --- a/lib/linalg/dgetri.cpp +++ b/lib/linalg/dgetri.cpp @@ -1,13 +1,13 @@ /* fortran/dgetri.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -138,31 +138,31 @@ f"> */ /* > \ingroup doubleGEcomputational */ /* ===================================================================== */ -/* Subroutine */ int dgetri_(integer *n, doublereal *a, integer *lda, integer - *ipiv, doublereal *work, integer *lwork, integer *info) +/* Subroutine */ int dgetri_(integer *n, doublereal *a, integer *lda, integer + *ipiv, doublereal *work, integer *lwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; /* Local variables */ integer i__, j, jb, nb, jj, jp, nn, iws; - extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen), - dgemv_(char *, integer *, integer *, doublereal *, doublereal *, - integer *, doublereal *, integer *, doublereal *, doublereal *, - integer *, ftnlen); + extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen), + dgemv_(char *, integer *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, ftnlen); integer nbmin; - extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, - doublereal *, integer *), dtrsm_(char *, char *, char *, char *, - integer *, integer *, doublereal *, doublereal *, integer *, - doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen), xerbla_( - char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, + doublereal *, integer *), dtrsm_(char *, char *, char *, char *, + integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen), xerbla_( + char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); integer ldwork; - extern /* Subroutine */ int dtrtri_(char *, char *, integer *, doublereal - *, integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dtrtri_(char *, char *, integer *, doublereal + *, integer *, integer *, ftnlen, ftnlen); integer lwkopt; logical lquery; @@ -202,55 +202,55 @@ f"> */ /* Function Body */ *info = 0; nb = ilaenv_(&c__1, (char *)"DGETRI", (char *)" ", n, &c_n1, &c_n1, &c_n1, (ftnlen)6, ( - ftnlen)1); + ftnlen)1); lwkopt = *n * nb; work[1] = (doublereal) lwkopt; lquery = *lwork == -1; if (*n < 0) { - *info = -1; + *info = -1; } else if (*lda < max(1,*n)) { - *info = -3; + *info = -3; } else if (*lwork < max(1,*n) && ! lquery) { - *info = -6; + *info = -6; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DGETRI", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DGETRI", &i__1, (ftnlen)6); + return 0; } else if (lquery) { - return 0; + return 0; } /* Quick return if possible */ if (*n == 0) { - return 0; + return 0; } /* Form inv(U). If INFO > 0 from DTRTRI, then U is singular, */ /* and the inverse is not computed. */ dtrtri_((char *)"Upper", (char *)"Non-unit", n, &a[a_offset], lda, info, (ftnlen)5, ( - ftnlen)8); + ftnlen)8); if (*info > 0) { - return 0; + return 0; } nbmin = 2; ldwork = *n; if (nb > 1 && nb < *n) { /* Computing MAX */ - i__1 = ldwork * nb; - iws = max(i__1,1); - if (*lwork < iws) { - nb = *lwork / ldwork; + i__1 = ldwork * nb; + iws = max(i__1,1); + if (*lwork < iws) { + nb = *lwork / ldwork; /* Computing MAX */ - i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DGETRI", (char *)" ", n, &c_n1, &c_n1, & - c_n1, (ftnlen)6, (ftnlen)1); - nbmin = max(i__1,i__2); - } + i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DGETRI", (char *)" ", n, &c_n1, &c_n1, & + c_n1, (ftnlen)6, (ftnlen)1); + nbmin = max(i__1,i__2); + } } else { - iws = *n; + iws = *n; } /* Solve the equation inv(A)*L = inv(U) for inv(A). */ @@ -259,75 +259,75 @@ f"> */ /* Use unblocked code. */ - for (j = *n; j >= 1; --j) { + for (j = *n; j >= 1; --j) { /* Copy current column of L to WORK and replace with zeros. */ - i__1 = *n; - for (i__ = j + 1; i__ <= i__1; ++i__) { - work[i__] = a[i__ + j * a_dim1]; - a[i__ + j * a_dim1] = 0.; + i__1 = *n; + for (i__ = j + 1; i__ <= i__1; ++i__) { + work[i__] = a[i__ + j * a_dim1]; + a[i__ + j * a_dim1] = 0.; /* L10: */ - } + } /* Compute current column of inv(A). */ - if (j < *n) { - i__1 = *n - j; - dgemv_((char *)"No transpose", n, &i__1, &c_b20, &a[(j + 1) * a_dim1 - + 1], lda, &work[j + 1], &c__1, &c_b22, &a[j * a_dim1 - + 1], &c__1, (ftnlen)12); - } + if (j < *n) { + i__1 = *n - j; + dgemv_((char *)"No transpose", n, &i__1, &c_b20, &a[(j + 1) * a_dim1 + + 1], lda, &work[j + 1], &c__1, &c_b22, &a[j * a_dim1 + + 1], &c__1, (ftnlen)12); + } /* L20: */ - } + } } else { /* Use blocked code. */ - nn = (*n - 1) / nb * nb + 1; - i__1 = -nb; - for (j = nn; i__1 < 0 ? j >= 1 : j <= 1; j += i__1) { + nn = (*n - 1) / nb * nb + 1; + i__1 = -nb; + for (j = nn; i__1 < 0 ? j >= 1 : j <= 1; j += i__1) { /* Computing MIN */ - i__2 = nb, i__3 = *n - j + 1; - jb = min(i__2,i__3); + i__2 = nb, i__3 = *n - j + 1; + jb = min(i__2,i__3); /* Copy current block column of L to WORK and replace with */ /* zeros. */ - i__2 = j + jb - 1; - for (jj = j; jj <= i__2; ++jj) { - i__3 = *n; - for (i__ = jj + 1; i__ <= i__3; ++i__) { - work[i__ + (jj - j) * ldwork] = a[i__ + jj * a_dim1]; - a[i__ + jj * a_dim1] = 0.; + i__2 = j + jb - 1; + for (jj = j; jj <= i__2; ++jj) { + i__3 = *n; + for (i__ = jj + 1; i__ <= i__3; ++i__) { + work[i__ + (jj - j) * ldwork] = a[i__ + jj * a_dim1]; + a[i__ + jj * a_dim1] = 0.; /* L30: */ - } + } /* L40: */ - } + } /* Compute current block column of inv(A). */ - if (j + jb <= *n) { - i__2 = *n - j - jb + 1; - dgemm_((char *)"No transpose", (char *)"No transpose", n, &jb, &i__2, &c_b20, - &a[(j + jb) * a_dim1 + 1], lda, &work[j + jb], & - ldwork, &c_b22, &a[j * a_dim1 + 1], lda, (ftnlen)12, ( - ftnlen)12); - } - dtrsm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", n, &jb, &c_b22, & - work[j], &ldwork, &a[j * a_dim1 + 1], lda, (ftnlen)5, ( - ftnlen)5, (ftnlen)12, (ftnlen)4); + if (j + jb <= *n) { + i__2 = *n - j - jb + 1; + dgemm_((char *)"No transpose", (char *)"No transpose", n, &jb, &i__2, &c_b20, + &a[(j + jb) * a_dim1 + 1], lda, &work[j + jb], & + ldwork, &c_b22, &a[j * a_dim1 + 1], lda, (ftnlen)12, ( + ftnlen)12); + } + dtrsm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", n, &jb, &c_b22, & + work[j], &ldwork, &a[j * a_dim1 + 1], lda, (ftnlen)5, ( + ftnlen)5, (ftnlen)12, (ftnlen)4); /* L50: */ - } + } } /* Apply column interchanges. */ for (j = *n - 1; j >= 1; --j) { - jp = ipiv[j]; - if (jp != j) { - dswap_(n, &a[j * a_dim1 + 1], &c__1, &a[jp * a_dim1 + 1], &c__1); - } + jp = ipiv[j]; + if (jp != j) { + dswap_(n, &a[j * a_dim1 + 1], &c__1, &a[jp * a_dim1 + 1], &c__1); + } /* L60: */ } @@ -339,5 +339,5 @@ f"> */ } /* dgetri_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dgetrs.cpp b/lib/linalg/dgetrs.cpp index 4df18e8650..ca10730a0b 100644 --- a/lib/linalg/dgetrs.cpp +++ b/lib/linalg/dgetrs.cpp @@ -1,13 +1,13 @@ /* fortran/dgetrs.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -143,20 +143,20 @@ f"> */ /* > \ingroup doubleGEcomputational */ /* ===================================================================== */ -/* Subroutine */ int dgetrs_(char *trans, integer *n, integer *nrhs, - doublereal *a, integer *lda, integer *ipiv, doublereal *b, integer * - ldb, integer *info, ftnlen trans_len) +/* Subroutine */ int dgetrs_(char *trans, integer *n, integer *nrhs, + doublereal *a, integer *lda, integer *ipiv, doublereal *b, integer * + ldb, integer *info, ftnlen trans_len) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1; /* Local variables */ extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, - integer *, integer *, doublereal *, doublereal *, integer *, - doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen), xerbla_( - char *, integer *, ftnlen), dlaswp_(integer *, doublereal *, - integer *, integer *, integer *, integer *, integer *); + extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, + integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen), xerbla_( + char *, integer *, ftnlen), dlaswp_(integer *, doublereal *, + integer *, integer *, integer *, integer *, integer *); logical notran; @@ -198,27 +198,27 @@ f"> */ *info = 0; notran = lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1); if (! notran && ! lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_( - trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { - *info = -1; + trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { + *info = -1; } else if (*n < 0) { - *info = -2; + *info = -2; } else if (*nrhs < 0) { - *info = -3; + *info = -3; } else if (*lda < max(1,*n)) { - *info = -5; + *info = -5; } else if (*ldb < max(1,*n)) { - *info = -8; + *info = -8; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DGETRS", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DGETRS", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*n == 0 || *nrhs == 0) { - return 0; + return 0; } if (notran) { @@ -227,38 +227,38 @@ f"> */ /* Apply row interchanges to the right hand sides. */ - dlaswp_(nrhs, &b[b_offset], ldb, &c__1, n, &ipiv[1], &c__1); + dlaswp_(nrhs, &b[b_offset], ldb, &c__1, n, &ipiv[1], &c__1); /* Solve L*X = B, overwriting B with X. */ - dtrsm_((char *)"Left", (char *)"Lower", (char *)"No transpose", (char *)"Unit", n, nrhs, &c_b12, &a[ - a_offset], lda, &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, ( - ftnlen)12, (ftnlen)4); + dtrsm_((char *)"Left", (char *)"Lower", (char *)"No transpose", (char *)"Unit", n, nrhs, &c_b12, &a[ + a_offset], lda, &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, ( + ftnlen)12, (ftnlen)4); /* Solve U*X = B, overwriting B with X. */ - dtrsm_((char *)"Left", (char *)"Upper", (char *)"No transpose", (char *)"Non-unit", n, nrhs, &c_b12, & - a[a_offset], lda, &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, ( - ftnlen)12, (ftnlen)8); + dtrsm_((char *)"Left", (char *)"Upper", (char *)"No transpose", (char *)"Non-unit", n, nrhs, &c_b12, & + a[a_offset], lda, &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, ( + ftnlen)12, (ftnlen)8); } else { /* Solve A**T * X = B. */ /* Solve U**T *X = B, overwriting B with X. */ - dtrsm_((char *)"Left", (char *)"Upper", (char *)"Transpose", (char *)"Non-unit", n, nrhs, &c_b12, &a[ - a_offset], lda, &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, ( - ftnlen)9, (ftnlen)8); + dtrsm_((char *)"Left", (char *)"Upper", (char *)"Transpose", (char *)"Non-unit", n, nrhs, &c_b12, &a[ + a_offset], lda, &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, ( + ftnlen)9, (ftnlen)8); /* Solve L**T *X = B, overwriting B with X. */ - dtrsm_((char *)"Left", (char *)"Lower", (char *)"Transpose", (char *)"Unit", n, nrhs, &c_b12, &a[ - a_offset], lda, &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, ( - ftnlen)9, (ftnlen)4); + dtrsm_((char *)"Left", (char *)"Lower", (char *)"Transpose", (char *)"Unit", n, nrhs, &c_b12, &a[ + a_offset], lda, &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, ( + ftnlen)9, (ftnlen)4); /* Apply row interchanges to the solution vectors. */ - dlaswp_(nrhs, &b[b_offset], ldb, &c__1, n, &ipiv[1], &c_n1); + dlaswp_(nrhs, &b[b_offset], ldb, &c__1, n, &ipiv[1], &c_n1); } return 0; @@ -268,5 +268,5 @@ f"> */ } /* dgetrs_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlabad.cpp b/lib/linalg/dlabad.cpp index 96eb6efcca..a753834632 100644 --- a/lib/linalg/dlabad.cpp +++ b/lib/linalg/dlabad.cpp @@ -1,13 +1,13 @@ /* fortran/dlabad.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -113,8 +113,8 @@ f"> */ /* SMALL and LARGE to avoid overflow and underflow problems. */ if (d_lg10(large) > 2e3) { - *small = sqrt(*small); - *large = sqrt(*large); + *small = sqrt(*small); + *large = sqrt(*large); } return 0; @@ -124,5 +124,5 @@ f"> */ } /* dlabad_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlabrd.cpp b/lib/linalg/dlabrd.cpp index 5775cc7bc1..a7f9113e5c 100644 --- a/lib/linalg/dlabrd.cpp +++ b/lib/linalg/dlabrd.cpp @@ -1,13 +1,13 @@ /* fortran/dlabrd.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -233,21 +233,21 @@ f"> */ /* > */ /* ===================================================================== */ /* Subroutine */ int dlabrd_(integer *m, integer *n, integer *nb, doublereal * - a, integer *lda, doublereal *d__, doublereal *e, doublereal *tauq, - doublereal *taup, doublereal *x, integer *ldx, doublereal *y, integer - *ldy) + a, integer *lda, doublereal *d__, doublereal *e, doublereal *tauq, + doublereal *taup, doublereal *x, integer *ldx, doublereal *y, integer + *ldy) { /* System generated locals */ - integer a_dim1, a_offset, x_dim1, x_offset, y_dim1, y_offset, i__1, i__2, - i__3; + integer a_dim1, a_offset, x_dim1, x_offset, y_dim1, y_offset, i__1, i__2, + i__3; /* Local variables */ integer i__; - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *), dgemv_(char *, integer *, integer *, doublereal *, - doublereal *, integer *, doublereal *, integer *, doublereal *, - doublereal *, integer *, ftnlen), dlarfg_(integer *, doublereal *, - doublereal *, integer *, doublereal *); + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *), dgemv_(char *, integer *, integer *, doublereal *, + doublereal *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, ftnlen), dlarfg_(integer *, doublereal *, + doublereal *, integer *, doublereal *); /* -- LAPACK auxiliary routine -- */ @@ -290,236 +290,236 @@ f"> */ /* Function Body */ if (*m <= 0 || *n <= 0) { - return 0; + return 0; } if (*m >= *n) { /* Reduce to upper bidiagonal form */ - i__1 = *nb; - for (i__ = 1; i__ <= i__1; ++i__) { + i__1 = *nb; + for (i__ = 1; i__ <= i__1; ++i__) { /* Update A(i:m,i) */ - i__2 = *m - i__ + 1; - i__3 = i__ - 1; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &a[i__ + a_dim1], lda, - &y[i__ + y_dim1], ldy, &c_b5, &a[i__ + i__ * a_dim1], & - c__1, (ftnlen)12); - i__2 = *m - i__ + 1; - i__3 = i__ - 1; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &x[i__ + x_dim1], ldx, - &a[i__ * a_dim1 + 1], &c__1, &c_b5, &a[i__ + i__ * - a_dim1], &c__1, (ftnlen)12); + i__2 = *m - i__ + 1; + i__3 = i__ - 1; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &a[i__ + a_dim1], lda, + &y[i__ + y_dim1], ldy, &c_b5, &a[i__ + i__ * a_dim1], & + c__1, (ftnlen)12); + i__2 = *m - i__ + 1; + i__3 = i__ - 1; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &x[i__ + x_dim1], ldx, + &a[i__ * a_dim1 + 1], &c__1, &c_b5, &a[i__ + i__ * + a_dim1], &c__1, (ftnlen)12); /* Generate reflection Q(i) to annihilate A(i+1:m,i) */ - i__2 = *m - i__ + 1; + i__2 = *m - i__ + 1; /* Computing MIN */ - i__3 = i__ + 1; - dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[min(i__3,*m) + i__ * - a_dim1], &c__1, &tauq[i__]); - d__[i__] = a[i__ + i__ * a_dim1]; - if (i__ < *n) { - a[i__ + i__ * a_dim1] = 1.; + i__3 = i__ + 1; + dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[min(i__3,*m) + i__ * + a_dim1], &c__1, &tauq[i__]); + d__[i__] = a[i__ + i__ * a_dim1]; + if (i__ < *n) { + a[i__ + i__ * a_dim1] = 1.; /* Compute Y(i+1:n,i) */ - i__2 = *m - i__ + 1; - i__3 = *n - i__; - dgemv_((char *)"Transpose", &i__2, &i__3, &c_b5, &a[i__ + (i__ + 1) * - a_dim1], lda, &a[i__ + i__ * a_dim1], &c__1, &c_b16, & - y[i__ + 1 + i__ * y_dim1], &c__1, (ftnlen)9); - i__2 = *m - i__ + 1; - i__3 = i__ - 1; - dgemv_((char *)"Transpose", &i__2, &i__3, &c_b5, &a[i__ + a_dim1], - lda, &a[i__ + i__ * a_dim1], &c__1, &c_b16, &y[i__ * - y_dim1 + 1], &c__1, (ftnlen)9); - i__2 = *n - i__; - i__3 = i__ - 1; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &y[i__ + 1 + - y_dim1], ldy, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[ - i__ + 1 + i__ * y_dim1], &c__1, (ftnlen)12); - i__2 = *m - i__ + 1; - i__3 = i__ - 1; - dgemv_((char *)"Transpose", &i__2, &i__3, &c_b5, &x[i__ + x_dim1], - ldx, &a[i__ + i__ * a_dim1], &c__1, &c_b16, &y[i__ * - y_dim1 + 1], &c__1, (ftnlen)9); - i__2 = i__ - 1; - i__3 = *n - i__; - dgemv_((char *)"Transpose", &i__2, &i__3, &c_b4, &a[(i__ + 1) * - a_dim1 + 1], lda, &y[i__ * y_dim1 + 1], &c__1, &c_b5, - &y[i__ + 1 + i__ * y_dim1], &c__1, (ftnlen)9); - i__2 = *n - i__; - dscal_(&i__2, &tauq[i__], &y[i__ + 1 + i__ * y_dim1], &c__1); + i__2 = *m - i__ + 1; + i__3 = *n - i__; + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b5, &a[i__ + (i__ + 1) * + a_dim1], lda, &a[i__ + i__ * a_dim1], &c__1, &c_b16, & + y[i__ + 1 + i__ * y_dim1], &c__1, (ftnlen)9); + i__2 = *m - i__ + 1; + i__3 = i__ - 1; + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b5, &a[i__ + a_dim1], + lda, &a[i__ + i__ * a_dim1], &c__1, &c_b16, &y[i__ * + y_dim1 + 1], &c__1, (ftnlen)9); + i__2 = *n - i__; + i__3 = i__ - 1; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &y[i__ + 1 + + y_dim1], ldy, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[ + i__ + 1 + i__ * y_dim1], &c__1, (ftnlen)12); + i__2 = *m - i__ + 1; + i__3 = i__ - 1; + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b5, &x[i__ + x_dim1], + ldx, &a[i__ + i__ * a_dim1], &c__1, &c_b16, &y[i__ * + y_dim1 + 1], &c__1, (ftnlen)9); + i__2 = i__ - 1; + i__3 = *n - i__; + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b4, &a[(i__ + 1) * + a_dim1 + 1], lda, &y[i__ * y_dim1 + 1], &c__1, &c_b5, + &y[i__ + 1 + i__ * y_dim1], &c__1, (ftnlen)9); + i__2 = *n - i__; + dscal_(&i__2, &tauq[i__], &y[i__ + 1 + i__ * y_dim1], &c__1); /* Update A(i,i+1:n) */ - i__2 = *n - i__; - dgemv_((char *)"No transpose", &i__2, &i__, &c_b4, &y[i__ + 1 + - y_dim1], ldy, &a[i__ + a_dim1], lda, &c_b5, &a[i__ + ( - i__ + 1) * a_dim1], lda, (ftnlen)12); - i__2 = i__ - 1; - i__3 = *n - i__; - dgemv_((char *)"Transpose", &i__2, &i__3, &c_b4, &a[(i__ + 1) * - a_dim1 + 1], lda, &x[i__ + x_dim1], ldx, &c_b5, &a[ - i__ + (i__ + 1) * a_dim1], lda, (ftnlen)9); + i__2 = *n - i__; + dgemv_((char *)"No transpose", &i__2, &i__, &c_b4, &y[i__ + 1 + + y_dim1], ldy, &a[i__ + a_dim1], lda, &c_b5, &a[i__ + ( + i__ + 1) * a_dim1], lda, (ftnlen)12); + i__2 = i__ - 1; + i__3 = *n - i__; + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b4, &a[(i__ + 1) * + a_dim1 + 1], lda, &x[i__ + x_dim1], ldx, &c_b5, &a[ + i__ + (i__ + 1) * a_dim1], lda, (ftnlen)9); /* Generate reflection P(i) to annihilate A(i,i+2:n) */ - i__2 = *n - i__; + i__2 = *n - i__; /* Computing MIN */ - i__3 = i__ + 2; - dlarfg_(&i__2, &a[i__ + (i__ + 1) * a_dim1], &a[i__ + min( - i__3,*n) * a_dim1], lda, &taup[i__]); - e[i__] = a[i__ + (i__ + 1) * a_dim1]; - a[i__ + (i__ + 1) * a_dim1] = 1.; + i__3 = i__ + 2; + dlarfg_(&i__2, &a[i__ + (i__ + 1) * a_dim1], &a[i__ + min( + i__3,*n) * a_dim1], lda, &taup[i__]); + e[i__] = a[i__ + (i__ + 1) * a_dim1]; + a[i__ + (i__ + 1) * a_dim1] = 1.; /* Compute X(i+1:m,i) */ - i__2 = *m - i__; - i__3 = *n - i__; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + (i__ - + 1) * a_dim1], lda, &a[i__ + (i__ + 1) * a_dim1], - lda, &c_b16, &x[i__ + 1 + i__ * x_dim1], &c__1, ( - ftnlen)12); - i__2 = *n - i__; - dgemv_((char *)"Transpose", &i__2, &i__, &c_b5, &y[i__ + 1 + y_dim1], - ldy, &a[i__ + (i__ + 1) * a_dim1], lda, &c_b16, &x[ - i__ * x_dim1 + 1], &c__1, (ftnlen)9); - i__2 = *m - i__; - dgemv_((char *)"No transpose", &i__2, &i__, &c_b4, &a[i__ + 1 + - a_dim1], lda, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[ - i__ + 1 + i__ * x_dim1], &c__1, (ftnlen)12); - i__2 = i__ - 1; - i__3 = *n - i__; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[(i__ + 1) * - a_dim1 + 1], lda, &a[i__ + (i__ + 1) * a_dim1], lda, & - c_b16, &x[i__ * x_dim1 + 1], &c__1, (ftnlen)12); - i__2 = *m - i__; - i__3 = i__ - 1; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &x[i__ + 1 + - x_dim1], ldx, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[ - i__ + 1 + i__ * x_dim1], &c__1, (ftnlen)12); - i__2 = *m - i__; - dscal_(&i__2, &taup[i__], &x[i__ + 1 + i__ * x_dim1], &c__1); - } + i__2 = *m - i__; + i__3 = *n - i__; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + (i__ + + 1) * a_dim1], lda, &a[i__ + (i__ + 1) * a_dim1], + lda, &c_b16, &x[i__ + 1 + i__ * x_dim1], &c__1, ( + ftnlen)12); + i__2 = *n - i__; + dgemv_((char *)"Transpose", &i__2, &i__, &c_b5, &y[i__ + 1 + y_dim1], + ldy, &a[i__ + (i__ + 1) * a_dim1], lda, &c_b16, &x[ + i__ * x_dim1 + 1], &c__1, (ftnlen)9); + i__2 = *m - i__; + dgemv_((char *)"No transpose", &i__2, &i__, &c_b4, &a[i__ + 1 + + a_dim1], lda, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[ + i__ + 1 + i__ * x_dim1], &c__1, (ftnlen)12); + i__2 = i__ - 1; + i__3 = *n - i__; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[(i__ + 1) * + a_dim1 + 1], lda, &a[i__ + (i__ + 1) * a_dim1], lda, & + c_b16, &x[i__ * x_dim1 + 1], &c__1, (ftnlen)12); + i__2 = *m - i__; + i__3 = i__ - 1; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &x[i__ + 1 + + x_dim1], ldx, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[ + i__ + 1 + i__ * x_dim1], &c__1, (ftnlen)12); + i__2 = *m - i__; + dscal_(&i__2, &taup[i__], &x[i__ + 1 + i__ * x_dim1], &c__1); + } /* L10: */ - } + } } else { /* Reduce to lower bidiagonal form */ - i__1 = *nb; - for (i__ = 1; i__ <= i__1; ++i__) { + i__1 = *nb; + for (i__ = 1; i__ <= i__1; ++i__) { /* Update A(i,i:n) */ - i__2 = *n - i__ + 1; - i__3 = i__ - 1; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &y[i__ + y_dim1], ldy, - &a[i__ + a_dim1], lda, &c_b5, &a[i__ + i__ * a_dim1], - lda, (ftnlen)12); - i__2 = i__ - 1; - i__3 = *n - i__ + 1; - dgemv_((char *)"Transpose", &i__2, &i__3, &c_b4, &a[i__ * a_dim1 + 1], - lda, &x[i__ + x_dim1], ldx, &c_b5, &a[i__ + i__ * a_dim1], - lda, (ftnlen)9); + i__2 = *n - i__ + 1; + i__3 = i__ - 1; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &y[i__ + y_dim1], ldy, + &a[i__ + a_dim1], lda, &c_b5, &a[i__ + i__ * a_dim1], + lda, (ftnlen)12); + i__2 = i__ - 1; + i__3 = *n - i__ + 1; + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b4, &a[i__ * a_dim1 + 1], + lda, &x[i__ + x_dim1], ldx, &c_b5, &a[i__ + i__ * a_dim1], + lda, (ftnlen)9); /* Generate reflection P(i) to annihilate A(i,i+1:n) */ - i__2 = *n - i__ + 1; + i__2 = *n - i__ + 1; /* Computing MIN */ - i__3 = i__ + 1; - dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[i__ + min(i__3,*n) * - a_dim1], lda, &taup[i__]); - d__[i__] = a[i__ + i__ * a_dim1]; - if (i__ < *m) { - a[i__ + i__ * a_dim1] = 1.; + i__3 = i__ + 1; + dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[i__ + min(i__3,*n) * + a_dim1], lda, &taup[i__]); + d__[i__] = a[i__ + i__ * a_dim1]; + if (i__ < *m) { + a[i__ + i__ * a_dim1] = 1.; /* Compute X(i+1:m,i) */ - i__2 = *m - i__; - i__3 = *n - i__ + 1; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + i__ * - a_dim1], lda, &a[i__ + i__ * a_dim1], lda, &c_b16, & - x[i__ + 1 + i__ * x_dim1], &c__1, (ftnlen)12); - i__2 = *n - i__ + 1; - i__3 = i__ - 1; - dgemv_((char *)"Transpose", &i__2, &i__3, &c_b5, &y[i__ + y_dim1], - ldy, &a[i__ + i__ * a_dim1], lda, &c_b16, &x[i__ * - x_dim1 + 1], &c__1, (ftnlen)9); - i__2 = *m - i__; - i__3 = i__ - 1; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &a[i__ + 1 + - a_dim1], lda, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[ - i__ + 1 + i__ * x_dim1], &c__1, (ftnlen)12); - i__2 = i__ - 1; - i__3 = *n - i__ + 1; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[i__ * a_dim1 + - 1], lda, &a[i__ + i__ * a_dim1], lda, &c_b16, &x[i__ * - x_dim1 + 1], &c__1, (ftnlen)12); - i__2 = *m - i__; - i__3 = i__ - 1; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &x[i__ + 1 + - x_dim1], ldx, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[ - i__ + 1 + i__ * x_dim1], &c__1, (ftnlen)12); - i__2 = *m - i__; - dscal_(&i__2, &taup[i__], &x[i__ + 1 + i__ * x_dim1], &c__1); + i__2 = *m - i__; + i__3 = *n - i__ + 1; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + i__ * + a_dim1], lda, &a[i__ + i__ * a_dim1], lda, &c_b16, & + x[i__ + 1 + i__ * x_dim1], &c__1, (ftnlen)12); + i__2 = *n - i__ + 1; + i__3 = i__ - 1; + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b5, &y[i__ + y_dim1], + ldy, &a[i__ + i__ * a_dim1], lda, &c_b16, &x[i__ * + x_dim1 + 1], &c__1, (ftnlen)9); + i__2 = *m - i__; + i__3 = i__ - 1; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &a[i__ + 1 + + a_dim1], lda, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[ + i__ + 1 + i__ * x_dim1], &c__1, (ftnlen)12); + i__2 = i__ - 1; + i__3 = *n - i__ + 1; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[i__ * a_dim1 + + 1], lda, &a[i__ + i__ * a_dim1], lda, &c_b16, &x[i__ * + x_dim1 + 1], &c__1, (ftnlen)12); + i__2 = *m - i__; + i__3 = i__ - 1; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &x[i__ + 1 + + x_dim1], ldx, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[ + i__ + 1 + i__ * x_dim1], &c__1, (ftnlen)12); + i__2 = *m - i__; + dscal_(&i__2, &taup[i__], &x[i__ + 1 + i__ * x_dim1], &c__1); /* Update A(i+1:m,i) */ - i__2 = *m - i__; - i__3 = i__ - 1; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &a[i__ + 1 + - a_dim1], lda, &y[i__ + y_dim1], ldy, &c_b5, &a[i__ + - 1 + i__ * a_dim1], &c__1, (ftnlen)12); - i__2 = *m - i__; - dgemv_((char *)"No transpose", &i__2, &i__, &c_b4, &x[i__ + 1 + - x_dim1], ldx, &a[i__ * a_dim1 + 1], &c__1, &c_b5, &a[ - i__ + 1 + i__ * a_dim1], &c__1, (ftnlen)12); + i__2 = *m - i__; + i__3 = i__ - 1; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &a[i__ + 1 + + a_dim1], lda, &y[i__ + y_dim1], ldy, &c_b5, &a[i__ + + 1 + i__ * a_dim1], &c__1, (ftnlen)12); + i__2 = *m - i__; + dgemv_((char *)"No transpose", &i__2, &i__, &c_b4, &x[i__ + 1 + + x_dim1], ldx, &a[i__ * a_dim1 + 1], &c__1, &c_b5, &a[ + i__ + 1 + i__ * a_dim1], &c__1, (ftnlen)12); /* Generate reflection Q(i) to annihilate A(i+2:m,i) */ - i__2 = *m - i__; + i__2 = *m - i__; /* Computing MIN */ - i__3 = i__ + 2; - dlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3,*m) + - i__ * a_dim1], &c__1, &tauq[i__]); - e[i__] = a[i__ + 1 + i__ * a_dim1]; - a[i__ + 1 + i__ * a_dim1] = 1.; + i__3 = i__ + 2; + dlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3,*m) + + i__ * a_dim1], &c__1, &tauq[i__]); + e[i__] = a[i__ + 1 + i__ * a_dim1]; + a[i__ + 1 + i__ * a_dim1] = 1.; /* Compute Y(i+1:n,i) */ - i__2 = *m - i__; - i__3 = *n - i__; - dgemv_((char *)"Transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + (i__ + - 1) * a_dim1], lda, &a[i__ + 1 + i__ * a_dim1], &c__1, - &c_b16, &y[i__ + 1 + i__ * y_dim1], &c__1, (ftnlen)9); - i__2 = *m - i__; - i__3 = i__ - 1; - dgemv_((char *)"Transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + a_dim1], - lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &y[ - i__ * y_dim1 + 1], &c__1, (ftnlen)9); - i__2 = *n - i__; - i__3 = i__ - 1; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &y[i__ + 1 + - y_dim1], ldy, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[ - i__ + 1 + i__ * y_dim1], &c__1, (ftnlen)12); - i__2 = *m - i__; - dgemv_((char *)"Transpose", &i__2, &i__, &c_b5, &x[i__ + 1 + x_dim1], - ldx, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &y[ - i__ * y_dim1 + 1], &c__1, (ftnlen)9); - i__2 = *n - i__; - dgemv_((char *)"Transpose", &i__, &i__2, &c_b4, &a[(i__ + 1) * a_dim1 - + 1], lda, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[i__ - + 1 + i__ * y_dim1], &c__1, (ftnlen)9); - i__2 = *n - i__; - dscal_(&i__2, &tauq[i__], &y[i__ + 1 + i__ * y_dim1], &c__1); - } + i__2 = *m - i__; + i__3 = *n - i__; + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + (i__ + + 1) * a_dim1], lda, &a[i__ + 1 + i__ * a_dim1], &c__1, + &c_b16, &y[i__ + 1 + i__ * y_dim1], &c__1, (ftnlen)9); + i__2 = *m - i__; + i__3 = i__ - 1; + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + a_dim1], + lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &y[ + i__ * y_dim1 + 1], &c__1, (ftnlen)9); + i__2 = *n - i__; + i__3 = i__ - 1; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &y[i__ + 1 + + y_dim1], ldy, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[ + i__ + 1 + i__ * y_dim1], &c__1, (ftnlen)12); + i__2 = *m - i__; + dgemv_((char *)"Transpose", &i__2, &i__, &c_b5, &x[i__ + 1 + x_dim1], + ldx, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &y[ + i__ * y_dim1 + 1], &c__1, (ftnlen)9); + i__2 = *n - i__; + dgemv_((char *)"Transpose", &i__, &i__2, &c_b4, &a[(i__ + 1) * a_dim1 + + 1], lda, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[i__ + + 1 + i__ * y_dim1], &c__1, (ftnlen)9); + i__2 = *n - i__; + dscal_(&i__2, &tauq[i__], &y[i__ + 1 + i__ * y_dim1], &c__1); + } /* L20: */ - } + } } return 0; @@ -528,5 +528,5 @@ f"> */ } /* dlabrd_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlacn2.cpp b/lib/linalg/dlacn2.cpp index befb0b4e52..7293447d88 100644 --- a/lib/linalg/dlacn2.cpp +++ b/lib/linalg/dlacn2.cpp @@ -1,13 +1,13 @@ /* fortran/dlacn2.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -157,8 +157,8 @@ f"> */ /* > ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988. */ /* > */ /* ===================================================================== */ -/* Subroutine */ int dlacn2_(integer *n, doublereal *v, doublereal *x, - integer *isgn, doublereal *est, integer *kase, integer *isave) +/* Subroutine */ int dlacn2_(integer *n, doublereal *v, doublereal *x, + integer *isgn, doublereal *est, integer *kase, integer *isave) { /* System generated locals */ integer i__1; @@ -172,8 +172,8 @@ f"> */ doublereal xs, temp; extern doublereal dasum_(integer *, doublereal *, integer *); integer jlast; - extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, - doublereal *, integer *); + extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, + doublereal *, integer *); extern integer idamax_(integer *, doublereal *, integer *); doublereal altsgn, estold; @@ -209,22 +209,22 @@ f"> */ /* Function Body */ if (*kase == 0) { - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - x[i__] = 1. / (doublereal) (*n); + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + x[i__] = 1. / (doublereal) (*n); /* L10: */ - } - *kase = 1; - isave[1] = 1; - return 0; + } + *kase = 1; + isave[1] = 1; + return 0; } switch (isave[1]) { - case 1: goto L20; - case 2: goto L40; - case 3: goto L70; - case 4: goto L110; - case 5: goto L140; + case 1: goto L20; + case 2: goto L40; + case 3: goto L70; + case 4: goto L110; + case 5: goto L140; } /* ................ ENTRY (ISAVE( 1 ) = 1) */ @@ -232,21 +232,21 @@ f"> */ L20: if (*n == 1) { - v[1] = x[1]; - *est = abs(v[1]); + v[1] = x[1]; + *est = abs(v[1]); /* ... QUIT */ - goto L150; + goto L150; } *est = dasum_(n, &x[1], &c__1); i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { - if (x[i__] >= 0.) { - x[i__] = 1.; - } else { - x[i__] = -1.; - } - isgn[i__] = i_dnnt(&x[i__]); + if (x[i__] >= 0.) { + x[i__] = 1.; + } else { + x[i__] = -1.; + } + isgn[i__] = i_dnnt(&x[i__]); /* L30: */ } *kase = 2; @@ -265,7 +265,7 @@ L40: L50: i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { - x[i__] = 0.; + x[i__] = 0.; /* L60: */ } x[isave[2]] = 1.; @@ -282,14 +282,14 @@ L70: *est = dasum_(n, &v[1], &c__1); i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { - if (x[i__] >= 0.) { - xs = 1.; - } else { - xs = -1.; - } - if (i_dnnt(&xs) != isgn[i__]) { - goto L90; - } + if (x[i__] >= 0.) { + xs = 1.; + } else { + xs = -1.; + } + if (i_dnnt(&xs) != isgn[i__]) { + goto L90; + } /* L80: */ } /* REPEATED SIGN VECTOR DETECTED, HENCE ALGORITHM HAS CONVERGED. */ @@ -298,17 +298,17 @@ L70: L90: /* TEST FOR CYCLING. */ if (*est <= estold) { - goto L120; + goto L120; } i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { - if (x[i__] >= 0.) { - x[i__] = 1.; - } else { - x[i__] = -1.; - } - isgn[i__] = i_dnnt(&x[i__]); + if (x[i__] >= 0.) { + x[i__] = 1.; + } else { + x[i__] = -1.; + } + isgn[i__] = i_dnnt(&x[i__]); /* L100: */ } *kase = 2; @@ -322,8 +322,8 @@ L110: jlast = isave[2]; isave[2] = idamax_(n, &x[1], &c__1); if (x[jlast] != (d__1 = x[isave[2]], abs(d__1)) && isave[3] < 5) { - ++isave[3]; - goto L50; + ++isave[3]; + goto L50; } /* ITERATION COMPLETE. FINAL STAGE. */ @@ -332,9 +332,9 @@ L120: altsgn = 1.; i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { - x[i__] = altsgn * ((doublereal) (i__ - 1) / (doublereal) (*n - 1) + - 1.); - altsgn = -altsgn; + x[i__] = altsgn * ((doublereal) (i__ - 1) / (doublereal) (*n - 1) + + 1.); + altsgn = -altsgn; /* L130: */ } *kase = 1; @@ -347,8 +347,8 @@ L120: L140: temp = dasum_(n, &x[1], &c__1) / (doublereal) (*n * 3) * 2.; if (temp > *est) { - dcopy_(n, &x[1], &c__1, &v[1], &c__1); - *est = temp; + dcopy_(n, &x[1], &c__1, &v[1], &c__1); + *est = temp; } L150: @@ -360,5 +360,5 @@ L150: } /* dlacn2_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlacpy.cpp b/lib/linalg/dlacpy.cpp index b1e62a5336..813a669202 100644 --- a/lib/linalg/dlacpy.cpp +++ b/lib/linalg/dlacpy.cpp @@ -1,13 +1,13 @@ /* fortran/dlacpy.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -120,7 +120,7 @@ f"> */ /* ===================================================================== */ /* Subroutine */ int dlacpy_(char *uplo, integer *m, integer *n, doublereal * - a, integer *lda, doublereal *b, integer *ldb, ftnlen uplo_len) + a, integer *lda, doublereal *b, integer *ldb, ftnlen uplo_len) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2; @@ -159,35 +159,35 @@ f"> */ /* Function Body */ if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = min(j,*m); - for (i__ = 1; i__ <= i__2; ++i__) { - b[i__ + j * b_dim1] = a[i__ + j * a_dim1]; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = min(j,*m); + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] = a[i__ + j * a_dim1]; /* L10: */ - } + } /* L20: */ - } + } } else if (lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = j; i__ <= i__2; ++i__) { - b[i__ + j * b_dim1] = a[i__ + j * a_dim1]; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = j; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] = a[i__ + j * a_dim1]; /* L30: */ - } + } /* L40: */ - } + } } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - b[i__ + j * b_dim1] = a[i__ + j * a_dim1]; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] = a[i__ + j * a_dim1]; /* L50: */ - } + } /* L60: */ - } + } } return 0; @@ -196,5 +196,5 @@ f"> */ } /* dlacpy_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dladiv.cpp b/lib/linalg/dladiv.cpp index 7ffd5485cc..d12fb854f0 100644 --- a/lib/linalg/dladiv.cpp +++ b/lib/linalg/dladiv.cpp @@ -1,13 +1,13 @@ /* fortran/dladiv.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -107,8 +107,8 @@ f"> */ /* > \ingroup doubleOTHERauxiliary */ /* ===================================================================== */ -/* Subroutine */ int dladiv_(doublereal *a, doublereal *b, doublereal *c__, - doublereal *d__, doublereal *p, doublereal *q) +/* Subroutine */ int dladiv_(doublereal *a, doublereal *b, doublereal *c__, + doublereal *d__, doublereal *p, doublereal *q) { /* System generated locals */ doublereal d__1, d__2; @@ -116,8 +116,8 @@ f"> */ /* Local variables */ doublereal s, aa, ab, bb, cc, cd, dd, be, un, ov, eps; extern doublereal dlamch_(char *, ftnlen); - extern /* Subroutine */ int dladiv1_(doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *, doublereal *); + extern /* Subroutine */ int dladiv1_(doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *, doublereal *); /* -- LAPACK auxiliary routine -- */ @@ -157,30 +157,30 @@ f"> */ eps = dlamch_((char *)"Epsilon", (ftnlen)7); be = 2. / (eps * eps); if (ab >= ov * .5) { - aa *= .5; - bb *= .5; - s *= 2.; + aa *= .5; + bb *= .5; + s *= 2.; } if (cd >= ov * .5) { - cc *= .5; - dd *= .5; - s *= .5; + cc *= .5; + dd *= .5; + s *= .5; } if (ab <= un * 2. / eps) { - aa *= be; - bb *= be; - s /= be; + aa *= be; + bb *= be; + s /= be; } if (cd <= un * 2. / eps) { - cc *= be; - dd *= be; - s *= be; + cc *= be; + dd *= be; + s *= be; } if (abs(*d__) <= abs(*c__)) { - dladiv1_(&aa, &bb, &cc, &dd, p, q); + dladiv1_(&aa, &bb, &cc, &dd, p, q); } else { - dladiv1_(&bb, &aa, &dd, &cc, p, q); - *q = -(*q); + dladiv1_(&bb, &aa, &dd, &cc, p, q); + *q = -(*q); } *p *= s; *q *= s; @@ -192,12 +192,12 @@ f"> */ } /* dladiv_ */ /* > \ingroup doubleOTHERauxiliary */ -/* Subroutine */ int dladiv1_(doublereal *a, doublereal *b, doublereal *c__, - doublereal *d__, doublereal *p, doublereal *q) +/* Subroutine */ int dladiv1_(doublereal *a, doublereal *b, doublereal *c__, + doublereal *d__, doublereal *p, doublereal *q) { doublereal r__, t; - extern doublereal dladiv2_(doublereal *, doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *); + extern doublereal dladiv2_(doublereal *, doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *); /* -- LAPACK auxiliary routine -- */ @@ -230,8 +230,8 @@ f"> */ } /* dladiv1_ */ /* > \ingroup doubleOTHERauxiliary */ -doublereal dladiv2_(doublereal *a, doublereal *b, doublereal *c__, doublereal - *d__, doublereal *r__, doublereal *t) +doublereal dladiv2_(doublereal *a, doublereal *b, doublereal *c__, doublereal + *d__, doublereal *r__, doublereal *t) { /* System generated locals */ doublereal ret_val; @@ -256,14 +256,14 @@ doublereal dladiv2_(doublereal *a, doublereal *b, doublereal *c__, doublereal /* .. Executable Statements .. */ if (*r__ != 0.) { - br = *b * *r__; - if (br != 0.) { - ret_val = (*a + br) * *t; - } else { - ret_val = *a * *t + *b * *t * *r__; - } + br = *b * *r__; + if (br != 0.) { + ret_val = (*a + br) * *t; + } else { + ret_val = *a * *t + *b * *t * *r__; + } } else { - ret_val = (*a + *d__ * (*b / *c__)) * *t; + ret_val = (*a + *d__ * (*b / *c__)) * *t; } return ret_val; @@ -273,5 +273,5 @@ doublereal dladiv2_(doublereal *a, doublereal *b, doublereal *c__, doublereal } /* dladiv2_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlae2.cpp b/lib/linalg/dlae2.cpp index 2a1be2816d..7351921b21 100644 --- a/lib/linalg/dlae2.cpp +++ b/lib/linalg/dlae2.cpp @@ -1,13 +1,13 @@ /* fortran/dlae2.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -118,8 +118,8 @@ extern "C" { /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int dlae2_(doublereal *a, doublereal *b, doublereal *c__, - doublereal *rt1, doublereal *rt2) +/* Subroutine */ int dlae2_(doublereal *a, doublereal *b, doublereal *c__, + doublereal *rt1, doublereal *rt2) { /* System generated locals */ doublereal d__1; @@ -156,48 +156,48 @@ extern "C" { tb = *b + *b; ab = abs(tb); if (abs(*a) > abs(*c__)) { - acmx = *a; - acmn = *c__; + acmx = *a; + acmn = *c__; } else { - acmx = *c__; - acmn = *a; + acmx = *c__; + acmn = *a; } if (adf > ab) { /* Computing 2nd power */ - d__1 = ab / adf; - rt = adf * sqrt(d__1 * d__1 + 1.); + d__1 = ab / adf; + rt = adf * sqrt(d__1 * d__1 + 1.); } else if (adf < ab) { /* Computing 2nd power */ - d__1 = adf / ab; - rt = ab * sqrt(d__1 * d__1 + 1.); + d__1 = adf / ab; + rt = ab * sqrt(d__1 * d__1 + 1.); } else { /* Includes case AB=ADF=0 */ - rt = ab * sqrt(2.); + rt = ab * sqrt(2.); } if (sm < 0.) { - *rt1 = (sm - rt) * .5; + *rt1 = (sm - rt) * .5; /* Order of execution important. */ /* To get fully accurate smaller eigenvalue, */ /* next line needs to be executed in higher precision. */ - *rt2 = acmx / *rt1 * acmn - *b / *rt1 * *b; + *rt2 = acmx / *rt1 * acmn - *b / *rt1 * *b; } else if (sm > 0.) { - *rt1 = (sm + rt) * .5; + *rt1 = (sm + rt) * .5; /* Order of execution important. */ /* To get fully accurate smaller eigenvalue, */ /* next line needs to be executed in higher precision. */ - *rt2 = acmx / *rt1 * acmn - *b / *rt1 * *b; + *rt2 = acmx / *rt1 * acmn - *b / *rt1 * *b; } else { /* Includes case RT1 = RT2 = 0 */ - *rt1 = rt * .5; - *rt2 = rt * -.5; + *rt1 = rt * .5; + *rt2 = rt * -.5; } return 0; @@ -206,5 +206,5 @@ extern "C" { } /* dlae2_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlaed0.cpp b/lib/linalg/dlaed0.cpp index 41b13a3cac..68fee93814 100644 --- a/lib/linalg/dlaed0.cpp +++ b/lib/linalg/dlaed0.cpp @@ -1,13 +1,13 @@ /* fortran/dlaed0.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -24,7 +24,7 @@ static doublereal c_b23 = 1.; static doublereal c_b24 = 0.; static integer c__1 = 1; -/* > \brief \b DLAED0 used by DSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced +/* > \brief \b DLAED0 used by DSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method. */ /* =========== DOCUMENTATION =========== */ @@ -197,10 +197,10 @@ f"> */ /* > at Berkeley, USA */ /* ===================================================================== */ -/* Subroutine */ int dlaed0_(integer *icompq, integer *qsiz, integer *n, - doublereal *d__, doublereal *e, doublereal *q, integer *ldq, - doublereal *qstore, integer *ldqs, doublereal *work, integer *iwork, - integer *info) +/* Subroutine */ int dlaed0_(integer *icompq, integer *qsiz, integer *n, + doublereal *d__, doublereal *e, doublereal *q, integer *ldq, + doublereal *qstore, integer *ldqs, doublereal *work, integer *iwork, + integer *info) { /* System generated locals */ integer q_dim1, q_offset, qstore_dim1, qstore_offset, i__1, i__2; @@ -214,33 +214,33 @@ f"> */ integer i__, j, k, iq, lgn, msd2, smm1, spm1, spm2; doublereal temp; integer curr; - extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); integer iperm; - extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, - doublereal *, integer *); + extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, + doublereal *, integer *); integer indxq, iwrem; extern /* Subroutine */ int dlaed1_(integer *, doublereal *, doublereal *, - integer *, integer *, doublereal *, integer *, doublereal *, - integer *, integer *); + integer *, integer *, doublereal *, integer *, doublereal *, + integer *, integer *); integer iqptr; - extern /* Subroutine */ int dlaed7_(integer *, integer *, integer *, - integer *, integer *, integer *, doublereal *, doublereal *, - integer *, integer *, doublereal *, integer *, doublereal *, - integer *, integer *, integer *, integer *, integer *, doublereal - *, doublereal *, integer *, integer *); + extern /* Subroutine */ int dlaed7_(integer *, integer *, integer *, + integer *, integer *, integer *, doublereal *, doublereal *, + integer *, integer *, doublereal *, integer *, doublereal *, + integer *, integer *, integer *, integer *, integer *, doublereal + *, doublereal *, integer *, integer *); integer tlvls; - extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, - doublereal *, integer *, doublereal *, integer *, ftnlen); + extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, + doublereal *, integer *, doublereal *, integer *, ftnlen); integer igivcl; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); integer igivnm, submat, curprb, subpbs, igivpt; - extern /* Subroutine */ int dsteqr_(char *, integer *, doublereal *, - doublereal *, doublereal *, integer *, doublereal *, integer *, - ftnlen); + extern /* Subroutine */ int dsteqr_(char *, integer *, doublereal *, + doublereal *, doublereal *, integer *, doublereal *, integer *, + ftnlen); integer curlvl, matsiz, iprmpt, smlsiz; @@ -285,30 +285,30 @@ f"> */ *info = 0; if (*icompq < 0 || *icompq > 2) { - *info = -1; + *info = -1; } else if (*icompq == 1 && *qsiz < max(0,*n)) { - *info = -2; + *info = -2; } else if (*n < 0) { - *info = -3; + *info = -3; } else if (*ldq < max(1,*n)) { - *info = -7; + *info = -7; } else if (*ldqs < max(1,*n)) { - *info = -9; + *info = -9; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DLAED0", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DLAED0", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*n == 0) { - return 0; + return 0; } smlsiz = ilaenv_(&c__9, (char *)"DLAED0", (char *)" ", &c__0, &c__0, &c__0, &c__0, ( - ftnlen)6, (ftnlen)1); + ftnlen)6, (ftnlen)1); /* Determine the size and placement of the submatrices, and save in */ /* the leading elements of IWORK. */ @@ -318,18 +318,18 @@ f"> */ tlvls = 0; L10: if (iwork[subpbs] > smlsiz) { - for (j = subpbs; j >= 1; --j) { - iwork[j * 2] = (iwork[j] + 1) / 2; - iwork[(j << 1) - 1] = iwork[j] / 2; + for (j = subpbs; j >= 1; --j) { + iwork[j * 2] = (iwork[j] + 1) / 2; + iwork[(j << 1) - 1] = iwork[j] / 2; /* L20: */ - } - ++tlvls; - subpbs <<= 1; - goto L10; + } + ++tlvls; + subpbs <<= 1; + goto L10; } i__1 = subpbs; for (j = 2; j <= i__1; ++j) { - iwork[j] += iwork[j - 1]; + iwork[j] += iwork[j - 1]; /* L30: */ } @@ -339,10 +339,10 @@ L10: spm1 = subpbs - 1; i__1 = spm1; for (i__ = 1; i__ <= i__1; ++i__) { - submat = iwork[i__] + 1; - smm1 = submat - 1; - d__[smm1] -= (d__1 = e[smm1], abs(d__1)); - d__[submat] -= (d__1 = e[smm1], abs(d__1)); + submat = iwork[i__] + 1; + smm1 = submat - 1; + d__[smm1] -= (d__1 = e[smm1], abs(d__1)); + d__[submat] -= (d__1 = e[smm1], abs(d__1)); /* L40: */ } @@ -352,35 +352,35 @@ L10: /* Set up workspaces for eigenvalues only/accumulate new vectors */ /* routine */ - temp = log((doublereal) (*n)) / log(2.); - lgn = (integer) temp; - if (pow_ii(&c__2, &lgn) < *n) { - ++lgn; - } - if (pow_ii(&c__2, &lgn) < *n) { - ++lgn; - } - iprmpt = indxq + *n + 1; - iperm = iprmpt + *n * lgn; - iqptr = iperm + *n * lgn; - igivpt = iqptr + *n + 2; - igivcl = igivpt + *n * lgn; + temp = log((doublereal) (*n)) / log(2.); + lgn = (integer) temp; + if (pow_ii(&c__2, &lgn) < *n) { + ++lgn; + } + if (pow_ii(&c__2, &lgn) < *n) { + ++lgn; + } + iprmpt = indxq + *n + 1; + iperm = iprmpt + *n * lgn; + iqptr = iperm + *n * lgn; + igivpt = iqptr + *n + 2; + igivcl = igivpt + *n * lgn; - igivnm = 1; - iq = igivnm + (*n << 1) * lgn; + igivnm = 1; + iq = igivnm + (*n << 1) * lgn; /* Computing 2nd power */ - i__1 = *n; - iwrem = iq + i__1 * i__1 + 1; + i__1 = *n; + iwrem = iq + i__1 * i__1 + 1; /* Initialize pointers */ - i__1 = subpbs; - for (i__ = 0; i__ <= i__1; ++i__) { - iwork[iprmpt + i__] = 1; - iwork[igivpt + i__] = 1; + i__1 = subpbs; + for (i__ = 0; i__ <= i__1; ++i__) { + iwork[iprmpt + i__] = 1; + iwork[igivpt + i__] = 1; /* L50: */ - } - iwork[iqptr] = 1; + } + iwork[iqptr] = 1; } /* Solve each submatrix eigenproblem at the bottom of the divide and */ @@ -389,43 +389,43 @@ L10: curr = 0; i__1 = spm1; for (i__ = 0; i__ <= i__1; ++i__) { - if (i__ == 0) { - submat = 1; - matsiz = iwork[1]; - } else { - submat = iwork[i__] + 1; - matsiz = iwork[i__ + 1] - iwork[i__]; - } - if (*icompq == 2) { - dsteqr_((char *)"I", &matsiz, &d__[submat], &e[submat], &q[submat + - submat * q_dim1], ldq, &work[1], info, (ftnlen)1); - if (*info != 0) { - goto L130; - } - } else { - dsteqr_((char *)"I", &matsiz, &d__[submat], &e[submat], &work[iq - 1 + - iwork[iqptr + curr]], &matsiz, &work[1], info, (ftnlen)1); - if (*info != 0) { - goto L130; - } - if (*icompq == 1) { - dgemm_((char *)"N", (char *)"N", qsiz, &matsiz, &matsiz, &c_b23, &q[submat * - q_dim1 + 1], ldq, &work[iq - 1 + iwork[iqptr + curr]], - &matsiz, &c_b24, &qstore[submat * qstore_dim1 + 1], - ldqs, (ftnlen)1, (ftnlen)1); - } + if (i__ == 0) { + submat = 1; + matsiz = iwork[1]; + } else { + submat = iwork[i__] + 1; + matsiz = iwork[i__ + 1] - iwork[i__]; + } + if (*icompq == 2) { + dsteqr_((char *)"I", &matsiz, &d__[submat], &e[submat], &q[submat + + submat * q_dim1], ldq, &work[1], info, (ftnlen)1); + if (*info != 0) { + goto L130; + } + } else { + dsteqr_((char *)"I", &matsiz, &d__[submat], &e[submat], &work[iq - 1 + + iwork[iqptr + curr]], &matsiz, &work[1], info, (ftnlen)1); + if (*info != 0) { + goto L130; + } + if (*icompq == 1) { + dgemm_((char *)"N", (char *)"N", qsiz, &matsiz, &matsiz, &c_b23, &q[submat * + q_dim1 + 1], ldq, &work[iq - 1 + iwork[iqptr + curr]], + &matsiz, &c_b24, &qstore[submat * qstore_dim1 + 1], + ldqs, (ftnlen)1, (ftnlen)1); + } /* Computing 2nd power */ - i__2 = matsiz; - iwork[iqptr + curr + 1] = iwork[iqptr + curr] + i__2 * i__2; - ++curr; - } - k = 1; - i__2 = iwork[i__ + 1]; - for (j = submat; j <= i__2; ++j) { - iwork[indxq + j] = k; - ++k; + i__2 = matsiz; + iwork[iqptr + curr + 1] = iwork[iqptr + curr] + i__2 * i__2; + ++curr; + } + k = 1; + i__2 = iwork[i__ + 1]; + for (j = submat; j <= i__2; ++j) { + iwork[indxq + j] = k; + ++k; /* L60: */ - } + } /* L70: */ } @@ -437,20 +437,20 @@ L10: curlvl = 1; L80: if (subpbs > 1) { - spm2 = subpbs - 2; - i__1 = spm2; - for (i__ = 0; i__ <= i__1; i__ += 2) { - if (i__ == 0) { - submat = 1; - matsiz = iwork[2]; - msd2 = iwork[1]; - curprb = 0; - } else { - submat = iwork[i__] + 1; - matsiz = iwork[i__ + 2] - iwork[i__]; - msd2 = matsiz / 2; - ++curprb; - } + spm2 = subpbs - 2; + i__1 = spm2; + for (i__ = 0; i__ <= i__1; i__ += 2) { + if (i__ == 0) { + submat = 1; + matsiz = iwork[2]; + msd2 = iwork[1]; + curprb = 0; + } else { + submat = iwork[i__] + 1; + matsiz = iwork[i__ + 2] - iwork[i__]; + msd2 = matsiz / 2; + ++curprb; + } /* Merge lower order eigensystems (of size MSD2 and MATSIZ - MSD2) */ /* into an eigensystem of size MATSIZ. */ @@ -460,27 +460,27 @@ L80: /* and eigenvectors of a full symmetric matrix (which was reduced to */ /* tridiagonal form) are desired. */ - if (*icompq == 2) { - dlaed1_(&matsiz, &d__[submat], &q[submat + submat * q_dim1], - ldq, &iwork[indxq + submat], &e[submat + msd2 - 1], & - msd2, &work[1], &iwork[subpbs + 1], info); - } else { - dlaed7_(icompq, &matsiz, qsiz, &tlvls, &curlvl, &curprb, &d__[ - submat], &qstore[submat * qstore_dim1 + 1], ldqs, & - iwork[indxq + submat], &e[submat + msd2 - 1], &msd2, & - work[iq], &iwork[iqptr], &iwork[iprmpt], &iwork[iperm] - , &iwork[igivpt], &iwork[igivcl], &work[igivnm], & - work[iwrem], &iwork[subpbs + 1], info); - } - if (*info != 0) { - goto L130; - } - iwork[i__ / 2 + 1] = iwork[i__ + 2]; + if (*icompq == 2) { + dlaed1_(&matsiz, &d__[submat], &q[submat + submat * q_dim1], + ldq, &iwork[indxq + submat], &e[submat + msd2 - 1], & + msd2, &work[1], &iwork[subpbs + 1], info); + } else { + dlaed7_(icompq, &matsiz, qsiz, &tlvls, &curlvl, &curprb, &d__[ + submat], &qstore[submat * qstore_dim1 + 1], ldqs, & + iwork[indxq + submat], &e[submat + msd2 - 1], &msd2, & + work[iq], &iwork[iqptr], &iwork[iprmpt], &iwork[iperm] + , &iwork[igivpt], &iwork[igivcl], &work[igivnm], & + work[iwrem], &iwork[subpbs + 1], info); + } + if (*info != 0) { + goto L130; + } + iwork[i__ / 2 + 1] = iwork[i__ + 2]; /* L90: */ - } - subpbs /= 2; - ++curlvl; - goto L80; + } + subpbs /= 2; + ++curlvl; + goto L80; } /* end while */ @@ -489,33 +489,33 @@ L80: /* merge step. */ if (*icompq == 1) { - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - j = iwork[indxq + i__]; - work[i__] = d__[j]; - dcopy_(qsiz, &qstore[j * qstore_dim1 + 1], &c__1, &q[i__ * q_dim1 - + 1], &c__1); + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + j = iwork[indxq + i__]; + work[i__] = d__[j]; + dcopy_(qsiz, &qstore[j * qstore_dim1 + 1], &c__1, &q[i__ * q_dim1 + + 1], &c__1); /* L100: */ - } - dcopy_(n, &work[1], &c__1, &d__[1], &c__1); + } + dcopy_(n, &work[1], &c__1, &d__[1], &c__1); } else if (*icompq == 2) { - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - j = iwork[indxq + i__]; - work[i__] = d__[j]; - dcopy_(n, &q[j * q_dim1 + 1], &c__1, &work[*n * i__ + 1], &c__1); + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + j = iwork[indxq + i__]; + work[i__] = d__[j]; + dcopy_(n, &q[j * q_dim1 + 1], &c__1, &work[*n * i__ + 1], &c__1); /* L110: */ - } - dcopy_(n, &work[1], &c__1, &d__[1], &c__1); - dlacpy_((char *)"A", n, n, &work[*n + 1], n, &q[q_offset], ldq, (ftnlen)1); + } + dcopy_(n, &work[1], &c__1, &d__[1], &c__1); + dlacpy_((char *)"A", n, n, &work[*n + 1], n, &q[q_offset], ldq, (ftnlen)1); } else { - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - j = iwork[indxq + i__]; - work[i__] = d__[j]; + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + j = iwork[indxq + i__]; + work[i__] = d__[j]; /* L120: */ - } - dcopy_(n, &work[1], &c__1, &d__[1], &c__1); + } + dcopy_(n, &work[1], &c__1, &d__[1], &c__1); } goto L140; @@ -530,5 +530,5 @@ L140: } /* dlaed0_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlaed1.cpp b/lib/linalg/dlaed1.cpp index a448e3363e..ff6c537c7c 100644 --- a/lib/linalg/dlaed1.cpp +++ b/lib/linalg/dlaed1.cpp @@ -1,13 +1,13 @@ /* fortran/dlaed1.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -184,29 +184,29 @@ f"> */ /* > Modified by Francoise Tisseur, University of Tennessee */ /* > */ /* ===================================================================== */ -/* Subroutine */ int dlaed1_(integer *n, doublereal *d__, doublereal *q, - integer *ldq, integer *indxq, doublereal *rho, integer *cutpnt, - doublereal *work, integer *iwork, integer *info) +/* Subroutine */ int dlaed1_(integer *n, doublereal *d__, doublereal *q, + integer *ldq, integer *indxq, doublereal *rho, integer *cutpnt, + doublereal *work, integer *iwork, integer *info) { /* System generated locals */ integer q_dim1, q_offset, i__1, i__2; /* Local variables */ integer i__, k, n1, n2, is, iw, iz, iq2, zpp1, indx, indxc; - extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, - doublereal *, integer *); + extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, + doublereal *, integer *); integer indxp; - extern /* Subroutine */ int dlaed2_(integer *, integer *, integer *, - doublereal *, doublereal *, integer *, integer *, doublereal *, - doublereal *, doublereal *, doublereal *, doublereal *, integer *, - integer *, integer *, integer *, integer *), dlaed3_(integer *, - integer *, integer *, doublereal *, doublereal *, integer *, - doublereal *, doublereal *, doublereal *, integer *, integer *, - doublereal *, doublereal *, integer *); + extern /* Subroutine */ int dlaed2_(integer *, integer *, integer *, + doublereal *, doublereal *, integer *, integer *, doublereal *, + doublereal *, doublereal *, doublereal *, doublereal *, integer *, + integer *, integer *, integer *, integer *), dlaed3_(integer *, + integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, doublereal *, doublereal *, integer *, integer *, + doublereal *, doublereal *, integer *); integer idlmda; - extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *, - integer *, integer *, integer *), xerbla_(char *, integer *, - ftnlen); + extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *, + integer *, integer *, integer *), xerbla_(char *, integer *, + ftnlen); integer coltyp; @@ -244,26 +244,26 @@ f"> */ *info = 0; if (*n < 0) { - *info = -1; + *info = -1; } else if (*ldq < max(1,*n)) { - *info = -4; + *info = -4; } else /* if(complicated condition) */ { /* Computing MIN */ - i__1 = 1, i__2 = *n / 2; - if (min(i__1,i__2) > *cutpnt || *n / 2 < *cutpnt) { - *info = -7; - } + i__1 = 1, i__2 = *n / 2; + if (min(i__1,i__2) > *cutpnt || *n / 2 < *cutpnt) { + *info = -7; + } } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DLAED1", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DLAED1", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*n == 0) { - return 0; + return 0; } /* The following values are integer pointers which indicate */ @@ -292,36 +292,36 @@ f"> */ /* Deflate eigenvalues. */ dlaed2_(&k, n, cutpnt, &d__[1], &q[q_offset], ldq, &indxq[1], rho, &work[ - iz], &work[idlmda], &work[iw], &work[iq2], &iwork[indx], &iwork[ - indxc], &iwork[indxp], &iwork[coltyp], info); + iz], &work[idlmda], &work[iw], &work[iq2], &iwork[indx], &iwork[ + indxc], &iwork[indxp], &iwork[coltyp], info); if (*info != 0) { - goto L20; + goto L20; } /* Solve Secular Equation. */ if (k != 0) { - is = (iwork[coltyp] + iwork[coltyp + 1]) * *cutpnt + (iwork[coltyp + - 1] + iwork[coltyp + 2]) * (*n - *cutpnt) + iq2; - dlaed3_(&k, n, cutpnt, &d__[1], &q[q_offset], ldq, rho, &work[idlmda], - &work[iq2], &iwork[indxc], &iwork[coltyp], &work[iw], &work[ - is], info); - if (*info != 0) { - goto L20; - } + is = (iwork[coltyp] + iwork[coltyp + 1]) * *cutpnt + (iwork[coltyp + + 1] + iwork[coltyp + 2]) * (*n - *cutpnt) + iq2; + dlaed3_(&k, n, cutpnt, &d__[1], &q[q_offset], ldq, rho, &work[idlmda], + &work[iq2], &iwork[indxc], &iwork[coltyp], &work[iw], &work[ + is], info); + if (*info != 0) { + goto L20; + } /* Prepare the INDXQ sorting permutation. */ - n1 = k; - n2 = *n - k; - dlamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &indxq[1]); + n1 = k; + n2 = *n - k; + dlamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &indxq[1]); } else { - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - indxq[i__] = i__; + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + indxq[i__] = i__; /* L10: */ - } + } } L20: @@ -332,5 +332,5 @@ L20: } /* dlaed1_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlaed2.cpp b/lib/linalg/dlaed2.cpp index 746c07ba33..c56d856171 100644 --- a/lib/linalg/dlaed2.cpp +++ b/lib/linalg/dlaed2.cpp @@ -1,13 +1,13 @@ /* fortran/dlaed2.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -234,10 +234,10 @@ f"> */ /* > */ /* ===================================================================== */ /* Subroutine */ int dlaed2_(integer *k, integer *n, integer *n1, doublereal * - d__, doublereal *q, integer *ldq, integer *indxq, doublereal *rho, - doublereal *z__, doublereal *dlamda, doublereal *w, doublereal *q2, - integer *indx, integer *indxc, integer *indxp, integer *coltyp, - integer *info) + d__, doublereal *q, integer *ldq, integer *indxq, doublereal *rho, + doublereal *z__, doublereal *dlamda, doublereal *w, doublereal *q2, + integer *indx, integer *indxc, integer *indxp, integer *coltyp, + integer *info) { /* System generated locals */ integer q_dim1, q_offset, i__1, i__2; @@ -253,19 +253,19 @@ f"> */ integer k2, n2, ct, nj, pj, js, iq1, iq2, n1p1; doublereal eps, tau, tol; integer psm[4], imax, jmax; - extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, - doublereal *, integer *, doublereal *, doublereal *); + extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, + doublereal *, integer *, doublereal *, doublereal *); integer ctot[4]; - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *), dcopy_(integer *, doublereal *, integer *, doublereal - *, integer *); - extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, - ftnlen); + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *), dcopy_(integer *, doublereal *, integer *, doublereal + *, integer *); + extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, + ftnlen); extern integer idamax_(integer *, doublereal *, integer *); - extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *, - integer *, integer *, integer *), dlacpy_(char *, integer *, - integer *, doublereal *, integer *, doublereal *, integer *, - ftnlen), xerbla_(char *, integer *, ftnlen); + extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *, + integer *, integer *, integer *), dlacpy_(char *, integer *, + integer *, doublereal *, integer *, doublereal *, integer *, + ftnlen), xerbla_(char *, integer *, ftnlen); /* -- LAPACK computational routine -- */ @@ -314,33 +314,33 @@ f"> */ *info = 0; if (*n < 0) { - *info = -2; + *info = -2; } else if (*ldq < max(1,*n)) { - *info = -6; + *info = -6; } else /* if(complicated condition) */ { /* Computing MIN */ - i__1 = 1, i__2 = *n / 2; - if (min(i__1,i__2) > *n1 || *n / 2 < *n1) { - *info = -3; - } + i__1 = 1, i__2 = *n / 2; + if (min(i__1,i__2) > *n1 || *n / 2 < *n1) { + *info = -3; + } } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DLAED2", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DLAED2", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*n == 0) { - return 0; + return 0; } n2 = *n - *n1; n1p1 = *n1 + 1; if (*rho < 0.) { - dscal_(&n2, &c_b3, &z__[n1p1], &c__1); + dscal_(&n2, &c_b3, &z__[n1p1], &c__1); } /* Normalize z so that norm(z) = 1. Since z is the concatenation of */ @@ -357,7 +357,7 @@ f"> */ i__1 = *n; for (i__ = n1p1; i__ <= i__1; ++i__) { - indxq[i__] += *n1; + indxq[i__] += *n1; /* L10: */ } @@ -365,13 +365,13 @@ f"> */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { - dlamda[i__] = d__[indxq[i__]]; + dlamda[i__] = d__[indxq[i__]]; /* L20: */ } dlamrg_(n1, &n2, &dlamda[1], &c__1, &c__1, &indxc[1]); i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { - indx[i__] = indxq[indxc[i__]]; + indx[i__] = indxq[indxc[i__]]; /* L30: */ } @@ -382,7 +382,7 @@ f"> */ eps = dlamch_((char *)"Epsilon", (ftnlen)7); /* Computing MAX */ d__3 = (d__1 = d__[jmax], abs(d__1)), d__4 = (d__2 = z__[imax], abs(d__2)) - ; + ; tol = eps * 8. * max(d__3,d__4); /* If the rank-1 modifier is small enough, no more needs to be done */ @@ -390,19 +390,19 @@ f"> */ /* elements in D. */ if (*rho * (d__1 = z__[imax], abs(d__1)) <= tol) { - *k = 0; - iq2 = 1; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__ = indx[j]; - dcopy_(n, &q[i__ * q_dim1 + 1], &c__1, &q2[iq2], &c__1); - dlamda[j] = d__[i__]; - iq2 += *n; + *k = 0; + iq2 = 1; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__ = indx[j]; + dcopy_(n, &q[i__ * q_dim1 + 1], &c__1, &q2[iq2], &c__1); + dlamda[j] = d__[i__]; + iq2 += *n; /* L40: */ - } - dlacpy_((char *)"A", n, n, &q2[1], n, &q[q_offset], ldq, (ftnlen)1); - dcopy_(n, &dlamda[1], &c__1, &d__[1], &c__1); - goto L190; + } + dlacpy_((char *)"A", n, n, &q2[1], n, &q[q_offset], ldq, (ftnlen)1); + dcopy_(n, &dlamda[1], &c__1, &d__[1], &c__1); + goto L190; } /* If there are multiple eigenvalues then the problem deflates. Here */ @@ -413,12 +413,12 @@ f"> */ i__1 = *n1; for (i__ = 1; i__ <= i__1; ++i__) { - coltyp[i__] = 1; + coltyp[i__] = 1; /* L50: */ } i__1 = *n; for (i__ = n1p1; i__ <= i__1; ++i__) { - coltyp[i__] = 3; + coltyp[i__] = 3; /* L60: */ } @@ -427,96 +427,96 @@ f"> */ k2 = *n + 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { - nj = indx[j]; - if (*rho * (d__1 = z__[nj], abs(d__1)) <= tol) { + nj = indx[j]; + if (*rho * (d__1 = z__[nj], abs(d__1)) <= tol) { /* Deflate due to small z component. */ - --k2; - coltyp[nj] = 4; - indxp[k2] = nj; - if (j == *n) { - goto L100; - } - } else { - pj = nj; - goto L80; - } + --k2; + coltyp[nj] = 4; + indxp[k2] = nj; + if (j == *n) { + goto L100; + } + } else { + pj = nj; + goto L80; + } /* L70: */ } L80: ++j; nj = indx[j]; if (j > *n) { - goto L100; + goto L100; } if (*rho * (d__1 = z__[nj], abs(d__1)) <= tol) { /* Deflate due to small z component. */ - --k2; - coltyp[nj] = 4; - indxp[k2] = nj; + --k2; + coltyp[nj] = 4; + indxp[k2] = nj; } else { /* Check if eigenvalues are close enough to allow deflation. */ - s = z__[pj]; - c__ = z__[nj]; + s = z__[pj]; + c__ = z__[nj]; /* Find sqrt(a**2+b**2) without overflow or */ /* destructive underflow. */ - tau = dlapy2_(&c__, &s); - t = d__[nj] - d__[pj]; - c__ /= tau; - s = -s / tau; - if ((d__1 = t * c__ * s, abs(d__1)) <= tol) { + tau = dlapy2_(&c__, &s); + t = d__[nj] - d__[pj]; + c__ /= tau; + s = -s / tau; + if ((d__1 = t * c__ * s, abs(d__1)) <= tol) { /* Deflation is possible. */ - z__[nj] = tau; - z__[pj] = 0.; - if (coltyp[nj] != coltyp[pj]) { - coltyp[nj] = 2; - } - coltyp[pj] = 4; - drot_(n, &q[pj * q_dim1 + 1], &c__1, &q[nj * q_dim1 + 1], &c__1, & - c__, &s); + z__[nj] = tau; + z__[pj] = 0.; + if (coltyp[nj] != coltyp[pj]) { + coltyp[nj] = 2; + } + coltyp[pj] = 4; + drot_(n, &q[pj * q_dim1 + 1], &c__1, &q[nj * q_dim1 + 1], &c__1, & + c__, &s); /* Computing 2nd power */ - d__1 = c__; + d__1 = c__; /* Computing 2nd power */ - d__2 = s; - t = d__[pj] * (d__1 * d__1) + d__[nj] * (d__2 * d__2); + d__2 = s; + t = d__[pj] * (d__1 * d__1) + d__[nj] * (d__2 * d__2); /* Computing 2nd power */ - d__1 = s; + d__1 = s; /* Computing 2nd power */ - d__2 = c__; - d__[nj] = d__[pj] * (d__1 * d__1) + d__[nj] * (d__2 * d__2); - d__[pj] = t; - --k2; - i__ = 1; + d__2 = c__; + d__[nj] = d__[pj] * (d__1 * d__1) + d__[nj] * (d__2 * d__2); + d__[pj] = t; + --k2; + i__ = 1; L90: - if (k2 + i__ <= *n) { - if (d__[pj] < d__[indxp[k2 + i__]]) { - indxp[k2 + i__ - 1] = indxp[k2 + i__]; - indxp[k2 + i__] = pj; - ++i__; - goto L90; - } else { - indxp[k2 + i__ - 1] = pj; - } - } else { - indxp[k2 + i__ - 1] = pj; - } - pj = nj; - } else { - ++(*k); - dlamda[*k] = d__[pj]; - w[*k] = z__[pj]; - indxp[*k] = pj; - pj = nj; - } + if (k2 + i__ <= *n) { + if (d__[pj] < d__[indxp[k2 + i__]]) { + indxp[k2 + i__ - 1] = indxp[k2 + i__]; + indxp[k2 + i__] = pj; + ++i__; + goto L90; + } else { + indxp[k2 + i__ - 1] = pj; + } + } else { + indxp[k2 + i__ - 1] = pj; + } + pj = nj; + } else { + ++(*k); + dlamda[*k] = d__[pj]; + w[*k] = z__[pj]; + indxp[*k] = pj; + pj = nj; + } } goto L80; L100: @@ -534,13 +534,13 @@ L100: /* empty). */ for (j = 1; j <= 4; ++j) { - ctot[j - 1] = 0; + ctot[j - 1] = 0; /* L110: */ } i__1 = *n; for (j = 1; j <= i__1; ++j) { - ct = coltyp[j]; - ++ctot[ct - 1]; + ct = coltyp[j]; + ++ctot[ct - 1]; /* L120: */ } @@ -558,11 +558,11 @@ L100: i__1 = *n; for (j = 1; j <= i__1; ++j) { - js = indxp[j]; - ct = coltyp[js]; - indx[psm[ct - 1]] = js; - indxc[psm[ct - 1]] = j; - ++psm[ct - 1]; + js = indxp[j]; + ct = coltyp[js]; + indx[psm[ct - 1]] = js; + indxc[psm[ct - 1]] = j; + ++psm[ct - 1]; /* L130: */ } @@ -576,44 +576,44 @@ L100: iq2 = (ctot[0] + ctot[1]) * *n1 + 1; i__1 = ctot[0]; for (j = 1; j <= i__1; ++j) { - js = indx[i__]; - dcopy_(n1, &q[js * q_dim1 + 1], &c__1, &q2[iq1], &c__1); - z__[i__] = d__[js]; - ++i__; - iq1 += *n1; + js = indx[i__]; + dcopy_(n1, &q[js * q_dim1 + 1], &c__1, &q2[iq1], &c__1); + z__[i__] = d__[js]; + ++i__; + iq1 += *n1; /* L140: */ } i__1 = ctot[1]; for (j = 1; j <= i__1; ++j) { - js = indx[i__]; - dcopy_(n1, &q[js * q_dim1 + 1], &c__1, &q2[iq1], &c__1); - dcopy_(&n2, &q[*n1 + 1 + js * q_dim1], &c__1, &q2[iq2], &c__1); - z__[i__] = d__[js]; - ++i__; - iq1 += *n1; - iq2 += n2; + js = indx[i__]; + dcopy_(n1, &q[js * q_dim1 + 1], &c__1, &q2[iq1], &c__1); + dcopy_(&n2, &q[*n1 + 1 + js * q_dim1], &c__1, &q2[iq2], &c__1); + z__[i__] = d__[js]; + ++i__; + iq1 += *n1; + iq2 += n2; /* L150: */ } i__1 = ctot[2]; for (j = 1; j <= i__1; ++j) { - js = indx[i__]; - dcopy_(&n2, &q[*n1 + 1 + js * q_dim1], &c__1, &q2[iq2], &c__1); - z__[i__] = d__[js]; - ++i__; - iq2 += n2; + js = indx[i__]; + dcopy_(&n2, &q[*n1 + 1 + js * q_dim1], &c__1, &q2[iq2], &c__1); + z__[i__] = d__[js]; + ++i__; + iq2 += n2; /* L160: */ } iq1 = iq2; i__1 = ctot[3]; for (j = 1; j <= i__1; ++j) { - js = indx[i__]; - dcopy_(n, &q[js * q_dim1 + 1], &c__1, &q2[iq2], &c__1); - iq2 += *n; - z__[i__] = d__[js]; - ++i__; + js = indx[i__]; + dcopy_(n, &q[js * q_dim1 + 1], &c__1, &q2[iq2], &c__1); + iq2 += *n; + z__[i__] = d__[js]; + ++i__; /* L170: */ } @@ -621,16 +621,16 @@ L100: /* into the last N - K slots of D and Q respectively. */ if (*k < *n) { - dlacpy_((char *)"A", n, &ctot[3], &q2[iq1], n, &q[(*k + 1) * q_dim1 + 1], ldq, - (ftnlen)1); - i__1 = *n - *k; - dcopy_(&i__1, &z__[*k + 1], &c__1, &d__[*k + 1], &c__1); + dlacpy_((char *)"A", n, &ctot[3], &q2[iq1], n, &q[(*k + 1) * q_dim1 + 1], ldq, + (ftnlen)1); + i__1 = *n - *k; + dcopy_(&i__1, &z__[*k + 1], &c__1, &d__[*k + 1], &c__1); } /* Copy CTOT into COLTYP for referencing in DLAED3. */ for (j = 1; j <= 4; ++j) { - coltyp[j] = ctot[j - 1]; + coltyp[j] = ctot[j - 1]; /* L180: */ } @@ -642,5 +642,5 @@ L190: } /* dlaed2_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlaed3.cpp b/lib/linalg/dlaed3.cpp index e56c3fb41b..c1f5e908dc 100644 --- a/lib/linalg/dlaed3.cpp +++ b/lib/linalg/dlaed3.cpp @@ -1,13 +1,13 @@ /* fortran/dlaed3.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -208,9 +208,9 @@ f"> */ /* > */ /* ===================================================================== */ /* Subroutine */ int dlaed3_(integer *k, integer *n, integer *n1, doublereal * - d__, doublereal *q, integer *ldq, doublereal *rho, doublereal *dlamda, - doublereal *q2, integer *indx, integer *ctot, doublereal *w, - doublereal *s, integer *info) + d__, doublereal *q, integer *ldq, doublereal *rho, doublereal *dlamda, + doublereal *q2, integer *indx, integer *ctot, doublereal *w, + doublereal *s, integer *info) { /* System generated locals */ integer q_dim1, q_offset, i__1, i__2; @@ -223,18 +223,18 @@ f"> */ integer i__, j, n2, n12, ii, n23, iq2; doublereal temp; extern doublereal dnrm2_(integer *, doublereal *, integer *); - extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen), - dcopy_(integer *, doublereal *, integer *, doublereal *, integer - *), dlaed4_(integer *, integer *, doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *, integer *); + extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen), + dcopy_(integer *, doublereal *, integer *, doublereal *, integer + *), dlaed4_(integer *, integer *, doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *, integer *); extern doublereal dlamc3_(doublereal *, doublereal *); - extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, - doublereal *, integer *, doublereal *, integer *, ftnlen), - dlaset_(char *, integer *, integer *, doublereal *, doublereal *, - doublereal *, integer *, ftnlen), xerbla_(char *, integer *, - ftnlen); + extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, + doublereal *, integer *, doublereal *, integer *, ftnlen), + dlaset_(char *, integer *, integer *, doublereal *, doublereal *, + doublereal *, integer *, ftnlen), xerbla_(char *, integer *, + ftnlen); /* -- LAPACK computational routine -- */ @@ -278,22 +278,22 @@ f"> */ *info = 0; if (*k < 0) { - *info = -1; + *info = -1; } else if (*n < *k) { - *info = -2; + *info = -2; } else if (*ldq < max(1,*n)) { - *info = -6; + *info = -6; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DLAED3", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DLAED3", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*k == 0) { - return 0; + return 0; } /* Modify values DLAMDA(i) to make sure all DLAMDA(i)-DLAMDA(j) can */ @@ -315,38 +315,38 @@ f"> */ i__1 = *k; for (i__ = 1; i__ <= i__1; ++i__) { - dlamda[i__] = dlamc3_(&dlamda[i__], &dlamda[i__]) - dlamda[i__]; + dlamda[i__] = dlamc3_(&dlamda[i__], &dlamda[i__]) - dlamda[i__]; /* L10: */ } i__1 = *k; for (j = 1; j <= i__1; ++j) { - dlaed4_(k, &j, &dlamda[1], &w[1], &q[j * q_dim1 + 1], rho, &d__[j], - info); + dlaed4_(k, &j, &dlamda[1], &w[1], &q[j * q_dim1 + 1], rho, &d__[j], + info); /* If the zero finder fails, the computation is terminated. */ - if (*info != 0) { - goto L120; - } + if (*info != 0) { + goto L120; + } /* L20: */ } if (*k == 1) { - goto L110; + goto L110; } if (*k == 2) { - i__1 = *k; - for (j = 1; j <= i__1; ++j) { - w[1] = q[j * q_dim1 + 1]; - w[2] = q[j * q_dim1 + 2]; - ii = indx[1]; - q[j * q_dim1 + 1] = w[ii]; - ii = indx[2]; - q[j * q_dim1 + 2] = w[ii]; + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + w[1] = q[j * q_dim1 + 1]; + w[2] = q[j * q_dim1 + 2]; + ii = indx[1]; + q[j * q_dim1 + 1] = w[ii]; + ii = indx[2]; + q[j * q_dim1 + 2] = w[ii]; /* L30: */ - } - goto L110; + } + goto L110; } /* Compute updated W. */ @@ -359,22 +359,22 @@ f"> */ dcopy_(k, &q[q_offset], &i__1, &w[1], &c__1); i__1 = *k; for (j = 1; j <= i__1; ++j) { - i__2 = j - 1; - for (i__ = 1; i__ <= i__2; ++i__) { - w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]); + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]); /* L40: */ - } - i__2 = *k; - for (i__ = j + 1; i__ <= i__2; ++i__) { - w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]); + } + i__2 = *k; + for (i__ = j + 1; i__ <= i__2; ++i__) { + w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]); /* L50: */ - } + } /* L60: */ } i__1 = *k; for (i__ = 1; i__ <= i__1; ++i__) { - d__1 = sqrt(-w[i__]); - w[i__] = d_sign(&d__1, &s[i__]); + d__1 = sqrt(-w[i__]); + w[i__] = d_sign(&d__1, &s[i__]); /* L70: */ } @@ -382,18 +382,18 @@ f"> */ i__1 = *k; for (j = 1; j <= i__1; ++j) { - i__2 = *k; - for (i__ = 1; i__ <= i__2; ++i__) { - s[i__] = w[i__] / q[i__ + j * q_dim1]; + i__2 = *k; + for (i__ = 1; i__ <= i__2; ++i__) { + s[i__] = w[i__] / q[i__ + j * q_dim1]; /* L80: */ - } - temp = dnrm2_(k, &s[1], &c__1); - i__2 = *k; - for (i__ = 1; i__ <= i__2; ++i__) { - ii = indx[i__]; - q[i__ + j * q_dim1] = s[ii] / temp; + } + temp = dnrm2_(k, &s[1], &c__1); + i__2 = *k; + for (i__ = 1; i__ <= i__2; ++i__) { + ii = indx[i__]; + q[i__ + j * q_dim1] = s[ii] / temp; /* L90: */ - } + } /* L100: */ } @@ -406,22 +406,22 @@ L110: n23 = ctot[2] + ctot[3]; dlacpy_((char *)"A", &n23, k, &q[ctot[1] + 1 + q_dim1], ldq, &s[1], &n23, (ftnlen) - 1); + 1); iq2 = *n1 * n12 + 1; if (n23 != 0) { - dgemm_((char *)"N", (char *)"N", &n2, k, &n23, &c_b22, &q2[iq2], &n2, &s[1], &n23, & - c_b23, &q[*n1 + 1 + q_dim1], ldq, (ftnlen)1, (ftnlen)1); + dgemm_((char *)"N", (char *)"N", &n2, k, &n23, &c_b22, &q2[iq2], &n2, &s[1], &n23, & + c_b23, &q[*n1 + 1 + q_dim1], ldq, (ftnlen)1, (ftnlen)1); } else { - dlaset_((char *)"A", &n2, k, &c_b23, &c_b23, &q[*n1 + 1 + q_dim1], ldq, ( - ftnlen)1); + dlaset_((char *)"A", &n2, k, &c_b23, &c_b23, &q[*n1 + 1 + q_dim1], ldq, ( + ftnlen)1); } dlacpy_((char *)"A", &n12, k, &q[q_offset], ldq, &s[1], &n12, (ftnlen)1); if (n12 != 0) { - dgemm_((char *)"N", (char *)"N", n1, k, &n12, &c_b22, &q2[1], n1, &s[1], &n12, &c_b23, - &q[q_offset], ldq, (ftnlen)1, (ftnlen)1); + dgemm_((char *)"N", (char *)"N", n1, k, &n12, &c_b22, &q2[1], n1, &s[1], &n12, &c_b23, + &q[q_offset], ldq, (ftnlen)1, (ftnlen)1); } else { - dlaset_((char *)"A", n1, k, &c_b23, &c_b23, &q[q_dim1 + 1], ldq, (ftnlen)1); + dlaset_((char *)"A", n1, k, &c_b23, &c_b23, &q[q_dim1 + 1], ldq, (ftnlen)1); } @@ -433,5 +433,5 @@ L120: } /* dlaed3_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlaed4.cpp b/lib/linalg/dlaed4.cpp index 5cc622887d..ca532571dd 100644 --- a/lib/linalg/dlaed4.cpp +++ b/lib/linalg/dlaed4.cpp @@ -1,13 +1,13 @@ /* fortran/dlaed4.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -161,9 +161,9 @@ f"> */ /* > at Berkeley, USA */ /* > */ /* ===================================================================== */ -/* Subroutine */ int dlaed4_(integer *n, integer *i__, doublereal *d__, - doublereal *z__, doublereal *delta, doublereal *rho, doublereal *dlam, - integer *info) +/* Subroutine */ int dlaed4_(integer *n, integer *i__, doublereal *d__, + doublereal *z__, doublereal *delta, doublereal *rho, doublereal *dlam, + integer *info) { /* System generated locals */ integer i__1; @@ -187,9 +187,9 @@ f"> */ integer niter; logical swtch; extern /* Subroutine */ int dlaed5_(integer *, doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *), dlaed6_(integer *, - logical *, doublereal *, doublereal *, doublereal *, doublereal *, - doublereal *, integer *); + doublereal *, doublereal *, doublereal *), dlaed6_(integer *, + logical *, doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, integer *); logical swtch3; extern doublereal dlamch_(char *, ftnlen); logical orgati; @@ -237,13 +237,13 @@ f"> */ /* Presumably, I=1 upon entry */ - *dlam = d__[1] + *rho * z__[1] * z__[1]; - delta[1] = 1.; - return 0; + *dlam = d__[1] + *rho * z__[1] * z__[1]; + delta[1] = 1.; + return 0; } if (*n == 2) { - dlaed5_(i__, &d__[1], &z__[1], &delta[1], rho, dlam); - return 0; + dlaed5_(i__, &d__[1], &z__[1], &delta[1], rho, dlam); + return 0; } /* Compute machine epsilon */ @@ -257,140 +257,140 @@ f"> */ /* Initialize some basic variables */ - ii = *n - 1; - niter = 1; + ii = *n - 1; + niter = 1; /* Calculate initial guess */ - midpt = *rho / 2.; + midpt = *rho / 2.; /* If ||Z||_2 is not one, then TEMP should be set to */ /* RHO * ||Z||_2^2 / TWO */ - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - delta[j] = d__[j] - d__[*i__] - midpt; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + delta[j] = d__[j] - d__[*i__] - midpt; /* L10: */ - } + } - psi = 0.; - i__1 = *n - 2; - for (j = 1; j <= i__1; ++j) { - psi += z__[j] * z__[j] / delta[j]; + psi = 0.; + i__1 = *n - 2; + for (j = 1; j <= i__1; ++j) { + psi += z__[j] * z__[j] / delta[j]; /* L20: */ - } + } - c__ = rhoinv + psi; - w = c__ + z__[ii] * z__[ii] / delta[ii] + z__[*n] * z__[*n] / delta[* - n]; + c__ = rhoinv + psi; + w = c__ + z__[ii] * z__[ii] / delta[ii] + z__[*n] * z__[*n] / delta[* + n]; - if (w <= 0.) { - temp = z__[*n - 1] * z__[*n - 1] / (d__[*n] - d__[*n - 1] + *rho) - + z__[*n] * z__[*n] / *rho; - if (c__ <= temp) { - tau = *rho; - } else { - del = d__[*n] - d__[*n - 1]; - a = -c__ * del + z__[*n - 1] * z__[*n - 1] + z__[*n] * z__[*n] - ; - b = z__[*n] * z__[*n] * del; - if (a < 0.) { - tau = b * 2. / (sqrt(a * a + b * 4. * c__) - a); - } else { - tau = (a + sqrt(a * a + b * 4. * c__)) / (c__ * 2.); - } - } + if (w <= 0.) { + temp = z__[*n - 1] * z__[*n - 1] / (d__[*n] - d__[*n - 1] + *rho) + + z__[*n] * z__[*n] / *rho; + if (c__ <= temp) { + tau = *rho; + } else { + del = d__[*n] - d__[*n - 1]; + a = -c__ * del + z__[*n - 1] * z__[*n - 1] + z__[*n] * z__[*n] + ; + b = z__[*n] * z__[*n] * del; + if (a < 0.) { + tau = b * 2. / (sqrt(a * a + b * 4. * c__) - a); + } else { + tau = (a + sqrt(a * a + b * 4. * c__)) / (c__ * 2.); + } + } /* It can be proved that */ /* D(N)+RHO/2 <= LAMBDA(N) < D(N)+TAU <= D(N)+RHO */ - dltlb = midpt; - dltub = *rho; - } else { - del = d__[*n] - d__[*n - 1]; - a = -c__ * del + z__[*n - 1] * z__[*n - 1] + z__[*n] * z__[*n]; - b = z__[*n] * z__[*n] * del; - if (a < 0.) { - tau = b * 2. / (sqrt(a * a + b * 4. * c__) - a); - } else { - tau = (a + sqrt(a * a + b * 4. * c__)) / (c__ * 2.); - } + dltlb = midpt; + dltub = *rho; + } else { + del = d__[*n] - d__[*n - 1]; + a = -c__ * del + z__[*n - 1] * z__[*n - 1] + z__[*n] * z__[*n]; + b = z__[*n] * z__[*n] * del; + if (a < 0.) { + tau = b * 2. / (sqrt(a * a + b * 4. * c__) - a); + } else { + tau = (a + sqrt(a * a + b * 4. * c__)) / (c__ * 2.); + } /* It can be proved that */ /* D(N) < D(N)+TAU < LAMBDA(N) < D(N)+RHO/2 */ - dltlb = 0.; - dltub = midpt; - } + dltlb = 0.; + dltub = midpt; + } - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - delta[j] = d__[j] - d__[*i__] - tau; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + delta[j] = d__[j] - d__[*i__] - tau; /* L30: */ - } + } /* Evaluate PSI and the derivative DPSI */ - dpsi = 0.; - psi = 0.; - erretm = 0.; - i__1 = ii; - for (j = 1; j <= i__1; ++j) { - temp = z__[j] / delta[j]; - psi += z__[j] * temp; - dpsi += temp * temp; - erretm += psi; + dpsi = 0.; + psi = 0.; + erretm = 0.; + i__1 = ii; + for (j = 1; j <= i__1; ++j) { + temp = z__[j] / delta[j]; + psi += z__[j] * temp; + dpsi += temp * temp; + erretm += psi; /* L40: */ - } - erretm = abs(erretm); + } + erretm = abs(erretm); /* Evaluate PHI and the derivative DPHI */ - temp = z__[*n] / delta[*n]; - phi = z__[*n] * temp; - dphi = temp * temp; - erretm = (-phi - psi) * 8. + erretm - phi + rhoinv + abs(tau) * (dpsi - + dphi); + temp = z__[*n] / delta[*n]; + phi = z__[*n] * temp; + dphi = temp * temp; + erretm = (-phi - psi) * 8. + erretm - phi + rhoinv + abs(tau) * (dpsi + + dphi); - w = rhoinv + phi + psi; + w = rhoinv + phi + psi; /* Test for convergence */ - if (abs(w) <= eps * erretm) { - *dlam = d__[*i__] + tau; - goto L250; - } + if (abs(w) <= eps * erretm) { + *dlam = d__[*i__] + tau; + goto L250; + } - if (w <= 0.) { - dltlb = max(dltlb,tau); - } else { - dltub = min(dltub,tau); - } + if (w <= 0.) { + dltlb = max(dltlb,tau); + } else { + dltub = min(dltub,tau); + } /* Calculate the new step */ - ++niter; - c__ = w - delta[*n - 1] * dpsi - delta[*n] * dphi; - a = (delta[*n - 1] + delta[*n]) * w - delta[*n - 1] * delta[*n] * ( - dpsi + dphi); - b = delta[*n - 1] * delta[*n] * w; - if (c__ < 0.) { - c__ = abs(c__); - } - if (c__ == 0.) { + ++niter; + c__ = w - delta[*n - 1] * dpsi - delta[*n] * dphi; + a = (delta[*n - 1] + delta[*n]) * w - delta[*n - 1] * delta[*n] * ( + dpsi + dphi); + b = delta[*n - 1] * delta[*n] * w; + if (c__ < 0.) { + c__ = abs(c__); + } + if (c__ == 0.) { /* ETA = B/A */ /* ETA = RHO - TAU */ /* ETA = DLTUB - TAU */ /* Update proposed by Li, Ren-Cang: */ - eta = -w / (dpsi + dphi); - } else if (a >= 0.) { - eta = (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (c__ - * 2.); - } else { - eta = b * 2. / (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1))) - ); - } + eta = -w / (dpsi + dphi); + } else if (a >= 0.) { + eta = (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (c__ + * 2.); + } else { + eta = b * 2. / (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1))) + ); + } /* Note, eta should be positive if w is negative, and */ /* eta should be negative otherwise. However, */ @@ -398,82 +398,82 @@ f"> */ /* we simply use one Newton step instead. This way */ /* will guarantee eta*w < 0. */ - if (w * eta > 0.) { - eta = -w / (dpsi + dphi); - } - temp = tau + eta; - if (temp > dltub || temp < dltlb) { - if (w < 0.) { - eta = (dltub - tau) / 2.; - } else { - eta = (dltlb - tau) / 2.; - } - } - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - delta[j] -= eta; + if (w * eta > 0.) { + eta = -w / (dpsi + dphi); + } + temp = tau + eta; + if (temp > dltub || temp < dltlb) { + if (w < 0.) { + eta = (dltub - tau) / 2.; + } else { + eta = (dltlb - tau) / 2.; + } + } + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + delta[j] -= eta; /* L50: */ - } + } - tau += eta; + tau += eta; /* Evaluate PSI and the derivative DPSI */ - dpsi = 0.; - psi = 0.; - erretm = 0.; - i__1 = ii; - for (j = 1; j <= i__1; ++j) { - temp = z__[j] / delta[j]; - psi += z__[j] * temp; - dpsi += temp * temp; - erretm += psi; + dpsi = 0.; + psi = 0.; + erretm = 0.; + i__1 = ii; + for (j = 1; j <= i__1; ++j) { + temp = z__[j] / delta[j]; + psi += z__[j] * temp; + dpsi += temp * temp; + erretm += psi; /* L60: */ - } - erretm = abs(erretm); + } + erretm = abs(erretm); /* Evaluate PHI and the derivative DPHI */ - temp = z__[*n] / delta[*n]; - phi = z__[*n] * temp; - dphi = temp * temp; - erretm = (-phi - psi) * 8. + erretm - phi + rhoinv + abs(tau) * (dpsi - + dphi); + temp = z__[*n] / delta[*n]; + phi = z__[*n] * temp; + dphi = temp * temp; + erretm = (-phi - psi) * 8. + erretm - phi + rhoinv + abs(tau) * (dpsi + + dphi); - w = rhoinv + phi + psi; + w = rhoinv + phi + psi; /* Main loop to update the values of the array DELTA */ - iter = niter + 1; + iter = niter + 1; - for (niter = iter; niter <= 30; ++niter) { + for (niter = iter; niter <= 30; ++niter) { /* Test for convergence */ - if (abs(w) <= eps * erretm) { - *dlam = d__[*i__] + tau; - goto L250; - } + if (abs(w) <= eps * erretm) { + *dlam = d__[*i__] + tau; + goto L250; + } - if (w <= 0.) { - dltlb = max(dltlb,tau); - } else { - dltub = min(dltub,tau); - } + if (w <= 0.) { + dltlb = max(dltlb,tau); + } else { + dltub = min(dltub,tau); + } /* Calculate the new step */ - c__ = w - delta[*n - 1] * dpsi - delta[*n] * dphi; - a = (delta[*n - 1] + delta[*n]) * w - delta[*n - 1] * delta[*n] * - (dpsi + dphi); - b = delta[*n - 1] * delta[*n] * w; - if (a >= 0.) { - eta = (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / ( - c__ * 2.); - } else { - eta = b * 2. / (a - sqrt((d__1 = a * a - b * 4. * c__, abs( - d__1)))); - } + c__ = w - delta[*n - 1] * dpsi - delta[*n] * dphi; + a = (delta[*n - 1] + delta[*n]) * w - delta[*n - 1] * delta[*n] * + (dpsi + dphi); + b = delta[*n - 1] * delta[*n] * w; + if (a >= 0.) { + eta = (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / ( + c__ * 2.); + } else { + eta = b * 2. / (a - sqrt((d__1 = a * a - b * 4. * c__, abs( + d__1)))); + } /* Note, eta should be positive if w is negative, and */ /* eta should be negative otherwise. However, */ @@ -481,57 +481,57 @@ f"> */ /* we simply use one Newton step instead. This way */ /* will guarantee eta*w < 0. */ - if (w * eta > 0.) { - eta = -w / (dpsi + dphi); - } - temp = tau + eta; - if (temp > dltub || temp < dltlb) { - if (w < 0.) { - eta = (dltub - tau) / 2.; - } else { - eta = (dltlb - tau) / 2.; - } - } - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - delta[j] -= eta; + if (w * eta > 0.) { + eta = -w / (dpsi + dphi); + } + temp = tau + eta; + if (temp > dltub || temp < dltlb) { + if (w < 0.) { + eta = (dltub - tau) / 2.; + } else { + eta = (dltlb - tau) / 2.; + } + } + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + delta[j] -= eta; /* L70: */ - } + } - tau += eta; + tau += eta; /* Evaluate PSI and the derivative DPSI */ - dpsi = 0.; - psi = 0.; - erretm = 0.; - i__1 = ii; - for (j = 1; j <= i__1; ++j) { - temp = z__[j] / delta[j]; - psi += z__[j] * temp; - dpsi += temp * temp; - erretm += psi; + dpsi = 0.; + psi = 0.; + erretm = 0.; + i__1 = ii; + for (j = 1; j <= i__1; ++j) { + temp = z__[j] / delta[j]; + psi += z__[j] * temp; + dpsi += temp * temp; + erretm += psi; /* L80: */ - } - erretm = abs(erretm); + } + erretm = abs(erretm); /* Evaluate PHI and the derivative DPHI */ - temp = z__[*n] / delta[*n]; - phi = z__[*n] * temp; - dphi = temp * temp; - erretm = (-phi - psi) * 8. + erretm - phi + rhoinv + abs(tau) * ( - dpsi + dphi); + temp = z__[*n] / delta[*n]; + phi = z__[*n] * temp; + dphi = temp * temp; + erretm = (-phi - psi) * 8. + erretm - phi + rhoinv + abs(tau) * ( + dpsi + dphi); - w = rhoinv + phi + psi; + w = rhoinv + phi + psi; /* L90: */ - } + } /* Return with INFO = 1, NITER = MAXIT and not converged */ - *info = 1; - *dlam = d__[*i__] + tau; - goto L250; + *info = 1; + *dlam = d__[*i__] + tau; + goto L250; /* End for the case I = N */ @@ -539,228 +539,228 @@ f"> */ /* The case for I < N */ - niter = 1; - ip1 = *i__ + 1; + niter = 1; + ip1 = *i__ + 1; /* Calculate initial guess */ - del = d__[ip1] - d__[*i__]; - midpt = del / 2.; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - delta[j] = d__[j] - d__[*i__] - midpt; + del = d__[ip1] - d__[*i__]; + midpt = del / 2.; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + delta[j] = d__[j] - d__[*i__] - midpt; /* L100: */ - } + } - psi = 0.; - i__1 = *i__ - 1; - for (j = 1; j <= i__1; ++j) { - psi += z__[j] * z__[j] / delta[j]; + psi = 0.; + i__1 = *i__ - 1; + for (j = 1; j <= i__1; ++j) { + psi += z__[j] * z__[j] / delta[j]; /* L110: */ - } + } - phi = 0.; - i__1 = *i__ + 2; - for (j = *n; j >= i__1; --j) { - phi += z__[j] * z__[j] / delta[j]; + phi = 0.; + i__1 = *i__ + 2; + for (j = *n; j >= i__1; --j) { + phi += z__[j] * z__[j] / delta[j]; /* L120: */ - } - c__ = rhoinv + psi + phi; - w = c__ + z__[*i__] * z__[*i__] / delta[*i__] + z__[ip1] * z__[ip1] / - delta[ip1]; + } + c__ = rhoinv + psi + phi; + w = c__ + z__[*i__] * z__[*i__] / delta[*i__] + z__[ip1] * z__[ip1] / + delta[ip1]; - if (w > 0.) { + if (w > 0.) { /* d(i)< the ith eigenvalue < (d(i)+d(i+1))/2 */ /* We choose d(i) as origin. */ - orgati = TRUE_; - a = c__ * del + z__[*i__] * z__[*i__] + z__[ip1] * z__[ip1]; - b = z__[*i__] * z__[*i__] * del; - if (a > 0.) { - tau = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs( - d__1)))); - } else { - tau = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / ( - c__ * 2.); - } - dltlb = 0.; - dltub = midpt; - } else { + orgati = TRUE_; + a = c__ * del + z__[*i__] * z__[*i__] + z__[ip1] * z__[ip1]; + b = z__[*i__] * z__[*i__] * del; + if (a > 0.) { + tau = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs( + d__1)))); + } else { + tau = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / ( + c__ * 2.); + } + dltlb = 0.; + dltub = midpt; + } else { /* (d(i)+d(i+1))/2 <= the ith eigenvalue < d(i+1) */ /* We choose d(i+1) as origin. */ - orgati = FALSE_; - a = c__ * del - z__[*i__] * z__[*i__] - z__[ip1] * z__[ip1]; - b = z__[ip1] * z__[ip1] * del; - if (a < 0.) { - tau = b * 2. / (a - sqrt((d__1 = a * a + b * 4. * c__, abs( - d__1)))); - } else { - tau = -(a + sqrt((d__1 = a * a + b * 4. * c__, abs(d__1)))) / - (c__ * 2.); - } - dltlb = -midpt; - dltub = 0.; - } + orgati = FALSE_; + a = c__ * del - z__[*i__] * z__[*i__] - z__[ip1] * z__[ip1]; + b = z__[ip1] * z__[ip1] * del; + if (a < 0.) { + tau = b * 2. / (a - sqrt((d__1 = a * a + b * 4. * c__, abs( + d__1)))); + } else { + tau = -(a + sqrt((d__1 = a * a + b * 4. * c__, abs(d__1)))) / + (c__ * 2.); + } + dltlb = -midpt; + dltub = 0.; + } - if (orgati) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - delta[j] = d__[j] - d__[*i__] - tau; + if (orgati) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + delta[j] = d__[j] - d__[*i__] - tau; /* L130: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - delta[j] = d__[j] - d__[ip1] - tau; + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + delta[j] = d__[j] - d__[ip1] - tau; /* L140: */ - } - } - if (orgati) { - ii = *i__; - } else { - ii = *i__ + 1; - } - iim1 = ii - 1; - iip1 = ii + 1; + } + } + if (orgati) { + ii = *i__; + } else { + ii = *i__ + 1; + } + iim1 = ii - 1; + iip1 = ii + 1; /* Evaluate PSI and the derivative DPSI */ - dpsi = 0.; - psi = 0.; - erretm = 0.; - i__1 = iim1; - for (j = 1; j <= i__1; ++j) { - temp = z__[j] / delta[j]; - psi += z__[j] * temp; - dpsi += temp * temp; - erretm += psi; + dpsi = 0.; + psi = 0.; + erretm = 0.; + i__1 = iim1; + for (j = 1; j <= i__1; ++j) { + temp = z__[j] / delta[j]; + psi += z__[j] * temp; + dpsi += temp * temp; + erretm += psi; /* L150: */ - } - erretm = abs(erretm); + } + erretm = abs(erretm); /* Evaluate PHI and the derivative DPHI */ - dphi = 0.; - phi = 0.; - i__1 = iip1; - for (j = *n; j >= i__1; --j) { - temp = z__[j] / delta[j]; - phi += z__[j] * temp; - dphi += temp * temp; - erretm += phi; + dphi = 0.; + phi = 0.; + i__1 = iip1; + for (j = *n; j >= i__1; --j) { + temp = z__[j] / delta[j]; + phi += z__[j] * temp; + dphi += temp * temp; + erretm += phi; /* L160: */ - } + } - w = rhoinv + phi + psi; + w = rhoinv + phi + psi; /* W is the value of the secular function with */ /* its ii-th element removed. */ - swtch3 = FALSE_; - if (orgati) { - if (w < 0.) { - swtch3 = TRUE_; - } - } else { - if (w > 0.) { - swtch3 = TRUE_; - } - } - if (ii == 1 || ii == *n) { - swtch3 = FALSE_; - } + swtch3 = FALSE_; + if (orgati) { + if (w < 0.) { + swtch3 = TRUE_; + } + } else { + if (w > 0.) { + swtch3 = TRUE_; + } + } + if (ii == 1 || ii == *n) { + swtch3 = FALSE_; + } - temp = z__[ii] / delta[ii]; - dw = dpsi + dphi + temp * temp; - temp = z__[ii] * temp; - w += temp; - erretm = (phi - psi) * 8. + erretm + rhoinv * 2. + abs(temp) * 3. + - abs(tau) * dw; + temp = z__[ii] / delta[ii]; + dw = dpsi + dphi + temp * temp; + temp = z__[ii] * temp; + w += temp; + erretm = (phi - psi) * 8. + erretm + rhoinv * 2. + abs(temp) * 3. + + abs(tau) * dw; /* Test for convergence */ - if (abs(w) <= eps * erretm) { - if (orgati) { - *dlam = d__[*i__] + tau; - } else { - *dlam = d__[ip1] + tau; - } - goto L250; - } + if (abs(w) <= eps * erretm) { + if (orgati) { + *dlam = d__[*i__] + tau; + } else { + *dlam = d__[ip1] + tau; + } + goto L250; + } - if (w <= 0.) { - dltlb = max(dltlb,tau); - } else { - dltub = min(dltub,tau); - } + if (w <= 0.) { + dltlb = max(dltlb,tau); + } else { + dltub = min(dltub,tau); + } /* Calculate the new step */ - ++niter; - if (! swtch3) { - if (orgati) { + ++niter; + if (! swtch3) { + if (orgati) { /* Computing 2nd power */ - d__1 = z__[*i__] / delta[*i__]; - c__ = w - delta[ip1] * dw - (d__[*i__] - d__[ip1]) * (d__1 * - d__1); - } else { + d__1 = z__[*i__] / delta[*i__]; + c__ = w - delta[ip1] * dw - (d__[*i__] - d__[ip1]) * (d__1 * + d__1); + } else { /* Computing 2nd power */ - d__1 = z__[ip1] / delta[ip1]; - c__ = w - delta[*i__] * dw - (d__[ip1] - d__[*i__]) * (d__1 * - d__1); - } - a = (delta[*i__] + delta[ip1]) * w - delta[*i__] * delta[ip1] * - dw; - b = delta[*i__] * delta[ip1] * w; - if (c__ == 0.) { - if (a == 0.) { - if (orgati) { - a = z__[*i__] * z__[*i__] + delta[ip1] * delta[ip1] * - (dpsi + dphi); - } else { - a = z__[ip1] * z__[ip1] + delta[*i__] * delta[*i__] * - (dpsi + dphi); - } - } - eta = b / a; - } else if (a <= 0.) { - eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / ( - c__ * 2.); - } else { - eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs( - d__1)))); - } - } else { + d__1 = z__[ip1] / delta[ip1]; + c__ = w - delta[*i__] * dw - (d__[ip1] - d__[*i__]) * (d__1 * + d__1); + } + a = (delta[*i__] + delta[ip1]) * w - delta[*i__] * delta[ip1] * + dw; + b = delta[*i__] * delta[ip1] * w; + if (c__ == 0.) { + if (a == 0.) { + if (orgati) { + a = z__[*i__] * z__[*i__] + delta[ip1] * delta[ip1] * + (dpsi + dphi); + } else { + a = z__[ip1] * z__[ip1] + delta[*i__] * delta[*i__] * + (dpsi + dphi); + } + } + eta = b / a; + } else if (a <= 0.) { + eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / ( + c__ * 2.); + } else { + eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs( + d__1)))); + } + } else { /* Interpolation using THREE most relevant poles */ - temp = rhoinv + psi + phi; - if (orgati) { - temp1 = z__[iim1] / delta[iim1]; - temp1 *= temp1; - c__ = temp - delta[iip1] * (dpsi + dphi) - (d__[iim1] - d__[ - iip1]) * temp1; - zz[0] = z__[iim1] * z__[iim1]; - zz[2] = delta[iip1] * delta[iip1] * (dpsi - temp1 + dphi); - } else { - temp1 = z__[iip1] / delta[iip1]; - temp1 *= temp1; - c__ = temp - delta[iim1] * (dpsi + dphi) - (d__[iip1] - d__[ - iim1]) * temp1; - zz[0] = delta[iim1] * delta[iim1] * (dpsi + (dphi - temp1)); - zz[2] = z__[iip1] * z__[iip1]; - } - zz[1] = z__[ii] * z__[ii]; - dlaed6_(&niter, &orgati, &c__, &delta[iim1], zz, &w, &eta, info); - if (*info != 0) { - goto L250; - } - } + temp = rhoinv + psi + phi; + if (orgati) { + temp1 = z__[iim1] / delta[iim1]; + temp1 *= temp1; + c__ = temp - delta[iip1] * (dpsi + dphi) - (d__[iim1] - d__[ + iip1]) * temp1; + zz[0] = z__[iim1] * z__[iim1]; + zz[2] = delta[iip1] * delta[iip1] * (dpsi - temp1 + dphi); + } else { + temp1 = z__[iip1] / delta[iip1]; + temp1 *= temp1; + c__ = temp - delta[iim1] * (dpsi + dphi) - (d__[iip1] - d__[ + iim1]) * temp1; + zz[0] = delta[iim1] * delta[iim1] * (dpsi + (dphi - temp1)); + zz[2] = z__[iip1] * z__[iip1]; + } + zz[1] = z__[ii] * z__[ii]; + dlaed6_(&niter, &orgati, &c__, &delta[iim1], zz, &w, &eta, info); + if (*info != 0) { + goto L250; + } + } /* Note, eta should be positive if w is negative, and */ /* eta should be negative otherwise. However, */ @@ -768,181 +768,181 @@ f"> */ /* we simply use one Newton step instead. This way */ /* will guarantee eta*w < 0. */ - if (w * eta >= 0.) { - eta = -w / dw; - } - temp = tau + eta; - if (temp > dltub || temp < dltlb) { - if (w < 0.) { - eta = (dltub - tau) / 2.; - } else { - eta = (dltlb - tau) / 2.; - } - } + if (w * eta >= 0.) { + eta = -w / dw; + } + temp = tau + eta; + if (temp > dltub || temp < dltlb) { + if (w < 0.) { + eta = (dltub - tau) / 2.; + } else { + eta = (dltlb - tau) / 2.; + } + } - prew = w; + prew = w; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - delta[j] -= eta; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + delta[j] -= eta; /* L180: */ - } + } /* Evaluate PSI and the derivative DPSI */ - dpsi = 0.; - psi = 0.; - erretm = 0.; - i__1 = iim1; - for (j = 1; j <= i__1; ++j) { - temp = z__[j] / delta[j]; - psi += z__[j] * temp; - dpsi += temp * temp; - erretm += psi; + dpsi = 0.; + psi = 0.; + erretm = 0.; + i__1 = iim1; + for (j = 1; j <= i__1; ++j) { + temp = z__[j] / delta[j]; + psi += z__[j] * temp; + dpsi += temp * temp; + erretm += psi; /* L190: */ - } - erretm = abs(erretm); + } + erretm = abs(erretm); /* Evaluate PHI and the derivative DPHI */ - dphi = 0.; - phi = 0.; - i__1 = iip1; - for (j = *n; j >= i__1; --j) { - temp = z__[j] / delta[j]; - phi += z__[j] * temp; - dphi += temp * temp; - erretm += phi; + dphi = 0.; + phi = 0.; + i__1 = iip1; + for (j = *n; j >= i__1; --j) { + temp = z__[j] / delta[j]; + phi += z__[j] * temp; + dphi += temp * temp; + erretm += phi; /* L200: */ - } + } - temp = z__[ii] / delta[ii]; - dw = dpsi + dphi + temp * temp; - temp = z__[ii] * temp; - w = rhoinv + phi + psi + temp; - erretm = (phi - psi) * 8. + erretm + rhoinv * 2. + abs(temp) * 3. + ( - d__1 = tau + eta, abs(d__1)) * dw; + temp = z__[ii] / delta[ii]; + dw = dpsi + dphi + temp * temp; + temp = z__[ii] * temp; + w = rhoinv + phi + psi + temp; + erretm = (phi - psi) * 8. + erretm + rhoinv * 2. + abs(temp) * 3. + ( + d__1 = tau + eta, abs(d__1)) * dw; - swtch = FALSE_; - if (orgati) { - if (-w > abs(prew) / 10.) { - swtch = TRUE_; - } - } else { - if (w > abs(prew) / 10.) { - swtch = TRUE_; - } - } + swtch = FALSE_; + if (orgati) { + if (-w > abs(prew) / 10.) { + swtch = TRUE_; + } + } else { + if (w > abs(prew) / 10.) { + swtch = TRUE_; + } + } - tau += eta; + tau += eta; /* Main loop to update the values of the array DELTA */ - iter = niter + 1; + iter = niter + 1; - for (niter = iter; niter <= 30; ++niter) { + for (niter = iter; niter <= 30; ++niter) { /* Test for convergence */ - if (abs(w) <= eps * erretm) { - if (orgati) { - *dlam = d__[*i__] + tau; - } else { - *dlam = d__[ip1] + tau; - } - goto L250; - } + if (abs(w) <= eps * erretm) { + if (orgati) { + *dlam = d__[*i__] + tau; + } else { + *dlam = d__[ip1] + tau; + } + goto L250; + } - if (w <= 0.) { - dltlb = max(dltlb,tau); - } else { - dltub = min(dltub,tau); - } + if (w <= 0.) { + dltlb = max(dltlb,tau); + } else { + dltub = min(dltub,tau); + } /* Calculate the new step */ - if (! swtch3) { - if (! swtch) { - if (orgati) { + if (! swtch3) { + if (! swtch) { + if (orgati) { /* Computing 2nd power */ - d__1 = z__[*i__] / delta[*i__]; - c__ = w - delta[ip1] * dw - (d__[*i__] - d__[ip1]) * ( - d__1 * d__1); - } else { + d__1 = z__[*i__] / delta[*i__]; + c__ = w - delta[ip1] * dw - (d__[*i__] - d__[ip1]) * ( + d__1 * d__1); + } else { /* Computing 2nd power */ - d__1 = z__[ip1] / delta[ip1]; - c__ = w - delta[*i__] * dw - (d__[ip1] - d__[*i__]) * - (d__1 * d__1); - } - } else { - temp = z__[ii] / delta[ii]; - if (orgati) { - dpsi += temp * temp; - } else { - dphi += temp * temp; - } - c__ = w - delta[*i__] * dpsi - delta[ip1] * dphi; - } - a = (delta[*i__] + delta[ip1]) * w - delta[*i__] * delta[ip1] - * dw; - b = delta[*i__] * delta[ip1] * w; - if (c__ == 0.) { - if (a == 0.) { - if (! swtch) { - if (orgati) { - a = z__[*i__] * z__[*i__] + delta[ip1] * - delta[ip1] * (dpsi + dphi); - } else { - a = z__[ip1] * z__[ip1] + delta[*i__] * delta[ - *i__] * (dpsi + dphi); - } - } else { - a = delta[*i__] * delta[*i__] * dpsi + delta[ip1] - * delta[ip1] * dphi; - } - } - eta = b / a; - } else if (a <= 0.) { - eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) - / (c__ * 2.); - } else { - eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, - abs(d__1)))); - } - } else { + d__1 = z__[ip1] / delta[ip1]; + c__ = w - delta[*i__] * dw - (d__[ip1] - d__[*i__]) * + (d__1 * d__1); + } + } else { + temp = z__[ii] / delta[ii]; + if (orgati) { + dpsi += temp * temp; + } else { + dphi += temp * temp; + } + c__ = w - delta[*i__] * dpsi - delta[ip1] * dphi; + } + a = (delta[*i__] + delta[ip1]) * w - delta[*i__] * delta[ip1] + * dw; + b = delta[*i__] * delta[ip1] * w; + if (c__ == 0.) { + if (a == 0.) { + if (! swtch) { + if (orgati) { + a = z__[*i__] * z__[*i__] + delta[ip1] * + delta[ip1] * (dpsi + dphi); + } else { + a = z__[ip1] * z__[ip1] + delta[*i__] * delta[ + *i__] * (dpsi + dphi); + } + } else { + a = delta[*i__] * delta[*i__] * dpsi + delta[ip1] + * delta[ip1] * dphi; + } + } + eta = b / a; + } else if (a <= 0.) { + eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) + / (c__ * 2.); + } else { + eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, + abs(d__1)))); + } + } else { /* Interpolation using THREE most relevant poles */ - temp = rhoinv + psi + phi; - if (swtch) { - c__ = temp - delta[iim1] * dpsi - delta[iip1] * dphi; - zz[0] = delta[iim1] * delta[iim1] * dpsi; - zz[2] = delta[iip1] * delta[iip1] * dphi; - } else { - if (orgati) { - temp1 = z__[iim1] / delta[iim1]; - temp1 *= temp1; - c__ = temp - delta[iip1] * (dpsi + dphi) - (d__[iim1] - - d__[iip1]) * temp1; - zz[0] = z__[iim1] * z__[iim1]; - zz[2] = delta[iip1] * delta[iip1] * (dpsi - temp1 + - dphi); - } else { - temp1 = z__[iip1] / delta[iip1]; - temp1 *= temp1; - c__ = temp - delta[iim1] * (dpsi + dphi) - (d__[iip1] - - d__[iim1]) * temp1; - zz[0] = delta[iim1] * delta[iim1] * (dpsi + (dphi - - temp1)); - zz[2] = z__[iip1] * z__[iip1]; - } - } - dlaed6_(&niter, &orgati, &c__, &delta[iim1], zz, &w, &eta, - info); - if (*info != 0) { - goto L250; - } - } + temp = rhoinv + psi + phi; + if (swtch) { + c__ = temp - delta[iim1] * dpsi - delta[iip1] * dphi; + zz[0] = delta[iim1] * delta[iim1] * dpsi; + zz[2] = delta[iip1] * delta[iip1] * dphi; + } else { + if (orgati) { + temp1 = z__[iim1] / delta[iim1]; + temp1 *= temp1; + c__ = temp - delta[iip1] * (dpsi + dphi) - (d__[iim1] + - d__[iip1]) * temp1; + zz[0] = z__[iim1] * z__[iim1]; + zz[2] = delta[iip1] * delta[iip1] * (dpsi - temp1 + + dphi); + } else { + temp1 = z__[iip1] / delta[iip1]; + temp1 *= temp1; + c__ = temp - delta[iim1] * (dpsi + dphi) - (d__[iip1] + - d__[iim1]) * temp1; + zz[0] = delta[iim1] * delta[iim1] * (dpsi + (dphi - + temp1)); + zz[2] = z__[iip1] * z__[iip1]; + } + } + dlaed6_(&niter, &orgati, &c__, &delta[iim1], zz, &w, &eta, + info); + if (*info != 0) { + goto L250; + } + } /* Note, eta should be positive if w is negative, and */ /* eta should be negative otherwise. However, */ @@ -950,76 +950,76 @@ f"> */ /* we simply use one Newton step instead. This way */ /* will guarantee eta*w < 0. */ - if (w * eta >= 0.) { - eta = -w / dw; - } - temp = tau + eta; - if (temp > dltub || temp < dltlb) { - if (w < 0.) { - eta = (dltub - tau) / 2.; - } else { - eta = (dltlb - tau) / 2.; - } - } + if (w * eta >= 0.) { + eta = -w / dw; + } + temp = tau + eta; + if (temp > dltub || temp < dltlb) { + if (w < 0.) { + eta = (dltub - tau) / 2.; + } else { + eta = (dltlb - tau) / 2.; + } + } - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - delta[j] -= eta; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + delta[j] -= eta; /* L210: */ - } + } - tau += eta; - prew = w; + tau += eta; + prew = w; /* Evaluate PSI and the derivative DPSI */ - dpsi = 0.; - psi = 0.; - erretm = 0.; - i__1 = iim1; - for (j = 1; j <= i__1; ++j) { - temp = z__[j] / delta[j]; - psi += z__[j] * temp; - dpsi += temp * temp; - erretm += psi; + dpsi = 0.; + psi = 0.; + erretm = 0.; + i__1 = iim1; + for (j = 1; j <= i__1; ++j) { + temp = z__[j] / delta[j]; + psi += z__[j] * temp; + dpsi += temp * temp; + erretm += psi; /* L220: */ - } - erretm = abs(erretm); + } + erretm = abs(erretm); /* Evaluate PHI and the derivative DPHI */ - dphi = 0.; - phi = 0.; - i__1 = iip1; - for (j = *n; j >= i__1; --j) { - temp = z__[j] / delta[j]; - phi += z__[j] * temp; - dphi += temp * temp; - erretm += phi; + dphi = 0.; + phi = 0.; + i__1 = iip1; + for (j = *n; j >= i__1; --j) { + temp = z__[j] / delta[j]; + phi += z__[j] * temp; + dphi += temp * temp; + erretm += phi; /* L230: */ - } + } - temp = z__[ii] / delta[ii]; - dw = dpsi + dphi + temp * temp; - temp = z__[ii] * temp; - w = rhoinv + phi + psi + temp; - erretm = (phi - psi) * 8. + erretm + rhoinv * 2. + abs(temp) * 3. - + abs(tau) * dw; - if (w * prew > 0. && abs(w) > abs(prew) / 10.) { - swtch = ! swtch; - } + temp = z__[ii] / delta[ii]; + dw = dpsi + dphi + temp * temp; + temp = z__[ii] * temp; + w = rhoinv + phi + psi + temp; + erretm = (phi - psi) * 8. + erretm + rhoinv * 2. + abs(temp) * 3. + + abs(tau) * dw; + if (w * prew > 0. && abs(w) > abs(prew) / 10.) { + swtch = ! swtch; + } /* L240: */ - } + } /* Return with INFO = 1, NITER = MAXIT and not converged */ - *info = 1; - if (orgati) { - *dlam = d__[*i__] + tau; - } else { - *dlam = d__[ip1] + tau; - } + *info = 1; + if (orgati) { + *dlam = d__[*i__] + tau; + } else { + *dlam = d__[ip1] + tau; + } } @@ -1032,5 +1032,5 @@ L250: } /* dlaed4_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlaed5.cpp b/lib/linalg/dlaed5.cpp index 14e8a429ee..558676d269 100644 --- a/lib/linalg/dlaed5.cpp +++ b/lib/linalg/dlaed5.cpp @@ -1,13 +1,13 @@ /* fortran/dlaed5.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -124,8 +124,8 @@ f"> */ /* > at Berkeley, USA */ /* > */ /* ===================================================================== */ -/* Subroutine */ int dlaed5_(integer *i__, doublereal *d__, doublereal *z__, - doublereal *delta, doublereal *rho, doublereal *dlam) +/* Subroutine */ int dlaed5_(integer *i__, doublereal *d__, doublereal *z__, + doublereal *delta, doublereal *rho, doublereal *dlam) { /* System generated locals */ doublereal d__1; @@ -164,49 +164,49 @@ f"> */ /* Function Body */ del = d__[2] - d__[1]; if (*i__ == 1) { - w = *rho * 2. * (z__[2] * z__[2] - z__[1] * z__[1]) / del + 1.; - if (w > 0.) { - b = del + *rho * (z__[1] * z__[1] + z__[2] * z__[2]); - c__ = *rho * z__[1] * z__[1] * del; + w = *rho * 2. * (z__[2] * z__[2] - z__[1] * z__[1]) / del + 1.; + if (w > 0.) { + b = del + *rho * (z__[1] * z__[1] + z__[2] * z__[2]); + c__ = *rho * z__[1] * z__[1] * del; /* B > ZERO, always */ - tau = c__ * 2. / (b + sqrt((d__1 = b * b - c__ * 4., abs(d__1)))); - *dlam = d__[1] + tau; - delta[1] = -z__[1] / tau; - delta[2] = z__[2] / (del - tau); - } else { - b = -del + *rho * (z__[1] * z__[1] + z__[2] * z__[2]); - c__ = *rho * z__[2] * z__[2] * del; - if (b > 0.) { - tau = c__ * -2. / (b + sqrt(b * b + c__ * 4.)); - } else { - tau = (b - sqrt(b * b + c__ * 4.)) / 2.; - } - *dlam = d__[2] + tau; - delta[1] = -z__[1] / (del + tau); - delta[2] = -z__[2] / tau; - } - temp = sqrt(delta[1] * delta[1] + delta[2] * delta[2]); - delta[1] /= temp; - delta[2] /= temp; + tau = c__ * 2. / (b + sqrt((d__1 = b * b - c__ * 4., abs(d__1)))); + *dlam = d__[1] + tau; + delta[1] = -z__[1] / tau; + delta[2] = z__[2] / (del - tau); + } else { + b = -del + *rho * (z__[1] * z__[1] + z__[2] * z__[2]); + c__ = *rho * z__[2] * z__[2] * del; + if (b > 0.) { + tau = c__ * -2. / (b + sqrt(b * b + c__ * 4.)); + } else { + tau = (b - sqrt(b * b + c__ * 4.)) / 2.; + } + *dlam = d__[2] + tau; + delta[1] = -z__[1] / (del + tau); + delta[2] = -z__[2] / tau; + } + temp = sqrt(delta[1] * delta[1] + delta[2] * delta[2]); + delta[1] /= temp; + delta[2] /= temp; } else { /* Now I=2 */ - b = -del + *rho * (z__[1] * z__[1] + z__[2] * z__[2]); - c__ = *rho * z__[2] * z__[2] * del; - if (b > 0.) { - tau = (b + sqrt(b * b + c__ * 4.)) / 2.; - } else { - tau = c__ * 2. / (-b + sqrt(b * b + c__ * 4.)); - } - *dlam = d__[2] + tau; - delta[1] = -z__[1] / (del + tau); - delta[2] = -z__[2] / tau; - temp = sqrt(delta[1] * delta[1] + delta[2] * delta[2]); - delta[1] /= temp; - delta[2] /= temp; + b = -del + *rho * (z__[1] * z__[1] + z__[2] * z__[2]); + c__ = *rho * z__[2] * z__[2] * del; + if (b > 0.) { + tau = (b + sqrt(b * b + c__ * 4.)) / 2.; + } else { + tau = c__ * 2. / (-b + sqrt(b * b + c__ * 4.)); + } + *dlam = d__[2] + tau; + delta[1] = -z__[1] / (del + tau); + delta[2] = -z__[2] / tau; + temp = sqrt(delta[1] * delta[1] + delta[2] * delta[2]); + delta[1] /= temp; + delta[2] /= temp; } return 0; @@ -215,5 +215,5 @@ f"> */ } /* dlaed5_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlaed6.cpp b/lib/linalg/dlaed6.cpp index 7a855780f0..aae975971f 100644 --- a/lib/linalg/dlaed6.cpp +++ b/lib/linalg/dlaed6.cpp @@ -1,13 +1,13 @@ /* fortran/dlaed6.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -157,8 +157,8 @@ f"> */ /* > */ /* ===================================================================== */ /* Subroutine */ int dlaed6_(integer *kniter, logical *orgati, doublereal * - rho, doublereal *d__, doublereal *z__, doublereal *finit, doublereal * - tau, integer *info) + rho, doublereal *d__, doublereal *z__, doublereal *finit, doublereal * + tau, integer *info) { /* System generated locals */ integer i__1; @@ -211,65 +211,65 @@ f"> */ *info = 0; if (*orgati) { - lbd = d__[2]; - ubd = d__[3]; + lbd = d__[2]; + ubd = d__[3]; } else { - lbd = d__[1]; - ubd = d__[2]; + lbd = d__[1]; + ubd = d__[2]; } if (*finit < 0.) { - lbd = 0.; + lbd = 0.; } else { - ubd = 0.; + ubd = 0.; } niter = 1; *tau = 0.; if (*kniter == 2) { - if (*orgati) { - temp = (d__[3] - d__[2]) / 2.; - c__ = *rho + z__[1] / (d__[1] - d__[2] - temp); - a = c__ * (d__[2] + d__[3]) + z__[2] + z__[3]; - b = c__ * d__[2] * d__[3] + z__[2] * d__[3] + z__[3] * d__[2]; - } else { - temp = (d__[1] - d__[2]) / 2.; - c__ = *rho + z__[3] / (d__[3] - d__[2] - temp); - a = c__ * (d__[1] + d__[2]) + z__[1] + z__[2]; - b = c__ * d__[1] * d__[2] + z__[1] * d__[2] + z__[2] * d__[1]; - } + if (*orgati) { + temp = (d__[3] - d__[2]) / 2.; + c__ = *rho + z__[1] / (d__[1] - d__[2] - temp); + a = c__ * (d__[2] + d__[3]) + z__[2] + z__[3]; + b = c__ * d__[2] * d__[3] + z__[2] * d__[3] + z__[3] * d__[2]; + } else { + temp = (d__[1] - d__[2]) / 2.; + c__ = *rho + z__[3] / (d__[3] - d__[2] - temp); + a = c__ * (d__[1] + d__[2]) + z__[1] + z__[2]; + b = c__ * d__[1] * d__[2] + z__[1] * d__[2] + z__[2] * d__[1]; + } /* Computing MAX */ - d__1 = abs(a), d__2 = abs(b), d__1 = max(d__1,d__2), d__2 = abs(c__); - temp = max(d__1,d__2); - a /= temp; - b /= temp; - c__ /= temp; - if (c__ == 0.) { - *tau = b / a; - } else if (a <= 0.) { - *tau = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / ( - c__ * 2.); - } else { - *tau = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)) - )); - } - if (*tau < lbd || *tau > ubd) { - *tau = (lbd + ubd) / 2.; - } - if (d__[1] == *tau || d__[2] == *tau || d__[3] == *tau) { - *tau = 0.; - } else { - temp = *finit + *tau * z__[1] / (d__[1] * (d__[1] - *tau)) + *tau - * z__[2] / (d__[2] * (d__[2] - *tau)) + *tau * z__[3] / ( - d__[3] * (d__[3] - *tau)); - if (temp <= 0.) { - lbd = *tau; - } else { - ubd = *tau; - } - if (abs(*finit) <= abs(temp)) { - *tau = 0.; - } - } + d__1 = abs(a), d__2 = abs(b), d__1 = max(d__1,d__2), d__2 = abs(c__); + temp = max(d__1,d__2); + a /= temp; + b /= temp; + c__ /= temp; + if (c__ == 0.) { + *tau = b / a; + } else if (a <= 0.) { + *tau = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / ( + c__ * 2.); + } else { + *tau = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)) + )); + } + if (*tau < lbd || *tau > ubd) { + *tau = (lbd + ubd) / 2.; + } + if (d__[1] == *tau || d__[2] == *tau || d__[3] == *tau) { + *tau = 0.; + } else { + temp = *finit + *tau * z__[1] / (d__[1] * (d__[1] - *tau)) + *tau + * z__[2] / (d__[2] * (d__[2] - *tau)) + *tau * z__[3] / ( + d__[3] * (d__[3] - *tau)); + if (temp <= 0.) { + lbd = *tau; + } else { + ubd = *tau; + } + if (abs(*finit) <= abs(temp)) { + *tau = 0.; + } + } } /* get machine parameters for possible scaling to avoid overflow */ @@ -291,75 +291,75 @@ f"> */ if (*orgati) { /* Computing MIN */ - d__3 = (d__1 = d__[2] - *tau, abs(d__1)), d__4 = (d__2 = d__[3] - * - tau, abs(d__2)); - temp = min(d__3,d__4); + d__3 = (d__1 = d__[2] - *tau, abs(d__1)), d__4 = (d__2 = d__[3] - * + tau, abs(d__2)); + temp = min(d__3,d__4); } else { /* Computing MIN */ - d__3 = (d__1 = d__[1] - *tau, abs(d__1)), d__4 = (d__2 = d__[2] - * - tau, abs(d__2)); - temp = min(d__3,d__4); + d__3 = (d__1 = d__[1] - *tau, abs(d__1)), d__4 = (d__2 = d__[2] - * + tau, abs(d__2)); + temp = min(d__3,d__4); } scale = FALSE_; if (temp <= small1) { - scale = TRUE_; - if (temp <= small2) { + scale = TRUE_; + if (temp <= small2) { /* Scale up by power of radix nearest 1/SAFMIN**(2/3) */ - sclfac = sminv2; - sclinv = small2; - } else { + sclfac = sminv2; + sclinv = small2; + } else { /* Scale up by power of radix nearest 1/SAFMIN**(1/3) */ - sclfac = sminv1; - sclinv = small1; - } + sclfac = sminv1; + sclinv = small1; + } /* Scaling up safe because D, Z, TAU scaled elsewhere to be O(1) */ - for (i__ = 1; i__ <= 3; ++i__) { - dscale[i__ - 1] = d__[i__] * sclfac; - zscale[i__ - 1] = z__[i__] * sclfac; + for (i__ = 1; i__ <= 3; ++i__) { + dscale[i__ - 1] = d__[i__] * sclfac; + zscale[i__ - 1] = z__[i__] * sclfac; /* L10: */ - } - *tau *= sclfac; - lbd *= sclfac; - ubd *= sclfac; + } + *tau *= sclfac; + lbd *= sclfac; + ubd *= sclfac; } else { /* Copy D and Z to DSCALE and ZSCALE */ - for (i__ = 1; i__ <= 3; ++i__) { - dscale[i__ - 1] = d__[i__]; - zscale[i__ - 1] = z__[i__]; + for (i__ = 1; i__ <= 3; ++i__) { + dscale[i__ - 1] = d__[i__]; + zscale[i__ - 1] = z__[i__]; /* L20: */ - } + } } fc = 0.; df = 0.; ddf = 0.; for (i__ = 1; i__ <= 3; ++i__) { - temp = 1. / (dscale[i__ - 1] - *tau); - temp1 = zscale[i__ - 1] * temp; - temp2 = temp1 * temp; - temp3 = temp2 * temp; - fc += temp1 / dscale[i__ - 1]; - df += temp2; - ddf += temp3; + temp = 1. / (dscale[i__ - 1] - *tau); + temp1 = zscale[i__ - 1] * temp; + temp2 = temp1 * temp; + temp3 = temp2 * temp; + fc += temp1 / dscale[i__ - 1]; + df += temp2; + ddf += temp3; /* L30: */ } f = *finit + *tau * fc; if (abs(f) <= 0.) { - goto L60; + goto L60; } if (f <= 0.) { - lbd = *tau; + lbd = *tau; } else { - ubd = *tau; + ubd = *tau; } /* Iteration begins -- Use Gragg-Thornton-Warner cubic convergent */ @@ -377,71 +377,71 @@ f"> */ for (niter = iter; niter <= 40; ++niter) { - if (*orgati) { - temp1 = dscale[1] - *tau; - temp2 = dscale[2] - *tau; - } else { - temp1 = dscale[0] - *tau; - temp2 = dscale[1] - *tau; - } - a = (temp1 + temp2) * f - temp1 * temp2 * df; - b = temp1 * temp2 * f; - c__ = f - (temp1 + temp2) * df + temp1 * temp2 * ddf; + if (*orgati) { + temp1 = dscale[1] - *tau; + temp2 = dscale[2] - *tau; + } else { + temp1 = dscale[0] - *tau; + temp2 = dscale[1] - *tau; + } + a = (temp1 + temp2) * f - temp1 * temp2 * df; + b = temp1 * temp2 * f; + c__ = f - (temp1 + temp2) * df + temp1 * temp2 * ddf; /* Computing MAX */ - d__1 = abs(a), d__2 = abs(b), d__1 = max(d__1,d__2), d__2 = abs(c__); - temp = max(d__1,d__2); - a /= temp; - b /= temp; - c__ /= temp; - if (c__ == 0.) { - eta = b / a; - } else if (a <= 0.) { - eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (c__ - * 2.); - } else { - eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1))) - ); - } - if (f * eta >= 0.) { - eta = -f / df; - } + d__1 = abs(a), d__2 = abs(b), d__1 = max(d__1,d__2), d__2 = abs(c__); + temp = max(d__1,d__2); + a /= temp; + b /= temp; + c__ /= temp; + if (c__ == 0.) { + eta = b / a; + } else if (a <= 0.) { + eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (c__ + * 2.); + } else { + eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1))) + ); + } + if (f * eta >= 0.) { + eta = -f / df; + } - *tau += eta; - if (*tau < lbd || *tau > ubd) { - *tau = (lbd + ubd) / 2.; - } + *tau += eta; + if (*tau < lbd || *tau > ubd) { + *tau = (lbd + ubd) / 2.; + } - fc = 0.; - erretm = 0.; - df = 0.; - ddf = 0.; - for (i__ = 1; i__ <= 3; ++i__) { - if (dscale[i__ - 1] - *tau != 0.) { - temp = 1. / (dscale[i__ - 1] - *tau); - temp1 = zscale[i__ - 1] * temp; - temp2 = temp1 * temp; - temp3 = temp2 * temp; - temp4 = temp1 / dscale[i__ - 1]; - fc += temp4; - erretm += abs(temp4); - df += temp2; - ddf += temp3; - } else { - goto L60; - } + fc = 0.; + erretm = 0.; + df = 0.; + ddf = 0.; + for (i__ = 1; i__ <= 3; ++i__) { + if (dscale[i__ - 1] - *tau != 0.) { + temp = 1. / (dscale[i__ - 1] - *tau); + temp1 = zscale[i__ - 1] * temp; + temp2 = temp1 * temp; + temp3 = temp2 * temp; + temp4 = temp1 / dscale[i__ - 1]; + fc += temp4; + erretm += abs(temp4); + df += temp2; + ddf += temp3; + } else { + goto L60; + } /* L40: */ - } - f = *finit + *tau * fc; - erretm = (abs(*finit) + abs(*tau) * erretm) * 8. + abs(*tau) * df; - if (abs(f) <= eps * 4. * erretm || ubd - lbd <= eps * 4. * abs(*tau)) - { - goto L60; - } - if (f <= 0.) { - lbd = *tau; - } else { - ubd = *tau; - } + } + f = *finit + *tau * fc; + erretm = (abs(*finit) + abs(*tau) * erretm) * 8. + abs(*tau) * df; + if (abs(f) <= eps * 4. * erretm || ubd - lbd <= eps * 4. * abs(*tau)) + { + goto L60; + } + if (f <= 0.) { + lbd = *tau; + } else { + ubd = *tau; + } /* L50: */ } *info = 1; @@ -450,7 +450,7 @@ L60: /* Undo scaling */ if (scale) { - *tau *= sclinv; + *tau *= sclinv; } return 0; @@ -459,5 +459,5 @@ L60: } /* dlaed6_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlaed7.cpp b/lib/linalg/dlaed7.cpp index 367bf37a46..1751f93559 100644 --- a/lib/linalg/dlaed7.cpp +++ b/lib/linalg/dlaed7.cpp @@ -1,13 +1,13 @@ /* fortran/dlaed7.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -282,12 +282,12 @@ f"> */ /* > at Berkeley, USA */ /* ===================================================================== */ -/* Subroutine */ int dlaed7_(integer *icompq, integer *n, integer *qsiz, - integer *tlvls, integer *curlvl, integer *curpbm, doublereal *d__, - doublereal *q, integer *ldq, integer *indxq, doublereal *rho, integer - *cutpnt, doublereal *qstore, integer *qptr, integer *prmptr, integer * - perm, integer *givptr, integer *givcol, doublereal *givnum, - doublereal *work, integer *iwork, integer *info) +/* Subroutine */ int dlaed7_(integer *icompq, integer *n, integer *qsiz, + integer *tlvls, integer *curlvl, integer *curpbm, doublereal *d__, + doublereal *q, integer *ldq, integer *indxq, doublereal *rho, integer + *cutpnt, doublereal *qstore, integer *qptr, integer *prmptr, integer * + perm, integer *givptr, integer *givcol, doublereal *givnum, + doublereal *work, integer *iwork, integer *info) { /* System generated locals */ integer q_dim1, q_offset, i__1, i__2; @@ -297,25 +297,25 @@ f"> */ /* Local variables */ integer i__, k, n1, n2, is, iw, iz, iq2, ptr, ldq2, indx, curr; - extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); integer indxc, indxp; - extern /* Subroutine */ int dlaed8_(integer *, integer *, integer *, - integer *, doublereal *, doublereal *, integer *, integer *, - doublereal *, integer *, doublereal *, doublereal *, doublereal *, - integer *, doublereal *, integer *, integer *, integer *, - doublereal *, integer *, integer *, integer *), dlaed9_(integer *, - integer *, integer *, integer *, doublereal *, doublereal *, - integer *, doublereal *, doublereal *, doublereal *, doublereal *, - integer *, integer *), dlaeda_(integer *, integer *, integer *, - integer *, integer *, integer *, integer *, integer *, doublereal - *, doublereal *, integer *, doublereal *, doublereal *, integer *) - ; + extern /* Subroutine */ int dlaed8_(integer *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, integer *, + doublereal *, integer *, doublereal *, doublereal *, doublereal *, + integer *, doublereal *, integer *, integer *, integer *, + doublereal *, integer *, integer *, integer *), dlaed9_(integer *, + integer *, integer *, integer *, doublereal *, doublereal *, + integer *, doublereal *, doublereal *, doublereal *, doublereal *, + integer *, integer *), dlaeda_(integer *, integer *, integer *, + integer *, integer *, integer *, integer *, integer *, doublereal + *, doublereal *, integer *, doublereal *, doublereal *, integer *) + ; integer idlmda; - extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *, - integer *, integer *, integer *), xerbla_(char *, integer *, - ftnlen); + extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *, + integer *, integer *, integer *), xerbla_(char *, integer *, + ftnlen); integer coltyp; @@ -362,26 +362,26 @@ f"> */ *info = 0; if (*icompq < 0 || *icompq > 1) { - *info = -1; + *info = -1; } else if (*n < 0) { - *info = -2; + *info = -2; } else if (*icompq == 1 && *qsiz < *n) { - *info = -3; + *info = -3; } else if (*ldq < max(1,*n)) { - *info = -9; + *info = -9; } else if (min(1,*n) > *cutpnt || *n < *cutpnt) { - *info = -12; + *info = -12; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DLAED7", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DLAED7", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*n == 0) { - return 0; + return 0; } /* The following values are for bookkeeping purposes only. They are */ @@ -389,9 +389,9 @@ f"> */ /* used by a particular array in DLAED8 and DLAED9. */ if (*icompq == 1) { - ldq2 = *qsiz; + ldq2 = *qsiz; } else { - ldq2 = *n; + ldq2 = *n; } iz = 1; @@ -411,64 +411,64 @@ f"> */ ptr = pow_ii(&c__2, tlvls) + 1; i__1 = *curlvl - 1; for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = *tlvls - i__; - ptr += pow_ii(&c__2, &i__2); + i__2 = *tlvls - i__; + ptr += pow_ii(&c__2, &i__2); /* L10: */ } curr = ptr + *curpbm; dlaeda_(n, tlvls, curlvl, curpbm, &prmptr[1], &perm[1], &givptr[1], & - givcol[3], &givnum[3], &qstore[1], &qptr[1], &work[iz], &work[iz - + *n], info); + givcol[3], &givnum[3], &qstore[1], &qptr[1], &work[iz], &work[iz + + *n], info); /* When solving the final problem, we no longer need the stored data, */ /* so we will overwrite the data from this level onto the previously */ /* used storage space. */ if (*curlvl == *tlvls) { - qptr[curr] = 1; - prmptr[curr] = 1; - givptr[curr] = 1; + qptr[curr] = 1; + prmptr[curr] = 1; + givptr[curr] = 1; } /* Sort and Deflate eigenvalues. */ - dlaed8_(icompq, &k, n, qsiz, &d__[1], &q[q_offset], ldq, &indxq[1], rho, - cutpnt, &work[iz], &work[idlmda], &work[iq2], &ldq2, &work[iw], & - perm[prmptr[curr]], &givptr[curr + 1], &givcol[(givptr[curr] << 1) - + 1], &givnum[(givptr[curr] << 1) + 1], &iwork[indxp], &iwork[ - indx], info); + dlaed8_(icompq, &k, n, qsiz, &d__[1], &q[q_offset], ldq, &indxq[1], rho, + cutpnt, &work[iz], &work[idlmda], &work[iq2], &ldq2, &work[iw], & + perm[prmptr[curr]], &givptr[curr + 1], &givcol[(givptr[curr] << 1) + + 1], &givnum[(givptr[curr] << 1) + 1], &iwork[indxp], &iwork[ + indx], info); prmptr[curr + 1] = prmptr[curr] + *n; givptr[curr + 1] += givptr[curr]; /* Solve Secular Equation. */ if (k != 0) { - dlaed9_(&k, &c__1, &k, n, &d__[1], &work[is], &k, rho, &work[idlmda], - &work[iw], &qstore[qptr[curr]], &k, info); - if (*info != 0) { - goto L30; - } - if (*icompq == 1) { - dgemm_((char *)"N", (char *)"N", qsiz, &k, &k, &c_b10, &work[iq2], &ldq2, &qstore[ - qptr[curr]], &k, &c_b11, &q[q_offset], ldq, (ftnlen)1, ( - ftnlen)1); - } + dlaed9_(&k, &c__1, &k, n, &d__[1], &work[is], &k, rho, &work[idlmda], + &work[iw], &qstore[qptr[curr]], &k, info); + if (*info != 0) { + goto L30; + } + if (*icompq == 1) { + dgemm_((char *)"N", (char *)"N", qsiz, &k, &k, &c_b10, &work[iq2], &ldq2, &qstore[ + qptr[curr]], &k, &c_b11, &q[q_offset], ldq, (ftnlen)1, ( + ftnlen)1); + } /* Computing 2nd power */ - i__1 = k; - qptr[curr + 1] = qptr[curr] + i__1 * i__1; + i__1 = k; + qptr[curr + 1] = qptr[curr] + i__1 * i__1; /* Prepare the INDXQ sorting permutation. */ - n1 = k; - n2 = *n - k; - dlamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &indxq[1]); + n1 = k; + n2 = *n - k; + dlamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &indxq[1]); } else { - qptr[curr + 1] = qptr[curr]; - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - indxq[i__] = i__; + qptr[curr + 1] = qptr[curr]; + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + indxq[i__] = i__; /* L20: */ - } + } } L30: @@ -479,5 +479,5 @@ L30: } /* dlaed7_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlaed8.cpp b/lib/linalg/dlaed8.cpp index 263bea75d5..8d1a7ae4b3 100644 --- a/lib/linalg/dlaed8.cpp +++ b/lib/linalg/dlaed8.cpp @@ -1,13 +1,13 @@ /* fortran/dlaed8.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -263,12 +263,12 @@ f"> */ /* > at Berkeley, USA */ /* ===================================================================== */ -/* Subroutine */ int dlaed8_(integer *icompq, integer *k, integer *n, integer - *qsiz, doublereal *d__, doublereal *q, integer *ldq, integer *indxq, - doublereal *rho, integer *cutpnt, doublereal *z__, doublereal *dlamda, - doublereal *q2, integer *ldq2, doublereal *w, integer *perm, integer - *givptr, integer *givcol, doublereal *givnum, integer *indxp, integer - *indx, integer *info) +/* Subroutine */ int dlaed8_(integer *icompq, integer *k, integer *n, integer + *qsiz, doublereal *d__, doublereal *q, integer *ldq, integer *indxq, + doublereal *rho, integer *cutpnt, doublereal *z__, doublereal *dlamda, + doublereal *q2, integer *ldq2, doublereal *w, integer *perm, integer + *givptr, integer *givcol, doublereal *givnum, integer *indxp, integer + *indx, integer *info) { /* System generated locals */ integer q_dim1, q_offset, q2_dim1, q2_offset, i__1; @@ -284,17 +284,17 @@ f"> */ integer k2, n1, n2, jp, n1p1; doublereal eps, tau, tol; integer jlam, imax, jmax; - extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, - doublereal *, integer *, doublereal *, doublereal *), dscal_( - integer *, doublereal *, doublereal *, integer *), dcopy_(integer - *, doublereal *, integer *, doublereal *, integer *); - extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, - ftnlen); + extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, + doublereal *, integer *, doublereal *, doublereal *), dscal_( + integer *, doublereal *, doublereal *, integer *), dcopy_(integer + *, doublereal *, integer *, doublereal *, integer *); + extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, + ftnlen); extern integer idamax_(integer *, doublereal *, integer *); - extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *, - integer *, integer *, integer *), dlacpy_(char *, integer *, - integer *, doublereal *, integer *, doublereal *, integer *, - ftnlen), xerbla_(char *, integer *, ftnlen); + extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *, + integer *, integer *, integer *), dlacpy_(char *, integer *, + integer *, doublereal *, integer *, doublereal *, integer *, + ftnlen), xerbla_(char *, integer *, ftnlen); /* -- LAPACK computational routine -- */ @@ -345,22 +345,22 @@ f"> */ *info = 0; if (*icompq < 0 || *icompq > 1) { - *info = -1; + *info = -1; } else if (*n < 0) { - *info = -3; + *info = -3; } else if (*icompq == 1 && *qsiz < *n) { - *info = -4; + *info = -4; } else if (*ldq < max(1,*n)) { - *info = -7; + *info = -7; } else if (*cutpnt < min(1,*n) || *cutpnt > *n) { - *info = -10; + *info = -10; } else if (*ldq2 < max(1,*n)) { - *info = -14; + *info = -14; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DLAED8", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DLAED8", &i__1, (ftnlen)6); + return 0; } /* Need to initialize GIVPTR to O here in case of quick exit */ @@ -373,7 +373,7 @@ f"> */ /* Quick return if possible */ if (*n == 0) { - return 0; + return 0; } n1 = *cutpnt; @@ -381,7 +381,7 @@ f"> */ n1p1 = n1 + 1; if (*rho < 0.) { - dscal_(&n2, &c_b3, &z__[n1p1], &c__1); + dscal_(&n2, &c_b3, &z__[n1p1], &c__1); } /* Normalize z so that norm(z) = 1 */ @@ -389,7 +389,7 @@ f"> */ t = 1. / sqrt(2.); i__1 = *n; for (j = 1; j <= i__1; ++j) { - indx[j] = j; + indx[j] = j; /* L10: */ } dscal_(n, &t, &z__[1], &c__1); @@ -399,13 +399,13 @@ f"> */ i__1 = *n; for (i__ = *cutpnt + 1; i__ <= i__1; ++i__) { - indxq[i__] += *cutpnt; + indxq[i__] += *cutpnt; /* L20: */ } i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { - dlamda[i__] = d__[indxq[i__]]; - w[i__] = z__[indxq[i__]]; + dlamda[i__] = d__[indxq[i__]]; + w[i__] = z__[indxq[i__]]; /* L30: */ } i__ = 1; @@ -413,8 +413,8 @@ f"> */ dlamrg_(&n1, &n2, &dlamda[1], &c__1, &c__1, &indx[1]); i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { - d__[i__] = dlamda[indx[i__]]; - z__[i__] = w[indx[i__]]; + d__[i__] = dlamda[indx[i__]]; + z__[i__] = w[indx[i__]]; /* L40: */ } @@ -430,25 +430,25 @@ f"> */ /* elements in D. */ if (*rho * (d__1 = z__[imax], abs(d__1)) <= tol) { - *k = 0; - if (*icompq == 0) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - perm[j] = indxq[indx[j]]; + *k = 0; + if (*icompq == 0) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + perm[j] = indxq[indx[j]]; /* L50: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - perm[j] = indxq[indx[j]]; - dcopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 - + 1], &c__1); + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + perm[j] = indxq[indx[j]]; + dcopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 + + 1], &c__1); /* L60: */ - } - dlacpy_((char *)"A", qsiz, n, &q2[q2_dim1 + 1], ldq2, &q[q_dim1 + 1], ldq, - (ftnlen)1); - } - return 0; + } + dlacpy_((char *)"A", qsiz, n, &q2[q2_dim1 + 1], ldq2, &q[q_dim1 + 1], ldq, + (ftnlen)1); + } + return 0; } /* If there are multiple eigenvalues then the problem deflates. Here */ @@ -461,90 +461,90 @@ f"> */ k2 = *n + 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { - if (*rho * (d__1 = z__[j], abs(d__1)) <= tol) { + if (*rho * (d__1 = z__[j], abs(d__1)) <= tol) { /* Deflate due to small z component. */ - --k2; - indxp[k2] = j; - if (j == *n) { - goto L110; - } - } else { - jlam = j; - goto L80; - } + --k2; + indxp[k2] = j; + if (j == *n) { + goto L110; + } + } else { + jlam = j; + goto L80; + } /* L70: */ } L80: ++j; if (j > *n) { - goto L100; + goto L100; } if (*rho * (d__1 = z__[j], abs(d__1)) <= tol) { /* Deflate due to small z component. */ - --k2; - indxp[k2] = j; + --k2; + indxp[k2] = j; } else { /* Check if eigenvalues are close enough to allow deflation. */ - s = z__[jlam]; - c__ = z__[j]; + s = z__[jlam]; + c__ = z__[j]; /* Find sqrt(a**2+b**2) without overflow or */ /* destructive underflow. */ - tau = dlapy2_(&c__, &s); - t = d__[j] - d__[jlam]; - c__ /= tau; - s = -s / tau; - if ((d__1 = t * c__ * s, abs(d__1)) <= tol) { + tau = dlapy2_(&c__, &s); + t = d__[j] - d__[jlam]; + c__ /= tau; + s = -s / tau; + if ((d__1 = t * c__ * s, abs(d__1)) <= tol) { /* Deflation is possible. */ - z__[j] = tau; - z__[jlam] = 0.; + z__[j] = tau; + z__[jlam] = 0.; /* Record the appropriate Givens rotation */ - ++(*givptr); - givcol[(*givptr << 1) + 1] = indxq[indx[jlam]]; - givcol[(*givptr << 1) + 2] = indxq[indx[j]]; - givnum[(*givptr << 1) + 1] = c__; - givnum[(*givptr << 1) + 2] = s; - if (*icompq == 1) { - drot_(qsiz, &q[indxq[indx[jlam]] * q_dim1 + 1], &c__1, &q[ - indxq[indx[j]] * q_dim1 + 1], &c__1, &c__, &s); - } - t = d__[jlam] * c__ * c__ + d__[j] * s * s; - d__[j] = d__[jlam] * s * s + d__[j] * c__ * c__; - d__[jlam] = t; - --k2; - i__ = 1; + ++(*givptr); + givcol[(*givptr << 1) + 1] = indxq[indx[jlam]]; + givcol[(*givptr << 1) + 2] = indxq[indx[j]]; + givnum[(*givptr << 1) + 1] = c__; + givnum[(*givptr << 1) + 2] = s; + if (*icompq == 1) { + drot_(qsiz, &q[indxq[indx[jlam]] * q_dim1 + 1], &c__1, &q[ + indxq[indx[j]] * q_dim1 + 1], &c__1, &c__, &s); + } + t = d__[jlam] * c__ * c__ + d__[j] * s * s; + d__[j] = d__[jlam] * s * s + d__[j] * c__ * c__; + d__[jlam] = t; + --k2; + i__ = 1; L90: - if (k2 + i__ <= *n) { - if (d__[jlam] < d__[indxp[k2 + i__]]) { - indxp[k2 + i__ - 1] = indxp[k2 + i__]; - indxp[k2 + i__] = jlam; - ++i__; - goto L90; - } else { - indxp[k2 + i__ - 1] = jlam; - } - } else { - indxp[k2 + i__ - 1] = jlam; - } - jlam = j; - } else { - ++(*k); - w[*k] = z__[jlam]; - dlamda[*k] = d__[jlam]; - indxp[*k] = jlam; - jlam = j; - } + if (k2 + i__ <= *n) { + if (d__[jlam] < d__[indxp[k2 + i__]]) { + indxp[k2 + i__ - 1] = indxp[k2 + i__]; + indxp[k2 + i__] = jlam; + ++i__; + goto L90; + } else { + indxp[k2 + i__ - 1] = jlam; + } + } else { + indxp[k2 + i__ - 1] = jlam; + } + jlam = j; + } else { + ++(*k); + w[*k] = z__[jlam]; + dlamda[*k] = d__[jlam]; + indxp[*k] = jlam; + jlam = j; + } } goto L80; L100: @@ -564,39 +564,39 @@ L110: /* while those which were deflated go into the last N - K slots. */ if (*icompq == 0) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - jp = indxp[j]; - dlamda[j] = d__[jp]; - perm[j] = indxq[indx[jp]]; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + jp = indxp[j]; + dlamda[j] = d__[jp]; + perm[j] = indxq[indx[jp]]; /* L120: */ - } + } } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - jp = indxp[j]; - dlamda[j] = d__[jp]; - perm[j] = indxq[indx[jp]]; - dcopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 + 1] - , &c__1); + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + jp = indxp[j]; + dlamda[j] = d__[jp]; + perm[j] = indxq[indx[jp]]; + dcopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 + 1] + , &c__1); /* L130: */ - } + } } /* The deflated eigenvalues and their corresponding vectors go back */ /* into the last N - K slots of D and Q respectively. */ if (*k < *n) { - if (*icompq == 0) { - i__1 = *n - *k; - dcopy_(&i__1, &dlamda[*k + 1], &c__1, &d__[*k + 1], &c__1); - } else { - i__1 = *n - *k; - dcopy_(&i__1, &dlamda[*k + 1], &c__1, &d__[*k + 1], &c__1); - i__1 = *n - *k; - dlacpy_((char *)"A", qsiz, &i__1, &q2[(*k + 1) * q2_dim1 + 1], ldq2, &q[(* - k + 1) * q_dim1 + 1], ldq, (ftnlen)1); - } + if (*icompq == 0) { + i__1 = *n - *k; + dcopy_(&i__1, &dlamda[*k + 1], &c__1, &d__[*k + 1], &c__1); + } else { + i__1 = *n - *k; + dcopy_(&i__1, &dlamda[*k + 1], &c__1, &d__[*k + 1], &c__1); + i__1 = *n - *k; + dlacpy_((char *)"A", qsiz, &i__1, &q2[(*k + 1) * q2_dim1 + 1], ldq2, &q[(* + k + 1) * q_dim1 + 1], ldq, (ftnlen)1); + } } return 0; @@ -606,5 +606,5 @@ L110: } /* dlaed8_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlaed9.cpp b/lib/linalg/dlaed9.cpp index f74b8f5bc0..d6a4f8bca3 100644 --- a/lib/linalg/dlaed9.cpp +++ b/lib/linalg/dlaed9.cpp @@ -1,13 +1,13 @@ /* fortran/dlaed9.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -176,10 +176,10 @@ f"> */ /* > at Berkeley, USA */ /* ===================================================================== */ -/* Subroutine */ int dlaed9_(integer *k, integer *kstart, integer *kstop, - integer *n, doublereal *d__, doublereal *q, integer *ldq, doublereal * - rho, doublereal *dlamda, doublereal *w, doublereal *s, integer *lds, - integer *info) +/* Subroutine */ int dlaed9_(integer *k, integer *kstart, integer *kstop, + integer *n, doublereal *d__, doublereal *q, integer *ldq, doublereal * + rho, doublereal *dlamda, doublereal *w, doublereal *s, integer *lds, + integer *info) { /* System generated locals */ integer q_dim1, q_offset, s_dim1, s_offset, i__1, i__2; @@ -192,10 +192,10 @@ f"> */ integer i__, j; doublereal temp; extern doublereal dnrm2_(integer *, doublereal *, integer *); - extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, - doublereal *, integer *), dlaed4_(integer *, integer *, - doublereal *, doublereal *, doublereal *, doublereal *, - doublereal *, integer *); + extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, + doublereal *, integer *), dlaed4_(integer *, integer *, + doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, integer *); extern doublereal dlamc3_(doublereal *, doublereal *); extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); @@ -238,28 +238,28 @@ f"> */ *info = 0; if (*k < 0) { - *info = -1; + *info = -1; } else if (*kstart < 1 || *kstart > max(1,*k)) { - *info = -2; + *info = -2; } else if (max(1,*kstop) < *kstart || *kstop > max(1,*k)) { - *info = -3; + *info = -3; } else if (*n < *k) { - *info = -4; + *info = -4; } else if (*ldq < max(1,*k)) { - *info = -7; + *info = -7; } else if (*lds < max(1,*k)) { - *info = -12; + *info = -12; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DLAED9", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DLAED9", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*k == 0) { - return 0; + return 0; } /* Modify values DLAMDA(i) to make sure all DLAMDA(i)-DLAMDA(j) can */ @@ -281,34 +281,34 @@ f"> */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { - dlamda[i__] = dlamc3_(&dlamda[i__], &dlamda[i__]) - dlamda[i__]; + dlamda[i__] = dlamc3_(&dlamda[i__], &dlamda[i__]) - dlamda[i__]; /* L10: */ } i__1 = *kstop; for (j = *kstart; j <= i__1; ++j) { - dlaed4_(k, &j, &dlamda[1], &w[1], &q[j * q_dim1 + 1], rho, &d__[j], - info); + dlaed4_(k, &j, &dlamda[1], &w[1], &q[j * q_dim1 + 1], rho, &d__[j], + info); /* If the zero finder fails, the computation is terminated. */ - if (*info != 0) { - goto L120; - } + if (*info != 0) { + goto L120; + } /* L20: */ } if (*k == 1 || *k == 2) { - i__1 = *k; - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = *k; - for (j = 1; j <= i__2; ++j) { - s[j + i__ * s_dim1] = q[j + i__ * q_dim1]; + i__1 = *k; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = *k; + for (j = 1; j <= i__2; ++j) { + s[j + i__ * s_dim1] = q[j + i__ * q_dim1]; /* L30: */ - } + } /* L40: */ - } - goto L120; + } + goto L120; } /* Compute updated W. */ @@ -321,22 +321,22 @@ f"> */ dcopy_(k, &q[q_offset], &i__1, &w[1], &c__1); i__1 = *k; for (j = 1; j <= i__1; ++j) { - i__2 = j - 1; - for (i__ = 1; i__ <= i__2; ++i__) { - w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]); + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]); /* L50: */ - } - i__2 = *k; - for (i__ = j + 1; i__ <= i__2; ++i__) { - w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]); + } + i__2 = *k; + for (i__ = j + 1; i__ <= i__2; ++i__) { + w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]); /* L60: */ - } + } /* L70: */ } i__1 = *k; for (i__ = 1; i__ <= i__1; ++i__) { - d__1 = sqrt(-w[i__]); - w[i__] = d_sign(&d__1, &s[i__ + s_dim1]); + d__1 = sqrt(-w[i__]); + w[i__] = d_sign(&d__1, &s[i__ + s_dim1]); /* L80: */ } @@ -344,17 +344,17 @@ f"> */ i__1 = *k; for (j = 1; j <= i__1; ++j) { - i__2 = *k; - for (i__ = 1; i__ <= i__2; ++i__) { - q[i__ + j * q_dim1] = w[i__] / q[i__ + j * q_dim1]; + i__2 = *k; + for (i__ = 1; i__ <= i__2; ++i__) { + q[i__ + j * q_dim1] = w[i__] / q[i__ + j * q_dim1]; /* L90: */ - } - temp = dnrm2_(k, &q[j * q_dim1 + 1], &c__1); - i__2 = *k; - for (i__ = 1; i__ <= i__2; ++i__) { - s[i__ + j * s_dim1] = q[i__ + j * q_dim1] / temp; + } + temp = dnrm2_(k, &q[j * q_dim1 + 1], &c__1); + i__2 = *k; + for (i__ = 1; i__ <= i__2; ++i__) { + s[i__ + j * s_dim1] = q[i__ + j * q_dim1] / temp; /* L100: */ - } + } /* L110: */ } @@ -366,5 +366,5 @@ L120: } /* dlaed9_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlaeda.cpp b/lib/linalg/dlaeda.cpp index f487609f82..39b4c8810f 100644 --- a/lib/linalg/dlaeda.cpp +++ b/lib/linalg/dlaeda.cpp @@ -1,13 +1,13 @@ /* fortran/dlaeda.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -189,10 +189,10 @@ f"> */ /* > at Berkeley, USA */ /* ===================================================================== */ -/* Subroutine */ int dlaeda_(integer *n, integer *tlvls, integer *curlvl, - integer *curpbm, integer *prmptr, integer *perm, integer *givptr, - integer *givcol, doublereal *givnum, doublereal *q, integer *qptr, - doublereal *z__, doublereal *ztemp, integer *info) +/* Subroutine */ int dlaeda_(integer *n, integer *tlvls, integer *curlvl, + integer *curpbm, integer *prmptr, integer *perm, integer *givptr, + integer *givcol, doublereal *givnum, doublereal *q, integer *qptr, + doublereal *z__, doublereal *ztemp, integer *info) { /* System generated locals */ integer i__1, i__2, i__3; @@ -203,14 +203,14 @@ f"> */ /* Local variables */ integer i__, k, mid, ptr; - extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, - doublereal *, integer *, doublereal *, doublereal *); + extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, + doublereal *, integer *, doublereal *, doublereal *); integer curr, bsiz1, bsiz2, psiz1, psiz2, zptr1; - extern /* Subroutine */ int dgemv_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, doublereal *, integer *, - doublereal *, doublereal *, integer *, ftnlen), dcopy_(integer *, - doublereal *, integer *, doublereal *, integer *), xerbla_(char *, - integer *, ftnlen); + extern /* Subroutine */ int dgemv_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, ftnlen), dcopy_(integer *, + doublereal *, integer *, doublereal *, integer *), xerbla_(char *, + integer *, ftnlen); /* -- LAPACK computational routine -- */ @@ -251,18 +251,18 @@ f"> */ *info = 0; if (*n < 0) { - *info = -1; + *info = -1; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DLAEDA", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DLAEDA", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*n == 0) { - return 0; + return 0; } /* Determine location of first number in second half. */ @@ -284,19 +284,19 @@ f"> */ /* roots. */ bsiz1 = (integer) (sqrt((doublereal) (qptr[curr + 1] - qptr[curr])) + .5); - bsiz2 = (integer) (sqrt((doublereal) (qptr[curr + 2] - qptr[curr + 1])) + - .5); + bsiz2 = (integer) (sqrt((doublereal) (qptr[curr + 2] - qptr[curr + 1])) + + .5); i__1 = mid - bsiz1 - 1; for (k = 1; k <= i__1; ++k) { - z__[k] = 0.; + z__[k] = 0.; /* L10: */ } dcopy_(&bsiz1, &q[qptr[curr] + bsiz1 - 1], &bsiz1, &z__[mid - bsiz1], & - c__1); + c__1); dcopy_(&bsiz2, &q[qptr[curr + 1]], &bsiz2, &z__[mid], &c__1); i__1 = *n; for (k = mid + bsiz2; k <= i__1; ++k) { - z__[k] = 0.; + z__[k] = 0.; /* L20: */ } @@ -307,43 +307,43 @@ f"> */ ptr = pow_ii(&c__2, tlvls) + 1; i__1 = *curlvl - 1; for (k = 1; k <= i__1; ++k) { - i__2 = *curlvl - k; - i__3 = *curlvl - k - 1; - curr = ptr + *curpbm * pow_ii(&c__2, &i__2) + pow_ii(&c__2, &i__3) - - 1; - psiz1 = prmptr[curr + 1] - prmptr[curr]; - psiz2 = prmptr[curr + 2] - prmptr[curr + 1]; - zptr1 = mid - psiz1; + i__2 = *curlvl - k; + i__3 = *curlvl - k - 1; + curr = ptr + *curpbm * pow_ii(&c__2, &i__2) + pow_ii(&c__2, &i__3) - + 1; + psiz1 = prmptr[curr + 1] - prmptr[curr]; + psiz2 = prmptr[curr + 2] - prmptr[curr + 1]; + zptr1 = mid - psiz1; /* Apply Givens at CURR and CURR+1 */ - i__2 = givptr[curr + 1] - 1; - for (i__ = givptr[curr]; i__ <= i__2; ++i__) { - drot_(&c__1, &z__[zptr1 + givcol[(i__ << 1) + 1] - 1], &c__1, & - z__[zptr1 + givcol[(i__ << 1) + 2] - 1], &c__1, &givnum[( - i__ << 1) + 1], &givnum[(i__ << 1) + 2]); + i__2 = givptr[curr + 1] - 1; + for (i__ = givptr[curr]; i__ <= i__2; ++i__) { + drot_(&c__1, &z__[zptr1 + givcol[(i__ << 1) + 1] - 1], &c__1, & + z__[zptr1 + givcol[(i__ << 1) + 2] - 1], &c__1, &givnum[( + i__ << 1) + 1], &givnum[(i__ << 1) + 2]); /* L30: */ - } - i__2 = givptr[curr + 2] - 1; - for (i__ = givptr[curr + 1]; i__ <= i__2; ++i__) { - drot_(&c__1, &z__[mid - 1 + givcol[(i__ << 1) + 1]], &c__1, &z__[ - mid - 1 + givcol[(i__ << 1) + 2]], &c__1, &givnum[(i__ << - 1) + 1], &givnum[(i__ << 1) + 2]); + } + i__2 = givptr[curr + 2] - 1; + for (i__ = givptr[curr + 1]; i__ <= i__2; ++i__) { + drot_(&c__1, &z__[mid - 1 + givcol[(i__ << 1) + 1]], &c__1, &z__[ + mid - 1 + givcol[(i__ << 1) + 2]], &c__1, &givnum[(i__ << + 1) + 1], &givnum[(i__ << 1) + 2]); /* L40: */ - } - psiz1 = prmptr[curr + 1] - prmptr[curr]; - psiz2 = prmptr[curr + 2] - prmptr[curr + 1]; - i__2 = psiz1 - 1; - for (i__ = 0; i__ <= i__2; ++i__) { - ztemp[i__ + 1] = z__[zptr1 + perm[prmptr[curr] + i__] - 1]; + } + psiz1 = prmptr[curr + 1] - prmptr[curr]; + psiz2 = prmptr[curr + 2] - prmptr[curr + 1]; + i__2 = psiz1 - 1; + for (i__ = 0; i__ <= i__2; ++i__) { + ztemp[i__ + 1] = z__[zptr1 + perm[prmptr[curr] + i__] - 1]; /* L50: */ - } - i__2 = psiz2 - 1; - for (i__ = 0; i__ <= i__2; ++i__) { - ztemp[psiz1 + i__ + 1] = z__[mid + perm[prmptr[curr + 1] + i__] - - 1]; + } + i__2 = psiz2 - 1; + for (i__ = 0; i__ <= i__2; ++i__) { + ztemp[psiz1 + i__ + 1] = z__[mid + perm[prmptr[curr + 1] + i__] - + 1]; /* L60: */ - } + } /* Multiply Blocks at CURR and CURR+1 */ @@ -351,27 +351,27 @@ f"> */ /* the SQRT in case the machine underestimates one of these */ /* square roots. */ - bsiz1 = (integer) (sqrt((doublereal) (qptr[curr + 1] - qptr[curr])) + - .5); - bsiz2 = (integer) (sqrt((doublereal) (qptr[curr + 2] - qptr[curr + 1]) - ) + .5); - if (bsiz1 > 0) { - dgemv_((char *)"T", &bsiz1, &bsiz1, &c_b24, &q[qptr[curr]], &bsiz1, & - ztemp[1], &c__1, &c_b26, &z__[zptr1], &c__1, (ftnlen)1); - } - i__2 = psiz1 - bsiz1; - dcopy_(&i__2, &ztemp[bsiz1 + 1], &c__1, &z__[zptr1 + bsiz1], &c__1); - if (bsiz2 > 0) { - dgemv_((char *)"T", &bsiz2, &bsiz2, &c_b24, &q[qptr[curr + 1]], &bsiz2, & - ztemp[psiz1 + 1], &c__1, &c_b26, &z__[mid], &c__1, ( - ftnlen)1); - } - i__2 = psiz2 - bsiz2; - dcopy_(&i__2, &ztemp[psiz1 + bsiz2 + 1], &c__1, &z__[mid + bsiz2], & - c__1); + bsiz1 = (integer) (sqrt((doublereal) (qptr[curr + 1] - qptr[curr])) + + .5); + bsiz2 = (integer) (sqrt((doublereal) (qptr[curr + 2] - qptr[curr + 1]) + ) + .5); + if (bsiz1 > 0) { + dgemv_((char *)"T", &bsiz1, &bsiz1, &c_b24, &q[qptr[curr]], &bsiz1, & + ztemp[1], &c__1, &c_b26, &z__[zptr1], &c__1, (ftnlen)1); + } + i__2 = psiz1 - bsiz1; + dcopy_(&i__2, &ztemp[bsiz1 + 1], &c__1, &z__[zptr1 + bsiz1], &c__1); + if (bsiz2 > 0) { + dgemv_((char *)"T", &bsiz2, &bsiz2, &c_b24, &q[qptr[curr + 1]], &bsiz2, & + ztemp[psiz1 + 1], &c__1, &c_b26, &z__[mid], &c__1, ( + ftnlen)1); + } + i__2 = psiz2 - bsiz2; + dcopy_(&i__2, &ztemp[psiz1 + bsiz2 + 1], &c__1, &z__[mid + bsiz2], & + c__1); - i__2 = *tlvls - k; - ptr += pow_ii(&c__2, &i__2); + i__2 = *tlvls - k; + ptr += pow_ii(&c__2, &i__2); /* L70: */ } @@ -382,5 +382,5 @@ f"> */ } /* dlaeda_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlaev2.cpp b/lib/linalg/dlaev2.cpp index 32f4eb5424..21bdbebe69 100644 --- a/lib/linalg/dlaev2.cpp +++ b/lib/linalg/dlaev2.cpp @@ -1,13 +1,13 @@ /* fortran/dlaev2.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -136,8 +136,8 @@ f"> */ /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int dlaev2_(doublereal *a, doublereal *b, doublereal *c__, - doublereal *rt1, doublereal *rt2, doublereal *cs1, doublereal *sn1) +/* Subroutine */ int dlaev2_(doublereal *a, doublereal *b, doublereal *c__, + doublereal *rt1, doublereal *rt2, doublereal *cs1, doublereal *sn1) { /* System generated locals */ doublereal d__1; @@ -176,81 +176,81 @@ f"> */ tb = *b + *b; ab = abs(tb); if (abs(*a) > abs(*c__)) { - acmx = *a; - acmn = *c__; + acmx = *a; + acmn = *c__; } else { - acmx = *c__; - acmn = *a; + acmx = *c__; + acmn = *a; } if (adf > ab) { /* Computing 2nd power */ - d__1 = ab / adf; - rt = adf * sqrt(d__1 * d__1 + 1.); + d__1 = ab / adf; + rt = adf * sqrt(d__1 * d__1 + 1.); } else if (adf < ab) { /* Computing 2nd power */ - d__1 = adf / ab; - rt = ab * sqrt(d__1 * d__1 + 1.); + d__1 = adf / ab; + rt = ab * sqrt(d__1 * d__1 + 1.); } else { /* Includes case AB=ADF=0 */ - rt = ab * sqrt(2.); + rt = ab * sqrt(2.); } if (sm < 0.) { - *rt1 = (sm - rt) * .5; - sgn1 = -1; + *rt1 = (sm - rt) * .5; + sgn1 = -1; /* Order of execution important. */ /* To get fully accurate smaller eigenvalue, */ /* next line needs to be executed in higher precision. */ - *rt2 = acmx / *rt1 * acmn - *b / *rt1 * *b; + *rt2 = acmx / *rt1 * acmn - *b / *rt1 * *b; } else if (sm > 0.) { - *rt1 = (sm + rt) * .5; - sgn1 = 1; + *rt1 = (sm + rt) * .5; + sgn1 = 1; /* Order of execution important. */ /* To get fully accurate smaller eigenvalue, */ /* next line needs to be executed in higher precision. */ - *rt2 = acmx / *rt1 * acmn - *b / *rt1 * *b; + *rt2 = acmx / *rt1 * acmn - *b / *rt1 * *b; } else { /* Includes case RT1 = RT2 = 0 */ - *rt1 = rt * .5; - *rt2 = rt * -.5; - sgn1 = 1; + *rt1 = rt * .5; + *rt2 = rt * -.5; + sgn1 = 1; } /* Compute the eigenvector */ if (df >= 0.) { - cs = df + rt; - sgn2 = 1; + cs = df + rt; + sgn2 = 1; } else { - cs = df - rt; - sgn2 = -1; + cs = df - rt; + sgn2 = -1; } acs = abs(cs); if (acs > ab) { - ct = -tb / cs; - *sn1 = 1. / sqrt(ct * ct + 1.); - *cs1 = ct * *sn1; + ct = -tb / cs; + *sn1 = 1. / sqrt(ct * ct + 1.); + *cs1 = ct * *sn1; } else { - if (ab == 0.) { - *cs1 = 1.; - *sn1 = 0.; - } else { - tn = -cs / tb; - *cs1 = 1. / sqrt(tn * tn + 1.); - *sn1 = tn * *cs1; - } + if (ab == 0.) { + *cs1 = 1.; + *sn1 = 0.; + } else { + tn = -cs / tb; + *cs1 = 1. / sqrt(tn * tn + 1.); + *sn1 = tn * *cs1; + } } if (sgn1 == sgn2) { - tn = *cs1; - *cs1 = -(*sn1); - *sn1 = tn; + tn = *cs1; + *cs1 = -(*sn1); + *sn1 = tn; } return 0; @@ -259,5 +259,5 @@ f"> */ } /* dlaev2_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlals0.cpp b/lib/linalg/dlals0.cpp index ce36d7d553..9dfb826915 100644 --- a/lib/linalg/dlals0.cpp +++ b/lib/linalg/dlals0.cpp @@ -1,13 +1,13 @@ /* fortran/dlals0.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -291,17 +291,17 @@ f"> */ /* > Osni Marques, LBNL/NERSC, USA \n */ /* ===================================================================== */ -/* Subroutine */ int dlals0_(integer *icompq, integer *nl, integer *nr, - integer *sqre, integer *nrhs, doublereal *b, integer *ldb, doublereal - *bx, integer *ldbx, integer *perm, integer *givptr, integer *givcol, - integer *ldgcol, doublereal *givnum, integer *ldgnum, doublereal * - poles, doublereal *difl, doublereal *difr, doublereal *z__, integer * - k, doublereal *c__, doublereal *s, doublereal *work, integer *info) +/* Subroutine */ int dlals0_(integer *icompq, integer *nl, integer *nr, + integer *sqre, integer *nrhs, doublereal *b, integer *ldb, doublereal + *bx, integer *ldbx, integer *perm, integer *givptr, integer *givcol, + integer *ldgcol, doublereal *givnum, integer *ldgnum, doublereal * + poles, doublereal *difl, doublereal *difr, doublereal *z__, integer * + k, doublereal *c__, doublereal *s, doublereal *work, integer *info) { /* System generated locals */ - integer givcol_dim1, givcol_offset, b_dim1, b_offset, bx_dim1, bx_offset, - difr_dim1, difr_offset, givnum_dim1, givnum_offset, poles_dim1, - poles_offset, i__1, i__2; + integer givcol_dim1, givcol_offset, b_dim1, b_offset, bx_dim1, bx_offset, + difr_dim1, difr_offset, givnum_dim1, givnum_offset, poles_dim1, + poles_offset, i__1, i__2; doublereal d__1; /* Local variables */ @@ -309,22 +309,22 @@ f"> */ doublereal dj; integer nlp1; doublereal temp; - extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, - doublereal *, integer *, doublereal *, doublereal *); + extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, + doublereal *, integer *, doublereal *, doublereal *); extern doublereal dnrm2_(integer *, doublereal *, integer *); - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *); + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *); doublereal diflj, difrj, dsigj; - extern /* Subroutine */ int dgemv_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, doublereal *, integer *, - doublereal *, doublereal *, integer *, ftnlen), dcopy_(integer *, - doublereal *, integer *, doublereal *, integer *); + extern /* Subroutine */ int dgemv_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, ftnlen), dcopy_(integer *, + doublereal *, integer *, doublereal *, integer *); extern doublereal dlamc3_(doublereal *, doublereal *); - extern /* Subroutine */ int dlascl_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, integer *, doublereal *, - integer *, integer *, ftnlen), dlacpy_(char *, integer *, integer - *, doublereal *, integer *, doublereal *, integer *, ftnlen), - xerbla_(char *, integer *, ftnlen); + extern /* Subroutine */ int dlascl_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, integer *, doublereal *, + integer *, integer *, ftnlen), dlacpy_(char *, integer *, integer + *, doublereal *, integer *, doublereal *, integer *, ftnlen), + xerbla_(char *, integer *, ftnlen); doublereal dsigjp; @@ -382,32 +382,32 @@ f"> */ n = *nl + *nr + 1; if (*icompq < 0 || *icompq > 1) { - *info = -1; + *info = -1; } else if (*nl < 1) { - *info = -2; + *info = -2; } else if (*nr < 1) { - *info = -3; + *info = -3; } else if (*sqre < 0 || *sqre > 1) { - *info = -4; + *info = -4; } else if (*nrhs < 1) { - *info = -5; + *info = -5; } else if (*ldb < n) { - *info = -7; + *info = -7; } else if (*ldbx < n) { - *info = -9; + *info = -9; } else if (*givptr < 0) { - *info = -11; + *info = -11; } else if (*ldgcol < n) { - *info = -13; + *info = -13; } else if (*ldgnum < n) { - *info = -15; + *info = -15; } else if (*k < 1) { - *info = -20; + *info = -20; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DLALS0", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DLALS0", &i__1, (ftnlen)6); + return 0; } m = n + *sqre; @@ -419,91 +419,91 @@ f"> */ /* Step (1L): apply back the Givens rotations performed. */ - i__1 = *givptr; - for (i__ = 1; i__ <= i__1; ++i__) { - drot_(nrhs, &b[givcol[i__ + (givcol_dim1 << 1)] + b_dim1], ldb, & - b[givcol[i__ + givcol_dim1] + b_dim1], ldb, &givnum[i__ + - (givnum_dim1 << 1)], &givnum[i__ + givnum_dim1]); + i__1 = *givptr; + for (i__ = 1; i__ <= i__1; ++i__) { + drot_(nrhs, &b[givcol[i__ + (givcol_dim1 << 1)] + b_dim1], ldb, & + b[givcol[i__ + givcol_dim1] + b_dim1], ldb, &givnum[i__ + + (givnum_dim1 << 1)], &givnum[i__ + givnum_dim1]); /* L10: */ - } + } /* Step (2L): permute rows of B. */ - dcopy_(nrhs, &b[nlp1 + b_dim1], ldb, &bx[bx_dim1 + 1], ldbx); - i__1 = n; - for (i__ = 2; i__ <= i__1; ++i__) { - dcopy_(nrhs, &b[perm[i__] + b_dim1], ldb, &bx[i__ + bx_dim1], - ldbx); + dcopy_(nrhs, &b[nlp1 + b_dim1], ldb, &bx[bx_dim1 + 1], ldbx); + i__1 = n; + for (i__ = 2; i__ <= i__1; ++i__) { + dcopy_(nrhs, &b[perm[i__] + b_dim1], ldb, &bx[i__ + bx_dim1], + ldbx); /* L20: */ - } + } /* Step (3L): apply the inverse of the left singular vector */ /* matrix to BX. */ - if (*k == 1) { - dcopy_(nrhs, &bx[bx_offset], ldbx, &b[b_offset], ldb); - if (z__[1] < 0.) { - dscal_(nrhs, &c_b5, &b[b_offset], ldb); - } - } else { - i__1 = *k; - for (j = 1; j <= i__1; ++j) { - diflj = difl[j]; - dj = poles[j + poles_dim1]; - dsigj = -poles[j + (poles_dim1 << 1)]; - if (j < *k) { - difrj = -difr[j + difr_dim1]; - dsigjp = -poles[j + 1 + (poles_dim1 << 1)]; - } - if (z__[j] == 0. || poles[j + (poles_dim1 << 1)] == 0.) { - work[j] = 0.; - } else { - work[j] = -poles[j + (poles_dim1 << 1)] * z__[j] / diflj / - (poles[j + (poles_dim1 << 1)] + dj); - } - i__2 = j - 1; - for (i__ = 1; i__ <= i__2; ++i__) { - if (z__[i__] == 0. || poles[i__ + (poles_dim1 << 1)] == - 0.) { - work[i__] = 0.; - } else { - work[i__] = poles[i__ + (poles_dim1 << 1)] * z__[i__] - / (dlamc3_(&poles[i__ + (poles_dim1 << 1)], & - dsigj) - diflj) / (poles[i__ + (poles_dim1 << - 1)] + dj); - } + if (*k == 1) { + dcopy_(nrhs, &bx[bx_offset], ldbx, &b[b_offset], ldb); + if (z__[1] < 0.) { + dscal_(nrhs, &c_b5, &b[b_offset], ldb); + } + } else { + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + diflj = difl[j]; + dj = poles[j + poles_dim1]; + dsigj = -poles[j + (poles_dim1 << 1)]; + if (j < *k) { + difrj = -difr[j + difr_dim1]; + dsigjp = -poles[j + 1 + (poles_dim1 << 1)]; + } + if (z__[j] == 0. || poles[j + (poles_dim1 << 1)] == 0.) { + work[j] = 0.; + } else { + work[j] = -poles[j + (poles_dim1 << 1)] * z__[j] / diflj / + (poles[j + (poles_dim1 << 1)] + dj); + } + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + if (z__[i__] == 0. || poles[i__ + (poles_dim1 << 1)] == + 0.) { + work[i__] = 0.; + } else { + work[i__] = poles[i__ + (poles_dim1 << 1)] * z__[i__] + / (dlamc3_(&poles[i__ + (poles_dim1 << 1)], & + dsigj) - diflj) / (poles[i__ + (poles_dim1 << + 1)] + dj); + } /* L30: */ - } - i__2 = *k; - for (i__ = j + 1; i__ <= i__2; ++i__) { - if (z__[i__] == 0. || poles[i__ + (poles_dim1 << 1)] == - 0.) { - work[i__] = 0.; - } else { - work[i__] = poles[i__ + (poles_dim1 << 1)] * z__[i__] - / (dlamc3_(&poles[i__ + (poles_dim1 << 1)], & - dsigjp) + difrj) / (poles[i__ + (poles_dim1 << - 1)] + dj); - } + } + i__2 = *k; + for (i__ = j + 1; i__ <= i__2; ++i__) { + if (z__[i__] == 0. || poles[i__ + (poles_dim1 << 1)] == + 0.) { + work[i__] = 0.; + } else { + work[i__] = poles[i__ + (poles_dim1 << 1)] * z__[i__] + / (dlamc3_(&poles[i__ + (poles_dim1 << 1)], & + dsigjp) + difrj) / (poles[i__ + (poles_dim1 << + 1)] + dj); + } /* L40: */ - } - work[1] = -1.; - temp = dnrm2_(k, &work[1], &c__1); - dgemv_((char *)"T", k, nrhs, &c_b11, &bx[bx_offset], ldbx, &work[1], & - c__1, &c_b13, &b[j + b_dim1], ldb, (ftnlen)1); - dlascl_((char *)"G", &c__0, &c__0, &temp, &c_b11, &c__1, nrhs, &b[j + - b_dim1], ldb, info, (ftnlen)1); + } + work[1] = -1.; + temp = dnrm2_(k, &work[1], &c__1); + dgemv_((char *)"T", k, nrhs, &c_b11, &bx[bx_offset], ldbx, &work[1], & + c__1, &c_b13, &b[j + b_dim1], ldb, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &temp, &c_b11, &c__1, nrhs, &b[j + + b_dim1], ldb, info, (ftnlen)1); /* L50: */ - } - } + } + } /* Move the deflated rows of BX to B also. */ - if (*k < max(m,n)) { - i__1 = n - *k; - dlacpy_((char *)"A", &i__1, nrhs, &bx[*k + 1 + bx_dim1], ldbx, &b[*k + 1 - + b_dim1], ldb, (ftnlen)1); - } + if (*k < max(m,n)) { + i__1 = n - *k; + dlacpy_((char *)"A", &i__1, nrhs, &bx[*k + 1 + bx_dim1], ldbx, &b[*k + 1 + + b_dim1], ldb, (ftnlen)1); + } } else { /* Apply back the right orthogonal transformations. */ @@ -511,84 +511,84 @@ f"> */ /* Step (1R): apply back the new right singular vector matrix */ /* to B. */ - if (*k == 1) { - dcopy_(nrhs, &b[b_offset], ldb, &bx[bx_offset], ldbx); - } else { - i__1 = *k; - for (j = 1; j <= i__1; ++j) { - dsigj = poles[j + (poles_dim1 << 1)]; - if (z__[j] == 0.) { - work[j] = 0.; - } else { - work[j] = -z__[j] / difl[j] / (dsigj + poles[j + - poles_dim1]) / difr[j + (difr_dim1 << 1)]; - } - i__2 = j - 1; - for (i__ = 1; i__ <= i__2; ++i__) { - if (z__[j] == 0.) { - work[i__] = 0.; - } else { - d__1 = -poles[i__ + 1 + (poles_dim1 << 1)]; - work[i__] = z__[j] / (dlamc3_(&dsigj, &d__1) - difr[ - i__ + difr_dim1]) / (dsigj + poles[i__ + - poles_dim1]) / difr[i__ + (difr_dim1 << 1)]; - } + if (*k == 1) { + dcopy_(nrhs, &b[b_offset], ldb, &bx[bx_offset], ldbx); + } else { + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + dsigj = poles[j + (poles_dim1 << 1)]; + if (z__[j] == 0.) { + work[j] = 0.; + } else { + work[j] = -z__[j] / difl[j] / (dsigj + poles[j + + poles_dim1]) / difr[j + (difr_dim1 << 1)]; + } + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + if (z__[j] == 0.) { + work[i__] = 0.; + } else { + d__1 = -poles[i__ + 1 + (poles_dim1 << 1)]; + work[i__] = z__[j] / (dlamc3_(&dsigj, &d__1) - difr[ + i__ + difr_dim1]) / (dsigj + poles[i__ + + poles_dim1]) / difr[i__ + (difr_dim1 << 1)]; + } /* L60: */ - } - i__2 = *k; - for (i__ = j + 1; i__ <= i__2; ++i__) { - if (z__[j] == 0.) { - work[i__] = 0.; - } else { - d__1 = -poles[i__ + (poles_dim1 << 1)]; - work[i__] = z__[j] / (dlamc3_(&dsigj, &d__1) - difl[ - i__]) / (dsigj + poles[i__ + poles_dim1]) / - difr[i__ + (difr_dim1 << 1)]; - } + } + i__2 = *k; + for (i__ = j + 1; i__ <= i__2; ++i__) { + if (z__[j] == 0.) { + work[i__] = 0.; + } else { + d__1 = -poles[i__ + (poles_dim1 << 1)]; + work[i__] = z__[j] / (dlamc3_(&dsigj, &d__1) - difl[ + i__]) / (dsigj + poles[i__ + poles_dim1]) / + difr[i__ + (difr_dim1 << 1)]; + } /* L70: */ - } - dgemv_((char *)"T", k, nrhs, &c_b11, &b[b_offset], ldb, &work[1], & - c__1, &c_b13, &bx[j + bx_dim1], ldbx, (ftnlen)1); + } + dgemv_((char *)"T", k, nrhs, &c_b11, &b[b_offset], ldb, &work[1], & + c__1, &c_b13, &bx[j + bx_dim1], ldbx, (ftnlen)1); /* L80: */ - } - } + } + } /* Step (2R): if SQRE = 1, apply back the rotation that is */ /* related to the right null space of the subproblem. */ - if (*sqre == 1) { - dcopy_(nrhs, &b[m + b_dim1], ldb, &bx[m + bx_dim1], ldbx); - drot_(nrhs, &bx[bx_dim1 + 1], ldbx, &bx[m + bx_dim1], ldbx, c__, - s); - } - if (*k < max(m,n)) { - i__1 = n - *k; - dlacpy_((char *)"A", &i__1, nrhs, &b[*k + 1 + b_dim1], ldb, &bx[*k + 1 + - bx_dim1], ldbx, (ftnlen)1); - } + if (*sqre == 1) { + dcopy_(nrhs, &b[m + b_dim1], ldb, &bx[m + bx_dim1], ldbx); + drot_(nrhs, &bx[bx_dim1 + 1], ldbx, &bx[m + bx_dim1], ldbx, c__, + s); + } + if (*k < max(m,n)) { + i__1 = n - *k; + dlacpy_((char *)"A", &i__1, nrhs, &b[*k + 1 + b_dim1], ldb, &bx[*k + 1 + + bx_dim1], ldbx, (ftnlen)1); + } /* Step (3R): permute rows of B. */ - dcopy_(nrhs, &bx[bx_dim1 + 1], ldbx, &b[nlp1 + b_dim1], ldb); - if (*sqre == 1) { - dcopy_(nrhs, &bx[m + bx_dim1], ldbx, &b[m + b_dim1], ldb); - } - i__1 = n; - for (i__ = 2; i__ <= i__1; ++i__) { - dcopy_(nrhs, &bx[i__ + bx_dim1], ldbx, &b[perm[i__] + b_dim1], - ldb); + dcopy_(nrhs, &bx[bx_dim1 + 1], ldbx, &b[nlp1 + b_dim1], ldb); + if (*sqre == 1) { + dcopy_(nrhs, &bx[m + bx_dim1], ldbx, &b[m + b_dim1], ldb); + } + i__1 = n; + for (i__ = 2; i__ <= i__1; ++i__) { + dcopy_(nrhs, &bx[i__ + bx_dim1], ldbx, &b[perm[i__] + b_dim1], + ldb); /* L90: */ - } + } /* Step (4R): apply back the Givens rotations performed. */ - for (i__ = *givptr; i__ >= 1; --i__) { - d__1 = -givnum[i__ + givnum_dim1]; - drot_(nrhs, &b[givcol[i__ + (givcol_dim1 << 1)] + b_dim1], ldb, & - b[givcol[i__ + givcol_dim1] + b_dim1], ldb, &givnum[i__ + - (givnum_dim1 << 1)], &d__1); + for (i__ = *givptr; i__ >= 1; --i__) { + d__1 = -givnum[i__ + givnum_dim1]; + drot_(nrhs, &b[givcol[i__ + (givcol_dim1 << 1)] + b_dim1], ldb, & + b[givcol[i__ + givcol_dim1] + b_dim1], ldb, &givnum[i__ + + (givnum_dim1 << 1)], &d__1); /* L100: */ - } + } } return 0; @@ -598,5 +598,5 @@ f"> */ } /* dlals0_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlalsa.cpp b/lib/linalg/dlalsa.cpp index 7c09a46de3..e68dabd8dd 100644 --- a/lib/linalg/dlalsa.cpp +++ b/lib/linalg/dlalsa.cpp @@ -1,13 +1,13 @@ /* fortran/dlalsa.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -286,40 +286,40 @@ f"> */ /* > Osni Marques, LBNL/NERSC, USA \n */ /* ===================================================================== */ -/* Subroutine */ int dlalsa_(integer *icompq, integer *smlsiz, integer *n, - integer *nrhs, doublereal *b, integer *ldb, doublereal *bx, integer * - ldbx, doublereal *u, integer *ldu, doublereal *vt, integer *k, - doublereal *difl, doublereal *difr, doublereal *z__, doublereal * - poles, integer *givptr, integer *givcol, integer *ldgcol, integer * - perm, doublereal *givnum, doublereal *c__, doublereal *s, doublereal * - work, integer *iwork, integer *info) +/* Subroutine */ int dlalsa_(integer *icompq, integer *smlsiz, integer *n, + integer *nrhs, doublereal *b, integer *ldb, doublereal *bx, integer * + ldbx, doublereal *u, integer *ldu, doublereal *vt, integer *k, + doublereal *difl, doublereal *difr, doublereal *z__, doublereal * + poles, integer *givptr, integer *givcol, integer *ldgcol, integer * + perm, doublereal *givnum, doublereal *c__, doublereal *s, doublereal * + work, integer *iwork, integer *info) { /* System generated locals */ - integer givcol_dim1, givcol_offset, perm_dim1, perm_offset, b_dim1, - b_offset, bx_dim1, bx_offset, difl_dim1, difl_offset, difr_dim1, - difr_offset, givnum_dim1, givnum_offset, poles_dim1, poles_offset, - u_dim1, u_offset, vt_dim1, vt_offset, z_dim1, z_offset, i__1, - i__2; + integer givcol_dim1, givcol_offset, perm_dim1, perm_offset, b_dim1, + b_offset, bx_dim1, bx_offset, difl_dim1, difl_offset, difr_dim1, + difr_offset, givnum_dim1, givnum_offset, poles_dim1, poles_offset, + u_dim1, u_offset, vt_dim1, vt_offset, z_dim1, z_offset, i__1, + i__2; /* Builtin functions */ integer pow_ii(integer *, integer *); /* Local variables */ - integer i__, j, i1, ic, lf, nd, ll, nl, nr, im1, nlf, nrf, lvl, ndb1, - nlp1, lvl2, nrp1, nlvl, sqre; - extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); + integer i__, j, i1, ic, lf, nd, ll, nl, nr, im1, nlf, nrf, lvl, ndb1, + nlp1, lvl2, nrp1, nlvl, sqre; + extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); integer inode, ndiml, ndimr; - extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, - doublereal *, integer *), dlals0_(integer *, integer *, integer *, - integer *, integer *, doublereal *, integer *, doublereal *, - integer *, integer *, integer *, integer *, integer *, doublereal - *, integer *, doublereal *, doublereal *, doublereal *, - doublereal *, integer *, doublereal *, doublereal *, doublereal *, - integer *), dlasdt_(integer *, integer *, integer *, integer *, - integer *, integer *, integer *), xerbla_(char *, integer *, - ftnlen); + extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, + doublereal *, integer *), dlals0_(integer *, integer *, integer *, + integer *, integer *, doublereal *, integer *, doublereal *, + integer *, integer *, integer *, integer *, integer *, doublereal + *, integer *, doublereal *, doublereal *, doublereal *, + doublereal *, integer *, doublereal *, doublereal *, doublereal *, + integer *), dlasdt_(integer *, integer *, integer *, integer *, + integer *, integer *, integer *), xerbla_(char *, integer *, + ftnlen); /* -- LAPACK computational routine -- */ @@ -388,26 +388,26 @@ f"> */ *info = 0; if (*icompq < 0 || *icompq > 1) { - *info = -1; + *info = -1; } else if (*smlsiz < 3) { - *info = -2; + *info = -2; } else if (*n < *smlsiz) { - *info = -3; + *info = -3; } else if (*nrhs < 1) { - *info = -4; + *info = -4; } else if (*ldb < *n) { - *info = -6; + *info = -6; } else if (*ldbx < *n) { - *info = -8; + *info = -8; } else if (*ldu < *n) { - *info = -10; + *info = -10; } else if (*ldgcol < *n) { - *info = -19; + *info = -19; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DLALSA", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DLALSA", &i__1, (ftnlen)6); + return 0; } /* Book-keeping and setting up the computation tree. */ @@ -416,14 +416,14 @@ f"> */ ndiml = inode + *n; ndimr = ndiml + *n; - dlasdt_(n, &nlvl, &nd, &iwork[inode], &iwork[ndiml], &iwork[ndimr], - smlsiz); + dlasdt_(n, &nlvl, &nd, &iwork[inode], &iwork[ndiml], &iwork[ndimr], + smlsiz); /* The following code applies back the left singular vector factors. */ /* For applying back the right singular vector factors, go to 50. */ if (*icompq == 1) { - goto L50; + goto L50; } /* The nodes on the bottom level of the tree were solved */ @@ -441,18 +441,18 @@ f"> */ /* NLF: starting row of the left subproblem */ /* NRF: starting row of the right subproblem */ - i1 = i__ - 1; - ic = iwork[inode + i1]; - nl = iwork[ndiml + i1]; - nr = iwork[ndimr + i1]; - nlf = ic - nl; - nrf = ic + 1; - dgemm_((char *)"T", (char *)"N", &nl, nrhs, &nl, &c_b7, &u[nlf + u_dim1], ldu, &b[nlf - + b_dim1], ldb, &c_b8, &bx[nlf + bx_dim1], ldbx, (ftnlen)1, ( - ftnlen)1); - dgemm_((char *)"T", (char *)"N", &nr, nrhs, &nr, &c_b7, &u[nrf + u_dim1], ldu, &b[nrf - + b_dim1], ldb, &c_b8, &bx[nrf + bx_dim1], ldbx, (ftnlen)1, ( - ftnlen)1); + i1 = i__ - 1; + ic = iwork[inode + i1]; + nl = iwork[ndiml + i1]; + nr = iwork[ndimr + i1]; + nlf = ic - nl; + nrf = ic + 1; + dgemm_((char *)"T", (char *)"N", &nl, nrhs, &nl, &c_b7, &u[nlf + u_dim1], ldu, &b[nlf + + b_dim1], ldb, &c_b8, &bx[nlf + bx_dim1], ldbx, (ftnlen)1, ( + ftnlen)1); + dgemm_((char *)"T", (char *)"N", &nr, nrhs, &nr, &c_b7, &u[nrf + u_dim1], ldu, &b[nrf + + b_dim1], ldb, &c_b8, &bx[nrf + bx_dim1], ldbx, (ftnlen)1, ( + ftnlen)1); /* L10: */ } @@ -461,8 +461,8 @@ f"> */ i__1 = nd; for (i__ = 1; i__ <= i__1; ++i__) { - ic = iwork[inode + i__ - 1]; - dcopy_(nrhs, &b[ic + b_dim1], ldb, &bx[ic + bx_dim1], ldbx); + ic = iwork[inode + i__ - 1]; + dcopy_(nrhs, &b[ic + b_dim1], ldb, &bx[ic + bx_dim1], ldbx); /* L20: */ } @@ -473,37 +473,37 @@ f"> */ sqre = 0; for (lvl = nlvl; lvl >= 1; --lvl) { - lvl2 = (lvl << 1) - 1; + lvl2 = (lvl << 1) - 1; /* find the first node LF and last node LL on */ /* the current level LVL */ - if (lvl == 1) { - lf = 1; - ll = 1; - } else { - i__1 = lvl - 1; - lf = pow_ii(&c__2, &i__1); - ll = (lf << 1) - 1; - } - i__1 = ll; - for (i__ = lf; i__ <= i__1; ++i__) { - im1 = i__ - 1; - ic = iwork[inode + im1]; - nl = iwork[ndiml + im1]; - nr = iwork[ndimr + im1]; - nlf = ic - nl; - nrf = ic + 1; - --j; - dlals0_(icompq, &nl, &nr, &sqre, nrhs, &bx[nlf + bx_dim1], ldbx, & - b[nlf + b_dim1], ldb, &perm[nlf + lvl * perm_dim1], & - givptr[j], &givcol[nlf + lvl2 * givcol_dim1], ldgcol, & - givnum[nlf + lvl2 * givnum_dim1], ldu, &poles[nlf + lvl2 * - poles_dim1], &difl[nlf + lvl * difl_dim1], &difr[nlf + - lvl2 * difr_dim1], &z__[nlf + lvl * z_dim1], &k[j], &c__[ - j], &s[j], &work[1], info); + if (lvl == 1) { + lf = 1; + ll = 1; + } else { + i__1 = lvl - 1; + lf = pow_ii(&c__2, &i__1); + ll = (lf << 1) - 1; + } + i__1 = ll; + for (i__ = lf; i__ <= i__1; ++i__) { + im1 = i__ - 1; + ic = iwork[inode + im1]; + nl = iwork[ndiml + im1]; + nr = iwork[ndimr + im1]; + nlf = ic - nl; + nrf = ic + 1; + --j; + dlals0_(icompq, &nl, &nr, &sqre, nrhs, &bx[nlf + bx_dim1], ldbx, & + b[nlf + b_dim1], ldb, &perm[nlf + lvl * perm_dim1], & + givptr[j], &givcol[nlf + lvl2 * givcol_dim1], ldgcol, & + givnum[nlf + lvl2 * givnum_dim1], ldu, &poles[nlf + lvl2 * + poles_dim1], &difl[nlf + lvl * difl_dim1], &difr[nlf + + lvl2 * difr_dim1], &z__[nlf + lvl * z_dim1], &k[j], &c__[ + j], &s[j], &work[1], info); /* L30: */ - } + } /* L40: */ } goto L90; @@ -518,42 +518,42 @@ L50: j = 0; i__1 = nlvl; for (lvl = 1; lvl <= i__1; ++lvl) { - lvl2 = (lvl << 1) - 1; + lvl2 = (lvl << 1) - 1; /* Find the first node LF and last node LL on */ /* the current level LVL. */ - if (lvl == 1) { - lf = 1; - ll = 1; - } else { - i__2 = lvl - 1; - lf = pow_ii(&c__2, &i__2); - ll = (lf << 1) - 1; - } - i__2 = lf; - for (i__ = ll; i__ >= i__2; --i__) { - im1 = i__ - 1; - ic = iwork[inode + im1]; - nl = iwork[ndiml + im1]; - nr = iwork[ndimr + im1]; - nlf = ic - nl; - nrf = ic + 1; - if (i__ == ll) { - sqre = 0; - } else { - sqre = 1; - } - ++j; - dlals0_(icompq, &nl, &nr, &sqre, nrhs, &b[nlf + b_dim1], ldb, &bx[ - nlf + bx_dim1], ldbx, &perm[nlf + lvl * perm_dim1], & - givptr[j], &givcol[nlf + lvl2 * givcol_dim1], ldgcol, & - givnum[nlf + lvl2 * givnum_dim1], ldu, &poles[nlf + lvl2 * - poles_dim1], &difl[nlf + lvl * difl_dim1], &difr[nlf + - lvl2 * difr_dim1], &z__[nlf + lvl * z_dim1], &k[j], &c__[ - j], &s[j], &work[1], info); + if (lvl == 1) { + lf = 1; + ll = 1; + } else { + i__2 = lvl - 1; + lf = pow_ii(&c__2, &i__2); + ll = (lf << 1) - 1; + } + i__2 = lf; + for (i__ = ll; i__ >= i__2; --i__) { + im1 = i__ - 1; + ic = iwork[inode + im1]; + nl = iwork[ndiml + im1]; + nr = iwork[ndimr + im1]; + nlf = ic - nl; + nrf = ic + 1; + if (i__ == ll) { + sqre = 0; + } else { + sqre = 1; + } + ++j; + dlals0_(icompq, &nl, &nr, &sqre, nrhs, &b[nlf + b_dim1], ldb, &bx[ + nlf + bx_dim1], ldbx, &perm[nlf + lvl * perm_dim1], & + givptr[j], &givcol[nlf + lvl2 * givcol_dim1], ldgcol, & + givnum[nlf + lvl2 * givnum_dim1], ldu, &poles[nlf + lvl2 * + poles_dim1], &difl[nlf + lvl * difl_dim1], &difr[nlf + + lvl2 * difr_dim1], &z__[nlf + lvl * z_dim1], &k[j], &c__[ + j], &s[j], &work[1], info); /* L60: */ - } + } /* L70: */ } @@ -564,24 +564,24 @@ L50: ndb1 = (nd + 1) / 2; i__1 = nd; for (i__ = ndb1; i__ <= i__1; ++i__) { - i1 = i__ - 1; - ic = iwork[inode + i1]; - nl = iwork[ndiml + i1]; - nr = iwork[ndimr + i1]; - nlp1 = nl + 1; - if (i__ == nd) { - nrp1 = nr; - } else { - nrp1 = nr + 1; - } - nlf = ic - nl; - nrf = ic + 1; - dgemm_((char *)"T", (char *)"N", &nlp1, nrhs, &nlp1, &c_b7, &vt[nlf + vt_dim1], ldu, & - b[nlf + b_dim1], ldb, &c_b8, &bx[nlf + bx_dim1], ldbx, ( - ftnlen)1, (ftnlen)1); - dgemm_((char *)"T", (char *)"N", &nrp1, nrhs, &nrp1, &c_b7, &vt[nrf + vt_dim1], ldu, & - b[nrf + b_dim1], ldb, &c_b8, &bx[nrf + bx_dim1], ldbx, ( - ftnlen)1, (ftnlen)1); + i1 = i__ - 1; + ic = iwork[inode + i1]; + nl = iwork[ndiml + i1]; + nr = iwork[ndimr + i1]; + nlp1 = nl + 1; + if (i__ == nd) { + nrp1 = nr; + } else { + nrp1 = nr + 1; + } + nlf = ic - nl; + nrf = ic + 1; + dgemm_((char *)"T", (char *)"N", &nlp1, nrhs, &nlp1, &c_b7, &vt[nlf + vt_dim1], ldu, & + b[nlf + b_dim1], ldb, &c_b8, &bx[nlf + bx_dim1], ldbx, ( + ftnlen)1, (ftnlen)1); + dgemm_((char *)"T", (char *)"N", &nrp1, nrhs, &nrp1, &c_b7, &vt[nrf + vt_dim1], ldu, & + b[nrf + b_dim1], ldb, &c_b8, &bx[nrf + bx_dim1], ldbx, ( + ftnlen)1, (ftnlen)1); /* L80: */ } @@ -594,5 +594,5 @@ L90: } /* dlalsa_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlalsd.cpp b/lib/linalg/dlalsd.cpp index 07c3ca57f0..a141fa6992 100644 --- a/lib/linalg/dlalsd.cpp +++ b/lib/linalg/dlalsd.cpp @@ -1,13 +1,13 @@ /* fortran/dlalsd.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -201,10 +201,10 @@ f"> */ /* > Osni Marques, LBNL/NERSC, USA \n */ /* ===================================================================== */ -/* Subroutine */ int dlalsd_(char *uplo, integer *smlsiz, integer *n, integer - *nrhs, doublereal *d__, doublereal *e, doublereal *b, integer *ldb, - doublereal *rcond, integer *rank, doublereal *work, integer *iwork, - integer *info, ftnlen uplo_len) +/* Subroutine */ int dlalsd_(char *uplo, integer *smlsiz, integer *n, integer + *nrhs, doublereal *d__, doublereal *e, doublereal *b, integer *ldb, + doublereal *rcond, integer *rank, doublereal *work, integer *iwork, + integer *info, ftnlen uplo_len) { /* System generated locals */ integer b_dim1, b_offset, i__1, i__2; @@ -227,44 +227,44 @@ f"> */ integer difl, difr; doublereal rcnd; integer perm, nsub; - extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, - doublereal *, integer *, doublereal *, doublereal *); + extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, + doublereal *, integer *, doublereal *, doublereal *); integer nlvl, sqre, bxst; - extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen), - dcopy_(integer *, doublereal *, integer *, doublereal *, integer - *); + extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen), + dcopy_(integer *, doublereal *, integer *, doublereal *, integer + *); integer poles, sizei, nsize, nwork, icmpq1, icmpq2; extern doublereal dlamch_(char *, ftnlen); - extern /* Subroutine */ int dlasda_(integer *, integer *, integer *, - integer *, doublereal *, doublereal *, doublereal *, integer *, - doublereal *, integer *, doublereal *, doublereal *, doublereal *, - doublereal *, integer *, integer *, integer *, integer *, - doublereal *, doublereal *, doublereal *, doublereal *, integer *, - integer *), dlalsa_(integer *, integer *, integer *, integer *, - doublereal *, integer *, doublereal *, integer *, doublereal *, - integer *, doublereal *, integer *, doublereal *, doublereal *, - doublereal *, doublereal *, integer *, integer *, integer *, - integer *, doublereal *, doublereal *, doublereal *, doublereal *, - integer *, integer *), dlascl_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, integer *, doublereal *, - integer *, integer *, ftnlen); + extern /* Subroutine */ int dlasda_(integer *, integer *, integer *, + integer *, doublereal *, doublereal *, doublereal *, integer *, + doublereal *, integer *, doublereal *, doublereal *, doublereal *, + doublereal *, integer *, integer *, integer *, integer *, + doublereal *, doublereal *, doublereal *, doublereal *, integer *, + integer *), dlalsa_(integer *, integer *, integer *, integer *, + doublereal *, integer *, doublereal *, integer *, doublereal *, + integer *, doublereal *, integer *, doublereal *, doublereal *, + doublereal *, doublereal *, integer *, integer *, integer *, + integer *, doublereal *, doublereal *, doublereal *, doublereal *, + integer *, integer *), dlascl_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, integer *, doublereal *, + integer *, integer *, ftnlen); extern integer idamax_(integer *, doublereal *, integer *); - extern /* Subroutine */ int dlasdq_(char *, integer *, integer *, integer - *, integer *, integer *, doublereal *, doublereal *, doublereal *, - integer *, doublereal *, integer *, doublereal *, integer *, - doublereal *, integer *, ftnlen), dlacpy_(char *, integer *, - integer *, doublereal *, integer *, doublereal *, integer *, - ftnlen), dlartg_(doublereal *, doublereal *, doublereal *, - doublereal *, doublereal *), dlaset_(char *, integer *, integer *, - doublereal *, doublereal *, doublereal *, integer *, ftnlen), - xerbla_(char *, integer *, ftnlen); + extern /* Subroutine */ int dlasdq_(char *, integer *, integer *, integer + *, integer *, integer *, doublereal *, doublereal *, doublereal *, + integer *, doublereal *, integer *, doublereal *, integer *, + doublereal *, integer *, ftnlen), dlacpy_(char *, integer *, + integer *, doublereal *, integer *, doublereal *, integer *, + ftnlen), dlartg_(doublereal *, doublereal *, doublereal *, + doublereal *, doublereal *), dlaset_(char *, integer *, integer *, + doublereal *, doublereal *, doublereal *, integer *, ftnlen), + xerbla_(char *, integer *, ftnlen); integer givcol; - extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *, - ftnlen); - extern /* Subroutine */ int dlasrt_(char *, integer *, doublereal *, - integer *, ftnlen); + extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *, + ftnlen); + extern /* Subroutine */ int dlasrt_(char *, integer *, doublereal *, + integer *, ftnlen); doublereal orgnrm; integer givnum, givptr, smlszp; @@ -307,16 +307,16 @@ f"> */ *info = 0; if (*n < 0) { - *info = -3; + *info = -3; } else if (*nrhs < 1) { - *info = -4; + *info = -4; } else if (*ldb < 1 || *ldb < *n) { - *info = -8; + *info = -8; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DLALSD", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DLALSD", &i__1, (ftnlen)6); + return 0; } eps = dlamch_((char *)"Epsilon", (ftnlen)7); @@ -324,9 +324,9 @@ f"> */ /* Set up the tolerance. */ if (*rcond <= 0. || *rcond >= 1.) { - rcnd = eps; + rcnd = eps; } else { - rcnd = *rcond; + rcnd = *rcond; } *rank = 0; @@ -334,52 +334,52 @@ f"> */ /* Quick return if possible. */ if (*n == 0) { - return 0; + return 0; } else if (*n == 1) { - if (d__[1] == 0.) { - dlaset_((char *)"A", &c__1, nrhs, &c_b6, &c_b6, &b[b_offset], ldb, ( - ftnlen)1); - } else { - *rank = 1; - dlascl_((char *)"G", &c__0, &c__0, &d__[1], &c_b11, &c__1, nrhs, &b[ - b_offset], ldb, info, (ftnlen)1); - d__[1] = abs(d__[1]); - } - return 0; + if (d__[1] == 0.) { + dlaset_((char *)"A", &c__1, nrhs, &c_b6, &c_b6, &b[b_offset], ldb, ( + ftnlen)1); + } else { + *rank = 1; + dlascl_((char *)"G", &c__0, &c__0, &d__[1], &c_b11, &c__1, nrhs, &b[ + b_offset], ldb, info, (ftnlen)1); + d__[1] = abs(d__[1]); + } + return 0; } /* Rotate the matrix if it is lower bidiagonal. */ if (*(unsigned char *)uplo == 'L') { - i__1 = *n - 1; - for (i__ = 1; i__ <= i__1; ++i__) { - dlartg_(&d__[i__], &e[i__], &cs, &sn, &r__); - d__[i__] = r__; - e[i__] = sn * d__[i__ + 1]; - d__[i__ + 1] = cs * d__[i__ + 1]; - if (*nrhs == 1) { - drot_(&c__1, &b[i__ + b_dim1], &c__1, &b[i__ + 1 + b_dim1], & - c__1, &cs, &sn); - } else { - work[(i__ << 1) - 1] = cs; - work[i__ * 2] = sn; - } + i__1 = *n - 1; + for (i__ = 1; i__ <= i__1; ++i__) { + dlartg_(&d__[i__], &e[i__], &cs, &sn, &r__); + d__[i__] = r__; + e[i__] = sn * d__[i__ + 1]; + d__[i__ + 1] = cs * d__[i__ + 1]; + if (*nrhs == 1) { + drot_(&c__1, &b[i__ + b_dim1], &c__1, &b[i__ + 1 + b_dim1], & + c__1, &cs, &sn); + } else { + work[(i__ << 1) - 1] = cs; + work[i__ * 2] = sn; + } /* L10: */ - } - if (*nrhs > 1) { - i__1 = *nrhs; - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = *n - 1; - for (j = 1; j <= i__2; ++j) { - cs = work[(j << 1) - 1]; - sn = work[j * 2]; - drot_(&c__1, &b[j + i__ * b_dim1], &c__1, &b[j + 1 + i__ * - b_dim1], &c__1, &cs, &sn); + } + if (*nrhs > 1) { + i__1 = *nrhs; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = *n - 1; + for (j = 1; j <= i__2; ++j) { + cs = work[(j << 1) - 1]; + sn = work[j * 2]; + drot_(&c__1, &b[j + i__ * b_dim1], &c__1, &b[j + 1 + i__ * + b_dim1], &c__1, &cs, &sn); /* L20: */ - } + } /* L30: */ - } - } + } + } } /* Scale. */ @@ -387,58 +387,58 @@ f"> */ nm1 = *n - 1; orgnrm = dlanst_((char *)"M", n, &d__[1], &e[1], (ftnlen)1); if (orgnrm == 0.) { - dlaset_((char *)"A", n, nrhs, &c_b6, &c_b6, &b[b_offset], ldb, (ftnlen)1); - return 0; + dlaset_((char *)"A", n, nrhs, &c_b6, &c_b6, &b[b_offset], ldb, (ftnlen)1); + return 0; } dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b11, n, &c__1, &d__[1], n, info, ( - ftnlen)1); - dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b11, &nm1, &c__1, &e[1], &nm1, - info, (ftnlen)1); + ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b11, &nm1, &c__1, &e[1], &nm1, + info, (ftnlen)1); /* If N is smaller than the minimum divide size SMLSIZ, then solve */ /* the problem with another solver. */ if (*n <= *smlsiz) { - nwork = *n * *n + 1; - dlaset_((char *)"A", n, n, &c_b6, &c_b11, &work[1], n, (ftnlen)1); - dlasdq_((char *)"U", &c__0, n, n, &c__0, nrhs, &d__[1], &e[1], &work[1], n, & - work[1], n, &b[b_offset], ldb, &work[nwork], info, (ftnlen)1); - if (*info != 0) { - return 0; - } - tol = rcnd * (d__1 = d__[idamax_(n, &d__[1], &c__1)], abs(d__1)); - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - if (d__[i__] <= tol) { - dlaset_((char *)"A", &c__1, nrhs, &c_b6, &c_b6, &b[i__ + b_dim1], ldb, - (ftnlen)1); - } else { - dlascl_((char *)"G", &c__0, &c__0, &d__[i__], &c_b11, &c__1, nrhs, &b[ - i__ + b_dim1], ldb, info, (ftnlen)1); - ++(*rank); - } + nwork = *n * *n + 1; + dlaset_((char *)"A", n, n, &c_b6, &c_b11, &work[1], n, (ftnlen)1); + dlasdq_((char *)"U", &c__0, n, n, &c__0, nrhs, &d__[1], &e[1], &work[1], n, & + work[1], n, &b[b_offset], ldb, &work[nwork], info, (ftnlen)1); + if (*info != 0) { + return 0; + } + tol = rcnd * (d__1 = d__[idamax_(n, &d__[1], &c__1)], abs(d__1)); + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + if (d__[i__] <= tol) { + dlaset_((char *)"A", &c__1, nrhs, &c_b6, &c_b6, &b[i__ + b_dim1], ldb, + (ftnlen)1); + } else { + dlascl_((char *)"G", &c__0, &c__0, &d__[i__], &c_b11, &c__1, nrhs, &b[ + i__ + b_dim1], ldb, info, (ftnlen)1); + ++(*rank); + } /* L40: */ - } - dgemm_((char *)"T", (char *)"N", n, nrhs, n, &c_b11, &work[1], n, &b[b_offset], ldb, & - c_b6, &work[nwork], n, (ftnlen)1, (ftnlen)1); - dlacpy_((char *)"A", n, nrhs, &work[nwork], n, &b[b_offset], ldb, (ftnlen)1); + } + dgemm_((char *)"T", (char *)"N", n, nrhs, n, &c_b11, &work[1], n, &b[b_offset], ldb, & + c_b6, &work[nwork], n, (ftnlen)1, (ftnlen)1); + dlacpy_((char *)"A", n, nrhs, &work[nwork], n, &b[b_offset], ldb, (ftnlen)1); /* Unscale. */ - dlascl_((char *)"G", &c__0, &c__0, &c_b11, &orgnrm, n, &c__1, &d__[1], n, - info, (ftnlen)1); - dlasrt_((char *)"D", n, &d__[1], info, (ftnlen)1); - dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b11, n, nrhs, &b[b_offset], - ldb, info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &c_b11, &orgnrm, n, &c__1, &d__[1], n, + info, (ftnlen)1); + dlasrt_((char *)"D", n, &d__[1], info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b11, n, nrhs, &b[b_offset], + ldb, info, (ftnlen)1); - return 0; + return 0; } /* Book-keeping and setting up some constants. */ - nlvl = (integer) (log((doublereal) (*n) / (doublereal) (*smlsiz + 1)) / - log(2.)) + 1; + nlvl = (integer) (log((doublereal) (*n) / (doublereal) (*smlsiz + 1)) / + log(2.)) + 1; smlszp = *smlsiz + 1; @@ -469,95 +469,95 @@ f"> */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { - if ((d__1 = d__[i__], abs(d__1)) < eps) { - d__[i__] = d_sign(&eps, &d__[i__]); - } + if ((d__1 = d__[i__], abs(d__1)) < eps) { + d__[i__] = d_sign(&eps, &d__[i__]); + } /* L50: */ } i__1 = nm1; for (i__ = 1; i__ <= i__1; ++i__) { - if ((d__1 = e[i__], abs(d__1)) < eps || i__ == nm1) { - ++nsub; - iwork[nsub] = st; + if ((d__1 = e[i__], abs(d__1)) < eps || i__ == nm1) { + ++nsub; + iwork[nsub] = st; /* Subproblem found. First determine its size and then */ /* apply divide and conquer on it. */ - if (i__ < nm1) { + if (i__ < nm1) { /* A subproblem with E(I) small for I < NM1. */ - nsize = i__ - st + 1; - iwork[sizei + nsub - 1] = nsize; - } else if ((d__1 = e[i__], abs(d__1)) >= eps) { + nsize = i__ - st + 1; + iwork[sizei + nsub - 1] = nsize; + } else if ((d__1 = e[i__], abs(d__1)) >= eps) { /* A subproblem with E(NM1) not too small but I = NM1. */ - nsize = *n - st + 1; - iwork[sizei + nsub - 1] = nsize; - } else { + nsize = *n - st + 1; + iwork[sizei + nsub - 1] = nsize; + } else { /* A subproblem with E(NM1) small. This implies an */ /* 1-by-1 subproblem at D(N), which is not solved */ /* explicitly. */ - nsize = i__ - st + 1; - iwork[sizei + nsub - 1] = nsize; - ++nsub; - iwork[nsub] = *n; - iwork[sizei + nsub - 1] = 1; - dcopy_(nrhs, &b[*n + b_dim1], ldb, &work[bx + nm1], n); - } - st1 = st - 1; - if (nsize == 1) { + nsize = i__ - st + 1; + iwork[sizei + nsub - 1] = nsize; + ++nsub; + iwork[nsub] = *n; + iwork[sizei + nsub - 1] = 1; + dcopy_(nrhs, &b[*n + b_dim1], ldb, &work[bx + nm1], n); + } + st1 = st - 1; + if (nsize == 1) { /* This is a 1-by-1 subproblem and is not solved */ /* explicitly. */ - dcopy_(nrhs, &b[st + b_dim1], ldb, &work[bx + st1], n); - } else if (nsize <= *smlsiz) { + dcopy_(nrhs, &b[st + b_dim1], ldb, &work[bx + st1], n); + } else if (nsize <= *smlsiz) { /* This is a small subproblem and is solved by DLASDQ. */ - dlaset_((char *)"A", &nsize, &nsize, &c_b6, &c_b11, &work[vt + st1], - n, (ftnlen)1); - dlasdq_((char *)"U", &c__0, &nsize, &nsize, &c__0, nrhs, &d__[st], &e[ - st], &work[vt + st1], n, &work[nwork], n, &b[st + - b_dim1], ldb, &work[nwork], info, (ftnlen)1); - if (*info != 0) { - return 0; - } - dlacpy_((char *)"A", &nsize, nrhs, &b[st + b_dim1], ldb, &work[bx + - st1], n, (ftnlen)1); - } else { + dlaset_((char *)"A", &nsize, &nsize, &c_b6, &c_b11, &work[vt + st1], + n, (ftnlen)1); + dlasdq_((char *)"U", &c__0, &nsize, &nsize, &c__0, nrhs, &d__[st], &e[ + st], &work[vt + st1], n, &work[nwork], n, &b[st + + b_dim1], ldb, &work[nwork], info, (ftnlen)1); + if (*info != 0) { + return 0; + } + dlacpy_((char *)"A", &nsize, nrhs, &b[st + b_dim1], ldb, &work[bx + + st1], n, (ftnlen)1); + } else { /* A large problem. Solve it using divide and conquer. */ - dlasda_(&icmpq1, smlsiz, &nsize, &sqre, &d__[st], &e[st], & - work[u + st1], n, &work[vt + st1], &iwork[k + st1], & - work[difl + st1], &work[difr + st1], &work[z__ + st1], - &work[poles + st1], &iwork[givptr + st1], &iwork[ - givcol + st1], n, &iwork[perm + st1], &work[givnum + - st1], &work[c__ + st1], &work[s + st1], &work[nwork], - &iwork[iwk], info); - if (*info != 0) { - return 0; - } - bxst = bx + st1; - dlalsa_(&icmpq2, smlsiz, &nsize, nrhs, &b[st + b_dim1], ldb, & - work[bxst], n, &work[u + st1], n, &work[vt + st1], & - iwork[k + st1], &work[difl + st1], &work[difr + st1], - &work[z__ + st1], &work[poles + st1], &iwork[givptr + - st1], &iwork[givcol + st1], n, &iwork[perm + st1], & - work[givnum + st1], &work[c__ + st1], &work[s + st1], - &work[nwork], &iwork[iwk], info); - if (*info != 0) { - return 0; - } - } - st = i__ + 1; - } + dlasda_(&icmpq1, smlsiz, &nsize, &sqre, &d__[st], &e[st], & + work[u + st1], n, &work[vt + st1], &iwork[k + st1], & + work[difl + st1], &work[difr + st1], &work[z__ + st1], + &work[poles + st1], &iwork[givptr + st1], &iwork[ + givcol + st1], n, &iwork[perm + st1], &work[givnum + + st1], &work[c__ + st1], &work[s + st1], &work[nwork], + &iwork[iwk], info); + if (*info != 0) { + return 0; + } + bxst = bx + st1; + dlalsa_(&icmpq2, smlsiz, &nsize, nrhs, &b[st + b_dim1], ldb, & + work[bxst], n, &work[u + st1], n, &work[vt + st1], & + iwork[k + st1], &work[difl + st1], &work[difr + st1], + &work[z__ + st1], &work[poles + st1], &iwork[givptr + + st1], &iwork[givcol + st1], n, &iwork[perm + st1], & + work[givnum + st1], &work[c__ + st1], &work[s + st1], + &work[nwork], &iwork[iwk], info); + if (*info != 0) { + return 0; + } + } + st = i__ + 1; + } /* L60: */ } @@ -571,15 +571,15 @@ f"> */ /* Some of the elements in D can be negative because 1-by-1 */ /* subproblems were not solved explicitly. */ - if ((d__1 = d__[i__], abs(d__1)) <= tol) { - dlaset_((char *)"A", &c__1, nrhs, &c_b6, &c_b6, &work[bx + i__ - 1], n, ( - ftnlen)1); - } else { - ++(*rank); - dlascl_((char *)"G", &c__0, &c__0, &d__[i__], &c_b11, &c__1, nrhs, &work[ - bx + i__ - 1], n, info, (ftnlen)1); - } - d__[i__] = (d__1 = d__[i__], abs(d__1)); + if ((d__1 = d__[i__], abs(d__1)) <= tol) { + dlaset_((char *)"A", &c__1, nrhs, &c_b6, &c_b6, &work[bx + i__ - 1], n, ( + ftnlen)1); + } else { + ++(*rank); + dlascl_((char *)"G", &c__0, &c__0, &d__[i__], &c_b11, &c__1, nrhs, &work[ + bx + i__ - 1], n, info, (ftnlen)1); + } + d__[i__] = (d__1 = d__[i__], abs(d__1)); /* L70: */ } @@ -588,38 +588,38 @@ f"> */ icmpq2 = 1; i__1 = nsub; for (i__ = 1; i__ <= i__1; ++i__) { - st = iwork[i__]; - st1 = st - 1; - nsize = iwork[sizei + i__ - 1]; - bxst = bx + st1; - if (nsize == 1) { - dcopy_(nrhs, &work[bxst], n, &b[st + b_dim1], ldb); - } else if (nsize <= *smlsiz) { - dgemm_((char *)"T", (char *)"N", &nsize, nrhs, &nsize, &c_b11, &work[vt + st1], n, - &work[bxst], n, &c_b6, &b[st + b_dim1], ldb, (ftnlen)1, ( - ftnlen)1); - } else { - dlalsa_(&icmpq2, smlsiz, &nsize, nrhs, &work[bxst], n, &b[st + - b_dim1], ldb, &work[u + st1], n, &work[vt + st1], &iwork[ - k + st1], &work[difl + st1], &work[difr + st1], &work[z__ - + st1], &work[poles + st1], &iwork[givptr + st1], &iwork[ - givcol + st1], n, &iwork[perm + st1], &work[givnum + st1], - &work[c__ + st1], &work[s + st1], &work[nwork], &iwork[ - iwk], info); - if (*info != 0) { - return 0; - } - } + st = iwork[i__]; + st1 = st - 1; + nsize = iwork[sizei + i__ - 1]; + bxst = bx + st1; + if (nsize == 1) { + dcopy_(nrhs, &work[bxst], n, &b[st + b_dim1], ldb); + } else if (nsize <= *smlsiz) { + dgemm_((char *)"T", (char *)"N", &nsize, nrhs, &nsize, &c_b11, &work[vt + st1], n, + &work[bxst], n, &c_b6, &b[st + b_dim1], ldb, (ftnlen)1, ( + ftnlen)1); + } else { + dlalsa_(&icmpq2, smlsiz, &nsize, nrhs, &work[bxst], n, &b[st + + b_dim1], ldb, &work[u + st1], n, &work[vt + st1], &iwork[ + k + st1], &work[difl + st1], &work[difr + st1], &work[z__ + + st1], &work[poles + st1], &iwork[givptr + st1], &iwork[ + givcol + st1], n, &iwork[perm + st1], &work[givnum + st1], + &work[c__ + st1], &work[s + st1], &work[nwork], &iwork[ + iwk], info); + if (*info != 0) { + return 0; + } + } /* L80: */ } /* Unscale and sort the singular values. */ dlascl_((char *)"G", &c__0, &c__0, &c_b11, &orgnrm, n, &c__1, &d__[1], n, info, ( - ftnlen)1); + ftnlen)1); dlasrt_((char *)"D", n, &d__[1], info, (ftnlen)1); - dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b11, n, nrhs, &b[b_offset], ldb, - info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b11, n, nrhs, &b[b_offset], ldb, + info, (ftnlen)1); return 0; @@ -628,5 +628,5 @@ f"> */ } /* dlalsd_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlamrg.cpp b/lib/linalg/dlamrg.cpp index 581a64fba7..810d1db154 100644 --- a/lib/linalg/dlamrg.cpp +++ b/lib/linalg/dlamrg.cpp @@ -1,13 +1,13 @@ /* fortran/dlamrg.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -15,7 +15,7 @@ extern "C" { #endif #include "lmp_f2c.h" -/* > \brief \b DLAMRG creates a permutation list to merge the entries of two independently sorted sets into a +/* > \brief \b DLAMRG creates a permutation list to merge the entries of two independently sorted sets into a single set sorted in ascending order. */ /* =========== DOCUMENTATION =========== */ @@ -116,8 +116,8 @@ f"> */ /* > \ingroup auxOTHERcomputational */ /* ===================================================================== */ -/* Subroutine */ int dlamrg_(integer *n1, integer *n2, doublereal *a, integer - *dtrd1, integer *dtrd2, integer *index) +/* Subroutine */ int dlamrg_(integer *n1, integer *n2, doublereal *a, integer + *dtrd1, integer *dtrd2, integer *index) { /* System generated locals */ integer i__1; @@ -149,50 +149,50 @@ f"> */ n1sv = *n1; n2sv = *n2; if (*dtrd1 > 0) { - ind1 = 1; + ind1 = 1; } else { - ind1 = *n1; + ind1 = *n1; } if (*dtrd2 > 0) { - ind2 = *n1 + 1; + ind2 = *n1 + 1; } else { - ind2 = *n1 + *n2; + ind2 = *n1 + *n2; } i__ = 1; /* while ( (N1SV > 0) & (N2SV > 0) ) */ L10: if (n1sv > 0 && n2sv > 0) { - if (a[ind1] <= a[ind2]) { - index[i__] = ind1; - ++i__; - ind1 += *dtrd1; - --n1sv; - } else { - index[i__] = ind2; - ++i__; - ind2 += *dtrd2; - --n2sv; - } - goto L10; + if (a[ind1] <= a[ind2]) { + index[i__] = ind1; + ++i__; + ind1 += *dtrd1; + --n1sv; + } else { + index[i__] = ind2; + ++i__; + ind2 += *dtrd2; + --n2sv; + } + goto L10; } /* end while */ if (n1sv == 0) { - i__1 = n2sv; - for (n1sv = 1; n1sv <= i__1; ++n1sv) { - index[i__] = ind2; - ++i__; - ind2 += *dtrd2; + i__1 = n2sv; + for (n1sv = 1; n1sv <= i__1; ++n1sv) { + index[i__] = ind2; + ++i__; + ind2 += *dtrd2; /* L20: */ - } + } } else { /* N2SV .EQ. 0 */ - i__1 = n1sv; - for (n2sv = 1; n2sv <= i__1; ++n2sv) { - index[i__] = ind1; - ++i__; - ind1 += *dtrd1; + i__1 = n1sv; + for (n2sv = 1; n2sv <= i__1; ++n2sv) { + index[i__] = ind1; + ++i__; + ind1 += *dtrd1; /* L30: */ - } + } } return 0; @@ -202,5 +202,5 @@ L10: } /* dlamrg_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlange.cpp b/lib/linalg/dlange.cpp index 1ccc6fae2b..ab88573259 100644 --- a/lib/linalg/dlange.cpp +++ b/lib/linalg/dlange.cpp @@ -1,13 +1,13 @@ /* fortran/dlange.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -19,7 +19,7 @@ extern "C" { static integer c__1 = 1; -/* > \brief \b DLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute +/* > \brief \b DLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general rectangular matrix. */ /* =========== DOCUMENTATION =========== */ @@ -135,8 +135,8 @@ f"> */ /* > \ingroup doubleGEauxiliary */ /* ===================================================================== */ -doublereal dlange_(char *norm, integer *m, integer *n, doublereal *a, integer - *lda, doublereal *work, ftnlen norm_len) +doublereal dlange_(char *norm, integer *m, integer *n, doublereal *a, integer + *lda, doublereal *work, ftnlen norm_len) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; @@ -151,8 +151,8 @@ doublereal dlange_(char *norm, integer *m, integer *n, doublereal *a, integer extern logical lsame_(char *, char *, ftnlen, ftnlen); doublereal value; extern logical disnan_(doublereal *); - extern /* Subroutine */ int dlassq_(integer *, doublereal *, integer *, - doublereal *, doublereal *); + extern /* Subroutine */ int dlassq_(integer *, doublereal *, integer *, + doublereal *, doublereal *); /* -- LAPACK auxiliary routine -- */ @@ -186,83 +186,83 @@ doublereal dlange_(char *norm, integer *m, integer *n, doublereal *a, integer /* Function Body */ if (min(*m,*n) == 0) { - value = 0.; + value = 0.; } else if (lsame_(norm, (char *)"M", (ftnlen)1, (ftnlen)1)) { /* Find max(abs(A(i,j))). */ - value = 0.; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - temp = (d__1 = a[i__ + j * a_dim1], abs(d__1)); - if (value < temp || disnan_(&temp)) { - value = temp; - } + value = 0.; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp = (d__1 = a[i__ + j * a_dim1], abs(d__1)); + if (value < temp || disnan_(&temp)) { + value = temp; + } /* L10: */ - } + } /* L20: */ - } + } } else if (lsame_(norm, (char *)"O", (ftnlen)1, (ftnlen)1) || *(unsigned char *) - norm == '1') { + norm == '1') { /* Find norm1(A). */ - value = 0.; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - sum = 0.; - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - sum += (d__1 = a[i__ + j * a_dim1], abs(d__1)); + value = 0.; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + sum = 0.; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + sum += (d__1 = a[i__ + j * a_dim1], abs(d__1)); /* L30: */ - } - if (value < sum || disnan_(&sum)) { - value = sum; - } + } + if (value < sum || disnan_(&sum)) { + value = sum; + } /* L40: */ - } + } } else if (lsame_(norm, (char *)"I", (ftnlen)1, (ftnlen)1)) { /* Find normI(A). */ - i__1 = *m; - for (i__ = 1; i__ <= i__1; ++i__) { - work[i__] = 0.; + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + work[i__] = 0.; /* L50: */ - } - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - work[i__] += (d__1 = a[i__ + j * a_dim1], abs(d__1)); + } + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + work[i__] += (d__1 = a[i__ + j * a_dim1], abs(d__1)); /* L60: */ - } + } /* L70: */ - } - value = 0.; - i__1 = *m; - for (i__ = 1; i__ <= i__1; ++i__) { - temp = work[i__]; - if (value < temp || disnan_(&temp)) { - value = temp; - } + } + value = 0.; + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + temp = work[i__]; + if (value < temp || disnan_(&temp)) { + value = temp; + } /* L80: */ - } + } } else if (lsame_(norm, (char *)"F", (ftnlen)1, (ftnlen)1) || lsame_(norm, (char *)"E", ( - ftnlen)1, (ftnlen)1)) { + ftnlen)1, (ftnlen)1)) { /* Find normF(A). */ - scale = 0.; - sum = 1.; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - dlassq_(m, &a[j * a_dim1 + 1], &c__1, &scale, &sum); + scale = 0.; + sum = 1.; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + dlassq_(m, &a[j * a_dim1 + 1], &c__1, &scale, &sum); /* L90: */ - } - value = scale * sqrt(sum); + } + value = scale * sqrt(sum); } ret_val = value; @@ -273,5 +273,5 @@ doublereal dlange_(char *norm, integer *m, integer *n, doublereal *a, integer } /* dlange_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlanst.cpp b/lib/linalg/dlanst.cpp index 8a71bcd12d..c216660b75 100644 --- a/lib/linalg/dlanst.cpp +++ b/lib/linalg/dlanst.cpp @@ -1,13 +1,13 @@ /* fortran/dlanst.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -121,8 +121,8 @@ f"> */ /* > \ingroup OTHERauxiliary */ /* ===================================================================== */ -doublereal dlanst_(char *norm, integer *n, doublereal *d__, doublereal *e, - ftnlen norm_len) +doublereal dlanst_(char *norm, integer *n, doublereal *d__, doublereal *e, + ftnlen norm_len) { /* System generated locals */ integer i__1; @@ -137,8 +137,8 @@ doublereal dlanst_(char *norm, integer *n, doublereal *d__, doublereal *e, extern logical lsame_(char *, char *, ftnlen, ftnlen); doublereal anorm; extern logical disnan_(doublereal *); - extern /* Subroutine */ int dlassq_(integer *, doublereal *, integer *, - doublereal *, doublereal *); + extern /* Subroutine */ int dlassq_(integer *, doublereal *, integer *, + doublereal *, doublereal *); /* -- LAPACK auxiliary routine -- */ @@ -170,61 +170,61 @@ doublereal dlanst_(char *norm, integer *n, doublereal *d__, doublereal *e, /* Function Body */ if (*n <= 0) { - anorm = 0.; + anorm = 0.; } else if (lsame_(norm, (char *)"M", (ftnlen)1, (ftnlen)1)) { /* Find max(abs(A(i,j))). */ - anorm = (d__1 = d__[*n], abs(d__1)); - i__1 = *n - 1; - for (i__ = 1; i__ <= i__1; ++i__) { - sum = (d__1 = d__[i__], abs(d__1)); - if (anorm < sum || disnan_(&sum)) { - anorm = sum; - } - sum = (d__1 = e[i__], abs(d__1)); - if (anorm < sum || disnan_(&sum)) { - anorm = sum; - } + anorm = (d__1 = d__[*n], abs(d__1)); + i__1 = *n - 1; + for (i__ = 1; i__ <= i__1; ++i__) { + sum = (d__1 = d__[i__], abs(d__1)); + if (anorm < sum || disnan_(&sum)) { + anorm = sum; + } + sum = (d__1 = e[i__], abs(d__1)); + if (anorm < sum || disnan_(&sum)) { + anorm = sum; + } /* L10: */ - } + } } else if (lsame_(norm, (char *)"O", (ftnlen)1, (ftnlen)1) || *(unsigned char *) - norm == '1' || lsame_(norm, (char *)"I", (ftnlen)1, (ftnlen)1)) { + norm == '1' || lsame_(norm, (char *)"I", (ftnlen)1, (ftnlen)1)) { /* Find norm1(A). */ - if (*n == 1) { - anorm = abs(d__[1]); - } else { - anorm = abs(d__[1]) + abs(e[1]); - sum = (d__1 = e[*n - 1], abs(d__1)) + (d__2 = d__[*n], abs(d__2)); - if (anorm < sum || disnan_(&sum)) { - anorm = sum; - } - i__1 = *n - 1; - for (i__ = 2; i__ <= i__1; ++i__) { - sum = (d__1 = d__[i__], abs(d__1)) + (d__2 = e[i__], abs(d__2) - ) + (d__3 = e[i__ - 1], abs(d__3)); - if (anorm < sum || disnan_(&sum)) { - anorm = sum; - } + if (*n == 1) { + anorm = abs(d__[1]); + } else { + anorm = abs(d__[1]) + abs(e[1]); + sum = (d__1 = e[*n - 1], abs(d__1)) + (d__2 = d__[*n], abs(d__2)); + if (anorm < sum || disnan_(&sum)) { + anorm = sum; + } + i__1 = *n - 1; + for (i__ = 2; i__ <= i__1; ++i__) { + sum = (d__1 = d__[i__], abs(d__1)) + (d__2 = e[i__], abs(d__2) + ) + (d__3 = e[i__ - 1], abs(d__3)); + if (anorm < sum || disnan_(&sum)) { + anorm = sum; + } /* L20: */ - } - } + } + } } else if (lsame_(norm, (char *)"F", (ftnlen)1, (ftnlen)1) || lsame_(norm, (char *)"E", ( - ftnlen)1, (ftnlen)1)) { + ftnlen)1, (ftnlen)1)) { /* Find normF(A). */ - scale = 0.; - sum = 1.; - if (*n > 1) { - i__1 = *n - 1; - dlassq_(&i__1, &e[1], &c__1, &scale, &sum); - sum *= 2; - } - dlassq_(n, &d__[1], &c__1, &scale, &sum); - anorm = scale * sqrt(sum); + scale = 0.; + sum = 1.; + if (*n > 1) { + i__1 = *n - 1; + dlassq_(&i__1, &e[1], &c__1, &scale, &sum); + sum *= 2; + } + dlassq_(n, &d__[1], &c__1, &scale, &sum); + anorm = scale * sqrt(sum); } ret_val = anorm; @@ -235,5 +235,5 @@ doublereal dlanst_(char *norm, integer *n, doublereal *d__, doublereal *e, } /* dlanst_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlansy.cpp b/lib/linalg/dlansy.cpp index 1c5a1fa24c..8d3cb42b7a 100644 --- a/lib/linalg/dlansy.cpp +++ b/lib/linalg/dlansy.cpp @@ -1,13 +1,13 @@ /* fortran/dlansy.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -143,8 +143,8 @@ f"> */ /* > \ingroup doubleSYauxiliary */ /* ===================================================================== */ -doublereal dlansy_(char *norm, char *uplo, integer *n, doublereal *a, integer - *lda, doublereal *work, ftnlen norm_len, ftnlen uplo_len) +doublereal dlansy_(char *norm, char *uplo, integer *n, doublereal *a, integer + *lda, doublereal *work, ftnlen norm_len, ftnlen uplo_len) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; @@ -159,8 +159,8 @@ doublereal dlansy_(char *norm, char *uplo, integer *n, doublereal *a, integer extern logical lsame_(char *, char *, ftnlen, ftnlen); doublereal value; extern logical disnan_(doublereal *); - extern /* Subroutine */ int dlassq_(integer *, doublereal *, integer *, - doublereal *, doublereal *); + extern /* Subroutine */ int dlassq_(integer *, doublereal *, integer *, + doublereal *, doublereal *); /* -- LAPACK auxiliary routine -- */ @@ -194,115 +194,115 @@ doublereal dlansy_(char *norm, char *uplo, integer *n, doublereal *a, integer /* Function Body */ if (*n == 0) { - value = 0.; + value = 0.; } else if (lsame_(norm, (char *)"M", (ftnlen)1, (ftnlen)1)) { /* Find max(abs(A(i,j))). */ - value = 0.; - if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = j; - for (i__ = 1; i__ <= i__2; ++i__) { - sum = (d__1 = a[i__ + j * a_dim1], abs(d__1)); - if (value < sum || disnan_(&sum)) { - value = sum; - } + value = 0.; + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + for (i__ = 1; i__ <= i__2; ++i__) { + sum = (d__1 = a[i__ + j * a_dim1], abs(d__1)); + if (value < sum || disnan_(&sum)) { + value = sum; + } /* L10: */ - } + } /* L20: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *n; - for (i__ = j; i__ <= i__2; ++i__) { - sum = (d__1 = a[i__ + j * a_dim1], abs(d__1)); - if (value < sum || disnan_(&sum)) { - value = sum; - } + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = j; i__ <= i__2; ++i__) { + sum = (d__1 = a[i__ + j * a_dim1], abs(d__1)); + if (value < sum || disnan_(&sum)) { + value = sum; + } /* L30: */ - } + } /* L40: */ - } - } + } + } } else if (lsame_(norm, (char *)"I", (ftnlen)1, (ftnlen)1) || lsame_(norm, (char *)"O", ( - ftnlen)1, (ftnlen)1) || *(unsigned char *)norm == '1') { + ftnlen)1, (ftnlen)1) || *(unsigned char *)norm == '1') { /* Find normI(A) ( = norm1(A), since A is symmetric). */ - value = 0.; - if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - sum = 0.; - i__2 = j - 1; - for (i__ = 1; i__ <= i__2; ++i__) { - absa = (d__1 = a[i__ + j * a_dim1], abs(d__1)); - sum += absa; - work[i__] += absa; + value = 0.; + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + sum = 0.; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + absa = (d__1 = a[i__ + j * a_dim1], abs(d__1)); + sum += absa; + work[i__] += absa; /* L50: */ - } - work[j] = sum + (d__1 = a[j + j * a_dim1], abs(d__1)); + } + work[j] = sum + (d__1 = a[j + j * a_dim1], abs(d__1)); /* L60: */ - } - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - sum = work[i__]; - if (value < sum || disnan_(&sum)) { - value = sum; - } + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + sum = work[i__]; + if (value < sum || disnan_(&sum)) { + value = sum; + } /* L70: */ - } - } else { - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - work[i__] = 0.; + } + } else { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + work[i__] = 0.; /* L80: */ - } - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - sum = work[j] + (d__1 = a[j + j * a_dim1], abs(d__1)); - i__2 = *n; - for (i__ = j + 1; i__ <= i__2; ++i__) { - absa = (d__1 = a[i__ + j * a_dim1], abs(d__1)); - sum += absa; - work[i__] += absa; + } + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + sum = work[j] + (d__1 = a[j + j * a_dim1], abs(d__1)); + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + absa = (d__1 = a[i__ + j * a_dim1], abs(d__1)); + sum += absa; + work[i__] += absa; /* L90: */ - } - if (value < sum || disnan_(&sum)) { - value = sum; - } + } + if (value < sum || disnan_(&sum)) { + value = sum; + } /* L100: */ - } - } + } + } } else if (lsame_(norm, (char *)"F", (ftnlen)1, (ftnlen)1) || lsame_(norm, (char *)"E", ( - ftnlen)1, (ftnlen)1)) { + ftnlen)1, (ftnlen)1)) { /* Find normF(A). */ - scale = 0.; - sum = 1.; - if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { - i__1 = *n; - for (j = 2; j <= i__1; ++j) { - i__2 = j - 1; - dlassq_(&i__2, &a[j * a_dim1 + 1], &c__1, &scale, &sum); + scale = 0.; + sum = 1.; + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + i__1 = *n; + for (j = 2; j <= i__1; ++j) { + i__2 = j - 1; + dlassq_(&i__2, &a[j * a_dim1 + 1], &c__1, &scale, &sum); /* L110: */ - } - } else { - i__1 = *n - 1; - for (j = 1; j <= i__1; ++j) { - i__2 = *n - j; - dlassq_(&i__2, &a[j + 1 + j * a_dim1], &c__1, &scale, &sum); + } + } else { + i__1 = *n - 1; + for (j = 1; j <= i__1; ++j) { + i__2 = *n - j; + dlassq_(&i__2, &a[j + 1 + j * a_dim1], &c__1, &scale, &sum); /* L120: */ - } - } - sum *= 2; - i__1 = *lda + 1; - dlassq_(n, &a[a_offset], &i__1, &scale, &sum); - value = scale * sqrt(sum); + } + } + sum *= 2; + i__1 = *lda + 1; + dlassq_(n, &a[a_offset], &i__1, &scale, &sum); + value = scale * sqrt(sum); } ret_val = value; @@ -313,5 +313,5 @@ doublereal dlansy_(char *norm, char *uplo, integer *n, doublereal *a, integer } /* dlansy_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlapy2.cpp b/lib/linalg/dlapy2.cpp index 6a5443d8df..d746e1f56a 100644 --- a/lib/linalg/dlapy2.cpp +++ b/lib/linalg/dlapy2.cpp @@ -1,13 +1,13 @@ /* fortran/dlapy2.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -119,25 +119,25 @@ doublereal dlapy2_(doublereal *x, doublereal *y) x_is_nan__ = disnan_(x); y_is_nan__ = disnan_(y); if (x_is_nan__) { - ret_val = *x; + ret_val = *x; } if (y_is_nan__) { - ret_val = *y; + ret_val = *y; } hugeval = dlamch_((char *)"Overflow", (ftnlen)8); if (! (x_is_nan__ || y_is_nan__)) { - xabs = abs(*x); - yabs = abs(*y); - w = max(xabs,yabs); - z__ = min(xabs,yabs); - if (z__ == 0. || w > hugeval) { - ret_val = w; - } else { + xabs = abs(*x); + yabs = abs(*y); + w = max(xabs,yabs); + z__ = min(xabs,yabs); + if (z__ == 0. || w > hugeval) { + ret_val = w; + } else { /* Computing 2nd power */ - d__1 = z__ / w; - ret_val = w * sqrt(d__1 * d__1 + 1.); - } + d__1 = z__ / w; + ret_val = w * sqrt(d__1 * d__1 + 1.); + } } return ret_val; @@ -146,5 +146,5 @@ doublereal dlapy2_(doublereal *x, doublereal *y) } /* dlapy2_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlapy3.cpp b/lib/linalg/dlapy3.cpp index 528afbf3d8..211f60dbf6 100644 --- a/lib/linalg/dlapy3.cpp +++ b/lib/linalg/dlapy3.cpp @@ -1,13 +1,13 @@ /* fortran/dlapy3.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -128,15 +128,15 @@ doublereal dlapy3_(doublereal *x, doublereal *y, doublereal *z__) /* W can be zero for max(0,nan,0) */ /* adding all three entries together will make sure */ /* NaN will not disappear. */ - ret_val = xabs + yabs + zabs; + ret_val = xabs + yabs + zabs; } else { /* Computing 2nd power */ - d__1 = xabs / w; + d__1 = xabs / w; /* Computing 2nd power */ - d__2 = yabs / w; + d__2 = yabs / w; /* Computing 2nd power */ - d__3 = zabs / w; - ret_val = w * sqrt(d__1 * d__1 + d__2 * d__2 + d__3 * d__3); + d__3 = zabs / w; + ret_val = w * sqrt(d__1 * d__1 + d__2 * d__2 + d__3 * d__3); } return ret_val; @@ -145,5 +145,5 @@ doublereal dlapy3_(doublereal *x, doublereal *y, doublereal *z__) } /* dlapy3_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlarf.cpp b/lib/linalg/dlarf.cpp index 5534559e63..8111d5fa2f 100644 --- a/lib/linalg/dlarf.cpp +++ b/lib/linalg/dlarf.cpp @@ -1,13 +1,13 @@ /* fortran/dlarf.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -147,8 +147,8 @@ static integer c__1 = 1; /* ===================================================================== */ /* Subroutine */ int dlarf_(char *side, integer *m, integer *n, doublereal *v, - integer *incv, doublereal *tau, doublereal *c__, integer *ldc, - doublereal *work, ftnlen side_len) + integer *incv, doublereal *tau, doublereal *c__, integer *ldc, + doublereal *work, ftnlen side_len) { /* System generated locals */ integer c_dim1, c_offset; @@ -157,16 +157,16 @@ static integer c__1 = 1; /* Local variables */ integer i__; logical applyleft; - extern /* Subroutine */ int dger_(integer *, integer *, doublereal *, - doublereal *, integer *, doublereal *, integer *, doublereal *, - integer *); + extern /* Subroutine */ int dger_(integer *, integer *, doublereal *, + doublereal *, integer *, doublereal *, integer *, doublereal *, + integer *); extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int dgemv_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, doublereal *, integer *, - doublereal *, doublereal *, integer *, ftnlen); + extern /* Subroutine */ int dgemv_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, ftnlen); integer lastc, lastv; - extern integer iladlc_(integer *, integer *, doublereal *, integer *), - iladlr_(integer *, integer *, doublereal *, integer *); + extern integer iladlc_(integer *, integer *, doublereal *, integer *), + iladlr_(integer *, integer *, doublereal *, integer *); /* -- LAPACK auxiliary routine -- */ @@ -204,28 +204,28 @@ static integer c__1 = 1; if (*tau != 0.) { /* Set up variables for scanning V. LASTV begins pointing to the end */ /* of V. */ - if (applyleft) { - lastv = *m; - } else { - lastv = *n; - } - if (*incv > 0) { - i__ = (lastv - 1) * *incv + 1; - } else { - i__ = 1; - } + if (applyleft) { + lastv = *m; + } else { + lastv = *n; + } + if (*incv > 0) { + i__ = (lastv - 1) * *incv + 1; + } else { + i__ = 1; + } /* Look for the last non-zero row in V. */ - while(lastv > 0 && v[i__] == 0.) { - --lastv; - i__ -= *incv; - } - if (applyleft) { + while(lastv > 0 && v[i__] == 0.) { + --lastv; + i__ -= *incv; + } + if (applyleft) { /* Scan for the last non-zero column in C(1:lastv,:). */ - lastc = iladlc_(&lastv, n, &c__[c_offset], ldc); - } else { + lastc = iladlc_(&lastv, n, &c__[c_offset], ldc); + } else { /* Scan for the last non-zero row in C(:,1:lastv). */ - lastc = iladlr_(m, &lastv, &c__[c_offset], ldc); - } + lastc = iladlr_(m, &lastv, &c__[c_offset], ldc); + } } /* Note that lastc.eq.0 renders the BLAS operations null; no special */ /* case is needed at this level. */ @@ -233,36 +233,36 @@ static integer c__1 = 1; /* Form H * C */ - if (lastv > 0) { + if (lastv > 0) { /* w(1:lastc,1) := C(1:lastv,1:lastc)**T * v(1:lastv,1) */ - dgemv_((char *)"Transpose", &lastv, &lastc, &c_b4, &c__[c_offset], ldc, & - v[1], incv, &c_b5, &work[1], &c__1, (ftnlen)9); + dgemv_((char *)"Transpose", &lastv, &lastc, &c_b4, &c__[c_offset], ldc, & + v[1], incv, &c_b5, &work[1], &c__1, (ftnlen)9); /* C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**T */ - d__1 = -(*tau); - dger_(&lastv, &lastc, &d__1, &v[1], incv, &work[1], &c__1, &c__[ - c_offset], ldc); - } + d__1 = -(*tau); + dger_(&lastv, &lastc, &d__1, &v[1], incv, &work[1], &c__1, &c__[ + c_offset], ldc); + } } else { /* Form C * H */ - if (lastv > 0) { + if (lastv > 0) { /* w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1) */ - dgemv_((char *)"No transpose", &lastc, &lastv, &c_b4, &c__[c_offset], ldc, - &v[1], incv, &c_b5, &work[1], &c__1, (ftnlen)12); + dgemv_((char *)"No transpose", &lastc, &lastv, &c_b4, &c__[c_offset], ldc, + &v[1], incv, &c_b5, &work[1], &c__1, (ftnlen)12); /* C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**T */ - d__1 = -(*tau); - dger_(&lastc, &lastv, &d__1, &work[1], &c__1, &v[1], incv, &c__[ - c_offset], ldc); - } + d__1 = -(*tau); + dger_(&lastc, &lastv, &d__1, &work[1], &c__1, &v[1], incv, &c__[ + c_offset], ldc); + } } return 0; @@ -271,5 +271,5 @@ static integer c__1 = 1; } /* dlarf_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlarfb.cpp b/lib/linalg/dlarfb.cpp index df15d11900..d282b19899 100644 --- a/lib/linalg/dlarfb.cpp +++ b/lib/linalg/dlarfb.cpp @@ -1,13 +1,13 @@ /* fortran/dlarfb.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -219,25 +219,25 @@ f"> */ /* > */ /* ===================================================================== */ /* Subroutine */ int dlarfb_(char *side, char *trans, char *direct, char * - storev, integer *m, integer *n, integer *k, doublereal *v, integer * - ldv, doublereal *t, integer *ldt, doublereal *c__, integer *ldc, - doublereal *work, integer *ldwork, ftnlen side_len, ftnlen trans_len, - ftnlen direct_len, ftnlen storev_len) + storev, integer *m, integer *n, integer *k, doublereal *v, integer * + ldv, doublereal *t, integer *ldt, doublereal *c__, integer *ldc, + doublereal *work, integer *ldwork, ftnlen side_len, ftnlen trans_len, + ftnlen direct_len, ftnlen storev_len) { /* System generated locals */ - integer c_dim1, c_offset, t_dim1, t_offset, v_dim1, v_offset, work_dim1, - work_offset, i__1, i__2; + integer c_dim1, c_offset, t_dim1, t_offset, v_dim1, v_offset, work_dim1, + work_offset, i__1, i__2; /* Local variables */ integer i__, j; - extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, - doublereal *, integer *), dtrmm_(char *, char *, char *, char *, - integer *, integer *, doublereal *, doublereal *, integer *, - doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, + doublereal *, integer *), dtrmm_(char *, char *, char *, char *, + integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); char transt[1]; @@ -280,24 +280,24 @@ f"> */ /* Function Body */ if (*m <= 0 || *n <= 0) { - return 0; + return 0; } if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { - *(unsigned char *)transt = 'T'; + *(unsigned char *)transt = 'T'; } else { - *(unsigned char *)transt = 'N'; + *(unsigned char *)transt = 'N'; } if (lsame_(storev, (char *)"C", (ftnlen)1, (ftnlen)1)) { - if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { + if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { /* Let V = ( V1 ) (first K rows) */ /* ( V2 ) */ /* where V1 is unit lower triangular. */ - if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { + if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { /* Form H * C or H**T * C where C = ( C1 ) */ /* ( C2 ) */ @@ -306,67 +306,67 @@ f"> */ /* W := C1**T */ - i__1 = *k; - for (j = 1; j <= i__1; ++j) { - dcopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1], - &c__1); + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + dcopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1], + &c__1); /* L10: */ - } + } /* W := W * V1 */ - dtrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", n, k, &c_b14, - &v[v_offset], ldv, &work[work_offset], ldwork, ( - ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); - if (*m > *k) { + dtrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", n, k, &c_b14, + &v[v_offset], ldv, &work[work_offset], ldwork, ( + ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); + if (*m > *k) { /* W := W + C2**T * V2 */ - i__1 = *m - *k; - dgemm_((char *)"Transpose", (char *)"No transpose", n, k, &i__1, &c_b14, & - c__[*k + 1 + c_dim1], ldc, &v[*k + 1 + v_dim1], - ldv, &c_b14, &work[work_offset], ldwork, (ftnlen) - 9, (ftnlen)12); - } + i__1 = *m - *k; + dgemm_((char *)"Transpose", (char *)"No transpose", n, k, &i__1, &c_b14, & + c__[*k + 1 + c_dim1], ldc, &v[*k + 1 + v_dim1], + ldv, &c_b14, &work[work_offset], ldwork, (ftnlen) + 9, (ftnlen)12); + } /* W := W * T**T or W * T */ - dtrmm_((char *)"Right", (char *)"Upper", transt, (char *)"Non-unit", n, k, &c_b14, &t[ - t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, - (ftnlen)5, (ftnlen)1, (ftnlen)8); + dtrmm_((char *)"Right", (char *)"Upper", transt, (char *)"Non-unit", n, k, &c_b14, &t[ + t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)1, (ftnlen)8); /* C := C - V * W**T */ - if (*m > *k) { + if (*m > *k) { /* C2 := C2 - V2 * W**T */ - i__1 = *m - *k; - dgemm_((char *)"No transpose", (char *)"Transpose", &i__1, n, k, &c_b25, & - v[*k + 1 + v_dim1], ldv, &work[work_offset], - ldwork, &c_b14, &c__[*k + 1 + c_dim1], ldc, ( - ftnlen)12, (ftnlen)9); - } + i__1 = *m - *k; + dgemm_((char *)"No transpose", (char *)"Transpose", &i__1, n, k, &c_b25, & + v[*k + 1 + v_dim1], ldv, &work[work_offset], + ldwork, &c_b14, &c__[*k + 1 + c_dim1], ldc, ( + ftnlen)12, (ftnlen)9); + } /* W := W * V1**T */ - dtrmm_((char *)"Right", (char *)"Lower", (char *)"Transpose", (char *)"Unit", n, k, &c_b14, & - v[v_offset], ldv, &work[work_offset], ldwork, (ftnlen) - 5, (ftnlen)5, (ftnlen)9, (ftnlen)4); + dtrmm_((char *)"Right", (char *)"Lower", (char *)"Transpose", (char *)"Unit", n, k, &c_b14, & + v[v_offset], ldv, &work[work_offset], ldwork, (ftnlen) + 5, (ftnlen)5, (ftnlen)9, (ftnlen)4); /* C1 := C1 - W**T */ - i__1 = *k; - for (j = 1; j <= i__1; ++j) { - i__2 = *n; - for (i__ = 1; i__ <= i__2; ++i__) { - c__[j + i__ * c_dim1] -= work[i__ + j * work_dim1]; + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[j + i__ * c_dim1] -= work[i__ + j * work_dim1]; /* L20: */ - } + } /* L30: */ - } + } - } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { /* Form C * H or C * H**T where C = ( C1 C2 ) */ @@ -374,74 +374,74 @@ f"> */ /* W := C1 */ - i__1 = *k; - for (j = 1; j <= i__1; ++j) { - dcopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j * - work_dim1 + 1], &c__1); + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + dcopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j * + work_dim1 + 1], &c__1); /* L40: */ - } + } /* W := W * V1 */ - dtrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", m, k, &c_b14, - &v[v_offset], ldv, &work[work_offset], ldwork, ( - ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); - if (*n > *k) { + dtrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", m, k, &c_b14, + &v[v_offset], ldv, &work[work_offset], ldwork, ( + ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); + if (*n > *k) { /* W := W + C2 * V2 */ - i__1 = *n - *k; - dgemm_((char *)"No transpose", (char *)"No transpose", m, k, &i__1, & - c_b14, &c__[(*k + 1) * c_dim1 + 1], ldc, &v[*k + - 1 + v_dim1], ldv, &c_b14, &work[work_offset], - ldwork, (ftnlen)12, (ftnlen)12); - } + i__1 = *n - *k; + dgemm_((char *)"No transpose", (char *)"No transpose", m, k, &i__1, & + c_b14, &c__[(*k + 1) * c_dim1 + 1], ldc, &v[*k + + 1 + v_dim1], ldv, &c_b14, &work[work_offset], + ldwork, (ftnlen)12, (ftnlen)12); + } /* W := W * T or W * T**T */ - dtrmm_((char *)"Right", (char *)"Upper", trans, (char *)"Non-unit", m, k, &c_b14, &t[ - t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, - (ftnlen)5, (ftnlen)1, (ftnlen)8); + dtrmm_((char *)"Right", (char *)"Upper", trans, (char *)"Non-unit", m, k, &c_b14, &t[ + t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)1, (ftnlen)8); /* C := C - W * V**T */ - if (*n > *k) { + if (*n > *k) { /* C2 := C2 - W * V2**T */ - i__1 = *n - *k; - dgemm_((char *)"No transpose", (char *)"Transpose", m, &i__1, k, &c_b25, & - work[work_offset], ldwork, &v[*k + 1 + v_dim1], - ldv, &c_b14, &c__[(*k + 1) * c_dim1 + 1], ldc, ( - ftnlen)12, (ftnlen)9); - } + i__1 = *n - *k; + dgemm_((char *)"No transpose", (char *)"Transpose", m, &i__1, k, &c_b25, & + work[work_offset], ldwork, &v[*k + 1 + v_dim1], + ldv, &c_b14, &c__[(*k + 1) * c_dim1 + 1], ldc, ( + ftnlen)12, (ftnlen)9); + } /* W := W * V1**T */ - dtrmm_((char *)"Right", (char *)"Lower", (char *)"Transpose", (char *)"Unit", m, k, &c_b14, & - v[v_offset], ldv, &work[work_offset], ldwork, (ftnlen) - 5, (ftnlen)5, (ftnlen)9, (ftnlen)4); + dtrmm_((char *)"Right", (char *)"Lower", (char *)"Transpose", (char *)"Unit", m, k, &c_b14, & + v[v_offset], ldv, &work[work_offset], ldwork, (ftnlen) + 5, (ftnlen)5, (ftnlen)9, (ftnlen)4); /* C1 := C1 - W */ - i__1 = *k; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - c__[i__ + j * c_dim1] -= work[i__ + j * work_dim1]; + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] -= work[i__ + j * work_dim1]; /* L50: */ - } + } /* L60: */ - } - } + } + } - } else { + } else { /* Let V = ( V1 ) */ /* ( V2 ) (last K rows) */ /* where V2 is unit upper triangular. */ - if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { + if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { /* Form H * C or H**T * C where C = ( C1 ) */ /* ( C2 ) */ @@ -450,67 +450,67 @@ f"> */ /* W := C2**T */ - i__1 = *k; - for (j = 1; j <= i__1; ++j) { - dcopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j * - work_dim1 + 1], &c__1); + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + dcopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j * + work_dim1 + 1], &c__1); /* L70: */ - } + } /* W := W * V2 */ - dtrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", n, k, &c_b14, - &v[*m - *k + 1 + v_dim1], ldv, &work[work_offset], - ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); - if (*m > *k) { + dtrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", n, k, &c_b14, + &v[*m - *k + 1 + v_dim1], ldv, &work[work_offset], + ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); + if (*m > *k) { /* W := W + C1**T * V1 */ - i__1 = *m - *k; - dgemm_((char *)"Transpose", (char *)"No transpose", n, k, &i__1, &c_b14, & - c__[c_offset], ldc, &v[v_offset], ldv, &c_b14, & - work[work_offset], ldwork, (ftnlen)9, (ftnlen)12); - } + i__1 = *m - *k; + dgemm_((char *)"Transpose", (char *)"No transpose", n, k, &i__1, &c_b14, & + c__[c_offset], ldc, &v[v_offset], ldv, &c_b14, & + work[work_offset], ldwork, (ftnlen)9, (ftnlen)12); + } /* W := W * T**T or W * T */ - dtrmm_((char *)"Right", (char *)"Lower", transt, (char *)"Non-unit", n, k, &c_b14, &t[ - t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, - (ftnlen)5, (ftnlen)1, (ftnlen)8); + dtrmm_((char *)"Right", (char *)"Lower", transt, (char *)"Non-unit", n, k, &c_b14, &t[ + t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)1, (ftnlen)8); /* C := C - V * W**T */ - if (*m > *k) { + if (*m > *k) { /* C1 := C1 - V1 * W**T */ - i__1 = *m - *k; - dgemm_((char *)"No transpose", (char *)"Transpose", &i__1, n, k, &c_b25, & - v[v_offset], ldv, &work[work_offset], ldwork, & - c_b14, &c__[c_offset], ldc, (ftnlen)12, (ftnlen)9) - ; - } + i__1 = *m - *k; + dgemm_((char *)"No transpose", (char *)"Transpose", &i__1, n, k, &c_b25, & + v[v_offset], ldv, &work[work_offset], ldwork, & + c_b14, &c__[c_offset], ldc, (ftnlen)12, (ftnlen)9) + ; + } /* W := W * V2**T */ - dtrmm_((char *)"Right", (char *)"Upper", (char *)"Transpose", (char *)"Unit", n, k, &c_b14, & - v[*m - *k + 1 + v_dim1], ldv, &work[work_offset], - ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)9, (ftnlen)4); + dtrmm_((char *)"Right", (char *)"Upper", (char *)"Transpose", (char *)"Unit", n, k, &c_b14, & + v[*m - *k + 1 + v_dim1], ldv, &work[work_offset], + ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)9, (ftnlen)4); /* C2 := C2 - W**T */ - i__1 = *k; - for (j = 1; j <= i__1; ++j) { - i__2 = *n; - for (i__ = 1; i__ <= i__2; ++i__) { - c__[*m - *k + j + i__ * c_dim1] -= work[i__ + j * - work_dim1]; + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[*m - *k + j + i__ * c_dim1] -= work[i__ + j * + work_dim1]; /* L80: */ - } + } /* L90: */ - } + } - } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { /* Form C * H or C * H**T where C = ( C1 C2 ) */ @@ -518,77 +518,77 @@ f"> */ /* W := C2 */ - i__1 = *k; - for (j = 1; j <= i__1; ++j) { - dcopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[ - j * work_dim1 + 1], &c__1); + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + dcopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[ + j * work_dim1 + 1], &c__1); /* L100: */ - } + } /* W := W * V2 */ - dtrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", m, k, &c_b14, - &v[*n - *k + 1 + v_dim1], ldv, &work[work_offset], - ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); - if (*n > *k) { + dtrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", m, k, &c_b14, + &v[*n - *k + 1 + v_dim1], ldv, &work[work_offset], + ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); + if (*n > *k) { /* W := W + C1 * V1 */ - i__1 = *n - *k; - dgemm_((char *)"No transpose", (char *)"No transpose", m, k, &i__1, & - c_b14, &c__[c_offset], ldc, &v[v_offset], ldv, & - c_b14, &work[work_offset], ldwork, (ftnlen)12, ( - ftnlen)12); - } + i__1 = *n - *k; + dgemm_((char *)"No transpose", (char *)"No transpose", m, k, &i__1, & + c_b14, &c__[c_offset], ldc, &v[v_offset], ldv, & + c_b14, &work[work_offset], ldwork, (ftnlen)12, ( + ftnlen)12); + } /* W := W * T or W * T**T */ - dtrmm_((char *)"Right", (char *)"Lower", trans, (char *)"Non-unit", m, k, &c_b14, &t[ - t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, - (ftnlen)5, (ftnlen)1, (ftnlen)8); + dtrmm_((char *)"Right", (char *)"Lower", trans, (char *)"Non-unit", m, k, &c_b14, &t[ + t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)1, (ftnlen)8); /* C := C - W * V**T */ - if (*n > *k) { + if (*n > *k) { /* C1 := C1 - W * V1**T */ - i__1 = *n - *k; - dgemm_((char *)"No transpose", (char *)"Transpose", m, &i__1, k, &c_b25, & - work[work_offset], ldwork, &v[v_offset], ldv, & - c_b14, &c__[c_offset], ldc, (ftnlen)12, (ftnlen)9) - ; - } + i__1 = *n - *k; + dgemm_((char *)"No transpose", (char *)"Transpose", m, &i__1, k, &c_b25, & + work[work_offset], ldwork, &v[v_offset], ldv, & + c_b14, &c__[c_offset], ldc, (ftnlen)12, (ftnlen)9) + ; + } /* W := W * V2**T */ - dtrmm_((char *)"Right", (char *)"Upper", (char *)"Transpose", (char *)"Unit", m, k, &c_b14, & - v[*n - *k + 1 + v_dim1], ldv, &work[work_offset], - ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)9, (ftnlen)4); + dtrmm_((char *)"Right", (char *)"Upper", (char *)"Transpose", (char *)"Unit", m, k, &c_b14, & + v[*n - *k + 1 + v_dim1], ldv, &work[work_offset], + ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)9, (ftnlen)4); /* C2 := C2 - W */ - i__1 = *k; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - c__[i__ + (*n - *k + j) * c_dim1] -= work[i__ + j * - work_dim1]; + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + (*n - *k + j) * c_dim1] -= work[i__ + j * + work_dim1]; /* L110: */ - } + } /* L120: */ - } - } - } + } + } + } } else if (lsame_(storev, (char *)"R", (ftnlen)1, (ftnlen)1)) { - if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { + if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { /* Let V = ( V1 V2 ) (V1: first K columns) */ /* where V1 is unit upper triangular. */ - if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { + if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { /* Form H * C or H**T * C where C = ( C1 ) */ /* ( C2 ) */ @@ -597,67 +597,67 @@ f"> */ /* W := C1**T */ - i__1 = *k; - for (j = 1; j <= i__1; ++j) { - dcopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1], - &c__1); + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + dcopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1], + &c__1); /* L130: */ - } + } /* W := W * V1**T */ - dtrmm_((char *)"Right", (char *)"Upper", (char *)"Transpose", (char *)"Unit", n, k, &c_b14, & - v[v_offset], ldv, &work[work_offset], ldwork, (ftnlen) - 5, (ftnlen)5, (ftnlen)9, (ftnlen)4); - if (*m > *k) { + dtrmm_((char *)"Right", (char *)"Upper", (char *)"Transpose", (char *)"Unit", n, k, &c_b14, & + v[v_offset], ldv, &work[work_offset], ldwork, (ftnlen) + 5, (ftnlen)5, (ftnlen)9, (ftnlen)4); + if (*m > *k) { /* W := W + C2**T * V2**T */ - i__1 = *m - *k; - dgemm_((char *)"Transpose", (char *)"Transpose", n, k, &i__1, &c_b14, & - c__[*k + 1 + c_dim1], ldc, &v[(*k + 1) * v_dim1 + - 1], ldv, &c_b14, &work[work_offset], ldwork, ( - ftnlen)9, (ftnlen)9); - } + i__1 = *m - *k; + dgemm_((char *)"Transpose", (char *)"Transpose", n, k, &i__1, &c_b14, & + c__[*k + 1 + c_dim1], ldc, &v[(*k + 1) * v_dim1 + + 1], ldv, &c_b14, &work[work_offset], ldwork, ( + ftnlen)9, (ftnlen)9); + } /* W := W * T**T or W * T */ - dtrmm_((char *)"Right", (char *)"Upper", transt, (char *)"Non-unit", n, k, &c_b14, &t[ - t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, - (ftnlen)5, (ftnlen)1, (ftnlen)8); + dtrmm_((char *)"Right", (char *)"Upper", transt, (char *)"Non-unit", n, k, &c_b14, &t[ + t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)1, (ftnlen)8); /* C := C - V**T * W**T */ - if (*m > *k) { + if (*m > *k) { /* C2 := C2 - V2**T * W**T */ - i__1 = *m - *k; - dgemm_((char *)"Transpose", (char *)"Transpose", &i__1, n, k, &c_b25, &v[( - *k + 1) * v_dim1 + 1], ldv, &work[work_offset], - ldwork, &c_b14, &c__[*k + 1 + c_dim1], ldc, ( - ftnlen)9, (ftnlen)9); - } + i__1 = *m - *k; + dgemm_((char *)"Transpose", (char *)"Transpose", &i__1, n, k, &c_b25, &v[( + *k + 1) * v_dim1 + 1], ldv, &work[work_offset], + ldwork, &c_b14, &c__[*k + 1 + c_dim1], ldc, ( + ftnlen)9, (ftnlen)9); + } /* W := W * V1 */ - dtrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", n, k, &c_b14, - &v[v_offset], ldv, &work[work_offset], ldwork, ( - ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); + dtrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", n, k, &c_b14, + &v[v_offset], ldv, &work[work_offset], ldwork, ( + ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); /* C1 := C1 - W**T */ - i__1 = *k; - for (j = 1; j <= i__1; ++j) { - i__2 = *n; - for (i__ = 1; i__ <= i__2; ++i__) { - c__[j + i__ * c_dim1] -= work[i__ + j * work_dim1]; + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[j + i__ * c_dim1] -= work[i__ + j * work_dim1]; /* L140: */ - } + } /* L150: */ - } + } - } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { /* Form C * H or C * H**T where C = ( C1 C2 ) */ @@ -665,74 +665,74 @@ f"> */ /* W := C1 */ - i__1 = *k; - for (j = 1; j <= i__1; ++j) { - dcopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j * - work_dim1 + 1], &c__1); + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + dcopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j * + work_dim1 + 1], &c__1); /* L160: */ - } + } /* W := W * V1**T */ - dtrmm_((char *)"Right", (char *)"Upper", (char *)"Transpose", (char *)"Unit", m, k, &c_b14, & - v[v_offset], ldv, &work[work_offset], ldwork, (ftnlen) - 5, (ftnlen)5, (ftnlen)9, (ftnlen)4); - if (*n > *k) { + dtrmm_((char *)"Right", (char *)"Upper", (char *)"Transpose", (char *)"Unit", m, k, &c_b14, & + v[v_offset], ldv, &work[work_offset], ldwork, (ftnlen) + 5, (ftnlen)5, (ftnlen)9, (ftnlen)4); + if (*n > *k) { /* W := W + C2 * V2**T */ - i__1 = *n - *k; - dgemm_((char *)"No transpose", (char *)"Transpose", m, k, &i__1, &c_b14, & - c__[(*k + 1) * c_dim1 + 1], ldc, &v[(*k + 1) * - v_dim1 + 1], ldv, &c_b14, &work[work_offset], - ldwork, (ftnlen)12, (ftnlen)9); - } + i__1 = *n - *k; + dgemm_((char *)"No transpose", (char *)"Transpose", m, k, &i__1, &c_b14, & + c__[(*k + 1) * c_dim1 + 1], ldc, &v[(*k + 1) * + v_dim1 + 1], ldv, &c_b14, &work[work_offset], + ldwork, (ftnlen)12, (ftnlen)9); + } /* W := W * T or W * T**T */ - dtrmm_((char *)"Right", (char *)"Upper", trans, (char *)"Non-unit", m, k, &c_b14, &t[ - t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, - (ftnlen)5, (ftnlen)1, (ftnlen)8); + dtrmm_((char *)"Right", (char *)"Upper", trans, (char *)"Non-unit", m, k, &c_b14, &t[ + t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)1, (ftnlen)8); /* C := C - W * V */ - if (*n > *k) { + if (*n > *k) { /* C2 := C2 - W * V2 */ - i__1 = *n - *k; - dgemm_((char *)"No transpose", (char *)"No transpose", m, &i__1, k, & - c_b25, &work[work_offset], ldwork, &v[(*k + 1) * - v_dim1 + 1], ldv, &c_b14, &c__[(*k + 1) * c_dim1 - + 1], ldc, (ftnlen)12, (ftnlen)12); - } + i__1 = *n - *k; + dgemm_((char *)"No transpose", (char *)"No transpose", m, &i__1, k, & + c_b25, &work[work_offset], ldwork, &v[(*k + 1) * + v_dim1 + 1], ldv, &c_b14, &c__[(*k + 1) * c_dim1 + + 1], ldc, (ftnlen)12, (ftnlen)12); + } /* W := W * V1 */ - dtrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", m, k, &c_b14, - &v[v_offset], ldv, &work[work_offset], ldwork, ( - ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); + dtrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", m, k, &c_b14, + &v[v_offset], ldv, &work[work_offset], ldwork, ( + ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); /* C1 := C1 - W */ - i__1 = *k; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - c__[i__ + j * c_dim1] -= work[i__ + j * work_dim1]; + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] -= work[i__ + j * work_dim1]; /* L170: */ - } + } /* L180: */ - } + } - } + } - } else { + } else { /* Let V = ( V1 V2 ) (V2: last K columns) */ /* where V2 is unit lower triangular. */ - if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { + if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { /* Form H * C or H**T * C where C = ( C1 ) */ /* ( C2 ) */ @@ -741,67 +741,67 @@ f"> */ /* W := C2**T */ - i__1 = *k; - for (j = 1; j <= i__1; ++j) { - dcopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j * - work_dim1 + 1], &c__1); + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + dcopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j * + work_dim1 + 1], &c__1); /* L190: */ - } + } /* W := W * V2**T */ - dtrmm_((char *)"Right", (char *)"Lower", (char *)"Transpose", (char *)"Unit", n, k, &c_b14, & - v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[work_offset] - , ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)9, (ftnlen)4); - if (*m > *k) { + dtrmm_((char *)"Right", (char *)"Lower", (char *)"Transpose", (char *)"Unit", n, k, &c_b14, & + v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[work_offset] + , ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)9, (ftnlen)4); + if (*m > *k) { /* W := W + C1**T * V1**T */ - i__1 = *m - *k; - dgemm_((char *)"Transpose", (char *)"Transpose", n, k, &i__1, &c_b14, & - c__[c_offset], ldc, &v[v_offset], ldv, &c_b14, & - work[work_offset], ldwork, (ftnlen)9, (ftnlen)9); - } + i__1 = *m - *k; + dgemm_((char *)"Transpose", (char *)"Transpose", n, k, &i__1, &c_b14, & + c__[c_offset], ldc, &v[v_offset], ldv, &c_b14, & + work[work_offset], ldwork, (ftnlen)9, (ftnlen)9); + } /* W := W * T**T or W * T */ - dtrmm_((char *)"Right", (char *)"Lower", transt, (char *)"Non-unit", n, k, &c_b14, &t[ - t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, - (ftnlen)5, (ftnlen)1, (ftnlen)8); + dtrmm_((char *)"Right", (char *)"Lower", transt, (char *)"Non-unit", n, k, &c_b14, &t[ + t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)1, (ftnlen)8); /* C := C - V**T * W**T */ - if (*m > *k) { + if (*m > *k) { /* C1 := C1 - V1**T * W**T */ - i__1 = *m - *k; - dgemm_((char *)"Transpose", (char *)"Transpose", &i__1, n, k, &c_b25, &v[ - v_offset], ldv, &work[work_offset], ldwork, & - c_b14, &c__[c_offset], ldc, (ftnlen)9, (ftnlen)9); - } + i__1 = *m - *k; + dgemm_((char *)"Transpose", (char *)"Transpose", &i__1, n, k, &c_b25, &v[ + v_offset], ldv, &work[work_offset], ldwork, & + c_b14, &c__[c_offset], ldc, (ftnlen)9, (ftnlen)9); + } /* W := W * V2 */ - dtrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", n, k, &c_b14, - &v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[ - work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen) - 12, (ftnlen)4); + dtrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", n, k, &c_b14, + &v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[ + work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen) + 12, (ftnlen)4); /* C2 := C2 - W**T */ - i__1 = *k; - for (j = 1; j <= i__1; ++j) { - i__2 = *n; - for (i__ = 1; i__ <= i__2; ++i__) { - c__[*m - *k + j + i__ * c_dim1] -= work[i__ + j * - work_dim1]; + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[*m - *k + j + i__ * c_dim1] -= work[i__ + j * + work_dim1]; /* L200: */ - } + } /* L210: */ - } + } - } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { /* Form C * H or C * H' where C = ( C1 C2 ) */ @@ -809,70 +809,70 @@ f"> */ /* W := C2 */ - i__1 = *k; - for (j = 1; j <= i__1; ++j) { - dcopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[ - j * work_dim1 + 1], &c__1); + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + dcopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[ + j * work_dim1 + 1], &c__1); /* L220: */ - } + } /* W := W * V2**T */ - dtrmm_((char *)"Right", (char *)"Lower", (char *)"Transpose", (char *)"Unit", m, k, &c_b14, & - v[(*n - *k + 1) * v_dim1 + 1], ldv, &work[work_offset] - , ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)9, (ftnlen)4); - if (*n > *k) { + dtrmm_((char *)"Right", (char *)"Lower", (char *)"Transpose", (char *)"Unit", m, k, &c_b14, & + v[(*n - *k + 1) * v_dim1 + 1], ldv, &work[work_offset] + , ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)9, (ftnlen)4); + if (*n > *k) { /* W := W + C1 * V1**T */ - i__1 = *n - *k; - dgemm_((char *)"No transpose", (char *)"Transpose", m, k, &i__1, &c_b14, & - c__[c_offset], ldc, &v[v_offset], ldv, &c_b14, & - work[work_offset], ldwork, (ftnlen)12, (ftnlen)9); - } + i__1 = *n - *k; + dgemm_((char *)"No transpose", (char *)"Transpose", m, k, &i__1, &c_b14, & + c__[c_offset], ldc, &v[v_offset], ldv, &c_b14, & + work[work_offset], ldwork, (ftnlen)12, (ftnlen)9); + } /* W := W * T or W * T**T */ - dtrmm_((char *)"Right", (char *)"Lower", trans, (char *)"Non-unit", m, k, &c_b14, &t[ - t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, - (ftnlen)5, (ftnlen)1, (ftnlen)8); + dtrmm_((char *)"Right", (char *)"Lower", trans, (char *)"Non-unit", m, k, &c_b14, &t[ + t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)1, (ftnlen)8); /* C := C - W * V */ - if (*n > *k) { + if (*n > *k) { /* C1 := C1 - W * V1 */ - i__1 = *n - *k; - dgemm_((char *)"No transpose", (char *)"No transpose", m, &i__1, k, & - c_b25, &work[work_offset], ldwork, &v[v_offset], - ldv, &c_b14, &c__[c_offset], ldc, (ftnlen)12, ( - ftnlen)12); - } + i__1 = *n - *k; + dgemm_((char *)"No transpose", (char *)"No transpose", m, &i__1, k, & + c_b25, &work[work_offset], ldwork, &v[v_offset], + ldv, &c_b14, &c__[c_offset], ldc, (ftnlen)12, ( + ftnlen)12); + } /* W := W * V2 */ - dtrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", m, k, &c_b14, - &v[(*n - *k + 1) * v_dim1 + 1], ldv, &work[ - work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen) - 12, (ftnlen)4); + dtrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", m, k, &c_b14, + &v[(*n - *k + 1) * v_dim1 + 1], ldv, &work[ + work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen) + 12, (ftnlen)4); /* C1 := C1 - W */ - i__1 = *k; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - c__[i__ + (*n - *k + j) * c_dim1] -= work[i__ + j * - work_dim1]; + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + (*n - *k + j) * c_dim1] -= work[i__ + j * + work_dim1]; /* L230: */ - } + } /* L240: */ - } + } - } + } - } + } } return 0; @@ -882,5 +882,5 @@ f"> */ } /* dlarfb_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlarfg.cpp b/lib/linalg/dlarfg.cpp index cb544ccf18..6693e1edb6 100644 --- a/lib/linalg/dlarfg.cpp +++ b/lib/linalg/dlarfg.cpp @@ -1,13 +1,13 @@ /* fortran/dlarfg.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -122,8 +122,8 @@ f"> */ /* > \ingroup doubleOTHERauxiliary */ /* ===================================================================== */ -/* Subroutine */ int dlarfg_(integer *n, doublereal *alpha, doublereal *x, - integer *incx, doublereal *tau) +/* Subroutine */ int dlarfg_(integer *n, doublereal *alpha, doublereal *x, + integer *incx, doublereal *tau) { /* System generated locals */ integer i__1; @@ -136,11 +136,11 @@ f"> */ integer j, knt; doublereal beta; extern doublereal dnrm2_(integer *, doublereal *, integer *); - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *); + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *); doublereal xnorm; - extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, - ftnlen); + extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, + ftnlen); doublereal safmin, rsafmn; @@ -172,8 +172,8 @@ f"> */ /* Function Body */ if (*n <= 1) { - *tau = 0.; - return 0; + *tau = 0.; + return 0; } i__1 = *n - 1; @@ -183,50 +183,50 @@ f"> */ /* H = I */ - *tau = 0.; + *tau = 0.; } else { /* general case */ - d__1 = dlapy2_(alpha, &xnorm); - beta = -d_sign(&d__1, alpha); - safmin = dlamch_((char *)"S", (ftnlen)1) / dlamch_((char *)"E", (ftnlen)1); - knt = 0; - if (abs(beta) < safmin) { + d__1 = dlapy2_(alpha, &xnorm); + beta = -d_sign(&d__1, alpha); + safmin = dlamch_((char *)"S", (ftnlen)1) / dlamch_((char *)"E", (ftnlen)1); + knt = 0; + if (abs(beta) < safmin) { /* XNORM, BETA may be inaccurate; scale X and recompute them */ - rsafmn = 1. / safmin; + rsafmn = 1. / safmin; L10: - ++knt; - i__1 = *n - 1; - dscal_(&i__1, &rsafmn, &x[1], incx); - beta *= rsafmn; - *alpha *= rsafmn; - if (abs(beta) < safmin && knt < 20) { - goto L10; - } + ++knt; + i__1 = *n - 1; + dscal_(&i__1, &rsafmn, &x[1], incx); + beta *= rsafmn; + *alpha *= rsafmn; + if (abs(beta) < safmin && knt < 20) { + goto L10; + } /* New BETA is at most 1, at least SAFMIN */ - i__1 = *n - 1; - xnorm = dnrm2_(&i__1, &x[1], incx); - d__1 = dlapy2_(alpha, &xnorm); - beta = -d_sign(&d__1, alpha); - } - *tau = (beta - *alpha) / beta; - i__1 = *n - 1; - d__1 = 1. / (*alpha - beta); - dscal_(&i__1, &d__1, &x[1], incx); + i__1 = *n - 1; + xnorm = dnrm2_(&i__1, &x[1], incx); + d__1 = dlapy2_(alpha, &xnorm); + beta = -d_sign(&d__1, alpha); + } + *tau = (beta - *alpha) / beta; + i__1 = *n - 1; + d__1 = 1. / (*alpha - beta); + dscal_(&i__1, &d__1, &x[1], incx); /* If ALPHA is subnormal, it may lose relative accuracy */ - i__1 = knt; - for (j = 1; j <= i__1; ++j) { - beta *= safmin; + i__1 = knt; + for (j = 1; j <= i__1; ++j) { + beta *= safmin; /* L20: */ - } - *alpha = beta; + } + *alpha = beta; } return 0; @@ -236,5 +236,5 @@ L10: } /* dlarfg_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlarft.cpp b/lib/linalg/dlarft.cpp index 220c9f0082..bd0874fa3c 100644 --- a/lib/linalg/dlarft.cpp +++ b/lib/linalg/dlarft.cpp @@ -1,13 +1,13 @@ /* static/dlarft.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -185,8 +185,8 @@ f"> */ /* > */ /* ===================================================================== */ /* Subroutine */ int dlarft_(char *direct, char *storev, integer *n, integer * - k, doublereal *v, integer *ldv, doublereal *tau, doublereal *t, - integer *ldt, ftnlen direct_len, ftnlen storev_len) + k, doublereal *v, integer *ldv, doublereal *tau, doublereal *t, + integer *ldt, ftnlen direct_len, ftnlen storev_len) { /* System generated locals */ integer t_dim1, t_offset, v_dim1, v_offset, i__1, i__2, i__3; @@ -195,13 +195,13 @@ f"> */ /* Local variables */ integer i__, j, prevlastv; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int dgemv_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, doublereal *, integer *, - doublereal *, doublereal *, integer *, ftnlen); + extern /* Subroutine */ int dgemv_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, ftnlen); integer lastv; - extern /* Subroutine */ int dtrmv_(char *, char *, char *, integer *, - doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, - ftnlen); + extern /* Subroutine */ int dtrmv_(char *, char *, char *, integer *, + doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, + ftnlen); /* -- LAPACK auxiliary routine -- */ @@ -238,173 +238,173 @@ f"> */ /* Function Body */ if (*n == 0) { - return 0; + return 0; } if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { - prevlastv = *n; - i__1 = *k; - for (i__ = 1; i__ <= i__1; ++i__) { - prevlastv = max(i__,prevlastv); - if (tau[i__] == 0.) { + prevlastv = *n; + i__1 = *k; + for (i__ = 1; i__ <= i__1; ++i__) { + prevlastv = max(i__,prevlastv); + if (tau[i__] == 0.) { /* H(i) = I */ - i__2 = i__; - for (j = 1; j <= i__2; ++j) { - t[j + i__ * t_dim1] = 0.; - } - } else { + i__2 = i__; + for (j = 1; j <= i__2; ++j) { + t[j + i__ * t_dim1] = 0.; + } + } else { /* general case */ - if (lsame_(storev, (char *)"C", (ftnlen)1, (ftnlen)1)) { + if (lsame_(storev, (char *)"C", (ftnlen)1, (ftnlen)1)) { /* Skip any trailing zeros. */ - i__2 = i__ + 1; - for (lastv = *n; lastv >= i__2; --lastv) { - if (v[lastv + i__ * v_dim1] != 0.) { - goto L219; - } - } + i__2 = i__ + 1; + for (lastv = *n; lastv >= i__2; --lastv) { + if (v[lastv + i__ * v_dim1] != 0.) { + goto L219; + } + } L219: - i__2 = i__ - 1; - for (j = 1; j <= i__2; ++j) { - t[j + i__ * t_dim1] = -tau[i__] * v[i__ + j * v_dim1]; - } - j = min(lastv,prevlastv); + i__2 = i__ - 1; + for (j = 1; j <= i__2; ++j) { + t[j + i__ * t_dim1] = -tau[i__] * v[i__ + j * v_dim1]; + } + j = min(lastv,prevlastv); /* T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**T * V(i:j,i) */ - i__2 = j - i__; - i__3 = i__ - 1; - d__1 = -tau[i__]; - dgemv_((char *)"Transpose", &i__2, &i__3, &d__1, &v[i__ + 1 + - v_dim1], ldv, &v[i__ + 1 + i__ * v_dim1], &c__1, & - c_b7, &t[i__ * t_dim1 + 1], &c__1, (ftnlen)9); - } else { + i__2 = j - i__; + i__3 = i__ - 1; + d__1 = -tau[i__]; + dgemv_((char *)"Transpose", &i__2, &i__3, &d__1, &v[i__ + 1 + + v_dim1], ldv, &v[i__ + 1 + i__ * v_dim1], &c__1, & + c_b7, &t[i__ * t_dim1 + 1], &c__1, (ftnlen)9); + } else { /* Skip any trailing zeros. */ - i__2 = i__ + 1; - for (lastv = *n; lastv >= i__2; --lastv) { - if (v[i__ + lastv * v_dim1] != 0.) { - goto L235; - } - } + i__2 = i__ + 1; + for (lastv = *n; lastv >= i__2; --lastv) { + if (v[i__ + lastv * v_dim1] != 0.) { + goto L235; + } + } L235: - i__2 = i__ - 1; - for (j = 1; j <= i__2; ++j) { - t[j + i__ * t_dim1] = -tau[i__] * v[j + i__ * v_dim1]; - } - j = min(lastv,prevlastv); + i__2 = i__ - 1; + for (j = 1; j <= i__2; ++j) { + t[j + i__ * t_dim1] = -tau[i__] * v[j + i__ * v_dim1]; + } + j = min(lastv,prevlastv); /* T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**T */ - i__2 = i__ - 1; - i__3 = j - i__; - d__1 = -tau[i__]; - dgemv_((char *)"No transpose", &i__2, &i__3, &d__1, &v[(i__ + 1) * - v_dim1 + 1], ldv, &v[i__ + (i__ + 1) * v_dim1], - ldv, &c_b7, &t[i__ * t_dim1 + 1], &c__1, (ftnlen) - 12); - } + i__2 = i__ - 1; + i__3 = j - i__; + d__1 = -tau[i__]; + dgemv_((char *)"No transpose", &i__2, &i__3, &d__1, &v[(i__ + 1) * + v_dim1 + 1], ldv, &v[i__ + (i__ + 1) * v_dim1], + ldv, &c_b7, &t[i__ * t_dim1 + 1], &c__1, (ftnlen) + 12); + } /* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) */ - i__2 = i__ - 1; - dtrmv_((char *)"Upper", (char *)"No transpose", (char *)"Non-unit", &i__2, &t[ - t_offset], ldt, &t[i__ * t_dim1 + 1], &c__1, (ftnlen) - 5, (ftnlen)12, (ftnlen)8); - t[i__ + i__ * t_dim1] = tau[i__]; - if (i__ > 1) { - prevlastv = max(prevlastv,lastv); - } else { - prevlastv = lastv; - } - } - } + i__2 = i__ - 1; + dtrmv_((char *)"Upper", (char *)"No transpose", (char *)"Non-unit", &i__2, &t[ + t_offset], ldt, &t[i__ * t_dim1 + 1], &c__1, (ftnlen) + 5, (ftnlen)12, (ftnlen)8); + t[i__ + i__ * t_dim1] = tau[i__]; + if (i__ > 1) { + prevlastv = max(prevlastv,lastv); + } else { + prevlastv = lastv; + } + } + } } else { - prevlastv = 1; - for (i__ = *k; i__ >= 1; --i__) { - if (tau[i__] == 0.) { + prevlastv = 1; + for (i__ = *k; i__ >= 1; --i__) { + if (tau[i__] == 0.) { /* H(i) = I */ - i__1 = *k; - for (j = i__; j <= i__1; ++j) { - t[j + i__ * t_dim1] = 0.; - } - } else { + i__1 = *k; + for (j = i__; j <= i__1; ++j) { + t[j + i__ * t_dim1] = 0.; + } + } else { /* general case */ - if (i__ < *k) { - if (lsame_(storev, (char *)"C", (ftnlen)1, (ftnlen)1)) { + if (i__ < *k) { + if (lsame_(storev, (char *)"C", (ftnlen)1, (ftnlen)1)) { /* Skip any leading zeros. */ - i__1 = i__ - 1; - for (lastv = 1; lastv <= i__1; ++lastv) { - if (v[lastv + i__ * v_dim1] != 0.) { - goto L280; - } - } + i__1 = i__ - 1; + for (lastv = 1; lastv <= i__1; ++lastv) { + if (v[lastv + i__ * v_dim1] != 0.) { + goto L280; + } + } L280: - i__1 = *k; - for (j = i__ + 1; j <= i__1; ++j) { - t[j + i__ * t_dim1] = -tau[i__] * v[*n - *k + i__ - + j * v_dim1]; - } - j = max(lastv,prevlastv); + i__1 = *k; + for (j = i__ + 1; j <= i__1; ++j) { + t[j + i__ * t_dim1] = -tau[i__] * v[*n - *k + i__ + + j * v_dim1]; + } + j = max(lastv,prevlastv); /* T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**T * V(j:n-k+i,i) */ - i__1 = *n - *k + i__ - j; - i__2 = *k - i__; - d__1 = -tau[i__]; - dgemv_((char *)"Transpose", &i__1, &i__2, &d__1, &v[j + (i__ - + 1) * v_dim1], ldv, &v[j + i__ * v_dim1], & - c__1, &c_b7, &t[i__ + 1 + i__ * t_dim1], & - c__1, (ftnlen)9); - } else { + i__1 = *n - *k + i__ - j; + i__2 = *k - i__; + d__1 = -tau[i__]; + dgemv_((char *)"Transpose", &i__1, &i__2, &d__1, &v[j + (i__ + + 1) * v_dim1], ldv, &v[j + i__ * v_dim1], & + c__1, &c_b7, &t[i__ + 1 + i__ * t_dim1], & + c__1, (ftnlen)9); + } else { /* Skip any leading zeros. */ - i__1 = i__ - 1; - for (lastv = 1; lastv <= i__1; ++lastv) { - if (v[i__ + lastv * v_dim1] != 0.) { - goto L296; - } - } + i__1 = i__ - 1; + for (lastv = 1; lastv <= i__1; ++lastv) { + if (v[i__ + lastv * v_dim1] != 0.) { + goto L296; + } + } L296: - i__1 = *k; - for (j = i__ + 1; j <= i__1; ++j) { - t[j + i__ * t_dim1] = -tau[i__] * v[j + (*n - *k - + i__) * v_dim1]; - } - j = max(lastv,prevlastv); + i__1 = *k; + for (j = i__ + 1; j <= i__1; ++j) { + t[j + i__ * t_dim1] = -tau[i__] * v[j + (*n - *k + + i__) * v_dim1]; + } + j = max(lastv,prevlastv); /* T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**T */ - i__1 = *k - i__; - i__2 = *n - *k + i__ - j; - d__1 = -tau[i__]; - dgemv_((char *)"No transpose", &i__1, &i__2, &d__1, &v[i__ + - 1 + j * v_dim1], ldv, &v[i__ + j * v_dim1], - ldv, &c_b7, &t[i__ + 1 + i__ * t_dim1], &c__1, - (ftnlen)12); - } + i__1 = *k - i__; + i__2 = *n - *k + i__ - j; + d__1 = -tau[i__]; + dgemv_((char *)"No transpose", &i__1, &i__2, &d__1, &v[i__ + + 1 + j * v_dim1], ldv, &v[i__ + j * v_dim1], + ldv, &c_b7, &t[i__ + 1 + i__ * t_dim1], &c__1, + (ftnlen)12); + } /* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) */ - i__1 = *k - i__; - dtrmv_((char *)"Lower", (char *)"No transpose", (char *)"Non-unit", &i__1, &t[i__ - + 1 + (i__ + 1) * t_dim1], ldt, &t[i__ + 1 + i__ * - t_dim1], &c__1, (ftnlen)5, (ftnlen)12, (ftnlen)8) - ; - if (i__ > 1) { - prevlastv = min(prevlastv,lastv); - } else { - prevlastv = lastv; - } - } - t[i__ + i__ * t_dim1] = tau[i__]; - } - } + i__1 = *k - i__; + dtrmv_((char *)"Lower", (char *)"No transpose", (char *)"Non-unit", &i__1, &t[i__ + + 1 + (i__ + 1) * t_dim1], ldt, &t[i__ + 1 + i__ * + t_dim1], &c__1, (ftnlen)5, (ftnlen)12, (ftnlen)8) + ; + if (i__ > 1) { + prevlastv = min(prevlastv,lastv); + } else { + prevlastv = lastv; + } + } + t[i__ + i__ * t_dim1] = tau[i__]; + } + } } return 0; @@ -413,5 +413,5 @@ L296: } /* dlarft_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlartg.cpp b/lib/linalg/dlartg.cpp index 118d7865f6..3f5832318e 100644 --- a/lib/linalg/dlartg.cpp +++ b/lib/linalg/dlartg.cpp @@ -1,13 +1,13 @@ /* fortran/dlartg.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -115,8 +115,8 @@ f"> */ /* > \ingroup OTHERauxiliary */ /* ===================================================================== */ -/* Subroutine */ int dlartg_(doublereal *f, doublereal *g, doublereal *cs, - doublereal *sn, doublereal *r__) +/* Subroutine */ int dlartg_(doublereal *f, doublereal *g, doublereal *cs, + doublereal *sn, doublereal *r__) { /* System generated locals */ integer i__1; @@ -171,81 +171,81 @@ f"> */ /* FIRST = .FALSE. */ /* END IF */ if (*g == 0.) { - *cs = 1.; - *sn = 0.; - *r__ = *f; + *cs = 1.; + *sn = 0.; + *r__ = *f; } else if (*f == 0.) { - *cs = 0.; - *sn = 1.; - *r__ = *g; + *cs = 0.; + *sn = 1.; + *r__ = *g; } else { - f1 = *f; - g1 = *g; + f1 = *f; + g1 = *g; /* Computing MAX */ - d__1 = abs(f1), d__2 = abs(g1); - scale = max(d__1,d__2); - if (scale >= safmx2) { - count = 0; + d__1 = abs(f1), d__2 = abs(g1); + scale = max(d__1,d__2); + if (scale >= safmx2) { + count = 0; L10: - ++count; - f1 *= safmn2; - g1 *= safmn2; + ++count; + f1 *= safmn2; + g1 *= safmn2; /* Computing MAX */ - d__1 = abs(f1), d__2 = abs(g1); - scale = max(d__1,d__2); - if (scale >= safmx2) { - goto L10; - } + d__1 = abs(f1), d__2 = abs(g1); + scale = max(d__1,d__2); + if (scale >= safmx2) { + goto L10; + } /* Computing 2nd power */ - d__1 = f1; + d__1 = f1; /* Computing 2nd power */ - d__2 = g1; - *r__ = sqrt(d__1 * d__1 + d__2 * d__2); - *cs = f1 / *r__; - *sn = g1 / *r__; - i__1 = count; - for (i__ = 1; i__ <= i__1; ++i__) { - *r__ *= safmx2; + d__2 = g1; + *r__ = sqrt(d__1 * d__1 + d__2 * d__2); + *cs = f1 / *r__; + *sn = g1 / *r__; + i__1 = count; + for (i__ = 1; i__ <= i__1; ++i__) { + *r__ *= safmx2; /* L20: */ - } - } else if (scale <= safmn2) { - count = 0; + } + } else if (scale <= safmn2) { + count = 0; L30: - ++count; - f1 *= safmx2; - g1 *= safmx2; + ++count; + f1 *= safmx2; + g1 *= safmx2; /* Computing MAX */ - d__1 = abs(f1), d__2 = abs(g1); - scale = max(d__1,d__2); - if (scale <= safmn2) { - goto L30; - } + d__1 = abs(f1), d__2 = abs(g1); + scale = max(d__1,d__2); + if (scale <= safmn2) { + goto L30; + } /* Computing 2nd power */ - d__1 = f1; + d__1 = f1; /* Computing 2nd power */ - d__2 = g1; - *r__ = sqrt(d__1 * d__1 + d__2 * d__2); - *cs = f1 / *r__; - *sn = g1 / *r__; - i__1 = count; - for (i__ = 1; i__ <= i__1; ++i__) { - *r__ *= safmn2; + d__2 = g1; + *r__ = sqrt(d__1 * d__1 + d__2 * d__2); + *cs = f1 / *r__; + *sn = g1 / *r__; + i__1 = count; + for (i__ = 1; i__ <= i__1; ++i__) { + *r__ *= safmn2; /* L40: */ - } - } else { + } + } else { /* Computing 2nd power */ - d__1 = f1; + d__1 = f1; /* Computing 2nd power */ - d__2 = g1; - *r__ = sqrt(d__1 * d__1 + d__2 * d__2); - *cs = f1 / *r__; - *sn = g1 / *r__; - } - if (abs(*f) > abs(*g) && *cs < 0.) { - *cs = -(*cs); - *sn = -(*sn); - *r__ = -(*r__); - } + d__2 = g1; + *r__ = sqrt(d__1 * d__1 + d__2 * d__2); + *cs = f1 / *r__; + *sn = g1 / *r__; + } + if (abs(*f) > abs(*g) && *cs < 0.) { + *cs = -(*cs); + *sn = -(*sn); + *r__ = -(*r__); + } } return 0; @@ -254,5 +254,5 @@ L30: } /* dlartg_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlas2.cpp b/lib/linalg/dlas2.cpp index e3a53a9bac..c590ed5819 100644 --- a/lib/linalg/dlas2.cpp +++ b/lib/linalg/dlas2.cpp @@ -1,13 +1,13 @@ /* fortran/dlas2.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -123,8 +123,8 @@ extern "C" { /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int dlas2_(doublereal *f, doublereal *g, doublereal *h__, - doublereal *ssmin, doublereal *ssmax) +/* Subroutine */ int dlas2_(doublereal *f, doublereal *g, doublereal *h__, + doublereal *ssmin, doublereal *ssmax) { /* System generated locals */ doublereal d__1, d__2; @@ -159,47 +159,47 @@ extern "C" { fhmn = min(fa,ha); fhmx = max(fa,ha); if (fhmn == 0.) { - *ssmin = 0.; - if (fhmx == 0.) { - *ssmax = ga; - } else { + *ssmin = 0.; + if (fhmx == 0.) { + *ssmax = ga; + } else { /* Computing 2nd power */ - d__1 = min(fhmx,ga) / max(fhmx,ga); - *ssmax = max(fhmx,ga) * sqrt(d__1 * d__1 + 1.); - } + d__1 = min(fhmx,ga) / max(fhmx,ga); + *ssmax = max(fhmx,ga) * sqrt(d__1 * d__1 + 1.); + } } else { - if (ga < fhmx) { - as = fhmn / fhmx + 1.; - at = (fhmx - fhmn) / fhmx; + if (ga < fhmx) { + as = fhmn / fhmx + 1.; + at = (fhmx - fhmn) / fhmx; /* Computing 2nd power */ - d__1 = ga / fhmx; - au = d__1 * d__1; - c__ = 2. / (sqrt(as * as + au) + sqrt(at * at + au)); - *ssmin = fhmn * c__; - *ssmax = fhmx / c__; - } else { - au = fhmx / ga; - if (au == 0.) { + d__1 = ga / fhmx; + au = d__1 * d__1; + c__ = 2. / (sqrt(as * as + au) + sqrt(at * at + au)); + *ssmin = fhmn * c__; + *ssmax = fhmx / c__; + } else { + au = fhmx / ga; + if (au == 0.) { /* Avoid possible harmful underflow if exponent range */ /* asymmetric (true SSMIN may not underflow even if */ /* AU underflows) */ - *ssmin = fhmn * fhmx / ga; - *ssmax = ga; - } else { - as = fhmn / fhmx + 1.; - at = (fhmx - fhmn) / fhmx; + *ssmin = fhmn * fhmx / ga; + *ssmax = ga; + } else { + as = fhmn / fhmx + 1.; + at = (fhmx - fhmn) / fhmx; /* Computing 2nd power */ - d__1 = as * au; + d__1 = as * au; /* Computing 2nd power */ - d__2 = at * au; - c__ = 1. / (sqrt(d__1 * d__1 + 1.) + sqrt(d__2 * d__2 + 1.)); - *ssmin = fhmn * c__ * au; - *ssmin += *ssmin; - *ssmax = ga / (c__ + c__); - } - } + d__2 = at * au; + c__ = 1. / (sqrt(d__1 * d__1 + 1.) + sqrt(d__2 * d__2 + 1.)); + *ssmin = fhmn * c__ * au; + *ssmin += *ssmin; + *ssmax = ga / (c__ + c__); + } + } } return 0; @@ -208,5 +208,5 @@ extern "C" { } /* dlas2_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlascl.cpp b/lib/linalg/dlascl.cpp index 932e1c63cb..7596a5c109 100644 --- a/lib/linalg/dlascl.cpp +++ b/lib/linalg/dlascl.cpp @@ -1,13 +1,13 @@ /* fortran/dlascl.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -159,9 +159,9 @@ f"> */ /* > \ingroup OTHERauxiliary */ /* ===================================================================== */ -/* Subroutine */ int dlascl_(char *type__, integer *kl, integer *ku, - doublereal *cfrom, doublereal *cto, integer *m, integer *n, - doublereal *a, integer *lda, integer *info, ftnlen type_len) +/* Subroutine */ int dlascl_(char *type__, integer *kl, integer *ku, + doublereal *cfrom, doublereal *cto, integer *m, integer *n, + doublereal *a, integer *lda, integer *info, ftnlen type_len) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; @@ -215,63 +215,63 @@ f"> */ *info = 0; if (lsame_(type__, (char *)"G", (ftnlen)1, (ftnlen)1)) { - itype = 0; + itype = 0; } else if (lsame_(type__, (char *)"L", (ftnlen)1, (ftnlen)1)) { - itype = 1; + itype = 1; } else if (lsame_(type__, (char *)"U", (ftnlen)1, (ftnlen)1)) { - itype = 2; + itype = 2; } else if (lsame_(type__, (char *)"H", (ftnlen)1, (ftnlen)1)) { - itype = 3; + itype = 3; } else if (lsame_(type__, (char *)"B", (ftnlen)1, (ftnlen)1)) { - itype = 4; + itype = 4; } else if (lsame_(type__, (char *)"Q", (ftnlen)1, (ftnlen)1)) { - itype = 5; + itype = 5; } else if (lsame_(type__, (char *)"Z", (ftnlen)1, (ftnlen)1)) { - itype = 6; + itype = 6; } else { - itype = -1; + itype = -1; } if (itype == -1) { - *info = -1; + *info = -1; } else if (*cfrom == 0. || disnan_(cfrom)) { - *info = -4; + *info = -4; } else if (disnan_(cto)) { - *info = -5; + *info = -5; } else if (*m < 0) { - *info = -6; + *info = -6; } else if (*n < 0 || itype == 4 && *n != *m || itype == 5 && *n != *m) { - *info = -7; + *info = -7; } else if (itype <= 3 && *lda < max(1,*m)) { - *info = -9; + *info = -9; } else if (itype >= 4) { /* Computing MAX */ - i__1 = *m - 1; - if (*kl < 0 || *kl > max(i__1,0)) { - *info = -2; - } else /* if(complicated condition) */ { + i__1 = *m - 1; + if (*kl < 0 || *kl > max(i__1,0)) { + *info = -2; + } else /* if(complicated condition) */ { /* Computing MAX */ - i__1 = *n - 1; - if (*ku < 0 || *ku > max(i__1,0) || (itype == 4 || itype == 5) && - *kl != *ku) { - *info = -3; - } else if (itype == 4 && *lda < *kl + 1 || itype == 5 && *lda < * - ku + 1 || itype == 6 && *lda < (*kl << 1) + *ku + 1) { - *info = -9; - } - } + i__1 = *n - 1; + if (*ku < 0 || *ku > max(i__1,0) || (itype == 4 || itype == 5) && + *kl != *ku) { + *info = -3; + } else if (itype == 4 && *lda < *kl + 1 || itype == 5 && *lda < * + ku + 1 || itype == 6 && *lda < (*kl << 1) + *ku + 1) { + *info = -9; + } + } } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DLASCL", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DLASCL", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*n == 0 || *m == 0) { - return 0; + return 0; } /* Get machine parameters */ @@ -287,154 +287,154 @@ L10: if (cfrom1 == cfromc) { /* CFROMC is an inf. Multiply by a correctly signed zero for */ /* finite CTOC, or a NaN if CTOC is infinite. */ - mul = ctoc / cfromc; - done = TRUE_; - cto1 = ctoc; + mul = ctoc / cfromc; + done = TRUE_; + cto1 = ctoc; } else { - cto1 = ctoc / bignum; - if (cto1 == ctoc) { + cto1 = ctoc / bignum; + if (cto1 == ctoc) { /* CTOC is either 0 or an inf. In both cases, CTOC itself */ /* serves as the correct multiplication factor. */ - mul = ctoc; - done = TRUE_; - cfromc = 1.; - } else if (abs(cfrom1) > abs(ctoc) && ctoc != 0.) { - mul = smlnum; - done = FALSE_; - cfromc = cfrom1; - } else if (abs(cto1) > abs(cfromc)) { - mul = bignum; - done = FALSE_; - ctoc = cto1; - } else { - mul = ctoc / cfromc; - done = TRUE_; - if (mul == 1.) { - return 0; - } - } + mul = ctoc; + done = TRUE_; + cfromc = 1.; + } else if (abs(cfrom1) > abs(ctoc) && ctoc != 0.) { + mul = smlnum; + done = FALSE_; + cfromc = cfrom1; + } else if (abs(cto1) > abs(cfromc)) { + mul = bignum; + done = FALSE_; + ctoc = cto1; + } else { + mul = ctoc / cfromc; + done = TRUE_; + if (mul == 1.) { + return 0; + } + } } if (itype == 0) { /* Full matrix */ - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - a[i__ + j * a_dim1] *= mul; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] *= mul; /* L20: */ - } + } /* L30: */ - } + } } else if (itype == 1) { /* Lower triangular matrix */ - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = j; i__ <= i__2; ++i__) { - a[i__ + j * a_dim1] *= mul; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = j; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] *= mul; /* L40: */ - } + } /* L50: */ - } + } } else if (itype == 2) { /* Upper triangular matrix */ - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = min(j,*m); - for (i__ = 1; i__ <= i__2; ++i__) { - a[i__ + j * a_dim1] *= mul; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = min(j,*m); + for (i__ = 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] *= mul; /* L60: */ - } + } /* L70: */ - } + } } else if (itype == 3) { /* Upper Hessenberg matrix */ - i__1 = *n; - for (j = 1; j <= i__1; ++j) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { /* Computing MIN */ - i__3 = j + 1; - i__2 = min(i__3,*m); - for (i__ = 1; i__ <= i__2; ++i__) { - a[i__ + j * a_dim1] *= mul; + i__3 = j + 1; + i__2 = min(i__3,*m); + for (i__ = 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] *= mul; /* L80: */ - } + } /* L90: */ - } + } } else if (itype == 4) { /* Lower half of a symmetric band matrix */ - k3 = *kl + 1; - k4 = *n + 1; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { + k3 = *kl + 1; + k4 = *n + 1; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { /* Computing MIN */ - i__3 = k3, i__4 = k4 - j; - i__2 = min(i__3,i__4); - for (i__ = 1; i__ <= i__2; ++i__) { - a[i__ + j * a_dim1] *= mul; + i__3 = k3, i__4 = k4 - j; + i__2 = min(i__3,i__4); + for (i__ = 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] *= mul; /* L100: */ - } + } /* L110: */ - } + } } else if (itype == 5) { /* Upper half of a symmetric band matrix */ - k1 = *ku + 2; - k3 = *ku + 1; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { + k1 = *ku + 2; + k3 = *ku + 1; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { /* Computing MAX */ - i__2 = k1 - j; - i__3 = k3; - for (i__ = max(i__2,1); i__ <= i__3; ++i__) { - a[i__ + j * a_dim1] *= mul; + i__2 = k1 - j; + i__3 = k3; + for (i__ = max(i__2,1); i__ <= i__3; ++i__) { + a[i__ + j * a_dim1] *= mul; /* L120: */ - } + } /* L130: */ - } + } } else if (itype == 6) { /* Band matrix */ - k1 = *kl + *ku + 2; - k2 = *kl + 1; - k3 = (*kl << 1) + *ku + 1; - k4 = *kl + *ku + 1 + *m; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { + k1 = *kl + *ku + 2; + k2 = *kl + 1; + k3 = (*kl << 1) + *ku + 1; + k4 = *kl + *ku + 1 + *m; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { /* Computing MAX */ - i__3 = k1 - j; + i__3 = k1 - j; /* Computing MIN */ - i__4 = k3, i__5 = k4 - j; - i__2 = min(i__4,i__5); - for (i__ = max(i__3,k2); i__ <= i__2; ++i__) { - a[i__ + j * a_dim1] *= mul; + i__4 = k3, i__5 = k4 - j; + i__2 = min(i__4,i__5); + for (i__ = max(i__3,k2); i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] *= mul; /* L140: */ - } + } /* L150: */ - } + } } if (! done) { - goto L10; + goto L10; } return 0; @@ -444,5 +444,5 @@ L10: } /* dlascl_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlasd4.cpp b/lib/linalg/dlasd4.cpp index b0d8d1f7fe..e7922d1199 100644 --- a/lib/linalg/dlasd4.cpp +++ b/lib/linalg/dlasd4.cpp @@ -1,13 +1,13 @@ /* fortran/dlasd4.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -170,9 +170,9 @@ f"> */ /* > at Berkeley, USA */ /* > */ /* ===================================================================== */ -/* Subroutine */ int dlasd4_(integer *n, integer *i__, doublereal *d__, - doublereal *z__, doublereal *delta, doublereal *rho, doublereal * - sigma, doublereal *work, integer *info) +/* Subroutine */ int dlasd4_(integer *n, integer *i__, doublereal *d__, + doublereal *z__, doublereal *delta, doublereal *rho, doublereal * + sigma, doublereal *work, integer *info) { /* System generated locals */ integer i__1; @@ -197,10 +197,10 @@ f"> */ doublereal dtisq; logical swtch; doublereal dtnsq; - extern /* Subroutine */ int dlaed6_(integer *, logical *, doublereal *, - doublereal *, doublereal *, doublereal *, doublereal *, integer *) - , dlasd5_(integer *, doublereal *, doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *); + extern /* Subroutine */ int dlaed6_(integer *, logical *, doublereal *, + doublereal *, doublereal *, doublereal *, doublereal *, integer *) + , dlasd5_(integer *, doublereal *, doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *); doublereal delsq2, dtnsq1; logical swtch3; extern doublereal dlamch_(char *, ftnlen); @@ -251,14 +251,14 @@ f"> */ /* Presumably, I=1 upon entry */ - *sigma = sqrt(d__[1] * d__[1] + *rho * z__[1] * z__[1]); - delta[1] = 1.; - work[1] = 1.; - return 0; + *sigma = sqrt(d__[1] * d__[1] + *rho * z__[1] * z__[1]); + delta[1] = 1.; + work[1] = 1.; + return 0; } if (*n == 2) { - dlasd5_(i__, &d__[1], &z__[1], &delta[1], rho, sigma, &work[1]); - return 0; + dlasd5_(i__, &d__[1], &z__[1], &delta[1], rho, sigma, &work[1]); + return 0; } /* Compute machine epsilon */ @@ -273,145 +273,145 @@ f"> */ /* Initialize some basic variables */ - ii = *n - 1; - niter = 1; + ii = *n - 1; + niter = 1; /* Calculate initial guess */ - temp = *rho / 2.; + temp = *rho / 2.; /* If ||Z||_2 is not one, then TEMP should be set to */ /* RHO * ||Z||_2^2 / TWO */ - temp1 = temp / (d__[*n] + sqrt(d__[*n] * d__[*n] + temp)); - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - work[j] = d__[j] + d__[*n] + temp1; - delta[j] = d__[j] - d__[*n] - temp1; + temp1 = temp / (d__[*n] + sqrt(d__[*n] * d__[*n] + temp)); + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + work[j] = d__[j] + d__[*n] + temp1; + delta[j] = d__[j] - d__[*n] - temp1; /* L10: */ - } + } - psi = 0.; - i__1 = *n - 2; - for (j = 1; j <= i__1; ++j) { - psi += z__[j] * z__[j] / (delta[j] * work[j]); + psi = 0.; + i__1 = *n - 2; + for (j = 1; j <= i__1; ++j) { + psi += z__[j] * z__[j] / (delta[j] * work[j]); /* L20: */ - } + } - c__ = rhoinv + psi; - w = c__ + z__[ii] * z__[ii] / (delta[ii] * work[ii]) + z__[*n] * z__[* - n] / (delta[*n] * work[*n]); + c__ = rhoinv + psi; + w = c__ + z__[ii] * z__[ii] / (delta[ii] * work[ii]) + z__[*n] * z__[* + n] / (delta[*n] * work[*n]); - if (w <= 0.) { - temp1 = sqrt(d__[*n] * d__[*n] + *rho); - temp = z__[*n - 1] * z__[*n - 1] / ((d__[*n - 1] + temp1) * (d__[* - n] - d__[*n - 1] + *rho / (d__[*n] + temp1))) + z__[*n] * - z__[*n] / *rho; + if (w <= 0.) { + temp1 = sqrt(d__[*n] * d__[*n] + *rho); + temp = z__[*n - 1] * z__[*n - 1] / ((d__[*n - 1] + temp1) * (d__[* + n] - d__[*n - 1] + *rho / (d__[*n] + temp1))) + z__[*n] * + z__[*n] / *rho; /* The following TAU2 is to approximate */ /* SIGMA_n^2 - D( N )*D( N ) */ - if (c__ <= temp) { - tau = *rho; - } else { - delsq = (d__[*n] - d__[*n - 1]) * (d__[*n] + d__[*n - 1]); - a = -c__ * delsq + z__[*n - 1] * z__[*n - 1] + z__[*n] * z__[* - n]; - b = z__[*n] * z__[*n] * delsq; - if (a < 0.) { - tau2 = b * 2. / (sqrt(a * a + b * 4. * c__) - a); - } else { - tau2 = (a + sqrt(a * a + b * 4. * c__)) / (c__ * 2.); - } - tau = tau2 / (d__[*n] + sqrt(d__[*n] * d__[*n] + tau2)); - } + if (c__ <= temp) { + tau = *rho; + } else { + delsq = (d__[*n] - d__[*n - 1]) * (d__[*n] + d__[*n - 1]); + a = -c__ * delsq + z__[*n - 1] * z__[*n - 1] + z__[*n] * z__[* + n]; + b = z__[*n] * z__[*n] * delsq; + if (a < 0.) { + tau2 = b * 2. / (sqrt(a * a + b * 4. * c__) - a); + } else { + tau2 = (a + sqrt(a * a + b * 4. * c__)) / (c__ * 2.); + } + tau = tau2 / (d__[*n] + sqrt(d__[*n] * d__[*n] + tau2)); + } /* It can be proved that */ /* D(N)^2+RHO/2 <= SIGMA_n^2 < D(N)^2+TAU2 <= D(N)^2+RHO */ - } else { - delsq = (d__[*n] - d__[*n - 1]) * (d__[*n] + d__[*n - 1]); - a = -c__ * delsq + z__[*n - 1] * z__[*n - 1] + z__[*n] * z__[*n]; - b = z__[*n] * z__[*n] * delsq; + } else { + delsq = (d__[*n] - d__[*n - 1]) * (d__[*n] + d__[*n - 1]); + a = -c__ * delsq + z__[*n - 1] * z__[*n - 1] + z__[*n] * z__[*n]; + b = z__[*n] * z__[*n] * delsq; /* The following TAU2 is to approximate */ /* SIGMA_n^2 - D( N )*D( N ) */ - if (a < 0.) { - tau2 = b * 2. / (sqrt(a * a + b * 4. * c__) - a); - } else { - tau2 = (a + sqrt(a * a + b * 4. * c__)) / (c__ * 2.); - } - tau = tau2 / (d__[*n] + sqrt(d__[*n] * d__[*n] + tau2)); + if (a < 0.) { + tau2 = b * 2. / (sqrt(a * a + b * 4. * c__) - a); + } else { + tau2 = (a + sqrt(a * a + b * 4. * c__)) / (c__ * 2.); + } + tau = tau2 / (d__[*n] + sqrt(d__[*n] * d__[*n] + tau2)); /* It can be proved that */ /* D(N)^2 < D(N)^2+TAU2 < SIGMA(N)^2 < D(N)^2+RHO/2 */ - } + } /* The following TAU is to approximate SIGMA_n - D( N ) */ /* TAU = TAU2 / ( D( N )+SQRT( D( N )*D( N )+TAU2 ) ) */ - *sigma = d__[*n] + tau; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - delta[j] = d__[j] - d__[*n] - tau; - work[j] = d__[j] + d__[*n] + tau; + *sigma = d__[*n] + tau; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + delta[j] = d__[j] - d__[*n] - tau; + work[j] = d__[j] + d__[*n] + tau; /* L30: */ - } + } /* Evaluate PSI and the derivative DPSI */ - dpsi = 0.; - psi = 0.; - erretm = 0.; - i__1 = ii; - for (j = 1; j <= i__1; ++j) { - temp = z__[j] / (delta[j] * work[j]); - psi += z__[j] * temp; - dpsi += temp * temp; - erretm += psi; + dpsi = 0.; + psi = 0.; + erretm = 0.; + i__1 = ii; + for (j = 1; j <= i__1; ++j) { + temp = z__[j] / (delta[j] * work[j]); + psi += z__[j] * temp; + dpsi += temp * temp; + erretm += psi; /* L40: */ - } - erretm = abs(erretm); + } + erretm = abs(erretm); /* Evaluate PHI and the derivative DPHI */ - temp = z__[*n] / (delta[*n] * work[*n]); - phi = z__[*n] * temp; - dphi = temp * temp; - erretm = (-phi - psi) * 8. + erretm - phi + rhoinv; + temp = z__[*n] / (delta[*n] * work[*n]); + phi = z__[*n] * temp; + dphi = temp * temp; + erretm = (-phi - psi) * 8. + erretm - phi + rhoinv; /* $ + ABS( TAU2 )*( DPSI+DPHI ) */ - w = rhoinv + phi + psi; + w = rhoinv + phi + psi; /* Test for convergence */ - if (abs(w) <= eps * erretm) { - goto L240; - } + if (abs(w) <= eps * erretm) { + goto L240; + } /* Calculate the new step */ - ++niter; - dtnsq1 = work[*n - 1] * delta[*n - 1]; - dtnsq = work[*n] * delta[*n]; - c__ = w - dtnsq1 * dpsi - dtnsq * dphi; - a = (dtnsq + dtnsq1) * w - dtnsq * dtnsq1 * (dpsi + dphi); - b = dtnsq * dtnsq1 * w; - if (c__ < 0.) { - c__ = abs(c__); - } - if (c__ == 0.) { - eta = *rho - *sigma * *sigma; - } else if (a >= 0.) { - eta = (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (c__ - * 2.); - } else { - eta = b * 2. / (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1))) - ); - } + ++niter; + dtnsq1 = work[*n - 1] * delta[*n - 1]; + dtnsq = work[*n] * delta[*n]; + c__ = w - dtnsq1 * dpsi - dtnsq * dphi; + a = (dtnsq + dtnsq1) * w - dtnsq * dtnsq1 * (dpsi + dphi); + b = dtnsq * dtnsq1 * w; + if (c__ < 0.) { + c__ = abs(c__); + } + if (c__ == 0.) { + eta = *rho - *sigma * *sigma; + } else if (a >= 0.) { + eta = (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (c__ + * 2.); + } else { + eta = b * 2. / (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1))) + ); + } /* Note, eta should be positive if w is negative, and */ /* eta should be negative otherwise. However, */ @@ -419,77 +419,77 @@ f"> */ /* we simply use one Newton step instead. This way */ /* will guarantee eta*w < 0. */ - if (w * eta > 0.) { - eta = -w / (dpsi + dphi); - } - temp = eta - dtnsq; - if (temp > *rho) { - eta = *rho + dtnsq; - } + if (w * eta > 0.) { + eta = -w / (dpsi + dphi); + } + temp = eta - dtnsq; + if (temp > *rho) { + eta = *rho + dtnsq; + } - eta /= *sigma + sqrt(eta + *sigma * *sigma); - tau += eta; - *sigma += eta; + eta /= *sigma + sqrt(eta + *sigma * *sigma); + tau += eta; + *sigma += eta; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - delta[j] -= eta; - work[j] += eta; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + delta[j] -= eta; + work[j] += eta; /* L50: */ - } + } /* Evaluate PSI and the derivative DPSI */ - dpsi = 0.; - psi = 0.; - erretm = 0.; - i__1 = ii; - for (j = 1; j <= i__1; ++j) { - temp = z__[j] / (work[j] * delta[j]); - psi += z__[j] * temp; - dpsi += temp * temp; - erretm += psi; + dpsi = 0.; + psi = 0.; + erretm = 0.; + i__1 = ii; + for (j = 1; j <= i__1; ++j) { + temp = z__[j] / (work[j] * delta[j]); + psi += z__[j] * temp; + dpsi += temp * temp; + erretm += psi; /* L60: */ - } - erretm = abs(erretm); + } + erretm = abs(erretm); /* Evaluate PHI and the derivative DPHI */ - tau2 = work[*n] * delta[*n]; - temp = z__[*n] / tau2; - phi = z__[*n] * temp; - dphi = temp * temp; - erretm = (-phi - psi) * 8. + erretm - phi + rhoinv; + tau2 = work[*n] * delta[*n]; + temp = z__[*n] / tau2; + phi = z__[*n] * temp; + dphi = temp * temp; + erretm = (-phi - psi) * 8. + erretm - phi + rhoinv; /* $ + ABS( TAU2 )*( DPSI+DPHI ) */ - w = rhoinv + phi + psi; + w = rhoinv + phi + psi; /* Main loop to update the values of the array DELTA */ - iter = niter + 1; + iter = niter + 1; - for (niter = iter; niter <= 400; ++niter) { + for (niter = iter; niter <= 400; ++niter) { /* Test for convergence */ - if (abs(w) <= eps * erretm) { - goto L240; - } + if (abs(w) <= eps * erretm) { + goto L240; + } /* Calculate the new step */ - dtnsq1 = work[*n - 1] * delta[*n - 1]; - dtnsq = work[*n] * delta[*n]; - c__ = w - dtnsq1 * dpsi - dtnsq * dphi; - a = (dtnsq + dtnsq1) * w - dtnsq1 * dtnsq * (dpsi + dphi); - b = dtnsq1 * dtnsq * w; - if (a >= 0.) { - eta = (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / ( - c__ * 2.); - } else { - eta = b * 2. / (a - sqrt((d__1 = a * a - b * 4. * c__, abs( - d__1)))); - } + dtnsq1 = work[*n - 1] * delta[*n - 1]; + dtnsq = work[*n] * delta[*n]; + c__ = w - dtnsq1 * dpsi - dtnsq * dphi; + a = (dtnsq + dtnsq1) * w - dtnsq1 * dtnsq * (dpsi + dphi); + b = dtnsq1 * dtnsq * w; + if (a >= 0.) { + eta = (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / ( + c__ * 2.); + } else { + eta = b * 2. / (a - sqrt((d__1 = a * a - b * 4. * c__, abs( + d__1)))); + } /* Note, eta should be positive if w is negative, and */ /* eta should be negative otherwise. However, */ @@ -497,57 +497,57 @@ f"> */ /* we simply use one Newton step instead. This way */ /* will guarantee eta*w < 0. */ - if (w * eta > 0.) { - eta = -w / (dpsi + dphi); - } - temp = eta - dtnsq; - if (temp <= 0.) { - eta /= 2.; - } + if (w * eta > 0.) { + eta = -w / (dpsi + dphi); + } + temp = eta - dtnsq; + if (temp <= 0.) { + eta /= 2.; + } - eta /= *sigma + sqrt(eta + *sigma * *sigma); - tau += eta; - *sigma += eta; + eta /= *sigma + sqrt(eta + *sigma * *sigma); + tau += eta; + *sigma += eta; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - delta[j] -= eta; - work[j] += eta; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + delta[j] -= eta; + work[j] += eta; /* L70: */ - } + } /* Evaluate PSI and the derivative DPSI */ - dpsi = 0.; - psi = 0.; - erretm = 0.; - i__1 = ii; - for (j = 1; j <= i__1; ++j) { - temp = z__[j] / (work[j] * delta[j]); - psi += z__[j] * temp; - dpsi += temp * temp; - erretm += psi; + dpsi = 0.; + psi = 0.; + erretm = 0.; + i__1 = ii; + for (j = 1; j <= i__1; ++j) { + temp = z__[j] / (work[j] * delta[j]); + psi += z__[j] * temp; + dpsi += temp * temp; + erretm += psi; /* L80: */ - } - erretm = abs(erretm); + } + erretm = abs(erretm); /* Evaluate PHI and the derivative DPHI */ - tau2 = work[*n] * delta[*n]; - temp = z__[*n] / tau2; - phi = z__[*n] * temp; - dphi = temp * temp; - erretm = (-phi - psi) * 8. + erretm - phi + rhoinv; + tau2 = work[*n] * delta[*n]; + temp = z__[*n] / tau2; + phi = z__[*n] * temp; + dphi = temp * temp; + erretm = (-phi - psi) * 8. + erretm - phi + rhoinv; /* $ + ABS( TAU2 )*( DPSI+DPHI ) */ - w = rhoinv + phi + psi; + w = rhoinv + phi + psi; /* L90: */ - } + } /* Return with INFO = 1, NITER = MAXIT and not converged */ - *info = 1; - goto L240; + *info = 1; + goto L240; /* End for the case I = N */ @@ -555,288 +555,288 @@ f"> */ /* The case for I < N */ - niter = 1; - ip1 = *i__ + 1; + niter = 1; + ip1 = *i__ + 1; /* Calculate initial guess */ - delsq = (d__[ip1] - d__[*i__]) * (d__[ip1] + d__[*i__]); - delsq2 = delsq / 2.; - sq2 = sqrt((d__[*i__] * d__[*i__] + d__[ip1] * d__[ip1]) / 2.); - temp = delsq2 / (d__[*i__] + sq2); - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - work[j] = d__[j] + d__[*i__] + temp; - delta[j] = d__[j] - d__[*i__] - temp; + delsq = (d__[ip1] - d__[*i__]) * (d__[ip1] + d__[*i__]); + delsq2 = delsq / 2.; + sq2 = sqrt((d__[*i__] * d__[*i__] + d__[ip1] * d__[ip1]) / 2.); + temp = delsq2 / (d__[*i__] + sq2); + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + work[j] = d__[j] + d__[*i__] + temp; + delta[j] = d__[j] - d__[*i__] - temp; /* L100: */ - } + } - psi = 0.; - i__1 = *i__ - 1; - for (j = 1; j <= i__1; ++j) { - psi += z__[j] * z__[j] / (work[j] * delta[j]); + psi = 0.; + i__1 = *i__ - 1; + for (j = 1; j <= i__1; ++j) { + psi += z__[j] * z__[j] / (work[j] * delta[j]); /* L110: */ - } + } - phi = 0.; - i__1 = *i__ + 2; - for (j = *n; j >= i__1; --j) { - phi += z__[j] * z__[j] / (work[j] * delta[j]); + phi = 0.; + i__1 = *i__ + 2; + for (j = *n; j >= i__1; --j) { + phi += z__[j] * z__[j] / (work[j] * delta[j]); /* L120: */ - } - c__ = rhoinv + psi + phi; - w = c__ + z__[*i__] * z__[*i__] / (work[*i__] * delta[*i__]) + z__[ - ip1] * z__[ip1] / (work[ip1] * delta[ip1]); + } + c__ = rhoinv + psi + phi; + w = c__ + z__[*i__] * z__[*i__] / (work[*i__] * delta[*i__]) + z__[ + ip1] * z__[ip1] / (work[ip1] * delta[ip1]); - geomavg = FALSE_; - if (w > 0.) { + geomavg = FALSE_; + if (w > 0.) { /* d(i)^2 < the ith sigma^2 < (d(i)^2+d(i+1)^2)/2 */ /* We choose d(i) as origin. */ - orgati = TRUE_; - ii = *i__; - sglb = 0.; - sgub = delsq2 / (d__[*i__] + sq2); - a = c__ * delsq + z__[*i__] * z__[*i__] + z__[ip1] * z__[ip1]; - b = z__[*i__] * z__[*i__] * delsq; - if (a > 0.) { - tau2 = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs( - d__1)))); - } else { - tau2 = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / - (c__ * 2.); - } + orgati = TRUE_; + ii = *i__; + sglb = 0.; + sgub = delsq2 / (d__[*i__] + sq2); + a = c__ * delsq + z__[*i__] * z__[*i__] + z__[ip1] * z__[ip1]; + b = z__[*i__] * z__[*i__] * delsq; + if (a > 0.) { + tau2 = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs( + d__1)))); + } else { + tau2 = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / + (c__ * 2.); + } /* TAU2 now is an estimation of SIGMA^2 - D( I )^2. The */ /* following, however, is the corresponding estimation of */ /* SIGMA - D( I ). */ - tau = tau2 / (d__[*i__] + sqrt(d__[*i__] * d__[*i__] + tau2)); - temp = sqrt(eps); - if (d__[*i__] <= temp * d__[ip1] && (d__1 = z__[*i__], abs(d__1)) - <= temp && d__[*i__] > 0.) { + tau = tau2 / (d__[*i__] + sqrt(d__[*i__] * d__[*i__] + tau2)); + temp = sqrt(eps); + if (d__[*i__] <= temp * d__[ip1] && (d__1 = z__[*i__], abs(d__1)) + <= temp && d__[*i__] > 0.) { /* Computing MIN */ - d__1 = d__[*i__] * 10.; - tau = min(d__1,sgub); - geomavg = TRUE_; - } - } else { + d__1 = d__[*i__] * 10.; + tau = min(d__1,sgub); + geomavg = TRUE_; + } + } else { /* (d(i)^2+d(i+1)^2)/2 <= the ith sigma^2 < d(i+1)^2/2 */ /* We choose d(i+1) as origin. */ - orgati = FALSE_; - ii = ip1; - sglb = -delsq2 / (d__[ii] + sq2); - sgub = 0.; - a = c__ * delsq - z__[*i__] * z__[*i__] - z__[ip1] * z__[ip1]; - b = z__[ip1] * z__[ip1] * delsq; - if (a < 0.) { - tau2 = b * 2. / (a - sqrt((d__1 = a * a + b * 4. * c__, abs( - d__1)))); - } else { - tau2 = -(a + sqrt((d__1 = a * a + b * 4. * c__, abs(d__1)))) / - (c__ * 2.); - } + orgati = FALSE_; + ii = ip1; + sglb = -delsq2 / (d__[ii] + sq2); + sgub = 0.; + a = c__ * delsq - z__[*i__] * z__[*i__] - z__[ip1] * z__[ip1]; + b = z__[ip1] * z__[ip1] * delsq; + if (a < 0.) { + tau2 = b * 2. / (a - sqrt((d__1 = a * a + b * 4. * c__, abs( + d__1)))); + } else { + tau2 = -(a + sqrt((d__1 = a * a + b * 4. * c__, abs(d__1)))) / + (c__ * 2.); + } /* TAU2 now is an estimation of SIGMA^2 - D( IP1 )^2. The */ /* following, however, is the corresponding estimation of */ /* SIGMA - D( IP1 ). */ - tau = tau2 / (d__[ip1] + sqrt((d__1 = d__[ip1] * d__[ip1] + tau2, - abs(d__1)))); - } + tau = tau2 / (d__[ip1] + sqrt((d__1 = d__[ip1] * d__[ip1] + tau2, + abs(d__1)))); + } - *sigma = d__[ii] + tau; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - work[j] = d__[j] + d__[ii] + tau; - delta[j] = d__[j] - d__[ii] - tau; + *sigma = d__[ii] + tau; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + work[j] = d__[j] + d__[ii] + tau; + delta[j] = d__[j] - d__[ii] - tau; /* L130: */ - } - iim1 = ii - 1; - iip1 = ii + 1; + } + iim1 = ii - 1; + iip1 = ii + 1; /* Evaluate PSI and the derivative DPSI */ - dpsi = 0.; - psi = 0.; - erretm = 0.; - i__1 = iim1; - for (j = 1; j <= i__1; ++j) { - temp = z__[j] / (work[j] * delta[j]); - psi += z__[j] * temp; - dpsi += temp * temp; - erretm += psi; + dpsi = 0.; + psi = 0.; + erretm = 0.; + i__1 = iim1; + for (j = 1; j <= i__1; ++j) { + temp = z__[j] / (work[j] * delta[j]); + psi += z__[j] * temp; + dpsi += temp * temp; + erretm += psi; /* L150: */ - } - erretm = abs(erretm); + } + erretm = abs(erretm); /* Evaluate PHI and the derivative DPHI */ - dphi = 0.; - phi = 0.; - i__1 = iip1; - for (j = *n; j >= i__1; --j) { - temp = z__[j] / (work[j] * delta[j]); - phi += z__[j] * temp; - dphi += temp * temp; - erretm += phi; + dphi = 0.; + phi = 0.; + i__1 = iip1; + for (j = *n; j >= i__1; --j) { + temp = z__[j] / (work[j] * delta[j]); + phi += z__[j] * temp; + dphi += temp * temp; + erretm += phi; /* L160: */ - } + } - w = rhoinv + phi + psi; + w = rhoinv + phi + psi; /* W is the value of the secular function with */ /* its ii-th element removed. */ - swtch3 = FALSE_; - if (orgati) { - if (w < 0.) { - swtch3 = TRUE_; - } - } else { - if (w > 0.) { - swtch3 = TRUE_; - } - } - if (ii == 1 || ii == *n) { - swtch3 = FALSE_; - } + swtch3 = FALSE_; + if (orgati) { + if (w < 0.) { + swtch3 = TRUE_; + } + } else { + if (w > 0.) { + swtch3 = TRUE_; + } + } + if (ii == 1 || ii == *n) { + swtch3 = FALSE_; + } - temp = z__[ii] / (work[ii] * delta[ii]); - dw = dpsi + dphi + temp * temp; - temp = z__[ii] * temp; - w += temp; - erretm = (phi - psi) * 8. + erretm + rhoinv * 2. + abs(temp) * 3.; + temp = z__[ii] / (work[ii] * delta[ii]); + dw = dpsi + dphi + temp * temp; + temp = z__[ii] * temp; + w += temp; + erretm = (phi - psi) * 8. + erretm + rhoinv * 2. + abs(temp) * 3.; /* $ + ABS( TAU2 )*DW */ /* Test for convergence */ - if (abs(w) <= eps * erretm) { - goto L240; - } + if (abs(w) <= eps * erretm) { + goto L240; + } - if (w <= 0.) { - sglb = max(sglb,tau); - } else { - sgub = min(sgub,tau); - } + if (w <= 0.) { + sglb = max(sglb,tau); + } else { + sgub = min(sgub,tau); + } /* Calculate the new step */ - ++niter; - if (! swtch3) { - dtipsq = work[ip1] * delta[ip1]; - dtisq = work[*i__] * delta[*i__]; - if (orgati) { + ++niter; + if (! swtch3) { + dtipsq = work[ip1] * delta[ip1]; + dtisq = work[*i__] * delta[*i__]; + if (orgati) { /* Computing 2nd power */ - d__1 = z__[*i__] / dtisq; - c__ = w - dtipsq * dw + delsq * (d__1 * d__1); - } else { + d__1 = z__[*i__] / dtisq; + c__ = w - dtipsq * dw + delsq * (d__1 * d__1); + } else { /* Computing 2nd power */ - d__1 = z__[ip1] / dtipsq; - c__ = w - dtisq * dw - delsq * (d__1 * d__1); - } - a = (dtipsq + dtisq) * w - dtipsq * dtisq * dw; - b = dtipsq * dtisq * w; - if (c__ == 0.) { - if (a == 0.) { - if (orgati) { - a = z__[*i__] * z__[*i__] + dtipsq * dtipsq * (dpsi + - dphi); - } else { - a = z__[ip1] * z__[ip1] + dtisq * dtisq * (dpsi + - dphi); - } - } - eta = b / a; - } else if (a <= 0.) { - eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / ( - c__ * 2.); - } else { - eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs( - d__1)))); - } - } else { + d__1 = z__[ip1] / dtipsq; + c__ = w - dtisq * dw - delsq * (d__1 * d__1); + } + a = (dtipsq + dtisq) * w - dtipsq * dtisq * dw; + b = dtipsq * dtisq * w; + if (c__ == 0.) { + if (a == 0.) { + if (orgati) { + a = z__[*i__] * z__[*i__] + dtipsq * dtipsq * (dpsi + + dphi); + } else { + a = z__[ip1] * z__[ip1] + dtisq * dtisq * (dpsi + + dphi); + } + } + eta = b / a; + } else if (a <= 0.) { + eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / ( + c__ * 2.); + } else { + eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs( + d__1)))); + } + } else { /* Interpolation using THREE most relevant poles */ - dtiim = work[iim1] * delta[iim1]; - dtiip = work[iip1] * delta[iip1]; - temp = rhoinv + psi + phi; - if (orgati) { - temp1 = z__[iim1] / dtiim; - temp1 *= temp1; - c__ = temp - dtiip * (dpsi + dphi) - (d__[iim1] - d__[iip1]) * - (d__[iim1] + d__[iip1]) * temp1; - zz[0] = z__[iim1] * z__[iim1]; - if (dpsi < temp1) { - zz[2] = dtiip * dtiip * dphi; - } else { - zz[2] = dtiip * dtiip * (dpsi - temp1 + dphi); - } - } else { - temp1 = z__[iip1] / dtiip; - temp1 *= temp1; - c__ = temp - dtiim * (dpsi + dphi) - (d__[iip1] - d__[iim1]) * - (d__[iim1] + d__[iip1]) * temp1; - if (dphi < temp1) { - zz[0] = dtiim * dtiim * dpsi; - } else { - zz[0] = dtiim * dtiim * (dpsi + (dphi - temp1)); - } - zz[2] = z__[iip1] * z__[iip1]; - } - zz[1] = z__[ii] * z__[ii]; - dd[0] = dtiim; - dd[1] = delta[ii] * work[ii]; - dd[2] = dtiip; - dlaed6_(&niter, &orgati, &c__, dd, zz, &w, &eta, info); + dtiim = work[iim1] * delta[iim1]; + dtiip = work[iip1] * delta[iip1]; + temp = rhoinv + psi + phi; + if (orgati) { + temp1 = z__[iim1] / dtiim; + temp1 *= temp1; + c__ = temp - dtiip * (dpsi + dphi) - (d__[iim1] - d__[iip1]) * + (d__[iim1] + d__[iip1]) * temp1; + zz[0] = z__[iim1] * z__[iim1]; + if (dpsi < temp1) { + zz[2] = dtiip * dtiip * dphi; + } else { + zz[2] = dtiip * dtiip * (dpsi - temp1 + dphi); + } + } else { + temp1 = z__[iip1] / dtiip; + temp1 *= temp1; + c__ = temp - dtiim * (dpsi + dphi) - (d__[iip1] - d__[iim1]) * + (d__[iim1] + d__[iip1]) * temp1; + if (dphi < temp1) { + zz[0] = dtiim * dtiim * dpsi; + } else { + zz[0] = dtiim * dtiim * (dpsi + (dphi - temp1)); + } + zz[2] = z__[iip1] * z__[iip1]; + } + zz[1] = z__[ii] * z__[ii]; + dd[0] = dtiim; + dd[1] = delta[ii] * work[ii]; + dd[2] = dtiip; + dlaed6_(&niter, &orgati, &c__, dd, zz, &w, &eta, info); - if (*info != 0) { + if (*info != 0) { /* If INFO is not 0, i.e., DLAED6 failed, switch back */ /* to 2 pole interpolation. */ - swtch3 = FALSE_; - *info = 0; - dtipsq = work[ip1] * delta[ip1]; - dtisq = work[*i__] * delta[*i__]; - if (orgati) { + swtch3 = FALSE_; + *info = 0; + dtipsq = work[ip1] * delta[ip1]; + dtisq = work[*i__] * delta[*i__]; + if (orgati) { /* Computing 2nd power */ - d__1 = z__[*i__] / dtisq; - c__ = w - dtipsq * dw + delsq * (d__1 * d__1); - } else { + d__1 = z__[*i__] / dtisq; + c__ = w - dtipsq * dw + delsq * (d__1 * d__1); + } else { /* Computing 2nd power */ - d__1 = z__[ip1] / dtipsq; - c__ = w - dtisq * dw - delsq * (d__1 * d__1); - } - a = (dtipsq + dtisq) * w - dtipsq * dtisq * dw; - b = dtipsq * dtisq * w; - if (c__ == 0.) { - if (a == 0.) { - if (orgati) { - a = z__[*i__] * z__[*i__] + dtipsq * dtipsq * ( - dpsi + dphi); - } else { - a = z__[ip1] * z__[ip1] + dtisq * dtisq * (dpsi + - dphi); - } - } - eta = b / a; - } else if (a <= 0.) { - eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) - / (c__ * 2.); - } else { - eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, - abs(d__1)))); - } - } - } + d__1 = z__[ip1] / dtipsq; + c__ = w - dtisq * dw - delsq * (d__1 * d__1); + } + a = (dtipsq + dtisq) * w - dtipsq * dtisq * dw; + b = dtipsq * dtisq * w; + if (c__ == 0.) { + if (a == 0.) { + if (orgati) { + a = z__[*i__] * z__[*i__] + dtipsq * dtipsq * ( + dpsi + dphi); + } else { + a = z__[ip1] * z__[ip1] + dtisq * dtisq * (dpsi + + dphi); + } + } + eta = b / a; + } else if (a <= 0.) { + eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) + / (c__ * 2.); + } else { + eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, + abs(d__1)))); + } + } + } /* Note, eta should be positive if w is negative, and */ /* eta should be negative otherwise. However, */ @@ -844,255 +844,255 @@ f"> */ /* we simply use one Newton step instead. This way */ /* will guarantee eta*w < 0. */ - if (w * eta >= 0.) { - eta = -w / dw; - } + if (w * eta >= 0.) { + eta = -w / dw; + } - eta /= *sigma + sqrt(*sigma * *sigma + eta); - temp = tau + eta; - if (temp > sgub || temp < sglb) { - if (w < 0.) { - eta = (sgub - tau) / 2.; - } else { - eta = (sglb - tau) / 2.; - } - if (geomavg) { - if (w < 0.) { - if (tau > 0.) { - eta = sqrt(sgub * tau) - tau; - } - } else { - if (sglb > 0.) { - eta = sqrt(sglb * tau) - tau; - } - } - } - } + eta /= *sigma + sqrt(*sigma * *sigma + eta); + temp = tau + eta; + if (temp > sgub || temp < sglb) { + if (w < 0.) { + eta = (sgub - tau) / 2.; + } else { + eta = (sglb - tau) / 2.; + } + if (geomavg) { + if (w < 0.) { + if (tau > 0.) { + eta = sqrt(sgub * tau) - tau; + } + } else { + if (sglb > 0.) { + eta = sqrt(sglb * tau) - tau; + } + } + } + } - prew = w; + prew = w; - tau += eta; - *sigma += eta; + tau += eta; + *sigma += eta; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - work[j] += eta; - delta[j] -= eta; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + work[j] += eta; + delta[j] -= eta; /* L170: */ - } + } /* Evaluate PSI and the derivative DPSI */ - dpsi = 0.; - psi = 0.; - erretm = 0.; - i__1 = iim1; - for (j = 1; j <= i__1; ++j) { - temp = z__[j] / (work[j] * delta[j]); - psi += z__[j] * temp; - dpsi += temp * temp; - erretm += psi; + dpsi = 0.; + psi = 0.; + erretm = 0.; + i__1 = iim1; + for (j = 1; j <= i__1; ++j) { + temp = z__[j] / (work[j] * delta[j]); + psi += z__[j] * temp; + dpsi += temp * temp; + erretm += psi; /* L180: */ - } - erretm = abs(erretm); + } + erretm = abs(erretm); /* Evaluate PHI and the derivative DPHI */ - dphi = 0.; - phi = 0.; - i__1 = iip1; - for (j = *n; j >= i__1; --j) { - temp = z__[j] / (work[j] * delta[j]); - phi += z__[j] * temp; - dphi += temp * temp; - erretm += phi; + dphi = 0.; + phi = 0.; + i__1 = iip1; + for (j = *n; j >= i__1; --j) { + temp = z__[j] / (work[j] * delta[j]); + phi += z__[j] * temp; + dphi += temp * temp; + erretm += phi; /* L190: */ - } + } - tau2 = work[ii] * delta[ii]; - temp = z__[ii] / tau2; - dw = dpsi + dphi + temp * temp; - temp = z__[ii] * temp; - w = rhoinv + phi + psi + temp; - erretm = (phi - psi) * 8. + erretm + rhoinv * 2. + abs(temp) * 3.; + tau2 = work[ii] * delta[ii]; + temp = z__[ii] / tau2; + dw = dpsi + dphi + temp * temp; + temp = z__[ii] * temp; + w = rhoinv + phi + psi + temp; + erretm = (phi - psi) * 8. + erretm + rhoinv * 2. + abs(temp) * 3.; /* $ + ABS( TAU2 )*DW */ - swtch = FALSE_; - if (orgati) { - if (-w > abs(prew) / 10.) { - swtch = TRUE_; - } - } else { - if (w > abs(prew) / 10.) { - swtch = TRUE_; - } - } + swtch = FALSE_; + if (orgati) { + if (-w > abs(prew) / 10.) { + swtch = TRUE_; + } + } else { + if (w > abs(prew) / 10.) { + swtch = TRUE_; + } + } /* Main loop to update the values of the array DELTA and WORK */ - iter = niter + 1; + iter = niter + 1; - for (niter = iter; niter <= 400; ++niter) { + for (niter = iter; niter <= 400; ++niter) { /* Test for convergence */ - if (abs(w) <= eps * erretm) { + if (abs(w) <= eps * erretm) { /* $ .OR. (SGUB-SGLB).LE.EIGHT*ABS(SGUB+SGLB) ) THEN */ - goto L240; - } + goto L240; + } - if (w <= 0.) { - sglb = max(sglb,tau); - } else { - sgub = min(sgub,tau); - } + if (w <= 0.) { + sglb = max(sglb,tau); + } else { + sgub = min(sgub,tau); + } /* Calculate the new step */ - if (! swtch3) { - dtipsq = work[ip1] * delta[ip1]; - dtisq = work[*i__] * delta[*i__]; - if (! swtch) { - if (orgati) { + if (! swtch3) { + dtipsq = work[ip1] * delta[ip1]; + dtisq = work[*i__] * delta[*i__]; + if (! swtch) { + if (orgati) { /* Computing 2nd power */ - d__1 = z__[*i__] / dtisq; - c__ = w - dtipsq * dw + delsq * (d__1 * d__1); - } else { + d__1 = z__[*i__] / dtisq; + c__ = w - dtipsq * dw + delsq * (d__1 * d__1); + } else { /* Computing 2nd power */ - d__1 = z__[ip1] / dtipsq; - c__ = w - dtisq * dw - delsq * (d__1 * d__1); - } - } else { - temp = z__[ii] / (work[ii] * delta[ii]); - if (orgati) { - dpsi += temp * temp; - } else { - dphi += temp * temp; - } - c__ = w - dtisq * dpsi - dtipsq * dphi; - } - a = (dtipsq + dtisq) * w - dtipsq * dtisq * dw; - b = dtipsq * dtisq * w; - if (c__ == 0.) { - if (a == 0.) { - if (! swtch) { - if (orgati) { - a = z__[*i__] * z__[*i__] + dtipsq * dtipsq * - (dpsi + dphi); - } else { - a = z__[ip1] * z__[ip1] + dtisq * dtisq * ( - dpsi + dphi); - } - } else { - a = dtisq * dtisq * dpsi + dtipsq * dtipsq * dphi; - } - } - eta = b / a; - } else if (a <= 0.) { - eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) - / (c__ * 2.); - } else { - eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, - abs(d__1)))); - } - } else { + d__1 = z__[ip1] / dtipsq; + c__ = w - dtisq * dw - delsq * (d__1 * d__1); + } + } else { + temp = z__[ii] / (work[ii] * delta[ii]); + if (orgati) { + dpsi += temp * temp; + } else { + dphi += temp * temp; + } + c__ = w - dtisq * dpsi - dtipsq * dphi; + } + a = (dtipsq + dtisq) * w - dtipsq * dtisq * dw; + b = dtipsq * dtisq * w; + if (c__ == 0.) { + if (a == 0.) { + if (! swtch) { + if (orgati) { + a = z__[*i__] * z__[*i__] + dtipsq * dtipsq * + (dpsi + dphi); + } else { + a = z__[ip1] * z__[ip1] + dtisq * dtisq * ( + dpsi + dphi); + } + } else { + a = dtisq * dtisq * dpsi + dtipsq * dtipsq * dphi; + } + } + eta = b / a; + } else if (a <= 0.) { + eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) + / (c__ * 2.); + } else { + eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, + abs(d__1)))); + } + } else { /* Interpolation using THREE most relevant poles */ - dtiim = work[iim1] * delta[iim1]; - dtiip = work[iip1] * delta[iip1]; - temp = rhoinv + psi + phi; - if (swtch) { - c__ = temp - dtiim * dpsi - dtiip * dphi; - zz[0] = dtiim * dtiim * dpsi; - zz[2] = dtiip * dtiip * dphi; - } else { - if (orgati) { - temp1 = z__[iim1] / dtiim; - temp1 *= temp1; - temp2 = (d__[iim1] - d__[iip1]) * (d__[iim1] + d__[ - iip1]) * temp1; - c__ = temp - dtiip * (dpsi + dphi) - temp2; - zz[0] = z__[iim1] * z__[iim1]; - if (dpsi < temp1) { - zz[2] = dtiip * dtiip * dphi; - } else { - zz[2] = dtiip * dtiip * (dpsi - temp1 + dphi); - } - } else { - temp1 = z__[iip1] / dtiip; - temp1 *= temp1; - temp2 = (d__[iip1] - d__[iim1]) * (d__[iim1] + d__[ - iip1]) * temp1; - c__ = temp - dtiim * (dpsi + dphi) - temp2; - if (dphi < temp1) { - zz[0] = dtiim * dtiim * dpsi; - } else { - zz[0] = dtiim * dtiim * (dpsi + (dphi - temp1)); - } - zz[2] = z__[iip1] * z__[iip1]; - } - } - dd[0] = dtiim; - dd[1] = delta[ii] * work[ii]; - dd[2] = dtiip; - dlaed6_(&niter, &orgati, &c__, dd, zz, &w, &eta, info); + dtiim = work[iim1] * delta[iim1]; + dtiip = work[iip1] * delta[iip1]; + temp = rhoinv + psi + phi; + if (swtch) { + c__ = temp - dtiim * dpsi - dtiip * dphi; + zz[0] = dtiim * dtiim * dpsi; + zz[2] = dtiip * dtiip * dphi; + } else { + if (orgati) { + temp1 = z__[iim1] / dtiim; + temp1 *= temp1; + temp2 = (d__[iim1] - d__[iip1]) * (d__[iim1] + d__[ + iip1]) * temp1; + c__ = temp - dtiip * (dpsi + dphi) - temp2; + zz[0] = z__[iim1] * z__[iim1]; + if (dpsi < temp1) { + zz[2] = dtiip * dtiip * dphi; + } else { + zz[2] = dtiip * dtiip * (dpsi - temp1 + dphi); + } + } else { + temp1 = z__[iip1] / dtiip; + temp1 *= temp1; + temp2 = (d__[iip1] - d__[iim1]) * (d__[iim1] + d__[ + iip1]) * temp1; + c__ = temp - dtiim * (dpsi + dphi) - temp2; + if (dphi < temp1) { + zz[0] = dtiim * dtiim * dpsi; + } else { + zz[0] = dtiim * dtiim * (dpsi + (dphi - temp1)); + } + zz[2] = z__[iip1] * z__[iip1]; + } + } + dd[0] = dtiim; + dd[1] = delta[ii] * work[ii]; + dd[2] = dtiip; + dlaed6_(&niter, &orgati, &c__, dd, zz, &w, &eta, info); - if (*info != 0) { + if (*info != 0) { /* If INFO is not 0, i.e., DLAED6 failed, switch */ /* back to two pole interpolation */ - swtch3 = FALSE_; - *info = 0; - dtipsq = work[ip1] * delta[ip1]; - dtisq = work[*i__] * delta[*i__]; - if (! swtch) { - if (orgati) { + swtch3 = FALSE_; + *info = 0; + dtipsq = work[ip1] * delta[ip1]; + dtisq = work[*i__] * delta[*i__]; + if (! swtch) { + if (orgati) { /* Computing 2nd power */ - d__1 = z__[*i__] / dtisq; - c__ = w - dtipsq * dw + delsq * (d__1 * d__1); - } else { + d__1 = z__[*i__] / dtisq; + c__ = w - dtipsq * dw + delsq * (d__1 * d__1); + } else { /* Computing 2nd power */ - d__1 = z__[ip1] / dtipsq; - c__ = w - dtisq * dw - delsq * (d__1 * d__1); - } - } else { - temp = z__[ii] / (work[ii] * delta[ii]); - if (orgati) { - dpsi += temp * temp; - } else { - dphi += temp * temp; - } - c__ = w - dtisq * dpsi - dtipsq * dphi; - } - a = (dtipsq + dtisq) * w - dtipsq * dtisq * dw; - b = dtipsq * dtisq * w; - if (c__ == 0.) { - if (a == 0.) { - if (! swtch) { - if (orgati) { - a = z__[*i__] * z__[*i__] + dtipsq * - dtipsq * (dpsi + dphi); - } else { - a = z__[ip1] * z__[ip1] + dtisq * dtisq * - (dpsi + dphi); - } - } else { - a = dtisq * dtisq * dpsi + dtipsq * dtipsq * - dphi; - } - } - eta = b / a; - } else if (a <= 0.) { - eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs( - d__1)))) / (c__ * 2.); - } else { - eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, - abs(d__1)))); - } - } - } + d__1 = z__[ip1] / dtipsq; + c__ = w - dtisq * dw - delsq * (d__1 * d__1); + } + } else { + temp = z__[ii] / (work[ii] * delta[ii]); + if (orgati) { + dpsi += temp * temp; + } else { + dphi += temp * temp; + } + c__ = w - dtisq * dpsi - dtipsq * dphi; + } + a = (dtipsq + dtisq) * w - dtipsq * dtisq * dw; + b = dtipsq * dtisq * w; + if (c__ == 0.) { + if (a == 0.) { + if (! swtch) { + if (orgati) { + a = z__[*i__] * z__[*i__] + dtipsq * + dtipsq * (dpsi + dphi); + } else { + a = z__[ip1] * z__[ip1] + dtisq * dtisq * + (dpsi + dphi); + } + } else { + a = dtisq * dtisq * dpsi + dtipsq * dtipsq * + dphi; + } + } + eta = b / a; + } else if (a <= 0.) { + eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs( + d__1)))) / (c__ * 2.); + } else { + eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, + abs(d__1)))); + } + } + } /* Note, eta should be positive if w is negative, and */ /* eta should be negative otherwise. However, */ @@ -1100,89 +1100,89 @@ f"> */ /* we simply use one Newton step instead. This way */ /* will guarantee eta*w < 0. */ - if (w * eta >= 0.) { - eta = -w / dw; - } + if (w * eta >= 0.) { + eta = -w / dw; + } - eta /= *sigma + sqrt(*sigma * *sigma + eta); - temp = tau + eta; - if (temp > sgub || temp < sglb) { - if (w < 0.) { - eta = (sgub - tau) / 2.; - } else { - eta = (sglb - tau) / 2.; - } - if (geomavg) { - if (w < 0.) { - if (tau > 0.) { - eta = sqrt(sgub * tau) - tau; - } - } else { - if (sglb > 0.) { - eta = sqrt(sglb * tau) - tau; - } - } - } - } + eta /= *sigma + sqrt(*sigma * *sigma + eta); + temp = tau + eta; + if (temp > sgub || temp < sglb) { + if (w < 0.) { + eta = (sgub - tau) / 2.; + } else { + eta = (sglb - tau) / 2.; + } + if (geomavg) { + if (w < 0.) { + if (tau > 0.) { + eta = sqrt(sgub * tau) - tau; + } + } else { + if (sglb > 0.) { + eta = sqrt(sglb * tau) - tau; + } + } + } + } - prew = w; + prew = w; - tau += eta; - *sigma += eta; + tau += eta; + *sigma += eta; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - work[j] += eta; - delta[j] -= eta; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + work[j] += eta; + delta[j] -= eta; /* L200: */ - } + } /* Evaluate PSI and the derivative DPSI */ - dpsi = 0.; - psi = 0.; - erretm = 0.; - i__1 = iim1; - for (j = 1; j <= i__1; ++j) { - temp = z__[j] / (work[j] * delta[j]); - psi += z__[j] * temp; - dpsi += temp * temp; - erretm += psi; + dpsi = 0.; + psi = 0.; + erretm = 0.; + i__1 = iim1; + for (j = 1; j <= i__1; ++j) { + temp = z__[j] / (work[j] * delta[j]); + psi += z__[j] * temp; + dpsi += temp * temp; + erretm += psi; /* L210: */ - } - erretm = abs(erretm); + } + erretm = abs(erretm); /* Evaluate PHI and the derivative DPHI */ - dphi = 0.; - phi = 0.; - i__1 = iip1; - for (j = *n; j >= i__1; --j) { - temp = z__[j] / (work[j] * delta[j]); - phi += z__[j] * temp; - dphi += temp * temp; - erretm += phi; + dphi = 0.; + phi = 0.; + i__1 = iip1; + for (j = *n; j >= i__1; --j) { + temp = z__[j] / (work[j] * delta[j]); + phi += z__[j] * temp; + dphi += temp * temp; + erretm += phi; /* L220: */ - } + } - tau2 = work[ii] * delta[ii]; - temp = z__[ii] / tau2; - dw = dpsi + dphi + temp * temp; - temp = z__[ii] * temp; - w = rhoinv + phi + psi + temp; - erretm = (phi - psi) * 8. + erretm + rhoinv * 2. + abs(temp) * 3.; + tau2 = work[ii] * delta[ii]; + temp = z__[ii] / tau2; + dw = dpsi + dphi + temp * temp; + temp = z__[ii] * temp; + w = rhoinv + phi + psi + temp; + erretm = (phi - psi) * 8. + erretm + rhoinv * 2. + abs(temp) * 3.; /* $ + ABS( TAU2 )*DW */ - if (w * prew > 0. && abs(w) > abs(prew) / 10.) { - swtch = ! swtch; - } + if (w * prew > 0. && abs(w) > abs(prew) / 10.) { + swtch = ! swtch; + } /* L230: */ - } + } /* Return with INFO = 1, NITER = MAXIT and not converged */ - *info = 1; + *info = 1; } @@ -1194,5 +1194,5 @@ L240: } /* dlasd4_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlasd5.cpp b/lib/linalg/dlasd5.cpp index a789475cad..a56f570c0b 100644 --- a/lib/linalg/dlasd5.cpp +++ b/lib/linalg/dlasd5.cpp @@ -1,13 +1,13 @@ /* fortran/dlasd5.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -133,9 +133,9 @@ f"> */ /* > at Berkeley, USA */ /* > */ /* ===================================================================== */ -/* Subroutine */ int dlasd5_(integer *i__, doublereal *d__, doublereal *z__, - doublereal *delta, doublereal *rho, doublereal *dsigma, doublereal * - work) +/* Subroutine */ int dlasd5_(integer *i__, doublereal *d__, doublereal *z__, + doublereal *delta, doublereal *rho, doublereal *dsigma, doublereal * + work) { /* System generated locals */ doublereal d__1; @@ -176,51 +176,51 @@ f"> */ del = d__[2] - d__[1]; delsq = del * (d__[2] + d__[1]); if (*i__ == 1) { - w = *rho * 4. * (z__[2] * z__[2] / (d__[1] + d__[2] * 3.) - z__[1] * - z__[1] / (d__[1] * 3. + d__[2])) / del + 1.; - if (w > 0.) { - b = delsq + *rho * (z__[1] * z__[1] + z__[2] * z__[2]); - c__ = *rho * z__[1] * z__[1] * delsq; + w = *rho * 4. * (z__[2] * z__[2] / (d__[1] + d__[2] * 3.) - z__[1] * + z__[1] / (d__[1] * 3. + d__[2])) / del + 1.; + if (w > 0.) { + b = delsq + *rho * (z__[1] * z__[1] + z__[2] * z__[2]); + c__ = *rho * z__[1] * z__[1] * delsq; /* B > ZERO, always */ /* The following TAU is DSIGMA * DSIGMA - D( 1 ) * D( 1 ) */ - tau = c__ * 2. / (b + sqrt((d__1 = b * b - c__ * 4., abs(d__1)))); + tau = c__ * 2. / (b + sqrt((d__1 = b * b - c__ * 4., abs(d__1)))); /* The following TAU is DSIGMA - D( 1 ) */ - tau /= d__[1] + sqrt(d__[1] * d__[1] + tau); - *dsigma = d__[1] + tau; - delta[1] = -tau; - delta[2] = del - tau; - work[1] = d__[1] * 2. + tau; - work[2] = d__[1] + tau + d__[2]; + tau /= d__[1] + sqrt(d__[1] * d__[1] + tau); + *dsigma = d__[1] + tau; + delta[1] = -tau; + delta[2] = del - tau; + work[1] = d__[1] * 2. + tau; + work[2] = d__[1] + tau + d__[2]; /* DELTA( 1 ) = -Z( 1 ) / TAU */ /* DELTA( 2 ) = Z( 2 ) / ( DEL-TAU ) */ - } else { - b = -delsq + *rho * (z__[1] * z__[1] + z__[2] * z__[2]); - c__ = *rho * z__[2] * z__[2] * delsq; + } else { + b = -delsq + *rho * (z__[1] * z__[1] + z__[2] * z__[2]); + c__ = *rho * z__[2] * z__[2] * delsq; /* The following TAU is DSIGMA * DSIGMA - D( 2 ) * D( 2 ) */ - if (b > 0.) { - tau = c__ * -2. / (b + sqrt(b * b + c__ * 4.)); - } else { - tau = (b - sqrt(b * b + c__ * 4.)) / 2.; - } + if (b > 0.) { + tau = c__ * -2. / (b + sqrt(b * b + c__ * 4.)); + } else { + tau = (b - sqrt(b * b + c__ * 4.)) / 2.; + } /* The following TAU is DSIGMA - D( 2 ) */ - tau /= d__[2] + sqrt((d__1 = d__[2] * d__[2] + tau, abs(d__1))); - *dsigma = d__[2] + tau; - delta[1] = -(del + tau); - delta[2] = -tau; - work[1] = d__[1] + tau + d__[2]; - work[2] = d__[2] * 2. + tau; + tau /= d__[2] + sqrt((d__1 = d__[2] * d__[2] + tau, abs(d__1))); + *dsigma = d__[2] + tau; + delta[1] = -(del + tau); + delta[2] = -tau; + work[1] = d__[1] + tau + d__[2]; + work[2] = d__[2] * 2. + tau; /* DELTA( 1 ) = -Z( 1 ) / ( DEL+TAU ) */ /* DELTA( 2 ) = -Z( 2 ) / TAU */ - } + } /* TEMP = SQRT( DELTA( 1 )*DELTA( 1 )+DELTA( 2 )*DELTA( 2 ) ) */ /* DELTA( 1 ) = DELTA( 1 ) / TEMP */ /* DELTA( 2 ) = DELTA( 2 ) / TEMP */ @@ -228,25 +228,25 @@ f"> */ /* Now I=2 */ - b = -delsq + *rho * (z__[1] * z__[1] + z__[2] * z__[2]); - c__ = *rho * z__[2] * z__[2] * delsq; + b = -delsq + *rho * (z__[1] * z__[1] + z__[2] * z__[2]); + c__ = *rho * z__[2] * z__[2] * delsq; /* The following TAU is DSIGMA * DSIGMA - D( 2 ) * D( 2 ) */ - if (b > 0.) { - tau = (b + sqrt(b * b + c__ * 4.)) / 2.; - } else { - tau = c__ * 2. / (-b + sqrt(b * b + c__ * 4.)); - } + if (b > 0.) { + tau = (b + sqrt(b * b + c__ * 4.)) / 2.; + } else { + tau = c__ * 2. / (-b + sqrt(b * b + c__ * 4.)); + } /* The following TAU is DSIGMA - D( 2 ) */ - tau /= d__[2] + sqrt(d__[2] * d__[2] + tau); - *dsigma = d__[2] + tau; - delta[1] = -(del + tau); - delta[2] = -tau; - work[1] = d__[1] + tau + d__[2]; - work[2] = d__[2] * 2. + tau; + tau /= d__[2] + sqrt(d__[2] * d__[2] + tau); + *dsigma = d__[2] + tau; + delta[1] = -(del + tau); + delta[2] = -tau; + work[1] = d__[1] + tau + d__[2]; + work[2] = d__[2] * 2. + tau; /* DELTA( 1 ) = -Z( 1 ) / ( DEL+TAU ) */ /* DELTA( 2 ) = -Z( 2 ) / TAU */ /* TEMP = SQRT( DELTA( 1 )*DELTA( 1 )+DELTA( 2 )*DELTA( 2 ) ) */ @@ -260,5 +260,5 @@ f"> */ } /* dlasd5_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlasd6.cpp b/lib/linalg/dlasd6.cpp index d3b6cddd86..48c7d8dd4f 100644 --- a/lib/linalg/dlasd6.cpp +++ b/lib/linalg/dlasd6.cpp @@ -1,13 +1,13 @@ /* fortran/dlasd6.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -334,34 +334,34 @@ f"> */ /* > California at Berkeley, USA */ /* > */ /* ===================================================================== */ -/* Subroutine */ int dlasd6_(integer *icompq, integer *nl, integer *nr, - integer *sqre, doublereal *d__, doublereal *vf, doublereal *vl, - doublereal *alpha, doublereal *beta, integer *idxq, integer *perm, - integer *givptr, integer *givcol, integer *ldgcol, doublereal *givnum, - integer *ldgnum, doublereal *poles, doublereal *difl, doublereal * - difr, doublereal *z__, integer *k, doublereal *c__, doublereal *s, - doublereal *work, integer *iwork, integer *info) +/* Subroutine */ int dlasd6_(integer *icompq, integer *nl, integer *nr, + integer *sqre, doublereal *d__, doublereal *vf, doublereal *vl, + doublereal *alpha, doublereal *beta, integer *idxq, integer *perm, + integer *givptr, integer *givcol, integer *ldgcol, doublereal *givnum, + integer *ldgnum, doublereal *poles, doublereal *difl, doublereal * + difr, doublereal *z__, integer *k, doublereal *c__, doublereal *s, + doublereal *work, integer *iwork, integer *info) { /* System generated locals */ - integer givcol_dim1, givcol_offset, givnum_dim1, givnum_offset, - poles_dim1, poles_offset, i__1; + integer givcol_dim1, givcol_offset, givnum_dim1, givnum_offset, + poles_dim1, poles_offset, i__1; doublereal d__1, d__2; /* Local variables */ integer i__, m, n, n1, n2, iw, idx, idxc, idxp, ivfw, ivlw; - extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, - doublereal *, integer *), dlasd7_(integer *, integer *, integer *, - integer *, integer *, doublereal *, doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *, integer *, integer *, - integer *, integer *, integer *, integer *, integer *, doublereal - *, integer *, doublereal *, doublereal *, integer *), dlasd8_( - integer *, integer *, doublereal *, doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *, integer *, doublereal *, - doublereal *, integer *), dlascl_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, integer *, doublereal *, - integer *, integer *, ftnlen), dlamrg_(integer *, integer *, - doublereal *, integer *, integer *, integer *); + extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, + doublereal *, integer *), dlasd7_(integer *, integer *, integer *, + integer *, integer *, doublereal *, doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *, integer *, integer *, + integer *, integer *, integer *, integer *, integer *, doublereal + *, integer *, doublereal *, doublereal *, integer *), dlasd8_( + integer *, integer *, doublereal *, doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *, integer *, doublereal *, + doublereal *, integer *), dlascl_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, integer *, doublereal *, + integer *, integer *, ftnlen), dlamrg_(integer *, integer *, + doublereal *, integer *, integer *, integer *); integer isigma; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); doublereal orgnrm; @@ -417,22 +417,22 @@ f"> */ m = n + *sqre; if (*icompq < 0 || *icompq > 1) { - *info = -1; + *info = -1; } else if (*nl < 1) { - *info = -2; + *info = -2; } else if (*nr < 1) { - *info = -3; + *info = -3; } else if (*sqre < 0 || *sqre > 1) { - *info = -4; + *info = -4; } else if (*ldgcol < n) { - *info = -14; + *info = -14; } else if (*ldgnum < n) { - *info = -16; + *info = -16; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DLASD6", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DLASD6", &i__1, (ftnlen)6); + return 0; } /* The following values are for bookkeeping purposes only. They are */ @@ -456,46 +456,46 @@ f"> */ d__[*nl + 1] = 0.; i__1 = n; for (i__ = 1; i__ <= i__1; ++i__) { - if ((d__1 = d__[i__], abs(d__1)) > orgnrm) { - orgnrm = (d__1 = d__[i__], abs(d__1)); - } + if ((d__1 = d__[i__], abs(d__1)) > orgnrm) { + orgnrm = (d__1 = d__[i__], abs(d__1)); + } /* L10: */ } dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b7, &n, &c__1, &d__[1], &n, info, ( - ftnlen)1); + ftnlen)1); *alpha /= orgnrm; *beta /= orgnrm; /* Sort and Deflate singular values. */ dlasd7_(icompq, nl, nr, sqre, k, &d__[1], &z__[1], &work[iw], &vf[1], & - work[ivfw], &vl[1], &work[ivlw], alpha, beta, &work[isigma], & - iwork[idx], &iwork[idxp], &idxq[1], &perm[1], givptr, &givcol[ - givcol_offset], ldgcol, &givnum[givnum_offset], ldgnum, c__, s, - info); + work[ivfw], &vl[1], &work[ivlw], alpha, beta, &work[isigma], & + iwork[idx], &iwork[idxp], &idxq[1], &perm[1], givptr, &givcol[ + givcol_offset], ldgcol, &givnum[givnum_offset], ldgnum, c__, s, + info); /* Solve Secular Equation, compute DIFL, DIFR, and update VF, VL. */ - dlasd8_(icompq, k, &d__[1], &z__[1], &vf[1], &vl[1], &difl[1], &difr[1], - ldgnum, &work[isigma], &work[iw], info); + dlasd8_(icompq, k, &d__[1], &z__[1], &vf[1], &vl[1], &difl[1], &difr[1], + ldgnum, &work[isigma], &work[iw], info); /* Report the possible convergence failure. */ if (*info != 0) { - return 0; + return 0; } /* Save the poles if ICOMPQ = 1. */ if (*icompq == 1) { - dcopy_(k, &d__[1], &c__1, &poles[poles_dim1 + 1], &c__1); - dcopy_(k, &work[isigma], &c__1, &poles[(poles_dim1 << 1) + 1], &c__1); + dcopy_(k, &d__[1], &c__1, &poles[poles_dim1 + 1], &c__1); + dcopy_(k, &work[isigma], &c__1, &poles[(poles_dim1 << 1) + 1], &c__1); } /* Unscale. */ dlascl_((char *)"G", &c__0, &c__0, &c_b7, &orgnrm, &n, &c__1, &d__[1], &n, info, ( - ftnlen)1); + ftnlen)1); /* Prepare the IDXQ sorting permutation. */ @@ -510,5 +510,5 @@ f"> */ } /* dlasd6_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlasd7.cpp b/lib/linalg/dlasd7.cpp index 29169c7a84..89a18cc81f 100644 --- a/lib/linalg/dlasd7.cpp +++ b/lib/linalg/dlasd7.cpp @@ -1,13 +1,13 @@ /* fortran/dlasd7.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -19,7 +19,7 @@ extern "C" { static integer c__1 = 1; -/* > \brief \b DLASD7 merges the two sets of singular values together into a single sorted set. Then it tries +/* > \brief \b DLASD7 merges the two sets of singular values together into a single sorted set. Then it tries to deflate the size of the problem. Used by sbdsdc. */ /* =========== DOCUMENTATION =========== */ @@ -298,13 +298,13 @@ f"> */ /* > California at Berkeley, USA */ /* > */ /* ===================================================================== */ -/* Subroutine */ int dlasd7_(integer *icompq, integer *nl, integer *nr, - integer *sqre, integer *k, doublereal *d__, doublereal *z__, - doublereal *zw, doublereal *vf, doublereal *vfw, doublereal *vl, - doublereal *vlw, doublereal *alpha, doublereal *beta, doublereal * - dsigma, integer *idx, integer *idxp, integer *idxq, integer *perm, - integer *givptr, integer *givcol, integer *ldgcol, doublereal *givnum, - integer *ldgnum, doublereal *c__, doublereal *s, integer *info) +/* Subroutine */ int dlasd7_(integer *icompq, integer *nl, integer *nr, + integer *sqre, integer *k, doublereal *d__, doublereal *z__, + doublereal *zw, doublereal *vf, doublereal *vfw, doublereal *vl, + doublereal *vlw, doublereal *alpha, doublereal *beta, doublereal * + dsigma, integer *idx, integer *idxp, integer *idxq, integer *perm, + integer *givptr, integer *givcol, integer *ldgcol, doublereal *givnum, + integer *ldgnum, doublereal *c__, doublereal *s, integer *info) { /* System generated locals */ integer givcol_dim1, givcol_offset, givnum_dim1, givnum_offset, i__1; @@ -316,17 +316,17 @@ f"> */ integer jp; doublereal eps, tau, tol; integer nlp1, nlp2, idxi, idxj; - extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, - doublereal *, integer *, doublereal *, doublereal *); + extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, + doublereal *, integer *, doublereal *, doublereal *); integer idxjp; - extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, - doublereal *, integer *); + extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, + doublereal *, integer *); integer jprev; - extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, - ftnlen); - extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *, - integer *, integer *, integer *), xerbla_(char *, integer *, - ftnlen); + extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, + ftnlen); + extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *, + integer *, integer *, integer *), xerbla_(char *, integer *, + ftnlen); doublereal hlftol; @@ -382,28 +382,28 @@ f"> */ m = n + *sqre; if (*icompq < 0 || *icompq > 1) { - *info = -1; + *info = -1; } else if (*nl < 1) { - *info = -2; + *info = -2; } else if (*nr < 1) { - *info = -3; + *info = -3; } else if (*sqre < 0 || *sqre > 1) { - *info = -4; + *info = -4; } else if (*ldgcol < n) { - *info = -22; + *info = -22; } else if (*ldgnum < n) { - *info = -24; + *info = -24; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DLASD7", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DLASD7", &i__1, (ftnlen)6); + return 0; } nlp1 = *nl + 1; nlp2 = *nl + 2; if (*icompq == 1) { - *givptr = 0; + *givptr = 0; } /* Generate the first part of the vector Z and move the singular */ @@ -413,11 +413,11 @@ f"> */ vl[nlp1] = 0.; tau = vf[nlp1]; for (i__ = *nl; i__ >= 1; --i__) { - z__[i__ + 1] = *alpha * vl[i__]; - vl[i__] = 0.; - vf[i__ + 1] = vf[i__]; - d__[i__ + 1] = d__[i__]; - idxq[i__ + 1] = idxq[i__] + 1; + z__[i__ + 1] = *alpha * vl[i__]; + vl[i__] = 0.; + vf[i__ + 1] = vf[i__]; + d__[i__ + 1] = d__[i__]; + idxq[i__ + 1] = idxq[i__] + 1; /* L10: */ } vf[1] = tau; @@ -426,8 +426,8 @@ f"> */ i__1 = m; for (i__ = nlp2; i__ <= i__1; ++i__) { - z__[i__] = *beta * vf[i__]; - vf[i__] = 0.; + z__[i__] = *beta * vf[i__]; + vf[i__] = 0.; /* L20: */ } @@ -435,7 +435,7 @@ f"> */ i__1 = n; for (i__ = nlp2; i__ <= i__1; ++i__) { - idxq[i__] += nlp1; + idxq[i__] += nlp1; /* L30: */ } @@ -443,10 +443,10 @@ f"> */ i__1 = n; for (i__ = 2; i__ <= i__1; ++i__) { - dsigma[i__] = d__[idxq[i__]]; - zw[i__] = z__[idxq[i__]]; - vfw[i__] = vf[idxq[i__]]; - vlw[i__] = vl[idxq[i__]]; + dsigma[i__] = d__[idxq[i__]]; + zw[i__] = z__[idxq[i__]]; + vfw[i__] = vf[idxq[i__]]; + vlw[i__] = vl[idxq[i__]]; /* L40: */ } @@ -454,11 +454,11 @@ f"> */ i__1 = n; for (i__ = 2; i__ <= i__1; ++i__) { - idxi = idx[i__] + 1; - d__[i__] = dsigma[idxi]; - z__[i__] = zw[idxi]; - vf[i__] = vfw[idxi]; - vl[i__] = vlw[idxi]; + idxi = idx[i__] + 1; + d__[i__] = dsigma[idxi]; + z__[i__] = zw[idxi]; + vf[i__] = vfw[idxi]; + vl[i__] = vlw[idxi]; /* L50: */ } @@ -495,19 +495,19 @@ f"> */ k2 = n + 1; i__1 = n; for (j = 2; j <= i__1; ++j) { - if ((d__1 = z__[j], abs(d__1)) <= tol) { + if ((d__1 = z__[j], abs(d__1)) <= tol) { /* Deflate due to small z component. */ - --k2; - idxp[k2] = j; - if (j == n) { - goto L100; - } - } else { - jprev = j; - goto L70; - } + --k2; + idxp[k2] = j; + if (j == n) { + goto L100; + } + } else { + jprev = j; + goto L70; + } /* L60: */ } L70: @@ -515,63 +515,63 @@ L70: L80: ++j; if (j > n) { - goto L90; + goto L90; } if ((d__1 = z__[j], abs(d__1)) <= tol) { /* Deflate due to small z component. */ - --k2; - idxp[k2] = j; + --k2; + idxp[k2] = j; } else { /* Check if singular values are close enough to allow deflation. */ - if ((d__1 = d__[j] - d__[jprev], abs(d__1)) <= tol) { + if ((d__1 = d__[j] - d__[jprev], abs(d__1)) <= tol) { /* Deflation is possible. */ - *s = z__[jprev]; - *c__ = z__[j]; + *s = z__[jprev]; + *c__ = z__[j]; /* Find sqrt(a**2+b**2) without overflow or */ /* destructive underflow. */ - tau = dlapy2_(c__, s); - z__[j] = tau; - z__[jprev] = 0.; - *c__ /= tau; - *s = -(*s) / tau; + tau = dlapy2_(c__, s); + z__[j] = tau; + z__[jprev] = 0.; + *c__ /= tau; + *s = -(*s) / tau; /* Record the appropriate Givens rotation */ - if (*icompq == 1) { - ++(*givptr); - idxjp = idxq[idx[jprev] + 1]; - idxj = idxq[idx[j] + 1]; - if (idxjp <= nlp1) { - --idxjp; - } - if (idxj <= nlp1) { - --idxj; - } - givcol[*givptr + (givcol_dim1 << 1)] = idxjp; - givcol[*givptr + givcol_dim1] = idxj; - givnum[*givptr + (givnum_dim1 << 1)] = *c__; - givnum[*givptr + givnum_dim1] = *s; - } - drot_(&c__1, &vf[jprev], &c__1, &vf[j], &c__1, c__, s); - drot_(&c__1, &vl[jprev], &c__1, &vl[j], &c__1, c__, s); - --k2; - idxp[k2] = jprev; - jprev = j; - } else { - ++(*k); - zw[*k] = z__[jprev]; - dsigma[*k] = d__[jprev]; - idxp[*k] = jprev; - jprev = j; - } + if (*icompq == 1) { + ++(*givptr); + idxjp = idxq[idx[jprev] + 1]; + idxj = idxq[idx[j] + 1]; + if (idxjp <= nlp1) { + --idxjp; + } + if (idxj <= nlp1) { + --idxj; + } + givcol[*givptr + (givcol_dim1 << 1)] = idxjp; + givcol[*givptr + givcol_dim1] = idxj; + givnum[*givptr + (givnum_dim1 << 1)] = *c__; + givnum[*givptr + givnum_dim1] = *s; + } + drot_(&c__1, &vf[jprev], &c__1, &vf[j], &c__1, c__, s); + drot_(&c__1, &vl[jprev], &c__1, &vl[j], &c__1, c__, s); + --k2; + idxp[k2] = jprev; + jprev = j; + } else { + ++(*k); + zw[*k] = z__[jprev]; + dsigma[*k] = d__[jprev]; + idxp[*k] = jprev; + jprev = j; + } } goto L80; L90: @@ -591,22 +591,22 @@ L100: i__1 = n; for (j = 2; j <= i__1; ++j) { - jp = idxp[j]; - dsigma[j] = d__[jp]; - vfw[j] = vf[jp]; - vlw[j] = vl[jp]; + jp = idxp[j]; + dsigma[j] = d__[jp]; + vfw[j] = vf[jp]; + vlw[j] = vl[jp]; /* L110: */ } if (*icompq == 1) { - i__1 = n; - for (j = 2; j <= i__1; ++j) { - jp = idxp[j]; - perm[j] = idxq[idx[jp] + 1]; - if (perm[j] <= nlp1) { - --perm[j]; - } + i__1 = n; + for (j = 2; j <= i__1; ++j) { + jp = idxp[j]; + perm[j] = idxq[idx[jp] + 1]; + if (perm[j] <= nlp1) { + --perm[j]; + } /* L120: */ - } + } } /* The deflated singular values go back into the last N - K slots of */ @@ -621,26 +621,26 @@ L100: dsigma[1] = 0.; hlftol = tol / 2.; if (abs(dsigma[2]) <= hlftol) { - dsigma[2] = hlftol; + dsigma[2] = hlftol; } if (m > n) { - z__[1] = dlapy2_(&z1, &z__[m]); - if (z__[1] <= tol) { - *c__ = 1.; - *s = 0.; - z__[1] = tol; - } else { - *c__ = z1 / z__[1]; - *s = -z__[m] / z__[1]; - } - drot_(&c__1, &vf[m], &c__1, &vf[1], &c__1, c__, s); - drot_(&c__1, &vl[m], &c__1, &vl[1], &c__1, c__, s); + z__[1] = dlapy2_(&z1, &z__[m]); + if (z__[1] <= tol) { + *c__ = 1.; + *s = 0.; + z__[1] = tol; + } else { + *c__ = z1 / z__[1]; + *s = -z__[m] / z__[1]; + } + drot_(&c__1, &vf[m], &c__1, &vf[1], &c__1, c__, s); + drot_(&c__1, &vl[m], &c__1, &vl[1], &c__1, c__, s); } else { - if (abs(z1) <= tol) { - z__[1] = tol; - } else { - z__[1] = z1; - } + if (abs(z1) <= tol) { + z__[1] = tol; + } else { + z__[1] = z1; + } } /* Restore Z, VF, and VL. */ @@ -659,5 +659,5 @@ L100: } /* dlasd7_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlasd8.cpp b/lib/linalg/dlasd8.cpp index b95d5b11cc..3ec481bb55 100644 --- a/lib/linalg/dlasd8.cpp +++ b/lib/linalg/dlasd8.cpp @@ -1,13 +1,13 @@ /* fortran/dlasd8.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -188,10 +188,10 @@ f"> */ /* > California at Berkeley, USA */ /* > */ /* ===================================================================== */ -/* Subroutine */ int dlasd8_(integer *icompq, integer *k, doublereal *d__, - doublereal *z__, doublereal *vf, doublereal *vl, doublereal *difl, - doublereal *difr, integer *lddifr, doublereal *dsigma, doublereal * - work, integer *info) +/* Subroutine */ int dlasd8_(integer *icompq, integer *k, doublereal *d__, + doublereal *z__, doublereal *vf, doublereal *vl, doublereal *difl, + doublereal *difr, integer *lddifr, doublereal *dsigma, doublereal * + work, integer *info) { /* System generated locals */ integer difr_dim1, difr_offset, i__1, i__2; @@ -204,22 +204,22 @@ f"> */ integer i__, j; doublereal dj, rho; integer iwk1, iwk2, iwk3; - extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, - integer *); + extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, + integer *); doublereal temp; extern doublereal dnrm2_(integer *, doublereal *, integer *); integer iwk2i, iwk3i; doublereal diflj, difrj, dsigj; - extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, - doublereal *, integer *); + extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, + doublereal *, integer *); extern doublereal dlamc3_(doublereal *, doublereal *); - extern /* Subroutine */ int dlasd4_(integer *, integer *, doublereal *, - doublereal *, doublereal *, doublereal *, doublereal *, - doublereal *, integer *), dlascl_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, integer *, doublereal *, - integer *, integer *, ftnlen), dlaset_(char *, integer *, integer - *, doublereal *, doublereal *, doublereal *, integer *, ftnlen), - xerbla_(char *, integer *, ftnlen); + extern /* Subroutine */ int dlasd4_(integer *, integer *, doublereal *, + doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, integer *), dlascl_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, integer *, doublereal *, + integer *, integer *, ftnlen), dlaset_(char *, integer *, integer + *, doublereal *, doublereal *, doublereal *, integer *, ftnlen), + xerbla_(char *, integer *, ftnlen); doublereal dsigjp; @@ -264,28 +264,28 @@ f"> */ *info = 0; if (*icompq < 0 || *icompq > 1) { - *info = -1; + *info = -1; } else if (*k < 1) { - *info = -2; + *info = -2; } else if (*lddifr < *k) { - *info = -9; + *info = -9; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DLASD8", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DLASD8", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*k == 1) { - d__[1] = abs(z__[1]); - difl[1] = d__[1]; - if (*icompq == 1) { - difl[2] = 1.; - difr[(difr_dim1 << 1) + 1] = 1.; - } - return 0; + d__[1] = abs(z__[1]); + difl[1] = d__[1]; + if (*icompq == 1) { + difl[2] = 1.; + difr[(difr_dim1 << 1) + 1] = 1.; + } + return 0; } /* Modify values DSIGMA(i) to make sure all DSIGMA(i)-DSIGMA(j) can */ @@ -307,7 +307,7 @@ f"> */ i__1 = *k; for (i__ = 1; i__ <= i__1; ++i__) { - dsigma[i__] = dlamc3_(&dsigma[i__], &dsigma[i__]) - dsigma[i__]; + dsigma[i__] = dlamc3_(&dsigma[i__], &dsigma[i__]) - dsigma[i__]; /* L10: */ } @@ -323,7 +323,7 @@ f"> */ rho = dnrm2_(k, &z__[1], &c__1); dlascl_((char *)"G", &c__0, &c__0, &rho, &c_b8, k, &c__1, &z__[1], k, info, ( - ftnlen)1); + ftnlen)1); rho *= rho; /* Initialize WORK(IWK3). */ @@ -335,31 +335,31 @@ f"> */ i__1 = *k; for (j = 1; j <= i__1; ++j) { - dlasd4_(k, &j, &dsigma[1], &z__[1], &work[iwk1], &rho, &d__[j], &work[ - iwk2], info); + dlasd4_(k, &j, &dsigma[1], &z__[1], &work[iwk1], &rho, &d__[j], &work[ + iwk2], info); /* If the root finder fails, report the convergence failure. */ - if (*info != 0) { - return 0; - } - work[iwk3i + j] = work[iwk3i + j] * work[j] * work[iwk2i + j]; - difl[j] = -work[j]; - difr[j + difr_dim1] = -work[j + 1]; - i__2 = j - 1; - for (i__ = 1; i__ <= i__2; ++i__) { - work[iwk3i + i__] = work[iwk3i + i__] * work[i__] * work[iwk2i + - i__] / (dsigma[i__] - dsigma[j]) / (dsigma[i__] + dsigma[ - j]); + if (*info != 0) { + return 0; + } + work[iwk3i + j] = work[iwk3i + j] * work[j] * work[iwk2i + j]; + difl[j] = -work[j]; + difr[j + difr_dim1] = -work[j + 1]; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + work[iwk3i + i__] = work[iwk3i + i__] * work[i__] * work[iwk2i + + i__] / (dsigma[i__] - dsigma[j]) / (dsigma[i__] + dsigma[ + j]); /* L20: */ - } - i__2 = *k; - for (i__ = j + 1; i__ <= i__2; ++i__) { - work[iwk3i + i__] = work[iwk3i + i__] * work[i__] * work[iwk2i + - i__] / (dsigma[i__] - dsigma[j]) / (dsigma[i__] + dsigma[ - j]); + } + i__2 = *k; + for (i__ = j + 1; i__ <= i__2; ++i__) { + work[iwk3i + i__] = work[iwk3i + i__] * work[i__] * work[iwk2i + + i__] / (dsigma[i__] - dsigma[j]) / (dsigma[i__] + dsigma[ + j]); /* L30: */ - } + } /* L40: */ } @@ -367,8 +367,8 @@ f"> */ i__1 = *k; for (i__ = 1; i__ <= i__1; ++i__) { - d__2 = sqrt((d__1 = work[iwk3i + i__], abs(d__1))); - z__[i__] = d_sign(&d__2, &z__[i__]); + d__2 = sqrt((d__1 = work[iwk3i + i__], abs(d__1))); + z__[i__] = d_sign(&d__2, &z__[i__]); /* L50: */ } @@ -376,32 +376,32 @@ f"> */ i__1 = *k; for (j = 1; j <= i__1; ++j) { - diflj = difl[j]; - dj = d__[j]; - dsigj = -dsigma[j]; - if (j < *k) { - difrj = -difr[j + difr_dim1]; - dsigjp = -dsigma[j + 1]; - } - work[j] = -z__[j] / diflj / (dsigma[j] + dj); - i__2 = j - 1; - for (i__ = 1; i__ <= i__2; ++i__) { - work[i__] = z__[i__] / (dlamc3_(&dsigma[i__], &dsigj) - diflj) / ( - dsigma[i__] + dj); + diflj = difl[j]; + dj = d__[j]; + dsigj = -dsigma[j]; + if (j < *k) { + difrj = -difr[j + difr_dim1]; + dsigjp = -dsigma[j + 1]; + } + work[j] = -z__[j] / diflj / (dsigma[j] + dj); + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + work[i__] = z__[i__] / (dlamc3_(&dsigma[i__], &dsigj) - diflj) / ( + dsigma[i__] + dj); /* L60: */ - } - i__2 = *k; - for (i__ = j + 1; i__ <= i__2; ++i__) { - work[i__] = z__[i__] / (dlamc3_(&dsigma[i__], &dsigjp) + difrj) / - (dsigma[i__] + dj); + } + i__2 = *k; + for (i__ = j + 1; i__ <= i__2; ++i__) { + work[i__] = z__[i__] / (dlamc3_(&dsigma[i__], &dsigjp) + difrj) / + (dsigma[i__] + dj); /* L70: */ - } - temp = dnrm2_(k, &work[1], &c__1); - work[iwk2i + j] = ddot_(k, &work[1], &c__1, &vf[1], &c__1) / temp; - work[iwk3i + j] = ddot_(k, &work[1], &c__1, &vl[1], &c__1) / temp; - if (*icompq == 1) { - difr[j + (difr_dim1 << 1)] = temp; - } + } + temp = dnrm2_(k, &work[1], &c__1); + work[iwk2i + j] = ddot_(k, &work[1], &c__1, &vf[1], &c__1) / temp; + work[iwk3i + j] = ddot_(k, &work[1], &c__1, &vl[1], &c__1) / temp; + if (*icompq == 1) { + difr[j + (difr_dim1 << 1)] = temp; + } /* L80: */ } @@ -415,5 +415,5 @@ f"> */ } /* dlasd8_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlasda.cpp b/lib/linalg/dlasda.cpp index a63dc14dec..d064a9af51 100644 --- a/lib/linalg/dlasda.cpp +++ b/lib/linalg/dlasda.cpp @@ -1,13 +1,13 @@ /* fortran/dlasda.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -296,47 +296,47 @@ f"> */ /* > California at Berkeley, USA */ /* > */ /* ===================================================================== */ -/* Subroutine */ int dlasda_(integer *icompq, integer *smlsiz, integer *n, - integer *sqre, doublereal *d__, doublereal *e, doublereal *u, integer - *ldu, doublereal *vt, integer *k, doublereal *difl, doublereal *difr, - doublereal *z__, doublereal *poles, integer *givptr, integer *givcol, - integer *ldgcol, integer *perm, doublereal *givnum, doublereal *c__, - doublereal *s, doublereal *work, integer *iwork, integer *info) +/* Subroutine */ int dlasda_(integer *icompq, integer *smlsiz, integer *n, + integer *sqre, doublereal *d__, doublereal *e, doublereal *u, integer + *ldu, doublereal *vt, integer *k, doublereal *difl, doublereal *difr, + doublereal *z__, doublereal *poles, integer *givptr, integer *givcol, + integer *ldgcol, integer *perm, doublereal *givnum, doublereal *c__, + doublereal *s, doublereal *work, integer *iwork, integer *info) { /* System generated locals */ - integer givcol_dim1, givcol_offset, perm_dim1, perm_offset, difl_dim1, - difl_offset, difr_dim1, difr_offset, givnum_dim1, givnum_offset, - poles_dim1, poles_offset, u_dim1, u_offset, vt_dim1, vt_offset, - z_dim1, z_offset, i__1, i__2; + integer givcol_dim1, givcol_offset, perm_dim1, perm_offset, difl_dim1, + difl_offset, difr_dim1, difr_offset, givnum_dim1, givnum_offset, + poles_dim1, poles_offset, u_dim1, u_offset, vt_dim1, vt_offset, + z_dim1, z_offset, i__1, i__2; /* Builtin functions */ integer pow_ii(integer *, integer *); /* Local variables */ integer i__, j, m, i1, ic, lf, nd, ll, nl, vf, nr, vl, im1, ncc, nlf, nrf, - vfi, iwk, vli, lvl, nru, ndb1, nlp1, lvl2, nrp1; + vfi, iwk, vli, lvl, nru, ndb1, nlp1, lvl2, nrp1; doublereal beta; integer idxq, nlvl; doublereal alpha; integer inode, ndiml, ndimr, idxqi, itemp; - extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, - doublereal *, integer *); + extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, + doublereal *, integer *); integer sqrei; - extern /* Subroutine */ int dlasd6_(integer *, integer *, integer *, - integer *, doublereal *, doublereal *, doublereal *, doublereal *, - doublereal *, integer *, integer *, integer *, integer *, - integer *, doublereal *, integer *, doublereal *, doublereal *, - doublereal *, doublereal *, integer *, doublereal *, doublereal *, - doublereal *, integer *, integer *); + extern /* Subroutine */ int dlasd6_(integer *, integer *, integer *, + integer *, doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, integer *, integer *, integer *, integer *, + integer *, doublereal *, integer *, doublereal *, doublereal *, + doublereal *, doublereal *, integer *, doublereal *, doublereal *, + doublereal *, integer *, integer *); integer nwork1, nwork2; - extern /* Subroutine */ int dlasdq_(char *, integer *, integer *, integer - *, integer *, integer *, doublereal *, doublereal *, doublereal *, - integer *, doublereal *, integer *, doublereal *, integer *, - doublereal *, integer *, ftnlen), dlasdt_(integer *, integer *, - integer *, integer *, integer *, integer *, integer *), dlaset_( - char *, integer *, integer *, doublereal *, doublereal *, - doublereal *, integer *, ftnlen), xerbla_(char *, integer *, - ftnlen); + extern /* Subroutine */ int dlasdq_(char *, integer *, integer *, integer + *, integer *, integer *, doublereal *, doublereal *, doublereal *, + integer *, doublereal *, integer *, doublereal *, integer *, + doublereal *, integer *, ftnlen), dlasdt_(integer *, integer *, + integer *, integer *, integer *, integer *, integer *), dlaset_( + char *, integer *, integer *, doublereal *, doublereal *, + doublereal *, integer *, ftnlen), xerbla_(char *, integer *, + ftnlen); integer smlszp; @@ -402,22 +402,22 @@ f"> */ *info = 0; if (*icompq < 0 || *icompq > 1) { - *info = -1; + *info = -1; } else if (*smlsiz < 3) { - *info = -2; + *info = -2; } else if (*n < 0) { - *info = -3; + *info = -3; } else if (*sqre < 0 || *sqre > 1) { - *info = -4; + *info = -4; } else if (*ldu < *n + *sqre) { - *info = -8; + *info = -8; } else if (*ldgcol < *n) { - *info = -17; + *info = -17; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DLASDA", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DLASDA", &i__1, (ftnlen)6); + return 0; } m = *n + *sqre; @@ -425,16 +425,16 @@ f"> */ /* If the input matrix is too small, call DLASDQ to find the SVD. */ if (*n <= *smlsiz) { - if (*icompq == 0) { - dlasdq_((char *)"U", sqre, n, &c__0, &c__0, &c__0, &d__[1], &e[1], &vt[ - vt_offset], ldu, &u[u_offset], ldu, &u[u_offset], ldu, & - work[1], info, (ftnlen)1); - } else { - dlasdq_((char *)"U", sqre, n, &m, n, &c__0, &d__[1], &e[1], &vt[vt_offset] - , ldu, &u[u_offset], ldu, &u[u_offset], ldu, &work[1], - info, (ftnlen)1); - } - return 0; + if (*icompq == 0) { + dlasdq_((char *)"U", sqre, n, &c__0, &c__0, &c__0, &d__[1], &e[1], &vt[ + vt_offset], ldu, &u[u_offset], ldu, &u[u_offset], ldu, & + work[1], info, (ftnlen)1); + } else { + dlasdq_((char *)"U", sqre, n, &m, n, &c__0, &d__[1], &e[1], &vt[vt_offset] + , ldu, &u[u_offset], ldu, &u[u_offset], ldu, &work[1], + info, (ftnlen)1); + } + return 0; } /* Book-keeping and set up the computation tree. */ @@ -454,8 +454,8 @@ f"> */ nwork1 = vl + m; nwork2 = nwork1 + smlszp * smlszp; - dlasdt_(n, &nlvl, &nd, &iwork[inode], &iwork[ndiml], &iwork[ndimr], - smlsiz); + dlasdt_(n, &nlvl, &nd, &iwork[inode], &iwork[ndiml], &iwork[ndimr], + smlsiz); /* for the nodes on bottom level of the tree, solve */ /* their subproblems by DLASDQ. */ @@ -470,84 +470,84 @@ f"> */ /* NLF: starting row of the left subproblem */ /* NRF: starting row of the right subproblem */ - i1 = i__ - 1; - ic = iwork[inode + i1]; - nl = iwork[ndiml + i1]; - nlp1 = nl + 1; - nr = iwork[ndimr + i1]; - nlf = ic - nl; - nrf = ic + 1; - idxqi = idxq + nlf - 2; - vfi = vf + nlf - 1; - vli = vl + nlf - 1; - sqrei = 1; - if (*icompq == 0) { - dlaset_((char *)"A", &nlp1, &nlp1, &c_b11, &c_b12, &work[nwork1], &smlszp, - (ftnlen)1); - dlasdq_((char *)"U", &sqrei, &nl, &nlp1, &nru, &ncc, &d__[nlf], &e[nlf], & - work[nwork1], &smlszp, &work[nwork2], &nl, &work[nwork2], - &nl, &work[nwork2], info, (ftnlen)1); - itemp = nwork1 + nl * smlszp; - dcopy_(&nlp1, &work[nwork1], &c__1, &work[vfi], &c__1); - dcopy_(&nlp1, &work[itemp], &c__1, &work[vli], &c__1); - } else { - dlaset_((char *)"A", &nl, &nl, &c_b11, &c_b12, &u[nlf + u_dim1], ldu, ( - ftnlen)1); - dlaset_((char *)"A", &nlp1, &nlp1, &c_b11, &c_b12, &vt[nlf + vt_dim1], - ldu, (ftnlen)1); - dlasdq_((char *)"U", &sqrei, &nl, &nlp1, &nl, &ncc, &d__[nlf], &e[nlf], & - vt[nlf + vt_dim1], ldu, &u[nlf + u_dim1], ldu, &u[nlf + - u_dim1], ldu, &work[nwork1], info, (ftnlen)1); - dcopy_(&nlp1, &vt[nlf + vt_dim1], &c__1, &work[vfi], &c__1); - dcopy_(&nlp1, &vt[nlf + nlp1 * vt_dim1], &c__1, &work[vli], &c__1) - ; - } - if (*info != 0) { - return 0; - } - i__2 = nl; - for (j = 1; j <= i__2; ++j) { - iwork[idxqi + j] = j; + i1 = i__ - 1; + ic = iwork[inode + i1]; + nl = iwork[ndiml + i1]; + nlp1 = nl + 1; + nr = iwork[ndimr + i1]; + nlf = ic - nl; + nrf = ic + 1; + idxqi = idxq + nlf - 2; + vfi = vf + nlf - 1; + vli = vl + nlf - 1; + sqrei = 1; + if (*icompq == 0) { + dlaset_((char *)"A", &nlp1, &nlp1, &c_b11, &c_b12, &work[nwork1], &smlszp, + (ftnlen)1); + dlasdq_((char *)"U", &sqrei, &nl, &nlp1, &nru, &ncc, &d__[nlf], &e[nlf], & + work[nwork1], &smlszp, &work[nwork2], &nl, &work[nwork2], + &nl, &work[nwork2], info, (ftnlen)1); + itemp = nwork1 + nl * smlszp; + dcopy_(&nlp1, &work[nwork1], &c__1, &work[vfi], &c__1); + dcopy_(&nlp1, &work[itemp], &c__1, &work[vli], &c__1); + } else { + dlaset_((char *)"A", &nl, &nl, &c_b11, &c_b12, &u[nlf + u_dim1], ldu, ( + ftnlen)1); + dlaset_((char *)"A", &nlp1, &nlp1, &c_b11, &c_b12, &vt[nlf + vt_dim1], + ldu, (ftnlen)1); + dlasdq_((char *)"U", &sqrei, &nl, &nlp1, &nl, &ncc, &d__[nlf], &e[nlf], & + vt[nlf + vt_dim1], ldu, &u[nlf + u_dim1], ldu, &u[nlf + + u_dim1], ldu, &work[nwork1], info, (ftnlen)1); + dcopy_(&nlp1, &vt[nlf + vt_dim1], &c__1, &work[vfi], &c__1); + dcopy_(&nlp1, &vt[nlf + nlp1 * vt_dim1], &c__1, &work[vli], &c__1) + ; + } + if (*info != 0) { + return 0; + } + i__2 = nl; + for (j = 1; j <= i__2; ++j) { + iwork[idxqi + j] = j; /* L10: */ - } - if (i__ == nd && *sqre == 0) { - sqrei = 0; - } else { - sqrei = 1; - } - idxqi += nlp1; - vfi += nlp1; - vli += nlp1; - nrp1 = nr + sqrei; - if (*icompq == 0) { - dlaset_((char *)"A", &nrp1, &nrp1, &c_b11, &c_b12, &work[nwork1], &smlszp, - (ftnlen)1); - dlasdq_((char *)"U", &sqrei, &nr, &nrp1, &nru, &ncc, &d__[nrf], &e[nrf], & - work[nwork1], &smlszp, &work[nwork2], &nr, &work[nwork2], - &nr, &work[nwork2], info, (ftnlen)1); - itemp = nwork1 + (nrp1 - 1) * smlszp; - dcopy_(&nrp1, &work[nwork1], &c__1, &work[vfi], &c__1); - dcopy_(&nrp1, &work[itemp], &c__1, &work[vli], &c__1); - } else { - dlaset_((char *)"A", &nr, &nr, &c_b11, &c_b12, &u[nrf + u_dim1], ldu, ( - ftnlen)1); - dlaset_((char *)"A", &nrp1, &nrp1, &c_b11, &c_b12, &vt[nrf + vt_dim1], - ldu, (ftnlen)1); - dlasdq_((char *)"U", &sqrei, &nr, &nrp1, &nr, &ncc, &d__[nrf], &e[nrf], & - vt[nrf + vt_dim1], ldu, &u[nrf + u_dim1], ldu, &u[nrf + - u_dim1], ldu, &work[nwork1], info, (ftnlen)1); - dcopy_(&nrp1, &vt[nrf + vt_dim1], &c__1, &work[vfi], &c__1); - dcopy_(&nrp1, &vt[nrf + nrp1 * vt_dim1], &c__1, &work[vli], &c__1) - ; - } - if (*info != 0) { - return 0; - } - i__2 = nr; - for (j = 1; j <= i__2; ++j) { - iwork[idxqi + j] = j; + } + if (i__ == nd && *sqre == 0) { + sqrei = 0; + } else { + sqrei = 1; + } + idxqi += nlp1; + vfi += nlp1; + vli += nlp1; + nrp1 = nr + sqrei; + if (*icompq == 0) { + dlaset_((char *)"A", &nrp1, &nrp1, &c_b11, &c_b12, &work[nwork1], &smlszp, + (ftnlen)1); + dlasdq_((char *)"U", &sqrei, &nr, &nrp1, &nru, &ncc, &d__[nrf], &e[nrf], & + work[nwork1], &smlszp, &work[nwork2], &nr, &work[nwork2], + &nr, &work[nwork2], info, (ftnlen)1); + itemp = nwork1 + (nrp1 - 1) * smlszp; + dcopy_(&nrp1, &work[nwork1], &c__1, &work[vfi], &c__1); + dcopy_(&nrp1, &work[itemp], &c__1, &work[vli], &c__1); + } else { + dlaset_((char *)"A", &nr, &nr, &c_b11, &c_b12, &u[nrf + u_dim1], ldu, ( + ftnlen)1); + dlaset_((char *)"A", &nrp1, &nrp1, &c_b11, &c_b12, &vt[nrf + vt_dim1], + ldu, (ftnlen)1); + dlasdq_((char *)"U", &sqrei, &nr, &nrp1, &nr, &ncc, &d__[nrf], &e[nrf], & + vt[nrf + vt_dim1], ldu, &u[nrf + u_dim1], ldu, &u[nrf + + u_dim1], ldu, &work[nwork1], info, (ftnlen)1); + dcopy_(&nrp1, &vt[nrf + vt_dim1], &c__1, &work[vfi], &c__1); + dcopy_(&nrp1, &vt[nrf + nrp1 * vt_dim1], &c__1, &work[vli], &c__1) + ; + } + if (*info != 0) { + return 0; + } + i__2 = nr; + for (j = 1; j <= i__2; ++j) { + iwork[idxqi + j] = j; /* L20: */ - } + } /* L30: */ } @@ -555,61 +555,61 @@ f"> */ j = pow_ii(&c__2, &nlvl); for (lvl = nlvl; lvl >= 1; --lvl) { - lvl2 = (lvl << 1) - 1; + lvl2 = (lvl << 1) - 1; /* Find the first node LF and last node LL on */ /* the current level LVL. */ - if (lvl == 1) { - lf = 1; - ll = 1; - } else { - i__1 = lvl - 1; - lf = pow_ii(&c__2, &i__1); - ll = (lf << 1) - 1; - } - i__1 = ll; - for (i__ = lf; i__ <= i__1; ++i__) { - im1 = i__ - 1; - ic = iwork[inode + im1]; - nl = iwork[ndiml + im1]; - nr = iwork[ndimr + im1]; - nlf = ic - nl; - nrf = ic + 1; - if (i__ == ll) { - sqrei = *sqre; - } else { - sqrei = 1; - } - vfi = vf + nlf - 1; - vli = vl + nlf - 1; - idxqi = idxq + nlf - 1; - alpha = d__[ic]; - beta = e[ic]; - if (*icompq == 0) { - dlasd6_(icompq, &nl, &nr, &sqrei, &d__[nlf], &work[vfi], & - work[vli], &alpha, &beta, &iwork[idxqi], &perm[ - perm_offset], &givptr[1], &givcol[givcol_offset], - ldgcol, &givnum[givnum_offset], ldu, &poles[ - poles_offset], &difl[difl_offset], &difr[difr_offset], - &z__[z_offset], &k[1], &c__[1], &s[1], &work[nwork1], - &iwork[iwk], info); - } else { - --j; - dlasd6_(icompq, &nl, &nr, &sqrei, &d__[nlf], &work[vfi], & - work[vli], &alpha, &beta, &iwork[idxqi], &perm[nlf + - lvl * perm_dim1], &givptr[j], &givcol[nlf + lvl2 * - givcol_dim1], ldgcol, &givnum[nlf + lvl2 * - givnum_dim1], ldu, &poles[nlf + lvl2 * poles_dim1], & - difl[nlf + lvl * difl_dim1], &difr[nlf + lvl2 * - difr_dim1], &z__[nlf + lvl * z_dim1], &k[j], &c__[j], - &s[j], &work[nwork1], &iwork[iwk], info); - } - if (*info != 0) { - return 0; - } + if (lvl == 1) { + lf = 1; + ll = 1; + } else { + i__1 = lvl - 1; + lf = pow_ii(&c__2, &i__1); + ll = (lf << 1) - 1; + } + i__1 = ll; + for (i__ = lf; i__ <= i__1; ++i__) { + im1 = i__ - 1; + ic = iwork[inode + im1]; + nl = iwork[ndiml + im1]; + nr = iwork[ndimr + im1]; + nlf = ic - nl; + nrf = ic + 1; + if (i__ == ll) { + sqrei = *sqre; + } else { + sqrei = 1; + } + vfi = vf + nlf - 1; + vli = vl + nlf - 1; + idxqi = idxq + nlf - 1; + alpha = d__[ic]; + beta = e[ic]; + if (*icompq == 0) { + dlasd6_(icompq, &nl, &nr, &sqrei, &d__[nlf], &work[vfi], & + work[vli], &alpha, &beta, &iwork[idxqi], &perm[ + perm_offset], &givptr[1], &givcol[givcol_offset], + ldgcol, &givnum[givnum_offset], ldu, &poles[ + poles_offset], &difl[difl_offset], &difr[difr_offset], + &z__[z_offset], &k[1], &c__[1], &s[1], &work[nwork1], + &iwork[iwk], info); + } else { + --j; + dlasd6_(icompq, &nl, &nr, &sqrei, &d__[nlf], &work[vfi], & + work[vli], &alpha, &beta, &iwork[idxqi], &perm[nlf + + lvl * perm_dim1], &givptr[j], &givcol[nlf + lvl2 * + givcol_dim1], ldgcol, &givnum[nlf + lvl2 * + givnum_dim1], ldu, &poles[nlf + lvl2 * poles_dim1], & + difl[nlf + lvl * difl_dim1], &difr[nlf + lvl2 * + difr_dim1], &z__[nlf + lvl * z_dim1], &k[j], &c__[j], + &s[j], &work[nwork1], &iwork[iwk], info); + } + if (*info != 0) { + return 0; + } /* L40: */ - } + } /* L50: */ } @@ -620,5 +620,5 @@ f"> */ } /* dlasda_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlasdq.cpp b/lib/linalg/dlasdq.cpp index efb468cef4..418be52678 100644 --- a/lib/linalg/dlasdq.cpp +++ b/lib/linalg/dlasdq.cpp @@ -1,13 +1,13 @@ /* fortran/dlasdq.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -232,14 +232,14 @@ f"> */ /* > */ /* ===================================================================== */ /* Subroutine */ int dlasdq_(char *uplo, integer *sqre, integer *n, integer * - ncvt, integer *nru, integer *ncc, doublereal *d__, doublereal *e, - doublereal *vt, integer *ldvt, doublereal *u, integer *ldu, - doublereal *c__, integer *ldc, doublereal *work, integer *info, - ftnlen uplo_len) + ncvt, integer *nru, integer *ncc, doublereal *d__, doublereal *e, + doublereal *vt, integer *ldvt, doublereal *u, integer *ldu, + doublereal *c__, integer *ldc, doublereal *work, integer *info, + ftnlen uplo_len) { /* System generated locals */ - integer c_dim1, c_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1, - i__2; + integer c_dim1, c_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1, + i__2; /* Local variables */ integer i__, j; @@ -248,17 +248,17 @@ f"> */ doublereal smin; integer sqre1; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int dlasr_(char *, char *, char *, integer *, - integer *, doublereal *, doublereal *, doublereal *, integer *, - ftnlen, ftnlen, ftnlen), dswap_(integer *, doublereal *, integer * - , doublereal *, integer *); + extern /* Subroutine */ int dlasr_(char *, char *, char *, integer *, + integer *, doublereal *, doublereal *, doublereal *, integer *, + ftnlen, ftnlen, ftnlen), dswap_(integer *, doublereal *, integer * + , doublereal *, integer *); integer iuplo; - extern /* Subroutine */ int dlartg_(doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *), xerbla_(char *, - integer *, ftnlen), dbdsqr_(char *, integer *, integer *, integer - *, integer *, doublereal *, doublereal *, doublereal *, integer *, - doublereal *, integer *, doublereal *, integer *, doublereal *, - integer *, ftnlen); + extern /* Subroutine */ int dlartg_(doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *), xerbla_(char *, + integer *, ftnlen), dbdsqr_(char *, integer *, integer *, integer + *, integer *, doublereal *, doublereal *, doublereal *, integer *, + doublereal *, integer *, doublereal *, integer *, doublereal *, + integer *, ftnlen); logical rotate; @@ -305,37 +305,37 @@ f"> */ *info = 0; iuplo = 0; if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { - iuplo = 1; + iuplo = 1; } if (lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { - iuplo = 2; + iuplo = 2; } if (iuplo == 0) { - *info = -1; + *info = -1; } else if (*sqre < 0 || *sqre > 1) { - *info = -2; + *info = -2; } else if (*n < 0) { - *info = -3; + *info = -3; } else if (*ncvt < 0) { - *info = -4; + *info = -4; } else if (*nru < 0) { - *info = -5; + *info = -5; } else if (*ncc < 0) { - *info = -6; + *info = -6; } else if (*ncvt == 0 && *ldvt < 1 || *ncvt > 0 && *ldvt < max(1,*n)) { - *info = -10; + *info = -10; } else if (*ldu < max(1,*nru)) { - *info = -12; + *info = -12; } else if (*ncc == 0 && *ldc < 1 || *ncc > 0 && *ldc < max(1,*n)) { - *info = -14; + *info = -14; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DLASDQ", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DLASDQ", &i__1, (ftnlen)6); + return 0; } if (*n == 0) { - return 0; + return 0; } /* ROTATE is true if any singular vectors desired, false otherwise */ @@ -348,92 +348,92 @@ f"> */ /* bidiagonal. The rotations are on the right. */ if (iuplo == 1 && sqre1 == 1) { - i__1 = *n - 1; - for (i__ = 1; i__ <= i__1; ++i__) { - dlartg_(&d__[i__], &e[i__], &cs, &sn, &r__); - d__[i__] = r__; - e[i__] = sn * d__[i__ + 1]; - d__[i__ + 1] = cs * d__[i__ + 1]; - if (rotate) { - work[i__] = cs; - work[*n + i__] = sn; - } + i__1 = *n - 1; + for (i__ = 1; i__ <= i__1; ++i__) { + dlartg_(&d__[i__], &e[i__], &cs, &sn, &r__); + d__[i__] = r__; + e[i__] = sn * d__[i__ + 1]; + d__[i__ + 1] = cs * d__[i__ + 1]; + if (rotate) { + work[i__] = cs; + work[*n + i__] = sn; + } /* L10: */ - } - dlartg_(&d__[*n], &e[*n], &cs, &sn, &r__); - d__[*n] = r__; - e[*n] = 0.; - if (rotate) { - work[*n] = cs; - work[*n + *n] = sn; - } - iuplo = 2; - sqre1 = 0; + } + dlartg_(&d__[*n], &e[*n], &cs, &sn, &r__); + d__[*n] = r__; + e[*n] = 0.; + if (rotate) { + work[*n] = cs; + work[*n + *n] = sn; + } + iuplo = 2; + sqre1 = 0; /* Update singular vectors if desired. */ - if (*ncvt > 0) { - dlasr_((char *)"L", (char *)"V", (char *)"F", &np1, ncvt, &work[1], &work[np1], &vt[ - vt_offset], ldvt, (ftnlen)1, (ftnlen)1, (ftnlen)1); - } + if (*ncvt > 0) { + dlasr_((char *)"L", (char *)"V", (char *)"F", &np1, ncvt, &work[1], &work[np1], &vt[ + vt_offset], ldvt, (ftnlen)1, (ftnlen)1, (ftnlen)1); + } } /* If matrix lower bidiagonal, rotate to be upper bidiagonal */ /* by applying Givens rotations on the left. */ if (iuplo == 2) { - i__1 = *n - 1; - for (i__ = 1; i__ <= i__1; ++i__) { - dlartg_(&d__[i__], &e[i__], &cs, &sn, &r__); - d__[i__] = r__; - e[i__] = sn * d__[i__ + 1]; - d__[i__ + 1] = cs * d__[i__ + 1]; - if (rotate) { - work[i__] = cs; - work[*n + i__] = sn; - } + i__1 = *n - 1; + for (i__ = 1; i__ <= i__1; ++i__) { + dlartg_(&d__[i__], &e[i__], &cs, &sn, &r__); + d__[i__] = r__; + e[i__] = sn * d__[i__ + 1]; + d__[i__ + 1] = cs * d__[i__ + 1]; + if (rotate) { + work[i__] = cs; + work[*n + i__] = sn; + } /* L20: */ - } + } /* If matrix (N+1)-by-N lower bidiagonal, one additional */ /* rotation is needed. */ - if (sqre1 == 1) { - dlartg_(&d__[*n], &e[*n], &cs, &sn, &r__); - d__[*n] = r__; - if (rotate) { - work[*n] = cs; - work[*n + *n] = sn; - } - } + if (sqre1 == 1) { + dlartg_(&d__[*n], &e[*n], &cs, &sn, &r__); + d__[*n] = r__; + if (rotate) { + work[*n] = cs; + work[*n + *n] = sn; + } + } /* Update singular vectors if desired. */ - if (*nru > 0) { - if (sqre1 == 0) { - dlasr_((char *)"R", (char *)"V", (char *)"F", nru, n, &work[1], &work[np1], &u[ - u_offset], ldu, (ftnlen)1, (ftnlen)1, (ftnlen)1); - } else { - dlasr_((char *)"R", (char *)"V", (char *)"F", nru, &np1, &work[1], &work[np1], &u[ - u_offset], ldu, (ftnlen)1, (ftnlen)1, (ftnlen)1); - } - } - if (*ncc > 0) { - if (sqre1 == 0) { - dlasr_((char *)"L", (char *)"V", (char *)"F", n, ncc, &work[1], &work[np1], &c__[ - c_offset], ldc, (ftnlen)1, (ftnlen)1, (ftnlen)1); - } else { - dlasr_((char *)"L", (char *)"V", (char *)"F", &np1, ncc, &work[1], &work[np1], &c__[ - c_offset], ldc, (ftnlen)1, (ftnlen)1, (ftnlen)1); - } - } + if (*nru > 0) { + if (sqre1 == 0) { + dlasr_((char *)"R", (char *)"V", (char *)"F", nru, n, &work[1], &work[np1], &u[ + u_offset], ldu, (ftnlen)1, (ftnlen)1, (ftnlen)1); + } else { + dlasr_((char *)"R", (char *)"V", (char *)"F", nru, &np1, &work[1], &work[np1], &u[ + u_offset], ldu, (ftnlen)1, (ftnlen)1, (ftnlen)1); + } + } + if (*ncc > 0) { + if (sqre1 == 0) { + dlasr_((char *)"L", (char *)"V", (char *)"F", n, ncc, &work[1], &work[np1], &c__[ + c_offset], ldc, (ftnlen)1, (ftnlen)1, (ftnlen)1); + } else { + dlasr_((char *)"L", (char *)"V", (char *)"F", &np1, ncc, &work[1], &work[np1], &c__[ + c_offset], ldc, (ftnlen)1, (ftnlen)1, (ftnlen)1); + } + } } /* Call DBDSQR to compute the SVD of the reduced real */ /* N-by-N upper bidiagonal matrix. */ dbdsqr_((char *)"U", n, ncvt, nru, ncc, &d__[1], &e[1], &vt[vt_offset], ldvt, &u[ - u_offset], ldu, &c__[c_offset], ldc, &work[1], info, (ftnlen)1); + u_offset], ldu, &c__[c_offset], ldc, &work[1], info, (ftnlen)1); /* Sort the singular values into ascending order (insertion sort on */ /* singular values, but only one transposition per singular vector) */ @@ -443,35 +443,35 @@ f"> */ /* Scan for smallest D(I). */ - isub = i__; - smin = d__[i__]; - i__2 = *n; - for (j = i__ + 1; j <= i__2; ++j) { - if (d__[j] < smin) { - isub = j; - smin = d__[j]; - } + isub = i__; + smin = d__[i__]; + i__2 = *n; + for (j = i__ + 1; j <= i__2; ++j) { + if (d__[j] < smin) { + isub = j; + smin = d__[j]; + } /* L30: */ - } - if (isub != i__) { + } + if (isub != i__) { /* Swap singular values and vectors. */ - d__[isub] = d__[i__]; - d__[i__] = smin; - if (*ncvt > 0) { - dswap_(ncvt, &vt[isub + vt_dim1], ldvt, &vt[i__ + vt_dim1], - ldvt); - } - if (*nru > 0) { - dswap_(nru, &u[isub * u_dim1 + 1], &c__1, &u[i__ * u_dim1 + 1] - , &c__1); - } - if (*ncc > 0) { - dswap_(ncc, &c__[isub + c_dim1], ldc, &c__[i__ + c_dim1], ldc) - ; - } - } + d__[isub] = d__[i__]; + d__[i__] = smin; + if (*ncvt > 0) { + dswap_(ncvt, &vt[isub + vt_dim1], ldvt, &vt[i__ + vt_dim1], + ldvt); + } + if (*nru > 0) { + dswap_(nru, &u[isub * u_dim1 + 1], &c__1, &u[i__ * u_dim1 + 1] + , &c__1); + } + if (*ncc > 0) { + dswap_(ncc, &c__[isub + c_dim1], ldc, &c__[i__ + c_dim1], ldc) + ; + } + } /* L40: */ } @@ -482,5 +482,5 @@ f"> */ } /* dlasdq_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlasdt.cpp b/lib/linalg/dlasdt.cpp index 0e507af8f2..77edcf93d4 100644 --- a/lib/linalg/dlasdt.cpp +++ b/lib/linalg/dlasdt.cpp @@ -1,13 +1,13 @@ /* fortran/dlasdt.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -122,7 +122,7 @@ f"> */ /* > */ /* ===================================================================== */ /* Subroutine */ int dlasdt_(integer *n, integer *lvl, integer *nd, integer * - inode, integer *ndiml, integer *ndimr, integer *msub) + inode, integer *ndiml, integer *ndimr, integer *msub) { /* System generated locals */ integer i__1, i__2; @@ -180,20 +180,20 @@ f"> */ /* Constructing the tree at (NLVL+1)-st level. The number of */ /* nodes created on this level is LLST * 2. */ - i__2 = llst - 1; - for (i__ = 0; i__ <= i__2; ++i__) { - il += 2; - ir += 2; - ncrnt = llst + i__; - ndiml[il] = ndiml[ncrnt] / 2; - ndimr[il] = ndiml[ncrnt] - ndiml[il] - 1; - inode[il] = inode[ncrnt] - ndimr[il] - 1; - ndiml[ir] = ndimr[ncrnt] / 2; - ndimr[ir] = ndimr[ncrnt] - ndiml[ir] - 1; - inode[ir] = inode[ncrnt] + ndiml[ir] + 1; + i__2 = llst - 1; + for (i__ = 0; i__ <= i__2; ++i__) { + il += 2; + ir += 2; + ncrnt = llst + i__; + ndiml[il] = ndiml[ncrnt] / 2; + ndimr[il] = ndiml[ncrnt] - ndiml[il] - 1; + inode[il] = inode[ncrnt] - ndimr[il] - 1; + ndiml[ir] = ndimr[ncrnt] / 2; + ndimr[ir] = ndimr[ncrnt] - ndiml[ir] - 1; + inode[ir] = inode[ncrnt] + ndiml[ir] + 1; /* L10: */ - } - llst <<= 1; + } + llst <<= 1; /* L20: */ } *nd = (llst << 1) - 1; @@ -205,5 +205,5 @@ f"> */ } /* dlasdt_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlaset.cpp b/lib/linalg/dlaset.cpp index 072bbf1500..4323f948e4 100644 --- a/lib/linalg/dlaset.cpp +++ b/lib/linalg/dlaset.cpp @@ -1,13 +1,13 @@ /* fortran/dlaset.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -128,7 +128,7 @@ f"> */ /* ===================================================================== */ /* Subroutine */ int dlaset_(char *uplo, integer *m, integer *n, doublereal * - alpha, doublereal *beta, doublereal *a, integer *lda, ftnlen uplo_len) + alpha, doublereal *beta, doublereal *a, integer *lda, ftnlen uplo_len) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; @@ -168,53 +168,53 @@ f"> */ /* Set the strictly upper triangular or trapezoidal part of the */ /* array to ALPHA. */ - i__1 = *n; - for (j = 2; j <= i__1; ++j) { + i__1 = *n; + for (j = 2; j <= i__1; ++j) { /* Computing MIN */ - i__3 = j - 1; - i__2 = min(i__3,*m); - for (i__ = 1; i__ <= i__2; ++i__) { - a[i__ + j * a_dim1] = *alpha; + i__3 = j - 1; + i__2 = min(i__3,*m); + for (i__ = 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] = *alpha; /* L10: */ - } + } /* L20: */ - } + } } else if (lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { /* Set the strictly lower triangular or trapezoidal part of the */ /* array to ALPHA. */ - i__1 = min(*m,*n); - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = j + 1; i__ <= i__2; ++i__) { - a[i__ + j * a_dim1] = *alpha; + i__1 = min(*m,*n); + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = j + 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] = *alpha; /* L30: */ - } + } /* L40: */ - } + } } else { /* Set the leading m-by-n submatrix to ALPHA. */ - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - a[i__ + j * a_dim1] = *alpha; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] = *alpha; /* L50: */ - } + } /* L60: */ - } + } } /* Set the first min(M,N) diagonal elements to BETA. */ i__1 = min(*m,*n); for (i__ = 1; i__ <= i__1; ++i__) { - a[i__ + i__ * a_dim1] = *beta; + a[i__ + i__ * a_dim1] = *beta; /* L70: */ } @@ -225,5 +225,5 @@ f"> */ } /* dlaset_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlasq1.cpp b/lib/linalg/dlasq1.cpp index 090f680525..0c9e0ca9f2 100644 --- a/lib/linalg/dlasq1.cpp +++ b/lib/linalg/dlasq1.cpp @@ -1,13 +1,13 @@ /* fortran/dlasq1.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -130,8 +130,8 @@ f"> */ /* > \ingroup auxOTHERcomputational */ /* ===================================================================== */ -/* Subroutine */ int dlasq1_(integer *n, doublereal *d__, doublereal *e, - doublereal *work, integer *info) +/* Subroutine */ int dlasq1_(integer *n, doublereal *d__, doublereal *e, + doublereal *work, integer *info) { /* System generated locals */ integer i__1, i__2; @@ -143,22 +143,22 @@ f"> */ /* Local variables */ integer i__; doublereal eps; - extern /* Subroutine */ int dlas2_(doublereal *, doublereal *, doublereal - *, doublereal *, doublereal *); + extern /* Subroutine */ int dlas2_(doublereal *, doublereal *, doublereal + *, doublereal *, doublereal *); doublereal scale; integer iinfo; doublereal sigmn; - extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, - doublereal *, integer *); + extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, + doublereal *, integer *); doublereal sigmx; extern /* Subroutine */ int dlasq2_(integer *, doublereal *, integer *); extern doublereal dlamch_(char *, ftnlen); - extern /* Subroutine */ int dlascl_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, integer *, doublereal *, - integer *, integer *, ftnlen); + extern /* Subroutine */ int dlascl_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, integer *, doublereal *, + integer *, integer *, ftnlen); doublereal safmin; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), dlasrt_( - char *, integer *, doublereal *, integer *, ftnlen); + char *, integer *, doublereal *, integer *, ftnlen); /* -- LAPACK computational routine -- */ @@ -192,20 +192,20 @@ f"> */ /* Function Body */ *info = 0; if (*n < 0) { - *info = -1; - i__1 = -(*info); - xerbla_((char *)"DLASQ1", &i__1, (ftnlen)6); - return 0; + *info = -1; + i__1 = -(*info); + xerbla_((char *)"DLASQ1", &i__1, (ftnlen)6); + return 0; } else if (*n == 0) { - return 0; + return 0; } else if (*n == 1) { - d__[1] = abs(d__[1]); - return 0; + d__[1] = abs(d__[1]); + return 0; } else if (*n == 2) { - dlas2_(&d__[1], &e[1], &d__[2], &sigmn, &sigmx); - d__[1] = sigmx; - d__[2] = sigmn; - return 0; + dlas2_(&d__[1], &e[1], &d__[2], &sigmn, &sigmx); + d__[1] = sigmx; + d__[2] = sigmn; + return 0; } /* Estimate the largest singular value. */ @@ -213,10 +213,10 @@ f"> */ sigmx = 0.; i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { - d__[i__] = (d__1 = d__[i__], abs(d__1)); + d__[i__] = (d__1 = d__[i__], abs(d__1)); /* Computing MAX */ - d__2 = sigmx, d__3 = (d__1 = e[i__], abs(d__1)); - sigmx = max(d__2,d__3); + d__2 = sigmx, d__3 = (d__1 = e[i__], abs(d__1)); + sigmx = max(d__2,d__3); /* L10: */ } d__[*n] = (d__1 = d__[*n], abs(d__1)); @@ -224,15 +224,15 @@ f"> */ /* Early return if SIGMX is zero (matrix is already diagonal). */ if (sigmx == 0.) { - dlasrt_((char *)"D", n, &d__[1], &iinfo, (ftnlen)1); - return 0; + dlasrt_((char *)"D", n, &d__[1], &iinfo, (ftnlen)1); + return 0; } i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { /* Computing MAX */ - d__1 = sigmx, d__2 = d__[i__]; - sigmx = max(d__1,d__2); + d__1 = sigmx, d__2 = d__[i__]; + sigmx = max(d__1,d__2); /* L20: */ } @@ -247,16 +247,16 @@ f"> */ dcopy_(&i__1, &e[1], &c__1, &work[2], &c__2); i__1 = (*n << 1) - 1; i__2 = (*n << 1) - 1; - dlascl_((char *)"G", &c__0, &c__0, &sigmx, &scale, &i__1, &c__1, &work[1], &i__2, - &iinfo, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &sigmx, &scale, &i__1, &c__1, &work[1], &i__2, + &iinfo, (ftnlen)1); /* Compute the q's and e's. */ i__1 = (*n << 1) - 1; for (i__ = 1; i__ <= i__1; ++i__) { /* Computing 2nd power */ - d__1 = work[i__]; - work[i__] = d__1 * d__1; + d__1 = work[i__]; + work[i__] = d__1 * d__1; /* L30: */ } work[*n * 2] = 0.; @@ -264,27 +264,27 @@ f"> */ dlasq2_(n, &work[1], info); if (*info == 0) { - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - d__[i__] = sqrt(work[i__]); + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + d__[i__] = sqrt(work[i__]); /* L40: */ - } - dlascl_((char *)"G", &c__0, &c__0, &scale, &sigmx, n, &c__1, &d__[1], n, & - iinfo, (ftnlen)1); + } + dlascl_((char *)"G", &c__0, &c__0, &scale, &sigmx, n, &c__1, &d__[1], n, & + iinfo, (ftnlen)1); } else if (*info == 2) { /* Maximum number of iterations exceeded. Move data from WORK */ /* into D and E so the calling subroutine can try to finish */ - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - d__[i__] = sqrt(work[(i__ << 1) - 1]); - e[i__] = sqrt(work[i__ * 2]); - } - dlascl_((char *)"G", &c__0, &c__0, &scale, &sigmx, n, &c__1, &d__[1], n, & - iinfo, (ftnlen)1); - dlascl_((char *)"G", &c__0, &c__0, &scale, &sigmx, n, &c__1, &e[1], n, &iinfo, - (ftnlen)1); + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + d__[i__] = sqrt(work[(i__ << 1) - 1]); + e[i__] = sqrt(work[i__ * 2]); + } + dlascl_((char *)"G", &c__0, &c__0, &scale, &sigmx, n, &c__1, &d__[1], n, & + iinfo, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &scale, &sigmx, n, &c__1, &e[1], n, &iinfo, + (ftnlen)1); } return 0; @@ -294,5 +294,5 @@ f"> */ } /* dlasq1_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlasq2.cpp b/lib/linalg/dlasq2.cpp index a6362ecfdf..c9e4b30884 100644 --- a/lib/linalg/dlasq2.cpp +++ b/lib/linalg/dlasq2.cpp @@ -1,13 +1,13 @@ /* fortran/dlasq2.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -168,20 +168,20 @@ f"> */ integer iinfo; doublereal tempe, tempq; integer ttype; - extern /* Subroutine */ int dlasq3_(integer *, integer *, doublereal *, - integer *, doublereal *, doublereal *, doublereal *, doublereal *, - integer *, integer *, integer *, logical *, integer *, - doublereal *, doublereal *, doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *); + extern /* Subroutine */ int dlasq3_(integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, doublereal *, doublereal *, + integer *, integer *, integer *, logical *, integer *, + doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *); extern doublereal dlamch_(char *, ftnlen); doublereal deemin; integer iwhila, iwhilb; doublereal oldemn, safmin; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - extern /* Subroutine */ int dlasrt_(char *, integer *, doublereal *, - integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dlasrt_(char *, integer *, doublereal *, + integer *, ftnlen); /* -- LAPACK computational routine -- */ @@ -223,57 +223,57 @@ f"> */ tol2 = d__1 * d__1; if (*n < 0) { - *info = -1; - xerbla_((char *)"DLASQ2", &c__1, (ftnlen)6); - return 0; + *info = -1; + xerbla_((char *)"DLASQ2", &c__1, (ftnlen)6); + return 0; } else if (*n == 0) { - return 0; + return 0; } else if (*n == 1) { /* 1-by-1 case. */ - if (z__[1] < 0.) { - *info = -201; - xerbla_((char *)"DLASQ2", &c__2, (ftnlen)6); - } - return 0; + if (z__[1] < 0.) { + *info = -201; + xerbla_((char *)"DLASQ2", &c__2, (ftnlen)6); + } + return 0; } else if (*n == 2) { /* 2-by-2 case. */ - if (z__[1] < 0.) { - *info = -201; - xerbla_((char *)"DLASQ2", &c__2, (ftnlen)6); - return 0; - } else if (z__[2] < 0.) { - *info = -202; - xerbla_((char *)"DLASQ2", &c__2, (ftnlen)6); - return 0; - } else if (z__[3] < 0.) { - *info = -203; - xerbla_((char *)"DLASQ2", &c__2, (ftnlen)6); - return 0; - } else if (z__[3] > z__[1]) { - d__ = z__[3]; - z__[3] = z__[1]; - z__[1] = d__; - } - z__[5] = z__[1] + z__[2] + z__[3]; - if (z__[2] > z__[3] * tol2) { - t = (z__[1] - z__[3] + z__[2]) * .5; - s = z__[3] * (z__[2] / t); - if (s <= t) { - s = z__[3] * (z__[2] / (t * (sqrt(s / t + 1.) + 1.))); - } else { - s = z__[3] * (z__[2] / (t + sqrt(t) * sqrt(t + s))); - } - t = z__[1] + (s + z__[2]); - z__[3] *= z__[1] / t; - z__[1] = t; - } - z__[2] = z__[3]; - z__[6] = z__[2] + z__[1]; - return 0; + if (z__[1] < 0.) { + *info = -201; + xerbla_((char *)"DLASQ2", &c__2, (ftnlen)6); + return 0; + } else if (z__[2] < 0.) { + *info = -202; + xerbla_((char *)"DLASQ2", &c__2, (ftnlen)6); + return 0; + } else if (z__[3] < 0.) { + *info = -203; + xerbla_((char *)"DLASQ2", &c__2, (ftnlen)6); + return 0; + } else if (z__[3] > z__[1]) { + d__ = z__[3]; + z__[3] = z__[1]; + z__[1] = d__; + } + z__[5] = z__[1] + z__[2] + z__[3]; + if (z__[2] > z__[3] * tol2) { + t = (z__[1] - z__[3] + z__[2]) * .5; + s = z__[3] * (z__[2] / t); + if (s <= t) { + s = z__[3] * (z__[2] / (t * (sqrt(s / t + 1.) + 1.))); + } else { + s = z__[3] * (z__[2] / (t + sqrt(t) * sqrt(t + s))); + } + t = z__[1] + (s + z__[2]); + z__[3] *= z__[1] / t; + z__[1] = t; + } + z__[2] = z__[3]; + z__[6] = z__[2] + z__[1]; + return 0; } /* Check for negative data and compute sums of q's and e's. */ @@ -287,32 +287,32 @@ f"> */ i__1 = *n - 1 << 1; for (k = 1; k <= i__1; k += 2) { - if (z__[k] < 0.) { - *info = -(k + 200); - xerbla_((char *)"DLASQ2", &c__2, (ftnlen)6); - return 0; - } else if (z__[k + 1] < 0.) { - *info = -(k + 201); - xerbla_((char *)"DLASQ2", &c__2, (ftnlen)6); - return 0; - } - d__ += z__[k]; - e += z__[k + 1]; + if (z__[k] < 0.) { + *info = -(k + 200); + xerbla_((char *)"DLASQ2", &c__2, (ftnlen)6); + return 0; + } else if (z__[k + 1] < 0.) { + *info = -(k + 201); + xerbla_((char *)"DLASQ2", &c__2, (ftnlen)6); + return 0; + } + d__ += z__[k]; + e += z__[k + 1]; /* Computing MAX */ - d__1 = qmax, d__2 = z__[k]; - qmax = max(d__1,d__2); + d__1 = qmax, d__2 = z__[k]; + qmax = max(d__1,d__2); /* Computing MIN */ - d__1 = emin, d__2 = z__[k + 1]; - emin = min(d__1,d__2); + d__1 = emin, d__2 = z__[k + 1]; + emin = min(d__1,d__2); /* Computing MAX */ - d__1 = max(qmax,zmax), d__2 = z__[k + 1]; - zmax = max(d__1,d__2); + d__1 = max(qmax,zmax), d__2 = z__[k + 1]; + zmax = max(d__1,d__2); /* L10: */ } if (z__[(*n << 1) - 1] < 0.) { - *info = -((*n << 1) + 199); - xerbla_((char *)"DLASQ2", &c__2, (ftnlen)6); - return 0; + *info = -((*n << 1) + 199); + xerbla_((char *)"DLASQ2", &c__2, (ftnlen)6); + return 0; } d__ += z__[(*n << 1) - 1]; /* Computing MAX */ @@ -323,14 +323,14 @@ f"> */ /* Check for diagonality. */ if (e == 0.) { - i__1 = *n; - for (k = 2; k <= i__1; ++k) { - z__[k] = z__[(k << 1) - 1]; + i__1 = *n; + for (k = 2; k <= i__1; ++k) { + z__[k] = z__[(k << 1) - 1]; /* L20: */ - } - dlasrt_((char *)"D", n, &z__[1], &iinfo, (ftnlen)1); - z__[(*n << 1) - 1] = d__; - return 0; + } + dlasrt_((char *)"D", n, &z__[1], &iinfo, (ftnlen)1); + z__[(*n << 1) - 1] = d__; + return 0; } trace = d__ + e; @@ -338,22 +338,22 @@ f"> */ /* Check for zero data. */ if (trace == 0.) { - z__[(*n << 1) - 1] = 0.; - return 0; + z__[(*n << 1) - 1] = 0.; + return 0; } /* Check whether the machine is IEEE conformable. */ ieee = ilaenv_(&c__10, (char *)"DLASQ2", (char *)"N", &c__1, &c__2, &c__3, &c__4, (ftnlen) - 6, (ftnlen)1) == 1; + 6, (ftnlen)1) == 1; /* Rearrange data for locality: Z=(q1,qq1,e1,ee1,q2,qq2,e2,ee2,...). */ for (k = *n << 1; k >= 2; k += -2) { - z__[k * 2] = 0.; - z__[(k << 1) - 1] = z__[k]; - z__[(k << 1) - 2] = 0.; - z__[(k << 1) - 3] = z__[k - 1]; + z__[k * 2] = 0.; + z__[(k << 1) - 1] = z__[k]; + z__[(k << 1) - 2] = 0.; + z__[(k << 1) - 3] = z__[k - 1]; /* L30: */ } @@ -363,17 +363,17 @@ f"> */ /* Reverse the qd-array, if warranted. */ if (z__[(i0 << 2) - 3] * 1.5 < z__[(n0 << 2) - 3]) { - ipn4 = i0 + n0 << 2; - i__1 = i0 + n0 - 1 << 1; - for (i4 = i0 << 2; i4 <= i__1; i4 += 4) { - temp = z__[i4 - 3]; - z__[i4 - 3] = z__[ipn4 - i4 - 3]; - z__[ipn4 - i4 - 3] = temp; - temp = z__[i4 - 1]; - z__[i4 - 1] = z__[ipn4 - i4 - 5]; - z__[ipn4 - i4 - 5] = temp; + ipn4 = i0 + n0 << 2; + i__1 = i0 + n0 - 1 << 1; + for (i4 = i0 << 2; i4 <= i__1; i4 += 4) { + temp = z__[i4 - 3]; + z__[i4 - 3] = z__[ipn4 - i4 - 3]; + z__[ipn4 - i4 - 3] = temp; + temp = z__[i4 - 1]; + z__[i4 - 1] = z__[ipn4 - i4 - 5]; + z__[ipn4 - i4 - 5] = temp; /* L40: */ - } + } } /* Initial split checking via dqd and Li's test. */ @@ -382,61 +382,61 @@ f"> */ for (k = 1; k <= 2; ++k) { - d__ = z__[(n0 << 2) + pp - 3]; - i__1 = (i0 << 2) + pp; - for (i4 = (n0 - 1 << 2) + pp; i4 >= i__1; i4 += -4) { - if (z__[i4 - 1] <= tol2 * d__) { - z__[i4 - 1] = -0.; - d__ = z__[i4 - 3]; - } else { - d__ = z__[i4 - 3] * (d__ / (d__ + z__[i4 - 1])); - } + d__ = z__[(n0 << 2) + pp - 3]; + i__1 = (i0 << 2) + pp; + for (i4 = (n0 - 1 << 2) + pp; i4 >= i__1; i4 += -4) { + if (z__[i4 - 1] <= tol2 * d__) { + z__[i4 - 1] = -0.; + d__ = z__[i4 - 3]; + } else { + d__ = z__[i4 - 3] * (d__ / (d__ + z__[i4 - 1])); + } /* L50: */ - } + } /* dqd maps Z to ZZ plus Li's test. */ - emin = z__[(i0 << 2) + pp + 1]; - d__ = z__[(i0 << 2) + pp - 3]; - i__1 = (n0 - 1 << 2) + pp; - for (i4 = (i0 << 2) + pp; i4 <= i__1; i4 += 4) { - z__[i4 - (pp << 1) - 2] = d__ + z__[i4 - 1]; - if (z__[i4 - 1] <= tol2 * d__) { - z__[i4 - 1] = -0.; - z__[i4 - (pp << 1) - 2] = d__; - z__[i4 - (pp << 1)] = 0.; - d__ = z__[i4 + 1]; - } else if (safmin * z__[i4 + 1] < z__[i4 - (pp << 1) - 2] && - safmin * z__[i4 - (pp << 1) - 2] < z__[i4 + 1]) { - temp = z__[i4 + 1] / z__[i4 - (pp << 1) - 2]; - z__[i4 - (pp << 1)] = z__[i4 - 1] * temp; - d__ *= temp; - } else { - z__[i4 - (pp << 1)] = z__[i4 + 1] * (z__[i4 - 1] / z__[i4 - ( - pp << 1) - 2]); - d__ = z__[i4 + 1] * (d__ / z__[i4 - (pp << 1) - 2]); - } + emin = z__[(i0 << 2) + pp + 1]; + d__ = z__[(i0 << 2) + pp - 3]; + i__1 = (n0 - 1 << 2) + pp; + for (i4 = (i0 << 2) + pp; i4 <= i__1; i4 += 4) { + z__[i4 - (pp << 1) - 2] = d__ + z__[i4 - 1]; + if (z__[i4 - 1] <= tol2 * d__) { + z__[i4 - 1] = -0.; + z__[i4 - (pp << 1) - 2] = d__; + z__[i4 - (pp << 1)] = 0.; + d__ = z__[i4 + 1]; + } else if (safmin * z__[i4 + 1] < z__[i4 - (pp << 1) - 2] && + safmin * z__[i4 - (pp << 1) - 2] < z__[i4 + 1]) { + temp = z__[i4 + 1] / z__[i4 - (pp << 1) - 2]; + z__[i4 - (pp << 1)] = z__[i4 - 1] * temp; + d__ *= temp; + } else { + z__[i4 - (pp << 1)] = z__[i4 + 1] * (z__[i4 - 1] / z__[i4 - ( + pp << 1) - 2]); + d__ = z__[i4 + 1] * (d__ / z__[i4 - (pp << 1) - 2]); + } /* Computing MIN */ - d__1 = emin, d__2 = z__[i4 - (pp << 1)]; - emin = min(d__1,d__2); + d__1 = emin, d__2 = z__[i4 - (pp << 1)]; + emin = min(d__1,d__2); /* L60: */ - } - z__[(n0 << 2) - pp - 2] = d__; + } + z__[(n0 << 2) - pp - 2] = d__; /* Now find qmax. */ - qmax = z__[(i0 << 2) - pp - 2]; - i__1 = (n0 << 2) - pp - 2; - for (i4 = (i0 << 2) - pp + 2; i4 <= i__1; i4 += 4) { + qmax = z__[(i0 << 2) - pp - 2]; + i__1 = (n0 << 2) - pp - 2; + for (i4 = (i0 << 2) - pp + 2; i4 <= i__1; i4 += 4) { /* Computing MAX */ - d__1 = qmax, d__2 = z__[i4]; - qmax = max(d__1,d__2); + d__1 = qmax, d__2 = z__[i4]; + qmax = max(d__1,d__2); /* L70: */ - } + } /* Prepare for the next iteration on K. */ - pp = 1 - pp; + pp = 1 - pp; /* L80: */ } @@ -457,104 +457,104 @@ f"> */ i__1 = *n + 1; for (iwhila = 1; iwhila <= i__1; ++iwhila) { - if (n0 < 1) { - goto L170; - } + if (n0 < 1) { + goto L170; + } /* While array unfinished do */ /* E(N0) holds the value of SIGMA when submatrix in I0:N0 */ /* splits from the rest of the array, but is negated. */ - desig = 0.; - if (n0 == *n) { - sigma = 0.; - } else { - sigma = -z__[(n0 << 2) - 1]; - } - if (sigma < 0.) { - *info = 1; - return 0; - } + desig = 0.; + if (n0 == *n) { + sigma = 0.; + } else { + sigma = -z__[(n0 << 2) - 1]; + } + if (sigma < 0.) { + *info = 1; + return 0; + } /* Find last unreduced submatrix's top index I0, find QMAX and */ /* EMIN. Find Gershgorin-type bound if Q's much greater than E's. */ - emax = 0.; - if (n0 > i0) { - emin = (d__1 = z__[(n0 << 2) - 5], abs(d__1)); - } else { - emin = 0.; - } - qmin = z__[(n0 << 2) - 3]; - qmax = qmin; - for (i4 = n0 << 2; i4 >= 8; i4 += -4) { - if (z__[i4 - 5] <= 0.) { - goto L100; - } - if (qmin >= emax * 4.) { + emax = 0.; + if (n0 > i0) { + emin = (d__1 = z__[(n0 << 2) - 5], abs(d__1)); + } else { + emin = 0.; + } + qmin = z__[(n0 << 2) - 3]; + qmax = qmin; + for (i4 = n0 << 2; i4 >= 8; i4 += -4) { + if (z__[i4 - 5] <= 0.) { + goto L100; + } + if (qmin >= emax * 4.) { /* Computing MIN */ - d__1 = qmin, d__2 = z__[i4 - 3]; - qmin = min(d__1,d__2); + d__1 = qmin, d__2 = z__[i4 - 3]; + qmin = min(d__1,d__2); /* Computing MAX */ - d__1 = emax, d__2 = z__[i4 - 5]; - emax = max(d__1,d__2); - } + d__1 = emax, d__2 = z__[i4 - 5]; + emax = max(d__1,d__2); + } /* Computing MAX */ - d__1 = qmax, d__2 = z__[i4 - 7] + z__[i4 - 5]; - qmax = max(d__1,d__2); + d__1 = qmax, d__2 = z__[i4 - 7] + z__[i4 - 5]; + qmax = max(d__1,d__2); /* Computing MIN */ - d__1 = emin, d__2 = z__[i4 - 5]; - emin = min(d__1,d__2); + d__1 = emin, d__2 = z__[i4 - 5]; + emin = min(d__1,d__2); /* L90: */ - } - i4 = 4; + } + i4 = 4; L100: - i0 = i4 / 4; - pp = 0; + i0 = i4 / 4; + pp = 0; - if (n0 - i0 > 1) { - dee = z__[(i0 << 2) - 3]; - deemin = dee; - kmin = i0; - i__2 = (n0 << 2) - 3; - for (i4 = (i0 << 2) + 1; i4 <= i__2; i4 += 4) { - dee = z__[i4] * (dee / (dee + z__[i4 - 2])); - if (dee <= deemin) { - deemin = dee; - kmin = (i4 + 3) / 4; - } + if (n0 - i0 > 1) { + dee = z__[(i0 << 2) - 3]; + deemin = dee; + kmin = i0; + i__2 = (n0 << 2) - 3; + for (i4 = (i0 << 2) + 1; i4 <= i__2; i4 += 4) { + dee = z__[i4] * (dee / (dee + z__[i4 - 2])); + if (dee <= deemin) { + deemin = dee; + kmin = (i4 + 3) / 4; + } /* L110: */ - } - if (kmin - i0 << 1 < n0 - kmin && deemin <= z__[(n0 << 2) - 3] * - .5) { - ipn4 = i0 + n0 << 2; - pp = 2; - i__2 = i0 + n0 - 1 << 1; - for (i4 = i0 << 2; i4 <= i__2; i4 += 4) { - temp = z__[i4 - 3]; - z__[i4 - 3] = z__[ipn4 - i4 - 3]; - z__[ipn4 - i4 - 3] = temp; - temp = z__[i4 - 2]; - z__[i4 - 2] = z__[ipn4 - i4 - 2]; - z__[ipn4 - i4 - 2] = temp; - temp = z__[i4 - 1]; - z__[i4 - 1] = z__[ipn4 - i4 - 5]; - z__[ipn4 - i4 - 5] = temp; - temp = z__[i4]; - z__[i4] = z__[ipn4 - i4 - 4]; - z__[ipn4 - i4 - 4] = temp; + } + if (kmin - i0 << 1 < n0 - kmin && deemin <= z__[(n0 << 2) - 3] * + .5) { + ipn4 = i0 + n0 << 2; + pp = 2; + i__2 = i0 + n0 - 1 << 1; + for (i4 = i0 << 2; i4 <= i__2; i4 += 4) { + temp = z__[i4 - 3]; + z__[i4 - 3] = z__[ipn4 - i4 - 3]; + z__[ipn4 - i4 - 3] = temp; + temp = z__[i4 - 2]; + z__[i4 - 2] = z__[ipn4 - i4 - 2]; + z__[ipn4 - i4 - 2] = temp; + temp = z__[i4 - 1]; + z__[i4 - 1] = z__[ipn4 - i4 - 5]; + z__[ipn4 - i4 - 5] = temp; + temp = z__[i4]; + z__[i4] = z__[ipn4 - i4 - 4]; + z__[ipn4 - i4 - 4] = temp; /* L120: */ - } - } - } + } + } + } /* Put -(initial shift) into DMIN. */ /* Computing MAX */ - d__1 = 0., d__2 = qmin - sqrt(qmin) * 2. * sqrt(emax); - dmin__ = -max(d__1,d__2); + d__1 = 0., d__2 = qmin - sqrt(qmin) * 2. * sqrt(emax); + dmin__ = -max(d__1,d__2); /* Now I0:N0 is unreduced. */ /* PP = 0 for ping, PP = 1 for pong. */ @@ -562,113 +562,113 @@ L100: /* and that the tests for deflation upon entry in DLASQ3 */ /* should not be performed. */ - nbig = (n0 - i0 + 1) * 100; - i__2 = nbig; - for (iwhilb = 1; iwhilb <= i__2; ++iwhilb) { - if (i0 > n0) { - goto L150; - } + nbig = (n0 - i0 + 1) * 100; + i__2 = nbig; + for (iwhilb = 1; iwhilb <= i__2; ++iwhilb) { + if (i0 > n0) { + goto L150; + } /* While submatrix unfinished take a good dqds step. */ - dlasq3_(&i0, &n0, &z__[1], &pp, &dmin__, &sigma, &desig, &qmax, & - nfail, &iter, &ndiv, &ieee, &ttype, &dmin1, &dmin2, &dn, & - dn1, &dn2, &g, &tau); + dlasq3_(&i0, &n0, &z__[1], &pp, &dmin__, &sigma, &desig, &qmax, & + nfail, &iter, &ndiv, &ieee, &ttype, &dmin1, &dmin2, &dn, & + dn1, &dn2, &g, &tau); - pp = 1 - pp; + pp = 1 - pp; /* When EMIN is very small check for splits. */ - if (pp == 0 && n0 - i0 >= 3) { - if (z__[n0 * 4] <= tol2 * qmax || z__[(n0 << 2) - 1] <= tol2 * - sigma) { - splt = i0 - 1; - qmax = z__[(i0 << 2) - 3]; - emin = z__[(i0 << 2) - 1]; - oldemn = z__[i0 * 4]; - i__3 = n0 - 3 << 2; - for (i4 = i0 << 2; i4 <= i__3; i4 += 4) { - if (z__[i4] <= tol2 * z__[i4 - 3] || z__[i4 - 1] <= - tol2 * sigma) { - z__[i4 - 1] = -sigma; - splt = i4 / 4; - qmax = 0.; - emin = z__[i4 + 3]; - oldemn = z__[i4 + 4]; - } else { + if (pp == 0 && n0 - i0 >= 3) { + if (z__[n0 * 4] <= tol2 * qmax || z__[(n0 << 2) - 1] <= tol2 * + sigma) { + splt = i0 - 1; + qmax = z__[(i0 << 2) - 3]; + emin = z__[(i0 << 2) - 1]; + oldemn = z__[i0 * 4]; + i__3 = n0 - 3 << 2; + for (i4 = i0 << 2; i4 <= i__3; i4 += 4) { + if (z__[i4] <= tol2 * z__[i4 - 3] || z__[i4 - 1] <= + tol2 * sigma) { + z__[i4 - 1] = -sigma; + splt = i4 / 4; + qmax = 0.; + emin = z__[i4 + 3]; + oldemn = z__[i4 + 4]; + } else { /* Computing MAX */ - d__1 = qmax, d__2 = z__[i4 + 1]; - qmax = max(d__1,d__2); + d__1 = qmax, d__2 = z__[i4 + 1]; + qmax = max(d__1,d__2); /* Computing MIN */ - d__1 = emin, d__2 = z__[i4 - 1]; - emin = min(d__1,d__2); + d__1 = emin, d__2 = z__[i4 - 1]; + emin = min(d__1,d__2); /* Computing MIN */ - d__1 = oldemn, d__2 = z__[i4]; - oldemn = min(d__1,d__2); - } + d__1 = oldemn, d__2 = z__[i4]; + oldemn = min(d__1,d__2); + } /* L130: */ - } - z__[(n0 << 2) - 1] = emin; - z__[n0 * 4] = oldemn; - i0 = splt + 1; - } - } + } + z__[(n0 << 2) - 1] = emin; + z__[n0 * 4] = oldemn; + i0 = splt + 1; + } + } /* L140: */ - } + } - *info = 2; + *info = 2; /* Maximum number of iterations exceeded, restore the shift */ /* SIGMA and place the new d's and e's in a qd array. */ /* This might need to be done for several blocks */ - i1 = i0; - n1 = n0; + i1 = i0; + n1 = n0; L145: - tempq = z__[(i0 << 2) - 3]; - z__[(i0 << 2) - 3] += sigma; - i__2 = n0; - for (k = i0 + 1; k <= i__2; ++k) { - tempe = z__[(k << 2) - 5]; - z__[(k << 2) - 5] *= tempq / z__[(k << 2) - 7]; - tempq = z__[(k << 2) - 3]; - z__[(k << 2) - 3] = z__[(k << 2) - 3] + sigma + tempe - z__[(k << - 2) - 5]; - } + tempq = z__[(i0 << 2) - 3]; + z__[(i0 << 2) - 3] += sigma; + i__2 = n0; + for (k = i0 + 1; k <= i__2; ++k) { + tempe = z__[(k << 2) - 5]; + z__[(k << 2) - 5] *= tempq / z__[(k << 2) - 7]; + tempq = z__[(k << 2) - 3]; + z__[(k << 2) - 3] = z__[(k << 2) - 3] + sigma + tempe - z__[(k << + 2) - 5]; + } /* Prepare to do this on the previous block if there is one */ - if (i1 > 1) { - n1 = i1 - 1; - while(i1 >= 2 && z__[(i1 << 2) - 5] >= 0.) { - --i1; - } - sigma = -z__[(n1 << 2) - 1]; - goto L145; - } - i__2 = *n; - for (k = 1; k <= i__2; ++k) { - z__[(k << 1) - 1] = z__[(k << 2) - 3]; + if (i1 > 1) { + n1 = i1 - 1; + while(i1 >= 2 && z__[(i1 << 2) - 5] >= 0.) { + --i1; + } + sigma = -z__[(n1 << 2) - 1]; + goto L145; + } + i__2 = *n; + for (k = 1; k <= i__2; ++k) { + z__[(k << 1) - 1] = z__[(k << 2) - 3]; /* Only the block 1..N0 is unfinished. The rest of the e's */ /* must be essentially zero, although sometimes other data */ /* has been stored in them. */ - if (k < n0) { - z__[k * 2] = z__[(k << 2) - 1]; - } else { - z__[k * 2] = 0.; - } - } - return 0; + if (k < n0) { + z__[k * 2] = z__[(k << 2) - 1]; + } else { + z__[k * 2] = 0.; + } + } + return 0; /* end IWHILB */ L150: /* L160: */ - ; + ; } *info = 3; @@ -682,7 +682,7 @@ L170: i__1 = *n; for (k = 2; k <= i__1; ++k) { - z__[k] = z__[(k << 2) - 3]; + z__[k] = z__[(k << 2) - 3]; /* L180: */ } @@ -692,7 +692,7 @@ L170: e = 0.; for (k = *n; k >= 1; --k) { - e += z__[k]; + e += z__[k]; /* L190: */ } @@ -712,5 +712,5 @@ L170: } /* dlasq2_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlasq3.cpp b/lib/linalg/dlasq3.cpp index e5974545a6..f43c67ca34 100644 --- a/lib/linalg/dlasq3.cpp +++ b/lib/linalg/dlasq3.cpp @@ -1,13 +1,13 @@ /* fortran/dlasq3.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -196,12 +196,12 @@ f"> */ /* > \ingroup auxOTHERcomputational */ /* ===================================================================== */ -/* Subroutine */ int dlasq3_(integer *i0, integer *n0, doublereal *z__, - integer *pp, doublereal *dmin__, doublereal *sigma, doublereal *desig, - doublereal *qmax, integer *nfail, integer *iter, integer *ndiv, - logical *ieee, integer *ttype, doublereal *dmin1, doublereal *dmin2, - doublereal *dn, doublereal *dn1, doublereal *dn2, doublereal *g, - doublereal *tau) +/* Subroutine */ int dlasq3_(integer *i0, integer *n0, doublereal *z__, + integer *pp, doublereal *dmin__, doublereal *sigma, doublereal *desig, + doublereal *qmax, integer *nfail, integer *iter, integer *ndiv, + logical *ieee, integer *ttype, doublereal *dmin1, doublereal *dmin2, + doublereal *dn, doublereal *dn1, doublereal *dn2, doublereal *g, + doublereal *tau) { /* System generated locals */ integer i__1; @@ -216,15 +216,15 @@ f"> */ doublereal eps, tol; integer n0in, ipn4; doublereal tol2, temp; - extern /* Subroutine */ int dlasq4_(integer *, integer *, doublereal *, - integer *, integer *, doublereal *, doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *, doublereal *, integer *, - doublereal *), dlasq5_(integer *, integer *, doublereal *, - integer *, doublereal *, doublereal *, doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *, doublereal *, logical * - , doublereal *), dlasq6_(integer *, integer *, doublereal *, - integer *, doublereal *, doublereal *, doublereal *, doublereal *, - doublereal *, doublereal *); + extern /* Subroutine */ int dlasq4_(integer *, integer *, doublereal *, + integer *, integer *, doublereal *, doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *, doublereal *, integer *, + doublereal *), dlasq5_(integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *, doublereal *, logical * + , doublereal *), dlasq6_(integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, doublereal *); extern doublereal dlamch_(char *, ftnlen); extern logical disnan_(doublereal *); @@ -268,21 +268,21 @@ f"> */ L10: if (*n0 < *i0) { - return 0; + return 0; } if (*n0 == *i0) { - goto L20; + goto L20; } nn = (*n0 << 2) + *pp; if (*n0 == *i0 + 1) { - goto L40; + goto L40; } /* Check whether E(N0-1) is negligible, 1 eigenvalue. */ - if (z__[nn - 5] > tol2 * (*sigma + z__[nn - 3]) && z__[nn - (*pp << 1) - - 4] > tol2 * z__[nn - 7]) { - goto L30; + if (z__[nn - 5] > tol2 * (*sigma + z__[nn - 3]) && z__[nn - (*pp << 1) - + 4] > tol2 * z__[nn - 7]) { + goto L30; } L20: @@ -296,28 +296,28 @@ L20: L30: if (z__[nn - 9] > tol2 * *sigma && z__[nn - (*pp << 1) - 8] > tol2 * z__[ - nn - 11]) { - goto L50; + nn - 11]) { + goto L50; } L40: if (z__[nn - 3] > z__[nn - 7]) { - s = z__[nn - 3]; - z__[nn - 3] = z__[nn - 7]; - z__[nn - 7] = s; + s = z__[nn - 3]; + z__[nn - 3] = z__[nn - 7]; + z__[nn - 7] = s; } t = (z__[nn - 7] - z__[nn - 3] + z__[nn - 5]) * .5; if (z__[nn - 5] > z__[nn - 3] * tol2 && t != 0.) { - s = z__[nn - 3] * (z__[nn - 5] / t); - if (s <= t) { - s = z__[nn - 3] * (z__[nn - 5] / (t * (sqrt(s / t + 1.) + 1.))); - } else { - s = z__[nn - 3] * (z__[nn - 5] / (t + sqrt(t) * sqrt(t + s))); - } - t = z__[nn - 7] + (s + z__[nn - 5]); - z__[nn - 3] *= z__[nn - 7] / t; - z__[nn - 7] = t; + s = z__[nn - 3] * (z__[nn - 5] / t); + if (s <= t) { + s = z__[nn - 3] * (z__[nn - 5] / (t * (sqrt(s / t + 1.) + 1.))); + } else { + s = z__[nn - 3] * (z__[nn - 5] / (t + sqrt(t) * sqrt(t + s))); + } + t = z__[nn - 7] + (s + z__[nn - 5]); + z__[nn - 3] *= z__[nn - 7] / t; + z__[nn - 7] = t; } z__[(*n0 << 2) - 7] = z__[nn - 7] + *sigma; z__[(*n0 << 2) - 3] = z__[nn - 3] + *sigma; @@ -326,64 +326,64 @@ L40: L50: if (*pp == 2) { - *pp = 0; + *pp = 0; } /* Reverse the qd-array, if warranted. */ if (*dmin__ <= 0. || *n0 < n0in) { - if (z__[(*i0 << 2) + *pp - 3] * 1.5 < z__[(*n0 << 2) + *pp - 3]) { - ipn4 = *i0 + *n0 << 2; - i__1 = *i0 + *n0 - 1 << 1; - for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { - temp = z__[j4 - 3]; - z__[j4 - 3] = z__[ipn4 - j4 - 3]; - z__[ipn4 - j4 - 3] = temp; - temp = z__[j4 - 2]; - z__[j4 - 2] = z__[ipn4 - j4 - 2]; - z__[ipn4 - j4 - 2] = temp; - temp = z__[j4 - 1]; - z__[j4 - 1] = z__[ipn4 - j4 - 5]; - z__[ipn4 - j4 - 5] = temp; - temp = z__[j4]; - z__[j4] = z__[ipn4 - j4 - 4]; - z__[ipn4 - j4 - 4] = temp; + if (z__[(*i0 << 2) + *pp - 3] * 1.5 < z__[(*n0 << 2) + *pp - 3]) { + ipn4 = *i0 + *n0 << 2; + i__1 = *i0 + *n0 - 1 << 1; + for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { + temp = z__[j4 - 3]; + z__[j4 - 3] = z__[ipn4 - j4 - 3]; + z__[ipn4 - j4 - 3] = temp; + temp = z__[j4 - 2]; + z__[j4 - 2] = z__[ipn4 - j4 - 2]; + z__[ipn4 - j4 - 2] = temp; + temp = z__[j4 - 1]; + z__[j4 - 1] = z__[ipn4 - j4 - 5]; + z__[ipn4 - j4 - 5] = temp; + temp = z__[j4]; + z__[j4] = z__[ipn4 - j4 - 4]; + z__[ipn4 - j4 - 4] = temp; /* L60: */ - } - if (*n0 - *i0 <= 4) { - z__[(*n0 << 2) + *pp - 1] = z__[(*i0 << 2) + *pp - 1]; - z__[(*n0 << 2) - *pp] = z__[(*i0 << 2) - *pp]; - } + } + if (*n0 - *i0 <= 4) { + z__[(*n0 << 2) + *pp - 1] = z__[(*i0 << 2) + *pp - 1]; + z__[(*n0 << 2) - *pp] = z__[(*i0 << 2) - *pp]; + } /* Computing MIN */ - d__1 = *dmin2, d__2 = z__[(*n0 << 2) + *pp - 1]; - *dmin2 = min(d__1,d__2); + d__1 = *dmin2, d__2 = z__[(*n0 << 2) + *pp - 1]; + *dmin2 = min(d__1,d__2); /* Computing MIN */ - d__1 = z__[(*n0 << 2) + *pp - 1], d__2 = z__[(*i0 << 2) + *pp - 1] - , d__1 = min(d__1,d__2), d__2 = z__[(*i0 << 2) + *pp + 3]; - z__[(*n0 << 2) + *pp - 1] = min(d__1,d__2); + d__1 = z__[(*n0 << 2) + *pp - 1], d__2 = z__[(*i0 << 2) + *pp - 1] + , d__1 = min(d__1,d__2), d__2 = z__[(*i0 << 2) + *pp + 3]; + z__[(*n0 << 2) + *pp - 1] = min(d__1,d__2); /* Computing MIN */ - d__1 = z__[(*n0 << 2) - *pp], d__2 = z__[(*i0 << 2) - *pp], d__1 = - min(d__1,d__2), d__2 = z__[(*i0 << 2) - *pp + 4]; - z__[(*n0 << 2) - *pp] = min(d__1,d__2); + d__1 = z__[(*n0 << 2) - *pp], d__2 = z__[(*i0 << 2) - *pp], d__1 = + min(d__1,d__2), d__2 = z__[(*i0 << 2) - *pp + 4]; + z__[(*n0 << 2) - *pp] = min(d__1,d__2); /* Computing MAX */ - d__1 = *qmax, d__2 = z__[(*i0 << 2) + *pp - 3], d__1 = max(d__1, - d__2), d__2 = z__[(*i0 << 2) + *pp + 1]; - *qmax = max(d__1,d__2); - *dmin__ = -0.; - } + d__1 = *qmax, d__2 = z__[(*i0 << 2) + *pp - 3], d__1 = max(d__1, + d__2), d__2 = z__[(*i0 << 2) + *pp + 1]; + *qmax = max(d__1,d__2); + *dmin__ = -0.; + } } /* Choose a shift. */ - dlasq4_(i0, n0, &z__[1], pp, &n0in, dmin__, dmin1, dmin2, dn, dn1, dn2, - tau, ttype, g); + dlasq4_(i0, n0, &z__[1], pp, &n0in, dmin__, dmin1, dmin2, dn, dn1, dn2, + tau, ttype, g); /* Call dqds until DMIN > 0. */ L70: - dlasq5_(i0, n0, &z__[1], pp, tau, sigma, dmin__, dmin1, dmin2, dn, dn1, - dn2, ieee, &eps); + dlasq5_(i0, n0, &z__[1], pp, tau, sigma, dmin__, dmin1, dmin2, dn, dn1, + dn2, ieee, &eps); *ndiv += *n0 - *i0 + 2; ++(*iter); @@ -394,55 +394,55 @@ L70: /* Success. */ - goto L90; + goto L90; - } else if (*dmin__ < 0. && *dmin1 > 0. && z__[(*n0 - 1 << 2) - *pp] < tol - * (*sigma + *dn1) && abs(*dn) < tol * *sigma) { + } else if (*dmin__ < 0. && *dmin1 > 0. && z__[(*n0 - 1 << 2) - *pp] < tol + * (*sigma + *dn1) && abs(*dn) < tol * *sigma) { /* Convergence hidden by negative DN. */ - z__[(*n0 - 1 << 2) - *pp + 2] = 0.; - *dmin__ = 0.; - goto L90; + z__[(*n0 - 1 << 2) - *pp + 2] = 0.; + *dmin__ = 0.; + goto L90; } else if (*dmin__ < 0.) { /* TAU too big. Select new TAU and try again. */ - ++(*nfail); - if (*ttype < -22) { + ++(*nfail); + if (*ttype < -22) { /* Failed twice. Play it safe. */ - *tau = 0.; - } else if (*dmin1 > 0.) { + *tau = 0.; + } else if (*dmin1 > 0.) { /* Late failure. Gives excellent shift. */ - *tau = (*tau + *dmin__) * (1. - eps * 2.); - *ttype += -11; - } else { + *tau = (*tau + *dmin__) * (1. - eps * 2.); + *ttype += -11; + } else { /* Early failure. Divide by 4. */ - *tau *= .25; - *ttype += -12; - } - goto L70; + *tau *= .25; + *ttype += -12; + } + goto L70; } else if (disnan_(dmin__)) { /* NaN. */ - if (*tau == 0.) { - goto L80; - } else { - *tau = 0.; - goto L70; - } + if (*tau == 0.) { + goto L80; + } else { + *tau = 0.; + goto L70; + } } else { /* Possible underflow. Play it safe. */ - goto L80; + goto L80; } /* Risk of underflow. */ @@ -455,12 +455,12 @@ L80: L90: if (*tau < *sigma) { - *desig += *tau; - t = *sigma + *desig; - *desig -= t - *sigma; + *desig += *tau; + t = *sigma + *desig; + *desig -= t - *sigma; } else { - t = *sigma + *tau; - *desig = *sigma - (t - *tau) + *desig; + t = *sigma + *tau; + *desig = *sigma - (t - *tau) + *desig; } *sigma = t; @@ -471,5 +471,5 @@ L90: } /* dlasq3_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlasq4.cpp b/lib/linalg/dlasq4.cpp index 4841ada1d2..9629f53161 100644 --- a/lib/linalg/dlasq4.cpp +++ b/lib/linalg/dlasq4.cpp @@ -1,13 +1,13 @@ /* fortran/dlasq4.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -167,10 +167,10 @@ f"> */ /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int dlasq4_(integer *i0, integer *n0, doublereal *z__, - integer *pp, integer *n0in, doublereal *dmin__, doublereal *dmin1, - doublereal *dmin2, doublereal *dn, doublereal *dn1, doublereal *dn2, - doublereal *tau, integer *ttype, doublereal *g) +/* Subroutine */ int dlasq4_(integer *i0, integer *n0, doublereal *z__, + integer *pp, integer *n0in, doublereal *dmin__, doublereal *dmin1, + doublereal *dmin2, doublereal *dn, doublereal *dn1, doublereal *dn2, + doublereal *tau, integer *ttype, doublereal *g) { /* System generated locals */ integer i__1; @@ -212,9 +212,9 @@ f"> */ /* Function Body */ if (*dmin__ <= 0.) { - *tau = -(*dmin__); - *ttype = -1; - return 0; + *tau = -(*dmin__); + *ttype = -1; + return 0; } nn = (*n0 << 2) + *pp; @@ -222,215 +222,215 @@ f"> */ /* No eigenvalues deflated. */ - if (*dmin__ == *dn || *dmin__ == *dn1) { + if (*dmin__ == *dn || *dmin__ == *dn1) { - b1 = sqrt(z__[nn - 3]) * sqrt(z__[nn - 5]); - b2 = sqrt(z__[nn - 7]) * sqrt(z__[nn - 9]); - a2 = z__[nn - 7] + z__[nn - 5]; + b1 = sqrt(z__[nn - 3]) * sqrt(z__[nn - 5]); + b2 = sqrt(z__[nn - 7]) * sqrt(z__[nn - 9]); + a2 = z__[nn - 7] + z__[nn - 5]; /* Cases 2 and 3. */ - if (*dmin__ == *dn && *dmin1 == *dn1) { - gap2 = *dmin2 - a2 - *dmin2 * .25; - if (gap2 > 0. && gap2 > b2) { - gap1 = a2 - *dn - b2 / gap2 * b2; - } else { - gap1 = a2 - *dn - (b1 + b2); - } - if (gap1 > 0. && gap1 > b1) { + if (*dmin__ == *dn && *dmin1 == *dn1) { + gap2 = *dmin2 - a2 - *dmin2 * .25; + if (gap2 > 0. && gap2 > b2) { + gap1 = a2 - *dn - b2 / gap2 * b2; + } else { + gap1 = a2 - *dn - (b1 + b2); + } + if (gap1 > 0. && gap1 > b1) { /* Computing MAX */ - d__1 = *dn - b1 / gap1 * b1, d__2 = *dmin__ * .5; - s = max(d__1,d__2); - *ttype = -2; - } else { - s = 0.; - if (*dn > b1) { - s = *dn - b1; - } - if (a2 > b1 + b2) { + d__1 = *dn - b1 / gap1 * b1, d__2 = *dmin__ * .5; + s = max(d__1,d__2); + *ttype = -2; + } else { + s = 0.; + if (*dn > b1) { + s = *dn - b1; + } + if (a2 > b1 + b2) { /* Computing MIN */ - d__1 = s, d__2 = a2 - (b1 + b2); - s = min(d__1,d__2); - } + d__1 = s, d__2 = a2 - (b1 + b2); + s = min(d__1,d__2); + } /* Computing MAX */ - d__1 = s, d__2 = *dmin__ * .333; - s = max(d__1,d__2); - *ttype = -3; - } - } else { + d__1 = s, d__2 = *dmin__ * .333; + s = max(d__1,d__2); + *ttype = -3; + } + } else { /* Case 4. */ - *ttype = -4; - s = *dmin__ * .25; - if (*dmin__ == *dn) { - gam = *dn; - a2 = 0.; - if (z__[nn - 5] > z__[nn - 7]) { - return 0; - } - b2 = z__[nn - 5] / z__[nn - 7]; - np = nn - 9; - } else { - np = nn - (*pp << 1); - gam = *dn1; - if (z__[np - 4] > z__[np - 2]) { - return 0; - } - a2 = z__[np - 4] / z__[np - 2]; - if (z__[nn - 9] > z__[nn - 11]) { - return 0; - } - b2 = z__[nn - 9] / z__[nn - 11]; - np = nn - 13; - } + *ttype = -4; + s = *dmin__ * .25; + if (*dmin__ == *dn) { + gam = *dn; + a2 = 0.; + if (z__[nn - 5] > z__[nn - 7]) { + return 0; + } + b2 = z__[nn - 5] / z__[nn - 7]; + np = nn - 9; + } else { + np = nn - (*pp << 1); + gam = *dn1; + if (z__[np - 4] > z__[np - 2]) { + return 0; + } + a2 = z__[np - 4] / z__[np - 2]; + if (z__[nn - 9] > z__[nn - 11]) { + return 0; + } + b2 = z__[nn - 9] / z__[nn - 11]; + np = nn - 13; + } /* Approximate contribution to norm squared from I < NN-1. */ - a2 += b2; - i__1 = (*i0 << 2) - 1 + *pp; - for (i4 = np; i4 >= i__1; i4 += -4) { - if (b2 == 0.) { - goto L20; - } - b1 = b2; - if (z__[i4] > z__[i4 - 2]) { - return 0; - } - b2 *= z__[i4] / z__[i4 - 2]; - a2 += b2; - if (max(b2,b1) * 100. < a2 || .563 < a2) { - goto L20; - } + a2 += b2; + i__1 = (*i0 << 2) - 1 + *pp; + for (i4 = np; i4 >= i__1; i4 += -4) { + if (b2 == 0.) { + goto L20; + } + b1 = b2; + if (z__[i4] > z__[i4 - 2]) { + return 0; + } + b2 *= z__[i4] / z__[i4 - 2]; + a2 += b2; + if (max(b2,b1) * 100. < a2 || .563 < a2) { + goto L20; + } /* L10: */ - } + } L20: - a2 *= 1.05; + a2 *= 1.05; /* Rayleigh quotient residual bound. */ - if (a2 < .563) { - s = gam * (1. - sqrt(a2)) / (a2 + 1.); - } - } - } else if (*dmin__ == *dn2) { + if (a2 < .563) { + s = gam * (1. - sqrt(a2)) / (a2 + 1.); + } + } + } else if (*dmin__ == *dn2) { /* Case 5. */ - *ttype = -5; - s = *dmin__ * .25; + *ttype = -5; + s = *dmin__ * .25; /* Compute contribution to norm squared from I > NN-2. */ - np = nn - (*pp << 1); - b1 = z__[np - 2]; - b2 = z__[np - 6]; - gam = *dn2; - if (z__[np - 8] > b2 || z__[np - 4] > b1) { - return 0; - } - a2 = z__[np - 8] / b2 * (z__[np - 4] / b1 + 1.); + np = nn - (*pp << 1); + b1 = z__[np - 2]; + b2 = z__[np - 6]; + gam = *dn2; + if (z__[np - 8] > b2 || z__[np - 4] > b1) { + return 0; + } + a2 = z__[np - 8] / b2 * (z__[np - 4] / b1 + 1.); /* Approximate contribution to norm squared from I < NN-2. */ - if (*n0 - *i0 > 2) { - b2 = z__[nn - 13] / z__[nn - 15]; - a2 += b2; - i__1 = (*i0 << 2) - 1 + *pp; - for (i4 = nn - 17; i4 >= i__1; i4 += -4) { - if (b2 == 0.) { - goto L40; - } - b1 = b2; - if (z__[i4] > z__[i4 - 2]) { - return 0; - } - b2 *= z__[i4] / z__[i4 - 2]; - a2 += b2; - if (max(b2,b1) * 100. < a2 || .563 < a2) { - goto L40; - } + if (*n0 - *i0 > 2) { + b2 = z__[nn - 13] / z__[nn - 15]; + a2 += b2; + i__1 = (*i0 << 2) - 1 + *pp; + for (i4 = nn - 17; i4 >= i__1; i4 += -4) { + if (b2 == 0.) { + goto L40; + } + b1 = b2; + if (z__[i4] > z__[i4 - 2]) { + return 0; + } + b2 *= z__[i4] / z__[i4 - 2]; + a2 += b2; + if (max(b2,b1) * 100. < a2 || .563 < a2) { + goto L40; + } /* L30: */ - } + } L40: - a2 *= 1.05; - } + a2 *= 1.05; + } - if (a2 < .563) { - s = gam * (1. - sqrt(a2)) / (a2 + 1.); - } - } else { + if (a2 < .563) { + s = gam * (1. - sqrt(a2)) / (a2 + 1.); + } + } else { /* Case 6, no information to guide us. */ - if (*ttype == -6) { - *g += (1. - *g) * .333; - } else if (*ttype == -18) { - *g = .083250000000000005; - } else { - *g = .25; - } - s = *g * *dmin__; - *ttype = -6; - } + if (*ttype == -6) { + *g += (1. - *g) * .333; + } else if (*ttype == -18) { + *g = .083250000000000005; + } else { + *g = .25; + } + s = *g * *dmin__; + *ttype = -6; + } } else if (*n0in == *n0 + 1) { /* One eigenvalue just deflated. Use DMIN1, DN1 for DMIN and DN. */ - if (*dmin1 == *dn1 && *dmin2 == *dn2) { + if (*dmin1 == *dn1 && *dmin2 == *dn2) { /* Cases 7 and 8. */ - *ttype = -7; - s = *dmin1 * .333; - if (z__[nn - 5] > z__[nn - 7]) { - return 0; - } - b1 = z__[nn - 5] / z__[nn - 7]; - b2 = b1; - if (b2 == 0.) { - goto L60; - } - i__1 = (*i0 << 2) - 1 + *pp; - for (i4 = (*n0 << 2) - 9 + *pp; i4 >= i__1; i4 += -4) { - a2 = b1; - if (z__[i4] > z__[i4 - 2]) { - return 0; - } - b1 *= z__[i4] / z__[i4 - 2]; - b2 += b1; - if (max(b1,a2) * 100. < b2) { - goto L60; - } + *ttype = -7; + s = *dmin1 * .333; + if (z__[nn - 5] > z__[nn - 7]) { + return 0; + } + b1 = z__[nn - 5] / z__[nn - 7]; + b2 = b1; + if (b2 == 0.) { + goto L60; + } + i__1 = (*i0 << 2) - 1 + *pp; + for (i4 = (*n0 << 2) - 9 + *pp; i4 >= i__1; i4 += -4) { + a2 = b1; + if (z__[i4] > z__[i4 - 2]) { + return 0; + } + b1 *= z__[i4] / z__[i4 - 2]; + b2 += b1; + if (max(b1,a2) * 100. < b2) { + goto L60; + } /* L50: */ - } + } L60: - b2 = sqrt(b2 * 1.05); + b2 = sqrt(b2 * 1.05); /* Computing 2nd power */ - d__1 = b2; - a2 = *dmin1 / (d__1 * d__1 + 1.); - gap2 = *dmin2 * .5 - a2; - if (gap2 > 0. && gap2 > b2 * a2) { + d__1 = b2; + a2 = *dmin1 / (d__1 * d__1 + 1.); + gap2 = *dmin2 * .5 - a2; + if (gap2 > 0. && gap2 > b2 * a2) { /* Computing MAX */ - d__1 = s, d__2 = a2 * (1. - a2 * 1.01 * (b2 / gap2) * b2); - s = max(d__1,d__2); - } else { + d__1 = s, d__2 = a2 * (1. - a2 * 1.01 * (b2 / gap2) * b2); + s = max(d__1,d__2); + } else { /* Computing MAX */ - d__1 = s, d__2 = a2 * (1. - b2 * 1.01); - s = max(d__1,d__2); - *ttype = -8; - } - } else { + d__1 = s, d__2 = a2 * (1. - b2 * 1.01); + s = max(d__1,d__2); + *ttype = -8; + } + } else { /* Case 9. */ - s = *dmin1 * .25; - if (*dmin1 == *dn1) { - s = *dmin1 * .5; - } - *ttype = -9; - } + s = *dmin1 * .25; + if (*dmin1 == *dn1) { + s = *dmin1 * .5; + } + *ttype = -9; + } } else if (*n0in == *n0 + 2) { @@ -438,55 +438,55 @@ L60: /* Cases 10 and 11. */ - if (*dmin2 == *dn2 && z__[nn - 5] * 2. < z__[nn - 7]) { - *ttype = -10; - s = *dmin2 * .333; - if (z__[nn - 5] > z__[nn - 7]) { - return 0; - } - b1 = z__[nn - 5] / z__[nn - 7]; - b2 = b1; - if (b2 == 0.) { - goto L80; - } - i__1 = (*i0 << 2) - 1 + *pp; - for (i4 = (*n0 << 2) - 9 + *pp; i4 >= i__1; i4 += -4) { - if (z__[i4] > z__[i4 - 2]) { - return 0; - } - b1 *= z__[i4] / z__[i4 - 2]; - b2 += b1; - if (b1 * 100. < b2) { - goto L80; - } + if (*dmin2 == *dn2 && z__[nn - 5] * 2. < z__[nn - 7]) { + *ttype = -10; + s = *dmin2 * .333; + if (z__[nn - 5] > z__[nn - 7]) { + return 0; + } + b1 = z__[nn - 5] / z__[nn - 7]; + b2 = b1; + if (b2 == 0.) { + goto L80; + } + i__1 = (*i0 << 2) - 1 + *pp; + for (i4 = (*n0 << 2) - 9 + *pp; i4 >= i__1; i4 += -4) { + if (z__[i4] > z__[i4 - 2]) { + return 0; + } + b1 *= z__[i4] / z__[i4 - 2]; + b2 += b1; + if (b1 * 100. < b2) { + goto L80; + } /* L70: */ - } + } L80: - b2 = sqrt(b2 * 1.05); + b2 = sqrt(b2 * 1.05); /* Computing 2nd power */ - d__1 = b2; - a2 = *dmin2 / (d__1 * d__1 + 1.); - gap2 = z__[nn - 7] + z__[nn - 9] - sqrt(z__[nn - 11]) * sqrt(z__[ - nn - 9]) - a2; - if (gap2 > 0. && gap2 > b2 * a2) { + d__1 = b2; + a2 = *dmin2 / (d__1 * d__1 + 1.); + gap2 = z__[nn - 7] + z__[nn - 9] - sqrt(z__[nn - 11]) * sqrt(z__[ + nn - 9]) - a2; + if (gap2 > 0. && gap2 > b2 * a2) { /* Computing MAX */ - d__1 = s, d__2 = a2 * (1. - a2 * 1.01 * (b2 / gap2) * b2); - s = max(d__1,d__2); - } else { + d__1 = s, d__2 = a2 * (1. - a2 * 1.01 * (b2 / gap2) * b2); + s = max(d__1,d__2); + } else { /* Computing MAX */ - d__1 = s, d__2 = a2 * (1. - b2 * 1.01); - s = max(d__1,d__2); - } - } else { - s = *dmin2 * .25; - *ttype = -11; - } + d__1 = s, d__2 = a2 * (1. - b2 * 1.01); + s = max(d__1,d__2); + } + } else { + s = *dmin2 * .25; + *ttype = -11; + } } else if (*n0in > *n0 + 2) { /* Case 12, more than two eigenvalues deflated. No information. */ - s = 0.; - *ttype = -12; + s = 0.; + *ttype = -12; } *tau = s; @@ -497,5 +497,5 @@ L80: } /* dlasq4_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlasq5.cpp b/lib/linalg/dlasq5.cpp index 13ae0ed20c..a7cd93932f 100644 --- a/lib/linalg/dlasq5.cpp +++ b/lib/linalg/dlasq5.cpp @@ -1,13 +1,13 @@ /* fortran/dlasq5.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -159,10 +159,10 @@ f"> */ /* > \ingroup auxOTHERcomputational */ /* ===================================================================== */ -/* Subroutine */ int dlasq5_(integer *i0, integer *n0, doublereal *z__, - integer *pp, doublereal *tau, doublereal *sigma, doublereal *dmin__, - doublereal *dmin1, doublereal *dmin2, doublereal *dn, doublereal * - dnm1, doublereal *dnm2, logical *ieee, doublereal *eps) +/* Subroutine */ int dlasq5_(integer *i0, integer *n0, doublereal *z__, + integer *pp, doublereal *tau, doublereal *sigma, doublereal *dmin__, + doublereal *dmin1, doublereal *dmin2, doublereal *dn, doublereal * + dnm1, doublereal *dnm2, logical *ieee, doublereal *eps) { /* System generated locals */ integer i__1; @@ -198,273 +198,273 @@ f"> */ /* Function Body */ if (*n0 - *i0 - 1 <= 0) { - return 0; + return 0; } dthresh = *eps * (*sigma + *tau); if (*tau < dthresh * .5) { - *tau = 0.; + *tau = 0.; } if (*tau != 0.) { - j4 = (*i0 << 2) + *pp - 3; - emin = z__[j4 + 4]; - d__ = z__[j4] - *tau; - *dmin__ = d__; - *dmin1 = -z__[j4]; + j4 = (*i0 << 2) + *pp - 3; + emin = z__[j4 + 4]; + d__ = z__[j4] - *tau; + *dmin__ = d__; + *dmin1 = -z__[j4]; - if (*ieee) { + if (*ieee) { /* Code for IEEE arithmetic. */ - if (*pp == 0) { - i__1 = *n0 - 3 << 2; - for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { - z__[j4 - 2] = d__ + z__[j4 - 1]; - temp = z__[j4 + 1] / z__[j4 - 2]; - d__ = d__ * temp - *tau; - *dmin__ = min(*dmin__,d__); - z__[j4] = z__[j4 - 1] * temp; + if (*pp == 0) { + i__1 = *n0 - 3 << 2; + for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { + z__[j4 - 2] = d__ + z__[j4 - 1]; + temp = z__[j4 + 1] / z__[j4 - 2]; + d__ = d__ * temp - *tau; + *dmin__ = min(*dmin__,d__); + z__[j4] = z__[j4 - 1] * temp; /* Computing MIN */ - d__1 = z__[j4]; - emin = min(d__1,emin); + d__1 = z__[j4]; + emin = min(d__1,emin); /* L10: */ - } - } else { - i__1 = *n0 - 3 << 2; - for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { - z__[j4 - 3] = d__ + z__[j4]; - temp = z__[j4 + 2] / z__[j4 - 3]; - d__ = d__ * temp - *tau; - *dmin__ = min(*dmin__,d__); - z__[j4 - 1] = z__[j4] * temp; + } + } else { + i__1 = *n0 - 3 << 2; + for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { + z__[j4 - 3] = d__ + z__[j4]; + temp = z__[j4 + 2] / z__[j4 - 3]; + d__ = d__ * temp - *tau; + *dmin__ = min(*dmin__,d__); + z__[j4 - 1] = z__[j4] * temp; /* Computing MIN */ - d__1 = z__[j4 - 1]; - emin = min(d__1,emin); + d__1 = z__[j4 - 1]; + emin = min(d__1,emin); /* L20: */ - } - } + } + } /* Unroll last two steps. */ - *dnm2 = d__; - *dmin2 = *dmin__; - j4 = (*n0 - 2 << 2) - *pp; - j4p2 = j4 + (*pp << 1) - 1; - z__[j4 - 2] = *dnm2 + z__[j4p2]; - z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); - *dnm1 = z__[j4p2 + 2] * (*dnm2 / z__[j4 - 2]) - *tau; - *dmin__ = min(*dmin__,*dnm1); + *dnm2 = d__; + *dmin2 = *dmin__; + j4 = (*n0 - 2 << 2) - *pp; + j4p2 = j4 + (*pp << 1) - 1; + z__[j4 - 2] = *dnm2 + z__[j4p2]; + z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); + *dnm1 = z__[j4p2 + 2] * (*dnm2 / z__[j4 - 2]) - *tau; + *dmin__ = min(*dmin__,*dnm1); - *dmin1 = *dmin__; - j4 += 4; - j4p2 = j4 + (*pp << 1) - 1; - z__[j4 - 2] = *dnm1 + z__[j4p2]; - z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); - *dn = z__[j4p2 + 2] * (*dnm1 / z__[j4 - 2]) - *tau; - *dmin__ = min(*dmin__,*dn); + *dmin1 = *dmin__; + j4 += 4; + j4p2 = j4 + (*pp << 1) - 1; + z__[j4 - 2] = *dnm1 + z__[j4p2]; + z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); + *dn = z__[j4p2 + 2] * (*dnm1 / z__[j4 - 2]) - *tau; + *dmin__ = min(*dmin__,*dn); - } else { + } else { /* Code for non IEEE arithmetic. */ - if (*pp == 0) { - i__1 = *n0 - 3 << 2; - for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { - z__[j4 - 2] = d__ + z__[j4 - 1]; - if (d__ < 0.) { - return 0; - } else { - z__[j4] = z__[j4 + 1] * (z__[j4 - 1] / z__[j4 - 2]); - d__ = z__[j4 + 1] * (d__ / z__[j4 - 2]) - *tau; - } - *dmin__ = min(*dmin__,d__); + if (*pp == 0) { + i__1 = *n0 - 3 << 2; + for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { + z__[j4 - 2] = d__ + z__[j4 - 1]; + if (d__ < 0.) { + return 0; + } else { + z__[j4] = z__[j4 + 1] * (z__[j4 - 1] / z__[j4 - 2]); + d__ = z__[j4 + 1] * (d__ / z__[j4 - 2]) - *tau; + } + *dmin__ = min(*dmin__,d__); /* Computing MIN */ - d__1 = emin, d__2 = z__[j4]; - emin = min(d__1,d__2); + d__1 = emin, d__2 = z__[j4]; + emin = min(d__1,d__2); /* L30: */ - } - } else { - i__1 = *n0 - 3 << 2; - for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { - z__[j4 - 3] = d__ + z__[j4]; - if (d__ < 0.) { - return 0; - } else { - z__[j4 - 1] = z__[j4 + 2] * (z__[j4] / z__[j4 - 3]); - d__ = z__[j4 + 2] * (d__ / z__[j4 - 3]) - *tau; - } - *dmin__ = min(*dmin__,d__); + } + } else { + i__1 = *n0 - 3 << 2; + for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { + z__[j4 - 3] = d__ + z__[j4]; + if (d__ < 0.) { + return 0; + } else { + z__[j4 - 1] = z__[j4 + 2] * (z__[j4] / z__[j4 - 3]); + d__ = z__[j4 + 2] * (d__ / z__[j4 - 3]) - *tau; + } + *dmin__ = min(*dmin__,d__); /* Computing MIN */ - d__1 = emin, d__2 = z__[j4 - 1]; - emin = min(d__1,d__2); + d__1 = emin, d__2 = z__[j4 - 1]; + emin = min(d__1,d__2); /* L40: */ - } - } + } + } /* Unroll last two steps. */ - *dnm2 = d__; - *dmin2 = *dmin__; - j4 = (*n0 - 2 << 2) - *pp; - j4p2 = j4 + (*pp << 1) - 1; - z__[j4 - 2] = *dnm2 + z__[j4p2]; - if (*dnm2 < 0.) { - return 0; - } else { - z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); - *dnm1 = z__[j4p2 + 2] * (*dnm2 / z__[j4 - 2]) - *tau; - } - *dmin__ = min(*dmin__,*dnm1); + *dnm2 = d__; + *dmin2 = *dmin__; + j4 = (*n0 - 2 << 2) - *pp; + j4p2 = j4 + (*pp << 1) - 1; + z__[j4 - 2] = *dnm2 + z__[j4p2]; + if (*dnm2 < 0.) { + return 0; + } else { + z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); + *dnm1 = z__[j4p2 + 2] * (*dnm2 / z__[j4 - 2]) - *tau; + } + *dmin__ = min(*dmin__,*dnm1); - *dmin1 = *dmin__; - j4 += 4; - j4p2 = j4 + (*pp << 1) - 1; - z__[j4 - 2] = *dnm1 + z__[j4p2]; - if (*dnm1 < 0.) { - return 0; - } else { - z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); - *dn = z__[j4p2 + 2] * (*dnm1 / z__[j4 - 2]) - *tau; - } - *dmin__ = min(*dmin__,*dn); + *dmin1 = *dmin__; + j4 += 4; + j4p2 = j4 + (*pp << 1) - 1; + z__[j4 - 2] = *dnm1 + z__[j4p2]; + if (*dnm1 < 0.) { + return 0; + } else { + z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); + *dn = z__[j4p2 + 2] * (*dnm1 / z__[j4 - 2]) - *tau; + } + *dmin__ = min(*dmin__,*dn); - } + } } else { /* This is the version that sets d's to zero if they are small enough */ - j4 = (*i0 << 2) + *pp - 3; - emin = z__[j4 + 4]; - d__ = z__[j4] - *tau; - *dmin__ = d__; - *dmin1 = -z__[j4]; - if (*ieee) { + j4 = (*i0 << 2) + *pp - 3; + emin = z__[j4 + 4]; + d__ = z__[j4] - *tau; + *dmin__ = d__; + *dmin1 = -z__[j4]; + if (*ieee) { /* Code for IEEE arithmetic. */ - if (*pp == 0) { - i__1 = *n0 - 3 << 2; - for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { - z__[j4 - 2] = d__ + z__[j4 - 1]; - temp = z__[j4 + 1] / z__[j4 - 2]; - d__ = d__ * temp - *tau; - if (d__ < dthresh) { - d__ = 0.; - } - *dmin__ = min(*dmin__,d__); - z__[j4] = z__[j4 - 1] * temp; + if (*pp == 0) { + i__1 = *n0 - 3 << 2; + for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { + z__[j4 - 2] = d__ + z__[j4 - 1]; + temp = z__[j4 + 1] / z__[j4 - 2]; + d__ = d__ * temp - *tau; + if (d__ < dthresh) { + d__ = 0.; + } + *dmin__ = min(*dmin__,d__); + z__[j4] = z__[j4 - 1] * temp; /* Computing MIN */ - d__1 = z__[j4]; - emin = min(d__1,emin); + d__1 = z__[j4]; + emin = min(d__1,emin); /* L50: */ - } - } else { - i__1 = *n0 - 3 << 2; - for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { - z__[j4 - 3] = d__ + z__[j4]; - temp = z__[j4 + 2] / z__[j4 - 3]; - d__ = d__ * temp - *tau; - if (d__ < dthresh) { - d__ = 0.; - } - *dmin__ = min(*dmin__,d__); - z__[j4 - 1] = z__[j4] * temp; + } + } else { + i__1 = *n0 - 3 << 2; + for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { + z__[j4 - 3] = d__ + z__[j4]; + temp = z__[j4 + 2] / z__[j4 - 3]; + d__ = d__ * temp - *tau; + if (d__ < dthresh) { + d__ = 0.; + } + *dmin__ = min(*dmin__,d__); + z__[j4 - 1] = z__[j4] * temp; /* Computing MIN */ - d__1 = z__[j4 - 1]; - emin = min(d__1,emin); + d__1 = z__[j4 - 1]; + emin = min(d__1,emin); /* L60: */ - } - } + } + } /* Unroll last two steps. */ - *dnm2 = d__; - *dmin2 = *dmin__; - j4 = (*n0 - 2 << 2) - *pp; - j4p2 = j4 + (*pp << 1) - 1; - z__[j4 - 2] = *dnm2 + z__[j4p2]; - z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); - *dnm1 = z__[j4p2 + 2] * (*dnm2 / z__[j4 - 2]) - *tau; - *dmin__ = min(*dmin__,*dnm1); + *dnm2 = d__; + *dmin2 = *dmin__; + j4 = (*n0 - 2 << 2) - *pp; + j4p2 = j4 + (*pp << 1) - 1; + z__[j4 - 2] = *dnm2 + z__[j4p2]; + z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); + *dnm1 = z__[j4p2 + 2] * (*dnm2 / z__[j4 - 2]) - *tau; + *dmin__ = min(*dmin__,*dnm1); - *dmin1 = *dmin__; - j4 += 4; - j4p2 = j4 + (*pp << 1) - 1; - z__[j4 - 2] = *dnm1 + z__[j4p2]; - z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); - *dn = z__[j4p2 + 2] * (*dnm1 / z__[j4 - 2]) - *tau; - *dmin__ = min(*dmin__,*dn); + *dmin1 = *dmin__; + j4 += 4; + j4p2 = j4 + (*pp << 1) - 1; + z__[j4 - 2] = *dnm1 + z__[j4p2]; + z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); + *dn = z__[j4p2 + 2] * (*dnm1 / z__[j4 - 2]) - *tau; + *dmin__ = min(*dmin__,*dn); - } else { + } else { /* Code for non IEEE arithmetic. */ - if (*pp == 0) { - i__1 = *n0 - 3 << 2; - for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { - z__[j4 - 2] = d__ + z__[j4 - 1]; - if (d__ < 0.) { - return 0; - } else { - z__[j4] = z__[j4 + 1] * (z__[j4 - 1] / z__[j4 - 2]); - d__ = z__[j4 + 1] * (d__ / z__[j4 - 2]) - *tau; - } - if (d__ < dthresh) { - d__ = 0.; - } - *dmin__ = min(*dmin__,d__); + if (*pp == 0) { + i__1 = *n0 - 3 << 2; + for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { + z__[j4 - 2] = d__ + z__[j4 - 1]; + if (d__ < 0.) { + return 0; + } else { + z__[j4] = z__[j4 + 1] * (z__[j4 - 1] / z__[j4 - 2]); + d__ = z__[j4 + 1] * (d__ / z__[j4 - 2]) - *tau; + } + if (d__ < dthresh) { + d__ = 0.; + } + *dmin__ = min(*dmin__,d__); /* Computing MIN */ - d__1 = emin, d__2 = z__[j4]; - emin = min(d__1,d__2); + d__1 = emin, d__2 = z__[j4]; + emin = min(d__1,d__2); /* L70: */ - } - } else { - i__1 = *n0 - 3 << 2; - for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { - z__[j4 - 3] = d__ + z__[j4]; - if (d__ < 0.) { - return 0; - } else { - z__[j4 - 1] = z__[j4 + 2] * (z__[j4] / z__[j4 - 3]); - d__ = z__[j4 + 2] * (d__ / z__[j4 - 3]) - *tau; - } - if (d__ < dthresh) { - d__ = 0.; - } - *dmin__ = min(*dmin__,d__); + } + } else { + i__1 = *n0 - 3 << 2; + for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { + z__[j4 - 3] = d__ + z__[j4]; + if (d__ < 0.) { + return 0; + } else { + z__[j4 - 1] = z__[j4 + 2] * (z__[j4] / z__[j4 - 3]); + d__ = z__[j4 + 2] * (d__ / z__[j4 - 3]) - *tau; + } + if (d__ < dthresh) { + d__ = 0.; + } + *dmin__ = min(*dmin__,d__); /* Computing MIN */ - d__1 = emin, d__2 = z__[j4 - 1]; - emin = min(d__1,d__2); + d__1 = emin, d__2 = z__[j4 - 1]; + emin = min(d__1,d__2); /* L80: */ - } - } + } + } /* Unroll last two steps. */ - *dnm2 = d__; - *dmin2 = *dmin__; - j4 = (*n0 - 2 << 2) - *pp; - j4p2 = j4 + (*pp << 1) - 1; - z__[j4 - 2] = *dnm2 + z__[j4p2]; - if (*dnm2 < 0.) { - return 0; - } else { - z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); - *dnm1 = z__[j4p2 + 2] * (*dnm2 / z__[j4 - 2]) - *tau; - } - *dmin__ = min(*dmin__,*dnm1); + *dnm2 = d__; + *dmin2 = *dmin__; + j4 = (*n0 - 2 << 2) - *pp; + j4p2 = j4 + (*pp << 1) - 1; + z__[j4 - 2] = *dnm2 + z__[j4p2]; + if (*dnm2 < 0.) { + return 0; + } else { + z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); + *dnm1 = z__[j4p2 + 2] * (*dnm2 / z__[j4 - 2]) - *tau; + } + *dmin__ = min(*dmin__,*dnm1); - *dmin1 = *dmin__; - j4 += 4; - j4p2 = j4 + (*pp << 1) - 1; - z__[j4 - 2] = *dnm1 + z__[j4p2]; - if (*dnm1 < 0.) { - return 0; - } else { - z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); - *dn = z__[j4p2 + 2] * (*dnm1 / z__[j4 - 2]) - *tau; - } - *dmin__ = min(*dmin__,*dn); + *dmin1 = *dmin__; + j4 += 4; + j4p2 = j4 + (*pp << 1) - 1; + z__[j4 - 2] = *dnm1 + z__[j4p2]; + if (*dnm1 < 0.) { + return 0; + } else { + z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); + *dn = z__[j4p2 + 2] * (*dnm1 / z__[j4 - 2]) - *tau; + } + *dmin__ = min(*dmin__,*dn); - } + } } z__[j4 + 2] = *dn; @@ -476,5 +476,5 @@ f"> */ } /* dlasq5_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlasq6.cpp b/lib/linalg/dlasq6.cpp index b06e9ad028..96bda77630 100644 --- a/lib/linalg/dlasq6.cpp +++ b/lib/linalg/dlasq6.cpp @@ -1,13 +1,13 @@ /* fortran/dlasq6.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -134,9 +134,9 @@ f"> */ /* > \ingroup auxOTHERcomputational */ /* ===================================================================== */ -/* Subroutine */ int dlasq6_(integer *i0, integer *n0, doublereal *z__, - integer *pp, doublereal *dmin__, doublereal *dmin1, doublereal *dmin2, - doublereal *dn, doublereal *dnm1, doublereal *dnm2) +/* Subroutine */ int dlasq6_(integer *i0, integer *n0, doublereal *z__, + integer *pp, doublereal *dmin__, doublereal *dmin1, doublereal *dmin2, + doublereal *dn, doublereal *dnm1, doublereal *dnm2) { /* System generated locals */ integer i__1; @@ -176,7 +176,7 @@ f"> */ /* Function Body */ if (*n0 - *i0 - 1 <= 0) { - return 0; + return 0; } safmin = dlamch_((char *)"Safe minimum", (ftnlen)12); @@ -186,53 +186,53 @@ f"> */ *dmin__ = d__; if (*pp == 0) { - i__1 = *n0 - 3 << 2; - for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { - z__[j4 - 2] = d__ + z__[j4 - 1]; - if (z__[j4 - 2] == 0.) { - z__[j4] = 0.; - d__ = z__[j4 + 1]; - *dmin__ = d__; - emin = 0.; - } else if (safmin * z__[j4 + 1] < z__[j4 - 2] && safmin * z__[j4 - - 2] < z__[j4 + 1]) { - temp = z__[j4 + 1] / z__[j4 - 2]; - z__[j4] = z__[j4 - 1] * temp; - d__ *= temp; - } else { - z__[j4] = z__[j4 + 1] * (z__[j4 - 1] / z__[j4 - 2]); - d__ = z__[j4 + 1] * (d__ / z__[j4 - 2]); - } - *dmin__ = min(*dmin__,d__); + i__1 = *n0 - 3 << 2; + for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { + z__[j4 - 2] = d__ + z__[j4 - 1]; + if (z__[j4 - 2] == 0.) { + z__[j4] = 0.; + d__ = z__[j4 + 1]; + *dmin__ = d__; + emin = 0.; + } else if (safmin * z__[j4 + 1] < z__[j4 - 2] && safmin * z__[j4 + - 2] < z__[j4 + 1]) { + temp = z__[j4 + 1] / z__[j4 - 2]; + z__[j4] = z__[j4 - 1] * temp; + d__ *= temp; + } else { + z__[j4] = z__[j4 + 1] * (z__[j4 - 1] / z__[j4 - 2]); + d__ = z__[j4 + 1] * (d__ / z__[j4 - 2]); + } + *dmin__ = min(*dmin__,d__); /* Computing MIN */ - d__1 = emin, d__2 = z__[j4]; - emin = min(d__1,d__2); + d__1 = emin, d__2 = z__[j4]; + emin = min(d__1,d__2); /* L10: */ - } + } } else { - i__1 = *n0 - 3 << 2; - for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { - z__[j4 - 3] = d__ + z__[j4]; - if (z__[j4 - 3] == 0.) { - z__[j4 - 1] = 0.; - d__ = z__[j4 + 2]; - *dmin__ = d__; - emin = 0.; - } else if (safmin * z__[j4 + 2] < z__[j4 - 3] && safmin * z__[j4 - - 3] < z__[j4 + 2]) { - temp = z__[j4 + 2] / z__[j4 - 3]; - z__[j4 - 1] = z__[j4] * temp; - d__ *= temp; - } else { - z__[j4 - 1] = z__[j4 + 2] * (z__[j4] / z__[j4 - 3]); - d__ = z__[j4 + 2] * (d__ / z__[j4 - 3]); - } - *dmin__ = min(*dmin__,d__); + i__1 = *n0 - 3 << 2; + for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { + z__[j4 - 3] = d__ + z__[j4]; + if (z__[j4 - 3] == 0.) { + z__[j4 - 1] = 0.; + d__ = z__[j4 + 2]; + *dmin__ = d__; + emin = 0.; + } else if (safmin * z__[j4 + 2] < z__[j4 - 3] && safmin * z__[j4 + - 3] < z__[j4 + 2]) { + temp = z__[j4 + 2] / z__[j4 - 3]; + z__[j4 - 1] = z__[j4] * temp; + d__ *= temp; + } else { + z__[j4 - 1] = z__[j4 + 2] * (z__[j4] / z__[j4 - 3]); + d__ = z__[j4 + 2] * (d__ / z__[j4 - 3]); + } + *dmin__ = min(*dmin__,d__); /* Computing MIN */ - d__1 = emin, d__2 = z__[j4 - 1]; - emin = min(d__1,d__2); + d__1 = emin, d__2 = z__[j4 - 1]; + emin = min(d__1,d__2); /* L20: */ - } + } } /* Unroll last two steps. */ @@ -243,18 +243,18 @@ f"> */ j4p2 = j4 + (*pp << 1) - 1; z__[j4 - 2] = *dnm2 + z__[j4p2]; if (z__[j4 - 2] == 0.) { - z__[j4] = 0.; - *dnm1 = z__[j4p2 + 2]; - *dmin__ = *dnm1; - emin = 0.; - } else if (safmin * z__[j4p2 + 2] < z__[j4 - 2] && safmin * z__[j4 - 2] < - z__[j4p2 + 2]) { - temp = z__[j4p2 + 2] / z__[j4 - 2]; - z__[j4] = z__[j4p2] * temp; - *dnm1 = *dnm2 * temp; + z__[j4] = 0.; + *dnm1 = z__[j4p2 + 2]; + *dmin__ = *dnm1; + emin = 0.; + } else if (safmin * z__[j4p2 + 2] < z__[j4 - 2] && safmin * z__[j4 - 2] < + z__[j4p2 + 2]) { + temp = z__[j4p2 + 2] / z__[j4 - 2]; + z__[j4] = z__[j4p2] * temp; + *dnm1 = *dnm2 * temp; } else { - z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); - *dnm1 = z__[j4p2 + 2] * (*dnm2 / z__[j4 - 2]); + z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); + *dnm1 = z__[j4p2 + 2] * (*dnm2 / z__[j4 - 2]); } *dmin__ = min(*dmin__,*dnm1); @@ -263,18 +263,18 @@ f"> */ j4p2 = j4 + (*pp << 1) - 1; z__[j4 - 2] = *dnm1 + z__[j4p2]; if (z__[j4 - 2] == 0.) { - z__[j4] = 0.; - *dn = z__[j4p2 + 2]; - *dmin__ = *dn; - emin = 0.; - } else if (safmin * z__[j4p2 + 2] < z__[j4 - 2] && safmin * z__[j4 - 2] < - z__[j4p2 + 2]) { - temp = z__[j4p2 + 2] / z__[j4 - 2]; - z__[j4] = z__[j4p2] * temp; - *dn = *dnm1 * temp; + z__[j4] = 0.; + *dn = z__[j4p2 + 2]; + *dmin__ = *dn; + emin = 0.; + } else if (safmin * z__[j4p2 + 2] < z__[j4 - 2] && safmin * z__[j4 - 2] < + z__[j4p2 + 2]) { + temp = z__[j4p2 + 2] / z__[j4 - 2]; + z__[j4] = z__[j4p2] * temp; + *dn = *dnm1 * temp; } else { - z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); - *dn = z__[j4p2 + 2] * (*dnm1 / z__[j4 - 2]); + z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); + *dn = z__[j4p2 + 2] * (*dnm1 / z__[j4 - 2]); } *dmin__ = min(*dmin__,*dn); @@ -287,5 +287,5 @@ f"> */ } /* dlasq6_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlasr.cpp b/lib/linalg/dlasr.cpp index c4de2f85a9..5baf2cd50c 100644 --- a/lib/linalg/dlasr.cpp +++ b/lib/linalg/dlasr.cpp @@ -1,13 +1,13 @@ /* fortran/dlasr.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -216,8 +216,8 @@ extern "C" { /* ===================================================================== */ /* Subroutine */ int dlasr_(char *side, char *pivot, char *direct, integer *m, - integer *n, doublereal *c__, doublereal *s, doublereal *a, integer * - lda, ftnlen side_len, ftnlen pivot_len, ftnlen direct_len) + integer *n, doublereal *c__, doublereal *s, doublereal *a, integer * + lda, ftnlen side_len, ftnlen pivot_len, ftnlen direct_len) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; @@ -265,264 +265,264 @@ extern "C" { /* Function Body */ info = 0; if (! (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1) || lsame_(side, (char *)"R", ( - ftnlen)1, (ftnlen)1))) { - info = 1; - } else if (! (lsame_(pivot, (char *)"V", (ftnlen)1, (ftnlen)1) || lsame_(pivot, - (char *)"T", (ftnlen)1, (ftnlen)1) || lsame_(pivot, (char *)"B", (ftnlen)1, ( - ftnlen)1))) { - info = 2; - } else if (! (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1) || lsame_(direct, - (char *)"B", (ftnlen)1, (ftnlen)1))) { - info = 3; + ftnlen)1, (ftnlen)1))) { + info = 1; + } else if (! (lsame_(pivot, (char *)"V", (ftnlen)1, (ftnlen)1) || lsame_(pivot, + (char *)"T", (ftnlen)1, (ftnlen)1) || lsame_(pivot, (char *)"B", (ftnlen)1, ( + ftnlen)1))) { + info = 2; + } else if (! (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1) || lsame_(direct, + (char *)"B", (ftnlen)1, (ftnlen)1))) { + info = 3; } else if (*m < 0) { - info = 4; + info = 4; } else if (*n < 0) { - info = 5; + info = 5; } else if (*lda < max(1,*m)) { - info = 9; + info = 9; } if (info != 0) { - xerbla_((char *)"DLASR ", &info, (ftnlen)6); - return 0; + xerbla_((char *)"DLASR ", &info, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*m == 0 || *n == 0) { - return 0; + return 0; } if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { /* Form P * A */ - if (lsame_(pivot, (char *)"V", (ftnlen)1, (ftnlen)1)) { - if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { - i__1 = *m - 1; - for (j = 1; j <= i__1; ++j) { - ctemp = c__[j]; - stemp = s[j]; - if (ctemp != 1. || stemp != 0.) { - i__2 = *n; - for (i__ = 1; i__ <= i__2; ++i__) { - temp = a[j + 1 + i__ * a_dim1]; - a[j + 1 + i__ * a_dim1] = ctemp * temp - stemp * - a[j + i__ * a_dim1]; - a[j + i__ * a_dim1] = stemp * temp + ctemp * a[j - + i__ * a_dim1]; + if (lsame_(pivot, (char *)"V", (ftnlen)1, (ftnlen)1)) { + if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { + i__1 = *m - 1; + for (j = 1; j <= i__1; ++j) { + ctemp = c__[j]; + stemp = s[j]; + if (ctemp != 1. || stemp != 0.) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + temp = a[j + 1 + i__ * a_dim1]; + a[j + 1 + i__ * a_dim1] = ctemp * temp - stemp * + a[j + i__ * a_dim1]; + a[j + i__ * a_dim1] = stemp * temp + ctemp * a[j + + i__ * a_dim1]; /* L10: */ - } - } + } + } /* L20: */ - } - } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { - for (j = *m - 1; j >= 1; --j) { - ctemp = c__[j]; - stemp = s[j]; - if (ctemp != 1. || stemp != 0.) { - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - temp = a[j + 1 + i__ * a_dim1]; - a[j + 1 + i__ * a_dim1] = ctemp * temp - stemp * - a[j + i__ * a_dim1]; - a[j + i__ * a_dim1] = stemp * temp + ctemp * a[j - + i__ * a_dim1]; + } + } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { + for (j = *m - 1; j >= 1; --j) { + ctemp = c__[j]; + stemp = s[j]; + if (ctemp != 1. || stemp != 0.) { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + temp = a[j + 1 + i__ * a_dim1]; + a[j + 1 + i__ * a_dim1] = ctemp * temp - stemp * + a[j + i__ * a_dim1]; + a[j + i__ * a_dim1] = stemp * temp + ctemp * a[j + + i__ * a_dim1]; /* L30: */ - } - } + } + } /* L40: */ - } - } - } else if (lsame_(pivot, (char *)"T", (ftnlen)1, (ftnlen)1)) { - if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { - i__1 = *m; - for (j = 2; j <= i__1; ++j) { - ctemp = c__[j - 1]; - stemp = s[j - 1]; - if (ctemp != 1. || stemp != 0.) { - i__2 = *n; - for (i__ = 1; i__ <= i__2; ++i__) { - temp = a[j + i__ * a_dim1]; - a[j + i__ * a_dim1] = ctemp * temp - stemp * a[ - i__ * a_dim1 + 1]; - a[i__ * a_dim1 + 1] = stemp * temp + ctemp * a[ - i__ * a_dim1 + 1]; + } + } + } else if (lsame_(pivot, (char *)"T", (ftnlen)1, (ftnlen)1)) { + if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { + i__1 = *m; + for (j = 2; j <= i__1; ++j) { + ctemp = c__[j - 1]; + stemp = s[j - 1]; + if (ctemp != 1. || stemp != 0.) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + temp = a[j + i__ * a_dim1]; + a[j + i__ * a_dim1] = ctemp * temp - stemp * a[ + i__ * a_dim1 + 1]; + a[i__ * a_dim1 + 1] = stemp * temp + ctemp * a[ + i__ * a_dim1 + 1]; /* L50: */ - } - } + } + } /* L60: */ - } - } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { - for (j = *m; j >= 2; --j) { - ctemp = c__[j - 1]; - stemp = s[j - 1]; - if (ctemp != 1. || stemp != 0.) { - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - temp = a[j + i__ * a_dim1]; - a[j + i__ * a_dim1] = ctemp * temp - stemp * a[ - i__ * a_dim1 + 1]; - a[i__ * a_dim1 + 1] = stemp * temp + ctemp * a[ - i__ * a_dim1 + 1]; + } + } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { + for (j = *m; j >= 2; --j) { + ctemp = c__[j - 1]; + stemp = s[j - 1]; + if (ctemp != 1. || stemp != 0.) { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + temp = a[j + i__ * a_dim1]; + a[j + i__ * a_dim1] = ctemp * temp - stemp * a[ + i__ * a_dim1 + 1]; + a[i__ * a_dim1 + 1] = stemp * temp + ctemp * a[ + i__ * a_dim1 + 1]; /* L70: */ - } - } + } + } /* L80: */ - } - } - } else if (lsame_(pivot, (char *)"B", (ftnlen)1, (ftnlen)1)) { - if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { - i__1 = *m - 1; - for (j = 1; j <= i__1; ++j) { - ctemp = c__[j]; - stemp = s[j]; - if (ctemp != 1. || stemp != 0.) { - i__2 = *n; - for (i__ = 1; i__ <= i__2; ++i__) { - temp = a[j + i__ * a_dim1]; - a[j + i__ * a_dim1] = stemp * a[*m + i__ * a_dim1] - + ctemp * temp; - a[*m + i__ * a_dim1] = ctemp * a[*m + i__ * - a_dim1] - stemp * temp; + } + } + } else if (lsame_(pivot, (char *)"B", (ftnlen)1, (ftnlen)1)) { + if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { + i__1 = *m - 1; + for (j = 1; j <= i__1; ++j) { + ctemp = c__[j]; + stemp = s[j]; + if (ctemp != 1. || stemp != 0.) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + temp = a[j + i__ * a_dim1]; + a[j + i__ * a_dim1] = stemp * a[*m + i__ * a_dim1] + + ctemp * temp; + a[*m + i__ * a_dim1] = ctemp * a[*m + i__ * + a_dim1] - stemp * temp; /* L90: */ - } - } + } + } /* L100: */ - } - } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { - for (j = *m - 1; j >= 1; --j) { - ctemp = c__[j]; - stemp = s[j]; - if (ctemp != 1. || stemp != 0.) { - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - temp = a[j + i__ * a_dim1]; - a[j + i__ * a_dim1] = stemp * a[*m + i__ * a_dim1] - + ctemp * temp; - a[*m + i__ * a_dim1] = ctemp * a[*m + i__ * - a_dim1] - stemp * temp; + } + } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { + for (j = *m - 1; j >= 1; --j) { + ctemp = c__[j]; + stemp = s[j]; + if (ctemp != 1. || stemp != 0.) { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + temp = a[j + i__ * a_dim1]; + a[j + i__ * a_dim1] = stemp * a[*m + i__ * a_dim1] + + ctemp * temp; + a[*m + i__ * a_dim1] = ctemp * a[*m + i__ * + a_dim1] - stemp * temp; /* L110: */ - } - } + } + } /* L120: */ - } - } - } + } + } + } } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { /* Form A * P**T */ - if (lsame_(pivot, (char *)"V", (ftnlen)1, (ftnlen)1)) { - if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { - i__1 = *n - 1; - for (j = 1; j <= i__1; ++j) { - ctemp = c__[j]; - stemp = s[j]; - if (ctemp != 1. || stemp != 0.) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - temp = a[i__ + (j + 1) * a_dim1]; - a[i__ + (j + 1) * a_dim1] = ctemp * temp - stemp * - a[i__ + j * a_dim1]; - a[i__ + j * a_dim1] = stemp * temp + ctemp * a[ - i__ + j * a_dim1]; + if (lsame_(pivot, (char *)"V", (ftnlen)1, (ftnlen)1)) { + if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { + i__1 = *n - 1; + for (j = 1; j <= i__1; ++j) { + ctemp = c__[j]; + stemp = s[j]; + if (ctemp != 1. || stemp != 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp = a[i__ + (j + 1) * a_dim1]; + a[i__ + (j + 1) * a_dim1] = ctemp * temp - stemp * + a[i__ + j * a_dim1]; + a[i__ + j * a_dim1] = stemp * temp + ctemp * a[ + i__ + j * a_dim1]; /* L130: */ - } - } + } + } /* L140: */ - } - } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { - for (j = *n - 1; j >= 1; --j) { - ctemp = c__[j]; - stemp = s[j]; - if (ctemp != 1. || stemp != 0.) { - i__1 = *m; - for (i__ = 1; i__ <= i__1; ++i__) { - temp = a[i__ + (j + 1) * a_dim1]; - a[i__ + (j + 1) * a_dim1] = ctemp * temp - stemp * - a[i__ + j * a_dim1]; - a[i__ + j * a_dim1] = stemp * temp + ctemp * a[ - i__ + j * a_dim1]; + } + } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { + for (j = *n - 1; j >= 1; --j) { + ctemp = c__[j]; + stemp = s[j]; + if (ctemp != 1. || stemp != 0.) { + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + temp = a[i__ + (j + 1) * a_dim1]; + a[i__ + (j + 1) * a_dim1] = ctemp * temp - stemp * + a[i__ + j * a_dim1]; + a[i__ + j * a_dim1] = stemp * temp + ctemp * a[ + i__ + j * a_dim1]; /* L150: */ - } - } + } + } /* L160: */ - } - } - } else if (lsame_(pivot, (char *)"T", (ftnlen)1, (ftnlen)1)) { - if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { - i__1 = *n; - for (j = 2; j <= i__1; ++j) { - ctemp = c__[j - 1]; - stemp = s[j - 1]; - if (ctemp != 1. || stemp != 0.) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - temp = a[i__ + j * a_dim1]; - a[i__ + j * a_dim1] = ctemp * temp - stemp * a[ - i__ + a_dim1]; - a[i__ + a_dim1] = stemp * temp + ctemp * a[i__ + - a_dim1]; + } + } + } else if (lsame_(pivot, (char *)"T", (ftnlen)1, (ftnlen)1)) { + if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { + i__1 = *n; + for (j = 2; j <= i__1; ++j) { + ctemp = c__[j - 1]; + stemp = s[j - 1]; + if (ctemp != 1. || stemp != 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp = a[i__ + j * a_dim1]; + a[i__ + j * a_dim1] = ctemp * temp - stemp * a[ + i__ + a_dim1]; + a[i__ + a_dim1] = stemp * temp + ctemp * a[i__ + + a_dim1]; /* L170: */ - } - } + } + } /* L180: */ - } - } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { - for (j = *n; j >= 2; --j) { - ctemp = c__[j - 1]; - stemp = s[j - 1]; - if (ctemp != 1. || stemp != 0.) { - i__1 = *m; - for (i__ = 1; i__ <= i__1; ++i__) { - temp = a[i__ + j * a_dim1]; - a[i__ + j * a_dim1] = ctemp * temp - stemp * a[ - i__ + a_dim1]; - a[i__ + a_dim1] = stemp * temp + ctemp * a[i__ + - a_dim1]; + } + } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { + for (j = *n; j >= 2; --j) { + ctemp = c__[j - 1]; + stemp = s[j - 1]; + if (ctemp != 1. || stemp != 0.) { + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + temp = a[i__ + j * a_dim1]; + a[i__ + j * a_dim1] = ctemp * temp - stemp * a[ + i__ + a_dim1]; + a[i__ + a_dim1] = stemp * temp + ctemp * a[i__ + + a_dim1]; /* L190: */ - } - } + } + } /* L200: */ - } - } - } else if (lsame_(pivot, (char *)"B", (ftnlen)1, (ftnlen)1)) { - if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { - i__1 = *n - 1; - for (j = 1; j <= i__1; ++j) { - ctemp = c__[j]; - stemp = s[j]; - if (ctemp != 1. || stemp != 0.) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - temp = a[i__ + j * a_dim1]; - a[i__ + j * a_dim1] = stemp * a[i__ + *n * a_dim1] - + ctemp * temp; - a[i__ + *n * a_dim1] = ctemp * a[i__ + *n * - a_dim1] - stemp * temp; + } + } + } else if (lsame_(pivot, (char *)"B", (ftnlen)1, (ftnlen)1)) { + if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { + i__1 = *n - 1; + for (j = 1; j <= i__1; ++j) { + ctemp = c__[j]; + stemp = s[j]; + if (ctemp != 1. || stemp != 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp = a[i__ + j * a_dim1]; + a[i__ + j * a_dim1] = stemp * a[i__ + *n * a_dim1] + + ctemp * temp; + a[i__ + *n * a_dim1] = ctemp * a[i__ + *n * + a_dim1] - stemp * temp; /* L210: */ - } - } + } + } /* L220: */ - } - } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { - for (j = *n - 1; j >= 1; --j) { - ctemp = c__[j]; - stemp = s[j]; - if (ctemp != 1. || stemp != 0.) { - i__1 = *m; - for (i__ = 1; i__ <= i__1; ++i__) { - temp = a[i__ + j * a_dim1]; - a[i__ + j * a_dim1] = stemp * a[i__ + *n * a_dim1] - + ctemp * temp; - a[i__ + *n * a_dim1] = ctemp * a[i__ + *n * - a_dim1] - stemp * temp; + } + } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { + for (j = *n - 1; j >= 1; --j) { + ctemp = c__[j]; + stemp = s[j]; + if (ctemp != 1. || stemp != 0.) { + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + temp = a[i__ + j * a_dim1]; + a[i__ + j * a_dim1] = stemp * a[i__ + *n * a_dim1] + + ctemp * temp; + a[i__ + *n * a_dim1] = ctemp * a[i__ + *n * + a_dim1] - stemp * temp; /* L230: */ - } - } + } + } /* L240: */ - } - } - } + } + } + } } return 0; @@ -532,5 +532,5 @@ extern "C" { } /* dlasr_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlasrt.cpp b/lib/linalg/dlasrt.cpp index 8c0eec5f2e..a796f6e568 100644 --- a/lib/linalg/dlasrt.cpp +++ b/lib/linalg/dlasrt.cpp @@ -1,13 +1,13 @@ /* fortran/dlasrt.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -105,7 +105,7 @@ f"> */ /* ===================================================================== */ /* Subroutine */ int dlasrt_(char *id, integer *n, doublereal *d__, integer * - info, ftnlen id_len) + info, ftnlen id_len) { /* System generated locals */ integer i__1, i__2; @@ -117,7 +117,7 @@ f"> */ doublereal tmp; integer endd; extern logical lsame_(char *, char *, ftnlen, ftnlen); - integer stack[64] /* was [2][32] */; + integer stack[64] /* was [2][32] */; doublereal dmnmx; integer start; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); @@ -156,25 +156,25 @@ f"> */ *info = 0; dir = -1; if (lsame_(id, (char *)"D", (ftnlen)1, (ftnlen)1)) { - dir = 0; + dir = 0; } else if (lsame_(id, (char *)"I", (ftnlen)1, (ftnlen)1)) { - dir = 1; + dir = 1; } if (dir == -1) { - *info = -1; + *info = -1; } else if (*n < 0) { - *info = -2; + *info = -2; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DLASRT", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DLASRT", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*n <= 1) { - return 0; + return 0; } stkpnt = 1; @@ -188,49 +188,49 @@ L10: /* Do Insertion sort on D( START:ENDD ) */ - if (dir == 0) { + if (dir == 0) { /* Sort into decreasing order */ - i__1 = endd; - for (i__ = start + 1; i__ <= i__1; ++i__) { - i__2 = start + 1; - for (j = i__; j >= i__2; --j) { - if (d__[j] > d__[j - 1]) { - dmnmx = d__[j]; - d__[j] = d__[j - 1]; - d__[j - 1] = dmnmx; - } else { - goto L30; - } + i__1 = endd; + for (i__ = start + 1; i__ <= i__1; ++i__) { + i__2 = start + 1; + for (j = i__; j >= i__2; --j) { + if (d__[j] > d__[j - 1]) { + dmnmx = d__[j]; + d__[j] = d__[j - 1]; + d__[j - 1] = dmnmx; + } else { + goto L30; + } /* L20: */ - } + } L30: - ; - } + ; + } - } else { + } else { /* Sort into increasing order */ - i__1 = endd; - for (i__ = start + 1; i__ <= i__1; ++i__) { - i__2 = start + 1; - for (j = i__; j >= i__2; --j) { - if (d__[j] < d__[j - 1]) { - dmnmx = d__[j]; - d__[j] = d__[j - 1]; - d__[j - 1] = dmnmx; - } else { - goto L50; - } + i__1 = endd; + for (i__ = start + 1; i__ <= i__1; ++i__) { + i__2 = start + 1; + for (j = i__; j >= i__2; --j) { + if (d__[j] < d__[j - 1]) { + dmnmx = d__[j]; + d__[j] = d__[j - 1]; + d__[j - 1] = dmnmx; + } else { + goto L50; + } /* L40: */ - } + } L50: - ; - } + ; + } - } + } } else if (endd - start > 20) { @@ -238,108 +238,108 @@ L50: /* Choose partition entry as median of 3 */ - d1 = d__[start]; - d2 = d__[endd]; - i__ = (start + endd) / 2; - d3 = d__[i__]; - if (d1 < d2) { - if (d3 < d1) { - dmnmx = d1; - } else if (d3 < d2) { - dmnmx = d3; - } else { - dmnmx = d2; - } - } else { - if (d3 < d2) { - dmnmx = d2; - } else if (d3 < d1) { - dmnmx = d3; - } else { - dmnmx = d1; - } - } + d1 = d__[start]; + d2 = d__[endd]; + i__ = (start + endd) / 2; + d3 = d__[i__]; + if (d1 < d2) { + if (d3 < d1) { + dmnmx = d1; + } else if (d3 < d2) { + dmnmx = d3; + } else { + dmnmx = d2; + } + } else { + if (d3 < d2) { + dmnmx = d2; + } else if (d3 < d1) { + dmnmx = d3; + } else { + dmnmx = d1; + } + } - if (dir == 0) { + if (dir == 0) { /* Sort into decreasing order */ - i__ = start - 1; - j = endd + 1; + i__ = start - 1; + j = endd + 1; L60: L70: - --j; - if (d__[j] < dmnmx) { - goto L70; - } + --j; + if (d__[j] < dmnmx) { + goto L70; + } L80: - ++i__; - if (d__[i__] > dmnmx) { - goto L80; - } - if (i__ < j) { - tmp = d__[i__]; - d__[i__] = d__[j]; - d__[j] = tmp; - goto L60; - } - if (j - start > endd - j - 1) { - ++stkpnt; - stack[(stkpnt << 1) - 2] = start; - stack[(stkpnt << 1) - 1] = j; - ++stkpnt; - stack[(stkpnt << 1) - 2] = j + 1; - stack[(stkpnt << 1) - 1] = endd; - } else { - ++stkpnt; - stack[(stkpnt << 1) - 2] = j + 1; - stack[(stkpnt << 1) - 1] = endd; - ++stkpnt; - stack[(stkpnt << 1) - 2] = start; - stack[(stkpnt << 1) - 1] = j; - } - } else { + ++i__; + if (d__[i__] > dmnmx) { + goto L80; + } + if (i__ < j) { + tmp = d__[i__]; + d__[i__] = d__[j]; + d__[j] = tmp; + goto L60; + } + if (j - start > endd - j - 1) { + ++stkpnt; + stack[(stkpnt << 1) - 2] = start; + stack[(stkpnt << 1) - 1] = j; + ++stkpnt; + stack[(stkpnt << 1) - 2] = j + 1; + stack[(stkpnt << 1) - 1] = endd; + } else { + ++stkpnt; + stack[(stkpnt << 1) - 2] = j + 1; + stack[(stkpnt << 1) - 1] = endd; + ++stkpnt; + stack[(stkpnt << 1) - 2] = start; + stack[(stkpnt << 1) - 1] = j; + } + } else { /* Sort into increasing order */ - i__ = start - 1; - j = endd + 1; + i__ = start - 1; + j = endd + 1; L90: L100: - --j; - if (d__[j] > dmnmx) { - goto L100; - } + --j; + if (d__[j] > dmnmx) { + goto L100; + } L110: - ++i__; - if (d__[i__] < dmnmx) { - goto L110; - } - if (i__ < j) { - tmp = d__[i__]; - d__[i__] = d__[j]; - d__[j] = tmp; - goto L90; - } - if (j - start > endd - j - 1) { - ++stkpnt; - stack[(stkpnt << 1) - 2] = start; - stack[(stkpnt << 1) - 1] = j; - ++stkpnt; - stack[(stkpnt << 1) - 2] = j + 1; - stack[(stkpnt << 1) - 1] = endd; - } else { - ++stkpnt; - stack[(stkpnt << 1) - 2] = j + 1; - stack[(stkpnt << 1) - 1] = endd; - ++stkpnt; - stack[(stkpnt << 1) - 2] = start; - stack[(stkpnt << 1) - 1] = j; - } - } + ++i__; + if (d__[i__] < dmnmx) { + goto L110; + } + if (i__ < j) { + tmp = d__[i__]; + d__[i__] = d__[j]; + d__[j] = tmp; + goto L90; + } + if (j - start > endd - j - 1) { + ++stkpnt; + stack[(stkpnt << 1) - 2] = start; + stack[(stkpnt << 1) - 1] = j; + ++stkpnt; + stack[(stkpnt << 1) - 2] = j + 1; + stack[(stkpnt << 1) - 1] = endd; + } else { + ++stkpnt; + stack[(stkpnt << 1) - 2] = j + 1; + stack[(stkpnt << 1) - 1] = endd; + ++stkpnt; + stack[(stkpnt << 1) - 2] = start; + stack[(stkpnt << 1) - 1] = j; + } + } } if (stkpnt > 0) { - goto L10; + goto L10; } return 0; @@ -348,5 +348,5 @@ L110: } /* dlasrt_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlassq.cpp b/lib/linalg/dlassq.cpp index fe346d2247..76391a54f9 100644 --- a/lib/linalg/dlassq.cpp +++ b/lib/linalg/dlassq.cpp @@ -1,13 +1,13 @@ /* fortran/dlassq.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -121,8 +121,8 @@ f"> */ /* > \ingroup OTHERauxiliary */ /* ===================================================================== */ -/* Subroutine */ int dlassq_(integer *n, doublereal *x, integer *incx, - doublereal *scale, doublereal *sumsq) +/* Subroutine */ int dlassq_(integer *n, doublereal *x, integer *incx, + doublereal *scale, doublereal *sumsq) { /* System generated locals */ integer i__1, i__2; @@ -161,24 +161,24 @@ f"> */ /* Function Body */ if (*n > 0) { - i__1 = (*n - 1) * *incx + 1; - i__2 = *incx; - for (ix = 1; i__2 < 0 ? ix >= i__1 : ix <= i__1; ix += i__2) { - absxi = (d__1 = x[ix], abs(d__1)); - if (absxi > 0. || disnan_(&absxi)) { - if (*scale < absxi) { + i__1 = (*n - 1) * *incx + 1; + i__2 = *incx; + for (ix = 1; i__2 < 0 ? ix >= i__1 : ix <= i__1; ix += i__2) { + absxi = (d__1 = x[ix], abs(d__1)); + if (absxi > 0. || disnan_(&absxi)) { + if (*scale < absxi) { /* Computing 2nd power */ - d__1 = *scale / absxi; - *sumsq = *sumsq * (d__1 * d__1) + 1; - *scale = absxi; - } else { + d__1 = *scale / absxi; + *sumsq = *sumsq * (d__1 * d__1) + 1; + *scale = absxi; + } else { /* Computing 2nd power */ - d__1 = absxi / *scale; - *sumsq += d__1 * d__1; - } - } + d__1 = absxi / *scale; + *sumsq += d__1 * d__1; + } + } /* L10: */ - } + } } return 0; @@ -187,5 +187,5 @@ f"> */ } /* dlassq_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlasv2.cpp b/lib/linalg/dlasv2.cpp index 4667b941d4..7bab630b39 100644 --- a/lib/linalg/dlasv2.cpp +++ b/lib/linalg/dlasv2.cpp @@ -1,13 +1,13 @@ /* fortran/dlasv2.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -159,9 +159,9 @@ f"> */ /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int dlasv2_(doublereal *f, doublereal *g, doublereal *h__, - doublereal *ssmin, doublereal *ssmax, doublereal *snr, doublereal * - csr, doublereal *snl, doublereal *csl) +/* Subroutine */ int dlasv2_(doublereal *f, doublereal *g, doublereal *h__, + doublereal *ssmin, doublereal *ssmax, doublereal *snr, doublereal * + csr, doublereal *snl, doublereal *csl) { /* System generated locals */ doublereal d__1; @@ -170,8 +170,8 @@ f"> */ double sqrt(doublereal), d_sign(doublereal *, doublereal *); /* Local variables */ - doublereal a, d__, l, m, r__, s, t, fa, ga, ha, ft, gt, ht, mm, tt, clt, - crt, slt, srt; + doublereal a, d__, l, m, r__, s, t, fa, ga, ha, ft, gt, ht, mm, tt, clt, + crt, slt, srt; integer pmax; doublereal temp; logical swap; @@ -212,13 +212,13 @@ f"> */ pmax = 1; swap = ha > fa; if (swap) { - pmax = 3; - temp = ft; - ft = ht; - ht = temp; - temp = fa; - fa = ha; - ha = temp; + pmax = 3; + temp = ft; + ft = ht; + ht = temp; + temp = fa; + fa = ha; + ha = temp; /* Now FA .ge. HA */ @@ -229,118 +229,118 @@ f"> */ /* Diagonal matrix */ - *ssmin = ha; - *ssmax = fa; - clt = 1.; - crt = 1.; - slt = 0.; - srt = 0.; + *ssmin = ha; + *ssmax = fa; + clt = 1.; + crt = 1.; + slt = 0.; + srt = 0.; } else { - gasmal = TRUE_; - if (ga > fa) { - pmax = 2; - if (fa / ga < dlamch_((char *)"EPS", (ftnlen)3)) { + gasmal = TRUE_; + if (ga > fa) { + pmax = 2; + if (fa / ga < dlamch_((char *)"EPS", (ftnlen)3)) { /* Case of very large GA */ - gasmal = FALSE_; - *ssmax = ga; - if (ha > 1.) { - *ssmin = fa / (ga / ha); - } else { - *ssmin = fa / ga * ha; - } - clt = 1.; - slt = ht / gt; - srt = 1.; - crt = ft / gt; - } - } - if (gasmal) { + gasmal = FALSE_; + *ssmax = ga; + if (ha > 1.) { + *ssmin = fa / (ga / ha); + } else { + *ssmin = fa / ga * ha; + } + clt = 1.; + slt = ht / gt; + srt = 1.; + crt = ft / gt; + } + } + if (gasmal) { /* Normal case */ - d__ = fa - ha; - if (d__ == fa) { + d__ = fa - ha; + if (d__ == fa) { /* Copes with infinite F or H */ - l = 1.; - } else { - l = d__ / fa; - } + l = 1.; + } else { + l = d__ / fa; + } /* Note that 0 .le. L .le. 1 */ - m = gt / ft; + m = gt / ft; /* Note that abs(M) .le. 1/macheps */ - t = 2. - l; + t = 2. - l; /* Note that T .ge. 1 */ - mm = m * m; - tt = t * t; - s = sqrt(tt + mm); + mm = m * m; + tt = t * t; + s = sqrt(tt + mm); /* Note that 1 .le. S .le. 1 + 1/macheps */ - if (l == 0.) { - r__ = abs(m); - } else { - r__ = sqrt(l * l + mm); - } + if (l == 0.) { + r__ = abs(m); + } else { + r__ = sqrt(l * l + mm); + } /* Note that 0 .le. R .le. 1 + 1/macheps */ - a = (s + r__) * .5; + a = (s + r__) * .5; /* Note that 1 .le. A .le. 1 + abs(M) */ - *ssmin = ha / a; - *ssmax = fa * a; - if (mm == 0.) { + *ssmin = ha / a; + *ssmax = fa * a; + if (mm == 0.) { /* Note that M is very tiny */ - if (l == 0.) { - t = d_sign(&c_b3, &ft) * d_sign(&c_b4, >); - } else { - t = gt / d_sign(&d__, &ft) + m / t; - } - } else { - t = (m / (s + t) + m / (r__ + l)) * (a + 1.); - } - l = sqrt(t * t + 4.); - crt = 2. / l; - srt = t / l; - clt = (crt + srt * m) / a; - slt = ht / ft * srt / a; - } + if (l == 0.) { + t = d_sign(&c_b3, &ft) * d_sign(&c_b4, >); + } else { + t = gt / d_sign(&d__, &ft) + m / t; + } + } else { + t = (m / (s + t) + m / (r__ + l)) * (a + 1.); + } + l = sqrt(t * t + 4.); + crt = 2. / l; + srt = t / l; + clt = (crt + srt * m) / a; + slt = ht / ft * srt / a; + } } if (swap) { - *csl = srt; - *snl = crt; - *csr = slt; - *snr = clt; + *csl = srt; + *snl = crt; + *csr = slt; + *snr = clt; } else { - *csl = clt; - *snl = slt; - *csr = crt; - *snr = srt; + *csl = clt; + *snl = slt; + *csr = crt; + *snr = srt; } /* Correct signs of SSMAX and SSMIN */ if (pmax == 1) { - tsign = d_sign(&c_b4, csr) * d_sign(&c_b4, csl) * d_sign(&c_b4, f); + tsign = d_sign(&c_b4, csr) * d_sign(&c_b4, csl) * d_sign(&c_b4, f); } if (pmax == 2) { - tsign = d_sign(&c_b4, snr) * d_sign(&c_b4, csl) * d_sign(&c_b4, g); + tsign = d_sign(&c_b4, snr) * d_sign(&c_b4, csl) * d_sign(&c_b4, g); } if (pmax == 3) { - tsign = d_sign(&c_b4, snr) * d_sign(&c_b4, snl) * d_sign(&c_b4, h__); + tsign = d_sign(&c_b4, snr) * d_sign(&c_b4, snl) * d_sign(&c_b4, h__); } *ssmax = d_sign(ssmax, &tsign); d__1 = tsign * d_sign(&c_b4, f) * d_sign(&c_b4, h__); @@ -352,5 +352,5 @@ f"> */ } /* dlasv2_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlaswp.cpp b/lib/linalg/dlaswp.cpp index db83b75947..05d911f30c 100644 --- a/lib/linalg/dlaswp.cpp +++ b/lib/linalg/dlaswp.cpp @@ -1,13 +1,13 @@ /* fortran/dlaswp.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -131,8 +131,8 @@ f"> */ /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int dlaswp_(integer *n, doublereal *a, integer *lda, integer - *k1, integer *k2, integer *ipiv, integer *incx) +/* Subroutine */ int dlaswp_(integer *n, doublereal *a, integer *lda, integer + *k1, integer *k2, integer *ipiv, integer *incx) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4; @@ -168,63 +168,63 @@ f"> */ /* Function Body */ if (*incx > 0) { - ix0 = *k1; - i1 = *k1; - i2 = *k2; - inc = 1; + ix0 = *k1; + i1 = *k1; + i2 = *k2; + inc = 1; } else if (*incx < 0) { - ix0 = *k1 + (*k1 - *k2) * *incx; - i1 = *k2; - i2 = *k1; - inc = -1; + ix0 = *k1 + (*k1 - *k2) * *incx; + i1 = *k2; + i2 = *k1; + inc = -1; } else { - return 0; + return 0; } n32 = *n / 32 << 5; if (n32 != 0) { - i__1 = n32; - for (j = 1; j <= i__1; j += 32) { - ix = ix0; - i__2 = i2; - i__3 = inc; - for (i__ = i1; i__3 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__3) - { - ip = ipiv[ix]; - if (ip != i__) { - i__4 = j + 31; - for (k = j; k <= i__4; ++k) { - temp = a[i__ + k * a_dim1]; - a[i__ + k * a_dim1] = a[ip + k * a_dim1]; - a[ip + k * a_dim1] = temp; + i__1 = n32; + for (j = 1; j <= i__1; j += 32) { + ix = ix0; + i__2 = i2; + i__3 = inc; + for (i__ = i1; i__3 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__3) + { + ip = ipiv[ix]; + if (ip != i__) { + i__4 = j + 31; + for (k = j; k <= i__4; ++k) { + temp = a[i__ + k * a_dim1]; + a[i__ + k * a_dim1] = a[ip + k * a_dim1]; + a[ip + k * a_dim1] = temp; /* L10: */ - } - } - ix += *incx; + } + } + ix += *incx; /* L20: */ - } + } /* L30: */ - } + } } if (n32 != *n) { - ++n32; - ix = ix0; - i__1 = i2; - i__3 = inc; - for (i__ = i1; i__3 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__3) { - ip = ipiv[ix]; - if (ip != i__) { - i__2 = *n; - for (k = n32; k <= i__2; ++k) { - temp = a[i__ + k * a_dim1]; - a[i__ + k * a_dim1] = a[ip + k * a_dim1]; - a[ip + k * a_dim1] = temp; + ++n32; + ix = ix0; + i__1 = i2; + i__3 = inc; + for (i__ = i1; i__3 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__3) { + ip = ipiv[ix]; + if (ip != i__) { + i__2 = *n; + for (k = n32; k <= i__2; ++k) { + temp = a[i__ + k * a_dim1]; + a[i__ + k * a_dim1] = a[ip + k * a_dim1]; + a[ip + k * a_dim1] = temp; /* L40: */ - } - } - ix += *incx; + } + } + ix += *incx; /* L50: */ - } + } } return 0; @@ -234,5 +234,5 @@ f"> */ } /* dlaswp_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlatrd.cpp b/lib/linalg/dlatrd.cpp index b291e1adbf..74fc5fcc87 100644 --- a/lib/linalg/dlatrd.cpp +++ b/lib/linalg/dlatrd.cpp @@ -1,13 +1,13 @@ /* fortran/dlatrd.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -223,28 +223,28 @@ f"> */ /* > */ /* ===================================================================== */ /* Subroutine */ int dlatrd_(char *uplo, integer *n, integer *nb, doublereal * - a, integer *lda, doublereal *e, doublereal *tau, doublereal *w, - integer *ldw, ftnlen uplo_len) + a, integer *lda, doublereal *e, doublereal *tau, doublereal *w, + integer *ldw, ftnlen uplo_len) { /* System generated locals */ integer a_dim1, a_offset, w_dim1, w_offset, i__1, i__2, i__3; /* Local variables */ integer i__, iw; - extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, - integer *); + extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, + integer *); doublereal alpha; - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *); + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *); extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int dgemv_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, doublereal *, integer *, - doublereal *, doublereal *, integer *, ftnlen), daxpy_(integer *, - doublereal *, doublereal *, integer *, doublereal *, integer *), - dsymv_(char *, integer *, doublereal *, doublereal *, integer *, - doublereal *, integer *, doublereal *, doublereal *, integer *, - ftnlen), dlarfg_(integer *, doublereal *, doublereal *, integer *, - doublereal *); + extern /* Subroutine */ int dgemv_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, ftnlen), daxpy_(integer *, + doublereal *, doublereal *, integer *, doublereal *, integer *), + dsymv_(char *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, + ftnlen), dlarfg_(integer *, doublereal *, doublereal *, integer *, + doublereal *); /* -- LAPACK auxiliary routine -- */ @@ -284,154 +284,154 @@ f"> */ /* Function Body */ if (*n <= 0) { - return 0; + return 0; } if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { /* Reduce last NB columns of upper triangle */ - i__1 = *n - *nb + 1; - for (i__ = *n; i__ >= i__1; --i__) { - iw = i__ - *n + *nb; - if (i__ < *n) { + i__1 = *n - *nb + 1; + for (i__ = *n; i__ >= i__1; --i__) { + iw = i__ - *n + *nb; + if (i__ < *n) { /* Update A(1:i,i) */ - i__2 = *n - i__; - dgemv_((char *)"No transpose", &i__, &i__2, &c_b5, &a[(i__ + 1) * - a_dim1 + 1], lda, &w[i__ + (iw + 1) * w_dim1], ldw, & - c_b6, &a[i__ * a_dim1 + 1], &c__1, (ftnlen)12); - i__2 = *n - i__; - dgemv_((char *)"No transpose", &i__, &i__2, &c_b5, &w[(iw + 1) * - w_dim1 + 1], ldw, &a[i__ + (i__ + 1) * a_dim1], lda, & - c_b6, &a[i__ * a_dim1 + 1], &c__1, (ftnlen)12); - } - if (i__ > 1) { + i__2 = *n - i__; + dgemv_((char *)"No transpose", &i__, &i__2, &c_b5, &a[(i__ + 1) * + a_dim1 + 1], lda, &w[i__ + (iw + 1) * w_dim1], ldw, & + c_b6, &a[i__ * a_dim1 + 1], &c__1, (ftnlen)12); + i__2 = *n - i__; + dgemv_((char *)"No transpose", &i__, &i__2, &c_b5, &w[(iw + 1) * + w_dim1 + 1], ldw, &a[i__ + (i__ + 1) * a_dim1], lda, & + c_b6, &a[i__ * a_dim1 + 1], &c__1, (ftnlen)12); + } + if (i__ > 1) { /* Generate elementary reflector H(i) to annihilate */ /* A(1:i-2,i) */ - i__2 = i__ - 1; - dlarfg_(&i__2, &a[i__ - 1 + i__ * a_dim1], &a[i__ * a_dim1 + - 1], &c__1, &tau[i__ - 1]); - e[i__ - 1] = a[i__ - 1 + i__ * a_dim1]; - a[i__ - 1 + i__ * a_dim1] = 1.; + i__2 = i__ - 1; + dlarfg_(&i__2, &a[i__ - 1 + i__ * a_dim1], &a[i__ * a_dim1 + + 1], &c__1, &tau[i__ - 1]); + e[i__ - 1] = a[i__ - 1 + i__ * a_dim1]; + a[i__ - 1 + i__ * a_dim1] = 1.; /* Compute W(1:i-1,i) */ - i__2 = i__ - 1; - dsymv_((char *)"Upper", &i__2, &c_b6, &a[a_offset], lda, &a[i__ * - a_dim1 + 1], &c__1, &c_b16, &w[iw * w_dim1 + 1], & - c__1, (ftnlen)5); - if (i__ < *n) { - i__2 = i__ - 1; - i__3 = *n - i__; - dgemv_((char *)"Transpose", &i__2, &i__3, &c_b6, &w[(iw + 1) * - w_dim1 + 1], ldw, &a[i__ * a_dim1 + 1], &c__1, & - c_b16, &w[i__ + 1 + iw * w_dim1], &c__1, (ftnlen) - 9); - i__2 = i__ - 1; - i__3 = *n - i__; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[(i__ + 1) * - a_dim1 + 1], lda, &w[i__ + 1 + iw * w_dim1], & - c__1, &c_b6, &w[iw * w_dim1 + 1], &c__1, (ftnlen) - 12); - i__2 = i__ - 1; - i__3 = *n - i__; - dgemv_((char *)"Transpose", &i__2, &i__3, &c_b6, &a[(i__ + 1) * - a_dim1 + 1], lda, &a[i__ * a_dim1 + 1], &c__1, & - c_b16, &w[i__ + 1 + iw * w_dim1], &c__1, (ftnlen) - 9); - i__2 = i__ - 1; - i__3 = *n - i__; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &w[(iw + 1) * - w_dim1 + 1], ldw, &w[i__ + 1 + iw * w_dim1], & - c__1, &c_b6, &w[iw * w_dim1 + 1], &c__1, (ftnlen) - 12); - } - i__2 = i__ - 1; - dscal_(&i__2, &tau[i__ - 1], &w[iw * w_dim1 + 1], &c__1); - i__2 = i__ - 1; - alpha = tau[i__ - 1] * -.5 * ddot_(&i__2, &w[iw * w_dim1 + 1], - &c__1, &a[i__ * a_dim1 + 1], &c__1); - i__2 = i__ - 1; - daxpy_(&i__2, &alpha, &a[i__ * a_dim1 + 1], &c__1, &w[iw * - w_dim1 + 1], &c__1); - } + i__2 = i__ - 1; + dsymv_((char *)"Upper", &i__2, &c_b6, &a[a_offset], lda, &a[i__ * + a_dim1 + 1], &c__1, &c_b16, &w[iw * w_dim1 + 1], & + c__1, (ftnlen)5); + if (i__ < *n) { + i__2 = i__ - 1; + i__3 = *n - i__; + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b6, &w[(iw + 1) * + w_dim1 + 1], ldw, &a[i__ * a_dim1 + 1], &c__1, & + c_b16, &w[i__ + 1 + iw * w_dim1], &c__1, (ftnlen) + 9); + i__2 = i__ - 1; + i__3 = *n - i__; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[(i__ + 1) * + a_dim1 + 1], lda, &w[i__ + 1 + iw * w_dim1], & + c__1, &c_b6, &w[iw * w_dim1 + 1], &c__1, (ftnlen) + 12); + i__2 = i__ - 1; + i__3 = *n - i__; + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b6, &a[(i__ + 1) * + a_dim1 + 1], lda, &a[i__ * a_dim1 + 1], &c__1, & + c_b16, &w[i__ + 1 + iw * w_dim1], &c__1, (ftnlen) + 9); + i__2 = i__ - 1; + i__3 = *n - i__; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &w[(iw + 1) * + w_dim1 + 1], ldw, &w[i__ + 1 + iw * w_dim1], & + c__1, &c_b6, &w[iw * w_dim1 + 1], &c__1, (ftnlen) + 12); + } + i__2 = i__ - 1; + dscal_(&i__2, &tau[i__ - 1], &w[iw * w_dim1 + 1], &c__1); + i__2 = i__ - 1; + alpha = tau[i__ - 1] * -.5 * ddot_(&i__2, &w[iw * w_dim1 + 1], + &c__1, &a[i__ * a_dim1 + 1], &c__1); + i__2 = i__ - 1; + daxpy_(&i__2, &alpha, &a[i__ * a_dim1 + 1], &c__1, &w[iw * + w_dim1 + 1], &c__1); + } /* L10: */ - } + } } else { /* Reduce first NB columns of lower triangle */ - i__1 = *nb; - for (i__ = 1; i__ <= i__1; ++i__) { + i__1 = *nb; + for (i__ = 1; i__ <= i__1; ++i__) { /* Update A(i:n,i) */ - i__2 = *n - i__ + 1; - i__3 = i__ - 1; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[i__ + a_dim1], lda, - &w[i__ + w_dim1], ldw, &c_b6, &a[i__ + i__ * a_dim1], & - c__1, (ftnlen)12); - i__2 = *n - i__ + 1; - i__3 = i__ - 1; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &w[i__ + w_dim1], ldw, - &a[i__ + a_dim1], lda, &c_b6, &a[i__ + i__ * a_dim1], & - c__1, (ftnlen)12); - if (i__ < *n) { + i__2 = *n - i__ + 1; + i__3 = i__ - 1; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[i__ + a_dim1], lda, + &w[i__ + w_dim1], ldw, &c_b6, &a[i__ + i__ * a_dim1], & + c__1, (ftnlen)12); + i__2 = *n - i__ + 1; + i__3 = i__ - 1; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &w[i__ + w_dim1], ldw, + &a[i__ + a_dim1], lda, &c_b6, &a[i__ + i__ * a_dim1], & + c__1, (ftnlen)12); + if (i__ < *n) { /* Generate elementary reflector H(i) to annihilate */ /* A(i+2:n,i) */ - i__2 = *n - i__; + i__2 = *n - i__; /* Computing MIN */ - i__3 = i__ + 2; - dlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3,*n) + - i__ * a_dim1], &c__1, &tau[i__]); - e[i__] = a[i__ + 1 + i__ * a_dim1]; - a[i__ + 1 + i__ * a_dim1] = 1.; + i__3 = i__ + 2; + dlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3,*n) + + i__ * a_dim1], &c__1, &tau[i__]); + e[i__] = a[i__ + 1 + i__ * a_dim1]; + a[i__ + 1 + i__ * a_dim1] = 1.; /* Compute W(i+1:n,i) */ - i__2 = *n - i__; - dsymv_((char *)"Lower", &i__2, &c_b6, &a[i__ + 1 + (i__ + 1) * a_dim1] - , lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[ - i__ + 1 + i__ * w_dim1], &c__1, (ftnlen)5); - i__2 = *n - i__; - i__3 = i__ - 1; - dgemv_((char *)"Transpose", &i__2, &i__3, &c_b6, &w[i__ + 1 + w_dim1], - ldw, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[ - i__ * w_dim1 + 1], &c__1, (ftnlen)9); - i__2 = *n - i__; - i__3 = i__ - 1; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + - a_dim1], lda, &w[i__ * w_dim1 + 1], &c__1, &c_b6, &w[ - i__ + 1 + i__ * w_dim1], &c__1, (ftnlen)12); - i__2 = *n - i__; - i__3 = i__ - 1; - dgemv_((char *)"Transpose", &i__2, &i__3, &c_b6, &a[i__ + 1 + a_dim1], - lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[ - i__ * w_dim1 + 1], &c__1, (ftnlen)9); - i__2 = *n - i__; - i__3 = i__ - 1; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &w[i__ + 1 + - w_dim1], ldw, &w[i__ * w_dim1 + 1], &c__1, &c_b6, &w[ - i__ + 1 + i__ * w_dim1], &c__1, (ftnlen)12); - i__2 = *n - i__; - dscal_(&i__2, &tau[i__], &w[i__ + 1 + i__ * w_dim1], &c__1); - i__2 = *n - i__; - alpha = tau[i__] * -.5 * ddot_(&i__2, &w[i__ + 1 + i__ * - w_dim1], &c__1, &a[i__ + 1 + i__ * a_dim1], &c__1); - i__2 = *n - i__; - daxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &w[ - i__ + 1 + i__ * w_dim1], &c__1); - } + i__2 = *n - i__; + dsymv_((char *)"Lower", &i__2, &c_b6, &a[i__ + 1 + (i__ + 1) * a_dim1] + , lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[ + i__ + 1 + i__ * w_dim1], &c__1, (ftnlen)5); + i__2 = *n - i__; + i__3 = i__ - 1; + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b6, &w[i__ + 1 + w_dim1], + ldw, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[ + i__ * w_dim1 + 1], &c__1, (ftnlen)9); + i__2 = *n - i__; + i__3 = i__ - 1; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + + a_dim1], lda, &w[i__ * w_dim1 + 1], &c__1, &c_b6, &w[ + i__ + 1 + i__ * w_dim1], &c__1, (ftnlen)12); + i__2 = *n - i__; + i__3 = i__ - 1; + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b6, &a[i__ + 1 + a_dim1], + lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[ + i__ * w_dim1 + 1], &c__1, (ftnlen)9); + i__2 = *n - i__; + i__3 = i__ - 1; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &w[i__ + 1 + + w_dim1], ldw, &w[i__ * w_dim1 + 1], &c__1, &c_b6, &w[ + i__ + 1 + i__ * w_dim1], &c__1, (ftnlen)12); + i__2 = *n - i__; + dscal_(&i__2, &tau[i__], &w[i__ + 1 + i__ * w_dim1], &c__1); + i__2 = *n - i__; + alpha = tau[i__] * -.5 * ddot_(&i__2, &w[i__ + 1 + i__ * + w_dim1], &c__1, &a[i__ + 1 + i__ * a_dim1], &c__1); + i__2 = *n - i__; + daxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &w[ + i__ + 1 + i__ * w_dim1], &c__1); + } /* L20: */ - } + } } return 0; @@ -441,5 +441,5 @@ f"> */ } /* dlatrd_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dlatrs.cpp b/lib/linalg/dlatrs.cpp index 0b68eac917..fc97690682 100644 --- a/lib/linalg/dlatrs.cpp +++ b/lib/linalg/dlatrs.cpp @@ -1,13 +1,13 @@ /* fortran/dlatrs.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -20,7 +20,7 @@ extern "C" { static integer c__1 = 1; static doublereal c_b46 = .5; -/* > \brief \b DLATRS solves a triangular system of equations with the scale factor set to prevent overflow. +/* > \brief \b DLATRS solves a triangular system of equations with the scale factor set to prevent overflow. */ /* =========== DOCUMENTATION =========== */ @@ -260,9 +260,9 @@ f"> */ /* > */ /* ===================================================================== */ /* Subroutine */ int dlatrs_(char *uplo, char *trans, char *diag, char * - normin, integer *n, doublereal *a, integer *lda, doublereal *x, - doublereal *scale, doublereal *cnorm, integer *info, ftnlen uplo_len, - ftnlen trans_len, ftnlen diag_len, ftnlen normin_len) + normin, integer *n, doublereal *a, integer *lda, doublereal *x, + doublereal *scale, doublereal *cnorm, integer *info, ftnlen uplo_len, + ftnlen trans_len, ftnlen diag_len, ftnlen normin_len) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; @@ -272,25 +272,25 @@ f"> */ integer i__, j; doublereal xj, rec, tjj; integer jinc; - extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, - integer *); + extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, + integer *); doublereal xbnd; integer imax; doublereal tmax, tjjs, xmax, grow, sumj; - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *); + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *); extern logical lsame_(char *, char *, ftnlen, ftnlen); doublereal tscal, uscal; extern doublereal dasum_(integer *, doublereal *, integer *); integer jlast; - extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *, - integer *, doublereal *, integer *); + extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *); logical upper; - extern /* Subroutine */ int dtrsv_(char *, char *, char *, integer *, - doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, - ftnlen); - extern doublereal dlamch_(char *, ftnlen), dlange_(char *, integer *, - integer *, doublereal *, integer *, doublereal *, ftnlen); + extern /* Subroutine */ int dtrsv_(char *, char *, char *, integer *, + doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, + ftnlen); + extern doublereal dlamch_(char *, ftnlen), dlange_(char *, integer *, + integer *, doublereal *, integer *, doublereal *, ftnlen); extern integer idamax_(integer *, doublereal *, integer *); extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); doublereal bignum; @@ -339,65 +339,65 @@ f"> */ /* Test the input parameters. */ if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { - *info = -1; - } else if (! notran && ! lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1) && ! - lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { - *info = -2; + *info = -1; + } else if (! notran && ! lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1) && ! + lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { + *info = -2; } else if (! nounit && ! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1)) { - *info = -3; + *info = -3; } else if (! lsame_(normin, (char *)"Y", (ftnlen)1, (ftnlen)1) && ! lsame_(normin, - (char *)"N", (ftnlen)1, (ftnlen)1)) { - *info = -4; + (char *)"N", (ftnlen)1, (ftnlen)1)) { + *info = -4; } else if (*n < 0) { - *info = -5; + *info = -5; } else if (*lda < max(1,*n)) { - *info = -7; + *info = -7; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DLATRS", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DLATRS", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ *scale = 1.; if (*n == 0) { - return 0; + return 0; } /* Determine machine dependent parameters to control overflow. */ smlnum = dlamch_((char *)"Safe minimum", (ftnlen)12) / dlamch_((char *)"Precision", ( - ftnlen)9); + ftnlen)9); bignum = 1. / smlnum; if (lsame_(normin, (char *)"N", (ftnlen)1, (ftnlen)1)) { /* Compute the 1-norm of each column, not including the diagonal. */ - if (upper) { + if (upper) { /* A is upper triangular. */ - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = j - 1; - cnorm[j] = dasum_(&i__2, &a[j * a_dim1 + 1], &c__1); + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j - 1; + cnorm[j] = dasum_(&i__2, &a[j * a_dim1 + 1], &c__1); /* L10: */ - } - } else { + } + } else { /* A is lower triangular. */ - i__1 = *n - 1; - for (j = 1; j <= i__1; ++j) { - i__2 = *n - j; - cnorm[j] = dasum_(&i__2, &a[j + 1 + j * a_dim1], &c__1); + i__1 = *n - 1; + for (j = 1; j <= i__1; ++j) { + i__2 = *n - j; + cnorm[j] = dasum_(&i__2, &a[j + 1 + j * a_dim1], &c__1); /* L20: */ - } - cnorm[*n] = 0.; - } + } + cnorm[*n] = 0.; + } } /* Scale the column norms by TSCAL if the maximum element in CNORM is */ @@ -406,81 +406,81 @@ f"> */ imax = idamax_(n, &cnorm[1], &c__1); tmax = cnorm[imax]; if (tmax <= bignum) { - tscal = 1.; + tscal = 1.; } else { /* Avoid NaN generation if entries in CNORM exceed the */ /* overflow threshold */ - if (tmax <= dlamch_((char *)"Overflow", (ftnlen)8)) { + if (tmax <= dlamch_((char *)"Overflow", (ftnlen)8)) { /* Case 1: All entries in CNORM are valid floating-point numbers */ - tscal = 1. / (smlnum * tmax); - dscal_(n, &tscal, &cnorm[1], &c__1); - } else { + tscal = 1. / (smlnum * tmax); + dscal_(n, &tscal, &cnorm[1], &c__1); + } else { /* Case 2: At least one column norm of A cannot be represented */ /* as floating-point number. Find the offdiagonal entry A( I, J ) */ /* with the largest absolute value. If this entry is not +/- Infinity, */ /* use this value as TSCAL. */ - tmax = 0.; - if (upper) { + tmax = 0.; + if (upper) { /* A is upper triangular. */ - i__1 = *n; - for (j = 2; j <= i__1; ++j) { + i__1 = *n; + for (j = 2; j <= i__1; ++j) { /* Computing MAX */ - i__2 = j - 1; - d__1 = dlange_((char *)"M", &i__2, &c__1, &a[j * a_dim1 + 1], & - c__1, &sumj, (ftnlen)1); - tmax = max(d__1,tmax); - } - } else { + i__2 = j - 1; + d__1 = dlange_((char *)"M", &i__2, &c__1, &a[j * a_dim1 + 1], & + c__1, &sumj, (ftnlen)1); + tmax = max(d__1,tmax); + } + } else { /* A is lower triangular. */ - i__1 = *n - 1; - for (j = 1; j <= i__1; ++j) { + i__1 = *n - 1; + for (j = 1; j <= i__1; ++j) { /* Computing MAX */ - i__2 = *n - j; - d__1 = dlange_((char *)"M", &i__2, &c__1, &a[j + 1 + j * a_dim1], - &c__1, &sumj, (ftnlen)1); - tmax = max(d__1,tmax); - } - } + i__2 = *n - j; + d__1 = dlange_((char *)"M", &i__2, &c__1, &a[j + 1 + j * a_dim1], + &c__1, &sumj, (ftnlen)1); + tmax = max(d__1,tmax); + } + } - if (tmax <= dlamch_((char *)"Overflow", (ftnlen)8)) { - tscal = 1. / (smlnum * tmax); - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - if (cnorm[j] <= dlamch_((char *)"Overflow", (ftnlen)8)) { - cnorm[j] *= tscal; - } else { + if (tmax <= dlamch_((char *)"Overflow", (ftnlen)8)) { + tscal = 1. / (smlnum * tmax); + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (cnorm[j] <= dlamch_((char *)"Overflow", (ftnlen)8)) { + cnorm[j] *= tscal; + } else { /* Recompute the 1-norm without introducing Infinity */ /* in the summation */ - cnorm[j] = 0.; - if (upper) { - i__2 = j - 1; - for (i__ = 1; i__ <= i__2; ++i__) { - cnorm[j] += tscal * (d__1 = a[i__ + j * - a_dim1], abs(d__1)); - } - } else { - i__2 = *n; - for (i__ = j + 1; i__ <= i__2; ++i__) { - cnorm[j] += tscal * (d__1 = a[i__ + j * - a_dim1], abs(d__1)); - } - } - } - } - } else { + cnorm[j] = 0.; + if (upper) { + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + cnorm[j] += tscal * (d__1 = a[i__ + j * + a_dim1], abs(d__1)); + } + } else { + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + cnorm[j] += tscal * (d__1 = a[i__ + j * + a_dim1], abs(d__1)); + } + } + } + } + } else { /* At least one entry of A is not a valid floating-point entry. */ /* Rely on TRSV to propagate Inf and NaN. */ - dtrsv_(uplo, trans, diag, n, &a[a_offset], lda, &x[1], &c__1, - (ftnlen)1, (ftnlen)1, (ftnlen)1); - return 0; - } - } + dtrsv_(uplo, trans, diag, n, &a[a_offset], lda, &x[1], &c__1, + (ftnlen)1, (ftnlen)1, (ftnlen)1); + return 0; + } + } } /* Compute a bound on the computed solution vector to see if the */ @@ -493,170 +493,170 @@ f"> */ /* Compute the growth in A * x = b. */ - if (upper) { - jfirst = *n; - jlast = 1; - jinc = -1; - } else { - jfirst = 1; - jlast = *n; - jinc = 1; - } + if (upper) { + jfirst = *n; + jlast = 1; + jinc = -1; + } else { + jfirst = 1; + jlast = *n; + jinc = 1; + } - if (tscal != 1.) { - grow = 0.; - goto L50; - } + if (tscal != 1.) { + grow = 0.; + goto L50; + } - if (nounit) { + if (nounit) { /* A is non-unit triangular. */ /* Compute GROW = 1/G(j) and XBND = 1/M(j). */ /* Initially, G(0) = max{x(i), i=1,...,n}. */ - grow = 1. / max(xbnd,smlnum); - xbnd = grow; - i__1 = jlast; - i__2 = jinc; - for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) { + grow = 1. / max(xbnd,smlnum); + xbnd = grow; + i__1 = jlast; + i__2 = jinc; + for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) { /* Exit the loop if the growth factor is too small. */ - if (grow <= smlnum) { - goto L50; - } + if (grow <= smlnum) { + goto L50; + } /* M(j) = G(j-1) / abs(A(j,j)) */ - tjj = (d__1 = a[j + j * a_dim1], abs(d__1)); + tjj = (d__1 = a[j + j * a_dim1], abs(d__1)); /* Computing MIN */ - d__1 = xbnd, d__2 = min(1.,tjj) * grow; - xbnd = min(d__1,d__2); - if (tjj + cnorm[j] >= smlnum) { + d__1 = xbnd, d__2 = min(1.,tjj) * grow; + xbnd = min(d__1,d__2); + if (tjj + cnorm[j] >= smlnum) { /* G(j) = G(j-1)*( 1 + CNORM(j) / abs(A(j,j)) ) */ - grow *= tjj / (tjj + cnorm[j]); - } else { + grow *= tjj / (tjj + cnorm[j]); + } else { /* G(j) could overflow, set GROW to 0. */ - grow = 0.; - } + grow = 0.; + } /* L30: */ - } - grow = xbnd; - } else { + } + grow = xbnd; + } else { /* A is unit triangular. */ /* Compute GROW = 1/G(j), where G(0) = max{x(i), i=1,...,n}. */ /* Computing MIN */ - d__1 = 1., d__2 = 1. / max(xbnd,smlnum); - grow = min(d__1,d__2); - i__2 = jlast; - i__1 = jinc; - for (j = jfirst; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) { + d__1 = 1., d__2 = 1. / max(xbnd,smlnum); + grow = min(d__1,d__2); + i__2 = jlast; + i__1 = jinc; + for (j = jfirst; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) { /* Exit the loop if the growth factor is too small. */ - if (grow <= smlnum) { - goto L50; - } + if (grow <= smlnum) { + goto L50; + } /* G(j) = G(j-1)*( 1 + CNORM(j) ) */ - grow *= 1. / (cnorm[j] + 1.); + grow *= 1. / (cnorm[j] + 1.); /* L40: */ - } - } + } + } L50: - ; + ; } else { /* Compute the growth in A**T * x = b. */ - if (upper) { - jfirst = 1; - jlast = *n; - jinc = 1; - } else { - jfirst = *n; - jlast = 1; - jinc = -1; - } + if (upper) { + jfirst = 1; + jlast = *n; + jinc = 1; + } else { + jfirst = *n; + jlast = 1; + jinc = -1; + } - if (tscal != 1.) { - grow = 0.; - goto L80; - } + if (tscal != 1.) { + grow = 0.; + goto L80; + } - if (nounit) { + if (nounit) { /* A is non-unit triangular. */ /* Compute GROW = 1/G(j) and XBND = 1/M(j). */ /* Initially, M(0) = max{x(i), i=1,...,n}. */ - grow = 1. / max(xbnd,smlnum); - xbnd = grow; - i__1 = jlast; - i__2 = jinc; - for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) { + grow = 1. / max(xbnd,smlnum); + xbnd = grow; + i__1 = jlast; + i__2 = jinc; + for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) { /* Exit the loop if the growth factor is too small. */ - if (grow <= smlnum) { - goto L80; - } + if (grow <= smlnum) { + goto L80; + } /* G(j) = max( G(j-1), M(j-1)*( 1 + CNORM(j) ) ) */ - xj = cnorm[j] + 1.; + xj = cnorm[j] + 1.; /* Computing MIN */ - d__1 = grow, d__2 = xbnd / xj; - grow = min(d__1,d__2); + d__1 = grow, d__2 = xbnd / xj; + grow = min(d__1,d__2); /* M(j) = M(j-1)*( 1 + CNORM(j) ) / abs(A(j,j)) */ - tjj = (d__1 = a[j + j * a_dim1], abs(d__1)); - if (xj > tjj) { - xbnd *= tjj / xj; - } + tjj = (d__1 = a[j + j * a_dim1], abs(d__1)); + if (xj > tjj) { + xbnd *= tjj / xj; + } /* L60: */ - } - grow = min(grow,xbnd); - } else { + } + grow = min(grow,xbnd); + } else { /* A is unit triangular. */ /* Compute GROW = 1/G(j), where G(0) = max{x(i), i=1,...,n}. */ /* Computing MIN */ - d__1 = 1., d__2 = 1. / max(xbnd,smlnum); - grow = min(d__1,d__2); - i__2 = jlast; - i__1 = jinc; - for (j = jfirst; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) { + d__1 = 1., d__2 = 1. / max(xbnd,smlnum); + grow = min(d__1,d__2); + i__2 = jlast; + i__1 = jinc; + for (j = jfirst; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) { /* Exit the loop if the growth factor is too small. */ - if (grow <= smlnum) { - goto L80; - } + if (grow <= smlnum) { + goto L80; + } /* G(j) = ( 1 + CNORM(j) )*G(j-1) */ - xj = cnorm[j] + 1.; - grow /= xj; + xj = cnorm[j] + 1.; + grow /= xj; /* L70: */ - } - } + } + } L80: - ; + ; } if (grow * tscal > smlnum) { @@ -664,313 +664,313 @@ L80: /* Use the Level 2 BLAS solve if the reciprocal of the bound on */ /* elements of X is not too small. */ - dtrsv_(uplo, trans, diag, n, &a[a_offset], lda, &x[1], &c__1, (ftnlen) - 1, (ftnlen)1, (ftnlen)1); + dtrsv_(uplo, trans, diag, n, &a[a_offset], lda, &x[1], &c__1, (ftnlen) + 1, (ftnlen)1, (ftnlen)1); } else { /* Use a Level 1 BLAS solve, scaling intermediate results. */ - if (xmax > bignum) { + if (xmax > bignum) { /* Scale X so that its components are less than or equal to */ /* BIGNUM in absolute value. */ - *scale = bignum / xmax; - dscal_(n, scale, &x[1], &c__1); - xmax = bignum; - } + *scale = bignum / xmax; + dscal_(n, scale, &x[1], &c__1); + xmax = bignum; + } - if (notran) { + if (notran) { /* Solve A * x = b */ - i__1 = jlast; - i__2 = jinc; - for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) { + i__1 = jlast; + i__2 = jinc; + for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) { /* Compute x(j) = b(j) / A(j,j), scaling x if necessary. */ - xj = (d__1 = x[j], abs(d__1)); - if (nounit) { - tjjs = a[j + j * a_dim1] * tscal; - } else { - tjjs = tscal; - if (tscal == 1.) { - goto L100; - } - } - tjj = abs(tjjs); - if (tjj > smlnum) { + xj = (d__1 = x[j], abs(d__1)); + if (nounit) { + tjjs = a[j + j * a_dim1] * tscal; + } else { + tjjs = tscal; + if (tscal == 1.) { + goto L100; + } + } + tjj = abs(tjjs); + if (tjj > smlnum) { /* abs(A(j,j)) > SMLNUM: */ - if (tjj < 1.) { - if (xj > tjj * bignum) { + if (tjj < 1.) { + if (xj > tjj * bignum) { /* Scale x by 1/b(j). */ - rec = 1. / xj; - dscal_(n, &rec, &x[1], &c__1); - *scale *= rec; - xmax *= rec; - } - } - x[j] /= tjjs; - xj = (d__1 = x[j], abs(d__1)); - } else if (tjj > 0.) { + rec = 1. / xj; + dscal_(n, &rec, &x[1], &c__1); + *scale *= rec; + xmax *= rec; + } + } + x[j] /= tjjs; + xj = (d__1 = x[j], abs(d__1)); + } else if (tjj > 0.) { /* 0 < abs(A(j,j)) <= SMLNUM: */ - if (xj > tjj * bignum) { + if (xj > tjj * bignum) { /* Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM */ /* to avoid overflow when dividing by A(j,j). */ - rec = tjj * bignum / xj; - if (cnorm[j] > 1.) { + rec = tjj * bignum / xj; + if (cnorm[j] > 1.) { /* Scale by 1/CNORM(j) to avoid overflow when */ /* multiplying x(j) times column j. */ - rec /= cnorm[j]; - } - dscal_(n, &rec, &x[1], &c__1); - *scale *= rec; - xmax *= rec; - } - x[j] /= tjjs; - xj = (d__1 = x[j], abs(d__1)); - } else { + rec /= cnorm[j]; + } + dscal_(n, &rec, &x[1], &c__1); + *scale *= rec; + xmax *= rec; + } + x[j] /= tjjs; + xj = (d__1 = x[j], abs(d__1)); + } else { /* A(j,j) = 0: Set x(1:n) = 0, x(j) = 1, and */ /* scale = 0, and compute a solution to A*x = 0. */ - i__3 = *n; - for (i__ = 1; i__ <= i__3; ++i__) { - x[i__] = 0.; + i__3 = *n; + for (i__ = 1; i__ <= i__3; ++i__) { + x[i__] = 0.; /* L90: */ - } - x[j] = 1.; - xj = 1.; - *scale = 0.; - xmax = 0.; - } + } + x[j] = 1.; + xj = 1.; + *scale = 0.; + xmax = 0.; + } L100: /* Scale x if necessary to avoid overflow when adding a */ /* multiple of column j of A. */ - if (xj > 1.) { - rec = 1. / xj; - if (cnorm[j] > (bignum - xmax) * rec) { + if (xj > 1.) { + rec = 1. / xj; + if (cnorm[j] > (bignum - xmax) * rec) { /* Scale x by 1/(2*abs(x(j))). */ - rec *= .5; - dscal_(n, &rec, &x[1], &c__1); - *scale *= rec; - } - } else if (xj * cnorm[j] > bignum - xmax) { + rec *= .5; + dscal_(n, &rec, &x[1], &c__1); + *scale *= rec; + } + } else if (xj * cnorm[j] > bignum - xmax) { /* Scale x by 1/2. */ - dscal_(n, &c_b46, &x[1], &c__1); - *scale *= .5; - } + dscal_(n, &c_b46, &x[1], &c__1); + *scale *= .5; + } - if (upper) { - if (j > 1) { + if (upper) { + if (j > 1) { /* Compute the update */ /* x(1:j-1) := x(1:j-1) - x(j) * A(1:j-1,j) */ - i__3 = j - 1; - d__1 = -x[j] * tscal; - daxpy_(&i__3, &d__1, &a[j * a_dim1 + 1], &c__1, &x[1], - &c__1); - i__3 = j - 1; - i__ = idamax_(&i__3, &x[1], &c__1); - xmax = (d__1 = x[i__], abs(d__1)); - } - } else { - if (j < *n) { + i__3 = j - 1; + d__1 = -x[j] * tscal; + daxpy_(&i__3, &d__1, &a[j * a_dim1 + 1], &c__1, &x[1], + &c__1); + i__3 = j - 1; + i__ = idamax_(&i__3, &x[1], &c__1); + xmax = (d__1 = x[i__], abs(d__1)); + } + } else { + if (j < *n) { /* Compute the update */ /* x(j+1:n) := x(j+1:n) - x(j) * A(j+1:n,j) */ - i__3 = *n - j; - d__1 = -x[j] * tscal; - daxpy_(&i__3, &d__1, &a[j + 1 + j * a_dim1], &c__1, & - x[j + 1], &c__1); - i__3 = *n - j; - i__ = j + idamax_(&i__3, &x[j + 1], &c__1); - xmax = (d__1 = x[i__], abs(d__1)); - } - } + i__3 = *n - j; + d__1 = -x[j] * tscal; + daxpy_(&i__3, &d__1, &a[j + 1 + j * a_dim1], &c__1, & + x[j + 1], &c__1); + i__3 = *n - j; + i__ = j + idamax_(&i__3, &x[j + 1], &c__1); + xmax = (d__1 = x[i__], abs(d__1)); + } + } /* L110: */ - } + } - } else { + } else { /* Solve A**T * x = b */ - i__2 = jlast; - i__1 = jinc; - for (j = jfirst; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) { + i__2 = jlast; + i__1 = jinc; + for (j = jfirst; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) { /* Compute x(j) = b(j) - sum A(k,j)*x(k). */ /* k<>j */ - xj = (d__1 = x[j], abs(d__1)); - uscal = tscal; - rec = 1. / max(xmax,1.); - if (cnorm[j] > (bignum - xj) * rec) { + xj = (d__1 = x[j], abs(d__1)); + uscal = tscal; + rec = 1. / max(xmax,1.); + if (cnorm[j] > (bignum - xj) * rec) { /* If x(j) could overflow, scale x by 1/(2*XMAX). */ - rec *= .5; - if (nounit) { - tjjs = a[j + j * a_dim1] * tscal; - } else { - tjjs = tscal; - } - tjj = abs(tjjs); - if (tjj > 1.) { + rec *= .5; + if (nounit) { + tjjs = a[j + j * a_dim1] * tscal; + } else { + tjjs = tscal; + } + tjj = abs(tjjs); + if (tjj > 1.) { /* Divide by A(j,j) when scaling x if A(j,j) > 1. */ /* Computing MIN */ - d__1 = 1., d__2 = rec * tjj; - rec = min(d__1,d__2); - uscal /= tjjs; - } - if (rec < 1.) { - dscal_(n, &rec, &x[1], &c__1); - *scale *= rec; - xmax *= rec; - } - } + d__1 = 1., d__2 = rec * tjj; + rec = min(d__1,d__2); + uscal /= tjjs; + } + if (rec < 1.) { + dscal_(n, &rec, &x[1], &c__1); + *scale *= rec; + xmax *= rec; + } + } - sumj = 0.; - if (uscal == 1.) { + sumj = 0.; + if (uscal == 1.) { /* If the scaling needed for A in the dot product is 1, */ /* call DDOT to perform the dot product. */ - if (upper) { - i__3 = j - 1; - sumj = ddot_(&i__3, &a[j * a_dim1 + 1], &c__1, &x[1], - &c__1); - } else if (j < *n) { - i__3 = *n - j; - sumj = ddot_(&i__3, &a[j + 1 + j * a_dim1], &c__1, &x[ - j + 1], &c__1); - } - } else { + if (upper) { + i__3 = j - 1; + sumj = ddot_(&i__3, &a[j * a_dim1 + 1], &c__1, &x[1], + &c__1); + } else if (j < *n) { + i__3 = *n - j; + sumj = ddot_(&i__3, &a[j + 1 + j * a_dim1], &c__1, &x[ + j + 1], &c__1); + } + } else { /* Otherwise, use in-line code for the dot product. */ - if (upper) { - i__3 = j - 1; - for (i__ = 1; i__ <= i__3; ++i__) { - sumj += a[i__ + j * a_dim1] * uscal * x[i__]; + if (upper) { + i__3 = j - 1; + for (i__ = 1; i__ <= i__3; ++i__) { + sumj += a[i__ + j * a_dim1] * uscal * x[i__]; /* L120: */ - } - } else if (j < *n) { - i__3 = *n; - for (i__ = j + 1; i__ <= i__3; ++i__) { - sumj += a[i__ + j * a_dim1] * uscal * x[i__]; + } + } else if (j < *n) { + i__3 = *n; + for (i__ = j + 1; i__ <= i__3; ++i__) { + sumj += a[i__ + j * a_dim1] * uscal * x[i__]; /* L130: */ - } - } - } + } + } + } - if (uscal == tscal) { + if (uscal == tscal) { /* Compute x(j) := ( x(j) - sumj ) / A(j,j) if 1/A(j,j) */ /* was not used to scale the dotproduct. */ - x[j] -= sumj; - xj = (d__1 = x[j], abs(d__1)); - if (nounit) { - tjjs = a[j + j * a_dim1] * tscal; - } else { - tjjs = tscal; - if (tscal == 1.) { - goto L150; - } - } + x[j] -= sumj; + xj = (d__1 = x[j], abs(d__1)); + if (nounit) { + tjjs = a[j + j * a_dim1] * tscal; + } else { + tjjs = tscal; + if (tscal == 1.) { + goto L150; + } + } /* Compute x(j) = x(j) / A(j,j), scaling if necessary. */ - tjj = abs(tjjs); - if (tjj > smlnum) { + tjj = abs(tjjs); + if (tjj > smlnum) { /* abs(A(j,j)) > SMLNUM: */ - if (tjj < 1.) { - if (xj > tjj * bignum) { + if (tjj < 1.) { + if (xj > tjj * bignum) { /* Scale X by 1/abs(x(j)). */ - rec = 1. / xj; - dscal_(n, &rec, &x[1], &c__1); - *scale *= rec; - xmax *= rec; - } - } - x[j] /= tjjs; - } else if (tjj > 0.) { + rec = 1. / xj; + dscal_(n, &rec, &x[1], &c__1); + *scale *= rec; + xmax *= rec; + } + } + x[j] /= tjjs; + } else if (tjj > 0.) { /* 0 < abs(A(j,j)) <= SMLNUM: */ - if (xj > tjj * bignum) { + if (xj > tjj * bignum) { /* Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM. */ - rec = tjj * bignum / xj; - dscal_(n, &rec, &x[1], &c__1); - *scale *= rec; - xmax *= rec; - } - x[j] /= tjjs; - } else { + rec = tjj * bignum / xj; + dscal_(n, &rec, &x[1], &c__1); + *scale *= rec; + xmax *= rec; + } + x[j] /= tjjs; + } else { /* A(j,j) = 0: Set x(1:n) = 0, x(j) = 1, and */ /* scale = 0, and compute a solution to A**T*x = 0. */ - i__3 = *n; - for (i__ = 1; i__ <= i__3; ++i__) { - x[i__] = 0.; + i__3 = *n; + for (i__ = 1; i__ <= i__3; ++i__) { + x[i__] = 0.; /* L140: */ - } - x[j] = 1.; - *scale = 0.; - xmax = 0.; - } + } + x[j] = 1.; + *scale = 0.; + xmax = 0.; + } L150: - ; - } else { + ; + } else { /* Compute x(j) := x(j) / A(j,j) - sumj if the dot */ /* product has already been divided by 1/A(j,j). */ - x[j] = x[j] / tjjs - sumj; - } + x[j] = x[j] / tjjs - sumj; + } /* Computing MAX */ - d__2 = xmax, d__3 = (d__1 = x[j], abs(d__1)); - xmax = max(d__2,d__3); + d__2 = xmax, d__3 = (d__1 = x[j], abs(d__1)); + xmax = max(d__2,d__3); /* L160: */ - } - } - *scale /= tscal; + } + } + *scale /= tscal; } /* Scale the column norms by 1/TSCAL for return. */ if (tscal != 1.) { - d__1 = 1. / tscal; - dscal_(n, &d__1, &cnorm[1], &c__1); + d__1 = 1. / tscal; + dscal_(n, &d__1, &cnorm[1], &c__1); } return 0; @@ -980,5 +980,5 @@ L150: } /* dlatrs_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dnrm2.cpp b/lib/linalg/dnrm2.cpp index 6ebf2d935e..dc2a59dfbd 100644 --- a/lib/linalg/dnrm2.cpp +++ b/lib/linalg/dnrm2.cpp @@ -1,13 +1,13 @@ /* fortran/dnrm2.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -126,35 +126,35 @@ doublereal dnrm2_(integer *n, doublereal *x, integer *incx) /* Function Body */ if (*n < 1 || *incx < 1) { - norm = 0.; + norm = 0.; } else if (*n == 1) { - norm = abs(x[1]); + norm = abs(x[1]); } else { - scale = 0.; - ssq = 1.; + scale = 0.; + ssq = 1.; /* The following loop is equivalent to this call to the LAPACK */ /* auxiliary routine: */ /* CALL DLASSQ( N, X, INCX, SCALE, SSQ ) */ - i__1 = (*n - 1) * *incx + 1; - i__2 = *incx; - for (ix = 1; i__2 < 0 ? ix >= i__1 : ix <= i__1; ix += i__2) { - if (x[ix] != 0.) { - absxi = (d__1 = x[ix], abs(d__1)); - if (scale < absxi) { + i__1 = (*n - 1) * *incx + 1; + i__2 = *incx; + for (ix = 1; i__2 < 0 ? ix >= i__1 : ix <= i__1; ix += i__2) { + if (x[ix] != 0.) { + absxi = (d__1 = x[ix], abs(d__1)); + if (scale < absxi) { /* Computing 2nd power */ - d__1 = scale / absxi; - ssq = ssq * (d__1 * d__1) + 1.; - scale = absxi; - } else { + d__1 = scale / absxi; + ssq = ssq * (d__1 * d__1) + 1.; + scale = absxi; + } else { /* Computing 2nd power */ - d__1 = absxi / scale; - ssq += d__1 * d__1; - } - } + d__1 = absxi / scale; + ssq += d__1 * d__1; + } + } /* L10: */ - } - norm = scale * sqrt(ssq); + } + norm = scale * sqrt(ssq); } ret_val = norm; @@ -165,5 +165,5 @@ doublereal dnrm2_(integer *n, doublereal *x, integer *incx) } /* dnrm2_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dorg2l.cpp b/lib/linalg/dorg2l.cpp index 5705f3b630..a028102645 100644 --- a/lib/linalg/dorg2l.cpp +++ b/lib/linalg/dorg2l.cpp @@ -1,13 +1,13 @@ /* fortran/dorg2l.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -136,7 +136,7 @@ f"> */ /* ===================================================================== */ /* Subroutine */ int dorg2l_(integer *m, integer *n, integer *k, doublereal * - a, integer *lda, doublereal *tau, doublereal *work, integer *info) + a, integer *lda, doublereal *tau, doublereal *work, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; @@ -144,10 +144,10 @@ f"> */ /* Local variables */ integer i__, j, l, ii; - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *), dlarf_(char *, integer *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - ftnlen), xerbla_(char *, integer *, ftnlen); + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *), dlarf_(char *, integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + ftnlen), xerbla_(char *, integer *, ftnlen); /* -- LAPACK computational routine -- */ @@ -183,62 +183,62 @@ f"> */ /* Function Body */ *info = 0; if (*m < 0) { - *info = -1; + *info = -1; } else if (*n < 0 || *n > *m) { - *info = -2; + *info = -2; } else if (*k < 0 || *k > *n) { - *info = -3; + *info = -3; } else if (*lda < max(1,*m)) { - *info = -5; + *info = -5; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DORG2L", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DORG2L", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*n <= 0) { - return 0; + return 0; } /* Initialise columns 1:n-k to columns of the unit matrix */ i__1 = *n - *k; for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (l = 1; l <= i__2; ++l) { - a[l + j * a_dim1] = 0.; + i__2 = *m; + for (l = 1; l <= i__2; ++l) { + a[l + j * a_dim1] = 0.; /* L10: */ - } - a[*m - *n + j + j * a_dim1] = 1.; + } + a[*m - *n + j + j * a_dim1] = 1.; /* L20: */ } i__1 = *k; for (i__ = 1; i__ <= i__1; ++i__) { - ii = *n - *k + i__; + ii = *n - *k + i__; /* Apply H(i) to A(1:m-k+i,1:n-k+i) from the left */ - a[*m - *n + ii + ii * a_dim1] = 1.; - i__2 = *m - *n + ii; - i__3 = ii - 1; - dlarf_((char *)"Left", &i__2, &i__3, &a[ii * a_dim1 + 1], &c__1, &tau[i__], & - a[a_offset], lda, &work[1], (ftnlen)4); - i__2 = *m - *n + ii - 1; - d__1 = -tau[i__]; - dscal_(&i__2, &d__1, &a[ii * a_dim1 + 1], &c__1); - a[*m - *n + ii + ii * a_dim1] = 1. - tau[i__]; + a[*m - *n + ii + ii * a_dim1] = 1.; + i__2 = *m - *n + ii; + i__3 = ii - 1; + dlarf_((char *)"Left", &i__2, &i__3, &a[ii * a_dim1 + 1], &c__1, &tau[i__], & + a[a_offset], lda, &work[1], (ftnlen)4); + i__2 = *m - *n + ii - 1; + d__1 = -tau[i__]; + dscal_(&i__2, &d__1, &a[ii * a_dim1 + 1], &c__1); + a[*m - *n + ii + ii * a_dim1] = 1. - tau[i__]; /* Set A(m-k+i+1:m,n-k+i) to zero */ - i__2 = *m; - for (l = *m - *n + ii + 1; l <= i__2; ++l) { - a[l + ii * a_dim1] = 0.; + i__2 = *m; + for (l = *m - *n + ii + 1; l <= i__2; ++l) { + a[l + ii * a_dim1] = 0.; /* L30: */ - } + } /* L40: */ } return 0; @@ -248,5 +248,5 @@ f"> */ } /* dorg2l_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dorg2r.cpp b/lib/linalg/dorg2r.cpp index 90ebed3963..f6d897beb6 100644 --- a/lib/linalg/dorg2r.cpp +++ b/lib/linalg/dorg2r.cpp @@ -1,13 +1,13 @@ /* fortran/dorg2r.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -136,7 +136,7 @@ f"> */ /* ===================================================================== */ /* Subroutine */ int dorg2r_(integer *m, integer *n, integer *k, doublereal * - a, integer *lda, doublereal *tau, doublereal *work, integer *info) + a, integer *lda, doublereal *tau, doublereal *work, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; @@ -144,10 +144,10 @@ f"> */ /* Local variables */ integer i__, j, l; - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *), dlarf_(char *, integer *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - ftnlen), xerbla_(char *, integer *, ftnlen); + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *), dlarf_(char *, integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + ftnlen), xerbla_(char *, integer *, ftnlen); /* -- LAPACK computational routine -- */ @@ -183,36 +183,36 @@ f"> */ /* Function Body */ *info = 0; if (*m < 0) { - *info = -1; + *info = -1; } else if (*n < 0 || *n > *m) { - *info = -2; + *info = -2; } else if (*k < 0 || *k > *n) { - *info = -3; + *info = -3; } else if (*lda < max(1,*m)) { - *info = -5; + *info = -5; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DORG2R", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DORG2R", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*n <= 0) { - return 0; + return 0; } /* Initialise columns k+1:n to columns of the unit matrix */ i__1 = *n; for (j = *k + 1; j <= i__1; ++j) { - i__2 = *m; - for (l = 1; l <= i__2; ++l) { - a[l + j * a_dim1] = 0.; + i__2 = *m; + for (l = 1; l <= i__2; ++l) { + a[l + j * a_dim1] = 0.; /* L10: */ - } - a[j + j * a_dim1] = 1.; + } + a[j + j * a_dim1] = 1.; /* L20: */ } @@ -220,28 +220,28 @@ f"> */ /* Apply H(i) to A(i:m,i:n) from the left */ - if (i__ < *n) { - a[i__ + i__ * a_dim1] = 1.; - i__1 = *m - i__ + 1; - i__2 = *n - i__; - dlarf_((char *)"Left", &i__1, &i__2, &a[i__ + i__ * a_dim1], &c__1, &tau[ - i__], &a[i__ + (i__ + 1) * a_dim1], lda, &work[1], ( - ftnlen)4); - } - if (i__ < *m) { - i__1 = *m - i__; - d__1 = -tau[i__]; - dscal_(&i__1, &d__1, &a[i__ + 1 + i__ * a_dim1], &c__1); - } - a[i__ + i__ * a_dim1] = 1. - tau[i__]; + if (i__ < *n) { + a[i__ + i__ * a_dim1] = 1.; + i__1 = *m - i__ + 1; + i__2 = *n - i__; + dlarf_((char *)"Left", &i__1, &i__2, &a[i__ + i__ * a_dim1], &c__1, &tau[ + i__], &a[i__ + (i__ + 1) * a_dim1], lda, &work[1], ( + ftnlen)4); + } + if (i__ < *m) { + i__1 = *m - i__; + d__1 = -tau[i__]; + dscal_(&i__1, &d__1, &a[i__ + 1 + i__ * a_dim1], &c__1); + } + a[i__ + i__ * a_dim1] = 1. - tau[i__]; /* Set A(1:i-1,i) to zero */ - i__1 = i__ - 1; - for (l = 1; l <= i__1; ++l) { - a[l + i__ * a_dim1] = 0.; + i__1 = i__ - 1; + for (l = 1; l <= i__1; ++l) { + a[l + i__ * a_dim1] = 0.; /* L30: */ - } + } /* L40: */ } return 0; @@ -251,5 +251,5 @@ f"> */ } /* dorg2r_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dorgbr.cpp b/lib/linalg/dorgbr.cpp index 4991344c01..a55e8aeca0 100644 --- a/lib/linalg/dorgbr.cpp +++ b/lib/linalg/dorgbr.cpp @@ -1,13 +1,13 @@ /* fortran/dorgbr.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -177,9 +177,9 @@ f"> */ /* > \ingroup doubleGBcomputational */ /* ===================================================================== */ -/* Subroutine */ int dorgbr_(char *vect, integer *m, integer *n, integer *k, - doublereal *a, integer *lda, doublereal *tau, doublereal *work, - integer *lwork, integer *info, ftnlen vect_len) +/* Subroutine */ int dorgbr_(char *vect, integer *m, integer *n, integer *k, + doublereal *a, integer *lda, doublereal *tau, doublereal *work, + integer *lwork, integer *info, ftnlen vect_len) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; @@ -190,10 +190,10 @@ f"> */ integer iinfo; logical wantq; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), dorglq_( - integer *, integer *, integer *, doublereal *, integer *, - doublereal *, doublereal *, integer *, integer *), dorgqr_( - integer *, integer *, integer *, doublereal *, integer *, - doublereal *, doublereal *, integer *, integer *); + integer *, integer *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, integer *), dorgqr_( + integer *, integer *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, integer *); integer lwkopt; logical lquery; @@ -236,67 +236,67 @@ f"> */ mn = min(*m,*n); lquery = *lwork == -1; if (! wantq && ! lsame_(vect, (char *)"P", (ftnlen)1, (ftnlen)1)) { - *info = -1; + *info = -1; } else if (*m < 0) { - *info = -2; + *info = -2; } else if (*n < 0 || wantq && (*n > *m || *n < min(*m,*k)) || ! wantq && ( - *m > *n || *m < min(*n,*k))) { - *info = -3; + *m > *n || *m < min(*n,*k))) { + *info = -3; } else if (*k < 0) { - *info = -4; + *info = -4; } else if (*lda < max(1,*m)) { - *info = -6; + *info = -6; } else if (*lwork < max(1,mn) && ! lquery) { - *info = -9; + *info = -9; } if (*info == 0) { - work[1] = 1.; - if (wantq) { - if (*m >= *k) { - dorgqr_(m, n, k, &a[a_offset], lda, &tau[1], &work[1], &c_n1, - &iinfo); - } else { - if (*m > 1) { - i__1 = *m - 1; - i__2 = *m - 1; - i__3 = *m - 1; - dorgqr_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], & - work[1], &c_n1, &iinfo); - } - } - } else { - if (*k < *n) { - dorglq_(m, n, k, &a[a_offset], lda, &tau[1], &work[1], &c_n1, - &iinfo); - } else { - if (*n > 1) { - i__1 = *n - 1; - i__2 = *n - 1; - i__3 = *n - 1; - dorglq_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], & - work[1], &c_n1, &iinfo); - } - } - } - lwkopt = (integer) work[1]; - lwkopt = max(lwkopt,mn); + work[1] = 1.; + if (wantq) { + if (*m >= *k) { + dorgqr_(m, n, k, &a[a_offset], lda, &tau[1], &work[1], &c_n1, + &iinfo); + } else { + if (*m > 1) { + i__1 = *m - 1; + i__2 = *m - 1; + i__3 = *m - 1; + dorgqr_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], & + work[1], &c_n1, &iinfo); + } + } + } else { + if (*k < *n) { + dorglq_(m, n, k, &a[a_offset], lda, &tau[1], &work[1], &c_n1, + &iinfo); + } else { + if (*n > 1) { + i__1 = *n - 1; + i__2 = *n - 1; + i__3 = *n - 1; + dorglq_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], & + work[1], &c_n1, &iinfo); + } + } + } + lwkopt = (integer) work[1]; + lwkopt = max(lwkopt,mn); } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DORGBR", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DORGBR", &i__1, (ftnlen)6); + return 0; } else if (lquery) { - work[1] = (doublereal) lwkopt; - return 0; + work[1] = (doublereal) lwkopt; + return 0; } /* Quick return if possible */ if (*m == 0 || *n == 0) { - work[1] = 1.; - return 0; + work[1] = 1.; + return 0; } if (wantq) { @@ -304,14 +304,14 @@ f"> */ /* Form Q, determined by a call to DGEBRD to reduce an m-by-k */ /* matrix */ - if (*m >= *k) { + if (*m >= *k) { /* If m >= k, assume m >= n >= k */ - dorgqr_(m, n, k, &a[a_offset], lda, &tau[1], &work[1], lwork, & - iinfo); + dorgqr_(m, n, k, &a[a_offset], lda, &tau[1], &work[1], lwork, & + iinfo); - } else { + } else { /* If m < k, assume m = n */ @@ -319,45 +319,45 @@ f"> */ /* column to the right, and set the first row and column of Q */ /* to those of the unit matrix */ - for (j = *m; j >= 2; --j) { - a[j * a_dim1 + 1] = 0.; - i__1 = *m; - for (i__ = j + 1; i__ <= i__1; ++i__) { - a[i__ + j * a_dim1] = a[i__ + (j - 1) * a_dim1]; + for (j = *m; j >= 2; --j) { + a[j * a_dim1 + 1] = 0.; + i__1 = *m; + for (i__ = j + 1; i__ <= i__1; ++i__) { + a[i__ + j * a_dim1] = a[i__ + (j - 1) * a_dim1]; /* L10: */ - } + } /* L20: */ - } - a[a_dim1 + 1] = 1.; - i__1 = *m; - for (i__ = 2; i__ <= i__1; ++i__) { - a[i__ + a_dim1] = 0.; + } + a[a_dim1 + 1] = 1.; + i__1 = *m; + for (i__ = 2; i__ <= i__1; ++i__) { + a[i__ + a_dim1] = 0.; /* L30: */ - } - if (*m > 1) { + } + if (*m > 1) { /* Form Q(2:m,2:m) */ - i__1 = *m - 1; - i__2 = *m - 1; - i__3 = *m - 1; - dorgqr_(&i__1, &i__2, &i__3, &a[(a_dim1 << 1) + 2], lda, &tau[ - 1], &work[1], lwork, &iinfo); - } - } + i__1 = *m - 1; + i__2 = *m - 1; + i__3 = *m - 1; + dorgqr_(&i__1, &i__2, &i__3, &a[(a_dim1 << 1) + 2], lda, &tau[ + 1], &work[1], lwork, &iinfo); + } + } } else { /* Form P**T, determined by a call to DGEBRD to reduce a k-by-n */ /* matrix */ - if (*k < *n) { + if (*k < *n) { /* If k < n, assume k <= m <= n */ - dorglq_(m, n, k, &a[a_offset], lda, &tau[1], &work[1], lwork, & - iinfo); + dorglq_(m, n, k, &a[a_offset], lda, &tau[1], &work[1], lwork, & + iinfo); - } else { + } else { /* If k >= n, assume m = n */ @@ -365,32 +365,32 @@ f"> */ /* row downward, and set the first row and column of P**T to */ /* those of the unit matrix */ - a[a_dim1 + 1] = 1.; - i__1 = *n; - for (i__ = 2; i__ <= i__1; ++i__) { - a[i__ + a_dim1] = 0.; + a[a_dim1 + 1] = 1.; + i__1 = *n; + for (i__ = 2; i__ <= i__1; ++i__) { + a[i__ + a_dim1] = 0.; /* L40: */ - } - i__1 = *n; - for (j = 2; j <= i__1; ++j) { - for (i__ = j - 1; i__ >= 2; --i__) { - a[i__ + j * a_dim1] = a[i__ - 1 + j * a_dim1]; + } + i__1 = *n; + for (j = 2; j <= i__1; ++j) { + for (i__ = j - 1; i__ >= 2; --i__) { + a[i__ + j * a_dim1] = a[i__ - 1 + j * a_dim1]; /* L50: */ - } - a[j * a_dim1 + 1] = 0.; + } + a[j * a_dim1 + 1] = 0.; /* L60: */ - } - if (*n > 1) { + } + if (*n > 1) { /* Form P**T(2:n,2:n) */ - i__1 = *n - 1; - i__2 = *n - 1; - i__3 = *n - 1; - dorglq_(&i__1, &i__2, &i__3, &a[(a_dim1 << 1) + 2], lda, &tau[ - 1], &work[1], lwork, &iinfo); - } - } + i__1 = *n - 1; + i__2 = *n - 1; + i__3 = *n - 1; + dorglq_(&i__1, &i__2, &i__3, &a[(a_dim1 << 1) + 2], lda, &tau[ + 1], &work[1], lwork, &iinfo); + } + } } work[1] = (doublereal) lwkopt; return 0; @@ -400,5 +400,5 @@ f"> */ } /* dorgbr_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dorgl2.cpp b/lib/linalg/dorgl2.cpp index a2cce985f3..68b6445522 100644 --- a/lib/linalg/dorgl2.cpp +++ b/lib/linalg/dorgl2.cpp @@ -1,13 +1,13 @@ /* fortran/dorgl2.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -130,7 +130,7 @@ f"> */ /* ===================================================================== */ /* Subroutine */ int dorgl2_(integer *m, integer *n, integer *k, doublereal * - a, integer *lda, doublereal *tau, doublereal *work, integer *info) + a, integer *lda, doublereal *tau, doublereal *work, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; @@ -138,10 +138,10 @@ f"> */ /* Local variables */ integer i__, j, l; - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *), dlarf_(char *, integer *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - ftnlen), xerbla_(char *, integer *, ftnlen); + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *), dlarf_(char *, integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + ftnlen), xerbla_(char *, integer *, ftnlen); /* -- LAPACK computational routine -- */ @@ -177,70 +177,70 @@ f"> */ /* Function Body */ *info = 0; if (*m < 0) { - *info = -1; + *info = -1; } else if (*n < *m) { - *info = -2; + *info = -2; } else if (*k < 0 || *k > *m) { - *info = -3; + *info = -3; } else if (*lda < max(1,*m)) { - *info = -5; + *info = -5; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DORGL2", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DORGL2", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*m <= 0) { - return 0; + return 0; } if (*k < *m) { /* Initialise rows k+1:m to rows of the unit matrix */ - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (l = *k + 1; l <= i__2; ++l) { - a[l + j * a_dim1] = 0.; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (l = *k + 1; l <= i__2; ++l) { + a[l + j * a_dim1] = 0.; /* L10: */ - } - if (j > *k && j <= *m) { - a[j + j * a_dim1] = 1.; - } + } + if (j > *k && j <= *m) { + a[j + j * a_dim1] = 1.; + } /* L20: */ - } + } } for (i__ = *k; i__ >= 1; --i__) { /* Apply H(i) to A(i:m,i:n) from the right */ - if (i__ < *n) { - if (i__ < *m) { - a[i__ + i__ * a_dim1] = 1.; - i__1 = *m - i__; - i__2 = *n - i__ + 1; - dlarf_((char *)"Right", &i__1, &i__2, &a[i__ + i__ * a_dim1], lda, & - tau[i__], &a[i__ + 1 + i__ * a_dim1], lda, &work[1], ( - ftnlen)5); - } - i__1 = *n - i__; - d__1 = -tau[i__]; - dscal_(&i__1, &d__1, &a[i__ + (i__ + 1) * a_dim1], lda); - } - a[i__ + i__ * a_dim1] = 1. - tau[i__]; + if (i__ < *n) { + if (i__ < *m) { + a[i__ + i__ * a_dim1] = 1.; + i__1 = *m - i__; + i__2 = *n - i__ + 1; + dlarf_((char *)"Right", &i__1, &i__2, &a[i__ + i__ * a_dim1], lda, & + tau[i__], &a[i__ + 1 + i__ * a_dim1], lda, &work[1], ( + ftnlen)5); + } + i__1 = *n - i__; + d__1 = -tau[i__]; + dscal_(&i__1, &d__1, &a[i__ + (i__ + 1) * a_dim1], lda); + } + a[i__ + i__ * a_dim1] = 1. - tau[i__]; /* Set A(i,1:i-1) to zero */ - i__1 = i__ - 1; - for (l = 1; l <= i__1; ++l) { - a[i__ + l * a_dim1] = 0.; + i__1 = i__ - 1; + for (l = 1; l <= i__1; ++l) { + a[i__ + l * a_dim1] = 0.; /* L30: */ - } + } /* L40: */ } return 0; @@ -250,5 +250,5 @@ f"> */ } /* dorgl2_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dorglq.cpp b/lib/linalg/dorglq.cpp index 3dc2d1986c..96eb224501 100644 --- a/lib/linalg/dorglq.cpp +++ b/lib/linalg/dorglq.cpp @@ -1,13 +1,13 @@ /* fortran/dorglq.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -151,24 +151,24 @@ f"> */ /* ===================================================================== */ /* Subroutine */ int dorglq_(integer *m, integer *n, integer *k, doublereal * - a, integer *lda, doublereal *tau, doublereal *work, integer *lwork, - integer *info) + a, integer *lda, doublereal *tau, doublereal *work, integer *lwork, + integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; /* Local variables */ integer i__, j, l, ib, nb, ki, kk, nx, iws, nbmin, iinfo; - extern /* Subroutine */ int dorgl2_(integer *, integer *, integer *, - doublereal *, integer *, doublereal *, doublereal *, integer *), - dlarfb_(char *, char *, char *, char *, integer *, integer *, - integer *, doublereal *, integer *, doublereal *, integer *, - doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, - ftnlen, ftnlen), dlarft_(char *, char *, integer *, integer *, - doublereal *, integer *, doublereal *, doublereal *, integer *, - ftnlen, ftnlen), xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dorgl2_(integer *, integer *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *), + dlarfb_(char *, char *, char *, char *, integer *, integer *, + integer *, doublereal *, integer *, doublereal *, integer *, + doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, + ftnlen, ftnlen), dlarft_(char *, char *, integer *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, + ftnlen, ftnlen), xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); integer ldwork, lwkopt; logical lquery; @@ -212,29 +212,29 @@ f"> */ work[1] = (doublereal) lwkopt; lquery = *lwork == -1; if (*m < 0) { - *info = -1; + *info = -1; } else if (*n < *m) { - *info = -2; + *info = -2; } else if (*k < 0 || *k > *m) { - *info = -3; + *info = -3; } else if (*lda < max(1,*m)) { - *info = -5; + *info = -5; } else if (*lwork < max(1,*m) && ! lquery) { - *info = -8; + *info = -8; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DORGLQ", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DORGLQ", &i__1, (ftnlen)6); + return 0; } else if (lquery) { - return 0; + return 0; } /* Quick return if possible */ if (*m <= 0) { - work[1] = 1.; - return 0; + work[1] = 1.; + return 0; } nbmin = 2; @@ -245,27 +245,27 @@ f"> */ /* Determine when to cross over from blocked to unblocked code. */ /* Computing MAX */ - i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"DORGLQ", (char *)" ", m, n, k, &c_n1, ( - ftnlen)6, (ftnlen)1); - nx = max(i__1,i__2); - if (nx < *k) { + i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"DORGLQ", (char *)" ", m, n, k, &c_n1, ( + ftnlen)6, (ftnlen)1); + nx = max(i__1,i__2); + if (nx < *k) { /* Determine if workspace is large enough for blocked code. */ - ldwork = *m; - iws = ldwork * nb; - if (*lwork < iws) { + ldwork = *m; + iws = ldwork * nb; + if (*lwork < iws) { /* Not enough workspace to use optimal NB: reduce NB and */ /* determine the minimum value of NB. */ - nb = *lwork / ldwork; + nb = *lwork / ldwork; /* Computing MAX */ - i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DORGLQ", (char *)" ", m, n, k, &c_n1, - (ftnlen)6, (ftnlen)1); - nbmin = max(i__1,i__2); - } - } + i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DORGLQ", (char *)" ", m, n, k, &c_n1, + (ftnlen)6, (ftnlen)1); + nbmin = max(i__1,i__2); + } + } } if (nb >= nbmin && nb < *k && nx < *k) { @@ -273,85 +273,85 @@ f"> */ /* Use blocked code after the last block. */ /* The first kk rows are handled by the block method. */ - ki = (*k - nx - 1) / nb * nb; + ki = (*k - nx - 1) / nb * nb; /* Computing MIN */ - i__1 = *k, i__2 = ki + nb; - kk = min(i__1,i__2); + i__1 = *k, i__2 = ki + nb; + kk = min(i__1,i__2); /* Set A(kk+1:m,1:kk) to zero. */ - i__1 = kk; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = kk + 1; i__ <= i__2; ++i__) { - a[i__ + j * a_dim1] = 0.; + i__1 = kk; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = kk + 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] = 0.; /* L10: */ - } + } /* L20: */ - } + } } else { - kk = 0; + kk = 0; } /* Use unblocked code for the last or only block. */ if (kk < *m) { - i__1 = *m - kk; - i__2 = *n - kk; - i__3 = *k - kk; - dorgl2_(&i__1, &i__2, &i__3, &a[kk + 1 + (kk + 1) * a_dim1], lda, & - tau[kk + 1], &work[1], &iinfo); + i__1 = *m - kk; + i__2 = *n - kk; + i__3 = *k - kk; + dorgl2_(&i__1, &i__2, &i__3, &a[kk + 1 + (kk + 1) * a_dim1], lda, & + tau[kk + 1], &work[1], &iinfo); } if (kk > 0) { /* Use blocked code */ - i__1 = -nb; - for (i__ = ki + 1; i__1 < 0 ? i__ >= 1 : i__ <= 1; i__ += i__1) { + i__1 = -nb; + for (i__ = ki + 1; i__1 < 0 ? i__ >= 1 : i__ <= 1; i__ += i__1) { /* Computing MIN */ - i__2 = nb, i__3 = *k - i__ + 1; - ib = min(i__2,i__3); - if (i__ + ib <= *m) { + i__2 = nb, i__3 = *k - i__ + 1; + ib = min(i__2,i__3); + if (i__ + ib <= *m) { /* Form the triangular factor of the block reflector */ /* H = H(i) H(i+1) . . . H(i+ib-1) */ - i__2 = *n - i__ + 1; - dlarft_((char *)"Forward", (char *)"Rowwise", &i__2, &ib, &a[i__ + i__ * - a_dim1], lda, &tau[i__], &work[1], &ldwork, (ftnlen)7, - (ftnlen)7); + i__2 = *n - i__ + 1; + dlarft_((char *)"Forward", (char *)"Rowwise", &i__2, &ib, &a[i__ + i__ * + a_dim1], lda, &tau[i__], &work[1], &ldwork, (ftnlen)7, + (ftnlen)7); /* Apply H**T to A(i+ib:m,i:n) from the right */ - i__2 = *m - i__ - ib + 1; - i__3 = *n - i__ + 1; - dlarfb_((char *)"Right", (char *)"Transpose", (char *)"Forward", (char *)"Rowwise", &i__2, & - i__3, &ib, &a[i__ + i__ * a_dim1], lda, &work[1], & - ldwork, &a[i__ + ib + i__ * a_dim1], lda, &work[ib + - 1], &ldwork, (ftnlen)5, (ftnlen)9, (ftnlen)7, (ftnlen) - 7); - } + i__2 = *m - i__ - ib + 1; + i__3 = *n - i__ + 1; + dlarfb_((char *)"Right", (char *)"Transpose", (char *)"Forward", (char *)"Rowwise", &i__2, & + i__3, &ib, &a[i__ + i__ * a_dim1], lda, &work[1], & + ldwork, &a[i__ + ib + i__ * a_dim1], lda, &work[ib + + 1], &ldwork, (ftnlen)5, (ftnlen)9, (ftnlen)7, (ftnlen) + 7); + } /* Apply H**T to columns i:n of current block */ - i__2 = *n - i__ + 1; - dorgl2_(&ib, &i__2, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], & - work[1], &iinfo); + i__2 = *n - i__ + 1; + dorgl2_(&ib, &i__2, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], & + work[1], &iinfo); /* Set columns 1:i-1 of current block to zero */ - i__2 = i__ - 1; - for (j = 1; j <= i__2; ++j) { - i__3 = i__ + ib - 1; - for (l = i__; l <= i__3; ++l) { - a[l + j * a_dim1] = 0.; + i__2 = i__ - 1; + for (j = 1; j <= i__2; ++j) { + i__3 = i__ + ib - 1; + for (l = i__; l <= i__3; ++l) { + a[l + j * a_dim1] = 0.; /* L30: */ - } + } /* L40: */ - } + } /* L50: */ - } + } } work[1] = (doublereal) iws; @@ -362,5 +362,5 @@ f"> */ } /* dorglq_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dorgql.cpp b/lib/linalg/dorgql.cpp index 22a9b05b4b..719b7aa685 100644 --- a/lib/linalg/dorgql.cpp +++ b/lib/linalg/dorgql.cpp @@ -1,13 +1,13 @@ /* fortran/dorgql.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -152,24 +152,24 @@ f"> */ /* ===================================================================== */ /* Subroutine */ int dorgql_(integer *m, integer *n, integer *k, doublereal * - a, integer *lda, doublereal *tau, doublereal *work, integer *lwork, - integer *info) + a, integer *lda, doublereal *tau, doublereal *work, integer *lwork, + integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4; /* Local variables */ integer i__, j, l, ib, nb, kk, nx, iws, nbmin, iinfo; - extern /* Subroutine */ int dorg2l_(integer *, integer *, integer *, - doublereal *, integer *, doublereal *, doublereal *, integer *), - dlarfb_(char *, char *, char *, char *, integer *, integer *, - integer *, doublereal *, integer *, doublereal *, integer *, - doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, - ftnlen, ftnlen), dlarft_(char *, char *, integer *, integer *, - doublereal *, integer *, doublereal *, doublereal *, integer *, - ftnlen, ftnlen), xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dorg2l_(integer *, integer *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *), + dlarfb_(char *, char *, char *, char *, integer *, integer *, + integer *, doublereal *, integer *, doublereal *, integer *, + doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, + ftnlen, ftnlen), dlarft_(char *, char *, integer *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, + ftnlen, ftnlen), xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); integer ldwork, lwkopt; logical lquery; @@ -210,42 +210,42 @@ f"> */ *info = 0; lquery = *lwork == -1; if (*m < 0) { - *info = -1; + *info = -1; } else if (*n < 0 || *n > *m) { - *info = -2; + *info = -2; } else if (*k < 0 || *k > *n) { - *info = -3; + *info = -3; } else if (*lda < max(1,*m)) { - *info = -5; + *info = -5; } if (*info == 0) { - if (*n == 0) { - lwkopt = 1; - } else { - nb = ilaenv_(&c__1, (char *)"DORGQL", (char *)" ", m, n, k, &c_n1, (ftnlen)6, ( - ftnlen)1); - lwkopt = *n * nb; - } - work[1] = (doublereal) lwkopt; + if (*n == 0) { + lwkopt = 1; + } else { + nb = ilaenv_(&c__1, (char *)"DORGQL", (char *)" ", m, n, k, &c_n1, (ftnlen)6, ( + ftnlen)1); + lwkopt = *n * nb; + } + work[1] = (doublereal) lwkopt; - if (*lwork < max(1,*n) && ! lquery) { - *info = -8; - } + if (*lwork < max(1,*n) && ! lquery) { + *info = -8; + } } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DORGQL", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DORGQL", &i__1, (ftnlen)6); + return 0; } else if (lquery) { - return 0; + return 0; } /* Quick return if possible */ if (*n <= 0) { - return 0; + return 0; } nbmin = 2; @@ -256,27 +256,27 @@ f"> */ /* Determine when to cross over from blocked to unblocked code. */ /* Computing MAX */ - i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"DORGQL", (char *)" ", m, n, k, &c_n1, ( - ftnlen)6, (ftnlen)1); - nx = max(i__1,i__2); - if (nx < *k) { + i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"DORGQL", (char *)" ", m, n, k, &c_n1, ( + ftnlen)6, (ftnlen)1); + nx = max(i__1,i__2); + if (nx < *k) { /* Determine if workspace is large enough for blocked code. */ - ldwork = *n; - iws = ldwork * nb; - if (*lwork < iws) { + ldwork = *n; + iws = ldwork * nb; + if (*lwork < iws) { /* Not enough workspace to use optimal NB: reduce NB and */ /* determine the minimum value of NB. */ - nb = *lwork / ldwork; + nb = *lwork / ldwork; /* Computing MAX */ - i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DORGQL", (char *)" ", m, n, k, &c_n1, - (ftnlen)6, (ftnlen)1); - nbmin = max(i__1,i__2); - } - } + i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DORGQL", (char *)" ", m, n, k, &c_n1, + (ftnlen)6, (ftnlen)1); + nbmin = max(i__1,i__2); + } + } } if (nb >= nbmin && nb < *k && nx < *k) { @@ -285,22 +285,22 @@ f"> */ /* The last kk columns are handled by the block method. */ /* Computing MIN */ - i__1 = *k, i__2 = (*k - nx + nb - 1) / nb * nb; - kk = min(i__1,i__2); + i__1 = *k, i__2 = (*k - nx + nb - 1) / nb * nb; + kk = min(i__1,i__2); /* Set A(m-kk+1:m,1:n-kk) to zero. */ - i__1 = *n - kk; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = *m - kk + 1; i__ <= i__2; ++i__) { - a[i__ + j * a_dim1] = 0.; + i__1 = *n - kk; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = *m - kk + 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] = 0.; /* L10: */ - } + } /* L20: */ - } + } } else { - kk = 0; + kk = 0; } /* Use unblocked code for the first or only block. */ @@ -309,59 +309,59 @@ f"> */ i__2 = *n - kk; i__3 = *k - kk; dorg2l_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], &work[1], &iinfo) - ; + ; if (kk > 0) { /* Use blocked code */ - i__1 = *k; - i__2 = nb; - for (i__ = *k - kk + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += - i__2) { + i__1 = *k; + i__2 = nb; + for (i__ = *k - kk + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += + i__2) { /* Computing MIN */ - i__3 = nb, i__4 = *k - i__ + 1; - ib = min(i__3,i__4); - if (*n - *k + i__ > 1) { + i__3 = nb, i__4 = *k - i__ + 1; + ib = min(i__3,i__4); + if (*n - *k + i__ > 1) { /* Form the triangular factor of the block reflector */ /* H = H(i+ib-1) . . . H(i+1) H(i) */ - i__3 = *m - *k + i__ + ib - 1; - dlarft_((char *)"Backward", (char *)"Columnwise", &i__3, &ib, &a[(*n - *k + - i__) * a_dim1 + 1], lda, &tau[i__], &work[1], &ldwork, - (ftnlen)8, (ftnlen)10); + i__3 = *m - *k + i__ + ib - 1; + dlarft_((char *)"Backward", (char *)"Columnwise", &i__3, &ib, &a[(*n - *k + + i__) * a_dim1 + 1], lda, &tau[i__], &work[1], &ldwork, + (ftnlen)8, (ftnlen)10); /* Apply H to A(1:m-k+i+ib-1,1:n-k+i-1) from the left */ - i__3 = *m - *k + i__ + ib - 1; - i__4 = *n - *k + i__ - 1; - dlarfb_((char *)"Left", (char *)"No transpose", (char *)"Backward", (char *)"Columnwise", & - i__3, &i__4, &ib, &a[(*n - *k + i__) * a_dim1 + 1], - lda, &work[1], &ldwork, &a[a_offset], lda, &work[ib + - 1], &ldwork, (ftnlen)4, (ftnlen)12, (ftnlen)8, ( - ftnlen)10); - } + i__3 = *m - *k + i__ + ib - 1; + i__4 = *n - *k + i__ - 1; + dlarfb_((char *)"Left", (char *)"No transpose", (char *)"Backward", (char *)"Columnwise", & + i__3, &i__4, &ib, &a[(*n - *k + i__) * a_dim1 + 1], + lda, &work[1], &ldwork, &a[a_offset], lda, &work[ib + + 1], &ldwork, (ftnlen)4, (ftnlen)12, (ftnlen)8, ( + ftnlen)10); + } /* Apply H to rows 1:m-k+i+ib-1 of current block */ - i__3 = *m - *k + i__ + ib - 1; - dorg2l_(&i__3, &ib, &ib, &a[(*n - *k + i__) * a_dim1 + 1], lda, & - tau[i__], &work[1], &iinfo); + i__3 = *m - *k + i__ + ib - 1; + dorg2l_(&i__3, &ib, &ib, &a[(*n - *k + i__) * a_dim1 + 1], lda, & + tau[i__], &work[1], &iinfo); /* Set rows m-k+i+ib:m of current block to zero */ - i__3 = *n - *k + i__ + ib - 1; - for (j = *n - *k + i__; j <= i__3; ++j) { - i__4 = *m; - for (l = *m - *k + i__ + ib; l <= i__4; ++l) { - a[l + j * a_dim1] = 0.; + i__3 = *n - *k + i__ + ib - 1; + for (j = *n - *k + i__; j <= i__3; ++j) { + i__4 = *m; + for (l = *m - *k + i__ + ib; l <= i__4; ++l) { + a[l + j * a_dim1] = 0.; /* L30: */ - } + } /* L40: */ - } + } /* L50: */ - } + } } work[1] = (doublereal) iws; @@ -372,5 +372,5 @@ f"> */ } /* dorgql_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dorgqr.cpp b/lib/linalg/dorgqr.cpp index 30f175f707..4fedb08864 100644 --- a/lib/linalg/dorgqr.cpp +++ b/lib/linalg/dorgqr.cpp @@ -1,13 +1,13 @@ /* fortran/dorgqr.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -152,24 +152,24 @@ f"> */ /* ===================================================================== */ /* Subroutine */ int dorgqr_(integer *m, integer *n, integer *k, doublereal * - a, integer *lda, doublereal *tau, doublereal *work, integer *lwork, - integer *info) + a, integer *lda, doublereal *tau, doublereal *work, integer *lwork, + integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; /* Local variables */ integer i__, j, l, ib, nb, ki, kk, nx, iws, nbmin, iinfo; - extern /* Subroutine */ int dorg2r_(integer *, integer *, integer *, - doublereal *, integer *, doublereal *, doublereal *, integer *), - dlarfb_(char *, char *, char *, char *, integer *, integer *, - integer *, doublereal *, integer *, doublereal *, integer *, - doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, - ftnlen, ftnlen), dlarft_(char *, char *, integer *, integer *, - doublereal *, integer *, doublereal *, doublereal *, integer *, - ftnlen, ftnlen), xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dorg2r_(integer *, integer *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *), + dlarfb_(char *, char *, char *, char *, integer *, integer *, + integer *, doublereal *, integer *, doublereal *, integer *, + doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, + ftnlen, ftnlen), dlarft_(char *, char *, integer *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, + ftnlen, ftnlen), xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); integer ldwork, lwkopt; logical lquery; @@ -213,29 +213,29 @@ f"> */ work[1] = (doublereal) lwkopt; lquery = *lwork == -1; if (*m < 0) { - *info = -1; + *info = -1; } else if (*n < 0 || *n > *m) { - *info = -2; + *info = -2; } else if (*k < 0 || *k > *n) { - *info = -3; + *info = -3; } else if (*lda < max(1,*m)) { - *info = -5; + *info = -5; } else if (*lwork < max(1,*n) && ! lquery) { - *info = -8; + *info = -8; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DORGQR", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DORGQR", &i__1, (ftnlen)6); + return 0; } else if (lquery) { - return 0; + return 0; } /* Quick return if possible */ if (*n <= 0) { - work[1] = 1.; - return 0; + work[1] = 1.; + return 0; } nbmin = 2; @@ -246,27 +246,27 @@ f"> */ /* Determine when to cross over from blocked to unblocked code. */ /* Computing MAX */ - i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"DORGQR", (char *)" ", m, n, k, &c_n1, ( - ftnlen)6, (ftnlen)1); - nx = max(i__1,i__2); - if (nx < *k) { + i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"DORGQR", (char *)" ", m, n, k, &c_n1, ( + ftnlen)6, (ftnlen)1); + nx = max(i__1,i__2); + if (nx < *k) { /* Determine if workspace is large enough for blocked code. */ - ldwork = *n; - iws = ldwork * nb; - if (*lwork < iws) { + ldwork = *n; + iws = ldwork * nb; + if (*lwork < iws) { /* Not enough workspace to use optimal NB: reduce NB and */ /* determine the minimum value of NB. */ - nb = *lwork / ldwork; + nb = *lwork / ldwork; /* Computing MAX */ - i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DORGQR", (char *)" ", m, n, k, &c_n1, - (ftnlen)6, (ftnlen)1); - nbmin = max(i__1,i__2); - } - } + i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DORGQR", (char *)" ", m, n, k, &c_n1, + (ftnlen)6, (ftnlen)1); + nbmin = max(i__1,i__2); + } + } } if (nb >= nbmin && nb < *k && nx < *k) { @@ -274,85 +274,85 @@ f"> */ /* Use blocked code after the last block. */ /* The first kk columns are handled by the block method. */ - ki = (*k - nx - 1) / nb * nb; + ki = (*k - nx - 1) / nb * nb; /* Computing MIN */ - i__1 = *k, i__2 = ki + nb; - kk = min(i__1,i__2); + i__1 = *k, i__2 = ki + nb; + kk = min(i__1,i__2); /* Set A(1:kk,kk+1:n) to zero. */ - i__1 = *n; - for (j = kk + 1; j <= i__1; ++j) { - i__2 = kk; - for (i__ = 1; i__ <= i__2; ++i__) { - a[i__ + j * a_dim1] = 0.; + i__1 = *n; + for (j = kk + 1; j <= i__1; ++j) { + i__2 = kk; + for (i__ = 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] = 0.; /* L10: */ - } + } /* L20: */ - } + } } else { - kk = 0; + kk = 0; } /* Use unblocked code for the last or only block. */ if (kk < *n) { - i__1 = *m - kk; - i__2 = *n - kk; - i__3 = *k - kk; - dorg2r_(&i__1, &i__2, &i__3, &a[kk + 1 + (kk + 1) * a_dim1], lda, & - tau[kk + 1], &work[1], &iinfo); + i__1 = *m - kk; + i__2 = *n - kk; + i__3 = *k - kk; + dorg2r_(&i__1, &i__2, &i__3, &a[kk + 1 + (kk + 1) * a_dim1], lda, & + tau[kk + 1], &work[1], &iinfo); } if (kk > 0) { /* Use blocked code */ - i__1 = -nb; - for (i__ = ki + 1; i__1 < 0 ? i__ >= 1 : i__ <= 1; i__ += i__1) { + i__1 = -nb; + for (i__ = ki + 1; i__1 < 0 ? i__ >= 1 : i__ <= 1; i__ += i__1) { /* Computing MIN */ - i__2 = nb, i__3 = *k - i__ + 1; - ib = min(i__2,i__3); - if (i__ + ib <= *n) { + i__2 = nb, i__3 = *k - i__ + 1; + ib = min(i__2,i__3); + if (i__ + ib <= *n) { /* Form the triangular factor of the block reflector */ /* H = H(i) H(i+1) . . . H(i+ib-1) */ - i__2 = *m - i__ + 1; - dlarft_((char *)"Forward", (char *)"Columnwise", &i__2, &ib, &a[i__ + i__ * - a_dim1], lda, &tau[i__], &work[1], &ldwork, (ftnlen)7, - (ftnlen)10); + i__2 = *m - i__ + 1; + dlarft_((char *)"Forward", (char *)"Columnwise", &i__2, &ib, &a[i__ + i__ * + a_dim1], lda, &tau[i__], &work[1], &ldwork, (ftnlen)7, + (ftnlen)10); /* Apply H to A(i:m,i+ib:n) from the left */ - i__2 = *m - i__ + 1; - i__3 = *n - i__ - ib + 1; - dlarfb_((char *)"Left", (char *)"No transpose", (char *)"Forward", (char *)"Columnwise", & - i__2, &i__3, &ib, &a[i__ + i__ * a_dim1], lda, &work[ - 1], &ldwork, &a[i__ + (i__ + ib) * a_dim1], lda, & - work[ib + 1], &ldwork, (ftnlen)4, (ftnlen)12, (ftnlen) - 7, (ftnlen)10); - } + i__2 = *m - i__ + 1; + i__3 = *n - i__ - ib + 1; + dlarfb_((char *)"Left", (char *)"No transpose", (char *)"Forward", (char *)"Columnwise", & + i__2, &i__3, &ib, &a[i__ + i__ * a_dim1], lda, &work[ + 1], &ldwork, &a[i__ + (i__ + ib) * a_dim1], lda, & + work[ib + 1], &ldwork, (ftnlen)4, (ftnlen)12, (ftnlen) + 7, (ftnlen)10); + } /* Apply H to rows i:m of current block */ - i__2 = *m - i__ + 1; - dorg2r_(&i__2, &ib, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], & - work[1], &iinfo); + i__2 = *m - i__ + 1; + dorg2r_(&i__2, &ib, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], & + work[1], &iinfo); /* Set rows 1:i-1 of current block to zero */ - i__2 = i__ + ib - 1; - for (j = i__; j <= i__2; ++j) { - i__3 = i__ - 1; - for (l = 1; l <= i__3; ++l) { - a[l + j * a_dim1] = 0.; + i__2 = i__ + ib - 1; + for (j = i__; j <= i__2; ++j) { + i__3 = i__ - 1; + for (l = 1; l <= i__3; ++l) { + a[l + j * a_dim1] = 0.; /* L30: */ - } + } /* L40: */ - } + } /* L50: */ - } + } } work[1] = (doublereal) iws; @@ -363,5 +363,5 @@ f"> */ } /* dorgqr_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dorgtr.cpp b/lib/linalg/dorgtr.cpp index 7686c56d19..0574de0d9b 100644 --- a/lib/linalg/dorgtr.cpp +++ b/lib/linalg/dorgtr.cpp @@ -1,13 +1,13 @@ /* fortran/dorgtr.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -145,8 +145,8 @@ f"> */ /* ===================================================================== */ /* Subroutine */ int dorgtr_(char *uplo, integer *n, doublereal *a, integer * - lda, doublereal *tau, doublereal *work, integer *lwork, integer *info, - ftnlen uplo_len) + lda, doublereal *tau, doublereal *work, integer *lwork, integer *info, + ftnlen uplo_len) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; @@ -157,12 +157,12 @@ f"> */ integer iinfo; logical upper; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - extern /* Subroutine */ int dorgql_(integer *, integer *, integer *, - doublereal *, integer *, doublereal *, doublereal *, integer *, - integer *), dorgqr_(integer *, integer *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, integer *); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dorgql_(integer *, integer *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, + integer *), dorgqr_(integer *, integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, integer *); integer lwkopt; logical lquery; @@ -204,52 +204,52 @@ f"> */ lquery = *lwork == -1; upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { - *info = -1; + *info = -1; } else if (*n < 0) { - *info = -2; + *info = -2; } else if (*lda < max(1,*n)) { - *info = -4; + *info = -4; } else /* if(complicated condition) */ { /* Computing MAX */ - i__1 = 1, i__2 = *n - 1; - if (*lwork < max(i__1,i__2) && ! lquery) { - *info = -7; - } + i__1 = 1, i__2 = *n - 1; + if (*lwork < max(i__1,i__2) && ! lquery) { + *info = -7; + } } if (*info == 0) { - if (upper) { - i__1 = *n - 1; - i__2 = *n - 1; - i__3 = *n - 1; - nb = ilaenv_(&c__1, (char *)"DORGQL", (char *)" ", &i__1, &i__2, &i__3, &c_n1, ( - ftnlen)6, (ftnlen)1); - } else { - i__1 = *n - 1; - i__2 = *n - 1; - i__3 = *n - 1; - nb = ilaenv_(&c__1, (char *)"DORGQR", (char *)" ", &i__1, &i__2, &i__3, &c_n1, ( - ftnlen)6, (ftnlen)1); - } + if (upper) { + i__1 = *n - 1; + i__2 = *n - 1; + i__3 = *n - 1; + nb = ilaenv_(&c__1, (char *)"DORGQL", (char *)" ", &i__1, &i__2, &i__3, &c_n1, ( + ftnlen)6, (ftnlen)1); + } else { + i__1 = *n - 1; + i__2 = *n - 1; + i__3 = *n - 1; + nb = ilaenv_(&c__1, (char *)"DORGQR", (char *)" ", &i__1, &i__2, &i__3, &c_n1, ( + ftnlen)6, (ftnlen)1); + } /* Computing MAX */ - i__1 = 1, i__2 = *n - 1; - lwkopt = max(i__1,i__2) * nb; - work[1] = (doublereal) lwkopt; + i__1 = 1, i__2 = *n - 1; + lwkopt = max(i__1,i__2) * nb; + work[1] = (doublereal) lwkopt; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DORGTR", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DORGTR", &i__1, (ftnlen)6); + return 0; } else if (lquery) { - return 0; + return 0; } /* Quick return if possible */ if (*n == 0) { - work[1] = 1.; - return 0; + work[1] = 1.; + return 0; } if (upper) { @@ -260,30 +260,30 @@ f"> */ /* column to the left, and set the last row and column of Q to */ /* those of the unit matrix */ - i__1 = *n - 1; - for (j = 1; j <= i__1; ++j) { - i__2 = j - 1; - for (i__ = 1; i__ <= i__2; ++i__) { - a[i__ + j * a_dim1] = a[i__ + (j + 1) * a_dim1]; + i__1 = *n - 1; + for (j = 1; j <= i__1; ++j) { + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] = a[i__ + (j + 1) * a_dim1]; /* L10: */ - } - a[*n + j * a_dim1] = 0.; + } + a[*n + j * a_dim1] = 0.; /* L20: */ - } - i__1 = *n - 1; - for (i__ = 1; i__ <= i__1; ++i__) { - a[i__ + *n * a_dim1] = 0.; + } + i__1 = *n - 1; + for (i__ = 1; i__ <= i__1; ++i__) { + a[i__ + *n * a_dim1] = 0.; /* L30: */ - } - a[*n + *n * a_dim1] = 1.; + } + a[*n + *n * a_dim1] = 1.; /* Generate Q(1:n-1,1:n-1) */ - i__1 = *n - 1; - i__2 = *n - 1; - i__3 = *n - 1; - dorgql_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], &work[1], - lwork, &iinfo); + i__1 = *n - 1; + i__2 = *n - 1; + i__3 = *n - 1; + dorgql_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], &work[1], + lwork, &iinfo); } else { @@ -293,31 +293,31 @@ f"> */ /* column to the right, and set the first row and column of Q to */ /* those of the unit matrix */ - for (j = *n; j >= 2; --j) { - a[j * a_dim1 + 1] = 0.; - i__1 = *n; - for (i__ = j + 1; i__ <= i__1; ++i__) { - a[i__ + j * a_dim1] = a[i__ + (j - 1) * a_dim1]; + for (j = *n; j >= 2; --j) { + a[j * a_dim1 + 1] = 0.; + i__1 = *n; + for (i__ = j + 1; i__ <= i__1; ++i__) { + a[i__ + j * a_dim1] = a[i__ + (j - 1) * a_dim1]; /* L40: */ - } + } /* L50: */ - } - a[a_dim1 + 1] = 1.; - i__1 = *n; - for (i__ = 2; i__ <= i__1; ++i__) { - a[i__ + a_dim1] = 0.; + } + a[a_dim1 + 1] = 1.; + i__1 = *n; + for (i__ = 2; i__ <= i__1; ++i__) { + a[i__ + a_dim1] = 0.; /* L60: */ - } - if (*n > 1) { + } + if (*n > 1) { /* Generate Q(2:n,2:n) */ - i__1 = *n - 1; - i__2 = *n - 1; - i__3 = *n - 1; - dorgqr_(&i__1, &i__2, &i__3, &a[(a_dim1 << 1) + 2], lda, &tau[1], - &work[1], lwork, &iinfo); - } + i__1 = *n - 1; + i__2 = *n - 1; + i__3 = *n - 1; + dorgqr_(&i__1, &i__2, &i__3, &a[(a_dim1 << 1) + 2], lda, &tau[1], + &work[1], lwork, &iinfo); + } } work[1] = (doublereal) lwkopt; return 0; @@ -327,5 +327,5 @@ f"> */ } /* dorgtr_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dorm2l.cpp b/lib/linalg/dorm2l.cpp index 6669a81614..6882f50cdb 100644 --- a/lib/linalg/dorm2l.cpp +++ b/lib/linalg/dorm2l.cpp @@ -1,13 +1,13 @@ /* fortran/dorm2l.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -19,7 +19,7 @@ extern "C" { static integer c__1 = 1; -/* > \brief \b DORM2L multiplies a general matrix by the orthogonal matrix from a QL factorization determined +/* > \brief \b DORM2L multiplies a general matrix by the orthogonal matrix from a QL factorization determined by sgeqlf (unblocked algorithm). */ /* =========== DOCUMENTATION =========== */ @@ -179,10 +179,10 @@ f"> */ /* > \ingroup doubleOTHERcomputational */ /* ===================================================================== */ -/* Subroutine */ int dorm2l_(char *side, char *trans, integer *m, integer *n, - integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal * - c__, integer *ldc, doublereal *work, integer *info, ftnlen side_len, - ftnlen trans_len) +/* Subroutine */ int dorm2l_(char *side, char *trans, integer *m, integer *n, + integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal * + c__, integer *ldc, doublereal *work, integer *info, ftnlen side_len, + ftnlen trans_len) { /* System generated locals */ integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2; @@ -191,9 +191,9 @@ f"> */ integer i__, i1, i2, i3, mi, ni, nq; doublereal aii; logical left; - extern /* Subroutine */ int dlarf_(char *, integer *, integer *, - doublereal *, integer *, doublereal *, doublereal *, integer *, - doublereal *, ftnlen); + extern /* Subroutine */ int dlarf_(char *, integer *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, + doublereal *, ftnlen); extern logical lsame_(char *, char *, ftnlen, ftnlen); extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); logical notran; @@ -242,75 +242,75 @@ f"> */ /* NQ is the order of Q */ if (left) { - nq = *m; + nq = *m; } else { - nq = *n; + nq = *n; } if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { - *info = -1; + *info = -1; } else if (! notran && ! lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1)) { - *info = -2; + *info = -2; } else if (*m < 0) { - *info = -3; + *info = -3; } else if (*n < 0) { - *info = -4; + *info = -4; } else if (*k < 0 || *k > nq) { - *info = -5; + *info = -5; } else if (*lda < max(1,nq)) { - *info = -7; + *info = -7; } else if (*ldc < max(1,*m)) { - *info = -10; + *info = -10; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DORM2L", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DORM2L", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*m == 0 || *n == 0 || *k == 0) { - return 0; + return 0; } if (left && notran || ! left && ! notran) { - i1 = 1; - i2 = *k; - i3 = 1; + i1 = 1; + i2 = *k; + i3 = 1; } else { - i1 = *k; - i2 = 1; - i3 = -1; + i1 = *k; + i2 = 1; + i3 = -1; } if (left) { - ni = *n; + ni = *n; } else { - mi = *m; + mi = *m; } i__1 = i2; i__2 = i3; for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { - if (left) { + if (left) { /* H(i) is applied to C(1:m-k+i,1:n) */ - mi = *m - *k + i__; - } else { + mi = *m - *k + i__; + } else { /* H(i) is applied to C(1:m,1:n-k+i) */ - ni = *n - *k + i__; - } + ni = *n - *k + i__; + } /* Apply H(i) */ - aii = a[nq - *k + i__ + i__ * a_dim1]; - a[nq - *k + i__ + i__ * a_dim1] = 1.; - dlarf_(side, &mi, &ni, &a[i__ * a_dim1 + 1], &c__1, &tau[i__], &c__[ - c_offset], ldc, &work[1], (ftnlen)1); - a[nq - *k + i__ + i__ * a_dim1] = aii; + aii = a[nq - *k + i__ + i__ * a_dim1]; + a[nq - *k + i__ + i__ * a_dim1] = 1.; + dlarf_(side, &mi, &ni, &a[i__ * a_dim1 + 1], &c__1, &tau[i__], &c__[ + c_offset], ldc, &work[1], (ftnlen)1); + a[nq - *k + i__ + i__ * a_dim1] = aii; /* L10: */ } return 0; @@ -320,5 +320,5 @@ f"> */ } /* dorm2l_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dorm2r.cpp b/lib/linalg/dorm2r.cpp index 13a74e8fe1..1b600a3507 100644 --- a/lib/linalg/dorm2r.cpp +++ b/lib/linalg/dorm2r.cpp @@ -1,13 +1,13 @@ /* fortran/dorm2r.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -19,7 +19,7 @@ extern "C" { static integer c__1 = 1; -/* > \brief \b DORM2R multiplies a general matrix by the orthogonal matrix from a QR factorization determined +/* > \brief \b DORM2R multiplies a general matrix by the orthogonal matrix from a QR factorization determined by sgeqrf (unblocked algorithm). */ /* =========== DOCUMENTATION =========== */ @@ -179,10 +179,10 @@ f"> */ /* > \ingroup doubleOTHERcomputational */ /* ===================================================================== */ -/* Subroutine */ int dorm2r_(char *side, char *trans, integer *m, integer *n, - integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal * - c__, integer *ldc, doublereal *work, integer *info, ftnlen side_len, - ftnlen trans_len) +/* Subroutine */ int dorm2r_(char *side, char *trans, integer *m, integer *n, + integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal * + c__, integer *ldc, doublereal *work, integer *info, ftnlen side_len, + ftnlen trans_len) { /* System generated locals */ integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2; @@ -191,9 +191,9 @@ f"> */ integer i__, i1, i2, i3, ic, jc, mi, ni, nq; doublereal aii; logical left; - extern /* Subroutine */ int dlarf_(char *, integer *, integer *, - doublereal *, integer *, doublereal *, doublereal *, integer *, - doublereal *, ftnlen); + extern /* Subroutine */ int dlarf_(char *, integer *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, + doublereal *, ftnlen); extern logical lsame_(char *, char *, ftnlen, ftnlen); extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); logical notran; @@ -242,79 +242,79 @@ f"> */ /* NQ is the order of Q */ if (left) { - nq = *m; + nq = *m; } else { - nq = *n; + nq = *n; } if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { - *info = -1; + *info = -1; } else if (! notran && ! lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1)) { - *info = -2; + *info = -2; } else if (*m < 0) { - *info = -3; + *info = -3; } else if (*n < 0) { - *info = -4; + *info = -4; } else if (*k < 0 || *k > nq) { - *info = -5; + *info = -5; } else if (*lda < max(1,nq)) { - *info = -7; + *info = -7; } else if (*ldc < max(1,*m)) { - *info = -10; + *info = -10; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DORM2R", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DORM2R", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*m == 0 || *n == 0 || *k == 0) { - return 0; + return 0; } if (left && ! notran || ! left && notran) { - i1 = 1; - i2 = *k; - i3 = 1; + i1 = 1; + i2 = *k; + i3 = 1; } else { - i1 = *k; - i2 = 1; - i3 = -1; + i1 = *k; + i2 = 1; + i3 = -1; } if (left) { - ni = *n; - jc = 1; + ni = *n; + jc = 1; } else { - mi = *m; - ic = 1; + mi = *m; + ic = 1; } i__1 = i2; i__2 = i3; for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { - if (left) { + if (left) { /* H(i) is applied to C(i:m,1:n) */ - mi = *m - i__ + 1; - ic = i__; - } else { + mi = *m - i__ + 1; + ic = i__; + } else { /* H(i) is applied to C(1:m,i:n) */ - ni = *n - i__ + 1; - jc = i__; - } + ni = *n - i__ + 1; + jc = i__; + } /* Apply H(i) */ - aii = a[i__ + i__ * a_dim1]; - a[i__ + i__ * a_dim1] = 1.; - dlarf_(side, &mi, &ni, &a[i__ + i__ * a_dim1], &c__1, &tau[i__], &c__[ - ic + jc * c_dim1], ldc, &work[1], (ftnlen)1); - a[i__ + i__ * a_dim1] = aii; + aii = a[i__ + i__ * a_dim1]; + a[i__ + i__ * a_dim1] = 1.; + dlarf_(side, &mi, &ni, &a[i__ + i__ * a_dim1], &c__1, &tau[i__], &c__[ + ic + jc * c_dim1], ldc, &work[1], (ftnlen)1); + a[i__ + i__ * a_dim1] = aii; /* L10: */ } return 0; @@ -324,5 +324,5 @@ f"> */ } /* dorm2r_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dormbr.cpp b/lib/linalg/dormbr.cpp index e00ec3ecb0..69283d95ef 100644 --- a/lib/linalg/dormbr.cpp +++ b/lib/linalg/dormbr.cpp @@ -1,13 +1,13 @@ /* fortran/dormbr.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -216,10 +216,10 @@ f"> */ /* > \ingroup doubleOTHERcomputational */ /* ===================================================================== */ -/* Subroutine */ int dormbr_(char *vect, char *side, char *trans, integer *m, - integer *n, integer *k, doublereal *a, integer *lda, doublereal *tau, - doublereal *c__, integer *ldc, doublereal *work, integer *lwork, - integer *info, ftnlen vect_len, ftnlen side_len, ftnlen trans_len) +/* Subroutine */ int dormbr_(char *vect, char *side, char *trans, integer *m, + integer *n, integer *k, doublereal *a, integer *lda, doublereal *tau, + doublereal *c__, integer *ldc, doublereal *work, integer *lwork, + integer *info, ftnlen vect_len, ftnlen side_len, ftnlen trans_len) { /* System generated locals */ address a__1[2]; @@ -235,15 +235,15 @@ f"> */ extern logical lsame_(char *, char *, ftnlen, ftnlen); integer iinfo; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - extern /* Subroutine */ int dormlq_(char *, char *, integer *, integer *, - integer *, doublereal *, integer *, doublereal *, doublereal *, - integer *, doublereal *, integer *, integer *, ftnlen, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dormlq_(char *, char *, integer *, integer *, + integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, integer *, ftnlen, ftnlen); logical notran; - extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *, - integer *, doublereal *, integer *, doublereal *, doublereal *, - integer *, doublereal *, integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *, + integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, integer *, ftnlen, ftnlen); logical applyq; char transt[1]; integer lwkopt; @@ -293,164 +293,164 @@ f"> */ /* NQ is the order of Q or P and NW is the minimum dimension of WORK */ if (left) { - nq = *m; - nw = max(1,*n); + nq = *m; + nw = max(1,*n); } else { - nq = *n; - nw = max(1,*m); + nq = *n; + nw = max(1,*m); } if (! applyq && ! lsame_(vect, (char *)"P", (ftnlen)1, (ftnlen)1)) { - *info = -1; + *info = -1; } else if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { - *info = -2; + *info = -2; } else if (! notran && ! lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1)) { - *info = -3; + *info = -3; } else if (*m < 0) { - *info = -4; + *info = -4; } else if (*n < 0) { - *info = -5; + *info = -5; } else if (*k < 0) { - *info = -6; + *info = -6; } else /* if(complicated condition) */ { /* Computing MAX */ - i__1 = 1, i__2 = min(nq,*k); - if (applyq && *lda < max(1,nq) || ! applyq && *lda < max(i__1,i__2)) { - *info = -8; - } else if (*ldc < max(1,*m)) { - *info = -11; - } else if (*lwork < nw && ! lquery) { - *info = -13; - } + i__1 = 1, i__2 = min(nq,*k); + if (applyq && *lda < max(1,nq) || ! applyq && *lda < max(i__1,i__2)) { + *info = -8; + } else if (*ldc < max(1,*m)) { + *info = -11; + } else if (*lwork < nw && ! lquery) { + *info = -13; + } } if (*info == 0) { - if (applyq) { - if (left) { + if (applyq) { + if (left) { /* Writing concatenation */ - i__3[0] = 1, a__1[0] = side; - i__3[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); - i__1 = *m - 1; - i__2 = *m - 1; - nb = ilaenv_(&c__1, (char *)"DORMQR", ch__1, &i__1, n, &i__2, &c_n1, ( - ftnlen)6, (ftnlen)2); - } else { + i__3[0] = 1, a__1[0] = side; + i__3[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + i__1 = *m - 1; + i__2 = *m - 1; + nb = ilaenv_(&c__1, (char *)"DORMQR", ch__1, &i__1, n, &i__2, &c_n1, ( + ftnlen)6, (ftnlen)2); + } else { /* Writing concatenation */ - i__3[0] = 1, a__1[0] = side; - i__3[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); - i__1 = *n - 1; - i__2 = *n - 1; - nb = ilaenv_(&c__1, (char *)"DORMQR", ch__1, m, &i__1, &i__2, &c_n1, ( - ftnlen)6, (ftnlen)2); - } - } else { - if (left) { + i__3[0] = 1, a__1[0] = side; + i__3[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + i__1 = *n - 1; + i__2 = *n - 1; + nb = ilaenv_(&c__1, (char *)"DORMQR", ch__1, m, &i__1, &i__2, &c_n1, ( + ftnlen)6, (ftnlen)2); + } + } else { + if (left) { /* Writing concatenation */ - i__3[0] = 1, a__1[0] = side; - i__3[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); - i__1 = *m - 1; - i__2 = *m - 1; - nb = ilaenv_(&c__1, (char *)"DORMLQ", ch__1, &i__1, n, &i__2, &c_n1, ( - ftnlen)6, (ftnlen)2); - } else { + i__3[0] = 1, a__1[0] = side; + i__3[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + i__1 = *m - 1; + i__2 = *m - 1; + nb = ilaenv_(&c__1, (char *)"DORMLQ", ch__1, &i__1, n, &i__2, &c_n1, ( + ftnlen)6, (ftnlen)2); + } else { /* Writing concatenation */ - i__3[0] = 1, a__1[0] = side; - i__3[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); - i__1 = *n - 1; - i__2 = *n - 1; - nb = ilaenv_(&c__1, (char *)"DORMLQ", ch__1, m, &i__1, &i__2, &c_n1, ( - ftnlen)6, (ftnlen)2); - } - } - lwkopt = nw * nb; - work[1] = (doublereal) lwkopt; + i__3[0] = 1, a__1[0] = side; + i__3[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + i__1 = *n - 1; + i__2 = *n - 1; + nb = ilaenv_(&c__1, (char *)"DORMLQ", ch__1, m, &i__1, &i__2, &c_n1, ( + ftnlen)6, (ftnlen)2); + } + } + lwkopt = nw * nb; + work[1] = (doublereal) lwkopt; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DORMBR", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DORMBR", &i__1, (ftnlen)6); + return 0; } else if (lquery) { - return 0; + return 0; } /* Quick return if possible */ work[1] = 1.; if (*m == 0 || *n == 0) { - return 0; + return 0; } if (applyq) { /* Apply Q */ - if (nq >= *k) { + if (nq >= *k) { /* Q was determined by a call to DGEBRD with nq >= k */ - dormqr_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[ - c_offset], ldc, &work[1], lwork, &iinfo, (ftnlen)1, ( - ftnlen)1); - } else if (nq > 1) { + dormqr_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[ + c_offset], ldc, &work[1], lwork, &iinfo, (ftnlen)1, ( + ftnlen)1); + } else if (nq > 1) { /* Q was determined by a call to DGEBRD with nq < k */ - if (left) { - mi = *m - 1; - ni = *n; - i1 = 2; - i2 = 1; - } else { - mi = *m; - ni = *n - 1; - i1 = 1; - i2 = 2; - } - i__1 = nq - 1; - dormqr_(side, trans, &mi, &ni, &i__1, &a[a_dim1 + 2], lda, &tau[1] - , &c__[i1 + i2 * c_dim1], ldc, &work[1], lwork, &iinfo, ( - ftnlen)1, (ftnlen)1); - } + if (left) { + mi = *m - 1; + ni = *n; + i1 = 2; + i2 = 1; + } else { + mi = *m; + ni = *n - 1; + i1 = 1; + i2 = 2; + } + i__1 = nq - 1; + dormqr_(side, trans, &mi, &ni, &i__1, &a[a_dim1 + 2], lda, &tau[1] + , &c__[i1 + i2 * c_dim1], ldc, &work[1], lwork, &iinfo, ( + ftnlen)1, (ftnlen)1); + } } else { /* Apply P */ - if (notran) { - *(unsigned char *)transt = 'T'; - } else { - *(unsigned char *)transt = 'N'; - } - if (nq > *k) { + if (notran) { + *(unsigned char *)transt = 'T'; + } else { + *(unsigned char *)transt = 'N'; + } + if (nq > *k) { /* P was determined by a call to DGEBRD with nq > k */ - dormlq_(side, transt, m, n, k, &a[a_offset], lda, &tau[1], &c__[ - c_offset], ldc, &work[1], lwork, &iinfo, (ftnlen)1, ( - ftnlen)1); - } else if (nq > 1) { + dormlq_(side, transt, m, n, k, &a[a_offset], lda, &tau[1], &c__[ + c_offset], ldc, &work[1], lwork, &iinfo, (ftnlen)1, ( + ftnlen)1); + } else if (nq > 1) { /* P was determined by a call to DGEBRD with nq <= k */ - if (left) { - mi = *m - 1; - ni = *n; - i1 = 2; - i2 = 1; - } else { - mi = *m; - ni = *n - 1; - i1 = 1; - i2 = 2; - } - i__1 = nq - 1; - dormlq_(side, transt, &mi, &ni, &i__1, &a[(a_dim1 << 1) + 1], lda, - &tau[1], &c__[i1 + i2 * c_dim1], ldc, &work[1], lwork, & - iinfo, (ftnlen)1, (ftnlen)1); - } + if (left) { + mi = *m - 1; + ni = *n; + i1 = 2; + i2 = 1; + } else { + mi = *m; + ni = *n - 1; + i1 = 1; + i2 = 2; + } + i__1 = nq - 1; + dormlq_(side, transt, &mi, &ni, &i__1, &a[(a_dim1 << 1) + 1], lda, + &tau[1], &c__[i1 + i2 * c_dim1], ldc, &work[1], lwork, & + iinfo, (ftnlen)1, (ftnlen)1); + } } work[1] = (doublereal) lwkopt; return 0; @@ -460,5 +460,5 @@ f"> */ } /* dormbr_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dorml2.cpp b/lib/linalg/dorml2.cpp index 9085a5a0ce..7fe1aac941 100644 --- a/lib/linalg/dorml2.cpp +++ b/lib/linalg/dorml2.cpp @@ -1,13 +1,13 @@ /* fortran/dorml2.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -15,7 +15,7 @@ extern "C" { #endif #include "lmp_f2c.h" -/* > \brief \b DORML2 multiplies a general matrix by the orthogonal matrix from a LQ factorization determined +/* > \brief \b DORML2 multiplies a general matrix by the orthogonal matrix from a LQ factorization determined by sgelqf (unblocked algorithm). */ /* =========== DOCUMENTATION =========== */ @@ -175,10 +175,10 @@ f"> */ /* > \ingroup doubleOTHERcomputational */ /* ===================================================================== */ -/* Subroutine */ int dorml2_(char *side, char *trans, integer *m, integer *n, - integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal * - c__, integer *ldc, doublereal *work, integer *info, ftnlen side_len, - ftnlen trans_len) +/* Subroutine */ int dorml2_(char *side, char *trans, integer *m, integer *n, + integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal * + c__, integer *ldc, doublereal *work, integer *info, ftnlen side_len, + ftnlen trans_len) { /* System generated locals */ integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2; @@ -187,9 +187,9 @@ f"> */ integer i__, i1, i2, i3, ic, jc, mi, ni, nq; doublereal aii; logical left; - extern /* Subroutine */ int dlarf_(char *, integer *, integer *, - doublereal *, integer *, doublereal *, doublereal *, integer *, - doublereal *, ftnlen); + extern /* Subroutine */ int dlarf_(char *, integer *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, + doublereal *, ftnlen); extern logical lsame_(char *, char *, ftnlen, ftnlen); extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); logical notran; @@ -238,79 +238,79 @@ f"> */ /* NQ is the order of Q */ if (left) { - nq = *m; + nq = *m; } else { - nq = *n; + nq = *n; } if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { - *info = -1; + *info = -1; } else if (! notran && ! lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1)) { - *info = -2; + *info = -2; } else if (*m < 0) { - *info = -3; + *info = -3; } else if (*n < 0) { - *info = -4; + *info = -4; } else if (*k < 0 || *k > nq) { - *info = -5; + *info = -5; } else if (*lda < max(1,*k)) { - *info = -7; + *info = -7; } else if (*ldc < max(1,*m)) { - *info = -10; + *info = -10; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DORML2", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DORML2", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*m == 0 || *n == 0 || *k == 0) { - return 0; + return 0; } if (left && notran || ! left && ! notran) { - i1 = 1; - i2 = *k; - i3 = 1; + i1 = 1; + i2 = *k; + i3 = 1; } else { - i1 = *k; - i2 = 1; - i3 = -1; + i1 = *k; + i2 = 1; + i3 = -1; } if (left) { - ni = *n; - jc = 1; + ni = *n; + jc = 1; } else { - mi = *m; - ic = 1; + mi = *m; + ic = 1; } i__1 = i2; i__2 = i3; for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { - if (left) { + if (left) { /* H(i) is applied to C(i:m,1:n) */ - mi = *m - i__ + 1; - ic = i__; - } else { + mi = *m - i__ + 1; + ic = i__; + } else { /* H(i) is applied to C(1:m,i:n) */ - ni = *n - i__ + 1; - jc = i__; - } + ni = *n - i__ + 1; + jc = i__; + } /* Apply H(i) */ - aii = a[i__ + i__ * a_dim1]; - a[i__ + i__ * a_dim1] = 1.; - dlarf_(side, &mi, &ni, &a[i__ + i__ * a_dim1], lda, &tau[i__], &c__[ - ic + jc * c_dim1], ldc, &work[1], (ftnlen)1); - a[i__ + i__ * a_dim1] = aii; + aii = a[i__ + i__ * a_dim1]; + a[i__ + i__ * a_dim1] = 1.; + dlarf_(side, &mi, &ni, &a[i__ + i__ * a_dim1], lda, &tau[i__], &c__[ + ic + jc * c_dim1], ldc, &work[1], (ftnlen)1); + a[i__ + i__ * a_dim1] = aii; /* L10: */ } return 0; @@ -320,5 +320,5 @@ f"> */ } /* dorml2_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dormlq.cpp b/lib/linalg/dormlq.cpp index e5ed90a9fa..bb14bbfc98 100644 --- a/lib/linalg/dormlq.cpp +++ b/lib/linalg/dormlq.cpp @@ -1,13 +1,13 @@ /* fortran/dormlq.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -189,15 +189,15 @@ f"> */ /* > \ingroup doubleOTHERcomputational */ /* ===================================================================== */ -/* Subroutine */ int dormlq_(char *side, char *trans, integer *m, integer *n, - integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal * - c__, integer *ldc, doublereal *work, integer *lwork, integer *info, - ftnlen side_len, ftnlen trans_len) +/* Subroutine */ int dormlq_(char *side, char *trans, integer *m, integer *n, + integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal * + c__, integer *ldc, doublereal *work, integer *lwork, integer *info, + ftnlen side_len, ftnlen trans_len) { /* System generated locals */ address a__1[2]; - integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4, - i__5; + integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4, + i__5; char ch__1[2]; /* Builtin functions */ @@ -208,17 +208,17 @@ f"> */ logical left; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer nbmin, iinfo; - extern /* Subroutine */ int dorml2_(char *, char *, integer *, integer *, - integer *, doublereal *, integer *, doublereal *, doublereal *, - integer *, doublereal *, integer *, ftnlen, ftnlen), dlarfb_(char - *, char *, char *, char *, integer *, integer *, integer *, - doublereal *, integer *, doublereal *, integer *, doublereal *, - integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, - ftnlen), dlarft_(char *, char *, integer *, integer *, doublereal - *, integer *, doublereal *, doublereal *, integer *, ftnlen, - ftnlen), xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dorml2_(char *, char *, integer *, integer *, + integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, ftnlen, ftnlen), dlarfb_(char + *, char *, char *, char *, integer *, integer *, integer *, + doublereal *, integer *, doublereal *, integer *, doublereal *, + integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, + ftnlen), dlarft_(char *, char *, integer *, integer *, doublereal + *, integer *, doublereal *, doublereal *, integer *, ftnlen, + ftnlen), xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); logical notran; integer ldwork; char transt[1]; @@ -270,28 +270,28 @@ f"> */ /* NQ is the order of Q and NW is the minimum dimension of WORK */ if (left) { - nq = *m; - nw = max(1,*n); + nq = *m; + nw = max(1,*n); } else { - nq = *n; - nw = max(1,*m); + nq = *n; + nw = max(1,*m); } if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { - *info = -1; + *info = -1; } else if (! notran && ! lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1)) { - *info = -2; + *info = -2; } else if (*m < 0) { - *info = -3; + *info = -3; } else if (*n < 0) { - *info = -4; + *info = -4; } else if (*k < 0 || *k > nq) { - *info = -5; + *info = -5; } else if (*lda < max(1,*k)) { - *info = -7; + *info = -7; } else if (*ldc < max(1,*m)) { - *info = -10; + *info = -10; } else if (*lwork < nw && ! lquery) { - *info = -12; + *info = -12; } if (*info == 0) { @@ -300,117 +300,117 @@ f"> */ /* Computing MIN */ /* Writing concatenation */ - i__3[0] = 1, a__1[0] = side; - i__3[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); - i__1 = 64, i__2 = ilaenv_(&c__1, (char *)"DORMLQ", ch__1, m, n, k, &c_n1, ( - ftnlen)6, (ftnlen)2); - nb = min(i__1,i__2); - lwkopt = nw * nb + 4160; - work[1] = (doublereal) lwkopt; + i__3[0] = 1, a__1[0] = side; + i__3[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + i__1 = 64, i__2 = ilaenv_(&c__1, (char *)"DORMLQ", ch__1, m, n, k, &c_n1, ( + ftnlen)6, (ftnlen)2); + nb = min(i__1,i__2); + lwkopt = nw * nb + 4160; + work[1] = (doublereal) lwkopt; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DORMLQ", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DORMLQ", &i__1, (ftnlen)6); + return 0; } else if (lquery) { - return 0; + return 0; } /* Quick return if possible */ if (*m == 0 || *n == 0 || *k == 0) { - work[1] = 1.; - return 0; + work[1] = 1.; + return 0; } nbmin = 2; ldwork = nw; if (nb > 1 && nb < *k) { - if (*lwork < lwkopt) { - nb = (*lwork - 4160) / ldwork; + if (*lwork < lwkopt) { + nb = (*lwork - 4160) / ldwork; /* Computing MAX */ /* Writing concatenation */ - i__3[0] = 1, a__1[0] = side; - i__3[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); - i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DORMLQ", ch__1, m, n, k, &c_n1, ( - ftnlen)6, (ftnlen)2); - nbmin = max(i__1,i__2); - } + i__3[0] = 1, a__1[0] = side; + i__3[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DORMLQ", ch__1, m, n, k, &c_n1, ( + ftnlen)6, (ftnlen)2); + nbmin = max(i__1,i__2); + } } if (nb < nbmin || nb >= *k) { /* Use unblocked code */ - dorml2_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[ - c_offset], ldc, &work[1], &iinfo, (ftnlen)1, (ftnlen)1); + dorml2_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[ + c_offset], ldc, &work[1], &iinfo, (ftnlen)1, (ftnlen)1); } else { /* Use blocked code */ - iwt = nw * nb + 1; - if (left && notran || ! left && ! notran) { - i1 = 1; - i2 = *k; - i3 = nb; - } else { - i1 = (*k - 1) / nb * nb + 1; - i2 = 1; - i3 = -nb; - } + iwt = nw * nb + 1; + if (left && notran || ! left && ! notran) { + i1 = 1; + i2 = *k; + i3 = nb; + } else { + i1 = (*k - 1) / nb * nb + 1; + i2 = 1; + i3 = -nb; + } - if (left) { - ni = *n; - jc = 1; - } else { - mi = *m; - ic = 1; - } + if (left) { + ni = *n; + jc = 1; + } else { + mi = *m; + ic = 1; + } - if (notran) { - *(unsigned char *)transt = 'T'; - } else { - *(unsigned char *)transt = 'N'; - } + if (notran) { + *(unsigned char *)transt = 'T'; + } else { + *(unsigned char *)transt = 'N'; + } - i__1 = i2; - i__2 = i3; - for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { + i__1 = i2; + i__2 = i3; + for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { /* Computing MIN */ - i__4 = nb, i__5 = *k - i__ + 1; - ib = min(i__4,i__5); + i__4 = nb, i__5 = *k - i__ + 1; + ib = min(i__4,i__5); /* Form the triangular factor of the block reflector */ /* H = H(i) H(i+1) . . . H(i+ib-1) */ - i__4 = nq - i__ + 1; - dlarft_((char *)"Forward", (char *)"Rowwise", &i__4, &ib, &a[i__ + i__ * a_dim1], - lda, &tau[i__], &work[iwt], &c__65, (ftnlen)7, (ftnlen)7); - if (left) { + i__4 = nq - i__ + 1; + dlarft_((char *)"Forward", (char *)"Rowwise", &i__4, &ib, &a[i__ + i__ * a_dim1], + lda, &tau[i__], &work[iwt], &c__65, (ftnlen)7, (ftnlen)7); + if (left) { /* H or H**T is applied to C(i:m,1:n) */ - mi = *m - i__ + 1; - ic = i__; - } else { + mi = *m - i__ + 1; + ic = i__; + } else { /* H or H**T is applied to C(1:m,i:n) */ - ni = *n - i__ + 1; - jc = i__; - } + ni = *n - i__ + 1; + jc = i__; + } /* Apply H or H**T */ - dlarfb_(side, transt, (char *)"Forward", (char *)"Rowwise", &mi, &ni, &ib, &a[i__ - + i__ * a_dim1], lda, &work[iwt], &c__65, &c__[ic + jc * - c_dim1], ldc, &work[1], &ldwork, (ftnlen)1, (ftnlen)1, ( - ftnlen)7, (ftnlen)7); + dlarfb_(side, transt, (char *)"Forward", (char *)"Rowwise", &mi, &ni, &ib, &a[i__ + + i__ * a_dim1], lda, &work[iwt], &c__65, &c__[ic + jc * + c_dim1], ldc, &work[1], &ldwork, (ftnlen)1, (ftnlen)1, ( + ftnlen)7, (ftnlen)7); /* L10: */ - } + } } work[1] = (doublereal) lwkopt; return 0; @@ -420,5 +420,5 @@ f"> */ } /* dormlq_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dormql.cpp b/lib/linalg/dormql.cpp index 735f9e3d2b..70694ed5f9 100644 --- a/lib/linalg/dormql.cpp +++ b/lib/linalg/dormql.cpp @@ -1,13 +1,13 @@ /* fortran/dormql.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -189,15 +189,15 @@ f"> */ /* > \ingroup doubleOTHERcomputational */ /* ===================================================================== */ -/* Subroutine */ int dormql_(char *side, char *trans, integer *m, integer *n, - integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal * - c__, integer *ldc, doublereal *work, integer *lwork, integer *info, - ftnlen side_len, ftnlen trans_len) +/* Subroutine */ int dormql_(char *side, char *trans, integer *m, integer *n, + integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal * + c__, integer *ldc, doublereal *work, integer *lwork, integer *info, + ftnlen side_len, ftnlen trans_len) { /* System generated locals */ address a__1[2]; - integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4, - i__5; + integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4, + i__5; char ch__1[2]; /* Builtin functions */ @@ -208,17 +208,17 @@ f"> */ logical left; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer nbmin, iinfo; - extern /* Subroutine */ int dorm2l_(char *, char *, integer *, integer *, - integer *, doublereal *, integer *, doublereal *, doublereal *, - integer *, doublereal *, integer *, ftnlen, ftnlen), dlarfb_(char - *, char *, char *, char *, integer *, integer *, integer *, - doublereal *, integer *, doublereal *, integer *, doublereal *, - integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, - ftnlen), dlarft_(char *, char *, integer *, integer *, doublereal - *, integer *, doublereal *, doublereal *, integer *, ftnlen, - ftnlen), xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dorm2l_(char *, char *, integer *, integer *, + integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, ftnlen, ftnlen), dlarfb_(char + *, char *, char *, char *, integer *, integer *, integer *, + doublereal *, integer *, doublereal *, integer *, doublereal *, + integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, + ftnlen), dlarft_(char *, char *, integer *, integer *, doublereal + *, integer *, doublereal *, doublereal *, integer *, ftnlen, + ftnlen), xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); logical notran; integer ldwork, lwkopt; logical lquery; @@ -268,141 +268,141 @@ f"> */ /* NQ is the order of Q and NW is the minimum dimension of WORK */ if (left) { - nq = *m; - nw = max(1,*n); + nq = *m; + nw = max(1,*n); } else { - nq = *n; - nw = max(1,*m); + nq = *n; + nw = max(1,*m); } if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { - *info = -1; + *info = -1; } else if (! notran && ! lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1)) { - *info = -2; + *info = -2; } else if (*m < 0) { - *info = -3; + *info = -3; } else if (*n < 0) { - *info = -4; + *info = -4; } else if (*k < 0 || *k > nq) { - *info = -5; + *info = -5; } else if (*lda < max(1,nq)) { - *info = -7; + *info = -7; } else if (*ldc < max(1,*m)) { - *info = -10; + *info = -10; } else if (*lwork < nw && ! lquery) { - *info = -12; + *info = -12; } if (*info == 0) { /* Compute the workspace requirements */ - if (*m == 0 || *n == 0) { - lwkopt = 1; - } else { + if (*m == 0 || *n == 0) { + lwkopt = 1; + } else { /* Computing MIN */ /* Writing concatenation */ - i__3[0] = 1, a__1[0] = side; - i__3[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); - i__1 = 64, i__2 = ilaenv_(&c__1, (char *)"DORMQL", ch__1, m, n, k, &c_n1, - (ftnlen)6, (ftnlen)2); - nb = min(i__1,i__2); - lwkopt = nw * nb + 4160; - } - work[1] = (doublereal) lwkopt; + i__3[0] = 1, a__1[0] = side; + i__3[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + i__1 = 64, i__2 = ilaenv_(&c__1, (char *)"DORMQL", ch__1, m, n, k, &c_n1, + (ftnlen)6, (ftnlen)2); + nb = min(i__1,i__2); + lwkopt = nw * nb + 4160; + } + work[1] = (doublereal) lwkopt; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DORMQL", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DORMQL", &i__1, (ftnlen)6); + return 0; } else if (lquery) { - return 0; + return 0; } /* Quick return if possible */ if (*m == 0 || *n == 0) { - return 0; + return 0; } nbmin = 2; ldwork = nw; if (nb > 1 && nb < *k) { - if (*lwork < lwkopt) { - nb = (*lwork - 4160) / ldwork; + if (*lwork < lwkopt) { + nb = (*lwork - 4160) / ldwork; /* Computing MAX */ /* Writing concatenation */ - i__3[0] = 1, a__1[0] = side; - i__3[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); - i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DORMQL", ch__1, m, n, k, &c_n1, ( - ftnlen)6, (ftnlen)2); - nbmin = max(i__1,i__2); - } + i__3[0] = 1, a__1[0] = side; + i__3[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DORMQL", ch__1, m, n, k, &c_n1, ( + ftnlen)6, (ftnlen)2); + nbmin = max(i__1,i__2); + } } if (nb < nbmin || nb >= *k) { /* Use unblocked code */ - dorm2l_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[ - c_offset], ldc, &work[1], &iinfo, (ftnlen)1, (ftnlen)1); + dorm2l_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[ + c_offset], ldc, &work[1], &iinfo, (ftnlen)1, (ftnlen)1); } else { /* Use blocked code */ - iwt = nw * nb + 1; - if (left && notran || ! left && ! notran) { - i1 = 1; - i2 = *k; - i3 = nb; - } else { - i1 = (*k - 1) / nb * nb + 1; - i2 = 1; - i3 = -nb; - } + iwt = nw * nb + 1; + if (left && notran || ! left && ! notran) { + i1 = 1; + i2 = *k; + i3 = nb; + } else { + i1 = (*k - 1) / nb * nb + 1; + i2 = 1; + i3 = -nb; + } - if (left) { - ni = *n; - } else { - mi = *m; - } + if (left) { + ni = *n; + } else { + mi = *m; + } - i__1 = i2; - i__2 = i3; - for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { + i__1 = i2; + i__2 = i3; + for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { /* Computing MIN */ - i__4 = nb, i__5 = *k - i__ + 1; - ib = min(i__4,i__5); + i__4 = nb, i__5 = *k - i__ + 1; + ib = min(i__4,i__5); /* Form the triangular factor of the block reflector */ /* H = H(i+ib-1) . . . H(i+1) H(i) */ - i__4 = nq - *k + i__ + ib - 1; - dlarft_((char *)"Backward", (char *)"Columnwise", &i__4, &ib, &a[i__ * a_dim1 + 1] - , lda, &tau[i__], &work[iwt], &c__65, (ftnlen)8, (ftnlen) - 10); - if (left) { + i__4 = nq - *k + i__ + ib - 1; + dlarft_((char *)"Backward", (char *)"Columnwise", &i__4, &ib, &a[i__ * a_dim1 + 1] + , lda, &tau[i__], &work[iwt], &c__65, (ftnlen)8, (ftnlen) + 10); + if (left) { /* H or H**T is applied to C(1:m-k+i+ib-1,1:n) */ - mi = *m - *k + i__ + ib - 1; - } else { + mi = *m - *k + i__ + ib - 1; + } else { /* H or H**T is applied to C(1:m,1:n-k+i+ib-1) */ - ni = *n - *k + i__ + ib - 1; - } + ni = *n - *k + i__ + ib - 1; + } /* Apply H or H**T */ - dlarfb_(side, trans, (char *)"Backward", (char *)"Columnwise", &mi, &ni, &ib, &a[ - i__ * a_dim1 + 1], lda, &work[iwt], &c__65, &c__[c_offset] - , ldc, &work[1], &ldwork, (ftnlen)1, (ftnlen)1, (ftnlen)8, - (ftnlen)10); + dlarfb_(side, trans, (char *)"Backward", (char *)"Columnwise", &mi, &ni, &ib, &a[ + i__ * a_dim1 + 1], lda, &work[iwt], &c__65, &c__[c_offset] + , ldc, &work[1], &ldwork, (ftnlen)1, (ftnlen)1, (ftnlen)8, + (ftnlen)10); /* L10: */ - } + } } work[1] = (doublereal) lwkopt; return 0; @@ -412,5 +412,5 @@ f"> */ } /* dormql_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dormqr.cpp b/lib/linalg/dormqr.cpp index 7fce43b587..17aaab62ba 100644 --- a/lib/linalg/dormqr.cpp +++ b/lib/linalg/dormqr.cpp @@ -1,13 +1,13 @@ /* fortran/dormqr.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -189,15 +189,15 @@ f"> */ /* > \ingroup doubleOTHERcomputational */ /* ===================================================================== */ -/* Subroutine */ int dormqr_(char *side, char *trans, integer *m, integer *n, - integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal * - c__, integer *ldc, doublereal *work, integer *lwork, integer *info, - ftnlen side_len, ftnlen trans_len) +/* Subroutine */ int dormqr_(char *side, char *trans, integer *m, integer *n, + integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal * + c__, integer *ldc, doublereal *work, integer *lwork, integer *info, + ftnlen side_len, ftnlen trans_len) { /* System generated locals */ address a__1[2]; - integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4, - i__5; + integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4, + i__5; char ch__1[2]; /* Builtin functions */ @@ -208,17 +208,17 @@ f"> */ logical left; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer nbmin, iinfo; - extern /* Subroutine */ int dorm2r_(char *, char *, integer *, integer *, - integer *, doublereal *, integer *, doublereal *, doublereal *, - integer *, doublereal *, integer *, ftnlen, ftnlen), dlarfb_(char - *, char *, char *, char *, integer *, integer *, integer *, - doublereal *, integer *, doublereal *, integer *, doublereal *, - integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, - ftnlen), dlarft_(char *, char *, integer *, integer *, doublereal - *, integer *, doublereal *, doublereal *, integer *, ftnlen, - ftnlen), xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dorm2r_(char *, char *, integer *, integer *, + integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, ftnlen, ftnlen), dlarfb_(char + *, char *, char *, char *, integer *, integer *, integer *, + doublereal *, integer *, doublereal *, integer *, doublereal *, + integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, + ftnlen), dlarft_(char *, char *, integer *, integer *, doublereal + *, integer *, doublereal *, doublereal *, integer *, ftnlen, + ftnlen), xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); logical notran; integer ldwork, lwkopt; logical lquery; @@ -268,28 +268,28 @@ f"> */ /* NQ is the order of Q and NW is the minimum dimension of WORK */ if (left) { - nq = *m; - nw = max(1,*n); + nq = *m; + nw = max(1,*n); } else { - nq = *n; - nw = max(1,*m); + nq = *n; + nw = max(1,*m); } if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { - *info = -1; + *info = -1; } else if (! notran && ! lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1)) { - *info = -2; + *info = -2; } else if (*m < 0) { - *info = -3; + *info = -3; } else if (*n < 0) { - *info = -4; + *info = -4; } else if (*k < 0 || *k > nq) { - *info = -5; + *info = -5; } else if (*lda < max(1,nq)) { - *info = -7; + *info = -7; } else if (*ldc < max(1,*m)) { - *info = -10; + *info = -10; } else if (*lwork < nw && ! lquery) { - *info = -12; + *info = -12; } if (*info == 0) { @@ -298,112 +298,112 @@ f"> */ /* Computing MIN */ /* Writing concatenation */ - i__3[0] = 1, a__1[0] = side; - i__3[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); - i__1 = 64, i__2 = ilaenv_(&c__1, (char *)"DORMQR", ch__1, m, n, k, &c_n1, ( - ftnlen)6, (ftnlen)2); - nb = min(i__1,i__2); - lwkopt = nw * nb + 4160; - work[1] = (doublereal) lwkopt; + i__3[0] = 1, a__1[0] = side; + i__3[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + i__1 = 64, i__2 = ilaenv_(&c__1, (char *)"DORMQR", ch__1, m, n, k, &c_n1, ( + ftnlen)6, (ftnlen)2); + nb = min(i__1,i__2); + lwkopt = nw * nb + 4160; + work[1] = (doublereal) lwkopt; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DORMQR", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DORMQR", &i__1, (ftnlen)6); + return 0; } else if (lquery) { - return 0; + return 0; } /* Quick return if possible */ if (*m == 0 || *n == 0 || *k == 0) { - work[1] = 1.; - return 0; + work[1] = 1.; + return 0; } nbmin = 2; ldwork = nw; if (nb > 1 && nb < *k) { - if (*lwork < lwkopt) { - nb = (*lwork - 4160) / ldwork; + if (*lwork < lwkopt) { + nb = (*lwork - 4160) / ldwork; /* Computing MAX */ /* Writing concatenation */ - i__3[0] = 1, a__1[0] = side; - i__3[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); - i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DORMQR", ch__1, m, n, k, &c_n1, ( - ftnlen)6, (ftnlen)2); - nbmin = max(i__1,i__2); - } + i__3[0] = 1, a__1[0] = side; + i__3[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DORMQR", ch__1, m, n, k, &c_n1, ( + ftnlen)6, (ftnlen)2); + nbmin = max(i__1,i__2); + } } if (nb < nbmin || nb >= *k) { /* Use unblocked code */ - dorm2r_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[ - c_offset], ldc, &work[1], &iinfo, (ftnlen)1, (ftnlen)1); + dorm2r_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[ + c_offset], ldc, &work[1], &iinfo, (ftnlen)1, (ftnlen)1); } else { /* Use blocked code */ - iwt = nw * nb + 1; - if (left && ! notran || ! left && notran) { - i1 = 1; - i2 = *k; - i3 = nb; - } else { - i1 = (*k - 1) / nb * nb + 1; - i2 = 1; - i3 = -nb; - } + iwt = nw * nb + 1; + if (left && ! notran || ! left && notran) { + i1 = 1; + i2 = *k; + i3 = nb; + } else { + i1 = (*k - 1) / nb * nb + 1; + i2 = 1; + i3 = -nb; + } - if (left) { - ni = *n; - jc = 1; - } else { - mi = *m; - ic = 1; - } + if (left) { + ni = *n; + jc = 1; + } else { + mi = *m; + ic = 1; + } - i__1 = i2; - i__2 = i3; - for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { + i__1 = i2; + i__2 = i3; + for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { /* Computing MIN */ - i__4 = nb, i__5 = *k - i__ + 1; - ib = min(i__4,i__5); + i__4 = nb, i__5 = *k - i__ + 1; + ib = min(i__4,i__5); /* Form the triangular factor of the block reflector */ /* H = H(i) H(i+1) . . . H(i+ib-1) */ - i__4 = nq - i__ + 1; - dlarft_((char *)"Forward", (char *)"Columnwise", &i__4, &ib, &a[i__ + i__ * - a_dim1], lda, &tau[i__], &work[iwt], &c__65, (ftnlen)7, ( - ftnlen)10); - if (left) { + i__4 = nq - i__ + 1; + dlarft_((char *)"Forward", (char *)"Columnwise", &i__4, &ib, &a[i__ + i__ * + a_dim1], lda, &tau[i__], &work[iwt], &c__65, (ftnlen)7, ( + ftnlen)10); + if (left) { /* H or H**T is applied to C(i:m,1:n) */ - mi = *m - i__ + 1; - ic = i__; - } else { + mi = *m - i__ + 1; + ic = i__; + } else { /* H or H**T is applied to C(1:m,i:n) */ - ni = *n - i__ + 1; - jc = i__; - } + ni = *n - i__ + 1; + jc = i__; + } /* Apply H or H**T */ - dlarfb_(side, trans, (char *)"Forward", (char *)"Columnwise", &mi, &ni, &ib, &a[ - i__ + i__ * a_dim1], lda, &work[iwt], &c__65, &c__[ic + - jc * c_dim1], ldc, &work[1], &ldwork, (ftnlen)1, (ftnlen) - 1, (ftnlen)7, (ftnlen)10); + dlarfb_(side, trans, (char *)"Forward", (char *)"Columnwise", &mi, &ni, &ib, &a[ + i__ + i__ * a_dim1], lda, &work[iwt], &c__65, &c__[ic + + jc * c_dim1], ldc, &work[1], &ldwork, (ftnlen)1, (ftnlen) + 1, (ftnlen)7, (ftnlen)10); /* L10: */ - } + } } work[1] = (doublereal) lwkopt; return 0; @@ -413,5 +413,5 @@ f"> */ } /* dormqr_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dormtr.cpp b/lib/linalg/dormtr.cpp index d917e95b06..a55ee5efbe 100644 --- a/lib/linalg/dormtr.cpp +++ b/lib/linalg/dormtr.cpp @@ -1,13 +1,13 @@ /* fortran/dormtr.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -192,10 +192,10 @@ f"> */ /* > \ingroup doubleOTHERcomputational */ /* ===================================================================== */ -/* Subroutine */ int dormtr_(char *side, char *uplo, char *trans, integer *m, - integer *n, doublereal *a, integer *lda, doublereal *tau, doublereal * - c__, integer *ldc, doublereal *work, integer *lwork, integer *info, - ftnlen side_len, ftnlen uplo_len, ftnlen trans_len) +/* Subroutine */ int dormtr_(char *side, char *uplo, char *trans, integer *m, + integer *n, doublereal *a, integer *lda, doublereal *tau, doublereal * + c__, integer *ldc, doublereal *work, integer *lwork, integer *info, + ftnlen side_len, ftnlen uplo_len, ftnlen trans_len) { /* System generated locals */ address a__1[2]; @@ -212,14 +212,14 @@ f"> */ integer iinfo; logical upper; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - extern /* Subroutine */ int dormql_(char *, char *, integer *, integer *, - integer *, doublereal *, integer *, doublereal *, doublereal *, - integer *, doublereal *, integer *, integer *, ftnlen, ftnlen), - dormqr_(char *, char *, integer *, integer *, integer *, - doublereal *, integer *, doublereal *, doublereal *, integer *, - doublereal *, integer *, integer *, ftnlen, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dormql_(char *, char *, integer *, integer *, + integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, integer *, ftnlen, ftnlen), + dormqr_(char *, char *, integer *, integer *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, integer *, ftnlen, ftnlen); integer lwkopt; logical lquery; @@ -266,123 +266,123 @@ f"> */ /* NQ is the order of Q and NW is the minimum dimension of WORK */ if (left) { - nq = *m; - nw = max(1,*n); + nq = *m; + nw = max(1,*n); } else { - nq = *n; - nw = max(1,*m); + nq = *n; + nw = max(1,*m); } if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { - *info = -1; + *info = -1; } else if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { - *info = -2; - } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, - (char *)"T", (ftnlen)1, (ftnlen)1)) { - *info = -3; + *info = -2; + } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, + (char *)"T", (ftnlen)1, (ftnlen)1)) { + *info = -3; } else if (*m < 0) { - *info = -4; + *info = -4; } else if (*n < 0) { - *info = -5; + *info = -5; } else if (*lda < max(1,nq)) { - *info = -7; + *info = -7; } else if (*ldc < max(1,*m)) { - *info = -10; + *info = -10; } else if (*lwork < nw && ! lquery) { - *info = -12; + *info = -12; } if (*info == 0) { - if (upper) { - if (left) { + if (upper) { + if (left) { /* Writing concatenation */ - i__1[0] = 1, a__1[0] = side; - i__1[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); - i__2 = *m - 1; - i__3 = *m - 1; - nb = ilaenv_(&c__1, (char *)"DORMQL", ch__1, &i__2, n, &i__3, &c_n1, ( - ftnlen)6, (ftnlen)2); - } else { + i__1[0] = 1, a__1[0] = side; + i__1[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); + i__2 = *m - 1; + i__3 = *m - 1; + nb = ilaenv_(&c__1, (char *)"DORMQL", ch__1, &i__2, n, &i__3, &c_n1, ( + ftnlen)6, (ftnlen)2); + } else { /* Writing concatenation */ - i__1[0] = 1, a__1[0] = side; - i__1[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); - i__2 = *n - 1; - i__3 = *n - 1; - nb = ilaenv_(&c__1, (char *)"DORMQL", ch__1, m, &i__2, &i__3, &c_n1, ( - ftnlen)6, (ftnlen)2); - } - } else { - if (left) { + i__1[0] = 1, a__1[0] = side; + i__1[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); + i__2 = *n - 1; + i__3 = *n - 1; + nb = ilaenv_(&c__1, (char *)"DORMQL", ch__1, m, &i__2, &i__3, &c_n1, ( + ftnlen)6, (ftnlen)2); + } + } else { + if (left) { /* Writing concatenation */ - i__1[0] = 1, a__1[0] = side; - i__1[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); - i__2 = *m - 1; - i__3 = *m - 1; - nb = ilaenv_(&c__1, (char *)"DORMQR", ch__1, &i__2, n, &i__3, &c_n1, ( - ftnlen)6, (ftnlen)2); - } else { + i__1[0] = 1, a__1[0] = side; + i__1[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); + i__2 = *m - 1; + i__3 = *m - 1; + nb = ilaenv_(&c__1, (char *)"DORMQR", ch__1, &i__2, n, &i__3, &c_n1, ( + ftnlen)6, (ftnlen)2); + } else { /* Writing concatenation */ - i__1[0] = 1, a__1[0] = side; - i__1[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); - i__2 = *n - 1; - i__3 = *n - 1; - nb = ilaenv_(&c__1, (char *)"DORMQR", ch__1, m, &i__2, &i__3, &c_n1, ( - ftnlen)6, (ftnlen)2); - } - } - lwkopt = nw * nb; - work[1] = (doublereal) lwkopt; + i__1[0] = 1, a__1[0] = side; + i__1[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); + i__2 = *n - 1; + i__3 = *n - 1; + nb = ilaenv_(&c__1, (char *)"DORMQR", ch__1, m, &i__2, &i__3, &c_n1, ( + ftnlen)6, (ftnlen)2); + } + } + lwkopt = nw * nb; + work[1] = (doublereal) lwkopt; } if (*info != 0) { - i__2 = -(*info); - xerbla_((char *)"DORMTR", &i__2, (ftnlen)6); - return 0; + i__2 = -(*info); + xerbla_((char *)"DORMTR", &i__2, (ftnlen)6); + return 0; } else if (lquery) { - return 0; + return 0; } /* Quick return if possible */ if (*m == 0 || *n == 0 || nq == 1) { - work[1] = 1.; - return 0; + work[1] = 1.; + return 0; } if (left) { - mi = *m - 1; - ni = *n; + mi = *m - 1; + ni = *n; } else { - mi = *m; - ni = *n - 1; + mi = *m; + ni = *n - 1; } if (upper) { /* Q was determined by a call to DSYTRD with UPLO = 'U' */ - i__2 = nq - 1; - dormql_(side, trans, &mi, &ni, &i__2, &a[(a_dim1 << 1) + 1], lda, & - tau[1], &c__[c_offset], ldc, &work[1], lwork, &iinfo, (ftnlen) - 1, (ftnlen)1); + i__2 = nq - 1; + dormql_(side, trans, &mi, &ni, &i__2, &a[(a_dim1 << 1) + 1], lda, & + tau[1], &c__[c_offset], ldc, &work[1], lwork, &iinfo, (ftnlen) + 1, (ftnlen)1); } else { /* Q was determined by a call to DSYTRD with UPLO = 'L' */ - if (left) { - i1 = 2; - i2 = 1; - } else { - i1 = 1; - i2 = 2; - } - i__2 = nq - 1; - dormqr_(side, trans, &mi, &ni, &i__2, &a[a_dim1 + 2], lda, &tau[1], & - c__[i1 + i2 * c_dim1], ldc, &work[1], lwork, &iinfo, (ftnlen) - 1, (ftnlen)1); + if (left) { + i1 = 2; + i2 = 1; + } else { + i1 = 1; + i2 = 2; + } + i__2 = nq - 1; + dormqr_(side, trans, &mi, &ni, &i__2, &a[a_dim1 + 2], lda, &tau[1], & + c__[i1 + i2 * c_dim1], ldc, &work[1], lwork, &iinfo, (ftnlen) + 1, (ftnlen)1); } work[1] = (doublereal) lwkopt; return 0; @@ -392,5 +392,5 @@ f"> */ } /* dormtr_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dposv.cpp b/lib/linalg/dposv.cpp index 6981ea843d..370c261bf0 100644 --- a/lib/linalg/dposv.cpp +++ b/lib/linalg/dposv.cpp @@ -1,13 +1,13 @@ /* fortran/dposv.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -146,9 +146,9 @@ extern "C" { /* > \ingroup doublePOsolve */ /* ===================================================================== */ -/* Subroutine */ int dposv_(char *uplo, integer *n, integer *nrhs, doublereal - *a, integer *lda, doublereal *b, integer *ldb, integer *info, ftnlen - uplo_len) +/* Subroutine */ int dposv_(char *uplo, integer *n, integer *nrhs, doublereal + *a, integer *lda, doublereal *b, integer *ldb, integer *info, ftnlen + uplo_len) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1; @@ -156,9 +156,9 @@ extern "C" { /* Local variables */ extern logical lsame_(char *, char *, ftnlen, ftnlen); extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), dpotrf_( - char *, integer *, doublereal *, integer *, integer *, ftnlen), - dpotrs_(char *, integer *, integer *, doublereal *, integer *, - doublereal *, integer *, integer *, ftnlen); + char *, integer *, doublereal *, integer *, integer *, ftnlen), + dpotrs_(char *, integer *, integer *, doublereal *, integer *, + doublereal *, integer *, integer *, ftnlen); /* -- LAPACK driver routine -- */ @@ -193,21 +193,21 @@ extern "C" { /* Function Body */ *info = 0; if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", ( - ftnlen)1, (ftnlen)1)) { - *info = -1; + ftnlen)1, (ftnlen)1)) { + *info = -1; } else if (*n < 0) { - *info = -2; + *info = -2; } else if (*nrhs < 0) { - *info = -3; + *info = -3; } else if (*lda < max(1,*n)) { - *info = -5; + *info = -5; } else if (*ldb < max(1,*n)) { - *info = -7; + *info = -7; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DPOSV ", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DPOSV ", &i__1, (ftnlen)6); + return 0; } /* Compute the Cholesky factorization A = U**T*U or A = L*L**T. */ @@ -217,8 +217,8 @@ extern "C" { /* Solve the system A*X = B, overwriting B with X. */ - dpotrs_(uplo, n, nrhs, &a[a_offset], lda, &b[b_offset], ldb, info, ( - ftnlen)1); + dpotrs_(uplo, n, nrhs, &a[a_offset], lda, &b[b_offset], ldb, info, ( + ftnlen)1); } return 0; @@ -228,5 +228,5 @@ extern "C" { } /* dposv_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dpotf2.cpp b/lib/linalg/dpotf2.cpp index e32a52c97c..987db22578 100644 --- a/lib/linalg/dpotf2.cpp +++ b/lib/linalg/dpotf2.cpp @@ -1,13 +1,13 @@ /* fortran/dpotf2.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -133,7 +133,7 @@ f"> */ /* ===================================================================== */ /* Subroutine */ int dpotf2_(char *uplo, integer *n, doublereal *a, integer * - lda, integer *info, ftnlen uplo_len) + lda, integer *info, ftnlen uplo_len) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; @@ -145,14 +145,14 @@ f"> */ /* Local variables */ integer j; doublereal ajj; - extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, - integer *); - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *); + extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, + integer *); + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *); extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int dgemv_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, doublereal *, integer *, - doublereal *, doublereal *, integer *, ftnlen); + extern /* Subroutine */ int dgemv_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, ftnlen); logical upper; extern logical disnan_(doublereal *); extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); @@ -192,90 +192,90 @@ f"> */ *info = 0; upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { - *info = -1; + *info = -1; } else if (*n < 0) { - *info = -2; + *info = -2; } else if (*lda < max(1,*n)) { - *info = -4; + *info = -4; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DPOTF2", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DPOTF2", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*n == 0) { - return 0; + return 0; } if (upper) { /* Compute the Cholesky factorization A = U**T *U. */ - i__1 = *n; - for (j = 1; j <= i__1; ++j) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { /* Compute U(J,J) and test for non-positive-definiteness. */ - i__2 = j - 1; - ajj = a[j + j * a_dim1] - ddot_(&i__2, &a[j * a_dim1 + 1], &c__1, - &a[j * a_dim1 + 1], &c__1); - if (ajj <= 0. || disnan_(&ajj)) { - a[j + j * a_dim1] = ajj; - goto L30; - } - ajj = sqrt(ajj); - a[j + j * a_dim1] = ajj; + i__2 = j - 1; + ajj = a[j + j * a_dim1] - ddot_(&i__2, &a[j * a_dim1 + 1], &c__1, + &a[j * a_dim1 + 1], &c__1); + if (ajj <= 0. || disnan_(&ajj)) { + a[j + j * a_dim1] = ajj; + goto L30; + } + ajj = sqrt(ajj); + a[j + j * a_dim1] = ajj; /* Compute elements J+1:N of row J. */ - if (j < *n) { - i__2 = j - 1; - i__3 = *n - j; - dgemv_((char *)"Transpose", &i__2, &i__3, &c_b10, &a[(j + 1) * a_dim1 - + 1], lda, &a[j * a_dim1 + 1], &c__1, &c_b12, &a[j + ( - j + 1) * a_dim1], lda, (ftnlen)9); - i__2 = *n - j; - d__1 = 1. / ajj; - dscal_(&i__2, &d__1, &a[j + (j + 1) * a_dim1], lda); - } + if (j < *n) { + i__2 = j - 1; + i__3 = *n - j; + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b10, &a[(j + 1) * a_dim1 + + 1], lda, &a[j * a_dim1 + 1], &c__1, &c_b12, &a[j + ( + j + 1) * a_dim1], lda, (ftnlen)9); + i__2 = *n - j; + d__1 = 1. / ajj; + dscal_(&i__2, &d__1, &a[j + (j + 1) * a_dim1], lda); + } /* L10: */ - } + } } else { /* Compute the Cholesky factorization A = L*L**T. */ - i__1 = *n; - for (j = 1; j <= i__1; ++j) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { /* Compute L(J,J) and test for non-positive-definiteness. */ - i__2 = j - 1; - ajj = a[j + j * a_dim1] - ddot_(&i__2, &a[j + a_dim1], lda, &a[j - + a_dim1], lda); - if (ajj <= 0. || disnan_(&ajj)) { - a[j + j * a_dim1] = ajj; - goto L30; - } - ajj = sqrt(ajj); - a[j + j * a_dim1] = ajj; + i__2 = j - 1; + ajj = a[j + j * a_dim1] - ddot_(&i__2, &a[j + a_dim1], lda, &a[j + + a_dim1], lda); + if (ajj <= 0. || disnan_(&ajj)) { + a[j + j * a_dim1] = ajj; + goto L30; + } + ajj = sqrt(ajj); + a[j + j * a_dim1] = ajj; /* Compute elements J+1:N of column J. */ - if (j < *n) { - i__2 = *n - j; - i__3 = j - 1; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b10, &a[j + 1 + - a_dim1], lda, &a[j + a_dim1], lda, &c_b12, &a[j + 1 + - j * a_dim1], &c__1, (ftnlen)12); - i__2 = *n - j; - d__1 = 1. / ajj; - dscal_(&i__2, &d__1, &a[j + 1 + j * a_dim1], &c__1); - } + if (j < *n) { + i__2 = *n - j; + i__3 = j - 1; + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b10, &a[j + 1 + + a_dim1], lda, &a[j + a_dim1], lda, &c_b12, &a[j + 1 + + j * a_dim1], &c__1, (ftnlen)12); + i__2 = *n - j; + d__1 = 1. / ajj; + dscal_(&i__2, &d__1, &a[j + 1 + j * a_dim1], &c__1); + } /* L20: */ - } + } } goto L40; @@ -290,5 +290,5 @@ L40: } /* dpotf2_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dpotrf.cpp b/lib/linalg/dpotrf.cpp index cd343efd77..6dc003ab93 100644 --- a/lib/linalg/dpotrf.cpp +++ b/lib/linalg/dpotrf.cpp @@ -1,13 +1,13 @@ /* fortran/dpotrf.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -131,28 +131,28 @@ f"> */ /* ===================================================================== */ /* Subroutine */ int dpotrf_(char *uplo, integer *n, doublereal *a, integer * - lda, integer *info, ftnlen uplo_len) + lda, integer *info, ftnlen uplo_len) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4; /* Local variables */ integer j, jb, nb; - extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, - integer *, integer *, doublereal *, doublereal *, integer *, - doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, + integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); logical upper; - extern /* Subroutine */ int dsyrk_(char *, char *, integer *, integer *, - doublereal *, doublereal *, integer *, doublereal *, doublereal *, - integer *, ftnlen, ftnlen), xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - extern /* Subroutine */ int dpotrf2_(char *, integer *, doublereal *, - integer *, integer *, ftnlen); + extern /* Subroutine */ int dsyrk_(char *, char *, integer *, integer *, + doublereal *, doublereal *, integer *, doublereal *, doublereal *, + integer *, ftnlen, ftnlen), xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dpotrf2_(char *, integer *, doublereal *, + integer *, integer *, ftnlen); /* -- LAPACK computational routine -- */ @@ -189,121 +189,121 @@ f"> */ *info = 0; upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { - *info = -1; + *info = -1; } else if (*n < 0) { - *info = -2; + *info = -2; } else if (*lda < max(1,*n)) { - *info = -4; + *info = -4; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DPOTRF", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DPOTRF", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*n == 0) { - return 0; + return 0; } /* Determine the block size for this environment. */ nb = ilaenv_(&c__1, (char *)"DPOTRF", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, ( - ftnlen)1); + ftnlen)1); if (nb <= 1 || nb >= *n) { /* Use unblocked code. */ - dpotrf2_(uplo, n, &a[a_offset], lda, info, (ftnlen)1); + dpotrf2_(uplo, n, &a[a_offset], lda, info, (ftnlen)1); } else { /* Use blocked code. */ - if (upper) { + if (upper) { /* Compute the Cholesky factorization A = U**T*U. */ - i__1 = *n; - i__2 = nb; - for (j = 1; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) { + i__1 = *n; + i__2 = nb; + for (j = 1; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) { /* Update and factorize the current diagonal block and test */ /* for non-positive-definiteness. */ /* Computing MIN */ - i__3 = nb, i__4 = *n - j + 1; - jb = min(i__3,i__4); - i__3 = j - 1; - dsyrk_((char *)"Upper", (char *)"Transpose", &jb, &i__3, &c_b13, &a[j * - a_dim1 + 1], lda, &c_b14, &a[j + j * a_dim1], lda, ( - ftnlen)5, (ftnlen)9); - dpotrf2_((char *)"Upper", &jb, &a[j + j * a_dim1], lda, info, (ftnlen) - 5); - if (*info != 0) { - goto L30; - } - if (j + jb <= *n) { + i__3 = nb, i__4 = *n - j + 1; + jb = min(i__3,i__4); + i__3 = j - 1; + dsyrk_((char *)"Upper", (char *)"Transpose", &jb, &i__3, &c_b13, &a[j * + a_dim1 + 1], lda, &c_b14, &a[j + j * a_dim1], lda, ( + ftnlen)5, (ftnlen)9); + dpotrf2_((char *)"Upper", &jb, &a[j + j * a_dim1], lda, info, (ftnlen) + 5); + if (*info != 0) { + goto L30; + } + if (j + jb <= *n) { /* Compute the current block row. */ - i__3 = *n - j - jb + 1; - i__4 = j - 1; - dgemm_((char *)"Transpose", (char *)"No transpose", &jb, &i__3, &i__4, & - c_b13, &a[j * a_dim1 + 1], lda, &a[(j + jb) * - a_dim1 + 1], lda, &c_b14, &a[j + (j + jb) * - a_dim1], lda, (ftnlen)9, (ftnlen)12); - i__3 = *n - j - jb + 1; - dtrsm_((char *)"Left", (char *)"Upper", (char *)"Transpose", (char *)"Non-unit", &jb, & - i__3, &c_b14, &a[j + j * a_dim1], lda, &a[j + (j - + jb) * a_dim1], lda, (ftnlen)4, (ftnlen)5, ( - ftnlen)9, (ftnlen)8); - } + i__3 = *n - j - jb + 1; + i__4 = j - 1; + dgemm_((char *)"Transpose", (char *)"No transpose", &jb, &i__3, &i__4, & + c_b13, &a[j * a_dim1 + 1], lda, &a[(j + jb) * + a_dim1 + 1], lda, &c_b14, &a[j + (j + jb) * + a_dim1], lda, (ftnlen)9, (ftnlen)12); + i__3 = *n - j - jb + 1; + dtrsm_((char *)"Left", (char *)"Upper", (char *)"Transpose", (char *)"Non-unit", &jb, & + i__3, &c_b14, &a[j + j * a_dim1], lda, &a[j + (j + + jb) * a_dim1], lda, (ftnlen)4, (ftnlen)5, ( + ftnlen)9, (ftnlen)8); + } /* L10: */ - } + } - } else { + } else { /* Compute the Cholesky factorization A = L*L**T. */ - i__2 = *n; - i__1 = nb; - for (j = 1; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) { + i__2 = *n; + i__1 = nb; + for (j = 1; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) { /* Update and factorize the current diagonal block and test */ /* for non-positive-definiteness. */ /* Computing MIN */ - i__3 = nb, i__4 = *n - j + 1; - jb = min(i__3,i__4); - i__3 = j - 1; - dsyrk_((char *)"Lower", (char *)"No transpose", &jb, &i__3, &c_b13, &a[j + - a_dim1], lda, &c_b14, &a[j + j * a_dim1], lda, ( - ftnlen)5, (ftnlen)12); - dpotrf2_((char *)"Lower", &jb, &a[j + j * a_dim1], lda, info, (ftnlen) - 5); - if (*info != 0) { - goto L30; - } - if (j + jb <= *n) { + i__3 = nb, i__4 = *n - j + 1; + jb = min(i__3,i__4); + i__3 = j - 1; + dsyrk_((char *)"Lower", (char *)"No transpose", &jb, &i__3, &c_b13, &a[j + + a_dim1], lda, &c_b14, &a[j + j * a_dim1], lda, ( + ftnlen)5, (ftnlen)12); + dpotrf2_((char *)"Lower", &jb, &a[j + j * a_dim1], lda, info, (ftnlen) + 5); + if (*info != 0) { + goto L30; + } + if (j + jb <= *n) { /* Compute the current block column. */ - i__3 = *n - j - jb + 1; - i__4 = j - 1; - dgemm_((char *)"No transpose", (char *)"Transpose", &i__3, &jb, &i__4, & - c_b13, &a[j + jb + a_dim1], lda, &a[j + a_dim1], - lda, &c_b14, &a[j + jb + j * a_dim1], lda, ( - ftnlen)12, (ftnlen)9); - i__3 = *n - j - jb + 1; - dtrsm_((char *)"Right", (char *)"Lower", (char *)"Transpose", (char *)"Non-unit", &i__3, & - jb, &c_b14, &a[j + j * a_dim1], lda, &a[j + jb + - j * a_dim1], lda, (ftnlen)5, (ftnlen)5, (ftnlen)9, - (ftnlen)8); - } + i__3 = *n - j - jb + 1; + i__4 = j - 1; + dgemm_((char *)"No transpose", (char *)"Transpose", &i__3, &jb, &i__4, & + c_b13, &a[j + jb + a_dim1], lda, &a[j + a_dim1], + lda, &c_b14, &a[j + jb + j * a_dim1], lda, ( + ftnlen)12, (ftnlen)9); + i__3 = *n - j - jb + 1; + dtrsm_((char *)"Right", (char *)"Lower", (char *)"Transpose", (char *)"Non-unit", &i__3, & + jb, &c_b14, &a[j + j * a_dim1], lda, &a[j + jb + + j * a_dim1], lda, (ftnlen)5, (ftnlen)5, (ftnlen)9, + (ftnlen)8); + } /* L20: */ - } - } + } + } } goto L40; @@ -318,5 +318,5 @@ L40: } /* dpotrf_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dpotrf2.cpp b/lib/linalg/dpotrf2.cpp index 9b882bb9e0..61f9c83af6 100644 --- a/lib/linalg/dpotrf2.cpp +++ b/lib/linalg/dpotrf2.cpp @@ -1,13 +1,13 @@ /* static/dpotrf2.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -125,7 +125,7 @@ static doublereal c_b11 = -1.; /* ===================================================================== */ /* Subroutine */ int dpotrf2_(char *uplo, integer *n, doublereal *a, integer * - lda, integer *info, ftnlen uplo_len) + lda, integer *info, ftnlen uplo_len) { /* System generated locals */ integer a_dim1, a_offset, i__1; @@ -137,13 +137,13 @@ static doublereal c_b11 = -1.; integer n1, n2; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer iinfo; - extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, - integer *, integer *, doublereal *, doublereal *, integer *, - doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, + integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); logical upper; - extern /* Subroutine */ int dsyrk_(char *, char *, integer *, integer *, - doublereal *, doublereal *, integer *, doublereal *, doublereal *, - integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dsyrk_(char *, char *, integer *, integer *, + doublereal *, doublereal *, integer *, doublereal *, doublereal *, + integer *, ftnlen, ftnlen); extern logical disnan_(doublereal *); extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); @@ -182,22 +182,22 @@ static doublereal c_b11 = -1.; *info = 0; upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { - *info = -1; + *info = -1; } else if (*n < 0) { - *info = -2; + *info = -2; } else if (*lda < max(1,*n)) { - *info = -4; + *info = -4; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DPOTRF2", &i__1, (ftnlen)7); - return 0; + i__1 = -(*info); + xerbla_((char *)"DPOTRF2", &i__1, (ftnlen)7); + return 0; } /* Quick return if possible */ if (*n == 0) { - return 0; + return 0; } /* N=1 case */ @@ -206,73 +206,73 @@ static doublereal c_b11 = -1.; /* Test for non-positive-definiteness */ - if (a[a_dim1 + 1] <= 0. || disnan_(&a[a_dim1 + 1])) { - *info = 1; - return 0; - } + if (a[a_dim1 + 1] <= 0. || disnan_(&a[a_dim1 + 1])) { + *info = 1; + return 0; + } /* Factor */ - a[a_dim1 + 1] = sqrt(a[a_dim1 + 1]); + a[a_dim1 + 1] = sqrt(a[a_dim1 + 1]); /* Use recursive code */ } else { - n1 = *n / 2; - n2 = *n - n1; + n1 = *n / 2; + n2 = *n - n1; /* Factor A11 */ - dpotrf2_(uplo, &n1, &a[a_dim1 + 1], lda, &iinfo, (ftnlen)1); - if (iinfo != 0) { - *info = iinfo; - return 0; - } + dpotrf2_(uplo, &n1, &a[a_dim1 + 1], lda, &iinfo, (ftnlen)1); + if (iinfo != 0) { + *info = iinfo; + return 0; + } /* Compute the Cholesky factorization A = U**T*U */ - if (upper) { + if (upper) { /* Update and scale A12 */ - dtrsm_((char *)"L", (char *)"U", (char *)"T", (char *)"N", &n1, &n2, &c_b9, &a[a_dim1 + 1], lda, & - a[(n1 + 1) * a_dim1 + 1], lda, (ftnlen)1, (ftnlen)1, ( - ftnlen)1, (ftnlen)1); + dtrsm_((char *)"L", (char *)"U", (char *)"T", (char *)"N", &n1, &n2, &c_b9, &a[a_dim1 + 1], lda, & + a[(n1 + 1) * a_dim1 + 1], lda, (ftnlen)1, (ftnlen)1, ( + ftnlen)1, (ftnlen)1); /* Update and factor A22 */ - dsyrk_(uplo, (char *)"T", &n2, &n1, &c_b11, &a[(n1 + 1) * a_dim1 + 1], - lda, &c_b9, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, (ftnlen) - 1, (ftnlen)1); - dpotrf2_(uplo, &n2, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, &iinfo, ( - ftnlen)1); - if (iinfo != 0) { - *info = iinfo + n1; - return 0; - } + dsyrk_(uplo, (char *)"T", &n2, &n1, &c_b11, &a[(n1 + 1) * a_dim1 + 1], + lda, &c_b9, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, (ftnlen) + 1, (ftnlen)1); + dpotrf2_(uplo, &n2, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, &iinfo, ( + ftnlen)1); + if (iinfo != 0) { + *info = iinfo + n1; + return 0; + } /* Compute the Cholesky factorization A = L*L**T */ - } else { + } else { /* Update and scale A21 */ - dtrsm_((char *)"R", (char *)"L", (char *)"T", (char *)"N", &n2, &n1, &c_b9, &a[a_dim1 + 1], lda, & - a[n1 + 1 + a_dim1], lda, (ftnlen)1, (ftnlen)1, (ftnlen)1, - (ftnlen)1); + dtrsm_((char *)"R", (char *)"L", (char *)"T", (char *)"N", &n2, &n1, &c_b9, &a[a_dim1 + 1], lda, & + a[n1 + 1 + a_dim1], lda, (ftnlen)1, (ftnlen)1, (ftnlen)1, + (ftnlen)1); /* Update and factor A22 */ - dsyrk_(uplo, (char *)"N", &n2, &n1, &c_b11, &a[n1 + 1 + a_dim1], lda, & - c_b9, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, (ftnlen)1, ( - ftnlen)1); - dpotrf2_(uplo, &n2, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, &iinfo, ( - ftnlen)1); - if (iinfo != 0) { - *info = iinfo + n1; - return 0; - } - } + dsyrk_(uplo, (char *)"N", &n2, &n1, &c_b11, &a[n1 + 1 + a_dim1], lda, & + c_b9, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, (ftnlen)1, ( + ftnlen)1); + dpotrf2_(uplo, &n2, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, &iinfo, ( + ftnlen)1); + if (iinfo != 0) { + *info = iinfo + n1; + return 0; + } + } } return 0; @@ -281,5 +281,5 @@ static doublereal c_b11 = -1.; } /* dpotrf2_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dpotrs.cpp b/lib/linalg/dpotrs.cpp index 169f851130..c8cc0e0d68 100644 --- a/lib/linalg/dpotrs.cpp +++ b/lib/linalg/dpotrs.cpp @@ -1,13 +1,13 @@ /* fortran/dpotrs.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -130,18 +130,18 @@ f"> */ /* > \ingroup doublePOcomputational */ /* ===================================================================== */ -/* Subroutine */ int dpotrs_(char *uplo, integer *n, integer *nrhs, - doublereal *a, integer *lda, doublereal *b, integer *ldb, integer * - info, ftnlen uplo_len) +/* Subroutine */ int dpotrs_(char *uplo, integer *n, integer *nrhs, + doublereal *a, integer *lda, doublereal *b, integer *ldb, integer * + info, ftnlen uplo_len) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1; /* Local variables */ extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, - integer *, integer *, doublereal *, doublereal *, integer *, - doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, + integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); logical upper; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); @@ -183,26 +183,26 @@ f"> */ *info = 0; upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { - *info = -1; + *info = -1; } else if (*n < 0) { - *info = -2; + *info = -2; } else if (*nrhs < 0) { - *info = -3; + *info = -3; } else if (*lda < max(1,*n)) { - *info = -5; + *info = -5; } else if (*ldb < max(1,*n)) { - *info = -7; + *info = -7; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DPOTRS", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DPOTRS", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*n == 0 || *nrhs == 0) { - return 0; + return 0; } if (upper) { @@ -211,30 +211,30 @@ f"> */ /* Solve U**T *X = B, overwriting B with X. */ - dtrsm_((char *)"Left", (char *)"Upper", (char *)"Transpose", (char *)"Non-unit", n, nrhs, &c_b9, &a[ - a_offset], lda, &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, ( - ftnlen)9, (ftnlen)8); + dtrsm_((char *)"Left", (char *)"Upper", (char *)"Transpose", (char *)"Non-unit", n, nrhs, &c_b9, &a[ + a_offset], lda, &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, ( + ftnlen)9, (ftnlen)8); /* Solve U*X = B, overwriting B with X. */ - dtrsm_((char *)"Left", (char *)"Upper", (char *)"No transpose", (char *)"Non-unit", n, nrhs, &c_b9, & - a[a_offset], lda, &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, ( - ftnlen)12, (ftnlen)8); + dtrsm_((char *)"Left", (char *)"Upper", (char *)"No transpose", (char *)"Non-unit", n, nrhs, &c_b9, & + a[a_offset], lda, &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, ( + ftnlen)12, (ftnlen)8); } else { /* Solve A*X = B where A = L*L**T. */ /* Solve L*X = B, overwriting B with X. */ - dtrsm_((char *)"Left", (char *)"Lower", (char *)"No transpose", (char *)"Non-unit", n, nrhs, &c_b9, & - a[a_offset], lda, &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, ( - ftnlen)12, (ftnlen)8); + dtrsm_((char *)"Left", (char *)"Lower", (char *)"No transpose", (char *)"Non-unit", n, nrhs, &c_b9, & + a[a_offset], lda, &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, ( + ftnlen)12, (ftnlen)8); /* Solve L**T *X = B, overwriting B with X. */ - dtrsm_((char *)"Left", (char *)"Lower", (char *)"Transpose", (char *)"Non-unit", n, nrhs, &c_b9, &a[ - a_offset], lda, &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, ( - ftnlen)9, (ftnlen)8); + dtrsm_((char *)"Left", (char *)"Lower", (char *)"Transpose", (char *)"Non-unit", n, nrhs, &c_b9, &a[ + a_offset], lda, &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, ( + ftnlen)9, (ftnlen)8); } return 0; @@ -244,5 +244,5 @@ f"> */ } /* dpotrs_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/drot.cpp b/lib/linalg/drot.cpp index efd339cdf0..1ed9c47a89 100644 --- a/lib/linalg/drot.cpp +++ b/lib/linalg/drot.cpp @@ -1,13 +1,13 @@ /* fortran/drot.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -105,8 +105,8 @@ extern "C" { /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int drot_(integer *n, doublereal *dx, integer *incx, - doublereal *dy, integer *incy, doublereal *c__, doublereal *s) +/* Subroutine */ int drot_(integer *n, doublereal *dx, integer *incx, + doublereal *dy, integer *incy, doublereal *c__, doublereal *s) { /* System generated locals */ integer i__1; @@ -135,39 +135,39 @@ extern "C" { /* Function Body */ if (*n <= 0) { - return 0; + return 0; } if (*incx == 1 && *incy == 1) { /* code for both increments equal to 1 */ - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - dtemp = *c__ * dx[i__] + *s * dy[i__]; - dy[i__] = *c__ * dy[i__] - *s * dx[i__]; - dx[i__] = dtemp; - } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + dtemp = *c__ * dx[i__] + *s * dy[i__]; + dy[i__] = *c__ * dy[i__] - *s * dx[i__]; + dx[i__] = dtemp; + } } else { /* code for unequal increments or equal increments not equal */ /* to 1 */ - ix = 1; - iy = 1; - if (*incx < 0) { - ix = (-(*n) + 1) * *incx + 1; - } - if (*incy < 0) { - iy = (-(*n) + 1) * *incy + 1; - } - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - dtemp = *c__ * dx[ix] + *s * dy[iy]; - dy[iy] = *c__ * dy[iy] - *s * dx[ix]; - dx[ix] = dtemp; - ix += *incx; - iy += *incy; - } + ix = 1; + iy = 1; + if (*incx < 0) { + ix = (-(*n) + 1) * *incx + 1; + } + if (*incy < 0) { + iy = (-(*n) + 1) * *incy + 1; + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + dtemp = *c__ * dx[ix] + *s * dy[iy]; + dy[iy] = *c__ * dy[iy] - *s * dx[ix]; + dx[ix] = dtemp; + ix += *incx; + iy += *incy; + } } return 0; @@ -176,5 +176,5 @@ extern "C" { } /* drot_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/drscl.cpp b/lib/linalg/drscl.cpp index 041c7fbba3..10904c478f 100644 --- a/lib/linalg/drscl.cpp +++ b/lib/linalg/drscl.cpp @@ -1,13 +1,13 @@ /* fortran/drscl.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -100,14 +100,14 @@ extern "C" { /* > \ingroup doubleOTHERauxiliary */ /* ===================================================================== */ -/* Subroutine */ int drscl_(integer *n, doublereal *sa, doublereal *sx, - integer *incx) +/* Subroutine */ int drscl_(integer *n, doublereal *sa, doublereal *sx, + integer *incx) { doublereal mul, cden; logical done; doublereal cnum, cden1, cnum1; - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *), dlabad_(doublereal *, doublereal *); + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *), dlabad_(doublereal *, doublereal *); extern doublereal dlamch_(char *, ftnlen); doublereal bignum, smlnum; @@ -142,7 +142,7 @@ extern "C" { /* Function Body */ if (*n <= 0) { - return 0; + return 0; } /* Get machine parameters */ @@ -163,22 +163,22 @@ L10: /* Pre-multiply X by SMLNUM if CDEN is large compared to CNUM. */ - mul = smlnum; - done = FALSE_; - cden = cden1; + mul = smlnum; + done = FALSE_; + cden = cden1; } else if (abs(cnum1) > abs(cden)) { /* Pre-multiply X by BIGNUM if CDEN is small compared to CNUM. */ - mul = bignum; - done = FALSE_; - cnum = cnum1; + mul = bignum; + done = FALSE_; + cnum = cnum1; } else { /* Multiply X by CNUM / CDEN and return. */ - mul = cnum / cden; - done = TRUE_; + mul = cnum / cden; + done = TRUE_; } /* Scale the vector X by MUL */ @@ -186,7 +186,7 @@ L10: dscal_(n, &mul, &sx[1], incx); if (! done) { - goto L10; + goto L10; } return 0; @@ -196,5 +196,5 @@ L10: } /* drscl_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dscal.cpp b/lib/linalg/dscal.cpp index d1fc1d43ee..e141f7352b 100644 --- a/lib/linalg/dscal.cpp +++ b/lib/linalg/dscal.cpp @@ -1,13 +1,13 @@ /* fortran/dscal.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -92,8 +92,8 @@ extern "C" { /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int dscal_(integer *n, doublereal *da, doublereal *dx, - integer *incx) +/* Subroutine */ int dscal_(integer *n, doublereal *da, doublereal *dx, + integer *incx) { /* System generated locals */ integer i__1, i__2; @@ -123,7 +123,7 @@ extern "C" { /* Function Body */ if (*n <= 0 || *incx <= 0 || *da == 1.) { - return 0; + return 0; } if (*incx == 1) { @@ -132,35 +132,35 @@ extern "C" { /* clean-up loop */ - m = *n % 5; - if (m != 0) { - i__1 = m; - for (i__ = 1; i__ <= i__1; ++i__) { - dx[i__] = *da * dx[i__]; - } - if (*n < 5) { - return 0; - } - } - mp1 = m + 1; - i__1 = *n; - for (i__ = mp1; i__ <= i__1; i__ += 5) { - dx[i__] = *da * dx[i__]; - dx[i__ + 1] = *da * dx[i__ + 1]; - dx[i__ + 2] = *da * dx[i__ + 2]; - dx[i__ + 3] = *da * dx[i__ + 3]; - dx[i__ + 4] = *da * dx[i__ + 4]; - } + m = *n % 5; + if (m != 0) { + i__1 = m; + for (i__ = 1; i__ <= i__1; ++i__) { + dx[i__] = *da * dx[i__]; + } + if (*n < 5) { + return 0; + } + } + mp1 = m + 1; + i__1 = *n; + for (i__ = mp1; i__ <= i__1; i__ += 5) { + dx[i__] = *da * dx[i__]; + dx[i__ + 1] = *da * dx[i__ + 1]; + dx[i__ + 2] = *da * dx[i__ + 2]; + dx[i__ + 3] = *da * dx[i__ + 3]; + dx[i__ + 4] = *da * dx[i__ + 4]; + } } else { /* code for increment not equal to 1 */ - nincx = *n * *incx; - i__1 = nincx; - i__2 = *incx; - for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { - dx[i__] = *da * dx[i__]; - } + nincx = *n * *incx; + i__1 = nincx; + i__2 = *incx; + for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { + dx[i__] = *da * dx[i__]; + } } return 0; @@ -169,5 +169,5 @@ extern "C" { } /* dscal_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dstedc.cpp b/lib/linalg/dstedc.cpp index e71b373994..f1b09e0f25 100644 --- a/lib/linalg/dstedc.cpp +++ b/lib/linalg/dstedc.cpp @@ -1,13 +1,13 @@ /* fortran/dstedc.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -212,10 +212,10 @@ f"> */ /* > Modified by Francoise Tisseur, University of Tennessee */ /* > */ /* ===================================================================== */ -/* Subroutine */ int dstedc_(char *compz, integer *n, doublereal *d__, - doublereal *e, doublereal *z__, integer *ldz, doublereal *work, - integer *lwork, integer *iwork, integer *liwork, integer *info, - ftnlen compz_len) +/* Subroutine */ int dstedc_(char *compz, integer *n, doublereal *d__, + doublereal *e, doublereal *z__, integer *ldz, doublereal *work, + integer *lwork, integer *iwork, integer *liwork, integer *info, + ftnlen compz_len) { /* System generated locals */ integer z_dim1, z_offset, i__1, i__2; @@ -231,37 +231,37 @@ f"> */ doublereal p; integer ii, lgn; doublereal eps, tiny; - extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, - doublereal *, integer *); + extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, + doublereal *, integer *); integer lwmin; - extern /* Subroutine */ int dlaed0_(integer *, integer *, integer *, - doublereal *, doublereal *, doublereal *, integer *, doublereal *, - integer *, doublereal *, integer *, integer *); + extern /* Subroutine */ int dlaed0_(integer *, integer *, integer *, + doublereal *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, integer *, integer *); integer start; extern doublereal dlamch_(char *, ftnlen); - extern /* Subroutine */ int dlascl_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, integer *, doublereal *, - integer *, integer *, ftnlen), dlacpy_(char *, integer *, integer - *, doublereal *, integer *, doublereal *, integer *, ftnlen), - dlaset_(char *, integer *, integer *, doublereal *, doublereal *, - doublereal *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dlascl_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, integer *, doublereal *, + integer *, integer *, ftnlen), dlacpy_(char *, integer *, integer + *, doublereal *, integer *, doublereal *, integer *, ftnlen), + dlaset_(char *, integer *, integer *, doublereal *, doublereal *, + doublereal *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); integer finish; - extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *, - ftnlen); + extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *, + ftnlen); extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *, - integer *), dlasrt_(char *, integer *, doublereal *, integer *, - ftnlen); + integer *), dlasrt_(char *, integer *, doublereal *, integer *, + ftnlen); integer liwmin, icompz; - extern /* Subroutine */ int dsteqr_(char *, integer *, doublereal *, - doublereal *, doublereal *, integer *, doublereal *, integer *, - ftnlen); + extern /* Subroutine */ int dsteqr_(char *, integer *, doublereal *, + doublereal *, doublereal *, integer *, doublereal *, integer *, + ftnlen); doublereal orgnrm; logical lquery; integer smlsiz, storez, strtrw; @@ -306,82 +306,82 @@ f"> */ lquery = *lwork == -1 || *liwork == -1; if (lsame_(compz, (char *)"N", (ftnlen)1, (ftnlen)1)) { - icompz = 0; + icompz = 0; } else if (lsame_(compz, (char *)"V", (ftnlen)1, (ftnlen)1)) { - icompz = 1; + icompz = 1; } else if (lsame_(compz, (char *)"I", (ftnlen)1, (ftnlen)1)) { - icompz = 2; + icompz = 2; } else { - icompz = -1; + icompz = -1; } if (icompz < 0) { - *info = -1; + *info = -1; } else if (*n < 0) { - *info = -2; + *info = -2; } else if (*ldz < 1 || icompz > 0 && *ldz < max(1,*n)) { - *info = -6; + *info = -6; } if (*info == 0) { /* Compute the workspace requirements */ - smlsiz = ilaenv_(&c__9, (char *)"DSTEDC", (char *)" ", &c__0, &c__0, &c__0, &c__0, ( - ftnlen)6, (ftnlen)1); - if (*n <= 1 || icompz == 0) { - liwmin = 1; - lwmin = 1; - } else if (*n <= smlsiz) { - liwmin = 1; - lwmin = *n - 1 << 1; - } else { - lgn = (integer) (log((doublereal) (*n)) / log(2.)); - if (pow_ii(&c__2, &lgn) < *n) { - ++lgn; - } - if (pow_ii(&c__2, &lgn) < *n) { - ++lgn; - } - if (icompz == 1) { + smlsiz = ilaenv_(&c__9, (char *)"DSTEDC", (char *)" ", &c__0, &c__0, &c__0, &c__0, ( + ftnlen)6, (ftnlen)1); + if (*n <= 1 || icompz == 0) { + liwmin = 1; + lwmin = 1; + } else if (*n <= smlsiz) { + liwmin = 1; + lwmin = *n - 1 << 1; + } else { + lgn = (integer) (log((doublereal) (*n)) / log(2.)); + if (pow_ii(&c__2, &lgn) < *n) { + ++lgn; + } + if (pow_ii(&c__2, &lgn) < *n) { + ++lgn; + } + if (icompz == 1) { /* Computing 2nd power */ - i__1 = *n; - lwmin = *n * 3 + 1 + (*n << 1) * lgn + (i__1 * i__1 << 2); - liwmin = *n * 6 + 6 + *n * 5 * lgn; - } else if (icompz == 2) { + i__1 = *n; + lwmin = *n * 3 + 1 + (*n << 1) * lgn + (i__1 * i__1 << 2); + liwmin = *n * 6 + 6 + *n * 5 * lgn; + } else if (icompz == 2) { /* Computing 2nd power */ - i__1 = *n; - lwmin = (*n << 2) + 1 + i__1 * i__1; - liwmin = *n * 5 + 3; - } - } - work[1] = (doublereal) lwmin; - iwork[1] = liwmin; + i__1 = *n; + lwmin = (*n << 2) + 1 + i__1 * i__1; + liwmin = *n * 5 + 3; + } + } + work[1] = (doublereal) lwmin; + iwork[1] = liwmin; - if (*lwork < lwmin && ! lquery) { - *info = -8; - } else if (*liwork < liwmin && ! lquery) { - *info = -10; - } + if (*lwork < lwmin && ! lquery) { + *info = -8; + } else if (*liwork < liwmin && ! lquery) { + *info = -10; + } } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DSTEDC", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DSTEDC", &i__1, (ftnlen)6); + return 0; } else if (lquery) { - return 0; + return 0; } /* Quick return if possible */ if (*n == 0) { - return 0; + return 0; } if (*n == 1) { - if (icompz != 0) { - z__[z_dim1 + 1] = 1.; - } - return 0; + if (icompz != 0) { + z__[z_dim1 + 1] = 1.; + } + return 0; } /* If the following conditional clause is removed, then the routine */ @@ -396,8 +396,8 @@ f"> */ /* If COMPZ = 'N', use DSTERF to compute the eigenvalues. */ if (icompz == 0) { - dsterf_(n, &d__[1], &e[1], info); - goto L50; + dsterf_(n, &d__[1], &e[1], info); + goto L50; } /* If N is smaller than the minimum divide size (SMLSIZ+1), then */ @@ -405,40 +405,40 @@ f"> */ if (*n <= smlsiz) { - dsteqr_(compz, n, &d__[1], &e[1], &z__[z_offset], ldz, &work[1], info, - (ftnlen)1); + dsteqr_(compz, n, &d__[1], &e[1], &z__[z_offset], ldz, &work[1], info, + (ftnlen)1); } else { /* If COMPZ = 'V', the Z matrix must be stored elsewhere for later */ /* use. */ - if (icompz == 1) { - storez = *n * *n + 1; - } else { - storez = 1; - } + if (icompz == 1) { + storez = *n * *n + 1; + } else { + storez = 1; + } - if (icompz == 2) { - dlaset_((char *)"Full", n, n, &c_b17, &c_b18, &z__[z_offset], ldz, ( - ftnlen)4); - } + if (icompz == 2) { + dlaset_((char *)"Full", n, n, &c_b17, &c_b18, &z__[z_offset], ldz, ( + ftnlen)4); + } /* Scale. */ - orgnrm = dlanst_((char *)"M", n, &d__[1], &e[1], (ftnlen)1); - if (orgnrm == 0.) { - goto L50; - } + orgnrm = dlanst_((char *)"M", n, &d__[1], &e[1], (ftnlen)1); + if (orgnrm == 0.) { + goto L50; + } - eps = dlamch_((char *)"Epsilon", (ftnlen)7); + eps = dlamch_((char *)"Epsilon", (ftnlen)7); - start = 1; + start = 1; /* while ( START <= N ) */ L10: - if (start <= *n) { + if (start <= *n) { /* Let FINISH be the position of the next subdiagonal entry */ /* such that E( FINISH ) <= TINY or FINISH = N if no such */ @@ -446,119 +446,119 @@ L10: /* between START and FINISH constitutes an independent */ /* sub-problem. */ - finish = start; + finish = start; L20: - if (finish < *n) { - tiny = eps * sqrt((d__1 = d__[finish], abs(d__1))) * sqrt(( - d__2 = d__[finish + 1], abs(d__2))); - if ((d__1 = e[finish], abs(d__1)) > tiny) { - ++finish; - goto L20; - } - } + if (finish < *n) { + tiny = eps * sqrt((d__1 = d__[finish], abs(d__1))) * sqrt(( + d__2 = d__[finish + 1], abs(d__2))); + if ((d__1 = e[finish], abs(d__1)) > tiny) { + ++finish; + goto L20; + } + } /* (Sub) Problem determined. Compute its size and solve it. */ - m = finish - start + 1; - if (m == 1) { - start = finish + 1; - goto L10; - } - if (m > smlsiz) { + m = finish - start + 1; + if (m == 1) { + start = finish + 1; + goto L10; + } + if (m > smlsiz) { /* Scale. */ - orgnrm = dlanst_((char *)"M", &m, &d__[start], &e[start], (ftnlen)1); - dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b18, &m, &c__1, &d__[ - start], &m, info, (ftnlen)1); - i__1 = m - 1; - i__2 = m - 1; - dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b18, &i__1, &c__1, &e[ - start], &i__2, info, (ftnlen)1); + orgnrm = dlanst_((char *)"M", &m, &d__[start], &e[start], (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b18, &m, &c__1, &d__[ + start], &m, info, (ftnlen)1); + i__1 = m - 1; + i__2 = m - 1; + dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b18, &i__1, &c__1, &e[ + start], &i__2, info, (ftnlen)1); - if (icompz == 1) { - strtrw = 1; - } else { - strtrw = start; - } - dlaed0_(&icompz, n, &m, &d__[start], &e[start], &z__[strtrw + - start * z_dim1], ldz, &work[1], n, &work[storez], & - iwork[1], info); - if (*info != 0) { - *info = (*info / (m + 1) + start - 1) * (*n + 1) + *info % - (m + 1) + start - 1; - goto L50; - } + if (icompz == 1) { + strtrw = 1; + } else { + strtrw = start; + } + dlaed0_(&icompz, n, &m, &d__[start], &e[start], &z__[strtrw + + start * z_dim1], ldz, &work[1], n, &work[storez], & + iwork[1], info); + if (*info != 0) { + *info = (*info / (m + 1) + start - 1) * (*n + 1) + *info % + (m + 1) + start - 1; + goto L50; + } /* Scale back. */ - dlascl_((char *)"G", &c__0, &c__0, &c_b18, &orgnrm, &m, &c__1, &d__[ - start], &m, info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &c_b18, &orgnrm, &m, &c__1, &d__[ + start], &m, info, (ftnlen)1); - } else { - if (icompz == 1) { + } else { + if (icompz == 1) { /* Since QR won't update a Z matrix which is larger than */ /* the length of D, we must solve the sub-problem in a */ /* workspace and then multiply back into Z. */ - dsteqr_((char *)"I", &m, &d__[start], &e[start], &work[1], &m, & - work[m * m + 1], info, (ftnlen)1); - dlacpy_((char *)"A", n, &m, &z__[start * z_dim1 + 1], ldz, &work[ - storez], n, (ftnlen)1); - dgemm_((char *)"N", (char *)"N", n, &m, &m, &c_b18, &work[storez], n, & - work[1], &m, &c_b17, &z__[start * z_dim1 + 1], - ldz, (ftnlen)1, (ftnlen)1); - } else if (icompz == 2) { - dsteqr_((char *)"I", &m, &d__[start], &e[start], &z__[start + - start * z_dim1], ldz, &work[1], info, (ftnlen)1); - } else { - dsterf_(&m, &d__[start], &e[start], info); - } - if (*info != 0) { - *info = start * (*n + 1) + finish; - goto L50; - } - } + dsteqr_((char *)"I", &m, &d__[start], &e[start], &work[1], &m, & + work[m * m + 1], info, (ftnlen)1); + dlacpy_((char *)"A", n, &m, &z__[start * z_dim1 + 1], ldz, &work[ + storez], n, (ftnlen)1); + dgemm_((char *)"N", (char *)"N", n, &m, &m, &c_b18, &work[storez], n, & + work[1], &m, &c_b17, &z__[start * z_dim1 + 1], + ldz, (ftnlen)1, (ftnlen)1); + } else if (icompz == 2) { + dsteqr_((char *)"I", &m, &d__[start], &e[start], &z__[start + + start * z_dim1], ldz, &work[1], info, (ftnlen)1); + } else { + dsterf_(&m, &d__[start], &e[start], info); + } + if (*info != 0) { + *info = start * (*n + 1) + finish; + goto L50; + } + } - start = finish + 1; - goto L10; - } + start = finish + 1; + goto L10; + } /* endwhile */ - if (icompz == 0) { + if (icompz == 0) { /* Use Quick Sort */ - dlasrt_((char *)"I", n, &d__[1], info, (ftnlen)1); + dlasrt_((char *)"I", n, &d__[1], info, (ftnlen)1); - } else { + } else { /* Use Selection Sort to minimize swaps of eigenvectors */ - i__1 = *n; - for (ii = 2; ii <= i__1; ++ii) { - i__ = ii - 1; - k = i__; - p = d__[i__]; - i__2 = *n; - for (j = ii; j <= i__2; ++j) { - if (d__[j] < p) { - k = j; - p = d__[j]; - } + i__1 = *n; + for (ii = 2; ii <= i__1; ++ii) { + i__ = ii - 1; + k = i__; + p = d__[i__]; + i__2 = *n; + for (j = ii; j <= i__2; ++j) { + if (d__[j] < p) { + k = j; + p = d__[j]; + } /* L30: */ - } - if (k != i__) { - d__[k] = d__[i__]; - d__[i__] = p; - dswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1 - + 1], &c__1); - } + } + if (k != i__) { + d__[k] = d__[i__]; + d__[i__] = p; + dswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1 + + 1], &c__1); + } /* L40: */ - } - } + } + } } L50: @@ -572,5 +572,5 @@ L50: } /* dstedc_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dsteqr.cpp b/lib/linalg/dsteqr.cpp index 65209d15d3..62a13f9d0b 100644 --- a/lib/linalg/dsteqr.cpp +++ b/lib/linalg/dsteqr.cpp @@ -1,13 +1,13 @@ /* fortran/dsteqr.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -155,9 +155,9 @@ f"> */ /* > \ingroup auxOTHERcomputational */ /* ===================================================================== */ -/* Subroutine */ int dsteqr_(char *compz, integer *n, doublereal *d__, - doublereal *e, doublereal *z__, integer *ldz, doublereal *work, - integer *info, ftnlen compz_len) +/* Subroutine */ int dsteqr_(char *compz, integer *n, doublereal *d__, + doublereal *e, doublereal *z__, integer *ldz, doublereal *work, + integer *info, ftnlen compz_len) { /* System generated locals */ integer z_dim1, z_offset, i__1, i__2; @@ -175,34 +175,34 @@ f"> */ integer lsv; doublereal tst, eps2; integer lend, jtot; - extern /* Subroutine */ int dlae2_(doublereal *, doublereal *, doublereal - *, doublereal *, doublereal *); + extern /* Subroutine */ int dlae2_(doublereal *, doublereal *, doublereal + *, doublereal *, doublereal *); extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int dlasr_(char *, char *, char *, integer *, - integer *, doublereal *, doublereal *, doublereal *, integer *, - ftnlen, ftnlen, ftnlen); + extern /* Subroutine */ int dlasr_(char *, char *, char *, integer *, + integer *, doublereal *, doublereal *, doublereal *, integer *, + ftnlen, ftnlen, ftnlen); doublereal anorm; - extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, - doublereal *, integer *), dlaev2_(doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *, doublereal *, - doublereal *); + extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, + doublereal *, integer *), dlaev2_(doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *); integer lendm1, lendp1; - extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, - ftnlen); + extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, + ftnlen); integer iscale; - extern /* Subroutine */ int dlascl_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, integer *, doublereal *, - integer *, integer *, ftnlen), dlaset_(char *, integer *, integer - *, doublereal *, doublereal *, doublereal *, integer *, ftnlen); + extern /* Subroutine */ int dlascl_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, integer *, doublereal *, + integer *, integer *, ftnlen), dlaset_(char *, integer *, integer + *, doublereal *, doublereal *, doublereal *, integer *, ftnlen); doublereal safmin; - extern /* Subroutine */ int dlartg_(doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *); + extern /* Subroutine */ int dlartg_(doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *); doublereal safmax; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *, - ftnlen); - extern /* Subroutine */ int dlasrt_(char *, integer *, doublereal *, - integer *, ftnlen); + extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *, + ftnlen); + extern /* Subroutine */ int dlasrt_(char *, integer *, doublereal *, + integer *, ftnlen); integer lendsv; doublereal ssfmin; integer nmaxit, icompz; @@ -246,38 +246,38 @@ f"> */ *info = 0; if (lsame_(compz, (char *)"N", (ftnlen)1, (ftnlen)1)) { - icompz = 0; + icompz = 0; } else if (lsame_(compz, (char *)"V", (ftnlen)1, (ftnlen)1)) { - icompz = 1; + icompz = 1; } else if (lsame_(compz, (char *)"I", (ftnlen)1, (ftnlen)1)) { - icompz = 2; + icompz = 2; } else { - icompz = -1; + icompz = -1; } if (icompz < 0) { - *info = -1; + *info = -1; } else if (*n < 0) { - *info = -2; + *info = -2; } else if (*ldz < 1 || icompz > 0 && *ldz < max(1,*n)) { - *info = -6; + *info = -6; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DSTEQR", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DSTEQR", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*n == 0) { - return 0; + return 0; } if (*n == 1) { - if (icompz == 2) { - z__[z_dim1 + 1] = 1.; - } - return 0; + if (icompz == 2) { + z__[z_dim1 + 1] = 1.; + } + return 0; } /* Determine the unit roundoff and over/underflow thresholds. */ @@ -295,7 +295,7 @@ f"> */ /* matrix. */ if (icompz == 2) { - dlaset_((char *)"Full", n, n, &c_b9, &c_b10, &z__[z_offset], ldz, (ftnlen)4); + dlaset_((char *)"Full", n, n, &c_b9, &c_b10, &z__[z_offset], ldz, (ftnlen)4); } nmaxit = *n * 30; @@ -310,25 +310,25 @@ f"> */ L10: if (l1 > *n) { - goto L160; + goto L160; } if (l1 > 1) { - e[l1 - 1] = 0.; + e[l1 - 1] = 0.; } if (l1 <= nm1) { - i__1 = nm1; - for (m = l1; m <= i__1; ++m) { - tst = (d__1 = e[m], abs(d__1)); - if (tst == 0.) { - goto L30; - } - if (tst <= sqrt((d__1 = d__[m], abs(d__1))) * sqrt((d__2 = d__[m - + 1], abs(d__2))) * eps) { - e[m] = 0.; - goto L30; - } + i__1 = nm1; + for (m = l1; m <= i__1; ++m) { + tst = (d__1 = e[m], abs(d__1)); + if (tst == 0.) { + goto L30; + } + if (tst <= sqrt((d__1 = d__[m], abs(d__1))) * sqrt((d__2 = d__[m + + 1], abs(d__2))) * eps) { + e[m] = 0.; + goto L30; + } /* L20: */ - } + } } m = *n; @@ -339,7 +339,7 @@ L30: lendsv = lend; l1 = m + 1; if (lend == l) { - goto L10; + goto L10; } /* Scale submatrix in rows and columns L to LEND */ @@ -348,31 +348,31 @@ L30: anorm = dlanst_((char *)"M", &i__1, &d__[l], &e[l], (ftnlen)1); iscale = 0; if (anorm == 0.) { - goto L10; + goto L10; } if (anorm > ssfmax) { - iscale = 1; - i__1 = lend - l + 1; - dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n, - info, (ftnlen)1); - i__1 = lend - l; - dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &e[l], n, - info, (ftnlen)1); + iscale = 1; + i__1 = lend - l + 1; + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n, + info, (ftnlen)1); + i__1 = lend - l; + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &e[l], n, + info, (ftnlen)1); } else if (anorm < ssfmin) { - iscale = 2; - i__1 = lend - l + 1; - dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n, - info, (ftnlen)1); - i__1 = lend - l; - dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n, - info, (ftnlen)1); + iscale = 2; + i__1 = lend - l + 1; + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n, + info, (ftnlen)1); + i__1 = lend - l; + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n, + info, (ftnlen)1); } /* Choose between QL and QR iteration */ if ((d__1 = d__[lend], abs(d__1)) < (d__2 = d__[l], abs(d__2))) { - lend = lsv; - l = lendsv; + lend = lsv; + l = lendsv; } if (lend > l) { @@ -382,120 +382,120 @@ L30: /* Look for small subdiagonal element. */ L40: - if (l != lend) { - lendm1 = lend - 1; - i__1 = lendm1; - for (m = l; m <= i__1; ++m) { + if (l != lend) { + lendm1 = lend - 1; + i__1 = lendm1; + for (m = l; m <= i__1; ++m) { /* Computing 2nd power */ - d__2 = (d__1 = e[m], abs(d__1)); - tst = d__2 * d__2; - if (tst <= eps2 * (d__1 = d__[m], abs(d__1)) * (d__2 = d__[m - + 1], abs(d__2)) + safmin) { - goto L60; - } + d__2 = (d__1 = e[m], abs(d__1)); + tst = d__2 * d__2; + if (tst <= eps2 * (d__1 = d__[m], abs(d__1)) * (d__2 = d__[m + + 1], abs(d__2)) + safmin) { + goto L60; + } /* L50: */ - } - } + } + } - m = lend; + m = lend; L60: - if (m < lend) { - e[m] = 0.; - } - p = d__[l]; - if (m == l) { - goto L80; - } + if (m < lend) { + e[m] = 0.; + } + p = d__[l]; + if (m == l) { + goto L80; + } /* If remaining matrix is 2-by-2, use DLAE2 or SLAEV2 */ /* to compute its eigensystem. */ - if (m == l + 1) { - if (icompz > 0) { - dlaev2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2, &c__, &s); - work[l] = c__; - work[*n - 1 + l] = s; - dlasr_((char *)"R", (char *)"V", (char *)"B", n, &c__2, &work[l], &work[*n - 1 + l], & - z__[l * z_dim1 + 1], ldz, (ftnlen)1, (ftnlen)1, ( - ftnlen)1); - } else { - dlae2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2); - } - d__[l] = rt1; - d__[l + 1] = rt2; - e[l] = 0.; - l += 2; - if (l <= lend) { - goto L40; - } - goto L140; - } + if (m == l + 1) { + if (icompz > 0) { + dlaev2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2, &c__, &s); + work[l] = c__; + work[*n - 1 + l] = s; + dlasr_((char *)"R", (char *)"V", (char *)"B", n, &c__2, &work[l], &work[*n - 1 + l], & + z__[l * z_dim1 + 1], ldz, (ftnlen)1, (ftnlen)1, ( + ftnlen)1); + } else { + dlae2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2); + } + d__[l] = rt1; + d__[l + 1] = rt2; + e[l] = 0.; + l += 2; + if (l <= lend) { + goto L40; + } + goto L140; + } - if (jtot == nmaxit) { - goto L140; - } - ++jtot; + if (jtot == nmaxit) { + goto L140; + } + ++jtot; /* Form shift. */ - g = (d__[l + 1] - p) / (e[l] * 2.); - r__ = dlapy2_(&g, &c_b10); - g = d__[m] - p + e[l] / (g + d_sign(&r__, &g)); + g = (d__[l + 1] - p) / (e[l] * 2.); + r__ = dlapy2_(&g, &c_b10); + g = d__[m] - p + e[l] / (g + d_sign(&r__, &g)); - s = 1.; - c__ = 1.; - p = 0.; + s = 1.; + c__ = 1.; + p = 0.; /* Inner loop */ - mm1 = m - 1; - i__1 = l; - for (i__ = mm1; i__ >= i__1; --i__) { - f = s * e[i__]; - b = c__ * e[i__]; - dlartg_(&g, &f, &c__, &s, &r__); - if (i__ != m - 1) { - e[i__ + 1] = r__; - } - g = d__[i__ + 1] - p; - r__ = (d__[i__] - g) * s + c__ * 2. * b; - p = s * r__; - d__[i__ + 1] = g + p; - g = c__ * r__ - b; + mm1 = m - 1; + i__1 = l; + for (i__ = mm1; i__ >= i__1; --i__) { + f = s * e[i__]; + b = c__ * e[i__]; + dlartg_(&g, &f, &c__, &s, &r__); + if (i__ != m - 1) { + e[i__ + 1] = r__; + } + g = d__[i__ + 1] - p; + r__ = (d__[i__] - g) * s + c__ * 2. * b; + p = s * r__; + d__[i__ + 1] = g + p; + g = c__ * r__ - b; /* If eigenvectors are desired, then save rotations. */ - if (icompz > 0) { - work[i__] = c__; - work[*n - 1 + i__] = -s; - } + if (icompz > 0) { + work[i__] = c__; + work[*n - 1 + i__] = -s; + } /* L70: */ - } + } /* If eigenvectors are desired, then apply saved rotations. */ - if (icompz > 0) { - mm = m - l + 1; - dlasr_((char *)"R", (char *)"V", (char *)"B", n, &mm, &work[l], &work[*n - 1 + l], &z__[l - * z_dim1 + 1], ldz, (ftnlen)1, (ftnlen)1, (ftnlen)1); - } + if (icompz > 0) { + mm = m - l + 1; + dlasr_((char *)"R", (char *)"V", (char *)"B", n, &mm, &work[l], &work[*n - 1 + l], &z__[l + * z_dim1 + 1], ldz, (ftnlen)1, (ftnlen)1, (ftnlen)1); + } - d__[l] -= p; - e[l] = g; - goto L40; + d__[l] -= p; + e[l] = g; + goto L40; /* Eigenvalue found. */ L80: - d__[l] = p; + d__[l] = p; - ++l; - if (l <= lend) { - goto L40; - } - goto L140; + ++l; + if (l <= lend) { + goto L40; + } + goto L140; } else { @@ -504,121 +504,121 @@ L80: /* Look for small superdiagonal element. */ L90: - if (l != lend) { - lendp1 = lend + 1; - i__1 = lendp1; - for (m = l; m >= i__1; --m) { + if (l != lend) { + lendp1 = lend + 1; + i__1 = lendp1; + for (m = l; m >= i__1; --m) { /* Computing 2nd power */ - d__2 = (d__1 = e[m - 1], abs(d__1)); - tst = d__2 * d__2; - if (tst <= eps2 * (d__1 = d__[m], abs(d__1)) * (d__2 = d__[m - - 1], abs(d__2)) + safmin) { - goto L110; - } + d__2 = (d__1 = e[m - 1], abs(d__1)); + tst = d__2 * d__2; + if (tst <= eps2 * (d__1 = d__[m], abs(d__1)) * (d__2 = d__[m + - 1], abs(d__2)) + safmin) { + goto L110; + } /* L100: */ - } - } + } + } - m = lend; + m = lend; L110: - if (m > lend) { - e[m - 1] = 0.; - } - p = d__[l]; - if (m == l) { - goto L130; - } + if (m > lend) { + e[m - 1] = 0.; + } + p = d__[l]; + if (m == l) { + goto L130; + } /* If remaining matrix is 2-by-2, use DLAE2 or SLAEV2 */ /* to compute its eigensystem. */ - if (m == l - 1) { - if (icompz > 0) { - dlaev2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2, &c__, &s) - ; - work[m] = c__; - work[*n - 1 + m] = s; - dlasr_((char *)"R", (char *)"V", (char *)"F", n, &c__2, &work[m], &work[*n - 1 + m], & - z__[(l - 1) * z_dim1 + 1], ldz, (ftnlen)1, (ftnlen)1, - (ftnlen)1); - } else { - dlae2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2); - } - d__[l - 1] = rt1; - d__[l] = rt2; - e[l - 1] = 0.; - l += -2; - if (l >= lend) { - goto L90; - } - goto L140; - } + if (m == l - 1) { + if (icompz > 0) { + dlaev2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2, &c__, &s) + ; + work[m] = c__; + work[*n - 1 + m] = s; + dlasr_((char *)"R", (char *)"V", (char *)"F", n, &c__2, &work[m], &work[*n - 1 + m], & + z__[(l - 1) * z_dim1 + 1], ldz, (ftnlen)1, (ftnlen)1, + (ftnlen)1); + } else { + dlae2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2); + } + d__[l - 1] = rt1; + d__[l] = rt2; + e[l - 1] = 0.; + l += -2; + if (l >= lend) { + goto L90; + } + goto L140; + } - if (jtot == nmaxit) { - goto L140; - } - ++jtot; + if (jtot == nmaxit) { + goto L140; + } + ++jtot; /* Form shift. */ - g = (d__[l - 1] - p) / (e[l - 1] * 2.); - r__ = dlapy2_(&g, &c_b10); - g = d__[m] - p + e[l - 1] / (g + d_sign(&r__, &g)); + g = (d__[l - 1] - p) / (e[l - 1] * 2.); + r__ = dlapy2_(&g, &c_b10); + g = d__[m] - p + e[l - 1] / (g + d_sign(&r__, &g)); - s = 1.; - c__ = 1.; - p = 0.; + s = 1.; + c__ = 1.; + p = 0.; /* Inner loop */ - lm1 = l - 1; - i__1 = lm1; - for (i__ = m; i__ <= i__1; ++i__) { - f = s * e[i__]; - b = c__ * e[i__]; - dlartg_(&g, &f, &c__, &s, &r__); - if (i__ != m) { - e[i__ - 1] = r__; - } - g = d__[i__] - p; - r__ = (d__[i__ + 1] - g) * s + c__ * 2. * b; - p = s * r__; - d__[i__] = g + p; - g = c__ * r__ - b; + lm1 = l - 1; + i__1 = lm1; + for (i__ = m; i__ <= i__1; ++i__) { + f = s * e[i__]; + b = c__ * e[i__]; + dlartg_(&g, &f, &c__, &s, &r__); + if (i__ != m) { + e[i__ - 1] = r__; + } + g = d__[i__] - p; + r__ = (d__[i__ + 1] - g) * s + c__ * 2. * b; + p = s * r__; + d__[i__] = g + p; + g = c__ * r__ - b; /* If eigenvectors are desired, then save rotations. */ - if (icompz > 0) { - work[i__] = c__; - work[*n - 1 + i__] = s; - } + if (icompz > 0) { + work[i__] = c__; + work[*n - 1 + i__] = s; + } /* L120: */ - } + } /* If eigenvectors are desired, then apply saved rotations. */ - if (icompz > 0) { - mm = l - m + 1; - dlasr_((char *)"R", (char *)"V", (char *)"F", n, &mm, &work[m], &work[*n - 1 + m], &z__[m - * z_dim1 + 1], ldz, (ftnlen)1, (ftnlen)1, (ftnlen)1); - } + if (icompz > 0) { + mm = l - m + 1; + dlasr_((char *)"R", (char *)"V", (char *)"F", n, &mm, &work[m], &work[*n - 1 + m], &z__[m + * z_dim1 + 1], ldz, (ftnlen)1, (ftnlen)1, (ftnlen)1); + } - d__[l] -= p; - e[lm1] = g; - goto L90; + d__[l] -= p; + e[lm1] = g; + goto L90; /* Eigenvalue found. */ L130: - d__[l] = p; + d__[l] = p; - --l; - if (l >= lend) { - goto L90; - } - goto L140; + --l; + if (l >= lend) { + goto L90; + } + goto L140; } @@ -626,32 +626,32 @@ L130: L140: if (iscale == 1) { - i__1 = lendsv - lsv + 1; - dlascl_((char *)"G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv], - n, info, (ftnlen)1); - i__1 = lendsv - lsv; - dlascl_((char *)"G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &e[lsv], n, - info, (ftnlen)1); + i__1 = lendsv - lsv + 1; + dlascl_((char *)"G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv], + n, info, (ftnlen)1); + i__1 = lendsv - lsv; + dlascl_((char *)"G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &e[lsv], n, + info, (ftnlen)1); } else if (iscale == 2) { - i__1 = lendsv - lsv + 1; - dlascl_((char *)"G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[lsv], - n, info, (ftnlen)1); - i__1 = lendsv - lsv; - dlascl_((char *)"G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &e[lsv], n, - info, (ftnlen)1); + i__1 = lendsv - lsv + 1; + dlascl_((char *)"G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[lsv], + n, info, (ftnlen)1); + i__1 = lendsv - lsv; + dlascl_((char *)"G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &e[lsv], n, + info, (ftnlen)1); } /* Check for no convergence to an eigenvalue after a total */ /* of N*MAXIT iterations. */ if (jtot < nmaxit) { - goto L10; + goto L10; } i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { - if (e[i__] != 0.) { - ++(*info); - } + if (e[i__] != 0.) { + ++(*info); + } /* L150: */ } goto L190; @@ -663,33 +663,33 @@ L160: /* Use Quick Sort */ - dlasrt_((char *)"I", n, &d__[1], info, (ftnlen)1); + dlasrt_((char *)"I", n, &d__[1], info, (ftnlen)1); } else { /* Use Selection Sort to minimize swaps of eigenvectors */ - i__1 = *n; - for (ii = 2; ii <= i__1; ++ii) { - i__ = ii - 1; - k = i__; - p = d__[i__]; - i__2 = *n; - for (j = ii; j <= i__2; ++j) { - if (d__[j] < p) { - k = j; - p = d__[j]; - } + i__1 = *n; + for (ii = 2; ii <= i__1; ++ii) { + i__ = ii - 1; + k = i__; + p = d__[i__]; + i__2 = *n; + for (j = ii; j <= i__2; ++j) { + if (d__[j] < p) { + k = j; + p = d__[j]; + } /* L170: */ - } - if (k != i__) { - d__[k] = d__[i__]; - d__[i__] = p; - dswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1 + 1], - &c__1); - } + } + if (k != i__) { + d__[k] = d__[i__]; + d__[i__] = p; + dswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1 + 1], + &c__1); + } /* L180: */ - } + } } L190: @@ -700,5 +700,5 @@ L190: } /* dsteqr_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dsterf.cpp b/lib/linalg/dsterf.cpp index 03172b87f3..981374d32a 100644 --- a/lib/linalg/dsterf.cpp +++ b/lib/linalg/dsterf.cpp @@ -1,13 +1,13 @@ /* fortran/dsterf.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -108,8 +108,8 @@ f"> */ /* > \ingroup auxOTHERcomputational */ /* ===================================================================== */ -/* Subroutine */ int dsterf_(integer *n, doublereal *d__, doublereal *e, - integer *info) +/* Subroutine */ int dsterf_(integer *n, doublereal *d__, doublereal *e, + integer *info) { /* System generated locals */ integer i__1; @@ -129,22 +129,22 @@ f"> */ integer lend; doublereal rmax; integer jtot; - extern /* Subroutine */ int dlae2_(doublereal *, doublereal *, doublereal - *, doublereal *, doublereal *); + extern /* Subroutine */ int dlae2_(doublereal *, doublereal *, doublereal + *, doublereal *, doublereal *); doublereal gamma, alpha, sigma, anorm; - extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, - ftnlen); + extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, + ftnlen); integer iscale; - extern /* Subroutine */ int dlascl_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, integer *, doublereal *, - integer *, integer *, ftnlen); + extern /* Subroutine */ int dlascl_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, integer *, doublereal *, + integer *, integer *, ftnlen); doublereal oldgam, safmin; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); doublereal safmax; - extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *, - ftnlen); - extern /* Subroutine */ int dlasrt_(char *, integer *, doublereal *, - integer *, ftnlen); + extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *, + ftnlen); + extern /* Subroutine */ int dlasrt_(char *, integer *, doublereal *, + integer *, ftnlen); integer lendsv; doublereal ssfmin; integer nmaxit; @@ -186,13 +186,13 @@ f"> */ /* Quick return if possible */ if (*n < 0) { - *info = -1; - i__1 = -(*info); - xerbla_((char *)"DSTERF", &i__1, (ftnlen)6); - return 0; + *info = -1; + i__1 = -(*info); + xerbla_((char *)"DSTERF", &i__1, (ftnlen)6); + return 0; } if (*n <= 1) { - return 0; + return 0; } /* Determine the unit roundoff for this environment. */ @@ -221,18 +221,18 @@ f"> */ L10: if (l1 > *n) { - goto L170; + goto L170; } if (l1 > 1) { - e[l1 - 1] = 0.; + e[l1 - 1] = 0.; } i__1 = *n - 1; for (m = l1; m <= i__1; ++m) { - if ((d__3 = e[m], abs(d__3)) <= sqrt((d__1 = d__[m], abs(d__1))) * - sqrt((d__2 = d__[m + 1], abs(d__2))) * eps) { - e[m] = 0.; - goto L30; - } + if ((d__3 = e[m], abs(d__3)) <= sqrt((d__1 = d__[m], abs(d__1))) * + sqrt((d__2 = d__[m + 1], abs(d__2))) * eps) { + e[m] = 0.; + goto L30; + } /* L20: */ } m = *n; @@ -244,7 +244,7 @@ L30: lendsv = lend; l1 = m + 1; if (lend == l) { - goto L10; + goto L10; } /* Scale submatrix in rows and columns L to LEND */ @@ -253,39 +253,39 @@ L30: anorm = dlanst_((char *)"M", &i__1, &d__[l], &e[l], (ftnlen)1); iscale = 0; if (anorm == 0.) { - goto L10; + goto L10; } if (anorm > ssfmax) { - iscale = 1; - i__1 = lend - l + 1; - dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n, - info, (ftnlen)1); - i__1 = lend - l; - dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &e[l], n, - info, (ftnlen)1); + iscale = 1; + i__1 = lend - l + 1; + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n, + info, (ftnlen)1); + i__1 = lend - l; + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &e[l], n, + info, (ftnlen)1); } else if (anorm < ssfmin) { - iscale = 2; - i__1 = lend - l + 1; - dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n, - info, (ftnlen)1); - i__1 = lend - l; - dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n, - info, (ftnlen)1); + iscale = 2; + i__1 = lend - l + 1; + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n, + info, (ftnlen)1); + i__1 = lend - l; + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n, + info, (ftnlen)1); } i__1 = lend - 1; for (i__ = l; i__ <= i__1; ++i__) { /* Computing 2nd power */ - d__1 = e[i__]; - e[i__] = d__1 * d__1; + d__1 = e[i__]; + e[i__] = d__1 * d__1; /* L40: */ } /* Choose between QL and QR iteration */ if ((d__1 = d__[lend], abs(d__1)) < (d__2 = d__[l], abs(d__2))) { - lend = lsv; - l = lendsv; + lend = lsv; + l = lendsv; } if (lend >= l) { @@ -295,98 +295,98 @@ L30: /* Look for small subdiagonal element. */ L50: - if (l != lend) { - i__1 = lend - 1; - for (m = l; m <= i__1; ++m) { - if ((d__2 = e[m], abs(d__2)) <= eps2 * (d__1 = d__[m] * d__[m - + 1], abs(d__1))) { - goto L70; - } + if (l != lend) { + i__1 = lend - 1; + for (m = l; m <= i__1; ++m) { + if ((d__2 = e[m], abs(d__2)) <= eps2 * (d__1 = d__[m] * d__[m + + 1], abs(d__1))) { + goto L70; + } /* L60: */ - } - } - m = lend; + } + } + m = lend; L70: - if (m < lend) { - e[m] = 0.; - } - p = d__[l]; - if (m == l) { - goto L90; - } + if (m < lend) { + e[m] = 0.; + } + p = d__[l]; + if (m == l) { + goto L90; + } /* If remaining matrix is 2 by 2, use DLAE2 to compute its */ /* eigenvalues. */ - if (m == l + 1) { - rte = sqrt(e[l]); - dlae2_(&d__[l], &rte, &d__[l + 1], &rt1, &rt2); - d__[l] = rt1; - d__[l + 1] = rt2; - e[l] = 0.; - l += 2; - if (l <= lend) { - goto L50; - } - goto L150; - } + if (m == l + 1) { + rte = sqrt(e[l]); + dlae2_(&d__[l], &rte, &d__[l + 1], &rt1, &rt2); + d__[l] = rt1; + d__[l + 1] = rt2; + e[l] = 0.; + l += 2; + if (l <= lend) { + goto L50; + } + goto L150; + } - if (jtot == nmaxit) { - goto L150; - } - ++jtot; + if (jtot == nmaxit) { + goto L150; + } + ++jtot; /* Form shift. */ - rte = sqrt(e[l]); - sigma = (d__[l + 1] - p) / (rte * 2.); - r__ = dlapy2_(&sigma, &c_b33); - sigma = p - rte / (sigma + d_sign(&r__, &sigma)); + rte = sqrt(e[l]); + sigma = (d__[l + 1] - p) / (rte * 2.); + r__ = dlapy2_(&sigma, &c_b33); + sigma = p - rte / (sigma + d_sign(&r__, &sigma)); - c__ = 1.; - s = 0.; - gamma = d__[m] - sigma; - p = gamma * gamma; + c__ = 1.; + s = 0.; + gamma = d__[m] - sigma; + p = gamma * gamma; /* Inner loop */ - i__1 = l; - for (i__ = m - 1; i__ >= i__1; --i__) { - bb = e[i__]; - r__ = p + bb; - if (i__ != m - 1) { - e[i__ + 1] = s * r__; - } - oldc = c__; - c__ = p / r__; - s = bb / r__; - oldgam = gamma; - alpha = d__[i__]; - gamma = c__ * (alpha - sigma) - s * oldgam; - d__[i__ + 1] = oldgam + (alpha - gamma); - if (c__ != 0.) { - p = gamma * gamma / c__; - } else { - p = oldc * bb; - } + i__1 = l; + for (i__ = m - 1; i__ >= i__1; --i__) { + bb = e[i__]; + r__ = p + bb; + if (i__ != m - 1) { + e[i__ + 1] = s * r__; + } + oldc = c__; + c__ = p / r__; + s = bb / r__; + oldgam = gamma; + alpha = d__[i__]; + gamma = c__ * (alpha - sigma) - s * oldgam; + d__[i__ + 1] = oldgam + (alpha - gamma); + if (c__ != 0.) { + p = gamma * gamma / c__; + } else { + p = oldc * bb; + } /* L80: */ - } + } - e[l] = s * p; - d__[l] = sigma + gamma; - goto L50; + e[l] = s * p; + d__[l] = sigma + gamma; + goto L50; /* Eigenvalue found. */ L90: - d__[l] = p; + d__[l] = p; - ++l; - if (l <= lend) { - goto L50; - } - goto L150; + ++l; + if (l <= lend) { + goto L50; + } + goto L150; } else { @@ -395,96 +395,96 @@ L90: /* Look for small superdiagonal element. */ L100: - i__1 = lend + 1; - for (m = l; m >= i__1; --m) { - if ((d__2 = e[m - 1], abs(d__2)) <= eps2 * (d__1 = d__[m] * d__[m - - 1], abs(d__1))) { - goto L120; - } + i__1 = lend + 1; + for (m = l; m >= i__1; --m) { + if ((d__2 = e[m - 1], abs(d__2)) <= eps2 * (d__1 = d__[m] * d__[m + - 1], abs(d__1))) { + goto L120; + } /* L110: */ - } - m = lend; + } + m = lend; L120: - if (m > lend) { - e[m - 1] = 0.; - } - p = d__[l]; - if (m == l) { - goto L140; - } + if (m > lend) { + e[m - 1] = 0.; + } + p = d__[l]; + if (m == l) { + goto L140; + } /* If remaining matrix is 2 by 2, use DLAE2 to compute its */ /* eigenvalues. */ - if (m == l - 1) { - rte = sqrt(e[l - 1]); - dlae2_(&d__[l], &rte, &d__[l - 1], &rt1, &rt2); - d__[l] = rt1; - d__[l - 1] = rt2; - e[l - 1] = 0.; - l += -2; - if (l >= lend) { - goto L100; - } - goto L150; - } + if (m == l - 1) { + rte = sqrt(e[l - 1]); + dlae2_(&d__[l], &rte, &d__[l - 1], &rt1, &rt2); + d__[l] = rt1; + d__[l - 1] = rt2; + e[l - 1] = 0.; + l += -2; + if (l >= lend) { + goto L100; + } + goto L150; + } - if (jtot == nmaxit) { - goto L150; - } - ++jtot; + if (jtot == nmaxit) { + goto L150; + } + ++jtot; /* Form shift. */ - rte = sqrt(e[l - 1]); - sigma = (d__[l - 1] - p) / (rte * 2.); - r__ = dlapy2_(&sigma, &c_b33); - sigma = p - rte / (sigma + d_sign(&r__, &sigma)); + rte = sqrt(e[l - 1]); + sigma = (d__[l - 1] - p) / (rte * 2.); + r__ = dlapy2_(&sigma, &c_b33); + sigma = p - rte / (sigma + d_sign(&r__, &sigma)); - c__ = 1.; - s = 0.; - gamma = d__[m] - sigma; - p = gamma * gamma; + c__ = 1.; + s = 0.; + gamma = d__[m] - sigma; + p = gamma * gamma; /* Inner loop */ - i__1 = l - 1; - for (i__ = m; i__ <= i__1; ++i__) { - bb = e[i__]; - r__ = p + bb; - if (i__ != m) { - e[i__ - 1] = s * r__; - } - oldc = c__; - c__ = p / r__; - s = bb / r__; - oldgam = gamma; - alpha = d__[i__ + 1]; - gamma = c__ * (alpha - sigma) - s * oldgam; - d__[i__] = oldgam + (alpha - gamma); - if (c__ != 0.) { - p = gamma * gamma / c__; - } else { - p = oldc * bb; - } + i__1 = l - 1; + for (i__ = m; i__ <= i__1; ++i__) { + bb = e[i__]; + r__ = p + bb; + if (i__ != m) { + e[i__ - 1] = s * r__; + } + oldc = c__; + c__ = p / r__; + s = bb / r__; + oldgam = gamma; + alpha = d__[i__ + 1]; + gamma = c__ * (alpha - sigma) - s * oldgam; + d__[i__] = oldgam + (alpha - gamma); + if (c__ != 0.) { + p = gamma * gamma / c__; + } else { + p = oldc * bb; + } /* L130: */ - } + } - e[l - 1] = s * p; - d__[l] = sigma + gamma; - goto L100; + e[l - 1] = s * p; + d__[l] = sigma + gamma; + goto L100; /* Eigenvalue found. */ L140: - d__[l] = p; + d__[l] = p; - --l; - if (l >= lend) { - goto L100; - } - goto L150; + --l; + if (l >= lend) { + goto L100; + } + goto L150; } @@ -492,27 +492,27 @@ L140: L150: if (iscale == 1) { - i__1 = lendsv - lsv + 1; - dlascl_((char *)"G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv], - n, info, (ftnlen)1); + i__1 = lendsv - lsv + 1; + dlascl_((char *)"G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv], + n, info, (ftnlen)1); } if (iscale == 2) { - i__1 = lendsv - lsv + 1; - dlascl_((char *)"G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[lsv], - n, info, (ftnlen)1); + i__1 = lendsv - lsv + 1; + dlascl_((char *)"G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[lsv], + n, info, (ftnlen)1); } /* Check for no convergence to an eigenvalue after a total */ /* of N*MAXIT iterations. */ if (jtot < nmaxit) { - goto L10; + goto L10; } i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { - if (e[i__] != 0.) { - ++(*info); - } + if (e[i__] != 0.) { + ++(*info); + } /* L160: */ } goto L180; @@ -530,5 +530,5 @@ L180: } /* dsterf_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dswap.cpp b/lib/linalg/dswap.cpp index a1eca4fc06..4cb6a77f67 100644 --- a/lib/linalg/dswap.cpp +++ b/lib/linalg/dswap.cpp @@ -1,13 +1,13 @@ /* fortran/dswap.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -95,8 +95,8 @@ extern "C" { /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int dswap_(integer *n, doublereal *dx, integer *incx, - doublereal *dy, integer *incy) +/* Subroutine */ int dswap_(integer *n, doublereal *dx, integer *incx, + doublereal *dy, integer *incy) { /* System generated locals */ integer i__1; @@ -127,7 +127,7 @@ extern "C" { /* Function Body */ if (*n <= 0) { - return 0; + return 0; } if (*incx == 1 && *incy == 1) { @@ -136,52 +136,52 @@ extern "C" { /* clean-up loop */ - m = *n % 3; - if (m != 0) { - i__1 = m; - for (i__ = 1; i__ <= i__1; ++i__) { - dtemp = dx[i__]; - dx[i__] = dy[i__]; - dy[i__] = dtemp; - } - if (*n < 3) { - return 0; - } - } - mp1 = m + 1; - i__1 = *n; - for (i__ = mp1; i__ <= i__1; i__ += 3) { - dtemp = dx[i__]; - dx[i__] = dy[i__]; - dy[i__] = dtemp; - dtemp = dx[i__ + 1]; - dx[i__ + 1] = dy[i__ + 1]; - dy[i__ + 1] = dtemp; - dtemp = dx[i__ + 2]; - dx[i__ + 2] = dy[i__ + 2]; - dy[i__ + 2] = dtemp; - } + m = *n % 3; + if (m != 0) { + i__1 = m; + for (i__ = 1; i__ <= i__1; ++i__) { + dtemp = dx[i__]; + dx[i__] = dy[i__]; + dy[i__] = dtemp; + } + if (*n < 3) { + return 0; + } + } + mp1 = m + 1; + i__1 = *n; + for (i__ = mp1; i__ <= i__1; i__ += 3) { + dtemp = dx[i__]; + dx[i__] = dy[i__]; + dy[i__] = dtemp; + dtemp = dx[i__ + 1]; + dx[i__ + 1] = dy[i__ + 1]; + dy[i__ + 1] = dtemp; + dtemp = dx[i__ + 2]; + dx[i__ + 2] = dy[i__ + 2]; + dy[i__ + 2] = dtemp; + } } else { /* code for unequal increments or equal increments not equal */ /* to 1 */ - ix = 1; - iy = 1; - if (*incx < 0) { - ix = (-(*n) + 1) * *incx + 1; - } - if (*incy < 0) { - iy = (-(*n) + 1) * *incy + 1; - } - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - dtemp = dx[ix]; - dx[ix] = dy[iy]; - dy[iy] = dtemp; - ix += *incx; - iy += *incy; - } + ix = 1; + iy = 1; + if (*incx < 0) { + ix = (-(*n) + 1) * *incx + 1; + } + if (*incy < 0) { + iy = (-(*n) + 1) * *incy + 1; + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + dtemp = dx[ix]; + dx[ix] = dy[iy]; + dy[iy] = dtemp; + ix += *incx; + iy += *incy; + } } return 0; @@ -190,5 +190,5 @@ extern "C" { } /* dswap_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dsyev.cpp b/lib/linalg/dsyev.cpp index 603b633195..a222fc4b09 100644 --- a/lib/linalg/dsyev.cpp +++ b/lib/linalg/dsyev.cpp @@ -1,13 +1,13 @@ /* fortran/dsyev.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -157,8 +157,8 @@ ices */ /* ===================================================================== */ /* Subroutine */ int dsyev_(char *jobz, char *uplo, integer *n, doublereal *a, - integer *lda, doublereal *w, doublereal *work, integer *lwork, - integer *info, ftnlen jobz_len, ftnlen uplo_len) + integer *lda, doublereal *w, doublereal *work, integer *lwork, + integer *info, ftnlen jobz_len, ftnlen uplo_len) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; @@ -174,35 +174,35 @@ ices */ doublereal anrm; integer imax; doublereal rmin, rmax; - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *); + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *); doublereal sigma; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer iinfo; logical lower, wantz; extern doublereal dlamch_(char *, ftnlen); integer iscale; - extern /* Subroutine */ int dlascl_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, integer *, doublereal *, - integer *, integer *, ftnlen); + extern /* Subroutine */ int dlascl_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, integer *, doublereal *, + integer *, integer *, ftnlen); doublereal safmin; - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); doublereal bignum; integer indtau; extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *, - integer *); - extern doublereal dlansy_(char *, char *, integer *, doublereal *, - integer *, doublereal *, ftnlen, ftnlen); + integer *); + extern doublereal dlansy_(char *, char *, integer *, doublereal *, + integer *, doublereal *, ftnlen, ftnlen); integer indwrk; - extern /* Subroutine */ int dorgtr_(char *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, integer *, - ftnlen), dsteqr_(char *, integer *, doublereal *, doublereal *, - doublereal *, integer *, doublereal *, integer *, ftnlen), - dsytrd_(char *, integer *, doublereal *, integer *, doublereal *, - doublereal *, doublereal *, doublereal *, integer *, integer *, - ftnlen); + extern /* Subroutine */ int dorgtr_(char *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, integer *, + ftnlen), dsteqr_(char *, integer *, doublereal *, doublereal *, + doublereal *, integer *, doublereal *, integer *, ftnlen), + dsytrd_(char *, integer *, doublereal *, integer *, doublereal *, + doublereal *, doublereal *, doublereal *, integer *, integer *, + ftnlen); integer llwork; doublereal smlnum; integer lwkopt; @@ -248,51 +248,51 @@ ices */ *info = 0; if (! (wantz || lsame_(jobz, (char *)"N", (ftnlen)1, (ftnlen)1))) { - *info = -1; + *info = -1; } else if (! (lower || lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1))) { - *info = -2; + *info = -2; } else if (*n < 0) { - *info = -3; + *info = -3; } else if (*lda < max(1,*n)) { - *info = -5; + *info = -5; } if (*info == 0) { - nb = ilaenv_(&c__1, (char *)"DSYTRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, - (ftnlen)1); + nb = ilaenv_(&c__1, (char *)"DSYTRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, + (ftnlen)1); /* Computing MAX */ - i__1 = 1, i__2 = (nb + 2) * *n; - lwkopt = max(i__1,i__2); - work[1] = (doublereal) lwkopt; + i__1 = 1, i__2 = (nb + 2) * *n; + lwkopt = max(i__1,i__2); + work[1] = (doublereal) lwkopt; /* Computing MAX */ - i__1 = 1, i__2 = *n * 3 - 1; - if (*lwork < max(i__1,i__2) && ! lquery) { - *info = -8; - } + i__1 = 1, i__2 = *n * 3 - 1; + if (*lwork < max(i__1,i__2) && ! lquery) { + *info = -8; + } } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DSYEV ", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DSYEV ", &i__1, (ftnlen)6); + return 0; } else if (lquery) { - return 0; + return 0; } /* Quick return if possible */ if (*n == 0) { - return 0; + return 0; } if (*n == 1) { - w[1] = a[a_dim1 + 1]; - work[1] = 2.; - if (wantz) { - a[a_dim1 + 1] = 1.; - } - return 0; + w[1] = a[a_dim1 + 1]; + work[1] = 2.; + if (wantz) { + a[a_dim1 + 1] = 1.; + } + return 0; } /* Get machine constants. */ @@ -307,18 +307,18 @@ ices */ /* Scale matrix to allowable range, if necessary. */ anrm = dlansy_((char *)"M", uplo, n, &a[a_offset], lda, &work[1], (ftnlen)1, ( - ftnlen)1); + ftnlen)1); iscale = 0; if (anrm > 0. && anrm < rmin) { - iscale = 1; - sigma = rmin / anrm; + iscale = 1; + sigma = rmin / anrm; } else if (anrm > rmax) { - iscale = 1; - sigma = rmax / anrm; + iscale = 1; + sigma = rmax / anrm; } if (iscale == 1) { - dlascl_(uplo, &c__0, &c__0, &c_b17, &sigma, n, n, &a[a_offset], lda, - info, (ftnlen)1); + dlascl_(uplo, &c__0, &c__0, &c_b17, &sigma, n, n, &a[a_offset], lda, + info, (ftnlen)1); } /* Call DSYTRD to reduce symmetric matrix to tridiagonal form. */ @@ -328,30 +328,30 @@ ices */ indwrk = indtau + *n; llwork = *lwork - indwrk + 1; dsytrd_(uplo, n, &a[a_offset], lda, &w[1], &work[inde], &work[indtau], & - work[indwrk], &llwork, &iinfo, (ftnlen)1); + work[indwrk], &llwork, &iinfo, (ftnlen)1); /* For eigenvalues only, call DSTERF. For eigenvectors, first call */ /* DORGTR to generate the orthogonal matrix, then call DSTEQR. */ if (! wantz) { - dsterf_(n, &w[1], &work[inde], info); + dsterf_(n, &w[1], &work[inde], info); } else { - dorgtr_(uplo, n, &a[a_offset], lda, &work[indtau], &work[indwrk], & - llwork, &iinfo, (ftnlen)1); - dsteqr_(jobz, n, &w[1], &work[inde], &a[a_offset], lda, &work[indtau], - info, (ftnlen)1); + dorgtr_(uplo, n, &a[a_offset], lda, &work[indtau], &work[indwrk], & + llwork, &iinfo, (ftnlen)1); + dsteqr_(jobz, n, &w[1], &work[inde], &a[a_offset], lda, &work[indtau], + info, (ftnlen)1); } /* If matrix was scaled, then rescale eigenvalues appropriately. */ if (iscale == 1) { - if (*info == 0) { - imax = *n; - } else { - imax = *info - 1; - } - d__1 = 1. / sigma; - dscal_(&imax, &d__1, &w[1], &c__1); + if (*info == 0) { + imax = *n; + } else { + imax = *info - 1; + } + d__1 = 1. / sigma; + dscal_(&imax, &d__1, &w[1], &c__1); } /* Set WORK(1) to optimal workspace size. */ @@ -365,5 +365,5 @@ ices */ } /* dsyev_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dsyevd.cpp b/lib/linalg/dsyevd.cpp index a0e0084884..2f8d5a145b 100644 --- a/lib/linalg/dsyevd.cpp +++ b/lib/linalg/dsyevd.cpp @@ -1,13 +1,13 @@ /* fortran/dsyevd.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -207,9 +207,9 @@ f"> */ /* > */ /* ===================================================================== */ /* Subroutine */ int dsyevd_(char *jobz, char *uplo, integer *n, doublereal * - a, integer *lda, doublereal *w, doublereal *work, integer *lwork, - integer *iwork, integer *liwork, integer *info, ftnlen jobz_len, - ftnlen uplo_len) + a, integer *lda, doublereal *w, doublereal *work, integer *lwork, + integer *iwork, integer *liwork, integer *info, ftnlen jobz_len, + ftnlen uplo_len) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; @@ -223,8 +223,8 @@ f"> */ integer inde; doublereal anrm, rmin, rmax; integer lopt; - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *); + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *); doublereal sigma; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer iinfo, lwmin, liopt; @@ -232,30 +232,30 @@ f"> */ integer indwk2, llwrk2; extern doublereal dlamch_(char *, ftnlen); integer iscale; - extern /* Subroutine */ int dlascl_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, integer *, doublereal *, - integer *, integer *, ftnlen), dstedc_(char *, integer *, - doublereal *, doublereal *, doublereal *, integer *, doublereal *, - integer *, integer *, integer *, integer *, ftnlen), dlacpy_( - char *, integer *, integer *, doublereal *, integer *, doublereal - *, integer *, ftnlen); + extern /* Subroutine */ int dlascl_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, integer *, doublereal *, + integer *, integer *, ftnlen), dstedc_(char *, integer *, + doublereal *, doublereal *, doublereal *, integer *, doublereal *, + integer *, integer *, integer *, integer *, ftnlen), dlacpy_( + char *, integer *, integer *, doublereal *, integer *, doublereal + *, integer *, ftnlen); doublereal safmin; - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); doublereal bignum; integer indtau; extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *, - integer *); - extern doublereal dlansy_(char *, char *, integer *, doublereal *, - integer *, doublereal *, ftnlen, ftnlen); + integer *); + extern doublereal dlansy_(char *, char *, integer *, doublereal *, + integer *, doublereal *, ftnlen, ftnlen); integer indwrk, liwmin; - extern /* Subroutine */ int dormtr_(char *, char *, char *, integer *, - integer *, doublereal *, integer *, doublereal *, doublereal *, - integer *, doublereal *, integer *, integer *, ftnlen, ftnlen, - ftnlen), dsytrd_(char *, integer *, doublereal *, integer *, - doublereal *, doublereal *, doublereal *, doublereal *, integer *, - integer *, ftnlen); + extern /* Subroutine */ int dormtr_(char *, char *, char *, integer *, + integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, integer *, ftnlen, ftnlen, + ftnlen), dsytrd_(char *, integer *, doublereal *, integer *, + doublereal *, doublereal *, doublereal *, doublereal *, integer *, + integer *, ftnlen); integer llwork; doublereal smlnum; logical lquery; @@ -302,67 +302,67 @@ f"> */ *info = 0; if (! (wantz || lsame_(jobz, (char *)"N", (ftnlen)1, (ftnlen)1))) { - *info = -1; + *info = -1; } else if (! (lower || lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1))) { - *info = -2; + *info = -2; } else if (*n < 0) { - *info = -3; + *info = -3; } else if (*lda < max(1,*n)) { - *info = -5; + *info = -5; } if (*info == 0) { - if (*n <= 1) { - liwmin = 1; - lwmin = 1; - lopt = lwmin; - liopt = liwmin; - } else { - if (wantz) { - liwmin = *n * 5 + 3; + if (*n <= 1) { + liwmin = 1; + lwmin = 1; + lopt = lwmin; + liopt = liwmin; + } else { + if (wantz) { + liwmin = *n * 5 + 3; /* Computing 2nd power */ - i__1 = *n; - lwmin = *n * 6 + 1 + (i__1 * i__1 << 1); - } else { - liwmin = 1; - lwmin = (*n << 1) + 1; - } + i__1 = *n; + lwmin = *n * 6 + 1 + (i__1 * i__1 << 1); + } else { + liwmin = 1; + lwmin = (*n << 1) + 1; + } /* Computing MAX */ - i__1 = lwmin, i__2 = (*n << 1) + *n * ilaenv_(&c__1, (char *)"DSYTRD", - uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); - lopt = max(i__1,i__2); - liopt = liwmin; - } - work[1] = (doublereal) lopt; - iwork[1] = liopt; + i__1 = lwmin, i__2 = (*n << 1) + *n * ilaenv_(&c__1, (char *)"DSYTRD", + uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); + lopt = max(i__1,i__2); + liopt = liwmin; + } + work[1] = (doublereal) lopt; + iwork[1] = liopt; - if (*lwork < lwmin && ! lquery) { - *info = -8; - } else if (*liwork < liwmin && ! lquery) { - *info = -10; - } + if (*lwork < lwmin && ! lquery) { + *info = -8; + } else if (*liwork < liwmin && ! lquery) { + *info = -10; + } } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DSYEVD", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DSYEVD", &i__1, (ftnlen)6); + return 0; } else if (lquery) { - return 0; + return 0; } /* Quick return if possible */ if (*n == 0) { - return 0; + return 0; } if (*n == 1) { - w[1] = a[a_dim1 + 1]; - if (wantz) { - a[a_dim1 + 1] = 1.; - } - return 0; + w[1] = a[a_dim1 + 1]; + if (wantz) { + a[a_dim1 + 1] = 1.; + } + return 0; } /* Get machine constants. */ @@ -377,18 +377,18 @@ f"> */ /* Scale matrix to allowable range, if necessary. */ anrm = dlansy_((char *)"M", uplo, n, &a[a_offset], lda, &work[1], (ftnlen)1, ( - ftnlen)1); + ftnlen)1); iscale = 0; if (anrm > 0. && anrm < rmin) { - iscale = 1; - sigma = rmin / anrm; + iscale = 1; + sigma = rmin / anrm; } else if (anrm > rmax) { - iscale = 1; - sigma = rmax / anrm; + iscale = 1; + sigma = rmax / anrm; } if (iscale == 1) { - dlascl_(uplo, &c__0, &c__0, &c_b17, &sigma, n, n, &a[a_offset], lda, - info, (ftnlen)1); + dlascl_(uplo, &c__0, &c__0, &c_b17, &sigma, n, n, &a[a_offset], lda, + info, (ftnlen)1); } /* Call DSYTRD to reduce symmetric matrix to tridiagonal form. */ @@ -401,7 +401,7 @@ f"> */ llwrk2 = *lwork - indwk2 + 1; dsytrd_(uplo, n, &a[a_offset], lda, &w[1], &work[inde], &work[indtau], & - work[indwrk], &llwork, &iinfo, (ftnlen)1); + work[indwrk], &llwork, &iinfo, (ftnlen)1); /* For eigenvalues only, call DSTERF. For eigenvectors, first call */ /* DSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the */ @@ -409,21 +409,21 @@ f"> */ /* Householder transformations stored in A. */ if (! wantz) { - dsterf_(n, &w[1], &work[inde], info); + dsterf_(n, &w[1], &work[inde], info); } else { - dstedc_((char *)"I", n, &w[1], &work[inde], &work[indwrk], n, &work[indwk2], & - llwrk2, &iwork[1], liwork, info, (ftnlen)1); - dormtr_((char *)"L", uplo, (char *)"N", n, n, &a[a_offset], lda, &work[indtau], &work[ - indwrk], n, &work[indwk2], &llwrk2, &iinfo, (ftnlen)1, ( - ftnlen)1, (ftnlen)1); - dlacpy_((char *)"A", n, n, &work[indwrk], n, &a[a_offset], lda, (ftnlen)1); + dstedc_((char *)"I", n, &w[1], &work[inde], &work[indwrk], n, &work[indwk2], & + llwrk2, &iwork[1], liwork, info, (ftnlen)1); + dormtr_((char *)"L", uplo, (char *)"N", n, n, &a[a_offset], lda, &work[indtau], &work[ + indwrk], n, &work[indwk2], &llwrk2, &iinfo, (ftnlen)1, ( + ftnlen)1, (ftnlen)1); + dlacpy_((char *)"A", n, n, &work[indwrk], n, &a[a_offset], lda, (ftnlen)1); } /* If matrix was scaled, then rescale eigenvalues appropriately. */ if (iscale == 1) { - d__1 = 1. / sigma; - dscal_(n, &d__1, &w[1], &c__1); + d__1 = 1. / sigma; + dscal_(n, &d__1, &w[1], &c__1); } work[1] = (doublereal) lopt; @@ -436,5 +436,5 @@ f"> */ } /* dsyevd_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dsygs2.cpp b/lib/linalg/dsygs2.cpp index 8b0089be28..785aeb4f27 100644 --- a/lib/linalg/dsygs2.cpp +++ b/lib/linalg/dsygs2.cpp @@ -1,13 +1,13 @@ /* fortran/dsygs2.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -150,9 +150,9 @@ f"> */ /* > \ingroup doubleSYcomputational */ /* ===================================================================== */ -/* Subroutine */ int dsygs2_(integer *itype, char *uplo, integer *n, - doublereal *a, integer *lda, doublereal *b, integer *ldb, integer * - info, ftnlen uplo_len) +/* Subroutine */ int dsygs2_(integer *itype, char *uplo, integer *n, + doublereal *a, integer *lda, doublereal *b, integer *ldb, integer * + info, ftnlen uplo_len) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2; @@ -161,19 +161,19 @@ f"> */ /* Local variables */ integer k; doublereal ct, akk, bkk; - extern /* Subroutine */ int dsyr2_(char *, integer *, doublereal *, - doublereal *, integer *, doublereal *, integer *, doublereal *, - integer *, ftnlen), dscal_(integer *, doublereal *, doublereal *, - integer *); + extern /* Subroutine */ int dsyr2_(char *, integer *, doublereal *, + doublereal *, integer *, doublereal *, integer *, doublereal *, + integer *, ftnlen), dscal_(integer *, doublereal *, doublereal *, + integer *); extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *, - integer *, doublereal *, integer *); + extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *); logical upper; - extern /* Subroutine */ int dtrmv_(char *, char *, char *, integer *, - doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, - ftnlen), dtrsv_(char *, char *, char *, integer *, doublereal *, - integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen), - xerbla_(char *, integer *, ftnlen); + extern /* Subroutine */ int dtrmv_(char *, char *, char *, integer *, + doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, + ftnlen), dtrsv_(char *, char *, char *, integer *, doublereal *, + integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen), + xerbla_(char *, integer *, ftnlen); /* -- LAPACK computational routine -- */ @@ -213,162 +213,162 @@ f"> */ *info = 0; upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); if (*itype < 1 || *itype > 3) { - *info = -1; + *info = -1; } else if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { - *info = -2; + *info = -2; } else if (*n < 0) { - *info = -3; + *info = -3; } else if (*lda < max(1,*n)) { - *info = -5; + *info = -5; } else if (*ldb < max(1,*n)) { - *info = -7; + *info = -7; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DSYGS2", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DSYGS2", &i__1, (ftnlen)6); + return 0; } if (*itype == 1) { - if (upper) { + if (upper) { /* Compute inv(U**T)*A*inv(U) */ - i__1 = *n; - for (k = 1; k <= i__1; ++k) { + i__1 = *n; + for (k = 1; k <= i__1; ++k) { /* Update the upper triangle of A(k:n,k:n) */ - akk = a[k + k * a_dim1]; - bkk = b[k + k * b_dim1]; + akk = a[k + k * a_dim1]; + bkk = b[k + k * b_dim1]; /* Computing 2nd power */ - d__1 = bkk; - akk /= d__1 * d__1; - a[k + k * a_dim1] = akk; - if (k < *n) { - i__2 = *n - k; - d__1 = 1. / bkk; - dscal_(&i__2, &d__1, &a[k + (k + 1) * a_dim1], lda); - ct = akk * -.5; - i__2 = *n - k; - daxpy_(&i__2, &ct, &b[k + (k + 1) * b_dim1], ldb, &a[k + ( - k + 1) * a_dim1], lda); - i__2 = *n - k; - dsyr2_(uplo, &i__2, &c_b6, &a[k + (k + 1) * a_dim1], lda, - &b[k + (k + 1) * b_dim1], ldb, &a[k + 1 + (k + 1) - * a_dim1], lda, (ftnlen)1); - i__2 = *n - k; - daxpy_(&i__2, &ct, &b[k + (k + 1) * b_dim1], ldb, &a[k + ( - k + 1) * a_dim1], lda); - i__2 = *n - k; - dtrsv_(uplo, (char *)"Transpose", (char *)"Non-unit", &i__2, &b[k + 1 + ( - k + 1) * b_dim1], ldb, &a[k + (k + 1) * a_dim1], - lda, (ftnlen)1, (ftnlen)9, (ftnlen)8); - } + d__1 = bkk; + akk /= d__1 * d__1; + a[k + k * a_dim1] = akk; + if (k < *n) { + i__2 = *n - k; + d__1 = 1. / bkk; + dscal_(&i__2, &d__1, &a[k + (k + 1) * a_dim1], lda); + ct = akk * -.5; + i__2 = *n - k; + daxpy_(&i__2, &ct, &b[k + (k + 1) * b_dim1], ldb, &a[k + ( + k + 1) * a_dim1], lda); + i__2 = *n - k; + dsyr2_(uplo, &i__2, &c_b6, &a[k + (k + 1) * a_dim1], lda, + &b[k + (k + 1) * b_dim1], ldb, &a[k + 1 + (k + 1) + * a_dim1], lda, (ftnlen)1); + i__2 = *n - k; + daxpy_(&i__2, &ct, &b[k + (k + 1) * b_dim1], ldb, &a[k + ( + k + 1) * a_dim1], lda); + i__2 = *n - k; + dtrsv_(uplo, (char *)"Transpose", (char *)"Non-unit", &i__2, &b[k + 1 + ( + k + 1) * b_dim1], ldb, &a[k + (k + 1) * a_dim1], + lda, (ftnlen)1, (ftnlen)9, (ftnlen)8); + } /* L10: */ - } - } else { + } + } else { /* Compute inv(L)*A*inv(L**T) */ - i__1 = *n; - for (k = 1; k <= i__1; ++k) { + i__1 = *n; + for (k = 1; k <= i__1; ++k) { /* Update the lower triangle of A(k:n,k:n) */ - akk = a[k + k * a_dim1]; - bkk = b[k + k * b_dim1]; + akk = a[k + k * a_dim1]; + bkk = b[k + k * b_dim1]; /* Computing 2nd power */ - d__1 = bkk; - akk /= d__1 * d__1; - a[k + k * a_dim1] = akk; - if (k < *n) { - i__2 = *n - k; - d__1 = 1. / bkk; - dscal_(&i__2, &d__1, &a[k + 1 + k * a_dim1], &c__1); - ct = akk * -.5; - i__2 = *n - k; - daxpy_(&i__2, &ct, &b[k + 1 + k * b_dim1], &c__1, &a[k + - 1 + k * a_dim1], &c__1); - i__2 = *n - k; - dsyr2_(uplo, &i__2, &c_b6, &a[k + 1 + k * a_dim1], &c__1, - &b[k + 1 + k * b_dim1], &c__1, &a[k + 1 + (k + 1) - * a_dim1], lda, (ftnlen)1); - i__2 = *n - k; - daxpy_(&i__2, &ct, &b[k + 1 + k * b_dim1], &c__1, &a[k + - 1 + k * a_dim1], &c__1); - i__2 = *n - k; - dtrsv_(uplo, (char *)"No transpose", (char *)"Non-unit", &i__2, &b[k + 1 - + (k + 1) * b_dim1], ldb, &a[k + 1 + k * a_dim1], - &c__1, (ftnlen)1, (ftnlen)12, (ftnlen)8); - } + d__1 = bkk; + akk /= d__1 * d__1; + a[k + k * a_dim1] = akk; + if (k < *n) { + i__2 = *n - k; + d__1 = 1. / bkk; + dscal_(&i__2, &d__1, &a[k + 1 + k * a_dim1], &c__1); + ct = akk * -.5; + i__2 = *n - k; + daxpy_(&i__2, &ct, &b[k + 1 + k * b_dim1], &c__1, &a[k + + 1 + k * a_dim1], &c__1); + i__2 = *n - k; + dsyr2_(uplo, &i__2, &c_b6, &a[k + 1 + k * a_dim1], &c__1, + &b[k + 1 + k * b_dim1], &c__1, &a[k + 1 + (k + 1) + * a_dim1], lda, (ftnlen)1); + i__2 = *n - k; + daxpy_(&i__2, &ct, &b[k + 1 + k * b_dim1], &c__1, &a[k + + 1 + k * a_dim1], &c__1); + i__2 = *n - k; + dtrsv_(uplo, (char *)"No transpose", (char *)"Non-unit", &i__2, &b[k + 1 + + (k + 1) * b_dim1], ldb, &a[k + 1 + k * a_dim1], + &c__1, (ftnlen)1, (ftnlen)12, (ftnlen)8); + } /* L20: */ - } - } + } + } } else { - if (upper) { + if (upper) { /* Compute U*A*U**T */ - i__1 = *n; - for (k = 1; k <= i__1; ++k) { + i__1 = *n; + for (k = 1; k <= i__1; ++k) { /* Update the upper triangle of A(1:k,1:k) */ - akk = a[k + k * a_dim1]; - bkk = b[k + k * b_dim1]; - i__2 = k - 1; - dtrmv_(uplo, (char *)"No transpose", (char *)"Non-unit", &i__2, &b[b_offset], - ldb, &a[k * a_dim1 + 1], &c__1, (ftnlen)1, (ftnlen)12, - (ftnlen)8); - ct = akk * .5; - i__2 = k - 1; - daxpy_(&i__2, &ct, &b[k * b_dim1 + 1], &c__1, &a[k * a_dim1 + - 1], &c__1); - i__2 = k - 1; - dsyr2_(uplo, &i__2, &c_b27, &a[k * a_dim1 + 1], &c__1, &b[k * - b_dim1 + 1], &c__1, &a[a_offset], lda, (ftnlen)1); - i__2 = k - 1; - daxpy_(&i__2, &ct, &b[k * b_dim1 + 1], &c__1, &a[k * a_dim1 + - 1], &c__1); - i__2 = k - 1; - dscal_(&i__2, &bkk, &a[k * a_dim1 + 1], &c__1); + akk = a[k + k * a_dim1]; + bkk = b[k + k * b_dim1]; + i__2 = k - 1; + dtrmv_(uplo, (char *)"No transpose", (char *)"Non-unit", &i__2, &b[b_offset], + ldb, &a[k * a_dim1 + 1], &c__1, (ftnlen)1, (ftnlen)12, + (ftnlen)8); + ct = akk * .5; + i__2 = k - 1; + daxpy_(&i__2, &ct, &b[k * b_dim1 + 1], &c__1, &a[k * a_dim1 + + 1], &c__1); + i__2 = k - 1; + dsyr2_(uplo, &i__2, &c_b27, &a[k * a_dim1 + 1], &c__1, &b[k * + b_dim1 + 1], &c__1, &a[a_offset], lda, (ftnlen)1); + i__2 = k - 1; + daxpy_(&i__2, &ct, &b[k * b_dim1 + 1], &c__1, &a[k * a_dim1 + + 1], &c__1); + i__2 = k - 1; + dscal_(&i__2, &bkk, &a[k * a_dim1 + 1], &c__1); /* Computing 2nd power */ - d__1 = bkk; - a[k + k * a_dim1] = akk * (d__1 * d__1); + d__1 = bkk; + a[k + k * a_dim1] = akk * (d__1 * d__1); /* L30: */ - } - } else { + } + } else { /* Compute L**T *A*L */ - i__1 = *n; - for (k = 1; k <= i__1; ++k) { + i__1 = *n; + for (k = 1; k <= i__1; ++k) { /* Update the lower triangle of A(1:k,1:k) */ - akk = a[k + k * a_dim1]; - bkk = b[k + k * b_dim1]; - i__2 = k - 1; - dtrmv_(uplo, (char *)"Transpose", (char *)"Non-unit", &i__2, &b[b_offset], - ldb, &a[k + a_dim1], lda, (ftnlen)1, (ftnlen)9, ( - ftnlen)8); - ct = akk * .5; - i__2 = k - 1; - daxpy_(&i__2, &ct, &b[k + b_dim1], ldb, &a[k + a_dim1], lda); - i__2 = k - 1; - dsyr2_(uplo, &i__2, &c_b27, &a[k + a_dim1], lda, &b[k + - b_dim1], ldb, &a[a_offset], lda, (ftnlen)1); - i__2 = k - 1; - daxpy_(&i__2, &ct, &b[k + b_dim1], ldb, &a[k + a_dim1], lda); - i__2 = k - 1; - dscal_(&i__2, &bkk, &a[k + a_dim1], lda); + akk = a[k + k * a_dim1]; + bkk = b[k + k * b_dim1]; + i__2 = k - 1; + dtrmv_(uplo, (char *)"Transpose", (char *)"Non-unit", &i__2, &b[b_offset], + ldb, &a[k + a_dim1], lda, (ftnlen)1, (ftnlen)9, ( + ftnlen)8); + ct = akk * .5; + i__2 = k - 1; + daxpy_(&i__2, &ct, &b[k + b_dim1], ldb, &a[k + a_dim1], lda); + i__2 = k - 1; + dsyr2_(uplo, &i__2, &c_b27, &a[k + a_dim1], lda, &b[k + + b_dim1], ldb, &a[a_offset], lda, (ftnlen)1); + i__2 = k - 1; + daxpy_(&i__2, &ct, &b[k + b_dim1], ldb, &a[k + a_dim1], lda); + i__2 = k - 1; + dscal_(&i__2, &bkk, &a[k + a_dim1], lda); /* Computing 2nd power */ - d__1 = bkk; - a[k + k * a_dim1] = akk * (d__1 * d__1); + d__1 = bkk; + a[k + k * a_dim1] = akk * (d__1 * d__1); /* L40: */ - } - } + } + } } return 0; @@ -377,5 +377,5 @@ f"> */ } /* dsygs2_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dsygst.cpp b/lib/linalg/dsygst.cpp index 2f5189a6f1..0ad89918d3 100644 --- a/lib/linalg/dsygst.cpp +++ b/lib/linalg/dsygst.cpp @@ -1,13 +1,13 @@ /* fortran/dsygst.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -152,9 +152,9 @@ f"> */ /* > \ingroup doubleSYcomputational */ /* ===================================================================== */ -/* Subroutine */ int dsygst_(integer *itype, char *uplo, integer *n, - doublereal *a, integer *lda, doublereal *b, integer *ldb, integer * - info, ftnlen uplo_len) +/* Subroutine */ int dsygst_(integer *itype, char *uplo, integer *n, + doublereal *a, integer *lda, doublereal *b, integer *ldb, integer * + info, ftnlen uplo_len) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3; @@ -162,23 +162,23 @@ f"> */ /* Local variables */ integer k, kb, nb; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int dtrmm_(char *, char *, char *, char *, - integer *, integer *, doublereal *, doublereal *, integer *, - doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen), dsymm_( - char *, char *, integer *, integer *, doublereal *, doublereal *, - integer *, doublereal *, integer *, doublereal *, doublereal *, - integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dtrmm_(char *, char *, char *, char *, + integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen), dsymm_( + char *, char *, integer *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, ftnlen, ftnlen); logical upper; - extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, - integer *, integer *, doublereal *, doublereal *, integer *, - doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen), dsygs2_( - integer *, char *, integer *, doublereal *, integer *, doublereal - *, integer *, integer *, ftnlen), dsyr2k_(char *, char *, integer - *, integer *, doublereal *, doublereal *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen) - , xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, + integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen), dsygs2_( + integer *, char *, integer *, doublereal *, integer *, doublereal + *, integer *, integer *, ftnlen), dsyr2k_(char *, char *, integer + *, integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen) + , xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); /* -- LAPACK computational routine -- */ @@ -218,212 +218,212 @@ f"> */ *info = 0; upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); if (*itype < 1 || *itype > 3) { - *info = -1; + *info = -1; } else if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { - *info = -2; + *info = -2; } else if (*n < 0) { - *info = -3; + *info = -3; } else if (*lda < max(1,*n)) { - *info = -5; + *info = -5; } else if (*ldb < max(1,*n)) { - *info = -7; + *info = -7; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DSYGST", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DSYGST", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*n == 0) { - return 0; + return 0; } /* Determine the block size for this environment. */ nb = ilaenv_(&c__1, (char *)"DSYGST", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, ( - ftnlen)1); + ftnlen)1); if (nb <= 1 || nb >= *n) { /* Use unblocked code */ - dsygs2_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info, ( - ftnlen)1); + dsygs2_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info, ( + ftnlen)1); } else { /* Use blocked code */ - if (*itype == 1) { - if (upper) { + if (*itype == 1) { + if (upper) { /* Compute inv(U**T)*A*inv(U) */ - i__1 = *n; - i__2 = nb; - for (k = 1; i__2 < 0 ? k >= i__1 : k <= i__1; k += i__2) { + i__1 = *n; + i__2 = nb; + for (k = 1; i__2 < 0 ? k >= i__1 : k <= i__1; k += i__2) { /* Computing MIN */ - i__3 = *n - k + 1; - kb = min(i__3,nb); + i__3 = *n - k + 1; + kb = min(i__3,nb); /* Update the upper triangle of A(k:n,k:n) */ - dsygs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k + - k * b_dim1], ldb, info, (ftnlen)1); - if (k + kb <= *n) { - i__3 = *n - k - kb + 1; - dtrsm_((char *)"Left", uplo, (char *)"Transpose", (char *)"Non-unit", &kb, & - i__3, &c_b14, &b[k + k * b_dim1], ldb, &a[k + - (k + kb) * a_dim1], lda, (ftnlen)4, (ftnlen)1, - (ftnlen)9, (ftnlen)8); - i__3 = *n - k - kb + 1; - dsymm_((char *)"Left", uplo, &kb, &i__3, &c_b16, &a[k + k * - a_dim1], lda, &b[k + (k + kb) * b_dim1], ldb, - &c_b14, &a[k + (k + kb) * a_dim1], lda, ( - ftnlen)4, (ftnlen)1); - i__3 = *n - k - kb + 1; - dsyr2k_(uplo, (char *)"Transpose", &i__3, &kb, &c_b19, &a[k + - (k + kb) * a_dim1], lda, &b[k + (k + kb) * - b_dim1], ldb, &c_b14, &a[k + kb + (k + kb) * - a_dim1], lda, (ftnlen)1, (ftnlen)9); - i__3 = *n - k - kb + 1; - dsymm_((char *)"Left", uplo, &kb, &i__3, &c_b16, &a[k + k * - a_dim1], lda, &b[k + (k + kb) * b_dim1], ldb, - &c_b14, &a[k + (k + kb) * a_dim1], lda, ( - ftnlen)4, (ftnlen)1); - i__3 = *n - k - kb + 1; - dtrsm_((char *)"Right", uplo, (char *)"No transpose", (char *)"Non-unit", &kb, - &i__3, &c_b14, &b[k + kb + (k + kb) * b_dim1] - , ldb, &a[k + (k + kb) * a_dim1], lda, ( - ftnlen)5, (ftnlen)1, (ftnlen)12, (ftnlen)8); - } + dsygs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k + + k * b_dim1], ldb, info, (ftnlen)1); + if (k + kb <= *n) { + i__3 = *n - k - kb + 1; + dtrsm_((char *)"Left", uplo, (char *)"Transpose", (char *)"Non-unit", &kb, & + i__3, &c_b14, &b[k + k * b_dim1], ldb, &a[k + + (k + kb) * a_dim1], lda, (ftnlen)4, (ftnlen)1, + (ftnlen)9, (ftnlen)8); + i__3 = *n - k - kb + 1; + dsymm_((char *)"Left", uplo, &kb, &i__3, &c_b16, &a[k + k * + a_dim1], lda, &b[k + (k + kb) * b_dim1], ldb, + &c_b14, &a[k + (k + kb) * a_dim1], lda, ( + ftnlen)4, (ftnlen)1); + i__3 = *n - k - kb + 1; + dsyr2k_(uplo, (char *)"Transpose", &i__3, &kb, &c_b19, &a[k + + (k + kb) * a_dim1], lda, &b[k + (k + kb) * + b_dim1], ldb, &c_b14, &a[k + kb + (k + kb) * + a_dim1], lda, (ftnlen)1, (ftnlen)9); + i__3 = *n - k - kb + 1; + dsymm_((char *)"Left", uplo, &kb, &i__3, &c_b16, &a[k + k * + a_dim1], lda, &b[k + (k + kb) * b_dim1], ldb, + &c_b14, &a[k + (k + kb) * a_dim1], lda, ( + ftnlen)4, (ftnlen)1); + i__3 = *n - k - kb + 1; + dtrsm_((char *)"Right", uplo, (char *)"No transpose", (char *)"Non-unit", &kb, + &i__3, &c_b14, &b[k + kb + (k + kb) * b_dim1] + , ldb, &a[k + (k + kb) * a_dim1], lda, ( + ftnlen)5, (ftnlen)1, (ftnlen)12, (ftnlen)8); + } /* L10: */ - } - } else { + } + } else { /* Compute inv(L)*A*inv(L**T) */ - i__2 = *n; - i__1 = nb; - for (k = 1; i__1 < 0 ? k >= i__2 : k <= i__2; k += i__1) { + i__2 = *n; + i__1 = nb; + for (k = 1; i__1 < 0 ? k >= i__2 : k <= i__2; k += i__1) { /* Computing MIN */ - i__3 = *n - k + 1; - kb = min(i__3,nb); + i__3 = *n - k + 1; + kb = min(i__3,nb); /* Update the lower triangle of A(k:n,k:n) */ - dsygs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k + - k * b_dim1], ldb, info, (ftnlen)1); - if (k + kb <= *n) { - i__3 = *n - k - kb + 1; - dtrsm_((char *)"Right", uplo, (char *)"Transpose", (char *)"Non-unit", &i__3, - &kb, &c_b14, &b[k + k * b_dim1], ldb, &a[k + - kb + k * a_dim1], lda, (ftnlen)5, (ftnlen)1, ( - ftnlen)9, (ftnlen)8); - i__3 = *n - k - kb + 1; - dsymm_((char *)"Right", uplo, &i__3, &kb, &c_b16, &a[k + k * - a_dim1], lda, &b[k + kb + k * b_dim1], ldb, & - c_b14, &a[k + kb + k * a_dim1], lda, (ftnlen) - 5, (ftnlen)1); - i__3 = *n - k - kb + 1; - dsyr2k_(uplo, (char *)"No transpose", &i__3, &kb, &c_b19, &a[ - k + kb + k * a_dim1], lda, &b[k + kb + k * - b_dim1], ldb, &c_b14, &a[k + kb + (k + kb) * - a_dim1], lda, (ftnlen)1, (ftnlen)12); - i__3 = *n - k - kb + 1; - dsymm_((char *)"Right", uplo, &i__3, &kb, &c_b16, &a[k + k * - a_dim1], lda, &b[k + kb + k * b_dim1], ldb, & - c_b14, &a[k + kb + k * a_dim1], lda, (ftnlen) - 5, (ftnlen)1); - i__3 = *n - k - kb + 1; - dtrsm_((char *)"Left", uplo, (char *)"No transpose", (char *)"Non-unit", & - i__3, &kb, &c_b14, &b[k + kb + (k + kb) * - b_dim1], ldb, &a[k + kb + k * a_dim1], lda, ( - ftnlen)4, (ftnlen)1, (ftnlen)12, (ftnlen)8); - } + dsygs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k + + k * b_dim1], ldb, info, (ftnlen)1); + if (k + kb <= *n) { + i__3 = *n - k - kb + 1; + dtrsm_((char *)"Right", uplo, (char *)"Transpose", (char *)"Non-unit", &i__3, + &kb, &c_b14, &b[k + k * b_dim1], ldb, &a[k + + kb + k * a_dim1], lda, (ftnlen)5, (ftnlen)1, ( + ftnlen)9, (ftnlen)8); + i__3 = *n - k - kb + 1; + dsymm_((char *)"Right", uplo, &i__3, &kb, &c_b16, &a[k + k * + a_dim1], lda, &b[k + kb + k * b_dim1], ldb, & + c_b14, &a[k + kb + k * a_dim1], lda, (ftnlen) + 5, (ftnlen)1); + i__3 = *n - k - kb + 1; + dsyr2k_(uplo, (char *)"No transpose", &i__3, &kb, &c_b19, &a[ + k + kb + k * a_dim1], lda, &b[k + kb + k * + b_dim1], ldb, &c_b14, &a[k + kb + (k + kb) * + a_dim1], lda, (ftnlen)1, (ftnlen)12); + i__3 = *n - k - kb + 1; + dsymm_((char *)"Right", uplo, &i__3, &kb, &c_b16, &a[k + k * + a_dim1], lda, &b[k + kb + k * b_dim1], ldb, & + c_b14, &a[k + kb + k * a_dim1], lda, (ftnlen) + 5, (ftnlen)1); + i__3 = *n - k - kb + 1; + dtrsm_((char *)"Left", uplo, (char *)"No transpose", (char *)"Non-unit", & + i__3, &kb, &c_b14, &b[k + kb + (k + kb) * + b_dim1], ldb, &a[k + kb + k * a_dim1], lda, ( + ftnlen)4, (ftnlen)1, (ftnlen)12, (ftnlen)8); + } /* L20: */ - } - } - } else { - if (upper) { + } + } + } else { + if (upper) { /* Compute U*A*U**T */ - i__1 = *n; - i__2 = nb; - for (k = 1; i__2 < 0 ? k >= i__1 : k <= i__1; k += i__2) { + i__1 = *n; + i__2 = nb; + for (k = 1; i__2 < 0 ? k >= i__1 : k <= i__1; k += i__2) { /* Computing MIN */ - i__3 = *n - k + 1; - kb = min(i__3,nb); + i__3 = *n - k + 1; + kb = min(i__3,nb); /* Update the upper triangle of A(1:k+kb-1,1:k+kb-1) */ - i__3 = k - 1; - dtrmm_((char *)"Left", uplo, (char *)"No transpose", (char *)"Non-unit", &i__3, & - kb, &c_b14, &b[b_offset], ldb, &a[k * a_dim1 + 1], - lda, (ftnlen)4, (ftnlen)1, (ftnlen)12, (ftnlen)8) - ; - i__3 = k - 1; - dsymm_((char *)"Right", uplo, &i__3, &kb, &c_b52, &a[k + k * - a_dim1], lda, &b[k * b_dim1 + 1], ldb, &c_b14, &a[ - k * a_dim1 + 1], lda, (ftnlen)5, (ftnlen)1); - i__3 = k - 1; - dsyr2k_(uplo, (char *)"No transpose", &i__3, &kb, &c_b14, &a[k * - a_dim1 + 1], lda, &b[k * b_dim1 + 1], ldb, &c_b14, - &a[a_offset], lda, (ftnlen)1, (ftnlen)12); - i__3 = k - 1; - dsymm_((char *)"Right", uplo, &i__3, &kb, &c_b52, &a[k + k * - a_dim1], lda, &b[k * b_dim1 + 1], ldb, &c_b14, &a[ - k * a_dim1 + 1], lda, (ftnlen)5, (ftnlen)1); - i__3 = k - 1; - dtrmm_((char *)"Right", uplo, (char *)"Transpose", (char *)"Non-unit", &i__3, &kb, - &c_b14, &b[k + k * b_dim1], ldb, &a[k * a_dim1 + - 1], lda, (ftnlen)5, (ftnlen)1, (ftnlen)9, (ftnlen) - 8); - dsygs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k + - k * b_dim1], ldb, info, (ftnlen)1); + i__3 = k - 1; + dtrmm_((char *)"Left", uplo, (char *)"No transpose", (char *)"Non-unit", &i__3, & + kb, &c_b14, &b[b_offset], ldb, &a[k * a_dim1 + 1], + lda, (ftnlen)4, (ftnlen)1, (ftnlen)12, (ftnlen)8) + ; + i__3 = k - 1; + dsymm_((char *)"Right", uplo, &i__3, &kb, &c_b52, &a[k + k * + a_dim1], lda, &b[k * b_dim1 + 1], ldb, &c_b14, &a[ + k * a_dim1 + 1], lda, (ftnlen)5, (ftnlen)1); + i__3 = k - 1; + dsyr2k_(uplo, (char *)"No transpose", &i__3, &kb, &c_b14, &a[k * + a_dim1 + 1], lda, &b[k * b_dim1 + 1], ldb, &c_b14, + &a[a_offset], lda, (ftnlen)1, (ftnlen)12); + i__3 = k - 1; + dsymm_((char *)"Right", uplo, &i__3, &kb, &c_b52, &a[k + k * + a_dim1], lda, &b[k * b_dim1 + 1], ldb, &c_b14, &a[ + k * a_dim1 + 1], lda, (ftnlen)5, (ftnlen)1); + i__3 = k - 1; + dtrmm_((char *)"Right", uplo, (char *)"Transpose", (char *)"Non-unit", &i__3, &kb, + &c_b14, &b[k + k * b_dim1], ldb, &a[k * a_dim1 + + 1], lda, (ftnlen)5, (ftnlen)1, (ftnlen)9, (ftnlen) + 8); + dsygs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k + + k * b_dim1], ldb, info, (ftnlen)1); /* L30: */ - } - } else { + } + } else { /* Compute L**T*A*L */ - i__2 = *n; - i__1 = nb; - for (k = 1; i__1 < 0 ? k >= i__2 : k <= i__2; k += i__1) { + i__2 = *n; + i__1 = nb; + for (k = 1; i__1 < 0 ? k >= i__2 : k <= i__2; k += i__1) { /* Computing MIN */ - i__3 = *n - k + 1; - kb = min(i__3,nb); + i__3 = *n - k + 1; + kb = min(i__3,nb); /* Update the lower triangle of A(1:k+kb-1,1:k+kb-1) */ - i__3 = k - 1; - dtrmm_((char *)"Right", uplo, (char *)"No transpose", (char *)"Non-unit", &kb, & - i__3, &c_b14, &b[b_offset], ldb, &a[k + a_dim1], - lda, (ftnlen)5, (ftnlen)1, (ftnlen)12, (ftnlen)8); - i__3 = k - 1; - dsymm_((char *)"Left", uplo, &kb, &i__3, &c_b52, &a[k + k * - a_dim1], lda, &b[k + b_dim1], ldb, &c_b14, &a[k + - a_dim1], lda, (ftnlen)4, (ftnlen)1); - i__3 = k - 1; - dsyr2k_(uplo, (char *)"Transpose", &i__3, &kb, &c_b14, &a[k + - a_dim1], lda, &b[k + b_dim1], ldb, &c_b14, &a[ - a_offset], lda, (ftnlen)1, (ftnlen)9); - i__3 = k - 1; - dsymm_((char *)"Left", uplo, &kb, &i__3, &c_b52, &a[k + k * - a_dim1], lda, &b[k + b_dim1], ldb, &c_b14, &a[k + - a_dim1], lda, (ftnlen)4, (ftnlen)1); - i__3 = k - 1; - dtrmm_((char *)"Left", uplo, (char *)"Transpose", (char *)"Non-unit", &kb, &i__3, - &c_b14, &b[k + k * b_dim1], ldb, &a[k + a_dim1], - lda, (ftnlen)4, (ftnlen)1, (ftnlen)9, (ftnlen)8); - dsygs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k + - k * b_dim1], ldb, info, (ftnlen)1); + i__3 = k - 1; + dtrmm_((char *)"Right", uplo, (char *)"No transpose", (char *)"Non-unit", &kb, & + i__3, &c_b14, &b[b_offset], ldb, &a[k + a_dim1], + lda, (ftnlen)5, (ftnlen)1, (ftnlen)12, (ftnlen)8); + i__3 = k - 1; + dsymm_((char *)"Left", uplo, &kb, &i__3, &c_b52, &a[k + k * + a_dim1], lda, &b[k + b_dim1], ldb, &c_b14, &a[k + + a_dim1], lda, (ftnlen)4, (ftnlen)1); + i__3 = k - 1; + dsyr2k_(uplo, (char *)"Transpose", &i__3, &kb, &c_b14, &a[k + + a_dim1], lda, &b[k + b_dim1], ldb, &c_b14, &a[ + a_offset], lda, (ftnlen)1, (ftnlen)9); + i__3 = k - 1; + dsymm_((char *)"Left", uplo, &kb, &i__3, &c_b52, &a[k + k * + a_dim1], lda, &b[k + b_dim1], ldb, &c_b14, &a[k + + a_dim1], lda, (ftnlen)4, (ftnlen)1); + i__3 = k - 1; + dtrmm_((char *)"Left", uplo, (char *)"Transpose", (char *)"Non-unit", &kb, &i__3, + &c_b14, &b[k + k * b_dim1], ldb, &a[k + a_dim1], + lda, (ftnlen)4, (ftnlen)1, (ftnlen)9, (ftnlen)8); + dsygs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k + + k * b_dim1], ldb, info, (ftnlen)1); /* L40: */ - } - } - } + } + } + } } return 0; @@ -432,5 +432,5 @@ f"> */ } /* dsygst_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dsygv.cpp b/lib/linalg/dsygv.cpp index e7078e8006..bc7ed2cc76 100644 --- a/lib/linalg/dsygv.cpp +++ b/lib/linalg/dsygv.cpp @@ -1,13 +1,13 @@ /* fortran/dsygv.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -197,9 +197,9 @@ static doublereal c_b16 = 1.; /* ===================================================================== */ /* Subroutine */ int dsygv_(integer *itype, char *jobz, char *uplo, integer * - n, doublereal *a, integer *lda, doublereal *b, integer *ldb, - doublereal *w, doublereal *work, integer *lwork, integer *info, - ftnlen jobz_len, ftnlen uplo_len) + n, doublereal *a, integer *lda, doublereal *b, integer *ldb, + doublereal *w, doublereal *work, integer *lwork, integer *info, + ftnlen jobz_len, ftnlen uplo_len) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2; @@ -207,27 +207,27 @@ static doublereal c_b16 = 1.; /* Local variables */ integer nb, neig; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int dtrmm_(char *, char *, char *, char *, - integer *, integer *, doublereal *, doublereal *, integer *, - doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + extern /* Subroutine */ int dtrmm_(char *, char *, char *, char *, + integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); char trans[1]; - extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, - integer *, integer *, doublereal *, doublereal *, integer *, - doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, + integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); logical upper; extern /* Subroutine */ int dsyev_(char *, char *, integer *, doublereal * - , integer *, doublereal *, doublereal *, integer *, integer *, - ftnlen, ftnlen); + , integer *, doublereal *, doublereal *, integer *, integer *, + ftnlen, ftnlen); logical wantz; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - extern /* Subroutine */ int dpotrf_(char *, integer *, doublereal *, - integer *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dpotrf_(char *, integer *, doublereal *, + integer *, integer *, ftnlen); integer lwkmin; - extern /* Subroutine */ int dsygst_(integer *, char *, integer *, - doublereal *, integer *, doublereal *, integer *, integer *, - ftnlen); + extern /* Subroutine */ int dsygst_(integer *, char *, integer *, + doublereal *, integer *, doublereal *, integer *, integer *, + ftnlen); integer lwkopt; logical lquery; @@ -274,102 +274,102 @@ static doublereal c_b16 = 1.; *info = 0; if (*itype < 1 || *itype > 3) { - *info = -1; + *info = -1; } else if (! (wantz || lsame_(jobz, (char *)"N", (ftnlen)1, (ftnlen)1))) { - *info = -2; + *info = -2; } else if (! (upper || lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1))) { - *info = -3; + *info = -3; } else if (*n < 0) { - *info = -4; + *info = -4; } else if (*lda < max(1,*n)) { - *info = -6; + *info = -6; } else if (*ldb < max(1,*n)) { - *info = -8; + *info = -8; } if (*info == 0) { /* Computing MAX */ - i__1 = 1, i__2 = *n * 3 - 1; - lwkmin = max(i__1,i__2); - nb = ilaenv_(&c__1, (char *)"DSYTRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, - (ftnlen)1); + i__1 = 1, i__2 = *n * 3 - 1; + lwkmin = max(i__1,i__2); + nb = ilaenv_(&c__1, (char *)"DSYTRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, + (ftnlen)1); /* Computing MAX */ - i__1 = lwkmin, i__2 = (nb + 2) * *n; - lwkopt = max(i__1,i__2); - work[1] = (doublereal) lwkopt; + i__1 = lwkmin, i__2 = (nb + 2) * *n; + lwkopt = max(i__1,i__2); + work[1] = (doublereal) lwkopt; - if (*lwork < lwkmin && ! lquery) { - *info = -11; - } + if (*lwork < lwkmin && ! lquery) { + *info = -11; + } } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DSYGV ", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DSYGV ", &i__1, (ftnlen)6); + return 0; } else if (lquery) { - return 0; + return 0; } /* Quick return if possible */ if (*n == 0) { - return 0; + return 0; } /* Form a Cholesky factorization of B. */ dpotrf_(uplo, n, &b[b_offset], ldb, info, (ftnlen)1); if (*info != 0) { - *info = *n + *info; - return 0; + *info = *n + *info; + return 0; } /* Transform problem to standard eigenvalue problem and solve. */ dsygst_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info, ( - ftnlen)1); + ftnlen)1); dsyev_(jobz, uplo, n, &a[a_offset], lda, &w[1], &work[1], lwork, info, ( - ftnlen)1, (ftnlen)1); + ftnlen)1, (ftnlen)1); if (wantz) { /* Backtransform eigenvectors to the original problem. */ - neig = *n; - if (*info > 0) { - neig = *info - 1; - } - if (*itype == 1 || *itype == 2) { + neig = *n; + if (*info > 0) { + neig = *info - 1; + } + if (*itype == 1 || *itype == 2) { /* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; */ /* backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y */ - if (upper) { - *(unsigned char *)trans = 'N'; - } else { - *(unsigned char *)trans = 'T'; - } + if (upper) { + *(unsigned char *)trans = 'N'; + } else { + *(unsigned char *)trans = 'T'; + } - dtrsm_((char *)"Left", uplo, trans, (char *)"Non-unit", n, &neig, &c_b16, &b[ - b_offset], ldb, &a[a_offset], lda, (ftnlen)4, (ftnlen)1, ( - ftnlen)1, (ftnlen)8); + dtrsm_((char *)"Left", uplo, trans, (char *)"Non-unit", n, &neig, &c_b16, &b[ + b_offset], ldb, &a[a_offset], lda, (ftnlen)4, (ftnlen)1, ( + ftnlen)1, (ftnlen)8); - } else if (*itype == 3) { + } else if (*itype == 3) { /* For B*A*x=(lambda)*x; */ /* backtransform eigenvectors: x = L*y or U**T*y */ - if (upper) { - *(unsigned char *)trans = 'T'; - } else { - *(unsigned char *)trans = 'N'; - } + if (upper) { + *(unsigned char *)trans = 'T'; + } else { + *(unsigned char *)trans = 'N'; + } - dtrmm_((char *)"Left", uplo, trans, (char *)"Non-unit", n, &neig, &c_b16, &b[ - b_offset], ldb, &a[a_offset], lda, (ftnlen)4, (ftnlen)1, ( - ftnlen)1, (ftnlen)8); - } + dtrmm_((char *)"Left", uplo, trans, (char *)"Non-unit", n, &neig, &c_b16, &b[ + b_offset], ldb, &a[a_offset], lda, (ftnlen)4, (ftnlen)1, ( + ftnlen)1, (ftnlen)8); + } } work[1] = (doublereal) lwkopt; @@ -380,5 +380,5 @@ static doublereal c_b16 = 1.; } /* dsygv_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dsygvd.cpp b/lib/linalg/dsygvd.cpp index 80513dfdcc..c44f6239f6 100644 --- a/lib/linalg/dsygvd.cpp +++ b/lib/linalg/dsygvd.cpp @@ -1,13 +1,13 @@ /* fortran/dsygvd.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -247,9 +247,9 @@ f"> */ /* > */ /* ===================================================================== */ /* Subroutine */ int dsygvd_(integer *itype, char *jobz, char *uplo, integer * - n, doublereal *a, integer *lda, doublereal *b, integer *ldb, - doublereal *w, doublereal *work, integer *lwork, integer *iwork, - integer *liwork, integer *info, ftnlen jobz_len, ftnlen uplo_len) + n, doublereal *a, integer *lda, doublereal *b, integer *ldb, + doublereal *w, doublereal *work, integer *lwork, integer *iwork, + integer *liwork, integer *info, ftnlen jobz_len, ftnlen uplo_len) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1; @@ -258,24 +258,24 @@ f"> */ /* Local variables */ integer lopt; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int dtrmm_(char *, char *, char *, char *, - integer *, integer *, doublereal *, doublereal *, integer *, - doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + extern /* Subroutine */ int dtrmm_(char *, char *, char *, char *, + integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); integer lwmin; char trans[1]; integer liopt; - extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, - integer *, integer *, doublereal *, doublereal *, integer *, - doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, + integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); logical upper, wantz; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), dpotrf_( - char *, integer *, doublereal *, integer *, integer *, ftnlen); + char *, integer *, doublereal *, integer *, integer *, ftnlen); integer liwmin; - extern /* Subroutine */ int dsyevd_(char *, char *, integer *, doublereal - *, integer *, doublereal *, doublereal *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen), dsygst_(integer *, char *, - integer *, doublereal *, integer *, doublereal *, integer *, - integer *, ftnlen); + extern /* Subroutine */ int dsyevd_(char *, char *, integer *, doublereal + *, integer *, doublereal *, doublereal *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen), dsygst_(integer *, char *, + integer *, doublereal *, integer *, doublereal *, integer *, + integer *, ftnlen); logical lquery; @@ -322,72 +322,72 @@ f"> */ *info = 0; if (*n <= 1) { - liwmin = 1; - lwmin = 1; + liwmin = 1; + lwmin = 1; } else if (wantz) { - liwmin = *n * 5 + 3; + liwmin = *n * 5 + 3; /* Computing 2nd power */ - i__1 = *n; - lwmin = *n * 6 + 1 + (i__1 * i__1 << 1); + i__1 = *n; + lwmin = *n * 6 + 1 + (i__1 * i__1 << 1); } else { - liwmin = 1; - lwmin = (*n << 1) + 1; + liwmin = 1; + lwmin = (*n << 1) + 1; } lopt = lwmin; liopt = liwmin; if (*itype < 1 || *itype > 3) { - *info = -1; + *info = -1; } else if (! (wantz || lsame_(jobz, (char *)"N", (ftnlen)1, (ftnlen)1))) { - *info = -2; + *info = -2; } else if (! (upper || lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1))) { - *info = -3; + *info = -3; } else if (*n < 0) { - *info = -4; + *info = -4; } else if (*lda < max(1,*n)) { - *info = -6; + *info = -6; } else if (*ldb < max(1,*n)) { - *info = -8; + *info = -8; } if (*info == 0) { - work[1] = (doublereal) lopt; - iwork[1] = liopt; + work[1] = (doublereal) lopt; + iwork[1] = liopt; - if (*lwork < lwmin && ! lquery) { - *info = -11; - } else if (*liwork < liwmin && ! lquery) { - *info = -13; - } + if (*lwork < lwmin && ! lquery) { + *info = -11; + } else if (*liwork < liwmin && ! lquery) { + *info = -13; + } } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DSYGVD", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DSYGVD", &i__1, (ftnlen)6); + return 0; } else if (lquery) { - return 0; + return 0; } /* Quick return if possible */ if (*n == 0) { - return 0; + return 0; } /* Form a Cholesky factorization of B. */ dpotrf_(uplo, n, &b[b_offset], ldb, info, (ftnlen)1); if (*info != 0) { - *info = *n + *info; - return 0; + *info = *n + *info; + return 0; } /* Transform problem to standard eigenvalue problem and solve. */ dsygst_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info, ( - ftnlen)1); + ftnlen)1); dsyevd_(jobz, uplo, n, &a[a_offset], lda, &w[1], &work[1], lwork, &iwork[ - 1], liwork, info, (ftnlen)1, (ftnlen)1); + 1], liwork, info, (ftnlen)1, (ftnlen)1); /* Computing MAX */ d__1 = (doublereal) lopt; lopt = (integer) max(d__1,work[1]); @@ -399,36 +399,36 @@ f"> */ /* Backtransform eigenvectors to the original problem. */ - if (*itype == 1 || *itype == 2) { + if (*itype == 1 || *itype == 2) { /* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; */ /* backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y */ - if (upper) { - *(unsigned char *)trans = 'N'; - } else { - *(unsigned char *)trans = 'T'; - } + if (upper) { + *(unsigned char *)trans = 'N'; + } else { + *(unsigned char *)trans = 'T'; + } - dtrsm_((char *)"Left", uplo, trans, (char *)"Non-unit", n, n, &c_b11, &b[b_offset] - , ldb, &a[a_offset], lda, (ftnlen)4, (ftnlen)1, (ftnlen)1, - (ftnlen)8); + dtrsm_((char *)"Left", uplo, trans, (char *)"Non-unit", n, n, &c_b11, &b[b_offset] + , ldb, &a[a_offset], lda, (ftnlen)4, (ftnlen)1, (ftnlen)1, + (ftnlen)8); - } else if (*itype == 3) { + } else if (*itype == 3) { /* For B*A*x=(lambda)*x; */ /* backtransform eigenvectors: x = L*y or U**T*y */ - if (upper) { - *(unsigned char *)trans = 'T'; - } else { - *(unsigned char *)trans = 'N'; - } + if (upper) { + *(unsigned char *)trans = 'T'; + } else { + *(unsigned char *)trans = 'N'; + } - dtrmm_((char *)"Left", uplo, trans, (char *)"Non-unit", n, n, &c_b11, &b[b_offset] - , ldb, &a[a_offset], lda, (ftnlen)4, (ftnlen)1, (ftnlen)1, - (ftnlen)8); - } + dtrmm_((char *)"Left", uplo, trans, (char *)"Non-unit", n, n, &c_b11, &b[b_offset] + , ldb, &a[a_offset], lda, (ftnlen)4, (ftnlen)1, (ftnlen)1, + (ftnlen)8); + } } work[1] = (doublereal) lopt; @@ -441,5 +441,5 @@ f"> */ } /* dsygvd_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dsymm.cpp b/lib/linalg/dsymm.cpp index 223551570d..83538c9c27 100644 --- a/lib/linalg/dsymm.cpp +++ b/lib/linalg/dsymm.cpp @@ -1,13 +1,13 @@ /* fortran/dsymm.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -202,14 +202,14 @@ extern "C" { /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int dsymm_(char *side, char *uplo, integer *m, integer *n, - doublereal *alpha, doublereal *a, integer *lda, doublereal *b, - integer *ldb, doublereal *beta, doublereal *c__, integer *ldc, ftnlen - side_len, ftnlen uplo_len) +/* Subroutine */ int dsymm_(char *side, char *uplo, integer *m, integer *n, + doublereal *alpha, doublereal *a, integer *lda, doublereal *b, + integer *ldb, doublereal *beta, doublereal *c__, integer *ldc, ftnlen + side_len, ftnlen uplo_len) { /* System generated locals */ - integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, - i__3; + integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, + i__3; /* Local variables */ integer i__, j, k, info; @@ -257,9 +257,9 @@ extern "C" { /* Function Body */ if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { - nrowa = *m; + nrowa = *m; } else { - nrowa = *n; + nrowa = *n; } upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); @@ -267,57 +267,57 @@ extern "C" { info = 0; if (! lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1) && ! lsame_(side, (char *)"R", ( - ftnlen)1, (ftnlen)1)) { - info = 1; + ftnlen)1, (ftnlen)1)) { + info = 1; } else if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { - info = 2; + info = 2; } else if (*m < 0) { - info = 3; + info = 3; } else if (*n < 0) { - info = 4; + info = 4; } else if (*lda < max(1,nrowa)) { - info = 7; + info = 7; } else if (*ldb < max(1,*m)) { - info = 9; + info = 9; } else if (*ldc < max(1,*m)) { - info = 12; + info = 12; } if (info != 0) { - xerbla_((char *)"DSYMM ", &info, (ftnlen)6); - return 0; + xerbla_((char *)"DSYMM ", &info, (ftnlen)6); + return 0; } /* Quick return if possible. */ if (*m == 0 || *n == 0 || *alpha == 0. && *beta == 1.) { - return 0; + return 0; } /* And when alpha.eq.zero. */ if (*alpha == 0.) { - if (*beta == 0.) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - c__[i__ + j * c_dim1] = 0.; + if (*beta == 0.) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = 0.; /* L10: */ - } + } /* L20: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; /* L30: */ - } + } /* L40: */ - } - } - return 0; + } + } + return 0; } /* Start the operations. */ @@ -326,107 +326,107 @@ extern "C" { /* Form C := alpha*A*B + beta*C. */ - if (upper) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - temp1 = *alpha * b[i__ + j * b_dim1]; - temp2 = 0.; - i__3 = i__ - 1; - for (k = 1; k <= i__3; ++k) { - c__[k + j * c_dim1] += temp1 * a[k + i__ * a_dim1]; - temp2 += b[k + j * b_dim1] * a[k + i__ * a_dim1]; + if (upper) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp1 = *alpha * b[i__ + j * b_dim1]; + temp2 = 0.; + i__3 = i__ - 1; + for (k = 1; k <= i__3; ++k) { + c__[k + j * c_dim1] += temp1 * a[k + i__ * a_dim1]; + temp2 += b[k + j * b_dim1] * a[k + i__ * a_dim1]; /* L50: */ - } - if (*beta == 0.) { - c__[i__ + j * c_dim1] = temp1 * a[i__ + i__ * a_dim1] - + *alpha * temp2; - } else { - c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1] - + temp1 * a[i__ + i__ * a_dim1] + *alpha * - temp2; - } + } + if (*beta == 0.) { + c__[i__ + j * c_dim1] = temp1 * a[i__ + i__ * a_dim1] + + *alpha * temp2; + } else { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1] + + temp1 * a[i__ + i__ * a_dim1] + *alpha * + temp2; + } /* L60: */ - } + } /* L70: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - for (i__ = *m; i__ >= 1; --i__) { - temp1 = *alpha * b[i__ + j * b_dim1]; - temp2 = 0.; - i__2 = *m; - for (k = i__ + 1; k <= i__2; ++k) { - c__[k + j * c_dim1] += temp1 * a[k + i__ * a_dim1]; - temp2 += b[k + j * b_dim1] * a[k + i__ * a_dim1]; + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + for (i__ = *m; i__ >= 1; --i__) { + temp1 = *alpha * b[i__ + j * b_dim1]; + temp2 = 0.; + i__2 = *m; + for (k = i__ + 1; k <= i__2; ++k) { + c__[k + j * c_dim1] += temp1 * a[k + i__ * a_dim1]; + temp2 += b[k + j * b_dim1] * a[k + i__ * a_dim1]; /* L80: */ - } - if (*beta == 0.) { - c__[i__ + j * c_dim1] = temp1 * a[i__ + i__ * a_dim1] - + *alpha * temp2; - } else { - c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1] - + temp1 * a[i__ + i__ * a_dim1] + *alpha * - temp2; - } + } + if (*beta == 0.) { + c__[i__ + j * c_dim1] = temp1 * a[i__ + i__ * a_dim1] + + *alpha * temp2; + } else { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1] + + temp1 * a[i__ + i__ * a_dim1] + *alpha * + temp2; + } /* L90: */ - } + } /* L100: */ - } - } + } + } } else { /* Form C := alpha*B*A + beta*C. */ - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - temp1 = *alpha * a[j + j * a_dim1]; - if (*beta == 0.) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - c__[i__ + j * c_dim1] = temp1 * b[i__ + j * b_dim1]; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp1 = *alpha * a[j + j * a_dim1]; + if (*beta == 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = temp1 * b[i__ + j * b_dim1]; /* L110: */ - } - } else { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1] + - temp1 * b[i__ + j * b_dim1]; + } + } else { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1] + + temp1 * b[i__ + j * b_dim1]; /* L120: */ - } - } - i__2 = j - 1; - for (k = 1; k <= i__2; ++k) { - if (upper) { - temp1 = *alpha * a[k + j * a_dim1]; - } else { - temp1 = *alpha * a[j + k * a_dim1]; - } - i__3 = *m; - for (i__ = 1; i__ <= i__3; ++i__) { - c__[i__ + j * c_dim1] += temp1 * b[i__ + k * b_dim1]; + } + } + i__2 = j - 1; + for (k = 1; k <= i__2; ++k) { + if (upper) { + temp1 = *alpha * a[k + j * a_dim1]; + } else { + temp1 = *alpha * a[j + k * a_dim1]; + } + i__3 = *m; + for (i__ = 1; i__ <= i__3; ++i__) { + c__[i__ + j * c_dim1] += temp1 * b[i__ + k * b_dim1]; /* L130: */ - } + } /* L140: */ - } - i__2 = *n; - for (k = j + 1; k <= i__2; ++k) { - if (upper) { - temp1 = *alpha * a[j + k * a_dim1]; - } else { - temp1 = *alpha * a[k + j * a_dim1]; - } - i__3 = *m; - for (i__ = 1; i__ <= i__3; ++i__) { - c__[i__ + j * c_dim1] += temp1 * b[i__ + k * b_dim1]; + } + i__2 = *n; + for (k = j + 1; k <= i__2; ++k) { + if (upper) { + temp1 = *alpha * a[j + k * a_dim1]; + } else { + temp1 = *alpha * a[k + j * a_dim1]; + } + i__3 = *m; + for (i__ = 1; i__ <= i__3; ++i__) { + c__[i__ + j * c_dim1] += temp1 * b[i__ + k * b_dim1]; /* L150: */ - } + } /* L160: */ - } + } /* L170: */ - } + } } return 0; @@ -436,5 +436,5 @@ extern "C" { } /* dsymm_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dsymv.cpp b/lib/linalg/dsymv.cpp index 4dc77ad743..542c12c97c 100644 --- a/lib/linalg/dsymv.cpp +++ b/lib/linalg/dsymv.cpp @@ -1,13 +1,13 @@ /* fortran/dsymv.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -165,9 +165,9 @@ extern "C" { /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int dsymv_(char *uplo, integer *n, doublereal *alpha, - doublereal *a, integer *lda, doublereal *x, integer *incx, doublereal - *beta, doublereal *y, integer *incy, ftnlen uplo_len) +/* Subroutine */ int dsymv_(char *uplo, integer *n, doublereal *alpha, + doublereal *a, integer *lda, doublereal *x, integer *incx, doublereal + *beta, doublereal *y, integer *incy, ftnlen uplo_len) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; @@ -213,39 +213,39 @@ extern "C" { /* Function Body */ info = 0; if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", ( - ftnlen)1, (ftnlen)1)) { - info = 1; + ftnlen)1, (ftnlen)1)) { + info = 1; } else if (*n < 0) { - info = 2; + info = 2; } else if (*lda < max(1,*n)) { - info = 5; + info = 5; } else if (*incx == 0) { - info = 7; + info = 7; } else if (*incy == 0) { - info = 10; + info = 10; } if (info != 0) { - xerbla_((char *)"DSYMV ", &info, (ftnlen)6); - return 0; + xerbla_((char *)"DSYMV ", &info, (ftnlen)6); + return 0; } /* Quick return if possible. */ if (*n == 0 || *alpha == 0. && *beta == 1.) { - return 0; + return 0; } /* Set up the start points in X and Y. */ if (*incx > 0) { - kx = 1; + kx = 1; } else { - kx = 1 - (*n - 1) * *incx; + kx = 1 - (*n - 1) * *incx; } if (*incy > 0) { - ky = 1; + ky = 1; } else { - ky = 1 - (*n - 1) * *incy; + ky = 1 - (*n - 1) * *incy; } /* Start the operations. In this version the elements of A are */ @@ -255,126 +255,126 @@ extern "C" { /* First form y := beta*y. */ if (*beta != 1.) { - if (*incy == 1) { - if (*beta == 0.) { - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - y[i__] = 0.; + if (*incy == 1) { + if (*beta == 0.) { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + y[i__] = 0.; /* L10: */ - } - } else { - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - y[i__] = *beta * y[i__]; + } + } else { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + y[i__] = *beta * y[i__]; /* L20: */ - } - } - } else { - iy = ky; - if (*beta == 0.) { - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - y[iy] = 0.; - iy += *incy; + } + } + } else { + iy = ky; + if (*beta == 0.) { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + y[iy] = 0.; + iy += *incy; /* L30: */ - } - } else { - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - y[iy] = *beta * y[iy]; - iy += *incy; + } + } else { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + y[iy] = *beta * y[iy]; + iy += *incy; /* L40: */ - } - } - } + } + } + } } if (*alpha == 0.) { - return 0; + return 0; } if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { /* Form y when A is stored in upper triangle. */ - if (*incx == 1 && *incy == 1) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - temp1 = *alpha * x[j]; - temp2 = 0.; - i__2 = j - 1; - for (i__ = 1; i__ <= i__2; ++i__) { - y[i__] += temp1 * a[i__ + j * a_dim1]; - temp2 += a[i__ + j * a_dim1] * x[i__]; + if (*incx == 1 && *incy == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp1 = *alpha * x[j]; + temp2 = 0.; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + y[i__] += temp1 * a[i__ + j * a_dim1]; + temp2 += a[i__ + j * a_dim1] * x[i__]; /* L50: */ - } - y[j] = y[j] + temp1 * a[j + j * a_dim1] + *alpha * temp2; + } + y[j] = y[j] + temp1 * a[j + j * a_dim1] + *alpha * temp2; /* L60: */ - } - } else { - jx = kx; - jy = ky; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - temp1 = *alpha * x[jx]; - temp2 = 0.; - ix = kx; - iy = ky; - i__2 = j - 1; - for (i__ = 1; i__ <= i__2; ++i__) { - y[iy] += temp1 * a[i__ + j * a_dim1]; - temp2 += a[i__ + j * a_dim1] * x[ix]; - ix += *incx; - iy += *incy; + } + } else { + jx = kx; + jy = ky; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp1 = *alpha * x[jx]; + temp2 = 0.; + ix = kx; + iy = ky; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + y[iy] += temp1 * a[i__ + j * a_dim1]; + temp2 += a[i__ + j * a_dim1] * x[ix]; + ix += *incx; + iy += *incy; /* L70: */ - } - y[jy] = y[jy] + temp1 * a[j + j * a_dim1] + *alpha * temp2; - jx += *incx; - jy += *incy; + } + y[jy] = y[jy] + temp1 * a[j + j * a_dim1] + *alpha * temp2; + jx += *incx; + jy += *incy; /* L80: */ - } - } + } + } } else { /* Form y when A is stored in lower triangle. */ - if (*incx == 1 && *incy == 1) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - temp1 = *alpha * x[j]; - temp2 = 0.; - y[j] += temp1 * a[j + j * a_dim1]; - i__2 = *n; - for (i__ = j + 1; i__ <= i__2; ++i__) { - y[i__] += temp1 * a[i__ + j * a_dim1]; - temp2 += a[i__ + j * a_dim1] * x[i__]; + if (*incx == 1 && *incy == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp1 = *alpha * x[j]; + temp2 = 0.; + y[j] += temp1 * a[j + j * a_dim1]; + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + y[i__] += temp1 * a[i__ + j * a_dim1]; + temp2 += a[i__ + j * a_dim1] * x[i__]; /* L90: */ - } - y[j] += *alpha * temp2; + } + y[j] += *alpha * temp2; /* L100: */ - } - } else { - jx = kx; - jy = ky; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - temp1 = *alpha * x[jx]; - temp2 = 0.; - y[jy] += temp1 * a[j + j * a_dim1]; - ix = jx; - iy = jy; - i__2 = *n; - for (i__ = j + 1; i__ <= i__2; ++i__) { - ix += *incx; - iy += *incy; - y[iy] += temp1 * a[i__ + j * a_dim1]; - temp2 += a[i__ + j * a_dim1] * x[ix]; + } + } else { + jx = kx; + jy = ky; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp1 = *alpha * x[jx]; + temp2 = 0.; + y[jy] += temp1 * a[j + j * a_dim1]; + ix = jx; + iy = jy; + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + ix += *incx; + iy += *incy; + y[iy] += temp1 * a[i__ + j * a_dim1]; + temp2 += a[i__ + j * a_dim1] * x[ix]; /* L110: */ - } - y[jy] += *alpha * temp2; - jx += *incx; - jy += *incy; + } + y[jy] += *alpha * temp2; + jx += *incx; + jy += *incy; /* L120: */ - } - } + } + } } return 0; @@ -384,5 +384,5 @@ extern "C" { } /* dsymv_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dsyr2.cpp b/lib/linalg/dsyr2.cpp index f017821e1d..d4395ee996 100644 --- a/lib/linalg/dsyr2.cpp +++ b/lib/linalg/dsyr2.cpp @@ -1,13 +1,13 @@ /* fortran/dsyr2.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -160,9 +160,9 @@ extern "C" { /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int dsyr2_(char *uplo, integer *n, doublereal *alpha, - doublereal *x, integer *incx, doublereal *y, integer *incy, - doublereal *a, integer *lda, ftnlen uplo_len) +/* Subroutine */ int dsyr2_(char *uplo, integer *n, doublereal *alpha, + doublereal *x, integer *incx, doublereal *y, integer *incy, + doublereal *a, integer *lda, ftnlen uplo_len) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; @@ -208,44 +208,44 @@ extern "C" { /* Function Body */ info = 0; if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", ( - ftnlen)1, (ftnlen)1)) { - info = 1; + ftnlen)1, (ftnlen)1)) { + info = 1; } else if (*n < 0) { - info = 2; + info = 2; } else if (*incx == 0) { - info = 5; + info = 5; } else if (*incy == 0) { - info = 7; + info = 7; } else if (*lda < max(1,*n)) { - info = 9; + info = 9; } if (info != 0) { - xerbla_((char *)"DSYR2 ", &info, (ftnlen)6); - return 0; + xerbla_((char *)"DSYR2 ", &info, (ftnlen)6); + return 0; } /* Quick return if possible. */ if (*n == 0 || *alpha == 0.) { - return 0; + return 0; } /* Set up the start points in X and Y if the increments are not both */ /* unity. */ if (*incx != 1 || *incy != 1) { - if (*incx > 0) { - kx = 1; - } else { - kx = 1 - (*n - 1) * *incx; - } - if (*incy > 0) { - ky = 1; - } else { - ky = 1 - (*n - 1) * *incy; - } - jx = kx; - jy = ky; + if (*incx > 0) { + kx = 1; + } else { + kx = 1 - (*n - 1) * *incx; + } + if (*incy > 0) { + ky = 1; + } else { + ky = 1 - (*n - 1) * *incy; + } + jx = kx; + jy = ky; } /* Start the operations. In this version the elements of A are */ @@ -256,84 +256,84 @@ extern "C" { /* Form A when A is stored in the upper triangle. */ - if (*incx == 1 && *incy == 1) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - if (x[j] != 0. || y[j] != 0.) { - temp1 = *alpha * y[j]; - temp2 = *alpha * x[j]; - i__2 = j; - for (i__ = 1; i__ <= i__2; ++i__) { - a[i__ + j * a_dim1] = a[i__ + j * a_dim1] + x[i__] * - temp1 + y[i__] * temp2; + if (*incx == 1 && *incy == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (x[j] != 0. || y[j] != 0.) { + temp1 = *alpha * y[j]; + temp2 = *alpha * x[j]; + i__2 = j; + for (i__ = 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] = a[i__ + j * a_dim1] + x[i__] * + temp1 + y[i__] * temp2; /* L10: */ - } - } + } + } /* L20: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - if (x[jx] != 0. || y[jy] != 0.) { - temp1 = *alpha * y[jy]; - temp2 = *alpha * x[jx]; - ix = kx; - iy = ky; - i__2 = j; - for (i__ = 1; i__ <= i__2; ++i__) { - a[i__ + j * a_dim1] = a[i__ + j * a_dim1] + x[ix] * - temp1 + y[iy] * temp2; - ix += *incx; - iy += *incy; + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (x[jx] != 0. || y[jy] != 0.) { + temp1 = *alpha * y[jy]; + temp2 = *alpha * x[jx]; + ix = kx; + iy = ky; + i__2 = j; + for (i__ = 1; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] = a[i__ + j * a_dim1] + x[ix] * + temp1 + y[iy] * temp2; + ix += *incx; + iy += *incy; /* L30: */ - } - } - jx += *incx; - jy += *incy; + } + } + jx += *incx; + jy += *incy; /* L40: */ - } - } + } + } } else { /* Form A when A is stored in the lower triangle. */ - if (*incx == 1 && *incy == 1) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - if (x[j] != 0. || y[j] != 0.) { - temp1 = *alpha * y[j]; - temp2 = *alpha * x[j]; - i__2 = *n; - for (i__ = j; i__ <= i__2; ++i__) { - a[i__ + j * a_dim1] = a[i__ + j * a_dim1] + x[i__] * - temp1 + y[i__] * temp2; + if (*incx == 1 && *incy == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (x[j] != 0. || y[j] != 0.) { + temp1 = *alpha * y[j]; + temp2 = *alpha * x[j]; + i__2 = *n; + for (i__ = j; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] = a[i__ + j * a_dim1] + x[i__] * + temp1 + y[i__] * temp2; /* L50: */ - } - } + } + } /* L60: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - if (x[jx] != 0. || y[jy] != 0.) { - temp1 = *alpha * y[jy]; - temp2 = *alpha * x[jx]; - ix = jx; - iy = jy; - i__2 = *n; - for (i__ = j; i__ <= i__2; ++i__) { - a[i__ + j * a_dim1] = a[i__ + j * a_dim1] + x[ix] * - temp1 + y[iy] * temp2; - ix += *incx; - iy += *incy; + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (x[jx] != 0. || y[jy] != 0.) { + temp1 = *alpha * y[jy]; + temp2 = *alpha * x[jx]; + ix = jx; + iy = jy; + i__2 = *n; + for (i__ = j; i__ <= i__2; ++i__) { + a[i__ + j * a_dim1] = a[i__ + j * a_dim1] + x[ix] * + temp1 + y[iy] * temp2; + ix += *incx; + iy += *incy; /* L70: */ - } - } - jx += *incx; - jy += *incy; + } + } + jx += *incx; + jy += *incy; /* L80: */ - } - } + } + } } return 0; @@ -343,5 +343,5 @@ extern "C" { } /* dsyr2_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dsyr2k.cpp b/lib/linalg/dsyr2k.cpp index 33d32b3440..29f16539b2 100644 --- a/lib/linalg/dsyr2k.cpp +++ b/lib/linalg/dsyr2k.cpp @@ -1,13 +1,13 @@ /* fortran/dsyr2k.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -205,14 +205,14 @@ extern "C" { /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int dsyr2k_(char *uplo, char *trans, integer *n, integer *k, - doublereal *alpha, doublereal *a, integer *lda, doublereal *b, - integer *ldb, doublereal *beta, doublereal *c__, integer *ldc, ftnlen - uplo_len, ftnlen trans_len) +/* Subroutine */ int dsyr2k_(char *uplo, char *trans, integer *n, integer *k, + doublereal *alpha, doublereal *a, integer *lda, doublereal *b, + integer *ldb, doublereal *beta, doublereal *c__, integer *ldc, ftnlen + uplo_len, ftnlen trans_len) { /* System generated locals */ - integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, - i__3; + integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, + i__3; /* Local variables */ integer i__, j, l, info; @@ -260,90 +260,90 @@ extern "C" { /* Function Body */ if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { - nrowa = *n; + nrowa = *n; } else { - nrowa = *k; + nrowa = *k; } upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); info = 0; if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { - info = 1; - } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, - (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, ( - ftnlen)1)) { - info = 2; + info = 1; + } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, + (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, ( + ftnlen)1)) { + info = 2; } else if (*n < 0) { - info = 3; + info = 3; } else if (*k < 0) { - info = 4; + info = 4; } else if (*lda < max(1,nrowa)) { - info = 7; + info = 7; } else if (*ldb < max(1,nrowa)) { - info = 9; + info = 9; } else if (*ldc < max(1,*n)) { - info = 12; + info = 12; } if (info != 0) { - xerbla_((char *)"DSYR2K", &info, (ftnlen)6); - return 0; + xerbla_((char *)"DSYR2K", &info, (ftnlen)6); + return 0; } /* Quick return if possible. */ if (*n == 0 || (*alpha == 0. || *k == 0) && *beta == 1.) { - return 0; + return 0; } /* And when alpha.eq.zero. */ if (*alpha == 0.) { - if (upper) { - if (*beta == 0.) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = j; - for (i__ = 1; i__ <= i__2; ++i__) { - c__[i__ + j * c_dim1] = 0.; + if (upper) { + if (*beta == 0.) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = 0.; /* L10: */ - } + } /* L20: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = j; - for (i__ = 1; i__ <= i__2; ++i__) { - c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; /* L30: */ - } + } /* L40: */ - } - } - } else { - if (*beta == 0.) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *n; - for (i__ = j; i__ <= i__2; ++i__) { - c__[i__ + j * c_dim1] = 0.; + } + } + } else { + if (*beta == 0.) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = j; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = 0.; /* L50: */ - } + } /* L60: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *n; - for (i__ = j; i__ <= i__2; ++i__) { - c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = j; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; /* L70: */ - } + } /* L80: */ - } - } - } - return 0; + } + } + } + return 0; } /* Start the operations. */ @@ -352,126 +352,126 @@ extern "C" { /* Form C := alpha*A*B**T + alpha*B*A**T + C. */ - if (upper) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - if (*beta == 0.) { - i__2 = j; - for (i__ = 1; i__ <= i__2; ++i__) { - c__[i__ + j * c_dim1] = 0.; + if (upper) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (*beta == 0.) { + i__2 = j; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = 0.; /* L90: */ - } - } else if (*beta != 1.) { - i__2 = j; - for (i__ = 1; i__ <= i__2; ++i__) { - c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; + } + } else if (*beta != 1.) { + i__2 = j; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; /* L100: */ - } - } - i__2 = *k; - for (l = 1; l <= i__2; ++l) { - if (a[j + l * a_dim1] != 0. || b[j + l * b_dim1] != 0.) { - temp1 = *alpha * b[j + l * b_dim1]; - temp2 = *alpha * a[j + l * a_dim1]; - i__3 = j; - for (i__ = 1; i__ <= i__3; ++i__) { - c__[i__ + j * c_dim1] = c__[i__ + j * c_dim1] + a[ - i__ + l * a_dim1] * temp1 + b[i__ + l * - b_dim1] * temp2; + } + } + i__2 = *k; + for (l = 1; l <= i__2; ++l) { + if (a[j + l * a_dim1] != 0. || b[j + l * b_dim1] != 0.) { + temp1 = *alpha * b[j + l * b_dim1]; + temp2 = *alpha * a[j + l * a_dim1]; + i__3 = j; + for (i__ = 1; i__ <= i__3; ++i__) { + c__[i__ + j * c_dim1] = c__[i__ + j * c_dim1] + a[ + i__ + l * a_dim1] * temp1 + b[i__ + l * + b_dim1] * temp2; /* L110: */ - } - } + } + } /* L120: */ - } + } /* L130: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - if (*beta == 0.) { - i__2 = *n; - for (i__ = j; i__ <= i__2; ++i__) { - c__[i__ + j * c_dim1] = 0.; + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (*beta == 0.) { + i__2 = *n; + for (i__ = j; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = 0.; /* L140: */ - } - } else if (*beta != 1.) { - i__2 = *n; - for (i__ = j; i__ <= i__2; ++i__) { - c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; + } + } else if (*beta != 1.) { + i__2 = *n; + for (i__ = j; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; /* L150: */ - } - } - i__2 = *k; - for (l = 1; l <= i__2; ++l) { - if (a[j + l * a_dim1] != 0. || b[j + l * b_dim1] != 0.) { - temp1 = *alpha * b[j + l * b_dim1]; - temp2 = *alpha * a[j + l * a_dim1]; - i__3 = *n; - for (i__ = j; i__ <= i__3; ++i__) { - c__[i__ + j * c_dim1] = c__[i__ + j * c_dim1] + a[ - i__ + l * a_dim1] * temp1 + b[i__ + l * - b_dim1] * temp2; + } + } + i__2 = *k; + for (l = 1; l <= i__2; ++l) { + if (a[j + l * a_dim1] != 0. || b[j + l * b_dim1] != 0.) { + temp1 = *alpha * b[j + l * b_dim1]; + temp2 = *alpha * a[j + l * a_dim1]; + i__3 = *n; + for (i__ = j; i__ <= i__3; ++i__) { + c__[i__ + j * c_dim1] = c__[i__ + j * c_dim1] + a[ + i__ + l * a_dim1] * temp1 + b[i__ + l * + b_dim1] * temp2; /* L160: */ - } - } + } + } /* L170: */ - } + } /* L180: */ - } - } + } + } } else { /* Form C := alpha*A**T*B + alpha*B**T*A + C. */ - if (upper) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = j; - for (i__ = 1; i__ <= i__2; ++i__) { - temp1 = 0.; - temp2 = 0.; - i__3 = *k; - for (l = 1; l <= i__3; ++l) { - temp1 += a[l + i__ * a_dim1] * b[l + j * b_dim1]; - temp2 += b[l + i__ * b_dim1] * a[l + j * a_dim1]; + if (upper) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + for (i__ = 1; i__ <= i__2; ++i__) { + temp1 = 0.; + temp2 = 0.; + i__3 = *k; + for (l = 1; l <= i__3; ++l) { + temp1 += a[l + i__ * a_dim1] * b[l + j * b_dim1]; + temp2 += b[l + i__ * b_dim1] * a[l + j * a_dim1]; /* L190: */ - } - if (*beta == 0.) { - c__[i__ + j * c_dim1] = *alpha * temp1 + *alpha * - temp2; - } else { - c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1] - + *alpha * temp1 + *alpha * temp2; - } + } + if (*beta == 0.) { + c__[i__ + j * c_dim1] = *alpha * temp1 + *alpha * + temp2; + } else { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1] + + *alpha * temp1 + *alpha * temp2; + } /* L200: */ - } + } /* L210: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *n; - for (i__ = j; i__ <= i__2; ++i__) { - temp1 = 0.; - temp2 = 0.; - i__3 = *k; - for (l = 1; l <= i__3; ++l) { - temp1 += a[l + i__ * a_dim1] * b[l + j * b_dim1]; - temp2 += b[l + i__ * b_dim1] * a[l + j * a_dim1]; + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = j; i__ <= i__2; ++i__) { + temp1 = 0.; + temp2 = 0.; + i__3 = *k; + for (l = 1; l <= i__3; ++l) { + temp1 += a[l + i__ * a_dim1] * b[l + j * b_dim1]; + temp2 += b[l + i__ * b_dim1] * a[l + j * a_dim1]; /* L220: */ - } - if (*beta == 0.) { - c__[i__ + j * c_dim1] = *alpha * temp1 + *alpha * - temp2; - } else { - c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1] - + *alpha * temp1 + *alpha * temp2; - } + } + if (*beta == 0.) { + c__[i__ + j * c_dim1] = *alpha * temp1 + *alpha * + temp2; + } else { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1] + + *alpha * temp1 + *alpha * temp2; + } /* L230: */ - } + } /* L240: */ - } - } + } + } } return 0; @@ -481,5 +481,5 @@ extern "C" { } /* dsyr2k_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dsyrk.cpp b/lib/linalg/dsyrk.cpp index 28dc601121..4fb3e554f9 100644 --- a/lib/linalg/dsyrk.cpp +++ b/lib/linalg/dsyrk.cpp @@ -1,13 +1,13 @@ /* fortran/dsyrk.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -182,9 +182,9 @@ extern "C" { /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int dsyrk_(char *uplo, char *trans, integer *n, integer *k, - doublereal *alpha, doublereal *a, integer *lda, doublereal *beta, - doublereal *c__, integer *ldc, ftnlen uplo_len, ftnlen trans_len) +/* Subroutine */ int dsyrk_(char *uplo, char *trans, integer *n, integer *k, + doublereal *alpha, doublereal *a, integer *lda, doublereal *beta, + doublereal *c__, integer *ldc, ftnlen uplo_len, ftnlen trans_len) { /* System generated locals */ integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3; @@ -232,88 +232,88 @@ extern "C" { /* Function Body */ if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { - nrowa = *n; + nrowa = *n; } else { - nrowa = *k; + nrowa = *k; } upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); info = 0; if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { - info = 1; - } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, - (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, ( - ftnlen)1)) { - info = 2; + info = 1; + } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, + (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, ( + ftnlen)1)) { + info = 2; } else if (*n < 0) { - info = 3; + info = 3; } else if (*k < 0) { - info = 4; + info = 4; } else if (*lda < max(1,nrowa)) { - info = 7; + info = 7; } else if (*ldc < max(1,*n)) { - info = 10; + info = 10; } if (info != 0) { - xerbla_((char *)"DSYRK ", &info, (ftnlen)6); - return 0; + xerbla_((char *)"DSYRK ", &info, (ftnlen)6); + return 0; } /* Quick return if possible. */ if (*n == 0 || (*alpha == 0. || *k == 0) && *beta == 1.) { - return 0; + return 0; } /* And when alpha.eq.zero. */ if (*alpha == 0.) { - if (upper) { - if (*beta == 0.) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = j; - for (i__ = 1; i__ <= i__2; ++i__) { - c__[i__ + j * c_dim1] = 0.; + if (upper) { + if (*beta == 0.) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = 0.; /* L10: */ - } + } /* L20: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = j; - for (i__ = 1; i__ <= i__2; ++i__) { - c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; /* L30: */ - } + } /* L40: */ - } - } - } else { - if (*beta == 0.) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *n; - for (i__ = j; i__ <= i__2; ++i__) { - c__[i__ + j * c_dim1] = 0.; + } + } + } else { + if (*beta == 0.) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = j; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = 0.; /* L50: */ - } + } /* L60: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *n; - for (i__ = j; i__ <= i__2; ++i__) { - c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = j; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; /* L70: */ - } + } /* L80: */ - } - } - } - return 0; + } + } + } + return 0; } /* Start the operations. */ @@ -322,116 +322,116 @@ extern "C" { /* Form C := alpha*A*A**T + beta*C. */ - if (upper) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - if (*beta == 0.) { - i__2 = j; - for (i__ = 1; i__ <= i__2; ++i__) { - c__[i__ + j * c_dim1] = 0.; + if (upper) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (*beta == 0.) { + i__2 = j; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = 0.; /* L90: */ - } - } else if (*beta != 1.) { - i__2 = j; - for (i__ = 1; i__ <= i__2; ++i__) { - c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; + } + } else if (*beta != 1.) { + i__2 = j; + for (i__ = 1; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; /* L100: */ - } - } - i__2 = *k; - for (l = 1; l <= i__2; ++l) { - if (a[j + l * a_dim1] != 0.) { - temp = *alpha * a[j + l * a_dim1]; - i__3 = j; - for (i__ = 1; i__ <= i__3; ++i__) { - c__[i__ + j * c_dim1] += temp * a[i__ + l * - a_dim1]; + } + } + i__2 = *k; + for (l = 1; l <= i__2; ++l) { + if (a[j + l * a_dim1] != 0.) { + temp = *alpha * a[j + l * a_dim1]; + i__3 = j; + for (i__ = 1; i__ <= i__3; ++i__) { + c__[i__ + j * c_dim1] += temp * a[i__ + l * + a_dim1]; /* L110: */ - } - } + } + } /* L120: */ - } + } /* L130: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - if (*beta == 0.) { - i__2 = *n; - for (i__ = j; i__ <= i__2; ++i__) { - c__[i__ + j * c_dim1] = 0.; + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (*beta == 0.) { + i__2 = *n; + for (i__ = j; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = 0.; /* L140: */ - } - } else if (*beta != 1.) { - i__2 = *n; - for (i__ = j; i__ <= i__2; ++i__) { - c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; + } + } else if (*beta != 1.) { + i__2 = *n; + for (i__ = j; i__ <= i__2; ++i__) { + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; /* L150: */ - } - } - i__2 = *k; - for (l = 1; l <= i__2; ++l) { - if (a[j + l * a_dim1] != 0.) { - temp = *alpha * a[j + l * a_dim1]; - i__3 = *n; - for (i__ = j; i__ <= i__3; ++i__) { - c__[i__ + j * c_dim1] += temp * a[i__ + l * - a_dim1]; + } + } + i__2 = *k; + for (l = 1; l <= i__2; ++l) { + if (a[j + l * a_dim1] != 0.) { + temp = *alpha * a[j + l * a_dim1]; + i__3 = *n; + for (i__ = j; i__ <= i__3; ++i__) { + c__[i__ + j * c_dim1] += temp * a[i__ + l * + a_dim1]; /* L160: */ - } - } + } + } /* L170: */ - } + } /* L180: */ - } - } + } + } } else { /* Form C := alpha*A**T*A + beta*C. */ - if (upper) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = j; - for (i__ = 1; i__ <= i__2; ++i__) { - temp = 0.; - i__3 = *k; - for (l = 1; l <= i__3; ++l) { - temp += a[l + i__ * a_dim1] * a[l + j * a_dim1]; + if (upper) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + for (i__ = 1; i__ <= i__2; ++i__) { + temp = 0.; + i__3 = *k; + for (l = 1; l <= i__3; ++l) { + temp += a[l + i__ * a_dim1] * a[l + j * a_dim1]; /* L190: */ - } - if (*beta == 0.) { - c__[i__ + j * c_dim1] = *alpha * temp; - } else { - c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[ - i__ + j * c_dim1]; - } + } + if (*beta == 0.) { + c__[i__ + j * c_dim1] = *alpha * temp; + } else { + c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[ + i__ + j * c_dim1]; + } /* L200: */ - } + } /* L210: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *n; - for (i__ = j; i__ <= i__2; ++i__) { - temp = 0.; - i__3 = *k; - for (l = 1; l <= i__3; ++l) { - temp += a[l + i__ * a_dim1] * a[l + j * a_dim1]; + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = j; i__ <= i__2; ++i__) { + temp = 0.; + i__3 = *k; + for (l = 1; l <= i__3; ++l) { + temp += a[l + i__ * a_dim1] * a[l + j * a_dim1]; /* L220: */ - } - if (*beta == 0.) { - c__[i__ + j * c_dim1] = *alpha * temp; - } else { - c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[ - i__ + j * c_dim1]; - } + } + if (*beta == 0.) { + c__[i__ + j * c_dim1] = *alpha * temp; + } else { + c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[ + i__ + j * c_dim1]; + } /* L230: */ - } + } /* L240: */ - } - } + } + } } return 0; @@ -441,5 +441,5 @@ extern "C" { } /* dsyrk_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dsytd2.cpp b/lib/linalg/dsytd2.cpp index 4035fd0d58..acf22710af 100644 --- a/lib/linalg/dsytd2.cpp +++ b/lib/linalg/dsytd2.cpp @@ -1,13 +1,13 @@ /* fortran/dsytd2.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -197,30 +197,30 @@ f"> */ /* > */ /* ===================================================================== */ /* Subroutine */ int dsytd2_(char *uplo, integer *n, doublereal *a, integer * - lda, doublereal *d__, doublereal *e, doublereal *tau, integer *info, - ftnlen uplo_len) + lda, doublereal *d__, doublereal *e, doublereal *tau, integer *info, + ftnlen uplo_len) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; /* Local variables */ integer i__; - extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, - integer *); + extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, + integer *); doublereal taui; - extern /* Subroutine */ int dsyr2_(char *, integer *, doublereal *, - doublereal *, integer *, doublereal *, integer *, doublereal *, - integer *, ftnlen); + extern /* Subroutine */ int dsyr2_(char *, integer *, doublereal *, + doublereal *, integer *, doublereal *, integer *, doublereal *, + integer *, ftnlen); doublereal alpha; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *, - integer *, doublereal *, integer *); + extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *); logical upper; - extern /* Subroutine */ int dsymv_(char *, integer *, doublereal *, - doublereal *, integer *, doublereal *, integer *, doublereal *, - doublereal *, integer *, ftnlen), dlarfg_(integer *, doublereal *, - doublereal *, integer *, doublereal *), xerbla_(char *, integer * - , ftnlen); + extern /* Subroutine */ int dsymv_(char *, integer *, doublereal *, + doublereal *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, ftnlen), dlarfg_(integer *, doublereal *, + doublereal *, integer *, doublereal *), xerbla_(char *, integer * + , ftnlen); /* -- LAPACK computational routine -- */ @@ -260,122 +260,122 @@ f"> */ *info = 0; upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { - *info = -1; + *info = -1; } else if (*n < 0) { - *info = -2; + *info = -2; } else if (*lda < max(1,*n)) { - *info = -4; + *info = -4; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DSYTD2", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DSYTD2", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*n <= 0) { - return 0; + return 0; } if (upper) { /* Reduce the upper triangle of A */ - for (i__ = *n - 1; i__ >= 1; --i__) { + for (i__ = *n - 1; i__ >= 1; --i__) { /* Generate elementary reflector H(i) = I - tau * v * v**T */ /* to annihilate A(1:i-1,i+1) */ - dlarfg_(&i__, &a[i__ + (i__ + 1) * a_dim1], &a[(i__ + 1) * a_dim1 - + 1], &c__1, &taui); - e[i__] = a[i__ + (i__ + 1) * a_dim1]; + dlarfg_(&i__, &a[i__ + (i__ + 1) * a_dim1], &a[(i__ + 1) * a_dim1 + + 1], &c__1, &taui); + e[i__] = a[i__ + (i__ + 1) * a_dim1]; - if (taui != 0.) { + if (taui != 0.) { /* Apply H(i) from both sides to A(1:i,1:i) */ - a[i__ + (i__ + 1) * a_dim1] = 1.; + a[i__ + (i__ + 1) * a_dim1] = 1.; /* Compute x := tau * A * v storing x in TAU(1:i) */ - dsymv_(uplo, &i__, &taui, &a[a_offset], lda, &a[(i__ + 1) * - a_dim1 + 1], &c__1, &c_b8, &tau[1], &c__1, (ftnlen)1); + dsymv_(uplo, &i__, &taui, &a[a_offset], lda, &a[(i__ + 1) * + a_dim1 + 1], &c__1, &c_b8, &tau[1], &c__1, (ftnlen)1); /* Compute w := x - 1/2 * tau * (x**T * v) * v */ - alpha = taui * -.5 * ddot_(&i__, &tau[1], &c__1, &a[(i__ + 1) - * a_dim1 + 1], &c__1); - daxpy_(&i__, &alpha, &a[(i__ + 1) * a_dim1 + 1], &c__1, &tau[ - 1], &c__1); + alpha = taui * -.5 * ddot_(&i__, &tau[1], &c__1, &a[(i__ + 1) + * a_dim1 + 1], &c__1); + daxpy_(&i__, &alpha, &a[(i__ + 1) * a_dim1 + 1], &c__1, &tau[ + 1], &c__1); /* Apply the transformation as a rank-2 update: */ /* A := A - v * w**T - w * v**T */ - dsyr2_(uplo, &i__, &c_b14, &a[(i__ + 1) * a_dim1 + 1], &c__1, - &tau[1], &c__1, &a[a_offset], lda, (ftnlen)1); + dsyr2_(uplo, &i__, &c_b14, &a[(i__ + 1) * a_dim1 + 1], &c__1, + &tau[1], &c__1, &a[a_offset], lda, (ftnlen)1); - a[i__ + (i__ + 1) * a_dim1] = e[i__]; - } - d__[i__ + 1] = a[i__ + 1 + (i__ + 1) * a_dim1]; - tau[i__] = taui; + a[i__ + (i__ + 1) * a_dim1] = e[i__]; + } + d__[i__ + 1] = a[i__ + 1 + (i__ + 1) * a_dim1]; + tau[i__] = taui; /* L10: */ - } - d__[1] = a[a_dim1 + 1]; + } + d__[1] = a[a_dim1 + 1]; } else { /* Reduce the lower triangle of A */ - i__1 = *n - 1; - for (i__ = 1; i__ <= i__1; ++i__) { + i__1 = *n - 1; + for (i__ = 1; i__ <= i__1; ++i__) { /* Generate elementary reflector H(i) = I - tau * v * v**T */ /* to annihilate A(i+2:n,i) */ - i__2 = *n - i__; + i__2 = *n - i__; /* Computing MIN */ - i__3 = i__ + 2; - dlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3,*n) + i__ * - a_dim1], &c__1, &taui); - e[i__] = a[i__ + 1 + i__ * a_dim1]; + i__3 = i__ + 2; + dlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3,*n) + i__ * + a_dim1], &c__1, &taui); + e[i__] = a[i__ + 1 + i__ * a_dim1]; - if (taui != 0.) { + if (taui != 0.) { /* Apply H(i) from both sides to A(i+1:n,i+1:n) */ - a[i__ + 1 + i__ * a_dim1] = 1.; + a[i__ + 1 + i__ * a_dim1] = 1.; /* Compute x := tau * A * v storing y in TAU(i:n-1) */ - i__2 = *n - i__; - dsymv_(uplo, &i__2, &taui, &a[i__ + 1 + (i__ + 1) * a_dim1], - lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b8, &tau[ - i__], &c__1, (ftnlen)1); + i__2 = *n - i__; + dsymv_(uplo, &i__2, &taui, &a[i__ + 1 + (i__ + 1) * a_dim1], + lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b8, &tau[ + i__], &c__1, (ftnlen)1); /* Compute w := x - 1/2 * tau * (x**T * v) * v */ - i__2 = *n - i__; - alpha = taui * -.5 * ddot_(&i__2, &tau[i__], &c__1, &a[i__ + - 1 + i__ * a_dim1], &c__1); - i__2 = *n - i__; - daxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &tau[ - i__], &c__1); + i__2 = *n - i__; + alpha = taui * -.5 * ddot_(&i__2, &tau[i__], &c__1, &a[i__ + + 1 + i__ * a_dim1], &c__1); + i__2 = *n - i__; + daxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &tau[ + i__], &c__1); /* Apply the transformation as a rank-2 update: */ /* A := A - v * w**T - w * v**T */ - i__2 = *n - i__; - dsyr2_(uplo, &i__2, &c_b14, &a[i__ + 1 + i__ * a_dim1], &c__1, - &tau[i__], &c__1, &a[i__ + 1 + (i__ + 1) * a_dim1], - lda, (ftnlen)1); + i__2 = *n - i__; + dsyr2_(uplo, &i__2, &c_b14, &a[i__ + 1 + i__ * a_dim1], &c__1, + &tau[i__], &c__1, &a[i__ + 1 + (i__ + 1) * a_dim1], + lda, (ftnlen)1); - a[i__ + 1 + i__ * a_dim1] = e[i__]; - } - d__[i__] = a[i__ + i__ * a_dim1]; - tau[i__] = taui; + a[i__ + 1 + i__ * a_dim1] = e[i__]; + } + d__[i__] = a[i__ + i__ * a_dim1]; + tau[i__] = taui; /* L20: */ - } - d__[*n] = a[*n + *n * a_dim1]; + } + d__[*n] = a[*n + *n * a_dim1]; } return 0; @@ -385,5 +385,5 @@ f"> */ } /* dsytd2_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dsytrd.cpp b/lib/linalg/dsytrd.cpp index 190dd8b1ac..b29df9fb10 100644 --- a/lib/linalg/dsytrd.cpp +++ b/lib/linalg/dsytrd.cpp @@ -1,13 +1,13 @@ /* fortran/dsytrd.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -218,8 +218,8 @@ f"> */ /* > */ /* ===================================================================== */ /* Subroutine */ int dsytrd_(char *uplo, integer *n, doublereal *a, integer * - lda, doublereal *d__, doublereal *e, doublereal *tau, doublereal * - work, integer *lwork, integer *info, ftnlen uplo_len) + lda, doublereal *d__, doublereal *e, doublereal *tau, doublereal * + work, integer *lwork, integer *info, ftnlen uplo_len) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; @@ -229,16 +229,16 @@ f"> */ extern logical lsame_(char *, char *, ftnlen, ftnlen); integer nbmin, iinfo; logical upper; - extern /* Subroutine */ int dsytd2_(char *, integer *, doublereal *, - integer *, doublereal *, doublereal *, doublereal *, integer *, - ftnlen), dsyr2k_(char *, char *, integer *, integer *, doublereal - *, doublereal *, integer *, doublereal *, integer *, doublereal *, - doublereal *, integer *, ftnlen, ftnlen), dlatrd_(char *, - integer *, integer *, doublereal *, integer *, doublereal *, - doublereal *, doublereal *, integer *, ftnlen), xerbla_(char *, - integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dsytd2_(char *, integer *, doublereal *, + integer *, doublereal *, doublereal *, doublereal *, integer *, + ftnlen), dsyr2k_(char *, char *, integer *, integer *, doublereal + *, doublereal *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, ftnlen, ftnlen), dlatrd_(char *, + integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, doublereal *, integer *, ftnlen), xerbla_(char *, + integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); integer ldwork, lwkopt; logical lquery; @@ -282,38 +282,38 @@ f"> */ upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); lquery = *lwork == -1; if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { - *info = -1; + *info = -1; } else if (*n < 0) { - *info = -2; + *info = -2; } else if (*lda < max(1,*n)) { - *info = -4; + *info = -4; } else if (*lwork < 1 && ! lquery) { - *info = -9; + *info = -9; } if (*info == 0) { /* Determine the block size. */ - nb = ilaenv_(&c__1, (char *)"DSYTRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, - (ftnlen)1); - lwkopt = *n * nb; - work[1] = (doublereal) lwkopt; + nb = ilaenv_(&c__1, (char *)"DSYTRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, + (ftnlen)1); + lwkopt = *n * nb; + work[1] = (doublereal) lwkopt; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DSYTRD", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DSYTRD", &i__1, (ftnlen)6); + return 0; } else if (lquery) { - return 0; + return 0; } /* Quick return if possible */ if (*n == 0) { - work[1] = 1.; - return 0; + work[1] = 1.; + return 0; } nx = *n; @@ -324,35 +324,35 @@ f"> */ /* (last block is always handled by unblocked code). */ /* Computing MAX */ - i__1 = nb, i__2 = ilaenv_(&c__3, (char *)"DSYTRD", uplo, n, &c_n1, &c_n1, & - c_n1, (ftnlen)6, (ftnlen)1); - nx = max(i__1,i__2); - if (nx < *n) { + i__1 = nb, i__2 = ilaenv_(&c__3, (char *)"DSYTRD", uplo, n, &c_n1, &c_n1, & + c_n1, (ftnlen)6, (ftnlen)1); + nx = max(i__1,i__2); + if (nx < *n) { /* Determine if workspace is large enough for blocked code. */ - ldwork = *n; - iws = ldwork * nb; - if (*lwork < iws) { + ldwork = *n; + iws = ldwork * nb; + if (*lwork < iws) { /* Not enough workspace to use optimal NB: determine the */ /* minimum value of NB, and reduce NB or force use of */ /* unblocked code by setting NX = N. */ /* Computing MAX */ - i__1 = *lwork / ldwork; - nb = max(i__1,1); - nbmin = ilaenv_(&c__2, (char *)"DSYTRD", uplo, n, &c_n1, &c_n1, &c_n1, - (ftnlen)6, (ftnlen)1); - if (nb < nbmin) { - nx = *n; - } - } - } else { - nx = *n; - } + i__1 = *lwork / ldwork; + nb = max(i__1,1); + nbmin = ilaenv_(&c__2, (char *)"DSYTRD", uplo, n, &c_n1, &c_n1, &c_n1, + (ftnlen)6, (ftnlen)1); + if (nb < nbmin) { + nx = *n; + } + } + } else { + nx = *n; + } } else { - nb = 1; + nb = 1; } if (upper) { @@ -360,86 +360,86 @@ f"> */ /* Reduce the upper triangle of A. */ /* Columns 1:kk are handled by the unblocked method. */ - kk = *n - (*n - nx + nb - 1) / nb * nb; - i__1 = kk + 1; - i__2 = -nb; - for (i__ = *n - nb + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += - i__2) { + kk = *n - (*n - nx + nb - 1) / nb * nb; + i__1 = kk + 1; + i__2 = -nb; + for (i__ = *n - nb + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += + i__2) { /* Reduce columns i:i+nb-1 to tridiagonal form and form the */ /* matrix W which is needed to update the unreduced part of */ /* the matrix */ - i__3 = i__ + nb - 1; - dlatrd_(uplo, &i__3, &nb, &a[a_offset], lda, &e[1], &tau[1], & - work[1], &ldwork, (ftnlen)1); + i__3 = i__ + nb - 1; + dlatrd_(uplo, &i__3, &nb, &a[a_offset], lda, &e[1], &tau[1], & + work[1], &ldwork, (ftnlen)1); /* Update the unreduced submatrix A(1:i-1,1:i-1), using an */ /* update of the form: A := A - V*W**T - W*V**T */ - i__3 = i__ - 1; - dsyr2k_(uplo, (char *)"No transpose", &i__3, &nb, &c_b22, &a[i__ * a_dim1 - + 1], lda, &work[1], &ldwork, &c_b23, &a[a_offset], lda, ( - ftnlen)1, (ftnlen)12); + i__3 = i__ - 1; + dsyr2k_(uplo, (char *)"No transpose", &i__3, &nb, &c_b22, &a[i__ * a_dim1 + + 1], lda, &work[1], &ldwork, &c_b23, &a[a_offset], lda, ( + ftnlen)1, (ftnlen)12); /* Copy superdiagonal elements back into A, and diagonal */ /* elements into D */ - i__3 = i__ + nb - 1; - for (j = i__; j <= i__3; ++j) { - a[j - 1 + j * a_dim1] = e[j - 1]; - d__[j] = a[j + j * a_dim1]; + i__3 = i__ + nb - 1; + for (j = i__; j <= i__3; ++j) { + a[j - 1 + j * a_dim1] = e[j - 1]; + d__[j] = a[j + j * a_dim1]; /* L10: */ - } + } /* L20: */ - } + } /* Use unblocked code to reduce the last or only block */ - dsytd2_(uplo, &kk, &a[a_offset], lda, &d__[1], &e[1], &tau[1], &iinfo, - (ftnlen)1); + dsytd2_(uplo, &kk, &a[a_offset], lda, &d__[1], &e[1], &tau[1], &iinfo, + (ftnlen)1); } else { /* Reduce the lower triangle of A */ - i__2 = *n - nx; - i__1 = nb; - for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) { + i__2 = *n - nx; + i__1 = nb; + for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) { /* Reduce columns i:i+nb-1 to tridiagonal form and form the */ /* matrix W which is needed to update the unreduced part of */ /* the matrix */ - i__3 = *n - i__ + 1; - dlatrd_(uplo, &i__3, &nb, &a[i__ + i__ * a_dim1], lda, &e[i__], & - tau[i__], &work[1], &ldwork, (ftnlen)1); + i__3 = *n - i__ + 1; + dlatrd_(uplo, &i__3, &nb, &a[i__ + i__ * a_dim1], lda, &e[i__], & + tau[i__], &work[1], &ldwork, (ftnlen)1); /* Update the unreduced submatrix A(i+ib:n,i+ib:n), using */ /* an update of the form: A := A - V*W**T - W*V**T */ - i__3 = *n - i__ - nb + 1; - dsyr2k_(uplo, (char *)"No transpose", &i__3, &nb, &c_b22, &a[i__ + nb + - i__ * a_dim1], lda, &work[nb + 1], &ldwork, &c_b23, &a[ - i__ + nb + (i__ + nb) * a_dim1], lda, (ftnlen)1, (ftnlen) - 12); + i__3 = *n - i__ - nb + 1; + dsyr2k_(uplo, (char *)"No transpose", &i__3, &nb, &c_b22, &a[i__ + nb + + i__ * a_dim1], lda, &work[nb + 1], &ldwork, &c_b23, &a[ + i__ + nb + (i__ + nb) * a_dim1], lda, (ftnlen)1, (ftnlen) + 12); /* Copy subdiagonal elements back into A, and diagonal */ /* elements into D */ - i__3 = i__ + nb - 1; - for (j = i__; j <= i__3; ++j) { - a[j + 1 + j * a_dim1] = e[j]; - d__[j] = a[j + j * a_dim1]; + i__3 = i__ + nb - 1; + for (j = i__; j <= i__3; ++j) { + a[j + 1 + j * a_dim1] = e[j]; + d__[j] = a[j + j * a_dim1]; /* L30: */ - } + } /* L40: */ - } + } /* Use unblocked code to reduce the last or only block */ - i__1 = *n - i__ + 1; - dsytd2_(uplo, &i__1, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[i__], - &tau[i__], &iinfo, (ftnlen)1); + i__1 = *n - i__ + 1; + dsytd2_(uplo, &i__1, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[i__], + &tau[i__], &iinfo, (ftnlen)1); } work[1] = (doublereal) lwkopt; @@ -450,5 +450,5 @@ f"> */ } /* dsytrd_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dtrmm.cpp b/lib/linalg/dtrmm.cpp index ffb6a1ad6b..1a61cf72b1 100644 --- a/lib/linalg/dtrmm.cpp +++ b/lib/linalg/dtrmm.cpp @@ -1,13 +1,13 @@ /* fortran/dtrmm.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -190,10 +190,10 @@ extern "C" { /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int dtrmm_(char *side, char *uplo, char *transa, char *diag, - integer *m, integer *n, doublereal *alpha, doublereal *a, integer * - lda, doublereal *b, integer *ldb, ftnlen side_len, ftnlen uplo_len, - ftnlen transa_len, ftnlen diag_len) +/* Subroutine */ int dtrmm_(char *side, char *uplo, char *transa, char *diag, + integer *m, integer *n, doublereal *alpha, doublereal *a, integer * + lda, doublereal *b, integer *ldb, ftnlen side_len, ftnlen uplo_len, + ftnlen transa_len, ftnlen diag_len) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3; @@ -244,276 +244,276 @@ extern "C" { /* Function Body */ lside = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); if (lside) { - nrowa = *m; + nrowa = *m; } else { - nrowa = *n; + nrowa = *n; } nounit = lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1); upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); info = 0; if (! lside && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { - info = 1; + info = 1; } else if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { - info = 2; + info = 2; } else if (! lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(transa, - (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(transa, (char *)"C", (ftnlen)1, ( - ftnlen)1)) { - info = 3; - } else if (! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, - (char *)"N", (ftnlen)1, (ftnlen)1)) { - info = 4; + (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(transa, (char *)"C", (ftnlen)1, ( + ftnlen)1)) { + info = 3; + } else if (! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, + (char *)"N", (ftnlen)1, (ftnlen)1)) { + info = 4; } else if (*m < 0) { - info = 5; + info = 5; } else if (*n < 0) { - info = 6; + info = 6; } else if (*lda < max(1,nrowa)) { - info = 9; + info = 9; } else if (*ldb < max(1,*m)) { - info = 11; + info = 11; } if (info != 0) { - xerbla_((char *)"DTRMM ", &info, (ftnlen)6); - return 0; + xerbla_((char *)"DTRMM ", &info, (ftnlen)6); + return 0; } /* Quick return if possible. */ if (*m == 0 || *n == 0) { - return 0; + return 0; } /* And when alpha.eq.zero. */ if (*alpha == 0.) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - b[i__ + j * b_dim1] = 0.; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] = 0.; /* L10: */ - } + } /* L20: */ - } - return 0; + } + return 0; } /* Start the operations. */ if (lside) { - if (lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1)) { + if (lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1)) { /* Form B := alpha*A*B. */ - if (upper) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (k = 1; k <= i__2; ++k) { - if (b[k + j * b_dim1] != 0.) { - temp = *alpha * b[k + j * b_dim1]; - i__3 = k - 1; - for (i__ = 1; i__ <= i__3; ++i__) { - b[i__ + j * b_dim1] += temp * a[i__ + k * - a_dim1]; + if (upper) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (k = 1; k <= i__2; ++k) { + if (b[k + j * b_dim1] != 0.) { + temp = *alpha * b[k + j * b_dim1]; + i__3 = k - 1; + for (i__ = 1; i__ <= i__3; ++i__) { + b[i__ + j * b_dim1] += temp * a[i__ + k * + a_dim1]; /* L30: */ - } - if (nounit) { - temp *= a[k + k * a_dim1]; - } - b[k + j * b_dim1] = temp; - } + } + if (nounit) { + temp *= a[k + k * a_dim1]; + } + b[k + j * b_dim1] = temp; + } /* L40: */ - } + } /* L50: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - for (k = *m; k >= 1; --k) { - if (b[k + j * b_dim1] != 0.) { - temp = *alpha * b[k + j * b_dim1]; - b[k + j * b_dim1] = temp; - if (nounit) { - b[k + j * b_dim1] *= a[k + k * a_dim1]; - } - i__2 = *m; - for (i__ = k + 1; i__ <= i__2; ++i__) { - b[i__ + j * b_dim1] += temp * a[i__ + k * - a_dim1]; + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + for (k = *m; k >= 1; --k) { + if (b[k + j * b_dim1] != 0.) { + temp = *alpha * b[k + j * b_dim1]; + b[k + j * b_dim1] = temp; + if (nounit) { + b[k + j * b_dim1] *= a[k + k * a_dim1]; + } + i__2 = *m; + for (i__ = k + 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] += temp * a[i__ + k * + a_dim1]; /* L60: */ - } - } + } + } /* L70: */ - } + } /* L80: */ - } - } - } else { + } + } + } else { /* Form B := alpha*A**T*B. */ - if (upper) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - for (i__ = *m; i__ >= 1; --i__) { - temp = b[i__ + j * b_dim1]; - if (nounit) { - temp *= a[i__ + i__ * a_dim1]; - } - i__2 = i__ - 1; - for (k = 1; k <= i__2; ++k) { - temp += a[k + i__ * a_dim1] * b[k + j * b_dim1]; + if (upper) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + for (i__ = *m; i__ >= 1; --i__) { + temp = b[i__ + j * b_dim1]; + if (nounit) { + temp *= a[i__ + i__ * a_dim1]; + } + i__2 = i__ - 1; + for (k = 1; k <= i__2; ++k) { + temp += a[k + i__ * a_dim1] * b[k + j * b_dim1]; /* L90: */ - } - b[i__ + j * b_dim1] = *alpha * temp; + } + b[i__ + j * b_dim1] = *alpha * temp; /* L100: */ - } + } /* L110: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - temp = b[i__ + j * b_dim1]; - if (nounit) { - temp *= a[i__ + i__ * a_dim1]; - } - i__3 = *m; - for (k = i__ + 1; k <= i__3; ++k) { - temp += a[k + i__ * a_dim1] * b[k + j * b_dim1]; + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp = b[i__ + j * b_dim1]; + if (nounit) { + temp *= a[i__ + i__ * a_dim1]; + } + i__3 = *m; + for (k = i__ + 1; k <= i__3; ++k) { + temp += a[k + i__ * a_dim1] * b[k + j * b_dim1]; /* L120: */ - } - b[i__ + j * b_dim1] = *alpha * temp; + } + b[i__ + j * b_dim1] = *alpha * temp; /* L130: */ - } + } /* L140: */ - } - } - } + } + } + } } else { - if (lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1)) { + if (lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1)) { /* Form B := alpha*B*A. */ - if (upper) { - for (j = *n; j >= 1; --j) { - temp = *alpha; - if (nounit) { - temp *= a[j + j * a_dim1]; - } - i__1 = *m; - for (i__ = 1; i__ <= i__1; ++i__) { - b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1]; + if (upper) { + for (j = *n; j >= 1; --j) { + temp = *alpha; + if (nounit) { + temp *= a[j + j * a_dim1]; + } + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1]; /* L150: */ - } - i__1 = j - 1; - for (k = 1; k <= i__1; ++k) { - if (a[k + j * a_dim1] != 0.) { - temp = *alpha * a[k + j * a_dim1]; - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - b[i__ + j * b_dim1] += temp * b[i__ + k * - b_dim1]; + } + i__1 = j - 1; + for (k = 1; k <= i__1; ++k) { + if (a[k + j * a_dim1] != 0.) { + temp = *alpha * a[k + j * a_dim1]; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] += temp * b[i__ + k * + b_dim1]; /* L160: */ - } - } + } + } /* L170: */ - } + } /* L180: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - temp = *alpha; - if (nounit) { - temp *= a[j + j * a_dim1]; - } - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1]; + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp = *alpha; + if (nounit) { + temp *= a[j + j * a_dim1]; + } + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1]; /* L190: */ - } - i__2 = *n; - for (k = j + 1; k <= i__2; ++k) { - if (a[k + j * a_dim1] != 0.) { - temp = *alpha * a[k + j * a_dim1]; - i__3 = *m; - for (i__ = 1; i__ <= i__3; ++i__) { - b[i__ + j * b_dim1] += temp * b[i__ + k * - b_dim1]; + } + i__2 = *n; + for (k = j + 1; k <= i__2; ++k) { + if (a[k + j * a_dim1] != 0.) { + temp = *alpha * a[k + j * a_dim1]; + i__3 = *m; + for (i__ = 1; i__ <= i__3; ++i__) { + b[i__ + j * b_dim1] += temp * b[i__ + k * + b_dim1]; /* L200: */ - } - } + } + } /* L210: */ - } + } /* L220: */ - } - } - } else { + } + } + } else { /* Form B := alpha*B*A**T. */ - if (upper) { - i__1 = *n; - for (k = 1; k <= i__1; ++k) { - i__2 = k - 1; - for (j = 1; j <= i__2; ++j) { - if (a[j + k * a_dim1] != 0.) { - temp = *alpha * a[j + k * a_dim1]; - i__3 = *m; - for (i__ = 1; i__ <= i__3; ++i__) { - b[i__ + j * b_dim1] += temp * b[i__ + k * - b_dim1]; + if (upper) { + i__1 = *n; + for (k = 1; k <= i__1; ++k) { + i__2 = k - 1; + for (j = 1; j <= i__2; ++j) { + if (a[j + k * a_dim1] != 0.) { + temp = *alpha * a[j + k * a_dim1]; + i__3 = *m; + for (i__ = 1; i__ <= i__3; ++i__) { + b[i__ + j * b_dim1] += temp * b[i__ + k * + b_dim1]; /* L230: */ - } - } + } + } /* L240: */ - } - temp = *alpha; - if (nounit) { - temp *= a[k + k * a_dim1]; - } - if (temp != 1.) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1]; + } + temp = *alpha; + if (nounit) { + temp *= a[k + k * a_dim1]; + } + if (temp != 1.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1]; /* L250: */ - } - } + } + } /* L260: */ - } - } else { - for (k = *n; k >= 1; --k) { - i__1 = *n; - for (j = k + 1; j <= i__1; ++j) { - if (a[j + k * a_dim1] != 0.) { - temp = *alpha * a[j + k * a_dim1]; - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - b[i__ + j * b_dim1] += temp * b[i__ + k * - b_dim1]; + } + } else { + for (k = *n; k >= 1; --k) { + i__1 = *n; + for (j = k + 1; j <= i__1; ++j) { + if (a[j + k * a_dim1] != 0.) { + temp = *alpha * a[j + k * a_dim1]; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] += temp * b[i__ + k * + b_dim1]; /* L270: */ - } - } + } + } /* L280: */ - } - temp = *alpha; - if (nounit) { - temp *= a[k + k * a_dim1]; - } - if (temp != 1.) { - i__1 = *m; - for (i__ = 1; i__ <= i__1; ++i__) { - b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1]; + } + temp = *alpha; + if (nounit) { + temp *= a[k + k * a_dim1]; + } + if (temp != 1.) { + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1]; /* L290: */ - } - } + } + } /* L300: */ - } - } - } + } + } + } } return 0; @@ -523,5 +523,5 @@ extern "C" { } /* dtrmm_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dtrmv.cpp b/lib/linalg/dtrmv.cpp index 77dbf2f66f..597fcae137 100644 --- a/lib/linalg/dtrmv.cpp +++ b/lib/linalg/dtrmv.cpp @@ -1,13 +1,13 @@ /* fortran/dtrmv.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -160,9 +160,9 @@ extern "C" { /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int dtrmv_(char *uplo, char *trans, char *diag, integer *n, - doublereal *a, integer *lda, doublereal *x, integer *incx, ftnlen - uplo_len, ftnlen trans_len, ftnlen diag_len) +/* Subroutine */ int dtrmv_(char *uplo, char *trans, char *diag, integer *n, + doublereal *a, integer *lda, doublereal *x, integer *incx, ftnlen + uplo_len, ftnlen trans_len, ftnlen diag_len) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; @@ -208,31 +208,31 @@ extern "C" { /* Function Body */ info = 0; if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", ( - ftnlen)1, (ftnlen)1)) { - info = 1; - } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, - (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, ( - ftnlen)1)) { - info = 2; - } else if (! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, - (char *)"N", (ftnlen)1, (ftnlen)1)) { - info = 3; + ftnlen)1, (ftnlen)1)) { + info = 1; + } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, + (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, ( + ftnlen)1)) { + info = 2; + } else if (! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, + (char *)"N", (ftnlen)1, (ftnlen)1)) { + info = 3; } else if (*n < 0) { - info = 4; + info = 4; } else if (*lda < max(1,*n)) { - info = 6; + info = 6; } else if (*incx == 0) { - info = 8; + info = 8; } if (info != 0) { - xerbla_((char *)"DTRMV ", &info, (ftnlen)6); - return 0; + xerbla_((char *)"DTRMV ", &info, (ftnlen)6); + return 0; } /* Quick return if possible. */ if (*n == 0) { - return 0; + return 0; } nounit = lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1); @@ -241,9 +241,9 @@ extern "C" { /* will be ( N - 1 )*INCX too small for descending loops. */ if (*incx <= 0) { - kx = 1 - (*n - 1) * *incx; + kx = 1 - (*n - 1) * *incx; } else if (*incx != 1) { - kx = 1; + kx = 1; } /* Start the operations. In this version the elements of A are */ @@ -253,155 +253,155 @@ extern "C" { /* Form x := A*x. */ - if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { - if (*incx == 1) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - if (x[j] != 0.) { - temp = x[j]; - i__2 = j - 1; - for (i__ = 1; i__ <= i__2; ++i__) { - x[i__] += temp * a[i__ + j * a_dim1]; + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + if (*incx == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (x[j] != 0.) { + temp = x[j]; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + x[i__] += temp * a[i__ + j * a_dim1]; /* L10: */ - } - if (nounit) { - x[j] *= a[j + j * a_dim1]; - } - } + } + if (nounit) { + x[j] *= a[j + j * a_dim1]; + } + } /* L20: */ - } - } else { - jx = kx; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - if (x[jx] != 0.) { - temp = x[jx]; - ix = kx; - i__2 = j - 1; - for (i__ = 1; i__ <= i__2; ++i__) { - x[ix] += temp * a[i__ + j * a_dim1]; - ix += *incx; + } + } else { + jx = kx; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (x[jx] != 0.) { + temp = x[jx]; + ix = kx; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + x[ix] += temp * a[i__ + j * a_dim1]; + ix += *incx; /* L30: */ - } - if (nounit) { - x[jx] *= a[j + j * a_dim1]; - } - } - jx += *incx; + } + if (nounit) { + x[jx] *= a[j + j * a_dim1]; + } + } + jx += *incx; /* L40: */ - } - } - } else { - if (*incx == 1) { - for (j = *n; j >= 1; --j) { - if (x[j] != 0.) { - temp = x[j]; - i__1 = j + 1; - for (i__ = *n; i__ >= i__1; --i__) { - x[i__] += temp * a[i__ + j * a_dim1]; + } + } + } else { + if (*incx == 1) { + for (j = *n; j >= 1; --j) { + if (x[j] != 0.) { + temp = x[j]; + i__1 = j + 1; + for (i__ = *n; i__ >= i__1; --i__) { + x[i__] += temp * a[i__ + j * a_dim1]; /* L50: */ - } - if (nounit) { - x[j] *= a[j + j * a_dim1]; - } - } + } + if (nounit) { + x[j] *= a[j + j * a_dim1]; + } + } /* L60: */ - } - } else { - kx += (*n - 1) * *incx; - jx = kx; - for (j = *n; j >= 1; --j) { - if (x[jx] != 0.) { - temp = x[jx]; - ix = kx; - i__1 = j + 1; - for (i__ = *n; i__ >= i__1; --i__) { - x[ix] += temp * a[i__ + j * a_dim1]; - ix -= *incx; + } + } else { + kx += (*n - 1) * *incx; + jx = kx; + for (j = *n; j >= 1; --j) { + if (x[jx] != 0.) { + temp = x[jx]; + ix = kx; + i__1 = j + 1; + for (i__ = *n; i__ >= i__1; --i__) { + x[ix] += temp * a[i__ + j * a_dim1]; + ix -= *incx; /* L70: */ - } - if (nounit) { - x[jx] *= a[j + j * a_dim1]; - } - } - jx -= *incx; + } + if (nounit) { + x[jx] *= a[j + j * a_dim1]; + } + } + jx -= *incx; /* L80: */ - } - } - } + } + } + } } else { /* Form x := A**T*x. */ - if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { - if (*incx == 1) { - for (j = *n; j >= 1; --j) { - temp = x[j]; - if (nounit) { - temp *= a[j + j * a_dim1]; - } - for (i__ = j - 1; i__ >= 1; --i__) { - temp += a[i__ + j * a_dim1] * x[i__]; + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + if (*incx == 1) { + for (j = *n; j >= 1; --j) { + temp = x[j]; + if (nounit) { + temp *= a[j + j * a_dim1]; + } + for (i__ = j - 1; i__ >= 1; --i__) { + temp += a[i__ + j * a_dim1] * x[i__]; /* L90: */ - } - x[j] = temp; + } + x[j] = temp; /* L100: */ - } - } else { - jx = kx + (*n - 1) * *incx; - for (j = *n; j >= 1; --j) { - temp = x[jx]; - ix = jx; - if (nounit) { - temp *= a[j + j * a_dim1]; - } - for (i__ = j - 1; i__ >= 1; --i__) { - ix -= *incx; - temp += a[i__ + j * a_dim1] * x[ix]; + } + } else { + jx = kx + (*n - 1) * *incx; + for (j = *n; j >= 1; --j) { + temp = x[jx]; + ix = jx; + if (nounit) { + temp *= a[j + j * a_dim1]; + } + for (i__ = j - 1; i__ >= 1; --i__) { + ix -= *incx; + temp += a[i__ + j * a_dim1] * x[ix]; /* L110: */ - } - x[jx] = temp; - jx -= *incx; + } + x[jx] = temp; + jx -= *incx; /* L120: */ - } - } - } else { - if (*incx == 1) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - temp = x[j]; - if (nounit) { - temp *= a[j + j * a_dim1]; - } - i__2 = *n; - for (i__ = j + 1; i__ <= i__2; ++i__) { - temp += a[i__ + j * a_dim1] * x[i__]; + } + } + } else { + if (*incx == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp = x[j]; + if (nounit) { + temp *= a[j + j * a_dim1]; + } + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + temp += a[i__ + j * a_dim1] * x[i__]; /* L130: */ - } - x[j] = temp; + } + x[j] = temp; /* L140: */ - } - } else { - jx = kx; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - temp = x[jx]; - ix = jx; - if (nounit) { - temp *= a[j + j * a_dim1]; - } - i__2 = *n; - for (i__ = j + 1; i__ <= i__2; ++i__) { - ix += *incx; - temp += a[i__ + j * a_dim1] * x[ix]; + } + } else { + jx = kx; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp = x[jx]; + ix = jx; + if (nounit) { + temp *= a[j + j * a_dim1]; + } + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + ix += *incx; + temp += a[i__ + j * a_dim1] * x[ix]; /* L150: */ - } - x[jx] = temp; - jx += *incx; + } + x[jx] = temp; + jx += *incx; /* L160: */ - } - } - } + } + } + } } return 0; @@ -411,5 +411,5 @@ extern "C" { } /* dtrmv_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dtrsm.cpp b/lib/linalg/dtrsm.cpp index 488da4ecdc..8b815c5300 100644 --- a/lib/linalg/dtrsm.cpp +++ b/lib/linalg/dtrsm.cpp @@ -1,13 +1,13 @@ /* fortran/dtrsm.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -194,10 +194,10 @@ extern "C" { /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int dtrsm_(char *side, char *uplo, char *transa, char *diag, - integer *m, integer *n, doublereal *alpha, doublereal *a, integer * - lda, doublereal *b, integer *ldb, ftnlen side_len, ftnlen uplo_len, - ftnlen transa_len, ftnlen diag_len) +/* Subroutine */ int dtrsm_(char *side, char *uplo, char *transa, char *diag, + integer *m, integer *n, doublereal *alpha, doublereal *a, integer * + lda, doublereal *b, integer *ldb, ftnlen side_len, ftnlen uplo_len, + ftnlen transa_len, ftnlen diag_len) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3; @@ -248,310 +248,310 @@ extern "C" { /* Function Body */ lside = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); if (lside) { - nrowa = *m; + nrowa = *m; } else { - nrowa = *n; + nrowa = *n; } nounit = lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1); upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); info = 0; if (! lside && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { - info = 1; + info = 1; } else if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { - info = 2; + info = 2; } else if (! lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(transa, - (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(transa, (char *)"C", (ftnlen)1, ( - ftnlen)1)) { - info = 3; - } else if (! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, - (char *)"N", (ftnlen)1, (ftnlen)1)) { - info = 4; + (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(transa, (char *)"C", (ftnlen)1, ( + ftnlen)1)) { + info = 3; + } else if (! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, + (char *)"N", (ftnlen)1, (ftnlen)1)) { + info = 4; } else if (*m < 0) { - info = 5; + info = 5; } else if (*n < 0) { - info = 6; + info = 6; } else if (*lda < max(1,nrowa)) { - info = 9; + info = 9; } else if (*ldb < max(1,*m)) { - info = 11; + info = 11; } if (info != 0) { - xerbla_((char *)"DTRSM ", &info, (ftnlen)6); - return 0; + xerbla_((char *)"DTRSM ", &info, (ftnlen)6); + return 0; } /* Quick return if possible. */ if (*m == 0 || *n == 0) { - return 0; + return 0; } /* And when alpha.eq.zero. */ if (*alpha == 0.) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - b[i__ + j * b_dim1] = 0.; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] = 0.; /* L10: */ - } + } /* L20: */ - } - return 0; + } + return 0; } /* Start the operations. */ if (lside) { - if (lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1)) { + if (lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1)) { /* Form B := alpha*inv( A )*B. */ - if (upper) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - if (*alpha != 1.) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1] - ; + if (upper) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (*alpha != 1.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1] + ; /* L30: */ - } - } - for (k = *m; k >= 1; --k) { - if (b[k + j * b_dim1] != 0.) { - if (nounit) { - b[k + j * b_dim1] /= a[k + k * a_dim1]; - } - i__2 = k - 1; - for (i__ = 1; i__ <= i__2; ++i__) { - b[i__ + j * b_dim1] -= b[k + j * b_dim1] * a[ - i__ + k * a_dim1]; + } + } + for (k = *m; k >= 1; --k) { + if (b[k + j * b_dim1] != 0.) { + if (nounit) { + b[k + j * b_dim1] /= a[k + k * a_dim1]; + } + i__2 = k - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] -= b[k + j * b_dim1] * a[ + i__ + k * a_dim1]; /* L40: */ - } - } + } + } /* L50: */ - } + } /* L60: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - if (*alpha != 1.) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1] - ; + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (*alpha != 1.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1] + ; /* L70: */ - } - } - i__2 = *m; - for (k = 1; k <= i__2; ++k) { - if (b[k + j * b_dim1] != 0.) { - if (nounit) { - b[k + j * b_dim1] /= a[k + k * a_dim1]; - } - i__3 = *m; - for (i__ = k + 1; i__ <= i__3; ++i__) { - b[i__ + j * b_dim1] -= b[k + j * b_dim1] * a[ - i__ + k * a_dim1]; + } + } + i__2 = *m; + for (k = 1; k <= i__2; ++k) { + if (b[k + j * b_dim1] != 0.) { + if (nounit) { + b[k + j * b_dim1] /= a[k + k * a_dim1]; + } + i__3 = *m; + for (i__ = k + 1; i__ <= i__3; ++i__) { + b[i__ + j * b_dim1] -= b[k + j * b_dim1] * a[ + i__ + k * a_dim1]; /* L80: */ - } - } + } + } /* L90: */ - } + } /* L100: */ - } - } - } else { + } + } + } else { /* Form B := alpha*inv( A**T )*B. */ - if (upper) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - temp = *alpha * b[i__ + j * b_dim1]; - i__3 = i__ - 1; - for (k = 1; k <= i__3; ++k) { - temp -= a[k + i__ * a_dim1] * b[k + j * b_dim1]; + if (upper) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp = *alpha * b[i__ + j * b_dim1]; + i__3 = i__ - 1; + for (k = 1; k <= i__3; ++k) { + temp -= a[k + i__ * a_dim1] * b[k + j * b_dim1]; /* L110: */ - } - if (nounit) { - temp /= a[i__ + i__ * a_dim1]; - } - b[i__ + j * b_dim1] = temp; + } + if (nounit) { + temp /= a[i__ + i__ * a_dim1]; + } + b[i__ + j * b_dim1] = temp; /* L120: */ - } + } /* L130: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - for (i__ = *m; i__ >= 1; --i__) { - temp = *alpha * b[i__ + j * b_dim1]; - i__2 = *m; - for (k = i__ + 1; k <= i__2; ++k) { - temp -= a[k + i__ * a_dim1] * b[k + j * b_dim1]; + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + for (i__ = *m; i__ >= 1; --i__) { + temp = *alpha * b[i__ + j * b_dim1]; + i__2 = *m; + for (k = i__ + 1; k <= i__2; ++k) { + temp -= a[k + i__ * a_dim1] * b[k + j * b_dim1]; /* L140: */ - } - if (nounit) { - temp /= a[i__ + i__ * a_dim1]; - } - b[i__ + j * b_dim1] = temp; + } + if (nounit) { + temp /= a[i__ + i__ * a_dim1]; + } + b[i__ + j * b_dim1] = temp; /* L150: */ - } + } /* L160: */ - } - } - } + } + } + } } else { - if (lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1)) { + if (lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1)) { /* Form B := alpha*B*inv( A ). */ - if (upper) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - if (*alpha != 1.) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1] - ; + if (upper) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (*alpha != 1.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1] + ; /* L170: */ - } - } - i__2 = j - 1; - for (k = 1; k <= i__2; ++k) { - if (a[k + j * a_dim1] != 0.) { - i__3 = *m; - for (i__ = 1; i__ <= i__3; ++i__) { - b[i__ + j * b_dim1] -= a[k + j * a_dim1] * b[ - i__ + k * b_dim1]; + } + } + i__2 = j - 1; + for (k = 1; k <= i__2; ++k) { + if (a[k + j * a_dim1] != 0.) { + i__3 = *m; + for (i__ = 1; i__ <= i__3; ++i__) { + b[i__ + j * b_dim1] -= a[k + j * a_dim1] * b[ + i__ + k * b_dim1]; /* L180: */ - } - } + } + } /* L190: */ - } - if (nounit) { - temp = 1. / a[j + j * a_dim1]; - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1]; + } + if (nounit) { + temp = 1. / a[j + j * a_dim1]; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1]; /* L200: */ - } - } + } + } /* L210: */ - } - } else { - for (j = *n; j >= 1; --j) { - if (*alpha != 1.) { - i__1 = *m; - for (i__ = 1; i__ <= i__1; ++i__) { - b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1] - ; + } + } else { + for (j = *n; j >= 1; --j) { + if (*alpha != 1.) { + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1] + ; /* L220: */ - } - } - i__1 = *n; - for (k = j + 1; k <= i__1; ++k) { - if (a[k + j * a_dim1] != 0.) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - b[i__ + j * b_dim1] -= a[k + j * a_dim1] * b[ - i__ + k * b_dim1]; + } + } + i__1 = *n; + for (k = j + 1; k <= i__1; ++k) { + if (a[k + j * a_dim1] != 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] -= a[k + j * a_dim1] * b[ + i__ + k * b_dim1]; /* L230: */ - } - } + } + } /* L240: */ - } - if (nounit) { - temp = 1. / a[j + j * a_dim1]; - i__1 = *m; - for (i__ = 1; i__ <= i__1; ++i__) { - b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1]; + } + if (nounit) { + temp = 1. / a[j + j * a_dim1]; + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1]; /* L250: */ - } - } + } + } /* L260: */ - } - } - } else { + } + } + } else { /* Form B := alpha*B*inv( A**T ). */ - if (upper) { - for (k = *n; k >= 1; --k) { - if (nounit) { - temp = 1. / a[k + k * a_dim1]; - i__1 = *m; - for (i__ = 1; i__ <= i__1; ++i__) { - b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1]; + if (upper) { + for (k = *n; k >= 1; --k) { + if (nounit) { + temp = 1. / a[k + k * a_dim1]; + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1]; /* L270: */ - } - } - i__1 = k - 1; - for (j = 1; j <= i__1; ++j) { - if (a[j + k * a_dim1] != 0.) { - temp = a[j + k * a_dim1]; - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - b[i__ + j * b_dim1] -= temp * b[i__ + k * - b_dim1]; + } + } + i__1 = k - 1; + for (j = 1; j <= i__1; ++j) { + if (a[j + k * a_dim1] != 0.) { + temp = a[j + k * a_dim1]; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + j * b_dim1] -= temp * b[i__ + k * + b_dim1]; /* L280: */ - } - } + } + } /* L290: */ - } - if (*alpha != 1.) { - i__1 = *m; - for (i__ = 1; i__ <= i__1; ++i__) { - b[i__ + k * b_dim1] = *alpha * b[i__ + k * b_dim1] - ; + } + if (*alpha != 1.) { + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + b[i__ + k * b_dim1] = *alpha * b[i__ + k * b_dim1] + ; /* L300: */ - } - } + } + } /* L310: */ - } - } else { - i__1 = *n; - for (k = 1; k <= i__1; ++k) { - if (nounit) { - temp = 1. / a[k + k * a_dim1]; - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1]; + } + } else { + i__1 = *n; + for (k = 1; k <= i__1; ++k) { + if (nounit) { + temp = 1. / a[k + k * a_dim1]; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1]; /* L320: */ - } - } - i__2 = *n; - for (j = k + 1; j <= i__2; ++j) { - if (a[j + k * a_dim1] != 0.) { - temp = a[j + k * a_dim1]; - i__3 = *m; - for (i__ = 1; i__ <= i__3; ++i__) { - b[i__ + j * b_dim1] -= temp * b[i__ + k * - b_dim1]; + } + } + i__2 = *n; + for (j = k + 1; j <= i__2; ++j) { + if (a[j + k * a_dim1] != 0.) { + temp = a[j + k * a_dim1]; + i__3 = *m; + for (i__ = 1; i__ <= i__3; ++i__) { + b[i__ + j * b_dim1] -= temp * b[i__ + k * + b_dim1]; /* L330: */ - } - } + } + } /* L340: */ - } - if (*alpha != 1.) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - b[i__ + k * b_dim1] = *alpha * b[i__ + k * b_dim1] - ; + } + if (*alpha != 1.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + b[i__ + k * b_dim1] = *alpha * b[i__ + k * b_dim1] + ; /* L350: */ - } - } + } + } /* L360: */ - } - } - } + } + } + } } return 0; @@ -561,5 +561,5 @@ extern "C" { } /* dtrsm_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dtrsv.cpp b/lib/linalg/dtrsv.cpp index 58b85f9206..4044c819f6 100644 --- a/lib/linalg/dtrsv.cpp +++ b/lib/linalg/dtrsv.cpp @@ -1,13 +1,13 @@ /* fortran/dtrsv.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -156,9 +156,9 @@ extern "C" { /* > \ingroup double_blas_level1 */ /* ===================================================================== */ -/* Subroutine */ int dtrsv_(char *uplo, char *trans, char *diag, integer *n, - doublereal *a, integer *lda, doublereal *x, integer *incx, ftnlen - uplo_len, ftnlen trans_len, ftnlen diag_len) +/* Subroutine */ int dtrsv_(char *uplo, char *trans, char *diag, integer *n, + doublereal *a, integer *lda, doublereal *x, integer *incx, ftnlen + uplo_len, ftnlen trans_len, ftnlen diag_len) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; @@ -204,31 +204,31 @@ extern "C" { /* Function Body */ info = 0; if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", ( - ftnlen)1, (ftnlen)1)) { - info = 1; - } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, - (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, ( - ftnlen)1)) { - info = 2; - } else if (! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, - (char *)"N", (ftnlen)1, (ftnlen)1)) { - info = 3; + ftnlen)1, (ftnlen)1)) { + info = 1; + } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, + (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, ( + ftnlen)1)) { + info = 2; + } else if (! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, + (char *)"N", (ftnlen)1, (ftnlen)1)) { + info = 3; } else if (*n < 0) { - info = 4; + info = 4; } else if (*lda < max(1,*n)) { - info = 6; + info = 6; } else if (*incx == 0) { - info = 8; + info = 8; } if (info != 0) { - xerbla_((char *)"DTRSV ", &info, (ftnlen)6); - return 0; + xerbla_((char *)"DTRSV ", &info, (ftnlen)6); + return 0; } /* Quick return if possible. */ if (*n == 0) { - return 0; + return 0; } nounit = lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1); @@ -237,9 +237,9 @@ extern "C" { /* will be ( N - 1 )*INCX too small for descending loops. */ if (*incx <= 0) { - kx = 1 - (*n - 1) * *incx; + kx = 1 - (*n - 1) * *incx; } else if (*incx != 1) { - kx = 1; + kx = 1; } /* Start the operations. In this version the elements of A are */ @@ -249,155 +249,155 @@ extern "C" { /* Form x := inv( A )*x. */ - if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { - if (*incx == 1) { - for (j = *n; j >= 1; --j) { - if (x[j] != 0.) { - if (nounit) { - x[j] /= a[j + j * a_dim1]; - } - temp = x[j]; - for (i__ = j - 1; i__ >= 1; --i__) { - x[i__] -= temp * a[i__ + j * a_dim1]; + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + if (*incx == 1) { + for (j = *n; j >= 1; --j) { + if (x[j] != 0.) { + if (nounit) { + x[j] /= a[j + j * a_dim1]; + } + temp = x[j]; + for (i__ = j - 1; i__ >= 1; --i__) { + x[i__] -= temp * a[i__ + j * a_dim1]; /* L10: */ - } - } + } + } /* L20: */ - } - } else { - jx = kx + (*n - 1) * *incx; - for (j = *n; j >= 1; --j) { - if (x[jx] != 0.) { - if (nounit) { - x[jx] /= a[j + j * a_dim1]; - } - temp = x[jx]; - ix = jx; - for (i__ = j - 1; i__ >= 1; --i__) { - ix -= *incx; - x[ix] -= temp * a[i__ + j * a_dim1]; + } + } else { + jx = kx + (*n - 1) * *incx; + for (j = *n; j >= 1; --j) { + if (x[jx] != 0.) { + if (nounit) { + x[jx] /= a[j + j * a_dim1]; + } + temp = x[jx]; + ix = jx; + for (i__ = j - 1; i__ >= 1; --i__) { + ix -= *incx; + x[ix] -= temp * a[i__ + j * a_dim1]; /* L30: */ - } - } - jx -= *incx; + } + } + jx -= *incx; /* L40: */ - } - } - } else { - if (*incx == 1) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - if (x[j] != 0.) { - if (nounit) { - x[j] /= a[j + j * a_dim1]; - } - temp = x[j]; - i__2 = *n; - for (i__ = j + 1; i__ <= i__2; ++i__) { - x[i__] -= temp * a[i__ + j * a_dim1]; + } + } + } else { + if (*incx == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (x[j] != 0.) { + if (nounit) { + x[j] /= a[j + j * a_dim1]; + } + temp = x[j]; + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + x[i__] -= temp * a[i__ + j * a_dim1]; /* L50: */ - } - } + } + } /* L60: */ - } - } else { - jx = kx; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - if (x[jx] != 0.) { - if (nounit) { - x[jx] /= a[j + j * a_dim1]; - } - temp = x[jx]; - ix = jx; - i__2 = *n; - for (i__ = j + 1; i__ <= i__2; ++i__) { - ix += *incx; - x[ix] -= temp * a[i__ + j * a_dim1]; + } + } else { + jx = kx; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (x[jx] != 0.) { + if (nounit) { + x[jx] /= a[j + j * a_dim1]; + } + temp = x[jx]; + ix = jx; + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + ix += *incx; + x[ix] -= temp * a[i__ + j * a_dim1]; /* L70: */ - } - } - jx += *incx; + } + } + jx += *incx; /* L80: */ - } - } - } + } + } + } } else { /* Form x := inv( A**T )*x. */ - if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { - if (*incx == 1) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - temp = x[j]; - i__2 = j - 1; - for (i__ = 1; i__ <= i__2; ++i__) { - temp -= a[i__ + j * a_dim1] * x[i__]; + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + if (*incx == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp = x[j]; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + temp -= a[i__ + j * a_dim1] * x[i__]; /* L90: */ - } - if (nounit) { - temp /= a[j + j * a_dim1]; - } - x[j] = temp; + } + if (nounit) { + temp /= a[j + j * a_dim1]; + } + x[j] = temp; /* L100: */ - } - } else { - jx = kx; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - temp = x[jx]; - ix = kx; - i__2 = j - 1; - for (i__ = 1; i__ <= i__2; ++i__) { - temp -= a[i__ + j * a_dim1] * x[ix]; - ix += *incx; + } + } else { + jx = kx; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp = x[jx]; + ix = kx; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + temp -= a[i__ + j * a_dim1] * x[ix]; + ix += *incx; /* L110: */ - } - if (nounit) { - temp /= a[j + j * a_dim1]; - } - x[jx] = temp; - jx += *incx; + } + if (nounit) { + temp /= a[j + j * a_dim1]; + } + x[jx] = temp; + jx += *incx; /* L120: */ - } - } - } else { - if (*incx == 1) { - for (j = *n; j >= 1; --j) { - temp = x[j]; - i__1 = j + 1; - for (i__ = *n; i__ >= i__1; --i__) { - temp -= a[i__ + j * a_dim1] * x[i__]; + } + } + } else { + if (*incx == 1) { + for (j = *n; j >= 1; --j) { + temp = x[j]; + i__1 = j + 1; + for (i__ = *n; i__ >= i__1; --i__) { + temp -= a[i__ + j * a_dim1] * x[i__]; /* L130: */ - } - if (nounit) { - temp /= a[j + j * a_dim1]; - } - x[j] = temp; + } + if (nounit) { + temp /= a[j + j * a_dim1]; + } + x[j] = temp; /* L140: */ - } - } else { - kx += (*n - 1) * *incx; - jx = kx; - for (j = *n; j >= 1; --j) { - temp = x[jx]; - ix = kx; - i__1 = j + 1; - for (i__ = *n; i__ >= i__1; --i__) { - temp -= a[i__ + j * a_dim1] * x[ix]; - ix -= *incx; + } + } else { + kx += (*n - 1) * *incx; + jx = kx; + for (j = *n; j >= 1; --j) { + temp = x[jx]; + ix = kx; + i__1 = j + 1; + for (i__ = *n; i__ >= i__1; --i__) { + temp -= a[i__ + j * a_dim1] * x[ix]; + ix -= *incx; /* L150: */ - } - if (nounit) { - temp /= a[j + j * a_dim1]; - } - x[jx] = temp; - jx -= *incx; + } + if (nounit) { + temp /= a[j + j * a_dim1]; + } + x[jx] = temp; + jx -= *incx; /* L160: */ - } - } - } + } + } + } } return 0; @@ -407,5 +407,5 @@ extern "C" { } /* dtrsv_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dtrti2.cpp b/lib/linalg/dtrti2.cpp index f159e31b0d..79cc64b359 100644 --- a/lib/linalg/dtrti2.cpp +++ b/lib/linalg/dtrti2.cpp @@ -1,13 +1,13 @@ /* fortran/dtrti2.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -131,7 +131,7 @@ f"> */ /* ===================================================================== */ /* Subroutine */ int dtrti2_(char *uplo, char *diag, integer *n, doublereal * - a, integer *lda, integer *info, ftnlen uplo_len, ftnlen diag_len) + a, integer *lda, integer *info, ftnlen uplo_len, ftnlen diag_len) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; @@ -139,13 +139,13 @@ f"> */ /* Local variables */ integer j; doublereal ajj; - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *); + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *); extern logical lsame_(char *, char *, ftnlen, ftnlen); logical upper; - extern /* Subroutine */ int dtrmv_(char *, char *, char *, integer *, - doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, - ftnlen), xerbla_(char *, integer *, ftnlen); + extern /* Subroutine */ int dtrmv_(char *, char *, char *, integer *, + doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, + ftnlen), xerbla_(char *, integer *, ftnlen); logical nounit; @@ -184,67 +184,67 @@ f"> */ upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); nounit = lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1); if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { - *info = -1; + *info = -1; } else if (! nounit && ! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1)) { - *info = -2; + *info = -2; } else if (*n < 0) { - *info = -3; + *info = -3; } else if (*lda < max(1,*n)) { - *info = -5; + *info = -5; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DTRTI2", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DTRTI2", &i__1, (ftnlen)6); + return 0; } if (upper) { /* Compute inverse of upper triangular matrix. */ - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - if (nounit) { - a[j + j * a_dim1] = 1. / a[j + j * a_dim1]; - ajj = -a[j + j * a_dim1]; - } else { - ajj = -1.; - } + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (nounit) { + a[j + j * a_dim1] = 1. / a[j + j * a_dim1]; + ajj = -a[j + j * a_dim1]; + } else { + ajj = -1.; + } /* Compute elements 1:j-1 of j-th column. */ - i__2 = j - 1; - dtrmv_((char *)"Upper", (char *)"No transpose", diag, &i__2, &a[a_offset], lda, & - a[j * a_dim1 + 1], &c__1, (ftnlen)5, (ftnlen)12, (ftnlen) - 1); - i__2 = j - 1; - dscal_(&i__2, &ajj, &a[j * a_dim1 + 1], &c__1); + i__2 = j - 1; + dtrmv_((char *)"Upper", (char *)"No transpose", diag, &i__2, &a[a_offset], lda, & + a[j * a_dim1 + 1], &c__1, (ftnlen)5, (ftnlen)12, (ftnlen) + 1); + i__2 = j - 1; + dscal_(&i__2, &ajj, &a[j * a_dim1 + 1], &c__1); /* L10: */ - } + } } else { /* Compute inverse of lower triangular matrix. */ - for (j = *n; j >= 1; --j) { - if (nounit) { - a[j + j * a_dim1] = 1. / a[j + j * a_dim1]; - ajj = -a[j + j * a_dim1]; - } else { - ajj = -1.; - } - if (j < *n) { + for (j = *n; j >= 1; --j) { + if (nounit) { + a[j + j * a_dim1] = 1. / a[j + j * a_dim1]; + ajj = -a[j + j * a_dim1]; + } else { + ajj = -1.; + } + if (j < *n) { /* Compute elements j+1:n of j-th column. */ - i__1 = *n - j; - dtrmv_((char *)"Lower", (char *)"No transpose", diag, &i__1, &a[j + 1 + (j + - 1) * a_dim1], lda, &a[j + 1 + j * a_dim1], &c__1, ( - ftnlen)5, (ftnlen)12, (ftnlen)1); - i__1 = *n - j; - dscal_(&i__1, &ajj, &a[j + 1 + j * a_dim1], &c__1); - } + i__1 = *n - j; + dtrmv_((char *)"Lower", (char *)"No transpose", diag, &i__1, &a[j + 1 + (j + + 1) * a_dim1], lda, &a[j + 1 + j * a_dim1], &c__1, ( + ftnlen)5, (ftnlen)12, (ftnlen)1); + i__1 = *n - j; + dscal_(&i__1, &ajj, &a[j + 1 + j * a_dim1], &c__1); + } /* L20: */ - } + } } return 0; @@ -254,5 +254,5 @@ f"> */ } /* dtrti2_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dtrtri.cpp b/lib/linalg/dtrtri.cpp index faecb3dd69..a80ece791c 100644 --- a/lib/linalg/dtrtri.cpp +++ b/lib/linalg/dtrtri.cpp @@ -1,13 +1,13 @@ /* fortran/dtrtri.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -134,7 +134,7 @@ f"> */ /* ===================================================================== */ /* Subroutine */ int dtrtri_(char *uplo, char *diag, integer *n, doublereal * - a, integer *lda, integer *info, ftnlen uplo_len, ftnlen diag_len) + a, integer *lda, integer *info, ftnlen uplo_len, ftnlen diag_len) { /* System generated locals */ address a__1[2]; @@ -147,18 +147,18 @@ f"> */ /* Local variables */ integer j, jb, nb, nn; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int dtrmm_(char *, char *, char *, char *, - integer *, integer *, doublereal *, doublereal *, integer *, - doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen), dtrsm_( - char *, char *, char *, char *, integer *, integer *, doublereal * - , doublereal *, integer *, doublereal *, integer *, ftnlen, - ftnlen, ftnlen, ftnlen); + extern /* Subroutine */ int dtrmm_(char *, char *, char *, char *, + integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen), dtrsm_( + char *, char *, char *, char *, integer *, integer *, doublereal * + , doublereal *, integer *, doublereal *, integer *, ftnlen, + ftnlen, ftnlen, ftnlen); logical upper; - extern /* Subroutine */ int dtrti2_(char *, char *, integer *, doublereal - *, integer *, integer *, ftnlen, ftnlen), xerbla_(char *, integer - *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dtrti2_(char *, char *, integer *, doublereal + *, integer *, integer *, ftnlen, ftnlen), xerbla_(char *, integer + *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); logical nounit; @@ -197,37 +197,37 @@ f"> */ upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); nounit = lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1); if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { - *info = -1; + *info = -1; } else if (! nounit && ! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1)) { - *info = -2; + *info = -2; } else if (*n < 0) { - *info = -3; + *info = -3; } else if (*lda < max(1,*n)) { - *info = -5; + *info = -5; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"DTRTRI", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"DTRTRI", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*n == 0) { - return 0; + return 0; } /* Check for singularity if non-unit. */ if (nounit) { - i__1 = *n; - for (*info = 1; *info <= i__1; ++(*info)) { - if (a[*info + *info * a_dim1] == 0.) { - return 0; - } + i__1 = *n; + for (*info = 1; *info <= i__1; ++(*info)) { + if (a[*info + *info * a_dim1] == 0.) { + return 0; + } /* L10: */ - } - *info = 0; + } + *info = 0; } /* Determine the block size for this environment. */ @@ -237,77 +237,77 @@ f"> */ i__2[1] = 1, a__1[1] = diag; s_cat(ch__1, a__1, i__2, &c__2, (ftnlen)2); nb = ilaenv_(&c__1, (char *)"DTRTRI", ch__1, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, ( - ftnlen)2); + ftnlen)2); if (nb <= 1 || nb >= *n) { /* Use unblocked code */ - dtrti2_(uplo, diag, n, &a[a_offset], lda, info, (ftnlen)1, (ftnlen)1); + dtrti2_(uplo, diag, n, &a[a_offset], lda, info, (ftnlen)1, (ftnlen)1); } else { /* Use blocked code */ - if (upper) { + if (upper) { /* Compute inverse of upper triangular matrix */ - i__1 = *n; - i__3 = nb; - for (j = 1; i__3 < 0 ? j >= i__1 : j <= i__1; j += i__3) { + i__1 = *n; + i__3 = nb; + for (j = 1; i__3 < 0 ? j >= i__1 : j <= i__1; j += i__3) { /* Computing MIN */ - i__4 = nb, i__5 = *n - j + 1; - jb = min(i__4,i__5); + i__4 = nb, i__5 = *n - j + 1; + jb = min(i__4,i__5); /* Compute rows 1:j-1 of current block column */ - i__4 = j - 1; - dtrmm_((char *)"Left", (char *)"Upper", (char *)"No transpose", diag, &i__4, &jb, & - c_b18, &a[a_offset], lda, &a[j * a_dim1 + 1], lda, ( - ftnlen)4, (ftnlen)5, (ftnlen)12, (ftnlen)1); - i__4 = j - 1; - dtrsm_((char *)"Right", (char *)"Upper", (char *)"No transpose", diag, &i__4, &jb, & - c_b22, &a[j + j * a_dim1], lda, &a[j * a_dim1 + 1], - lda, (ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)1); + i__4 = j - 1; + dtrmm_((char *)"Left", (char *)"Upper", (char *)"No transpose", diag, &i__4, &jb, & + c_b18, &a[a_offset], lda, &a[j * a_dim1 + 1], lda, ( + ftnlen)4, (ftnlen)5, (ftnlen)12, (ftnlen)1); + i__4 = j - 1; + dtrsm_((char *)"Right", (char *)"Upper", (char *)"No transpose", diag, &i__4, &jb, & + c_b22, &a[j + j * a_dim1], lda, &a[j * a_dim1 + 1], + lda, (ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)1); /* Compute inverse of current diagonal block */ - dtrti2_((char *)"Upper", diag, &jb, &a[j + j * a_dim1], lda, info, ( - ftnlen)5, (ftnlen)1); + dtrti2_((char *)"Upper", diag, &jb, &a[j + j * a_dim1], lda, info, ( + ftnlen)5, (ftnlen)1); /* L20: */ - } - } else { + } + } else { /* Compute inverse of lower triangular matrix */ - nn = (*n - 1) / nb * nb + 1; - i__3 = -nb; - for (j = nn; i__3 < 0 ? j >= 1 : j <= 1; j += i__3) { + nn = (*n - 1) / nb * nb + 1; + i__3 = -nb; + for (j = nn; i__3 < 0 ? j >= 1 : j <= 1; j += i__3) { /* Computing MIN */ - i__1 = nb, i__4 = *n - j + 1; - jb = min(i__1,i__4); - if (j + jb <= *n) { + i__1 = nb, i__4 = *n - j + 1; + jb = min(i__1,i__4); + if (j + jb <= *n) { /* Compute rows j+jb:n of current block column */ - i__1 = *n - j - jb + 1; - dtrmm_((char *)"Left", (char *)"Lower", (char *)"No transpose", diag, &i__1, &jb, - &c_b18, &a[j + jb + (j + jb) * a_dim1], lda, &a[j - + jb + j * a_dim1], lda, (ftnlen)4, (ftnlen)5, ( - ftnlen)12, (ftnlen)1); - i__1 = *n - j - jb + 1; - dtrsm_((char *)"Right", (char *)"Lower", (char *)"No transpose", diag, &i__1, &jb, - &c_b22, &a[j + j * a_dim1], lda, &a[j + jb + j * - a_dim1], lda, (ftnlen)5, (ftnlen)5, (ftnlen)12, ( - ftnlen)1); - } + i__1 = *n - j - jb + 1; + dtrmm_((char *)"Left", (char *)"Lower", (char *)"No transpose", diag, &i__1, &jb, + &c_b18, &a[j + jb + (j + jb) * a_dim1], lda, &a[j + + jb + j * a_dim1], lda, (ftnlen)4, (ftnlen)5, ( + ftnlen)12, (ftnlen)1); + i__1 = *n - j - jb + 1; + dtrsm_((char *)"Right", (char *)"Lower", (char *)"No transpose", diag, &i__1, &jb, + &c_b22, &a[j + j * a_dim1], lda, &a[j + jb + j * + a_dim1], lda, (ftnlen)5, (ftnlen)5, (ftnlen)12, ( + ftnlen)1); + } /* Compute inverse of current diagonal block */ - dtrti2_((char *)"Lower", diag, &jb, &a[j + j * a_dim1], lda, info, ( - ftnlen)5, (ftnlen)1); + dtrti2_((char *)"Lower", diag, &jb, &a[j + j * a_dim1], lda, info, ( + ftnlen)5, (ftnlen)1); /* L30: */ - } - } + } + } } return 0; @@ -317,5 +317,5 @@ f"> */ } /* dtrtri_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/dznrm2.cpp b/lib/linalg/dznrm2.cpp index ec71aa201b..7a92e63831 100644 --- a/lib/linalg/dznrm2.cpp +++ b/lib/linalg/dznrm2.cpp @@ -1,13 +1,13 @@ /* fortran/dznrm2.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -127,48 +127,48 @@ doublereal dznrm2_(integer *n, doublecomplex *x, integer *incx) /* Function Body */ if (*n < 1 || *incx < 1) { - norm = 0.; + norm = 0.; } else { - scale = 0.; - ssq = 1.; + scale = 0.; + ssq = 1.; /* The following loop is equivalent to this call to the LAPACK */ /* auxiliary routine: */ /* CALL ZLASSQ( N, X, INCX, SCALE, SSQ ) */ - i__1 = (*n - 1) * *incx + 1; - i__2 = *incx; - for (ix = 1; i__2 < 0 ? ix >= i__1 : ix <= i__1; ix += i__2) { - i__3 = ix; - if (x[i__3].r != 0.) { - i__3 = ix; - temp = (d__1 = x[i__3].r, abs(d__1)); - if (scale < temp) { + i__1 = (*n - 1) * *incx + 1; + i__2 = *incx; + for (ix = 1; i__2 < 0 ? ix >= i__1 : ix <= i__1; ix += i__2) { + i__3 = ix; + if (x[i__3].r != 0.) { + i__3 = ix; + temp = (d__1 = x[i__3].r, abs(d__1)); + if (scale < temp) { /* Computing 2nd power */ - d__1 = scale / temp; - ssq = ssq * (d__1 * d__1) + 1.; - scale = temp; - } else { + d__1 = scale / temp; + ssq = ssq * (d__1 * d__1) + 1.; + scale = temp; + } else { /* Computing 2nd power */ - d__1 = temp / scale; - ssq += d__1 * d__1; - } - } - if (d_imag(&x[ix]) != 0.) { - temp = (d__1 = d_imag(&x[ix]), abs(d__1)); - if (scale < temp) { + d__1 = temp / scale; + ssq += d__1 * d__1; + } + } + if (d_imag(&x[ix]) != 0.) { + temp = (d__1 = d_imag(&x[ix]), abs(d__1)); + if (scale < temp) { /* Computing 2nd power */ - d__1 = scale / temp; - ssq = ssq * (d__1 * d__1) + 1.; - scale = temp; - } else { + d__1 = scale / temp; + ssq = ssq * (d__1 * d__1) + 1.; + scale = temp; + } else { /* Computing 2nd power */ - d__1 = temp / scale; - ssq += d__1 * d__1; - } - } + d__1 = temp / scale; + ssq += d__1 * d__1; + } + } /* L10: */ - } - norm = scale * sqrt(ssq); + } + norm = scale * sqrt(ssq); } ret_val = norm; @@ -179,5 +179,5 @@ doublereal dznrm2_(integer *n, doublecomplex *x, integer *incx) } /* dznrm2_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/idamax.cpp b/lib/linalg/idamax.cpp index edcf861435..e50c15bd38 100644 --- a/lib/linalg/idamax.cpp +++ b/lib/linalg/idamax.cpp @@ -1,13 +1,13 @@ /* fortran/idamax.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -116,39 +116,39 @@ integer idamax_(integer *n, doublereal *dx, integer *incx) /* Function Body */ ret_val = 0; if (*n < 1 || *incx <= 0) { - return ret_val; + return ret_val; } ret_val = 1; if (*n == 1) { - return ret_val; + return ret_val; } if (*incx == 1) { /* code for increment equal to 1 */ - dmax__ = abs(dx[1]); - i__1 = *n; - for (i__ = 2; i__ <= i__1; ++i__) { - if ((d__1 = dx[i__], abs(d__1)) > dmax__) { - ret_val = i__; - dmax__ = (d__1 = dx[i__], abs(d__1)); - } - } + dmax__ = abs(dx[1]); + i__1 = *n; + for (i__ = 2; i__ <= i__1; ++i__) { + if ((d__1 = dx[i__], abs(d__1)) > dmax__) { + ret_val = i__; + dmax__ = (d__1 = dx[i__], abs(d__1)); + } + } } else { /* code for increment not equal to 1 */ - ix = 1; - dmax__ = abs(dx[1]); - ix += *incx; - i__1 = *n; - for (i__ = 2; i__ <= i__1; ++i__) { - if ((d__1 = dx[ix], abs(d__1)) > dmax__) { - ret_val = i__; - dmax__ = (d__1 = dx[ix], abs(d__1)); - } - ix += *incx; - } + ix = 1; + dmax__ = abs(dx[1]); + ix += *incx; + i__1 = *n; + for (i__ = 2; i__ <= i__1; ++i__) { + if ((d__1 = dx[ix], abs(d__1)) > dmax__) { + ret_val = i__; + dmax__ = (d__1 = dx[ix], abs(d__1)); + } + ix += *incx; + } } return ret_val; @@ -157,5 +157,5 @@ integer idamax_(integer *n, doublereal *dx, integer *incx) } /* idamax_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/ieeeck.cpp b/lib/linalg/ieeeck.cpp index 16626acf9d..783a87df9d 100644 --- a/lib/linalg/ieeeck.cpp +++ b/lib/linalg/ieeeck.cpp @@ -1,13 +1,13 @@ /* fortran/ieeeck.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -123,50 +123,50 @@ integer ieeeck_(integer *ispec, real *zero, real *one) posinf = *one / *zero; if (posinf <= *one) { - ret_val = 0; - return ret_val; + ret_val = 0; + return ret_val; } neginf = -(*one) / *zero; if (neginf >= *zero) { - ret_val = 0; - return ret_val; + ret_val = 0; + return ret_val; } negzro = *one / (neginf + *one); if (negzro != *zero) { - ret_val = 0; - return ret_val; + ret_val = 0; + return ret_val; } neginf = *one / negzro; if (neginf >= *zero) { - ret_val = 0; - return ret_val; + ret_val = 0; + return ret_val; } newzro = negzro + *zero; if (newzro != *zero) { - ret_val = 0; - return ret_val; + ret_val = 0; + return ret_val; } posinf = *one / newzro; if (posinf <= *one) { - ret_val = 0; - return ret_val; + ret_val = 0; + return ret_val; } neginf *= posinf; if (neginf >= *zero) { - ret_val = 0; - return ret_val; + ret_val = 0; + return ret_val; } posinf *= posinf; if (posinf <= *one) { - ret_val = 0; - return ret_val; + ret_val = 0; + return ret_val; } @@ -175,7 +175,7 @@ integer ieeeck_(integer *ispec, real *zero, real *one) /* Return if we were only asked to check infinity arithmetic */ if (*ispec == 0) { - return ret_val; + return ret_val; } nan1 = posinf + neginf; @@ -191,38 +191,38 @@ integer ieeeck_(integer *ispec, real *zero, real *one) nan6 = nan5 * *zero; if (nan1 == nan1) { - ret_val = 0; - return ret_val; + ret_val = 0; + return ret_val; } if (nan2 == nan2) { - ret_val = 0; - return ret_val; + ret_val = 0; + return ret_val; } if (nan3 == nan3) { - ret_val = 0; - return ret_val; + ret_val = 0; + return ret_val; } if (nan4 == nan4) { - ret_val = 0; - return ret_val; + ret_val = 0; + return ret_val; } if (nan5 == nan5) { - ret_val = 0; - return ret_val; + ret_val = 0; + return ret_val; } if (nan6 == nan6) { - ret_val = 0; - return ret_val; + ret_val = 0; + return ret_val; } return ret_val; } /* ieeeck_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/iladlc.cpp b/lib/linalg/iladlc.cpp index 21b05e970a..20355f1a94 100644 --- a/lib/linalg/iladlc.cpp +++ b/lib/linalg/iladlc.cpp @@ -1,13 +1,13 @@ /* fortran/iladlc.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -128,23 +128,23 @@ integer iladlc_(integer *m, integer *n, doublereal *a, integer *lda) /* Function Body */ if (*n == 0) { - ret_val = *n; + ret_val = *n; } else if (a[*n * a_dim1 + 1] != 0. || a[*m + *n * a_dim1] != 0.) { - ret_val = *n; + ret_val = *n; } else { /* Now scan each column from the end, returning with the first non-zero. */ - for (ret_val = *n; ret_val >= 1; --ret_val) { - i__1 = *m; - for (i__ = 1; i__ <= i__1; ++i__) { - if (a[i__ + ret_val * a_dim1] != 0.) { - return ret_val; - } - } - } + for (ret_val = *n; ret_val >= 1; --ret_val) { + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + if (a[i__ + ret_val * a_dim1] != 0.) { + return ret_val; + } + } + } } return ret_val; } /* iladlc_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/iladlr.cpp b/lib/linalg/iladlr.cpp index a301b66170..a68f2a665e 100644 --- a/lib/linalg/iladlr.cpp +++ b/lib/linalg/iladlr.cpp @@ -1,13 +1,13 @@ /* fortran/iladlr.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -128,24 +128,24 @@ integer iladlr_(integer *m, integer *n, doublereal *a, integer *lda) /* Function Body */ if (*m == 0) { - ret_val = *m; + ret_val = *m; } else if (a[*m + a_dim1] != 0. || a[*m + *n * a_dim1] != 0.) { - ret_val = *m; + ret_val = *m; } else { /* Scan up each column tracking the last zero row seen. */ - ret_val = 0; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__ = *m; - while(a[max(i__,1) + j * a_dim1] == 0. && i__ >= 1) { - --i__; - } - ret_val = max(ret_val,i__); - } + ret_val = 0; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__ = *m; + while(a[max(i__,1) + j * a_dim1] == 0. && i__ >= 1) { + --i__; + } + ret_val = max(ret_val,i__); + } } return ret_val; } /* iladlr_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/ilaenv.cpp b/lib/linalg/ilaenv.cpp index 0e9a051222..6c94f00e6f 100644 --- a/lib/linalg/ilaenv.cpp +++ b/lib/linalg/ilaenv.cpp @@ -1,13 +1,13 @@ /* fortran/ilaenv.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -185,9 +185,9 @@ f"> */ /* > \endverbatim */ /* > */ /* ===================================================================== */ -integer ilaenv_(integer *ispec, char *name__, char *opts, integer *n1, - integer *n2, integer *n3, integer *n4, ftnlen name_len, ftnlen - opts_len) +integer ilaenv_(integer *ispec, char *name__, char *opts, integer *n1, + integer *n2, integer *n3, integer *n4, ftnlen name_len, ftnlen + opts_len) { /* System generated locals */ integer ret_val, i__1, i__2, i__3; @@ -206,8 +206,8 @@ integer ilaenv_(integer *ispec, char *name__, char *opts, integer *n1, logical sname; extern integer ieeeck_(integer *, real *, real *); char subnam[16]; - extern integer iparmq_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern integer iparmq_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); /* -- LAPACK auxiliary routine -- */ @@ -228,23 +228,23 @@ integer ilaenv_(integer *ispec, char *name__, char *opts, integer *n1, /* .. Executable Statements .. */ switch (*ispec) { - case 1: goto L10; - case 2: goto L10; - case 3: goto L10; - case 4: goto L80; - case 5: goto L90; - case 6: goto L100; - case 7: goto L110; - case 8: goto L120; - case 9: goto L130; - case 10: goto L140; - case 11: goto L150; - case 12: goto L160; - case 13: goto L160; - case 14: goto L160; - case 15: goto L160; - case 16: goto L160; - case 17: goto L160; + case 1: goto L10; + case 2: goto L10; + case 3: goto L10; + case 4: goto L80; + case 5: goto L90; + case 6: goto L100; + case 7: goto L110; + case 8: goto L120; + case 9: goto L130; + case 10: goto L140; + case 11: goto L150; + case 12: goto L160; + case 13: goto L160; + case 14: goto L160; + case 15: goto L160; + case 16: goto L160; + case 17: goto L160; } /* Invalid value for ISPEC */ @@ -264,66 +264,66 @@ L10: /* ASCII character set */ - if (ic >= 97 && ic <= 122) { - *(unsigned char *)subnam = (char) (ic - 32); - for (i__ = 2; i__ <= 6; ++i__) { - ic = *(unsigned char *)&subnam[i__ - 1]; - if (ic >= 97 && ic <= 122) { - *(unsigned char *)&subnam[i__ - 1] = (char) (ic - 32); - } + if (ic >= 97 && ic <= 122) { + *(unsigned char *)subnam = (char) (ic - 32); + for (i__ = 2; i__ <= 6; ++i__) { + ic = *(unsigned char *)&subnam[i__ - 1]; + if (ic >= 97 && ic <= 122) { + *(unsigned char *)&subnam[i__ - 1] = (char) (ic - 32); + } /* L20: */ - } - } + } + } } else if (iz == 233 || iz == 169) { /* EBCDIC character set */ - if (ic >= 129 && ic <= 137 || ic >= 145 && ic <= 153 || ic >= 162 && - ic <= 169) { - *(unsigned char *)subnam = (char) (ic + 64); - for (i__ = 2; i__ <= 6; ++i__) { - ic = *(unsigned char *)&subnam[i__ - 1]; - if (ic >= 129 && ic <= 137 || ic >= 145 && ic <= 153 || ic >= - 162 && ic <= 169) { - *(unsigned char *)&subnam[i__ - 1] = (char) (ic + 64); - } + if (ic >= 129 && ic <= 137 || ic >= 145 && ic <= 153 || ic >= 162 && + ic <= 169) { + *(unsigned char *)subnam = (char) (ic + 64); + for (i__ = 2; i__ <= 6; ++i__) { + ic = *(unsigned char *)&subnam[i__ - 1]; + if (ic >= 129 && ic <= 137 || ic >= 145 && ic <= 153 || ic >= + 162 && ic <= 169) { + *(unsigned char *)&subnam[i__ - 1] = (char) (ic + 64); + } /* L30: */ - } - } + } + } } else if (iz == 218 || iz == 250) { /* Prime machines: ASCII+128 */ - if (ic >= 225 && ic <= 250) { - *(unsigned char *)subnam = (char) (ic - 32); - for (i__ = 2; i__ <= 6; ++i__) { - ic = *(unsigned char *)&subnam[i__ - 1]; - if (ic >= 225 && ic <= 250) { - *(unsigned char *)&subnam[i__ - 1] = (char) (ic - 32); - } + if (ic >= 225 && ic <= 250) { + *(unsigned char *)subnam = (char) (ic - 32); + for (i__ = 2; i__ <= 6; ++i__) { + ic = *(unsigned char *)&subnam[i__ - 1]; + if (ic >= 225 && ic <= 250) { + *(unsigned char *)&subnam[i__ - 1] = (char) (ic - 32); + } /* L40: */ - } - } + } + } } *(unsigned char *)c1 = *(unsigned char *)subnam; sname = *(unsigned char *)c1 == 'S' || *(unsigned char *)c1 == 'D'; cname = *(unsigned char *)c1 == 'C' || *(unsigned char *)c1 == 'Z'; if (! (cname || sname)) { - return ret_val; + return ret_val; } s_copy(c2, subnam + 1, (ftnlen)2, (ftnlen)2); s_copy(c3, subnam + 3, (ftnlen)3, (ftnlen)3); s_copy(c4, c3 + 1, (ftnlen)2, (ftnlen)2); twostage = i_len(subnam, (ftnlen)16) >= 11 && *(unsigned char *)&subnam[ - 10] == '2'; + 10] == '2'; switch (*ispec) { - case 1: goto L50; - case 2: goto L60; - case 3: goto L70; + case 1: goto L50; + case 2: goto L60; + case 3: goto L70; } L50: @@ -340,260 +340,260 @@ L50: /* This is for *LAORHR_GETRFNP routine */ - if (sname) { - nb = 32; - } else { - nb = 32; - } + if (sname) { + nb = 32; + } else { + nb = 32; + } } else if (s_cmp(c2, (char *)"GE", (ftnlen)2, (ftnlen)2) == 0) { - if (s_cmp(c3, (char *)"TRF", (ftnlen)3, (ftnlen)3) == 0) { - if (sname) { - nb = 64; - } else { - nb = 64; - } - } else if (s_cmp(c3, (char *)"QRF", (ftnlen)3, (ftnlen)3) == 0 || s_cmp(c3, - (char *)"RQF", (ftnlen)3, (ftnlen)3) == 0 || s_cmp(c3, (char *)"LQF", (ftnlen) - 3, (ftnlen)3) == 0 || s_cmp(c3, (char *)"QLF", (ftnlen)3, (ftnlen)3) - == 0) { - if (sname) { - nb = 32; - } else { - nb = 32; - } - } else if (s_cmp(c3, (char *)"QR ", (ftnlen)3, (ftnlen)3) == 0) { - if (*n3 == 1) { - if (sname) { + if (s_cmp(c3, (char *)"TRF", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nb = 64; + } else { + nb = 64; + } + } else if (s_cmp(c3, (char *)"QRF", (ftnlen)3, (ftnlen)3) == 0 || s_cmp(c3, + (char *)"RQF", (ftnlen)3, (ftnlen)3) == 0 || s_cmp(c3, (char *)"LQF", (ftnlen) + 3, (ftnlen)3) == 0 || s_cmp(c3, (char *)"QLF", (ftnlen)3, (ftnlen)3) + == 0) { + if (sname) { + nb = 32; + } else { + nb = 32; + } + } else if (s_cmp(c3, (char *)"QR ", (ftnlen)3, (ftnlen)3) == 0) { + if (*n3 == 1) { + if (sname) { /* M*N */ - if (*n1 * *n2 <= 131072 || *n1 <= 8192) { - nb = *n1; - } else { - nb = 32768 / *n2; - } - } else { - if (*n1 * *n2 <= 131072 || *n1 <= 8192) { - nb = *n1; - } else { - nb = 32768 / *n2; - } - } - } else { - if (sname) { - nb = 1; - } else { - nb = 1; - } - } - } else if (s_cmp(c3, (char *)"LQ ", (ftnlen)3, (ftnlen)3) == 0) { - if (*n3 == 2) { - if (sname) { + if (*n1 * *n2 <= 131072 || *n1 <= 8192) { + nb = *n1; + } else { + nb = 32768 / *n2; + } + } else { + if (*n1 * *n2 <= 131072 || *n1 <= 8192) { + nb = *n1; + } else { + nb = 32768 / *n2; + } + } + } else { + if (sname) { + nb = 1; + } else { + nb = 1; + } + } + } else if (s_cmp(c3, (char *)"LQ ", (ftnlen)3, (ftnlen)3) == 0) { + if (*n3 == 2) { + if (sname) { /* M*N */ - if (*n1 * *n2 <= 131072 || *n1 <= 8192) { - nb = *n1; - } else { - nb = 32768 / *n2; - } - } else { - if (*n1 * *n2 <= 131072 || *n1 <= 8192) { - nb = *n1; - } else { - nb = 32768 / *n2; - } - } - } else { - if (sname) { - nb = 1; - } else { - nb = 1; - } - } - } else if (s_cmp(c3, (char *)"HRD", (ftnlen)3, (ftnlen)3) == 0) { - if (sname) { - nb = 32; - } else { - nb = 32; - } - } else if (s_cmp(c3, (char *)"BRD", (ftnlen)3, (ftnlen)3) == 0) { - if (sname) { - nb = 32; - } else { - nb = 32; - } - } else if (s_cmp(c3, (char *)"TRI", (ftnlen)3, (ftnlen)3) == 0) { - if (sname) { - nb = 64; - } else { - nb = 64; - } - } + if (*n1 * *n2 <= 131072 || *n1 <= 8192) { + nb = *n1; + } else { + nb = 32768 / *n2; + } + } else { + if (*n1 * *n2 <= 131072 || *n1 <= 8192) { + nb = *n1; + } else { + nb = 32768 / *n2; + } + } + } else { + if (sname) { + nb = 1; + } else { + nb = 1; + } + } + } else if (s_cmp(c3, (char *)"HRD", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nb = 32; + } else { + nb = 32; + } + } else if (s_cmp(c3, (char *)"BRD", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nb = 32; + } else { + nb = 32; + } + } else if (s_cmp(c3, (char *)"TRI", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nb = 64; + } else { + nb = 64; + } + } } else if (s_cmp(c2, (char *)"PO", (ftnlen)2, (ftnlen)2) == 0) { - if (s_cmp(c3, (char *)"TRF", (ftnlen)3, (ftnlen)3) == 0) { - if (sname) { - nb = 64; - } else { - nb = 64; - } - } + if (s_cmp(c3, (char *)"TRF", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nb = 64; + } else { + nb = 64; + } + } } else if (s_cmp(c2, (char *)"SY", (ftnlen)2, (ftnlen)2) == 0) { - if (s_cmp(c3, (char *)"TRF", (ftnlen)3, (ftnlen)3) == 0) { - if (sname) { - if (twostage) { - nb = 192; - } else { - nb = 64; - } - } else { - if (twostage) { - nb = 192; - } else { - nb = 64; - } - } - } else if (sname && s_cmp(c3, (char *)"TRD", (ftnlen)3, (ftnlen)3) == 0) { - nb = 32; - } else if (sname && s_cmp(c3, (char *)"GST", (ftnlen)3, (ftnlen)3) == 0) { - nb = 64; - } + if (s_cmp(c3, (char *)"TRF", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + if (twostage) { + nb = 192; + } else { + nb = 64; + } + } else { + if (twostage) { + nb = 192; + } else { + nb = 64; + } + } + } else if (sname && s_cmp(c3, (char *)"TRD", (ftnlen)3, (ftnlen)3) == 0) { + nb = 32; + } else if (sname && s_cmp(c3, (char *)"GST", (ftnlen)3, (ftnlen)3) == 0) { + nb = 64; + } } else if (cname && s_cmp(c2, (char *)"HE", (ftnlen)2, (ftnlen)2) == 0) { - if (s_cmp(c3, (char *)"TRF", (ftnlen)3, (ftnlen)3) == 0) { - if (twostage) { - nb = 192; - } else { - nb = 64; - } - } else if (s_cmp(c3, (char *)"TRD", (ftnlen)3, (ftnlen)3) == 0) { - nb = 32; - } else if (s_cmp(c3, (char *)"GST", (ftnlen)3, (ftnlen)3) == 0) { - nb = 64; - } + if (s_cmp(c3, (char *)"TRF", (ftnlen)3, (ftnlen)3) == 0) { + if (twostage) { + nb = 192; + } else { + nb = 64; + } + } else if (s_cmp(c3, (char *)"TRD", (ftnlen)3, (ftnlen)3) == 0) { + nb = 32; + } else if (s_cmp(c3, (char *)"GST", (ftnlen)3, (ftnlen)3) == 0) { + nb = 64; + } } else if (sname && s_cmp(c2, (char *)"OR", (ftnlen)2, (ftnlen)2) == 0) { - if (*(unsigned char *)c3 == 'G') { - if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", - (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( - ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == - 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( - c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( - ftnlen)2, (ftnlen)2) == 0) { - nb = 32; - } - } else if (*(unsigned char *)c3 == 'M') { - if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", - (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( - ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == - 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( - c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( - ftnlen)2, (ftnlen)2) == 0) { - nb = 32; - } - } + if (*(unsigned char *)c3 == 'G') { + if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == + 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( + c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( + ftnlen)2, (ftnlen)2) == 0) { + nb = 32; + } + } else if (*(unsigned char *)c3 == 'M') { + if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == + 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( + c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( + ftnlen)2, (ftnlen)2) == 0) { + nb = 32; + } + } } else if (cname && s_cmp(c2, (char *)"UN", (ftnlen)2, (ftnlen)2) == 0) { - if (*(unsigned char *)c3 == 'G') { - if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", - (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( - ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == - 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( - c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( - ftnlen)2, (ftnlen)2) == 0) { - nb = 32; - } - } else if (*(unsigned char *)c3 == 'M') { - if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", - (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( - ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == - 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( - c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( - ftnlen)2, (ftnlen)2) == 0) { - nb = 32; - } - } + if (*(unsigned char *)c3 == 'G') { + if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == + 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( + c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( + ftnlen)2, (ftnlen)2) == 0) { + nb = 32; + } + } else if (*(unsigned char *)c3 == 'M') { + if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == + 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( + c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( + ftnlen)2, (ftnlen)2) == 0) { + nb = 32; + } + } } else if (s_cmp(c2, (char *)"GB", (ftnlen)2, (ftnlen)2) == 0) { - if (s_cmp(c3, (char *)"TRF", (ftnlen)3, (ftnlen)3) == 0) { - if (sname) { - if (*n4 <= 64) { - nb = 1; - } else { - nb = 32; - } - } else { - if (*n4 <= 64) { - nb = 1; - } else { - nb = 32; - } - } - } + if (s_cmp(c3, (char *)"TRF", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + if (*n4 <= 64) { + nb = 1; + } else { + nb = 32; + } + } else { + if (*n4 <= 64) { + nb = 1; + } else { + nb = 32; + } + } + } } else if (s_cmp(c2, (char *)"PB", (ftnlen)2, (ftnlen)2) == 0) { - if (s_cmp(c3, (char *)"TRF", (ftnlen)3, (ftnlen)3) == 0) { - if (sname) { - if (*n2 <= 64) { - nb = 1; - } else { - nb = 32; - } - } else { - if (*n2 <= 64) { - nb = 1; - } else { - nb = 32; - } - } - } + if (s_cmp(c3, (char *)"TRF", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + if (*n2 <= 64) { + nb = 1; + } else { + nb = 32; + } + } else { + if (*n2 <= 64) { + nb = 1; + } else { + nb = 32; + } + } + } } else if (s_cmp(c2, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0) { - if (s_cmp(c3, (char *)"TRI", (ftnlen)3, (ftnlen)3) == 0) { - if (sname) { - nb = 64; - } else { - nb = 64; - } - } else if (s_cmp(c3, (char *)"EVC", (ftnlen)3, (ftnlen)3) == 0) { - if (sname) { - nb = 64; - } else { - nb = 64; - } - } else if (s_cmp(c3, (char *)"SYL", (ftnlen)3, (ftnlen)3) == 0) { + if (s_cmp(c3, (char *)"TRI", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nb = 64; + } else { + nb = 64; + } + } else if (s_cmp(c3, (char *)"EVC", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nb = 64; + } else { + nb = 64; + } + } else if (s_cmp(c3, (char *)"SYL", (ftnlen)3, (ftnlen)3) == 0) { /* The upper bound is to prevent overly aggressive scaling. */ - if (sname) { + if (sname) { /* Computing MIN */ /* Computing MAX */ - i__2 = 48, i__3 = (min(*n1,*n2) << 4) / 100; - i__1 = max(i__2,i__3); - nb = min(i__1,240); - } else { + i__2 = 48, i__3 = (min(*n1,*n2) << 4) / 100; + i__1 = max(i__2,i__3); + nb = min(i__1,240); + } else { /* Computing MIN */ /* Computing MAX */ - i__2 = 24, i__3 = (min(*n1,*n2) << 3) / 100; - i__1 = max(i__2,i__3); - nb = min(i__1,80); - } - } + i__2 = 24, i__3 = (min(*n1,*n2) << 3) / 100; + i__1 = max(i__2,i__3); + nb = min(i__1,80); + } + } } else if (s_cmp(c2, (char *)"LA", (ftnlen)2, (ftnlen)2) == 0) { - if (s_cmp(c3, (char *)"UUM", (ftnlen)3, (ftnlen)3) == 0) { - if (sname) { - nb = 64; - } else { - nb = 64; - } - } else if (s_cmp(c3, (char *)"TRS", (ftnlen)3, (ftnlen)3) == 0) { - if (sname) { - nb = 32; - } else { - nb = 32; - } - } + if (s_cmp(c3, (char *)"UUM", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nb = 64; + } else { + nb = 64; + } + } else if (s_cmp(c3, (char *)"TRS", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nb = 32; + } else { + nb = 32; + } + } } else if (sname && s_cmp(c2, (char *)"ST", (ftnlen)2, (ftnlen)2) == 0) { - if (s_cmp(c3, (char *)"EBZ", (ftnlen)3, (ftnlen)3) == 0) { - nb = 1; - } + if (s_cmp(c3, (char *)"EBZ", (ftnlen)3, (ftnlen)3) == 0) { + nb = 1; + } } else if (s_cmp(c2, (char *)"GG", (ftnlen)2, (ftnlen)2) == 0) { - nb = 32; - if (s_cmp(c3, (char *)"HD3", (ftnlen)3, (ftnlen)3) == 0) { - if (sname) { - nb = 32; - } else { - nb = 32; - } - } + nb = 32; + if (s_cmp(c3, (char *)"HD3", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nb = 32; + } else { + nb = 32; + } + } } ret_val = nb; return ret_val; @@ -604,93 +604,93 @@ L60: nbmin = 2; if (s_cmp(c2, (char *)"GE", (ftnlen)2, (ftnlen)2) == 0) { - if (s_cmp(c3, (char *)"QRF", (ftnlen)3, (ftnlen)3) == 0 || s_cmp(c3, (char *)"RQF", ( - ftnlen)3, (ftnlen)3) == 0 || s_cmp(c3, (char *)"LQF", (ftnlen)3, ( - ftnlen)3) == 0 || s_cmp(c3, (char *)"QLF", (ftnlen)3, (ftnlen)3) == 0) - { - if (sname) { - nbmin = 2; - } else { - nbmin = 2; - } - } else if (s_cmp(c3, (char *)"HRD", (ftnlen)3, (ftnlen)3) == 0) { - if (sname) { - nbmin = 2; - } else { - nbmin = 2; - } - } else if (s_cmp(c3, (char *)"BRD", (ftnlen)3, (ftnlen)3) == 0) { - if (sname) { - nbmin = 2; - } else { - nbmin = 2; - } - } else if (s_cmp(c3, (char *)"TRI", (ftnlen)3, (ftnlen)3) == 0) { - if (sname) { - nbmin = 2; - } else { - nbmin = 2; - } - } + if (s_cmp(c3, (char *)"QRF", (ftnlen)3, (ftnlen)3) == 0 || s_cmp(c3, (char *)"RQF", ( + ftnlen)3, (ftnlen)3) == 0 || s_cmp(c3, (char *)"LQF", (ftnlen)3, ( + ftnlen)3) == 0 || s_cmp(c3, (char *)"QLF", (ftnlen)3, (ftnlen)3) == 0) + { + if (sname) { + nbmin = 2; + } else { + nbmin = 2; + } + } else if (s_cmp(c3, (char *)"HRD", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nbmin = 2; + } else { + nbmin = 2; + } + } else if (s_cmp(c3, (char *)"BRD", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nbmin = 2; + } else { + nbmin = 2; + } + } else if (s_cmp(c3, (char *)"TRI", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nbmin = 2; + } else { + nbmin = 2; + } + } } else if (s_cmp(c2, (char *)"SY", (ftnlen)2, (ftnlen)2) == 0) { - if (s_cmp(c3, (char *)"TRF", (ftnlen)3, (ftnlen)3) == 0) { - if (sname) { - nbmin = 8; - } else { - nbmin = 8; - } - } else if (sname && s_cmp(c3, (char *)"TRD", (ftnlen)3, (ftnlen)3) == 0) { - nbmin = 2; - } + if (s_cmp(c3, (char *)"TRF", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nbmin = 8; + } else { + nbmin = 8; + } + } else if (sname && s_cmp(c3, (char *)"TRD", (ftnlen)3, (ftnlen)3) == 0) { + nbmin = 2; + } } else if (cname && s_cmp(c2, (char *)"HE", (ftnlen)2, (ftnlen)2) == 0) { - if (s_cmp(c3, (char *)"TRD", (ftnlen)3, (ftnlen)3) == 0) { - nbmin = 2; - } + if (s_cmp(c3, (char *)"TRD", (ftnlen)3, (ftnlen)3) == 0) { + nbmin = 2; + } } else if (sname && s_cmp(c2, (char *)"OR", (ftnlen)2, (ftnlen)2) == 0) { - if (*(unsigned char *)c3 == 'G') { - if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", - (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( - ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == - 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( - c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( - ftnlen)2, (ftnlen)2) == 0) { - nbmin = 2; - } - } else if (*(unsigned char *)c3 == 'M') { - if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", - (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( - ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == - 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( - c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( - ftnlen)2, (ftnlen)2) == 0) { - nbmin = 2; - } - } + if (*(unsigned char *)c3 == 'G') { + if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == + 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( + c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( + ftnlen)2, (ftnlen)2) == 0) { + nbmin = 2; + } + } else if (*(unsigned char *)c3 == 'M') { + if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == + 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( + c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( + ftnlen)2, (ftnlen)2) == 0) { + nbmin = 2; + } + } } else if (cname && s_cmp(c2, (char *)"UN", (ftnlen)2, (ftnlen)2) == 0) { - if (*(unsigned char *)c3 == 'G') { - if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", - (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( - ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == - 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( - c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( - ftnlen)2, (ftnlen)2) == 0) { - nbmin = 2; - } - } else if (*(unsigned char *)c3 == 'M') { - if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", - (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( - ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == - 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( - c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( - ftnlen)2, (ftnlen)2) == 0) { - nbmin = 2; - } - } + if (*(unsigned char *)c3 == 'G') { + if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == + 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( + c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( + ftnlen)2, (ftnlen)2) == 0) { + nbmin = 2; + } + } else if (*(unsigned char *)c3 == 'M') { + if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == + 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( + c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( + ftnlen)2, (ftnlen)2) == 0) { + nbmin = 2; + } + } } else if (s_cmp(c2, (char *)"GG", (ftnlen)2, (ftnlen)2) == 0) { - nbmin = 2; - if (s_cmp(c3, (char *)"HD3", (ftnlen)3, (ftnlen)3) == 0) { - nbmin = 2; - } + nbmin = 2; + if (s_cmp(c3, (char *)"HD3", (ftnlen)3, (ftnlen)3) == 0) { + nbmin = 2; + } } ret_val = nbmin; return ret_val; @@ -701,63 +701,63 @@ L70: nx = 0; if (s_cmp(c2, (char *)"GE", (ftnlen)2, (ftnlen)2) == 0) { - if (s_cmp(c3, (char *)"QRF", (ftnlen)3, (ftnlen)3) == 0 || s_cmp(c3, (char *)"RQF", ( - ftnlen)3, (ftnlen)3) == 0 || s_cmp(c3, (char *)"LQF", (ftnlen)3, ( - ftnlen)3) == 0 || s_cmp(c3, (char *)"QLF", (ftnlen)3, (ftnlen)3) == 0) - { - if (sname) { - nx = 128; - } else { - nx = 128; - } - } else if (s_cmp(c3, (char *)"HRD", (ftnlen)3, (ftnlen)3) == 0) { - if (sname) { - nx = 128; - } else { - nx = 128; - } - } else if (s_cmp(c3, (char *)"BRD", (ftnlen)3, (ftnlen)3) == 0) { - if (sname) { - nx = 128; - } else { - nx = 128; - } - } + if (s_cmp(c3, (char *)"QRF", (ftnlen)3, (ftnlen)3) == 0 || s_cmp(c3, (char *)"RQF", ( + ftnlen)3, (ftnlen)3) == 0 || s_cmp(c3, (char *)"LQF", (ftnlen)3, ( + ftnlen)3) == 0 || s_cmp(c3, (char *)"QLF", (ftnlen)3, (ftnlen)3) == 0) + { + if (sname) { + nx = 128; + } else { + nx = 128; + } + } else if (s_cmp(c3, (char *)"HRD", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nx = 128; + } else { + nx = 128; + } + } else if (s_cmp(c3, (char *)"BRD", (ftnlen)3, (ftnlen)3) == 0) { + if (sname) { + nx = 128; + } else { + nx = 128; + } + } } else if (s_cmp(c2, (char *)"SY", (ftnlen)2, (ftnlen)2) == 0) { - if (sname && s_cmp(c3, (char *)"TRD", (ftnlen)3, (ftnlen)3) == 0) { - nx = 32; - } + if (sname && s_cmp(c3, (char *)"TRD", (ftnlen)3, (ftnlen)3) == 0) { + nx = 32; + } } else if (cname && s_cmp(c2, (char *)"HE", (ftnlen)2, (ftnlen)2) == 0) { - if (s_cmp(c3, (char *)"TRD", (ftnlen)3, (ftnlen)3) == 0) { - nx = 32; - } + if (s_cmp(c3, (char *)"TRD", (ftnlen)3, (ftnlen)3) == 0) { + nx = 32; + } } else if (sname && s_cmp(c2, (char *)"OR", (ftnlen)2, (ftnlen)2) == 0) { - if (*(unsigned char *)c3 == 'G') { - if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", - (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( - ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == - 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( - c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( - ftnlen)2, (ftnlen)2) == 0) { - nx = 128; - } - } + if (*(unsigned char *)c3 == 'G') { + if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == + 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( + c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( + ftnlen)2, (ftnlen)2) == 0) { + nx = 128; + } + } } else if (cname && s_cmp(c2, (char *)"UN", (ftnlen)2, (ftnlen)2) == 0) { - if (*(unsigned char *)c3 == 'G') { - if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", - (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( - ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == - 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( - c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( - ftnlen)2, (ftnlen)2) == 0) { - nx = 128; - } - } + if (*(unsigned char *)c3 == 'G') { + if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == + 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( + c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( + ftnlen)2, (ftnlen)2) == 0) { + nx = 128; + } + } } else if (s_cmp(c2, (char *)"GG", (ftnlen)2, (ftnlen)2) == 0) { - nx = 128; - if (s_cmp(c3, (char *)"HD3", (ftnlen)3, (ftnlen)3) == 0) { - nx = 128; - } + nx = 128; + if (s_cmp(c3, (char *)"HD3", (ftnlen)3, (ftnlen)3) == 0) { + nx = 128; + } } ret_val = nx; return ret_val; @@ -813,7 +813,7 @@ L140: /* ILAENV = 0 */ ret_val = 1; if (ret_val == 1) { - ret_val = ieeeck_(&c__1, &c_b176, &c_b177); + ret_val = ieeeck_(&c__1, &c_b176, &c_b177); } return ret_val; @@ -824,7 +824,7 @@ L150: /* ILAENV = 0 */ ret_val = 1; if (ret_val == 1) { - ret_val = ieeeck_(&c__0, &c_b176, &c_b177); + ret_val = ieeeck_(&c__0, &c_b176, &c_b177); } return ret_val; @@ -833,7 +833,7 @@ L160: /* 12 <= ISPEC <= 17: xHSEQR or related subroutines. */ ret_val = iparmq_(ispec, name__, opts, n1, n2, n3, n4, name_len, opts_len) - ; + ; return ret_val; /* End of ILAENV */ @@ -841,5 +841,5 @@ L160: } /* ilaenv_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/ilazlc.cpp b/lib/linalg/ilazlc.cpp index 309c9e5edb..eb3f9ed604 100644 --- a/lib/linalg/ilazlc.cpp +++ b/lib/linalg/ilazlc.cpp @@ -1,13 +1,13 @@ /* fortran/ilazlc.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -128,29 +128,29 @@ integer ilazlc_(integer *m, integer *n, doublecomplex *a, integer *lda) /* Function Body */ if (*n == 0) { - ret_val = *n; + ret_val = *n; } else /* if(complicated condition) */ { - i__1 = *n * a_dim1 + 1; - i__2 = *m + *n * a_dim1; - if (a[i__1].r != 0. || a[i__1].i != 0. || (a[i__2].r != 0. || a[i__2] - .i != 0.)) { - ret_val = *n; - } else { + i__1 = *n * a_dim1 + 1; + i__2 = *m + *n * a_dim1; + if (a[i__1].r != 0. || a[i__1].i != 0. || (a[i__2].r != 0. || a[i__2] + .i != 0.)) { + ret_val = *n; + } else { /* Now scan each column from the end, returning with the first non-zero. */ - for (ret_val = *n; ret_val >= 1; --ret_val) { - i__1 = *m; - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = i__ + ret_val * a_dim1; - if (a[i__2].r != 0. || a[i__2].i != 0.) { - return ret_val; - } - } - } - } + for (ret_val = *n; ret_val >= 1; --ret_val) { + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__ + ret_val * a_dim1; + if (a[i__2].r != 0. || a[i__2].i != 0.) { + return ret_val; + } + } + } + } } return ret_val; } /* ilazlc_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/ilazlr.cpp b/lib/linalg/ilazlr.cpp index 8ca4fd8029..ebef3fa0e1 100644 --- a/lib/linalg/ilazlr.cpp +++ b/lib/linalg/ilazlr.cpp @@ -1,13 +1,13 @@ /* fortran/ilazlr.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -128,32 +128,32 @@ integer ilazlr_(integer *m, integer *n, doublecomplex *a, integer *lda) /* Function Body */ if (*m == 0) { - ret_val = *m; + ret_val = *m; } else /* if(complicated condition) */ { - i__1 = *m + a_dim1; - i__2 = *m + *n * a_dim1; - if (a[i__1].r != 0. || a[i__1].i != 0. || (a[i__2].r != 0. || a[i__2] - .i != 0.)) { - ret_val = *m; - } else { + i__1 = *m + a_dim1; + i__2 = *m + *n * a_dim1; + if (a[i__1].r != 0. || a[i__1].i != 0. || (a[i__2].r != 0. || a[i__2] + .i != 0.)) { + ret_val = *m; + } else { /* Scan up each column tracking the last zero row seen. */ - ret_val = 0; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__ = *m; - for(;;) { /* while(complicated condition) */ - i__2 = max(i__,1) + j * a_dim1; - if (!(a[i__2].r == 0. && a[i__2].i == 0. && i__ >= 1)) - break; - --i__; - } - ret_val = max(ret_val,i__); - } - } + ret_val = 0; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__ = *m; + for(;;) { /* while(complicated condition) */ + i__2 = max(i__,1) + j * a_dim1; + if (!(a[i__2].r == 0. && a[i__2].i == 0. && i__ >= 1)) + break; + --i__; + } + ret_val = max(ret_val,i__); + } + } } return ret_val; } /* ilazlr_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/iparmq.cpp b/lib/linalg/iparmq.cpp index 12f3b7f7f6..ad22d9f869 100644 --- a/lib/linalg/iparmq.cpp +++ b/lib/linalg/iparmq.cpp @@ -1,13 +1,13 @@ /* fortran/iparmq.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -246,8 +246,8 @@ f"> */ /* > \endverbatim */ /* > */ /* ===================================================================== */ -integer iparmq_(integer *ispec, char *name__, char *opts, integer *n, integer - *ilo, integer *ihi, integer *lwork, ftnlen name_len, ftnlen opts_len) +integer iparmq_(integer *ispec, char *name__, char *opts, integer *n, integer + *ilo, integer *ihi, integer *lwork, ftnlen name_len, ftnlen opts_len) { /* System generated locals */ integer ret_val, i__1, i__2; @@ -282,32 +282,32 @@ integer iparmq_(integer *ispec, char *name__, char *opts, integer *n, integer /* ==== Set the number simultaneous shifts ==== */ - nh = *ihi - *ilo + 1; - ns = 2; - if (nh >= 30) { - ns = 4; - } - if (nh >= 60) { - ns = 10; - } - if (nh >= 150) { + nh = *ihi - *ilo + 1; + ns = 2; + if (nh >= 30) { + ns = 4; + } + if (nh >= 60) { + ns = 10; + } + if (nh >= 150) { /* Computing MAX */ - r__1 = log((real) nh) / log((float)2.); - i__1 = 10, i__2 = nh / i_nint(&r__1); - ns = max(i__1,i__2); - } - if (nh >= 590) { - ns = 64; - } - if (nh >= 3000) { - ns = 128; - } - if (nh >= 6000) { - ns = 256; - } + r__1 = log((real) nh) / log((float)2.); + i__1 = 10, i__2 = nh / i_nint(&r__1); + ns = max(i__1,i__2); + } + if (nh >= 590) { + ns = 64; + } + if (nh >= 3000) { + ns = 128; + } + if (nh >= 6000) { + ns = 256; + } /* Computing MAX */ - i__1 = 2, i__2 = ns - ns % 2; - ns = max(i__1,i__2); + i__1 = 2, i__2 = ns - ns % 2; + ns = max(i__1,i__2); } if (*ispec == 12) { @@ -317,7 +317,7 @@ integer iparmq_(integer *ispec, char *name__, char *opts, integer *n, integer /* . to xLAHQR, the classic double shift algorithm. */ /* . This must be at least 11. ==== */ - ret_val = 75; + ret_val = 75; } else if (*ispec == 14) { @@ -325,23 +325,23 @@ integer iparmq_(integer *ispec, char *name__, char *opts, integer *n, integer /* . whenever aggressive early deflation finds */ /* . at least (NIBBLE*(window size)/100) deflations. ==== */ - ret_val = 14; + ret_val = 14; } else if (*ispec == 15) { /* ==== NSHFTS: The number of simultaneous shifts ===== */ - ret_val = ns; + ret_val = ns; } else if (*ispec == 13) { /* ==== NW: deflation window size. ==== */ - if (nh <= 500) { - ret_val = ns; - } else { - ret_val = ns * 3 / 2; - } + if (nh <= 500) { + ret_val = ns; + } else { + ret_val = ns * 3 / 2; + } } else if (*ispec == 16) { @@ -355,87 +355,87 @@ integer iparmq_(integer *ispec, char *name__, char *opts, integer *n, integer /* Convert NAME to upper case if the first character is lower case. */ - ret_val = 0; - s_copy(subnam, name__, (ftnlen)6, name_len); - ic = *(unsigned char *)subnam; - iz = 'Z'; - if (iz == 90 || iz == 122) { + ret_val = 0; + s_copy(subnam, name__, (ftnlen)6, name_len); + ic = *(unsigned char *)subnam; + iz = 'Z'; + if (iz == 90 || iz == 122) { /* ASCII character set */ - if (ic >= 97 && ic <= 122) { - *(unsigned char *)subnam = (char) (ic - 32); - for (i__ = 2; i__ <= 6; ++i__) { - ic = *(unsigned char *)&subnam[i__ - 1]; - if (ic >= 97 && ic <= 122) { - *(unsigned char *)&subnam[i__ - 1] = (char) (ic - 32); - } - } - } + if (ic >= 97 && ic <= 122) { + *(unsigned char *)subnam = (char) (ic - 32); + for (i__ = 2; i__ <= 6; ++i__) { + ic = *(unsigned char *)&subnam[i__ - 1]; + if (ic >= 97 && ic <= 122) { + *(unsigned char *)&subnam[i__ - 1] = (char) (ic - 32); + } + } + } - } else if (iz == 233 || iz == 169) { + } else if (iz == 233 || iz == 169) { /* EBCDIC character set */ - if (ic >= 129 && ic <= 137 || ic >= 145 && ic <= 153 || ic >= 162 - && ic <= 169) { - *(unsigned char *)subnam = (char) (ic + 64); - for (i__ = 2; i__ <= 6; ++i__) { - ic = *(unsigned char *)&subnam[i__ - 1]; - if (ic >= 129 && ic <= 137 || ic >= 145 && ic <= 153 || - ic >= 162 && ic <= 169) { - *(unsigned char *)&subnam[i__ - 1] = (char) (ic + 64); - } - } - } + if (ic >= 129 && ic <= 137 || ic >= 145 && ic <= 153 || ic >= 162 + && ic <= 169) { + *(unsigned char *)subnam = (char) (ic + 64); + for (i__ = 2; i__ <= 6; ++i__) { + ic = *(unsigned char *)&subnam[i__ - 1]; + if (ic >= 129 && ic <= 137 || ic >= 145 && ic <= 153 || + ic >= 162 && ic <= 169) { + *(unsigned char *)&subnam[i__ - 1] = (char) (ic + 64); + } + } + } - } else if (iz == 218 || iz == 250) { + } else if (iz == 218 || iz == 250) { /* Prime machines: ASCII+128 */ - if (ic >= 225 && ic <= 250) { - *(unsigned char *)subnam = (char) (ic - 32); - for (i__ = 2; i__ <= 6; ++i__) { - ic = *(unsigned char *)&subnam[i__ - 1]; - if (ic >= 225 && ic <= 250) { - *(unsigned char *)&subnam[i__ - 1] = (char) (ic - 32); - } - } - } - } + if (ic >= 225 && ic <= 250) { + *(unsigned char *)subnam = (char) (ic - 32); + for (i__ = 2; i__ <= 6; ++i__) { + ic = *(unsigned char *)&subnam[i__ - 1]; + if (ic >= 225 && ic <= 250) { + *(unsigned char *)&subnam[i__ - 1] = (char) (ic - 32); + } + } + } + } - if (s_cmp(subnam + 1, (char *)"GGHRD", (ftnlen)5, (ftnlen)5) == 0 || s_cmp( - subnam + 1, (char *)"GGHD3", (ftnlen)5, (ftnlen)5) == 0) { - ret_val = 1; - if (nh >= 14) { - ret_val = 2; - } - } else if (s_cmp(subnam + 3, (char *)"EXC", (ftnlen)3, (ftnlen)3) == 0) { - if (nh >= 14) { - ret_val = 1; - } - if (nh >= 14) { - ret_val = 2; - } - } else if (s_cmp(subnam + 1, (char *)"HSEQR", (ftnlen)5, (ftnlen)5) == 0 || - s_cmp(subnam + 1, (char *)"LAQR", (ftnlen)4, (ftnlen)4) == 0) { - if (ns >= 14) { - ret_val = 1; - } - if (ns >= 14) { - ret_val = 2; - } - } + if (s_cmp(subnam + 1, (char *)"GGHRD", (ftnlen)5, (ftnlen)5) == 0 || s_cmp( + subnam + 1, (char *)"GGHD3", (ftnlen)5, (ftnlen)5) == 0) { + ret_val = 1; + if (nh >= 14) { + ret_val = 2; + } + } else if (s_cmp(subnam + 3, (char *)"EXC", (ftnlen)3, (ftnlen)3) == 0) { + if (nh >= 14) { + ret_val = 1; + } + if (nh >= 14) { + ret_val = 2; + } + } else if (s_cmp(subnam + 1, (char *)"HSEQR", (ftnlen)5, (ftnlen)5) == 0 || + s_cmp(subnam + 1, (char *)"LAQR", (ftnlen)4, (ftnlen)4) == 0) { + if (ns >= 14) { + ret_val = 1; + } + if (ns >= 14) { + ret_val = 2; + } + } } else if (*ispec == 17) { /* === Relative cost of near-the-diagonal chase vs */ /* BLAS updates === */ - ret_val = 10; + ret_val = 10; } else { /* ===== invalid value of ispec ===== */ - ret_val = -1; + ret_val = -1; } @@ -445,5 +445,5 @@ integer iparmq_(integer *ispec, char *name__, char *opts, integer *n, integer } /* iparmq_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/lmp_f2c.h b/lib/linalg/lmp_f2c.h index 0b1ebac99c..7483a147ea 100644 --- a/lib/linalg/lmp_f2c.h +++ b/lib/linalg/lmp_f2c.h @@ -2,7 +2,7 @@ /** barf [ba:rf] 2. "He suggested using FORTRAN, and everybody barfed." - - From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */ + - From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */ #ifndef F2C_INCLUDE #define F2C_INCLUDE @@ -19,11 +19,11 @@ typedef long int logical; typedef short int shortlogical; typedef char logical1; typedef char integer1; -#ifdef INTEGER_STAR_8 /* Adjust for integer*8. */ -typedef long long longint; /* system-dependent */ -typedef unsigned long long ulongint; /* system-dependent */ -#define qbit_clear(a,b) ((a) & ~((ulongint)1 << (b))) -#define qbit_set(a,b) ((a) | ((ulongint)1 << (b))) +#ifdef INTEGER_STAR_8 /* Adjust for integer*8. */ +typedef long long longint; /* system-dependent */ +typedef unsigned long long ulongint; /* system-dependent */ +#define qbit_clear(a,b) ((a) & ~((ulongint)1 << (b))) +#define qbit_set(a,b) ((a) | ((ulongint)1 << (b))) #endif #define TRUE_ (1) @@ -49,109 +49,109 @@ typedef long int ftnint; /*external read, write*/ typedef struct -{ flag cierr; - ftnint ciunit; - flag ciend; - char *cifmt; - ftnint cirec; +{ flag cierr; + ftnint ciunit; + flag ciend; + char *cifmt; + ftnint cirec; } cilist; /*internal read, write*/ typedef struct -{ flag icierr; - char *iciunit; - flag iciend; - char *icifmt; - ftnint icirlen; - ftnint icirnum; +{ flag icierr; + char *iciunit; + flag iciend; + char *icifmt; + ftnint icirlen; + ftnint icirnum; } icilist; /*open*/ typedef struct -{ flag oerr; - ftnint ounit; - char *ofnm; - ftnlen ofnmlen; - char *osta; - char *oacc; - char *ofm; - ftnint orl; - char *oblnk; +{ flag oerr; + ftnint ounit; + char *ofnm; + ftnlen ofnmlen; + char *osta; + char *oacc; + char *ofm; + ftnint orl; + char *oblnk; } olist; /*close*/ typedef struct -{ flag cerr; - ftnint cunit; - char *csta; +{ flag cerr; + ftnint cunit; + char *csta; } cllist; /*rewind, backspace, endfile*/ typedef struct -{ flag aerr; - ftnint aunit; +{ flag aerr; + ftnint aunit; } alist; /* inquire */ typedef struct -{ flag inerr; - ftnint inunit; - char *infile; - ftnlen infilen; - ftnint *inex; /*parameters in standard's order*/ - ftnint *inopen; - ftnint *innum; - ftnint *innamed; - char *inname; - ftnlen innamlen; - char *inacc; - ftnlen inacclen; - char *inseq; - ftnlen inseqlen; - char *indir; - ftnlen indirlen; - char *infmt; - ftnlen infmtlen; - char *inform; - ftnint informlen; - char *inunf; - ftnlen inunflen; - ftnint *inrecl; - ftnint *innrec; - char *inblank; - ftnlen inblanklen; +{ flag inerr; + ftnint inunit; + char *infile; + ftnlen infilen; + ftnint *inex; /*parameters in standard's order*/ + ftnint *inopen; + ftnint *innum; + ftnint *innamed; + char *inname; + ftnlen innamlen; + char *inacc; + ftnlen inacclen; + char *inseq; + ftnlen inseqlen; + char *indir; + ftnlen indirlen; + char *infmt; + ftnlen infmtlen; + char *inform; + ftnint informlen; + char *inunf; + ftnlen inunflen; + ftnint *inrecl; + ftnint *innrec; + char *inblank; + ftnlen inblanklen; } inlist; #define VOID void -union Multitype { /* for multiple entry points */ - integer1 g; - shortint h; - integer i; - /* longint j; */ - real r; - doublereal d; - complex c; - doublecomplex z; - }; +union Multitype { /* for multiple entry points */ + integer1 g; + shortint h; + integer i; + /* longint j; */ + real r; + doublereal d; + complex c; + doublecomplex z; + }; typedef union Multitype Multitype; -/*typedef long int Long;*/ /* No longer used; formerly in Namelist */ +/*typedef long int Long;*/ /* No longer used; formerly in Namelist */ -struct Vardesc { /* for Namelist */ - char *name; - char *addr; - ftnlen *dims; - int type; - }; +struct Vardesc { /* for Namelist */ + char *name; + char *addr; + ftnlen *dims; + int type; + }; typedef struct Vardesc Vardesc; struct Namelist { - char *name; - Vardesc **vars; - int nvars; - }; + char *name; + Vardesc **vars; + int nvars; + }; typedef struct Namelist Namelist; #define abs(x) ((x) >= 0 ? (x) : -(x)) @@ -160,9 +160,9 @@ typedef struct Namelist Namelist; #define max(a,b) ((a) >= (b) ? (a) : (b)) #define dmin(a,b) (doublereal)min(a,b) #define dmax(a,b) (doublereal)max(a,b) -#define bit_test(a,b) ((a) >> (b) & 1) -#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b))) -#define bit_set(a,b) ((a) | ((uinteger)1 << (b))) +#define bit_test(a,b) ((a) >> (b) & 1) +#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b))) +#define bit_set(a,b) ((a) | ((uinteger)1 << (b))) /* procedure parameter types for -A and -C++ */ @@ -193,10 +193,10 @@ typedef /* Character */ VOID (*H_fp)(); typedef /* Subroutine */ int (*S_fp)(); #endif /* E_fp is for real functions when -R is not specified */ -typedef VOID C_f; /* complex function */ -typedef VOID H_f; /* character function */ -typedef VOID Z_f; /* double complex function */ -typedef doublereal E_f; /* real function with -R not specified */ +typedef VOID C_f; /* complex function */ +typedef VOID H_f; /* character function */ +typedef VOID Z_f; /* double complex function */ +typedef doublereal E_f; /* real function with -R not specified */ /* undef any lower-case symbols that your C compiler predefines, e.g.: */ diff --git a/lib/linalg/zaxpy.cpp b/lib/linalg/zaxpy.cpp index 2788743a40..6939872757 100644 --- a/lib/linalg/zaxpy.cpp +++ b/lib/linalg/zaxpy.cpp @@ -1,13 +1,13 @@ /* fortran/zaxpy.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -101,8 +101,8 @@ extern "C" { /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int zaxpy_(integer *n, doublecomplex *za, doublecomplex *zx, - integer *incx, doublecomplex *zy, integer *incy) +/* Subroutine */ int zaxpy_(integer *n, doublecomplex *za, doublecomplex *zx, + integer *incx, doublecomplex *zy, integer *incy) { /* System generated locals */ integer i__1, i__2, i__3, i__4; @@ -134,50 +134,50 @@ extern "C" { /* Function Body */ if (*n <= 0) { - return 0; + return 0; } if (dcabs1_(za) == 0.) { - return 0; + return 0; } if (*incx == 1 && *incy == 1) { /* code for both increments equal to 1 */ - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = i__; - i__3 = i__; - i__4 = i__; - z__2.r = za->r * zx[i__4].r - za->i * zx[i__4].i, z__2.i = za->r * - zx[i__4].i + za->i * zx[i__4].r; - z__1.r = zy[i__3].r + z__2.r, z__1.i = zy[i__3].i + z__2.i; - zy[i__2].r = z__1.r, zy[i__2].i = z__1.i; - } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__; + i__3 = i__; + i__4 = i__; + z__2.r = za->r * zx[i__4].r - za->i * zx[i__4].i, z__2.i = za->r * + zx[i__4].i + za->i * zx[i__4].r; + z__1.r = zy[i__3].r + z__2.r, z__1.i = zy[i__3].i + z__2.i; + zy[i__2].r = z__1.r, zy[i__2].i = z__1.i; + } } else { /* code for unequal increments or equal increments */ /* not equal to 1 */ - ix = 1; - iy = 1; - if (*incx < 0) { - ix = (-(*n) + 1) * *incx + 1; - } - if (*incy < 0) { - iy = (-(*n) + 1) * *incy + 1; - } - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = iy; - i__3 = iy; - i__4 = ix; - z__2.r = za->r * zx[i__4].r - za->i * zx[i__4].i, z__2.i = za->r * - zx[i__4].i + za->i * zx[i__4].r; - z__1.r = zy[i__3].r + z__2.r, z__1.i = zy[i__3].i + z__2.i; - zy[i__2].r = z__1.r, zy[i__2].i = z__1.i; - ix += *incx; - iy += *incy; - } + ix = 1; + iy = 1; + if (*incx < 0) { + ix = (-(*n) + 1) * *incx + 1; + } + if (*incy < 0) { + iy = (-(*n) + 1) * *incy + 1; + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = iy; + i__3 = iy; + i__4 = ix; + z__2.r = za->r * zx[i__4].r - za->i * zx[i__4].i, z__2.i = za->r * + zx[i__4].i + za->i * zx[i__4].r; + z__1.r = zy[i__3].r + z__2.r, z__1.i = zy[i__3].i + z__2.i; + zy[i__2].r = z__1.r, zy[i__2].i = z__1.i; + ix += *incx; + iy += *incy; + } } return 0; @@ -187,5 +187,5 @@ extern "C" { } /* zaxpy_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zcopy.cpp b/lib/linalg/zcopy.cpp index 357bd961a0..97d1250228 100644 --- a/lib/linalg/zcopy.cpp +++ b/lib/linalg/zcopy.cpp @@ -1,13 +1,13 @@ /* fortran/zcopy.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -94,8 +94,8 @@ extern "C" { /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int zcopy_(integer *n, doublecomplex *zx, integer *incx, - doublecomplex *zy, integer *incy) +/* Subroutine */ int zcopy_(integer *n, doublecomplex *zx, integer *incx, + doublecomplex *zy, integer *incy) { /* System generated locals */ integer i__1, i__2, i__3; @@ -123,39 +123,39 @@ extern "C" { /* Function Body */ if (*n <= 0) { - return 0; + return 0; } if (*incx == 1 && *incy == 1) { /* code for both increments equal to 1 */ - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = i__; - i__3 = i__; - zy[i__2].r = zx[i__3].r, zy[i__2].i = zx[i__3].i; - } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__; + i__3 = i__; + zy[i__2].r = zx[i__3].r, zy[i__2].i = zx[i__3].i; + } } else { /* code for unequal increments or equal increments */ /* not equal to 1 */ - ix = 1; - iy = 1; - if (*incx < 0) { - ix = (-(*n) + 1) * *incx + 1; - } - if (*incy < 0) { - iy = (-(*n) + 1) * *incy + 1; - } - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = iy; - i__3 = ix; - zy[i__2].r = zx[i__3].r, zy[i__2].i = zx[i__3].i; - ix += *incx; - iy += *incy; - } + ix = 1; + iy = 1; + if (*incx < 0) { + ix = (-(*n) + 1) * *incx + 1; + } + if (*incy < 0) { + iy = (-(*n) + 1) * *incy + 1; + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = iy; + i__3 = ix; + zy[i__2].r = zx[i__3].r, zy[i__2].i = zx[i__3].i; + ix += *incx; + iy += *incy; + } } return 0; @@ -164,5 +164,5 @@ extern "C" { } /* zcopy_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zdotc.cpp b/lib/linalg/zdotc.cpp index 943f923bea..e0c614e843 100644 --- a/lib/linalg/zdotc.cpp +++ b/lib/linalg/zdotc.cpp @@ -1,13 +1,13 @@ /* fortran/zdotc.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -96,8 +96,8 @@ extern "C" { /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Double Complex */ VOID zdotc_(doublecomplex * ret_val, integer *n, - doublecomplex *zx, integer *incx, doublecomplex *zy, integer *incy) +/* Double Complex */ VOID zdotc_(doublecomplex * ret_val, integer *n, + doublecomplex *zx, integer *incx, doublecomplex *zy, integer *incy) { /* System generated locals */ integer i__1, i__2; @@ -134,45 +134,45 @@ extern "C" { ztemp.r = 0., ztemp.i = 0.; ret_val->r = 0., ret_val->i = 0.; if (*n <= 0) { - return ; + return ; } if (*incx == 1 && *incy == 1) { /* code for both increments equal to 1 */ - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - d_cnjg(&z__3, &zx[i__]); - i__2 = i__; - z__2.r = z__3.r * zy[i__2].r - z__3.i * zy[i__2].i, z__2.i = - z__3.r * zy[i__2].i + z__3.i * zy[i__2].r; - z__1.r = ztemp.r + z__2.r, z__1.i = ztemp.i + z__2.i; - ztemp.r = z__1.r, ztemp.i = z__1.i; - } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + d_cnjg(&z__3, &zx[i__]); + i__2 = i__; + z__2.r = z__3.r * zy[i__2].r - z__3.i * zy[i__2].i, z__2.i = + z__3.r * zy[i__2].i + z__3.i * zy[i__2].r; + z__1.r = ztemp.r + z__2.r, z__1.i = ztemp.i + z__2.i; + ztemp.r = z__1.r, ztemp.i = z__1.i; + } } else { /* code for unequal increments or equal increments */ /* not equal to 1 */ - ix = 1; - iy = 1; - if (*incx < 0) { - ix = (-(*n) + 1) * *incx + 1; - } - if (*incy < 0) { - iy = (-(*n) + 1) * *incy + 1; - } - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - d_cnjg(&z__3, &zx[ix]); - i__2 = iy; - z__2.r = z__3.r * zy[i__2].r - z__3.i * zy[i__2].i, z__2.i = - z__3.r * zy[i__2].i + z__3.i * zy[i__2].r; - z__1.r = ztemp.r + z__2.r, z__1.i = ztemp.i + z__2.i; - ztemp.r = z__1.r, ztemp.i = z__1.i; - ix += *incx; - iy += *incy; - } + ix = 1; + iy = 1; + if (*incx < 0) { + ix = (-(*n) + 1) * *incx + 1; + } + if (*incy < 0) { + iy = (-(*n) + 1) * *incy + 1; + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + d_cnjg(&z__3, &zx[ix]); + i__2 = iy; + z__2.r = z__3.r * zy[i__2].r - z__3.i * zy[i__2].i, z__2.i = + z__3.r * zy[i__2].i + z__3.i * zy[i__2].r; + z__1.r = ztemp.r + z__2.r, z__1.i = ztemp.i + z__2.i; + ztemp.r = z__1.r, ztemp.i = z__1.i; + ix += *incx; + iy += *incy; + } } ret_val->r = ztemp.r, ret_val->i = ztemp.i; return ; @@ -182,5 +182,5 @@ extern "C" { } /* zdotc_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zdrot.cpp b/lib/linalg/zdrot.cpp index c6ec16b053..e4c66f5480 100644 --- a/lib/linalg/zdrot.cpp +++ b/lib/linalg/zdrot.cpp @@ -1,13 +1,13 @@ /* fortran/zdrot.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -111,8 +111,8 @@ extern "C" { /* > \ingroup complex16_blas_level1 */ /* ===================================================================== */ -/* Subroutine */ int zdrot_(integer *n, doublecomplex *zx, integer *incx, - doublecomplex *zy, integer *incy, doublereal *c__, doublereal *s) +/* Subroutine */ int zdrot_(integer *n, doublecomplex *zx, integer *incx, + doublecomplex *zy, integer *incy, doublereal *c__, doublereal *s) { /* System generated locals */ integer i__1, i__2, i__3, i__4; @@ -144,63 +144,63 @@ extern "C" { /* Function Body */ if (*n <= 0) { - return 0; + return 0; } if (*incx == 1 && *incy == 1) { /* code for both increments equal to 1 */ - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = i__; - z__2.r = *c__ * zx[i__2].r, z__2.i = *c__ * zx[i__2].i; - i__3 = i__; - z__3.r = *s * zy[i__3].r, z__3.i = *s * zy[i__3].i; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; - ctemp.r = z__1.r, ctemp.i = z__1.i; - i__2 = i__; - i__3 = i__; - z__2.r = *c__ * zy[i__3].r, z__2.i = *c__ * zy[i__3].i; - i__4 = i__; - z__3.r = *s * zx[i__4].r, z__3.i = *s * zx[i__4].i; - z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i; - zy[i__2].r = z__1.r, zy[i__2].i = z__1.i; - i__2 = i__; - zx[i__2].r = ctemp.r, zx[i__2].i = ctemp.i; - } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__; + z__2.r = *c__ * zx[i__2].r, z__2.i = *c__ * zx[i__2].i; + i__3 = i__; + z__3.r = *s * zy[i__3].r, z__3.i = *s * zy[i__3].i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; + ctemp.r = z__1.r, ctemp.i = z__1.i; + i__2 = i__; + i__3 = i__; + z__2.r = *c__ * zy[i__3].r, z__2.i = *c__ * zy[i__3].i; + i__4 = i__; + z__3.r = *s * zx[i__4].r, z__3.i = *s * zx[i__4].i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i; + zy[i__2].r = z__1.r, zy[i__2].i = z__1.i; + i__2 = i__; + zx[i__2].r = ctemp.r, zx[i__2].i = ctemp.i; + } } else { /* code for unequal increments or equal increments not equal */ /* to 1 */ - ix = 1; - iy = 1; - if (*incx < 0) { - ix = (-(*n) + 1) * *incx + 1; - } - if (*incy < 0) { - iy = (-(*n) + 1) * *incy + 1; - } - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = ix; - z__2.r = *c__ * zx[i__2].r, z__2.i = *c__ * zx[i__2].i; - i__3 = iy; - z__3.r = *s * zy[i__3].r, z__3.i = *s * zy[i__3].i; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; - ctemp.r = z__1.r, ctemp.i = z__1.i; - i__2 = iy; - i__3 = iy; - z__2.r = *c__ * zy[i__3].r, z__2.i = *c__ * zy[i__3].i; - i__4 = ix; - z__3.r = *s * zx[i__4].r, z__3.i = *s * zx[i__4].i; - z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i; - zy[i__2].r = z__1.r, zy[i__2].i = z__1.i; - i__2 = ix; - zx[i__2].r = ctemp.r, zx[i__2].i = ctemp.i; - ix += *incx; - iy += *incy; - } + ix = 1; + iy = 1; + if (*incx < 0) { + ix = (-(*n) + 1) * *incx + 1; + } + if (*incy < 0) { + iy = (-(*n) + 1) * *incy + 1; + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = ix; + z__2.r = *c__ * zx[i__2].r, z__2.i = *c__ * zx[i__2].i; + i__3 = iy; + z__3.r = *s * zy[i__3].r, z__3.i = *s * zy[i__3].i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; + ctemp.r = z__1.r, ctemp.i = z__1.i; + i__2 = iy; + i__3 = iy; + z__2.r = *c__ * zy[i__3].r, z__2.i = *c__ * zy[i__3].i; + i__4 = ix; + z__3.r = *s * zx[i__4].r, z__3.i = *s * zx[i__4].i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i; + zy[i__2].r = z__1.r, zy[i__2].i = z__1.i; + i__2 = ix; + zx[i__2].r = ctemp.r, zx[i__2].i = ctemp.i; + ix += *incx; + iy += *incy; + } } return 0; @@ -209,5 +209,5 @@ extern "C" { } /* zdrot_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zdscal.cpp b/lib/linalg/zdscal.cpp index c7c6406782..fd444bdf71 100644 --- a/lib/linalg/zdscal.cpp +++ b/lib/linalg/zdscal.cpp @@ -1,13 +1,13 @@ /* fortran/zdscal.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -91,8 +91,8 @@ extern "C" { /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int zdscal_(integer *n, doublereal *da, doublecomplex *zx, - integer *incx) +/* Subroutine */ int zdscal_(integer *n, doublereal *da, doublecomplex *zx, + integer *incx) { /* System generated locals */ integer i__1, i__2, i__3, i__4; @@ -127,36 +127,36 @@ extern "C" { /* Function Body */ if (*n <= 0 || *incx <= 0 || *da == 1.) { - return 0; + return 0; } if (*incx == 1) { /* code for increment equal to 1 */ - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = i__; - i__3 = i__; - d__1 = *da * zx[i__3].r; - d__2 = *da * d_imag(&zx[i__]); - z__1.r = d__1, z__1.i = d__2; - zx[i__2].r = z__1.r, zx[i__2].i = z__1.i; - } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__; + i__3 = i__; + d__1 = *da * zx[i__3].r; + d__2 = *da * d_imag(&zx[i__]); + z__1.r = d__1, z__1.i = d__2; + zx[i__2].r = z__1.r, zx[i__2].i = z__1.i; + } } else { /* code for increment not equal to 1 */ - nincx = *n * *incx; - i__1 = nincx; - i__2 = *incx; - for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { - i__3 = i__; - i__4 = i__; - d__1 = *da * zx[i__4].r; - d__2 = *da * d_imag(&zx[i__]); - z__1.r = d__1, z__1.i = d__2; - zx[i__3].r = z__1.r, zx[i__3].i = z__1.i; - } + nincx = *n * *incx; + i__1 = nincx; + i__2 = *incx; + for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { + i__3 = i__; + i__4 = i__; + d__1 = *da * zx[i__4].r; + d__2 = *da * d_imag(&zx[i__]); + z__1.r = d__1, z__1.i = d__2; + zx[i__3].r = z__1.r, zx[i__3].i = z__1.i; + } } return 0; @@ -165,5 +165,5 @@ extern "C" { } /* zdscal_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zgemm.cpp b/lib/linalg/zgemm.cpp index 92434e720f..53020bef2d 100644 --- a/lib/linalg/zgemm.cpp +++ b/lib/linalg/zgemm.cpp @@ -1,13 +1,13 @@ /* fortran/zgemm.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -201,13 +201,13 @@ extern "C" { /* > */ /* ===================================================================== */ /* Subroutine */ int zgemm_(char *transa, char *transb, integer *m, integer * - n, integer *k, doublecomplex *alpha, doublecomplex *a, integer *lda, - doublecomplex *b, integer *ldb, doublecomplex *beta, doublecomplex * - c__, integer *ldc, ftnlen transa_len, ftnlen transb_len) + n, integer *k, doublecomplex *alpha, doublecomplex *a, integer *lda, + doublecomplex *b, integer *ldb, doublecomplex *beta, doublecomplex * + c__, integer *ldc, ftnlen transa_len, ftnlen transb_len) { /* System generated locals */ - integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, - i__3, i__4, i__5, i__6; + integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, + i__3, i__4, i__5, i__6; doublecomplex z__1, z__2, z__3, z__4; /* Builtin functions */ @@ -267,489 +267,489 @@ extern "C" { conja = lsame_(transa, (char *)"C", (ftnlen)1, (ftnlen)1); conjb = lsame_(transb, (char *)"C", (ftnlen)1, (ftnlen)1); if (nota) { - nrowa = *m; + nrowa = *m; } else { - nrowa = *k; + nrowa = *k; } if (notb) { - nrowb = *k; + nrowb = *k; } else { - nrowb = *n; + nrowb = *n; } /* Test the input parameters. */ info = 0; if (! nota && ! conja && ! lsame_(transa, (char *)"T", (ftnlen)1, (ftnlen)1)) { - info = 1; + info = 1; } else if (! notb && ! conjb && ! lsame_(transb, (char *)"T", (ftnlen)1, (ftnlen) - 1)) { - info = 2; + 1)) { + info = 2; } else if (*m < 0) { - info = 3; + info = 3; } else if (*n < 0) { - info = 4; + info = 4; } else if (*k < 0) { - info = 5; + info = 5; } else if (*lda < max(1,nrowa)) { - info = 8; + info = 8; } else if (*ldb < max(1,nrowb)) { - info = 10; + info = 10; } else if (*ldc < max(1,*m)) { - info = 13; + info = 13; } if (info != 0) { - xerbla_((char *)"ZGEMM ", &info, (ftnlen)6); - return 0; + xerbla_((char *)"ZGEMM ", &info, (ftnlen)6); + return 0; } /* Quick return if possible. */ if (*m == 0 || *n == 0 || (alpha->r == 0. && alpha->i == 0. || *k == 0) && - (beta->r == 1. && beta->i == 0.)) { - return 0; + (beta->r == 1. && beta->i == 0.)) { + return 0; } /* And when alpha.eq.zero. */ if (alpha->r == 0. && alpha->i == 0.) { - if (beta->r == 0. && beta->i == 0.) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * c_dim1; - c__[i__3].r = 0., c__[i__3].i = 0.; + if (beta->r == 0. && beta->i == 0.) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + c__[i__3].r = 0., c__[i__3].i = 0.; /* L10: */ - } + } /* L20: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * c_dim1; - i__4 = i__ + j * c_dim1; - z__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4].i, - z__1.i = beta->r * c__[i__4].i + beta->i * c__[ - i__4].r; - c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + i__4 = i__ + j * c_dim1; + z__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4].i, + z__1.i = beta->r * c__[i__4].i + beta->i * c__[ + i__4].r; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; /* L30: */ - } + } /* L40: */ - } - } - return 0; + } + } + return 0; } /* Start the operations. */ if (notb) { - if (nota) { + if (nota) { /* Form C := alpha*A*B + beta*C. */ - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - if (beta->r == 0. && beta->i == 0.) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * c_dim1; - c__[i__3].r = 0., c__[i__3].i = 0.; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (beta->r == 0. && beta->i == 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + c__[i__3].r = 0., c__[i__3].i = 0.; /* L50: */ - } - } else if (beta->r != 1. || beta->i != 0.) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * c_dim1; - i__4 = i__ + j * c_dim1; - z__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4] - .i, z__1.i = beta->r * c__[i__4].i + beta->i * - c__[i__4].r; - c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } + } else if (beta->r != 1. || beta->i != 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + i__4 = i__ + j * c_dim1; + z__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4] + .i, z__1.i = beta->r * c__[i__4].i + beta->i * + c__[i__4].r; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; /* L60: */ - } - } - i__2 = *k; - for (l = 1; l <= i__2; ++l) { - i__3 = l + j * b_dim1; - z__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3].i, - z__1.i = alpha->r * b[i__3].i + alpha->i * b[i__3] - .r; - temp.r = z__1.r, temp.i = z__1.i; - i__3 = *m; - for (i__ = 1; i__ <= i__3; ++i__) { - i__4 = i__ + j * c_dim1; - i__5 = i__ + j * c_dim1; - i__6 = i__ + l * a_dim1; - z__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i, - z__2.i = temp.r * a[i__6].i + temp.i * a[i__6] - .r; - z__1.r = c__[i__5].r + z__2.r, z__1.i = c__[i__5].i + - z__2.i; - c__[i__4].r = z__1.r, c__[i__4].i = z__1.i; + } + } + i__2 = *k; + for (l = 1; l <= i__2; ++l) { + i__3 = l + j * b_dim1; + z__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3].i, + z__1.i = alpha->r * b[i__3].i + alpha->i * b[i__3] + .r; + temp.r = z__1.r, temp.i = z__1.i; + i__3 = *m; + for (i__ = 1; i__ <= i__3; ++i__) { + i__4 = i__ + j * c_dim1; + i__5 = i__ + j * c_dim1; + i__6 = i__ + l * a_dim1; + z__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i, + z__2.i = temp.r * a[i__6].i + temp.i * a[i__6] + .r; + z__1.r = c__[i__5].r + z__2.r, z__1.i = c__[i__5].i + + z__2.i; + c__[i__4].r = z__1.r, c__[i__4].i = z__1.i; /* L70: */ - } + } /* L80: */ - } + } /* L90: */ - } - } else if (conja) { + } + } else if (conja) { /* Form C := alpha*A**H*B + beta*C. */ - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - temp.r = 0., temp.i = 0.; - i__3 = *k; - for (l = 1; l <= i__3; ++l) { - d_cnjg(&z__3, &a[l + i__ * a_dim1]); - i__4 = l + j * b_dim1; - z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4].i, - z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4] - .r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; - temp.r = z__1.r, temp.i = z__1.i; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp.r = 0., temp.i = 0.; + i__3 = *k; + for (l = 1; l <= i__3; ++l) { + d_cnjg(&z__3, &a[l + i__ * a_dim1]); + i__4 = l + j * b_dim1; + z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4].i, + z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4] + .r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; /* L100: */ - } - if (beta->r == 0. && beta->i == 0.) { - i__3 = i__ + j * c_dim1; - z__1.r = alpha->r * temp.r - alpha->i * temp.i, - z__1.i = alpha->r * temp.i + alpha->i * - temp.r; - c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; - } else { - i__3 = i__ + j * c_dim1; - z__2.r = alpha->r * temp.r - alpha->i * temp.i, - z__2.i = alpha->r * temp.i + alpha->i * - temp.r; - i__4 = i__ + j * c_dim1; - z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4] - .i, z__3.i = beta->r * c__[i__4].i + beta->i * - c__[i__4].r; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; - c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; - } + } + if (beta->r == 0. && beta->i == 0.) { + i__3 = i__ + j * c_dim1; + z__1.r = alpha->r * temp.r - alpha->i * temp.i, + z__1.i = alpha->r * temp.i + alpha->i * + temp.r; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } else { + i__3 = i__ + j * c_dim1; + z__2.r = alpha->r * temp.r - alpha->i * temp.i, + z__2.i = alpha->r * temp.i + alpha->i * + temp.r; + i__4 = i__ + j * c_dim1; + z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4] + .i, z__3.i = beta->r * c__[i__4].i + beta->i * + c__[i__4].r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } /* L110: */ - } + } /* L120: */ - } - } else { + } + } else { /* Form C := alpha*A**T*B + beta*C */ - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - temp.r = 0., temp.i = 0.; - i__3 = *k; - for (l = 1; l <= i__3; ++l) { - i__4 = l + i__ * a_dim1; - i__5 = l + j * b_dim1; - z__2.r = a[i__4].r * b[i__5].r - a[i__4].i * b[i__5] - .i, z__2.i = a[i__4].r * b[i__5].i + a[i__4] - .i * b[i__5].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; - temp.r = z__1.r, temp.i = z__1.i; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp.r = 0., temp.i = 0.; + i__3 = *k; + for (l = 1; l <= i__3; ++l) { + i__4 = l + i__ * a_dim1; + i__5 = l + j * b_dim1; + z__2.r = a[i__4].r * b[i__5].r - a[i__4].i * b[i__5] + .i, z__2.i = a[i__4].r * b[i__5].i + a[i__4] + .i * b[i__5].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; /* L130: */ - } - if (beta->r == 0. && beta->i == 0.) { - i__3 = i__ + j * c_dim1; - z__1.r = alpha->r * temp.r - alpha->i * temp.i, - z__1.i = alpha->r * temp.i + alpha->i * - temp.r; - c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; - } else { - i__3 = i__ + j * c_dim1; - z__2.r = alpha->r * temp.r - alpha->i * temp.i, - z__2.i = alpha->r * temp.i + alpha->i * - temp.r; - i__4 = i__ + j * c_dim1; - z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4] - .i, z__3.i = beta->r * c__[i__4].i + beta->i * - c__[i__4].r; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; - c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; - } + } + if (beta->r == 0. && beta->i == 0.) { + i__3 = i__ + j * c_dim1; + z__1.r = alpha->r * temp.r - alpha->i * temp.i, + z__1.i = alpha->r * temp.i + alpha->i * + temp.r; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } else { + i__3 = i__ + j * c_dim1; + z__2.r = alpha->r * temp.r - alpha->i * temp.i, + z__2.i = alpha->r * temp.i + alpha->i * + temp.r; + i__4 = i__ + j * c_dim1; + z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4] + .i, z__3.i = beta->r * c__[i__4].i + beta->i * + c__[i__4].r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } /* L140: */ - } + } /* L150: */ - } - } + } + } } else if (nota) { - if (conjb) { + if (conjb) { /* Form C := alpha*A*B**H + beta*C. */ - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - if (beta->r == 0. && beta->i == 0.) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * c_dim1; - c__[i__3].r = 0., c__[i__3].i = 0.; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (beta->r == 0. && beta->i == 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + c__[i__3].r = 0., c__[i__3].i = 0.; /* L160: */ - } - } else if (beta->r != 1. || beta->i != 0.) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * c_dim1; - i__4 = i__ + j * c_dim1; - z__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4] - .i, z__1.i = beta->r * c__[i__4].i + beta->i * - c__[i__4].r; - c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } + } else if (beta->r != 1. || beta->i != 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + i__4 = i__ + j * c_dim1; + z__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4] + .i, z__1.i = beta->r * c__[i__4].i + beta->i * + c__[i__4].r; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; /* L170: */ - } - } - i__2 = *k; - for (l = 1; l <= i__2; ++l) { - d_cnjg(&z__2, &b[j + l * b_dim1]); - z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = - alpha->r * z__2.i + alpha->i * z__2.r; - temp.r = z__1.r, temp.i = z__1.i; - i__3 = *m; - for (i__ = 1; i__ <= i__3; ++i__) { - i__4 = i__ + j * c_dim1; - i__5 = i__ + j * c_dim1; - i__6 = i__ + l * a_dim1; - z__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i, - z__2.i = temp.r * a[i__6].i + temp.i * a[i__6] - .r; - z__1.r = c__[i__5].r + z__2.r, z__1.i = c__[i__5].i + - z__2.i; - c__[i__4].r = z__1.r, c__[i__4].i = z__1.i; + } + } + i__2 = *k; + for (l = 1; l <= i__2; ++l) { + d_cnjg(&z__2, &b[j + l * b_dim1]); + z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = + alpha->r * z__2.i + alpha->i * z__2.r; + temp.r = z__1.r, temp.i = z__1.i; + i__3 = *m; + for (i__ = 1; i__ <= i__3; ++i__) { + i__4 = i__ + j * c_dim1; + i__5 = i__ + j * c_dim1; + i__6 = i__ + l * a_dim1; + z__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i, + z__2.i = temp.r * a[i__6].i + temp.i * a[i__6] + .r; + z__1.r = c__[i__5].r + z__2.r, z__1.i = c__[i__5].i + + z__2.i; + c__[i__4].r = z__1.r, c__[i__4].i = z__1.i; /* L180: */ - } + } /* L190: */ - } + } /* L200: */ - } - } else { + } + } else { /* Form C := alpha*A*B**T + beta*C */ - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - if (beta->r == 0. && beta->i == 0.) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * c_dim1; - c__[i__3].r = 0., c__[i__3].i = 0.; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (beta->r == 0. && beta->i == 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + c__[i__3].r = 0., c__[i__3].i = 0.; /* L210: */ - } - } else if (beta->r != 1. || beta->i != 0.) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * c_dim1; - i__4 = i__ + j * c_dim1; - z__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4] - .i, z__1.i = beta->r * c__[i__4].i + beta->i * - c__[i__4].r; - c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } + } else if (beta->r != 1. || beta->i != 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + i__4 = i__ + j * c_dim1; + z__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4] + .i, z__1.i = beta->r * c__[i__4].i + beta->i * + c__[i__4].r; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; /* L220: */ - } - } - i__2 = *k; - for (l = 1; l <= i__2; ++l) { - i__3 = j + l * b_dim1; - z__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3].i, - z__1.i = alpha->r * b[i__3].i + alpha->i * b[i__3] - .r; - temp.r = z__1.r, temp.i = z__1.i; - i__3 = *m; - for (i__ = 1; i__ <= i__3; ++i__) { - i__4 = i__ + j * c_dim1; - i__5 = i__ + j * c_dim1; - i__6 = i__ + l * a_dim1; - z__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i, - z__2.i = temp.r * a[i__6].i + temp.i * a[i__6] - .r; - z__1.r = c__[i__5].r + z__2.r, z__1.i = c__[i__5].i + - z__2.i; - c__[i__4].r = z__1.r, c__[i__4].i = z__1.i; + } + } + i__2 = *k; + for (l = 1; l <= i__2; ++l) { + i__3 = j + l * b_dim1; + z__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3].i, + z__1.i = alpha->r * b[i__3].i + alpha->i * b[i__3] + .r; + temp.r = z__1.r, temp.i = z__1.i; + i__3 = *m; + for (i__ = 1; i__ <= i__3; ++i__) { + i__4 = i__ + j * c_dim1; + i__5 = i__ + j * c_dim1; + i__6 = i__ + l * a_dim1; + z__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i, + z__2.i = temp.r * a[i__6].i + temp.i * a[i__6] + .r; + z__1.r = c__[i__5].r + z__2.r, z__1.i = c__[i__5].i + + z__2.i; + c__[i__4].r = z__1.r, c__[i__4].i = z__1.i; /* L230: */ - } + } /* L240: */ - } + } /* L250: */ - } - } + } + } } else if (conja) { - if (conjb) { + if (conjb) { /* Form C := alpha*A**H*B**H + beta*C. */ - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - temp.r = 0., temp.i = 0.; - i__3 = *k; - for (l = 1; l <= i__3; ++l) { - d_cnjg(&z__3, &a[l + i__ * a_dim1]); - d_cnjg(&z__4, &b[j + l * b_dim1]); - z__2.r = z__3.r * z__4.r - z__3.i * z__4.i, z__2.i = - z__3.r * z__4.i + z__3.i * z__4.r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; - temp.r = z__1.r, temp.i = z__1.i; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp.r = 0., temp.i = 0.; + i__3 = *k; + for (l = 1; l <= i__3; ++l) { + d_cnjg(&z__3, &a[l + i__ * a_dim1]); + d_cnjg(&z__4, &b[j + l * b_dim1]); + z__2.r = z__3.r * z__4.r - z__3.i * z__4.i, z__2.i = + z__3.r * z__4.i + z__3.i * z__4.r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; /* L260: */ - } - if (beta->r == 0. && beta->i == 0.) { - i__3 = i__ + j * c_dim1; - z__1.r = alpha->r * temp.r - alpha->i * temp.i, - z__1.i = alpha->r * temp.i + alpha->i * - temp.r; - c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; - } else { - i__3 = i__ + j * c_dim1; - z__2.r = alpha->r * temp.r - alpha->i * temp.i, - z__2.i = alpha->r * temp.i + alpha->i * - temp.r; - i__4 = i__ + j * c_dim1; - z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4] - .i, z__3.i = beta->r * c__[i__4].i + beta->i * - c__[i__4].r; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; - c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; - } + } + if (beta->r == 0. && beta->i == 0.) { + i__3 = i__ + j * c_dim1; + z__1.r = alpha->r * temp.r - alpha->i * temp.i, + z__1.i = alpha->r * temp.i + alpha->i * + temp.r; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } else { + i__3 = i__ + j * c_dim1; + z__2.r = alpha->r * temp.r - alpha->i * temp.i, + z__2.i = alpha->r * temp.i + alpha->i * + temp.r; + i__4 = i__ + j * c_dim1; + z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4] + .i, z__3.i = beta->r * c__[i__4].i + beta->i * + c__[i__4].r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } /* L270: */ - } + } /* L280: */ - } - } else { + } + } else { /* Form C := alpha*A**H*B**T + beta*C */ - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - temp.r = 0., temp.i = 0.; - i__3 = *k; - for (l = 1; l <= i__3; ++l) { - d_cnjg(&z__3, &a[l + i__ * a_dim1]); - i__4 = j + l * b_dim1; - z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4].i, - z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4] - .r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; - temp.r = z__1.r, temp.i = z__1.i; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp.r = 0., temp.i = 0.; + i__3 = *k; + for (l = 1; l <= i__3; ++l) { + d_cnjg(&z__3, &a[l + i__ * a_dim1]); + i__4 = j + l * b_dim1; + z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4].i, + z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4] + .r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; /* L290: */ - } - if (beta->r == 0. && beta->i == 0.) { - i__3 = i__ + j * c_dim1; - z__1.r = alpha->r * temp.r - alpha->i * temp.i, - z__1.i = alpha->r * temp.i + alpha->i * - temp.r; - c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; - } else { - i__3 = i__ + j * c_dim1; - z__2.r = alpha->r * temp.r - alpha->i * temp.i, - z__2.i = alpha->r * temp.i + alpha->i * - temp.r; - i__4 = i__ + j * c_dim1; - z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4] - .i, z__3.i = beta->r * c__[i__4].i + beta->i * - c__[i__4].r; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; - c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; - } + } + if (beta->r == 0. && beta->i == 0.) { + i__3 = i__ + j * c_dim1; + z__1.r = alpha->r * temp.r - alpha->i * temp.i, + z__1.i = alpha->r * temp.i + alpha->i * + temp.r; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } else { + i__3 = i__ + j * c_dim1; + z__2.r = alpha->r * temp.r - alpha->i * temp.i, + z__2.i = alpha->r * temp.i + alpha->i * + temp.r; + i__4 = i__ + j * c_dim1; + z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4] + .i, z__3.i = beta->r * c__[i__4].i + beta->i * + c__[i__4].r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } /* L300: */ - } + } /* L310: */ - } - } + } + } } else { - if (conjb) { + if (conjb) { /* Form C := alpha*A**T*B**H + beta*C */ - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - temp.r = 0., temp.i = 0.; - i__3 = *k; - for (l = 1; l <= i__3; ++l) { - i__4 = l + i__ * a_dim1; - d_cnjg(&z__3, &b[j + l * b_dim1]); - z__2.r = a[i__4].r * z__3.r - a[i__4].i * z__3.i, - z__2.i = a[i__4].r * z__3.i + a[i__4].i * - z__3.r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; - temp.r = z__1.r, temp.i = z__1.i; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp.r = 0., temp.i = 0.; + i__3 = *k; + for (l = 1; l <= i__3; ++l) { + i__4 = l + i__ * a_dim1; + d_cnjg(&z__3, &b[j + l * b_dim1]); + z__2.r = a[i__4].r * z__3.r - a[i__4].i * z__3.i, + z__2.i = a[i__4].r * z__3.i + a[i__4].i * + z__3.r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; /* L320: */ - } - if (beta->r == 0. && beta->i == 0.) { - i__3 = i__ + j * c_dim1; - z__1.r = alpha->r * temp.r - alpha->i * temp.i, - z__1.i = alpha->r * temp.i + alpha->i * - temp.r; - c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; - } else { - i__3 = i__ + j * c_dim1; - z__2.r = alpha->r * temp.r - alpha->i * temp.i, - z__2.i = alpha->r * temp.i + alpha->i * - temp.r; - i__4 = i__ + j * c_dim1; - z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4] - .i, z__3.i = beta->r * c__[i__4].i + beta->i * - c__[i__4].r; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; - c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; - } + } + if (beta->r == 0. && beta->i == 0.) { + i__3 = i__ + j * c_dim1; + z__1.r = alpha->r * temp.r - alpha->i * temp.i, + z__1.i = alpha->r * temp.i + alpha->i * + temp.r; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } else { + i__3 = i__ + j * c_dim1; + z__2.r = alpha->r * temp.r - alpha->i * temp.i, + z__2.i = alpha->r * temp.i + alpha->i * + temp.r; + i__4 = i__ + j * c_dim1; + z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4] + .i, z__3.i = beta->r * c__[i__4].i + beta->i * + c__[i__4].r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } /* L330: */ - } + } /* L340: */ - } - } else { + } + } else { /* Form C := alpha*A**T*B**T + beta*C */ - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - temp.r = 0., temp.i = 0.; - i__3 = *k; - for (l = 1; l <= i__3; ++l) { - i__4 = l + i__ * a_dim1; - i__5 = j + l * b_dim1; - z__2.r = a[i__4].r * b[i__5].r - a[i__4].i * b[i__5] - .i, z__2.i = a[i__4].r * b[i__5].i + a[i__4] - .i * b[i__5].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; - temp.r = z__1.r, temp.i = z__1.i; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + temp.r = 0., temp.i = 0.; + i__3 = *k; + for (l = 1; l <= i__3; ++l) { + i__4 = l + i__ * a_dim1; + i__5 = j + l * b_dim1; + z__2.r = a[i__4].r * b[i__5].r - a[i__4].i * b[i__5] + .i, z__2.i = a[i__4].r * b[i__5].i + a[i__4] + .i * b[i__5].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; /* L350: */ - } - if (beta->r == 0. && beta->i == 0.) { - i__3 = i__ + j * c_dim1; - z__1.r = alpha->r * temp.r - alpha->i * temp.i, - z__1.i = alpha->r * temp.i + alpha->i * - temp.r; - c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; - } else { - i__3 = i__ + j * c_dim1; - z__2.r = alpha->r * temp.r - alpha->i * temp.i, - z__2.i = alpha->r * temp.i + alpha->i * - temp.r; - i__4 = i__ + j * c_dim1; - z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4] - .i, z__3.i = beta->r * c__[i__4].i + beta->i * - c__[i__4].r; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; - c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; - } + } + if (beta->r == 0. && beta->i == 0.) { + i__3 = i__ + j * c_dim1; + z__1.r = alpha->r * temp.r - alpha->i * temp.i, + z__1.i = alpha->r * temp.i + alpha->i * + temp.r; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } else { + i__3 = i__ + j * c_dim1; + z__2.r = alpha->r * temp.r - alpha->i * temp.i, + z__2.i = alpha->r * temp.i + alpha->i * + temp.r; + i__4 = i__ + j * c_dim1; + z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4] + .i, z__3.i = beta->r * c__[i__4].i + beta->i * + c__[i__4].r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } /* L360: */ - } + } /* L370: */ - } - } + } + } } return 0; @@ -759,5 +759,5 @@ extern "C" { } /* zgemm_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zgemv.cpp b/lib/linalg/zgemv.cpp index 9524445dba..99b8cf9d0a 100644 --- a/lib/linalg/zgemv.cpp +++ b/lib/linalg/zgemv.cpp @@ -1,13 +1,13 @@ /* fortran/zgemv.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -171,10 +171,10 @@ extern "C" { /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int zgemv_(char *trans, integer *m, integer *n, - doublecomplex *alpha, doublecomplex *a, integer *lda, doublecomplex * - x, integer *incx, doublecomplex *beta, doublecomplex *y, integer * - incy, ftnlen trans_len) +/* Subroutine */ int zgemv_(char *trans, integer *m, integer *n, + doublecomplex *alpha, doublecomplex *a, integer *lda, doublecomplex * + x, integer *incx, doublecomplex *beta, doublecomplex *y, integer * + incy, ftnlen trans_len) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; @@ -226,30 +226,30 @@ extern "C" { /* Function Body */ info = 0; if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"T", ( - ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1) - ) { - info = 1; + ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1) + ) { + info = 1; } else if (*m < 0) { - info = 2; + info = 2; } else if (*n < 0) { - info = 3; + info = 3; } else if (*lda < max(1,*m)) { - info = 6; + info = 6; } else if (*incx == 0) { - info = 8; + info = 8; } else if (*incy == 0) { - info = 11; + info = 11; } if (info != 0) { - xerbla_((char *)"ZGEMV ", &info, (ftnlen)6); - return 0; + xerbla_((char *)"ZGEMV ", &info, (ftnlen)6); + return 0; } /* Quick return if possible. */ - if (*m == 0 || *n == 0 || alpha->r == 0. && alpha->i == 0. && (beta->r == - 1. && beta->i == 0.)) { - return 0; + if (*m == 0 || *n == 0 || alpha->r == 0. && alpha->i == 0. && (beta->r == + 1. && beta->i == 0.)) { + return 0; } noconj = lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1); @@ -258,21 +258,21 @@ extern "C" { /* up the start points in X and Y. */ if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { - lenx = *n; - leny = *m; + lenx = *n; + leny = *m; } else { - lenx = *m; - leny = *n; + lenx = *m; + leny = *n; } if (*incx > 0) { - kx = 1; + kx = 1; } else { - kx = 1 - (lenx - 1) * *incx; + kx = 1 - (lenx - 1) * *incx; } if (*incy > 0) { - ky = 1; + ky = 1; } else { - ky = 1 - (leny - 1) * *incy; + ky = 1 - (leny - 1) * *incy; } /* Start the operations. In this version the elements of A are */ @@ -281,189 +281,189 @@ extern "C" { /* First form y := beta*y. */ if (beta->r != 1. || beta->i != 0.) { - if (*incy == 1) { - if (beta->r == 0. && beta->i == 0.) { - i__1 = leny; - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = i__; - y[i__2].r = 0., y[i__2].i = 0.; + if (*incy == 1) { + if (beta->r == 0. && beta->i == 0.) { + i__1 = leny; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__; + y[i__2].r = 0., y[i__2].i = 0.; /* L10: */ - } - } else { - i__1 = leny; - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = i__; - i__3 = i__; - z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i, - z__1.i = beta->r * y[i__3].i + beta->i * y[i__3] - .r; - y[i__2].r = z__1.r, y[i__2].i = z__1.i; + } + } else { + i__1 = leny; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__; + i__3 = i__; + z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i, + z__1.i = beta->r * y[i__3].i + beta->i * y[i__3] + .r; + y[i__2].r = z__1.r, y[i__2].i = z__1.i; /* L20: */ - } - } - } else { - iy = ky; - if (beta->r == 0. && beta->i == 0.) { - i__1 = leny; - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = iy; - y[i__2].r = 0., y[i__2].i = 0.; - iy += *incy; + } + } + } else { + iy = ky; + if (beta->r == 0. && beta->i == 0.) { + i__1 = leny; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = iy; + y[i__2].r = 0., y[i__2].i = 0.; + iy += *incy; /* L30: */ - } - } else { - i__1 = leny; - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = iy; - i__3 = iy; - z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i, - z__1.i = beta->r * y[i__3].i + beta->i * y[i__3] - .r; - y[i__2].r = z__1.r, y[i__2].i = z__1.i; - iy += *incy; + } + } else { + i__1 = leny; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = iy; + i__3 = iy; + z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i, + z__1.i = beta->r * y[i__3].i + beta->i * y[i__3] + .r; + y[i__2].r = z__1.r, y[i__2].i = z__1.i; + iy += *incy; /* L40: */ - } - } - } + } + } + } } if (alpha->r == 0. && alpha->i == 0.) { - return 0; + return 0; } if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { /* Form y := alpha*A*x + y. */ - jx = kx; - if (*incy == 1) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = jx; - z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i = - alpha->r * x[i__2].i + alpha->i * x[i__2].r; - temp.r = z__1.r, temp.i = z__1.i; - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__; - i__4 = i__; - i__5 = i__ + j * a_dim1; - z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, z__2.i = - temp.r * a[i__5].i + temp.i * a[i__5].r; - z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; - y[i__3].r = z__1.r, y[i__3].i = z__1.i; + jx = kx; + if (*incy == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = jx; + z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i = + alpha->r * x[i__2].i + alpha->i * x[i__2].r; + temp.r = z__1.r, temp.i = z__1.i; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__; + i__4 = i__; + i__5 = i__ + j * a_dim1; + z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, z__2.i = + temp.r * a[i__5].i + temp.i * a[i__5].r; + z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; + y[i__3].r = z__1.r, y[i__3].i = z__1.i; /* L50: */ - } - jx += *incx; + } + jx += *incx; /* L60: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = jx; - z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i = - alpha->r * x[i__2].i + alpha->i * x[i__2].r; - temp.r = z__1.r, temp.i = z__1.i; - iy = ky; - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = iy; - i__4 = iy; - i__5 = i__ + j * a_dim1; - z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, z__2.i = - temp.r * a[i__5].i + temp.i * a[i__5].r; - z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; - y[i__3].r = z__1.r, y[i__3].i = z__1.i; - iy += *incy; + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = jx; + z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i = + alpha->r * x[i__2].i + alpha->i * x[i__2].r; + temp.r = z__1.r, temp.i = z__1.i; + iy = ky; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = iy; + i__4 = iy; + i__5 = i__ + j * a_dim1; + z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, z__2.i = + temp.r * a[i__5].i + temp.i * a[i__5].r; + z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; + y[i__3].r = z__1.r, y[i__3].i = z__1.i; + iy += *incy; /* L70: */ - } - jx += *incx; + } + jx += *incx; /* L80: */ - } - } + } + } } else { /* Form y := alpha*A**T*x + y or y := alpha*A**H*x + y. */ - jy = ky; - if (*incx == 1) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - temp.r = 0., temp.i = 0.; - if (noconj) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * a_dim1; - i__4 = i__; - z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[i__4] - .i, z__2.i = a[i__3].r * x[i__4].i + a[i__3] - .i * x[i__4].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; - temp.r = z__1.r, temp.i = z__1.i; + jy = ky; + if (*incx == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp.r = 0., temp.i = 0.; + if (noconj) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + i__4 = i__; + z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[i__4] + .i, z__2.i = a[i__3].r * x[i__4].i + a[i__3] + .i * x[i__4].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; /* L90: */ - } - } else { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - d_cnjg(&z__3, &a[i__ + j * a_dim1]); - i__3 = i__; - z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, - z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3] - .r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; - temp.r = z__1.r, temp.i = z__1.i; + } + } else { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + d_cnjg(&z__3, &a[i__ + j * a_dim1]); + i__3 = i__; + z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, + z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3] + .r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; /* L100: */ - } - } - i__2 = jy; - i__3 = jy; - z__2.r = alpha->r * temp.r - alpha->i * temp.i, z__2.i = - alpha->r * temp.i + alpha->i * temp.r; - z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i; - y[i__2].r = z__1.r, y[i__2].i = z__1.i; - jy += *incy; + } + } + i__2 = jy; + i__3 = jy; + z__2.r = alpha->r * temp.r - alpha->i * temp.i, z__2.i = + alpha->r * temp.i + alpha->i * temp.r; + z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i; + y[i__2].r = z__1.r, y[i__2].i = z__1.i; + jy += *incy; /* L110: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - temp.r = 0., temp.i = 0.; - ix = kx; - if (noconj) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * a_dim1; - i__4 = ix; - z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[i__4] - .i, z__2.i = a[i__3].r * x[i__4].i + a[i__3] - .i * x[i__4].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; - temp.r = z__1.r, temp.i = z__1.i; - ix += *incx; + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp.r = 0., temp.i = 0.; + ix = kx; + if (noconj) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + i__4 = ix; + z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[i__4] + .i, z__2.i = a[i__3].r * x[i__4].i + a[i__3] + .i * x[i__4].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + ix += *incx; /* L120: */ - } - } else { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - d_cnjg(&z__3, &a[i__ + j * a_dim1]); - i__3 = ix; - z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, - z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3] - .r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; - temp.r = z__1.r, temp.i = z__1.i; - ix += *incx; + } + } else { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + d_cnjg(&z__3, &a[i__ + j * a_dim1]); + i__3 = ix; + z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, + z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3] + .r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + ix += *incx; /* L130: */ - } - } - i__2 = jy; - i__3 = jy; - z__2.r = alpha->r * temp.r - alpha->i * temp.i, z__2.i = - alpha->r * temp.i + alpha->i * temp.r; - z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i; - y[i__2].r = z__1.r, y[i__2].i = z__1.i; - jy += *incy; + } + } + i__2 = jy; + i__3 = jy; + z__2.r = alpha->r * temp.r - alpha->i * temp.i, z__2.i = + alpha->r * temp.i + alpha->i * temp.r; + z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i; + y[i__2].r = z__1.r, y[i__2].i = z__1.i; + jy += *incy; /* L140: */ - } - } + } + } } return 0; @@ -473,5 +473,5 @@ extern "C" { } /* zgemv_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zgerc.cpp b/lib/linalg/zgerc.cpp index db1e60a2eb..668c4c4f64 100644 --- a/lib/linalg/zgerc.cpp +++ b/lib/linalg/zgerc.cpp @@ -1,13 +1,13 @@ /* fortran/zgerc.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -143,9 +143,9 @@ extern "C" { /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int zgerc_(integer *m, integer *n, doublecomplex *alpha, - doublecomplex *x, integer *incx, doublecomplex *y, integer *incy, - doublecomplex *a, integer *lda) +/* Subroutine */ int zgerc_(integer *m, integer *n, doublecomplex *alpha, + doublecomplex *x, integer *incx, doublecomplex *y, integer *incy, + doublecomplex *a, integer *lda) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; @@ -192,90 +192,90 @@ extern "C" { /* Function Body */ info = 0; if (*m < 0) { - info = 1; + info = 1; } else if (*n < 0) { - info = 2; + info = 2; } else if (*incx == 0) { - info = 5; + info = 5; } else if (*incy == 0) { - info = 7; + info = 7; } else if (*lda < max(1,*m)) { - info = 9; + info = 9; } if (info != 0) { - xerbla_((char *)"ZGERC ", &info, (ftnlen)6); - return 0; + xerbla_((char *)"ZGERC ", &info, (ftnlen)6); + return 0; } /* Quick return if possible. */ if (*m == 0 || *n == 0 || alpha->r == 0. && alpha->i == 0.) { - return 0; + return 0; } /* Start the operations. In this version the elements of A are */ /* accessed sequentially with one pass through A. */ if (*incy > 0) { - jy = 1; + jy = 1; } else { - jy = 1 - (*n - 1) * *incy; + jy = 1 - (*n - 1) * *incy; } if (*incx == 1) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = jy; - if (y[i__2].r != 0. || y[i__2].i != 0.) { - d_cnjg(&z__2, &y[jy]); - z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = - alpha->r * z__2.i + alpha->i * z__2.r; - temp.r = z__1.r, temp.i = z__1.i; - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * a_dim1; - i__4 = i__ + j * a_dim1; - i__5 = i__; - z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, z__2.i = - x[i__5].r * temp.i + x[i__5].i * temp.r; - z__1.r = a[i__4].r + z__2.r, z__1.i = a[i__4].i + z__2.i; - a[i__3].r = z__1.r, a[i__3].i = z__1.i; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = jy; + if (y[i__2].r != 0. || y[i__2].i != 0.) { + d_cnjg(&z__2, &y[jy]); + z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = + alpha->r * z__2.i + alpha->i * z__2.r; + temp.r = z__1.r, temp.i = z__1.i; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + i__4 = i__ + j * a_dim1; + i__5 = i__; + z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, z__2.i = + x[i__5].r * temp.i + x[i__5].i * temp.r; + z__1.r = a[i__4].r + z__2.r, z__1.i = a[i__4].i + z__2.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; /* L10: */ - } - } - jy += *incy; + } + } + jy += *incy; /* L20: */ - } + } } else { - if (*incx > 0) { - kx = 1; - } else { - kx = 1 - (*m - 1) * *incx; - } - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = jy; - if (y[i__2].r != 0. || y[i__2].i != 0.) { - d_cnjg(&z__2, &y[jy]); - z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = - alpha->r * z__2.i + alpha->i * z__2.r; - temp.r = z__1.r, temp.i = z__1.i; - ix = kx; - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * a_dim1; - i__4 = i__ + j * a_dim1; - i__5 = ix; - z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, z__2.i = - x[i__5].r * temp.i + x[i__5].i * temp.r; - z__1.r = a[i__4].r + z__2.r, z__1.i = a[i__4].i + z__2.i; - a[i__3].r = z__1.r, a[i__3].i = z__1.i; - ix += *incx; + if (*incx > 0) { + kx = 1; + } else { + kx = 1 - (*m - 1) * *incx; + } + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = jy; + if (y[i__2].r != 0. || y[i__2].i != 0.) { + d_cnjg(&z__2, &y[jy]); + z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = + alpha->r * z__2.i + alpha->i * z__2.r; + temp.r = z__1.r, temp.i = z__1.i; + ix = kx; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + i__4 = i__ + j * a_dim1; + i__5 = ix; + z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, z__2.i = + x[i__5].r * temp.i + x[i__5].i * temp.r; + z__1.r = a[i__4].r + z__2.r, z__1.i = a[i__4].i + z__2.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; + ix += *incx; /* L30: */ - } - } - jy += *incy; + } + } + jy += *incy; /* L40: */ - } + } } return 0; @@ -285,5 +285,5 @@ extern "C" { } /* zgerc_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zheev.cpp b/lib/linalg/zheev.cpp index f421e49090..52661d9511 100644 --- a/lib/linalg/zheev.cpp +++ b/lib/linalg/zheev.cpp @@ -1,13 +1,13 @@ /* fortran/zheev.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -163,9 +163,9 @@ ices */ /* > \ingroup complex16HEeigen */ /* ===================================================================== */ -/* Subroutine */ int zheev_(char *jobz, char *uplo, integer *n, doublecomplex - *a, integer *lda, doublereal *w, doublecomplex *work, integer *lwork, - doublereal *rwork, integer *info, ftnlen jobz_len, ftnlen uplo_len) +/* Subroutine */ int zheev_(char *jobz, char *uplo, integer *n, doublecomplex + *a, integer *lda, doublereal *w, doublecomplex *work, integer *lwork, + doublereal *rwork, integer *info, ftnlen jobz_len, ftnlen uplo_len) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; @@ -181,8 +181,8 @@ ices */ doublereal anrm; integer imax; doublereal rmin, rmax; - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *); + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *); doublereal sigma; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer iinfo; @@ -190,29 +190,29 @@ ices */ extern doublereal dlamch_(char *, ftnlen); integer iscale; doublereal safmin; - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); doublereal bignum; - extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *, - integer *, doublereal *, ftnlen, ftnlen); + extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *, + integer *, doublereal *, ftnlen, ftnlen); integer indtau; extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *, - integer *), zlascl_(char *, integer *, integer *, doublereal *, - doublereal *, integer *, integer *, doublecomplex *, integer *, - integer *, ftnlen); + integer *), zlascl_(char *, integer *, integer *, doublereal *, + doublereal *, integer *, integer *, doublecomplex *, integer *, + integer *, ftnlen); integer indwrk; - extern /* Subroutine */ int zhetrd_(char *, integer *, doublecomplex *, - integer *, doublereal *, doublereal *, doublecomplex *, - doublecomplex *, integer *, integer *, ftnlen); + extern /* Subroutine */ int zhetrd_(char *, integer *, doublecomplex *, + integer *, doublereal *, doublereal *, doublecomplex *, + doublecomplex *, integer *, integer *, ftnlen); integer llwork; doublereal smlnum; integer lwkopt; logical lquery; - extern /* Subroutine */ int zsteqr_(char *, integer *, doublereal *, - doublereal *, doublecomplex *, integer *, doublereal *, integer *, - ftnlen), zungtr_(char *, integer *, doublecomplex *, integer *, - doublecomplex *, doublecomplex *, integer *, integer *, ftnlen); + extern /* Subroutine */ int zsteqr_(char *, integer *, doublereal *, + doublereal *, doublecomplex *, integer *, doublereal *, integer *, + ftnlen), zungtr_(char *, integer *, doublecomplex *, integer *, + doublecomplex *, doublecomplex *, integer *, integer *, ftnlen); /* -- LAPACK driver routine -- */ @@ -255,53 +255,53 @@ ices */ *info = 0; if (! (wantz || lsame_(jobz, (char *)"N", (ftnlen)1, (ftnlen)1))) { - *info = -1; + *info = -1; } else if (! (lower || lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1))) { - *info = -2; + *info = -2; } else if (*n < 0) { - *info = -3; + *info = -3; } else if (*lda < max(1,*n)) { - *info = -5; + *info = -5; } if (*info == 0) { - nb = ilaenv_(&c__1, (char *)"ZHETRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, - (ftnlen)1); + nb = ilaenv_(&c__1, (char *)"ZHETRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, + (ftnlen)1); /* Computing MAX */ - i__1 = 1, i__2 = (nb + 1) * *n; - lwkopt = max(i__1,i__2); - work[1].r = (doublereal) lwkopt, work[1].i = 0.; + i__1 = 1, i__2 = (nb + 1) * *n; + lwkopt = max(i__1,i__2); + work[1].r = (doublereal) lwkopt, work[1].i = 0.; /* Computing MAX */ - i__1 = 1, i__2 = (*n << 1) - 1; - if (*lwork < max(i__1,i__2) && ! lquery) { - *info = -8; - } + i__1 = 1, i__2 = (*n << 1) - 1; + if (*lwork < max(i__1,i__2) && ! lquery) { + *info = -8; + } } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"ZHEEV ", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"ZHEEV ", &i__1, (ftnlen)6); + return 0; } else if (lquery) { - return 0; + return 0; } /* Quick return if possible */ if (*n == 0) { - return 0; + return 0; } if (*n == 1) { - i__1 = a_dim1 + 1; - w[1] = a[i__1].r; - work[1].r = 1., work[1].i = 0.; - if (wantz) { - i__1 = a_dim1 + 1; - a[i__1].r = 1., a[i__1].i = 0.; - } - return 0; + i__1 = a_dim1 + 1; + w[1] = a[i__1].r; + work[1].r = 1., work[1].i = 0.; + if (wantz) { + i__1 = a_dim1 + 1; + a[i__1].r = 1., a[i__1].i = 0.; + } + return 0; } /* Get machine constants. */ @@ -316,18 +316,18 @@ ices */ /* Scale matrix to allowable range, if necessary. */ anrm = zlanhe_((char *)"M", uplo, n, &a[a_offset], lda, &rwork[1], (ftnlen)1, ( - ftnlen)1); + ftnlen)1); iscale = 0; if (anrm > 0. && anrm < rmin) { - iscale = 1; - sigma = rmin / anrm; + iscale = 1; + sigma = rmin / anrm; } else if (anrm > rmax) { - iscale = 1; - sigma = rmax / anrm; + iscale = 1; + sigma = rmax / anrm; } if (iscale == 1) { - zlascl_(uplo, &c__0, &c__0, &c_b18, &sigma, n, n, &a[a_offset], lda, - info, (ftnlen)1); + zlascl_(uplo, &c__0, &c__0, &c_b18, &sigma, n, n, &a[a_offset], lda, + info, (ftnlen)1); } /* Call ZHETRD to reduce Hermitian matrix to tridiagonal form. */ @@ -337,31 +337,31 @@ ices */ indwrk = indtau + *n; llwork = *lwork - indwrk + 1; zhetrd_(uplo, n, &a[a_offset], lda, &w[1], &rwork[inde], &work[indtau], & - work[indwrk], &llwork, &iinfo, (ftnlen)1); + work[indwrk], &llwork, &iinfo, (ftnlen)1); /* For eigenvalues only, call DSTERF. For eigenvectors, first call */ /* ZUNGTR to generate the unitary matrix, then call ZSTEQR. */ if (! wantz) { - dsterf_(n, &w[1], &rwork[inde], info); + dsterf_(n, &w[1], &rwork[inde], info); } else { - zungtr_(uplo, n, &a[a_offset], lda, &work[indtau], &work[indwrk], & - llwork, &iinfo, (ftnlen)1); - indwrk = inde + *n; - zsteqr_(jobz, n, &w[1], &rwork[inde], &a[a_offset], lda, &rwork[ - indwrk], info, (ftnlen)1); + zungtr_(uplo, n, &a[a_offset], lda, &work[indtau], &work[indwrk], & + llwork, &iinfo, (ftnlen)1); + indwrk = inde + *n; + zsteqr_(jobz, n, &w[1], &rwork[inde], &a[a_offset], lda, &rwork[ + indwrk], info, (ftnlen)1); } /* If matrix was scaled, then rescale eigenvalues appropriately. */ if (iscale == 1) { - if (*info == 0) { - imax = *n; - } else { - imax = *info - 1; - } - d__1 = 1. / sigma; - dscal_(&imax, &d__1, &w[1], &c__1); + if (*info == 0) { + imax = *n; + } else { + imax = *info - 1; + } + d__1 = 1. / sigma; + dscal_(&imax, &d__1, &w[1], &c__1); } /* Set WORK(1) to optimal complex workspace size. */ @@ -375,5 +375,5 @@ ices */ } /* zheev_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zheevd.cpp b/lib/linalg/zheevd.cpp index c340c17718..83747a7962 100644 --- a/lib/linalg/zheevd.cpp +++ b/lib/linalg/zheevd.cpp @@ -1,13 +1,13 @@ /* fortran/zheevd.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -228,10 +228,10 @@ f"> */ /* > at Berkeley, USA */ /* > */ /* ===================================================================== */ -/* Subroutine */ int zheevd_(char *jobz, char *uplo, integer *n, - doublecomplex *a, integer *lda, doublereal *w, doublecomplex *work, - integer *lwork, doublereal *rwork, integer *lrwork, integer *iwork, - integer *liwork, integer *info, ftnlen jobz_len, ftnlen uplo_len) +/* Subroutine */ int zheevd_(char *jobz, char *uplo, integer *n, + doublecomplex *a, integer *lda, doublereal *w, doublecomplex *work, + integer *lwork, doublereal *rwork, integer *lrwork, integer *iwork, + integer *liwork, integer *info, ftnlen jobz_len, ftnlen uplo_len) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; @@ -247,8 +247,8 @@ f"> */ integer imax; doublereal rmin, rmax; integer lopt; - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *); + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *); doublereal sigma; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer iinfo, lwmin, liopt; @@ -259,33 +259,33 @@ f"> */ extern doublereal dlamch_(char *, ftnlen); integer iscale; doublereal safmin; - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); doublereal bignum; - extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *, - integer *, doublereal *, ftnlen, ftnlen); + extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *, + integer *, doublereal *, ftnlen, ftnlen); integer indtau; extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *, - integer *), zlascl_(char *, integer *, integer *, doublereal *, - doublereal *, integer *, integer *, doublecomplex *, integer *, - integer *, ftnlen), zstedc_(char *, integer *, doublereal *, - doublereal *, doublecomplex *, integer *, doublecomplex *, - integer *, doublereal *, integer *, integer *, integer *, integer - *, ftnlen); + integer *), zlascl_(char *, integer *, integer *, doublereal *, + doublereal *, integer *, integer *, doublecomplex *, integer *, + integer *, ftnlen), zstedc_(char *, integer *, doublereal *, + doublereal *, doublecomplex *, integer *, doublecomplex *, + integer *, doublereal *, integer *, integer *, integer *, integer + *, ftnlen); integer indrwk, indwrk, liwmin; - extern /* Subroutine */ int zhetrd_(char *, integer *, doublecomplex *, - integer *, doublereal *, doublereal *, doublecomplex *, - doublecomplex *, integer *, integer *, ftnlen), zlacpy_(char *, - integer *, integer *, doublecomplex *, integer *, doublecomplex *, - integer *, ftnlen); + extern /* Subroutine */ int zhetrd_(char *, integer *, doublecomplex *, + integer *, doublereal *, doublereal *, doublecomplex *, + doublecomplex *, integer *, integer *, ftnlen), zlacpy_(char *, + integer *, integer *, doublecomplex *, integer *, doublecomplex *, + integer *, ftnlen); integer lrwmin, llwork; doublereal smlnum; logical lquery; - extern /* Subroutine */ int zunmtr_(char *, char *, char *, integer *, - integer *, doublecomplex *, integer *, doublecomplex *, - doublecomplex *, integer *, doublecomplex *, integer *, integer *, - ftnlen, ftnlen, ftnlen); + extern /* Subroutine */ int zunmtr_(char *, char *, char *, integer *, + integer *, doublecomplex *, integer *, doublecomplex *, + doublecomplex *, integer *, doublecomplex *, integer *, integer *, + ftnlen, ftnlen, ftnlen); /* -- LAPACK driver routine -- */ @@ -329,77 +329,77 @@ f"> */ *info = 0; if (! (wantz || lsame_(jobz, (char *)"N", (ftnlen)1, (ftnlen)1))) { - *info = -1; + *info = -1; } else if (! (lower || lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1))) { - *info = -2; + *info = -2; } else if (*n < 0) { - *info = -3; + *info = -3; } else if (*lda < max(1,*n)) { - *info = -5; + *info = -5; } if (*info == 0) { - if (*n <= 1) { - lwmin = 1; - lrwmin = 1; - liwmin = 1; - lopt = lwmin; - lropt = lrwmin; - liopt = liwmin; - } else { - if (wantz) { - lwmin = (*n << 1) + *n * *n; + if (*n <= 1) { + lwmin = 1; + lrwmin = 1; + liwmin = 1; + lopt = lwmin; + lropt = lrwmin; + liopt = liwmin; + } else { + if (wantz) { + lwmin = (*n << 1) + *n * *n; /* Computing 2nd power */ - i__1 = *n; - lrwmin = *n * 5 + 1 + (i__1 * i__1 << 1); - liwmin = *n * 5 + 3; - } else { - lwmin = *n + 1; - lrwmin = *n; - liwmin = 1; - } + i__1 = *n; + lrwmin = *n * 5 + 1 + (i__1 * i__1 << 1); + liwmin = *n * 5 + 3; + } else { + lwmin = *n + 1; + lrwmin = *n; + liwmin = 1; + } /* Computing MAX */ - i__1 = lwmin, i__2 = *n + *n * ilaenv_(&c__1, (char *)"ZHETRD", uplo, n, & - c_n1, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); - lopt = max(i__1,i__2); - lropt = lrwmin; - liopt = liwmin; - } - work[1].r = (doublereal) lopt, work[1].i = 0.; - rwork[1] = (doublereal) lropt; - iwork[1] = liopt; + i__1 = lwmin, i__2 = *n + *n * ilaenv_(&c__1, (char *)"ZHETRD", uplo, n, & + c_n1, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); + lopt = max(i__1,i__2); + lropt = lrwmin; + liopt = liwmin; + } + work[1].r = (doublereal) lopt, work[1].i = 0.; + rwork[1] = (doublereal) lropt; + iwork[1] = liopt; - if (*lwork < lwmin && ! lquery) { - *info = -8; - } else if (*lrwork < lrwmin && ! lquery) { - *info = -10; - } else if (*liwork < liwmin && ! lquery) { - *info = -12; - } + if (*lwork < lwmin && ! lquery) { + *info = -8; + } else if (*lrwork < lrwmin && ! lquery) { + *info = -10; + } else if (*liwork < liwmin && ! lquery) { + *info = -12; + } } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"ZHEEVD", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"ZHEEVD", &i__1, (ftnlen)6); + return 0; } else if (lquery) { - return 0; + return 0; } /* Quick return if possible */ if (*n == 0) { - return 0; + return 0; } if (*n == 1) { - i__1 = a_dim1 + 1; - w[1] = a[i__1].r; - if (wantz) { - i__1 = a_dim1 + 1; - a[i__1].r = 1., a[i__1].i = 0.; - } - return 0; + i__1 = a_dim1 + 1; + w[1] = a[i__1].r; + if (wantz) { + i__1 = a_dim1 + 1; + a[i__1].r = 1., a[i__1].i = 0.; + } + return 0; } /* Get machine constants. */ @@ -414,18 +414,18 @@ f"> */ /* Scale matrix to allowable range, if necessary. */ anrm = zlanhe_((char *)"M", uplo, n, &a[a_offset], lda, &rwork[1], (ftnlen)1, ( - ftnlen)1); + ftnlen)1); iscale = 0; if (anrm > 0. && anrm < rmin) { - iscale = 1; - sigma = rmin / anrm; + iscale = 1; + sigma = rmin / anrm; } else if (anrm > rmax) { - iscale = 1; - sigma = rmax / anrm; + iscale = 1; + sigma = rmax / anrm; } if (iscale == 1) { - zlascl_(uplo, &c__0, &c__0, &c_b18, &sigma, n, n, &a[a_offset], lda, - info, (ftnlen)1); + zlascl_(uplo, &c__0, &c__0, &c_b18, &sigma, n, n, &a[a_offset], lda, + info, (ftnlen)1); } /* Call ZHETRD to reduce Hermitian matrix to tridiagonal form. */ @@ -439,7 +439,7 @@ f"> */ llwrk2 = *lwork - indwk2 + 1; llrwk = *lrwork - indrwk + 1; zhetrd_(uplo, n, &a[a_offset], lda, &w[1], &rwork[inde], &work[indtau], & - work[indwrk], &llwork, &iinfo, (ftnlen)1); + work[indwrk], &llwork, &iinfo, (ftnlen)1); /* For eigenvalues only, call DSTERF. For eigenvectors, first call */ /* ZSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the */ @@ -448,27 +448,27 @@ f"> */ /* A. */ if (! wantz) { - dsterf_(n, &w[1], &rwork[inde], info); + dsterf_(n, &w[1], &rwork[inde], info); } else { - zstedc_((char *)"I", n, &w[1], &rwork[inde], &work[indwrk], n, &work[indwk2], - &llwrk2, &rwork[indrwk], &llrwk, &iwork[1], liwork, info, ( - ftnlen)1); - zunmtr_((char *)"L", uplo, (char *)"N", n, n, &a[a_offset], lda, &work[indtau], &work[ - indwrk], n, &work[indwk2], &llwrk2, &iinfo, (ftnlen)1, ( - ftnlen)1, (ftnlen)1); - zlacpy_((char *)"A", n, n, &work[indwrk], n, &a[a_offset], lda, (ftnlen)1); + zstedc_((char *)"I", n, &w[1], &rwork[inde], &work[indwrk], n, &work[indwk2], + &llwrk2, &rwork[indrwk], &llrwk, &iwork[1], liwork, info, ( + ftnlen)1); + zunmtr_((char *)"L", uplo, (char *)"N", n, n, &a[a_offset], lda, &work[indtau], &work[ + indwrk], n, &work[indwk2], &llwrk2, &iinfo, (ftnlen)1, ( + ftnlen)1, (ftnlen)1); + zlacpy_((char *)"A", n, n, &work[indwrk], n, &a[a_offset], lda, (ftnlen)1); } /* If matrix was scaled, then rescale eigenvalues appropriately. */ if (iscale == 1) { - if (*info == 0) { - imax = *n; - } else { - imax = *info - 1; - } - d__1 = 1. / sigma; - dscal_(&imax, &d__1, &w[1], &c__1); + if (*info == 0) { + imax = *n; + } else { + imax = *info - 1; + } + d__1 = 1. / sigma; + dscal_(&imax, &d__1, &w[1], &c__1); } work[1].r = (doublereal) lopt, work[1].i = 0.; @@ -482,5 +482,5 @@ f"> */ } /* zheevd_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zhemv.cpp b/lib/linalg/zhemv.cpp index f965dcfcdf..132915183b 100644 --- a/lib/linalg/zhemv.cpp +++ b/lib/linalg/zhemv.cpp @@ -1,13 +1,13 @@ /* fortran/zhemv.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -167,9 +167,9 @@ extern "C" { /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int zhemv_(char *uplo, integer *n, doublecomplex *alpha, - doublecomplex *a, integer *lda, doublecomplex *x, integer *incx, - doublecomplex *beta, doublecomplex *y, integer *incy, ftnlen uplo_len) +/* Subroutine */ int zhemv_(char *uplo, integer *n, doublecomplex *alpha, + doublecomplex *a, integer *lda, doublecomplex *x, integer *incx, + doublecomplex *beta, doublecomplex *y, integer *incy, ftnlen uplo_len) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; @@ -220,40 +220,40 @@ extern "C" { /* Function Body */ info = 0; if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", ( - ftnlen)1, (ftnlen)1)) { - info = 1; + ftnlen)1, (ftnlen)1)) { + info = 1; } else if (*n < 0) { - info = 2; + info = 2; } else if (*lda < max(1,*n)) { - info = 5; + info = 5; } else if (*incx == 0) { - info = 7; + info = 7; } else if (*incy == 0) { - info = 10; + info = 10; } if (info != 0) { - xerbla_((char *)"ZHEMV ", &info, (ftnlen)6); - return 0; + xerbla_((char *)"ZHEMV ", &info, (ftnlen)6); + return 0; } /* Quick return if possible. */ - if (*n == 0 || alpha->r == 0. && alpha->i == 0. && (beta->r == 1. && - beta->i == 0.)) { - return 0; + if (*n == 0 || alpha->r == 0. && alpha->i == 0. && (beta->r == 1. && + beta->i == 0.)) { + return 0; } /* Set up the start points in X and Y. */ if (*incx > 0) { - kx = 1; + kx = 1; } else { - kx = 1 - (*n - 1) * *incx; + kx = 1 - (*n - 1) * *incx; } if (*incy > 0) { - ky = 1; + ky = 1; } else { - ky = 1 - (*n - 1) * *incy; + ky = 1 - (*n - 1) * *incy; } /* Start the operations. In this version the elements of A are */ @@ -263,238 +263,238 @@ extern "C" { /* First form y := beta*y. */ if (beta->r != 1. || beta->i != 0.) { - if (*incy == 1) { - if (beta->r == 0. && beta->i == 0.) { - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = i__; - y[i__2].r = 0., y[i__2].i = 0.; + if (*incy == 1) { + if (beta->r == 0. && beta->i == 0.) { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__; + y[i__2].r = 0., y[i__2].i = 0.; /* L10: */ - } - } else { - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = i__; - i__3 = i__; - z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i, - z__1.i = beta->r * y[i__3].i + beta->i * y[i__3] - .r; - y[i__2].r = z__1.r, y[i__2].i = z__1.i; + } + } else { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__; + i__3 = i__; + z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i, + z__1.i = beta->r * y[i__3].i + beta->i * y[i__3] + .r; + y[i__2].r = z__1.r, y[i__2].i = z__1.i; /* L20: */ - } - } - } else { - iy = ky; - if (beta->r == 0. && beta->i == 0.) { - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = iy; - y[i__2].r = 0., y[i__2].i = 0.; - iy += *incy; + } + } + } else { + iy = ky; + if (beta->r == 0. && beta->i == 0.) { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = iy; + y[i__2].r = 0., y[i__2].i = 0.; + iy += *incy; /* L30: */ - } - } else { - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = iy; - i__3 = iy; - z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i, - z__1.i = beta->r * y[i__3].i + beta->i * y[i__3] - .r; - y[i__2].r = z__1.r, y[i__2].i = z__1.i; - iy += *incy; + } + } else { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = iy; + i__3 = iy; + z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i, + z__1.i = beta->r * y[i__3].i + beta->i * y[i__3] + .r; + y[i__2].r = z__1.r, y[i__2].i = z__1.i; + iy += *incy; /* L40: */ - } - } - } + } + } + } } if (alpha->r == 0. && alpha->i == 0.) { - return 0; + return 0; } if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { /* Form y when A is stored in upper triangle. */ - if (*incx == 1 && *incy == 1) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = j; - z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i = - alpha->r * x[i__2].i + alpha->i * x[i__2].r; - temp1.r = z__1.r, temp1.i = z__1.i; - temp2.r = 0., temp2.i = 0.; - i__2 = j - 1; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__; - i__4 = i__; - i__5 = i__ + j * a_dim1; - z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, - z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5] - .r; - z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; - y[i__3].r = z__1.r, y[i__3].i = z__1.i; - d_cnjg(&z__3, &a[i__ + j * a_dim1]); - i__3 = i__; - z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = - z__3.r * x[i__3].i + z__3.i * x[i__3].r; - z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; - temp2.r = z__1.r, temp2.i = z__1.i; + if (*incx == 1 && *incy == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i = + alpha->r * x[i__2].i + alpha->i * x[i__2].r; + temp1.r = z__1.r, temp1.i = z__1.i; + temp2.r = 0., temp2.i = 0.; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__; + i__4 = i__; + i__5 = i__ + j * a_dim1; + z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, + z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5] + .r; + z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; + y[i__3].r = z__1.r, y[i__3].i = z__1.i; + d_cnjg(&z__3, &a[i__ + j * a_dim1]); + i__3 = i__; + z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = + z__3.r * x[i__3].i + z__3.i * x[i__3].r; + z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; + temp2.r = z__1.r, temp2.i = z__1.i; /* L50: */ - } - i__2 = j; - i__3 = j; - i__4 = j + j * a_dim1; - d__1 = a[i__4].r; - z__3.r = d__1 * temp1.r, z__3.i = d__1 * temp1.i; - z__2.r = y[i__3].r + z__3.r, z__2.i = y[i__3].i + z__3.i; - z__4.r = alpha->r * temp2.r - alpha->i * temp2.i, z__4.i = - alpha->r * temp2.i + alpha->i * temp2.r; - z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; - y[i__2].r = z__1.r, y[i__2].i = z__1.i; + } + i__2 = j; + i__3 = j; + i__4 = j + j * a_dim1; + d__1 = a[i__4].r; + z__3.r = d__1 * temp1.r, z__3.i = d__1 * temp1.i; + z__2.r = y[i__3].r + z__3.r, z__2.i = y[i__3].i + z__3.i; + z__4.r = alpha->r * temp2.r - alpha->i * temp2.i, z__4.i = + alpha->r * temp2.i + alpha->i * temp2.r; + z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; + y[i__2].r = z__1.r, y[i__2].i = z__1.i; /* L60: */ - } - } else { - jx = kx; - jy = ky; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = jx; - z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i = - alpha->r * x[i__2].i + alpha->i * x[i__2].r; - temp1.r = z__1.r, temp1.i = z__1.i; - temp2.r = 0., temp2.i = 0.; - ix = kx; - iy = ky; - i__2 = j - 1; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = iy; - i__4 = iy; - i__5 = i__ + j * a_dim1; - z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, - z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5] - .r; - z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; - y[i__3].r = z__1.r, y[i__3].i = z__1.i; - d_cnjg(&z__3, &a[i__ + j * a_dim1]); - i__3 = ix; - z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = - z__3.r * x[i__3].i + z__3.i * x[i__3].r; - z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; - temp2.r = z__1.r, temp2.i = z__1.i; - ix += *incx; - iy += *incy; + } + } else { + jx = kx; + jy = ky; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = jx; + z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i = + alpha->r * x[i__2].i + alpha->i * x[i__2].r; + temp1.r = z__1.r, temp1.i = z__1.i; + temp2.r = 0., temp2.i = 0.; + ix = kx; + iy = ky; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = iy; + i__4 = iy; + i__5 = i__ + j * a_dim1; + z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, + z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5] + .r; + z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; + y[i__3].r = z__1.r, y[i__3].i = z__1.i; + d_cnjg(&z__3, &a[i__ + j * a_dim1]); + i__3 = ix; + z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = + z__3.r * x[i__3].i + z__3.i * x[i__3].r; + z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; + temp2.r = z__1.r, temp2.i = z__1.i; + ix += *incx; + iy += *incy; /* L70: */ - } - i__2 = jy; - i__3 = jy; - i__4 = j + j * a_dim1; - d__1 = a[i__4].r; - z__3.r = d__1 * temp1.r, z__3.i = d__1 * temp1.i; - z__2.r = y[i__3].r + z__3.r, z__2.i = y[i__3].i + z__3.i; - z__4.r = alpha->r * temp2.r - alpha->i * temp2.i, z__4.i = - alpha->r * temp2.i + alpha->i * temp2.r; - z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; - y[i__2].r = z__1.r, y[i__2].i = z__1.i; - jx += *incx; - jy += *incy; + } + i__2 = jy; + i__3 = jy; + i__4 = j + j * a_dim1; + d__1 = a[i__4].r; + z__3.r = d__1 * temp1.r, z__3.i = d__1 * temp1.i; + z__2.r = y[i__3].r + z__3.r, z__2.i = y[i__3].i + z__3.i; + z__4.r = alpha->r * temp2.r - alpha->i * temp2.i, z__4.i = + alpha->r * temp2.i + alpha->i * temp2.r; + z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; + y[i__2].r = z__1.r, y[i__2].i = z__1.i; + jx += *incx; + jy += *incy; /* L80: */ - } - } + } + } } else { /* Form y when A is stored in lower triangle. */ - if (*incx == 1 && *incy == 1) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = j; - z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i = - alpha->r * x[i__2].i + alpha->i * x[i__2].r; - temp1.r = z__1.r, temp1.i = z__1.i; - temp2.r = 0., temp2.i = 0.; - i__2 = j; - i__3 = j; - i__4 = j + j * a_dim1; - d__1 = a[i__4].r; - z__2.r = d__1 * temp1.r, z__2.i = d__1 * temp1.i; - z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i; - y[i__2].r = z__1.r, y[i__2].i = z__1.i; - i__2 = *n; - for (i__ = j + 1; i__ <= i__2; ++i__) { - i__3 = i__; - i__4 = i__; - i__5 = i__ + j * a_dim1; - z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, - z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5] - .r; - z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; - y[i__3].r = z__1.r, y[i__3].i = z__1.i; - d_cnjg(&z__3, &a[i__ + j * a_dim1]); - i__3 = i__; - z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = - z__3.r * x[i__3].i + z__3.i * x[i__3].r; - z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; - temp2.r = z__1.r, temp2.i = z__1.i; + if (*incx == 1 && *incy == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i = + alpha->r * x[i__2].i + alpha->i * x[i__2].r; + temp1.r = z__1.r, temp1.i = z__1.i; + temp2.r = 0., temp2.i = 0.; + i__2 = j; + i__3 = j; + i__4 = j + j * a_dim1; + d__1 = a[i__4].r; + z__2.r = d__1 * temp1.r, z__2.i = d__1 * temp1.i; + z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i; + y[i__2].r = z__1.r, y[i__2].i = z__1.i; + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + i__3 = i__; + i__4 = i__; + i__5 = i__ + j * a_dim1; + z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, + z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5] + .r; + z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; + y[i__3].r = z__1.r, y[i__3].i = z__1.i; + d_cnjg(&z__3, &a[i__ + j * a_dim1]); + i__3 = i__; + z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = + z__3.r * x[i__3].i + z__3.i * x[i__3].r; + z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; + temp2.r = z__1.r, temp2.i = z__1.i; /* L90: */ - } - i__2 = j; - i__3 = j; - z__2.r = alpha->r * temp2.r - alpha->i * temp2.i, z__2.i = - alpha->r * temp2.i + alpha->i * temp2.r; - z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i; - y[i__2].r = z__1.r, y[i__2].i = z__1.i; + } + i__2 = j; + i__3 = j; + z__2.r = alpha->r * temp2.r - alpha->i * temp2.i, z__2.i = + alpha->r * temp2.i + alpha->i * temp2.r; + z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i; + y[i__2].r = z__1.r, y[i__2].i = z__1.i; /* L100: */ - } - } else { - jx = kx; - jy = ky; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = jx; - z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i = - alpha->r * x[i__2].i + alpha->i * x[i__2].r; - temp1.r = z__1.r, temp1.i = z__1.i; - temp2.r = 0., temp2.i = 0.; - i__2 = jy; - i__3 = jy; - i__4 = j + j * a_dim1; - d__1 = a[i__4].r; - z__2.r = d__1 * temp1.r, z__2.i = d__1 * temp1.i; - z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i; - y[i__2].r = z__1.r, y[i__2].i = z__1.i; - ix = jx; - iy = jy; - i__2 = *n; - for (i__ = j + 1; i__ <= i__2; ++i__) { - ix += *incx; - iy += *incy; - i__3 = iy; - i__4 = iy; - i__5 = i__ + j * a_dim1; - z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, - z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5] - .r; - z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; - y[i__3].r = z__1.r, y[i__3].i = z__1.i; - d_cnjg(&z__3, &a[i__ + j * a_dim1]); - i__3 = ix; - z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = - z__3.r * x[i__3].i + z__3.i * x[i__3].r; - z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; - temp2.r = z__1.r, temp2.i = z__1.i; + } + } else { + jx = kx; + jy = ky; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = jx; + z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i = + alpha->r * x[i__2].i + alpha->i * x[i__2].r; + temp1.r = z__1.r, temp1.i = z__1.i; + temp2.r = 0., temp2.i = 0.; + i__2 = jy; + i__3 = jy; + i__4 = j + j * a_dim1; + d__1 = a[i__4].r; + z__2.r = d__1 * temp1.r, z__2.i = d__1 * temp1.i; + z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i; + y[i__2].r = z__1.r, y[i__2].i = z__1.i; + ix = jx; + iy = jy; + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + ix += *incx; + iy += *incy; + i__3 = iy; + i__4 = iy; + i__5 = i__ + j * a_dim1; + z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, + z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5] + .r; + z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; + y[i__3].r = z__1.r, y[i__3].i = z__1.i; + d_cnjg(&z__3, &a[i__ + j * a_dim1]); + i__3 = ix; + z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = + z__3.r * x[i__3].i + z__3.i * x[i__3].r; + z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; + temp2.r = z__1.r, temp2.i = z__1.i; /* L110: */ - } - i__2 = jy; - i__3 = jy; - z__2.r = alpha->r * temp2.r - alpha->i * temp2.i, z__2.i = - alpha->r * temp2.i + alpha->i * temp2.r; - z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i; - y[i__2].r = z__1.r, y[i__2].i = z__1.i; - jx += *incx; - jy += *incy; + } + i__2 = jy; + i__3 = jy; + z__2.r = alpha->r * temp2.r - alpha->i * temp2.i, z__2.i = + alpha->r * temp2.i + alpha->i * temp2.r; + z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i; + y[i__2].r = z__1.r, y[i__2].i = z__1.i; + jx += *incx; + jy += *incy; /* L120: */ - } - } + } + } } return 0; @@ -504,5 +504,5 @@ extern "C" { } /* zhemv_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zher2.cpp b/lib/linalg/zher2.cpp index 2f77acd257..07d95f7917 100644 --- a/lib/linalg/zher2.cpp +++ b/lib/linalg/zher2.cpp @@ -1,13 +1,13 @@ /* fortran/zher2.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -163,9 +163,9 @@ extern "C" { /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int zher2_(char *uplo, integer *n, doublecomplex *alpha, - doublecomplex *x, integer *incx, doublecomplex *y, integer *incy, - doublecomplex *a, integer *lda, ftnlen uplo_len) +/* Subroutine */ int zher2_(char *uplo, integer *n, doublecomplex *alpha, + doublecomplex *x, integer *incx, doublecomplex *y, integer *incy, + doublecomplex *a, integer *lda, ftnlen uplo_len) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6; @@ -216,44 +216,44 @@ extern "C" { /* Function Body */ info = 0; if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", ( - ftnlen)1, (ftnlen)1)) { - info = 1; + ftnlen)1, (ftnlen)1)) { + info = 1; } else if (*n < 0) { - info = 2; + info = 2; } else if (*incx == 0) { - info = 5; + info = 5; } else if (*incy == 0) { - info = 7; + info = 7; } else if (*lda < max(1,*n)) { - info = 9; + info = 9; } if (info != 0) { - xerbla_((char *)"ZHER2 ", &info, (ftnlen)6); - return 0; + xerbla_((char *)"ZHER2 ", &info, (ftnlen)6); + return 0; } /* Quick return if possible. */ if (*n == 0 || alpha->r == 0. && alpha->i == 0.) { - return 0; + return 0; } /* Set up the start points in X and Y if the increments are not both */ /* unity. */ if (*incx != 1 || *incy != 1) { - if (*incx > 0) { - kx = 1; - } else { - kx = 1 - (*n - 1) * *incx; - } - if (*incy > 0) { - ky = 1; - } else { - ky = 1 - (*n - 1) * *incy; - } - jx = kx; - jy = ky; + if (*incx > 0) { + kx = 1; + } else { + kx = 1 - (*n - 1) * *incx; + } + if (*incy > 0) { + ky = 1; + } else { + ky = 1 - (*n - 1) * *incy; + } + jx = kx; + jy = ky; } /* Start the operations. In this version the elements of A are */ @@ -264,248 +264,248 @@ extern "C" { /* Form A when A is stored in the upper triangle. */ - if (*incx == 1 && *incy == 1) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = j; - i__3 = j; - if (x[i__2].r != 0. || x[i__2].i != 0. || (y[i__3].r != 0. || - y[i__3].i != 0.)) { - d_cnjg(&z__2, &y[j]); - z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = - alpha->r * z__2.i + alpha->i * z__2.r; - temp1.r = z__1.r, temp1.i = z__1.i; - i__2 = j; - z__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, - z__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2] - .r; - d_cnjg(&z__1, &z__2); - temp2.r = z__1.r, temp2.i = z__1.i; - i__2 = j - 1; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * a_dim1; - i__4 = i__ + j * a_dim1; - i__5 = i__; - z__3.r = x[i__5].r * temp1.r - x[i__5].i * temp1.i, - z__3.i = x[i__5].r * temp1.i + x[i__5].i * - temp1.r; - z__2.r = a[i__4].r + z__3.r, z__2.i = a[i__4].i + - z__3.i; - i__6 = i__; - z__4.r = y[i__6].r * temp2.r - y[i__6].i * temp2.i, - z__4.i = y[i__6].r * temp2.i + y[i__6].i * - temp2.r; - z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; - a[i__3].r = z__1.r, a[i__3].i = z__1.i; + if (*incx == 1 && *incy == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + i__3 = j; + if (x[i__2].r != 0. || x[i__2].i != 0. || (y[i__3].r != 0. || + y[i__3].i != 0.)) { + d_cnjg(&z__2, &y[j]); + z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = + alpha->r * z__2.i + alpha->i * z__2.r; + temp1.r = z__1.r, temp1.i = z__1.i; + i__2 = j; + z__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, + z__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2] + .r; + d_cnjg(&z__1, &z__2); + temp2.r = z__1.r, temp2.i = z__1.i; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + i__4 = i__ + j * a_dim1; + i__5 = i__; + z__3.r = x[i__5].r * temp1.r - x[i__5].i * temp1.i, + z__3.i = x[i__5].r * temp1.i + x[i__5].i * + temp1.r; + z__2.r = a[i__4].r + z__3.r, z__2.i = a[i__4].i + + z__3.i; + i__6 = i__; + z__4.r = y[i__6].r * temp2.r - y[i__6].i * temp2.i, + z__4.i = y[i__6].r * temp2.i + y[i__6].i * + temp2.r; + z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; /* L10: */ - } - i__2 = j + j * a_dim1; - i__3 = j + j * a_dim1; - i__4 = j; - z__2.r = x[i__4].r * temp1.r - x[i__4].i * temp1.i, - z__2.i = x[i__4].r * temp1.i + x[i__4].i * - temp1.r; - i__5 = j; - z__3.r = y[i__5].r * temp2.r - y[i__5].i * temp2.i, - z__3.i = y[i__5].r * temp2.i + y[i__5].i * - temp2.r; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; - d__1 = a[i__3].r + z__1.r; - a[i__2].r = d__1, a[i__2].i = 0.; - } else { - i__2 = j + j * a_dim1; - i__3 = j + j * a_dim1; - d__1 = a[i__3].r; - a[i__2].r = d__1, a[i__2].i = 0.; - } + } + i__2 = j + j * a_dim1; + i__3 = j + j * a_dim1; + i__4 = j; + z__2.r = x[i__4].r * temp1.r - x[i__4].i * temp1.i, + z__2.i = x[i__4].r * temp1.i + x[i__4].i * + temp1.r; + i__5 = j; + z__3.r = y[i__5].r * temp2.r - y[i__5].i * temp2.i, + z__3.i = y[i__5].r * temp2.i + y[i__5].i * + temp2.r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; + d__1 = a[i__3].r + z__1.r; + a[i__2].r = d__1, a[i__2].i = 0.; + } else { + i__2 = j + j * a_dim1; + i__3 = j + j * a_dim1; + d__1 = a[i__3].r; + a[i__2].r = d__1, a[i__2].i = 0.; + } /* L20: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = jx; - i__3 = jy; - if (x[i__2].r != 0. || x[i__2].i != 0. || (y[i__3].r != 0. || - y[i__3].i != 0.)) { - d_cnjg(&z__2, &y[jy]); - z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = - alpha->r * z__2.i + alpha->i * z__2.r; - temp1.r = z__1.r, temp1.i = z__1.i; - i__2 = jx; - z__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, - z__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2] - .r; - d_cnjg(&z__1, &z__2); - temp2.r = z__1.r, temp2.i = z__1.i; - ix = kx; - iy = ky; - i__2 = j - 1; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * a_dim1; - i__4 = i__ + j * a_dim1; - i__5 = ix; - z__3.r = x[i__5].r * temp1.r - x[i__5].i * temp1.i, - z__3.i = x[i__5].r * temp1.i + x[i__5].i * - temp1.r; - z__2.r = a[i__4].r + z__3.r, z__2.i = a[i__4].i + - z__3.i; - i__6 = iy; - z__4.r = y[i__6].r * temp2.r - y[i__6].i * temp2.i, - z__4.i = y[i__6].r * temp2.i + y[i__6].i * - temp2.r; - z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; - a[i__3].r = z__1.r, a[i__3].i = z__1.i; - ix += *incx; - iy += *incy; + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = jx; + i__3 = jy; + if (x[i__2].r != 0. || x[i__2].i != 0. || (y[i__3].r != 0. || + y[i__3].i != 0.)) { + d_cnjg(&z__2, &y[jy]); + z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = + alpha->r * z__2.i + alpha->i * z__2.r; + temp1.r = z__1.r, temp1.i = z__1.i; + i__2 = jx; + z__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, + z__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2] + .r; + d_cnjg(&z__1, &z__2); + temp2.r = z__1.r, temp2.i = z__1.i; + ix = kx; + iy = ky; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + i__4 = i__ + j * a_dim1; + i__5 = ix; + z__3.r = x[i__5].r * temp1.r - x[i__5].i * temp1.i, + z__3.i = x[i__5].r * temp1.i + x[i__5].i * + temp1.r; + z__2.r = a[i__4].r + z__3.r, z__2.i = a[i__4].i + + z__3.i; + i__6 = iy; + z__4.r = y[i__6].r * temp2.r - y[i__6].i * temp2.i, + z__4.i = y[i__6].r * temp2.i + y[i__6].i * + temp2.r; + z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; + ix += *incx; + iy += *incy; /* L30: */ - } - i__2 = j + j * a_dim1; - i__3 = j + j * a_dim1; - i__4 = jx; - z__2.r = x[i__4].r * temp1.r - x[i__4].i * temp1.i, - z__2.i = x[i__4].r * temp1.i + x[i__4].i * - temp1.r; - i__5 = jy; - z__3.r = y[i__5].r * temp2.r - y[i__5].i * temp2.i, - z__3.i = y[i__5].r * temp2.i + y[i__5].i * - temp2.r; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; - d__1 = a[i__3].r + z__1.r; - a[i__2].r = d__1, a[i__2].i = 0.; - } else { - i__2 = j + j * a_dim1; - i__3 = j + j * a_dim1; - d__1 = a[i__3].r; - a[i__2].r = d__1, a[i__2].i = 0.; - } - jx += *incx; - jy += *incy; + } + i__2 = j + j * a_dim1; + i__3 = j + j * a_dim1; + i__4 = jx; + z__2.r = x[i__4].r * temp1.r - x[i__4].i * temp1.i, + z__2.i = x[i__4].r * temp1.i + x[i__4].i * + temp1.r; + i__5 = jy; + z__3.r = y[i__5].r * temp2.r - y[i__5].i * temp2.i, + z__3.i = y[i__5].r * temp2.i + y[i__5].i * + temp2.r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; + d__1 = a[i__3].r + z__1.r; + a[i__2].r = d__1, a[i__2].i = 0.; + } else { + i__2 = j + j * a_dim1; + i__3 = j + j * a_dim1; + d__1 = a[i__3].r; + a[i__2].r = d__1, a[i__2].i = 0.; + } + jx += *incx; + jy += *incy; /* L40: */ - } - } + } + } } else { /* Form A when A is stored in the lower triangle. */ - if (*incx == 1 && *incy == 1) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = j; - i__3 = j; - if (x[i__2].r != 0. || x[i__2].i != 0. || (y[i__3].r != 0. || - y[i__3].i != 0.)) { - d_cnjg(&z__2, &y[j]); - z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = - alpha->r * z__2.i + alpha->i * z__2.r; - temp1.r = z__1.r, temp1.i = z__1.i; - i__2 = j; - z__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, - z__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2] - .r; - d_cnjg(&z__1, &z__2); - temp2.r = z__1.r, temp2.i = z__1.i; - i__2 = j + j * a_dim1; - i__3 = j + j * a_dim1; - i__4 = j; - z__2.r = x[i__4].r * temp1.r - x[i__4].i * temp1.i, - z__2.i = x[i__4].r * temp1.i + x[i__4].i * - temp1.r; - i__5 = j; - z__3.r = y[i__5].r * temp2.r - y[i__5].i * temp2.i, - z__3.i = y[i__5].r * temp2.i + y[i__5].i * - temp2.r; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; - d__1 = a[i__3].r + z__1.r; - a[i__2].r = d__1, a[i__2].i = 0.; - i__2 = *n; - for (i__ = j + 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * a_dim1; - i__4 = i__ + j * a_dim1; - i__5 = i__; - z__3.r = x[i__5].r * temp1.r - x[i__5].i * temp1.i, - z__3.i = x[i__5].r * temp1.i + x[i__5].i * - temp1.r; - z__2.r = a[i__4].r + z__3.r, z__2.i = a[i__4].i + - z__3.i; - i__6 = i__; - z__4.r = y[i__6].r * temp2.r - y[i__6].i * temp2.i, - z__4.i = y[i__6].r * temp2.i + y[i__6].i * - temp2.r; - z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; - a[i__3].r = z__1.r, a[i__3].i = z__1.i; + if (*incx == 1 && *incy == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + i__3 = j; + if (x[i__2].r != 0. || x[i__2].i != 0. || (y[i__3].r != 0. || + y[i__3].i != 0.)) { + d_cnjg(&z__2, &y[j]); + z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = + alpha->r * z__2.i + alpha->i * z__2.r; + temp1.r = z__1.r, temp1.i = z__1.i; + i__2 = j; + z__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, + z__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2] + .r; + d_cnjg(&z__1, &z__2); + temp2.r = z__1.r, temp2.i = z__1.i; + i__2 = j + j * a_dim1; + i__3 = j + j * a_dim1; + i__4 = j; + z__2.r = x[i__4].r * temp1.r - x[i__4].i * temp1.i, + z__2.i = x[i__4].r * temp1.i + x[i__4].i * + temp1.r; + i__5 = j; + z__3.r = y[i__5].r * temp2.r - y[i__5].i * temp2.i, + z__3.i = y[i__5].r * temp2.i + y[i__5].i * + temp2.r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; + d__1 = a[i__3].r + z__1.r; + a[i__2].r = d__1, a[i__2].i = 0.; + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + i__4 = i__ + j * a_dim1; + i__5 = i__; + z__3.r = x[i__5].r * temp1.r - x[i__5].i * temp1.i, + z__3.i = x[i__5].r * temp1.i + x[i__5].i * + temp1.r; + z__2.r = a[i__4].r + z__3.r, z__2.i = a[i__4].i + + z__3.i; + i__6 = i__; + z__4.r = y[i__6].r * temp2.r - y[i__6].i * temp2.i, + z__4.i = y[i__6].r * temp2.i + y[i__6].i * + temp2.r; + z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; /* L50: */ - } - } else { - i__2 = j + j * a_dim1; - i__3 = j + j * a_dim1; - d__1 = a[i__3].r; - a[i__2].r = d__1, a[i__2].i = 0.; - } + } + } else { + i__2 = j + j * a_dim1; + i__3 = j + j * a_dim1; + d__1 = a[i__3].r; + a[i__2].r = d__1, a[i__2].i = 0.; + } /* L60: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = jx; - i__3 = jy; - if (x[i__2].r != 0. || x[i__2].i != 0. || (y[i__3].r != 0. || - y[i__3].i != 0.)) { - d_cnjg(&z__2, &y[jy]); - z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = - alpha->r * z__2.i + alpha->i * z__2.r; - temp1.r = z__1.r, temp1.i = z__1.i; - i__2 = jx; - z__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, - z__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2] - .r; - d_cnjg(&z__1, &z__2); - temp2.r = z__1.r, temp2.i = z__1.i; - i__2 = j + j * a_dim1; - i__3 = j + j * a_dim1; - i__4 = jx; - z__2.r = x[i__4].r * temp1.r - x[i__4].i * temp1.i, - z__2.i = x[i__4].r * temp1.i + x[i__4].i * - temp1.r; - i__5 = jy; - z__3.r = y[i__5].r * temp2.r - y[i__5].i * temp2.i, - z__3.i = y[i__5].r * temp2.i + y[i__5].i * - temp2.r; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; - d__1 = a[i__3].r + z__1.r; - a[i__2].r = d__1, a[i__2].i = 0.; - ix = jx; - iy = jy; - i__2 = *n; - for (i__ = j + 1; i__ <= i__2; ++i__) { - ix += *incx; - iy += *incy; - i__3 = i__ + j * a_dim1; - i__4 = i__ + j * a_dim1; - i__5 = ix; - z__3.r = x[i__5].r * temp1.r - x[i__5].i * temp1.i, - z__3.i = x[i__5].r * temp1.i + x[i__5].i * - temp1.r; - z__2.r = a[i__4].r + z__3.r, z__2.i = a[i__4].i + - z__3.i; - i__6 = iy; - z__4.r = y[i__6].r * temp2.r - y[i__6].i * temp2.i, - z__4.i = y[i__6].r * temp2.i + y[i__6].i * - temp2.r; - z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; - a[i__3].r = z__1.r, a[i__3].i = z__1.i; + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = jx; + i__3 = jy; + if (x[i__2].r != 0. || x[i__2].i != 0. || (y[i__3].r != 0. || + y[i__3].i != 0.)) { + d_cnjg(&z__2, &y[jy]); + z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = + alpha->r * z__2.i + alpha->i * z__2.r; + temp1.r = z__1.r, temp1.i = z__1.i; + i__2 = jx; + z__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, + z__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2] + .r; + d_cnjg(&z__1, &z__2); + temp2.r = z__1.r, temp2.i = z__1.i; + i__2 = j + j * a_dim1; + i__3 = j + j * a_dim1; + i__4 = jx; + z__2.r = x[i__4].r * temp1.r - x[i__4].i * temp1.i, + z__2.i = x[i__4].r * temp1.i + x[i__4].i * + temp1.r; + i__5 = jy; + z__3.r = y[i__5].r * temp2.r - y[i__5].i * temp2.i, + z__3.i = y[i__5].r * temp2.i + y[i__5].i * + temp2.r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; + d__1 = a[i__3].r + z__1.r; + a[i__2].r = d__1, a[i__2].i = 0.; + ix = jx; + iy = jy; + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + ix += *incx; + iy += *incy; + i__3 = i__ + j * a_dim1; + i__4 = i__ + j * a_dim1; + i__5 = ix; + z__3.r = x[i__5].r * temp1.r - x[i__5].i * temp1.i, + z__3.i = x[i__5].r * temp1.i + x[i__5].i * + temp1.r; + z__2.r = a[i__4].r + z__3.r, z__2.i = a[i__4].i + + z__3.i; + i__6 = iy; + z__4.r = y[i__6].r * temp2.r - y[i__6].i * temp2.i, + z__4.i = y[i__6].r * temp2.i + y[i__6].i * + temp2.r; + z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; /* L70: */ - } - } else { - i__2 = j + j * a_dim1; - i__3 = j + j * a_dim1; - d__1 = a[i__3].r; - a[i__2].r = d__1, a[i__2].i = 0.; - } - jx += *incx; - jy += *incy; + } + } else { + i__2 = j + j * a_dim1; + i__3 = j + j * a_dim1; + d__1 = a[i__3].r; + a[i__2].r = d__1, a[i__2].i = 0.; + } + jx += *incx; + jy += *incy; /* L80: */ - } - } + } + } } return 0; @@ -515,5 +515,5 @@ extern "C" { } /* zher2_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zher2k.cpp b/lib/linalg/zher2k.cpp index 1b94010d33..7b5553add1 100644 --- a/lib/linalg/zher2k.cpp +++ b/lib/linalg/zher2k.cpp @@ -1,13 +1,13 @@ /* fortran/zher2k.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -211,14 +211,14 @@ extern "C" { /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int zher2k_(char *uplo, char *trans, integer *n, integer *k, - doublecomplex *alpha, doublecomplex *a, integer *lda, doublecomplex * - b, integer *ldb, doublereal *beta, doublecomplex *c__, integer *ldc, - ftnlen uplo_len, ftnlen trans_len) +/* Subroutine */ int zher2k_(char *uplo, char *trans, integer *n, integer *k, + doublecomplex *alpha, doublecomplex *a, integer *lda, doublecomplex * + b, integer *ldb, doublereal *beta, doublecomplex *c__, integer *ldc, + ftnlen uplo_len, ftnlen trans_len) { /* System generated locals */ - integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, - i__3, i__4, i__5, i__6, i__7; + integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, + i__3, i__4, i__5, i__6, i__7; doublereal d__1; doublecomplex z__1, z__2, z__3, z__4, z__5, z__6; @@ -271,108 +271,108 @@ extern "C" { /* Function Body */ if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { - nrowa = *n; + nrowa = *n; } else { - nrowa = *k; + nrowa = *k; } upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); info = 0; if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { - info = 1; - } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, - (char *)"C", (ftnlen)1, (ftnlen)1)) { - info = 2; + info = 1; + } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, + (char *)"C", (ftnlen)1, (ftnlen)1)) { + info = 2; } else if (*n < 0) { - info = 3; + info = 3; } else if (*k < 0) { - info = 4; + info = 4; } else if (*lda < max(1,nrowa)) { - info = 7; + info = 7; } else if (*ldb < max(1,nrowa)) { - info = 9; + info = 9; } else if (*ldc < max(1,*n)) { - info = 12; + info = 12; } if (info != 0) { - xerbla_((char *)"ZHER2K", &info, (ftnlen)6); - return 0; + xerbla_((char *)"ZHER2K", &info, (ftnlen)6); + return 0; } /* Quick return if possible. */ - if (*n == 0 || (alpha->r == 0. && alpha->i == 0. || *k == 0) && *beta == - 1.) { - return 0; + if (*n == 0 || (alpha->r == 0. && alpha->i == 0. || *k == 0) && *beta == + 1.) { + return 0; } /* And when alpha.eq.zero. */ if (alpha->r == 0. && alpha->i == 0.) { - if (upper) { - if (*beta == 0.) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = j; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * c_dim1; - c__[i__3].r = 0., c__[i__3].i = 0.; + if (upper) { + if (*beta == 0.) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + c__[i__3].r = 0., c__[i__3].i = 0.; /* L10: */ - } + } /* L20: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = j - 1; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * c_dim1; - i__4 = i__ + j * c_dim1; - z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[ - i__4].i; - c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + i__4 = i__ + j * c_dim1; + z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[ + i__4].i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; /* L30: */ - } - i__2 = j + j * c_dim1; - i__3 = j + j * c_dim1; - d__1 = *beta * c__[i__3].r; - c__[i__2].r = d__1, c__[i__2].i = 0.; + } + i__2 = j + j * c_dim1; + i__3 = j + j * c_dim1; + d__1 = *beta * c__[i__3].r; + c__[i__2].r = d__1, c__[i__2].i = 0.; /* L40: */ - } - } - } else { - if (*beta == 0.) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *n; - for (i__ = j; i__ <= i__2; ++i__) { - i__3 = i__ + j * c_dim1; - c__[i__3].r = 0., c__[i__3].i = 0.; + } + } + } else { + if (*beta == 0.) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = j; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + c__[i__3].r = 0., c__[i__3].i = 0.; /* L50: */ - } + } /* L60: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = j + j * c_dim1; - i__3 = j + j * c_dim1; - d__1 = *beta * c__[i__3].r; - c__[i__2].r = d__1, c__[i__2].i = 0.; - i__2 = *n; - for (i__ = j + 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * c_dim1; - i__4 = i__ + j * c_dim1; - z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[ - i__4].i; - c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j + j * c_dim1; + i__3 = j + j * c_dim1; + d__1 = *beta * c__[i__3].r; + c__[i__2].r = d__1, c__[i__2].i = 0.; + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + i__4 = i__ + j * c_dim1; + z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[ + i__4].i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; /* L70: */ - } + } /* L80: */ - } - } - } - return 0; + } + } + } + return 0; } /* Start the operations. */ @@ -382,361 +382,361 @@ extern "C" { /* Form C := alpha*A*B**H + conjg( alpha )*B*A**H + */ /* C. */ - if (upper) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - if (*beta == 0.) { - i__2 = j; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * c_dim1; - c__[i__3].r = 0., c__[i__3].i = 0.; + if (upper) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (*beta == 0.) { + i__2 = j; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + c__[i__3].r = 0., c__[i__3].i = 0.; /* L90: */ - } - } else if (*beta != 1.) { - i__2 = j - 1; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * c_dim1; - i__4 = i__ + j * c_dim1; - z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[ - i__4].i; - c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } + } else if (*beta != 1.) { + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + i__4 = i__ + j * c_dim1; + z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[ + i__4].i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; /* L100: */ - } - i__2 = j + j * c_dim1; - i__3 = j + j * c_dim1; - d__1 = *beta * c__[i__3].r; - c__[i__2].r = d__1, c__[i__2].i = 0.; - } else { - i__2 = j + j * c_dim1; - i__3 = j + j * c_dim1; - d__1 = c__[i__3].r; - c__[i__2].r = d__1, c__[i__2].i = 0.; - } - i__2 = *k; - for (l = 1; l <= i__2; ++l) { - i__3 = j + l * a_dim1; - i__4 = j + l * b_dim1; - if (a[i__3].r != 0. || a[i__3].i != 0. || (b[i__4].r != - 0. || b[i__4].i != 0.)) { - d_cnjg(&z__2, &b[j + l * b_dim1]); - z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, - z__1.i = alpha->r * z__2.i + alpha->i * - z__2.r; - temp1.r = z__1.r, temp1.i = z__1.i; - i__3 = j + l * a_dim1; - z__2.r = alpha->r * a[i__3].r - alpha->i * a[i__3].i, - z__2.i = alpha->r * a[i__3].i + alpha->i * a[ - i__3].r; - d_cnjg(&z__1, &z__2); - temp2.r = z__1.r, temp2.i = z__1.i; - i__3 = j - 1; - for (i__ = 1; i__ <= i__3; ++i__) { - i__4 = i__ + j * c_dim1; - i__5 = i__ + j * c_dim1; - i__6 = i__ + l * a_dim1; - z__3.r = a[i__6].r * temp1.r - a[i__6].i * - temp1.i, z__3.i = a[i__6].r * temp1.i + a[ - i__6].i * temp1.r; - z__2.r = c__[i__5].r + z__3.r, z__2.i = c__[i__5] - .i + z__3.i; - i__7 = i__ + l * b_dim1; - z__4.r = b[i__7].r * temp2.r - b[i__7].i * - temp2.i, z__4.i = b[i__7].r * temp2.i + b[ - i__7].i * temp2.r; - z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + - z__4.i; - c__[i__4].r = z__1.r, c__[i__4].i = z__1.i; + } + i__2 = j + j * c_dim1; + i__3 = j + j * c_dim1; + d__1 = *beta * c__[i__3].r; + c__[i__2].r = d__1, c__[i__2].i = 0.; + } else { + i__2 = j + j * c_dim1; + i__3 = j + j * c_dim1; + d__1 = c__[i__3].r; + c__[i__2].r = d__1, c__[i__2].i = 0.; + } + i__2 = *k; + for (l = 1; l <= i__2; ++l) { + i__3 = j + l * a_dim1; + i__4 = j + l * b_dim1; + if (a[i__3].r != 0. || a[i__3].i != 0. || (b[i__4].r != + 0. || b[i__4].i != 0.)) { + d_cnjg(&z__2, &b[j + l * b_dim1]); + z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, + z__1.i = alpha->r * z__2.i + alpha->i * + z__2.r; + temp1.r = z__1.r, temp1.i = z__1.i; + i__3 = j + l * a_dim1; + z__2.r = alpha->r * a[i__3].r - alpha->i * a[i__3].i, + z__2.i = alpha->r * a[i__3].i + alpha->i * a[ + i__3].r; + d_cnjg(&z__1, &z__2); + temp2.r = z__1.r, temp2.i = z__1.i; + i__3 = j - 1; + for (i__ = 1; i__ <= i__3; ++i__) { + i__4 = i__ + j * c_dim1; + i__5 = i__ + j * c_dim1; + i__6 = i__ + l * a_dim1; + z__3.r = a[i__6].r * temp1.r - a[i__6].i * + temp1.i, z__3.i = a[i__6].r * temp1.i + a[ + i__6].i * temp1.r; + z__2.r = c__[i__5].r + z__3.r, z__2.i = c__[i__5] + .i + z__3.i; + i__7 = i__ + l * b_dim1; + z__4.r = b[i__7].r * temp2.r - b[i__7].i * + temp2.i, z__4.i = b[i__7].r * temp2.i + b[ + i__7].i * temp2.r; + z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + + z__4.i; + c__[i__4].r = z__1.r, c__[i__4].i = z__1.i; /* L110: */ - } - i__3 = j + j * c_dim1; - i__4 = j + j * c_dim1; - i__5 = j + l * a_dim1; - z__2.r = a[i__5].r * temp1.r - a[i__5].i * temp1.i, - z__2.i = a[i__5].r * temp1.i + a[i__5].i * - temp1.r; - i__6 = j + l * b_dim1; - z__3.r = b[i__6].r * temp2.r - b[i__6].i * temp2.i, - z__3.i = b[i__6].r * temp2.i + b[i__6].i * - temp2.r; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; - d__1 = c__[i__4].r + z__1.r; - c__[i__3].r = d__1, c__[i__3].i = 0.; - } + } + i__3 = j + j * c_dim1; + i__4 = j + j * c_dim1; + i__5 = j + l * a_dim1; + z__2.r = a[i__5].r * temp1.r - a[i__5].i * temp1.i, + z__2.i = a[i__5].r * temp1.i + a[i__5].i * + temp1.r; + i__6 = j + l * b_dim1; + z__3.r = b[i__6].r * temp2.r - b[i__6].i * temp2.i, + z__3.i = b[i__6].r * temp2.i + b[i__6].i * + temp2.r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; + d__1 = c__[i__4].r + z__1.r; + c__[i__3].r = d__1, c__[i__3].i = 0.; + } /* L120: */ - } + } /* L130: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - if (*beta == 0.) { - i__2 = *n; - for (i__ = j; i__ <= i__2; ++i__) { - i__3 = i__ + j * c_dim1; - c__[i__3].r = 0., c__[i__3].i = 0.; + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (*beta == 0.) { + i__2 = *n; + for (i__ = j; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + c__[i__3].r = 0., c__[i__3].i = 0.; /* L140: */ - } - } else if (*beta != 1.) { - i__2 = *n; - for (i__ = j + 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * c_dim1; - i__4 = i__ + j * c_dim1; - z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[ - i__4].i; - c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } + } else if (*beta != 1.) { + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + i__4 = i__ + j * c_dim1; + z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[ + i__4].i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; /* L150: */ - } - i__2 = j + j * c_dim1; - i__3 = j + j * c_dim1; - d__1 = *beta * c__[i__3].r; - c__[i__2].r = d__1, c__[i__2].i = 0.; - } else { - i__2 = j + j * c_dim1; - i__3 = j + j * c_dim1; - d__1 = c__[i__3].r; - c__[i__2].r = d__1, c__[i__2].i = 0.; - } - i__2 = *k; - for (l = 1; l <= i__2; ++l) { - i__3 = j + l * a_dim1; - i__4 = j + l * b_dim1; - if (a[i__3].r != 0. || a[i__3].i != 0. || (b[i__4].r != - 0. || b[i__4].i != 0.)) { - d_cnjg(&z__2, &b[j + l * b_dim1]); - z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, - z__1.i = alpha->r * z__2.i + alpha->i * - z__2.r; - temp1.r = z__1.r, temp1.i = z__1.i; - i__3 = j + l * a_dim1; - z__2.r = alpha->r * a[i__3].r - alpha->i * a[i__3].i, - z__2.i = alpha->r * a[i__3].i + alpha->i * a[ - i__3].r; - d_cnjg(&z__1, &z__2); - temp2.r = z__1.r, temp2.i = z__1.i; - i__3 = *n; - for (i__ = j + 1; i__ <= i__3; ++i__) { - i__4 = i__ + j * c_dim1; - i__5 = i__ + j * c_dim1; - i__6 = i__ + l * a_dim1; - z__3.r = a[i__6].r * temp1.r - a[i__6].i * - temp1.i, z__3.i = a[i__6].r * temp1.i + a[ - i__6].i * temp1.r; - z__2.r = c__[i__5].r + z__3.r, z__2.i = c__[i__5] - .i + z__3.i; - i__7 = i__ + l * b_dim1; - z__4.r = b[i__7].r * temp2.r - b[i__7].i * - temp2.i, z__4.i = b[i__7].r * temp2.i + b[ - i__7].i * temp2.r; - z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + - z__4.i; - c__[i__4].r = z__1.r, c__[i__4].i = z__1.i; + } + i__2 = j + j * c_dim1; + i__3 = j + j * c_dim1; + d__1 = *beta * c__[i__3].r; + c__[i__2].r = d__1, c__[i__2].i = 0.; + } else { + i__2 = j + j * c_dim1; + i__3 = j + j * c_dim1; + d__1 = c__[i__3].r; + c__[i__2].r = d__1, c__[i__2].i = 0.; + } + i__2 = *k; + for (l = 1; l <= i__2; ++l) { + i__3 = j + l * a_dim1; + i__4 = j + l * b_dim1; + if (a[i__3].r != 0. || a[i__3].i != 0. || (b[i__4].r != + 0. || b[i__4].i != 0.)) { + d_cnjg(&z__2, &b[j + l * b_dim1]); + z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, + z__1.i = alpha->r * z__2.i + alpha->i * + z__2.r; + temp1.r = z__1.r, temp1.i = z__1.i; + i__3 = j + l * a_dim1; + z__2.r = alpha->r * a[i__3].r - alpha->i * a[i__3].i, + z__2.i = alpha->r * a[i__3].i + alpha->i * a[ + i__3].r; + d_cnjg(&z__1, &z__2); + temp2.r = z__1.r, temp2.i = z__1.i; + i__3 = *n; + for (i__ = j + 1; i__ <= i__3; ++i__) { + i__4 = i__ + j * c_dim1; + i__5 = i__ + j * c_dim1; + i__6 = i__ + l * a_dim1; + z__3.r = a[i__6].r * temp1.r - a[i__6].i * + temp1.i, z__3.i = a[i__6].r * temp1.i + a[ + i__6].i * temp1.r; + z__2.r = c__[i__5].r + z__3.r, z__2.i = c__[i__5] + .i + z__3.i; + i__7 = i__ + l * b_dim1; + z__4.r = b[i__7].r * temp2.r - b[i__7].i * + temp2.i, z__4.i = b[i__7].r * temp2.i + b[ + i__7].i * temp2.r; + z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + + z__4.i; + c__[i__4].r = z__1.r, c__[i__4].i = z__1.i; /* L160: */ - } - i__3 = j + j * c_dim1; - i__4 = j + j * c_dim1; - i__5 = j + l * a_dim1; - z__2.r = a[i__5].r * temp1.r - a[i__5].i * temp1.i, - z__2.i = a[i__5].r * temp1.i + a[i__5].i * - temp1.r; - i__6 = j + l * b_dim1; - z__3.r = b[i__6].r * temp2.r - b[i__6].i * temp2.i, - z__3.i = b[i__6].r * temp2.i + b[i__6].i * - temp2.r; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; - d__1 = c__[i__4].r + z__1.r; - c__[i__3].r = d__1, c__[i__3].i = 0.; - } + } + i__3 = j + j * c_dim1; + i__4 = j + j * c_dim1; + i__5 = j + l * a_dim1; + z__2.r = a[i__5].r * temp1.r - a[i__5].i * temp1.i, + z__2.i = a[i__5].r * temp1.i + a[i__5].i * + temp1.r; + i__6 = j + l * b_dim1; + z__3.r = b[i__6].r * temp2.r - b[i__6].i * temp2.i, + z__3.i = b[i__6].r * temp2.i + b[i__6].i * + temp2.r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; + d__1 = c__[i__4].r + z__1.r; + c__[i__3].r = d__1, c__[i__3].i = 0.; + } /* L170: */ - } + } /* L180: */ - } - } + } + } } else { /* Form C := alpha*A**H*B + conjg( alpha )*B**H*A + */ /* C. */ - if (upper) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = j; - for (i__ = 1; i__ <= i__2; ++i__) { - temp1.r = 0., temp1.i = 0.; - temp2.r = 0., temp2.i = 0.; - i__3 = *k; - for (l = 1; l <= i__3; ++l) { - d_cnjg(&z__3, &a[l + i__ * a_dim1]); - i__4 = l + j * b_dim1; - z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4].i, - z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4] - .r; - z__1.r = temp1.r + z__2.r, z__1.i = temp1.i + z__2.i; - temp1.r = z__1.r, temp1.i = z__1.i; - d_cnjg(&z__3, &b[l + i__ * b_dim1]); - i__4 = l + j * a_dim1; - z__2.r = z__3.r * a[i__4].r - z__3.i * a[i__4].i, - z__2.i = z__3.r * a[i__4].i + z__3.i * a[i__4] - .r; - z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; - temp2.r = z__1.r, temp2.i = z__1.i; + if (upper) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + for (i__ = 1; i__ <= i__2; ++i__) { + temp1.r = 0., temp1.i = 0.; + temp2.r = 0., temp2.i = 0.; + i__3 = *k; + for (l = 1; l <= i__3; ++l) { + d_cnjg(&z__3, &a[l + i__ * a_dim1]); + i__4 = l + j * b_dim1; + z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4].i, + z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4] + .r; + z__1.r = temp1.r + z__2.r, z__1.i = temp1.i + z__2.i; + temp1.r = z__1.r, temp1.i = z__1.i; + d_cnjg(&z__3, &b[l + i__ * b_dim1]); + i__4 = l + j * a_dim1; + z__2.r = z__3.r * a[i__4].r - z__3.i * a[i__4].i, + z__2.i = z__3.r * a[i__4].i + z__3.i * a[i__4] + .r; + z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; + temp2.r = z__1.r, temp2.i = z__1.i; /* L190: */ - } - if (i__ == j) { - if (*beta == 0.) { - i__3 = j + j * c_dim1; - z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, - z__2.i = alpha->r * temp1.i + alpha->i * - temp1.r; - d_cnjg(&z__4, alpha); - z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, - z__3.i = z__4.r * temp2.i + z__4.i * - temp2.r; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; - d__1 = z__1.r; - c__[i__3].r = d__1, c__[i__3].i = 0.; - } else { - i__3 = j + j * c_dim1; - i__4 = j + j * c_dim1; - z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, - z__2.i = alpha->r * temp1.i + alpha->i * - temp1.r; - d_cnjg(&z__4, alpha); - z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, - z__3.i = z__4.r * temp2.i + z__4.i * - temp2.r; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; - d__1 = *beta * c__[i__4].r + z__1.r; - c__[i__3].r = d__1, c__[i__3].i = 0.; - } - } else { - if (*beta == 0.) { - i__3 = i__ + j * c_dim1; - z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, - z__2.i = alpha->r * temp1.i + alpha->i * - temp1.r; - d_cnjg(&z__4, alpha); - z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, - z__3.i = z__4.r * temp2.i + z__4.i * - temp2.r; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; - c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; - } else { - i__3 = i__ + j * c_dim1; - i__4 = i__ + j * c_dim1; - z__3.r = *beta * c__[i__4].r, z__3.i = *beta * - c__[i__4].i; - z__4.r = alpha->r * temp1.r - alpha->i * temp1.i, - z__4.i = alpha->r * temp1.i + alpha->i * - temp1.r; - z__2.r = z__3.r + z__4.r, z__2.i = z__3.i + - z__4.i; - d_cnjg(&z__6, alpha); - z__5.r = z__6.r * temp2.r - z__6.i * temp2.i, - z__5.i = z__6.r * temp2.i + z__6.i * - temp2.r; - z__1.r = z__2.r + z__5.r, z__1.i = z__2.i + - z__5.i; - c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; - } - } + } + if (i__ == j) { + if (*beta == 0.) { + i__3 = j + j * c_dim1; + z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, + z__2.i = alpha->r * temp1.i + alpha->i * + temp1.r; + d_cnjg(&z__4, alpha); + z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, + z__3.i = z__4.r * temp2.i + z__4.i * + temp2.r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + d__1 = z__1.r; + c__[i__3].r = d__1, c__[i__3].i = 0.; + } else { + i__3 = j + j * c_dim1; + i__4 = j + j * c_dim1; + z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, + z__2.i = alpha->r * temp1.i + alpha->i * + temp1.r; + d_cnjg(&z__4, alpha); + z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, + z__3.i = z__4.r * temp2.i + z__4.i * + temp2.r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + d__1 = *beta * c__[i__4].r + z__1.r; + c__[i__3].r = d__1, c__[i__3].i = 0.; + } + } else { + if (*beta == 0.) { + i__3 = i__ + j * c_dim1; + z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, + z__2.i = alpha->r * temp1.i + alpha->i * + temp1.r; + d_cnjg(&z__4, alpha); + z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, + z__3.i = z__4.r * temp2.i + z__4.i * + temp2.r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } else { + i__3 = i__ + j * c_dim1; + i__4 = i__ + j * c_dim1; + z__3.r = *beta * c__[i__4].r, z__3.i = *beta * + c__[i__4].i; + z__4.r = alpha->r * temp1.r - alpha->i * temp1.i, + z__4.i = alpha->r * temp1.i + alpha->i * + temp1.r; + z__2.r = z__3.r + z__4.r, z__2.i = z__3.i + + z__4.i; + d_cnjg(&z__6, alpha); + z__5.r = z__6.r * temp2.r - z__6.i * temp2.i, + z__5.i = z__6.r * temp2.i + z__6.i * + temp2.r; + z__1.r = z__2.r + z__5.r, z__1.i = z__2.i + + z__5.i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } + } /* L200: */ - } + } /* L210: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *n; - for (i__ = j; i__ <= i__2; ++i__) { - temp1.r = 0., temp1.i = 0.; - temp2.r = 0., temp2.i = 0.; - i__3 = *k; - for (l = 1; l <= i__3; ++l) { - d_cnjg(&z__3, &a[l + i__ * a_dim1]); - i__4 = l + j * b_dim1; - z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4].i, - z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4] - .r; - z__1.r = temp1.r + z__2.r, z__1.i = temp1.i + z__2.i; - temp1.r = z__1.r, temp1.i = z__1.i; - d_cnjg(&z__3, &b[l + i__ * b_dim1]); - i__4 = l + j * a_dim1; - z__2.r = z__3.r * a[i__4].r - z__3.i * a[i__4].i, - z__2.i = z__3.r * a[i__4].i + z__3.i * a[i__4] - .r; - z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; - temp2.r = z__1.r, temp2.i = z__1.i; + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = j; i__ <= i__2; ++i__) { + temp1.r = 0., temp1.i = 0.; + temp2.r = 0., temp2.i = 0.; + i__3 = *k; + for (l = 1; l <= i__3; ++l) { + d_cnjg(&z__3, &a[l + i__ * a_dim1]); + i__4 = l + j * b_dim1; + z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4].i, + z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4] + .r; + z__1.r = temp1.r + z__2.r, z__1.i = temp1.i + z__2.i; + temp1.r = z__1.r, temp1.i = z__1.i; + d_cnjg(&z__3, &b[l + i__ * b_dim1]); + i__4 = l + j * a_dim1; + z__2.r = z__3.r * a[i__4].r - z__3.i * a[i__4].i, + z__2.i = z__3.r * a[i__4].i + z__3.i * a[i__4] + .r; + z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; + temp2.r = z__1.r, temp2.i = z__1.i; /* L220: */ - } - if (i__ == j) { - if (*beta == 0.) { - i__3 = j + j * c_dim1; - z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, - z__2.i = alpha->r * temp1.i + alpha->i * - temp1.r; - d_cnjg(&z__4, alpha); - z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, - z__3.i = z__4.r * temp2.i + z__4.i * - temp2.r; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; - d__1 = z__1.r; - c__[i__3].r = d__1, c__[i__3].i = 0.; - } else { - i__3 = j + j * c_dim1; - i__4 = j + j * c_dim1; - z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, - z__2.i = alpha->r * temp1.i + alpha->i * - temp1.r; - d_cnjg(&z__4, alpha); - z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, - z__3.i = z__4.r * temp2.i + z__4.i * - temp2.r; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; - d__1 = *beta * c__[i__4].r + z__1.r; - c__[i__3].r = d__1, c__[i__3].i = 0.; - } - } else { - if (*beta == 0.) { - i__3 = i__ + j * c_dim1; - z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, - z__2.i = alpha->r * temp1.i + alpha->i * - temp1.r; - d_cnjg(&z__4, alpha); - z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, - z__3.i = z__4.r * temp2.i + z__4.i * - temp2.r; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; - c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; - } else { - i__3 = i__ + j * c_dim1; - i__4 = i__ + j * c_dim1; - z__3.r = *beta * c__[i__4].r, z__3.i = *beta * - c__[i__4].i; - z__4.r = alpha->r * temp1.r - alpha->i * temp1.i, - z__4.i = alpha->r * temp1.i + alpha->i * - temp1.r; - z__2.r = z__3.r + z__4.r, z__2.i = z__3.i + - z__4.i; - d_cnjg(&z__6, alpha); - z__5.r = z__6.r * temp2.r - z__6.i * temp2.i, - z__5.i = z__6.r * temp2.i + z__6.i * - temp2.r; - z__1.r = z__2.r + z__5.r, z__1.i = z__2.i + - z__5.i; - c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; - } - } + } + if (i__ == j) { + if (*beta == 0.) { + i__3 = j + j * c_dim1; + z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, + z__2.i = alpha->r * temp1.i + alpha->i * + temp1.r; + d_cnjg(&z__4, alpha); + z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, + z__3.i = z__4.r * temp2.i + z__4.i * + temp2.r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + d__1 = z__1.r; + c__[i__3].r = d__1, c__[i__3].i = 0.; + } else { + i__3 = j + j * c_dim1; + i__4 = j + j * c_dim1; + z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, + z__2.i = alpha->r * temp1.i + alpha->i * + temp1.r; + d_cnjg(&z__4, alpha); + z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, + z__3.i = z__4.r * temp2.i + z__4.i * + temp2.r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + d__1 = *beta * c__[i__4].r + z__1.r; + c__[i__3].r = d__1, c__[i__3].i = 0.; + } + } else { + if (*beta == 0.) { + i__3 = i__ + j * c_dim1; + z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, + z__2.i = alpha->r * temp1.i + alpha->i * + temp1.r; + d_cnjg(&z__4, alpha); + z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, + z__3.i = z__4.r * temp2.i + z__4.i * + temp2.r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } else { + i__3 = i__ + j * c_dim1; + i__4 = i__ + j * c_dim1; + z__3.r = *beta * c__[i__4].r, z__3.i = *beta * + c__[i__4].i; + z__4.r = alpha->r * temp1.r - alpha->i * temp1.i, + z__4.i = alpha->r * temp1.i + alpha->i * + temp1.r; + z__2.r = z__3.r + z__4.r, z__2.i = z__3.i + + z__4.i; + d_cnjg(&z__6, alpha); + z__5.r = z__6.r * temp2.r - z__6.i * temp2.i, + z__5.i = z__6.r * temp2.i + z__6.i * + temp2.r; + z__1.r = z__2.r + z__5.r, z__1.i = z__2.i + + z__5.i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + } + } /* L230: */ - } + } /* L240: */ - } - } + } + } } return 0; @@ -746,5 +746,5 @@ extern "C" { } /* zher2k_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zhetd2.cpp b/lib/linalg/zhetd2.cpp index c6c59ad6d5..71ad2aeab4 100644 --- a/lib/linalg/zhetd2.cpp +++ b/lib/linalg/zhetd2.cpp @@ -1,13 +1,13 @@ /* fortran/zhetd2.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -197,9 +197,9 @@ f"> */ /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int zhetd2_(char *uplo, integer *n, doublecomplex *a, - integer *lda, doublereal *d__, doublereal *e, doublecomplex *tau, - integer *info, ftnlen uplo_len) +/* Subroutine */ int zhetd2_(char *uplo, integer *n, doublecomplex *a, + integer *lda, doublereal *d__, doublereal *e, doublecomplex *tau, + integer *info, ftnlen uplo_len) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; @@ -209,21 +209,21 @@ f"> */ /* Local variables */ integer i__; doublecomplex taui; - extern /* Subroutine */ int zher2_(char *, integer *, doublecomplex *, - doublecomplex *, integer *, doublecomplex *, integer *, - doublecomplex *, integer *, ftnlen); + extern /* Subroutine */ int zher2_(char *, integer *, doublecomplex *, + doublecomplex *, integer *, doublecomplex *, integer *, + doublecomplex *, integer *, ftnlen); doublecomplex alpha; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *, - doublecomplex *, integer *, doublecomplex *, integer *); - extern /* Subroutine */ int zhemv_(char *, integer *, doublecomplex *, - doublecomplex *, integer *, doublecomplex *, integer *, - doublecomplex *, doublecomplex *, integer *, ftnlen); + extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *, + doublecomplex *, integer *, doublecomplex *, integer *); + extern /* Subroutine */ int zhemv_(char *, integer *, doublecomplex *, + doublecomplex *, integer *, doublecomplex *, integer *, + doublecomplex *, doublecomplex *, integer *, ftnlen); logical upper; - extern /* Subroutine */ int zaxpy_(integer *, doublecomplex *, - doublecomplex *, integer *, doublecomplex *, integer *), xerbla_( - char *, integer *, ftnlen), zlarfg_(integer *, doublecomplex *, - doublecomplex *, integer *, doublecomplex *); + extern /* Subroutine */ int zaxpy_(integer *, doublecomplex *, + doublecomplex *, integer *, doublecomplex *, integer *), xerbla_( + char *, integer *, ftnlen), zlarfg_(integer *, doublecomplex *, + doublecomplex *, integer *, doublecomplex *); /* -- LAPACK computational routine -- */ @@ -263,169 +263,169 @@ f"> */ *info = 0; upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { - *info = -1; + *info = -1; } else if (*n < 0) { - *info = -2; + *info = -2; } else if (*lda < max(1,*n)) { - *info = -4; + *info = -4; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"ZHETD2", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"ZHETD2", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*n <= 0) { - return 0; + return 0; } if (upper) { /* Reduce the upper triangle of A */ - i__1 = *n + *n * a_dim1; - i__2 = *n + *n * a_dim1; - d__1 = a[i__2].r; - a[i__1].r = d__1, a[i__1].i = 0.; - for (i__ = *n - 1; i__ >= 1; --i__) { + i__1 = *n + *n * a_dim1; + i__2 = *n + *n * a_dim1; + d__1 = a[i__2].r; + a[i__1].r = d__1, a[i__1].i = 0.; + for (i__ = *n - 1; i__ >= 1; --i__) { /* Generate elementary reflector H(i) = I - tau * v * v**H */ /* to annihilate A(1:i-1,i+1) */ - i__1 = i__ + (i__ + 1) * a_dim1; - alpha.r = a[i__1].r, alpha.i = a[i__1].i; - zlarfg_(&i__, &alpha, &a[(i__ + 1) * a_dim1 + 1], &c__1, &taui); - e[i__] = alpha.r; + i__1 = i__ + (i__ + 1) * a_dim1; + alpha.r = a[i__1].r, alpha.i = a[i__1].i; + zlarfg_(&i__, &alpha, &a[(i__ + 1) * a_dim1 + 1], &c__1, &taui); + e[i__] = alpha.r; - if (taui.r != 0. || taui.i != 0.) { + if (taui.r != 0. || taui.i != 0.) { /* Apply H(i) from both sides to A(1:i,1:i) */ - i__1 = i__ + (i__ + 1) * a_dim1; - a[i__1].r = 1., a[i__1].i = 0.; + i__1 = i__ + (i__ + 1) * a_dim1; + a[i__1].r = 1., a[i__1].i = 0.; /* Compute x := tau * A * v storing x in TAU(1:i) */ - zhemv_(uplo, &i__, &taui, &a[a_offset], lda, &a[(i__ + 1) * - a_dim1 + 1], &c__1, &c_b2, &tau[1], &c__1, (ftnlen)1); + zhemv_(uplo, &i__, &taui, &a[a_offset], lda, &a[(i__ + 1) * + a_dim1 + 1], &c__1, &c_b2, &tau[1], &c__1, (ftnlen)1); /* Compute w := x - 1/2 * tau * (x**H * v) * v */ - z__3.r = -.5, z__3.i = -0.; - z__2.r = z__3.r * taui.r - z__3.i * taui.i, z__2.i = z__3.r * - taui.i + z__3.i * taui.r; - zdotc_(&z__4, &i__, &tau[1], &c__1, &a[(i__ + 1) * a_dim1 + 1] - , &c__1); - z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, z__1.i = z__2.r * - z__4.i + z__2.i * z__4.r; - alpha.r = z__1.r, alpha.i = z__1.i; - zaxpy_(&i__, &alpha, &a[(i__ + 1) * a_dim1 + 1], &c__1, &tau[ - 1], &c__1); + z__3.r = -.5, z__3.i = -0.; + z__2.r = z__3.r * taui.r - z__3.i * taui.i, z__2.i = z__3.r * + taui.i + z__3.i * taui.r; + zdotc_(&z__4, &i__, &tau[1], &c__1, &a[(i__ + 1) * a_dim1 + 1] + , &c__1); + z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, z__1.i = z__2.r * + z__4.i + z__2.i * z__4.r; + alpha.r = z__1.r, alpha.i = z__1.i; + zaxpy_(&i__, &alpha, &a[(i__ + 1) * a_dim1 + 1], &c__1, &tau[ + 1], &c__1); /* Apply the transformation as a rank-2 update: */ /* A := A - v * w**H - w * v**H */ - z__1.r = -1., z__1.i = -0.; - zher2_(uplo, &i__, &z__1, &a[(i__ + 1) * a_dim1 + 1], &c__1, & - tau[1], &c__1, &a[a_offset], lda, (ftnlen)1); + z__1.r = -1., z__1.i = -0.; + zher2_(uplo, &i__, &z__1, &a[(i__ + 1) * a_dim1 + 1], &c__1, & + tau[1], &c__1, &a[a_offset], lda, (ftnlen)1); - } else { - i__1 = i__ + i__ * a_dim1; - i__2 = i__ + i__ * a_dim1; - d__1 = a[i__2].r; - a[i__1].r = d__1, a[i__1].i = 0.; - } - i__1 = i__ + (i__ + 1) * a_dim1; - i__2 = i__; - a[i__1].r = e[i__2], a[i__1].i = 0.; - i__1 = i__ + 1 + (i__ + 1) * a_dim1; - d__[i__ + 1] = a[i__1].r; - i__1 = i__; - tau[i__1].r = taui.r, tau[i__1].i = taui.i; + } else { + i__1 = i__ + i__ * a_dim1; + i__2 = i__ + i__ * a_dim1; + d__1 = a[i__2].r; + a[i__1].r = d__1, a[i__1].i = 0.; + } + i__1 = i__ + (i__ + 1) * a_dim1; + i__2 = i__; + a[i__1].r = e[i__2], a[i__1].i = 0.; + i__1 = i__ + 1 + (i__ + 1) * a_dim1; + d__[i__ + 1] = a[i__1].r; + i__1 = i__; + tau[i__1].r = taui.r, tau[i__1].i = taui.i; /* L10: */ - } - i__1 = a_dim1 + 1; - d__[1] = a[i__1].r; + } + i__1 = a_dim1 + 1; + d__[1] = a[i__1].r; } else { /* Reduce the lower triangle of A */ - i__1 = a_dim1 + 1; - i__2 = a_dim1 + 1; - d__1 = a[i__2].r; - a[i__1].r = d__1, a[i__1].i = 0.; - i__1 = *n - 1; - for (i__ = 1; i__ <= i__1; ++i__) { + i__1 = a_dim1 + 1; + i__2 = a_dim1 + 1; + d__1 = a[i__2].r; + a[i__1].r = d__1, a[i__1].i = 0.; + i__1 = *n - 1; + for (i__ = 1; i__ <= i__1; ++i__) { /* Generate elementary reflector H(i) = I - tau * v * v**H */ /* to annihilate A(i+2:n,i) */ - i__2 = i__ + 1 + i__ * a_dim1; - alpha.r = a[i__2].r, alpha.i = a[i__2].i; - i__2 = *n - i__; + i__2 = i__ + 1 + i__ * a_dim1; + alpha.r = a[i__2].r, alpha.i = a[i__2].i; + i__2 = *n - i__; /* Computing MIN */ - i__3 = i__ + 2; - zlarfg_(&i__2, &alpha, &a[min(i__3,*n) + i__ * a_dim1], &c__1, & - taui); - e[i__] = alpha.r; + i__3 = i__ + 2; + zlarfg_(&i__2, &alpha, &a[min(i__3,*n) + i__ * a_dim1], &c__1, & + taui); + e[i__] = alpha.r; - if (taui.r != 0. || taui.i != 0.) { + if (taui.r != 0. || taui.i != 0.) { /* Apply H(i) from both sides to A(i+1:n,i+1:n) */ - i__2 = i__ + 1 + i__ * a_dim1; - a[i__2].r = 1., a[i__2].i = 0.; + i__2 = i__ + 1 + i__ * a_dim1; + a[i__2].r = 1., a[i__2].i = 0.; /* Compute x := tau * A * v storing y in TAU(i:n-1) */ - i__2 = *n - i__; - zhemv_(uplo, &i__2, &taui, &a[i__ + 1 + (i__ + 1) * a_dim1], - lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b2, &tau[ - i__], &c__1, (ftnlen)1); + i__2 = *n - i__; + zhemv_(uplo, &i__2, &taui, &a[i__ + 1 + (i__ + 1) * a_dim1], + lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b2, &tau[ + i__], &c__1, (ftnlen)1); /* Compute w := x - 1/2 * tau * (x**H * v) * v */ - z__3.r = -.5, z__3.i = -0.; - z__2.r = z__3.r * taui.r - z__3.i * taui.i, z__2.i = z__3.r * - taui.i + z__3.i * taui.r; - i__2 = *n - i__; - zdotc_(&z__4, &i__2, &tau[i__], &c__1, &a[i__ + 1 + i__ * - a_dim1], &c__1); - z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, z__1.i = z__2.r * - z__4.i + z__2.i * z__4.r; - alpha.r = z__1.r, alpha.i = z__1.i; - i__2 = *n - i__; - zaxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &tau[ - i__], &c__1); + z__3.r = -.5, z__3.i = -0.; + z__2.r = z__3.r * taui.r - z__3.i * taui.i, z__2.i = z__3.r * + taui.i + z__3.i * taui.r; + i__2 = *n - i__; + zdotc_(&z__4, &i__2, &tau[i__], &c__1, &a[i__ + 1 + i__ * + a_dim1], &c__1); + z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, z__1.i = z__2.r * + z__4.i + z__2.i * z__4.r; + alpha.r = z__1.r, alpha.i = z__1.i; + i__2 = *n - i__; + zaxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &tau[ + i__], &c__1); /* Apply the transformation as a rank-2 update: */ /* A := A - v * w**H - w * v**H */ - i__2 = *n - i__; - z__1.r = -1., z__1.i = -0.; - zher2_(uplo, &i__2, &z__1, &a[i__ + 1 + i__ * a_dim1], &c__1, - &tau[i__], &c__1, &a[i__ + 1 + (i__ + 1) * a_dim1], - lda, (ftnlen)1); + i__2 = *n - i__; + z__1.r = -1., z__1.i = -0.; + zher2_(uplo, &i__2, &z__1, &a[i__ + 1 + i__ * a_dim1], &c__1, + &tau[i__], &c__1, &a[i__ + 1 + (i__ + 1) * a_dim1], + lda, (ftnlen)1); - } else { - i__2 = i__ + 1 + (i__ + 1) * a_dim1; - i__3 = i__ + 1 + (i__ + 1) * a_dim1; - d__1 = a[i__3].r; - a[i__2].r = d__1, a[i__2].i = 0.; - } - i__2 = i__ + 1 + i__ * a_dim1; - i__3 = i__; - a[i__2].r = e[i__3], a[i__2].i = 0.; - i__2 = i__ + i__ * a_dim1; - d__[i__] = a[i__2].r; - i__2 = i__; - tau[i__2].r = taui.r, tau[i__2].i = taui.i; + } else { + i__2 = i__ + 1 + (i__ + 1) * a_dim1; + i__3 = i__ + 1 + (i__ + 1) * a_dim1; + d__1 = a[i__3].r; + a[i__2].r = d__1, a[i__2].i = 0.; + } + i__2 = i__ + 1 + i__ * a_dim1; + i__3 = i__; + a[i__2].r = e[i__3], a[i__2].i = 0.; + i__2 = i__ + i__ * a_dim1; + d__[i__] = a[i__2].r; + i__2 = i__; + tau[i__2].r = taui.r, tau[i__2].i = taui.i; /* L20: */ - } - i__1 = *n + *n * a_dim1; - d__[*n] = a[i__1].r; + } + i__1 = *n + *n * a_dim1; + d__[*n] = a[i__1].r; } return 0; @@ -435,5 +435,5 @@ f"> */ } /* zhetd2_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zhetrd.cpp b/lib/linalg/zhetrd.cpp index e1c8481bbb..ed3de347ef 100644 --- a/lib/linalg/zhetrd.cpp +++ b/lib/linalg/zhetrd.cpp @@ -1,13 +1,13 @@ /* fortran/zhetrd.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -216,9 +216,9 @@ f"> */ /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int zhetrd_(char *uplo, integer *n, doublecomplex *a, - integer *lda, doublereal *d__, doublereal *e, doublecomplex *tau, - doublecomplex *work, integer *lwork, integer *info, ftnlen uplo_len) +/* Subroutine */ int zhetrd_(char *uplo, integer *n, doublecomplex *a, + integer *lda, doublereal *d__, doublereal *e, doublecomplex *tau, + doublecomplex *work, integer *lwork, integer *info, ftnlen uplo_len) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; @@ -229,17 +229,17 @@ f"> */ extern logical lsame_(char *, char *, ftnlen, ftnlen); integer nbmin, iinfo; logical upper; - extern /* Subroutine */ int zhetd2_(char *, integer *, doublecomplex *, - integer *, doublereal *, doublereal *, doublecomplex *, integer *, - ftnlen), zher2k_(char *, char *, integer *, integer *, - doublecomplex *, doublecomplex *, integer *, doublecomplex *, - integer *, doublereal *, doublecomplex *, integer *, ftnlen, - ftnlen), xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - extern /* Subroutine */ int zlatrd_(char *, integer *, integer *, - doublecomplex *, integer *, doublereal *, doublecomplex *, - doublecomplex *, integer *, ftnlen); + extern /* Subroutine */ int zhetd2_(char *, integer *, doublecomplex *, + integer *, doublereal *, doublereal *, doublecomplex *, integer *, + ftnlen), zher2k_(char *, char *, integer *, integer *, + doublecomplex *, doublecomplex *, integer *, doublecomplex *, + integer *, doublereal *, doublecomplex *, integer *, ftnlen, + ftnlen), xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int zlatrd_(char *, integer *, integer *, + doublecomplex *, integer *, doublereal *, doublecomplex *, + doublecomplex *, integer *, ftnlen); integer ldwork, lwkopt; logical lquery; @@ -283,38 +283,38 @@ f"> */ upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); lquery = *lwork == -1; if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { - *info = -1; + *info = -1; } else if (*n < 0) { - *info = -2; + *info = -2; } else if (*lda < max(1,*n)) { - *info = -4; + *info = -4; } else if (*lwork < 1 && ! lquery) { - *info = -9; + *info = -9; } if (*info == 0) { /* Determine the block size. */ - nb = ilaenv_(&c__1, (char *)"ZHETRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, - (ftnlen)1); - lwkopt = *n * nb; - work[1].r = (doublereal) lwkopt, work[1].i = 0.; + nb = ilaenv_(&c__1, (char *)"ZHETRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, + (ftnlen)1); + lwkopt = *n * nb; + work[1].r = (doublereal) lwkopt, work[1].i = 0.; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"ZHETRD", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"ZHETRD", &i__1, (ftnlen)6); + return 0; } else if (lquery) { - return 0; + return 0; } /* Quick return if possible */ if (*n == 0) { - work[1].r = 1., work[1].i = 0.; - return 0; + work[1].r = 1., work[1].i = 0.; + return 0; } nx = *n; @@ -325,35 +325,35 @@ f"> */ /* (last block is always handled by unblocked code). */ /* Computing MAX */ - i__1 = nb, i__2 = ilaenv_(&c__3, (char *)"ZHETRD", uplo, n, &c_n1, &c_n1, & - c_n1, (ftnlen)6, (ftnlen)1); - nx = max(i__1,i__2); - if (nx < *n) { + i__1 = nb, i__2 = ilaenv_(&c__3, (char *)"ZHETRD", uplo, n, &c_n1, &c_n1, & + c_n1, (ftnlen)6, (ftnlen)1); + nx = max(i__1,i__2); + if (nx < *n) { /* Determine if workspace is large enough for blocked code. */ - ldwork = *n; - iws = ldwork * nb; - if (*lwork < iws) { + ldwork = *n; + iws = ldwork * nb; + if (*lwork < iws) { /* Not enough workspace to use optimal NB: determine the */ /* minimum value of NB, and reduce NB or force use of */ /* unblocked code by setting NX = N. */ /* Computing MAX */ - i__1 = *lwork / ldwork; - nb = max(i__1,1); - nbmin = ilaenv_(&c__2, (char *)"ZHETRD", uplo, n, &c_n1, &c_n1, &c_n1, - (ftnlen)6, (ftnlen)1); - if (nb < nbmin) { - nx = *n; - } - } - } else { - nx = *n; - } + i__1 = *lwork / ldwork; + nb = max(i__1,1); + nbmin = ilaenv_(&c__2, (char *)"ZHETRD", uplo, n, &c_n1, &c_n1, &c_n1, + (ftnlen)6, (ftnlen)1); + if (nb < nbmin) { + nx = *n; + } + } + } else { + nx = *n; + } } else { - nb = 1; + nb = 1; } if (upper) { @@ -361,94 +361,94 @@ f"> */ /* Reduce the upper triangle of A. */ /* Columns 1:kk are handled by the unblocked method. */ - kk = *n - (*n - nx + nb - 1) / nb * nb; - i__1 = kk + 1; - i__2 = -nb; - for (i__ = *n - nb + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += - i__2) { + kk = *n - (*n - nx + nb - 1) / nb * nb; + i__1 = kk + 1; + i__2 = -nb; + for (i__ = *n - nb + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += + i__2) { /* Reduce columns i:i+nb-1 to tridiagonal form and form the */ /* matrix W which is needed to update the unreduced part of */ /* the matrix */ - i__3 = i__ + nb - 1; - zlatrd_(uplo, &i__3, &nb, &a[a_offset], lda, &e[1], &tau[1], & - work[1], &ldwork, (ftnlen)1); + i__3 = i__ + nb - 1; + zlatrd_(uplo, &i__3, &nb, &a[a_offset], lda, &e[1], &tau[1], & + work[1], &ldwork, (ftnlen)1); /* Update the unreduced submatrix A(1:i-1,1:i-1), using an */ /* update of the form: A := A - V*W**H - W*V**H */ - i__3 = i__ - 1; - z__1.r = -1., z__1.i = -0.; - zher2k_(uplo, (char *)"No transpose", &i__3, &nb, &z__1, &a[i__ * a_dim1 - + 1], lda, &work[1], &ldwork, &c_b23, &a[a_offset], lda, ( - ftnlen)1, (ftnlen)12); + i__3 = i__ - 1; + z__1.r = -1., z__1.i = -0.; + zher2k_(uplo, (char *)"No transpose", &i__3, &nb, &z__1, &a[i__ * a_dim1 + + 1], lda, &work[1], &ldwork, &c_b23, &a[a_offset], lda, ( + ftnlen)1, (ftnlen)12); /* Copy superdiagonal elements back into A, and diagonal */ /* elements into D */ - i__3 = i__ + nb - 1; - for (j = i__; j <= i__3; ++j) { - i__4 = j - 1 + j * a_dim1; - i__5 = j - 1; - a[i__4].r = e[i__5], a[i__4].i = 0.; - i__4 = j + j * a_dim1; - d__[j] = a[i__4].r; + i__3 = i__ + nb - 1; + for (j = i__; j <= i__3; ++j) { + i__4 = j - 1 + j * a_dim1; + i__5 = j - 1; + a[i__4].r = e[i__5], a[i__4].i = 0.; + i__4 = j + j * a_dim1; + d__[j] = a[i__4].r; /* L10: */ - } + } /* L20: */ - } + } /* Use unblocked code to reduce the last or only block */ - zhetd2_(uplo, &kk, &a[a_offset], lda, &d__[1], &e[1], &tau[1], &iinfo, - (ftnlen)1); + zhetd2_(uplo, &kk, &a[a_offset], lda, &d__[1], &e[1], &tau[1], &iinfo, + (ftnlen)1); } else { /* Reduce the lower triangle of A */ - i__2 = *n - nx; - i__1 = nb; - for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) { + i__2 = *n - nx; + i__1 = nb; + for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) { /* Reduce columns i:i+nb-1 to tridiagonal form and form the */ /* matrix W which is needed to update the unreduced part of */ /* the matrix */ - i__3 = *n - i__ + 1; - zlatrd_(uplo, &i__3, &nb, &a[i__ + i__ * a_dim1], lda, &e[i__], & - tau[i__], &work[1], &ldwork, (ftnlen)1); + i__3 = *n - i__ + 1; + zlatrd_(uplo, &i__3, &nb, &a[i__ + i__ * a_dim1], lda, &e[i__], & + tau[i__], &work[1], &ldwork, (ftnlen)1); /* Update the unreduced submatrix A(i+nb:n,i+nb:n), using */ /* an update of the form: A := A - V*W**H - W*V**H */ - i__3 = *n - i__ - nb + 1; - z__1.r = -1., z__1.i = -0.; - zher2k_(uplo, (char *)"No transpose", &i__3, &nb, &z__1, &a[i__ + nb + - i__ * a_dim1], lda, &work[nb + 1], &ldwork, &c_b23, &a[ - i__ + nb + (i__ + nb) * a_dim1], lda, (ftnlen)1, (ftnlen) - 12); + i__3 = *n - i__ - nb + 1; + z__1.r = -1., z__1.i = -0.; + zher2k_(uplo, (char *)"No transpose", &i__3, &nb, &z__1, &a[i__ + nb + + i__ * a_dim1], lda, &work[nb + 1], &ldwork, &c_b23, &a[ + i__ + nb + (i__ + nb) * a_dim1], lda, (ftnlen)1, (ftnlen) + 12); /* Copy subdiagonal elements back into A, and diagonal */ /* elements into D */ - i__3 = i__ + nb - 1; - for (j = i__; j <= i__3; ++j) { - i__4 = j + 1 + j * a_dim1; - i__5 = j; - a[i__4].r = e[i__5], a[i__4].i = 0.; - i__4 = j + j * a_dim1; - d__[j] = a[i__4].r; + i__3 = i__ + nb - 1; + for (j = i__; j <= i__3; ++j) { + i__4 = j + 1 + j * a_dim1; + i__5 = j; + a[i__4].r = e[i__5], a[i__4].i = 0.; + i__4 = j + j * a_dim1; + d__[j] = a[i__4].r; /* L30: */ - } + } /* L40: */ - } + } /* Use unblocked code to reduce the last or only block */ - i__1 = *n - i__ + 1; - zhetd2_(uplo, &i__1, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[i__], - &tau[i__], &iinfo, (ftnlen)1); + i__1 = *n - i__ + 1; + zhetd2_(uplo, &i__1, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[i__], + &tau[i__], &iinfo, (ftnlen)1); } work[1].r = (doublereal) lwkopt, work[1].i = 0.; @@ -459,5 +459,5 @@ f"> */ } /* zhetrd_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zhpr.cpp b/lib/linalg/zhpr.cpp index f3c36d5826..b977b2ce1e 100644 --- a/lib/linalg/zhpr.cpp +++ b/lib/linalg/zhpr.cpp @@ -1,13 +1,13 @@ /* fortran/zhpr.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -143,8 +143,8 @@ extern "C" { /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int zhpr_(char *uplo, integer *n, doublereal *alpha, - doublecomplex *x, integer *incx, doublecomplex *ap, ftnlen uplo_len) +/* Subroutine */ int zhpr_(char *uplo, integer *n, doublereal *alpha, + doublecomplex *x, integer *incx, doublecomplex *ap, ftnlen uplo_len) { /* System generated locals */ integer i__1, i__2, i__3, i__4, i__5; @@ -192,30 +192,30 @@ extern "C" { /* Function Body */ info = 0; if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", ( - ftnlen)1, (ftnlen)1)) { - info = 1; + ftnlen)1, (ftnlen)1)) { + info = 1; } else if (*n < 0) { - info = 2; + info = 2; } else if (*incx == 0) { - info = 5; + info = 5; } if (info != 0) { - xerbla_((char *)"ZHPR ", &info, (ftnlen)6); - return 0; + xerbla_((char *)"ZHPR ", &info, (ftnlen)6); + return 0; } /* Quick return if possible. */ if (*n == 0 || *alpha == 0.) { - return 0; + return 0; } /* Set the start point in X if the increment is not unity. */ if (*incx <= 0) { - kx = 1 - (*n - 1) * *incx; + kx = 1 - (*n - 1) * *incx; } else if (*incx != 1) { - kx = 1; + kx = 1; } /* Start the operations. In this version the elements of the array AP */ @@ -226,172 +226,172 @@ extern "C" { /* Form A when upper triangle is stored in AP. */ - if (*incx == 1) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = j; - if (x[i__2].r != 0. || x[i__2].i != 0.) { - d_cnjg(&z__2, &x[j]); - z__1.r = *alpha * z__2.r, z__1.i = *alpha * z__2.i; - temp.r = z__1.r, temp.i = z__1.i; - k = kk; - i__2 = j - 1; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = k; - i__4 = k; - i__5 = i__; - z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, - z__2.i = x[i__5].r * temp.i + x[i__5].i * - temp.r; - z__1.r = ap[i__4].r + z__2.r, z__1.i = ap[i__4].i + - z__2.i; - ap[i__3].r = z__1.r, ap[i__3].i = z__1.i; - ++k; + if (*incx == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + if (x[i__2].r != 0. || x[i__2].i != 0.) { + d_cnjg(&z__2, &x[j]); + z__1.r = *alpha * z__2.r, z__1.i = *alpha * z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + k = kk; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = k; + i__4 = k; + i__5 = i__; + z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, + z__2.i = x[i__5].r * temp.i + x[i__5].i * + temp.r; + z__1.r = ap[i__4].r + z__2.r, z__1.i = ap[i__4].i + + z__2.i; + ap[i__3].r = z__1.r, ap[i__3].i = z__1.i; + ++k; /* L10: */ - } - i__2 = kk + j - 1; - i__3 = kk + j - 1; - i__4 = j; - z__1.r = x[i__4].r * temp.r - x[i__4].i * temp.i, z__1.i = - x[i__4].r * temp.i + x[i__4].i * temp.r; - d__1 = ap[i__3].r + z__1.r; - ap[i__2].r = d__1, ap[i__2].i = 0.; - } else { - i__2 = kk + j - 1; - i__3 = kk + j - 1; - d__1 = ap[i__3].r; - ap[i__2].r = d__1, ap[i__2].i = 0.; - } - kk += j; + } + i__2 = kk + j - 1; + i__3 = kk + j - 1; + i__4 = j; + z__1.r = x[i__4].r * temp.r - x[i__4].i * temp.i, z__1.i = + x[i__4].r * temp.i + x[i__4].i * temp.r; + d__1 = ap[i__3].r + z__1.r; + ap[i__2].r = d__1, ap[i__2].i = 0.; + } else { + i__2 = kk + j - 1; + i__3 = kk + j - 1; + d__1 = ap[i__3].r; + ap[i__2].r = d__1, ap[i__2].i = 0.; + } + kk += j; /* L20: */ - } - } else { - jx = kx; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = jx; - if (x[i__2].r != 0. || x[i__2].i != 0.) { - d_cnjg(&z__2, &x[jx]); - z__1.r = *alpha * z__2.r, z__1.i = *alpha * z__2.i; - temp.r = z__1.r, temp.i = z__1.i; - ix = kx; - i__2 = kk + j - 2; - for (k = kk; k <= i__2; ++k) { - i__3 = k; - i__4 = k; - i__5 = ix; - z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, - z__2.i = x[i__5].r * temp.i + x[i__5].i * - temp.r; - z__1.r = ap[i__4].r + z__2.r, z__1.i = ap[i__4].i + - z__2.i; - ap[i__3].r = z__1.r, ap[i__3].i = z__1.i; - ix += *incx; + } + } else { + jx = kx; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = jx; + if (x[i__2].r != 0. || x[i__2].i != 0.) { + d_cnjg(&z__2, &x[jx]); + z__1.r = *alpha * z__2.r, z__1.i = *alpha * z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + ix = kx; + i__2 = kk + j - 2; + for (k = kk; k <= i__2; ++k) { + i__3 = k; + i__4 = k; + i__5 = ix; + z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, + z__2.i = x[i__5].r * temp.i + x[i__5].i * + temp.r; + z__1.r = ap[i__4].r + z__2.r, z__1.i = ap[i__4].i + + z__2.i; + ap[i__3].r = z__1.r, ap[i__3].i = z__1.i; + ix += *incx; /* L30: */ - } - i__2 = kk + j - 1; - i__3 = kk + j - 1; - i__4 = jx; - z__1.r = x[i__4].r * temp.r - x[i__4].i * temp.i, z__1.i = - x[i__4].r * temp.i + x[i__4].i * temp.r; - d__1 = ap[i__3].r + z__1.r; - ap[i__2].r = d__1, ap[i__2].i = 0.; - } else { - i__2 = kk + j - 1; - i__3 = kk + j - 1; - d__1 = ap[i__3].r; - ap[i__2].r = d__1, ap[i__2].i = 0.; - } - jx += *incx; - kk += j; + } + i__2 = kk + j - 1; + i__3 = kk + j - 1; + i__4 = jx; + z__1.r = x[i__4].r * temp.r - x[i__4].i * temp.i, z__1.i = + x[i__4].r * temp.i + x[i__4].i * temp.r; + d__1 = ap[i__3].r + z__1.r; + ap[i__2].r = d__1, ap[i__2].i = 0.; + } else { + i__2 = kk + j - 1; + i__3 = kk + j - 1; + d__1 = ap[i__3].r; + ap[i__2].r = d__1, ap[i__2].i = 0.; + } + jx += *incx; + kk += j; /* L40: */ - } - } + } + } } else { /* Form A when lower triangle is stored in AP. */ - if (*incx == 1) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = j; - if (x[i__2].r != 0. || x[i__2].i != 0.) { - d_cnjg(&z__2, &x[j]); - z__1.r = *alpha * z__2.r, z__1.i = *alpha * z__2.i; - temp.r = z__1.r, temp.i = z__1.i; - i__2 = kk; - i__3 = kk; - i__4 = j; - z__1.r = temp.r * x[i__4].r - temp.i * x[i__4].i, z__1.i = - temp.r * x[i__4].i + temp.i * x[i__4].r; - d__1 = ap[i__3].r + z__1.r; - ap[i__2].r = d__1, ap[i__2].i = 0.; - k = kk + 1; - i__2 = *n; - for (i__ = j + 1; i__ <= i__2; ++i__) { - i__3 = k; - i__4 = k; - i__5 = i__; - z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, - z__2.i = x[i__5].r * temp.i + x[i__5].i * - temp.r; - z__1.r = ap[i__4].r + z__2.r, z__1.i = ap[i__4].i + - z__2.i; - ap[i__3].r = z__1.r, ap[i__3].i = z__1.i; - ++k; + if (*incx == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + if (x[i__2].r != 0. || x[i__2].i != 0.) { + d_cnjg(&z__2, &x[j]); + z__1.r = *alpha * z__2.r, z__1.i = *alpha * z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + i__2 = kk; + i__3 = kk; + i__4 = j; + z__1.r = temp.r * x[i__4].r - temp.i * x[i__4].i, z__1.i = + temp.r * x[i__4].i + temp.i * x[i__4].r; + d__1 = ap[i__3].r + z__1.r; + ap[i__2].r = d__1, ap[i__2].i = 0.; + k = kk + 1; + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + i__3 = k; + i__4 = k; + i__5 = i__; + z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, + z__2.i = x[i__5].r * temp.i + x[i__5].i * + temp.r; + z__1.r = ap[i__4].r + z__2.r, z__1.i = ap[i__4].i + + z__2.i; + ap[i__3].r = z__1.r, ap[i__3].i = z__1.i; + ++k; /* L50: */ - } - } else { - i__2 = kk; - i__3 = kk; - d__1 = ap[i__3].r; - ap[i__2].r = d__1, ap[i__2].i = 0.; - } - kk = kk + *n - j + 1; + } + } else { + i__2 = kk; + i__3 = kk; + d__1 = ap[i__3].r; + ap[i__2].r = d__1, ap[i__2].i = 0.; + } + kk = kk + *n - j + 1; /* L60: */ - } - } else { - jx = kx; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = jx; - if (x[i__2].r != 0. || x[i__2].i != 0.) { - d_cnjg(&z__2, &x[jx]); - z__1.r = *alpha * z__2.r, z__1.i = *alpha * z__2.i; - temp.r = z__1.r, temp.i = z__1.i; - i__2 = kk; - i__3 = kk; - i__4 = jx; - z__1.r = temp.r * x[i__4].r - temp.i * x[i__4].i, z__1.i = - temp.r * x[i__4].i + temp.i * x[i__4].r; - d__1 = ap[i__3].r + z__1.r; - ap[i__2].r = d__1, ap[i__2].i = 0.; - ix = jx; - i__2 = kk + *n - j; - for (k = kk + 1; k <= i__2; ++k) { - ix += *incx; - i__3 = k; - i__4 = k; - i__5 = ix; - z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, - z__2.i = x[i__5].r * temp.i + x[i__5].i * - temp.r; - z__1.r = ap[i__4].r + z__2.r, z__1.i = ap[i__4].i + - z__2.i; - ap[i__3].r = z__1.r, ap[i__3].i = z__1.i; + } + } else { + jx = kx; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = jx; + if (x[i__2].r != 0. || x[i__2].i != 0.) { + d_cnjg(&z__2, &x[jx]); + z__1.r = *alpha * z__2.r, z__1.i = *alpha * z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + i__2 = kk; + i__3 = kk; + i__4 = jx; + z__1.r = temp.r * x[i__4].r - temp.i * x[i__4].i, z__1.i = + temp.r * x[i__4].i + temp.i * x[i__4].r; + d__1 = ap[i__3].r + z__1.r; + ap[i__2].r = d__1, ap[i__2].i = 0.; + ix = jx; + i__2 = kk + *n - j; + for (k = kk + 1; k <= i__2; ++k) { + ix += *incx; + i__3 = k; + i__4 = k; + i__5 = ix; + z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, + z__2.i = x[i__5].r * temp.i + x[i__5].i * + temp.r; + z__1.r = ap[i__4].r + z__2.r, z__1.i = ap[i__4].i + + z__2.i; + ap[i__3].r = z__1.r, ap[i__3].i = z__1.i; /* L70: */ - } - } else { - i__2 = kk; - i__3 = kk; - d__1 = ap[i__3].r; - ap[i__2].r = d__1, ap[i__2].i = 0.; - } - jx += *incx; - kk = kk + *n - j + 1; + } + } else { + i__2 = kk; + i__3 = kk; + d__1 = ap[i__3].r; + ap[i__2].r = d__1, ap[i__2].i = 0.; + } + jx += *incx; + kk = kk + *n - j + 1; /* L80: */ - } - } + } + } } return 0; @@ -401,5 +401,5 @@ extern "C" { } /* zhpr_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zlacgv.cpp b/lib/linalg/zlacgv.cpp index 46c1c5c0ce..9e9a4050b2 100644 --- a/lib/linalg/zlacgv.cpp +++ b/lib/linalg/zlacgv.cpp @@ -1,13 +1,13 @@ /* fortran/zlacgv.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -125,26 +125,26 @@ f"> */ /* Function Body */ if (*incx == 1) { - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = i__; - d_cnjg(&z__1, &x[i__]); - x[i__2].r = z__1.r, x[i__2].i = z__1.i; + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__; + d_cnjg(&z__1, &x[i__]); + x[i__2].r = z__1.r, x[i__2].i = z__1.i; /* L10: */ - } + } } else { - ioff = 1; - if (*incx < 0) { - ioff = 1 - (*n - 1) * *incx; - } - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = ioff; - d_cnjg(&z__1, &x[ioff]); - x[i__2].r = z__1.r, x[i__2].i = z__1.i; - ioff += *incx; + ioff = 1; + if (*incx < 0) { + ioff = 1 - (*n - 1) * *incx; + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = ioff; + d_cnjg(&z__1, &x[ioff]); + x[i__2].r = z__1.r, x[i__2].i = z__1.i; + ioff += *incx; /* L20: */ - } + } } return 0; @@ -153,5 +153,5 @@ f"> */ } /* zlacgv_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zlacpy.cpp b/lib/linalg/zlacpy.cpp index 1cb52d4c0a..4a68cd9e07 100644 --- a/lib/linalg/zlacpy.cpp +++ b/lib/linalg/zlacpy.cpp @@ -1,13 +1,13 @@ /* fortran/zlacpy.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -119,9 +119,9 @@ f"> */ /* > \ingroup complex16OTHERauxiliary */ /* ===================================================================== */ -/* Subroutine */ int zlacpy_(char *uplo, integer *m, integer *n, - doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, - ftnlen uplo_len) +/* Subroutine */ int zlacpy_(char *uplo, integer *m, integer *n, + doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, + ftnlen uplo_len) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4; @@ -160,43 +160,43 @@ f"> */ /* Function Body */ if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = min(j,*m); - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * b_dim1; - i__4 = i__ + j * a_dim1; - b[i__3].r = a[i__4].r, b[i__3].i = a[i__4].i; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = min(j,*m); + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * b_dim1; + i__4 = i__ + j * a_dim1; + b[i__3].r = a[i__4].r, b[i__3].i = a[i__4].i; /* L10: */ - } + } /* L20: */ - } + } } else if (lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = j; i__ <= i__2; ++i__) { - i__3 = i__ + j * b_dim1; - i__4 = i__ + j * a_dim1; - b[i__3].r = a[i__4].r, b[i__3].i = a[i__4].i; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = j; i__ <= i__2; ++i__) { + i__3 = i__ + j * b_dim1; + i__4 = i__ + j * a_dim1; + b[i__3].r = a[i__4].r, b[i__3].i = a[i__4].i; /* L30: */ - } + } /* L40: */ - } + } } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * b_dim1; - i__4 = i__ + j * a_dim1; - b[i__3].r = a[i__4].r, b[i__3].i = a[i__4].i; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * b_dim1; + i__4 = i__ + j * a_dim1; + b[i__3].r = a[i__4].r, b[i__3].i = a[i__4].i; /* L50: */ - } + } /* L60: */ - } + } } return 0; @@ -206,5 +206,5 @@ f"> */ } /* zlacpy_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zlacrm.cpp b/lib/linalg/zlacrm.cpp index e993f79aa5..46508ae4a9 100644 --- a/lib/linalg/zlacrm.cpp +++ b/lib/linalg/zlacrm.cpp @@ -1,13 +1,13 @@ /* fortran/zlacrm.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -135,13 +135,13 @@ f"> */ /* > \ingroup complex16OTHERauxiliary */ /* ===================================================================== */ -/* Subroutine */ int zlacrm_(integer *m, integer *n, doublecomplex *a, - integer *lda, doublereal *b, integer *ldb, doublecomplex *c__, - integer *ldc, doublereal *rwork) +/* Subroutine */ int zlacrm_(integer *m, integer *n, doublecomplex *a, + integer *lda, doublereal *b, integer *ldb, doublecomplex *c__, + integer *ldc, doublereal *rwork) { /* System generated locals */ - integer b_dim1, b_offset, a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, - i__3, i__4, i__5; + integer b_dim1, b_offset, a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, + i__3, i__4, i__5; doublereal d__1; doublecomplex z__1; @@ -150,9 +150,9 @@ f"> */ /* Local variables */ integer i__, j, l; - extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); /* -- LAPACK auxiliary routine -- */ @@ -192,58 +192,58 @@ f"> */ /* Function Body */ if (*m == 0 || *n == 0) { - return 0; + return 0; } i__1 = *n; for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * a_dim1; - rwork[(j - 1) * *m + i__] = a[i__3].r; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + rwork[(j - 1) * *m + i__] = a[i__3].r; /* L10: */ - } + } /* L20: */ } l = *m * *n + 1; dgemm_((char *)"N", (char *)"N", m, n, n, &c_b6, &rwork[1], m, &b[b_offset], ldb, &c_b7, & - rwork[l], m, (ftnlen)1, (ftnlen)1); + rwork[l], m, (ftnlen)1, (ftnlen)1); i__1 = *n; for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * c_dim1; - i__4 = l + (j - 1) * *m + i__ - 1; - c__[i__3].r = rwork[i__4], c__[i__3].i = 0.; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + i__4 = l + (j - 1) * *m + i__ - 1; + c__[i__3].r = rwork[i__4], c__[i__3].i = 0.; /* L30: */ - } + } /* L40: */ } i__1 = *n; for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - rwork[(j - 1) * *m + i__] = d_imag(&a[i__ + j * a_dim1]); + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + rwork[(j - 1) * *m + i__] = d_imag(&a[i__ + j * a_dim1]); /* L50: */ - } + } /* L60: */ } dgemm_((char *)"N", (char *)"N", m, n, n, &c_b6, &rwork[1], m, &b[b_offset], ldb, &c_b7, & - rwork[l], m, (ftnlen)1, (ftnlen)1); + rwork[l], m, (ftnlen)1, (ftnlen)1); i__1 = *n; for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * c_dim1; - i__4 = i__ + j * c_dim1; - d__1 = c__[i__4].r; - i__5 = l + (j - 1) * *m + i__ - 1; - z__1.r = d__1, z__1.i = rwork[i__5]; - c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + i__4 = i__ + j * c_dim1; + d__1 = c__[i__4].r; + i__5 = l + (j - 1) * *m + i__ - 1; + z__1.r = d__1, z__1.i = rwork[i__5]; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; /* L70: */ - } + } /* L80: */ } @@ -254,5 +254,5 @@ f"> */ } /* zlacrm_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zladiv.cpp b/lib/linalg/zladiv.cpp index 6e80b3371a..6b065d5ce0 100644 --- a/lib/linalg/zladiv.cpp +++ b/lib/linalg/zladiv.cpp @@ -1,13 +1,13 @@ /* fortran/zladiv.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -80,8 +80,8 @@ f"> */ /* > \ingroup complex16OTHERauxiliary */ /* ===================================================================== */ -/* Double Complex */ VOID zladiv_(doublecomplex * ret_val, doublecomplex *x, - doublecomplex *y) +/* Double Complex */ VOID zladiv_(doublecomplex * ret_val, doublecomplex *x, + doublecomplex *y) { /* System generated locals */ doublereal d__1, d__2, d__3, d__4; @@ -92,8 +92,8 @@ f"> */ /* Local variables */ doublereal zi, zr; - extern /* Subroutine */ int dladiv_(doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *, doublereal *); + extern /* Subroutine */ int dladiv_(doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *, doublereal *); /* -- LAPACK auxiliary routine -- */ @@ -128,5 +128,5 @@ f"> */ } /* zladiv_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zlaed0.cpp b/lib/linalg/zlaed0.cpp index 680dd85054..98bc39611d 100644 --- a/lib/linalg/zlaed0.cpp +++ b/lib/linalg/zlaed0.cpp @@ -1,13 +1,13 @@ /* fortran/zlaed0.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -22,7 +22,7 @@ static integer c__0 = 0; static integer c__2 = 2; static integer c__1 = 1; -/* > \brief \b ZLAED0 used by ZSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced +/* > \brief \b ZLAED0 used by ZSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method. */ /* =========== DOCUMENTATION =========== */ @@ -168,9 +168,9 @@ f"> */ /* > \ingroup complex16OTHERcomputational */ /* ===================================================================== */ -/* Subroutine */ int zlaed0_(integer *qsiz, integer *n, doublereal *d__, - doublereal *e, doublecomplex *q, integer *ldq, doublecomplex *qstore, - integer *ldqs, doublereal *rwork, integer *iwork, integer *info) +/* Subroutine */ int zlaed0_(integer *qsiz, integer *n, doublereal *d__, + doublereal *e, doublecomplex *q, integer *ldq, doublecomplex *qstore, + integer *ldqs, doublereal *rwork, integer *iwork, integer *info) { /* System generated locals */ integer q_dim1, q_offset, qstore_dim1, qstore_offset, i__1, i__2; @@ -184,27 +184,27 @@ f"> */ integer i__, j, k, ll, iq, lgn, msd2, smm1, spm1, spm2; doublereal temp; integer curr, iperm; - extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, - doublereal *, integer *); + extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, + doublereal *, integer *); integer indxq, iwrem, iqptr, tlvls; - extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, - doublecomplex *, integer *), zlaed7_(integer *, integer *, - integer *, integer *, integer *, integer *, doublereal *, - doublecomplex *, integer *, doublereal *, integer *, doublereal *, - integer *, integer *, integer *, integer *, integer *, - doublereal *, doublecomplex *, doublereal *, integer *, integer *) - ; + extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, + doublecomplex *, integer *), zlaed7_(integer *, integer *, + integer *, integer *, integer *, integer *, doublereal *, + doublecomplex *, integer *, doublereal *, integer *, doublereal *, + integer *, integer *, integer *, integer *, integer *, + doublereal *, doublecomplex *, doublereal *, integer *, integer *) + ; integer igivcl; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); extern /* Subroutine */ int zlacrm_(integer *, integer *, doublecomplex *, - integer *, doublereal *, integer *, doublecomplex *, integer *, - doublereal *); + integer *, doublereal *, integer *, doublecomplex *, integer *, + doublereal *); integer igivnm, submat, curprb, subpbs, igivpt; - extern /* Subroutine */ int dsteqr_(char *, integer *, doublereal *, - doublereal *, doublereal *, integer *, doublereal *, integer *, - ftnlen); + extern /* Subroutine */ int dsteqr_(char *, integer *, doublereal *, + doublereal *, doublereal *, integer *, doublereal *, integer *, + ftnlen); integer curlvl, matsiz, iprmpt, smlsiz; @@ -255,28 +255,28 @@ f"> */ /* ELSE IF( ( ICOMPQ .EQ. 1 ) .AND. ( QSIZ .LT. MAX( 0, N ) ) ) */ /* $ THEN */ if (*qsiz < max(0,*n)) { - *info = -1; + *info = -1; } else if (*n < 0) { - *info = -2; + *info = -2; } else if (*ldq < max(1,*n)) { - *info = -6; + *info = -6; } else if (*ldqs < max(1,*n)) { - *info = -8; + *info = -8; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"ZLAED0", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"ZLAED0", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*n == 0) { - return 0; + return 0; } smlsiz = ilaenv_(&c__9, (char *)"ZLAED0", (char *)" ", &c__0, &c__0, &c__0, &c__0, ( - ftnlen)6, (ftnlen)1); + ftnlen)6, (ftnlen)1); /* Determine the size and placement of the submatrices, and save in */ /* the leading elements of IWORK. */ @@ -286,18 +286,18 @@ f"> */ tlvls = 0; L10: if (iwork[subpbs] > smlsiz) { - for (j = subpbs; j >= 1; --j) { - iwork[j * 2] = (iwork[j] + 1) / 2; - iwork[(j << 1) - 1] = iwork[j] / 2; + for (j = subpbs; j >= 1; --j) { + iwork[j * 2] = (iwork[j] + 1) / 2; + iwork[(j << 1) - 1] = iwork[j] / 2; /* L20: */ - } - ++tlvls; - subpbs <<= 1; - goto L10; + } + ++tlvls; + subpbs <<= 1; + goto L10; } i__1 = subpbs; for (j = 2; j <= i__1; ++j) { - iwork[j] += iwork[j - 1]; + iwork[j] += iwork[j - 1]; /* L30: */ } @@ -307,10 +307,10 @@ L10: spm1 = subpbs - 1; i__1 = spm1; for (i__ = 1; i__ <= i__1; ++i__) { - submat = iwork[i__] + 1; - smm1 = submat - 1; - d__[smm1] -= (d__1 = e[smm1], abs(d__1)); - d__[submat] -= (d__1 = e[smm1], abs(d__1)); + submat = iwork[i__] + 1; + smm1 = submat - 1; + d__[smm1] -= (d__1 = e[smm1], abs(d__1)); + d__[submat] -= (d__1 = e[smm1], abs(d__1)); /* L40: */ } @@ -322,10 +322,10 @@ L10: temp = log((doublereal) (*n)) / log(2.); lgn = (integer) temp; if (pow_ii(&c__2, &lgn) < *n) { - ++lgn; + ++lgn; } if (pow_ii(&c__2, &lgn) < *n) { - ++lgn; + ++lgn; } iprmpt = indxq + *n + 1; iperm = iprmpt + *n * lgn; @@ -341,8 +341,8 @@ L10: /* Initialize pointers */ i__1 = subpbs; for (i__ = 0; i__ <= i__1; ++i__) { - iwork[iprmpt + i__] = 1; - iwork[igivpt + i__] = 1; + iwork[iprmpt + i__] = 1; + iwork[igivpt + i__] = 1; /* L50: */ } iwork[iqptr] = 1; @@ -353,34 +353,34 @@ L10: curr = 0; i__1 = spm1; for (i__ = 0; i__ <= i__1; ++i__) { - if (i__ == 0) { - submat = 1; - matsiz = iwork[1]; - } else { - submat = iwork[i__] + 1; - matsiz = iwork[i__ + 1] - iwork[i__]; - } - ll = iq - 1 + iwork[iqptr + curr]; - dsteqr_((char *)"I", &matsiz, &d__[submat], &e[submat], &rwork[ll], &matsiz, & - rwork[1], info, (ftnlen)1); - zlacrm_(qsiz, &matsiz, &q[submat * q_dim1 + 1], ldq, &rwork[ll], & - matsiz, &qstore[submat * qstore_dim1 + 1], ldqs, &rwork[iwrem] - ); + if (i__ == 0) { + submat = 1; + matsiz = iwork[1]; + } else { + submat = iwork[i__] + 1; + matsiz = iwork[i__ + 1] - iwork[i__]; + } + ll = iq - 1 + iwork[iqptr + curr]; + dsteqr_((char *)"I", &matsiz, &d__[submat], &e[submat], &rwork[ll], &matsiz, & + rwork[1], info, (ftnlen)1); + zlacrm_(qsiz, &matsiz, &q[submat * q_dim1 + 1], ldq, &rwork[ll], & + matsiz, &qstore[submat * qstore_dim1 + 1], ldqs, &rwork[iwrem] + ); /* Computing 2nd power */ - i__2 = matsiz; - iwork[iqptr + curr + 1] = iwork[iqptr + curr] + i__2 * i__2; - ++curr; - if (*info > 0) { - *info = submat * (*n + 1) + submat + matsiz - 1; - return 0; - } - k = 1; - i__2 = iwork[i__ + 1]; - for (j = submat; j <= i__2; ++j) { - iwork[indxq + j] = k; - ++k; + i__2 = matsiz; + iwork[iqptr + curr + 1] = iwork[iqptr + curr] + i__2 * i__2; + ++curr; + if (*info > 0) { + *info = submat * (*n + 1) + submat + matsiz - 1; + return 0; + } + k = 1; + i__2 = iwork[i__ + 1]; + for (j = submat; j <= i__2; ++j) { + iwork[indxq + j] = k; + ++k; /* L60: */ - } + } /* L70: */ } @@ -392,20 +392,20 @@ L10: curlvl = 1; L80: if (subpbs > 1) { - spm2 = subpbs - 2; - i__1 = spm2; - for (i__ = 0; i__ <= i__1; i__ += 2) { - if (i__ == 0) { - submat = 1; - matsiz = iwork[2]; - msd2 = iwork[1]; - curprb = 0; - } else { - submat = iwork[i__] + 1; - matsiz = iwork[i__ + 2] - iwork[i__]; - msd2 = matsiz / 2; - ++curprb; - } + spm2 = subpbs - 2; + i__1 = spm2; + for (i__ = 0; i__ <= i__1; i__ += 2) { + if (i__ == 0) { + submat = 1; + matsiz = iwork[2]; + msd2 = iwork[1]; + curprb = 0; + } else { + submat = iwork[i__] + 1; + matsiz = iwork[i__ + 2] - iwork[i__]; + msd2 = matsiz / 2; + ++curprb; + } /* Merge lower order eigensystems (of size MSD2 and MATSIZ - MSD2) */ /* into an eigensystem of size MATSIZ. ZLAED7 handles the case */ @@ -414,22 +414,22 @@ L80: /* I am free to use Q as a valuable working space until Loop 150. */ - zlaed7_(&matsiz, &msd2, qsiz, &tlvls, &curlvl, &curprb, &d__[ - submat], &qstore[submat * qstore_dim1 + 1], ldqs, &e[ - submat + msd2 - 1], &iwork[indxq + submat], &rwork[iq], & - iwork[iqptr], &iwork[iprmpt], &iwork[iperm], &iwork[ - igivpt], &iwork[igivcl], &rwork[igivnm], &q[submat * - q_dim1 + 1], &rwork[iwrem], &iwork[subpbs + 1], info); - if (*info > 0) { - *info = submat * (*n + 1) + submat + matsiz - 1; - return 0; - } - iwork[i__ / 2 + 1] = iwork[i__ + 2]; + zlaed7_(&matsiz, &msd2, qsiz, &tlvls, &curlvl, &curprb, &d__[ + submat], &qstore[submat * qstore_dim1 + 1], ldqs, &e[ + submat + msd2 - 1], &iwork[indxq + submat], &rwork[iq], & + iwork[iqptr], &iwork[iprmpt], &iwork[iperm], &iwork[ + igivpt], &iwork[igivcl], &rwork[igivnm], &q[submat * + q_dim1 + 1], &rwork[iwrem], &iwork[subpbs + 1], info); + if (*info > 0) { + *info = submat * (*n + 1) + submat + matsiz - 1; + return 0; + } + iwork[i__ / 2 + 1] = iwork[i__ + 2]; /* L90: */ - } - subpbs /= 2; - ++curlvl; - goto L80; + } + subpbs /= 2; + ++curlvl; + goto L80; } /* end while */ @@ -439,10 +439,10 @@ L80: i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { - j = iwork[indxq + i__]; - rwork[i__] = d__[j]; - zcopy_(qsiz, &qstore[j * qstore_dim1 + 1], &c__1, &q[i__ * q_dim1 + 1] - , &c__1); + j = iwork[indxq + i__]; + rwork[i__] = d__[j]; + zcopy_(qsiz, &qstore[j * qstore_dim1 + 1], &c__1, &q[i__ * q_dim1 + 1] + , &c__1); /* L100: */ } dcopy_(n, &rwork[1], &c__1, &d__[1], &c__1); @@ -454,5 +454,5 @@ L80: } /* zlaed0_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zlaed7.cpp b/lib/linalg/zlaed7.cpp index 9c06a0c334..b20d805e62 100644 --- a/lib/linalg/zlaed7.cpp +++ b/lib/linalg/zlaed7.cpp @@ -1,13 +1,13 @@ /* fortran/zlaed7.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -269,12 +269,12 @@ f"> */ /* > \ingroup complex16OTHERcomputational */ /* ===================================================================== */ -/* Subroutine */ int zlaed7_(integer *n, integer *cutpnt, integer *qsiz, - integer *tlvls, integer *curlvl, integer *curpbm, doublereal *d__, - doublecomplex *q, integer *ldq, doublereal *rho, integer *indxq, - doublereal *qstore, integer *qptr, integer *prmptr, integer *perm, - integer *givptr, integer *givcol, doublereal *givnum, doublecomplex * - work, doublereal *rwork, integer *iwork, integer *info) +/* Subroutine */ int zlaed7_(integer *n, integer *cutpnt, integer *qsiz, + integer *tlvls, integer *curlvl, integer *curpbm, doublereal *d__, + doublecomplex *q, integer *ldq, doublereal *rho, integer *indxq, + doublereal *qstore, integer *qptr, integer *prmptr, integer *perm, + integer *givptr, integer *givcol, doublereal *givnum, doublecomplex * + work, doublereal *rwork, integer *iwork, integer *info) { /* System generated locals */ integer q_dim1, q_offset, i__1, i__2; @@ -284,23 +284,23 @@ f"> */ /* Local variables */ integer i__, k, n1, n2, iq, iw, iz, ptr, indx, curr, indxc, indxp; - extern /* Subroutine */ int dlaed9_(integer *, integer *, integer *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - doublereal *, doublereal *, doublereal *, integer *, integer *), - zlaed8_(integer *, integer *, integer *, doublecomplex *, integer - *, doublereal *, doublereal *, integer *, doublereal *, - doublereal *, doublecomplex *, integer *, doublereal *, integer *, - integer *, integer *, integer *, integer *, integer *, - doublereal *, integer *), dlaeda_(integer *, integer *, integer *, - integer *, integer *, integer *, integer *, integer *, - doublereal *, doublereal *, integer *, doublereal *, doublereal *, - integer *); + extern /* Subroutine */ int dlaed9_(integer *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, doublereal *, + doublereal *, doublereal *, doublereal *, integer *, integer *), + zlaed8_(integer *, integer *, integer *, doublecomplex *, integer + *, doublereal *, doublereal *, integer *, doublereal *, + doublereal *, doublecomplex *, integer *, doublereal *, integer *, + integer *, integer *, integer *, integer *, integer *, + doublereal *, integer *), dlaeda_(integer *, integer *, integer *, + integer *, integer *, integer *, integer *, integer *, + doublereal *, doublereal *, integer *, doublereal *, doublereal *, + integer *); integer idlmda; - extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *, - integer *, integer *, integer *), xerbla_(char *, integer *, - ftnlen), zlacrm_(integer *, integer *, doublecomplex *, integer *, - doublereal *, integer *, doublecomplex *, integer *, doublereal * - ); + extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *, + integer *, integer *, integer *), xerbla_(char *, integer *, + ftnlen), zlacrm_(integer *, integer *, doublecomplex *, integer *, + doublereal *, integer *, doublecomplex *, integer *, doublereal * + ); integer coltyp; @@ -349,24 +349,24 @@ f"> */ /* INFO = -1 */ /* ELSE IF( N.LT.0 ) THEN */ if (*n < 0) { - *info = -1; + *info = -1; } else if (min(1,*n) > *cutpnt || *n < *cutpnt) { - *info = -2; + *info = -2; } else if (*qsiz < *n) { - *info = -3; + *info = -3; } else if (*ldq < max(1,*n)) { - *info = -9; + *info = -9; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"ZLAED7", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"ZLAED7", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*n == 0) { - return 0; + return 0; } /* The following values are for bookkeeping purposes only. They are */ @@ -389,60 +389,60 @@ f"> */ ptr = pow_ii(&c__2, tlvls) + 1; i__1 = *curlvl - 1; for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = *tlvls - i__; - ptr += pow_ii(&c__2, &i__2); + i__2 = *tlvls - i__; + ptr += pow_ii(&c__2, &i__2); /* L10: */ } curr = ptr + *curpbm; dlaeda_(n, tlvls, curlvl, curpbm, &prmptr[1], &perm[1], &givptr[1], & - givcol[3], &givnum[3], &qstore[1], &qptr[1], &rwork[iz], &rwork[ - iz + *n], info); + givcol[3], &givnum[3], &qstore[1], &qptr[1], &rwork[iz], &rwork[ + iz + *n], info); /* When solving the final problem, we no longer need the stored data, */ /* so we will overwrite the data from this level onto the previously */ /* used storage space. */ if (*curlvl == *tlvls) { - qptr[curr] = 1; - prmptr[curr] = 1; - givptr[curr] = 1; + qptr[curr] = 1; + prmptr[curr] = 1; + givptr[curr] = 1; } /* Sort and Deflate eigenvalues. */ - zlaed8_(&k, n, qsiz, &q[q_offset], ldq, &d__[1], rho, cutpnt, &rwork[iz], - &rwork[idlmda], &work[1], qsiz, &rwork[iw], &iwork[indxp], &iwork[ - indx], &indxq[1], &perm[prmptr[curr]], &givptr[curr + 1], &givcol[ - (givptr[curr] << 1) + 1], &givnum[(givptr[curr] << 1) + 1], info); + zlaed8_(&k, n, qsiz, &q[q_offset], ldq, &d__[1], rho, cutpnt, &rwork[iz], + &rwork[idlmda], &work[1], qsiz, &rwork[iw], &iwork[indxp], &iwork[ + indx], &indxq[1], &perm[prmptr[curr]], &givptr[curr + 1], &givcol[ + (givptr[curr] << 1) + 1], &givnum[(givptr[curr] << 1) + 1], info); prmptr[curr + 1] = prmptr[curr] + *n; givptr[curr + 1] += givptr[curr]; /* Solve Secular Equation. */ if (k != 0) { - dlaed9_(&k, &c__1, &k, n, &d__[1], &rwork[iq], &k, rho, &rwork[idlmda] - , &rwork[iw], &qstore[qptr[curr]], &k, info); - zlacrm_(qsiz, &k, &work[1], qsiz, &qstore[qptr[curr]], &k, &q[ - q_offset], ldq, &rwork[iq]); + dlaed9_(&k, &c__1, &k, n, &d__[1], &rwork[iq], &k, rho, &rwork[idlmda] + , &rwork[iw], &qstore[qptr[curr]], &k, info); + zlacrm_(qsiz, &k, &work[1], qsiz, &qstore[qptr[curr]], &k, &q[ + q_offset], ldq, &rwork[iq]); /* Computing 2nd power */ - i__1 = k; - qptr[curr + 1] = qptr[curr] + i__1 * i__1; - if (*info != 0) { - return 0; - } + i__1 = k; + qptr[curr + 1] = qptr[curr] + i__1 * i__1; + if (*info != 0) { + return 0; + } /* Prepare the INDXQ sorting premutation. */ - n1 = k; - n2 = *n - k; - dlamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &indxq[1]); + n1 = k; + n2 = *n - k; + dlamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &indxq[1]); } else { - qptr[curr + 1] = qptr[curr]; - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - indxq[i__] = i__; + qptr[curr + 1] = qptr[curr]; + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + indxq[i__] = i__; /* L20: */ - } + } } return 0; @@ -452,5 +452,5 @@ f"> */ } /* zlaed7_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zlaed8.cpp b/lib/linalg/zlaed8.cpp index 00f4db857b..77c07f385e 100644 --- a/lib/linalg/zlaed8.cpp +++ b/lib/linalg/zlaed8.cpp @@ -1,13 +1,13 @@ /* fortran/zlaed8.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -248,12 +248,12 @@ f"> */ /* > \ingroup complex16OTHERcomputational */ /* ===================================================================== */ -/* Subroutine */ int zlaed8_(integer *k, integer *n, integer *qsiz, - doublecomplex *q, integer *ldq, doublereal *d__, doublereal *rho, - integer *cutpnt, doublereal *z__, doublereal *dlamda, doublecomplex * - q2, integer *ldq2, doublereal *w, integer *indxp, integer *indx, - integer *indxq, integer *perm, integer *givptr, integer *givcol, - doublereal *givnum, integer *info) +/* Subroutine */ int zlaed8_(integer *k, integer *n, integer *qsiz, + doublecomplex *q, integer *ldq, doublereal *d__, doublereal *rho, + integer *cutpnt, doublereal *z__, doublereal *dlamda, doublecomplex * + q2, integer *ldq2, doublereal *w, integer *indxp, integer *indx, + integer *indxq, integer *perm, integer *givptr, integer *givcol, + doublereal *givnum, integer *info) { /* System generated locals */ integer q_dim1, q_offset, q2_dim1, q2_offset, i__1; @@ -269,19 +269,19 @@ f"> */ integer k2, n1, n2, jp, n1p1; doublereal eps, tau, tol; integer jlam, imax, jmax; - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *), dcopy_(integer *, doublereal *, integer *, doublereal - *, integer *), zdrot_(integer *, doublecomplex *, integer *, - doublecomplex *, integer *, doublereal *, doublereal *), zcopy_( - integer *, doublecomplex *, integer *, doublecomplex *, integer *) - ; - extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, - ftnlen); + extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, + integer *), dcopy_(integer *, doublereal *, integer *, doublereal + *, integer *), zdrot_(integer *, doublecomplex *, integer *, + doublecomplex *, integer *, doublereal *, doublereal *), zcopy_( + integer *, doublecomplex *, integer *, doublecomplex *, integer *) + ; + extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, + ftnlen); extern integer idamax_(integer *, doublereal *, integer *); - extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *, - integer *, integer *, integer *), xerbla_(char *, integer *, - ftnlen), zlacpy_(char *, integer *, integer *, doublecomplex *, - integer *, doublecomplex *, integer *, ftnlen); + extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *, + integer *, integer *, integer *), xerbla_(char *, integer *, + ftnlen), zlacpy_(char *, integer *, integer *, doublecomplex *, + integer *, doublecomplex *, integer *, ftnlen); /* -- LAPACK computational routine -- */ @@ -331,20 +331,20 @@ f"> */ *info = 0; if (*n < 0) { - *info = -2; + *info = -2; } else if (*qsiz < *n) { - *info = -3; + *info = -3; } else if (*ldq < max(1,*n)) { - *info = -5; + *info = -5; } else if (*cutpnt < min(1,*n) || *cutpnt > *n) { - *info = -8; + *info = -8; } else if (*ldq2 < max(1,*n)) { - *info = -12; + *info = -12; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"ZLAED8", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"ZLAED8", &i__1, (ftnlen)6); + return 0; } /* Need to initialize GIVPTR to O here in case of quick exit */ @@ -357,7 +357,7 @@ f"> */ /* Quick return if possible */ if (*n == 0) { - return 0; + return 0; } n1 = *cutpnt; @@ -365,7 +365,7 @@ f"> */ n1p1 = n1 + 1; if (*rho < 0.) { - dscal_(&n2, &c_b3, &z__[n1p1], &c__1); + dscal_(&n2, &c_b3, &z__[n1p1], &c__1); } /* Normalize z so that norm(z) = 1 */ @@ -373,7 +373,7 @@ f"> */ t = 1. / sqrt(2.); i__1 = *n; for (j = 1; j <= i__1; ++j) { - indx[j] = j; + indx[j] = j; /* L10: */ } dscal_(n, &t, &z__[1], &c__1); @@ -383,13 +383,13 @@ f"> */ i__1 = *n; for (i__ = *cutpnt + 1; i__ <= i__1; ++i__) { - indxq[i__] += *cutpnt; + indxq[i__] += *cutpnt; /* L20: */ } i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { - dlamda[i__] = d__[indxq[i__]]; - w[i__] = z__[indxq[i__]]; + dlamda[i__] = d__[indxq[i__]]; + w[i__] = z__[indxq[i__]]; /* L30: */ } i__ = 1; @@ -397,8 +397,8 @@ f"> */ dlamrg_(&n1, &n2, &dlamda[1], &c__1, &c__1, &indx[1]); i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { - d__[i__] = dlamda[indx[i__]]; - z__[i__] = w[indx[i__]]; + d__[i__] = dlamda[indx[i__]]; + z__[i__] = w[indx[i__]]; /* L40: */ } @@ -414,17 +414,17 @@ f"> */ /* elements in D. */ if (*rho * (d__1 = z__[imax], abs(d__1)) <= tol) { - *k = 0; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - perm[j] = indxq[indx[j]]; - zcopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 + 1] - , &c__1); + *k = 0; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + perm[j] = indxq[indx[j]]; + zcopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 + 1] + , &c__1); /* L50: */ - } - zlacpy_((char *)"A", qsiz, n, &q2[q2_dim1 + 1], ldq2, &q[q_dim1 + 1], ldq, ( - ftnlen)1); - return 0; + } + zlacpy_((char *)"A", qsiz, n, &q2[q2_dim1 + 1], ldq2, &q[q_dim1 + 1], ldq, ( + ftnlen)1); + return 0; } /* If there are multiple eigenvalues then the problem deflates. Here */ @@ -437,88 +437,88 @@ f"> */ k2 = *n + 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { - if (*rho * (d__1 = z__[j], abs(d__1)) <= tol) { + if (*rho * (d__1 = z__[j], abs(d__1)) <= tol) { /* Deflate due to small z component. */ - --k2; - indxp[k2] = j; - if (j == *n) { - goto L100; - } - } else { - jlam = j; - goto L70; - } + --k2; + indxp[k2] = j; + if (j == *n) { + goto L100; + } + } else { + jlam = j; + goto L70; + } /* L60: */ } L70: ++j; if (j > *n) { - goto L90; + goto L90; } if (*rho * (d__1 = z__[j], abs(d__1)) <= tol) { /* Deflate due to small z component. */ - --k2; - indxp[k2] = j; + --k2; + indxp[k2] = j; } else { /* Check if eigenvalues are close enough to allow deflation. */ - s = z__[jlam]; - c__ = z__[j]; + s = z__[jlam]; + c__ = z__[j]; /* Find sqrt(a**2+b**2) without overflow or */ /* destructive underflow. */ - tau = dlapy2_(&c__, &s); - t = d__[j] - d__[jlam]; - c__ /= tau; - s = -s / tau; - if ((d__1 = t * c__ * s, abs(d__1)) <= tol) { + tau = dlapy2_(&c__, &s); + t = d__[j] - d__[jlam]; + c__ /= tau; + s = -s / tau; + if ((d__1 = t * c__ * s, abs(d__1)) <= tol) { /* Deflation is possible. */ - z__[j] = tau; - z__[jlam] = 0.; + z__[j] = tau; + z__[jlam] = 0.; /* Record the appropriate Givens rotation */ - ++(*givptr); - givcol[(*givptr << 1) + 1] = indxq[indx[jlam]]; - givcol[(*givptr << 1) + 2] = indxq[indx[j]]; - givnum[(*givptr << 1) + 1] = c__; - givnum[(*givptr << 1) + 2] = s; - zdrot_(qsiz, &q[indxq[indx[jlam]] * q_dim1 + 1], &c__1, &q[indxq[ - indx[j]] * q_dim1 + 1], &c__1, &c__, &s); - t = d__[jlam] * c__ * c__ + d__[j] * s * s; - d__[j] = d__[jlam] * s * s + d__[j] * c__ * c__; - d__[jlam] = t; - --k2; - i__ = 1; + ++(*givptr); + givcol[(*givptr << 1) + 1] = indxq[indx[jlam]]; + givcol[(*givptr << 1) + 2] = indxq[indx[j]]; + givnum[(*givptr << 1) + 1] = c__; + givnum[(*givptr << 1) + 2] = s; + zdrot_(qsiz, &q[indxq[indx[jlam]] * q_dim1 + 1], &c__1, &q[indxq[ + indx[j]] * q_dim1 + 1], &c__1, &c__, &s); + t = d__[jlam] * c__ * c__ + d__[j] * s * s; + d__[j] = d__[jlam] * s * s + d__[j] * c__ * c__; + d__[jlam] = t; + --k2; + i__ = 1; L80: - if (k2 + i__ <= *n) { - if (d__[jlam] < d__[indxp[k2 + i__]]) { - indxp[k2 + i__ - 1] = indxp[k2 + i__]; - indxp[k2 + i__] = jlam; - ++i__; - goto L80; - } else { - indxp[k2 + i__ - 1] = jlam; - } - } else { - indxp[k2 + i__ - 1] = jlam; - } - jlam = j; - } else { - ++(*k); - w[*k] = z__[jlam]; - dlamda[*k] = d__[jlam]; - indxp[*k] = jlam; - jlam = j; - } + if (k2 + i__ <= *n) { + if (d__[jlam] < d__[indxp[k2 + i__]]) { + indxp[k2 + i__ - 1] = indxp[k2 + i__]; + indxp[k2 + i__] = jlam; + ++i__; + goto L80; + } else { + indxp[k2 + i__ - 1] = jlam; + } + } else { + indxp[k2 + i__ - 1] = jlam; + } + jlam = j; + } else { + ++(*k); + w[*k] = z__[jlam]; + dlamda[*k] = d__[jlam]; + indxp[*k] = jlam; + jlam = j; + } } goto L70; L90: @@ -539,11 +539,11 @@ L100: i__1 = *n; for (j = 1; j <= i__1; ++j) { - jp = indxp[j]; - dlamda[j] = d__[jp]; - perm[j] = indxq[indx[jp]]; - zcopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 + 1], & - c__1); + jp = indxp[j]; + dlamda[j] = d__[jp]; + perm[j] = indxq[indx[jp]]; + zcopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 + 1], & + c__1); /* L110: */ } @@ -551,11 +551,11 @@ L100: /* into the last N - K slots of D and Q respectively. */ if (*k < *n) { - i__1 = *n - *k; - dcopy_(&i__1, &dlamda[*k + 1], &c__1, &d__[*k + 1], &c__1); - i__1 = *n - *k; - zlacpy_((char *)"A", qsiz, &i__1, &q2[(*k + 1) * q2_dim1 + 1], ldq2, &q[(*k + - 1) * q_dim1 + 1], ldq, (ftnlen)1); + i__1 = *n - *k; + dcopy_(&i__1, &dlamda[*k + 1], &c__1, &d__[*k + 1], &c__1); + i__1 = *n - *k; + zlacpy_((char *)"A", qsiz, &i__1, &q2[(*k + 1) * q2_dim1 + 1], ldq2, &q[(*k + + 1) * q_dim1 + 1], ldq, (ftnlen)1); } return 0; @@ -565,5 +565,5 @@ L100: } /* zlaed8_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zlanhe.cpp b/lib/linalg/zlanhe.cpp index 2522e8d500..c54482158a 100644 --- a/lib/linalg/zlanhe.cpp +++ b/lib/linalg/zlanhe.cpp @@ -1,13 +1,13 @@ /* fortran/zlanhe.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -145,8 +145,8 @@ f"> */ /* > \ingroup complex16HEauxiliary */ /* ===================================================================== */ -doublereal zlanhe_(char *norm, char *uplo, integer *n, doublecomplex *a, - integer *lda, doublereal *work, ftnlen norm_len, ftnlen uplo_len) +doublereal zlanhe_(char *norm, char *uplo, integer *n, doublecomplex *a, + integer *lda, doublereal *work, ftnlen norm_len, ftnlen uplo_len) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; @@ -162,7 +162,7 @@ doublereal zlanhe_(char *norm, char *uplo, integer *n, doublecomplex *a, doublereal value; extern logical disnan_(doublereal *); extern /* Subroutine */ int zlassq_(integer *, doublecomplex *, integer *, - doublereal *, doublereal *); + doublereal *, doublereal *); /* -- LAPACK auxiliary routine -- */ @@ -196,144 +196,144 @@ doublereal zlanhe_(char *norm, char *uplo, integer *n, doublecomplex *a, /* Function Body */ if (*n == 0) { - value = 0.; + value = 0.; } else if (lsame_(norm, (char *)"M", (ftnlen)1, (ftnlen)1)) { /* Find max(abs(A(i,j))). */ - value = 0.; - if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = j - 1; - for (i__ = 1; i__ <= i__2; ++i__) { - sum = z_abs(&a[i__ + j * a_dim1]); - if (value < sum || disnan_(&sum)) { - value = sum; - } + value = 0.; + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + sum = z_abs(&a[i__ + j * a_dim1]); + if (value < sum || disnan_(&sum)) { + value = sum; + } /* L10: */ - } - i__2 = j + j * a_dim1; - sum = (d__1 = a[i__2].r, abs(d__1)); - if (value < sum || disnan_(&sum)) { - value = sum; - } + } + i__2 = j + j * a_dim1; + sum = (d__1 = a[i__2].r, abs(d__1)); + if (value < sum || disnan_(&sum)) { + value = sum; + } /* L20: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = j + j * a_dim1; - sum = (d__1 = a[i__2].r, abs(d__1)); - if (value < sum || disnan_(&sum)) { - value = sum; - } - i__2 = *n; - for (i__ = j + 1; i__ <= i__2; ++i__) { - sum = z_abs(&a[i__ + j * a_dim1]); - if (value < sum || disnan_(&sum)) { - value = sum; - } + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j + j * a_dim1; + sum = (d__1 = a[i__2].r, abs(d__1)); + if (value < sum || disnan_(&sum)) { + value = sum; + } + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + sum = z_abs(&a[i__ + j * a_dim1]); + if (value < sum || disnan_(&sum)) { + value = sum; + } /* L30: */ - } + } /* L40: */ - } - } + } + } } else if (lsame_(norm, (char *)"I", (ftnlen)1, (ftnlen)1) || lsame_(norm, (char *)"O", ( - ftnlen)1, (ftnlen)1) || *(unsigned char *)norm == '1') { + ftnlen)1, (ftnlen)1) || *(unsigned char *)norm == '1') { /* Find normI(A) ( = norm1(A), since A is hermitian). */ - value = 0.; - if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - sum = 0.; - i__2 = j - 1; - for (i__ = 1; i__ <= i__2; ++i__) { - absa = z_abs(&a[i__ + j * a_dim1]); - sum += absa; - work[i__] += absa; + value = 0.; + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + sum = 0.; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + absa = z_abs(&a[i__ + j * a_dim1]); + sum += absa; + work[i__] += absa; /* L50: */ - } - i__2 = j + j * a_dim1; - work[j] = sum + (d__1 = a[i__2].r, abs(d__1)); + } + i__2 = j + j * a_dim1; + work[j] = sum + (d__1 = a[i__2].r, abs(d__1)); /* L60: */ - } - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - sum = work[i__]; - if (value < sum || disnan_(&sum)) { - value = sum; - } + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + sum = work[i__]; + if (value < sum || disnan_(&sum)) { + value = sum; + } /* L70: */ - } - } else { - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - work[i__] = 0.; + } + } else { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + work[i__] = 0.; /* L80: */ - } - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = j + j * a_dim1; - sum = work[j] + (d__1 = a[i__2].r, abs(d__1)); - i__2 = *n; - for (i__ = j + 1; i__ <= i__2; ++i__) { - absa = z_abs(&a[i__ + j * a_dim1]); - sum += absa; - work[i__] += absa; + } + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j + j * a_dim1; + sum = work[j] + (d__1 = a[i__2].r, abs(d__1)); + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + absa = z_abs(&a[i__ + j * a_dim1]); + sum += absa; + work[i__] += absa; /* L90: */ - } - if (value < sum || disnan_(&sum)) { - value = sum; - } + } + if (value < sum || disnan_(&sum)) { + value = sum; + } /* L100: */ - } - } + } + } } else if (lsame_(norm, (char *)"F", (ftnlen)1, (ftnlen)1) || lsame_(norm, (char *)"E", ( - ftnlen)1, (ftnlen)1)) { + ftnlen)1, (ftnlen)1)) { /* Find normF(A). */ - scale = 0.; - sum = 1.; - if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { - i__1 = *n; - for (j = 2; j <= i__1; ++j) { - i__2 = j - 1; - zlassq_(&i__2, &a[j * a_dim1 + 1], &c__1, &scale, &sum); + scale = 0.; + sum = 1.; + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + i__1 = *n; + for (j = 2; j <= i__1; ++j) { + i__2 = j - 1; + zlassq_(&i__2, &a[j * a_dim1 + 1], &c__1, &scale, &sum); /* L110: */ - } - } else { - i__1 = *n - 1; - for (j = 1; j <= i__1; ++j) { - i__2 = *n - j; - zlassq_(&i__2, &a[j + 1 + j * a_dim1], &c__1, &scale, &sum); + } + } else { + i__1 = *n - 1; + for (j = 1; j <= i__1; ++j) { + i__2 = *n - j; + zlassq_(&i__2, &a[j + 1 + j * a_dim1], &c__1, &scale, &sum); /* L120: */ - } - } - sum *= 2; - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = i__ + i__ * a_dim1; - if (a[i__2].r != 0.) { - i__2 = i__ + i__ * a_dim1; - absa = (d__1 = a[i__2].r, abs(d__1)); - if (scale < absa) { + } + } + sum *= 2; + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__ + i__ * a_dim1; + if (a[i__2].r != 0.) { + i__2 = i__ + i__ * a_dim1; + absa = (d__1 = a[i__2].r, abs(d__1)); + if (scale < absa) { /* Computing 2nd power */ - d__1 = scale / absa; - sum = sum * (d__1 * d__1) + 1.; - scale = absa; - } else { + d__1 = scale / absa; + sum = sum * (d__1 * d__1) + 1.; + scale = absa; + } else { /* Computing 2nd power */ - d__1 = absa / scale; - sum += d__1 * d__1; - } - } + d__1 = absa / scale; + sum += d__1 * d__1; + } + } /* L130: */ - } - value = scale * sqrt(sum); + } + value = scale * sqrt(sum); } ret_val = value; @@ -344,5 +344,5 @@ doublereal zlanhe_(char *norm, char *uplo, integer *n, doublecomplex *a, } /* zlanhe_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zlarf.cpp b/lib/linalg/zlarf.cpp index 453644e7d9..7bee520eae 100644 --- a/lib/linalg/zlarf.cpp +++ b/lib/linalg/zlarf.cpp @@ -1,13 +1,13 @@ /* fortran/zlarf.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -150,9 +150,9 @@ static integer c__1 = 1; /* > \ingroup complex16OTHERauxiliary */ /* ===================================================================== */ -/* Subroutine */ int zlarf_(char *side, integer *m, integer *n, doublecomplex - *v, integer *incv, doublecomplex *tau, doublecomplex *c__, integer * - ldc, doublecomplex *work, ftnlen side_len) +/* Subroutine */ int zlarf_(char *side, integer *m, integer *n, doublecomplex + *v, integer *incv, doublecomplex *tau, doublecomplex *c__, integer * + ldc, doublecomplex *work, ftnlen side_len) { /* System generated locals */ integer c_dim1, c_offset, i__1; @@ -163,14 +163,14 @@ static integer c__1 = 1; logical applyleft; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer lastc; - extern /* Subroutine */ int zgerc_(integer *, integer *, doublecomplex *, - doublecomplex *, integer *, doublecomplex *, integer *, - doublecomplex *, integer *), zgemv_(char *, integer *, integer *, - doublecomplex *, doublecomplex *, integer *, doublecomplex *, - integer *, doublecomplex *, doublecomplex *, integer *, ftnlen); + extern /* Subroutine */ int zgerc_(integer *, integer *, doublecomplex *, + doublecomplex *, integer *, doublecomplex *, integer *, + doublecomplex *, integer *), zgemv_(char *, integer *, integer *, + doublecomplex *, doublecomplex *, integer *, doublecomplex *, + integer *, doublecomplex *, doublecomplex *, integer *, ftnlen); integer lastv; - extern integer ilazlc_(integer *, integer *, doublecomplex *, integer *), - ilazlr_(integer *, integer *, doublecomplex *, integer *); + extern integer ilazlc_(integer *, integer *, doublecomplex *, integer *), + ilazlr_(integer *, integer *, doublecomplex *, integer *); /* -- LAPACK auxiliary routine -- */ @@ -208,31 +208,31 @@ static integer c__1 = 1; if (tau->r != 0. || tau->i != 0.) { /* Set up variables for scanning V. LASTV begins pointing to the end */ /* of V. */ - if (applyleft) { - lastv = *m; - } else { - lastv = *n; - } - if (*incv > 0) { - i__ = (lastv - 1) * *incv + 1; - } else { - i__ = 1; - } + if (applyleft) { + lastv = *m; + } else { + lastv = *n; + } + if (*incv > 0) { + i__ = (lastv - 1) * *incv + 1; + } else { + i__ = 1; + } /* Look for the last non-zero row in V. */ - for(;;) { /* while(complicated condition) */ - i__1 = i__; - if (!(lastv > 0 && (v[i__1].r == 0. && v[i__1].i == 0.))) - break; - --lastv; - i__ -= *incv; - } - if (applyleft) { + for(;;) { /* while(complicated condition) */ + i__1 = i__; + if (!(lastv > 0 && (v[i__1].r == 0. && v[i__1].i == 0.))) + break; + --lastv; + i__ -= *incv; + } + if (applyleft) { /* Scan for the last non-zero column in C(1:lastv,:). */ - lastc = ilazlc_(&lastv, n, &c__[c_offset], ldc); - } else { + lastc = ilazlc_(&lastv, n, &c__[c_offset], ldc); + } else { /* Scan for the last non-zero row in C(:,1:lastv). */ - lastc = ilazlr_(m, &lastv, &c__[c_offset], ldc); - } + lastc = ilazlr_(m, &lastv, &c__[c_offset], ldc); + } } /* Note that lastc.eq.0 renders the BLAS operations null; no special */ /* case is needed at this level. */ @@ -240,37 +240,37 @@ static integer c__1 = 1; /* Form H * C */ - if (lastv > 0) { + if (lastv > 0) { /* w(1:lastc,1) := C(1:lastv,1:lastc)**H * v(1:lastv,1) */ - zgemv_((char *)"Conjugate transpose", &lastv, &lastc, &c_b1, &c__[ - c_offset], ldc, &v[1], incv, &c_b2, &work[1], &c__1, ( - ftnlen)19); + zgemv_((char *)"Conjugate transpose", &lastv, &lastc, &c_b1, &c__[ + c_offset], ldc, &v[1], incv, &c_b2, &work[1], &c__1, ( + ftnlen)19); /* C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**H */ - z__1.r = -tau->r, z__1.i = -tau->i; - zgerc_(&lastv, &lastc, &z__1, &v[1], incv, &work[1], &c__1, &c__[ - c_offset], ldc); - } + z__1.r = -tau->r, z__1.i = -tau->i; + zgerc_(&lastv, &lastc, &z__1, &v[1], incv, &work[1], &c__1, &c__[ + c_offset], ldc); + } } else { /* Form C * H */ - if (lastv > 0) { + if (lastv > 0) { /* w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1) */ - zgemv_((char *)"No transpose", &lastc, &lastv, &c_b1, &c__[c_offset], ldc, - &v[1], incv, &c_b2, &work[1], &c__1, (ftnlen)12); + zgemv_((char *)"No transpose", &lastc, &lastv, &c_b1, &c__[c_offset], ldc, + &v[1], incv, &c_b2, &work[1], &c__1, (ftnlen)12); /* C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**H */ - z__1.r = -tau->r, z__1.i = -tau->i; - zgerc_(&lastc, &lastv, &z__1, &work[1], &c__1, &v[1], incv, &c__[ - c_offset], ldc); - } + z__1.r = -tau->r, z__1.i = -tau->i; + zgerc_(&lastc, &lastv, &z__1, &work[1], &c__1, &v[1], incv, &c__[ + c_offset], ldc); + } } return 0; @@ -279,5 +279,5 @@ static integer c__1 = 1; } /* zlarf_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zlarfb.cpp b/lib/linalg/zlarfb.cpp index 0ea0c17bd4..b09fdf4917 100644 --- a/lib/linalg/zlarfb.cpp +++ b/lib/linalg/zlarfb.cpp @@ -1,13 +1,13 @@ /* fortran/zlarfb.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -218,14 +218,14 @@ f"> */ /* > */ /* ===================================================================== */ /* Subroutine */ int zlarfb_(char *side, char *trans, char *direct, char * - storev, integer *m, integer *n, integer *k, doublecomplex *v, integer - *ldv, doublecomplex *t, integer *ldt, doublecomplex *c__, integer * - ldc, doublecomplex *work, integer *ldwork, ftnlen side_len, ftnlen - trans_len, ftnlen direct_len, ftnlen storev_len) + storev, integer *m, integer *n, integer *k, doublecomplex *v, integer + *ldv, doublecomplex *t, integer *ldt, doublecomplex *c__, integer * + ldc, doublecomplex *work, integer *ldwork, ftnlen side_len, ftnlen + trans_len, ftnlen direct_len, ftnlen storev_len) { /* System generated locals */ - integer c_dim1, c_offset, t_dim1, t_offset, v_dim1, v_offset, work_dim1, - work_offset, i__1, i__2, i__3, i__4, i__5; + integer c_dim1, c_offset, t_dim1, t_offset, v_dim1, v_offset, work_dim1, + work_offset, i__1, i__2, i__3, i__4, i__5; doublecomplex z__1, z__2; /* Builtin functions */ @@ -234,15 +234,15 @@ f"> */ /* Local variables */ integer i__, j; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *, - integer *, doublecomplex *, doublecomplex *, integer *, - doublecomplex *, integer *, doublecomplex *, doublecomplex *, - integer *, ftnlen, ftnlen), zcopy_(integer *, doublecomplex *, - integer *, doublecomplex *, integer *), ztrmm_(char *, char *, - char *, char *, integer *, integer *, doublecomplex *, - doublecomplex *, integer *, doublecomplex *, integer *, ftnlen, - ftnlen, ftnlen, ftnlen), zlacgv_(integer *, doublecomplex *, - integer *); + extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *, + integer *, doublecomplex *, doublecomplex *, integer *, + doublecomplex *, integer *, doublecomplex *, doublecomplex *, + integer *, ftnlen, ftnlen), zcopy_(integer *, doublecomplex *, + integer *, doublecomplex *, integer *), ztrmm_(char *, char *, + char *, char *, integer *, integer *, doublecomplex *, + doublecomplex *, integer *, doublecomplex *, integer *, ftnlen, + ftnlen, ftnlen, ftnlen), zlacgv_(integer *, doublecomplex *, + integer *); char transt[1]; @@ -287,24 +287,24 @@ f"> */ /* Function Body */ if (*m <= 0 || *n <= 0) { - return 0; + return 0; } if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { - *(unsigned char *)transt = 'C'; + *(unsigned char *)transt = 'C'; } else { - *(unsigned char *)transt = 'N'; + *(unsigned char *)transt = 'N'; } if (lsame_(storev, (char *)"C", (ftnlen)1, (ftnlen)1)) { - if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { + if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { /* Let V = ( V1 ) (first K rows) */ /* ( V2 ) */ /* where V1 is unit lower triangular. */ - if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { + if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { /* Form H * C or H**H * C where C = ( C1 ) */ /* ( C2 ) */ @@ -313,74 +313,74 @@ f"> */ /* W := C1**H */ - i__1 = *k; - for (j = 1; j <= i__1; ++j) { - zcopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1], - &c__1); - zlacgv_(n, &work[j * work_dim1 + 1], &c__1); + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + zcopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1], + &c__1); + zlacgv_(n, &work[j * work_dim1 + 1], &c__1); /* L10: */ - } + } /* W := W * V1 */ - ztrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", n, k, &c_b1, - &v[v_offset], ldv, &work[work_offset], ldwork, ( - ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); - if (*m > *k) { + ztrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", n, k, &c_b1, + &v[v_offset], ldv, &work[work_offset], ldwork, ( + ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); + if (*m > *k) { /* W := W + C2**H * V2 */ - i__1 = *m - *k; - zgemm_((char *)"Conjugate transpose", (char *)"No transpose", n, k, &i__1, - &c_b1, &c__[*k + 1 + c_dim1], ldc, &v[*k + 1 + - v_dim1], ldv, &c_b1, &work[work_offset], ldwork, ( - ftnlen)19, (ftnlen)12); - } + i__1 = *m - *k; + zgemm_((char *)"Conjugate transpose", (char *)"No transpose", n, k, &i__1, + &c_b1, &c__[*k + 1 + c_dim1], ldc, &v[*k + 1 + + v_dim1], ldv, &c_b1, &work[work_offset], ldwork, ( + ftnlen)19, (ftnlen)12); + } /* W := W * T**H or W * T */ - ztrmm_((char *)"Right", (char *)"Upper", transt, (char *)"Non-unit", n, k, &c_b1, &t[ - t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, - (ftnlen)5, (ftnlen)1, (ftnlen)8); + ztrmm_((char *)"Right", (char *)"Upper", transt, (char *)"Non-unit", n, k, &c_b1, &t[ + t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)1, (ftnlen)8); /* C := C - V * W**H */ - if (*m > *k) { + if (*m > *k) { /* C2 := C2 - V2 * W**H */ - i__1 = *m - *k; - z__1.r = -1., z__1.i = -0.; - zgemm_((char *)"No transpose", (char *)"Conjugate transpose", &i__1, n, k, - &z__1, &v[*k + 1 + v_dim1], ldv, &work[ - work_offset], ldwork, &c_b1, &c__[*k + 1 + c_dim1] - , ldc, (ftnlen)12, (ftnlen)19); - } + i__1 = *m - *k; + z__1.r = -1., z__1.i = -0.; + zgemm_((char *)"No transpose", (char *)"Conjugate transpose", &i__1, n, k, + &z__1, &v[*k + 1 + v_dim1], ldv, &work[ + work_offset], ldwork, &c_b1, &c__[*k + 1 + c_dim1] + , ldc, (ftnlen)12, (ftnlen)19); + } /* W := W * V1**H */ - ztrmm_((char *)"Right", (char *)"Lower", (char *)"Conjugate transpose", (char *)"Unit", n, k, - &c_b1, &v[v_offset], ldv, &work[work_offset], ldwork, - (ftnlen)5, (ftnlen)5, (ftnlen)19, (ftnlen)4); + ztrmm_((char *)"Right", (char *)"Lower", (char *)"Conjugate transpose", (char *)"Unit", n, k, + &c_b1, &v[v_offset], ldv, &work[work_offset], ldwork, + (ftnlen)5, (ftnlen)5, (ftnlen)19, (ftnlen)4); /* C1 := C1 - W**H */ - i__1 = *k; - for (j = 1; j <= i__1; ++j) { - i__2 = *n; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = j + i__ * c_dim1; - i__4 = j + i__ * c_dim1; - d_cnjg(&z__2, &work[i__ + j * work_dim1]); - z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i - - z__2.i; - c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = j + i__ * c_dim1; + i__4 = j + i__ * c_dim1; + d_cnjg(&z__2, &work[i__ + j * work_dim1]); + z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i - + z__2.i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; /* L20: */ - } + } /* L30: */ - } + } - } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { /* Form C * H or C * H**H where C = ( C1 C2 ) */ @@ -388,80 +388,80 @@ f"> */ /* W := C1 */ - i__1 = *k; - for (j = 1; j <= i__1; ++j) { - zcopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j * - work_dim1 + 1], &c__1); + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + zcopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j * + work_dim1 + 1], &c__1); /* L40: */ - } + } /* W := W * V1 */ - ztrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", m, k, &c_b1, - &v[v_offset], ldv, &work[work_offset], ldwork, ( - ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); - if (*n > *k) { + ztrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", m, k, &c_b1, + &v[v_offset], ldv, &work[work_offset], ldwork, ( + ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); + if (*n > *k) { /* W := W + C2 * V2 */ - i__1 = *n - *k; - zgemm_((char *)"No transpose", (char *)"No transpose", m, k, &i__1, &c_b1, - &c__[(*k + 1) * c_dim1 + 1], ldc, &v[*k + 1 + - v_dim1], ldv, &c_b1, &work[work_offset], ldwork, ( - ftnlen)12, (ftnlen)12); - } + i__1 = *n - *k; + zgemm_((char *)"No transpose", (char *)"No transpose", m, k, &i__1, &c_b1, + &c__[(*k + 1) * c_dim1 + 1], ldc, &v[*k + 1 + + v_dim1], ldv, &c_b1, &work[work_offset], ldwork, ( + ftnlen)12, (ftnlen)12); + } /* W := W * T or W * T**H */ - ztrmm_((char *)"Right", (char *)"Upper", trans, (char *)"Non-unit", m, k, &c_b1, &t[ - t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, - (ftnlen)5, (ftnlen)1, (ftnlen)8); + ztrmm_((char *)"Right", (char *)"Upper", trans, (char *)"Non-unit", m, k, &c_b1, &t[ + t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)1, (ftnlen)8); /* C := C - W * V**H */ - if (*n > *k) { + if (*n > *k) { /* C2 := C2 - W * V2**H */ - i__1 = *n - *k; - z__1.r = -1., z__1.i = -0.; - zgemm_((char *)"No transpose", (char *)"Conjugate transpose", m, &i__1, k, - &z__1, &work[work_offset], ldwork, &v[*k + 1 + - v_dim1], ldv, &c_b1, &c__[(*k + 1) * c_dim1 + 1], - ldc, (ftnlen)12, (ftnlen)19); - } + i__1 = *n - *k; + z__1.r = -1., z__1.i = -0.; + zgemm_((char *)"No transpose", (char *)"Conjugate transpose", m, &i__1, k, + &z__1, &work[work_offset], ldwork, &v[*k + 1 + + v_dim1], ldv, &c_b1, &c__[(*k + 1) * c_dim1 + 1], + ldc, (ftnlen)12, (ftnlen)19); + } /* W := W * V1**H */ - ztrmm_((char *)"Right", (char *)"Lower", (char *)"Conjugate transpose", (char *)"Unit", m, k, - &c_b1, &v[v_offset], ldv, &work[work_offset], ldwork, - (ftnlen)5, (ftnlen)5, (ftnlen)19, (ftnlen)4); + ztrmm_((char *)"Right", (char *)"Lower", (char *)"Conjugate transpose", (char *)"Unit", m, k, + &c_b1, &v[v_offset], ldv, &work[work_offset], ldwork, + (ftnlen)5, (ftnlen)5, (ftnlen)19, (ftnlen)4); /* C1 := C1 - W */ - i__1 = *k; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * c_dim1; - i__4 = i__ + j * c_dim1; - i__5 = i__ + j * work_dim1; - z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[ - i__4].i - work[i__5].i; - c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + i__4 = i__ + j * c_dim1; + i__5 = i__ + j * work_dim1; + z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[ + i__4].i - work[i__5].i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; /* L50: */ - } + } /* L60: */ - } - } + } + } - } else { + } else { /* Let V = ( V1 ) */ /* ( V2 ) (last K rows) */ /* where V2 is unit upper triangular. */ - if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { + if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { /* Form H * C or H**H * C where C = ( C1 ) */ /* ( C2 ) */ @@ -470,75 +470,75 @@ f"> */ /* W := C2**H */ - i__1 = *k; - for (j = 1; j <= i__1; ++j) { - zcopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j * - work_dim1 + 1], &c__1); - zlacgv_(n, &work[j * work_dim1 + 1], &c__1); + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + zcopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j * + work_dim1 + 1], &c__1); + zlacgv_(n, &work[j * work_dim1 + 1], &c__1); /* L70: */ - } + } /* W := W * V2 */ - ztrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", n, k, &c_b1, - &v[*m - *k + 1 + v_dim1], ldv, &work[work_offset], - ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); - if (*m > *k) { + ztrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", n, k, &c_b1, + &v[*m - *k + 1 + v_dim1], ldv, &work[work_offset], + ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); + if (*m > *k) { /* W := W + C1**H * V1 */ - i__1 = *m - *k; - zgemm_((char *)"Conjugate transpose", (char *)"No transpose", n, k, &i__1, - &c_b1, &c__[c_offset], ldc, &v[v_offset], ldv, & - c_b1, &work[work_offset], ldwork, (ftnlen)19, ( - ftnlen)12); - } + i__1 = *m - *k; + zgemm_((char *)"Conjugate transpose", (char *)"No transpose", n, k, &i__1, + &c_b1, &c__[c_offset], ldc, &v[v_offset], ldv, & + c_b1, &work[work_offset], ldwork, (ftnlen)19, ( + ftnlen)12); + } /* W := W * T**H or W * T */ - ztrmm_((char *)"Right", (char *)"Lower", transt, (char *)"Non-unit", n, k, &c_b1, &t[ - t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, - (ftnlen)5, (ftnlen)1, (ftnlen)8); + ztrmm_((char *)"Right", (char *)"Lower", transt, (char *)"Non-unit", n, k, &c_b1, &t[ + t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)1, (ftnlen)8); /* C := C - V * W**H */ - if (*m > *k) { + if (*m > *k) { /* C1 := C1 - V1 * W**H */ - i__1 = *m - *k; - z__1.r = -1., z__1.i = -0.; - zgemm_((char *)"No transpose", (char *)"Conjugate transpose", &i__1, n, k, - &z__1, &v[v_offset], ldv, &work[work_offset], - ldwork, &c_b1, &c__[c_offset], ldc, (ftnlen)12, ( - ftnlen)19); - } + i__1 = *m - *k; + z__1.r = -1., z__1.i = -0.; + zgemm_((char *)"No transpose", (char *)"Conjugate transpose", &i__1, n, k, + &z__1, &v[v_offset], ldv, &work[work_offset], + ldwork, &c_b1, &c__[c_offset], ldc, (ftnlen)12, ( + ftnlen)19); + } /* W := W * V2**H */ - ztrmm_((char *)"Right", (char *)"Upper", (char *)"Conjugate transpose", (char *)"Unit", n, k, - &c_b1, &v[*m - *k + 1 + v_dim1], ldv, &work[ - work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen) - 19, (ftnlen)4); + ztrmm_((char *)"Right", (char *)"Upper", (char *)"Conjugate transpose", (char *)"Unit", n, k, + &c_b1, &v[*m - *k + 1 + v_dim1], ldv, &work[ + work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen) + 19, (ftnlen)4); /* C2 := C2 - W**H */ - i__1 = *k; - for (j = 1; j <= i__1; ++j) { - i__2 = *n; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = *m - *k + j + i__ * c_dim1; - i__4 = *m - *k + j + i__ * c_dim1; - d_cnjg(&z__2, &work[i__ + j * work_dim1]); - z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i - - z__2.i; - c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = *m - *k + j + i__ * c_dim1; + i__4 = *m - *k + j + i__ * c_dim1; + d_cnjg(&z__2, &work[i__ + j * work_dim1]); + z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i - + z__2.i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; /* L80: */ - } + } /* L90: */ - } + } - } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { /* Form C * H or C * H**H where C = ( C1 C2 ) */ @@ -546,83 +546,83 @@ f"> */ /* W := C2 */ - i__1 = *k; - for (j = 1; j <= i__1; ++j) { - zcopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[ - j * work_dim1 + 1], &c__1); + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + zcopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[ + j * work_dim1 + 1], &c__1); /* L100: */ - } + } /* W := W * V2 */ - ztrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", m, k, &c_b1, - &v[*n - *k + 1 + v_dim1], ldv, &work[work_offset], - ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); - if (*n > *k) { + ztrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", m, k, &c_b1, + &v[*n - *k + 1 + v_dim1], ldv, &work[work_offset], + ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); + if (*n > *k) { /* W := W + C1 * V1 */ - i__1 = *n - *k; - zgemm_((char *)"No transpose", (char *)"No transpose", m, k, &i__1, &c_b1, - &c__[c_offset], ldc, &v[v_offset], ldv, &c_b1, & - work[work_offset], ldwork, (ftnlen)12, (ftnlen)12) - ; - } + i__1 = *n - *k; + zgemm_((char *)"No transpose", (char *)"No transpose", m, k, &i__1, &c_b1, + &c__[c_offset], ldc, &v[v_offset], ldv, &c_b1, & + work[work_offset], ldwork, (ftnlen)12, (ftnlen)12) + ; + } /* W := W * T or W * T**H */ - ztrmm_((char *)"Right", (char *)"Lower", trans, (char *)"Non-unit", m, k, &c_b1, &t[ - t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, - (ftnlen)5, (ftnlen)1, (ftnlen)8); + ztrmm_((char *)"Right", (char *)"Lower", trans, (char *)"Non-unit", m, k, &c_b1, &t[ + t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)1, (ftnlen)8); /* C := C - W * V**H */ - if (*n > *k) { + if (*n > *k) { /* C1 := C1 - W * V1**H */ - i__1 = *n - *k; - z__1.r = -1., z__1.i = -0.; - zgemm_((char *)"No transpose", (char *)"Conjugate transpose", m, &i__1, k, - &z__1, &work[work_offset], ldwork, &v[v_offset], - ldv, &c_b1, &c__[c_offset], ldc, (ftnlen)12, ( - ftnlen)19); - } + i__1 = *n - *k; + z__1.r = -1., z__1.i = -0.; + zgemm_((char *)"No transpose", (char *)"Conjugate transpose", m, &i__1, k, + &z__1, &work[work_offset], ldwork, &v[v_offset], + ldv, &c_b1, &c__[c_offset], ldc, (ftnlen)12, ( + ftnlen)19); + } /* W := W * V2**H */ - ztrmm_((char *)"Right", (char *)"Upper", (char *)"Conjugate transpose", (char *)"Unit", m, k, - &c_b1, &v[*n - *k + 1 + v_dim1], ldv, &work[ - work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen) - 19, (ftnlen)4); + ztrmm_((char *)"Right", (char *)"Upper", (char *)"Conjugate transpose", (char *)"Unit", m, k, + &c_b1, &v[*n - *k + 1 + v_dim1], ldv, &work[ + work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen) + 19, (ftnlen)4); /* C2 := C2 - W */ - i__1 = *k; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + (*n - *k + j) * c_dim1; - i__4 = i__ + (*n - *k + j) * c_dim1; - i__5 = i__ + j * work_dim1; - z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[ - i__4].i - work[i__5].i; - c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + (*n - *k + j) * c_dim1; + i__4 = i__ + (*n - *k + j) * c_dim1; + i__5 = i__ + j * work_dim1; + z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[ + i__4].i - work[i__5].i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; /* L110: */ - } + } /* L120: */ - } - } - } + } + } + } } else if (lsame_(storev, (char *)"R", (ftnlen)1, (ftnlen)1)) { - if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { + if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { /* Let V = ( V1 V2 ) (V1: first K columns) */ /* where V1 is unit upper triangular. */ - if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { + if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { /* Form H * C or H**H * C where C = ( C1 ) */ /* ( C2 ) */ @@ -631,74 +631,74 @@ f"> */ /* W := C1**H */ - i__1 = *k; - for (j = 1; j <= i__1; ++j) { - zcopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1], - &c__1); - zlacgv_(n, &work[j * work_dim1 + 1], &c__1); + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + zcopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1], + &c__1); + zlacgv_(n, &work[j * work_dim1 + 1], &c__1); /* L130: */ - } + } /* W := W * V1**H */ - ztrmm_((char *)"Right", (char *)"Upper", (char *)"Conjugate transpose", (char *)"Unit", n, k, - &c_b1, &v[v_offset], ldv, &work[work_offset], ldwork, - (ftnlen)5, (ftnlen)5, (ftnlen)19, (ftnlen)4); - if (*m > *k) { + ztrmm_((char *)"Right", (char *)"Upper", (char *)"Conjugate transpose", (char *)"Unit", n, k, + &c_b1, &v[v_offset], ldv, &work[work_offset], ldwork, + (ftnlen)5, (ftnlen)5, (ftnlen)19, (ftnlen)4); + if (*m > *k) { /* W := W + C2**H * V2**H */ - i__1 = *m - *k; - zgemm_((char *)"Conjugate transpose", (char *)"Conjugate transpose", n, k, - &i__1, &c_b1, &c__[*k + 1 + c_dim1], ldc, &v[(*k - + 1) * v_dim1 + 1], ldv, &c_b1, &work[work_offset] - , ldwork, (ftnlen)19, (ftnlen)19); - } + i__1 = *m - *k; + zgemm_((char *)"Conjugate transpose", (char *)"Conjugate transpose", n, k, + &i__1, &c_b1, &c__[*k + 1 + c_dim1], ldc, &v[(*k + + 1) * v_dim1 + 1], ldv, &c_b1, &work[work_offset] + , ldwork, (ftnlen)19, (ftnlen)19); + } /* W := W * T**H or W * T */ - ztrmm_((char *)"Right", (char *)"Upper", transt, (char *)"Non-unit", n, k, &c_b1, &t[ - t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, - (ftnlen)5, (ftnlen)1, (ftnlen)8); + ztrmm_((char *)"Right", (char *)"Upper", transt, (char *)"Non-unit", n, k, &c_b1, &t[ + t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)1, (ftnlen)8); /* C := C - V**H * W**H */ - if (*m > *k) { + if (*m > *k) { /* C2 := C2 - V2**H * W**H */ - i__1 = *m - *k; - z__1.r = -1., z__1.i = -0.; - zgemm_((char *)"Conjugate transpose", (char *)"Conjugate transpose", & - i__1, n, k, &z__1, &v[(*k + 1) * v_dim1 + 1], ldv, - &work[work_offset], ldwork, &c_b1, &c__[*k + 1 + - c_dim1], ldc, (ftnlen)19, (ftnlen)19); - } + i__1 = *m - *k; + z__1.r = -1., z__1.i = -0.; + zgemm_((char *)"Conjugate transpose", (char *)"Conjugate transpose", & + i__1, n, k, &z__1, &v[(*k + 1) * v_dim1 + 1], ldv, + &work[work_offset], ldwork, &c_b1, &c__[*k + 1 + + c_dim1], ldc, (ftnlen)19, (ftnlen)19); + } /* W := W * V1 */ - ztrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", n, k, &c_b1, - &v[v_offset], ldv, &work[work_offset], ldwork, ( - ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); + ztrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", n, k, &c_b1, + &v[v_offset], ldv, &work[work_offset], ldwork, ( + ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); /* C1 := C1 - W**H */ - i__1 = *k; - for (j = 1; j <= i__1; ++j) { - i__2 = *n; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = j + i__ * c_dim1; - i__4 = j + i__ * c_dim1; - d_cnjg(&z__2, &work[i__ + j * work_dim1]); - z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i - - z__2.i; - c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = j + i__ * c_dim1; + i__4 = j + i__ * c_dim1; + d_cnjg(&z__2, &work[i__ + j * work_dim1]); + z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i - + z__2.i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; /* L140: */ - } + } /* L150: */ - } + } - } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { /* Form C * H or C * H**H where C = ( C1 C2 ) */ @@ -706,80 +706,80 @@ f"> */ /* W := C1 */ - i__1 = *k; - for (j = 1; j <= i__1; ++j) { - zcopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j * - work_dim1 + 1], &c__1); + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + zcopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j * + work_dim1 + 1], &c__1); /* L160: */ - } + } /* W := W * V1**H */ - ztrmm_((char *)"Right", (char *)"Upper", (char *)"Conjugate transpose", (char *)"Unit", m, k, - &c_b1, &v[v_offset], ldv, &work[work_offset], ldwork, - (ftnlen)5, (ftnlen)5, (ftnlen)19, (ftnlen)4); - if (*n > *k) { + ztrmm_((char *)"Right", (char *)"Upper", (char *)"Conjugate transpose", (char *)"Unit", m, k, + &c_b1, &v[v_offset], ldv, &work[work_offset], ldwork, + (ftnlen)5, (ftnlen)5, (ftnlen)19, (ftnlen)4); + if (*n > *k) { /* W := W + C2 * V2**H */ - i__1 = *n - *k; - zgemm_((char *)"No transpose", (char *)"Conjugate transpose", m, k, &i__1, - &c_b1, &c__[(*k + 1) * c_dim1 + 1], ldc, &v[(*k - + 1) * v_dim1 + 1], ldv, &c_b1, &work[work_offset] - , ldwork, (ftnlen)12, (ftnlen)19); - } + i__1 = *n - *k; + zgemm_((char *)"No transpose", (char *)"Conjugate transpose", m, k, &i__1, + &c_b1, &c__[(*k + 1) * c_dim1 + 1], ldc, &v[(*k + + 1) * v_dim1 + 1], ldv, &c_b1, &work[work_offset] + , ldwork, (ftnlen)12, (ftnlen)19); + } /* W := W * T or W * T**H */ - ztrmm_((char *)"Right", (char *)"Upper", trans, (char *)"Non-unit", m, k, &c_b1, &t[ - t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, - (ftnlen)5, (ftnlen)1, (ftnlen)8); + ztrmm_((char *)"Right", (char *)"Upper", trans, (char *)"Non-unit", m, k, &c_b1, &t[ + t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)1, (ftnlen)8); /* C := C - W * V */ - if (*n > *k) { + if (*n > *k) { /* C2 := C2 - W * V2 */ - i__1 = *n - *k; - z__1.r = -1., z__1.i = -0.; - zgemm_((char *)"No transpose", (char *)"No transpose", m, &i__1, k, &z__1, - &work[work_offset], ldwork, &v[(*k + 1) * v_dim1 - + 1], ldv, &c_b1, &c__[(*k + 1) * c_dim1 + 1], - ldc, (ftnlen)12, (ftnlen)12); - } + i__1 = *n - *k; + z__1.r = -1., z__1.i = -0.; + zgemm_((char *)"No transpose", (char *)"No transpose", m, &i__1, k, &z__1, + &work[work_offset], ldwork, &v[(*k + 1) * v_dim1 + + 1], ldv, &c_b1, &c__[(*k + 1) * c_dim1 + 1], + ldc, (ftnlen)12, (ftnlen)12); + } /* W := W * V1 */ - ztrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", m, k, &c_b1, - &v[v_offset], ldv, &work[work_offset], ldwork, ( - ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); + ztrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", m, k, &c_b1, + &v[v_offset], ldv, &work[work_offset], ldwork, ( + ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); /* C1 := C1 - W */ - i__1 = *k; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * c_dim1; - i__4 = i__ + j * c_dim1; - i__5 = i__ + j * work_dim1; - z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[ - i__4].i - work[i__5].i; - c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * c_dim1; + i__4 = i__ + j * c_dim1; + i__5 = i__ + j * work_dim1; + z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[ + i__4].i - work[i__5].i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; /* L170: */ - } + } /* L180: */ - } + } - } + } - } else { + } else { /* Let V = ( V1 V2 ) (V2: last K columns) */ /* where V2 is unit lower triangular. */ - if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { + if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { /* Form H * C or H**H * C where C = ( C1 ) */ /* ( C2 ) */ @@ -788,76 +788,76 @@ f"> */ /* W := C2**H */ - i__1 = *k; - for (j = 1; j <= i__1; ++j) { - zcopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j * - work_dim1 + 1], &c__1); - zlacgv_(n, &work[j * work_dim1 + 1], &c__1); + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + zcopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j * + work_dim1 + 1], &c__1); + zlacgv_(n, &work[j * work_dim1 + 1], &c__1); /* L190: */ - } + } /* W := W * V2**H */ - ztrmm_((char *)"Right", (char *)"Lower", (char *)"Conjugate transpose", (char *)"Unit", n, k, - &c_b1, &v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[ - work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen) - 19, (ftnlen)4); - if (*m > *k) { + ztrmm_((char *)"Right", (char *)"Lower", (char *)"Conjugate transpose", (char *)"Unit", n, k, + &c_b1, &v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[ + work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen) + 19, (ftnlen)4); + if (*m > *k) { /* W := W + C1**H * V1**H */ - i__1 = *m - *k; - zgemm_((char *)"Conjugate transpose", (char *)"Conjugate transpose", n, k, - &i__1, &c_b1, &c__[c_offset], ldc, &v[v_offset], - ldv, &c_b1, &work[work_offset], ldwork, (ftnlen) - 19, (ftnlen)19); - } + i__1 = *m - *k; + zgemm_((char *)"Conjugate transpose", (char *)"Conjugate transpose", n, k, + &i__1, &c_b1, &c__[c_offset], ldc, &v[v_offset], + ldv, &c_b1, &work[work_offset], ldwork, (ftnlen) + 19, (ftnlen)19); + } /* W := W * T**H or W * T */ - ztrmm_((char *)"Right", (char *)"Lower", transt, (char *)"Non-unit", n, k, &c_b1, &t[ - t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, - (ftnlen)5, (ftnlen)1, (ftnlen)8); + ztrmm_((char *)"Right", (char *)"Lower", transt, (char *)"Non-unit", n, k, &c_b1, &t[ + t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)1, (ftnlen)8); /* C := C - V**H * W**H */ - if (*m > *k) { + if (*m > *k) { /* C1 := C1 - V1**H * W**H */ - i__1 = *m - *k; - z__1.r = -1., z__1.i = -0.; - zgemm_((char *)"Conjugate transpose", (char *)"Conjugate transpose", & - i__1, n, k, &z__1, &v[v_offset], ldv, &work[ - work_offset], ldwork, &c_b1, &c__[c_offset], ldc, - (ftnlen)19, (ftnlen)19); - } + i__1 = *m - *k; + z__1.r = -1., z__1.i = -0.; + zgemm_((char *)"Conjugate transpose", (char *)"Conjugate transpose", & + i__1, n, k, &z__1, &v[v_offset], ldv, &work[ + work_offset], ldwork, &c_b1, &c__[c_offset], ldc, + (ftnlen)19, (ftnlen)19); + } /* W := W * V2 */ - ztrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", n, k, &c_b1, - &v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[ - work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen) - 12, (ftnlen)4); + ztrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", n, k, &c_b1, + &v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[ + work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen) + 12, (ftnlen)4); /* C2 := C2 - W**H */ - i__1 = *k; - for (j = 1; j <= i__1; ++j) { - i__2 = *n; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = *m - *k + j + i__ * c_dim1; - i__4 = *m - *k + j + i__ * c_dim1; - d_cnjg(&z__2, &work[i__ + j * work_dim1]); - z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i - - z__2.i; - c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = *m - *k + j + i__ * c_dim1; + i__4 = *m - *k + j + i__ * c_dim1; + d_cnjg(&z__2, &work[i__ + j * work_dim1]); + z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i - + z__2.i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; /* L200: */ - } + } /* L210: */ - } + } - } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { /* Form C * H or C * H**H where C = ( C1 C2 ) */ @@ -865,77 +865,77 @@ f"> */ /* W := C2 */ - i__1 = *k; - for (j = 1; j <= i__1; ++j) { - zcopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[ - j * work_dim1 + 1], &c__1); + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + zcopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[ + j * work_dim1 + 1], &c__1); /* L220: */ - } + } /* W := W * V2**H */ - ztrmm_((char *)"Right", (char *)"Lower", (char *)"Conjugate transpose", (char *)"Unit", m, k, - &c_b1, &v[(*n - *k + 1) * v_dim1 + 1], ldv, &work[ - work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen) - 19, (ftnlen)4); - if (*n > *k) { + ztrmm_((char *)"Right", (char *)"Lower", (char *)"Conjugate transpose", (char *)"Unit", m, k, + &c_b1, &v[(*n - *k + 1) * v_dim1 + 1], ldv, &work[ + work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen) + 19, (ftnlen)4); + if (*n > *k) { /* W := W + C1 * V1**H */ - i__1 = *n - *k; - zgemm_((char *)"No transpose", (char *)"Conjugate transpose", m, k, &i__1, - &c_b1, &c__[c_offset], ldc, &v[v_offset], ldv, & - c_b1, &work[work_offset], ldwork, (ftnlen)12, ( - ftnlen)19); - } + i__1 = *n - *k; + zgemm_((char *)"No transpose", (char *)"Conjugate transpose", m, k, &i__1, + &c_b1, &c__[c_offset], ldc, &v[v_offset], ldv, & + c_b1, &work[work_offset], ldwork, (ftnlen)12, ( + ftnlen)19); + } /* W := W * T or W * T**H */ - ztrmm_((char *)"Right", (char *)"Lower", trans, (char *)"Non-unit", m, k, &c_b1, &t[ - t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, - (ftnlen)5, (ftnlen)1, (ftnlen)8); + ztrmm_((char *)"Right", (char *)"Lower", trans, (char *)"Non-unit", m, k, &c_b1, &t[ + t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)1, (ftnlen)8); /* C := C - W * V */ - if (*n > *k) { + if (*n > *k) { /* C1 := C1 - W * V1 */ - i__1 = *n - *k; - z__1.r = -1., z__1.i = -0.; - zgemm_((char *)"No transpose", (char *)"No transpose", m, &i__1, k, &z__1, - &work[work_offset], ldwork, &v[v_offset], ldv, & - c_b1, &c__[c_offset], ldc, (ftnlen)12, (ftnlen)12) - ; - } + i__1 = *n - *k; + z__1.r = -1., z__1.i = -0.; + zgemm_((char *)"No transpose", (char *)"No transpose", m, &i__1, k, &z__1, + &work[work_offset], ldwork, &v[v_offset], ldv, & + c_b1, &c__[c_offset], ldc, (ftnlen)12, (ftnlen)12) + ; + } /* W := W * V2 */ - ztrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", m, k, &c_b1, - &v[(*n - *k + 1) * v_dim1 + 1], ldv, &work[ - work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen) - 12, (ftnlen)4); + ztrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", m, k, &c_b1, + &v[(*n - *k + 1) * v_dim1 + 1], ldv, &work[ + work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen) + 12, (ftnlen)4); /* C1 := C1 - W */ - i__1 = *k; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + (*n - *k + j) * c_dim1; - i__4 = i__ + (*n - *k + j) * c_dim1; - i__5 = i__ + j * work_dim1; - z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[ - i__4].i - work[i__5].i; - c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; + i__1 = *k; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + (*n - *k + j) * c_dim1; + i__4 = i__ + (*n - *k + j) * c_dim1; + i__5 = i__ + j * work_dim1; + z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[ + i__4].i - work[i__5].i; + c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; /* L230: */ - } + } /* L240: */ - } + } - } + } - } + } } return 0; @@ -945,5 +945,5 @@ f"> */ } /* zlarfb_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zlarfg.cpp b/lib/linalg/zlarfg.cpp index e3d58be892..71e2add68c 100644 --- a/lib/linalg/zlarfg.cpp +++ b/lib/linalg/zlarfg.cpp @@ -1,13 +1,13 @@ /* fortran/zlarfg.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -127,7 +127,7 @@ f"> */ /* ===================================================================== */ /* Subroutine */ int zlarfg_(integer *n, doublecomplex *alpha, doublecomplex * - x, integer *incx, doublecomplex *tau) + x, integer *incx, doublecomplex *tau) { /* System generated locals */ integer i__1; @@ -140,18 +140,18 @@ f"> */ /* Local variables */ integer j, knt; doublereal beta, alphi, alphr; - extern /* Subroutine */ int zscal_(integer *, doublecomplex *, - doublecomplex *, integer *); + extern /* Subroutine */ int zscal_(integer *, doublecomplex *, + doublecomplex *, integer *); doublereal xnorm; - extern doublereal dlapy3_(doublereal *, doublereal *, doublereal *), - dznrm2_(integer *, doublecomplex *, integer *), dlamch_(char *, - ftnlen); + extern doublereal dlapy3_(doublereal *, doublereal *, doublereal *), + dznrm2_(integer *, doublecomplex *, integer *), dlamch_(char *, + ftnlen); doublereal safmin; - extern /* Subroutine */ int zdscal_(integer *, doublereal *, - doublecomplex *, integer *); + extern /* Subroutine */ int zdscal_(integer *, doublereal *, + doublecomplex *, integer *); doublereal rsafmn; extern /* Double Complex */ VOID zladiv_(doublecomplex *, doublecomplex *, - doublecomplex *); + doublecomplex *); /* -- LAPACK auxiliary routine -- */ @@ -182,8 +182,8 @@ f"> */ /* Function Body */ if (*n <= 0) { - tau->r = 0., tau->i = 0.; - return 0; + tau->r = 0., tau->i = 0.; + return 0; } i__1 = *n - 1; @@ -195,59 +195,59 @@ f"> */ /* H = I */ - tau->r = 0., tau->i = 0.; + tau->r = 0., tau->i = 0.; } else { /* general case */ - d__1 = dlapy3_(&alphr, &alphi, &xnorm); - beta = -d_sign(&d__1, &alphr); - safmin = dlamch_((char *)"S", (ftnlen)1) / dlamch_((char *)"E", (ftnlen)1); - rsafmn = 1. / safmin; + d__1 = dlapy3_(&alphr, &alphi, &xnorm); + beta = -d_sign(&d__1, &alphr); + safmin = dlamch_((char *)"S", (ftnlen)1) / dlamch_((char *)"E", (ftnlen)1); + rsafmn = 1. / safmin; - knt = 0; - if (abs(beta) < safmin) { + knt = 0; + if (abs(beta) < safmin) { /* XNORM, BETA may be inaccurate; scale X and recompute them */ L10: - ++knt; - i__1 = *n - 1; - zdscal_(&i__1, &rsafmn, &x[1], incx); - beta *= rsafmn; - alphi *= rsafmn; - alphr *= rsafmn; - if (abs(beta) < safmin && knt < 20) { - goto L10; - } + ++knt; + i__1 = *n - 1; + zdscal_(&i__1, &rsafmn, &x[1], incx); + beta *= rsafmn; + alphi *= rsafmn; + alphr *= rsafmn; + if (abs(beta) < safmin && knt < 20) { + goto L10; + } /* New BETA is at most 1, at least SAFMIN */ - i__1 = *n - 1; - xnorm = dznrm2_(&i__1, &x[1], incx); - z__1.r = alphr, z__1.i = alphi; - alpha->r = z__1.r, alpha->i = z__1.i; - d__1 = dlapy3_(&alphr, &alphi, &xnorm); - beta = -d_sign(&d__1, &alphr); - } - d__1 = (beta - alphr) / beta; - d__2 = -alphi / beta; - z__1.r = d__1, z__1.i = d__2; - tau->r = z__1.r, tau->i = z__1.i; - z__2.r = alpha->r - beta, z__2.i = alpha->i; - zladiv_(&z__1, &c_b5, &z__2); - alpha->r = z__1.r, alpha->i = z__1.i; - i__1 = *n - 1; - zscal_(&i__1, alpha, &x[1], incx); + i__1 = *n - 1; + xnorm = dznrm2_(&i__1, &x[1], incx); + z__1.r = alphr, z__1.i = alphi; + alpha->r = z__1.r, alpha->i = z__1.i; + d__1 = dlapy3_(&alphr, &alphi, &xnorm); + beta = -d_sign(&d__1, &alphr); + } + d__1 = (beta - alphr) / beta; + d__2 = -alphi / beta; + z__1.r = d__1, z__1.i = d__2; + tau->r = z__1.r, tau->i = z__1.i; + z__2.r = alpha->r - beta, z__2.i = alpha->i; + zladiv_(&z__1, &c_b5, &z__2); + alpha->r = z__1.r, alpha->i = z__1.i; + i__1 = *n - 1; + zscal_(&i__1, alpha, &x[1], incx); /* If ALPHA is subnormal, it may lose relative accuracy */ - i__1 = knt; - for (j = 1; j <= i__1; ++j) { - beta *= safmin; + i__1 = knt; + for (j = 1; j <= i__1; ++j) { + beta *= safmin; /* L20: */ - } - alpha->r = beta, alpha->i = 0.; + } + alpha->r = beta, alpha->i = 0.; } return 0; @@ -257,5 +257,5 @@ L10: } /* zlarfg_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zlarft.cpp b/lib/linalg/zlarft.cpp index d907f6792d..ad5e46b910 100644 --- a/lib/linalg/zlarft.cpp +++ b/lib/linalg/zlarft.cpp @@ -1,13 +1,13 @@ /* static/zlarft.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -185,8 +185,8 @@ f"> */ /* > */ /* ===================================================================== */ /* Subroutine */ int zlarft_(char *direct, char *storev, integer *n, integer * - k, doublecomplex *v, integer *ldv, doublecomplex *tau, doublecomplex * - t, integer *ldt, ftnlen direct_len, ftnlen storev_len) + k, doublecomplex *v, integer *ldv, doublecomplex *tau, doublecomplex * + t, integer *ldt, ftnlen direct_len, ftnlen storev_len) { /* System generated locals */ integer t_dim1, t_offset, v_dim1, v_offset, i__1, i__2, i__3, i__4, i__5; @@ -198,16 +198,16 @@ f"> */ /* Local variables */ integer i__, j, prevlastv; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *, - integer *, doublecomplex *, doublecomplex *, integer *, - doublecomplex *, integer *, doublecomplex *, doublecomplex *, - integer *, ftnlen, ftnlen), zgemv_(char *, integer *, integer *, - doublecomplex *, doublecomplex *, integer *, doublecomplex *, - integer *, doublecomplex *, doublecomplex *, integer *, ftnlen); + extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *, + integer *, doublecomplex *, doublecomplex *, integer *, + doublecomplex *, integer *, doublecomplex *, doublecomplex *, + integer *, ftnlen, ftnlen), zgemv_(char *, integer *, integer *, + doublecomplex *, doublecomplex *, integer *, doublecomplex *, + integer *, doublecomplex *, doublecomplex *, integer *, ftnlen); integer lastv; - extern /* Subroutine */ int ztrmv_(char *, char *, char *, integer *, - doublecomplex *, integer *, doublecomplex *, integer *, ftnlen, - ftnlen, ftnlen); + extern /* Subroutine */ int ztrmv_(char *, char *, char *, integer *, + doublecomplex *, integer *, doublecomplex *, integer *, ftnlen, + ftnlen, ftnlen); /* -- LAPACK auxiliary routine -- */ @@ -244,215 +244,215 @@ f"> */ /* Function Body */ if (*n == 0) { - return 0; + return 0; } if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { - prevlastv = *n; - i__1 = *k; - for (i__ = 1; i__ <= i__1; ++i__) { - prevlastv = max(prevlastv,i__); - i__2 = i__; - if (tau[i__2].r == 0. && tau[i__2].i == 0.) { + prevlastv = *n; + i__1 = *k; + for (i__ = 1; i__ <= i__1; ++i__) { + prevlastv = max(prevlastv,i__); + i__2 = i__; + if (tau[i__2].r == 0. && tau[i__2].i == 0.) { /* H(i) = I */ - i__2 = i__; - for (j = 1; j <= i__2; ++j) { - i__3 = j + i__ * t_dim1; - t[i__3].r = 0., t[i__3].i = 0.; - } - } else { + i__2 = i__; + for (j = 1; j <= i__2; ++j) { + i__3 = j + i__ * t_dim1; + t[i__3].r = 0., t[i__3].i = 0.; + } + } else { /* general case */ - if (lsame_(storev, (char *)"C", (ftnlen)1, (ftnlen)1)) { + if (lsame_(storev, (char *)"C", (ftnlen)1, (ftnlen)1)) { /* Skip any trailing zeros. */ - i__2 = i__ + 1; - for (lastv = *n; lastv >= i__2; --lastv) { - i__3 = lastv + i__ * v_dim1; - if (v[i__3].r != 0. || v[i__3].i != 0.) { - goto L220; - } - } + i__2 = i__ + 1; + for (lastv = *n; lastv >= i__2; --lastv) { + i__3 = lastv + i__ * v_dim1; + if (v[i__3].r != 0. || v[i__3].i != 0.) { + goto L220; + } + } L220: - i__2 = i__ - 1; - for (j = 1; j <= i__2; ++j) { - i__3 = j + i__ * t_dim1; - i__4 = i__; - z__2.r = -tau[i__4].r, z__2.i = -tau[i__4].i; - d_cnjg(&z__3, &v[i__ + j * v_dim1]); - z__1.r = z__2.r * z__3.r - z__2.i * z__3.i, z__1.i = - z__2.r * z__3.i + z__2.i * z__3.r; - t[i__3].r = z__1.r, t[i__3].i = z__1.i; - } - j = min(lastv,prevlastv); + i__2 = i__ - 1; + for (j = 1; j <= i__2; ++j) { + i__3 = j + i__ * t_dim1; + i__4 = i__; + z__2.r = -tau[i__4].r, z__2.i = -tau[i__4].i; + d_cnjg(&z__3, &v[i__ + j * v_dim1]); + z__1.r = z__2.r * z__3.r - z__2.i * z__3.i, z__1.i = + z__2.r * z__3.i + z__2.i * z__3.r; + t[i__3].r = z__1.r, t[i__3].i = z__1.i; + } + j = min(lastv,prevlastv); /* T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**H * V(i:j,i) */ - i__2 = j - i__; - i__3 = i__ - 1; - i__4 = i__; - z__1.r = -tau[i__4].r, z__1.i = -tau[i__4].i; - zgemv_((char *)"Conjugate transpose", &i__2, &i__3, &z__1, &v[i__ - + 1 + v_dim1], ldv, &v[i__ + 1 + i__ * v_dim1], & - c__1, &c_b1, &t[i__ * t_dim1 + 1], &c__1, (ftnlen) - 19); - } else { + i__2 = j - i__; + i__3 = i__ - 1; + i__4 = i__; + z__1.r = -tau[i__4].r, z__1.i = -tau[i__4].i; + zgemv_((char *)"Conjugate transpose", &i__2, &i__3, &z__1, &v[i__ + + 1 + v_dim1], ldv, &v[i__ + 1 + i__ * v_dim1], & + c__1, &c_b1, &t[i__ * t_dim1 + 1], &c__1, (ftnlen) + 19); + } else { /* Skip any trailing zeros. */ - i__2 = i__ + 1; - for (lastv = *n; lastv >= i__2; --lastv) { - i__3 = i__ + lastv * v_dim1; - if (v[i__3].r != 0. || v[i__3].i != 0.) { - goto L236; - } - } + i__2 = i__ + 1; + for (lastv = *n; lastv >= i__2; --lastv) { + i__3 = i__ + lastv * v_dim1; + if (v[i__3].r != 0. || v[i__3].i != 0.) { + goto L236; + } + } L236: - i__2 = i__ - 1; - for (j = 1; j <= i__2; ++j) { - i__3 = j + i__ * t_dim1; - i__4 = i__; - z__2.r = -tau[i__4].r, z__2.i = -tau[i__4].i; - i__5 = j + i__ * v_dim1; - z__1.r = z__2.r * v[i__5].r - z__2.i * v[i__5].i, - z__1.i = z__2.r * v[i__5].i + z__2.i * v[i__5] - .r; - t[i__3].r = z__1.r, t[i__3].i = z__1.i; - } - j = min(lastv,prevlastv); + i__2 = i__ - 1; + for (j = 1; j <= i__2; ++j) { + i__3 = j + i__ * t_dim1; + i__4 = i__; + z__2.r = -tau[i__4].r, z__2.i = -tau[i__4].i; + i__5 = j + i__ * v_dim1; + z__1.r = z__2.r * v[i__5].r - z__2.i * v[i__5].i, + z__1.i = z__2.r * v[i__5].i + z__2.i * v[i__5] + .r; + t[i__3].r = z__1.r, t[i__3].i = z__1.i; + } + j = min(lastv,prevlastv); /* T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**H */ - i__2 = i__ - 1; - i__3 = j - i__; - i__4 = i__; - z__1.r = -tau[i__4].r, z__1.i = -tau[i__4].i; - zgemm_((char *)"N", (char *)"C", &i__2, &c__1, &i__3, &z__1, &v[(i__ + 1) - * v_dim1 + 1], ldv, &v[i__ + (i__ + 1) * v_dim1], - ldv, &c_b1, &t[i__ * t_dim1 + 1], ldt, (ftnlen)1, - (ftnlen)1); - } + i__2 = i__ - 1; + i__3 = j - i__; + i__4 = i__; + z__1.r = -tau[i__4].r, z__1.i = -tau[i__4].i; + zgemm_((char *)"N", (char *)"C", &i__2, &c__1, &i__3, &z__1, &v[(i__ + 1) + * v_dim1 + 1], ldv, &v[i__ + (i__ + 1) * v_dim1], + ldv, &c_b1, &t[i__ * t_dim1 + 1], ldt, (ftnlen)1, + (ftnlen)1); + } /* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) */ - i__2 = i__ - 1; - ztrmv_((char *)"Upper", (char *)"No transpose", (char *)"Non-unit", &i__2, &t[ - t_offset], ldt, &t[i__ * t_dim1 + 1], &c__1, (ftnlen) - 5, (ftnlen)12, (ftnlen)8); - i__2 = i__ + i__ * t_dim1; - i__3 = i__; - t[i__2].r = tau[i__3].r, t[i__2].i = tau[i__3].i; - if (i__ > 1) { - prevlastv = max(prevlastv,lastv); - } else { - prevlastv = lastv; - } - } - } + i__2 = i__ - 1; + ztrmv_((char *)"Upper", (char *)"No transpose", (char *)"Non-unit", &i__2, &t[ + t_offset], ldt, &t[i__ * t_dim1 + 1], &c__1, (ftnlen) + 5, (ftnlen)12, (ftnlen)8); + i__2 = i__ + i__ * t_dim1; + i__3 = i__; + t[i__2].r = tau[i__3].r, t[i__2].i = tau[i__3].i; + if (i__ > 1) { + prevlastv = max(prevlastv,lastv); + } else { + prevlastv = lastv; + } + } + } } else { - prevlastv = 1; - for (i__ = *k; i__ >= 1; --i__) { - i__1 = i__; - if (tau[i__1].r == 0. && tau[i__1].i == 0.) { + prevlastv = 1; + for (i__ = *k; i__ >= 1; --i__) { + i__1 = i__; + if (tau[i__1].r == 0. && tau[i__1].i == 0.) { /* H(i) = I */ - i__1 = *k; - for (j = i__; j <= i__1; ++j) { - i__2 = j + i__ * t_dim1; - t[i__2].r = 0., t[i__2].i = 0.; - } - } else { + i__1 = *k; + for (j = i__; j <= i__1; ++j) { + i__2 = j + i__ * t_dim1; + t[i__2].r = 0., t[i__2].i = 0.; + } + } else { /* general case */ - if (i__ < *k) { - if (lsame_(storev, (char *)"C", (ftnlen)1, (ftnlen)1)) { + if (i__ < *k) { + if (lsame_(storev, (char *)"C", (ftnlen)1, (ftnlen)1)) { /* Skip any leading zeros. */ - i__1 = i__ - 1; - for (lastv = 1; lastv <= i__1; ++lastv) { - i__2 = lastv + i__ * v_dim1; - if (v[i__2].r != 0. || v[i__2].i != 0.) { - goto L281; - } - } + i__1 = i__ - 1; + for (lastv = 1; lastv <= i__1; ++lastv) { + i__2 = lastv + i__ * v_dim1; + if (v[i__2].r != 0. || v[i__2].i != 0.) { + goto L281; + } + } L281: - i__1 = *k; - for (j = i__ + 1; j <= i__1; ++j) { - i__2 = j + i__ * t_dim1; - i__3 = i__; - z__2.r = -tau[i__3].r, z__2.i = -tau[i__3].i; - d_cnjg(&z__3, &v[*n - *k + i__ + j * v_dim1]); - z__1.r = z__2.r * z__3.r - z__2.i * z__3.i, - z__1.i = z__2.r * z__3.i + z__2.i * - z__3.r; - t[i__2].r = z__1.r, t[i__2].i = z__1.i; - } - j = max(lastv,prevlastv); + i__1 = *k; + for (j = i__ + 1; j <= i__1; ++j) { + i__2 = j + i__ * t_dim1; + i__3 = i__; + z__2.r = -tau[i__3].r, z__2.i = -tau[i__3].i; + d_cnjg(&z__3, &v[*n - *k + i__ + j * v_dim1]); + z__1.r = z__2.r * z__3.r - z__2.i * z__3.i, + z__1.i = z__2.r * z__3.i + z__2.i * + z__3.r; + t[i__2].r = z__1.r, t[i__2].i = z__1.i; + } + j = max(lastv,prevlastv); /* T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**H * V(j:n-k+i,i) */ - i__1 = *n - *k + i__ - j; - i__2 = *k - i__; - i__3 = i__; - z__1.r = -tau[i__3].r, z__1.i = -tau[i__3].i; - zgemv_((char *)"Conjugate transpose", &i__1, &i__2, &z__1, &v[ - j + (i__ + 1) * v_dim1], ldv, &v[j + i__ * - v_dim1], &c__1, &c_b1, &t[i__ + 1 + i__ * - t_dim1], &c__1, (ftnlen)19); - } else { + i__1 = *n - *k + i__ - j; + i__2 = *k - i__; + i__3 = i__; + z__1.r = -tau[i__3].r, z__1.i = -tau[i__3].i; + zgemv_((char *)"Conjugate transpose", &i__1, &i__2, &z__1, &v[ + j + (i__ + 1) * v_dim1], ldv, &v[j + i__ * + v_dim1], &c__1, &c_b1, &t[i__ + 1 + i__ * + t_dim1], &c__1, (ftnlen)19); + } else { /* Skip any leading zeros. */ - i__1 = i__ - 1; - for (lastv = 1; lastv <= i__1; ++lastv) { - i__2 = i__ + lastv * v_dim1; - if (v[i__2].r != 0. || v[i__2].i != 0.) { - goto L297; - } - } + i__1 = i__ - 1; + for (lastv = 1; lastv <= i__1; ++lastv) { + i__2 = i__ + lastv * v_dim1; + if (v[i__2].r != 0. || v[i__2].i != 0.) { + goto L297; + } + } L297: - i__1 = *k; - for (j = i__ + 1; j <= i__1; ++j) { - i__2 = j + i__ * t_dim1; - i__3 = i__; - z__2.r = -tau[i__3].r, z__2.i = -tau[i__3].i; - i__4 = j + (*n - *k + i__) * v_dim1; - z__1.r = z__2.r * v[i__4].r - z__2.i * v[i__4].i, - z__1.i = z__2.r * v[i__4].i + z__2.i * v[ - i__4].r; - t[i__2].r = z__1.r, t[i__2].i = z__1.i; - } - j = max(lastv,prevlastv); + i__1 = *k; + for (j = i__ + 1; j <= i__1; ++j) { + i__2 = j + i__ * t_dim1; + i__3 = i__; + z__2.r = -tau[i__3].r, z__2.i = -tau[i__3].i; + i__4 = j + (*n - *k + i__) * v_dim1; + z__1.r = z__2.r * v[i__4].r - z__2.i * v[i__4].i, + z__1.i = z__2.r * v[i__4].i + z__2.i * v[ + i__4].r; + t[i__2].r = z__1.r, t[i__2].i = z__1.i; + } + j = max(lastv,prevlastv); /* T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**H */ - i__1 = *k - i__; - i__2 = *n - *k + i__ - j; - i__3 = i__; - z__1.r = -tau[i__3].r, z__1.i = -tau[i__3].i; - zgemm_((char *)"N", (char *)"C", &i__1, &c__1, &i__2, &z__1, &v[i__ + - 1 + j * v_dim1], ldv, &v[i__ + j * v_dim1], - ldv, &c_b1, &t[i__ + 1 + i__ * t_dim1], ldt, ( - ftnlen)1, (ftnlen)1); - } + i__1 = *k - i__; + i__2 = *n - *k + i__ - j; + i__3 = i__; + z__1.r = -tau[i__3].r, z__1.i = -tau[i__3].i; + zgemm_((char *)"N", (char *)"C", &i__1, &c__1, &i__2, &z__1, &v[i__ + + 1 + j * v_dim1], ldv, &v[i__ + j * v_dim1], + ldv, &c_b1, &t[i__ + 1 + i__ * t_dim1], ldt, ( + ftnlen)1, (ftnlen)1); + } /* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) */ - i__1 = *k - i__; - ztrmv_((char *)"Lower", (char *)"No transpose", (char *)"Non-unit", &i__1, &t[i__ - + 1 + (i__ + 1) * t_dim1], ldt, &t[i__ + 1 + i__ * - t_dim1], &c__1, (ftnlen)5, (ftnlen)12, (ftnlen)8) - ; - if (i__ > 1) { - prevlastv = min(prevlastv,lastv); - } else { - prevlastv = lastv; - } - } - i__1 = i__ + i__ * t_dim1; - i__2 = i__; - t[i__1].r = tau[i__2].r, t[i__1].i = tau[i__2].i; - } - } + i__1 = *k - i__; + ztrmv_((char *)"Lower", (char *)"No transpose", (char *)"Non-unit", &i__1, &t[i__ + + 1 + (i__ + 1) * t_dim1], ldt, &t[i__ + 1 + i__ * + t_dim1], &c__1, (ftnlen)5, (ftnlen)12, (ftnlen)8) + ; + if (i__ > 1) { + prevlastv = min(prevlastv,lastv); + } else { + prevlastv = lastv; + } + } + i__1 = i__ + i__ * t_dim1; + i__2 = i__; + t[i__1].r = tau[i__2].r, t[i__1].i = tau[i__2].i; + } + } } return 0; @@ -461,5 +461,5 @@ L297: } /* zlarft_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zlascl.cpp b/lib/linalg/zlascl.cpp index 337dd64793..8cea99ddb0 100644 --- a/lib/linalg/zlascl.cpp +++ b/lib/linalg/zlascl.cpp @@ -1,13 +1,13 @@ /* fortran/zlascl.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -159,9 +159,9 @@ f"> */ /* > \ingroup complex16OTHERauxiliary */ /* ===================================================================== */ -/* Subroutine */ int zlascl_(char *type__, integer *kl, integer *ku, - doublereal *cfrom, doublereal *cto, integer *m, integer *n, - doublecomplex *a, integer *lda, integer *info, ftnlen type_len) +/* Subroutine */ int zlascl_(char *type__, integer *kl, integer *ku, + doublereal *cfrom, doublereal *cto, integer *m, integer *n, + doublecomplex *a, integer *lda, integer *info, ftnlen type_len) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; @@ -216,63 +216,63 @@ f"> */ *info = 0; if (lsame_(type__, (char *)"G", (ftnlen)1, (ftnlen)1)) { - itype = 0; + itype = 0; } else if (lsame_(type__, (char *)"L", (ftnlen)1, (ftnlen)1)) { - itype = 1; + itype = 1; } else if (lsame_(type__, (char *)"U", (ftnlen)1, (ftnlen)1)) { - itype = 2; + itype = 2; } else if (lsame_(type__, (char *)"H", (ftnlen)1, (ftnlen)1)) { - itype = 3; + itype = 3; } else if (lsame_(type__, (char *)"B", (ftnlen)1, (ftnlen)1)) { - itype = 4; + itype = 4; } else if (lsame_(type__, (char *)"Q", (ftnlen)1, (ftnlen)1)) { - itype = 5; + itype = 5; } else if (lsame_(type__, (char *)"Z", (ftnlen)1, (ftnlen)1)) { - itype = 6; + itype = 6; } else { - itype = -1; + itype = -1; } if (itype == -1) { - *info = -1; + *info = -1; } else if (*cfrom == 0. || disnan_(cfrom)) { - *info = -4; + *info = -4; } else if (disnan_(cto)) { - *info = -5; + *info = -5; } else if (*m < 0) { - *info = -6; + *info = -6; } else if (*n < 0 || itype == 4 && *n != *m || itype == 5 && *n != *m) { - *info = -7; + *info = -7; } else if (itype <= 3 && *lda < max(1,*m)) { - *info = -9; + *info = -9; } else if (itype >= 4) { /* Computing MAX */ - i__1 = *m - 1; - if (*kl < 0 || *kl > max(i__1,0)) { - *info = -2; - } else /* if(complicated condition) */ { + i__1 = *m - 1; + if (*kl < 0 || *kl > max(i__1,0)) { + *info = -2; + } else /* if(complicated condition) */ { /* Computing MAX */ - i__1 = *n - 1; - if (*ku < 0 || *ku > max(i__1,0) || (itype == 4 || itype == 5) && - *kl != *ku) { - *info = -3; - } else if (itype == 4 && *lda < *kl + 1 || itype == 5 && *lda < * - ku + 1 || itype == 6 && *lda < (*kl << 1) + *ku + 1) { - *info = -9; - } - } + i__1 = *n - 1; + if (*ku < 0 || *ku > max(i__1,0) || (itype == 4 || itype == 5) && + *kl != *ku) { + *info = -3; + } else if (itype == 4 && *lda < *kl + 1 || itype == 5 && *lda < * + ku + 1 || itype == 6 && *lda < (*kl << 1) + *ku + 1) { + *info = -9; + } + } } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"ZLASCL", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"ZLASCL", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*n == 0 || *m == 0) { - return 0; + return 0; } /* Get machine parameters */ @@ -288,175 +288,175 @@ L10: if (cfrom1 == cfromc) { /* CFROMC is an inf. Multiply by a correctly signed zero for */ /* finite CTOC, or a NaN if CTOC is infinite. */ - mul = ctoc / cfromc; - done = TRUE_; - cto1 = ctoc; + mul = ctoc / cfromc; + done = TRUE_; + cto1 = ctoc; } else { - cto1 = ctoc / bignum; - if (cto1 == ctoc) { + cto1 = ctoc / bignum; + if (cto1 == ctoc) { /* CTOC is either 0 or an inf. In both cases, CTOC itself */ /* serves as the correct multiplication factor. */ - mul = ctoc; - done = TRUE_; - cfromc = 1.; - } else if (abs(cfrom1) > abs(ctoc) && ctoc != 0.) { - mul = smlnum; - done = FALSE_; - cfromc = cfrom1; - } else if (abs(cto1) > abs(cfromc)) { - mul = bignum; - done = FALSE_; - ctoc = cto1; - } else { - mul = ctoc / cfromc; - done = TRUE_; - if (mul == 1.) { - return 0; - } - } + mul = ctoc; + done = TRUE_; + cfromc = 1.; + } else if (abs(cfrom1) > abs(ctoc) && ctoc != 0.) { + mul = smlnum; + done = FALSE_; + cfromc = cfrom1; + } else if (abs(cto1) > abs(cfromc)) { + mul = bignum; + done = FALSE_; + ctoc = cto1; + } else { + mul = ctoc / cfromc; + done = TRUE_; + if (mul == 1.) { + return 0; + } + } } if (itype == 0) { /* Full matrix */ - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * a_dim1; - i__4 = i__ + j * a_dim1; - z__1.r = mul * a[i__4].r, z__1.i = mul * a[i__4].i; - a[i__3].r = z__1.r, a[i__3].i = z__1.i; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + i__4 = i__ + j * a_dim1; + z__1.r = mul * a[i__4].r, z__1.i = mul * a[i__4].i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; /* L20: */ - } + } /* L30: */ - } + } } else if (itype == 1) { /* Lower triangular matrix */ - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = j; i__ <= i__2; ++i__) { - i__3 = i__ + j * a_dim1; - i__4 = i__ + j * a_dim1; - z__1.r = mul * a[i__4].r, z__1.i = mul * a[i__4].i; - a[i__3].r = z__1.r, a[i__3].i = z__1.i; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = j; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + i__4 = i__ + j * a_dim1; + z__1.r = mul * a[i__4].r, z__1.i = mul * a[i__4].i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; /* L40: */ - } + } /* L50: */ - } + } } else if (itype == 2) { /* Upper triangular matrix */ - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = min(j,*m); - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * a_dim1; - i__4 = i__ + j * a_dim1; - z__1.r = mul * a[i__4].r, z__1.i = mul * a[i__4].i; - a[i__3].r = z__1.r, a[i__3].i = z__1.i; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = min(j,*m); + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + i__4 = i__ + j * a_dim1; + z__1.r = mul * a[i__4].r, z__1.i = mul * a[i__4].i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; /* L60: */ - } + } /* L70: */ - } + } } else if (itype == 3) { /* Upper Hessenberg matrix */ - i__1 = *n; - for (j = 1; j <= i__1; ++j) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { /* Computing MIN */ - i__3 = j + 1; - i__2 = min(i__3,*m); - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * a_dim1; - i__4 = i__ + j * a_dim1; - z__1.r = mul * a[i__4].r, z__1.i = mul * a[i__4].i; - a[i__3].r = z__1.r, a[i__3].i = z__1.i; + i__3 = j + 1; + i__2 = min(i__3,*m); + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + i__4 = i__ + j * a_dim1; + z__1.r = mul * a[i__4].r, z__1.i = mul * a[i__4].i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; /* L80: */ - } + } /* L90: */ - } + } } else if (itype == 4) { /* Lower half of a symmetric band matrix */ - k3 = *kl + 1; - k4 = *n + 1; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { + k3 = *kl + 1; + k4 = *n + 1; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { /* Computing MIN */ - i__3 = k3, i__4 = k4 - j; - i__2 = min(i__3,i__4); - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * a_dim1; - i__4 = i__ + j * a_dim1; - z__1.r = mul * a[i__4].r, z__1.i = mul * a[i__4].i; - a[i__3].r = z__1.r, a[i__3].i = z__1.i; + i__3 = k3, i__4 = k4 - j; + i__2 = min(i__3,i__4); + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + i__4 = i__ + j * a_dim1; + z__1.r = mul * a[i__4].r, z__1.i = mul * a[i__4].i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; /* L100: */ - } + } /* L110: */ - } + } } else if (itype == 5) { /* Upper half of a symmetric band matrix */ - k1 = *ku + 2; - k3 = *ku + 1; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { + k1 = *ku + 2; + k3 = *ku + 1; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { /* Computing MAX */ - i__2 = k1 - j; - i__3 = k3; - for (i__ = max(i__2,1); i__ <= i__3; ++i__) { - i__2 = i__ + j * a_dim1; - i__4 = i__ + j * a_dim1; - z__1.r = mul * a[i__4].r, z__1.i = mul * a[i__4].i; - a[i__2].r = z__1.r, a[i__2].i = z__1.i; + i__2 = k1 - j; + i__3 = k3; + for (i__ = max(i__2,1); i__ <= i__3; ++i__) { + i__2 = i__ + j * a_dim1; + i__4 = i__ + j * a_dim1; + z__1.r = mul * a[i__4].r, z__1.i = mul * a[i__4].i; + a[i__2].r = z__1.r, a[i__2].i = z__1.i; /* L120: */ - } + } /* L130: */ - } + } } else if (itype == 6) { /* Band matrix */ - k1 = *kl + *ku + 2; - k2 = *kl + 1; - k3 = (*kl << 1) + *ku + 1; - k4 = *kl + *ku + 1 + *m; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { + k1 = *kl + *ku + 2; + k2 = *kl + 1; + k3 = (*kl << 1) + *ku + 1; + k4 = *kl + *ku + 1 + *m; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { /* Computing MAX */ - i__3 = k1 - j; + i__3 = k1 - j; /* Computing MIN */ - i__4 = k3, i__5 = k4 - j; - i__2 = min(i__4,i__5); - for (i__ = max(i__3,k2); i__ <= i__2; ++i__) { - i__3 = i__ + j * a_dim1; - i__4 = i__ + j * a_dim1; - z__1.r = mul * a[i__4].r, z__1.i = mul * a[i__4].i; - a[i__3].r = z__1.r, a[i__3].i = z__1.i; + i__4 = k3, i__5 = k4 - j; + i__2 = min(i__4,i__5); + for (i__ = max(i__3,k2); i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + i__4 = i__ + j * a_dim1; + z__1.r = mul * a[i__4].r, z__1.i = mul * a[i__4].i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; /* L140: */ - } + } /* L150: */ - } + } } if (! done) { - goto L10; + goto L10; } return 0; @@ -466,5 +466,5 @@ L10: } /* zlascl_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zlaset.cpp b/lib/linalg/zlaset.cpp index e402ea02fe..782cc99055 100644 --- a/lib/linalg/zlaset.cpp +++ b/lib/linalg/zlaset.cpp @@ -1,13 +1,13 @@ /* fortran/zlaset.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -123,9 +123,9 @@ f"> */ /* > \ingroup complex16OTHERauxiliary */ /* ===================================================================== */ -/* Subroutine */ int zlaset_(char *uplo, integer *m, integer *n, - doublecomplex *alpha, doublecomplex *beta, doublecomplex *a, integer * - lda, ftnlen uplo_len) +/* Subroutine */ int zlaset_(char *uplo, integer *m, integer *n, + doublecomplex *alpha, doublecomplex *beta, doublecomplex *a, integer * + lda, ftnlen uplo_len) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; @@ -165,68 +165,68 @@ f"> */ /* Set the diagonal to BETA and the strictly upper triangular */ /* part of the array to ALPHA. */ - i__1 = *n; - for (j = 2; j <= i__1; ++j) { + i__1 = *n; + for (j = 2; j <= i__1; ++j) { /* Computing MIN */ - i__3 = j - 1; - i__2 = min(i__3,*m); - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * a_dim1; - a[i__3].r = alpha->r, a[i__3].i = alpha->i; + i__3 = j - 1; + i__2 = min(i__3,*m); + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + a[i__3].r = alpha->r, a[i__3].i = alpha->i; /* L10: */ - } + } /* L20: */ - } - i__1 = min(*n,*m); - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = i__ + i__ * a_dim1; - a[i__2].r = beta->r, a[i__2].i = beta->i; + } + i__1 = min(*n,*m); + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__ + i__ * a_dim1; + a[i__2].r = beta->r, a[i__2].i = beta->i; /* L30: */ - } + } } else if (lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { /* Set the diagonal to BETA and the strictly lower triangular */ /* part of the array to ALPHA. */ - i__1 = min(*m,*n); - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = j + 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * a_dim1; - a[i__3].r = alpha->r, a[i__3].i = alpha->i; + i__1 = min(*m,*n); + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = j + 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + a[i__3].r = alpha->r, a[i__3].i = alpha->i; /* L40: */ - } + } /* L50: */ - } - i__1 = min(*n,*m); - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = i__ + i__ * a_dim1; - a[i__2].r = beta->r, a[i__2].i = beta->i; + } + i__1 = min(*n,*m); + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__ + i__ * a_dim1; + a[i__2].r = beta->r, a[i__2].i = beta->i; /* L60: */ - } + } } else { /* Set the array to BETA on the diagonal and ALPHA on the */ /* offdiagonal. */ - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * a_dim1; - a[i__3].r = alpha->r, a[i__3].i = alpha->i; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + a[i__3].r = alpha->r, a[i__3].i = alpha->i; /* L70: */ - } + } /* L80: */ - } - i__1 = min(*m,*n); - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = i__ + i__ * a_dim1; - a[i__2].r = beta->r, a[i__2].i = beta->i; + } + i__1 = min(*m,*n); + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__ + i__ * a_dim1; + a[i__2].r = beta->r, a[i__2].i = beta->i; /* L90: */ - } + } } return 0; @@ -236,5 +236,5 @@ f"> */ } /* zlaset_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zlasr.cpp b/lib/linalg/zlasr.cpp index 23d68bf82f..51c9797679 100644 --- a/lib/linalg/zlasr.cpp +++ b/lib/linalg/zlasr.cpp @@ -1,13 +1,13 @@ /* fortran/zlasr.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -217,8 +217,8 @@ extern "C" { /* ===================================================================== */ /* Subroutine */ int zlasr_(char *side, char *pivot, char *direct, integer *m, - integer *n, doublereal *c__, doublereal *s, doublecomplex *a, - integer *lda, ftnlen side_len, ftnlen pivot_len, ftnlen direct_len) + integer *n, doublereal *c__, doublereal *s, doublecomplex *a, + integer *lda, ftnlen side_len, ftnlen pivot_len, ftnlen direct_len) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4; @@ -267,420 +267,420 @@ extern "C" { /* Function Body */ info = 0; if (! (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1) || lsame_(side, (char *)"R", ( - ftnlen)1, (ftnlen)1))) { - info = 1; - } else if (! (lsame_(pivot, (char *)"V", (ftnlen)1, (ftnlen)1) || lsame_(pivot, - (char *)"T", (ftnlen)1, (ftnlen)1) || lsame_(pivot, (char *)"B", (ftnlen)1, ( - ftnlen)1))) { - info = 2; - } else if (! (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1) || lsame_(direct, - (char *)"B", (ftnlen)1, (ftnlen)1))) { - info = 3; + ftnlen)1, (ftnlen)1))) { + info = 1; + } else if (! (lsame_(pivot, (char *)"V", (ftnlen)1, (ftnlen)1) || lsame_(pivot, + (char *)"T", (ftnlen)1, (ftnlen)1) || lsame_(pivot, (char *)"B", (ftnlen)1, ( + ftnlen)1))) { + info = 2; + } else if (! (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1) || lsame_(direct, + (char *)"B", (ftnlen)1, (ftnlen)1))) { + info = 3; } else if (*m < 0) { - info = 4; + info = 4; } else if (*n < 0) { - info = 5; + info = 5; } else if (*lda < max(1,*m)) { - info = 9; + info = 9; } if (info != 0) { - xerbla_((char *)"ZLASR ", &info, (ftnlen)6); - return 0; + xerbla_((char *)"ZLASR ", &info, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*m == 0 || *n == 0) { - return 0; + return 0; } if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { /* Form P * A */ - if (lsame_(pivot, (char *)"V", (ftnlen)1, (ftnlen)1)) { - if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { - i__1 = *m - 1; - for (j = 1; j <= i__1; ++j) { - ctemp = c__[j]; - stemp = s[j]; - if (ctemp != 1. || stemp != 0.) { - i__2 = *n; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = j + 1 + i__ * a_dim1; - temp.r = a[i__3].r, temp.i = a[i__3].i; - i__3 = j + 1 + i__ * a_dim1; - z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i; - i__4 = j + i__ * a_dim1; - z__3.r = stemp * a[i__4].r, z__3.i = stemp * a[ - i__4].i; - z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - - z__3.i; - a[i__3].r = z__1.r, a[i__3].i = z__1.i; - i__3 = j + i__ * a_dim1; - z__2.r = stemp * temp.r, z__2.i = stemp * temp.i; - i__4 = j + i__ * a_dim1; - z__3.r = ctemp * a[i__4].r, z__3.i = ctemp * a[ - i__4].i; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; - a[i__3].r = z__1.r, a[i__3].i = z__1.i; + if (lsame_(pivot, (char *)"V", (ftnlen)1, (ftnlen)1)) { + if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { + i__1 = *m - 1; + for (j = 1; j <= i__1; ++j) { + ctemp = c__[j]; + stemp = s[j]; + if (ctemp != 1. || stemp != 0.) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = j + 1 + i__ * a_dim1; + temp.r = a[i__3].r, temp.i = a[i__3].i; + i__3 = j + 1 + i__ * a_dim1; + z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i; + i__4 = j + i__ * a_dim1; + z__3.r = stemp * a[i__4].r, z__3.i = stemp * a[ + i__4].i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - + z__3.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; + i__3 = j + i__ * a_dim1; + z__2.r = stemp * temp.r, z__2.i = stemp * temp.i; + i__4 = j + i__ * a_dim1; + z__3.r = ctemp * a[i__4].r, z__3.i = ctemp * a[ + i__4].i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; /* L10: */ - } - } + } + } /* L20: */ - } - } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { - for (j = *m - 1; j >= 1; --j) { - ctemp = c__[j]; - stemp = s[j]; - if (ctemp != 1. || stemp != 0.) { - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = j + 1 + i__ * a_dim1; - temp.r = a[i__2].r, temp.i = a[i__2].i; - i__2 = j + 1 + i__ * a_dim1; - z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i; - i__3 = j + i__ * a_dim1; - z__3.r = stemp * a[i__3].r, z__3.i = stemp * a[ - i__3].i; - z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - - z__3.i; - a[i__2].r = z__1.r, a[i__2].i = z__1.i; - i__2 = j + i__ * a_dim1; - z__2.r = stemp * temp.r, z__2.i = stemp * temp.i; - i__3 = j + i__ * a_dim1; - z__3.r = ctemp * a[i__3].r, z__3.i = ctemp * a[ - i__3].i; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; - a[i__2].r = z__1.r, a[i__2].i = z__1.i; + } + } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { + for (j = *m - 1; j >= 1; --j) { + ctemp = c__[j]; + stemp = s[j]; + if (ctemp != 1. || stemp != 0.) { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = j + 1 + i__ * a_dim1; + temp.r = a[i__2].r, temp.i = a[i__2].i; + i__2 = j + 1 + i__ * a_dim1; + z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i; + i__3 = j + i__ * a_dim1; + z__3.r = stemp * a[i__3].r, z__3.i = stemp * a[ + i__3].i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - + z__3.i; + a[i__2].r = z__1.r, a[i__2].i = z__1.i; + i__2 = j + i__ * a_dim1; + z__2.r = stemp * temp.r, z__2.i = stemp * temp.i; + i__3 = j + i__ * a_dim1; + z__3.r = ctemp * a[i__3].r, z__3.i = ctemp * a[ + i__3].i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + a[i__2].r = z__1.r, a[i__2].i = z__1.i; /* L30: */ - } - } + } + } /* L40: */ - } - } - } else if (lsame_(pivot, (char *)"T", (ftnlen)1, (ftnlen)1)) { - if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { - i__1 = *m; - for (j = 2; j <= i__1; ++j) { - ctemp = c__[j - 1]; - stemp = s[j - 1]; - if (ctemp != 1. || stemp != 0.) { - i__2 = *n; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = j + i__ * a_dim1; - temp.r = a[i__3].r, temp.i = a[i__3].i; - i__3 = j + i__ * a_dim1; - z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i; - i__4 = i__ * a_dim1 + 1; - z__3.r = stemp * a[i__4].r, z__3.i = stemp * a[ - i__4].i; - z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - - z__3.i; - a[i__3].r = z__1.r, a[i__3].i = z__1.i; - i__3 = i__ * a_dim1 + 1; - z__2.r = stemp * temp.r, z__2.i = stemp * temp.i; - i__4 = i__ * a_dim1 + 1; - z__3.r = ctemp * a[i__4].r, z__3.i = ctemp * a[ - i__4].i; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; - a[i__3].r = z__1.r, a[i__3].i = z__1.i; + } + } + } else if (lsame_(pivot, (char *)"T", (ftnlen)1, (ftnlen)1)) { + if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { + i__1 = *m; + for (j = 2; j <= i__1; ++j) { + ctemp = c__[j - 1]; + stemp = s[j - 1]; + if (ctemp != 1. || stemp != 0.) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = j + i__ * a_dim1; + temp.r = a[i__3].r, temp.i = a[i__3].i; + i__3 = j + i__ * a_dim1; + z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i; + i__4 = i__ * a_dim1 + 1; + z__3.r = stemp * a[i__4].r, z__3.i = stemp * a[ + i__4].i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - + z__3.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; + i__3 = i__ * a_dim1 + 1; + z__2.r = stemp * temp.r, z__2.i = stemp * temp.i; + i__4 = i__ * a_dim1 + 1; + z__3.r = ctemp * a[i__4].r, z__3.i = ctemp * a[ + i__4].i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; /* L50: */ - } - } + } + } /* L60: */ - } - } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { - for (j = *m; j >= 2; --j) { - ctemp = c__[j - 1]; - stemp = s[j - 1]; - if (ctemp != 1. || stemp != 0.) { - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = j + i__ * a_dim1; - temp.r = a[i__2].r, temp.i = a[i__2].i; - i__2 = j + i__ * a_dim1; - z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i; - i__3 = i__ * a_dim1 + 1; - z__3.r = stemp * a[i__3].r, z__3.i = stemp * a[ - i__3].i; - z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - - z__3.i; - a[i__2].r = z__1.r, a[i__2].i = z__1.i; - i__2 = i__ * a_dim1 + 1; - z__2.r = stemp * temp.r, z__2.i = stemp * temp.i; - i__3 = i__ * a_dim1 + 1; - z__3.r = ctemp * a[i__3].r, z__3.i = ctemp * a[ - i__3].i; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; - a[i__2].r = z__1.r, a[i__2].i = z__1.i; + } + } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { + for (j = *m; j >= 2; --j) { + ctemp = c__[j - 1]; + stemp = s[j - 1]; + if (ctemp != 1. || stemp != 0.) { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = j + i__ * a_dim1; + temp.r = a[i__2].r, temp.i = a[i__2].i; + i__2 = j + i__ * a_dim1; + z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i; + i__3 = i__ * a_dim1 + 1; + z__3.r = stemp * a[i__3].r, z__3.i = stemp * a[ + i__3].i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - + z__3.i; + a[i__2].r = z__1.r, a[i__2].i = z__1.i; + i__2 = i__ * a_dim1 + 1; + z__2.r = stemp * temp.r, z__2.i = stemp * temp.i; + i__3 = i__ * a_dim1 + 1; + z__3.r = ctemp * a[i__3].r, z__3.i = ctemp * a[ + i__3].i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + a[i__2].r = z__1.r, a[i__2].i = z__1.i; /* L70: */ - } - } + } + } /* L80: */ - } - } - } else if (lsame_(pivot, (char *)"B", (ftnlen)1, (ftnlen)1)) { - if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { - i__1 = *m - 1; - for (j = 1; j <= i__1; ++j) { - ctemp = c__[j]; - stemp = s[j]; - if (ctemp != 1. || stemp != 0.) { - i__2 = *n; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = j + i__ * a_dim1; - temp.r = a[i__3].r, temp.i = a[i__3].i; - i__3 = j + i__ * a_dim1; - i__4 = *m + i__ * a_dim1; - z__2.r = stemp * a[i__4].r, z__2.i = stemp * a[ - i__4].i; - z__3.r = ctemp * temp.r, z__3.i = ctemp * temp.i; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; - a[i__3].r = z__1.r, a[i__3].i = z__1.i; - i__3 = *m + i__ * a_dim1; - i__4 = *m + i__ * a_dim1; - z__2.r = ctemp * a[i__4].r, z__2.i = ctemp * a[ - i__4].i; - z__3.r = stemp * temp.r, z__3.i = stemp * temp.i; - z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - - z__3.i; - a[i__3].r = z__1.r, a[i__3].i = z__1.i; + } + } + } else if (lsame_(pivot, (char *)"B", (ftnlen)1, (ftnlen)1)) { + if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { + i__1 = *m - 1; + for (j = 1; j <= i__1; ++j) { + ctemp = c__[j]; + stemp = s[j]; + if (ctemp != 1. || stemp != 0.) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = j + i__ * a_dim1; + temp.r = a[i__3].r, temp.i = a[i__3].i; + i__3 = j + i__ * a_dim1; + i__4 = *m + i__ * a_dim1; + z__2.r = stemp * a[i__4].r, z__2.i = stemp * a[ + i__4].i; + z__3.r = ctemp * temp.r, z__3.i = ctemp * temp.i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; + i__3 = *m + i__ * a_dim1; + i__4 = *m + i__ * a_dim1; + z__2.r = ctemp * a[i__4].r, z__2.i = ctemp * a[ + i__4].i; + z__3.r = stemp * temp.r, z__3.i = stemp * temp.i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - + z__3.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; /* L90: */ - } - } + } + } /* L100: */ - } - } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { - for (j = *m - 1; j >= 1; --j) { - ctemp = c__[j]; - stemp = s[j]; - if (ctemp != 1. || stemp != 0.) { - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = j + i__ * a_dim1; - temp.r = a[i__2].r, temp.i = a[i__2].i; - i__2 = j + i__ * a_dim1; - i__3 = *m + i__ * a_dim1; - z__2.r = stemp * a[i__3].r, z__2.i = stemp * a[ - i__3].i; - z__3.r = ctemp * temp.r, z__3.i = ctemp * temp.i; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; - a[i__2].r = z__1.r, a[i__2].i = z__1.i; - i__2 = *m + i__ * a_dim1; - i__3 = *m + i__ * a_dim1; - z__2.r = ctemp * a[i__3].r, z__2.i = ctemp * a[ - i__3].i; - z__3.r = stemp * temp.r, z__3.i = stemp * temp.i; - z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - - z__3.i; - a[i__2].r = z__1.r, a[i__2].i = z__1.i; + } + } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { + for (j = *m - 1; j >= 1; --j) { + ctemp = c__[j]; + stemp = s[j]; + if (ctemp != 1. || stemp != 0.) { + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = j + i__ * a_dim1; + temp.r = a[i__2].r, temp.i = a[i__2].i; + i__2 = j + i__ * a_dim1; + i__3 = *m + i__ * a_dim1; + z__2.r = stemp * a[i__3].r, z__2.i = stemp * a[ + i__3].i; + z__3.r = ctemp * temp.r, z__3.i = ctemp * temp.i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + a[i__2].r = z__1.r, a[i__2].i = z__1.i; + i__2 = *m + i__ * a_dim1; + i__3 = *m + i__ * a_dim1; + z__2.r = ctemp * a[i__3].r, z__2.i = ctemp * a[ + i__3].i; + z__3.r = stemp * temp.r, z__3.i = stemp * temp.i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - + z__3.i; + a[i__2].r = z__1.r, a[i__2].i = z__1.i; /* L110: */ - } - } + } + } /* L120: */ - } - } - } + } + } + } } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { /* Form A * P**T */ - if (lsame_(pivot, (char *)"V", (ftnlen)1, (ftnlen)1)) { - if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { - i__1 = *n - 1; - for (j = 1; j <= i__1; ++j) { - ctemp = c__[j]; - stemp = s[j]; - if (ctemp != 1. || stemp != 0.) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + (j + 1) * a_dim1; - temp.r = a[i__3].r, temp.i = a[i__3].i; - i__3 = i__ + (j + 1) * a_dim1; - z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i; - i__4 = i__ + j * a_dim1; - z__3.r = stemp * a[i__4].r, z__3.i = stemp * a[ - i__4].i; - z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - - z__3.i; - a[i__3].r = z__1.r, a[i__3].i = z__1.i; - i__3 = i__ + j * a_dim1; - z__2.r = stemp * temp.r, z__2.i = stemp * temp.i; - i__4 = i__ + j * a_dim1; - z__3.r = ctemp * a[i__4].r, z__3.i = ctemp * a[ - i__4].i; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; - a[i__3].r = z__1.r, a[i__3].i = z__1.i; + if (lsame_(pivot, (char *)"V", (ftnlen)1, (ftnlen)1)) { + if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { + i__1 = *n - 1; + for (j = 1; j <= i__1; ++j) { + ctemp = c__[j]; + stemp = s[j]; + if (ctemp != 1. || stemp != 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + (j + 1) * a_dim1; + temp.r = a[i__3].r, temp.i = a[i__3].i; + i__3 = i__ + (j + 1) * a_dim1; + z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i; + i__4 = i__ + j * a_dim1; + z__3.r = stemp * a[i__4].r, z__3.i = stemp * a[ + i__4].i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - + z__3.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; + i__3 = i__ + j * a_dim1; + z__2.r = stemp * temp.r, z__2.i = stemp * temp.i; + i__4 = i__ + j * a_dim1; + z__3.r = ctemp * a[i__4].r, z__3.i = ctemp * a[ + i__4].i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; /* L130: */ - } - } + } + } /* L140: */ - } - } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { - for (j = *n - 1; j >= 1; --j) { - ctemp = c__[j]; - stemp = s[j]; - if (ctemp != 1. || stemp != 0.) { - i__1 = *m; - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = i__ + (j + 1) * a_dim1; - temp.r = a[i__2].r, temp.i = a[i__2].i; - i__2 = i__ + (j + 1) * a_dim1; - z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i; - i__3 = i__ + j * a_dim1; - z__3.r = stemp * a[i__3].r, z__3.i = stemp * a[ - i__3].i; - z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - - z__3.i; - a[i__2].r = z__1.r, a[i__2].i = z__1.i; - i__2 = i__ + j * a_dim1; - z__2.r = stemp * temp.r, z__2.i = stemp * temp.i; - i__3 = i__ + j * a_dim1; - z__3.r = ctemp * a[i__3].r, z__3.i = ctemp * a[ - i__3].i; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; - a[i__2].r = z__1.r, a[i__2].i = z__1.i; + } + } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { + for (j = *n - 1; j >= 1; --j) { + ctemp = c__[j]; + stemp = s[j]; + if (ctemp != 1. || stemp != 0.) { + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__ + (j + 1) * a_dim1; + temp.r = a[i__2].r, temp.i = a[i__2].i; + i__2 = i__ + (j + 1) * a_dim1; + z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i; + i__3 = i__ + j * a_dim1; + z__3.r = stemp * a[i__3].r, z__3.i = stemp * a[ + i__3].i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - + z__3.i; + a[i__2].r = z__1.r, a[i__2].i = z__1.i; + i__2 = i__ + j * a_dim1; + z__2.r = stemp * temp.r, z__2.i = stemp * temp.i; + i__3 = i__ + j * a_dim1; + z__3.r = ctemp * a[i__3].r, z__3.i = ctemp * a[ + i__3].i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + a[i__2].r = z__1.r, a[i__2].i = z__1.i; /* L150: */ - } - } + } + } /* L160: */ - } - } - } else if (lsame_(pivot, (char *)"T", (ftnlen)1, (ftnlen)1)) { - if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { - i__1 = *n; - for (j = 2; j <= i__1; ++j) { - ctemp = c__[j - 1]; - stemp = s[j - 1]; - if (ctemp != 1. || stemp != 0.) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * a_dim1; - temp.r = a[i__3].r, temp.i = a[i__3].i; - i__3 = i__ + j * a_dim1; - z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i; - i__4 = i__ + a_dim1; - z__3.r = stemp * a[i__4].r, z__3.i = stemp * a[ - i__4].i; - z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - - z__3.i; - a[i__3].r = z__1.r, a[i__3].i = z__1.i; - i__3 = i__ + a_dim1; - z__2.r = stemp * temp.r, z__2.i = stemp * temp.i; - i__4 = i__ + a_dim1; - z__3.r = ctemp * a[i__4].r, z__3.i = ctemp * a[ - i__4].i; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; - a[i__3].r = z__1.r, a[i__3].i = z__1.i; + } + } + } else if (lsame_(pivot, (char *)"T", (ftnlen)1, (ftnlen)1)) { + if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { + i__1 = *n; + for (j = 2; j <= i__1; ++j) { + ctemp = c__[j - 1]; + stemp = s[j - 1]; + if (ctemp != 1. || stemp != 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + temp.r = a[i__3].r, temp.i = a[i__3].i; + i__3 = i__ + j * a_dim1; + z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i; + i__4 = i__ + a_dim1; + z__3.r = stemp * a[i__4].r, z__3.i = stemp * a[ + i__4].i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - + z__3.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; + i__3 = i__ + a_dim1; + z__2.r = stemp * temp.r, z__2.i = stemp * temp.i; + i__4 = i__ + a_dim1; + z__3.r = ctemp * a[i__4].r, z__3.i = ctemp * a[ + i__4].i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; /* L170: */ - } - } + } + } /* L180: */ - } - } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { - for (j = *n; j >= 2; --j) { - ctemp = c__[j - 1]; - stemp = s[j - 1]; - if (ctemp != 1. || stemp != 0.) { - i__1 = *m; - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = i__ + j * a_dim1; - temp.r = a[i__2].r, temp.i = a[i__2].i; - i__2 = i__ + j * a_dim1; - z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i; - i__3 = i__ + a_dim1; - z__3.r = stemp * a[i__3].r, z__3.i = stemp * a[ - i__3].i; - z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - - z__3.i; - a[i__2].r = z__1.r, a[i__2].i = z__1.i; - i__2 = i__ + a_dim1; - z__2.r = stemp * temp.r, z__2.i = stemp * temp.i; - i__3 = i__ + a_dim1; - z__3.r = ctemp * a[i__3].r, z__3.i = ctemp * a[ - i__3].i; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; - a[i__2].r = z__1.r, a[i__2].i = z__1.i; + } + } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { + for (j = *n; j >= 2; --j) { + ctemp = c__[j - 1]; + stemp = s[j - 1]; + if (ctemp != 1. || stemp != 0.) { + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__ + j * a_dim1; + temp.r = a[i__2].r, temp.i = a[i__2].i; + i__2 = i__ + j * a_dim1; + z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i; + i__3 = i__ + a_dim1; + z__3.r = stemp * a[i__3].r, z__3.i = stemp * a[ + i__3].i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - + z__3.i; + a[i__2].r = z__1.r, a[i__2].i = z__1.i; + i__2 = i__ + a_dim1; + z__2.r = stemp * temp.r, z__2.i = stemp * temp.i; + i__3 = i__ + a_dim1; + z__3.r = ctemp * a[i__3].r, z__3.i = ctemp * a[ + i__3].i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + a[i__2].r = z__1.r, a[i__2].i = z__1.i; /* L190: */ - } - } + } + } /* L200: */ - } - } - } else if (lsame_(pivot, (char *)"B", (ftnlen)1, (ftnlen)1)) { - if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { - i__1 = *n - 1; - for (j = 1; j <= i__1; ++j) { - ctemp = c__[j]; - stemp = s[j]; - if (ctemp != 1. || stemp != 0.) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * a_dim1; - temp.r = a[i__3].r, temp.i = a[i__3].i; - i__3 = i__ + j * a_dim1; - i__4 = i__ + *n * a_dim1; - z__2.r = stemp * a[i__4].r, z__2.i = stemp * a[ - i__4].i; - z__3.r = ctemp * temp.r, z__3.i = ctemp * temp.i; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; - a[i__3].r = z__1.r, a[i__3].i = z__1.i; - i__3 = i__ + *n * a_dim1; - i__4 = i__ + *n * a_dim1; - z__2.r = ctemp * a[i__4].r, z__2.i = ctemp * a[ - i__4].i; - z__3.r = stemp * temp.r, z__3.i = stemp * temp.i; - z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - - z__3.i; - a[i__3].r = z__1.r, a[i__3].i = z__1.i; + } + } + } else if (lsame_(pivot, (char *)"B", (ftnlen)1, (ftnlen)1)) { + if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { + i__1 = *n - 1; + for (j = 1; j <= i__1; ++j) { + ctemp = c__[j]; + stemp = s[j]; + if (ctemp != 1. || stemp != 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + temp.r = a[i__3].r, temp.i = a[i__3].i; + i__3 = i__ + j * a_dim1; + i__4 = i__ + *n * a_dim1; + z__2.r = stemp * a[i__4].r, z__2.i = stemp * a[ + i__4].i; + z__3.r = ctemp * temp.r, z__3.i = ctemp * temp.i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; + i__3 = i__ + *n * a_dim1; + i__4 = i__ + *n * a_dim1; + z__2.r = ctemp * a[i__4].r, z__2.i = ctemp * a[ + i__4].i; + z__3.r = stemp * temp.r, z__3.i = stemp * temp.i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - + z__3.i; + a[i__3].r = z__1.r, a[i__3].i = z__1.i; /* L210: */ - } - } + } + } /* L220: */ - } - } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { - for (j = *n - 1; j >= 1; --j) { - ctemp = c__[j]; - stemp = s[j]; - if (ctemp != 1. || stemp != 0.) { - i__1 = *m; - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = i__ + j * a_dim1; - temp.r = a[i__2].r, temp.i = a[i__2].i; - i__2 = i__ + j * a_dim1; - i__3 = i__ + *n * a_dim1; - z__2.r = stemp * a[i__3].r, z__2.i = stemp * a[ - i__3].i; - z__3.r = ctemp * temp.r, z__3.i = ctemp * temp.i; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; - a[i__2].r = z__1.r, a[i__2].i = z__1.i; - i__2 = i__ + *n * a_dim1; - i__3 = i__ + *n * a_dim1; - z__2.r = ctemp * a[i__3].r, z__2.i = ctemp * a[ - i__3].i; - z__3.r = stemp * temp.r, z__3.i = stemp * temp.i; - z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - - z__3.i; - a[i__2].r = z__1.r, a[i__2].i = z__1.i; + } + } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { + for (j = *n - 1; j >= 1; --j) { + ctemp = c__[j]; + stemp = s[j]; + if (ctemp != 1. || stemp != 0.) { + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__ + j * a_dim1; + temp.r = a[i__2].r, temp.i = a[i__2].i; + i__2 = i__ + j * a_dim1; + i__3 = i__ + *n * a_dim1; + z__2.r = stemp * a[i__3].r, z__2.i = stemp * a[ + i__3].i; + z__3.r = ctemp * temp.r, z__3.i = ctemp * temp.i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + + z__3.i; + a[i__2].r = z__1.r, a[i__2].i = z__1.i; + i__2 = i__ + *n * a_dim1; + i__3 = i__ + *n * a_dim1; + z__2.r = ctemp * a[i__3].r, z__2.i = ctemp * a[ + i__3].i; + z__3.r = stemp * temp.r, z__3.i = stemp * temp.i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - + z__3.i; + a[i__2].r = z__1.r, a[i__2].i = z__1.i; /* L230: */ - } - } + } + } /* L240: */ - } - } - } + } + } + } } return 0; @@ -690,5 +690,5 @@ extern "C" { } /* zlasr_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zlassq.cpp b/lib/linalg/zlassq.cpp index 1fa44450fe..2e2a5ba539 100644 --- a/lib/linalg/zlassq.cpp +++ b/lib/linalg/zlassq.cpp @@ -1,13 +1,13 @@ /* fortran/zlassq.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -124,8 +124,8 @@ f"> */ /* > \ingroup complex16OTHERauxiliary */ /* ===================================================================== */ -/* Subroutine */ int zlassq_(integer *n, doublecomplex *x, integer *incx, - doublereal *scale, doublereal *sumsq) +/* Subroutine */ int zlassq_(integer *n, doublecomplex *x, integer *incx, + doublereal *scale, doublereal *sumsq) { /* System generated locals */ integer i__1, i__2, i__3; @@ -167,38 +167,38 @@ f"> */ /* Function Body */ if (*n > 0) { - i__1 = (*n - 1) * *incx + 1; - i__2 = *incx; - for (ix = 1; i__2 < 0 ? ix >= i__1 : ix <= i__1; ix += i__2) { - i__3 = ix; - temp1 = (d__1 = x[i__3].r, abs(d__1)); - if (temp1 > 0. || disnan_(&temp1)) { - if (*scale < temp1) { + i__1 = (*n - 1) * *incx + 1; + i__2 = *incx; + for (ix = 1; i__2 < 0 ? ix >= i__1 : ix <= i__1; ix += i__2) { + i__3 = ix; + temp1 = (d__1 = x[i__3].r, abs(d__1)); + if (temp1 > 0. || disnan_(&temp1)) { + if (*scale < temp1) { /* Computing 2nd power */ - d__1 = *scale / temp1; - *sumsq = *sumsq * (d__1 * d__1) + 1; - *scale = temp1; - } else { + d__1 = *scale / temp1; + *sumsq = *sumsq * (d__1 * d__1) + 1; + *scale = temp1; + } else { /* Computing 2nd power */ - d__1 = temp1 / *scale; - *sumsq += d__1 * d__1; - } - } - temp1 = (d__1 = d_imag(&x[ix]), abs(d__1)); - if (temp1 > 0. || disnan_(&temp1)) { - if (*scale < temp1) { + d__1 = temp1 / *scale; + *sumsq += d__1 * d__1; + } + } + temp1 = (d__1 = d_imag(&x[ix]), abs(d__1)); + if (temp1 > 0. || disnan_(&temp1)) { + if (*scale < temp1) { /* Computing 2nd power */ - d__1 = *scale / temp1; - *sumsq = *sumsq * (d__1 * d__1) + 1; - *scale = temp1; - } else { + d__1 = *scale / temp1; + *sumsq = *sumsq * (d__1 * d__1) + 1; + *scale = temp1; + } else { /* Computing 2nd power */ - d__1 = temp1 / *scale; - *sumsq += d__1 * d__1; - } - } + d__1 = temp1 / *scale; + *sumsq += d__1 * d__1; + } + } /* L10: */ - } + } } return 0; @@ -208,5 +208,5 @@ f"> */ } /* zlassq_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zlatrd.cpp b/lib/linalg/zlatrd.cpp index eaa0fc1826..d471ea96eb 100644 --- a/lib/linalg/zlatrd.cpp +++ b/lib/linalg/zlatrd.cpp @@ -1,13 +1,13 @@ /* fortran/zlatrd.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -222,9 +222,9 @@ f"> */ /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int zlatrd_(char *uplo, integer *n, integer *nb, - doublecomplex *a, integer *lda, doublereal *e, doublecomplex *tau, - doublecomplex *w, integer *ldw, ftnlen uplo_len) +/* Subroutine */ int zlatrd_(char *uplo, integer *n, integer *nb, + doublecomplex *a, integer *lda, doublereal *e, doublecomplex *tau, + doublecomplex *w, integer *ldw, ftnlen uplo_len) { /* System generated locals */ integer a_dim1, a_offset, w_dim1, w_offset, i__1, i__2, i__3; @@ -235,20 +235,20 @@ f"> */ integer i__, iw; doublecomplex alpha; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int zscal_(integer *, doublecomplex *, - doublecomplex *, integer *); - extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *, - doublecomplex *, integer *, doublecomplex *, integer *); - extern /* Subroutine */ int zgemv_(char *, integer *, integer *, - doublecomplex *, doublecomplex *, integer *, doublecomplex *, - integer *, doublecomplex *, doublecomplex *, integer *, ftnlen), - zhemv_(char *, integer *, doublecomplex *, doublecomplex *, - integer *, doublecomplex *, integer *, doublecomplex *, - doublecomplex *, integer *, ftnlen), zaxpy_(integer *, - doublecomplex *, doublecomplex *, integer *, doublecomplex *, - integer *), zlarfg_(integer *, doublecomplex *, doublecomplex *, - integer *, doublecomplex *), zlacgv_(integer *, doublecomplex *, - integer *); + extern /* Subroutine */ int zscal_(integer *, doublecomplex *, + doublecomplex *, integer *); + extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *, + doublecomplex *, integer *, doublecomplex *, integer *); + extern /* Subroutine */ int zgemv_(char *, integer *, integer *, + doublecomplex *, doublecomplex *, integer *, doublecomplex *, + integer *, doublecomplex *, doublecomplex *, integer *, ftnlen), + zhemv_(char *, integer *, doublecomplex *, doublecomplex *, + integer *, doublecomplex *, integer *, doublecomplex *, + doublecomplex *, integer *, ftnlen), zaxpy_(integer *, + doublecomplex *, doublecomplex *, integer *, doublecomplex *, + integer *), zlarfg_(integer *, doublecomplex *, doublecomplex *, + integer *, doublecomplex *), zlacgv_(integer *, doublecomplex *, + integer *); /* -- LAPACK auxiliary routine -- */ @@ -288,214 +288,214 @@ f"> */ /* Function Body */ if (*n <= 0) { - return 0; + return 0; } if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { /* Reduce last NB columns of upper triangle */ - i__1 = *n - *nb + 1; - for (i__ = *n; i__ >= i__1; --i__) { - iw = i__ - *n + *nb; - if (i__ < *n) { + i__1 = *n - *nb + 1; + for (i__ = *n; i__ >= i__1; --i__) { + iw = i__ - *n + *nb; + if (i__ < *n) { /* Update A(1:i,i) */ - i__2 = i__ + i__ * a_dim1; - i__3 = i__ + i__ * a_dim1; - d__1 = a[i__3].r; - a[i__2].r = d__1, a[i__2].i = 0.; - i__2 = *n - i__; - zlacgv_(&i__2, &w[i__ + (iw + 1) * w_dim1], ldw); - i__2 = *n - i__; - z__1.r = -1., z__1.i = -0.; - zgemv_((char *)"No transpose", &i__, &i__2, &z__1, &a[(i__ + 1) * - a_dim1 + 1], lda, &w[i__ + (iw + 1) * w_dim1], ldw, & - c_b2, &a[i__ * a_dim1 + 1], &c__1, (ftnlen)12); - i__2 = *n - i__; - zlacgv_(&i__2, &w[i__ + (iw + 1) * w_dim1], ldw); - i__2 = *n - i__; - zlacgv_(&i__2, &a[i__ + (i__ + 1) * a_dim1], lda); - i__2 = *n - i__; - z__1.r = -1., z__1.i = -0.; - zgemv_((char *)"No transpose", &i__, &i__2, &z__1, &w[(iw + 1) * - w_dim1 + 1], ldw, &a[i__ + (i__ + 1) * a_dim1], lda, & - c_b2, &a[i__ * a_dim1 + 1], &c__1, (ftnlen)12); - i__2 = *n - i__; - zlacgv_(&i__2, &a[i__ + (i__ + 1) * a_dim1], lda); - i__2 = i__ + i__ * a_dim1; - i__3 = i__ + i__ * a_dim1; - d__1 = a[i__3].r; - a[i__2].r = d__1, a[i__2].i = 0.; - } - if (i__ > 1) { + i__2 = i__ + i__ * a_dim1; + i__3 = i__ + i__ * a_dim1; + d__1 = a[i__3].r; + a[i__2].r = d__1, a[i__2].i = 0.; + i__2 = *n - i__; + zlacgv_(&i__2, &w[i__ + (iw + 1) * w_dim1], ldw); + i__2 = *n - i__; + z__1.r = -1., z__1.i = -0.; + zgemv_((char *)"No transpose", &i__, &i__2, &z__1, &a[(i__ + 1) * + a_dim1 + 1], lda, &w[i__ + (iw + 1) * w_dim1], ldw, & + c_b2, &a[i__ * a_dim1 + 1], &c__1, (ftnlen)12); + i__2 = *n - i__; + zlacgv_(&i__2, &w[i__ + (iw + 1) * w_dim1], ldw); + i__2 = *n - i__; + zlacgv_(&i__2, &a[i__ + (i__ + 1) * a_dim1], lda); + i__2 = *n - i__; + z__1.r = -1., z__1.i = -0.; + zgemv_((char *)"No transpose", &i__, &i__2, &z__1, &w[(iw + 1) * + w_dim1 + 1], ldw, &a[i__ + (i__ + 1) * a_dim1], lda, & + c_b2, &a[i__ * a_dim1 + 1], &c__1, (ftnlen)12); + i__2 = *n - i__; + zlacgv_(&i__2, &a[i__ + (i__ + 1) * a_dim1], lda); + i__2 = i__ + i__ * a_dim1; + i__3 = i__ + i__ * a_dim1; + d__1 = a[i__3].r; + a[i__2].r = d__1, a[i__2].i = 0.; + } + if (i__ > 1) { /* Generate elementary reflector H(i) to annihilate */ /* A(1:i-2,i) */ - i__2 = i__ - 1 + i__ * a_dim1; - alpha.r = a[i__2].r, alpha.i = a[i__2].i; - i__2 = i__ - 1; - zlarfg_(&i__2, &alpha, &a[i__ * a_dim1 + 1], &c__1, &tau[i__ - - 1]); - e[i__ - 1] = alpha.r; - i__2 = i__ - 1 + i__ * a_dim1; - a[i__2].r = 1., a[i__2].i = 0.; + i__2 = i__ - 1 + i__ * a_dim1; + alpha.r = a[i__2].r, alpha.i = a[i__2].i; + i__2 = i__ - 1; + zlarfg_(&i__2, &alpha, &a[i__ * a_dim1 + 1], &c__1, &tau[i__ + - 1]); + e[i__ - 1] = alpha.r; + i__2 = i__ - 1 + i__ * a_dim1; + a[i__2].r = 1., a[i__2].i = 0.; /* Compute W(1:i-1,i) */ - i__2 = i__ - 1; - zhemv_((char *)"Upper", &i__2, &c_b2, &a[a_offset], lda, &a[i__ * - a_dim1 + 1], &c__1, &c_b1, &w[iw * w_dim1 + 1], &c__1, - (ftnlen)5); - if (i__ < *n) { - i__2 = i__ - 1; - i__3 = *n - i__; - zgemv_((char *)"Conjugate transpose", &i__2, &i__3, &c_b2, &w[(iw - + 1) * w_dim1 + 1], ldw, &a[i__ * a_dim1 + 1], & - c__1, &c_b1, &w[i__ + 1 + iw * w_dim1], &c__1, ( - ftnlen)19); - i__2 = i__ - 1; - i__3 = *n - i__; - z__1.r = -1., z__1.i = -0.; - zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &a[(i__ + 1) * - a_dim1 + 1], lda, &w[i__ + 1 + iw * w_dim1], & - c__1, &c_b2, &w[iw * w_dim1 + 1], &c__1, (ftnlen) - 12); - i__2 = i__ - 1; - i__3 = *n - i__; - zgemv_((char *)"Conjugate transpose", &i__2, &i__3, &c_b2, &a[( - i__ + 1) * a_dim1 + 1], lda, &a[i__ * a_dim1 + 1], - &c__1, &c_b1, &w[i__ + 1 + iw * w_dim1], &c__1, ( - ftnlen)19); - i__2 = i__ - 1; - i__3 = *n - i__; - z__1.r = -1., z__1.i = -0.; - zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &w[(iw + 1) * - w_dim1 + 1], ldw, &w[i__ + 1 + iw * w_dim1], & - c__1, &c_b2, &w[iw * w_dim1 + 1], &c__1, (ftnlen) - 12); - } - i__2 = i__ - 1; - zscal_(&i__2, &tau[i__ - 1], &w[iw * w_dim1 + 1], &c__1); - z__3.r = -.5, z__3.i = -0.; - i__2 = i__ - 1; - z__2.r = z__3.r * tau[i__2].r - z__3.i * tau[i__2].i, z__2.i = - z__3.r * tau[i__2].i + z__3.i * tau[i__2].r; - i__3 = i__ - 1; - zdotc_(&z__4, &i__3, &w[iw * w_dim1 + 1], &c__1, &a[i__ * - a_dim1 + 1], &c__1); - z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, z__1.i = z__2.r * - z__4.i + z__2.i * z__4.r; - alpha.r = z__1.r, alpha.i = z__1.i; - i__2 = i__ - 1; - zaxpy_(&i__2, &alpha, &a[i__ * a_dim1 + 1], &c__1, &w[iw * - w_dim1 + 1], &c__1); - } + i__2 = i__ - 1; + zhemv_((char *)"Upper", &i__2, &c_b2, &a[a_offset], lda, &a[i__ * + a_dim1 + 1], &c__1, &c_b1, &w[iw * w_dim1 + 1], &c__1, + (ftnlen)5); + if (i__ < *n) { + i__2 = i__ - 1; + i__3 = *n - i__; + zgemv_((char *)"Conjugate transpose", &i__2, &i__3, &c_b2, &w[(iw + + 1) * w_dim1 + 1], ldw, &a[i__ * a_dim1 + 1], & + c__1, &c_b1, &w[i__ + 1 + iw * w_dim1], &c__1, ( + ftnlen)19); + i__2 = i__ - 1; + i__3 = *n - i__; + z__1.r = -1., z__1.i = -0.; + zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &a[(i__ + 1) * + a_dim1 + 1], lda, &w[i__ + 1 + iw * w_dim1], & + c__1, &c_b2, &w[iw * w_dim1 + 1], &c__1, (ftnlen) + 12); + i__2 = i__ - 1; + i__3 = *n - i__; + zgemv_((char *)"Conjugate transpose", &i__2, &i__3, &c_b2, &a[( + i__ + 1) * a_dim1 + 1], lda, &a[i__ * a_dim1 + 1], + &c__1, &c_b1, &w[i__ + 1 + iw * w_dim1], &c__1, ( + ftnlen)19); + i__2 = i__ - 1; + i__3 = *n - i__; + z__1.r = -1., z__1.i = -0.; + zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &w[(iw + 1) * + w_dim1 + 1], ldw, &w[i__ + 1 + iw * w_dim1], & + c__1, &c_b2, &w[iw * w_dim1 + 1], &c__1, (ftnlen) + 12); + } + i__2 = i__ - 1; + zscal_(&i__2, &tau[i__ - 1], &w[iw * w_dim1 + 1], &c__1); + z__3.r = -.5, z__3.i = -0.; + i__2 = i__ - 1; + z__2.r = z__3.r * tau[i__2].r - z__3.i * tau[i__2].i, z__2.i = + z__3.r * tau[i__2].i + z__3.i * tau[i__2].r; + i__3 = i__ - 1; + zdotc_(&z__4, &i__3, &w[iw * w_dim1 + 1], &c__1, &a[i__ * + a_dim1 + 1], &c__1); + z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, z__1.i = z__2.r * + z__4.i + z__2.i * z__4.r; + alpha.r = z__1.r, alpha.i = z__1.i; + i__2 = i__ - 1; + zaxpy_(&i__2, &alpha, &a[i__ * a_dim1 + 1], &c__1, &w[iw * + w_dim1 + 1], &c__1); + } /* L10: */ - } + } } else { /* Reduce first NB columns of lower triangle */ - i__1 = *nb; - for (i__ = 1; i__ <= i__1; ++i__) { + i__1 = *nb; + for (i__ = 1; i__ <= i__1; ++i__) { /* Update A(i:n,i) */ - i__2 = i__ + i__ * a_dim1; - i__3 = i__ + i__ * a_dim1; - d__1 = a[i__3].r; - a[i__2].r = d__1, a[i__2].i = 0.; - i__2 = i__ - 1; - zlacgv_(&i__2, &w[i__ + w_dim1], ldw); - i__2 = *n - i__ + 1; - i__3 = i__ - 1; - z__1.r = -1., z__1.i = -0.; - zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &a[i__ + a_dim1], lda, - &w[i__ + w_dim1], ldw, &c_b2, &a[i__ + i__ * a_dim1], & - c__1, (ftnlen)12); - i__2 = i__ - 1; - zlacgv_(&i__2, &w[i__ + w_dim1], ldw); - i__2 = i__ - 1; - zlacgv_(&i__2, &a[i__ + a_dim1], lda); - i__2 = *n - i__ + 1; - i__3 = i__ - 1; - z__1.r = -1., z__1.i = -0.; - zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &w[i__ + w_dim1], ldw, - &a[i__ + a_dim1], lda, &c_b2, &a[i__ + i__ * a_dim1], & - c__1, (ftnlen)12); - i__2 = i__ - 1; - zlacgv_(&i__2, &a[i__ + a_dim1], lda); - i__2 = i__ + i__ * a_dim1; - i__3 = i__ + i__ * a_dim1; - d__1 = a[i__3].r; - a[i__2].r = d__1, a[i__2].i = 0.; - if (i__ < *n) { + i__2 = i__ + i__ * a_dim1; + i__3 = i__ + i__ * a_dim1; + d__1 = a[i__3].r; + a[i__2].r = d__1, a[i__2].i = 0.; + i__2 = i__ - 1; + zlacgv_(&i__2, &w[i__ + w_dim1], ldw); + i__2 = *n - i__ + 1; + i__3 = i__ - 1; + z__1.r = -1., z__1.i = -0.; + zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &a[i__ + a_dim1], lda, + &w[i__ + w_dim1], ldw, &c_b2, &a[i__ + i__ * a_dim1], & + c__1, (ftnlen)12); + i__2 = i__ - 1; + zlacgv_(&i__2, &w[i__ + w_dim1], ldw); + i__2 = i__ - 1; + zlacgv_(&i__2, &a[i__ + a_dim1], lda); + i__2 = *n - i__ + 1; + i__3 = i__ - 1; + z__1.r = -1., z__1.i = -0.; + zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &w[i__ + w_dim1], ldw, + &a[i__ + a_dim1], lda, &c_b2, &a[i__ + i__ * a_dim1], & + c__1, (ftnlen)12); + i__2 = i__ - 1; + zlacgv_(&i__2, &a[i__ + a_dim1], lda); + i__2 = i__ + i__ * a_dim1; + i__3 = i__ + i__ * a_dim1; + d__1 = a[i__3].r; + a[i__2].r = d__1, a[i__2].i = 0.; + if (i__ < *n) { /* Generate elementary reflector H(i) to annihilate */ /* A(i+2:n,i) */ - i__2 = i__ + 1 + i__ * a_dim1; - alpha.r = a[i__2].r, alpha.i = a[i__2].i; - i__2 = *n - i__; + i__2 = i__ + 1 + i__ * a_dim1; + alpha.r = a[i__2].r, alpha.i = a[i__2].i; + i__2 = *n - i__; /* Computing MIN */ - i__3 = i__ + 2; - zlarfg_(&i__2, &alpha, &a[min(i__3,*n) + i__ * a_dim1], &c__1, - &tau[i__]); - e[i__] = alpha.r; - i__2 = i__ + 1 + i__ * a_dim1; - a[i__2].r = 1., a[i__2].i = 0.; + i__3 = i__ + 2; + zlarfg_(&i__2, &alpha, &a[min(i__3,*n) + i__ * a_dim1], &c__1, + &tau[i__]); + e[i__] = alpha.r; + i__2 = i__ + 1 + i__ * a_dim1; + a[i__2].r = 1., a[i__2].i = 0.; /* Compute W(i+1:n,i) */ - i__2 = *n - i__; - zhemv_((char *)"Lower", &i__2, &c_b2, &a[i__ + 1 + (i__ + 1) * a_dim1] - , lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b1, &w[ - i__ + 1 + i__ * w_dim1], &c__1, (ftnlen)5); - i__2 = *n - i__; - i__3 = i__ - 1; - zgemv_((char *)"Conjugate transpose", &i__2, &i__3, &c_b2, &w[i__ + 1 - + w_dim1], ldw, &a[i__ + 1 + i__ * a_dim1], &c__1, & - c_b1, &w[i__ * w_dim1 + 1], &c__1, (ftnlen)19); - i__2 = *n - i__; - i__3 = i__ - 1; - z__1.r = -1., z__1.i = -0.; - zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &a[i__ + 1 + - a_dim1], lda, &w[i__ * w_dim1 + 1], &c__1, &c_b2, &w[ - i__ + 1 + i__ * w_dim1], &c__1, (ftnlen)12); - i__2 = *n - i__; - i__3 = i__ - 1; - zgemv_((char *)"Conjugate transpose", &i__2, &i__3, &c_b2, &a[i__ + 1 - + a_dim1], lda, &a[i__ + 1 + i__ * a_dim1], &c__1, & - c_b1, &w[i__ * w_dim1 + 1], &c__1, (ftnlen)19); - i__2 = *n - i__; - i__3 = i__ - 1; - z__1.r = -1., z__1.i = -0.; - zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &w[i__ + 1 + - w_dim1], ldw, &w[i__ * w_dim1 + 1], &c__1, &c_b2, &w[ - i__ + 1 + i__ * w_dim1], &c__1, (ftnlen)12); - i__2 = *n - i__; - zscal_(&i__2, &tau[i__], &w[i__ + 1 + i__ * w_dim1], &c__1); - z__3.r = -.5, z__3.i = -0.; - i__2 = i__; - z__2.r = z__3.r * tau[i__2].r - z__3.i * tau[i__2].i, z__2.i = - z__3.r * tau[i__2].i + z__3.i * tau[i__2].r; - i__3 = *n - i__; - zdotc_(&z__4, &i__3, &w[i__ + 1 + i__ * w_dim1], &c__1, &a[ - i__ + 1 + i__ * a_dim1], &c__1); - z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, z__1.i = z__2.r * - z__4.i + z__2.i * z__4.r; - alpha.r = z__1.r, alpha.i = z__1.i; - i__2 = *n - i__; - zaxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &w[ - i__ + 1 + i__ * w_dim1], &c__1); - } + i__2 = *n - i__; + zhemv_((char *)"Lower", &i__2, &c_b2, &a[i__ + 1 + (i__ + 1) * a_dim1] + , lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b1, &w[ + i__ + 1 + i__ * w_dim1], &c__1, (ftnlen)5); + i__2 = *n - i__; + i__3 = i__ - 1; + zgemv_((char *)"Conjugate transpose", &i__2, &i__3, &c_b2, &w[i__ + 1 + + w_dim1], ldw, &a[i__ + 1 + i__ * a_dim1], &c__1, & + c_b1, &w[i__ * w_dim1 + 1], &c__1, (ftnlen)19); + i__2 = *n - i__; + i__3 = i__ - 1; + z__1.r = -1., z__1.i = -0.; + zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &a[i__ + 1 + + a_dim1], lda, &w[i__ * w_dim1 + 1], &c__1, &c_b2, &w[ + i__ + 1 + i__ * w_dim1], &c__1, (ftnlen)12); + i__2 = *n - i__; + i__3 = i__ - 1; + zgemv_((char *)"Conjugate transpose", &i__2, &i__3, &c_b2, &a[i__ + 1 + + a_dim1], lda, &a[i__ + 1 + i__ * a_dim1], &c__1, & + c_b1, &w[i__ * w_dim1 + 1], &c__1, (ftnlen)19); + i__2 = *n - i__; + i__3 = i__ - 1; + z__1.r = -1., z__1.i = -0.; + zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &w[i__ + 1 + + w_dim1], ldw, &w[i__ * w_dim1 + 1], &c__1, &c_b2, &w[ + i__ + 1 + i__ * w_dim1], &c__1, (ftnlen)12); + i__2 = *n - i__; + zscal_(&i__2, &tau[i__], &w[i__ + 1 + i__ * w_dim1], &c__1); + z__3.r = -.5, z__3.i = -0.; + i__2 = i__; + z__2.r = z__3.r * tau[i__2].r - z__3.i * tau[i__2].i, z__2.i = + z__3.r * tau[i__2].i + z__3.i * tau[i__2].r; + i__3 = *n - i__; + zdotc_(&z__4, &i__3, &w[i__ + 1 + i__ * w_dim1], &c__1, &a[ + i__ + 1 + i__ * a_dim1], &c__1); + z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, z__1.i = z__2.r * + z__4.i + z__2.i * z__4.r; + alpha.r = z__1.r, alpha.i = z__1.i; + i__2 = *n - i__; + zaxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &w[ + i__ + 1 + i__ * w_dim1], &c__1); + } /* L20: */ - } + } } return 0; @@ -505,5 +505,5 @@ f"> */ } /* zlatrd_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zpptrf.cpp b/lib/linalg/zpptrf.cpp index ebf3b7df9a..d14e3678be 100644 --- a/lib/linalg/zpptrf.cpp +++ b/lib/linalg/zpptrf.cpp @@ -1,13 +1,13 @@ /* fortran/zpptrf.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -140,8 +140,8 @@ f"> */ /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int zpptrf_(char *uplo, integer *n, doublecomplex *ap, - integer *info, ftnlen uplo_len) +/* Subroutine */ int zpptrf_(char *uplo, integer *n, doublecomplex *ap, + integer *info, ftnlen uplo_len) { /* System generated locals */ integer i__1, i__2, i__3; @@ -154,16 +154,16 @@ f"> */ /* Local variables */ integer j, jc, jj; doublereal ajj; - extern /* Subroutine */ int zhpr_(char *, integer *, doublereal *, - doublecomplex *, integer *, doublecomplex *, ftnlen); + extern /* Subroutine */ int zhpr_(char *, integer *, doublereal *, + doublecomplex *, integer *, doublecomplex *, ftnlen); extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *, - doublecomplex *, integer *, doublecomplex *, integer *); + extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *, + doublecomplex *, integer *, doublecomplex *, integer *); logical upper; - extern /* Subroutine */ int ztpsv_(char *, char *, char *, integer *, - doublecomplex *, doublecomplex *, integer *, ftnlen, ftnlen, - ftnlen), xerbla_(char *, integer *, ftnlen), zdscal_(integer *, - doublereal *, doublecomplex *, integer *); + extern /* Subroutine */ int ztpsv_(char *, char *, char *, integer *, + doublecomplex *, doublecomplex *, integer *, ftnlen, ftnlen, + ftnlen), xerbla_(char *, integer *, ftnlen), zdscal_(integer *, + doublereal *, doublecomplex *, integer *); /* -- LAPACK computational routine -- */ @@ -198,91 +198,91 @@ f"> */ *info = 0; upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { - *info = -1; + *info = -1; } else if (*n < 0) { - *info = -2; + *info = -2; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"ZPPTRF", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"ZPPTRF", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*n == 0) { - return 0; + return 0; } if (upper) { /* Compute the Cholesky factorization A = U**H * U. */ - jj = 0; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - jc = jj + 1; - jj += j; + jj = 0; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + jc = jj + 1; + jj += j; /* Compute elements 1:J-1 of column J. */ - if (j > 1) { - i__2 = j - 1; - ztpsv_((char *)"Upper", (char *)"Conjugate transpose", (char *)"Non-unit", &i__2, &ap[ - 1], &ap[jc], &c__1, (ftnlen)5, (ftnlen)19, (ftnlen)8); - } + if (j > 1) { + i__2 = j - 1; + ztpsv_((char *)"Upper", (char *)"Conjugate transpose", (char *)"Non-unit", &i__2, &ap[ + 1], &ap[jc], &c__1, (ftnlen)5, (ftnlen)19, (ftnlen)8); + } /* Compute U(J,J) and test for non-positive-definiteness. */ - i__2 = jj; - i__3 = j - 1; - zdotc_(&z__1, &i__3, &ap[jc], &c__1, &ap[jc], &c__1); - ajj = ap[i__2].r - z__1.r; - if (ajj <= 0.) { - i__2 = jj; - ap[i__2].r = ajj, ap[i__2].i = 0.; - goto L30; - } - i__2 = jj; - d__1 = sqrt(ajj); - ap[i__2].r = d__1, ap[i__2].i = 0.; + i__2 = jj; + i__3 = j - 1; + zdotc_(&z__1, &i__3, &ap[jc], &c__1, &ap[jc], &c__1); + ajj = ap[i__2].r - z__1.r; + if (ajj <= 0.) { + i__2 = jj; + ap[i__2].r = ajj, ap[i__2].i = 0.; + goto L30; + } + i__2 = jj; + d__1 = sqrt(ajj); + ap[i__2].r = d__1, ap[i__2].i = 0.; /* L10: */ - } + } } else { /* Compute the Cholesky factorization A = L * L**H. */ - jj = 1; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { + jj = 1; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { /* Compute L(J,J) and test for non-positive-definiteness. */ - i__2 = jj; - ajj = ap[i__2].r; - if (ajj <= 0.) { - i__2 = jj; - ap[i__2].r = ajj, ap[i__2].i = 0.; - goto L30; - } - ajj = sqrt(ajj); - i__2 = jj; - ap[i__2].r = ajj, ap[i__2].i = 0.; + i__2 = jj; + ajj = ap[i__2].r; + if (ajj <= 0.) { + i__2 = jj; + ap[i__2].r = ajj, ap[i__2].i = 0.; + goto L30; + } + ajj = sqrt(ajj); + i__2 = jj; + ap[i__2].r = ajj, ap[i__2].i = 0.; /* Compute elements J+1:N of column J and update the trailing */ /* submatrix. */ - if (j < *n) { - i__2 = *n - j; - d__1 = 1. / ajj; - zdscal_(&i__2, &d__1, &ap[jj + 1], &c__1); - i__2 = *n - j; - zhpr_((char *)"Lower", &i__2, &c_b16, &ap[jj + 1], &c__1, &ap[jj + *n - - j + 1], (ftnlen)5); - jj = jj + *n - j + 1; - } + if (j < *n) { + i__2 = *n - j; + d__1 = 1. / ajj; + zdscal_(&i__2, &d__1, &ap[jj + 1], &c__1); + i__2 = *n - j; + zhpr_((char *)"Lower", &i__2, &c_b16, &ap[jj + 1], &c__1, &ap[jj + *n + - j + 1], (ftnlen)5); + jj = jj + *n - j + 1; + } /* L20: */ - } + } } goto L40; @@ -297,5 +297,5 @@ L40: } /* zpptrf_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zpptri.cpp b/lib/linalg/zpptri.cpp index fc11e435b1..e804683c79 100644 --- a/lib/linalg/zpptri.cpp +++ b/lib/linalg/zpptri.cpp @@ -1,13 +1,13 @@ /* fortran/zpptri.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -114,8 +114,8 @@ f"> */ /* > \ingroup complex16OTHERcomputational */ /* ===================================================================== */ -/* Subroutine */ int zpptri_(char *uplo, integer *n, doublecomplex *ap, - integer *info, ftnlen uplo_len) +/* Subroutine */ int zpptri_(char *uplo, integer *n, doublecomplex *ap, + integer *info, ftnlen uplo_len) { /* System generated locals */ integer i__1, i__2, i__3; @@ -126,17 +126,17 @@ f"> */ integer j, jc, jj; doublereal ajj; integer jjn; - extern /* Subroutine */ int zhpr_(char *, integer *, doublereal *, - doublecomplex *, integer *, doublecomplex *, ftnlen); + extern /* Subroutine */ int zhpr_(char *, integer *, doublereal *, + doublecomplex *, integer *, doublecomplex *, ftnlen); extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *, - doublecomplex *, integer *, doublecomplex *, integer *); + extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *, + doublecomplex *, integer *, doublecomplex *, integer *); logical upper; - extern /* Subroutine */ int ztpmv_(char *, char *, char *, integer *, - doublecomplex *, doublecomplex *, integer *, ftnlen, ftnlen, - ftnlen), xerbla_(char *, integer *, ftnlen), zdscal_(integer *, - doublereal *, doublecomplex *, integer *), ztptri_(char *, char *, - integer *, doublecomplex *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int ztpmv_(char *, char *, char *, integer *, + doublecomplex *, doublecomplex *, integer *, ftnlen, ftnlen, + ftnlen), xerbla_(char *, integer *, ftnlen), zdscal_(integer *, + doublereal *, doublecomplex *, integer *), ztptri_(char *, char *, + integer *, doublecomplex *, integer *, ftnlen, ftnlen); /* -- LAPACK computational routine -- */ @@ -171,70 +171,70 @@ f"> */ *info = 0; upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { - *info = -1; + *info = -1; } else if (*n < 0) { - *info = -2; + *info = -2; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"ZPPTRI", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"ZPPTRI", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*n == 0) { - return 0; + return 0; } /* Invert the triangular Cholesky factor U or L. */ ztptri_(uplo, (char *)"Non-unit", n, &ap[1], info, (ftnlen)1, (ftnlen)8); if (*info > 0) { - return 0; + return 0; } if (upper) { /* Compute the product inv(U) * inv(U)**H. */ - jj = 0; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - jc = jj + 1; - jj += j; - if (j > 1) { - i__2 = j - 1; - zhpr_((char *)"Upper", &i__2, &c_b8, &ap[jc], &c__1, &ap[1], (ftnlen) - 5); - } - i__2 = jj; - ajj = ap[i__2].r; - zdscal_(&j, &ajj, &ap[jc], &c__1); + jj = 0; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + jc = jj + 1; + jj += j; + if (j > 1) { + i__2 = j - 1; + zhpr_((char *)"Upper", &i__2, &c_b8, &ap[jc], &c__1, &ap[1], (ftnlen) + 5); + } + i__2 = jj; + ajj = ap[i__2].r; + zdscal_(&j, &ajj, &ap[jc], &c__1); /* L10: */ - } + } } else { /* Compute the product inv(L)**H * inv(L). */ - jj = 1; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - jjn = jj + *n - j + 1; - i__2 = jj; - i__3 = *n - j + 1; - zdotc_(&z__1, &i__3, &ap[jj], &c__1, &ap[jj], &c__1); - d__1 = z__1.r; - ap[i__2].r = d__1, ap[i__2].i = 0.; - if (j < *n) { - i__2 = *n - j; - ztpmv_((char *)"Lower", (char *)"Conjugate transpose", (char *)"Non-unit", &i__2, &ap[ - jjn], &ap[jj + 1], &c__1, (ftnlen)5, (ftnlen)19, ( - ftnlen)8); - } - jj = jjn; + jj = 1; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + jjn = jj + *n - j + 1; + i__2 = jj; + i__3 = *n - j + 1; + zdotc_(&z__1, &i__3, &ap[jj], &c__1, &ap[jj], &c__1); + d__1 = z__1.r; + ap[i__2].r = d__1, ap[i__2].i = 0.; + if (j < *n) { + i__2 = *n - j; + ztpmv_((char *)"Lower", (char *)"Conjugate transpose", (char *)"Non-unit", &i__2, &ap[ + jjn], &ap[jj + 1], &c__1, (ftnlen)5, (ftnlen)19, ( + ftnlen)8); + } + jj = jjn; /* L20: */ - } + } } return 0; @@ -244,5 +244,5 @@ f"> */ } /* zpptri_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zscal.cpp b/lib/linalg/zscal.cpp index 5985adebaf..6efc02ee5e 100644 --- a/lib/linalg/zscal.cpp +++ b/lib/linalg/zscal.cpp @@ -1,13 +1,13 @@ /* fortran/zscal.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -91,8 +91,8 @@ extern "C" { /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int zscal_(integer *n, doublecomplex *za, doublecomplex *zx, - integer *incx) +/* Subroutine */ int zscal_(integer *n, doublecomplex *za, doublecomplex *zx, + integer *incx) { /* System generated locals */ integer i__1, i__2, i__3, i__4; @@ -122,34 +122,34 @@ extern "C" { /* Function Body */ if (*n <= 0 || *incx <= 0 || za->r == 1. && za->i == 0.) { - return 0; + return 0; } if (*incx == 1) { /* code for increment equal to 1 */ - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = i__; - i__3 = i__; - z__1.r = za->r * zx[i__3].r - za->i * zx[i__3].i, z__1.i = za->r * - zx[i__3].i + za->i * zx[i__3].r; - zx[i__2].r = z__1.r, zx[i__2].i = z__1.i; - } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__; + i__3 = i__; + z__1.r = za->r * zx[i__3].r - za->i * zx[i__3].i, z__1.i = za->r * + zx[i__3].i + za->i * zx[i__3].r; + zx[i__2].r = z__1.r, zx[i__2].i = z__1.i; + } } else { /* code for increment not equal to 1 */ - nincx = *n * *incx; - i__1 = nincx; - i__2 = *incx; - for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { - i__3 = i__; - i__4 = i__; - z__1.r = za->r * zx[i__4].r - za->i * zx[i__4].i, z__1.i = za->r * - zx[i__4].i + za->i * zx[i__4].r; - zx[i__3].r = z__1.r, zx[i__3].i = z__1.i; - } + nincx = *n * *incx; + i__1 = nincx; + i__2 = *incx; + for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { + i__3 = i__; + i__4 = i__; + z__1.r = za->r * zx[i__4].r - za->i * zx[i__4].i, z__1.i = za->r * + zx[i__4].i + za->i * zx[i__4].r; + zx[i__3].r = z__1.r, zx[i__3].i = z__1.i; + } } return 0; @@ -158,5 +158,5 @@ extern "C" { } /* zscal_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zstedc.cpp b/lib/linalg/zstedc.cpp index fb52b344b1..1a4d71cf50 100644 --- a/lib/linalg/zstedc.cpp +++ b/lib/linalg/zstedc.cpp @@ -1,13 +1,13 @@ /* fortran/zstedc.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -236,10 +236,10 @@ f"> */ /* > at Berkeley, USA */ /* ===================================================================== */ -/* Subroutine */ int zstedc_(char *compz, integer *n, doublereal *d__, - doublereal *e, doublecomplex *z__, integer *ldz, doublecomplex *work, - integer *lwork, doublereal *rwork, integer *lrwork, integer *iwork, - integer *liwork, integer *info, ftnlen compz_len) +/* Subroutine */ int zstedc_(char *compz, integer *n, doublereal *d__, + doublereal *e, doublecomplex *z__, integer *ldz, doublecomplex *work, + integer *lwork, doublereal *rwork, integer *lrwork, integer *iwork, + integer *liwork, integer *info, ftnlen compz_len) { /* System generated locals */ integer z_dim1, z_offset, i__1, i__2, i__3, i__4; @@ -257,40 +257,40 @@ f"> */ doublereal eps, tiny; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer lwmin, start; - extern /* Subroutine */ int zswap_(integer *, doublecomplex *, integer *, - doublecomplex *, integer *), zlaed0_(integer *, integer *, - doublereal *, doublereal *, doublecomplex *, integer *, - doublecomplex *, integer *, doublereal *, integer *, integer *); + extern /* Subroutine */ int zswap_(integer *, doublecomplex *, integer *, + doublecomplex *, integer *), zlaed0_(integer *, integer *, + doublereal *, doublereal *, doublecomplex *, integer *, + doublecomplex *, integer *, doublereal *, integer *, integer *); extern doublereal dlamch_(char *, ftnlen); - extern /* Subroutine */ int dlascl_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, integer *, doublereal *, - integer *, integer *, ftnlen), dstedc_(char *, integer *, - doublereal *, doublereal *, doublereal *, integer *, doublereal *, - integer *, integer *, integer *, integer *, ftnlen), dlaset_( - char *, integer *, integer *, doublereal *, doublereal *, - doublereal *, integer *, ftnlen), xerbla_(char *, integer *, - ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int dlascl_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, integer *, doublereal *, + integer *, integer *, ftnlen), dstedc_(char *, integer *, + doublereal *, doublereal *, doublereal *, integer *, doublereal *, + integer *, integer *, integer *, integer *, ftnlen), dlaset_( + char *, integer *, integer *, doublereal *, doublereal *, + doublereal *, integer *, ftnlen), xerbla_(char *, integer *, + ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); integer finish; - extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *, - ftnlen); + extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *, + ftnlen); extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *, - integer *), zlacrm_(integer *, integer *, doublecomplex *, - integer *, doublereal *, integer *, doublecomplex *, integer *, - doublereal *); + integer *), zlacrm_(integer *, integer *, doublecomplex *, + integer *, doublereal *, integer *, doublecomplex *, integer *, + doublereal *); integer liwmin, icompz; - extern /* Subroutine */ int dsteqr_(char *, integer *, doublereal *, - doublereal *, doublereal *, integer *, doublereal *, integer *, - ftnlen), zlacpy_(char *, integer *, integer *, doublecomplex *, - integer *, doublecomplex *, integer *, ftnlen); + extern /* Subroutine */ int dsteqr_(char *, integer *, doublereal *, + doublereal *, doublereal *, integer *, doublereal *, integer *, + ftnlen), zlacpy_(char *, integer *, integer *, doublecomplex *, + integer *, doublecomplex *, integer *, ftnlen); doublereal orgnrm; integer lrwmin; logical lquery; integer smlsiz; - extern /* Subroutine */ int zsteqr_(char *, integer *, doublereal *, - doublereal *, doublecomplex *, integer *, doublereal *, integer *, - ftnlen); + extern /* Subroutine */ int zsteqr_(char *, integer *, doublereal *, + doublereal *, doublecomplex *, integer *, doublereal *, integer *, + ftnlen); /* -- LAPACK computational routine -- */ @@ -333,88 +333,88 @@ f"> */ lquery = *lwork == -1 || *lrwork == -1 || *liwork == -1; if (lsame_(compz, (char *)"N", (ftnlen)1, (ftnlen)1)) { - icompz = 0; + icompz = 0; } else if (lsame_(compz, (char *)"V", (ftnlen)1, (ftnlen)1)) { - icompz = 1; + icompz = 1; } else if (lsame_(compz, (char *)"I", (ftnlen)1, (ftnlen)1)) { - icompz = 2; + icompz = 2; } else { - icompz = -1; + icompz = -1; } if (icompz < 0) { - *info = -1; + *info = -1; } else if (*n < 0) { - *info = -2; + *info = -2; } else if (*ldz < 1 || icompz > 0 && *ldz < max(1,*n)) { - *info = -6; + *info = -6; } if (*info == 0) { /* Compute the workspace requirements */ - smlsiz = ilaenv_(&c__9, (char *)"ZSTEDC", (char *)" ", &c__0, &c__0, &c__0, &c__0, ( - ftnlen)6, (ftnlen)1); - if (*n <= 1 || icompz == 0) { - lwmin = 1; - liwmin = 1; - lrwmin = 1; - } else if (*n <= smlsiz) { - lwmin = 1; - liwmin = 1; - lrwmin = *n - 1 << 1; - } else if (icompz == 1) { - lgn = (integer) (log((doublereal) (*n)) / log(2.)); - if (pow_ii(&c__2, &lgn) < *n) { - ++lgn; - } - if (pow_ii(&c__2, &lgn) < *n) { - ++lgn; - } - lwmin = *n * *n; + smlsiz = ilaenv_(&c__9, (char *)"ZSTEDC", (char *)" ", &c__0, &c__0, &c__0, &c__0, ( + ftnlen)6, (ftnlen)1); + if (*n <= 1 || icompz == 0) { + lwmin = 1; + liwmin = 1; + lrwmin = 1; + } else if (*n <= smlsiz) { + lwmin = 1; + liwmin = 1; + lrwmin = *n - 1 << 1; + } else if (icompz == 1) { + lgn = (integer) (log((doublereal) (*n)) / log(2.)); + if (pow_ii(&c__2, &lgn) < *n) { + ++lgn; + } + if (pow_ii(&c__2, &lgn) < *n) { + ++lgn; + } + lwmin = *n * *n; /* Computing 2nd power */ - i__1 = *n; - lrwmin = *n * 3 + 1 + (*n << 1) * lgn + (i__1 * i__1 << 2); - liwmin = *n * 6 + 6 + *n * 5 * lgn; - } else if (icompz == 2) { - lwmin = 1; + i__1 = *n; + lrwmin = *n * 3 + 1 + (*n << 1) * lgn + (i__1 * i__1 << 2); + liwmin = *n * 6 + 6 + *n * 5 * lgn; + } else if (icompz == 2) { + lwmin = 1; /* Computing 2nd power */ - i__1 = *n; - lrwmin = (*n << 2) + 1 + (i__1 * i__1 << 1); - liwmin = *n * 5 + 3; - } - work[1].r = (doublereal) lwmin, work[1].i = 0.; - rwork[1] = (doublereal) lrwmin; - iwork[1] = liwmin; + i__1 = *n; + lrwmin = (*n << 2) + 1 + (i__1 * i__1 << 1); + liwmin = *n * 5 + 3; + } + work[1].r = (doublereal) lwmin, work[1].i = 0.; + rwork[1] = (doublereal) lrwmin; + iwork[1] = liwmin; - if (*lwork < lwmin && ! lquery) { - *info = -8; - } else if (*lrwork < lrwmin && ! lquery) { - *info = -10; - } else if (*liwork < liwmin && ! lquery) { - *info = -12; - } + if (*lwork < lwmin && ! lquery) { + *info = -8; + } else if (*lrwork < lrwmin && ! lquery) { + *info = -10; + } else if (*liwork < liwmin && ! lquery) { + *info = -12; + } } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"ZSTEDC", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"ZSTEDC", &i__1, (ftnlen)6); + return 0; } else if (lquery) { - return 0; + return 0; } /* Quick return if possible */ if (*n == 0) { - return 0; + return 0; } if (*n == 1) { - if (icompz != 0) { - i__1 = z_dim1 + 1; - z__[i__1].r = 1., z__[i__1].i = 0.; - } - return 0; + if (icompz != 0) { + i__1 = z_dim1 + 1; + z__[i__1].r = 1., z__[i__1].i = 0.; + } + return 0; } /* If the following conditional clause is removed, then the routine */ @@ -429,8 +429,8 @@ f"> */ /* If COMPZ = 'N', use DSTERF to compute the eigenvalues. */ if (icompz == 0) { - dsterf_(n, &d__[1], &e[1], info); - goto L70; + dsterf_(n, &d__[1], &e[1], info); + goto L70; } /* If N is smaller than the minimum divide size (SMLSIZ+1), then */ @@ -438,51 +438,51 @@ f"> */ if (*n <= smlsiz) { - zsteqr_(compz, n, &d__[1], &e[1], &z__[z_offset], ldz, &rwork[1], - info, (ftnlen)1); + zsteqr_(compz, n, &d__[1], &e[1], &z__[z_offset], ldz, &rwork[1], + info, (ftnlen)1); } else { /* If COMPZ = 'I', we simply call DSTEDC instead. */ - if (icompz == 2) { - dlaset_((char *)"Full", n, n, &c_b17, &c_b18, &rwork[1], n, (ftnlen)4); - ll = *n * *n + 1; - i__1 = *lrwork - ll + 1; - dstedc_((char *)"I", n, &d__[1], &e[1], &rwork[1], n, &rwork[ll], &i__1, & - iwork[1], liwork, info, (ftnlen)1); - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *n; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * z_dim1; - i__4 = (j - 1) * *n + i__; - z__[i__3].r = rwork[i__4], z__[i__3].i = 0.; + if (icompz == 2) { + dlaset_((char *)"Full", n, n, &c_b17, &c_b18, &rwork[1], n, (ftnlen)4); + ll = *n * *n + 1; + i__1 = *lrwork - ll + 1; + dstedc_((char *)"I", n, &d__[1], &e[1], &rwork[1], n, &rwork[ll], &i__1, & + iwork[1], liwork, info, (ftnlen)1); + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *n; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * z_dim1; + i__4 = (j - 1) * *n + i__; + z__[i__3].r = rwork[i__4], z__[i__3].i = 0.; /* L10: */ - } + } /* L20: */ - } - goto L70; - } + } + goto L70; + } /* From now on, only option left to be handled is COMPZ = 'V', */ /* i.e. ICOMPZ = 1. */ /* Scale. */ - orgnrm = dlanst_((char *)"M", n, &d__[1], &e[1], (ftnlen)1); - if (orgnrm == 0.) { - goto L70; - } + orgnrm = dlanst_((char *)"M", n, &d__[1], &e[1], (ftnlen)1); + if (orgnrm == 0.) { + goto L70; + } - eps = dlamch_((char *)"Epsilon", (ftnlen)7); + eps = dlamch_((char *)"Epsilon", (ftnlen)7); - start = 1; + start = 1; /* while ( START <= N ) */ L30: - if (start <= *n) { + if (start <= *n) { /* Let FINISH be the position of the next subdiagonal entry */ /* such that E( FINISH ) <= TINY or FINISH = N if no such */ @@ -490,88 +490,88 @@ L30: /* between START and FINISH constitutes an independent */ /* sub-problem. */ - finish = start; + finish = start; L40: - if (finish < *n) { - tiny = eps * sqrt((d__1 = d__[finish], abs(d__1))) * sqrt(( - d__2 = d__[finish + 1], abs(d__2))); - if ((d__1 = e[finish], abs(d__1)) > tiny) { - ++finish; - goto L40; - } - } + if (finish < *n) { + tiny = eps * sqrt((d__1 = d__[finish], abs(d__1))) * sqrt(( + d__2 = d__[finish + 1], abs(d__2))); + if ((d__1 = e[finish], abs(d__1)) > tiny) { + ++finish; + goto L40; + } + } /* (Sub) Problem determined. Compute its size and solve it. */ - m = finish - start + 1; - if (m > smlsiz) { + m = finish - start + 1; + if (m > smlsiz) { /* Scale. */ - orgnrm = dlanst_((char *)"M", &m, &d__[start], &e[start], (ftnlen)1); - dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b18, &m, &c__1, &d__[ - start], &m, info, (ftnlen)1); - i__1 = m - 1; - i__2 = m - 1; - dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b18, &i__1, &c__1, &e[ - start], &i__2, info, (ftnlen)1); + orgnrm = dlanst_((char *)"M", &m, &d__[start], &e[start], (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b18, &m, &c__1, &d__[ + start], &m, info, (ftnlen)1); + i__1 = m - 1; + i__2 = m - 1; + dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b18, &i__1, &c__1, &e[ + start], &i__2, info, (ftnlen)1); - zlaed0_(n, &m, &d__[start], &e[start], &z__[start * z_dim1 + - 1], ldz, &work[1], n, &rwork[1], &iwork[1], info); - if (*info > 0) { - *info = (*info / (m + 1) + start - 1) * (*n + 1) + *info % - (m + 1) + start - 1; - goto L70; - } + zlaed0_(n, &m, &d__[start], &e[start], &z__[start * z_dim1 + + 1], ldz, &work[1], n, &rwork[1], &iwork[1], info); + if (*info > 0) { + *info = (*info / (m + 1) + start - 1) * (*n + 1) + *info % + (m + 1) + start - 1; + goto L70; + } /* Scale back. */ - dlascl_((char *)"G", &c__0, &c__0, &c_b18, &orgnrm, &m, &c__1, &d__[ - start], &m, info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &c_b18, &orgnrm, &m, &c__1, &d__[ + start], &m, info, (ftnlen)1); - } else { - dsteqr_((char *)"I", &m, &d__[start], &e[start], &rwork[1], &m, & - rwork[m * m + 1], info, (ftnlen)1); - zlacrm_(n, &m, &z__[start * z_dim1 + 1], ldz, &rwork[1], &m, & - work[1], n, &rwork[m * m + 1]); - zlacpy_((char *)"A", n, &m, &work[1], n, &z__[start * z_dim1 + 1], - ldz, (ftnlen)1); - if (*info > 0) { - *info = start * (*n + 1) + finish; - goto L70; - } - } + } else { + dsteqr_((char *)"I", &m, &d__[start], &e[start], &rwork[1], &m, & + rwork[m * m + 1], info, (ftnlen)1); + zlacrm_(n, &m, &z__[start * z_dim1 + 1], ldz, &rwork[1], &m, & + work[1], n, &rwork[m * m + 1]); + zlacpy_((char *)"A", n, &m, &work[1], n, &z__[start * z_dim1 + 1], + ldz, (ftnlen)1); + if (*info > 0) { + *info = start * (*n + 1) + finish; + goto L70; + } + } - start = finish + 1; - goto L30; - } + start = finish + 1; + goto L30; + } /* endwhile */ /* Use Selection Sort to minimize swaps of eigenvectors */ - i__1 = *n; - for (ii = 2; ii <= i__1; ++ii) { - i__ = ii - 1; - k = i__; - p = d__[i__]; - i__2 = *n; - for (j = ii; j <= i__2; ++j) { - if (d__[j] < p) { - k = j; - p = d__[j]; - } + i__1 = *n; + for (ii = 2; ii <= i__1; ++ii) { + i__ = ii - 1; + k = i__; + p = d__[i__]; + i__2 = *n; + for (j = ii; j <= i__2; ++j) { + if (d__[j] < p) { + k = j; + p = d__[j]; + } /* L50: */ - } - if (k != i__) { - d__[k] = d__[i__]; - d__[i__] = p; - zswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1 + 1], - &c__1); - } + } + if (k != i__) { + d__[k] = d__[i__]; + d__[i__] = p; + zswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1 + 1], + &c__1); + } /* L60: */ - } + } } L70: @@ -586,5 +586,5 @@ L70: } /* zstedc_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zsteqr.cpp b/lib/linalg/zsteqr.cpp index 21cb31cc10..ce75593d28 100644 --- a/lib/linalg/zsteqr.cpp +++ b/lib/linalg/zsteqr.cpp @@ -1,13 +1,13 @@ /* fortran/zsteqr.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -157,9 +157,9 @@ f"> */ /* > \ingroup complex16OTHERcomputational */ /* ===================================================================== */ -/* Subroutine */ int zsteqr_(char *compz, integer *n, doublereal *d__, - doublereal *e, doublecomplex *z__, integer *ldz, doublereal *work, - integer *info, ftnlen compz_len) +/* Subroutine */ int zsteqr_(char *compz, integer *n, doublereal *d__, + doublereal *e, doublecomplex *z__, integer *ldz, doublereal *work, + integer *info, ftnlen compz_len) { /* System generated locals */ integer z_dim1, z_offset, i__1, i__2; @@ -177,39 +177,39 @@ f"> */ integer lsv; doublereal tst, eps2; integer lend, jtot; - extern /* Subroutine */ int dlae2_(doublereal *, doublereal *, doublereal - *, doublereal *, doublereal *); + extern /* Subroutine */ int dlae2_(doublereal *, doublereal *, doublereal + *, doublereal *, doublereal *); extern logical lsame_(char *, char *, ftnlen, ftnlen); doublereal anorm; - extern /* Subroutine */ int zlasr_(char *, char *, char *, integer *, - integer *, doublereal *, doublereal *, doublecomplex *, integer *, - ftnlen, ftnlen, ftnlen), zswap_(integer *, doublecomplex *, - integer *, doublecomplex *, integer *), dlaev2_(doublereal *, - doublereal *, doublereal *, doublereal *, doublereal *, - doublereal *, doublereal *); + extern /* Subroutine */ int zlasr_(char *, char *, char *, integer *, + integer *, doublereal *, doublereal *, doublecomplex *, integer *, + ftnlen, ftnlen, ftnlen), zswap_(integer *, doublecomplex *, + integer *, doublecomplex *, integer *), dlaev2_(doublereal *, + doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, doublereal *); integer lendm1, lendp1; - extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, - ftnlen); + extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, + ftnlen); integer iscale; - extern /* Subroutine */ int dlascl_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, integer *, doublereal *, - integer *, integer *, ftnlen); + extern /* Subroutine */ int dlascl_(char *, integer *, integer *, + doublereal *, doublereal *, integer *, integer *, doublereal *, + integer *, integer *, ftnlen); doublereal safmin; - extern /* Subroutine */ int dlartg_(doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *); + extern /* Subroutine */ int dlartg_(doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *); doublereal safmax; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *, - ftnlen); - extern /* Subroutine */ int dlasrt_(char *, integer *, doublereal *, - integer *, ftnlen); + extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *, + ftnlen); + extern /* Subroutine */ int dlasrt_(char *, integer *, doublereal *, + integer *, ftnlen); integer lendsv; doublereal ssfmin; integer nmaxit, icompz; doublereal ssfmax; - extern /* Subroutine */ int zlaset_(char *, integer *, integer *, - doublecomplex *, doublecomplex *, doublecomplex *, integer *, - ftnlen); + extern /* Subroutine */ int zlaset_(char *, integer *, integer *, + doublecomplex *, doublecomplex *, doublecomplex *, integer *, + ftnlen); /* -- LAPACK computational routine -- */ @@ -249,39 +249,39 @@ f"> */ *info = 0; if (lsame_(compz, (char *)"N", (ftnlen)1, (ftnlen)1)) { - icompz = 0; + icompz = 0; } else if (lsame_(compz, (char *)"V", (ftnlen)1, (ftnlen)1)) { - icompz = 1; + icompz = 1; } else if (lsame_(compz, (char *)"I", (ftnlen)1, (ftnlen)1)) { - icompz = 2; + icompz = 2; } else { - icompz = -1; + icompz = -1; } if (icompz < 0) { - *info = -1; + *info = -1; } else if (*n < 0) { - *info = -2; + *info = -2; } else if (*ldz < 1 || icompz > 0 && *ldz < max(1,*n)) { - *info = -6; + *info = -6; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"ZSTEQR", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"ZSTEQR", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*n == 0) { - return 0; + return 0; } if (*n == 1) { - if (icompz == 2) { - i__1 = z_dim1 + 1; - z__[i__1].r = 1., z__[i__1].i = 0.; - } - return 0; + if (icompz == 2) { + i__1 = z_dim1 + 1; + z__[i__1].r = 1., z__[i__1].i = 0.; + } + return 0; } /* Determine the unit roundoff and over/underflow thresholds. */ @@ -299,7 +299,7 @@ f"> */ /* matrix. */ if (icompz == 2) { - zlaset_((char *)"Full", n, n, &c_b1, &c_b2, &z__[z_offset], ldz, (ftnlen)4); + zlaset_((char *)"Full", n, n, &c_b1, &c_b2, &z__[z_offset], ldz, (ftnlen)4); } nmaxit = *n * 30; @@ -314,25 +314,25 @@ f"> */ L10: if (l1 > *n) { - goto L160; + goto L160; } if (l1 > 1) { - e[l1 - 1] = 0.; + e[l1 - 1] = 0.; } if (l1 <= nm1) { - i__1 = nm1; - for (m = l1; m <= i__1; ++m) { - tst = (d__1 = e[m], abs(d__1)); - if (tst == 0.) { - goto L30; - } - if (tst <= sqrt((d__1 = d__[m], abs(d__1))) * sqrt((d__2 = d__[m - + 1], abs(d__2))) * eps) { - e[m] = 0.; - goto L30; - } + i__1 = nm1; + for (m = l1; m <= i__1; ++m) { + tst = (d__1 = e[m], abs(d__1)); + if (tst == 0.) { + goto L30; + } + if (tst <= sqrt((d__1 = d__[m], abs(d__1))) * sqrt((d__2 = d__[m + + 1], abs(d__2))) * eps) { + e[m] = 0.; + goto L30; + } /* L20: */ - } + } } m = *n; @@ -343,7 +343,7 @@ L30: lendsv = lend; l1 = m + 1; if (lend == l) { - goto L10; + goto L10; } /* Scale submatrix in rows and columns L to LEND */ @@ -352,31 +352,31 @@ L30: anorm = dlanst_((char *)"I", &i__1, &d__[l], &e[l], (ftnlen)1); iscale = 0; if (anorm == 0.) { - goto L10; + goto L10; } if (anorm > ssfmax) { - iscale = 1; - i__1 = lend - l + 1; - dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n, - info, (ftnlen)1); - i__1 = lend - l; - dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &e[l], n, - info, (ftnlen)1); + iscale = 1; + i__1 = lend - l + 1; + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n, + info, (ftnlen)1); + i__1 = lend - l; + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &e[l], n, + info, (ftnlen)1); } else if (anorm < ssfmin) { - iscale = 2; - i__1 = lend - l + 1; - dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n, - info, (ftnlen)1); - i__1 = lend - l; - dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n, - info, (ftnlen)1); + iscale = 2; + i__1 = lend - l + 1; + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n, + info, (ftnlen)1); + i__1 = lend - l; + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n, + info, (ftnlen)1); } /* Choose between QL and QR iteration */ if ((d__1 = d__[lend], abs(d__1)) < (d__2 = d__[l], abs(d__2))) { - lend = lsv; - l = lendsv; + lend = lsv; + l = lendsv; } if (lend > l) { @@ -386,120 +386,120 @@ L30: /* Look for small subdiagonal element. */ L40: - if (l != lend) { - lendm1 = lend - 1; - i__1 = lendm1; - for (m = l; m <= i__1; ++m) { + if (l != lend) { + lendm1 = lend - 1; + i__1 = lendm1; + for (m = l; m <= i__1; ++m) { /* Computing 2nd power */ - d__2 = (d__1 = e[m], abs(d__1)); - tst = d__2 * d__2; - if (tst <= eps2 * (d__1 = d__[m], abs(d__1)) * (d__2 = d__[m - + 1], abs(d__2)) + safmin) { - goto L60; - } + d__2 = (d__1 = e[m], abs(d__1)); + tst = d__2 * d__2; + if (tst <= eps2 * (d__1 = d__[m], abs(d__1)) * (d__2 = d__[m + + 1], abs(d__2)) + safmin) { + goto L60; + } /* L50: */ - } - } + } + } - m = lend; + m = lend; L60: - if (m < lend) { - e[m] = 0.; - } - p = d__[l]; - if (m == l) { - goto L80; - } + if (m < lend) { + e[m] = 0.; + } + p = d__[l]; + if (m == l) { + goto L80; + } /* If remaining matrix is 2-by-2, use DLAE2 or SLAEV2 */ /* to compute its eigensystem. */ - if (m == l + 1) { - if (icompz > 0) { - dlaev2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2, &c__, &s); - work[l] = c__; - work[*n - 1 + l] = s; - zlasr_((char *)"R", (char *)"V", (char *)"B", n, &c__2, &work[l], &work[*n - 1 + l], & - z__[l * z_dim1 + 1], ldz, (ftnlen)1, (ftnlen)1, ( - ftnlen)1); - } else { - dlae2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2); - } - d__[l] = rt1; - d__[l + 1] = rt2; - e[l] = 0.; - l += 2; - if (l <= lend) { - goto L40; - } - goto L140; - } + if (m == l + 1) { + if (icompz > 0) { + dlaev2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2, &c__, &s); + work[l] = c__; + work[*n - 1 + l] = s; + zlasr_((char *)"R", (char *)"V", (char *)"B", n, &c__2, &work[l], &work[*n - 1 + l], & + z__[l * z_dim1 + 1], ldz, (ftnlen)1, (ftnlen)1, ( + ftnlen)1); + } else { + dlae2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2); + } + d__[l] = rt1; + d__[l + 1] = rt2; + e[l] = 0.; + l += 2; + if (l <= lend) { + goto L40; + } + goto L140; + } - if (jtot == nmaxit) { - goto L140; - } - ++jtot; + if (jtot == nmaxit) { + goto L140; + } + ++jtot; /* Form shift. */ - g = (d__[l + 1] - p) / (e[l] * 2.); - r__ = dlapy2_(&g, &c_b41); - g = d__[m] - p + e[l] / (g + d_sign(&r__, &g)); + g = (d__[l + 1] - p) / (e[l] * 2.); + r__ = dlapy2_(&g, &c_b41); + g = d__[m] - p + e[l] / (g + d_sign(&r__, &g)); - s = 1.; - c__ = 1.; - p = 0.; + s = 1.; + c__ = 1.; + p = 0.; /* Inner loop */ - mm1 = m - 1; - i__1 = l; - for (i__ = mm1; i__ >= i__1; --i__) { - f = s * e[i__]; - b = c__ * e[i__]; - dlartg_(&g, &f, &c__, &s, &r__); - if (i__ != m - 1) { - e[i__ + 1] = r__; - } - g = d__[i__ + 1] - p; - r__ = (d__[i__] - g) * s + c__ * 2. * b; - p = s * r__; - d__[i__ + 1] = g + p; - g = c__ * r__ - b; + mm1 = m - 1; + i__1 = l; + for (i__ = mm1; i__ >= i__1; --i__) { + f = s * e[i__]; + b = c__ * e[i__]; + dlartg_(&g, &f, &c__, &s, &r__); + if (i__ != m - 1) { + e[i__ + 1] = r__; + } + g = d__[i__ + 1] - p; + r__ = (d__[i__] - g) * s + c__ * 2. * b; + p = s * r__; + d__[i__ + 1] = g + p; + g = c__ * r__ - b; /* If eigenvectors are desired, then save rotations. */ - if (icompz > 0) { - work[i__] = c__; - work[*n - 1 + i__] = -s; - } + if (icompz > 0) { + work[i__] = c__; + work[*n - 1 + i__] = -s; + } /* L70: */ - } + } /* If eigenvectors are desired, then apply saved rotations. */ - if (icompz > 0) { - mm = m - l + 1; - zlasr_((char *)"R", (char *)"V", (char *)"B", n, &mm, &work[l], &work[*n - 1 + l], &z__[l - * z_dim1 + 1], ldz, (ftnlen)1, (ftnlen)1, (ftnlen)1); - } + if (icompz > 0) { + mm = m - l + 1; + zlasr_((char *)"R", (char *)"V", (char *)"B", n, &mm, &work[l], &work[*n - 1 + l], &z__[l + * z_dim1 + 1], ldz, (ftnlen)1, (ftnlen)1, (ftnlen)1); + } - d__[l] -= p; - e[l] = g; - goto L40; + d__[l] -= p; + e[l] = g; + goto L40; /* Eigenvalue found. */ L80: - d__[l] = p; + d__[l] = p; - ++l; - if (l <= lend) { - goto L40; - } - goto L140; + ++l; + if (l <= lend) { + goto L40; + } + goto L140; } else { @@ -508,121 +508,121 @@ L80: /* Look for small superdiagonal element. */ L90: - if (l != lend) { - lendp1 = lend + 1; - i__1 = lendp1; - for (m = l; m >= i__1; --m) { + if (l != lend) { + lendp1 = lend + 1; + i__1 = lendp1; + for (m = l; m >= i__1; --m) { /* Computing 2nd power */ - d__2 = (d__1 = e[m - 1], abs(d__1)); - tst = d__2 * d__2; - if (tst <= eps2 * (d__1 = d__[m], abs(d__1)) * (d__2 = d__[m - - 1], abs(d__2)) + safmin) { - goto L110; - } + d__2 = (d__1 = e[m - 1], abs(d__1)); + tst = d__2 * d__2; + if (tst <= eps2 * (d__1 = d__[m], abs(d__1)) * (d__2 = d__[m + - 1], abs(d__2)) + safmin) { + goto L110; + } /* L100: */ - } - } + } + } - m = lend; + m = lend; L110: - if (m > lend) { - e[m - 1] = 0.; - } - p = d__[l]; - if (m == l) { - goto L130; - } + if (m > lend) { + e[m - 1] = 0.; + } + p = d__[l]; + if (m == l) { + goto L130; + } /* If remaining matrix is 2-by-2, use DLAE2 or SLAEV2 */ /* to compute its eigensystem. */ - if (m == l - 1) { - if (icompz > 0) { - dlaev2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2, &c__, &s) - ; - work[m] = c__; - work[*n - 1 + m] = s; - zlasr_((char *)"R", (char *)"V", (char *)"F", n, &c__2, &work[m], &work[*n - 1 + m], & - z__[(l - 1) * z_dim1 + 1], ldz, (ftnlen)1, (ftnlen)1, - (ftnlen)1); - } else { - dlae2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2); - } - d__[l - 1] = rt1; - d__[l] = rt2; - e[l - 1] = 0.; - l += -2; - if (l >= lend) { - goto L90; - } - goto L140; - } + if (m == l - 1) { + if (icompz > 0) { + dlaev2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2, &c__, &s) + ; + work[m] = c__; + work[*n - 1 + m] = s; + zlasr_((char *)"R", (char *)"V", (char *)"F", n, &c__2, &work[m], &work[*n - 1 + m], & + z__[(l - 1) * z_dim1 + 1], ldz, (ftnlen)1, (ftnlen)1, + (ftnlen)1); + } else { + dlae2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2); + } + d__[l - 1] = rt1; + d__[l] = rt2; + e[l - 1] = 0.; + l += -2; + if (l >= lend) { + goto L90; + } + goto L140; + } - if (jtot == nmaxit) { - goto L140; - } - ++jtot; + if (jtot == nmaxit) { + goto L140; + } + ++jtot; /* Form shift. */ - g = (d__[l - 1] - p) / (e[l - 1] * 2.); - r__ = dlapy2_(&g, &c_b41); - g = d__[m] - p + e[l - 1] / (g + d_sign(&r__, &g)); + g = (d__[l - 1] - p) / (e[l - 1] * 2.); + r__ = dlapy2_(&g, &c_b41); + g = d__[m] - p + e[l - 1] / (g + d_sign(&r__, &g)); - s = 1.; - c__ = 1.; - p = 0.; + s = 1.; + c__ = 1.; + p = 0.; /* Inner loop */ - lm1 = l - 1; - i__1 = lm1; - for (i__ = m; i__ <= i__1; ++i__) { - f = s * e[i__]; - b = c__ * e[i__]; - dlartg_(&g, &f, &c__, &s, &r__); - if (i__ != m) { - e[i__ - 1] = r__; - } - g = d__[i__] - p; - r__ = (d__[i__ + 1] - g) * s + c__ * 2. * b; - p = s * r__; - d__[i__] = g + p; - g = c__ * r__ - b; + lm1 = l - 1; + i__1 = lm1; + for (i__ = m; i__ <= i__1; ++i__) { + f = s * e[i__]; + b = c__ * e[i__]; + dlartg_(&g, &f, &c__, &s, &r__); + if (i__ != m) { + e[i__ - 1] = r__; + } + g = d__[i__] - p; + r__ = (d__[i__ + 1] - g) * s + c__ * 2. * b; + p = s * r__; + d__[i__] = g + p; + g = c__ * r__ - b; /* If eigenvectors are desired, then save rotations. */ - if (icompz > 0) { - work[i__] = c__; - work[*n - 1 + i__] = s; - } + if (icompz > 0) { + work[i__] = c__; + work[*n - 1 + i__] = s; + } /* L120: */ - } + } /* If eigenvectors are desired, then apply saved rotations. */ - if (icompz > 0) { - mm = l - m + 1; - zlasr_((char *)"R", (char *)"V", (char *)"F", n, &mm, &work[m], &work[*n - 1 + m], &z__[m - * z_dim1 + 1], ldz, (ftnlen)1, (ftnlen)1, (ftnlen)1); - } + if (icompz > 0) { + mm = l - m + 1; + zlasr_((char *)"R", (char *)"V", (char *)"F", n, &mm, &work[m], &work[*n - 1 + m], &z__[m + * z_dim1 + 1], ldz, (ftnlen)1, (ftnlen)1, (ftnlen)1); + } - d__[l] -= p; - e[lm1] = g; - goto L90; + d__[l] -= p; + e[lm1] = g; + goto L90; /* Eigenvalue found. */ L130: - d__[l] = p; + d__[l] = p; - --l; - if (l >= lend) { - goto L90; - } - goto L140; + --l; + if (l >= lend) { + goto L90; + } + goto L140; } @@ -630,33 +630,33 @@ L130: L140: if (iscale == 1) { - i__1 = lendsv - lsv + 1; - dlascl_((char *)"G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv], - n, info, (ftnlen)1); - i__1 = lendsv - lsv; - dlascl_((char *)"G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &e[lsv], n, - info, (ftnlen)1); + i__1 = lendsv - lsv + 1; + dlascl_((char *)"G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv], + n, info, (ftnlen)1); + i__1 = lendsv - lsv; + dlascl_((char *)"G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &e[lsv], n, + info, (ftnlen)1); } else if (iscale == 2) { - i__1 = lendsv - lsv + 1; - dlascl_((char *)"G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[lsv], - n, info, (ftnlen)1); - i__1 = lendsv - lsv; - dlascl_((char *)"G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &e[lsv], n, - info, (ftnlen)1); + i__1 = lendsv - lsv + 1; + dlascl_((char *)"G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[lsv], + n, info, (ftnlen)1); + i__1 = lendsv - lsv; + dlascl_((char *)"G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &e[lsv], n, + info, (ftnlen)1); } /* Check for no convergence to an eigenvalue after a total */ /* of N*MAXIT iterations. */ if (jtot == nmaxit) { - i__1 = *n - 1; - for (i__ = 1; i__ <= i__1; ++i__) { - if (e[i__] != 0.) { - ++(*info); - } + i__1 = *n - 1; + for (i__ = 1; i__ <= i__1; ++i__) { + if (e[i__] != 0.) { + ++(*info); + } /* L150: */ - } - return 0; + } + return 0; } goto L10; @@ -667,33 +667,33 @@ L160: /* Use Quick Sort */ - dlasrt_((char *)"I", n, &d__[1], info, (ftnlen)1); + dlasrt_((char *)"I", n, &d__[1], info, (ftnlen)1); } else { /* Use Selection Sort to minimize swaps of eigenvectors */ - i__1 = *n; - for (ii = 2; ii <= i__1; ++ii) { - i__ = ii - 1; - k = i__; - p = d__[i__]; - i__2 = *n; - for (j = ii; j <= i__2; ++j) { - if (d__[j] < p) { - k = j; - p = d__[j]; - } + i__1 = *n; + for (ii = 2; ii <= i__1; ++ii) { + i__ = ii - 1; + k = i__; + p = d__[i__]; + i__2 = *n; + for (j = ii; j <= i__2; ++j) { + if (d__[j] < p) { + k = j; + p = d__[j]; + } /* L170: */ - } - if (k != i__) { - d__[k] = d__[i__]; - d__[i__] = p; - zswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1 + 1], - &c__1); - } + } + if (k != i__) { + d__[k] = d__[i__]; + d__[i__] = p; + zswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1 + 1], + &c__1); + } /* L180: */ - } + } } return 0; @@ -702,5 +702,5 @@ L160: } /* zsteqr_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zswap.cpp b/lib/linalg/zswap.cpp index d00bb044fd..ff04833b04 100644 --- a/lib/linalg/zswap.cpp +++ b/lib/linalg/zswap.cpp @@ -1,13 +1,13 @@ /* fortran/zswap.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -94,8 +94,8 @@ extern "C" { /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int zswap_(integer *n, doublecomplex *zx, integer *incx, - doublecomplex *zy, integer *incy) +/* Subroutine */ int zswap_(integer *n, doublecomplex *zx, integer *incx, + doublecomplex *zy, integer *incy) { /* System generated locals */ integer i__1, i__2, i__3; @@ -124,46 +124,46 @@ extern "C" { /* Function Body */ if (*n <= 0) { - return 0; + return 0; } if (*incx == 1 && *incy == 1) { /* code for both increments equal to 1 */ - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = i__; - ztemp.r = zx[i__2].r, ztemp.i = zx[i__2].i; - i__2 = i__; - i__3 = i__; - zx[i__2].r = zy[i__3].r, zx[i__2].i = zy[i__3].i; - i__2 = i__; - zy[i__2].r = ztemp.r, zy[i__2].i = ztemp.i; - } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__; + ztemp.r = zx[i__2].r, ztemp.i = zx[i__2].i; + i__2 = i__; + i__3 = i__; + zx[i__2].r = zy[i__3].r, zx[i__2].i = zy[i__3].i; + i__2 = i__; + zy[i__2].r = ztemp.r, zy[i__2].i = ztemp.i; + } } else { /* code for unequal increments or equal increments not equal */ /* to 1 */ - ix = 1; - iy = 1; - if (*incx < 0) { - ix = (-(*n) + 1) * *incx + 1; - } - if (*incy < 0) { - iy = (-(*n) + 1) * *incy + 1; - } - i__1 = *n; - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = ix; - ztemp.r = zx[i__2].r, ztemp.i = zx[i__2].i; - i__2 = ix; - i__3 = iy; - zx[i__2].r = zy[i__3].r, zx[i__2].i = zy[i__3].i; - i__2 = iy; - zy[i__2].r = ztemp.r, zy[i__2].i = ztemp.i; - ix += *incx; - iy += *incy; - } + ix = 1; + iy = 1; + if (*incx < 0) { + ix = (-(*n) + 1) * *incx + 1; + } + if (*incy < 0) { + iy = (-(*n) + 1) * *incy + 1; + } + i__1 = *n; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = ix; + ztemp.r = zx[i__2].r, ztemp.i = zx[i__2].i; + i__2 = ix; + i__3 = iy; + zx[i__2].r = zy[i__3].r, zx[i__2].i = zy[i__3].i; + i__2 = iy; + zy[i__2].r = ztemp.r, zy[i__2].i = ztemp.i; + ix += *incx; + iy += *incy; + } } return 0; @@ -172,5 +172,5 @@ extern "C" { } /* zswap_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/ztpmv.cpp b/lib/linalg/ztpmv.cpp index a29145d6bd..adb1db10f4 100644 --- a/lib/linalg/ztpmv.cpp +++ b/lib/linalg/ztpmv.cpp @@ -1,13 +1,13 @@ /* fortran/ztpmv.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -155,9 +155,9 @@ extern "C" { /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int ztpmv_(char *uplo, char *trans, char *diag, integer *n, - doublecomplex *ap, doublecomplex *x, integer *incx, ftnlen uplo_len, - ftnlen trans_len, ftnlen diag_len) +/* Subroutine */ int ztpmv_(char *uplo, char *trans, char *diag, integer *n, + doublecomplex *ap, doublecomplex *x, integer *incx, ftnlen uplo_len, + ftnlen trans_len, ftnlen diag_len) { /* System generated locals */ integer i__1, i__2, i__3, i__4, i__5; @@ -205,29 +205,29 @@ extern "C" { /* Function Body */ info = 0; if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", ( - ftnlen)1, (ftnlen)1)) { - info = 1; - } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, - (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, ( - ftnlen)1)) { - info = 2; - } else if (! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, - (char *)"N", (ftnlen)1, (ftnlen)1)) { - info = 3; + ftnlen)1, (ftnlen)1)) { + info = 1; + } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, + (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, ( + ftnlen)1)) { + info = 2; + } else if (! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, + (char *)"N", (ftnlen)1, (ftnlen)1)) { + info = 3; } else if (*n < 0) { - info = 4; + info = 4; } else if (*incx == 0) { - info = 7; + info = 7; } if (info != 0) { - xerbla_((char *)"ZTPMV ", &info, (ftnlen)6); - return 0; + xerbla_((char *)"ZTPMV ", &info, (ftnlen)6); + return 0; } /* Quick return if possible. */ if (*n == 0) { - return 0; + return 0; } noconj = lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1); @@ -237,9 +237,9 @@ extern "C" { /* will be ( N - 1 )*INCX too small for descending loops. */ if (*incx <= 0) { - kx = 1 - (*n - 1) * *incx; + kx = 1 - (*n - 1) * *incx; } else if (*incx != 1) { - kx = 1; + kx = 1; } /* Start the operations. In this version the elements of AP are */ @@ -249,383 +249,383 @@ extern "C" { /* Form x:= A*x. */ - if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { - kk = 1; - if (*incx == 1) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = j; - if (x[i__2].r != 0. || x[i__2].i != 0.) { - i__2 = j; - temp.r = x[i__2].r, temp.i = x[i__2].i; - k = kk; - i__2 = j - 1; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__; - i__4 = i__; - i__5 = k; - z__2.r = temp.r * ap[i__5].r - temp.i * ap[i__5] - .i, z__2.i = temp.r * ap[i__5].i + temp.i - * ap[i__5].r; - z__1.r = x[i__4].r + z__2.r, z__1.i = x[i__4].i + - z__2.i; - x[i__3].r = z__1.r, x[i__3].i = z__1.i; - ++k; + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + kk = 1; + if (*incx == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + if (x[i__2].r != 0. || x[i__2].i != 0.) { + i__2 = j; + temp.r = x[i__2].r, temp.i = x[i__2].i; + k = kk; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__; + i__4 = i__; + i__5 = k; + z__2.r = temp.r * ap[i__5].r - temp.i * ap[i__5] + .i, z__2.i = temp.r * ap[i__5].i + temp.i + * ap[i__5].r; + z__1.r = x[i__4].r + z__2.r, z__1.i = x[i__4].i + + z__2.i; + x[i__3].r = z__1.r, x[i__3].i = z__1.i; + ++k; /* L10: */ - } - if (nounit) { - i__2 = j; - i__3 = j; - i__4 = kk + j - 1; - z__1.r = x[i__3].r * ap[i__4].r - x[i__3].i * ap[ - i__4].i, z__1.i = x[i__3].r * ap[i__4].i - + x[i__3].i * ap[i__4].r; - x[i__2].r = z__1.r, x[i__2].i = z__1.i; - } - } - kk += j; + } + if (nounit) { + i__2 = j; + i__3 = j; + i__4 = kk + j - 1; + z__1.r = x[i__3].r * ap[i__4].r - x[i__3].i * ap[ + i__4].i, z__1.i = x[i__3].r * ap[i__4].i + + x[i__3].i * ap[i__4].r; + x[i__2].r = z__1.r, x[i__2].i = z__1.i; + } + } + kk += j; /* L20: */ - } - } else { - jx = kx; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = jx; - if (x[i__2].r != 0. || x[i__2].i != 0.) { - i__2 = jx; - temp.r = x[i__2].r, temp.i = x[i__2].i; - ix = kx; - i__2 = kk + j - 2; - for (k = kk; k <= i__2; ++k) { - i__3 = ix; - i__4 = ix; - i__5 = k; - z__2.r = temp.r * ap[i__5].r - temp.i * ap[i__5] - .i, z__2.i = temp.r * ap[i__5].i + temp.i - * ap[i__5].r; - z__1.r = x[i__4].r + z__2.r, z__1.i = x[i__4].i + - z__2.i; - x[i__3].r = z__1.r, x[i__3].i = z__1.i; - ix += *incx; + } + } else { + jx = kx; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = jx; + if (x[i__2].r != 0. || x[i__2].i != 0.) { + i__2 = jx; + temp.r = x[i__2].r, temp.i = x[i__2].i; + ix = kx; + i__2 = kk + j - 2; + for (k = kk; k <= i__2; ++k) { + i__3 = ix; + i__4 = ix; + i__5 = k; + z__2.r = temp.r * ap[i__5].r - temp.i * ap[i__5] + .i, z__2.i = temp.r * ap[i__5].i + temp.i + * ap[i__5].r; + z__1.r = x[i__4].r + z__2.r, z__1.i = x[i__4].i + + z__2.i; + x[i__3].r = z__1.r, x[i__3].i = z__1.i; + ix += *incx; /* L30: */ - } - if (nounit) { - i__2 = jx; - i__3 = jx; - i__4 = kk + j - 1; - z__1.r = x[i__3].r * ap[i__4].r - x[i__3].i * ap[ - i__4].i, z__1.i = x[i__3].r * ap[i__4].i - + x[i__3].i * ap[i__4].r; - x[i__2].r = z__1.r, x[i__2].i = z__1.i; - } - } - jx += *incx; - kk += j; + } + if (nounit) { + i__2 = jx; + i__3 = jx; + i__4 = kk + j - 1; + z__1.r = x[i__3].r * ap[i__4].r - x[i__3].i * ap[ + i__4].i, z__1.i = x[i__3].r * ap[i__4].i + + x[i__3].i * ap[i__4].r; + x[i__2].r = z__1.r, x[i__2].i = z__1.i; + } + } + jx += *incx; + kk += j; /* L40: */ - } - } - } else { - kk = *n * (*n + 1) / 2; - if (*incx == 1) { - for (j = *n; j >= 1; --j) { - i__1 = j; - if (x[i__1].r != 0. || x[i__1].i != 0.) { - i__1 = j; - temp.r = x[i__1].r, temp.i = x[i__1].i; - k = kk; - i__1 = j + 1; - for (i__ = *n; i__ >= i__1; --i__) { - i__2 = i__; - i__3 = i__; - i__4 = k; - z__2.r = temp.r * ap[i__4].r - temp.i * ap[i__4] - .i, z__2.i = temp.r * ap[i__4].i + temp.i - * ap[i__4].r; - z__1.r = x[i__3].r + z__2.r, z__1.i = x[i__3].i + - z__2.i; - x[i__2].r = z__1.r, x[i__2].i = z__1.i; - --k; + } + } + } else { + kk = *n * (*n + 1) / 2; + if (*incx == 1) { + for (j = *n; j >= 1; --j) { + i__1 = j; + if (x[i__1].r != 0. || x[i__1].i != 0.) { + i__1 = j; + temp.r = x[i__1].r, temp.i = x[i__1].i; + k = kk; + i__1 = j + 1; + for (i__ = *n; i__ >= i__1; --i__) { + i__2 = i__; + i__3 = i__; + i__4 = k; + z__2.r = temp.r * ap[i__4].r - temp.i * ap[i__4] + .i, z__2.i = temp.r * ap[i__4].i + temp.i + * ap[i__4].r; + z__1.r = x[i__3].r + z__2.r, z__1.i = x[i__3].i + + z__2.i; + x[i__2].r = z__1.r, x[i__2].i = z__1.i; + --k; /* L50: */ - } - if (nounit) { - i__1 = j; - i__2 = j; - i__3 = kk - *n + j; - z__1.r = x[i__2].r * ap[i__3].r - x[i__2].i * ap[ - i__3].i, z__1.i = x[i__2].r * ap[i__3].i - + x[i__2].i * ap[i__3].r; - x[i__1].r = z__1.r, x[i__1].i = z__1.i; - } - } - kk -= *n - j + 1; + } + if (nounit) { + i__1 = j; + i__2 = j; + i__3 = kk - *n + j; + z__1.r = x[i__2].r * ap[i__3].r - x[i__2].i * ap[ + i__3].i, z__1.i = x[i__2].r * ap[i__3].i + + x[i__2].i * ap[i__3].r; + x[i__1].r = z__1.r, x[i__1].i = z__1.i; + } + } + kk -= *n - j + 1; /* L60: */ - } - } else { - kx += (*n - 1) * *incx; - jx = kx; - for (j = *n; j >= 1; --j) { - i__1 = jx; - if (x[i__1].r != 0. || x[i__1].i != 0.) { - i__1 = jx; - temp.r = x[i__1].r, temp.i = x[i__1].i; - ix = kx; - i__1 = kk - (*n - (j + 1)); - for (k = kk; k >= i__1; --k) { - i__2 = ix; - i__3 = ix; - i__4 = k; - z__2.r = temp.r * ap[i__4].r - temp.i * ap[i__4] - .i, z__2.i = temp.r * ap[i__4].i + temp.i - * ap[i__4].r; - z__1.r = x[i__3].r + z__2.r, z__1.i = x[i__3].i + - z__2.i; - x[i__2].r = z__1.r, x[i__2].i = z__1.i; - ix -= *incx; + } + } else { + kx += (*n - 1) * *incx; + jx = kx; + for (j = *n; j >= 1; --j) { + i__1 = jx; + if (x[i__1].r != 0. || x[i__1].i != 0.) { + i__1 = jx; + temp.r = x[i__1].r, temp.i = x[i__1].i; + ix = kx; + i__1 = kk - (*n - (j + 1)); + for (k = kk; k >= i__1; --k) { + i__2 = ix; + i__3 = ix; + i__4 = k; + z__2.r = temp.r * ap[i__4].r - temp.i * ap[i__4] + .i, z__2.i = temp.r * ap[i__4].i + temp.i + * ap[i__4].r; + z__1.r = x[i__3].r + z__2.r, z__1.i = x[i__3].i + + z__2.i; + x[i__2].r = z__1.r, x[i__2].i = z__1.i; + ix -= *incx; /* L70: */ - } - if (nounit) { - i__1 = jx; - i__2 = jx; - i__3 = kk - *n + j; - z__1.r = x[i__2].r * ap[i__3].r - x[i__2].i * ap[ - i__3].i, z__1.i = x[i__2].r * ap[i__3].i - + x[i__2].i * ap[i__3].r; - x[i__1].r = z__1.r, x[i__1].i = z__1.i; - } - } - jx -= *incx; - kk -= *n - j + 1; + } + if (nounit) { + i__1 = jx; + i__2 = jx; + i__3 = kk - *n + j; + z__1.r = x[i__2].r * ap[i__3].r - x[i__2].i * ap[ + i__3].i, z__1.i = x[i__2].r * ap[i__3].i + + x[i__2].i * ap[i__3].r; + x[i__1].r = z__1.r, x[i__1].i = z__1.i; + } + } + jx -= *incx; + kk -= *n - j + 1; /* L80: */ - } - } - } + } + } + } } else { /* Form x := A**T*x or x := A**H*x. */ - if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { - kk = *n * (*n + 1) / 2; - if (*incx == 1) { - for (j = *n; j >= 1; --j) { - i__1 = j; - temp.r = x[i__1].r, temp.i = x[i__1].i; - k = kk - 1; - if (noconj) { - if (nounit) { - i__1 = kk; - z__1.r = temp.r * ap[i__1].r - temp.i * ap[i__1] - .i, z__1.i = temp.r * ap[i__1].i + temp.i - * ap[i__1].r; - temp.r = z__1.r, temp.i = z__1.i; - } - for (i__ = j - 1; i__ >= 1; --i__) { - i__1 = k; - i__2 = i__; - z__2.r = ap[i__1].r * x[i__2].r - ap[i__1].i * x[ - i__2].i, z__2.i = ap[i__1].r * x[i__2].i - + ap[i__1].i * x[i__2].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; - temp.r = z__1.r, temp.i = z__1.i; - --k; + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + kk = *n * (*n + 1) / 2; + if (*incx == 1) { + for (j = *n; j >= 1; --j) { + i__1 = j; + temp.r = x[i__1].r, temp.i = x[i__1].i; + k = kk - 1; + if (noconj) { + if (nounit) { + i__1 = kk; + z__1.r = temp.r * ap[i__1].r - temp.i * ap[i__1] + .i, z__1.i = temp.r * ap[i__1].i + temp.i + * ap[i__1].r; + temp.r = z__1.r, temp.i = z__1.i; + } + for (i__ = j - 1; i__ >= 1; --i__) { + i__1 = k; + i__2 = i__; + z__2.r = ap[i__1].r * x[i__2].r - ap[i__1].i * x[ + i__2].i, z__2.i = ap[i__1].r * x[i__2].i + + ap[i__1].i * x[i__2].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + --k; /* L90: */ - } - } else { - if (nounit) { - d_cnjg(&z__2, &ap[kk]); - z__1.r = temp.r * z__2.r - temp.i * z__2.i, - z__1.i = temp.r * z__2.i + temp.i * - z__2.r; - temp.r = z__1.r, temp.i = z__1.i; - } - for (i__ = j - 1; i__ >= 1; --i__) { - d_cnjg(&z__3, &ap[k]); - i__1 = i__; - z__2.r = z__3.r * x[i__1].r - z__3.i * x[i__1].i, - z__2.i = z__3.r * x[i__1].i + z__3.i * x[ - i__1].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; - temp.r = z__1.r, temp.i = z__1.i; - --k; + } + } else { + if (nounit) { + d_cnjg(&z__2, &ap[kk]); + z__1.r = temp.r * z__2.r - temp.i * z__2.i, + z__1.i = temp.r * z__2.i + temp.i * + z__2.r; + temp.r = z__1.r, temp.i = z__1.i; + } + for (i__ = j - 1; i__ >= 1; --i__) { + d_cnjg(&z__3, &ap[k]); + i__1 = i__; + z__2.r = z__3.r * x[i__1].r - z__3.i * x[i__1].i, + z__2.i = z__3.r * x[i__1].i + z__3.i * x[ + i__1].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + --k; /* L100: */ - } - } - i__1 = j; - x[i__1].r = temp.r, x[i__1].i = temp.i; - kk -= j; + } + } + i__1 = j; + x[i__1].r = temp.r, x[i__1].i = temp.i; + kk -= j; /* L110: */ - } - } else { - jx = kx + (*n - 1) * *incx; - for (j = *n; j >= 1; --j) { - i__1 = jx; - temp.r = x[i__1].r, temp.i = x[i__1].i; - ix = jx; - if (noconj) { - if (nounit) { - i__1 = kk; - z__1.r = temp.r * ap[i__1].r - temp.i * ap[i__1] - .i, z__1.i = temp.r * ap[i__1].i + temp.i - * ap[i__1].r; - temp.r = z__1.r, temp.i = z__1.i; - } - i__1 = kk - j + 1; - for (k = kk - 1; k >= i__1; --k) { - ix -= *incx; - i__2 = k; - i__3 = ix; - z__2.r = ap[i__2].r * x[i__3].r - ap[i__2].i * x[ - i__3].i, z__2.i = ap[i__2].r * x[i__3].i - + ap[i__2].i * x[i__3].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; - temp.r = z__1.r, temp.i = z__1.i; + } + } else { + jx = kx + (*n - 1) * *incx; + for (j = *n; j >= 1; --j) { + i__1 = jx; + temp.r = x[i__1].r, temp.i = x[i__1].i; + ix = jx; + if (noconj) { + if (nounit) { + i__1 = kk; + z__1.r = temp.r * ap[i__1].r - temp.i * ap[i__1] + .i, z__1.i = temp.r * ap[i__1].i + temp.i + * ap[i__1].r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__1 = kk - j + 1; + for (k = kk - 1; k >= i__1; --k) { + ix -= *incx; + i__2 = k; + i__3 = ix; + z__2.r = ap[i__2].r * x[i__3].r - ap[i__2].i * x[ + i__3].i, z__2.i = ap[i__2].r * x[i__3].i + + ap[i__2].i * x[i__3].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; /* L120: */ - } - } else { - if (nounit) { - d_cnjg(&z__2, &ap[kk]); - z__1.r = temp.r * z__2.r - temp.i * z__2.i, - z__1.i = temp.r * z__2.i + temp.i * - z__2.r; - temp.r = z__1.r, temp.i = z__1.i; - } - i__1 = kk - j + 1; - for (k = kk - 1; k >= i__1; --k) { - ix -= *incx; - d_cnjg(&z__3, &ap[k]); - i__2 = ix; - z__2.r = z__3.r * x[i__2].r - z__3.i * x[i__2].i, - z__2.i = z__3.r * x[i__2].i + z__3.i * x[ - i__2].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; - temp.r = z__1.r, temp.i = z__1.i; + } + } else { + if (nounit) { + d_cnjg(&z__2, &ap[kk]); + z__1.r = temp.r * z__2.r - temp.i * z__2.i, + z__1.i = temp.r * z__2.i + temp.i * + z__2.r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__1 = kk - j + 1; + for (k = kk - 1; k >= i__1; --k) { + ix -= *incx; + d_cnjg(&z__3, &ap[k]); + i__2 = ix; + z__2.r = z__3.r * x[i__2].r - z__3.i * x[i__2].i, + z__2.i = z__3.r * x[i__2].i + z__3.i * x[ + i__2].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; /* L130: */ - } - } - i__1 = jx; - x[i__1].r = temp.r, x[i__1].i = temp.i; - jx -= *incx; - kk -= j; + } + } + i__1 = jx; + x[i__1].r = temp.r, x[i__1].i = temp.i; + jx -= *incx; + kk -= j; /* L140: */ - } - } - } else { - kk = 1; - if (*incx == 1) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = j; - temp.r = x[i__2].r, temp.i = x[i__2].i; - k = kk + 1; - if (noconj) { - if (nounit) { - i__2 = kk; - z__1.r = temp.r * ap[i__2].r - temp.i * ap[i__2] - .i, z__1.i = temp.r * ap[i__2].i + temp.i - * ap[i__2].r; - temp.r = z__1.r, temp.i = z__1.i; - } - i__2 = *n; - for (i__ = j + 1; i__ <= i__2; ++i__) { - i__3 = k; - i__4 = i__; - z__2.r = ap[i__3].r * x[i__4].r - ap[i__3].i * x[ - i__4].i, z__2.i = ap[i__3].r * x[i__4].i - + ap[i__3].i * x[i__4].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; - temp.r = z__1.r, temp.i = z__1.i; - ++k; + } + } + } else { + kk = 1; + if (*incx == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + temp.r = x[i__2].r, temp.i = x[i__2].i; + k = kk + 1; + if (noconj) { + if (nounit) { + i__2 = kk; + z__1.r = temp.r * ap[i__2].r - temp.i * ap[i__2] + .i, z__1.i = temp.r * ap[i__2].i + temp.i + * ap[i__2].r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + i__3 = k; + i__4 = i__; + z__2.r = ap[i__3].r * x[i__4].r - ap[i__3].i * x[ + i__4].i, z__2.i = ap[i__3].r * x[i__4].i + + ap[i__3].i * x[i__4].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + ++k; /* L150: */ - } - } else { - if (nounit) { - d_cnjg(&z__2, &ap[kk]); - z__1.r = temp.r * z__2.r - temp.i * z__2.i, - z__1.i = temp.r * z__2.i + temp.i * - z__2.r; - temp.r = z__1.r, temp.i = z__1.i; - } - i__2 = *n; - for (i__ = j + 1; i__ <= i__2; ++i__) { - d_cnjg(&z__3, &ap[k]); - i__3 = i__; - z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, - z__2.i = z__3.r * x[i__3].i + z__3.i * x[ - i__3].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; - temp.r = z__1.r, temp.i = z__1.i; - ++k; + } + } else { + if (nounit) { + d_cnjg(&z__2, &ap[kk]); + z__1.r = temp.r * z__2.r - temp.i * z__2.i, + z__1.i = temp.r * z__2.i + temp.i * + z__2.r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + d_cnjg(&z__3, &ap[k]); + i__3 = i__; + z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, + z__2.i = z__3.r * x[i__3].i + z__3.i * x[ + i__3].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + ++k; /* L160: */ - } - } - i__2 = j; - x[i__2].r = temp.r, x[i__2].i = temp.i; - kk += *n - j + 1; + } + } + i__2 = j; + x[i__2].r = temp.r, x[i__2].i = temp.i; + kk += *n - j + 1; /* L170: */ - } - } else { - jx = kx; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = jx; - temp.r = x[i__2].r, temp.i = x[i__2].i; - ix = jx; - if (noconj) { - if (nounit) { - i__2 = kk; - z__1.r = temp.r * ap[i__2].r - temp.i * ap[i__2] - .i, z__1.i = temp.r * ap[i__2].i + temp.i - * ap[i__2].r; - temp.r = z__1.r, temp.i = z__1.i; - } - i__2 = kk + *n - j; - for (k = kk + 1; k <= i__2; ++k) { - ix += *incx; - i__3 = k; - i__4 = ix; - z__2.r = ap[i__3].r * x[i__4].r - ap[i__3].i * x[ - i__4].i, z__2.i = ap[i__3].r * x[i__4].i - + ap[i__3].i * x[i__4].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; - temp.r = z__1.r, temp.i = z__1.i; + } + } else { + jx = kx; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = jx; + temp.r = x[i__2].r, temp.i = x[i__2].i; + ix = jx; + if (noconj) { + if (nounit) { + i__2 = kk; + z__1.r = temp.r * ap[i__2].r - temp.i * ap[i__2] + .i, z__1.i = temp.r * ap[i__2].i + temp.i + * ap[i__2].r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__2 = kk + *n - j; + for (k = kk + 1; k <= i__2; ++k) { + ix += *incx; + i__3 = k; + i__4 = ix; + z__2.r = ap[i__3].r * x[i__4].r - ap[i__3].i * x[ + i__4].i, z__2.i = ap[i__3].r * x[i__4].i + + ap[i__3].i * x[i__4].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; /* L180: */ - } - } else { - if (nounit) { - d_cnjg(&z__2, &ap[kk]); - z__1.r = temp.r * z__2.r - temp.i * z__2.i, - z__1.i = temp.r * z__2.i + temp.i * - z__2.r; - temp.r = z__1.r, temp.i = z__1.i; - } - i__2 = kk + *n - j; - for (k = kk + 1; k <= i__2; ++k) { - ix += *incx; - d_cnjg(&z__3, &ap[k]); - i__3 = ix; - z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, - z__2.i = z__3.r * x[i__3].i + z__3.i * x[ - i__3].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; - temp.r = z__1.r, temp.i = z__1.i; + } + } else { + if (nounit) { + d_cnjg(&z__2, &ap[kk]); + z__1.r = temp.r * z__2.r - temp.i * z__2.i, + z__1.i = temp.r * z__2.i + temp.i * + z__2.r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__2 = kk + *n - j; + for (k = kk + 1; k <= i__2; ++k) { + ix += *incx; + d_cnjg(&z__3, &ap[k]); + i__3 = ix; + z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, + z__2.i = z__3.r * x[i__3].i + z__3.i * x[ + i__3].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; /* L190: */ - } - } - i__2 = jx; - x[i__2].r = temp.r, x[i__2].i = temp.i; - jx += *incx; - kk += *n - j + 1; + } + } + i__2 = jx; + x[i__2].r = temp.r, x[i__2].i = temp.i; + jx += *incx; + kk += *n - j + 1; /* L200: */ - } - } - } + } + } + } } return 0; @@ -635,5 +635,5 @@ extern "C" { } /* ztpmv_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/ztpsv.cpp b/lib/linalg/ztpsv.cpp index 7e7e64d721..c3c564acd2 100644 --- a/lib/linalg/ztpsv.cpp +++ b/lib/linalg/ztpsv.cpp @@ -1,13 +1,13 @@ /* fortran/ztpsv.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -157,9 +157,9 @@ extern "C" { /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int ztpsv_(char *uplo, char *trans, char *diag, integer *n, - doublecomplex *ap, doublecomplex *x, integer *incx, ftnlen uplo_len, - ftnlen trans_len, ftnlen diag_len) +/* Subroutine */ int ztpsv_(char *uplo, char *trans, char *diag, integer *n, + doublecomplex *ap, doublecomplex *x, integer *incx, ftnlen uplo_len, + ftnlen trans_len, ftnlen diag_len) { /* System generated locals */ integer i__1, i__2, i__3, i__4, i__5; @@ -167,7 +167,7 @@ extern "C" { /* Builtin functions */ void z_div(doublecomplex *, doublecomplex *, doublecomplex *), d_cnjg( - doublecomplex *, doublecomplex *); + doublecomplex *, doublecomplex *); /* Local variables */ integer i__, j, k, kk, ix, jx, kx, info; @@ -208,29 +208,29 @@ extern "C" { /* Function Body */ info = 0; if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", ( - ftnlen)1, (ftnlen)1)) { - info = 1; - } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, - (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, ( - ftnlen)1)) { - info = 2; - } else if (! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, - (char *)"N", (ftnlen)1, (ftnlen)1)) { - info = 3; + ftnlen)1, (ftnlen)1)) { + info = 1; + } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, + (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, ( + ftnlen)1)) { + info = 2; + } else if (! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, + (char *)"N", (ftnlen)1, (ftnlen)1)) { + info = 3; } else if (*n < 0) { - info = 4; + info = 4; } else if (*incx == 0) { - info = 7; + info = 7; } if (info != 0) { - xerbla_((char *)"ZTPSV ", &info, (ftnlen)6); - return 0; + xerbla_((char *)"ZTPSV ", &info, (ftnlen)6); + return 0; } /* Quick return if possible. */ if (*n == 0) { - return 0; + return 0; } noconj = lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1); @@ -240,9 +240,9 @@ extern "C" { /* will be ( N - 1 )*INCX too small for descending loops. */ if (*incx <= 0) { - kx = 1 - (*n - 1) * *incx; + kx = 1 - (*n - 1) * *incx; } else if (*incx != 1) { - kx = 1; + kx = 1; } /* Start the operations. In this version the elements of AP are */ @@ -252,348 +252,348 @@ extern "C" { /* Form x := inv( A )*x. */ - if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { - kk = *n * (*n + 1) / 2; - if (*incx == 1) { - for (j = *n; j >= 1; --j) { - i__1 = j; - if (x[i__1].r != 0. || x[i__1].i != 0.) { - if (nounit) { - i__1 = j; - z_div(&z__1, &x[j], &ap[kk]); - x[i__1].r = z__1.r, x[i__1].i = z__1.i; - } - i__1 = j; - temp.r = x[i__1].r, temp.i = x[i__1].i; - k = kk - 1; - for (i__ = j - 1; i__ >= 1; --i__) { - i__1 = i__; - i__2 = i__; - i__3 = k; - z__2.r = temp.r * ap[i__3].r - temp.i * ap[i__3] - .i, z__2.i = temp.r * ap[i__3].i + temp.i - * ap[i__3].r; - z__1.r = x[i__2].r - z__2.r, z__1.i = x[i__2].i - - z__2.i; - x[i__1].r = z__1.r, x[i__1].i = z__1.i; - --k; + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + kk = *n * (*n + 1) / 2; + if (*incx == 1) { + for (j = *n; j >= 1; --j) { + i__1 = j; + if (x[i__1].r != 0. || x[i__1].i != 0.) { + if (nounit) { + i__1 = j; + z_div(&z__1, &x[j], &ap[kk]); + x[i__1].r = z__1.r, x[i__1].i = z__1.i; + } + i__1 = j; + temp.r = x[i__1].r, temp.i = x[i__1].i; + k = kk - 1; + for (i__ = j - 1; i__ >= 1; --i__) { + i__1 = i__; + i__2 = i__; + i__3 = k; + z__2.r = temp.r * ap[i__3].r - temp.i * ap[i__3] + .i, z__2.i = temp.r * ap[i__3].i + temp.i + * ap[i__3].r; + z__1.r = x[i__2].r - z__2.r, z__1.i = x[i__2].i - + z__2.i; + x[i__1].r = z__1.r, x[i__1].i = z__1.i; + --k; /* L10: */ - } - } - kk -= j; + } + } + kk -= j; /* L20: */ - } - } else { - jx = kx + (*n - 1) * *incx; - for (j = *n; j >= 1; --j) { - i__1 = jx; - if (x[i__1].r != 0. || x[i__1].i != 0.) { - if (nounit) { - i__1 = jx; - z_div(&z__1, &x[jx], &ap[kk]); - x[i__1].r = z__1.r, x[i__1].i = z__1.i; - } - i__1 = jx; - temp.r = x[i__1].r, temp.i = x[i__1].i; - ix = jx; - i__1 = kk - j + 1; - for (k = kk - 1; k >= i__1; --k) { - ix -= *incx; - i__2 = ix; - i__3 = ix; - i__4 = k; - z__2.r = temp.r * ap[i__4].r - temp.i * ap[i__4] - .i, z__2.i = temp.r * ap[i__4].i + temp.i - * ap[i__4].r; - z__1.r = x[i__3].r - z__2.r, z__1.i = x[i__3].i - - z__2.i; - x[i__2].r = z__1.r, x[i__2].i = z__1.i; + } + } else { + jx = kx + (*n - 1) * *incx; + for (j = *n; j >= 1; --j) { + i__1 = jx; + if (x[i__1].r != 0. || x[i__1].i != 0.) { + if (nounit) { + i__1 = jx; + z_div(&z__1, &x[jx], &ap[kk]); + x[i__1].r = z__1.r, x[i__1].i = z__1.i; + } + i__1 = jx; + temp.r = x[i__1].r, temp.i = x[i__1].i; + ix = jx; + i__1 = kk - j + 1; + for (k = kk - 1; k >= i__1; --k) { + ix -= *incx; + i__2 = ix; + i__3 = ix; + i__4 = k; + z__2.r = temp.r * ap[i__4].r - temp.i * ap[i__4] + .i, z__2.i = temp.r * ap[i__4].i + temp.i + * ap[i__4].r; + z__1.r = x[i__3].r - z__2.r, z__1.i = x[i__3].i - + z__2.i; + x[i__2].r = z__1.r, x[i__2].i = z__1.i; /* L30: */ - } - } - jx -= *incx; - kk -= j; + } + } + jx -= *incx; + kk -= j; /* L40: */ - } - } - } else { - kk = 1; - if (*incx == 1) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = j; - if (x[i__2].r != 0. || x[i__2].i != 0.) { - if (nounit) { - i__2 = j; - z_div(&z__1, &x[j], &ap[kk]); - x[i__2].r = z__1.r, x[i__2].i = z__1.i; - } - i__2 = j; - temp.r = x[i__2].r, temp.i = x[i__2].i; - k = kk + 1; - i__2 = *n; - for (i__ = j + 1; i__ <= i__2; ++i__) { - i__3 = i__; - i__4 = i__; - i__5 = k; - z__2.r = temp.r * ap[i__5].r - temp.i * ap[i__5] - .i, z__2.i = temp.r * ap[i__5].i + temp.i - * ap[i__5].r; - z__1.r = x[i__4].r - z__2.r, z__1.i = x[i__4].i - - z__2.i; - x[i__3].r = z__1.r, x[i__3].i = z__1.i; - ++k; + } + } + } else { + kk = 1; + if (*incx == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + if (x[i__2].r != 0. || x[i__2].i != 0.) { + if (nounit) { + i__2 = j; + z_div(&z__1, &x[j], &ap[kk]); + x[i__2].r = z__1.r, x[i__2].i = z__1.i; + } + i__2 = j; + temp.r = x[i__2].r, temp.i = x[i__2].i; + k = kk + 1; + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + i__3 = i__; + i__4 = i__; + i__5 = k; + z__2.r = temp.r * ap[i__5].r - temp.i * ap[i__5] + .i, z__2.i = temp.r * ap[i__5].i + temp.i + * ap[i__5].r; + z__1.r = x[i__4].r - z__2.r, z__1.i = x[i__4].i - + z__2.i; + x[i__3].r = z__1.r, x[i__3].i = z__1.i; + ++k; /* L50: */ - } - } - kk += *n - j + 1; + } + } + kk += *n - j + 1; /* L60: */ - } - } else { - jx = kx; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = jx; - if (x[i__2].r != 0. || x[i__2].i != 0.) { - if (nounit) { - i__2 = jx; - z_div(&z__1, &x[jx], &ap[kk]); - x[i__2].r = z__1.r, x[i__2].i = z__1.i; - } - i__2 = jx; - temp.r = x[i__2].r, temp.i = x[i__2].i; - ix = jx; - i__2 = kk + *n - j; - for (k = kk + 1; k <= i__2; ++k) { - ix += *incx; - i__3 = ix; - i__4 = ix; - i__5 = k; - z__2.r = temp.r * ap[i__5].r - temp.i * ap[i__5] - .i, z__2.i = temp.r * ap[i__5].i + temp.i - * ap[i__5].r; - z__1.r = x[i__4].r - z__2.r, z__1.i = x[i__4].i - - z__2.i; - x[i__3].r = z__1.r, x[i__3].i = z__1.i; + } + } else { + jx = kx; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = jx; + if (x[i__2].r != 0. || x[i__2].i != 0.) { + if (nounit) { + i__2 = jx; + z_div(&z__1, &x[jx], &ap[kk]); + x[i__2].r = z__1.r, x[i__2].i = z__1.i; + } + i__2 = jx; + temp.r = x[i__2].r, temp.i = x[i__2].i; + ix = jx; + i__2 = kk + *n - j; + for (k = kk + 1; k <= i__2; ++k) { + ix += *incx; + i__3 = ix; + i__4 = ix; + i__5 = k; + z__2.r = temp.r * ap[i__5].r - temp.i * ap[i__5] + .i, z__2.i = temp.r * ap[i__5].i + temp.i + * ap[i__5].r; + z__1.r = x[i__4].r - z__2.r, z__1.i = x[i__4].i - + z__2.i; + x[i__3].r = z__1.r, x[i__3].i = z__1.i; /* L70: */ - } - } - jx += *incx; - kk += *n - j + 1; + } + } + jx += *incx; + kk += *n - j + 1; /* L80: */ - } - } - } + } + } + } } else { /* Form x := inv( A**T )*x or x := inv( A**H )*x. */ - if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { - kk = 1; - if (*incx == 1) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = j; - temp.r = x[i__2].r, temp.i = x[i__2].i; - k = kk; - if (noconj) { - i__2 = j - 1; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = k; - i__4 = i__; - z__2.r = ap[i__3].r * x[i__4].r - ap[i__3].i * x[ - i__4].i, z__2.i = ap[i__3].r * x[i__4].i - + ap[i__3].i * x[i__4].r; - z__1.r = temp.r - z__2.r, z__1.i = temp.i - - z__2.i; - temp.r = z__1.r, temp.i = z__1.i; - ++k; + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + kk = 1; + if (*incx == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + temp.r = x[i__2].r, temp.i = x[i__2].i; + k = kk; + if (noconj) { + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = k; + i__4 = i__; + z__2.r = ap[i__3].r * x[i__4].r - ap[i__3].i * x[ + i__4].i, z__2.i = ap[i__3].r * x[i__4].i + + ap[i__3].i * x[i__4].r; + z__1.r = temp.r - z__2.r, z__1.i = temp.i - + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + ++k; /* L90: */ - } - if (nounit) { - z_div(&z__1, &temp, &ap[kk + j - 1]); - temp.r = z__1.r, temp.i = z__1.i; - } - } else { - i__2 = j - 1; - for (i__ = 1; i__ <= i__2; ++i__) { - d_cnjg(&z__3, &ap[k]); - i__3 = i__; - z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, - z__2.i = z__3.r * x[i__3].i + z__3.i * x[ - i__3].r; - z__1.r = temp.r - z__2.r, z__1.i = temp.i - - z__2.i; - temp.r = z__1.r, temp.i = z__1.i; - ++k; + } + if (nounit) { + z_div(&z__1, &temp, &ap[kk + j - 1]); + temp.r = z__1.r, temp.i = z__1.i; + } + } else { + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + d_cnjg(&z__3, &ap[k]); + i__3 = i__; + z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, + z__2.i = z__3.r * x[i__3].i + z__3.i * x[ + i__3].r; + z__1.r = temp.r - z__2.r, z__1.i = temp.i - + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + ++k; /* L100: */ - } - if (nounit) { - d_cnjg(&z__2, &ap[kk + j - 1]); - z_div(&z__1, &temp, &z__2); - temp.r = z__1.r, temp.i = z__1.i; - } - } - i__2 = j; - x[i__2].r = temp.r, x[i__2].i = temp.i; - kk += j; + } + if (nounit) { + d_cnjg(&z__2, &ap[kk + j - 1]); + z_div(&z__1, &temp, &z__2); + temp.r = z__1.r, temp.i = z__1.i; + } + } + i__2 = j; + x[i__2].r = temp.r, x[i__2].i = temp.i; + kk += j; /* L110: */ - } - } else { - jx = kx; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = jx; - temp.r = x[i__2].r, temp.i = x[i__2].i; - ix = kx; - if (noconj) { - i__2 = kk + j - 2; - for (k = kk; k <= i__2; ++k) { - i__3 = k; - i__4 = ix; - z__2.r = ap[i__3].r * x[i__4].r - ap[i__3].i * x[ - i__4].i, z__2.i = ap[i__3].r * x[i__4].i - + ap[i__3].i * x[i__4].r; - z__1.r = temp.r - z__2.r, z__1.i = temp.i - - z__2.i; - temp.r = z__1.r, temp.i = z__1.i; - ix += *incx; + } + } else { + jx = kx; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = jx; + temp.r = x[i__2].r, temp.i = x[i__2].i; + ix = kx; + if (noconj) { + i__2 = kk + j - 2; + for (k = kk; k <= i__2; ++k) { + i__3 = k; + i__4 = ix; + z__2.r = ap[i__3].r * x[i__4].r - ap[i__3].i * x[ + i__4].i, z__2.i = ap[i__3].r * x[i__4].i + + ap[i__3].i * x[i__4].r; + z__1.r = temp.r - z__2.r, z__1.i = temp.i - + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + ix += *incx; /* L120: */ - } - if (nounit) { - z_div(&z__1, &temp, &ap[kk + j - 1]); - temp.r = z__1.r, temp.i = z__1.i; - } - } else { - i__2 = kk + j - 2; - for (k = kk; k <= i__2; ++k) { - d_cnjg(&z__3, &ap[k]); - i__3 = ix; - z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, - z__2.i = z__3.r * x[i__3].i + z__3.i * x[ - i__3].r; - z__1.r = temp.r - z__2.r, z__1.i = temp.i - - z__2.i; - temp.r = z__1.r, temp.i = z__1.i; - ix += *incx; + } + if (nounit) { + z_div(&z__1, &temp, &ap[kk + j - 1]); + temp.r = z__1.r, temp.i = z__1.i; + } + } else { + i__2 = kk + j - 2; + for (k = kk; k <= i__2; ++k) { + d_cnjg(&z__3, &ap[k]); + i__3 = ix; + z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, + z__2.i = z__3.r * x[i__3].i + z__3.i * x[ + i__3].r; + z__1.r = temp.r - z__2.r, z__1.i = temp.i - + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + ix += *incx; /* L130: */ - } - if (nounit) { - d_cnjg(&z__2, &ap[kk + j - 1]); - z_div(&z__1, &temp, &z__2); - temp.r = z__1.r, temp.i = z__1.i; - } - } - i__2 = jx; - x[i__2].r = temp.r, x[i__2].i = temp.i; - jx += *incx; - kk += j; + } + if (nounit) { + d_cnjg(&z__2, &ap[kk + j - 1]); + z_div(&z__1, &temp, &z__2); + temp.r = z__1.r, temp.i = z__1.i; + } + } + i__2 = jx; + x[i__2].r = temp.r, x[i__2].i = temp.i; + jx += *incx; + kk += j; /* L140: */ - } - } - } else { - kk = *n * (*n + 1) / 2; - if (*incx == 1) { - for (j = *n; j >= 1; --j) { - i__1 = j; - temp.r = x[i__1].r, temp.i = x[i__1].i; - k = kk; - if (noconj) { - i__1 = j + 1; - for (i__ = *n; i__ >= i__1; --i__) { - i__2 = k; - i__3 = i__; - z__2.r = ap[i__2].r * x[i__3].r - ap[i__2].i * x[ - i__3].i, z__2.i = ap[i__2].r * x[i__3].i - + ap[i__2].i * x[i__3].r; - z__1.r = temp.r - z__2.r, z__1.i = temp.i - - z__2.i; - temp.r = z__1.r, temp.i = z__1.i; - --k; + } + } + } else { + kk = *n * (*n + 1) / 2; + if (*incx == 1) { + for (j = *n; j >= 1; --j) { + i__1 = j; + temp.r = x[i__1].r, temp.i = x[i__1].i; + k = kk; + if (noconj) { + i__1 = j + 1; + for (i__ = *n; i__ >= i__1; --i__) { + i__2 = k; + i__3 = i__; + z__2.r = ap[i__2].r * x[i__3].r - ap[i__2].i * x[ + i__3].i, z__2.i = ap[i__2].r * x[i__3].i + + ap[i__2].i * x[i__3].r; + z__1.r = temp.r - z__2.r, z__1.i = temp.i - + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + --k; /* L150: */ - } - if (nounit) { - z_div(&z__1, &temp, &ap[kk - *n + j]); - temp.r = z__1.r, temp.i = z__1.i; - } - } else { - i__1 = j + 1; - for (i__ = *n; i__ >= i__1; --i__) { - d_cnjg(&z__3, &ap[k]); - i__2 = i__; - z__2.r = z__3.r * x[i__2].r - z__3.i * x[i__2].i, - z__2.i = z__3.r * x[i__2].i + z__3.i * x[ - i__2].r; - z__1.r = temp.r - z__2.r, z__1.i = temp.i - - z__2.i; - temp.r = z__1.r, temp.i = z__1.i; - --k; + } + if (nounit) { + z_div(&z__1, &temp, &ap[kk - *n + j]); + temp.r = z__1.r, temp.i = z__1.i; + } + } else { + i__1 = j + 1; + for (i__ = *n; i__ >= i__1; --i__) { + d_cnjg(&z__3, &ap[k]); + i__2 = i__; + z__2.r = z__3.r * x[i__2].r - z__3.i * x[i__2].i, + z__2.i = z__3.r * x[i__2].i + z__3.i * x[ + i__2].r; + z__1.r = temp.r - z__2.r, z__1.i = temp.i - + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + --k; /* L160: */ - } - if (nounit) { - d_cnjg(&z__2, &ap[kk - *n + j]); - z_div(&z__1, &temp, &z__2); - temp.r = z__1.r, temp.i = z__1.i; - } - } - i__1 = j; - x[i__1].r = temp.r, x[i__1].i = temp.i; - kk -= *n - j + 1; + } + if (nounit) { + d_cnjg(&z__2, &ap[kk - *n + j]); + z_div(&z__1, &temp, &z__2); + temp.r = z__1.r, temp.i = z__1.i; + } + } + i__1 = j; + x[i__1].r = temp.r, x[i__1].i = temp.i; + kk -= *n - j + 1; /* L170: */ - } - } else { - kx += (*n - 1) * *incx; - jx = kx; - for (j = *n; j >= 1; --j) { - i__1 = jx; - temp.r = x[i__1].r, temp.i = x[i__1].i; - ix = kx; - if (noconj) { - i__1 = kk - (*n - (j + 1)); - for (k = kk; k >= i__1; --k) { - i__2 = k; - i__3 = ix; - z__2.r = ap[i__2].r * x[i__3].r - ap[i__2].i * x[ - i__3].i, z__2.i = ap[i__2].r * x[i__3].i - + ap[i__2].i * x[i__3].r; - z__1.r = temp.r - z__2.r, z__1.i = temp.i - - z__2.i; - temp.r = z__1.r, temp.i = z__1.i; - ix -= *incx; + } + } else { + kx += (*n - 1) * *incx; + jx = kx; + for (j = *n; j >= 1; --j) { + i__1 = jx; + temp.r = x[i__1].r, temp.i = x[i__1].i; + ix = kx; + if (noconj) { + i__1 = kk - (*n - (j + 1)); + for (k = kk; k >= i__1; --k) { + i__2 = k; + i__3 = ix; + z__2.r = ap[i__2].r * x[i__3].r - ap[i__2].i * x[ + i__3].i, z__2.i = ap[i__2].r * x[i__3].i + + ap[i__2].i * x[i__3].r; + z__1.r = temp.r - z__2.r, z__1.i = temp.i - + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + ix -= *incx; /* L180: */ - } - if (nounit) { - z_div(&z__1, &temp, &ap[kk - *n + j]); - temp.r = z__1.r, temp.i = z__1.i; - } - } else { - i__1 = kk - (*n - (j + 1)); - for (k = kk; k >= i__1; --k) { - d_cnjg(&z__3, &ap[k]); - i__2 = ix; - z__2.r = z__3.r * x[i__2].r - z__3.i * x[i__2].i, - z__2.i = z__3.r * x[i__2].i + z__3.i * x[ - i__2].r; - z__1.r = temp.r - z__2.r, z__1.i = temp.i - - z__2.i; - temp.r = z__1.r, temp.i = z__1.i; - ix -= *incx; + } + if (nounit) { + z_div(&z__1, &temp, &ap[kk - *n + j]); + temp.r = z__1.r, temp.i = z__1.i; + } + } else { + i__1 = kk - (*n - (j + 1)); + for (k = kk; k >= i__1; --k) { + d_cnjg(&z__3, &ap[k]); + i__2 = ix; + z__2.r = z__3.r * x[i__2].r - z__3.i * x[i__2].i, + z__2.i = z__3.r * x[i__2].i + z__3.i * x[ + i__2].r; + z__1.r = temp.r - z__2.r, z__1.i = temp.i - + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; + ix -= *incx; /* L190: */ - } - if (nounit) { - d_cnjg(&z__2, &ap[kk - *n + j]); - z_div(&z__1, &temp, &z__2); - temp.r = z__1.r, temp.i = z__1.i; - } - } - i__1 = jx; - x[i__1].r = temp.r, x[i__1].i = temp.i; - jx -= *incx; - kk -= *n - j + 1; + } + if (nounit) { + d_cnjg(&z__2, &ap[kk - *n + j]); + z_div(&z__1, &temp, &z__2); + temp.r = z__1.r, temp.i = z__1.i; + } + } + i__1 = jx; + x[i__1].r = temp.r, x[i__1].i = temp.i; + jx -= *incx; + kk -= *n - j + 1; /* L200: */ - } - } - } + } + } + } } return 0; @@ -603,5 +603,5 @@ extern "C" { } /* ztpsv_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/ztptri.cpp b/lib/linalg/ztptri.cpp index c781cb964f..eb5c2988e3 100644 --- a/lib/linalg/ztptri.cpp +++ b/lib/linalg/ztptri.cpp @@ -1,13 +1,13 @@ /* fortran/ztptri.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -138,8 +138,8 @@ f"> */ /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int ztptri_(char *uplo, char *diag, integer *n, - doublecomplex *ap, integer *info, ftnlen uplo_len, ftnlen diag_len) +/* Subroutine */ int ztptri_(char *uplo, char *diag, integer *n, + doublecomplex *ap, integer *info, ftnlen uplo_len, ftnlen diag_len) { /* System generated locals */ integer i__1, i__2; @@ -152,12 +152,12 @@ f"> */ integer j, jc, jj; doublecomplex ajj; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int zscal_(integer *, doublecomplex *, - doublecomplex *, integer *); + extern /* Subroutine */ int zscal_(integer *, doublecomplex *, + doublecomplex *, integer *); logical upper; - extern /* Subroutine */ int ztpmv_(char *, char *, char *, integer *, - doublecomplex *, doublecomplex *, integer *, ftnlen, ftnlen, - ftnlen), xerbla_(char *, integer *, ftnlen); + extern /* Subroutine */ int ztpmv_(char *, char *, char *, integer *, + doublecomplex *, doublecomplex *, integer *, ftnlen, ftnlen, + ftnlen), xerbla_(char *, integer *, ftnlen); integer jclast; logical nounit; @@ -193,108 +193,108 @@ f"> */ upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); nounit = lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1); if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { - *info = -1; + *info = -1; } else if (! nounit && ! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1)) { - *info = -2; + *info = -2; } else if (*n < 0) { - *info = -3; + *info = -3; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"ZTPTRI", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"ZTPTRI", &i__1, (ftnlen)6); + return 0; } /* Check for singularity if non-unit. */ if (nounit) { - if (upper) { - jj = 0; - i__1 = *n; - for (*info = 1; *info <= i__1; ++(*info)) { - jj += *info; - i__2 = jj; - if (ap[i__2].r == 0. && ap[i__2].i == 0.) { - return 0; - } + if (upper) { + jj = 0; + i__1 = *n; + for (*info = 1; *info <= i__1; ++(*info)) { + jj += *info; + i__2 = jj; + if (ap[i__2].r == 0. && ap[i__2].i == 0.) { + return 0; + } /* L10: */ - } - } else { - jj = 1; - i__1 = *n; - for (*info = 1; *info <= i__1; ++(*info)) { - i__2 = jj; - if (ap[i__2].r == 0. && ap[i__2].i == 0.) { - return 0; - } - jj = jj + *n - *info + 1; + } + } else { + jj = 1; + i__1 = *n; + for (*info = 1; *info <= i__1; ++(*info)) { + i__2 = jj; + if (ap[i__2].r == 0. && ap[i__2].i == 0.) { + return 0; + } + jj = jj + *n - *info + 1; /* L20: */ - } - } - *info = 0; + } + } + *info = 0; } if (upper) { /* Compute inverse of upper triangular matrix. */ - jc = 1; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - if (nounit) { - i__2 = jc + j - 1; - z_div(&z__1, &c_b1, &ap[jc + j - 1]); - ap[i__2].r = z__1.r, ap[i__2].i = z__1.i; - i__2 = jc + j - 1; - z__1.r = -ap[i__2].r, z__1.i = -ap[i__2].i; - ajj.r = z__1.r, ajj.i = z__1.i; - } else { - z__1.r = -1., z__1.i = -0.; - ajj.r = z__1.r, ajj.i = z__1.i; - } + jc = 1; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + if (nounit) { + i__2 = jc + j - 1; + z_div(&z__1, &c_b1, &ap[jc + j - 1]); + ap[i__2].r = z__1.r, ap[i__2].i = z__1.i; + i__2 = jc + j - 1; + z__1.r = -ap[i__2].r, z__1.i = -ap[i__2].i; + ajj.r = z__1.r, ajj.i = z__1.i; + } else { + z__1.r = -1., z__1.i = -0.; + ajj.r = z__1.r, ajj.i = z__1.i; + } /* Compute elements 1:j-1 of j-th column. */ - i__2 = j - 1; - ztpmv_((char *)"Upper", (char *)"No transpose", diag, &i__2, &ap[1], &ap[jc], & - c__1, (ftnlen)5, (ftnlen)12, (ftnlen)1); - i__2 = j - 1; - zscal_(&i__2, &ajj, &ap[jc], &c__1); - jc += j; + i__2 = j - 1; + ztpmv_((char *)"Upper", (char *)"No transpose", diag, &i__2, &ap[1], &ap[jc], & + c__1, (ftnlen)5, (ftnlen)12, (ftnlen)1); + i__2 = j - 1; + zscal_(&i__2, &ajj, &ap[jc], &c__1); + jc += j; /* L30: */ - } + } } else { /* Compute inverse of lower triangular matrix. */ - jc = *n * (*n + 1) / 2; - for (j = *n; j >= 1; --j) { - if (nounit) { - i__1 = jc; - z_div(&z__1, &c_b1, &ap[jc]); - ap[i__1].r = z__1.r, ap[i__1].i = z__1.i; - i__1 = jc; - z__1.r = -ap[i__1].r, z__1.i = -ap[i__1].i; - ajj.r = z__1.r, ajj.i = z__1.i; - } else { - z__1.r = -1., z__1.i = -0.; - ajj.r = z__1.r, ajj.i = z__1.i; - } - if (j < *n) { + jc = *n * (*n + 1) / 2; + for (j = *n; j >= 1; --j) { + if (nounit) { + i__1 = jc; + z_div(&z__1, &c_b1, &ap[jc]); + ap[i__1].r = z__1.r, ap[i__1].i = z__1.i; + i__1 = jc; + z__1.r = -ap[i__1].r, z__1.i = -ap[i__1].i; + ajj.r = z__1.r, ajj.i = z__1.i; + } else { + z__1.r = -1., z__1.i = -0.; + ajj.r = z__1.r, ajj.i = z__1.i; + } + if (j < *n) { /* Compute elements j+1:n of j-th column. */ - i__1 = *n - j; - ztpmv_((char *)"Lower", (char *)"No transpose", diag, &i__1, &ap[jclast], &ap[ - jc + 1], &c__1, (ftnlen)5, (ftnlen)12, (ftnlen)1); - i__1 = *n - j; - zscal_(&i__1, &ajj, &ap[jc + 1], &c__1); - } - jclast = jc; - jc = jc - *n + j - 2; + i__1 = *n - j; + ztpmv_((char *)"Lower", (char *)"No transpose", diag, &i__1, &ap[jclast], &ap[ + jc + 1], &c__1, (ftnlen)5, (ftnlen)12, (ftnlen)1); + i__1 = *n - j; + zscal_(&i__1, &ajj, &ap[jc + 1], &c__1); + } + jclast = jc; + jc = jc - *n + j - 2; /* L40: */ - } + } } return 0; @@ -304,5 +304,5 @@ f"> */ } /* ztptri_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/ztrmm.cpp b/lib/linalg/ztrmm.cpp index cd71371d5b..3fec24189e 100644 --- a/lib/linalg/ztrmm.cpp +++ b/lib/linalg/ztrmm.cpp @@ -1,13 +1,13 @@ /* fortran/ztrmm.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -190,14 +190,14 @@ extern "C" { /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int ztrmm_(char *side, char *uplo, char *transa, char *diag, - integer *m, integer *n, doublecomplex *alpha, doublecomplex *a, - integer *lda, doublecomplex *b, integer *ldb, ftnlen side_len, ftnlen - uplo_len, ftnlen transa_len, ftnlen diag_len) +/* Subroutine */ int ztrmm_(char *side, char *uplo, char *transa, char *diag, + integer *m, integer *n, doublecomplex *alpha, doublecomplex *a, + integer *lda, doublecomplex *b, integer *ldb, ftnlen side_len, ftnlen + uplo_len, ftnlen transa_len, ftnlen diag_len) { /* System generated locals */ - integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4, i__5, - i__6; + integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4, i__5, + i__6; doublecomplex z__1, z__2, z__3; /* Builtin functions */ @@ -249,9 +249,9 @@ extern "C" { /* Function Body */ lside = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); if (lside) { - nrowa = *m; + nrowa = *m; } else { - nrowa = *n; + nrowa = *n; } noconj = lsame_(transa, (char *)"T", (ftnlen)1, (ftnlen)1); nounit = lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1); @@ -259,496 +259,496 @@ extern "C" { info = 0; if (! lside && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { - info = 1; + info = 1; } else if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { - info = 2; + info = 2; } else if (! lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(transa, - (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(transa, (char *)"C", (ftnlen)1, ( - ftnlen)1)) { - info = 3; - } else if (! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, - (char *)"N", (ftnlen)1, (ftnlen)1)) { - info = 4; + (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(transa, (char *)"C", (ftnlen)1, ( + ftnlen)1)) { + info = 3; + } else if (! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, + (char *)"N", (ftnlen)1, (ftnlen)1)) { + info = 4; } else if (*m < 0) { - info = 5; + info = 5; } else if (*n < 0) { - info = 6; + info = 6; } else if (*lda < max(1,nrowa)) { - info = 9; + info = 9; } else if (*ldb < max(1,*m)) { - info = 11; + info = 11; } if (info != 0) { - xerbla_((char *)"ZTRMM ", &info, (ftnlen)6); - return 0; + xerbla_((char *)"ZTRMM ", &info, (ftnlen)6); + return 0; } /* Quick return if possible. */ if (*m == 0 || *n == 0) { - return 0; + return 0; } /* And when alpha.eq.zero. */ if (alpha->r == 0. && alpha->i == 0.) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * b_dim1; - b[i__3].r = 0., b[i__3].i = 0.; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * b_dim1; + b[i__3].r = 0., b[i__3].i = 0.; /* L10: */ - } + } /* L20: */ - } - return 0; + } + return 0; } /* Start the operations. */ if (lside) { - if (lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1)) { + if (lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1)) { /* Form B := alpha*A*B. */ - if (upper) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (k = 1; k <= i__2; ++k) { - i__3 = k + j * b_dim1; - if (b[i__3].r != 0. || b[i__3].i != 0.) { - i__3 = k + j * b_dim1; - z__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3] - .i, z__1.i = alpha->r * b[i__3].i + - alpha->i * b[i__3].r; - temp.r = z__1.r, temp.i = z__1.i; - i__3 = k - 1; - for (i__ = 1; i__ <= i__3; ++i__) { - i__4 = i__ + j * b_dim1; - i__5 = i__ + j * b_dim1; - i__6 = i__ + k * a_dim1; - z__2.r = temp.r * a[i__6].r - temp.i * a[i__6] - .i, z__2.i = temp.r * a[i__6].i + - temp.i * a[i__6].r; - z__1.r = b[i__5].r + z__2.r, z__1.i = b[i__5] - .i + z__2.i; - b[i__4].r = z__1.r, b[i__4].i = z__1.i; + if (upper) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (k = 1; k <= i__2; ++k) { + i__3 = k + j * b_dim1; + if (b[i__3].r != 0. || b[i__3].i != 0.) { + i__3 = k + j * b_dim1; + z__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3] + .i, z__1.i = alpha->r * b[i__3].i + + alpha->i * b[i__3].r; + temp.r = z__1.r, temp.i = z__1.i; + i__3 = k - 1; + for (i__ = 1; i__ <= i__3; ++i__) { + i__4 = i__ + j * b_dim1; + i__5 = i__ + j * b_dim1; + i__6 = i__ + k * a_dim1; + z__2.r = temp.r * a[i__6].r - temp.i * a[i__6] + .i, z__2.i = temp.r * a[i__6].i + + temp.i * a[i__6].r; + z__1.r = b[i__5].r + z__2.r, z__1.i = b[i__5] + .i + z__2.i; + b[i__4].r = z__1.r, b[i__4].i = z__1.i; /* L30: */ - } - if (nounit) { - i__3 = k + k * a_dim1; - z__1.r = temp.r * a[i__3].r - temp.i * a[i__3] - .i, z__1.i = temp.r * a[i__3].i + - temp.i * a[i__3].r; - temp.r = z__1.r, temp.i = z__1.i; - } - i__3 = k + j * b_dim1; - b[i__3].r = temp.r, b[i__3].i = temp.i; - } + } + if (nounit) { + i__3 = k + k * a_dim1; + z__1.r = temp.r * a[i__3].r - temp.i * a[i__3] + .i, z__1.i = temp.r * a[i__3].i + + temp.i * a[i__3].r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__3 = k + j * b_dim1; + b[i__3].r = temp.r, b[i__3].i = temp.i; + } /* L40: */ - } + } /* L50: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - for (k = *m; k >= 1; --k) { - i__2 = k + j * b_dim1; - if (b[i__2].r != 0. || b[i__2].i != 0.) { - i__2 = k + j * b_dim1; - z__1.r = alpha->r * b[i__2].r - alpha->i * b[i__2] - .i, z__1.i = alpha->r * b[i__2].i + - alpha->i * b[i__2].r; - temp.r = z__1.r, temp.i = z__1.i; - i__2 = k + j * b_dim1; - b[i__2].r = temp.r, b[i__2].i = temp.i; - if (nounit) { - i__2 = k + j * b_dim1; - i__3 = k + j * b_dim1; - i__4 = k + k * a_dim1; - z__1.r = b[i__3].r * a[i__4].r - b[i__3].i * - a[i__4].i, z__1.i = b[i__3].r * a[ - i__4].i + b[i__3].i * a[i__4].r; - b[i__2].r = z__1.r, b[i__2].i = z__1.i; - } - i__2 = *m; - for (i__ = k + 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * b_dim1; - i__4 = i__ + j * b_dim1; - i__5 = i__ + k * a_dim1; - z__2.r = temp.r * a[i__5].r - temp.i * a[i__5] - .i, z__2.i = temp.r * a[i__5].i + - temp.i * a[i__5].r; - z__1.r = b[i__4].r + z__2.r, z__1.i = b[i__4] - .i + z__2.i; - b[i__3].r = z__1.r, b[i__3].i = z__1.i; + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + for (k = *m; k >= 1; --k) { + i__2 = k + j * b_dim1; + if (b[i__2].r != 0. || b[i__2].i != 0.) { + i__2 = k + j * b_dim1; + z__1.r = alpha->r * b[i__2].r - alpha->i * b[i__2] + .i, z__1.i = alpha->r * b[i__2].i + + alpha->i * b[i__2].r; + temp.r = z__1.r, temp.i = z__1.i; + i__2 = k + j * b_dim1; + b[i__2].r = temp.r, b[i__2].i = temp.i; + if (nounit) { + i__2 = k + j * b_dim1; + i__3 = k + j * b_dim1; + i__4 = k + k * a_dim1; + z__1.r = b[i__3].r * a[i__4].r - b[i__3].i * + a[i__4].i, z__1.i = b[i__3].r * a[ + i__4].i + b[i__3].i * a[i__4].r; + b[i__2].r = z__1.r, b[i__2].i = z__1.i; + } + i__2 = *m; + for (i__ = k + 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * b_dim1; + i__4 = i__ + j * b_dim1; + i__5 = i__ + k * a_dim1; + z__2.r = temp.r * a[i__5].r - temp.i * a[i__5] + .i, z__2.i = temp.r * a[i__5].i + + temp.i * a[i__5].r; + z__1.r = b[i__4].r + z__2.r, z__1.i = b[i__4] + .i + z__2.i; + b[i__3].r = z__1.r, b[i__3].i = z__1.i; /* L60: */ - } - } + } + } /* L70: */ - } + } /* L80: */ - } - } - } else { + } + } + } else { /* Form B := alpha*A**T*B or B := alpha*A**H*B. */ - if (upper) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - for (i__ = *m; i__ >= 1; --i__) { - i__2 = i__ + j * b_dim1; - temp.r = b[i__2].r, temp.i = b[i__2].i; - if (noconj) { - if (nounit) { - i__2 = i__ + i__ * a_dim1; - z__1.r = temp.r * a[i__2].r - temp.i * a[i__2] - .i, z__1.i = temp.r * a[i__2].i + - temp.i * a[i__2].r; - temp.r = z__1.r, temp.i = z__1.i; - } - i__2 = i__ - 1; - for (k = 1; k <= i__2; ++k) { - i__3 = k + i__ * a_dim1; - i__4 = k + j * b_dim1; - z__2.r = a[i__3].r * b[i__4].r - a[i__3].i * - b[i__4].i, z__2.i = a[i__3].r * b[ - i__4].i + a[i__3].i * b[i__4].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; - temp.r = z__1.r, temp.i = z__1.i; + if (upper) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + for (i__ = *m; i__ >= 1; --i__) { + i__2 = i__ + j * b_dim1; + temp.r = b[i__2].r, temp.i = b[i__2].i; + if (noconj) { + if (nounit) { + i__2 = i__ + i__ * a_dim1; + z__1.r = temp.r * a[i__2].r - temp.i * a[i__2] + .i, z__1.i = temp.r * a[i__2].i + + temp.i * a[i__2].r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__2 = i__ - 1; + for (k = 1; k <= i__2; ++k) { + i__3 = k + i__ * a_dim1; + i__4 = k + j * b_dim1; + z__2.r = a[i__3].r * b[i__4].r - a[i__3].i * + b[i__4].i, z__2.i = a[i__3].r * b[ + i__4].i + a[i__3].i * b[i__4].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; /* L90: */ - } - } else { - if (nounit) { - d_cnjg(&z__2, &a[i__ + i__ * a_dim1]); - z__1.r = temp.r * z__2.r - temp.i * z__2.i, - z__1.i = temp.r * z__2.i + temp.i * - z__2.r; - temp.r = z__1.r, temp.i = z__1.i; - } - i__2 = i__ - 1; - for (k = 1; k <= i__2; ++k) { - d_cnjg(&z__3, &a[k + i__ * a_dim1]); - i__3 = k + j * b_dim1; - z__2.r = z__3.r * b[i__3].r - z__3.i * b[i__3] - .i, z__2.i = z__3.r * b[i__3].i + - z__3.i * b[i__3].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; - temp.r = z__1.r, temp.i = z__1.i; + } + } else { + if (nounit) { + d_cnjg(&z__2, &a[i__ + i__ * a_dim1]); + z__1.r = temp.r * z__2.r - temp.i * z__2.i, + z__1.i = temp.r * z__2.i + temp.i * + z__2.r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__2 = i__ - 1; + for (k = 1; k <= i__2; ++k) { + d_cnjg(&z__3, &a[k + i__ * a_dim1]); + i__3 = k + j * b_dim1; + z__2.r = z__3.r * b[i__3].r - z__3.i * b[i__3] + .i, z__2.i = z__3.r * b[i__3].i + + z__3.i * b[i__3].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; /* L100: */ - } - } - i__2 = i__ + j * b_dim1; - z__1.r = alpha->r * temp.r - alpha->i * temp.i, - z__1.i = alpha->r * temp.i + alpha->i * - temp.r; - b[i__2].r = z__1.r, b[i__2].i = z__1.i; + } + } + i__2 = i__ + j * b_dim1; + z__1.r = alpha->r * temp.r - alpha->i * temp.i, + z__1.i = alpha->r * temp.i + alpha->i * + temp.r; + b[i__2].r = z__1.r, b[i__2].i = z__1.i; /* L110: */ - } + } /* L120: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * b_dim1; - temp.r = b[i__3].r, temp.i = b[i__3].i; - if (noconj) { - if (nounit) { - i__3 = i__ + i__ * a_dim1; - z__1.r = temp.r * a[i__3].r - temp.i * a[i__3] - .i, z__1.i = temp.r * a[i__3].i + - temp.i * a[i__3].r; - temp.r = z__1.r, temp.i = z__1.i; - } - i__3 = *m; - for (k = i__ + 1; k <= i__3; ++k) { - i__4 = k + i__ * a_dim1; - i__5 = k + j * b_dim1; - z__2.r = a[i__4].r * b[i__5].r - a[i__4].i * - b[i__5].i, z__2.i = a[i__4].r * b[ - i__5].i + a[i__4].i * b[i__5].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; - temp.r = z__1.r, temp.i = z__1.i; + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * b_dim1; + temp.r = b[i__3].r, temp.i = b[i__3].i; + if (noconj) { + if (nounit) { + i__3 = i__ + i__ * a_dim1; + z__1.r = temp.r * a[i__3].r - temp.i * a[i__3] + .i, z__1.i = temp.r * a[i__3].i + + temp.i * a[i__3].r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__3 = *m; + for (k = i__ + 1; k <= i__3; ++k) { + i__4 = k + i__ * a_dim1; + i__5 = k + j * b_dim1; + z__2.r = a[i__4].r * b[i__5].r - a[i__4].i * + b[i__5].i, z__2.i = a[i__4].r * b[ + i__5].i + a[i__4].i * b[i__5].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; /* L130: */ - } - } else { - if (nounit) { - d_cnjg(&z__2, &a[i__ + i__ * a_dim1]); - z__1.r = temp.r * z__2.r - temp.i * z__2.i, - z__1.i = temp.r * z__2.i + temp.i * - z__2.r; - temp.r = z__1.r, temp.i = z__1.i; - } - i__3 = *m; - for (k = i__ + 1; k <= i__3; ++k) { - d_cnjg(&z__3, &a[k + i__ * a_dim1]); - i__4 = k + j * b_dim1; - z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4] - .i, z__2.i = z__3.r * b[i__4].i + - z__3.i * b[i__4].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; - temp.r = z__1.r, temp.i = z__1.i; + } + } else { + if (nounit) { + d_cnjg(&z__2, &a[i__ + i__ * a_dim1]); + z__1.r = temp.r * z__2.r - temp.i * z__2.i, + z__1.i = temp.r * z__2.i + temp.i * + z__2.r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__3 = *m; + for (k = i__ + 1; k <= i__3; ++k) { + d_cnjg(&z__3, &a[k + i__ * a_dim1]); + i__4 = k + j * b_dim1; + z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4] + .i, z__2.i = z__3.r * b[i__4].i + + z__3.i * b[i__4].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; /* L140: */ - } - } - i__3 = i__ + j * b_dim1; - z__1.r = alpha->r * temp.r - alpha->i * temp.i, - z__1.i = alpha->r * temp.i + alpha->i * - temp.r; - b[i__3].r = z__1.r, b[i__3].i = z__1.i; + } + } + i__3 = i__ + j * b_dim1; + z__1.r = alpha->r * temp.r - alpha->i * temp.i, + z__1.i = alpha->r * temp.i + alpha->i * + temp.r; + b[i__3].r = z__1.r, b[i__3].i = z__1.i; /* L150: */ - } + } /* L160: */ - } - } - } + } + } + } } else { - if (lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1)) { + if (lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1)) { /* Form B := alpha*B*A. */ - if (upper) { - for (j = *n; j >= 1; --j) { - temp.r = alpha->r, temp.i = alpha->i; - if (nounit) { - i__1 = j + j * a_dim1; - z__1.r = temp.r * a[i__1].r - temp.i * a[i__1].i, - z__1.i = temp.r * a[i__1].i + temp.i * a[i__1] - .r; - temp.r = z__1.r, temp.i = z__1.i; - } - i__1 = *m; - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = i__ + j * b_dim1; - i__3 = i__ + j * b_dim1; - z__1.r = temp.r * b[i__3].r - temp.i * b[i__3].i, - z__1.i = temp.r * b[i__3].i + temp.i * b[i__3] - .r; - b[i__2].r = z__1.r, b[i__2].i = z__1.i; + if (upper) { + for (j = *n; j >= 1; --j) { + temp.r = alpha->r, temp.i = alpha->i; + if (nounit) { + i__1 = j + j * a_dim1; + z__1.r = temp.r * a[i__1].r - temp.i * a[i__1].i, + z__1.i = temp.r * a[i__1].i + temp.i * a[i__1] + .r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__ + j * b_dim1; + i__3 = i__ + j * b_dim1; + z__1.r = temp.r * b[i__3].r - temp.i * b[i__3].i, + z__1.i = temp.r * b[i__3].i + temp.i * b[i__3] + .r; + b[i__2].r = z__1.r, b[i__2].i = z__1.i; /* L170: */ - } - i__1 = j - 1; - for (k = 1; k <= i__1; ++k) { - i__2 = k + j * a_dim1; - if (a[i__2].r != 0. || a[i__2].i != 0.) { - i__2 = k + j * a_dim1; - z__1.r = alpha->r * a[i__2].r - alpha->i * a[i__2] - .i, z__1.i = alpha->r * a[i__2].i + - alpha->i * a[i__2].r; - temp.r = z__1.r, temp.i = z__1.i; - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * b_dim1; - i__4 = i__ + j * b_dim1; - i__5 = i__ + k * b_dim1; - z__2.r = temp.r * b[i__5].r - temp.i * b[i__5] - .i, z__2.i = temp.r * b[i__5].i + - temp.i * b[i__5].r; - z__1.r = b[i__4].r + z__2.r, z__1.i = b[i__4] - .i + z__2.i; - b[i__3].r = z__1.r, b[i__3].i = z__1.i; + } + i__1 = j - 1; + for (k = 1; k <= i__1; ++k) { + i__2 = k + j * a_dim1; + if (a[i__2].r != 0. || a[i__2].i != 0.) { + i__2 = k + j * a_dim1; + z__1.r = alpha->r * a[i__2].r - alpha->i * a[i__2] + .i, z__1.i = alpha->r * a[i__2].i + + alpha->i * a[i__2].r; + temp.r = z__1.r, temp.i = z__1.i; + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * b_dim1; + i__4 = i__ + j * b_dim1; + i__5 = i__ + k * b_dim1; + z__2.r = temp.r * b[i__5].r - temp.i * b[i__5] + .i, z__2.i = temp.r * b[i__5].i + + temp.i * b[i__5].r; + z__1.r = b[i__4].r + z__2.r, z__1.i = b[i__4] + .i + z__2.i; + b[i__3].r = z__1.r, b[i__3].i = z__1.i; /* L180: */ - } - } + } + } /* L190: */ - } + } /* L200: */ - } - } else { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - temp.r = alpha->r, temp.i = alpha->i; - if (nounit) { - i__2 = j + j * a_dim1; - z__1.r = temp.r * a[i__2].r - temp.i * a[i__2].i, - z__1.i = temp.r * a[i__2].i + temp.i * a[i__2] - .r; - temp.r = z__1.r, temp.i = z__1.i; - } - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * b_dim1; - i__4 = i__ + j * b_dim1; - z__1.r = temp.r * b[i__4].r - temp.i * b[i__4].i, - z__1.i = temp.r * b[i__4].i + temp.i * b[i__4] - .r; - b[i__3].r = z__1.r, b[i__3].i = z__1.i; + } + } else { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + temp.r = alpha->r, temp.i = alpha->i; + if (nounit) { + i__2 = j + j * a_dim1; + z__1.r = temp.r * a[i__2].r - temp.i * a[i__2].i, + z__1.i = temp.r * a[i__2].i + temp.i * a[i__2] + .r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * b_dim1; + i__4 = i__ + j * b_dim1; + z__1.r = temp.r * b[i__4].r - temp.i * b[i__4].i, + z__1.i = temp.r * b[i__4].i + temp.i * b[i__4] + .r; + b[i__3].r = z__1.r, b[i__3].i = z__1.i; /* L210: */ - } - i__2 = *n; - for (k = j + 1; k <= i__2; ++k) { - i__3 = k + j * a_dim1; - if (a[i__3].r != 0. || a[i__3].i != 0.) { - i__3 = k + j * a_dim1; - z__1.r = alpha->r * a[i__3].r - alpha->i * a[i__3] - .i, z__1.i = alpha->r * a[i__3].i + - alpha->i * a[i__3].r; - temp.r = z__1.r, temp.i = z__1.i; - i__3 = *m; - for (i__ = 1; i__ <= i__3; ++i__) { - i__4 = i__ + j * b_dim1; - i__5 = i__ + j * b_dim1; - i__6 = i__ + k * b_dim1; - z__2.r = temp.r * b[i__6].r - temp.i * b[i__6] - .i, z__2.i = temp.r * b[i__6].i + - temp.i * b[i__6].r; - z__1.r = b[i__5].r + z__2.r, z__1.i = b[i__5] - .i + z__2.i; - b[i__4].r = z__1.r, b[i__4].i = z__1.i; + } + i__2 = *n; + for (k = j + 1; k <= i__2; ++k) { + i__3 = k + j * a_dim1; + if (a[i__3].r != 0. || a[i__3].i != 0.) { + i__3 = k + j * a_dim1; + z__1.r = alpha->r * a[i__3].r - alpha->i * a[i__3] + .i, z__1.i = alpha->r * a[i__3].i + + alpha->i * a[i__3].r; + temp.r = z__1.r, temp.i = z__1.i; + i__3 = *m; + for (i__ = 1; i__ <= i__3; ++i__) { + i__4 = i__ + j * b_dim1; + i__5 = i__ + j * b_dim1; + i__6 = i__ + k * b_dim1; + z__2.r = temp.r * b[i__6].r - temp.i * b[i__6] + .i, z__2.i = temp.r * b[i__6].i + + temp.i * b[i__6].r; + z__1.r = b[i__5].r + z__2.r, z__1.i = b[i__5] + .i + z__2.i; + b[i__4].r = z__1.r, b[i__4].i = z__1.i; /* L220: */ - } - } + } + } /* L230: */ - } + } /* L240: */ - } - } - } else { + } + } + } else { /* Form B := alpha*B*A**T or B := alpha*B*A**H. */ - if (upper) { - i__1 = *n; - for (k = 1; k <= i__1; ++k) { - i__2 = k - 1; - for (j = 1; j <= i__2; ++j) { - i__3 = j + k * a_dim1; - if (a[i__3].r != 0. || a[i__3].i != 0.) { - if (noconj) { - i__3 = j + k * a_dim1; - z__1.r = alpha->r * a[i__3].r - alpha->i * a[ - i__3].i, z__1.i = alpha->r * a[i__3] - .i + alpha->i * a[i__3].r; - temp.r = z__1.r, temp.i = z__1.i; - } else { - d_cnjg(&z__2, &a[j + k * a_dim1]); - z__1.r = alpha->r * z__2.r - alpha->i * - z__2.i, z__1.i = alpha->r * z__2.i + - alpha->i * z__2.r; - temp.r = z__1.r, temp.i = z__1.i; - } - i__3 = *m; - for (i__ = 1; i__ <= i__3; ++i__) { - i__4 = i__ + j * b_dim1; - i__5 = i__ + j * b_dim1; - i__6 = i__ + k * b_dim1; - z__2.r = temp.r * b[i__6].r - temp.i * b[i__6] - .i, z__2.i = temp.r * b[i__6].i + - temp.i * b[i__6].r; - z__1.r = b[i__5].r + z__2.r, z__1.i = b[i__5] - .i + z__2.i; - b[i__4].r = z__1.r, b[i__4].i = z__1.i; + if (upper) { + i__1 = *n; + for (k = 1; k <= i__1; ++k) { + i__2 = k - 1; + for (j = 1; j <= i__2; ++j) { + i__3 = j + k * a_dim1; + if (a[i__3].r != 0. || a[i__3].i != 0.) { + if (noconj) { + i__3 = j + k * a_dim1; + z__1.r = alpha->r * a[i__3].r - alpha->i * a[ + i__3].i, z__1.i = alpha->r * a[i__3] + .i + alpha->i * a[i__3].r; + temp.r = z__1.r, temp.i = z__1.i; + } else { + d_cnjg(&z__2, &a[j + k * a_dim1]); + z__1.r = alpha->r * z__2.r - alpha->i * + z__2.i, z__1.i = alpha->r * z__2.i + + alpha->i * z__2.r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__3 = *m; + for (i__ = 1; i__ <= i__3; ++i__) { + i__4 = i__ + j * b_dim1; + i__5 = i__ + j * b_dim1; + i__6 = i__ + k * b_dim1; + z__2.r = temp.r * b[i__6].r - temp.i * b[i__6] + .i, z__2.i = temp.r * b[i__6].i + + temp.i * b[i__6].r; + z__1.r = b[i__5].r + z__2.r, z__1.i = b[i__5] + .i + z__2.i; + b[i__4].r = z__1.r, b[i__4].i = z__1.i; /* L250: */ - } - } + } + } /* L260: */ - } - temp.r = alpha->r, temp.i = alpha->i; - if (nounit) { - if (noconj) { - i__2 = k + k * a_dim1; - z__1.r = temp.r * a[i__2].r - temp.i * a[i__2].i, - z__1.i = temp.r * a[i__2].i + temp.i * a[ - i__2].r; - temp.r = z__1.r, temp.i = z__1.i; - } else { - d_cnjg(&z__2, &a[k + k * a_dim1]); - z__1.r = temp.r * z__2.r - temp.i * z__2.i, - z__1.i = temp.r * z__2.i + temp.i * - z__2.r; - temp.r = z__1.r, temp.i = z__1.i; - } - } - if (temp.r != 1. || temp.i != 0.) { - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + k * b_dim1; - i__4 = i__ + k * b_dim1; - z__1.r = temp.r * b[i__4].r - temp.i * b[i__4].i, - z__1.i = temp.r * b[i__4].i + temp.i * b[ - i__4].r; - b[i__3].r = z__1.r, b[i__3].i = z__1.i; + } + temp.r = alpha->r, temp.i = alpha->i; + if (nounit) { + if (noconj) { + i__2 = k + k * a_dim1; + z__1.r = temp.r * a[i__2].r - temp.i * a[i__2].i, + z__1.i = temp.r * a[i__2].i + temp.i * a[ + i__2].r; + temp.r = z__1.r, temp.i = z__1.i; + } else { + d_cnjg(&z__2, &a[k + k * a_dim1]); + z__1.r = temp.r * z__2.r - temp.i * z__2.i, + z__1.i = temp.r * z__2.i + temp.i * + z__2.r; + temp.r = z__1.r, temp.i = z__1.i; + } + } + if (temp.r != 1. || temp.i != 0.) { + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + k * b_dim1; + i__4 = i__ + k * b_dim1; + z__1.r = temp.r * b[i__4].r - temp.i * b[i__4].i, + z__1.i = temp.r * b[i__4].i + temp.i * b[ + i__4].r; + b[i__3].r = z__1.r, b[i__3].i = z__1.i; /* L270: */ - } - } + } + } /* L280: */ - } - } else { - for (k = *n; k >= 1; --k) { - i__1 = *n; - for (j = k + 1; j <= i__1; ++j) { - i__2 = j + k * a_dim1; - if (a[i__2].r != 0. || a[i__2].i != 0.) { - if (noconj) { - i__2 = j + k * a_dim1; - z__1.r = alpha->r * a[i__2].r - alpha->i * a[ - i__2].i, z__1.i = alpha->r * a[i__2] - .i + alpha->i * a[i__2].r; - temp.r = z__1.r, temp.i = z__1.i; - } else { - d_cnjg(&z__2, &a[j + k * a_dim1]); - z__1.r = alpha->r * z__2.r - alpha->i * - z__2.i, z__1.i = alpha->r * z__2.i + - alpha->i * z__2.r; - temp.r = z__1.r, temp.i = z__1.i; - } - i__2 = *m; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * b_dim1; - i__4 = i__ + j * b_dim1; - i__5 = i__ + k * b_dim1; - z__2.r = temp.r * b[i__5].r - temp.i * b[i__5] - .i, z__2.i = temp.r * b[i__5].i + - temp.i * b[i__5].r; - z__1.r = b[i__4].r + z__2.r, z__1.i = b[i__4] - .i + z__2.i; - b[i__3].r = z__1.r, b[i__3].i = z__1.i; + } + } else { + for (k = *n; k >= 1; --k) { + i__1 = *n; + for (j = k + 1; j <= i__1; ++j) { + i__2 = j + k * a_dim1; + if (a[i__2].r != 0. || a[i__2].i != 0.) { + if (noconj) { + i__2 = j + k * a_dim1; + z__1.r = alpha->r * a[i__2].r - alpha->i * a[ + i__2].i, z__1.i = alpha->r * a[i__2] + .i + alpha->i * a[i__2].r; + temp.r = z__1.r, temp.i = z__1.i; + } else { + d_cnjg(&z__2, &a[j + k * a_dim1]); + z__1.r = alpha->r * z__2.r - alpha->i * + z__2.i, z__1.i = alpha->r * z__2.i + + alpha->i * z__2.r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__2 = *m; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * b_dim1; + i__4 = i__ + j * b_dim1; + i__5 = i__ + k * b_dim1; + z__2.r = temp.r * b[i__5].r - temp.i * b[i__5] + .i, z__2.i = temp.r * b[i__5].i + + temp.i * b[i__5].r; + z__1.r = b[i__4].r + z__2.r, z__1.i = b[i__4] + .i + z__2.i; + b[i__3].r = z__1.r, b[i__3].i = z__1.i; /* L290: */ - } - } + } + } /* L300: */ - } - temp.r = alpha->r, temp.i = alpha->i; - if (nounit) { - if (noconj) { - i__1 = k + k * a_dim1; - z__1.r = temp.r * a[i__1].r - temp.i * a[i__1].i, - z__1.i = temp.r * a[i__1].i + temp.i * a[ - i__1].r; - temp.r = z__1.r, temp.i = z__1.i; - } else { - d_cnjg(&z__2, &a[k + k * a_dim1]); - z__1.r = temp.r * z__2.r - temp.i * z__2.i, - z__1.i = temp.r * z__2.i + temp.i * - z__2.r; - temp.r = z__1.r, temp.i = z__1.i; - } - } - if (temp.r != 1. || temp.i != 0.) { - i__1 = *m; - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = i__ + k * b_dim1; - i__3 = i__ + k * b_dim1; - z__1.r = temp.r * b[i__3].r - temp.i * b[i__3].i, - z__1.i = temp.r * b[i__3].i + temp.i * b[ - i__3].r; - b[i__2].r = z__1.r, b[i__2].i = z__1.i; + } + temp.r = alpha->r, temp.i = alpha->i; + if (nounit) { + if (noconj) { + i__1 = k + k * a_dim1; + z__1.r = temp.r * a[i__1].r - temp.i * a[i__1].i, + z__1.i = temp.r * a[i__1].i + temp.i * a[ + i__1].r; + temp.r = z__1.r, temp.i = z__1.i; + } else { + d_cnjg(&z__2, &a[k + k * a_dim1]); + z__1.r = temp.r * z__2.r - temp.i * z__2.i, + z__1.i = temp.r * z__2.i + temp.i * + z__2.r; + temp.r = z__1.r, temp.i = z__1.i; + } + } + if (temp.r != 1. || temp.i != 0.) { + i__1 = *m; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__ + k * b_dim1; + i__3 = i__ + k * b_dim1; + z__1.r = temp.r * b[i__3].r - temp.i * b[i__3].i, + z__1.i = temp.r * b[i__3].i + temp.i * b[ + i__3].r; + b[i__2].r = z__1.r, b[i__2].i = z__1.i; /* L310: */ - } - } + } + } /* L320: */ - } - } - } + } + } + } } return 0; @@ -758,5 +758,5 @@ extern "C" { } /* ztrmm_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/ztrmv.cpp b/lib/linalg/ztrmv.cpp index ffc55b16fe..77f93e41a6 100644 --- a/lib/linalg/ztrmv.cpp +++ b/lib/linalg/ztrmv.cpp @@ -1,13 +1,13 @@ /* fortran/ztrmv.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -160,9 +160,9 @@ extern "C" { /* > \endverbatim */ /* > */ /* ===================================================================== */ -/* Subroutine */ int ztrmv_(char *uplo, char *trans, char *diag, integer *n, - doublecomplex *a, integer *lda, doublecomplex *x, integer *incx, - ftnlen uplo_len, ftnlen trans_len, ftnlen diag_len) +/* Subroutine */ int ztrmv_(char *uplo, char *trans, char *diag, integer *n, + doublecomplex *a, integer *lda, doublecomplex *x, integer *incx, + ftnlen uplo_len, ftnlen trans_len, ftnlen diag_len) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; @@ -212,31 +212,31 @@ extern "C" { /* Function Body */ info = 0; if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", ( - ftnlen)1, (ftnlen)1)) { - info = 1; - } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, - (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, ( - ftnlen)1)) { - info = 2; - } else if (! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, - (char *)"N", (ftnlen)1, (ftnlen)1)) { - info = 3; + ftnlen)1, (ftnlen)1)) { + info = 1; + } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, + (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, ( + ftnlen)1)) { + info = 2; + } else if (! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, + (char *)"N", (ftnlen)1, (ftnlen)1)) { + info = 3; } else if (*n < 0) { - info = 4; + info = 4; } else if (*lda < max(1,*n)) { - info = 6; + info = 6; } else if (*incx == 0) { - info = 8; + info = 8; } if (info != 0) { - xerbla_((char *)"ZTRMV ", &info, (ftnlen)6); - return 0; + xerbla_((char *)"ZTRMV ", &info, (ftnlen)6); + return 0; } /* Quick return if possible. */ if (*n == 0) { - return 0; + return 0; } noconj = lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1); @@ -246,9 +246,9 @@ extern "C" { /* will be ( N - 1 )*INCX too small for descending loops. */ if (*incx <= 0) { - kx = 1 - (*n - 1) * *incx; + kx = 1 - (*n - 1) * *incx; } else if (*incx != 1) { - kx = 1; + kx = 1; } /* Start the operations. In this version the elements of A are */ @@ -258,359 +258,359 @@ extern "C" { /* Form x := A*x. */ - if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { - if (*incx == 1) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = j; - if (x[i__2].r != 0. || x[i__2].i != 0.) { - i__2 = j; - temp.r = x[i__2].r, temp.i = x[i__2].i; - i__2 = j - 1; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__; - i__4 = i__; - i__5 = i__ + j * a_dim1; - z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, - z__2.i = temp.r * a[i__5].i + temp.i * a[ - i__5].r; - z__1.r = x[i__4].r + z__2.r, z__1.i = x[i__4].i + - z__2.i; - x[i__3].r = z__1.r, x[i__3].i = z__1.i; + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + if (*incx == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + if (x[i__2].r != 0. || x[i__2].i != 0.) { + i__2 = j; + temp.r = x[i__2].r, temp.i = x[i__2].i; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__; + i__4 = i__; + i__5 = i__ + j * a_dim1; + z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, + z__2.i = temp.r * a[i__5].i + temp.i * a[ + i__5].r; + z__1.r = x[i__4].r + z__2.r, z__1.i = x[i__4].i + + z__2.i; + x[i__3].r = z__1.r, x[i__3].i = z__1.i; /* L10: */ - } - if (nounit) { - i__2 = j; - i__3 = j; - i__4 = j + j * a_dim1; - z__1.r = x[i__3].r * a[i__4].r - x[i__3].i * a[ - i__4].i, z__1.i = x[i__3].r * a[i__4].i + - x[i__3].i * a[i__4].r; - x[i__2].r = z__1.r, x[i__2].i = z__1.i; - } - } + } + if (nounit) { + i__2 = j; + i__3 = j; + i__4 = j + j * a_dim1; + z__1.r = x[i__3].r * a[i__4].r - x[i__3].i * a[ + i__4].i, z__1.i = x[i__3].r * a[i__4].i + + x[i__3].i * a[i__4].r; + x[i__2].r = z__1.r, x[i__2].i = z__1.i; + } + } /* L20: */ - } - } else { - jx = kx; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = jx; - if (x[i__2].r != 0. || x[i__2].i != 0.) { - i__2 = jx; - temp.r = x[i__2].r, temp.i = x[i__2].i; - ix = kx; - i__2 = j - 1; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = ix; - i__4 = ix; - i__5 = i__ + j * a_dim1; - z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, - z__2.i = temp.r * a[i__5].i + temp.i * a[ - i__5].r; - z__1.r = x[i__4].r + z__2.r, z__1.i = x[i__4].i + - z__2.i; - x[i__3].r = z__1.r, x[i__3].i = z__1.i; - ix += *incx; + } + } else { + jx = kx; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = jx; + if (x[i__2].r != 0. || x[i__2].i != 0.) { + i__2 = jx; + temp.r = x[i__2].r, temp.i = x[i__2].i; + ix = kx; + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = ix; + i__4 = ix; + i__5 = i__ + j * a_dim1; + z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, + z__2.i = temp.r * a[i__5].i + temp.i * a[ + i__5].r; + z__1.r = x[i__4].r + z__2.r, z__1.i = x[i__4].i + + z__2.i; + x[i__3].r = z__1.r, x[i__3].i = z__1.i; + ix += *incx; /* L30: */ - } - if (nounit) { - i__2 = jx; - i__3 = jx; - i__4 = j + j * a_dim1; - z__1.r = x[i__3].r * a[i__4].r - x[i__3].i * a[ - i__4].i, z__1.i = x[i__3].r * a[i__4].i + - x[i__3].i * a[i__4].r; - x[i__2].r = z__1.r, x[i__2].i = z__1.i; - } - } - jx += *incx; + } + if (nounit) { + i__2 = jx; + i__3 = jx; + i__4 = j + j * a_dim1; + z__1.r = x[i__3].r * a[i__4].r - x[i__3].i * a[ + i__4].i, z__1.i = x[i__3].r * a[i__4].i + + x[i__3].i * a[i__4].r; + x[i__2].r = z__1.r, x[i__2].i = z__1.i; + } + } + jx += *incx; /* L40: */ - } - } - } else { - if (*incx == 1) { - for (j = *n; j >= 1; --j) { - i__1 = j; - if (x[i__1].r != 0. || x[i__1].i != 0.) { - i__1 = j; - temp.r = x[i__1].r, temp.i = x[i__1].i; - i__1 = j + 1; - for (i__ = *n; i__ >= i__1; --i__) { - i__2 = i__; - i__3 = i__; - i__4 = i__ + j * a_dim1; - z__2.r = temp.r * a[i__4].r - temp.i * a[i__4].i, - z__2.i = temp.r * a[i__4].i + temp.i * a[ - i__4].r; - z__1.r = x[i__3].r + z__2.r, z__1.i = x[i__3].i + - z__2.i; - x[i__2].r = z__1.r, x[i__2].i = z__1.i; + } + } + } else { + if (*incx == 1) { + for (j = *n; j >= 1; --j) { + i__1 = j; + if (x[i__1].r != 0. || x[i__1].i != 0.) { + i__1 = j; + temp.r = x[i__1].r, temp.i = x[i__1].i; + i__1 = j + 1; + for (i__ = *n; i__ >= i__1; --i__) { + i__2 = i__; + i__3 = i__; + i__4 = i__ + j * a_dim1; + z__2.r = temp.r * a[i__4].r - temp.i * a[i__4].i, + z__2.i = temp.r * a[i__4].i + temp.i * a[ + i__4].r; + z__1.r = x[i__3].r + z__2.r, z__1.i = x[i__3].i + + z__2.i; + x[i__2].r = z__1.r, x[i__2].i = z__1.i; /* L50: */ - } - if (nounit) { - i__1 = j; - i__2 = j; - i__3 = j + j * a_dim1; - z__1.r = x[i__2].r * a[i__3].r - x[i__2].i * a[ - i__3].i, z__1.i = x[i__2].r * a[i__3].i + - x[i__2].i * a[i__3].r; - x[i__1].r = z__1.r, x[i__1].i = z__1.i; - } - } + } + if (nounit) { + i__1 = j; + i__2 = j; + i__3 = j + j * a_dim1; + z__1.r = x[i__2].r * a[i__3].r - x[i__2].i * a[ + i__3].i, z__1.i = x[i__2].r * a[i__3].i + + x[i__2].i * a[i__3].r; + x[i__1].r = z__1.r, x[i__1].i = z__1.i; + } + } /* L60: */ - } - } else { - kx += (*n - 1) * *incx; - jx = kx; - for (j = *n; j >= 1; --j) { - i__1 = jx; - if (x[i__1].r != 0. || x[i__1].i != 0.) { - i__1 = jx; - temp.r = x[i__1].r, temp.i = x[i__1].i; - ix = kx; - i__1 = j + 1; - for (i__ = *n; i__ >= i__1; --i__) { - i__2 = ix; - i__3 = ix; - i__4 = i__ + j * a_dim1; - z__2.r = temp.r * a[i__4].r - temp.i * a[i__4].i, - z__2.i = temp.r * a[i__4].i + temp.i * a[ - i__4].r; - z__1.r = x[i__3].r + z__2.r, z__1.i = x[i__3].i + - z__2.i; - x[i__2].r = z__1.r, x[i__2].i = z__1.i; - ix -= *incx; + } + } else { + kx += (*n - 1) * *incx; + jx = kx; + for (j = *n; j >= 1; --j) { + i__1 = jx; + if (x[i__1].r != 0. || x[i__1].i != 0.) { + i__1 = jx; + temp.r = x[i__1].r, temp.i = x[i__1].i; + ix = kx; + i__1 = j + 1; + for (i__ = *n; i__ >= i__1; --i__) { + i__2 = ix; + i__3 = ix; + i__4 = i__ + j * a_dim1; + z__2.r = temp.r * a[i__4].r - temp.i * a[i__4].i, + z__2.i = temp.r * a[i__4].i + temp.i * a[ + i__4].r; + z__1.r = x[i__3].r + z__2.r, z__1.i = x[i__3].i + + z__2.i; + x[i__2].r = z__1.r, x[i__2].i = z__1.i; + ix -= *incx; /* L70: */ - } - if (nounit) { - i__1 = jx; - i__2 = jx; - i__3 = j + j * a_dim1; - z__1.r = x[i__2].r * a[i__3].r - x[i__2].i * a[ - i__3].i, z__1.i = x[i__2].r * a[i__3].i + - x[i__2].i * a[i__3].r; - x[i__1].r = z__1.r, x[i__1].i = z__1.i; - } - } - jx -= *incx; + } + if (nounit) { + i__1 = jx; + i__2 = jx; + i__3 = j + j * a_dim1; + z__1.r = x[i__2].r * a[i__3].r - x[i__2].i * a[ + i__3].i, z__1.i = x[i__2].r * a[i__3].i + + x[i__2].i * a[i__3].r; + x[i__1].r = z__1.r, x[i__1].i = z__1.i; + } + } + jx -= *incx; /* L80: */ - } - } - } + } + } + } } else { /* Form x := A**T*x or x := A**H*x. */ - if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { - if (*incx == 1) { - for (j = *n; j >= 1; --j) { - i__1 = j; - temp.r = x[i__1].r, temp.i = x[i__1].i; - if (noconj) { - if (nounit) { - i__1 = j + j * a_dim1; - z__1.r = temp.r * a[i__1].r - temp.i * a[i__1].i, - z__1.i = temp.r * a[i__1].i + temp.i * a[ - i__1].r; - temp.r = z__1.r, temp.i = z__1.i; - } - for (i__ = j - 1; i__ >= 1; --i__) { - i__1 = i__ + j * a_dim1; - i__2 = i__; - z__2.r = a[i__1].r * x[i__2].r - a[i__1].i * x[ - i__2].i, z__2.i = a[i__1].r * x[i__2].i + - a[i__1].i * x[i__2].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; - temp.r = z__1.r, temp.i = z__1.i; + if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { + if (*incx == 1) { + for (j = *n; j >= 1; --j) { + i__1 = j; + temp.r = x[i__1].r, temp.i = x[i__1].i; + if (noconj) { + if (nounit) { + i__1 = j + j * a_dim1; + z__1.r = temp.r * a[i__1].r - temp.i * a[i__1].i, + z__1.i = temp.r * a[i__1].i + temp.i * a[ + i__1].r; + temp.r = z__1.r, temp.i = z__1.i; + } + for (i__ = j - 1; i__ >= 1; --i__) { + i__1 = i__ + j * a_dim1; + i__2 = i__; + z__2.r = a[i__1].r * x[i__2].r - a[i__1].i * x[ + i__2].i, z__2.i = a[i__1].r * x[i__2].i + + a[i__1].i * x[i__2].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; /* L90: */ - } - } else { - if (nounit) { - d_cnjg(&z__2, &a[j + j * a_dim1]); - z__1.r = temp.r * z__2.r - temp.i * z__2.i, - z__1.i = temp.r * z__2.i + temp.i * - z__2.r; - temp.r = z__1.r, temp.i = z__1.i; - } - for (i__ = j - 1; i__ >= 1; --i__) { - d_cnjg(&z__3, &a[i__ + j * a_dim1]); - i__1 = i__; - z__2.r = z__3.r * x[i__1].r - z__3.i * x[i__1].i, - z__2.i = z__3.r * x[i__1].i + z__3.i * x[ - i__1].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; - temp.r = z__1.r, temp.i = z__1.i; + } + } else { + if (nounit) { + d_cnjg(&z__2, &a[j + j * a_dim1]); + z__1.r = temp.r * z__2.r - temp.i * z__2.i, + z__1.i = temp.r * z__2.i + temp.i * + z__2.r; + temp.r = z__1.r, temp.i = z__1.i; + } + for (i__ = j - 1; i__ >= 1; --i__) { + d_cnjg(&z__3, &a[i__ + j * a_dim1]); + i__1 = i__; + z__2.r = z__3.r * x[i__1].r - z__3.i * x[i__1].i, + z__2.i = z__3.r * x[i__1].i + z__3.i * x[ + i__1].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; /* L100: */ - } - } - i__1 = j; - x[i__1].r = temp.r, x[i__1].i = temp.i; + } + } + i__1 = j; + x[i__1].r = temp.r, x[i__1].i = temp.i; /* L110: */ - } - } else { - jx = kx + (*n - 1) * *incx; - for (j = *n; j >= 1; --j) { - i__1 = jx; - temp.r = x[i__1].r, temp.i = x[i__1].i; - ix = jx; - if (noconj) { - if (nounit) { - i__1 = j + j * a_dim1; - z__1.r = temp.r * a[i__1].r - temp.i * a[i__1].i, - z__1.i = temp.r * a[i__1].i + temp.i * a[ - i__1].r; - temp.r = z__1.r, temp.i = z__1.i; - } - for (i__ = j - 1; i__ >= 1; --i__) { - ix -= *incx; - i__1 = i__ + j * a_dim1; - i__2 = ix; - z__2.r = a[i__1].r * x[i__2].r - a[i__1].i * x[ - i__2].i, z__2.i = a[i__1].r * x[i__2].i + - a[i__1].i * x[i__2].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; - temp.r = z__1.r, temp.i = z__1.i; + } + } else { + jx = kx + (*n - 1) * *incx; + for (j = *n; j >= 1; --j) { + i__1 = jx; + temp.r = x[i__1].r, temp.i = x[i__1].i; + ix = jx; + if (noconj) { + if (nounit) { + i__1 = j + j * a_dim1; + z__1.r = temp.r * a[i__1].r - temp.i * a[i__1].i, + z__1.i = temp.r * a[i__1].i + temp.i * a[ + i__1].r; + temp.r = z__1.r, temp.i = z__1.i; + } + for (i__ = j - 1; i__ >= 1; --i__) { + ix -= *incx; + i__1 = i__ + j * a_dim1; + i__2 = ix; + z__2.r = a[i__1].r * x[i__2].r - a[i__1].i * x[ + i__2].i, z__2.i = a[i__1].r * x[i__2].i + + a[i__1].i * x[i__2].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; /* L120: */ - } - } else { - if (nounit) { - d_cnjg(&z__2, &a[j + j * a_dim1]); - z__1.r = temp.r * z__2.r - temp.i * z__2.i, - z__1.i = temp.r * z__2.i + temp.i * - z__2.r; - temp.r = z__1.r, temp.i = z__1.i; - } - for (i__ = j - 1; i__ >= 1; --i__) { - ix -= *incx; - d_cnjg(&z__3, &a[i__ + j * a_dim1]); - i__1 = ix; - z__2.r = z__3.r * x[i__1].r - z__3.i * x[i__1].i, - z__2.i = z__3.r * x[i__1].i + z__3.i * x[ - i__1].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; - temp.r = z__1.r, temp.i = z__1.i; + } + } else { + if (nounit) { + d_cnjg(&z__2, &a[j + j * a_dim1]); + z__1.r = temp.r * z__2.r - temp.i * z__2.i, + z__1.i = temp.r * z__2.i + temp.i * + z__2.r; + temp.r = z__1.r, temp.i = z__1.i; + } + for (i__ = j - 1; i__ >= 1; --i__) { + ix -= *incx; + d_cnjg(&z__3, &a[i__ + j * a_dim1]); + i__1 = ix; + z__2.r = z__3.r * x[i__1].r - z__3.i * x[i__1].i, + z__2.i = z__3.r * x[i__1].i + z__3.i * x[ + i__1].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; /* L130: */ - } - } - i__1 = jx; - x[i__1].r = temp.r, x[i__1].i = temp.i; - jx -= *incx; + } + } + i__1 = jx; + x[i__1].r = temp.r, x[i__1].i = temp.i; + jx -= *incx; /* L140: */ - } - } - } else { - if (*incx == 1) { - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = j; - temp.r = x[i__2].r, temp.i = x[i__2].i; - if (noconj) { - if (nounit) { - i__2 = j + j * a_dim1; - z__1.r = temp.r * a[i__2].r - temp.i * a[i__2].i, - z__1.i = temp.r * a[i__2].i + temp.i * a[ - i__2].r; - temp.r = z__1.r, temp.i = z__1.i; - } - i__2 = *n; - for (i__ = j + 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * a_dim1; - i__4 = i__; - z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[ - i__4].i, z__2.i = a[i__3].r * x[i__4].i + - a[i__3].i * x[i__4].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; - temp.r = z__1.r, temp.i = z__1.i; + } + } + } else { + if (*incx == 1) { + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = j; + temp.r = x[i__2].r, temp.i = x[i__2].i; + if (noconj) { + if (nounit) { + i__2 = j + j * a_dim1; + z__1.r = temp.r * a[i__2].r - temp.i * a[i__2].i, + z__1.i = temp.r * a[i__2].i + temp.i * a[ + i__2].r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + i__4 = i__; + z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[ + i__4].i, z__2.i = a[i__3].r * x[i__4].i + + a[i__3].i * x[i__4].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; /* L150: */ - } - } else { - if (nounit) { - d_cnjg(&z__2, &a[j + j * a_dim1]); - z__1.r = temp.r * z__2.r - temp.i * z__2.i, - z__1.i = temp.r * z__2.i + temp.i * - z__2.r; - temp.r = z__1.r, temp.i = z__1.i; - } - i__2 = *n; - for (i__ = j + 1; i__ <= i__2; ++i__) { - d_cnjg(&z__3, &a[i__ + j * a_dim1]); - i__3 = i__; - z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, - z__2.i = z__3.r * x[i__3].i + z__3.i * x[ - i__3].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; - temp.r = z__1.r, temp.i = z__1.i; + } + } else { + if (nounit) { + d_cnjg(&z__2, &a[j + j * a_dim1]); + z__1.r = temp.r * z__2.r - temp.i * z__2.i, + z__1.i = temp.r * z__2.i + temp.i * + z__2.r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + d_cnjg(&z__3, &a[i__ + j * a_dim1]); + i__3 = i__; + z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, + z__2.i = z__3.r * x[i__3].i + z__3.i * x[ + i__3].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; /* L160: */ - } - } - i__2 = j; - x[i__2].r = temp.r, x[i__2].i = temp.i; + } + } + i__2 = j; + x[i__2].r = temp.r, x[i__2].i = temp.i; /* L170: */ - } - } else { - jx = kx; - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = jx; - temp.r = x[i__2].r, temp.i = x[i__2].i; - ix = jx; - if (noconj) { - if (nounit) { - i__2 = j + j * a_dim1; - z__1.r = temp.r * a[i__2].r - temp.i * a[i__2].i, - z__1.i = temp.r * a[i__2].i + temp.i * a[ - i__2].r; - temp.r = z__1.r, temp.i = z__1.i; - } - i__2 = *n; - for (i__ = j + 1; i__ <= i__2; ++i__) { - ix += *incx; - i__3 = i__ + j * a_dim1; - i__4 = ix; - z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[ - i__4].i, z__2.i = a[i__3].r * x[i__4].i + - a[i__3].i * x[i__4].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; - temp.r = z__1.r, temp.i = z__1.i; + } + } else { + jx = kx; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = jx; + temp.r = x[i__2].r, temp.i = x[i__2].i; + ix = jx; + if (noconj) { + if (nounit) { + i__2 = j + j * a_dim1; + z__1.r = temp.r * a[i__2].r - temp.i * a[i__2].i, + z__1.i = temp.r * a[i__2].i + temp.i * a[ + i__2].r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + ix += *incx; + i__3 = i__ + j * a_dim1; + i__4 = ix; + z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[ + i__4].i, z__2.i = a[i__3].r * x[i__4].i + + a[i__3].i * x[i__4].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; /* L180: */ - } - } else { - if (nounit) { - d_cnjg(&z__2, &a[j + j * a_dim1]); - z__1.r = temp.r * z__2.r - temp.i * z__2.i, - z__1.i = temp.r * z__2.i + temp.i * - z__2.r; - temp.r = z__1.r, temp.i = z__1.i; - } - i__2 = *n; - for (i__ = j + 1; i__ <= i__2; ++i__) { - ix += *incx; - d_cnjg(&z__3, &a[i__ + j * a_dim1]); - i__3 = ix; - z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, - z__2.i = z__3.r * x[i__3].i + z__3.i * x[ - i__3].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; - temp.r = z__1.r, temp.i = z__1.i; + } + } else { + if (nounit) { + d_cnjg(&z__2, &a[j + j * a_dim1]); + z__1.r = temp.r * z__2.r - temp.i * z__2.i, + z__1.i = temp.r * z__2.i + temp.i * + z__2.r; + temp.r = z__1.r, temp.i = z__1.i; + } + i__2 = *n; + for (i__ = j + 1; i__ <= i__2; ++i__) { + ix += *incx; + d_cnjg(&z__3, &a[i__ + j * a_dim1]); + i__3 = ix; + z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, + z__2.i = z__3.r * x[i__3].i + z__3.i * x[ + i__3].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + + z__2.i; + temp.r = z__1.r, temp.i = z__1.i; /* L190: */ - } - } - i__2 = jx; - x[i__2].r = temp.r, x[i__2].i = temp.i; - jx += *incx; + } + } + i__2 = jx; + x[i__2].r = temp.r, x[i__2].i = temp.i; + jx += *incx; /* L200: */ - } - } - } + } + } + } } return 0; @@ -620,5 +620,5 @@ extern "C" { } /* ztrmv_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zung2l.cpp b/lib/linalg/zung2l.cpp index 45c03e5c78..4c4f96c5b0 100644 --- a/lib/linalg/zung2l.cpp +++ b/lib/linalg/zung2l.cpp @@ -1,13 +1,13 @@ /* fortran/zung2l.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -135,9 +135,9 @@ f"> */ /* > \ingroup complex16OTHERcomputational */ /* ===================================================================== */ -/* Subroutine */ int zung2l_(integer *m, integer *n, integer *k, - doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex * - work, integer *info) +/* Subroutine */ int zung2l_(integer *m, integer *n, integer *k, + doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex * + work, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; @@ -145,11 +145,11 @@ f"> */ /* Local variables */ integer i__, j, l, ii; - extern /* Subroutine */ int zscal_(integer *, doublecomplex *, - doublecomplex *, integer *), zlarf_(char *, integer *, integer *, - doublecomplex *, integer *, doublecomplex *, doublecomplex *, - integer *, doublecomplex *, ftnlen), xerbla_(char *, integer *, - ftnlen); + extern /* Subroutine */ int zscal_(integer *, doublecomplex *, + doublecomplex *, integer *), zlarf_(char *, integer *, integer *, + doublecomplex *, integer *, doublecomplex *, doublecomplex *, + integer *, doublecomplex *, ftnlen), xerbla_(char *, integer *, + ftnlen); /* -- LAPACK computational routine -- */ @@ -185,70 +185,70 @@ f"> */ /* Function Body */ *info = 0; if (*m < 0) { - *info = -1; + *info = -1; } else if (*n < 0 || *n > *m) { - *info = -2; + *info = -2; } else if (*k < 0 || *k > *n) { - *info = -3; + *info = -3; } else if (*lda < max(1,*m)) { - *info = -5; + *info = -5; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"ZUNG2L", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"ZUNG2L", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*n <= 0) { - return 0; + return 0; } /* Initialise columns 1:n-k to columns of the unit matrix */ i__1 = *n - *k; for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (l = 1; l <= i__2; ++l) { - i__3 = l + j * a_dim1; - a[i__3].r = 0., a[i__3].i = 0.; + i__2 = *m; + for (l = 1; l <= i__2; ++l) { + i__3 = l + j * a_dim1; + a[i__3].r = 0., a[i__3].i = 0.; /* L10: */ - } - i__2 = *m - *n + j + j * a_dim1; - a[i__2].r = 1., a[i__2].i = 0.; + } + i__2 = *m - *n + j + j * a_dim1; + a[i__2].r = 1., a[i__2].i = 0.; /* L20: */ } i__1 = *k; for (i__ = 1; i__ <= i__1; ++i__) { - ii = *n - *k + i__; + ii = *n - *k + i__; /* Apply H(i) to A(1:m-k+i,1:n-k+i) from the left */ - i__2 = *m - *n + ii + ii * a_dim1; - a[i__2].r = 1., a[i__2].i = 0.; - i__2 = *m - *n + ii; - i__3 = ii - 1; - zlarf_((char *)"Left", &i__2, &i__3, &a[ii * a_dim1 + 1], &c__1, &tau[i__], & - a[a_offset], lda, &work[1], (ftnlen)4); - i__2 = *m - *n + ii - 1; - i__3 = i__; - z__1.r = -tau[i__3].r, z__1.i = -tau[i__3].i; - zscal_(&i__2, &z__1, &a[ii * a_dim1 + 1], &c__1); - i__2 = *m - *n + ii + ii * a_dim1; - i__3 = i__; - z__1.r = 1. - tau[i__3].r, z__1.i = 0. - tau[i__3].i; - a[i__2].r = z__1.r, a[i__2].i = z__1.i; + i__2 = *m - *n + ii + ii * a_dim1; + a[i__2].r = 1., a[i__2].i = 0.; + i__2 = *m - *n + ii; + i__3 = ii - 1; + zlarf_((char *)"Left", &i__2, &i__3, &a[ii * a_dim1 + 1], &c__1, &tau[i__], & + a[a_offset], lda, &work[1], (ftnlen)4); + i__2 = *m - *n + ii - 1; + i__3 = i__; + z__1.r = -tau[i__3].r, z__1.i = -tau[i__3].i; + zscal_(&i__2, &z__1, &a[ii * a_dim1 + 1], &c__1); + i__2 = *m - *n + ii + ii * a_dim1; + i__3 = i__; + z__1.r = 1. - tau[i__3].r, z__1.i = 0. - tau[i__3].i; + a[i__2].r = z__1.r, a[i__2].i = z__1.i; /* Set A(m-k+i+1:m,n-k+i) to zero */ - i__2 = *m; - for (l = *m - *n + ii + 1; l <= i__2; ++l) { - i__3 = l + ii * a_dim1; - a[i__3].r = 0., a[i__3].i = 0.; + i__2 = *m; + for (l = *m - *n + ii + 1; l <= i__2; ++l) { + i__3 = l + ii * a_dim1; + a[i__3].r = 0., a[i__3].i = 0.; /* L30: */ - } + } /* L40: */ } return 0; @@ -258,5 +258,5 @@ f"> */ } /* zung2l_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zung2r.cpp b/lib/linalg/zung2r.cpp index 4bd9202caa..044df4d2b0 100644 --- a/lib/linalg/zung2r.cpp +++ b/lib/linalg/zung2r.cpp @@ -1,13 +1,13 @@ /* fortran/zung2r.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -134,9 +134,9 @@ f"> */ /* > \ingroup complex16OTHERcomputational */ /* ===================================================================== */ -/* Subroutine */ int zung2r_(integer *m, integer *n, integer *k, - doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex * - work, integer *info) +/* Subroutine */ int zung2r_(integer *m, integer *n, integer *k, + doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex * + work, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; @@ -144,11 +144,11 @@ f"> */ /* Local variables */ integer i__, j, l; - extern /* Subroutine */ int zscal_(integer *, doublecomplex *, - doublecomplex *, integer *), zlarf_(char *, integer *, integer *, - doublecomplex *, integer *, doublecomplex *, doublecomplex *, - integer *, doublecomplex *, ftnlen), xerbla_(char *, integer *, - ftnlen); + extern /* Subroutine */ int zscal_(integer *, doublecomplex *, + doublecomplex *, integer *), zlarf_(char *, integer *, integer *, + doublecomplex *, integer *, doublecomplex *, doublecomplex *, + integer *, doublecomplex *, ftnlen), xerbla_(char *, integer *, + ftnlen); /* -- LAPACK computational routine -- */ @@ -184,38 +184,38 @@ f"> */ /* Function Body */ *info = 0; if (*m < 0) { - *info = -1; + *info = -1; } else if (*n < 0 || *n > *m) { - *info = -2; + *info = -2; } else if (*k < 0 || *k > *n) { - *info = -3; + *info = -3; } else if (*lda < max(1,*m)) { - *info = -5; + *info = -5; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"ZUNG2R", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"ZUNG2R", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*n <= 0) { - return 0; + return 0; } /* Initialise columns k+1:n to columns of the unit matrix */ i__1 = *n; for (j = *k + 1; j <= i__1; ++j) { - i__2 = *m; - for (l = 1; l <= i__2; ++l) { - i__3 = l + j * a_dim1; - a[i__3].r = 0., a[i__3].i = 0.; + i__2 = *m; + for (l = 1; l <= i__2; ++l) { + i__3 = l + j * a_dim1; + a[i__3].r = 0., a[i__3].i = 0.; /* L10: */ - } - i__2 = j + j * a_dim1; - a[i__2].r = 1., a[i__2].i = 0.; + } + i__2 = j + j * a_dim1; + a[i__2].r = 1., a[i__2].i = 0.; /* L20: */ } @@ -223,34 +223,34 @@ f"> */ /* Apply H(i) to A(i:m,i:n) from the left */ - if (i__ < *n) { - i__1 = i__ + i__ * a_dim1; - a[i__1].r = 1., a[i__1].i = 0.; - i__1 = *m - i__ + 1; - i__2 = *n - i__; - zlarf_((char *)"Left", &i__1, &i__2, &a[i__ + i__ * a_dim1], &c__1, &tau[ - i__], &a[i__ + (i__ + 1) * a_dim1], lda, &work[1], ( - ftnlen)4); - } - if (i__ < *m) { - i__1 = *m - i__; - i__2 = i__; - z__1.r = -tau[i__2].r, z__1.i = -tau[i__2].i; - zscal_(&i__1, &z__1, &a[i__ + 1 + i__ * a_dim1], &c__1); - } - i__1 = i__ + i__ * a_dim1; - i__2 = i__; - z__1.r = 1. - tau[i__2].r, z__1.i = 0. - tau[i__2].i; - a[i__1].r = z__1.r, a[i__1].i = z__1.i; + if (i__ < *n) { + i__1 = i__ + i__ * a_dim1; + a[i__1].r = 1., a[i__1].i = 0.; + i__1 = *m - i__ + 1; + i__2 = *n - i__; + zlarf_((char *)"Left", &i__1, &i__2, &a[i__ + i__ * a_dim1], &c__1, &tau[ + i__], &a[i__ + (i__ + 1) * a_dim1], lda, &work[1], ( + ftnlen)4); + } + if (i__ < *m) { + i__1 = *m - i__; + i__2 = i__; + z__1.r = -tau[i__2].r, z__1.i = -tau[i__2].i; + zscal_(&i__1, &z__1, &a[i__ + 1 + i__ * a_dim1], &c__1); + } + i__1 = i__ + i__ * a_dim1; + i__2 = i__; + z__1.r = 1. - tau[i__2].r, z__1.i = 0. - tau[i__2].i; + a[i__1].r = z__1.r, a[i__1].i = z__1.i; /* Set A(1:i-1,i) to zero */ - i__1 = i__ - 1; - for (l = 1; l <= i__1; ++l) { - i__2 = l + i__ * a_dim1; - a[i__2].r = 0., a[i__2].i = 0.; + i__1 = i__ - 1; + for (l = 1; l <= i__1; ++l) { + i__2 = l + i__ * a_dim1; + a[i__2].r = 0., a[i__2].i = 0.; /* L30: */ - } + } /* L40: */ } return 0; @@ -260,5 +260,5 @@ f"> */ } /* zung2r_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zungl2.cpp b/lib/linalg/zungl2.cpp index bd40069fd6..d4b85486c6 100644 --- a/lib/linalg/zungl2.cpp +++ b/lib/linalg/zungl2.cpp @@ -1,13 +1,13 @@ /* fortran/zungl2.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -130,9 +130,9 @@ f"> */ /* > \ingroup complex16OTHERcomputational */ /* ===================================================================== */ -/* Subroutine */ int zungl2_(integer *m, integer *n, integer *k, - doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex * - work, integer *info) +/* Subroutine */ int zungl2_(integer *m, integer *n, integer *k, + doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex * + work, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; @@ -143,11 +143,11 @@ f"> */ /* Local variables */ integer i__, j, l; - extern /* Subroutine */ int zscal_(integer *, doublecomplex *, - doublecomplex *, integer *), zlarf_(char *, integer *, integer *, - doublecomplex *, integer *, doublecomplex *, doublecomplex *, - integer *, doublecomplex *, ftnlen), xerbla_(char *, integer *, - ftnlen), zlacgv_(integer *, doublecomplex *, integer *); + extern /* Subroutine */ int zscal_(integer *, doublecomplex *, + doublecomplex *, integer *), zlarf_(char *, integer *, integer *, + doublecomplex *, integer *, doublecomplex *, doublecomplex *, + integer *, doublecomplex *, ftnlen), xerbla_(char *, integer *, + ftnlen), zlacgv_(integer *, doublecomplex *, integer *); /* -- LAPACK computational routine -- */ @@ -183,83 +183,83 @@ f"> */ /* Function Body */ *info = 0; if (*m < 0) { - *info = -1; + *info = -1; } else if (*n < *m) { - *info = -2; + *info = -2; } else if (*k < 0 || *k > *m) { - *info = -3; + *info = -3; } else if (*lda < max(1,*m)) { - *info = -5; + *info = -5; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"ZUNGL2", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"ZUNGL2", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*m <= 0) { - return 0; + return 0; } if (*k < *m) { /* Initialise rows k+1:m to rows of the unit matrix */ - i__1 = *n; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (l = *k + 1; l <= i__2; ++l) { - i__3 = l + j * a_dim1; - a[i__3].r = 0., a[i__3].i = 0.; + i__1 = *n; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (l = *k + 1; l <= i__2; ++l) { + i__3 = l + j * a_dim1; + a[i__3].r = 0., a[i__3].i = 0.; /* L10: */ - } - if (j > *k && j <= *m) { - i__2 = j + j * a_dim1; - a[i__2].r = 1., a[i__2].i = 0.; - } + } + if (j > *k && j <= *m) { + i__2 = j + j * a_dim1; + a[i__2].r = 1., a[i__2].i = 0.; + } /* L20: */ - } + } } for (i__ = *k; i__ >= 1; --i__) { /* Apply H(i)**H to A(i:m,i:n) from the right */ - if (i__ < *n) { - i__1 = *n - i__; - zlacgv_(&i__1, &a[i__ + (i__ + 1) * a_dim1], lda); - if (i__ < *m) { - i__1 = i__ + i__ * a_dim1; - a[i__1].r = 1., a[i__1].i = 0.; - i__1 = *m - i__; - i__2 = *n - i__ + 1; - d_cnjg(&z__1, &tau[i__]); - zlarf_((char *)"Right", &i__1, &i__2, &a[i__ + i__ * a_dim1], lda, & - z__1, &a[i__ + 1 + i__ * a_dim1], lda, &work[1], ( - ftnlen)5); - } - i__1 = *n - i__; - i__2 = i__; - z__1.r = -tau[i__2].r, z__1.i = -tau[i__2].i; - zscal_(&i__1, &z__1, &a[i__ + (i__ + 1) * a_dim1], lda); - i__1 = *n - i__; - zlacgv_(&i__1, &a[i__ + (i__ + 1) * a_dim1], lda); - } - i__1 = i__ + i__ * a_dim1; - d_cnjg(&z__2, &tau[i__]); - z__1.r = 1. - z__2.r, z__1.i = 0. - z__2.i; - a[i__1].r = z__1.r, a[i__1].i = z__1.i; + if (i__ < *n) { + i__1 = *n - i__; + zlacgv_(&i__1, &a[i__ + (i__ + 1) * a_dim1], lda); + if (i__ < *m) { + i__1 = i__ + i__ * a_dim1; + a[i__1].r = 1., a[i__1].i = 0.; + i__1 = *m - i__; + i__2 = *n - i__ + 1; + d_cnjg(&z__1, &tau[i__]); + zlarf_((char *)"Right", &i__1, &i__2, &a[i__ + i__ * a_dim1], lda, & + z__1, &a[i__ + 1 + i__ * a_dim1], lda, &work[1], ( + ftnlen)5); + } + i__1 = *n - i__; + i__2 = i__; + z__1.r = -tau[i__2].r, z__1.i = -tau[i__2].i; + zscal_(&i__1, &z__1, &a[i__ + (i__ + 1) * a_dim1], lda); + i__1 = *n - i__; + zlacgv_(&i__1, &a[i__ + (i__ + 1) * a_dim1], lda); + } + i__1 = i__ + i__ * a_dim1; + d_cnjg(&z__2, &tau[i__]); + z__1.r = 1. - z__2.r, z__1.i = 0. - z__2.i; + a[i__1].r = z__1.r, a[i__1].i = z__1.i; /* Set A(i,1:i-1) to zero */ - i__1 = i__ - 1; - for (l = 1; l <= i__1; ++l) { - i__2 = i__ + l * a_dim1; - a[i__2].r = 0., a[i__2].i = 0.; + i__1 = i__ - 1; + for (l = 1; l <= i__1; ++l) { + i__2 = i__ + l * a_dim1; + a[i__2].r = 0., a[i__2].i = 0.; /* L30: */ - } + } /* L40: */ } return 0; @@ -269,5 +269,5 @@ f"> */ } /* zungl2_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zungql.cpp b/lib/linalg/zungql.cpp index 006c4859eb..8ee03838d4 100644 --- a/lib/linalg/zungql.cpp +++ b/lib/linalg/zungql.cpp @@ -1,13 +1,13 @@ /* fortran/zungql.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -151,28 +151,28 @@ f"> */ /* > \ingroup complex16OTHERcomputational */ /* ===================================================================== */ -/* Subroutine */ int zungql_(integer *m, integer *n, integer *k, - doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex * - work, integer *lwork, integer *info) +/* Subroutine */ int zungql_(integer *m, integer *n, integer *k, + doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex * + work, integer *lwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; /* Local variables */ integer i__, j, l, ib, nb, kk, nx, iws, nbmin, iinfo; - extern /* Subroutine */ int zung2l_(integer *, integer *, integer *, - doublecomplex *, integer *, doublecomplex *, doublecomplex *, - integer *), xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *, - integer *, integer *, integer *, doublecomplex *, integer *, - doublecomplex *, integer *, doublecomplex *, integer *, - doublecomplex *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + extern /* Subroutine */ int zung2l_(integer *, integer *, integer *, + doublecomplex *, integer *, doublecomplex *, doublecomplex *, + integer *), xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *, + integer *, integer *, integer *, doublecomplex *, integer *, + doublecomplex *, integer *, doublecomplex *, integer *, + doublecomplex *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); integer ldwork; - extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *, - doublecomplex *, integer *, doublecomplex *, doublecomplex *, - integer *, ftnlen, ftnlen); + extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *, + doublecomplex *, integer *, doublecomplex *, doublecomplex *, + integer *, ftnlen, ftnlen); logical lquery; integer lwkopt; @@ -213,42 +213,42 @@ f"> */ *info = 0; lquery = *lwork == -1; if (*m < 0) { - *info = -1; + *info = -1; } else if (*n < 0 || *n > *m) { - *info = -2; + *info = -2; } else if (*k < 0 || *k > *n) { - *info = -3; + *info = -3; } else if (*lda < max(1,*m)) { - *info = -5; + *info = -5; } if (*info == 0) { - if (*n == 0) { - lwkopt = 1; - } else { - nb = ilaenv_(&c__1, (char *)"ZUNGQL", (char *)" ", m, n, k, &c_n1, (ftnlen)6, ( - ftnlen)1); - lwkopt = *n * nb; - } - work[1].r = (doublereal) lwkopt, work[1].i = 0.; + if (*n == 0) { + lwkopt = 1; + } else { + nb = ilaenv_(&c__1, (char *)"ZUNGQL", (char *)" ", m, n, k, &c_n1, (ftnlen)6, ( + ftnlen)1); + lwkopt = *n * nb; + } + work[1].r = (doublereal) lwkopt, work[1].i = 0.; - if (*lwork < max(1,*n) && ! lquery) { - *info = -8; - } + if (*lwork < max(1,*n) && ! lquery) { + *info = -8; + } } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"ZUNGQL", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"ZUNGQL", &i__1, (ftnlen)6); + return 0; } else if (lquery) { - return 0; + return 0; } /* Quick return if possible */ if (*n <= 0) { - return 0; + return 0; } nbmin = 2; @@ -259,27 +259,27 @@ f"> */ /* Determine when to cross over from blocked to unblocked code. */ /* Computing MAX */ - i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"ZUNGQL", (char *)" ", m, n, k, &c_n1, ( - ftnlen)6, (ftnlen)1); - nx = max(i__1,i__2); - if (nx < *k) { + i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"ZUNGQL", (char *)" ", m, n, k, &c_n1, ( + ftnlen)6, (ftnlen)1); + nx = max(i__1,i__2); + if (nx < *k) { /* Determine if workspace is large enough for blocked code. */ - ldwork = *n; - iws = ldwork * nb; - if (*lwork < iws) { + ldwork = *n; + iws = ldwork * nb; + if (*lwork < iws) { /* Not enough workspace to use optimal NB: reduce NB and */ /* determine the minimum value of NB. */ - nb = *lwork / ldwork; + nb = *lwork / ldwork; /* Computing MAX */ - i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"ZUNGQL", (char *)" ", m, n, k, &c_n1, - (ftnlen)6, (ftnlen)1); - nbmin = max(i__1,i__2); - } - } + i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"ZUNGQL", (char *)" ", m, n, k, &c_n1, + (ftnlen)6, (ftnlen)1); + nbmin = max(i__1,i__2); + } + } } if (nb >= nbmin && nb < *k && nx < *k) { @@ -288,23 +288,23 @@ f"> */ /* The last kk columns are handled by the block method. */ /* Computing MIN */ - i__1 = *k, i__2 = (*k - nx + nb - 1) / nb * nb; - kk = min(i__1,i__2); + i__1 = *k, i__2 = (*k - nx + nb - 1) / nb * nb; + kk = min(i__1,i__2); /* Set A(m-kk+1:m,1:n-kk) to zero. */ - i__1 = *n - kk; - for (j = 1; j <= i__1; ++j) { - i__2 = *m; - for (i__ = *m - kk + 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * a_dim1; - a[i__3].r = 0., a[i__3].i = 0.; + i__1 = *n - kk; + for (j = 1; j <= i__1; ++j) { + i__2 = *m; + for (i__ = *m - kk + 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + a[i__3].r = 0., a[i__3].i = 0.; /* L10: */ - } + } /* L20: */ - } + } } else { - kk = 0; + kk = 0; } /* Use unblocked code for the first or only block. */ @@ -313,60 +313,60 @@ f"> */ i__2 = *n - kk; i__3 = *k - kk; zung2l_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], &work[1], &iinfo) - ; + ; if (kk > 0) { /* Use blocked code */ - i__1 = *k; - i__2 = nb; - for (i__ = *k - kk + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += - i__2) { + i__1 = *k; + i__2 = nb; + for (i__ = *k - kk + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += + i__2) { /* Computing MIN */ - i__3 = nb, i__4 = *k - i__ + 1; - ib = min(i__3,i__4); - if (*n - *k + i__ > 1) { + i__3 = nb, i__4 = *k - i__ + 1; + ib = min(i__3,i__4); + if (*n - *k + i__ > 1) { /* Form the triangular factor of the block reflector */ /* H = H(i+ib-1) . . . H(i+1) H(i) */ - i__3 = *m - *k + i__ + ib - 1; - zlarft_((char *)"Backward", (char *)"Columnwise", &i__3, &ib, &a[(*n - *k + - i__) * a_dim1 + 1], lda, &tau[i__], &work[1], &ldwork, - (ftnlen)8, (ftnlen)10); + i__3 = *m - *k + i__ + ib - 1; + zlarft_((char *)"Backward", (char *)"Columnwise", &i__3, &ib, &a[(*n - *k + + i__) * a_dim1 + 1], lda, &tau[i__], &work[1], &ldwork, + (ftnlen)8, (ftnlen)10); /* Apply H to A(1:m-k+i+ib-1,1:n-k+i-1) from the left */ - i__3 = *m - *k + i__ + ib - 1; - i__4 = *n - *k + i__ - 1; - zlarfb_((char *)"Left", (char *)"No transpose", (char *)"Backward", (char *)"Columnwise", & - i__3, &i__4, &ib, &a[(*n - *k + i__) * a_dim1 + 1], - lda, &work[1], &ldwork, &a[a_offset], lda, &work[ib + - 1], &ldwork, (ftnlen)4, (ftnlen)12, (ftnlen)8, ( - ftnlen)10); - } + i__3 = *m - *k + i__ + ib - 1; + i__4 = *n - *k + i__ - 1; + zlarfb_((char *)"Left", (char *)"No transpose", (char *)"Backward", (char *)"Columnwise", & + i__3, &i__4, &ib, &a[(*n - *k + i__) * a_dim1 + 1], + lda, &work[1], &ldwork, &a[a_offset], lda, &work[ib + + 1], &ldwork, (ftnlen)4, (ftnlen)12, (ftnlen)8, ( + ftnlen)10); + } /* Apply H to rows 1:m-k+i+ib-1 of current block */ - i__3 = *m - *k + i__ + ib - 1; - zung2l_(&i__3, &ib, &ib, &a[(*n - *k + i__) * a_dim1 + 1], lda, & - tau[i__], &work[1], &iinfo); + i__3 = *m - *k + i__ + ib - 1; + zung2l_(&i__3, &ib, &ib, &a[(*n - *k + i__) * a_dim1 + 1], lda, & + tau[i__], &work[1], &iinfo); /* Set rows m-k+i+ib:m of current block to zero */ - i__3 = *n - *k + i__ + ib - 1; - for (j = *n - *k + i__; j <= i__3; ++j) { - i__4 = *m; - for (l = *m - *k + i__ + ib; l <= i__4; ++l) { - i__5 = l + j * a_dim1; - a[i__5].r = 0., a[i__5].i = 0.; + i__3 = *n - *k + i__ + ib - 1; + for (j = *n - *k + i__; j <= i__3; ++j) { + i__4 = *m; + for (l = *m - *k + i__ + ib; l <= i__4; ++l) { + i__5 = l + j * a_dim1; + a[i__5].r = 0., a[i__5].i = 0.; /* L30: */ - } + } /* L40: */ - } + } /* L50: */ - } + } } work[1].r = (doublereal) iws, work[1].i = 0.; @@ -377,5 +377,5 @@ f"> */ } /* zungql_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zungqr.cpp b/lib/linalg/zungqr.cpp index 7ce6a2a40d..a79c87eedd 100644 --- a/lib/linalg/zungqr.cpp +++ b/lib/linalg/zungqr.cpp @@ -1,13 +1,13 @@ /* fortran/zungqr.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -151,28 +151,28 @@ f"> */ /* > \ingroup complex16OTHERcomputational */ /* ===================================================================== */ -/* Subroutine */ int zungqr_(integer *m, integer *n, integer *k, - doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex * - work, integer *lwork, integer *info) +/* Subroutine */ int zungqr_(integer *m, integer *n, integer *k, + doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex * + work, integer *lwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4; /* Local variables */ integer i__, j, l, ib, nb, ki, kk, nx, iws, nbmin, iinfo; - extern /* Subroutine */ int zung2r_(integer *, integer *, integer *, - doublecomplex *, integer *, doublecomplex *, doublecomplex *, - integer *), xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *, - integer *, integer *, integer *, doublecomplex *, integer *, - doublecomplex *, integer *, doublecomplex *, integer *, - doublecomplex *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + extern /* Subroutine */ int zung2r_(integer *, integer *, integer *, + doublecomplex *, integer *, doublecomplex *, doublecomplex *, + integer *), xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *, + integer *, integer *, integer *, doublecomplex *, integer *, + doublecomplex *, integer *, doublecomplex *, integer *, + doublecomplex *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); integer ldwork; - extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *, - doublecomplex *, integer *, doublecomplex *, doublecomplex *, - integer *, ftnlen, ftnlen); + extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *, + doublecomplex *, integer *, doublecomplex *, doublecomplex *, + integer *, ftnlen, ftnlen); integer lwkopt; logical lquery; @@ -216,29 +216,29 @@ f"> */ work[1].r = (doublereal) lwkopt, work[1].i = 0.; lquery = *lwork == -1; if (*m < 0) { - *info = -1; + *info = -1; } else if (*n < 0 || *n > *m) { - *info = -2; + *info = -2; } else if (*k < 0 || *k > *n) { - *info = -3; + *info = -3; } else if (*lda < max(1,*m)) { - *info = -5; + *info = -5; } else if (*lwork < max(1,*n) && ! lquery) { - *info = -8; + *info = -8; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"ZUNGQR", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"ZUNGQR", &i__1, (ftnlen)6); + return 0; } else if (lquery) { - return 0; + return 0; } /* Quick return if possible */ if (*n <= 0) { - work[1].r = 1., work[1].i = 0.; - return 0; + work[1].r = 1., work[1].i = 0.; + return 0; } nbmin = 2; @@ -249,27 +249,27 @@ f"> */ /* Determine when to cross over from blocked to unblocked code. */ /* Computing MAX */ - i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"ZUNGQR", (char *)" ", m, n, k, &c_n1, ( - ftnlen)6, (ftnlen)1); - nx = max(i__1,i__2); - if (nx < *k) { + i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"ZUNGQR", (char *)" ", m, n, k, &c_n1, ( + ftnlen)6, (ftnlen)1); + nx = max(i__1,i__2); + if (nx < *k) { /* Determine if workspace is large enough for blocked code. */ - ldwork = *n; - iws = ldwork * nb; - if (*lwork < iws) { + ldwork = *n; + iws = ldwork * nb; + if (*lwork < iws) { /* Not enough workspace to use optimal NB: reduce NB and */ /* determine the minimum value of NB. */ - nb = *lwork / ldwork; + nb = *lwork / ldwork; /* Computing MAX */ - i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"ZUNGQR", (char *)" ", m, n, k, &c_n1, - (ftnlen)6, (ftnlen)1); - nbmin = max(i__1,i__2); - } - } + i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"ZUNGQR", (char *)" ", m, n, k, &c_n1, + (ftnlen)6, (ftnlen)1); + nbmin = max(i__1,i__2); + } + } } if (nb >= nbmin && nb < *k && nx < *k) { @@ -277,87 +277,87 @@ f"> */ /* Use blocked code after the last block. */ /* The first kk columns are handled by the block method. */ - ki = (*k - nx - 1) / nb * nb; + ki = (*k - nx - 1) / nb * nb; /* Computing MIN */ - i__1 = *k, i__2 = ki + nb; - kk = min(i__1,i__2); + i__1 = *k, i__2 = ki + nb; + kk = min(i__1,i__2); /* Set A(1:kk,kk+1:n) to zero. */ - i__1 = *n; - for (j = kk + 1; j <= i__1; ++j) { - i__2 = kk; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * a_dim1; - a[i__3].r = 0., a[i__3].i = 0.; + i__1 = *n; + for (j = kk + 1; j <= i__1; ++j) { + i__2 = kk; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + a[i__3].r = 0., a[i__3].i = 0.; /* L10: */ - } + } /* L20: */ - } + } } else { - kk = 0; + kk = 0; } /* Use unblocked code for the last or only block. */ if (kk < *n) { - i__1 = *m - kk; - i__2 = *n - kk; - i__3 = *k - kk; - zung2r_(&i__1, &i__2, &i__3, &a[kk + 1 + (kk + 1) * a_dim1], lda, & - tau[kk + 1], &work[1], &iinfo); + i__1 = *m - kk; + i__2 = *n - kk; + i__3 = *k - kk; + zung2r_(&i__1, &i__2, &i__3, &a[kk + 1 + (kk + 1) * a_dim1], lda, & + tau[kk + 1], &work[1], &iinfo); } if (kk > 0) { /* Use blocked code */ - i__1 = -nb; - for (i__ = ki + 1; i__1 < 0 ? i__ >= 1 : i__ <= 1; i__ += i__1) { + i__1 = -nb; + for (i__ = ki + 1; i__1 < 0 ? i__ >= 1 : i__ <= 1; i__ += i__1) { /* Computing MIN */ - i__2 = nb, i__3 = *k - i__ + 1; - ib = min(i__2,i__3); - if (i__ + ib <= *n) { + i__2 = nb, i__3 = *k - i__ + 1; + ib = min(i__2,i__3); + if (i__ + ib <= *n) { /* Form the triangular factor of the block reflector */ /* H = H(i) H(i+1) . . . H(i+ib-1) */ - i__2 = *m - i__ + 1; - zlarft_((char *)"Forward", (char *)"Columnwise", &i__2, &ib, &a[i__ + i__ * - a_dim1], lda, &tau[i__], &work[1], &ldwork, (ftnlen)7, - (ftnlen)10); + i__2 = *m - i__ + 1; + zlarft_((char *)"Forward", (char *)"Columnwise", &i__2, &ib, &a[i__ + i__ * + a_dim1], lda, &tau[i__], &work[1], &ldwork, (ftnlen)7, + (ftnlen)10); /* Apply H to A(i:m,i+ib:n) from the left */ - i__2 = *m - i__ + 1; - i__3 = *n - i__ - ib + 1; - zlarfb_((char *)"Left", (char *)"No transpose", (char *)"Forward", (char *)"Columnwise", & - i__2, &i__3, &ib, &a[i__ + i__ * a_dim1], lda, &work[ - 1], &ldwork, &a[i__ + (i__ + ib) * a_dim1], lda, & - work[ib + 1], &ldwork, (ftnlen)4, (ftnlen)12, (ftnlen) - 7, (ftnlen)10); - } + i__2 = *m - i__ + 1; + i__3 = *n - i__ - ib + 1; + zlarfb_((char *)"Left", (char *)"No transpose", (char *)"Forward", (char *)"Columnwise", & + i__2, &i__3, &ib, &a[i__ + i__ * a_dim1], lda, &work[ + 1], &ldwork, &a[i__ + (i__ + ib) * a_dim1], lda, & + work[ib + 1], &ldwork, (ftnlen)4, (ftnlen)12, (ftnlen) + 7, (ftnlen)10); + } /* Apply H to rows i:m of current block */ - i__2 = *m - i__ + 1; - zung2r_(&i__2, &ib, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], & - work[1], &iinfo); + i__2 = *m - i__ + 1; + zung2r_(&i__2, &ib, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], & + work[1], &iinfo); /* Set rows 1:i-1 of current block to zero */ - i__2 = i__ + ib - 1; - for (j = i__; j <= i__2; ++j) { - i__3 = i__ - 1; - for (l = 1; l <= i__3; ++l) { - i__4 = l + j * a_dim1; - a[i__4].r = 0., a[i__4].i = 0.; + i__2 = i__ + ib - 1; + for (j = i__; j <= i__2; ++j) { + i__3 = i__ - 1; + for (l = 1; l <= i__3; ++l) { + i__4 = l + j * a_dim1; + a[i__4].r = 0., a[i__4].i = 0.; /* L30: */ - } + } /* L40: */ - } + } /* L50: */ - } + } } work[1].r = (doublereal) iws, work[1].i = 0.; @@ -368,5 +368,5 @@ f"> */ } /* zungqr_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zungtr.cpp b/lib/linalg/zungtr.cpp index c8f42b6e21..86c03cb474 100644 --- a/lib/linalg/zungtr.cpp +++ b/lib/linalg/zungtr.cpp @@ -1,13 +1,13 @@ /* fortran/zungtr.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -144,9 +144,9 @@ f"> */ /* > \ingroup complex16OTHERcomputational */ /* ===================================================================== */ -/* Subroutine */ int zungtr_(char *uplo, integer *n, doublecomplex *a, - integer *lda, doublecomplex *tau, doublecomplex *work, integer *lwork, - integer *info, ftnlen uplo_len) +/* Subroutine */ int zungtr_(char *uplo, integer *n, doublecomplex *a, + integer *lda, doublecomplex *tau, doublecomplex *work, integer *lwork, + integer *info, ftnlen uplo_len) { /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4; @@ -157,15 +157,15 @@ f"> */ integer iinfo; logical upper; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); integer lwkopt; logical lquery; - extern /* Subroutine */ int zungql_(integer *, integer *, integer *, - doublecomplex *, integer *, doublecomplex *, doublecomplex *, - integer *, integer *), zungqr_(integer *, integer *, integer *, - doublecomplex *, integer *, doublecomplex *, doublecomplex *, - integer *, integer *); + extern /* Subroutine */ int zungql_(integer *, integer *, integer *, + doublecomplex *, integer *, doublecomplex *, doublecomplex *, + integer *, integer *), zungqr_(integer *, integer *, integer *, + doublecomplex *, integer *, doublecomplex *, doublecomplex *, + integer *, integer *); /* -- LAPACK computational routine -- */ @@ -205,52 +205,52 @@ f"> */ lquery = *lwork == -1; upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { - *info = -1; + *info = -1; } else if (*n < 0) { - *info = -2; + *info = -2; } else if (*lda < max(1,*n)) { - *info = -4; + *info = -4; } else /* if(complicated condition) */ { /* Computing MAX */ - i__1 = 1, i__2 = *n - 1; - if (*lwork < max(i__1,i__2) && ! lquery) { - *info = -7; - } + i__1 = 1, i__2 = *n - 1; + if (*lwork < max(i__1,i__2) && ! lquery) { + *info = -7; + } } if (*info == 0) { - if (upper) { - i__1 = *n - 1; - i__2 = *n - 1; - i__3 = *n - 1; - nb = ilaenv_(&c__1, (char *)"ZUNGQL", (char *)" ", &i__1, &i__2, &i__3, &c_n1, ( - ftnlen)6, (ftnlen)1); - } else { - i__1 = *n - 1; - i__2 = *n - 1; - i__3 = *n - 1; - nb = ilaenv_(&c__1, (char *)"ZUNGQR", (char *)" ", &i__1, &i__2, &i__3, &c_n1, ( - ftnlen)6, (ftnlen)1); - } + if (upper) { + i__1 = *n - 1; + i__2 = *n - 1; + i__3 = *n - 1; + nb = ilaenv_(&c__1, (char *)"ZUNGQL", (char *)" ", &i__1, &i__2, &i__3, &c_n1, ( + ftnlen)6, (ftnlen)1); + } else { + i__1 = *n - 1; + i__2 = *n - 1; + i__3 = *n - 1; + nb = ilaenv_(&c__1, (char *)"ZUNGQR", (char *)" ", &i__1, &i__2, &i__3, &c_n1, ( + ftnlen)6, (ftnlen)1); + } /* Computing MAX */ - i__1 = 1, i__2 = *n - 1; - lwkopt = max(i__1,i__2) * nb; - work[1].r = (doublereal) lwkopt, work[1].i = 0.; + i__1 = 1, i__2 = *n - 1; + lwkopt = max(i__1,i__2) * nb; + work[1].r = (doublereal) lwkopt, work[1].i = 0.; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"ZUNGTR", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"ZUNGTR", &i__1, (ftnlen)6); + return 0; } else if (lquery) { - return 0; + return 0; } /* Quick return if possible */ if (*n == 0) { - work[1].r = 1., work[1].i = 0.; - return 0; + work[1].r = 1., work[1].i = 0.; + return 0; } if (upper) { @@ -261,35 +261,35 @@ f"> */ /* column to the left, and set the last row and column of Q to */ /* those of the unit matrix */ - i__1 = *n - 1; - for (j = 1; j <= i__1; ++j) { - i__2 = j - 1; - for (i__ = 1; i__ <= i__2; ++i__) { - i__3 = i__ + j * a_dim1; - i__4 = i__ + (j + 1) * a_dim1; - a[i__3].r = a[i__4].r, a[i__3].i = a[i__4].i; + i__1 = *n - 1; + for (j = 1; j <= i__1; ++j) { + i__2 = j - 1; + for (i__ = 1; i__ <= i__2; ++i__) { + i__3 = i__ + j * a_dim1; + i__4 = i__ + (j + 1) * a_dim1; + a[i__3].r = a[i__4].r, a[i__3].i = a[i__4].i; /* L10: */ - } - i__2 = *n + j * a_dim1; - a[i__2].r = 0., a[i__2].i = 0.; + } + i__2 = *n + j * a_dim1; + a[i__2].r = 0., a[i__2].i = 0.; /* L20: */ - } - i__1 = *n - 1; - for (i__ = 1; i__ <= i__1; ++i__) { - i__2 = i__ + *n * a_dim1; - a[i__2].r = 0., a[i__2].i = 0.; + } + i__1 = *n - 1; + for (i__ = 1; i__ <= i__1; ++i__) { + i__2 = i__ + *n * a_dim1; + a[i__2].r = 0., a[i__2].i = 0.; /* L30: */ - } - i__1 = *n + *n * a_dim1; - a[i__1].r = 1., a[i__1].i = 0.; + } + i__1 = *n + *n * a_dim1; + a[i__1].r = 1., a[i__1].i = 0.; /* Generate Q(1:n-1,1:n-1) */ - i__1 = *n - 1; - i__2 = *n - 1; - i__3 = *n - 1; - zungql_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], &work[1], - lwork, &iinfo); + i__1 = *n - 1; + i__2 = *n - 1; + i__3 = *n - 1; + zungql_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], &work[1], + lwork, &iinfo); } else { @@ -299,36 +299,36 @@ f"> */ /* column to the right, and set the first row and column of Q to */ /* those of the unit matrix */ - for (j = *n; j >= 2; --j) { - i__1 = j * a_dim1 + 1; - a[i__1].r = 0., a[i__1].i = 0.; - i__1 = *n; - for (i__ = j + 1; i__ <= i__1; ++i__) { - i__2 = i__ + j * a_dim1; - i__3 = i__ + (j - 1) * a_dim1; - a[i__2].r = a[i__3].r, a[i__2].i = a[i__3].i; + for (j = *n; j >= 2; --j) { + i__1 = j * a_dim1 + 1; + a[i__1].r = 0., a[i__1].i = 0.; + i__1 = *n; + for (i__ = j + 1; i__ <= i__1; ++i__) { + i__2 = i__ + j * a_dim1; + i__3 = i__ + (j - 1) * a_dim1; + a[i__2].r = a[i__3].r, a[i__2].i = a[i__3].i; /* L40: */ - } + } /* L50: */ - } - i__1 = a_dim1 + 1; - a[i__1].r = 1., a[i__1].i = 0.; - i__1 = *n; - for (i__ = 2; i__ <= i__1; ++i__) { - i__2 = i__ + a_dim1; - a[i__2].r = 0., a[i__2].i = 0.; + } + i__1 = a_dim1 + 1; + a[i__1].r = 1., a[i__1].i = 0.; + i__1 = *n; + for (i__ = 2; i__ <= i__1; ++i__) { + i__2 = i__ + a_dim1; + a[i__2].r = 0., a[i__2].i = 0.; /* L60: */ - } - if (*n > 1) { + } + if (*n > 1) { /* Generate Q(2:n,2:n) */ - i__1 = *n - 1; - i__2 = *n - 1; - i__3 = *n - 1; - zungqr_(&i__1, &i__2, &i__3, &a[(a_dim1 << 1) + 2], lda, &tau[1], - &work[1], lwork, &iinfo); - } + i__1 = *n - 1; + i__2 = *n - 1; + i__3 = *n - 1; + zungqr_(&i__1, &i__2, &i__3, &a[(a_dim1 << 1) + 2], lda, &tau[1], + &work[1], lwork, &iinfo); + } } work[1].r = (doublereal) lwkopt, work[1].i = 0.; return 0; @@ -338,5 +338,5 @@ f"> */ } /* zungtr_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zunm2l.cpp b/lib/linalg/zunm2l.cpp index d7fc940517..d9bc80e8c7 100644 --- a/lib/linalg/zunm2l.cpp +++ b/lib/linalg/zunm2l.cpp @@ -1,13 +1,13 @@ /* fortran/zunm2l.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -19,7 +19,7 @@ extern "C" { static integer c__1 = 1; -/* > \brief \b ZUNM2L multiplies a general matrix by the unitary matrix from a QL factorization determined by +/* > \brief \b ZUNM2L multiplies a general matrix by the unitary matrix from a QL factorization determined by cgeqlf (unblocked algorithm). */ /* =========== DOCUMENTATION =========== */ @@ -179,10 +179,10 @@ f"> */ /* > \ingroup complex16OTHERcomputational */ /* ===================================================================== */ -/* Subroutine */ int zunm2l_(char *side, char *trans, integer *m, integer *n, - integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, - doublecomplex *c__, integer *ldc, doublecomplex *work, integer *info, - ftnlen side_len, ftnlen trans_len) +/* Subroutine */ int zunm2l_(char *side, char *trans, integer *m, integer *n, + integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, + doublecomplex *c__, integer *ldc, doublecomplex *work, integer *info, + ftnlen side_len, ftnlen trans_len) { /* System generated locals */ integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3; @@ -197,10 +197,10 @@ f"> */ logical left; doublecomplex taui; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int zlarf_(char *, integer *, integer *, - doublecomplex *, integer *, doublecomplex *, doublecomplex *, - integer *, doublecomplex *, ftnlen), xerbla_(char *, integer *, - ftnlen); + extern /* Subroutine */ int zlarf_(char *, integer *, integer *, + doublecomplex *, integer *, doublecomplex *, doublecomplex *, + integer *, doublecomplex *, ftnlen), xerbla_(char *, integer *, + ftnlen); logical notran; @@ -247,85 +247,85 @@ f"> */ /* NQ is the order of Q */ if (left) { - nq = *m; + nq = *m; } else { - nq = *n; + nq = *n; } if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { - *info = -1; + *info = -1; } else if (! notran && ! lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { - *info = -2; + *info = -2; } else if (*m < 0) { - *info = -3; + *info = -3; } else if (*n < 0) { - *info = -4; + *info = -4; } else if (*k < 0 || *k > nq) { - *info = -5; + *info = -5; } else if (*lda < max(1,nq)) { - *info = -7; + *info = -7; } else if (*ldc < max(1,*m)) { - *info = -10; + *info = -10; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"ZUNM2L", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"ZUNM2L", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*m == 0 || *n == 0 || *k == 0) { - return 0; + return 0; } if (left && notran || ! left && ! notran) { - i1 = 1; - i2 = *k; - i3 = 1; + i1 = 1; + i2 = *k; + i3 = 1; } else { - i1 = *k; - i2 = 1; - i3 = -1; + i1 = *k; + i2 = 1; + i3 = -1; } if (left) { - ni = *n; + ni = *n; } else { - mi = *m; + mi = *m; } i__1 = i2; i__2 = i3; for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { - if (left) { + if (left) { /* H(i) or H(i)**H is applied to C(1:m-k+i,1:n) */ - mi = *m - *k + i__; - } else { + mi = *m - *k + i__; + } else { /* H(i) or H(i)**H is applied to C(1:m,1:n-k+i) */ - ni = *n - *k + i__; - } + ni = *n - *k + i__; + } /* Apply H(i) or H(i)**H */ - if (notran) { - i__3 = i__; - taui.r = tau[i__3].r, taui.i = tau[i__3].i; - } else { - d_cnjg(&z__1, &tau[i__]); - taui.r = z__1.r, taui.i = z__1.i; - } - i__3 = nq - *k + i__ + i__ * a_dim1; - aii.r = a[i__3].r, aii.i = a[i__3].i; - i__3 = nq - *k + i__ + i__ * a_dim1; - a[i__3].r = 1., a[i__3].i = 0.; - zlarf_(side, &mi, &ni, &a[i__ * a_dim1 + 1], &c__1, &taui, &c__[ - c_offset], ldc, &work[1], (ftnlen)1); - i__3 = nq - *k + i__ + i__ * a_dim1; - a[i__3].r = aii.r, a[i__3].i = aii.i; + if (notran) { + i__3 = i__; + taui.r = tau[i__3].r, taui.i = tau[i__3].i; + } else { + d_cnjg(&z__1, &tau[i__]); + taui.r = z__1.r, taui.i = z__1.i; + } + i__3 = nq - *k + i__ + i__ * a_dim1; + aii.r = a[i__3].r, aii.i = a[i__3].i; + i__3 = nq - *k + i__ + i__ * a_dim1; + a[i__3].r = 1., a[i__3].i = 0.; + zlarf_(side, &mi, &ni, &a[i__ * a_dim1 + 1], &c__1, &taui, &c__[ + c_offset], ldc, &work[1], (ftnlen)1); + i__3 = nq - *k + i__ + i__ * a_dim1; + a[i__3].r = aii.r, a[i__3].i = aii.i; /* L10: */ } return 0; @@ -335,5 +335,5 @@ f"> */ } /* zunm2l_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zunm2r.cpp b/lib/linalg/zunm2r.cpp index 56ad0d944a..a84cf72ba6 100644 --- a/lib/linalg/zunm2r.cpp +++ b/lib/linalg/zunm2r.cpp @@ -1,13 +1,13 @@ /* fortran/zunm2r.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -19,7 +19,7 @@ extern "C" { static integer c__1 = 1; -/* > \brief \b ZUNM2R multiplies a general matrix by the unitary matrix from a QR factorization determined by +/* > \brief \b ZUNM2R multiplies a general matrix by the unitary matrix from a QR factorization determined by cgeqrf (unblocked algorithm). */ /* =========== DOCUMENTATION =========== */ @@ -179,10 +179,10 @@ f"> */ /* > \ingroup complex16OTHERcomputational */ /* ===================================================================== */ -/* Subroutine */ int zunm2r_(char *side, char *trans, integer *m, integer *n, - integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, - doublecomplex *c__, integer *ldc, doublecomplex *work, integer *info, - ftnlen side_len, ftnlen trans_len) +/* Subroutine */ int zunm2r_(char *side, char *trans, integer *m, integer *n, + integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, + doublecomplex *c__, integer *ldc, doublecomplex *work, integer *info, + ftnlen side_len, ftnlen trans_len) { /* System generated locals */ integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3; @@ -197,10 +197,10 @@ f"> */ logical left; doublecomplex taui; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int zlarf_(char *, integer *, integer *, - doublecomplex *, integer *, doublecomplex *, doublecomplex *, - integer *, doublecomplex *, ftnlen), xerbla_(char *, integer *, - ftnlen); + extern /* Subroutine */ int zlarf_(char *, integer *, integer *, + doublecomplex *, integer *, doublecomplex *, doublecomplex *, + integer *, doublecomplex *, ftnlen), xerbla_(char *, integer *, + ftnlen); logical notran; @@ -247,89 +247,89 @@ f"> */ /* NQ is the order of Q */ if (left) { - nq = *m; + nq = *m; } else { - nq = *n; + nq = *n; } if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { - *info = -1; + *info = -1; } else if (! notran && ! lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { - *info = -2; + *info = -2; } else if (*m < 0) { - *info = -3; + *info = -3; } else if (*n < 0) { - *info = -4; + *info = -4; } else if (*k < 0 || *k > nq) { - *info = -5; + *info = -5; } else if (*lda < max(1,nq)) { - *info = -7; + *info = -7; } else if (*ldc < max(1,*m)) { - *info = -10; + *info = -10; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"ZUNM2R", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"ZUNM2R", &i__1, (ftnlen)6); + return 0; } /* Quick return if possible */ if (*m == 0 || *n == 0 || *k == 0) { - return 0; + return 0; } if (left && ! notran || ! left && notran) { - i1 = 1; - i2 = *k; - i3 = 1; + i1 = 1; + i2 = *k; + i3 = 1; } else { - i1 = *k; - i2 = 1; - i3 = -1; + i1 = *k; + i2 = 1; + i3 = -1; } if (left) { - ni = *n; - jc = 1; + ni = *n; + jc = 1; } else { - mi = *m; - ic = 1; + mi = *m; + ic = 1; } i__1 = i2; i__2 = i3; for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { - if (left) { + if (left) { /* H(i) or H(i)**H is applied to C(i:m,1:n) */ - mi = *m - i__ + 1; - ic = i__; - } else { + mi = *m - i__ + 1; + ic = i__; + } else { /* H(i) or H(i)**H is applied to C(1:m,i:n) */ - ni = *n - i__ + 1; - jc = i__; - } + ni = *n - i__ + 1; + jc = i__; + } /* Apply H(i) or H(i)**H */ - if (notran) { - i__3 = i__; - taui.r = tau[i__3].r, taui.i = tau[i__3].i; - } else { - d_cnjg(&z__1, &tau[i__]); - taui.r = z__1.r, taui.i = z__1.i; - } - i__3 = i__ + i__ * a_dim1; - aii.r = a[i__3].r, aii.i = a[i__3].i; - i__3 = i__ + i__ * a_dim1; - a[i__3].r = 1., a[i__3].i = 0.; - zlarf_(side, &mi, &ni, &a[i__ + i__ * a_dim1], &c__1, &taui, &c__[ic - + jc * c_dim1], ldc, &work[1], (ftnlen)1); - i__3 = i__ + i__ * a_dim1; - a[i__3].r = aii.r, a[i__3].i = aii.i; + if (notran) { + i__3 = i__; + taui.r = tau[i__3].r, taui.i = tau[i__3].i; + } else { + d_cnjg(&z__1, &tau[i__]); + taui.r = z__1.r, taui.i = z__1.i; + } + i__3 = i__ + i__ * a_dim1; + aii.r = a[i__3].r, aii.i = a[i__3].i; + i__3 = i__ + i__ * a_dim1; + a[i__3].r = 1., a[i__3].i = 0.; + zlarf_(side, &mi, &ni, &a[i__ + i__ * a_dim1], &c__1, &taui, &c__[ic + + jc * c_dim1], ldc, &work[1], (ftnlen)1); + i__3 = i__ + i__ * a_dim1; + a[i__3].r = aii.r, a[i__3].i = aii.i; /* L10: */ } return 0; @@ -339,5 +339,5 @@ f"> */ } /* zunm2r_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zunmql.cpp b/lib/linalg/zunmql.cpp index c7e6134831..facff63c71 100644 --- a/lib/linalg/zunmql.cpp +++ b/lib/linalg/zunmql.cpp @@ -1,13 +1,13 @@ /* fortran/zunmql.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -189,15 +189,15 @@ f"> */ /* > \ingroup complex16OTHERcomputational */ /* ===================================================================== */ -/* Subroutine */ int zunmql_(char *side, char *trans, integer *m, integer *n, - integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, - doublecomplex *c__, integer *ldc, doublecomplex *work, integer *lwork, - integer *info, ftnlen side_len, ftnlen trans_len) +/* Subroutine */ int zunmql_(char *side, char *trans, integer *m, integer *n, + integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, + doublecomplex *c__, integer *ldc, doublecomplex *work, integer *lwork, + integer *info, ftnlen side_len, ftnlen trans_len) { /* System generated locals */ address a__1[2]; - integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4, - i__5; + integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4, + i__5; char ch__1[2]; /* Builtin functions */ @@ -208,21 +208,21 @@ f"> */ logical left; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer nbmin, iinfo; - extern /* Subroutine */ int zunm2l_(char *, char *, integer *, integer *, - integer *, doublecomplex *, integer *, doublecomplex *, - doublecomplex *, integer *, doublecomplex *, integer *, ftnlen, - ftnlen), xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *, - integer *, integer *, integer *, doublecomplex *, integer *, - doublecomplex *, integer *, doublecomplex *, integer *, - doublecomplex *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + extern /* Subroutine */ int zunm2l_(char *, char *, integer *, integer *, + integer *, doublecomplex *, integer *, doublecomplex *, + doublecomplex *, integer *, doublecomplex *, integer *, ftnlen, + ftnlen), xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *, + integer *, integer *, integer *, doublecomplex *, integer *, + doublecomplex *, integer *, doublecomplex *, integer *, + doublecomplex *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); logical notran; integer ldwork; - extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *, - doublecomplex *, integer *, doublecomplex *, doublecomplex *, - integer *, ftnlen, ftnlen); + extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *, + doublecomplex *, integer *, doublecomplex *, doublecomplex *, + integer *, ftnlen, ftnlen); integer lwkopt; logical lquery; @@ -271,141 +271,141 @@ f"> */ /* NQ is the order of Q and NW is the minimum dimension of WORK */ if (left) { - nq = *m; - nw = max(1,*n); + nq = *m; + nw = max(1,*n); } else { - nq = *n; - nw = max(1,*m); + nq = *n; + nw = max(1,*m); } if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { - *info = -1; + *info = -1; } else if (! notran && ! lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { - *info = -2; + *info = -2; } else if (*m < 0) { - *info = -3; + *info = -3; } else if (*n < 0) { - *info = -4; + *info = -4; } else if (*k < 0 || *k > nq) { - *info = -5; + *info = -5; } else if (*lda < max(1,nq)) { - *info = -7; + *info = -7; } else if (*ldc < max(1,*m)) { - *info = -10; + *info = -10; } else if (*lwork < nw && ! lquery) { - *info = -12; + *info = -12; } if (*info == 0) { /* Compute the workspace requirements */ - if (*m == 0 || *n == 0) { - lwkopt = 1; - } else { + if (*m == 0 || *n == 0) { + lwkopt = 1; + } else { /* Computing MIN */ /* Writing concatenation */ - i__3[0] = 1, a__1[0] = side; - i__3[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); - i__1 = 64, i__2 = ilaenv_(&c__1, (char *)"ZUNMQL", ch__1, m, n, k, &c_n1, - (ftnlen)6, (ftnlen)2); - nb = min(i__1,i__2); - lwkopt = nw * nb + 4160; - } - work[1].r = (doublereal) lwkopt, work[1].i = 0.; + i__3[0] = 1, a__1[0] = side; + i__3[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + i__1 = 64, i__2 = ilaenv_(&c__1, (char *)"ZUNMQL", ch__1, m, n, k, &c_n1, + (ftnlen)6, (ftnlen)2); + nb = min(i__1,i__2); + lwkopt = nw * nb + 4160; + } + work[1].r = (doublereal) lwkopt, work[1].i = 0.; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"ZUNMQL", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"ZUNMQL", &i__1, (ftnlen)6); + return 0; } else if (lquery) { - return 0; + return 0; } /* Quick return if possible */ if (*m == 0 || *n == 0) { - return 0; + return 0; } nbmin = 2; ldwork = nw; if (nb > 1 && nb < *k) { - if (*lwork < lwkopt) { - nb = (*lwork - 4160) / ldwork; + if (*lwork < lwkopt) { + nb = (*lwork - 4160) / ldwork; /* Computing MAX */ /* Writing concatenation */ - i__3[0] = 1, a__1[0] = side; - i__3[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); - i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"ZUNMQL", ch__1, m, n, k, &c_n1, ( - ftnlen)6, (ftnlen)2); - nbmin = max(i__1,i__2); - } + i__3[0] = 1, a__1[0] = side; + i__3[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"ZUNMQL", ch__1, m, n, k, &c_n1, ( + ftnlen)6, (ftnlen)2); + nbmin = max(i__1,i__2); + } } if (nb < nbmin || nb >= *k) { /* Use unblocked code */ - zunm2l_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[ - c_offset], ldc, &work[1], &iinfo, (ftnlen)1, (ftnlen)1); + zunm2l_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[ + c_offset], ldc, &work[1], &iinfo, (ftnlen)1, (ftnlen)1); } else { /* Use blocked code */ - iwt = nw * nb + 1; - if (left && notran || ! left && ! notran) { - i1 = 1; - i2 = *k; - i3 = nb; - } else { - i1 = (*k - 1) / nb * nb + 1; - i2 = 1; - i3 = -nb; - } + iwt = nw * nb + 1; + if (left && notran || ! left && ! notran) { + i1 = 1; + i2 = *k; + i3 = nb; + } else { + i1 = (*k - 1) / nb * nb + 1; + i2 = 1; + i3 = -nb; + } - if (left) { - ni = *n; - } else { - mi = *m; - } + if (left) { + ni = *n; + } else { + mi = *m; + } - i__1 = i2; - i__2 = i3; - for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { + i__1 = i2; + i__2 = i3; + for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { /* Computing MIN */ - i__4 = nb, i__5 = *k - i__ + 1; - ib = min(i__4,i__5); + i__4 = nb, i__5 = *k - i__ + 1; + ib = min(i__4,i__5); /* Form the triangular factor of the block reflector */ /* H = H(i+ib-1) . . . H(i+1) H(i) */ - i__4 = nq - *k + i__ + ib - 1; - zlarft_((char *)"Backward", (char *)"Columnwise", &i__4, &ib, &a[i__ * a_dim1 + 1] - , lda, &tau[i__], &work[iwt], &c__65, (ftnlen)8, (ftnlen) - 10); - if (left) { + i__4 = nq - *k + i__ + ib - 1; + zlarft_((char *)"Backward", (char *)"Columnwise", &i__4, &ib, &a[i__ * a_dim1 + 1] + , lda, &tau[i__], &work[iwt], &c__65, (ftnlen)8, (ftnlen) + 10); + if (left) { /* H or H**H is applied to C(1:m-k+i+ib-1,1:n) */ - mi = *m - *k + i__ + ib - 1; - } else { + mi = *m - *k + i__ + ib - 1; + } else { /* H or H**H is applied to C(1:m,1:n-k+i+ib-1) */ - ni = *n - *k + i__ + ib - 1; - } + ni = *n - *k + i__ + ib - 1; + } /* Apply H or H**H */ - zlarfb_(side, trans, (char *)"Backward", (char *)"Columnwise", &mi, &ni, &ib, &a[ - i__ * a_dim1 + 1], lda, &work[iwt], &c__65, &c__[c_offset] - , ldc, &work[1], &ldwork, (ftnlen)1, (ftnlen)1, (ftnlen)8, - (ftnlen)10); + zlarfb_(side, trans, (char *)"Backward", (char *)"Columnwise", &mi, &ni, &ib, &a[ + i__ * a_dim1 + 1], lda, &work[iwt], &c__65, &c__[c_offset] + , ldc, &work[1], &ldwork, (ftnlen)1, (ftnlen)1, (ftnlen)8, + (ftnlen)10); /* L10: */ - } + } } work[1].r = (doublereal) lwkopt, work[1].i = 0.; return 0; @@ -415,5 +415,5 @@ f"> */ } /* zunmql_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zunmqr.cpp b/lib/linalg/zunmqr.cpp index dc127fe1aa..8659499dab 100644 --- a/lib/linalg/zunmqr.cpp +++ b/lib/linalg/zunmqr.cpp @@ -1,13 +1,13 @@ /* fortran/zunmqr.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -189,15 +189,15 @@ f"> */ /* > \ingroup complex16OTHERcomputational */ /* ===================================================================== */ -/* Subroutine */ int zunmqr_(char *side, char *trans, integer *m, integer *n, - integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, - doublecomplex *c__, integer *ldc, doublecomplex *work, integer *lwork, - integer *info, ftnlen side_len, ftnlen trans_len) +/* Subroutine */ int zunmqr_(char *side, char *trans, integer *m, integer *n, + integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, + doublecomplex *c__, integer *ldc, doublecomplex *work, integer *lwork, + integer *info, ftnlen side_len, ftnlen trans_len) { /* System generated locals */ address a__1[2]; - integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4, - i__5; + integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4, + i__5; char ch__1[2]; /* Builtin functions */ @@ -208,21 +208,21 @@ f"> */ logical left; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer nbmin, iinfo; - extern /* Subroutine */ int zunm2r_(char *, char *, integer *, integer *, - integer *, doublecomplex *, integer *, doublecomplex *, - doublecomplex *, integer *, doublecomplex *, integer *, ftnlen, - ftnlen), xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *, - integer *, integer *, integer *, doublecomplex *, integer *, - doublecomplex *, integer *, doublecomplex *, integer *, - doublecomplex *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + extern /* Subroutine */ int zunm2r_(char *, char *, integer *, integer *, + integer *, doublecomplex *, integer *, doublecomplex *, + doublecomplex *, integer *, doublecomplex *, integer *, ftnlen, + ftnlen), xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); + extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *, + integer *, integer *, integer *, doublecomplex *, integer *, + doublecomplex *, integer *, doublecomplex *, integer *, + doublecomplex *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); logical notran; integer ldwork; - extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *, - doublecomplex *, integer *, doublecomplex *, doublecomplex *, - integer *, ftnlen, ftnlen); + extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *, + doublecomplex *, integer *, doublecomplex *, doublecomplex *, + integer *, ftnlen, ftnlen); integer lwkopt; logical lquery; @@ -271,28 +271,28 @@ f"> */ /* NQ is the order of Q and NW is the minimum dimension of WORK */ if (left) { - nq = *m; - nw = max(1,*n); + nq = *m; + nw = max(1,*n); } else { - nq = *n; - nw = max(1,*m); + nq = *n; + nw = max(1,*m); } if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { - *info = -1; + *info = -1; } else if (! notran && ! lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { - *info = -2; + *info = -2; } else if (*m < 0) { - *info = -3; + *info = -3; } else if (*n < 0) { - *info = -4; + *info = -4; } else if (*k < 0 || *k > nq) { - *info = -5; + *info = -5; } else if (*lda < max(1,nq)) { - *info = -7; + *info = -7; } else if (*ldc < max(1,*m)) { - *info = -10; + *info = -10; } else if (*lwork < nw && ! lquery) { - *info = -12; + *info = -12; } if (*info == 0) { @@ -301,112 +301,112 @@ f"> */ /* Computing MIN */ /* Writing concatenation */ - i__3[0] = 1, a__1[0] = side; - i__3[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); - i__1 = 64, i__2 = ilaenv_(&c__1, (char *)"ZUNMQR", ch__1, m, n, k, &c_n1, ( - ftnlen)6, (ftnlen)2); - nb = min(i__1,i__2); - lwkopt = nw * nb + 4160; - work[1].r = (doublereal) lwkopt, work[1].i = 0.; + i__3[0] = 1, a__1[0] = side; + i__3[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + i__1 = 64, i__2 = ilaenv_(&c__1, (char *)"ZUNMQR", ch__1, m, n, k, &c_n1, ( + ftnlen)6, (ftnlen)2); + nb = min(i__1,i__2); + lwkopt = nw * nb + 4160; + work[1].r = (doublereal) lwkopt, work[1].i = 0.; } if (*info != 0) { - i__1 = -(*info); - xerbla_((char *)"ZUNMQR", &i__1, (ftnlen)6); - return 0; + i__1 = -(*info); + xerbla_((char *)"ZUNMQR", &i__1, (ftnlen)6); + return 0; } else if (lquery) { - return 0; + return 0; } /* Quick return if possible */ if (*m == 0 || *n == 0 || *k == 0) { - work[1].r = 1., work[1].i = 0.; - return 0; + work[1].r = 1., work[1].i = 0.; + return 0; } nbmin = 2; ldwork = nw; if (nb > 1 && nb < *k) { - if (*lwork < lwkopt) { - nb = (*lwork - 4160) / ldwork; + if (*lwork < lwkopt) { + nb = (*lwork - 4160) / ldwork; /* Computing MAX */ /* Writing concatenation */ - i__3[0] = 1, a__1[0] = side; - i__3[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); - i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"ZUNMQR", ch__1, m, n, k, &c_n1, ( - ftnlen)6, (ftnlen)2); - nbmin = max(i__1,i__2); - } + i__3[0] = 1, a__1[0] = side; + i__3[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"ZUNMQR", ch__1, m, n, k, &c_n1, ( + ftnlen)6, (ftnlen)2); + nbmin = max(i__1,i__2); + } } if (nb < nbmin || nb >= *k) { /* Use unblocked code */ - zunm2r_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[ - c_offset], ldc, &work[1], &iinfo, (ftnlen)1, (ftnlen)1); + zunm2r_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[ + c_offset], ldc, &work[1], &iinfo, (ftnlen)1, (ftnlen)1); } else { /* Use blocked code */ - iwt = nw * nb + 1; - if (left && ! notran || ! left && notran) { - i1 = 1; - i2 = *k; - i3 = nb; - } else { - i1 = (*k - 1) / nb * nb + 1; - i2 = 1; - i3 = -nb; - } + iwt = nw * nb + 1; + if (left && ! notran || ! left && notran) { + i1 = 1; + i2 = *k; + i3 = nb; + } else { + i1 = (*k - 1) / nb * nb + 1; + i2 = 1; + i3 = -nb; + } - if (left) { - ni = *n; - jc = 1; - } else { - mi = *m; - ic = 1; - } + if (left) { + ni = *n; + jc = 1; + } else { + mi = *m; + ic = 1; + } - i__1 = i2; - i__2 = i3; - for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { + i__1 = i2; + i__2 = i3; + for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { /* Computing MIN */ - i__4 = nb, i__5 = *k - i__ + 1; - ib = min(i__4,i__5); + i__4 = nb, i__5 = *k - i__ + 1; + ib = min(i__4,i__5); /* Form the triangular factor of the block reflector */ /* H = H(i) H(i+1) . . . H(i+ib-1) */ - i__4 = nq - i__ + 1; - zlarft_((char *)"Forward", (char *)"Columnwise", &i__4, &ib, &a[i__ + i__ * - a_dim1], lda, &tau[i__], &work[iwt], &c__65, (ftnlen)7, ( - ftnlen)10); - if (left) { + i__4 = nq - i__ + 1; + zlarft_((char *)"Forward", (char *)"Columnwise", &i__4, &ib, &a[i__ + i__ * + a_dim1], lda, &tau[i__], &work[iwt], &c__65, (ftnlen)7, ( + ftnlen)10); + if (left) { /* H or H**H is applied to C(i:m,1:n) */ - mi = *m - i__ + 1; - ic = i__; - } else { + mi = *m - i__ + 1; + ic = i__; + } else { /* H or H**H is applied to C(1:m,i:n) */ - ni = *n - i__ + 1; - jc = i__; - } + ni = *n - i__ + 1; + jc = i__; + } /* Apply H or H**H */ - zlarfb_(side, trans, (char *)"Forward", (char *)"Columnwise", &mi, &ni, &ib, &a[ - i__ + i__ * a_dim1], lda, &work[iwt], &c__65, &c__[ic + - jc * c_dim1], ldc, &work[1], &ldwork, (ftnlen)1, (ftnlen) - 1, (ftnlen)7, (ftnlen)10); + zlarfb_(side, trans, (char *)"Forward", (char *)"Columnwise", &mi, &ni, &ib, &a[ + i__ + i__ * a_dim1], lda, &work[iwt], &c__65, &c__[ic + + jc * c_dim1], ldc, &work[1], &ldwork, (ftnlen)1, (ftnlen) + 1, (ftnlen)7, (ftnlen)10); /* L10: */ - } + } } work[1].r = (doublereal) lwkopt, work[1].i = 0.; return 0; @@ -416,5 +416,5 @@ f"> */ } /* zunmqr_ */ #ifdef __cplusplus - } + } #endif diff --git a/lib/linalg/zunmtr.cpp b/lib/linalg/zunmtr.cpp index ab5e7eacb8..be224d7e93 100644 --- a/lib/linalg/zunmtr.cpp +++ b/lib/linalg/zunmtr.cpp @@ -1,13 +1,13 @@ /* fortran/zunmtr.f -- translated by f2c (version 20200916). You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - http://www.netlib.org/f2c/libf2c.zip + http://www.netlib.org/f2c/libf2c.zip */ #ifdef __cplusplus @@ -192,10 +192,10 @@ f"> */ /* > \ingroup complex16OTHERcomputational */ /* ===================================================================== */ -/* Subroutine */ int zunmtr_(char *side, char *uplo, char *trans, integer *m, - integer *n, doublecomplex *a, integer *lda, doublecomplex *tau, - doublecomplex *c__, integer *ldc, doublecomplex *work, integer *lwork, - integer *info, ftnlen side_len, ftnlen uplo_len, ftnlen trans_len) +/* Subroutine */ int zunmtr_(char *side, char *uplo, char *trans, integer *m, + integer *n, doublecomplex *a, integer *lda, doublecomplex *tau, + doublecomplex *c__, integer *ldc, doublecomplex *work, integer *lwork, + integer *info, ftnlen side_len, ftnlen uplo_len, ftnlen trans_len) { /* System generated locals */ address a__1[2]; @@ -212,17 +212,17 @@ f"> */ integer iinfo; logical upper; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, + integer *, integer *, ftnlen, ftnlen); integer lwkopt; logical lquery; - extern /* Subroutine */ int zunmql_(char *, char *, integer *, integer *, - integer *, doublecomplex *, integer *, doublecomplex *, - doublecomplex *, integer *, doublecomplex *, integer *, integer *, - ftnlen, ftnlen), zunmqr_(char *, char *, integer *, integer *, - integer *, doublecomplex *, integer *, doublecomplex *, - doublecomplex *, integer *, doublecomplex *, integer *, integer *, - ftnlen, ftnlen); + extern /* Subroutine */ int zunmql_(char *, char *, integer *, integer *, + integer *, doublecomplex *, integer *, doublecomplex *, + doublecomplex *, integer *, doublecomplex *, integer *, integer *, + ftnlen, ftnlen), zunmqr_(char *, char *, integer *, integer *, + integer *, doublecomplex *, integer *, doublecomplex *, + doublecomplex *, integer *, doublecomplex *, integer *, integer *, + ftnlen, ftnlen); /* -- LAPACK computational routine -- */ @@ -267,123 +267,123 @@ f"> */ /* NQ is the order of Q and NW is the minimum dimension of WORK */ if (left) { - nq = *m; - nw = max(1,*n); + nq = *m; + nw = max(1,*n); } else { - nq = *n; - nw = max(1,*m); + nq = *n; + nw = max(1,*m); } if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { - *info = -1; + *info = -1; } else if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { - *info = -2; - } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, - (char *)"C", (ftnlen)1, (ftnlen)1)) { - *info = -3; + *info = -2; + } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, + (char *)"C", (ftnlen)1, (ftnlen)1)) { + *info = -3; } else if (*m < 0) { - *info = -4; + *info = -4; } else if (*n < 0) { - *info = -5; + *info = -5; } else if (*lda < max(1,nq)) { - *info = -7; + *info = -7; } else if (*ldc < max(1,*m)) { - *info = -10; + *info = -10; } else if (*lwork < nw && ! lquery) { - *info = -12; + *info = -12; } if (*info == 0) { - if (upper) { - if (left) { + if (upper) { + if (left) { /* Writing concatenation */ - i__1[0] = 1, a__1[0] = side; - i__1[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); - i__2 = *m - 1; - i__3 = *m - 1; - nb = ilaenv_(&c__1, (char *)"ZUNMQL", ch__1, &i__2, n, &i__3, &c_n1, ( - ftnlen)6, (ftnlen)2); - } else { + i__1[0] = 1, a__1[0] = side; + i__1[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); + i__2 = *m - 1; + i__3 = *m - 1; + nb = ilaenv_(&c__1, (char *)"ZUNMQL", ch__1, &i__2, n, &i__3, &c_n1, ( + ftnlen)6, (ftnlen)2); + } else { /* Writing concatenation */ - i__1[0] = 1, a__1[0] = side; - i__1[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); - i__2 = *n - 1; - i__3 = *n - 1; - nb = ilaenv_(&c__1, (char *)"ZUNMQL", ch__1, m, &i__2, &i__3, &c_n1, ( - ftnlen)6, (ftnlen)2); - } - } else { - if (left) { + i__1[0] = 1, a__1[0] = side; + i__1[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); + i__2 = *n - 1; + i__3 = *n - 1; + nb = ilaenv_(&c__1, (char *)"ZUNMQL", ch__1, m, &i__2, &i__3, &c_n1, ( + ftnlen)6, (ftnlen)2); + } + } else { + if (left) { /* Writing concatenation */ - i__1[0] = 1, a__1[0] = side; - i__1[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); - i__2 = *m - 1; - i__3 = *m - 1; - nb = ilaenv_(&c__1, (char *)"ZUNMQR", ch__1, &i__2, n, &i__3, &c_n1, ( - ftnlen)6, (ftnlen)2); - } else { + i__1[0] = 1, a__1[0] = side; + i__1[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); + i__2 = *m - 1; + i__3 = *m - 1; + nb = ilaenv_(&c__1, (char *)"ZUNMQR", ch__1, &i__2, n, &i__3, &c_n1, ( + ftnlen)6, (ftnlen)2); + } else { /* Writing concatenation */ - i__1[0] = 1, a__1[0] = side; - i__1[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); - i__2 = *n - 1; - i__3 = *n - 1; - nb = ilaenv_(&c__1, (char *)"ZUNMQR", ch__1, m, &i__2, &i__3, &c_n1, ( - ftnlen)6, (ftnlen)2); - } - } - lwkopt = nw * nb; - work[1].r = (doublereal) lwkopt, work[1].i = 0.; + i__1[0] = 1, a__1[0] = side; + i__1[1] = 1, a__1[1] = trans; + s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); + i__2 = *n - 1; + i__3 = *n - 1; + nb = ilaenv_(&c__1, (char *)"ZUNMQR", ch__1, m, &i__2, &i__3, &c_n1, ( + ftnlen)6, (ftnlen)2); + } + } + lwkopt = nw * nb; + work[1].r = (doublereal) lwkopt, work[1].i = 0.; } if (*info != 0) { - i__2 = -(*info); - xerbla_((char *)"ZUNMTR", &i__2, (ftnlen)6); - return 0; + i__2 = -(*info); + xerbla_((char *)"ZUNMTR", &i__2, (ftnlen)6); + return 0; } else if (lquery) { - return 0; + return 0; } /* Quick return if possible */ if (*m == 0 || *n == 0 || nq == 1) { - work[1].r = 1., work[1].i = 0.; - return 0; + work[1].r = 1., work[1].i = 0.; + return 0; } if (left) { - mi = *m - 1; - ni = *n; + mi = *m - 1; + ni = *n; } else { - mi = *m; - ni = *n - 1; + mi = *m; + ni = *n - 1; } if (upper) { /* Q was determined by a call to ZHETRD with UPLO = 'U' */ - i__2 = nq - 1; - zunmql_(side, trans, &mi, &ni, &i__2, &a[(a_dim1 << 1) + 1], lda, & - tau[1], &c__[c_offset], ldc, &work[1], lwork, &iinfo, (ftnlen) - 1, (ftnlen)1); + i__2 = nq - 1; + zunmql_(side, trans, &mi, &ni, &i__2, &a[(a_dim1 << 1) + 1], lda, & + tau[1], &c__[c_offset], ldc, &work[1], lwork, &iinfo, (ftnlen) + 1, (ftnlen)1); } else { /* Q was determined by a call to ZHETRD with UPLO = 'L' */ - if (left) { - i1 = 2; - i2 = 1; - } else { - i1 = 1; - i2 = 2; - } - i__2 = nq - 1; - zunmqr_(side, trans, &mi, &ni, &i__2, &a[a_dim1 + 2], lda, &tau[1], & - c__[i1 + i2 * c_dim1], ldc, &work[1], lwork, &iinfo, (ftnlen) - 1, (ftnlen)1); + if (left) { + i1 = 2; + i2 = 1; + } else { + i1 = 1; + i2 = 2; + } + i__2 = nq - 1; + zunmqr_(side, trans, &mi, &ni, &i__2, &a[a_dim1 + 2], lda, &tau[1], & + c__[i1 + i2 * c_dim1], ldc, &work[1], lwork, &iinfo, (ftnlen) + 1, (ftnlen)1); } work[1].r = (doublereal) lwkopt, work[1].i = 0.; return 0; @@ -393,5 +393,5 @@ f"> */ } /* zunmtr_ */ #ifdef __cplusplus - } + } #endif From f157ba2389790097e6fd85b1e78e2e1d4086edaa Mon Sep 17 00:00:00 2001 From: Axel Kohlmeyer Date: Wed, 28 Dec 2022 15:31:49 -0500 Subject: [PATCH 29/47] add some f2c runtime functions, remove exception, avoid name conflict with libgfortran --- lib/linalg/convert.sh | 20 ++- lib/linalg/d_lmp_cnjg.cpp | 13 ++ lib/linalg/d_lmp_imag.cpp | 10 ++ lib/linalg/d_lmp_lg10.cpp | 14 ++ lib/linalg/d_lmp_sign.cpp | 12 ++ lib/linalg/dbdsqr.cpp | 8 +- lib/linalg/dcabs1.cpp | 4 +- lib/linalg/dgesvd.cpp | 6 +- lib/linalg/dlabad.cpp | 4 +- lib/linalg/dlacn2.cpp | 8 +- lib/linalg/dlaed0.cpp | 6 +- lib/linalg/dlaed3.cpp | 4 +- lib/linalg/dlaed6.cpp | 4 +- lib/linalg/dlaed7.cpp | 6 +- lib/linalg/dlaed9.cpp | 4 +- lib/linalg/dlaeda.cpp | 10 +- lib/linalg/dlalsa.cpp | 8 +- lib/linalg/dlalsd.cpp | 4 +- lib/linalg/dlamc3.cpp | 68 +++++++++ lib/linalg/dlarfg.cpp | 6 +- lib/linalg/dlartg.cpp | 4 +- lib/linalg/dlasd8.cpp | 4 +- lib/linalg/dlasda.cpp | 6 +- lib/linalg/dlasv2.cpp | 18 +-- lib/linalg/dormbr.cpp | 10 +- lib/linalg/dormlq.cpp | 6 +- lib/linalg/dormql.cpp | 6 +- lib/linalg/dormqr.cpp | 6 +- lib/linalg/dormtr.cpp | 10 +- lib/linalg/dstedc.cpp | 6 +- lib/linalg/dsteqr.cpp | 6 +- lib/linalg/dsterf.cpp | 6 +- lib/linalg/dtrtri.cpp | 4 +- lib/linalg/dznrm2.cpp | 6 +- lib/linalg/i_lmp_dnnt.cpp | 12 ++ lib/linalg/i_lmp_len.cpp | 10 ++ lib/linalg/i_lmp_nint.cpp | 13 ++ lib/linalg/ilaenv.cpp | 250 +++++++++++++++---------------- lib/linalg/iparmq.cpp | 18 +-- lib/linalg/pow_lmp_dd.cpp | 12 ++ lib/linalg/pow_lmp_di.cpp | 31 ++++ lib/linalg/pow_lmp_ii.cpp | 29 ++++ lib/linalg/s_lmp_cat.cpp | 23 +++ lib/linalg/s_lmp_cmp.cpp | 45 ++++++ lib/linalg/s_lmp_copy.cpp | 26 ++++ lib/linalg/static/.clang-format | 23 +++ lib/linalg/static/README | 9 +- lib/linalg/static/d_lmp_cnjg.cpp | 13 ++ lib/linalg/static/d_lmp_imag.cpp | 10 ++ lib/linalg/static/d_lmp_lg10.cpp | 14 ++ lib/linalg/static/d_lmp_sign.cpp | 12 ++ lib/linalg/static/dlamc3.f | 45 ++++++ lib/linalg/static/i_lmp_dnnt.cpp | 12 ++ lib/linalg/static/i_lmp_len.cpp | 10 ++ lib/linalg/static/i_lmp_nint.cpp | 13 ++ lib/linalg/static/pow_lmp_dd.cpp | 12 ++ lib/linalg/static/pow_lmp_di.cpp | 31 ++++ lib/linalg/static/pow_lmp_ii.cpp | 29 ++++ lib/linalg/static/s_lmp_cat.cpp | 23 +++ lib/linalg/static/s_lmp_cmp.cpp | 45 ++++++ lib/linalg/static/s_lmp_copy.cpp | 26 ++++ lib/linalg/static/xerbla.cpp | 47 +++--- lib/linalg/static/z_lmp_abs.cpp | 31 ++++ lib/linalg/static/z_lmp_div.cpp | 31 ++++ lib/linalg/whitespace.conf | 13 ++ lib/linalg/xerbla.cpp | 47 +++--- lib/linalg/z_lmp_abs.cpp | 31 ++++ lib/linalg/z_lmp_div.cpp | 31 ++++ lib/linalg/zdotc.cpp | 6 +- lib/linalg/zdscal.cpp | 6 +- lib/linalg/zgemm.cpp | 14 +- lib/linalg/zgemv.cpp | 6 +- lib/linalg/zgerc.cpp | 6 +- lib/linalg/zhemv.cpp | 10 +- lib/linalg/zher2.cpp | 18 +-- lib/linalg/zher2k.cpp | 34 ++--- lib/linalg/zhpr.cpp | 10 +- lib/linalg/zlacgv.cpp | 6 +- lib/linalg/zlacrm.cpp | 4 +- lib/linalg/zladiv.cpp | 6 +- lib/linalg/zlaed0.cpp | 6 +- lib/linalg/zlaed7.cpp | 6 +- lib/linalg/zlanhe.cpp | 10 +- lib/linalg/zlarfb.cpp | 10 +- lib/linalg/zlarfg.cpp | 8 +- lib/linalg/zlarft.cpp | 6 +- lib/linalg/zlassq.cpp | 4 +- lib/linalg/zstedc.cpp | 6 +- lib/linalg/zsteqr.cpp | 6 +- lib/linalg/ztpmv.cpp | 18 +-- lib/linalg/ztpsv.cpp | 42 +++--- lib/linalg/ztptri.cpp | 6 +- lib/linalg/ztrmm.cpp | 18 +-- lib/linalg/ztrmv.cpp | 18 +-- lib/linalg/zungl2.cpp | 6 +- lib/linalg/zunm2l.cpp | 4 +- lib/linalg/zunm2r.cpp | 4 +- lib/linalg/zunmql.cpp | 6 +- lib/linalg/zunmqr.cpp | 6 +- lib/linalg/zunmtr.cpp | 10 +- 100 files changed, 1233 insertions(+), 437 deletions(-) create mode 100644 lib/linalg/d_lmp_cnjg.cpp create mode 100644 lib/linalg/d_lmp_imag.cpp create mode 100644 lib/linalg/d_lmp_lg10.cpp create mode 100644 lib/linalg/d_lmp_sign.cpp create mode 100644 lib/linalg/dlamc3.cpp create mode 100644 lib/linalg/i_lmp_dnnt.cpp create mode 100644 lib/linalg/i_lmp_len.cpp create mode 100644 lib/linalg/i_lmp_nint.cpp create mode 100644 lib/linalg/pow_lmp_dd.cpp create mode 100644 lib/linalg/pow_lmp_di.cpp create mode 100644 lib/linalg/pow_lmp_ii.cpp create mode 100644 lib/linalg/s_lmp_cat.cpp create mode 100644 lib/linalg/s_lmp_cmp.cpp create mode 100644 lib/linalg/s_lmp_copy.cpp create mode 100644 lib/linalg/static/.clang-format create mode 100644 lib/linalg/static/d_lmp_cnjg.cpp create mode 100644 lib/linalg/static/d_lmp_imag.cpp create mode 100644 lib/linalg/static/d_lmp_lg10.cpp create mode 100644 lib/linalg/static/d_lmp_sign.cpp create mode 100644 lib/linalg/static/dlamc3.f create mode 100644 lib/linalg/static/i_lmp_dnnt.cpp create mode 100644 lib/linalg/static/i_lmp_len.cpp create mode 100644 lib/linalg/static/i_lmp_nint.cpp create mode 100644 lib/linalg/static/pow_lmp_dd.cpp create mode 100644 lib/linalg/static/pow_lmp_di.cpp create mode 100644 lib/linalg/static/pow_lmp_ii.cpp create mode 100644 lib/linalg/static/s_lmp_cat.cpp create mode 100644 lib/linalg/static/s_lmp_cmp.cpp create mode 100644 lib/linalg/static/s_lmp_copy.cpp create mode 100644 lib/linalg/static/z_lmp_abs.cpp create mode 100644 lib/linalg/static/z_lmp_div.cpp create mode 100644 lib/linalg/whitespace.conf create mode 100644 lib/linalg/z_lmp_abs.cpp create mode 100644 lib/linalg/z_lmp_div.cpp diff --git a/lib/linalg/convert.sh b/lib/linalg/convert.sh index c73e0d3393..0b2cdec0f2 100755 --- a/lib/linalg/convert.sh +++ b/lib/linalg/convert.sh @@ -10,20 +10,28 @@ fi # cleanup rm -f *.c *.cpp *.P *~ *.orig *.bak *.rej -# translate files directly, skip those for which we have replacements. +# translate original files directly for f in fortran/*.f do \ b=$(basename $f .f) + # skip files for which we have replacements if test $b == dgetrf2 || test $b == disnan || test $b == dlaisnan || \ test $b == dlamch || test $b == dlarft || test $b == dpotrf2 || \ test $b == lsame || test $b == xerbla || test $b == zlarft then echo Skipping $b else + # convert to C++ with f2c. Make local variables dynamic. f2c -C++ -a -f $f && mv $b.c $b.cpp || exit 2 # silence c++ compiler warnings about string constants sed -i -e 's/\("[^"]\+"\)/(char *)\1/g' -e 's/^extern.*"C"/extern "C"/' \ -e 's/^#include.*"f2c.h"/#include "lmp_f2c.h"/' $b.cpp + # replace libf2c functions with local versions under a different name + sed -i -e 's/s_\(cat\|cmp\|copy\)(/s_lmp_\1(/g' \ + -e 's/d_\(sign\|cnjg\|imag\|lg10\)(/d_lmp_\1(/g' \ + -e 's/z_\(abs\|div\)(/z_lmp_\1(/g' \ + -e 's/i_\(len\|nint\|dnnt\)(/i_lmp_\1(/g' \ + -e 's/pow_\(dd\|di\|ii\)(/pow_lmp_\1(/g' $b.cpp fi done @@ -31,10 +39,17 @@ done for f in static/*.f do \ b=$(basename $f .f) + # convert to C++ with f2c. Make local variables dynamic. f2c -C++ -a -f $f && mv $b.c $b.cpp || exit 2 # silence c++ compiler warnings about string constants sed -i -e 's/\("[^"]\+"\)/(char *)\1/g' -e 's/^extern.*"C"/extern "C"/' \ -e 's/^#include.*"f2c.h"/#include "lmp_f2c.h"/' $b.cpp + # replace libf2c functions with local versions under a different name + sed -i -e 's/s_\(cat\|cmp\|copy\)(/s_lmp_\1(/g' \ + -e 's/d_\(sign\|cnjg\|imag\|lg10\)(/d_lmp_\1(/g' \ + -e 's/z_\(abs\|div\)(/z_lmp_\1(/g' \ + -e 's/i_\(len\|nint\|dnnt\)(/i_lmp_\1(/g' \ + -e 's/pow_\(dd\|di\|ii\)(/pow_lmp_\1(/g' $b.cpp done # copy direct C++ alternatives @@ -42,3 +57,6 @@ for c in static/*.cpp do \ cp -v $c . done + +# fix whitespace +python ../../tools/coding_standard/whitespace.py -c whitespace.conf -f . diff --git a/lib/linalg/d_lmp_cnjg.cpp b/lib/linalg/d_lmp_cnjg.cpp new file mode 100644 index 0000000000..03ca8f98fd --- /dev/null +++ b/lib/linalg/d_lmp_cnjg.cpp @@ -0,0 +1,13 @@ + +#include "lmp_f2c.h" + +extern "C" { + +void d_lmp_cnjg(doublecomplex *r, doublecomplex *z) +{ + doublereal zi = z->i; + + r->r = z->r; + r->i = -zi; +} +} diff --git a/lib/linalg/d_lmp_imag.cpp b/lib/linalg/d_lmp_imag.cpp new file mode 100644 index 0000000000..f0443f7828 --- /dev/null +++ b/lib/linalg/d_lmp_imag.cpp @@ -0,0 +1,10 @@ + +#include "lmp_f2c.h" + +extern "C" { + +double d_lmp_imag(doublecomplex *z) +{ + return (z->i); +} +} diff --git a/lib/linalg/d_lmp_lg10.cpp b/lib/linalg/d_lmp_lg10.cpp new file mode 100644 index 0000000000..ec48c99839 --- /dev/null +++ b/lib/linalg/d_lmp_lg10.cpp @@ -0,0 +1,14 @@ + +#include "lmp_f2c.h" +#undef abs + +static constexpr double log10e = 0.43429448190325182765; + +#include + +extern "C" { +double d_lmp_lg10(doublereal *x) +{ + return (log10e * log(*x)); +} +} diff --git a/lib/linalg/d_lmp_sign.cpp b/lib/linalg/d_lmp_sign.cpp new file mode 100644 index 0000000000..fb0a1e79ff --- /dev/null +++ b/lib/linalg/d_lmp_sign.cpp @@ -0,0 +1,12 @@ + +#include "lmp_f2c.h" + +extern "C" { + +double d_lmp_sign(doublereal *a, doublereal *b) +{ + double x; + x = (*a >= 0 ? *a : -*a); + return (*b >= 0 ? x : -x); +} +} diff --git a/lib/linalg/dbdsqr.cpp b/lib/linalg/dbdsqr.cpp index 5f5c1b1d6f..e8fef63745 100644 --- a/lib/linalg/dbdsqr.cpp +++ b/lib/linalg/dbdsqr.cpp @@ -274,7 +274,7 @@ f"> */ doublereal d__1, d__2, d__3, d__4; /* Builtin functions */ - double pow_dd(doublereal *, doublereal *), sqrt(doublereal), d_sign( + double pow_lmp_dd(doublereal *, doublereal *), sqrt(doublereal), d_lmp_sign( doublereal *, doublereal *); /* Local variables */ @@ -454,7 +454,7 @@ f"> */ /* Computing MAX */ /* Computing MIN */ - d__3 = 100., d__4 = pow_dd(&eps, &c_b15); + d__3 = 100., d__4 = pow_lmp_dd(&eps, &c_b15); d__1 = 10., d__2 = min(d__3,d__4); tolmul = max(d__1,d__2); tol = tolmul * eps; @@ -852,7 +852,7 @@ L90: /* Chase bulge from top to bottom */ /* Save cosines and sines for later singular vector updates */ - f = ((d__1 = d__[ll], abs(d__1)) - shift) * (d_sign(&c_b49, &d__[ + f = ((d__1 = d__[ll], abs(d__1)) - shift) * (d_lmp_sign(&c_b49, &d__[ ll]) + shift / d__[ll]); g = e[ll]; i__1 = m - 1; @@ -912,7 +912,7 @@ L90: /* Chase bulge from bottom to top */ /* Save cosines and sines for later singular vector updates */ - f = ((d__1 = d__[m], abs(d__1)) - shift) * (d_sign(&c_b49, &d__[m] + f = ((d__1 = d__[m], abs(d__1)) - shift) * (d_lmp_sign(&c_b49, &d__[m] ) + shift / d__[m]); g = e[m - 1]; i__1 = ll + 1; diff --git a/lib/linalg/dcabs1.cpp b/lib/linalg/dcabs1.cpp index bdaf645a57..54b2b57eab 100644 --- a/lib/linalg/dcabs1.cpp +++ b/lib/linalg/dcabs1.cpp @@ -66,7 +66,7 @@ doublereal dcabs1_(doublecomplex *z__) doublereal ret_val, d__1, d__2; /* Builtin functions */ - double d_imag(doublecomplex *); + double d_lmp_imag(doublecomplex *); /* -- Reference BLAS level1 routine -- */ @@ -80,7 +80,7 @@ doublereal dcabs1_(doublecomplex *z__) /* .. Intrinsic Functions .. */ - ret_val = (d__1 = z__->r, abs(d__1)) + (d__2 = d_imag(z__), abs(d__2)); + ret_val = (d__1 = z__->r, abs(d__1)) + (d__2 = d_lmp_imag(z__), abs(d__2)); return ret_val; /* End of DCABS1 */ diff --git a/lib/linalg/dgesvd.cpp b/lib/linalg/dgesvd.cpp index 6a2e70640f..b5f4f1e8de 100644 --- a/lib/linalg/dgesvd.cpp +++ b/lib/linalg/dgesvd.cpp @@ -248,7 +248,7 @@ f"> */ char ch__1[2]; /* Builtin functions */ - /* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen); + /* Subroutine */ int s_lmp_cat(char *, char **, integer *, integer *, ftnlen); double sqrt(doublereal); /* Local variables */ @@ -391,7 +391,7 @@ f"> */ /* Writing concatenation */ i__1[0] = 1, a__1[0] = jobu; i__1[1] = 1, a__1[1] = jobvt; - s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); + s_lmp_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); mnthr = ilaenv_(&c__6, (char *)"DGESVD", ch__1, m, n, &c__0, &c__0, ( ftnlen)6, (ftnlen)2); bdspac = *n * 5; @@ -650,7 +650,7 @@ f"> */ /* Writing concatenation */ i__1[0] = 1, a__1[0] = jobu; i__1[1] = 1, a__1[1] = jobvt; - s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); + s_lmp_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); mnthr = ilaenv_(&c__6, (char *)"DGESVD", ch__1, m, n, &c__0, &c__0, ( ftnlen)6, (ftnlen)2); bdspac = *m * 5; diff --git a/lib/linalg/dlabad.cpp b/lib/linalg/dlabad.cpp index a753834632..45de813f49 100644 --- a/lib/linalg/dlabad.cpp +++ b/lib/linalg/dlabad.cpp @@ -93,7 +93,7 @@ f"> */ /* Subroutine */ int dlabad_(doublereal *small, doublereal *large) { /* Builtin functions */ - double d_lg10(doublereal *), sqrt(doublereal); + double d_lmp_lg10(doublereal *), sqrt(doublereal); /* -- LAPACK auxiliary routine -- */ @@ -112,7 +112,7 @@ f"> */ /* If it looks like we're on a Cray, take the square root of */ /* SMALL and LARGE to avoid overflow and underflow problems. */ - if (d_lg10(large) > 2e3) { + if (d_lmp_lg10(large) > 2e3) { *small = sqrt(*small); *large = sqrt(*large); } diff --git a/lib/linalg/dlacn2.cpp b/lib/linalg/dlacn2.cpp index 7293447d88..bee9fb7e25 100644 --- a/lib/linalg/dlacn2.cpp +++ b/lib/linalg/dlacn2.cpp @@ -165,7 +165,7 @@ f"> */ doublereal d__1; /* Builtin functions */ - integer i_dnnt(doublereal *); + integer i_lmp_dnnt(doublereal *); /* Local variables */ integer i__; @@ -246,7 +246,7 @@ L20: } else { x[i__] = -1.; } - isgn[i__] = i_dnnt(&x[i__]); + isgn[i__] = i_lmp_dnnt(&x[i__]); /* L30: */ } *kase = 2; @@ -287,7 +287,7 @@ L70: } else { xs = -1.; } - if (i_dnnt(&xs) != isgn[i__]) { + if (i_lmp_dnnt(&xs) != isgn[i__]) { goto L90; } /* L80: */ @@ -308,7 +308,7 @@ L90: } else { x[i__] = -1.; } - isgn[i__] = i_dnnt(&x[i__]); + isgn[i__] = i_lmp_dnnt(&x[i__]); /* L100: */ } *kase = 2; diff --git a/lib/linalg/dlaed0.cpp b/lib/linalg/dlaed0.cpp index 68fee93814..5c40115e77 100644 --- a/lib/linalg/dlaed0.cpp +++ b/lib/linalg/dlaed0.cpp @@ -208,7 +208,7 @@ f"> */ /* Builtin functions */ double log(doublereal); - integer pow_ii(integer *, integer *); + integer pow_lmp_ii(integer *, integer *); /* Local variables */ integer i__, j, k, iq, lgn, msd2, smm1, spm1, spm2; @@ -354,10 +354,10 @@ L10: temp = log((doublereal) (*n)) / log(2.); lgn = (integer) temp; - if (pow_ii(&c__2, &lgn) < *n) { + if (pow_lmp_ii(&c__2, &lgn) < *n) { ++lgn; } - if (pow_ii(&c__2, &lgn) < *n) { + if (pow_lmp_ii(&c__2, &lgn) < *n) { ++lgn; } iprmpt = indxq + *n + 1; diff --git a/lib/linalg/dlaed3.cpp b/lib/linalg/dlaed3.cpp index c1f5e908dc..5c7d2a8596 100644 --- a/lib/linalg/dlaed3.cpp +++ b/lib/linalg/dlaed3.cpp @@ -217,7 +217,7 @@ f"> */ doublereal d__1; /* Builtin functions */ - double sqrt(doublereal), d_sign(doublereal *, doublereal *); + double sqrt(doublereal), d_lmp_sign(doublereal *, doublereal *); /* Local variables */ integer i__, j, n2, n12, ii, n23, iq2; @@ -374,7 +374,7 @@ f"> */ i__1 = *k; for (i__ = 1; i__ <= i__1; ++i__) { d__1 = sqrt(-w[i__]); - w[i__] = d_sign(&d__1, &s[i__]); + w[i__] = d_lmp_sign(&d__1, &s[i__]); /* L70: */ } diff --git a/lib/linalg/dlaed6.cpp b/lib/linalg/dlaed6.cpp index aae975971f..d884bbd67e 100644 --- a/lib/linalg/dlaed6.cpp +++ b/lib/linalg/dlaed6.cpp @@ -165,7 +165,7 @@ f"> */ doublereal d__1, d__2, d__3, d__4; /* Builtin functions */ - double sqrt(doublereal), log(doublereal), pow_di(doublereal *, integer *); + double sqrt(doublereal), log(doublereal), pow_lmp_di(doublereal *, integer *); /* Local variables */ doublereal a, b, c__, f; @@ -281,7 +281,7 @@ f"> */ eps = dlamch_((char *)"Epsilon", (ftnlen)7); base = dlamch_((char *)"Base", (ftnlen)4); i__1 = (integer) (log(dlamch_((char *)"SafMin", (ftnlen)6)) / log(base) / 3.); - small1 = pow_di(&base, &i__1); + small1 = pow_lmp_di(&base, &i__1); sminv1 = 1. / small1; small2 = small1 * small1; sminv2 = sminv1 * sminv1; diff --git a/lib/linalg/dlaed7.cpp b/lib/linalg/dlaed7.cpp index 1751f93559..bc763aa9df 100644 --- a/lib/linalg/dlaed7.cpp +++ b/lib/linalg/dlaed7.cpp @@ -293,7 +293,7 @@ f"> */ integer q_dim1, q_offset, i__1, i__2; /* Builtin functions */ - integer pow_ii(integer *, integer *); + integer pow_lmp_ii(integer *, integer *); /* Local variables */ integer i__, k, n1, n2, is, iw, iz, iq2, ptr, ldq2, indx, curr; @@ -408,11 +408,11 @@ f"> */ /* Form the z-vector which consists of the last row of Q_1 and the */ /* first row of Q_2. */ - ptr = pow_ii(&c__2, tlvls) + 1; + ptr = pow_lmp_ii(&c__2, tlvls) + 1; i__1 = *curlvl - 1; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = *tlvls - i__; - ptr += pow_ii(&c__2, &i__2); + ptr += pow_lmp_ii(&c__2, &i__2); /* L10: */ } curr = ptr + *curpbm; diff --git a/lib/linalg/dlaed9.cpp b/lib/linalg/dlaed9.cpp index d6a4f8bca3..f6f01b7098 100644 --- a/lib/linalg/dlaed9.cpp +++ b/lib/linalg/dlaed9.cpp @@ -186,7 +186,7 @@ f"> */ doublereal d__1; /* Builtin functions */ - double sqrt(doublereal), d_sign(doublereal *, doublereal *); + double sqrt(doublereal), d_lmp_sign(doublereal *, doublereal *); /* Local variables */ integer i__, j; @@ -336,7 +336,7 @@ f"> */ i__1 = *k; for (i__ = 1; i__ <= i__1; ++i__) { d__1 = sqrt(-w[i__]); - w[i__] = d_sign(&d__1, &s[i__ + s_dim1]); + w[i__] = d_lmp_sign(&d__1, &s[i__ + s_dim1]); /* L80: */ } diff --git a/lib/linalg/dlaeda.cpp b/lib/linalg/dlaeda.cpp index 39b4c8810f..81389d8db0 100644 --- a/lib/linalg/dlaeda.cpp +++ b/lib/linalg/dlaeda.cpp @@ -198,7 +198,7 @@ f"> */ integer i__1, i__2, i__3; /* Builtin functions */ - integer pow_ii(integer *, integer *); + integer pow_lmp_ii(integer *, integer *); double sqrt(doublereal); /* Local variables */ @@ -277,7 +277,7 @@ f"> */ /* scheme */ i__1 = *curlvl - 1; - curr = ptr + *curpbm * pow_ii(&c__2, curlvl) + pow_ii(&c__2, &i__1) - 1; + curr = ptr + *curpbm * pow_lmp_ii(&c__2, curlvl) + pow_lmp_ii(&c__2, &i__1) - 1; /* Determine size of these matrices. We add HALF to the value of */ /* the SQRT in case the machine underestimates one of these square */ @@ -304,12 +304,12 @@ f"> */ /* rotations and permutation and then multiplying the center matrices */ /* against the current Z. */ - ptr = pow_ii(&c__2, tlvls) + 1; + ptr = pow_lmp_ii(&c__2, tlvls) + 1; i__1 = *curlvl - 1; for (k = 1; k <= i__1; ++k) { i__2 = *curlvl - k; i__3 = *curlvl - k - 1; - curr = ptr + *curpbm * pow_ii(&c__2, &i__2) + pow_ii(&c__2, &i__3) - + curr = ptr + *curpbm * pow_lmp_ii(&c__2, &i__2) + pow_lmp_ii(&c__2, &i__3) - 1; psiz1 = prmptr[curr + 1] - prmptr[curr]; psiz2 = prmptr[curr + 2] - prmptr[curr + 1]; @@ -371,7 +371,7 @@ f"> */ c__1); i__2 = *tlvls - k; - ptr += pow_ii(&c__2, &i__2); + ptr += pow_lmp_ii(&c__2, &i__2); /* L70: */ } diff --git a/lib/linalg/dlalsa.cpp b/lib/linalg/dlalsa.cpp index e68dabd8dd..a428ee8c3d 100644 --- a/lib/linalg/dlalsa.cpp +++ b/lib/linalg/dlalsa.cpp @@ -302,7 +302,7 @@ f"> */ i__2; /* Builtin functions */ - integer pow_ii(integer *, integer *); + integer pow_lmp_ii(integer *, integer *); /* Local variables */ integer i__, j, i1, ic, lf, nd, ll, nl, nr, im1, nlf, nrf, lvl, ndb1, @@ -469,7 +469,7 @@ f"> */ /* Finally go through the left singular vector matrices of all */ /* the other subproblems bottom-up on the tree. */ - j = pow_ii(&c__2, &nlvl); + j = pow_lmp_ii(&c__2, &nlvl); sqre = 0; for (lvl = nlvl; lvl >= 1; --lvl) { @@ -483,7 +483,7 @@ f"> */ ll = 1; } else { i__1 = lvl - 1; - lf = pow_ii(&c__2, &i__1); + lf = pow_lmp_ii(&c__2, &i__1); ll = (lf << 1) - 1; } i__1 = ll; @@ -528,7 +528,7 @@ L50: ll = 1; } else { i__2 = lvl - 1; - lf = pow_ii(&c__2, &i__2); + lf = pow_lmp_ii(&c__2, &i__2); ll = (lf << 1) - 1; } i__2 = lf; diff --git a/lib/linalg/dlalsd.cpp b/lib/linalg/dlalsd.cpp index a141fa6992..f3678a1bfd 100644 --- a/lib/linalg/dlalsd.cpp +++ b/lib/linalg/dlalsd.cpp @@ -211,7 +211,7 @@ f"> */ doublereal d__1; /* Builtin functions */ - double log(doublereal), d_sign(doublereal *, doublereal *); + double log(doublereal), d_lmp_sign(doublereal *, doublereal *); /* Local variables */ integer c__, i__, j, k; @@ -470,7 +470,7 @@ f"> */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { if ((d__1 = d__[i__], abs(d__1)) < eps) { - d__[i__] = d_sign(&eps, &d__[i__]); + d__[i__] = d_lmp_sign(&eps, &d__[i__]); } /* L50: */ } diff --git a/lib/linalg/dlamc3.cpp b/lib/linalg/dlamc3.cpp new file mode 100644 index 0000000000..a7dbd89bc0 --- /dev/null +++ b/lib/linalg/dlamc3.cpp @@ -0,0 +1,68 @@ +/* static/dlamc3.f -- translated by f2c (version 20200916). + You must link the resulting object file with libf2c: + on Microsoft Windows system, link with libf2c.lib; + on Linux or Unix systems, link with .../path/to/libf2c.a -lm + or, if you install libf2c.a in a standard place, with -lf2c -lm + -- in that order, at the end of the command line, as in + cc *.o -lf2c -lm + Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., + + http://www.netlib.org/f2c/libf2c.zip +*/ + +#ifdef __cplusplus +extern "C" { +#endif +#include "lmp_f2c.h" + +/* > \brief \b DLAMC3 */ +/* > \details */ +/* > \b Purpose: */ +/* > \verbatim */ +/* > DLAMC3 is intended to force A and B to be stored prior to doing */ +/* > the addition of A and B , for use in situations where optimizers */ +/* > might hold one of these in a register. */ +/* > \endverbatim */ +/* > \author LAPACK is a software package provided by Univ. of Tennessee, Univ. of California Berkeley, Univ. +of Colorado Denver and NAG Ltd.. */ +/* > \date December 2016 */ +/* > \ingroup auxOTHERauxiliary */ +/* > */ +/* > \param[in] A */ +/* > \verbatim */ +/* > A is a DOUBLE PRECISION */ +/* > \endverbatim */ +/* > */ +/* > \param[in] B */ +/* > \verbatim */ +/* > B is a DOUBLE PRECISION */ +/* > The values A and B. */ +/* > \endverbatim */ +/* > */ +doublereal dlamc3_(doublereal *a, doublereal *b) +{ + /* System generated locals */ + doublereal ret_val; + + +/* -- LAPACK auxiliary routine (version 3.7.0) -- */ +/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ +/* November 2010 */ + +/* .. Scalar Arguments .. */ +/* .. */ +/* ===================================================================== */ + +/* .. Executable Statements .. */ + + ret_val = *a + *b; + + return ret_val; + +/* End of DLAMC3 */ + +} /* dlamc3_ */ + +#ifdef __cplusplus + } +#endif diff --git a/lib/linalg/dlarfg.cpp b/lib/linalg/dlarfg.cpp index 6693e1edb6..546db1171e 100644 --- a/lib/linalg/dlarfg.cpp +++ b/lib/linalg/dlarfg.cpp @@ -130,7 +130,7 @@ f"> */ doublereal d__1; /* Builtin functions */ - double d_sign(doublereal *, doublereal *); + double d_lmp_sign(doublereal *, doublereal *); /* Local variables */ integer j, knt; @@ -189,7 +189,7 @@ f"> */ /* general case */ d__1 = dlapy2_(alpha, &xnorm); - beta = -d_sign(&d__1, alpha); + beta = -d_lmp_sign(&d__1, alpha); safmin = dlamch_((char *)"S", (ftnlen)1) / dlamch_((char *)"E", (ftnlen)1); knt = 0; if (abs(beta) < safmin) { @@ -212,7 +212,7 @@ L10: i__1 = *n - 1; xnorm = dnrm2_(&i__1, &x[1], incx); d__1 = dlapy2_(alpha, &xnorm); - beta = -d_sign(&d__1, alpha); + beta = -d_lmp_sign(&d__1, alpha); } *tau = (beta - *alpha) / beta; i__1 = *n - 1; diff --git a/lib/linalg/dlartg.cpp b/lib/linalg/dlartg.cpp index 3f5832318e..c18a8c6d43 100644 --- a/lib/linalg/dlartg.cpp +++ b/lib/linalg/dlartg.cpp @@ -123,7 +123,7 @@ f"> */ doublereal d__1, d__2; /* Builtin functions */ - double log(doublereal), pow_di(doublereal *, integer *), sqrt(doublereal); + double log(doublereal), pow_lmp_di(doublereal *, integer *), sqrt(doublereal); /* Local variables */ integer i__; @@ -166,7 +166,7 @@ f"> */ eps = dlamch_((char *)"E", (ftnlen)1); d__1 = dlamch_((char *)"B", (ftnlen)1); i__1 = (integer) (log(safmin / eps) / log(dlamch_((char *)"B", (ftnlen)1)) / 2.); - safmn2 = pow_di(&d__1, &i__1); + safmn2 = pow_lmp_di(&d__1, &i__1); safmx2 = 1. / safmn2; /* FIRST = .FALSE. */ /* END IF */ diff --git a/lib/linalg/dlasd8.cpp b/lib/linalg/dlasd8.cpp index 3ec481bb55..5d0890e27b 100644 --- a/lib/linalg/dlasd8.cpp +++ b/lib/linalg/dlasd8.cpp @@ -198,7 +198,7 @@ f"> */ doublereal d__1, d__2; /* Builtin functions */ - double sqrt(doublereal), d_sign(doublereal *, doublereal *); + double sqrt(doublereal), d_lmp_sign(doublereal *, doublereal *); /* Local variables */ integer i__, j; @@ -368,7 +368,7 @@ f"> */ i__1 = *k; for (i__ = 1; i__ <= i__1; ++i__) { d__2 = sqrt((d__1 = work[iwk3i + i__], abs(d__1))); - z__[i__] = d_sign(&d__2, &z__[i__]); + z__[i__] = d_lmp_sign(&d__2, &z__[i__]); /* L50: */ } diff --git a/lib/linalg/dlasda.cpp b/lib/linalg/dlasda.cpp index d064a9af51..b50a48f625 100644 --- a/lib/linalg/dlasda.cpp +++ b/lib/linalg/dlasda.cpp @@ -310,7 +310,7 @@ f"> */ z_dim1, z_offset, i__1, i__2; /* Builtin functions */ - integer pow_ii(integer *, integer *); + integer pow_lmp_ii(integer *, integer *); /* Local variables */ integer i__, j, m, i1, ic, lf, nd, ll, nl, vf, nr, vl, im1, ncc, nlf, nrf, @@ -553,7 +553,7 @@ f"> */ /* Now conquer each subproblem bottom-up. */ - j = pow_ii(&c__2, &nlvl); + j = pow_lmp_ii(&c__2, &nlvl); for (lvl = nlvl; lvl >= 1; --lvl) { lvl2 = (lvl << 1) - 1; @@ -565,7 +565,7 @@ f"> */ ll = 1; } else { i__1 = lvl - 1; - lf = pow_ii(&c__2, &i__1); + lf = pow_lmp_ii(&c__2, &i__1); ll = (lf << 1) - 1; } i__1 = ll; diff --git a/lib/linalg/dlasv2.cpp b/lib/linalg/dlasv2.cpp index 7bab630b39..7dde3369fc 100644 --- a/lib/linalg/dlasv2.cpp +++ b/lib/linalg/dlasv2.cpp @@ -167,7 +167,7 @@ f"> */ doublereal d__1; /* Builtin functions */ - double sqrt(doublereal), d_sign(doublereal *, doublereal *); + double sqrt(doublereal), d_lmp_sign(doublereal *, doublereal *); /* Local variables */ doublereal a, d__, l, m, r__, s, t, fa, ga, ha, ft, gt, ht, mm, tt, clt, @@ -305,9 +305,9 @@ f"> */ /* Note that M is very tiny */ if (l == 0.) { - t = d_sign(&c_b3, &ft) * d_sign(&c_b4, >); + t = d_lmp_sign(&c_b3, &ft) * d_lmp_sign(&c_b4, >); } else { - t = gt / d_sign(&d__, &ft) + m / t; + t = gt / d_lmp_sign(&d__, &ft) + m / t; } } else { t = (m / (s + t) + m / (r__ + l)) * (a + 1.); @@ -334,17 +334,17 @@ f"> */ /* Correct signs of SSMAX and SSMIN */ if (pmax == 1) { - tsign = d_sign(&c_b4, csr) * d_sign(&c_b4, csl) * d_sign(&c_b4, f); + tsign = d_lmp_sign(&c_b4, csr) * d_lmp_sign(&c_b4, csl) * d_lmp_sign(&c_b4, f); } if (pmax == 2) { - tsign = d_sign(&c_b4, snr) * d_sign(&c_b4, csl) * d_sign(&c_b4, g); + tsign = d_lmp_sign(&c_b4, snr) * d_lmp_sign(&c_b4, csl) * d_lmp_sign(&c_b4, g); } if (pmax == 3) { - tsign = d_sign(&c_b4, snr) * d_sign(&c_b4, snl) * d_sign(&c_b4, h__); + tsign = d_lmp_sign(&c_b4, snr) * d_lmp_sign(&c_b4, snl) * d_lmp_sign(&c_b4, h__); } - *ssmax = d_sign(ssmax, &tsign); - d__1 = tsign * d_sign(&c_b4, f) * d_sign(&c_b4, h__); - *ssmin = d_sign(ssmin, &d__1); + *ssmax = d_lmp_sign(ssmax, &tsign); + d__1 = tsign * d_lmp_sign(&c_b4, f) * d_lmp_sign(&c_b4, h__); + *ssmin = d_lmp_sign(ssmin, &d__1); return 0; /* End of DLASV2 */ diff --git a/lib/linalg/dormbr.cpp b/lib/linalg/dormbr.cpp index 69283d95ef..8d6bdd60b0 100644 --- a/lib/linalg/dormbr.cpp +++ b/lib/linalg/dormbr.cpp @@ -227,7 +227,7 @@ f"> */ char ch__1[2]; /* Builtin functions */ - /* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen); + /* Subroutine */ int s_lmp_cat(char *, char **, integer *, integer *, ftnlen); /* Local variables */ integer i1, i2, nb, mi, ni, nq, nw; @@ -329,7 +329,7 @@ f"> */ /* Writing concatenation */ i__3[0] = 1, a__1[0] = side; i__3[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + s_lmp_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); i__1 = *m - 1; i__2 = *m - 1; nb = ilaenv_(&c__1, (char *)"DORMQR", ch__1, &i__1, n, &i__2, &c_n1, ( @@ -338,7 +338,7 @@ f"> */ /* Writing concatenation */ i__3[0] = 1, a__1[0] = side; i__3[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + s_lmp_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); i__1 = *n - 1; i__2 = *n - 1; nb = ilaenv_(&c__1, (char *)"DORMQR", ch__1, m, &i__1, &i__2, &c_n1, ( @@ -349,7 +349,7 @@ f"> */ /* Writing concatenation */ i__3[0] = 1, a__1[0] = side; i__3[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + s_lmp_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); i__1 = *m - 1; i__2 = *m - 1; nb = ilaenv_(&c__1, (char *)"DORMLQ", ch__1, &i__1, n, &i__2, &c_n1, ( @@ -358,7 +358,7 @@ f"> */ /* Writing concatenation */ i__3[0] = 1, a__1[0] = side; i__3[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + s_lmp_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); i__1 = *n - 1; i__2 = *n - 1; nb = ilaenv_(&c__1, (char *)"DORMLQ", ch__1, m, &i__1, &i__2, &c_n1, ( diff --git a/lib/linalg/dormlq.cpp b/lib/linalg/dormlq.cpp index bb14bbfc98..79106afb5c 100644 --- a/lib/linalg/dormlq.cpp +++ b/lib/linalg/dormlq.cpp @@ -201,7 +201,7 @@ f"> */ char ch__1[2]; /* Builtin functions */ - /* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen); + /* Subroutine */ int s_lmp_cat(char *, char **, integer *, integer *, ftnlen); /* Local variables */ integer i__, i1, i2, i3, ib, ic, jc, nb, mi, ni, nq, nw, iwt; @@ -302,7 +302,7 @@ f"> */ /* Writing concatenation */ i__3[0] = 1, a__1[0] = side; i__3[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + s_lmp_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); i__1 = 64, i__2 = ilaenv_(&c__1, (char *)"DORMLQ", ch__1, m, n, k, &c_n1, ( ftnlen)6, (ftnlen)2); nb = min(i__1,i__2); @@ -334,7 +334,7 @@ f"> */ /* Writing concatenation */ i__3[0] = 1, a__1[0] = side; i__3[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + s_lmp_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DORMLQ", ch__1, m, n, k, &c_n1, ( ftnlen)6, (ftnlen)2); nbmin = max(i__1,i__2); diff --git a/lib/linalg/dormql.cpp b/lib/linalg/dormql.cpp index 70694ed5f9..eea324bc69 100644 --- a/lib/linalg/dormql.cpp +++ b/lib/linalg/dormql.cpp @@ -201,7 +201,7 @@ f"> */ char ch__1[2]; /* Builtin functions */ - /* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen); + /* Subroutine */ int s_lmp_cat(char *, char **, integer *, integer *, ftnlen); /* Local variables */ integer i__, i1, i2, i3, ib, nb, mi, ni, nq, nw, iwt; @@ -303,7 +303,7 @@ f"> */ /* Writing concatenation */ i__3[0] = 1, a__1[0] = side; i__3[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + s_lmp_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); i__1 = 64, i__2 = ilaenv_(&c__1, (char *)"DORMQL", ch__1, m, n, k, &c_n1, (ftnlen)6, (ftnlen)2); nb = min(i__1,i__2); @@ -335,7 +335,7 @@ f"> */ /* Writing concatenation */ i__3[0] = 1, a__1[0] = side; i__3[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + s_lmp_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DORMQL", ch__1, m, n, k, &c_n1, ( ftnlen)6, (ftnlen)2); nbmin = max(i__1,i__2); diff --git a/lib/linalg/dormqr.cpp b/lib/linalg/dormqr.cpp index 17aaab62ba..eb43ba8045 100644 --- a/lib/linalg/dormqr.cpp +++ b/lib/linalg/dormqr.cpp @@ -201,7 +201,7 @@ f"> */ char ch__1[2]; /* Builtin functions */ - /* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen); + /* Subroutine */ int s_lmp_cat(char *, char **, integer *, integer *, ftnlen); /* Local variables */ integer i__, i1, i2, i3, ib, ic, jc, nb, mi, ni, nq, nw, iwt; @@ -300,7 +300,7 @@ f"> */ /* Writing concatenation */ i__3[0] = 1, a__1[0] = side; i__3[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + s_lmp_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); i__1 = 64, i__2 = ilaenv_(&c__1, (char *)"DORMQR", ch__1, m, n, k, &c_n1, ( ftnlen)6, (ftnlen)2); nb = min(i__1,i__2); @@ -332,7 +332,7 @@ f"> */ /* Writing concatenation */ i__3[0] = 1, a__1[0] = side; i__3[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + s_lmp_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DORMQR", ch__1, m, n, k, &c_n1, ( ftnlen)6, (ftnlen)2); nbmin = max(i__1,i__2); diff --git a/lib/linalg/dormtr.cpp b/lib/linalg/dormtr.cpp index a55ee5efbe..0f0cdac3db 100644 --- a/lib/linalg/dormtr.cpp +++ b/lib/linalg/dormtr.cpp @@ -203,7 +203,7 @@ f"> */ char ch__1[2]; /* Builtin functions */ - /* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen); + /* Subroutine */ int s_lmp_cat(char *, char **, integer *, integer *, ftnlen); /* Local variables */ integer i1, i2, nb, mi, ni, nq, nw; @@ -297,7 +297,7 @@ f"> */ /* Writing concatenation */ i__1[0] = 1, a__1[0] = side; i__1[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); + s_lmp_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); i__2 = *m - 1; i__3 = *m - 1; nb = ilaenv_(&c__1, (char *)"DORMQL", ch__1, &i__2, n, &i__3, &c_n1, ( @@ -306,7 +306,7 @@ f"> */ /* Writing concatenation */ i__1[0] = 1, a__1[0] = side; i__1[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); + s_lmp_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); i__2 = *n - 1; i__3 = *n - 1; nb = ilaenv_(&c__1, (char *)"DORMQL", ch__1, m, &i__2, &i__3, &c_n1, ( @@ -317,7 +317,7 @@ f"> */ /* Writing concatenation */ i__1[0] = 1, a__1[0] = side; i__1[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); + s_lmp_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); i__2 = *m - 1; i__3 = *m - 1; nb = ilaenv_(&c__1, (char *)"DORMQR", ch__1, &i__2, n, &i__3, &c_n1, ( @@ -326,7 +326,7 @@ f"> */ /* Writing concatenation */ i__1[0] = 1, a__1[0] = side; i__1[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); + s_lmp_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); i__2 = *n - 1; i__3 = *n - 1; nb = ilaenv_(&c__1, (char *)"DORMQR", ch__1, m, &i__2, &i__3, &c_n1, ( diff --git a/lib/linalg/dstedc.cpp b/lib/linalg/dstedc.cpp index f1b09e0f25..1a55346056 100644 --- a/lib/linalg/dstedc.cpp +++ b/lib/linalg/dstedc.cpp @@ -223,7 +223,7 @@ f"> */ /* Builtin functions */ double log(doublereal); - integer pow_ii(integer *, integer *); + integer pow_lmp_ii(integer *, integer *); double sqrt(doublereal); /* Local variables */ @@ -336,10 +336,10 @@ f"> */ lwmin = *n - 1 << 1; } else { lgn = (integer) (log((doublereal) (*n)) / log(2.)); - if (pow_ii(&c__2, &lgn) < *n) { + if (pow_lmp_ii(&c__2, &lgn) < *n) { ++lgn; } - if (pow_ii(&c__2, &lgn) < *n) { + if (pow_lmp_ii(&c__2, &lgn) < *n) { ++lgn; } if (icompz == 1) { diff --git a/lib/linalg/dsteqr.cpp b/lib/linalg/dsteqr.cpp index 62a13f9d0b..2f590595e7 100644 --- a/lib/linalg/dsteqr.cpp +++ b/lib/linalg/dsteqr.cpp @@ -164,7 +164,7 @@ f"> */ doublereal d__1, d__2; /* Builtin functions */ - double sqrt(doublereal), d_sign(doublereal *, doublereal *); + double sqrt(doublereal), d_lmp_sign(doublereal *, doublereal *); /* Local variables */ doublereal b, c__, f, g; @@ -441,7 +441,7 @@ L60: g = (d__[l + 1] - p) / (e[l] * 2.); r__ = dlapy2_(&g, &c_b10); - g = d__[m] - p + e[l] / (g + d_sign(&r__, &g)); + g = d__[m] - p + e[l] / (g + d_lmp_sign(&r__, &g)); s = 1.; c__ = 1.; @@ -564,7 +564,7 @@ L110: g = (d__[l - 1] - p) / (e[l - 1] * 2.); r__ = dlapy2_(&g, &c_b10); - g = d__[m] - p + e[l - 1] / (g + d_sign(&r__, &g)); + g = d__[m] - p + e[l - 1] / (g + d_lmp_sign(&r__, &g)); s = 1.; c__ = 1.; diff --git a/lib/linalg/dsterf.cpp b/lib/linalg/dsterf.cpp index 981374d32a..687cbf943b 100644 --- a/lib/linalg/dsterf.cpp +++ b/lib/linalg/dsterf.cpp @@ -116,7 +116,7 @@ f"> */ doublereal d__1, d__2, d__3; /* Builtin functions */ - double sqrt(doublereal), d_sign(doublereal *, doublereal *); + double sqrt(doublereal), d_lmp_sign(doublereal *, doublereal *); /* Local variables */ doublereal c__; @@ -342,7 +342,7 @@ L70: rte = sqrt(e[l]); sigma = (d__[l + 1] - p) / (rte * 2.); r__ = dlapy2_(&sigma, &c_b33); - sigma = p - rte / (sigma + d_sign(&r__, &sigma)); + sigma = p - rte / (sigma + d_lmp_sign(&r__, &sigma)); c__ = 1.; s = 0.; @@ -440,7 +440,7 @@ L120: rte = sqrt(e[l - 1]); sigma = (d__[l - 1] - p) / (rte * 2.); r__ = dlapy2_(&sigma, &c_b33); - sigma = p - rte / (sigma + d_sign(&r__, &sigma)); + sigma = p - rte / (sigma + d_lmp_sign(&r__, &sigma)); c__ = 1.; s = 0.; diff --git a/lib/linalg/dtrtri.cpp b/lib/linalg/dtrtri.cpp index a80ece791c..91742619b0 100644 --- a/lib/linalg/dtrtri.cpp +++ b/lib/linalg/dtrtri.cpp @@ -142,7 +142,7 @@ f"> */ char ch__1[2]; /* Builtin functions */ - /* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen); + /* Subroutine */ int s_lmp_cat(char *, char **, integer *, integer *, ftnlen); /* Local variables */ integer j, jb, nb, nn; @@ -235,7 +235,7 @@ f"> */ /* Writing concatenation */ i__2[0] = 1, a__1[0] = uplo; i__2[1] = 1, a__1[1] = diag; - s_cat(ch__1, a__1, i__2, &c__2, (ftnlen)2); + s_lmp_cat(ch__1, a__1, i__2, &c__2, (ftnlen)2); nb = ilaenv_(&c__1, (char *)"DTRTRI", ch__1, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, ( ftnlen)2); if (nb <= 1 || nb >= *n) { diff --git a/lib/linalg/dznrm2.cpp b/lib/linalg/dznrm2.cpp index 7a92e63831..5041b7280e 100644 --- a/lib/linalg/dznrm2.cpp +++ b/lib/linalg/dznrm2.cpp @@ -97,7 +97,7 @@ doublereal dznrm2_(integer *n, doublecomplex *x, integer *incx) doublereal ret_val, d__1; /* Builtin functions */ - double d_imag(doublecomplex *), sqrt(doublereal); + double d_lmp_imag(doublecomplex *), sqrt(doublereal); /* Local variables */ integer ix; @@ -153,8 +153,8 @@ doublereal dznrm2_(integer *n, doublecomplex *x, integer *incx) ssq += d__1 * d__1; } } - if (d_imag(&x[ix]) != 0.) { - temp = (d__1 = d_imag(&x[ix]), abs(d__1)); + if (d_lmp_imag(&x[ix]) != 0.) { + temp = (d__1 = d_lmp_imag(&x[ix]), abs(d__1)); if (scale < temp) { /* Computing 2nd power */ d__1 = scale / temp; diff --git a/lib/linalg/i_lmp_dnnt.cpp b/lib/linalg/i_lmp_dnnt.cpp new file mode 100644 index 0000000000..8050697bb9 --- /dev/null +++ b/lib/linalg/i_lmp_dnnt.cpp @@ -0,0 +1,12 @@ + +#include "lmp_f2c.h" + +#undef abs +#include + +extern "C" { +integer i_lmp_dnnt(doublereal *x) +{ + return (integer)(*x >= 0. ? floor(*x + .5) : -floor(.5 - *x)); +} +} diff --git a/lib/linalg/i_lmp_len.cpp b/lib/linalg/i_lmp_len.cpp new file mode 100644 index 0000000000..b6101b29ad --- /dev/null +++ b/lib/linalg/i_lmp_len.cpp @@ -0,0 +1,10 @@ + +#include "lmp_f2c.h" + +extern "C" { + +integer i_lmp_len(char *s, ftnlen n) +{ + return (n); +} +} diff --git a/lib/linalg/i_lmp_nint.cpp b/lib/linalg/i_lmp_nint.cpp new file mode 100644 index 0000000000..f41ca6b3eb --- /dev/null +++ b/lib/linalg/i_lmp_nint.cpp @@ -0,0 +1,13 @@ + +#include "lmp_f2c.h" +#undef abs + +#include + +extern "C" { + +integer i_lmp_nint(real *x) +{ + return (integer)(*x >= 0 ? floor(*x + .5) : -floor(.5 - *x)); +} +} diff --git a/lib/linalg/ilaenv.cpp b/lib/linalg/ilaenv.cpp index 6c94f00e6f..355b2a9429 100644 --- a/lib/linalg/ilaenv.cpp +++ b/lib/linalg/ilaenv.cpp @@ -193,8 +193,8 @@ integer ilaenv_(integer *ispec, char *name__, char *opts, integer *n1, integer ret_val, i__1, i__2, i__3; /* Builtin functions */ - /* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen); - integer i_len(char *, ftnlen), s_cmp(char *, char *, ftnlen, ftnlen); + /* Subroutine */ int s_lmp_copy(char *, char *, ftnlen, ftnlen); + integer i_lmp_len(char *, ftnlen), s_lmp_cmp(char *, char *, ftnlen, ftnlen); /* Local variables */ logical twostage; @@ -257,7 +257,7 @@ L10: /* Convert NAME to upper case if the first character is lower case. */ ret_val = 1; - s_copy(subnam, name__, (ftnlen)16, name_len); + s_lmp_copy(subnam, name__, (ftnlen)16, name_len); ic = *(unsigned char *)subnam; iz = 'Z'; if (iz == 90 || iz == 122) { @@ -314,10 +314,10 @@ L10: if (! (cname || sname)) { return ret_val; } - s_copy(c2, subnam + 1, (ftnlen)2, (ftnlen)2); - s_copy(c3, subnam + 3, (ftnlen)3, (ftnlen)3); - s_copy(c4, c3 + 1, (ftnlen)2, (ftnlen)2); - twostage = i_len(subnam, (ftnlen)16) >= 11 && *(unsigned char *)&subnam[ + s_lmp_copy(c2, subnam + 1, (ftnlen)2, (ftnlen)2); + s_lmp_copy(c3, subnam + 3, (ftnlen)3, (ftnlen)3); + s_lmp_copy(c4, c3 + 1, (ftnlen)2, (ftnlen)2); + twostage = i_lmp_len(subnam, (ftnlen)16) >= 11 && *(unsigned char *)&subnam[ 10] == '2'; switch (*ispec) { @@ -336,7 +336,7 @@ L50: nb = 1; - if (s_cmp(subnam + 1, (char *)"LAORH", (ftnlen)5, (ftnlen)5) == 0) { + if (s_lmp_cmp(subnam + 1, (char *)"LAORH", (ftnlen)5, (ftnlen)5) == 0) { /* This is for *LAORHR_GETRFNP routine */ @@ -345,23 +345,23 @@ L50: } else { nb = 32; } - } else if (s_cmp(c2, (char *)"GE", (ftnlen)2, (ftnlen)2) == 0) { - if (s_cmp(c3, (char *)"TRF", (ftnlen)3, (ftnlen)3) == 0) { + } else if (s_lmp_cmp(c2, (char *)"GE", (ftnlen)2, (ftnlen)2) == 0) { + if (s_lmp_cmp(c3, (char *)"TRF", (ftnlen)3, (ftnlen)3) == 0) { if (sname) { nb = 64; } else { nb = 64; } - } else if (s_cmp(c3, (char *)"QRF", (ftnlen)3, (ftnlen)3) == 0 || s_cmp(c3, - (char *)"RQF", (ftnlen)3, (ftnlen)3) == 0 || s_cmp(c3, (char *)"LQF", (ftnlen) - 3, (ftnlen)3) == 0 || s_cmp(c3, (char *)"QLF", (ftnlen)3, (ftnlen)3) + } else if (s_lmp_cmp(c3, (char *)"QRF", (ftnlen)3, (ftnlen)3) == 0 || s_lmp_cmp(c3, + (char *)"RQF", (ftnlen)3, (ftnlen)3) == 0 || s_lmp_cmp(c3, (char *)"LQF", (ftnlen) + 3, (ftnlen)3) == 0 || s_lmp_cmp(c3, (char *)"QLF", (ftnlen)3, (ftnlen)3) == 0) { if (sname) { nb = 32; } else { nb = 32; } - } else if (s_cmp(c3, (char *)"QR ", (ftnlen)3, (ftnlen)3) == 0) { + } else if (s_lmp_cmp(c3, (char *)"QR ", (ftnlen)3, (ftnlen)3) == 0) { if (*n3 == 1) { if (sname) { /* M*N */ @@ -384,7 +384,7 @@ L50: nb = 1; } } - } else if (s_cmp(c3, (char *)"LQ ", (ftnlen)3, (ftnlen)3) == 0) { + } else if (s_lmp_cmp(c3, (char *)"LQ ", (ftnlen)3, (ftnlen)3) == 0) { if (*n3 == 2) { if (sname) { /* M*N */ @@ -407,35 +407,35 @@ L50: nb = 1; } } - } else if (s_cmp(c3, (char *)"HRD", (ftnlen)3, (ftnlen)3) == 0) { + } else if (s_lmp_cmp(c3, (char *)"HRD", (ftnlen)3, (ftnlen)3) == 0) { if (sname) { nb = 32; } else { nb = 32; } - } else if (s_cmp(c3, (char *)"BRD", (ftnlen)3, (ftnlen)3) == 0) { + } else if (s_lmp_cmp(c3, (char *)"BRD", (ftnlen)3, (ftnlen)3) == 0) { if (sname) { nb = 32; } else { nb = 32; } - } else if (s_cmp(c3, (char *)"TRI", (ftnlen)3, (ftnlen)3) == 0) { + } else if (s_lmp_cmp(c3, (char *)"TRI", (ftnlen)3, (ftnlen)3) == 0) { if (sname) { nb = 64; } else { nb = 64; } } - } else if (s_cmp(c2, (char *)"PO", (ftnlen)2, (ftnlen)2) == 0) { - if (s_cmp(c3, (char *)"TRF", (ftnlen)3, (ftnlen)3) == 0) { + } else if (s_lmp_cmp(c2, (char *)"PO", (ftnlen)2, (ftnlen)2) == 0) { + if (s_lmp_cmp(c3, (char *)"TRF", (ftnlen)3, (ftnlen)3) == 0) { if (sname) { nb = 64; } else { nb = 64; } } - } else if (s_cmp(c2, (char *)"SY", (ftnlen)2, (ftnlen)2) == 0) { - if (s_cmp(c3, (char *)"TRF", (ftnlen)3, (ftnlen)3) == 0) { + } else if (s_lmp_cmp(c2, (char *)"SY", (ftnlen)2, (ftnlen)2) == 0) { + if (s_lmp_cmp(c3, (char *)"TRF", (ftnlen)3, (ftnlen)3) == 0) { if (sname) { if (twostage) { nb = 192; @@ -449,65 +449,65 @@ L50: nb = 64; } } - } else if (sname && s_cmp(c3, (char *)"TRD", (ftnlen)3, (ftnlen)3) == 0) { + } else if (sname && s_lmp_cmp(c3, (char *)"TRD", (ftnlen)3, (ftnlen)3) == 0) { nb = 32; - } else if (sname && s_cmp(c3, (char *)"GST", (ftnlen)3, (ftnlen)3) == 0) { + } else if (sname && s_lmp_cmp(c3, (char *)"GST", (ftnlen)3, (ftnlen)3) == 0) { nb = 64; } - } else if (cname && s_cmp(c2, (char *)"HE", (ftnlen)2, (ftnlen)2) == 0) { - if (s_cmp(c3, (char *)"TRF", (ftnlen)3, (ftnlen)3) == 0) { + } else if (cname && s_lmp_cmp(c2, (char *)"HE", (ftnlen)2, (ftnlen)2) == 0) { + if (s_lmp_cmp(c3, (char *)"TRF", (ftnlen)3, (ftnlen)3) == 0) { if (twostage) { nb = 192; } else { nb = 64; } - } else if (s_cmp(c3, (char *)"TRD", (ftnlen)3, (ftnlen)3) == 0) { + } else if (s_lmp_cmp(c3, (char *)"TRD", (ftnlen)3, (ftnlen)3) == 0) { nb = 32; - } else if (s_cmp(c3, (char *)"GST", (ftnlen)3, (ftnlen)3) == 0) { + } else if (s_lmp_cmp(c3, (char *)"GST", (ftnlen)3, (ftnlen)3) == 0) { nb = 64; } - } else if (sname && s_cmp(c2, (char *)"OR", (ftnlen)2, (ftnlen)2) == 0) { + } else if (sname && s_lmp_cmp(c2, (char *)"OR", (ftnlen)2, (ftnlen)2) == 0) { if (*(unsigned char *)c3 == 'G') { - if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", - (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( - ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == - 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( - c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( + if (s_lmp_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == + 0 || s_lmp_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp( + c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"BR", ( ftnlen)2, (ftnlen)2) == 0) { nb = 32; } } else if (*(unsigned char *)c3 == 'M') { - if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", - (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( - ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == - 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( - c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( + if (s_lmp_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == + 0 || s_lmp_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp( + c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"BR", ( ftnlen)2, (ftnlen)2) == 0) { nb = 32; } } - } else if (cname && s_cmp(c2, (char *)"UN", (ftnlen)2, (ftnlen)2) == 0) { + } else if (cname && s_lmp_cmp(c2, (char *)"UN", (ftnlen)2, (ftnlen)2) == 0) { if (*(unsigned char *)c3 == 'G') { - if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", - (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( - ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == - 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( - c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( + if (s_lmp_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == + 0 || s_lmp_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp( + c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"BR", ( ftnlen)2, (ftnlen)2) == 0) { nb = 32; } } else if (*(unsigned char *)c3 == 'M') { - if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", - (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( - ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == - 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( - c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( + if (s_lmp_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == + 0 || s_lmp_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp( + c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"BR", ( ftnlen)2, (ftnlen)2) == 0) { nb = 32; } } - } else if (s_cmp(c2, (char *)"GB", (ftnlen)2, (ftnlen)2) == 0) { - if (s_cmp(c3, (char *)"TRF", (ftnlen)3, (ftnlen)3) == 0) { + } else if (s_lmp_cmp(c2, (char *)"GB", (ftnlen)2, (ftnlen)2) == 0) { + if (s_lmp_cmp(c3, (char *)"TRF", (ftnlen)3, (ftnlen)3) == 0) { if (sname) { if (*n4 <= 64) { nb = 1; @@ -522,8 +522,8 @@ L50: } } } - } else if (s_cmp(c2, (char *)"PB", (ftnlen)2, (ftnlen)2) == 0) { - if (s_cmp(c3, (char *)"TRF", (ftnlen)3, (ftnlen)3) == 0) { + } else if (s_lmp_cmp(c2, (char *)"PB", (ftnlen)2, (ftnlen)2) == 0) { + if (s_lmp_cmp(c3, (char *)"TRF", (ftnlen)3, (ftnlen)3) == 0) { if (sname) { if (*n2 <= 64) { nb = 1; @@ -538,20 +538,20 @@ L50: } } } - } else if (s_cmp(c2, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0) { - if (s_cmp(c3, (char *)"TRI", (ftnlen)3, (ftnlen)3) == 0) { + } else if (s_lmp_cmp(c2, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0) { + if (s_lmp_cmp(c3, (char *)"TRI", (ftnlen)3, (ftnlen)3) == 0) { if (sname) { nb = 64; } else { nb = 64; } - } else if (s_cmp(c3, (char *)"EVC", (ftnlen)3, (ftnlen)3) == 0) { + } else if (s_lmp_cmp(c3, (char *)"EVC", (ftnlen)3, (ftnlen)3) == 0) { if (sname) { nb = 64; } else { nb = 64; } - } else if (s_cmp(c3, (char *)"SYL", (ftnlen)3, (ftnlen)3) == 0) { + } else if (s_lmp_cmp(c3, (char *)"SYL", (ftnlen)3, (ftnlen)3) == 0) { /* The upper bound is to prevent overly aggressive scaling. */ if (sname) { /* Computing MIN */ @@ -567,27 +567,27 @@ L50: nb = min(i__1,80); } } - } else if (s_cmp(c2, (char *)"LA", (ftnlen)2, (ftnlen)2) == 0) { - if (s_cmp(c3, (char *)"UUM", (ftnlen)3, (ftnlen)3) == 0) { + } else if (s_lmp_cmp(c2, (char *)"LA", (ftnlen)2, (ftnlen)2) == 0) { + if (s_lmp_cmp(c3, (char *)"UUM", (ftnlen)3, (ftnlen)3) == 0) { if (sname) { nb = 64; } else { nb = 64; } - } else if (s_cmp(c3, (char *)"TRS", (ftnlen)3, (ftnlen)3) == 0) { + } else if (s_lmp_cmp(c3, (char *)"TRS", (ftnlen)3, (ftnlen)3) == 0) { if (sname) { nb = 32; } else { nb = 32; } } - } else if (sname && s_cmp(c2, (char *)"ST", (ftnlen)2, (ftnlen)2) == 0) { - if (s_cmp(c3, (char *)"EBZ", (ftnlen)3, (ftnlen)3) == 0) { + } else if (sname && s_lmp_cmp(c2, (char *)"ST", (ftnlen)2, (ftnlen)2) == 0) { + if (s_lmp_cmp(c3, (char *)"EBZ", (ftnlen)3, (ftnlen)3) == 0) { nb = 1; } - } else if (s_cmp(c2, (char *)"GG", (ftnlen)2, (ftnlen)2) == 0) { + } else if (s_lmp_cmp(c2, (char *)"GG", (ftnlen)2, (ftnlen)2) == 0) { nb = 32; - if (s_cmp(c3, (char *)"HD3", (ftnlen)3, (ftnlen)3) == 0) { + if (s_lmp_cmp(c3, (char *)"HD3", (ftnlen)3, (ftnlen)3) == 0) { if (sname) { nb = 32; } else { @@ -603,92 +603,92 @@ L60: /* ISPEC = 2: minimum block size */ nbmin = 2; - if (s_cmp(c2, (char *)"GE", (ftnlen)2, (ftnlen)2) == 0) { - if (s_cmp(c3, (char *)"QRF", (ftnlen)3, (ftnlen)3) == 0 || s_cmp(c3, (char *)"RQF", ( - ftnlen)3, (ftnlen)3) == 0 || s_cmp(c3, (char *)"LQF", (ftnlen)3, ( - ftnlen)3) == 0 || s_cmp(c3, (char *)"QLF", (ftnlen)3, (ftnlen)3) == 0) + if (s_lmp_cmp(c2, (char *)"GE", (ftnlen)2, (ftnlen)2) == 0) { + if (s_lmp_cmp(c3, (char *)"QRF", (ftnlen)3, (ftnlen)3) == 0 || s_lmp_cmp(c3, (char *)"RQF", ( + ftnlen)3, (ftnlen)3) == 0 || s_lmp_cmp(c3, (char *)"LQF", (ftnlen)3, ( + ftnlen)3) == 0 || s_lmp_cmp(c3, (char *)"QLF", (ftnlen)3, (ftnlen)3) == 0) { if (sname) { nbmin = 2; } else { nbmin = 2; } - } else if (s_cmp(c3, (char *)"HRD", (ftnlen)3, (ftnlen)3) == 0) { + } else if (s_lmp_cmp(c3, (char *)"HRD", (ftnlen)3, (ftnlen)3) == 0) { if (sname) { nbmin = 2; } else { nbmin = 2; } - } else if (s_cmp(c3, (char *)"BRD", (ftnlen)3, (ftnlen)3) == 0) { + } else if (s_lmp_cmp(c3, (char *)"BRD", (ftnlen)3, (ftnlen)3) == 0) { if (sname) { nbmin = 2; } else { nbmin = 2; } - } else if (s_cmp(c3, (char *)"TRI", (ftnlen)3, (ftnlen)3) == 0) { + } else if (s_lmp_cmp(c3, (char *)"TRI", (ftnlen)3, (ftnlen)3) == 0) { if (sname) { nbmin = 2; } else { nbmin = 2; } } - } else if (s_cmp(c2, (char *)"SY", (ftnlen)2, (ftnlen)2) == 0) { - if (s_cmp(c3, (char *)"TRF", (ftnlen)3, (ftnlen)3) == 0) { + } else if (s_lmp_cmp(c2, (char *)"SY", (ftnlen)2, (ftnlen)2) == 0) { + if (s_lmp_cmp(c3, (char *)"TRF", (ftnlen)3, (ftnlen)3) == 0) { if (sname) { nbmin = 8; } else { nbmin = 8; } - } else if (sname && s_cmp(c3, (char *)"TRD", (ftnlen)3, (ftnlen)3) == 0) { + } else if (sname && s_lmp_cmp(c3, (char *)"TRD", (ftnlen)3, (ftnlen)3) == 0) { nbmin = 2; } - } else if (cname && s_cmp(c2, (char *)"HE", (ftnlen)2, (ftnlen)2) == 0) { - if (s_cmp(c3, (char *)"TRD", (ftnlen)3, (ftnlen)3) == 0) { + } else if (cname && s_lmp_cmp(c2, (char *)"HE", (ftnlen)2, (ftnlen)2) == 0) { + if (s_lmp_cmp(c3, (char *)"TRD", (ftnlen)3, (ftnlen)3) == 0) { nbmin = 2; } - } else if (sname && s_cmp(c2, (char *)"OR", (ftnlen)2, (ftnlen)2) == 0) { + } else if (sname && s_lmp_cmp(c2, (char *)"OR", (ftnlen)2, (ftnlen)2) == 0) { if (*(unsigned char *)c3 == 'G') { - if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", - (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( - ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == - 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( - c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( + if (s_lmp_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == + 0 || s_lmp_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp( + c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"BR", ( ftnlen)2, (ftnlen)2) == 0) { nbmin = 2; } } else if (*(unsigned char *)c3 == 'M') { - if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", - (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( - ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == - 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( - c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( + if (s_lmp_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == + 0 || s_lmp_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp( + c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"BR", ( ftnlen)2, (ftnlen)2) == 0) { nbmin = 2; } } - } else if (cname && s_cmp(c2, (char *)"UN", (ftnlen)2, (ftnlen)2) == 0) { + } else if (cname && s_lmp_cmp(c2, (char *)"UN", (ftnlen)2, (ftnlen)2) == 0) { if (*(unsigned char *)c3 == 'G') { - if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", - (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( - ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == - 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( - c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( + if (s_lmp_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == + 0 || s_lmp_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp( + c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"BR", ( ftnlen)2, (ftnlen)2) == 0) { nbmin = 2; } } else if (*(unsigned char *)c3 == 'M') { - if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", - (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( - ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == - 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( - c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( + if (s_lmp_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == + 0 || s_lmp_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp( + c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"BR", ( ftnlen)2, (ftnlen)2) == 0) { nbmin = 2; } } - } else if (s_cmp(c2, (char *)"GG", (ftnlen)2, (ftnlen)2) == 0) { + } else if (s_lmp_cmp(c2, (char *)"GG", (ftnlen)2, (ftnlen)2) == 0) { nbmin = 2; - if (s_cmp(c3, (char *)"HD3", (ftnlen)3, (ftnlen)3) == 0) { + if (s_lmp_cmp(c3, (char *)"HD3", (ftnlen)3, (ftnlen)3) == 0) { nbmin = 2; } } @@ -700,62 +700,62 @@ L70: /* ISPEC = 3: crossover point */ nx = 0; - if (s_cmp(c2, (char *)"GE", (ftnlen)2, (ftnlen)2) == 0) { - if (s_cmp(c3, (char *)"QRF", (ftnlen)3, (ftnlen)3) == 0 || s_cmp(c3, (char *)"RQF", ( - ftnlen)3, (ftnlen)3) == 0 || s_cmp(c3, (char *)"LQF", (ftnlen)3, ( - ftnlen)3) == 0 || s_cmp(c3, (char *)"QLF", (ftnlen)3, (ftnlen)3) == 0) + if (s_lmp_cmp(c2, (char *)"GE", (ftnlen)2, (ftnlen)2) == 0) { + if (s_lmp_cmp(c3, (char *)"QRF", (ftnlen)3, (ftnlen)3) == 0 || s_lmp_cmp(c3, (char *)"RQF", ( + ftnlen)3, (ftnlen)3) == 0 || s_lmp_cmp(c3, (char *)"LQF", (ftnlen)3, ( + ftnlen)3) == 0 || s_lmp_cmp(c3, (char *)"QLF", (ftnlen)3, (ftnlen)3) == 0) { if (sname) { nx = 128; } else { nx = 128; } - } else if (s_cmp(c3, (char *)"HRD", (ftnlen)3, (ftnlen)3) == 0) { + } else if (s_lmp_cmp(c3, (char *)"HRD", (ftnlen)3, (ftnlen)3) == 0) { if (sname) { nx = 128; } else { nx = 128; } - } else if (s_cmp(c3, (char *)"BRD", (ftnlen)3, (ftnlen)3) == 0) { + } else if (s_lmp_cmp(c3, (char *)"BRD", (ftnlen)3, (ftnlen)3) == 0) { if (sname) { nx = 128; } else { nx = 128; } } - } else if (s_cmp(c2, (char *)"SY", (ftnlen)2, (ftnlen)2) == 0) { - if (sname && s_cmp(c3, (char *)"TRD", (ftnlen)3, (ftnlen)3) == 0) { + } else if (s_lmp_cmp(c2, (char *)"SY", (ftnlen)2, (ftnlen)2) == 0) { + if (sname && s_lmp_cmp(c3, (char *)"TRD", (ftnlen)3, (ftnlen)3) == 0) { nx = 32; } - } else if (cname && s_cmp(c2, (char *)"HE", (ftnlen)2, (ftnlen)2) == 0) { - if (s_cmp(c3, (char *)"TRD", (ftnlen)3, (ftnlen)3) == 0) { + } else if (cname && s_lmp_cmp(c2, (char *)"HE", (ftnlen)2, (ftnlen)2) == 0) { + if (s_lmp_cmp(c3, (char *)"TRD", (ftnlen)3, (ftnlen)3) == 0) { nx = 32; } - } else if (sname && s_cmp(c2, (char *)"OR", (ftnlen)2, (ftnlen)2) == 0) { + } else if (sname && s_lmp_cmp(c2, (char *)"OR", (ftnlen)2, (ftnlen)2) == 0) { if (*(unsigned char *)c3 == 'G') { - if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", - (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( - ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == - 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( - c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( + if (s_lmp_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == + 0 || s_lmp_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp( + c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"BR", ( ftnlen)2, (ftnlen)2) == 0) { nx = 128; } } - } else if (cname && s_cmp(c2, (char *)"UN", (ftnlen)2, (ftnlen)2) == 0) { + } else if (cname && s_lmp_cmp(c2, (char *)"UN", (ftnlen)2, (ftnlen)2) == 0) { if (*(unsigned char *)c3 == 'G') { - if (s_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"RQ", - (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"LQ", (ftnlen)2, ( - ftnlen)2) == 0 || s_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == - 0 || s_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp( - c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_cmp(c4, (char *)"BR", ( + if (s_lmp_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"RQ", + (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"LQ", (ftnlen)2, ( + ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == + 0 || s_lmp_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp( + c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"BR", ( ftnlen)2, (ftnlen)2) == 0) { nx = 128; } } - } else if (s_cmp(c2, (char *)"GG", (ftnlen)2, (ftnlen)2) == 0) { + } else if (s_lmp_cmp(c2, (char *)"GG", (ftnlen)2, (ftnlen)2) == 0) { nx = 128; - if (s_cmp(c3, (char *)"HD3", (ftnlen)3, (ftnlen)3) == 0) { + if (s_lmp_cmp(c3, (char *)"HD3", (ftnlen)3, (ftnlen)3) == 0) { nx = 128; } } diff --git a/lib/linalg/iparmq.cpp b/lib/linalg/iparmq.cpp index ad22d9f869..0b8e981525 100644 --- a/lib/linalg/iparmq.cpp +++ b/lib/linalg/iparmq.cpp @@ -255,9 +255,9 @@ integer iparmq_(integer *ispec, char *name__, char *opts, integer *n, integer /* Builtin functions */ double log(doublereal); - integer i_nint(real *); - /* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen); - integer s_cmp(char *, char *, ftnlen, ftnlen); + integer i_lmp_nint(real *); + /* Subroutine */ int s_lmp_copy(char *, char *, ftnlen, ftnlen); + integer s_lmp_cmp(char *, char *, ftnlen, ftnlen); /* Local variables */ integer i__, ic, nh, ns, iz; @@ -293,7 +293,7 @@ integer iparmq_(integer *ispec, char *name__, char *opts, integer *n, integer if (nh >= 150) { /* Computing MAX */ r__1 = log((real) nh) / log((float)2.); - i__1 = 10, i__2 = nh / i_nint(&r__1); + i__1 = 10, i__2 = nh / i_lmp_nint(&r__1); ns = max(i__1,i__2); } if (nh >= 590) { @@ -356,7 +356,7 @@ integer iparmq_(integer *ispec, char *name__, char *opts, integer *n, integer /* Convert NAME to upper case if the first character is lower case. */ ret_val = 0; - s_copy(subnam, name__, (ftnlen)6, name_len); + s_lmp_copy(subnam, name__, (ftnlen)6, name_len); ic = *(unsigned char *)subnam; iz = 'Z'; if (iz == 90 || iz == 122) { @@ -404,21 +404,21 @@ integer iparmq_(integer *ispec, char *name__, char *opts, integer *n, integer } } - if (s_cmp(subnam + 1, (char *)"GGHRD", (ftnlen)5, (ftnlen)5) == 0 || s_cmp( + if (s_lmp_cmp(subnam + 1, (char *)"GGHRD", (ftnlen)5, (ftnlen)5) == 0 || s_lmp_cmp( subnam + 1, (char *)"GGHD3", (ftnlen)5, (ftnlen)5) == 0) { ret_val = 1; if (nh >= 14) { ret_val = 2; } - } else if (s_cmp(subnam + 3, (char *)"EXC", (ftnlen)3, (ftnlen)3) == 0) { + } else if (s_lmp_cmp(subnam + 3, (char *)"EXC", (ftnlen)3, (ftnlen)3) == 0) { if (nh >= 14) { ret_val = 1; } if (nh >= 14) { ret_val = 2; } - } else if (s_cmp(subnam + 1, (char *)"HSEQR", (ftnlen)5, (ftnlen)5) == 0 || - s_cmp(subnam + 1, (char *)"LAQR", (ftnlen)4, (ftnlen)4) == 0) { + } else if (s_lmp_cmp(subnam + 1, (char *)"HSEQR", (ftnlen)5, (ftnlen)5) == 0 || + s_lmp_cmp(subnam + 1, (char *)"LAQR", (ftnlen)4, (ftnlen)4) == 0) { if (ns >= 14) { ret_val = 1; } diff --git a/lib/linalg/pow_lmp_dd.cpp b/lib/linalg/pow_lmp_dd.cpp new file mode 100644 index 0000000000..4963b04bbc --- /dev/null +++ b/lib/linalg/pow_lmp_dd.cpp @@ -0,0 +1,12 @@ + +#include "lmp_f2c.h" +#undef abs + +#include + +extern "C" { +double pow_lmp_dd(doublereal *ap, doublereal *bp) +{ + return (pow(*ap, *bp)); +} +} diff --git a/lib/linalg/pow_lmp_di.cpp b/lib/linalg/pow_lmp_di.cpp new file mode 100644 index 0000000000..9c3d89d536 --- /dev/null +++ b/lib/linalg/pow_lmp_di.cpp @@ -0,0 +1,31 @@ + +#include "lmp_f2c.h" + +extern "C" { + +double pow_lmp_di(doublereal *ap, integer *bp) +{ + double pow, x; + integer n; + unsigned long u; + + pow = 1; + x = *ap; + n = *bp; + + if (n != 0) { + if (n < 0) { + n = -n; + x = 1 / x; + } + for (u = n;;) { + if (u & 01) pow *= x; + if (u >>= 1) + x *= x; + else + break; + } + } + return (pow); +} +} diff --git a/lib/linalg/pow_lmp_ii.cpp b/lib/linalg/pow_lmp_ii.cpp new file mode 100644 index 0000000000..ff28c8fd5a --- /dev/null +++ b/lib/linalg/pow_lmp_ii.cpp @@ -0,0 +1,29 @@ + +#include "lmp_f2c.h" + +extern "C" { + +integer pow_lmp_ii(integer *ap, integer *bp) +{ + integer pow, x, n; + unsigned long u; + + x = *ap; + n = *bp; + + if (n <= 0) { + if (n == 0 || x == 1) return 1; + if (x != -1) return x == 0 ? 1 / x : 0; + n = -n; + } + u = n; + for (pow = 1;;) { + if (u & 01) pow *= x; + if (u >>= 1) + x *= x; + else + break; + } + return (pow); +} +} diff --git a/lib/linalg/s_lmp_cat.cpp b/lib/linalg/s_lmp_cat.cpp new file mode 100644 index 0000000000..323b0b671d --- /dev/null +++ b/lib/linalg/s_lmp_cat.cpp @@ -0,0 +1,23 @@ + +#include "lmp_f2c.h" + +// concatenate two strings + +extern "C" { +void s_lmp_cat(char *lp, char *rpp[], ftnint rnp[], ftnint *np, ftnlen ll) +{ + ftnlen i, nc; + char *rp; + ftnlen n = *np; + for (i = 0; i < n; ++i) { + nc = ll; + if (rnp[i] < nc) nc = rnp[i]; + ll -= nc; + rp = rpp[i]; + while (--nc >= 0) + *lp++ = *rp++; + } + while (--ll >= 0) + *lp++ = ' '; +} +} diff --git a/lib/linalg/s_lmp_cmp.cpp b/lib/linalg/s_lmp_cmp.cpp new file mode 100644 index 0000000000..b51817defa --- /dev/null +++ b/lib/linalg/s_lmp_cmp.cpp @@ -0,0 +1,45 @@ + +#include "lmp_f2c.h" + +extern "C" { + +// compare two strings + +integer s_lmp_cmp(char *a0, char *b0, ftnlen la, ftnlen lb) +{ + register unsigned char *a, *aend, *b, *bend; + a = (unsigned char *)a0; + b = (unsigned char *)b0; + aend = a + la; + bend = b + lb; + + if (la <= lb) { + while (a < aend) + if (*a != *b) + return (*a - *b); + else { + ++a; + ++b; + } + + while (b < bend) + if (*b != ' ') + return (' ' - *b); + else + ++b; + } else { + while (b < bend) + if (*a == *b) { + ++a; + ++b; + } else + return (*a - *b); + while (a < aend) + if (*a != ' ') + return (*a - ' '); + else + ++a; + } + return (0); +} +} diff --git a/lib/linalg/s_lmp_copy.cpp b/lib/linalg/s_lmp_copy.cpp new file mode 100644 index 0000000000..9b432e08ca --- /dev/null +++ b/lib/linalg/s_lmp_copy.cpp @@ -0,0 +1,26 @@ + +#include "lmp_f2c.h" + +extern "C" { + +/* assign strings: a = b */ + +void s_lmp_copy(register char *a, register char *b, ftnlen la, ftnlen lb) +{ + register char *aend, *bend; + + aend = a + la; + + if (la <= lb) + while (a < aend) + *a++ = *b++; + + else { + bend = b + lb; + while (b < bend) + *a++ = *b++; + while (a < aend) + *a++ = ' '; + } +} +} diff --git a/lib/linalg/static/.clang-format b/lib/linalg/static/.clang-format new file mode 100644 index 0000000000..cb352b37f5 --- /dev/null +++ b/lib/linalg/static/.clang-format @@ -0,0 +1,23 @@ +--- +Language: Cpp +BasedOnStyle: LLVM +AccessModifierOffset: -4 +AlignConsecutiveAssignments: true +AlignEscapedNewlines: Left +AllowShortFunctionsOnASingleLine: Inline +AllowShortLambdasOnASingleLine: None +AllowShortIfStatementsOnASingleLine: WithoutElse +BraceWrapping: + AfterFunction: true +BreakBeforeBraces: Custom +BreakInheritanceList: AfterColon +BreakConstructorInitializers: AfterColon +ColumnLimit: 100 +IndentCaseLabels: true +IndentWidth: 4 +ObjCBlockIndentWidth: 4 +PenaltyBreakAssignment: 4 +Standard: Cpp11 +TabWidth: 4 +UseTab: Never +... diff --git a/lib/linalg/static/README b/lib/linalg/static/README index c06337c2dd..2d0271db7c 100644 --- a/lib/linalg/static/README +++ b/lib/linalg/static/README @@ -1,5 +1,8 @@ -The C++ files in this folder are direct C++ implementations of their -Fortran equivalents using the C++ runtime. -. +The C++ files in this folder are either direct C++ implementations of +their Fortran equivalents using the C++ runtime, or they are adapted +copies of functions from the libf2c runtime. The runtime functions +needed to be renamed to avoid conflics with libgfortran which uses +some of the same function names. + The Fortran files in this folder are modified from their original versions, so that f2c can correctly translate them. diff --git a/lib/linalg/static/d_lmp_cnjg.cpp b/lib/linalg/static/d_lmp_cnjg.cpp new file mode 100644 index 0000000000..03ca8f98fd --- /dev/null +++ b/lib/linalg/static/d_lmp_cnjg.cpp @@ -0,0 +1,13 @@ + +#include "lmp_f2c.h" + +extern "C" { + +void d_lmp_cnjg(doublecomplex *r, doublecomplex *z) +{ + doublereal zi = z->i; + + r->r = z->r; + r->i = -zi; +} +} diff --git a/lib/linalg/static/d_lmp_imag.cpp b/lib/linalg/static/d_lmp_imag.cpp new file mode 100644 index 0000000000..f0443f7828 --- /dev/null +++ b/lib/linalg/static/d_lmp_imag.cpp @@ -0,0 +1,10 @@ + +#include "lmp_f2c.h" + +extern "C" { + +double d_lmp_imag(doublecomplex *z) +{ + return (z->i); +} +} diff --git a/lib/linalg/static/d_lmp_lg10.cpp b/lib/linalg/static/d_lmp_lg10.cpp new file mode 100644 index 0000000000..ec48c99839 --- /dev/null +++ b/lib/linalg/static/d_lmp_lg10.cpp @@ -0,0 +1,14 @@ + +#include "lmp_f2c.h" +#undef abs + +static constexpr double log10e = 0.43429448190325182765; + +#include + +extern "C" { +double d_lmp_lg10(doublereal *x) +{ + return (log10e * log(*x)); +} +} diff --git a/lib/linalg/static/d_lmp_sign.cpp b/lib/linalg/static/d_lmp_sign.cpp new file mode 100644 index 0000000000..fb0a1e79ff --- /dev/null +++ b/lib/linalg/static/d_lmp_sign.cpp @@ -0,0 +1,12 @@ + +#include "lmp_f2c.h" + +extern "C" { + +double d_lmp_sign(doublereal *a, doublereal *b) +{ + double x; + x = (*a >= 0 ? *a : -*a); + return (*b >= 0 ? x : -x); +} +} diff --git a/lib/linalg/static/dlamc3.f b/lib/linalg/static/dlamc3.f new file mode 100644 index 0000000000..1108297707 --- /dev/null +++ b/lib/linalg/static/dlamc3.f @@ -0,0 +1,45 @@ +*> \brief \b DLAMC3 +*> \details +*> \b Purpose: +*> \verbatim +*> DLAMC3 is intended to force A and B to be stored prior to doing +*> the addition of A and B , for use in situations where optimizers +*> might hold one of these in a register. +*> \endverbatim +*> \author LAPACK is a software package provided by Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd.. +*> \date December 2016 +*> \ingroup auxOTHERauxiliary +*> +*> \param[in] A +*> \verbatim +*> A is a DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is a DOUBLE PRECISION +*> The values A and B. +*> \endverbatim +*> + DOUBLE PRECISION FUNCTION DLAMC3( A, B ) +* +* -- LAPACK auxiliary routine (version 3.7.0) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2010 +* +* .. Scalar Arguments .. + DOUBLE PRECISION A, B +* .. +* ===================================================================== +* +* .. Executable Statements .. +* + DLAMC3 = A + B +* + RETURN +* +* End of DLAMC3 +* + END +* +************************************************************************ diff --git a/lib/linalg/static/i_lmp_dnnt.cpp b/lib/linalg/static/i_lmp_dnnt.cpp new file mode 100644 index 0000000000..8050697bb9 --- /dev/null +++ b/lib/linalg/static/i_lmp_dnnt.cpp @@ -0,0 +1,12 @@ + +#include "lmp_f2c.h" + +#undef abs +#include + +extern "C" { +integer i_lmp_dnnt(doublereal *x) +{ + return (integer)(*x >= 0. ? floor(*x + .5) : -floor(.5 - *x)); +} +} diff --git a/lib/linalg/static/i_lmp_len.cpp b/lib/linalg/static/i_lmp_len.cpp new file mode 100644 index 0000000000..b6101b29ad --- /dev/null +++ b/lib/linalg/static/i_lmp_len.cpp @@ -0,0 +1,10 @@ + +#include "lmp_f2c.h" + +extern "C" { + +integer i_lmp_len(char *s, ftnlen n) +{ + return (n); +} +} diff --git a/lib/linalg/static/i_lmp_nint.cpp b/lib/linalg/static/i_lmp_nint.cpp new file mode 100644 index 0000000000..f41ca6b3eb --- /dev/null +++ b/lib/linalg/static/i_lmp_nint.cpp @@ -0,0 +1,13 @@ + +#include "lmp_f2c.h" +#undef abs + +#include + +extern "C" { + +integer i_lmp_nint(real *x) +{ + return (integer)(*x >= 0 ? floor(*x + .5) : -floor(.5 - *x)); +} +} diff --git a/lib/linalg/static/pow_lmp_dd.cpp b/lib/linalg/static/pow_lmp_dd.cpp new file mode 100644 index 0000000000..4963b04bbc --- /dev/null +++ b/lib/linalg/static/pow_lmp_dd.cpp @@ -0,0 +1,12 @@ + +#include "lmp_f2c.h" +#undef abs + +#include + +extern "C" { +double pow_lmp_dd(doublereal *ap, doublereal *bp) +{ + return (pow(*ap, *bp)); +} +} diff --git a/lib/linalg/static/pow_lmp_di.cpp b/lib/linalg/static/pow_lmp_di.cpp new file mode 100644 index 0000000000..9c3d89d536 --- /dev/null +++ b/lib/linalg/static/pow_lmp_di.cpp @@ -0,0 +1,31 @@ + +#include "lmp_f2c.h" + +extern "C" { + +double pow_lmp_di(doublereal *ap, integer *bp) +{ + double pow, x; + integer n; + unsigned long u; + + pow = 1; + x = *ap; + n = *bp; + + if (n != 0) { + if (n < 0) { + n = -n; + x = 1 / x; + } + for (u = n;;) { + if (u & 01) pow *= x; + if (u >>= 1) + x *= x; + else + break; + } + } + return (pow); +} +} diff --git a/lib/linalg/static/pow_lmp_ii.cpp b/lib/linalg/static/pow_lmp_ii.cpp new file mode 100644 index 0000000000..ff28c8fd5a --- /dev/null +++ b/lib/linalg/static/pow_lmp_ii.cpp @@ -0,0 +1,29 @@ + +#include "lmp_f2c.h" + +extern "C" { + +integer pow_lmp_ii(integer *ap, integer *bp) +{ + integer pow, x, n; + unsigned long u; + + x = *ap; + n = *bp; + + if (n <= 0) { + if (n == 0 || x == 1) return 1; + if (x != -1) return x == 0 ? 1 / x : 0; + n = -n; + } + u = n; + for (pow = 1;;) { + if (u & 01) pow *= x; + if (u >>= 1) + x *= x; + else + break; + } + return (pow); +} +} diff --git a/lib/linalg/static/s_lmp_cat.cpp b/lib/linalg/static/s_lmp_cat.cpp new file mode 100644 index 0000000000..323b0b671d --- /dev/null +++ b/lib/linalg/static/s_lmp_cat.cpp @@ -0,0 +1,23 @@ + +#include "lmp_f2c.h" + +// concatenate two strings + +extern "C" { +void s_lmp_cat(char *lp, char *rpp[], ftnint rnp[], ftnint *np, ftnlen ll) +{ + ftnlen i, nc; + char *rp; + ftnlen n = *np; + for (i = 0; i < n; ++i) { + nc = ll; + if (rnp[i] < nc) nc = rnp[i]; + ll -= nc; + rp = rpp[i]; + while (--nc >= 0) + *lp++ = *rp++; + } + while (--ll >= 0) + *lp++ = ' '; +} +} diff --git a/lib/linalg/static/s_lmp_cmp.cpp b/lib/linalg/static/s_lmp_cmp.cpp new file mode 100644 index 0000000000..b51817defa --- /dev/null +++ b/lib/linalg/static/s_lmp_cmp.cpp @@ -0,0 +1,45 @@ + +#include "lmp_f2c.h" + +extern "C" { + +// compare two strings + +integer s_lmp_cmp(char *a0, char *b0, ftnlen la, ftnlen lb) +{ + register unsigned char *a, *aend, *b, *bend; + a = (unsigned char *)a0; + b = (unsigned char *)b0; + aend = a + la; + bend = b + lb; + + if (la <= lb) { + while (a < aend) + if (*a != *b) + return (*a - *b); + else { + ++a; + ++b; + } + + while (b < bend) + if (*b != ' ') + return (' ' - *b); + else + ++b; + } else { + while (b < bend) + if (*a == *b) { + ++a; + ++b; + } else + return (*a - *b); + while (a < aend) + if (*a != ' ') + return (*a - ' '); + else + ++a; + } + return (0); +} +} diff --git a/lib/linalg/static/s_lmp_copy.cpp b/lib/linalg/static/s_lmp_copy.cpp new file mode 100644 index 0000000000..9b432e08ca --- /dev/null +++ b/lib/linalg/static/s_lmp_copy.cpp @@ -0,0 +1,26 @@ + +#include "lmp_f2c.h" + +extern "C" { + +/* assign strings: a = b */ + +void s_lmp_copy(register char *a, register char *b, ftnlen la, ftnlen lb) +{ + register char *aend, *bend; + + aend = a + la; + + if (la <= lb) + while (a < aend) + *a++ = *b++; + + else { + bend = b + lb; + while (b < bend) + *a++ = *b++; + while (a < aend) + *a++ = ' '; + } +} +} diff --git a/lib/linalg/static/xerbla.cpp b/lib/linalg/static/xerbla.cpp index cf2f7b1c69..325bd7030d 100644 --- a/lib/linalg/static/xerbla.cpp +++ b/lib/linalg/static/xerbla.cpp @@ -1,30 +1,31 @@ -#include -#include - -class LinalgException : public std::exception { - std::string message; - - public: - LinalgException() = delete; - - explicit LinalgException(const std::string &msg) { message = msg; } - const char *what() const noexcept override { return message.c_str(); } -}; - -extern "C" { - #include "lmp_f2c.h" +#undef abs +#include +#include +#include + +extern "C" { + +static constexpr int BUFSZ = 1024; + integer xerbla_(const char *srname, integer *info) { - std::string mesg = " ** On entry to "; - for (int i = 0; i < 1024; ++i) { - if ((srname[i] == '\0') || (srname[i] == ' ')) break; - mesg.push_back(srname[i]); - } - mesg += " parameter number " + std::to_string(*info) + " had an illegal value\n"; - throw LinalgException(mesg); - return 0; + char buf[BUFSZ]; + buf[0] = '\0'; + + strcat(buf, " ** On entry to "); + for (int i = 0; i < BUFSZ - 16; ++i) { + if ((srname[i] == '\0') || (srname[i] == ' ')) { + buf[i + 16] = '\0'; + break; + } + buf[i + 16] = srname[i]; + } + int len = strlen(buf); + snprintf(buf+len, BUFSZ-len, " parameter number %d had an illegal value\n", *info); + exit(1); + return 0; } } diff --git a/lib/linalg/static/z_lmp_abs.cpp b/lib/linalg/static/z_lmp_abs.cpp new file mode 100644 index 0000000000..2b79d56457 --- /dev/null +++ b/lib/linalg/static/z_lmp_abs.cpp @@ -0,0 +1,31 @@ + +#include "lmp_f2c.h" +#undef abs + +#include + +extern "C" { + +static double f__cabs(double real, double imag) +{ + double temp; + + if (real < 0) real = -real; + if (imag < 0) imag = -imag; + if (imag > real) { + temp = real; + real = imag; + imag = temp; + } + if ((real + imag) == real) return (real); + + temp = imag / real; + temp = real * sqrt(1.0 + temp * temp); /*overflow!!*/ + return (temp); +} + +double z_lmp_abs(doublecomplex *z) +{ + return (f__cabs(z->r, z->i)); +} +} diff --git a/lib/linalg/static/z_lmp_div.cpp b/lib/linalg/static/z_lmp_div.cpp new file mode 100644 index 0000000000..5f742506da --- /dev/null +++ b/lib/linalg/static/z_lmp_div.cpp @@ -0,0 +1,31 @@ + +#include "lmp_f2c.h" + +extern "C" { + +void z_lmp_div(doublecomplex *c, doublecomplex *a, doublecomplex *b) +{ + double ratio, den; + double abr, abi, cr; + + if ((abr = b->r) < 0.) abr = -abr; + if ((abi = b->i) < 0.) abi = -abi; + if (abr <= abi) { + if (abi == 0) { + if (a->i != 0 || a->r != 0) abi = 1.; + c->i = c->r = abi / abr; + return; + } + ratio = b->r / b->i; + den = b->i * (1 + ratio * ratio); + cr = (a->r * ratio + a->i) / den; + c->i = (a->i * ratio - a->r) / den; + } else { + ratio = b->i / b->r; + den = b->r * (1 + ratio * ratio); + cr = (a->r + a->i * ratio) / den; + c->i = (a->i - a->r * ratio) / den; + } + c->r = cr; +} +} diff --git a/lib/linalg/whitespace.conf b/lib/linalg/whitespace.conf new file mode 100644 index 0000000000..7988edc506 --- /dev/null +++ b/lib/linalg/whitespace.conf @@ -0,0 +1,13 @@ +--- +recursive: false +include: + - "." + - "static/**" +exclude: + - "Makefile.*" + - "*.py" +patterns: + - "*.cpp" + - "*.h" + - "README" +... diff --git a/lib/linalg/xerbla.cpp b/lib/linalg/xerbla.cpp index cf2f7b1c69..325bd7030d 100644 --- a/lib/linalg/xerbla.cpp +++ b/lib/linalg/xerbla.cpp @@ -1,30 +1,31 @@ -#include -#include - -class LinalgException : public std::exception { - std::string message; - - public: - LinalgException() = delete; - - explicit LinalgException(const std::string &msg) { message = msg; } - const char *what() const noexcept override { return message.c_str(); } -}; - -extern "C" { - #include "lmp_f2c.h" +#undef abs +#include +#include +#include + +extern "C" { + +static constexpr int BUFSZ = 1024; + integer xerbla_(const char *srname, integer *info) { - std::string mesg = " ** On entry to "; - for (int i = 0; i < 1024; ++i) { - if ((srname[i] == '\0') || (srname[i] == ' ')) break; - mesg.push_back(srname[i]); - } - mesg += " parameter number " + std::to_string(*info) + " had an illegal value\n"; - throw LinalgException(mesg); - return 0; + char buf[BUFSZ]; + buf[0] = '\0'; + + strcat(buf, " ** On entry to "); + for (int i = 0; i < BUFSZ - 16; ++i) { + if ((srname[i] == '\0') || (srname[i] == ' ')) { + buf[i + 16] = '\0'; + break; + } + buf[i + 16] = srname[i]; + } + int len = strlen(buf); + snprintf(buf+len, BUFSZ-len, " parameter number %d had an illegal value\n", *info); + exit(1); + return 0; } } diff --git a/lib/linalg/z_lmp_abs.cpp b/lib/linalg/z_lmp_abs.cpp new file mode 100644 index 0000000000..2b79d56457 --- /dev/null +++ b/lib/linalg/z_lmp_abs.cpp @@ -0,0 +1,31 @@ + +#include "lmp_f2c.h" +#undef abs + +#include + +extern "C" { + +static double f__cabs(double real, double imag) +{ + double temp; + + if (real < 0) real = -real; + if (imag < 0) imag = -imag; + if (imag > real) { + temp = real; + real = imag; + imag = temp; + } + if ((real + imag) == real) return (real); + + temp = imag / real; + temp = real * sqrt(1.0 + temp * temp); /*overflow!!*/ + return (temp); +} + +double z_lmp_abs(doublecomplex *z) +{ + return (f__cabs(z->r, z->i)); +} +} diff --git a/lib/linalg/z_lmp_div.cpp b/lib/linalg/z_lmp_div.cpp new file mode 100644 index 0000000000..5f742506da --- /dev/null +++ b/lib/linalg/z_lmp_div.cpp @@ -0,0 +1,31 @@ + +#include "lmp_f2c.h" + +extern "C" { + +void z_lmp_div(doublecomplex *c, doublecomplex *a, doublecomplex *b) +{ + double ratio, den; + double abr, abi, cr; + + if ((abr = b->r) < 0.) abr = -abr; + if ((abi = b->i) < 0.) abi = -abi; + if (abr <= abi) { + if (abi == 0) { + if (a->i != 0 || a->r != 0) abi = 1.; + c->i = c->r = abi / abr; + return; + } + ratio = b->r / b->i; + den = b->i * (1 + ratio * ratio); + cr = (a->r * ratio + a->i) / den; + c->i = (a->i * ratio - a->r) / den; + } else { + ratio = b->i / b->r; + den = b->r * (1 + ratio * ratio); + cr = (a->r + a->i * ratio) / den; + c->i = (a->i - a->r * ratio) / den; + } + c->r = cr; +} +} diff --git a/lib/linalg/zdotc.cpp b/lib/linalg/zdotc.cpp index e0c614e843..2697cc1c2c 100644 --- a/lib/linalg/zdotc.cpp +++ b/lib/linalg/zdotc.cpp @@ -104,7 +104,7 @@ extern "C" { doublecomplex z__1, z__2, z__3; /* Builtin functions */ - void d_cnjg(doublecomplex *, doublecomplex *); + void d_lmp_cnjg(doublecomplex *, doublecomplex *); /* Local variables */ integer i__, ix, iy; @@ -142,7 +142,7 @@ extern "C" { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { - d_cnjg(&z__3, &zx[i__]); + d_lmp_cnjg(&z__3, &zx[i__]); i__2 = i__; z__2.r = z__3.r * zy[i__2].r - z__3.i * zy[i__2].i, z__2.i = z__3.r * zy[i__2].i + z__3.i * zy[i__2].r; @@ -164,7 +164,7 @@ extern "C" { } i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { - d_cnjg(&z__3, &zx[ix]); + d_lmp_cnjg(&z__3, &zx[ix]); i__2 = iy; z__2.r = z__3.r * zy[i__2].r - z__3.i * zy[i__2].i, z__2.i = z__3.r * zy[i__2].i + z__3.i * zy[i__2].r; diff --git a/lib/linalg/zdscal.cpp b/lib/linalg/zdscal.cpp index fd444bdf71..ebe50c247d 100644 --- a/lib/linalg/zdscal.cpp +++ b/lib/linalg/zdscal.cpp @@ -100,7 +100,7 @@ extern "C" { doublecomplex z__1; /* Builtin functions */ - double d_imag(doublecomplex *); + double d_lmp_imag(doublecomplex *); /* Local variables */ integer i__, nincx; @@ -138,7 +138,7 @@ extern "C" { i__2 = i__; i__3 = i__; d__1 = *da * zx[i__3].r; - d__2 = *da * d_imag(&zx[i__]); + d__2 = *da * d_lmp_imag(&zx[i__]); z__1.r = d__1, z__1.i = d__2; zx[i__2].r = z__1.r, zx[i__2].i = z__1.i; } @@ -153,7 +153,7 @@ extern "C" { i__3 = i__; i__4 = i__; d__1 = *da * zx[i__4].r; - d__2 = *da * d_imag(&zx[i__]); + d__2 = *da * d_lmp_imag(&zx[i__]); z__1.r = d__1, z__1.i = d__2; zx[i__3].r = z__1.r, zx[i__3].i = z__1.i; } diff --git a/lib/linalg/zgemm.cpp b/lib/linalg/zgemm.cpp index 53020bef2d..c49b0a4e57 100644 --- a/lib/linalg/zgemm.cpp +++ b/lib/linalg/zgemm.cpp @@ -211,7 +211,7 @@ extern "C" { doublecomplex z__1, z__2, z__3, z__4; /* Builtin functions */ - void d_cnjg(doublecomplex *, doublecomplex *); + void d_lmp_cnjg(doublecomplex *, doublecomplex *); /* Local variables */ integer i__, j, l, info; @@ -406,7 +406,7 @@ extern "C" { temp.r = 0., temp.i = 0.; i__3 = *k; for (l = 1; l <= i__3; ++l) { - d_cnjg(&z__3, &a[l + i__ * a_dim1]); + d_lmp_cnjg(&z__3, &a[l + i__ * a_dim1]); i__4 = l + j * b_dim1; z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4].i, z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4] @@ -508,7 +508,7 @@ extern "C" { } i__2 = *k; for (l = 1; l <= i__2; ++l) { - d_cnjg(&z__2, &b[j + l * b_dim1]); + d_lmp_cnjg(&z__2, &b[j + l * b_dim1]); z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = alpha->r * z__2.i + alpha->i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; @@ -591,8 +591,8 @@ extern "C" { temp.r = 0., temp.i = 0.; i__3 = *k; for (l = 1; l <= i__3; ++l) { - d_cnjg(&z__3, &a[l + i__ * a_dim1]); - d_cnjg(&z__4, &b[j + l * b_dim1]); + d_lmp_cnjg(&z__3, &a[l + i__ * a_dim1]); + d_lmp_cnjg(&z__4, &b[j + l * b_dim1]); z__2.r = z__3.r * z__4.r - z__3.i * z__4.i, z__2.i = z__3.r * z__4.i + z__3.i * z__4.r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; @@ -632,7 +632,7 @@ extern "C" { temp.r = 0., temp.i = 0.; i__3 = *k; for (l = 1; l <= i__3; ++l) { - d_cnjg(&z__3, &a[l + i__ * a_dim1]); + d_lmp_cnjg(&z__3, &a[l + i__ * a_dim1]); i__4 = j + l * b_dim1; z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4].i, z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4] @@ -677,7 +677,7 @@ extern "C" { i__3 = *k; for (l = 1; l <= i__3; ++l) { i__4 = l + i__ * a_dim1; - d_cnjg(&z__3, &b[j + l * b_dim1]); + d_lmp_cnjg(&z__3, &b[j + l * b_dim1]); z__2.r = a[i__4].r * z__3.r - a[i__4].i * z__3.i, z__2.i = a[i__4].r * z__3.i + a[i__4].i * z__3.r; diff --git a/lib/linalg/zgemv.cpp b/lib/linalg/zgemv.cpp index 99b8cf9d0a..68736014b7 100644 --- a/lib/linalg/zgemv.cpp +++ b/lib/linalg/zgemv.cpp @@ -181,7 +181,7 @@ extern "C" { doublecomplex z__1, z__2, z__3; /* Builtin functions */ - void d_cnjg(doublecomplex *, doublecomplex *); + void d_lmp_cnjg(doublecomplex *, doublecomplex *); /* Local variables */ integer i__, j, ix, iy, jx, jy, kx, ky, info; @@ -403,7 +403,7 @@ extern "C" { } else { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { - d_cnjg(&z__3, &a[i__ + j * a_dim1]); + d_lmp_cnjg(&z__3, &a[i__ + j * a_dim1]); i__3 = i__; z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3] @@ -443,7 +443,7 @@ extern "C" { } else { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { - d_cnjg(&z__3, &a[i__ + j * a_dim1]); + d_lmp_cnjg(&z__3, &a[i__ + j * a_dim1]); i__3 = ix; z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3] diff --git a/lib/linalg/zgerc.cpp b/lib/linalg/zgerc.cpp index 668c4c4f64..04dde8606a 100644 --- a/lib/linalg/zgerc.cpp +++ b/lib/linalg/zgerc.cpp @@ -152,7 +152,7 @@ extern "C" { doublecomplex z__1, z__2; /* Builtin functions */ - void d_cnjg(doublecomplex *, doublecomplex *); + void d_lmp_cnjg(doublecomplex *, doublecomplex *); /* Local variables */ integer i__, j, ix, jy, kx, info; @@ -226,7 +226,7 @@ extern "C" { for (j = 1; j <= i__1; ++j) { i__2 = jy; if (y[i__2].r != 0. || y[i__2].i != 0.) { - d_cnjg(&z__2, &y[jy]); + d_lmp_cnjg(&z__2, &y[jy]); z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = alpha->r * z__2.i + alpha->i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; @@ -255,7 +255,7 @@ extern "C" { for (j = 1; j <= i__1; ++j) { i__2 = jy; if (y[i__2].r != 0. || y[i__2].i != 0.) { - d_cnjg(&z__2, &y[jy]); + d_lmp_cnjg(&z__2, &y[jy]); z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = alpha->r * z__2.i + alpha->i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; diff --git a/lib/linalg/zhemv.cpp b/lib/linalg/zhemv.cpp index 132915183b..f26dbadf2b 100644 --- a/lib/linalg/zhemv.cpp +++ b/lib/linalg/zhemv.cpp @@ -177,7 +177,7 @@ extern "C" { doublecomplex z__1, z__2, z__3, z__4; /* Builtin functions */ - void d_cnjg(doublecomplex *, doublecomplex *); + void d_lmp_cnjg(doublecomplex *, doublecomplex *); /* Local variables */ integer i__, j, ix, iy, jx, jy, kx, ky, info; @@ -333,7 +333,7 @@ extern "C" { .r; z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; y[i__3].r = z__1.r, y[i__3].i = z__1.i; - d_cnjg(&z__3, &a[i__ + j * a_dim1]); + d_lmp_cnjg(&z__3, &a[i__ + j * a_dim1]); i__3 = i__; z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3].r; @@ -375,7 +375,7 @@ extern "C" { .r; z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; y[i__3].r = z__1.r, y[i__3].i = z__1.i; - d_cnjg(&z__3, &a[i__ + j * a_dim1]); + d_lmp_cnjg(&z__3, &a[i__ + j * a_dim1]); i__3 = ix; z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3].r; @@ -429,7 +429,7 @@ extern "C" { .r; z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; y[i__3].r = z__1.r, y[i__3].i = z__1.i; - d_cnjg(&z__3, &a[i__ + j * a_dim1]); + d_lmp_cnjg(&z__3, &a[i__ + j * a_dim1]); i__3 = i__; z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3].r; @@ -476,7 +476,7 @@ extern "C" { .r; z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; y[i__3].r = z__1.r, y[i__3].i = z__1.i; - d_cnjg(&z__3, &a[i__ + j * a_dim1]); + d_lmp_cnjg(&z__3, &a[i__ + j * a_dim1]); i__3 = ix; z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3].r; diff --git a/lib/linalg/zher2.cpp b/lib/linalg/zher2.cpp index 07d95f7917..6f66534dd4 100644 --- a/lib/linalg/zher2.cpp +++ b/lib/linalg/zher2.cpp @@ -173,7 +173,7 @@ extern "C" { doublecomplex z__1, z__2, z__3, z__4; /* Builtin functions */ - void d_cnjg(doublecomplex *, doublecomplex *); + void d_lmp_cnjg(doublecomplex *, doublecomplex *); /* Local variables */ integer i__, j, ix, iy, jx, jy, kx, ky, info; @@ -271,7 +271,7 @@ extern "C" { i__3 = j; if (x[i__2].r != 0. || x[i__2].i != 0. || (y[i__3].r != 0. || y[i__3].i != 0.)) { - d_cnjg(&z__2, &y[j]); + d_lmp_cnjg(&z__2, &y[j]); z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = alpha->r * z__2.i + alpha->i * z__2.r; temp1.r = z__1.r, temp1.i = z__1.i; @@ -279,7 +279,7 @@ extern "C" { z__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2] .r; - d_cnjg(&z__1, &z__2); + d_lmp_cnjg(&z__1, &z__2); temp2.r = z__1.r, temp2.i = z__1.i; i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { @@ -327,7 +327,7 @@ extern "C" { i__3 = jy; if (x[i__2].r != 0. || x[i__2].i != 0. || (y[i__3].r != 0. || y[i__3].i != 0.)) { - d_cnjg(&z__2, &y[jy]); + d_lmp_cnjg(&z__2, &y[jy]); z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = alpha->r * z__2.i + alpha->i * z__2.r; temp1.r = z__1.r, temp1.i = z__1.i; @@ -335,7 +335,7 @@ extern "C" { z__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2] .r; - d_cnjg(&z__1, &z__2); + d_lmp_cnjg(&z__1, &z__2); temp2.r = z__1.r, temp2.i = z__1.i; ix = kx; iy = ky; @@ -394,7 +394,7 @@ extern "C" { i__3 = j; if (x[i__2].r != 0. || x[i__2].i != 0. || (y[i__3].r != 0. || y[i__3].i != 0.)) { - d_cnjg(&z__2, &y[j]); + d_lmp_cnjg(&z__2, &y[j]); z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = alpha->r * z__2.i + alpha->i * z__2.r; temp1.r = z__1.r, temp1.i = z__1.i; @@ -402,7 +402,7 @@ extern "C" { z__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2] .r; - d_cnjg(&z__1, &z__2); + d_lmp_cnjg(&z__1, &z__2); temp2.r = z__1.r, temp2.i = z__1.i; i__2 = j + j * a_dim1; i__3 = j + j * a_dim1; @@ -450,7 +450,7 @@ extern "C" { i__3 = jy; if (x[i__2].r != 0. || x[i__2].i != 0. || (y[i__3].r != 0. || y[i__3].i != 0.)) { - d_cnjg(&z__2, &y[jy]); + d_lmp_cnjg(&z__2, &y[jy]); z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = alpha->r * z__2.i + alpha->i * z__2.r; temp1.r = z__1.r, temp1.i = z__1.i; @@ -458,7 +458,7 @@ extern "C" { z__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2] .r; - d_cnjg(&z__1, &z__2); + d_lmp_cnjg(&z__1, &z__2); temp2.r = z__1.r, temp2.i = z__1.i; i__2 = j + j * a_dim1; i__3 = j + j * a_dim1; diff --git a/lib/linalg/zher2k.cpp b/lib/linalg/zher2k.cpp index 7b5553add1..01ce32deb9 100644 --- a/lib/linalg/zher2k.cpp +++ b/lib/linalg/zher2k.cpp @@ -223,7 +223,7 @@ extern "C" { doublecomplex z__1, z__2, z__3, z__4, z__5, z__6; /* Builtin functions */ - void d_cnjg(doublecomplex *, doublecomplex *); + void d_lmp_cnjg(doublecomplex *, doublecomplex *); /* Local variables */ integer i__, j, l, info; @@ -418,7 +418,7 @@ extern "C" { i__4 = j + l * b_dim1; if (a[i__3].r != 0. || a[i__3].i != 0. || (b[i__4].r != 0. || b[i__4].i != 0.)) { - d_cnjg(&z__2, &b[j + l * b_dim1]); + d_lmp_cnjg(&z__2, &b[j + l * b_dim1]); z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = alpha->r * z__2.i + alpha->i * z__2.r; @@ -427,7 +427,7 @@ extern "C" { z__2.r = alpha->r * a[i__3].r - alpha->i * a[i__3].i, z__2.i = alpha->r * a[i__3].i + alpha->i * a[ i__3].r; - d_cnjg(&z__1, &z__2); + d_lmp_cnjg(&z__1, &z__2); temp2.r = z__1.r, temp2.i = z__1.i; i__3 = j - 1; for (i__ = 1; i__ <= i__3; ++i__) { @@ -502,7 +502,7 @@ extern "C" { i__4 = j + l * b_dim1; if (a[i__3].r != 0. || a[i__3].i != 0. || (b[i__4].r != 0. || b[i__4].i != 0.)) { - d_cnjg(&z__2, &b[j + l * b_dim1]); + d_lmp_cnjg(&z__2, &b[j + l * b_dim1]); z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = alpha->r * z__2.i + alpha->i * z__2.r; @@ -511,7 +511,7 @@ extern "C" { z__2.r = alpha->r * a[i__3].r - alpha->i * a[i__3].i, z__2.i = alpha->r * a[i__3].i + alpha->i * a[ i__3].r; - d_cnjg(&z__1, &z__2); + d_lmp_cnjg(&z__1, &z__2); temp2.r = z__1.r, temp2.i = z__1.i; i__3 = *n; for (i__ = j + 1; i__ <= i__3; ++i__) { @@ -565,14 +565,14 @@ extern "C" { temp2.r = 0., temp2.i = 0.; i__3 = *k; for (l = 1; l <= i__3; ++l) { - d_cnjg(&z__3, &a[l + i__ * a_dim1]); + d_lmp_cnjg(&z__3, &a[l + i__ * a_dim1]); i__4 = l + j * b_dim1; z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4].i, z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4] .r; z__1.r = temp1.r + z__2.r, z__1.i = temp1.i + z__2.i; temp1.r = z__1.r, temp1.i = z__1.i; - d_cnjg(&z__3, &b[l + i__ * b_dim1]); + d_lmp_cnjg(&z__3, &b[l + i__ * b_dim1]); i__4 = l + j * a_dim1; z__2.r = z__3.r * a[i__4].r - z__3.i * a[i__4].i, z__2.i = z__3.r * a[i__4].i + z__3.i * a[i__4] @@ -587,7 +587,7 @@ extern "C" { z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, z__2.i = alpha->r * temp1.i + alpha->i * temp1.r; - d_cnjg(&z__4, alpha); + d_lmp_cnjg(&z__4, alpha); z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, z__3.i = z__4.r * temp2.i + z__4.i * temp2.r; @@ -601,7 +601,7 @@ extern "C" { z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, z__2.i = alpha->r * temp1.i + alpha->i * temp1.r; - d_cnjg(&z__4, alpha); + d_lmp_cnjg(&z__4, alpha); z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, z__3.i = z__4.r * temp2.i + z__4.i * temp2.r; @@ -616,7 +616,7 @@ extern "C" { z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, z__2.i = alpha->r * temp1.i + alpha->i * temp1.r; - d_cnjg(&z__4, alpha); + d_lmp_cnjg(&z__4, alpha); z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, z__3.i = z__4.r * temp2.i + z__4.i * temp2.r; @@ -633,7 +633,7 @@ extern "C" { temp1.r; z__2.r = z__3.r + z__4.r, z__2.i = z__3.i + z__4.i; - d_cnjg(&z__6, alpha); + d_lmp_cnjg(&z__6, alpha); z__5.r = z__6.r * temp2.r - z__6.i * temp2.i, z__5.i = z__6.r * temp2.i + z__6.i * temp2.r; @@ -655,14 +655,14 @@ extern "C" { temp2.r = 0., temp2.i = 0.; i__3 = *k; for (l = 1; l <= i__3; ++l) { - d_cnjg(&z__3, &a[l + i__ * a_dim1]); + d_lmp_cnjg(&z__3, &a[l + i__ * a_dim1]); i__4 = l + j * b_dim1; z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4].i, z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4] .r; z__1.r = temp1.r + z__2.r, z__1.i = temp1.i + z__2.i; temp1.r = z__1.r, temp1.i = z__1.i; - d_cnjg(&z__3, &b[l + i__ * b_dim1]); + d_lmp_cnjg(&z__3, &b[l + i__ * b_dim1]); i__4 = l + j * a_dim1; z__2.r = z__3.r * a[i__4].r - z__3.i * a[i__4].i, z__2.i = z__3.r * a[i__4].i + z__3.i * a[i__4] @@ -677,7 +677,7 @@ extern "C" { z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, z__2.i = alpha->r * temp1.i + alpha->i * temp1.r; - d_cnjg(&z__4, alpha); + d_lmp_cnjg(&z__4, alpha); z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, z__3.i = z__4.r * temp2.i + z__4.i * temp2.r; @@ -691,7 +691,7 @@ extern "C" { z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, z__2.i = alpha->r * temp1.i + alpha->i * temp1.r; - d_cnjg(&z__4, alpha); + d_lmp_cnjg(&z__4, alpha); z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, z__3.i = z__4.r * temp2.i + z__4.i * temp2.r; @@ -706,7 +706,7 @@ extern "C" { z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, z__2.i = alpha->r * temp1.i + alpha->i * temp1.r; - d_cnjg(&z__4, alpha); + d_lmp_cnjg(&z__4, alpha); z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, z__3.i = z__4.r * temp2.i + z__4.i * temp2.r; @@ -723,7 +723,7 @@ extern "C" { temp1.r; z__2.r = z__3.r + z__4.r, z__2.i = z__3.i + z__4.i; - d_cnjg(&z__6, alpha); + d_lmp_cnjg(&z__6, alpha); z__5.r = z__6.r * temp2.r - z__6.i * temp2.i, z__5.i = z__6.r * temp2.i + z__6.i * temp2.r; diff --git a/lib/linalg/zhpr.cpp b/lib/linalg/zhpr.cpp index b977b2ce1e..29ed826c46 100644 --- a/lib/linalg/zhpr.cpp +++ b/lib/linalg/zhpr.cpp @@ -152,7 +152,7 @@ extern "C" { doublecomplex z__1, z__2; /* Builtin functions */ - void d_cnjg(doublecomplex *, doublecomplex *); + void d_lmp_cnjg(doublecomplex *, doublecomplex *); /* Local variables */ integer i__, j, k, kk, ix, jx, kx, info; @@ -231,7 +231,7 @@ extern "C" { for (j = 1; j <= i__1; ++j) { i__2 = j; if (x[i__2].r != 0. || x[i__2].i != 0.) { - d_cnjg(&z__2, &x[j]); + d_lmp_cnjg(&z__2, &x[j]); z__1.r = *alpha * z__2.r, z__1.i = *alpha * z__2.i; temp.r = z__1.r, temp.i = z__1.i; k = kk; @@ -271,7 +271,7 @@ extern "C" { for (j = 1; j <= i__1; ++j) { i__2 = jx; if (x[i__2].r != 0. || x[i__2].i != 0.) { - d_cnjg(&z__2, &x[jx]); + d_lmp_cnjg(&z__2, &x[jx]); z__1.r = *alpha * z__2.r, z__1.i = *alpha * z__2.i; temp.r = z__1.r, temp.i = z__1.i; ix = kx; @@ -316,7 +316,7 @@ extern "C" { for (j = 1; j <= i__1; ++j) { i__2 = j; if (x[i__2].r != 0. || x[i__2].i != 0.) { - d_cnjg(&z__2, &x[j]); + d_lmp_cnjg(&z__2, &x[j]); z__1.r = *alpha * z__2.r, z__1.i = *alpha * z__2.i; temp.r = z__1.r, temp.i = z__1.i; i__2 = kk; @@ -356,7 +356,7 @@ extern "C" { for (j = 1; j <= i__1; ++j) { i__2 = jx; if (x[i__2].r != 0. || x[i__2].i != 0.) { - d_cnjg(&z__2, &x[jx]); + d_lmp_cnjg(&z__2, &x[jx]); z__1.r = *alpha * z__2.r, z__1.i = *alpha * z__2.i; temp.r = z__1.r, temp.i = z__1.i; i__2 = kk; diff --git a/lib/linalg/zlacgv.cpp b/lib/linalg/zlacgv.cpp index 9e9a4050b2..d73cd7b759 100644 --- a/lib/linalg/zlacgv.cpp +++ b/lib/linalg/zlacgv.cpp @@ -97,7 +97,7 @@ f"> */ doublecomplex z__1; /* Builtin functions */ - void d_cnjg(doublecomplex *, doublecomplex *); + void d_lmp_cnjg(doublecomplex *, doublecomplex *); /* Local variables */ integer i__, ioff; @@ -128,7 +128,7 @@ f"> */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; - d_cnjg(&z__1, &x[i__]); + d_lmp_cnjg(&z__1, &x[i__]); x[i__2].r = z__1.r, x[i__2].i = z__1.i; /* L10: */ } @@ -140,7 +140,7 @@ f"> */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = ioff; - d_cnjg(&z__1, &x[ioff]); + d_lmp_cnjg(&z__1, &x[ioff]); x[i__2].r = z__1.r, x[i__2].i = z__1.i; ioff += *incx; /* L20: */ diff --git a/lib/linalg/zlacrm.cpp b/lib/linalg/zlacrm.cpp index 46508ae4a9..c3415cb29b 100644 --- a/lib/linalg/zlacrm.cpp +++ b/lib/linalg/zlacrm.cpp @@ -146,7 +146,7 @@ f"> */ doublecomplex z__1; /* Builtin functions */ - double d_imag(doublecomplex *); + double d_lmp_imag(doublecomplex *); /* Local variables */ integer i__, j, l; @@ -225,7 +225,7 @@ f"> */ for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { - rwork[(j - 1) * *m + i__] = d_imag(&a[i__ + j * a_dim1]); + rwork[(j - 1) * *m + i__] = d_lmp_imag(&a[i__ + j * a_dim1]); /* L50: */ } /* L60: */ diff --git a/lib/linalg/zladiv.cpp b/lib/linalg/zladiv.cpp index 6b065d5ce0..105560e1a5 100644 --- a/lib/linalg/zladiv.cpp +++ b/lib/linalg/zladiv.cpp @@ -88,7 +88,7 @@ f"> */ doublecomplex z__1; /* Builtin functions */ - double d_imag(doublecomplex *); + double d_lmp_imag(doublecomplex *); /* Local variables */ doublereal zi, zr; @@ -114,9 +114,9 @@ f"> */ /* .. Executable Statements .. */ d__1 = x->r; - d__2 = d_imag(x); + d__2 = d_lmp_imag(x); d__3 = y->r; - d__4 = d_imag(y); + d__4 = d_lmp_imag(y); dladiv_(&d__1, &d__2, &d__3, &d__4, &zr, &zi); z__1.r = zr, z__1.i = zi; ret_val->r = z__1.r, ret_val->i = z__1.i; diff --git a/lib/linalg/zlaed0.cpp b/lib/linalg/zlaed0.cpp index 98bc39611d..5895127d75 100644 --- a/lib/linalg/zlaed0.cpp +++ b/lib/linalg/zlaed0.cpp @@ -178,7 +178,7 @@ f"> */ /* Builtin functions */ double log(doublereal); - integer pow_ii(integer *, integer *); + integer pow_lmp_ii(integer *, integer *); /* Local variables */ integer i__, j, k, ll, iq, lgn, msd2, smm1, spm1, spm2; @@ -321,10 +321,10 @@ L10: temp = log((doublereal) (*n)) / log(2.); lgn = (integer) temp; - if (pow_ii(&c__2, &lgn) < *n) { + if (pow_lmp_ii(&c__2, &lgn) < *n) { ++lgn; } - if (pow_ii(&c__2, &lgn) < *n) { + if (pow_lmp_ii(&c__2, &lgn) < *n) { ++lgn; } iprmpt = indxq + *n + 1; diff --git a/lib/linalg/zlaed7.cpp b/lib/linalg/zlaed7.cpp index b20d805e62..11b29341bb 100644 --- a/lib/linalg/zlaed7.cpp +++ b/lib/linalg/zlaed7.cpp @@ -280,7 +280,7 @@ f"> */ integer q_dim1, q_offset, i__1, i__2; /* Builtin functions */ - integer pow_ii(integer *, integer *); + integer pow_lmp_ii(integer *, integer *); /* Local variables */ integer i__, k, n1, n2, iq, iw, iz, ptr, indx, curr, indxc, indxp; @@ -386,11 +386,11 @@ f"> */ /* Form the z-vector which consists of the last row of Q_1 and the */ /* first row of Q_2. */ - ptr = pow_ii(&c__2, tlvls) + 1; + ptr = pow_lmp_ii(&c__2, tlvls) + 1; i__1 = *curlvl - 1; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = *tlvls - i__; - ptr += pow_ii(&c__2, &i__2); + ptr += pow_lmp_ii(&c__2, &i__2); /* L10: */ } curr = ptr + *curpbm; diff --git a/lib/linalg/zlanhe.cpp b/lib/linalg/zlanhe.cpp index c54482158a..6db6cc5cef 100644 --- a/lib/linalg/zlanhe.cpp +++ b/lib/linalg/zlanhe.cpp @@ -153,7 +153,7 @@ doublereal zlanhe_(char *norm, char *uplo, integer *n, doublecomplex *a, doublereal ret_val, d__1; /* Builtin functions */ - double z_abs(doublecomplex *), sqrt(doublereal); + double z_lmp_abs(doublecomplex *), sqrt(doublereal); /* Local variables */ integer i__, j; @@ -207,7 +207,7 @@ doublereal zlanhe_(char *norm, char *uplo, integer *n, doublecomplex *a, for (j = 1; j <= i__1; ++j) { i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { - sum = z_abs(&a[i__ + j * a_dim1]); + sum = z_lmp_abs(&a[i__ + j * a_dim1]); if (value < sum || disnan_(&sum)) { value = sum; } @@ -230,7 +230,7 @@ doublereal zlanhe_(char *norm, char *uplo, integer *n, doublecomplex *a, } i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { - sum = z_abs(&a[i__ + j * a_dim1]); + sum = z_lmp_abs(&a[i__ + j * a_dim1]); if (value < sum || disnan_(&sum)) { value = sum; } @@ -251,7 +251,7 @@ doublereal zlanhe_(char *norm, char *uplo, integer *n, doublecomplex *a, sum = 0.; i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { - absa = z_abs(&a[i__ + j * a_dim1]); + absa = z_lmp_abs(&a[i__ + j * a_dim1]); sum += absa; work[i__] += absa; /* L50: */ @@ -280,7 +280,7 @@ doublereal zlanhe_(char *norm, char *uplo, integer *n, doublecomplex *a, sum = work[j] + (d__1 = a[i__2].r, abs(d__1)); i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { - absa = z_abs(&a[i__ + j * a_dim1]); + absa = z_lmp_abs(&a[i__ + j * a_dim1]); sum += absa; work[i__] += absa; /* L90: */ diff --git a/lib/linalg/zlarfb.cpp b/lib/linalg/zlarfb.cpp index b09fdf4917..e9015669ca 100644 --- a/lib/linalg/zlarfb.cpp +++ b/lib/linalg/zlarfb.cpp @@ -229,7 +229,7 @@ f"> */ doublecomplex z__1, z__2; /* Builtin functions */ - void d_cnjg(doublecomplex *, doublecomplex *); + void d_lmp_cnjg(doublecomplex *, doublecomplex *); /* Local variables */ integer i__, j; @@ -371,7 +371,7 @@ f"> */ for (i__ = 1; i__ <= i__2; ++i__) { i__3 = j + i__ * c_dim1; i__4 = j + i__ * c_dim1; - d_cnjg(&z__2, &work[i__ + j * work_dim1]); + d_lmp_cnjg(&z__2, &work[i__ + j * work_dim1]); z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i - z__2.i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; @@ -529,7 +529,7 @@ f"> */ for (i__ = 1; i__ <= i__2; ++i__) { i__3 = *m - *k + j + i__ * c_dim1; i__4 = *m - *k + j + i__ * c_dim1; - d_cnjg(&z__2, &work[i__ + j * work_dim1]); + d_lmp_cnjg(&z__2, &work[i__ + j * work_dim1]); z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i - z__2.i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; @@ -689,7 +689,7 @@ f"> */ for (i__ = 1; i__ <= i__2; ++i__) { i__3 = j + i__ * c_dim1; i__4 = j + i__ * c_dim1; - d_cnjg(&z__2, &work[i__ + j * work_dim1]); + d_lmp_cnjg(&z__2, &work[i__ + j * work_dim1]); z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i - z__2.i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; @@ -848,7 +848,7 @@ f"> */ for (i__ = 1; i__ <= i__2; ++i__) { i__3 = *m - *k + j + i__ * c_dim1; i__4 = *m - *k + j + i__ * c_dim1; - d_cnjg(&z__2, &work[i__ + j * work_dim1]); + d_lmp_cnjg(&z__2, &work[i__ + j * work_dim1]); z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i - z__2.i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; diff --git a/lib/linalg/zlarfg.cpp b/lib/linalg/zlarfg.cpp index 71e2add68c..518ba9bcbb 100644 --- a/lib/linalg/zlarfg.cpp +++ b/lib/linalg/zlarfg.cpp @@ -135,7 +135,7 @@ f"> */ doublecomplex z__1, z__2; /* Builtin functions */ - double d_imag(doublecomplex *), d_sign(doublereal *, doublereal *); + double d_lmp_imag(doublecomplex *), d_lmp_sign(doublereal *, doublereal *); /* Local variables */ integer j, knt; @@ -189,7 +189,7 @@ f"> */ i__1 = *n - 1; xnorm = dznrm2_(&i__1, &x[1], incx); alphr = alpha->r; - alphi = d_imag(alpha); + alphi = d_lmp_imag(alpha); if (xnorm == 0. && alphi == 0.) { @@ -201,7 +201,7 @@ f"> */ /* general case */ d__1 = dlapy3_(&alphr, &alphi, &xnorm); - beta = -d_sign(&d__1, &alphr); + beta = -d_lmp_sign(&d__1, &alphr); safmin = dlamch_((char *)"S", (ftnlen)1) / dlamch_((char *)"E", (ftnlen)1); rsafmn = 1. / safmin; @@ -228,7 +228,7 @@ L10: z__1.r = alphr, z__1.i = alphi; alpha->r = z__1.r, alpha->i = z__1.i; d__1 = dlapy3_(&alphr, &alphi, &xnorm); - beta = -d_sign(&d__1, &alphr); + beta = -d_lmp_sign(&d__1, &alphr); } d__1 = (beta - alphr) / beta; d__2 = -alphi / beta; diff --git a/lib/linalg/zlarft.cpp b/lib/linalg/zlarft.cpp index ad5e46b910..391de106cf 100644 --- a/lib/linalg/zlarft.cpp +++ b/lib/linalg/zlarft.cpp @@ -193,7 +193,7 @@ f"> */ doublecomplex z__1, z__2, z__3; /* Builtin functions */ - void d_cnjg(doublecomplex *, doublecomplex *); + void d_lmp_cnjg(doublecomplex *, doublecomplex *); /* Local variables */ integer i__, j, prevlastv; @@ -281,7 +281,7 @@ L220: i__3 = j + i__ * t_dim1; i__4 = i__; z__2.r = -tau[i__4].r, z__2.i = -tau[i__4].i; - d_cnjg(&z__3, &v[i__ + j * v_dim1]); + d_lmp_cnjg(&z__3, &v[i__ + j * v_dim1]); z__1.r = z__2.r * z__3.r - z__2.i * z__3.i, z__1.i = z__2.r * z__3.i + z__2.i * z__3.r; t[i__3].r = z__1.r, t[i__3].i = z__1.i; @@ -382,7 +382,7 @@ L281: i__2 = j + i__ * t_dim1; i__3 = i__; z__2.r = -tau[i__3].r, z__2.i = -tau[i__3].i; - d_cnjg(&z__3, &v[*n - *k + i__ + j * v_dim1]); + d_lmp_cnjg(&z__3, &v[*n - *k + i__ + j * v_dim1]); z__1.r = z__2.r * z__3.r - z__2.i * z__3.i, z__1.i = z__2.r * z__3.i + z__2.i * z__3.r; diff --git a/lib/linalg/zlassq.cpp b/lib/linalg/zlassq.cpp index 2e2a5ba539..31c0f15f4c 100644 --- a/lib/linalg/zlassq.cpp +++ b/lib/linalg/zlassq.cpp @@ -132,7 +132,7 @@ f"> */ doublereal d__1; /* Builtin functions */ - double d_imag(doublecomplex *); + double d_lmp_imag(doublecomplex *); /* Local variables */ integer ix; @@ -184,7 +184,7 @@ f"> */ *sumsq += d__1 * d__1; } } - temp1 = (d__1 = d_imag(&x[ix]), abs(d__1)); + temp1 = (d__1 = d_lmp_imag(&x[ix]), abs(d__1)); if (temp1 > 0. || disnan_(&temp1)) { if (*scale < temp1) { /* Computing 2nd power */ diff --git a/lib/linalg/zstedc.cpp b/lib/linalg/zstedc.cpp index 1a4d71cf50..fc6d9a782b 100644 --- a/lib/linalg/zstedc.cpp +++ b/lib/linalg/zstedc.cpp @@ -247,7 +247,7 @@ f"> */ /* Builtin functions */ double log(doublereal); - integer pow_ii(integer *, integer *); + integer pow_lmp_ii(integer *, integer *); double sqrt(doublereal); /* Local variables */ @@ -365,10 +365,10 @@ f"> */ lrwmin = *n - 1 << 1; } else if (icompz == 1) { lgn = (integer) (log((doublereal) (*n)) / log(2.)); - if (pow_ii(&c__2, &lgn) < *n) { + if (pow_lmp_ii(&c__2, &lgn) < *n) { ++lgn; } - if (pow_ii(&c__2, &lgn) < *n) { + if (pow_lmp_ii(&c__2, &lgn) < *n) { ++lgn; } lwmin = *n * *n; diff --git a/lib/linalg/zsteqr.cpp b/lib/linalg/zsteqr.cpp index ce75593d28..2085ccbaae 100644 --- a/lib/linalg/zsteqr.cpp +++ b/lib/linalg/zsteqr.cpp @@ -166,7 +166,7 @@ f"> */ doublereal d__1, d__2; /* Builtin functions */ - double sqrt(doublereal), d_sign(doublereal *, doublereal *); + double sqrt(doublereal), d_lmp_sign(doublereal *, doublereal *); /* Local variables */ doublereal b, c__, f, g; @@ -445,7 +445,7 @@ L60: g = (d__[l + 1] - p) / (e[l] * 2.); r__ = dlapy2_(&g, &c_b41); - g = d__[m] - p + e[l] / (g + d_sign(&r__, &g)); + g = d__[m] - p + e[l] / (g + d_lmp_sign(&r__, &g)); s = 1.; c__ = 1.; @@ -568,7 +568,7 @@ L110: g = (d__[l - 1] - p) / (e[l - 1] * 2.); r__ = dlapy2_(&g, &c_b41); - g = d__[m] - p + e[l - 1] / (g + d_sign(&r__, &g)); + g = d__[m] - p + e[l - 1] / (g + d_lmp_sign(&r__, &g)); s = 1.; c__ = 1.; diff --git a/lib/linalg/ztpmv.cpp b/lib/linalg/ztpmv.cpp index adb1db10f4..9e4a16df42 100644 --- a/lib/linalg/ztpmv.cpp +++ b/lib/linalg/ztpmv.cpp @@ -164,7 +164,7 @@ extern "C" { doublecomplex z__1, z__2, z__3; /* Builtin functions */ - void d_cnjg(doublecomplex *, doublecomplex *); + void d_lmp_cnjg(doublecomplex *, doublecomplex *); /* Local variables */ integer i__, j, k, kk, ix, jx, kx, info; @@ -432,14 +432,14 @@ extern "C" { } } else { if (nounit) { - d_cnjg(&z__2, &ap[kk]); + d_lmp_cnjg(&z__2, &ap[kk]); z__1.r = temp.r * z__2.r - temp.i * z__2.i, z__1.i = temp.r * z__2.i + temp.i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } for (i__ = j - 1; i__ >= 1; --i__) { - d_cnjg(&z__3, &ap[k]); + d_lmp_cnjg(&z__3, &ap[k]); i__1 = i__; z__2.r = z__3.r * x[i__1].r - z__3.i * x[i__1].i, z__2.i = z__3.r * x[i__1].i + z__3.i * x[ @@ -485,7 +485,7 @@ extern "C" { } } else { if (nounit) { - d_cnjg(&z__2, &ap[kk]); + d_lmp_cnjg(&z__2, &ap[kk]); z__1.r = temp.r * z__2.r - temp.i * z__2.i, z__1.i = temp.r * z__2.i + temp.i * z__2.r; @@ -494,7 +494,7 @@ extern "C" { i__1 = kk - j + 1; for (k = kk - 1; k >= i__1; --k) { ix -= *incx; - d_cnjg(&z__3, &ap[k]); + d_lmp_cnjg(&z__3, &ap[k]); i__2 = ix; z__2.r = z__3.r * x[i__2].r - z__3.i * x[i__2].i, z__2.i = z__3.r * x[i__2].i + z__3.i * x[ @@ -543,7 +543,7 @@ extern "C" { } } else { if (nounit) { - d_cnjg(&z__2, &ap[kk]); + d_lmp_cnjg(&z__2, &ap[kk]); z__1.r = temp.r * z__2.r - temp.i * z__2.i, z__1.i = temp.r * z__2.i + temp.i * z__2.r; @@ -551,7 +551,7 @@ extern "C" { } i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { - d_cnjg(&z__3, &ap[k]); + d_lmp_cnjg(&z__3, &ap[k]); i__3 = i__; z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = z__3.r * x[i__3].i + z__3.i * x[ @@ -598,7 +598,7 @@ extern "C" { } } else { if (nounit) { - d_cnjg(&z__2, &ap[kk]); + d_lmp_cnjg(&z__2, &ap[kk]); z__1.r = temp.r * z__2.r - temp.i * z__2.i, z__1.i = temp.r * z__2.i + temp.i * z__2.r; @@ -607,7 +607,7 @@ extern "C" { i__2 = kk + *n - j; for (k = kk + 1; k <= i__2; ++k) { ix += *incx; - d_cnjg(&z__3, &ap[k]); + d_lmp_cnjg(&z__3, &ap[k]); i__3 = ix; z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = z__3.r * x[i__3].i + z__3.i * x[ diff --git a/lib/linalg/ztpsv.cpp b/lib/linalg/ztpsv.cpp index c3c564acd2..a1bddbbeb9 100644 --- a/lib/linalg/ztpsv.cpp +++ b/lib/linalg/ztpsv.cpp @@ -166,7 +166,7 @@ extern "C" { doublecomplex z__1, z__2, z__3; /* Builtin functions */ - void z_div(doublecomplex *, doublecomplex *, doublecomplex *), d_cnjg( + void z_lmp_div(doublecomplex *, doublecomplex *, doublecomplex *), d_lmp_cnjg( doublecomplex *, doublecomplex *); /* Local variables */ @@ -260,7 +260,7 @@ extern "C" { if (x[i__1].r != 0. || x[i__1].i != 0.) { if (nounit) { i__1 = j; - z_div(&z__1, &x[j], &ap[kk]); + z_lmp_div(&z__1, &x[j], &ap[kk]); x[i__1].r = z__1.r, x[i__1].i = z__1.i; } i__1 = j; @@ -290,7 +290,7 @@ extern "C" { if (x[i__1].r != 0. || x[i__1].i != 0.) { if (nounit) { i__1 = jx; - z_div(&z__1, &x[jx], &ap[kk]); + z_lmp_div(&z__1, &x[jx], &ap[kk]); x[i__1].r = z__1.r, x[i__1].i = z__1.i; } i__1 = jx; @@ -325,7 +325,7 @@ extern "C" { if (x[i__2].r != 0. || x[i__2].i != 0.) { if (nounit) { i__2 = j; - z_div(&z__1, &x[j], &ap[kk]); + z_lmp_div(&z__1, &x[j], &ap[kk]); x[i__2].r = z__1.r, x[i__2].i = z__1.i; } i__2 = j; @@ -357,7 +357,7 @@ extern "C" { if (x[i__2].r != 0. || x[i__2].i != 0.) { if (nounit) { i__2 = jx; - z_div(&z__1, &x[jx], &ap[kk]); + z_lmp_div(&z__1, &x[jx], &ap[kk]); x[i__2].r = z__1.r, x[i__2].i = z__1.i; } i__2 = jx; @@ -411,13 +411,13 @@ extern "C" { /* L90: */ } if (nounit) { - z_div(&z__1, &temp, &ap[kk + j - 1]); + z_lmp_div(&z__1, &temp, &ap[kk + j - 1]); temp.r = z__1.r, temp.i = z__1.i; } } else { i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { - d_cnjg(&z__3, &ap[k]); + d_lmp_cnjg(&z__3, &ap[k]); i__3 = i__; z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = z__3.r * x[i__3].i + z__3.i * x[ @@ -429,8 +429,8 @@ extern "C" { /* L100: */ } if (nounit) { - d_cnjg(&z__2, &ap[kk + j - 1]); - z_div(&z__1, &temp, &z__2); + d_lmp_cnjg(&z__2, &ap[kk + j - 1]); + z_lmp_div(&z__1, &temp, &z__2); temp.r = z__1.r, temp.i = z__1.i; } } @@ -461,13 +461,13 @@ extern "C" { /* L120: */ } if (nounit) { - z_div(&z__1, &temp, &ap[kk + j - 1]); + z_lmp_div(&z__1, &temp, &ap[kk + j - 1]); temp.r = z__1.r, temp.i = z__1.i; } } else { i__2 = kk + j - 2; for (k = kk; k <= i__2; ++k) { - d_cnjg(&z__3, &ap[k]); + d_lmp_cnjg(&z__3, &ap[k]); i__3 = ix; z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = z__3.r * x[i__3].i + z__3.i * x[ @@ -479,8 +479,8 @@ extern "C" { /* L130: */ } if (nounit) { - d_cnjg(&z__2, &ap[kk + j - 1]); - z_div(&z__1, &temp, &z__2); + d_lmp_cnjg(&z__2, &ap[kk + j - 1]); + z_lmp_div(&z__1, &temp, &z__2); temp.r = z__1.r, temp.i = z__1.i; } } @@ -513,13 +513,13 @@ extern "C" { /* L150: */ } if (nounit) { - z_div(&z__1, &temp, &ap[kk - *n + j]); + z_lmp_div(&z__1, &temp, &ap[kk - *n + j]); temp.r = z__1.r, temp.i = z__1.i; } } else { i__1 = j + 1; for (i__ = *n; i__ >= i__1; --i__) { - d_cnjg(&z__3, &ap[k]); + d_lmp_cnjg(&z__3, &ap[k]); i__2 = i__; z__2.r = z__3.r * x[i__2].r - z__3.i * x[i__2].i, z__2.i = z__3.r * x[i__2].i + z__3.i * x[ @@ -531,8 +531,8 @@ extern "C" { /* L160: */ } if (nounit) { - d_cnjg(&z__2, &ap[kk - *n + j]); - z_div(&z__1, &temp, &z__2); + d_lmp_cnjg(&z__2, &ap[kk - *n + j]); + z_lmp_div(&z__1, &temp, &z__2); temp.r = z__1.r, temp.i = z__1.i; } } @@ -563,13 +563,13 @@ extern "C" { /* L180: */ } if (nounit) { - z_div(&z__1, &temp, &ap[kk - *n + j]); + z_lmp_div(&z__1, &temp, &ap[kk - *n + j]); temp.r = z__1.r, temp.i = z__1.i; } } else { i__1 = kk - (*n - (j + 1)); for (k = kk; k >= i__1; --k) { - d_cnjg(&z__3, &ap[k]); + d_lmp_cnjg(&z__3, &ap[k]); i__2 = ix; z__2.r = z__3.r * x[i__2].r - z__3.i * x[i__2].i, z__2.i = z__3.r * x[i__2].i + z__3.i * x[ @@ -581,8 +581,8 @@ extern "C" { /* L190: */ } if (nounit) { - d_cnjg(&z__2, &ap[kk - *n + j]); - z_div(&z__1, &temp, &z__2); + d_lmp_cnjg(&z__2, &ap[kk - *n + j]); + z_lmp_div(&z__1, &temp, &z__2); temp.r = z__1.r, temp.i = z__1.i; } } diff --git a/lib/linalg/ztptri.cpp b/lib/linalg/ztptri.cpp index eb5c2988e3..29377adc03 100644 --- a/lib/linalg/ztptri.cpp +++ b/lib/linalg/ztptri.cpp @@ -146,7 +146,7 @@ f"> */ doublecomplex z__1; /* Builtin functions */ - void z_div(doublecomplex *, doublecomplex *, doublecomplex *); + void z_lmp_div(doublecomplex *, doublecomplex *, doublecomplex *); /* Local variables */ integer j, jc, jj; @@ -243,7 +243,7 @@ f"> */ for (j = 1; j <= i__1; ++j) { if (nounit) { i__2 = jc + j - 1; - z_div(&z__1, &c_b1, &ap[jc + j - 1]); + z_lmp_div(&z__1, &c_b1, &ap[jc + j - 1]); ap[i__2].r = z__1.r, ap[i__2].i = z__1.i; i__2 = jc + j - 1; z__1.r = -ap[i__2].r, z__1.i = -ap[i__2].i; @@ -272,7 +272,7 @@ f"> */ for (j = *n; j >= 1; --j) { if (nounit) { i__1 = jc; - z_div(&z__1, &c_b1, &ap[jc]); + z_lmp_div(&z__1, &c_b1, &ap[jc]); ap[i__1].r = z__1.r, ap[i__1].i = z__1.i; i__1 = jc; z__1.r = -ap[i__1].r, z__1.i = -ap[i__1].i; diff --git a/lib/linalg/ztrmm.cpp b/lib/linalg/ztrmm.cpp index 3fec24189e..a44eec9bb1 100644 --- a/lib/linalg/ztrmm.cpp +++ b/lib/linalg/ztrmm.cpp @@ -201,7 +201,7 @@ extern "C" { doublecomplex z__1, z__2, z__3; /* Builtin functions */ - void d_cnjg(doublecomplex *, doublecomplex *); + void d_lmp_cnjg(doublecomplex *, doublecomplex *); /* Local variables */ integer i__, j, k, info; @@ -424,7 +424,7 @@ extern "C" { } } else { if (nounit) { - d_cnjg(&z__2, &a[i__ + i__ * a_dim1]); + d_lmp_cnjg(&z__2, &a[i__ + i__ * a_dim1]); z__1.r = temp.r * z__2.r - temp.i * z__2.i, z__1.i = temp.r * z__2.i + temp.i * z__2.r; @@ -432,7 +432,7 @@ extern "C" { } i__2 = i__ - 1; for (k = 1; k <= i__2; ++k) { - d_cnjg(&z__3, &a[k + i__ * a_dim1]); + d_lmp_cnjg(&z__3, &a[k + i__ * a_dim1]); i__3 = k + j * b_dim1; z__2.r = z__3.r * b[i__3].r - z__3.i * b[i__3] .i, z__2.i = z__3.r * b[i__3].i + @@ -481,7 +481,7 @@ extern "C" { } } else { if (nounit) { - d_cnjg(&z__2, &a[i__ + i__ * a_dim1]); + d_lmp_cnjg(&z__2, &a[i__ + i__ * a_dim1]); z__1.r = temp.r * z__2.r - temp.i * z__2.i, z__1.i = temp.r * z__2.i + temp.i * z__2.r; @@ -489,7 +489,7 @@ extern "C" { } i__3 = *m; for (k = i__ + 1; k <= i__3; ++k) { - d_cnjg(&z__3, &a[k + i__ * a_dim1]); + d_lmp_cnjg(&z__3, &a[k + i__ * a_dim1]); i__4 = k + j * b_dim1; z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4] .i, z__2.i = z__3.r * b[i__4].i + @@ -630,7 +630,7 @@ extern "C" { .i + alpha->i * a[i__3].r; temp.r = z__1.r, temp.i = z__1.i; } else { - d_cnjg(&z__2, &a[j + k * a_dim1]); + d_lmp_cnjg(&z__2, &a[j + k * a_dim1]); z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = alpha->r * z__2.i + alpha->i * z__2.r; @@ -661,7 +661,7 @@ extern "C" { i__2].r; temp.r = z__1.r, temp.i = z__1.i; } else { - d_cnjg(&z__2, &a[k + k * a_dim1]); + d_lmp_cnjg(&z__2, &a[k + k * a_dim1]); z__1.r = temp.r * z__2.r - temp.i * z__2.i, z__1.i = temp.r * z__2.i + temp.i * z__2.r; @@ -695,7 +695,7 @@ extern "C" { .i + alpha->i * a[i__2].r; temp.r = z__1.r, temp.i = z__1.i; } else { - d_cnjg(&z__2, &a[j + k * a_dim1]); + d_lmp_cnjg(&z__2, &a[j + k * a_dim1]); z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = alpha->r * z__2.i + alpha->i * z__2.r; @@ -726,7 +726,7 @@ extern "C" { i__1].r; temp.r = z__1.r, temp.i = z__1.i; } else { - d_cnjg(&z__2, &a[k + k * a_dim1]); + d_lmp_cnjg(&z__2, &a[k + k * a_dim1]); z__1.r = temp.r * z__2.r - temp.i * z__2.i, z__1.i = temp.r * z__2.i + temp.i * z__2.r; diff --git a/lib/linalg/ztrmv.cpp b/lib/linalg/ztrmv.cpp index 77f93e41a6..9d9877638f 100644 --- a/lib/linalg/ztrmv.cpp +++ b/lib/linalg/ztrmv.cpp @@ -169,7 +169,7 @@ extern "C" { doublecomplex z__1, z__2, z__3; /* Builtin functions */ - void d_cnjg(doublecomplex *, doublecomplex *); + void d_lmp_cnjg(doublecomplex *, doublecomplex *); /* Local variables */ integer i__, j, ix, jx, kx, info; @@ -428,14 +428,14 @@ extern "C" { } } else { if (nounit) { - d_cnjg(&z__2, &a[j + j * a_dim1]); + d_lmp_cnjg(&z__2, &a[j + j * a_dim1]); z__1.r = temp.r * z__2.r - temp.i * z__2.i, z__1.i = temp.r * z__2.i + temp.i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } for (i__ = j - 1; i__ >= 1; --i__) { - d_cnjg(&z__3, &a[i__ + j * a_dim1]); + d_lmp_cnjg(&z__3, &a[i__ + j * a_dim1]); i__1 = i__; z__2.r = z__3.r * x[i__1].r - z__3.i * x[i__1].i, z__2.i = z__3.r * x[i__1].i + z__3.i * x[ @@ -478,7 +478,7 @@ extern "C" { } } else { if (nounit) { - d_cnjg(&z__2, &a[j + j * a_dim1]); + d_lmp_cnjg(&z__2, &a[j + j * a_dim1]); z__1.r = temp.r * z__2.r - temp.i * z__2.i, z__1.i = temp.r * z__2.i + temp.i * z__2.r; @@ -486,7 +486,7 @@ extern "C" { } for (i__ = j - 1; i__ >= 1; --i__) { ix -= *incx; - d_cnjg(&z__3, &a[i__ + j * a_dim1]); + d_lmp_cnjg(&z__3, &a[i__ + j * a_dim1]); i__1 = ix; z__2.r = z__3.r * x[i__1].r - z__3.i * x[i__1].i, z__2.i = z__3.r * x[i__1].i + z__3.i * x[ @@ -531,7 +531,7 @@ extern "C" { } } else { if (nounit) { - d_cnjg(&z__2, &a[j + j * a_dim1]); + d_lmp_cnjg(&z__2, &a[j + j * a_dim1]); z__1.r = temp.r * z__2.r - temp.i * z__2.i, z__1.i = temp.r * z__2.i + temp.i * z__2.r; @@ -539,7 +539,7 @@ extern "C" { } i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { - d_cnjg(&z__3, &a[i__ + j * a_dim1]); + d_lmp_cnjg(&z__3, &a[i__ + j * a_dim1]); i__3 = i__; z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = z__3.r * x[i__3].i + z__3.i * x[ @@ -584,7 +584,7 @@ extern "C" { } } else { if (nounit) { - d_cnjg(&z__2, &a[j + j * a_dim1]); + d_lmp_cnjg(&z__2, &a[j + j * a_dim1]); z__1.r = temp.r * z__2.r - temp.i * z__2.i, z__1.i = temp.r * z__2.i + temp.i * z__2.r; @@ -593,7 +593,7 @@ extern "C" { i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { ix += *incx; - d_cnjg(&z__3, &a[i__ + j * a_dim1]); + d_lmp_cnjg(&z__3, &a[i__ + j * a_dim1]); i__3 = ix; z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = z__3.r * x[i__3].i + z__3.i * x[ diff --git a/lib/linalg/zungl2.cpp b/lib/linalg/zungl2.cpp index d4b85486c6..44213e5927 100644 --- a/lib/linalg/zungl2.cpp +++ b/lib/linalg/zungl2.cpp @@ -139,7 +139,7 @@ f"> */ doublecomplex z__1, z__2; /* Builtin functions */ - void d_cnjg(doublecomplex *, doublecomplex *); + void d_lmp_cnjg(doublecomplex *, doublecomplex *); /* Local variables */ integer i__, j, l; @@ -235,7 +235,7 @@ f"> */ a[i__1].r = 1., a[i__1].i = 0.; i__1 = *m - i__; i__2 = *n - i__ + 1; - d_cnjg(&z__1, &tau[i__]); + d_lmp_cnjg(&z__1, &tau[i__]); zlarf_((char *)"Right", &i__1, &i__2, &a[i__ + i__ * a_dim1], lda, & z__1, &a[i__ + 1 + i__ * a_dim1], lda, &work[1], ( ftnlen)5); @@ -248,7 +248,7 @@ f"> */ zlacgv_(&i__1, &a[i__ + (i__ + 1) * a_dim1], lda); } i__1 = i__ + i__ * a_dim1; - d_cnjg(&z__2, &tau[i__]); + d_lmp_cnjg(&z__2, &tau[i__]); z__1.r = 1. - z__2.r, z__1.i = 0. - z__2.i; a[i__1].r = z__1.r, a[i__1].i = z__1.i; diff --git a/lib/linalg/zunm2l.cpp b/lib/linalg/zunm2l.cpp index d9bc80e8c7..3e5b63f574 100644 --- a/lib/linalg/zunm2l.cpp +++ b/lib/linalg/zunm2l.cpp @@ -189,7 +189,7 @@ f"> */ doublecomplex z__1; /* Builtin functions */ - void d_cnjg(doublecomplex *, doublecomplex *); + void d_lmp_cnjg(doublecomplex *, doublecomplex *); /* Local variables */ integer i__, i1, i2, i3, mi, ni, nq; @@ -315,7 +315,7 @@ f"> */ i__3 = i__; taui.r = tau[i__3].r, taui.i = tau[i__3].i; } else { - d_cnjg(&z__1, &tau[i__]); + d_lmp_cnjg(&z__1, &tau[i__]); taui.r = z__1.r, taui.i = z__1.i; } i__3 = nq - *k + i__ + i__ * a_dim1; diff --git a/lib/linalg/zunm2r.cpp b/lib/linalg/zunm2r.cpp index a84cf72ba6..cbfdfb2f42 100644 --- a/lib/linalg/zunm2r.cpp +++ b/lib/linalg/zunm2r.cpp @@ -189,7 +189,7 @@ f"> */ doublecomplex z__1; /* Builtin functions */ - void d_cnjg(doublecomplex *, doublecomplex *); + void d_lmp_cnjg(doublecomplex *, doublecomplex *); /* Local variables */ integer i__, i1, i2, i3, ic, jc, mi, ni, nq; @@ -319,7 +319,7 @@ f"> */ i__3 = i__; taui.r = tau[i__3].r, taui.i = tau[i__3].i; } else { - d_cnjg(&z__1, &tau[i__]); + d_lmp_cnjg(&z__1, &tau[i__]); taui.r = z__1.r, taui.i = z__1.i; } i__3 = i__ + i__ * a_dim1; diff --git a/lib/linalg/zunmql.cpp b/lib/linalg/zunmql.cpp index facff63c71..694c8f776c 100644 --- a/lib/linalg/zunmql.cpp +++ b/lib/linalg/zunmql.cpp @@ -201,7 +201,7 @@ f"> */ char ch__1[2]; /* Builtin functions */ - /* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen); + /* Subroutine */ int s_lmp_cat(char *, char **, integer *, integer *, ftnlen); /* Local variables */ integer i__, i1, i2, i3, ib, nb, mi, ni, nq, nw, iwt; @@ -306,7 +306,7 @@ f"> */ /* Writing concatenation */ i__3[0] = 1, a__1[0] = side; i__3[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + s_lmp_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); i__1 = 64, i__2 = ilaenv_(&c__1, (char *)"ZUNMQL", ch__1, m, n, k, &c_n1, (ftnlen)6, (ftnlen)2); nb = min(i__1,i__2); @@ -338,7 +338,7 @@ f"> */ /* Writing concatenation */ i__3[0] = 1, a__1[0] = side; i__3[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + s_lmp_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"ZUNMQL", ch__1, m, n, k, &c_n1, ( ftnlen)6, (ftnlen)2); nbmin = max(i__1,i__2); diff --git a/lib/linalg/zunmqr.cpp b/lib/linalg/zunmqr.cpp index 8659499dab..6718cdc001 100644 --- a/lib/linalg/zunmqr.cpp +++ b/lib/linalg/zunmqr.cpp @@ -201,7 +201,7 @@ f"> */ char ch__1[2]; /* Builtin functions */ - /* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen); + /* Subroutine */ int s_lmp_cat(char *, char **, integer *, integer *, ftnlen); /* Local variables */ integer i__, i1, i2, i3, ib, ic, jc, nb, mi, ni, nq, nw, iwt; @@ -303,7 +303,7 @@ f"> */ /* Writing concatenation */ i__3[0] = 1, a__1[0] = side; i__3[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + s_lmp_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); i__1 = 64, i__2 = ilaenv_(&c__1, (char *)"ZUNMQR", ch__1, m, n, k, &c_n1, ( ftnlen)6, (ftnlen)2); nb = min(i__1,i__2); @@ -335,7 +335,7 @@ f"> */ /* Writing concatenation */ i__3[0] = 1, a__1[0] = side; i__3[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); + s_lmp_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"ZUNMQR", ch__1, m, n, k, &c_n1, ( ftnlen)6, (ftnlen)2); nbmin = max(i__1,i__2); diff --git a/lib/linalg/zunmtr.cpp b/lib/linalg/zunmtr.cpp index be224d7e93..f4f4f55761 100644 --- a/lib/linalg/zunmtr.cpp +++ b/lib/linalg/zunmtr.cpp @@ -203,7 +203,7 @@ f"> */ char ch__1[2]; /* Builtin functions */ - /* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen); + /* Subroutine */ int s_lmp_cat(char *, char **, integer *, integer *, ftnlen); /* Local variables */ integer i1, i2, nb, mi, ni, nq, nw; @@ -298,7 +298,7 @@ f"> */ /* Writing concatenation */ i__1[0] = 1, a__1[0] = side; i__1[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); + s_lmp_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); i__2 = *m - 1; i__3 = *m - 1; nb = ilaenv_(&c__1, (char *)"ZUNMQL", ch__1, &i__2, n, &i__3, &c_n1, ( @@ -307,7 +307,7 @@ f"> */ /* Writing concatenation */ i__1[0] = 1, a__1[0] = side; i__1[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); + s_lmp_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); i__2 = *n - 1; i__3 = *n - 1; nb = ilaenv_(&c__1, (char *)"ZUNMQL", ch__1, m, &i__2, &i__3, &c_n1, ( @@ -318,7 +318,7 @@ f"> */ /* Writing concatenation */ i__1[0] = 1, a__1[0] = side; i__1[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); + s_lmp_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); i__2 = *m - 1; i__3 = *m - 1; nb = ilaenv_(&c__1, (char *)"ZUNMQR", ch__1, &i__2, n, &i__3, &c_n1, ( @@ -327,7 +327,7 @@ f"> */ /* Writing concatenation */ i__1[0] = 1, a__1[0] = side; i__1[1] = 1, a__1[1] = trans; - s_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); + s_lmp_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); i__2 = *n - 1; i__3 = *n - 1; nb = ilaenv_(&c__1, (char *)"ZUNMQR", ch__1, m, &i__2, &i__3, &c_n1, ( From 57713cf9a3f7095f88be791706f18cd9f63ae8a0 Mon Sep 17 00:00:00 2001 From: Axel Kohlmeyer Date: Wed, 28 Dec 2022 16:31:50 -0500 Subject: [PATCH 30/47] remove redundant comments from generated C++ files. clean up with clang-format. --- lib/linalg/convert.sh | 25 +- lib/linalg/dasum.cpp | 128 +- lib/linalg/daxpy.cpp | 144 +- lib/linalg/dbdsqr.cpp | 699 +----- lib/linalg/dcabs1.cpp | 82 +- lib/linalg/dcopy.cpp | 137 +- lib/linalg/ddot.cpp | 137 +- lib/linalg/dgebd2.cpp | 338 +-- lib/linalg/dgebrd.cpp | 378 +-- lib/linalg/dgecon.cpp | 258 +- lib/linalg/dgelq2.cpp | 218 +- lib/linalg/dgelqf.cpp | 305 +-- lib/linalg/dgelsd.cpp | 795 ++---- lib/linalg/dgelss.cpp | 930 ++------ lib/linalg/dgemm.cpp | 317 +-- lib/linalg/dgemv.cpp | 254 +- lib/linalg/dgeqr2.cpp | 222 +- lib/linalg/dgeqrf.cpp | 311 +-- lib/linalg/dger.cpp | 200 +- lib/linalg/dgesv.cpp | 197 +- lib/linalg/dgesvd.cpp | 3844 +++++++----------------------- lib/linalg/dgetf2.cpp | 216 +- lib/linalg/dgetrf.cpp | 261 +- lib/linalg/dgetrf2.cpp | 271 +-- lib/linalg/dgetri.cpp | 286 +-- lib/linalg/dgetrs.cpp | 249 +- lib/linalg/disnan.cpp | 4 +- lib/linalg/dlabad.cpp | 118 +- lib/linalg/dlabrd.cpp | 510 +--- lib/linalg/dlacn2.cpp | 264 +- lib/linalg/dlacpy.cpp | 164 +- lib/linalg/dladiv.cpp | 221 +- lib/linalg/dlae2.cpp | 171 +- lib/linalg/dlaed0.cpp | 386 +-- lib/linalg/dlaed1.cpp | 292 +-- lib/linalg/dlaed2.cpp | 429 +--- lib/linalg/dlaed3.cpp | 347 +-- lib/linalg/dlaed4.cpp | 595 +---- lib/linalg/dlaed5.cpp | 169 +- lib/linalg/dlaed6.cpp | 296 +-- lib/linalg/dlaed7.cpp | 418 +--- lib/linalg/dlaed8.cpp | 434 +--- lib/linalg/dlaed9.cpp | 289 +-- lib/linalg/dlaeda.cpp | 331 +-- lib/linalg/dlaev2.cpp | 193 +- lib/linalg/dlals0.cpp | 493 +--- lib/linalg/dlalsa.cpp | 475 +--- lib/linalg/dlalsd.cpp | 498 +--- lib/linalg/dlamc3.cpp | 59 +- lib/linalg/dlamch.cpp | 38 +- lib/linalg/dlamrg.cpp | 154 +- lib/linalg/dlange.cpp | 210 +- lib/linalg/dlanst.cpp | 188 +- lib/linalg/dlansy.cpp | 217 +- lib/linalg/dlapy2.cpp | 121 +- lib/linalg/dlapy3.cpp | 127 +- lib/linalg/dlarf.cpp | 236 +- lib/linalg/dlarfb.cpp | 831 +------ lib/linalg/dlarfg.cpp | 191 +- lib/linalg/dlarft.cpp | 336 +-- lib/linalg/dlartg.cpp | 184 +- lib/linalg/dlas2.cpp | 173 +- lib/linalg/dlascl.cpp | 299 +-- lib/linalg/dlasd4.cpp | 629 +---- lib/linalg/dlasd5.cpp | 215 +- lib/linalg/dlasd6.cpp | 460 +--- lib/linalg/dlasd7.cpp | 459 +--- lib/linalg/dlasd8.cpp | 329 +-- lib/linalg/dlasda.cpp | 498 +--- lib/linalg/dlasdq.cpp | 378 +-- lib/linalg/dlasdt.cpp | 176 +- lib/linalg/dlaset.cpp | 195 +- lib/linalg/dlasq1.cpp | 230 +- lib/linalg/dlasq2.cpp | 407 +--- lib/linalg/dlasq3.cpp | 365 +-- lib/linalg/dlasq4.cpp | 306 +-- lib/linalg/dlasq5.cpp | 299 +-- lib/linalg/dlasq6.cpp | 210 +- lib/linalg/dlasr.cpp | 383 +-- lib/linalg/dlasrt.cpp | 198 +- lib/linalg/dlassq.cpp | 163 +- lib/linalg/dlasv2.cpp | 242 +- lib/linalg/dlaswp.cpp | 177 +- lib/linalg/dlatrd.cpp | 424 +--- lib/linalg/dlatrs.cpp | 658 +---- lib/linalg/dnrm2.cpp | 131 +- lib/linalg/dorg2l.cpp | 206 +- lib/linalg/dorg2r.cpp | 207 +- lib/linalg/dorgbr.cpp | 326 +-- lib/linalg/dorgl2.cpp | 203 +- lib/linalg/dorglq.cpp | 307 +-- lib/linalg/dorgql.cpp | 315 +-- lib/linalg/dorgqr.cpp | 309 +-- lib/linalg/dorgtr.cpp | 262 +- lib/linalg/dorm2l.cpp | 264 +- lib/linalg/dorm2r.cpp | 264 +- lib/linalg/dormbr.cpp | 367 +-- lib/linalg/dorml2.cpp | 261 +- lib/linalg/dormlq.cpp | 348 +-- lib/linalg/dormql.cpp | 348 +-- lib/linalg/dormqr.cpp | 348 +-- lib/linalg/dormtr.cpp | 319 +-- lib/linalg/dposv.cpp | 211 +- lib/linalg/dpotf2.cpp | 233 +- lib/linalg/dpotrf.cpp | 287 +-- lib/linalg/dpotrf2.cpp | 245 +- lib/linalg/dpotrs.cpp | 228 +- lib/linalg/drot.cpp | 143 +- lib/linalg/drscl.cpp | 166 +- lib/linalg/dscal.cpp | 134 +- lib/linalg/dstedc.cpp | 448 +--- lib/linalg/dsteqr.cpp | 427 +--- lib/linalg/dsterf.cpp | 300 +-- lib/linalg/dswap.cpp | 137 +- lib/linalg/dsyev.cpp | 298 +-- lib/linalg/dsyevd.cpp | 363 +-- lib/linalg/dsygs2.cpp | 308 +-- lib/linalg/dsygst.cpp | 431 +--- lib/linalg/dsygv.cpp | 338 +-- lib/linalg/dsygvd.cpp | 390 +-- lib/linalg/dsymm.cpp | 319 +-- lib/linalg/dsymv.cpp | 247 +- lib/linalg/dsyr2.cpp | 249 +- lib/linalg/dsyr2k.cpp | 336 +-- lib/linalg/dsyrk.cpp | 293 +-- lib/linalg/dsytd2.cpp | 351 +-- lib/linalg/dsytrd.cpp | 397 +-- lib/linalg/dtrmm.cpp | 326 +-- lib/linalg/dtrmv.cpp | 255 +- lib/linalg/dtrsm.cpp | 354 +-- lib/linalg/dtrsv.cpp | 251 +- lib/linalg/dtrti2.cpp | 213 +- lib/linalg/dtrtri.cpp | 280 +-- lib/linalg/dznrm2.cpp | 134 +- lib/linalg/idamax.cpp | 119 +- lib/linalg/ieeeck.cpp | 145 +- lib/linalg/iladlc.cpp | 124 +- lib/linalg/iladlr.cpp | 128 +- lib/linalg/ilaenv.cpp | 566 ++--- lib/linalg/ilazlc.cpp | 129 +- lib/linalg/ilazlr.cpp | 138 +- lib/linalg/iparmq.cpp | 365 +-- lib/linalg/lsame.cpp | 10 +- lib/linalg/pow_lmp_di.cpp | 4 +- lib/linalg/s_lmp_cmp.cpp | 4 +- lib/linalg/static/.clang-format | 2 +- lib/linalg/static/disnan.cpp | 4 +- lib/linalg/static/dlamch.cpp | 38 +- lib/linalg/static/lsame.cpp | 10 +- lib/linalg/static/pow_lmp_di.cpp | 4 +- lib/linalg/static/s_lmp_cmp.cpp | 4 +- lib/linalg/static/xerbla.cpp | 2 +- lib/linalg/static/z_lmp_div.cpp | 12 +- lib/linalg/whitespace.conf | 13 - lib/linalg/xerbla.cpp | 2 +- lib/linalg/z_lmp_div.cpp | 12 +- lib/linalg/zaxpy.cpp | 150 +- lib/linalg/zcopy.cpp | 131 +- lib/linalg/zdotc.cpp | 154 +- lib/linalg/zdrot.cpp | 151 +- lib/linalg/zdscal.cpp | 132 +- lib/linalg/zgemm.cpp | 483 +--- lib/linalg/zgemv.cpp | 312 +-- lib/linalg/zgerc.cpp | 218 +- lib/linalg/zheev.cpp | 305 +-- lib/linalg/zheevd.cpp | 393 +-- lib/linalg/zhemv.cpp | 321 +-- lib/linalg/zher2.cpp | 342 +-- lib/linalg/zher2k.cpp | 494 +--- lib/linalg/zhetd2.cpp | 369 +-- lib/linalg/zhetrd.cpp | 399 +--- lib/linalg/zhpr.cpp | 257 +- lib/linalg/zlacgv.cpp | 127 +- lib/linalg/zlacpy.cpp | 168 +- lib/linalg/zlacrm.cpp | 206 +- lib/linalg/zladiv.cpp | 122 +- lib/linalg/zlaed0.cpp | 339 +-- lib/linalg/zlaed7.cpp | 403 +--- lib/linalg/zlaed8.cpp | 419 +--- lib/linalg/zlanhe.cpp | 222 +- lib/linalg/zlarf.cpp | 247 +- lib/linalg/zlarfb.cpp | 863 ++----- lib/linalg/zlarfg.cpp | 203 +- lib/linalg/zlarft.cpp | 355 +-- lib/linalg/zlascl.cpp | 299 +-- lib/linalg/zlaset.cpp | 196 +- lib/linalg/zlasr.cpp | 456 +--- lib/linalg/zlassq.cpp | 171 +- lib/linalg/zlatrd.cpp | 446 +--- lib/linalg/zpptrf.cpp | 234 +- lib/linalg/zpptri.cpp | 198 +- lib/linalg/zscal.cpp | 137 +- lib/linalg/zstedc.cpp | 471 +--- lib/linalg/zsteqr.cpp | 432 +--- lib/linalg/zswap.cpp | 130 +- lib/linalg/ztpmv.cpp | 394 +-- lib/linalg/ztpsv.cpp | 348 +-- lib/linalg/ztptri.cpp | 224 +- lib/linalg/ztrmm.cpp | 497 +--- lib/linalg/ztrmv.cpp | 385 +-- lib/linalg/zung2l.cpp | 208 +- lib/linalg/zung2r.cpp | 208 +- lib/linalg/zungl2.cpp | 208 +- lib/linalg/zungql.cpp | 317 +-- lib/linalg/zungqr.cpp | 311 +-- lib/linalg/zungtr.cpp | 263 +- lib/linalg/zunm2l.cpp | 266 +-- lib/linalg/zunm2r.cpp | 266 +-- lib/linalg/zunmql.cpp | 350 +-- lib/linalg/zunmqr.cpp | 350 +-- lib/linalg/zunmtr.cpp | 320 +-- 211 files changed, 6255 insertions(+), 54891 deletions(-) delete mode 100644 lib/linalg/whitespace.conf diff --git a/lib/linalg/convert.sh b/lib/linalg/convert.sh index 0b2cdec0f2..0dba27c9e3 100755 --- a/lib/linalg/convert.sh +++ b/lib/linalg/convert.sh @@ -21,12 +21,15 @@ do \ then echo Skipping $b else - # convert to C++ with f2c. Make local variables dynamic. - f2c -C++ -a -f $f && mv $b.c $b.cpp || exit 2 - # silence c++ compiler warnings about string constants + # convert to C++ with f2c, make local variables dynamic, + # strip comments, and reindent with clang-format. + f2c -C++ -a -f < $f \ + | g++ -fpreprocessed -dD -P -E - \ + | clang-format -style=file:static/.clang-format > $b.cpp || exit 2 + # silence c++ compiler warnings about string constants, use custom f2c header sed -i -e 's/\("[^"]\+"\)/(char *)\1/g' -e 's/^extern.*"C"/extern "C"/' \ -e 's/^#include.*"f2c.h"/#include "lmp_f2c.h"/' $b.cpp - # replace libf2c functions with local versions under a different name + # replace libf2c functions with local versions under different names sed -i -e 's/s_\(cat\|cmp\|copy\)(/s_lmp_\1(/g' \ -e 's/d_\(sign\|cnjg\|imag\|lg10\)(/d_lmp_\1(/g' \ -e 's/z_\(abs\|div\)(/z_lmp_\1(/g' \ @@ -39,12 +42,15 @@ done for f in static/*.f do \ b=$(basename $f .f) - # convert to C++ with f2c. Make local variables dynamic. - f2c -C++ -a -f $f && mv $b.c $b.cpp || exit 2 - # silence c++ compiler warnings about string constants + # convert to C++ with f2c, make local variables dynamic, + # strip comments, and reindent with clang-format. + f2c -C++ -a -f < $f \ + | g++ -fpreprocessed -dD -P -E - \ + | clang-format -style=file:static/.clang-format > $b.cpp || exit 2 + # silence c++ compiler warnings about string constants, use custom f2c header sed -i -e 's/\("[^"]\+"\)/(char *)\1/g' -e 's/^extern.*"C"/extern "C"/' \ -e 's/^#include.*"f2c.h"/#include "lmp_f2c.h"/' $b.cpp - # replace libf2c functions with local versions under a different name + # replace libf2c functions with local versions under different names sed -i -e 's/s_\(cat\|cmp\|copy\)(/s_lmp_\1(/g' \ -e 's/d_\(sign\|cnjg\|imag\|lg10\)(/d_lmp_\1(/g' \ -e 's/z_\(abs\|div\)(/z_lmp_\1(/g' \ @@ -57,6 +63,3 @@ for c in static/*.cpp do \ cp -v $c . done - -# fix whitespace -python ../../tools/coding_standard/whitespace.py -c whitespace.conf -f . diff --git a/lib/linalg/dasum.cpp b/lib/linalg/dasum.cpp index 93e40126c0..faf6f38081 100644 --- a/lib/linalg/dasum.cpp +++ b/lib/linalg/dasum.cpp @@ -1,131 +1,21 @@ -/* fortran/dasum.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DASUM */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* DOUBLE PRECISION FUNCTION DASUM(N,DX,INCX) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INCX,N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION DX(*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DASUM takes the sum of the absolute values. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > number of elements in input vector(s) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DX */ -/* > \verbatim */ -/* > DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > storage spacing between elements of DX */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup double_blas_level1 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > jack dongarra, linpack, 3/11/78. */ -/* > modified 3/93 to return if incx .le. 0. */ -/* > modified 12/3/93, array(1) declarations changed to array(*) */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ doublereal dasum_(integer *n, doublereal *dx, integer *incx) { - /* System generated locals */ integer i__1, i__2; doublereal ret_val, d__1, d__2, d__3, d__4, d__5, d__6; - - /* Local variables */ integer i__, m, mp1; doublereal dtemp; integer nincx; - - -/* -- Reference BLAS level1 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Local Scalars .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ - /* Parameter adjustments */ --dx; - - /* Function Body */ ret_val = 0.; dtemp = 0.; if (*n <= 0 || *incx <= 0) { return ret_val; } if (*incx == 1) { -/* code for increment equal to 1 */ - - -/* clean-up loop */ - m = *n % 6; if (m != 0) { i__1 = m; @@ -140,15 +30,11 @@ doublereal dasum_(integer *n, doublereal *dx, integer *incx) mp1 = m + 1; i__1 = *n; for (i__ = mp1; i__ <= i__1; i__ += 6) { - dtemp = dtemp + (d__1 = dx[i__], abs(d__1)) + (d__2 = dx[i__ + 1], - abs(d__2)) + (d__3 = dx[i__ + 2], abs(d__3)) + (d__4 = - dx[i__ + 3], abs(d__4)) + (d__5 = dx[i__ + 4], abs(d__5)) - + (d__6 = dx[i__ + 5], abs(d__6)); + dtemp = dtemp + (d__1 = dx[i__], abs(d__1)) + (d__2 = dx[i__ + 1], abs(d__2)) + + (d__3 = dx[i__ + 2], abs(d__3)) + (d__4 = dx[i__ + 3], abs(d__4)) + + (d__5 = dx[i__ + 4], abs(d__5)) + (d__6 = dx[i__ + 5], abs(d__6)); } } else { - -/* code for increment not equal to 1 */ - nincx = *n * *incx; i__1 = nincx; i__2 = *incx; @@ -158,11 +44,7 @@ doublereal dasum_(integer *n, doublereal *dx, integer *incx) } ret_val = dtemp; return ret_val; - -/* End of DASUM */ - -} /* dasum_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/daxpy.cpp b/lib/linalg/daxpy.cpp index 54105d1426..1f820f6fc4 100644 --- a/lib/linalg/daxpy.cpp +++ b/lib/linalg/daxpy.cpp @@ -1,137 +1,13 @@ -/* fortran/daxpy.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DAXPY */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DAXPY(N,DA,DX,INCX,DY,INCY) */ - -/* .. Scalar Arguments .. */ -/* DOUBLE PRECISION DA */ -/* INTEGER INCX,INCY,N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION DX(*),DY(*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DAXPY constant times a vector plus a vector. */ -/* > uses unrolled loops for increments equal to one. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > number of elements in input vector(s) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DA */ -/* > \verbatim */ -/* > DA is DOUBLE PRECISION */ -/* > On entry, DA specifies the scalar alpha. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DX */ -/* > \verbatim */ -/* > DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > storage spacing between elements of DX */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] DY */ -/* > \verbatim */ -/* > DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCY */ -/* > \verbatim */ -/* > INCY is INTEGER */ -/* > storage spacing between elements of DY */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup double_blas_level1 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > jack dongarra, linpack, 3/11/78. */ -/* > modified 12/3/93, array(1) declarations changed to array(*) */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int daxpy_(integer *n, doublereal *da, doublereal *dx, - integer *incx, doublereal *dy, integer *incy) +int daxpy_(integer *n, doublereal *da, doublereal *dx, integer *incx, doublereal *dy, integer *incy) { - /* System generated locals */ integer i__1; - - /* Local variables */ integer i__, m, ix, iy, mp1; - - -/* -- Reference BLAS level1 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Local Scalars .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ - /* Parameter adjustments */ --dy; --dx; - - /* Function Body */ if (*n <= 0) { return 0; } @@ -139,12 +15,6 @@ extern "C" { return 0; } if (*incx == 1 && *incy == 1) { - -/* code for both increments equal to 1 */ - - -/* clean-up loop */ - m = *n % 4; if (m != 0) { i__1 = m; @@ -164,10 +34,6 @@ extern "C" { dy[i__ + 3] += *da * dx[i__ + 3]; } } else { - -/* code for unequal increments or equal increments */ -/* not equal to 1 */ - ix = 1; iy = 1; if (*incx < 0) { @@ -184,11 +50,7 @@ extern "C" { } } return 0; - -/* End of DAXPY */ - -} /* daxpy_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dbdsqr.cpp b/lib/linalg/dbdsqr.cpp index e8fef63745..59498b4ae6 100644 --- a/lib/linalg/dbdsqr.cpp +++ b/lib/linalg/dbdsqr.cpp @@ -1,283 +1,18 @@ -/* fortran/dbdsqr.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static doublereal c_b15 = -.125; static integer c__1 = 1; static doublereal c_b49 = 1.; static doublereal c_b72 = -1.; - -/* > \brief \b DBDSQR */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DBDSQR + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DBDSQR( UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, */ -/* LDU, C, LDC, WORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER UPLO */ -/* INTEGER INFO, LDC, LDU, LDVT, N, NCC, NCVT, NRU */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION C( LDC, * ), D( * ), E( * ), U( LDU, * ), */ -/* $ VT( LDVT, * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DBDSQR computes the singular values and, optionally, the right and/or */ -/* > left singular vectors from the singular value decomposition (SVD) of */ -/* > a real N-by-N (upper or lower) bidiagonal matrix B using the implicit */ -/* > zero-shift QR algorithm. The SVD of B has the form */ -/* > */ -/* > B = Q * S * P**T */ -/* > */ -/* > where S is the diagonal matrix of singular values, Q is an orthogonal */ -/* > matrix of left singular vectors, and P is an orthogonal matrix of */ -/* > right singular vectors. If left singular vectors are requested, this */ -/* > subroutine actually returns U*Q instead of Q, and, if right singular */ -/* > vectors are requested, this subroutine returns P**T*VT instead of */ -/* > P**T, for given real input matrices U and VT. When U and VT are the */ -/* > orthogonal matrices that reduce a general matrix A to bidiagonal */ -/* > form: A = U*B*VT, as computed by DGEBRD, then */ -/* > */ -/* > A = (U*Q) * S * (P**T*VT) */ -/* > */ -/* > is the SVD of A. Optionally, the subroutine may also compute Q**T*C */ -/* > for a given real input matrix C. */ -/* > */ -/* > See "Computing Small Singular Values of Bidiagonal Matrices With */ -/* > Guaranteed High Relative Accuracy," by J. Demmel and W. Kahan, */ -/* > LAPACK Working Note #3 (or SIAM J. Sci. Statist. Comput. vol. 11, */ -/* > no. 5, pp. 873-912, Sept 1990) and */ -/* > (char *)"Accurate singular values and differential qd algorithms," by */ -/* > B. Parlett and V. Fernando, Technical Report CPAM-554, Mathematics */ -/* > Department, University of California at Berkeley, July 1992 */ -/* > for a detailed description of the algorithm. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > = 'U': B is upper bidiagonal; */ -/* > = 'L': B is lower bidiagonal. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrix B. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] NCVT */ -/* > \verbatim */ -/* > NCVT is INTEGER */ -/* > The number of columns of the matrix VT. NCVT >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] NRU */ -/* > \verbatim */ -/* > NRU is INTEGER */ -/* > The number of rows of the matrix U. NRU >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] NCC */ -/* > \verbatim */ -/* > NCC is INTEGER */ -/* > The number of columns of the matrix C. NCC >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension (N) */ -/* > On entry, the n diagonal elements of the bidiagonal matrix B. */ -/* > On exit, if INFO=0, the singular values of B in decreasing */ -/* > order. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] E */ -/* > \verbatim */ -/* > E is DOUBLE PRECISION array, dimension (N-1) */ -/* > On entry, the N-1 offdiagonal elements of the bidiagonal */ -/* > matrix B. */ -/* > On exit, if INFO = 0, E is destroyed; if INFO > 0, D and E */ -/* > will contain the diagonal and superdiagonal elements of a */ -/* > bidiagonal matrix orthogonally equivalent to the one given */ -/* > as input. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] VT */ -/* > \verbatim */ -/* > VT is DOUBLE PRECISION array, dimension (LDVT, NCVT) */ -/* > On entry, an N-by-NCVT matrix VT. */ -/* > On exit, VT is overwritten by P**T * VT. */ -/* > Not referenced if NCVT = 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDVT */ -/* > \verbatim */ -/* > LDVT is INTEGER */ -/* > The leading dimension of the array VT. */ -/* > LDVT >= max(1,N) if NCVT > 0; LDVT >= 1 if NCVT = 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] U */ -/* > \verbatim */ -/* > U is DOUBLE PRECISION array, dimension (LDU, N) */ -/* > On entry, an NRU-by-N matrix U. */ -/* > On exit, U is overwritten by U * Q. */ -/* > Not referenced if NRU = 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDU */ -/* > \verbatim */ -/* > LDU is INTEGER */ -/* > The leading dimension of the array U. LDU >= max(1,NRU). */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] C */ -/* > \verbatim */ -/* > C is DOUBLE PRECISION array, dimension (LDC, NCC) */ -/* > On entry, an N-by-NCC matrix C. */ -/* > On exit, C is overwritten by Q**T * C. */ -/* > Not referenced if NCC = 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDC */ -/* > \verbatim */ -/* > LDC is INTEGER */ -/* > The leading dimension of the array C. */ -/* > LDC >= max(1,N) if NCC > 0; LDC >=1 if NCC = 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (4*(N-1)) */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: If INFO = -i, the i-th argument had an illegal value */ -/* > > 0: */ -/* > if NCVT = NRU = NCC = 0, */ -/* > = 1, a split was marked by a positive value in E */ -/* > = 2, current block of Z not diagonalized after 30*N */ -/* > iterations (in inner while loop) */ -/* > = 3, termination criterion of outer while loop not met */ -/* > (program created more than N unreduced blocks) */ -/* > else NCVT = NRU = NCC = 0, */ -/* > the algorithm did not converge; D and E contain the */ -/* > elements of a bidiagonal matrix which is orthogonally */ -/* > similar to the input matrix B; if INFO = i, i */ -/* > elements of E have not converged to zero. */ -/* > \endverbatim */ - -/* > \par Internal Parameters: */ -/* ========================= */ -/* > */ -/* > \verbatim */ -/* > TOLMUL DOUBLE PRECISION, default = max(10,min(100,EPS**(-1/8))) */ -/* > TOLMUL controls the convergence criterion of the QR loop. */ -/* > If it is positive, TOLMUL*EPS is the desired relative */ -/* > precision in the computed singular values. */ -/* > If it is negative, abs(TOLMUL*EPS*sigma_max) is the */ -/* > desired absolute accuracy in the computed singular */ -/* > values (corresponds to relative accuracy */ -/* > abs(TOLMUL*EPS) in the largest singular value. */ -/* > abs(TOLMUL) should be between 1 and 1/EPS, and preferably */ -/* > between 10 (for fast convergence) and .1/EPS */ -/* > (for there to be some accuracy in the results). */ -/* > Default is to lose at either one eighth or 2 of the */ -/* > available decimal digits in each computed singular value */ -/* > (whichever is smaller). */ -/* > */ -/* > MAXITR INTEGER, default = 6 */ -/* > MAXITR controls the maximum number of passes of the */ -/* > algorithm through its inner loop. The algorithms stops */ -/* > (and so fails to converge) if the number of passes */ -/* > through the inner loop exceeds MAXITR*N**2. */ -/* > */ -/* > \endverbatim */ - -/* > \par Note: */ -/* =========== */ -/* > */ -/* > \verbatim */ -/* > Bug report from Cezary Dendek. */ -/* > On March 23rd 2017, the INTEGER variable MAXIT = MAXITR*N**2 is */ -/* > removed since it can overflow pretty easily (for N larger or equal */ -/* > than 18,919). We instead use MAXITDIVN = MAXITR*N. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup auxOTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dbdsqr_(char *uplo, integer *n, integer *ncvt, integer * - nru, integer *ncc, doublereal *d__, doublereal *e, doublereal *vt, - integer *ldvt, doublereal *u, integer *ldu, doublereal *c__, integer * - ldc, doublereal *work, integer *info, ftnlen uplo_len) +int dbdsqr_(char *uplo, integer *n, integer *ncvt, integer *nru, integer *ncc, doublereal *d__, + doublereal *e, doublereal *vt, integer *ldvt, doublereal *u, integer *ldu, + doublereal *c__, integer *ldc, doublereal *work, integer *info, ftnlen uplo_len) { - /* System generated locals */ - integer c_dim1, c_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1, - i__2; + integer c_dim1, c_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1, i__2; doublereal d__1, d__2, d__3, d__4; - - /* Builtin functions */ - double pow_lmp_dd(doublereal *, doublereal *), sqrt(doublereal), d_lmp_sign( - doublereal *, doublereal *); - - /* Local variables */ + double pow_lmp_dd(doublereal *, doublereal *), sqrt(doublereal), d_lmp_sign(doublereal *, doublereal *); integer iterdivn; doublereal f, g, h__; integer i__, j, m; @@ -294,61 +29,28 @@ f"> */ doublereal cosl; integer isub, iter; doublereal unfl, sinl, cosr, smin, smax, sinr; - extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, - doublereal *, integer *, doublereal *, doublereal *), dlas2_( - doublereal *, doublereal *, doublereal *, doublereal *, - doublereal *), dscal_(integer *, doublereal *, doublereal *, - integer *); + extern int drot_(integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, + doublereal *), + dlas2_(doublereal *, doublereal *, doublereal *, doublereal *, doublereal *), + dscal_(integer *, doublereal *, doublereal *, integer *); extern logical lsame_(char *, char *, ftnlen, ftnlen); doublereal oldcs; - extern /* Subroutine */ int dlasr_(char *, char *, char *, integer *, - integer *, doublereal *, doublereal *, doublereal *, integer *, - ftnlen, ftnlen, ftnlen); + extern int dlasr_(char *, char *, char *, integer *, integer *, doublereal *, doublereal *, + doublereal *, integer *, ftnlen, ftnlen, ftnlen); integer oldll; doublereal shift, sigmn, oldsn; - extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, - doublereal *, integer *); + extern int dswap_(integer *, doublereal *, integer *, doublereal *, integer *); doublereal sminl, sigmx; logical lower; - extern /* Subroutine */ int dlasq1_(integer *, doublereal *, doublereal *, - doublereal *, integer *), dlasv2_(doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *); + extern int dlasq1_(integer *, doublereal *, doublereal *, doublereal *, integer *), + dlasv2_(doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *); extern doublereal dlamch_(char *, ftnlen); - extern /* Subroutine */ int dlartg_(doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *), xerbla_(char *, - integer *, ftnlen); + extern int dlartg_(doublereal *, doublereal *, doublereal *, doublereal *, doublereal *), + xerbla_(char *, integer *, ftnlen); doublereal sminoa, thresh; logical rotate; doublereal tolmul; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ --d__; --e; vt_dim1 = *ldvt; @@ -361,11 +63,9 @@ f"> */ c_offset = 1 + c_dim1; c__ -= c_offset; --work; - - /* Function Body */ *info = 0; lower = lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1); - if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lower) { + if (!lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && !lower) { *info = -1; } else if (*n < 0) { *info = -2; @@ -375,11 +75,11 @@ f"> */ *info = -4; } else if (*ncc < 0) { *info = -5; - } else if (*ncvt == 0 && *ldvt < 1 || *ncvt > 0 && *ldvt < max(1,*n)) { + } else if (*ncvt == 0 && *ldvt < 1 || *ncvt > 0 && *ldvt < max(1, *n)) { *info = -9; - } else if (*ldu < max(1,*nru)) { + } else if (*ldu < max(1, *nru)) { *info = -11; - } else if (*ncc == 0 && *ldc < 1 || *ncc > 0 && *ldc < max(1,*n)) { + } else if (*ncc == 0 && *ldc < 1 || *ncc > 0 && *ldc < max(1, *n)) { *info = -13; } if (*info != 0) { @@ -393,37 +93,20 @@ f"> */ if (*n == 1) { goto L160; } - -/* ROTATE is true if any singular vectors desired, false otherwise */ - rotate = *ncvt > 0 || *nru > 0 || *ncc > 0; - -/* If no singular vectors desired, use qd algorithm */ - - if (! rotate) { + if (!rotate) { dlasq1_(n, &d__[1], &e[1], &work[1], info); - -/* If INFO equals 2, dqds didn't finish, try to finish */ - if (*info != 2) { return 0; } *info = 0; } - nm1 = *n - 1; nm12 = nm1 + nm1; nm13 = nm12 + nm1; idir = 0; - -/* Get machine constants */ - eps = dlamch_((char *)"Epsilon", (ftnlen)7); unfl = dlamch_((char *)"Safe minimum", (ftnlen)12); - -/* If matrix lower bidiagonal, rotate to be upper bidiagonal */ -/* by applying Givens rotations on the left */ - if (lower) { i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { @@ -433,54 +116,33 @@ f"> */ d__[i__ + 1] = cs * d__[i__ + 1]; work[i__] = cs; work[nm1 + i__] = sn; -/* L10: */ } - -/* Update singular vectors if desired */ - if (*nru > 0) { - dlasr_((char *)"R", (char *)"V", (char *)"F", nru, n, &work[1], &work[*n], &u[u_offset], - ldu, (ftnlen)1, (ftnlen)1, (ftnlen)1); + dlasr_((char *)"R", (char *)"V", (char *)"F", nru, n, &work[1], &work[*n], &u[u_offset], ldu, (ftnlen)1, + (ftnlen)1, (ftnlen)1); } if (*ncc > 0) { - dlasr_((char *)"L", (char *)"V", (char *)"F", n, ncc, &work[1], &work[*n], &c__[c_offset], - ldc, (ftnlen)1, (ftnlen)1, (ftnlen)1); + dlasr_((char *)"L", (char *)"V", (char *)"F", n, ncc, &work[1], &work[*n], &c__[c_offset], ldc, (ftnlen)1, + (ftnlen)1, (ftnlen)1); } } - -/* Compute singular values to relative accuracy TOL */ -/* (By setting TOL to be negative, algorithm will compute */ -/* singular values to absolute accuracy ABS(TOL)*norm(input matrix)) */ - -/* Computing MAX */ -/* Computing MIN */ d__3 = 100., d__4 = pow_lmp_dd(&eps, &c_b15); - d__1 = 10., d__2 = min(d__3,d__4); - tolmul = max(d__1,d__2); + d__1 = 10., d__2 = min(d__3, d__4); + tolmul = max(d__1, d__2); tol = tolmul * eps; - -/* Compute approximate maximum, minimum singular values */ - smax = 0.; i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { -/* Computing MAX */ d__2 = smax, d__3 = (d__1 = d__[i__], abs(d__1)); - smax = max(d__2,d__3); -/* L20: */ + smax = max(d__2, d__3); } i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { -/* Computing MAX */ d__2 = smax, d__3 = (d__1 = e[i__], abs(d__1)); - smax = max(d__2,d__3); -/* L30: */ + smax = max(d__2, d__3); } sminl = 0.; if (tol >= 0.) { - -/* Relative accuracy desired */ - sminoa = abs(d__[1]); if (sminoa == 0.) { goto L50; @@ -488,52 +150,30 @@ f"> */ mu = sminoa; i__1 = *n; for (i__ = 2; i__ <= i__1; ++i__) { - mu = (d__2 = d__[i__], abs(d__2)) * (mu / (mu + (d__1 = e[i__ - 1] - , abs(d__1)))); - sminoa = min(sminoa,mu); + mu = (d__2 = d__[i__], abs(d__2)) * (mu / (mu + (d__1 = e[i__ - 1], abs(d__1)))); + sminoa = min(sminoa, mu); if (sminoa == 0.) { goto L50; } -/* L40: */ } -L50: - sminoa /= sqrt((doublereal) (*n)); -/* Computing MAX */ + L50: + sminoa /= sqrt((doublereal)(*n)); d__1 = tol * sminoa, d__2 = *n * (*n * unfl) * 6; - thresh = max(d__1,d__2); + thresh = max(d__1, d__2); } else { - -/* Absolute accuracy desired */ - -/* Computing MAX */ d__1 = abs(tol) * smax, d__2 = *n * (*n * unfl) * 6; - thresh = max(d__1,d__2); + thresh = max(d__1, d__2); } - -/* Prepare for main iteration loop for the singular values */ -/* (MAXIT is the maximum number of passes through the inner */ -/* loop permitted before nonconvergence signalled.) */ - maxitdivn = *n * 6; iterdivn = 0; iter = -1; oldll = -1; oldm = -1; - -/* M points to last element of unconverged part of matrix */ - m = *n; - -/* Begin main iteration loop */ - L60: - -/* Check for convergence or exceeding iteration count */ - if (m <= 1) { goto L160; } - if (iter >= *n) { iter -= *n; ++iterdivn; @@ -541,9 +181,6 @@ L60: goto L200; } } - -/* Find diagonal block of matrix to work on */ - if (tol < 0. && (d__1 = d__[m], abs(d__1)) <= thresh) { d__[m] = 0.; } @@ -560,95 +197,51 @@ L60: if (abse <= thresh) { goto L80; } - smin = min(smin,abss); -/* Computing MAX */ - d__1 = max(smax,abss); - smax = max(d__1,abse); -/* L70: */ + smin = min(smin, abss); + d__1 = max(smax, abss); + smax = max(d__1, abse); } ll = 0; goto L90; L80: e[ll] = 0.; - -/* Matrix splits since E(LL) = 0 */ - if (ll == m - 1) { - -/* Convergence of bottom singular value, return to top of loop */ - --m; goto L60; } L90: ++ll; - -/* E(LL) through E(M-1) are nonzero, E(LL-1) is zero */ - if (ll == m - 1) { - -/* 2 by 2 block, handle separately */ - - dlasv2_(&d__[m - 1], &e[m - 1], &d__[m], &sigmn, &sigmx, &sinr, &cosr, - &sinl, &cosl); + dlasv2_(&d__[m - 1], &e[m - 1], &d__[m], &sigmn, &sigmx, &sinr, &cosr, &sinl, &cosl); d__[m - 1] = sigmx; e[m - 1] = 0.; d__[m] = sigmn; - -/* Compute singular vectors, if desired */ - if (*ncvt > 0) { - drot_(ncvt, &vt[m - 1 + vt_dim1], ldvt, &vt[m + vt_dim1], ldvt, & - cosr, &sinr); + drot_(ncvt, &vt[m - 1 + vt_dim1], ldvt, &vt[m + vt_dim1], ldvt, &cosr, &sinr); } if (*nru > 0) { - drot_(nru, &u[(m - 1) * u_dim1 + 1], &c__1, &u[m * u_dim1 + 1], & - c__1, &cosl, &sinl); + drot_(nru, &u[(m - 1) * u_dim1 + 1], &c__1, &u[m * u_dim1 + 1], &c__1, &cosl, &sinl); } if (*ncc > 0) { - drot_(ncc, &c__[m - 1 + c_dim1], ldc, &c__[m + c_dim1], ldc, & - cosl, &sinl); + drot_(ncc, &c__[m - 1 + c_dim1], ldc, &c__[m + c_dim1], ldc, &cosl, &sinl); } m += -2; goto L60; } - -/* If working on new submatrix, choose shift direction */ -/* (from larger end diagonal element towards smaller) */ - if (ll > oldm || m < oldll) { if ((d__1 = d__[ll], abs(d__1)) >= (d__2 = d__[m], abs(d__2))) { - -/* Chase bulge from top (big end) to bottom (small end) */ - idir = 1; } else { - -/* Chase bulge from bottom (big end) to top (small end) */ - idir = 2; } } - -/* Apply convergence tests */ - if (idir == 1) { - -/* Run convergence test in forward direction */ -/* First apply standard test to bottom of matrix */ - - if ((d__2 = e[m - 1], abs(d__2)) <= abs(tol) * (d__1 = d__[m], abs( - d__1)) || tol < 0. && (d__3 = e[m - 1], abs(d__3)) <= thresh) - { + if ((d__2 = e[m - 1], abs(d__2)) <= abs(tol) * (d__1 = d__[m], abs(d__1)) || + tol < 0. && (d__3 = e[m - 1], abs(d__3)) <= thresh) { e[m - 1] = 0.; goto L60; } - if (tol >= 0.) { - -/* If relative accuracy desired, */ -/* apply convergence criterion forward */ - mu = (d__1 = d__[ll], abs(d__1)); sminl = mu; i__1 = m - 1; @@ -657,29 +250,17 @@ L90: e[lll] = 0.; goto L60; } - mu = (d__2 = d__[lll + 1], abs(d__2)) * (mu / (mu + (d__1 = e[ - lll], abs(d__1)))); - sminl = min(sminl,mu); -/* L100: */ + mu = (d__2 = d__[lll + 1], abs(d__2)) * (mu / (mu + (d__1 = e[lll], abs(d__1)))); + sminl = min(sminl, mu); } } - } else { - -/* Run convergence test in backward direction */ -/* First apply standard test to top of matrix */ - - if ((d__2 = e[ll], abs(d__2)) <= abs(tol) * (d__1 = d__[ll], abs(d__1) - ) || tol < 0. && (d__3 = e[ll], abs(d__3)) <= thresh) { + if ((d__2 = e[ll], abs(d__2)) <= abs(tol) * (d__1 = d__[ll], abs(d__1)) || + tol < 0. && (d__3 = e[ll], abs(d__3)) <= thresh) { e[ll] = 0.; goto L60; } - if (tol >= 0.) { - -/* If relative accuracy desired, */ -/* apply convergence criterion backward */ - mu = (d__1 = d__[m], abs(d__1)); sminl = mu; i__1 = ll; @@ -688,30 +269,17 @@ L90: e[lll] = 0.; goto L60; } - mu = (d__2 = d__[lll], abs(d__2)) * (mu / (mu + (d__1 = e[lll] - , abs(d__1)))); - sminl = min(sminl,mu); -/* L110: */ + mu = (d__2 = d__[lll], abs(d__2)) * (mu / (mu + (d__1 = e[lll], abs(d__1)))); + sminl = min(sminl, mu); } } } oldll = ll; oldm = m; - -/* Compute shift. First, test if shifting would ruin relative */ -/* accuracy, and if so set the shift to zero. */ - -/* Computing MAX */ d__1 = eps, d__2 = tol * .01; - if (tol >= 0. && *n * tol * (sminl / smax) <= max(d__1,d__2)) { - -/* Use a zero shift to avoid loss of relative accuracy */ - + if (tol >= 0. && *n * tol * (sminl / smax) <= max(d__1, d__2)) { shift = 0.; } else { - -/* Compute the shift from 2-by-2 block at end of matrix */ - if (idir == 1) { sll = (d__1 = d__[ll], abs(d__1)); dlas2_(&d__[m - 1], &e[m - 1], &d__[m], &shift, &r__); @@ -719,30 +287,16 @@ L90: sll = (d__1 = d__[m], abs(d__1)); dlas2_(&d__[ll], &e[ll], &d__[ll + 1], &shift, &r__); } - -/* Test if shift negligible, and if so set to zero */ - if (sll > 0.) { -/* Computing 2nd power */ d__1 = shift / sll; if (d__1 * d__1 < eps) { shift = 0.; } } } - -/* Increment iteration count */ - iter = iter + m - ll; - -/* If SHIFT = 0, do simplified QR iteration */ - if (shift == 0.) { if (idir == 1) { - -/* Chase bulge from top to bottom */ -/* Save cosines and sines for later singular vector updates */ - cs = 1.; oldcs = 1.; i__1 = m - 1; @@ -759,43 +313,29 @@ L90: work[i__ - ll + 1 + nm1] = sn; work[i__ - ll + 1 + nm12] = oldcs; work[i__ - ll + 1 + nm13] = oldsn; -/* L120: */ } h__ = d__[m] * cs; d__[m] = h__ * oldcs; e[m - 1] = h__ * oldsn; - -/* Update singular vectors */ - if (*ncvt > 0) { i__1 = m - ll + 1; - dlasr_((char *)"L", (char *)"V", (char *)"F", &i__1, ncvt, &work[1], &work[*n], &vt[ - ll + vt_dim1], ldvt, (ftnlen)1, (ftnlen)1, (ftnlen)1); + dlasr_((char *)"L", (char *)"V", (char *)"F", &i__1, ncvt, &work[1], &work[*n], &vt[ll + vt_dim1], ldvt, + (ftnlen)1, (ftnlen)1, (ftnlen)1); } if (*nru > 0) { i__1 = m - ll + 1; - dlasr_((char *)"R", (char *)"V", (char *)"F", nru, &i__1, &work[nm12 + 1], &work[nm13 - + 1], &u[ll * u_dim1 + 1], ldu, (ftnlen)1, (ftnlen)1, - (ftnlen)1); + dlasr_((char *)"R", (char *)"V", (char *)"F", nru, &i__1, &work[nm12 + 1], &work[nm13 + 1], + &u[ll * u_dim1 + 1], ldu, (ftnlen)1, (ftnlen)1, (ftnlen)1); } if (*ncc > 0) { i__1 = m - ll + 1; - dlasr_((char *)"L", (char *)"V", (char *)"F", &i__1, ncc, &work[nm12 + 1], &work[nm13 - + 1], &c__[ll + c_dim1], ldc, (ftnlen)1, (ftnlen)1, ( - ftnlen)1); + dlasr_((char *)"L", (char *)"V", (char *)"F", &i__1, ncc, &work[nm12 + 1], &work[nm13 + 1], + &c__[ll + c_dim1], ldc, (ftnlen)1, (ftnlen)1, (ftnlen)1); } - -/* Test convergence */ - if ((d__1 = e[m - 1], abs(d__1)) <= thresh) { e[m - 1] = 0.; } - } else { - -/* Chase bulge from bottom to top */ -/* Save cosines and sines for later singular vector updates */ - cs = 1.; oldcs = 1.; i__1 = ll + 1; @@ -812,48 +352,33 @@ L90: work[i__ - ll + nm1] = -sn; work[i__ - ll + nm12] = oldcs; work[i__ - ll + nm13] = -oldsn; -/* L130: */ } h__ = d__[ll] * cs; d__[ll] = h__ * oldcs; e[ll] = h__ * oldsn; - -/* Update singular vectors */ - if (*ncvt > 0) { i__1 = m - ll + 1; - dlasr_((char *)"L", (char *)"V", (char *)"B", &i__1, ncvt, &work[nm12 + 1], &work[ - nm13 + 1], &vt[ll + vt_dim1], ldvt, (ftnlen)1, ( - ftnlen)1, (ftnlen)1); + dlasr_((char *)"L", (char *)"V", (char *)"B", &i__1, ncvt, &work[nm12 + 1], &work[nm13 + 1], + &vt[ll + vt_dim1], ldvt, (ftnlen)1, (ftnlen)1, (ftnlen)1); } if (*nru > 0) { i__1 = m - ll + 1; - dlasr_((char *)"R", (char *)"V", (char *)"B", nru, &i__1, &work[1], &work[*n], &u[ll * - u_dim1 + 1], ldu, (ftnlen)1, (ftnlen)1, (ftnlen)1); + dlasr_((char *)"R", (char *)"V", (char *)"B", nru, &i__1, &work[1], &work[*n], &u[ll * u_dim1 + 1], ldu, + (ftnlen)1, (ftnlen)1, (ftnlen)1); } if (*ncc > 0) { i__1 = m - ll + 1; - dlasr_((char *)"L", (char *)"V", (char *)"B", &i__1, ncc, &work[1], &work[*n], &c__[ - ll + c_dim1], ldc, (ftnlen)1, (ftnlen)1, (ftnlen)1); + dlasr_((char *)"L", (char *)"V", (char *)"B", &i__1, ncc, &work[1], &work[*n], &c__[ll + c_dim1], ldc, + (ftnlen)1, (ftnlen)1, (ftnlen)1); } - -/* Test convergence */ - if ((d__1 = e[ll], abs(d__1)) <= thresh) { e[ll] = 0.; } } } else { - -/* Use nonzero shift */ - if (idir == 1) { - -/* Chase bulge from top to bottom */ -/* Save cosines and sines for later singular vector updates */ - - f = ((d__1 = d__[ll], abs(d__1)) - shift) * (d_lmp_sign(&c_b49, &d__[ - ll]) + shift / d__[ll]); + f = ((d__1 = d__[ll], abs(d__1)) - shift) * + (d_lmp_sign(&c_b49, &d__[ll]) + shift / d__[ll]); g = e[ll]; i__1 = m - 1; for (i__ = ll; i__ <= i__1; ++i__) { @@ -877,43 +402,28 @@ L90: work[i__ - ll + 1 + nm1] = sinr; work[i__ - ll + 1 + nm12] = cosl; work[i__ - ll + 1 + nm13] = sinl; -/* L140: */ } e[m - 1] = f; - -/* Update singular vectors */ - if (*ncvt > 0) { i__1 = m - ll + 1; - dlasr_((char *)"L", (char *)"V", (char *)"F", &i__1, ncvt, &work[1], &work[*n], &vt[ - ll + vt_dim1], ldvt, (ftnlen)1, (ftnlen)1, (ftnlen)1); + dlasr_((char *)"L", (char *)"V", (char *)"F", &i__1, ncvt, &work[1], &work[*n], &vt[ll + vt_dim1], ldvt, + (ftnlen)1, (ftnlen)1, (ftnlen)1); } if (*nru > 0) { i__1 = m - ll + 1; - dlasr_((char *)"R", (char *)"V", (char *)"F", nru, &i__1, &work[nm12 + 1], &work[nm13 - + 1], &u[ll * u_dim1 + 1], ldu, (ftnlen)1, (ftnlen)1, - (ftnlen)1); + dlasr_((char *)"R", (char *)"V", (char *)"F", nru, &i__1, &work[nm12 + 1], &work[nm13 + 1], + &u[ll * u_dim1 + 1], ldu, (ftnlen)1, (ftnlen)1, (ftnlen)1); } if (*ncc > 0) { i__1 = m - ll + 1; - dlasr_((char *)"L", (char *)"V", (char *)"F", &i__1, ncc, &work[nm12 + 1], &work[nm13 - + 1], &c__[ll + c_dim1], ldc, (ftnlen)1, (ftnlen)1, ( - ftnlen)1); + dlasr_((char *)"L", (char *)"V", (char *)"F", &i__1, ncc, &work[nm12 + 1], &work[nm13 + 1], + &c__[ll + c_dim1], ldc, (ftnlen)1, (ftnlen)1, (ftnlen)1); } - -/* Test convergence */ - if ((d__1 = e[m - 1], abs(d__1)) <= thresh) { e[m - 1] = 0.; } - } else { - -/* Chase bulge from bottom to top */ -/* Save cosines and sines for later singular vector updates */ - - f = ((d__1 = d__[m], abs(d__1)) - shift) * (d_lmp_sign(&c_b49, &d__[m] - ) + shift / d__[m]); + f = ((d__1 = d__[m], abs(d__1)) - shift) * (d_lmp_sign(&c_b49, &d__[m]) + shift / d__[m]); g = e[m - 1]; i__1 = ll + 1; for (i__ = m; i__ >= i__1; --i__) { @@ -937,66 +447,41 @@ L90: work[i__ - ll + nm1] = -sinr; work[i__ - ll + nm12] = cosl; work[i__ - ll + nm13] = -sinl; -/* L150: */ } e[ll] = f; - -/* Test convergence */ - if ((d__1 = e[ll], abs(d__1)) <= thresh) { e[ll] = 0.; } - -/* Update singular vectors if desired */ - if (*ncvt > 0) { i__1 = m - ll + 1; - dlasr_((char *)"L", (char *)"V", (char *)"B", &i__1, ncvt, &work[nm12 + 1], &work[ - nm13 + 1], &vt[ll + vt_dim1], ldvt, (ftnlen)1, ( - ftnlen)1, (ftnlen)1); + dlasr_((char *)"L", (char *)"V", (char *)"B", &i__1, ncvt, &work[nm12 + 1], &work[nm13 + 1], + &vt[ll + vt_dim1], ldvt, (ftnlen)1, (ftnlen)1, (ftnlen)1); } if (*nru > 0) { i__1 = m - ll + 1; - dlasr_((char *)"R", (char *)"V", (char *)"B", nru, &i__1, &work[1], &work[*n], &u[ll * - u_dim1 + 1], ldu, (ftnlen)1, (ftnlen)1, (ftnlen)1); + dlasr_((char *)"R", (char *)"V", (char *)"B", nru, &i__1, &work[1], &work[*n], &u[ll * u_dim1 + 1], ldu, + (ftnlen)1, (ftnlen)1, (ftnlen)1); } if (*ncc > 0) { i__1 = m - ll + 1; - dlasr_((char *)"L", (char *)"V", (char *)"B", &i__1, ncc, &work[1], &work[*n], &c__[ - ll + c_dim1], ldc, (ftnlen)1, (ftnlen)1, (ftnlen)1); + dlasr_((char *)"L", (char *)"V", (char *)"B", &i__1, ncc, &work[1], &work[*n], &c__[ll + c_dim1], ldc, + (ftnlen)1, (ftnlen)1, (ftnlen)1); } } } - -/* QR iteration finished, go back and check convergence */ - goto L60; - -/* All singular values converged, so make them positive */ - L160: i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { if (d__[i__] < 0.) { d__[i__] = -d__[i__]; - -/* Change sign of singular vectors, if desired */ - if (*ncvt > 0) { dscal_(ncvt, &c_b72, &vt[i__ + vt_dim1], ldvt); } } -/* L170: */ } - -/* Sort the singular values into decreasing order (insertion sort on */ -/* singular values, but only one transposition per singular vector) */ - i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { - -/* Scan for smallest D(I) */ - isub = 1; smin = d__[1]; i__2 = *n + 1 - i__; @@ -1005,33 +490,22 @@ L160: isub = j; smin = d__[j]; } -/* L180: */ } if (isub != *n + 1 - i__) { - -/* Swap singular values and vectors */ - d__[isub] = d__[*n + 1 - i__]; d__[*n + 1 - i__] = smin; if (*ncvt > 0) { - dswap_(ncvt, &vt[isub + vt_dim1], ldvt, &vt[*n + 1 - i__ + - vt_dim1], ldvt); + dswap_(ncvt, &vt[isub + vt_dim1], ldvt, &vt[*n + 1 - i__ + vt_dim1], ldvt); } if (*nru > 0) { - dswap_(nru, &u[isub * u_dim1 + 1], &c__1, &u[(*n + 1 - i__) * - u_dim1 + 1], &c__1); + dswap_(nru, &u[isub * u_dim1 + 1], &c__1, &u[(*n + 1 - i__) * u_dim1 + 1], &c__1); } if (*ncc > 0) { - dswap_(ncc, &c__[isub + c_dim1], ldc, &c__[*n + 1 - i__ + - c_dim1], ldc); + dswap_(ncc, &c__[isub + c_dim1], ldc, &c__[*n + 1 - i__ + c_dim1], ldc); } } -/* L190: */ } goto L220; - -/* Maximum number of iterations exceeded, failure to converge */ - L200: *info = 0; i__1 = *n - 1; @@ -1039,15 +513,10 @@ L200: if (e[i__] != 0.) { ++(*info); } -/* L210: */ } L220: return 0; - -/* End of DBDSQR */ - -} /* dbdsqr_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dcabs1.cpp b/lib/linalg/dcabs1.cpp index 54b2b57eab..83332f3177 100644 --- a/lib/linalg/dcabs1.cpp +++ b/lib/linalg/dcabs1.cpp @@ -1,92 +1,14 @@ -/* fortran/dcabs1.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DCABS1 */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* DOUBLE PRECISION FUNCTION DCABS1(Z) */ - -/* .. Scalar Arguments .. */ -/* COMPLEX*16 Z */ -/* .. */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DCABS1 computes |Re(.)| + |Im(.)| of a double complex number */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] Z */ -/* > \verbatim */ -/* > Z is COMPLEX*16 */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup double_blas_level1 */ - -/* ===================================================================== */ doublereal dcabs1_(doublecomplex *z__) { - /* System generated locals */ doublereal ret_val, d__1, d__2; - - /* Builtin functions */ double d_lmp_imag(doublecomplex *); - - -/* -- Reference BLAS level1 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. */ -/* ===================================================================== */ - -/* .. Intrinsic Functions .. */ - ret_val = (d__1 = z__->r, abs(d__1)) + (d__2 = d_lmp_imag(z__), abs(d__2)); return ret_val; - -/* End of DCABS1 */ - -} /* dcabs1_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dcopy.cpp b/lib/linalg/dcopy.cpp index dceb6ad727..1a7d65fc23 100644 --- a/lib/linalg/dcopy.cpp +++ b/lib/linalg/dcopy.cpp @@ -1,140 +1,17 @@ -/* fortran/dcopy.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DCOPY */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DCOPY(N,DX,INCX,DY,INCY) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INCX,INCY,N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION DX(*),DY(*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DCOPY copies a vector, x, to a vector, y. */ -/* > uses unrolled loops for increments equal to 1. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > number of elements in input vector(s) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DX */ -/* > \verbatim */ -/* > DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > storage spacing between elements of DX */ -/* > \endverbatim */ -/* > */ -/* > \param[out] DY */ -/* > \verbatim */ -/* > DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCY */ -/* > \verbatim */ -/* > INCY is INTEGER */ -/* > storage spacing between elements of DY */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup double_blas_level1 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > jack dongarra, linpack, 3/11/78. */ -/* > modified 12/3/93, array(1) declarations changed to array(*) */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dcopy_(integer *n, doublereal *dx, integer *incx, - doublereal *dy, integer *incy) +int dcopy_(integer *n, doublereal *dx, integer *incx, doublereal *dy, integer *incy) { - /* System generated locals */ integer i__1; - - /* Local variables */ integer i__, m, ix, iy, mp1; - - -/* -- Reference BLAS level1 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Local Scalars .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ - /* Parameter adjustments */ --dy; --dx; - - /* Function Body */ if (*n <= 0) { return 0; } if (*incx == 1 && *incy == 1) { - -/* code for both increments equal to 1 */ - - -/* clean-up loop */ - m = *n % 7; if (m != 0) { i__1 = m; @@ -157,10 +34,6 @@ extern "C" { dy[i__ + 6] = dx[i__ + 6]; } } else { - -/* code for unequal increments or equal increments */ -/* not equal to 1 */ - ix = 1; iy = 1; if (*incx < 0) { @@ -177,11 +50,7 @@ extern "C" { } } return 0; - -/* End of DCOPY */ - -} /* dcopy_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/ddot.cpp b/lib/linalg/ddot.cpp index e2319f6803..58a7075238 100644 --- a/lib/linalg/ddot.cpp +++ b/lib/linalg/ddot.cpp @@ -1,144 +1,21 @@ -/* fortran/ddot.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DDOT */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* DOUBLE PRECISION FUNCTION DDOT(N,DX,INCX,DY,INCY) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INCX,INCY,N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION DX(*),DY(*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DDOT forms the dot product of two vectors. */ -/* > uses unrolled loops for increments equal to one. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > number of elements in input vector(s) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DX */ -/* > \verbatim */ -/* > DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > storage spacing between elements of DX */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DY */ -/* > \verbatim */ -/* > DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCY */ -/* > \verbatim */ -/* > INCY is INTEGER */ -/* > storage spacing between elements of DY */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup double_blas_level1 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > jack dongarra, linpack, 3/11/78. */ -/* > modified 12/3/93, array(1) declarations changed to array(*) */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -doublereal ddot_(integer *n, doublereal *dx, integer *incx, doublereal *dy, - integer *incy) +doublereal ddot_(integer *n, doublereal *dx, integer *incx, doublereal *dy, integer *incy) { - /* System generated locals */ integer i__1; doublereal ret_val; - - /* Local variables */ integer i__, m, ix, iy, mp1; doublereal dtemp; - - -/* -- Reference BLAS level1 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Local Scalars .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ - /* Parameter adjustments */ --dy; --dx; - - /* Function Body */ ret_val = 0.; dtemp = 0.; if (*n <= 0) { return ret_val; } if (*incx == 1 && *incy == 1) { - -/* code for both increments equal to 1 */ - - -/* clean-up loop */ - m = *n % 5; if (m != 0) { i__1 = m; @@ -158,10 +35,6 @@ doublereal ddot_(integer *n, doublereal *dx, integer *incx, doublereal *dy, dx[i__ + 4] * dy[i__ + 4]; } } else { - -/* code for unequal increments or equal increments */ -/* not equal to 1 */ - ix = 1; iy = 1; if (*incx < 0) { @@ -179,11 +52,7 @@ doublereal ddot_(integer *n, doublereal *dx, integer *incx, doublereal *dy, } ret_val = dtemp; return ret_val; - -/* End of DDOT */ - -} /* ddot_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dgebd2.cpp b/lib/linalg/dgebd2.cpp index 8c95869e21..ea2ff1bce9 100644 --- a/lib/linalg/dgebd2.cpp +++ b/lib/linalg/dgebd2.cpp @@ -1,254 +1,17 @@ -/* fortran/dgebd2.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; - -/* > \brief \b DGEBD2 reduces a general matrix to bidiagonal form using an unblocked algorithm. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DGEBD2 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DGEBD2( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INFO, LDA, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), TAUP( * ), */ -/* $ TAUQ( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DGEBD2 reduces a real general m by n matrix A to upper or lower */ -/* > bidiagonal form B by an orthogonal transformation: Q**T * A * P = B. */ -/* > */ -/* > If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows in the matrix A. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns in the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On entry, the m by n general matrix to be reduced. */ -/* > On exit, */ -/* > if m >= n, the diagonal and the first superdiagonal are */ -/* > overwritten with the upper bidiagonal matrix B; the */ -/* > elements below the diagonal, with the array TAUQ, represent */ -/* > the orthogonal matrix Q as a product of elementary */ -/* > reflectors, and the elements above the first superdiagonal, */ -/* > with the array TAUP, represent the orthogonal matrix P as */ -/* > a product of elementary reflectors; */ -/* > if m < n, the diagonal and the first subdiagonal are */ -/* > overwritten with the lower bidiagonal matrix B; the */ -/* > elements below the first subdiagonal, with the array TAUQ, */ -/* > represent the orthogonal matrix Q as a product of */ -/* > elementary reflectors, and the elements above the diagonal, */ -/* > with the array TAUP, represent the orthogonal matrix P as */ -/* > a product of elementary reflectors. */ -/* > See Further Details. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension (min(M,N)) */ -/* > The diagonal elements of the bidiagonal matrix B: */ -/* > D(i) = A(i,i). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] E */ -/* > \verbatim */ -/* > E is DOUBLE PRECISION array, dimension (min(M,N)-1) */ -/* > The off-diagonal elements of the bidiagonal matrix B: */ -/* > if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1; */ -/* > if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] TAUQ */ -/* > \verbatim */ -/* > TAUQ is DOUBLE PRECISION array, dimension (min(M,N)) */ -/* > The scalar factors of the elementary reflectors which */ -/* > represent the orthogonal matrix Q. See Further Details. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] TAUP */ -/* > \verbatim */ -/* > TAUP is DOUBLE PRECISION array, dimension (min(M,N)) */ -/* > The scalar factors of the elementary reflectors which */ -/* > represent the orthogonal matrix P. See Further Details. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (max(M,N)) */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit. */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleGEcomputational */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > The matrices Q and P are represented as products of elementary */ -/* > reflectors: */ -/* > */ -/* > If m >= n, */ -/* > */ -/* > Q = H(1) H(2) . . . H(n) and P = G(1) G(2) . . . G(n-1) */ -/* > */ -/* > Each H(i) and G(i) has the form: */ -/* > */ -/* > H(i) = I - tauq * v * v**T and G(i) = I - taup * u * u**T */ -/* > */ -/* > where tauq and taup are real scalars, and v and u are real vectors; */ -/* > v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in A(i+1:m,i); */ -/* > u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in A(i,i+2:n); */ -/* > tauq is stored in TAUQ(i) and taup in TAUP(i). */ -/* > */ -/* > If m < n, */ -/* > */ -/* > Q = H(1) H(2) . . . H(m-1) and P = G(1) G(2) . . . G(m) */ -/* > */ -/* > Each H(i) and G(i) has the form: */ -/* > */ -/* > H(i) = I - tauq * v * v**T and G(i) = I - taup * u * u**T */ -/* > */ -/* > where tauq and taup are real scalars, and v and u are real vectors; */ -/* > v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i); */ -/* > u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n); */ -/* > tauq is stored in TAUQ(i) and taup in TAUP(i). */ -/* > */ -/* > The contents of A on exit are illustrated by the following examples: */ -/* > */ -/* > m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n): */ -/* > */ -/* > ( d e u1 u1 u1 ) ( d u1 u1 u1 u1 u1 ) */ -/* > ( v1 d e u2 u2 ) ( e d u2 u2 u2 u2 ) */ -/* > ( v1 v2 d e u3 ) ( v1 e d u3 u3 u3 ) */ -/* > ( v1 v2 v3 d e ) ( v1 v2 e d u4 u4 ) */ -/* > ( v1 v2 v3 v4 d ) ( v1 v2 v3 e d u5 ) */ -/* > ( v1 v2 v3 v4 v5 ) */ -/* > */ -/* > where d and e denote diagonal and off-diagonal elements of B, vi */ -/* > denotes an element of the vector defining H(i), and ui an element of */ -/* > the vector defining G(i). */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dgebd2_(integer *m, integer *n, doublereal *a, integer * - lda, doublereal *d__, doublereal *e, doublereal *tauq, doublereal * - taup, doublereal *work, integer *info) +int dgebd2_(integer *m, integer *n, doublereal *a, integer *lda, doublereal *d__, doublereal *e, + doublereal *tauq, doublereal *taup, doublereal *work, integer *info) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; - - /* Local variables */ integer i__; - extern /* Subroutine */ int dlarf_(char *, integer *, integer *, - doublereal *, integer *, doublereal *, doublereal *, integer *, - doublereal *, ftnlen), dlarfg_(integer *, doublereal *, - doublereal *, integer *, doublereal *), xerbla_(char *, integer *, - ftnlen); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters */ - - /* Parameter adjustments */ + extern int dlarf_(char *, integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, doublereal *, ftnlen), + dlarfg_(integer *, doublereal *, doublereal *, integer *, doublereal *), + xerbla_(char *, integer *, ftnlen); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; @@ -257,14 +20,12 @@ f"> */ --tauq; --taup; --work; - - /* Function Body */ *info = 0; if (*m < 0) { *info = -1; } else if (*n < 0) { *info = -2; - } else if (*lda < max(1,*m)) { + } else if (*lda < max(1, *m)) { *info = -4; } if (*info < 0) { @@ -272,122 +33,73 @@ f"> */ xerbla_((char *)"DGEBD2", &i__1, (ftnlen)6); return 0; } - if (*m >= *n) { - -/* Reduce to upper bidiagonal form */ - i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { - -/* Generate elementary reflector H(i) to annihilate A(i+1:m,i) */ - i__2 = *m - i__ + 1; -/* Computing MIN */ i__3 = i__ + 1; - dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[min(i__3,*m) + i__ * - a_dim1], &c__1, &tauq[i__]); + dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[min(i__3, *m) + i__ * a_dim1], &c__1, + &tauq[i__]); d__[i__] = a[i__ + i__ * a_dim1]; a[i__ + i__ * a_dim1] = 1.; - -/* Apply H(i) to A(i:m,i+1:n) from the left */ - if (i__ < *n) { i__2 = *m - i__ + 1; i__3 = *n - i__; - dlarf_((char *)"Left", &i__2, &i__3, &a[i__ + i__ * a_dim1], &c__1, & - tauq[i__], &a[i__ + (i__ + 1) * a_dim1], lda, &work[1] - , (ftnlen)4); + dlarf_((char *)"Left", &i__2, &i__3, &a[i__ + i__ * a_dim1], &c__1, &tauq[i__], + &a[i__ + (i__ + 1) * a_dim1], lda, &work[1], (ftnlen)4); } a[i__ + i__ * a_dim1] = d__[i__]; - if (i__ < *n) { - -/* Generate elementary reflector G(i) to annihilate */ -/* A(i,i+2:n) */ - i__2 = *n - i__; -/* Computing MIN */ i__3 = i__ + 2; - dlarfg_(&i__2, &a[i__ + (i__ + 1) * a_dim1], &a[i__ + min( - i__3,*n) * a_dim1], lda, &taup[i__]); + dlarfg_(&i__2, &a[i__ + (i__ + 1) * a_dim1], &a[i__ + min(i__3, *n) * a_dim1], lda, + &taup[i__]); e[i__] = a[i__ + (i__ + 1) * a_dim1]; a[i__ + (i__ + 1) * a_dim1] = 1.; - -/* Apply G(i) to A(i+1:m,i+1:n) from the right */ - i__2 = *m - i__; i__3 = *n - i__; - dlarf_((char *)"Right", &i__2, &i__3, &a[i__ + (i__ + 1) * a_dim1], - lda, &taup[i__], &a[i__ + 1 + (i__ + 1) * a_dim1], - lda, &work[1], (ftnlen)5); + dlarf_((char *)"Right", &i__2, &i__3, &a[i__ + (i__ + 1) * a_dim1], lda, &taup[i__], + &a[i__ + 1 + (i__ + 1) * a_dim1], lda, &work[1], (ftnlen)5); a[i__ + (i__ + 1) * a_dim1] = e[i__]; } else { taup[i__] = 0.; } -/* L10: */ } } else { - -/* Reduce to lower bidiagonal form */ - i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { - -/* Generate elementary reflector G(i) to annihilate A(i,i+1:n) */ - i__2 = *n - i__ + 1; -/* Computing MIN */ i__3 = i__ + 1; - dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[i__ + min(i__3,*n) * - a_dim1], lda, &taup[i__]); + dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[i__ + min(i__3, *n) * a_dim1], lda, + &taup[i__]); d__[i__] = a[i__ + i__ * a_dim1]; a[i__ + i__ * a_dim1] = 1.; - -/* Apply G(i) to A(i+1:m,i:n) from the right */ - if (i__ < *m) { i__2 = *m - i__; i__3 = *n - i__ + 1; - dlarf_((char *)"Right", &i__2, &i__3, &a[i__ + i__ * a_dim1], lda, & - taup[i__], &a[i__ + 1 + i__ * a_dim1], lda, &work[1], - (ftnlen)5); + dlarf_((char *)"Right", &i__2, &i__3, &a[i__ + i__ * a_dim1], lda, &taup[i__], + &a[i__ + 1 + i__ * a_dim1], lda, &work[1], (ftnlen)5); } a[i__ + i__ * a_dim1] = d__[i__]; - if (i__ < *m) { - -/* Generate elementary reflector H(i) to annihilate */ -/* A(i+2:m,i) */ - i__2 = *m - i__; -/* Computing MIN */ i__3 = i__ + 2; - dlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3,*m) + - i__ * a_dim1], &c__1, &tauq[i__]); + dlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3, *m) + i__ * a_dim1], &c__1, + &tauq[i__]); e[i__] = a[i__ + 1 + i__ * a_dim1]; a[i__ + 1 + i__ * a_dim1] = 1.; - -/* Apply H(i) to A(i+1:m,i+1:n) from the left */ - i__2 = *m - i__; i__3 = *n - i__; - dlarf_((char *)"Left", &i__2, &i__3, &a[i__ + 1 + i__ * a_dim1], & - c__1, &tauq[i__], &a[i__ + 1 + (i__ + 1) * a_dim1], - lda, &work[1], (ftnlen)4); + dlarf_((char *)"Left", &i__2, &i__3, &a[i__ + 1 + i__ * a_dim1], &c__1, &tauq[i__], + &a[i__ + 1 + (i__ + 1) * a_dim1], lda, &work[1], (ftnlen)4); a[i__ + 1 + i__ * a_dim1] = e[i__]; } else { tauq[i__] = 0.; } -/* L20: */ } } return 0; - -/* End of DGEBD2 */ - -} /* dgebd2_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dgebrd.cpp b/lib/linalg/dgebrd.cpp index 0be33bde5c..d62e506c41 100644 --- a/lib/linalg/dgebrd.cpp +++ b/lib/linalg/dgebrd.cpp @@ -1,285 +1,32 @@ -/* fortran/dgebrd.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static integer c_n1 = -1; static integer c__3 = 3; static integer c__2 = 2; static doublereal c_b21 = -1.; static doublereal c_b22 = 1.; - -/* > \brief \b DGEBRD */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DGEBRD + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DGEBRD( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK, */ -/* INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INFO, LDA, LWORK, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), TAUP( * ), */ -/* $ TAUQ( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DGEBRD reduces a general real M-by-N matrix A to upper or lower */ -/* > bidiagonal form B by an orthogonal transformation: Q**T * A * P = B. */ -/* > */ -/* > If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows in the matrix A. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns in the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On entry, the M-by-N general matrix to be reduced. */ -/* > On exit, */ -/* > if m >= n, the diagonal and the first superdiagonal are */ -/* > overwritten with the upper bidiagonal matrix B; the */ -/* > elements below the diagonal, with the array TAUQ, represent */ -/* > the orthogonal matrix Q as a product of elementary */ -/* > reflectors, and the elements above the first superdiagonal, */ -/* > with the array TAUP, represent the orthogonal matrix P as */ -/* > a product of elementary reflectors; */ -/* > if m < n, the diagonal and the first subdiagonal are */ -/* > overwritten with the lower bidiagonal matrix B; the */ -/* > elements below the first subdiagonal, with the array TAUQ, */ -/* > represent the orthogonal matrix Q as a product of */ -/* > elementary reflectors, and the elements above the diagonal, */ -/* > with the array TAUP, represent the orthogonal matrix P as */ -/* > a product of elementary reflectors. */ -/* > See Further Details. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension (min(M,N)) */ -/* > The diagonal elements of the bidiagonal matrix B: */ -/* > D(i) = A(i,i). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] E */ -/* > \verbatim */ -/* > E is DOUBLE PRECISION array, dimension (min(M,N)-1) */ -/* > The off-diagonal elements of the bidiagonal matrix B: */ -/* > if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1; */ -/* > if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] TAUQ */ -/* > \verbatim */ -/* > TAUQ is DOUBLE PRECISION array, dimension (min(M,N)) */ -/* > The scalar factors of the elementary reflectors which */ -/* > represent the orthogonal matrix Q. See Further Details. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] TAUP */ -/* > \verbatim */ -/* > TAUP is DOUBLE PRECISION array, dimension (min(M,N)) */ -/* > The scalar factors of the elementary reflectors which */ -/* > represent the orthogonal matrix P. See Further Details. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ -/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LWORK */ -/* > \verbatim */ -/* > LWORK is INTEGER */ -/* > The length of the array WORK. LWORK >= max(1,M,N). */ -/* > For optimum performance LWORK >= (M+N)*NB, where NB */ -/* > is the optimal blocksize. */ -/* > */ -/* > If LWORK = -1, then a workspace query is assumed; the routine */ -/* > only calculates the optimal size of the WORK array, returns */ -/* > this value as the first entry of the WORK array, and no error */ -/* > message related to LWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleGEcomputational */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > The matrices Q and P are represented as products of elementary */ -/* > reflectors: */ -/* > */ -/* > If m >= n, */ -/* > */ -/* > Q = H(1) H(2) . . . H(n) and P = G(1) G(2) . . . G(n-1) */ -/* > */ -/* > Each H(i) and G(i) has the form: */ -/* > */ -/* > H(i) = I - tauq * v * v**T and G(i) = I - taup * u * u**T */ -/* > */ -/* > where tauq and taup are real scalars, and v and u are real vectors; */ -/* > v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in A(i+1:m,i); */ -/* > u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in A(i,i+2:n); */ -/* > tauq is stored in TAUQ(i) and taup in TAUP(i). */ -/* > */ -/* > If m < n, */ -/* > */ -/* > Q = H(1) H(2) . . . H(m-1) and P = G(1) G(2) . . . G(m) */ -/* > */ -/* > Each H(i) and G(i) has the form: */ -/* > */ -/* > H(i) = I - tauq * v * v**T and G(i) = I - taup * u * u**T */ -/* > */ -/* > where tauq and taup are real scalars, and v and u are real vectors; */ -/* > v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i); */ -/* > u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n); */ -/* > tauq is stored in TAUQ(i) and taup in TAUP(i). */ -/* > */ -/* > The contents of A on exit are illustrated by the following examples: */ -/* > */ -/* > m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n): */ -/* > */ -/* > ( d e u1 u1 u1 ) ( d u1 u1 u1 u1 u1 ) */ -/* > ( v1 d e u2 u2 ) ( e d u2 u2 u2 u2 ) */ -/* > ( v1 v2 d e u3 ) ( v1 e d u3 u3 u3 ) */ -/* > ( v1 v2 v3 d e ) ( v1 v2 e d u4 u4 ) */ -/* > ( v1 v2 v3 v4 d ) ( v1 v2 v3 e d u5 ) */ -/* > ( v1 v2 v3 v4 v5 ) */ -/* > */ -/* > where d and e denote diagonal and off-diagonal elements of B, vi */ -/* > denotes an element of the vector defining H(i), and ui an element of */ -/* > the vector defining G(i). */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dgebrd_(integer *m, integer *n, doublereal *a, integer * - lda, doublereal *d__, doublereal *e, doublereal *tauq, doublereal * - taup, doublereal *work, integer *lwork, integer *info) +int dgebrd_(integer *m, integer *n, doublereal *a, integer *lda, doublereal *d__, doublereal *e, + doublereal *tauq, doublereal *taup, doublereal *work, integer *lwork, integer *info) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4; - - /* Local variables */ integer i__, j, nb, nx, ws; - extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); + extern int dgemm_(char *, char *, integer *, integer *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, + ftnlen, ftnlen); integer nbmin, iinfo, minmn; - extern /* Subroutine */ int dgebd2_(integer *, integer *, doublereal *, - integer *, doublereal *, doublereal *, doublereal *, doublereal *, - doublereal *, integer *), dlabrd_(integer *, integer *, integer * - , doublereal *, integer *, doublereal *, doublereal *, doublereal - *, doublereal *, doublereal *, integer *, doublereal *, integer *) - , xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern int dgebd2_(integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *, integer *), + dlabrd_(integer *, integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, + integer *), + xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); integer ldwrkx, ldwrky, lwkopt; logical lquery; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; @@ -288,26 +35,21 @@ f"> */ --tauq; --taup; --work; - - /* Function Body */ *info = 0; -/* Computing MAX */ - i__1 = 1, i__2 = ilaenv_(&c__1, (char *)"DGEBRD", (char *)" ", m, n, &c_n1, &c_n1, ( - ftnlen)6, (ftnlen)1); - nb = max(i__1,i__2); + i__1 = 1, i__2 = ilaenv_(&c__1, (char *)"DGEBRD", (char *)" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); + nb = max(i__1, i__2); lwkopt = (*m + *n) * nb; - work[1] = (doublereal) lwkopt; + work[1] = (doublereal)lwkopt; lquery = *lwork == -1; if (*m < 0) { *info = -1; } else if (*n < 0) { *info = -2; - } else if (*lda < max(1,*m)) { + } else if (*lda < max(1, *m)) { *info = -4; - } else /* if(complicated condition) */ { -/* Computing MAX */ - i__1 = max(1,*m); - if (*lwork < max(i__1,*n) && ! lquery) { + } else { + i__1 = max(1, *m); + if (*lwork < max(i__1, *n) && !lquery) { *info = -10; } } @@ -318,39 +60,21 @@ f"> */ } else if (lquery) { return 0; } - -/* Quick return if possible */ - - minmn = min(*m,*n); + minmn = min(*m, *n); if (minmn == 0) { work[1] = 1.; return 0; } - - ws = max(*m,*n); + ws = max(*m, *n); ldwrkx = *m; ldwrky = *n; - if (nb > 1 && nb < minmn) { - -/* Set the crossover point NX. */ - -/* Computing MAX */ - i__1 = nb, i__2 = ilaenv_(&c__3, (char *)"DGEBRD", (char *)" ", m, n, &c_n1, &c_n1, ( - ftnlen)6, (ftnlen)1); - nx = max(i__1,i__2); - -/* Determine when to switch from blocked to unblocked code. */ - + i__1 = nb, i__2 = ilaenv_(&c__3, (char *)"DGEBRD", (char *)" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); + nx = max(i__1, i__2); if (nx < minmn) { ws = (*m + *n) * nb; if (*lwork < ws) { - -/* Not enough work space for the optimal NB, consider using */ -/* a smaller block size. */ - - nbmin = ilaenv_(&c__2, (char *)"DGEBRD", (char *)" ", m, n, &c_n1, &c_n1, ( - ftnlen)6, (ftnlen)1); + nbmin = ilaenv_(&c__2, (char *)"DGEBRD", (char *)" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); if (*lwork >= (*m + *n) * nbmin) { nb = *lwork / (*m + *n); } else { @@ -362,70 +86,44 @@ f"> */ } else { nx = minmn; } - i__1 = minmn - nx; i__2 = nb; for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { - -/* Reduce rows and columns i:i+nb-1 to bidiagonal form and return */ -/* the matrices X and Y which are needed to update the unreduced */ -/* part of the matrix */ - i__3 = *m - i__ + 1; i__4 = *n - i__ + 1; - dlabrd_(&i__3, &i__4, &nb, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[ - i__], &tauq[i__], &taup[i__], &work[1], &ldwrkx, &work[ldwrkx - * nb + 1], &ldwrky); - -/* Update the trailing submatrix A(i+nb:m,i+nb:n), using an update */ -/* of the form A := A - V*Y**T - X*U**T */ - + dlabrd_(&i__3, &i__4, &nb, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[i__], &tauq[i__], + &taup[i__], &work[1], &ldwrkx, &work[ldwrkx * nb + 1], &ldwrky); i__3 = *m - i__ - nb + 1; i__4 = *n - i__ - nb + 1; - dgemm_((char *)"No transpose", (char *)"Transpose", &i__3, &i__4, &nb, &c_b21, &a[i__ - + nb + i__ * a_dim1], lda, &work[ldwrkx * nb + nb + 1], & - ldwrky, &c_b22, &a[i__ + nb + (i__ + nb) * a_dim1], lda, ( - ftnlen)12, (ftnlen)9); + dgemm_((char *)"No transpose", (char *)"Transpose", &i__3, &i__4, &nb, &c_b21, &a[i__ + nb + i__ * a_dim1], + lda, &work[ldwrkx * nb + nb + 1], &ldwrky, &c_b22, + &a[i__ + nb + (i__ + nb) * a_dim1], lda, (ftnlen)12, (ftnlen)9); i__3 = *m - i__ - nb + 1; i__4 = *n - i__ - nb + 1; - dgemm_((char *)"No transpose", (char *)"No transpose", &i__3, &i__4, &nb, &c_b21, & - work[nb + 1], &ldwrkx, &a[i__ + (i__ + nb) * a_dim1], lda, & - c_b22, &a[i__ + nb + (i__ + nb) * a_dim1], lda, (ftnlen)12, ( - ftnlen)12); - -/* Copy diagonal and off-diagonal elements of B back into A */ - + dgemm_((char *)"No transpose", (char *)"No transpose", &i__3, &i__4, &nb, &c_b21, &work[nb + 1], &ldwrkx, + &a[i__ + (i__ + nb) * a_dim1], lda, &c_b22, &a[i__ + nb + (i__ + nb) * a_dim1], lda, + (ftnlen)12, (ftnlen)12); if (*m >= *n) { i__3 = i__ + nb - 1; for (j = i__; j <= i__3; ++j) { a[j + j * a_dim1] = d__[j]; a[j + (j + 1) * a_dim1] = e[j]; -/* L10: */ } } else { i__3 = i__ + nb - 1; for (j = i__; j <= i__3; ++j) { a[j + j * a_dim1] = d__[j]; a[j + 1 + j * a_dim1] = e[j]; -/* L20: */ } } -/* L30: */ } - -/* Use unblocked code to reduce the remainder of the matrix */ - i__2 = *m - i__ + 1; i__1 = *n - i__ + 1; - dgebd2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[i__], & - tauq[i__], &taup[i__], &work[1], &iinfo); - work[1] = (doublereal) ws; + dgebd2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[i__], &tauq[i__], &taup[i__], + &work[1], &iinfo); + work[1] = (doublereal)ws; return 0; - -/* End of DGEBRD */ - -} /* dgebrd_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dgecon.cpp b/lib/linalg/dgecon.cpp index 76a0186cc8..01604f5f5d 100644 --- a/lib/linalg/dgecon.cpp +++ b/lib/linalg/dgecon.cpp @@ -1,157 +1,13 @@ -/* fortran/dgecon.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; - -/* > \brief \b DGECON */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DGECON + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DGECON( NORM, N, A, LDA, ANORM, RCOND, WORK, IWORK, */ -/* INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER NORM */ -/* INTEGER INFO, LDA, N */ -/* DOUBLE PRECISION ANORM, RCOND */ -/* .. */ -/* .. Array Arguments .. */ -/* INTEGER IWORK( * ) */ -/* DOUBLE PRECISION A( LDA, * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DGECON estimates the reciprocal of the condition number of a general */ -/* > real matrix A, in either the 1-norm or the infinity-norm, using */ -/* > the LU factorization computed by DGETRF. */ -/* > */ -/* > An estimate is obtained for norm(inv(A)), and the reciprocal of the */ -/* > condition number is computed as */ -/* > RCOND = 1 / ( norm(A) * norm(inv(A)) ). */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] NORM */ -/* > \verbatim */ -/* > NORM is CHARACTER*1 */ -/* > Specifies whether the 1-norm condition number or the */ -/* > infinity-norm condition number is required: */ -/* > = '1' or 'O': 1-norm; */ -/* > = 'I': Infinity-norm. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > The factors L and U from the factorization A = P*L*U */ -/* > as computed by DGETRF. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] ANORM */ -/* > \verbatim */ -/* > ANORM is DOUBLE PRECISION */ -/* > If NORM = '1' or 'O', the 1-norm of the original matrix A. */ -/* > If NORM = 'I', the infinity-norm of the original matrix A. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] RCOND */ -/* > \verbatim */ -/* > RCOND is DOUBLE PRECISION */ -/* > The reciprocal of the condition number of the matrix A, */ -/* > computed as RCOND = 1/(norm(A) * norm(inv(A))). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (4*N) */ -/* > \endverbatim */ -/* > */ -/* > \param[out] IWORK */ -/* > \verbatim */ -/* > IWORK is INTEGER array, dimension (N) */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleGEcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dgecon_(char *norm, integer *n, doublereal *a, integer * - lda, doublereal *anorm, doublereal *rcond, doublereal *work, integer * - iwork, integer *info, ftnlen norm_len) +int dgecon_(char *norm, integer *n, doublereal *a, integer *lda, doublereal *anorm, + doublereal *rcond, doublereal *work, integer *iwork, integer *info, ftnlen norm_len) { - /* System generated locals */ integer a_dim1, a_offset, i__1; doublereal d__1; - - /* Local variables */ doublereal sl; integer ix; doublereal su; @@ -159,64 +15,31 @@ f"> */ doublereal scale; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer isave[3]; - extern /* Subroutine */ int drscl_(integer *, doublereal *, doublereal *, - integer *), dlacn2_(integer *, doublereal *, doublereal *, - integer *, doublereal *, integer *, integer *); + extern int drscl_(integer *, doublereal *, doublereal *, integer *), + dlacn2_(integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, + integer *); extern doublereal dlamch_(char *, ftnlen); extern integer idamax_(integer *, doublereal *, integer *); - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern int xerbla_(char *, integer *, ftnlen); doublereal ainvnm; - extern /* Subroutine */ int dlatrs_(char *, char *, char *, char *, - integer *, doublereal *, integer *, doublereal *, doublereal *, - doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + extern int dlatrs_(char *, char *, char *, char *, integer *, doublereal *, integer *, + doublereal *, doublereal *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, + ftnlen); logical onenrm; char normin[1]; doublereal smlnum; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. Local Arrays .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --work; --iwork; - - /* Function Body */ *info = 0; - onenrm = *(unsigned char *)norm == '1' || lsame_(norm, (char *)"O", (ftnlen)1, ( - ftnlen)1); - if (! onenrm && ! lsame_(norm, (char *)"I", (ftnlen)1, (ftnlen)1)) { + onenrm = *(unsigned char *)norm == '1' || lsame_(norm, (char *)"O", (ftnlen)1, (ftnlen)1); + if (!onenrm && !lsame_(norm, (char *)"I", (ftnlen)1, (ftnlen)1)) { *info = -1; } else if (*n < 0) { *info = -2; - } else if (*lda < max(1,*n)) { + } else if (*lda < max(1, *n)) { *info = -4; } else if (*anorm < 0.) { *info = -5; @@ -226,9 +49,6 @@ f"> */ xerbla_((char *)"DGECON", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - *rcond = 0.; if (*n == 0) { *rcond = 1.; @@ -236,11 +56,7 @@ f"> */ } else if (*anorm == 0.) { return 0; } - smlnum = dlamch_((char *)"Safe minimum", (ftnlen)12); - -/* Estimate the norm of inv(A). */ - ainvnm = 0.; *(unsigned char *)normin = 'N'; if (onenrm) { @@ -253,61 +69,33 @@ L10: dlacn2_(n, &work[*n + 1], &work[1], &iwork[1], &ainvnm, &kase, isave); if (kase != 0) { if (kase == kase1) { - -/* Multiply by inv(L). */ - - dlatrs_((char *)"Lower", (char *)"No transpose", (char *)"Unit", normin, n, &a[a_offset], - lda, &work[1], &sl, &work[(*n << 1) + 1], info, (ftnlen)5, - (ftnlen)12, (ftnlen)4, (ftnlen)1); - -/* Multiply by inv(U). */ - - dlatrs_((char *)"Upper", (char *)"No transpose", (char *)"Non-unit", normin, n, &a[ - a_offset], lda, &work[1], &su, &work[*n * 3 + 1], info, ( - ftnlen)5, (ftnlen)12, (ftnlen)8, (ftnlen)1); + dlatrs_((char *)"Lower", (char *)"No transpose", (char *)"Unit", normin, n, &a[a_offset], lda, &work[1], &sl, + &work[(*n << 1) + 1], info, (ftnlen)5, (ftnlen)12, (ftnlen)4, (ftnlen)1); + dlatrs_((char *)"Upper", (char *)"No transpose", (char *)"Non-unit", normin, n, &a[a_offset], lda, &work[1], + &su, &work[*n * 3 + 1], info, (ftnlen)5, (ftnlen)12, (ftnlen)8, (ftnlen)1); } else { - -/* Multiply by inv(U**T). */ - - dlatrs_((char *)"Upper", (char *)"Transpose", (char *)"Non-unit", normin, n, &a[a_offset], - lda, &work[1], &su, &work[*n * 3 + 1], info, (ftnlen)5, ( - ftnlen)9, (ftnlen)8, (ftnlen)1); - -/* Multiply by inv(L**T). */ - - dlatrs_((char *)"Lower", (char *)"Transpose", (char *)"Unit", normin, n, &a[a_offset], - lda, &work[1], &sl, &work[(*n << 1) + 1], info, (ftnlen)5, - (ftnlen)9, (ftnlen)4, (ftnlen)1); + dlatrs_((char *)"Upper", (char *)"Transpose", (char *)"Non-unit", normin, n, &a[a_offset], lda, &work[1], &su, + &work[*n * 3 + 1], info, (ftnlen)5, (ftnlen)9, (ftnlen)8, (ftnlen)1); + dlatrs_((char *)"Lower", (char *)"Transpose", (char *)"Unit", normin, n, &a[a_offset], lda, &work[1], &sl, + &work[(*n << 1) + 1], info, (ftnlen)5, (ftnlen)9, (ftnlen)4, (ftnlen)1); } - -/* Divide X by 1/(SL*SU) if doing so will not cause overflow. */ - scale = sl * su; *(unsigned char *)normin = 'Y'; if (scale != 1.) { ix = idamax_(n, &work[1], &c__1); - if (scale < (d__1 = work[ix], abs(d__1)) * smlnum || scale == 0.) - { + if (scale < (d__1 = work[ix], abs(d__1)) * smlnum || scale == 0.) { goto L20; } drscl_(n, &scale, &work[1], &c__1); } goto L10; } - -/* Compute the estimate of the reciprocal condition number. */ - if (ainvnm != 0.) { *rcond = 1. / ainvnm / *anorm; } - L20: return 0; - -/* End of DGECON */ - -} /* dgecon_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dgelq2.cpp b/lib/linalg/dgelq2.cpp index fec5ae2c50..dbb3e17a27 100644 --- a/lib/linalg/dgelq2.cpp +++ b/lib/linalg/dgelq2.cpp @@ -1,204 +1,28 @@ -/* fortran/dgelq2.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorit -hm. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DGELQ2 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DGELQ2( M, N, A, LDA, TAU, WORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INFO, LDA, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DGELQ2 computes an LQ factorization of a real m-by-n matrix A: */ -/* > */ -/* > A = ( L 0 ) * Q */ -/* > */ -/* > where: */ -/* > */ -/* > Q is a n-by-n orthogonal matrix; */ -/* > L is a lower-triangular m-by-m matrix; */ -/* > 0 is a m-by-(n-m) zero matrix, if m < n. */ -/* > */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix A. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On entry, the m by n matrix A. */ -/* > On exit, the elements on and below the diagonal of the array */ -/* > contain the m by min(m,n) lower trapezoidal matrix L (L is */ -/* > lower triangular if m <= n); the elements above the diagonal, */ -/* > with the array TAU, represent the orthogonal matrix Q as a */ -/* > product of elementary reflectors (see Further Details). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] TAU */ -/* > \verbatim */ -/* > TAU is DOUBLE PRECISION array, dimension (min(M,N)) */ -/* > The scalar factors of the elementary reflectors (see Further */ -/* > Details). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (M) */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleGEcomputational */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > The matrix Q is represented as a product of elementary reflectors */ -/* > */ -/* > Q = H(k) . . . H(2) H(1), where k = min(m,n). */ -/* > */ -/* > Each H(i) has the form */ -/* > */ -/* > H(i) = I - tau * v * v**T */ -/* > */ -/* > where tau is a real scalar, and v is a real vector with */ -/* > v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n), */ -/* > and tau in TAU(i). */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dgelq2_(integer *m, integer *n, doublereal *a, integer * - lda, doublereal *tau, doublereal *work, integer *info) +int dgelq2_(integer *m, integer *n, doublereal *a, integer *lda, doublereal *tau, doublereal *work, + integer *info) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; - - /* Local variables */ integer i__, k; doublereal aii; - extern /* Subroutine */ int dlarf_(char *, integer *, integer *, - doublereal *, integer *, doublereal *, doublereal *, integer *, - doublereal *, ftnlen), dlarfg_(integer *, doublereal *, - doublereal *, integer *, doublereal *), xerbla_(char *, integer *, - ftnlen); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments */ - - /* Parameter adjustments */ + extern int dlarf_(char *, integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, doublereal *, ftnlen), + dlarfg_(integer *, doublereal *, doublereal *, integer *, doublereal *), + xerbla_(char *, integer *, ftnlen); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --tau; --work; - - /* Function Body */ *info = 0; if (*m < 0) { *info = -1; } else if (*n < 0) { *info = -2; - } else if (*lda < max(1,*m)) { + } else if (*lda < max(1, *m)) { *info = -4; } if (*info != 0) { @@ -206,40 +30,24 @@ f"> */ xerbla_((char *)"DGELQ2", &i__1, (ftnlen)6); return 0; } - - k = min(*m,*n); - + k = min(*m, *n); i__1 = k; for (i__ = 1; i__ <= i__1; ++i__) { - -/* Generate elementary reflector H(i) to annihilate A(i,i+1:n) */ - i__2 = *n - i__ + 1; -/* Computing MIN */ i__3 = i__ + 1; - dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[i__ + min(i__3,*n) * a_dim1] - , lda, &tau[i__]); + dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[i__ + min(i__3, *n) * a_dim1], lda, &tau[i__]); if (i__ < *m) { - -/* Apply H(i) to A(i+1:m,i:n) from the right */ - aii = a[i__ + i__ * a_dim1]; a[i__ + i__ * a_dim1] = 1.; i__2 = *m - i__; i__3 = *n - i__ + 1; - dlarf_((char *)"Right", &i__2, &i__3, &a[i__ + i__ * a_dim1], lda, &tau[ - i__], &a[i__ + 1 + i__ * a_dim1], lda, &work[1], (ftnlen) - 5); + dlarf_((char *)"Right", &i__2, &i__3, &a[i__ + i__ * a_dim1], lda, &tau[i__], + &a[i__ + 1 + i__ * a_dim1], lda, &work[1], (ftnlen)5); a[i__ + i__ * a_dim1] = aii; } -/* L10: */ } return 0; - -/* End of DGELQ2 */ - -} /* dgelq2_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dgelqf.cpp b/lib/linalg/dgelqf.cpp index f6e60e5bcf..0d48361669 100644 --- a/lib/linalg/dgelqf.cpp +++ b/lib/linalg/dgelqf.cpp @@ -1,237 +1,45 @@ -/* fortran/dgelqf.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static integer c_n1 = -1; static integer c__3 = 3; static integer c__2 = 2; - -/* > \brief \b DGELQF */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DGELQF + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INFO, LDA, LWORK, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DGELQF computes an LQ factorization of a real M-by-N matrix A: */ -/* > */ -/* > A = ( L 0 ) * Q */ -/* > */ -/* > where: */ -/* > */ -/* > Q is a N-by-N orthogonal matrix; */ -/* > L is a lower-triangular M-by-M matrix; */ -/* > 0 is a M-by-(N-M) zero matrix, if M < N. */ -/* > */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix A. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On entry, the M-by-N matrix A. */ -/* > On exit, the elements on and below the diagonal of the array */ -/* > contain the m-by-min(m,n) lower trapezoidal matrix L (L is */ -/* > lower triangular if m <= n); the elements above the diagonal, */ -/* > with the array TAU, represent the orthogonal matrix Q as a */ -/* > product of elementary reflectors (see Further Details). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] TAU */ -/* > \verbatim */ -/* > TAU is DOUBLE PRECISION array, dimension (min(M,N)) */ -/* > The scalar factors of the elementary reflectors (see Further */ -/* > Details). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ -/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LWORK */ -/* > \verbatim */ -/* > LWORK is INTEGER */ -/* > The dimension of the array WORK. LWORK >= max(1,M). */ -/* > For optimum performance LWORK >= M*NB, where NB is the */ -/* > optimal blocksize. */ -/* > */ -/* > If LWORK = -1, then a workspace query is assumed; the routine */ -/* > only calculates the optimal size of the WORK array, returns */ -/* > this value as the first entry of the WORK array, and no error */ -/* > message related to LWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleGEcomputational */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > The matrix Q is represented as a product of elementary reflectors */ -/* > */ -/* > Q = H(k) . . . H(2) H(1), where k = min(m,n). */ -/* > */ -/* > Each H(i) has the form */ -/* > */ -/* > H(i) = I - tau * v * v**T */ -/* > */ -/* > where tau is a real scalar, and v is a real vector with */ -/* > v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n), */ -/* > and tau in TAU(i). */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dgelqf_(integer *m, integer *n, doublereal *a, integer * - lda, doublereal *tau, doublereal *work, integer *lwork, integer *info) +int dgelqf_(integer *m, integer *n, doublereal *a, integer *lda, doublereal *tau, doublereal *work, + integer *lwork, integer *info) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4; - - /* Local variables */ integer i__, k, ib, nb, nx, iws, nbmin, iinfo; - extern /* Subroutine */ int dgelq2_(integer *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *), dlarfb_(char *, - char *, char *, char *, integer *, integer *, integer *, - doublereal *, integer *, doublereal *, integer *, doublereal *, - integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, - ftnlen), dlarft_(char *, char *, integer *, integer *, doublereal - *, integer *, doublereal *, doublereal *, integer *, ftnlen, - ftnlen), xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern int dgelq2_(integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *), + dlarfb_(char *, char *, char *, char *, integer *, integer *, integer *, doublereal *, + integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, + integer *, ftnlen, ftnlen, ftnlen, ftnlen), + dlarft_(char *, char *, integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, ftnlen, ftnlen), + xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); integer ldwork, lwkopt; logical lquery; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --tau; --work; - - /* Function Body */ *info = 0; - nb = ilaenv_(&c__1, (char *)"DGELQF", (char *)" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen) - 1); + nb = ilaenv_(&c__1, (char *)"DGELQF", (char *)" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); lwkopt = *m * nb; - work[1] = (doublereal) lwkopt; + work[1] = (doublereal)lwkopt; lquery = *lwork == -1; if (*m < 0) { *info = -1; } else if (*n < 0) { *info = -2; - } else if (*lda < max(1,*m)) { + } else if (*lda < max(1, *m)) { *info = -4; - } else if (*lwork < max(1,*m) && ! lquery) { + } else if (*lwork < max(1, *m) && !lquery) { *info = -7; } if (*info != 0) { @@ -241,105 +49,58 @@ f"> */ } else if (lquery) { return 0; } - -/* Quick return if possible */ - - k = min(*m,*n); + k = min(*m, *n); if (k == 0) { work[1] = 1.; return 0; } - nbmin = 2; nx = 0; iws = *m; if (nb > 1 && nb < k) { - -/* Determine when to cross over from blocked to unblocked code. */ - -/* Computing MAX */ - i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"DGELQF", (char *)" ", m, n, &c_n1, &c_n1, ( - ftnlen)6, (ftnlen)1); - nx = max(i__1,i__2); + i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"DGELQF", (char *)" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); + nx = max(i__1, i__2); if (nx < k) { - -/* Determine if workspace is large enough for blocked code. */ - ldwork = *m; iws = ldwork * nb; if (*lwork < iws) { - -/* Not enough workspace to use optimal NB: reduce NB and */ -/* determine the minimum value of NB. */ - nb = *lwork / ldwork; -/* Computing MAX */ - i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DGELQF", (char *)" ", m, n, &c_n1, & - c_n1, (ftnlen)6, (ftnlen)1); - nbmin = max(i__1,i__2); + i__1 = 2, + i__2 = ilaenv_(&c__2, (char *)"DGELQF", (char *)" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); + nbmin = max(i__1, i__2); } } } - if (nb >= nbmin && nb < k && nx < k) { - -/* Use blocked code initially */ - i__1 = k - nx; i__2 = nb; for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { -/* Computing MIN */ i__3 = k - i__ + 1; - ib = min(i__3,nb); - -/* Compute the LQ factorization of the current block */ -/* A(i:i+ib-1,i:n) */ - + ib = min(i__3, nb); i__3 = *n - i__ + 1; - dgelq2_(&ib, &i__3, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[ - 1], &iinfo); + dgelq2_(&ib, &i__3, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[1], &iinfo); if (i__ + ib <= *m) { - -/* Form the triangular factor of the block reflector */ -/* H = H(i) H(i+1) . . . H(i+ib-1) */ - i__3 = *n - i__ + 1; - dlarft_((char *)"Forward", (char *)"Rowwise", &i__3, &ib, &a[i__ + i__ * - a_dim1], lda, &tau[i__], &work[1], &ldwork, (ftnlen)7, - (ftnlen)7); - -/* Apply H to A(i+ib:m,i:n) from the right */ - + dlarft_((char *)"Forward", (char *)"Rowwise", &i__3, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], + &work[1], &ldwork, (ftnlen)7, (ftnlen)7); i__3 = *m - i__ - ib + 1; i__4 = *n - i__ + 1; - dlarfb_((char *)"Right", (char *)"No transpose", (char *)"Forward", (char *)"Rowwise", &i__3, - &i__4, &ib, &a[i__ + i__ * a_dim1], lda, &work[1], & - ldwork, &a[i__ + ib + i__ * a_dim1], lda, &work[ib + - 1], &ldwork, (ftnlen)5, (ftnlen)12, (ftnlen)7, ( - ftnlen)7); + dlarfb_((char *)"Right", (char *)"No transpose", (char *)"Forward", (char *)"Rowwise", &i__3, &i__4, &ib, + &a[i__ + i__ * a_dim1], lda, &work[1], &ldwork, &a[i__ + ib + i__ * a_dim1], + lda, &work[ib + 1], &ldwork, (ftnlen)5, (ftnlen)12, (ftnlen)7, (ftnlen)7); } -/* L10: */ } } else { i__ = 1; } - -/* Use unblocked code to factor the last or only block. */ - if (i__ <= k) { i__2 = *m - i__ + 1; i__1 = *n - i__ + 1; - dgelq2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[1] - , &iinfo); + dgelq2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[1], &iinfo); } - - work[1] = (doublereal) iws; + work[1] = (doublereal)iws; return 0; - -/* End of DGELQF */ - -} /* dgelqf_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dgelsd.cpp b/lib/linalg/dgelsd.cpp index ffe7446f85..479d95dd61 100644 --- a/lib/linalg/dgelsd.cpp +++ b/lib/linalg/dgelsd.cpp @@ -1,322 +1,60 @@ -/* fortran/dgelsd.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__6 = 6; static integer c_n1 = -1; static integer c__9 = 9; static integer c__0 = 0; static integer c__1 = 1; static doublereal c_b82 = 0.; - -/* > \brief DGELSD computes the minimum-norm solution to a linear least squares problem for GE matrices */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DGELSD + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DGELSD( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, */ -/* WORK, LWORK, IWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS, RANK */ -/* DOUBLE PRECISION RCOND */ -/* .. */ -/* .. Array Arguments .. */ -/* INTEGER IWORK( * ) */ -/* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), S( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DGELSD computes the minimum-norm solution to a real linear least */ -/* > squares problem: */ -/* > minimize 2-norm(| b - A*x |) */ -/* > using the singular value decomposition (SVD) of A. A is an M-by-N */ -/* > matrix which may be rank-deficient. */ -/* > */ -/* > Several right hand side vectors b and solution vectors x can be */ -/* > handled in a single call; they are stored as the columns of the */ -/* > M-by-NRHS right hand side matrix B and the N-by-NRHS solution */ -/* > matrix X. */ -/* > */ -/* > The problem is solved in three steps: */ -/* > (1) Reduce the coefficient matrix A to bidiagonal form with */ -/* > Householder transformations, reducing the original problem */ -/* > into a (char *)"bidiagonal least squares problem" (BLS) */ -/* > (2) Solve the BLS using a divide and conquer approach. */ -/* > (3) Apply back all the Householder transformations to solve */ -/* > the original least squares problem. */ -/* > */ -/* > The effective rank of A is determined by treating as zero those */ -/* > singular values which are less than RCOND times the largest singular */ -/* > value. */ -/* > */ -/* > The divide and conquer algorithm makes very mild assumptions about */ -/* > floating point arithmetic. It will work on machines with a guard */ -/* > digit in add/subtract, or on those binary machines without guard */ -/* > digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */ -/* > Cray-2. It could conceivably fail on hexadecimal or decimal machines */ -/* > without guard digits, but we know of none. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of A. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] NRHS */ -/* > \verbatim */ -/* > NRHS is INTEGER */ -/* > The number of right hand sides, i.e., the number of columns */ -/* > of the matrices B and X. NRHS >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On entry, the M-by-N matrix A. */ -/* > On exit, A has been destroyed. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] B */ -/* > \verbatim */ -/* > B is DOUBLE PRECISION array, dimension (LDB,NRHS) */ -/* > On entry, the M-by-NRHS right hand side matrix B. */ -/* > On exit, B is overwritten by the N-by-NRHS solution */ -/* > matrix X. If m >= n and RANK = n, the residual */ -/* > sum-of-squares for the solution in the i-th column is given */ -/* > by the sum of squares of elements n+1:m in that column. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDB */ -/* > \verbatim */ -/* > LDB is INTEGER */ -/* > The leading dimension of the array B. LDB >= max(1,max(M,N)). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] S */ -/* > \verbatim */ -/* > S is DOUBLE PRECISION array, dimension (min(M,N)) */ -/* > The singular values of A in decreasing order. */ -/* > The condition number of A in the 2-norm = S(1)/S(min(m,n)). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] RCOND */ -/* > \verbatim */ -/* > RCOND is DOUBLE PRECISION */ -/* > RCOND is used to determine the effective rank of A. */ -/* > Singular values S(i) <= RCOND*S(1) are treated as zero. */ -/* > If RCOND < 0, machine precision is used instead. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] RANK */ -/* > \verbatim */ -/* > RANK is INTEGER */ -/* > The effective rank of A, i.e., the number of singular values */ -/* > which are greater than RCOND*S(1). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ -/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LWORK */ -/* > \verbatim */ -/* > LWORK is INTEGER */ -/* > The dimension of the array WORK. LWORK must be at least 1. */ -/* > The exact minimum amount of workspace needed depends on M, */ -/* > N and NRHS. As long as LWORK is at least */ -/* > 12*N + 2*N*SMLSIZ + 8*N*NLVL + N*NRHS + (SMLSIZ+1)**2, */ -/* > if M is greater than or equal to N or */ -/* > 12*M + 2*M*SMLSIZ + 8*M*NLVL + M*NRHS + (SMLSIZ+1)**2, */ -/* > if M is less than N, the code will execute correctly. */ -/* > SMLSIZ is returned by ILAENV and is equal to the maximum */ -/* > size of the subproblems at the bottom of the computation */ -/* > tree (usually about 25), and */ -/* > NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 ) */ -/* > For good performance, LWORK should generally be larger. */ -/* > */ -/* > If LWORK = -1, then a workspace query is assumed; the routine */ -/* > only calculates the optimal size of the WORK array, returns */ -/* > this value as the first entry of the WORK array, and no error */ -/* > message related to LWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] IWORK */ -/* > \verbatim */ -/* > IWORK is INTEGER array, dimension (MAX(1,LIWORK)) */ -/* > LIWORK >= max(1, 3 * MINMN * NLVL + 11 * MINMN), */ -/* > where MINMN = MIN( M,N ). */ -/* > On exit, if INFO = 0, IWORK(1) returns the minimum LIWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ -/* > > 0: the algorithm for computing the SVD failed to converge; */ -/* > if INFO = i, i off-diagonal elements of an intermediate */ -/* > bidiagonal form did not converge to zero. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleGEsolve */ - -/* > \par Contributors: */ -/* ================== */ -/* > */ -/* > Ming Gu and Ren-Cang Li, Computer Science Division, University of */ -/* > California at Berkeley, USA \n */ -/* > Osni Marques, LBNL/NERSC, USA \n */ - -/* ===================================================================== */ -/* Subroutine */ int dgelsd_(integer *m, integer *n, integer *nrhs, - doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal * - s, doublereal *rcond, integer *rank, doublereal *work, integer *lwork, - integer *iwork, integer *info) +int dgelsd_(integer *m, integer *n, integer *nrhs, doublereal *a, integer *lda, doublereal *b, + integer *ldb, doublereal *s, doublereal *rcond, integer *rank, doublereal *work, + integer *lwork, integer *iwork, integer *info) { - /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4; - - /* Builtin functions */ double log(doublereal); - - /* Local variables */ integer ie, il, mm; doublereal eps, anrm, bnrm; integer itau, nlvl, iascl, ibscl; doublereal sfmin; integer minmn, maxmn, itaup, itauq, mnthr, nwork; - extern /* Subroutine */ int dlabad_(doublereal *, doublereal *), dgebrd_( - integer *, integer *, doublereal *, integer *, doublereal *, - doublereal *, doublereal *, doublereal *, doublereal *, integer *, - integer *); - extern doublereal dlamch_(char *, ftnlen), dlange_(char *, integer *, - integer *, doublereal *, integer *, doublereal *, ftnlen); - extern /* Subroutine */ int dgelqf_(integer *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, integer *), - dlalsd_(char *, integer *, integer *, integer *, doublereal *, - doublereal *, doublereal *, integer *, doublereal *, integer *, - doublereal *, integer *, integer *, ftnlen), dlascl_(char *, - integer *, integer *, doublereal *, doublereal *, integer *, - integer *, doublereal *, integer *, integer *, ftnlen), dgeqrf_( - integer *, integer *, doublereal *, integer *, doublereal *, - doublereal *, integer *, integer *), dlacpy_(char *, integer *, - integer *, doublereal *, integer *, doublereal *, integer *, - ftnlen), dlaset_(char *, integer *, integer *, doublereal *, - doublereal *, doublereal *, integer *, ftnlen), xerbla_(char *, - integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern int dlabad_(doublereal *, doublereal *), + dgebrd_(integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *, integer *, integer *); + extern doublereal dlamch_(char *, ftnlen), + dlange_(char *, integer *, integer *, doublereal *, integer *, doublereal *, ftnlen); + extern int dgelqf_(integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, integer *), + dlalsd_(char *, integer *, integer *, integer *, doublereal *, doublereal *, doublereal *, + integer *, doublereal *, integer *, doublereal *, integer *, integer *, ftnlen), + dlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, integer *, + doublereal *, integer *, integer *, ftnlen), + dgeqrf_(integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, integer *), + dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, + ftnlen), + dlaset_(char *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, + ftnlen), + xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); doublereal bignum; - extern /* Subroutine */ int dormbr_(char *, char *, char *, integer *, - integer *, integer *, doublereal *, integer *, doublereal *, - doublereal *, integer *, doublereal *, integer *, integer *, - ftnlen, ftnlen, ftnlen); + extern int dormbr_(char *, char *, char *, integer *, integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, + integer *, ftnlen, ftnlen, ftnlen); integer wlalsd; - extern /* Subroutine */ int dormlq_(char *, char *, integer *, integer *, - integer *, doublereal *, integer *, doublereal *, doublereal *, - integer *, doublereal *, integer *, integer *, ftnlen, ftnlen); + extern int dormlq_(char *, char *, integer *, integer *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, doublereal *, integer *, integer *, + ftnlen, ftnlen); integer ldwork; - extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *, - integer *, doublereal *, integer *, doublereal *, doublereal *, - integer *, doublereal *, integer *, integer *, ftnlen, ftnlen); + extern int dormqr_(char *, char *, integer *, integer *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, doublereal *, integer *, integer *, + ftnlen, ftnlen); integer liwork, minwrk, maxwrk; doublereal smlnum; logical lquery; integer smlsiz; - - -/* -- LAPACK driver routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments. */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; @@ -326,13 +64,10 @@ f"> */ --s; --work; --iwork; - - /* Function Body */ *info = 0; - minmn = min(*m,*n); - maxmn = max(*m,*n); - mnthr = ilaenv_(&c__6, (char *)"DGELSD", (char *)" ", m, n, nrhs, &c_n1, (ftnlen)6, ( - ftnlen)1); + minmn = min(*m, *n); + maxmn = max(*m, *n); + mnthr = ilaenv_(&c__6, (char *)"DGELSD", (char *)" ", m, n, nrhs, &c_n1, (ftnlen)6, (ftnlen)1); lquery = *lwork == -1; if (*m < 0) { *info = -1; @@ -340,158 +75,105 @@ f"> */ *info = -2; } else if (*nrhs < 0) { *info = -3; - } else if (*lda < max(1,*m)) { + } else if (*lda < max(1, *m)) { *info = -5; - } else if (*ldb < max(1,maxmn)) { + } else if (*ldb < max(1, maxmn)) { *info = -7; } - - smlsiz = ilaenv_(&c__9, (char *)"DGELSD", (char *)" ", &c__0, &c__0, &c__0, &c__0, ( - ftnlen)6, (ftnlen)1); - -/* Compute workspace. */ -/* (Note: Comments in the code beginning (char *)"Workspace:" describe the */ -/* minimal amount of workspace needed at that point in the code, */ -/* as well as the preferred amount for good performance. */ -/* NB refers to the optimal block size for the immediately */ -/* following subroutine, as returned by ILAENV.) */ - + smlsiz = ilaenv_(&c__9, (char *)"DGELSD", (char *)" ", &c__0, &c__0, &c__0, &c__0, (ftnlen)6, (ftnlen)1); minwrk = 1; liwork = 1; - minmn = max(1,minmn); -/* Computing MAX */ - i__1 = (integer) (log((doublereal) minmn / (doublereal) (smlsiz + 1)) / - log(2.)) + 1; - nlvl = max(i__1,0); - + minmn = max(1, minmn); + i__1 = (integer)(log((doublereal)minmn / (doublereal)(smlsiz + 1)) / log(2.)) + 1; + nlvl = max(i__1, 0); if (*info == 0) { maxwrk = 0; liwork = minmn * 3 * nlvl + minmn * 11; mm = *m; if (*m >= *n && *m >= mnthr) { - -/* Path 1a - overdetermined, with many more rows than columns. */ - mm = *n; -/* Computing MAX */ - i__1 = maxwrk, i__2 = *n + *n * ilaenv_(&c__1, (char *)"DGEQRF", (char *)" ", m, - n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); - maxwrk = max(i__1,i__2); -/* Computing MAX */ - i__1 = maxwrk, i__2 = *n + *nrhs * ilaenv_(&c__1, (char *)"DORMQR", (char *)"LT", - m, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)2); - maxwrk = max(i__1,i__2); + i__1 = maxwrk, i__2 = *n + *n * ilaenv_(&c__1, (char *)"DGEQRF", (char *)" ", m, n, &c_n1, &c_n1, + (ftnlen)6, (ftnlen)1); + maxwrk = max(i__1, i__2); + i__1 = maxwrk, i__2 = *n + *nrhs * ilaenv_(&c__1, (char *)"DORMQR", (char *)"LT", m, nrhs, n, &c_n1, + (ftnlen)6, (ftnlen)2); + maxwrk = max(i__1, i__2); } if (*m >= *n) { - -/* Path 1 - overdetermined or exactly determined. */ - -/* Computing MAX */ - i__1 = maxwrk, i__2 = *n * 3 + (mm + *n) * ilaenv_(&c__1, (char *)"DGEBRD" - , (char *)" ", &mm, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); - maxwrk = max(i__1,i__2); -/* Computing MAX */ - i__1 = maxwrk, i__2 = *n * 3 + *nrhs * ilaenv_(&c__1, (char *)"DORMBR", - (char *)"QLT", &mm, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)3); - maxwrk = max(i__1,i__2); -/* Computing MAX */ - i__1 = maxwrk, i__2 = *n * 3 + (*n - 1) * ilaenv_(&c__1, (char *)"DORMBR", - (char *)"PLN", n, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)3); - maxwrk = max(i__1,i__2); -/* Computing 2nd power */ + i__1 = maxwrk, i__2 = *n * 3 + (mm + *n) * ilaenv_(&c__1, (char *)"DGEBRD", (char *)" ", &mm, n, &c_n1, + &c_n1, (ftnlen)6, (ftnlen)1); + maxwrk = max(i__1, i__2); + i__1 = maxwrk, i__2 = *n * 3 + *nrhs * ilaenv_(&c__1, (char *)"DORMBR", (char *)"QLT", &mm, nrhs, n, + &c_n1, (ftnlen)6, (ftnlen)3); + maxwrk = max(i__1, i__2); + i__1 = maxwrk, i__2 = *n * 3 + (*n - 1) * ilaenv_(&c__1, (char *)"DORMBR", (char *)"PLN", n, nrhs, n, + &c_n1, (ftnlen)6, (ftnlen)3); + maxwrk = max(i__1, i__2); i__1 = smlsiz + 1; - wlalsd = *n * 9 + (*n << 1) * smlsiz + (*n << 3) * nlvl + *n * * - nrhs + i__1 * i__1; -/* Computing MAX */ + wlalsd = *n * 9 + (*n << 1) * smlsiz + (*n << 3) * nlvl + *n * *nrhs + i__1 * i__1; i__1 = maxwrk, i__2 = *n * 3 + wlalsd; - maxwrk = max(i__1,i__2); -/* Computing MAX */ - i__1 = *n * 3 + mm, i__2 = *n * 3 + *nrhs, i__1 = max(i__1,i__2), - i__2 = *n * 3 + wlalsd; - minwrk = max(i__1,i__2); + maxwrk = max(i__1, i__2); + i__1 = *n * 3 + mm, i__2 = *n * 3 + *nrhs, i__1 = max(i__1, i__2), + i__2 = *n * 3 + wlalsd; + minwrk = max(i__1, i__2); } if (*n > *m) { -/* Computing 2nd power */ i__1 = smlsiz + 1; - wlalsd = *m * 9 + (*m << 1) * smlsiz + (*m << 3) * nlvl + *m * * - nrhs + i__1 * i__1; + wlalsd = *m * 9 + (*m << 1) * smlsiz + (*m << 3) * nlvl + *m * *nrhs + i__1 * i__1; if (*n >= mnthr) { - -/* Path 2a - underdetermined, with many more columns */ -/* than rows. */ - - maxwrk = *m + *m * ilaenv_(&c__1, (char *)"DGELQF", (char *)" ", m, n, &c_n1, - &c_n1, (ftnlen)6, (ftnlen)1); -/* Computing MAX */ - i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m << 1) * - ilaenv_(&c__1, (char *)"DGEBRD", (char *)" ", m, m, &c_n1, &c_n1, ( - ftnlen)6, (ftnlen)1); - maxwrk = max(i__1,i__2); -/* Computing MAX */ - i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + *nrhs * ilaenv_(& - c__1, (char *)"DORMBR", (char *)"QLT", m, nrhs, m, &c_n1, (ftnlen)6, ( - ftnlen)3); - maxwrk = max(i__1,i__2); -/* Computing MAX */ - i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + (*m - 1) * - ilaenv_(&c__1, (char *)"DORMBR", (char *)"PLN", m, nrhs, m, &c_n1, ( - ftnlen)6, (ftnlen)3); - maxwrk = max(i__1,i__2); + maxwrk = *m + *m * ilaenv_(&c__1, (char *)"DGELQF", (char *)" ", m, n, &c_n1, &c_n1, (ftnlen)6, + (ftnlen)1); + i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + + (*m << 1) * ilaenv_(&c__1, (char *)"DGEBRD", (char *)" ", m, m, &c_n1, &c_n1, + (ftnlen)6, (ftnlen)1); + maxwrk = max(i__1, i__2); + i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + + *nrhs * ilaenv_(&c__1, (char *)"DORMBR", (char *)"QLT", m, nrhs, m, &c_n1, + (ftnlen)6, (ftnlen)3); + maxwrk = max(i__1, i__2); + i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + + (*m - 1) * ilaenv_(&c__1, (char *)"DORMBR", (char *)"PLN", m, nrhs, m, &c_n1, + (ftnlen)6, (ftnlen)3); + maxwrk = max(i__1, i__2); if (*nrhs > 1) { -/* Computing MAX */ i__1 = maxwrk, i__2 = *m * *m + *m + *m * *nrhs; - maxwrk = max(i__1,i__2); + maxwrk = max(i__1, i__2); } else { -/* Computing MAX */ i__1 = maxwrk, i__2 = *m * *m + (*m << 1); - maxwrk = max(i__1,i__2); + maxwrk = max(i__1, i__2); } -/* Computing MAX */ - i__1 = maxwrk, i__2 = *m + *nrhs * ilaenv_(&c__1, (char *)"DORMLQ", - (char *)"LT", n, nrhs, m, &c_n1, (ftnlen)6, (ftnlen)2); - maxwrk = max(i__1,i__2); -/* Computing MAX */ + i__1 = maxwrk, i__2 = *m + *nrhs * ilaenv_(&c__1, (char *)"DORMLQ", (char *)"LT", n, nrhs, m, &c_n1, + (ftnlen)6, (ftnlen)2); + maxwrk = max(i__1, i__2); i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + wlalsd; - maxwrk = max(i__1,i__2); -/* XXX: Ensure the Path 2a case below is triggered. The workspace */ -/* calculation should use queries for all routines eventually. */ -/* Computing MAX */ -/* Computing MAX */ - i__3 = *m, i__4 = (*m << 1) - 4, i__3 = max(i__3,i__4), i__3 = - max(i__3,*nrhs), i__4 = *n - *m * 3; - i__1 = maxwrk, i__2 = (*m << 2) + *m * *m + max(i__3,i__4); - maxwrk = max(i__1,i__2); + maxwrk = max(i__1, i__2); + i__3 = *m, i__4 = (*m << 1) - 4, i__3 = max(i__3, i__4), i__3 = max(i__3, *nrhs), + i__4 = *n - *m * 3; + i__1 = maxwrk, i__2 = (*m << 2) + *m * *m + max(i__3, i__4); + maxwrk = max(i__1, i__2); } else { - -/* Path 2 - remaining underdetermined cases. */ - - maxwrk = *m * 3 + (*n + *m) * ilaenv_(&c__1, (char *)"DGEBRD", (char *)" ", m, - n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); -/* Computing MAX */ - i__1 = maxwrk, i__2 = *m * 3 + *nrhs * ilaenv_(&c__1, (char *)"DORMBR" - , (char *)"QLT", m, nrhs, n, &c_n1, (ftnlen)6, (ftnlen)3); - maxwrk = max(i__1,i__2); -/* Computing MAX */ - i__1 = maxwrk, i__2 = *m * 3 + *m * ilaenv_(&c__1, (char *)"DORMBR", - (char *)"PLN", n, nrhs, m, &c_n1, (ftnlen)6, (ftnlen)3); - maxwrk = max(i__1,i__2); -/* Computing MAX */ + maxwrk = *m * 3 + (*n + *m) * ilaenv_(&c__1, (char *)"DGEBRD", (char *)" ", m, n, &c_n1, &c_n1, + (ftnlen)6, (ftnlen)1); + i__1 = maxwrk, i__2 = *m * 3 + *nrhs * ilaenv_(&c__1, (char *)"DORMBR", (char *)"QLT", m, nrhs, n, + &c_n1, (ftnlen)6, (ftnlen)3); + maxwrk = max(i__1, i__2); + i__1 = maxwrk, i__2 = *m * 3 + *m * ilaenv_(&c__1, (char *)"DORMBR", (char *)"PLN", n, nrhs, m, + &c_n1, (ftnlen)6, (ftnlen)3); + maxwrk = max(i__1, i__2); i__1 = maxwrk, i__2 = *m * 3 + wlalsd; - maxwrk = max(i__1,i__2); + maxwrk = max(i__1, i__2); } -/* Computing MAX */ - i__1 = *m * 3 + *nrhs, i__2 = *m * 3 + *m, i__1 = max(i__1,i__2), - i__2 = *m * 3 + wlalsd; - minwrk = max(i__1,i__2); + i__1 = *m * 3 + *nrhs, i__2 = *m * 3 + *m, i__1 = max(i__1, i__2), + i__2 = *m * 3 + wlalsd; + minwrk = max(i__1, i__2); } - minwrk = min(minwrk,maxwrk); - work[1] = (doublereal) maxwrk; + minwrk = min(minwrk, maxwrk); + work[1] = (doublereal)maxwrk; iwork[1] = liwork; - if (*lwork < minwrk && ! lquery) { + if (*lwork < minwrk && !lquery) { *info = -12; } } - if (*info != 0) { i__1 = -(*info); xerbla_((char *)"DGELSD", &i__1, (ftnlen)6); @@ -499,318 +181,161 @@ f"> */ } else if (lquery) { goto L10; } - -/* Quick return if possible. */ - if (*m == 0 || *n == 0) { *rank = 0; return 0; } - -/* Get machine parameters. */ - eps = dlamch_((char *)"P", (ftnlen)1); sfmin = dlamch_((char *)"S", (ftnlen)1); smlnum = sfmin / eps; bignum = 1. / smlnum; dlabad_(&smlnum, &bignum); - -/* Scale A if max entry outside range [SMLNUM,BIGNUM]. */ - anrm = dlange_((char *)"M", m, n, &a[a_offset], lda, &work[1], (ftnlen)1); iascl = 0; if (anrm > 0. && anrm < smlnum) { - -/* Scale matrix norm up to SMLNUM. */ - - dlascl_((char *)"G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, - info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, info, (ftnlen)1); iascl = 1; } else if (anrm > bignum) { - -/* Scale matrix norm down to BIGNUM. */ - - dlascl_((char *)"G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, - info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, info, (ftnlen)1); iascl = 2; } else if (anrm == 0.) { - -/* Matrix all zero. Return zero solution. */ - - i__1 = max(*m,*n); - dlaset_((char *)"F", &i__1, nrhs, &c_b82, &c_b82, &b[b_offset], ldb, (ftnlen) - 1); + i__1 = max(*m, *n); + dlaset_((char *)"F", &i__1, nrhs, &c_b82, &c_b82, &b[b_offset], ldb, (ftnlen)1); dlaset_((char *)"F", &minmn, &c__1, &c_b82, &c_b82, &s[1], &c__1, (ftnlen)1); *rank = 0; goto L10; } - -/* Scale B if max entry outside range [SMLNUM,BIGNUM]. */ - bnrm = dlange_((char *)"M", m, nrhs, &b[b_offset], ldb, &work[1], (ftnlen)1); ibscl = 0; if (bnrm > 0. && bnrm < smlnum) { - -/* Scale matrix norm up to SMLNUM. */ - - dlascl_((char *)"G", &c__0, &c__0, &bnrm, &smlnum, m, nrhs, &b[b_offset], ldb, - info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &bnrm, &smlnum, m, nrhs, &b[b_offset], ldb, info, (ftnlen)1); ibscl = 1; } else if (bnrm > bignum) { - -/* Scale matrix norm down to BIGNUM. */ - - dlascl_((char *)"G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb, - info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb, info, (ftnlen)1); ibscl = 2; } - -/* If M < N make sure certain entries of B are zero. */ - if (*m < *n) { i__1 = *n - *m; - dlaset_((char *)"F", &i__1, nrhs, &c_b82, &c_b82, &b[*m + 1 + b_dim1], ldb, ( - ftnlen)1); + dlaset_((char *)"F", &i__1, nrhs, &c_b82, &c_b82, &b[*m + 1 + b_dim1], ldb, (ftnlen)1); } - -/* Overdetermined case. */ - if (*m >= *n) { - -/* Path 1 - overdetermined or exactly determined. */ - mm = *m; if (*m >= mnthr) { - -/* Path 1a - overdetermined, with many more rows than columns. */ - mm = *n; itau = 1; nwork = itau + *n; - -/* Compute A=Q*R. */ -/* (Workspace: need 2*N, prefer N+N*NB) */ - i__1 = *lwork - nwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__1, - info); - -/* Multiply B by transpose(Q). */ -/* (Workspace: need N+NRHS, prefer N+NRHS*NB) */ - + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__1, info); i__1 = *lwork - nwork + 1; - dormqr_((char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, &work[itau], &b[ - b_offset], ldb, &work[nwork], &i__1, info, (ftnlen)1, ( - ftnlen)1); - -/* Zero out below R. */ - + dormqr_((char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, &work[itau], &b[b_offset], ldb, + &work[nwork], &i__1, info, (ftnlen)1, (ftnlen)1); if (*n > 1) { i__1 = *n - 1; i__2 = *n - 1; - dlaset_((char *)"L", &i__1, &i__2, &c_b82, &c_b82, &a[a_dim1 + 2], - lda, (ftnlen)1); + dlaset_((char *)"L", &i__1, &i__2, &c_b82, &c_b82, &a[a_dim1 + 2], lda, (ftnlen)1); } } - ie = 1; itauq = ie + *n; itaup = itauq + *n; nwork = itaup + *n; - -/* Bidiagonalize R in A. */ -/* (Workspace: need 3*N+MM, prefer 3*N+(MM+N)*NB) */ - i__1 = *lwork - nwork + 1; - dgebrd_(&mm, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], & - work[itaup], &work[nwork], &i__1, info); - -/* Multiply B by transpose of left bidiagonalizing vectors of R. */ -/* (Workspace: need 3*N+NRHS, prefer 3*N+NRHS*NB) */ - + dgebrd_(&mm, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &work[itaup], + &work[nwork], &i__1, info); i__1 = *lwork - nwork + 1; - dormbr_((char *)"Q", (char *)"L", (char *)"T", &mm, nrhs, n, &a[a_offset], lda, &work[itauq], - &b[b_offset], ldb, &work[nwork], &i__1, info, (ftnlen)1, ( - ftnlen)1, (ftnlen)1); - -/* Solve the bidiagonal least squares problem. */ - - dlalsd_((char *)"U", &smlsiz, n, nrhs, &s[1], &work[ie], &b[b_offset], ldb, - rcond, rank, &work[nwork], &iwork[1], info, (ftnlen)1); + dormbr_((char *)"Q", (char *)"L", (char *)"T", &mm, nrhs, n, &a[a_offset], lda, &work[itauq], &b[b_offset], ldb, + &work[nwork], &i__1, info, (ftnlen)1, (ftnlen)1, (ftnlen)1); + dlalsd_((char *)"U", &smlsiz, n, nrhs, &s[1], &work[ie], &b[b_offset], ldb, rcond, rank, + &work[nwork], &iwork[1], info, (ftnlen)1); if (*info != 0) { goto L10; } - -/* Multiply B by right bidiagonalizing vectors of R. */ - i__1 = *lwork - nwork + 1; - dormbr_((char *)"P", (char *)"L", (char *)"N", n, nrhs, n, &a[a_offset], lda, &work[itaup], & - b[b_offset], ldb, &work[nwork], &i__1, info, (ftnlen)1, ( - ftnlen)1, (ftnlen)1); - - } else /* if(complicated condition) */ { -/* Computing MAX */ - i__1 = *m, i__2 = (*m << 1) - 4, i__1 = max(i__1,i__2), i__1 = max( - i__1,*nrhs), i__2 = *n - *m * 3, i__1 = max(i__1,i__2); - if (*n >= mnthr && *lwork >= (*m << 2) + *m * *m + max(i__1,wlalsd)) { - -/* Path 2a - underdetermined, with many more columns than rows */ -/* and sufficient workspace for an efficient algorithm. */ - + dormbr_((char *)"P", (char *)"L", (char *)"N", n, nrhs, n, &a[a_offset], lda, &work[itaup], &b[b_offset], ldb, + &work[nwork], &i__1, info, (ftnlen)1, (ftnlen)1, (ftnlen)1); + } else { + i__1 = *m, i__2 = (*m << 1) - 4, i__1 = max(i__1, i__2), i__1 = max(i__1, *nrhs), + i__2 = *n - *m * 3, i__1 = max(i__1, i__2); + if (*n >= mnthr && *lwork >= (*m << 2) + *m * *m + max(i__1, wlalsd)) { ldwork = *m; -/* Computing MAX */ -/* Computing MAX */ - i__3 = *m, i__4 = (*m << 1) - 4, i__3 = max(i__3,i__4), i__3 = - max(i__3,*nrhs), i__4 = *n - *m * 3; - i__1 = (*m << 2) + *m * *lda + max(i__3,i__4), i__2 = *m * *lda + - *m + *m * *nrhs, i__1 = max(i__1,i__2), i__2 = (*m << 2) - + *m * *lda + wlalsd; - if (*lwork >= max(i__1,i__2)) { + i__3 = *m, i__4 = (*m << 1) - 4, i__3 = max(i__3, i__4), i__3 = max(i__3, *nrhs), + i__4 = *n - *m * 3; + i__1 = (*m << 2) + *m * *lda + max(i__3, i__4), i__2 = *m * *lda + *m + *m * *nrhs, + i__1 = max(i__1, i__2), i__2 = (*m << 2) + *m * *lda + wlalsd; + if (*lwork >= max(i__1, i__2)) { ldwork = *lda; } itau = 1; nwork = *m + 1; - -/* Compute A=L*Q. */ -/* (Workspace: need 2*M, prefer M+M*NB) */ - i__1 = *lwork - nwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__1, - info); + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[nwork], &i__1, info); il = nwork; - -/* Copy L to WORK(IL), zeroing out above its diagonal. */ - - dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[il], &ldwork, (ftnlen) - 1); + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[il], &ldwork, (ftnlen)1); i__1 = *m - 1; i__2 = *m - 1; - dlaset_((char *)"U", &i__1, &i__2, &c_b82, &c_b82, &work[il + ldwork], & - ldwork, (ftnlen)1); + dlaset_((char *)"U", &i__1, &i__2, &c_b82, &c_b82, &work[il + ldwork], &ldwork, (ftnlen)1); ie = il + ldwork * *m; itauq = ie + *m; itaup = itauq + *m; nwork = itaup + *m; - -/* Bidiagonalize L in WORK(IL). */ -/* (Workspace: need M*M+5*M, prefer M*M+4*M+2*M*NB) */ - i__1 = *lwork - nwork + 1; - dgebrd_(m, m, &work[il], &ldwork, &s[1], &work[ie], &work[itauq], - &work[itaup], &work[nwork], &i__1, info); - -/* Multiply B by transpose of left bidiagonalizing vectors of L. */ -/* (Workspace: need M*M+4*M+NRHS, prefer M*M+4*M+NRHS*NB) */ - + dgebrd_(m, m, &work[il], &ldwork, &s[1], &work[ie], &work[itauq], &work[itaup], + &work[nwork], &i__1, info); i__1 = *lwork - nwork + 1; - dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, m, &work[il], &ldwork, &work[ - itauq], &b[b_offset], ldb, &work[nwork], &i__1, info, ( - ftnlen)1, (ftnlen)1, (ftnlen)1); - -/* Solve the bidiagonal least squares problem. */ - - dlalsd_((char *)"U", &smlsiz, m, nrhs, &s[1], &work[ie], &b[b_offset], - ldb, rcond, rank, &work[nwork], &iwork[1], info, (ftnlen) - 1); + dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, m, &work[il], &ldwork, &work[itauq], &b[b_offset], ldb, + &work[nwork], &i__1, info, (ftnlen)1, (ftnlen)1, (ftnlen)1); + dlalsd_((char *)"U", &smlsiz, m, nrhs, &s[1], &work[ie], &b[b_offset], ldb, rcond, rank, + &work[nwork], &iwork[1], info, (ftnlen)1); if (*info != 0) { goto L10; } - -/* Multiply B by right bidiagonalizing vectors of L. */ - i__1 = *lwork - nwork + 1; - dormbr_((char *)"P", (char *)"L", (char *)"N", m, nrhs, m, &work[il], &ldwork, &work[ - itaup], &b[b_offset], ldb, &work[nwork], &i__1, info, ( - ftnlen)1, (ftnlen)1, (ftnlen)1); - -/* Zero out below first M rows of B. */ - + dormbr_((char *)"P", (char *)"L", (char *)"N", m, nrhs, m, &work[il], &ldwork, &work[itaup], &b[b_offset], ldb, + &work[nwork], &i__1, info, (ftnlen)1, (ftnlen)1, (ftnlen)1); i__1 = *n - *m; - dlaset_((char *)"F", &i__1, nrhs, &c_b82, &c_b82, &b[*m + 1 + b_dim1], - ldb, (ftnlen)1); + dlaset_((char *)"F", &i__1, nrhs, &c_b82, &c_b82, &b[*m + 1 + b_dim1], ldb, (ftnlen)1); nwork = itau + *m; - -/* Multiply transpose(Q) by B. */ -/* (Workspace: need M+NRHS, prefer M+NRHS*NB) */ - i__1 = *lwork - nwork + 1; - dormlq_((char *)"L", (char *)"T", n, nrhs, m, &a[a_offset], lda, &work[itau], &b[ - b_offset], ldb, &work[nwork], &i__1, info, (ftnlen)1, ( - ftnlen)1); - + dormlq_((char *)"L", (char *)"T", n, nrhs, m, &a[a_offset], lda, &work[itau], &b[b_offset], ldb, + &work[nwork], &i__1, info, (ftnlen)1, (ftnlen)1); } else { - -/* Path 2 - remaining underdetermined cases. */ - ie = 1; itauq = ie + *m; itaup = itauq + *m; nwork = itaup + *m; - -/* Bidiagonalize A. */ -/* (Workspace: need 3*M+N, prefer 3*M+(M+N)*NB) */ - i__1 = *lwork - nwork + 1; - dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], & - work[itaup], &work[nwork], &i__1, info); - -/* Multiply B by transpose of left bidiagonalizing vectors. */ -/* (Workspace: need 3*M+NRHS, prefer 3*M+NRHS*NB) */ - + dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &work[itaup], + &work[nwork], &i__1, info); i__1 = *lwork - nwork + 1; - dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, &work[itauq] - , &b[b_offset], ldb, &work[nwork], &i__1, info, (ftnlen)1, - (ftnlen)1, (ftnlen)1); - -/* Solve the bidiagonal least squares problem. */ - - dlalsd_((char *)"L", &smlsiz, m, nrhs, &s[1], &work[ie], &b[b_offset], - ldb, rcond, rank, &work[nwork], &iwork[1], info, (ftnlen) - 1); + dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, &work[itauq], &b[b_offset], ldb, + &work[nwork], &i__1, info, (ftnlen)1, (ftnlen)1, (ftnlen)1); + dlalsd_((char *)"L", &smlsiz, m, nrhs, &s[1], &work[ie], &b[b_offset], ldb, rcond, rank, + &work[nwork], &iwork[1], info, (ftnlen)1); if (*info != 0) { goto L10; } - -/* Multiply B by right bidiagonalizing vectors of A. */ - i__1 = *lwork - nwork + 1; - dormbr_((char *)"P", (char *)"L", (char *)"N", n, nrhs, m, &a[a_offset], lda, &work[itaup] - , &b[b_offset], ldb, &work[nwork], &i__1, info, (ftnlen)1, - (ftnlen)1, (ftnlen)1); - + dormbr_((char *)"P", (char *)"L", (char *)"N", n, nrhs, m, &a[a_offset], lda, &work[itaup], &b[b_offset], ldb, + &work[nwork], &i__1, info, (ftnlen)1, (ftnlen)1, (ftnlen)1); } } - -/* Undo scaling. */ - if (iascl == 1) { - dlascl_((char *)"G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb, - info, (ftnlen)1); - dlascl_((char *)"G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], & - minmn, info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb, info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], &minmn, info, (ftnlen)1); } else if (iascl == 2) { - dlascl_((char *)"G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb, - info, (ftnlen)1); - dlascl_((char *)"G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], & - minmn, info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb, info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], &minmn, info, (ftnlen)1); } if (ibscl == 1) { - dlascl_((char *)"G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb, - info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb, info, (ftnlen)1); } else if (ibscl == 2) { - dlascl_((char *)"G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb, - info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb, info, (ftnlen)1); } - L10: - work[1] = (doublereal) maxwrk; + work[1] = (doublereal)maxwrk; iwork[1] = liwork; return 0; - -/* End of DGELSD */ - -} /* dgelsd_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dgelss.cpp b/lib/linalg/dgelss.cpp index 86036f9179..e10906f4e9 100644 --- a/lib/linalg/dgelss.cpp +++ b/lib/linalg/dgelss.cpp @@ -1,298 +1,73 @@ -/* fortran/dgelss.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__6 = 6; static integer c_n1 = -1; static integer c__0 = 0; static doublereal c_b46 = 0.; static integer c__1 = 1; static doublereal c_b79 = 1.; - -/* > \brief DGELSS solves overdetermined or underdetermined systems for GE matrices */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DGELSS + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DGELSS( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, */ -/* WORK, LWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS, RANK */ -/* DOUBLE PRECISION RCOND */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), S( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DGELSS computes the minimum norm solution to a real linear least */ -/* > squares problem: */ -/* > */ -/* > Minimize 2-norm(| b - A*x |). */ -/* > */ -/* > using the singular value decomposition (SVD) of A. A is an M-by-N */ -/* > matrix which may be rank-deficient. */ -/* > */ -/* > Several right hand side vectors b and solution vectors x can be */ -/* > handled in a single call; they are stored as the columns of the */ -/* > M-by-NRHS right hand side matrix B and the N-by-NRHS solution matrix */ -/* > X. */ -/* > */ -/* > The effective rank of A is determined by treating as zero those */ -/* > singular values which are less than RCOND times the largest singular */ -/* > value. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix A. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] NRHS */ -/* > \verbatim */ -/* > NRHS is INTEGER */ -/* > The number of right hand sides, i.e., the number of columns */ -/* > of the matrices B and X. NRHS >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On entry, the M-by-N matrix A. */ -/* > On exit, the first min(m,n) rows of A are overwritten with */ -/* > its right singular vectors, stored rowwise. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] B */ -/* > \verbatim */ -/* > B is DOUBLE PRECISION array, dimension (LDB,NRHS) */ -/* > On entry, the M-by-NRHS right hand side matrix B. */ -/* > On exit, B is overwritten by the N-by-NRHS solution */ -/* > matrix X. If m >= n and RANK = n, the residual */ -/* > sum-of-squares for the solution in the i-th column is given */ -/* > by the sum of squares of elements n+1:m in that column. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDB */ -/* > \verbatim */ -/* > LDB is INTEGER */ -/* > The leading dimension of the array B. LDB >= max(1,max(M,N)). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] S */ -/* > \verbatim */ -/* > S is DOUBLE PRECISION array, dimension (min(M,N)) */ -/* > The singular values of A in decreasing order. */ -/* > The condition number of A in the 2-norm = S(1)/S(min(m,n)). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] RCOND */ -/* > \verbatim */ -/* > RCOND is DOUBLE PRECISION */ -/* > RCOND is used to determine the effective rank of A. */ -/* > Singular values S(i) <= RCOND*S(1) are treated as zero. */ -/* > If RCOND < 0, machine precision is used instead. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] RANK */ -/* > \verbatim */ -/* > RANK is INTEGER */ -/* > The effective rank of A, i.e., the number of singular values */ -/* > which are greater than RCOND*S(1). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ -/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LWORK */ -/* > \verbatim */ -/* > LWORK is INTEGER */ -/* > The dimension of the array WORK. LWORK >= 1, and also: */ -/* > LWORK >= 3*min(M,N) + max( 2*min(M,N), max(M,N), NRHS ) */ -/* > For good performance, LWORK should generally be larger. */ -/* > */ -/* > If LWORK = -1, then a workspace query is assumed; the routine */ -/* > only calculates the optimal size of the WORK array, returns */ -/* > this value as the first entry of the WORK array, and no error */ -/* > message related to LWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ -/* > > 0: the algorithm for computing the SVD failed to converge; */ -/* > if INFO = i, i off-diagonal elements of an intermediate */ -/* > bidiagonal form did not converge to zero. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleGEsolve */ - -/* ===================================================================== */ -/* Subroutine */ int dgelss_(integer *m, integer *n, integer *nrhs, - doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal * - s, doublereal *rcond, integer *rank, doublereal *work, integer *lwork, - integer *info) +int dgelss_(integer *m, integer *n, integer *nrhs, doublereal *a, integer *lda, doublereal *b, + integer *ldb, doublereal *s, doublereal *rcond, integer *rank, doublereal *work, + integer *lwork, integer *info) { - /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4; doublereal d__1; - - /* Local variables */ integer i__, bl, ie, il, mm; doublereal dum[1], eps, thr, anrm, bnrm; - integer itau, lwork_dgebrd__, lwork_dgelqf__, lwork_dgeqrf__, - lwork_dorgbr__, lwork_dormbr__, lwork_dormlq__, lwork_dormqr__; - extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); + integer itau, lwork_dgebrd__, lwork_dgelqf__, lwork_dgeqrf__, lwork_dorgbr__, lwork_dormbr__, + lwork_dormlq__, lwork_dormqr__; + extern int dgemm_(char *, char *, integer *, integer *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, + ftnlen, ftnlen); integer iascl, ibscl; - extern /* Subroutine */ int dgemv_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, doublereal *, integer *, - doublereal *, doublereal *, integer *, ftnlen), drscl_(integer *, - doublereal *, doublereal *, integer *); + extern int dgemv_(char *, integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, ftnlen), + drscl_(integer *, doublereal *, doublereal *, integer *); integer chunk; doublereal sfmin; integer minmn; - extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, - doublereal *, integer *); + extern int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *); integer maxmn, itaup, itauq, mnthr, iwork; - extern /* Subroutine */ int dlabad_(doublereal *, doublereal *), dgebrd_( - integer *, integer *, doublereal *, integer *, doublereal *, - doublereal *, doublereal *, doublereal *, doublereal *, integer *, - integer *); - extern doublereal dlamch_(char *, ftnlen), dlange_(char *, integer *, - integer *, doublereal *, integer *, doublereal *, ftnlen); + extern int dlabad_(doublereal *, doublereal *), + dgebrd_(integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *, integer *, integer *); + extern doublereal dlamch_(char *, ftnlen), + dlange_(char *, integer *, integer *, doublereal *, integer *, doublereal *, ftnlen); integer bdspac; - extern /* Subroutine */ int dgelqf_(integer *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, integer *), - dlascl_(char *, integer *, integer *, doublereal *, doublereal *, - integer *, integer *, doublereal *, integer *, integer *, ftnlen), - dgeqrf_(integer *, integer *, doublereal *, integer *, - doublereal *, doublereal *, integer *, integer *), dlacpy_(char *, - integer *, integer *, doublereal *, integer *, doublereal *, - integer *, ftnlen), dlaset_(char *, integer *, integer *, - doublereal *, doublereal *, doublereal *, integer *, ftnlen), - xerbla_(char *, integer *, ftnlen), dbdsqr_(char *, integer *, - integer *, integer *, integer *, doublereal *, doublereal *, - doublereal *, integer *, doublereal *, integer *, doublereal *, - integer *, doublereal *, integer *, ftnlen), dorgbr_(char *, - integer *, integer *, integer *, doublereal *, integer *, - doublereal *, doublereal *, integer *, integer *, ftnlen); + extern int dgelqf_(integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, integer *), + dlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, integer *, + doublereal *, integer *, integer *, ftnlen), + dgeqrf_(integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, integer *), + dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, + ftnlen), + dlaset_(char *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, + ftnlen), + xerbla_(char *, integer *, ftnlen), + dbdsqr_(char *, integer *, integer *, integer *, integer *, doublereal *, doublereal *, + doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, + doublereal *, integer *, ftnlen), + dorgbr_(char *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, integer *, ftnlen); doublereal bignum; - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - extern /* Subroutine */ int dormbr_(char *, char *, char *, integer *, - integer *, integer *, doublereal *, integer *, doublereal *, - doublereal *, integer *, doublereal *, integer *, integer *, - ftnlen, ftnlen, ftnlen), dormlq_(char *, char *, integer *, - integer *, integer *, doublereal *, integer *, doublereal *, - doublereal *, integer *, doublereal *, integer *, integer *, - ftnlen, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); + extern int dormbr_(char *, char *, char *, integer *, integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, + integer *, ftnlen, ftnlen, ftnlen), + dormlq_(char *, char *, integer *, integer *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, doublereal *, integer *, integer *, ftnlen, + ftnlen); integer ldwork; - extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *, - integer *, doublereal *, integer *, doublereal *, doublereal *, - integer *, doublereal *, integer *, integer *, ftnlen, ftnlen); + extern int dormqr_(char *, char *, integer *, integer *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, doublereal *, integer *, integer *, + ftnlen, ftnlen); integer minwrk, maxwrk; doublereal smlnum; logical lquery; - - -/* -- LAPACK driver routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. Local Arrays .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; @@ -301,11 +76,9 @@ f"> */ b -= b_offset; --s; --work; - - /* Function Body */ *info = 0; - minmn = min(*m,*n); - maxmn = max(*m,*n); + minmn = min(*m, *n); + maxmn = max(*m, *n); lquery = *lwork == -1; if (*m < 0) { *info = -1; @@ -313,194 +86,113 @@ f"> */ *info = -2; } else if (*nrhs < 0) { *info = -3; - } else if (*lda < max(1,*m)) { + } else if (*lda < max(1, *m)) { *info = -5; - } else if (*ldb < max(1,maxmn)) { + } else if (*ldb < max(1, maxmn)) { *info = -7; } - -/* Compute workspace */ -/* (Note: Comments in the code beginning (char *)"Workspace:" describe the */ -/* minimal amount of workspace needed at that point in the code, */ -/* as well as the preferred amount for good performance. */ -/* NB refers to the optimal block size for the immediately */ -/* following subroutine, as returned by ILAENV.) */ - if (*info == 0) { minwrk = 1; maxwrk = 1; if (minmn > 0) { mm = *m; - mnthr = ilaenv_(&c__6, (char *)"DGELSS", (char *)" ", m, n, nrhs, &c_n1, (ftnlen) - 6, (ftnlen)1); + mnthr = ilaenv_(&c__6, (char *)"DGELSS", (char *)" ", m, n, nrhs, &c_n1, (ftnlen)6, (ftnlen)1); if (*m >= *n && *m >= mnthr) { - -/* Path 1a - overdetermined, with many more rows than */ -/* columns */ - -/* Compute space needed for DGEQRF */ dgeqrf_(m, n, &a[a_offset], lda, dum, dum, &c_n1, info); - lwork_dgeqrf__ = (integer) dum[0]; -/* Compute space needed for DORMQR */ - dormqr_((char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, dum, &b[ - b_offset], ldb, dum, &c_n1, info, (ftnlen)1, (ftnlen) - 1); - lwork_dormqr__ = (integer) dum[0]; + lwork_dgeqrf__ = (integer)dum[0]; + dormqr_((char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, dum, &b[b_offset], ldb, dum, &c_n1, + info, (ftnlen)1, (ftnlen)1); + lwork_dormqr__ = (integer)dum[0]; mm = *n; -/* Computing MAX */ i__1 = maxwrk, i__2 = *n + lwork_dgeqrf__; - maxwrk = max(i__1,i__2); -/* Computing MAX */ + maxwrk = max(i__1, i__2); i__1 = maxwrk, i__2 = *n + lwork_dormqr__; - maxwrk = max(i__1,i__2); + maxwrk = max(i__1, i__2); } if (*m >= *n) { - -/* Path 1 - overdetermined or exactly determined */ - -/* Compute workspace needed for DBDSQR */ - -/* Computing MAX */ i__1 = 1, i__2 = *n * 5; - bdspac = max(i__1,i__2); -/* Compute space needed for DGEBRD */ - dgebrd_(&mm, n, &a[a_offset], lda, &s[1], dum, dum, dum, dum, - &c_n1, info); - lwork_dgebrd__ = (integer) dum[0]; -/* Compute space needed for DORMBR */ - dormbr_((char *)"Q", (char *)"L", (char *)"T", &mm, nrhs, n, &a[a_offset], lda, dum, & - b[b_offset], ldb, dum, &c_n1, info, (ftnlen)1, ( - ftnlen)1, (ftnlen)1); - lwork_dormbr__ = (integer) dum[0]; -/* Compute space needed for DORGBR */ - dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, dum, dum, &c_n1, - info, (ftnlen)1); - lwork_dorgbr__ = (integer) dum[0]; -/* Compute total workspace needed */ -/* Computing MAX */ + bdspac = max(i__1, i__2); + dgebrd_(&mm, n, &a[a_offset], lda, &s[1], dum, dum, dum, dum, &c_n1, info); + lwork_dgebrd__ = (integer)dum[0]; + dormbr_((char *)"Q", (char *)"L", (char *)"T", &mm, nrhs, n, &a[a_offset], lda, dum, &b[b_offset], ldb, dum, + &c_n1, info, (ftnlen)1, (ftnlen)1, (ftnlen)1); + lwork_dormbr__ = (integer)dum[0]; + dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, dum, dum, &c_n1, info, (ftnlen)1); + lwork_dorgbr__ = (integer)dum[0]; i__1 = maxwrk, i__2 = *n * 3 + lwork_dgebrd__; - maxwrk = max(i__1,i__2); -/* Computing MAX */ + maxwrk = max(i__1, i__2); i__1 = maxwrk, i__2 = *n * 3 + lwork_dormbr__; - maxwrk = max(i__1,i__2); -/* Computing MAX */ + maxwrk = max(i__1, i__2); i__1 = maxwrk, i__2 = *n * 3 + lwork_dorgbr__; - maxwrk = max(i__1,i__2); - maxwrk = max(maxwrk,bdspac); -/* Computing MAX */ + maxwrk = max(i__1, i__2); + maxwrk = max(maxwrk, bdspac); i__1 = maxwrk, i__2 = *n * *nrhs; - maxwrk = max(i__1,i__2); -/* Computing MAX */ - i__1 = *n * 3 + mm, i__2 = *n * 3 + *nrhs, i__1 = max(i__1, - i__2); - minwrk = max(i__1,bdspac); - maxwrk = max(minwrk,maxwrk); + maxwrk = max(i__1, i__2); + i__1 = *n * 3 + mm, i__2 = *n * 3 + *nrhs, i__1 = max(i__1, i__2); + minwrk = max(i__1, bdspac); + maxwrk = max(minwrk, maxwrk); } if (*n > *m) { - -/* Compute workspace needed for DBDSQR */ - -/* Computing MAX */ i__1 = 1, i__2 = *m * 5; - bdspac = max(i__1,i__2); -/* Computing MAX */ - i__1 = *m * 3 + *nrhs, i__2 = *m * 3 + *n, i__1 = max(i__1, - i__2); - minwrk = max(i__1,bdspac); + bdspac = max(i__1, i__2); + i__1 = *m * 3 + *nrhs, i__2 = *m * 3 + *n, i__1 = max(i__1, i__2); + minwrk = max(i__1, bdspac); if (*n >= mnthr) { - -/* Path 2a - underdetermined, with many more columns */ -/* than rows */ - -/* Compute space needed for DGELQF */ dgelqf_(m, n, &a[a_offset], lda, dum, dum, &c_n1, info); - lwork_dgelqf__ = (integer) dum[0]; -/* Compute space needed for DGEBRD */ - dgebrd_(m, m, &a[a_offset], lda, &s[1], dum, dum, dum, - dum, &c_n1, info); - lwork_dgebrd__ = (integer) dum[0]; -/* Compute space needed for DORMBR */ - dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, dum, - &b[b_offset], ldb, dum, &c_n1, info, (ftnlen)1, ( - ftnlen)1, (ftnlen)1); - lwork_dormbr__ = (integer) dum[0]; -/* Compute space needed for DORGBR */ - dorgbr_((char *)"P", m, m, m, &a[a_offset], lda, dum, dum, &c_n1, - info, (ftnlen)1); - lwork_dorgbr__ = (integer) dum[0]; -/* Compute space needed for DORMLQ */ - dormlq_((char *)"L", (char *)"T", n, nrhs, m, &a[a_offset], lda, dum, &b[ - b_offset], ldb, dum, &c_n1, info, (ftnlen)1, ( - ftnlen)1); - lwork_dormlq__ = (integer) dum[0]; -/* Compute total workspace needed */ + lwork_dgelqf__ = (integer)dum[0]; + dgebrd_(m, m, &a[a_offset], lda, &s[1], dum, dum, dum, dum, &c_n1, info); + lwork_dgebrd__ = (integer)dum[0]; + dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, dum, &b[b_offset], ldb, + dum, &c_n1, info, (ftnlen)1, (ftnlen)1, (ftnlen)1); + lwork_dormbr__ = (integer)dum[0]; + dorgbr_((char *)"P", m, m, m, &a[a_offset], lda, dum, dum, &c_n1, info, (ftnlen)1); + lwork_dorgbr__ = (integer)dum[0]; + dormlq_((char *)"L", (char *)"T", n, nrhs, m, &a[a_offset], lda, dum, &b[b_offset], ldb, dum, + &c_n1, info, (ftnlen)1, (ftnlen)1); + lwork_dormlq__ = (integer)dum[0]; maxwrk = *m + lwork_dgelqf__; -/* Computing MAX */ - i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + - lwork_dgebrd__; - maxwrk = max(i__1,i__2); -/* Computing MAX */ - i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + - lwork_dormbr__; - maxwrk = max(i__1,i__2); -/* Computing MAX */ - i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + - lwork_dorgbr__; - maxwrk = max(i__1,i__2); -/* Computing MAX */ + i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + lwork_dgebrd__; + maxwrk = max(i__1, i__2); + i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + lwork_dormbr__; + maxwrk = max(i__1, i__2); + i__1 = maxwrk, i__2 = *m * *m + (*m << 2) + lwork_dorgbr__; + maxwrk = max(i__1, i__2); i__1 = maxwrk, i__2 = *m * *m + *m + bdspac; - maxwrk = max(i__1,i__2); + maxwrk = max(i__1, i__2); if (*nrhs > 1) { -/* Computing MAX */ i__1 = maxwrk, i__2 = *m * *m + *m + *m * *nrhs; - maxwrk = max(i__1,i__2); + maxwrk = max(i__1, i__2); } else { -/* Computing MAX */ i__1 = maxwrk, i__2 = *m * *m + (*m << 1); - maxwrk = max(i__1,i__2); + maxwrk = max(i__1, i__2); } -/* Computing MAX */ i__1 = maxwrk, i__2 = *m + lwork_dormlq__; - maxwrk = max(i__1,i__2); + maxwrk = max(i__1, i__2); } else { - -/* Path 2 - underdetermined */ - -/* Compute space needed for DGEBRD */ - dgebrd_(m, n, &a[a_offset], lda, &s[1], dum, dum, dum, - dum, &c_n1, info); - lwork_dgebrd__ = (integer) dum[0]; -/* Compute space needed for DORMBR */ - dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, m, &a[a_offset], lda, dum, - &b[b_offset], ldb, dum, &c_n1, info, (ftnlen)1, ( - ftnlen)1, (ftnlen)1); - lwork_dormbr__ = (integer) dum[0]; -/* Compute space needed for DORGBR */ - dorgbr_((char *)"P", m, n, m, &a[a_offset], lda, dum, dum, &c_n1, - info, (ftnlen)1); - lwork_dorgbr__ = (integer) dum[0]; + dgebrd_(m, n, &a[a_offset], lda, &s[1], dum, dum, dum, dum, &c_n1, info); + lwork_dgebrd__ = (integer)dum[0]; + dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, m, &a[a_offset], lda, dum, &b[b_offset], ldb, + dum, &c_n1, info, (ftnlen)1, (ftnlen)1, (ftnlen)1); + lwork_dormbr__ = (integer)dum[0]; + dorgbr_((char *)"P", m, n, m, &a[a_offset], lda, dum, dum, &c_n1, info, (ftnlen)1); + lwork_dorgbr__ = (integer)dum[0]; maxwrk = *m * 3 + lwork_dgebrd__; -/* Computing MAX */ i__1 = maxwrk, i__2 = *m * 3 + lwork_dormbr__; - maxwrk = max(i__1,i__2); -/* Computing MAX */ + maxwrk = max(i__1, i__2); i__1 = maxwrk, i__2 = *m * 3 + lwork_dorgbr__; - maxwrk = max(i__1,i__2); - maxwrk = max(maxwrk,bdspac); -/* Computing MAX */ + maxwrk = max(i__1, i__2); + maxwrk = max(maxwrk, bdspac); i__1 = maxwrk, i__2 = *n * *nrhs; - maxwrk = max(i__1,i__2); + maxwrk = max(i__1, i__2); } } - maxwrk = max(minwrk,maxwrk); + maxwrk = max(minwrk, maxwrk); } - work[1] = (doublereal) maxwrk; - - if (*lwork < minwrk && ! lquery) { + work[1] = (doublereal)maxwrk; + if (*lwork < minwrk && !lquery) { *info = -12; } } - if (*info != 0) { i__1 = -(*info); xerbla_((char *)"DGELSS", &i__1, (ftnlen)6); @@ -508,160 +200,80 @@ f"> */ } else if (lquery) { return 0; } - -/* Quick return if possible */ - if (*m == 0 || *n == 0) { *rank = 0; return 0; } - -/* Get machine parameters */ - eps = dlamch_((char *)"P", (ftnlen)1); sfmin = dlamch_((char *)"S", (ftnlen)1); smlnum = sfmin / eps; bignum = 1. / smlnum; dlabad_(&smlnum, &bignum); - -/* Scale A if max element outside range [SMLNUM,BIGNUM] */ - anrm = dlange_((char *)"M", m, n, &a[a_offset], lda, &work[1], (ftnlen)1); iascl = 0; if (anrm > 0. && anrm < smlnum) { - -/* Scale matrix norm up to SMLNUM */ - - dlascl_((char *)"G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, - info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, info, (ftnlen)1); iascl = 1; } else if (anrm > bignum) { - -/* Scale matrix norm down to BIGNUM */ - - dlascl_((char *)"G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, - info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, info, (ftnlen)1); iascl = 2; } else if (anrm == 0.) { - -/* Matrix all zero. Return zero solution. */ - - i__1 = max(*m,*n); - dlaset_((char *)"F", &i__1, nrhs, &c_b46, &c_b46, &b[b_offset], ldb, (ftnlen) - 1); + i__1 = max(*m, *n); + dlaset_((char *)"F", &i__1, nrhs, &c_b46, &c_b46, &b[b_offset], ldb, (ftnlen)1); dlaset_((char *)"F", &minmn, &c__1, &c_b46, &c_b46, &s[1], &minmn, (ftnlen)1); *rank = 0; goto L70; } - -/* Scale B if max element outside range [SMLNUM,BIGNUM] */ - bnrm = dlange_((char *)"M", m, nrhs, &b[b_offset], ldb, &work[1], (ftnlen)1); ibscl = 0; if (bnrm > 0. && bnrm < smlnum) { - -/* Scale matrix norm up to SMLNUM */ - - dlascl_((char *)"G", &c__0, &c__0, &bnrm, &smlnum, m, nrhs, &b[b_offset], ldb, - info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &bnrm, &smlnum, m, nrhs, &b[b_offset], ldb, info, (ftnlen)1); ibscl = 1; } else if (bnrm > bignum) { - -/* Scale matrix norm down to BIGNUM */ - - dlascl_((char *)"G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb, - info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb, info, (ftnlen)1); ibscl = 2; } - -/* Overdetermined case */ - if (*m >= *n) { - -/* Path 1 - overdetermined or exactly determined */ - mm = *m; if (*m >= mnthr) { - -/* Path 1a - overdetermined, with many more rows than columns */ - mm = *n; itau = 1; iwork = itau + *n; - -/* Compute A=Q*R */ -/* (Workspace: need 2*N, prefer N+N*NB) */ - i__1 = *lwork - iwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__1, - info); - -/* Multiply B by transpose(Q) */ -/* (Workspace: need N+NRHS, prefer N+NRHS*NB) */ - + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__1, info); i__1 = *lwork - iwork + 1; - dormqr_((char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, &work[itau], &b[ - b_offset], ldb, &work[iwork], &i__1, info, (ftnlen)1, ( - ftnlen)1); - -/* Zero out below R */ - + dormqr_((char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, &work[itau], &b[b_offset], ldb, + &work[iwork], &i__1, info, (ftnlen)1, (ftnlen)1); if (*n > 1) { i__1 = *n - 1; i__2 = *n - 1; - dlaset_((char *)"L", &i__1, &i__2, &c_b46, &c_b46, &a[a_dim1 + 2], - lda, (ftnlen)1); + dlaset_((char *)"L", &i__1, &i__2, &c_b46, &c_b46, &a[a_dim1 + 2], lda, (ftnlen)1); } } - ie = 1; itauq = ie + *n; itaup = itauq + *n; iwork = itaup + *n; - -/* Bidiagonalize R in A */ -/* (Workspace: need 3*N+MM, prefer 3*N+(MM+N)*NB) */ - i__1 = *lwork - iwork + 1; - dgebrd_(&mm, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], & - work[itaup], &work[iwork], &i__1, info); - -/* Multiply B by transpose of left bidiagonalizing vectors of R */ -/* (Workspace: need 3*N+NRHS, prefer 3*N+NRHS*NB) */ - + dgebrd_(&mm, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &work[itaup], + &work[iwork], &i__1, info); i__1 = *lwork - iwork + 1; - dormbr_((char *)"Q", (char *)"L", (char *)"T", &mm, nrhs, n, &a[a_offset], lda, &work[itauq], - &b[b_offset], ldb, &work[iwork], &i__1, info, (ftnlen)1, ( - ftnlen)1, (ftnlen)1); - -/* Generate right bidiagonalizing vectors of R in A */ -/* (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB) */ - + dormbr_((char *)"Q", (char *)"L", (char *)"T", &mm, nrhs, n, &a[a_offset], lda, &work[itauq], &b[b_offset], ldb, + &work[iwork], &i__1, info, (ftnlen)1, (ftnlen)1, (ftnlen)1); i__1 = *lwork - iwork + 1; - dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, &work[itaup], &work[iwork], & - i__1, info, (ftnlen)1); + dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, &work[itaup], &work[iwork], &i__1, info, + (ftnlen)1); iwork = ie + *n; - -/* Perform bidiagonal QR iteration */ -/* multiply B by transpose of left singular vectors */ -/* compute right singular vectors in A */ -/* (Workspace: need BDSPAC) */ - - dbdsqr_((char *)"U", n, n, &c__0, nrhs, &s[1], &work[ie], &a[a_offset], lda, - dum, &c__1, &b[b_offset], ldb, &work[iwork], info, (ftnlen)1); + dbdsqr_((char *)"U", n, n, &c__0, nrhs, &s[1], &work[ie], &a[a_offset], lda, dum, &c__1, + &b[b_offset], ldb, &work[iwork], info, (ftnlen)1); if (*info != 0) { goto L70; } - -/* Multiply B by reciprocals of singular values */ - -/* Computing MAX */ d__1 = *rcond * s[1]; - thr = max(d__1,sfmin); + thr = max(d__1, sfmin); if (*rcond < 0.) { -/* Computing MAX */ d__1 = eps * s[1]; - thr = max(d__1,sfmin); + thr = max(d__1, sfmin); } *rank = 0; i__1 = *n; @@ -670,129 +282,73 @@ f"> */ drscl_(nrhs, &s[i__], &b[i__ + b_dim1], ldb); ++(*rank); } else { - dlaset_((char *)"F", &c__1, nrhs, &c_b46, &c_b46, &b[i__ + b_dim1], - ldb, (ftnlen)1); + dlaset_((char *)"F", &c__1, nrhs, &c_b46, &c_b46, &b[i__ + b_dim1], ldb, (ftnlen)1); } -/* L10: */ } - -/* Multiply B by right singular vectors */ -/* (Workspace: need N, prefer N*NRHS) */ - if (*lwork >= *ldb * *nrhs && *nrhs > 1) { - dgemm_((char *)"T", (char *)"N", n, nrhs, n, &c_b79, &a[a_offset], lda, &b[ - b_offset], ldb, &c_b46, &work[1], ldb, (ftnlen)1, (ftnlen) - 1); - dlacpy_((char *)"G", n, nrhs, &work[1], ldb, &b[b_offset], ldb, (ftnlen)1) - ; + dgemm_((char *)"T", (char *)"N", n, nrhs, n, &c_b79, &a[a_offset], lda, &b[b_offset], ldb, &c_b46, + &work[1], ldb, (ftnlen)1, (ftnlen)1); + dlacpy_((char *)"G", n, nrhs, &work[1], ldb, &b[b_offset], ldb, (ftnlen)1); } else if (*nrhs > 1) { chunk = *lwork / *n; i__1 = *nrhs; i__2 = chunk; for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { -/* Computing MIN */ i__3 = *nrhs - i__ + 1; - bl = min(i__3,chunk); - dgemm_((char *)"T", (char *)"N", n, &bl, n, &c_b79, &a[a_offset], lda, &b[i__ - * b_dim1 + 1], ldb, &c_b46, &work[1], n, (ftnlen)1, ( - ftnlen)1); - dlacpy_((char *)"G", n, &bl, &work[1], n, &b[i__ * b_dim1 + 1], ldb, ( - ftnlen)1); -/* L20: */ + bl = min(i__3, chunk); + dgemm_((char *)"T", (char *)"N", n, &bl, n, &c_b79, &a[a_offset], lda, &b[i__ * b_dim1 + 1], ldb, + &c_b46, &work[1], n, (ftnlen)1, (ftnlen)1); + dlacpy_((char *)"G", n, &bl, &work[1], n, &b[i__ * b_dim1 + 1], ldb, (ftnlen)1); } } else { - dgemv_((char *)"T", n, n, &c_b79, &a[a_offset], lda, &b[b_offset], &c__1, - &c_b46, &work[1], &c__1, (ftnlen)1); + dgemv_((char *)"T", n, n, &c_b79, &a[a_offset], lda, &b[b_offset], &c__1, &c_b46, &work[1], + &c__1, (ftnlen)1); dcopy_(n, &work[1], &c__1, &b[b_offset], &c__1); } - - } else /* if(complicated condition) */ { -/* Computing MAX */ - i__2 = *m, i__1 = (*m << 1) - 4, i__2 = max(i__2,i__1), i__2 = max( - i__2,*nrhs), i__1 = *n - *m * 3; - if (*n >= mnthr && *lwork >= (*m << 2) + *m * *m + max(i__2,i__1)) { - -/* Path 2a - underdetermined, with many more columns than rows */ -/* and sufficient workspace for an efficient algorithm */ - + } else { + i__2 = *m, i__1 = (*m << 1) - 4, i__2 = max(i__2, i__1), i__2 = max(i__2, *nrhs), + i__1 = *n - *m * 3; + if (*n >= mnthr && *lwork >= (*m << 2) + *m * *m + max(i__2, i__1)) { ldwork = *m; -/* Computing MAX */ -/* Computing MAX */ - i__3 = *m, i__4 = (*m << 1) - 4, i__3 = max(i__3,i__4), i__3 = - max(i__3,*nrhs), i__4 = *n - *m * 3; - i__2 = (*m << 2) + *m * *lda + max(i__3,i__4), i__1 = *m * *lda + - *m + *m * *nrhs; - if (*lwork >= max(i__2,i__1)) { + i__3 = *m, i__4 = (*m << 1) - 4, i__3 = max(i__3, i__4), i__3 = max(i__3, *nrhs), + i__4 = *n - *m * 3; + i__2 = (*m << 2) + *m * *lda + max(i__3, i__4), i__1 = *m * *lda + *m + *m * *nrhs; + if (*lwork >= max(i__2, i__1)) { ldwork = *lda; } itau = 1; iwork = *m + 1; - -/* Compute A=L*Q */ -/* (Workspace: need 2*M, prefer M+M*NB) */ - i__2 = *lwork - iwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, - info); + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, info); il = iwork; - -/* Copy L to WORK(IL), zeroing out above it */ - - dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[il], &ldwork, (ftnlen) - 1); + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[il], &ldwork, (ftnlen)1); i__2 = *m - 1; i__1 = *m - 1; - dlaset_((char *)"U", &i__2, &i__1, &c_b46, &c_b46, &work[il + ldwork], & - ldwork, (ftnlen)1); + dlaset_((char *)"U", &i__2, &i__1, &c_b46, &c_b46, &work[il + ldwork], &ldwork, (ftnlen)1); ie = il + ldwork * *m; itauq = ie + *m; itaup = itauq + *m; iwork = itaup + *m; - -/* Bidiagonalize L in WORK(IL) */ -/* (Workspace: need M*M+5*M, prefer M*M+4*M+2*M*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(m, m, &work[il], &ldwork, &s[1], &work[ie], &work[itauq], - &work[itaup], &work[iwork], &i__2, info); - -/* Multiply B by transpose of left bidiagonalizing vectors of L */ -/* (Workspace: need M*M+4*M+NRHS, prefer M*M+4*M+NRHS*NB) */ - + dgebrd_(m, m, &work[il], &ldwork, &s[1], &work[ie], &work[itauq], &work[itaup], + &work[iwork], &i__2, info); i__2 = *lwork - iwork + 1; - dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, m, &work[il], &ldwork, &work[ - itauq], &b[b_offset], ldb, &work[iwork], &i__2, info, ( - ftnlen)1, (ftnlen)1, (ftnlen)1); - -/* Generate right bidiagonalizing vectors of R in WORK(IL) */ -/* (Workspace: need M*M+5*M-1, prefer M*M+4*M+(M-1)*NB) */ - + dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, m, &work[il], &ldwork, &work[itauq], &b[b_offset], ldb, + &work[iwork], &i__2, info, (ftnlen)1, (ftnlen)1, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", m, m, m, &work[il], &ldwork, &work[itaup], &work[ - iwork], &i__2, info, (ftnlen)1); + dorgbr_((char *)"P", m, m, m, &work[il], &ldwork, &work[itaup], &work[iwork], &i__2, info, + (ftnlen)1); iwork = ie + *m; - -/* Perform bidiagonal QR iteration, */ -/* computing right singular vectors of L in WORK(IL) and */ -/* multiplying B by transpose of left singular vectors */ -/* (Workspace: need M*M+M+BDSPAC) */ - - dbdsqr_((char *)"U", m, m, &c__0, nrhs, &s[1], &work[ie], &work[il], & - ldwork, &a[a_offset], lda, &b[b_offset], ldb, &work[iwork] - , info, (ftnlen)1); + dbdsqr_((char *)"U", m, m, &c__0, nrhs, &s[1], &work[ie], &work[il], &ldwork, &a[a_offset], lda, + &b[b_offset], ldb, &work[iwork], info, (ftnlen)1); if (*info != 0) { goto L70; } - -/* Multiply B by reciprocals of singular values */ - -/* Computing MAX */ d__1 = *rcond * s[1]; - thr = max(d__1,sfmin); + thr = max(d__1, sfmin); if (*rcond < 0.) { -/* Computing MAX */ d__1 = eps * s[1]; - thr = max(d__1,sfmin); + thr = max(d__1, sfmin); } *rank = 0; i__2 = *m; @@ -801,112 +357,61 @@ f"> */ drscl_(nrhs, &s[i__], &b[i__ + b_dim1], ldb); ++(*rank); } else { - dlaset_((char *)"F", &c__1, nrhs, &c_b46, &c_b46, &b[i__ + b_dim1] - , ldb, (ftnlen)1); + dlaset_((char *)"F", &c__1, nrhs, &c_b46, &c_b46, &b[i__ + b_dim1], ldb, (ftnlen)1); } -/* L30: */ } iwork = ie; - -/* Multiply B by right singular vectors of L in WORK(IL) */ -/* (Workspace: need M*M+2*M, prefer M*M+M+M*NRHS) */ - if (*lwork >= *ldb * *nrhs + iwork - 1 && *nrhs > 1) { - dgemm_((char *)"T", (char *)"N", m, nrhs, m, &c_b79, &work[il], &ldwork, &b[ - b_offset], ldb, &c_b46, &work[iwork], ldb, (ftnlen)1, - (ftnlen)1); - dlacpy_((char *)"G", m, nrhs, &work[iwork], ldb, &b[b_offset], ldb, ( - ftnlen)1); + dgemm_((char *)"T", (char *)"N", m, nrhs, m, &c_b79, &work[il], &ldwork, &b[b_offset], ldb, &c_b46, + &work[iwork], ldb, (ftnlen)1, (ftnlen)1); + dlacpy_((char *)"G", m, nrhs, &work[iwork], ldb, &b[b_offset], ldb, (ftnlen)1); } else if (*nrhs > 1) { chunk = (*lwork - iwork + 1) / *m; i__2 = *nrhs; i__1 = chunk; - for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += - i__1) { -/* Computing MIN */ + for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) { i__3 = *nrhs - i__ + 1; - bl = min(i__3,chunk); - dgemm_((char *)"T", (char *)"N", m, &bl, m, &c_b79, &work[il], &ldwork, & - b[i__ * b_dim1 + 1], ldb, &c_b46, &work[iwork], m, - (ftnlen)1, (ftnlen)1); - dlacpy_((char *)"G", m, &bl, &work[iwork], m, &b[i__ * b_dim1 + 1] - , ldb, (ftnlen)1); -/* L40: */ + bl = min(i__3, chunk); + dgemm_((char *)"T", (char *)"N", m, &bl, m, &c_b79, &work[il], &ldwork, &b[i__ * b_dim1 + 1], + ldb, &c_b46, &work[iwork], m, (ftnlen)1, (ftnlen)1); + dlacpy_((char *)"G", m, &bl, &work[iwork], m, &b[i__ * b_dim1 + 1], ldb, (ftnlen)1); } } else { - dgemv_((char *)"T", m, m, &c_b79, &work[il], &ldwork, &b[b_dim1 + 1], - &c__1, &c_b46, &work[iwork], &c__1, (ftnlen)1); + dgemv_((char *)"T", m, m, &c_b79, &work[il], &ldwork, &b[b_dim1 + 1], &c__1, &c_b46, + &work[iwork], &c__1, (ftnlen)1); dcopy_(m, &work[iwork], &c__1, &b[b_dim1 + 1], &c__1); } - -/* Zero out below first M rows of B */ - i__1 = *n - *m; - dlaset_((char *)"F", &i__1, nrhs, &c_b46, &c_b46, &b[*m + 1 + b_dim1], - ldb, (ftnlen)1); + dlaset_((char *)"F", &i__1, nrhs, &c_b46, &c_b46, &b[*m + 1 + b_dim1], ldb, (ftnlen)1); iwork = itau + *m; - -/* Multiply transpose(Q) by B */ -/* (Workspace: need M+NRHS, prefer M+NRHS*NB) */ - i__1 = *lwork - iwork + 1; - dormlq_((char *)"L", (char *)"T", n, nrhs, m, &a[a_offset], lda, &work[itau], &b[ - b_offset], ldb, &work[iwork], &i__1, info, (ftnlen)1, ( - ftnlen)1); - + dormlq_((char *)"L", (char *)"T", n, nrhs, m, &a[a_offset], lda, &work[itau], &b[b_offset], ldb, + &work[iwork], &i__1, info, (ftnlen)1, (ftnlen)1); } else { - -/* Path 2 - remaining underdetermined cases */ - ie = 1; itauq = ie + *m; itaup = itauq + *m; iwork = itaup + *m; - -/* Bidiagonalize A */ -/* (Workspace: need 3*M+N, prefer 3*M+(M+N)*NB) */ - i__1 = *lwork - iwork + 1; - dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], & - work[itaup], &work[iwork], &i__1, info); - -/* Multiply B by transpose of left bidiagonalizing vectors */ -/* (Workspace: need 3*M+NRHS, prefer 3*M+NRHS*NB) */ - + dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &work[itaup], + &work[iwork], &i__1, info); i__1 = *lwork - iwork + 1; - dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, &work[itauq] - , &b[b_offset], ldb, &work[iwork], &i__1, info, (ftnlen)1, - (ftnlen)1, (ftnlen)1); - -/* Generate right bidiagonalizing vectors in A */ -/* (Workspace: need 4*M, prefer 3*M+M*NB) */ - + dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, &work[itauq], &b[b_offset], ldb, + &work[iwork], &i__1, info, (ftnlen)1, (ftnlen)1, (ftnlen)1); i__1 = *lwork - iwork + 1; - dorgbr_((char *)"P", m, n, m, &a[a_offset], lda, &work[itaup], &work[ - iwork], &i__1, info, (ftnlen)1); + dorgbr_((char *)"P", m, n, m, &a[a_offset], lda, &work[itaup], &work[iwork], &i__1, info, + (ftnlen)1); iwork = ie + *m; - -/* Perform bidiagonal QR iteration, */ -/* computing right singular vectors of A in A and */ -/* multiplying B by transpose of left singular vectors */ -/* (Workspace: need BDSPAC) */ - - dbdsqr_((char *)"L", m, n, &c__0, nrhs, &s[1], &work[ie], &a[a_offset], - lda, dum, &c__1, &b[b_offset], ldb, &work[iwork], info, ( - ftnlen)1); + dbdsqr_((char *)"L", m, n, &c__0, nrhs, &s[1], &work[ie], &a[a_offset], lda, dum, &c__1, + &b[b_offset], ldb, &work[iwork], info, (ftnlen)1); if (*info != 0) { goto L70; } - -/* Multiply B by reciprocals of singular values */ - -/* Computing MAX */ d__1 = *rcond * s[1]; - thr = max(d__1,sfmin); + thr = max(d__1, sfmin); if (*rcond < 0.) { -/* Computing MAX */ d__1 = eps * s[1]; - thr = max(d__1,sfmin); + thr = max(d__1, sfmin); } *rank = 0; i__1 = *m; @@ -915,74 +420,47 @@ f"> */ drscl_(nrhs, &s[i__], &b[i__ + b_dim1], ldb); ++(*rank); } else { - dlaset_((char *)"F", &c__1, nrhs, &c_b46, &c_b46, &b[i__ + b_dim1] - , ldb, (ftnlen)1); + dlaset_((char *)"F", &c__1, nrhs, &c_b46, &c_b46, &b[i__ + b_dim1], ldb, (ftnlen)1); } -/* L50: */ } - -/* Multiply B by right singular vectors of A */ -/* (Workspace: need N, prefer N*NRHS) */ - if (*lwork >= *ldb * *nrhs && *nrhs > 1) { - dgemm_((char *)"T", (char *)"N", n, nrhs, m, &c_b79, &a[a_offset], lda, &b[ - b_offset], ldb, &c_b46, &work[1], ldb, (ftnlen)1, ( - ftnlen)1); - dlacpy_((char *)"F", n, nrhs, &work[1], ldb, &b[b_offset], ldb, ( - ftnlen)1); + dgemm_((char *)"T", (char *)"N", n, nrhs, m, &c_b79, &a[a_offset], lda, &b[b_offset], ldb, &c_b46, + &work[1], ldb, (ftnlen)1, (ftnlen)1); + dlacpy_((char *)"F", n, nrhs, &work[1], ldb, &b[b_offset], ldb, (ftnlen)1); } else if (*nrhs > 1) { chunk = *lwork / *n; i__1 = *nrhs; i__2 = chunk; - for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += - i__2) { -/* Computing MIN */ + for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { i__3 = *nrhs - i__ + 1; - bl = min(i__3,chunk); - dgemm_((char *)"T", (char *)"N", n, &bl, m, &c_b79, &a[a_offset], lda, &b[ - i__ * b_dim1 + 1], ldb, &c_b46, &work[1], n, ( - ftnlen)1, (ftnlen)1); - dlacpy_((char *)"F", n, &bl, &work[1], n, &b[i__ * b_dim1 + 1], - ldb, (ftnlen)1); -/* L60: */ + bl = min(i__3, chunk); + dgemm_((char *)"T", (char *)"N", n, &bl, m, &c_b79, &a[a_offset], lda, &b[i__ * b_dim1 + 1], + ldb, &c_b46, &work[1], n, (ftnlen)1, (ftnlen)1); + dlacpy_((char *)"F", n, &bl, &work[1], n, &b[i__ * b_dim1 + 1], ldb, (ftnlen)1); } } else { - dgemv_((char *)"T", m, n, &c_b79, &a[a_offset], lda, &b[b_offset], & - c__1, &c_b46, &work[1], &c__1, (ftnlen)1); + dgemv_((char *)"T", m, n, &c_b79, &a[a_offset], lda, &b[b_offset], &c__1, &c_b46, &work[1], + &c__1, (ftnlen)1); dcopy_(n, &work[1], &c__1, &b[b_offset], &c__1); } } } - -/* Undo scaling */ - if (iascl == 1) { - dlascl_((char *)"G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb, - info, (ftnlen)1); - dlascl_((char *)"G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], & - minmn, info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb, info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], &minmn, info, (ftnlen)1); } else if (iascl == 2) { - dlascl_((char *)"G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb, - info, (ftnlen)1); - dlascl_((char *)"G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], & - minmn, info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb, info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], &minmn, info, (ftnlen)1); } if (ibscl == 1) { - dlascl_((char *)"G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb, - info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb, info, (ftnlen)1); } else if (ibscl == 2) { - dlascl_((char *)"G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb, - info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb, info, (ftnlen)1); } - L70: - work[1] = (doublereal) maxwrk; + work[1] = (doublereal)maxwrk; return 0; - -/* End of DGELSS */ - -} /* dgelss_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dgemm.cpp b/lib/linalg/dgemm.cpp index 360584e254..6ffa0440c7 100644 --- a/lib/linalg/dgemm.cpp +++ b/lib/linalg/dgemm.cpp @@ -1,250 +1,18 @@ -/* fortran/dgemm.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DGEMM */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) */ - -/* .. Scalar Arguments .. */ -/* DOUBLE PRECISION ALPHA,BETA */ -/* INTEGER K,LDA,LDB,LDC,M,N */ -/* CHARACTER TRANSA,TRANSB */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DGEMM performs one of the matrix-matrix operations */ -/* > */ -/* > C := alpha*op( A )*op( B ) + beta*C, */ -/* > */ -/* > where op( X ) is one of */ -/* > */ -/* > op( X ) = X or op( X ) = X**T, */ -/* > */ -/* > alpha and beta are scalars, and A, B and C are matrices, with op( A ) */ -/* > an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] TRANSA */ -/* > \verbatim */ -/* > TRANSA is CHARACTER*1 */ -/* > On entry, TRANSA specifies the form of op( A ) to be used in */ -/* > the matrix multiplication as follows: */ -/* > */ -/* > TRANSA = 'N' or 'n', op( A ) = A. */ -/* > */ -/* > TRANSA = 'T' or 't', op( A ) = A**T. */ -/* > */ -/* > TRANSA = 'C' or 'c', op( A ) = A**T. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TRANSB */ -/* > \verbatim */ -/* > TRANSB is CHARACTER*1 */ -/* > On entry, TRANSB specifies the form of op( B ) to be used in */ -/* > the matrix multiplication as follows: */ -/* > */ -/* > TRANSB = 'N' or 'n', op( B ) = B. */ -/* > */ -/* > TRANSB = 'T' or 't', op( B ) = B**T. */ -/* > */ -/* > TRANSB = 'C' or 'c', op( B ) = B**T. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > On entry, M specifies the number of rows of the matrix */ -/* > op( A ) and of the matrix C. M must be at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > On entry, N specifies the number of columns of the matrix */ -/* > op( B ) and the number of columns of the matrix C. N must be */ -/* > at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > On entry, K specifies the number of columns of the matrix */ -/* > op( A ) and the number of rows of the matrix op( B ). K must */ -/* > be at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] ALPHA */ -/* > \verbatim */ -/* > ALPHA is DOUBLE PRECISION. */ -/* > On entry, ALPHA specifies the scalar alpha. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is */ -/* > k when TRANSA = 'N' or 'n', and is m otherwise. */ -/* > Before entry with TRANSA = 'N' or 'n', the leading m by k */ -/* > part of the array A must contain the matrix A, otherwise */ -/* > the leading k by m part of the array A must contain the */ -/* > matrix A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > On entry, LDA specifies the first dimension of A as declared */ -/* > in the calling (sub) program. When TRANSA = 'N' or 'n' then */ -/* > LDA must be at least max( 1, m ), otherwise LDA must be at */ -/* > least max( 1, k ). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] B */ -/* > \verbatim */ -/* > B is DOUBLE PRECISION array, dimension ( LDB, kb ), where kb is */ -/* > n when TRANSB = 'N' or 'n', and is k otherwise. */ -/* > Before entry with TRANSB = 'N' or 'n', the leading k by n */ -/* > part of the array B must contain the matrix B, otherwise */ -/* > the leading n by k part of the array B must contain the */ -/* > matrix B. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDB */ -/* > \verbatim */ -/* > LDB is INTEGER */ -/* > On entry, LDB specifies the first dimension of B as declared */ -/* > in the calling (sub) program. When TRANSB = 'N' or 'n' then */ -/* > LDB must be at least max( 1, k ), otherwise LDB must be at */ -/* > least max( 1, n ). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] BETA */ -/* > \verbatim */ -/* > BETA is DOUBLE PRECISION. */ -/* > On entry, BETA specifies the scalar beta. When BETA is */ -/* > supplied as zero then C need not be set on input. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] C */ -/* > \verbatim */ -/* > C is DOUBLE PRECISION array, dimension ( LDC, N ) */ -/* > Before entry, the leading m by n part of the array C must */ -/* > contain the matrix C, except when beta is zero, in which */ -/* > case C need not be set on entry. */ -/* > On exit, the array C is overwritten by the m by n matrix */ -/* > ( alpha*op( A )*op( B ) + beta*C ). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDC */ -/* > \verbatim */ -/* > LDC is INTEGER */ -/* > On entry, LDC specifies the first dimension of C as declared */ -/* > in the calling (sub) program. LDC must be at least */ -/* > max( 1, m ). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup double_blas_level3 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > Level 3 Blas routine. */ -/* > */ -/* > -- Written on 8-February-1989. */ -/* > Jack Dongarra, Argonne National Laboratory. */ -/* > Iain Duff, AERE Harwell. */ -/* > Jeremy Du Croz, Numerical Algorithms Group Ltd. */ -/* > Sven Hammarling, Numerical Algorithms Group Ltd. */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dgemm_(char *transa, char *transb, integer *m, integer * - n, integer *k, doublereal *alpha, doublereal *a, integer *lda, - doublereal *b, integer *ldb, doublereal *beta, doublereal *c__, - integer *ldc, ftnlen transa_len, ftnlen transb_len) +int dgemm_(char *transa, char *transb, integer *m, integer *n, integer *k, doublereal *alpha, + doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal *beta, + doublereal *c__, integer *ldc, ftnlen transa_len, ftnlen transb_len) { - /* System generated locals */ - integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, - i__3; - - /* Local variables */ + integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, i__3; integer i__, j, l, info; logical nota, notb; doublereal temp; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer nrowa, nrowb; - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - - -/* -- Reference BLAS level3 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. Parameters .. */ -/* .. */ - -/* Set NOTA and NOTB as true if A and B respectively are not */ -/* transposed and set NROWA and NROWB as the number of rows of A */ -/* and B respectively. */ - - /* Parameter adjustments */ + extern int xerbla_(char *, integer *, ftnlen); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; @@ -254,8 +22,6 @@ extern "C" { c_dim1 = *ldc; c_offset = 1 + c_dim1; c__ -= c_offset; - - /* Function Body */ nota = lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1); notb = lsame_(transb, (char *)"N", (ftnlen)1, (ftnlen)1); if (nota) { @@ -268,15 +34,12 @@ extern "C" { } else { nrowb = *n; } - -/* Test the input parameters. */ - info = 0; - if (! nota && ! lsame_(transa, (char *)"C", (ftnlen)1, (ftnlen)1) && ! lsame_( - transa, (char *)"T", (ftnlen)1, (ftnlen)1)) { + if (!nota && !lsame_(transa, (char *)"C", (ftnlen)1, (ftnlen)1) && + !lsame_(transa, (char *)"T", (ftnlen)1, (ftnlen)1)) { info = 1; - } else if (! notb && ! lsame_(transb, (char *)"C", (ftnlen)1, (ftnlen)1) && ! - lsame_(transb, (char *)"T", (ftnlen)1, (ftnlen)1)) { + } else if (!notb && !lsame_(transb, (char *)"C", (ftnlen)1, (ftnlen)1) && + !lsame_(transb, (char *)"T", (ftnlen)1, (ftnlen)1)) { info = 2; } else if (*m < 0) { info = 3; @@ -284,26 +47,20 @@ extern "C" { info = 4; } else if (*k < 0) { info = 5; - } else if (*lda < max(1,nrowa)) { + } else if (*lda < max(1, nrowa)) { info = 8; - } else if (*ldb < max(1,nrowb)) { + } else if (*ldb < max(1, nrowb)) { info = 10; - } else if (*ldc < max(1,*m)) { + } else if (*ldc < max(1, *m)) { info = 13; } if (info != 0) { xerbla_((char *)"DGEMM ", &info, (ftnlen)6); return 0; } - -/* Quick return if possible. */ - if (*m == 0 || *n == 0 || (*alpha == 0. || *k == 0) && *beta == 1.) { return 0; } - -/* And if alpha.eq.zero. */ - if (*alpha == 0.) { if (*beta == 0.) { i__1 = *n; @@ -311,9 +68,7 @@ extern "C" { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { c__[i__ + j * c_dim1] = 0.; -/* L10: */ } -/* L20: */ } } else { i__1 = *n; @@ -321,34 +76,24 @@ extern "C" { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; -/* L30: */ } -/* L40: */ } } return 0; } - -/* Start the operations. */ - if (notb) { if (nota) { - -/* Form C := alpha*A*B + beta*C. */ - i__1 = *n; for (j = 1; j <= i__1; ++j) { if (*beta == 0.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { c__[i__ + j * c_dim1] = 0.; -/* L50: */ } } else if (*beta != 1.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; -/* L60: */ } } i__2 = *k; @@ -357,16 +102,10 @@ extern "C" { i__3 = *m; for (i__ = 1; i__ <= i__3; ++i__) { c__[i__ + j * c_dim1] += temp * a[i__ + l * a_dim1]; -/* L70: */ } -/* L80: */ } -/* L90: */ } } else { - -/* Form C := alpha*A**T*B + beta*C */ - i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; @@ -375,37 +114,28 @@ extern "C" { i__3 = *k; for (l = 1; l <= i__3; ++l) { temp += a[l + i__ * a_dim1] * b[l + j * b_dim1]; -/* L100: */ } if (*beta == 0.) { c__[i__ + j * c_dim1] = *alpha * temp; } else { - c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[ - i__ + j * c_dim1]; + c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[i__ + j * c_dim1]; } -/* L110: */ } -/* L120: */ } } } else { if (nota) { - -/* Form C := alpha*A*B**T + beta*C */ - i__1 = *n; for (j = 1; j <= i__1; ++j) { if (*beta == 0.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { c__[i__ + j * c_dim1] = 0.; -/* L130: */ } } else if (*beta != 1.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; -/* L140: */ } } i__2 = *k; @@ -414,16 +144,10 @@ extern "C" { i__3 = *m; for (i__ = 1; i__ <= i__3; ++i__) { c__[i__ + j * c_dim1] += temp * a[i__ + l * a_dim1]; -/* L150: */ } -/* L160: */ } -/* L170: */ } } else { - -/* Form C := alpha*A**T*B**T + beta*C */ - i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; @@ -432,27 +156,18 @@ extern "C" { i__3 = *k; for (l = 1; l <= i__3; ++l) { temp += a[l + i__ * a_dim1] * b[j + l * b_dim1]; -/* L180: */ } if (*beta == 0.) { c__[i__ + j * c_dim1] = *alpha * temp; } else { - c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[ - i__ + j * c_dim1]; + c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[i__ + j * c_dim1]; } -/* L190: */ } -/* L200: */ } } } - return 0; - -/* End of DGEMM */ - -} /* dgemm_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dgemv.cpp b/lib/linalg/dgemv.cpp index 5e82c1144c..1ec78f9529 100644 --- a/lib/linalg/dgemv.cpp +++ b/lib/linalg/dgemv.cpp @@ -1,231 +1,31 @@ -/* fortran/dgemv.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DGEMV */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) */ - -/* .. Scalar Arguments .. */ -/* DOUBLE PRECISION ALPHA,BETA */ -/* INTEGER INCX,INCY,LDA,M,N */ -/* CHARACTER TRANS */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A(LDA,*),X(*),Y(*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DGEMV performs one of the matrix-vector operations */ -/* > */ -/* > y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, */ -/* > */ -/* > where alpha and beta are scalars, x and y are vectors and A is an */ -/* > m by n matrix. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] TRANS */ -/* > \verbatim */ -/* > TRANS is CHARACTER*1 */ -/* > On entry, TRANS specifies the operation to be performed as */ -/* > follows: */ -/* > */ -/* > TRANS = 'N' or 'n' y := alpha*A*x + beta*y. */ -/* > */ -/* > TRANS = 'T' or 't' y := alpha*A**T*x + beta*y. */ -/* > */ -/* > TRANS = 'C' or 'c' y := alpha*A**T*x + beta*y. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > On entry, M specifies the number of rows of the matrix A. */ -/* > M must be at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > On entry, N specifies the number of columns of the matrix A. */ -/* > N must be at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] ALPHA */ -/* > \verbatim */ -/* > ALPHA is DOUBLE PRECISION. */ -/* > On entry, ALPHA specifies the scalar alpha. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension ( LDA, N ) */ -/* > Before entry, the leading m by n part of the array A must */ -/* > contain the matrix of coefficients. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > On entry, LDA specifies the first dimension of A as declared */ -/* > in the calling (sub) program. LDA must be at least */ -/* > max( 1, m ). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] X */ -/* > \verbatim */ -/* > X is DOUBLE PRECISION array, dimension at least */ -/* > ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' */ -/* > and at least */ -/* > ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. */ -/* > Before entry, the incremented array X must contain the */ -/* > vector x. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > On entry, INCX specifies the increment for the elements of */ -/* > X. INCX must not be zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] BETA */ -/* > \verbatim */ -/* > BETA is DOUBLE PRECISION. */ -/* > On entry, BETA specifies the scalar beta. When BETA is */ -/* > supplied as zero then Y need not be set on input. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] Y */ -/* > \verbatim */ -/* > Y is DOUBLE PRECISION array, dimension at least */ -/* > ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' */ -/* > and at least */ -/* > ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. */ -/* > Before entry with BETA non-zero, the incremented array Y */ -/* > must contain the vector y. On exit, Y is overwritten by the */ -/* > updated vector y. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCY */ -/* > \verbatim */ -/* > INCY is INTEGER */ -/* > On entry, INCY specifies the increment for the elements of */ -/* > Y. INCY must not be zero. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup double_blas_level2 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > Level 2 Blas routine. */ -/* > The vector and matrix arguments are not referenced when N = 0, or M = 0 */ -/* > */ -/* > -- Written on 22-October-1986. */ -/* > Jack Dongarra, Argonne National Lab. */ -/* > Jeremy Du Croz, Nag Central Office. */ -/* > Sven Hammarling, Nag Central Office. */ -/* > Richard Hanson, Sandia National Labs. */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dgemv_(char *trans, integer *m, integer *n, doublereal * - alpha, doublereal *a, integer *lda, doublereal *x, integer *incx, - doublereal *beta, doublereal *y, integer *incy, ftnlen trans_len) +int dgemv_(char *trans, integer *m, integer *n, doublereal *alpha, doublereal *a, integer *lda, + doublereal *x, integer *incx, doublereal *beta, doublereal *y, integer *incy, + ftnlen trans_len) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; - - /* Local variables */ integer i__, j, ix, iy, jx, jy, kx, ky, info; doublereal temp; integer lenx, leny; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - - -/* -- Reference BLAS level2 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ + extern int xerbla_(char *, integer *, ftnlen); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --x; --y; - - /* Function Body */ info = 0; - if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"T", ( - ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1) - ) { + if (!lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && !lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1) && + !lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { info = 1; } else if (*m < 0) { info = 2; } else if (*n < 0) { info = 3; - } else if (*lda < max(1,*m)) { + } else if (*lda < max(1, *m)) { info = 6; } else if (*incx == 0) { info = 8; @@ -236,16 +36,9 @@ extern "C" { xerbla_((char *)"DGEMV ", &info, (ftnlen)6); return 0; } - -/* Quick return if possible. */ - if (*m == 0 || *n == 0 || *alpha == 0. && *beta == 1.) { return 0; } - -/* Set LENX and LENY, the lengths of the vectors x and y, and set */ -/* up the start points in X and Y. */ - if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { lenx = *n; leny = *m; @@ -263,25 +56,17 @@ extern "C" { } else { ky = 1 - (leny - 1) * *incy; } - -/* Start the operations. In this version the elements of A are */ -/* accessed sequentially with one pass through A. */ - -/* First form y := beta*y. */ - if (*beta != 1.) { if (*incy == 1) { if (*beta == 0.) { i__1 = leny; for (i__ = 1; i__ <= i__1; ++i__) { y[i__] = 0.; -/* L10: */ } } else { i__1 = leny; for (i__ = 1; i__ <= i__1; ++i__) { y[i__] = *beta * y[i__]; -/* L20: */ } } } else { @@ -291,14 +76,12 @@ extern "C" { for (i__ = 1; i__ <= i__1; ++i__) { y[iy] = 0.; iy += *incy; -/* L30: */ } } else { i__1 = leny; for (i__ = 1; i__ <= i__1; ++i__) { y[iy] = *beta * y[iy]; iy += *incy; -/* L40: */ } } } @@ -307,9 +90,6 @@ extern "C" { return 0; } if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { - -/* Form y := alpha*A*x + y. */ - jx = kx; if (*incy == 1) { i__1 = *n; @@ -318,10 +98,8 @@ extern "C" { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { y[i__] += temp * a[i__ + j * a_dim1]; -/* L50: */ } jx += *incx; -/* L60: */ } } else { i__1 = *n; @@ -332,16 +110,11 @@ extern "C" { for (i__ = 1; i__ <= i__2; ++i__) { y[iy] += temp * a[i__ + j * a_dim1]; iy += *incy; -/* L70: */ } jx += *incx; -/* L80: */ } } } else { - -/* Form y := alpha*A**T*x + y. */ - jy = ky; if (*incx == 1) { i__1 = *n; @@ -350,11 +123,9 @@ extern "C" { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { temp += a[i__ + j * a_dim1] * x[i__]; -/* L90: */ } y[jy] += *alpha * temp; jy += *incy; -/* L100: */ } } else { i__1 = *n; @@ -365,21 +136,14 @@ extern "C" { for (i__ = 1; i__ <= i__2; ++i__) { temp += a[i__ + j * a_dim1] * x[ix]; ix += *incx; -/* L110: */ } y[jy] += *alpha * temp; jy += *incy; -/* L120: */ } } } - return 0; - -/* End of DGEMV */ - -} /* dgemv_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dgeqr2.cpp b/lib/linalg/dgeqr2.cpp index 6cc1bc8400..5c3b885bfb 100644 --- a/lib/linalg/dgeqr2.cpp +++ b/lib/linalg/dgeqr2.cpp @@ -1,209 +1,29 @@ -/* fortran/dgeqr2.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; - -/* > \brief \b DGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorit -hm. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DGEQR2 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DGEQR2( M, N, A, LDA, TAU, WORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INFO, LDA, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DGEQR2 computes a QR factorization of a real m-by-n matrix A: */ -/* > */ -/* > A = Q * ( R ), */ -/* > ( 0 ) */ -/* > */ -/* > where: */ -/* > */ -/* > Q is a m-by-m orthogonal matrix; */ -/* > R is an upper-triangular n-by-n matrix; */ -/* > 0 is a (m-n)-by-n zero matrix, if m > n. */ -/* > */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix A. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On entry, the m by n matrix A. */ -/* > On exit, the elements on and above the diagonal of the array */ -/* > contain the min(m,n) by n upper trapezoidal matrix R (R is */ -/* > upper triangular if m >= n); the elements below the diagonal, */ -/* > with the array TAU, represent the orthogonal matrix Q as a */ -/* > product of elementary reflectors (see Further Details). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] TAU */ -/* > \verbatim */ -/* > TAU is DOUBLE PRECISION array, dimension (min(M,N)) */ -/* > The scalar factors of the elementary reflectors (see Further */ -/* > Details). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (N) */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleGEcomputational */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > The matrix Q is represented as a product of elementary reflectors */ -/* > */ -/* > Q = H(1) H(2) . . . H(k), where k = min(m,n). */ -/* > */ -/* > Each H(i) has the form */ -/* > */ -/* > H(i) = I - tau * v * v**T */ -/* > */ -/* > where tau is a real scalar, and v is a real vector with */ -/* > v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), */ -/* > and tau in TAU(i). */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dgeqr2_(integer *m, integer *n, doublereal *a, integer * - lda, doublereal *tau, doublereal *work, integer *info) +int dgeqr2_(integer *m, integer *n, doublereal *a, integer *lda, doublereal *tau, doublereal *work, + integer *info) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; - - /* Local variables */ integer i__, k; doublereal aii; - extern /* Subroutine */ int dlarf_(char *, integer *, integer *, - doublereal *, integer *, doublereal *, doublereal *, integer *, - doublereal *, ftnlen), dlarfg_(integer *, doublereal *, - doublereal *, integer *, doublereal *), xerbla_(char *, integer *, - ftnlen); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments */ - - /* Parameter adjustments */ + extern int dlarf_(char *, integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, doublereal *, ftnlen), + dlarfg_(integer *, doublereal *, doublereal *, integer *, doublereal *), + xerbla_(char *, integer *, ftnlen); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --tau; --work; - - /* Function Body */ *info = 0; if (*m < 0) { *info = -1; } else if (*n < 0) { *info = -2; - } else if (*lda < max(1,*m)) { + } else if (*lda < max(1, *m)) { *info = -4; } if (*info != 0) { @@ -211,40 +31,24 @@ f"> */ xerbla_((char *)"DGEQR2", &i__1, (ftnlen)6); return 0; } - - k = min(*m,*n); - + k = min(*m, *n); i__1 = k; for (i__ = 1; i__ <= i__1; ++i__) { - -/* Generate elementary reflector H(i) to annihilate A(i+1:m,i) */ - i__2 = *m - i__ + 1; -/* Computing MIN */ i__3 = i__ + 1; - dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[min(i__3,*m) + i__ * a_dim1] - , &c__1, &tau[i__]); + dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[min(i__3, *m) + i__ * a_dim1], &c__1, &tau[i__]); if (i__ < *n) { - -/* Apply H(i) to A(i:m,i+1:n) from the left */ - aii = a[i__ + i__ * a_dim1]; a[i__ + i__ * a_dim1] = 1.; i__2 = *m - i__ + 1; i__3 = *n - i__; - dlarf_((char *)"Left", &i__2, &i__3, &a[i__ + i__ * a_dim1], &c__1, &tau[ - i__], &a[i__ + (i__ + 1) * a_dim1], lda, &work[1], ( - ftnlen)4); + dlarf_((char *)"Left", &i__2, &i__3, &a[i__ + i__ * a_dim1], &c__1, &tau[i__], + &a[i__ + (i__ + 1) * a_dim1], lda, &work[1], (ftnlen)4); a[i__ + i__ * a_dim1] = aii; } -/* L10: */ } return 0; - -/* End of DGEQR2 */ - -} /* dgeqr2_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dgeqrf.cpp b/lib/linalg/dgeqrf.cpp index 57b92689b9..6c70b9f7f7 100644 --- a/lib/linalg/dgeqrf.cpp +++ b/lib/linalg/dgeqrf.cpp @@ -1,240 +1,45 @@ -/* fortran/dgeqrf.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static integer c_n1 = -1; static integer c__3 = 3; static integer c__2 = 2; - -/* > \brief \b DGEQRF */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DGEQRF + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DGEQRF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INFO, LDA, LWORK, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DGEQRF computes a QR factorization of a real M-by-N matrix A: */ -/* > */ -/* > A = Q * ( R ), */ -/* > ( 0 ) */ -/* > */ -/* > where: */ -/* > */ -/* > Q is a M-by-M orthogonal matrix; */ -/* > R is an upper-triangular N-by-N matrix; */ -/* > 0 is a (M-N)-by-N zero matrix, if M > N. */ -/* > */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix A. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On entry, the M-by-N matrix A. */ -/* > On exit, the elements on and above the diagonal of the array */ -/* > contain the min(M,N)-by-N upper trapezoidal matrix R (R is */ -/* > upper triangular if m >= n); the elements below the diagonal, */ -/* > with the array TAU, represent the orthogonal matrix Q as a */ -/* > product of min(m,n) elementary reflectors (see Further */ -/* > Details). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] TAU */ -/* > \verbatim */ -/* > TAU is DOUBLE PRECISION array, dimension (min(M,N)) */ -/* > The scalar factors of the elementary reflectors (see Further */ -/* > Details). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ -/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LWORK */ -/* > \verbatim */ -/* > LWORK is INTEGER */ -/* > The dimension of the array WORK. */ -/* > LWORK >= 1, if MIN(M,N) = 0, and LWORK >= N, otherwise. */ -/* > For optimum performance LWORK >= N*NB, where NB is */ -/* > the optimal blocksize. */ -/* > */ -/* > If LWORK = -1, then a workspace query is assumed; the routine */ -/* > only calculates the optimal size of the WORK array, returns */ -/* > this value as the first entry of the WORK array, and no error */ -/* > message related to LWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleGEcomputational */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > The matrix Q is represented as a product of elementary reflectors */ -/* > */ -/* > Q = H(1) H(2) . . . H(k), where k = min(m,n). */ -/* > */ -/* > Each H(i) has the form */ -/* > */ -/* > H(i) = I - tau * v * v**T */ -/* > */ -/* > where tau is a real scalar, and v is a real vector with */ -/* > v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), */ -/* > and tau in TAU(i). */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dgeqrf_(integer *m, integer *n, doublereal *a, integer * - lda, doublereal *tau, doublereal *work, integer *lwork, integer *info) +int dgeqrf_(integer *m, integer *n, doublereal *a, integer *lda, doublereal *tau, doublereal *work, + integer *lwork, integer *info) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4; - - /* Local variables */ integer i__, k, ib, nb, nx, iws, nbmin, iinfo; - extern /* Subroutine */ int dgeqr2_(integer *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *), dlarfb_(char *, - char *, char *, char *, integer *, integer *, integer *, - doublereal *, integer *, doublereal *, integer *, doublereal *, - integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, - ftnlen), dlarft_(char *, char *, integer *, integer *, doublereal - *, integer *, doublereal *, doublereal *, integer *, ftnlen, - ftnlen), xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern int dgeqr2_(integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *), + dlarfb_(char *, char *, char *, char *, integer *, integer *, integer *, doublereal *, + integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, + integer *, ftnlen, ftnlen, ftnlen, ftnlen), + dlarft_(char *, char *, integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, ftnlen, ftnlen), + xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); integer ldwork, lwkopt; logical lquery; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --tau; --work; - - /* Function Body */ - k = min(*m,*n); + k = min(*m, *n); *info = 0; - nb = ilaenv_(&c__1, (char *)"DGEQRF", (char *)" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen) - 1); + nb = ilaenv_(&c__1, (char *)"DGEQRF", (char *)" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); lquery = *lwork == -1; if (*m < 0) { *info = -1; } else if (*n < 0) { *info = -2; - } else if (*lda < max(1,*m)) { + } else if (*lda < max(1, *m)) { *info = -4; - } else if (! lquery) { - if (*lwork <= 0 || *m > 0 && *lwork < max(1,*n)) { + } else if (!lquery) { + if (*lwork <= 0 || *m > 0 && *lwork < max(1, *n)) { *info = -7; } } @@ -248,107 +53,61 @@ f"> */ } else { lwkopt = *n * nb; } - work[1] = (doublereal) lwkopt; + work[1] = (doublereal)lwkopt; return 0; } - -/* Quick return if possible */ - if (k == 0) { work[1] = 1.; return 0; } - nbmin = 2; nx = 0; iws = *n; if (nb > 1 && nb < k) { - -/* Determine when to cross over from blocked to unblocked code. */ - -/* Computing MAX */ - i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"DGEQRF", (char *)" ", m, n, &c_n1, &c_n1, ( - ftnlen)6, (ftnlen)1); - nx = max(i__1,i__2); + i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"DGEQRF", (char *)" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); + nx = max(i__1, i__2); if (nx < k) { - -/* Determine if workspace is large enough for blocked code. */ - ldwork = *n; iws = ldwork * nb; if (*lwork < iws) { - -/* Not enough workspace to use optimal NB: reduce NB and */ -/* determine the minimum value of NB. */ - nb = *lwork / ldwork; -/* Computing MAX */ - i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DGEQRF", (char *)" ", m, n, &c_n1, & - c_n1, (ftnlen)6, (ftnlen)1); - nbmin = max(i__1,i__2); + i__1 = 2, + i__2 = ilaenv_(&c__2, (char *)"DGEQRF", (char *)" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); + nbmin = max(i__1, i__2); } } } - if (nb >= nbmin && nb < k && nx < k) { - -/* Use blocked code initially */ - i__1 = k - nx; i__2 = nb; for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { -/* Computing MIN */ i__3 = k - i__ + 1; - ib = min(i__3,nb); - -/* Compute the QR factorization of the current block */ -/* A(i:m,i:i+ib-1) */ - + ib = min(i__3, nb); i__3 = *m - i__ + 1; - dgeqr2_(&i__3, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[ - 1], &iinfo); + dgeqr2_(&i__3, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[1], &iinfo); if (i__ + ib <= *n) { - -/* Form the triangular factor of the block reflector */ -/* H = H(i) H(i+1) . . . H(i+ib-1) */ - i__3 = *m - i__ + 1; - dlarft_((char *)"Forward", (char *)"Columnwise", &i__3, &ib, &a[i__ + i__ * - a_dim1], lda, &tau[i__], &work[1], &ldwork, (ftnlen)7, - (ftnlen)10); - -/* Apply H**T to A(i:m,i+ib:n) from the left */ - + dlarft_((char *)"Forward", (char *)"Columnwise", &i__3, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], + &work[1], &ldwork, (ftnlen)7, (ftnlen)10); i__3 = *m - i__ + 1; i__4 = *n - i__ - ib + 1; - dlarfb_((char *)"Left", (char *)"Transpose", (char *)"Forward", (char *)"Columnwise", &i__3, & - i__4, &ib, &a[i__ + i__ * a_dim1], lda, &work[1], & - ldwork, &a[i__ + (i__ + ib) * a_dim1], lda, &work[ib - + 1], &ldwork, (ftnlen)4, (ftnlen)9, (ftnlen)7, ( - ftnlen)10); + dlarfb_((char *)"Left", (char *)"Transpose", (char *)"Forward", (char *)"Columnwise", &i__3, &i__4, &ib, + &a[i__ + i__ * a_dim1], lda, &work[1], &ldwork, + &a[i__ + (i__ + ib) * a_dim1], lda, &work[ib + 1], &ldwork, (ftnlen)4, + (ftnlen)9, (ftnlen)7, (ftnlen)10); } -/* L10: */ } } else { i__ = 1; } - -/* Use unblocked code to factor the last or only block. */ - if (i__ <= k) { i__2 = *m - i__ + 1; i__1 = *n - i__ + 1; - dgeqr2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[1] - , &iinfo); + dgeqr2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[1], &iinfo); } - - work[1] = (doublereal) iws; + work[1] = (doublereal)iws; return 0; - -/* End of DGEQRF */ - -} /* dgeqrf_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dger.cpp b/lib/linalg/dger.cpp index 9bb0d19982..46447e29f3 100644 --- a/lib/linalg/dger.cpp +++ b/lib/linalg/dger.cpp @@ -1,191 +1,19 @@ -/* fortran/dger.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DGER */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DGER(M,N,ALPHA,X,INCX,Y,INCY,A,LDA) */ - -/* .. Scalar Arguments .. */ -/* DOUBLE PRECISION ALPHA */ -/* INTEGER INCX,INCY,LDA,M,N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A(LDA,*),X(*),Y(*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DGER performs the rank 1 operation */ -/* > */ -/* > A := alpha*x*y**T + A, */ -/* > */ -/* > where alpha is a scalar, x is an m element vector, y is an n element */ -/* > vector and A is an m by n matrix. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > On entry, M specifies the number of rows of the matrix A. */ -/* > M must be at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > On entry, N specifies the number of columns of the matrix A. */ -/* > N must be at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] ALPHA */ -/* > \verbatim */ -/* > ALPHA is DOUBLE PRECISION. */ -/* > On entry, ALPHA specifies the scalar alpha. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] X */ -/* > \verbatim */ -/* > X is DOUBLE PRECISION array, dimension at least */ -/* > ( 1 + ( m - 1 )*abs( INCX ) ). */ -/* > Before entry, the incremented array X must contain the m */ -/* > element vector x. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > On entry, INCX specifies the increment for the elements of */ -/* > X. INCX must not be zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] Y */ -/* > \verbatim */ -/* > Y is DOUBLE PRECISION array, dimension at least */ -/* > ( 1 + ( n - 1 )*abs( INCY ) ). */ -/* > Before entry, the incremented array Y must contain the n */ -/* > element vector y. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCY */ -/* > \verbatim */ -/* > INCY is INTEGER */ -/* > On entry, INCY specifies the increment for the elements of */ -/* > Y. INCY must not be zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension ( LDA, N ) */ -/* > Before entry, the leading m by n part of the array A must */ -/* > contain the matrix of coefficients. On exit, A is */ -/* > overwritten by the updated matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > On entry, LDA specifies the first dimension of A as declared */ -/* > in the calling (sub) program. LDA must be at least */ -/* > max( 1, m ). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup double_blas_level2 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > Level 2 Blas routine. */ -/* > */ -/* > -- Written on 22-October-1986. */ -/* > Jack Dongarra, Argonne National Lab. */ -/* > Jeremy Du Croz, Nag Central Office. */ -/* > Sven Hammarling, Nag Central Office. */ -/* > Richard Hanson, Sandia National Labs. */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dger_(integer *m, integer *n, doublereal *alpha, - doublereal *x, integer *incx, doublereal *y, integer *incy, - doublereal *a, integer *lda) +int dger_(integer *m, integer *n, doublereal *alpha, doublereal *x, integer *incx, doublereal *y, + integer *incy, doublereal *a, integer *lda) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; - - /* Local variables */ integer i__, j, ix, jy, kx, info; doublereal temp; - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - - -/* -- Reference BLAS level2 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ + extern int xerbla_(char *, integer *, ftnlen); --x; --y; a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; - - /* Function Body */ info = 0; if (*m < 0) { info = 1; @@ -195,23 +23,16 @@ extern "C" { info = 5; } else if (*incy == 0) { info = 7; - } else if (*lda < max(1,*m)) { + } else if (*lda < max(1, *m)) { info = 9; } if (info != 0) { xerbla_((char *)"DGER ", &info, (ftnlen)6); return 0; } - -/* Quick return if possible. */ - if (*m == 0 || *n == 0 || *alpha == 0.) { return 0; } - -/* Start the operations. In this version the elements of A are */ -/* accessed sequentially with one pass through A. */ - if (*incy > 0) { jy = 1; } else { @@ -225,11 +46,9 @@ extern "C" { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { a[i__ + j * a_dim1] += x[i__] * temp; -/* L10: */ } } jy += *incy; -/* L20: */ } } else { if (*incx > 0) { @@ -246,20 +65,13 @@ extern "C" { for (i__ = 1; i__ <= i__2; ++i__) { a[i__ + j * a_dim1] += x[ix] * temp; ix += *incx; -/* L30: */ } } jy += *incy; -/* L40: */ } } - return 0; - -/* End of DGER */ - -} /* dger_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dgesv.cpp b/lib/linalg/dgesv.cpp index c2e0232c37..41f85f4566 100644 --- a/lib/linalg/dgesv.cpp +++ b/lib/linalg/dgesv.cpp @@ -1,176 +1,15 @@ -/* fortran/dgesv.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief DGESV computes the solution to system of linear equations A * X = B for GE matrices */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DGESV + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DGESV( N, NRHS, A, LDA, IPIV, B, LDB, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INFO, LDA, LDB, N, NRHS */ -/* .. */ -/* .. Array Arguments .. */ -/* INTEGER IPIV( * ) */ -/* DOUBLE PRECISION A( LDA, * ), B( LDB, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DGESV computes the solution to a real system of linear equations */ -/* > A * X = B, */ -/* > where A is an N-by-N matrix and X and B are N-by-NRHS matrices. */ -/* > */ -/* > The LU decomposition with partial pivoting and row interchanges is */ -/* > used to factor A as */ -/* > A = P * L * U, */ -/* > where P is a permutation matrix, L is unit lower triangular, and U is */ -/* > upper triangular. The factored form of A is then used to solve the */ -/* > system of equations A * X = B. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of linear equations, i.e., the order of the */ -/* > matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] NRHS */ -/* > \verbatim */ -/* > NRHS is INTEGER */ -/* > The number of right hand sides, i.e., the number of columns */ -/* > of the matrix B. NRHS >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On entry, the N-by-N coefficient matrix A. */ -/* > On exit, the factors L and U from the factorization */ -/* > A = P*L*U; the unit diagonal elements of L are not stored. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] IPIV */ -/* > \verbatim */ -/* > IPIV is INTEGER array, dimension (N) */ -/* > The pivot indices that define the permutation matrix P; */ -/* > row i of the matrix was interchanged with row IPIV(i). */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] B */ -/* > \verbatim */ -/* > B is DOUBLE PRECISION array, dimension (LDB,NRHS) */ -/* > On entry, the N-by-NRHS matrix of right hand side matrix B. */ -/* > On exit, if INFO = 0, the N-by-NRHS solution matrix X. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDB */ -/* > \verbatim */ -/* > LDB is INTEGER */ -/* > The leading dimension of the array B. LDB >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > > 0: if INFO = i, U(i,i) is exactly zero. The factorization */ -/* > has been completed, but the factor U is exactly */ -/* > singular, so the solution could not be computed. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleGEsolve */ - -/* ===================================================================== */ -/* Subroutine */ int dgesv_(integer *n, integer *nrhs, doublereal *a, integer - *lda, integer *ipiv, doublereal *b, integer *ldb, integer *info) +int dgesv_(integer *n, integer *nrhs, doublereal *a, integer *lda, integer *ipiv, doublereal *b, + integer *ldb, integer *info) { - /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1; - - /* Local variables */ - extern /* Subroutine */ int dgetrf_(integer *, integer *, doublereal *, - integer *, integer *, integer *), xerbla_(char *, integer *, - ftnlen), dgetrs_(char *, integer *, integer *, doublereal *, - integer *, integer *, doublereal *, integer *, integer *, ftnlen); - - -/* -- LAPACK driver routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ + extern int dgetrf_(integer *, integer *, doublereal *, integer *, integer *, integer *), + xerbla_(char *, integer *, ftnlen), + dgetrs_(char *, integer *, integer *, doublereal *, integer *, integer *, doublereal *, + integer *, integer *, ftnlen); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; @@ -178,16 +17,14 @@ extern "C" { b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; - - /* Function Body */ *info = 0; if (*n < 0) { *info = -1; } else if (*nrhs < 0) { *info = -2; - } else if (*lda < max(1,*n)) { + } else if (*lda < max(1, *n)) { *info = -4; - } else if (*ldb < max(1,*n)) { + } else if (*ldb < max(1, *n)) { *info = -7; } if (*info != 0) { @@ -195,23 +32,13 @@ extern "C" { xerbla_((char *)"DGESV ", &i__1, (ftnlen)6); return 0; } - -/* Compute the LU factorization of A. */ - dgetrf_(n, n, &a[a_offset], lda, &ipiv[1], info); if (*info == 0) { - -/* Solve the system A*X = B, overwriting B with X. */ - - dgetrs_((char *)"No transpose", n, nrhs, &a[a_offset], lda, &ipiv[1], &b[ - b_offset], ldb, info, (ftnlen)12); + dgetrs_((char *)"No transpose", n, nrhs, &a[a_offset], lda, &ipiv[1], &b[b_offset], ldb, info, + (ftnlen)12); } return 0; - -/* End of DGESV */ - -} /* dgesv_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dgesvd.cpp b/lib/linalg/dgesvd.cpp index b5f4f1e8de..43765bce16 100644 --- a/lib/linalg/dgesvd.cpp +++ b/lib/linalg/dgesvd.cpp @@ -1,22 +1,7 @@ -/* fortran/dgesvd.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__6 = 6; static integer c__0 = 0; static integer c__2 = 2; @@ -24,313 +9,62 @@ static integer c_n1 = -1; static doublereal c_b57 = 0.; static integer c__1 = 1; static doublereal c_b79 = 1.; - -/* > \brief DGESVD computes the singular value decomposition (SVD) for GE matrices */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DGESVD + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, */ -/* WORK, LWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER JOBU, JOBVT */ -/* INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), S( * ), U( LDU, * ), */ -/* $ VT( LDVT, * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DGESVD computes the singular value decomposition (SVD) of a real */ -/* > M-by-N matrix A, optionally computing the left and/or right singular */ -/* > vectors. The SVD is written */ -/* > */ -/* > A = U * SIGMA * transpose(V) */ -/* > */ -/* > where SIGMA is an M-by-N matrix which is zero except for its */ -/* > min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and */ -/* > V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA */ -/* > are the singular values of A; they are real and non-negative, and */ -/* > are returned in descending order. The first min(m,n) columns of */ -/* > U and V are the left and right singular vectors of A. */ -/* > */ -/* > Note that the routine returns V**T, not V. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] JOBU */ -/* > \verbatim */ -/* > JOBU is CHARACTER*1 */ -/* > Specifies options for computing all or part of the matrix U: */ -/* > = 'A': all M columns of U are returned in array U: */ -/* > = 'S': the first min(m,n) columns of U (the left singular */ -/* > vectors) are returned in the array U; */ -/* > = 'O': the first min(m,n) columns of U (the left singular */ -/* > vectors) are overwritten on the array A; */ -/* > = 'N': no columns of U (no left singular vectors) are */ -/* > computed. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] JOBVT */ -/* > \verbatim */ -/* > JOBVT is CHARACTER*1 */ -/* > Specifies options for computing all or part of the matrix */ -/* > V**T: */ -/* > = 'A': all N rows of V**T are returned in the array VT; */ -/* > = 'S': the first min(m,n) rows of V**T (the right singular */ -/* > vectors) are returned in the array VT; */ -/* > = 'O': the first min(m,n) rows of V**T (the right singular */ -/* > vectors) are overwritten on the array A; */ -/* > = 'N': no rows of V**T (no right singular vectors) are */ -/* > computed. */ -/* > */ -/* > JOBVT and JOBU cannot both be 'O'. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the input matrix A. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the input matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On entry, the M-by-N matrix A. */ -/* > On exit, */ -/* > if JOBU = 'O', A is overwritten with the first min(m,n) */ -/* > columns of U (the left singular vectors, */ -/* > stored columnwise); */ -/* > if JOBVT = 'O', A is overwritten with the first min(m,n) */ -/* > rows of V**T (the right singular vectors, */ -/* > stored rowwise); */ -/* > if JOBU .ne. 'O' and JOBVT .ne. 'O', the contents of A */ -/* > are destroyed. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] S */ -/* > \verbatim */ -/* > S is DOUBLE PRECISION array, dimension (min(M,N)) */ -/* > The singular values of A, sorted so that S(i) >= S(i+1). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] U */ -/* > \verbatim */ -/* > U is DOUBLE PRECISION array, dimension (LDU,UCOL) */ -/* > (LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'S'. */ -/* > If JOBU = 'A', U contains the M-by-M orthogonal matrix U; */ -/* > if JOBU = 'S', U contains the first min(m,n) columns of U */ -/* > (the left singular vectors, stored columnwise); */ -/* > if JOBU = 'N' or 'O', U is not referenced. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDU */ -/* > \verbatim */ -/* > LDU is INTEGER */ -/* > The leading dimension of the array U. LDU >= 1; if */ -/* > JOBU = 'S' or 'A', LDU >= M. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] VT */ -/* > \verbatim */ -/* > VT is DOUBLE PRECISION array, dimension (LDVT,N) */ -/* > If JOBVT = 'A', VT contains the N-by-N orthogonal matrix */ -/* > V**T; */ -/* > if JOBVT = 'S', VT contains the first min(m,n) rows of */ -/* > V**T (the right singular vectors, stored rowwise); */ -/* > if JOBVT = 'N' or 'O', VT is not referenced. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDVT */ -/* > \verbatim */ -/* > LDVT is INTEGER */ -/* > The leading dimension of the array VT. LDVT >= 1; if */ -/* > JOBVT = 'A', LDVT >= N; if JOBVT = 'S', LDVT >= min(M,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ -/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK; */ -/* > if INFO > 0, WORK(2:MIN(M,N)) contains the unconverged */ -/* > superdiagonal elements of an upper bidiagonal matrix B */ -/* > whose diagonal is in S (not necessarily sorted). B */ -/* > satisfies A = U * B * VT, so it has the same singular values */ -/* > as A, and singular vectors related by U and VT. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LWORK */ -/* > \verbatim */ -/* > LWORK is INTEGER */ -/* > The dimension of the array WORK. */ -/* > LWORK >= MAX(1,5*MIN(M,N)) for the paths (see comments inside code): */ -/* > - PATH 1 (M much larger than N, JOBU='N') */ -/* > - PATH 1t (N much larger than M, JOBVT='N') */ -/* > LWORK >= MAX(1,3*MIN(M,N) + MAX(M,N),5*MIN(M,N)) for the other paths */ -/* > For good performance, LWORK should generally be larger. */ -/* > */ -/* > If LWORK = -1, then a workspace query is assumed; the routine */ -/* > only calculates the optimal size of the WORK array, returns */ -/* > this value as the first entry of the WORK array, and no error */ -/* > message related to LWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit. */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ -/* > > 0: if DBDSQR did not converge, INFO specifies how many */ -/* > superdiagonals of an intermediate bidiagonal form B */ -/* > did not converge to zero. See the description of WORK */ -/* > above for details. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleGEsing */ - -/* ===================================================================== */ -/* Subroutine */ int dgesvd_(char *jobu, char *jobvt, integer *m, integer *n, - doublereal *a, integer *lda, doublereal *s, doublereal *u, integer * - ldu, doublereal *vt, integer *ldvt, doublereal *work, integer *lwork, - integer *info, ftnlen jobu_len, ftnlen jobvt_len) +int dgesvd_(char *jobu, char *jobvt, integer *m, integer *n, doublereal *a, integer *lda, + doublereal *s, doublereal *u, integer *ldu, doublereal *vt, integer *ldvt, + doublereal *work, integer *lwork, integer *info, ftnlen jobu_len, ftnlen jobvt_len) { - /* System generated locals */ address a__1[2]; - integer a_dim1, a_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1[2], - i__2, i__3, i__4; + integer a_dim1, a_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1[2], i__2, i__3, i__4; char ch__1[2]; - - /* Builtin functions */ - /* Subroutine */ int s_lmp_cat(char *, char **, integer *, integer *, ftnlen); + int s_lmp_cat(char *, char **, integer *, integer *, ftnlen); double sqrt(doublereal); - - /* Local variables */ integer i__, ie, ir, iu, blk, ncu; doublereal dum[1], eps; integer nru, iscl; doublereal anrm; - integer ierr, itau, ncvt, nrvt, lwork_dgebrd__, lwork_dgelqf__, - lwork_dgeqrf__; - extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); + integer ierr, itau, ncvt, nrvt, lwork_dgebrd__, lwork_dgelqf__, lwork_dgeqrf__; + extern int dgemm_(char *, char *, integer *, integer *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, + ftnlen, ftnlen); extern logical lsame_(char *, char *, ftnlen, ftnlen); integer chunk, minmn, wrkbl, itaup, itauq, mnthr, iwork; logical wntua, wntva, wntun, wntuo, wntvn, wntvo, wntus, wntvs; - extern /* Subroutine */ int dgebrd_(integer *, integer *, doublereal *, - integer *, doublereal *, doublereal *, doublereal *, doublereal *, - doublereal *, integer *, integer *); - extern doublereal dlamch_(char *, ftnlen), dlange_(char *, integer *, - integer *, doublereal *, integer *, doublereal *, ftnlen); + extern int dgebrd_(integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *, integer *, integer *); + extern doublereal dlamch_(char *, ftnlen), + dlange_(char *, integer *, integer *, doublereal *, integer *, doublereal *, ftnlen); integer bdspac; - extern /* Subroutine */ int dgelqf_(integer *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, integer *), - dlascl_(char *, integer *, integer *, doublereal *, doublereal *, - integer *, integer *, doublereal *, integer *, integer *, ftnlen), - dgeqrf_(integer *, integer *, doublereal *, integer *, - doublereal *, doublereal *, integer *, integer *), dlacpy_(char *, - integer *, integer *, doublereal *, integer *, doublereal *, - integer *, ftnlen), dlaset_(char *, integer *, integer *, - doublereal *, doublereal *, doublereal *, integer *, ftnlen), - dbdsqr_(char *, integer *, integer *, integer *, integer *, - doublereal *, doublereal *, doublereal *, integer *, doublereal *, - integer *, doublereal *, integer *, doublereal *, integer *, - ftnlen), dorgbr_(char *, integer *, integer *, integer *, - doublereal *, integer *, doublereal *, doublereal *, integer *, - integer *, ftnlen); + extern int dgelqf_(integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, integer *), + dlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, integer *, + doublereal *, integer *, integer *, ftnlen), + dgeqrf_(integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, integer *), + dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, + ftnlen), + dlaset_(char *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, + ftnlen), + dbdsqr_(char *, integer *, integer *, integer *, integer *, doublereal *, doublereal *, + doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, + doublereal *, integer *, ftnlen), + dorgbr_(char *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, integer *, ftnlen); doublereal bignum; - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - extern /* Subroutine */ int dormbr_(char *, char *, char *, integer *, - integer *, integer *, doublereal *, integer *, doublereal *, - doublereal *, integer *, doublereal *, integer *, integer *, - ftnlen, ftnlen, ftnlen), dorglq_(integer *, integer *, integer *, - doublereal *, integer *, doublereal *, doublereal *, integer *, - integer *), dorgqr_(integer *, integer *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, integer *); + extern int xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); + extern int dormbr_(char *, char *, char *, integer *, integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, + integer *, ftnlen, ftnlen, ftnlen), + dorglq_(integer *, integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, integer *), + dorgqr_(integer *, integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, integer *); integer ldwrkr, minwrk, ldwrku, maxwrk; doublereal smlnum; logical lquery, wntuas, wntvas; - integer lwork_dorgbr_p__, lwork_dorgbr_q__, lwork_dorglq_m__, - lwork_dorglq_n__, lwork_dorgqr_m__, lwork_dorgqr_n__; - - -/* -- LAPACK driver routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. Local Arrays .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments */ - - /* Parameter adjustments */ + integer lwork_dorgbr_p__, lwork_dorgbr_q__, lwork_dorglq_m__, lwork_dorglq_n__, + lwork_dorgqr_m__, lwork_dorgqr_n__; a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; @@ -342,10 +76,8 @@ f"> */ vt_offset = 1 + vt_dim1; vt -= vt_offset; --work; - - /* Function Body */ *info = 0; - minmn = min(*m,*n); + minmn = min(*m, *n); wntua = lsame_(jobu, (char *)"A", (ftnlen)1, (ftnlen)1); wntus = lsame_(jobu, (char *)"S", (ftnlen)1, (ftnlen)1); wntuas = wntua || wntus; @@ -357,560 +89,357 @@ f"> */ wntvo = lsame_(jobvt, (char *)"O", (ftnlen)1, (ftnlen)1); wntvn = lsame_(jobvt, (char *)"N", (ftnlen)1, (ftnlen)1); lquery = *lwork == -1; - - if (! (wntua || wntus || wntuo || wntun)) { + if (!(wntua || wntus || wntuo || wntun)) { *info = -1; - } else if (! (wntva || wntvs || wntvo || wntvn) || wntvo && wntuo) { + } else if (!(wntva || wntvs || wntvo || wntvn) || wntvo && wntuo) { *info = -2; } else if (*m < 0) { *info = -3; } else if (*n < 0) { *info = -4; - } else if (*lda < max(1,*m)) { + } else if (*lda < max(1, *m)) { *info = -6; } else if (*ldu < 1 || wntuas && *ldu < *m) { *info = -9; } else if (*ldvt < 1 || wntva && *ldvt < *n || wntvs && *ldvt < minmn) { *info = -11; } - -/* Compute workspace */ -/* (Note: Comments in the code beginning (char *)"Workspace:" describe the */ -/* minimal amount of workspace needed at that point in the code, */ -/* as well as the preferred amount for good performance. */ -/* NB refers to the optimal block size for the immediately */ -/* following subroutine, as returned by ILAENV.) */ - if (*info == 0) { minwrk = 1; maxwrk = 1; if (*m >= *n && minmn > 0) { - -/* Compute space needed for DBDSQR */ - -/* Writing concatenation */ i__1[0] = 1, a__1[0] = jobu; i__1[1] = 1, a__1[1] = jobvt; s_lmp_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); - mnthr = ilaenv_(&c__6, (char *)"DGESVD", ch__1, m, n, &c__0, &c__0, ( - ftnlen)6, (ftnlen)2); + mnthr = ilaenv_(&c__6, (char *)"DGESVD", ch__1, m, n, &c__0, &c__0, (ftnlen)6, (ftnlen)2); bdspac = *n * 5; -/* Compute space needed for DGEQRF */ dgeqrf_(m, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr); - lwork_dgeqrf__ = (integer) dum[0]; -/* Compute space needed for DORGQR */ + lwork_dgeqrf__ = (integer)dum[0]; dorgqr_(m, n, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr); - lwork_dorgqr_n__ = (integer) dum[0]; + lwork_dorgqr_n__ = (integer)dum[0]; dorgqr_(m, m, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr); - lwork_dorgqr_m__ = (integer) dum[0]; -/* Compute space needed for DGEBRD */ - dgebrd_(n, n, &a[a_offset], lda, &s[1], dum, dum, dum, dum, &c_n1, - &ierr); - lwork_dgebrd__ = (integer) dum[0]; -/* Compute space needed for DORGBR P */ - dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr, ( - ftnlen)1); - lwork_dorgbr_p__ = (integer) dum[0]; -/* Compute space needed for DORGBR Q */ - dorgbr_((char *)"Q", n, n, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr, ( - ftnlen)1); - lwork_dorgbr_q__ = (integer) dum[0]; - + lwork_dorgqr_m__ = (integer)dum[0]; + dgebrd_(n, n, &a[a_offset], lda, &s[1], dum, dum, dum, dum, &c_n1, &ierr); + lwork_dgebrd__ = (integer)dum[0]; + dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr, (ftnlen)1); + lwork_dorgbr_p__ = (integer)dum[0]; + dorgbr_((char *)"Q", n, n, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr, (ftnlen)1); + lwork_dorgbr_q__ = (integer)dum[0]; if (*m >= mnthr) { if (wntun) { - -/* Path 1 (M much larger than N, JOBU='N') */ - maxwrk = *n + lwork_dgeqrf__; -/* Computing MAX */ i__2 = maxwrk, i__3 = *n * 3 + lwork_dgebrd__; - maxwrk = max(i__2,i__3); + maxwrk = max(i__2, i__3); if (wntvo || wntvas) { -/* Computing MAX */ i__2 = maxwrk, i__3 = *n * 3 + lwork_dorgbr_p__; - maxwrk = max(i__2,i__3); + maxwrk = max(i__2, i__3); } - maxwrk = max(maxwrk,bdspac); -/* Computing MAX */ + maxwrk = max(maxwrk, bdspac); i__2 = *n << 2; - minwrk = max(i__2,bdspac); + minwrk = max(i__2, bdspac); } else if (wntuo && wntvn) { - -/* Path 2 (M much larger than N, JOBU='O', JOBVT='N') */ - wrkbl = *n + lwork_dgeqrf__; -/* Computing MAX */ i__2 = wrkbl, i__3 = *n + lwork_dorgqr_n__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__; - wrkbl = max(i__2,i__3); - wrkbl = max(wrkbl,bdspac); -/* Computing MAX */ + wrkbl = max(i__2, i__3); + wrkbl = max(wrkbl, bdspac); i__2 = *n * *n + wrkbl, i__3 = *n * *n + *m * *n + *n; - maxwrk = max(i__2,i__3); -/* Computing MAX */ + maxwrk = max(i__2, i__3); i__2 = *n * 3 + *m; - minwrk = max(i__2,bdspac); + minwrk = max(i__2, bdspac); } else if (wntuo && wntvas) { - -/* Path 3 (M much larger than N, JOBU='O', JOBVT='S' or */ -/* 'A') */ - wrkbl = *n + lwork_dgeqrf__; -/* Computing MAX */ i__2 = wrkbl, i__3 = *n + lwork_dorgqr_n__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_p__; - wrkbl = max(i__2,i__3); - wrkbl = max(wrkbl,bdspac); -/* Computing MAX */ + wrkbl = max(i__2, i__3); + wrkbl = max(wrkbl, bdspac); i__2 = *n * *n + wrkbl, i__3 = *n * *n + *m * *n + *n; - maxwrk = max(i__2,i__3); -/* Computing MAX */ + maxwrk = max(i__2, i__3); i__2 = *n * 3 + *m; - minwrk = max(i__2,bdspac); + minwrk = max(i__2, bdspac); } else if (wntus && wntvn) { - -/* Path 4 (M much larger than N, JOBU='S', JOBVT='N') */ - wrkbl = *n + lwork_dgeqrf__; -/* Computing MAX */ i__2 = wrkbl, i__3 = *n + lwork_dorgqr_n__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__; - wrkbl = max(i__2,i__3); - wrkbl = max(wrkbl,bdspac); + wrkbl = max(i__2, i__3); + wrkbl = max(wrkbl, bdspac); maxwrk = *n * *n + wrkbl; -/* Computing MAX */ i__2 = *n * 3 + *m; - minwrk = max(i__2,bdspac); + minwrk = max(i__2, bdspac); } else if (wntus && wntvo) { - -/* Path 5 (M much larger than N, JOBU='S', JOBVT='O') */ - wrkbl = *n + lwork_dgeqrf__; -/* Computing MAX */ i__2 = wrkbl, i__3 = *n + lwork_dorgqr_n__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_p__; - wrkbl = max(i__2,i__3); - wrkbl = max(wrkbl,bdspac); + wrkbl = max(i__2, i__3); + wrkbl = max(wrkbl, bdspac); maxwrk = (*n << 1) * *n + wrkbl; -/* Computing MAX */ i__2 = *n * 3 + *m; - minwrk = max(i__2,bdspac); + minwrk = max(i__2, bdspac); } else if (wntus && wntvas) { - -/* Path 6 (M much larger than N, JOBU='S', JOBVT='S' or */ -/* 'A') */ - wrkbl = *n + lwork_dgeqrf__; -/* Computing MAX */ i__2 = wrkbl, i__3 = *n + lwork_dorgqr_n__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_p__; - wrkbl = max(i__2,i__3); - wrkbl = max(wrkbl,bdspac); + wrkbl = max(i__2, i__3); + wrkbl = max(wrkbl, bdspac); maxwrk = *n * *n + wrkbl; -/* Computing MAX */ i__2 = *n * 3 + *m; - minwrk = max(i__2,bdspac); + minwrk = max(i__2, bdspac); } else if (wntua && wntvn) { - -/* Path 7 (M much larger than N, JOBU='A', JOBVT='N') */ - wrkbl = *n + lwork_dgeqrf__; -/* Computing MAX */ i__2 = wrkbl, i__3 = *n + lwork_dorgqr_m__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__; - wrkbl = max(i__2,i__3); - wrkbl = max(wrkbl,bdspac); + wrkbl = max(i__2, i__3); + wrkbl = max(wrkbl, bdspac); maxwrk = *n * *n + wrkbl; -/* Computing MAX */ i__2 = *n * 3 + *m; - minwrk = max(i__2,bdspac); + minwrk = max(i__2, bdspac); } else if (wntua && wntvo) { - -/* Path 8 (M much larger than N, JOBU='A', JOBVT='O') */ - wrkbl = *n + lwork_dgeqrf__; -/* Computing MAX */ i__2 = wrkbl, i__3 = *n + lwork_dorgqr_m__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_p__; - wrkbl = max(i__2,i__3); - wrkbl = max(wrkbl,bdspac); + wrkbl = max(i__2, i__3); + wrkbl = max(wrkbl, bdspac); maxwrk = (*n << 1) * *n + wrkbl; -/* Computing MAX */ i__2 = *n * 3 + *m; - minwrk = max(i__2,bdspac); + minwrk = max(i__2, bdspac); } else if (wntua && wntvas) { - -/* Path 9 (M much larger than N, JOBU='A', JOBVT='S' or */ -/* 'A') */ - wrkbl = *n + lwork_dgeqrf__; -/* Computing MAX */ i__2 = wrkbl, i__3 = *n + lwork_dorgqr_m__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *n * 3 + lwork_dgebrd__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_q__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *n * 3 + lwork_dorgbr_p__; - wrkbl = max(i__2,i__3); - wrkbl = max(wrkbl,bdspac); + wrkbl = max(i__2, i__3); + wrkbl = max(wrkbl, bdspac); maxwrk = *n * *n + wrkbl; -/* Computing MAX */ i__2 = *n * 3 + *m; - minwrk = max(i__2,bdspac); + minwrk = max(i__2, bdspac); } } else { - -/* Path 10 (M at least N, but not much larger) */ - - dgebrd_(m, n, &a[a_offset], lda, &s[1], dum, dum, dum, dum, & - c_n1, &ierr); - lwork_dgebrd__ = (integer) dum[0]; + dgebrd_(m, n, &a[a_offset], lda, &s[1], dum, dum, dum, dum, &c_n1, &ierr); + lwork_dgebrd__ = (integer)dum[0]; maxwrk = *n * 3 + lwork_dgebrd__; if (wntus || wntuo) { - dorgbr_((char *)"Q", m, n, n, &a[a_offset], lda, dum, dum, &c_n1, - &ierr, (ftnlen)1); - lwork_dorgbr_q__ = (integer) dum[0]; -/* Computing MAX */ + dorgbr_((char *)"Q", m, n, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr, (ftnlen)1); + lwork_dorgbr_q__ = (integer)dum[0]; i__2 = maxwrk, i__3 = *n * 3 + lwork_dorgbr_q__; - maxwrk = max(i__2,i__3); + maxwrk = max(i__2, i__3); } if (wntua) { - dorgbr_((char *)"Q", m, m, n, &a[a_offset], lda, dum, dum, &c_n1, - &ierr, (ftnlen)1); - lwork_dorgbr_q__ = (integer) dum[0]; -/* Computing MAX */ + dorgbr_((char *)"Q", m, m, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr, (ftnlen)1); + lwork_dorgbr_q__ = (integer)dum[0]; i__2 = maxwrk, i__3 = *n * 3 + lwork_dorgbr_q__; - maxwrk = max(i__2,i__3); + maxwrk = max(i__2, i__3); } - if (! wntvn) { -/* Computing MAX */ + if (!wntvn) { i__2 = maxwrk, i__3 = *n * 3 + lwork_dorgbr_p__; - maxwrk = max(i__2,i__3); + maxwrk = max(i__2, i__3); } - maxwrk = max(maxwrk,bdspac); -/* Computing MAX */ + maxwrk = max(maxwrk, bdspac); i__2 = *n * 3 + *m; - minwrk = max(i__2,bdspac); + minwrk = max(i__2, bdspac); } } else if (minmn > 0) { - -/* Compute space needed for DBDSQR */ - -/* Writing concatenation */ i__1[0] = 1, a__1[0] = jobu; i__1[1] = 1, a__1[1] = jobvt; s_lmp_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); - mnthr = ilaenv_(&c__6, (char *)"DGESVD", ch__1, m, n, &c__0, &c__0, ( - ftnlen)6, (ftnlen)2); + mnthr = ilaenv_(&c__6, (char *)"DGESVD", ch__1, m, n, &c__0, &c__0, (ftnlen)6, (ftnlen)2); bdspac = *m * 5; -/* Compute space needed for DGELQF */ dgelqf_(m, n, &a[a_offset], lda, dum, dum, &c_n1, &ierr); - lwork_dgelqf__ = (integer) dum[0]; -/* Compute space needed for DORGLQ */ + lwork_dgelqf__ = (integer)dum[0]; dorglq_(n, n, m, dum, n, dum, dum, &c_n1, &ierr); - lwork_dorglq_n__ = (integer) dum[0]; + lwork_dorglq_n__ = (integer)dum[0]; dorglq_(m, n, m, &a[a_offset], lda, dum, dum, &c_n1, &ierr); - lwork_dorglq_m__ = (integer) dum[0]; -/* Compute space needed for DGEBRD */ - dgebrd_(m, m, &a[a_offset], lda, &s[1], dum, dum, dum, dum, &c_n1, - &ierr); - lwork_dgebrd__ = (integer) dum[0]; -/* Compute space needed for DORGBR P */ - dorgbr_((char *)"P", m, m, m, &a[a_offset], n, dum, dum, &c_n1, &ierr, ( - ftnlen)1); - lwork_dorgbr_p__ = (integer) dum[0]; -/* Compute space needed for DORGBR Q */ - dorgbr_((char *)"Q", m, m, m, &a[a_offset], n, dum, dum, &c_n1, &ierr, ( - ftnlen)1); - lwork_dorgbr_q__ = (integer) dum[0]; + lwork_dorglq_m__ = (integer)dum[0]; + dgebrd_(m, m, &a[a_offset], lda, &s[1], dum, dum, dum, dum, &c_n1, &ierr); + lwork_dgebrd__ = (integer)dum[0]; + dorgbr_((char *)"P", m, m, m, &a[a_offset], n, dum, dum, &c_n1, &ierr, (ftnlen)1); + lwork_dorgbr_p__ = (integer)dum[0]; + dorgbr_((char *)"Q", m, m, m, &a[a_offset], n, dum, dum, &c_n1, &ierr, (ftnlen)1); + lwork_dorgbr_q__ = (integer)dum[0]; if (*n >= mnthr) { if (wntvn) { - -/* Path 1t(N much larger than M, JOBVT='N') */ - maxwrk = *m + lwork_dgelqf__; -/* Computing MAX */ i__2 = maxwrk, i__3 = *m * 3 + lwork_dgebrd__; - maxwrk = max(i__2,i__3); + maxwrk = max(i__2, i__3); if (wntuo || wntuas) { -/* Computing MAX */ i__2 = maxwrk, i__3 = *m * 3 + lwork_dorgbr_q__; - maxwrk = max(i__2,i__3); + maxwrk = max(i__2, i__3); } - maxwrk = max(maxwrk,bdspac); -/* Computing MAX */ + maxwrk = max(maxwrk, bdspac); i__2 = *m << 2; - minwrk = max(i__2,bdspac); + minwrk = max(i__2, bdspac); } else if (wntvo && wntun) { - -/* Path 2t(N much larger than M, JOBU='N', JOBVT='O') */ - wrkbl = *m + lwork_dgelqf__; -/* Computing MAX */ i__2 = wrkbl, i__3 = *m + lwork_dorglq_m__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__; - wrkbl = max(i__2,i__3); - wrkbl = max(wrkbl,bdspac); -/* Computing MAX */ + wrkbl = max(i__2, i__3); + wrkbl = max(wrkbl, bdspac); i__2 = *m * *m + wrkbl, i__3 = *m * *m + *m * *n + *m; - maxwrk = max(i__2,i__3); -/* Computing MAX */ + maxwrk = max(i__2, i__3); i__2 = *m * 3 + *n; - minwrk = max(i__2,bdspac); + minwrk = max(i__2, bdspac); } else if (wntvo && wntuas) { - -/* Path 3t(N much larger than M, JOBU='S' or 'A', */ -/* JOBVT='O') */ - wrkbl = *m + lwork_dgelqf__; -/* Computing MAX */ i__2 = wrkbl, i__3 = *m + lwork_dorglq_m__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_q__; - wrkbl = max(i__2,i__3); - wrkbl = max(wrkbl,bdspac); -/* Computing MAX */ + wrkbl = max(i__2, i__3); + wrkbl = max(wrkbl, bdspac); i__2 = *m * *m + wrkbl, i__3 = *m * *m + *m * *n + *m; - maxwrk = max(i__2,i__3); -/* Computing MAX */ + maxwrk = max(i__2, i__3); i__2 = *m * 3 + *n; - minwrk = max(i__2,bdspac); + minwrk = max(i__2, bdspac); } else if (wntvs && wntun) { - -/* Path 4t(N much larger than M, JOBU='N', JOBVT='S') */ - wrkbl = *m + lwork_dgelqf__; -/* Computing MAX */ i__2 = wrkbl, i__3 = *m + lwork_dorglq_m__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__; - wrkbl = max(i__2,i__3); - wrkbl = max(wrkbl,bdspac); + wrkbl = max(i__2, i__3); + wrkbl = max(wrkbl, bdspac); maxwrk = *m * *m + wrkbl; -/* Computing MAX */ i__2 = *m * 3 + *n; - minwrk = max(i__2,bdspac); + minwrk = max(i__2, bdspac); } else if (wntvs && wntuo) { - -/* Path 5t(N much larger than M, JOBU='O', JOBVT='S') */ - wrkbl = *m + lwork_dgelqf__; -/* Computing MAX */ i__2 = wrkbl, i__3 = *m + lwork_dorglq_m__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_q__; - wrkbl = max(i__2,i__3); - wrkbl = max(wrkbl,bdspac); + wrkbl = max(i__2, i__3); + wrkbl = max(wrkbl, bdspac); maxwrk = (*m << 1) * *m + wrkbl; -/* Computing MAX */ i__2 = *m * 3 + *n; - minwrk = max(i__2,bdspac); + minwrk = max(i__2, bdspac); } else if (wntvs && wntuas) { - -/* Path 6t(N much larger than M, JOBU='S' or 'A', */ -/* JOBVT='S') */ - wrkbl = *m + lwork_dgelqf__; -/* Computing MAX */ i__2 = wrkbl, i__3 = *m + lwork_dorglq_m__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_q__; - wrkbl = max(i__2,i__3); - wrkbl = max(wrkbl,bdspac); + wrkbl = max(i__2, i__3); + wrkbl = max(wrkbl, bdspac); maxwrk = *m * *m + wrkbl; -/* Computing MAX */ i__2 = *m * 3 + *n; - minwrk = max(i__2,bdspac); + minwrk = max(i__2, bdspac); } else if (wntva && wntun) { - -/* Path 7t(N much larger than M, JOBU='N', JOBVT='A') */ - wrkbl = *m + lwork_dgelqf__; -/* Computing MAX */ i__2 = wrkbl, i__3 = *m + lwork_dorglq_n__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__; - wrkbl = max(i__2,i__3); - wrkbl = max(wrkbl,bdspac); + wrkbl = max(i__2, i__3); + wrkbl = max(wrkbl, bdspac); maxwrk = *m * *m + wrkbl; -/* Computing MAX */ i__2 = *m * 3 + *n; - minwrk = max(i__2,bdspac); + minwrk = max(i__2, bdspac); } else if (wntva && wntuo) { - -/* Path 8t(N much larger than M, JOBU='O', JOBVT='A') */ - wrkbl = *m + lwork_dgelqf__; -/* Computing MAX */ i__2 = wrkbl, i__3 = *m + lwork_dorglq_n__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_q__; - wrkbl = max(i__2,i__3); - wrkbl = max(wrkbl,bdspac); + wrkbl = max(i__2, i__3); + wrkbl = max(wrkbl, bdspac); maxwrk = (*m << 1) * *m + wrkbl; -/* Computing MAX */ i__2 = *m * 3 + *n; - minwrk = max(i__2,bdspac); + minwrk = max(i__2, bdspac); } else if (wntva && wntuas) { - -/* Path 9t(N much larger than M, JOBU='S' or 'A', */ -/* JOBVT='A') */ - wrkbl = *m + lwork_dgelqf__; -/* Computing MAX */ i__2 = wrkbl, i__3 = *m + lwork_dorglq_n__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *m * 3 + lwork_dgebrd__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_p__; - wrkbl = max(i__2,i__3); -/* Computing MAX */ + wrkbl = max(i__2, i__3); i__2 = wrkbl, i__3 = *m * 3 + lwork_dorgbr_q__; - wrkbl = max(i__2,i__3); - wrkbl = max(wrkbl,bdspac); + wrkbl = max(i__2, i__3); + wrkbl = max(wrkbl, bdspac); maxwrk = *m * *m + wrkbl; -/* Computing MAX */ i__2 = *m * 3 + *n; - minwrk = max(i__2,bdspac); + minwrk = max(i__2, bdspac); } } else { - -/* Path 10t(N greater than M, but not much larger) */ - - dgebrd_(m, n, &a[a_offset], lda, &s[1], dum, dum, dum, dum, & - c_n1, &ierr); - lwork_dgebrd__ = (integer) dum[0]; + dgebrd_(m, n, &a[a_offset], lda, &s[1], dum, dum, dum, dum, &c_n1, &ierr); + lwork_dgebrd__ = (integer)dum[0]; maxwrk = *m * 3 + lwork_dgebrd__; if (wntvs || wntvo) { -/* Compute space needed for DORGBR P */ - dorgbr_((char *)"P", m, n, m, &a[a_offset], n, dum, dum, &c_n1, & - ierr, (ftnlen)1); - lwork_dorgbr_p__ = (integer) dum[0]; -/* Computing MAX */ + dorgbr_((char *)"P", m, n, m, &a[a_offset], n, dum, dum, &c_n1, &ierr, (ftnlen)1); + lwork_dorgbr_p__ = (integer)dum[0]; i__2 = maxwrk, i__3 = *m * 3 + lwork_dorgbr_p__; - maxwrk = max(i__2,i__3); + maxwrk = max(i__2, i__3); } if (wntva) { - dorgbr_((char *)"P", n, n, m, &a[a_offset], n, dum, dum, &c_n1, & - ierr, (ftnlen)1); - lwork_dorgbr_p__ = (integer) dum[0]; -/* Computing MAX */ + dorgbr_((char *)"P", n, n, m, &a[a_offset], n, dum, dum, &c_n1, &ierr, (ftnlen)1); + lwork_dorgbr_p__ = (integer)dum[0]; i__2 = maxwrk, i__3 = *m * 3 + lwork_dorgbr_p__; - maxwrk = max(i__2,i__3); + maxwrk = max(i__2, i__3); } - if (! wntun) { -/* Computing MAX */ + if (!wntun) { i__2 = maxwrk, i__3 = *m * 3 + lwork_dorgbr_q__; - maxwrk = max(i__2,i__3); + maxwrk = max(i__2, i__3); } - maxwrk = max(maxwrk,bdspac); -/* Computing MAX */ + maxwrk = max(maxwrk, bdspac); i__2 = *m * 3 + *n; - minwrk = max(i__2,bdspac); + minwrk = max(i__2, bdspac); } } - maxwrk = max(maxwrk,minwrk); - work[1] = (doublereal) maxwrk; - - if (*lwork < minwrk && ! lquery) { + maxwrk = max(maxwrk, minwrk); + work[1] = (doublereal)maxwrk; + if (*lwork < minwrk && !lquery) { *info = -13; } } - if (*info != 0) { i__2 = -(*info); xerbla_((char *)"DGESVD", &i__2, (ftnlen)6); @@ -918,1527 +447,676 @@ f"> */ } else if (lquery) { return 0; } - -/* Quick return if possible */ - if (*m == 0 || *n == 0) { return 0; } - -/* Get machine constants */ - eps = dlamch_((char *)"P", (ftnlen)1); smlnum = sqrt(dlamch_((char *)"S", (ftnlen)1)) / eps; bignum = 1. / smlnum; - -/* Scale A if max element outside range [SMLNUM,BIGNUM] */ - anrm = dlange_((char *)"M", m, n, &a[a_offset], lda, dum, (ftnlen)1); iscl = 0; if (anrm > 0. && anrm < smlnum) { iscl = 1; - dlascl_((char *)"G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, & - ierr, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda, &ierr, (ftnlen)1); } else if (anrm > bignum) { iscl = 1; - dlascl_((char *)"G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, & - ierr, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda, &ierr, (ftnlen)1); } - if (*m >= *n) { - -/* A has at least as many rows as columns. If A has sufficiently */ -/* more rows than columns, first reduce using the QR */ -/* decomposition (if sufficient workspace available) */ - if (*m >= mnthr) { - if (wntun) { - -/* Path 1 (M much larger than N, JOBU='N') */ -/* No left singular vectors to be computed */ - itau = 1; iwork = itau + *n; - -/* Compute A=Q*R */ -/* (Workspace: need 2*N, prefer N + N*NB) */ - i__2 = *lwork - iwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], & - i__2, &ierr); - -/* Zero out below R */ - + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, &ierr); if (*n > 1) { i__2 = *n - 1; i__3 = *n - 1; - dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &a[a_dim1 + 2], - lda, (ftnlen)1); + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &a[a_dim1 + 2], lda, (ftnlen)1); } ie = 1; itauq = ie + *n; itaup = itauq + *n; iwork = itaup + *n; - -/* Bidiagonalize R in A */ -/* (Workspace: need 4*N, prefer 3*N + 2*N*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &work[ - itauq], &work[itaup], &work[iwork], &i__2, &ierr); + dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &work[itaup], + &work[iwork], &i__2, &ierr); ncvt = 0; if (wntvo || wntvas) { - -/* If right singular vectors desired, generate P'. */ -/* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, &work[itaup], & - work[iwork], &i__2, &ierr, (ftnlen)1); + dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, &work[itaup], &work[iwork], &i__2, + &ierr, (ftnlen)1); ncvt = *n; } iwork = ie + *n; - -/* Perform bidiagonal QR iteration, computing right */ -/* singular vectors of A in A if desired */ -/* (Workspace: need BDSPAC) */ - - dbdsqr_((char *)"U", n, &ncvt, &c__0, &c__0, &s[1], &work[ie], &a[ - a_offset], lda, dum, &c__1, dum, &c__1, &work[iwork], - info, (ftnlen)1); - -/* If right singular vectors desired in VT, copy them there */ - + dbdsqr_((char *)"U", n, &ncvt, &c__0, &c__0, &s[1], &work[ie], &a[a_offset], lda, dum, + &c__1, dum, &c__1, &work[iwork], info, (ftnlen)1); if (wntvas) { - dlacpy_((char *)"F", n, n, &a[a_offset], lda, &vt[vt_offset], - ldvt, (ftnlen)1); + dlacpy_((char *)"F", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt, (ftnlen)1); } - } else if (wntuo && wntvn) { - -/* Path 2 (M much larger than N, JOBU='O', JOBVT='N') */ -/* N left singular vectors to be overwritten on A and */ -/* no right singular vectors to be computed */ - -/* Computing MAX */ i__2 = *n << 2; - if (*lwork >= *n * *n + max(i__2,bdspac)) { - -/* Sufficient workspace for a fast algorithm */ - + if (*lwork >= *n * *n + max(i__2, bdspac)) { ir = 1; -/* Computing MAX */ i__2 = wrkbl, i__3 = *lda * *n + *n; - if (*lwork >= max(i__2,i__3) + *lda * *n) { - -/* WORK(IU) is LDA by N, WORK(IR) is LDA by N */ - + if (*lwork >= max(i__2, i__3) + *lda * *n) { ldwrku = *lda; ldwrkr = *lda; - } else /* if(complicated condition) */ { -/* Computing MAX */ + } else { i__2 = wrkbl, i__3 = *lda * *n + *n; - if (*lwork >= max(i__2,i__3) + *n * *n) { - -/* WORK(IU) is LDA by N, WORK(IR) is N by N */ - + if (*lwork >= max(i__2, i__3) + *n * *n) { ldwrku = *lda; ldwrkr = *n; } else { - -/* WORK(IU) is LDWRKU by N, WORK(IR) is N by N */ - ldwrku = (*lwork - *n * *n - *n) / *n; ldwrkr = *n; } } itau = ir + ldwrkr * *n; iwork = itau + *n; - -/* Compute A=Q*R */ -/* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */ - i__2 = *lwork - iwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork] - , &i__2, &ierr); - -/* Copy R to WORK(IR) and zero out below it */ - - dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr, - (ftnlen)1); + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr, (ftnlen)1); i__2 = *n - 1; i__3 = *n - 1; - dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[ir + 1], - &ldwrkr, (ftnlen)1); - -/* Generate Q in A */ -/* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */ - + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[ir + 1], &ldwrkr, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); + dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, &ierr); ie = itau; itauq = ie + *n; itaup = itauq + *n; iwork = itaup + *n; - -/* Bidiagonalize R in WORK(IR) */ -/* (Workspace: need N*N + 4*N, prefer N*N + 3*N + 2*N*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], &work[ - itauq], &work[itaup], &work[iwork], &i__2, &ierr); - -/* Generate left vectors bidiagonalizing R */ -/* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB) */ - + dgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], &work[itauq], &work[itaup], + &work[iwork], &i__2, &ierr); i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", n, n, n, &work[ir], &ldwrkr, &work[itauq], & - work[iwork], &i__2, &ierr, (ftnlen)1); + dorgbr_((char *)"Q", n, n, n, &work[ir], &ldwrkr, &work[itauq], &work[iwork], &i__2, + &ierr, (ftnlen)1); iwork = ie + *n; - -/* Perform bidiagonal QR iteration, computing left */ -/* singular vectors of R in WORK(IR) */ -/* (Workspace: need N*N + BDSPAC) */ - - dbdsqr_((char *)"U", n, &c__0, n, &c__0, &s[1], &work[ie], dum, & - c__1, &work[ir], &ldwrkr, dum, &c__1, &work[iwork] - , info, (ftnlen)1); + dbdsqr_((char *)"U", n, &c__0, n, &c__0, &s[1], &work[ie], dum, &c__1, &work[ir], + &ldwrkr, dum, &c__1, &work[iwork], info, (ftnlen)1); iu = ie + *n; - -/* Multiply Q in A by left singular vectors of R in */ -/* WORK(IR), storing result in WORK(IU) and copying to A */ -/* (Workspace: need N*N + 2*N, prefer N*N + M*N + N) */ - i__2 = *m; i__3 = ldwrku; - for (i__ = 1; i__3 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += - i__3) { -/* Computing MIN */ + for (i__ = 1; i__3 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__3) { i__4 = *m - i__ + 1; - chunk = min(i__4,ldwrku); - dgemm_((char *)"N", (char *)"N", &chunk, n, n, &c_b79, &a[i__ + - a_dim1], lda, &work[ir], &ldwrkr, &c_b57, & - work[iu], &ldwrku, (ftnlen)1, (ftnlen)1); - dlacpy_((char *)"F", &chunk, n, &work[iu], &ldwrku, &a[i__ + - a_dim1], lda, (ftnlen)1); -/* L10: */ + chunk = min(i__4, ldwrku); + dgemm_((char *)"N", (char *)"N", &chunk, n, n, &c_b79, &a[i__ + a_dim1], lda, &work[ir], + &ldwrkr, &c_b57, &work[iu], &ldwrku, (ftnlen)1, (ftnlen)1); + dlacpy_((char *)"F", &chunk, n, &work[iu], &ldwrku, &a[i__ + a_dim1], lda, + (ftnlen)1); } - } else { - -/* Insufficient workspace for a fast algorithm */ - ie = 1; itauq = ie + *n; itaup = itauq + *n; iwork = itaup + *n; - -/* Bidiagonalize A */ -/* (Workspace: need 3*N + M, prefer 3*N + (M + N)*NB) */ - i__3 = *lwork - iwork + 1; - dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[ - itauq], &work[itaup], &work[iwork], &i__3, &ierr); - -/* Generate left vectors bidiagonalizing A */ -/* (Workspace: need 4*N, prefer 3*N + N*NB) */ - + dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &work[itaup], + &work[iwork], &i__3, &ierr); i__3 = *lwork - iwork + 1; - dorgbr_((char *)"Q", m, n, n, &a[a_offset], lda, &work[itauq], & - work[iwork], &i__3, &ierr, (ftnlen)1); + dorgbr_((char *)"Q", m, n, n, &a[a_offset], lda, &work[itauq], &work[iwork], &i__3, + &ierr, (ftnlen)1); iwork = ie + *n; - -/* Perform bidiagonal QR iteration, computing left */ -/* singular vectors of A in A */ -/* (Workspace: need BDSPAC) */ - - dbdsqr_((char *)"U", n, &c__0, m, &c__0, &s[1], &work[ie], dum, & - c__1, &a[a_offset], lda, dum, &c__1, &work[iwork], - info, (ftnlen)1); - + dbdsqr_((char *)"U", n, &c__0, m, &c__0, &s[1], &work[ie], dum, &c__1, &a[a_offset], + lda, dum, &c__1, &work[iwork], info, (ftnlen)1); } - } else if (wntuo && wntvas) { - -/* Path 3 (M much larger than N, JOBU='O', JOBVT='S' or 'A') */ -/* N left singular vectors to be overwritten on A and */ -/* N right singular vectors to be computed in VT */ - -/* Computing MAX */ i__3 = *n << 2; - if (*lwork >= *n * *n + max(i__3,bdspac)) { - -/* Sufficient workspace for a fast algorithm */ - + if (*lwork >= *n * *n + max(i__3, bdspac)) { ir = 1; -/* Computing MAX */ i__3 = wrkbl, i__2 = *lda * *n + *n; - if (*lwork >= max(i__3,i__2) + *lda * *n) { - -/* WORK(IU) is LDA by N and WORK(IR) is LDA by N */ - + if (*lwork >= max(i__3, i__2) + *lda * *n) { ldwrku = *lda; ldwrkr = *lda; - } else /* if(complicated condition) */ { -/* Computing MAX */ + } else { i__3 = wrkbl, i__2 = *lda * *n + *n; - if (*lwork >= max(i__3,i__2) + *n * *n) { - -/* WORK(IU) is LDA by N and WORK(IR) is N by N */ - + if (*lwork >= max(i__3, i__2) + *n * *n) { ldwrku = *lda; ldwrkr = *n; } else { - -/* WORK(IU) is LDWRKU by N and WORK(IR) is N by N */ - ldwrku = (*lwork - *n * *n - *n) / *n; ldwrkr = *n; } } itau = ir + ldwrkr * *n; iwork = itau + *n; - -/* Compute A=Q*R */ -/* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */ - i__3 = *lwork - iwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork] - , &i__3, &ierr); - -/* Copy R to VT, zeroing out below it */ - - dlacpy_((char *)"U", n, n, &a[a_offset], lda, &vt[vt_offset], - ldvt, (ftnlen)1); + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__3, &ierr); + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt, (ftnlen)1); if (*n > 1) { i__3 = *n - 1; i__2 = *n - 1; - dlaset_((char *)"L", &i__3, &i__2, &c_b57, &c_b57, &vt[ - vt_dim1 + 2], ldvt, (ftnlen)1); + dlaset_((char *)"L", &i__3, &i__2, &c_b57, &c_b57, &vt[vt_dim1 + 2], ldvt, + (ftnlen)1); } - -/* Generate Q in A */ -/* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */ - i__3 = *lwork - iwork + 1; - dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__3, &ierr); + dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__3, &ierr); ie = itau; itauq = ie + *n; itaup = itauq + *n; iwork = itaup + *n; - -/* Bidiagonalize R in VT, copying result to WORK(IR) */ -/* (Workspace: need N*N + 4*N, prefer N*N + 3*N + 2*N*NB) */ - i__3 = *lwork - iwork + 1; - dgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], &i__3, & - ierr); - dlacpy_((char *)"L", n, n, &vt[vt_offset], ldvt, &work[ir], & - ldwrkr, (ftnlen)1); - -/* Generate left vectors bidiagonalizing R in WORK(IR) */ -/* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB) */ - + dgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &work[ie], &work[itauq], + &work[itaup], &work[iwork], &i__3, &ierr); + dlacpy_((char *)"L", n, n, &vt[vt_offset], ldvt, &work[ir], &ldwrkr, (ftnlen)1); i__3 = *lwork - iwork + 1; - dorgbr_((char *)"Q", n, n, n, &work[ir], &ldwrkr, &work[itauq], & - work[iwork], &i__3, &ierr, (ftnlen)1); - -/* Generate right vectors bidiagonalizing R in VT */ -/* (Workspace: need N*N + 4*N-1, prefer N*N + 3*N + (N-1)*NB) */ - + dorgbr_((char *)"Q", n, n, n, &work[ir], &ldwrkr, &work[itauq], &work[iwork], &i__3, + &ierr, (ftnlen)1); i__3 = *lwork - iwork + 1; - dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], - &work[iwork], &i__3, &ierr, (ftnlen)1); + dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], &work[iwork], &i__3, + &ierr, (ftnlen)1); iwork = ie + *n; - -/* Perform bidiagonal QR iteration, computing left */ -/* singular vectors of R in WORK(IR) and computing right */ -/* singular vectors of R in VT */ -/* (Workspace: need N*N + BDSPAC) */ - - dbdsqr_((char *)"U", n, n, n, &c__0, &s[1], &work[ie], &vt[ - vt_offset], ldvt, &work[ir], &ldwrkr, dum, &c__1, - &work[iwork], info, (ftnlen)1); + dbdsqr_((char *)"U", n, n, n, &c__0, &s[1], &work[ie], &vt[vt_offset], ldvt, &work[ir], + &ldwrkr, dum, &c__1, &work[iwork], info, (ftnlen)1); iu = ie + *n; - -/* Multiply Q in A by left singular vectors of R in */ -/* WORK(IR), storing result in WORK(IU) and copying to A */ -/* (Workspace: need N*N + 2*N, prefer N*N + M*N + N) */ - i__3 = *m; i__2 = ldwrku; - for (i__ = 1; i__2 < 0 ? i__ >= i__3 : i__ <= i__3; i__ += - i__2) { -/* Computing MIN */ + for (i__ = 1; i__2 < 0 ? i__ >= i__3 : i__ <= i__3; i__ += i__2) { i__4 = *m - i__ + 1; - chunk = min(i__4,ldwrku); - dgemm_((char *)"N", (char *)"N", &chunk, n, n, &c_b79, &a[i__ + - a_dim1], lda, &work[ir], &ldwrkr, &c_b57, & - work[iu], &ldwrku, (ftnlen)1, (ftnlen)1); - dlacpy_((char *)"F", &chunk, n, &work[iu], &ldwrku, &a[i__ + - a_dim1], lda, (ftnlen)1); -/* L20: */ + chunk = min(i__4, ldwrku); + dgemm_((char *)"N", (char *)"N", &chunk, n, n, &c_b79, &a[i__ + a_dim1], lda, &work[ir], + &ldwrkr, &c_b57, &work[iu], &ldwrku, (ftnlen)1, (ftnlen)1); + dlacpy_((char *)"F", &chunk, n, &work[iu], &ldwrku, &a[i__ + a_dim1], lda, + (ftnlen)1); } - } else { - -/* Insufficient workspace for a fast algorithm */ - itau = 1; iwork = itau + *n; - -/* Compute A=Q*R */ -/* (Workspace: need 2*N, prefer N + N*NB) */ - i__2 = *lwork - iwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork] - , &i__2, &ierr); - -/* Copy R to VT, zeroing out below it */ - - dlacpy_((char *)"U", n, n, &a[a_offset], lda, &vt[vt_offset], - ldvt, (ftnlen)1); + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt, (ftnlen)1); if (*n > 1) { i__2 = *n - 1; i__3 = *n - 1; - dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &vt[ - vt_dim1 + 2], ldvt, (ftnlen)1); + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &vt[vt_dim1 + 2], ldvt, + (ftnlen)1); } - -/* Generate Q in A */ -/* (Workspace: need 2*N, prefer N + N*NB) */ - i__2 = *lwork - iwork + 1; - dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); + dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, &ierr); ie = itau; itauq = ie + *n; itaup = itauq + *n; iwork = itaup + *n; - -/* Bidiagonalize R in VT */ -/* (Workspace: need 4*N, prefer 3*N + 2*N*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], &i__2, & - ierr); - -/* Multiply Q in A by left vectors bidiagonalizing R */ -/* (Workspace: need 3*N + M, prefer 3*N + M*NB) */ - + dgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &work[ie], &work[itauq], + &work[itaup], &work[iwork], &i__2, &ierr); i__2 = *lwork - iwork + 1; - dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &vt[vt_offset], ldvt, & - work[itauq], &a[a_offset], lda, &work[iwork], & - i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen)1); - -/* Generate right vectors bidiagonalizing R in VT */ -/* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) */ - + dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &vt[vt_offset], ldvt, &work[itauq], + &a[a_offset], lda, &work[iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, + (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], - &work[iwork], &i__2, &ierr, (ftnlen)1); + dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], &work[iwork], &i__2, + &ierr, (ftnlen)1); iwork = ie + *n; - -/* Perform bidiagonal QR iteration, computing left */ -/* singular vectors of A in A and computing right */ -/* singular vectors of A in VT */ -/* (Workspace: need BDSPAC) */ - - dbdsqr_((char *)"U", n, n, m, &c__0, &s[1], &work[ie], &vt[ - vt_offset], ldvt, &a[a_offset], lda, dum, &c__1, & - work[iwork], info, (ftnlen)1); - + dbdsqr_((char *)"U", n, n, m, &c__0, &s[1], &work[ie], &vt[vt_offset], ldvt, + &a[a_offset], lda, dum, &c__1, &work[iwork], info, (ftnlen)1); } - } else if (wntus) { - if (wntvn) { - -/* Path 4 (M much larger than N, JOBU='S', JOBVT='N') */ -/* N left singular vectors to be computed in U and */ -/* no right singular vectors to be computed */ - -/* Computing MAX */ i__2 = *n << 2; - if (*lwork >= *n * *n + max(i__2,bdspac)) { - -/* Sufficient workspace for a fast algorithm */ - + if (*lwork >= *n * *n + max(i__2, bdspac)) { ir = 1; if (*lwork >= wrkbl + *lda * *n) { - -/* WORK(IR) is LDA by N */ - ldwrkr = *lda; } else { - -/* WORK(IR) is N by N */ - ldwrkr = *n; } itau = ir + ldwrkr * *n; iwork = itau + *n; - -/* Compute A=Q*R */ -/* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */ - i__2 = *lwork - iwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - -/* Copy R to WORK(IR), zeroing out below it */ - - dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[ir], & - ldwrkr, (ftnlen)1); + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr, (ftnlen)1); i__2 = *n - 1; i__3 = *n - 1; - dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[ir + - 1], &ldwrkr, (ftnlen)1); - -/* Generate Q in A */ -/* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */ - + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[ir + 1], &ldwrkr, + (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], & - work[iwork], &i__2, &ierr); + dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, + &ierr); ie = itau; itauq = ie + *n; itaup = itauq + *n; iwork = itaup + *n; - -/* Bidiagonalize R in WORK(IR) */ -/* (Workspace: need N*N + 4*N, prefer N*N + 3*N + 2*N*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); - -/* Generate left vectors bidiagonalizing R in WORK(IR) */ -/* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB) */ - + dgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], &work[itauq], + &work[itaup], &work[iwork], &i__2, &ierr); i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", n, n, n, &work[ir], &ldwrkr, &work[itauq] - , &work[iwork], &i__2, &ierr, (ftnlen)1); + dorgbr_((char *)"Q", n, n, n, &work[ir], &ldwrkr, &work[itauq], &work[iwork], &i__2, + &ierr, (ftnlen)1); iwork = ie + *n; - -/* Perform bidiagonal QR iteration, computing left */ -/* singular vectors of R in WORK(IR) */ -/* (Workspace: need N*N + BDSPAC) */ - - dbdsqr_((char *)"U", n, &c__0, n, &c__0, &s[1], &work[ie], - dum, &c__1, &work[ir], &ldwrkr, dum, &c__1, & - work[iwork], info, (ftnlen)1); - -/* Multiply Q in A by left singular vectors of R in */ -/* WORK(IR), storing result in U */ -/* (Workspace: need N*N) */ - - dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &a[a_offset], lda, & - work[ir], &ldwrkr, &c_b57, &u[u_offset], ldu, - (ftnlen)1, (ftnlen)1); - + dbdsqr_((char *)"U", n, &c__0, n, &c__0, &s[1], &work[ie], dum, &c__1, &work[ir], + &ldwrkr, dum, &c__1, &work[iwork], info, (ftnlen)1); + dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &a[a_offset], lda, &work[ir], &ldwrkr, + &c_b57, &u[u_offset], ldu, (ftnlen)1, (ftnlen)1); } else { - -/* Insufficient workspace for a fast algorithm */ - itau = 1; iwork = itau + *n; - -/* Compute A=Q*R, copying result to U */ -/* (Workspace: need 2*N, prefer N + N*NB) */ - i__2 = *lwork - iwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], - ldu, (ftnlen)1); - -/* Generate Q in U */ -/* (Workspace: need 2*N, prefer N + N*NB) */ - + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], ldu, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgqr_(m, n, n, &u[u_offset], ldu, &work[itau], & - work[iwork], &i__2, &ierr); + dorgqr_(m, n, n, &u[u_offset], ldu, &work[itau], &work[iwork], &i__2, + &ierr); ie = itau; itauq = ie + *n; itaup = itauq + *n; iwork = itaup + *n; - -/* Zero out below R in A */ - if (*n > 1) { i__2 = *n - 1; i__3 = *n - 1; - dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &a[ - a_dim1 + 2], lda, (ftnlen)1); + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &a[a_dim1 + 2], lda, + (ftnlen)1); } - -/* Bidiagonalize R in A */ -/* (Workspace: need 4*N, prefer 3*N + 2*N*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); - -/* Multiply Q in U by left vectors bidiagonalizing R */ -/* (Workspace: need 3*N + M, prefer 3*N + M*NB) */ - + dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], + &work[itaup], &work[iwork], &i__2, &ierr); i__2 = *lwork - iwork + 1; - dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &a[a_offset], lda, & - work[itauq], &u[u_offset], ldu, &work[iwork], - &i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen)1) - ; + dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &a[a_offset], lda, &work[itauq], + &u[u_offset], ldu, &work[iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, + (ftnlen)1); iwork = ie + *n; - -/* Perform bidiagonal QR iteration, computing left */ -/* singular vectors of A in U */ -/* (Workspace: need BDSPAC) */ - - dbdsqr_((char *)"U", n, &c__0, m, &c__0, &s[1], &work[ie], - dum, &c__1, &u[u_offset], ldu, dum, &c__1, & - work[iwork], info, (ftnlen)1); - + dbdsqr_((char *)"U", n, &c__0, m, &c__0, &s[1], &work[ie], dum, &c__1, &u[u_offset], + ldu, dum, &c__1, &work[iwork], info, (ftnlen)1); } - } else if (wntvo) { - -/* Path 5 (M much larger than N, JOBU='S', JOBVT='O') */ -/* N left singular vectors to be computed in U and */ -/* N right singular vectors to be overwritten on A */ - -/* Computing MAX */ i__2 = *n << 2; - if (*lwork >= (*n << 1) * *n + max(i__2,bdspac)) { - -/* Sufficient workspace for a fast algorithm */ - + if (*lwork >= (*n << 1) * *n + max(i__2, bdspac)) { iu = 1; if (*lwork >= wrkbl + (*lda << 1) * *n) { - -/* WORK(IU) is LDA by N and WORK(IR) is LDA by N */ - ldwrku = *lda; ir = iu + ldwrku * *n; ldwrkr = *lda; } else if (*lwork >= wrkbl + (*lda + *n) * *n) { - -/* WORK(IU) is LDA by N and WORK(IR) is N by N */ - ldwrku = *lda; ir = iu + ldwrku * *n; ldwrkr = *n; } else { - -/* WORK(IU) is N by N and WORK(IR) is N by N */ - ldwrku = *n; ir = iu + ldwrku * *n; ldwrkr = *n; } itau = ir + ldwrkr * *n; iwork = itau + *n; - -/* Compute A=Q*R */ -/* (Workspace: need 2*N*N + 2*N, prefer 2*N*N + N + N*NB) */ - i__2 = *lwork - iwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - -/* Copy R to WORK(IU), zeroing out below it */ - - dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[iu], & - ldwrku, (ftnlen)1); + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[iu], &ldwrku, (ftnlen)1); i__2 = *n - 1; i__3 = *n - 1; - dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[iu + - 1], &ldwrku, (ftnlen)1); - -/* Generate Q in A */ -/* (Workspace: need 2*N*N + 2*N, prefer 2*N*N + N + N*NB) */ - + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[iu + 1], &ldwrku, + (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], & - work[iwork], &i__2, &ierr); + dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, + &ierr); ie = itau; itauq = ie + *n; itaup = itauq + *n; iwork = itaup + *n; - -/* Bidiagonalize R in WORK(IU), copying result to */ -/* WORK(IR) */ -/* (Workspace: need 2*N*N + 4*N, */ -/* prefer 2*N*N+3*N+2*N*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(n, n, &work[iu], &ldwrku, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); - dlacpy_((char *)"U", n, n, &work[iu], &ldwrku, &work[ir], & - ldwrkr, (ftnlen)1); - -/* Generate left bidiagonalizing vectors in WORK(IU) */ -/* (Workspace: need 2*N*N + 4*N, prefer 2*N*N + 3*N + N*NB) */ - + dgebrd_(n, n, &work[iu], &ldwrku, &s[1], &work[ie], &work[itauq], + &work[itaup], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"U", n, n, &work[iu], &ldwrku, &work[ir], &ldwrkr, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", n, n, n, &work[iu], &ldwrku, &work[itauq] - , &work[iwork], &i__2, &ierr, (ftnlen)1); - -/* Generate right bidiagonalizing vectors in WORK(IR) */ -/* (Workspace: need 2*N*N + 4*N-1, */ -/* prefer 2*N*N+3*N+(N-1)*NB) */ - + dorgbr_((char *)"Q", n, n, n, &work[iu], &ldwrku, &work[itauq], &work[iwork], &i__2, + &ierr, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", n, n, n, &work[ir], &ldwrkr, &work[itaup] - , &work[iwork], &i__2, &ierr, (ftnlen)1); + dorgbr_((char *)"P", n, n, n, &work[ir], &ldwrkr, &work[itaup], &work[iwork], &i__2, + &ierr, (ftnlen)1); iwork = ie + *n; - -/* Perform bidiagonal QR iteration, computing left */ -/* singular vectors of R in WORK(IU) and computing */ -/* right singular vectors of R in WORK(IR) */ -/* (Workspace: need 2*N*N + BDSPAC) */ - - dbdsqr_((char *)"U", n, n, n, &c__0, &s[1], &work[ie], &work[ - ir], &ldwrkr, &work[iu], &ldwrku, dum, &c__1, - &work[iwork], info, (ftnlen)1); - -/* Multiply Q in A by left singular vectors of R in */ -/* WORK(IU), storing result in U */ -/* (Workspace: need N*N) */ - - dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &a[a_offset], lda, & - work[iu], &ldwrku, &c_b57, &u[u_offset], ldu, - (ftnlen)1, (ftnlen)1); - -/* Copy right singular vectors of R to A */ -/* (Workspace: need N*N) */ - - dlacpy_((char *)"F", n, n, &work[ir], &ldwrkr, &a[a_offset], - lda, (ftnlen)1); - + dbdsqr_((char *)"U", n, n, n, &c__0, &s[1], &work[ie], &work[ir], &ldwrkr, + &work[iu], &ldwrku, dum, &c__1, &work[iwork], info, (ftnlen)1); + dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &a[a_offset], lda, &work[iu], &ldwrku, + &c_b57, &u[u_offset], ldu, (ftnlen)1, (ftnlen)1); + dlacpy_((char *)"F", n, n, &work[ir], &ldwrkr, &a[a_offset], lda, (ftnlen)1); } else { - -/* Insufficient workspace for a fast algorithm */ - itau = 1; iwork = itau + *n; - -/* Compute A=Q*R, copying result to U */ -/* (Workspace: need 2*N, prefer N + N*NB) */ - i__2 = *lwork - iwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], - ldu, (ftnlen)1); - -/* Generate Q in U */ -/* (Workspace: need 2*N, prefer N + N*NB) */ - + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], ldu, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgqr_(m, n, n, &u[u_offset], ldu, &work[itau], & - work[iwork], &i__2, &ierr); + dorgqr_(m, n, n, &u[u_offset], ldu, &work[itau], &work[iwork], &i__2, + &ierr); ie = itau; itauq = ie + *n; itaup = itauq + *n; iwork = itaup + *n; - -/* Zero out below R in A */ - if (*n > 1) { i__2 = *n - 1; i__3 = *n - 1; - dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &a[ - a_dim1 + 2], lda, (ftnlen)1); + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &a[a_dim1 + 2], lda, + (ftnlen)1); } - -/* Bidiagonalize R in A */ -/* (Workspace: need 4*N, prefer 3*N + 2*N*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); - -/* Multiply Q in U by left vectors bidiagonalizing R */ -/* (Workspace: need 3*N + M, prefer 3*N + M*NB) */ - + dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], + &work[itaup], &work[iwork], &i__2, &ierr); i__2 = *lwork - iwork + 1; - dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &a[a_offset], lda, & - work[itauq], &u[u_offset], ldu, &work[iwork], - &i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen)1) - ; - -/* Generate right vectors bidiagonalizing R in A */ -/* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) */ - + dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &a[a_offset], lda, &work[itauq], + &u[u_offset], ldu, &work[iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, + (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, &work[itaup], - &work[iwork], &i__2, &ierr, (ftnlen)1); + dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, &work[itaup], &work[iwork], &i__2, + &ierr, (ftnlen)1); iwork = ie + *n; - -/* Perform bidiagonal QR iteration, computing left */ -/* singular vectors of A in U and computing right */ -/* singular vectors of A in A */ -/* (Workspace: need BDSPAC) */ - - dbdsqr_((char *)"U", n, n, m, &c__0, &s[1], &work[ie], &a[ - a_offset], lda, &u[u_offset], ldu, dum, &c__1, - &work[iwork], info, (ftnlen)1); - + dbdsqr_((char *)"U", n, n, m, &c__0, &s[1], &work[ie], &a[a_offset], lda, + &u[u_offset], ldu, dum, &c__1, &work[iwork], info, (ftnlen)1); } - } else if (wntvas) { - -/* Path 6 (M much larger than N, JOBU='S', JOBVT='S' */ -/* or 'A') */ -/* N left singular vectors to be computed in U and */ -/* N right singular vectors to be computed in VT */ - -/* Computing MAX */ i__2 = *n << 2; - if (*lwork >= *n * *n + max(i__2,bdspac)) { - -/* Sufficient workspace for a fast algorithm */ - + if (*lwork >= *n * *n + max(i__2, bdspac)) { iu = 1; if (*lwork >= wrkbl + *lda * *n) { - -/* WORK(IU) is LDA by N */ - ldwrku = *lda; } else { - -/* WORK(IU) is N by N */ - ldwrku = *n; } itau = iu + ldwrku * *n; iwork = itau + *n; - -/* Compute A=Q*R */ -/* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */ - i__2 = *lwork - iwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - -/* Copy R to WORK(IU), zeroing out below it */ - - dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[iu], & - ldwrku, (ftnlen)1); + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[iu], &ldwrku, (ftnlen)1); i__2 = *n - 1; i__3 = *n - 1; - dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[iu + - 1], &ldwrku, (ftnlen)1); - -/* Generate Q in A */ -/* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */ - + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[iu + 1], &ldwrku, + (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], & - work[iwork], &i__2, &ierr); + dorgqr_(m, n, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, + &ierr); ie = itau; itauq = ie + *n; itaup = itauq + *n; iwork = itaup + *n; - -/* Bidiagonalize R in WORK(IU), copying result to VT */ -/* (Workspace: need N*N + 4*N, prefer N*N + 3*N + 2*N*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(n, n, &work[iu], &ldwrku, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); - dlacpy_((char *)"U", n, n, &work[iu], &ldwrku, &vt[vt_offset], - ldvt, (ftnlen)1); - -/* Generate left bidiagonalizing vectors in WORK(IU) */ -/* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB) */ - + dgebrd_(n, n, &work[iu], &ldwrku, &s[1], &work[ie], &work[itauq], + &work[itaup], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"U", n, n, &work[iu], &ldwrku, &vt[vt_offset], ldvt, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", n, n, n, &work[iu], &ldwrku, &work[itauq] - , &work[iwork], &i__2, &ierr, (ftnlen)1); - -/* Generate right bidiagonalizing vectors in VT */ -/* (Workspace: need N*N + 4*N-1, */ -/* prefer N*N+3*N+(N-1)*NB) */ - + dorgbr_((char *)"Q", n, n, n, &work[iu], &ldwrku, &work[itauq], &work[iwork], &i__2, + &ierr, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[ - itaup], &work[iwork], &i__2, &ierr, (ftnlen)1) - ; + dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], &work[iwork], + &i__2, &ierr, (ftnlen)1); iwork = ie + *n; - -/* Perform bidiagonal QR iteration, computing left */ -/* singular vectors of R in WORK(IU) and computing */ -/* right singular vectors of R in VT */ -/* (Workspace: need N*N + BDSPAC) */ - - dbdsqr_((char *)"U", n, n, n, &c__0, &s[1], &work[ie], &vt[ - vt_offset], ldvt, &work[iu], &ldwrku, dum, & - c__1, &work[iwork], info, (ftnlen)1); - -/* Multiply Q in A by left singular vectors of R in */ -/* WORK(IU), storing result in U */ -/* (Workspace: need N*N) */ - - dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &a[a_offset], lda, & - work[iu], &ldwrku, &c_b57, &u[u_offset], ldu, - (ftnlen)1, (ftnlen)1); - + dbdsqr_((char *)"U", n, n, n, &c__0, &s[1], &work[ie], &vt[vt_offset], ldvt, + &work[iu], &ldwrku, dum, &c__1, &work[iwork], info, (ftnlen)1); + dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &a[a_offset], lda, &work[iu], &ldwrku, + &c_b57, &u[u_offset], ldu, (ftnlen)1, (ftnlen)1); } else { - -/* Insufficient workspace for a fast algorithm */ - itau = 1; iwork = itau + *n; - -/* Compute A=Q*R, copying result to U */ -/* (Workspace: need 2*N, prefer N + N*NB) */ - i__2 = *lwork - iwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], - ldu, (ftnlen)1); - -/* Generate Q in U */ -/* (Workspace: need 2*N, prefer N + N*NB) */ - + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], ldu, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgqr_(m, n, n, &u[u_offset], ldu, &work[itau], & - work[iwork], &i__2, &ierr); - -/* Copy R to VT, zeroing out below it */ - - dlacpy_((char *)"U", n, n, &a[a_offset], lda, &vt[vt_offset], - ldvt, (ftnlen)1); + dorgqr_(m, n, n, &u[u_offset], ldu, &work[itau], &work[iwork], &i__2, + &ierr); + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt, (ftnlen)1); if (*n > 1) { i__2 = *n - 1; i__3 = *n - 1; - dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &vt[ - vt_dim1 + 2], ldvt, (ftnlen)1); + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &vt[vt_dim1 + 2], ldvt, + (ftnlen)1); } ie = itau; itauq = ie + *n; itaup = itauq + *n; iwork = itaup + *n; - -/* Bidiagonalize R in VT */ -/* (Workspace: need 4*N, prefer 3*N + 2*N*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &work[ie], - &work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); - -/* Multiply Q in U by left bidiagonalizing vectors */ -/* in VT */ -/* (Workspace: need 3*N + M, prefer 3*N + M*NB) */ - + dgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &work[ie], &work[itauq], + &work[itaup], &work[iwork], &i__2, &ierr); i__2 = *lwork - iwork + 1; - dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &vt[vt_offset], ldvt, - &work[itauq], &u[u_offset], ldu, &work[iwork], - &i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen) - 1); - -/* Generate right bidiagonalizing vectors in VT */ -/* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) */ - + dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &vt[vt_offset], ldvt, &work[itauq], + &u[u_offset], ldu, &work[iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, + (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[ - itaup], &work[iwork], &i__2, &ierr, (ftnlen)1) - ; + dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], &work[iwork], + &i__2, &ierr, (ftnlen)1); iwork = ie + *n; - -/* Perform bidiagonal QR iteration, computing left */ -/* singular vectors of A in U and computing right */ -/* singular vectors of A in VT */ -/* (Workspace: need BDSPAC) */ - - dbdsqr_((char *)"U", n, n, m, &c__0, &s[1], &work[ie], &vt[ - vt_offset], ldvt, &u[u_offset], ldu, dum, & - c__1, &work[iwork], info, (ftnlen)1); - + dbdsqr_((char *)"U", n, n, m, &c__0, &s[1], &work[ie], &vt[vt_offset], ldvt, + &u[u_offset], ldu, dum, &c__1, &work[iwork], info, (ftnlen)1); } - } - } else if (wntua) { - if (wntvn) { - -/* Path 7 (M much larger than N, JOBU='A', JOBVT='N') */ -/* M left singular vectors to be computed in U and */ -/* no right singular vectors to be computed */ - -/* Computing MAX */ - i__2 = *n + *m, i__3 = *n << 2, i__2 = max(i__2,i__3); - if (*lwork >= *n * *n + max(i__2,bdspac)) { - -/* Sufficient workspace for a fast algorithm */ - + i__2 = *n + *m, i__3 = *n << 2, i__2 = max(i__2, i__3); + if (*lwork >= *n * *n + max(i__2, bdspac)) { ir = 1; if (*lwork >= wrkbl + *lda * *n) { - -/* WORK(IR) is LDA by N */ - ldwrkr = *lda; } else { - -/* WORK(IR) is N by N */ - ldwrkr = *n; } itau = ir + ldwrkr * *n; iwork = itau + *n; - -/* Compute A=Q*R, copying result to U */ -/* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */ - i__2 = *lwork - iwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], - ldu, (ftnlen)1); - -/* Copy R to WORK(IR), zeroing out below it */ - - dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[ir], & - ldwrkr, (ftnlen)1); + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], ldu, (ftnlen)1); + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[ir], &ldwrkr, (ftnlen)1); i__2 = *n - 1; i__3 = *n - 1; - dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[ir + - 1], &ldwrkr, (ftnlen)1); - -/* Generate Q in U */ -/* (Workspace: need N*N + N + M, prefer N*N + N + M*NB) */ - + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[ir + 1], &ldwrkr, + (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], & - work[iwork], &i__2, &ierr); + dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], &work[iwork], &i__2, + &ierr); ie = itau; itauq = ie + *n; itaup = itauq + *n; iwork = itaup + *n; - -/* Bidiagonalize R in WORK(IR) */ -/* (Workspace: need N*N + 4*N, prefer N*N + 3*N + 2*N*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); - -/* Generate left bidiagonalizing vectors in WORK(IR) */ -/* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB) */ - + dgebrd_(n, n, &work[ir], &ldwrkr, &s[1], &work[ie], &work[itauq], + &work[itaup], &work[iwork], &i__2, &ierr); i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", n, n, n, &work[ir], &ldwrkr, &work[itauq] - , &work[iwork], &i__2, &ierr, (ftnlen)1); + dorgbr_((char *)"Q", n, n, n, &work[ir], &ldwrkr, &work[itauq], &work[iwork], &i__2, + &ierr, (ftnlen)1); iwork = ie + *n; - -/* Perform bidiagonal QR iteration, computing left */ -/* singular vectors of R in WORK(IR) */ -/* (Workspace: need N*N + BDSPAC) */ - - dbdsqr_((char *)"U", n, &c__0, n, &c__0, &s[1], &work[ie], - dum, &c__1, &work[ir], &ldwrkr, dum, &c__1, & - work[iwork], info, (ftnlen)1); - -/* Multiply Q in U by left singular vectors of R in */ -/* WORK(IR), storing result in A */ -/* (Workspace: need N*N) */ - - dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &u[u_offset], ldu, & - work[ir], &ldwrkr, &c_b57, &a[a_offset], lda, - (ftnlen)1, (ftnlen)1); - -/* Copy left singular vectors of A from A to U */ - - dlacpy_((char *)"F", m, n, &a[a_offset], lda, &u[u_offset], - ldu, (ftnlen)1); - + dbdsqr_((char *)"U", n, &c__0, n, &c__0, &s[1], &work[ie], dum, &c__1, &work[ir], + &ldwrkr, dum, &c__1, &work[iwork], info, (ftnlen)1); + dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &u[u_offset], ldu, &work[ir], &ldwrkr, + &c_b57, &a[a_offset], lda, (ftnlen)1, (ftnlen)1); + dlacpy_((char *)"F", m, n, &a[a_offset], lda, &u[u_offset], ldu, (ftnlen)1); } else { - -/* Insufficient workspace for a fast algorithm */ - itau = 1; iwork = itau + *n; - -/* Compute A=Q*R, copying result to U */ -/* (Workspace: need 2*N, prefer N + N*NB) */ - i__2 = *lwork - iwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], - ldu, (ftnlen)1); - -/* Generate Q in U */ -/* (Workspace: need N + M, prefer N + M*NB) */ - + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], ldu, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], & - work[iwork], &i__2, &ierr); + dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], &work[iwork], &i__2, + &ierr); ie = itau; itauq = ie + *n; itaup = itauq + *n; iwork = itaup + *n; - -/* Zero out below R in A */ - if (*n > 1) { i__2 = *n - 1; i__3 = *n - 1; - dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &a[ - a_dim1 + 2], lda, (ftnlen)1); + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &a[a_dim1 + 2], lda, + (ftnlen)1); } - -/* Bidiagonalize R in A */ -/* (Workspace: need 4*N, prefer 3*N + 2*N*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); - -/* Multiply Q in U by left bidiagonalizing vectors */ -/* in A */ -/* (Workspace: need 3*N + M, prefer 3*N + M*NB) */ - + dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], + &work[itaup], &work[iwork], &i__2, &ierr); i__2 = *lwork - iwork + 1; - dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &a[a_offset], lda, & - work[itauq], &u[u_offset], ldu, &work[iwork], - &i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen)1) - ; + dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &a[a_offset], lda, &work[itauq], + &u[u_offset], ldu, &work[iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, + (ftnlen)1); iwork = ie + *n; - -/* Perform bidiagonal QR iteration, computing left */ -/* singular vectors of A in U */ -/* (Workspace: need BDSPAC) */ - - dbdsqr_((char *)"U", n, &c__0, m, &c__0, &s[1], &work[ie], - dum, &c__1, &u[u_offset], ldu, dum, &c__1, & - work[iwork], info, (ftnlen)1); - + dbdsqr_((char *)"U", n, &c__0, m, &c__0, &s[1], &work[ie], dum, &c__1, &u[u_offset], + ldu, dum, &c__1, &work[iwork], info, (ftnlen)1); } - } else if (wntvo) { - -/* Path 8 (M much larger than N, JOBU='A', JOBVT='O') */ -/* M left singular vectors to be computed in U and */ -/* N right singular vectors to be overwritten on A */ - -/* Computing MAX */ - i__2 = *n + *m, i__3 = *n << 2, i__2 = max(i__2,i__3); - if (*lwork >= (*n << 1) * *n + max(i__2,bdspac)) { - -/* Sufficient workspace for a fast algorithm */ - + i__2 = *n + *m, i__3 = *n << 2, i__2 = max(i__2, i__3); + if (*lwork >= (*n << 1) * *n + max(i__2, bdspac)) { iu = 1; if (*lwork >= wrkbl + (*lda << 1) * *n) { - -/* WORK(IU) is LDA by N and WORK(IR) is LDA by N */ - ldwrku = *lda; ir = iu + ldwrku * *n; ldwrkr = *lda; } else if (*lwork >= wrkbl + (*lda + *n) * *n) { - -/* WORK(IU) is LDA by N and WORK(IR) is N by N */ - ldwrku = *lda; ir = iu + ldwrku * *n; ldwrkr = *n; } else { - -/* WORK(IU) is N by N and WORK(IR) is N by N */ - ldwrku = *n; ir = iu + ldwrku * *n; ldwrkr = *n; } itau = ir + ldwrkr * *n; iwork = itau + *n; - -/* Compute A=Q*R, copying result to U */ -/* (Workspace: need 2*N*N + 2*N, prefer 2*N*N + N + N*NB) */ - i__2 = *lwork - iwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], - ldu, (ftnlen)1); - -/* Generate Q in U */ -/* (Workspace: need 2*N*N + N + M, prefer 2*N*N + N + M*NB) */ - + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], ldu, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], & - work[iwork], &i__2, &ierr); - -/* Copy R to WORK(IU), zeroing out below it */ - - dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[iu], & - ldwrku, (ftnlen)1); + dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], &work[iwork], &i__2, + &ierr); + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[iu], &ldwrku, (ftnlen)1); i__2 = *n - 1; i__3 = *n - 1; - dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[iu + - 1], &ldwrku, (ftnlen)1); + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[iu + 1], &ldwrku, + (ftnlen)1); ie = itau; itauq = ie + *n; itaup = itauq + *n; iwork = itaup + *n; - -/* Bidiagonalize R in WORK(IU), copying result to */ -/* WORK(IR) */ -/* (Workspace: need 2*N*N + 4*N, */ -/* prefer 2*N*N+3*N+2*N*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(n, n, &work[iu], &ldwrku, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); - dlacpy_((char *)"U", n, n, &work[iu], &ldwrku, &work[ir], & - ldwrkr, (ftnlen)1); - -/* Generate left bidiagonalizing vectors in WORK(IU) */ -/* (Workspace: need 2*N*N + 4*N, prefer 2*N*N + 3*N + N*NB) */ - + dgebrd_(n, n, &work[iu], &ldwrku, &s[1], &work[ie], &work[itauq], + &work[itaup], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"U", n, n, &work[iu], &ldwrku, &work[ir], &ldwrkr, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", n, n, n, &work[iu], &ldwrku, &work[itauq] - , &work[iwork], &i__2, &ierr, (ftnlen)1); - -/* Generate right bidiagonalizing vectors in WORK(IR) */ -/* (Workspace: need 2*N*N + 4*N-1, */ -/* prefer 2*N*N+3*N+(N-1)*NB) */ - + dorgbr_((char *)"Q", n, n, n, &work[iu], &ldwrku, &work[itauq], &work[iwork], &i__2, + &ierr, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", n, n, n, &work[ir], &ldwrkr, &work[itaup] - , &work[iwork], &i__2, &ierr, (ftnlen)1); + dorgbr_((char *)"P", n, n, n, &work[ir], &ldwrkr, &work[itaup], &work[iwork], &i__2, + &ierr, (ftnlen)1); iwork = ie + *n; - -/* Perform bidiagonal QR iteration, computing left */ -/* singular vectors of R in WORK(IU) and computing */ -/* right singular vectors of R in WORK(IR) */ -/* (Workspace: need 2*N*N + BDSPAC) */ - - dbdsqr_((char *)"U", n, n, n, &c__0, &s[1], &work[ie], &work[ - ir], &ldwrkr, &work[iu], &ldwrku, dum, &c__1, - &work[iwork], info, (ftnlen)1); - -/* Multiply Q in U by left singular vectors of R in */ -/* WORK(IU), storing result in A */ -/* (Workspace: need N*N) */ - - dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &u[u_offset], ldu, & - work[iu], &ldwrku, &c_b57, &a[a_offset], lda, - (ftnlen)1, (ftnlen)1); - -/* Copy left singular vectors of A from A to U */ - - dlacpy_((char *)"F", m, n, &a[a_offset], lda, &u[u_offset], - ldu, (ftnlen)1); - -/* Copy right singular vectors of R from WORK(IR) to A */ - - dlacpy_((char *)"F", n, n, &work[ir], &ldwrkr, &a[a_offset], - lda, (ftnlen)1); - + dbdsqr_((char *)"U", n, n, n, &c__0, &s[1], &work[ie], &work[ir], &ldwrkr, + &work[iu], &ldwrku, dum, &c__1, &work[iwork], info, (ftnlen)1); + dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &u[u_offset], ldu, &work[iu], &ldwrku, + &c_b57, &a[a_offset], lda, (ftnlen)1, (ftnlen)1); + dlacpy_((char *)"F", m, n, &a[a_offset], lda, &u[u_offset], ldu, (ftnlen)1); + dlacpy_((char *)"F", n, n, &work[ir], &ldwrkr, &a[a_offset], lda, (ftnlen)1); } else { - -/* Insufficient workspace for a fast algorithm */ - itau = 1; iwork = itau + *n; - -/* Compute A=Q*R, copying result to U */ -/* (Workspace: need 2*N, prefer N + N*NB) */ - i__2 = *lwork - iwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], - ldu, (ftnlen)1); - -/* Generate Q in U */ -/* (Workspace: need N + M, prefer N + M*NB) */ - + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], ldu, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], & - work[iwork], &i__2, &ierr); + dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], &work[iwork], &i__2, + &ierr); ie = itau; itauq = ie + *n; itaup = itauq + *n; iwork = itaup + *n; - -/* Zero out below R in A */ - if (*n > 1) { i__2 = *n - 1; i__3 = *n - 1; - dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &a[ - a_dim1 + 2], lda, (ftnlen)1); + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &a[a_dim1 + 2], lda, + (ftnlen)1); } - -/* Bidiagonalize R in A */ -/* (Workspace: need 4*N, prefer 3*N + 2*N*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); - -/* Multiply Q in U by left bidiagonalizing vectors */ -/* in A */ -/* (Workspace: need 3*N + M, prefer 3*N + M*NB) */ - + dgebrd_(n, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], + &work[itaup], &work[iwork], &i__2, &ierr); i__2 = *lwork - iwork + 1; - dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &a[a_offset], lda, & - work[itauq], &u[u_offset], ldu, &work[iwork], - &i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen)1) - ; - -/* Generate right bidiagonalizing vectors in A */ -/* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) */ - + dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &a[a_offset], lda, &work[itauq], + &u[u_offset], ldu, &work[iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, + (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, &work[itaup], - &work[iwork], &i__2, &ierr, (ftnlen)1); + dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, &work[itaup], &work[iwork], &i__2, + &ierr, (ftnlen)1); iwork = ie + *n; - -/* Perform bidiagonal QR iteration, computing left */ -/* singular vectors of A in U and computing right */ -/* singular vectors of A in A */ -/* (Workspace: need BDSPAC) */ - - dbdsqr_((char *)"U", n, n, m, &c__0, &s[1], &work[ie], &a[ - a_offset], lda, &u[u_offset], ldu, dum, &c__1, - &work[iwork], info, (ftnlen)1); - + dbdsqr_((char *)"U", n, n, m, &c__0, &s[1], &work[ie], &a[a_offset], lda, + &u[u_offset], ldu, dum, &c__1, &work[iwork], info, (ftnlen)1); } - } else if (wntvas) { - -/* Path 9 (M much larger than N, JOBU='A', JOBVT='S' */ -/* or 'A') */ -/* M left singular vectors to be computed in U and */ -/* N right singular vectors to be computed in VT */ - -/* Computing MAX */ - i__2 = *n + *m, i__3 = *n << 2, i__2 = max(i__2,i__3); - if (*lwork >= *n * *n + max(i__2,bdspac)) { - -/* Sufficient workspace for a fast algorithm */ - + i__2 = *n + *m, i__3 = *n << 2, i__2 = max(i__2, i__3); + if (*lwork >= *n * *n + max(i__2, bdspac)) { iu = 1; if (*lwork >= wrkbl + *lda * *n) { - -/* WORK(IU) is LDA by N */ - ldwrku = *lda; } else { - -/* WORK(IU) is N by N */ - ldwrku = *n; } itau = iu + ldwrku * *n; iwork = itau + *n; - -/* Compute A=Q*R, copying result to U */ -/* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) */ - i__2 = *lwork - iwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], - ldu, (ftnlen)1); - -/* Generate Q in U */ -/* (Workspace: need N*N + N + M, prefer N*N + N + M*NB) */ - + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], ldu, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], & - work[iwork], &i__2, &ierr); - -/* Copy R to WORK(IU), zeroing out below it */ - - dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[iu], & - ldwrku, (ftnlen)1); + dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], &work[iwork], &i__2, + &ierr); + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &work[iu], &ldwrku, (ftnlen)1); i__2 = *n - 1; i__3 = *n - 1; - dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[iu + - 1], &ldwrku, (ftnlen)1); + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &work[iu + 1], &ldwrku, + (ftnlen)1); ie = itau; itauq = ie + *n; itaup = itauq + *n; iwork = itaup + *n; - -/* Bidiagonalize R in WORK(IU), copying result to VT */ -/* (Workspace: need N*N + 4*N, prefer N*N + 3*N + 2*N*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(n, n, &work[iu], &ldwrku, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); - dlacpy_((char *)"U", n, n, &work[iu], &ldwrku, &vt[vt_offset], - ldvt, (ftnlen)1); - -/* Generate left bidiagonalizing vectors in WORK(IU) */ -/* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB) */ - + dgebrd_(n, n, &work[iu], &ldwrku, &s[1], &work[ie], &work[itauq], + &work[itaup], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"U", n, n, &work[iu], &ldwrku, &vt[vt_offset], ldvt, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", n, n, n, &work[iu], &ldwrku, &work[itauq] - , &work[iwork], &i__2, &ierr, (ftnlen)1); - -/* Generate right bidiagonalizing vectors in VT */ -/* (Workspace: need N*N + 4*N-1, */ -/* prefer N*N+3*N+(N-1)*NB) */ - + dorgbr_((char *)"Q", n, n, n, &work[iu], &ldwrku, &work[itauq], &work[iwork], &i__2, + &ierr, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[ - itaup], &work[iwork], &i__2, &ierr, (ftnlen)1) - ; + dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], &work[iwork], + &i__2, &ierr, (ftnlen)1); iwork = ie + *n; - -/* Perform bidiagonal QR iteration, computing left */ -/* singular vectors of R in WORK(IU) and computing */ -/* right singular vectors of R in VT */ -/* (Workspace: need N*N + BDSPAC) */ - - dbdsqr_((char *)"U", n, n, n, &c__0, &s[1], &work[ie], &vt[ - vt_offset], ldvt, &work[iu], &ldwrku, dum, & - c__1, &work[iwork], info, (ftnlen)1); - -/* Multiply Q in U by left singular vectors of R in */ -/* WORK(IU), storing result in A */ -/* (Workspace: need N*N) */ - - dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &u[u_offset], ldu, & - work[iu], &ldwrku, &c_b57, &a[a_offset], lda, - (ftnlen)1, (ftnlen)1); - -/* Copy left singular vectors of A from A to U */ - - dlacpy_((char *)"F", m, n, &a[a_offset], lda, &u[u_offset], - ldu, (ftnlen)1); - + dbdsqr_((char *)"U", n, n, n, &c__0, &s[1], &work[ie], &vt[vt_offset], ldvt, + &work[iu], &ldwrku, dum, &c__1, &work[iwork], info, (ftnlen)1); + dgemm_((char *)"N", (char *)"N", m, n, n, &c_b79, &u[u_offset], ldu, &work[iu], &ldwrku, + &c_b57, &a[a_offset], lda, (ftnlen)1, (ftnlen)1); + dlacpy_((char *)"F", m, n, &a[a_offset], lda, &u[u_offset], ldu, (ftnlen)1); } else { - -/* Insufficient workspace for a fast algorithm */ - itau = 1; iwork = itau + *n; - -/* Compute A=Q*R, copying result to U */ -/* (Workspace: need 2*N, prefer N + N*NB) */ - i__2 = *lwork - iwork + 1; - dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], - ldu, (ftnlen)1); - -/* Generate Q in U */ -/* (Workspace: need N + M, prefer N + M*NB) */ - + dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], ldu, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], & - work[iwork], &i__2, &ierr); - -/* Copy R from A to VT, zeroing out below it */ - - dlacpy_((char *)"U", n, n, &a[a_offset], lda, &vt[vt_offset], - ldvt, (ftnlen)1); + dorgqr_(m, m, n, &u[u_offset], ldu, &work[itau], &work[iwork], &i__2, + &ierr); + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt, (ftnlen)1); if (*n > 1) { i__2 = *n - 1; i__3 = *n - 1; - dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &vt[ - vt_dim1 + 2], ldvt, (ftnlen)1); + dlaset_((char *)"L", &i__2, &i__3, &c_b57, &c_b57, &vt[vt_dim1 + 2], ldvt, + (ftnlen)1); } ie = itau; itauq = ie + *n; itaup = itauq + *n; iwork = itaup + *n; - -/* Bidiagonalize R in VT */ -/* (Workspace: need 4*N, prefer 3*N + 2*N*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &work[ie], - &work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); - -/* Multiply Q in U by left bidiagonalizing vectors */ -/* in VT */ -/* (Workspace: need 3*N + M, prefer 3*N + M*NB) */ - + dgebrd_(n, n, &vt[vt_offset], ldvt, &s[1], &work[ie], &work[itauq], + &work[itaup], &work[iwork], &i__2, &ierr); i__2 = *lwork - iwork + 1; - dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &vt[vt_offset], ldvt, - &work[itauq], &u[u_offset], ldu, &work[iwork], - &i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen) - 1); - -/* Generate right bidiagonalizing vectors in VT */ -/* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) */ - + dormbr_((char *)"Q", (char *)"R", (char *)"N", m, n, n, &vt[vt_offset], ldvt, &work[itauq], + &u[u_offset], ldu, &work[iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, + (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[ - itaup], &work[iwork], &i__2, &ierr, (ftnlen)1) - ; + dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], &work[iwork], + &i__2, &ierr, (ftnlen)1); iwork = ie + *n; - -/* Perform bidiagonal QR iteration, computing left */ -/* singular vectors of A in U and computing right */ -/* singular vectors of A in VT */ -/* (Workspace: need BDSPAC) */ - - dbdsqr_((char *)"U", n, n, m, &c__0, &s[1], &work[ie], &vt[ - vt_offset], ldvt, &u[u_offset], ldu, dum, & - c__1, &work[iwork], info, (ftnlen)1); - + dbdsqr_((char *)"U", n, n, m, &c__0, &s[1], &work[ie], &vt[vt_offset], ldvt, + &u[u_offset], ldu, dum, &c__1, &work[iwork], info, (ftnlen)1); } - } - } - } else { - -/* M .LT. MNTHR */ - -/* Path 10 (M at least N, but not much larger) */ -/* Reduce to bidiagonal form without QR decomposition */ - ie = 1; itauq = ie + *n; itaup = itauq + *n; iwork = itaup + *n; - -/* Bidiagonalize A */ -/* (Workspace: need 3*N + M, prefer 3*N + (M + N)*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], & - work[itaup], &work[iwork], &i__2, &ierr); + dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &work[itaup], + &work[iwork], &i__2, &ierr); if (wntuas) { - -/* If left singular vectors desired in U, copy result to U */ -/* and generate left bidiagonalizing vectors in U */ -/* (Workspace: need 3*N + NCU, prefer 3*N + NCU*NB) */ - - dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], ldu, ( - ftnlen)1); + dlacpy_((char *)"L", m, n, &a[a_offset], lda, &u[u_offset], ldu, (ftnlen)1); if (wntus) { ncu = *n; } @@ -2446,40 +1124,24 @@ f"> */ ncu = *m; } i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", m, &ncu, n, &u[u_offset], ldu, &work[itauq], & - work[iwork], &i__2, &ierr, (ftnlen)1); + dorgbr_((char *)"Q", m, &ncu, n, &u[u_offset], ldu, &work[itauq], &work[iwork], &i__2, + &ierr, (ftnlen)1); } if (wntvas) { - -/* If right singular vectors desired in VT, copy result to */ -/* VT and generate right bidiagonalizing vectors in VT */ -/* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) */ - - dlacpy_((char *)"U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt, ( - ftnlen)1); + dlacpy_((char *)"U", n, n, &a[a_offset], lda, &vt[vt_offset], ldvt, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], & - work[iwork], &i__2, &ierr, (ftnlen)1); + dorgbr_((char *)"P", n, n, n, &vt[vt_offset], ldvt, &work[itaup], &work[iwork], &i__2, + &ierr, (ftnlen)1); } if (wntuo) { - -/* If left singular vectors desired in A, generate left */ -/* bidiagonalizing vectors in A */ -/* (Workspace: need 4*N, prefer 3*N + N*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", m, n, n, &a[a_offset], lda, &work[itauq], &work[ - iwork], &i__2, &ierr, (ftnlen)1); + dorgbr_((char *)"Q", m, n, n, &a[a_offset], lda, &work[itauq], &work[iwork], &i__2, &ierr, + (ftnlen)1); } if (wntvo) { - -/* If right singular vectors desired in A, generate right */ -/* bidiagonalizing vectors in A */ -/* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, &work[itaup], &work[ - iwork], &i__2, &ierr, (ftnlen)1); + dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, &work[itaup], &work[iwork], &i__2, &ierr, + (ftnlen)1); } iwork = ie + *n; if (wntuas || wntuo) { @@ -2494,146 +1156,65 @@ f"> */ if (wntvn) { ncvt = 0; } - if (! wntuo && ! wntvo) { - -/* Perform bidiagonal QR iteration, if desired, computing */ -/* left singular vectors in U and computing right singular */ -/* vectors in VT */ -/* (Workspace: need BDSPAC) */ - - dbdsqr_((char *)"U", n, &ncvt, &nru, &c__0, &s[1], &work[ie], &vt[ - vt_offset], ldvt, &u[u_offset], ldu, dum, &c__1, & - work[iwork], info, (ftnlen)1); - } else if (! wntuo && wntvo) { - -/* Perform bidiagonal QR iteration, if desired, computing */ -/* left singular vectors in U and computing right singular */ -/* vectors in A */ -/* (Workspace: need BDSPAC) */ - - dbdsqr_((char *)"U", n, &ncvt, &nru, &c__0, &s[1], &work[ie], &a[ - a_offset], lda, &u[u_offset], ldu, dum, &c__1, &work[ - iwork], info, (ftnlen)1); + if (!wntuo && !wntvo) { + dbdsqr_((char *)"U", n, &ncvt, &nru, &c__0, &s[1], &work[ie], &vt[vt_offset], ldvt, + &u[u_offset], ldu, dum, &c__1, &work[iwork], info, (ftnlen)1); + } else if (!wntuo && wntvo) { + dbdsqr_((char *)"U", n, &ncvt, &nru, &c__0, &s[1], &work[ie], &a[a_offset], lda, + &u[u_offset], ldu, dum, &c__1, &work[iwork], info, (ftnlen)1); } else { - -/* Perform bidiagonal QR iteration, if desired, computing */ -/* left singular vectors in A and computing right singular */ -/* vectors in VT */ -/* (Workspace: need BDSPAC) */ - - dbdsqr_((char *)"U", n, &ncvt, &nru, &c__0, &s[1], &work[ie], &vt[ - vt_offset], ldvt, &a[a_offset], lda, dum, &c__1, & - work[iwork], info, (ftnlen)1); + dbdsqr_((char *)"U", n, &ncvt, &nru, &c__0, &s[1], &work[ie], &vt[vt_offset], ldvt, + &a[a_offset], lda, dum, &c__1, &work[iwork], info, (ftnlen)1); } - } - } else { - -/* A has more columns than rows. If A has sufficiently more */ -/* columns than rows, first reduce using the LQ decomposition (if */ -/* sufficient workspace available) */ - if (*n >= mnthr) { - if (wntvn) { - -/* Path 1t(N much larger than M, JOBVT='N') */ -/* No right singular vectors to be computed */ - itau = 1; iwork = itau + *m; - -/* Compute A=L*Q */ -/* (Workspace: need 2*M, prefer M + M*NB) */ - i__2 = *lwork - iwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], & - i__2, &ierr); - -/* Zero out above L */ - + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, &ierr); i__2 = *m - 1; i__3 = *m - 1; - dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &a[(a_dim1 << 1) + - 1], lda, (ftnlen)1); + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &a[(a_dim1 << 1) + 1], lda, (ftnlen)1); ie = 1; itauq = ie + *m; itaup = itauq + *m; iwork = itaup + *m; - -/* Bidiagonalize L in A */ -/* (Workspace: need 4*M, prefer 3*M + 2*M*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &work[ - itauq], &work[itaup], &work[iwork], &i__2, &ierr); + dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &work[itaup], + &work[iwork], &i__2, &ierr); if (wntuo || wntuas) { - -/* If left singular vectors desired, generate Q */ -/* (Workspace: need 4*M, prefer 3*M + M*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", m, m, m, &a[a_offset], lda, &work[itauq], & - work[iwork], &i__2, &ierr, (ftnlen)1); + dorgbr_((char *)"Q", m, m, m, &a[a_offset], lda, &work[itauq], &work[iwork], &i__2, + &ierr, (ftnlen)1); } iwork = ie + *m; nru = 0; if (wntuo || wntuas) { nru = *m; } - -/* Perform bidiagonal QR iteration, computing left singular */ -/* vectors of A in A if desired */ -/* (Workspace: need BDSPAC) */ - - dbdsqr_((char *)"U", m, &c__0, &nru, &c__0, &s[1], &work[ie], dum, & - c__1, &a[a_offset], lda, dum, &c__1, &work[iwork], - info, (ftnlen)1); - -/* If left singular vectors desired in U, copy them there */ - + dbdsqr_((char *)"U", m, &c__0, &nru, &c__0, &s[1], &work[ie], dum, &c__1, &a[a_offset], lda, + dum, &c__1, &work[iwork], info, (ftnlen)1); if (wntuas) { - dlacpy_((char *)"F", m, m, &a[a_offset], lda, &u[u_offset], ldu, ( - ftnlen)1); + dlacpy_((char *)"F", m, m, &a[a_offset], lda, &u[u_offset], ldu, (ftnlen)1); } - } else if (wntvo && wntun) { - -/* Path 2t(N much larger than M, JOBU='N', JOBVT='O') */ -/* M right singular vectors to be overwritten on A and */ -/* no left singular vectors to be computed */ - -/* Computing MAX */ i__2 = *m << 2; - if (*lwork >= *m * *m + max(i__2,bdspac)) { - -/* Sufficient workspace for a fast algorithm */ - + if (*lwork >= *m * *m + max(i__2, bdspac)) { ir = 1; -/* Computing MAX */ i__2 = wrkbl, i__3 = *lda * *n + *m; - if (*lwork >= max(i__2,i__3) + *lda * *m) { - -/* WORK(IU) is LDA by N and WORK(IR) is LDA by M */ - + if (*lwork >= max(i__2, i__3) + *lda * *m) { ldwrku = *lda; chunk = *n; ldwrkr = *lda; - } else /* if(complicated condition) */ { -/* Computing MAX */ + } else { i__2 = wrkbl, i__3 = *lda * *n + *m; - if (*lwork >= max(i__2,i__3) + *m * *m) { - -/* WORK(IU) is LDA by N and WORK(IR) is M by M */ - + if (*lwork >= max(i__2, i__3) + *m * *m) { ldwrku = *lda; chunk = *n; ldwrkr = *m; } else { - -/* WORK(IU) is M by CHUNK and WORK(IR) is M by M */ - ldwrku = *m; chunk = (*lwork - *m * *m - *m) / *m; ldwrkr = *m; @@ -2641,147 +1222,71 @@ f"> */ } itau = ir + ldwrkr * *m; iwork = itau + *m; - -/* Compute A=L*Q */ -/* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */ - i__2 = *lwork - iwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork] - , &i__2, &ierr); - -/* Copy L to WORK(IR) and zero out above it */ - - dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[ir], &ldwrkr, - (ftnlen)1); + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[ir], &ldwrkr, (ftnlen)1); i__2 = *m - 1; i__3 = *m - 1; - dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[ir + - ldwrkr], &ldwrkr, (ftnlen)1); - -/* Generate Q in A */ -/* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */ - + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[ir + ldwrkr], &ldwrkr, + (ftnlen)1); i__2 = *lwork - iwork + 1; - dorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); + dorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, &ierr); ie = itau; itauq = ie + *m; itaup = itauq + *m; iwork = itaup + *m; - -/* Bidiagonalize L in WORK(IR) */ -/* (Workspace: need M*M + 4*M, prefer M*M + 3*M + 2*M*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &work[ie], &work[ - itauq], &work[itaup], &work[iwork], &i__2, &ierr); - -/* Generate right vectors bidiagonalizing L */ -/* (Workspace: need M*M + 4*M-1, prefer M*M + 3*M + (M-1)*NB) */ - + dgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &work[ie], &work[itauq], &work[itaup], + &work[iwork], &i__2, &ierr); i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", m, m, m, &work[ir], &ldwrkr, &work[itaup], & - work[iwork], &i__2, &ierr, (ftnlen)1); + dorgbr_((char *)"P", m, m, m, &work[ir], &ldwrkr, &work[itaup], &work[iwork], &i__2, + &ierr, (ftnlen)1); iwork = ie + *m; - -/* Perform bidiagonal QR iteration, computing right */ -/* singular vectors of L in WORK(IR) */ -/* (Workspace: need M*M + BDSPAC) */ - - dbdsqr_((char *)"U", m, m, &c__0, &c__0, &s[1], &work[ie], &work[ - ir], &ldwrkr, dum, &c__1, dum, &c__1, &work[iwork] - , info, (ftnlen)1); + dbdsqr_((char *)"U", m, m, &c__0, &c__0, &s[1], &work[ie], &work[ir], &ldwrkr, dum, + &c__1, dum, &c__1, &work[iwork], info, (ftnlen)1); iu = ie + *m; - -/* Multiply right singular vectors of L in WORK(IR) by Q */ -/* in A, storing result in WORK(IU) and copying to A */ -/* (Workspace: need M*M + 2*M, prefer M*M + M*N + M) */ - i__2 = *n; i__3 = chunk; - for (i__ = 1; i__3 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += - i__3) { -/* Computing MIN */ + for (i__ = 1; i__3 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__3) { i__4 = *n - i__ + 1; - blk = min(i__4,chunk); - dgemm_((char *)"N", (char *)"N", m, &blk, m, &c_b79, &work[ir], & - ldwrkr, &a[i__ * a_dim1 + 1], lda, &c_b57, & - work[iu], &ldwrku, (ftnlen)1, (ftnlen)1); - dlacpy_((char *)"F", m, &blk, &work[iu], &ldwrku, &a[i__ * - a_dim1 + 1], lda, (ftnlen)1); -/* L30: */ + blk = min(i__4, chunk); + dgemm_((char *)"N", (char *)"N", m, &blk, m, &c_b79, &work[ir], &ldwrkr, + &a[i__ * a_dim1 + 1], lda, &c_b57, &work[iu], &ldwrku, (ftnlen)1, + (ftnlen)1); + dlacpy_((char *)"F", m, &blk, &work[iu], &ldwrku, &a[i__ * a_dim1 + 1], lda, + (ftnlen)1); } - } else { - -/* Insufficient workspace for a fast algorithm */ - ie = 1; itauq = ie + *m; itaup = itauq + *m; iwork = itaup + *m; - -/* Bidiagonalize A */ -/* (Workspace: need 3*M + N, prefer 3*M + (M + N)*NB) */ - i__3 = *lwork - iwork + 1; - dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[ - itauq], &work[itaup], &work[iwork], &i__3, &ierr); - -/* Generate right vectors bidiagonalizing A */ -/* (Workspace: need 4*M, prefer 3*M + M*NB) */ - + dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &work[itaup], + &work[iwork], &i__3, &ierr); i__3 = *lwork - iwork + 1; - dorgbr_((char *)"P", m, n, m, &a[a_offset], lda, &work[itaup], & - work[iwork], &i__3, &ierr, (ftnlen)1); + dorgbr_((char *)"P", m, n, m, &a[a_offset], lda, &work[itaup], &work[iwork], &i__3, + &ierr, (ftnlen)1); iwork = ie + *m; - -/* Perform bidiagonal QR iteration, computing right */ -/* singular vectors of A in A */ -/* (Workspace: need BDSPAC) */ - - dbdsqr_((char *)"L", m, n, &c__0, &c__0, &s[1], &work[ie], &a[ - a_offset], lda, dum, &c__1, dum, &c__1, &work[ - iwork], info, (ftnlen)1); - + dbdsqr_((char *)"L", m, n, &c__0, &c__0, &s[1], &work[ie], &a[a_offset], lda, dum, + &c__1, dum, &c__1, &work[iwork], info, (ftnlen)1); } - } else if (wntvo && wntuas) { - -/* Path 3t(N much larger than M, JOBU='S' or 'A', JOBVT='O') */ -/* M right singular vectors to be overwritten on A and */ -/* M left singular vectors to be computed in U */ - -/* Computing MAX */ i__3 = *m << 2; - if (*lwork >= *m * *m + max(i__3,bdspac)) { - -/* Sufficient workspace for a fast algorithm */ - + if (*lwork >= *m * *m + max(i__3, bdspac)) { ir = 1; -/* Computing MAX */ i__3 = wrkbl, i__2 = *lda * *n + *m; - if (*lwork >= max(i__3,i__2) + *lda * *m) { - -/* WORK(IU) is LDA by N and WORK(IR) is LDA by M */ - + if (*lwork >= max(i__3, i__2) + *lda * *m) { ldwrku = *lda; chunk = *n; ldwrkr = *lda; - } else /* if(complicated condition) */ { -/* Computing MAX */ + } else { i__3 = wrkbl, i__2 = *lda * *n + *m; - if (*lwork >= max(i__3,i__2) + *m * *m) { - -/* WORK(IU) is LDA by N and WORK(IR) is M by M */ - + if (*lwork >= max(i__3, i__2) + *m * *m) { ldwrku = *lda; chunk = *n; ldwrkr = *m; } else { - -/* WORK(IU) is M by CHUNK and WORK(IR) is M by M */ - ldwrku = *m; chunk = (*lwork - *m * *m - *m) / *m; ldwrkr = *m; @@ -2789,1239 +1294,532 @@ f"> */ } itau = ir + ldwrkr * *m; iwork = itau + *m; - -/* Compute A=L*Q */ -/* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */ - i__3 = *lwork - iwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork] - , &i__3, &ierr); - -/* Copy L to U, zeroing about above it */ - - dlacpy_((char *)"L", m, m, &a[a_offset], lda, &u[u_offset], ldu, ( - ftnlen)1); + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__3, &ierr); + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &u[u_offset], ldu, (ftnlen)1); i__3 = *m - 1; i__2 = *m - 1; - dlaset_((char *)"U", &i__3, &i__2, &c_b57, &c_b57, &u[(u_dim1 << - 1) + 1], ldu, (ftnlen)1); - -/* Generate Q in A */ -/* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */ - + dlaset_((char *)"U", &i__3, &i__2, &c_b57, &c_b57, &u[(u_dim1 << 1) + 1], ldu, + (ftnlen)1); i__3 = *lwork - iwork + 1; - dorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__3, &ierr); + dorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[iwork], &i__3, &ierr); ie = itau; itauq = ie + *m; itaup = itauq + *m; iwork = itaup + *m; - -/* Bidiagonalize L in U, copying result to WORK(IR) */ -/* (Workspace: need M*M + 4*M, prefer M*M + 3*M + 2*M*NB) */ - i__3 = *lwork - iwork + 1; - dgebrd_(m, m, &u[u_offset], ldu, &s[1], &work[ie], &work[ - itauq], &work[itaup], &work[iwork], &i__3, &ierr); - dlacpy_((char *)"U", m, m, &u[u_offset], ldu, &work[ir], &ldwrkr, - (ftnlen)1); - -/* Generate right vectors bidiagonalizing L in WORK(IR) */ -/* (Workspace: need M*M + 4*M-1, prefer M*M + 3*M + (M-1)*NB) */ - + dgebrd_(m, m, &u[u_offset], ldu, &s[1], &work[ie], &work[itauq], &work[itaup], + &work[iwork], &i__3, &ierr); + dlacpy_((char *)"U", m, m, &u[u_offset], ldu, &work[ir], &ldwrkr, (ftnlen)1); i__3 = *lwork - iwork + 1; - dorgbr_((char *)"P", m, m, m, &work[ir], &ldwrkr, &work[itaup], & - work[iwork], &i__3, &ierr, (ftnlen)1); - -/* Generate left vectors bidiagonalizing L in U */ -/* (Workspace: need M*M + 4*M, prefer M*M + 3*M + M*NB) */ - + dorgbr_((char *)"P", m, m, m, &work[ir], &ldwrkr, &work[itaup], &work[iwork], &i__3, + &ierr, (ftnlen)1); i__3 = *lwork - iwork + 1; - dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq], & - work[iwork], &i__3, &ierr, (ftnlen)1); + dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq], &work[iwork], &i__3, + &ierr, (ftnlen)1); iwork = ie + *m; - -/* Perform bidiagonal QR iteration, computing left */ -/* singular vectors of L in U, and computing right */ -/* singular vectors of L in WORK(IR) */ -/* (Workspace: need M*M + BDSPAC) */ - - dbdsqr_((char *)"U", m, m, m, &c__0, &s[1], &work[ie], &work[ir], - &ldwrkr, &u[u_offset], ldu, dum, &c__1, &work[ - iwork], info, (ftnlen)1); + dbdsqr_((char *)"U", m, m, m, &c__0, &s[1], &work[ie], &work[ir], &ldwrkr, &u[u_offset], + ldu, dum, &c__1, &work[iwork], info, (ftnlen)1); iu = ie + *m; - -/* Multiply right singular vectors of L in WORK(IR) by Q */ -/* in A, storing result in WORK(IU) and copying to A */ -/* (Workspace: need M*M + 2*M, prefer M*M + M*N + M)) */ - i__3 = *n; i__2 = chunk; - for (i__ = 1; i__2 < 0 ? i__ >= i__3 : i__ <= i__3; i__ += - i__2) { -/* Computing MIN */ + for (i__ = 1; i__2 < 0 ? i__ >= i__3 : i__ <= i__3; i__ += i__2) { i__4 = *n - i__ + 1; - blk = min(i__4,chunk); - dgemm_((char *)"N", (char *)"N", m, &blk, m, &c_b79, &work[ir], & - ldwrkr, &a[i__ * a_dim1 + 1], lda, &c_b57, & - work[iu], &ldwrku, (ftnlen)1, (ftnlen)1); - dlacpy_((char *)"F", m, &blk, &work[iu], &ldwrku, &a[i__ * - a_dim1 + 1], lda, (ftnlen)1); -/* L40: */ + blk = min(i__4, chunk); + dgemm_((char *)"N", (char *)"N", m, &blk, m, &c_b79, &work[ir], &ldwrkr, + &a[i__ * a_dim1 + 1], lda, &c_b57, &work[iu], &ldwrku, (ftnlen)1, + (ftnlen)1); + dlacpy_((char *)"F", m, &blk, &work[iu], &ldwrku, &a[i__ * a_dim1 + 1], lda, + (ftnlen)1); } - } else { - -/* Insufficient workspace for a fast algorithm */ - itau = 1; iwork = itau + *m; - -/* Compute A=L*Q */ -/* (Workspace: need 2*M, prefer M + M*NB) */ - i__2 = *lwork - iwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork] - , &i__2, &ierr); - -/* Copy L to U, zeroing out above it */ - - dlacpy_((char *)"L", m, m, &a[a_offset], lda, &u[u_offset], ldu, ( - ftnlen)1); + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &u[u_offset], ldu, (ftnlen)1); i__2 = *m - 1; i__3 = *m - 1; - dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &u[(u_dim1 << - 1) + 1], ldu, (ftnlen)1); - -/* Generate Q in A */ -/* (Workspace: need 2*M, prefer M + M*NB) */ - + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &u[(u_dim1 << 1) + 1], ldu, + (ftnlen)1); i__2 = *lwork - iwork + 1; - dorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); + dorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, &ierr); ie = itau; itauq = ie + *m; itaup = itauq + *m; iwork = itaup + *m; - -/* Bidiagonalize L in U */ -/* (Workspace: need 4*M, prefer 3*M + 2*M*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(m, m, &u[u_offset], ldu, &s[1], &work[ie], &work[ - itauq], &work[itaup], &work[iwork], &i__2, &ierr); - -/* Multiply right vectors bidiagonalizing L by Q in A */ -/* (Workspace: need 3*M + N, prefer 3*M + N*NB) */ - + dgebrd_(m, m, &u[u_offset], ldu, &s[1], &work[ie], &work[itauq], &work[itaup], + &work[iwork], &i__2, &ierr); i__2 = *lwork - iwork + 1; - dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &u[u_offset], ldu, &work[ - itaup], &a[a_offset], lda, &work[iwork], &i__2, & - ierr, (ftnlen)1, (ftnlen)1, (ftnlen)1); - -/* Generate left vectors bidiagonalizing L in U */ -/* (Workspace: need 4*M, prefer 3*M + M*NB) */ - + dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &u[u_offset], ldu, &work[itaup], &a[a_offset], + lda, &work[iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq], & - work[iwork], &i__2, &ierr, (ftnlen)1); + dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq], &work[iwork], &i__2, + &ierr, (ftnlen)1); iwork = ie + *m; - -/* Perform bidiagonal QR iteration, computing left */ -/* singular vectors of A in U and computing right */ -/* singular vectors of A in A */ -/* (Workspace: need BDSPAC) */ - - dbdsqr_((char *)"U", m, n, m, &c__0, &s[1], &work[ie], &a[ - a_offset], lda, &u[u_offset], ldu, dum, &c__1, & - work[iwork], info, (ftnlen)1); - + dbdsqr_((char *)"U", m, n, m, &c__0, &s[1], &work[ie], &a[a_offset], lda, &u[u_offset], + ldu, dum, &c__1, &work[iwork], info, (ftnlen)1); } - } else if (wntvs) { - if (wntun) { - -/* Path 4t(N much larger than M, JOBU='N', JOBVT='S') */ -/* M right singular vectors to be computed in VT and */ -/* no left singular vectors to be computed */ - -/* Computing MAX */ i__2 = *m << 2; - if (*lwork >= *m * *m + max(i__2,bdspac)) { - -/* Sufficient workspace for a fast algorithm */ - + if (*lwork >= *m * *m + max(i__2, bdspac)) { ir = 1; if (*lwork >= wrkbl + *lda * *m) { - -/* WORK(IR) is LDA by M */ - ldwrkr = *lda; } else { - -/* WORK(IR) is M by M */ - ldwrkr = *m; } itau = ir + ldwrkr * *m; iwork = itau + *m; - -/* Compute A=L*Q */ -/* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */ - i__2 = *lwork - iwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - -/* Copy L to WORK(IR), zeroing out above it */ - - dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[ir], & - ldwrkr, (ftnlen)1); + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[ir], &ldwrkr, (ftnlen)1); i__2 = *m - 1; i__3 = *m - 1; - dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[ir + - ldwrkr], &ldwrkr, (ftnlen)1); - -/* Generate Q in A */ -/* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */ - + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[ir + ldwrkr], &ldwrkr, + (ftnlen)1); i__2 = *lwork - iwork + 1; - dorglq_(m, n, m, &a[a_offset], lda, &work[itau], & - work[iwork], &i__2, &ierr); + dorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, + &ierr); ie = itau; itauq = ie + *m; itaup = itauq + *m; iwork = itaup + *m; - -/* Bidiagonalize L in WORK(IR) */ -/* (Workspace: need M*M + 4*M, prefer M*M + 3*M + 2*M*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); - -/* Generate right vectors bidiagonalizing L in */ -/* WORK(IR) */ -/* (Workspace: need M*M + 4*M, prefer M*M + 3*M + (M-1)*NB) */ - + dgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &work[ie], &work[itauq], + &work[itaup], &work[iwork], &i__2, &ierr); i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", m, m, m, &work[ir], &ldwrkr, &work[itaup] - , &work[iwork], &i__2, &ierr, (ftnlen)1); + dorgbr_((char *)"P", m, m, m, &work[ir], &ldwrkr, &work[itaup], &work[iwork], &i__2, + &ierr, (ftnlen)1); iwork = ie + *m; - -/* Perform bidiagonal QR iteration, computing right */ -/* singular vectors of L in WORK(IR) */ -/* (Workspace: need M*M + BDSPAC) */ - - dbdsqr_((char *)"U", m, m, &c__0, &c__0, &s[1], &work[ie], & - work[ir], &ldwrkr, dum, &c__1, dum, &c__1, & - work[iwork], info, (ftnlen)1); - -/* Multiply right singular vectors of L in WORK(IR) by */ -/* Q in A, storing result in VT */ -/* (Workspace: need M*M) */ - - dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[ir], &ldwrkr, - &a[a_offset], lda, &c_b57, &vt[vt_offset], - ldvt, (ftnlen)1, (ftnlen)1); - + dbdsqr_((char *)"U", m, m, &c__0, &c__0, &s[1], &work[ie], &work[ir], &ldwrkr, dum, + &c__1, dum, &c__1, &work[iwork], info, (ftnlen)1); + dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[ir], &ldwrkr, &a[a_offset], lda, + &c_b57, &vt[vt_offset], ldvt, (ftnlen)1, (ftnlen)1); } else { - -/* Insufficient workspace for a fast algorithm */ - itau = 1; iwork = itau + *m; - -/* Compute A=L*Q */ -/* (Workspace: need 2*M, prefer M + M*NB) */ - i__2 = *lwork - iwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - -/* Copy result to VT */ - - dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], - ldvt, (ftnlen)1); - -/* Generate Q in VT */ -/* (Workspace: need 2*M, prefer M + M*NB) */ - + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], & - work[iwork], &i__2, &ierr); + dorglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], &work[iwork], &i__2, + &ierr); ie = itau; itauq = ie + *m; itaup = itauq + *m; iwork = itaup + *m; - -/* Zero out above L in A */ - i__2 = *m - 1; i__3 = *m - 1; - dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &a[(a_dim1 - << 1) + 1], lda, (ftnlen)1); - -/* Bidiagonalize L in A */ -/* (Workspace: need 4*M, prefer 3*M + 2*M*NB) */ - + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &a[(a_dim1 << 1) + 1], lda, + (ftnlen)1); i__2 = *lwork - iwork + 1; - dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); - -/* Multiply right vectors bidiagonalizing L by Q in VT */ -/* (Workspace: need 3*M + N, prefer 3*M + N*NB) */ - + dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], + &work[itaup], &work[iwork], &i__2, &ierr); i__2 = *lwork - iwork + 1; - dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &a[a_offset], lda, & - work[itaup], &vt[vt_offset], ldvt, &work[ - iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, ( - ftnlen)1); + dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &a[a_offset], lda, &work[itaup], + &vt[vt_offset], ldvt, &work[iwork], &i__2, &ierr, (ftnlen)1, + (ftnlen)1, (ftnlen)1); iwork = ie + *m; - -/* Perform bidiagonal QR iteration, computing right */ -/* singular vectors of A in VT */ -/* (Workspace: need BDSPAC) */ - - dbdsqr_((char *)"U", m, n, &c__0, &c__0, &s[1], &work[ie], & - vt[vt_offset], ldvt, dum, &c__1, dum, &c__1, & - work[iwork], info, (ftnlen)1); - + dbdsqr_((char *)"U", m, n, &c__0, &c__0, &s[1], &work[ie], &vt[vt_offset], ldvt, + dum, &c__1, dum, &c__1, &work[iwork], info, (ftnlen)1); } - } else if (wntuo) { - -/* Path 5t(N much larger than M, JOBU='O', JOBVT='S') */ -/* M right singular vectors to be computed in VT and */ -/* M left singular vectors to be overwritten on A */ - -/* Computing MAX */ i__2 = *m << 2; - if (*lwork >= (*m << 1) * *m + max(i__2,bdspac)) { - -/* Sufficient workspace for a fast algorithm */ - + if (*lwork >= (*m << 1) * *m + max(i__2, bdspac)) { iu = 1; if (*lwork >= wrkbl + (*lda << 1) * *m) { - -/* WORK(IU) is LDA by M and WORK(IR) is LDA by M */ - ldwrku = *lda; ir = iu + ldwrku * *m; ldwrkr = *lda; } else if (*lwork >= wrkbl + (*lda + *m) * *m) { - -/* WORK(IU) is LDA by M and WORK(IR) is M by M */ - ldwrku = *lda; ir = iu + ldwrku * *m; ldwrkr = *m; } else { - -/* WORK(IU) is M by M and WORK(IR) is M by M */ - ldwrku = *m; ir = iu + ldwrku * *m; ldwrkr = *m; } itau = ir + ldwrkr * *m; iwork = itau + *m; - -/* Compute A=L*Q */ -/* (Workspace: need 2*M*M + 2*M, prefer 2*M*M + M + M*NB) */ - i__2 = *lwork - iwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - -/* Copy L to WORK(IU), zeroing out below it */ - - dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[iu], & - ldwrku, (ftnlen)1); + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[iu], &ldwrku, (ftnlen)1); i__2 = *m - 1; i__3 = *m - 1; - dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[iu + - ldwrku], &ldwrku, (ftnlen)1); - -/* Generate Q in A */ -/* (Workspace: need 2*M*M + 2*M, prefer 2*M*M + M + M*NB) */ - + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[iu + ldwrku], &ldwrku, + (ftnlen)1); i__2 = *lwork - iwork + 1; - dorglq_(m, n, m, &a[a_offset], lda, &work[itau], & - work[iwork], &i__2, &ierr); + dorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, + &ierr); ie = itau; itauq = ie + *m; itaup = itauq + *m; iwork = itaup + *m; - -/* Bidiagonalize L in WORK(IU), copying result to */ -/* WORK(IR) */ -/* (Workspace: need 2*M*M + 4*M, */ -/* prefer 2*M*M+3*M+2*M*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(m, m, &work[iu], &ldwrku, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); - dlacpy_((char *)"L", m, m, &work[iu], &ldwrku, &work[ir], & - ldwrkr, (ftnlen)1); - -/* Generate right bidiagonalizing vectors in WORK(IU) */ -/* (Workspace: need 2*M*M + 4*M-1, */ -/* prefer 2*M*M+3*M+(M-1)*NB) */ - + dgebrd_(m, m, &work[iu], &ldwrku, &s[1], &work[ie], &work[itauq], + &work[itaup], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, m, &work[iu], &ldwrku, &work[ir], &ldwrkr, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", m, m, m, &work[iu], &ldwrku, &work[itaup] - , &work[iwork], &i__2, &ierr, (ftnlen)1); - -/* Generate left bidiagonalizing vectors in WORK(IR) */ -/* (Workspace: need 2*M*M + 4*M, prefer 2*M*M + 3*M + M*NB) */ - + dorgbr_((char *)"P", m, m, m, &work[iu], &ldwrku, &work[itaup], &work[iwork], &i__2, + &ierr, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", m, m, m, &work[ir], &ldwrkr, &work[itauq] - , &work[iwork], &i__2, &ierr, (ftnlen)1); + dorgbr_((char *)"Q", m, m, m, &work[ir], &ldwrkr, &work[itauq], &work[iwork], &i__2, + &ierr, (ftnlen)1); iwork = ie + *m; - -/* Perform bidiagonal QR iteration, computing left */ -/* singular vectors of L in WORK(IR) and computing */ -/* right singular vectors of L in WORK(IU) */ -/* (Workspace: need 2*M*M + BDSPAC) */ - - dbdsqr_((char *)"U", m, m, m, &c__0, &s[1], &work[ie], &work[ - iu], &ldwrku, &work[ir], &ldwrkr, dum, &c__1, - &work[iwork], info, (ftnlen)1); - -/* Multiply right singular vectors of L in WORK(IU) by */ -/* Q in A, storing result in VT */ -/* (Workspace: need M*M) */ - - dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[iu], &ldwrku, - &a[a_offset], lda, &c_b57, &vt[vt_offset], - ldvt, (ftnlen)1, (ftnlen)1); - -/* Copy left singular vectors of L to A */ -/* (Workspace: need M*M) */ - - dlacpy_((char *)"F", m, m, &work[ir], &ldwrkr, &a[a_offset], - lda, (ftnlen)1); - + dbdsqr_((char *)"U", m, m, m, &c__0, &s[1], &work[ie], &work[iu], &ldwrku, + &work[ir], &ldwrkr, dum, &c__1, &work[iwork], info, (ftnlen)1); + dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[iu], &ldwrku, &a[a_offset], lda, + &c_b57, &vt[vt_offset], ldvt, (ftnlen)1, (ftnlen)1); + dlacpy_((char *)"F", m, m, &work[ir], &ldwrkr, &a[a_offset], lda, (ftnlen)1); } else { - -/* Insufficient workspace for a fast algorithm */ - itau = 1; iwork = itau + *m; - -/* Compute A=L*Q, copying result to VT */ -/* (Workspace: need 2*M, prefer M + M*NB) */ - i__2 = *lwork - iwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], - ldvt, (ftnlen)1); - -/* Generate Q in VT */ -/* (Workspace: need 2*M, prefer M + M*NB) */ - + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], & - work[iwork], &i__2, &ierr); + dorglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], &work[iwork], &i__2, + &ierr); ie = itau; itauq = ie + *m; itaup = itauq + *m; iwork = itaup + *m; - -/* Zero out above L in A */ - i__2 = *m - 1; i__3 = *m - 1; - dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &a[(a_dim1 - << 1) + 1], lda, (ftnlen)1); - -/* Bidiagonalize L in A */ -/* (Workspace: need 4*M, prefer 3*M + 2*M*NB) */ - + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &a[(a_dim1 << 1) + 1], lda, + (ftnlen)1); i__2 = *lwork - iwork + 1; - dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); - -/* Multiply right vectors bidiagonalizing L by Q in VT */ -/* (Workspace: need 3*M + N, prefer 3*M + N*NB) */ - + dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], + &work[itaup], &work[iwork], &i__2, &ierr); i__2 = *lwork - iwork + 1; - dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &a[a_offset], lda, & - work[itaup], &vt[vt_offset], ldvt, &work[ - iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, ( - ftnlen)1); - -/* Generate left bidiagonalizing vectors of L in A */ -/* (Workspace: need 4*M, prefer 3*M + M*NB) */ - + dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &a[a_offset], lda, &work[itaup], + &vt[vt_offset], ldvt, &work[iwork], &i__2, &ierr, (ftnlen)1, + (ftnlen)1, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", m, m, m, &a[a_offset], lda, &work[itauq], - &work[iwork], &i__2, &ierr, (ftnlen)1); + dorgbr_((char *)"Q", m, m, m, &a[a_offset], lda, &work[itauq], &work[iwork], &i__2, + &ierr, (ftnlen)1); iwork = ie + *m; - -/* Perform bidiagonal QR iteration, compute left */ -/* singular vectors of A in A and compute right */ -/* singular vectors of A in VT */ -/* (Workspace: need BDSPAC) */ - - dbdsqr_((char *)"U", m, n, m, &c__0, &s[1], &work[ie], &vt[ - vt_offset], ldvt, &a[a_offset], lda, dum, & - c__1, &work[iwork], info, (ftnlen)1); - + dbdsqr_((char *)"U", m, n, m, &c__0, &s[1], &work[ie], &vt[vt_offset], ldvt, + &a[a_offset], lda, dum, &c__1, &work[iwork], info, (ftnlen)1); } - } else if (wntuas) { - -/* Path 6t(N much larger than M, JOBU='S' or 'A', */ -/* JOBVT='S') */ -/* M right singular vectors to be computed in VT and */ -/* M left singular vectors to be computed in U */ - -/* Computing MAX */ i__2 = *m << 2; - if (*lwork >= *m * *m + max(i__2,bdspac)) { - -/* Sufficient workspace for a fast algorithm */ - + if (*lwork >= *m * *m + max(i__2, bdspac)) { iu = 1; if (*lwork >= wrkbl + *lda * *m) { - -/* WORK(IU) is LDA by N */ - ldwrku = *lda; } else { - -/* WORK(IU) is LDA by M */ - ldwrku = *m; } itau = iu + ldwrku * *m; iwork = itau + *m; - -/* Compute A=L*Q */ -/* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */ - i__2 = *lwork - iwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - -/* Copy L to WORK(IU), zeroing out above it */ - - dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[iu], & - ldwrku, (ftnlen)1); + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[iu], &ldwrku, (ftnlen)1); i__2 = *m - 1; i__3 = *m - 1; - dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[iu + - ldwrku], &ldwrku, (ftnlen)1); - -/* Generate Q in A */ -/* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */ - + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[iu + ldwrku], &ldwrku, + (ftnlen)1); i__2 = *lwork - iwork + 1; - dorglq_(m, n, m, &a[a_offset], lda, &work[itau], & - work[iwork], &i__2, &ierr); + dorglq_(m, n, m, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, + &ierr); ie = itau; itauq = ie + *m; itaup = itauq + *m; iwork = itaup + *m; - -/* Bidiagonalize L in WORK(IU), copying result to U */ -/* (Workspace: need M*M + 4*M, prefer M*M + 3*M + 2*M*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(m, m, &work[iu], &ldwrku, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); - dlacpy_((char *)"L", m, m, &work[iu], &ldwrku, &u[u_offset], - ldu, (ftnlen)1); - -/* Generate right bidiagonalizing vectors in WORK(IU) */ -/* (Workspace: need M*M + 4*M-1, */ -/* prefer M*M+3*M+(M-1)*NB) */ - + dgebrd_(m, m, &work[iu], &ldwrku, &s[1], &work[ie], &work[itauq], + &work[itaup], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, m, &work[iu], &ldwrku, &u[u_offset], ldu, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", m, m, m, &work[iu], &ldwrku, &work[itaup] - , &work[iwork], &i__2, &ierr, (ftnlen)1); - -/* Generate left bidiagonalizing vectors in U */ -/* (Workspace: need M*M + 4*M, prefer M*M + 3*M + M*NB) */ - + dorgbr_((char *)"P", m, m, m, &work[iu], &ldwrku, &work[itaup], &work[iwork], &i__2, + &ierr, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq], - &work[iwork], &i__2, &ierr, (ftnlen)1); + dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq], &work[iwork], &i__2, + &ierr, (ftnlen)1); iwork = ie + *m; - -/* Perform bidiagonal QR iteration, computing left */ -/* singular vectors of L in U and computing right */ -/* singular vectors of L in WORK(IU) */ -/* (Workspace: need M*M + BDSPAC) */ - - dbdsqr_((char *)"U", m, m, m, &c__0, &s[1], &work[ie], &work[ - iu], &ldwrku, &u[u_offset], ldu, dum, &c__1, & - work[iwork], info, (ftnlen)1); - -/* Multiply right singular vectors of L in WORK(IU) by */ -/* Q in A, storing result in VT */ -/* (Workspace: need M*M) */ - - dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[iu], &ldwrku, - &a[a_offset], lda, &c_b57, &vt[vt_offset], - ldvt, (ftnlen)1, (ftnlen)1); - + dbdsqr_((char *)"U", m, m, m, &c__0, &s[1], &work[ie], &work[iu], &ldwrku, + &u[u_offset], ldu, dum, &c__1, &work[iwork], info, (ftnlen)1); + dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[iu], &ldwrku, &a[a_offset], lda, + &c_b57, &vt[vt_offset], ldvt, (ftnlen)1, (ftnlen)1); } else { - -/* Insufficient workspace for a fast algorithm */ - itau = 1; iwork = itau + *m; - -/* Compute A=L*Q, copying result to VT */ -/* (Workspace: need 2*M, prefer M + M*NB) */ - i__2 = *lwork - iwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], - ldvt, (ftnlen)1); - -/* Generate Q in VT */ -/* (Workspace: need 2*M, prefer M + M*NB) */ - + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], & - work[iwork], &i__2, &ierr); - -/* Copy L to U, zeroing out above it */ - - dlacpy_((char *)"L", m, m, &a[a_offset], lda, &u[u_offset], - ldu, (ftnlen)1); + dorglq_(m, n, m, &vt[vt_offset], ldvt, &work[itau], &work[iwork], &i__2, + &ierr); + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &u[u_offset], ldu, (ftnlen)1); i__2 = *m - 1; i__3 = *m - 1; - dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &u[(u_dim1 - << 1) + 1], ldu, (ftnlen)1); + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &u[(u_dim1 << 1) + 1], ldu, + (ftnlen)1); ie = itau; itauq = ie + *m; itaup = itauq + *m; iwork = itaup + *m; - -/* Bidiagonalize L in U */ -/* (Workspace: need 4*M, prefer 3*M + 2*M*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(m, m, &u[u_offset], ldu, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); - -/* Multiply right bidiagonalizing vectors in U by Q */ -/* in VT */ -/* (Workspace: need 3*M + N, prefer 3*M + N*NB) */ - + dgebrd_(m, m, &u[u_offset], ldu, &s[1], &work[ie], &work[itauq], + &work[itaup], &work[iwork], &i__2, &ierr); i__2 = *lwork - iwork + 1; - dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &u[u_offset], ldu, & - work[itaup], &vt[vt_offset], ldvt, &work[ - iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, ( - ftnlen)1); - -/* Generate left bidiagonalizing vectors in U */ -/* (Workspace: need 4*M, prefer 3*M + M*NB) */ - + dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &u[u_offset], ldu, &work[itaup], + &vt[vt_offset], ldvt, &work[iwork], &i__2, &ierr, (ftnlen)1, + (ftnlen)1, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq], - &work[iwork], &i__2, &ierr, (ftnlen)1); + dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq], &work[iwork], &i__2, + &ierr, (ftnlen)1); iwork = ie + *m; - -/* Perform bidiagonal QR iteration, computing left */ -/* singular vectors of A in U and computing right */ -/* singular vectors of A in VT */ -/* (Workspace: need BDSPAC) */ - - dbdsqr_((char *)"U", m, n, m, &c__0, &s[1], &work[ie], &vt[ - vt_offset], ldvt, &u[u_offset], ldu, dum, & - c__1, &work[iwork], info, (ftnlen)1); - + dbdsqr_((char *)"U", m, n, m, &c__0, &s[1], &work[ie], &vt[vt_offset], ldvt, + &u[u_offset], ldu, dum, &c__1, &work[iwork], info, (ftnlen)1); } - } - } else if (wntva) { - if (wntun) { - -/* Path 7t(N much larger than M, JOBU='N', JOBVT='A') */ -/* N right singular vectors to be computed in VT and */ -/* no left singular vectors to be computed */ - -/* Computing MAX */ - i__2 = *n + *m, i__3 = *m << 2, i__2 = max(i__2,i__3); - if (*lwork >= *m * *m + max(i__2,bdspac)) { - -/* Sufficient workspace for a fast algorithm */ - + i__2 = *n + *m, i__3 = *m << 2, i__2 = max(i__2, i__3); + if (*lwork >= *m * *m + max(i__2, bdspac)) { ir = 1; if (*lwork >= wrkbl + *lda * *m) { - -/* WORK(IR) is LDA by M */ - ldwrkr = *lda; } else { - -/* WORK(IR) is M by M */ - ldwrkr = *m; } itau = ir + ldwrkr * *m; iwork = itau + *m; - -/* Compute A=L*Q, copying result to VT */ -/* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */ - i__2 = *lwork - iwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], - ldvt, (ftnlen)1); - -/* Copy L to WORK(IR), zeroing out above it */ - - dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[ir], & - ldwrkr, (ftnlen)1); + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt, (ftnlen)1); + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[ir], &ldwrkr, (ftnlen)1); i__2 = *m - 1; i__3 = *m - 1; - dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[ir + - ldwrkr], &ldwrkr, (ftnlen)1); - -/* Generate Q in VT */ -/* (Workspace: need M*M + M + N, prefer M*M + M + N*NB) */ - + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[ir + ldwrkr], &ldwrkr, + (ftnlen)1); i__2 = *lwork - iwork + 1; - dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], & - work[iwork], &i__2, &ierr); + dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &work[iwork], &i__2, + &ierr); ie = itau; itauq = ie + *m; itaup = itauq + *m; iwork = itaup + *m; - -/* Bidiagonalize L in WORK(IR) */ -/* (Workspace: need M*M + 4*M, prefer M*M + 3*M + 2*M*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); - -/* Generate right bidiagonalizing vectors in WORK(IR) */ -/* (Workspace: need M*M + 4*M-1, */ -/* prefer M*M+3*M+(M-1)*NB) */ - + dgebrd_(m, m, &work[ir], &ldwrkr, &s[1], &work[ie], &work[itauq], + &work[itaup], &work[iwork], &i__2, &ierr); i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", m, m, m, &work[ir], &ldwrkr, &work[itaup] - , &work[iwork], &i__2, &ierr, (ftnlen)1); + dorgbr_((char *)"P", m, m, m, &work[ir], &ldwrkr, &work[itaup], &work[iwork], &i__2, + &ierr, (ftnlen)1); iwork = ie + *m; - -/* Perform bidiagonal QR iteration, computing right */ -/* singular vectors of L in WORK(IR) */ -/* (Workspace: need M*M + BDSPAC) */ - - dbdsqr_((char *)"U", m, m, &c__0, &c__0, &s[1], &work[ie], & - work[ir], &ldwrkr, dum, &c__1, dum, &c__1, & - work[iwork], info, (ftnlen)1); - -/* Multiply right singular vectors of L in WORK(IR) by */ -/* Q in VT, storing result in A */ -/* (Workspace: need M*M) */ - - dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[ir], &ldwrkr, - &vt[vt_offset], ldvt, &c_b57, &a[a_offset], - lda, (ftnlen)1, (ftnlen)1); - -/* Copy right singular vectors of A from A to VT */ - - dlacpy_((char *)"F", m, n, &a[a_offset], lda, &vt[vt_offset], - ldvt, (ftnlen)1); - + dbdsqr_((char *)"U", m, m, &c__0, &c__0, &s[1], &work[ie], &work[ir], &ldwrkr, dum, + &c__1, dum, &c__1, &work[iwork], info, (ftnlen)1); + dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[ir], &ldwrkr, &vt[vt_offset], ldvt, + &c_b57, &a[a_offset], lda, (ftnlen)1, (ftnlen)1); + dlacpy_((char *)"F", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt, (ftnlen)1); } else { - -/* Insufficient workspace for a fast algorithm */ - itau = 1; iwork = itau + *m; - -/* Compute A=L*Q, copying result to VT */ -/* (Workspace: need 2*M, prefer M + M*NB) */ - i__2 = *lwork - iwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], - ldvt, (ftnlen)1); - -/* Generate Q in VT */ -/* (Workspace: need M + N, prefer M + N*NB) */ - + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], & - work[iwork], &i__2, &ierr); + dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &work[iwork], &i__2, + &ierr); ie = itau; itauq = ie + *m; itaup = itauq + *m; iwork = itaup + *m; - -/* Zero out above L in A */ - i__2 = *m - 1; i__3 = *m - 1; - dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &a[(a_dim1 - << 1) + 1], lda, (ftnlen)1); - -/* Bidiagonalize L in A */ -/* (Workspace: need 4*M, prefer 3*M + 2*M*NB) */ - + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &a[(a_dim1 << 1) + 1], lda, + (ftnlen)1); i__2 = *lwork - iwork + 1; - dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); - -/* Multiply right bidiagonalizing vectors in A by Q */ -/* in VT */ -/* (Workspace: need 3*M + N, prefer 3*M + N*NB) */ - + dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], + &work[itaup], &work[iwork], &i__2, &ierr); i__2 = *lwork - iwork + 1; - dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &a[a_offset], lda, & - work[itaup], &vt[vt_offset], ldvt, &work[ - iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, ( - ftnlen)1); + dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &a[a_offset], lda, &work[itaup], + &vt[vt_offset], ldvt, &work[iwork], &i__2, &ierr, (ftnlen)1, + (ftnlen)1, (ftnlen)1); iwork = ie + *m; - -/* Perform bidiagonal QR iteration, computing right */ -/* singular vectors of A in VT */ -/* (Workspace: need BDSPAC) */ - - dbdsqr_((char *)"U", m, n, &c__0, &c__0, &s[1], &work[ie], & - vt[vt_offset], ldvt, dum, &c__1, dum, &c__1, & - work[iwork], info, (ftnlen)1); - + dbdsqr_((char *)"U", m, n, &c__0, &c__0, &s[1], &work[ie], &vt[vt_offset], ldvt, + dum, &c__1, dum, &c__1, &work[iwork], info, (ftnlen)1); } - } else if (wntuo) { - -/* Path 8t(N much larger than M, JOBU='O', JOBVT='A') */ -/* N right singular vectors to be computed in VT and */ -/* M left singular vectors to be overwritten on A */ - -/* Computing MAX */ - i__2 = *n + *m, i__3 = *m << 2, i__2 = max(i__2,i__3); - if (*lwork >= (*m << 1) * *m + max(i__2,bdspac)) { - -/* Sufficient workspace for a fast algorithm */ - + i__2 = *n + *m, i__3 = *m << 2, i__2 = max(i__2, i__3); + if (*lwork >= (*m << 1) * *m + max(i__2, bdspac)) { iu = 1; if (*lwork >= wrkbl + (*lda << 1) * *m) { - -/* WORK(IU) is LDA by M and WORK(IR) is LDA by M */ - ldwrku = *lda; ir = iu + ldwrku * *m; ldwrkr = *lda; } else if (*lwork >= wrkbl + (*lda + *m) * *m) { - -/* WORK(IU) is LDA by M and WORK(IR) is M by M */ - ldwrku = *lda; ir = iu + ldwrku * *m; ldwrkr = *m; } else { - -/* WORK(IU) is M by M and WORK(IR) is M by M */ - ldwrku = *m; ir = iu + ldwrku * *m; ldwrkr = *m; } itau = ir + ldwrkr * *m; iwork = itau + *m; - -/* Compute A=L*Q, copying result to VT */ -/* (Workspace: need 2*M*M + 2*M, prefer 2*M*M + M + M*NB) */ - i__2 = *lwork - iwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], - ldvt, (ftnlen)1); - -/* Generate Q in VT */ -/* (Workspace: need 2*M*M + M + N, prefer 2*M*M + M + N*NB) */ - + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], & - work[iwork], &i__2, &ierr); - -/* Copy L to WORK(IU), zeroing out above it */ - - dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[iu], & - ldwrku, (ftnlen)1); + dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &work[iwork], &i__2, + &ierr); + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[iu], &ldwrku, (ftnlen)1); i__2 = *m - 1; i__3 = *m - 1; - dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[iu + - ldwrku], &ldwrku, (ftnlen)1); + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[iu + ldwrku], &ldwrku, + (ftnlen)1); ie = itau; itauq = ie + *m; itaup = itauq + *m; iwork = itaup + *m; - -/* Bidiagonalize L in WORK(IU), copying result to */ -/* WORK(IR) */ -/* (Workspace: need 2*M*M + 4*M, */ -/* prefer 2*M*M+3*M+2*M*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(m, m, &work[iu], &ldwrku, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); - dlacpy_((char *)"L", m, m, &work[iu], &ldwrku, &work[ir], & - ldwrkr, (ftnlen)1); - -/* Generate right bidiagonalizing vectors in WORK(IU) */ -/* (Workspace: need 2*M*M + 4*M-1, */ -/* prefer 2*M*M+3*M+(M-1)*NB) */ - + dgebrd_(m, m, &work[iu], &ldwrku, &s[1], &work[ie], &work[itauq], + &work[itaup], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, m, &work[iu], &ldwrku, &work[ir], &ldwrkr, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", m, m, m, &work[iu], &ldwrku, &work[itaup] - , &work[iwork], &i__2, &ierr, (ftnlen)1); - -/* Generate left bidiagonalizing vectors in WORK(IR) */ -/* (Workspace: need 2*M*M + 4*M, prefer 2*M*M + 3*M + M*NB) */ - + dorgbr_((char *)"P", m, m, m, &work[iu], &ldwrku, &work[itaup], &work[iwork], &i__2, + &ierr, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", m, m, m, &work[ir], &ldwrkr, &work[itauq] - , &work[iwork], &i__2, &ierr, (ftnlen)1); + dorgbr_((char *)"Q", m, m, m, &work[ir], &ldwrkr, &work[itauq], &work[iwork], &i__2, + &ierr, (ftnlen)1); iwork = ie + *m; - -/* Perform bidiagonal QR iteration, computing left */ -/* singular vectors of L in WORK(IR) and computing */ -/* right singular vectors of L in WORK(IU) */ -/* (Workspace: need 2*M*M + BDSPAC) */ - - dbdsqr_((char *)"U", m, m, m, &c__0, &s[1], &work[ie], &work[ - iu], &ldwrku, &work[ir], &ldwrkr, dum, &c__1, - &work[iwork], info, (ftnlen)1); - -/* Multiply right singular vectors of L in WORK(IU) by */ -/* Q in VT, storing result in A */ -/* (Workspace: need M*M) */ - - dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[iu], &ldwrku, - &vt[vt_offset], ldvt, &c_b57, &a[a_offset], - lda, (ftnlen)1, (ftnlen)1); - -/* Copy right singular vectors of A from A to VT */ - - dlacpy_((char *)"F", m, n, &a[a_offset], lda, &vt[vt_offset], - ldvt, (ftnlen)1); - -/* Copy left singular vectors of A from WORK(IR) to A */ - - dlacpy_((char *)"F", m, m, &work[ir], &ldwrkr, &a[a_offset], - lda, (ftnlen)1); - + dbdsqr_((char *)"U", m, m, m, &c__0, &s[1], &work[ie], &work[iu], &ldwrku, + &work[ir], &ldwrkr, dum, &c__1, &work[iwork], info, (ftnlen)1); + dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[iu], &ldwrku, &vt[vt_offset], ldvt, + &c_b57, &a[a_offset], lda, (ftnlen)1, (ftnlen)1); + dlacpy_((char *)"F", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt, (ftnlen)1); + dlacpy_((char *)"F", m, m, &work[ir], &ldwrkr, &a[a_offset], lda, (ftnlen)1); } else { - -/* Insufficient workspace for a fast algorithm */ - itau = 1; iwork = itau + *m; - -/* Compute A=L*Q, copying result to VT */ -/* (Workspace: need 2*M, prefer M + M*NB) */ - i__2 = *lwork - iwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], - ldvt, (ftnlen)1); - -/* Generate Q in VT */ -/* (Workspace: need M + N, prefer M + N*NB) */ - + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], & - work[iwork], &i__2, &ierr); + dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &work[iwork], &i__2, + &ierr); ie = itau; itauq = ie + *m; itaup = itauq + *m; iwork = itaup + *m; - -/* Zero out above L in A */ - i__2 = *m - 1; i__3 = *m - 1; - dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &a[(a_dim1 - << 1) + 1], lda, (ftnlen)1); - -/* Bidiagonalize L in A */ -/* (Workspace: need 4*M, prefer 3*M + 2*M*NB) */ - + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &a[(a_dim1 << 1) + 1], lda, + (ftnlen)1); i__2 = *lwork - iwork + 1; - dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); - -/* Multiply right bidiagonalizing vectors in A by Q */ -/* in VT */ -/* (Workspace: need 3*M + N, prefer 3*M + N*NB) */ - + dgebrd_(m, m, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], + &work[itaup], &work[iwork], &i__2, &ierr); i__2 = *lwork - iwork + 1; - dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &a[a_offset], lda, & - work[itaup], &vt[vt_offset], ldvt, &work[ - iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, ( - ftnlen)1); - -/* Generate left bidiagonalizing vectors in A */ -/* (Workspace: need 4*M, prefer 3*M + M*NB) */ - + dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &a[a_offset], lda, &work[itaup], + &vt[vt_offset], ldvt, &work[iwork], &i__2, &ierr, (ftnlen)1, + (ftnlen)1, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", m, m, m, &a[a_offset], lda, &work[itauq], - &work[iwork], &i__2, &ierr, (ftnlen)1); + dorgbr_((char *)"Q", m, m, m, &a[a_offset], lda, &work[itauq], &work[iwork], &i__2, + &ierr, (ftnlen)1); iwork = ie + *m; - -/* Perform bidiagonal QR iteration, computing left */ -/* singular vectors of A in A and computing right */ -/* singular vectors of A in VT */ -/* (Workspace: need BDSPAC) */ - - dbdsqr_((char *)"U", m, n, m, &c__0, &s[1], &work[ie], &vt[ - vt_offset], ldvt, &a[a_offset], lda, dum, & - c__1, &work[iwork], info, (ftnlen)1); - + dbdsqr_((char *)"U", m, n, m, &c__0, &s[1], &work[ie], &vt[vt_offset], ldvt, + &a[a_offset], lda, dum, &c__1, &work[iwork], info, (ftnlen)1); } - } else if (wntuas) { - -/* Path 9t(N much larger than M, JOBU='S' or 'A', */ -/* JOBVT='A') */ -/* N right singular vectors to be computed in VT and */ -/* M left singular vectors to be computed in U */ - -/* Computing MAX */ - i__2 = *n + *m, i__3 = *m << 2, i__2 = max(i__2,i__3); - if (*lwork >= *m * *m + max(i__2,bdspac)) { - -/* Sufficient workspace for a fast algorithm */ - + i__2 = *n + *m, i__3 = *m << 2, i__2 = max(i__2, i__3); + if (*lwork >= *m * *m + max(i__2, bdspac)) { iu = 1; if (*lwork >= wrkbl + *lda * *m) { - -/* WORK(IU) is LDA by M */ - ldwrku = *lda; } else { - -/* WORK(IU) is M by M */ - ldwrku = *m; } itau = iu + ldwrku * *m; iwork = itau + *m; - -/* Compute A=L*Q, copying result to VT */ -/* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) */ - i__2 = *lwork - iwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], - ldvt, (ftnlen)1); - -/* Generate Q in VT */ -/* (Workspace: need M*M + M + N, prefer M*M + M + N*NB) */ - + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], & - work[iwork], &i__2, &ierr); - -/* Copy L to WORK(IU), zeroing out above it */ - - dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[iu], & - ldwrku, (ftnlen)1); + dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &work[iwork], &i__2, + &ierr); + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[iu], &ldwrku, (ftnlen)1); i__2 = *m - 1; i__3 = *m - 1; - dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[iu + - ldwrku], &ldwrku, (ftnlen)1); + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &work[iu + ldwrku], &ldwrku, + (ftnlen)1); ie = itau; itauq = ie + *m; itaup = itauq + *m; iwork = itaup + *m; - -/* Bidiagonalize L in WORK(IU), copying result to U */ -/* (Workspace: need M*M + 4*M, prefer M*M + 3*M + 2*M*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(m, m, &work[iu], &ldwrku, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); - dlacpy_((char *)"L", m, m, &work[iu], &ldwrku, &u[u_offset], - ldu, (ftnlen)1); - -/* Generate right bidiagonalizing vectors in WORK(IU) */ -/* (Workspace: need M*M + 4*M, prefer M*M + 3*M + (M-1)*NB) */ - + dgebrd_(m, m, &work[iu], &ldwrku, &s[1], &work[ie], &work[itauq], + &work[itaup], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"L", m, m, &work[iu], &ldwrku, &u[u_offset], ldu, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", m, m, m, &work[iu], &ldwrku, &work[itaup] - , &work[iwork], &i__2, &ierr, (ftnlen)1); - -/* Generate left bidiagonalizing vectors in U */ -/* (Workspace: need M*M + 4*M, prefer M*M + 3*M + M*NB) */ - + dorgbr_((char *)"P", m, m, m, &work[iu], &ldwrku, &work[itaup], &work[iwork], &i__2, + &ierr, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq], - &work[iwork], &i__2, &ierr, (ftnlen)1); + dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq], &work[iwork], &i__2, + &ierr, (ftnlen)1); iwork = ie + *m; - -/* Perform bidiagonal QR iteration, computing left */ -/* singular vectors of L in U and computing right */ -/* singular vectors of L in WORK(IU) */ -/* (Workspace: need M*M + BDSPAC) */ - - dbdsqr_((char *)"U", m, m, m, &c__0, &s[1], &work[ie], &work[ - iu], &ldwrku, &u[u_offset], ldu, dum, &c__1, & - work[iwork], info, (ftnlen)1); - -/* Multiply right singular vectors of L in WORK(IU) by */ -/* Q in VT, storing result in A */ -/* (Workspace: need M*M) */ - - dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[iu], &ldwrku, - &vt[vt_offset], ldvt, &c_b57, &a[a_offset], - lda, (ftnlen)1, (ftnlen)1); - -/* Copy right singular vectors of A from A to VT */ - - dlacpy_((char *)"F", m, n, &a[a_offset], lda, &vt[vt_offset], - ldvt, (ftnlen)1); - + dbdsqr_((char *)"U", m, m, m, &c__0, &s[1], &work[ie], &work[iu], &ldwrku, + &u[u_offset], ldu, dum, &c__1, &work[iwork], info, (ftnlen)1); + dgemm_((char *)"N", (char *)"N", m, n, m, &c_b79, &work[iu], &ldwrku, &vt[vt_offset], ldvt, + &c_b57, &a[a_offset], lda, (ftnlen)1, (ftnlen)1); + dlacpy_((char *)"F", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt, (ftnlen)1); } else { - -/* Insufficient workspace for a fast algorithm */ - itau = 1; iwork = itau + *m; - -/* Compute A=L*Q, copying result to VT */ -/* (Workspace: need 2*M, prefer M + M*NB) */ - i__2 = *lwork - iwork + 1; - dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[ - iwork], &i__2, &ierr); - dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], - ldvt, (ftnlen)1); - -/* Generate Q in VT */ -/* (Workspace: need M + N, prefer M + N*NB) */ - + dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2, &ierr); + dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], & - work[iwork], &i__2, &ierr); - -/* Copy L to U, zeroing out above it */ - - dlacpy_((char *)"L", m, m, &a[a_offset], lda, &u[u_offset], - ldu, (ftnlen)1); + dorglq_(n, n, m, &vt[vt_offset], ldvt, &work[itau], &work[iwork], &i__2, + &ierr); + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &u[u_offset], ldu, (ftnlen)1); i__2 = *m - 1; i__3 = *m - 1; - dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &u[(u_dim1 - << 1) + 1], ldu, (ftnlen)1); + dlaset_((char *)"U", &i__2, &i__3, &c_b57, &c_b57, &u[(u_dim1 << 1) + 1], ldu, + (ftnlen)1); ie = itau; itauq = ie + *m; itaup = itauq + *m; iwork = itaup + *m; - -/* Bidiagonalize L in U */ -/* (Workspace: need 4*M, prefer 3*M + 2*M*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(m, m, &u[u_offset], ldu, &s[1], &work[ie], & - work[itauq], &work[itaup], &work[iwork], & - i__2, &ierr); - -/* Multiply right bidiagonalizing vectors in U by Q */ -/* in VT */ -/* (Workspace: need 3*M + N, prefer 3*M + N*NB) */ - + dgebrd_(m, m, &u[u_offset], ldu, &s[1], &work[ie], &work[itauq], + &work[itaup], &work[iwork], &i__2, &ierr); i__2 = *lwork - iwork + 1; - dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &u[u_offset], ldu, & - work[itaup], &vt[vt_offset], ldvt, &work[ - iwork], &i__2, &ierr, (ftnlen)1, (ftnlen)1, ( - ftnlen)1); - -/* Generate left bidiagonalizing vectors in U */ -/* (Workspace: need 4*M, prefer 3*M + M*NB) */ - + dormbr_((char *)"P", (char *)"L", (char *)"T", m, n, m, &u[u_offset], ldu, &work[itaup], + &vt[vt_offset], ldvt, &work[iwork], &i__2, &ierr, (ftnlen)1, + (ftnlen)1, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq], - &work[iwork], &i__2, &ierr, (ftnlen)1); + dorgbr_((char *)"Q", m, m, m, &u[u_offset], ldu, &work[itauq], &work[iwork], &i__2, + &ierr, (ftnlen)1); iwork = ie + *m; - -/* Perform bidiagonal QR iteration, computing left */ -/* singular vectors of A in U and computing right */ -/* singular vectors of A in VT */ -/* (Workspace: need BDSPAC) */ - - dbdsqr_((char *)"U", m, n, m, &c__0, &s[1], &work[ie], &vt[ - vt_offset], ldvt, &u[u_offset], ldu, dum, & - c__1, &work[iwork], info, (ftnlen)1); - + dbdsqr_((char *)"U", m, n, m, &c__0, &s[1], &work[ie], &vt[vt_offset], ldvt, + &u[u_offset], ldu, dum, &c__1, &work[iwork], info, (ftnlen)1); } - } - } - } else { - -/* N .LT. MNTHR */ - -/* Path 10t(N greater than M, but not much larger) */ -/* Reduce to bidiagonal form without LQ decomposition */ - ie = 1; itauq = ie + *m; itaup = itauq + *m; iwork = itaup + *m; - -/* Bidiagonalize A */ -/* (Workspace: need 3*M + N, prefer 3*M + (M + N)*NB) */ - i__2 = *lwork - iwork + 1; - dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], & - work[itaup], &work[iwork], &i__2, &ierr); + dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &work[itaup], + &work[iwork], &i__2, &ierr); if (wntuas) { - -/* If left singular vectors desired in U, copy result to U */ -/* and generate left bidiagonalizing vectors in U */ -/* (Workspace: need 4*M-1, prefer 3*M + (M-1)*NB) */ - - dlacpy_((char *)"L", m, m, &a[a_offset], lda, &u[u_offset], ldu, ( - ftnlen)1); + dlacpy_((char *)"L", m, m, &a[a_offset], lda, &u[u_offset], ldu, (ftnlen)1); i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[ - iwork], &i__2, &ierr, (ftnlen)1); + dorgbr_((char *)"Q", m, m, n, &u[u_offset], ldu, &work[itauq], &work[iwork], &i__2, &ierr, + (ftnlen)1); } if (wntvas) { - -/* If right singular vectors desired in VT, copy result to */ -/* VT and generate right bidiagonalizing vectors in VT */ -/* (Workspace: need 3*M + NRVT, prefer 3*M + NRVT*NB) */ - - dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt, ( - ftnlen)1); + dlacpy_((char *)"U", m, n, &a[a_offset], lda, &vt[vt_offset], ldvt, (ftnlen)1); if (wntva) { nrvt = *n; } @@ -4029,28 +1827,18 @@ f"> */ nrvt = *m; } i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", &nrvt, n, m, &vt[vt_offset], ldvt, &work[itaup], - &work[iwork], &i__2, &ierr, (ftnlen)1); + dorgbr_((char *)"P", &nrvt, n, m, &vt[vt_offset], ldvt, &work[itaup], &work[iwork], &i__2, + &ierr, (ftnlen)1); } if (wntuo) { - -/* If left singular vectors desired in A, generate left */ -/* bidiagonalizing vectors in A */ -/* (Workspace: need 4*M-1, prefer 3*M + (M-1)*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"Q", m, m, n, &a[a_offset], lda, &work[itauq], &work[ - iwork], &i__2, &ierr, (ftnlen)1); + dorgbr_((char *)"Q", m, m, n, &a[a_offset], lda, &work[itauq], &work[iwork], &i__2, &ierr, + (ftnlen)1); } if (wntvo) { - -/* If right singular vectors desired in A, generate right */ -/* bidiagonalizing vectors in A */ -/* (Workspace: need 4*M, prefer 3*M + M*NB) */ - i__2 = *lwork - iwork + 1; - dorgbr_((char *)"P", m, n, m, &a[a_offset], lda, &work[itaup], &work[ - iwork], &i__2, &ierr, (ftnlen)1); + dorgbr_((char *)"P", m, n, m, &a[a_offset], lda, &work[itaup], &work[iwork], &i__2, &ierr, + (ftnlen)1); } iwork = ie + *m; if (wntuas || wntuo) { @@ -4065,94 +1853,54 @@ f"> */ if (wntvn) { ncvt = 0; } - if (! wntuo && ! wntvo) { - -/* Perform bidiagonal QR iteration, if desired, computing */ -/* left singular vectors in U and computing right singular */ -/* vectors in VT */ -/* (Workspace: need BDSPAC) */ - - dbdsqr_((char *)"L", m, &ncvt, &nru, &c__0, &s[1], &work[ie], &vt[ - vt_offset], ldvt, &u[u_offset], ldu, dum, &c__1, & - work[iwork], info, (ftnlen)1); - } else if (! wntuo && wntvo) { - -/* Perform bidiagonal QR iteration, if desired, computing */ -/* left singular vectors in U and computing right singular */ -/* vectors in A */ -/* (Workspace: need BDSPAC) */ - - dbdsqr_((char *)"L", m, &ncvt, &nru, &c__0, &s[1], &work[ie], &a[ - a_offset], lda, &u[u_offset], ldu, dum, &c__1, &work[ - iwork], info, (ftnlen)1); + if (!wntuo && !wntvo) { + dbdsqr_((char *)"L", m, &ncvt, &nru, &c__0, &s[1], &work[ie], &vt[vt_offset], ldvt, + &u[u_offset], ldu, dum, &c__1, &work[iwork], info, (ftnlen)1); + } else if (!wntuo && wntvo) { + dbdsqr_((char *)"L", m, &ncvt, &nru, &c__0, &s[1], &work[ie], &a[a_offset], lda, + &u[u_offset], ldu, dum, &c__1, &work[iwork], info, (ftnlen)1); } else { - -/* Perform bidiagonal QR iteration, if desired, computing */ -/* left singular vectors in A and computing right singular */ -/* vectors in VT */ -/* (Workspace: need BDSPAC) */ - - dbdsqr_((char *)"L", m, &ncvt, &nru, &c__0, &s[1], &work[ie], &vt[ - vt_offset], ldvt, &a[a_offset], lda, dum, &c__1, & - work[iwork], info, (ftnlen)1); + dbdsqr_((char *)"L", m, &ncvt, &nru, &c__0, &s[1], &work[ie], &vt[vt_offset], ldvt, + &a[a_offset], lda, dum, &c__1, &work[iwork], info, (ftnlen)1); } - } - } - -/* If DBDSQR failed to converge, copy unconverged superdiagonals */ -/* to WORK( 2:MINMN ) */ - if (*info != 0) { if (ie > 2) { i__2 = minmn - 1; for (i__ = 1; i__ <= i__2; ++i__) { work[i__ + 1] = work[i__ + ie - 1]; -/* L50: */ } } if (ie < 2) { for (i__ = minmn - 1; i__ >= 1; --i__) { work[i__ + 1] = work[i__ + ie - 1]; -/* L60: */ } } } - -/* Undo scaling if necessary */ - if (iscl == 1) { if (anrm > bignum) { - dlascl_((char *)"G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], & - minmn, &ierr, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], &minmn, &ierr, + (ftnlen)1); } if (*info != 0 && anrm > bignum) { i__2 = minmn - 1; - dlascl_((char *)"G", &c__0, &c__0, &bignum, &anrm, &i__2, &c__1, &work[2], - &minmn, &ierr, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &bignum, &anrm, &i__2, &c__1, &work[2], &minmn, &ierr, + (ftnlen)1); } if (anrm < smlnum) { - dlascl_((char *)"G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], & - minmn, &ierr, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], &minmn, &ierr, + (ftnlen)1); } if (*info != 0 && anrm < smlnum) { i__2 = minmn - 1; - dlascl_((char *)"G", &c__0, &c__0, &smlnum, &anrm, &i__2, &c__1, &work[2], - &minmn, &ierr, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &smlnum, &anrm, &i__2, &c__1, &work[2], &minmn, &ierr, + (ftnlen)1); } } - -/* Return optimal workspace in WORK(1) */ - - work[1] = (doublereal) maxwrk; - + work[1] = (doublereal)maxwrk; return 0; - -/* End of DGESVD */ - -} /* dgesvd_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dgetf2.cpp b/lib/linalg/dgetf2.cpp index c5951c8703..debebd53a0 100644 --- a/lib/linalg/dgetf2.cpp +++ b/lib/linalg/dgetf2.cpp @@ -1,194 +1,32 @@ -/* fortran/dgetf2.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static doublereal c_b8 = -1.; - -/* > \brief \b DGETF2 computes the LU factorization of a general m-by-n matrix using partial pivoting with row - interchanges (unblocked algorithm). */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DGETF2 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DGETF2( M, N, A, LDA, IPIV, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INFO, LDA, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* INTEGER IPIV( * ) */ -/* DOUBLE PRECISION A( LDA, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DGETF2 computes an LU factorization of a general m-by-n matrix A */ -/* > using partial pivoting with row interchanges. */ -/* > */ -/* > The factorization has the form */ -/* > A = P * L * U */ -/* > where P is a permutation matrix, L is lower triangular with unit */ -/* > diagonal elements (lower trapezoidal if m > n), and U is upper */ -/* > triangular (upper trapezoidal if m < n). */ -/* > */ -/* > This is the right-looking Level 2 BLAS version of the algorithm. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix A. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On entry, the m by n matrix to be factored. */ -/* > On exit, the factors L and U from the factorization */ -/* > A = P*L*U; the unit diagonal elements of L are not stored. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] IPIV */ -/* > \verbatim */ -/* > IPIV is INTEGER array, dimension (min(M,N)) */ -/* > The pivot indices; for 1 <= i <= min(M,N), row i of the */ -/* > matrix was interchanged with row IPIV(i). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -k, the k-th argument had an illegal value */ -/* > > 0: if INFO = k, U(k,k) is exactly zero. The factorization */ -/* > has been completed, but the factor U is exactly */ -/* > singular, and division by zero will occur if it is used */ -/* > to solve a system of equations. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleGEcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dgetf2_(integer *m, integer *n, doublereal *a, integer * - lda, integer *ipiv, integer *info) +int dgetf2_(integer *m, integer *n, doublereal *a, integer *lda, integer *ipiv, integer *info) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; doublereal d__1; - - /* Local variables */ integer i__, j, jp; - extern /* Subroutine */ int dger_(integer *, integer *, doublereal *, - doublereal *, integer *, doublereal *, integer *, doublereal *, - integer *), dscal_(integer *, doublereal *, doublereal *, integer - *); + extern int dger_(integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, integer *), + dscal_(integer *, doublereal *, doublereal *, integer *); doublereal sfmin; - extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, - doublereal *, integer *); + extern int dswap_(integer *, doublereal *, integer *, doublereal *, integer *); extern doublereal dlamch_(char *, ftnlen); extern integer idamax_(integer *, doublereal *, integer *); - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ + extern int xerbla_(char *, integer *, ftnlen); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --ipiv; - - /* Function Body */ *info = 0; if (*m < 0) { *info = -1; } else if (*n < 0) { *info = -2; - } else if (*lda < max(1,*m)) { + } else if (*lda < max(1, *m)) { *info = -4; } if (*info != 0) { @@ -196,35 +34,19 @@ f"> */ xerbla_((char *)"DGETF2", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*m == 0 || *n == 0) { return 0; } - -/* Compute machine safe minimum */ - sfmin = dlamch_((char *)"S", (ftnlen)1); - - i__1 = min(*m,*n); + i__1 = min(*m, *n); for (j = 1; j <= i__1; ++j) { - -/* Find pivot and test for singularity. */ - i__2 = *m - j + 1; jp = j - 1 + idamax_(&i__2, &a[j + j * a_dim1], &c__1); ipiv[j] = jp; if (a[jp + j * a_dim1] != 0.) { - -/* Apply the interchange to columns 1:N. */ - if (jp != j) { dswap_(n, &a[j + a_dim1], lda, &a[jp + a_dim1], lda); } - -/* Compute elements J+1:M of J-th column. */ - if (j < *m) { if ((d__1 = a[j + j * a_dim1], abs(d__1)) >= sfmin) { i__2 = *m - j; @@ -234,33 +56,21 @@ f"> */ i__2 = *m - j; for (i__ = 1; i__ <= i__2; ++i__) { a[j + i__ + j * a_dim1] /= a[j + j * a_dim1]; -/* L20: */ } } } - } else if (*info == 0) { - *info = j; } - - if (j < min(*m,*n)) { - -/* Update trailing submatrix. */ - + if (j < min(*m, *n)) { i__2 = *m - j; i__3 = *n - j; - dger_(&i__2, &i__3, &c_b8, &a[j + 1 + j * a_dim1], &c__1, &a[j + ( - j + 1) * a_dim1], lda, &a[j + 1 + (j + 1) * a_dim1], lda); + dger_(&i__2, &i__3, &c_b8, &a[j + 1 + j * a_dim1], &c__1, &a[j + (j + 1) * a_dim1], lda, + &a[j + 1 + (j + 1) * a_dim1], lda); } -/* L10: */ } return 0; - -/* End of DGETF2 */ - -} /* dgetf2_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dgetrf.cpp b/lib/linalg/dgetrf.cpp index cd1e8b50fe..a41a6ae69f 100644 --- a/lib/linalg/dgetrf.cpp +++ b/lib/linalg/dgetrf.cpp @@ -1,197 +1,38 @@ -/* fortran/dgetrf.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static integer c_n1 = -1; static doublereal c_b16 = 1.; static doublereal c_b19 = -1.; - -/* > \brief \b DGETRF */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DGETRF + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DGETRF( M, N, A, LDA, IPIV, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INFO, LDA, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* INTEGER IPIV( * ) */ -/* DOUBLE PRECISION A( LDA, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DGETRF computes an LU factorization of a general M-by-N matrix A */ -/* > using partial pivoting with row interchanges. */ -/* > */ -/* > The factorization has the form */ -/* > A = P * L * U */ -/* > where P is a permutation matrix, L is lower triangular with unit */ -/* > diagonal elements (lower trapezoidal if m > n), and U is upper */ -/* > triangular (upper trapezoidal if m < n). */ -/* > */ -/* > This is the right-looking Level 3 BLAS version of the algorithm. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix A. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On entry, the M-by-N matrix to be factored. */ -/* > On exit, the factors L and U from the factorization */ -/* > A = P*L*U; the unit diagonal elements of L are not stored. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] IPIV */ -/* > \verbatim */ -/* > IPIV is INTEGER array, dimension (min(M,N)) */ -/* > The pivot indices; for 1 <= i <= min(M,N), row i of the */ -/* > matrix was interchanged with row IPIV(i). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > > 0: if INFO = i, U(i,i) is exactly zero. The factorization */ -/* > has been completed, but the factor U is exactly */ -/* > singular, and division by zero will occur if it is used */ -/* > to solve a system of equations. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleGEcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dgetrf_(integer *m, integer *n, doublereal *a, integer * - lda, integer *ipiv, integer *info) +int dgetrf_(integer *m, integer *n, doublereal *a, integer *lda, integer *ipiv, integer *info) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; - - /* Local variables */ integer i__, j, jb, nb; - extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); + extern int dgemm_(char *, char *, integer *, integer *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, + ftnlen, ftnlen); integer iinfo; - extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, - integer *, integer *, doublereal *, doublereal *, integer *, - doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen), xerbla_( - char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - extern /* Subroutine */ int dlaswp_(integer *, doublereal *, integer *, - integer *, integer *, integer *, integer *), dgetrf2_(integer *, - integer *, doublereal *, integer *, integer *, integer *); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ + extern int dtrsm_(char *, char *, char *, char *, integer *, integer *, doublereal *, + doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, + ftnlen), + xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); + extern int dlaswp_(integer *, doublereal *, integer *, integer *, integer *, integer *, + integer *), + dgetrf2_(integer *, integer *, doublereal *, integer *, integer *, integer *); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --ipiv; - - /* Function Body */ *info = 0; if (*m < 0) { *info = -1; } else if (*n < 0) { *info = -2; - } else if (*lda < max(1,*m)) { + } else if (*lda < max(1, *m)) { *info = -4; } if (*info != 0) { @@ -199,95 +40,51 @@ f"> */ xerbla_((char *)"DGETRF", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*m == 0 || *n == 0) { return 0; } - -/* Determine the block size for this environment. */ - - nb = ilaenv_(&c__1, (char *)"DGETRF", (char *)" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen) - 1); - if (nb <= 1 || nb >= min(*m,*n)) { - -/* Use unblocked code. */ - + nb = ilaenv_(&c__1, (char *)"DGETRF", (char *)" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); + if (nb <= 1 || nb >= min(*m, *n)) { dgetrf2_(m, n, &a[a_offset], lda, &ipiv[1], info); } else { - -/* Use blocked code. */ - - i__1 = min(*m,*n); + i__1 = min(*m, *n); i__2 = nb; for (j = 1; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) { -/* Computing MIN */ - i__3 = min(*m,*n) - j + 1; - jb = min(i__3,nb); - -/* Factor diagonal and subdiagonal blocks and test for exact */ -/* singularity. */ - + i__3 = min(*m, *n) - j + 1; + jb = min(i__3, nb); i__3 = *m - j + 1; dgetrf2_(&i__3, &jb, &a[j + j * a_dim1], lda, &ipiv[j], &iinfo); - -/* Adjust INFO and the pivot indices. */ - if (*info == 0 && iinfo > 0) { *info = iinfo + j - 1; } -/* Computing MIN */ i__4 = *m, i__5 = j + jb - 1; - i__3 = min(i__4,i__5); + i__3 = min(i__4, i__5); for (i__ = j; i__ <= i__3; ++i__) { ipiv[i__] = j - 1 + ipiv[i__]; -/* L10: */ } - -/* Apply interchanges to columns 1:J-1. */ - i__3 = j - 1; i__4 = j + jb - 1; dlaswp_(&i__3, &a[a_offset], lda, &j, &i__4, &ipiv[1], &c__1); - if (j + jb <= *n) { - -/* Apply interchanges to columns J+JB:N. */ - i__3 = *n - j - jb + 1; i__4 = j + jb - 1; - dlaswp_(&i__3, &a[(j + jb) * a_dim1 + 1], lda, &j, &i__4, & - ipiv[1], &c__1); - -/* Compute block row of U. */ - + dlaswp_(&i__3, &a[(j + jb) * a_dim1 + 1], lda, &j, &i__4, &ipiv[1], &c__1); i__3 = *n - j - jb + 1; - dtrsm_((char *)"Left", (char *)"Lower", (char *)"No transpose", (char *)"Unit", &jb, &i__3, & - c_b16, &a[j + j * a_dim1], lda, &a[j + (j + jb) * - a_dim1], lda, (ftnlen)4, (ftnlen)5, (ftnlen)12, ( - ftnlen)4); + dtrsm_((char *)"Left", (char *)"Lower", (char *)"No transpose", (char *)"Unit", &jb, &i__3, &c_b16, + &a[j + j * a_dim1], lda, &a[j + (j + jb) * a_dim1], lda, (ftnlen)4, + (ftnlen)5, (ftnlen)12, (ftnlen)4); if (j + jb <= *m) { - -/* Update trailing submatrix. */ - i__3 = *m - j - jb + 1; i__4 = *n - j - jb + 1; - dgemm_((char *)"No transpose", (char *)"No transpose", &i__3, &i__4, &jb, - &c_b19, &a[j + jb + j * a_dim1], lda, &a[j + (j + - jb) * a_dim1], lda, &c_b16, &a[j + jb + (j + jb) * - a_dim1], lda, (ftnlen)12, (ftnlen)12); + dgemm_((char *)"No transpose", (char *)"No transpose", &i__3, &i__4, &jb, &c_b19, + &a[j + jb + j * a_dim1], lda, &a[j + (j + jb) * a_dim1], lda, &c_b16, + &a[j + jb + (j + jb) * a_dim1], lda, (ftnlen)12, (ftnlen)12); } } -/* L20: */ } } return 0; - -/* End of DGETRF */ - -} /* dgetrf_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dgetrf2.cpp b/lib/linalg/dgetrf2.cpp index c7097bbfed..e3f6b1c48d 100644 --- a/lib/linalg/dgetrf2.cpp +++ b/lib/linalg/dgetrf2.cpp @@ -1,201 +1,39 @@ -/* static/dgetrf2.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static doublereal c_b13 = 1.; static doublereal c_b16 = -1.; - -/* > \brief \b DGETRF2 */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* RECURSIVE SUBROUTINE DGETRF2( M, N, A, LDA, IPIV, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INFO, LDA, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* INTEGER IPIV( * ) */ -/* DOUBLE PRECISION A( LDA, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DGETRF2 computes an LU factorization of a general M-by-N matrix A */ -/* > using partial pivoting with row interchanges. */ -/* > */ -/* > The factorization has the form */ -/* > A = P * L * U */ -/* > where P is a permutation matrix, L is lower triangular with unit */ -/* > diagonal elements (lower trapezoidal if m > n), and U is upper */ -/* > triangular (upper trapezoidal if m < n). */ -/* > */ -/* > This is the recursive version of the algorithm. It divides */ -/* > the matrix into four submatrices: */ -/* > */ -/* > [ A11 | A12 ] where A11 is n1 by n1 and A22 is n2 by n2 */ -/* > A = [ -----|----- ] with n1 = min(m,n)/2 */ -/* > [ A21 | A22 ] n2 = n-n1 */ -/* > */ -/* > [ A11 ] */ -/* > The subroutine calls itself to factor [ --- ], */ -/* > [ A12 ] */ -/* > [ A12 ] */ -/* > do the swaps on [ --- ], solve A12, update A22, */ -/* > [ A22 ] */ -/* > */ -/* > then calls itself to factor A22 and do the swaps on A21. */ -/* > */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix A. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On entry, the M-by-N matrix to be factored. */ -/* > On exit, the factors L and U from the factorization */ -/* > A = P*L*U; the unit diagonal elements of L are not stored. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] IPIV */ -/* > \verbatim */ -/* > IPIV is INTEGER array, dimension (min(M,N)) */ -/* > The pivot indices; for 1 <= i <= min(M,N), row i of the */ -/* > matrix was interchanged with row IPIV(i). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > > 0: if INFO = i, U(i,i) is exactly zero. The factorization */ -/* > has been completed, but the factor U is exactly */ -/* > singular, and division by zero will occur if it is used */ -/* > to solve a system of equations. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleGEcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dgetrf2_(integer *m, integer *n, doublereal *a, integer * - lda, integer *ipiv, integer *info) +int dgetrf2_(integer *m, integer *n, doublereal *a, integer *lda, integer *ipiv, integer *info) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; doublereal d__1; - - /* Local variables */ integer i__, n1, n2; doublereal temp; - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *), dgemm_(char *, char *, integer *, integer *, integer * - , doublereal *, doublereal *, integer *, doublereal *, integer *, - doublereal *, doublereal *, integer *, ftnlen, ftnlen); + extern int dscal_(integer *, doublereal *, doublereal *, integer *), + dgemm_(char *, char *, integer *, integer *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, ftnlen, + ftnlen); integer iinfo; doublereal sfmin; - extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, - integer *, integer *, doublereal *, doublereal *, integer *, - doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + extern int dtrsm_(char *, char *, char *, char *, integer *, integer *, doublereal *, + doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, + ftnlen); extern doublereal dlamch_(char *, ftnlen); extern integer idamax_(integer *, doublereal *, integer *); - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), dlaswp_( - integer *, doublereal *, integer *, integer *, integer *, integer - *, integer *); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters */ - - /* Parameter adjustments */ + extern int xerbla_(char *, integer *, ftnlen), + dlaswp_(integer *, doublereal *, integer *, integer *, integer *, integer *, integer *); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --ipiv; - - /* Function Body */ *info = 0; if (*m < 0) { *info = -1; } else if (*n < 0) { *info = -2; - } else if (*lda < max(1,*m)) { + } else if (*lda < max(1, *m)) { *info = -4; } if (*info != 0) { @@ -203,47 +41,24 @@ static doublereal c_b16 = -1.; xerbla_((char *)"DGETRF2", &i__1, (ftnlen)7); return 0; } - -/* Quick return if possible */ - if (*m == 0 || *n == 0) { return 0; } if (*m == 1) { - -/* Use unblocked code for one row case */ -/* Just need to handle IPIV and INFO */ - ipiv[1] = 1; if (a[a_dim1 + 1] == 0.) { *info = 1; } - } else if (*n == 1) { - -/* Use unblocked code for one column case */ - - -/* Compute machine safe minimum */ - sfmin = dlamch_((char *)"S", (ftnlen)1); - -/* Find pivot and test for singularity */ - i__ = idamax_(m, &a[a_dim1 + 1], &c__1); ipiv[1] = i__; if (a[i__ + a_dim1] != 0.) { - -/* Apply the interchange */ - if (i__ != 1) { temp = a[a_dim1 + 1]; a[a_dim1 + 1] = a[i__ + a_dim1]; a[i__ + a_dim1] = temp; } - -/* Compute elements 2:M of the column */ - if ((d__1 = a[a_dim1 + 1], abs(d__1)) >= sfmin) { i__1 = *m - 1; d__1 = 1. / a[a_dim1 + 1]; @@ -252,80 +67,40 @@ static doublereal c_b16 = -1.; i__1 = *m - 1; for (i__ = 1; i__ <= i__1; ++i__) { a[i__ + 1 + a_dim1] /= a[a_dim1 + 1]; -/* L10: */ } } - } else { *info = 1; } - } else { - -/* Use recursive code */ - - n1 = min(*m,*n) / 2; + n1 = min(*m, *n) / 2; n2 = *n - n1; - -/* [ A11 ] */ -/* Factor [ --- ] */ -/* [ A21 ] */ - dgetrf2_(m, &n1, &a[a_offset], lda, &ipiv[1], &iinfo); if (*info == 0 && iinfo > 0) { *info = iinfo; } - -/* [ A12 ] */ -/* Apply interchanges to [ --- ] */ -/* [ A22 ] */ - - dlaswp_(&n2, &a[(n1 + 1) * a_dim1 + 1], lda, &c__1, &n1, &ipiv[1], & - c__1); - -/* Solve A12 */ - - dtrsm_((char *)"L", (char *)"L", (char *)"N", (char *)"U", &n1, &n2, &c_b13, &a[a_offset], lda, &a[( - n1 + 1) * a_dim1 + 1], lda, (ftnlen)1, (ftnlen)1, (ftnlen)1, ( - ftnlen)1); - -/* Update A22 */ - + dlaswp_(&n2, &a[(n1 + 1) * a_dim1 + 1], lda, &c__1, &n1, &ipiv[1], &c__1); + dtrsm_((char *)"L", (char *)"L", (char *)"N", (char *)"U", &n1, &n2, &c_b13, &a[a_offset], lda, &a[(n1 + 1) * a_dim1 + 1], + lda, (ftnlen)1, (ftnlen)1, (ftnlen)1, (ftnlen)1); i__1 = *m - n1; - dgemm_((char *)"N", (char *)"N", &i__1, &n2, &n1, &c_b16, &a[n1 + 1 + a_dim1], lda, & - a[(n1 + 1) * a_dim1 + 1], lda, &c_b13, &a[n1 + 1 + (n1 + 1) * - a_dim1], lda, (ftnlen)1, (ftnlen)1); - -/* Factor A22 */ - + dgemm_((char *)"N", (char *)"N", &i__1, &n2, &n1, &c_b16, &a[n1 + 1 + a_dim1], lda, + &a[(n1 + 1) * a_dim1 + 1], lda, &c_b13, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, + (ftnlen)1, (ftnlen)1); i__1 = *m - n1; - dgetrf2_(&i__1, &n2, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, &ipiv[n1 + - 1], &iinfo); - -/* Adjust INFO and the pivot indices */ - + dgetrf2_(&i__1, &n2, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, &ipiv[n1 + 1], &iinfo); if (*info == 0 && iinfo > 0) { *info = iinfo + n1; } - i__1 = min(*m,*n); + i__1 = min(*m, *n); for (i__ = n1 + 1; i__ <= i__1; ++i__) { ipiv[i__] += n1; -/* L20: */ } - -/* Apply interchanges to A21 */ - i__1 = n1 + 1; - i__2 = min(*m,*n); + i__2 = min(*m, *n); dlaswp_(&n1, &a[a_dim1 + 1], lda, &i__1, &i__2, &ipiv[1], &c__1); - } return 0; - -/* End of DGETRF2 */ - -} /* dgetrf2_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dgetri.cpp b/lib/linalg/dgetri.cpp index 368c6701ac..9e522bff50 100644 --- a/lib/linalg/dgetri.cpp +++ b/lib/linalg/dgetri.cpp @@ -1,216 +1,49 @@ -/* fortran/dgetri.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static integer c_n1 = -1; static integer c__2 = 2; static doublereal c_b20 = -1.; static doublereal c_b22 = 1.; - -/* > \brief \b DGETRI */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DGETRI + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INFO, LDA, LWORK, N */ -/* .. */ -/* .. Array Arguments .. */ -/* INTEGER IPIV( * ) */ -/* DOUBLE PRECISION A( LDA, * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DGETRI computes the inverse of a matrix using the LU factorization */ -/* > computed by DGETRF. */ -/* > */ -/* > This method inverts U and then computes inv(A) by solving the system */ -/* > inv(A)*L = inv(U) for inv(A). */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On entry, the factors L and U from the factorization */ -/* > A = P*L*U as computed by DGETRF. */ -/* > On exit, if INFO = 0, the inverse of the original matrix A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] IPIV */ -/* > \verbatim */ -/* > IPIV is INTEGER array, dimension (N) */ -/* > The pivot indices from DGETRF; for 1<=i<=N, row i of the */ -/* > matrix was interchanged with row IPIV(i). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ -/* > On exit, if INFO=0, then WORK(1) returns the optimal LWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LWORK */ -/* > \verbatim */ -/* > LWORK is INTEGER */ -/* > The dimension of the array WORK. LWORK >= max(1,N). */ -/* > For optimal performance LWORK >= N*NB, where NB is */ -/* > the optimal blocksize returned by ILAENV. */ -/* > */ -/* > If LWORK = -1, then a workspace query is assumed; the routine */ -/* > only calculates the optimal size of the WORK array, returns */ -/* > this value as the first entry of the WORK array, and no error */ -/* > message related to LWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > > 0: if INFO = i, U(i,i) is exactly zero; the matrix is */ -/* > singular and its inverse could not be computed. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleGEcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dgetri_(integer *n, doublereal *a, integer *lda, integer - *ipiv, doublereal *work, integer *lwork, integer *info) +int dgetri_(integer *n, doublereal *a, integer *lda, integer *ipiv, doublereal *work, + integer *lwork, integer *info) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; - - /* Local variables */ integer i__, j, jb, nb, jj, jp, nn, iws; - extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen), - dgemv_(char *, integer *, integer *, doublereal *, doublereal *, - integer *, doublereal *, integer *, doublereal *, doublereal *, - integer *, ftnlen); + extern int dgemm_(char *, char *, integer *, integer *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, + ftnlen, ftnlen), + dgemv_(char *, integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, ftnlen); integer nbmin; - extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, - doublereal *, integer *), dtrsm_(char *, char *, char *, char *, - integer *, integer *, doublereal *, doublereal *, integer *, - doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen), xerbla_( - char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern int dswap_(integer *, doublereal *, integer *, doublereal *, integer *), + dtrsm_(char *, char *, char *, char *, integer *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen), + xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); integer ldwork; - extern /* Subroutine */ int dtrtri_(char *, char *, integer *, doublereal - *, integer *, integer *, ftnlen, ftnlen); + extern int dtrtri_(char *, char *, integer *, doublereal *, integer *, integer *, ftnlen, + ftnlen); integer lwkopt; logical lquery; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --ipiv; --work; - - /* Function Body */ *info = 0; - nb = ilaenv_(&c__1, (char *)"DGETRI", (char *)" ", n, &c_n1, &c_n1, &c_n1, (ftnlen)6, ( - ftnlen)1); + nb = ilaenv_(&c__1, (char *)"DGETRI", (char *)" ", n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); lwkopt = *n * nb; - work[1] = (doublereal) lwkopt; + work[1] = (doublereal)lwkopt; lquery = *lwork == -1; if (*n < 0) { *info = -1; - } else if (*lda < max(1,*n)) { + } else if (*lda < max(1, *n)) { *info = -3; - } else if (*lwork < max(1,*n) && ! lquery) { + } else if (*lwork < max(1, *n) && !lquery) { *info = -6; } if (*info != 0) { @@ -220,124 +53,73 @@ f"> */ } else if (lquery) { return 0; } - -/* Quick return if possible */ - if (*n == 0) { return 0; } - -/* Form inv(U). If INFO > 0 from DTRTRI, then U is singular, */ -/* and the inverse is not computed. */ - - dtrtri_((char *)"Upper", (char *)"Non-unit", n, &a[a_offset], lda, info, (ftnlen)5, ( - ftnlen)8); + dtrtri_((char *)"Upper", (char *)"Non-unit", n, &a[a_offset], lda, info, (ftnlen)5, (ftnlen)8); if (*info > 0) { return 0; } - nbmin = 2; ldwork = *n; if (nb > 1 && nb < *n) { -/* Computing MAX */ i__1 = ldwork * nb; - iws = max(i__1,1); + iws = max(i__1, 1); if (*lwork < iws) { nb = *lwork / ldwork; -/* Computing MAX */ - i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DGETRI", (char *)" ", n, &c_n1, &c_n1, & - c_n1, (ftnlen)6, (ftnlen)1); - nbmin = max(i__1,i__2); + i__1 = 2, + i__2 = ilaenv_(&c__2, (char *)"DGETRI", (char *)" ", n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); + nbmin = max(i__1, i__2); } } else { iws = *n; } - -/* Solve the equation inv(A)*L = inv(U) for inv(A). */ - if (nb < nbmin || nb >= *n) { - -/* Use unblocked code. */ - for (j = *n; j >= 1; --j) { - -/* Copy current column of L to WORK and replace with zeros. */ - i__1 = *n; for (i__ = j + 1; i__ <= i__1; ++i__) { work[i__] = a[i__ + j * a_dim1]; a[i__ + j * a_dim1] = 0.; -/* L10: */ } - -/* Compute current column of inv(A). */ - if (j < *n) { i__1 = *n - j; - dgemv_((char *)"No transpose", n, &i__1, &c_b20, &a[(j + 1) * a_dim1 - + 1], lda, &work[j + 1], &c__1, &c_b22, &a[j * a_dim1 - + 1], &c__1, (ftnlen)12); + dgemv_((char *)"No transpose", n, &i__1, &c_b20, &a[(j + 1) * a_dim1 + 1], lda, + &work[j + 1], &c__1, &c_b22, &a[j * a_dim1 + 1], &c__1, (ftnlen)12); } -/* L20: */ } } else { - -/* Use blocked code. */ - nn = (*n - 1) / nb * nb + 1; i__1 = -nb; for (j = nn; i__1 < 0 ? j >= 1 : j <= 1; j += i__1) { -/* Computing MIN */ i__2 = nb, i__3 = *n - j + 1; - jb = min(i__2,i__3); - -/* Copy current block column of L to WORK and replace with */ -/* zeros. */ - + jb = min(i__2, i__3); i__2 = j + jb - 1; for (jj = j; jj <= i__2; ++jj) { i__3 = *n; for (i__ = jj + 1; i__ <= i__3; ++i__) { work[i__ + (jj - j) * ldwork] = a[i__ + jj * a_dim1]; a[i__ + jj * a_dim1] = 0.; -/* L30: */ } -/* L40: */ } - -/* Compute current block column of inv(A). */ - if (j + jb <= *n) { i__2 = *n - j - jb + 1; dgemm_((char *)"No transpose", (char *)"No transpose", n, &jb, &i__2, &c_b20, - &a[(j + jb) * a_dim1 + 1], lda, &work[j + jb], & - ldwork, &c_b22, &a[j * a_dim1 + 1], lda, (ftnlen)12, ( - ftnlen)12); + &a[(j + jb) * a_dim1 + 1], lda, &work[j + jb], &ldwork, &c_b22, + &a[j * a_dim1 + 1], lda, (ftnlen)12, (ftnlen)12); } - dtrsm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", n, &jb, &c_b22, & - work[j], &ldwork, &a[j * a_dim1 + 1], lda, (ftnlen)5, ( - ftnlen)5, (ftnlen)12, (ftnlen)4); -/* L50: */ + dtrsm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", n, &jb, &c_b22, &work[j], &ldwork, + &a[j * a_dim1 + 1], lda, (ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); } } - -/* Apply column interchanges. */ - for (j = *n - 1; j >= 1; --j) { jp = ipiv[j]; if (jp != j) { dswap_(n, &a[j * a_dim1 + 1], &c__1, &a[jp * a_dim1 + 1], &c__1); } -/* L60: */ } - - work[1] = (doublereal) iws; + work[1] = (doublereal)iws; return 0; - -/* End of DGETRI */ - -} /* dgetri_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dgetrs.cpp b/lib/linalg/dgetrs.cpp index ca10730a0b..c45250cc95 100644 --- a/lib/linalg/dgetrs.cpp +++ b/lib/linalg/dgetrs.cpp @@ -1,191 +1,21 @@ -/* fortran/dgetrs.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static doublereal c_b12 = 1.; static integer c_n1 = -1; - -/* > \brief \b DGETRS */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DGETRS + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DGETRS( TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER TRANS */ -/* INTEGER INFO, LDA, LDB, N, NRHS */ -/* .. */ -/* .. Array Arguments .. */ -/* INTEGER IPIV( * ) */ -/* DOUBLE PRECISION A( LDA, * ), B( LDB, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DGETRS solves a system of linear equations */ -/* > A * X = B or A**T * X = B */ -/* > with a general N-by-N matrix A using the LU factorization computed */ -/* > by DGETRF. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] TRANS */ -/* > \verbatim */ -/* > TRANS is CHARACTER*1 */ -/* > Specifies the form of the system of equations: */ -/* > = 'N': A * X = B (No transpose) */ -/* > = 'T': A**T* X = B (Transpose) */ -/* > = 'C': A**T* X = B (Conjugate transpose = Transpose) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] NRHS */ -/* > \verbatim */ -/* > NRHS is INTEGER */ -/* > The number of right hand sides, i.e., the number of columns */ -/* > of the matrix B. NRHS >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > The factors L and U from the factorization A = P*L*U */ -/* > as computed by DGETRF. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] IPIV */ -/* > \verbatim */ -/* > IPIV is INTEGER array, dimension (N) */ -/* > The pivot indices from DGETRF; for 1<=i<=N, row i of the */ -/* > matrix was interchanged with row IPIV(i). */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] B */ -/* > \verbatim */ -/* > B is DOUBLE PRECISION array, dimension (LDB,NRHS) */ -/* > On entry, the right hand side matrix B. */ -/* > On exit, the solution matrix X. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDB */ -/* > \verbatim */ -/* > LDB is INTEGER */ -/* > The leading dimension of the array B. LDB >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleGEcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dgetrs_(char *trans, integer *n, integer *nrhs, - doublereal *a, integer *lda, integer *ipiv, doublereal *b, integer * - ldb, integer *info, ftnlen trans_len) +int dgetrs_(char *trans, integer *n, integer *nrhs, doublereal *a, integer *lda, integer *ipiv, + doublereal *b, integer *ldb, integer *info, ftnlen trans_len) { - /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1; - - /* Local variables */ extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, - integer *, integer *, doublereal *, doublereal *, integer *, - doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen), xerbla_( - char *, integer *, ftnlen), dlaswp_(integer *, doublereal *, - integer *, integer *, integer *, integer *, integer *); + extern int dtrsm_(char *, char *, char *, char *, integer *, integer *, doublereal *, + doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, + ftnlen), + xerbla_(char *, integer *, ftnlen), + dlaswp_(integer *, doublereal *, integer *, integer *, integer *, integer *, integer *); logical notran; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; @@ -193,20 +23,18 @@ f"> */ b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; - - /* Function Body */ *info = 0; notran = lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1); - if (! notran && ! lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_( - trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { + if (!notran && !lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1) && + !lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*nrhs < 0) { *info = -3; - } else if (*lda < max(1,*n)) { + } else if (*lda < max(1, *n)) { *info = -5; - } else if (*ldb < max(1,*n)) { + } else if (*ldb < max(1, *n)) { *info = -8; } if (*info != 0) { @@ -214,59 +42,24 @@ f"> */ xerbla_((char *)"DGETRS", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*n == 0 || *nrhs == 0) { return 0; } - if (notran) { - -/* Solve A * X = B. */ - -/* Apply row interchanges to the right hand sides. */ - dlaswp_(nrhs, &b[b_offset], ldb, &c__1, n, &ipiv[1], &c__1); - -/* Solve L*X = B, overwriting B with X. */ - - dtrsm_((char *)"Left", (char *)"Lower", (char *)"No transpose", (char *)"Unit", n, nrhs, &c_b12, &a[ - a_offset], lda, &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, ( - ftnlen)12, (ftnlen)4); - -/* Solve U*X = B, overwriting B with X. */ - - dtrsm_((char *)"Left", (char *)"Upper", (char *)"No transpose", (char *)"Non-unit", n, nrhs, &c_b12, & - a[a_offset], lda, &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, ( - ftnlen)12, (ftnlen)8); + dtrsm_((char *)"Left", (char *)"Lower", (char *)"No transpose", (char *)"Unit", n, nrhs, &c_b12, &a[a_offset], lda, + &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, (ftnlen)12, (ftnlen)4); + dtrsm_((char *)"Left", (char *)"Upper", (char *)"No transpose", (char *)"Non-unit", n, nrhs, &c_b12, &a[a_offset], lda, + &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, (ftnlen)12, (ftnlen)8); } else { - -/* Solve A**T * X = B. */ - -/* Solve U**T *X = B, overwriting B with X. */ - - dtrsm_((char *)"Left", (char *)"Upper", (char *)"Transpose", (char *)"Non-unit", n, nrhs, &c_b12, &a[ - a_offset], lda, &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, ( - ftnlen)9, (ftnlen)8); - -/* Solve L**T *X = B, overwriting B with X. */ - - dtrsm_((char *)"Left", (char *)"Lower", (char *)"Transpose", (char *)"Unit", n, nrhs, &c_b12, &a[ - a_offset], lda, &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, ( - ftnlen)9, (ftnlen)4); - -/* Apply row interchanges to the solution vectors. */ - + dtrsm_((char *)"Left", (char *)"Upper", (char *)"Transpose", (char *)"Non-unit", n, nrhs, &c_b12, &a[a_offset], lda, + &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, (ftnlen)9, (ftnlen)8); + dtrsm_((char *)"Left", (char *)"Lower", (char *)"Transpose", (char *)"Unit", n, nrhs, &c_b12, &a[a_offset], lda, + &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, (ftnlen)9, (ftnlen)4); dlaswp_(nrhs, &b[b_offset], ldb, &c__1, n, &ipiv[1], &c_n1); } - return 0; - -/* End of DGETRS */ - -} /* dgetrs_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/disnan.cpp b/lib/linalg/disnan.cpp index 9e5bc1094e..dcdaad77e1 100644 --- a/lib/linalg/disnan.cpp +++ b/lib/linalg/disnan.cpp @@ -7,8 +7,8 @@ extern "C" { logical disnan_(const doublereal *din) { - if (!din) return TRUE_; + if (!din) return TRUE_; - return std::isnan(*din) ? TRUE_ : FALSE_; + return std::isnan(*din) ? TRUE_ : FALSE_; } } diff --git a/lib/linalg/dlabad.cpp b/lib/linalg/dlabad.cpp index 45de813f49..790163be3c 100644 --- a/lib/linalg/dlabad.cpp +++ b/lib/linalg/dlabad.cpp @@ -1,128 +1,16 @@ -/* fortran/dlabad.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DLABAD */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLABAD + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLABAD( SMALL, LARGE ) */ - -/* .. Scalar Arguments .. */ -/* DOUBLE PRECISION LARGE, SMALL */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLABAD takes as input the values computed by DLAMCH for underflow and */ -/* > overflow, and returns the square root of each of these values if the */ -/* > log of LARGE is sufficiently large. This subroutine is intended to */ -/* > identify machines with a large exponent range, such as the Crays, and */ -/* > redefine the underflow and overflow limits to be the square roots of */ -/* > the values computed by DLAMCH. This subroutine is needed because */ -/* > DLAMCH does not compensate for poor arithmetic in the upper half of */ -/* > the exponent range, as is found on a Cray. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in,out] SMALL */ -/* > \verbatim */ -/* > SMALL is DOUBLE PRECISION */ -/* > On entry, the underflow threshold as computed by DLAMCH. */ -/* > On exit, if LOG10(LARGE) is sufficiently large, the square */ -/* > root of SMALL, otherwise unchanged. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] LARGE */ -/* > \verbatim */ -/* > LARGE is DOUBLE PRECISION */ -/* > On entry, the overflow threshold as computed by DLAMCH. */ -/* > On exit, if LOG10(LARGE) is sufficiently large, the square */ -/* > root of LARGE, otherwise unchanged. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup OTHERauxiliary */ - -/* ===================================================================== */ -/* Subroutine */ int dlabad_(doublereal *small, doublereal *large) +int dlabad_(doublereal *small, doublereal *large) { - /* Builtin functions */ double d_lmp_lg10(doublereal *), sqrt(doublereal); - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* If it looks like we're on a Cray, take the square root of */ -/* SMALL and LARGE to avoid overflow and underflow problems. */ - if (d_lmp_lg10(large) > 2e3) { *small = sqrt(*small); *large = sqrt(*large); } - return 0; - -/* End of DLABAD */ - -} /* dlabad_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlabrd.cpp b/lib/linalg/dlabrd.cpp index a7f9113e5c..d58ebe9a39 100644 --- a/lib/linalg/dlabrd.cpp +++ b/lib/linalg/dlabrd.cpp @@ -1,279 +1,21 @@ -/* fortran/dlabrd.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static doublereal c_b4 = -1.; static doublereal c_b5 = 1.; static integer c__1 = 1; static doublereal c_b16 = 0.; - -/* > \brief \b DLABRD reduces the first nb rows and columns of a general matrix to a bidiagonal form. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLABRD + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLABRD( M, N, NB, A, LDA, D, E, TAUQ, TAUP, X, LDX, Y, */ -/* LDY ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER LDA, LDX, LDY, M, N, NB */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), TAUP( * ), */ -/* $ TAUQ( * ), X( LDX, * ), Y( LDY, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLABRD reduces the first NB rows and columns of a real general */ -/* > m by n matrix A to upper or lower bidiagonal form by an orthogonal */ -/* > transformation Q**T * A * P, and returns the matrices X and Y which */ -/* > are needed to apply the transformation to the unreduced part of A. */ -/* > */ -/* > If m >= n, A is reduced to upper bidiagonal form; if m < n, to lower */ -/* > bidiagonal form. */ -/* > */ -/* > This is an auxiliary routine called by DGEBRD */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows in the matrix A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns in the matrix A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] NB */ -/* > \verbatim */ -/* > NB is INTEGER */ -/* > The number of leading rows and columns of A to be reduced. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On entry, the m by n general matrix to be reduced. */ -/* > On exit, the first NB rows and columns of the matrix are */ -/* > overwritten; the rest of the array is unchanged. */ -/* > If m >= n, elements on and below the diagonal in the first NB */ -/* > columns, with the array TAUQ, represent the orthogonal */ -/* > matrix Q as a product of elementary reflectors; and */ -/* > elements above the diagonal in the first NB rows, with the */ -/* > array TAUP, represent the orthogonal matrix P as a product */ -/* > of elementary reflectors. */ -/* > If m < n, elements below the diagonal in the first NB */ -/* > columns, with the array TAUQ, represent the orthogonal */ -/* > matrix Q as a product of elementary reflectors, and */ -/* > elements on and above the diagonal in the first NB rows, */ -/* > with the array TAUP, represent the orthogonal matrix P as */ -/* > a product of elementary reflectors. */ -/* > See Further Details. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension (NB) */ -/* > The diagonal elements of the first NB rows and columns of */ -/* > the reduced matrix. D(i) = A(i,i). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] E */ -/* > \verbatim */ -/* > E is DOUBLE PRECISION array, dimension (NB) */ -/* > The off-diagonal elements of the first NB rows and columns of */ -/* > the reduced matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] TAUQ */ -/* > \verbatim */ -/* > TAUQ is DOUBLE PRECISION array, dimension (NB) */ -/* > The scalar factors of the elementary reflectors which */ -/* > represent the orthogonal matrix Q. See Further Details. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] TAUP */ -/* > \verbatim */ -/* > TAUP is DOUBLE PRECISION array, dimension (NB) */ -/* > The scalar factors of the elementary reflectors which */ -/* > represent the orthogonal matrix P. See Further Details. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] X */ -/* > \verbatim */ -/* > X is DOUBLE PRECISION array, dimension (LDX,NB) */ -/* > The m-by-nb matrix X required to update the unreduced part */ -/* > of A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDX */ -/* > \verbatim */ -/* > LDX is INTEGER */ -/* > The leading dimension of the array X. LDX >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] Y */ -/* > \verbatim */ -/* > Y is DOUBLE PRECISION array, dimension (LDY,NB) */ -/* > The n-by-nb matrix Y required to update the unreduced part */ -/* > of A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDY */ -/* > \verbatim */ -/* > LDY is INTEGER */ -/* > The leading dimension of the array Y. LDY >= max(1,N). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleOTHERauxiliary */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > The matrices Q and P are represented as products of elementary */ -/* > reflectors: */ -/* > */ -/* > Q = H(1) H(2) . . . H(nb) and P = G(1) G(2) . . . G(nb) */ -/* > */ -/* > Each H(i) and G(i) has the form: */ -/* > */ -/* > H(i) = I - tauq * v * v**T and G(i) = I - taup * u * u**T */ -/* > */ -/* > where tauq and taup are real scalars, and v and u are real vectors. */ -/* > */ -/* > If m >= n, v(1:i-1) = 0, v(i) = 1, and v(i:m) is stored on exit in */ -/* > A(i:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+1:n) is stored on exit in */ -/* > A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i). */ -/* > */ -/* > If m < n, v(1:i) = 0, v(i+1) = 1, and v(i+1:m) is stored on exit in */ -/* > A(i+2:m,i); u(1:i-1) = 0, u(i) = 1, and u(i:n) is stored on exit in */ -/* > A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i). */ -/* > */ -/* > The elements of the vectors v and u together form the m-by-nb matrix */ -/* > V and the nb-by-n matrix U**T which are needed, with X and Y, to apply */ -/* > the transformation to the unreduced part of the matrix, using a block */ -/* > update of the form: A := A - V*Y**T - X*U**T. */ -/* > */ -/* > The contents of A on exit are illustrated by the following examples */ -/* > with nb = 2: */ -/* > */ -/* > m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n): */ -/* > */ -/* > ( 1 1 u1 u1 u1 ) ( 1 u1 u1 u1 u1 u1 ) */ -/* > ( v1 1 1 u2 u2 ) ( 1 1 u2 u2 u2 u2 ) */ -/* > ( v1 v2 a a a ) ( v1 1 a a a a ) */ -/* > ( v1 v2 a a a ) ( v1 v2 a a a a ) */ -/* > ( v1 v2 a a a ) ( v1 v2 a a a a ) */ -/* > ( v1 v2 a a a ) */ -/* > */ -/* > where a denotes an element of the original matrix which is unchanged, */ -/* > vi denotes an element of the vector defining H(i), and ui an element */ -/* > of the vector defining G(i). */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dlabrd_(integer *m, integer *n, integer *nb, doublereal * - a, integer *lda, doublereal *d__, doublereal *e, doublereal *tauq, - doublereal *taup, doublereal *x, integer *ldx, doublereal *y, integer - *ldy) +int dlabrd_(integer *m, integer *n, integer *nb, doublereal *a, integer *lda, doublereal *d__, + doublereal *e, doublereal *tauq, doublereal *taup, doublereal *x, integer *ldx, + doublereal *y, integer *ldy) { - /* System generated locals */ - integer a_dim1, a_offset, x_dim1, x_offset, y_dim1, y_offset, i__1, i__2, - i__3; - - /* Local variables */ + integer a_dim1, a_offset, x_dim1, x_offset, y_dim1, y_offset, i__1, i__2, i__3; integer i__; - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *), dgemv_(char *, integer *, integer *, doublereal *, - doublereal *, integer *, doublereal *, integer *, doublereal *, - doublereal *, integer *, ftnlen), dlarfg_(integer *, doublereal *, - doublereal *, integer *, doublereal *); - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Quick return if possible */ - - /* Parameter adjustments */ + extern int dscal_(integer *, doublereal *, doublereal *, integer *), + dgemv_(char *, integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, ftnlen), + dlarfg_(integer *, doublereal *, doublereal *, integer *, doublereal *); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; @@ -287,246 +29,182 @@ f"> */ y_dim1 = *ldy; y_offset = 1 + y_dim1; y -= y_offset; - - /* Function Body */ if (*m <= 0 || *n <= 0) { return 0; } - if (*m >= *n) { - -/* Reduce to upper bidiagonal form */ - i__1 = *nb; for (i__ = 1; i__ <= i__1; ++i__) { - -/* Update A(i:m,i) */ - i__2 = *m - i__ + 1; i__3 = i__ - 1; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &a[i__ + a_dim1], lda, - &y[i__ + y_dim1], ldy, &c_b5, &a[i__ + i__ * a_dim1], & - c__1, (ftnlen)12); + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &a[i__ + a_dim1], lda, &y[i__ + y_dim1], + ldy, &c_b5, &a[i__ + i__ * a_dim1], &c__1, (ftnlen)12); i__2 = *m - i__ + 1; i__3 = i__ - 1; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &x[i__ + x_dim1], ldx, - &a[i__ * a_dim1 + 1], &c__1, &c_b5, &a[i__ + i__ * - a_dim1], &c__1, (ftnlen)12); - -/* Generate reflection Q(i) to annihilate A(i+1:m,i) */ - + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &x[i__ + x_dim1], ldx, &a[i__ * a_dim1 + 1], + &c__1, &c_b5, &a[i__ + i__ * a_dim1], &c__1, (ftnlen)12); i__2 = *m - i__ + 1; -/* Computing MIN */ i__3 = i__ + 1; - dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[min(i__3,*m) + i__ * - a_dim1], &c__1, &tauq[i__]); + dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[min(i__3, *m) + i__ * a_dim1], &c__1, + &tauq[i__]); d__[i__] = a[i__ + i__ * a_dim1]; if (i__ < *n) { a[i__ + i__ * a_dim1] = 1.; - -/* Compute Y(i+1:n,i) */ - i__2 = *m - i__ + 1; i__3 = *n - i__; - dgemv_((char *)"Transpose", &i__2, &i__3, &c_b5, &a[i__ + (i__ + 1) * - a_dim1], lda, &a[i__ + i__ * a_dim1], &c__1, &c_b16, & - y[i__ + 1 + i__ * y_dim1], &c__1, (ftnlen)9); + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b5, &a[i__ + (i__ + 1) * a_dim1], lda, + &a[i__ + i__ * a_dim1], &c__1, &c_b16, &y[i__ + 1 + i__ * y_dim1], &c__1, + (ftnlen)9); i__2 = *m - i__ + 1; i__3 = i__ - 1; - dgemv_((char *)"Transpose", &i__2, &i__3, &c_b5, &a[i__ + a_dim1], - lda, &a[i__ + i__ * a_dim1], &c__1, &c_b16, &y[i__ * - y_dim1 + 1], &c__1, (ftnlen)9); + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b5, &a[i__ + a_dim1], lda, + &a[i__ + i__ * a_dim1], &c__1, &c_b16, &y[i__ * y_dim1 + 1], &c__1, + (ftnlen)9); i__2 = *n - i__; i__3 = i__ - 1; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &y[i__ + 1 + - y_dim1], ldy, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[ - i__ + 1 + i__ * y_dim1], &c__1, (ftnlen)12); + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &y[i__ + 1 + y_dim1], ldy, + &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[i__ + 1 + i__ * y_dim1], &c__1, + (ftnlen)12); i__2 = *m - i__ + 1; i__3 = i__ - 1; - dgemv_((char *)"Transpose", &i__2, &i__3, &c_b5, &x[i__ + x_dim1], - ldx, &a[i__ + i__ * a_dim1], &c__1, &c_b16, &y[i__ * - y_dim1 + 1], &c__1, (ftnlen)9); + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b5, &x[i__ + x_dim1], ldx, + &a[i__ + i__ * a_dim1], &c__1, &c_b16, &y[i__ * y_dim1 + 1], &c__1, + (ftnlen)9); i__2 = i__ - 1; i__3 = *n - i__; - dgemv_((char *)"Transpose", &i__2, &i__3, &c_b4, &a[(i__ + 1) * - a_dim1 + 1], lda, &y[i__ * y_dim1 + 1], &c__1, &c_b5, - &y[i__ + 1 + i__ * y_dim1], &c__1, (ftnlen)9); + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b4, &a[(i__ + 1) * a_dim1 + 1], lda, + &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[i__ + 1 + i__ * y_dim1], &c__1, + (ftnlen)9); i__2 = *n - i__; dscal_(&i__2, &tauq[i__], &y[i__ + 1 + i__ * y_dim1], &c__1); - -/* Update A(i,i+1:n) */ - i__2 = *n - i__; - dgemv_((char *)"No transpose", &i__2, &i__, &c_b4, &y[i__ + 1 + - y_dim1], ldy, &a[i__ + a_dim1], lda, &c_b5, &a[i__ + ( - i__ + 1) * a_dim1], lda, (ftnlen)12); + dgemv_((char *)"No transpose", &i__2, &i__, &c_b4, &y[i__ + 1 + y_dim1], ldy, + &a[i__ + a_dim1], lda, &c_b5, &a[i__ + (i__ + 1) * a_dim1], lda, (ftnlen)12); i__2 = i__ - 1; i__3 = *n - i__; - dgemv_((char *)"Transpose", &i__2, &i__3, &c_b4, &a[(i__ + 1) * - a_dim1 + 1], lda, &x[i__ + x_dim1], ldx, &c_b5, &a[ - i__ + (i__ + 1) * a_dim1], lda, (ftnlen)9); - -/* Generate reflection P(i) to annihilate A(i,i+2:n) */ - + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b4, &a[(i__ + 1) * a_dim1 + 1], lda, + &x[i__ + x_dim1], ldx, &c_b5, &a[i__ + (i__ + 1) * a_dim1], lda, (ftnlen)9); i__2 = *n - i__; -/* Computing MIN */ i__3 = i__ + 2; - dlarfg_(&i__2, &a[i__ + (i__ + 1) * a_dim1], &a[i__ + min( - i__3,*n) * a_dim1], lda, &taup[i__]); + dlarfg_(&i__2, &a[i__ + (i__ + 1) * a_dim1], &a[i__ + min(i__3, *n) * a_dim1], lda, + &taup[i__]); e[i__] = a[i__ + (i__ + 1) * a_dim1]; a[i__ + (i__ + 1) * a_dim1] = 1.; - -/* Compute X(i+1:m,i) */ - i__2 = *m - i__; i__3 = *n - i__; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + (i__ - + 1) * a_dim1], lda, &a[i__ + (i__ + 1) * a_dim1], - lda, &c_b16, &x[i__ + 1 + i__ * x_dim1], &c__1, ( - ftnlen)12); + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + (i__ + 1) * a_dim1], lda, + &a[i__ + (i__ + 1) * a_dim1], lda, &c_b16, &x[i__ + 1 + i__ * x_dim1], &c__1, + (ftnlen)12); i__2 = *n - i__; - dgemv_((char *)"Transpose", &i__2, &i__, &c_b5, &y[i__ + 1 + y_dim1], - ldy, &a[i__ + (i__ + 1) * a_dim1], lda, &c_b16, &x[ - i__ * x_dim1 + 1], &c__1, (ftnlen)9); + dgemv_((char *)"Transpose", &i__2, &i__, &c_b5, &y[i__ + 1 + y_dim1], ldy, + &a[i__ + (i__ + 1) * a_dim1], lda, &c_b16, &x[i__ * x_dim1 + 1], &c__1, + (ftnlen)9); i__2 = *m - i__; - dgemv_((char *)"No transpose", &i__2, &i__, &c_b4, &a[i__ + 1 + - a_dim1], lda, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[ - i__ + 1 + i__ * x_dim1], &c__1, (ftnlen)12); + dgemv_((char *)"No transpose", &i__2, &i__, &c_b4, &a[i__ + 1 + a_dim1], lda, + &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[i__ + 1 + i__ * x_dim1], &c__1, + (ftnlen)12); i__2 = i__ - 1; i__3 = *n - i__; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[(i__ + 1) * - a_dim1 + 1], lda, &a[i__ + (i__ + 1) * a_dim1], lda, & - c_b16, &x[i__ * x_dim1 + 1], &c__1, (ftnlen)12); + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[(i__ + 1) * a_dim1 + 1], lda, + &a[i__ + (i__ + 1) * a_dim1], lda, &c_b16, &x[i__ * x_dim1 + 1], &c__1, + (ftnlen)12); i__2 = *m - i__; i__3 = i__ - 1; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &x[i__ + 1 + - x_dim1], ldx, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[ - i__ + 1 + i__ * x_dim1], &c__1, (ftnlen)12); + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &x[i__ + 1 + x_dim1], ldx, + &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[i__ + 1 + i__ * x_dim1], &c__1, + (ftnlen)12); i__2 = *m - i__; dscal_(&i__2, &taup[i__], &x[i__ + 1 + i__ * x_dim1], &c__1); } -/* L10: */ } } else { - -/* Reduce to lower bidiagonal form */ - i__1 = *nb; for (i__ = 1; i__ <= i__1; ++i__) { - -/* Update A(i,i:n) */ - i__2 = *n - i__ + 1; i__3 = i__ - 1; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &y[i__ + y_dim1], ldy, - &a[i__ + a_dim1], lda, &c_b5, &a[i__ + i__ * a_dim1], - lda, (ftnlen)12); + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &y[i__ + y_dim1], ldy, &a[i__ + a_dim1], + lda, &c_b5, &a[i__ + i__ * a_dim1], lda, (ftnlen)12); i__2 = i__ - 1; i__3 = *n - i__ + 1; - dgemv_((char *)"Transpose", &i__2, &i__3, &c_b4, &a[i__ * a_dim1 + 1], - lda, &x[i__ + x_dim1], ldx, &c_b5, &a[i__ + i__ * a_dim1], - lda, (ftnlen)9); - -/* Generate reflection P(i) to annihilate A(i,i+1:n) */ - + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b4, &a[i__ * a_dim1 + 1], lda, &x[i__ + x_dim1], + ldx, &c_b5, &a[i__ + i__ * a_dim1], lda, (ftnlen)9); i__2 = *n - i__ + 1; -/* Computing MIN */ i__3 = i__ + 1; - dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[i__ + min(i__3,*n) * - a_dim1], lda, &taup[i__]); + dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[i__ + min(i__3, *n) * a_dim1], lda, + &taup[i__]); d__[i__] = a[i__ + i__ * a_dim1]; if (i__ < *m) { a[i__ + i__ * a_dim1] = 1.; - -/* Compute X(i+1:m,i) */ - i__2 = *m - i__; i__3 = *n - i__ + 1; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + i__ * - a_dim1], lda, &a[i__ + i__ * a_dim1], lda, &c_b16, & - x[i__ + 1 + i__ * x_dim1], &c__1, (ftnlen)12); + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + i__ * a_dim1], lda, + &a[i__ + i__ * a_dim1], lda, &c_b16, &x[i__ + 1 + i__ * x_dim1], &c__1, + (ftnlen)12); i__2 = *n - i__ + 1; i__3 = i__ - 1; - dgemv_((char *)"Transpose", &i__2, &i__3, &c_b5, &y[i__ + y_dim1], - ldy, &a[i__ + i__ * a_dim1], lda, &c_b16, &x[i__ * - x_dim1 + 1], &c__1, (ftnlen)9); + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b5, &y[i__ + y_dim1], ldy, + &a[i__ + i__ * a_dim1], lda, &c_b16, &x[i__ * x_dim1 + 1], &c__1, (ftnlen)9); i__2 = *m - i__; i__3 = i__ - 1; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &a[i__ + 1 + - a_dim1], lda, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[ - i__ + 1 + i__ * x_dim1], &c__1, (ftnlen)12); + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &a[i__ + 1 + a_dim1], lda, + &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[i__ + 1 + i__ * x_dim1], &c__1, + (ftnlen)12); i__2 = i__ - 1; i__3 = *n - i__ + 1; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[i__ * a_dim1 + - 1], lda, &a[i__ + i__ * a_dim1], lda, &c_b16, &x[i__ * - x_dim1 + 1], &c__1, (ftnlen)12); + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[i__ * a_dim1 + 1], lda, + &a[i__ + i__ * a_dim1], lda, &c_b16, &x[i__ * x_dim1 + 1], &c__1, + (ftnlen)12); i__2 = *m - i__; i__3 = i__ - 1; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &x[i__ + 1 + - x_dim1], ldx, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[ - i__ + 1 + i__ * x_dim1], &c__1, (ftnlen)12); + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &x[i__ + 1 + x_dim1], ldx, + &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[i__ + 1 + i__ * x_dim1], &c__1, + (ftnlen)12); i__2 = *m - i__; dscal_(&i__2, &taup[i__], &x[i__ + 1 + i__ * x_dim1], &c__1); - -/* Update A(i+1:m,i) */ - i__2 = *m - i__; i__3 = i__ - 1; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &a[i__ + 1 + - a_dim1], lda, &y[i__ + y_dim1], ldy, &c_b5, &a[i__ + - 1 + i__ * a_dim1], &c__1, (ftnlen)12); + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &a[i__ + 1 + a_dim1], lda, + &y[i__ + y_dim1], ldy, &c_b5, &a[i__ + 1 + i__ * a_dim1], &c__1, (ftnlen)12); i__2 = *m - i__; - dgemv_((char *)"No transpose", &i__2, &i__, &c_b4, &x[i__ + 1 + - x_dim1], ldx, &a[i__ * a_dim1 + 1], &c__1, &c_b5, &a[ - i__ + 1 + i__ * a_dim1], &c__1, (ftnlen)12); - -/* Generate reflection Q(i) to annihilate A(i+2:m,i) */ - + dgemv_((char *)"No transpose", &i__2, &i__, &c_b4, &x[i__ + 1 + x_dim1], ldx, + &a[i__ * a_dim1 + 1], &c__1, &c_b5, &a[i__ + 1 + i__ * a_dim1], &c__1, + (ftnlen)12); i__2 = *m - i__; -/* Computing MIN */ i__3 = i__ + 2; - dlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3,*m) + - i__ * a_dim1], &c__1, &tauq[i__]); + dlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3, *m) + i__ * a_dim1], &c__1, + &tauq[i__]); e[i__] = a[i__ + 1 + i__ * a_dim1]; a[i__ + 1 + i__ * a_dim1] = 1.; - -/* Compute Y(i+1:n,i) */ - i__2 = *m - i__; i__3 = *n - i__; - dgemv_((char *)"Transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + (i__ + - 1) * a_dim1], lda, &a[i__ + 1 + i__ * a_dim1], &c__1, - &c_b16, &y[i__ + 1 + i__ * y_dim1], &c__1, (ftnlen)9); + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + (i__ + 1) * a_dim1], lda, + &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &y[i__ + 1 + i__ * y_dim1], &c__1, + (ftnlen)9); i__2 = *m - i__; i__3 = i__ - 1; - dgemv_((char *)"Transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + a_dim1], - lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &y[ - i__ * y_dim1 + 1], &c__1, (ftnlen)9); + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + a_dim1], lda, + &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &y[i__ * y_dim1 + 1], &c__1, + (ftnlen)9); i__2 = *n - i__; i__3 = i__ - 1; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &y[i__ + 1 + - y_dim1], ldy, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[ - i__ + 1 + i__ * y_dim1], &c__1, (ftnlen)12); + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b4, &y[i__ + 1 + y_dim1], ldy, + &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[i__ + 1 + i__ * y_dim1], &c__1, + (ftnlen)12); i__2 = *m - i__; - dgemv_((char *)"Transpose", &i__2, &i__, &c_b5, &x[i__ + 1 + x_dim1], - ldx, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &y[ - i__ * y_dim1 + 1], &c__1, (ftnlen)9); + dgemv_((char *)"Transpose", &i__2, &i__, &c_b5, &x[i__ + 1 + x_dim1], ldx, + &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &y[i__ * y_dim1 + 1], &c__1, + (ftnlen)9); i__2 = *n - i__; - dgemv_((char *)"Transpose", &i__, &i__2, &c_b4, &a[(i__ + 1) * a_dim1 - + 1], lda, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[i__ - + 1 + i__ * y_dim1], &c__1, (ftnlen)9); + dgemv_((char *)"Transpose", &i__, &i__2, &c_b4, &a[(i__ + 1) * a_dim1 + 1], lda, + &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[i__ + 1 + i__ * y_dim1], &c__1, + (ftnlen)9); i__2 = *n - i__; dscal_(&i__2, &tauq[i__], &y[i__ + 1 + i__ * y_dim1], &c__1); } -/* L20: */ } } return 0; - -/* End of DLABRD */ - -} /* dlabrd_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlacn2.cpp b/lib/linalg/dlacn2.cpp index bee9fb7e25..3f9bea59d8 100644 --- a/lib/linalg/dlacn2.cpp +++ b/lib/linalg/dlacn2.cpp @@ -1,244 +1,53 @@ -/* fortran/dlacn2.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; - -/* > \brief \b DLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matr -ix-vector products. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLACN2 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLACN2( N, V, X, ISGN, EST, KASE, ISAVE ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER KASE, N */ -/* DOUBLE PRECISION EST */ -/* .. */ -/* .. Array Arguments .. */ -/* INTEGER ISGN( * ), ISAVE( 3 ) */ -/* DOUBLE PRECISION V( * ), X( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLACN2 estimates the 1-norm of a square, real matrix A. */ -/* > Reverse communication is used for evaluating matrix-vector products. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrix. N >= 1. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] V */ -/* > \verbatim */ -/* > V is DOUBLE PRECISION array, dimension (N) */ -/* > On the final return, V = A*W, where EST = norm(V)/norm(W) */ -/* > (W is not returned). */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] X */ -/* > \verbatim */ -/* > X is DOUBLE PRECISION array, dimension (N) */ -/* > On an intermediate return, X should be overwritten by */ -/* > A * X, if KASE=1, */ -/* > A**T * X, if KASE=2, */ -/* > and DLACN2 must be re-called with all the other parameters */ -/* > unchanged. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] ISGN */ -/* > \verbatim */ -/* > ISGN is INTEGER array, dimension (N) */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] EST */ -/* > \verbatim */ -/* > EST is DOUBLE PRECISION */ -/* > On entry with KASE = 1 or 2 and ISAVE(1) = 3, EST should be */ -/* > unchanged from the previous call to DLACN2. */ -/* > On exit, EST is an estimate (a lower bound) for norm(A). */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] KASE */ -/* > \verbatim */ -/* > KASE is INTEGER */ -/* > On the initial call to DLACN2, KASE should be 0. */ -/* > On an intermediate return, KASE will be 1 or 2, indicating */ -/* > whether X should be overwritten by A * X or A**T * X. */ -/* > On the final return from DLACN2, KASE will again be 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] ISAVE */ -/* > \verbatim */ -/* > ISAVE is INTEGER array, dimension (3) */ -/* > ISAVE is used to save variables between calls to DLACN2 */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleOTHERauxiliary */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > Originally named SONEST, dated March 16, 1988. */ -/* > */ -/* > This is a thread safe version of DLACON, which uses the array ISAVE */ -/* > in place of a SAVE statement, as follows: */ -/* > */ -/* > DLACON DLACN2 */ -/* > JUMP ISAVE(1) */ -/* > J ISAVE(2) */ -/* > ITER ISAVE(3) */ -/* > \endverbatim */ - -/* > \par Contributors: */ -/* ================== */ -/* > */ -/* > Nick Higham, University of Manchester */ - -/* > \par References: */ -/* ================ */ -/* > */ -/* > N.J. Higham, "FORTRAN codes for estimating the one-norm of */ -/* > a real or complex matrix, with applications to condition estimation", */ -/* > ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988. */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dlacn2_(integer *n, doublereal *v, doublereal *x, - integer *isgn, doublereal *est, integer *kase, integer *isave) +int dlacn2_(integer *n, doublereal *v, doublereal *x, integer *isgn, doublereal *est, integer *kase, + integer *isave) { - /* System generated locals */ integer i__1; doublereal d__1; - - /* Builtin functions */ integer i_lmp_dnnt(doublereal *); - - /* Local variables */ integer i__; doublereal xs, temp; extern doublereal dasum_(integer *, doublereal *, integer *); integer jlast; - extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, - doublereal *, integer *); + extern int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *); extern integer idamax_(integer *, doublereal *, integer *); doublereal altsgn, estold; - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - - /* Parameter adjustments */ --isave; --isgn; --x; --v; - - /* Function Body */ if (*kase == 0) { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { - x[i__] = 1. / (doublereal) (*n); -/* L10: */ + x[i__] = 1. / (doublereal)(*n); } *kase = 1; isave[1] = 1; return 0; } - switch (isave[1]) { - case 1: goto L20; - case 2: goto L40; - case 3: goto L70; - case 4: goto L110; - case 5: goto L140; + case 1: + goto L20; + case 2: + goto L40; + case 3: + goto L70; + case 4: + goto L110; + case 5: + goto L140; } - -/* ................ ENTRY (ISAVE( 1 ) = 1) */ -/* FIRST ITERATION. X HAS BEEN OVERWRITTEN BY A*X. */ - L20: if (*n == 1) { v[1] = x[1]; *est = abs(v[1]); -/* ... QUIT */ goto L150; } *est = dasum_(n, &x[1], &c__1); - i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { if (x[i__] >= 0.) { @@ -247,35 +56,22 @@ L20: x[i__] = -1.; } isgn[i__] = i_lmp_dnnt(&x[i__]); -/* L30: */ } *kase = 2; isave[1] = 2; return 0; - -/* ................ ENTRY (ISAVE( 1 ) = 2) */ -/* FIRST ITERATION. X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X. */ - L40: isave[2] = idamax_(n, &x[1], &c__1); isave[3] = 2; - -/* MAIN LOOP - ITERATIONS 2,3,...,ITMAX. */ - L50: i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { x[i__] = 0.; -/* L60: */ } x[isave[2]] = 1.; *kase = 1; isave[1] = 3; return 0; - -/* ................ ENTRY (ISAVE( 1 ) = 3) */ -/* X HAS BEEN OVERWRITTEN BY A*X. */ - L70: dcopy_(n, &x[1], &c__1, &v[1], &c__1); estold = *est; @@ -290,17 +86,12 @@ L70: if (i_lmp_dnnt(&xs) != isgn[i__]) { goto L90; } -/* L80: */ } -/* REPEATED SIGN VECTOR DETECTED, HENCE ALGORITHM HAS CONVERGED. */ goto L120; - L90: -/* TEST FOR CYCLING. */ if (*est <= estold) { goto L120; } - i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { if (x[i__] >= 0.) { @@ -309,15 +100,10 @@ L90: x[i__] = -1.; } isgn[i__] = i_lmp_dnnt(&x[i__]); -/* L100: */ } *kase = 2; isave[1] = 4; return 0; - -/* ................ ENTRY (ISAVE( 1 ) = 4) */ -/* X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X. */ - L110: jlast = isave[2]; isave[2] = idamax_(n, &x[1], &c__1); @@ -325,40 +111,26 @@ L110: ++isave[3]; goto L50; } - -/* ITERATION COMPLETE. FINAL STAGE. */ - L120: altsgn = 1.; i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { - x[i__] = altsgn * ((doublereal) (i__ - 1) / (doublereal) (*n - 1) + - 1.); + x[i__] = altsgn * ((doublereal)(i__ - 1) / (doublereal)(*n - 1) + 1.); altsgn = -altsgn; -/* L130: */ } *kase = 1; isave[1] = 5; return 0; - -/* ................ ENTRY (ISAVE( 1 ) = 5) */ -/* X HAS BEEN OVERWRITTEN BY A*X. */ - L140: - temp = dasum_(n, &x[1], &c__1) / (doublereal) (*n * 3) * 2.; + temp = dasum_(n, &x[1], &c__1) / (doublereal)(*n * 3) * 2.; if (temp > *est) { dcopy_(n, &x[1], &c__1, &v[1], &c__1); *est = temp; } - L150: *kase = 0; return 0; - -/* End of DLACN2 */ - -} /* dlacn2_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlacpy.cpp b/lib/linalg/dlacpy.cpp index 813a669202..361ee09b9e 100644 --- a/lib/linalg/dlacpy.cpp +++ b/lib/linalg/dlacpy.cpp @@ -1,172 +1,26 @@ -/* fortran/dlacpy.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DLACPY copies all or part of one two-dimensional array to another. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLACPY + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLACPY( UPLO, M, N, A, LDA, B, LDB ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER UPLO */ -/* INTEGER LDA, LDB, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), B( LDB, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLACPY copies all or part of a two-dimensional matrix A to another */ -/* > matrix B. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > Specifies the part of the matrix A to be copied to B. */ -/* > = 'U': Upper triangular part */ -/* > = 'L': Lower triangular part */ -/* > Otherwise: All of the matrix A */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix A. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > The m by n matrix A. If UPLO = 'U', only the upper triangle */ -/* > or trapezoid is accessed; if UPLO = 'L', only the lower */ -/* > triangle or trapezoid is accessed. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] B */ -/* > \verbatim */ -/* > B is DOUBLE PRECISION array, dimension (LDB,N) */ -/* > On exit, B = A in the locations specified by UPLO. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDB */ -/* > \verbatim */ -/* > LDB is INTEGER */ -/* > The leading dimension of the array B. LDB >= max(1,M). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup OTHERauxiliary */ - -/* ===================================================================== */ -/* Subroutine */ int dlacpy_(char *uplo, integer *m, integer *n, doublereal * - a, integer *lda, doublereal *b, integer *ldb, ftnlen uplo_len) +int dlacpy_(char *uplo, integer *m, integer *n, doublereal *a, integer *lda, doublereal *b, + integer *ldb, ftnlen uplo_len) { - /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2; - - /* Local variables */ integer i__, j; extern logical lsame_(char *, char *, ftnlen, ftnlen); - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; - - /* Function Body */ if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { i__1 = *n; for (j = 1; j <= i__1; ++j) { - i__2 = min(j,*m); + i__2 = min(j, *m); for (i__ = 1; i__ <= i__2; ++i__) { b[i__ + j * b_dim1] = a[i__ + j * a_dim1]; -/* L10: */ } -/* L20: */ } } else if (lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { i__1 = *n; @@ -174,9 +28,7 @@ f"> */ i__2 = *m; for (i__ = j; i__ <= i__2; ++i__) { b[i__ + j * b_dim1] = a[i__ + j * a_dim1]; -/* L30: */ } -/* L40: */ } } else { i__1 = *n; @@ -184,17 +36,11 @@ f"> */ i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { b[i__ + j * b_dim1] = a[i__ + j * a_dim1]; -/* L50: */ } -/* L60: */ } } return 0; - -/* End of DLACPY */ - -} /* dlacpy_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dladiv.cpp b/lib/linalg/dladiv.cpp index d12fb854f0..52f48222b0 100644 --- a/lib/linalg/dladiv.cpp +++ b/lib/linalg/dladiv.cpp @@ -1,156 +1,23 @@ -/* fortran/dladiv.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DLADIV performs complex division in real arithmetic, avoiding unnecessary overflow. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLADIV + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLADIV( A, B, C, D, P, Q ) */ - -/* .. Scalar Arguments .. */ -/* DOUBLE PRECISION A, B, C, D, P, Q */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLADIV performs complex division in real arithmetic */ -/* > */ -/* > a + i*b */ -/* > p + i*q = --------- */ -/* > c + i*d */ -/* > */ -/* > The algorithm is due to Michael Baudin and Robert L. Smith */ -/* > and can be found in the paper */ -/* > (char *)"A Robust Complex Division in Scilab" */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION */ -/* > \endverbatim */ -/* > */ -/* > \param[in] B */ -/* > \verbatim */ -/* > B is DOUBLE PRECISION */ -/* > \endverbatim */ -/* > */ -/* > \param[in] C */ -/* > \verbatim */ -/* > C is DOUBLE PRECISION */ -/* > \endverbatim */ -/* > */ -/* > \param[in] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION */ -/* > The scalars a, b, c, and d in the above expression. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] P */ -/* > \verbatim */ -/* > P is DOUBLE PRECISION */ -/* > \endverbatim */ -/* > */ -/* > \param[out] Q */ -/* > \verbatim */ -/* > Q is DOUBLE PRECISION */ -/* > The scalars p and q in the above expression. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleOTHERauxiliary */ - -/* ===================================================================== */ -/* Subroutine */ int dladiv_(doublereal *a, doublereal *b, doublereal *c__, - doublereal *d__, doublereal *p, doublereal *q) +int dladiv_(doublereal *a, doublereal *b, doublereal *c__, doublereal *d__, doublereal *p, + doublereal *q) { - /* System generated locals */ doublereal d__1, d__2; - - /* Local variables */ doublereal s, aa, ab, bb, cc, cd, dd, be, un, ov, eps; extern doublereal dlamch_(char *, ftnlen); - extern /* Subroutine */ int dladiv1_(doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *, doublereal *); - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ - -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - + extern int dladiv1_(doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *); aa = *a; bb = *b; cc = *c__; dd = *d__; -/* Computing MAX */ d__1 = abs(*a), d__2 = abs(*b); - ab = max(d__1,d__2); -/* Computing MAX */ + ab = max(d__1, d__2); d__1 = abs(*c__), d__2 = abs(*d__); - cd = max(d__1,d__2); + cd = max(d__1, d__2); s = 1.; ov = dlamch_((char *)"Overflow threshold", (ftnlen)18); un = dlamch_((char *)"Safe minimum", (ftnlen)12); @@ -184,77 +51,26 @@ f"> */ } *p *= s; *q *= s; - return 0; - -/* End of DLADIV */ - -} /* dladiv_ */ - -/* > \ingroup doubleOTHERauxiliary */ -/* Subroutine */ int dladiv1_(doublereal *a, doublereal *b, doublereal *c__, - doublereal *d__, doublereal *p, doublereal *q) +} +int dladiv1_(doublereal *a, doublereal *b, doublereal *c__, doublereal *d__, doublereal *p, + doublereal *q) { doublereal r__, t; - extern doublereal dladiv2_(doublereal *, doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *); - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ - -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - + extern doublereal dladiv2_(doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *); r__ = *d__ / *c__; t = 1. / (*c__ + *d__ * r__); *p = dladiv2_(a, b, c__, d__, &r__, &t); *a = -(*a); *q = dladiv2_(b, a, c__, d__, &r__, &t); - return 0; - -/* End of DLADIV1 */ - -} /* dladiv1_ */ - -/* > \ingroup doubleOTHERauxiliary */ -doublereal dladiv2_(doublereal *a, doublereal *b, doublereal *c__, doublereal - *d__, doublereal *r__, doublereal *t) +} +doublereal dladiv2_(doublereal *a, doublereal *b, doublereal *c__, doublereal *d__, doublereal *r__, + doublereal *t) { - /* System generated locals */ doublereal ret_val; - - /* Local variables */ doublereal br; - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ - -/* .. Local Scalars .. */ -/* .. */ -/* .. Executable Statements .. */ - if (*r__ != 0.) { br = *b * *r__; if (br != 0.) { @@ -265,13 +81,8 @@ doublereal dladiv2_(doublereal *a, doublereal *b, doublereal *c__, doublereal } else { ret_val = (*a + *d__ * (*b / *c__)) * *t; } - return ret_val; - -/* End of DLADIV2 */ - -} /* dladiv2_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlae2.cpp b/lib/linalg/dlae2.cpp index 7351921b21..985e03a608 100644 --- a/lib/linalg/dlae2.cpp +++ b/lib/linalg/dlae2.cpp @@ -1,155 +1,12 @@ -/* fortran/dlae2.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLAE2 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLAE2( A, B, C, RT1, RT2 ) */ - -/* .. Scalar Arguments .. */ -/* DOUBLE PRECISION A, B, C, RT1, RT2 */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix */ -/* > [ A B ] */ -/* > [ B C ]. */ -/* > On return, RT1 is the eigenvalue of larger absolute value, and RT2 */ -/* > is the eigenvalue of smaller absolute value. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION */ -/* > The (1,1) element of the 2-by-2 matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] B */ -/* > \verbatim */ -/* > B is DOUBLE PRECISION */ -/* > The (1,2) and (2,1) elements of the 2-by-2 matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] C */ -/* > \verbatim */ -/* > C is DOUBLE PRECISION */ -/* > The (2,2) element of the 2-by-2 matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] RT1 */ -/* > \verbatim */ -/* > RT1 is DOUBLE PRECISION */ -/* > The eigenvalue of larger absolute value. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] RT2 */ -/* > \verbatim */ -/* > RT2 is DOUBLE PRECISION */ -/* > The eigenvalue of smaller absolute value. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup OTHERauxiliary */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > RT1 is accurate to a few ulps barring over/underflow. */ -/* > */ -/* > RT2 may be inaccurate if there is massive cancellation in the */ -/* > determinant A*C-B*B; higher precision or correctly rounded or */ -/* > correctly truncated arithmetic would be needed to compute RT2 */ -/* > accurately in all cases. */ -/* > */ -/* > Overflow is possible only if RT1 is within a factor of 5 of overflow. */ -/* > Underflow is harmless if the input data is 0 or exceeds */ -/* > underflow_threshold / macheps. */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dlae2_(doublereal *a, doublereal *b, doublereal *c__, - doublereal *rt1, doublereal *rt2) +int dlae2_(doublereal *a, doublereal *b, doublereal *c__, doublereal *rt1, doublereal *rt2) { - /* System generated locals */ doublereal d__1; - - /* Builtin functions */ double sqrt(doublereal); - - /* Local variables */ doublereal ab, df, tb, sm, rt, adf, acmn, acmx; - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Compute the eigenvalues */ - sm = *a + *c__; df = *a - *c__; adf = abs(df); @@ -163,48 +20,26 @@ extern "C" { acmn = *a; } if (adf > ab) { -/* Computing 2nd power */ d__1 = ab / adf; rt = adf * sqrt(d__1 * d__1 + 1.); } else if (adf < ab) { -/* Computing 2nd power */ d__1 = adf / ab; rt = ab * sqrt(d__1 * d__1 + 1.); } else { - -/* Includes case AB=ADF=0 */ - rt = ab * sqrt(2.); } if (sm < 0.) { *rt1 = (sm - rt) * .5; - -/* Order of execution important. */ -/* To get fully accurate smaller eigenvalue, */ -/* next line needs to be executed in higher precision. */ - *rt2 = acmx / *rt1 * acmn - *b / *rt1 * *b; } else if (sm > 0.) { *rt1 = (sm + rt) * .5; - -/* Order of execution important. */ -/* To get fully accurate smaller eigenvalue, */ -/* next line needs to be executed in higher precision. */ - *rt2 = acmx / *rt1 * acmn - *b / *rt1 * *b; } else { - -/* Includes case RT1 = RT2 = 0 */ - *rt1 = rt * .5; *rt2 = rt * -.5; } return 0; - -/* End of DLAE2 */ - -} /* dlae2_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlaed0.cpp b/lib/linalg/dlaed0.cpp index 5c40115e77..b1a243175b 100644 --- a/lib/linalg/dlaed0.cpp +++ b/lib/linalg/dlaed0.cpp @@ -1,275 +1,48 @@ -/* fortran/dlaed0.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__9 = 9; static integer c__0 = 0; static integer c__2 = 2; static doublereal c_b23 = 1.; static doublereal c_b24 = 0.; static integer c__1 = 1; - -/* > \brief \b DLAED0 used by DSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced -symmetric tridiagonal matrix using the divide and conquer method. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLAED0 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, */ -/* WORK, IWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER ICOMPQ, INFO, LDQ, LDQS, N, QSIZ */ -/* .. */ -/* .. Array Arguments .. */ -/* INTEGER IWORK( * ) */ -/* DOUBLE PRECISION D( * ), E( * ), Q( LDQ, * ), QSTORE( LDQS, * ), */ -/* $ WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLAED0 computes all eigenvalues and corresponding eigenvectors of a */ -/* > symmetric tridiagonal matrix using the divide and conquer method. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] ICOMPQ */ -/* > \verbatim */ -/* > ICOMPQ is INTEGER */ -/* > = 0: Compute eigenvalues only. */ -/* > = 1: Compute eigenvectors of original dense symmetric matrix */ -/* > also. On entry, Q contains the orthogonal matrix used */ -/* > to reduce the original matrix to tridiagonal form. */ -/* > = 2: Compute eigenvalues and eigenvectors of tridiagonal */ -/* > matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] QSIZ */ -/* > \verbatim */ -/* > QSIZ is INTEGER */ -/* > The dimension of the orthogonal matrix used to reduce */ -/* > the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The dimension of the symmetric tridiagonal matrix. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension (N) */ -/* > On entry, the main diagonal of the tridiagonal matrix. */ -/* > On exit, its eigenvalues. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] E */ -/* > \verbatim */ -/* > E is DOUBLE PRECISION array, dimension (N-1) */ -/* > The off-diagonal elements of the tridiagonal matrix. */ -/* > On exit, E has been destroyed. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] Q */ -/* > \verbatim */ -/* > Q is DOUBLE PRECISION array, dimension (LDQ, N) */ -/* > On entry, Q must contain an N-by-N orthogonal matrix. */ -/* > If ICOMPQ = 0 Q is not referenced. */ -/* > If ICOMPQ = 1 On entry, Q is a subset of the columns of the */ -/* > orthogonal matrix used to reduce the full */ -/* > matrix to tridiagonal form corresponding to */ -/* > the subset of the full matrix which is being */ -/* > decomposed at this time. */ -/* > If ICOMPQ = 2 On entry, Q will be the identity matrix. */ -/* > On exit, Q contains the eigenvectors of the */ -/* > tridiagonal matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDQ */ -/* > \verbatim */ -/* > LDQ is INTEGER */ -/* > The leading dimension of the array Q. If eigenvectors are */ -/* > desired, then LDQ >= max(1,N). In any case, LDQ >= 1. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] QSTORE */ -/* > \verbatim */ -/* > QSTORE is DOUBLE PRECISION array, dimension (LDQS, N) */ -/* > Referenced only when ICOMPQ = 1. Used to store parts of */ -/* > the eigenvector matrix when the updating matrix multiplies */ -/* > take place. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDQS */ -/* > \verbatim */ -/* > LDQS is INTEGER */ -/* > The leading dimension of the array QSTORE. If ICOMPQ = 1, */ -/* > then LDQS >= max(1,N). In any case, LDQS >= 1. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, */ -/* > If ICOMPQ = 0 or 1, the dimension of WORK must be at least */ -/* > 1 + 3*N + 2*N*lg N + 3*N**2 */ -/* > ( lg( N ) = smallest integer k */ -/* > such that 2^k >= N ) */ -/* > If ICOMPQ = 2, the dimension of WORK must be at least */ -/* > 4*N + N**2. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] IWORK */ -/* > \verbatim */ -/* > IWORK is INTEGER array, */ -/* > If ICOMPQ = 0 or 1, the dimension of IWORK must be at least */ -/* > 6 + 6*N + 5*N*lg N. */ -/* > ( lg( N ) = smallest integer k */ -/* > such that 2^k >= N ) */ -/* > If ICOMPQ = 2, the dimension of IWORK must be at least */ -/* > 3 + 5*N. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit. */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ -/* > > 0: The algorithm failed to compute an eigenvalue while */ -/* > working on the submatrix lying in rows and columns */ -/* > INFO/(N+1) through mod(INFO,N+1). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup auxOTHERcomputational */ - -/* > \par Contributors: */ -/* ================== */ -/* > */ -/* > Jeff Rutter, Computer Science Division, University of California */ -/* > at Berkeley, USA */ - -/* ===================================================================== */ -/* Subroutine */ int dlaed0_(integer *icompq, integer *qsiz, integer *n, - doublereal *d__, doublereal *e, doublereal *q, integer *ldq, - doublereal *qstore, integer *ldqs, doublereal *work, integer *iwork, - integer *info) +int dlaed0_(integer *icompq, integer *qsiz, integer *n, doublereal *d__, doublereal *e, + doublereal *q, integer *ldq, doublereal *qstore, integer *ldqs, doublereal *work, + integer *iwork, integer *info) { - /* System generated locals */ integer q_dim1, q_offset, qstore_dim1, qstore_offset, i__1, i__2; doublereal d__1; - - /* Builtin functions */ double log(doublereal); integer pow_lmp_ii(integer *, integer *); - - /* Local variables */ integer i__, j, k, iq, lgn, msd2, smm1, spm1, spm2; doublereal temp; integer curr; - extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); + extern int dgemm_(char *, char *, integer *, integer *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, + ftnlen, ftnlen); integer iperm; - extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, - doublereal *, integer *); + extern int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *); integer indxq, iwrem; - extern /* Subroutine */ int dlaed1_(integer *, doublereal *, doublereal *, - integer *, integer *, doublereal *, integer *, doublereal *, - integer *, integer *); + extern int dlaed1_(integer *, doublereal *, doublereal *, integer *, integer *, doublereal *, + integer *, doublereal *, integer *, integer *); integer iqptr; - extern /* Subroutine */ int dlaed7_(integer *, integer *, integer *, - integer *, integer *, integer *, doublereal *, doublereal *, - integer *, integer *, doublereal *, integer *, doublereal *, - integer *, integer *, integer *, integer *, integer *, doublereal - *, doublereal *, integer *, integer *); + extern int dlaed7_(integer *, integer *, integer *, integer *, integer *, integer *, + doublereal *, doublereal *, integer *, integer *, doublereal *, integer *, + doublereal *, integer *, integer *, integer *, integer *, integer *, + doublereal *, doublereal *, integer *, integer *); integer tlvls; - extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, - doublereal *, integer *, doublereal *, integer *, ftnlen); + extern int dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, + integer *, ftnlen); integer igivcl; - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern int xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); integer igivnm, submat, curprb, subpbs, igivpt; - extern /* Subroutine */ int dsteqr_(char *, integer *, doublereal *, - doublereal *, doublereal *, integer *, doublereal *, integer *, - ftnlen); + extern int dsteqr_(char *, integer *, doublereal *, doublereal *, doublereal *, integer *, + doublereal *, integer *, ftnlen); integer curlvl, matsiz, iprmpt, smlsiz; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ --d__; --e; q_dim1 = *ldq; @@ -280,19 +53,16 @@ f"> */ qstore -= qstore_offset; --work; --iwork; - - /* Function Body */ *info = 0; - if (*icompq < 0 || *icompq > 2) { *info = -1; - } else if (*icompq == 1 && *qsiz < max(0,*n)) { + } else if (*icompq == 1 && *qsiz < max(0, *n)) { *info = -2; } else if (*n < 0) { *info = -3; - } else if (*ldq < max(1,*n)) { + } else if (*ldq < max(1, *n)) { *info = -7; - } else if (*ldqs < max(1,*n)) { + } else if (*ldqs < max(1, *n)) { *info = -9; } if (*info != 0) { @@ -300,19 +70,10 @@ f"> */ xerbla_((char *)"DLAED0", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*n == 0) { return 0; } - - smlsiz = ilaenv_(&c__9, (char *)"DLAED0", (char *)" ", &c__0, &c__0, &c__0, &c__0, ( - ftnlen)6, (ftnlen)1); - -/* Determine the size and placement of the submatrices, and save in */ -/* the leading elements of IWORK. */ - + smlsiz = ilaenv_(&c__9, (char *)"DLAED0", (char *)" ", &c__0, &c__0, &c__0, &c__0, (ftnlen)6, (ftnlen)1); iwork[1] = *n; subpbs = 1; tlvls = 0; @@ -321,7 +82,6 @@ L10: for (j = subpbs; j >= 1; --j) { iwork[j * 2] = (iwork[j] + 1) / 2; iwork[(j << 1) - 1] = iwork[j] / 2; -/* L20: */ } ++tlvls; subpbs <<= 1; @@ -330,12 +90,7 @@ L10: i__1 = subpbs; for (j = 2; j <= i__1; ++j) { iwork[j] += iwork[j - 1]; -/* L30: */ } - -/* Divide the matrix into SUBPBS submatrices of size at most SMLSIZ+1 */ -/* using rank-1 modifications (cuts). */ - spm1 = subpbs - 1; i__1 = spm1; for (i__ = 1; i__ <= i__1; ++i__) { @@ -343,17 +98,11 @@ L10: smm1 = submat - 1; d__[smm1] -= (d__1 = e[smm1], abs(d__1)); d__[submat] -= (d__1 = e[smm1], abs(d__1)); -/* L40: */ } - indxq = (*n << 2) + 3; if (*icompq != 2) { - -/* Set up workspaces for eigenvalues only/accumulate new vectors */ -/* routine */ - - temp = log((doublereal) (*n)) / log(2.); - lgn = (integer) temp; + temp = log((doublereal)(*n)) / log(2.); + lgn = (integer)temp; if (pow_lmp_ii(&c__2, &lgn) < *n) { ++lgn; } @@ -365,27 +114,17 @@ L10: iqptr = iperm + *n * lgn; igivpt = iqptr + *n + 2; igivcl = igivpt + *n * lgn; - igivnm = 1; iq = igivnm + (*n << 1) * lgn; -/* Computing 2nd power */ i__1 = *n; iwrem = iq + i__1 * i__1 + 1; - -/* Initialize pointers */ - i__1 = subpbs; for (i__ = 0; i__ <= i__1; ++i__) { iwork[iprmpt + i__] = 1; iwork[igivpt + i__] = 1; -/* L50: */ } iwork[iqptr] = 1; } - -/* Solve each submatrix eigenproblem at the bottom of the divide and */ -/* conquer tree. */ - curr = 0; i__1 = spm1; for (i__ = 0; i__ <= i__1; ++i__) { @@ -397,24 +136,22 @@ L10: matsiz = iwork[i__ + 1] - iwork[i__]; } if (*icompq == 2) { - dsteqr_((char *)"I", &matsiz, &d__[submat], &e[submat], &q[submat + - submat * q_dim1], ldq, &work[1], info, (ftnlen)1); + dsteqr_((char *)"I", &matsiz, &d__[submat], &e[submat], &q[submat + submat * q_dim1], ldq, + &work[1], info, (ftnlen)1); if (*info != 0) { goto L130; } } else { - dsteqr_((char *)"I", &matsiz, &d__[submat], &e[submat], &work[iq - 1 + - iwork[iqptr + curr]], &matsiz, &work[1], info, (ftnlen)1); + dsteqr_((char *)"I", &matsiz, &d__[submat], &e[submat], &work[iq - 1 + iwork[iqptr + curr]], + &matsiz, &work[1], info, (ftnlen)1); if (*info != 0) { goto L130; } if (*icompq == 1) { - dgemm_((char *)"N", (char *)"N", qsiz, &matsiz, &matsiz, &c_b23, &q[submat * - q_dim1 + 1], ldq, &work[iq - 1 + iwork[iqptr + curr]], - &matsiz, &c_b24, &qstore[submat * qstore_dim1 + 1], - ldqs, (ftnlen)1, (ftnlen)1); + dgemm_((char *)"N", (char *)"N", qsiz, &matsiz, &matsiz, &c_b23, &q[submat * q_dim1 + 1], ldq, + &work[iq - 1 + iwork[iqptr + curr]], &matsiz, &c_b24, + &qstore[submat * qstore_dim1 + 1], ldqs, (ftnlen)1, (ftnlen)1); } -/* Computing 2nd power */ i__2 = matsiz; iwork[iqptr + curr + 1] = iwork[iqptr + curr] + i__2 * i__2; ++curr; @@ -424,16 +161,8 @@ L10: for (j = submat; j <= i__2; ++j) { iwork[indxq + j] = k; ++k; -/* L60: */ } -/* L70: */ } - -/* Successively merge eigensystems of adjacent submatrices */ -/* into eigensystem for the corresponding larger matrix. */ - -/* while ( SUBPBS > 1 ) */ - curlvl = 1; L80: if (subpbs > 1) { @@ -451,51 +180,32 @@ L80: msd2 = matsiz / 2; ++curprb; } - -/* Merge lower order eigensystems (of size MSD2 and MATSIZ - MSD2) */ -/* into an eigensystem of size MATSIZ. */ -/* DLAED1 is used only for the full eigensystem of a tridiagonal */ -/* matrix. */ -/* DLAED7 handles the cases in which eigenvalues only or eigenvalues */ -/* and eigenvectors of a full symmetric matrix (which was reduced to */ -/* tridiagonal form) are desired. */ - if (*icompq == 2) { - dlaed1_(&matsiz, &d__[submat], &q[submat + submat * q_dim1], - ldq, &iwork[indxq + submat], &e[submat + msd2 - 1], & - msd2, &work[1], &iwork[subpbs + 1], info); + dlaed1_(&matsiz, &d__[submat], &q[submat + submat * q_dim1], ldq, + &iwork[indxq + submat], &e[submat + msd2 - 1], &msd2, &work[1], + &iwork[subpbs + 1], info); } else { - dlaed7_(icompq, &matsiz, qsiz, &tlvls, &curlvl, &curprb, &d__[ - submat], &qstore[submat * qstore_dim1 + 1], ldqs, & - iwork[indxq + submat], &e[submat + msd2 - 1], &msd2, & - work[iq], &iwork[iqptr], &iwork[iprmpt], &iwork[iperm] - , &iwork[igivpt], &iwork[igivcl], &work[igivnm], & - work[iwrem], &iwork[subpbs + 1], info); + dlaed7_(icompq, &matsiz, qsiz, &tlvls, &curlvl, &curprb, &d__[submat], + &qstore[submat * qstore_dim1 + 1], ldqs, &iwork[indxq + submat], + &e[submat + msd2 - 1], &msd2, &work[iq], &iwork[iqptr], &iwork[iprmpt], + &iwork[iperm], &iwork[igivpt], &iwork[igivcl], &work[igivnm], &work[iwrem], + &iwork[subpbs + 1], info); } if (*info != 0) { goto L130; } iwork[i__ / 2 + 1] = iwork[i__ + 2]; -/* L90: */ } subpbs /= 2; ++curlvl; goto L80; } - -/* end while */ - -/* Re-merge the eigenvalues/vectors which were deflated at the final */ -/* merge step. */ - if (*icompq == 1) { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { j = iwork[indxq + i__]; work[i__] = d__[j]; - dcopy_(qsiz, &qstore[j * qstore_dim1 + 1], &c__1, &q[i__ * q_dim1 - + 1], &c__1); -/* L100: */ + dcopy_(qsiz, &qstore[j * qstore_dim1 + 1], &c__1, &q[i__ * q_dim1 + 1], &c__1); } dcopy_(n, &work[1], &c__1, &d__[1], &c__1); } else if (*icompq == 2) { @@ -504,7 +214,6 @@ L80: j = iwork[indxq + i__]; work[i__] = d__[j]; dcopy_(n, &q[j * q_dim1 + 1], &c__1, &work[*n * i__ + 1], &c__1); -/* L110: */ } dcopy_(n, &work[1], &c__1, &d__[1], &c__1); dlacpy_((char *)"A", n, n, &work[*n + 1], n, &q[q_offset], ldq, (ftnlen)1); @@ -513,22 +222,15 @@ L80: for (i__ = 1; i__ <= i__1; ++i__) { j = iwork[indxq + i__]; work[i__] = d__[j]; -/* L120: */ } dcopy_(n, &work[1], &c__1, &d__[1], &c__1); } goto L140; - L130: *info = submat * (*n + 1) + submat + matsiz - 1; - L140: return 0; - -/* End of DLAED0 */ - -} /* dlaed0_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlaed1.cpp b/lib/linalg/dlaed1.cpp index ff6c537c7c..2d40bdfcd8 100644 --- a/lib/linalg/dlaed1.cpp +++ b/lib/linalg/dlaed1.cpp @@ -1,237 +1,26 @@ -/* fortran/dlaed1.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static integer c_n1 = -1; - -/* > \brief \b DLAED1 used by DSTEDC. Computes the updated eigensystem of a diagonal matrix after modification - by a rank-one symmetric matrix. Used when the original matrix is tridiagonal. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLAED1 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLAED1( N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK, */ -/* INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER CUTPNT, INFO, LDQ, N */ -/* DOUBLE PRECISION RHO */ -/* .. */ -/* .. Array Arguments .. */ -/* INTEGER INDXQ( * ), IWORK( * ) */ -/* DOUBLE PRECISION D( * ), Q( LDQ, * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLAED1 computes the updated eigensystem of a diagonal */ -/* > matrix after modification by a rank-one symmetric matrix. This */ -/* > routine is used only for the eigenproblem which requires all */ -/* > eigenvalues and eigenvectors of a tridiagonal matrix. DLAED7 handles */ -/* > the case in which eigenvalues only or eigenvalues and eigenvectors */ -/* > of a full symmetric matrix (which was reduced to tridiagonal form) */ -/* > are desired. */ -/* > */ -/* > T = Q(in) ( D(in) + RHO * Z*Z**T ) Q**T(in) = Q(out) * D(out) * Q**T(out) */ -/* > */ -/* > where Z = Q**T*u, u is a vector of length N with ones in the */ -/* > CUTPNT and CUTPNT + 1 th elements and zeros elsewhere. */ -/* > */ -/* > The eigenvectors of the original matrix are stored in Q, and the */ -/* > eigenvalues are in D. The algorithm consists of three stages: */ -/* > */ -/* > The first stage consists of deflating the size of the problem */ -/* > when there are multiple eigenvalues or if there is a zero in */ -/* > the Z vector. For each such occurrence the dimension of the */ -/* > secular equation problem is reduced by one. This stage is */ -/* > performed by the routine DLAED2. */ -/* > */ -/* > The second stage consists of calculating the updated */ -/* > eigenvalues. This is done by finding the roots of the secular */ -/* > equation via the routine DLAED4 (as called by DLAED3). */ -/* > This routine also calculates the eigenvectors of the current */ -/* > problem. */ -/* > */ -/* > The final stage consists of computing the updated eigenvectors */ -/* > directly using the updated eigenvalues. The eigenvectors for */ -/* > the current problem are multiplied with the eigenvectors from */ -/* > the overall problem. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The dimension of the symmetric tridiagonal matrix. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension (N) */ -/* > On entry, the eigenvalues of the rank-1-perturbed matrix. */ -/* > On exit, the eigenvalues of the repaired matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] Q */ -/* > \verbatim */ -/* > Q is DOUBLE PRECISION array, dimension (LDQ,N) */ -/* > On entry, the eigenvectors of the rank-1-perturbed matrix. */ -/* > On exit, the eigenvectors of the repaired tridiagonal matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDQ */ -/* > \verbatim */ -/* > LDQ is INTEGER */ -/* > The leading dimension of the array Q. LDQ >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] INDXQ */ -/* > \verbatim */ -/* > INDXQ is INTEGER array, dimension (N) */ -/* > On entry, the permutation which separately sorts the two */ -/* > subproblems in D into ascending order. */ -/* > On exit, the permutation which will reintegrate the */ -/* > subproblems back into sorted order, */ -/* > i.e. D( INDXQ( I = 1, N ) ) will be in ascending order. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] RHO */ -/* > \verbatim */ -/* > RHO is DOUBLE PRECISION */ -/* > The subdiagonal entry used to create the rank-1 modification. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] CUTPNT */ -/* > \verbatim */ -/* > CUTPNT is INTEGER */ -/* > The location of the last eigenvalue in the leading sub-matrix. */ -/* > min(1,N) <= CUTPNT <= N/2. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (4*N + N**2) */ -/* > \endverbatim */ -/* > */ -/* > \param[out] IWORK */ -/* > \verbatim */ -/* > IWORK is INTEGER array, dimension (4*N) */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit. */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ -/* > > 0: if INFO = 1, an eigenvalue did not converge */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup auxOTHERcomputational */ - -/* > \par Contributors: */ -/* ================== */ -/* > */ -/* > Jeff Rutter, Computer Science Division, University of California */ -/* > at Berkeley, USA \n */ -/* > Modified by Francoise Tisseur, University of Tennessee */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dlaed1_(integer *n, doublereal *d__, doublereal *q, - integer *ldq, integer *indxq, doublereal *rho, integer *cutpnt, - doublereal *work, integer *iwork, integer *info) +int dlaed1_(integer *n, doublereal *d__, doublereal *q, integer *ldq, integer *indxq, + doublereal *rho, integer *cutpnt, doublereal *work, integer *iwork, integer *info) { - /* System generated locals */ integer q_dim1, q_offset, i__1, i__2; - - /* Local variables */ integer i__, k, n1, n2, is, iw, iz, iq2, zpp1, indx, indxc; - extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, - doublereal *, integer *); + extern int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *); integer indxp; - extern /* Subroutine */ int dlaed2_(integer *, integer *, integer *, - doublereal *, doublereal *, integer *, integer *, doublereal *, - doublereal *, doublereal *, doublereal *, doublereal *, integer *, - integer *, integer *, integer *, integer *), dlaed3_(integer *, - integer *, integer *, doublereal *, doublereal *, integer *, - doublereal *, doublereal *, doublereal *, integer *, integer *, - doublereal *, doublereal *, integer *); + extern int dlaed2_(integer *, integer *, integer *, doublereal *, doublereal *, integer *, + integer *, doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, integer *, integer *, integer *, integer *, integer *), + dlaed3_(integer *, integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, doublereal *, doublereal *, integer *, integer *, doublereal *, + doublereal *, integer *); integer idlmda; - extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *, - integer *, integer *, integer *), xerbla_(char *, integer *, - ftnlen); + extern int dlamrg_(integer *, integer *, doublereal *, integer *, integer *, integer *), + xerbla_(char *, integer *, ftnlen); integer coltyp; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ --d__; q_dim1 = *ldq; q_offset = 1 + q_dim1; @@ -239,18 +28,14 @@ f"> */ --indxq; --work; --iwork; - - /* Function Body */ *info = 0; - if (*n < 0) { *info = -1; - } else if (*ldq < max(1,*n)) { + } else if (*ldq < max(1, *n)) { *info = -4; - } else /* if(complicated condition) */ { -/* Computing MIN */ + } else { i__1 = 1, i__2 = *n / 2; - if (min(i__1,i__2) > *cutpnt || *n / 2 < *cutpnt) { + if (min(i__1, i__2) > *cutpnt || *n / 2 < *cutpnt) { *info = -7; } } @@ -259,60 +44,35 @@ f"> */ xerbla_((char *)"DLAED1", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*n == 0) { return 0; } - -/* The following values are integer pointers which indicate */ -/* the portion of the workspace */ -/* used by a particular array in DLAED2 and DLAED3. */ - iz = 1; idlmda = iz + *n; iw = idlmda + *n; iq2 = iw + *n; - indx = 1; indxc = indx + *n; coltyp = indxc + *n; indxp = coltyp + *n; - - -/* Form the z-vector which consists of the last row of Q_1 and the */ -/* first row of Q_2. */ - dcopy_(cutpnt, &q[*cutpnt + q_dim1], ldq, &work[iz], &c__1); zpp1 = *cutpnt + 1; i__1 = *n - *cutpnt; dcopy_(&i__1, &q[zpp1 + zpp1 * q_dim1], ldq, &work[iz + *cutpnt], &c__1); - -/* Deflate eigenvalues. */ - - dlaed2_(&k, n, cutpnt, &d__[1], &q[q_offset], ldq, &indxq[1], rho, &work[ - iz], &work[idlmda], &work[iw], &work[iq2], &iwork[indx], &iwork[ - indxc], &iwork[indxp], &iwork[coltyp], info); - + dlaed2_(&k, n, cutpnt, &d__[1], &q[q_offset], ldq, &indxq[1], rho, &work[iz], &work[idlmda], + &work[iw], &work[iq2], &iwork[indx], &iwork[indxc], &iwork[indxp], &iwork[coltyp], + info); if (*info != 0) { goto L20; } - -/* Solve Secular Equation. */ - if (k != 0) { - is = (iwork[coltyp] + iwork[coltyp + 1]) * *cutpnt + (iwork[coltyp + - 1] + iwork[coltyp + 2]) * (*n - *cutpnt) + iq2; - dlaed3_(&k, n, cutpnt, &d__[1], &q[q_offset], ldq, rho, &work[idlmda], - &work[iq2], &iwork[indxc], &iwork[coltyp], &work[iw], &work[ - is], info); + is = (iwork[coltyp] + iwork[coltyp + 1]) * *cutpnt + + (iwork[coltyp + 1] + iwork[coltyp + 2]) * (*n - *cutpnt) + iq2; + dlaed3_(&k, n, cutpnt, &d__[1], &q[q_offset], ldq, rho, &work[idlmda], &work[iq2], + &iwork[indxc], &iwork[coltyp], &work[iw], &work[is], info); if (*info != 0) { goto L20; } - -/* Prepare the INDXQ sorting permutation. */ - n1 = k; n2 = *n - k; dlamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &indxq[1]); @@ -320,17 +80,11 @@ f"> */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { indxq[i__] = i__; -/* L10: */ } } - L20: return 0; - -/* End of DLAED1 */ - -} /* dlaed1_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlaed2.cpp b/lib/linalg/dlaed2.cpp index c56d856171..4f0461bab9 100644 --- a/lib/linalg/dlaed2.cpp +++ b/lib/linalg/dlaed2.cpp @@ -1,301 +1,34 @@ -/* fortran/dlaed2.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static doublereal c_b3 = -1.; static integer c__1 = 1; - -/* > \brief \b DLAED2 used by DSTEDC. Merges eigenvalues and deflates secular equation. Used when the original - matrix is tridiagonal. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLAED2 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLAED2( K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W, */ -/* Q2, INDX, INDXC, INDXP, COLTYP, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INFO, K, LDQ, N, N1 */ -/* DOUBLE PRECISION RHO */ -/* .. */ -/* .. Array Arguments .. */ -/* INTEGER COLTYP( * ), INDX( * ), INDXC( * ), INDXP( * ), */ -/* $ INDXQ( * ) */ -/* DOUBLE PRECISION D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( * ), */ -/* $ W( * ), Z( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLAED2 merges the two sets of eigenvalues together into a single */ -/* > sorted set. Then it tries to deflate the size of the problem. */ -/* > There are two ways in which deflation can occur: when two or more */ -/* > eigenvalues are close together or if there is a tiny entry in the */ -/* > Z vector. For each such occurrence the order of the related secular */ -/* > equation problem is reduced by one. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[out] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > The number of non-deflated eigenvalues, and the order of the */ -/* > related secular equation. 0 <= K <=N. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The dimension of the symmetric tridiagonal matrix. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N1 */ -/* > \verbatim */ -/* > N1 is INTEGER */ -/* > The location of the last eigenvalue in the leading sub-matrix. */ -/* > min(1,N) <= N1 <= N/2. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension (N) */ -/* > On entry, D contains the eigenvalues of the two submatrices to */ -/* > be combined. */ -/* > On exit, D contains the trailing (N-K) updated eigenvalues */ -/* > (those which were deflated) sorted into increasing order. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] Q */ -/* > \verbatim */ -/* > Q is DOUBLE PRECISION array, dimension (LDQ, N) */ -/* > On entry, Q contains the eigenvectors of two submatrices in */ -/* > the two square blocks with corners at (1,1), (N1,N1) */ -/* > and (N1+1, N1+1), (N,N). */ -/* > On exit, Q contains the trailing (N-K) updated eigenvectors */ -/* > (those which were deflated) in its last N-K columns. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDQ */ -/* > \verbatim */ -/* > LDQ is INTEGER */ -/* > The leading dimension of the array Q. LDQ >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] INDXQ */ -/* > \verbatim */ -/* > INDXQ is INTEGER array, dimension (N) */ -/* > The permutation which separately sorts the two sub-problems */ -/* > in D into ascending order. Note that elements in the second */ -/* > half of this permutation must first have N1 added to their */ -/* > values. Destroyed on exit. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] RHO */ -/* > \verbatim */ -/* > RHO is DOUBLE PRECISION */ -/* > On entry, the off-diagonal element associated with the rank-1 */ -/* > cut which originally split the two submatrices which are now */ -/* > being recombined. */ -/* > On exit, RHO has been modified to the value required by */ -/* > DLAED3. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] Z */ -/* > \verbatim */ -/* > Z is DOUBLE PRECISION array, dimension (N) */ -/* > On entry, Z contains the updating vector (the last */ -/* > row of the first sub-eigenvector matrix and the first row of */ -/* > the second sub-eigenvector matrix). */ -/* > On exit, the contents of Z have been destroyed by the updating */ -/* > process. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] DLAMDA */ -/* > \verbatim */ -/* > DLAMDA is DOUBLE PRECISION array, dimension (N) */ -/* > A copy of the first K eigenvalues which will be used by */ -/* > DLAED3 to form the secular equation. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] W */ -/* > \verbatim */ -/* > W is DOUBLE PRECISION array, dimension (N) */ -/* > The first k values of the final deflation-altered z-vector */ -/* > which will be passed to DLAED3. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] Q2 */ -/* > \verbatim */ -/* > Q2 is DOUBLE PRECISION array, dimension (N1**2+(N-N1)**2) */ -/* > A copy of the first K eigenvectors which will be used by */ -/* > DLAED3 in a matrix multiply (DGEMM) to solve for the new */ -/* > eigenvectors. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INDX */ -/* > \verbatim */ -/* > INDX is INTEGER array, dimension (N) */ -/* > The permutation used to sort the contents of DLAMDA into */ -/* > ascending order. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INDXC */ -/* > \verbatim */ -/* > INDXC is INTEGER array, dimension (N) */ -/* > The permutation used to arrange the columns of the deflated */ -/* > Q matrix into three groups: the first group contains non-zero */ -/* > elements only at and above N1, the second contains */ -/* > non-zero elements only below N1, and the third is dense. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INDXP */ -/* > \verbatim */ -/* > INDXP is INTEGER array, dimension (N) */ -/* > The permutation used to place deflated values of D at the end */ -/* > of the array. INDXP(1:K) points to the nondeflated D-values */ -/* > and INDXP(K+1:N) points to the deflated eigenvalues. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] COLTYP */ -/* > \verbatim */ -/* > COLTYP is INTEGER array, dimension (N) */ -/* > During execution, a label which will indicate which of the */ -/* > following types a column in the Q2 matrix is: */ -/* > 1 : non-zero in the upper half only; */ -/* > 2 : dense; */ -/* > 3 : non-zero in the lower half only; */ -/* > 4 : deflated. */ -/* > On exit, COLTYP(i) is the number of columns of type i, */ -/* > for i=1 to 4 only. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit. */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup auxOTHERcomputational */ - -/* > \par Contributors: */ -/* ================== */ -/* > */ -/* > Jeff Rutter, Computer Science Division, University of California */ -/* > at Berkeley, USA \n */ -/* > Modified by Francoise Tisseur, University of Tennessee */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dlaed2_(integer *k, integer *n, integer *n1, doublereal * - d__, doublereal *q, integer *ldq, integer *indxq, doublereal *rho, - doublereal *z__, doublereal *dlamda, doublereal *w, doublereal *q2, - integer *indx, integer *indxc, integer *indxp, integer *coltyp, - integer *info) +int dlaed2_(integer *k, integer *n, integer *n1, doublereal *d__, doublereal *q, integer *ldq, + integer *indxq, doublereal *rho, doublereal *z__, doublereal *dlamda, doublereal *w, + doublereal *q2, integer *indx, integer *indxc, integer *indxp, integer *coltyp, + integer *info) { - /* System generated locals */ integer q_dim1, q_offset, i__1, i__2; doublereal d__1, d__2, d__3, d__4; - - /* Builtin functions */ double sqrt(doublereal); - - /* Local variables */ doublereal c__; integer i__, j; doublereal s, t; integer k2, n2, ct, nj, pj, js, iq1, iq2, n1p1; doublereal eps, tau, tol; integer psm[4], imax, jmax; - extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, - doublereal *, integer *, doublereal *, doublereal *); + extern int drot_(integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, + doublereal *); integer ctot[4]; - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *), dcopy_(integer *, doublereal *, integer *, doublereal - *, integer *); - extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, - ftnlen); + extern int dscal_(integer *, doublereal *, doublereal *, integer *), + dcopy_(integer *, doublereal *, integer *, doublereal *, integer *); + extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, ftnlen); extern integer idamax_(integer *, doublereal *, integer *); - extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *, - integer *, integer *, integer *), dlacpy_(char *, integer *, - integer *, doublereal *, integer *, doublereal *, integer *, - ftnlen), xerbla_(char *, integer *, ftnlen); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Arrays .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ + extern int dlamrg_(integer *, integer *, doublereal *, integer *, integer *, integer *), + dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, + ftnlen), + xerbla_(char *, integer *, ftnlen); --d__; q_dim1 = *ldq; q_offset = 1 + q_dim1; @@ -309,18 +42,14 @@ f"> */ --indxc; --indxp; --coltyp; - - /* Function Body */ *info = 0; - if (*n < 0) { *info = -2; - } else if (*ldq < max(1,*n)) { + } else if (*ldq < max(1, *n)) { *info = -6; - } else /* if(complicated condition) */ { -/* Computing MIN */ + } else { i__1 = 1, i__2 = *n / 2; - if (min(i__1,i__2) > *n1 || *n / 2 < *n1) { + if (min(i__1, i__2) > *n1 || *n / 2 < *n1) { *info = -3; } } @@ -329,66 +58,35 @@ f"> */ xerbla_((char *)"DLAED2", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*n == 0) { return 0; } - n2 = *n - *n1; n1p1 = *n1 + 1; - if (*rho < 0.) { dscal_(&n2, &c_b3, &z__[n1p1], &c__1); } - -/* Normalize z so that norm(z) = 1. Since z is the concatenation of */ -/* two normalized vectors, norm2(z) = sqrt(2). */ - t = 1. / sqrt(2.); dscal_(n, &t, &z__[1], &c__1); - -/* RHO = ABS( norm(z)**2 * RHO ) */ - *rho = (d__1 = *rho * 2., abs(d__1)); - -/* Sort the eigenvalues into increasing order */ - i__1 = *n; for (i__ = n1p1; i__ <= i__1; ++i__) { indxq[i__] += *n1; -/* L10: */ } - -/* re-integrate the deflated parts from the last pass */ - i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { dlamda[i__] = d__[indxq[i__]]; -/* L20: */ } dlamrg_(n1, &n2, &dlamda[1], &c__1, &c__1, &indxc[1]); i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { indx[i__] = indxq[indxc[i__]]; -/* L30: */ } - -/* Calculate the allowable deflation tolerance */ - imax = idamax_(n, &z__[1], &c__1); jmax = idamax_(n, &d__[1], &c__1); eps = dlamch_((char *)"Epsilon", (ftnlen)7); -/* Computing MAX */ - d__3 = (d__1 = d__[jmax], abs(d__1)), d__4 = (d__2 = z__[imax], abs(d__2)) - ; - tol = eps * 8. * max(d__3,d__4); - -/* If the rank-1 modifier is small enough, no more needs to be done */ -/* except to reorganize Q so that its columns correspond with the */ -/* elements in D. */ - + d__3 = (d__1 = d__[jmax], abs(d__1)), d__4 = (d__2 = z__[imax], abs(d__2)); + tol = eps * 8. * max(d__3, d__4); if (*rho * (d__1 = z__[imax], abs(d__1)) <= tol) { *k = 0; iq2 = 1; @@ -398,40 +96,25 @@ f"> */ dcopy_(n, &q[i__ * q_dim1 + 1], &c__1, &q2[iq2], &c__1); dlamda[j] = d__[i__]; iq2 += *n; -/* L40: */ } dlacpy_((char *)"A", n, n, &q2[1], n, &q[q_offset], ldq, (ftnlen)1); dcopy_(n, &dlamda[1], &c__1, &d__[1], &c__1); goto L190; } - -/* If there are multiple eigenvalues then the problem deflates. Here */ -/* the number of equal eigenvalues are found. As each equal */ -/* eigenvalue is found, an elementary reflector is computed to rotate */ -/* the corresponding eigensubspace so that the corresponding */ -/* components of Z are zero in this new basis. */ - i__1 = *n1; for (i__ = 1; i__ <= i__1; ++i__) { coltyp[i__] = 1; -/* L50: */ } i__1 = *n; for (i__ = n1p1; i__ <= i__1; ++i__) { coltyp[i__] = 3; -/* L60: */ } - - *k = 0; k2 = *n + 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { nj = indx[j]; if (*rho * (d__1 = z__[nj], abs(d__1)) <= tol) { - -/* Deflate due to small z component. */ - --k2; coltyp[nj] = 4; indxp[k2] = nj; @@ -442,7 +125,6 @@ f"> */ pj = nj; goto L80; } -/* L70: */ } L80: ++j; @@ -451,52 +133,34 @@ L80: goto L100; } if (*rho * (d__1 = z__[nj], abs(d__1)) <= tol) { - -/* Deflate due to small z component. */ - --k2; coltyp[nj] = 4; indxp[k2] = nj; } else { - -/* Check if eigenvalues are close enough to allow deflation. */ - s = z__[pj]; c__ = z__[nj]; - -/* Find sqrt(a**2+b**2) without overflow or */ -/* destructive underflow. */ - tau = dlapy2_(&c__, &s); t = d__[nj] - d__[pj]; c__ /= tau; s = -s / tau; if ((d__1 = t * c__ * s, abs(d__1)) <= tol) { - -/* Deflation is possible. */ - z__[nj] = tau; z__[pj] = 0.; if (coltyp[nj] != coltyp[pj]) { coltyp[nj] = 2; } coltyp[pj] = 4; - drot_(n, &q[pj * q_dim1 + 1], &c__1, &q[nj * q_dim1 + 1], &c__1, & - c__, &s); -/* Computing 2nd power */ + drot_(n, &q[pj * q_dim1 + 1], &c__1, &q[nj * q_dim1 + 1], &c__1, &c__, &s); d__1 = c__; -/* Computing 2nd power */ d__2 = s; t = d__[pj] * (d__1 * d__1) + d__[nj] * (d__2 * d__2); -/* Computing 2nd power */ d__1 = s; -/* Computing 2nd power */ d__2 = c__; d__[nj] = d__[pj] * (d__1 * d__1) + d__[nj] * (d__2 * d__2); d__[pj] = t; --k2; i__ = 1; -L90: + L90: if (k2 + i__ <= *n) { if (d__[pj] < d__[indxp[k2 + i__]]) { indxp[k2 + i__ - 1] = indxp[k2 + i__]; @@ -520,42 +184,23 @@ L90: } goto L80; L100: - -/* Record the last eigenvalue. */ - ++(*k); dlamda[*k] = d__[pj]; w[*k] = z__[pj]; indxp[*k] = pj; - -/* Count up the total number of the various types of columns, then */ -/* form a permutation which positions the four column types into */ -/* four uniform groups (although one or more of these groups may be */ -/* empty). */ - for (j = 1; j <= 4; ++j) { ctot[j - 1] = 0; -/* L110: */ } i__1 = *n; for (j = 1; j <= i__1; ++j) { ct = coltyp[j]; ++ctot[ct - 1]; -/* L120: */ } - -/* PSM(*) = Position in SubMatrix (of types 1 through 4) */ - psm[0] = 1; psm[1] = ctot[0] + 1; psm[2] = psm[1] + ctot[1]; psm[3] = psm[2] + ctot[2]; *k = *n - ctot[3]; - -/* Fill out the INDXC array so that the permutation which it induces */ -/* will place all type-1 columns first, all type-2 columns next, */ -/* then all type-3's, and finally all type-4's. */ - i__1 = *n; for (j = 1; j <= i__1; ++j) { js = indxp[j]; @@ -563,14 +208,7 @@ L100: indx[psm[ct - 1]] = js; indxc[psm[ct - 1]] = j; ++psm[ct - 1]; -/* L130: */ } - -/* Sort the eigenvalues and corresponding eigenvectors into DLAMDA */ -/* and Q2 respectively. The eigenvalues/vectors which were not */ -/* deflated go into the first K slots of DLAMDA and Q2 respectively, */ -/* while those which were deflated go into the last N - K slots. */ - i__ = 1; iq1 = 1; iq2 = (ctot[0] + ctot[1]) * *n1 + 1; @@ -581,9 +219,7 @@ L100: z__[i__] = d__[js]; ++i__; iq1 += *n1; -/* L140: */ } - i__1 = ctot[1]; for (j = 1; j <= i__1; ++j) { js = indx[i__]; @@ -593,9 +229,7 @@ L100: ++i__; iq1 += *n1; iq2 += n2; -/* L150: */ } - i__1 = ctot[2]; for (j = 1; j <= i__1; ++j) { js = indx[i__]; @@ -603,9 +237,7 @@ L100: z__[i__] = d__[js]; ++i__; iq2 += n2; -/* L160: */ } - iq1 = iq2; i__1 = ctot[3]; for (j = 1; j <= i__1; ++j) { @@ -614,33 +246,18 @@ L100: iq2 += *n; z__[i__] = d__[js]; ++i__; -/* L170: */ } - -/* The deflated eigenvalues and their corresponding vectors go back */ -/* into the last N - K slots of D and Q respectively. */ - if (*k < *n) { - dlacpy_((char *)"A", n, &ctot[3], &q2[iq1], n, &q[(*k + 1) * q_dim1 + 1], ldq, - (ftnlen)1); + dlacpy_((char *)"A", n, &ctot[3], &q2[iq1], n, &q[(*k + 1) * q_dim1 + 1], ldq, (ftnlen)1); i__1 = *n - *k; dcopy_(&i__1, &z__[*k + 1], &c__1, &d__[*k + 1], &c__1); } - -/* Copy CTOT into COLTYP for referencing in DLAED3. */ - for (j = 1; j <= 4; ++j) { coltyp[j] = ctot[j - 1]; -/* L180: */ } - L190: return 0; - -/* End of DLAED2 */ - -} /* dlaed2_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlaed3.cpp b/lib/linalg/dlaed3.cpp index 5c7d2a8596..926b0ecd7a 100644 --- a/lib/linalg/dlaed3.cpp +++ b/lib/linalg/dlaed3.cpp @@ -1,268 +1,32 @@ -/* fortran/dlaed3.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static doublereal c_b22 = 1.; static doublereal c_b23 = 0.; - -/* > \brief \b DLAED3 used by DSTEDC. Finds the roots of the secular equation and updates the eigenvectors. Us -ed when the original matrix is tridiagonal. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLAED3 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLAED3( K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX, */ -/* CTOT, W, S, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INFO, K, LDQ, N, N1 */ -/* DOUBLE PRECISION RHO */ -/* .. */ -/* .. Array Arguments .. */ -/* INTEGER CTOT( * ), INDX( * ) */ -/* DOUBLE PRECISION D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( * ), */ -/* $ S( * ), W( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLAED3 finds the roots of the secular equation, as defined by the */ -/* > values in D, W, and RHO, between 1 and K. It makes the */ -/* > appropriate calls to DLAED4 and then updates the eigenvectors by */ -/* > multiplying the matrix of eigenvectors of the pair of eigensystems */ -/* > being combined by the matrix of eigenvectors of the K-by-K system */ -/* > which is solved here. */ -/* > */ -/* > This code makes very mild assumptions about floating point */ -/* > arithmetic. It will work on machines with a guard digit in */ -/* > add/subtract, or on those binary machines without guard digits */ -/* > which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. */ -/* > It could conceivably fail on hexadecimal or decimal machines */ -/* > without guard digits, but we know of none. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > The number of terms in the rational function to be solved by */ -/* > DLAED4. K >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of rows and columns in the Q matrix. */ -/* > N >= K (deflation may result in N>K). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N1 */ -/* > \verbatim */ -/* > N1 is INTEGER */ -/* > The location of the last eigenvalue in the leading submatrix. */ -/* > min(1,N) <= N1 <= N/2. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension (N) */ -/* > D(I) contains the updated eigenvalues for */ -/* > 1 <= I <= K. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] Q */ -/* > \verbatim */ -/* > Q is DOUBLE PRECISION array, dimension (LDQ,N) */ -/* > Initially the first K columns are used as workspace. */ -/* > On output the columns 1 to K contain */ -/* > the updated eigenvectors. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDQ */ -/* > \verbatim */ -/* > LDQ is INTEGER */ -/* > The leading dimension of the array Q. LDQ >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] RHO */ -/* > \verbatim */ -/* > RHO is DOUBLE PRECISION */ -/* > The value of the parameter in the rank one update equation. */ -/* > RHO >= 0 required. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] DLAMDA */ -/* > \verbatim */ -/* > DLAMDA is DOUBLE PRECISION array, dimension (K) */ -/* > The first K elements of this array contain the old roots */ -/* > of the deflated updating problem. These are the poles */ -/* > of the secular equation. May be changed on output by */ -/* > having lowest order bit set to zero on Cray X-MP, Cray Y-MP, */ -/* > Cray-2, or Cray C-90, as described above. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] Q2 */ -/* > \verbatim */ -/* > Q2 is DOUBLE PRECISION array, dimension (LDQ2*N) */ -/* > The first K columns of this matrix contain the non-deflated */ -/* > eigenvectors for the split problem. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INDX */ -/* > \verbatim */ -/* > INDX is INTEGER array, dimension (N) */ -/* > The permutation used to arrange the columns of the deflated */ -/* > Q matrix into three groups (see DLAED2). */ -/* > The rows of the eigenvectors found by DLAED4 must be likewise */ -/* > permuted before the matrix multiply can take place. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] CTOT */ -/* > \verbatim */ -/* > CTOT is INTEGER array, dimension (4) */ -/* > A count of the total number of the various types of columns */ -/* > in Q, as described in INDX. The fourth column type is any */ -/* > column which has been deflated. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] W */ -/* > \verbatim */ -/* > W is DOUBLE PRECISION array, dimension (K) */ -/* > The first K elements of this array contain the components */ -/* > of the deflation-adjusted updating vector. Destroyed on */ -/* > output. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] S */ -/* > \verbatim */ -/* > S is DOUBLE PRECISION array, dimension (N1 + 1)*K */ -/* > Will contain the eigenvectors of the repaired matrix which */ -/* > will be multiplied by the previously accumulated eigenvectors */ -/* > to update the system. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit. */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ -/* > > 0: if INFO = 1, an eigenvalue did not converge */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup auxOTHERcomputational */ - -/* > \par Contributors: */ -/* ================== */ -/* > */ -/* > Jeff Rutter, Computer Science Division, University of California */ -/* > at Berkeley, USA \n */ -/* > Modified by Francoise Tisseur, University of Tennessee */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dlaed3_(integer *k, integer *n, integer *n1, doublereal * - d__, doublereal *q, integer *ldq, doublereal *rho, doublereal *dlamda, - doublereal *q2, integer *indx, integer *ctot, doublereal *w, - doublereal *s, integer *info) +int dlaed3_(integer *k, integer *n, integer *n1, doublereal *d__, doublereal *q, integer *ldq, + doublereal *rho, doublereal *dlamda, doublereal *q2, integer *indx, integer *ctot, + doublereal *w, doublereal *s, integer *info) { - /* System generated locals */ integer q_dim1, q_offset, i__1, i__2; doublereal d__1; - - /* Builtin functions */ double sqrt(doublereal), d_lmp_sign(doublereal *, doublereal *); - - /* Local variables */ integer i__, j, n2, n12, ii, n23, iq2; doublereal temp; extern doublereal dnrm2_(integer *, doublereal *, integer *); - extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen), - dcopy_(integer *, doublereal *, integer *, doublereal *, integer - *), dlaed4_(integer *, integer *, doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *, integer *); + extern int dgemm_(char *, char *, integer *, integer *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, + ftnlen, ftnlen), + dcopy_(integer *, doublereal *, integer *, doublereal *, integer *), + dlaed4_(integer *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, integer *); extern doublereal dlamc3_(doublereal *, doublereal *); - extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, - doublereal *, integer *, doublereal *, integer *, ftnlen), - dlaset_(char *, integer *, integer *, doublereal *, doublereal *, - doublereal *, integer *, ftnlen), xerbla_(char *, integer *, - ftnlen); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ + extern int dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, + integer *, ftnlen), + dlaset_(char *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, + ftnlen), + xerbla_(char *, integer *, ftnlen); --d__; q_dim1 = *ldq; q_offset = 1 + q_dim1; @@ -273,15 +37,12 @@ f"> */ --ctot; --w; --s; - - /* Function Body */ *info = 0; - if (*k < 0) { *info = -1; } else if (*n < *k) { *info = -2; - } else if (*ldq < max(1,*n)) { + } else if (*ldq < max(1, *n)) { *info = -6; } if (*info != 0) { @@ -289,49 +50,20 @@ f"> */ xerbla_((char *)"DLAED3", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*k == 0) { return 0; } - -/* Modify values DLAMDA(i) to make sure all DLAMDA(i)-DLAMDA(j) can */ -/* be computed with high relative accuracy (barring over/underflow). */ -/* This is a problem on machines without a guard digit in */ -/* add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2). */ -/* The following code replaces DLAMDA(I) by 2*DLAMDA(I)-DLAMDA(I), */ -/* which on any of these machines zeros out the bottommost */ -/* bit of DLAMDA(I) if it is 1; this makes the subsequent */ -/* subtractions DLAMDA(I)-DLAMDA(J) unproblematic when cancellation */ -/* occurs. On binary machines with a guard digit (almost all */ -/* machines) it does not change DLAMDA(I) at all. On hexadecimal */ -/* and decimal machines with a guard digit, it slightly */ -/* changes the bottommost bits of DLAMDA(I). It does not account */ -/* for hexadecimal or decimal machines without guard digits */ -/* (we know of none). We use a subroutine call to compute */ -/* 2*DLAMBDA(I) to prevent optimizing compilers from eliminating */ -/* this code. */ - i__1 = *k; for (i__ = 1; i__ <= i__1; ++i__) { dlamda[i__] = dlamc3_(&dlamda[i__], &dlamda[i__]) - dlamda[i__]; -/* L10: */ } - i__1 = *k; for (j = 1; j <= i__1; ++j) { - dlaed4_(k, &j, &dlamda[1], &w[1], &q[j * q_dim1 + 1], rho, &d__[j], - info); - -/* If the zero finder fails, the computation is terminated. */ - + dlaed4_(k, &j, &dlamda[1], &w[1], &q[j * q_dim1 + 1], rho, &d__[j], info); if (*info != 0) { goto L120; } -/* L20: */ } - if (*k == 1) { goto L110; } @@ -344,17 +76,10 @@ f"> */ q[j * q_dim1 + 1] = w[ii]; ii = indx[2]; q[j * q_dim1 + 2] = w[ii]; -/* L30: */ } goto L110; } - -/* Compute updated W. */ - dcopy_(k, &w[1], &c__1, &s[1], &c__1); - -/* Initialize W(I) = Q(I,I) */ - i__1 = *ldq + 1; dcopy_(k, &q[q_offset], &i__1, &w[1], &c__1); i__1 = *k; @@ -362,76 +87,52 @@ f"> */ i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]); -/* L40: */ } i__2 = *k; for (i__ = j + 1; i__ <= i__2; ++i__) { w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]); -/* L50: */ } -/* L60: */ } i__1 = *k; for (i__ = 1; i__ <= i__1; ++i__) { d__1 = sqrt(-w[i__]); w[i__] = d_lmp_sign(&d__1, &s[i__]); -/* L70: */ } - -/* Compute eigenvectors of the modified rank-1 modification. */ - i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *k; for (i__ = 1; i__ <= i__2; ++i__) { s[i__] = w[i__] / q[i__ + j * q_dim1]; -/* L80: */ } temp = dnrm2_(k, &s[1], &c__1); i__2 = *k; for (i__ = 1; i__ <= i__2; ++i__) { ii = indx[i__]; q[i__ + j * q_dim1] = s[ii] / temp; -/* L90: */ } -/* L100: */ } - -/* Compute the updated eigenvectors. */ - L110: - n2 = *n - *n1; n12 = ctot[1] + ctot[2]; n23 = ctot[2] + ctot[3]; - - dlacpy_((char *)"A", &n23, k, &q[ctot[1] + 1 + q_dim1], ldq, &s[1], &n23, (ftnlen) - 1); + dlacpy_((char *)"A", &n23, k, &q[ctot[1] + 1 + q_dim1], ldq, &s[1], &n23, (ftnlen)1); iq2 = *n1 * n12 + 1; if (n23 != 0) { - dgemm_((char *)"N", (char *)"N", &n2, k, &n23, &c_b22, &q2[iq2], &n2, &s[1], &n23, & - c_b23, &q[*n1 + 1 + q_dim1], ldq, (ftnlen)1, (ftnlen)1); + dgemm_((char *)"N", (char *)"N", &n2, k, &n23, &c_b22, &q2[iq2], &n2, &s[1], &n23, &c_b23, + &q[*n1 + 1 + q_dim1], ldq, (ftnlen)1, (ftnlen)1); } else { - dlaset_((char *)"A", &n2, k, &c_b23, &c_b23, &q[*n1 + 1 + q_dim1], ldq, ( - ftnlen)1); + dlaset_((char *)"A", &n2, k, &c_b23, &c_b23, &q[*n1 + 1 + q_dim1], ldq, (ftnlen)1); } - dlacpy_((char *)"A", &n12, k, &q[q_offset], ldq, &s[1], &n12, (ftnlen)1); if (n12 != 0) { - dgemm_((char *)"N", (char *)"N", n1, k, &n12, &c_b22, &q2[1], n1, &s[1], &n12, &c_b23, - &q[q_offset], ldq, (ftnlen)1, (ftnlen)1); + dgemm_((char *)"N", (char *)"N", n1, k, &n12, &c_b22, &q2[1], n1, &s[1], &n12, &c_b23, &q[q_offset], ldq, + (ftnlen)1, (ftnlen)1); } else { dlaset_((char *)"A", n1, k, &c_b23, &c_b23, &q[q_dim1 + 1], ldq, (ftnlen)1); } - - L120: return 0; - -/* End of DLAED3 */ - -} /* dlaed3_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlaed4.cpp b/lib/linalg/dlaed4.cpp index ca532571dd..9bc4f35caf 100644 --- a/lib/linalg/dlaed4.cpp +++ b/lib/linalg/dlaed4.cpp @@ -1,178 +1,13 @@ -/* fortran/dlaed4.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DLAED4 used by DSTEDC. Finds a single root of the secular equation. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLAED4 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLAED4( N, I, D, Z, DELTA, RHO, DLAM, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER I, INFO, N */ -/* DOUBLE PRECISION DLAM, RHO */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION D( * ), DELTA( * ), Z( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > This subroutine computes the I-th updated eigenvalue of a symmetric */ -/* > rank-one modification to a diagonal matrix whose elements are */ -/* > given in the array d, and that */ -/* > */ -/* > D(i) < D(j) for i < j */ -/* > */ -/* > and that RHO > 0. This is arranged by the calling routine, and is */ -/* > no loss in generality. The rank-one modified system is thus */ -/* > */ -/* > diag( D ) + RHO * Z * Z_transpose. */ -/* > */ -/* > where we assume the Euclidean norm of Z is 1. */ -/* > */ -/* > The method consists of approximating the rational functions in the */ -/* > secular equation by simpler interpolating rational functions. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The length of all arrays. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] I */ -/* > \verbatim */ -/* > I is INTEGER */ -/* > The index of the eigenvalue to be computed. 1 <= I <= N. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension (N) */ -/* > The original eigenvalues. It is assumed that they are in */ -/* > order, D(I) < D(J) for I < J. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] Z */ -/* > \verbatim */ -/* > Z is DOUBLE PRECISION array, dimension (N) */ -/* > The components of the updating vector. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] DELTA */ -/* > \verbatim */ -/* > DELTA is DOUBLE PRECISION array, dimension (N) */ -/* > If N > 2, DELTA contains (D(j) - lambda_I) in its j-th */ -/* > component. If N = 1, then DELTA(1) = 1. If N = 2, see DLAED5 */ -/* > for detail. The vector DELTA contains the information necessary */ -/* > to construct the eigenvectors by DLAED3 and DLAED9. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] RHO */ -/* > \verbatim */ -/* > RHO is DOUBLE PRECISION */ -/* > The scalar in the symmetric updating formula. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] DLAM */ -/* > \verbatim */ -/* > DLAM is DOUBLE PRECISION */ -/* > The computed lambda_I, the I-th updated eigenvalue. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > > 0: if INFO = 1, the updating process failed. */ -/* > \endverbatim */ - -/* > \par Internal Parameters: */ -/* ========================= */ -/* > */ -/* > \verbatim */ -/* > Logical variable ORGATI (origin-at-i?) is used for distinguishing */ -/* > whether D(i) or D(i+1) is treated as the origin. */ -/* > */ -/* > ORGATI = .true. origin at i */ -/* > ORGATI = .false. origin at i+1 */ -/* > */ -/* > Logical variable SWTCH3 (switch-for-3-poles?) is for noting */ -/* > if we are working with THREE poles! */ -/* > */ -/* > MAXIT is the maximum number of iterations allowed for each */ -/* > eigenvalue. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup auxOTHERcomputational */ - -/* > \par Contributors: */ -/* ================== */ -/* > */ -/* > Ren-Cang Li, Computer Science Division, University of California */ -/* > at Berkeley, USA */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dlaed4_(integer *n, integer *i__, doublereal *d__, - doublereal *z__, doublereal *delta, doublereal *rho, doublereal *dlam, - integer *info) +int dlaed4_(integer *n, integer *i__, doublereal *d__, doublereal *z__, doublereal *delta, + doublereal *rho, doublereal *dlam, integer *info) { - /* System generated locals */ integer i__1; doublereal d__1; - - /* Builtin functions */ double sqrt(doublereal); - - /* Local variables */ doublereal a, b, c__; integer j; doublereal w; @@ -186,57 +21,19 @@ f"> */ doublereal temp, prew, temp1, dltlb, dltub, midpt; integer niter; logical swtch; - extern /* Subroutine */ int dlaed5_(integer *, doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *), dlaed6_(integer *, - logical *, doublereal *, doublereal *, doublereal *, doublereal *, - doublereal *, integer *); + extern int dlaed5_(integer *, doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *), + dlaed6_(integer *, logical *, doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, integer *); logical swtch3; extern doublereal dlamch_(char *, ftnlen); logical orgati; doublereal erretm, rhoinv; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. Local Arrays .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Since this routine is called in an inner loop, we do no argument */ -/* checking. */ - -/* Quick return for N=1 and 2. */ - - /* Parameter adjustments */ --delta; --z__; --d__; - - /* Function Body */ *info = 0; if (*n == 1) { - -/* Presumably, I=1 upon entry */ - *dlam = d__[1] + *rho * z__[1] * z__[1]; delta[1] = 1.; return 0; @@ -245,54 +42,31 @@ f"> */ dlaed5_(i__, &d__[1], &z__[1], &delta[1], rho, dlam); return 0; } - -/* Compute machine epsilon */ - eps = dlamch_((char *)"Epsilon", (ftnlen)7); rhoinv = 1. / *rho; - -/* The case I = N */ - if (*i__ == *n) { - -/* Initialize some basic variables */ - ii = *n - 1; niter = 1; - -/* Calculate initial guess */ - midpt = *rho / 2.; - -/* If ||Z||_2 is not one, then TEMP should be set to */ -/* RHO * ||Z||_2^2 / TWO */ - i__1 = *n; for (j = 1; j <= i__1; ++j) { delta[j] = d__[j] - d__[*i__] - midpt; -/* L10: */ } - psi = 0.; i__1 = *n - 2; for (j = 1; j <= i__1; ++j) { psi += z__[j] * z__[j] / delta[j]; -/* L20: */ } - c__ = rhoinv + psi; - w = c__ + z__[ii] * z__[ii] / delta[ii] + z__[*n] * z__[*n] / delta[* - n]; - + w = c__ + z__[ii] * z__[ii] / delta[ii] + z__[*n] * z__[*n] / delta[*n]; if (w <= 0.) { - temp = z__[*n - 1] * z__[*n - 1] / (d__[*n] - d__[*n - 1] + *rho) - + z__[*n] * z__[*n] / *rho; + temp = z__[*n - 1] * z__[*n - 1] / (d__[*n] - d__[*n - 1] + *rho) + + z__[*n] * z__[*n] / *rho; if (c__ <= temp) { tau = *rho; } else { del = d__[*n] - d__[*n - 1]; - a = -c__ * del + z__[*n - 1] * z__[*n - 1] + z__[*n] * z__[*n] - ; + a = -c__ * del + z__[*n - 1] * z__[*n - 1] + z__[*n] * z__[*n]; b = z__[*n] * z__[*n] * del; if (a < 0.) { tau = b * 2. / (sqrt(a * a + b * 4. * c__) - a); @@ -300,10 +74,6 @@ f"> */ tau = (a + sqrt(a * a + b * 4. * c__)) / (c__ * 2.); } } - -/* It can be proved that */ -/* D(N)+RHO/2 <= LAMBDA(N) < D(N)+TAU <= D(N)+RHO */ - dltlb = midpt; dltub = *rho; } else { @@ -315,22 +85,13 @@ f"> */ } else { tau = (a + sqrt(a * a + b * 4. * c__)) / (c__ * 2.); } - -/* It can be proved that */ -/* D(N) < D(N)+TAU < LAMBDA(N) < D(N)+RHO/2 */ - dltlb = 0.; dltub = midpt; } - i__1 = *n; for (j = 1; j <= i__1; ++j) { delta[j] = d__[j] - d__[*i__] - tau; -/* L30: */ } - -/* Evaluate PSI and the derivative DPSI */ - dpsi = 0.; psi = 0.; erretm = 0.; @@ -340,64 +101,36 @@ f"> */ psi += z__[j] * temp; dpsi += temp * temp; erretm += psi; -/* L40: */ } erretm = abs(erretm); - -/* Evaluate PHI and the derivative DPHI */ - temp = z__[*n] / delta[*n]; phi = z__[*n] * temp; dphi = temp * temp; - erretm = (-phi - psi) * 8. + erretm - phi + rhoinv + abs(tau) * (dpsi - + dphi); - + erretm = (-phi - psi) * 8. + erretm - phi + rhoinv + abs(tau) * (dpsi + dphi); w = rhoinv + phi + psi; - -/* Test for convergence */ - if (abs(w) <= eps * erretm) { *dlam = d__[*i__] + tau; goto L250; } - if (w <= 0.) { - dltlb = max(dltlb,tau); + dltlb = max(dltlb, tau); } else { - dltub = min(dltub,tau); + dltub = min(dltub, tau); } - -/* Calculate the new step */ - ++niter; c__ = w - delta[*n - 1] * dpsi - delta[*n] * dphi; - a = (delta[*n - 1] + delta[*n]) * w - delta[*n - 1] * delta[*n] * ( - dpsi + dphi); + a = (delta[*n - 1] + delta[*n]) * w - delta[*n - 1] * delta[*n] * (dpsi + dphi); b = delta[*n - 1] * delta[*n] * w; if (c__ < 0.) { c__ = abs(c__); } if (c__ == 0.) { -/* ETA = B/A */ -/* ETA = RHO - TAU */ -/* ETA = DLTUB - TAU */ - -/* Update proposed by Li, Ren-Cang: */ eta = -w / (dpsi + dphi); } else if (a >= 0.) { - eta = (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (c__ - * 2.); + eta = (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (c__ * 2.); } else { - eta = b * 2. / (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1))) - ); + eta = b * 2. / (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))); } - -/* Note, eta should be positive if w is negative, and */ -/* eta should be negative otherwise. However, */ -/* if for some reason caused by roundoff, eta*w > 0, */ -/* we simply use one Newton step instead. This way */ -/* will guarantee eta*w < 0. */ - if (w * eta > 0.) { eta = -w / (dpsi + dphi); } @@ -412,13 +145,8 @@ f"> */ i__1 = *n; for (j = 1; j <= i__1; ++j) { delta[j] -= eta; -/* L50: */ } - tau += eta; - -/* Evaluate PSI and the derivative DPSI */ - dpsi = 0.; psi = 0.; erretm = 0.; @@ -428,59 +156,32 @@ f"> */ psi += z__[j] * temp; dpsi += temp * temp; erretm += psi; -/* L60: */ } erretm = abs(erretm); - -/* Evaluate PHI and the derivative DPHI */ - temp = z__[*n] / delta[*n]; phi = z__[*n] * temp; dphi = temp * temp; - erretm = (-phi - psi) * 8. + erretm - phi + rhoinv + abs(tau) * (dpsi - + dphi); - + erretm = (-phi - psi) * 8. + erretm - phi + rhoinv + abs(tau) * (dpsi + dphi); w = rhoinv + phi + psi; - -/* Main loop to update the values of the array DELTA */ - iter = niter + 1; - for (niter = iter; niter <= 30; ++niter) { - -/* Test for convergence */ - if (abs(w) <= eps * erretm) { *dlam = d__[*i__] + tau; goto L250; } - if (w <= 0.) { - dltlb = max(dltlb,tau); + dltlb = max(dltlb, tau); } else { - dltub = min(dltub,tau); + dltub = min(dltub, tau); } - -/* Calculate the new step */ - c__ = w - delta[*n - 1] * dpsi - delta[*n] * dphi; - a = (delta[*n - 1] + delta[*n]) * w - delta[*n - 1] * delta[*n] * - (dpsi + dphi); + a = (delta[*n - 1] + delta[*n]) * w - delta[*n - 1] * delta[*n] * (dpsi + dphi); b = delta[*n - 1] * delta[*n] * w; if (a >= 0.) { - eta = (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / ( - c__ * 2.); + eta = (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (c__ * 2.); } else { - eta = b * 2. / (a - sqrt((d__1 = a * a - b * 4. * c__, abs( - d__1)))); + eta = b * 2. / (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))); } - -/* Note, eta should be positive if w is negative, and */ -/* eta should be negative otherwise. However, */ -/* if for some reason caused by roundoff, eta*w > 0, */ -/* we simply use one Newton step instead. This way */ -/* will guarantee eta*w < 0. */ - if (w * eta > 0.) { eta = -w / (dpsi + dphi); } @@ -495,13 +196,8 @@ f"> */ i__1 = *n; for (j = 1; j <= i__1; ++j) { delta[j] -= eta; -/* L70: */ } - tau += eta; - -/* Evaluate PSI and the derivative DPSI */ - dpsi = 0.; psi = 0.; erretm = 0.; @@ -511,113 +207,70 @@ f"> */ psi += z__[j] * temp; dpsi += temp * temp; erretm += psi; -/* L80: */ } erretm = abs(erretm); - -/* Evaluate PHI and the derivative DPHI */ - temp = z__[*n] / delta[*n]; phi = z__[*n] * temp; dphi = temp * temp; - erretm = (-phi - psi) * 8. + erretm - phi + rhoinv + abs(tau) * ( - dpsi + dphi); - + erretm = (-phi - psi) * 8. + erretm - phi + rhoinv + abs(tau) * (dpsi + dphi); w = rhoinv + phi + psi; -/* L90: */ } - -/* Return with INFO = 1, NITER = MAXIT and not converged */ - *info = 1; *dlam = d__[*i__] + tau; goto L250; - -/* End for the case I = N */ - } else { - -/* The case for I < N */ - niter = 1; ip1 = *i__ + 1; - -/* Calculate initial guess */ - del = d__[ip1] - d__[*i__]; midpt = del / 2.; i__1 = *n; for (j = 1; j <= i__1; ++j) { delta[j] = d__[j] - d__[*i__] - midpt; -/* L100: */ } - psi = 0.; i__1 = *i__ - 1; for (j = 1; j <= i__1; ++j) { psi += z__[j] * z__[j] / delta[j]; -/* L110: */ } - phi = 0.; i__1 = *i__ + 2; for (j = *n; j >= i__1; --j) { phi += z__[j] * z__[j] / delta[j]; -/* L120: */ } c__ = rhoinv + psi + phi; - w = c__ + z__[*i__] * z__[*i__] / delta[*i__] + z__[ip1] * z__[ip1] / - delta[ip1]; - + w = c__ + z__[*i__] * z__[*i__] / delta[*i__] + z__[ip1] * z__[ip1] / delta[ip1]; if (w > 0.) { - -/* d(i)< the ith eigenvalue < (d(i)+d(i+1))/2 */ - -/* We choose d(i) as origin. */ - orgati = TRUE_; a = c__ * del + z__[*i__] * z__[*i__] + z__[ip1] * z__[ip1]; b = z__[*i__] * z__[*i__] * del; if (a > 0.) { - tau = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs( - d__1)))); + tau = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))); } else { - tau = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / ( - c__ * 2.); + tau = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (c__ * 2.); } dltlb = 0.; dltub = midpt; } else { - -/* (d(i)+d(i+1))/2 <= the ith eigenvalue < d(i+1) */ - -/* We choose d(i+1) as origin. */ - orgati = FALSE_; a = c__ * del - z__[*i__] * z__[*i__] - z__[ip1] * z__[ip1]; b = z__[ip1] * z__[ip1] * del; if (a < 0.) { - tau = b * 2. / (a - sqrt((d__1 = a * a + b * 4. * c__, abs( - d__1)))); + tau = b * 2. / (a - sqrt((d__1 = a * a + b * 4. * c__, abs(d__1)))); } else { - tau = -(a + sqrt((d__1 = a * a + b * 4. * c__, abs(d__1)))) / - (c__ * 2.); + tau = -(a + sqrt((d__1 = a * a + b * 4. * c__, abs(d__1)))) / (c__ * 2.); } dltlb = -midpt; dltub = 0.; } - if (orgati) { i__1 = *n; for (j = 1; j <= i__1; ++j) { delta[j] = d__[j] - d__[*i__] - tau; -/* L130: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { delta[j] = d__[j] - d__[ip1] - tau; -/* L140: */ } } if (orgati) { @@ -627,9 +280,6 @@ f"> */ } iim1 = ii - 1; iip1 = ii + 1; - -/* Evaluate PSI and the derivative DPSI */ - dpsi = 0.; psi = 0.; erretm = 0.; @@ -639,12 +289,8 @@ f"> */ psi += z__[j] * temp; dpsi += temp * temp; erretm += psi; -/* L150: */ } erretm = abs(erretm); - -/* Evaluate PHI and the derivative DPHI */ - dphi = 0.; phi = 0.; i__1 = iip1; @@ -653,14 +299,8 @@ f"> */ phi += z__[j] * temp; dphi += temp * temp; erretm += phi; -/* L160: */ } - w = rhoinv + phi + psi; - -/* W is the value of the secular function with */ -/* its ii-th element removed. */ - swtch3 = FALSE_; if (orgati) { if (w < 0.) { @@ -674,16 +314,11 @@ f"> */ if (ii == 1 || ii == *n) { swtch3 = FALSE_; } - temp = z__[ii] / delta[ii]; dw = dpsi + dphi + temp * temp; temp = z__[ii] * temp; w += temp; - erretm = (phi - psi) * 8. + erretm + rhoinv * 2. + abs(temp) * 3. + - abs(tau) * dw; - -/* Test for convergence */ - + erretm = (phi - psi) * 8. + erretm + rhoinv * 2. + abs(temp) * 3. + abs(tau) * dw; if (abs(w) <= eps * erretm) { if (orgati) { *dlam = d__[*i__] + tau; @@ -692,66 +327,48 @@ f"> */ } goto L250; } - if (w <= 0.) { - dltlb = max(dltlb,tau); + dltlb = max(dltlb, tau); } else { - dltub = min(dltub,tau); + dltub = min(dltub, tau); } - -/* Calculate the new step */ - ++niter; - if (! swtch3) { + if (!swtch3) { if (orgati) { -/* Computing 2nd power */ d__1 = z__[*i__] / delta[*i__]; - c__ = w - delta[ip1] * dw - (d__[*i__] - d__[ip1]) * (d__1 * - d__1); + c__ = w - delta[ip1] * dw - (d__[*i__] - d__[ip1]) * (d__1 * d__1); } else { -/* Computing 2nd power */ d__1 = z__[ip1] / delta[ip1]; - c__ = w - delta[*i__] * dw - (d__[ip1] - d__[*i__]) * (d__1 * - d__1); + c__ = w - delta[*i__] * dw - (d__[ip1] - d__[*i__]) * (d__1 * d__1); } - a = (delta[*i__] + delta[ip1]) * w - delta[*i__] * delta[ip1] * - dw; + a = (delta[*i__] + delta[ip1]) * w - delta[*i__] * delta[ip1] * dw; b = delta[*i__] * delta[ip1] * w; if (c__ == 0.) { if (a == 0.) { if (orgati) { - a = z__[*i__] * z__[*i__] + delta[ip1] * delta[ip1] * - (dpsi + dphi); + a = z__[*i__] * z__[*i__] + delta[ip1] * delta[ip1] * (dpsi + dphi); } else { - a = z__[ip1] * z__[ip1] + delta[*i__] * delta[*i__] * - (dpsi + dphi); + a = z__[ip1] * z__[ip1] + delta[*i__] * delta[*i__] * (dpsi + dphi); } } eta = b / a; } else if (a <= 0.) { - eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / ( - c__ * 2.); + eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (c__ * 2.); } else { - eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs( - d__1)))); + eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))); } } else { - -/* Interpolation using THREE most relevant poles */ - temp = rhoinv + psi + phi; if (orgati) { temp1 = z__[iim1] / delta[iim1]; temp1 *= temp1; - c__ = temp - delta[iip1] * (dpsi + dphi) - (d__[iim1] - d__[ - iip1]) * temp1; + c__ = temp - delta[iip1] * (dpsi + dphi) - (d__[iim1] - d__[iip1]) * temp1; zz[0] = z__[iim1] * z__[iim1]; zz[2] = delta[iip1] * delta[iip1] * (dpsi - temp1 + dphi); } else { temp1 = z__[iip1] / delta[iip1]; temp1 *= temp1; - c__ = temp - delta[iim1] * (dpsi + dphi) - (d__[iip1] - d__[ - iim1]) * temp1; + c__ = temp - delta[iim1] * (dpsi + dphi) - (d__[iip1] - d__[iim1]) * temp1; zz[0] = delta[iim1] * delta[iim1] * (dpsi + (dphi - temp1)); zz[2] = z__[iip1] * z__[iip1]; } @@ -761,13 +378,6 @@ f"> */ goto L250; } } - -/* Note, eta should be positive if w is negative, and */ -/* eta should be negative otherwise. However, */ -/* if for some reason caused by roundoff, eta*w > 0, */ -/* we simply use one Newton step instead. This way */ -/* will guarantee eta*w < 0. */ - if (w * eta >= 0.) { eta = -w / dw; } @@ -779,17 +389,11 @@ f"> */ eta = (dltlb - tau) / 2.; } } - prew = w; - i__1 = *n; for (j = 1; j <= i__1; ++j) { delta[j] -= eta; -/* L180: */ } - -/* Evaluate PSI and the derivative DPSI */ - dpsi = 0.; psi = 0.; erretm = 0.; @@ -799,12 +403,8 @@ f"> */ psi += z__[j] * temp; dpsi += temp * temp; erretm += psi; -/* L190: */ } erretm = abs(erretm); - -/* Evaluate PHI and the derivative DPHI */ - dphi = 0.; phi = 0.; i__1 = iip1; @@ -813,16 +413,13 @@ f"> */ phi += z__[j] * temp; dphi += temp * temp; erretm += phi; -/* L200: */ } - temp = z__[ii] / delta[ii]; dw = dpsi + dphi + temp * temp; temp = z__[ii] * temp; w = rhoinv + phi + psi + temp; - erretm = (phi - psi) * 8. + erretm + rhoinv * 2. + abs(temp) * 3. + ( - d__1 = tau + eta, abs(d__1)) * dw; - + erretm = (phi - psi) * 8. + erretm + rhoinv * 2. + abs(temp) * 3. + + (d__1 = tau + eta, abs(d__1)) * dw; swtch = FALSE_; if (orgati) { if (-w > abs(prew) / 10.) { @@ -833,17 +430,9 @@ f"> */ swtch = TRUE_; } } - tau += eta; - -/* Main loop to update the values of the array DELTA */ - iter = niter + 1; - for (niter = iter; niter <= 30; ++niter) { - -/* Test for convergence */ - if (abs(w) <= eps * erretm) { if (orgati) { *dlam = d__[*i__] + tau; @@ -852,27 +441,19 @@ f"> */ } goto L250; } - if (w <= 0.) { - dltlb = max(dltlb,tau); + dltlb = max(dltlb, tau); } else { - dltub = min(dltub,tau); + dltub = min(dltub, tau); } - -/* Calculate the new step */ - - if (! swtch3) { - if (! swtch) { + if (!swtch3) { + if (!swtch) { if (orgati) { -/* Computing 2nd power */ d__1 = z__[*i__] / delta[*i__]; - c__ = w - delta[ip1] * dw - (d__[*i__] - d__[ip1]) * ( - d__1 * d__1); + c__ = w - delta[ip1] * dw - (d__[*i__] - d__[ip1]) * (d__1 * d__1); } else { -/* Computing 2nd power */ d__1 = z__[ip1] / delta[ip1]; - c__ = w - delta[*i__] * dw - (d__[ip1] - d__[*i__]) * - (d__1 * d__1); + c__ = w - delta[*i__] * dw - (d__[ip1] - d__[*i__]) * (d__1 * d__1); } } else { temp = z__[ii] / delta[ii]; @@ -883,36 +464,27 @@ f"> */ } c__ = w - delta[*i__] * dpsi - delta[ip1] * dphi; } - a = (delta[*i__] + delta[ip1]) * w - delta[*i__] * delta[ip1] - * dw; + a = (delta[*i__] + delta[ip1]) * w - delta[*i__] * delta[ip1] * dw; b = delta[*i__] * delta[ip1] * w; if (c__ == 0.) { if (a == 0.) { - if (! swtch) { + if (!swtch) { if (orgati) { - a = z__[*i__] * z__[*i__] + delta[ip1] * - delta[ip1] * (dpsi + dphi); + a = z__[*i__] * z__[*i__] + delta[ip1] * delta[ip1] * (dpsi + dphi); } else { - a = z__[ip1] * z__[ip1] + delta[*i__] * delta[ - *i__] * (dpsi + dphi); + a = z__[ip1] * z__[ip1] + delta[*i__] * delta[*i__] * (dpsi + dphi); } } else { - a = delta[*i__] * delta[*i__] * dpsi + delta[ip1] - * delta[ip1] * dphi; + a = delta[*i__] * delta[*i__] * dpsi + delta[ip1] * delta[ip1] * dphi; } } eta = b / a; } else if (a <= 0.) { - eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) - / (c__ * 2.); + eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (c__ * 2.); } else { - eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, - abs(d__1)))); + eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))); } } else { - -/* Interpolation using THREE most relevant poles */ - temp = rhoinv + psi + phi; if (swtch) { c__ = temp - delta[iim1] * dpsi - delta[iip1] * dphi; @@ -922,34 +494,22 @@ f"> */ if (orgati) { temp1 = z__[iim1] / delta[iim1]; temp1 *= temp1; - c__ = temp - delta[iip1] * (dpsi + dphi) - (d__[iim1] - - d__[iip1]) * temp1; + c__ = temp - delta[iip1] * (dpsi + dphi) - (d__[iim1] - d__[iip1]) * temp1; zz[0] = z__[iim1] * z__[iim1]; - zz[2] = delta[iip1] * delta[iip1] * (dpsi - temp1 + - dphi); + zz[2] = delta[iip1] * delta[iip1] * (dpsi - temp1 + dphi); } else { temp1 = z__[iip1] / delta[iip1]; temp1 *= temp1; - c__ = temp - delta[iim1] * (dpsi + dphi) - (d__[iip1] - - d__[iim1]) * temp1; - zz[0] = delta[iim1] * delta[iim1] * (dpsi + (dphi - - temp1)); + c__ = temp - delta[iim1] * (dpsi + dphi) - (d__[iip1] - d__[iim1]) * temp1; + zz[0] = delta[iim1] * delta[iim1] * (dpsi + (dphi - temp1)); zz[2] = z__[iip1] * z__[iip1]; } } - dlaed6_(&niter, &orgati, &c__, &delta[iim1], zz, &w, &eta, - info); + dlaed6_(&niter, &orgati, &c__, &delta[iim1], zz, &w, &eta, info); if (*info != 0) { goto L250; } } - -/* Note, eta should be positive if w is negative, and */ -/* eta should be negative otherwise. However, */ -/* if for some reason caused by roundoff, eta*w > 0, */ -/* we simply use one Newton step instead. This way */ -/* will guarantee eta*w < 0. */ - if (w * eta >= 0.) { eta = -w / dw; } @@ -961,18 +521,12 @@ f"> */ eta = (dltlb - tau) / 2.; } } - i__1 = *n; for (j = 1; j <= i__1; ++j) { delta[j] -= eta; -/* L210: */ } - tau += eta; prew = w; - -/* Evaluate PSI and the derivative DPSI */ - dpsi = 0.; psi = 0.; erretm = 0.; @@ -982,12 +536,8 @@ f"> */ psi += z__[j] * temp; dpsi += temp * temp; erretm += psi; -/* L220: */ } erretm = abs(erretm); - -/* Evaluate PHI and the derivative DPHI */ - dphi = 0.; phi = 0.; i__1 = iip1; @@ -996,41 +546,26 @@ f"> */ phi += z__[j] * temp; dphi += temp * temp; erretm += phi; -/* L230: */ } - temp = z__[ii] / delta[ii]; dw = dpsi + dphi + temp * temp; temp = z__[ii] * temp; w = rhoinv + phi + psi + temp; - erretm = (phi - psi) * 8. + erretm + rhoinv * 2. + abs(temp) * 3. - + abs(tau) * dw; + erretm = (phi - psi) * 8. + erretm + rhoinv * 2. + abs(temp) * 3. + abs(tau) * dw; if (w * prew > 0. && abs(w) > abs(prew) / 10.) { - swtch = ! swtch; + swtch = !swtch; } - -/* L240: */ } - -/* Return with INFO = 1, NITER = MAXIT and not converged */ - *info = 1; if (orgati) { *dlam = d__[*i__] + tau; } else { *dlam = d__[ip1] + tau; } - } - L250: - return 0; - -/* End of DLAED4 */ - -} /* dlaed4_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlaed5.cpp b/lib/linalg/dlaed5.cpp index 558676d269..30671066fa 100644 --- a/lib/linalg/dlaed5.cpp +++ b/lib/linalg/dlaed5.cpp @@ -1,176 +1,22 @@ -/* fortran/dlaed5.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DLAED5 used by DSTEDC. Solves the 2-by-2 secular equation. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLAED5 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLAED5( I, D, Z, DELTA, RHO, DLAM ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER I */ -/* DOUBLE PRECISION DLAM, RHO */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION D( 2 ), DELTA( 2 ), Z( 2 ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > This subroutine computes the I-th eigenvalue of a symmetric rank-one */ -/* > modification of a 2-by-2 diagonal matrix */ -/* > */ -/* > diag( D ) + RHO * Z * transpose(Z) . */ -/* > */ -/* > The diagonal elements in the array D are assumed to satisfy */ -/* > */ -/* > D(i) < D(j) for i < j . */ -/* > */ -/* > We also assume RHO > 0 and that the Euclidean norm of the vector */ -/* > Z is one. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] I */ -/* > \verbatim */ -/* > I is INTEGER */ -/* > The index of the eigenvalue to be computed. I = 1 or I = 2. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension (2) */ -/* > The original eigenvalues. We assume D(1) < D(2). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] Z */ -/* > \verbatim */ -/* > Z is DOUBLE PRECISION array, dimension (2) */ -/* > The components of the updating vector. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] DELTA */ -/* > \verbatim */ -/* > DELTA is DOUBLE PRECISION array, dimension (2) */ -/* > The vector DELTA contains the information necessary */ -/* > to construct the eigenvectors. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] RHO */ -/* > \verbatim */ -/* > RHO is DOUBLE PRECISION */ -/* > The scalar in the symmetric updating formula. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] DLAM */ -/* > \verbatim */ -/* > DLAM is DOUBLE PRECISION */ -/* > The computed lambda_I, the I-th updated eigenvalue. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup auxOTHERcomputational */ - -/* > \par Contributors: */ -/* ================== */ -/* > */ -/* > Ren-Cang Li, Computer Science Division, University of California */ -/* > at Berkeley, USA */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dlaed5_(integer *i__, doublereal *d__, doublereal *z__, - doublereal *delta, doublereal *rho, doublereal *dlam) +int dlaed5_(integer *i__, doublereal *d__, doublereal *z__, doublereal *delta, doublereal *rho, + doublereal *dlam) { - /* System generated locals */ doublereal d__1; - - /* Builtin functions */ double sqrt(doublereal); - - /* Local variables */ doublereal b, c__, w, del, tau, temp; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - - /* Parameter adjustments */ --delta; --z__; --d__; - - /* Function Body */ del = d__[2] - d__[1]; if (*i__ == 1) { w = *rho * 2. * (z__[2] * z__[2] - z__[1] * z__[1]) / del + 1.; if (w > 0.) { b = del + *rho * (z__[1] * z__[1] + z__[2] * z__[2]); c__ = *rho * z__[1] * z__[1] * del; - -/* B > ZERO, always */ - tau = c__ * 2. / (b + sqrt((d__1 = b * b - c__ * 4., abs(d__1)))); *dlam = d__[1] + tau; delta[1] = -z__[1] / tau; @@ -191,9 +37,6 @@ f"> */ delta[1] /= temp; delta[2] /= temp; } else { - -/* Now I=2 */ - b = -del + *rho * (z__[1] * z__[1] + z__[2] * z__[2]); c__ = *rho * z__[2] * z__[2] * del; if (b > 0.) { @@ -209,11 +52,7 @@ f"> */ delta[2] /= temp; } return 0; - -/* End of DLAED5 */ - -} /* dlaed5_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlaed6.cpp b/lib/linalg/dlaed6.cpp index d884bbd67e..083046b822 100644 --- a/lib/linalg/dlaed6.cpp +++ b/lib/linalg/dlaed6.cpp @@ -1,173 +1,13 @@ -/* fortran/dlaed6.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DLAED6 used by DSTEDC. Computes one Newton step in solution of the secular equation. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLAED6 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLAED6( KNITER, ORGATI, RHO, D, Z, FINIT, TAU, INFO ) */ - -/* .. Scalar Arguments .. */ -/* LOGICAL ORGATI */ -/* INTEGER INFO, KNITER */ -/* DOUBLE PRECISION FINIT, RHO, TAU */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION D( 3 ), Z( 3 ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLAED6 computes the positive or negative root (closest to the origin) */ -/* > of */ -/* > z(1) z(2) z(3) */ -/* > f(x) = rho + --------- + ---------- + --------- */ -/* > d(1)-x d(2)-x d(3)-x */ -/* > */ -/* > It is assumed that */ -/* > */ -/* > if ORGATI = .true. the root is between d(2) and d(3); */ -/* > otherwise it is between d(1) and d(2) */ -/* > */ -/* > This routine will be called by DLAED4 when necessary. In most cases, */ -/* > the root sought is the smallest in magnitude, though it might not be */ -/* > in some extremely rare situations. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] KNITER */ -/* > \verbatim */ -/* > KNITER is INTEGER */ -/* > Refer to DLAED4 for its significance. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] ORGATI */ -/* > \verbatim */ -/* > ORGATI is LOGICAL */ -/* > If ORGATI is true, the needed root is between d(2) and */ -/* > d(3); otherwise it is between d(1) and d(2). See */ -/* > DLAED4 for further details. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] RHO */ -/* > \verbatim */ -/* > RHO is DOUBLE PRECISION */ -/* > Refer to the equation f(x) above. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension (3) */ -/* > D satisfies d(1) < d(2) < d(3). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] Z */ -/* > \verbatim */ -/* > Z is DOUBLE PRECISION array, dimension (3) */ -/* > Each of the elements in z must be positive. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] FINIT */ -/* > \verbatim */ -/* > FINIT is DOUBLE PRECISION */ -/* > The value of f at 0. It is more accurate than the one */ -/* > evaluated inside this routine (if someone wants to do */ -/* > so). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] TAU */ -/* > \verbatim */ -/* > TAU is DOUBLE PRECISION */ -/* > The root of the equation f(x). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > > 0: if INFO = 1, failure to converge */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup auxOTHERcomputational */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > 10/02/03: This version has a few statements commented out for thread */ -/* > safety (machine parameters are computed on each entry). SJH. */ -/* > */ -/* > 05/10/06: Modified from a new version of Ren-Cang Li, use */ -/* > Gragg-Thornton-Warner cubic convergent scheme for better stability. */ -/* > \endverbatim */ - -/* > \par Contributors: */ -/* ================== */ -/* > */ -/* > Ren-Cang Li, Computer Science Division, University of California */ -/* > at Berkeley, USA */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dlaed6_(integer *kniter, logical *orgati, doublereal * - rho, doublereal *d__, doublereal *z__, doublereal *finit, doublereal * - tau, integer *info) +int dlaed6_(integer *kniter, logical *orgati, doublereal *rho, doublereal *d__, doublereal *z__, + doublereal *finit, doublereal *tau, integer *info) { - /* System generated locals */ integer i__1; doublereal d__1, d__2, d__3, d__4; - - /* Builtin functions */ double sqrt(doublereal), log(doublereal), pow_lmp_di(doublereal *, integer *); - - /* Local variables */ doublereal a, b, c__, f; integer i__; doublereal fc, df, ddf, lbd, eta, ubd, eps, base; @@ -178,38 +18,9 @@ f"> */ doublereal small1, small2, sminv1, sminv2; extern doublereal dlamch_(char *, ftnlen); doublereal dscale[3], sclfac, zscale[3], erretm, sclinv; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Local Arrays .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - - /* Parameter adjustments */ --z__; --d__; - - /* Function Body */ *info = 0; - if (*orgati) { lbd = d__[2]; ubd = d__[3]; @@ -222,7 +33,6 @@ f"> */ } else { ubd = 0.; } - niter = 1; *tau = 0.; if (*kniter == 2) { @@ -237,20 +47,17 @@ f"> */ a = c__ * (d__[1] + d__[2]) + z__[1] + z__[2]; b = c__ * d__[1] * d__[2] + z__[1] * d__[2] + z__[2] * d__[1]; } -/* Computing MAX */ - d__1 = abs(a), d__2 = abs(b), d__1 = max(d__1,d__2), d__2 = abs(c__); - temp = max(d__1,d__2); + d__1 = abs(a), d__2 = abs(b), d__1 = max(d__1, d__2), d__2 = abs(c__); + temp = max(d__1, d__2); a /= temp; b /= temp; c__ /= temp; if (c__ == 0.) { *tau = b / a; } else if (a <= 0.) { - *tau = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / ( - c__ * 2.); + *tau = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (c__ * 2.); } else { - *tau = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)) - )); + *tau = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))); } if (*tau < lbd || *tau > ubd) { *tau = (lbd + ubd) / 2.; @@ -258,9 +65,9 @@ f"> */ if (d__[1] == *tau || d__[2] == *tau || d__[3] == *tau) { *tau = 0.; } else { - temp = *finit + *tau * z__[1] / (d__[1] * (d__[1] - *tau)) + *tau - * z__[2] / (d__[2] * (d__[2] - *tau)) + *tau * z__[3] / ( - d__[3] * (d__[3] - *tau)); + temp = *finit + *tau * z__[1] / (d__[1] * (d__[1] - *tau)) + + *tau * z__[2] / (d__[2] * (d__[2] - *tau)) + + *tau * z__[3] / (d__[3] * (d__[3] - *tau)); if (temp <= 0.) { lbd = *tau; } else { @@ -271,73 +78,43 @@ f"> */ } } } - -/* get machine parameters for possible scaling to avoid overflow */ - -/* modified by Sven: parameters SMALL1, SMINV1, SMALL2, */ -/* SMINV2, EPS are not SAVEd anymore between one call to the */ -/* others but recomputed at each call */ - eps = dlamch_((char *)"Epsilon", (ftnlen)7); base = dlamch_((char *)"Base", (ftnlen)4); - i__1 = (integer) (log(dlamch_((char *)"SafMin", (ftnlen)6)) / log(base) / 3.); + i__1 = (integer)(log(dlamch_((char *)"SafMin", (ftnlen)6)) / log(base) / 3.); small1 = pow_lmp_di(&base, &i__1); sminv1 = 1. / small1; small2 = small1 * small1; sminv2 = sminv1 * sminv1; - -/* Determine if scaling of inputs necessary to avoid overflow */ -/* when computing 1/TEMP**3 */ - if (*orgati) { -/* Computing MIN */ - d__3 = (d__1 = d__[2] - *tau, abs(d__1)), d__4 = (d__2 = d__[3] - * - tau, abs(d__2)); - temp = min(d__3,d__4); + d__3 = (d__1 = d__[2] - *tau, abs(d__1)), d__4 = (d__2 = d__[3] - *tau, abs(d__2)); + temp = min(d__3, d__4); } else { -/* Computing MIN */ - d__3 = (d__1 = d__[1] - *tau, abs(d__1)), d__4 = (d__2 = d__[2] - * - tau, abs(d__2)); - temp = min(d__3,d__4); + d__3 = (d__1 = d__[1] - *tau, abs(d__1)), d__4 = (d__2 = d__[2] - *tau, abs(d__2)); + temp = min(d__3, d__4); } scale = FALSE_; if (temp <= small1) { scale = TRUE_; if (temp <= small2) { - -/* Scale up by power of radix nearest 1/SAFMIN**(2/3) */ - sclfac = sminv2; sclinv = small2; } else { - -/* Scale up by power of radix nearest 1/SAFMIN**(1/3) */ - sclfac = sminv1; sclinv = small1; } - -/* Scaling up safe because D, Z, TAU scaled elsewhere to be O(1) */ - for (i__ = 1; i__ <= 3; ++i__) { dscale[i__ - 1] = d__[i__] * sclfac; zscale[i__ - 1] = z__[i__] * sclfac; -/* L10: */ } *tau *= sclfac; lbd *= sclfac; ubd *= sclfac; } else { - -/* Copy D and Z to DSCALE and ZSCALE */ - for (i__ = 1; i__ <= 3; ++i__) { dscale[i__ - 1] = d__[i__]; zscale[i__ - 1] = z__[i__]; -/* L20: */ } } - fc = 0.; df = 0.; ddf = 0.; @@ -349,10 +126,8 @@ f"> */ fc += temp1 / dscale[i__ - 1]; df += temp2; ddf += temp3; -/* L30: */ } f = *finit + *tau * fc; - if (abs(f) <= 0.) { goto L60; } @@ -361,22 +136,8 @@ f"> */ } else { ubd = *tau; } - -/* Iteration begins -- Use Gragg-Thornton-Warner cubic convergent */ -/* scheme */ - -/* It is not hard to see that */ - -/* 1) Iterations will go up monotonically */ -/* if FINIT < 0; */ - -/* 2) Iterations will go down monotonically */ -/* if FINIT > 0. */ - iter = niter + 1; - for (niter = iter; niter <= 40; ++niter) { - if (*orgati) { temp1 = dscale[1] - *tau; temp2 = dscale[2] - *tau; @@ -387,30 +148,25 @@ f"> */ a = (temp1 + temp2) * f - temp1 * temp2 * df; b = temp1 * temp2 * f; c__ = f - (temp1 + temp2) * df + temp1 * temp2 * ddf; -/* Computing MAX */ - d__1 = abs(a), d__2 = abs(b), d__1 = max(d__1,d__2), d__2 = abs(c__); - temp = max(d__1,d__2); + d__1 = abs(a), d__2 = abs(b), d__1 = max(d__1, d__2), d__2 = abs(c__); + temp = max(d__1, d__2); a /= temp; b /= temp; c__ /= temp; if (c__ == 0.) { eta = b / a; } else if (a <= 0.) { - eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (c__ - * 2.); + eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (c__ * 2.); } else { - eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1))) - ); + eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))); } if (f * eta >= 0.) { eta = -f / df; } - *tau += eta; if (*tau < lbd || *tau > ubd) { *tau = (lbd + ubd) / 2.; } - fc = 0.; erretm = 0.; df = 0.; @@ -429,12 +185,10 @@ f"> */ } else { goto L60; } -/* L40: */ } f = *finit + *tau * fc; erretm = (abs(*finit) + abs(*tau) * erretm) * 8. + abs(*tau) * df; - if (abs(f) <= eps * 4. * erretm || ubd - lbd <= eps * 4. * abs(*tau)) - { + if (abs(f) <= eps * 4. * erretm || ubd - lbd <= eps * 4. * abs(*tau)) { goto L60; } if (f <= 0.) { @@ -442,22 +196,14 @@ f"> */ } else { ubd = *tau; } -/* L50: */ } *info = 1; L60: - -/* Undo scaling */ - if (scale) { *tau *= sclinv; } return 0; - -/* End of DLAED6 */ - -} /* dlaed6_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlaed7.cpp b/lib/linalg/dlaed7.cpp index bc763aa9df..036fdeff6f 100644 --- a/lib/linalg/dlaed7.cpp +++ b/lib/linalg/dlaed7.cpp @@ -1,348 +1,38 @@ -/* fortran/dlaed7.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__2 = 2; static integer c__1 = 1; static doublereal c_b10 = 1.; static doublereal c_b11 = 0.; static integer c_n1 = -1; - -/* > \brief \b DLAED7 used by DSTEDC. Computes the updated eigensystem of a diagonal matrix after modification - by a rank-one symmetric matrix. Used when the original matrix is dense. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLAED7 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLAED7( ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, */ -/* LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR, */ -/* PERM, GIVPTR, GIVCOL, GIVNUM, WORK, IWORK, */ -/* INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER CURLVL, CURPBM, CUTPNT, ICOMPQ, INFO, LDQ, N, */ -/* $ QSIZ, TLVLS */ -/* DOUBLE PRECISION RHO */ -/* .. */ -/* .. Array Arguments .. */ -/* INTEGER GIVCOL( 2, * ), GIVPTR( * ), INDXQ( * ), */ -/* $ IWORK( * ), PERM( * ), PRMPTR( * ), QPTR( * ) */ -/* DOUBLE PRECISION D( * ), GIVNUM( 2, * ), Q( LDQ, * ), */ -/* $ QSTORE( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLAED7 computes the updated eigensystem of a diagonal */ -/* > matrix after modification by a rank-one symmetric matrix. This */ -/* > routine is used only for the eigenproblem which requires all */ -/* > eigenvalues and optionally eigenvectors of a dense symmetric matrix */ -/* > that has been reduced to tridiagonal form. DLAED1 handles */ -/* > the case in which all eigenvalues and eigenvectors of a symmetric */ -/* > tridiagonal matrix are desired. */ -/* > */ -/* > T = Q(in) ( D(in) + RHO * Z*Z**T ) Q**T(in) = Q(out) * D(out) * Q**T(out) */ -/* > */ -/* > where Z = Q**Tu, u is a vector of length N with ones in the */ -/* > CUTPNT and CUTPNT + 1 th elements and zeros elsewhere. */ -/* > */ -/* > The eigenvectors of the original matrix are stored in Q, and the */ -/* > eigenvalues are in D. The algorithm consists of three stages: */ -/* > */ -/* > The first stage consists of deflating the size of the problem */ -/* > when there are multiple eigenvalues or if there is a zero in */ -/* > the Z vector. For each such occurrence the dimension of the */ -/* > secular equation problem is reduced by one. This stage is */ -/* > performed by the routine DLAED8. */ -/* > */ -/* > The second stage consists of calculating the updated */ -/* > eigenvalues. This is done by finding the roots of the secular */ -/* > equation via the routine DLAED4 (as called by DLAED9). */ -/* > This routine also calculates the eigenvectors of the current */ -/* > problem. */ -/* > */ -/* > The final stage consists of computing the updated eigenvectors */ -/* > directly using the updated eigenvalues. The eigenvectors for */ -/* > the current problem are multiplied with the eigenvectors from */ -/* > the overall problem. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] ICOMPQ */ -/* > \verbatim */ -/* > ICOMPQ is INTEGER */ -/* > = 0: Compute eigenvalues only. */ -/* > = 1: Compute eigenvectors of original dense symmetric matrix */ -/* > also. On entry, Q contains the orthogonal matrix used */ -/* > to reduce the original matrix to tridiagonal form. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The dimension of the symmetric tridiagonal matrix. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] QSIZ */ -/* > \verbatim */ -/* > QSIZ is INTEGER */ -/* > The dimension of the orthogonal matrix used to reduce */ -/* > the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TLVLS */ -/* > \verbatim */ -/* > TLVLS is INTEGER */ -/* > The total number of merging levels in the overall divide and */ -/* > conquer tree. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] CURLVL */ -/* > \verbatim */ -/* > CURLVL is INTEGER */ -/* > The current level in the overall merge routine, */ -/* > 0 <= CURLVL <= TLVLS. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] CURPBM */ -/* > \verbatim */ -/* > CURPBM is INTEGER */ -/* > The current problem in the current level in the overall */ -/* > merge routine (counting from upper left to lower right). */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension (N) */ -/* > On entry, the eigenvalues of the rank-1-perturbed matrix. */ -/* > On exit, the eigenvalues of the repaired matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] Q */ -/* > \verbatim */ -/* > Q is DOUBLE PRECISION array, dimension (LDQ, N) */ -/* > On entry, the eigenvectors of the rank-1-perturbed matrix. */ -/* > On exit, the eigenvectors of the repaired tridiagonal matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDQ */ -/* > \verbatim */ -/* > LDQ is INTEGER */ -/* > The leading dimension of the array Q. LDQ >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INDXQ */ -/* > \verbatim */ -/* > INDXQ is INTEGER array, dimension (N) */ -/* > The permutation which will reintegrate the subproblem just */ -/* > solved back into sorted order, i.e., D( INDXQ( I = 1, N ) ) */ -/* > will be in ascending order. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] RHO */ -/* > \verbatim */ -/* > RHO is DOUBLE PRECISION */ -/* > The subdiagonal element used to create the rank-1 */ -/* > modification. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] CUTPNT */ -/* > \verbatim */ -/* > CUTPNT is INTEGER */ -/* > Contains the location of the last eigenvalue in the leading */ -/* > sub-matrix. min(1,N) <= CUTPNT <= N. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] QSTORE */ -/* > \verbatim */ -/* > QSTORE is DOUBLE PRECISION array, dimension (N**2+1) */ -/* > Stores eigenvectors of submatrices encountered during */ -/* > divide and conquer, packed together. QPTR points to */ -/* > beginning of the submatrices. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] QPTR */ -/* > \verbatim */ -/* > QPTR is INTEGER array, dimension (N+2) */ -/* > List of indices pointing to beginning of submatrices stored */ -/* > in QSTORE. The submatrices are numbered starting at the */ -/* > bottom left of the divide and conquer tree, from left to */ -/* > right and bottom to top. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] PRMPTR */ -/* > \verbatim */ -/* > PRMPTR is INTEGER array, dimension (N lg N) */ -/* > Contains a list of pointers which indicate where in PERM a */ -/* > level's permutation is stored. PRMPTR(i+1) - PRMPTR(i) */ -/* > indicates the size of the permutation and also the size of */ -/* > the full, non-deflated problem. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] PERM */ -/* > \verbatim */ -/* > PERM is INTEGER array, dimension (N lg N) */ -/* > Contains the permutations (from deflation and sorting) to be */ -/* > applied to each eigenblock. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] GIVPTR */ -/* > \verbatim */ -/* > GIVPTR is INTEGER array, dimension (N lg N) */ -/* > Contains a list of pointers which indicate where in GIVCOL a */ -/* > level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i) */ -/* > indicates the number of Givens rotations. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] GIVCOL */ -/* > \verbatim */ -/* > GIVCOL is INTEGER array, dimension (2, N lg N) */ -/* > Each pair of numbers indicates a pair of columns to take place */ -/* > in a Givens rotation. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] GIVNUM */ -/* > \verbatim */ -/* > GIVNUM is DOUBLE PRECISION array, dimension (2, N lg N) */ -/* > Each number indicates the S value to be used in the */ -/* > corresponding Givens rotation. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (3*N+2*QSIZ*N) */ -/* > \endverbatim */ -/* > */ -/* > \param[out] IWORK */ -/* > \verbatim */ -/* > IWORK is INTEGER array, dimension (4*N) */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit. */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ -/* > > 0: if INFO = 1, an eigenvalue did not converge */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup auxOTHERcomputational */ - -/* > \par Contributors: */ -/* ================== */ -/* > */ -/* > Jeff Rutter, Computer Science Division, University of California */ -/* > at Berkeley, USA */ - -/* ===================================================================== */ -/* Subroutine */ int dlaed7_(integer *icompq, integer *n, integer *qsiz, - integer *tlvls, integer *curlvl, integer *curpbm, doublereal *d__, - doublereal *q, integer *ldq, integer *indxq, doublereal *rho, integer - *cutpnt, doublereal *qstore, integer *qptr, integer *prmptr, integer * - perm, integer *givptr, integer *givcol, doublereal *givnum, - doublereal *work, integer *iwork, integer *info) +int dlaed7_(integer *icompq, integer *n, integer *qsiz, integer *tlvls, integer *curlvl, + integer *curpbm, doublereal *d__, doublereal *q, integer *ldq, integer *indxq, + doublereal *rho, integer *cutpnt, doublereal *qstore, integer *qptr, integer *prmptr, + integer *perm, integer *givptr, integer *givcol, doublereal *givnum, doublereal *work, + integer *iwork, integer *info) { - /* System generated locals */ integer q_dim1, q_offset, i__1, i__2; - - /* Builtin functions */ integer pow_lmp_ii(integer *, integer *); - - /* Local variables */ integer i__, k, n1, n2, is, iw, iz, iq2, ptr, ldq2, indx, curr; - extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); + extern int dgemm_(char *, char *, integer *, integer *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, + ftnlen, ftnlen); integer indxc, indxp; - extern /* Subroutine */ int dlaed8_(integer *, integer *, integer *, - integer *, doublereal *, doublereal *, integer *, integer *, - doublereal *, integer *, doublereal *, doublereal *, doublereal *, - integer *, doublereal *, integer *, integer *, integer *, - doublereal *, integer *, integer *, integer *), dlaed9_(integer *, - integer *, integer *, integer *, doublereal *, doublereal *, - integer *, doublereal *, doublereal *, doublereal *, doublereal *, - integer *, integer *), dlaeda_(integer *, integer *, integer *, - integer *, integer *, integer *, integer *, integer *, doublereal - *, doublereal *, integer *, doublereal *, doublereal *, integer *) - ; + extern int dlaed8_(integer *, integer *, integer *, integer *, doublereal *, doublereal *, + integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, + doublereal *, integer *, doublereal *, integer *, integer *, integer *, + doublereal *, integer *, integer *, integer *), + dlaed9_(integer *, integer *, integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, doublereal *, doublereal *, doublereal *, integer *, integer *), + dlaeda_(integer *, integer *, integer *, integer *, integer *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, doublereal *, doublereal *, + integer *); integer idlmda; - extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *, - integer *, integer *, integer *), xerbla_(char *, integer *, - ftnlen); + extern int dlamrg_(integer *, integer *, doublereal *, integer *, integer *, integer *), + xerbla_(char *, integer *, ftnlen); integer coltyp; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ --d__; q_dim1 = *ldq; q_offset = 1 + q_dim1; @@ -357,19 +47,16 @@ f"> */ givnum -= 3; --work; --iwork; - - /* Function Body */ *info = 0; - if (*icompq < 0 || *icompq > 1) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*icompq == 1 && *qsiz < *n) { *info = -3; - } else if (*ldq < max(1,*n)) { + } else if (*ldq < max(1, *n)) { *info = -9; - } else if (min(1,*n) > *cutpnt || *n < *cutpnt) { + } else if (min(1, *n) > *cutpnt || *n < *cutpnt) { *info = -12; } if (*info != 0) { @@ -377,88 +64,55 @@ f"> */ xerbla_((char *)"DLAED7", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*n == 0) { return 0; } - -/* The following values are for bookkeeping purposes only. They are */ -/* integer pointers which indicate the portion of the workspace */ -/* used by a particular array in DLAED8 and DLAED9. */ - if (*icompq == 1) { ldq2 = *qsiz; } else { ldq2 = *n; } - iz = 1; idlmda = iz + *n; iw = idlmda + *n; iq2 = iw + *n; is = iq2 + *n * ldq2; - indx = 1; indxc = indx + *n; coltyp = indxc + *n; indxp = coltyp + *n; - -/* Form the z-vector which consists of the last row of Q_1 and the */ -/* first row of Q_2. */ - ptr = pow_lmp_ii(&c__2, tlvls) + 1; i__1 = *curlvl - 1; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = *tlvls - i__; ptr += pow_lmp_ii(&c__2, &i__2); -/* L10: */ } curr = ptr + *curpbm; - dlaeda_(n, tlvls, curlvl, curpbm, &prmptr[1], &perm[1], &givptr[1], & - givcol[3], &givnum[3], &qstore[1], &qptr[1], &work[iz], &work[iz - + *n], info); - -/* When solving the final problem, we no longer need the stored data, */ -/* so we will overwrite the data from this level onto the previously */ -/* used storage space. */ - + dlaeda_(n, tlvls, curlvl, curpbm, &prmptr[1], &perm[1], &givptr[1], &givcol[3], &givnum[3], + &qstore[1], &qptr[1], &work[iz], &work[iz + *n], info); if (*curlvl == *tlvls) { qptr[curr] = 1; prmptr[curr] = 1; givptr[curr] = 1; } - -/* Sort and Deflate eigenvalues. */ - - dlaed8_(icompq, &k, n, qsiz, &d__[1], &q[q_offset], ldq, &indxq[1], rho, - cutpnt, &work[iz], &work[idlmda], &work[iq2], &ldq2, &work[iw], & - perm[prmptr[curr]], &givptr[curr + 1], &givcol[(givptr[curr] << 1) - + 1], &givnum[(givptr[curr] << 1) + 1], &iwork[indxp], &iwork[ - indx], info); + dlaed8_(icompq, &k, n, qsiz, &d__[1], &q[q_offset], ldq, &indxq[1], rho, cutpnt, &work[iz], + &work[idlmda], &work[iq2], &ldq2, &work[iw], &perm[prmptr[curr]], &givptr[curr + 1], + &givcol[(givptr[curr] << 1) + 1], &givnum[(givptr[curr] << 1) + 1], &iwork[indxp], + &iwork[indx], info); prmptr[curr + 1] = prmptr[curr] + *n; givptr[curr + 1] += givptr[curr]; - -/* Solve Secular Equation. */ - if (k != 0) { - dlaed9_(&k, &c__1, &k, n, &d__[1], &work[is], &k, rho, &work[idlmda], - &work[iw], &qstore[qptr[curr]], &k, info); + dlaed9_(&k, &c__1, &k, n, &d__[1], &work[is], &k, rho, &work[idlmda], &work[iw], + &qstore[qptr[curr]], &k, info); if (*info != 0) { goto L30; } if (*icompq == 1) { - dgemm_((char *)"N", (char *)"N", qsiz, &k, &k, &c_b10, &work[iq2], &ldq2, &qstore[ - qptr[curr]], &k, &c_b11, &q[q_offset], ldq, (ftnlen)1, ( - ftnlen)1); + dgemm_((char *)"N", (char *)"N", qsiz, &k, &k, &c_b10, &work[iq2], &ldq2, &qstore[qptr[curr]], &k, + &c_b11, &q[q_offset], ldq, (ftnlen)1, (ftnlen)1); } -/* Computing 2nd power */ i__1 = k; qptr[curr + 1] = qptr[curr] + i__1 * i__1; - -/* Prepare the INDXQ sorting permutation. */ - n1 = k; n2 = *n - k; dlamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &indxq[1]); @@ -467,17 +121,11 @@ f"> */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { indxq[i__] = i__; -/* L20: */ } } - L30: return 0; - -/* End of DLAED7 */ - -} /* dlaed7_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlaed8.cpp b/lib/linalg/dlaed8.cpp index 8d1a7ae4b3..46580ce44f 100644 --- a/lib/linalg/dlaed8.cpp +++ b/lib/linalg/dlaed8.cpp @@ -1,329 +1,34 @@ -/* fortran/dlaed8.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static doublereal c_b3 = -1.; static integer c__1 = 1; - -/* > \brief \b DLAED8 used by DSTEDC. Merges eigenvalues and deflates secular equation. Used when the original - matrix is dense. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLAED8 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLAED8( ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, */ -/* CUTPNT, Z, DLAMDA, Q2, LDQ2, W, PERM, GIVPTR, */ -/* GIVCOL, GIVNUM, INDXP, INDX, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER CUTPNT, GIVPTR, ICOMPQ, INFO, K, LDQ, LDQ2, N, */ -/* $ QSIZ */ -/* DOUBLE PRECISION RHO */ -/* .. */ -/* .. Array Arguments .. */ -/* INTEGER GIVCOL( 2, * ), INDX( * ), INDXP( * ), */ -/* $ INDXQ( * ), PERM( * ) */ -/* DOUBLE PRECISION D( * ), DLAMDA( * ), GIVNUM( 2, * ), */ -/* $ Q( LDQ, * ), Q2( LDQ2, * ), W( * ), Z( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLAED8 merges the two sets of eigenvalues together into a single */ -/* > sorted set. Then it tries to deflate the size of the problem. */ -/* > There are two ways in which deflation can occur: when two or more */ -/* > eigenvalues are close together or if there is a tiny element in the */ -/* > Z vector. For each such occurrence the order of the related secular */ -/* > equation problem is reduced by one. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] ICOMPQ */ -/* > \verbatim */ -/* > ICOMPQ is INTEGER */ -/* > = 0: Compute eigenvalues only. */ -/* > = 1: Compute eigenvectors of original dense symmetric matrix */ -/* > also. On entry, Q contains the orthogonal matrix used */ -/* > to reduce the original matrix to tridiagonal form. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > The number of non-deflated eigenvalues, and the order of the */ -/* > related secular equation. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The dimension of the symmetric tridiagonal matrix. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] QSIZ */ -/* > \verbatim */ -/* > QSIZ is INTEGER */ -/* > The dimension of the orthogonal matrix used to reduce */ -/* > the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension (N) */ -/* > On entry, the eigenvalues of the two submatrices to be */ -/* > combined. On exit, the trailing (N-K) updated eigenvalues */ -/* > (those which were deflated) sorted into increasing order. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] Q */ -/* > \verbatim */ -/* > Q is DOUBLE PRECISION array, dimension (LDQ,N) */ -/* > If ICOMPQ = 0, Q is not referenced. Otherwise, */ -/* > on entry, Q contains the eigenvectors of the partially solved */ -/* > system which has been previously updated in matrix */ -/* > multiplies with other partially solved eigensystems. */ -/* > On exit, Q contains the trailing (N-K) updated eigenvectors */ -/* > (those which were deflated) in its last N-K columns. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDQ */ -/* > \verbatim */ -/* > LDQ is INTEGER */ -/* > The leading dimension of the array Q. LDQ >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INDXQ */ -/* > \verbatim */ -/* > INDXQ is INTEGER array, dimension (N) */ -/* > The permutation which separately sorts the two sub-problems */ -/* > in D into ascending order. Note that elements in the second */ -/* > half of this permutation must first have CUTPNT added to */ -/* > their values in order to be accurate. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] RHO */ -/* > \verbatim */ -/* > RHO is DOUBLE PRECISION */ -/* > On entry, the off-diagonal element associated with the rank-1 */ -/* > cut which originally split the two submatrices which are now */ -/* > being recombined. */ -/* > On exit, RHO has been modified to the value required by */ -/* > DLAED3. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] CUTPNT */ -/* > \verbatim */ -/* > CUTPNT is INTEGER */ -/* > The location of the last eigenvalue in the leading */ -/* > sub-matrix. min(1,N) <= CUTPNT <= N. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] Z */ -/* > \verbatim */ -/* > Z is DOUBLE PRECISION array, dimension (N) */ -/* > On entry, Z contains the updating vector (the last row of */ -/* > the first sub-eigenvector matrix and the first row of the */ -/* > second sub-eigenvector matrix). */ -/* > On exit, the contents of Z are destroyed by the updating */ -/* > process. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] DLAMDA */ -/* > \verbatim */ -/* > DLAMDA is DOUBLE PRECISION array, dimension (N) */ -/* > A copy of the first K eigenvalues which will be used by */ -/* > DLAED3 to form the secular equation. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] Q2 */ -/* > \verbatim */ -/* > Q2 is DOUBLE PRECISION array, dimension (LDQ2,N) */ -/* > If ICOMPQ = 0, Q2 is not referenced. Otherwise, */ -/* > a copy of the first K eigenvectors which will be used by */ -/* > DLAED7 in a matrix multiply (DGEMM) to update the new */ -/* > eigenvectors. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDQ2 */ -/* > \verbatim */ -/* > LDQ2 is INTEGER */ -/* > The leading dimension of the array Q2. LDQ2 >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] W */ -/* > \verbatim */ -/* > W is DOUBLE PRECISION array, dimension (N) */ -/* > The first k values of the final deflation-altered z-vector and */ -/* > will be passed to DLAED3. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] PERM */ -/* > \verbatim */ -/* > PERM is INTEGER array, dimension (N) */ -/* > The permutations (from deflation and sorting) to be applied */ -/* > to each eigenblock. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] GIVPTR */ -/* > \verbatim */ -/* > GIVPTR is INTEGER */ -/* > The number of Givens rotations which took place in this */ -/* > subproblem. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] GIVCOL */ -/* > \verbatim */ -/* > GIVCOL is INTEGER array, dimension (2, N) */ -/* > Each pair of numbers indicates a pair of columns to take place */ -/* > in a Givens rotation. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] GIVNUM */ -/* > \verbatim */ -/* > GIVNUM is DOUBLE PRECISION array, dimension (2, N) */ -/* > Each number indicates the S value to be used in the */ -/* > corresponding Givens rotation. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INDXP */ -/* > \verbatim */ -/* > INDXP is INTEGER array, dimension (N) */ -/* > The permutation used to place deflated values of D at the end */ -/* > of the array. INDXP(1:K) points to the nondeflated D-values */ -/* > and INDXP(K+1:N) points to the deflated eigenvalues. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INDX */ -/* > \verbatim */ -/* > INDX is INTEGER array, dimension (N) */ -/* > The permutation used to sort the contents of D into ascending */ -/* > order. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit. */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup auxOTHERcomputational */ - -/* > \par Contributors: */ -/* ================== */ -/* > */ -/* > Jeff Rutter, Computer Science Division, University of California */ -/* > at Berkeley, USA */ - -/* ===================================================================== */ -/* Subroutine */ int dlaed8_(integer *icompq, integer *k, integer *n, integer - *qsiz, doublereal *d__, doublereal *q, integer *ldq, integer *indxq, - doublereal *rho, integer *cutpnt, doublereal *z__, doublereal *dlamda, - doublereal *q2, integer *ldq2, doublereal *w, integer *perm, integer - *givptr, integer *givcol, doublereal *givnum, integer *indxp, integer - *indx, integer *info) +int dlaed8_(integer *icompq, integer *k, integer *n, integer *qsiz, doublereal *d__, doublereal *q, + integer *ldq, integer *indxq, doublereal *rho, integer *cutpnt, doublereal *z__, + doublereal *dlamda, doublereal *q2, integer *ldq2, doublereal *w, integer *perm, + integer *givptr, integer *givcol, doublereal *givnum, integer *indxp, integer *indx, + integer *info) { - /* System generated locals */ integer q_dim1, q_offset, q2_dim1, q2_offset, i__1; doublereal d__1; - - /* Builtin functions */ double sqrt(doublereal); - - /* Local variables */ doublereal c__; integer i__, j; doublereal s, t; integer k2, n1, n2, jp, n1p1; doublereal eps, tau, tol; integer jlam, imax, jmax; - extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, - doublereal *, integer *, doublereal *, doublereal *), dscal_( - integer *, doublereal *, doublereal *, integer *), dcopy_(integer - *, doublereal *, integer *, doublereal *, integer *); - extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, - ftnlen); + extern int drot_(integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, + doublereal *), + dscal_(integer *, doublereal *, doublereal *, integer *), + dcopy_(integer *, doublereal *, integer *, doublereal *, integer *); + extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, ftnlen); extern integer idamax_(integer *, doublereal *, integer *); - extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *, - integer *, integer *, integer *), dlacpy_(char *, integer *, - integer *, doublereal *, integer *, doublereal *, integer *, - ftnlen), xerbla_(char *, integer *, ftnlen); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ - -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ + extern int dlamrg_(integer *, integer *, doublereal *, integer *, integer *, integer *), + dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, + ftnlen), + xerbla_(char *, integer *, ftnlen); --d__; q_dim1 = *ldq; q_offset = 1 + q_dim1; @@ -340,21 +45,18 @@ f"> */ givnum -= 3; --indxp; --indx; - - /* Function Body */ *info = 0; - if (*icompq < 0 || *icompq > 1) { *info = -1; } else if (*n < 0) { *info = -3; } else if (*icompq == 1 && *qsiz < *n) { *info = -4; - } else if (*ldq < max(1,*n)) { + } else if (*ldq < max(1, *n)) { *info = -7; - } else if (*cutpnt < min(1,*n) || *cutpnt > *n) { + } else if (*cutpnt < min(1, *n) || *cutpnt > *n) { *info = -10; - } else if (*ldq2 < max(1,*n)) { + } else if (*ldq2 < max(1, *n)) { *info = -14; } if (*info != 0) { @@ -362,51 +64,31 @@ f"> */ xerbla_((char *)"DLAED8", &i__1, (ftnlen)6); return 0; } - -/* Need to initialize GIVPTR to O here in case of quick exit */ -/* to prevent an unspecified code behavior (usually sigfault) */ -/* when IWORK array on entry to *stedc is not zeroed */ -/* (or at least some IWORK entries which used in *laed7 for GIVPTR). */ - *givptr = 0; - -/* Quick return if possible */ - if (*n == 0) { return 0; } - n1 = *cutpnt; n2 = *n - n1; n1p1 = n1 + 1; - if (*rho < 0.) { dscal_(&n2, &c_b3, &z__[n1p1], &c__1); } - -/* Normalize z so that norm(z) = 1 */ - t = 1. / sqrt(2.); i__1 = *n; for (j = 1; j <= i__1; ++j) { indx[j] = j; -/* L10: */ } dscal_(n, &t, &z__[1], &c__1); *rho = (d__1 = *rho * 2., abs(d__1)); - -/* Sort the eigenvalues into increasing order */ - i__1 = *n; for (i__ = *cutpnt + 1; i__ <= i__1; ++i__) { indxq[i__] += *cutpnt; -/* L20: */ } i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { dlamda[i__] = d__[indxq[i__]]; w[i__] = z__[indxq[i__]]; -/* L30: */ } i__ = 1; j = *cutpnt + 1; @@ -415,56 +97,33 @@ f"> */ for (i__ = 1; i__ <= i__1; ++i__) { d__[i__] = dlamda[indx[i__]]; z__[i__] = w[indx[i__]]; -/* L40: */ } - -/* Calculate the allowable deflation tolerance */ - imax = idamax_(n, &z__[1], &c__1); jmax = idamax_(n, &d__[1], &c__1); eps = dlamch_((char *)"Epsilon", (ftnlen)7); tol = eps * 8. * (d__1 = d__[jmax], abs(d__1)); - -/* If the rank-1 modifier is small enough, no more needs to be done */ -/* except to reorganize Q so that its columns correspond with the */ -/* elements in D. */ - if (*rho * (d__1 = z__[imax], abs(d__1)) <= tol) { *k = 0; if (*icompq == 0) { i__1 = *n; for (j = 1; j <= i__1; ++j) { perm[j] = indxq[indx[j]]; -/* L50: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { perm[j] = indxq[indx[j]]; - dcopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 - + 1], &c__1); -/* L60: */ + dcopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 + 1], &c__1); } - dlacpy_((char *)"A", qsiz, n, &q2[q2_dim1 + 1], ldq2, &q[q_dim1 + 1], ldq, - (ftnlen)1); + dlacpy_((char *)"A", qsiz, n, &q2[q2_dim1 + 1], ldq2, &q[q_dim1 + 1], ldq, (ftnlen)1); } return 0; } - -/* If there are multiple eigenvalues then the problem deflates. Here */ -/* the number of equal eigenvalues are found. As each equal */ -/* eigenvalue is found, an elementary reflector is computed to rotate */ -/* the corresponding eigensubspace so that the corresponding */ -/* components of Z are zero in this new basis. */ - *k = 0; k2 = *n + 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { if (*rho * (d__1 = z__[j], abs(d__1)) <= tol) { - -/* Deflate due to small z component. */ - --k2; indxp[k2] = j; if (j == *n) { @@ -474,7 +133,6 @@ f"> */ jlam = j; goto L80; } -/* L70: */ } L80: ++j; @@ -482,49 +140,33 @@ L80: goto L100; } if (*rho * (d__1 = z__[j], abs(d__1)) <= tol) { - -/* Deflate due to small z component. */ - --k2; indxp[k2] = j; } else { - -/* Check if eigenvalues are close enough to allow deflation. */ - s = z__[jlam]; c__ = z__[j]; - -/* Find sqrt(a**2+b**2) without overflow or */ -/* destructive underflow. */ - tau = dlapy2_(&c__, &s); t = d__[j] - d__[jlam]; c__ /= tau; s = -s / tau; if ((d__1 = t * c__ * s, abs(d__1)) <= tol) { - -/* Deflation is possible. */ - z__[j] = tau; z__[jlam] = 0.; - -/* Record the appropriate Givens rotation */ - ++(*givptr); givcol[(*givptr << 1) + 1] = indxq[indx[jlam]]; givcol[(*givptr << 1) + 2] = indxq[indx[j]]; givnum[(*givptr << 1) + 1] = c__; givnum[(*givptr << 1) + 2] = s; if (*icompq == 1) { - drot_(qsiz, &q[indxq[indx[jlam]] * q_dim1 + 1], &c__1, &q[ - indxq[indx[j]] * q_dim1 + 1], &c__1, &c__, &s); + drot_(qsiz, &q[indxq[indx[jlam]] * q_dim1 + 1], &c__1, + &q[indxq[indx[j]] * q_dim1 + 1], &c__1, &c__, &s); } t = d__[jlam] * c__ * c__ + d__[j] * s * s; d__[j] = d__[jlam] * s * s + d__[j] * c__ * c__; d__[jlam] = t; --k2; i__ = 1; -L90: + L90: if (k2 + i__ <= *n) { if (d__[jlam] < d__[indxp[k2 + i__]]) { indxp[k2 + i__ - 1] = indxp[k2 + i__]; @@ -548,28 +190,17 @@ L90: } goto L80; L100: - -/* Record the last eigenvalue. */ - ++(*k); w[*k] = z__[jlam]; dlamda[*k] = d__[jlam]; indxp[*k] = jlam; - L110: - -/* Sort the eigenvalues and corresponding eigenvectors into DLAMDA */ -/* and Q2 respectively. The eigenvalues/vectors which were not */ -/* deflated go into the first K slots of DLAMDA and Q2 respectively, */ -/* while those which were deflated go into the last N - K slots. */ - if (*icompq == 0) { i__1 = *n; for (j = 1; j <= i__1; ++j) { jp = indxp[j]; dlamda[j] = d__[jp]; perm[j] = indxq[indx[jp]]; -/* L120: */ } } else { i__1 = *n; @@ -577,15 +208,9 @@ L110: jp = indxp[j]; dlamda[j] = d__[jp]; perm[j] = indxq[indx[jp]]; - dcopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 + 1] - , &c__1); -/* L130: */ + dcopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 + 1], &c__1); } } - -/* The deflated eigenvalues and their corresponding vectors go back */ -/* into the last N - K slots of D and Q respectively. */ - if (*k < *n) { if (*icompq == 0) { i__1 = *n - *k; @@ -594,17 +219,12 @@ L110: i__1 = *n - *k; dcopy_(&i__1, &dlamda[*k + 1], &c__1, &d__[*k + 1], &c__1); i__1 = *n - *k; - dlacpy_((char *)"A", qsiz, &i__1, &q2[(*k + 1) * q2_dim1 + 1], ldq2, &q[(* - k + 1) * q_dim1 + 1], ldq, (ftnlen)1); + dlacpy_((char *)"A", qsiz, &i__1, &q2[(*k + 1) * q2_dim1 + 1], ldq2, &q[(*k + 1) * q_dim1 + 1], + ldq, (ftnlen)1); } } - return 0; - -/* End of DLAED8 */ - -} /* dlaed8_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlaed9.cpp b/lib/linalg/dlaed9.cpp index f6f01b7098..2ca15ee0d7 100644 --- a/lib/linalg/dlaed9.cpp +++ b/lib/linalg/dlaed9.cpp @@ -1,229 +1,23 @@ -/* fortran/dlaed9.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; - -/* > \brief \b DLAED9 used by DSTEDC. Finds the roots of the secular equation and updates the eigenvectors. Us -ed when the original matrix is dense. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLAED9 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLAED9( K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA, W, */ -/* S, LDS, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INFO, K, KSTART, KSTOP, LDQ, LDS, N */ -/* DOUBLE PRECISION RHO */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION D( * ), DLAMDA( * ), Q( LDQ, * ), S( LDS, * ), */ -/* $ W( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLAED9 finds the roots of the secular equation, as defined by the */ -/* > values in D, Z, and RHO, between KSTART and KSTOP. It makes the */ -/* > appropriate calls to DLAED4 and then stores the new matrix of */ -/* > eigenvectors for use in calculating the next level of Z vectors. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > The number of terms in the rational function to be solved by */ -/* > DLAED4. K >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] KSTART */ -/* > \verbatim */ -/* > KSTART is INTEGER */ -/* > \endverbatim */ -/* > */ -/* > \param[in] KSTOP */ -/* > \verbatim */ -/* > KSTOP is INTEGER */ -/* > The updated eigenvalues Lambda(I), KSTART <= I <= KSTOP */ -/* > are to be computed. 1 <= KSTART <= KSTOP <= K. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of rows and columns in the Q matrix. */ -/* > N >= K (delation may result in N > K). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension (N) */ -/* > D(I) contains the updated eigenvalues */ -/* > for KSTART <= I <= KSTOP. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] Q */ -/* > \verbatim */ -/* > Q is DOUBLE PRECISION array, dimension (LDQ,N) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDQ */ -/* > \verbatim */ -/* > LDQ is INTEGER */ -/* > The leading dimension of the array Q. LDQ >= max( 1, N ). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] RHO */ -/* > \verbatim */ -/* > RHO is DOUBLE PRECISION */ -/* > The value of the parameter in the rank one update equation. */ -/* > RHO >= 0 required. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DLAMDA */ -/* > \verbatim */ -/* > DLAMDA is DOUBLE PRECISION array, dimension (K) */ -/* > The first K elements of this array contain the old roots */ -/* > of the deflated updating problem. These are the poles */ -/* > of the secular equation. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] W */ -/* > \verbatim */ -/* > W is DOUBLE PRECISION array, dimension (K) */ -/* > The first K elements of this array contain the components */ -/* > of the deflation-adjusted updating vector. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] S */ -/* > \verbatim */ -/* > S is DOUBLE PRECISION array, dimension (LDS, K) */ -/* > Will contain the eigenvectors of the repaired matrix which */ -/* > will be stored for subsequent Z vector calculation and */ -/* > multiplied by the previously accumulated eigenvectors */ -/* > to update the system. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDS */ -/* > \verbatim */ -/* > LDS is INTEGER */ -/* > The leading dimension of S. LDS >= max( 1, K ). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit. */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ -/* > > 0: if INFO = 1, an eigenvalue did not converge */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup auxOTHERcomputational */ - -/* > \par Contributors: */ -/* ================== */ -/* > */ -/* > Jeff Rutter, Computer Science Division, University of California */ -/* > at Berkeley, USA */ - -/* ===================================================================== */ -/* Subroutine */ int dlaed9_(integer *k, integer *kstart, integer *kstop, - integer *n, doublereal *d__, doublereal *q, integer *ldq, doublereal * - rho, doublereal *dlamda, doublereal *w, doublereal *s, integer *lds, - integer *info) +int dlaed9_(integer *k, integer *kstart, integer *kstop, integer *n, doublereal *d__, doublereal *q, + integer *ldq, doublereal *rho, doublereal *dlamda, doublereal *w, doublereal *s, + integer *lds, integer *info) { - /* System generated locals */ integer q_dim1, q_offset, s_dim1, s_offset, i__1, i__2; doublereal d__1; - - /* Builtin functions */ double sqrt(doublereal), d_lmp_sign(doublereal *, doublereal *); - - /* Local variables */ integer i__, j; doublereal temp; extern doublereal dnrm2_(integer *, doublereal *, integer *); - extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, - doublereal *, integer *), dlaed4_(integer *, integer *, - doublereal *, doublereal *, doublereal *, doublereal *, - doublereal *, integer *); + extern int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *), + dlaed4_(integer *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, integer *); extern doublereal dlamc3_(doublereal *, doublereal *); - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ + extern int xerbla_(char *, integer *, ftnlen); --d__; q_dim1 = *ldq; q_offset = 1 + q_dim1; @@ -233,21 +27,18 @@ f"> */ s_dim1 = *lds; s_offset = 1 + s_dim1; s -= s_offset; - - /* Function Body */ *info = 0; - if (*k < 0) { *info = -1; - } else if (*kstart < 1 || *kstart > max(1,*k)) { + } else if (*kstart < 1 || *kstart > max(1, *k)) { *info = -2; - } else if (max(1,*kstop) < *kstart || *kstop > max(1,*k)) { + } else if (max(1, *kstop) < *kstart || *kstop > max(1, *k)) { *info = -3; } else if (*n < *k) { *info = -4; - } else if (*ldq < max(1,*k)) { + } else if (*ldq < max(1, *k)) { *info = -7; - } else if (*lds < max(1,*k)) { + } else if (*lds < max(1, *k)) { *info = -12; } if (*info != 0) { @@ -255,68 +46,31 @@ f"> */ xerbla_((char *)"DLAED9", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*k == 0) { return 0; } - -/* Modify values DLAMDA(i) to make sure all DLAMDA(i)-DLAMDA(j) can */ -/* be computed with high relative accuracy (barring over/underflow). */ -/* This is a problem on machines without a guard digit in */ -/* add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2). */ -/* The following code replaces DLAMDA(I) by 2*DLAMDA(I)-DLAMDA(I), */ -/* which on any of these machines zeros out the bottommost */ -/* bit of DLAMDA(I) if it is 1; this makes the subsequent */ -/* subtractions DLAMDA(I)-DLAMDA(J) unproblematic when cancellation */ -/* occurs. On binary machines with a guard digit (almost all */ -/* machines) it does not change DLAMDA(I) at all. On hexadecimal */ -/* and decimal machines with a guard digit, it slightly */ -/* changes the bottommost bits of DLAMDA(I). It does not account */ -/* for hexadecimal or decimal machines without guard digits */ -/* (we know of none). We use a subroutine call to compute */ -/* 2*DLAMBDA(I) to prevent optimizing compilers from eliminating */ -/* this code. */ - i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { dlamda[i__] = dlamc3_(&dlamda[i__], &dlamda[i__]) - dlamda[i__]; -/* L10: */ } - i__1 = *kstop; for (j = *kstart; j <= i__1; ++j) { - dlaed4_(k, &j, &dlamda[1], &w[1], &q[j * q_dim1 + 1], rho, &d__[j], - info); - -/* If the zero finder fails, the computation is terminated. */ - + dlaed4_(k, &j, &dlamda[1], &w[1], &q[j * q_dim1 + 1], rho, &d__[j], info); if (*info != 0) { goto L120; } -/* L20: */ } - if (*k == 1 || *k == 2) { i__1 = *k; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = *k; for (j = 1; j <= i__2; ++j) { s[j + i__ * s_dim1] = q[j + i__ * q_dim1]; -/* L30: */ } -/* L40: */ } goto L120; } - -/* Compute updated W. */ - dcopy_(k, &w[1], &c__1, &s[s_offset], &c__1); - -/* Initialize W(I) = Q(I,I) */ - i__1 = *ldq + 1; dcopy_(k, &q[q_offset], &i__1, &w[1], &c__1); i__1 = *k; @@ -324,47 +78,32 @@ f"> */ i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]); -/* L50: */ } i__2 = *k; for (i__ = j + 1; i__ <= i__2; ++i__) { w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]); -/* L60: */ } -/* L70: */ } i__1 = *k; for (i__ = 1; i__ <= i__1; ++i__) { d__1 = sqrt(-w[i__]); w[i__] = d_lmp_sign(&d__1, &s[i__ + s_dim1]); -/* L80: */ } - -/* Compute eigenvectors of the modified rank-1 modification. */ - i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *k; for (i__ = 1; i__ <= i__2; ++i__) { q[i__ + j * q_dim1] = w[i__] / q[i__ + j * q_dim1]; -/* L90: */ } temp = dnrm2_(k, &q[j * q_dim1 + 1], &c__1); i__2 = *k; for (i__ = 1; i__ <= i__2; ++i__) { s[i__ + j * s_dim1] = q[i__ + j * q_dim1] / temp; -/* L100: */ } -/* L110: */ } - L120: return 0; - -/* End of DLAED9 */ - -} /* dlaed9_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlaeda.cpp b/lib/linalg/dlaeda.cpp index 81389d8db0..32ab3718a3 100644 --- a/lib/linalg/dlaeda.cpp +++ b/lib/linalg/dlaeda.cpp @@ -1,242 +1,26 @@ -/* fortran/dlaeda.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__2 = 2; static integer c__1 = 1; static doublereal c_b24 = 1.; static doublereal c_b26 = 0.; - -/* > \brief \b DLAEDA used by DSTEDC. Computes the Z vector determining the rank-one modification of the diago -nal matrix. Used when the original matrix is dense. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLAEDA + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLAEDA( N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR, */ -/* GIVCOL, GIVNUM, Q, QPTR, Z, ZTEMP, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER CURLVL, CURPBM, INFO, N, TLVLS */ -/* .. */ -/* .. Array Arguments .. */ -/* INTEGER GIVCOL( 2, * ), GIVPTR( * ), PERM( * ), */ -/* $ PRMPTR( * ), QPTR( * ) */ -/* DOUBLE PRECISION GIVNUM( 2, * ), Q( * ), Z( * ), ZTEMP( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLAEDA computes the Z vector corresponding to the merge step in the */ -/* > CURLVLth step of the merge process with TLVLS steps for the CURPBMth */ -/* > problem. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The dimension of the symmetric tridiagonal matrix. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TLVLS */ -/* > \verbatim */ -/* > TLVLS is INTEGER */ -/* > The total number of merging levels in the overall divide and */ -/* > conquer tree. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] CURLVL */ -/* > \verbatim */ -/* > CURLVL is INTEGER */ -/* > The current level in the overall merge routine, */ -/* > 0 <= curlvl <= tlvls. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] CURPBM */ -/* > \verbatim */ -/* > CURPBM is INTEGER */ -/* > The current problem in the current level in the overall */ -/* > merge routine (counting from upper left to lower right). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] PRMPTR */ -/* > \verbatim */ -/* > PRMPTR is INTEGER array, dimension (N lg N) */ -/* > Contains a list of pointers which indicate where in PERM a */ -/* > level's permutation is stored. PRMPTR(i+1) - PRMPTR(i) */ -/* > indicates the size of the permutation and incidentally the */ -/* > size of the full, non-deflated problem. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] PERM */ -/* > \verbatim */ -/* > PERM is INTEGER array, dimension (N lg N) */ -/* > Contains the permutations (from deflation and sorting) to be */ -/* > applied to each eigenblock. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] GIVPTR */ -/* > \verbatim */ -/* > GIVPTR is INTEGER array, dimension (N lg N) */ -/* > Contains a list of pointers which indicate where in GIVCOL a */ -/* > level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i) */ -/* > indicates the number of Givens rotations. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] GIVCOL */ -/* > \verbatim */ -/* > GIVCOL is INTEGER array, dimension (2, N lg N) */ -/* > Each pair of numbers indicates a pair of columns to take place */ -/* > in a Givens rotation. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] GIVNUM */ -/* > \verbatim */ -/* > GIVNUM is DOUBLE PRECISION array, dimension (2, N lg N) */ -/* > Each number indicates the S value to be used in the */ -/* > corresponding Givens rotation. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] Q */ -/* > \verbatim */ -/* > Q is DOUBLE PRECISION array, dimension (N**2) */ -/* > Contains the square eigenblocks from previous levels, the */ -/* > starting positions for blocks are given by QPTR. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] QPTR */ -/* > \verbatim */ -/* > QPTR is INTEGER array, dimension (N+2) */ -/* > Contains a list of pointers which indicate where in Q an */ -/* > eigenblock is stored. SQRT( QPTR(i+1) - QPTR(i) ) indicates */ -/* > the size of the block. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] Z */ -/* > \verbatim */ -/* > Z is DOUBLE PRECISION array, dimension (N) */ -/* > On output this vector contains the updating vector (the last */ -/* > row of the first sub-eigenvector matrix and the first row of */ -/* > the second sub-eigenvector matrix). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] ZTEMP */ -/* > \verbatim */ -/* > ZTEMP is DOUBLE PRECISION array, dimension (N) */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit. */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup auxOTHERcomputational */ - -/* > \par Contributors: */ -/* ================== */ -/* > */ -/* > Jeff Rutter, Computer Science Division, University of California */ -/* > at Berkeley, USA */ - -/* ===================================================================== */ -/* Subroutine */ int dlaeda_(integer *n, integer *tlvls, integer *curlvl, - integer *curpbm, integer *prmptr, integer *perm, integer *givptr, - integer *givcol, doublereal *givnum, doublereal *q, integer *qptr, - doublereal *z__, doublereal *ztemp, integer *info) +int dlaeda_(integer *n, integer *tlvls, integer *curlvl, integer *curpbm, integer *prmptr, + integer *perm, integer *givptr, integer *givcol, doublereal *givnum, doublereal *q, + integer *qptr, doublereal *z__, doublereal *ztemp, integer *info) { - /* System generated locals */ integer i__1, i__2, i__3; - - /* Builtin functions */ integer pow_lmp_ii(integer *, integer *); double sqrt(doublereal); - - /* Local variables */ integer i__, k, mid, ptr; - extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, - doublereal *, integer *, doublereal *, doublereal *); + extern int drot_(integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, + doublereal *); integer curr, bsiz1, bsiz2, psiz1, psiz2, zptr1; - extern /* Subroutine */ int dgemv_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, doublereal *, integer *, - doublereal *, doublereal *, integer *, ftnlen), dcopy_(integer *, - doublereal *, integer *, doublereal *, integer *), xerbla_(char *, - integer *, ftnlen); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ + extern int dgemv_(char *, integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, ftnlen), + dcopy_(integer *, doublereal *, integer *, doublereal *, integer *), + xerbla_(char *, integer *, ftnlen); --ztemp; --z__; --qptr; @@ -246,10 +30,7 @@ f"> */ --givptr; --perm; --prmptr; - - /* Function Body */ *info = 0; - if (*n < 0) { *info = -1; } @@ -258,129 +39,75 @@ f"> */ xerbla_((char *)"DLAEDA", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*n == 0) { return 0; } - -/* Determine location of first number in second half. */ - mid = *n / 2 + 1; - -/* Gather last/first rows of appropriate eigenblocks into center of Z */ - ptr = 1; - -/* Determine location of lowest level subproblem in the full storage */ -/* scheme */ - i__1 = *curlvl - 1; curr = ptr + *curpbm * pow_lmp_ii(&c__2, curlvl) + pow_lmp_ii(&c__2, &i__1) - 1; - -/* Determine size of these matrices. We add HALF to the value of */ -/* the SQRT in case the machine underestimates one of these square */ -/* roots. */ - - bsiz1 = (integer) (sqrt((doublereal) (qptr[curr + 1] - qptr[curr])) + .5); - bsiz2 = (integer) (sqrt((doublereal) (qptr[curr + 2] - qptr[curr + 1])) + - .5); + bsiz1 = (integer)(sqrt((doublereal)(qptr[curr + 1] - qptr[curr])) + .5); + bsiz2 = (integer)(sqrt((doublereal)(qptr[curr + 2] - qptr[curr + 1])) + .5); i__1 = mid - bsiz1 - 1; for (k = 1; k <= i__1; ++k) { z__[k] = 0.; -/* L10: */ } - dcopy_(&bsiz1, &q[qptr[curr] + bsiz1 - 1], &bsiz1, &z__[mid - bsiz1], & - c__1); + dcopy_(&bsiz1, &q[qptr[curr] + bsiz1 - 1], &bsiz1, &z__[mid - bsiz1], &c__1); dcopy_(&bsiz2, &q[qptr[curr + 1]], &bsiz2, &z__[mid], &c__1); i__1 = *n; for (k = mid + bsiz2; k <= i__1; ++k) { z__[k] = 0.; -/* L20: */ } - -/* Loop through remaining levels 1 -> CURLVL applying the Givens */ -/* rotations and permutation and then multiplying the center matrices */ -/* against the current Z. */ - ptr = pow_lmp_ii(&c__2, tlvls) + 1; i__1 = *curlvl - 1; for (k = 1; k <= i__1; ++k) { i__2 = *curlvl - k; i__3 = *curlvl - k - 1; - curr = ptr + *curpbm * pow_lmp_ii(&c__2, &i__2) + pow_lmp_ii(&c__2, &i__3) - - 1; + curr = ptr + *curpbm * pow_lmp_ii(&c__2, &i__2) + pow_lmp_ii(&c__2, &i__3) - 1; psiz1 = prmptr[curr + 1] - prmptr[curr]; psiz2 = prmptr[curr + 2] - prmptr[curr + 1]; zptr1 = mid - psiz1; - -/* Apply Givens at CURR and CURR+1 */ - i__2 = givptr[curr + 1] - 1; for (i__ = givptr[curr]; i__ <= i__2; ++i__) { - drot_(&c__1, &z__[zptr1 + givcol[(i__ << 1) + 1] - 1], &c__1, & - z__[zptr1 + givcol[(i__ << 1) + 2] - 1], &c__1, &givnum[( - i__ << 1) + 1], &givnum[(i__ << 1) + 2]); -/* L30: */ + drot_(&c__1, &z__[zptr1 + givcol[(i__ << 1) + 1] - 1], &c__1, + &z__[zptr1 + givcol[(i__ << 1) + 2] - 1], &c__1, &givnum[(i__ << 1) + 1], + &givnum[(i__ << 1) + 2]); } i__2 = givptr[curr + 2] - 1; for (i__ = givptr[curr + 1]; i__ <= i__2; ++i__) { - drot_(&c__1, &z__[mid - 1 + givcol[(i__ << 1) + 1]], &c__1, &z__[ - mid - 1 + givcol[(i__ << 1) + 2]], &c__1, &givnum[(i__ << - 1) + 1], &givnum[(i__ << 1) + 2]); -/* L40: */ + drot_(&c__1, &z__[mid - 1 + givcol[(i__ << 1) + 1]], &c__1, + &z__[mid - 1 + givcol[(i__ << 1) + 2]], &c__1, &givnum[(i__ << 1) + 1], + &givnum[(i__ << 1) + 2]); } psiz1 = prmptr[curr + 1] - prmptr[curr]; psiz2 = prmptr[curr + 2] - prmptr[curr + 1]; i__2 = psiz1 - 1; for (i__ = 0; i__ <= i__2; ++i__) { ztemp[i__ + 1] = z__[zptr1 + perm[prmptr[curr] + i__] - 1]; -/* L50: */ } i__2 = psiz2 - 1; for (i__ = 0; i__ <= i__2; ++i__) { - ztemp[psiz1 + i__ + 1] = z__[mid + perm[prmptr[curr + 1] + i__] - - 1]; -/* L60: */ + ztemp[psiz1 + i__ + 1] = z__[mid + perm[prmptr[curr + 1] + i__] - 1]; } - -/* Multiply Blocks at CURR and CURR+1 */ - -/* Determine size of these matrices. We add HALF to the value of */ -/* the SQRT in case the machine underestimates one of these */ -/* square roots. */ - - bsiz1 = (integer) (sqrt((doublereal) (qptr[curr + 1] - qptr[curr])) + - .5); - bsiz2 = (integer) (sqrt((doublereal) (qptr[curr + 2] - qptr[curr + 1]) - ) + .5); + bsiz1 = (integer)(sqrt((doublereal)(qptr[curr + 1] - qptr[curr])) + .5); + bsiz2 = (integer)(sqrt((doublereal)(qptr[curr + 2] - qptr[curr + 1])) + .5); if (bsiz1 > 0) { - dgemv_((char *)"T", &bsiz1, &bsiz1, &c_b24, &q[qptr[curr]], &bsiz1, & - ztemp[1], &c__1, &c_b26, &z__[zptr1], &c__1, (ftnlen)1); + dgemv_((char *)"T", &bsiz1, &bsiz1, &c_b24, &q[qptr[curr]], &bsiz1, &ztemp[1], &c__1, &c_b26, + &z__[zptr1], &c__1, (ftnlen)1); } i__2 = psiz1 - bsiz1; dcopy_(&i__2, &ztemp[bsiz1 + 1], &c__1, &z__[zptr1 + bsiz1], &c__1); if (bsiz2 > 0) { - dgemv_((char *)"T", &bsiz2, &bsiz2, &c_b24, &q[qptr[curr + 1]], &bsiz2, & - ztemp[psiz1 + 1], &c__1, &c_b26, &z__[mid], &c__1, ( - ftnlen)1); + dgemv_((char *)"T", &bsiz2, &bsiz2, &c_b24, &q[qptr[curr + 1]], &bsiz2, &ztemp[psiz1 + 1], + &c__1, &c_b26, &z__[mid], &c__1, (ftnlen)1); } i__2 = psiz2 - bsiz2; - dcopy_(&i__2, &ztemp[psiz1 + bsiz2 + 1], &c__1, &z__[mid + bsiz2], & - c__1); - + dcopy_(&i__2, &ztemp[psiz1 + bsiz2 + 1], &c__1, &z__[mid + bsiz2], &c__1); i__2 = *tlvls - k; ptr += pow_lmp_ii(&c__2, &i__2); -/* L70: */ } - return 0; - -/* End of DLAEDA */ - -} /* dlaeda_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlaev2.cpp b/lib/linalg/dlaev2.cpp index 21bdbebe69..454b0b9c40 100644 --- a/lib/linalg/dlaev2.cpp +++ b/lib/linalg/dlaev2.cpp @@ -1,175 +1,15 @@ -/* fortran/dlaev2.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLAEV2 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLAEV2( A, B, C, RT1, RT2, CS1, SN1 ) */ - -/* .. Scalar Arguments .. */ -/* DOUBLE PRECISION A, B, C, CS1, RT1, RT2, SN1 */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix */ -/* > [ A B ] */ -/* > [ B C ]. */ -/* > On return, RT1 is the eigenvalue of larger absolute value, RT2 is the */ -/* > eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right */ -/* > eigenvector for RT1, giving the decomposition */ -/* > */ -/* > [ CS1 SN1 ] [ A B ] [ CS1 -SN1 ] = [ RT1 0 ] */ -/* > [-SN1 CS1 ] [ B C ] [ SN1 CS1 ] [ 0 RT2 ]. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION */ -/* > The (1,1) element of the 2-by-2 matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] B */ -/* > \verbatim */ -/* > B is DOUBLE PRECISION */ -/* > The (1,2) element and the conjugate of the (2,1) element of */ -/* > the 2-by-2 matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] C */ -/* > \verbatim */ -/* > C is DOUBLE PRECISION */ -/* > The (2,2) element of the 2-by-2 matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] RT1 */ -/* > \verbatim */ -/* > RT1 is DOUBLE PRECISION */ -/* > The eigenvalue of larger absolute value. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] RT2 */ -/* > \verbatim */ -/* > RT2 is DOUBLE PRECISION */ -/* > The eigenvalue of smaller absolute value. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] CS1 */ -/* > \verbatim */ -/* > CS1 is DOUBLE PRECISION */ -/* > \endverbatim */ -/* > */ -/* > \param[out] SN1 */ -/* > \verbatim */ -/* > SN1 is DOUBLE PRECISION */ -/* > The vector (CS1, SN1) is a unit right eigenvector for RT1. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup OTHERauxiliary */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > RT1 is accurate to a few ulps barring over/underflow. */ -/* > */ -/* > RT2 may be inaccurate if there is massive cancellation in the */ -/* > determinant A*C-B*B; higher precision or correctly rounded or */ -/* > correctly truncated arithmetic would be needed to compute RT2 */ -/* > accurately in all cases. */ -/* > */ -/* > CS1 and SN1 are accurate to a few ulps barring over/underflow. */ -/* > */ -/* > Overflow is possible only if RT1 is within a factor of 5 of overflow. */ -/* > Underflow is harmless if the input data is 0 or exceeds */ -/* > underflow_threshold / macheps. */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dlaev2_(doublereal *a, doublereal *b, doublereal *c__, - doublereal *rt1, doublereal *rt2, doublereal *cs1, doublereal *sn1) +int dlaev2_(doublereal *a, doublereal *b, doublereal *c__, doublereal *rt1, doublereal *rt2, + doublereal *cs1, doublereal *sn1) { - /* System generated locals */ doublereal d__1; - - /* Builtin functions */ double sqrt(doublereal); - - /* Local variables */ doublereal ab, df, cs, ct, tb, sm, tn, rt, adf, acs; integer sgn1, sgn2; doublereal acmn, acmx; - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Compute the eigenvalues */ - sm = *a + *c__; df = *a - *c__; adf = abs(df); @@ -183,48 +23,27 @@ f"> */ acmn = *a; } if (adf > ab) { -/* Computing 2nd power */ d__1 = ab / adf; rt = adf * sqrt(d__1 * d__1 + 1.); } else if (adf < ab) { -/* Computing 2nd power */ d__1 = adf / ab; rt = ab * sqrt(d__1 * d__1 + 1.); } else { - -/* Includes case AB=ADF=0 */ - rt = ab * sqrt(2.); } if (sm < 0.) { *rt1 = (sm - rt) * .5; sgn1 = -1; - -/* Order of execution important. */ -/* To get fully accurate smaller eigenvalue, */ -/* next line needs to be executed in higher precision. */ - *rt2 = acmx / *rt1 * acmn - *b / *rt1 * *b; } else if (sm > 0.) { *rt1 = (sm + rt) * .5; sgn1 = 1; - -/* Order of execution important. */ -/* To get fully accurate smaller eigenvalue, */ -/* next line needs to be executed in higher precision. */ - *rt2 = acmx / *rt1 * acmn - *b / *rt1 * *b; } else { - -/* Includes case RT1 = RT2 = 0 */ - *rt1 = rt * .5; *rt2 = rt * -.5; sgn1 = 1; } - -/* Compute the eigenvector */ - if (df >= 0.) { cs = df + rt; sgn2 = 1; @@ -253,11 +72,7 @@ f"> */ *sn1 = tn; } return 0; - -/* End of DLAEV2 */ - -} /* dlaev2_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlals0.cpp b/lib/linalg/dlals0.cpp index 9dfb826915..6623506f7e 100644 --- a/lib/linalg/dlals0.cpp +++ b/lib/linalg/dlals0.cpp @@ -1,359 +1,40 @@ -/* fortran/dlals0.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static doublereal c_b5 = -1.; static integer c__1 = 1; static doublereal c_b11 = 1.; static doublereal c_b13 = 0.; static integer c__0 = 0; - -/* > \brief \b DLALS0 applies back multiplying factors in solving the least squares problem using divide and c -onquer SVD approach. Used by sgelsd. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLALS0 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLALS0( ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX, */ -/* PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, */ -/* POLES, DIFL, DIFR, Z, K, C, S, WORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER GIVPTR, ICOMPQ, INFO, K, LDB, LDBX, LDGCOL, */ -/* $ LDGNUM, NL, NR, NRHS, SQRE */ -/* DOUBLE PRECISION C, S */ -/* .. */ -/* .. Array Arguments .. */ -/* INTEGER GIVCOL( LDGCOL, * ), PERM( * ) */ -/* DOUBLE PRECISION B( LDB, * ), BX( LDBX, * ), DIFL( * ), */ -/* $ DIFR( LDGNUM, * ), GIVNUM( LDGNUM, * ), */ -/* $ POLES( LDGNUM, * ), WORK( * ), Z( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLALS0 applies back the multiplying factors of either the left or the */ -/* > right singular vector matrix of a diagonal matrix appended by a row */ -/* > to the right hand side matrix B in solving the least squares problem */ -/* > using the divide-and-conquer SVD approach. */ -/* > */ -/* > For the left singular vector matrix, three types of orthogonal */ -/* > matrices are involved: */ -/* > */ -/* > (1L) Givens rotations: the number of such rotations is GIVPTR; the */ -/* > pairs of columns/rows they were applied to are stored in GIVCOL; */ -/* > and the C- and S-values of these rotations are stored in GIVNUM. */ -/* > */ -/* > (2L) Permutation. The (NL+1)-st row of B is to be moved to the first */ -/* > row, and for J=2:N, PERM(J)-th row of B is to be moved to the */ -/* > J-th row. */ -/* > */ -/* > (3L) The left singular vector matrix of the remaining matrix. */ -/* > */ -/* > For the right singular vector matrix, four types of orthogonal */ -/* > matrices are involved: */ -/* > */ -/* > (1R) The right singular vector matrix of the remaining matrix. */ -/* > */ -/* > (2R) If SQRE = 1, one extra Givens rotation to generate the right */ -/* > null space. */ -/* > */ -/* > (3R) The inverse transformation of (2L). */ -/* > */ -/* > (4R) The inverse transformation of (1L). */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] ICOMPQ */ -/* > \verbatim */ -/* > ICOMPQ is INTEGER */ -/* > Specifies whether singular vectors are to be computed in */ -/* > factored form: */ -/* > = 0: Left singular vector matrix. */ -/* > = 1: Right singular vector matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] NL */ -/* > \verbatim */ -/* > NL is INTEGER */ -/* > The row dimension of the upper block. NL >= 1. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] NR */ -/* > \verbatim */ -/* > NR is INTEGER */ -/* > The row dimension of the lower block. NR >= 1. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] SQRE */ -/* > \verbatim */ -/* > SQRE is INTEGER */ -/* > = 0: the lower block is an NR-by-NR square matrix. */ -/* > = 1: the lower block is an NR-by-(NR+1) rectangular matrix. */ -/* > */ -/* > The bidiagonal matrix has row dimension N = NL + NR + 1, */ -/* > and column dimension M = N + SQRE. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] NRHS */ -/* > \verbatim */ -/* > NRHS is INTEGER */ -/* > The number of columns of B and BX. NRHS must be at least 1. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] B */ -/* > \verbatim */ -/* > B is DOUBLE PRECISION array, dimension ( LDB, NRHS ) */ -/* > On input, B contains the right hand sides of the least */ -/* > squares problem in rows 1 through M. On output, B contains */ -/* > the solution X in rows 1 through N. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDB */ -/* > \verbatim */ -/* > LDB is INTEGER */ -/* > The leading dimension of B. LDB must be at least */ -/* > max(1,MAX( M, N ) ). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] BX */ -/* > \verbatim */ -/* > BX is DOUBLE PRECISION array, dimension ( LDBX, NRHS ) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDBX */ -/* > \verbatim */ -/* > LDBX is INTEGER */ -/* > The leading dimension of BX. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] PERM */ -/* > \verbatim */ -/* > PERM is INTEGER array, dimension ( N ) */ -/* > The permutations (from deflation and sorting) applied */ -/* > to the two blocks. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] GIVPTR */ -/* > \verbatim */ -/* > GIVPTR is INTEGER */ -/* > The number of Givens rotations which took place in this */ -/* > subproblem. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] GIVCOL */ -/* > \verbatim */ -/* > GIVCOL is INTEGER array, dimension ( LDGCOL, 2 ) */ -/* > Each pair of numbers indicates a pair of rows/columns */ -/* > involved in a Givens rotation. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDGCOL */ -/* > \verbatim */ -/* > LDGCOL is INTEGER */ -/* > The leading dimension of GIVCOL, must be at least N. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] GIVNUM */ -/* > \verbatim */ -/* > GIVNUM is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) */ -/* > Each number indicates the C or S value used in the */ -/* > corresponding Givens rotation. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDGNUM */ -/* > \verbatim */ -/* > LDGNUM is INTEGER */ -/* > The leading dimension of arrays DIFR, POLES and */ -/* > GIVNUM, must be at least K. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] POLES */ -/* > \verbatim */ -/* > POLES is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) */ -/* > On entry, POLES(1:K, 1) contains the new singular */ -/* > values obtained from solving the secular equation, and */ -/* > POLES(1:K, 2) is an array containing the poles in the secular */ -/* > equation. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DIFL */ -/* > \verbatim */ -/* > DIFL is DOUBLE PRECISION array, dimension ( K ). */ -/* > On entry, DIFL(I) is the distance between I-th updated */ -/* > (undeflated) singular value and the I-th (undeflated) old */ -/* > singular value. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DIFR */ -/* > \verbatim */ -/* > DIFR is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ). */ -/* > On entry, DIFR(I, 1) contains the distances between I-th */ -/* > updated (undeflated) singular value and the I+1-th */ -/* > (undeflated) old singular value. And DIFR(I, 2) is the */ -/* > normalizing factor for the I-th right singular vector. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] Z */ -/* > \verbatim */ -/* > Z is DOUBLE PRECISION array, dimension ( K ) */ -/* > Contain the components of the deflation-adjusted updating row */ -/* > vector. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > Contains the dimension of the non-deflated matrix, */ -/* > This is the order of the related secular equation. 1 <= K <=N. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] C */ -/* > \verbatim */ -/* > C is DOUBLE PRECISION */ -/* > C contains garbage if SQRE =0 and the C-value of a Givens */ -/* > rotation related to the right null space if SQRE = 1. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] S */ -/* > \verbatim */ -/* > S is DOUBLE PRECISION */ -/* > S contains garbage if SQRE =0 and the S-value of a Givens */ -/* > rotation related to the right null space if SQRE = 1. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension ( K ) */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit. */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleOTHERcomputational */ - -/* > \par Contributors: */ -/* ================== */ -/* > */ -/* > Ming Gu and Ren-Cang Li, Computer Science Division, University of */ -/* > California at Berkeley, USA \n */ -/* > Osni Marques, LBNL/NERSC, USA \n */ - -/* ===================================================================== */ -/* Subroutine */ int dlals0_(integer *icompq, integer *nl, integer *nr, - integer *sqre, integer *nrhs, doublereal *b, integer *ldb, doublereal - *bx, integer *ldbx, integer *perm, integer *givptr, integer *givcol, - integer *ldgcol, doublereal *givnum, integer *ldgnum, doublereal * - poles, doublereal *difl, doublereal *difr, doublereal *z__, integer * - k, doublereal *c__, doublereal *s, doublereal *work, integer *info) +int dlals0_(integer *icompq, integer *nl, integer *nr, integer *sqre, integer *nrhs, doublereal *b, + integer *ldb, doublereal *bx, integer *ldbx, integer *perm, integer *givptr, + integer *givcol, integer *ldgcol, doublereal *givnum, integer *ldgnum, + doublereal *poles, doublereal *difl, doublereal *difr, doublereal *z__, integer *k, + doublereal *c__, doublereal *s, doublereal *work, integer *info) { - /* System generated locals */ - integer givcol_dim1, givcol_offset, b_dim1, b_offset, bx_dim1, bx_offset, - difr_dim1, difr_offset, givnum_dim1, givnum_offset, poles_dim1, - poles_offset, i__1, i__2; + integer givcol_dim1, givcol_offset, b_dim1, b_offset, bx_dim1, bx_offset, difr_dim1, + difr_offset, givnum_dim1, givnum_offset, poles_dim1, poles_offset, i__1, i__2; doublereal d__1; - - /* Local variables */ integer i__, j, m, n; doublereal dj; integer nlp1; doublereal temp; - extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, - doublereal *, integer *, doublereal *, doublereal *); + extern int drot_(integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, + doublereal *); extern doublereal dnrm2_(integer *, doublereal *, integer *); - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *); + extern int dscal_(integer *, doublereal *, doublereal *, integer *); doublereal diflj, difrj, dsigj; - extern /* Subroutine */ int dgemv_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, doublereal *, integer *, - doublereal *, doublereal *, integer *, ftnlen), dcopy_(integer *, - doublereal *, integer *, doublereal *, integer *); + extern int dgemv_(char *, integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, ftnlen), + dcopy_(integer *, doublereal *, integer *, doublereal *, integer *); extern doublereal dlamc3_(doublereal *, doublereal *); - extern /* Subroutine */ int dlascl_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, integer *, doublereal *, - integer *, integer *, ftnlen), dlacpy_(char *, integer *, integer - *, doublereal *, integer *, doublereal *, integer *, ftnlen), - xerbla_(char *, integer *, ftnlen); + extern int dlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, + integer *, doublereal *, integer *, integer *, ftnlen), + dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, + ftnlen), + xerbla_(char *, integer *, ftnlen); doublereal dsigjp; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; @@ -376,11 +57,8 @@ f"> */ --difl; --z__; --work; - - /* Function Body */ *info = 0; n = *nl + *nr + 1; - if (*icompq < 0 || *icompq > 1) { *info = -1; } else if (*nl < 1) { @@ -409,37 +87,20 @@ f"> */ xerbla_((char *)"DLALS0", &i__1, (ftnlen)6); return 0; } - m = n + *sqre; nlp1 = *nl + 1; - if (*icompq == 0) { - -/* Apply back orthogonal transformations from the left. */ - -/* Step (1L): apply back the Givens rotations performed. */ - i__1 = *givptr; for (i__ = 1; i__ <= i__1; ++i__) { - drot_(nrhs, &b[givcol[i__ + (givcol_dim1 << 1)] + b_dim1], ldb, & - b[givcol[i__ + givcol_dim1] + b_dim1], ldb, &givnum[i__ + - (givnum_dim1 << 1)], &givnum[i__ + givnum_dim1]); -/* L10: */ + drot_(nrhs, &b[givcol[i__ + (givcol_dim1 << 1)] + b_dim1], ldb, + &b[givcol[i__ + givcol_dim1] + b_dim1], ldb, &givnum[i__ + (givnum_dim1 << 1)], + &givnum[i__ + givnum_dim1]); } - -/* Step (2L): permute rows of B. */ - dcopy_(nrhs, &b[nlp1 + b_dim1], ldb, &bx[bx_dim1 + 1], ldbx); i__1 = n; for (i__ = 2; i__ <= i__1; ++i__) { - dcopy_(nrhs, &b[perm[i__] + b_dim1], ldb, &bx[i__ + bx_dim1], - ldbx); -/* L20: */ + dcopy_(nrhs, &b[perm[i__] + b_dim1], ldb, &bx[i__ + bx_dim1], ldbx); } - -/* Step (3L): apply the inverse of the left singular vector */ -/* matrix to BX. */ - if (*k == 1) { dcopy_(nrhs, &bx[bx_offset], ldbx, &b[b_offset], ldb); if (z__[1] < 0.) { @@ -459,58 +120,42 @@ f"> */ work[j] = 0.; } else { work[j] = -poles[j + (poles_dim1 << 1)] * z__[j] / diflj / - (poles[j + (poles_dim1 << 1)] + dj); + (poles[j + (poles_dim1 << 1)] + dj); } i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { - if (z__[i__] == 0. || poles[i__ + (poles_dim1 << 1)] == - 0.) { + if (z__[i__] == 0. || poles[i__ + (poles_dim1 << 1)] == 0.) { work[i__] = 0.; } else { - work[i__] = poles[i__ + (poles_dim1 << 1)] * z__[i__] - / (dlamc3_(&poles[i__ + (poles_dim1 << 1)], & - dsigj) - diflj) / (poles[i__ + (poles_dim1 << - 1)] + dj); + work[i__] = poles[i__ + (poles_dim1 << 1)] * z__[i__] / + (dlamc3_(&poles[i__ + (poles_dim1 << 1)], &dsigj) - diflj) / + (poles[i__ + (poles_dim1 << 1)] + dj); } -/* L30: */ } i__2 = *k; for (i__ = j + 1; i__ <= i__2; ++i__) { - if (z__[i__] == 0. || poles[i__ + (poles_dim1 << 1)] == - 0.) { + if (z__[i__] == 0. || poles[i__ + (poles_dim1 << 1)] == 0.) { work[i__] = 0.; } else { - work[i__] = poles[i__ + (poles_dim1 << 1)] * z__[i__] - / (dlamc3_(&poles[i__ + (poles_dim1 << 1)], & - dsigjp) + difrj) / (poles[i__ + (poles_dim1 << - 1)] + dj); + work[i__] = poles[i__ + (poles_dim1 << 1)] * z__[i__] / + (dlamc3_(&poles[i__ + (poles_dim1 << 1)], &dsigjp) + difrj) / + (poles[i__ + (poles_dim1 << 1)] + dj); } -/* L40: */ } work[1] = -1.; temp = dnrm2_(k, &work[1], &c__1); - dgemv_((char *)"T", k, nrhs, &c_b11, &bx[bx_offset], ldbx, &work[1], & - c__1, &c_b13, &b[j + b_dim1], ldb, (ftnlen)1); - dlascl_((char *)"G", &c__0, &c__0, &temp, &c_b11, &c__1, nrhs, &b[j + - b_dim1], ldb, info, (ftnlen)1); -/* L50: */ + dgemv_((char *)"T", k, nrhs, &c_b11, &bx[bx_offset], ldbx, &work[1], &c__1, &c_b13, + &b[j + b_dim1], ldb, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &temp, &c_b11, &c__1, nrhs, &b[j + b_dim1], ldb, info, + (ftnlen)1); } } - -/* Move the deflated rows of BX to B also. */ - - if (*k < max(m,n)) { + if (*k < max(m, n)) { i__1 = n - *k; - dlacpy_((char *)"A", &i__1, nrhs, &bx[*k + 1 + bx_dim1], ldbx, &b[*k + 1 - + b_dim1], ldb, (ftnlen)1); + dlacpy_((char *)"A", &i__1, nrhs, &bx[*k + 1 + bx_dim1], ldbx, &b[*k + 1 + b_dim1], ldb, + (ftnlen)1); } } else { - -/* Apply back the right orthogonal transformations. */ - -/* Step (1R): apply back the new right singular vector matrix */ -/* to B. */ - if (*k == 1) { dcopy_(nrhs, &b[b_offset], ldb, &bx[bx_offset], ldbx); } else { @@ -520,8 +165,8 @@ f"> */ if (z__[j] == 0.) { work[j] = 0.; } else { - work[j] = -z__[j] / difl[j] / (dsigj + poles[j + - poles_dim1]) / difr[j + (difr_dim1 << 1)]; + work[j] = -z__[j] / difl[j] / (dsigj + poles[j + poles_dim1]) / + difr[j + (difr_dim1 << 1)]; } i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { @@ -529,11 +174,10 @@ f"> */ work[i__] = 0.; } else { d__1 = -poles[i__ + 1 + (poles_dim1 << 1)]; - work[i__] = z__[j] / (dlamc3_(&dsigj, &d__1) - difr[ - i__ + difr_dim1]) / (dsigj + poles[i__ + - poles_dim1]) / difr[i__ + (difr_dim1 << 1)]; + work[i__] = z__[j] / (dlamc3_(&dsigj, &d__1) - difr[i__ + difr_dim1]) / + (dsigj + poles[i__ + poles_dim1]) / + difr[i__ + (difr_dim1 << 1)]; } -/* L60: */ } i__2 = *k; for (i__ = j + 1; i__ <= i__2; ++i__) { @@ -541,62 +185,41 @@ f"> */ work[i__] = 0.; } else { d__1 = -poles[i__ + (poles_dim1 << 1)]; - work[i__] = z__[j] / (dlamc3_(&dsigj, &d__1) - difl[ - i__]) / (dsigj + poles[i__ + poles_dim1]) / - difr[i__ + (difr_dim1 << 1)]; + work[i__] = z__[j] / (dlamc3_(&dsigj, &d__1) - difl[i__]) / + (dsigj + poles[i__ + poles_dim1]) / + difr[i__ + (difr_dim1 << 1)]; } -/* L70: */ } - dgemv_((char *)"T", k, nrhs, &c_b11, &b[b_offset], ldb, &work[1], & - c__1, &c_b13, &bx[j + bx_dim1], ldbx, (ftnlen)1); -/* L80: */ + dgemv_((char *)"T", k, nrhs, &c_b11, &b[b_offset], ldb, &work[1], &c__1, &c_b13, + &bx[j + bx_dim1], ldbx, (ftnlen)1); } } - -/* Step (2R): if SQRE = 1, apply back the rotation that is */ -/* related to the right null space of the subproblem. */ - if (*sqre == 1) { dcopy_(nrhs, &b[m + b_dim1], ldb, &bx[m + bx_dim1], ldbx); - drot_(nrhs, &bx[bx_dim1 + 1], ldbx, &bx[m + bx_dim1], ldbx, c__, - s); + drot_(nrhs, &bx[bx_dim1 + 1], ldbx, &bx[m + bx_dim1], ldbx, c__, s); } - if (*k < max(m,n)) { + if (*k < max(m, n)) { i__1 = n - *k; - dlacpy_((char *)"A", &i__1, nrhs, &b[*k + 1 + b_dim1], ldb, &bx[*k + 1 + - bx_dim1], ldbx, (ftnlen)1); + dlacpy_((char *)"A", &i__1, nrhs, &b[*k + 1 + b_dim1], ldb, &bx[*k + 1 + bx_dim1], ldbx, + (ftnlen)1); } - -/* Step (3R): permute rows of B. */ - dcopy_(nrhs, &bx[bx_dim1 + 1], ldbx, &b[nlp1 + b_dim1], ldb); if (*sqre == 1) { dcopy_(nrhs, &bx[m + bx_dim1], ldbx, &b[m + b_dim1], ldb); } i__1 = n; for (i__ = 2; i__ <= i__1; ++i__) { - dcopy_(nrhs, &bx[i__ + bx_dim1], ldbx, &b[perm[i__] + b_dim1], - ldb); -/* L90: */ + dcopy_(nrhs, &bx[i__ + bx_dim1], ldbx, &b[perm[i__] + b_dim1], ldb); } - -/* Step (4R): apply back the Givens rotations performed. */ - for (i__ = *givptr; i__ >= 1; --i__) { d__1 = -givnum[i__ + givnum_dim1]; - drot_(nrhs, &b[givcol[i__ + (givcol_dim1 << 1)] + b_dim1], ldb, & - b[givcol[i__ + givcol_dim1] + b_dim1], ldb, &givnum[i__ + - (givnum_dim1 << 1)], &d__1); -/* L100: */ + drot_(nrhs, &b[givcol[i__ + (givcol_dim1 << 1)] + b_dim1], ldb, + &b[givcol[i__ + givcol_dim1] + b_dim1], ldb, &givnum[i__ + (givnum_dim1 << 1)], + &d__1); } } - return 0; - -/* End of DLALS0 */ - -} /* dlals0_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlalsa.cpp b/lib/linalg/dlalsa.cpp index a428ee8c3d..82b9d56562 100644 --- a/lib/linalg/dlalsa.cpp +++ b/lib/linalg/dlalsa.cpp @@ -1,349 +1,35 @@ -/* fortran/dlalsa.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static doublereal c_b7 = 1.; static doublereal c_b8 = 0.; static integer c__2 = 2; - -/* > \brief \b DLALSA computes the SVD of the coefficient matrix in compact form. Used by sgelsd. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLALSA + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLALSA( ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U, */ -/* LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR, */ -/* GIVCOL, LDGCOL, PERM, GIVNUM, C, S, WORK, */ -/* IWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER ICOMPQ, INFO, LDB, LDBX, LDGCOL, LDU, N, NRHS, */ -/* $ SMLSIZ */ -/* .. */ -/* .. Array Arguments .. */ -/* INTEGER GIVCOL( LDGCOL, * ), GIVPTR( * ), IWORK( * ), */ -/* $ K( * ), PERM( LDGCOL, * ) */ -/* DOUBLE PRECISION B( LDB, * ), BX( LDBX, * ), C( * ), */ -/* $ DIFL( LDU, * ), DIFR( LDU, * ), */ -/* $ GIVNUM( LDU, * ), POLES( LDU, * ), S( * ), */ -/* $ U( LDU, * ), VT( LDU, * ), WORK( * ), */ -/* $ Z( LDU, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLALSA is an itermediate step in solving the least squares problem */ -/* > by computing the SVD of the coefficient matrix in compact form (The */ -/* > singular vectors are computed as products of simple orthorgonal */ -/* > matrices.). */ -/* > */ -/* > If ICOMPQ = 0, DLALSA applies the inverse of the left singular vector */ -/* > matrix of an upper bidiagonal matrix to the right hand side; and if */ -/* > ICOMPQ = 1, DLALSA applies the right singular vector matrix to the */ -/* > right hand side. The singular vector matrices were generated in */ -/* > compact form by DLALSA. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] ICOMPQ */ -/* > \verbatim */ -/* > ICOMPQ is INTEGER */ -/* > Specifies whether the left or the right singular vector */ -/* > matrix is involved. */ -/* > = 0: Left singular vector matrix */ -/* > = 1: Right singular vector matrix */ -/* > \endverbatim */ -/* > */ -/* > \param[in] SMLSIZ */ -/* > \verbatim */ -/* > SMLSIZ is INTEGER */ -/* > The maximum size of the subproblems at the bottom of the */ -/* > computation tree. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The row and column dimensions of the upper bidiagonal matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] NRHS */ -/* > \verbatim */ -/* > NRHS is INTEGER */ -/* > The number of columns of B and BX. NRHS must be at least 1. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] B */ -/* > \verbatim */ -/* > B is DOUBLE PRECISION array, dimension ( LDB, NRHS ) */ -/* > On input, B contains the right hand sides of the least */ -/* > squares problem in rows 1 through M. */ -/* > On output, B contains the solution X in rows 1 through N. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDB */ -/* > \verbatim */ -/* > LDB is INTEGER */ -/* > The leading dimension of B in the calling subprogram. */ -/* > LDB must be at least max(1,MAX( M, N ) ). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] BX */ -/* > \verbatim */ -/* > BX is DOUBLE PRECISION array, dimension ( LDBX, NRHS ) */ -/* > On exit, the result of applying the left or right singular */ -/* > vector matrix to B. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDBX */ -/* > \verbatim */ -/* > LDBX is INTEGER */ -/* > The leading dimension of BX. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] U */ -/* > \verbatim */ -/* > U is DOUBLE PRECISION array, dimension ( LDU, SMLSIZ ). */ -/* > On entry, U contains the left singular vector matrices of all */ -/* > subproblems at the bottom level. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDU */ -/* > \verbatim */ -/* > LDU is INTEGER, LDU = > N. */ -/* > The leading dimension of arrays U, VT, DIFL, DIFR, */ -/* > POLES, GIVNUM, and Z. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] VT */ -/* > \verbatim */ -/* > VT is DOUBLE PRECISION array, dimension ( LDU, SMLSIZ+1 ). */ -/* > On entry, VT**T contains the right singular vector matrices of */ -/* > all subproblems at the bottom level. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER array, dimension ( N ). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DIFL */ -/* > \verbatim */ -/* > DIFL is DOUBLE PRECISION array, dimension ( LDU, NLVL ). */ -/* > where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DIFR */ -/* > \verbatim */ -/* > DIFR is DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ). */ -/* > On entry, DIFL(*, I) and DIFR(*, 2 * I -1) record */ -/* > distances between singular values on the I-th level and */ -/* > singular values on the (I -1)-th level, and DIFR(*, 2 * I) */ -/* > record the normalizing factors of the right singular vectors */ -/* > matrices of subproblems on I-th level. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] Z */ -/* > \verbatim */ -/* > Z is DOUBLE PRECISION array, dimension ( LDU, NLVL ). */ -/* > On entry, Z(1, I) contains the components of the deflation- */ -/* > adjusted updating row vector for subproblems on the I-th */ -/* > level. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] POLES */ -/* > \verbatim */ -/* > POLES is DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ). */ -/* > On entry, POLES(*, 2 * I -1: 2 * I) contains the new and old */ -/* > singular values involved in the secular equations on the I-th */ -/* > level. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] GIVPTR */ -/* > \verbatim */ -/* > GIVPTR is INTEGER array, dimension ( N ). */ -/* > On entry, GIVPTR( I ) records the number of Givens */ -/* > rotations performed on the I-th problem on the computation */ -/* > tree. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] GIVCOL */ -/* > \verbatim */ -/* > GIVCOL is INTEGER array, dimension ( LDGCOL, 2 * NLVL ). */ -/* > On entry, for each I, GIVCOL(*, 2 * I - 1: 2 * I) records the */ -/* > locations of Givens rotations performed on the I-th level on */ -/* > the computation tree. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDGCOL */ -/* > \verbatim */ -/* > LDGCOL is INTEGER, LDGCOL = > N. */ -/* > The leading dimension of arrays GIVCOL and PERM. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] PERM */ -/* > \verbatim */ -/* > PERM is INTEGER array, dimension ( LDGCOL, NLVL ). */ -/* > On entry, PERM(*, I) records permutations done on the I-th */ -/* > level of the computation tree. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] GIVNUM */ -/* > \verbatim */ -/* > GIVNUM is DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ). */ -/* > On entry, GIVNUM(*, 2 *I -1 : 2 * I) records the C- and S- */ -/* > values of Givens rotations performed on the I-th level on the */ -/* > computation tree. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] C */ -/* > \verbatim */ -/* > C is DOUBLE PRECISION array, dimension ( N ). */ -/* > On entry, if the I-th subproblem is not square, */ -/* > C( I ) contains the C-value of a Givens rotation related to */ -/* > the right null space of the I-th subproblem. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] S */ -/* > \verbatim */ -/* > S is DOUBLE PRECISION array, dimension ( N ). */ -/* > On entry, if the I-th subproblem is not square, */ -/* > S( I ) contains the S-value of a Givens rotation related to */ -/* > the right null space of the I-th subproblem. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (N) */ -/* > \endverbatim */ -/* > */ -/* > \param[out] IWORK */ -/* > \verbatim */ -/* > IWORK is INTEGER array, dimension (3*N) */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit. */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleOTHERcomputational */ - -/* > \par Contributors: */ -/* ================== */ -/* > */ -/* > Ming Gu and Ren-Cang Li, Computer Science Division, University of */ -/* > California at Berkeley, USA \n */ -/* > Osni Marques, LBNL/NERSC, USA \n */ - -/* ===================================================================== */ -/* Subroutine */ int dlalsa_(integer *icompq, integer *smlsiz, integer *n, - integer *nrhs, doublereal *b, integer *ldb, doublereal *bx, integer * - ldbx, doublereal *u, integer *ldu, doublereal *vt, integer *k, - doublereal *difl, doublereal *difr, doublereal *z__, doublereal * - poles, integer *givptr, integer *givcol, integer *ldgcol, integer * - perm, doublereal *givnum, doublereal *c__, doublereal *s, doublereal * - work, integer *iwork, integer *info) +int dlalsa_(integer *icompq, integer *smlsiz, integer *n, integer *nrhs, doublereal *b, + integer *ldb, doublereal *bx, integer *ldbx, doublereal *u, integer *ldu, + doublereal *vt, integer *k, doublereal *difl, doublereal *difr, doublereal *z__, + doublereal *poles, integer *givptr, integer *givcol, integer *ldgcol, integer *perm, + doublereal *givnum, doublereal *c__, doublereal *s, doublereal *work, integer *iwork, + integer *info) { - /* System generated locals */ - integer givcol_dim1, givcol_offset, perm_dim1, perm_offset, b_dim1, - b_offset, bx_dim1, bx_offset, difl_dim1, difl_offset, difr_dim1, - difr_offset, givnum_dim1, givnum_offset, poles_dim1, poles_offset, - u_dim1, u_offset, vt_dim1, vt_offset, z_dim1, z_offset, i__1, - i__2; - - /* Builtin functions */ + integer givcol_dim1, givcol_offset, perm_dim1, perm_offset, b_dim1, b_offset, bx_dim1, + bx_offset, difl_dim1, difl_offset, difr_dim1, difr_offset, givnum_dim1, givnum_offset, + poles_dim1, poles_offset, u_dim1, u_offset, vt_dim1, vt_offset, z_dim1, z_offset, i__1, + i__2; integer pow_lmp_ii(integer *, integer *); - - /* Local variables */ - integer i__, j, i1, ic, lf, nd, ll, nl, nr, im1, nlf, nrf, lvl, ndb1, - nlp1, lvl2, nrp1, nlvl, sqre; - extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); + integer i__, j, i1, ic, lf, nd, ll, nl, nr, im1, nlf, nrf, lvl, ndb1, nlp1, lvl2, nrp1, nlvl, + sqre; + extern int dgemm_(char *, char *, integer *, integer *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, + ftnlen, ftnlen); integer inode, ndiml, ndimr; - extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, - doublereal *, integer *), dlals0_(integer *, integer *, integer *, - integer *, integer *, doublereal *, integer *, doublereal *, - integer *, integer *, integer *, integer *, integer *, doublereal - *, integer *, doublereal *, doublereal *, doublereal *, - doublereal *, integer *, doublereal *, doublereal *, doublereal *, - integer *), dlasdt_(integer *, integer *, integer *, integer *, - integer *, integer *, integer *), xerbla_(char *, integer *, - ftnlen); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ + extern int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *), + dlals0_(integer *, integer *, integer *, integer *, integer *, doublereal *, integer *, + doublereal *, integer *, integer *, integer *, integer *, integer *, doublereal *, + integer *, doublereal *, doublereal *, doublereal *, doublereal *, integer *, + doublereal *, doublereal *, doublereal *, integer *), + dlasdt_(integer *, integer *, integer *, integer *, integer *, integer *, integer *), + xerbla_(char *, integer *, ftnlen); b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; @@ -383,10 +69,7 @@ f"> */ --s; --work; --iwork; - - /* Function Body */ *info = 0; - if (*icompq < 0 || *icompq > 1) { *info = -1; } else if (*smlsiz < 3) { @@ -409,75 +92,36 @@ f"> */ xerbla_((char *)"DLALSA", &i__1, (ftnlen)6); return 0; } - -/* Book-keeping and setting up the computation tree. */ - inode = 1; ndiml = inode + *n; ndimr = ndiml + *n; - - dlasdt_(n, &nlvl, &nd, &iwork[inode], &iwork[ndiml], &iwork[ndimr], - smlsiz); - -/* The following code applies back the left singular vector factors. */ -/* For applying back the right singular vector factors, go to 50. */ - + dlasdt_(n, &nlvl, &nd, &iwork[inode], &iwork[ndiml], &iwork[ndimr], smlsiz); if (*icompq == 1) { goto L50; } - -/* The nodes on the bottom level of the tree were solved */ -/* by DLASDQ. The corresponding left and right singular vector */ -/* matrices are in explicit form. First apply back the left */ -/* singular vector matrices. */ - ndb1 = (nd + 1) / 2; i__1 = nd; for (i__ = ndb1; i__ <= i__1; ++i__) { - -/* IC : center row of each node */ -/* NL : number of rows of left subproblem */ -/* NR : number of rows of right subproblem */ -/* NLF: starting row of the left subproblem */ -/* NRF: starting row of the right subproblem */ - i1 = i__ - 1; ic = iwork[inode + i1]; nl = iwork[ndiml + i1]; nr = iwork[ndimr + i1]; nlf = ic - nl; nrf = ic + 1; - dgemm_((char *)"T", (char *)"N", &nl, nrhs, &nl, &c_b7, &u[nlf + u_dim1], ldu, &b[nlf - + b_dim1], ldb, &c_b8, &bx[nlf + bx_dim1], ldbx, (ftnlen)1, ( - ftnlen)1); - dgemm_((char *)"T", (char *)"N", &nr, nrhs, &nr, &c_b7, &u[nrf + u_dim1], ldu, &b[nrf - + b_dim1], ldb, &c_b8, &bx[nrf + bx_dim1], ldbx, (ftnlen)1, ( - ftnlen)1); -/* L10: */ + dgemm_((char *)"T", (char *)"N", &nl, nrhs, &nl, &c_b7, &u[nlf + u_dim1], ldu, &b[nlf + b_dim1], ldb, &c_b8, + &bx[nlf + bx_dim1], ldbx, (ftnlen)1, (ftnlen)1); + dgemm_((char *)"T", (char *)"N", &nr, nrhs, &nr, &c_b7, &u[nrf + u_dim1], ldu, &b[nrf + b_dim1], ldb, &c_b8, + &bx[nrf + bx_dim1], ldbx, (ftnlen)1, (ftnlen)1); } - -/* Next copy the rows of B that correspond to unchanged rows */ -/* in the bidiagonal matrix to BX. */ - i__1 = nd; for (i__ = 1; i__ <= i__1; ++i__) { ic = iwork[inode + i__ - 1]; dcopy_(nrhs, &b[ic + b_dim1], ldb, &bx[ic + bx_dim1], ldbx); -/* L20: */ } - -/* Finally go through the left singular vector matrices of all */ -/* the other subproblems bottom-up on the tree. */ - j = pow_lmp_ii(&c__2, &nlvl); sqre = 0; - for (lvl = nlvl; lvl >= 1; --lvl) { lvl2 = (lvl << 1) - 1; - -/* find the first node LF and last node LL on */ -/* the current level LVL */ - if (lvl == 1) { lf = 1; ll = 1; @@ -495,34 +139,19 @@ f"> */ nlf = ic - nl; nrf = ic + 1; --j; - dlals0_(icompq, &nl, &nr, &sqre, nrhs, &bx[nlf + bx_dim1], ldbx, & - b[nlf + b_dim1], ldb, &perm[nlf + lvl * perm_dim1], & - givptr[j], &givcol[nlf + lvl2 * givcol_dim1], ldgcol, & - givnum[nlf + lvl2 * givnum_dim1], ldu, &poles[nlf + lvl2 * - poles_dim1], &difl[nlf + lvl * difl_dim1], &difr[nlf + - lvl2 * difr_dim1], &z__[nlf + lvl * z_dim1], &k[j], &c__[ - j], &s[j], &work[1], info); -/* L30: */ + dlals0_(icompq, &nl, &nr, &sqre, nrhs, &bx[nlf + bx_dim1], ldbx, &b[nlf + b_dim1], ldb, + &perm[nlf + lvl * perm_dim1], &givptr[j], &givcol[nlf + lvl2 * givcol_dim1], + ldgcol, &givnum[nlf + lvl2 * givnum_dim1], ldu, &poles[nlf + lvl2 * poles_dim1], + &difl[nlf + lvl * difl_dim1], &difr[nlf + lvl2 * difr_dim1], + &z__[nlf + lvl * z_dim1], &k[j], &c__[j], &s[j], &work[1], info); } -/* L40: */ } goto L90; - -/* ICOMPQ = 1: applying back the right singular vector factors. */ - L50: - -/* First now go through the right singular vector matrices of all */ -/* the tree nodes top-down. */ - j = 0; i__1 = nlvl; for (lvl = 1; lvl <= i__1; ++lvl) { lvl2 = (lvl << 1) - 1; - -/* Find the first node LF and last node LL on */ -/* the current level LVL. */ - if (lvl == 1) { lf = 1; ll = 1; @@ -545,22 +174,13 @@ L50: sqre = 1; } ++j; - dlals0_(icompq, &nl, &nr, &sqre, nrhs, &b[nlf + b_dim1], ldb, &bx[ - nlf + bx_dim1], ldbx, &perm[nlf + lvl * perm_dim1], & - givptr[j], &givcol[nlf + lvl2 * givcol_dim1], ldgcol, & - givnum[nlf + lvl2 * givnum_dim1], ldu, &poles[nlf + lvl2 * - poles_dim1], &difl[nlf + lvl * difl_dim1], &difr[nlf + - lvl2 * difr_dim1], &z__[nlf + lvl * z_dim1], &k[j], &c__[ - j], &s[j], &work[1], info); -/* L60: */ + dlals0_(icompq, &nl, &nr, &sqre, nrhs, &b[nlf + b_dim1], ldb, &bx[nlf + bx_dim1], ldbx, + &perm[nlf + lvl * perm_dim1], &givptr[j], &givcol[nlf + lvl2 * givcol_dim1], + ldgcol, &givnum[nlf + lvl2 * givnum_dim1], ldu, &poles[nlf + lvl2 * poles_dim1], + &difl[nlf + lvl * difl_dim1], &difr[nlf + lvl2 * difr_dim1], + &z__[nlf + lvl * z_dim1], &k[j], &c__[j], &s[j], &work[1], info); } -/* L70: */ } - -/* The nodes on the bottom level of the tree were solved */ -/* by DLASDQ. The corresponding right singular vector */ -/* matrices are in explicit form. Apply them back. */ - ndb1 = (nd + 1) / 2; i__1 = nd; for (i__ = ndb1; i__ <= i__1; ++i__) { @@ -576,23 +196,14 @@ L50: } nlf = ic - nl; nrf = ic + 1; - dgemm_((char *)"T", (char *)"N", &nlp1, nrhs, &nlp1, &c_b7, &vt[nlf + vt_dim1], ldu, & - b[nlf + b_dim1], ldb, &c_b8, &bx[nlf + bx_dim1], ldbx, ( - ftnlen)1, (ftnlen)1); - dgemm_((char *)"T", (char *)"N", &nrp1, nrhs, &nrp1, &c_b7, &vt[nrf + vt_dim1], ldu, & - b[nrf + b_dim1], ldb, &c_b8, &bx[nrf + bx_dim1], ldbx, ( - ftnlen)1, (ftnlen)1); -/* L80: */ + dgemm_((char *)"T", (char *)"N", &nlp1, nrhs, &nlp1, &c_b7, &vt[nlf + vt_dim1], ldu, &b[nlf + b_dim1], ldb, + &c_b8, &bx[nlf + bx_dim1], ldbx, (ftnlen)1, (ftnlen)1); + dgemm_((char *)"T", (char *)"N", &nrp1, nrhs, &nrp1, &c_b7, &vt[nrf + vt_dim1], ldu, &b[nrf + b_dim1], ldb, + &c_b8, &bx[nrf + bx_dim1], ldbx, (ftnlen)1, (ftnlen)1); } - L90: - return 0; - -/* End of DLALSA */ - -} /* dlalsa_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlalsd.cpp b/lib/linalg/dlalsd.cpp index f3678a1bfd..a68eb9b93e 100644 --- a/lib/linalg/dlalsd.cpp +++ b/lib/linalg/dlalsd.cpp @@ -1,219 +1,18 @@ -/* fortran/dlalsd.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static doublereal c_b6 = 0.; static integer c__0 = 0; static doublereal c_b11 = 1.; - -/* > \brief \b DLALSD uses the singular value decomposition of A to solve the least squares problem. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLALSD + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND, */ -/* RANK, WORK, IWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER UPLO */ -/* INTEGER INFO, LDB, N, NRHS, RANK, SMLSIZ */ -/* DOUBLE PRECISION RCOND */ -/* .. */ -/* .. Array Arguments .. */ -/* INTEGER IWORK( * ) */ -/* DOUBLE PRECISION B( LDB, * ), D( * ), E( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLALSD uses the singular value decomposition of A to solve the least */ -/* > squares problem of finding X to minimize the Euclidean norm of each */ -/* > column of A*X-B, where A is N-by-N upper bidiagonal, and X and B */ -/* > are N-by-NRHS. The solution X overwrites B. */ -/* > */ -/* > The singular values of A smaller than RCOND times the largest */ -/* > singular value are treated as zero in solving the least squares */ -/* > problem; in this case a minimum norm solution is returned. */ -/* > The actual singular values are returned in D in ascending order. */ -/* > */ -/* > This code makes very mild assumptions about floating point */ -/* > arithmetic. It will work on machines with a guard digit in */ -/* > add/subtract, or on those binary machines without guard digits */ -/* > which subtract like the Cray XMP, Cray YMP, Cray C 90, or Cray 2. */ -/* > It could conceivably fail on hexadecimal or decimal machines */ -/* > without guard digits, but we know of none. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > = 'U': D and E define an upper bidiagonal matrix. */ -/* > = 'L': D and E define a lower bidiagonal matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] SMLSIZ */ -/* > \verbatim */ -/* > SMLSIZ is INTEGER */ -/* > The maximum size of the subproblems at the bottom of the */ -/* > computation tree. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The dimension of the bidiagonal matrix. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] NRHS */ -/* > \verbatim */ -/* > NRHS is INTEGER */ -/* > The number of columns of B. NRHS must be at least 1. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension (N) */ -/* > On entry D contains the main diagonal of the bidiagonal */ -/* > matrix. On exit, if INFO = 0, D contains its singular values. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] E */ -/* > \verbatim */ -/* > E is DOUBLE PRECISION array, dimension (N-1) */ -/* > Contains the super-diagonal entries of the bidiagonal matrix. */ -/* > On exit, E has been destroyed. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] B */ -/* > \verbatim */ -/* > B is DOUBLE PRECISION array, dimension (LDB,NRHS) */ -/* > On input, B contains the right hand sides of the least */ -/* > squares problem. On output, B contains the solution X. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDB */ -/* > \verbatim */ -/* > LDB is INTEGER */ -/* > The leading dimension of B in the calling subprogram. */ -/* > LDB must be at least max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] RCOND */ -/* > \verbatim */ -/* > RCOND is DOUBLE PRECISION */ -/* > The singular values of A less than or equal to RCOND times */ -/* > the largest singular value are treated as zero in solving */ -/* > the least squares problem. If RCOND is negative, */ -/* > machine precision is used instead. */ -/* > For example, if diag(S)*X=B were the least squares problem, */ -/* > where diag(S) is a diagonal matrix of singular values, the */ -/* > solution would be X(i) = B(i) / S(i) if S(i) is greater than */ -/* > RCOND*max(S), and X(i) = 0 if S(i) is less than or equal to */ -/* > RCOND*max(S). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] RANK */ -/* > \verbatim */ -/* > RANK is INTEGER */ -/* > The number of singular values of A greater than RCOND times */ -/* > the largest singular value. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension at least */ -/* > (9*N + 2*N*SMLSIZ + 8*N*NLVL + N*NRHS + (SMLSIZ+1)**2), */ -/* > where NLVL = max(0, INT(log_2 (N/(SMLSIZ+1))) + 1). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] IWORK */ -/* > \verbatim */ -/* > IWORK is INTEGER array, dimension at least */ -/* > (3*N*NLVL + 11*N) */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit. */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ -/* > > 0: The algorithm failed to compute a singular value while */ -/* > working on the submatrix lying in rows and columns */ -/* > INFO/(N+1) through MOD(INFO,N+1). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleOTHERcomputational */ - -/* > \par Contributors: */ -/* ================== */ -/* > */ -/* > Ming Gu and Ren-Cang Li, Computer Science Division, University of */ -/* > California at Berkeley, USA \n */ -/* > Osni Marques, LBNL/NERSC, USA \n */ - -/* ===================================================================== */ -/* Subroutine */ int dlalsd_(char *uplo, integer *smlsiz, integer *n, integer - *nrhs, doublereal *d__, doublereal *e, doublereal *b, integer *ldb, - doublereal *rcond, integer *rank, doublereal *work, integer *iwork, - integer *info, ftnlen uplo_len) +int dlalsd_(char *uplo, integer *smlsiz, integer *n, integer *nrhs, doublereal *d__, doublereal *e, + doublereal *b, integer *ldb, doublereal *rcond, integer *rank, doublereal *work, + integer *iwork, integer *info, ftnlen uplo_len) { - /* System generated locals */ integer b_dim1, b_offset, i__1, i__2; doublereal d__1; - - /* Builtin functions */ double log(doublereal), d_lmp_sign(doublereal *, doublereal *); - - /* Local variables */ integer c__, i__, j, k; doublereal r__; integer s, u, z__; @@ -227,74 +26,42 @@ f"> */ integer difl, difr; doublereal rcnd; integer perm, nsub; - extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, - doublereal *, integer *, doublereal *, doublereal *); + extern int drot_(integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, + doublereal *); integer nlvl, sqre, bxst; - extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen), - dcopy_(integer *, doublereal *, integer *, doublereal *, integer - *); + extern int dgemm_(char *, char *, integer *, integer *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, + ftnlen, ftnlen), + dcopy_(integer *, doublereal *, integer *, doublereal *, integer *); integer poles, sizei, nsize, nwork, icmpq1, icmpq2; extern doublereal dlamch_(char *, ftnlen); - extern /* Subroutine */ int dlasda_(integer *, integer *, integer *, - integer *, doublereal *, doublereal *, doublereal *, integer *, - doublereal *, integer *, doublereal *, doublereal *, doublereal *, - doublereal *, integer *, integer *, integer *, integer *, - doublereal *, doublereal *, doublereal *, doublereal *, integer *, - integer *), dlalsa_(integer *, integer *, integer *, integer *, - doublereal *, integer *, doublereal *, integer *, doublereal *, - integer *, doublereal *, integer *, doublereal *, doublereal *, - doublereal *, doublereal *, integer *, integer *, integer *, - integer *, doublereal *, doublereal *, doublereal *, doublereal *, - integer *, integer *), dlascl_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, integer *, doublereal *, - integer *, integer *, ftnlen); + extern int dlasda_(integer *, integer *, integer *, integer *, doublereal *, doublereal *, + doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, + doublereal *, doublereal *, integer *, integer *, integer *, integer *, + doublereal *, doublereal *, doublereal *, doublereal *, integer *, + integer *), + dlalsa_(integer *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, + integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, + doublereal *, doublereal *, doublereal *, integer *, integer *, integer *, + integer *, doublereal *, doublereal *, doublereal *, doublereal *, integer *, + integer *), + dlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, integer *, + doublereal *, integer *, integer *, ftnlen); extern integer idamax_(integer *, doublereal *, integer *); - extern /* Subroutine */ int dlasdq_(char *, integer *, integer *, integer - *, integer *, integer *, doublereal *, doublereal *, doublereal *, - integer *, doublereal *, integer *, doublereal *, integer *, - doublereal *, integer *, ftnlen), dlacpy_(char *, integer *, - integer *, doublereal *, integer *, doublereal *, integer *, - ftnlen), dlartg_(doublereal *, doublereal *, doublereal *, - doublereal *, doublereal *), dlaset_(char *, integer *, integer *, - doublereal *, doublereal *, doublereal *, integer *, ftnlen), - xerbla_(char *, integer *, ftnlen); + extern int dlasdq_(char *, integer *, integer *, integer *, integer *, integer *, doublereal *, + doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, + integer *, doublereal *, integer *, ftnlen), + dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, + ftnlen), + dlartg_(doublereal *, doublereal *, doublereal *, doublereal *, doublereal *), + dlaset_(char *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, + ftnlen), + xerbla_(char *, integer *, ftnlen); integer givcol; - extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *, - ftnlen); - extern /* Subroutine */ int dlasrt_(char *, integer *, doublereal *, - integer *, ftnlen); + extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *, ftnlen); + extern int dlasrt_(char *, integer *, doublereal *, integer *, ftnlen); doublereal orgnrm; integer givnum, givptr, smlszp; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ --d__; --e; b_dim1 = *ldb; @@ -302,10 +69,7 @@ f"> */ b -= b_offset; --work; --iwork; - - /* Function Body */ *info = 0; - if (*n < 0) { *info = -3; } else if (*nrhs < 1) { @@ -318,38 +82,26 @@ f"> */ xerbla_((char *)"DLALSD", &i__1, (ftnlen)6); return 0; } - eps = dlamch_((char *)"Epsilon", (ftnlen)7); - -/* Set up the tolerance. */ - if (*rcond <= 0. || *rcond >= 1.) { rcnd = eps; } else { rcnd = *rcond; } - *rank = 0; - -/* Quick return if possible. */ - if (*n == 0) { return 0; } else if (*n == 1) { if (d__[1] == 0.) { - dlaset_((char *)"A", &c__1, nrhs, &c_b6, &c_b6, &b[b_offset], ldb, ( - ftnlen)1); + dlaset_((char *)"A", &c__1, nrhs, &c_b6, &c_b6, &b[b_offset], ldb, (ftnlen)1); } else { *rank = 1; - dlascl_((char *)"G", &c__0, &c__0, &d__[1], &c_b11, &c__1, nrhs, &b[ - b_offset], ldb, info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &d__[1], &c_b11, &c__1, nrhs, &b[b_offset], ldb, info, + (ftnlen)1); d__[1] = abs(d__[1]); } return 0; } - -/* Rotate the matrix if it is lower bidiagonal. */ - if (*(unsigned char *)uplo == 'L') { i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { @@ -358,13 +110,11 @@ f"> */ e[i__] = sn * d__[i__ + 1]; d__[i__ + 1] = cs * d__[i__ + 1]; if (*nrhs == 1) { - drot_(&c__1, &b[i__ + b_dim1], &c__1, &b[i__ + 1 + b_dim1], & - c__1, &cs, &sn); + drot_(&c__1, &b[i__ + b_dim1], &c__1, &b[i__ + 1 + b_dim1], &c__1, &cs, &sn); } else { work[(i__ << 1) - 1] = cs; work[i__ * 2] = sn; } -/* L10: */ } if (*nrhs > 1) { i__1 = *nrhs; @@ -373,37 +123,25 @@ f"> */ for (j = 1; j <= i__2; ++j) { cs = work[(j << 1) - 1]; sn = work[j * 2]; - drot_(&c__1, &b[j + i__ * b_dim1], &c__1, &b[j + 1 + i__ * - b_dim1], &c__1, &cs, &sn); -/* L20: */ + drot_(&c__1, &b[j + i__ * b_dim1], &c__1, &b[j + 1 + i__ * b_dim1], &c__1, &cs, + &sn); } -/* L30: */ } } } - -/* Scale. */ - nm1 = *n - 1; orgnrm = dlanst_((char *)"M", n, &d__[1], &e[1], (ftnlen)1); if (orgnrm == 0.) { dlaset_((char *)"A", n, nrhs, &c_b6, &c_b6, &b[b_offset], ldb, (ftnlen)1); return 0; } - - dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b11, n, &c__1, &d__[1], n, info, ( - ftnlen)1); - dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b11, &nm1, &c__1, &e[1], &nm1, - info, (ftnlen)1); - -/* If N is smaller than the minimum divide size SMLSIZ, then solve */ -/* the problem with another solver. */ - + dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b11, n, &c__1, &d__[1], n, info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b11, &nm1, &c__1, &e[1], &nm1, info, (ftnlen)1); if (*n <= *smlsiz) { nwork = *n * *n + 1; dlaset_((char *)"A", n, n, &c_b6, &c_b11, &work[1], n, (ftnlen)1); - dlasdq_((char *)"U", &c__0, n, n, &c__0, nrhs, &d__[1], &e[1], &work[1], n, & - work[1], n, &b[b_offset], ldb, &work[nwork], info, (ftnlen)1); + dlasdq_((char *)"U", &c__0, n, n, &c__0, nrhs, &d__[1], &e[1], &work[1], n, &work[1], n, + &b[b_offset], ldb, &work[nwork], info, (ftnlen)1); if (*info != 0) { return 0; } @@ -411,37 +149,23 @@ f"> */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { if (d__[i__] <= tol) { - dlaset_((char *)"A", &c__1, nrhs, &c_b6, &c_b6, &b[i__ + b_dim1], ldb, - (ftnlen)1); + dlaset_((char *)"A", &c__1, nrhs, &c_b6, &c_b6, &b[i__ + b_dim1], ldb, (ftnlen)1); } else { - dlascl_((char *)"G", &c__0, &c__0, &d__[i__], &c_b11, &c__1, nrhs, &b[ - i__ + b_dim1], ldb, info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &d__[i__], &c_b11, &c__1, nrhs, &b[i__ + b_dim1], ldb, + info, (ftnlen)1); ++(*rank); } -/* L40: */ } - dgemm_((char *)"T", (char *)"N", n, nrhs, n, &c_b11, &work[1], n, &b[b_offset], ldb, & - c_b6, &work[nwork], n, (ftnlen)1, (ftnlen)1); + dgemm_((char *)"T", (char *)"N", n, nrhs, n, &c_b11, &work[1], n, &b[b_offset], ldb, &c_b6, &work[nwork], n, + (ftnlen)1, (ftnlen)1); dlacpy_((char *)"A", n, nrhs, &work[nwork], n, &b[b_offset], ldb, (ftnlen)1); - -/* Unscale. */ - - dlascl_((char *)"G", &c__0, &c__0, &c_b11, &orgnrm, n, &c__1, &d__[1], n, - info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &c_b11, &orgnrm, n, &c__1, &d__[1], n, info, (ftnlen)1); dlasrt_((char *)"D", n, &d__[1], info, (ftnlen)1); - dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b11, n, nrhs, &b[b_offset], - ldb, info, (ftnlen)1); - + dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b11, n, nrhs, &b[b_offset], ldb, info, (ftnlen)1); return 0; } - -/* Book-keeping and setting up some constants. */ - - nlvl = (integer) (log((doublereal) (*n) / (doublereal) (*smlsiz + 1)) / - log(2.)) + 1; - + nlvl = (integer)(log((doublereal)(*n) / (doublereal)(*smlsiz + 1)) / log(2.)) + 1; smlszp = *smlsiz + 1; - u = 1; vt = *smlsiz * *n + 1; difl = vt + smlszp * *n; @@ -453,55 +177,35 @@ f"> */ givnum = poles + (nlvl << 1) * *n; bx = givnum + (nlvl << 1) * *n; nwork = bx + *n * *nrhs; - sizei = *n + 1; k = sizei + *n; givptr = k + *n; perm = givptr + *n; givcol = perm + nlvl * *n; iwk = givcol + (nlvl * *n << 1); - st = 1; sqre = 0; icmpq1 = 1; icmpq2 = 0; nsub = 0; - i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { if ((d__1 = d__[i__], abs(d__1)) < eps) { d__[i__] = d_lmp_sign(&eps, &d__[i__]); } -/* L50: */ } - i__1 = nm1; for (i__ = 1; i__ <= i__1; ++i__) { if ((d__1 = e[i__], abs(d__1)) < eps || i__ == nm1) { ++nsub; iwork[nsub] = st; - -/* Subproblem found. First determine its size and then */ -/* apply divide and conquer on it. */ - if (i__ < nm1) { - -/* A subproblem with E(I) small for I < NM1. */ - nsize = i__ - st + 1; iwork[sizei + nsub - 1] = nsize; } else if ((d__1 = e[i__], abs(d__1)) >= eps) { - -/* A subproblem with E(NM1) not too small but I = NM1. */ - nsize = *n - st + 1; iwork[sizei + nsub - 1] = nsize; } else { - -/* A subproblem with E(NM1) small. This implies an */ -/* 1-by-1 subproblem at D(N), which is not solved */ -/* explicitly. */ - nsize = i__ - st + 1; iwork[sizei + nsub - 1] = nsize; ++nsub; @@ -511,80 +215,50 @@ f"> */ } st1 = st - 1; if (nsize == 1) { - -/* This is a 1-by-1 subproblem and is not solved */ -/* explicitly. */ - dcopy_(nrhs, &b[st + b_dim1], ldb, &work[bx + st1], n); } else if (nsize <= *smlsiz) { - -/* This is a small subproblem and is solved by DLASDQ. */ - - dlaset_((char *)"A", &nsize, &nsize, &c_b6, &c_b11, &work[vt + st1], - n, (ftnlen)1); - dlasdq_((char *)"U", &c__0, &nsize, &nsize, &c__0, nrhs, &d__[st], &e[ - st], &work[vt + st1], n, &work[nwork], n, &b[st + - b_dim1], ldb, &work[nwork], info, (ftnlen)1); + dlaset_((char *)"A", &nsize, &nsize, &c_b6, &c_b11, &work[vt + st1], n, (ftnlen)1); + dlasdq_((char *)"U", &c__0, &nsize, &nsize, &c__0, nrhs, &d__[st], &e[st], &work[vt + st1], + n, &work[nwork], n, &b[st + b_dim1], ldb, &work[nwork], info, (ftnlen)1); if (*info != 0) { return 0; } - dlacpy_((char *)"A", &nsize, nrhs, &b[st + b_dim1], ldb, &work[bx + - st1], n, (ftnlen)1); + dlacpy_((char *)"A", &nsize, nrhs, &b[st + b_dim1], ldb, &work[bx + st1], n, (ftnlen)1); } else { - -/* A large problem. Solve it using divide and conquer. */ - - dlasda_(&icmpq1, smlsiz, &nsize, &sqre, &d__[st], &e[st], & - work[u + st1], n, &work[vt + st1], &iwork[k + st1], & - work[difl + st1], &work[difr + st1], &work[z__ + st1], - &work[poles + st1], &iwork[givptr + st1], &iwork[ - givcol + st1], n, &iwork[perm + st1], &work[givnum + - st1], &work[c__ + st1], &work[s + st1], &work[nwork], - &iwork[iwk], info); + dlasda_(&icmpq1, smlsiz, &nsize, &sqre, &d__[st], &e[st], &work[u + st1], n, + &work[vt + st1], &iwork[k + st1], &work[difl + st1], &work[difr + st1], + &work[z__ + st1], &work[poles + st1], &iwork[givptr + st1], + &iwork[givcol + st1], n, &iwork[perm + st1], &work[givnum + st1], + &work[c__ + st1], &work[s + st1], &work[nwork], &iwork[iwk], info); if (*info != 0) { return 0; } bxst = bx + st1; - dlalsa_(&icmpq2, smlsiz, &nsize, nrhs, &b[st + b_dim1], ldb, & - work[bxst], n, &work[u + st1], n, &work[vt + st1], & - iwork[k + st1], &work[difl + st1], &work[difr + st1], - &work[z__ + st1], &work[poles + st1], &iwork[givptr + - st1], &iwork[givcol + st1], n, &iwork[perm + st1], & - work[givnum + st1], &work[c__ + st1], &work[s + st1], - &work[nwork], &iwork[iwk], info); + dlalsa_(&icmpq2, smlsiz, &nsize, nrhs, &b[st + b_dim1], ldb, &work[bxst], n, + &work[u + st1], n, &work[vt + st1], &iwork[k + st1], &work[difl + st1], + &work[difr + st1], &work[z__ + st1], &work[poles + st1], + &iwork[givptr + st1], &iwork[givcol + st1], n, &iwork[perm + st1], + &work[givnum + st1], &work[c__ + st1], &work[s + st1], &work[nwork], + &iwork[iwk], info); if (*info != 0) { return 0; } } st = i__ + 1; } -/* L60: */ } - -/* Apply the singular values and treat the tiny ones as zero. */ - tol = rcnd * (d__1 = d__[idamax_(n, &d__[1], &c__1)], abs(d__1)); - i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { - -/* Some of the elements in D can be negative because 1-by-1 */ -/* subproblems were not solved explicitly. */ - if ((d__1 = d__[i__], abs(d__1)) <= tol) { - dlaset_((char *)"A", &c__1, nrhs, &c_b6, &c_b6, &work[bx + i__ - 1], n, ( - ftnlen)1); + dlaset_((char *)"A", &c__1, nrhs, &c_b6, &c_b6, &work[bx + i__ - 1], n, (ftnlen)1); } else { ++(*rank); - dlascl_((char *)"G", &c__0, &c__0, &d__[i__], &c_b11, &c__1, nrhs, &work[ - bx + i__ - 1], n, info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &d__[i__], &c_b11, &c__1, nrhs, &work[bx + i__ - 1], n, info, + (ftnlen)1); } d__[i__] = (d__1 = d__[i__], abs(d__1)); -/* L70: */ } - -/* Now apply back the right singular vectors. */ - icmpq2 = 1; i__1 = nsub; for (i__ = 1; i__ <= i__1; ++i__) { @@ -595,38 +269,24 @@ f"> */ if (nsize == 1) { dcopy_(nrhs, &work[bxst], n, &b[st + b_dim1], ldb); } else if (nsize <= *smlsiz) { - dgemm_((char *)"T", (char *)"N", &nsize, nrhs, &nsize, &c_b11, &work[vt + st1], n, - &work[bxst], n, &c_b6, &b[st + b_dim1], ldb, (ftnlen)1, ( - ftnlen)1); + dgemm_((char *)"T", (char *)"N", &nsize, nrhs, &nsize, &c_b11, &work[vt + st1], n, &work[bxst], n, + &c_b6, &b[st + b_dim1], ldb, (ftnlen)1, (ftnlen)1); } else { - dlalsa_(&icmpq2, smlsiz, &nsize, nrhs, &work[bxst], n, &b[st + - b_dim1], ldb, &work[u + st1], n, &work[vt + st1], &iwork[ - k + st1], &work[difl + st1], &work[difr + st1], &work[z__ - + st1], &work[poles + st1], &iwork[givptr + st1], &iwork[ - givcol + st1], n, &iwork[perm + st1], &work[givnum + st1], - &work[c__ + st1], &work[s + st1], &work[nwork], &iwork[ - iwk], info); + dlalsa_(&icmpq2, smlsiz, &nsize, nrhs, &work[bxst], n, &b[st + b_dim1], ldb, + &work[u + st1], n, &work[vt + st1], &iwork[k + st1], &work[difl + st1], + &work[difr + st1], &work[z__ + st1], &work[poles + st1], &iwork[givptr + st1], + &iwork[givcol + st1], n, &iwork[perm + st1], &work[givnum + st1], + &work[c__ + st1], &work[s + st1], &work[nwork], &iwork[iwk], info); if (*info != 0) { return 0; } } -/* L80: */ } - -/* Unscale and sort the singular values. */ - - dlascl_((char *)"G", &c__0, &c__0, &c_b11, &orgnrm, n, &c__1, &d__[1], n, info, ( - ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &c_b11, &orgnrm, n, &c__1, &d__[1], n, info, (ftnlen)1); dlasrt_((char *)"D", n, &d__[1], info, (ftnlen)1); - dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b11, n, nrhs, &b[b_offset], ldb, - info, (ftnlen)1); - + dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b11, n, nrhs, &b[b_offset], ldb, info, (ftnlen)1); return 0; - -/* End of DLALSD */ - -} /* dlalsd_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlamc3.cpp b/lib/linalg/dlamc3.cpp index a7dbd89bc0..0c33327867 100644 --- a/lib/linalg/dlamc3.cpp +++ b/lib/linalg/dlamc3.cpp @@ -1,68 +1,13 @@ -/* static/dlamc3.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DLAMC3 */ -/* > \details */ -/* > \b Purpose: */ -/* > \verbatim */ -/* > DLAMC3 is intended to force A and B to be stored prior to doing */ -/* > the addition of A and B , for use in situations where optimizers */ -/* > might hold one of these in a register. */ -/* > \endverbatim */ -/* > \author LAPACK is a software package provided by Univ. of Tennessee, Univ. of California Berkeley, Univ. -of Colorado Denver and NAG Ltd.. */ -/* > \date December 2016 */ -/* > \ingroup auxOTHERauxiliary */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is a DOUBLE PRECISION */ -/* > \endverbatim */ -/* > */ -/* > \param[in] B */ -/* > \verbatim */ -/* > B is a DOUBLE PRECISION */ -/* > The values A and B. */ -/* > \endverbatim */ -/* > */ doublereal dlamc3_(doublereal *a, doublereal *b) { - /* System generated locals */ doublereal ret_val; - - -/* -- LAPACK auxiliary routine (version 3.7.0) -- */ -/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ -/* November 2010 */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* ===================================================================== */ - -/* .. Executable Statements .. */ - ret_val = *a + *b; - return ret_val; - -/* End of DLAMC3 */ - -} /* dlamc3_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlamch.cpp b/lib/linalg/dlamch.cpp index 3d616d95d2..277096e6f3 100644 --- a/lib/linalg/dlamch.cpp +++ b/lib/linalg/dlamch.cpp @@ -12,34 +12,34 @@ extern "C" { doublereal dlamch_(const char *cmach) { - if (!cmach) return 0.0; - char select = toupper(*cmach); + if (!cmach) return 0.0; + char select = toupper(*cmach); - // BLAS assumes rounding not truncation => epsilon is half - const double eps = 0.5 * std::numeric_limits::epsilon(); - if (select == 'E') return eps; + // BLAS assumes rounding not truncation => epsilon is half + const double eps = 0.5 * std::numeric_limits::epsilon(); + if (select == 'E') return eps; - double min = std::numeric_limits::min(); - const double max = std::numeric_limits::max(); - double small = 1.0 / max; - if (small >= min) min = small * (1.0 + eps); - if (select == 'S') return min; + double min = std::numeric_limits::min(); + const double max = std::numeric_limits::max(); + double small = 1.0 / max; + if (small >= min) min = small * (1.0 + eps); + if (select == 'S') return min; - const double radix = std::numeric_limits::radix; - if (select == 'B') return radix; + const double radix = std::numeric_limits::radix; + if (select == 'B') return radix; - if (select == 'P') return eps * radix; + if (select == 'P') return eps * radix; - if (select == 'N') return std::numeric_limits::digits; + if (select == 'N') return std::numeric_limits::digits; - if (select == 'M') return std::numeric_limits::min_exponent; + if (select == 'M') return std::numeric_limits::min_exponent; - if (select == 'U') return min; + if (select == 'U') return min; - if (select == 'L') return std::numeric_limits::max_exponent; + if (select == 'L') return std::numeric_limits::max_exponent; - if (select == 'O') return max; + if (select == 'O') return max; - return 0.0; + return 0.0; } } diff --git a/lib/linalg/dlamrg.cpp b/lib/linalg/dlamrg.cpp index 810d1db154..cb4d918840 100644 --- a/lib/linalg/dlamrg.cpp +++ b/lib/linalg/dlamrg.cpp @@ -1,151 +1,13 @@ -/* fortran/dlamrg.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DLAMRG creates a permutation list to merge the entries of two independently sorted sets into a -single set sorted in ascending order. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLAMRG + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLAMRG( N1, N2, A, DTRD1, DTRD2, INDEX ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER DTRD1, DTRD2, N1, N2 */ -/* .. */ -/* .. Array Arguments .. */ -/* INTEGER INDEX( * ) */ -/* DOUBLE PRECISION A( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLAMRG will create a permutation list which will merge the elements */ -/* > of A (which is composed of two independently sorted sets) into a */ -/* > single set which is sorted in ascending order. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N1 */ -/* > \verbatim */ -/* > N1 is INTEGER */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N2 */ -/* > \verbatim */ -/* > N2 is INTEGER */ -/* > These arguments contain the respective lengths of the two */ -/* > sorted lists to be merged. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (N1+N2) */ -/* > The first N1 elements of A contain a list of numbers which */ -/* > are sorted in either ascending or descending order. Likewise */ -/* > for the final N2 elements. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DTRD1 */ -/* > \verbatim */ -/* > DTRD1 is INTEGER */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DTRD2 */ -/* > \verbatim */ -/* > DTRD2 is INTEGER */ -/* > These are the strides to be taken through the array A. */ -/* > Allowable strides are 1 and -1. They indicate whether a */ -/* > subset of A is sorted in ascending (DTRDx = 1) or descending */ -/* > (DTRDx = -1) order. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INDEX */ -/* > \verbatim */ -/* > INDEX is INTEGER array, dimension (N1+N2) */ -/* > On exit this array will contain a permutation such that */ -/* > if B( I ) = A( INDEX( I ) ) for I=1,N1+N2, then B will be */ -/* > sorted in ascending order. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup auxOTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dlamrg_(integer *n1, integer *n2, doublereal *a, integer - *dtrd1, integer *dtrd2, integer *index) +int dlamrg_(integer *n1, integer *n2, doublereal *a, integer *dtrd1, integer *dtrd2, integer *index) { - /* System generated locals */ integer i__1; - - /* Local variables */ integer i__, ind1, ind2, n1sv, n2sv; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Local Scalars .. */ -/* .. */ -/* .. Executable Statements .. */ - - /* Parameter adjustments */ --index; --a; - - /* Function Body */ n1sv = *n1; n2sv = *n2; if (*dtrd1 > 0) { @@ -159,7 +21,6 @@ f"> */ ind2 = *n1 + *n2; } i__ = 1; -/* while ( (N1SV > 0) & (N2SV > 0) ) */ L10: if (n1sv > 0 && n2sv > 0) { if (a[ind1] <= a[ind2]) { @@ -175,32 +36,23 @@ L10: } goto L10; } -/* end while */ if (n1sv == 0) { i__1 = n2sv; for (n1sv = 1; n1sv <= i__1; ++n1sv) { index[i__] = ind2; ++i__; ind2 += *dtrd2; -/* L20: */ } } else { -/* N2SV .EQ. 0 */ i__1 = n1sv; for (n2sv = 1; n2sv <= i__1; ++n2sv) { index[i__] = ind1; ++i__; ind1 += *dtrd1; -/* L30: */ } } - return 0; - -/* End of DLAMRG */ - -} /* dlamrg_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlange.cpp b/lib/linalg/dlange.cpp index ab88573259..f6ef58d0b2 100644 --- a/lib/linalg/dlange.cpp +++ b/lib/linalg/dlange.cpp @@ -1,196 +1,27 @@ -/* fortran/dlange.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; - -/* > \brief \b DLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute -value of any element of a general rectangular matrix. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLANGE + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* DOUBLE PRECISION FUNCTION DLANGE( NORM, M, N, A, LDA, WORK ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER NORM */ -/* INTEGER LDA, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLANGE returns the value of the one norm, or the Frobenius norm, or */ -/* > the infinity norm, or the element of largest absolute value of a */ -/* > real matrix A. */ -/* > \endverbatim */ -/* > */ -/* > \return DLANGE */ -/* > \verbatim */ -/* > */ -/* > DLANGE = ( max(abs(A(i,j))), NORM = 'M' or 'm' */ -/* > ( */ -/* > ( norm1(A), NORM = '1', 'O' or 'o' */ -/* > ( */ -/* > ( normI(A), NORM = 'I' or 'i' */ -/* > ( */ -/* > ( normF(A), NORM = 'F', 'f', 'E' or 'e' */ -/* > */ -/* > where norm1 denotes the one norm of a matrix (maximum column sum), */ -/* > normI denotes the infinity norm of a matrix (maximum row sum) and */ -/* > normF denotes the Frobenius norm of a matrix (square root of sum of */ -/* > squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] NORM */ -/* > \verbatim */ -/* > NORM is CHARACTER*1 */ -/* > Specifies the value to be returned in DLANGE as described */ -/* > above. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix A. M >= 0. When M = 0, */ -/* > DLANGE is set to zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix A. N >= 0. When N = 0, */ -/* > DLANGE is set to zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > The m by n matrix A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(M,1). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), */ -/* > where LWORK >= M when NORM = 'I'; otherwise, WORK is not */ -/* > referenced. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleGEauxiliary */ - -/* ===================================================================== */ -doublereal dlange_(char *norm, integer *m, integer *n, doublereal *a, integer - *lda, doublereal *work, ftnlen norm_len) +doublereal dlange_(char *norm, integer *m, integer *n, doublereal *a, integer *lda, + doublereal *work, ftnlen norm_len) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; doublereal ret_val, d__1; - - /* Builtin functions */ double sqrt(doublereal); - - /* Local variables */ integer i__, j; doublereal sum, temp, scale; extern logical lsame_(char *, char *, ftnlen, ftnlen); doublereal value; extern logical disnan_(doublereal *); - extern /* Subroutine */ int dlassq_(integer *, doublereal *, integer *, - doublereal *, doublereal *); - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - - /* Parameter adjustments */ + extern int dlassq_(integer *, doublereal *, integer *, doublereal *, doublereal *); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --work; - - /* Function Body */ - if (min(*m,*n) == 0) { + if (min(*m, *n) == 0) { value = 0.; } else if (lsame_(norm, (char *)"M", (ftnlen)1, (ftnlen)1)) { - -/* Find max(abs(A(i,j))). */ - value = 0.; i__1 = *n; for (j = 1; j <= i__1; ++j) { @@ -200,15 +31,9 @@ doublereal dlange_(char *norm, integer *m, integer *n, doublereal *a, integer if (value < temp || disnan_(&temp)) { value = temp; } -/* L10: */ } -/* L20: */ } - } else if (lsame_(norm, (char *)"O", (ftnlen)1, (ftnlen)1) || *(unsigned char *) - norm == '1') { - -/* Find norm1(A). */ - + } else if (lsame_(norm, (char *)"O", (ftnlen)1, (ftnlen)1) || *(unsigned char *)norm == '1') { value = 0.; i__1 = *n; for (j = 1; j <= i__1; ++j) { @@ -216,30 +41,22 @@ doublereal dlange_(char *norm, integer *m, integer *n, doublereal *a, integer i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { sum += (d__1 = a[i__ + j * a_dim1], abs(d__1)); -/* L30: */ } if (value < sum || disnan_(&sum)) { value = sum; } -/* L40: */ } } else if (lsame_(norm, (char *)"I", (ftnlen)1, (ftnlen)1)) { - -/* Find normI(A). */ - i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { work[i__] = 0.; -/* L50: */ } i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { work[i__] += (d__1 = a[i__ + j * a_dim1], abs(d__1)); -/* L60: */ } -/* L70: */ } value = 0.; i__1 = *m; @@ -248,30 +65,19 @@ doublereal dlange_(char *norm, integer *m, integer *n, doublereal *a, integer if (value < temp || disnan_(&temp)) { value = temp; } -/* L80: */ } - } else if (lsame_(norm, (char *)"F", (ftnlen)1, (ftnlen)1) || lsame_(norm, (char *)"E", ( - ftnlen)1, (ftnlen)1)) { - -/* Find normF(A). */ - + } else if (lsame_(norm, (char *)"F", (ftnlen)1, (ftnlen)1) || lsame_(norm, (char *)"E", (ftnlen)1, (ftnlen)1)) { scale = 0.; sum = 1.; i__1 = *n; for (j = 1; j <= i__1; ++j) { dlassq_(m, &a[j * a_dim1 + 1], &c__1, &scale, &sum); -/* L90: */ } value = scale * sqrt(sum); } - ret_val = value; return ret_val; - -/* End of DLANGE */ - -} /* dlange_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlanst.cpp b/lib/linalg/dlanst.cpp index c216660b75..5b401bd0d9 100644 --- a/lib/linalg/dlanst.cpp +++ b/lib/linalg/dlanst.cpp @@ -1,180 +1,24 @@ -/* fortran/dlanst.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; - -/* > \brief \b DLANST returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the ele -ment of largest absolute value of a real symmetric tridiagonal matrix. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLANST + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* DOUBLE PRECISION FUNCTION DLANST( NORM, N, D, E ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER NORM */ -/* INTEGER N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION D( * ), E( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLANST returns the value of the one norm, or the Frobenius norm, or */ -/* > the infinity norm, or the element of largest absolute value of a */ -/* > real symmetric tridiagonal matrix A. */ -/* > \endverbatim */ -/* > */ -/* > \return DLANST */ -/* > \verbatim */ -/* > */ -/* > DLANST = ( max(abs(A(i,j))), NORM = 'M' or 'm' */ -/* > ( */ -/* > ( norm1(A), NORM = '1', 'O' or 'o' */ -/* > ( */ -/* > ( normI(A), NORM = 'I' or 'i' */ -/* > ( */ -/* > ( normF(A), NORM = 'F', 'f', 'E' or 'e' */ -/* > */ -/* > where norm1 denotes the one norm of a matrix (maximum column sum), */ -/* > normI denotes the infinity norm of a matrix (maximum row sum) and */ -/* > normF denotes the Frobenius norm of a matrix (square root of sum of */ -/* > squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] NORM */ -/* > \verbatim */ -/* > NORM is CHARACTER*1 */ -/* > Specifies the value to be returned in DLANST as described */ -/* > above. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrix A. N >= 0. When N = 0, DLANST is */ -/* > set to zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension (N) */ -/* > The diagonal elements of A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] E */ -/* > \verbatim */ -/* > E is DOUBLE PRECISION array, dimension (N-1) */ -/* > The (n-1) sub-diagonal or super-diagonal elements of A. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup OTHERauxiliary */ - -/* ===================================================================== */ -doublereal dlanst_(char *norm, integer *n, doublereal *d__, doublereal *e, - ftnlen norm_len) +doublereal dlanst_(char *norm, integer *n, doublereal *d__, doublereal *e, ftnlen norm_len) { - /* System generated locals */ integer i__1; doublereal ret_val, d__1, d__2, d__3; - - /* Builtin functions */ double sqrt(doublereal); - - /* Local variables */ integer i__; doublereal sum, scale; extern logical lsame_(char *, char *, ftnlen, ftnlen); doublereal anorm; extern logical disnan_(doublereal *); - extern /* Subroutine */ int dlassq_(integer *, doublereal *, integer *, - doublereal *, doublereal *); - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - - /* Parameter adjustments */ + extern int dlassq_(integer *, doublereal *, integer *, doublereal *, doublereal *); --e; --d__; - - /* Function Body */ if (*n <= 0) { anorm = 0.; } else if (lsame_(norm, (char *)"M", (ftnlen)1, (ftnlen)1)) { - -/* Find max(abs(A(i,j))). */ - anorm = (d__1 = d__[*n], abs(d__1)); i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { @@ -186,13 +30,9 @@ doublereal dlanst_(char *norm, integer *n, doublereal *d__, doublereal *e, if (anorm < sum || disnan_(&sum)) { anorm = sum; } -/* L10: */ } - } else if (lsame_(norm, (char *)"O", (ftnlen)1, (ftnlen)1) || *(unsigned char *) - norm == '1' || lsame_(norm, (char *)"I", (ftnlen)1, (ftnlen)1)) { - -/* Find norm1(A). */ - + } else if (lsame_(norm, (char *)"O", (ftnlen)1, (ftnlen)1) || *(unsigned char *)norm == '1' || + lsame_(norm, (char *)"I", (ftnlen)1, (ftnlen)1)) { if (*n == 1) { anorm = abs(d__[1]); } else { @@ -203,19 +43,14 @@ doublereal dlanst_(char *norm, integer *n, doublereal *d__, doublereal *e, } i__1 = *n - 1; for (i__ = 2; i__ <= i__1; ++i__) { - sum = (d__1 = d__[i__], abs(d__1)) + (d__2 = e[i__], abs(d__2) - ) + (d__3 = e[i__ - 1], abs(d__3)); + sum = (d__1 = d__[i__], abs(d__1)) + (d__2 = e[i__], abs(d__2)) + + (d__3 = e[i__ - 1], abs(d__3)); if (anorm < sum || disnan_(&sum)) { anorm = sum; } -/* L20: */ } } - } else if (lsame_(norm, (char *)"F", (ftnlen)1, (ftnlen)1) || lsame_(norm, (char *)"E", ( - ftnlen)1, (ftnlen)1)) { - -/* Find normF(A). */ - + } else if (lsame_(norm, (char *)"F", (ftnlen)1, (ftnlen)1) || lsame_(norm, (char *)"E", (ftnlen)1, (ftnlen)1)) { scale = 0.; sum = 1.; if (*n > 1) { @@ -226,14 +61,9 @@ doublereal dlanst_(char *norm, integer *n, doublereal *d__, doublereal *e, dlassq_(n, &d__[1], &c__1, &scale, &sum); anorm = scale * sqrt(sum); } - ret_val = anorm; return ret_val; - -/* End of DLANST */ - -} /* dlanst_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlansy.cpp b/lib/linalg/dlansy.cpp index 8d3cb42b7a..296605e896 100644 --- a/lib/linalg/dlansy.cpp +++ b/lib/linalg/dlansy.cpp @@ -1,204 +1,27 @@ -/* fortran/dlansy.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; - -/* > \brief \b DLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the ele -ment of largest absolute value of a real symmetric matrix. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLANSY + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* DOUBLE PRECISION FUNCTION DLANSY( NORM, UPLO, N, A, LDA, WORK ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER NORM, UPLO */ -/* INTEGER LDA, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLANSY returns the value of the one norm, or the Frobenius norm, or */ -/* > the infinity norm, or the element of largest absolute value of a */ -/* > real symmetric matrix A. */ -/* > \endverbatim */ -/* > */ -/* > \return DLANSY */ -/* > \verbatim */ -/* > */ -/* > DLANSY = ( max(abs(A(i,j))), NORM = 'M' or 'm' */ -/* > ( */ -/* > ( norm1(A), NORM = '1', 'O' or 'o' */ -/* > ( */ -/* > ( normI(A), NORM = 'I' or 'i' */ -/* > ( */ -/* > ( normF(A), NORM = 'F', 'f', 'E' or 'e' */ -/* > */ -/* > where norm1 denotes the one norm of a matrix (maximum column sum), */ -/* > normI denotes the infinity norm of a matrix (maximum row sum) and */ -/* > normF denotes the Frobenius norm of a matrix (square root of sum of */ -/* > squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] NORM */ -/* > \verbatim */ -/* > NORM is CHARACTER*1 */ -/* > Specifies the value to be returned in DLANSY as described */ -/* > above. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > Specifies whether the upper or lower triangular part of the */ -/* > symmetric matrix A is to be referenced. */ -/* > = 'U': Upper triangular part of A is referenced */ -/* > = 'L': Lower triangular part of A is referenced */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrix A. N >= 0. When N = 0, DLANSY is */ -/* > set to zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > The symmetric matrix A. If UPLO = 'U', the leading n by n */ -/* > upper triangular part of A contains the upper triangular part */ -/* > of the matrix A, and the strictly lower triangular part of A */ -/* > is not referenced. If UPLO = 'L', the leading n by n lower */ -/* > triangular part of A contains the lower triangular part of */ -/* > the matrix A, and the strictly upper triangular part of A is */ -/* > not referenced. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(N,1). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), */ -/* > where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, */ -/* > WORK is not referenced. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleSYauxiliary */ - -/* ===================================================================== */ -doublereal dlansy_(char *norm, char *uplo, integer *n, doublereal *a, integer - *lda, doublereal *work, ftnlen norm_len, ftnlen uplo_len) +doublereal dlansy_(char *norm, char *uplo, integer *n, doublereal *a, integer *lda, + doublereal *work, ftnlen norm_len, ftnlen uplo_len) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; doublereal ret_val, d__1; - - /* Builtin functions */ double sqrt(doublereal); - - /* Local variables */ integer i__, j; doublereal sum, absa, scale; extern logical lsame_(char *, char *, ftnlen, ftnlen); doublereal value; extern logical disnan_(doublereal *); - extern /* Subroutine */ int dlassq_(integer *, doublereal *, integer *, - doublereal *, doublereal *); - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - - /* Parameter adjustments */ + extern int dlassq_(integer *, doublereal *, integer *, doublereal *, doublereal *); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --work; - - /* Function Body */ if (*n == 0) { value = 0.; } else if (lsame_(norm, (char *)"M", (ftnlen)1, (ftnlen)1)) { - -/* Find max(abs(A(i,j))). */ - value = 0.; if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { i__1 = *n; @@ -209,9 +32,7 @@ doublereal dlansy_(char *norm, char *uplo, integer *n, doublereal *a, integer if (value < sum || disnan_(&sum)) { value = sum; } -/* L10: */ } -/* L20: */ } } else { i__1 = *n; @@ -222,16 +43,11 @@ doublereal dlansy_(char *norm, char *uplo, integer *n, doublereal *a, integer if (value < sum || disnan_(&sum)) { value = sum; } -/* L30: */ } -/* L40: */ } } - } else if (lsame_(norm, (char *)"I", (ftnlen)1, (ftnlen)1) || lsame_(norm, (char *)"O", ( - ftnlen)1, (ftnlen)1) || *(unsigned char *)norm == '1') { - -/* Find normI(A) ( = norm1(A), since A is symmetric). */ - + } else if (lsame_(norm, (char *)"I", (ftnlen)1, (ftnlen)1) || lsame_(norm, (char *)"O", (ftnlen)1, (ftnlen)1) || + *(unsigned char *)norm == '1') { value = 0.; if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { i__1 = *n; @@ -242,10 +58,8 @@ doublereal dlansy_(char *norm, char *uplo, integer *n, doublereal *a, integer absa = (d__1 = a[i__ + j * a_dim1], abs(d__1)); sum += absa; work[i__] += absa; -/* L50: */ } work[j] = sum + (d__1 = a[j + j * a_dim1], abs(d__1)); -/* L60: */ } i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { @@ -253,13 +67,11 @@ doublereal dlansy_(char *norm, char *uplo, integer *n, doublereal *a, integer if (value < sum || disnan_(&sum)) { value = sum; } -/* L70: */ } } else { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { work[i__] = 0.; -/* L80: */ } i__1 = *n; for (j = 1; j <= i__1; ++j) { @@ -269,19 +81,13 @@ doublereal dlansy_(char *norm, char *uplo, integer *n, doublereal *a, integer absa = (d__1 = a[i__ + j * a_dim1], abs(d__1)); sum += absa; work[i__] += absa; -/* L90: */ } if (value < sum || disnan_(&sum)) { value = sum; } -/* L100: */ } } - } else if (lsame_(norm, (char *)"F", (ftnlen)1, (ftnlen)1) || lsame_(norm, (char *)"E", ( - ftnlen)1, (ftnlen)1)) { - -/* Find normF(A). */ - + } else if (lsame_(norm, (char *)"F", (ftnlen)1, (ftnlen)1) || lsame_(norm, (char *)"E", (ftnlen)1, (ftnlen)1)) { scale = 0.; sum = 1.; if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { @@ -289,14 +95,12 @@ doublereal dlansy_(char *norm, char *uplo, integer *n, doublereal *a, integer for (j = 2; j <= i__1; ++j) { i__2 = j - 1; dlassq_(&i__2, &a[j * a_dim1 + 1], &c__1, &scale, &sum); -/* L110: */ } } else { i__1 = *n - 1; for (j = 1; j <= i__1; ++j) { i__2 = *n - j; dlassq_(&i__2, &a[j + 1 + j * a_dim1], &c__1, &scale, &sum); -/* L120: */ } } sum *= 2; @@ -304,14 +108,9 @@ doublereal dlansy_(char *norm, char *uplo, integer *n, doublereal *a, integer dlassq_(n, &a[a_offset], &i__1, &scale, &sum); value = scale * sqrt(sum); } - ret_val = value; return ret_val; - -/* End of DLANSY */ - -} /* dlansy_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlapy2.cpp b/lib/linalg/dlapy2.cpp index d746e1f56a..996878faaa 100644 --- a/lib/linalg/dlapy2.cpp +++ b/lib/linalg/dlapy2.cpp @@ -1,121 +1,16 @@ -/* fortran/dlapy2.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DLAPY2 returns sqrt(x2+y2). */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLAPY2 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* DOUBLE PRECISION FUNCTION DLAPY2( X, Y ) */ - -/* .. Scalar Arguments .. */ -/* DOUBLE PRECISION X, Y */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLAPY2 returns sqrt(x**2+y**2), taking care not to cause unnecessary */ -/* > overflow and unnecessary underflow. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] X */ -/* > \verbatim */ -/* > X is DOUBLE PRECISION */ -/* > \endverbatim */ -/* > */ -/* > \param[in] Y */ -/* > \verbatim */ -/* > Y is DOUBLE PRECISION */ -/* > X and Y specify the values x and y. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup OTHERauxiliary */ - -/* ===================================================================== */ doublereal dlapy2_(doublereal *x, doublereal *y) { - /* System generated locals */ doublereal ret_val, d__1; - - /* Builtin functions */ double sqrt(doublereal); - - /* Local variables */ logical x_is_nan__, y_is_nan__; doublereal w, z__, xabs, yabs; extern doublereal dlamch_(char *, ftnlen); extern logical disnan_(doublereal *); doublereal hugeval; - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - x_is_nan__ = disnan_(x); y_is_nan__ = disnan_(y); if (x_is_nan__) { @@ -125,26 +20,20 @@ doublereal dlapy2_(doublereal *x, doublereal *y) ret_val = *y; } hugeval = dlamch_((char *)"Overflow", (ftnlen)8); - - if (! (x_is_nan__ || y_is_nan__)) { + if (!(x_is_nan__ || y_is_nan__)) { xabs = abs(*x); yabs = abs(*y); - w = max(xabs,yabs); - z__ = min(xabs,yabs); + w = max(xabs, yabs); + z__ = min(xabs, yabs); if (z__ == 0. || w > hugeval) { ret_val = w; } else { -/* Computing 2nd power */ d__1 = z__ / w; ret_val = w * sqrt(d__1 * d__1 + 1.); } } return ret_val; - -/* End of DLAPY2 */ - -} /* dlapy2_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlapy3.cpp b/lib/linalg/dlapy3.cpp index 211f60dbf6..c6fd054f4a 100644 --- a/lib/linalg/dlapy3.cpp +++ b/lib/linalg/dlapy3.cpp @@ -1,149 +1,30 @@ -/* fortran/dlapy3.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DLAPY3 returns sqrt(x2+y2+z2). */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLAPY3 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* DOUBLE PRECISION FUNCTION DLAPY3( X, Y, Z ) */ - -/* .. Scalar Arguments .. */ -/* DOUBLE PRECISION X, Y, Z */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLAPY3 returns sqrt(x**2+y**2+z**2), taking care not to cause */ -/* > unnecessary overflow and unnecessary underflow. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] X */ -/* > \verbatim */ -/* > X is DOUBLE PRECISION */ -/* > \endverbatim */ -/* > */ -/* > \param[in] Y */ -/* > \verbatim */ -/* > Y is DOUBLE PRECISION */ -/* > \endverbatim */ -/* > */ -/* > \param[in] Z */ -/* > \verbatim */ -/* > Z is DOUBLE PRECISION */ -/* > X, Y and Z specify the values x, y and z. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup OTHERauxiliary */ - -/* ===================================================================== */ doublereal dlapy3_(doublereal *x, doublereal *y, doublereal *z__) { - /* System generated locals */ doublereal ret_val, d__1, d__2, d__3; - - /* Builtin functions */ double sqrt(doublereal); - - /* Local variables */ doublereal w, xabs, yabs, zabs; extern doublereal dlamch_(char *, ftnlen); doublereal hugeval; - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - hugeval = dlamch_((char *)"Overflow", (ftnlen)8); xabs = abs(*x); yabs = abs(*y); zabs = abs(*z__); -/* Computing MAX */ - d__1 = max(xabs,yabs); - w = max(d__1,zabs); + d__1 = max(xabs, yabs); + w = max(d__1, zabs); if (w == 0. || w > hugeval) { -/* W can be zero for max(0,nan,0) */ -/* adding all three entries together will make sure */ -/* NaN will not disappear. */ ret_val = xabs + yabs + zabs; } else { -/* Computing 2nd power */ d__1 = xabs / w; -/* Computing 2nd power */ d__2 = yabs / w; -/* Computing 2nd power */ d__3 = zabs / w; ret_val = w * sqrt(d__1 * d__1 + d__2 * d__2 + d__3 * d__3); } return ret_val; - -/* End of DLAPY3 */ - -} /* dlapy3_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlarf.cpp b/lib/linalg/dlarf.cpp index 8111d5fa2f..8fcb290abb 100644 --- a/lib/linalg/dlarf.cpp +++ b/lib/linalg/dlarf.cpp @@ -1,209 +1,34 @@ -/* fortran/dlarf.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static doublereal c_b4 = 1.; static doublereal c_b5 = 0.; static integer c__1 = 1; - -/* > \brief \b DLARF applies an elementary reflector to a general rectangular matrix. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLARF + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER SIDE */ -/* INTEGER INCV, LDC, M, N */ -/* DOUBLE PRECISION TAU */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION C( LDC, * ), V( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLARF applies a real elementary reflector H to a real m by n matrix */ -/* > C, from either the left or the right. H is represented in the form */ -/* > */ -/* > H = I - tau * v * v**T */ -/* > */ -/* > where tau is a real scalar and v is a real vector. */ -/* > */ -/* > If tau = 0, then H is taken to be the unit matrix. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] SIDE */ -/* > \verbatim */ -/* > SIDE is CHARACTER*1 */ -/* > = 'L': form H * C */ -/* > = 'R': form C * H */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix C. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix C. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] V */ -/* > \verbatim */ -/* > V is DOUBLE PRECISION array, dimension */ -/* > (1 + (M-1)*abs(INCV)) if SIDE = 'L' */ -/* > or (1 + (N-1)*abs(INCV)) if SIDE = 'R' */ -/* > The vector v in the representation of H. V is not used if */ -/* > TAU = 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCV */ -/* > \verbatim */ -/* > INCV is INTEGER */ -/* > The increment between elements of v. INCV <> 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TAU */ -/* > \verbatim */ -/* > TAU is DOUBLE PRECISION */ -/* > The value tau in the representation of H. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] C */ -/* > \verbatim */ -/* > C is DOUBLE PRECISION array, dimension (LDC,N) */ -/* > On entry, the m by n matrix C. */ -/* > On exit, C is overwritten by the matrix H * C if SIDE = 'L', */ -/* > or C * H if SIDE = 'R'. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDC */ -/* > \verbatim */ -/* > LDC is INTEGER */ -/* > The leading dimension of the array C. LDC >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension */ -/* > (N) if SIDE = 'L' */ -/* > or (M) if SIDE = 'R' */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleOTHERauxiliary */ - -/* ===================================================================== */ -/* Subroutine */ int dlarf_(char *side, integer *m, integer *n, doublereal *v, - integer *incv, doublereal *tau, doublereal *c__, integer *ldc, - doublereal *work, ftnlen side_len) +int dlarf_(char *side, integer *m, integer *n, doublereal *v, integer *incv, doublereal *tau, + doublereal *c__, integer *ldc, doublereal *work, ftnlen side_len) { - /* System generated locals */ integer c_dim1, c_offset; doublereal d__1; - - /* Local variables */ integer i__; logical applyleft; - extern /* Subroutine */ int dger_(integer *, integer *, doublereal *, - doublereal *, integer *, doublereal *, integer *, doublereal *, - integer *); + extern int dger_(integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, integer *); extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int dgemv_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, doublereal *, integer *, - doublereal *, doublereal *, integer *, ftnlen); + extern int dgemv_(char *, integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, ftnlen); integer lastc, lastv; extern integer iladlc_(integer *, integer *, doublereal *, integer *), - iladlr_(integer *, integer *, doublereal *, integer *); - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - - /* Parameter adjustments */ + iladlr_(integer *, integer *, doublereal *, integer *); --v; c_dim1 = *ldc; c_offset = 1 + c_dim1; c__ -= c_offset; --work; - - /* Function Body */ applyleft = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); lastv = 0; lastc = 0; if (*tau != 0.) { -/* Set up variables for scanning V. LASTV begins pointing to the end */ -/* of V. */ if (applyleft) { lastv = *m; } else { @@ -214,62 +39,33 @@ static integer c__1 = 1; } else { i__ = 1; } -/* Look for the last non-zero row in V. */ - while(lastv > 0 && v[i__] == 0.) { + while (lastv > 0 && v[i__] == 0.) { --lastv; i__ -= *incv; } if (applyleft) { -/* Scan for the last non-zero column in C(1:lastv,:). */ lastc = iladlc_(&lastv, n, &c__[c_offset], ldc); } else { -/* Scan for the last non-zero row in C(:,1:lastv). */ lastc = iladlr_(m, &lastv, &c__[c_offset], ldc); } } -/* Note that lastc.eq.0 renders the BLAS operations null; no special */ -/* case is needed at this level. */ if (applyleft) { - -/* Form H * C */ - if (lastv > 0) { - -/* w(1:lastc,1) := C(1:lastv,1:lastc)**T * v(1:lastv,1) */ - - dgemv_((char *)"Transpose", &lastv, &lastc, &c_b4, &c__[c_offset], ldc, & - v[1], incv, &c_b5, &work[1], &c__1, (ftnlen)9); - -/* C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**T */ - + dgemv_((char *)"Transpose", &lastv, &lastc, &c_b4, &c__[c_offset], ldc, &v[1], incv, &c_b5, + &work[1], &c__1, (ftnlen)9); d__1 = -(*tau); - dger_(&lastv, &lastc, &d__1, &v[1], incv, &work[1], &c__1, &c__[ - c_offset], ldc); + dger_(&lastv, &lastc, &d__1, &v[1], incv, &work[1], &c__1, &c__[c_offset], ldc); } } else { - -/* Form C * H */ - if (lastv > 0) { - -/* w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1) */ - - dgemv_((char *)"No transpose", &lastc, &lastv, &c_b4, &c__[c_offset], ldc, - &v[1], incv, &c_b5, &work[1], &c__1, (ftnlen)12); - -/* C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**T */ - + dgemv_((char *)"No transpose", &lastc, &lastv, &c_b4, &c__[c_offset], ldc, &v[1], incv, &c_b5, + &work[1], &c__1, (ftnlen)12); d__1 = -(*tau); - dger_(&lastc, &lastv, &d__1, &work[1], &c__1, &v[1], incv, &c__[ - c_offset], ldc); + dger_(&lastc, &lastv, &d__1, &work[1], &c__1, &v[1], incv, &c__[c_offset], ldc); } } return 0; - -/* End of DLARF */ - -} /* dlarf_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlarfb.cpp b/lib/linalg/dlarfb.cpp index d282b19899..83f301f9d2 100644 --- a/lib/linalg/dlarfb.cpp +++ b/lib/linalg/dlarfb.cpp @@ -1,270 +1,26 @@ -/* fortran/dlarfb.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static doublereal c_b14 = 1.; static doublereal c_b25 = -1.; - -/* > \brief \b DLARFB applies a block reflector or its transpose to a general rectangular matrix. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLARFB + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, */ -/* T, LDT, C, LDC, WORK, LDWORK ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER DIRECT, SIDE, STOREV, TRANS */ -/* INTEGER K, LDC, LDT, LDV, LDWORK, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION C( LDC, * ), T( LDT, * ), V( LDV, * ), */ -/* $ WORK( LDWORK, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLARFB applies a real block reflector H or its transpose H**T to a */ -/* > real m by n matrix C, from either the left or the right. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] SIDE */ -/* > \verbatim */ -/* > SIDE is CHARACTER*1 */ -/* > = 'L': apply H or H**T from the Left */ -/* > = 'R': apply H or H**T from the Right */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TRANS */ -/* > \verbatim */ -/* > TRANS is CHARACTER*1 */ -/* > = 'N': apply H (No transpose) */ -/* > = 'T': apply H**T (Transpose) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DIRECT */ -/* > \verbatim */ -/* > DIRECT is CHARACTER*1 */ -/* > Indicates how H is formed from a product of elementary */ -/* > reflectors */ -/* > = 'F': H = H(1) H(2) . . . H(k) (Forward) */ -/* > = 'B': H = H(k) . . . H(2) H(1) (Backward) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] STOREV */ -/* > \verbatim */ -/* > STOREV is CHARACTER*1 */ -/* > Indicates how the vectors which define the elementary */ -/* > reflectors are stored: */ -/* > = 'C': Columnwise */ -/* > = 'R': Rowwise */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix C. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix C. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > The order of the matrix T (= the number of elementary */ -/* > reflectors whose product defines the block reflector). */ -/* > If SIDE = 'L', M >= K >= 0; */ -/* > if SIDE = 'R', N >= K >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] V */ -/* > \verbatim */ -/* > V is DOUBLE PRECISION array, dimension */ -/* > (LDV,K) if STOREV = 'C' */ -/* > (LDV,M) if STOREV = 'R' and SIDE = 'L' */ -/* > (LDV,N) if STOREV = 'R' and SIDE = 'R' */ -/* > The matrix V. See Further Details. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDV */ -/* > \verbatim */ -/* > LDV is INTEGER */ -/* > The leading dimension of the array V. */ -/* > If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M); */ -/* > if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N); */ -/* > if STOREV = 'R', LDV >= K. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] T */ -/* > \verbatim */ -/* > T is DOUBLE PRECISION array, dimension (LDT,K) */ -/* > The triangular k by k matrix T in the representation of the */ -/* > block reflector. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDT */ -/* > \verbatim */ -/* > LDT is INTEGER */ -/* > The leading dimension of the array T. LDT >= K. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] C */ -/* > \verbatim */ -/* > C is DOUBLE PRECISION array, dimension (LDC,N) */ -/* > On entry, the m by n matrix C. */ -/* > On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDC */ -/* > \verbatim */ -/* > LDC is INTEGER */ -/* > The leading dimension of the array C. LDC >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (LDWORK,K) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDWORK */ -/* > \verbatim */ -/* > LDWORK is INTEGER */ -/* > The leading dimension of the array WORK. */ -/* > If SIDE = 'L', LDWORK >= max(1,N); */ -/* > if SIDE = 'R', LDWORK >= max(1,M). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleOTHERauxiliary */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > The shape of the matrix V and the storage of the vectors which define */ -/* > the H(i) is best illustrated by the following example with n = 5 and */ -/* > k = 3. The elements equal to 1 are not stored; the corresponding */ -/* > array elements are modified but restored on exit. The rest of the */ -/* > array is not used. */ -/* > */ -/* > DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': */ -/* > */ -/* > V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) */ -/* > ( v1 1 ) ( 1 v2 v2 v2 ) */ -/* > ( v1 v2 1 ) ( 1 v3 v3 ) */ -/* > ( v1 v2 v3 ) */ -/* > ( v1 v2 v3 ) */ -/* > */ -/* > DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': */ -/* > */ -/* > V = ( v1 v2 v3 ) V = ( v1 v1 1 ) */ -/* > ( v1 v2 v3 ) ( v2 v2 v2 1 ) */ -/* > ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) */ -/* > ( 1 v3 ) */ -/* > ( 1 ) */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dlarfb_(char *side, char *trans, char *direct, char * - storev, integer *m, integer *n, integer *k, doublereal *v, integer * - ldv, doublereal *t, integer *ldt, doublereal *c__, integer *ldc, - doublereal *work, integer *ldwork, ftnlen side_len, ftnlen trans_len, - ftnlen direct_len, ftnlen storev_len) +int dlarfb_(char *side, char *trans, char *direct, char *storev, integer *m, integer *n, integer *k, + doublereal *v, integer *ldv, doublereal *t, integer *ldt, doublereal *c__, integer *ldc, + doublereal *work, integer *ldwork, ftnlen side_len, ftnlen trans_len, ftnlen direct_len, + ftnlen storev_len) { - /* System generated locals */ - integer c_dim1, c_offset, t_dim1, t_offset, v_dim1, v_offset, work_dim1, - work_offset, i__1, i__2; - - /* Local variables */ + integer c_dim1, c_offset, t_dim1, t_offset, v_dim1, v_offset, work_dim1, work_offset, i__1, + i__2; integer i__, j; - extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); + extern int dgemm_(char *, char *, integer *, integer *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, + ftnlen, ftnlen); extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, - doublereal *, integer *), dtrmm_(char *, char *, char *, char *, - integer *, integer *, doublereal *, doublereal *, integer *, - doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + extern int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *), + dtrmm_(char *, char *, char *, char *, integer *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); char transt[1]; - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Quick return if possible */ - - /* Parameter adjustments */ v_dim1 = *ldv; v_offset = 1 + v_dim1; v -= v_offset; @@ -277,610 +33,279 @@ f"> */ work_dim1 = *ldwork; work_offset = 1 + work_dim1; work -= work_offset; - - /* Function Body */ if (*m <= 0 || *n <= 0) { return 0; } - if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { *(unsigned char *)transt = 'T'; } else { *(unsigned char *)transt = 'N'; } - if (lsame_(storev, (char *)"C", (ftnlen)1, (ftnlen)1)) { - if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { - -/* Let V = ( V1 ) (first K rows) */ -/* ( V2 ) */ -/* where V1 is unit lower triangular. */ - if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { - -/* Form H * C or H**T * C where C = ( C1 ) */ -/* ( C2 ) */ - -/* W := C**T * V = (C1**T * V1 + C2**T * V2) (stored in WORK) */ - -/* W := C1**T */ - i__1 = *k; for (j = 1; j <= i__1; ++j) { - dcopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1], - &c__1); -/* L10: */ + dcopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1], &c__1); } - -/* W := W * V1 */ - - dtrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", n, k, &c_b14, - &v[v_offset], ldv, &work[work_offset], ldwork, ( - ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); + dtrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", n, k, &c_b14, &v[v_offset], ldv, + &work[work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); if (*m > *k) { - -/* W := W + C2**T * V2 */ - i__1 = *m - *k; - dgemm_((char *)"Transpose", (char *)"No transpose", n, k, &i__1, &c_b14, & - c__[*k + 1 + c_dim1], ldc, &v[*k + 1 + v_dim1], - ldv, &c_b14, &work[work_offset], ldwork, (ftnlen) - 9, (ftnlen)12); + dgemm_((char *)"Transpose", (char *)"No transpose", n, k, &i__1, &c_b14, &c__[*k + 1 + c_dim1], + ldc, &v[*k + 1 + v_dim1], ldv, &c_b14, &work[work_offset], ldwork, + (ftnlen)9, (ftnlen)12); } - -/* W := W * T**T or W * T */ - - dtrmm_((char *)"Right", (char *)"Upper", transt, (char *)"Non-unit", n, k, &c_b14, &t[ - t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, - (ftnlen)5, (ftnlen)1, (ftnlen)8); - -/* C := C - V * W**T */ - + dtrmm_((char *)"Right", (char *)"Upper", transt, (char *)"Non-unit", n, k, &c_b14, &t[t_offset], ldt, + &work[work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)1, (ftnlen)8); if (*m > *k) { - -/* C2 := C2 - V2 * W**T */ - i__1 = *m - *k; - dgemm_((char *)"No transpose", (char *)"Transpose", &i__1, n, k, &c_b25, & - v[*k + 1 + v_dim1], ldv, &work[work_offset], - ldwork, &c_b14, &c__[*k + 1 + c_dim1], ldc, ( - ftnlen)12, (ftnlen)9); + dgemm_((char *)"No transpose", (char *)"Transpose", &i__1, n, k, &c_b25, &v[*k + 1 + v_dim1], + ldv, &work[work_offset], ldwork, &c_b14, &c__[*k + 1 + c_dim1], ldc, + (ftnlen)12, (ftnlen)9); } - -/* W := W * V1**T */ - - dtrmm_((char *)"Right", (char *)"Lower", (char *)"Transpose", (char *)"Unit", n, k, &c_b14, & - v[v_offset], ldv, &work[work_offset], ldwork, (ftnlen) - 5, (ftnlen)5, (ftnlen)9, (ftnlen)4); - -/* C1 := C1 - W**T */ - + dtrmm_((char *)"Right", (char *)"Lower", (char *)"Transpose", (char *)"Unit", n, k, &c_b14, &v[v_offset], ldv, + &work[work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)9, (ftnlen)4); i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { c__[j + i__ * c_dim1] -= work[i__ + j * work_dim1]; -/* L20: */ } -/* L30: */ } - } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { - -/* Form C * H or C * H**T where C = ( C1 C2 ) */ - -/* W := C * V = (C1*V1 + C2*V2) (stored in WORK) */ - -/* W := C1 */ - i__1 = *k; for (j = 1; j <= i__1; ++j) { - dcopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j * - work_dim1 + 1], &c__1); -/* L40: */ + dcopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j * work_dim1 + 1], &c__1); } - -/* W := W * V1 */ - - dtrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", m, k, &c_b14, - &v[v_offset], ldv, &work[work_offset], ldwork, ( - ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); + dtrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", m, k, &c_b14, &v[v_offset], ldv, + &work[work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); if (*n > *k) { - -/* W := W + C2 * V2 */ - i__1 = *n - *k; - dgemm_((char *)"No transpose", (char *)"No transpose", m, k, &i__1, & - c_b14, &c__[(*k + 1) * c_dim1 + 1], ldc, &v[*k + - 1 + v_dim1], ldv, &c_b14, &work[work_offset], - ldwork, (ftnlen)12, (ftnlen)12); + dgemm_((char *)"No transpose", (char *)"No transpose", m, k, &i__1, &c_b14, + &c__[(*k + 1) * c_dim1 + 1], ldc, &v[*k + 1 + v_dim1], ldv, &c_b14, + &work[work_offset], ldwork, (ftnlen)12, (ftnlen)12); } - -/* W := W * T or W * T**T */ - - dtrmm_((char *)"Right", (char *)"Upper", trans, (char *)"Non-unit", m, k, &c_b14, &t[ - t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, - (ftnlen)5, (ftnlen)1, (ftnlen)8); - -/* C := C - W * V**T */ - + dtrmm_((char *)"Right", (char *)"Upper", trans, (char *)"Non-unit", m, k, &c_b14, &t[t_offset], ldt, + &work[work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)1, (ftnlen)8); if (*n > *k) { - -/* C2 := C2 - W * V2**T */ - i__1 = *n - *k; - dgemm_((char *)"No transpose", (char *)"Transpose", m, &i__1, k, &c_b25, & - work[work_offset], ldwork, &v[*k + 1 + v_dim1], - ldv, &c_b14, &c__[(*k + 1) * c_dim1 + 1], ldc, ( - ftnlen)12, (ftnlen)9); + dgemm_((char *)"No transpose", (char *)"Transpose", m, &i__1, k, &c_b25, &work[work_offset], + ldwork, &v[*k + 1 + v_dim1], ldv, &c_b14, &c__[(*k + 1) * c_dim1 + 1], + ldc, (ftnlen)12, (ftnlen)9); } - -/* W := W * V1**T */ - - dtrmm_((char *)"Right", (char *)"Lower", (char *)"Transpose", (char *)"Unit", m, k, &c_b14, & - v[v_offset], ldv, &work[work_offset], ldwork, (ftnlen) - 5, (ftnlen)5, (ftnlen)9, (ftnlen)4); - -/* C1 := C1 - W */ - + dtrmm_((char *)"Right", (char *)"Lower", (char *)"Transpose", (char *)"Unit", m, k, &c_b14, &v[v_offset], ldv, + &work[work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)9, (ftnlen)4); i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { c__[i__ + j * c_dim1] -= work[i__ + j * work_dim1]; -/* L50: */ } -/* L60: */ } } - } else { - -/* Let V = ( V1 ) */ -/* ( V2 ) (last K rows) */ -/* where V2 is unit upper triangular. */ - if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { - -/* Form H * C or H**T * C where C = ( C1 ) */ -/* ( C2 ) */ - -/* W := C**T * V = (C1**T * V1 + C2**T * V2) (stored in WORK) */ - -/* W := C2**T */ - i__1 = *k; for (j = 1; j <= i__1; ++j) { - dcopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j * - work_dim1 + 1], &c__1); -/* L70: */ + dcopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j * work_dim1 + 1], &c__1); } - -/* W := W * V2 */ - dtrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", n, k, &c_b14, - &v[*m - *k + 1 + v_dim1], ldv, &work[work_offset], - ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); + &v[*m - *k + 1 + v_dim1], ldv, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)12, (ftnlen)4); if (*m > *k) { - -/* W := W + C1**T * V1 */ - i__1 = *m - *k; - dgemm_((char *)"Transpose", (char *)"No transpose", n, k, &i__1, &c_b14, & - c__[c_offset], ldc, &v[v_offset], ldv, &c_b14, & - work[work_offset], ldwork, (ftnlen)9, (ftnlen)12); + dgemm_((char *)"Transpose", (char *)"No transpose", n, k, &i__1, &c_b14, &c__[c_offset], ldc, + &v[v_offset], ldv, &c_b14, &work[work_offset], ldwork, (ftnlen)9, + (ftnlen)12); } - -/* W := W * T**T or W * T */ - - dtrmm_((char *)"Right", (char *)"Lower", transt, (char *)"Non-unit", n, k, &c_b14, &t[ - t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, - (ftnlen)5, (ftnlen)1, (ftnlen)8); - -/* C := C - V * W**T */ - + dtrmm_((char *)"Right", (char *)"Lower", transt, (char *)"Non-unit", n, k, &c_b14, &t[t_offset], ldt, + &work[work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)1, (ftnlen)8); if (*m > *k) { - -/* C1 := C1 - V1 * W**T */ - i__1 = *m - *k; - dgemm_((char *)"No transpose", (char *)"Transpose", &i__1, n, k, &c_b25, & - v[v_offset], ldv, &work[work_offset], ldwork, & - c_b14, &c__[c_offset], ldc, (ftnlen)12, (ftnlen)9) - ; + dgemm_((char *)"No transpose", (char *)"Transpose", &i__1, n, k, &c_b25, &v[v_offset], ldv, + &work[work_offset], ldwork, &c_b14, &c__[c_offset], ldc, (ftnlen)12, + (ftnlen)9); } - -/* W := W * V2**T */ - - dtrmm_((char *)"Right", (char *)"Upper", (char *)"Transpose", (char *)"Unit", n, k, &c_b14, & - v[*m - *k + 1 + v_dim1], ldv, &work[work_offset], - ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)9, (ftnlen)4); - -/* C2 := C2 - W**T */ - + dtrmm_((char *)"Right", (char *)"Upper", (char *)"Transpose", (char *)"Unit", n, k, &c_b14, + &v[*m - *k + 1 + v_dim1], ldv, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)9, (ftnlen)4); i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { - c__[*m - *k + j + i__ * c_dim1] -= work[i__ + j * - work_dim1]; -/* L80: */ + c__[*m - *k + j + i__ * c_dim1] -= work[i__ + j * work_dim1]; } -/* L90: */ } - } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { - -/* Form C * H or C * H**T where C = ( C1 C2 ) */ - -/* W := C * V = (C1*V1 + C2*V2) (stored in WORK) */ - -/* W := C2 */ - i__1 = *k; for (j = 1; j <= i__1; ++j) { - dcopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[ - j * work_dim1 + 1], &c__1); -/* L100: */ + dcopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[j * work_dim1 + 1], + &c__1); } - -/* W := W * V2 */ - dtrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", m, k, &c_b14, - &v[*n - *k + 1 + v_dim1], ldv, &work[work_offset], - ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); + &v[*n - *k + 1 + v_dim1], ldv, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)12, (ftnlen)4); if (*n > *k) { - -/* W := W + C1 * V1 */ - i__1 = *n - *k; - dgemm_((char *)"No transpose", (char *)"No transpose", m, k, &i__1, & - c_b14, &c__[c_offset], ldc, &v[v_offset], ldv, & - c_b14, &work[work_offset], ldwork, (ftnlen)12, ( - ftnlen)12); + dgemm_((char *)"No transpose", (char *)"No transpose", m, k, &i__1, &c_b14, &c__[c_offset], ldc, + &v[v_offset], ldv, &c_b14, &work[work_offset], ldwork, (ftnlen)12, + (ftnlen)12); } - -/* W := W * T or W * T**T */ - - dtrmm_((char *)"Right", (char *)"Lower", trans, (char *)"Non-unit", m, k, &c_b14, &t[ - t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, - (ftnlen)5, (ftnlen)1, (ftnlen)8); - -/* C := C - W * V**T */ - + dtrmm_((char *)"Right", (char *)"Lower", trans, (char *)"Non-unit", m, k, &c_b14, &t[t_offset], ldt, + &work[work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)1, (ftnlen)8); if (*n > *k) { - -/* C1 := C1 - W * V1**T */ - i__1 = *n - *k; - dgemm_((char *)"No transpose", (char *)"Transpose", m, &i__1, k, &c_b25, & - work[work_offset], ldwork, &v[v_offset], ldv, & - c_b14, &c__[c_offset], ldc, (ftnlen)12, (ftnlen)9) - ; + dgemm_((char *)"No transpose", (char *)"Transpose", m, &i__1, k, &c_b25, &work[work_offset], + ldwork, &v[v_offset], ldv, &c_b14, &c__[c_offset], ldc, (ftnlen)12, + (ftnlen)9); } - -/* W := W * V2**T */ - - dtrmm_((char *)"Right", (char *)"Upper", (char *)"Transpose", (char *)"Unit", m, k, &c_b14, & - v[*n - *k + 1 + v_dim1], ldv, &work[work_offset], - ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)9, (ftnlen)4); - -/* C2 := C2 - W */ - + dtrmm_((char *)"Right", (char *)"Upper", (char *)"Transpose", (char *)"Unit", m, k, &c_b14, + &v[*n - *k + 1 + v_dim1], ldv, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)9, (ftnlen)4); i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { - c__[i__ + (*n - *k + j) * c_dim1] -= work[i__ + j * - work_dim1]; -/* L110: */ + c__[i__ + (*n - *k + j) * c_dim1] -= work[i__ + j * work_dim1]; } -/* L120: */ } } } - } else if (lsame_(storev, (char *)"R", (ftnlen)1, (ftnlen)1)) { - if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { - -/* Let V = ( V1 V2 ) (V1: first K columns) */ -/* where V1 is unit upper triangular. */ - if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { - -/* Form H * C or H**T * C where C = ( C1 ) */ -/* ( C2 ) */ - -/* W := C**T * V**T = (C1**T * V1**T + C2**T * V2**T) (stored in WORK) */ - -/* W := C1**T */ - i__1 = *k; for (j = 1; j <= i__1; ++j) { - dcopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1], - &c__1); -/* L130: */ + dcopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1], &c__1); } - -/* W := W * V1**T */ - - dtrmm_((char *)"Right", (char *)"Upper", (char *)"Transpose", (char *)"Unit", n, k, &c_b14, & - v[v_offset], ldv, &work[work_offset], ldwork, (ftnlen) - 5, (ftnlen)5, (ftnlen)9, (ftnlen)4); + dtrmm_((char *)"Right", (char *)"Upper", (char *)"Transpose", (char *)"Unit", n, k, &c_b14, &v[v_offset], ldv, + &work[work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)9, (ftnlen)4); if (*m > *k) { - -/* W := W + C2**T * V2**T */ - i__1 = *m - *k; - dgemm_((char *)"Transpose", (char *)"Transpose", n, k, &i__1, &c_b14, & - c__[*k + 1 + c_dim1], ldc, &v[(*k + 1) * v_dim1 + - 1], ldv, &c_b14, &work[work_offset], ldwork, ( - ftnlen)9, (ftnlen)9); + dgemm_((char *)"Transpose", (char *)"Transpose", n, k, &i__1, &c_b14, &c__[*k + 1 + c_dim1], + ldc, &v[(*k + 1) * v_dim1 + 1], ldv, &c_b14, &work[work_offset], ldwork, + (ftnlen)9, (ftnlen)9); } - -/* W := W * T**T or W * T */ - - dtrmm_((char *)"Right", (char *)"Upper", transt, (char *)"Non-unit", n, k, &c_b14, &t[ - t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, - (ftnlen)5, (ftnlen)1, (ftnlen)8); - -/* C := C - V**T * W**T */ - + dtrmm_((char *)"Right", (char *)"Upper", transt, (char *)"Non-unit", n, k, &c_b14, &t[t_offset], ldt, + &work[work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)1, (ftnlen)8); if (*m > *k) { - -/* C2 := C2 - V2**T * W**T */ - i__1 = *m - *k; - dgemm_((char *)"Transpose", (char *)"Transpose", &i__1, n, k, &c_b25, &v[( - *k + 1) * v_dim1 + 1], ldv, &work[work_offset], - ldwork, &c_b14, &c__[*k + 1 + c_dim1], ldc, ( - ftnlen)9, (ftnlen)9); + dgemm_((char *)"Transpose", (char *)"Transpose", &i__1, n, k, &c_b25, &v[(*k + 1) * v_dim1 + 1], + ldv, &work[work_offset], ldwork, &c_b14, &c__[*k + 1 + c_dim1], ldc, + (ftnlen)9, (ftnlen)9); } - -/* W := W * V1 */ - - dtrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", n, k, &c_b14, - &v[v_offset], ldv, &work[work_offset], ldwork, ( - ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); - -/* C1 := C1 - W**T */ - + dtrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", n, k, &c_b14, &v[v_offset], ldv, + &work[work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { c__[j + i__ * c_dim1] -= work[i__ + j * work_dim1]; -/* L140: */ } -/* L150: */ } - } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { - -/* Form C * H or C * H**T where C = ( C1 C2 ) */ - -/* W := C * V**T = (C1*V1**T + C2*V2**T) (stored in WORK) */ - -/* W := C1 */ - i__1 = *k; for (j = 1; j <= i__1; ++j) { - dcopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j * - work_dim1 + 1], &c__1); -/* L160: */ + dcopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j * work_dim1 + 1], &c__1); } - -/* W := W * V1**T */ - - dtrmm_((char *)"Right", (char *)"Upper", (char *)"Transpose", (char *)"Unit", m, k, &c_b14, & - v[v_offset], ldv, &work[work_offset], ldwork, (ftnlen) - 5, (ftnlen)5, (ftnlen)9, (ftnlen)4); + dtrmm_((char *)"Right", (char *)"Upper", (char *)"Transpose", (char *)"Unit", m, k, &c_b14, &v[v_offset], ldv, + &work[work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)9, (ftnlen)4); if (*n > *k) { - -/* W := W + C2 * V2**T */ - i__1 = *n - *k; - dgemm_((char *)"No transpose", (char *)"Transpose", m, k, &i__1, &c_b14, & - c__[(*k + 1) * c_dim1 + 1], ldc, &v[(*k + 1) * - v_dim1 + 1], ldv, &c_b14, &work[work_offset], - ldwork, (ftnlen)12, (ftnlen)9); + dgemm_((char *)"No transpose", (char *)"Transpose", m, k, &i__1, &c_b14, + &c__[(*k + 1) * c_dim1 + 1], ldc, &v[(*k + 1) * v_dim1 + 1], ldv, &c_b14, + &work[work_offset], ldwork, (ftnlen)12, (ftnlen)9); } - -/* W := W * T or W * T**T */ - - dtrmm_((char *)"Right", (char *)"Upper", trans, (char *)"Non-unit", m, k, &c_b14, &t[ - t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, - (ftnlen)5, (ftnlen)1, (ftnlen)8); - -/* C := C - W * V */ - + dtrmm_((char *)"Right", (char *)"Upper", trans, (char *)"Non-unit", m, k, &c_b14, &t[t_offset], ldt, + &work[work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)1, (ftnlen)8); if (*n > *k) { - -/* C2 := C2 - W * V2 */ - i__1 = *n - *k; - dgemm_((char *)"No transpose", (char *)"No transpose", m, &i__1, k, & - c_b25, &work[work_offset], ldwork, &v[(*k + 1) * - v_dim1 + 1], ldv, &c_b14, &c__[(*k + 1) * c_dim1 - + 1], ldc, (ftnlen)12, (ftnlen)12); + dgemm_((char *)"No transpose", (char *)"No transpose", m, &i__1, k, &c_b25, &work[work_offset], + ldwork, &v[(*k + 1) * v_dim1 + 1], ldv, &c_b14, + &c__[(*k + 1) * c_dim1 + 1], ldc, (ftnlen)12, (ftnlen)12); } - -/* W := W * V1 */ - - dtrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", m, k, &c_b14, - &v[v_offset], ldv, &work[work_offset], ldwork, ( - ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); - -/* C1 := C1 - W */ - + dtrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", m, k, &c_b14, &v[v_offset], ldv, + &work[work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { c__[i__ + j * c_dim1] -= work[i__ + j * work_dim1]; -/* L170: */ } -/* L180: */ } - } - } else { - -/* Let V = ( V1 V2 ) (V2: last K columns) */ -/* where V2 is unit lower triangular. */ - if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { - -/* Form H * C or H**T * C where C = ( C1 ) */ -/* ( C2 ) */ - -/* W := C**T * V**T = (C1**T * V1**T + C2**T * V2**T) (stored in WORK) */ - -/* W := C2**T */ - i__1 = *k; for (j = 1; j <= i__1; ++j) { - dcopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j * - work_dim1 + 1], &c__1); -/* L190: */ + dcopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j * work_dim1 + 1], &c__1); } - -/* W := W * V2**T */ - - dtrmm_((char *)"Right", (char *)"Lower", (char *)"Transpose", (char *)"Unit", n, k, &c_b14, & - v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[work_offset] - , ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)9, (ftnlen)4); + dtrmm_((char *)"Right", (char *)"Lower", (char *)"Transpose", (char *)"Unit", n, k, &c_b14, + &v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)9, (ftnlen)4); if (*m > *k) { - -/* W := W + C1**T * V1**T */ - i__1 = *m - *k; - dgemm_((char *)"Transpose", (char *)"Transpose", n, k, &i__1, &c_b14, & - c__[c_offset], ldc, &v[v_offset], ldv, &c_b14, & - work[work_offset], ldwork, (ftnlen)9, (ftnlen)9); + dgemm_((char *)"Transpose", (char *)"Transpose", n, k, &i__1, &c_b14, &c__[c_offset], ldc, + &v[v_offset], ldv, &c_b14, &work[work_offset], ldwork, (ftnlen)9, + (ftnlen)9); } - -/* W := W * T**T or W * T */ - - dtrmm_((char *)"Right", (char *)"Lower", transt, (char *)"Non-unit", n, k, &c_b14, &t[ - t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, - (ftnlen)5, (ftnlen)1, (ftnlen)8); - -/* C := C - V**T * W**T */ - + dtrmm_((char *)"Right", (char *)"Lower", transt, (char *)"Non-unit", n, k, &c_b14, &t[t_offset], ldt, + &work[work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)1, (ftnlen)8); if (*m > *k) { - -/* C1 := C1 - V1**T * W**T */ - i__1 = *m - *k; - dgemm_((char *)"Transpose", (char *)"Transpose", &i__1, n, k, &c_b25, &v[ - v_offset], ldv, &work[work_offset], ldwork, & - c_b14, &c__[c_offset], ldc, (ftnlen)9, (ftnlen)9); + dgemm_((char *)"Transpose", (char *)"Transpose", &i__1, n, k, &c_b25, &v[v_offset], ldv, + &work[work_offset], ldwork, &c_b14, &c__[c_offset], ldc, (ftnlen)9, + (ftnlen)9); } - -/* W := W * V2 */ - dtrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", n, k, &c_b14, - &v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[ - work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen) - 12, (ftnlen)4); - -/* C2 := C2 - W**T */ - + &v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)12, (ftnlen)4); i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { - c__[*m - *k + j + i__ * c_dim1] -= work[i__ + j * - work_dim1]; -/* L200: */ + c__[*m - *k + j + i__ * c_dim1] -= work[i__ + j * work_dim1]; } -/* L210: */ } - } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { - -/* Form C * H or C * H' where C = ( C1 C2 ) */ - -/* W := C * V**T = (C1*V1**T + C2*V2**T) (stored in WORK) */ - -/* W := C2 */ - i__1 = *k; for (j = 1; j <= i__1; ++j) { - dcopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[ - j * work_dim1 + 1], &c__1); -/* L220: */ + dcopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[j * work_dim1 + 1], + &c__1); } - -/* W := W * V2**T */ - - dtrmm_((char *)"Right", (char *)"Lower", (char *)"Transpose", (char *)"Unit", m, k, &c_b14, & - v[(*n - *k + 1) * v_dim1 + 1], ldv, &work[work_offset] - , ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)9, (ftnlen)4); + dtrmm_((char *)"Right", (char *)"Lower", (char *)"Transpose", (char *)"Unit", m, k, &c_b14, + &v[(*n - *k + 1) * v_dim1 + 1], ldv, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)9, (ftnlen)4); if (*n > *k) { - -/* W := W + C1 * V1**T */ - i__1 = *n - *k; - dgemm_((char *)"No transpose", (char *)"Transpose", m, k, &i__1, &c_b14, & - c__[c_offset], ldc, &v[v_offset], ldv, &c_b14, & - work[work_offset], ldwork, (ftnlen)12, (ftnlen)9); + dgemm_((char *)"No transpose", (char *)"Transpose", m, k, &i__1, &c_b14, &c__[c_offset], ldc, + &v[v_offset], ldv, &c_b14, &work[work_offset], ldwork, (ftnlen)12, + (ftnlen)9); } - -/* W := W * T or W * T**T */ - - dtrmm_((char *)"Right", (char *)"Lower", trans, (char *)"Non-unit", m, k, &c_b14, &t[ - t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, - (ftnlen)5, (ftnlen)1, (ftnlen)8); - -/* C := C - W * V */ - + dtrmm_((char *)"Right", (char *)"Lower", trans, (char *)"Non-unit", m, k, &c_b14, &t[t_offset], ldt, + &work[work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)1, (ftnlen)8); if (*n > *k) { - -/* C1 := C1 - W * V1 */ - i__1 = *n - *k; - dgemm_((char *)"No transpose", (char *)"No transpose", m, &i__1, k, & - c_b25, &work[work_offset], ldwork, &v[v_offset], - ldv, &c_b14, &c__[c_offset], ldc, (ftnlen)12, ( - ftnlen)12); + dgemm_((char *)"No transpose", (char *)"No transpose", m, &i__1, k, &c_b25, &work[work_offset], + ldwork, &v[v_offset], ldv, &c_b14, &c__[c_offset], ldc, (ftnlen)12, + (ftnlen)12); } - -/* W := W * V2 */ - dtrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", m, k, &c_b14, - &v[(*n - *k + 1) * v_dim1 + 1], ldv, &work[ - work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen) - 12, (ftnlen)4); - -/* C1 := C1 - W */ - + &v[(*n - *k + 1) * v_dim1 + 1], ldv, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)12, (ftnlen)4); i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { - c__[i__ + (*n - *k + j) * c_dim1] -= work[i__ + j * - work_dim1]; -/* L230: */ + c__[i__ + (*n - *k + j) * c_dim1] -= work[i__ + j * work_dim1]; } -/* L240: */ } - } - } } - return 0; - -/* End of DLARFB */ - -} /* dlarfb_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlarfg.cpp b/lib/linalg/dlarfg.cpp index 546db1171e..1dbdd82f66 100644 --- a/lib/linalg/dlarfg.cpp +++ b/lib/linalg/dlarfg.cpp @@ -1,203 +1,36 @@ -/* fortran/dlarfg.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DLARFG generates an elementary reflector (Householder matrix). */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLARFG + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INCX, N */ -/* DOUBLE PRECISION ALPHA, TAU */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION X( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLARFG generates a real elementary reflector H of order n, such */ -/* > that */ -/* > */ -/* > H * ( alpha ) = ( beta ), H**T * H = I. */ -/* > ( x ) ( 0 ) */ -/* > */ -/* > where alpha and beta are scalars, and x is an (n-1)-element real */ -/* > vector. H is represented in the form */ -/* > */ -/* > H = I - tau * ( 1 ) * ( 1 v**T ) , */ -/* > ( v ) */ -/* > */ -/* > where tau is a real scalar and v is a real (n-1)-element */ -/* > vector. */ -/* > */ -/* > If the elements of x are all zero, then tau = 0 and H is taken to be */ -/* > the unit matrix. */ -/* > */ -/* > Otherwise 1 <= tau <= 2. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the elementary reflector. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] ALPHA */ -/* > \verbatim */ -/* > ALPHA is DOUBLE PRECISION */ -/* > On entry, the value alpha. */ -/* > On exit, it is overwritten with the value beta. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] X */ -/* > \verbatim */ -/* > X is DOUBLE PRECISION array, dimension */ -/* > (1+(N-2)*abs(INCX)) */ -/* > On entry, the vector x. */ -/* > On exit, it is overwritten with the vector v. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > The increment between elements of X. INCX > 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] TAU */ -/* > \verbatim */ -/* > TAU is DOUBLE PRECISION */ -/* > The value tau. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleOTHERauxiliary */ - -/* ===================================================================== */ -/* Subroutine */ int dlarfg_(integer *n, doublereal *alpha, doublereal *x, - integer *incx, doublereal *tau) +int dlarfg_(integer *n, doublereal *alpha, doublereal *x, integer *incx, doublereal *tau) { - /* System generated locals */ integer i__1; doublereal d__1; - - /* Builtin functions */ double d_lmp_sign(doublereal *, doublereal *); - - /* Local variables */ integer j, knt; doublereal beta; extern doublereal dnrm2_(integer *, doublereal *, integer *); - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *); + extern int dscal_(integer *, doublereal *, doublereal *, integer *); doublereal xnorm; - extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, - ftnlen); + extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, ftnlen); doublereal safmin, rsafmn; - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Executable Statements .. */ - - /* Parameter adjustments */ --x; - - /* Function Body */ if (*n <= 1) { *tau = 0.; return 0; } - i__1 = *n - 1; xnorm = dnrm2_(&i__1, &x[1], incx); - if (xnorm == 0.) { - -/* H = I */ - *tau = 0.; } else { - -/* general case */ - d__1 = dlapy2_(alpha, &xnorm); beta = -d_lmp_sign(&d__1, alpha); safmin = dlamch_((char *)"S", (ftnlen)1) / dlamch_((char *)"E", (ftnlen)1); knt = 0; if (abs(beta) < safmin) { - -/* XNORM, BETA may be inaccurate; scale X and recompute them */ - rsafmn = 1. / safmin; -L10: + L10: ++knt; i__1 = *n - 1; dscal_(&i__1, &rsafmn, &x[1], incx); @@ -206,9 +39,6 @@ L10: if (abs(beta) < safmin && knt < 20) { goto L10; } - -/* New BETA is at most 1, at least SAFMIN */ - i__1 = *n - 1; xnorm = dnrm2_(&i__1, &x[1], incx); d__1 = dlapy2_(alpha, &xnorm); @@ -218,23 +48,14 @@ L10: i__1 = *n - 1; d__1 = 1. / (*alpha - beta); dscal_(&i__1, &d__1, &x[1], incx); - -/* If ALPHA is subnormal, it may lose relative accuracy */ - i__1 = knt; for (j = 1; j <= i__1; ++j) { beta *= safmin; -/* L20: */ } *alpha = beta; } - return 0; - -/* End of DLARFG */ - -} /* dlarfg_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlarft.cpp b/lib/linalg/dlarft.cpp index bd0874fa3c..79881a08a4 100644 --- a/lib/linalg/dlarft.cpp +++ b/lib/linalg/dlarft.cpp @@ -1,233 +1,21 @@ -/* static/dlarft.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static doublereal c_b7 = 1.; - -/* > \brief \b DLARFT forms the triangular factor T of a block reflector H = I - vtvH */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLARFT + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER DIRECT, STOREV */ -/* INTEGER K, LDT, LDV, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLARFT forms the triangular factor T of a real block reflector H */ -/* > of order n, which is defined as a product of k elementary reflectors. */ -/* > */ -/* > If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; */ -/* > */ -/* > If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. */ -/* > */ -/* > If STOREV = 'C', the vector which defines the elementary reflector */ -/* > H(i) is stored in the i-th column of the array V, and */ -/* > */ -/* > H = I - V * T * V**T */ -/* > */ -/* > If STOREV = 'R', the vector which defines the elementary reflector */ -/* > H(i) is stored in the i-th row of the array V, and */ -/* > */ -/* > H = I - V**T * T * V */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] DIRECT */ -/* > \verbatim */ -/* > DIRECT is CHARACTER*1 */ -/* > Specifies the order in which the elementary reflectors are */ -/* > multiplied to form the block reflector: */ -/* > = 'F': H = H(1) H(2) . . . H(k) (Forward) */ -/* > = 'B': H = H(k) . . . H(2) H(1) (Backward) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] STOREV */ -/* > \verbatim */ -/* > STOREV is CHARACTER*1 */ -/* > Specifies how the vectors which define the elementary */ -/* > reflectors are stored (see also Further Details): */ -/* > = 'C': columnwise */ -/* > = 'R': rowwise */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the block reflector H. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > The order of the triangular factor T (= the number of */ -/* > elementary reflectors). K >= 1. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] V */ -/* > \verbatim */ -/* > V is DOUBLE PRECISION array, dimension */ -/* > (LDV,K) if STOREV = 'C' */ -/* > (LDV,N) if STOREV = 'R' */ -/* > The matrix V. See further details. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDV */ -/* > \verbatim */ -/* > LDV is INTEGER */ -/* > The leading dimension of the array V. */ -/* > If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TAU */ -/* > \verbatim */ -/* > TAU is DOUBLE PRECISION array, dimension (K) */ -/* > TAU(i) must contain the scalar factor of the elementary */ -/* > reflector H(i). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] T */ -/* > \verbatim */ -/* > T is DOUBLE PRECISION array, dimension (LDT,K) */ -/* > The k by k triangular factor T of the block reflector. */ -/* > If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is */ -/* > lower triangular. The rest of the array is not used. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDT */ -/* > \verbatim */ -/* > LDT is INTEGER */ -/* > The leading dimension of the array T. LDT >= K. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleOTHERauxiliary */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > The shape of the matrix V and the storage of the vectors which define */ -/* > the H(i) is best illustrated by the following example with n = 5 and */ -/* > k = 3. The elements equal to 1 are not stored. */ -/* > */ -/* > DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': */ -/* > */ -/* > V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) */ -/* > ( v1 1 ) ( 1 v2 v2 v2 ) */ -/* > ( v1 v2 1 ) ( 1 v3 v3 ) */ -/* > ( v1 v2 v3 ) */ -/* > ( v1 v2 v3 ) */ -/* > */ -/* > DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': */ -/* > */ -/* > V = ( v1 v2 v3 ) V = ( v1 v1 1 ) */ -/* > ( v1 v2 v3 ) ( v2 v2 v2 1 ) */ -/* > ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) */ -/* > ( 1 v3 ) */ -/* > ( 1 ) */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dlarft_(char *direct, char *storev, integer *n, integer * - k, doublereal *v, integer *ldv, doublereal *tau, doublereal *t, - integer *ldt, ftnlen direct_len, ftnlen storev_len) +int dlarft_(char *direct, char *storev, integer *n, integer *k, doublereal *v, integer *ldv, + doublereal *tau, doublereal *t, integer *ldt, ftnlen direct_len, ftnlen storev_len) { - /* System generated locals */ integer t_dim1, t_offset, v_dim1, v_offset, i__1, i__2, i__3; doublereal d__1; - - /* Local variables */ integer i__, j, prevlastv; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int dgemv_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, doublereal *, integer *, - doublereal *, doublereal *, integer *, ftnlen); + extern int dgemv_(char *, integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, ftnlen); integer lastv; - extern /* Subroutine */ int dtrmv_(char *, char *, char *, integer *, - doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, - ftnlen); - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Quick return if possible */ - - /* Parameter adjustments */ + extern int dtrmv_(char *, char *, char *, integer *, doublereal *, integer *, doublereal *, + integer *, ftnlen, ftnlen, ftnlen); v_dim1 = *ldv; v_offset = 1 + v_dim1; v -= v_offset; @@ -235,87 +23,65 @@ f"> */ t_dim1 = *ldt; t_offset = 1 + t_dim1; t -= t_offset; - - /* Function Body */ if (*n == 0) { return 0; } - if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { prevlastv = *n; i__1 = *k; for (i__ = 1; i__ <= i__1; ++i__) { - prevlastv = max(i__,prevlastv); + prevlastv = max(i__, prevlastv); if (tau[i__] == 0.) { - -/* H(i) = I */ - i__2 = i__; for (j = 1; j <= i__2; ++j) { t[j + i__ * t_dim1] = 0.; } } else { - -/* general case */ - if (lsame_(storev, (char *)"C", (ftnlen)1, (ftnlen)1)) { -/* Skip any trailing zeros. */ i__2 = i__ + 1; for (lastv = *n; lastv >= i__2; --lastv) { if (v[lastv + i__ * v_dim1] != 0.) { goto L219; } } -L219: + L219: i__2 = i__ - 1; for (j = 1; j <= i__2; ++j) { t[j + i__ * t_dim1] = -tau[i__] * v[i__ + j * v_dim1]; } - j = min(lastv,prevlastv); - -/* T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**T * V(i:j,i) */ - + j = min(lastv, prevlastv); i__2 = j - i__; i__3 = i__ - 1; d__1 = -tau[i__]; - dgemv_((char *)"Transpose", &i__2, &i__3, &d__1, &v[i__ + 1 + - v_dim1], ldv, &v[i__ + 1 + i__ * v_dim1], &c__1, & - c_b7, &t[i__ * t_dim1 + 1], &c__1, (ftnlen)9); + dgemv_((char *)"Transpose", &i__2, &i__3, &d__1, &v[i__ + 1 + v_dim1], ldv, + &v[i__ + 1 + i__ * v_dim1], &c__1, &c_b7, &t[i__ * t_dim1 + 1], &c__1, + (ftnlen)9); } else { -/* Skip any trailing zeros. */ i__2 = i__ + 1; for (lastv = *n; lastv >= i__2; --lastv) { if (v[i__ + lastv * v_dim1] != 0.) { goto L235; } } -L235: + L235: i__2 = i__ - 1; for (j = 1; j <= i__2; ++j) { t[j + i__ * t_dim1] = -tau[i__] * v[j + i__ * v_dim1]; } - j = min(lastv,prevlastv); - -/* T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**T */ - + j = min(lastv, prevlastv); i__2 = i__ - 1; i__3 = j - i__; d__1 = -tau[i__]; - dgemv_((char *)"No transpose", &i__2, &i__3, &d__1, &v[(i__ + 1) * - v_dim1 + 1], ldv, &v[i__ + (i__ + 1) * v_dim1], - ldv, &c_b7, &t[i__ * t_dim1 + 1], &c__1, (ftnlen) - 12); + dgemv_((char *)"No transpose", &i__2, &i__3, &d__1, &v[(i__ + 1) * v_dim1 + 1], ldv, + &v[i__ + (i__ + 1) * v_dim1], ldv, &c_b7, &t[i__ * t_dim1 + 1], &c__1, + (ftnlen)12); } - -/* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) */ - i__2 = i__ - 1; - dtrmv_((char *)"Upper", (char *)"No transpose", (char *)"Non-unit", &i__2, &t[ - t_offset], ldt, &t[i__ * t_dim1 + 1], &c__1, (ftnlen) - 5, (ftnlen)12, (ftnlen)8); + dtrmv_((char *)"Upper", (char *)"No transpose", (char *)"Non-unit", &i__2, &t[t_offset], ldt, + &t[i__ * t_dim1 + 1], &c__1, (ftnlen)5, (ftnlen)12, (ftnlen)8); t[i__ + i__ * t_dim1] = tau[i__]; if (i__ > 1) { - prevlastv = max(prevlastv,lastv); + prevlastv = max(prevlastv, lastv); } else { prevlastv = lastv; } @@ -325,79 +91,57 @@ L235: prevlastv = 1; for (i__ = *k; i__ >= 1; --i__) { if (tau[i__] == 0.) { - -/* H(i) = I */ - i__1 = *k; for (j = i__; j <= i__1; ++j) { t[j + i__ * t_dim1] = 0.; } } else { - -/* general case */ - if (i__ < *k) { if (lsame_(storev, (char *)"C", (ftnlen)1, (ftnlen)1)) { -/* Skip any leading zeros. */ i__1 = i__ - 1; for (lastv = 1; lastv <= i__1; ++lastv) { if (v[lastv + i__ * v_dim1] != 0.) { goto L280; } } -L280: + L280: i__1 = *k; for (j = i__ + 1; j <= i__1; ++j) { - t[j + i__ * t_dim1] = -tau[i__] * v[*n - *k + i__ - + j * v_dim1]; + t[j + i__ * t_dim1] = -tau[i__] * v[*n - *k + i__ + j * v_dim1]; } - j = max(lastv,prevlastv); - -/* T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**T * V(j:n-k+i,i) */ - + j = max(lastv, prevlastv); i__1 = *n - *k + i__ - j; i__2 = *k - i__; d__1 = -tau[i__]; - dgemv_((char *)"Transpose", &i__1, &i__2, &d__1, &v[j + (i__ - + 1) * v_dim1], ldv, &v[j + i__ * v_dim1], & - c__1, &c_b7, &t[i__ + 1 + i__ * t_dim1], & - c__1, (ftnlen)9); + dgemv_((char *)"Transpose", &i__1, &i__2, &d__1, &v[j + (i__ + 1) * v_dim1], ldv, + &v[j + i__ * v_dim1], &c__1, &c_b7, &t[i__ + 1 + i__ * t_dim1], + &c__1, (ftnlen)9); } else { -/* Skip any leading zeros. */ i__1 = i__ - 1; for (lastv = 1; lastv <= i__1; ++lastv) { if (v[i__ + lastv * v_dim1] != 0.) { goto L296; } } -L296: + L296: i__1 = *k; for (j = i__ + 1; j <= i__1; ++j) { - t[j + i__ * t_dim1] = -tau[i__] * v[j + (*n - *k - + i__) * v_dim1]; + t[j + i__ * t_dim1] = -tau[i__] * v[j + (*n - *k + i__) * v_dim1]; } - j = max(lastv,prevlastv); - -/* T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**T */ - + j = max(lastv, prevlastv); i__1 = *k - i__; i__2 = *n - *k + i__ - j; d__1 = -tau[i__]; - dgemv_((char *)"No transpose", &i__1, &i__2, &d__1, &v[i__ + - 1 + j * v_dim1], ldv, &v[i__ + j * v_dim1], - ldv, &c_b7, &t[i__ + 1 + i__ * t_dim1], &c__1, - (ftnlen)12); + dgemv_((char *)"No transpose", &i__1, &i__2, &d__1, &v[i__ + 1 + j * v_dim1], ldv, + &v[i__ + j * v_dim1], ldv, &c_b7, &t[i__ + 1 + i__ * t_dim1], &c__1, + (ftnlen)12); } - -/* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) */ - i__1 = *k - i__; - dtrmv_((char *)"Lower", (char *)"No transpose", (char *)"Non-unit", &i__1, &t[i__ - + 1 + (i__ + 1) * t_dim1], ldt, &t[i__ + 1 + i__ * - t_dim1], &c__1, (ftnlen)5, (ftnlen)12, (ftnlen)8) - ; + dtrmv_((char *)"Lower", (char *)"No transpose", (char *)"Non-unit", &i__1, + &t[i__ + 1 + (i__ + 1) * t_dim1], ldt, &t[i__ + 1 + i__ * t_dim1], &c__1, + (ftnlen)5, (ftnlen)12, (ftnlen)8); if (i__ > 1) { - prevlastv = min(prevlastv,lastv); + prevlastv = min(prevlastv, lastv); } else { prevlastv = lastv; } @@ -407,11 +151,7 @@ L296: } } return 0; - -/* End of DLARFT */ - -} /* dlarft_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlartg.cpp b/lib/linalg/dlartg.cpp index c18a8c6d43..c388e3b2d4 100644 --- a/lib/linalg/dlartg.cpp +++ b/lib/linalg/dlartg.cpp @@ -1,175 +1,24 @@ -/* fortran/dlartg.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DLARTG generates a plane rotation with real cosine and real sine. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLARTG + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLARTG( F, G, CS, SN, R ) */ - -/* .. Scalar Arguments .. */ -/* DOUBLE PRECISION CS, F, G, R, SN */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLARTG generate a plane rotation so that */ -/* > */ -/* > [ CS SN ] . [ F ] = [ R ] where CS**2 + SN**2 = 1. */ -/* > [ -SN CS ] [ G ] [ 0 ] */ -/* > */ -/* > This is a slower, more accurate version of the BLAS1 routine DROTG, */ -/* > with the following other differences: */ -/* > F and G are unchanged on return. */ -/* > If G=0, then CS=1 and SN=0. */ -/* > If F=0 and (G .ne. 0), then CS=0 and SN=1 without doing any */ -/* > floating point operations (saves work in DBDSQR when */ -/* > there are zeros on the diagonal). */ -/* > */ -/* > If F exceeds G in magnitude, CS will be positive. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] F */ -/* > \verbatim */ -/* > F is DOUBLE PRECISION */ -/* > The first component of vector to be rotated. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] G */ -/* > \verbatim */ -/* > G is DOUBLE PRECISION */ -/* > The second component of vector to be rotated. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] CS */ -/* > \verbatim */ -/* > CS is DOUBLE PRECISION */ -/* > The cosine of the rotation. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] SN */ -/* > \verbatim */ -/* > SN is DOUBLE PRECISION */ -/* > The sine of the rotation. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] R */ -/* > \verbatim */ -/* > R is DOUBLE PRECISION */ -/* > The nonzero component of the rotated vector. */ -/* > */ -/* > This version has a few statements commented out for thread safety */ -/* > (machine parameters are computed on each entry). 10 feb 03, SJH. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \date December 2016 */ - -/* > \ingroup OTHERauxiliary */ - -/* ===================================================================== */ -/* Subroutine */ int dlartg_(doublereal *f, doublereal *g, doublereal *cs, - doublereal *sn, doublereal *r__) +int dlartg_(doublereal *f, doublereal *g, doublereal *cs, doublereal *sn, doublereal *r__) { - /* System generated locals */ integer i__1; doublereal d__1, d__2; - - /* Builtin functions */ double log(doublereal), pow_lmp_di(doublereal *, integer *), sqrt(doublereal); - - /* Local variables */ integer i__; doublereal f1, g1, eps, scale; integer count; doublereal safmn2, safmx2; extern doublereal dlamch_(char *, ftnlen); doublereal safmin; - - -/* -- LAPACK auxiliary routine (version 3.7.0) -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ -/* December 2016 */ - -/* .. Scalar Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* LOGICAL FIRST */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Save statement .. */ -/* SAVE FIRST, SAFMX2, SAFMIN, SAFMN2 */ -/* .. */ -/* .. Data statements .. */ -/* DATA FIRST / .TRUE. / */ -/* .. */ -/* .. Executable Statements .. */ - -/* IF( FIRST ) THEN */ safmin = dlamch_((char *)"S", (ftnlen)1); eps = dlamch_((char *)"E", (ftnlen)1); d__1 = dlamch_((char *)"B", (ftnlen)1); - i__1 = (integer) (log(safmin / eps) / log(dlamch_((char *)"B", (ftnlen)1)) / 2.); + i__1 = (integer)(log(safmin / eps) / log(dlamch_((char *)"B", (ftnlen)1)) / 2.); safmn2 = pow_lmp_di(&d__1, &i__1); safmx2 = 1. / safmn2; -/* FIRST = .FALSE. */ -/* END IF */ if (*g == 0.) { *cs = 1.; *sn = 0.; @@ -181,24 +30,20 @@ f"> */ } else { f1 = *f; g1 = *g; -/* Computing MAX */ d__1 = abs(f1), d__2 = abs(g1); - scale = max(d__1,d__2); + scale = max(d__1, d__2); if (scale >= safmx2) { count = 0; -L10: + L10: ++count; f1 *= safmn2; g1 *= safmn2; -/* Computing MAX */ d__1 = abs(f1), d__2 = abs(g1); - scale = max(d__1,d__2); + scale = max(d__1, d__2); if (scale >= safmx2) { goto L10; } -/* Computing 2nd power */ d__1 = f1; -/* Computing 2nd power */ d__2 = g1; *r__ = sqrt(d__1 * d__1 + d__2 * d__2); *cs = f1 / *r__; @@ -206,23 +51,19 @@ L10: i__1 = count; for (i__ = 1; i__ <= i__1; ++i__) { *r__ *= safmx2; -/* L20: */ } } else if (scale <= safmn2) { count = 0; -L30: + L30: ++count; f1 *= safmx2; g1 *= safmx2; -/* Computing MAX */ d__1 = abs(f1), d__2 = abs(g1); - scale = max(d__1,d__2); + scale = max(d__1, d__2); if (scale <= safmn2) { goto L30; } -/* Computing 2nd power */ d__1 = f1; -/* Computing 2nd power */ d__2 = g1; *r__ = sqrt(d__1 * d__1 + d__2 * d__2); *cs = f1 / *r__; @@ -230,12 +71,9 @@ L30: i__1 = count; for (i__ = 1; i__ <= i__1; ++i__) { *r__ *= safmn2; -/* L40: */ } } else { -/* Computing 2nd power */ d__1 = f1; -/* Computing 2nd power */ d__2 = g1; *r__ = sqrt(d__1 * d__1 + d__2 * d__2); *cs = f1 / *r__; @@ -248,11 +86,7 @@ L30: } } return 0; - -/* End of DLARTG */ - -} /* dlartg_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlas2.cpp b/lib/linalg/dlas2.cpp index c590ed5819..4271202477 100644 --- a/lib/linalg/dlas2.cpp +++ b/lib/linalg/dlas2.cpp @@ -1,177 +1,29 @@ -/* fortran/dlas2.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DLAS2 computes singular values of a 2-by-2 triangular matrix. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLAS2 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLAS2( F, G, H, SSMIN, SSMAX ) */ - -/* .. Scalar Arguments .. */ -/* DOUBLE PRECISION F, G, H, SSMAX, SSMIN */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLAS2 computes the singular values of the 2-by-2 matrix */ -/* > [ F G ] */ -/* > [ 0 H ]. */ -/* > On return, SSMIN is the smaller singular value and SSMAX is the */ -/* > larger singular value. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] F */ -/* > \verbatim */ -/* > F is DOUBLE PRECISION */ -/* > The (1,1) element of the 2-by-2 matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] G */ -/* > \verbatim */ -/* > G is DOUBLE PRECISION */ -/* > The (1,2) element of the 2-by-2 matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] H */ -/* > \verbatim */ -/* > H is DOUBLE PRECISION */ -/* > The (2,2) element of the 2-by-2 matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] SSMIN */ -/* > \verbatim */ -/* > SSMIN is DOUBLE PRECISION */ -/* > The smaller singular value. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] SSMAX */ -/* > \verbatim */ -/* > SSMAX is DOUBLE PRECISION */ -/* > The larger singular value. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup OTHERauxiliary */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > Barring over/underflow, all output quantities are correct to within */ -/* > a few units in the last place (ulps), even in the absence of a guard */ -/* > digit in addition/subtraction. */ -/* > */ -/* > In IEEE arithmetic, the code works correctly if one matrix element is */ -/* > infinite. */ -/* > */ -/* > Overflow will not occur unless the largest singular value itself */ -/* > overflows, or is within a few ulps of overflow. (On machines with */ -/* > partial overflow, like the Cray, overflow may occur if the largest */ -/* > singular value is within a factor of 2 of overflow.) */ -/* > */ -/* > Underflow is harmless if underflow is gradual. Otherwise, results */ -/* > may correspond to a matrix modified by perturbations of size near */ -/* > the underflow threshold. */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dlas2_(doublereal *f, doublereal *g, doublereal *h__, - doublereal *ssmin, doublereal *ssmax) +int dlas2_(doublereal *f, doublereal *g, doublereal *h__, doublereal *ssmin, doublereal *ssmax) { - /* System generated locals */ doublereal d__1, d__2; - - /* Builtin functions */ double sqrt(doublereal); - - /* Local variables */ doublereal c__, fa, ga, ha, as, at, au, fhmn, fhmx; - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ - -/* ==================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - fa = abs(*f); ga = abs(*g); ha = abs(*h__); - fhmn = min(fa,ha); - fhmx = max(fa,ha); + fhmn = min(fa, ha); + fhmx = max(fa, ha); if (fhmn == 0.) { *ssmin = 0.; if (fhmx == 0.) { *ssmax = ga; } else { -/* Computing 2nd power */ - d__1 = min(fhmx,ga) / max(fhmx,ga); - *ssmax = max(fhmx,ga) * sqrt(d__1 * d__1 + 1.); + d__1 = min(fhmx, ga) / max(fhmx, ga); + *ssmax = max(fhmx, ga) * sqrt(d__1 * d__1 + 1.); } } else { if (ga < fhmx) { as = fhmn / fhmx + 1.; at = (fhmx - fhmn) / fhmx; -/* Computing 2nd power */ d__1 = ga / fhmx; au = d__1 * d__1; c__ = 2. / (sqrt(as * as + au) + sqrt(at * at + au)); @@ -180,19 +32,12 @@ extern "C" { } else { au = fhmx / ga; if (au == 0.) { - -/* Avoid possible harmful underflow if exponent range */ -/* asymmetric (true SSMIN may not underflow even if */ -/* AU underflows) */ - *ssmin = fhmn * fhmx / ga; *ssmax = ga; } else { as = fhmn / fhmx + 1.; at = (fhmx - fhmn) / fhmx; -/* Computing 2nd power */ d__1 = as * au; -/* Computing 2nd power */ d__2 = at * au; c__ = 1. / (sqrt(d__1 * d__1 + 1.) + sqrt(d__2 * d__2 + 1.)); *ssmin = fhmn * c__ * au; @@ -202,11 +47,7 @@ extern "C" { } } return 0; - -/* End of DLAS2 */ - -} /* dlas2_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlascl.cpp b/lib/linalg/dlascl.cpp index 7596a5c109..3248e1b8a9 100644 --- a/lib/linalg/dlascl.cpp +++ b/lib/linalg/dlascl.cpp @@ -1,172 +1,11 @@ -/* fortran/dlascl.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLASCL + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLASCL( TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER TYPE */ -/* INTEGER INFO, KL, KU, LDA, M, N */ -/* DOUBLE PRECISION CFROM, CTO */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLASCL multiplies the M by N real matrix A by the real scalar */ -/* > CTO/CFROM. This is done without over/underflow as long as the final */ -/* > result CTO*A(I,J)/CFROM does not over/underflow. TYPE specifies that */ -/* > A may be full, upper triangular, lower triangular, upper Hessenberg, */ -/* > or banded. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] TYPE */ -/* > \verbatim */ -/* > TYPE is CHARACTER*1 */ -/* > TYPE indices the storage type of the input matrix. */ -/* > = 'G': A is a full matrix. */ -/* > = 'L': A is a lower triangular matrix. */ -/* > = 'U': A is an upper triangular matrix. */ -/* > = 'H': A is an upper Hessenberg matrix. */ -/* > = 'B': A is a symmetric band matrix with lower bandwidth KL */ -/* > and upper bandwidth KU and with the only the lower */ -/* > half stored. */ -/* > = 'Q': A is a symmetric band matrix with lower bandwidth KL */ -/* > and upper bandwidth KU and with the only the upper */ -/* > half stored. */ -/* > = 'Z': A is a band matrix with lower bandwidth KL and upper */ -/* > bandwidth KU. See DGBTRF for storage details. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] KL */ -/* > \verbatim */ -/* > KL is INTEGER */ -/* > The lower bandwidth of A. Referenced only if TYPE = 'B', */ -/* > 'Q' or 'Z'. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] KU */ -/* > \verbatim */ -/* > KU is INTEGER */ -/* > The upper bandwidth of A. Referenced only if TYPE = 'B', */ -/* > 'Q' or 'Z'. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] CFROM */ -/* > \verbatim */ -/* > CFROM is DOUBLE PRECISION */ -/* > \endverbatim */ -/* > */ -/* > \param[in] CTO */ -/* > \verbatim */ -/* > CTO is DOUBLE PRECISION */ -/* > */ -/* > The matrix A is multiplied by CTO/CFROM. A(I,J) is computed */ -/* > without over/underflow if the final result CTO*A(I,J)/CFROM */ -/* > can be represented without over/underflow. CFROM must be */ -/* > nonzero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix A. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > The matrix to be multiplied by CTO/CFROM. See TYPE for the */ -/* > storage type. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. */ -/* > If TYPE = 'G', 'L', 'U', 'H', LDA >= max(1,M); */ -/* > TYPE = 'B', LDA >= KL+1; */ -/* > TYPE = 'Q', LDA >= KU+1; */ -/* > TYPE = 'Z', LDA >= 2*KL+KU+1. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > 0 - successful exit */ -/* > <0 - if INFO = -i, the i-th argument had an illegal value. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup OTHERauxiliary */ - -/* ===================================================================== */ -/* Subroutine */ int dlascl_(char *type__, integer *kl, integer *ku, - doublereal *cfrom, doublereal *cto, integer *m, integer *n, - doublereal *a, integer *lda, integer *info, ftnlen type_len) +int dlascl_(char *type__, integer *kl, integer *ku, doublereal *cfrom, doublereal *cto, integer *m, + integer *n, doublereal *a, integer *lda, integer *info, ftnlen type_len) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; - - /* Local variables */ integer i__, j, k1, k2, k3, k4; doublereal mul, cto1; logical done; @@ -177,43 +16,12 @@ f"> */ extern doublereal dlamch_(char *, ftnlen); doublereal cfromc; extern logical disnan_(doublereal *); - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern int xerbla_(char *, integer *, ftnlen); doublereal bignum, smlnum; - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; - - /* Function Body */ *info = 0; - if (lsame_(type__, (char *)"G", (ftnlen)1, (ftnlen)1)) { itype = 0; } else if (lsame_(type__, (char *)"L", (ftnlen)1, (ftnlen)1)) { @@ -231,7 +39,6 @@ f"> */ } else { itype = -1; } - if (itype == -1) { *info = -1; } else if (*cfrom == 0. || disnan_(cfrom)) { @@ -242,59 +49,43 @@ f"> */ *info = -6; } else if (*n < 0 || itype == 4 && *n != *m || itype == 5 && *n != *m) { *info = -7; - } else if (itype <= 3 && *lda < max(1,*m)) { + } else if (itype <= 3 && *lda < max(1, *m)) { *info = -9; } else if (itype >= 4) { -/* Computing MAX */ i__1 = *m - 1; - if (*kl < 0 || *kl > max(i__1,0)) { + if (*kl < 0 || *kl > max(i__1, 0)) { *info = -2; - } else /* if(complicated condition) */ { -/* Computing MAX */ + } else { i__1 = *n - 1; - if (*ku < 0 || *ku > max(i__1,0) || (itype == 4 || itype == 5) && - *kl != *ku) { + if (*ku < 0 || *ku > max(i__1, 0) || (itype == 4 || itype == 5) && *kl != *ku) { *info = -3; - } else if (itype == 4 && *lda < *kl + 1 || itype == 5 && *lda < * - ku + 1 || itype == 6 && *lda < (*kl << 1) + *ku + 1) { + } else if (itype == 4 && *lda < *kl + 1 || itype == 5 && *lda < *ku + 1 || + itype == 6 && *lda < (*kl << 1) + *ku + 1) { *info = -9; } } } - if (*info != 0) { i__1 = -(*info); xerbla_((char *)"DLASCL", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*n == 0 || *m == 0) { return 0; } - -/* Get machine parameters */ - smlnum = dlamch_((char *)"S", (ftnlen)1); bignum = 1. / smlnum; - cfromc = *cfrom; ctoc = *cto; - L10: cfrom1 = cfromc * smlnum; if (cfrom1 == cfromc) { -/* CFROMC is an inf. Multiply by a correctly signed zero for */ -/* finite CTOC, or a NaN if CTOC is infinite. */ mul = ctoc / cfromc; done = TRUE_; cto1 = ctoc; } else { cto1 = ctoc / bignum; if (cto1 == ctoc) { -/* CTOC is either 0 or an inf. In both cases, CTOC itself */ -/* serves as the correct multiplication factor. */ mul = ctoc; done = TRUE_; cfromc = 1.; @@ -314,135 +105,81 @@ L10: } } } - if (itype == 0) { - -/* Full matrix */ - i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { a[i__ + j * a_dim1] *= mul; -/* L20: */ } -/* L30: */ } - } else if (itype == 1) { - -/* Lower triangular matrix */ - i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = j; i__ <= i__2; ++i__) { a[i__ + j * a_dim1] *= mul; -/* L40: */ } -/* L50: */ } - } else if (itype == 2) { - -/* Upper triangular matrix */ - i__1 = *n; for (j = 1; j <= i__1; ++j) { - i__2 = min(j,*m); + i__2 = min(j, *m); for (i__ = 1; i__ <= i__2; ++i__) { a[i__ + j * a_dim1] *= mul; -/* L60: */ } -/* L70: */ } - } else if (itype == 3) { - -/* Upper Hessenberg matrix */ - i__1 = *n; for (j = 1; j <= i__1; ++j) { -/* Computing MIN */ i__3 = j + 1; - i__2 = min(i__3,*m); + i__2 = min(i__3, *m); for (i__ = 1; i__ <= i__2; ++i__) { a[i__ + j * a_dim1] *= mul; -/* L80: */ } -/* L90: */ } - } else if (itype == 4) { - -/* Lower half of a symmetric band matrix */ - k3 = *kl + 1; k4 = *n + 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { -/* Computing MIN */ i__3 = k3, i__4 = k4 - j; - i__2 = min(i__3,i__4); + i__2 = min(i__3, i__4); for (i__ = 1; i__ <= i__2; ++i__) { a[i__ + j * a_dim1] *= mul; -/* L100: */ } -/* L110: */ } - } else if (itype == 5) { - -/* Upper half of a symmetric band matrix */ - k1 = *ku + 2; k3 = *ku + 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { -/* Computing MAX */ i__2 = k1 - j; i__3 = k3; - for (i__ = max(i__2,1); i__ <= i__3; ++i__) { + for (i__ = max(i__2, 1); i__ <= i__3; ++i__) { a[i__ + j * a_dim1] *= mul; -/* L120: */ } -/* L130: */ } - } else if (itype == 6) { - -/* Band matrix */ - k1 = *kl + *ku + 2; k2 = *kl + 1; k3 = (*kl << 1) + *ku + 1; k4 = *kl + *ku + 1 + *m; i__1 = *n; for (j = 1; j <= i__1; ++j) { -/* Computing MAX */ i__3 = k1 - j; -/* Computing MIN */ i__4 = k3, i__5 = k4 - j; - i__2 = min(i__4,i__5); - for (i__ = max(i__3,k2); i__ <= i__2; ++i__) { + i__2 = min(i__4, i__5); + for (i__ = max(i__3, k2); i__ <= i__2; ++i__) { a[i__ + j * a_dim1] *= mul; -/* L140: */ } -/* L150: */ } - } - - if (! done) { + if (!done) { goto L10; } - return 0; - -/* End of DLASCL */ - -} /* dlascl_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlasd4.cpp b/lib/linalg/dlasd4.cpp index e7922d1199..c51c15370e 100644 --- a/lib/linalg/dlasd4.cpp +++ b/lib/linalg/dlasd4.cpp @@ -1,187 +1,13 @@ -/* fortran/dlasd4.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DLASD4 computes the square root of the i-th updated eigenvalue of a positive symmetric rank-one - modification to a positive diagonal matrix. Used by dbdsdc. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLASD4 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLASD4( N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER I, INFO, N */ -/* DOUBLE PRECISION RHO, SIGMA */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION D( * ), DELTA( * ), WORK( * ), Z( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > This subroutine computes the square root of the I-th updated */ -/* > eigenvalue of a positive symmetric rank-one modification to */ -/* > a positive diagonal matrix whose entries are given as the squares */ -/* > of the corresponding entries in the array d, and that */ -/* > */ -/* > 0 <= D(i) < D(j) for i < j */ -/* > */ -/* > and that RHO > 0. This is arranged by the calling routine, and is */ -/* > no loss in generality. The rank-one modified system is thus */ -/* > */ -/* > diag( D ) * diag( D ) + RHO * Z * Z_transpose. */ -/* > */ -/* > where we assume the Euclidean norm of Z is 1. */ -/* > */ -/* > The method consists of approximating the rational functions in the */ -/* > secular equation by simpler interpolating rational functions. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The length of all arrays. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] I */ -/* > \verbatim */ -/* > I is INTEGER */ -/* > The index of the eigenvalue to be computed. 1 <= I <= N. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension ( N ) */ -/* > The original eigenvalues. It is assumed that they are in */ -/* > order, 0 <= D(I) < D(J) for I < J. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] Z */ -/* > \verbatim */ -/* > Z is DOUBLE PRECISION array, dimension ( N ) */ -/* > The components of the updating vector. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] DELTA */ -/* > \verbatim */ -/* > DELTA is DOUBLE PRECISION array, dimension ( N ) */ -/* > If N .ne. 1, DELTA contains (D(j) - sigma_I) in its j-th */ -/* > component. If N = 1, then DELTA(1) = 1. The vector DELTA */ -/* > contains the information necessary to construct the */ -/* > (singular) eigenvectors. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] RHO */ -/* > \verbatim */ -/* > RHO is DOUBLE PRECISION */ -/* > The scalar in the symmetric updating formula. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] SIGMA */ -/* > \verbatim */ -/* > SIGMA is DOUBLE PRECISION */ -/* > The computed sigma_I, the I-th updated eigenvalue. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension ( N ) */ -/* > If N .ne. 1, WORK contains (D(j) + sigma_I) in its j-th */ -/* > component. If N = 1, then WORK( 1 ) = 1. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > > 0: if INFO = 1, the updating process failed. */ -/* > \endverbatim */ - -/* > \par Internal Parameters: */ -/* ========================= */ -/* > */ -/* > \verbatim */ -/* > Logical variable ORGATI (origin-at-i?) is used for distinguishing */ -/* > whether D(i) or D(i+1) is treated as the origin. */ -/* > */ -/* > ORGATI = .true. origin at i */ -/* > ORGATI = .false. origin at i+1 */ -/* > */ -/* > Logical variable SWTCH3 (switch-for-3-poles?) is for noting */ -/* > if we are working with THREE poles! */ -/* > */ -/* > MAXIT is the maximum number of iterations allowed for each */ -/* > eigenvalue. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup OTHERauxiliary */ - -/* > \par Contributors: */ -/* ================== */ -/* > */ -/* > Ren-Cang Li, Computer Science Division, University of California */ -/* > at Berkeley, USA */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dlasd4_(integer *n, integer *i__, doublereal *d__, - doublereal *z__, doublereal *delta, doublereal *rho, doublereal * - sigma, doublereal *work, integer *info) +int dlasd4_(integer *n, integer *i__, doublereal *d__, doublereal *z__, doublereal *delta, + doublereal *rho, doublereal *sigma, doublereal *work, integer *info) { - /* System generated locals */ integer i__1; doublereal d__1; - - /* Builtin functions */ double sqrt(doublereal); - - /* Local variables */ doublereal a, b, c__; integer j; doublereal w, dd[3]; @@ -197,60 +23,22 @@ f"> */ doublereal dtisq; logical swtch; doublereal dtnsq; - extern /* Subroutine */ int dlaed6_(integer *, logical *, doublereal *, - doublereal *, doublereal *, doublereal *, doublereal *, integer *) - , dlasd5_(integer *, doublereal *, doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *); + extern int dlaed6_(integer *, logical *, doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, integer *), + dlasd5_(integer *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *); doublereal delsq2, dtnsq1; logical swtch3; extern doublereal dlamch_(char *, ftnlen); logical orgati; doublereal erretm, dtipsq, rhoinv; logical geomavg; - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. Local Arrays .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Since this routine is called in an inner loop, we do no argument */ -/* checking. */ - -/* Quick return for N=1 and 2. */ - - /* Parameter adjustments */ --work; --delta; --z__; --d__; - - /* Function Body */ *info = 0; if (*n == 1) { - -/* Presumably, I=1 upon entry */ - *sigma = sqrt(d__[1] * d__[1] + *rho * z__[1] * z__[1]); delta[1] = 1.; work[1] = 1.; @@ -260,63 +48,38 @@ f"> */ dlasd5_(i__, &d__[1], &z__[1], &delta[1], rho, sigma, &work[1]); return 0; } - -/* Compute machine epsilon */ - eps = dlamch_((char *)"Epsilon", (ftnlen)7); rhoinv = 1. / *rho; tau2 = 0.; - -/* The case I = N */ - if (*i__ == *n) { - -/* Initialize some basic variables */ - ii = *n - 1; niter = 1; - -/* Calculate initial guess */ - temp = *rho / 2.; - -/* If ||Z||_2 is not one, then TEMP should be set to */ -/* RHO * ||Z||_2^2 / TWO */ - temp1 = temp / (d__[*n] + sqrt(d__[*n] * d__[*n] + temp)); i__1 = *n; for (j = 1; j <= i__1; ++j) { work[j] = d__[j] + d__[*n] + temp1; delta[j] = d__[j] - d__[*n] - temp1; -/* L10: */ } - psi = 0.; i__1 = *n - 2; for (j = 1; j <= i__1; ++j) { psi += z__[j] * z__[j] / (delta[j] * work[j]); -/* L20: */ } - c__ = rhoinv + psi; - w = c__ + z__[ii] * z__[ii] / (delta[ii] * work[ii]) + z__[*n] * z__[* - n] / (delta[*n] * work[*n]); - + w = c__ + z__[ii] * z__[ii] / (delta[ii] * work[ii]) + + z__[*n] * z__[*n] / (delta[*n] * work[*n]); if (w <= 0.) { temp1 = sqrt(d__[*n] * d__[*n] + *rho); - temp = z__[*n - 1] * z__[*n - 1] / ((d__[*n - 1] + temp1) * (d__[* - n] - d__[*n - 1] + *rho / (d__[*n] + temp1))) + z__[*n] * - z__[*n] / *rho; - -/* The following TAU2 is to approximate */ -/* SIGMA_n^2 - D( N )*D( N ) */ - + temp = + z__[*n - 1] * z__[*n - 1] / + ((d__[*n - 1] + temp1) * (d__[*n] - d__[*n - 1] + *rho / (d__[*n] + temp1))) + + z__[*n] * z__[*n] / *rho; if (c__ <= temp) { tau = *rho; } else { delsq = (d__[*n] - d__[*n - 1]) * (d__[*n] + d__[*n - 1]); - a = -c__ * delsq + z__[*n - 1] * z__[*n - 1] + z__[*n] * z__[* - n]; + a = -c__ * delsq + z__[*n - 1] * z__[*n - 1] + z__[*n] * z__[*n]; b = z__[*n] * z__[*n] * delsq; if (a < 0.) { tau2 = b * 2. / (sqrt(a * a + b * 4. * c__) - a); @@ -325,44 +88,23 @@ f"> */ } tau = tau2 / (d__[*n] + sqrt(d__[*n] * d__[*n] + tau2)); } - -/* It can be proved that */ -/* D(N)^2+RHO/2 <= SIGMA_n^2 < D(N)^2+TAU2 <= D(N)^2+RHO */ - } else { delsq = (d__[*n] - d__[*n - 1]) * (d__[*n] + d__[*n - 1]); a = -c__ * delsq + z__[*n - 1] * z__[*n - 1] + z__[*n] * z__[*n]; b = z__[*n] * z__[*n] * delsq; - -/* The following TAU2 is to approximate */ -/* SIGMA_n^2 - D( N )*D( N ) */ - if (a < 0.) { tau2 = b * 2. / (sqrt(a * a + b * 4. * c__) - a); } else { tau2 = (a + sqrt(a * a + b * 4. * c__)) / (c__ * 2.); } tau = tau2 / (d__[*n] + sqrt(d__[*n] * d__[*n] + tau2)); - -/* It can be proved that */ -/* D(N)^2 < D(N)^2+TAU2 < SIGMA(N)^2 < D(N)^2+RHO/2 */ - } - -/* The following TAU is to approximate SIGMA_n - D( N ) */ - -/* TAU = TAU2 / ( D( N )+SQRT( D( N )*D( N )+TAU2 ) ) */ - *sigma = d__[*n] + tau; i__1 = *n; for (j = 1; j <= i__1; ++j) { delta[j] = d__[j] - d__[*n] - tau; work[j] = d__[j] + d__[*n] + tau; -/* L30: */ } - -/* Evaluate PSI and the derivative DPSI */ - dpsi = 0.; psi = 0.; erretm = 0.; @@ -372,28 +114,16 @@ f"> */ psi += z__[j] * temp; dpsi += temp * temp; erretm += psi; -/* L40: */ } erretm = abs(erretm); - -/* Evaluate PHI and the derivative DPHI */ - temp = z__[*n] / (delta[*n] * work[*n]); phi = z__[*n] * temp; dphi = temp * temp; erretm = (-phi - psi) * 8. + erretm - phi + rhoinv; -/* $ + ABS( TAU2 )*( DPSI+DPHI ) */ - w = rhoinv + phi + psi; - -/* Test for convergence */ - if (abs(w) <= eps * erretm) { goto L240; } - -/* Calculate the new step */ - ++niter; dtnsq1 = work[*n - 1] * delta[*n - 1]; dtnsq = work[*n] * delta[*n]; @@ -406,19 +136,10 @@ f"> */ if (c__ == 0.) { eta = *rho - *sigma * *sigma; } else if (a >= 0.) { - eta = (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (c__ - * 2.); + eta = (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (c__ * 2.); } else { - eta = b * 2. / (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1))) - ); + eta = b * 2. / (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))); } - -/* Note, eta should be positive if w is negative, and */ -/* eta should be negative otherwise. However, */ -/* if for some reason caused by roundoff, eta*w > 0, */ -/* we simply use one Newton step instead. This way */ -/* will guarantee eta*w < 0. */ - if (w * eta > 0.) { eta = -w / (dpsi + dphi); } @@ -426,20 +147,14 @@ f"> */ if (temp > *rho) { eta = *rho + dtnsq; } - eta /= *sigma + sqrt(eta + *sigma * *sigma); tau += eta; *sigma += eta; - i__1 = *n; for (j = 1; j <= i__1; ++j) { delta[j] -= eta; work[j] += eta; -/* L50: */ } - -/* Evaluate PSI and the derivative DPSI */ - dpsi = 0.; psi = 0.; erretm = 0.; @@ -449,54 +164,29 @@ f"> */ psi += z__[j] * temp; dpsi += temp * temp; erretm += psi; -/* L60: */ } erretm = abs(erretm); - -/* Evaluate PHI and the derivative DPHI */ - tau2 = work[*n] * delta[*n]; temp = z__[*n] / tau2; phi = z__[*n] * temp; dphi = temp * temp; erretm = (-phi - psi) * 8. + erretm - phi + rhoinv; -/* $ + ABS( TAU2 )*( DPSI+DPHI ) */ - w = rhoinv + phi + psi; - -/* Main loop to update the values of the array DELTA */ - iter = niter + 1; - for (niter = iter; niter <= 400; ++niter) { - -/* Test for convergence */ - if (abs(w) <= eps * erretm) { goto L240; } - -/* Calculate the new step */ - dtnsq1 = work[*n - 1] * delta[*n - 1]; dtnsq = work[*n] * delta[*n]; c__ = w - dtnsq1 * dpsi - dtnsq * dphi; a = (dtnsq + dtnsq1) * w - dtnsq1 * dtnsq * (dpsi + dphi); b = dtnsq1 * dtnsq * w; if (a >= 0.) { - eta = (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / ( - c__ * 2.); + eta = (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (c__ * 2.); } else { - eta = b * 2. / (a - sqrt((d__1 = a * a - b * 4. * c__, abs( - d__1)))); + eta = b * 2. / (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))); } - -/* Note, eta should be positive if w is negative, and */ -/* eta should be negative otherwise. However, */ -/* if for some reason caused by roundoff, eta*w > 0, */ -/* we simply use one Newton step instead. This way */ -/* will guarantee eta*w < 0. */ - if (w * eta > 0.) { eta = -w / (dpsi + dphi); } @@ -504,20 +194,14 @@ f"> */ if (temp <= 0.) { eta /= 2.; } - eta /= *sigma + sqrt(eta + *sigma * *sigma); tau += eta; *sigma += eta; - i__1 = *n; for (j = 1; j <= i__1; ++j) { delta[j] -= eta; work[j] += eta; -/* L70: */ } - -/* Evaluate PSI and the derivative DPSI */ - dpsi = 0.; psi = 0.; erretm = 0.; @@ -527,39 +211,20 @@ f"> */ psi += z__[j] * temp; dpsi += temp * temp; erretm += psi; -/* L80: */ } erretm = abs(erretm); - -/* Evaluate PHI and the derivative DPHI */ - tau2 = work[*n] * delta[*n]; temp = z__[*n] / tau2; phi = z__[*n] * temp; dphi = temp * temp; erretm = (-phi - psi) * 8. + erretm - phi + rhoinv; -/* $ + ABS( TAU2 )*( DPSI+DPHI ) */ - w = rhoinv + phi + psi; -/* L90: */ } - -/* Return with INFO = 1, NITER = MAXIT and not converged */ - *info = 1; goto L240; - -/* End for the case I = N */ - } else { - -/* The case for I < N */ - niter = 1; ip1 = *i__ + 1; - -/* Calculate initial guess */ - delsq = (d__[ip1] - d__[*i__]) * (d__[ip1] + d__[*i__]); delsq2 = delsq / 2.; sq2 = sqrt((d__[*i__] * d__[*i__] + d__[ip1] * d__[ip1]) / 2.); @@ -568,33 +233,22 @@ f"> */ for (j = 1; j <= i__1; ++j) { work[j] = d__[j] + d__[*i__] + temp; delta[j] = d__[j] - d__[*i__] - temp; -/* L100: */ } - psi = 0.; i__1 = *i__ - 1; for (j = 1; j <= i__1; ++j) { psi += z__[j] * z__[j] / (work[j] * delta[j]); -/* L110: */ } - phi = 0.; i__1 = *i__ + 2; for (j = *n; j >= i__1; --j) { phi += z__[j] * z__[j] / (work[j] * delta[j]); -/* L120: */ } c__ = rhoinv + psi + phi; - w = c__ + z__[*i__] * z__[*i__] / (work[*i__] * delta[*i__]) + z__[ - ip1] * z__[ip1] / (work[ip1] * delta[ip1]); - + w = c__ + z__[*i__] * z__[*i__] / (work[*i__] * delta[*i__]) + + z__[ip1] * z__[ip1] / (work[ip1] * delta[ip1]); geomavg = FALSE_; if (w > 0.) { - -/* d(i)^2 < the ith sigma^2 < (d(i)^2+d(i+1)^2)/2 */ - -/* We choose d(i) as origin. */ - orgati = TRUE_; ii = *i__; sglb = 0.; @@ -602,32 +256,19 @@ f"> */ a = c__ * delsq + z__[*i__] * z__[*i__] + z__[ip1] * z__[ip1]; b = z__[*i__] * z__[*i__] * delsq; if (a > 0.) { - tau2 = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs( - d__1)))); + tau2 = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))); } else { - tau2 = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / - (c__ * 2.); + tau2 = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (c__ * 2.); } - -/* TAU2 now is an estimation of SIGMA^2 - D( I )^2. The */ -/* following, however, is the corresponding estimation of */ -/* SIGMA - D( I ). */ - tau = tau2 / (d__[*i__] + sqrt(d__[*i__] * d__[*i__] + tau2)); temp = sqrt(eps); - if (d__[*i__] <= temp * d__[ip1] && (d__1 = z__[*i__], abs(d__1)) - <= temp && d__[*i__] > 0.) { -/* Computing MIN */ + if (d__[*i__] <= temp * d__[ip1] && (d__1 = z__[*i__], abs(d__1)) <= temp && + d__[*i__] > 0.) { d__1 = d__[*i__] * 10.; - tau = min(d__1,sgub); + tau = min(d__1, sgub); geomavg = TRUE_; } } else { - -/* (d(i)^2+d(i+1)^2)/2 <= the ith sigma^2 < d(i+1)^2/2 */ - -/* We choose d(i+1) as origin. */ - orgati = FALSE_; ii = ip1; sglb = -delsq2 / (d__[ii] + sq2); @@ -635,33 +276,20 @@ f"> */ a = c__ * delsq - z__[*i__] * z__[*i__] - z__[ip1] * z__[ip1]; b = z__[ip1] * z__[ip1] * delsq; if (a < 0.) { - tau2 = b * 2. / (a - sqrt((d__1 = a * a + b * 4. * c__, abs( - d__1)))); + tau2 = b * 2. / (a - sqrt((d__1 = a * a + b * 4. * c__, abs(d__1)))); } else { - tau2 = -(a + sqrt((d__1 = a * a + b * 4. * c__, abs(d__1)))) / - (c__ * 2.); + tau2 = -(a + sqrt((d__1 = a * a + b * 4. * c__, abs(d__1)))) / (c__ * 2.); } - -/* TAU2 now is an estimation of SIGMA^2 - D( IP1 )^2. The */ -/* following, however, is the corresponding estimation of */ -/* SIGMA - D( IP1 ). */ - - tau = tau2 / (d__[ip1] + sqrt((d__1 = d__[ip1] * d__[ip1] + tau2, - abs(d__1)))); + tau = tau2 / (d__[ip1] + sqrt((d__1 = d__[ip1] * d__[ip1] + tau2, abs(d__1)))); } - *sigma = d__[ii] + tau; i__1 = *n; for (j = 1; j <= i__1; ++j) { work[j] = d__[j] + d__[ii] + tau; delta[j] = d__[j] - d__[ii] - tau; -/* L130: */ } iim1 = ii - 1; iip1 = ii + 1; - -/* Evaluate PSI and the derivative DPSI */ - dpsi = 0.; psi = 0.; erretm = 0.; @@ -671,12 +299,8 @@ f"> */ psi += z__[j] * temp; dpsi += temp * temp; erretm += psi; -/* L150: */ } erretm = abs(erretm); - -/* Evaluate PHI and the derivative DPHI */ - dphi = 0.; phi = 0.; i__1 = iip1; @@ -685,14 +309,8 @@ f"> */ phi += z__[j] * temp; dphi += temp * temp; erretm += phi; -/* L160: */ } - w = rhoinv + phi + psi; - -/* W is the value of the secular function with */ -/* its ii-th element removed. */ - swtch3 = FALSE_; if (orgati) { if (w < 0.) { @@ -706,38 +324,27 @@ f"> */ if (ii == 1 || ii == *n) { swtch3 = FALSE_; } - temp = z__[ii] / (work[ii] * delta[ii]); dw = dpsi + dphi + temp * temp; temp = z__[ii] * temp; w += temp; erretm = (phi - psi) * 8. + erretm + rhoinv * 2. + abs(temp) * 3.; -/* $ + ABS( TAU2 )*DW */ - -/* Test for convergence */ - if (abs(w) <= eps * erretm) { goto L240; } - if (w <= 0.) { - sglb = max(sglb,tau); + sglb = max(sglb, tau); } else { - sgub = min(sgub,tau); + sgub = min(sgub, tau); } - -/* Calculate the new step */ - ++niter; - if (! swtch3) { + if (!swtch3) { dtipsq = work[ip1] * delta[ip1]; dtisq = work[*i__] * delta[*i__]; if (orgati) { -/* Computing 2nd power */ d__1 = z__[*i__] / dtisq; c__ = w - dtipsq * dw + delsq * (d__1 * d__1); } else { -/* Computing 2nd power */ d__1 = z__[ip1] / dtipsq; c__ = w - dtisq * dw - delsq * (d__1 * d__1); } @@ -746,33 +353,26 @@ f"> */ if (c__ == 0.) { if (a == 0.) { if (orgati) { - a = z__[*i__] * z__[*i__] + dtipsq * dtipsq * (dpsi + - dphi); + a = z__[*i__] * z__[*i__] + dtipsq * dtipsq * (dpsi + dphi); } else { - a = z__[ip1] * z__[ip1] + dtisq * dtisq * (dpsi + - dphi); + a = z__[ip1] * z__[ip1] + dtisq * dtisq * (dpsi + dphi); } } eta = b / a; } else if (a <= 0.) { - eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / ( - c__ * 2.); + eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (c__ * 2.); } else { - eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs( - d__1)))); + eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))); } } else { - -/* Interpolation using THREE most relevant poles */ - dtiim = work[iim1] * delta[iim1]; dtiip = work[iip1] * delta[iip1]; temp = rhoinv + psi + phi; if (orgati) { temp1 = z__[iim1] / dtiim; temp1 *= temp1; - c__ = temp - dtiip * (dpsi + dphi) - (d__[iim1] - d__[iip1]) * - (d__[iim1] + d__[iip1]) * temp1; + c__ = temp - dtiip * (dpsi + dphi) - + (d__[iim1] - d__[iip1]) * (d__[iim1] + d__[iip1]) * temp1; zz[0] = z__[iim1] * z__[iim1]; if (dpsi < temp1) { zz[2] = dtiip * dtiip * dphi; @@ -782,8 +382,8 @@ f"> */ } else { temp1 = z__[iip1] / dtiip; temp1 *= temp1; - c__ = temp - dtiim * (dpsi + dphi) - (d__[iip1] - d__[iim1]) * - (d__[iim1] + d__[iip1]) * temp1; + c__ = temp - dtiim * (dpsi + dphi) - + (d__[iip1] - d__[iim1]) * (d__[iim1] + d__[iip1]) * temp1; if (dphi < temp1) { zz[0] = dtiim * dtiim * dpsi; } else { @@ -796,22 +396,15 @@ f"> */ dd[1] = delta[ii] * work[ii]; dd[2] = dtiip; dlaed6_(&niter, &orgati, &c__, dd, zz, &w, &eta, info); - if (*info != 0) { - -/* If INFO is not 0, i.e., DLAED6 failed, switch back */ -/* to 2 pole interpolation. */ - swtch3 = FALSE_; *info = 0; dtipsq = work[ip1] * delta[ip1]; dtisq = work[*i__] * delta[*i__]; if (orgati) { -/* Computing 2nd power */ d__1 = z__[*i__] / dtisq; c__ = w - dtipsq * dw + delsq * (d__1 * d__1); } else { -/* Computing 2nd power */ d__1 = z__[ip1] / dtipsq; c__ = w - dtisq * dw - delsq * (d__1 * d__1); } @@ -820,34 +413,22 @@ f"> */ if (c__ == 0.) { if (a == 0.) { if (orgati) { - a = z__[*i__] * z__[*i__] + dtipsq * dtipsq * ( - dpsi + dphi); + a = z__[*i__] * z__[*i__] + dtipsq * dtipsq * (dpsi + dphi); } else { - a = z__[ip1] * z__[ip1] + dtisq * dtisq * (dpsi + - dphi); + a = z__[ip1] * z__[ip1] + dtisq * dtisq * (dpsi + dphi); } } eta = b / a; } else if (a <= 0.) { - eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) - / (c__ * 2.); + eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (c__ * 2.); } else { - eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, - abs(d__1)))); + eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))); } } } - -/* Note, eta should be positive if w is negative, and */ -/* eta should be negative otherwise. However, */ -/* if for some reason caused by roundoff, eta*w > 0, */ -/* we simply use one Newton step instead. This way */ -/* will guarantee eta*w < 0. */ - if (w * eta >= 0.) { eta = -w / dw; } - eta /= *sigma + sqrt(*sigma * *sigma + eta); temp = tau + eta; if (temp > sgub || temp < sglb) { @@ -868,21 +449,14 @@ f"> */ } } } - prew = w; - tau += eta; *sigma += eta; - i__1 = *n; for (j = 1; j <= i__1; ++j) { work[j] += eta; delta[j] -= eta; -/* L170: */ } - -/* Evaluate PSI and the derivative DPSI */ - dpsi = 0.; psi = 0.; erretm = 0.; @@ -892,12 +466,8 @@ f"> */ psi += z__[j] * temp; dpsi += temp * temp; erretm += psi; -/* L180: */ } erretm = abs(erretm); - -/* Evaluate PHI and the derivative DPHI */ - dphi = 0.; phi = 0.; i__1 = iip1; @@ -906,17 +476,13 @@ f"> */ phi += z__[j] * temp; dphi += temp * temp; erretm += phi; -/* L190: */ } - tau2 = work[ii] * delta[ii]; temp = z__[ii] / tau2; dw = dpsi + dphi + temp * temp; temp = z__[ii] * temp; w = rhoinv + phi + psi + temp; erretm = (phi - psi) * 8. + erretm + rhoinv * 2. + abs(temp) * 3.; -/* $ + ABS( TAU2 )*DW */ - swtch = FALSE_; if (orgati) { if (-w > abs(prew) / 10.) { @@ -927,38 +493,24 @@ f"> */ swtch = TRUE_; } } - -/* Main loop to update the values of the array DELTA and WORK */ - iter = niter + 1; - for (niter = iter; niter <= 400; ++niter) { - -/* Test for convergence */ - if (abs(w) <= eps * erretm) { -/* $ .OR. (SGUB-SGLB).LE.EIGHT*ABS(SGUB+SGLB) ) THEN */ goto L240; } - if (w <= 0.) { - sglb = max(sglb,tau); + sglb = max(sglb, tau); } else { - sgub = min(sgub,tau); + sgub = min(sgub, tau); } - -/* Calculate the new step */ - - if (! swtch3) { + if (!swtch3) { dtipsq = work[ip1] * delta[ip1]; dtisq = work[*i__] * delta[*i__]; - if (! swtch) { + if (!swtch) { if (orgati) { -/* Computing 2nd power */ d__1 = z__[*i__] / dtisq; c__ = w - dtipsq * dw + delsq * (d__1 * d__1); } else { -/* Computing 2nd power */ d__1 = z__[ip1] / dtipsq; c__ = w - dtisq * dw - delsq * (d__1 * d__1); } @@ -975,13 +527,11 @@ f"> */ b = dtipsq * dtisq * w; if (c__ == 0.) { if (a == 0.) { - if (! swtch) { + if (!swtch) { if (orgati) { - a = z__[*i__] * z__[*i__] + dtipsq * dtipsq * - (dpsi + dphi); + a = z__[*i__] * z__[*i__] + dtipsq * dtipsq * (dpsi + dphi); } else { - a = z__[ip1] * z__[ip1] + dtisq * dtisq * ( - dpsi + dphi); + a = z__[ip1] * z__[ip1] + dtisq * dtisq * (dpsi + dphi); } } else { a = dtisq * dtisq * dpsi + dtipsq * dtipsq * dphi; @@ -989,16 +539,11 @@ f"> */ } eta = b / a; } else if (a <= 0.) { - eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) - / (c__ * 2.); + eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (c__ * 2.); } else { - eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, - abs(d__1)))); + eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))); } } else { - -/* Interpolation using THREE most relevant poles */ - dtiim = work[iim1] * delta[iim1]; dtiip = work[iip1] * delta[iip1]; temp = rhoinv + psi + phi; @@ -1010,8 +555,7 @@ f"> */ if (orgati) { temp1 = z__[iim1] / dtiim; temp1 *= temp1; - temp2 = (d__[iim1] - d__[iip1]) * (d__[iim1] + d__[ - iip1]) * temp1; + temp2 = (d__[iim1] - d__[iip1]) * (d__[iim1] + d__[iip1]) * temp1; c__ = temp - dtiip * (dpsi + dphi) - temp2; zz[0] = z__[iim1] * z__[iim1]; if (dpsi < temp1) { @@ -1022,8 +566,7 @@ f"> */ } else { temp1 = z__[iip1] / dtiip; temp1 *= temp1; - temp2 = (d__[iip1] - d__[iim1]) * (d__[iim1] + d__[ - iip1]) * temp1; + temp2 = (d__[iip1] - d__[iim1]) * (d__[iim1] + d__[iip1]) * temp1; c__ = temp - dtiim * (dpsi + dphi) - temp2; if (dphi < temp1) { zz[0] = dtiim * dtiim * dpsi; @@ -1037,23 +580,16 @@ f"> */ dd[1] = delta[ii] * work[ii]; dd[2] = dtiip; dlaed6_(&niter, &orgati, &c__, dd, zz, &w, &eta, info); - if (*info != 0) { - -/* If INFO is not 0, i.e., DLAED6 failed, switch */ -/* back to two pole interpolation */ - swtch3 = FALSE_; *info = 0; dtipsq = work[ip1] * delta[ip1]; dtisq = work[*i__] * delta[*i__]; - if (! swtch) { + if (!swtch) { if (orgati) { -/* Computing 2nd power */ d__1 = z__[*i__] / dtisq; c__ = w - dtipsq * dw + delsq * (d__1 * d__1); } else { -/* Computing 2nd power */ d__1 = z__[ip1] / dtipsq; c__ = w - dtisq * dw - delsq * (d__1 * d__1); } @@ -1070,40 +606,27 @@ f"> */ b = dtipsq * dtisq * w; if (c__ == 0.) { if (a == 0.) { - if (! swtch) { + if (!swtch) { if (orgati) { - a = z__[*i__] * z__[*i__] + dtipsq * - dtipsq * (dpsi + dphi); + a = z__[*i__] * z__[*i__] + dtipsq * dtipsq * (dpsi + dphi); } else { - a = z__[ip1] * z__[ip1] + dtisq * dtisq * - (dpsi + dphi); + a = z__[ip1] * z__[ip1] + dtisq * dtisq * (dpsi + dphi); } } else { - a = dtisq * dtisq * dpsi + dtipsq * dtipsq * - dphi; + a = dtisq * dtisq * dpsi + dtipsq * dtipsq * dphi; } } eta = b / a; } else if (a <= 0.) { - eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs( - d__1)))) / (c__ * 2.); + eta = (a - sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))) / (c__ * 2.); } else { - eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, - abs(d__1)))); + eta = b * 2. / (a + sqrt((d__1 = a * a - b * 4. * c__, abs(d__1)))); } } } - -/* Note, eta should be positive if w is negative, and */ -/* eta should be negative otherwise. However, */ -/* if for some reason caused by roundoff, eta*w > 0, */ -/* we simply use one Newton step instead. This way */ -/* will guarantee eta*w < 0. */ - if (w * eta >= 0.) { eta = -w / dw; } - eta /= *sigma + sqrt(*sigma * *sigma + eta); temp = tau + eta; if (temp > sgub || temp < sglb) { @@ -1124,21 +647,14 @@ f"> */ } } } - prew = w; - tau += eta; *sigma += eta; - i__1 = *n; for (j = 1; j <= i__1; ++j) { work[j] += eta; delta[j] -= eta; -/* L200: */ } - -/* Evaluate PSI and the derivative DPSI */ - dpsi = 0.; psi = 0.; erretm = 0.; @@ -1148,12 +664,8 @@ f"> */ psi += z__[j] * temp; dpsi += temp * temp; erretm += psi; -/* L210: */ } erretm = abs(erretm); - -/* Evaluate PHI and the derivative DPHI */ - dphi = 0.; phi = 0.; i__1 = iip1; @@ -1162,37 +674,22 @@ f"> */ phi += z__[j] * temp; dphi += temp * temp; erretm += phi; -/* L220: */ } - tau2 = work[ii] * delta[ii]; temp = z__[ii] / tau2; dw = dpsi + dphi + temp * temp; temp = z__[ii] * temp; w = rhoinv + phi + psi + temp; erretm = (phi - psi) * 8. + erretm + rhoinv * 2. + abs(temp) * 3.; -/* $ + ABS( TAU2 )*DW */ - if (w * prew > 0. && abs(w) > abs(prew) / 10.) { - swtch = ! swtch; + swtch = !swtch; } - -/* L230: */ } - -/* Return with INFO = 1, NITER = MAXIT and not converged */ - *info = 1; - } - L240: return 0; - -/* End of DLASD4 */ - -} /* dlasd4_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlasd5.cpp b/lib/linalg/dlasd5.cpp index a56f570c0b..7bade73f84 100644 --- a/lib/linalg/dlasd5.cpp +++ b/lib/linalg/dlasd5.cpp @@ -1,264 +1,67 @@ -/* fortran/dlasd5.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DLASD5 computes the square root of the i-th eigenvalue of a positive symmetric rank-one modific -ation of a 2-by-2 diagonal matrix. Used by sbdsdc. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLASD5 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLASD5( I, D, Z, DELTA, RHO, DSIGMA, WORK ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER I */ -/* DOUBLE PRECISION DSIGMA, RHO */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION D( 2 ), DELTA( 2 ), WORK( 2 ), Z( 2 ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > This subroutine computes the square root of the I-th eigenvalue */ -/* > of a positive symmetric rank-one modification of a 2-by-2 diagonal */ -/* > matrix */ -/* > */ -/* > diag( D ) * diag( D ) + RHO * Z * transpose(Z) . */ -/* > */ -/* > The diagonal entries in the array D are assumed to satisfy */ -/* > */ -/* > 0 <= D(i) < D(j) for i < j . */ -/* > */ -/* > We also assume RHO > 0 and that the Euclidean norm of the vector */ -/* > Z is one. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] I */ -/* > \verbatim */ -/* > I is INTEGER */ -/* > The index of the eigenvalue to be computed. I = 1 or I = 2. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension ( 2 ) */ -/* > The original eigenvalues. We assume 0 <= D(1) < D(2). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] Z */ -/* > \verbatim */ -/* > Z is DOUBLE PRECISION array, dimension ( 2 ) */ -/* > The components of the updating vector. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] DELTA */ -/* > \verbatim */ -/* > DELTA is DOUBLE PRECISION array, dimension ( 2 ) */ -/* > Contains (D(j) - sigma_I) in its j-th component. */ -/* > The vector DELTA contains the information necessary */ -/* > to construct the eigenvectors. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] RHO */ -/* > \verbatim */ -/* > RHO is DOUBLE PRECISION */ -/* > The scalar in the symmetric updating formula. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] DSIGMA */ -/* > \verbatim */ -/* > DSIGMA is DOUBLE PRECISION */ -/* > The computed sigma_I, the I-th updated eigenvalue. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension ( 2 ) */ -/* > WORK contains (D(j) + sigma_I) in its j-th component. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup OTHERauxiliary */ - -/* > \par Contributors: */ -/* ================== */ -/* > */ -/* > Ren-Cang Li, Computer Science Division, University of California */ -/* > at Berkeley, USA */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dlasd5_(integer *i__, doublereal *d__, doublereal *z__, - doublereal *delta, doublereal *rho, doublereal *dsigma, doublereal * - work) +int dlasd5_(integer *i__, doublereal *d__, doublereal *z__, doublereal *delta, doublereal *rho, + doublereal *dsigma, doublereal *work) { - /* System generated locals */ doublereal d__1; - - /* Builtin functions */ double sqrt(doublereal); - - /* Local variables */ doublereal b, c__, w, del, tau, delsq; - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - - /* Parameter adjustments */ --work; --delta; --z__; --d__; - - /* Function Body */ del = d__[2] - d__[1]; delsq = del * (d__[2] + d__[1]); if (*i__ == 1) { - w = *rho * 4. * (z__[2] * z__[2] / (d__[1] + d__[2] * 3.) - z__[1] * - z__[1] / (d__[1] * 3. + d__[2])) / del + 1.; + w = *rho * 4. * + (z__[2] * z__[2] / (d__[1] + d__[2] * 3.) - + z__[1] * z__[1] / (d__[1] * 3. + d__[2])) / + del + + 1.; if (w > 0.) { b = delsq + *rho * (z__[1] * z__[1] + z__[2] * z__[2]); c__ = *rho * z__[1] * z__[1] * delsq; - -/* B > ZERO, always */ - -/* The following TAU is DSIGMA * DSIGMA - D( 1 ) * D( 1 ) */ - tau = c__ * 2. / (b + sqrt((d__1 = b * b - c__ * 4., abs(d__1)))); - -/* The following TAU is DSIGMA - D( 1 ) */ - tau /= d__[1] + sqrt(d__[1] * d__[1] + tau); *dsigma = d__[1] + tau; delta[1] = -tau; delta[2] = del - tau; work[1] = d__[1] * 2. + tau; work[2] = d__[1] + tau + d__[2]; -/* DELTA( 1 ) = -Z( 1 ) / TAU */ -/* DELTA( 2 ) = Z( 2 ) / ( DEL-TAU ) */ } else { b = -delsq + *rho * (z__[1] * z__[1] + z__[2] * z__[2]); c__ = *rho * z__[2] * z__[2] * delsq; - -/* The following TAU is DSIGMA * DSIGMA - D( 2 ) * D( 2 ) */ - if (b > 0.) { tau = c__ * -2. / (b + sqrt(b * b + c__ * 4.)); } else { tau = (b - sqrt(b * b + c__ * 4.)) / 2.; } - -/* The following TAU is DSIGMA - D( 2 ) */ - tau /= d__[2] + sqrt((d__1 = d__[2] * d__[2] + tau, abs(d__1))); *dsigma = d__[2] + tau; delta[1] = -(del + tau); delta[2] = -tau; work[1] = d__[1] + tau + d__[2]; work[2] = d__[2] * 2. + tau; -/* DELTA( 1 ) = -Z( 1 ) / ( DEL+TAU ) */ -/* DELTA( 2 ) = -Z( 2 ) / TAU */ } -/* TEMP = SQRT( DELTA( 1 )*DELTA( 1 )+DELTA( 2 )*DELTA( 2 ) ) */ -/* DELTA( 1 ) = DELTA( 1 ) / TEMP */ -/* DELTA( 2 ) = DELTA( 2 ) / TEMP */ } else { - -/* Now I=2 */ - b = -delsq + *rho * (z__[1] * z__[1] + z__[2] * z__[2]); c__ = *rho * z__[2] * z__[2] * delsq; - -/* The following TAU is DSIGMA * DSIGMA - D( 2 ) * D( 2 ) */ - if (b > 0.) { tau = (b + sqrt(b * b + c__ * 4.)) / 2.; } else { tau = c__ * 2. / (-b + sqrt(b * b + c__ * 4.)); } - -/* The following TAU is DSIGMA - D( 2 ) */ - tau /= d__[2] + sqrt(d__[2] * d__[2] + tau); *dsigma = d__[2] + tau; delta[1] = -(del + tau); delta[2] = -tau; work[1] = d__[1] + tau + d__[2]; work[2] = d__[2] * 2. + tau; -/* DELTA( 1 ) = -Z( 1 ) / ( DEL+TAU ) */ -/* DELTA( 2 ) = -Z( 2 ) / TAU */ -/* TEMP = SQRT( DELTA( 1 )*DELTA( 1 )+DELTA( 2 )*DELTA( 2 ) ) */ -/* DELTA( 1 ) = DELTA( 1 ) / TEMP */ -/* DELTA( 2 ) = DELTA( 2 ) / TEMP */ } return 0; - -/* End of DLASD5 */ - -} /* dlasd5_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlasd6.cpp b/lib/linalg/dlasd6.cpp index 48c7d8dd4f..a631245cf5 100644 --- a/lib/linalg/dlasd6.cpp +++ b/lib/linalg/dlasd6.cpp @@ -1,396 +1,35 @@ -/* fortran/dlasd6.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__0 = 0; static doublereal c_b7 = 1.; static integer c__1 = 1; static integer c_n1 = -1; - -/* > \brief \b DLASD6 computes the SVD of an updated upper bidiagonal matrix obtained by merging two smaller o -nes by appending a row. Used by sbdsdc. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLASD6 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLASD6( ICOMPQ, NL, NR, SQRE, D, VF, VL, ALPHA, BETA, */ -/* IDXQ, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, */ -/* LDGNUM, POLES, DIFL, DIFR, Z, K, C, S, WORK, */ -/* IWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER GIVPTR, ICOMPQ, INFO, K, LDGCOL, LDGNUM, NL, */ -/* $ NR, SQRE */ -/* DOUBLE PRECISION ALPHA, BETA, C, S */ -/* .. */ -/* .. Array Arguments .. */ -/* INTEGER GIVCOL( LDGCOL, * ), IDXQ( * ), IWORK( * ), */ -/* $ PERM( * ) */ -/* DOUBLE PRECISION D( * ), DIFL( * ), DIFR( * ), */ -/* $ GIVNUM( LDGNUM, * ), POLES( LDGNUM, * ), */ -/* $ VF( * ), VL( * ), WORK( * ), Z( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLASD6 computes the SVD of an updated upper bidiagonal matrix B */ -/* > obtained by merging two smaller ones by appending a row. This */ -/* > routine is used only for the problem which requires all singular */ -/* > values and optionally singular vector matrices in factored form. */ -/* > B is an N-by-M matrix with N = NL + NR + 1 and M = N + SQRE. */ -/* > A related subroutine, DLASD1, handles the case in which all singular */ -/* > values and singular vectors of the bidiagonal matrix are desired. */ -/* > */ -/* > DLASD6 computes the SVD as follows: */ -/* > */ -/* > ( D1(in) 0 0 0 ) */ -/* > B = U(in) * ( Z1**T a Z2**T b ) * VT(in) */ -/* > ( 0 0 D2(in) 0 ) */ -/* > */ -/* > = U(out) * ( D(out) 0) * VT(out) */ -/* > */ -/* > where Z**T = (Z1**T a Z2**T b) = u**T VT**T, and u is a vector of dimension M */ -/* > with ALPHA and BETA in the NL+1 and NL+2 th entries and zeros */ -/* > elsewhere; and the entry b is empty if SQRE = 0. */ -/* > */ -/* > The singular values of B can be computed using D1, D2, the first */ -/* > components of all the right singular vectors of the lower block, and */ -/* > the last components of all the right singular vectors of the upper */ -/* > block. These components are stored and updated in VF and VL, */ -/* > respectively, in DLASD6. Hence U and VT are not explicitly */ -/* > referenced. */ -/* > */ -/* > The singular values are stored in D. The algorithm consists of two */ -/* > stages: */ -/* > */ -/* > The first stage consists of deflating the size of the problem */ -/* > when there are multiple singular values or if there is a zero */ -/* > in the Z vector. For each such occurrence the dimension of the */ -/* > secular equation problem is reduced by one. This stage is */ -/* > performed by the routine DLASD7. */ -/* > */ -/* > The second stage consists of calculating the updated */ -/* > singular values. This is done by finding the roots of the */ -/* > secular equation via the routine DLASD4 (as called by DLASD8). */ -/* > This routine also updates VF and VL and computes the distances */ -/* > between the updated singular values and the old singular */ -/* > values. */ -/* > */ -/* > DLASD6 is called from DLASDA. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] ICOMPQ */ -/* > \verbatim */ -/* > ICOMPQ is INTEGER */ -/* > Specifies whether singular vectors are to be computed in */ -/* > factored form: */ -/* > = 0: Compute singular values only. */ -/* > = 1: Compute singular vectors in factored form as well. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] NL */ -/* > \verbatim */ -/* > NL is INTEGER */ -/* > The row dimension of the upper block. NL >= 1. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] NR */ -/* > \verbatim */ -/* > NR is INTEGER */ -/* > The row dimension of the lower block. NR >= 1. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] SQRE */ -/* > \verbatim */ -/* > SQRE is INTEGER */ -/* > = 0: the lower block is an NR-by-NR square matrix. */ -/* > = 1: the lower block is an NR-by-(NR+1) rectangular matrix. */ -/* > */ -/* > The bidiagonal matrix has row dimension N = NL + NR + 1, */ -/* > and column dimension M = N + SQRE. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension ( NL+NR+1 ). */ -/* > On entry D(1:NL,1:NL) contains the singular values of the */ -/* > upper block, and D(NL+2:N) contains the singular values */ -/* > of the lower block. On exit D(1:N) contains the singular */ -/* > values of the modified matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] VF */ -/* > \verbatim */ -/* > VF is DOUBLE PRECISION array, dimension ( M ) */ -/* > On entry, VF(1:NL+1) contains the first components of all */ -/* > right singular vectors of the upper block; and VF(NL+2:M) */ -/* > contains the first components of all right singular vectors */ -/* > of the lower block. On exit, VF contains the first components */ -/* > of all right singular vectors of the bidiagonal matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] VL */ -/* > \verbatim */ -/* > VL is DOUBLE PRECISION array, dimension ( M ) */ -/* > On entry, VL(1:NL+1) contains the last components of all */ -/* > right singular vectors of the upper block; and VL(NL+2:M) */ -/* > contains the last components of all right singular vectors of */ -/* > the lower block. On exit, VL contains the last components of */ -/* > all right singular vectors of the bidiagonal matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] ALPHA */ -/* > \verbatim */ -/* > ALPHA is DOUBLE PRECISION */ -/* > Contains the diagonal element associated with the added row. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] BETA */ -/* > \verbatim */ -/* > BETA is DOUBLE PRECISION */ -/* > Contains the off-diagonal element associated with the added */ -/* > row. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] IDXQ */ -/* > \verbatim */ -/* > IDXQ is INTEGER array, dimension ( N ) */ -/* > This contains the permutation which will reintegrate the */ -/* > subproblem just solved back into sorted order, i.e. */ -/* > D( IDXQ( I = 1, N ) ) will be in ascending order. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] PERM */ -/* > \verbatim */ -/* > PERM is INTEGER array, dimension ( N ) */ -/* > The permutations (from deflation and sorting) to be applied */ -/* > to each block. Not referenced if ICOMPQ = 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] GIVPTR */ -/* > \verbatim */ -/* > GIVPTR is INTEGER */ -/* > The number of Givens rotations which took place in this */ -/* > subproblem. Not referenced if ICOMPQ = 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] GIVCOL */ -/* > \verbatim */ -/* > GIVCOL is INTEGER array, dimension ( LDGCOL, 2 ) */ -/* > Each pair of numbers indicates a pair of columns to take place */ -/* > in a Givens rotation. Not referenced if ICOMPQ = 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDGCOL */ -/* > \verbatim */ -/* > LDGCOL is INTEGER */ -/* > leading dimension of GIVCOL, must be at least N. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] GIVNUM */ -/* > \verbatim */ -/* > GIVNUM is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) */ -/* > Each number indicates the C or S value to be used in the */ -/* > corresponding Givens rotation. Not referenced if ICOMPQ = 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDGNUM */ -/* > \verbatim */ -/* > LDGNUM is INTEGER */ -/* > The leading dimension of GIVNUM and POLES, must be at least N. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] POLES */ -/* > \verbatim */ -/* > POLES is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) */ -/* > On exit, POLES(1,*) is an array containing the new singular */ -/* > values obtained from solving the secular equation, and */ -/* > POLES(2,*) is an array containing the poles in the secular */ -/* > equation. Not referenced if ICOMPQ = 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] DIFL */ -/* > \verbatim */ -/* > DIFL is DOUBLE PRECISION array, dimension ( N ) */ -/* > On exit, DIFL(I) is the distance between I-th updated */ -/* > (undeflated) singular value and the I-th (undeflated) old */ -/* > singular value. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] DIFR */ -/* > \verbatim */ -/* > DIFR is DOUBLE PRECISION array, */ -/* > dimension ( LDDIFR, 2 ) if ICOMPQ = 1 and */ -/* > dimension ( K ) if ICOMPQ = 0. */ -/* > On exit, DIFR(I,1) = D(I) - DSIGMA(I+1), DIFR(K,1) is not */ -/* > defined and will not be referenced. */ -/* > */ -/* > If ICOMPQ = 1, DIFR(1:K,2) is an array containing the */ -/* > normalizing factors for the right singular vector matrix. */ -/* > */ -/* > See DLASD8 for details on DIFL and DIFR. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] Z */ -/* > \verbatim */ -/* > Z is DOUBLE PRECISION array, dimension ( M ) */ -/* > The first elements of this array contain the components */ -/* > of the deflation-adjusted updating row vector. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > Contains the dimension of the non-deflated matrix, */ -/* > This is the order of the related secular equation. 1 <= K <=N. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] C */ -/* > \verbatim */ -/* > C is DOUBLE PRECISION */ -/* > C contains garbage if SQRE =0 and the C-value of a Givens */ -/* > rotation related to the right null space if SQRE = 1. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] S */ -/* > \verbatim */ -/* > S is DOUBLE PRECISION */ -/* > S contains garbage if SQRE =0 and the S-value of a Givens */ -/* > rotation related to the right null space if SQRE = 1. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension ( 4 * M ) */ -/* > \endverbatim */ -/* > */ -/* > \param[out] IWORK */ -/* > \verbatim */ -/* > IWORK is INTEGER array, dimension ( 3 * N ) */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit. */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ -/* > > 0: if INFO = 1, a singular value did not converge */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup OTHERauxiliary */ - -/* > \par Contributors: */ -/* ================== */ -/* > */ -/* > Ming Gu and Huan Ren, Computer Science Division, University of */ -/* > California at Berkeley, USA */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dlasd6_(integer *icompq, integer *nl, integer *nr, - integer *sqre, doublereal *d__, doublereal *vf, doublereal *vl, - doublereal *alpha, doublereal *beta, integer *idxq, integer *perm, - integer *givptr, integer *givcol, integer *ldgcol, doublereal *givnum, - integer *ldgnum, doublereal *poles, doublereal *difl, doublereal * - difr, doublereal *z__, integer *k, doublereal *c__, doublereal *s, - doublereal *work, integer *iwork, integer *info) +int dlasd6_(integer *icompq, integer *nl, integer *nr, integer *sqre, doublereal *d__, + doublereal *vf, doublereal *vl, doublereal *alpha, doublereal *beta, integer *idxq, + integer *perm, integer *givptr, integer *givcol, integer *ldgcol, doublereal *givnum, + integer *ldgnum, doublereal *poles, doublereal *difl, doublereal *difr, doublereal *z__, + integer *k, doublereal *c__, doublereal *s, doublereal *work, integer *iwork, + integer *info) { - /* System generated locals */ - integer givcol_dim1, givcol_offset, givnum_dim1, givnum_offset, - poles_dim1, poles_offset, i__1; + integer givcol_dim1, givcol_offset, givnum_dim1, givnum_offset, poles_dim1, poles_offset, i__1; doublereal d__1, d__2; - - /* Local variables */ integer i__, m, n, n1, n2, iw, idx, idxc, idxp, ivfw, ivlw; - extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, - doublereal *, integer *), dlasd7_(integer *, integer *, integer *, - integer *, integer *, doublereal *, doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *, integer *, integer *, - integer *, integer *, integer *, integer *, integer *, doublereal - *, integer *, doublereal *, doublereal *, integer *), dlasd8_( - integer *, integer *, doublereal *, doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *, integer *, doublereal *, - doublereal *, integer *), dlascl_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, integer *, doublereal *, - integer *, integer *, ftnlen), dlamrg_(integer *, integer *, - doublereal *, integer *, integer *, integer *); + extern int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *), + dlasd7_(integer *, integer *, integer *, integer *, integer *, doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, doublereal *, integer *, integer *, integer *, integer *, integer *, + integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *), + dlasd8_(integer *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, doublereal *, integer *, doublereal *, doublereal *, integer *), + dlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, integer *, + doublereal *, integer *, integer *, ftnlen), + dlamrg_(integer *, integer *, doublereal *, integer *, integer *, integer *); integer isigma; - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern int xerbla_(char *, integer *, ftnlen); doublereal orgnrm; - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ --d__; --vf; --vl; @@ -410,12 +49,9 @@ f"> */ --z__; --work; --iwork; - - /* Function Body */ *info = 0; n = *nl + *nr + 1; m = n + *sqre; - if (*icompq < 0 || *icompq > 1) { *info = -1; } else if (*nl < 1) { @@ -434,81 +70,43 @@ f"> */ xerbla_((char *)"DLASD6", &i__1, (ftnlen)6); return 0; } - -/* The following values are for bookkeeping purposes only. They are */ -/* integer pointers which indicate the portion of the workspace */ -/* used by a particular array in DLASD7 and DLASD8. */ - isigma = 1; iw = isigma + n; ivfw = iw + m; ivlw = ivfw + m; - idx = 1; idxc = idx + n; idxp = idxc + n; - -/* Scale. */ - -/* Computing MAX */ d__1 = abs(*alpha), d__2 = abs(*beta); - orgnrm = max(d__1,d__2); + orgnrm = max(d__1, d__2); d__[*nl + 1] = 0.; i__1 = n; for (i__ = 1; i__ <= i__1; ++i__) { if ((d__1 = d__[i__], abs(d__1)) > orgnrm) { orgnrm = (d__1 = d__[i__], abs(d__1)); } -/* L10: */ } - dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b7, &n, &c__1, &d__[1], &n, info, ( - ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b7, &n, &c__1, &d__[1], &n, info, (ftnlen)1); *alpha /= orgnrm; *beta /= orgnrm; - -/* Sort and Deflate singular values. */ - - dlasd7_(icompq, nl, nr, sqre, k, &d__[1], &z__[1], &work[iw], &vf[1], & - work[ivfw], &vl[1], &work[ivlw], alpha, beta, &work[isigma], & - iwork[idx], &iwork[idxp], &idxq[1], &perm[1], givptr, &givcol[ - givcol_offset], ldgcol, &givnum[givnum_offset], ldgnum, c__, s, - info); - -/* Solve Secular Equation, compute DIFL, DIFR, and update VF, VL. */ - - dlasd8_(icompq, k, &d__[1], &z__[1], &vf[1], &vl[1], &difl[1], &difr[1], - ldgnum, &work[isigma], &work[iw], info); - -/* Report the possible convergence failure. */ - + dlasd7_(icompq, nl, nr, sqre, k, &d__[1], &z__[1], &work[iw], &vf[1], &work[ivfw], &vl[1], + &work[ivlw], alpha, beta, &work[isigma], &iwork[idx], &iwork[idxp], &idxq[1], &perm[1], + givptr, &givcol[givcol_offset], ldgcol, &givnum[givnum_offset], ldgnum, c__, s, info); + dlasd8_(icompq, k, &d__[1], &z__[1], &vf[1], &vl[1], &difl[1], &difr[1], ldgnum, &work[isigma], + &work[iw], info); if (*info != 0) { return 0; } - -/* Save the poles if ICOMPQ = 1. */ - if (*icompq == 1) { dcopy_(k, &d__[1], &c__1, &poles[poles_dim1 + 1], &c__1); dcopy_(k, &work[isigma], &c__1, &poles[(poles_dim1 << 1) + 1], &c__1); } - -/* Unscale. */ - - dlascl_((char *)"G", &c__0, &c__0, &c_b7, &orgnrm, &n, &c__1, &d__[1], &n, info, ( - ftnlen)1); - -/* Prepare the IDXQ sorting permutation. */ - + dlascl_((char *)"G", &c__0, &c__0, &c_b7, &orgnrm, &n, &c__1, &d__[1], &n, info, (ftnlen)1); n1 = *k; n2 = n - *k; dlamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &idxq[1]); - return 0; - -/* End of DLASD6 */ - -} /* dlasd6_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlasd7.cpp b/lib/linalg/dlasd7.cpp index 89a18cc81f..989771ca01 100644 --- a/lib/linalg/dlasd7.cpp +++ b/lib/linalg/dlasd7.cpp @@ -1,362 +1,31 @@ -/* fortran/dlasd7.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; - -/* > \brief \b DLASD7 merges the two sets of singular values together into a single sorted set. Then it tries -to deflate the size of the problem. Used by sbdsdc. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLASD7 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLASD7( ICOMPQ, NL, NR, SQRE, K, D, Z, ZW, VF, VFW, VL, */ -/* VLW, ALPHA, BETA, DSIGMA, IDX, IDXP, IDXQ, */ -/* PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, */ -/* C, S, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER GIVPTR, ICOMPQ, INFO, K, LDGCOL, LDGNUM, NL, */ -/* $ NR, SQRE */ -/* DOUBLE PRECISION ALPHA, BETA, C, S */ -/* .. */ -/* .. Array Arguments .. */ -/* INTEGER GIVCOL( LDGCOL, * ), IDX( * ), IDXP( * ), */ -/* $ IDXQ( * ), PERM( * ) */ -/* DOUBLE PRECISION D( * ), DSIGMA( * ), GIVNUM( LDGNUM, * ), */ -/* $ VF( * ), VFW( * ), VL( * ), VLW( * ), Z( * ), */ -/* $ ZW( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLASD7 merges the two sets of singular values together into a single */ -/* > sorted set. Then it tries to deflate the size of the problem. There */ -/* > are two ways in which deflation can occur: when two or more singular */ -/* > values are close together or if there is a tiny entry in the Z */ -/* > vector. For each such occurrence the order of the related */ -/* > secular equation problem is reduced by one. */ -/* > */ -/* > DLASD7 is called from DLASD6. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] ICOMPQ */ -/* > \verbatim */ -/* > ICOMPQ is INTEGER */ -/* > Specifies whether singular vectors are to be computed */ -/* > in compact form, as follows: */ -/* > = 0: Compute singular values only. */ -/* > = 1: Compute singular vectors of upper */ -/* > bidiagonal matrix in compact form. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] NL */ -/* > \verbatim */ -/* > NL is INTEGER */ -/* > The row dimension of the upper block. NL >= 1. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] NR */ -/* > \verbatim */ -/* > NR is INTEGER */ -/* > The row dimension of the lower block. NR >= 1. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] SQRE */ -/* > \verbatim */ -/* > SQRE is INTEGER */ -/* > = 0: the lower block is an NR-by-NR square matrix. */ -/* > = 1: the lower block is an NR-by-(NR+1) rectangular matrix. */ -/* > */ -/* > The bidiagonal matrix has */ -/* > N = NL + NR + 1 rows and */ -/* > M = N + SQRE >= N columns. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > Contains the dimension of the non-deflated matrix, this is */ -/* > the order of the related secular equation. 1 <= K <=N. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension ( N ) */ -/* > On entry D contains the singular values of the two submatrices */ -/* > to be combined. On exit D contains the trailing (N-K) updated */ -/* > singular values (those which were deflated) sorted into */ -/* > increasing order. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] Z */ -/* > \verbatim */ -/* > Z is DOUBLE PRECISION array, dimension ( M ) */ -/* > On exit Z contains the updating row vector in the secular */ -/* > equation. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] ZW */ -/* > \verbatim */ -/* > ZW is DOUBLE PRECISION array, dimension ( M ) */ -/* > Workspace for Z. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] VF */ -/* > \verbatim */ -/* > VF is DOUBLE PRECISION array, dimension ( M ) */ -/* > On entry, VF(1:NL+1) contains the first components of all */ -/* > right singular vectors of the upper block; and VF(NL+2:M) */ -/* > contains the first components of all right singular vectors */ -/* > of the lower block. On exit, VF contains the first components */ -/* > of all right singular vectors of the bidiagonal matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] VFW */ -/* > \verbatim */ -/* > VFW is DOUBLE PRECISION array, dimension ( M ) */ -/* > Workspace for VF. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] VL */ -/* > \verbatim */ -/* > VL is DOUBLE PRECISION array, dimension ( M ) */ -/* > On entry, VL(1:NL+1) contains the last components of all */ -/* > right singular vectors of the upper block; and VL(NL+2:M) */ -/* > contains the last components of all right singular vectors */ -/* > of the lower block. On exit, VL contains the last components */ -/* > of all right singular vectors of the bidiagonal matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] VLW */ -/* > \verbatim */ -/* > VLW is DOUBLE PRECISION array, dimension ( M ) */ -/* > Workspace for VL. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] ALPHA */ -/* > \verbatim */ -/* > ALPHA is DOUBLE PRECISION */ -/* > Contains the diagonal element associated with the added row. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] BETA */ -/* > \verbatim */ -/* > BETA is DOUBLE PRECISION */ -/* > Contains the off-diagonal element associated with the added */ -/* > row. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] DSIGMA */ -/* > \verbatim */ -/* > DSIGMA is DOUBLE PRECISION array, dimension ( N ) */ -/* > Contains a copy of the diagonal elements (K-1 singular values */ -/* > and one zero) in the secular equation. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] IDX */ -/* > \verbatim */ -/* > IDX is INTEGER array, dimension ( N ) */ -/* > This will contain the permutation used to sort the contents of */ -/* > D into ascending order. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] IDXP */ -/* > \verbatim */ -/* > IDXP is INTEGER array, dimension ( N ) */ -/* > This will contain the permutation used to place deflated */ -/* > values of D at the end of the array. On output IDXP(2:K) */ -/* > points to the nondeflated D-values and IDXP(K+1:N) */ -/* > points to the deflated singular values. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] IDXQ */ -/* > \verbatim */ -/* > IDXQ is INTEGER array, dimension ( N ) */ -/* > This contains the permutation which separately sorts the two */ -/* > sub-problems in D into ascending order. Note that entries in */ -/* > the first half of this permutation must first be moved one */ -/* > position backward; and entries in the second half */ -/* > must first have NL+1 added to their values. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] PERM */ -/* > \verbatim */ -/* > PERM is INTEGER array, dimension ( N ) */ -/* > The permutations (from deflation and sorting) to be applied */ -/* > to each singular block. Not referenced if ICOMPQ = 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] GIVPTR */ -/* > \verbatim */ -/* > GIVPTR is INTEGER */ -/* > The number of Givens rotations which took place in this */ -/* > subproblem. Not referenced if ICOMPQ = 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] GIVCOL */ -/* > \verbatim */ -/* > GIVCOL is INTEGER array, dimension ( LDGCOL, 2 ) */ -/* > Each pair of numbers indicates a pair of columns to take place */ -/* > in a Givens rotation. Not referenced if ICOMPQ = 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDGCOL */ -/* > \verbatim */ -/* > LDGCOL is INTEGER */ -/* > The leading dimension of GIVCOL, must be at least N. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] GIVNUM */ -/* > \verbatim */ -/* > GIVNUM is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) */ -/* > Each number indicates the C or S value to be used in the */ -/* > corresponding Givens rotation. Not referenced if ICOMPQ = 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDGNUM */ -/* > \verbatim */ -/* > LDGNUM is INTEGER */ -/* > The leading dimension of GIVNUM, must be at least N. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] C */ -/* > \verbatim */ -/* > C is DOUBLE PRECISION */ -/* > C contains garbage if SQRE =0 and the C-value of a Givens */ -/* > rotation related to the right null space if SQRE = 1. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] S */ -/* > \verbatim */ -/* > S is DOUBLE PRECISION */ -/* > S contains garbage if SQRE =0 and the S-value of a Givens */ -/* > rotation related to the right null space if SQRE = 1. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit. */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup OTHERauxiliary */ - -/* > \par Contributors: */ -/* ================== */ -/* > */ -/* > Ming Gu and Huan Ren, Computer Science Division, University of */ -/* > California at Berkeley, USA */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dlasd7_(integer *icompq, integer *nl, integer *nr, - integer *sqre, integer *k, doublereal *d__, doublereal *z__, - doublereal *zw, doublereal *vf, doublereal *vfw, doublereal *vl, - doublereal *vlw, doublereal *alpha, doublereal *beta, doublereal * - dsigma, integer *idx, integer *idxp, integer *idxq, integer *perm, - integer *givptr, integer *givcol, integer *ldgcol, doublereal *givnum, - integer *ldgnum, doublereal *c__, doublereal *s, integer *info) +int dlasd7_(integer *icompq, integer *nl, integer *nr, integer *sqre, integer *k, doublereal *d__, + doublereal *z__, doublereal *zw, doublereal *vf, doublereal *vfw, doublereal *vl, + doublereal *vlw, doublereal *alpha, doublereal *beta, doublereal *dsigma, integer *idx, + integer *idxp, integer *idxq, integer *perm, integer *givptr, integer *givcol, + integer *ldgcol, doublereal *givnum, integer *ldgnum, doublereal *c__, doublereal *s, + integer *info) { - /* System generated locals */ integer givcol_dim1, givcol_offset, givnum_dim1, givnum_offset, i__1; doublereal d__1, d__2; - - /* Local variables */ integer i__, j, m, n, k2; doublereal z1; integer jp; doublereal eps, tau, tol; integer nlp1, nlp2, idxi, idxj; - extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, - doublereal *, integer *, doublereal *, doublereal *); + extern int drot_(integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, + doublereal *); integer idxjp; - extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, - doublereal *, integer *); + extern int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *); integer jprev; - extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, - ftnlen); - extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *, - integer *, integer *, integer *), xerbla_(char *, integer *, - ftnlen); + extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, ftnlen); + extern int dlamrg_(integer *, integer *, doublereal *, integer *, integer *, integer *), + xerbla_(char *, integer *, ftnlen); doublereal hlftol; - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ - -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ --d__; --z__; --zw; @@ -375,12 +44,9 @@ f"> */ givnum_dim1 = *ldgnum; givnum_offset = 1 + givnum_dim1; givnum -= givnum_offset; - - /* Function Body */ *info = 0; n = *nl + *nr + 1; m = n + *sqre; - if (*icompq < 0 || *icompq > 1) { *info = -1; } else if (*nl < 1) { @@ -399,16 +65,11 @@ f"> */ xerbla_((char *)"DLASD7", &i__1, (ftnlen)6); return 0; } - nlp1 = *nl + 1; nlp2 = *nl + 2; if (*icompq == 1) { *givptr = 0; } - -/* Generate the first part of the vector Z and move the singular */ -/* values in the first part of D one position backward. */ - z1 = *alpha * vl[nlp1]; vl[nlp1] = 0.; tau = vf[nlp1]; @@ -418,40 +79,25 @@ f"> */ vf[i__ + 1] = vf[i__]; d__[i__ + 1] = d__[i__]; idxq[i__ + 1] = idxq[i__] + 1; -/* L10: */ } vf[1] = tau; - -/* Generate the second part of the vector Z. */ - i__1 = m; for (i__ = nlp2; i__ <= i__1; ++i__) { z__[i__] = *beta * vf[i__]; vf[i__] = 0.; -/* L20: */ } - -/* Sort the singular values into increasing order */ - i__1 = n; for (i__ = nlp2; i__ <= i__1; ++i__) { idxq[i__] += nlp1; -/* L30: */ } - -/* DSIGMA, IDXC, IDXC, and ZW are used as storage space. */ - i__1 = n; for (i__ = 2; i__ <= i__1; ++i__) { dsigma[i__] = d__[idxq[i__]]; zw[i__] = z__[idxq[i__]]; vfw[i__] = vf[idxq[i__]]; vlw[i__] = vl[idxq[i__]]; -/* L40: */ } - dlamrg_(nl, nr, &dsigma[2], &c__1, &c__1, &idx[2]); - i__1 = n; for (i__ = 2; i__ <= i__1; ++i__) { idxi = idx[i__] + 1; @@ -459,46 +105,17 @@ f"> */ z__[i__] = zw[idxi]; vf[i__] = vfw[idxi]; vl[i__] = vlw[idxi]; -/* L50: */ } - -/* Calculate the allowable deflation tolerance */ - eps = dlamch_((char *)"Epsilon", (ftnlen)7); -/* Computing MAX */ d__1 = abs(*alpha), d__2 = abs(*beta); - tol = max(d__1,d__2); -/* Computing MAX */ + tol = max(d__1, d__2); d__2 = (d__1 = d__[n], abs(d__1)); - tol = eps * 64. * max(d__2,tol); - -/* There are 2 kinds of deflation -- first a value in the z-vector */ -/* is small, second two (or more) singular values are very close */ -/* together (their difference is small). */ - -/* If the value in the z-vector is small, we simply permute the */ -/* array so that the corresponding singular value is moved to the */ -/* end. */ - -/* If two values in the D-vector are close, we perform a two-sided */ -/* rotation designed to make one of the corresponding z-vector */ -/* entries zero, and then permute the array so that the deflated */ -/* singular value is moved to the end. */ - -/* If there are multiple singular values then the problem deflates. */ -/* Here the number of equal singular values are found. As each equal */ -/* singular value is found, an elementary reflector is computed to */ -/* rotate the corresponding singular subspace so that the */ -/* corresponding components of Z are zero in this new basis. */ - + tol = eps * 64. * max(d__2, tol); *k = 1; k2 = n + 1; i__1 = n; for (j = 2; j <= i__1; ++j) { if ((d__1 = z__[j], abs(d__1)) <= tol) { - -/* Deflate due to small z component. */ - --k2; idxp[k2] = j; if (j == n) { @@ -508,7 +125,6 @@ f"> */ jprev = j; goto L70; } -/* L60: */ } L70: j = jprev; @@ -518,33 +134,17 @@ L80: goto L90; } if ((d__1 = z__[j], abs(d__1)) <= tol) { - -/* Deflate due to small z component. */ - --k2; idxp[k2] = j; } else { - -/* Check if singular values are close enough to allow deflation. */ - if ((d__1 = d__[j] - d__[jprev], abs(d__1)) <= tol) { - -/* Deflation is possible. */ - *s = z__[jprev]; *c__ = z__[j]; - -/* Find sqrt(a**2+b**2) without overflow or */ -/* destructive underflow. */ - tau = dlapy2_(c__, s); z__[j] = tau; z__[jprev] = 0.; *c__ /= tau; *s = -(*s) / tau; - -/* Record the appropriate Givens rotation */ - if (*icompq == 1) { ++(*givptr); idxjp = idxq[idx[jprev] + 1]; @@ -575,27 +175,17 @@ L80: } goto L80; L90: - -/* Record the last singular value. */ - ++(*k); zw[*k] = z__[jprev]; dsigma[*k] = d__[jprev]; idxp[*k] = jprev; - L100: - -/* Sort the singular values into DSIGMA. The singular values which */ -/* were not deflated go into the first K slots of DSIGMA, except */ -/* that DSIGMA(1) is treated separately. */ - i__1 = n; for (j = 2; j <= i__1; ++j) { jp = idxp[j]; dsigma[j] = d__[jp]; vfw[j] = vf[jp]; vlw[j] = vl[jp]; -/* L110: */ } if (*icompq == 1) { i__1 = n; @@ -605,19 +195,10 @@ L100: if (perm[j] <= nlp1) { --perm[j]; } -/* L120: */ } } - -/* The deflated singular values go back into the last N - K slots of */ -/* D. */ - i__1 = n - *k; dcopy_(&i__1, &dsigma[*k + 1], &c__1, &d__[*k + 1], &c__1); - -/* Determine DSIGMA(1), DSIGMA(2), Z(1), VF(1), VL(1), VF(M), and */ -/* VL(M). */ - dsigma[1] = 0.; hlftol = tol / 2.; if (abs(dsigma[2]) <= hlftol) { @@ -642,22 +223,14 @@ L100: z__[1] = z1; } } - -/* Restore Z, VF, and VL. */ - i__1 = *k - 1; dcopy_(&i__1, &zw[2], &c__1, &z__[2], &c__1); i__1 = n - 1; dcopy_(&i__1, &vfw[2], &c__1, &vf[2], &c__1); i__1 = n - 1; dcopy_(&i__1, &vlw[2], &c__1, &vl[2], &c__1); - return 0; - -/* End of DLASD7 */ - -} /* dlasd7_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlasd8.cpp b/lib/linalg/dlasd8.cpp index 5d0890e27b..ba92932435 100644 --- a/lib/linalg/dlasd8.cpp +++ b/lib/linalg/dlasd8.cpp @@ -1,254 +1,35 @@ -/* fortran/dlasd8.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static integer c__0 = 0; static doublereal c_b8 = 1.; - -/* > \brief \b DLASD8 finds the square roots of the roots of the secular equation, and stores, for each elemen -t in D, the distance to its two nearest poles. Used by sbdsdc. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLASD8 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLASD8( ICOMPQ, K, D, Z, VF, VL, DIFL, DIFR, LDDIFR, */ -/* DSIGMA, WORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER ICOMPQ, INFO, K, LDDIFR */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION D( * ), DIFL( * ), DIFR( LDDIFR, * ), */ -/* $ DSIGMA( * ), VF( * ), VL( * ), WORK( * ), */ -/* $ Z( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLASD8 finds the square roots of the roots of the secular equation, */ -/* > as defined by the values in DSIGMA and Z. It makes the appropriate */ -/* > calls to DLASD4, and stores, for each element in D, the distance */ -/* > to its two nearest poles (elements in DSIGMA). It also updates */ -/* > the arrays VF and VL, the first and last components of all the */ -/* > right singular vectors of the original bidiagonal matrix. */ -/* > */ -/* > DLASD8 is called from DLASD6. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] ICOMPQ */ -/* > \verbatim */ -/* > ICOMPQ is INTEGER */ -/* > Specifies whether singular vectors are to be computed in */ -/* > factored form in the calling routine: */ -/* > = 0: Compute singular values only. */ -/* > = 1: Compute singular vectors in factored form as well. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > The number of terms in the rational function to be solved */ -/* > by DLASD4. K >= 1. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension ( K ) */ -/* > On output, D contains the updated singular values. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] Z */ -/* > \verbatim */ -/* > Z is DOUBLE PRECISION array, dimension ( K ) */ -/* > On entry, the first K elements of this array contain the */ -/* > components of the deflation-adjusted updating row vector. */ -/* > On exit, Z is updated. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] VF */ -/* > \verbatim */ -/* > VF is DOUBLE PRECISION array, dimension ( K ) */ -/* > On entry, VF contains information passed through DBEDE8. */ -/* > On exit, VF contains the first K components of the first */ -/* > components of all right singular vectors of the bidiagonal */ -/* > matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] VL */ -/* > \verbatim */ -/* > VL is DOUBLE PRECISION array, dimension ( K ) */ -/* > On entry, VL contains information passed through DBEDE8. */ -/* > On exit, VL contains the first K components of the last */ -/* > components of all right singular vectors of the bidiagonal */ -/* > matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] DIFL */ -/* > \verbatim */ -/* > DIFL is DOUBLE PRECISION array, dimension ( K ) */ -/* > On exit, DIFL(I) = D(I) - DSIGMA(I). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] DIFR */ -/* > \verbatim */ -/* > DIFR is DOUBLE PRECISION array, */ -/* > dimension ( LDDIFR, 2 ) if ICOMPQ = 1 and */ -/* > dimension ( K ) if ICOMPQ = 0. */ -/* > On exit, DIFR(I,1) = D(I) - DSIGMA(I+1), DIFR(K,1) is not */ -/* > defined and will not be referenced. */ -/* > */ -/* > If ICOMPQ = 1, DIFR(1:K,2) is an array containing the */ -/* > normalizing factors for the right singular vector matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDDIFR */ -/* > \verbatim */ -/* > LDDIFR is INTEGER */ -/* > The leading dimension of DIFR, must be at least K. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] DSIGMA */ -/* > \verbatim */ -/* > DSIGMA is DOUBLE PRECISION array, dimension ( K ) */ -/* > On entry, the first K elements of this array contain the old */ -/* > roots of the deflated updating problem. These are the poles */ -/* > of the secular equation. */ -/* > On exit, the elements of DSIGMA may be very slightly altered */ -/* > in value. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (3*K) */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit. */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ -/* > > 0: if INFO = 1, a singular value did not converge */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup OTHERauxiliary */ - -/* > \par Contributors: */ -/* ================== */ -/* > */ -/* > Ming Gu and Huan Ren, Computer Science Division, University of */ -/* > California at Berkeley, USA */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dlasd8_(integer *icompq, integer *k, doublereal *d__, - doublereal *z__, doublereal *vf, doublereal *vl, doublereal *difl, - doublereal *difr, integer *lddifr, doublereal *dsigma, doublereal * - work, integer *info) +int dlasd8_(integer *icompq, integer *k, doublereal *d__, doublereal *z__, doublereal *vf, + doublereal *vl, doublereal *difl, doublereal *difr, integer *lddifr, doublereal *dsigma, + doublereal *work, integer *info) { - /* System generated locals */ integer difr_dim1, difr_offset, i__1, i__2; doublereal d__1, d__2; - - /* Builtin functions */ double sqrt(doublereal), d_lmp_sign(doublereal *, doublereal *); - - /* Local variables */ integer i__, j; doublereal dj, rho; integer iwk1, iwk2, iwk3; - extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, - integer *); + extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, integer *); doublereal temp; extern doublereal dnrm2_(integer *, doublereal *, integer *); integer iwk2i, iwk3i; doublereal diflj, difrj, dsigj; - extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, - doublereal *, integer *); + extern int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *); extern doublereal dlamc3_(doublereal *, doublereal *); - extern /* Subroutine */ int dlasd4_(integer *, integer *, doublereal *, - doublereal *, doublereal *, doublereal *, doublereal *, - doublereal *, integer *), dlascl_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, integer *, doublereal *, - integer *, integer *, ftnlen), dlaset_(char *, integer *, integer - *, doublereal *, doublereal *, doublereal *, integer *, ftnlen), - xerbla_(char *, integer *, ftnlen); + extern int dlasd4_(integer *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, doublereal *, integer *), + dlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, integer *, + doublereal *, integer *, integer *, ftnlen), + dlaset_(char *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, + ftnlen), + xerbla_(char *, integer *, ftnlen); doublereal dsigjp; - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ --d__; --z__; --vf; @@ -259,10 +40,7 @@ f"> */ difr -= difr_offset; --dsigma; --work; - - /* Function Body */ *info = 0; - if (*icompq < 0 || *icompq > 1) { *info = -1; } else if (*k < 1) { @@ -275,9 +53,6 @@ f"> */ xerbla_((char *)"DLASD8", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*k == 1) { d__[1] = abs(z__[1]); difl[1] = d__[1]; @@ -287,59 +62,22 @@ f"> */ } return 0; } - -/* Modify values DSIGMA(i) to make sure all DSIGMA(i)-DSIGMA(j) can */ -/* be computed with high relative accuracy (barring over/underflow). */ -/* This is a problem on machines without a guard digit in */ -/* add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2). */ -/* The following code replaces DSIGMA(I) by 2*DSIGMA(I)-DSIGMA(I), */ -/* which on any of these machines zeros out the bottommost */ -/* bit of DSIGMA(I) if it is 1; this makes the subsequent */ -/* subtractions DSIGMA(I)-DSIGMA(J) unproblematic when cancellation */ -/* occurs. On binary machines with a guard digit (almost all */ -/* machines) it does not change DSIGMA(I) at all. On hexadecimal */ -/* and decimal machines with a guard digit, it slightly */ -/* changes the bottommost bits of DSIGMA(I). It does not account */ -/* for hexadecimal or decimal machines without guard digits */ -/* (we know of none). We use a subroutine call to compute */ -/* 2*DLAMBDA(I) to prevent optimizing compilers from eliminating */ -/* this code. */ - i__1 = *k; for (i__ = 1; i__ <= i__1; ++i__) { dsigma[i__] = dlamc3_(&dsigma[i__], &dsigma[i__]) - dsigma[i__]; -/* L10: */ } - -/* Book keeping. */ - iwk1 = 1; iwk2 = iwk1 + *k; iwk3 = iwk2 + *k; iwk2i = iwk2 - 1; iwk3i = iwk3 - 1; - -/* Normalize Z. */ - rho = dnrm2_(k, &z__[1], &c__1); - dlascl_((char *)"G", &c__0, &c__0, &rho, &c_b8, k, &c__1, &z__[1], k, info, ( - ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &rho, &c_b8, k, &c__1, &z__[1], k, info, (ftnlen)1); rho *= rho; - -/* Initialize WORK(IWK3). */ - dlaset_((char *)"A", k, &c__1, &c_b8, &c_b8, &work[iwk3], k, (ftnlen)1); - -/* Compute the updated singular values, the arrays DIFL, DIFR, */ -/* and the updated Z. */ - i__1 = *k; for (j = 1; j <= i__1; ++j) { - dlasd4_(k, &j, &dsigma[1], &z__[1], &work[iwk1], &rho, &d__[j], &work[ - iwk2], info); - -/* If the root finder fails, report the convergence failure. */ - + dlasd4_(k, &j, &dsigma[1], &z__[1], &work[iwk1], &rho, &d__[j], &work[iwk2], info); if (*info != 0) { return 0; } @@ -348,32 +86,20 @@ f"> */ difr[j + difr_dim1] = -work[j + 1]; i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { - work[iwk3i + i__] = work[iwk3i + i__] * work[i__] * work[iwk2i + - i__] / (dsigma[i__] - dsigma[j]) / (dsigma[i__] + dsigma[ - j]); -/* L20: */ + work[iwk3i + i__] = work[iwk3i + i__] * work[i__] * work[iwk2i + i__] / + (dsigma[i__] - dsigma[j]) / (dsigma[i__] + dsigma[j]); } i__2 = *k; for (i__ = j + 1; i__ <= i__2; ++i__) { - work[iwk3i + i__] = work[iwk3i + i__] * work[i__] * work[iwk2i + - i__] / (dsigma[i__] - dsigma[j]) / (dsigma[i__] + dsigma[ - j]); -/* L30: */ + work[iwk3i + i__] = work[iwk3i + i__] * work[i__] * work[iwk2i + i__] / + (dsigma[i__] - dsigma[j]) / (dsigma[i__] + dsigma[j]); } -/* L40: */ } - -/* Compute updated Z. */ - i__1 = *k; for (i__ = 1; i__ <= i__1; ++i__) { d__2 = sqrt((d__1 = work[iwk3i + i__], abs(d__1))); z__[i__] = d_lmp_sign(&d__2, &z__[i__]); -/* L50: */ } - -/* Update VF and VL. */ - i__1 = *k; for (j = 1; j <= i__1; ++j) { diflj = difl[j]; @@ -386,15 +112,11 @@ f"> */ work[j] = -z__[j] / diflj / (dsigma[j] + dj); i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { - work[i__] = z__[i__] / (dlamc3_(&dsigma[i__], &dsigj) - diflj) / ( - dsigma[i__] + dj); -/* L60: */ + work[i__] = z__[i__] / (dlamc3_(&dsigma[i__], &dsigj) - diflj) / (dsigma[i__] + dj); } i__2 = *k; for (i__ = j + 1; i__ <= i__2; ++i__) { - work[i__] = z__[i__] / (dlamc3_(&dsigma[i__], &dsigjp) + difrj) / - (dsigma[i__] + dj); -/* L70: */ + work[i__] = z__[i__] / (dlamc3_(&dsigma[i__], &dsigjp) + difrj) / (dsigma[i__] + dj); } temp = dnrm2_(k, &work[1], &c__1); work[iwk2i + j] = ddot_(k, &work[1], &c__1, &vf[1], &c__1) / temp; @@ -402,18 +124,11 @@ f"> */ if (*icompq == 1) { difr[j + (difr_dim1 << 1)] = temp; } -/* L80: */ } - dcopy_(k, &work[iwk2], &c__1, &vf[1], &c__1); dcopy_(k, &work[iwk3], &c__1, &vl[1], &c__1); - return 0; - -/* End of DLASD8 */ - -} /* dlasd8_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlasda.cpp b/lib/linalg/dlasda.cpp index b50a48f625..47f76ed32d 100644 --- a/lib/linalg/dlasda.cpp +++ b/lib/linalg/dlasda.cpp @@ -1,367 +1,44 @@ -/* fortran/dlasda.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__0 = 0; static doublereal c_b11 = 0.; static doublereal c_b12 = 1.; static integer c__1 = 1; static integer c__2 = 2; - -/* > \brief \b DLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal matrix with d -iagonal d and off-diagonal e. Used by sbdsdc. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLASDA + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLASDA( ICOMPQ, SMLSIZ, N, SQRE, D, E, U, LDU, VT, K, */ -/* DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, */ -/* PERM, GIVNUM, C, S, WORK, IWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER ICOMPQ, INFO, LDGCOL, LDU, N, SMLSIZ, SQRE */ -/* .. */ -/* .. Array Arguments .. */ -/* INTEGER GIVCOL( LDGCOL, * ), GIVPTR( * ), IWORK( * ), */ -/* $ K( * ), PERM( LDGCOL, * ) */ -/* DOUBLE PRECISION C( * ), D( * ), DIFL( LDU, * ), DIFR( LDU, * ), */ -/* $ E( * ), GIVNUM( LDU, * ), POLES( LDU, * ), */ -/* $ S( * ), U( LDU, * ), VT( LDU, * ), WORK( * ), */ -/* $ Z( LDU, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > Using a divide and conquer approach, DLASDA computes the singular */ -/* > value decomposition (SVD) of a real upper bidiagonal N-by-M matrix */ -/* > B with diagonal D and offdiagonal E, where M = N + SQRE. The */ -/* > algorithm computes the singular values in the SVD B = U * S * VT. */ -/* > The orthogonal matrices U and VT are optionally computed in */ -/* > compact form. */ -/* > */ -/* > A related subroutine, DLASD0, computes the singular values and */ -/* > the singular vectors in explicit form. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] ICOMPQ */ -/* > \verbatim */ -/* > ICOMPQ is INTEGER */ -/* > Specifies whether singular vectors are to be computed */ -/* > in compact form, as follows */ -/* > = 0: Compute singular values only. */ -/* > = 1: Compute singular vectors of upper bidiagonal */ -/* > matrix in compact form. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] SMLSIZ */ -/* > \verbatim */ -/* > SMLSIZ is INTEGER */ -/* > The maximum size of the subproblems at the bottom of the */ -/* > computation tree. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The row dimension of the upper bidiagonal matrix. This is */ -/* > also the dimension of the main diagonal array D. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] SQRE */ -/* > \verbatim */ -/* > SQRE is INTEGER */ -/* > Specifies the column dimension of the bidiagonal matrix. */ -/* > = 0: The bidiagonal matrix has column dimension M = N; */ -/* > = 1: The bidiagonal matrix has column dimension M = N + 1. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension ( N ) */ -/* > On entry D contains the main diagonal of the bidiagonal */ -/* > matrix. On exit D, if INFO = 0, contains its singular values. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] E */ -/* > \verbatim */ -/* > E is DOUBLE PRECISION array, dimension ( M-1 ) */ -/* > Contains the subdiagonal entries of the bidiagonal matrix. */ -/* > On exit, E has been destroyed. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] U */ -/* > \verbatim */ -/* > U is DOUBLE PRECISION array, */ -/* > dimension ( LDU, SMLSIZ ) if ICOMPQ = 1, and not referenced */ -/* > if ICOMPQ = 0. If ICOMPQ = 1, on exit, U contains the left */ -/* > singular vector matrices of all subproblems at the bottom */ -/* > level. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDU */ -/* > \verbatim */ -/* > LDU is INTEGER, LDU = > N. */ -/* > The leading dimension of arrays U, VT, DIFL, DIFR, POLES, */ -/* > GIVNUM, and Z. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] VT */ -/* > \verbatim */ -/* > VT is DOUBLE PRECISION array, */ -/* > dimension ( LDU, SMLSIZ+1 ) if ICOMPQ = 1, and not referenced */ -/* > if ICOMPQ = 0. If ICOMPQ = 1, on exit, VT**T contains the right */ -/* > singular vector matrices of all subproblems at the bottom */ -/* > level. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] K */ -/* > \verbatim */ -/* > K is INTEGER array, */ -/* > dimension ( N ) if ICOMPQ = 1 and dimension 1 if ICOMPQ = 0. */ -/* > If ICOMPQ = 1, on exit, K(I) is the dimension of the I-th */ -/* > secular equation on the computation tree. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] DIFL */ -/* > \verbatim */ -/* > DIFL is DOUBLE PRECISION array, dimension ( LDU, NLVL ), */ -/* > where NLVL = floor(log_2 (N/SMLSIZ))). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] DIFR */ -/* > \verbatim */ -/* > DIFR is DOUBLE PRECISION array, */ -/* > dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1 and */ -/* > dimension ( N ) if ICOMPQ = 0. */ -/* > If ICOMPQ = 1, on exit, DIFL(1:N, I) and DIFR(1:N, 2 * I - 1) */ -/* > record distances between singular values on the I-th */ -/* > level and singular values on the (I -1)-th level, and */ -/* > DIFR(1:N, 2 * I ) contains the normalizing factors for */ -/* > the right singular vector matrix. See DLASD8 for details. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] Z */ -/* > \verbatim */ -/* > Z is DOUBLE PRECISION array, */ -/* > dimension ( LDU, NLVL ) if ICOMPQ = 1 and */ -/* > dimension ( N ) if ICOMPQ = 0. */ -/* > The first K elements of Z(1, I) contain the components of */ -/* > the deflation-adjusted updating row vector for subproblems */ -/* > on the I-th level. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] POLES */ -/* > \verbatim */ -/* > POLES is DOUBLE PRECISION array, */ -/* > dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not referenced */ -/* > if ICOMPQ = 0. If ICOMPQ = 1, on exit, POLES(1, 2*I - 1) and */ -/* > POLES(1, 2*I) contain the new and old singular values */ -/* > involved in the secular equations on the I-th level. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] GIVPTR */ -/* > \verbatim */ -/* > GIVPTR is INTEGER array, */ -/* > dimension ( N ) if ICOMPQ = 1, and not referenced if */ -/* > ICOMPQ = 0. If ICOMPQ = 1, on exit, GIVPTR( I ) records */ -/* > the number of Givens rotations performed on the I-th */ -/* > problem on the computation tree. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] GIVCOL */ -/* > \verbatim */ -/* > GIVCOL is INTEGER array, */ -/* > dimension ( LDGCOL, 2 * NLVL ) if ICOMPQ = 1, and not */ -/* > referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, */ -/* > GIVCOL(1, 2 *I - 1) and GIVCOL(1, 2 *I) record the locations */ -/* > of Givens rotations performed on the I-th level on the */ -/* > computation tree. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDGCOL */ -/* > \verbatim */ -/* > LDGCOL is INTEGER, LDGCOL = > N. */ -/* > The leading dimension of arrays GIVCOL and PERM. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] PERM */ -/* > \verbatim */ -/* > PERM is INTEGER array, */ -/* > dimension ( LDGCOL, NLVL ) if ICOMPQ = 1, and not referenced */ -/* > if ICOMPQ = 0. If ICOMPQ = 1, on exit, PERM(1, I) records */ -/* > permutations done on the I-th level of the computation tree. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] GIVNUM */ -/* > \verbatim */ -/* > GIVNUM is DOUBLE PRECISION array, */ -/* > dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not */ -/* > referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, */ -/* > GIVNUM(1, 2 *I - 1) and GIVNUM(1, 2 *I) record the C- and S- */ -/* > values of Givens rotations performed on the I-th level on */ -/* > the computation tree. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] C */ -/* > \verbatim */ -/* > C is DOUBLE PRECISION array, */ -/* > dimension ( N ) if ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. */ -/* > If ICOMPQ = 1 and the I-th subproblem is not square, on exit, */ -/* > C( I ) contains the C-value of a Givens rotation related to */ -/* > the right null space of the I-th subproblem. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] S */ -/* > \verbatim */ -/* > S is DOUBLE PRECISION array, dimension ( N ) if */ -/* > ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1 */ -/* > and the I-th subproblem is not square, on exit, S( I ) */ -/* > contains the S-value of a Givens rotation related to */ -/* > the right null space of the I-th subproblem. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension */ -/* > (6 * N + (SMLSIZ + 1)*(SMLSIZ + 1)). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] IWORK */ -/* > \verbatim */ -/* > IWORK is INTEGER array, dimension (7*N) */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit. */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ -/* > > 0: if INFO = 1, a singular value did not converge */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup OTHERauxiliary */ - -/* > \par Contributors: */ -/* ================== */ -/* > */ -/* > Ming Gu and Huan Ren, Computer Science Division, University of */ -/* > California at Berkeley, USA */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dlasda_(integer *icompq, integer *smlsiz, integer *n, - integer *sqre, doublereal *d__, doublereal *e, doublereal *u, integer - *ldu, doublereal *vt, integer *k, doublereal *difl, doublereal *difr, - doublereal *z__, doublereal *poles, integer *givptr, integer *givcol, - integer *ldgcol, integer *perm, doublereal *givnum, doublereal *c__, - doublereal *s, doublereal *work, integer *iwork, integer *info) +int dlasda_(integer *icompq, integer *smlsiz, integer *n, integer *sqre, doublereal *d__, + doublereal *e, doublereal *u, integer *ldu, doublereal *vt, integer *k, + doublereal *difl, doublereal *difr, doublereal *z__, doublereal *poles, integer *givptr, + integer *givcol, integer *ldgcol, integer *perm, doublereal *givnum, doublereal *c__, + doublereal *s, doublereal *work, integer *iwork, integer *info) { - /* System generated locals */ - integer givcol_dim1, givcol_offset, perm_dim1, perm_offset, difl_dim1, - difl_offset, difr_dim1, difr_offset, givnum_dim1, givnum_offset, - poles_dim1, poles_offset, u_dim1, u_offset, vt_dim1, vt_offset, - z_dim1, z_offset, i__1, i__2; - - /* Builtin functions */ + integer givcol_dim1, givcol_offset, perm_dim1, perm_offset, difl_dim1, difl_offset, difr_dim1, + difr_offset, givnum_dim1, givnum_offset, poles_dim1, poles_offset, u_dim1, u_offset, + vt_dim1, vt_offset, z_dim1, z_offset, i__1, i__2; integer pow_lmp_ii(integer *, integer *); - - /* Local variables */ - integer i__, j, m, i1, ic, lf, nd, ll, nl, vf, nr, vl, im1, ncc, nlf, nrf, - vfi, iwk, vli, lvl, nru, ndb1, nlp1, lvl2, nrp1; + integer i__, j, m, i1, ic, lf, nd, ll, nl, vf, nr, vl, im1, ncc, nlf, nrf, vfi, iwk, vli, lvl, + nru, ndb1, nlp1, lvl2, nrp1; doublereal beta; integer idxq, nlvl; doublereal alpha; integer inode, ndiml, ndimr, idxqi, itemp; - extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, - doublereal *, integer *); + extern int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *); integer sqrei; - extern /* Subroutine */ int dlasd6_(integer *, integer *, integer *, - integer *, doublereal *, doublereal *, doublereal *, doublereal *, - doublereal *, integer *, integer *, integer *, integer *, - integer *, doublereal *, integer *, doublereal *, doublereal *, - doublereal *, doublereal *, integer *, doublereal *, doublereal *, - doublereal *, integer *, integer *); + extern int dlasd6_(integer *, integer *, integer *, integer *, doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *, integer *, integer *, integer *, + integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, + doublereal *, doublereal *, integer *, doublereal *, doublereal *, + doublereal *, integer *, integer *); integer nwork1, nwork2; - extern /* Subroutine */ int dlasdq_(char *, integer *, integer *, integer - *, integer *, integer *, doublereal *, doublereal *, doublereal *, - integer *, doublereal *, integer *, doublereal *, integer *, - doublereal *, integer *, ftnlen), dlasdt_(integer *, integer *, - integer *, integer *, integer *, integer *, integer *), dlaset_( - char *, integer *, integer *, doublereal *, doublereal *, - doublereal *, integer *, ftnlen), xerbla_(char *, integer *, - ftnlen); + extern int dlasdq_(char *, integer *, integer *, integer *, integer *, integer *, doublereal *, + doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, + integer *, doublereal *, integer *, ftnlen), + dlasdt_(integer *, integer *, integer *, integer *, integer *, integer *, integer *), + dlaset_(char *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, + ftnlen), + xerbla_(char *, integer *, ftnlen); integer smlszp; - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ --d__; --e; givnum_dim1 = *ldu; @@ -397,10 +74,7 @@ f"> */ --s; --work; --iwork; - - /* Function Body */ *info = 0; - if (*icompq < 0 || *icompq > 1) { *info = -1; } else if (*smlsiz < 3) { @@ -419,57 +93,33 @@ f"> */ xerbla_((char *)"DLASDA", &i__1, (ftnlen)6); return 0; } - m = *n + *sqre; - -/* If the input matrix is too small, call DLASDQ to find the SVD. */ - if (*n <= *smlsiz) { if (*icompq == 0) { - dlasdq_((char *)"U", sqre, n, &c__0, &c__0, &c__0, &d__[1], &e[1], &vt[ - vt_offset], ldu, &u[u_offset], ldu, &u[u_offset], ldu, & - work[1], info, (ftnlen)1); + dlasdq_((char *)"U", sqre, n, &c__0, &c__0, &c__0, &d__[1], &e[1], &vt[vt_offset], ldu, + &u[u_offset], ldu, &u[u_offset], ldu, &work[1], info, (ftnlen)1); } else { - dlasdq_((char *)"U", sqre, n, &m, n, &c__0, &d__[1], &e[1], &vt[vt_offset] - , ldu, &u[u_offset], ldu, &u[u_offset], ldu, &work[1], - info, (ftnlen)1); + dlasdq_((char *)"U", sqre, n, &m, n, &c__0, &d__[1], &e[1], &vt[vt_offset], ldu, &u[u_offset], + ldu, &u[u_offset], ldu, &work[1], info, (ftnlen)1); } return 0; } - -/* Book-keeping and set up the computation tree. */ - inode = 1; ndiml = inode + *n; ndimr = ndiml + *n; idxq = ndimr + *n; iwk = idxq + *n; - ncc = 0; nru = 0; - smlszp = *smlsiz + 1; vf = 1; vl = vf + m; nwork1 = vl + m; nwork2 = nwork1 + smlszp * smlszp; - - dlasdt_(n, &nlvl, &nd, &iwork[inode], &iwork[ndiml], &iwork[ndimr], - smlsiz); - -/* for the nodes on bottom level of the tree, solve */ -/* their subproblems by DLASDQ. */ - + dlasdt_(n, &nlvl, &nd, &iwork[inode], &iwork[ndiml], &iwork[ndimr], smlsiz); ndb1 = (nd + 1) / 2; i__1 = nd; for (i__ = ndb1; i__ <= i__1; ++i__) { - -/* IC : center row of each node */ -/* NL : number of rows of left subproblem */ -/* NR : number of rows of right subproblem */ -/* NLF: starting row of the left subproblem */ -/* NRF: starting row of the right subproblem */ - i1 = i__ - 1; ic = iwork[inode + i1]; nl = iwork[ndiml + i1]; @@ -482,25 +132,19 @@ f"> */ vli = vl + nlf - 1; sqrei = 1; if (*icompq == 0) { - dlaset_((char *)"A", &nlp1, &nlp1, &c_b11, &c_b12, &work[nwork1], &smlszp, - (ftnlen)1); - dlasdq_((char *)"U", &sqrei, &nl, &nlp1, &nru, &ncc, &d__[nlf], &e[nlf], & - work[nwork1], &smlszp, &work[nwork2], &nl, &work[nwork2], - &nl, &work[nwork2], info, (ftnlen)1); + dlaset_((char *)"A", &nlp1, &nlp1, &c_b11, &c_b12, &work[nwork1], &smlszp, (ftnlen)1); + dlasdq_((char *)"U", &sqrei, &nl, &nlp1, &nru, &ncc, &d__[nlf], &e[nlf], &work[nwork1], &smlszp, + &work[nwork2], &nl, &work[nwork2], &nl, &work[nwork2], info, (ftnlen)1); itemp = nwork1 + nl * smlszp; dcopy_(&nlp1, &work[nwork1], &c__1, &work[vfi], &c__1); dcopy_(&nlp1, &work[itemp], &c__1, &work[vli], &c__1); } else { - dlaset_((char *)"A", &nl, &nl, &c_b11, &c_b12, &u[nlf + u_dim1], ldu, ( - ftnlen)1); - dlaset_((char *)"A", &nlp1, &nlp1, &c_b11, &c_b12, &vt[nlf + vt_dim1], - ldu, (ftnlen)1); - dlasdq_((char *)"U", &sqrei, &nl, &nlp1, &nl, &ncc, &d__[nlf], &e[nlf], & - vt[nlf + vt_dim1], ldu, &u[nlf + u_dim1], ldu, &u[nlf + - u_dim1], ldu, &work[nwork1], info, (ftnlen)1); + dlaset_((char *)"A", &nl, &nl, &c_b11, &c_b12, &u[nlf + u_dim1], ldu, (ftnlen)1); + dlaset_((char *)"A", &nlp1, &nlp1, &c_b11, &c_b12, &vt[nlf + vt_dim1], ldu, (ftnlen)1); + dlasdq_((char *)"U", &sqrei, &nl, &nlp1, &nl, &ncc, &d__[nlf], &e[nlf], &vt[nlf + vt_dim1], ldu, + &u[nlf + u_dim1], ldu, &u[nlf + u_dim1], ldu, &work[nwork1], info, (ftnlen)1); dcopy_(&nlp1, &vt[nlf + vt_dim1], &c__1, &work[vfi], &c__1); - dcopy_(&nlp1, &vt[nlf + nlp1 * vt_dim1], &c__1, &work[vli], &c__1) - ; + dcopy_(&nlp1, &vt[nlf + nlp1 * vt_dim1], &c__1, &work[vli], &c__1); } if (*info != 0) { return 0; @@ -508,7 +152,6 @@ f"> */ i__2 = nl; for (j = 1; j <= i__2; ++j) { iwork[idxqi + j] = j; -/* L10: */ } if (i__ == nd && *sqre == 0) { sqrei = 0; @@ -520,25 +163,19 @@ f"> */ vli += nlp1; nrp1 = nr + sqrei; if (*icompq == 0) { - dlaset_((char *)"A", &nrp1, &nrp1, &c_b11, &c_b12, &work[nwork1], &smlszp, - (ftnlen)1); - dlasdq_((char *)"U", &sqrei, &nr, &nrp1, &nru, &ncc, &d__[nrf], &e[nrf], & - work[nwork1], &smlszp, &work[nwork2], &nr, &work[nwork2], - &nr, &work[nwork2], info, (ftnlen)1); + dlaset_((char *)"A", &nrp1, &nrp1, &c_b11, &c_b12, &work[nwork1], &smlszp, (ftnlen)1); + dlasdq_((char *)"U", &sqrei, &nr, &nrp1, &nru, &ncc, &d__[nrf], &e[nrf], &work[nwork1], &smlszp, + &work[nwork2], &nr, &work[nwork2], &nr, &work[nwork2], info, (ftnlen)1); itemp = nwork1 + (nrp1 - 1) * smlszp; dcopy_(&nrp1, &work[nwork1], &c__1, &work[vfi], &c__1); dcopy_(&nrp1, &work[itemp], &c__1, &work[vli], &c__1); } else { - dlaset_((char *)"A", &nr, &nr, &c_b11, &c_b12, &u[nrf + u_dim1], ldu, ( - ftnlen)1); - dlaset_((char *)"A", &nrp1, &nrp1, &c_b11, &c_b12, &vt[nrf + vt_dim1], - ldu, (ftnlen)1); - dlasdq_((char *)"U", &sqrei, &nr, &nrp1, &nr, &ncc, &d__[nrf], &e[nrf], & - vt[nrf + vt_dim1], ldu, &u[nrf + u_dim1], ldu, &u[nrf + - u_dim1], ldu, &work[nwork1], info, (ftnlen)1); + dlaset_((char *)"A", &nr, &nr, &c_b11, &c_b12, &u[nrf + u_dim1], ldu, (ftnlen)1); + dlaset_((char *)"A", &nrp1, &nrp1, &c_b11, &c_b12, &vt[nrf + vt_dim1], ldu, (ftnlen)1); + dlasdq_((char *)"U", &sqrei, &nr, &nrp1, &nr, &ncc, &d__[nrf], &e[nrf], &vt[nrf + vt_dim1], ldu, + &u[nrf + u_dim1], ldu, &u[nrf + u_dim1], ldu, &work[nwork1], info, (ftnlen)1); dcopy_(&nrp1, &vt[nrf + vt_dim1], &c__1, &work[vfi], &c__1); - dcopy_(&nrp1, &vt[nrf + nrp1 * vt_dim1], &c__1, &work[vli], &c__1) - ; + dcopy_(&nrp1, &vt[nrf + nrp1 * vt_dim1], &c__1, &work[vli], &c__1); } if (*info != 0) { return 0; @@ -546,20 +183,11 @@ f"> */ i__2 = nr; for (j = 1; j <= i__2; ++j) { iwork[idxqi + j] = j; -/* L20: */ } -/* L30: */ } - -/* Now conquer each subproblem bottom-up. */ - j = pow_lmp_ii(&c__2, &nlvl); for (lvl = nlvl; lvl >= 1; --lvl) { lvl2 = (lvl << 1) - 1; - -/* Find the first node LF and last node LL on */ -/* the current level LVL. */ - if (lvl == 1) { lf = 1; ll = 1; @@ -587,38 +215,28 @@ f"> */ alpha = d__[ic]; beta = e[ic]; if (*icompq == 0) { - dlasd6_(icompq, &nl, &nr, &sqrei, &d__[nlf], &work[vfi], & - work[vli], &alpha, &beta, &iwork[idxqi], &perm[ - perm_offset], &givptr[1], &givcol[givcol_offset], - ldgcol, &givnum[givnum_offset], ldu, &poles[ - poles_offset], &difl[difl_offset], &difr[difr_offset], - &z__[z_offset], &k[1], &c__[1], &s[1], &work[nwork1], - &iwork[iwk], info); + dlasd6_(icompq, &nl, &nr, &sqrei, &d__[nlf], &work[vfi], &work[vli], &alpha, &beta, + &iwork[idxqi], &perm[perm_offset], &givptr[1], &givcol[givcol_offset], + ldgcol, &givnum[givnum_offset], ldu, &poles[poles_offset], + &difl[difl_offset], &difr[difr_offset], &z__[z_offset], &k[1], &c__[1], + &s[1], &work[nwork1], &iwork[iwk], info); } else { --j; - dlasd6_(icompq, &nl, &nr, &sqrei, &d__[nlf], &work[vfi], & - work[vli], &alpha, &beta, &iwork[idxqi], &perm[nlf + - lvl * perm_dim1], &givptr[j], &givcol[nlf + lvl2 * - givcol_dim1], ldgcol, &givnum[nlf + lvl2 * - givnum_dim1], ldu, &poles[nlf + lvl2 * poles_dim1], & - difl[nlf + lvl * difl_dim1], &difr[nlf + lvl2 * - difr_dim1], &z__[nlf + lvl * z_dim1], &k[j], &c__[j], - &s[j], &work[nwork1], &iwork[iwk], info); + dlasd6_(icompq, &nl, &nr, &sqrei, &d__[nlf], &work[vfi], &work[vli], &alpha, &beta, + &iwork[idxqi], &perm[nlf + lvl * perm_dim1], &givptr[j], + &givcol[nlf + lvl2 * givcol_dim1], ldgcol, + &givnum[nlf + lvl2 * givnum_dim1], ldu, &poles[nlf + lvl2 * poles_dim1], + &difl[nlf + lvl * difl_dim1], &difr[nlf + lvl2 * difr_dim1], + &z__[nlf + lvl * z_dim1], &k[j], &c__[j], &s[j], &work[nwork1], &iwork[iwk], + info); } if (*info != 0) { return 0; } -/* L40: */ } -/* L50: */ } - return 0; - -/* End of DLASDA */ - -} /* dlasda_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlasdq.cpp b/lib/linalg/dlasdq.cpp index 418be52678..9b97d9258f 100644 --- a/lib/linalg/dlasdq.cpp +++ b/lib/linalg/dlasdq.cpp @@ -1,293 +1,30 @@ -/* fortran/dlasdq.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; - -/* > \brief \b DLASDQ computes the SVD of a real bidiagonal matrix with diagonal d and off-diagonal e. Used by - sbdsdc. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLASDQ + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLASDQ( UPLO, SQRE, N, NCVT, NRU, NCC, D, E, VT, LDVT, */ -/* U, LDU, C, LDC, WORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER UPLO */ -/* INTEGER INFO, LDC, LDU, LDVT, N, NCC, NCVT, NRU, SQRE */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION C( LDC, * ), D( * ), E( * ), U( LDU, * ), */ -/* $ VT( LDVT, * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLASDQ computes the singular value decomposition (SVD) of a real */ -/* > (upper or lower) bidiagonal matrix with diagonal D and offdiagonal */ -/* > E, accumulating the transformations if desired. Letting B denote */ -/* > the input bidiagonal matrix, the algorithm computes orthogonal */ -/* > matrices Q and P such that B = Q * S * P**T (P**T denotes the transpose */ -/* > of P). The singular values S are overwritten on D. */ -/* > */ -/* > The input matrix U is changed to U * Q if desired. */ -/* > The input matrix VT is changed to P**T * VT if desired. */ -/* > The input matrix C is changed to Q**T * C if desired. */ -/* > */ -/* > See "Computing Small Singular Values of Bidiagonal Matrices With */ -/* > Guaranteed High Relative Accuracy," by J. Demmel and W. Kahan, */ -/* > LAPACK Working Note #3, for a detailed description of the algorithm. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > On entry, UPLO specifies whether the input bidiagonal matrix */ -/* > is upper or lower bidiagonal, and whether it is square are */ -/* > not. */ -/* > UPLO = 'U' or 'u' B is upper bidiagonal. */ -/* > UPLO = 'L' or 'l' B is lower bidiagonal. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] SQRE */ -/* > \verbatim */ -/* > SQRE is INTEGER */ -/* > = 0: then the input matrix is N-by-N. */ -/* > = 1: then the input matrix is N-by-(N+1) if UPLU = 'U' and */ -/* > (N+1)-by-N if UPLU = 'L'. */ -/* > */ -/* > The bidiagonal matrix has */ -/* > N = NL + NR + 1 rows and */ -/* > M = N + SQRE >= N columns. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > On entry, N specifies the number of rows and columns */ -/* > in the matrix. N must be at least 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] NCVT */ -/* > \verbatim */ -/* > NCVT is INTEGER */ -/* > On entry, NCVT specifies the number of columns of */ -/* > the matrix VT. NCVT must be at least 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] NRU */ -/* > \verbatim */ -/* > NRU is INTEGER */ -/* > On entry, NRU specifies the number of rows of */ -/* > the matrix U. NRU must be at least 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] NCC */ -/* > \verbatim */ -/* > NCC is INTEGER */ -/* > On entry, NCC specifies the number of columns of */ -/* > the matrix C. NCC must be at least 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension (N) */ -/* > On entry, D contains the diagonal entries of the */ -/* > bidiagonal matrix whose SVD is desired. On normal exit, */ -/* > D contains the singular values in ascending order. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] E */ -/* > \verbatim */ -/* > E is DOUBLE PRECISION array. */ -/* > dimension is (N-1) if SQRE = 0 and N if SQRE = 1. */ -/* > On entry, the entries of E contain the offdiagonal entries */ -/* > of the bidiagonal matrix whose SVD is desired. On normal */ -/* > exit, E will contain 0. If the algorithm does not converge, */ -/* > D and E will contain the diagonal and superdiagonal entries */ -/* > of a bidiagonal matrix orthogonally equivalent to the one */ -/* > given as input. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] VT */ -/* > \verbatim */ -/* > VT is DOUBLE PRECISION array, dimension (LDVT, NCVT) */ -/* > On entry, contains a matrix which on exit has been */ -/* > premultiplied by P**T, dimension N-by-NCVT if SQRE = 0 */ -/* > and (N+1)-by-NCVT if SQRE = 1 (not referenced if NCVT=0). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDVT */ -/* > \verbatim */ -/* > LDVT is INTEGER */ -/* > On entry, LDVT specifies the leading dimension of VT as */ -/* > declared in the calling (sub) program. LDVT must be at */ -/* > least 1. If NCVT is nonzero LDVT must also be at least N. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] U */ -/* > \verbatim */ -/* > U is DOUBLE PRECISION array, dimension (LDU, N) */ -/* > On entry, contains a matrix which on exit has been */ -/* > postmultiplied by Q, dimension NRU-by-N if SQRE = 0 */ -/* > and NRU-by-(N+1) if SQRE = 1 (not referenced if NRU=0). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDU */ -/* > \verbatim */ -/* > LDU is INTEGER */ -/* > On entry, LDU specifies the leading dimension of U as */ -/* > declared in the calling (sub) program. LDU must be at */ -/* > least max( 1, NRU ) . */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] C */ -/* > \verbatim */ -/* > C is DOUBLE PRECISION array, dimension (LDC, NCC) */ -/* > On entry, contains an N-by-NCC matrix which on exit */ -/* > has been premultiplied by Q**T dimension N-by-NCC if SQRE = 0 */ -/* > and (N+1)-by-NCC if SQRE = 1 (not referenced if NCC=0). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDC */ -/* > \verbatim */ -/* > LDC is INTEGER */ -/* > On entry, LDC specifies the leading dimension of C as */ -/* > declared in the calling (sub) program. LDC must be at */ -/* > least 1. If NCC is nonzero, LDC must also be at least N. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (4*N) */ -/* > Workspace. Only referenced if one of NCVT, NRU, or NCC is */ -/* > nonzero, and if N is at least 2. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > On exit, a value of 0 indicates a successful exit. */ -/* > If INFO < 0, argument number -INFO is illegal. */ -/* > If INFO > 0, the algorithm did not converge, and INFO */ -/* > specifies how many superdiagonals did not converge. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup OTHERauxiliary */ - -/* > \par Contributors: */ -/* ================== */ -/* > */ -/* > Ming Gu and Huan Ren, Computer Science Division, University of */ -/* > California at Berkeley, USA */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dlasdq_(char *uplo, integer *sqre, integer *n, integer * - ncvt, integer *nru, integer *ncc, doublereal *d__, doublereal *e, - doublereal *vt, integer *ldvt, doublereal *u, integer *ldu, - doublereal *c__, integer *ldc, doublereal *work, integer *info, - ftnlen uplo_len) +int dlasdq_(char *uplo, integer *sqre, integer *n, integer *ncvt, integer *nru, integer *ncc, + doublereal *d__, doublereal *e, doublereal *vt, integer *ldvt, doublereal *u, + integer *ldu, doublereal *c__, integer *ldc, doublereal *work, integer *info, + ftnlen uplo_len) { - /* System generated locals */ - integer c_dim1, c_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1, - i__2; - - /* Local variables */ + integer c_dim1, c_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1, i__2; integer i__, j; doublereal r__, cs, sn; integer np1, isub; doublereal smin; integer sqre1; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int dlasr_(char *, char *, char *, integer *, - integer *, doublereal *, doublereal *, doublereal *, integer *, - ftnlen, ftnlen, ftnlen), dswap_(integer *, doublereal *, integer * - , doublereal *, integer *); + extern int dlasr_(char *, char *, char *, integer *, integer *, doublereal *, doublereal *, + doublereal *, integer *, ftnlen, ftnlen, ftnlen), + dswap_(integer *, doublereal *, integer *, doublereal *, integer *); integer iuplo; - extern /* Subroutine */ int dlartg_(doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *), xerbla_(char *, - integer *, ftnlen), dbdsqr_(char *, integer *, integer *, integer - *, integer *, doublereal *, doublereal *, doublereal *, integer *, - doublereal *, integer *, doublereal *, integer *, doublereal *, - integer *, ftnlen); + extern int dlartg_(doublereal *, doublereal *, doublereal *, doublereal *, doublereal *), + xerbla_(char *, integer *, ftnlen), + dbdsqr_(char *, integer *, integer *, integer *, integer *, doublereal *, doublereal *, + doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, + doublereal *, integer *, ftnlen); logical rotate; - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ --d__; --e; vt_dim1 = *ldvt; @@ -300,8 +37,6 @@ f"> */ c_offset = 1 + c_dim1; c__ -= c_offset; --work; - - /* Function Body */ *info = 0; iuplo = 0; if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { @@ -322,11 +57,11 @@ f"> */ *info = -5; } else if (*ncc < 0) { *info = -6; - } else if (*ncvt == 0 && *ldvt < 1 || *ncvt > 0 && *ldvt < max(1,*n)) { + } else if (*ncvt == 0 && *ldvt < 1 || *ncvt > 0 && *ldvt < max(1, *n)) { *info = -10; - } else if (*ldu < max(1,*nru)) { + } else if (*ldu < max(1, *nru)) { *info = -12; - } else if (*ncc == 0 && *ldc < 1 || *ncc > 0 && *ldc < max(1,*n)) { + } else if (*ncc == 0 && *ldc < 1 || *ncc > 0 && *ldc < max(1, *n)) { *info = -14; } if (*info != 0) { @@ -337,16 +72,9 @@ f"> */ if (*n == 0) { return 0; } - -/* ROTATE is true if any singular vectors desired, false otherwise */ - rotate = *ncvt > 0 || *nru > 0 || *ncc > 0; np1 = *n + 1; sqre1 = *sqre; - -/* If matrix non-square upper bidiagonal, rotate to be lower */ -/* bidiagonal. The rotations are on the right. */ - if (iuplo == 1 && sqre1 == 1) { i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { @@ -358,7 +86,6 @@ f"> */ work[i__] = cs; work[*n + i__] = sn; } -/* L10: */ } dlartg_(&d__[*n], &e[*n], &cs, &sn, &r__); d__[*n] = r__; @@ -369,18 +96,11 @@ f"> */ } iuplo = 2; sqre1 = 0; - -/* Update singular vectors if desired. */ - if (*ncvt > 0) { - dlasr_((char *)"L", (char *)"V", (char *)"F", &np1, ncvt, &work[1], &work[np1], &vt[ - vt_offset], ldvt, (ftnlen)1, (ftnlen)1, (ftnlen)1); + dlasr_((char *)"L", (char *)"V", (char *)"F", &np1, ncvt, &work[1], &work[np1], &vt[vt_offset], ldvt, (ftnlen)1, + (ftnlen)1, (ftnlen)1); } } - -/* If matrix lower bidiagonal, rotate to be upper bidiagonal */ -/* by applying Givens rotations on the left. */ - if (iuplo == 2) { i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { @@ -392,12 +112,7 @@ f"> */ work[i__] = cs; work[*n + i__] = sn; } -/* L20: */ } - -/* If matrix (N+1)-by-N lower bidiagonal, one additional */ -/* rotation is needed. */ - if (sqre1 == 1) { dlartg_(&d__[*n], &e[*n], &cs, &sn, &r__); d__[*n] = r__; @@ -406,43 +121,29 @@ f"> */ work[*n + *n] = sn; } } - -/* Update singular vectors if desired. */ - if (*nru > 0) { if (sqre1 == 0) { - dlasr_((char *)"R", (char *)"V", (char *)"F", nru, n, &work[1], &work[np1], &u[ - u_offset], ldu, (ftnlen)1, (ftnlen)1, (ftnlen)1); + dlasr_((char *)"R", (char *)"V", (char *)"F", nru, n, &work[1], &work[np1], &u[u_offset], ldu, (ftnlen)1, + (ftnlen)1, (ftnlen)1); } else { - dlasr_((char *)"R", (char *)"V", (char *)"F", nru, &np1, &work[1], &work[np1], &u[ - u_offset], ldu, (ftnlen)1, (ftnlen)1, (ftnlen)1); + dlasr_((char *)"R", (char *)"V", (char *)"F", nru, &np1, &work[1], &work[np1], &u[u_offset], ldu, (ftnlen)1, + (ftnlen)1, (ftnlen)1); } } if (*ncc > 0) { if (sqre1 == 0) { - dlasr_((char *)"L", (char *)"V", (char *)"F", n, ncc, &work[1], &work[np1], &c__[ - c_offset], ldc, (ftnlen)1, (ftnlen)1, (ftnlen)1); + dlasr_((char *)"L", (char *)"V", (char *)"F", n, ncc, &work[1], &work[np1], &c__[c_offset], ldc, (ftnlen)1, + (ftnlen)1, (ftnlen)1); } else { - dlasr_((char *)"L", (char *)"V", (char *)"F", &np1, ncc, &work[1], &work[np1], &c__[ - c_offset], ldc, (ftnlen)1, (ftnlen)1, (ftnlen)1); + dlasr_((char *)"L", (char *)"V", (char *)"F", &np1, ncc, &work[1], &work[np1], &c__[c_offset], ldc, + (ftnlen)1, (ftnlen)1, (ftnlen)1); } } } - -/* Call DBDSQR to compute the SVD of the reduced real */ -/* N-by-N upper bidiagonal matrix. */ - - dbdsqr_((char *)"U", n, ncvt, nru, ncc, &d__[1], &e[1], &vt[vt_offset], ldvt, &u[ - u_offset], ldu, &c__[c_offset], ldc, &work[1], info, (ftnlen)1); - -/* Sort the singular values into ascending order (insertion sort on */ -/* singular values, but only one transposition per singular vector) */ - + dbdsqr_((char *)"U", n, ncvt, nru, ncc, &d__[1], &e[1], &vt[vt_offset], ldvt, &u[u_offset], ldu, + &c__[c_offset], ldc, &work[1], info, (ftnlen)1); i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { - -/* Scan for smallest D(I). */ - isub = i__; smin = d__[i__]; i__2 = *n; @@ -451,36 +152,23 @@ f"> */ isub = j; smin = d__[j]; } -/* L30: */ } if (isub != i__) { - -/* Swap singular values and vectors. */ - d__[isub] = d__[i__]; d__[i__] = smin; if (*ncvt > 0) { - dswap_(ncvt, &vt[isub + vt_dim1], ldvt, &vt[i__ + vt_dim1], - ldvt); + dswap_(ncvt, &vt[isub + vt_dim1], ldvt, &vt[i__ + vt_dim1], ldvt); } if (*nru > 0) { - dswap_(nru, &u[isub * u_dim1 + 1], &c__1, &u[i__ * u_dim1 + 1] - , &c__1); + dswap_(nru, &u[isub * u_dim1 + 1], &c__1, &u[i__ * u_dim1 + 1], &c__1); } if (*ncc > 0) { - dswap_(ncc, &c__[isub + c_dim1], ldc, &c__[i__ + c_dim1], ldc) - ; + dswap_(ncc, &c__[isub + c_dim1], ldc, &c__[i__ + c_dim1], ldc); } } -/* L40: */ } - return 0; - -/* End of DLASDQ */ - -} /* dlasdq_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlasdt.cpp b/lib/linalg/dlasdt.cpp index 77edcf93d4..ddc7df74ba 100644 --- a/lib/linalg/dlasdt.cpp +++ b/lib/linalg/dlasdt.cpp @@ -1,172 +1,21 @@ -/* fortran/dlasdt.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DLASDT creates a tree of subproblems for bidiagonal divide and conquer. Used by sbdsdc. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLASDT + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLASDT( N, LVL, ND, INODE, NDIML, NDIMR, MSUB ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER LVL, MSUB, N, ND */ -/* .. */ -/* .. Array Arguments .. */ -/* INTEGER INODE( * ), NDIML( * ), NDIMR( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLASDT creates a tree of subproblems for bidiagonal divide and */ -/* > conquer. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > On entry, the number of diagonal elements of the */ -/* > bidiagonal matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] LVL */ -/* > \verbatim */ -/* > LVL is INTEGER */ -/* > On exit, the number of levels on the computation tree. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] ND */ -/* > \verbatim */ -/* > ND is INTEGER */ -/* > On exit, the number of nodes on the tree. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INODE */ -/* > \verbatim */ -/* > INODE is INTEGER array, dimension ( N ) */ -/* > On exit, centers of subproblems. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] NDIML */ -/* > \verbatim */ -/* > NDIML is INTEGER array, dimension ( N ) */ -/* > On exit, row dimensions of left children. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] NDIMR */ -/* > \verbatim */ -/* > NDIMR is INTEGER array, dimension ( N ) */ -/* > On exit, row dimensions of right children. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] MSUB */ -/* > \verbatim */ -/* > MSUB is INTEGER */ -/* > On entry, the maximum row dimension each subproblem at the */ -/* > bottom of the tree can be of. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup OTHERauxiliary */ - -/* > \par Contributors: */ -/* ================== */ -/* > */ -/* > Ming Gu and Huan Ren, Computer Science Division, University of */ -/* > California at Berkeley, USA */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dlasdt_(integer *n, integer *lvl, integer *nd, integer * - inode, integer *ndiml, integer *ndimr, integer *msub) +int dlasdt_(integer *n, integer *lvl, integer *nd, integer *inode, integer *ndiml, integer *ndimr, + integer *msub) { - /* System generated locals */ integer i__1, i__2; - - /* Builtin functions */ double log(doublereal); - - /* Local variables */ integer i__, il, ir, maxn; doublereal temp; integer nlvl, llst, ncrnt; - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Find the number of levels on the tree. */ - - /* Parameter adjustments */ --ndimr; --ndiml; --inode; - - /* Function Body */ - maxn = max(1,*n); - temp = log((doublereal) maxn / (doublereal) (*msub + 1)) / log(2.); - *lvl = (integer) temp + 1; - + maxn = max(1, *n); + temp = log((doublereal)maxn / (doublereal)(*msub + 1)) / log(2.); + *lvl = (integer)temp + 1; i__ = *n / 2; inode[1] = i__ + 1; ndiml[1] = i__; @@ -176,10 +25,6 @@ f"> */ llst = 1; i__1 = *lvl - 1; for (nlvl = 1; nlvl <= i__1; ++nlvl) { - -/* Constructing the tree at (NLVL+1)-st level. The number of */ -/* nodes created on this level is LLST * 2. */ - i__2 = llst - 1; for (i__ = 0; i__ <= i__2; ++i__) { il += 2; @@ -191,19 +36,12 @@ f"> */ ndiml[ir] = ndimr[ncrnt] / 2; ndimr[ir] = ndimr[ncrnt] - ndiml[ir] - 1; inode[ir] = inode[ncrnt] + ndiml[ir] + 1; -/* L10: */ } llst <<= 1; -/* L20: */ } *nd = (llst << 1) - 1; - return 0; - -/* End of DLASDT */ - -} /* dlasdt_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlaset.cpp b/lib/linalg/dlaset.cpp index 4323f948e4..b3cea88292 100644 --- a/lib/linalg/dlaset.cpp +++ b/lib/linalg/dlaset.cpp @@ -1,229 +1,48 @@ -/* fortran/dlaset.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given val -ues. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLASET + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLASET( UPLO, M, N, ALPHA, BETA, A, LDA ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER UPLO */ -/* INTEGER LDA, M, N */ -/* DOUBLE PRECISION ALPHA, BETA */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLASET initializes an m-by-n matrix A to BETA on the diagonal and */ -/* > ALPHA on the offdiagonals. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > Specifies the part of the matrix A to be set. */ -/* > = 'U': Upper triangular part is set; the strictly lower */ -/* > triangular part of A is not changed. */ -/* > = 'L': Lower triangular part is set; the strictly upper */ -/* > triangular part of A is not changed. */ -/* > Otherwise: All of the matrix A is set. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix A. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] ALPHA */ -/* > \verbatim */ -/* > ALPHA is DOUBLE PRECISION */ -/* > The constant to which the offdiagonal elements are to be set. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] BETA */ -/* > \verbatim */ -/* > BETA is DOUBLE PRECISION */ -/* > The constant to which the diagonal elements are to be set. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On exit, the leading m-by-n submatrix of A is set as follows: */ -/* > */ -/* > if UPLO = 'U', A(i,j) = ALPHA, 1<=i<=j-1, 1<=j<=n, */ -/* > if UPLO = 'L', A(i,j) = ALPHA, j+1<=i<=m, 1<=j<=n, */ -/* > otherwise, A(i,j) = ALPHA, 1<=i<=m, 1<=j<=n, i.ne.j, */ -/* > */ -/* > and, for all UPLO, A(i,i) = BETA, 1<=i<=min(m,n). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,M). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup OTHERauxiliary */ - -/* ===================================================================== */ -/* Subroutine */ int dlaset_(char *uplo, integer *m, integer *n, doublereal * - alpha, doublereal *beta, doublereal *a, integer *lda, ftnlen uplo_len) +int dlaset_(char *uplo, integer *m, integer *n, doublereal *alpha, doublereal *beta, doublereal *a, + integer *lda, ftnlen uplo_len) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; - - /* Local variables */ integer i__, j; extern logical lsame_(char *, char *, ftnlen, ftnlen); - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; - - /* Function Body */ if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { - -/* Set the strictly upper triangular or trapezoidal part of the */ -/* array to ALPHA. */ - i__1 = *n; for (j = 2; j <= i__1; ++j) { -/* Computing MIN */ i__3 = j - 1; - i__2 = min(i__3,*m); + i__2 = min(i__3, *m); for (i__ = 1; i__ <= i__2; ++i__) { a[i__ + j * a_dim1] = *alpha; -/* L10: */ } -/* L20: */ } - } else if (lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { - -/* Set the strictly lower triangular or trapezoidal part of the */ -/* array to ALPHA. */ - - i__1 = min(*m,*n); + i__1 = min(*m, *n); for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = j + 1; i__ <= i__2; ++i__) { a[i__ + j * a_dim1] = *alpha; -/* L30: */ } -/* L40: */ } - } else { - -/* Set the leading m-by-n submatrix to ALPHA. */ - i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { a[i__ + j * a_dim1] = *alpha; -/* L50: */ } -/* L60: */ } } - -/* Set the first min(M,N) diagonal elements to BETA. */ - - i__1 = min(*m,*n); + i__1 = min(*m, *n); for (i__ = 1; i__ <= i__1; ++i__) { a[i__ + i__ * a_dim1] = *beta; -/* L70: */ } - return 0; - -/* End of DLASET */ - -} /* dlaset_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlasq1.cpp b/lib/linalg/dlasq1.cpp index 0c9e0ca9f2..1a719c6ee3 100644 --- a/lib/linalg/dlasq1.cpp +++ b/lib/linalg/dlasq1.cpp @@ -1,195 +1,33 @@ -/* fortran/dlasq1.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static integer c__2 = 2; static integer c__0 = 0; - -/* > \brief \b DLASQ1 computes the singular values of a real square bidiagonal matrix. Used by sbdsqr. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLASQ1 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLASQ1( N, D, E, WORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INFO, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION D( * ), E( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLASQ1 computes the singular values of a real N-by-N bidiagonal */ -/* > matrix with diagonal D and off-diagonal E. The singular values */ -/* > are computed to high relative accuracy, in the absence of */ -/* > denormalization, underflow and overflow. The algorithm was first */ -/* > presented in */ -/* > */ -/* > (char *)"Accurate singular values and differential qd algorithms" by K. V. */ -/* > Fernando and B. N. Parlett, Numer. Math., Vol-67, No. 2, pp. 191-230, */ -/* > 1994, */ -/* > */ -/* > and the present implementation is described in "An implementation of */ -/* > the dqds Algorithm (Positive Case)", LAPACK Working Note. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of rows and columns in the matrix. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension (N) */ -/* > On entry, D contains the diagonal elements of the */ -/* > bidiagonal matrix whose SVD is desired. On normal exit, */ -/* > D contains the singular values in decreasing order. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] E */ -/* > \verbatim */ -/* > E is DOUBLE PRECISION array, dimension (N) */ -/* > On entry, elements E(1:N-1) contain the off-diagonal elements */ -/* > of the bidiagonal matrix whose SVD is desired. */ -/* > On exit, E is overwritten. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (4*N) */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > > 0: the algorithm failed */ -/* > = 1, a split was marked by a positive value in E */ -/* > = 2, current block of Z not diagonalized after 100*N */ -/* > iterations (in inner while loop) On exit D and E */ -/* > represent a matrix with the same singular values */ -/* > which the calling subroutine could use to finish the */ -/* > computation, or even feed back into DLASQ1 */ -/* > = 3, termination criterion of outer while loop not met */ -/* > (program created more than N unreduced blocks) */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup auxOTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dlasq1_(integer *n, doublereal *d__, doublereal *e, - doublereal *work, integer *info) +int dlasq1_(integer *n, doublereal *d__, doublereal *e, doublereal *work, integer *info) { - /* System generated locals */ integer i__1, i__2; doublereal d__1, d__2, d__3; - - /* Builtin functions */ double sqrt(doublereal); - - /* Local variables */ integer i__; doublereal eps; - extern /* Subroutine */ int dlas2_(doublereal *, doublereal *, doublereal - *, doublereal *, doublereal *); + extern int dlas2_(doublereal *, doublereal *, doublereal *, doublereal *, doublereal *); doublereal scale; integer iinfo; doublereal sigmn; - extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, - doublereal *, integer *); + extern int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *); doublereal sigmx; - extern /* Subroutine */ int dlasq2_(integer *, doublereal *, integer *); + extern int dlasq2_(integer *, doublereal *, integer *); extern doublereal dlamch_(char *, ftnlen); - extern /* Subroutine */ int dlascl_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, integer *, doublereal *, - integer *, integer *, ftnlen); + extern int dlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, + integer *, doublereal *, integer *, integer *, ftnlen); doublereal safmin; - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), dlasrt_( - char *, integer *, doublereal *, integer *, ftnlen); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - - /* Parameter adjustments */ + extern int xerbla_(char *, integer *, ftnlen), + dlasrt_(char *, integer *, doublereal *, integer *, ftnlen); --work; --e; --d__; - - /* Function Body */ *info = 0; if (*n < 0) { *info = -1; @@ -207,38 +45,23 @@ f"> */ d__[2] = sigmn; return 0; } - -/* Estimate the largest singular value. */ - sigmx = 0.; i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { d__[i__] = (d__1 = d__[i__], abs(d__1)); -/* Computing MAX */ d__2 = sigmx, d__3 = (d__1 = e[i__], abs(d__1)); - sigmx = max(d__2,d__3); -/* L10: */ + sigmx = max(d__2, d__3); } d__[*n] = (d__1 = d__[*n], abs(d__1)); - -/* Early return if SIGMX is zero (matrix is already diagonal). */ - if (sigmx == 0.) { dlasrt_((char *)"D", n, &d__[1], &iinfo, (ftnlen)1); return 0; } - i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { -/* Computing MAX */ d__1 = sigmx, d__2 = d__[i__]; - sigmx = max(d__1,d__2); -/* L20: */ + sigmx = max(d__1, d__2); } - -/* Copy D and E into WORK (in the Z format) and scale (squaring the */ -/* input data makes scaling by a power of the radix pointless). */ - eps = dlamch_((char *)"Precision", (ftnlen)9); safmin = dlamch_((char *)"Safe minimum", (ftnlen)12); scale = sqrt(eps / safmin); @@ -247,52 +70,31 @@ f"> */ dcopy_(&i__1, &e[1], &c__1, &work[2], &c__2); i__1 = (*n << 1) - 1; i__2 = (*n << 1) - 1; - dlascl_((char *)"G", &c__0, &c__0, &sigmx, &scale, &i__1, &c__1, &work[1], &i__2, - &iinfo, (ftnlen)1); - -/* Compute the q's and e's. */ - + dlascl_((char *)"G", &c__0, &c__0, &sigmx, &scale, &i__1, &c__1, &work[1], &i__2, &iinfo, (ftnlen)1); i__1 = (*n << 1) - 1; for (i__ = 1; i__ <= i__1; ++i__) { -/* Computing 2nd power */ d__1 = work[i__]; work[i__] = d__1 * d__1; -/* L30: */ } work[*n * 2] = 0.; - dlasq2_(n, &work[1], info); - if (*info == 0) { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { d__[i__] = sqrt(work[i__]); -/* L40: */ } - dlascl_((char *)"G", &c__0, &c__0, &scale, &sigmx, n, &c__1, &d__[1], n, & - iinfo, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &scale, &sigmx, n, &c__1, &d__[1], n, &iinfo, (ftnlen)1); } else if (*info == 2) { - -/* Maximum number of iterations exceeded. Move data from WORK */ -/* into D and E so the calling subroutine can try to finish */ - i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { d__[i__] = sqrt(work[(i__ << 1) - 1]); e[i__] = sqrt(work[i__ * 2]); } - dlascl_((char *)"G", &c__0, &c__0, &scale, &sigmx, n, &c__1, &d__[1], n, & - iinfo, (ftnlen)1); - dlascl_((char *)"G", &c__0, &c__0, &scale, &sigmx, n, &c__1, &e[1], n, &iinfo, - (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &scale, &sigmx, n, &c__1, &d__[1], n, &iinfo, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &scale, &sigmx, n, &c__1, &e[1], n, &iinfo, (ftnlen)1); } - return 0; - -/* End of DLASQ1 */ - -} /* dlasq1_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlasq2.cpp b/lib/linalg/dlasq2.cpp index c9e4b30884..37bc963975 100644 --- a/lib/linalg/dlasq2.cpp +++ b/lib/linalg/dlasq2.cpp @@ -1,152 +1,17 @@ -/* fortran/dlasq2.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static integer c__2 = 2; static integer c__10 = 10; static integer c__3 = 3; static integer c__4 = 4; - -/* > \brief \b DLASQ2 computes all the eigenvalues of the symmetric positive definite tridiagonal matrix assoc -iated with the qd Array Z to high relative accuracy. Used by sbdsqr and sstegr. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLASQ2 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLASQ2( N, Z, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INFO, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION Z( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLASQ2 computes all the eigenvalues of the symmetric positive */ -/* > definite tridiagonal matrix associated with the qd array Z to high */ -/* > relative accuracy are computed to high relative accuracy, in the */ -/* > absence of denormalization, underflow and overflow. */ -/* > */ -/* > To see the relation of Z to the tridiagonal matrix, let L be a */ -/* > unit lower bidiagonal matrix with subdiagonals Z(2,4,6,,..) and */ -/* > let U be an upper bidiagonal matrix with 1's above and diagonal */ -/* > Z(1,3,5,,..). The tridiagonal is L*U or, if you prefer, the */ -/* > symmetric tridiagonal to which it is similar. */ -/* > */ -/* > Note : DLASQ2 defines a logical variable, IEEE, which is true */ -/* > on machines which follow ieee-754 floating-point standard in their */ -/* > handling of infinities and NaNs, and false otherwise. This variable */ -/* > is passed to DLASQ3. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of rows and columns in the matrix. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] Z */ -/* > \verbatim */ -/* > Z is DOUBLE PRECISION array, dimension ( 4*N ) */ -/* > On entry Z holds the qd array. On exit, entries 1 to N hold */ -/* > the eigenvalues in decreasing order, Z( 2*N+1 ) holds the */ -/* > trace, and Z( 2*N+2 ) holds the sum of the eigenvalues. If */ -/* > N > 2, then Z( 2*N+3 ) holds the iteration count, Z( 2*N+4 ) */ -/* > holds NDIVS/NIN^2, and Z( 2*N+5 ) holds the percentage of */ -/* > shifts that failed. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if the i-th argument is a scalar and had an illegal */ -/* > value, then INFO = -i, if the i-th argument is an */ -/* > array and the j-entry had an illegal value, then */ -/* > INFO = -(i*100+j) */ -/* > > 0: the algorithm failed */ -/* > = 1, a split was marked by a positive value in E */ -/* > = 2, current block of Z not diagonalized after 100*N */ -/* > iterations (in inner while loop). On exit Z holds */ -/* > a qd array with the same eigenvalues as the given Z. */ -/* > = 3, termination criterion of outer while loop not met */ -/* > (program created more than N unreduced blocks) */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup auxOTHERcomputational */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > Local Variables: I0:N0 defines a current unreduced segment of Z. */ -/* > The shifts are accumulated in SIGMA. Iteration count is in ITER. */ -/* > Ping-pong is controlled by PP (alternates between 0 and 1). */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dlasq2_(integer *n, doublereal *z__, integer *info) +int dlasq2_(integer *n, doublereal *z__, integer *info) { - /* System generated locals */ integer i__1, i__2, i__3; doublereal d__1, d__2; - - /* Builtin functions */ double sqrt(doublereal); - - /* Local variables */ doublereal d__, e, g; integer k; doublereal s, t; @@ -168,60 +33,25 @@ f"> */ integer iinfo; doublereal tempe, tempq; integer ttype; - extern /* Subroutine */ int dlasq3_(integer *, integer *, doublereal *, - integer *, doublereal *, doublereal *, doublereal *, doublereal *, - integer *, integer *, integer *, logical *, integer *, - doublereal *, doublereal *, doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *); + extern int dlasq3_(integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, + doublereal *, doublereal *, integer *, integer *, integer *, logical *, + integer *, doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *); extern doublereal dlamch_(char *, ftnlen); doublereal deemin; integer iwhila, iwhilb; doublereal oldemn, safmin; - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - extern /* Subroutine */ int dlasrt_(char *, integer *, doublereal *, - integer *, ftnlen); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments. */ -/* (in case DLASQ2 is not called by DLASQ1) */ - - /* Parameter adjustments */ + extern int xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); + extern int dlasrt_(char *, integer *, doublereal *, integer *, ftnlen); --z__; - - /* Function Body */ *info = 0; eps = dlamch_((char *)"Precision", (ftnlen)9); safmin = dlamch_((char *)"Safe minimum", (ftnlen)12); tol = eps * 100.; -/* Computing 2nd power */ d__1 = tol; tol2 = d__1 * d__1; - if (*n < 0) { *info = -1; xerbla_((char *)"DLASQ2", &c__1, (ftnlen)6); @@ -229,18 +59,12 @@ f"> */ } else if (*n == 0) { return 0; } else if (*n == 1) { - -/* 1-by-1 case. */ - if (z__[1] < 0.) { *info = -201; xerbla_((char *)"DLASQ2", &c__2, (ftnlen)6); } return 0; } else if (*n == 2) { - -/* 2-by-2 case. */ - if (z__[1] < 0.) { *info = -201; xerbla_((char *)"DLASQ2", &c__2, (ftnlen)6); @@ -275,16 +99,12 @@ f"> */ z__[6] = z__[2] + z__[1]; return 0; } - -/* Check for negative data and compute sums of q's and e's. */ - z__[*n * 2] = 0.; emin = z__[2]; qmax = 0.; zmax = 0.; d__ = 0.; e = 0.; - i__1 = *n - 1 << 1; for (k = 1; k <= i__1; k += 2) { if (z__[k] < 0.) { @@ -298,16 +118,12 @@ f"> */ } d__ += z__[k]; e += z__[k + 1]; -/* Computing MAX */ d__1 = qmax, d__2 = z__[k]; - qmax = max(d__1,d__2); -/* Computing MIN */ + qmax = max(d__1, d__2); d__1 = emin, d__2 = z__[k + 1]; - emin = min(d__1,d__2); -/* Computing MAX */ - d__1 = max(qmax,zmax), d__2 = z__[k + 1]; - zmax = max(d__1,d__2); -/* L10: */ + emin = min(d__1, d__2); + d__1 = max(qmax, zmax), d__2 = z__[k + 1]; + zmax = max(d__1, d__2); } if (z__[(*n << 1) - 1] < 0.) { *info = -((*n << 1) + 199); @@ -315,53 +131,32 @@ f"> */ return 0; } d__ += z__[(*n << 1) - 1]; -/* Computing MAX */ d__1 = qmax, d__2 = z__[(*n << 1) - 1]; - qmax = max(d__1,d__2); - zmax = max(qmax,zmax); - -/* Check for diagonality. */ - + qmax = max(d__1, d__2); + zmax = max(qmax, zmax); if (e == 0.) { i__1 = *n; for (k = 2; k <= i__1; ++k) { z__[k] = z__[(k << 1) - 1]; -/* L20: */ } dlasrt_((char *)"D", n, &z__[1], &iinfo, (ftnlen)1); z__[(*n << 1) - 1] = d__; return 0; } - trace = d__ + e; - -/* Check for zero data. */ - if (trace == 0.) { z__[(*n << 1) - 1] = 0.; return 0; } - -/* Check whether the machine is IEEE conformable. */ - - ieee = ilaenv_(&c__10, (char *)"DLASQ2", (char *)"N", &c__1, &c__2, &c__3, &c__4, (ftnlen) - 6, (ftnlen)1) == 1; - -/* Rearrange data for locality: Z=(q1,qq1,e1,ee1,q2,qq2,e2,ee2,...). */ - + ieee = ilaenv_(&c__10, (char *)"DLASQ2", (char *)"N", &c__1, &c__2, &c__3, &c__4, (ftnlen)6, (ftnlen)1) == 1; for (k = *n << 1; k >= 2; k += -2) { z__[k * 2] = 0.; z__[(k << 1) - 1] = z__[k]; z__[(k << 1) - 2] = 0.; z__[(k << 1) - 3] = z__[k - 1]; -/* L30: */ } - i0 = 1; n0 = *n; - -/* Reverse the qd-array, if warranted. */ - if (z__[(i0 << 2) - 3] * 1.5 < z__[(n0 << 2) - 3]) { ipn4 = i0 + n0 << 2; i__1 = i0 + n0 - 1 << 1; @@ -372,16 +167,10 @@ f"> */ temp = z__[i4 - 1]; z__[i4 - 1] = z__[ipn4 - i4 - 5]; z__[ipn4 - i4 - 5] = temp; -/* L40: */ } } - -/* Initial split checking via dqd and Li's test. */ - pp = 0; - for (k = 1; k <= 2; ++k) { - d__ = z__[(n0 << 2) + pp - 3]; i__1 = (i0 << 2) + pp; for (i4 = (n0 - 1 << 2) + pp; i4 >= i__1; i4 += -4) { @@ -391,11 +180,7 @@ f"> */ } else { d__ = z__[i4 - 3] * (d__ / (d__ + z__[i4 - 1])); } -/* L50: */ } - -/* dqd maps Z to ZZ plus Li's test. */ - emin = z__[(i0 << 2) + pp + 1]; d__ = z__[(i0 << 2) + pp - 3]; i__1 = (n0 - 1 << 2) + pp; @@ -407,41 +192,26 @@ f"> */ z__[i4 - (pp << 1)] = 0.; d__ = z__[i4 + 1]; } else if (safmin * z__[i4 + 1] < z__[i4 - (pp << 1) - 2] && - safmin * z__[i4 - (pp << 1) - 2] < z__[i4 + 1]) { + safmin * z__[i4 - (pp << 1) - 2] < z__[i4 + 1]) { temp = z__[i4 + 1] / z__[i4 - (pp << 1) - 2]; z__[i4 - (pp << 1)] = z__[i4 - 1] * temp; d__ *= temp; } else { - z__[i4 - (pp << 1)] = z__[i4 + 1] * (z__[i4 - 1] / z__[i4 - ( - pp << 1) - 2]); + z__[i4 - (pp << 1)] = z__[i4 + 1] * (z__[i4 - 1] / z__[i4 - (pp << 1) - 2]); d__ = z__[i4 + 1] * (d__ / z__[i4 - (pp << 1) - 2]); } -/* Computing MIN */ d__1 = emin, d__2 = z__[i4 - (pp << 1)]; - emin = min(d__1,d__2); -/* L60: */ + emin = min(d__1, d__2); } z__[(n0 << 2) - pp - 2] = d__; - -/* Now find qmax. */ - qmax = z__[(i0 << 2) - pp - 2]; i__1 = (n0 << 2) - pp - 2; for (i4 = (i0 << 2) - pp + 2; i4 <= i__1; i4 += 4) { -/* Computing MAX */ d__1 = qmax, d__2 = z__[i4]; - qmax = max(d__1,d__2); -/* L70: */ + qmax = max(d__1, d__2); } - -/* Prepare for the next iteration on K. */ - pp = 1 - pp; -/* L80: */ } - -/* Initialise variables to pass to DLASQ3. */ - ttype = 0; dmin1 = 0.; dmin2 = 0.; @@ -450,22 +220,14 @@ f"> */ dn2 = 0.; g = 0.; tau = 0.; - iter = 2; nfail = 0; ndiv = n0 - i0 << 1; - i__1 = *n + 1; for (iwhila = 1; iwhila <= i__1; ++iwhila) { if (n0 < 1) { goto L170; } - -/* While array unfinished do */ - -/* E(N0) holds the value of SIGMA when submatrix in I0:N0 */ -/* splits from the rest of the array, but is negated. */ - desig = 0.; if (n0 == *n) { sigma = 0.; @@ -476,10 +238,6 @@ f"> */ *info = 1; return 0; } - -/* Find last unreduced submatrix's top index I0, find QMAX and */ -/* EMIN. Find Gershgorin-type bound if Q's much greater than E's. */ - emax = 0.; if (n0 > i0) { emin = (d__1 = z__[(n0 << 2) - 5], abs(d__1)); @@ -493,27 +251,20 @@ f"> */ goto L100; } if (qmin >= emax * 4.) { -/* Computing MIN */ d__1 = qmin, d__2 = z__[i4 - 3]; - qmin = min(d__1,d__2); -/* Computing MAX */ + qmin = min(d__1, d__2); d__1 = emax, d__2 = z__[i4 - 5]; - emax = max(d__1,d__2); + emax = max(d__1, d__2); } -/* Computing MAX */ d__1 = qmax, d__2 = z__[i4 - 7] + z__[i4 - 5]; - qmax = max(d__1,d__2); -/* Computing MIN */ + qmax = max(d__1, d__2); d__1 = emin, d__2 = z__[i4 - 5]; - emin = min(d__1,d__2); -/* L90: */ + emin = min(d__1, d__2); } i4 = 4; - -L100: + L100: i0 = i4 / 4; pp = 0; - if (n0 - i0 > 1) { dee = z__[(i0 << 2) - 3]; deemin = dee; @@ -525,10 +276,8 @@ L100: deemin = dee; kmin = (i4 + 3) / 4; } -/* L110: */ } - if (kmin - i0 << 1 < n0 - kmin && deemin <= z__[(n0 << 2) - 3] * - .5) { + if (kmin - i0 << 1 < n0 - kmin && deemin <= z__[(n0 << 2) - 3] * .5) { ipn4 = i0 + n0 << 2; pp = 2; i__2 = i0 + n0 - 1 << 1; @@ -545,87 +294,53 @@ L100: temp = z__[i4]; z__[i4] = z__[ipn4 - i4 - 4]; z__[ipn4 - i4 - 4] = temp; -/* L120: */ } } } - -/* Put -(initial shift) into DMIN. */ - -/* Computing MAX */ d__1 = 0., d__2 = qmin - sqrt(qmin) * 2. * sqrt(emax); - dmin__ = -max(d__1,d__2); - -/* Now I0:N0 is unreduced. */ -/* PP = 0 for ping, PP = 1 for pong. */ -/* PP = 2 indicates that flipping was applied to the Z array and */ -/* and that the tests for deflation upon entry in DLASQ3 */ -/* should not be performed. */ - + dmin__ = -max(d__1, d__2); nbig = (n0 - i0 + 1) * 100; i__2 = nbig; for (iwhilb = 1; iwhilb <= i__2; ++iwhilb) { if (i0 > n0) { goto L150; } - -/* While submatrix unfinished take a good dqds step. */ - - dlasq3_(&i0, &n0, &z__[1], &pp, &dmin__, &sigma, &desig, &qmax, & - nfail, &iter, &ndiv, &ieee, &ttype, &dmin1, &dmin2, &dn, & - dn1, &dn2, &g, &tau); - + dlasq3_(&i0, &n0, &z__[1], &pp, &dmin__, &sigma, &desig, &qmax, &nfail, &iter, &ndiv, + &ieee, &ttype, &dmin1, &dmin2, &dn, &dn1, &dn2, &g, &tau); pp = 1 - pp; - -/* When EMIN is very small check for splits. */ - if (pp == 0 && n0 - i0 >= 3) { - if (z__[n0 * 4] <= tol2 * qmax || z__[(n0 << 2) - 1] <= tol2 * - sigma) { + if (z__[n0 * 4] <= tol2 * qmax || z__[(n0 << 2) - 1] <= tol2 * sigma) { splt = i0 - 1; qmax = z__[(i0 << 2) - 3]; emin = z__[(i0 << 2) - 1]; oldemn = z__[i0 * 4]; i__3 = n0 - 3 << 2; for (i4 = i0 << 2; i4 <= i__3; i4 += 4) { - if (z__[i4] <= tol2 * z__[i4 - 3] || z__[i4 - 1] <= - tol2 * sigma) { + if (z__[i4] <= tol2 * z__[i4 - 3] || z__[i4 - 1] <= tol2 * sigma) { z__[i4 - 1] = -sigma; splt = i4 / 4; qmax = 0.; emin = z__[i4 + 3]; oldemn = z__[i4 + 4]; } else { -/* Computing MAX */ d__1 = qmax, d__2 = z__[i4 + 1]; - qmax = max(d__1,d__2); -/* Computing MIN */ + qmax = max(d__1, d__2); d__1 = emin, d__2 = z__[i4 - 1]; - emin = min(d__1,d__2); -/* Computing MIN */ + emin = min(d__1, d__2); d__1 = oldemn, d__2 = z__[i4]; - oldemn = min(d__1,d__2); + oldemn = min(d__1, d__2); } -/* L130: */ } z__[(n0 << 2) - 1] = emin; z__[n0 * 4] = oldemn; i0 = splt + 1; } } - -/* L140: */ } - *info = 2; - -/* Maximum number of iterations exceeded, restore the shift */ -/* SIGMA and place the new d's and e's in a qd array. */ -/* This might need to be done for several blocks */ - i1 = i0; n1 = n0; -L145: + L145: tempq = z__[(i0 << 2) - 3]; z__[(i0 << 2) - 3] += sigma; i__2 = n0; @@ -633,15 +348,11 @@ L145: tempe = z__[(k << 2) - 5]; z__[(k << 2) - 5] *= tempq / z__[(k << 2) - 7]; tempq = z__[(k << 2) - 3]; - z__[(k << 2) - 3] = z__[(k << 2) - 3] + sigma + tempe - z__[(k << - 2) - 5]; + z__[(k << 2) - 3] = z__[(k << 2) - 3] + sigma + tempe - z__[(k << 2) - 5]; } - -/* Prepare to do this on the previous block if there is one */ - if (i1 > 1) { n1 = i1 - 1; - while(i1 >= 2 && z__[(i1 << 2) - 5] >= 0.) { + while (i1 >= 2 && z__[(i1 << 2) - 5] >= 0.) { --i1; } sigma = -z__[(n1 << 2) - 1]; @@ -650,11 +361,6 @@ L145: i__2 = *n; for (k = 1; k <= i__2; ++k) { z__[(k << 1) - 1] = z__[(k << 2) - 3]; - -/* Only the block 1..N0 is unfinished. The rest of the e's */ -/* must be essentially zero, although sometimes other data */ -/* has been stored in them. */ - if (k < n0) { z__[k * 2] = z__[(k << 2) - 1]; } else { @@ -662,55 +368,28 @@ L145: } } return 0; - -/* end IWHILB */ - -L150: - -/* L160: */ - ; + L150:; } - *info = 3; return 0; - -/* end IWHILA */ - L170: - -/* Move q's to the front. */ - i__1 = *n; for (k = 2; k <= i__1; ++k) { z__[k] = z__[(k << 2) - 3]; -/* L180: */ } - -/* Sort and compute sum of eigenvalues. */ - dlasrt_((char *)"D", n, &z__[1], &iinfo, (ftnlen)1); - e = 0.; for (k = *n; k >= 1; --k) { e += z__[k]; -/* L190: */ } - -/* Store trace, sum(eigenvalues) and information on performance. */ - z__[(*n << 1) + 1] = trace; z__[(*n << 1) + 2] = e; - z__[(*n << 1) + 3] = (doublereal) iter; -/* Computing 2nd power */ + z__[(*n << 1) + 3] = (doublereal)iter; i__1 = *n; - z__[(*n << 1) + 4] = (doublereal) ndiv / (doublereal) (i__1 * i__1); - z__[(*n << 1) + 5] = nfail * 100. / (doublereal) iter; + z__[(*n << 1) + 4] = (doublereal)ndiv / (doublereal)(i__1 * i__1); + z__[(*n << 1) + 5] = nfail * 100. / (doublereal)iter; return 0; - -/* End of DLASQ2 */ - -} /* dlasq2_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlasq3.cpp b/lib/linalg/dlasq3.cpp index f43c67ca34..62819cf77f 100644 --- a/lib/linalg/dlasq3.cpp +++ b/lib/linalg/dlasq3.cpp @@ -1,272 +1,37 @@ -/* fortran/dlasq3.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DLASQ3 checks for deflation, computes a shift and calls dqds. Used by sbdsqr. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLASQ3 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLASQ3( I0, N0, Z, PP, DMIN, SIGMA, DESIG, QMAX, NFAIL, */ -/* ITER, NDIV, IEEE, TTYPE, DMIN1, DMIN2, DN, DN1, */ -/* DN2, G, TAU ) */ - -/* .. Scalar Arguments .. */ -/* LOGICAL IEEE */ -/* INTEGER I0, ITER, N0, NDIV, NFAIL, PP */ -/* DOUBLE PRECISION DESIG, DMIN, DMIN1, DMIN2, DN, DN1, DN2, G, */ -/* $ QMAX, SIGMA, TAU */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION Z( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLASQ3 checks for deflation, computes a shift (TAU) and calls dqds. */ -/* > In case of failure it changes shifts, and tries again until output */ -/* > is positive. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] I0 */ -/* > \verbatim */ -/* > I0 is INTEGER */ -/* > First index. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] N0 */ -/* > \verbatim */ -/* > N0 is INTEGER */ -/* > Last index. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] Z */ -/* > \verbatim */ -/* > Z is DOUBLE PRECISION array, dimension ( 4*N0 ) */ -/* > Z holds the qd array. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] PP */ -/* > \verbatim */ -/* > PP is INTEGER */ -/* > PP=0 for ping, PP=1 for pong. */ -/* > PP=2 indicates that flipping was applied to the Z array */ -/* > and that the initial tests for deflation should not be */ -/* > performed. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] DMIN */ -/* > \verbatim */ -/* > DMIN is DOUBLE PRECISION */ -/* > Minimum value of d. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] SIGMA */ -/* > \verbatim */ -/* > SIGMA is DOUBLE PRECISION */ -/* > Sum of shifts used in current segment. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] DESIG */ -/* > \verbatim */ -/* > DESIG is DOUBLE PRECISION */ -/* > Lower order part of SIGMA */ -/* > \endverbatim */ -/* > */ -/* > \param[in] QMAX */ -/* > \verbatim */ -/* > QMAX is DOUBLE PRECISION */ -/* > Maximum value of q. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] NFAIL */ -/* > \verbatim */ -/* > NFAIL is INTEGER */ -/* > Increment NFAIL by 1 each time the shift was too big. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] ITER */ -/* > \verbatim */ -/* > ITER is INTEGER */ -/* > Increment ITER by 1 for each iteration. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] NDIV */ -/* > \verbatim */ -/* > NDIV is INTEGER */ -/* > Increment NDIV by 1 for each division. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] IEEE */ -/* > \verbatim */ -/* > IEEE is LOGICAL */ -/* > Flag for IEEE or non IEEE arithmetic (passed to DLASQ5). */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] TTYPE */ -/* > \verbatim */ -/* > TTYPE is INTEGER */ -/* > Shift type. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] DMIN1 */ -/* > \verbatim */ -/* > DMIN1 is DOUBLE PRECISION */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] DMIN2 */ -/* > \verbatim */ -/* > DMIN2 is DOUBLE PRECISION */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] DN */ -/* > \verbatim */ -/* > DN is DOUBLE PRECISION */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] DN1 */ -/* > \verbatim */ -/* > DN1 is DOUBLE PRECISION */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] DN2 */ -/* > \verbatim */ -/* > DN2 is DOUBLE PRECISION */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] G */ -/* > \verbatim */ -/* > G is DOUBLE PRECISION */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] TAU */ -/* > \verbatim */ -/* > TAU is DOUBLE PRECISION */ -/* > */ -/* > These are passed as arguments in order to save their values */ -/* > between calls to DLASQ3. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup auxOTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dlasq3_(integer *i0, integer *n0, doublereal *z__, - integer *pp, doublereal *dmin__, doublereal *sigma, doublereal *desig, - doublereal *qmax, integer *nfail, integer *iter, integer *ndiv, - logical *ieee, integer *ttype, doublereal *dmin1, doublereal *dmin2, - doublereal *dn, doublereal *dn1, doublereal *dn2, doublereal *g, - doublereal *tau) +int dlasq3_(integer *i0, integer *n0, doublereal *z__, integer *pp, doublereal *dmin__, + doublereal *sigma, doublereal *desig, doublereal *qmax, integer *nfail, integer *iter, + integer *ndiv, logical *ieee, integer *ttype, doublereal *dmin1, doublereal *dmin2, + doublereal *dn, doublereal *dn1, doublereal *dn2, doublereal *g, doublereal *tau) { - /* System generated locals */ integer i__1; doublereal d__1, d__2; - - /* Builtin functions */ double sqrt(doublereal); - - /* Local variables */ doublereal s, t; integer j4, nn; doublereal eps, tol; integer n0in, ipn4; doublereal tol2, temp; - extern /* Subroutine */ int dlasq4_(integer *, integer *, doublereal *, - integer *, integer *, doublereal *, doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *, doublereal *, integer *, - doublereal *), dlasq5_(integer *, integer *, doublereal *, - integer *, doublereal *, doublereal *, doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *, doublereal *, logical * - , doublereal *), dlasq6_(integer *, integer *, doublereal *, - integer *, doublereal *, doublereal *, doublereal *, doublereal *, - doublereal *, doublereal *); + extern int dlasq4_(integer *, integer *, doublereal *, integer *, integer *, doublereal *, + doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *, integer *, doublereal *), + dlasq5_(integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, + logical *, doublereal *), + dlasq6_(integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, + doublereal *, doublereal *, doublereal *, doublereal *); extern doublereal dlamch_(char *, ftnlen); extern logical disnan_(doublereal *); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. External Function .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - - /* Parameter adjustments */ --z__; - - /* Function Body */ n0in = *n0; eps = dlamch_((char *)"Precision", (ftnlen)9); tol = eps * 100.; -/* Computing 2nd power */ d__1 = tol; tol2 = d__1 * d__1; - -/* Check for deflation. */ - L10: - if (*n0 < *i0) { return 0; } @@ -277,31 +42,19 @@ L10: if (*n0 == *i0 + 1) { goto L40; } - -/* Check whether E(N0-1) is negligible, 1 eigenvalue. */ - - if (z__[nn - 5] > tol2 * (*sigma + z__[nn - 3]) && z__[nn - (*pp << 1) - - 4] > tol2 * z__[nn - 7]) { + if (z__[nn - 5] > tol2 * (*sigma + z__[nn - 3]) && + z__[nn - (*pp << 1) - 4] > tol2 * z__[nn - 7]) { goto L30; } - L20: - z__[(*n0 << 2) - 3] = z__[(*n0 << 2) + *pp - 3] + *sigma; --(*n0); goto L10; - -/* Check whether E(N0-2) is negligible, 2 eigenvalues. */ - L30: - - if (z__[nn - 9] > tol2 * *sigma && z__[nn - (*pp << 1) - 8] > tol2 * z__[ - nn - 11]) { + if (z__[nn - 9] > tol2 * *sigma && z__[nn - (*pp << 1) - 8] > tol2 * z__[nn - 11]) { goto L50; } - L40: - if (z__[nn - 3] > z__[nn - 7]) { s = z__[nn - 3]; z__[nn - 3] = z__[nn - 7]; @@ -323,14 +76,10 @@ L40: z__[(*n0 << 2) - 3] = z__[nn - 3] + *sigma; *n0 += -2; goto L10; - L50: if (*pp == 2) { *pp = 0; } - -/* Reverse the qd-array, if warranted. */ - if (*dmin__ <= 0. || *n0 < n0in) { if (z__[(*i0 << 2) + *pp - 3] * 1.5 < z__[(*n0 << 2) + *pp - 3]) { ipn4 = *i0 + *n0 << 2; @@ -348,90 +97,50 @@ L50: temp = z__[j4]; z__[j4] = z__[ipn4 - j4 - 4]; z__[ipn4 - j4 - 4] = temp; -/* L60: */ } if (*n0 - *i0 <= 4) { z__[(*n0 << 2) + *pp - 1] = z__[(*i0 << 2) + *pp - 1]; z__[(*n0 << 2) - *pp] = z__[(*i0 << 2) - *pp]; } -/* Computing MIN */ d__1 = *dmin2, d__2 = z__[(*n0 << 2) + *pp - 1]; - *dmin2 = min(d__1,d__2); -/* Computing MIN */ - d__1 = z__[(*n0 << 2) + *pp - 1], d__2 = z__[(*i0 << 2) + *pp - 1] - , d__1 = min(d__1,d__2), d__2 = z__[(*i0 << 2) + *pp + 3]; - z__[(*n0 << 2) + *pp - 1] = min(d__1,d__2); -/* Computing MIN */ - d__1 = z__[(*n0 << 2) - *pp], d__2 = z__[(*i0 << 2) - *pp], d__1 = - min(d__1,d__2), d__2 = z__[(*i0 << 2) - *pp + 4]; - z__[(*n0 << 2) - *pp] = min(d__1,d__2); -/* Computing MAX */ - d__1 = *qmax, d__2 = z__[(*i0 << 2) + *pp - 3], d__1 = max(d__1, - d__2), d__2 = z__[(*i0 << 2) + *pp + 1]; - *qmax = max(d__1,d__2); + *dmin2 = min(d__1, d__2); + d__1 = z__[(*n0 << 2) + *pp - 1], d__2 = z__[(*i0 << 2) + *pp - 1], + d__1 = min(d__1, d__2), d__2 = z__[(*i0 << 2) + *pp + 3]; + z__[(*n0 << 2) + *pp - 1] = min(d__1, d__2); + d__1 = z__[(*n0 << 2) - *pp], d__2 = z__[(*i0 << 2) - *pp], d__1 = min(d__1, d__2), + d__2 = z__[(*i0 << 2) - *pp + 4]; + z__[(*n0 << 2) - *pp] = min(d__1, d__2); + d__1 = *qmax, d__2 = z__[(*i0 << 2) + *pp - 3], d__1 = max(d__1, d__2), + d__2 = z__[(*i0 << 2) + *pp + 1]; + *qmax = max(d__1, d__2); *dmin__ = -0.; } } - -/* Choose a shift. */ - - dlasq4_(i0, n0, &z__[1], pp, &n0in, dmin__, dmin1, dmin2, dn, dn1, dn2, - tau, ttype, g); - -/* Call dqds until DMIN > 0. */ - + dlasq4_(i0, n0, &z__[1], pp, &n0in, dmin__, dmin1, dmin2, dn, dn1, dn2, tau, ttype, g); L70: - - dlasq5_(i0, n0, &z__[1], pp, tau, sigma, dmin__, dmin1, dmin2, dn, dn1, - dn2, ieee, &eps); - + dlasq5_(i0, n0, &z__[1], pp, tau, sigma, dmin__, dmin1, dmin2, dn, dn1, dn2, ieee, &eps); *ndiv += *n0 - *i0 + 2; ++(*iter); - -/* Check status. */ - if (*dmin__ >= 0. && *dmin1 >= 0.) { - -/* Success. */ - goto L90; - - } else if (*dmin__ < 0. && *dmin1 > 0. && z__[(*n0 - 1 << 2) - *pp] < tol - * (*sigma + *dn1) && abs(*dn) < tol * *sigma) { - -/* Convergence hidden by negative DN. */ - + } else if (*dmin__ < 0. && *dmin1 > 0. && z__[(*n0 - 1 << 2) - *pp] < tol * (*sigma + *dn1) && + abs(*dn) < tol * *sigma) { z__[(*n0 - 1 << 2) - *pp + 2] = 0.; *dmin__ = 0.; goto L90; } else if (*dmin__ < 0.) { - -/* TAU too big. Select new TAU and try again. */ - ++(*nfail); if (*ttype < -22) { - -/* Failed twice. Play it safe. */ - *tau = 0.; } else if (*dmin1 > 0.) { - -/* Late failure. Gives excellent shift. */ - *tau = (*tau + *dmin__) * (1. - eps * 2.); *ttype += -11; } else { - -/* Early failure. Divide by 4. */ - *tau *= .25; *ttype += -12; } goto L70; } else if (disnan_(dmin__)) { - -/* NaN. */ - if (*tau == 0.) { goto L80; } else { @@ -439,20 +148,13 @@ L70: goto L70; } } else { - -/* Possible underflow. Play it safe. */ - goto L80; } - -/* Risk of underflow. */ - L80: dlasq6_(i0, n0, &z__[1], pp, dmin__, dmin1, dmin2, dn, dn1, dn2); *ndiv += *n0 - *i0 + 2; ++(*iter); *tau = 0.; - L90: if (*tau < *sigma) { *desig += *tau; @@ -463,13 +165,8 @@ L90: *desig = *sigma - (t - *tau) + *desig; } *sigma = t; - return 0; - -/* End of DLASQ3 */ - -} /* dlasq3_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlasq4.cpp b/lib/linalg/dlasq4.cpp index 9629f53161..524c89a2ac 100644 --- a/lib/linalg/dlasq4.cpp +++ b/lib/linalg/dlasq4.cpp @@ -1,235 +1,29 @@ -/* fortran/dlasq4.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DLASQ4 computes an approximation to the smallest eigenvalue using values of d from the previous - transform. Used by sbdsqr. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLASQ4 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLASQ4( I0, N0, Z, PP, N0IN, DMIN, DMIN1, DMIN2, DN, */ -/* DN1, DN2, TAU, TTYPE, G ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER I0, N0, N0IN, PP, TTYPE */ -/* DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DN1, DN2, G, TAU */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION Z( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLASQ4 computes an approximation TAU to the smallest eigenvalue */ -/* > using values of d from the previous transform. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] I0 */ -/* > \verbatim */ -/* > I0 is INTEGER */ -/* > First index. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N0 */ -/* > \verbatim */ -/* > N0 is INTEGER */ -/* > Last index. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] Z */ -/* > \verbatim */ -/* > Z is DOUBLE PRECISION array, dimension ( 4*N0 ) */ -/* > Z holds the qd array. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] PP */ -/* > \verbatim */ -/* > PP is INTEGER */ -/* > PP=0 for ping, PP=1 for pong. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N0IN */ -/* > \verbatim */ -/* > N0IN is INTEGER */ -/* > The value of N0 at start of EIGTEST. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DMIN */ -/* > \verbatim */ -/* > DMIN is DOUBLE PRECISION */ -/* > Minimum value of d. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DMIN1 */ -/* > \verbatim */ -/* > DMIN1 is DOUBLE PRECISION */ -/* > Minimum value of d, excluding D( N0 ). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DMIN2 */ -/* > \verbatim */ -/* > DMIN2 is DOUBLE PRECISION */ -/* > Minimum value of d, excluding D( N0 ) and D( N0-1 ). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DN */ -/* > \verbatim */ -/* > DN is DOUBLE PRECISION */ -/* > d(N) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DN1 */ -/* > \verbatim */ -/* > DN1 is DOUBLE PRECISION */ -/* > d(N-1) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DN2 */ -/* > \verbatim */ -/* > DN2 is DOUBLE PRECISION */ -/* > d(N-2) */ -/* > \endverbatim */ -/* > */ -/* > \param[out] TAU */ -/* > \verbatim */ -/* > TAU is DOUBLE PRECISION */ -/* > This is the shift. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] TTYPE */ -/* > \verbatim */ -/* > TTYPE is INTEGER */ -/* > Shift type. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] G */ -/* > \verbatim */ -/* > G is DOUBLE PRECISION */ -/* > G is passed as an argument in order to save its value between */ -/* > calls to DLASQ4. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup auxOTHERcomputational */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > CNST1 = 9/16 */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dlasq4_(integer *i0, integer *n0, doublereal *z__, - integer *pp, integer *n0in, doublereal *dmin__, doublereal *dmin1, - doublereal *dmin2, doublereal *dn, doublereal *dn1, doublereal *dn2, - doublereal *tau, integer *ttype, doublereal *g) +int dlasq4_(integer *i0, integer *n0, doublereal *z__, integer *pp, integer *n0in, + doublereal *dmin__, doublereal *dmin1, doublereal *dmin2, doublereal *dn, + doublereal *dn1, doublereal *dn2, doublereal *tau, integer *ttype, doublereal *g) { - /* System generated locals */ integer i__1; doublereal d__1, d__2; - - /* Builtin functions */ double sqrt(doublereal); - - /* Local variables */ doublereal s, a2, b1, b2; integer i4, nn, np; doublereal gam, gap1, gap2; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* A negative DMIN forces the shift to take that absolute value */ -/* TTYPE records the type of shift. */ - - /* Parameter adjustments */ --z__; - - /* Function Body */ if (*dmin__ <= 0.) { *tau = -(*dmin__); *ttype = -1; return 0; } - nn = (*n0 << 2) + *pp; if (*n0in == *n0) { - -/* No eigenvalues deflated. */ - if (*dmin__ == *dn || *dmin__ == *dn1) { - b1 = sqrt(z__[nn - 3]) * sqrt(z__[nn - 5]); b2 = sqrt(z__[nn - 7]) * sqrt(z__[nn - 9]); a2 = z__[nn - 7] + z__[nn - 5]; - -/* Cases 2 and 3. */ - if (*dmin__ == *dn && *dmin1 == *dn1) { gap2 = *dmin2 - a2 - *dmin2 * .25; if (gap2 > 0. && gap2 > b2) { @@ -238,9 +32,8 @@ f"> */ gap1 = a2 - *dn - (b1 + b2); } if (gap1 > 0. && gap1 > b1) { -/* Computing MAX */ d__1 = *dn - b1 / gap1 * b1, d__2 = *dmin__ * .5; - s = max(d__1,d__2); + s = max(d__1, d__2); *ttype = -2; } else { s = 0.; @@ -248,19 +41,14 @@ f"> */ s = *dn - b1; } if (a2 > b1 + b2) { -/* Computing MIN */ d__1 = s, d__2 = a2 - (b1 + b2); - s = min(d__1,d__2); + s = min(d__1, d__2); } -/* Computing MAX */ d__1 = s, d__2 = *dmin__ * .333; - s = max(d__1,d__2); + s = max(d__1, d__2); *ttype = -3; } } else { - -/* Case 4. */ - *ttype = -4; s = *dmin__ * .25; if (*dmin__ == *dn) { @@ -284,9 +72,6 @@ f"> */ b2 = z__[nn - 9] / z__[nn - 11]; np = nn - 13; } - -/* Approximate contribution to norm squared from I < NN-1. */ - a2 += b2; i__1 = (*i0 << 2) - 1 + *pp; for (i4 = np; i4 >= i__1; i4 += -4) { @@ -299,29 +84,19 @@ f"> */ } b2 *= z__[i4] / z__[i4 - 2]; a2 += b2; - if (max(b2,b1) * 100. < a2 || .563 < a2) { + if (max(b2, b1) * 100. < a2 || .563 < a2) { goto L20; } -/* L10: */ } -L20: + L20: a2 *= 1.05; - -/* Rayleigh quotient residual bound. */ - if (a2 < .563) { s = gam * (1. - sqrt(a2)) / (a2 + 1.); } } } else if (*dmin__ == *dn2) { - -/* Case 5. */ - *ttype = -5; s = *dmin__ * .25; - -/* Compute contribution to norm squared from I > NN-2. */ - np = nn - (*pp << 1); b1 = z__[np - 2]; b2 = z__[np - 6]; @@ -330,9 +105,6 @@ L20: return 0; } a2 = z__[np - 8] / b2 * (z__[np - 4] / b1 + 1.); - -/* Approximate contribution to norm squared from I < NN-2. */ - if (*n0 - *i0 > 2) { b2 = z__[nn - 13] / z__[nn - 15]; a2 += b2; @@ -347,22 +119,17 @@ L20: } b2 *= z__[i4] / z__[i4 - 2]; a2 += b2; - if (max(b2,b1) * 100. < a2 || .563 < a2) { + if (max(b2, b1) * 100. < a2 || .563 < a2) { goto L40; } -/* L30: */ } -L40: + L40: a2 *= 1.05; } - if (a2 < .563) { s = gam * (1. - sqrt(a2)) / (a2 + 1.); } } else { - -/* Case 6, no information to guide us. */ - if (*ttype == -6) { *g += (1. - *g) * .333; } else if (*ttype == -18) { @@ -373,15 +140,8 @@ L40: s = *g * *dmin__; *ttype = -6; } - } else if (*n0in == *n0 + 1) { - -/* One eigenvalue just deflated. Use DMIN1, DN1 for DMIN and DN. */ - if (*dmin1 == *dn1 && *dmin2 == *dn2) { - -/* Cases 7 and 8. */ - *ttype = -7; s = *dmin1 * .333; if (z__[nn - 5] > z__[nn - 7]) { @@ -400,44 +160,31 @@ L40: } b1 *= z__[i4] / z__[i4 - 2]; b2 += b1; - if (max(b1,a2) * 100. < b2) { + if (max(b1, a2) * 100. < b2) { goto L60; } -/* L50: */ } -L60: + L60: b2 = sqrt(b2 * 1.05); -/* Computing 2nd power */ d__1 = b2; a2 = *dmin1 / (d__1 * d__1 + 1.); gap2 = *dmin2 * .5 - a2; if (gap2 > 0. && gap2 > b2 * a2) { -/* Computing MAX */ d__1 = s, d__2 = a2 * (1. - a2 * 1.01 * (b2 / gap2) * b2); - s = max(d__1,d__2); + s = max(d__1, d__2); } else { -/* Computing MAX */ d__1 = s, d__2 = a2 * (1. - b2 * 1.01); - s = max(d__1,d__2); + s = max(d__1, d__2); *ttype = -8; } } else { - -/* Case 9. */ - s = *dmin1 * .25; if (*dmin1 == *dn1) { s = *dmin1 * .5; } *ttype = -9; } - } else if (*n0in == *n0 + 2) { - -/* Two eigenvalues deflated. Use DMIN2, DN2 for DMIN and DN. */ - -/* Cases 10 and 11. */ - if (*dmin2 == *dn2 && z__[nn - 5] * 2. < z__[nn - 7]) { *ttype = -10; s = *dmin2 * .333; @@ -459,43 +206,30 @@ L60: if (b1 * 100. < b2) { goto L80; } -/* L70: */ } -L80: + L80: b2 = sqrt(b2 * 1.05); -/* Computing 2nd power */ d__1 = b2; a2 = *dmin2 / (d__1 * d__1 + 1.); - gap2 = z__[nn - 7] + z__[nn - 9] - sqrt(z__[nn - 11]) * sqrt(z__[ - nn - 9]) - a2; + gap2 = z__[nn - 7] + z__[nn - 9] - sqrt(z__[nn - 11]) * sqrt(z__[nn - 9]) - a2; if (gap2 > 0. && gap2 > b2 * a2) { -/* Computing MAX */ d__1 = s, d__2 = a2 * (1. - a2 * 1.01 * (b2 / gap2) * b2); - s = max(d__1,d__2); + s = max(d__1, d__2); } else { -/* Computing MAX */ d__1 = s, d__2 = a2 * (1. - b2 * 1.01); - s = max(d__1,d__2); + s = max(d__1, d__2); } } else { s = *dmin2 * .25; *ttype = -11; } } else if (*n0in > *n0 + 2) { - -/* Case 12, more than two eigenvalues deflated. No information. */ - s = 0.; *ttype = -12; } - *tau = s; return 0; - -/* End of DLASQ4 */ - -} /* dlasq4_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlasq5.cpp b/lib/linalg/dlasq5.cpp index a7cd93932f..b242f3ceb8 100644 --- a/lib/linalg/dlasq5.cpp +++ b/lib/linalg/dlasq5.cpp @@ -1,206 +1,20 @@ -/* fortran/dlasq5.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DLASQ5 computes one dqds transform in ping-pong form. Used by sbdsqr and sstegr. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLASQ5 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLASQ5( I0, N0, Z, PP, TAU, SIGMA, DMIN, DMIN1, DMIN2, DN, */ -/* DNM1, DNM2, IEEE, EPS ) */ - -/* .. Scalar Arguments .. */ -/* LOGICAL IEEE */ -/* INTEGER I0, N0, PP */ -/* DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DNM1, DNM2, TAU, SIGMA, EPS */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION Z( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLASQ5 computes one dqds transform in ping-pong form, one */ -/* > version for IEEE machines another for non IEEE machines. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] I0 */ -/* > \verbatim */ -/* > I0 is INTEGER */ -/* > First index. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N0 */ -/* > \verbatim */ -/* > N0 is INTEGER */ -/* > Last index. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] Z */ -/* > \verbatim */ -/* > Z is DOUBLE PRECISION array, dimension ( 4*N ) */ -/* > Z holds the qd array. EMIN is stored in Z(4*N0) to avoid */ -/* > an extra argument. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] PP */ -/* > \verbatim */ -/* > PP is INTEGER */ -/* > PP=0 for ping, PP=1 for pong. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TAU */ -/* > \verbatim */ -/* > TAU is DOUBLE PRECISION */ -/* > This is the shift. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] SIGMA */ -/* > \verbatim */ -/* > SIGMA is DOUBLE PRECISION */ -/* > This is the accumulated shift up to this step. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] DMIN */ -/* > \verbatim */ -/* > DMIN is DOUBLE PRECISION */ -/* > Minimum value of d. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] DMIN1 */ -/* > \verbatim */ -/* > DMIN1 is DOUBLE PRECISION */ -/* > Minimum value of d, excluding D( N0 ). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] DMIN2 */ -/* > \verbatim */ -/* > DMIN2 is DOUBLE PRECISION */ -/* > Minimum value of d, excluding D( N0 ) and D( N0-1 ). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] DN */ -/* > \verbatim */ -/* > DN is DOUBLE PRECISION */ -/* > d(N0), the last value of d. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] DNM1 */ -/* > \verbatim */ -/* > DNM1 is DOUBLE PRECISION */ -/* > d(N0-1). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] DNM2 */ -/* > \verbatim */ -/* > DNM2 is DOUBLE PRECISION */ -/* > d(N0-2). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] IEEE */ -/* > \verbatim */ -/* > IEEE is LOGICAL */ -/* > Flag for IEEE or non IEEE arithmetic. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] EPS */ -/* > \verbatim */ -/* > EPS is DOUBLE PRECISION */ -/* > This is the value of epsilon used. */ -/* > \endverbatim */ -/* > */ -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup auxOTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dlasq5_(integer *i0, integer *n0, doublereal *z__, - integer *pp, doublereal *tau, doublereal *sigma, doublereal *dmin__, - doublereal *dmin1, doublereal *dmin2, doublereal *dn, doublereal * - dnm1, doublereal *dnm2, logical *ieee, doublereal *eps) +int dlasq5_(integer *i0, integer *n0, doublereal *z__, integer *pp, doublereal *tau, + doublereal *sigma, doublereal *dmin__, doublereal *dmin1, doublereal *dmin2, + doublereal *dn, doublereal *dnm1, doublereal *dnm2, logical *ieee, doublereal *eps) { - /* System generated locals */ integer i__1; doublereal d__1, d__2; - - /* Local variables */ doublereal d__; integer j4, j4p2; doublereal emin, temp, dthresh; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameter .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - - /* Parameter adjustments */ --z__; - - /* Function Body */ if (*n0 - *i0 - 1 <= 0) { return 0; } - dthresh = *eps * (*sigma + *tau); if (*tau < dthresh * .5) { *tau = 0.; @@ -211,23 +25,17 @@ f"> */ d__ = z__[j4] - *tau; *dmin__ = d__; *dmin1 = -z__[j4]; - if (*ieee) { - -/* Code for IEEE arithmetic. */ - if (*pp == 0) { i__1 = *n0 - 3 << 2; for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { z__[j4 - 2] = d__ + z__[j4 - 1]; temp = z__[j4 + 1] / z__[j4 - 2]; d__ = d__ * temp - *tau; - *dmin__ = min(*dmin__,d__); + *dmin__ = min(*dmin__, d__); z__[j4] = z__[j4 - 1] * temp; -/* Computing MIN */ d__1 = z__[j4]; - emin = min(d__1,emin); -/* L10: */ + emin = min(d__1, emin); } } else { i__1 = *n0 - 3 << 2; @@ -235,17 +43,12 @@ f"> */ z__[j4 - 3] = d__ + z__[j4]; temp = z__[j4 + 2] / z__[j4 - 3]; d__ = d__ * temp - *tau; - *dmin__ = min(*dmin__,d__); + *dmin__ = min(*dmin__, d__); z__[j4 - 1] = z__[j4] * temp; -/* Computing MIN */ d__1 = z__[j4 - 1]; - emin = min(d__1,emin); -/* L20: */ + emin = min(d__1, emin); } } - -/* Unroll last two steps. */ - *dnm2 = d__; *dmin2 = *dmin__; j4 = (*n0 - 2 << 2) - *pp; @@ -253,20 +56,15 @@ f"> */ z__[j4 - 2] = *dnm2 + z__[j4p2]; z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); *dnm1 = z__[j4p2 + 2] * (*dnm2 / z__[j4 - 2]) - *tau; - *dmin__ = min(*dmin__,*dnm1); - + *dmin__ = min(*dmin__, *dnm1); *dmin1 = *dmin__; j4 += 4; j4p2 = j4 + (*pp << 1) - 1; z__[j4 - 2] = *dnm1 + z__[j4p2]; z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); *dn = z__[j4p2 + 2] * (*dnm1 / z__[j4 - 2]) - *tau; - *dmin__ = min(*dmin__,*dn); - + *dmin__ = min(*dmin__, *dn); } else { - -/* Code for non IEEE arithmetic. */ - if (*pp == 0) { i__1 = *n0 - 3 << 2; for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { @@ -277,11 +75,9 @@ f"> */ z__[j4] = z__[j4 + 1] * (z__[j4 - 1] / z__[j4 - 2]); d__ = z__[j4 + 1] * (d__ / z__[j4 - 2]) - *tau; } - *dmin__ = min(*dmin__,d__); -/* Computing MIN */ + *dmin__ = min(*dmin__, d__); d__1 = emin, d__2 = z__[j4]; - emin = min(d__1,d__2); -/* L30: */ + emin = min(d__1, d__2); } } else { i__1 = *n0 - 3 << 2; @@ -293,16 +89,11 @@ f"> */ z__[j4 - 1] = z__[j4 + 2] * (z__[j4] / z__[j4 - 3]); d__ = z__[j4 + 2] * (d__ / z__[j4 - 3]) - *tau; } - *dmin__ = min(*dmin__,d__); -/* Computing MIN */ + *dmin__ = min(*dmin__, d__); d__1 = emin, d__2 = z__[j4 - 1]; - emin = min(d__1,d__2); -/* L40: */ + emin = min(d__1, d__2); } } - -/* Unroll last two steps. */ - *dnm2 = d__; *dmin2 = *dmin__; j4 = (*n0 - 2 << 2) - *pp; @@ -314,8 +105,7 @@ f"> */ z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); *dnm1 = z__[j4p2 + 2] * (*dnm2 / z__[j4 - 2]) - *tau; } - *dmin__ = min(*dmin__,*dnm1); - + *dmin__ = min(*dmin__, *dnm1); *dmin1 = *dmin__; j4 += 4; j4p2 = j4 + (*pp << 1) - 1; @@ -326,20 +116,15 @@ f"> */ z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); *dn = z__[j4p2 + 2] * (*dnm1 / z__[j4 - 2]) - *tau; } - *dmin__ = min(*dmin__,*dn); - + *dmin__ = min(*dmin__, *dn); } } else { -/* This is the version that sets d's to zero if they are small enough */ j4 = (*i0 << 2) + *pp - 3; emin = z__[j4 + 4]; d__ = z__[j4] - *tau; *dmin__ = d__; *dmin1 = -z__[j4]; if (*ieee) { - -/* Code for IEEE arithmetic. */ - if (*pp == 0) { i__1 = *n0 - 3 << 2; for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { @@ -349,12 +134,10 @@ f"> */ if (d__ < dthresh) { d__ = 0.; } - *dmin__ = min(*dmin__,d__); + *dmin__ = min(*dmin__, d__); z__[j4] = z__[j4 - 1] * temp; -/* Computing MIN */ d__1 = z__[j4]; - emin = min(d__1,emin); -/* L50: */ + emin = min(d__1, emin); } } else { i__1 = *n0 - 3 << 2; @@ -365,17 +148,12 @@ f"> */ if (d__ < dthresh) { d__ = 0.; } - *dmin__ = min(*dmin__,d__); + *dmin__ = min(*dmin__, d__); z__[j4 - 1] = z__[j4] * temp; -/* Computing MIN */ d__1 = z__[j4 - 1]; - emin = min(d__1,emin); -/* L60: */ + emin = min(d__1, emin); } } - -/* Unroll last two steps. */ - *dnm2 = d__; *dmin2 = *dmin__; j4 = (*n0 - 2 << 2) - *pp; @@ -383,20 +161,15 @@ f"> */ z__[j4 - 2] = *dnm2 + z__[j4p2]; z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); *dnm1 = z__[j4p2 + 2] * (*dnm2 / z__[j4 - 2]) - *tau; - *dmin__ = min(*dmin__,*dnm1); - + *dmin__ = min(*dmin__, *dnm1); *dmin1 = *dmin__; j4 += 4; j4p2 = j4 + (*pp << 1) - 1; z__[j4 - 2] = *dnm1 + z__[j4p2]; z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); *dn = z__[j4p2 + 2] * (*dnm1 / z__[j4 - 2]) - *tau; - *dmin__ = min(*dmin__,*dn); - + *dmin__ = min(*dmin__, *dn); } else { - -/* Code for non IEEE arithmetic. */ - if (*pp == 0) { i__1 = *n0 - 3 << 2; for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { @@ -410,11 +183,9 @@ f"> */ if (d__ < dthresh) { d__ = 0.; } - *dmin__ = min(*dmin__,d__); -/* Computing MIN */ + *dmin__ = min(*dmin__, d__); d__1 = emin, d__2 = z__[j4]; - emin = min(d__1,d__2); -/* L70: */ + emin = min(d__1, d__2); } } else { i__1 = *n0 - 3 << 2; @@ -429,16 +200,11 @@ f"> */ if (d__ < dthresh) { d__ = 0.; } - *dmin__ = min(*dmin__,d__); -/* Computing MIN */ + *dmin__ = min(*dmin__, d__); d__1 = emin, d__2 = z__[j4 - 1]; - emin = min(d__1,d__2); -/* L80: */ + emin = min(d__1, d__2); } } - -/* Unroll last two steps. */ - *dnm2 = d__; *dmin2 = *dmin__; j4 = (*n0 - 2 << 2) - *pp; @@ -450,8 +216,7 @@ f"> */ z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); *dnm1 = z__[j4p2 + 2] * (*dnm2 / z__[j4 - 2]) - *tau; } - *dmin__ = min(*dmin__,*dnm1); - + *dmin__ = min(*dmin__, *dnm1); *dmin1 = *dmin__; j4 += 4; j4p2 = j4 + (*pp << 1) - 1; @@ -462,19 +227,13 @@ f"> */ z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); *dn = z__[j4p2 + 2] * (*dnm1 / z__[j4 - 2]) - *tau; } - *dmin__ = min(*dmin__,*dn); - + *dmin__ = min(*dmin__, *dn); } } - z__[j4 + 2] = *dn; z__[(*n0 << 2) - *pp] = emin; return 0; - -/* End of DLASQ5 */ - -} /* dlasq5_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlasq6.cpp b/lib/linalg/dlasq6.cpp index 96bda77630..b60dcdd9d6 100644 --- a/lib/linalg/dlasq6.cpp +++ b/lib/linalg/dlasq6.cpp @@ -1,190 +1,27 @@ -/* fortran/dlasq6.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DLASQ6 computes one dqd transform in ping-pong form. Used by sbdsqr and sstegr. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLASQ6 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLASQ6( I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN, */ -/* DNM1, DNM2 ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER I0, N0, PP */ -/* DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DNM1, DNM2 */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION Z( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLASQ6 computes one dqd (shift equal to zero) transform in */ -/* > ping-pong form, with protection against underflow and overflow. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] I0 */ -/* > \verbatim */ -/* > I0 is INTEGER */ -/* > First index. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N0 */ -/* > \verbatim */ -/* > N0 is INTEGER */ -/* > Last index. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] Z */ -/* > \verbatim */ -/* > Z is DOUBLE PRECISION array, dimension ( 4*N ) */ -/* > Z holds the qd array. EMIN is stored in Z(4*N0) to avoid */ -/* > an extra argument. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] PP */ -/* > \verbatim */ -/* > PP is INTEGER */ -/* > PP=0 for ping, PP=1 for pong. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] DMIN */ -/* > \verbatim */ -/* > DMIN is DOUBLE PRECISION */ -/* > Minimum value of d. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] DMIN1 */ -/* > \verbatim */ -/* > DMIN1 is DOUBLE PRECISION */ -/* > Minimum value of d, excluding D( N0 ). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] DMIN2 */ -/* > \verbatim */ -/* > DMIN2 is DOUBLE PRECISION */ -/* > Minimum value of d, excluding D( N0 ) and D( N0-1 ). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] DN */ -/* > \verbatim */ -/* > DN is DOUBLE PRECISION */ -/* > d(N0), the last value of d. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] DNM1 */ -/* > \verbatim */ -/* > DNM1 is DOUBLE PRECISION */ -/* > d(N0-1). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] DNM2 */ -/* > \verbatim */ -/* > DNM2 is DOUBLE PRECISION */ -/* > d(N0-2). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup auxOTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dlasq6_(integer *i0, integer *n0, doublereal *z__, - integer *pp, doublereal *dmin__, doublereal *dmin1, doublereal *dmin2, - doublereal *dn, doublereal *dnm1, doublereal *dnm2) +int dlasq6_(integer *i0, integer *n0, doublereal *z__, integer *pp, doublereal *dmin__, + doublereal *dmin1, doublereal *dmin2, doublereal *dn, doublereal *dnm1, + doublereal *dnm2) { - /* System generated locals */ integer i__1; doublereal d__1, d__2; - - /* Local variables */ doublereal d__; integer j4, j4p2; doublereal emin, temp; extern doublereal dlamch_(char *, ftnlen); doublereal safmin; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameter .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Function .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - - /* Parameter adjustments */ --z__; - - /* Function Body */ if (*n0 - *i0 - 1 <= 0) { return 0; } - safmin = dlamch_((char *)"Safe minimum", (ftnlen)12); j4 = (*i0 << 2) + *pp - 3; emin = z__[j4 + 4]; d__ = z__[j4]; *dmin__ = d__; - if (*pp == 0) { i__1 = *n0 - 3 << 2; for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) { @@ -194,8 +31,7 @@ f"> */ d__ = z__[j4 + 1]; *dmin__ = d__; emin = 0.; - } else if (safmin * z__[j4 + 1] < z__[j4 - 2] && safmin * z__[j4 - - 2] < z__[j4 + 1]) { + } else if (safmin * z__[j4 + 1] < z__[j4 - 2] && safmin * z__[j4 - 2] < z__[j4 + 1]) { temp = z__[j4 + 1] / z__[j4 - 2]; z__[j4] = z__[j4 - 1] * temp; d__ *= temp; @@ -203,11 +39,9 @@ f"> */ z__[j4] = z__[j4 + 1] * (z__[j4 - 1] / z__[j4 - 2]); d__ = z__[j4 + 1] * (d__ / z__[j4 - 2]); } - *dmin__ = min(*dmin__,d__); -/* Computing MIN */ + *dmin__ = min(*dmin__, d__); d__1 = emin, d__2 = z__[j4]; - emin = min(d__1,d__2); -/* L10: */ + emin = min(d__1, d__2); } } else { i__1 = *n0 - 3 << 2; @@ -218,8 +52,7 @@ f"> */ d__ = z__[j4 + 2]; *dmin__ = d__; emin = 0.; - } else if (safmin * z__[j4 + 2] < z__[j4 - 3] && safmin * z__[j4 - - 3] < z__[j4 + 2]) { + } else if (safmin * z__[j4 + 2] < z__[j4 - 3] && safmin * z__[j4 - 3] < z__[j4 + 2]) { temp = z__[j4 + 2] / z__[j4 - 3]; z__[j4 - 1] = z__[j4] * temp; d__ *= temp; @@ -227,16 +60,11 @@ f"> */ z__[j4 - 1] = z__[j4 + 2] * (z__[j4] / z__[j4 - 3]); d__ = z__[j4 + 2] * (d__ / z__[j4 - 3]); } - *dmin__ = min(*dmin__,d__); -/* Computing MIN */ + *dmin__ = min(*dmin__, d__); d__1 = emin, d__2 = z__[j4 - 1]; - emin = min(d__1,d__2); -/* L20: */ + emin = min(d__1, d__2); } } - -/* Unroll last two steps. */ - *dnm2 = d__; *dmin2 = *dmin__; j4 = (*n0 - 2 << 2) - *pp; @@ -247,8 +75,7 @@ f"> */ *dnm1 = z__[j4p2 + 2]; *dmin__ = *dnm1; emin = 0.; - } else if (safmin * z__[j4p2 + 2] < z__[j4 - 2] && safmin * z__[j4 - 2] < - z__[j4p2 + 2]) { + } else if (safmin * z__[j4p2 + 2] < z__[j4 - 2] && safmin * z__[j4 - 2] < z__[j4p2 + 2]) { temp = z__[j4p2 + 2] / z__[j4 - 2]; z__[j4] = z__[j4p2] * temp; *dnm1 = *dnm2 * temp; @@ -256,8 +83,7 @@ f"> */ z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); *dnm1 = z__[j4p2 + 2] * (*dnm2 / z__[j4 - 2]); } - *dmin__ = min(*dmin__,*dnm1); - + *dmin__ = min(*dmin__, *dnm1); *dmin1 = *dmin__; j4 += 4; j4p2 = j4 + (*pp << 1) - 1; @@ -267,8 +93,7 @@ f"> */ *dn = z__[j4p2 + 2]; *dmin__ = *dn; emin = 0.; - } else if (safmin * z__[j4p2 + 2] < z__[j4 - 2] && safmin * z__[j4 - 2] < - z__[j4p2 + 2]) { + } else if (safmin * z__[j4p2 + 2] < z__[j4 - 2] && safmin * z__[j4 - 2] < z__[j4p2 + 2]) { temp = z__[j4p2 + 2] / z__[j4 - 2]; z__[j4] = z__[j4p2] * temp; *dn = *dnm1 * temp; @@ -276,16 +101,11 @@ f"> */ z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]); *dn = z__[j4p2 + 2] * (*dnm1 / z__[j4 - 2]); } - *dmin__ = min(*dmin__,*dn); - + *dmin__ = min(*dmin__, *dn); z__[j4 + 2] = *dn; z__[(*n0 << 2) - *pp] = emin; return 0; - -/* End of DLASQ6 */ - -} /* dlasq6_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlasr.cpp b/lib/linalg/dlasr.cpp index 5baf2cd50c..83784179fa 100644 --- a/lib/linalg/dlasr.cpp +++ b/lib/linalg/dlasr.cpp @@ -1,300 +1,47 @@ -/* fortran/dlasr.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DLASR applies a sequence of plane rotations to a general rectangular matrix. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLASR + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER DIRECT, PIVOT, SIDE */ -/* INTEGER LDA, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), C( * ), S( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLASR applies a sequence of plane rotations to a real matrix A, */ -/* > from either the left or the right. */ -/* > */ -/* > When SIDE = 'L', the transformation takes the form */ -/* > */ -/* > A := P*A */ -/* > */ -/* > and when SIDE = 'R', the transformation takes the form */ -/* > */ -/* > A := A*P**T */ -/* > */ -/* > where P is an orthogonal matrix consisting of a sequence of z plane */ -/* > rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R', */ -/* > and P**T is the transpose of P. */ -/* > */ -/* > When DIRECT = 'F' (Forward sequence), then */ -/* > */ -/* > P = P(z-1) * ... * P(2) * P(1) */ -/* > */ -/* > and when DIRECT = 'B' (Backward sequence), then */ -/* > */ -/* > P = P(1) * P(2) * ... * P(z-1) */ -/* > */ -/* > where P(k) is a plane rotation matrix defined by the 2-by-2 rotation */ -/* > */ -/* > R(k) = ( c(k) s(k) ) */ -/* > = ( -s(k) c(k) ). */ -/* > */ -/* > When PIVOT = 'V' (Variable pivot), the rotation is performed */ -/* > for the plane (k,k+1), i.e., P(k) has the form */ -/* > */ -/* > P(k) = ( 1 ) */ -/* > ( ... ) */ -/* > ( 1 ) */ -/* > ( c(k) s(k) ) */ -/* > ( -s(k) c(k) ) */ -/* > ( 1 ) */ -/* > ( ... ) */ -/* > ( 1 ) */ -/* > */ -/* > where R(k) appears as a rank-2 modification to the identity matrix in */ -/* > rows and columns k and k+1. */ -/* > */ -/* > When PIVOT = 'T' (Top pivot), the rotation is performed for the */ -/* > plane (1,k+1), so P(k) has the form */ -/* > */ -/* > P(k) = ( c(k) s(k) ) */ -/* > ( 1 ) */ -/* > ( ... ) */ -/* > ( 1 ) */ -/* > ( -s(k) c(k) ) */ -/* > ( 1 ) */ -/* > ( ... ) */ -/* > ( 1 ) */ -/* > */ -/* > where R(k) appears in rows and columns 1 and k+1. */ -/* > */ -/* > Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is */ -/* > performed for the plane (k,z), giving P(k) the form */ -/* > */ -/* > P(k) = ( 1 ) */ -/* > ( ... ) */ -/* > ( 1 ) */ -/* > ( c(k) s(k) ) */ -/* > ( 1 ) */ -/* > ( ... ) */ -/* > ( 1 ) */ -/* > ( -s(k) c(k) ) */ -/* > */ -/* > where R(k) appears in rows and columns k and z. The rotations are */ -/* > performed without ever forming P(k) explicitly. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] SIDE */ -/* > \verbatim */ -/* > SIDE is CHARACTER*1 */ -/* > Specifies whether the plane rotation matrix P is applied to */ -/* > A on the left or the right. */ -/* > = 'L': Left, compute A := P*A */ -/* > = 'R': Right, compute A:= A*P**T */ -/* > \endverbatim */ -/* > */ -/* > \param[in] PIVOT */ -/* > \verbatim */ -/* > PIVOT is CHARACTER*1 */ -/* > Specifies the plane for which P(k) is a plane rotation */ -/* > matrix. */ -/* > = 'V': Variable pivot, the plane (k,k+1) */ -/* > = 'T': Top pivot, the plane (1,k+1) */ -/* > = 'B': Bottom pivot, the plane (k,z) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DIRECT */ -/* > \verbatim */ -/* > DIRECT is CHARACTER*1 */ -/* > Specifies whether P is a forward or backward sequence of */ -/* > plane rotations. */ -/* > = 'F': Forward, P = P(z-1)*...*P(2)*P(1) */ -/* > = 'B': Backward, P = P(1)*P(2)*...*P(z-1) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix A. If m <= 1, an immediate */ -/* > return is effected. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix A. If n <= 1, an */ -/* > immediate return is effected. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] C */ -/* > \verbatim */ -/* > C is DOUBLE PRECISION array, dimension */ -/* > (M-1) if SIDE = 'L' */ -/* > (N-1) if SIDE = 'R' */ -/* > The cosines c(k) of the plane rotations. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] S */ -/* > \verbatim */ -/* > S is DOUBLE PRECISION array, dimension */ -/* > (M-1) if SIDE = 'L' */ -/* > (N-1) if SIDE = 'R' */ -/* > The sines s(k) of the plane rotations. The 2-by-2 plane */ -/* > rotation part of the matrix P(k), R(k), has the form */ -/* > R(k) = ( c(k) s(k) ) */ -/* > ( -s(k) c(k) ). */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > The M-by-N matrix A. On exit, A is overwritten by P*A if */ -/* > SIDE = 'L' or by A*P**T if SIDE = 'R'. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,M). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup OTHERauxiliary */ - -/* ===================================================================== */ -/* Subroutine */ int dlasr_(char *side, char *pivot, char *direct, integer *m, - integer *n, doublereal *c__, doublereal *s, doublereal *a, integer * - lda, ftnlen side_len, ftnlen pivot_len, ftnlen direct_len) +int dlasr_(char *side, char *pivot, char *direct, integer *m, integer *n, doublereal *c__, + doublereal *s, doublereal *a, integer *lda, ftnlen side_len, ftnlen pivot_len, + ftnlen direct_len) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; - - /* Local variables */ integer i__, j, info; doublereal temp; extern logical lsame_(char *, char *, ftnlen, ftnlen); doublereal ctemp, stemp; - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters */ - - /* Parameter adjustments */ + extern int xerbla_(char *, integer *, ftnlen); --c__; --s; a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; - - /* Function Body */ info = 0; - if (! (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1) || lsame_(side, (char *)"R", ( - ftnlen)1, (ftnlen)1))) { + if (!(lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1) || lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1))) { info = 1; - } else if (! (lsame_(pivot, (char *)"V", (ftnlen)1, (ftnlen)1) || lsame_(pivot, - (char *)"T", (ftnlen)1, (ftnlen)1) || lsame_(pivot, (char *)"B", (ftnlen)1, ( - ftnlen)1))) { + } else if (!(lsame_(pivot, (char *)"V", (ftnlen)1, (ftnlen)1) || + lsame_(pivot, (char *)"T", (ftnlen)1, (ftnlen)1) || + lsame_(pivot, (char *)"B", (ftnlen)1, (ftnlen)1))) { info = 2; - } else if (! (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1) || lsame_(direct, - (char *)"B", (ftnlen)1, (ftnlen)1))) { + } else if (!(lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1) || + lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1))) { info = 3; } else if (*m < 0) { info = 4; } else if (*n < 0) { info = 5; - } else if (*lda < max(1,*m)) { + } else if (*lda < max(1, *m)) { info = 9; } if (info != 0) { xerbla_((char *)"DLASR ", &info, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*m == 0 || *n == 0) { return 0; } if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { - -/* Form P * A */ - if (lsame_(pivot, (char *)"V", (ftnlen)1, (ftnlen)1)) { if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { i__1 = *m - 1; @@ -305,14 +52,10 @@ extern "C" { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { temp = a[j + 1 + i__ * a_dim1]; - a[j + 1 + i__ * a_dim1] = ctemp * temp - stemp * - a[j + i__ * a_dim1]; - a[j + i__ * a_dim1] = stemp * temp + ctemp * a[j - + i__ * a_dim1]; -/* L10: */ + a[j + 1 + i__ * a_dim1] = ctemp * temp - stemp * a[j + i__ * a_dim1]; + a[j + i__ * a_dim1] = stemp * temp + ctemp * a[j + i__ * a_dim1]; } } -/* L20: */ } } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { for (j = *m - 1; j >= 1; --j) { @@ -322,14 +65,10 @@ extern "C" { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { temp = a[j + 1 + i__ * a_dim1]; - a[j + 1 + i__ * a_dim1] = ctemp * temp - stemp * - a[j + i__ * a_dim1]; - a[j + i__ * a_dim1] = stemp * temp + ctemp * a[j - + i__ * a_dim1]; -/* L30: */ + a[j + 1 + i__ * a_dim1] = ctemp * temp - stemp * a[j + i__ * a_dim1]; + a[j + i__ * a_dim1] = stemp * temp + ctemp * a[j + i__ * a_dim1]; } } -/* L40: */ } } } else if (lsame_(pivot, (char *)"T", (ftnlen)1, (ftnlen)1)) { @@ -342,14 +81,10 @@ extern "C" { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { temp = a[j + i__ * a_dim1]; - a[j + i__ * a_dim1] = ctemp * temp - stemp * a[ - i__ * a_dim1 + 1]; - a[i__ * a_dim1 + 1] = stemp * temp + ctemp * a[ - i__ * a_dim1 + 1]; -/* L50: */ + a[j + i__ * a_dim1] = ctemp * temp - stemp * a[i__ * a_dim1 + 1]; + a[i__ * a_dim1 + 1] = stemp * temp + ctemp * a[i__ * a_dim1 + 1]; } } -/* L60: */ } } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { for (j = *m; j >= 2; --j) { @@ -359,14 +94,10 @@ extern "C" { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { temp = a[j + i__ * a_dim1]; - a[j + i__ * a_dim1] = ctemp * temp - stemp * a[ - i__ * a_dim1 + 1]; - a[i__ * a_dim1 + 1] = stemp * temp + ctemp * a[ - i__ * a_dim1 + 1]; -/* L70: */ + a[j + i__ * a_dim1] = ctemp * temp - stemp * a[i__ * a_dim1 + 1]; + a[i__ * a_dim1 + 1] = stemp * temp + ctemp * a[i__ * a_dim1 + 1]; } } -/* L80: */ } } } else if (lsame_(pivot, (char *)"B", (ftnlen)1, (ftnlen)1)) { @@ -379,14 +110,10 @@ extern "C" { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { temp = a[j + i__ * a_dim1]; - a[j + i__ * a_dim1] = stemp * a[*m + i__ * a_dim1] - + ctemp * temp; - a[*m + i__ * a_dim1] = ctemp * a[*m + i__ * - a_dim1] - stemp * temp; -/* L90: */ + a[j + i__ * a_dim1] = stemp * a[*m + i__ * a_dim1] + ctemp * temp; + a[*m + i__ * a_dim1] = ctemp * a[*m + i__ * a_dim1] - stemp * temp; } } -/* L100: */ } } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { for (j = *m - 1; j >= 1; --j) { @@ -396,21 +123,14 @@ extern "C" { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { temp = a[j + i__ * a_dim1]; - a[j + i__ * a_dim1] = stemp * a[*m + i__ * a_dim1] - + ctemp * temp; - a[*m + i__ * a_dim1] = ctemp * a[*m + i__ * - a_dim1] - stemp * temp; -/* L110: */ + a[j + i__ * a_dim1] = stemp * a[*m + i__ * a_dim1] + ctemp * temp; + a[*m + i__ * a_dim1] = ctemp * a[*m + i__ * a_dim1] - stemp * temp; } } -/* L120: */ } } } } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { - -/* Form A * P**T */ - if (lsame_(pivot, (char *)"V", (ftnlen)1, (ftnlen)1)) { if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { i__1 = *n - 1; @@ -421,14 +141,10 @@ extern "C" { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { temp = a[i__ + (j + 1) * a_dim1]; - a[i__ + (j + 1) * a_dim1] = ctemp * temp - stemp * - a[i__ + j * a_dim1]; - a[i__ + j * a_dim1] = stemp * temp + ctemp * a[ - i__ + j * a_dim1]; -/* L130: */ + a[i__ + (j + 1) * a_dim1] = ctemp * temp - stemp * a[i__ + j * a_dim1]; + a[i__ + j * a_dim1] = stemp * temp + ctemp * a[i__ + j * a_dim1]; } } -/* L140: */ } } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { for (j = *n - 1; j >= 1; --j) { @@ -438,14 +154,10 @@ extern "C" { i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { temp = a[i__ + (j + 1) * a_dim1]; - a[i__ + (j + 1) * a_dim1] = ctemp * temp - stemp * - a[i__ + j * a_dim1]; - a[i__ + j * a_dim1] = stemp * temp + ctemp * a[ - i__ + j * a_dim1]; -/* L150: */ + a[i__ + (j + 1) * a_dim1] = ctemp * temp - stemp * a[i__ + j * a_dim1]; + a[i__ + j * a_dim1] = stemp * temp + ctemp * a[i__ + j * a_dim1]; } } -/* L160: */ } } } else if (lsame_(pivot, (char *)"T", (ftnlen)1, (ftnlen)1)) { @@ -458,14 +170,10 @@ extern "C" { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { temp = a[i__ + j * a_dim1]; - a[i__ + j * a_dim1] = ctemp * temp - stemp * a[ - i__ + a_dim1]; - a[i__ + a_dim1] = stemp * temp + ctemp * a[i__ + - a_dim1]; -/* L170: */ + a[i__ + j * a_dim1] = ctemp * temp - stemp * a[i__ + a_dim1]; + a[i__ + a_dim1] = stemp * temp + ctemp * a[i__ + a_dim1]; } } -/* L180: */ } } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { for (j = *n; j >= 2; --j) { @@ -475,14 +183,10 @@ extern "C" { i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { temp = a[i__ + j * a_dim1]; - a[i__ + j * a_dim1] = ctemp * temp - stemp * a[ - i__ + a_dim1]; - a[i__ + a_dim1] = stemp * temp + ctemp * a[i__ + - a_dim1]; -/* L190: */ + a[i__ + j * a_dim1] = ctemp * temp - stemp * a[i__ + a_dim1]; + a[i__ + a_dim1] = stemp * temp + ctemp * a[i__ + a_dim1]; } } -/* L200: */ } } } else if (lsame_(pivot, (char *)"B", (ftnlen)1, (ftnlen)1)) { @@ -495,14 +199,10 @@ extern "C" { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { temp = a[i__ + j * a_dim1]; - a[i__ + j * a_dim1] = stemp * a[i__ + *n * a_dim1] - + ctemp * temp; - a[i__ + *n * a_dim1] = ctemp * a[i__ + *n * - a_dim1] - stemp * temp; -/* L210: */ + a[i__ + j * a_dim1] = stemp * a[i__ + *n * a_dim1] + ctemp * temp; + a[i__ + *n * a_dim1] = ctemp * a[i__ + *n * a_dim1] - stemp * temp; } } -/* L220: */ } } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { for (j = *n - 1; j >= 1; --j) { @@ -512,25 +212,16 @@ extern "C" { i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { temp = a[i__ + j * a_dim1]; - a[i__ + j * a_dim1] = stemp * a[i__ + *n * a_dim1] - + ctemp * temp; - a[i__ + *n * a_dim1] = ctemp * a[i__ + *n * - a_dim1] - stemp * temp; -/* L230: */ + a[i__ + j * a_dim1] = stemp * a[i__ + *n * a_dim1] + ctemp * temp; + a[i__ + *n * a_dim1] = ctemp * a[i__ + *n * a_dim1] - stemp * temp; } } -/* L240: */ } } } } - return 0; - -/* End of DLASR */ - -} /* dlasr_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlasrt.cpp b/lib/linalg/dlasrt.cpp index a796f6e568..9724ce322b 100644 --- a/lib/linalg/dlasrt.cpp +++ b/lib/linalg/dlasrt.cpp @@ -1,158 +1,22 @@ -/* fortran/dlasrt.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DLASRT sorts numbers in increasing or decreasing order. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLASRT + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLASRT( ID, N, D, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER ID */ -/* INTEGER INFO, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION D( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > Sort the numbers in D in increasing order (if ID = 'I') or */ -/* > in decreasing order (if ID = 'D' ). */ -/* > */ -/* > Use Quick Sort, reverting to Insertion sort on arrays of */ -/* > size <= 20. Dimension of STACK limits N to about 2**32. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] ID */ -/* > \verbatim */ -/* > ID is CHARACTER*1 */ -/* > = 'I': sort D in increasing order; */ -/* > = 'D': sort D in decreasing order. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The length of the array D. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension (N) */ -/* > On entry, the array to be sorted. */ -/* > On exit, D has been sorted into increasing order */ -/* > (D(1) <= ... <= D(N) ) or into decreasing order */ -/* > (D(1) >= ... >= D(N) ), depending on ID. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup auxOTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dlasrt_(char *id, integer *n, doublereal *d__, integer * - info, ftnlen id_len) +int dlasrt_(char *id, integer *n, doublereal *d__, integer *info, ftnlen id_len) { - /* System generated locals */ integer i__1, i__2; - - /* Local variables */ integer i__, j; doublereal d1, d2, d3; integer dir; doublereal tmp; integer endd; extern logical lsame_(char *, char *, ftnlen, ftnlen); - integer stack[64] /* was [2][32] */; + integer stack[64]; doublereal dmnmx; integer start; - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern int xerbla_(char *, integer *, ftnlen); integer stkpnt; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. Local Arrays .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ --d__; - - /* Function Body */ *info = 0; dir = -1; if (lsame_(id, (char *)"D", (ftnlen)1, (ftnlen)1)) { @@ -170,13 +34,9 @@ f"> */ xerbla_((char *)"DLASRT", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*n <= 1) { return 0; } - stkpnt = 1; stack[0] = 1; stack[1] = *n; @@ -185,13 +45,7 @@ L10: endd = stack[(stkpnt << 1) - 1]; --stkpnt; if (endd - start <= 20 && endd - start > 0) { - -/* Do Insertion sort on D( START:ENDD ) */ - if (dir == 0) { - -/* Sort into decreasing order */ - i__1 = endd; for (i__ = start + 1; i__ <= i__1; ++i__) { i__2 = start + 1; @@ -203,16 +57,10 @@ L10: } else { goto L30; } -/* L20: */ } -L30: - ; + L30:; } - } else { - -/* Sort into increasing order */ - i__1 = endd; for (i__ = start + 1; i__ <= i__1; ++i__) { i__2 = start + 1; @@ -224,20 +72,11 @@ L30: } else { goto L50; } -/* L40: */ } -L50: - ; + L50:; } - } - } else if (endd - start > 20) { - -/* Partition D( START:ENDD ) and stack parts, largest one first */ - -/* Choose partition entry as median of 3 */ - d1 = d__[start]; d2 = d__[endd]; i__ = (start + endd) / 2; @@ -259,20 +98,16 @@ L50: dmnmx = d1; } } - if (dir == 0) { - -/* Sort into decreasing order */ - i__ = start - 1; j = endd + 1; -L60: -L70: + L60: + L70: --j; if (d__[j] < dmnmx) { goto L70; } -L80: + L80: ++i__; if (d__[i__] > dmnmx) { goto L80; @@ -299,18 +134,15 @@ L80: stack[(stkpnt << 1) - 1] = j; } } else { - -/* Sort into increasing order */ - i__ = start - 1; j = endd + 1; -L90: -L100: + L90: + L100: --j; if (d__[j] > dmnmx) { goto L100; } -L110: + L110: ++i__; if (d__[i__] < dmnmx) { goto L110; @@ -342,11 +174,7 @@ L110: goto L10; } return 0; - -/* End of DLASRT */ - -} /* dlasrt_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlassq.cpp b/lib/linalg/dlassq.cpp index 76391a54f9..84e8690a14 100644 --- a/lib/linalg/dlassq.cpp +++ b/lib/linalg/dlassq.cpp @@ -1,165 +1,15 @@ -/* fortran/dlassq.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DLASSQ updates a sum of squares represented in scaled form. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLASSQ + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLASSQ( N, X, INCX, SCALE, SUMSQ ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INCX, N */ -/* DOUBLE PRECISION SCALE, SUMSQ */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION X( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLASSQ returns the values scl and smsq such that */ -/* > */ -/* > ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq, */ -/* > */ -/* > where x( i ) = X( 1 + ( i - 1 )*INCX ). The value of sumsq is */ -/* > assumed to be non-negative and scl returns the value */ -/* > */ -/* > scl = max( scale, abs( x( i ) ) ). */ -/* > */ -/* > scale and sumsq must be supplied in SCALE and SUMSQ and */ -/* > scl and smsq are overwritten on SCALE and SUMSQ respectively. */ -/* > */ -/* > The routine makes only one pass through the vector x. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of elements to be used from the vector X. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] X */ -/* > \verbatim */ -/* > X is DOUBLE PRECISION array, dimension (N) */ -/* > The vector for which a scaled sum of squares is computed. */ -/* > x( i ) = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > The increment between successive values of the vector X. */ -/* > INCX > 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] SCALE */ -/* > \verbatim */ -/* > SCALE is DOUBLE PRECISION */ -/* > On entry, the value scale in the equation above. */ -/* > On exit, SCALE is overwritten with scl , the scaling factor */ -/* > for the sum of squares. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] SUMSQ */ -/* > \verbatim */ -/* > SUMSQ is DOUBLE PRECISION */ -/* > On entry, the value sumsq in the equation above. */ -/* > On exit, SUMSQ is overwritten with smsq , the basic sum of */ -/* > squares from which scl has been factored out. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \date December 2016 */ - -/* > \ingroup OTHERauxiliary */ - -/* ===================================================================== */ -/* Subroutine */ int dlassq_(integer *n, doublereal *x, integer *incx, - doublereal *scale, doublereal *sumsq) +int dlassq_(integer *n, doublereal *x, integer *incx, doublereal *scale, doublereal *sumsq) { - /* System generated locals */ integer i__1, i__2; doublereal d__1; - - /* Local variables */ integer ix; doublereal absxi; extern logical disnan_(doublereal *); - - -/* -- LAPACK auxiliary routine (version 3.7.0) -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ -/* December 2016 */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - - /* Parameter adjustments */ --x; - - /* Function Body */ if (*n > 0) { i__1 = (*n - 1) * *incx + 1; i__2 = *incx; @@ -167,25 +17,18 @@ f"> */ absxi = (d__1 = x[ix], abs(d__1)); if (absxi > 0. || disnan_(&absxi)) { if (*scale < absxi) { -/* Computing 2nd power */ d__1 = *scale / absxi; *sumsq = *sumsq * (d__1 * d__1) + 1; *scale = absxi; } else { -/* Computing 2nd power */ d__1 = absxi / *scale; *sumsq += d__1 * d__1; } } -/* L10: */ } } return 0; - -/* End of DLASSQ */ - -} /* dlassq_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlasv2.cpp b/lib/linalg/dlasv2.cpp index 7dde3369fc..6de3269b8f 100644 --- a/lib/linalg/dlasv2.cpp +++ b/lib/linalg/dlasv2.cpp @@ -1,214 +1,25 @@ -/* fortran/dlasv2.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static doublereal c_b3 = 2.; static doublereal c_b4 = 1.; - -/* > \brief \b DLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLASV2 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLASV2( F, G, H, SSMIN, SSMAX, SNR, CSR, SNL, CSL ) */ - -/* .. Scalar Arguments .. */ -/* DOUBLE PRECISION CSL, CSR, F, G, H, SNL, SNR, SSMAX, SSMIN */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLASV2 computes the singular value decomposition of a 2-by-2 */ -/* > triangular matrix */ -/* > [ F G ] */ -/* > [ 0 H ]. */ -/* > On return, abs(SSMAX) is the larger singular value, abs(SSMIN) is the */ -/* > smaller singular value, and (CSL,SNL) and (CSR,SNR) are the left and */ -/* > right singular vectors for abs(SSMAX), giving the decomposition */ -/* > */ -/* > [ CSL SNL ] [ F G ] [ CSR -SNR ] = [ SSMAX 0 ] */ -/* > [-SNL CSL ] [ 0 H ] [ SNR CSR ] [ 0 SSMIN ]. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] F */ -/* > \verbatim */ -/* > F is DOUBLE PRECISION */ -/* > The (1,1) element of the 2-by-2 matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] G */ -/* > \verbatim */ -/* > G is DOUBLE PRECISION */ -/* > The (1,2) element of the 2-by-2 matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] H */ -/* > \verbatim */ -/* > H is DOUBLE PRECISION */ -/* > The (2,2) element of the 2-by-2 matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] SSMIN */ -/* > \verbatim */ -/* > SSMIN is DOUBLE PRECISION */ -/* > abs(SSMIN) is the smaller singular value. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] SSMAX */ -/* > \verbatim */ -/* > SSMAX is DOUBLE PRECISION */ -/* > abs(SSMAX) is the larger singular value. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] SNL */ -/* > \verbatim */ -/* > SNL is DOUBLE PRECISION */ -/* > \endverbatim */ -/* > */ -/* > \param[out] CSL */ -/* > \verbatim */ -/* > CSL is DOUBLE PRECISION */ -/* > The vector (CSL, SNL) is a unit left singular vector for the */ -/* > singular value abs(SSMAX). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] SNR */ -/* > \verbatim */ -/* > SNR is DOUBLE PRECISION */ -/* > \endverbatim */ -/* > */ -/* > \param[out] CSR */ -/* > \verbatim */ -/* > CSR is DOUBLE PRECISION */ -/* > The vector (CSR, SNR) is a unit right singular vector for the */ -/* > singular value abs(SSMAX). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup OTHERauxiliary */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > Any input parameter may be aliased with any output parameter. */ -/* > */ -/* > Barring over/underflow and assuming a guard digit in subtraction, all */ -/* > output quantities are correct to within a few units in the last */ -/* > place (ulps). */ -/* > */ -/* > In IEEE arithmetic, the code works correctly if one matrix element is */ -/* > infinite. */ -/* > */ -/* > Overflow will not occur unless the largest singular value itself */ -/* > overflows or is within a few ulps of overflow. (On machines with */ -/* > partial overflow, like the Cray, overflow may occur if the largest */ -/* > singular value is within a factor of 2 of overflow.) */ -/* > */ -/* > Underflow is harmless if underflow is gradual. Otherwise, results */ -/* > may correspond to a matrix modified by perturbations of size near */ -/* > the underflow threshold. */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dlasv2_(doublereal *f, doublereal *g, doublereal *h__, - doublereal *ssmin, doublereal *ssmax, doublereal *snr, doublereal * - csr, doublereal *snl, doublereal *csl) +int dlasv2_(doublereal *f, doublereal *g, doublereal *h__, doublereal *ssmin, doublereal *ssmax, + doublereal *snr, doublereal *csr, doublereal *snl, doublereal *csl) { - /* System generated locals */ doublereal d__1; - - /* Builtin functions */ double sqrt(doublereal), d_lmp_sign(doublereal *, doublereal *); - - /* Local variables */ - doublereal a, d__, l, m, r__, s, t, fa, ga, ha, ft, gt, ht, mm, tt, clt, - crt, slt, srt; + doublereal a, d__, l, m, r__, s, t, fa, ga, ha, ft, gt, ht, mm, tt, clt, crt, slt, srt; integer pmax; doublereal temp; logical swap; doublereal tsign; extern doublereal dlamch_(char *, ftnlen); logical gasmal; - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - ft = *f; fa = abs(ft); ht = *h__; ha = abs(*h__); - -/* PMAX points to the maximum absolute element of matrix */ -/* PMAX = 1 if F largest in absolute values */ -/* PMAX = 2 if G largest in absolute values */ -/* PMAX = 3 if H largest in absolute values */ - pmax = 1; swap = ha > fa; if (swap) { @@ -219,16 +30,10 @@ f"> */ temp = fa; fa = ha; ha = temp; - -/* Now FA .ge. HA */ - } gt = *g; ga = abs(gt); if (ga == 0.) { - -/* Diagonal matrix */ - *ssmin = ha; *ssmax = fa; clt = 1.; @@ -240,9 +45,6 @@ f"> */ if (ga > fa) { pmax = 2; if (fa / ga < dlamch_((char *)"EPS", (ftnlen)3)) { - -/* Case of very large GA */ - gasmal = FALSE_; *ssmax = ga; if (ha > 1.) { @@ -257,53 +59,26 @@ f"> */ } } if (gasmal) { - -/* Normal case */ - d__ = fa - ha; if (d__ == fa) { - -/* Copes with infinite F or H */ - l = 1.; } else { l = d__ / fa; } - -/* Note that 0 .le. L .le. 1 */ - m = gt / ft; - -/* Note that abs(M) .le. 1/macheps */ - t = 2. - l; - -/* Note that T .ge. 1 */ - mm = m * m; tt = t * t; s = sqrt(tt + mm); - -/* Note that 1 .le. S .le. 1 + 1/macheps */ - if (l == 0.) { r__ = abs(m); } else { r__ = sqrt(l * l + mm); } - -/* Note that 0 .le. R .le. 1 + 1/macheps */ - a = (s + r__) * .5; - -/* Note that 1 .le. A .le. 1 + abs(M) */ - *ssmin = ha / a; *ssmax = fa * a; if (mm == 0.) { - -/* Note that M is very tiny */ - if (l == 0.) { t = d_lmp_sign(&c_b3, &ft) * d_lmp_sign(&c_b4, >); } else { @@ -330,9 +105,6 @@ f"> */ *csr = crt; *snr = srt; } - -/* Correct signs of SSMAX and SSMIN */ - if (pmax == 1) { tsign = d_lmp_sign(&c_b4, csr) * d_lmp_sign(&c_b4, csl) * d_lmp_sign(&c_b4, f); } @@ -346,11 +118,7 @@ f"> */ d__1 = tsign * d_lmp_sign(&c_b4, f) * d_lmp_sign(&c_b4, h__); *ssmin = d_lmp_sign(ssmin, &d__1); return 0; - -/* End of DLASV2 */ - -} /* dlasv2_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlaswp.cpp b/lib/linalg/dlaswp.cpp index 05d911f30c..d52226729f 100644 --- a/lib/linalg/dlaswp.cpp +++ b/lib/linalg/dlaswp.cpp @@ -1,172 +1,17 @@ -/* fortran/dlaswp.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DLASWP performs a series of row interchanges on a general rectangular matrix. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLASWP + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLASWP( N, A, LDA, K1, K2, IPIV, INCX ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INCX, K1, K2, LDA, N */ -/* .. */ -/* .. Array Arguments .. */ -/* INTEGER IPIV( * ) */ -/* DOUBLE PRECISION A( LDA, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLASWP performs a series of row interchanges on the matrix A. */ -/* > One row interchange is initiated for each of rows K1 through K2 of A. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On entry, the matrix of column dimension N to which the row */ -/* > interchanges will be applied. */ -/* > On exit, the permuted matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K1 */ -/* > \verbatim */ -/* > K1 is INTEGER */ -/* > The first element of IPIV for which a row interchange will */ -/* > be done. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K2 */ -/* > \verbatim */ -/* > K2 is INTEGER */ -/* > (K2-K1+1) is the number of elements of IPIV for which a row */ -/* > interchange will be done. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] IPIV */ -/* > \verbatim */ -/* > IPIV is INTEGER array, dimension (K1+(K2-K1)*abs(INCX)) */ -/* > The vector of pivot indices. Only the elements in positions */ -/* > K1 through K1+(K2-K1)*abs(INCX) of IPIV are accessed. */ -/* > IPIV(K1+(K-K1)*abs(INCX)) = L implies rows K and L are to be */ -/* > interchanged. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > The increment between successive values of IPIV. If INCX */ -/* > is negative, the pivots are applied in reverse order. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleOTHERauxiliary */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > Modified by */ -/* > R. C. Whaley, Computer Science Dept., Univ. of Tenn., Knoxville, USA */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dlaswp_(integer *n, doublereal *a, integer *lda, integer - *k1, integer *k2, integer *ipiv, integer *incx) +int dlaswp_(integer *n, doublereal *a, integer *lda, integer *k1, integer *k2, integer *ipiv, + integer *incx) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4; - - /* Local variables */ integer i__, j, k, i1, i2, n32, ip, ix, ix0, inc; doublereal temp; - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Local Scalars .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Interchange row I with row IPIV(K1+(I-K1)*abs(INCX)) for each of rows */ -/* K1 through K2. */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --ipiv; - - /* Function Body */ if (*incx > 0) { ix0 = *k1; i1 = *k1; @@ -180,7 +25,6 @@ f"> */ } else { return 0; } - n32 = *n / 32 << 5; if (n32 != 0) { i__1 = n32; @@ -188,8 +32,7 @@ f"> */ ix = ix0; i__2 = i2; i__3 = inc; - for (i__ = i1; i__3 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__3) - { + for (i__ = i1; i__3 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__3) { ip = ipiv[ix]; if (ip != i__) { i__4 = j + 31; @@ -197,13 +40,10 @@ f"> */ temp = a[i__ + k * a_dim1]; a[i__ + k * a_dim1] = a[ip + k * a_dim1]; a[ip + k * a_dim1] = temp; -/* L10: */ } } ix += *incx; -/* L20: */ } -/* L30: */ } } if (n32 != *n) { @@ -219,20 +59,13 @@ f"> */ temp = a[i__ + k * a_dim1]; a[i__ + k * a_dim1] = a[ip + k * a_dim1]; a[ip + k * a_dim1] = temp; -/* L40: */ } } ix += *incx; -/* L50: */ } } - return 0; - -/* End of DLASWP */ - -} /* dlaswp_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlatrd.cpp b/lib/linalg/dlatrd.cpp index 74fc5fcc87..32b131c233 100644 --- a/lib/linalg/dlatrd.cpp +++ b/lib/linalg/dlatrd.cpp @@ -1,278 +1,26 @@ -/* fortran/dlatrd.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static doublereal c_b5 = -1.; static doublereal c_b6 = 1.; static integer c__1 = 1; static doublereal c_b16 = 0.; - -/* > \brief \b DLATRD reduces the first nb rows and columns of a symmetric/Hermitian matrix A to real tridiago -nal form by an orthogonal similarity transformation. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLATRD + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLATRD( UPLO, N, NB, A, LDA, E, TAU, W, LDW ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER UPLO */ -/* INTEGER LDA, LDW, N, NB */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), E( * ), TAU( * ), W( LDW, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLATRD reduces NB rows and columns of a real symmetric matrix A to */ -/* > symmetric tridiagonal form by an orthogonal similarity */ -/* > transformation Q**T * A * Q, and returns the matrices V and W which are */ -/* > needed to apply the transformation to the unreduced part of A. */ -/* > */ -/* > If UPLO = 'U', DLATRD reduces the last NB rows and columns of a */ -/* > matrix, of which the upper triangle is supplied; */ -/* > if UPLO = 'L', DLATRD reduces the first NB rows and columns of a */ -/* > matrix, of which the lower triangle is supplied. */ -/* > */ -/* > This is an auxiliary routine called by DSYTRD. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > Specifies whether the upper or lower triangular part of the */ -/* > symmetric matrix A is stored: */ -/* > = 'U': Upper triangular */ -/* > = 'L': Lower triangular */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrix A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] NB */ -/* > \verbatim */ -/* > NB is INTEGER */ -/* > The number of rows and columns to be reduced. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On entry, the symmetric matrix A. If UPLO = 'U', the leading */ -/* > n-by-n upper triangular part of A contains the upper */ -/* > triangular part of the matrix A, and the strictly lower */ -/* > triangular part of A is not referenced. If UPLO = 'L', the */ -/* > leading n-by-n lower triangular part of A contains the lower */ -/* > triangular part of the matrix A, and the strictly upper */ -/* > triangular part of A is not referenced. */ -/* > On exit: */ -/* > if UPLO = 'U', the last NB columns have been reduced to */ -/* > tridiagonal form, with the diagonal elements overwriting */ -/* > the diagonal elements of A; the elements above the diagonal */ -/* > with the array TAU, represent the orthogonal matrix Q as a */ -/* > product of elementary reflectors; */ -/* > if UPLO = 'L', the first NB columns have been reduced to */ -/* > tridiagonal form, with the diagonal elements overwriting */ -/* > the diagonal elements of A; the elements below the diagonal */ -/* > with the array TAU, represent the orthogonal matrix Q as a */ -/* > product of elementary reflectors. */ -/* > See Further Details. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= (1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] E */ -/* > \verbatim */ -/* > E is DOUBLE PRECISION array, dimension (N-1) */ -/* > If UPLO = 'U', E(n-nb:n-1) contains the superdiagonal */ -/* > elements of the last NB columns of the reduced matrix; */ -/* > if UPLO = 'L', E(1:nb) contains the subdiagonal elements of */ -/* > the first NB columns of the reduced matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] TAU */ -/* > \verbatim */ -/* > TAU is DOUBLE PRECISION array, dimension (N-1) */ -/* > The scalar factors of the elementary reflectors, stored in */ -/* > TAU(n-nb:n-1) if UPLO = 'U', and in TAU(1:nb) if UPLO = 'L'. */ -/* > See Further Details. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] W */ -/* > \verbatim */ -/* > W is DOUBLE PRECISION array, dimension (LDW,NB) */ -/* > The n-by-nb matrix W required to update the unreduced part */ -/* > of A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDW */ -/* > \verbatim */ -/* > LDW is INTEGER */ -/* > The leading dimension of the array W. LDW >= max(1,N). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleOTHERauxiliary */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > If UPLO = 'U', the matrix Q is represented as a product of elementary */ -/* > reflectors */ -/* > */ -/* > Q = H(n) H(n-1) . . . H(n-nb+1). */ -/* > */ -/* > Each H(i) has the form */ -/* > */ -/* > H(i) = I - tau * v * v**T */ -/* > */ -/* > where tau is a real scalar, and v is a real vector with */ -/* > v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i), */ -/* > and tau in TAU(i-1). */ -/* > */ -/* > If UPLO = 'L', the matrix Q is represented as a product of elementary */ -/* > reflectors */ -/* > */ -/* > Q = H(1) H(2) . . . H(nb). */ -/* > */ -/* > Each H(i) has the form */ -/* > */ -/* > H(i) = I - tau * v * v**T */ -/* > */ -/* > where tau is a real scalar, and v is a real vector with */ -/* > v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i), */ -/* > and tau in TAU(i). */ -/* > */ -/* > The elements of the vectors v together form the n-by-nb matrix V */ -/* > which is needed, with W, to apply the transformation to the unreduced */ -/* > part of the matrix, using a symmetric rank-2k update of the form: */ -/* > A := A - V*W**T - W*V**T. */ -/* > */ -/* > The contents of A on exit are illustrated by the following examples */ -/* > with n = 5 and nb = 2: */ -/* > */ -/* > if UPLO = 'U': if UPLO = 'L': */ -/* > */ -/* > ( a a a v4 v5 ) ( d ) */ -/* > ( a a v4 v5 ) ( 1 d ) */ -/* > ( a 1 v5 ) ( v1 1 a ) */ -/* > ( d 1 ) ( v1 v2 a a ) */ -/* > ( d ) ( v1 v2 a a a ) */ -/* > */ -/* > where d denotes a diagonal element of the reduced matrix, a denotes */ -/* > an element of the original matrix that is unchanged, and vi denotes */ -/* > an element of the vector defining H(i). */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dlatrd_(char *uplo, integer *n, integer *nb, doublereal * - a, integer *lda, doublereal *e, doublereal *tau, doublereal *w, - integer *ldw, ftnlen uplo_len) +int dlatrd_(char *uplo, integer *n, integer *nb, doublereal *a, integer *lda, doublereal *e, + doublereal *tau, doublereal *w, integer *ldw, ftnlen uplo_len) { - /* System generated locals */ integer a_dim1, a_offset, w_dim1, w_offset, i__1, i__2, i__3; - - /* Local variables */ integer i__, iw; - extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, - integer *); + extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, integer *); doublereal alpha; - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *); + extern int dscal_(integer *, doublereal *, doublereal *, integer *); extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int dgemv_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, doublereal *, integer *, - doublereal *, doublereal *, integer *, ftnlen), daxpy_(integer *, - doublereal *, doublereal *, integer *, doublereal *, integer *), - dsymv_(char *, integer *, doublereal *, doublereal *, integer *, - doublereal *, integer *, doublereal *, doublereal *, integer *, - ftnlen), dlarfg_(integer *, doublereal *, doublereal *, integer *, - doublereal *); - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Quick return if possible */ - - /* Parameter adjustments */ + extern int dgemv_(char *, integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, ftnlen), + daxpy_(integer *, doublereal *, doublereal *, integer *, doublereal *, integer *), + dsymv_(char *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, ftnlen), + dlarfg_(integer *, doublereal *, doublereal *, integer *, doublereal *); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; @@ -281,165 +29,119 @@ f"> */ w_dim1 = *ldw; w_offset = 1 + w_dim1; w -= w_offset; - - /* Function Body */ if (*n <= 0) { return 0; } - if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { - -/* Reduce last NB columns of upper triangle */ - i__1 = *n - *nb + 1; for (i__ = *n; i__ >= i__1; --i__) { iw = i__ - *n + *nb; if (i__ < *n) { - -/* Update A(1:i,i) */ - i__2 = *n - i__; - dgemv_((char *)"No transpose", &i__, &i__2, &c_b5, &a[(i__ + 1) * - a_dim1 + 1], lda, &w[i__ + (iw + 1) * w_dim1], ldw, & - c_b6, &a[i__ * a_dim1 + 1], &c__1, (ftnlen)12); + dgemv_((char *)"No transpose", &i__, &i__2, &c_b5, &a[(i__ + 1) * a_dim1 + 1], lda, + &w[i__ + (iw + 1) * w_dim1], ldw, &c_b6, &a[i__ * a_dim1 + 1], &c__1, + (ftnlen)12); i__2 = *n - i__; - dgemv_((char *)"No transpose", &i__, &i__2, &c_b5, &w[(iw + 1) * - w_dim1 + 1], ldw, &a[i__ + (i__ + 1) * a_dim1], lda, & - c_b6, &a[i__ * a_dim1 + 1], &c__1, (ftnlen)12); + dgemv_((char *)"No transpose", &i__, &i__2, &c_b5, &w[(iw + 1) * w_dim1 + 1], ldw, + &a[i__ + (i__ + 1) * a_dim1], lda, &c_b6, &a[i__ * a_dim1 + 1], &c__1, + (ftnlen)12); } if (i__ > 1) { - -/* Generate elementary reflector H(i) to annihilate */ -/* A(1:i-2,i) */ - i__2 = i__ - 1; - dlarfg_(&i__2, &a[i__ - 1 + i__ * a_dim1], &a[i__ * a_dim1 + - 1], &c__1, &tau[i__ - 1]); + dlarfg_(&i__2, &a[i__ - 1 + i__ * a_dim1], &a[i__ * a_dim1 + 1], &c__1, + &tau[i__ - 1]); e[i__ - 1] = a[i__ - 1 + i__ * a_dim1]; a[i__ - 1 + i__ * a_dim1] = 1.; - -/* Compute W(1:i-1,i) */ - i__2 = i__ - 1; - dsymv_((char *)"Upper", &i__2, &c_b6, &a[a_offset], lda, &a[i__ * - a_dim1 + 1], &c__1, &c_b16, &w[iw * w_dim1 + 1], & - c__1, (ftnlen)5); + dsymv_((char *)"Upper", &i__2, &c_b6, &a[a_offset], lda, &a[i__ * a_dim1 + 1], &c__1, + &c_b16, &w[iw * w_dim1 + 1], &c__1, (ftnlen)5); if (i__ < *n) { i__2 = i__ - 1; i__3 = *n - i__; - dgemv_((char *)"Transpose", &i__2, &i__3, &c_b6, &w[(iw + 1) * - w_dim1 + 1], ldw, &a[i__ * a_dim1 + 1], &c__1, & - c_b16, &w[i__ + 1 + iw * w_dim1], &c__1, (ftnlen) - 9); + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b6, &w[(iw + 1) * w_dim1 + 1], ldw, + &a[i__ * a_dim1 + 1], &c__1, &c_b16, &w[i__ + 1 + iw * w_dim1], &c__1, + (ftnlen)9); i__2 = i__ - 1; i__3 = *n - i__; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[(i__ + 1) * - a_dim1 + 1], lda, &w[i__ + 1 + iw * w_dim1], & - c__1, &c_b6, &w[iw * w_dim1 + 1], &c__1, (ftnlen) - 12); + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[(i__ + 1) * a_dim1 + 1], lda, + &w[i__ + 1 + iw * w_dim1], &c__1, &c_b6, &w[iw * w_dim1 + 1], &c__1, + (ftnlen)12); i__2 = i__ - 1; i__3 = *n - i__; - dgemv_((char *)"Transpose", &i__2, &i__3, &c_b6, &a[(i__ + 1) * - a_dim1 + 1], lda, &a[i__ * a_dim1 + 1], &c__1, & - c_b16, &w[i__ + 1 + iw * w_dim1], &c__1, (ftnlen) - 9); + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b6, &a[(i__ + 1) * a_dim1 + 1], lda, + &a[i__ * a_dim1 + 1], &c__1, &c_b16, &w[i__ + 1 + iw * w_dim1], &c__1, + (ftnlen)9); i__2 = i__ - 1; i__3 = *n - i__; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &w[(iw + 1) * - w_dim1 + 1], ldw, &w[i__ + 1 + iw * w_dim1], & - c__1, &c_b6, &w[iw * w_dim1 + 1], &c__1, (ftnlen) - 12); + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &w[(iw + 1) * w_dim1 + 1], ldw, + &w[i__ + 1 + iw * w_dim1], &c__1, &c_b6, &w[iw * w_dim1 + 1], &c__1, + (ftnlen)12); } i__2 = i__ - 1; dscal_(&i__2, &tau[i__ - 1], &w[iw * w_dim1 + 1], &c__1); i__2 = i__ - 1; - alpha = tau[i__ - 1] * -.5 * ddot_(&i__2, &w[iw * w_dim1 + 1], - &c__1, &a[i__ * a_dim1 + 1], &c__1); + alpha = tau[i__ - 1] * -.5 * + ddot_(&i__2, &w[iw * w_dim1 + 1], &c__1, &a[i__ * a_dim1 + 1], &c__1); i__2 = i__ - 1; - daxpy_(&i__2, &alpha, &a[i__ * a_dim1 + 1], &c__1, &w[iw * - w_dim1 + 1], &c__1); + daxpy_(&i__2, &alpha, &a[i__ * a_dim1 + 1], &c__1, &w[iw * w_dim1 + 1], &c__1); } - -/* L10: */ } } else { - -/* Reduce first NB columns of lower triangle */ - i__1 = *nb; for (i__ = 1; i__ <= i__1; ++i__) { - -/* Update A(i:n,i) */ - i__2 = *n - i__ + 1; i__3 = i__ - 1; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[i__ + a_dim1], lda, - &w[i__ + w_dim1], ldw, &c_b6, &a[i__ + i__ * a_dim1], & - c__1, (ftnlen)12); + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[i__ + a_dim1], lda, &w[i__ + w_dim1], + ldw, &c_b6, &a[i__ + i__ * a_dim1], &c__1, (ftnlen)12); i__2 = *n - i__ + 1; i__3 = i__ - 1; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &w[i__ + w_dim1], ldw, - &a[i__ + a_dim1], lda, &c_b6, &a[i__ + i__ * a_dim1], & - c__1, (ftnlen)12); + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &w[i__ + w_dim1], ldw, &a[i__ + a_dim1], + lda, &c_b6, &a[i__ + i__ * a_dim1], &c__1, (ftnlen)12); if (i__ < *n) { - -/* Generate elementary reflector H(i) to annihilate */ -/* A(i+2:n,i) */ - i__2 = *n - i__; -/* Computing MIN */ i__3 = i__ + 2; - dlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3,*n) + - i__ * a_dim1], &c__1, &tau[i__]); + dlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3, *n) + i__ * a_dim1], &c__1, + &tau[i__]); e[i__] = a[i__ + 1 + i__ * a_dim1]; a[i__ + 1 + i__ * a_dim1] = 1.; - -/* Compute W(i+1:n,i) */ - i__2 = *n - i__; - dsymv_((char *)"Lower", &i__2, &c_b6, &a[i__ + 1 + (i__ + 1) * a_dim1] - , lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[ - i__ + 1 + i__ * w_dim1], &c__1, (ftnlen)5); + dsymv_((char *)"Lower", &i__2, &c_b6, &a[i__ + 1 + (i__ + 1) * a_dim1], lda, + &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[i__ + 1 + i__ * w_dim1], &c__1, + (ftnlen)5); i__2 = *n - i__; i__3 = i__ - 1; - dgemv_((char *)"Transpose", &i__2, &i__3, &c_b6, &w[i__ + 1 + w_dim1], - ldw, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[ - i__ * w_dim1 + 1], &c__1, (ftnlen)9); + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b6, &w[i__ + 1 + w_dim1], ldw, + &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[i__ * w_dim1 + 1], &c__1, + (ftnlen)9); i__2 = *n - i__; i__3 = i__ - 1; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + - a_dim1], lda, &w[i__ * w_dim1 + 1], &c__1, &c_b6, &w[ - i__ + 1 + i__ * w_dim1], &c__1, (ftnlen)12); + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + a_dim1], lda, + &w[i__ * w_dim1 + 1], &c__1, &c_b6, &w[i__ + 1 + i__ * w_dim1], &c__1, + (ftnlen)12); i__2 = *n - i__; i__3 = i__ - 1; - dgemv_((char *)"Transpose", &i__2, &i__3, &c_b6, &a[i__ + 1 + a_dim1], - lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[ - i__ * w_dim1 + 1], &c__1, (ftnlen)9); + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b6, &a[i__ + 1 + a_dim1], lda, + &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &w[i__ * w_dim1 + 1], &c__1, + (ftnlen)9); i__2 = *n - i__; i__3 = i__ - 1; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &w[i__ + 1 + - w_dim1], ldw, &w[i__ * w_dim1 + 1], &c__1, &c_b6, &w[ - i__ + 1 + i__ * w_dim1], &c__1, (ftnlen)12); + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b5, &w[i__ + 1 + w_dim1], ldw, + &w[i__ * w_dim1 + 1], &c__1, &c_b6, &w[i__ + 1 + i__ * w_dim1], &c__1, + (ftnlen)12); i__2 = *n - i__; dscal_(&i__2, &tau[i__], &w[i__ + 1 + i__ * w_dim1], &c__1); i__2 = *n - i__; - alpha = tau[i__] * -.5 * ddot_(&i__2, &w[i__ + 1 + i__ * - w_dim1], &c__1, &a[i__ + 1 + i__ * a_dim1], &c__1); + alpha = tau[i__] * -.5 * + ddot_(&i__2, &w[i__ + 1 + i__ * w_dim1], &c__1, &a[i__ + 1 + i__ * a_dim1], + &c__1); i__2 = *n - i__; - daxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &w[ - i__ + 1 + i__ * w_dim1], &c__1); + daxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &w[i__ + 1 + i__ * w_dim1], + &c__1); } - -/* L20: */ } } - return 0; - -/* End of DLATRD */ - -} /* dlatrd_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dlatrs.cpp b/lib/linalg/dlatrs.cpp index fc97690682..bd2af669dc 100644 --- a/lib/linalg/dlatrs.cpp +++ b/lib/linalg/dlatrs.cpp @@ -1,356 +1,62 @@ -/* fortran/dlatrs.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static doublereal c_b46 = .5; - -/* > \brief \b DLATRS solves a triangular system of equations with the scale factor set to prevent overflow. -*/ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DLATRS + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DLATRS( UPLO, TRANS, DIAG, NORMIN, N, A, LDA, X, SCALE, */ -/* CNORM, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER DIAG, NORMIN, TRANS, UPLO */ -/* INTEGER INFO, LDA, N */ -/* DOUBLE PRECISION SCALE */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), CNORM( * ), X( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DLATRS solves one of the triangular systems */ -/* > */ -/* > A *x = s*b or A**T *x = s*b */ -/* > */ -/* > with scaling to prevent overflow. Here A is an upper or lower */ -/* > triangular matrix, A**T denotes the transpose of A, x and b are */ -/* > n-element vectors, and s is a scaling factor, usually less than */ -/* > or equal to 1, chosen so that the components of x will be less than */ -/* > the overflow threshold. If the unscaled problem will not cause */ -/* > overflow, the Level 2 BLAS routine DTRSV is called. If the matrix A */ -/* > is singular (A(j,j) = 0 for some j), then s is set to 0 and a */ -/* > non-trivial solution to A*x = 0 is returned. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > Specifies whether the matrix A is upper or lower triangular. */ -/* > = 'U': Upper triangular */ -/* > = 'L': Lower triangular */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TRANS */ -/* > \verbatim */ -/* > TRANS is CHARACTER*1 */ -/* > Specifies the operation applied to A. */ -/* > = 'N': Solve A * x = s*b (No transpose) */ -/* > = 'T': Solve A**T* x = s*b (Transpose) */ -/* > = 'C': Solve A**T* x = s*b (Conjugate transpose = Transpose) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DIAG */ -/* > \verbatim */ -/* > DIAG is CHARACTER*1 */ -/* > Specifies whether or not the matrix A is unit triangular. */ -/* > = 'N': Non-unit triangular */ -/* > = 'U': Unit triangular */ -/* > \endverbatim */ -/* > */ -/* > \param[in] NORMIN */ -/* > \verbatim */ -/* > NORMIN is CHARACTER*1 */ -/* > Specifies whether CNORM has been set or not. */ -/* > = 'Y': CNORM contains the column norms on entry */ -/* > = 'N': CNORM is not set on entry. On exit, the norms will */ -/* > be computed and stored in CNORM. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > The triangular matrix A. If UPLO = 'U', the leading n by n */ -/* > upper triangular part of the array A contains the upper */ -/* > triangular matrix, and the strictly lower triangular part of */ -/* > A is not referenced. If UPLO = 'L', the leading n by n lower */ -/* > triangular part of the array A contains the lower triangular */ -/* > matrix, and the strictly upper triangular part of A is not */ -/* > referenced. If DIAG = 'U', the diagonal elements of A are */ -/* > also not referenced and are assumed to be 1. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max (1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] X */ -/* > \verbatim */ -/* > X is DOUBLE PRECISION array, dimension (N) */ -/* > On entry, the right hand side b of the triangular system. */ -/* > On exit, X is overwritten by the solution vector x. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] SCALE */ -/* > \verbatim */ -/* > SCALE is DOUBLE PRECISION */ -/* > The scaling factor s for the triangular system */ -/* > A * x = s*b or A**T* x = s*b. */ -/* > If SCALE = 0, the matrix A is singular or badly scaled, and */ -/* > the vector x is an exact or approximate solution to A*x = 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] CNORM */ -/* > \verbatim */ -/* > CNORM is DOUBLE PRECISION array, dimension (N) */ -/* > */ -/* > If NORMIN = 'Y', CNORM is an input argument and CNORM(j) */ -/* > contains the norm of the off-diagonal part of the j-th column */ -/* > of A. If TRANS = 'N', CNORM(j) must be greater than or equal */ -/* > to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j) */ -/* > must be greater than or equal to the 1-norm. */ -/* > */ -/* > If NORMIN = 'N', CNORM is an output argument and CNORM(j) */ -/* > returns the 1-norm of the offdiagonal part of the j-th column */ -/* > of A. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -k, the k-th argument had an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleOTHERauxiliary */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > A rough bound on x is computed; if that is less than overflow, DTRSV */ -/* > is called, otherwise, specific code is used which checks for possible */ -/* > overflow or divide-by-zero at every operation. */ -/* > */ -/* > A columnwise scheme is used for solving A*x = b. The basic algorithm */ -/* > if A is lower triangular is */ -/* > */ -/* > x[1:n] := b[1:n] */ -/* > for j = 1, ..., n */ -/* > x(j) := x(j) / A(j,j) */ -/* > x[j+1:n] := x[j+1:n] - x(j) * A[j+1:n,j] */ -/* > end */ -/* > */ -/* > Define bounds on the components of x after j iterations of the loop: */ -/* > M(j) = bound on x[1:j] */ -/* > G(j) = bound on x[j+1:n] */ -/* > Initially, let M(0) = 0 and G(0) = max{x(i), i=1,...,n}. */ -/* > */ -/* > Then for iteration j+1 we have */ -/* > M(j+1) <= G(j) / | A(j+1,j+1) | */ -/* > G(j+1) <= G(j) + M(j+1) * | A[j+2:n,j+1] | */ -/* > <= G(j) ( 1 + CNORM(j+1) / | A(j+1,j+1) | ) */ -/* > */ -/* > where CNORM(j+1) is greater than or equal to the infinity-norm of */ -/* > column j+1 of A, not counting the diagonal. Hence */ -/* > */ -/* > G(j) <= G(0) product ( 1 + CNORM(i) / | A(i,i) | ) */ -/* > 1<=i<=j */ -/* > and */ -/* > */ -/* > |x(j)| <= ( G(0) / |A(j,j)| ) product ( 1 + CNORM(i) / |A(i,i)| ) */ -/* > 1<=i< j */ -/* > */ -/* > Since |x(j)| <= M(j), we use the Level 2 BLAS routine DTRSV if the */ -/* > reciprocal of the largest M(j), j=1,..,n, is larger than */ -/* > max(underflow, 1/overflow). */ -/* > */ -/* > The bound on x(j) is also used to determine when a step in the */ -/* > columnwise method can be performed without fear of overflow. If */ -/* > the computed bound is greater than a large constant, x is scaled to */ -/* > prevent overflow, but if the bound overflows, x is set to 0, x(j) to */ -/* > 1, and scale to 0, and a non-trivial solution to A*x = 0 is found. */ -/* > */ -/* > Similarly, a row-wise scheme is used to solve A**T*x = b. The basic */ -/* > algorithm for A upper triangular is */ -/* > */ -/* > for j = 1, ..., n */ -/* > x(j) := ( b(j) - A[1:j-1,j]**T * x[1:j-1] ) / A(j,j) */ -/* > end */ -/* > */ -/* > We simultaneously compute two bounds */ -/* > G(j) = bound on ( b(i) - A[1:i-1,i]**T * x[1:i-1] ), 1<=i<=j */ -/* > M(j) = bound on x(i), 1<=i<=j */ -/* > */ -/* > The initial values are G(0) = 0, M(0) = max{b(i), i=1,..,n}, and we */ -/* > add the constraint G(j) >= G(j-1) and M(j) >= M(j-1) for j >= 1. */ -/* > Then the bound on x(j) is */ -/* > */ -/* > M(j) <= M(j-1) * ( 1 + CNORM(j) ) / | A(j,j) | */ -/* > */ -/* > <= M(0) * product ( ( 1 + CNORM(i) ) / |A(i,i)| ) */ -/* > 1<=i<=j */ -/* > */ -/* > and we can safely call DTRSV if 1/M(n) and 1/G(n) are both greater */ -/* > than max(underflow, 1/overflow). */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dlatrs_(char *uplo, char *trans, char *diag, char * - normin, integer *n, doublereal *a, integer *lda, doublereal *x, - doublereal *scale, doublereal *cnorm, integer *info, ftnlen uplo_len, - ftnlen trans_len, ftnlen diag_len, ftnlen normin_len) +int dlatrs_(char *uplo, char *trans, char *diag, char *normin, integer *n, doublereal *a, + integer *lda, doublereal *x, doublereal *scale, doublereal *cnorm, integer *info, + ftnlen uplo_len, ftnlen trans_len, ftnlen diag_len, ftnlen normin_len) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; doublereal d__1, d__2, d__3; - - /* Local variables */ integer i__, j; doublereal xj, rec, tjj; integer jinc; - extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, - integer *); + extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, integer *); doublereal xbnd; integer imax; doublereal tmax, tjjs, xmax, grow, sumj; - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *); + extern int dscal_(integer *, doublereal *, doublereal *, integer *); extern logical lsame_(char *, char *, ftnlen, ftnlen); doublereal tscal, uscal; extern doublereal dasum_(integer *, doublereal *, integer *); integer jlast; - extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *, - integer *, doublereal *, integer *); + extern int daxpy_(integer *, doublereal *, doublereal *, integer *, doublereal *, integer *); logical upper; - extern /* Subroutine */ int dtrsv_(char *, char *, char *, integer *, - doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, - ftnlen); - extern doublereal dlamch_(char *, ftnlen), dlange_(char *, integer *, - integer *, doublereal *, integer *, doublereal *, ftnlen); + extern int dtrsv_(char *, char *, char *, integer *, doublereal *, integer *, doublereal *, + integer *, ftnlen, ftnlen, ftnlen); + extern doublereal dlamch_(char *, ftnlen), + dlange_(char *, integer *, integer *, doublereal *, integer *, doublereal *, ftnlen); extern integer idamax_(integer *, doublereal *, integer *); - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern int xerbla_(char *, integer *, ftnlen); doublereal bignum; logical notran; integer jfirst; doublereal smlnum; logical nounit; - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --x; --cnorm; - - /* Function Body */ *info = 0; upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); notran = lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1); nounit = lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1); - -/* Test the input parameters. */ - - if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + if (!upper && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { *info = -1; - } else if (! notran && ! lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1) && ! - lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { + } else if (!notran && !lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1) && + !lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { *info = -2; - } else if (! nounit && ! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1)) { + } else if (!nounit && !lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1)) { *info = -3; - } else if (! lsame_(normin, (char *)"Y", (ftnlen)1, (ftnlen)1) && ! lsame_(normin, - (char *)"N", (ftnlen)1, (ftnlen)1)) { + } else if (!lsame_(normin, (char *)"Y", (ftnlen)1, (ftnlen)1) && + !lsame_(normin, (char *)"N", (ftnlen)1, (ftnlen)1)) { *info = -4; } else if (*n < 0) { *info = -5; - } else if (*lda < max(1,*n)) { + } else if (*lda < max(1, *n)) { *info = -7; } if (*info != 0) { @@ -358,96 +64,54 @@ f"> */ xerbla_((char *)"DLATRS", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - *scale = 1.; if (*n == 0) { return 0; } - -/* Determine machine dependent parameters to control overflow. */ - - smlnum = dlamch_((char *)"Safe minimum", (ftnlen)12) / dlamch_((char *)"Precision", ( - ftnlen)9); + smlnum = dlamch_((char *)"Safe minimum", (ftnlen)12) / dlamch_((char *)"Precision", (ftnlen)9); bignum = 1. / smlnum; - if (lsame_(normin, (char *)"N", (ftnlen)1, (ftnlen)1)) { - -/* Compute the 1-norm of each column, not including the diagonal. */ - if (upper) { - -/* A is upper triangular. */ - i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j - 1; cnorm[j] = dasum_(&i__2, &a[j * a_dim1 + 1], &c__1); -/* L10: */ } } else { - -/* A is lower triangular. */ - i__1 = *n - 1; for (j = 1; j <= i__1; ++j) { i__2 = *n - j; cnorm[j] = dasum_(&i__2, &a[j + 1 + j * a_dim1], &c__1); -/* L20: */ } cnorm[*n] = 0.; } } - -/* Scale the column norms by TSCAL if the maximum element in CNORM is */ -/* greater than BIGNUM. */ - imax = idamax_(n, &cnorm[1], &c__1); tmax = cnorm[imax]; if (tmax <= bignum) { tscal = 1.; } else { - -/* Avoid NaN generation if entries in CNORM exceed the */ -/* overflow threshold */ - if (tmax <= dlamch_((char *)"Overflow", (ftnlen)8)) { -/* Case 1: All entries in CNORM are valid floating-point numbers */ tscal = 1. / (smlnum * tmax); dscal_(n, &tscal, &cnorm[1], &c__1); } else { -/* Case 2: At least one column norm of A cannot be represented */ -/* as floating-point number. Find the offdiagonal entry A( I, J ) */ -/* with the largest absolute value. If this entry is not +/- Infinity, */ -/* use this value as TSCAL. */ tmax = 0.; if (upper) { - -/* A is upper triangular. */ - i__1 = *n; for (j = 2; j <= i__1; ++j) { -/* Computing MAX */ i__2 = j - 1; - d__1 = dlange_((char *)"M", &i__2, &c__1, &a[j * a_dim1 + 1], & - c__1, &sumj, (ftnlen)1); - tmax = max(d__1,tmax); + d__1 = dlange_((char *)"M", &i__2, &c__1, &a[j * a_dim1 + 1], &c__1, &sumj, (ftnlen)1); + tmax = max(d__1, tmax); } } else { - -/* A is lower triangular. */ - i__1 = *n - 1; for (j = 1; j <= i__1; ++j) { -/* Computing MAX */ i__2 = *n - j; - d__1 = dlange_((char *)"M", &i__2, &c__1, &a[j + 1 + j * a_dim1], - &c__1, &sumj, (ftnlen)1); - tmax = max(d__1,tmax); + d__1 = + dlange_((char *)"M", &i__2, &c__1, &a[j + 1 + j * a_dim1], &c__1, &sumj, (ftnlen)1); + tmax = max(d__1, tmax); } } - if (tmax <= dlamch_((char *)"Overflow", (ftnlen)8)) { tscal = 1. / (smlnum * tmax); i__1 = *n; @@ -455,44 +119,31 @@ f"> */ if (cnorm[j] <= dlamch_((char *)"Overflow", (ftnlen)8)) { cnorm[j] *= tscal; } else { -/* Recompute the 1-norm without introducing Infinity */ -/* in the summation */ cnorm[j] = 0.; if (upper) { i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { - cnorm[j] += tscal * (d__1 = a[i__ + j * - a_dim1], abs(d__1)); + cnorm[j] += tscal * (d__1 = a[i__ + j * a_dim1], abs(d__1)); } } else { i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { - cnorm[j] += tscal * (d__1 = a[i__ + j * - a_dim1], abs(d__1)); + cnorm[j] += tscal * (d__1 = a[i__ + j * a_dim1], abs(d__1)); } } } } } else { -/* At least one entry of A is not a valid floating-point entry. */ -/* Rely on TRSV to propagate Inf and NaN. */ - dtrsv_(uplo, trans, diag, n, &a[a_offset], lda, &x[1], &c__1, - (ftnlen)1, (ftnlen)1, (ftnlen)1); + dtrsv_(uplo, trans, diag, n, &a[a_offset], lda, &x[1], &c__1, (ftnlen)1, (ftnlen)1, + (ftnlen)1); return 0; } } } - -/* Compute a bound on the computed solution vector to see if the */ -/* Level 2 BLAS routine DTRSV can be used. */ - j = idamax_(n, &x[1], &c__1); xmax = (d__1 = x[j], abs(d__1)); xbnd = xmax; if (notran) { - -/* Compute the growth in A * x = b. */ - if (upper) { jfirst = *n; jlast = 1; @@ -502,83 +153,43 @@ f"> */ jlast = *n; jinc = 1; } - if (tscal != 1.) { grow = 0.; goto L50; } - if (nounit) { - -/* A is non-unit triangular. */ - -/* Compute GROW = 1/G(j) and XBND = 1/M(j). */ -/* Initially, G(0) = max{x(i), i=1,...,n}. */ - - grow = 1. / max(xbnd,smlnum); + grow = 1. / max(xbnd, smlnum); xbnd = grow; i__1 = jlast; i__2 = jinc; for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) { - -/* Exit the loop if the growth factor is too small. */ - if (grow <= smlnum) { goto L50; } - -/* M(j) = G(j-1) / abs(A(j,j)) */ - tjj = (d__1 = a[j + j * a_dim1], abs(d__1)); -/* Computing MIN */ - d__1 = xbnd, d__2 = min(1.,tjj) * grow; - xbnd = min(d__1,d__2); + d__1 = xbnd, d__2 = min(1., tjj) * grow; + xbnd = min(d__1, d__2); if (tjj + cnorm[j] >= smlnum) { - -/* G(j) = G(j-1)*( 1 + CNORM(j) / abs(A(j,j)) ) */ - grow *= tjj / (tjj + cnorm[j]); } else { - -/* G(j) could overflow, set GROW to 0. */ - grow = 0.; } -/* L30: */ } grow = xbnd; } else { - -/* A is unit triangular. */ - -/* Compute GROW = 1/G(j), where G(0) = max{x(i), i=1,...,n}. */ - -/* Computing MIN */ - d__1 = 1., d__2 = 1. / max(xbnd,smlnum); - grow = min(d__1,d__2); + d__1 = 1., d__2 = 1. / max(xbnd, smlnum); + grow = min(d__1, d__2); i__2 = jlast; i__1 = jinc; for (j = jfirst; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) { - -/* Exit the loop if the growth factor is too small. */ - if (grow <= smlnum) { goto L50; } - -/* G(j) = G(j-1)*( 1 + CNORM(j) ) */ - grow *= 1. / (cnorm[j] + 1.); -/* L40: */ } } -L50: - - ; + L50:; } else { - -/* Compute the growth in A**T * x = b. */ - if (upper) { jfirst = 1; jlast = *n; @@ -588,108 +199,56 @@ L50: jlast = 1; jinc = -1; } - if (tscal != 1.) { grow = 0.; goto L80; } - if (nounit) { - -/* A is non-unit triangular. */ - -/* Compute GROW = 1/G(j) and XBND = 1/M(j). */ -/* Initially, M(0) = max{x(i), i=1,...,n}. */ - - grow = 1. / max(xbnd,smlnum); + grow = 1. / max(xbnd, smlnum); xbnd = grow; i__1 = jlast; i__2 = jinc; for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) { - -/* Exit the loop if the growth factor is too small. */ - if (grow <= smlnum) { goto L80; } - -/* G(j) = max( G(j-1), M(j-1)*( 1 + CNORM(j) ) ) */ - xj = cnorm[j] + 1.; -/* Computing MIN */ d__1 = grow, d__2 = xbnd / xj; - grow = min(d__1,d__2); - -/* M(j) = M(j-1)*( 1 + CNORM(j) ) / abs(A(j,j)) */ - + grow = min(d__1, d__2); tjj = (d__1 = a[j + j * a_dim1], abs(d__1)); if (xj > tjj) { xbnd *= tjj / xj; } -/* L60: */ } - grow = min(grow,xbnd); + grow = min(grow, xbnd); } else { - -/* A is unit triangular. */ - -/* Compute GROW = 1/G(j), where G(0) = max{x(i), i=1,...,n}. */ - -/* Computing MIN */ - d__1 = 1., d__2 = 1. / max(xbnd,smlnum); - grow = min(d__1,d__2); + d__1 = 1., d__2 = 1. / max(xbnd, smlnum); + grow = min(d__1, d__2); i__2 = jlast; i__1 = jinc; for (j = jfirst; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) { - -/* Exit the loop if the growth factor is too small. */ - if (grow <= smlnum) { goto L80; } - -/* G(j) = ( 1 + CNORM(j) )*G(j-1) */ - xj = cnorm[j] + 1.; grow /= xj; -/* L70: */ } } -L80: - ; + L80:; } - if (grow * tscal > smlnum) { - -/* Use the Level 2 BLAS solve if the reciprocal of the bound on */ -/* elements of X is not too small. */ - - dtrsv_(uplo, trans, diag, n, &a[a_offset], lda, &x[1], &c__1, (ftnlen) - 1, (ftnlen)1, (ftnlen)1); + dtrsv_(uplo, trans, diag, n, &a[a_offset], lda, &x[1], &c__1, (ftnlen)1, (ftnlen)1, + (ftnlen)1); } else { - -/* Use a Level 1 BLAS solve, scaling intermediate results. */ - if (xmax > bignum) { - -/* Scale X so that its components are less than or equal to */ -/* BIGNUM in absolute value. */ - *scale = bignum / xmax; dscal_(n, scale, &x[1], &c__1); xmax = bignum; } - if (notran) { - -/* Solve A * x = b */ - i__1 = jlast; i__2 = jinc; for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) { - -/* Compute x(j) = b(j) / A(j,j), scaling x if necessary. */ - xj = (d__1 = x[j], abs(d__1)); if (nounit) { tjjs = a[j + j * a_dim1] * tscal; @@ -701,14 +260,8 @@ L80: } tjj = abs(tjjs); if (tjj > smlnum) { - -/* abs(A(j,j)) > SMLNUM: */ - if (tjj < 1.) { if (xj > tjj * bignum) { - -/* Scale x by 1/b(j). */ - rec = 1. / xj; dscal_(n, &rec, &x[1], &c__1); *scale *= rec; @@ -718,20 +271,9 @@ L80: x[j] /= tjjs; xj = (d__1 = x[j], abs(d__1)); } else if (tjj > 0.) { - -/* 0 < abs(A(j,j)) <= SMLNUM: */ - if (xj > tjj * bignum) { - -/* Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM */ -/* to avoid overflow when dividing by A(j,j). */ - rec = tjj * bignum / xj; if (cnorm[j] > 1.) { - -/* Scale by 1/CNORM(j) to avoid overflow when */ -/* multiplying x(j) times column j. */ - rec /= cnorm[j]; } dscal_(n, &rec, &x[1], &c__1); @@ -741,93 +283,55 @@ L80: x[j] /= tjjs; xj = (d__1 = x[j], abs(d__1)); } else { - -/* A(j,j) = 0: Set x(1:n) = 0, x(j) = 1, and */ -/* scale = 0, and compute a solution to A*x = 0. */ - i__3 = *n; for (i__ = 1; i__ <= i__3; ++i__) { x[i__] = 0.; -/* L90: */ } x[j] = 1.; xj = 1.; *scale = 0.; xmax = 0.; } -L100: - -/* Scale x if necessary to avoid overflow when adding a */ -/* multiple of column j of A. */ - + L100: if (xj > 1.) { rec = 1. / xj; if (cnorm[j] > (bignum - xmax) * rec) { - -/* Scale x by 1/(2*abs(x(j))). */ - rec *= .5; dscal_(n, &rec, &x[1], &c__1); *scale *= rec; } } else if (xj * cnorm[j] > bignum - xmax) { - -/* Scale x by 1/2. */ - dscal_(n, &c_b46, &x[1], &c__1); *scale *= .5; } - if (upper) { if (j > 1) { - -/* Compute the update */ -/* x(1:j-1) := x(1:j-1) - x(j) * A(1:j-1,j) */ - i__3 = j - 1; d__1 = -x[j] * tscal; - daxpy_(&i__3, &d__1, &a[j * a_dim1 + 1], &c__1, &x[1], - &c__1); + daxpy_(&i__3, &d__1, &a[j * a_dim1 + 1], &c__1, &x[1], &c__1); i__3 = j - 1; i__ = idamax_(&i__3, &x[1], &c__1); xmax = (d__1 = x[i__], abs(d__1)); } } else { if (j < *n) { - -/* Compute the update */ -/* x(j+1:n) := x(j+1:n) - x(j) * A(j+1:n,j) */ - i__3 = *n - j; d__1 = -x[j] * tscal; - daxpy_(&i__3, &d__1, &a[j + 1 + j * a_dim1], &c__1, & - x[j + 1], &c__1); + daxpy_(&i__3, &d__1, &a[j + 1 + j * a_dim1], &c__1, &x[j + 1], &c__1); i__3 = *n - j; i__ = j + idamax_(&i__3, &x[j + 1], &c__1); xmax = (d__1 = x[i__], abs(d__1)); } } -/* L110: */ } - } else { - -/* Solve A**T * x = b */ - i__2 = jlast; i__1 = jinc; for (j = jfirst; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) { - -/* Compute x(j) = b(j) - sum A(k,j)*x(k). */ -/* k<>j */ - xj = (d__1 = x[j], abs(d__1)); uscal = tscal; - rec = 1. / max(xmax,1.); + rec = 1. / max(xmax, 1.); if (cnorm[j] > (bignum - xj) * rec) { - -/* If x(j) could overflow, scale x by 1/(2*XMAX). */ - rec *= .5; if (nounit) { tjjs = a[j + j * a_dim1] * tscal; @@ -836,12 +340,8 @@ L100: } tjj = abs(tjjs); if (tjj > 1.) { - -/* Divide by A(j,j) when scaling x if A(j,j) > 1. */ - -/* Computing MIN */ d__1 = 1., d__2 = rec * tjj; - rec = min(d__1,d__2); + rec = min(d__1, d__2); uscal /= tjjs; } if (rec < 1.) { @@ -850,46 +350,29 @@ L100: xmax *= rec; } } - sumj = 0.; if (uscal == 1.) { - -/* If the scaling needed for A in the dot product is 1, */ -/* call DDOT to perform the dot product. */ - if (upper) { i__3 = j - 1; - sumj = ddot_(&i__3, &a[j * a_dim1 + 1], &c__1, &x[1], - &c__1); + sumj = ddot_(&i__3, &a[j * a_dim1 + 1], &c__1, &x[1], &c__1); } else if (j < *n) { i__3 = *n - j; - sumj = ddot_(&i__3, &a[j + 1 + j * a_dim1], &c__1, &x[ - j + 1], &c__1); + sumj = ddot_(&i__3, &a[j + 1 + j * a_dim1], &c__1, &x[j + 1], &c__1); } } else { - -/* Otherwise, use in-line code for the dot product. */ - if (upper) { i__3 = j - 1; for (i__ = 1; i__ <= i__3; ++i__) { sumj += a[i__ + j * a_dim1] * uscal * x[i__]; -/* L120: */ } } else if (j < *n) { i__3 = *n; for (i__ = j + 1; i__ <= i__3; ++i__) { sumj += a[i__ + j * a_dim1] * uscal * x[i__]; -/* L130: */ } } } - if (uscal == tscal) { - -/* Compute x(j) := ( x(j) - sumj ) / A(j,j) if 1/A(j,j) */ -/* was not used to scale the dotproduct. */ - x[j] -= sumj; xj = (d__1 = x[j], abs(d__1)); if (nounit) { @@ -900,19 +383,10 @@ L100: goto L150; } } - -/* Compute x(j) = x(j) / A(j,j), scaling if necessary. */ - tjj = abs(tjjs); if (tjj > smlnum) { - -/* abs(A(j,j)) > SMLNUM: */ - if (tjj < 1.) { if (xj > tjj * bignum) { - -/* Scale X by 1/abs(x(j)). */ - rec = 1. / xj; dscal_(n, &rec, &x[1], &c__1); *scale *= rec; @@ -921,13 +395,7 @@ L100: } x[j] /= tjjs; } else if (tjj > 0.) { - -/* 0 < abs(A(j,j)) <= SMLNUM: */ - if (xj > tjj * bignum) { - -/* Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM. */ - rec = tjj * bignum / xj; dscal_(n, &rec, &x[1], &c__1); *scale *= rec; @@ -935,50 +403,30 @@ L100: } x[j] /= tjjs; } else { - -/* A(j,j) = 0: Set x(1:n) = 0, x(j) = 1, and */ -/* scale = 0, and compute a solution to A**T*x = 0. */ - i__3 = *n; for (i__ = 1; i__ <= i__3; ++i__) { x[i__] = 0.; -/* L140: */ } x[j] = 1.; *scale = 0.; xmax = 0.; } -L150: - ; + L150:; } else { - -/* Compute x(j) := x(j) / A(j,j) - sumj if the dot */ -/* product has already been divided by 1/A(j,j). */ - x[j] = x[j] / tjjs - sumj; } -/* Computing MAX */ d__2 = xmax, d__3 = (d__1 = x[j], abs(d__1)); - xmax = max(d__2,d__3); -/* L160: */ + xmax = max(d__2, d__3); } } *scale /= tscal; } - -/* Scale the column norms by 1/TSCAL for return. */ - if (tscal != 1.) { d__1 = 1. / tscal; dscal_(n, &d__1, &cnorm[1], &c__1); } - return 0; - -/* End of DLATRS */ - -} /* dlatrs_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dnrm2.cpp b/lib/linalg/dnrm2.cpp index dc2a59dfbd..fc34e88c78 100644 --- a/lib/linalg/dnrm2.cpp +++ b/lib/linalg/dnrm2.cpp @@ -1,130 +1,15 @@ -/* fortran/dnrm2.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DNRM2 */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* DOUBLE PRECISION FUNCTION DNRM2(N,X,INCX) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INCX,N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION X(*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DNRM2 returns the euclidean norm of a vector via the function */ -/* > name, so that */ -/* > */ -/* > DNRM2 := sqrt( x'*x ) */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > number of elements in input vector(s) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] X */ -/* > \verbatim */ -/* > X is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > storage spacing between elements of DX */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \date December 2016 */ - -/* > \ingroup double_blas_level1 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > -- This version written on 25-October-1982. */ -/* > Modified on 14-October-1993 to inline the call to DLASSQ. */ -/* > Sven Hammarling, Nag Ltd. */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ doublereal dnrm2_(integer *n, doublereal *x, integer *incx) { - /* System generated locals */ integer i__1, i__2; doublereal ret_val, d__1; - - /* Builtin functions */ double sqrt(doublereal); - - /* Local variables */ integer ix; doublereal ssq, norm, scale, absxi; - - -/* -- Reference BLAS level1 routine (version 3.7.0) -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ -/* December 2016 */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ - /* Parameter adjustments */ --x; - - /* Function Body */ if (*n < 1 || *incx < 1) { norm = 0.; } else if (*n == 1) { @@ -132,38 +17,26 @@ doublereal dnrm2_(integer *n, doublereal *x, integer *incx) } else { scale = 0.; ssq = 1.; -/* The following loop is equivalent to this call to the LAPACK */ -/* auxiliary routine: */ -/* CALL DLASSQ( N, X, INCX, SCALE, SSQ ) */ - i__1 = (*n - 1) * *incx + 1; i__2 = *incx; for (ix = 1; i__2 < 0 ? ix >= i__1 : ix <= i__1; ix += i__2) { if (x[ix] != 0.) { absxi = (d__1 = x[ix], abs(d__1)); if (scale < absxi) { -/* Computing 2nd power */ d__1 = scale / absxi; ssq = ssq * (d__1 * d__1) + 1.; scale = absxi; } else { -/* Computing 2nd power */ d__1 = absxi / scale; ssq += d__1 * d__1; } } -/* L10: */ } norm = scale * sqrt(ssq); } - ret_val = norm; return ret_val; - -/* End of DNRM2. */ - -} /* dnrm2_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dorg2l.cpp b/lib/linalg/dorg2l.cpp index a028102645..42899af042 100644 --- a/lib/linalg/dorg2l.cpp +++ b/lib/linalg/dorg2l.cpp @@ -1,186 +1,23 @@ -/* fortran/dorg2l.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; - -/* > \brief \b DORG2L generates all or part of the orthogonal matrix Q from a QL factorization determined by s -geqlf (unblocked algorithm). */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DORG2L + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DORG2L( M, N, K, A, LDA, TAU, WORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INFO, K, LDA, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DORG2L generates an m by n real matrix Q with orthonormal columns, */ -/* > which is defined as the last n columns of a product of k elementary */ -/* > reflectors of order m */ -/* > */ -/* > Q = H(k) . . . H(2) H(1) */ -/* > */ -/* > as returned by DGEQLF. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix Q. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix Q. M >= N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > The number of elementary reflectors whose product defines the */ -/* > matrix Q. N >= K >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On entry, the (n-k+i)-th column must contain the vector which */ -/* > defines the elementary reflector H(i), for i = 1,2,...,k, as */ -/* > returned by DGEQLF in the last k columns of its array */ -/* > argument A. */ -/* > On exit, the m by n matrix Q. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The first dimension of the array A. LDA >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TAU */ -/* > \verbatim */ -/* > TAU is DOUBLE PRECISION array, dimension (K) */ -/* > TAU(i) must contain the scalar factor of the elementary */ -/* > reflector H(i), as returned by DGEQLF. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (N) */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument has an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleOTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dorg2l_(integer *m, integer *n, integer *k, doublereal * - a, integer *lda, doublereal *tau, doublereal *work, integer *info) +int dorg2l_(integer *m, integer *n, integer *k, doublereal *a, integer *lda, doublereal *tau, + doublereal *work, integer *info) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; doublereal d__1; - - /* Local variables */ integer i__, j, l, ii; - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *), dlarf_(char *, integer *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - ftnlen), xerbla_(char *, integer *, ftnlen); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments */ - - /* Parameter adjustments */ + extern int dscal_(integer *, doublereal *, doublereal *, integer *), + dlarf_(char *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, doublereal *, ftnlen), + xerbla_(char *, integer *, ftnlen); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --tau; --work; - - /* Function Body */ *info = 0; if (*m < 0) { *info = -1; @@ -188,7 +25,7 @@ f"> */ *info = -2; } else if (*k < 0 || *k > *n) { *info = -3; - } else if (*lda < max(1,*m)) { + } else if (*lda < max(1, *m)) { *info = -5; } if (*info != 0) { @@ -196,57 +33,36 @@ f"> */ xerbla_((char *)"DORG2L", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*n <= 0) { return 0; } - -/* Initialise columns 1:n-k to columns of the unit matrix */ - i__1 = *n - *k; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (l = 1; l <= i__2; ++l) { a[l + j * a_dim1] = 0.; -/* L10: */ } a[*m - *n + j + j * a_dim1] = 1.; -/* L20: */ } - i__1 = *k; for (i__ = 1; i__ <= i__1; ++i__) { ii = *n - *k + i__; - -/* Apply H(i) to A(1:m-k+i,1:n-k+i) from the left */ - a[*m - *n + ii + ii * a_dim1] = 1.; i__2 = *m - *n + ii; i__3 = ii - 1; - dlarf_((char *)"Left", &i__2, &i__3, &a[ii * a_dim1 + 1], &c__1, &tau[i__], & - a[a_offset], lda, &work[1], (ftnlen)4); + dlarf_((char *)"Left", &i__2, &i__3, &a[ii * a_dim1 + 1], &c__1, &tau[i__], &a[a_offset], lda, + &work[1], (ftnlen)4); i__2 = *m - *n + ii - 1; d__1 = -tau[i__]; dscal_(&i__2, &d__1, &a[ii * a_dim1 + 1], &c__1); a[*m - *n + ii + ii * a_dim1] = 1. - tau[i__]; - -/* Set A(m-k+i+1:m,n-k+i) to zero */ - i__2 = *m; for (l = *m - *n + ii + 1; l <= i__2; ++l) { a[l + ii * a_dim1] = 0.; -/* L30: */ } -/* L40: */ } return 0; - -/* End of DORG2L */ - -} /* dorg2l_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dorg2r.cpp b/lib/linalg/dorg2r.cpp index f6d897beb6..b9be1488c9 100644 --- a/lib/linalg/dorg2r.cpp +++ b/lib/linalg/dorg2r.cpp @@ -1,186 +1,23 @@ -/* fortran/dorg2r.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; - -/* > \brief \b DORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by s -geqrf (unblocked algorithm). */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DORG2R + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DORG2R( M, N, K, A, LDA, TAU, WORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INFO, K, LDA, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DORG2R generates an m by n real matrix Q with orthonormal columns, */ -/* > which is defined as the first n columns of a product of k elementary */ -/* > reflectors of order m */ -/* > */ -/* > Q = H(1) H(2) . . . H(k) */ -/* > */ -/* > as returned by DGEQRF. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix Q. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix Q. M >= N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > The number of elementary reflectors whose product defines the */ -/* > matrix Q. N >= K >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On entry, the i-th column must contain the vector which */ -/* > defines the elementary reflector H(i), for i = 1,2,...,k, as */ -/* > returned by DGEQRF in the first k columns of its array */ -/* > argument A. */ -/* > On exit, the m-by-n matrix Q. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The first dimension of the array A. LDA >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TAU */ -/* > \verbatim */ -/* > TAU is DOUBLE PRECISION array, dimension (K) */ -/* > TAU(i) must contain the scalar factor of the elementary */ -/* > reflector H(i), as returned by DGEQRF. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (N) */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument has an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleOTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dorg2r_(integer *m, integer *n, integer *k, doublereal * - a, integer *lda, doublereal *tau, doublereal *work, integer *info) +int dorg2r_(integer *m, integer *n, integer *k, doublereal *a, integer *lda, doublereal *tau, + doublereal *work, integer *info) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; doublereal d__1; - - /* Local variables */ integer i__, j, l; - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *), dlarf_(char *, integer *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - ftnlen), xerbla_(char *, integer *, ftnlen); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments */ - - /* Parameter adjustments */ + extern int dscal_(integer *, doublereal *, doublereal *, integer *), + dlarf_(char *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, doublereal *, ftnlen), + xerbla_(char *, integer *, ftnlen); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --tau; --work; - - /* Function Body */ *info = 0; if (*m < 0) { *info = -1; @@ -188,7 +25,7 @@ f"> */ *info = -2; } else if (*k < 0 || *k > *n) { *info = -3; - } else if (*lda < max(1,*m)) { + } else if (*lda < max(1, *m)) { *info = -5; } if (*info != 0) { @@ -196,37 +33,24 @@ f"> */ xerbla_((char *)"DORG2R", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*n <= 0) { return 0; } - -/* Initialise columns k+1:n to columns of the unit matrix */ - i__1 = *n; for (j = *k + 1; j <= i__1; ++j) { i__2 = *m; for (l = 1; l <= i__2; ++l) { a[l + j * a_dim1] = 0.; -/* L10: */ } a[j + j * a_dim1] = 1.; -/* L20: */ } - for (i__ = *k; i__ >= 1; --i__) { - -/* Apply H(i) to A(i:m,i:n) from the left */ - if (i__ < *n) { a[i__ + i__ * a_dim1] = 1.; i__1 = *m - i__ + 1; i__2 = *n - i__; - dlarf_((char *)"Left", &i__1, &i__2, &a[i__ + i__ * a_dim1], &c__1, &tau[ - i__], &a[i__ + (i__ + 1) * a_dim1], lda, &work[1], ( - ftnlen)4); + dlarf_((char *)"Left", &i__1, &i__2, &a[i__ + i__ * a_dim1], &c__1, &tau[i__], + &a[i__ + (i__ + 1) * a_dim1], lda, &work[1], (ftnlen)4); } if (i__ < *m) { i__1 = *m - i__; @@ -234,22 +58,13 @@ f"> */ dscal_(&i__1, &d__1, &a[i__ + 1 + i__ * a_dim1], &c__1); } a[i__ + i__ * a_dim1] = 1. - tau[i__]; - -/* Set A(1:i-1,i) to zero */ - i__1 = i__ - 1; for (l = 1; l <= i__1; ++l) { a[l + i__ * a_dim1] = 0.; -/* L30: */ } -/* L40: */ } return 0; - -/* End of DORG2R */ - -} /* dorg2r_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dorgbr.cpp b/lib/linalg/dorgbr.cpp index a55e8aeca0..27f94eb51f 100644 --- a/lib/linalg/dorgbr.cpp +++ b/lib/linalg/dorgbr.cpp @@ -1,404 +1,140 @@ -/* fortran/dorgbr.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c_n1 = -1; - -/* > \brief \b DORGBR */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DORGBR + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER VECT */ -/* INTEGER INFO, K, LDA, LWORK, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DORGBR generates one of the real orthogonal matrices Q or P**T */ -/* > determined by DGEBRD when reducing a real matrix A to bidiagonal */ -/* > form: A = Q * B * P**T. Q and P**T are defined as products of */ -/* > elementary reflectors H(i) or G(i) respectively. */ -/* > */ -/* > If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q */ -/* > is of order M: */ -/* > if m >= k, Q = H(1) H(2) . . . H(k) and DORGBR returns the first n */ -/* > columns of Q, where m >= n >= k; */ -/* > if m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR returns Q as an */ -/* > M-by-M matrix. */ -/* > */ -/* > If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T */ -/* > is of order N: */ -/* > if k < n, P**T = G(k) . . . G(2) G(1) and DORGBR returns the first m */ -/* > rows of P**T, where n >= m >= k; */ -/* > if k >= n, P**T = G(n-1) . . . G(2) G(1) and DORGBR returns P**T as */ -/* > an N-by-N matrix. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] VECT */ -/* > \verbatim */ -/* > VECT is CHARACTER*1 */ -/* > Specifies whether the matrix Q or the matrix P**T is */ -/* > required, as defined in the transformation applied by DGEBRD: */ -/* > = 'Q': generate Q; */ -/* > = 'P': generate P**T. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix Q or P**T to be returned. */ -/* > M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix Q or P**T to be returned. */ -/* > N >= 0. */ -/* > If VECT = 'Q', M >= N >= min(M,K); */ -/* > if VECT = 'P', N >= M >= min(N,K). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > If VECT = 'Q', the number of columns in the original M-by-K */ -/* > matrix reduced by DGEBRD. */ -/* > If VECT = 'P', the number of rows in the original K-by-N */ -/* > matrix reduced by DGEBRD. */ -/* > K >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On entry, the vectors which define the elementary reflectors, */ -/* > as returned by DGEBRD. */ -/* > On exit, the M-by-N matrix Q or P**T. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TAU */ -/* > \verbatim */ -/* > TAU is DOUBLE PRECISION array, dimension */ -/* > (min(M,K)) if VECT = 'Q' */ -/* > (min(N,K)) if VECT = 'P' */ -/* > TAU(i) must contain the scalar factor of the elementary */ -/* > reflector H(i) or G(i), which determines Q or P**T, as */ -/* > returned by DGEBRD in its array argument TAUQ or TAUP. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ -/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LWORK */ -/* > \verbatim */ -/* > LWORK is INTEGER */ -/* > The dimension of the array WORK. LWORK >= max(1,min(M,N)). */ -/* > For optimum performance LWORK >= min(M,N)*NB, where NB */ -/* > is the optimal blocksize. */ -/* > */ -/* > If LWORK = -1, then a workspace query is assumed; the routine */ -/* > only calculates the optimal size of the WORK array, returns */ -/* > this value as the first entry of the WORK array, and no error */ -/* > message related to LWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleGBcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dorgbr_(char *vect, integer *m, integer *n, integer *k, - doublereal *a, integer *lda, doublereal *tau, doublereal *work, - integer *lwork, integer *info, ftnlen vect_len) +int dorgbr_(char *vect, integer *m, integer *n, integer *k, doublereal *a, integer *lda, + doublereal *tau, doublereal *work, integer *lwork, integer *info, ftnlen vect_len) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; - - /* Local variables */ integer i__, j, mn; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer iinfo; logical wantq; - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), dorglq_( - integer *, integer *, integer *, doublereal *, integer *, - doublereal *, doublereal *, integer *, integer *), dorgqr_( - integer *, integer *, integer *, doublereal *, integer *, - doublereal *, doublereal *, integer *, integer *); + extern int xerbla_(char *, integer *, ftnlen), + dorglq_(integer *, integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, integer *), + dorgqr_(integer *, integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, integer *); integer lwkopt; logical lquery; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --tau; --work; - - /* Function Body */ *info = 0; wantq = lsame_(vect, (char *)"Q", (ftnlen)1, (ftnlen)1); - mn = min(*m,*n); + mn = min(*m, *n); lquery = *lwork == -1; - if (! wantq && ! lsame_(vect, (char *)"P", (ftnlen)1, (ftnlen)1)) { + if (!wantq && !lsame_(vect, (char *)"P", (ftnlen)1, (ftnlen)1)) { *info = -1; } else if (*m < 0) { *info = -2; - } else if (*n < 0 || wantq && (*n > *m || *n < min(*m,*k)) || ! wantq && ( - *m > *n || *m < min(*n,*k))) { + } else if (*n < 0 || wantq && (*n > *m || *n < min(*m, *k)) || + !wantq && (*m > *n || *m < min(*n, *k))) { *info = -3; } else if (*k < 0) { *info = -4; - } else if (*lda < max(1,*m)) { + } else if (*lda < max(1, *m)) { *info = -6; - } else if (*lwork < max(1,mn) && ! lquery) { + } else if (*lwork < max(1, mn) && !lquery) { *info = -9; } - if (*info == 0) { work[1] = 1.; if (wantq) { if (*m >= *k) { - dorgqr_(m, n, k, &a[a_offset], lda, &tau[1], &work[1], &c_n1, - &iinfo); + dorgqr_(m, n, k, &a[a_offset], lda, &tau[1], &work[1], &c_n1, &iinfo); } else { if (*m > 1) { i__1 = *m - 1; i__2 = *m - 1; i__3 = *m - 1; - dorgqr_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], & - work[1], &c_n1, &iinfo); + dorgqr_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], &work[1], &c_n1, + &iinfo); } } } else { if (*k < *n) { - dorglq_(m, n, k, &a[a_offset], lda, &tau[1], &work[1], &c_n1, - &iinfo); + dorglq_(m, n, k, &a[a_offset], lda, &tau[1], &work[1], &c_n1, &iinfo); } else { if (*n > 1) { i__1 = *n - 1; i__2 = *n - 1; i__3 = *n - 1; - dorglq_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], & - work[1], &c_n1, &iinfo); + dorglq_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], &work[1], &c_n1, + &iinfo); } } } - lwkopt = (integer) work[1]; - lwkopt = max(lwkopt,mn); + lwkopt = (integer)work[1]; + lwkopt = max(lwkopt, mn); } - if (*info != 0) { i__1 = -(*info); xerbla_((char *)"DORGBR", &i__1, (ftnlen)6); return 0; } else if (lquery) { - work[1] = (doublereal) lwkopt; + work[1] = (doublereal)lwkopt; return 0; } - -/* Quick return if possible */ - if (*m == 0 || *n == 0) { work[1] = 1.; return 0; } - if (wantq) { - -/* Form Q, determined by a call to DGEBRD to reduce an m-by-k */ -/* matrix */ - if (*m >= *k) { - -/* If m >= k, assume m >= n >= k */ - - dorgqr_(m, n, k, &a[a_offset], lda, &tau[1], &work[1], lwork, & - iinfo); - + dorgqr_(m, n, k, &a[a_offset], lda, &tau[1], &work[1], lwork, &iinfo); } else { - -/* If m < k, assume m = n */ - -/* Shift the vectors which define the elementary reflectors one */ -/* column to the right, and set the first row and column of Q */ -/* to those of the unit matrix */ - for (j = *m; j >= 2; --j) { a[j * a_dim1 + 1] = 0.; i__1 = *m; for (i__ = j + 1; i__ <= i__1; ++i__) { a[i__ + j * a_dim1] = a[i__ + (j - 1) * a_dim1]; -/* L10: */ } -/* L20: */ } a[a_dim1 + 1] = 1.; i__1 = *m; for (i__ = 2; i__ <= i__1; ++i__) { a[i__ + a_dim1] = 0.; -/* L30: */ } if (*m > 1) { - -/* Form Q(2:m,2:m) */ - i__1 = *m - 1; i__2 = *m - 1; i__3 = *m - 1; - dorgqr_(&i__1, &i__2, &i__3, &a[(a_dim1 << 1) + 2], lda, &tau[ - 1], &work[1], lwork, &iinfo); + dorgqr_(&i__1, &i__2, &i__3, &a[(a_dim1 << 1) + 2], lda, &tau[1], &work[1], lwork, + &iinfo); } } } else { - -/* Form P**T, determined by a call to DGEBRD to reduce a k-by-n */ -/* matrix */ - if (*k < *n) { - -/* If k < n, assume k <= m <= n */ - - dorglq_(m, n, k, &a[a_offset], lda, &tau[1], &work[1], lwork, & - iinfo); - + dorglq_(m, n, k, &a[a_offset], lda, &tau[1], &work[1], lwork, &iinfo); } else { - -/* If k >= n, assume m = n */ - -/* Shift the vectors which define the elementary reflectors one */ -/* row downward, and set the first row and column of P**T to */ -/* those of the unit matrix */ - a[a_dim1 + 1] = 1.; i__1 = *n; for (i__ = 2; i__ <= i__1; ++i__) { a[i__ + a_dim1] = 0.; -/* L40: */ } i__1 = *n; for (j = 2; j <= i__1; ++j) { for (i__ = j - 1; i__ >= 2; --i__) { a[i__ + j * a_dim1] = a[i__ - 1 + j * a_dim1]; -/* L50: */ } a[j * a_dim1 + 1] = 0.; -/* L60: */ } if (*n > 1) { - -/* Form P**T(2:n,2:n) */ - i__1 = *n - 1; i__2 = *n - 1; i__3 = *n - 1; - dorglq_(&i__1, &i__2, &i__3, &a[(a_dim1 << 1) + 2], lda, &tau[ - 1], &work[1], lwork, &iinfo); + dorglq_(&i__1, &i__2, &i__3, &a[(a_dim1 << 1) + 2], lda, &tau[1], &work[1], lwork, + &iinfo); } } } - work[1] = (doublereal) lwkopt; + work[1] = (doublereal)lwkopt; return 0; - -/* End of DORGBR */ - -} /* dorgbr_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dorgl2.cpp b/lib/linalg/dorgl2.cpp index 68b6445522..78561a4ba8 100644 --- a/lib/linalg/dorgl2.cpp +++ b/lib/linalg/dorgl2.cpp @@ -1,180 +1,22 @@ -/* fortran/dorgl2.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DORGL2 */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DORGL2 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DORGL2( M, N, K, A, LDA, TAU, WORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INFO, K, LDA, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DORGL2 generates an m by n real matrix Q with orthonormal rows, */ -/* > which is defined as the first m rows of a product of k elementary */ -/* > reflectors of order n */ -/* > */ -/* > Q = H(k) . . . H(2) H(1) */ -/* > */ -/* > as returned by DGELQF. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix Q. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix Q. N >= M. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > The number of elementary reflectors whose product defines the */ -/* > matrix Q. M >= K >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On entry, the i-th row must contain the vector which defines */ -/* > the elementary reflector H(i), for i = 1,2,...,k, as returned */ -/* > by DGELQF in the first k rows of its array argument A. */ -/* > On exit, the m-by-n matrix Q. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The first dimension of the array A. LDA >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TAU */ -/* > \verbatim */ -/* > TAU is DOUBLE PRECISION array, dimension (K) */ -/* > TAU(i) must contain the scalar factor of the elementary */ -/* > reflector H(i), as returned by DGELQF. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (M) */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument has an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleOTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dorgl2_(integer *m, integer *n, integer *k, doublereal * - a, integer *lda, doublereal *tau, doublereal *work, integer *info) +int dorgl2_(integer *m, integer *n, integer *k, doublereal *a, integer *lda, doublereal *tau, + doublereal *work, integer *info) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; doublereal d__1; - - /* Local variables */ integer i__, j, l; - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *), dlarf_(char *, integer *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - ftnlen), xerbla_(char *, integer *, ftnlen); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments */ - - /* Parameter adjustments */ + extern int dscal_(integer *, doublereal *, doublereal *, integer *), + dlarf_(char *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, doublereal *, ftnlen), + xerbla_(char *, integer *, ftnlen); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --tau; --work; - - /* Function Body */ *info = 0; if (*m < 0) { *info = -1; @@ -182,7 +24,7 @@ f"> */ *info = -2; } else if (*k < 0 || *k > *m) { *info = -3; - } else if (*lda < max(1,*m)) { + } else if (*lda < max(1, *m)) { *info = -5; } if (*info != 0) { @@ -190,65 +32,42 @@ f"> */ xerbla_((char *)"DORGL2", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*m <= 0) { return 0; } - if (*k < *m) { - -/* Initialise rows k+1:m to rows of the unit matrix */ - i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (l = *k + 1; l <= i__2; ++l) { a[l + j * a_dim1] = 0.; -/* L10: */ } if (j > *k && j <= *m) { a[j + j * a_dim1] = 1.; } -/* L20: */ } } - for (i__ = *k; i__ >= 1; --i__) { - -/* Apply H(i) to A(i:m,i:n) from the right */ - if (i__ < *n) { if (i__ < *m) { a[i__ + i__ * a_dim1] = 1.; i__1 = *m - i__; i__2 = *n - i__ + 1; - dlarf_((char *)"Right", &i__1, &i__2, &a[i__ + i__ * a_dim1], lda, & - tau[i__], &a[i__ + 1 + i__ * a_dim1], lda, &work[1], ( - ftnlen)5); + dlarf_((char *)"Right", &i__1, &i__2, &a[i__ + i__ * a_dim1], lda, &tau[i__], + &a[i__ + 1 + i__ * a_dim1], lda, &work[1], (ftnlen)5); } i__1 = *n - i__; d__1 = -tau[i__]; dscal_(&i__1, &d__1, &a[i__ + (i__ + 1) * a_dim1], lda); } a[i__ + i__ * a_dim1] = 1. - tau[i__]; - -/* Set A(i,1:i-1) to zero */ - i__1 = i__ - 1; for (l = 1; l <= i__1; ++l) { a[i__ + l * a_dim1] = 0.; -/* L30: */ } -/* L40: */ } return 0; - -/* End of DORGL2 */ - -} /* dorgl2_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dorglq.cpp b/lib/linalg/dorglq.cpp index 96eb224501..a43e7e86d2 100644 --- a/lib/linalg/dorglq.cpp +++ b/lib/linalg/dorglq.cpp @@ -1,215 +1,37 @@ -/* fortran/dorglq.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static integer c_n1 = -1; static integer c__3 = 3; static integer c__2 = 2; - -/* > \brief \b DORGLQ */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DORGLQ + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DORGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INFO, K, LDA, LWORK, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DORGLQ generates an M-by-N real matrix Q with orthonormal rows, */ -/* > which is defined as the first M rows of a product of K elementary */ -/* > reflectors of order N */ -/* > */ -/* > Q = H(k) . . . H(2) H(1) */ -/* > */ -/* > as returned by DGELQF. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix Q. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix Q. N >= M. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > The number of elementary reflectors whose product defines the */ -/* > matrix Q. M >= K >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On entry, the i-th row must contain the vector which defines */ -/* > the elementary reflector H(i), for i = 1,2,...,k, as returned */ -/* > by DGELQF in the first k rows of its array argument A. */ -/* > On exit, the M-by-N matrix Q. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The first dimension of the array A. LDA >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TAU */ -/* > \verbatim */ -/* > TAU is DOUBLE PRECISION array, dimension (K) */ -/* > TAU(i) must contain the scalar factor of the elementary */ -/* > reflector H(i), as returned by DGELQF. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ -/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LWORK */ -/* > \verbatim */ -/* > LWORK is INTEGER */ -/* > The dimension of the array WORK. LWORK >= max(1,M). */ -/* > For optimum performance LWORK >= M*NB, where NB is */ -/* > the optimal blocksize. */ -/* > */ -/* > If LWORK = -1, then a workspace query is assumed; the routine */ -/* > only calculates the optimal size of the WORK array, returns */ -/* > this value as the first entry of the WORK array, and no error */ -/* > message related to LWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument has an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleOTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dorglq_(integer *m, integer *n, integer *k, doublereal * - a, integer *lda, doublereal *tau, doublereal *work, integer *lwork, - integer *info) +int dorglq_(integer *m, integer *n, integer *k, doublereal *a, integer *lda, doublereal *tau, + doublereal *work, integer *lwork, integer *info) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; - - /* Local variables */ integer i__, j, l, ib, nb, ki, kk, nx, iws, nbmin, iinfo; - extern /* Subroutine */ int dorgl2_(integer *, integer *, integer *, - doublereal *, integer *, doublereal *, doublereal *, integer *), - dlarfb_(char *, char *, char *, char *, integer *, integer *, - integer *, doublereal *, integer *, doublereal *, integer *, - doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, - ftnlen, ftnlen), dlarft_(char *, char *, integer *, integer *, - doublereal *, integer *, doublereal *, doublereal *, integer *, - ftnlen, ftnlen), xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern int dorgl2_(integer *, integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *), + dlarfb_(char *, char *, char *, char *, integer *, integer *, integer *, doublereal *, + integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, + integer *, ftnlen, ftnlen, ftnlen, ftnlen), + dlarft_(char *, char *, integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, ftnlen, ftnlen), + xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); integer ldwork, lwkopt; logical lquery; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --tau; --work; - - /* Function Body */ *info = 0; nb = ilaenv_(&c__1, (char *)"DORGLQ", (char *)" ", m, n, k, &c_n1, (ftnlen)6, (ftnlen)1); - lwkopt = max(1,*m) * nb; - work[1] = (doublereal) lwkopt; + lwkopt = max(1, *m) * nb; + work[1] = (doublereal)lwkopt; lquery = *lwork == -1; if (*m < 0) { *info = -1; @@ -217,9 +39,9 @@ f"> */ *info = -2; } else if (*k < 0 || *k > *m) { *info = -3; - } else if (*lda < max(1,*m)) { + } else if (*lda < max(1, *m)) { *info = -5; - } else if (*lwork < max(1,*m) && ! lquery) { + } else if (*lwork < max(1, *m) && !lquery) { *info = -8; } if (*info != 0) { @@ -229,138 +51,77 @@ f"> */ } else if (lquery) { return 0; } - -/* Quick return if possible */ - if (*m <= 0) { work[1] = 1.; return 0; } - nbmin = 2; nx = 0; iws = *m; if (nb > 1 && nb < *k) { - -/* Determine when to cross over from blocked to unblocked code. */ - -/* Computing MAX */ - i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"DORGLQ", (char *)" ", m, n, k, &c_n1, ( - ftnlen)6, (ftnlen)1); - nx = max(i__1,i__2); + i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"DORGLQ", (char *)" ", m, n, k, &c_n1, (ftnlen)6, (ftnlen)1); + nx = max(i__1, i__2); if (nx < *k) { - -/* Determine if workspace is large enough for blocked code. */ - ldwork = *m; iws = ldwork * nb; if (*lwork < iws) { - -/* Not enough workspace to use optimal NB: reduce NB and */ -/* determine the minimum value of NB. */ - nb = *lwork / ldwork; -/* Computing MAX */ - i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DORGLQ", (char *)" ", m, n, k, &c_n1, - (ftnlen)6, (ftnlen)1); - nbmin = max(i__1,i__2); + i__1 = 2, + i__2 = ilaenv_(&c__2, (char *)"DORGLQ", (char *)" ", m, n, k, &c_n1, (ftnlen)6, (ftnlen)1); + nbmin = max(i__1, i__2); } } } - if (nb >= nbmin && nb < *k && nx < *k) { - -/* Use blocked code after the last block. */ -/* The first kk rows are handled by the block method. */ - ki = (*k - nx - 1) / nb * nb; -/* Computing MIN */ i__1 = *k, i__2 = ki + nb; - kk = min(i__1,i__2); - -/* Set A(kk+1:m,1:kk) to zero. */ - + kk = min(i__1, i__2); i__1 = kk; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = kk + 1; i__ <= i__2; ++i__) { a[i__ + j * a_dim1] = 0.; -/* L10: */ } -/* L20: */ } } else { kk = 0; } - -/* Use unblocked code for the last or only block. */ - if (kk < *m) { i__1 = *m - kk; i__2 = *n - kk; i__3 = *k - kk; - dorgl2_(&i__1, &i__2, &i__3, &a[kk + 1 + (kk + 1) * a_dim1], lda, & - tau[kk + 1], &work[1], &iinfo); + dorgl2_(&i__1, &i__2, &i__3, &a[kk + 1 + (kk + 1) * a_dim1], lda, &tau[kk + 1], &work[1], + &iinfo); } - if (kk > 0) { - -/* Use blocked code */ - i__1 = -nb; for (i__ = ki + 1; i__1 < 0 ? i__ >= 1 : i__ <= 1; i__ += i__1) { -/* Computing MIN */ i__2 = nb, i__3 = *k - i__ + 1; - ib = min(i__2,i__3); + ib = min(i__2, i__3); if (i__ + ib <= *m) { - -/* Form the triangular factor of the block reflector */ -/* H = H(i) H(i+1) . . . H(i+ib-1) */ - i__2 = *n - i__ + 1; - dlarft_((char *)"Forward", (char *)"Rowwise", &i__2, &ib, &a[i__ + i__ * - a_dim1], lda, &tau[i__], &work[1], &ldwork, (ftnlen)7, - (ftnlen)7); - -/* Apply H**T to A(i+ib:m,i:n) from the right */ - + dlarft_((char *)"Forward", (char *)"Rowwise", &i__2, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], + &work[1], &ldwork, (ftnlen)7, (ftnlen)7); i__2 = *m - i__ - ib + 1; i__3 = *n - i__ + 1; - dlarfb_((char *)"Right", (char *)"Transpose", (char *)"Forward", (char *)"Rowwise", &i__2, & - i__3, &ib, &a[i__ + i__ * a_dim1], lda, &work[1], & - ldwork, &a[i__ + ib + i__ * a_dim1], lda, &work[ib + - 1], &ldwork, (ftnlen)5, (ftnlen)9, (ftnlen)7, (ftnlen) - 7); + dlarfb_((char *)"Right", (char *)"Transpose", (char *)"Forward", (char *)"Rowwise", &i__2, &i__3, &ib, + &a[i__ + i__ * a_dim1], lda, &work[1], &ldwork, &a[i__ + ib + i__ * a_dim1], + lda, &work[ib + 1], &ldwork, (ftnlen)5, (ftnlen)9, (ftnlen)7, (ftnlen)7); } - -/* Apply H**T to columns i:n of current block */ - i__2 = *n - i__ + 1; - dorgl2_(&ib, &i__2, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], & - work[1], &iinfo); - -/* Set columns 1:i-1 of current block to zero */ - + dorgl2_(&ib, &i__2, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[1], &iinfo); i__2 = i__ - 1; for (j = 1; j <= i__2; ++j) { i__3 = i__ + ib - 1; for (l = i__; l <= i__3; ++l) { a[l + j * a_dim1] = 0.; -/* L30: */ } -/* L40: */ } -/* L50: */ } } - - work[1] = (doublereal) iws; + work[1] = (doublereal)iws; return 0; - -/* End of DORGLQ */ - -} /* dorglq_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dorgql.cpp b/lib/linalg/dorgql.cpp index 719b7aa685..53c6e01be0 100644 --- a/lib/linalg/dorgql.cpp +++ b/lib/linalg/dorgql.cpp @@ -1,212 +1,33 @@ -/* fortran/dorgql.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static integer c_n1 = -1; static integer c__3 = 3; static integer c__2 = 2; - -/* > \brief \b DORGQL */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DORGQL + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DORGQL( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INFO, K, LDA, LWORK, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DORGQL generates an M-by-N real matrix Q with orthonormal columns, */ -/* > which is defined as the last N columns of a product of K elementary */ -/* > reflectors of order M */ -/* > */ -/* > Q = H(k) . . . H(2) H(1) */ -/* > */ -/* > as returned by DGEQLF. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix Q. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix Q. M >= N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > The number of elementary reflectors whose product defines the */ -/* > matrix Q. N >= K >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On entry, the (n-k+i)-th column must contain the vector which */ -/* > defines the elementary reflector H(i), for i = 1,2,...,k, as */ -/* > returned by DGEQLF in the last k columns of its array */ -/* > argument A. */ -/* > On exit, the M-by-N matrix Q. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The first dimension of the array A. LDA >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TAU */ -/* > \verbatim */ -/* > TAU is DOUBLE PRECISION array, dimension (K) */ -/* > TAU(i) must contain the scalar factor of the elementary */ -/* > reflector H(i), as returned by DGEQLF. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ -/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LWORK */ -/* > \verbatim */ -/* > LWORK is INTEGER */ -/* > The dimension of the array WORK. LWORK >= max(1,N). */ -/* > For optimum performance LWORK >= N*NB, where NB is the */ -/* > optimal blocksize. */ -/* > */ -/* > If LWORK = -1, then a workspace query is assumed; the routine */ -/* > only calculates the optimal size of the WORK array, returns */ -/* > this value as the first entry of the WORK array, and no error */ -/* > message related to LWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument has an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleOTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dorgql_(integer *m, integer *n, integer *k, doublereal * - a, integer *lda, doublereal *tau, doublereal *work, integer *lwork, - integer *info) +int dorgql_(integer *m, integer *n, integer *k, doublereal *a, integer *lda, doublereal *tau, + doublereal *work, integer *lwork, integer *info) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4; - - /* Local variables */ integer i__, j, l, ib, nb, kk, nx, iws, nbmin, iinfo; - extern /* Subroutine */ int dorg2l_(integer *, integer *, integer *, - doublereal *, integer *, doublereal *, doublereal *, integer *), - dlarfb_(char *, char *, char *, char *, integer *, integer *, - integer *, doublereal *, integer *, doublereal *, integer *, - doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, - ftnlen, ftnlen), dlarft_(char *, char *, integer *, integer *, - doublereal *, integer *, doublereal *, doublereal *, integer *, - ftnlen, ftnlen), xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern int dorg2l_(integer *, integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *), + dlarfb_(char *, char *, char *, char *, integer *, integer *, integer *, doublereal *, + integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, + integer *, ftnlen, ftnlen, ftnlen, ftnlen), + dlarft_(char *, char *, integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, ftnlen, ftnlen), + xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); integer ldwork, lwkopt; logical lquery; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --tau; --work; - - /* Function Body */ *info = 0; lquery = *lwork == -1; if (*m < 0) { @@ -215,25 +36,21 @@ f"> */ *info = -2; } else if (*k < 0 || *k > *n) { *info = -3; - } else if (*lda < max(1,*m)) { + } else if (*lda < max(1, *m)) { *info = -5; } - if (*info == 0) { if (*n == 0) { lwkopt = 1; } else { - nb = ilaenv_(&c__1, (char *)"DORGQL", (char *)" ", m, n, k, &c_n1, (ftnlen)6, ( - ftnlen)1); + nb = ilaenv_(&c__1, (char *)"DORGQL", (char *)" ", m, n, k, &c_n1, (ftnlen)6, (ftnlen)1); lwkopt = *n * nb; } - work[1] = (doublereal) lwkopt; - - if (*lwork < max(1,*n) && ! lquery) { + work[1] = (doublereal)lwkopt; + if (*lwork < max(1, *n) && !lquery) { *info = -8; } } - if (*info != 0) { i__1 = -(*info); xerbla_((char *)"DORGQL", &i__1, (ftnlen)6); @@ -241,136 +58,74 @@ f"> */ } else if (lquery) { return 0; } - -/* Quick return if possible */ - if (*n <= 0) { return 0; } - nbmin = 2; nx = 0; iws = *n; if (nb > 1 && nb < *k) { - -/* Determine when to cross over from blocked to unblocked code. */ - -/* Computing MAX */ - i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"DORGQL", (char *)" ", m, n, k, &c_n1, ( - ftnlen)6, (ftnlen)1); - nx = max(i__1,i__2); + i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"DORGQL", (char *)" ", m, n, k, &c_n1, (ftnlen)6, (ftnlen)1); + nx = max(i__1, i__2); if (nx < *k) { - -/* Determine if workspace is large enough for blocked code. */ - ldwork = *n; iws = ldwork * nb; if (*lwork < iws) { - -/* Not enough workspace to use optimal NB: reduce NB and */ -/* determine the minimum value of NB. */ - nb = *lwork / ldwork; -/* Computing MAX */ - i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DORGQL", (char *)" ", m, n, k, &c_n1, - (ftnlen)6, (ftnlen)1); - nbmin = max(i__1,i__2); + i__1 = 2, + i__2 = ilaenv_(&c__2, (char *)"DORGQL", (char *)" ", m, n, k, &c_n1, (ftnlen)6, (ftnlen)1); + nbmin = max(i__1, i__2); } } } - if (nb >= nbmin && nb < *k && nx < *k) { - -/* Use blocked code after the first block. */ -/* The last kk columns are handled by the block method. */ - -/* Computing MIN */ i__1 = *k, i__2 = (*k - nx + nb - 1) / nb * nb; - kk = min(i__1,i__2); - -/* Set A(m-kk+1:m,1:n-kk) to zero. */ - + kk = min(i__1, i__2); i__1 = *n - kk; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = *m - kk + 1; i__ <= i__2; ++i__) { a[i__ + j * a_dim1] = 0.; -/* L10: */ } -/* L20: */ } } else { kk = 0; } - -/* Use unblocked code for the first or only block. */ - i__1 = *m - kk; i__2 = *n - kk; i__3 = *k - kk; - dorg2l_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], &work[1], &iinfo) - ; - + dorg2l_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], &work[1], &iinfo); if (kk > 0) { - -/* Use blocked code */ - i__1 = *k; i__2 = nb; - for (i__ = *k - kk + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += - i__2) { -/* Computing MIN */ + for (i__ = *k - kk + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { i__3 = nb, i__4 = *k - i__ + 1; - ib = min(i__3,i__4); + ib = min(i__3, i__4); if (*n - *k + i__ > 1) { - -/* Form the triangular factor of the block reflector */ -/* H = H(i+ib-1) . . . H(i+1) H(i) */ - i__3 = *m - *k + i__ + ib - 1; - dlarft_((char *)"Backward", (char *)"Columnwise", &i__3, &ib, &a[(*n - *k + - i__) * a_dim1 + 1], lda, &tau[i__], &work[1], &ldwork, - (ftnlen)8, (ftnlen)10); - -/* Apply H to A(1:m-k+i+ib-1,1:n-k+i-1) from the left */ - + dlarft_((char *)"Backward", (char *)"Columnwise", &i__3, &ib, &a[(*n - *k + i__) * a_dim1 + 1], lda, + &tau[i__], &work[1], &ldwork, (ftnlen)8, (ftnlen)10); i__3 = *m - *k + i__ + ib - 1; i__4 = *n - *k + i__ - 1; - dlarfb_((char *)"Left", (char *)"No transpose", (char *)"Backward", (char *)"Columnwise", & - i__3, &i__4, &ib, &a[(*n - *k + i__) * a_dim1 + 1], - lda, &work[1], &ldwork, &a[a_offset], lda, &work[ib + - 1], &ldwork, (ftnlen)4, (ftnlen)12, (ftnlen)8, ( - ftnlen)10); + dlarfb_((char *)"Left", (char *)"No transpose", (char *)"Backward", (char *)"Columnwise", &i__3, &i__4, &ib, + &a[(*n - *k + i__) * a_dim1 + 1], lda, &work[1], &ldwork, &a[a_offset], lda, + &work[ib + 1], &ldwork, (ftnlen)4, (ftnlen)12, (ftnlen)8, (ftnlen)10); } - -/* Apply H to rows 1:m-k+i+ib-1 of current block */ - i__3 = *m - *k + i__ + ib - 1; - dorg2l_(&i__3, &ib, &ib, &a[(*n - *k + i__) * a_dim1 + 1], lda, & - tau[i__], &work[1], &iinfo); - -/* Set rows m-k+i+ib:m of current block to zero */ - + dorg2l_(&i__3, &ib, &ib, &a[(*n - *k + i__) * a_dim1 + 1], lda, &tau[i__], &work[1], + &iinfo); i__3 = *n - *k + i__ + ib - 1; for (j = *n - *k + i__; j <= i__3; ++j) { i__4 = *m; for (l = *m - *k + i__ + ib; l <= i__4; ++l) { a[l + j * a_dim1] = 0.; -/* L30: */ } -/* L40: */ } -/* L50: */ } } - - work[1] = (doublereal) iws; + work[1] = (doublereal)iws; return 0; - -/* End of DORGQL */ - -} /* dorgql_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dorgqr.cpp b/lib/linalg/dorgqr.cpp index 4fedb08864..9f4e8f5da1 100644 --- a/lib/linalg/dorgqr.cpp +++ b/lib/linalg/dorgqr.cpp @@ -1,216 +1,37 @@ -/* fortran/dorgqr.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static integer c_n1 = -1; static integer c__3 = 3; static integer c__2 = 2; - -/* > \brief \b DORGQR */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DORGQR + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INFO, K, LDA, LWORK, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DORGQR generates an M-by-N real matrix Q with orthonormal columns, */ -/* > which is defined as the first N columns of a product of K elementary */ -/* > reflectors of order M */ -/* > */ -/* > Q = H(1) H(2) . . . H(k) */ -/* > */ -/* > as returned by DGEQRF. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix Q. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix Q. M >= N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > The number of elementary reflectors whose product defines the */ -/* > matrix Q. N >= K >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On entry, the i-th column must contain the vector which */ -/* > defines the elementary reflector H(i), for i = 1,2,...,k, as */ -/* > returned by DGEQRF in the first k columns of its array */ -/* > argument A. */ -/* > On exit, the M-by-N matrix Q. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The first dimension of the array A. LDA >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TAU */ -/* > \verbatim */ -/* > TAU is DOUBLE PRECISION array, dimension (K) */ -/* > TAU(i) must contain the scalar factor of the elementary */ -/* > reflector H(i), as returned by DGEQRF. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ -/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LWORK */ -/* > \verbatim */ -/* > LWORK is INTEGER */ -/* > The dimension of the array WORK. LWORK >= max(1,N). */ -/* > For optimum performance LWORK >= N*NB, where NB is the */ -/* > optimal blocksize. */ -/* > */ -/* > If LWORK = -1, then a workspace query is assumed; the routine */ -/* > only calculates the optimal size of the WORK array, returns */ -/* > this value as the first entry of the WORK array, and no error */ -/* > message related to LWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument has an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleOTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dorgqr_(integer *m, integer *n, integer *k, doublereal * - a, integer *lda, doublereal *tau, doublereal *work, integer *lwork, - integer *info) +int dorgqr_(integer *m, integer *n, integer *k, doublereal *a, integer *lda, doublereal *tau, + doublereal *work, integer *lwork, integer *info) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; - - /* Local variables */ integer i__, j, l, ib, nb, ki, kk, nx, iws, nbmin, iinfo; - extern /* Subroutine */ int dorg2r_(integer *, integer *, integer *, - doublereal *, integer *, doublereal *, doublereal *, integer *), - dlarfb_(char *, char *, char *, char *, integer *, integer *, - integer *, doublereal *, integer *, doublereal *, integer *, - doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, - ftnlen, ftnlen), dlarft_(char *, char *, integer *, integer *, - doublereal *, integer *, doublereal *, doublereal *, integer *, - ftnlen, ftnlen), xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern int dorg2r_(integer *, integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *), + dlarfb_(char *, char *, char *, char *, integer *, integer *, integer *, doublereal *, + integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, + integer *, ftnlen, ftnlen, ftnlen, ftnlen), + dlarft_(char *, char *, integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, ftnlen, ftnlen), + xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); integer ldwork, lwkopt; logical lquery; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --tau; --work; - - /* Function Body */ *info = 0; nb = ilaenv_(&c__1, (char *)"DORGQR", (char *)" ", m, n, k, &c_n1, (ftnlen)6, (ftnlen)1); - lwkopt = max(1,*n) * nb; - work[1] = (doublereal) lwkopt; + lwkopt = max(1, *n) * nb; + work[1] = (doublereal)lwkopt; lquery = *lwork == -1; if (*m < 0) { *info = -1; @@ -218,9 +39,9 @@ f"> */ *info = -2; } else if (*k < 0 || *k > *n) { *info = -3; - } else if (*lda < max(1,*m)) { + } else if (*lda < max(1, *m)) { *info = -5; - } else if (*lwork < max(1,*n) && ! lquery) { + } else if (*lwork < max(1, *n) && !lquery) { *info = -8; } if (*info != 0) { @@ -230,138 +51,78 @@ f"> */ } else if (lquery) { return 0; } - -/* Quick return if possible */ - if (*n <= 0) { work[1] = 1.; return 0; } - nbmin = 2; nx = 0; iws = *n; if (nb > 1 && nb < *k) { - -/* Determine when to cross over from blocked to unblocked code. */ - -/* Computing MAX */ - i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"DORGQR", (char *)" ", m, n, k, &c_n1, ( - ftnlen)6, (ftnlen)1); - nx = max(i__1,i__2); + i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"DORGQR", (char *)" ", m, n, k, &c_n1, (ftnlen)6, (ftnlen)1); + nx = max(i__1, i__2); if (nx < *k) { - -/* Determine if workspace is large enough for blocked code. */ - ldwork = *n; iws = ldwork * nb; if (*lwork < iws) { - -/* Not enough workspace to use optimal NB: reduce NB and */ -/* determine the minimum value of NB. */ - nb = *lwork / ldwork; -/* Computing MAX */ - i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DORGQR", (char *)" ", m, n, k, &c_n1, - (ftnlen)6, (ftnlen)1); - nbmin = max(i__1,i__2); + i__1 = 2, + i__2 = ilaenv_(&c__2, (char *)"DORGQR", (char *)" ", m, n, k, &c_n1, (ftnlen)6, (ftnlen)1); + nbmin = max(i__1, i__2); } } } - if (nb >= nbmin && nb < *k && nx < *k) { - -/* Use blocked code after the last block. */ -/* The first kk columns are handled by the block method. */ - ki = (*k - nx - 1) / nb * nb; -/* Computing MIN */ i__1 = *k, i__2 = ki + nb; - kk = min(i__1,i__2); - -/* Set A(1:kk,kk+1:n) to zero. */ - + kk = min(i__1, i__2); i__1 = *n; for (j = kk + 1; j <= i__1; ++j) { i__2 = kk; for (i__ = 1; i__ <= i__2; ++i__) { a[i__ + j * a_dim1] = 0.; -/* L10: */ } -/* L20: */ } } else { kk = 0; } - -/* Use unblocked code for the last or only block. */ - if (kk < *n) { i__1 = *m - kk; i__2 = *n - kk; i__3 = *k - kk; - dorg2r_(&i__1, &i__2, &i__3, &a[kk + 1 + (kk + 1) * a_dim1], lda, & - tau[kk + 1], &work[1], &iinfo); + dorg2r_(&i__1, &i__2, &i__3, &a[kk + 1 + (kk + 1) * a_dim1], lda, &tau[kk + 1], &work[1], + &iinfo); } - if (kk > 0) { - -/* Use blocked code */ - i__1 = -nb; for (i__ = ki + 1; i__1 < 0 ? i__ >= 1 : i__ <= 1; i__ += i__1) { -/* Computing MIN */ i__2 = nb, i__3 = *k - i__ + 1; - ib = min(i__2,i__3); + ib = min(i__2, i__3); if (i__ + ib <= *n) { - -/* Form the triangular factor of the block reflector */ -/* H = H(i) H(i+1) . . . H(i+ib-1) */ - i__2 = *m - i__ + 1; - dlarft_((char *)"Forward", (char *)"Columnwise", &i__2, &ib, &a[i__ + i__ * - a_dim1], lda, &tau[i__], &work[1], &ldwork, (ftnlen)7, - (ftnlen)10); - -/* Apply H to A(i:m,i+ib:n) from the left */ - + dlarft_((char *)"Forward", (char *)"Columnwise", &i__2, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], + &work[1], &ldwork, (ftnlen)7, (ftnlen)10); i__2 = *m - i__ + 1; i__3 = *n - i__ - ib + 1; - dlarfb_((char *)"Left", (char *)"No transpose", (char *)"Forward", (char *)"Columnwise", & - i__2, &i__3, &ib, &a[i__ + i__ * a_dim1], lda, &work[ - 1], &ldwork, &a[i__ + (i__ + ib) * a_dim1], lda, & - work[ib + 1], &ldwork, (ftnlen)4, (ftnlen)12, (ftnlen) - 7, (ftnlen)10); + dlarfb_((char *)"Left", (char *)"No transpose", (char *)"Forward", (char *)"Columnwise", &i__2, &i__3, &ib, + &a[i__ + i__ * a_dim1], lda, &work[1], &ldwork, + &a[i__ + (i__ + ib) * a_dim1], lda, &work[ib + 1], &ldwork, (ftnlen)4, + (ftnlen)12, (ftnlen)7, (ftnlen)10); } - -/* Apply H to rows i:m of current block */ - i__2 = *m - i__ + 1; - dorg2r_(&i__2, &ib, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], & - work[1], &iinfo); - -/* Set rows 1:i-1 of current block to zero */ - + dorg2r_(&i__2, &ib, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[1], &iinfo); i__2 = i__ + ib - 1; for (j = i__; j <= i__2; ++j) { i__3 = i__ - 1; for (l = 1; l <= i__3; ++l) { a[l + j * a_dim1] = 0.; -/* L30: */ } -/* L40: */ } -/* L50: */ } } - - work[1] = (doublereal) iws; + work[1] = (doublereal)iws; return 0; - -/* End of DORGQR */ - -} /* dorgqr_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dorgtr.cpp b/lib/linalg/dorgtr.cpp index 0574de0d9b..692b6c4945 100644 --- a/lib/linalg/dorgtr.cpp +++ b/lib/linalg/dorgtr.cpp @@ -1,242 +1,62 @@ -/* fortran/dorgtr.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static integer c_n1 = -1; - -/* > \brief \b DORGTR */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DORGTR + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DORGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER UPLO */ -/* INTEGER INFO, LDA, LWORK, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DORGTR generates a real orthogonal matrix Q which is defined as the */ -/* > product of n-1 elementary reflectors of order N, as returned by */ -/* > DSYTRD: */ -/* > */ -/* > if UPLO = 'U', Q = H(n-1) . . . H(2) H(1), */ -/* > */ -/* > if UPLO = 'L', Q = H(1) H(2) . . . H(n-1). */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > = 'U': Upper triangle of A contains elementary reflectors */ -/* > from DSYTRD; */ -/* > = 'L': Lower triangle of A contains elementary reflectors */ -/* > from DSYTRD. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrix Q. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On entry, the vectors which define the elementary reflectors, */ -/* > as returned by DSYTRD. */ -/* > On exit, the N-by-N orthogonal matrix Q. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TAU */ -/* > \verbatim */ -/* > TAU is DOUBLE PRECISION array, dimension (N-1) */ -/* > TAU(i) must contain the scalar factor of the elementary */ -/* > reflector H(i), as returned by DSYTRD. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ -/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LWORK */ -/* > \verbatim */ -/* > LWORK is INTEGER */ -/* > The dimension of the array WORK. LWORK >= max(1,N-1). */ -/* > For optimum performance LWORK >= (N-1)*NB, where NB is */ -/* > the optimal blocksize. */ -/* > */ -/* > If LWORK = -1, then a workspace query is assumed; the routine */ -/* > only calculates the optimal size of the WORK array, returns */ -/* > this value as the first entry of the WORK array, and no error */ -/* > message related to LWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleOTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dorgtr_(char *uplo, integer *n, doublereal *a, integer * - lda, doublereal *tau, doublereal *work, integer *lwork, integer *info, - ftnlen uplo_len) +int dorgtr_(char *uplo, integer *n, doublereal *a, integer *lda, doublereal *tau, doublereal *work, + integer *lwork, integer *info, ftnlen uplo_len) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; - - /* Local variables */ integer i__, j, nb; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer iinfo; logical upper; - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - extern /* Subroutine */ int dorgql_(integer *, integer *, integer *, - doublereal *, integer *, doublereal *, doublereal *, integer *, - integer *), dorgqr_(integer *, integer *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, integer *); + extern int xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); + extern int dorgql_(integer *, integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, integer *), + dorgqr_(integer *, integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, integer *); integer lwkopt; logical lquery; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --tau; --work; - - /* Function Body */ *info = 0; lquery = *lwork == -1; upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); - if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + if (!upper && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { *info = -1; } else if (*n < 0) { *info = -2; - } else if (*lda < max(1,*n)) { + } else if (*lda < max(1, *n)) { *info = -4; - } else /* if(complicated condition) */ { -/* Computing MAX */ + } else { i__1 = 1, i__2 = *n - 1; - if (*lwork < max(i__1,i__2) && ! lquery) { + if (*lwork < max(i__1, i__2) && !lquery) { *info = -7; } } - if (*info == 0) { if (upper) { i__1 = *n - 1; i__2 = *n - 1; i__3 = *n - 1; - nb = ilaenv_(&c__1, (char *)"DORGQL", (char *)" ", &i__1, &i__2, &i__3, &c_n1, ( - ftnlen)6, (ftnlen)1); + nb = ilaenv_(&c__1, (char *)"DORGQL", (char *)" ", &i__1, &i__2, &i__3, &c_n1, (ftnlen)6, (ftnlen)1); } else { i__1 = *n - 1; i__2 = *n - 1; i__3 = *n - 1; - nb = ilaenv_(&c__1, (char *)"DORGQR", (char *)" ", &i__1, &i__2, &i__3, &c_n1, ( - ftnlen)6, (ftnlen)1); + nb = ilaenv_(&c__1, (char *)"DORGQR", (char *)" ", &i__1, &i__2, &i__3, &c_n1, (ftnlen)6, (ftnlen)1); } -/* Computing MAX */ i__1 = 1, i__2 = *n - 1; - lwkopt = max(i__1,i__2) * nb; - work[1] = (doublereal) lwkopt; + lwkopt = max(i__1, i__2) * nb; + work[1] = (doublereal)lwkopt; } - if (*info != 0) { i__1 = -(*info); xerbla_((char *)"DORGTR", &i__1, (ftnlen)6); @@ -244,88 +64,52 @@ f"> */ } else if (lquery) { return 0; } - -/* Quick return if possible */ - if (*n == 0) { work[1] = 1.; return 0; } - if (upper) { - -/* Q was determined by a call to DSYTRD with UPLO = 'U' */ - -/* Shift the vectors which define the elementary reflectors one */ -/* column to the left, and set the last row and column of Q to */ -/* those of the unit matrix */ - i__1 = *n - 1; for (j = 1; j <= i__1; ++j) { i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { a[i__ + j * a_dim1] = a[i__ + (j + 1) * a_dim1]; -/* L10: */ } a[*n + j * a_dim1] = 0.; -/* L20: */ } i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { a[i__ + *n * a_dim1] = 0.; -/* L30: */ } a[*n + *n * a_dim1] = 1.; - -/* Generate Q(1:n-1,1:n-1) */ - i__1 = *n - 1; i__2 = *n - 1; i__3 = *n - 1; - dorgql_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], &work[1], - lwork, &iinfo); - + dorgql_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], &work[1], lwork, &iinfo); } else { - -/* Q was determined by a call to DSYTRD with UPLO = 'L'. */ - -/* Shift the vectors which define the elementary reflectors one */ -/* column to the right, and set the first row and column of Q to */ -/* those of the unit matrix */ - for (j = *n; j >= 2; --j) { a[j * a_dim1 + 1] = 0.; i__1 = *n; for (i__ = j + 1; i__ <= i__1; ++i__) { a[i__ + j * a_dim1] = a[i__ + (j - 1) * a_dim1]; -/* L40: */ } -/* L50: */ } a[a_dim1 + 1] = 1.; i__1 = *n; for (i__ = 2; i__ <= i__1; ++i__) { a[i__ + a_dim1] = 0.; -/* L60: */ } if (*n > 1) { - -/* Generate Q(2:n,2:n) */ - i__1 = *n - 1; i__2 = *n - 1; i__3 = *n - 1; - dorgqr_(&i__1, &i__2, &i__3, &a[(a_dim1 << 1) + 2], lda, &tau[1], - &work[1], lwork, &iinfo); + dorgqr_(&i__1, &i__2, &i__3, &a[(a_dim1 << 1) + 2], lda, &tau[1], &work[1], lwork, + &iinfo); } } - work[1] = (doublereal) lwkopt; + work[1] = (doublereal)lwkopt; return 0; - -/* End of DORGTR */ - -} /* dorgtr_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dorm2l.cpp b/lib/linalg/dorm2l.cpp index 6882f50cdb..35d3b346a5 100644 --- a/lib/linalg/dorm2l.cpp +++ b/lib/linalg/dorm2l.cpp @@ -1,230 +1,21 @@ -/* fortran/dorm2l.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; - -/* > \brief \b DORM2L multiplies a general matrix by the orthogonal matrix from a QL factorization determined -by sgeqlf (unblocked algorithm). */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DORM2L + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DORM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, */ -/* WORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER SIDE, TRANS */ -/* INTEGER INFO, K, LDA, LDC, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DORM2L overwrites the general real m by n matrix C with */ -/* > */ -/* > Q * C if SIDE = 'L' and TRANS = 'N', or */ -/* > */ -/* > Q**T * C if SIDE = 'L' and TRANS = 'T', or */ -/* > */ -/* > C * Q if SIDE = 'R' and TRANS = 'N', or */ -/* > */ -/* > C * Q**T if SIDE = 'R' and TRANS = 'T', */ -/* > */ -/* > where Q is a real orthogonal matrix defined as the product of k */ -/* > elementary reflectors */ -/* > */ -/* > Q = H(k) . . . H(2) H(1) */ -/* > */ -/* > as returned by DGEQLF. Q is of order m if SIDE = 'L' and of order n */ -/* > if SIDE = 'R'. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] SIDE */ -/* > \verbatim */ -/* > SIDE is CHARACTER*1 */ -/* > = 'L': apply Q or Q**T from the Left */ -/* > = 'R': apply Q or Q**T from the Right */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TRANS */ -/* > \verbatim */ -/* > TRANS is CHARACTER*1 */ -/* > = 'N': apply Q (No transpose) */ -/* > = 'T': apply Q**T (Transpose) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix C. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix C. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > The number of elementary reflectors whose product defines */ -/* > the matrix Q. */ -/* > If SIDE = 'L', M >= K >= 0; */ -/* > if SIDE = 'R', N >= K >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,K) */ -/* > The i-th column must contain the vector which defines the */ -/* > elementary reflector H(i), for i = 1,2,...,k, as returned by */ -/* > DGEQLF in the last k columns of its array argument A. */ -/* > A is modified by the routine but restored on exit. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. */ -/* > If SIDE = 'L', LDA >= max(1,M); */ -/* > if SIDE = 'R', LDA >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TAU */ -/* > \verbatim */ -/* > TAU is DOUBLE PRECISION array, dimension (K) */ -/* > TAU(i) must contain the scalar factor of the elementary */ -/* > reflector H(i), as returned by DGEQLF. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] C */ -/* > \verbatim */ -/* > C is DOUBLE PRECISION array, dimension (LDC,N) */ -/* > On entry, the m by n matrix C. */ -/* > On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDC */ -/* > \verbatim */ -/* > LDC is INTEGER */ -/* > The leading dimension of the array C. LDC >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension */ -/* > (N) if SIDE = 'L', */ -/* > (M) if SIDE = 'R' */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleOTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dorm2l_(char *side, char *trans, integer *m, integer *n, - integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal * - c__, integer *ldc, doublereal *work, integer *info, ftnlen side_len, - ftnlen trans_len) +int dorm2l_(char *side, char *trans, integer *m, integer *n, integer *k, doublereal *a, + integer *lda, doublereal *tau, doublereal *c__, integer *ldc, doublereal *work, + integer *info, ftnlen side_len, ftnlen trans_len) { - /* System generated locals */ integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2; - - /* Local variables */ integer i__, i1, i2, i3, mi, ni, nq; doublereal aii; logical left; - extern /* Subroutine */ int dlarf_(char *, integer *, integer *, - doublereal *, integer *, doublereal *, doublereal *, integer *, - doublereal *, ftnlen); + extern int dlarf_(char *, integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, doublereal *, ftnlen); extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern int xerbla_(char *, integer *, ftnlen); logical notran; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; @@ -233,22 +24,17 @@ f"> */ c_offset = 1 + c_dim1; c__ -= c_offset; --work; - - /* Function Body */ *info = 0; left = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); notran = lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1); - -/* NQ is the order of Q */ - if (left) { nq = *m; } else { nq = *n; } - if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + if (!left && !lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { *info = -1; - } else if (! notran && ! lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1)) { + } else if (!notran && !lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1)) { *info = -2; } else if (*m < 0) { *info = -3; @@ -256,9 +42,9 @@ f"> */ *info = -4; } else if (*k < 0 || *k > nq) { *info = -5; - } else if (*lda < max(1,nq)) { + } else if (*lda < max(1, nq)) { *info = -7; - } else if (*ldc < max(1,*m)) { + } else if (*ldc < max(1, *m)) { *info = -10; } if (*info != 0) { @@ -266,14 +52,10 @@ f"> */ xerbla_((char *)"DORM2L", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*m == 0 || *n == 0 || *k == 0) { return 0; } - - if (left && notran || ! left && ! notran) { + if (left && notran || !left && !notran) { i1 = 1; i2 = *k; i3 = 1; @@ -282,43 +64,27 @@ f"> */ i2 = 1; i3 = -1; } - if (left) { ni = *n; } else { mi = *m; } - i__1 = i2; i__2 = i3; for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { if (left) { - -/* H(i) is applied to C(1:m-k+i,1:n) */ - mi = *m - *k + i__; } else { - -/* H(i) is applied to C(1:m,1:n-k+i) */ - ni = *n - *k + i__; } - -/* Apply H(i) */ - aii = a[nq - *k + i__ + i__ * a_dim1]; a[nq - *k + i__ + i__ * a_dim1] = 1.; - dlarf_(side, &mi, &ni, &a[i__ * a_dim1 + 1], &c__1, &tau[i__], &c__[ - c_offset], ldc, &work[1], (ftnlen)1); + dlarf_(side, &mi, &ni, &a[i__ * a_dim1 + 1], &c__1, &tau[i__], &c__[c_offset], ldc, + &work[1], (ftnlen)1); a[nq - *k + i__ + i__ * a_dim1] = aii; -/* L10: */ } return 0; - -/* End of DORM2L */ - -} /* dorm2l_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dorm2r.cpp b/lib/linalg/dorm2r.cpp index 1b600a3507..6594725f24 100644 --- a/lib/linalg/dorm2r.cpp +++ b/lib/linalg/dorm2r.cpp @@ -1,230 +1,21 @@ -/* fortran/dorm2r.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; - -/* > \brief \b DORM2R multiplies a general matrix by the orthogonal matrix from a QR factorization determined -by sgeqrf (unblocked algorithm). */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DORM2R + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DORM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, */ -/* WORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER SIDE, TRANS */ -/* INTEGER INFO, K, LDA, LDC, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DORM2R overwrites the general real m by n matrix C with */ -/* > */ -/* > Q * C if SIDE = 'L' and TRANS = 'N', or */ -/* > */ -/* > Q**T* C if SIDE = 'L' and TRANS = 'T', or */ -/* > */ -/* > C * Q if SIDE = 'R' and TRANS = 'N', or */ -/* > */ -/* > C * Q**T if SIDE = 'R' and TRANS = 'T', */ -/* > */ -/* > where Q is a real orthogonal matrix defined as the product of k */ -/* > elementary reflectors */ -/* > */ -/* > Q = H(1) H(2) . . . H(k) */ -/* > */ -/* > as returned by DGEQRF. Q is of order m if SIDE = 'L' and of order n */ -/* > if SIDE = 'R'. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] SIDE */ -/* > \verbatim */ -/* > SIDE is CHARACTER*1 */ -/* > = 'L': apply Q or Q**T from the Left */ -/* > = 'R': apply Q or Q**T from the Right */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TRANS */ -/* > \verbatim */ -/* > TRANS is CHARACTER*1 */ -/* > = 'N': apply Q (No transpose) */ -/* > = 'T': apply Q**T (Transpose) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix C. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix C. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > The number of elementary reflectors whose product defines */ -/* > the matrix Q. */ -/* > If SIDE = 'L', M >= K >= 0; */ -/* > if SIDE = 'R', N >= K >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,K) */ -/* > The i-th column must contain the vector which defines the */ -/* > elementary reflector H(i), for i = 1,2,...,k, as returned by */ -/* > DGEQRF in the first k columns of its array argument A. */ -/* > A is modified by the routine but restored on exit. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. */ -/* > If SIDE = 'L', LDA >= max(1,M); */ -/* > if SIDE = 'R', LDA >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TAU */ -/* > \verbatim */ -/* > TAU is DOUBLE PRECISION array, dimension (K) */ -/* > TAU(i) must contain the scalar factor of the elementary */ -/* > reflector H(i), as returned by DGEQRF. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] C */ -/* > \verbatim */ -/* > C is DOUBLE PRECISION array, dimension (LDC,N) */ -/* > On entry, the m by n matrix C. */ -/* > On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDC */ -/* > \verbatim */ -/* > LDC is INTEGER */ -/* > The leading dimension of the array C. LDC >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension */ -/* > (N) if SIDE = 'L', */ -/* > (M) if SIDE = 'R' */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleOTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dorm2r_(char *side, char *trans, integer *m, integer *n, - integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal * - c__, integer *ldc, doublereal *work, integer *info, ftnlen side_len, - ftnlen trans_len) +int dorm2r_(char *side, char *trans, integer *m, integer *n, integer *k, doublereal *a, + integer *lda, doublereal *tau, doublereal *c__, integer *ldc, doublereal *work, + integer *info, ftnlen side_len, ftnlen trans_len) { - /* System generated locals */ integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2; - - /* Local variables */ integer i__, i1, i2, i3, ic, jc, mi, ni, nq; doublereal aii; logical left; - extern /* Subroutine */ int dlarf_(char *, integer *, integer *, - doublereal *, integer *, doublereal *, doublereal *, integer *, - doublereal *, ftnlen); + extern int dlarf_(char *, integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, doublereal *, ftnlen); extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern int xerbla_(char *, integer *, ftnlen); logical notran; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; @@ -233,22 +24,17 @@ f"> */ c_offset = 1 + c_dim1; c__ -= c_offset; --work; - - /* Function Body */ *info = 0; left = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); notran = lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1); - -/* NQ is the order of Q */ - if (left) { nq = *m; } else { nq = *n; } - if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + if (!left && !lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { *info = -1; - } else if (! notran && ! lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1)) { + } else if (!notran && !lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1)) { *info = -2; } else if (*m < 0) { *info = -3; @@ -256,9 +42,9 @@ f"> */ *info = -4; } else if (*k < 0 || *k > nq) { *info = -5; - } else if (*lda < max(1,nq)) { + } else if (*lda < max(1, nq)) { *info = -7; - } else if (*ldc < max(1,*m)) { + } else if (*ldc < max(1, *m)) { *info = -10; } if (*info != 0) { @@ -266,14 +52,10 @@ f"> */ xerbla_((char *)"DORM2R", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*m == 0 || *n == 0 || *k == 0) { return 0; } - - if (left && ! notran || ! left && notran) { + if (left && !notran || !left && notran) { i1 = 1; i2 = *k; i3 = 1; @@ -282,7 +64,6 @@ f"> */ i2 = 1; i3 = -1; } - if (left) { ni = *n; jc = 1; @@ -290,39 +71,24 @@ f"> */ mi = *m; ic = 1; } - i__1 = i2; i__2 = i3; for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { if (left) { - -/* H(i) is applied to C(i:m,1:n) */ - mi = *m - i__ + 1; ic = i__; } else { - -/* H(i) is applied to C(1:m,i:n) */ - ni = *n - i__ + 1; jc = i__; } - -/* Apply H(i) */ - aii = a[i__ + i__ * a_dim1]; a[i__ + i__ * a_dim1] = 1.; - dlarf_(side, &mi, &ni, &a[i__ + i__ * a_dim1], &c__1, &tau[i__], &c__[ - ic + jc * c_dim1], ldc, &work[1], (ftnlen)1); + dlarf_(side, &mi, &ni, &a[i__ + i__ * a_dim1], &c__1, &tau[i__], &c__[ic + jc * c_dim1], + ldc, &work[1], (ftnlen)1); a[i__ + i__ * a_dim1] = aii; -/* L10: */ } return 0; - -/* End of DORM2R */ - -} /* dorm2r_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dormbr.cpp b/lib/linalg/dormbr.cpp index 8d6bdd60b0..8be8ab13d8 100644 --- a/lib/linalg/dormbr.cpp +++ b/lib/linalg/dormbr.cpp @@ -1,279 +1,36 @@ -/* fortran/dormbr.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static integer c_n1 = -1; static integer c__2 = 2; - -/* > \brief \b DORMBR */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DORMBR + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, */ -/* LDC, WORK, LWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER SIDE, TRANS, VECT */ -/* INTEGER INFO, K, LDA, LDC, LWORK, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > If VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C */ -/* > with */ -/* > SIDE = 'L' SIDE = 'R' */ -/* > TRANS = 'N': Q * C C * Q */ -/* > TRANS = 'T': Q**T * C C * Q**T */ -/* > */ -/* > If VECT = 'P', DORMBR overwrites the general real M-by-N matrix C */ -/* > with */ -/* > SIDE = 'L' SIDE = 'R' */ -/* > TRANS = 'N': P * C C * P */ -/* > TRANS = 'T': P**T * C C * P**T */ -/* > */ -/* > Here Q and P**T are the orthogonal matrices determined by DGEBRD when */ -/* > reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and */ -/* > P**T are defined as products of elementary reflectors H(i) and G(i) */ -/* > respectively. */ -/* > */ -/* > Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the */ -/* > order of the orthogonal matrix Q or P**T that is applied. */ -/* > */ -/* > If VECT = 'Q', A is assumed to have been an NQ-by-K matrix: */ -/* > if nq >= k, Q = H(1) H(2) . . . H(k); */ -/* > if nq < k, Q = H(1) H(2) . . . H(nq-1). */ -/* > */ -/* > If VECT = 'P', A is assumed to have been a K-by-NQ matrix: */ -/* > if k < nq, P = G(1) G(2) . . . G(k); */ -/* > if k >= nq, P = G(1) G(2) . . . G(nq-1). */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] VECT */ -/* > \verbatim */ -/* > VECT is CHARACTER*1 */ -/* > = 'Q': apply Q or Q**T; */ -/* > = 'P': apply P or P**T. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] SIDE */ -/* > \verbatim */ -/* > SIDE is CHARACTER*1 */ -/* > = 'L': apply Q, Q**T, P or P**T from the Left; */ -/* > = 'R': apply Q, Q**T, P or P**T from the Right. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TRANS */ -/* > \verbatim */ -/* > TRANS is CHARACTER*1 */ -/* > = 'N': No transpose, apply Q or P; */ -/* > = 'T': Transpose, apply Q**T or P**T. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix C. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix C. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > If VECT = 'Q', the number of columns in the original */ -/* > matrix reduced by DGEBRD. */ -/* > If VECT = 'P', the number of rows in the original */ -/* > matrix reduced by DGEBRD. */ -/* > K >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension */ -/* > (LDA,min(nq,K)) if VECT = 'Q' */ -/* > (LDA,nq) if VECT = 'P' */ -/* > The vectors which define the elementary reflectors H(i) and */ -/* > G(i), whose products determine the matrices Q and P, as */ -/* > returned by DGEBRD. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. */ -/* > If VECT = 'Q', LDA >= max(1,nq); */ -/* > if VECT = 'P', LDA >= max(1,min(nq,K)). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TAU */ -/* > \verbatim */ -/* > TAU is DOUBLE PRECISION array, dimension (min(nq,K)) */ -/* > TAU(i) must contain the scalar factor of the elementary */ -/* > reflector H(i) or G(i) which determines Q or P, as returned */ -/* > by DGEBRD in the array argument TAUQ or TAUP. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] C */ -/* > \verbatim */ -/* > C is DOUBLE PRECISION array, dimension (LDC,N) */ -/* > On entry, the M-by-N matrix C. */ -/* > On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q */ -/* > or P*C or P**T*C or C*P or C*P**T. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDC */ -/* > \verbatim */ -/* > LDC is INTEGER */ -/* > The leading dimension of the array C. LDC >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ -/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LWORK */ -/* > \verbatim */ -/* > LWORK is INTEGER */ -/* > The dimension of the array WORK. */ -/* > If SIDE = 'L', LWORK >= max(1,N); */ -/* > if SIDE = 'R', LWORK >= max(1,M). */ -/* > For optimum performance LWORK >= N*NB if SIDE = 'L', and */ -/* > LWORK >= M*NB if SIDE = 'R', where NB is the optimal */ -/* > blocksize. */ -/* > */ -/* > If LWORK = -1, then a workspace query is assumed; the routine */ -/* > only calculates the optimal size of the WORK array, returns */ -/* > this value as the first entry of the WORK array, and no error */ -/* > message related to LWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleOTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dormbr_(char *vect, char *side, char *trans, integer *m, - integer *n, integer *k, doublereal *a, integer *lda, doublereal *tau, - doublereal *c__, integer *ldc, doublereal *work, integer *lwork, - integer *info, ftnlen vect_len, ftnlen side_len, ftnlen trans_len) +int dormbr_(char *vect, char *side, char *trans, integer *m, integer *n, integer *k, doublereal *a, + integer *lda, doublereal *tau, doublereal *c__, integer *ldc, doublereal *work, + integer *lwork, integer *info, ftnlen vect_len, ftnlen side_len, ftnlen trans_len) { - /* System generated locals */ address a__1[2]; integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2]; char ch__1[2]; - - /* Builtin functions */ - /* Subroutine */ int s_lmp_cat(char *, char **, integer *, integer *, ftnlen); - - /* Local variables */ + int s_lmp_cat(char *, char **, integer *, integer *, ftnlen); integer i1, i2, nb, mi, ni, nq, nw; logical left; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer iinfo; - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - extern /* Subroutine */ int dormlq_(char *, char *, integer *, integer *, - integer *, doublereal *, integer *, doublereal *, doublereal *, - integer *, doublereal *, integer *, integer *, ftnlen, ftnlen); + extern int xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); + extern int dormlq_(char *, char *, integer *, integer *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, doublereal *, integer *, integer *, + ftnlen, ftnlen); logical notran; - extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *, - integer *, doublereal *, integer *, doublereal *, doublereal *, - integer *, doublereal *, integer *, integer *, ftnlen, ftnlen); + extern int dormqr_(char *, char *, integer *, integer *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, doublereal *, integer *, integer *, + ftnlen, ftnlen); logical applyq; char transt[1]; integer lwkopt; logical lquery; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; @@ -282,28 +39,23 @@ f"> */ c_offset = 1 + c_dim1; c__ -= c_offset; --work; - - /* Function Body */ *info = 0; applyq = lsame_(vect, (char *)"Q", (ftnlen)1, (ftnlen)1); left = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); notran = lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1); lquery = *lwork == -1; - -/* NQ is the order of Q or P and NW is the minimum dimension of WORK */ - if (left) { nq = *m; - nw = max(1,*n); + nw = max(1, *n); } else { nq = *n; - nw = max(1,*m); + nw = max(1, *m); } - if (! applyq && ! lsame_(vect, (char *)"P", (ftnlen)1, (ftnlen)1)) { + if (!applyq && !lsame_(vect, (char *)"P", (ftnlen)1, (ftnlen)1)) { *info = -1; - } else if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + } else if (!left && !lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { *info = -2; - } else if (! notran && ! lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1)) { + } else if (!notran && !lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1)) { *info = -3; } else if (*m < 0) { *info = -4; @@ -311,64 +63,53 @@ f"> */ *info = -5; } else if (*k < 0) { *info = -6; - } else /* if(complicated condition) */ { -/* Computing MAX */ - i__1 = 1, i__2 = min(nq,*k); - if (applyq && *lda < max(1,nq) || ! applyq && *lda < max(i__1,i__2)) { + } else { + i__1 = 1, i__2 = min(nq, *k); + if (applyq && *lda < max(1, nq) || !applyq && *lda < max(i__1, i__2)) { *info = -8; - } else if (*ldc < max(1,*m)) { + } else if (*ldc < max(1, *m)) { *info = -11; - } else if (*lwork < nw && ! lquery) { + } else if (*lwork < nw && !lquery) { *info = -13; } } - if (*info == 0) { if (applyq) { if (left) { -/* Writing concatenation */ i__3[0] = 1, a__1[0] = side; i__3[1] = 1, a__1[1] = trans; s_lmp_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); i__1 = *m - 1; i__2 = *m - 1; - nb = ilaenv_(&c__1, (char *)"DORMQR", ch__1, &i__1, n, &i__2, &c_n1, ( - ftnlen)6, (ftnlen)2); + nb = ilaenv_(&c__1, (char *)"DORMQR", ch__1, &i__1, n, &i__2, &c_n1, (ftnlen)6, (ftnlen)2); } else { -/* Writing concatenation */ i__3[0] = 1, a__1[0] = side; i__3[1] = 1, a__1[1] = trans; s_lmp_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); i__1 = *n - 1; i__2 = *n - 1; - nb = ilaenv_(&c__1, (char *)"DORMQR", ch__1, m, &i__1, &i__2, &c_n1, ( - ftnlen)6, (ftnlen)2); + nb = ilaenv_(&c__1, (char *)"DORMQR", ch__1, m, &i__1, &i__2, &c_n1, (ftnlen)6, (ftnlen)2); } } else { if (left) { -/* Writing concatenation */ i__3[0] = 1, a__1[0] = side; i__3[1] = 1, a__1[1] = trans; s_lmp_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); i__1 = *m - 1; i__2 = *m - 1; - nb = ilaenv_(&c__1, (char *)"DORMLQ", ch__1, &i__1, n, &i__2, &c_n1, ( - ftnlen)6, (ftnlen)2); + nb = ilaenv_(&c__1, (char *)"DORMLQ", ch__1, &i__1, n, &i__2, &c_n1, (ftnlen)6, (ftnlen)2); } else { -/* Writing concatenation */ i__3[0] = 1, a__1[0] = side; i__3[1] = 1, a__1[1] = trans; s_lmp_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); i__1 = *n - 1; i__2 = *n - 1; - nb = ilaenv_(&c__1, (char *)"DORMLQ", ch__1, m, &i__1, &i__2, &c_n1, ( - ftnlen)6, (ftnlen)2); + nb = ilaenv_(&c__1, (char *)"DORMLQ", ch__1, m, &i__1, &i__2, &c_n1, (ftnlen)6, (ftnlen)2); } } lwkopt = nw * nb; - work[1] = (doublereal) lwkopt; + work[1] = (doublereal)lwkopt; } - if (*info != 0) { i__1 = -(*info); xerbla_((char *)"DORMBR", &i__1, (ftnlen)6); @@ -376,29 +117,15 @@ f"> */ } else if (lquery) { return 0; } - -/* Quick return if possible */ - work[1] = 1.; if (*m == 0 || *n == 0) { return 0; } - if (applyq) { - -/* Apply Q */ - if (nq >= *k) { - -/* Q was determined by a call to DGEBRD with nq >= k */ - - dormqr_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[ - c_offset], ldc, &work[1], lwork, &iinfo, (ftnlen)1, ( - ftnlen)1); + dormqr_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[c_offset], ldc, &work[1], + lwork, &iinfo, (ftnlen)1, (ftnlen)1); } else if (nq > 1) { - -/* Q was determined by a call to DGEBRD with nq < k */ - if (left) { mi = *m - 1; ni = *n; @@ -411,30 +138,19 @@ f"> */ i2 = 2; } i__1 = nq - 1; - dormqr_(side, trans, &mi, &ni, &i__1, &a[a_dim1 + 2], lda, &tau[1] - , &c__[i1 + i2 * c_dim1], ldc, &work[1], lwork, &iinfo, ( - ftnlen)1, (ftnlen)1); + dormqr_(side, trans, &mi, &ni, &i__1, &a[a_dim1 + 2], lda, &tau[1], + &c__[i1 + i2 * c_dim1], ldc, &work[1], lwork, &iinfo, (ftnlen)1, (ftnlen)1); } } else { - -/* Apply P */ - if (notran) { *(unsigned char *)transt = 'T'; } else { *(unsigned char *)transt = 'N'; } if (nq > *k) { - -/* P was determined by a call to DGEBRD with nq > k */ - - dormlq_(side, transt, m, n, k, &a[a_offset], lda, &tau[1], &c__[ - c_offset], ldc, &work[1], lwork, &iinfo, (ftnlen)1, ( - ftnlen)1); + dormlq_(side, transt, m, n, k, &a[a_offset], lda, &tau[1], &c__[c_offset], ldc, + &work[1], lwork, &iinfo, (ftnlen)1, (ftnlen)1); } else if (nq > 1) { - -/* P was determined by a call to DGEBRD with nq <= k */ - if (left) { mi = *m - 1; ni = *n; @@ -447,18 +163,13 @@ f"> */ i2 = 2; } i__1 = nq - 1; - dormlq_(side, transt, &mi, &ni, &i__1, &a[(a_dim1 << 1) + 1], lda, - &tau[1], &c__[i1 + i2 * c_dim1], ldc, &work[1], lwork, & - iinfo, (ftnlen)1, (ftnlen)1); + dormlq_(side, transt, &mi, &ni, &i__1, &a[(a_dim1 << 1) + 1], lda, &tau[1], + &c__[i1 + i2 * c_dim1], ldc, &work[1], lwork, &iinfo, (ftnlen)1, (ftnlen)1); } } - work[1] = (doublereal) lwkopt; + work[1] = (doublereal)lwkopt; return 0; - -/* End of DORMBR */ - -} /* dormbr_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dorml2.cpp b/lib/linalg/dorml2.cpp index 7fe1aac941..109315fb14 100644 --- a/lib/linalg/dorml2.cpp +++ b/lib/linalg/dorml2.cpp @@ -1,226 +1,20 @@ -/* fortran/dorml2.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DORML2 multiplies a general matrix by the orthogonal matrix from a LQ factorization determined -by sgelqf (unblocked algorithm). */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DORML2 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DORML2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, */ -/* WORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER SIDE, TRANS */ -/* INTEGER INFO, K, LDA, LDC, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DORML2 overwrites the general real m by n matrix C with */ -/* > */ -/* > Q * C if SIDE = 'L' and TRANS = 'N', or */ -/* > */ -/* > Q**T* C if SIDE = 'L' and TRANS = 'T', or */ -/* > */ -/* > C * Q if SIDE = 'R' and TRANS = 'N', or */ -/* > */ -/* > C * Q**T if SIDE = 'R' and TRANS = 'T', */ -/* > */ -/* > where Q is a real orthogonal matrix defined as the product of k */ -/* > elementary reflectors */ -/* > */ -/* > Q = H(k) . . . H(2) H(1) */ -/* > */ -/* > as returned by DGELQF. Q is of order m if SIDE = 'L' and of order n */ -/* > if SIDE = 'R'. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] SIDE */ -/* > \verbatim */ -/* > SIDE is CHARACTER*1 */ -/* > = 'L': apply Q or Q**T from the Left */ -/* > = 'R': apply Q or Q**T from the Right */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TRANS */ -/* > \verbatim */ -/* > TRANS is CHARACTER*1 */ -/* > = 'N': apply Q (No transpose) */ -/* > = 'T': apply Q**T (Transpose) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix C. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix C. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > The number of elementary reflectors whose product defines */ -/* > the matrix Q. */ -/* > If SIDE = 'L', M >= K >= 0; */ -/* > if SIDE = 'R', N >= K >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension */ -/* > (LDA,M) if SIDE = 'L', */ -/* > (LDA,N) if SIDE = 'R' */ -/* > The i-th row must contain the vector which defines the */ -/* > elementary reflector H(i), for i = 1,2,...,k, as returned by */ -/* > DGELQF in the first k rows of its array argument A. */ -/* > A is modified by the routine but restored on exit. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,K). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TAU */ -/* > \verbatim */ -/* > TAU is DOUBLE PRECISION array, dimension (K) */ -/* > TAU(i) must contain the scalar factor of the elementary */ -/* > reflector H(i), as returned by DGELQF. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] C */ -/* > \verbatim */ -/* > C is DOUBLE PRECISION array, dimension (LDC,N) */ -/* > On entry, the m by n matrix C. */ -/* > On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDC */ -/* > \verbatim */ -/* > LDC is INTEGER */ -/* > The leading dimension of the array C. LDC >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension */ -/* > (N) if SIDE = 'L', */ -/* > (M) if SIDE = 'R' */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleOTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dorml2_(char *side, char *trans, integer *m, integer *n, - integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal * - c__, integer *ldc, doublereal *work, integer *info, ftnlen side_len, - ftnlen trans_len) +int dorml2_(char *side, char *trans, integer *m, integer *n, integer *k, doublereal *a, + integer *lda, doublereal *tau, doublereal *c__, integer *ldc, doublereal *work, + integer *info, ftnlen side_len, ftnlen trans_len) { - /* System generated locals */ integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2; - - /* Local variables */ integer i__, i1, i2, i3, ic, jc, mi, ni, nq; doublereal aii; logical left; - extern /* Subroutine */ int dlarf_(char *, integer *, integer *, - doublereal *, integer *, doublereal *, doublereal *, integer *, - doublereal *, ftnlen); + extern int dlarf_(char *, integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, doublereal *, ftnlen); extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern int xerbla_(char *, integer *, ftnlen); logical notran; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; @@ -229,22 +23,17 @@ f"> */ c_offset = 1 + c_dim1; c__ -= c_offset; --work; - - /* Function Body */ *info = 0; left = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); notran = lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1); - -/* NQ is the order of Q */ - if (left) { nq = *m; } else { nq = *n; } - if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + if (!left && !lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { *info = -1; - } else if (! notran && ! lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1)) { + } else if (!notran && !lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1)) { *info = -2; } else if (*m < 0) { *info = -3; @@ -252,9 +41,9 @@ f"> */ *info = -4; } else if (*k < 0 || *k > nq) { *info = -5; - } else if (*lda < max(1,*k)) { + } else if (*lda < max(1, *k)) { *info = -7; - } else if (*ldc < max(1,*m)) { + } else if (*ldc < max(1, *m)) { *info = -10; } if (*info != 0) { @@ -262,14 +51,10 @@ f"> */ xerbla_((char *)"DORML2", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*m == 0 || *n == 0 || *k == 0) { return 0; } - - if (left && notran || ! left && ! notran) { + if (left && notran || !left && !notran) { i1 = 1; i2 = *k; i3 = 1; @@ -278,7 +63,6 @@ f"> */ i2 = 1; i3 = -1; } - if (left) { ni = *n; jc = 1; @@ -286,39 +70,24 @@ f"> */ mi = *m; ic = 1; } - i__1 = i2; i__2 = i3; for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { if (left) { - -/* H(i) is applied to C(i:m,1:n) */ - mi = *m - i__ + 1; ic = i__; } else { - -/* H(i) is applied to C(1:m,i:n) */ - ni = *n - i__ + 1; jc = i__; } - -/* Apply H(i) */ - aii = a[i__ + i__ * a_dim1]; a[i__ + i__ * a_dim1] = 1.; - dlarf_(side, &mi, &ni, &a[i__ + i__ * a_dim1], lda, &tau[i__], &c__[ - ic + jc * c_dim1], ldc, &work[1], (ftnlen)1); + dlarf_(side, &mi, &ni, &a[i__ + i__ * a_dim1], lda, &tau[i__], &c__[ic + jc * c_dim1], ldc, + &work[1], (ftnlen)1); a[i__ + i__ * a_dim1] = aii; -/* L10: */ } return 0; - -/* End of DORML2 */ - -} /* dorml2_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dormlq.cpp b/lib/linalg/dormlq.cpp index 79106afb5c..d8bedae2f9 100644 --- a/lib/linalg/dormlq.cpp +++ b/lib/linalg/dormlq.cpp @@ -1,257 +1,39 @@ -/* fortran/dormlq.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static integer c_n1 = -1; static integer c__2 = 2; static integer c__65 = 65; - -/* > \brief \b DORMLQ */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DORMLQ + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DORMLQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, */ -/* WORK, LWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER SIDE, TRANS */ -/* INTEGER INFO, K, LDA, LDC, LWORK, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DORMLQ overwrites the general real M-by-N matrix C with */ -/* > */ -/* > SIDE = 'L' SIDE = 'R' */ -/* > TRANS = 'N': Q * C C * Q */ -/* > TRANS = 'T': Q**T * C C * Q**T */ -/* > */ -/* > where Q is a real orthogonal matrix defined as the product of k */ -/* > elementary reflectors */ -/* > */ -/* > Q = H(k) . . . H(2) H(1) */ -/* > */ -/* > as returned by DGELQF. Q is of order M if SIDE = 'L' and of order N */ -/* > if SIDE = 'R'. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] SIDE */ -/* > \verbatim */ -/* > SIDE is CHARACTER*1 */ -/* > = 'L': apply Q or Q**T from the Left; */ -/* > = 'R': apply Q or Q**T from the Right. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TRANS */ -/* > \verbatim */ -/* > TRANS is CHARACTER*1 */ -/* > = 'N': No transpose, apply Q; */ -/* > = 'T': Transpose, apply Q**T. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix C. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix C. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > The number of elementary reflectors whose product defines */ -/* > the matrix Q. */ -/* > If SIDE = 'L', M >= K >= 0; */ -/* > if SIDE = 'R', N >= K >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension */ -/* > (LDA,M) if SIDE = 'L', */ -/* > (LDA,N) if SIDE = 'R' */ -/* > The i-th row must contain the vector which defines the */ -/* > elementary reflector H(i), for i = 1,2,...,k, as returned by */ -/* > DGELQF in the first k rows of its array argument A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,K). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TAU */ -/* > \verbatim */ -/* > TAU is DOUBLE PRECISION array, dimension (K) */ -/* > TAU(i) must contain the scalar factor of the elementary */ -/* > reflector H(i), as returned by DGELQF. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] C */ -/* > \verbatim */ -/* > C is DOUBLE PRECISION array, dimension (LDC,N) */ -/* > On entry, the M-by-N matrix C. */ -/* > On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDC */ -/* > \verbatim */ -/* > LDC is INTEGER */ -/* > The leading dimension of the array C. LDC >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ -/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LWORK */ -/* > \verbatim */ -/* > LWORK is INTEGER */ -/* > The dimension of the array WORK. */ -/* > If SIDE = 'L', LWORK >= max(1,N); */ -/* > if SIDE = 'R', LWORK >= max(1,M). */ -/* > For good performance, LWORK should generally be larger. */ -/* > */ -/* > If LWORK = -1, then a workspace query is assumed; the routine */ -/* > only calculates the optimal size of the WORK array, returns */ -/* > this value as the first entry of the WORK array, and no error */ -/* > message related to LWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleOTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dormlq_(char *side, char *trans, integer *m, integer *n, - integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal * - c__, integer *ldc, doublereal *work, integer *lwork, integer *info, - ftnlen side_len, ftnlen trans_len) +int dormlq_(char *side, char *trans, integer *m, integer *n, integer *k, doublereal *a, + integer *lda, doublereal *tau, doublereal *c__, integer *ldc, doublereal *work, + integer *lwork, integer *info, ftnlen side_len, ftnlen trans_len) { - /* System generated locals */ address a__1[2]; - integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4, - i__5; + integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4, i__5; char ch__1[2]; - - /* Builtin functions */ - /* Subroutine */ int s_lmp_cat(char *, char **, integer *, integer *, ftnlen); - - /* Local variables */ + int s_lmp_cat(char *, char **, integer *, integer *, ftnlen); integer i__, i1, i2, i3, ib, ic, jc, nb, mi, ni, nq, nw, iwt; logical left; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer nbmin, iinfo; - extern /* Subroutine */ int dorml2_(char *, char *, integer *, integer *, - integer *, doublereal *, integer *, doublereal *, doublereal *, - integer *, doublereal *, integer *, ftnlen, ftnlen), dlarfb_(char - *, char *, char *, char *, integer *, integer *, integer *, - doublereal *, integer *, doublereal *, integer *, doublereal *, - integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, - ftnlen), dlarft_(char *, char *, integer *, integer *, doublereal - *, integer *, doublereal *, doublereal *, integer *, ftnlen, - ftnlen), xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern int dorml2_(char *, char *, integer *, integer *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, doublereal *, integer *, ftnlen, + ftnlen), + dlarfb_(char *, char *, char *, char *, integer *, integer *, integer *, doublereal *, + integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, + integer *, ftnlen, ftnlen, ftnlen, ftnlen), + dlarft_(char *, char *, integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, ftnlen, ftnlen), + xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); logical notran; integer ldwork; char transt[1]; integer lwkopt; logical lquery; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; @@ -260,25 +42,20 @@ f"> */ c_offset = 1 + c_dim1; c__ -= c_offset; --work; - - /* Function Body */ *info = 0; left = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); notran = lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1); lquery = *lwork == -1; - -/* NQ is the order of Q and NW is the minimum dimension of WORK */ - if (left) { nq = *m; - nw = max(1,*n); + nw = max(1, *n); } else { nq = *n; - nw = max(1,*m); + nw = max(1, *m); } - if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + if (!left && !lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { *info = -1; - } else if (! notran && ! lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1)) { + } else if (!notran && !lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1)) { *info = -2; } else if (*m < 0) { *info = -3; @@ -286,30 +63,22 @@ f"> */ *info = -4; } else if (*k < 0 || *k > nq) { *info = -5; - } else if (*lda < max(1,*k)) { + } else if (*lda < max(1, *k)) { *info = -7; - } else if (*ldc < max(1,*m)) { + } else if (*ldc < max(1, *m)) { *info = -10; - } else if (*lwork < nw && ! lquery) { + } else if (*lwork < nw && !lquery) { *info = -12; } - if (*info == 0) { - -/* Compute the workspace requirements */ - -/* Computing MIN */ -/* Writing concatenation */ i__3[0] = 1, a__1[0] = side; i__3[1] = 1, a__1[1] = trans; s_lmp_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); - i__1 = 64, i__2 = ilaenv_(&c__1, (char *)"DORMLQ", ch__1, m, n, k, &c_n1, ( - ftnlen)6, (ftnlen)2); - nb = min(i__1,i__2); + i__1 = 64, i__2 = ilaenv_(&c__1, (char *)"DORMLQ", ch__1, m, n, k, &c_n1, (ftnlen)6, (ftnlen)2); + nb = min(i__1, i__2); lwkopt = nw * nb + 4160; - work[1] = (doublereal) lwkopt; + work[1] = (doublereal)lwkopt; } - if (*info != 0) { i__1 = -(*info); xerbla_((char *)"DORMLQ", &i__1, (ftnlen)6); @@ -317,42 +86,28 @@ f"> */ } else if (lquery) { return 0; } - -/* Quick return if possible */ - if (*m == 0 || *n == 0 || *k == 0) { work[1] = 1.; return 0; } - nbmin = 2; ldwork = nw; if (nb > 1 && nb < *k) { if (*lwork < lwkopt) { nb = (*lwork - 4160) / ldwork; -/* Computing MAX */ -/* Writing concatenation */ i__3[0] = 1, a__1[0] = side; i__3[1] = 1, a__1[1] = trans; s_lmp_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); - i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DORMLQ", ch__1, m, n, k, &c_n1, ( - ftnlen)6, (ftnlen)2); - nbmin = max(i__1,i__2); + i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DORMLQ", ch__1, m, n, k, &c_n1, (ftnlen)6, (ftnlen)2); + nbmin = max(i__1, i__2); } } - if (nb < nbmin || nb >= *k) { - -/* Use unblocked code */ - - dorml2_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[ - c_offset], ldc, &work[1], &iinfo, (ftnlen)1, (ftnlen)1); + dorml2_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[c_offset], ldc, &work[1], + &iinfo, (ftnlen)1, (ftnlen)1); } else { - -/* Use blocked code */ - iwt = nw * nb + 1; - if (left && notran || ! left && ! notran) { + if (left && notran || !left && !notran) { i1 = 1; i2 = *k; i3 = nb; @@ -361,7 +116,6 @@ f"> */ i2 = 1; i3 = -nb; } - if (left) { ni = *n; jc = 1; @@ -369,56 +123,34 @@ f"> */ mi = *m; ic = 1; } - if (notran) { *(unsigned char *)transt = 'T'; } else { *(unsigned char *)transt = 'N'; } - i__1 = i2; i__2 = i3; for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { -/* Computing MIN */ i__4 = nb, i__5 = *k - i__ + 1; - ib = min(i__4,i__5); - -/* Form the triangular factor of the block reflector */ -/* H = H(i) H(i+1) . . . H(i+ib-1) */ - + ib = min(i__4, i__5); i__4 = nq - i__ + 1; - dlarft_((char *)"Forward", (char *)"Rowwise", &i__4, &ib, &a[i__ + i__ * a_dim1], - lda, &tau[i__], &work[iwt], &c__65, (ftnlen)7, (ftnlen)7); + dlarft_((char *)"Forward", (char *)"Rowwise", &i__4, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], + &work[iwt], &c__65, (ftnlen)7, (ftnlen)7); if (left) { - -/* H or H**T is applied to C(i:m,1:n) */ - mi = *m - i__ + 1; ic = i__; } else { - -/* H or H**T is applied to C(1:m,i:n) */ - ni = *n - i__ + 1; jc = i__; } - -/* Apply H or H**T */ - - dlarfb_(side, transt, (char *)"Forward", (char *)"Rowwise", &mi, &ni, &ib, &a[i__ - + i__ * a_dim1], lda, &work[iwt], &c__65, &c__[ic + jc * - c_dim1], ldc, &work[1], &ldwork, (ftnlen)1, (ftnlen)1, ( - ftnlen)7, (ftnlen)7); -/* L10: */ + dlarfb_(side, transt, (char *)"Forward", (char *)"Rowwise", &mi, &ni, &ib, &a[i__ + i__ * a_dim1], lda, + &work[iwt], &c__65, &c__[ic + jc * c_dim1], ldc, &work[1], &ldwork, (ftnlen)1, + (ftnlen)1, (ftnlen)7, (ftnlen)7); } } - work[1] = (doublereal) lwkopt; + work[1] = (doublereal)lwkopt; return 0; - -/* End of DORMLQ */ - -} /* dormlq_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dormql.cpp b/lib/linalg/dormql.cpp index eea324bc69..45c0801c56 100644 --- a/lib/linalg/dormql.cpp +++ b/lib/linalg/dormql.cpp @@ -1,255 +1,37 @@ -/* fortran/dormql.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static integer c_n1 = -1; static integer c__2 = 2; static integer c__65 = 65; - -/* > \brief \b DORMQL */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DORMQL + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DORMQL( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, */ -/* WORK, LWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER SIDE, TRANS */ -/* INTEGER INFO, K, LDA, LDC, LWORK, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DORMQL overwrites the general real M-by-N matrix C with */ -/* > */ -/* > SIDE = 'L' SIDE = 'R' */ -/* > TRANS = 'N': Q * C C * Q */ -/* > TRANS = 'T': Q**T * C C * Q**T */ -/* > */ -/* > where Q is a real orthogonal matrix defined as the product of k */ -/* > elementary reflectors */ -/* > */ -/* > Q = H(k) . . . H(2) H(1) */ -/* > */ -/* > as returned by DGEQLF. Q is of order M if SIDE = 'L' and of order N */ -/* > if SIDE = 'R'. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] SIDE */ -/* > \verbatim */ -/* > SIDE is CHARACTER*1 */ -/* > = 'L': apply Q or Q**T from the Left; */ -/* > = 'R': apply Q or Q**T from the Right. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TRANS */ -/* > \verbatim */ -/* > TRANS is CHARACTER*1 */ -/* > = 'N': No transpose, apply Q; */ -/* > = 'T': Transpose, apply Q**T. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix C. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix C. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > The number of elementary reflectors whose product defines */ -/* > the matrix Q. */ -/* > If SIDE = 'L', M >= K >= 0; */ -/* > if SIDE = 'R', N >= K >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,K) */ -/* > The i-th column must contain the vector which defines the */ -/* > elementary reflector H(i), for i = 1,2,...,k, as returned by */ -/* > DGEQLF in the last k columns of its array argument A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. */ -/* > If SIDE = 'L', LDA >= max(1,M); */ -/* > if SIDE = 'R', LDA >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TAU */ -/* > \verbatim */ -/* > TAU is DOUBLE PRECISION array, dimension (K) */ -/* > TAU(i) must contain the scalar factor of the elementary */ -/* > reflector H(i), as returned by DGEQLF. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] C */ -/* > \verbatim */ -/* > C is DOUBLE PRECISION array, dimension (LDC,N) */ -/* > On entry, the M-by-N matrix C. */ -/* > On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDC */ -/* > \verbatim */ -/* > LDC is INTEGER */ -/* > The leading dimension of the array C. LDC >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ -/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LWORK */ -/* > \verbatim */ -/* > LWORK is INTEGER */ -/* > The dimension of the array WORK. */ -/* > If SIDE = 'L', LWORK >= max(1,N); */ -/* > if SIDE = 'R', LWORK >= max(1,M). */ -/* > For good performance, LWORK should generally be larger. */ -/* > */ -/* > If LWORK = -1, then a workspace query is assumed; the routine */ -/* > only calculates the optimal size of the WORK array, returns */ -/* > this value as the first entry of the WORK array, and no error */ -/* > message related to LWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleOTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dormql_(char *side, char *trans, integer *m, integer *n, - integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal * - c__, integer *ldc, doublereal *work, integer *lwork, integer *info, - ftnlen side_len, ftnlen trans_len) +int dormql_(char *side, char *trans, integer *m, integer *n, integer *k, doublereal *a, + integer *lda, doublereal *tau, doublereal *c__, integer *ldc, doublereal *work, + integer *lwork, integer *info, ftnlen side_len, ftnlen trans_len) { - /* System generated locals */ address a__1[2]; - integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4, - i__5; + integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4, i__5; char ch__1[2]; - - /* Builtin functions */ - /* Subroutine */ int s_lmp_cat(char *, char **, integer *, integer *, ftnlen); - - /* Local variables */ + int s_lmp_cat(char *, char **, integer *, integer *, ftnlen); integer i__, i1, i2, i3, ib, nb, mi, ni, nq, nw, iwt; logical left; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer nbmin, iinfo; - extern /* Subroutine */ int dorm2l_(char *, char *, integer *, integer *, - integer *, doublereal *, integer *, doublereal *, doublereal *, - integer *, doublereal *, integer *, ftnlen, ftnlen), dlarfb_(char - *, char *, char *, char *, integer *, integer *, integer *, - doublereal *, integer *, doublereal *, integer *, doublereal *, - integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, - ftnlen), dlarft_(char *, char *, integer *, integer *, doublereal - *, integer *, doublereal *, doublereal *, integer *, ftnlen, - ftnlen), xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern int dorm2l_(char *, char *, integer *, integer *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, doublereal *, integer *, ftnlen, + ftnlen), + dlarfb_(char *, char *, char *, char *, integer *, integer *, integer *, doublereal *, + integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, + integer *, ftnlen, ftnlen, ftnlen, ftnlen), + dlarft_(char *, char *, integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, ftnlen, ftnlen), + xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); logical notran; integer ldwork, lwkopt; logical lquery; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; @@ -258,25 +40,20 @@ f"> */ c_offset = 1 + c_dim1; c__ -= c_offset; --work; - - /* Function Body */ *info = 0; left = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); notran = lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1); lquery = *lwork == -1; - -/* NQ is the order of Q and NW is the minimum dimension of WORK */ - if (left) { nq = *m; - nw = max(1,*n); + nw = max(1, *n); } else { nq = *n; - nw = max(1,*m); + nw = max(1, *m); } - if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + if (!left && !lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { *info = -1; - } else if (! notran && ! lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1)) { + } else if (!notran && !lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1)) { *info = -2; } else if (*m < 0) { *info = -3; @@ -284,34 +61,26 @@ f"> */ *info = -4; } else if (*k < 0 || *k > nq) { *info = -5; - } else if (*lda < max(1,nq)) { + } else if (*lda < max(1, nq)) { *info = -7; - } else if (*ldc < max(1,*m)) { + } else if (*ldc < max(1, *m)) { *info = -10; - } else if (*lwork < nw && ! lquery) { + } else if (*lwork < nw && !lquery) { *info = -12; } - if (*info == 0) { - -/* Compute the workspace requirements */ - if (*m == 0 || *n == 0) { lwkopt = 1; } else { -/* Computing MIN */ -/* Writing concatenation */ i__3[0] = 1, a__1[0] = side; i__3[1] = 1, a__1[1] = trans; s_lmp_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); - i__1 = 64, i__2 = ilaenv_(&c__1, (char *)"DORMQL", ch__1, m, n, k, &c_n1, - (ftnlen)6, (ftnlen)2); - nb = min(i__1,i__2); + i__1 = 64, i__2 = ilaenv_(&c__1, (char *)"DORMQL", ch__1, m, n, k, &c_n1, (ftnlen)6, (ftnlen)2); + nb = min(i__1, i__2); lwkopt = nw * nb + 4160; } - work[1] = (doublereal) lwkopt; + work[1] = (doublereal)lwkopt; } - if (*info != 0) { i__1 = -(*info); xerbla_((char *)"DORMQL", &i__1, (ftnlen)6); @@ -319,41 +88,27 @@ f"> */ } else if (lquery) { return 0; } - -/* Quick return if possible */ - if (*m == 0 || *n == 0) { return 0; } - nbmin = 2; ldwork = nw; if (nb > 1 && nb < *k) { if (*lwork < lwkopt) { nb = (*lwork - 4160) / ldwork; -/* Computing MAX */ -/* Writing concatenation */ i__3[0] = 1, a__1[0] = side; i__3[1] = 1, a__1[1] = trans; s_lmp_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); - i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DORMQL", ch__1, m, n, k, &c_n1, ( - ftnlen)6, (ftnlen)2); - nbmin = max(i__1,i__2); + i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DORMQL", ch__1, m, n, k, &c_n1, (ftnlen)6, (ftnlen)2); + nbmin = max(i__1, i__2); } } - if (nb < nbmin || nb >= *k) { - -/* Use unblocked code */ - - dorm2l_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[ - c_offset], ldc, &work[1], &iinfo, (ftnlen)1, (ftnlen)1); + dorm2l_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[c_offset], ldc, &work[1], + &iinfo, (ftnlen)1, (ftnlen)1); } else { - -/* Use blocked code */ - iwt = nw * nb + 1; - if (left && notran || ! left && ! notran) { + if (left && notran || !left && !notran) { i1 = 1; i2 = *k; i3 = nb; @@ -362,55 +117,32 @@ f"> */ i2 = 1; i3 = -nb; } - if (left) { ni = *n; } else { mi = *m; } - i__1 = i2; i__2 = i3; for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { -/* Computing MIN */ i__4 = nb, i__5 = *k - i__ + 1; - ib = min(i__4,i__5); - -/* Form the triangular factor of the block reflector */ -/* H = H(i+ib-1) . . . H(i+1) H(i) */ - + ib = min(i__4, i__5); i__4 = nq - *k + i__ + ib - 1; - dlarft_((char *)"Backward", (char *)"Columnwise", &i__4, &ib, &a[i__ * a_dim1 + 1] - , lda, &tau[i__], &work[iwt], &c__65, (ftnlen)8, (ftnlen) - 10); + dlarft_((char *)"Backward", (char *)"Columnwise", &i__4, &ib, &a[i__ * a_dim1 + 1], lda, &tau[i__], + &work[iwt], &c__65, (ftnlen)8, (ftnlen)10); if (left) { - -/* H or H**T is applied to C(1:m-k+i+ib-1,1:n) */ - mi = *m - *k + i__ + ib - 1; } else { - -/* H or H**T is applied to C(1:m,1:n-k+i+ib-1) */ - ni = *n - *k + i__ + ib - 1; } - -/* Apply H or H**T */ - - dlarfb_(side, trans, (char *)"Backward", (char *)"Columnwise", &mi, &ni, &ib, &a[ - i__ * a_dim1 + 1], lda, &work[iwt], &c__65, &c__[c_offset] - , ldc, &work[1], &ldwork, (ftnlen)1, (ftnlen)1, (ftnlen)8, - (ftnlen)10); -/* L10: */ + dlarfb_(side, trans, (char *)"Backward", (char *)"Columnwise", &mi, &ni, &ib, &a[i__ * a_dim1 + 1], lda, + &work[iwt], &c__65, &c__[c_offset], ldc, &work[1], &ldwork, (ftnlen)1, + (ftnlen)1, (ftnlen)8, (ftnlen)10); } } - work[1] = (doublereal) lwkopt; + work[1] = (doublereal)lwkopt; return 0; - -/* End of DORMQL */ - -} /* dormql_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dormqr.cpp b/lib/linalg/dormqr.cpp index eb43ba8045..25d0c11f60 100644 --- a/lib/linalg/dormqr.cpp +++ b/lib/linalg/dormqr.cpp @@ -1,255 +1,37 @@ -/* fortran/dormqr.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static integer c_n1 = -1; static integer c__2 = 2; static integer c__65 = 65; - -/* > \brief \b DORMQR */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DORMQR + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DORMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, */ -/* WORK, LWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER SIDE, TRANS */ -/* INTEGER INFO, K, LDA, LDC, LWORK, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DORMQR overwrites the general real M-by-N matrix C with */ -/* > */ -/* > SIDE = 'L' SIDE = 'R' */ -/* > TRANS = 'N': Q * C C * Q */ -/* > TRANS = 'T': Q**T * C C * Q**T */ -/* > */ -/* > where Q is a real orthogonal matrix defined as the product of k */ -/* > elementary reflectors */ -/* > */ -/* > Q = H(1) H(2) . . . H(k) */ -/* > */ -/* > as returned by DGEQRF. Q is of order M if SIDE = 'L' and of order N */ -/* > if SIDE = 'R'. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] SIDE */ -/* > \verbatim */ -/* > SIDE is CHARACTER*1 */ -/* > = 'L': apply Q or Q**T from the Left; */ -/* > = 'R': apply Q or Q**T from the Right. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TRANS */ -/* > \verbatim */ -/* > TRANS is CHARACTER*1 */ -/* > = 'N': No transpose, apply Q; */ -/* > = 'T': Transpose, apply Q**T. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix C. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix C. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > The number of elementary reflectors whose product defines */ -/* > the matrix Q. */ -/* > If SIDE = 'L', M >= K >= 0; */ -/* > if SIDE = 'R', N >= K >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,K) */ -/* > The i-th column must contain the vector which defines the */ -/* > elementary reflector H(i), for i = 1,2,...,k, as returned by */ -/* > DGEQRF in the first k columns of its array argument A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. */ -/* > If SIDE = 'L', LDA >= max(1,M); */ -/* > if SIDE = 'R', LDA >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TAU */ -/* > \verbatim */ -/* > TAU is DOUBLE PRECISION array, dimension (K) */ -/* > TAU(i) must contain the scalar factor of the elementary */ -/* > reflector H(i), as returned by DGEQRF. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] C */ -/* > \verbatim */ -/* > C is DOUBLE PRECISION array, dimension (LDC,N) */ -/* > On entry, the M-by-N matrix C. */ -/* > On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDC */ -/* > \verbatim */ -/* > LDC is INTEGER */ -/* > The leading dimension of the array C. LDC >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ -/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LWORK */ -/* > \verbatim */ -/* > LWORK is INTEGER */ -/* > The dimension of the array WORK. */ -/* > If SIDE = 'L', LWORK >= max(1,N); */ -/* > if SIDE = 'R', LWORK >= max(1,M). */ -/* > For good performance, LWORK should generally be larger. */ -/* > */ -/* > If LWORK = -1, then a workspace query is assumed; the routine */ -/* > only calculates the optimal size of the WORK array, returns */ -/* > this value as the first entry of the WORK array, and no error */ -/* > message related to LWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleOTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dormqr_(char *side, char *trans, integer *m, integer *n, - integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal * - c__, integer *ldc, doublereal *work, integer *lwork, integer *info, - ftnlen side_len, ftnlen trans_len) +int dormqr_(char *side, char *trans, integer *m, integer *n, integer *k, doublereal *a, + integer *lda, doublereal *tau, doublereal *c__, integer *ldc, doublereal *work, + integer *lwork, integer *info, ftnlen side_len, ftnlen trans_len) { - /* System generated locals */ address a__1[2]; - integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4, - i__5; + integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4, i__5; char ch__1[2]; - - /* Builtin functions */ - /* Subroutine */ int s_lmp_cat(char *, char **, integer *, integer *, ftnlen); - - /* Local variables */ + int s_lmp_cat(char *, char **, integer *, integer *, ftnlen); integer i__, i1, i2, i3, ib, ic, jc, nb, mi, ni, nq, nw, iwt; logical left; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer nbmin, iinfo; - extern /* Subroutine */ int dorm2r_(char *, char *, integer *, integer *, - integer *, doublereal *, integer *, doublereal *, doublereal *, - integer *, doublereal *, integer *, ftnlen, ftnlen), dlarfb_(char - *, char *, char *, char *, integer *, integer *, integer *, - doublereal *, integer *, doublereal *, integer *, doublereal *, - integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, - ftnlen), dlarft_(char *, char *, integer *, integer *, doublereal - *, integer *, doublereal *, doublereal *, integer *, ftnlen, - ftnlen), xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern int dorm2r_(char *, char *, integer *, integer *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, doublereal *, integer *, ftnlen, + ftnlen), + dlarfb_(char *, char *, char *, char *, integer *, integer *, integer *, doublereal *, + integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, + integer *, ftnlen, ftnlen, ftnlen, ftnlen), + dlarft_(char *, char *, integer *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, ftnlen, ftnlen), + xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); logical notran; integer ldwork, lwkopt; logical lquery; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; @@ -258,25 +40,20 @@ f"> */ c_offset = 1 + c_dim1; c__ -= c_offset; --work; - - /* Function Body */ *info = 0; left = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); notran = lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1); lquery = *lwork == -1; - -/* NQ is the order of Q and NW is the minimum dimension of WORK */ - if (left) { nq = *m; - nw = max(1,*n); + nw = max(1, *n); } else { nq = *n; - nw = max(1,*m); + nw = max(1, *m); } - if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + if (!left && !lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { *info = -1; - } else if (! notran && ! lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1)) { + } else if (!notran && !lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1)) { *info = -2; } else if (*m < 0) { *info = -3; @@ -284,30 +61,22 @@ f"> */ *info = -4; } else if (*k < 0 || *k > nq) { *info = -5; - } else if (*lda < max(1,nq)) { + } else if (*lda < max(1, nq)) { *info = -7; - } else if (*ldc < max(1,*m)) { + } else if (*ldc < max(1, *m)) { *info = -10; - } else if (*lwork < nw && ! lquery) { + } else if (*lwork < nw && !lquery) { *info = -12; } - if (*info == 0) { - -/* Compute the workspace requirements */ - -/* Computing MIN */ -/* Writing concatenation */ i__3[0] = 1, a__1[0] = side; i__3[1] = 1, a__1[1] = trans; s_lmp_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); - i__1 = 64, i__2 = ilaenv_(&c__1, (char *)"DORMQR", ch__1, m, n, k, &c_n1, ( - ftnlen)6, (ftnlen)2); - nb = min(i__1,i__2); + i__1 = 64, i__2 = ilaenv_(&c__1, (char *)"DORMQR", ch__1, m, n, k, &c_n1, (ftnlen)6, (ftnlen)2); + nb = min(i__1, i__2); lwkopt = nw * nb + 4160; - work[1] = (doublereal) lwkopt; + work[1] = (doublereal)lwkopt; } - if (*info != 0) { i__1 = -(*info); xerbla_((char *)"DORMQR", &i__1, (ftnlen)6); @@ -315,42 +84,28 @@ f"> */ } else if (lquery) { return 0; } - -/* Quick return if possible */ - if (*m == 0 || *n == 0 || *k == 0) { work[1] = 1.; return 0; } - nbmin = 2; ldwork = nw; if (nb > 1 && nb < *k) { if (*lwork < lwkopt) { nb = (*lwork - 4160) / ldwork; -/* Computing MAX */ -/* Writing concatenation */ i__3[0] = 1, a__1[0] = side; i__3[1] = 1, a__1[1] = trans; s_lmp_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); - i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DORMQR", ch__1, m, n, k, &c_n1, ( - ftnlen)6, (ftnlen)2); - nbmin = max(i__1,i__2); + i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DORMQR", ch__1, m, n, k, &c_n1, (ftnlen)6, (ftnlen)2); + nbmin = max(i__1, i__2); } } - if (nb < nbmin || nb >= *k) { - -/* Use unblocked code */ - - dorm2r_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[ - c_offset], ldc, &work[1], &iinfo, (ftnlen)1, (ftnlen)1); + dorm2r_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[c_offset], ldc, &work[1], + &iinfo, (ftnlen)1, (ftnlen)1); } else { - -/* Use blocked code */ - iwt = nw * nb + 1; - if (left && ! notran || ! left && notran) { + if (left && !notran || !left && notran) { i1 = 1; i2 = *k; i3 = nb; @@ -359,7 +114,6 @@ f"> */ i2 = 1; i3 = -nb; } - if (left) { ni = *n; jc = 1; @@ -367,51 +121,29 @@ f"> */ mi = *m; ic = 1; } - i__1 = i2; i__2 = i3; for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { -/* Computing MIN */ i__4 = nb, i__5 = *k - i__ + 1; - ib = min(i__4,i__5); - -/* Form the triangular factor of the block reflector */ -/* H = H(i) H(i+1) . . . H(i+ib-1) */ - + ib = min(i__4, i__5); i__4 = nq - i__ + 1; - dlarft_((char *)"Forward", (char *)"Columnwise", &i__4, &ib, &a[i__ + i__ * - a_dim1], lda, &tau[i__], &work[iwt], &c__65, (ftnlen)7, ( - ftnlen)10); + dlarft_((char *)"Forward", (char *)"Columnwise", &i__4, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], + &work[iwt], &c__65, (ftnlen)7, (ftnlen)10); if (left) { - -/* H or H**T is applied to C(i:m,1:n) */ - mi = *m - i__ + 1; ic = i__; } else { - -/* H or H**T is applied to C(1:m,i:n) */ - ni = *n - i__ + 1; jc = i__; } - -/* Apply H or H**T */ - - dlarfb_(side, trans, (char *)"Forward", (char *)"Columnwise", &mi, &ni, &ib, &a[ - i__ + i__ * a_dim1], lda, &work[iwt], &c__65, &c__[ic + - jc * c_dim1], ldc, &work[1], &ldwork, (ftnlen)1, (ftnlen) - 1, (ftnlen)7, (ftnlen)10); -/* L10: */ + dlarfb_(side, trans, (char *)"Forward", (char *)"Columnwise", &mi, &ni, &ib, &a[i__ + i__ * a_dim1], + lda, &work[iwt], &c__65, &c__[ic + jc * c_dim1], ldc, &work[1], &ldwork, + (ftnlen)1, (ftnlen)1, (ftnlen)7, (ftnlen)10); } } - work[1] = (doublereal) lwkopt; + work[1] = (doublereal)lwkopt; return 0; - -/* End of DORMQR */ - -} /* dormqr_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dormtr.cpp b/lib/linalg/dormtr.cpp index 0f0cdac3db..9fc489ef42 100644 --- a/lib/linalg/dormtr.cpp +++ b/lib/linalg/dormtr.cpp @@ -1,253 +1,34 @@ -/* fortran/dormtr.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static integer c_n1 = -1; static integer c__2 = 2; - -/* > \brief \b DORMTR */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DORMTR + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DORMTR( SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC, */ -/* WORK, LWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER SIDE, TRANS, UPLO */ -/* INTEGER INFO, LDA, LDC, LWORK, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DORMTR overwrites the general real M-by-N matrix C with */ -/* > */ -/* > SIDE = 'L' SIDE = 'R' */ -/* > TRANS = 'N': Q * C C * Q */ -/* > TRANS = 'T': Q**T * C C * Q**T */ -/* > */ -/* > where Q is a real orthogonal matrix of order nq, with nq = m if */ -/* > SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of */ -/* > nq-1 elementary reflectors, as returned by DSYTRD: */ -/* > */ -/* > if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1); */ -/* > */ -/* > if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1). */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] SIDE */ -/* > \verbatim */ -/* > SIDE is CHARACTER*1 */ -/* > = 'L': apply Q or Q**T from the Left; */ -/* > = 'R': apply Q or Q**T from the Right. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > = 'U': Upper triangle of A contains elementary reflectors */ -/* > from DSYTRD; */ -/* > = 'L': Lower triangle of A contains elementary reflectors */ -/* > from DSYTRD. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TRANS */ -/* > \verbatim */ -/* > TRANS is CHARACTER*1 */ -/* > = 'N': No transpose, apply Q; */ -/* > = 'T': Transpose, apply Q**T. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix C. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix C. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension */ -/* > (LDA,M) if SIDE = 'L' */ -/* > (LDA,N) if SIDE = 'R' */ -/* > The vectors which define the elementary reflectors, as */ -/* > returned by DSYTRD. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. */ -/* > LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TAU */ -/* > \verbatim */ -/* > TAU is DOUBLE PRECISION array, dimension */ -/* > (M-1) if SIDE = 'L' */ -/* > (N-1) if SIDE = 'R' */ -/* > TAU(i) must contain the scalar factor of the elementary */ -/* > reflector H(i), as returned by DSYTRD. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] C */ -/* > \verbatim */ -/* > C is DOUBLE PRECISION array, dimension (LDC,N) */ -/* > On entry, the M-by-N matrix C. */ -/* > On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDC */ -/* > \verbatim */ -/* > LDC is INTEGER */ -/* > The leading dimension of the array C. LDC >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ -/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LWORK */ -/* > \verbatim */ -/* > LWORK is INTEGER */ -/* > The dimension of the array WORK. */ -/* > If SIDE = 'L', LWORK >= max(1,N); */ -/* > if SIDE = 'R', LWORK >= max(1,M). */ -/* > For optimum performance LWORK >= N*NB if SIDE = 'L', and */ -/* > LWORK >= M*NB if SIDE = 'R', where NB is the optimal */ -/* > blocksize. */ -/* > */ -/* > If LWORK = -1, then a workspace query is assumed; the routine */ -/* > only calculates the optimal size of the WORK array, returns */ -/* > this value as the first entry of the WORK array, and no error */ -/* > message related to LWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleOTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dormtr_(char *side, char *uplo, char *trans, integer *m, - integer *n, doublereal *a, integer *lda, doublereal *tau, doublereal * - c__, integer *ldc, doublereal *work, integer *lwork, integer *info, - ftnlen side_len, ftnlen uplo_len, ftnlen trans_len) +int dormtr_(char *side, char *uplo, char *trans, integer *m, integer *n, doublereal *a, + integer *lda, doublereal *tau, doublereal *c__, integer *ldc, doublereal *work, + integer *lwork, integer *info, ftnlen side_len, ftnlen uplo_len, ftnlen trans_len) { - /* System generated locals */ address a__1[2]; integer a_dim1, a_offset, c_dim1, c_offset, i__1[2], i__2, i__3; char ch__1[2]; - - /* Builtin functions */ - /* Subroutine */ int s_lmp_cat(char *, char **, integer *, integer *, ftnlen); - - /* Local variables */ + int s_lmp_cat(char *, char **, integer *, integer *, ftnlen); integer i1, i2, nb, mi, ni, nq, nw; logical left; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer iinfo; logical upper; - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - extern /* Subroutine */ int dormql_(char *, char *, integer *, integer *, - integer *, doublereal *, integer *, doublereal *, doublereal *, - integer *, doublereal *, integer *, integer *, ftnlen, ftnlen), - dormqr_(char *, char *, integer *, integer *, integer *, - doublereal *, integer *, doublereal *, doublereal *, integer *, - doublereal *, integer *, integer *, ftnlen, ftnlen); + extern int xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); + extern int dormql_(char *, char *, integer *, integer *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, doublereal *, integer *, integer *, + ftnlen, ftnlen), + dormqr_(char *, char *, integer *, integer *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, doublereal *, integer *, integer *, ftnlen, + ftnlen); integer lwkopt; logical lquery; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; @@ -256,87 +37,72 @@ f"> */ c_offset = 1 + c_dim1; c__ -= c_offset; --work; - - /* Function Body */ *info = 0; left = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); lquery = *lwork == -1; - -/* NQ is the order of Q and NW is the minimum dimension of WORK */ - if (left) { nq = *m; - nw = max(1,*n); + nw = max(1, *n); } else { nq = *n; - nw = max(1,*m); + nw = max(1, *m); } - if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + if (!left && !lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { *info = -1; - } else if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + } else if (!upper && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { *info = -2; - } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, - (char *)"T", (ftnlen)1, (ftnlen)1)) { + } else if (!lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && + !lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1)) { *info = -3; } else if (*m < 0) { *info = -4; } else if (*n < 0) { *info = -5; - } else if (*lda < max(1,nq)) { + } else if (*lda < max(1, nq)) { *info = -7; - } else if (*ldc < max(1,*m)) { + } else if (*ldc < max(1, *m)) { *info = -10; - } else if (*lwork < nw && ! lquery) { + } else if (*lwork < nw && !lquery) { *info = -12; } - if (*info == 0) { if (upper) { if (left) { -/* Writing concatenation */ i__1[0] = 1, a__1[0] = side; i__1[1] = 1, a__1[1] = trans; s_lmp_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); i__2 = *m - 1; i__3 = *m - 1; - nb = ilaenv_(&c__1, (char *)"DORMQL", ch__1, &i__2, n, &i__3, &c_n1, ( - ftnlen)6, (ftnlen)2); + nb = ilaenv_(&c__1, (char *)"DORMQL", ch__1, &i__2, n, &i__3, &c_n1, (ftnlen)6, (ftnlen)2); } else { -/* Writing concatenation */ i__1[0] = 1, a__1[0] = side; i__1[1] = 1, a__1[1] = trans; s_lmp_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); i__2 = *n - 1; i__3 = *n - 1; - nb = ilaenv_(&c__1, (char *)"DORMQL", ch__1, m, &i__2, &i__3, &c_n1, ( - ftnlen)6, (ftnlen)2); + nb = ilaenv_(&c__1, (char *)"DORMQL", ch__1, m, &i__2, &i__3, &c_n1, (ftnlen)6, (ftnlen)2); } } else { if (left) { -/* Writing concatenation */ i__1[0] = 1, a__1[0] = side; i__1[1] = 1, a__1[1] = trans; s_lmp_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); i__2 = *m - 1; i__3 = *m - 1; - nb = ilaenv_(&c__1, (char *)"DORMQR", ch__1, &i__2, n, &i__3, &c_n1, ( - ftnlen)6, (ftnlen)2); + nb = ilaenv_(&c__1, (char *)"DORMQR", ch__1, &i__2, n, &i__3, &c_n1, (ftnlen)6, (ftnlen)2); } else { -/* Writing concatenation */ i__1[0] = 1, a__1[0] = side; i__1[1] = 1, a__1[1] = trans; s_lmp_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); i__2 = *n - 1; i__3 = *n - 1; - nb = ilaenv_(&c__1, (char *)"DORMQR", ch__1, m, &i__2, &i__3, &c_n1, ( - ftnlen)6, (ftnlen)2); + nb = ilaenv_(&c__1, (char *)"DORMQR", ch__1, m, &i__2, &i__3, &c_n1, (ftnlen)6, (ftnlen)2); } } lwkopt = nw * nb; - work[1] = (doublereal) lwkopt; + work[1] = (doublereal)lwkopt; } - if (*info != 0) { i__2 = -(*info); xerbla_((char *)"DORMTR", &i__2, (ftnlen)6); @@ -344,14 +110,10 @@ f"> */ } else if (lquery) { return 0; } - -/* Quick return if possible */ - if (*m == 0 || *n == 0 || nq == 1) { work[1] = 1.; return 0; } - if (left) { mi = *m - 1; ni = *n; @@ -359,19 +121,11 @@ f"> */ mi = *m; ni = *n - 1; } - if (upper) { - -/* Q was determined by a call to DSYTRD with UPLO = 'U' */ - i__2 = nq - 1; - dormql_(side, trans, &mi, &ni, &i__2, &a[(a_dim1 << 1) + 1], lda, & - tau[1], &c__[c_offset], ldc, &work[1], lwork, &iinfo, (ftnlen) - 1, (ftnlen)1); + dormql_(side, trans, &mi, &ni, &i__2, &a[(a_dim1 << 1) + 1], lda, &tau[1], &c__[c_offset], + ldc, &work[1], lwork, &iinfo, (ftnlen)1, (ftnlen)1); } else { - -/* Q was determined by a call to DSYTRD with UPLO = 'L' */ - if (left) { i1 = 2; i2 = 1; @@ -380,17 +134,12 @@ f"> */ i2 = 2; } i__2 = nq - 1; - dormqr_(side, trans, &mi, &ni, &i__2, &a[a_dim1 + 2], lda, &tau[1], & - c__[i1 + i2 * c_dim1], ldc, &work[1], lwork, &iinfo, (ftnlen) - 1, (ftnlen)1); + dormqr_(side, trans, &mi, &ni, &i__2, &a[a_dim1 + 2], lda, &tau[1], &c__[i1 + i2 * c_dim1], + ldc, &work[1], lwork, &iinfo, (ftnlen)1, (ftnlen)1); } - work[1] = (doublereal) lwkopt; + work[1] = (doublereal)lwkopt; return 0; - -/* End of DORMTR */ - -} /* dormtr_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dposv.cpp b/lib/linalg/dposv.cpp index 370c261bf0..c61c591e0a 100644 --- a/lib/linalg/dposv.cpp +++ b/lib/linalg/dposv.cpp @@ -1,207 +1,32 @@ -/* fortran/dposv.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief DPOSV computes the solution to system of linear equations A * X = B for PO matrices */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DPOSV + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DPOSV( UPLO, N, NRHS, A, LDA, B, LDB, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER UPLO */ -/* INTEGER INFO, LDA, LDB, N, NRHS */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), B( LDB, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DPOSV computes the solution to a real system of linear equations */ -/* > A * X = B, */ -/* > where A is an N-by-N symmetric positive definite matrix and X and B */ -/* > are N-by-NRHS matrices. */ -/* > */ -/* > The Cholesky decomposition is used to factor A as */ -/* > A = U**T* U, if UPLO = 'U', or */ -/* > A = L * L**T, if UPLO = 'L', */ -/* > where U is an upper triangular matrix and L is a lower triangular */ -/* > matrix. The factored form of A is then used to solve the system of */ -/* > equations A * X = B. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > = 'U': Upper triangle of A is stored; */ -/* > = 'L': Lower triangle of A is stored. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of linear equations, i.e., the order of the */ -/* > matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] NRHS */ -/* > \verbatim */ -/* > NRHS is INTEGER */ -/* > The number of right hand sides, i.e., the number of columns */ -/* > of the matrix B. NRHS >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On entry, the symmetric matrix A. If UPLO = 'U', the leading */ -/* > N-by-N upper triangular part of A contains the upper */ -/* > triangular part of the matrix A, and the strictly lower */ -/* > triangular part of A is not referenced. If UPLO = 'L', the */ -/* > leading N-by-N lower triangular part of A contains the lower */ -/* > triangular part of the matrix A, and the strictly upper */ -/* > triangular part of A is not referenced. */ -/* > */ -/* > On exit, if INFO = 0, the factor U or L from the Cholesky */ -/* > factorization A = U**T*U or A = L*L**T. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] B */ -/* > \verbatim */ -/* > B is DOUBLE PRECISION array, dimension (LDB,NRHS) */ -/* > On entry, the N-by-NRHS right hand side matrix B. */ -/* > On exit, if INFO = 0, the N-by-NRHS solution matrix X. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDB */ -/* > \verbatim */ -/* > LDB is INTEGER */ -/* > The leading dimension of the array B. LDB >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > > 0: if INFO = i, the leading minor of order i of A is not */ -/* > positive definite, so the factorization could not be */ -/* > completed, and the solution has not been computed. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doublePOsolve */ - -/* ===================================================================== */ -/* Subroutine */ int dposv_(char *uplo, integer *n, integer *nrhs, doublereal - *a, integer *lda, doublereal *b, integer *ldb, integer *info, ftnlen - uplo_len) +int dposv_(char *uplo, integer *n, integer *nrhs, doublereal *a, integer *lda, doublereal *b, + integer *ldb, integer *info, ftnlen uplo_len) { - /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1; - - /* Local variables */ extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), dpotrf_( - char *, integer *, doublereal *, integer *, integer *, ftnlen), - dpotrs_(char *, integer *, integer *, doublereal *, integer *, - doublereal *, integer *, integer *, ftnlen); - - -/* -- LAPACK driver routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ + extern int xerbla_(char *, integer *, ftnlen), + dpotrf_(char *, integer *, doublereal *, integer *, integer *, ftnlen), + dpotrs_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, + integer *, ftnlen); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; - - /* Function Body */ *info = 0; - if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", ( - ftnlen)1, (ftnlen)1)) { + if (!lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*nrhs < 0) { *info = -3; - } else if (*lda < max(1,*n)) { + } else if (*lda < max(1, *n)) { *info = -5; - } else if (*ldb < max(1,*n)) { + } else if (*ldb < max(1, *n)) { *info = -7; } if (*info != 0) { @@ -209,24 +34,12 @@ extern "C" { xerbla_((char *)"DPOSV ", &i__1, (ftnlen)6); return 0; } - -/* Compute the Cholesky factorization A = U**T*U or A = L*L**T. */ - dpotrf_(uplo, n, &a[a_offset], lda, info, (ftnlen)1); if (*info == 0) { - -/* Solve the system A*X = B, overwriting B with X. */ - - dpotrs_(uplo, n, nrhs, &a[a_offset], lda, &b[b_offset], ldb, info, ( - ftnlen)1); - + dpotrs_(uplo, n, nrhs, &a[a_offset], lda, &b[b_offset], ldb, info, (ftnlen)1); } return 0; - -/* End of DPOSV */ - -} /* dposv_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dpotf2.cpp b/lib/linalg/dpotf2.cpp index 987db22578..4a2e84af28 100644 --- a/lib/linalg/dpotf2.cpp +++ b/lib/linalg/dpotf2.cpp @@ -1,201 +1,35 @@ -/* fortran/dpotf2.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static doublereal c_b10 = -1.; static doublereal c_b12 = 1.; - -/* > \brief \b DPOTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix (u -nblocked algorithm). */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DPOTF2 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DPOTF2( UPLO, N, A, LDA, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER UPLO */ -/* INTEGER INFO, LDA, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DPOTF2 computes the Cholesky factorization of a real symmetric */ -/* > positive definite matrix A. */ -/* > */ -/* > The factorization has the form */ -/* > A = U**T * U , if UPLO = 'U', or */ -/* > A = L * L**T, if UPLO = 'L', */ -/* > where U is an upper triangular matrix and L is lower triangular. */ -/* > */ -/* > This is the unblocked version of the algorithm, calling Level 2 BLAS. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > Specifies whether the upper or lower triangular part of the */ -/* > symmetric matrix A is stored. */ -/* > = 'U': Upper triangular */ -/* > = 'L': Lower triangular */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On entry, the symmetric matrix A. If UPLO = 'U', the leading */ -/* > n by n upper triangular part of A contains the upper */ -/* > triangular part of the matrix A, and the strictly lower */ -/* > triangular part of A is not referenced. If UPLO = 'L', the */ -/* > leading n by n lower triangular part of A contains the lower */ -/* > triangular part of the matrix A, and the strictly upper */ -/* > triangular part of A is not referenced. */ -/* > */ -/* > On exit, if INFO = 0, the factor U or L from the Cholesky */ -/* > factorization A = U**T *U or A = L*L**T. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -k, the k-th argument had an illegal value */ -/* > > 0: if INFO = k, the leading minor of order k is not */ -/* > positive definite, and the factorization could not be */ -/* > completed. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doublePOcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dpotf2_(char *uplo, integer *n, doublereal *a, integer * - lda, integer *info, ftnlen uplo_len) +int dpotf2_(char *uplo, integer *n, doublereal *a, integer *lda, integer *info, ftnlen uplo_len) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; doublereal d__1; - - /* Builtin functions */ double sqrt(doublereal); - - /* Local variables */ integer j; doublereal ajj; - extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, - integer *); - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *); + extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, integer *); + extern int dscal_(integer *, doublereal *, doublereal *, integer *); extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int dgemv_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, doublereal *, integer *, - doublereal *, doublereal *, integer *, ftnlen); + extern int dgemv_(char *, integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, ftnlen); logical upper; extern logical disnan_(doublereal *); - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ + extern int xerbla_(char *, integer *, ftnlen); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; - - /* Function Body */ *info = 0; upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); - if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + if (!upper && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { *info = -1; } else if (*n < 0) { *info = -2; - } else if (*lda < max(1,*n)) { + } else if (*lda < max(1, *n)) { *info = -4; } if (*info != 0) { @@ -203,92 +37,59 @@ f"> */ xerbla_((char *)"DPOTF2", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*n == 0) { return 0; } - if (upper) { - -/* Compute the Cholesky factorization A = U**T *U. */ - i__1 = *n; for (j = 1; j <= i__1; ++j) { - -/* Compute U(J,J) and test for non-positive-definiteness. */ - i__2 = j - 1; - ajj = a[j + j * a_dim1] - ddot_(&i__2, &a[j * a_dim1 + 1], &c__1, - &a[j * a_dim1 + 1], &c__1); + ajj = a[j + j * a_dim1] - + ddot_(&i__2, &a[j * a_dim1 + 1], &c__1, &a[j * a_dim1 + 1], &c__1); if (ajj <= 0. || disnan_(&ajj)) { a[j + j * a_dim1] = ajj; goto L30; } ajj = sqrt(ajj); a[j + j * a_dim1] = ajj; - -/* Compute elements J+1:N of row J. */ - if (j < *n) { i__2 = j - 1; i__3 = *n - j; - dgemv_((char *)"Transpose", &i__2, &i__3, &c_b10, &a[(j + 1) * a_dim1 - + 1], lda, &a[j * a_dim1 + 1], &c__1, &c_b12, &a[j + ( - j + 1) * a_dim1], lda, (ftnlen)9); + dgemv_((char *)"Transpose", &i__2, &i__3, &c_b10, &a[(j + 1) * a_dim1 + 1], lda, + &a[j * a_dim1 + 1], &c__1, &c_b12, &a[j + (j + 1) * a_dim1], lda, (ftnlen)9); i__2 = *n - j; d__1 = 1. / ajj; dscal_(&i__2, &d__1, &a[j + (j + 1) * a_dim1], lda); } -/* L10: */ } } else { - -/* Compute the Cholesky factorization A = L*L**T. */ - i__1 = *n; for (j = 1; j <= i__1; ++j) { - -/* Compute L(J,J) and test for non-positive-definiteness. */ - i__2 = j - 1; - ajj = a[j + j * a_dim1] - ddot_(&i__2, &a[j + a_dim1], lda, &a[j - + a_dim1], lda); + ajj = a[j + j * a_dim1] - ddot_(&i__2, &a[j + a_dim1], lda, &a[j + a_dim1], lda); if (ajj <= 0. || disnan_(&ajj)) { a[j + j * a_dim1] = ajj; goto L30; } ajj = sqrt(ajj); a[j + j * a_dim1] = ajj; - -/* Compute elements J+1:N of column J. */ - if (j < *n) { i__2 = *n - j; i__3 = j - 1; - dgemv_((char *)"No transpose", &i__2, &i__3, &c_b10, &a[j + 1 + - a_dim1], lda, &a[j + a_dim1], lda, &c_b12, &a[j + 1 + - j * a_dim1], &c__1, (ftnlen)12); + dgemv_((char *)"No transpose", &i__2, &i__3, &c_b10, &a[j + 1 + a_dim1], lda, + &a[j + a_dim1], lda, &c_b12, &a[j + 1 + j * a_dim1], &c__1, (ftnlen)12); i__2 = *n - j; d__1 = 1. / ajj; dscal_(&i__2, &d__1, &a[j + 1 + j * a_dim1], &c__1); } -/* L20: */ } } goto L40; - L30: *info = j; - L40: return 0; - -/* End of DPOTF2 */ - -} /* dpotf2_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dpotrf.cpp b/lib/linalg/dpotrf.cpp index 6dc003ab93..63caf94920 100644 --- a/lib/linalg/dpotrf.cpp +++ b/lib/linalg/dpotrf.cpp @@ -1,198 +1,39 @@ -/* fortran/dpotrf.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static integer c_n1 = -1; static doublereal c_b13 = -1.; static doublereal c_b14 = 1.; - -/* > \brief \b DPOTRF */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DPOTRF + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DPOTRF( UPLO, N, A, LDA, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER UPLO */ -/* INTEGER INFO, LDA, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DPOTRF computes the Cholesky factorization of a real symmetric */ -/* > positive definite matrix A. */ -/* > */ -/* > The factorization has the form */ -/* > A = U**T * U, if UPLO = 'U', or */ -/* > A = L * L**T, if UPLO = 'L', */ -/* > where U is an upper triangular matrix and L is lower triangular. */ -/* > */ -/* > This is the block version of the algorithm, calling Level 3 BLAS. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > = 'U': Upper triangle of A is stored; */ -/* > = 'L': Lower triangle of A is stored. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On entry, the symmetric matrix A. If UPLO = 'U', the leading */ -/* > N-by-N upper triangular part of A contains the upper */ -/* > triangular part of the matrix A, and the strictly lower */ -/* > triangular part of A is not referenced. If UPLO = 'L', the */ -/* > leading N-by-N lower triangular part of A contains the lower */ -/* > triangular part of the matrix A, and the strictly upper */ -/* > triangular part of A is not referenced. */ -/* > */ -/* > On exit, if INFO = 0, the factor U or L from the Cholesky */ -/* > factorization A = U**T*U or A = L*L**T. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > > 0: if INFO = i, the leading minor of order i is not */ -/* > positive definite, and the factorization could not be */ -/* > completed. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doublePOcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dpotrf_(char *uplo, integer *n, doublereal *a, integer * - lda, integer *info, ftnlen uplo_len) +int dpotrf_(char *uplo, integer *n, doublereal *a, integer *lda, integer *info, ftnlen uplo_len) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4; - - /* Local variables */ integer j, jb, nb; - extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); + extern int dgemm_(char *, char *, integer *, integer *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, + ftnlen, ftnlen); extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, - integer *, integer *, doublereal *, doublereal *, integer *, - doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + extern int dtrsm_(char *, char *, char *, char *, integer *, integer *, doublereal *, + doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, + ftnlen); logical upper; - extern /* Subroutine */ int dsyrk_(char *, char *, integer *, integer *, - doublereal *, doublereal *, integer *, doublereal *, doublereal *, - integer *, ftnlen, ftnlen), xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - extern /* Subroutine */ int dpotrf2_(char *, integer *, doublereal *, - integer *, integer *, ftnlen); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ + extern int dsyrk_(char *, char *, integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, doublereal *, integer *, ftnlen, ftnlen), + xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); + extern int dpotrf2_(char *, integer *, doublereal *, integer *, integer *, ftnlen); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; - - /* Function Body */ *info = 0; upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); - if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + if (!upper && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { *info = -1; } else if (*n < 0) { *info = -2; - } else if (*lda < max(1,*n)) { + } else if (*lda < max(1, *n)) { *info = -4; } if (*info != 0) { @@ -200,123 +41,71 @@ f"> */ xerbla_((char *)"DPOTRF", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*n == 0) { return 0; } - -/* Determine the block size for this environment. */ - - nb = ilaenv_(&c__1, (char *)"DPOTRF", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, ( - ftnlen)1); + nb = ilaenv_(&c__1, (char *)"DPOTRF", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); if (nb <= 1 || nb >= *n) { - -/* Use unblocked code. */ - dpotrf2_(uplo, n, &a[a_offset], lda, info, (ftnlen)1); } else { - -/* Use blocked code. */ - if (upper) { - -/* Compute the Cholesky factorization A = U**T*U. */ - i__1 = *n; i__2 = nb; for (j = 1; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) { - -/* Update and factorize the current diagonal block and test */ -/* for non-positive-definiteness. */ - -/* Computing MIN */ i__3 = nb, i__4 = *n - j + 1; - jb = min(i__3,i__4); + jb = min(i__3, i__4); i__3 = j - 1; - dsyrk_((char *)"Upper", (char *)"Transpose", &jb, &i__3, &c_b13, &a[j * - a_dim1 + 1], lda, &c_b14, &a[j + j * a_dim1], lda, ( - ftnlen)5, (ftnlen)9); - dpotrf2_((char *)"Upper", &jb, &a[j + j * a_dim1], lda, info, (ftnlen) - 5); + dsyrk_((char *)"Upper", (char *)"Transpose", &jb, &i__3, &c_b13, &a[j * a_dim1 + 1], lda, &c_b14, + &a[j + j * a_dim1], lda, (ftnlen)5, (ftnlen)9); + dpotrf2_((char *)"Upper", &jb, &a[j + j * a_dim1], lda, info, (ftnlen)5); if (*info != 0) { goto L30; } if (j + jb <= *n) { - -/* Compute the current block row. */ - i__3 = *n - j - jb + 1; i__4 = j - 1; - dgemm_((char *)"Transpose", (char *)"No transpose", &jb, &i__3, &i__4, & - c_b13, &a[j * a_dim1 + 1], lda, &a[(j + jb) * - a_dim1 + 1], lda, &c_b14, &a[j + (j + jb) * - a_dim1], lda, (ftnlen)9, (ftnlen)12); + dgemm_((char *)"Transpose", (char *)"No transpose", &jb, &i__3, &i__4, &c_b13, + &a[j * a_dim1 + 1], lda, &a[(j + jb) * a_dim1 + 1], lda, &c_b14, + &a[j + (j + jb) * a_dim1], lda, (ftnlen)9, (ftnlen)12); i__3 = *n - j - jb + 1; - dtrsm_((char *)"Left", (char *)"Upper", (char *)"Transpose", (char *)"Non-unit", &jb, & - i__3, &c_b14, &a[j + j * a_dim1], lda, &a[j + (j - + jb) * a_dim1], lda, (ftnlen)4, (ftnlen)5, ( - ftnlen)9, (ftnlen)8); + dtrsm_((char *)"Left", (char *)"Upper", (char *)"Transpose", (char *)"Non-unit", &jb, &i__3, &c_b14, + &a[j + j * a_dim1], lda, &a[j + (j + jb) * a_dim1], lda, (ftnlen)4, + (ftnlen)5, (ftnlen)9, (ftnlen)8); } -/* L10: */ } - } else { - -/* Compute the Cholesky factorization A = L*L**T. */ - i__2 = *n; i__1 = nb; for (j = 1; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) { - -/* Update and factorize the current diagonal block and test */ -/* for non-positive-definiteness. */ - -/* Computing MIN */ i__3 = nb, i__4 = *n - j + 1; - jb = min(i__3,i__4); + jb = min(i__3, i__4); i__3 = j - 1; - dsyrk_((char *)"Lower", (char *)"No transpose", &jb, &i__3, &c_b13, &a[j + - a_dim1], lda, &c_b14, &a[j + j * a_dim1], lda, ( - ftnlen)5, (ftnlen)12); - dpotrf2_((char *)"Lower", &jb, &a[j + j * a_dim1], lda, info, (ftnlen) - 5); + dsyrk_((char *)"Lower", (char *)"No transpose", &jb, &i__3, &c_b13, &a[j + a_dim1], lda, &c_b14, + &a[j + j * a_dim1], lda, (ftnlen)5, (ftnlen)12); + dpotrf2_((char *)"Lower", &jb, &a[j + j * a_dim1], lda, info, (ftnlen)5); if (*info != 0) { goto L30; } if (j + jb <= *n) { - -/* Compute the current block column. */ - i__3 = *n - j - jb + 1; i__4 = j - 1; - dgemm_((char *)"No transpose", (char *)"Transpose", &i__3, &jb, &i__4, & - c_b13, &a[j + jb + a_dim1], lda, &a[j + a_dim1], - lda, &c_b14, &a[j + jb + j * a_dim1], lda, ( - ftnlen)12, (ftnlen)9); + dgemm_((char *)"No transpose", (char *)"Transpose", &i__3, &jb, &i__4, &c_b13, + &a[j + jb + a_dim1], lda, &a[j + a_dim1], lda, &c_b14, + &a[j + jb + j * a_dim1], lda, (ftnlen)12, (ftnlen)9); i__3 = *n - j - jb + 1; - dtrsm_((char *)"Right", (char *)"Lower", (char *)"Transpose", (char *)"Non-unit", &i__3, & - jb, &c_b14, &a[j + j * a_dim1], lda, &a[j + jb + - j * a_dim1], lda, (ftnlen)5, (ftnlen)5, (ftnlen)9, - (ftnlen)8); + dtrsm_((char *)"Right", (char *)"Lower", (char *)"Transpose", (char *)"Non-unit", &i__3, &jb, &c_b14, + &a[j + j * a_dim1], lda, &a[j + jb + j * a_dim1], lda, (ftnlen)5, + (ftnlen)5, (ftnlen)9, (ftnlen)8); } -/* L20: */ } } } goto L40; - L30: *info = *info + j - 1; - L40: return 0; - -/* End of DPOTRF */ - -} /* dpotrf_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dpotrf2.cpp b/lib/linalg/dpotrf2.cpp index 61f9c83af6..af2e45eb36 100644 --- a/lib/linalg/dpotrf2.cpp +++ b/lib/linalg/dpotrf2.cpp @@ -1,191 +1,34 @@ -/* static/dpotrf2.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static doublereal c_b9 = 1.; static doublereal c_b11 = -1.; - -/* > \brief \b DPOTRF2 */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* RECURSIVE SUBROUTINE DPOTRF2( UPLO, N, A, LDA, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER UPLO */ -/* INTEGER INFO, LDA, N */ -/* .. */ -/* .. Array Arguments .. */ -/* REAL A( LDA, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DPOTRF2 computes the Cholesky factorization of a real symmetric */ -/* > positive definite matrix A using the recursive algorithm. */ -/* > */ -/* > The factorization has the form */ -/* > A = U**T * U, if UPLO = 'U', or */ -/* > A = L * L**T, if UPLO = 'L', */ -/* > where U is an upper triangular matrix and L is lower triangular. */ -/* > */ -/* > This is the recursive version of the algorithm. It divides */ -/* > the matrix into four submatrices: */ -/* > */ -/* > [ A11 | A12 ] where A11 is n1 by n1 and A22 is n2 by n2 */ -/* > A = [ -----|----- ] with n1 = n/2 */ -/* > [ A21 | A22 ] n2 = n-n1 */ -/* > */ -/* > The subroutine calls itself to factor A11. Update and scale A21 */ -/* > or A12, update A22 then calls itself to factor A22. */ -/* > */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > = 'U': Upper triangle of A is stored; */ -/* > = 'L': Lower triangle of A is stored. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On entry, the symmetric matrix A. If UPLO = 'U', the leading */ -/* > N-by-N upper triangular part of A contains the upper */ -/* > triangular part of the matrix A, and the strictly lower */ -/* > triangular part of A is not referenced. If UPLO = 'L', the */ -/* > leading N-by-N lower triangular part of A contains the lower */ -/* > triangular part of the matrix A, and the strictly upper */ -/* > triangular part of A is not referenced. */ -/* > */ -/* > On exit, if INFO = 0, the factor U or L from the Cholesky */ -/* > factorization A = U**T*U or A = L*L**T. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > > 0: if INFO = i, the leading minor of order i is not */ -/* > positive definite, and the factorization could not be */ -/* > completed. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doublePOcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dpotrf2_(char *uplo, integer *n, doublereal *a, integer * - lda, integer *info, ftnlen uplo_len) +int dpotrf2_(char *uplo, integer *n, doublereal *a, integer *lda, integer *info, ftnlen uplo_len) { - /* System generated locals */ integer a_dim1, a_offset, i__1; - - /* Builtin functions */ double sqrt(doublereal); - - /* Local variables */ integer n1, n2; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer iinfo; - extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, - integer *, integer *, doublereal *, doublereal *, integer *, - doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + extern int dtrsm_(char *, char *, char *, char *, integer *, integer *, doublereal *, + doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, + ftnlen); logical upper; - extern /* Subroutine */ int dsyrk_(char *, char *, integer *, integer *, - doublereal *, doublereal *, integer *, doublereal *, doublereal *, - integer *, ftnlen, ftnlen); + extern int dsyrk_(char *, char *, integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, doublereal *, integer *, ftnlen, ftnlen); extern logical disnan_(doublereal *); - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters */ - - /* Parameter adjustments */ + extern int xerbla_(char *, integer *, ftnlen); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; - - /* Function Body */ *info = 0; upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); - if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + if (!upper && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { *info = -1; } else if (*n < 0) { *info = -2; - } else if (*lda < max(1,*n)) { + } else if (*lda < max(1, *n)) { *info = -4; } if (*info != 0) { @@ -193,81 +36,39 @@ static doublereal c_b11 = -1.; xerbla_((char *)"DPOTRF2", &i__1, (ftnlen)7); return 0; } - -/* Quick return if possible */ - if (*n == 0) { return 0; } - -/* N=1 case */ - if (*n == 1) { - -/* Test for non-positive-definiteness */ - if (a[a_dim1 + 1] <= 0. || disnan_(&a[a_dim1 + 1])) { *info = 1; return 0; } - -/* Factor */ - a[a_dim1 + 1] = sqrt(a[a_dim1 + 1]); - -/* Use recursive code */ - } else { n1 = *n / 2; n2 = *n - n1; - -/* Factor A11 */ - dpotrf2_(uplo, &n1, &a[a_dim1 + 1], lda, &iinfo, (ftnlen)1); if (iinfo != 0) { *info = iinfo; return 0; } - -/* Compute the Cholesky factorization A = U**T*U */ - if (upper) { - -/* Update and scale A12 */ - - dtrsm_((char *)"L", (char *)"U", (char *)"T", (char *)"N", &n1, &n2, &c_b9, &a[a_dim1 + 1], lda, & - a[(n1 + 1) * a_dim1 + 1], lda, (ftnlen)1, (ftnlen)1, ( - ftnlen)1, (ftnlen)1); - -/* Update and factor A22 */ - - dsyrk_(uplo, (char *)"T", &n2, &n1, &c_b11, &a[(n1 + 1) * a_dim1 + 1], - lda, &c_b9, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, (ftnlen) - 1, (ftnlen)1); - dpotrf2_(uplo, &n2, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, &iinfo, ( - ftnlen)1); + dtrsm_((char *)"L", (char *)"U", (char *)"T", (char *)"N", &n1, &n2, &c_b9, &a[a_dim1 + 1], lda, + &a[(n1 + 1) * a_dim1 + 1], lda, (ftnlen)1, (ftnlen)1, (ftnlen)1, (ftnlen)1); + dsyrk_(uplo, (char *)"T", &n2, &n1, &c_b11, &a[(n1 + 1) * a_dim1 + 1], lda, &c_b9, + &a[n1 + 1 + (n1 + 1) * a_dim1], lda, (ftnlen)1, (ftnlen)1); + dpotrf2_(uplo, &n2, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, &iinfo, (ftnlen)1); if (iinfo != 0) { *info = iinfo + n1; return 0; } - -/* Compute the Cholesky factorization A = L*L**T */ - } else { - -/* Update and scale A21 */ - - dtrsm_((char *)"R", (char *)"L", (char *)"T", (char *)"N", &n2, &n1, &c_b9, &a[a_dim1 + 1], lda, & - a[n1 + 1 + a_dim1], lda, (ftnlen)1, (ftnlen)1, (ftnlen)1, - (ftnlen)1); - -/* Update and factor A22 */ - - dsyrk_(uplo, (char *)"N", &n2, &n1, &c_b11, &a[n1 + 1 + a_dim1], lda, & - c_b9, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, (ftnlen)1, ( - ftnlen)1); - dpotrf2_(uplo, &n2, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, &iinfo, ( - ftnlen)1); + dtrsm_((char *)"R", (char *)"L", (char *)"T", (char *)"N", &n2, &n1, &c_b9, &a[a_dim1 + 1], lda, &a[n1 + 1 + a_dim1], + lda, (ftnlen)1, (ftnlen)1, (ftnlen)1, (ftnlen)1); + dsyrk_(uplo, (char *)"N", &n2, &n1, &c_b11, &a[n1 + 1 + a_dim1], lda, &c_b9, + &a[n1 + 1 + (n1 + 1) * a_dim1], lda, (ftnlen)1, (ftnlen)1); + dpotrf2_(uplo, &n2, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, &iinfo, (ftnlen)1); if (iinfo != 0) { *info = iinfo + n1; return 0; @@ -275,11 +76,7 @@ static doublereal c_b11 = -1.; } } return 0; - -/* End of DPOTRF2 */ - -} /* dpotrf2_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dpotrs.cpp b/lib/linalg/dpotrs.cpp index c8cc0e0d68..c9ccf42f6d 100644 --- a/lib/linalg/dpotrs.cpp +++ b/lib/linalg/dpotrs.cpp @@ -1,196 +1,35 @@ -/* fortran/dpotrs.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static doublereal c_b9 = 1.; - -/* > \brief \b DPOTRS */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DPOTRS + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DPOTRS( UPLO, N, NRHS, A, LDA, B, LDB, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER UPLO */ -/* INTEGER INFO, LDA, LDB, N, NRHS */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), B( LDB, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DPOTRS solves a system of linear equations A*X = B with a symmetric */ -/* > positive definite matrix A using the Cholesky factorization */ -/* > A = U**T*U or A = L*L**T computed by DPOTRF. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > = 'U': Upper triangle of A is stored; */ -/* > = 'L': Lower triangle of A is stored. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] NRHS */ -/* > \verbatim */ -/* > NRHS is INTEGER */ -/* > The number of right hand sides, i.e., the number of columns */ -/* > of the matrix B. NRHS >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > The triangular factor U or L from the Cholesky factorization */ -/* > A = U**T*U or A = L*L**T, as computed by DPOTRF. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] B */ -/* > \verbatim */ -/* > B is DOUBLE PRECISION array, dimension (LDB,NRHS) */ -/* > On entry, the right hand side matrix B. */ -/* > On exit, the solution matrix X. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDB */ -/* > \verbatim */ -/* > LDB is INTEGER */ -/* > The leading dimension of the array B. LDB >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doublePOcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dpotrs_(char *uplo, integer *n, integer *nrhs, - doublereal *a, integer *lda, doublereal *b, integer *ldb, integer * - info, ftnlen uplo_len) +int dpotrs_(char *uplo, integer *n, integer *nrhs, doublereal *a, integer *lda, doublereal *b, + integer *ldb, integer *info, ftnlen uplo_len) { - /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1; - - /* Local variables */ extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, - integer *, integer *, doublereal *, doublereal *, integer *, - doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + extern int dtrsm_(char *, char *, char *, char *, integer *, integer *, doublereal *, + doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, + ftnlen); logical upper; - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ + extern int xerbla_(char *, integer *, ftnlen); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; - - /* Function Body */ *info = 0; upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); - if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + if (!upper && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*nrhs < 0) { *info = -3; - } else if (*lda < max(1,*n)) { + } else if (*lda < max(1, *n)) { *info = -5; - } else if (*ldb < max(1,*n)) { + } else if (*ldb < max(1, *n)) { *info = -7; } if (*info != 0) { @@ -198,51 +37,22 @@ f"> */ xerbla_((char *)"DPOTRS", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*n == 0 || *nrhs == 0) { return 0; } - if (upper) { - -/* Solve A*X = B where A = U**T *U. */ - -/* Solve U**T *X = B, overwriting B with X. */ - - dtrsm_((char *)"Left", (char *)"Upper", (char *)"Transpose", (char *)"Non-unit", n, nrhs, &c_b9, &a[ - a_offset], lda, &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, ( - ftnlen)9, (ftnlen)8); - -/* Solve U*X = B, overwriting B with X. */ - - dtrsm_((char *)"Left", (char *)"Upper", (char *)"No transpose", (char *)"Non-unit", n, nrhs, &c_b9, & - a[a_offset], lda, &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, ( - ftnlen)12, (ftnlen)8); + dtrsm_((char *)"Left", (char *)"Upper", (char *)"Transpose", (char *)"Non-unit", n, nrhs, &c_b9, &a[a_offset], lda, + &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, (ftnlen)9, (ftnlen)8); + dtrsm_((char *)"Left", (char *)"Upper", (char *)"No transpose", (char *)"Non-unit", n, nrhs, &c_b9, &a[a_offset], lda, + &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, (ftnlen)12, (ftnlen)8); } else { - -/* Solve A*X = B where A = L*L**T. */ - -/* Solve L*X = B, overwriting B with X. */ - - dtrsm_((char *)"Left", (char *)"Lower", (char *)"No transpose", (char *)"Non-unit", n, nrhs, &c_b9, & - a[a_offset], lda, &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, ( - ftnlen)12, (ftnlen)8); - -/* Solve L**T *X = B, overwriting B with X. */ - - dtrsm_((char *)"Left", (char *)"Lower", (char *)"Transpose", (char *)"Non-unit", n, nrhs, &c_b9, &a[ - a_offset], lda, &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, ( - ftnlen)9, (ftnlen)8); + dtrsm_((char *)"Left", (char *)"Lower", (char *)"No transpose", (char *)"Non-unit", n, nrhs, &c_b9, &a[a_offset], lda, + &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, (ftnlen)12, (ftnlen)8); + dtrsm_((char *)"Left", (char *)"Lower", (char *)"Transpose", (char *)"Non-unit", n, nrhs, &c_b9, &a[a_offset], lda, + &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, (ftnlen)9, (ftnlen)8); } - return 0; - -/* End of DPOTRS */ - -} /* dpotrs_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/drot.cpp b/lib/linalg/drot.cpp index 1ed9c47a89..aabbf00356 100644 --- a/lib/linalg/drot.cpp +++ b/lib/linalg/drot.cpp @@ -1,146 +1,19 @@ -/* fortran/drot.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DROT */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DROT(N,DX,INCX,DY,INCY,C,S) */ - -/* .. Scalar Arguments .. */ -/* DOUBLE PRECISION C,S */ -/* INTEGER INCX,INCY,N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION DX(*),DY(*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DROT applies a plane rotation. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > number of elements in input vector(s) */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] DX */ -/* > \verbatim */ -/* > DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > storage spacing between elements of DX */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] DY */ -/* > \verbatim */ -/* > DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCY */ -/* > \verbatim */ -/* > INCY is INTEGER */ -/* > storage spacing between elements of DY */ -/* > \endverbatim */ -/* > */ -/* > \param[in] C */ -/* > \verbatim */ -/* > C is DOUBLE PRECISION */ -/* > \endverbatim */ -/* > */ -/* > \param[in] S */ -/* > \verbatim */ -/* > S is DOUBLE PRECISION */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup double_blas_level1 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > jack dongarra, linpack, 3/11/78. */ -/* > modified 12/3/93, array(1) declarations changed to array(*) */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int drot_(integer *n, doublereal *dx, integer *incx, - doublereal *dy, integer *incy, doublereal *c__, doublereal *s) +int drot_(integer *n, doublereal *dx, integer *incx, doublereal *dy, integer *incy, doublereal *c__, + doublereal *s) { - /* System generated locals */ integer i__1; - - /* Local variables */ integer i__, ix, iy; doublereal dtemp; - - -/* -- Reference BLAS level1 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Local Scalars .. */ -/* .. */ - /* Parameter adjustments */ --dy; --dx; - - /* Function Body */ if (*n <= 0) { return 0; } if (*incx == 1 && *incy == 1) { - -/* code for both increments equal to 1 */ - i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { dtemp = *c__ * dx[i__] + *s * dy[i__]; @@ -148,10 +21,6 @@ extern "C" { dx[i__] = dtemp; } } else { - -/* code for unequal increments or equal increments not equal */ -/* to 1 */ - ix = 1; iy = 1; if (*incx < 0) { @@ -170,11 +39,7 @@ extern "C" { } } return 0; - -/* End of DROT */ - -} /* drot_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/drscl.cpp b/lib/linalg/drscl.cpp index 10904c478f..90e278a709 100644 --- a/lib/linalg/drscl.cpp +++ b/lib/linalg/drscl.cpp @@ -1,200 +1,46 @@ -/* fortran/drscl.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DRSCL multiplies a vector by the reciprocal of a real scalar. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DRSCL + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DRSCL( N, SA, SX, INCX ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INCX, N */ -/* DOUBLE PRECISION SA */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION SX( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DRSCL multiplies an n-element real vector x by the real scalar 1/a. */ -/* > This is done without overflow or underflow as long as */ -/* > the final result x/a does not overflow or underflow. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of components of the vector x. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] SA */ -/* > \verbatim */ -/* > SA is DOUBLE PRECISION */ -/* > The scalar a which is used to divide each component of x. */ -/* > SA must be >= 0, or the subroutine will divide by zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] SX */ -/* > \verbatim */ -/* > SX is DOUBLE PRECISION array, dimension */ -/* > (1+(N-1)*abs(INCX)) */ -/* > The n-element vector x. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > The increment between successive values of the vector SX. */ -/* > > 0: SX(1) = X(1) and SX(1+(i-1)*INCX) = x(i), 1< i<= n */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleOTHERauxiliary */ - -/* ===================================================================== */ -/* Subroutine */ int drscl_(integer *n, doublereal *sa, doublereal *sx, - integer *incx) +int drscl_(integer *n, doublereal *sa, doublereal *sx, integer *incx) { doublereal mul, cden; logical done; doublereal cnum, cden1, cnum1; - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *), dlabad_(doublereal *, doublereal *); + extern int dscal_(integer *, doublereal *, doublereal *, integer *), + dlabad_(doublereal *, doublereal *); extern doublereal dlamch_(char *, ftnlen); doublereal bignum, smlnum; - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Quick return if possible */ - - /* Parameter adjustments */ --sx; - - /* Function Body */ if (*n <= 0) { return 0; } - -/* Get machine parameters */ - smlnum = dlamch_((char *)"S", (ftnlen)1); bignum = 1. / smlnum; dlabad_(&smlnum, &bignum); - -/* Initialize the denominator to SA and the numerator to 1. */ - cden = *sa; cnum = 1.; - L10: cden1 = cden * smlnum; cnum1 = cnum / bignum; if (abs(cden1) > abs(cnum) && cnum != 0.) { - -/* Pre-multiply X by SMLNUM if CDEN is large compared to CNUM. */ - mul = smlnum; done = FALSE_; cden = cden1; } else if (abs(cnum1) > abs(cden)) { - -/* Pre-multiply X by BIGNUM if CDEN is small compared to CNUM. */ - mul = bignum; done = FALSE_; cnum = cnum1; } else { - -/* Multiply X by CNUM / CDEN and return. */ - mul = cnum / cden; done = TRUE_; } - -/* Scale the vector X by MUL */ - dscal_(n, &mul, &sx[1], incx); - - if (! done) { + if (!done) { goto L10; } - return 0; - -/* End of DRSCL */ - -} /* drscl_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dscal.cpp b/lib/linalg/dscal.cpp index e141f7352b..321aedfd73 100644 --- a/lib/linalg/dscal.cpp +++ b/lib/linalg/dscal.cpp @@ -1,137 +1,16 @@ -/* fortran/dscal.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DSCAL */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DSCAL(N,DA,DX,INCX) */ - -/* .. Scalar Arguments .. */ -/* DOUBLE PRECISION DA */ -/* INTEGER INCX,N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION DX(*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DSCAL scales a vector by a constant. */ -/* > uses unrolled loops for increment equal to 1. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > number of elements in input vector(s) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DA */ -/* > \verbatim */ -/* > DA is DOUBLE PRECISION */ -/* > On entry, DA specifies the scalar alpha. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] DX */ -/* > \verbatim */ -/* > DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > storage spacing between elements of DX */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup double_blas_level1 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > jack dongarra, linpack, 3/11/78. */ -/* > modified 3/93 to return if incx .le. 0. */ -/* > modified 12/3/93, array(1) declarations changed to array(*) */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dscal_(integer *n, doublereal *da, doublereal *dx, - integer *incx) +int dscal_(integer *n, doublereal *da, doublereal *dx, integer *incx) { - /* System generated locals */ integer i__1, i__2; - - /* Local variables */ integer i__, m, mp1, nincx; - - -/* -- Reference BLAS level1 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Local Scalars .. */ -/* .. Parameters .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ - /* Parameter adjustments */ --dx; - - /* Function Body */ if (*n <= 0 || *incx <= 0 || *da == 1.) { return 0; } if (*incx == 1) { - -/* code for increment equal to 1 */ - - -/* clean-up loop */ - m = *n % 5; if (m != 0) { i__1 = m; @@ -152,9 +31,6 @@ extern "C" { dx[i__ + 4] = *da * dx[i__ + 4]; } } else { - -/* code for increment not equal to 1 */ - nincx = *n * *incx; i__1 = nincx; i__2 = *incx; @@ -163,11 +39,7 @@ extern "C" { } } return 0; - -/* End of DSCAL */ - -} /* dscal_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dstedc.cpp b/lib/linalg/dstedc.cpp index 1a55346056..136723dde7 100644 --- a/lib/linalg/dstedc.cpp +++ b/lib/linalg/dstedc.cpp @@ -1,298 +1,55 @@ -/* fortran/dstedc.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__9 = 9; static integer c__0 = 0; static integer c__2 = 2; static doublereal c_b17 = 0.; static doublereal c_b18 = 1.; static integer c__1 = 1; - -/* > \brief \b DSTEDC */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DSTEDC + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, */ -/* LIWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER COMPZ */ -/* INTEGER INFO, LDZ, LIWORK, LWORK, N */ -/* .. */ -/* .. Array Arguments .. */ -/* INTEGER IWORK( * ) */ -/* DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DSTEDC computes all eigenvalues and, optionally, eigenvectors of a */ -/* > symmetric tridiagonal matrix using the divide and conquer method. */ -/* > The eigenvectors of a full or band real symmetric matrix can also be */ -/* > found if DSYTRD or DSPTRD or DSBTRD has been used to reduce this */ -/* > matrix to tridiagonal form. */ -/* > */ -/* > This code makes very mild assumptions about floating point */ -/* > arithmetic. It will work on machines with a guard digit in */ -/* > add/subtract, or on those binary machines without guard digits */ -/* > which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. */ -/* > It could conceivably fail on hexadecimal or decimal machines */ -/* > without guard digits, but we know of none. See DLAED3 for details. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] COMPZ */ -/* > \verbatim */ -/* > COMPZ is CHARACTER*1 */ -/* > = 'N': Compute eigenvalues only. */ -/* > = 'I': Compute eigenvectors of tridiagonal matrix also. */ -/* > = 'V': Compute eigenvectors of original dense symmetric */ -/* > matrix also. On entry, Z contains the orthogonal */ -/* > matrix used to reduce the original matrix to */ -/* > tridiagonal form. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The dimension of the symmetric tridiagonal matrix. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension (N) */ -/* > On entry, the diagonal elements of the tridiagonal matrix. */ -/* > On exit, if INFO = 0, the eigenvalues in ascending order. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] E */ -/* > \verbatim */ -/* > E is DOUBLE PRECISION array, dimension (N-1) */ -/* > On entry, the subdiagonal elements of the tridiagonal matrix. */ -/* > On exit, E has been destroyed. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] Z */ -/* > \verbatim */ -/* > Z is DOUBLE PRECISION array, dimension (LDZ,N) */ -/* > On entry, if COMPZ = 'V', then Z contains the orthogonal */ -/* > matrix used in the reduction to tridiagonal form. */ -/* > On exit, if INFO = 0, then if COMPZ = 'V', Z contains the */ -/* > orthonormal eigenvectors of the original symmetric matrix, */ -/* > and if COMPZ = 'I', Z contains the orthonormal eigenvectors */ -/* > of the symmetric tridiagonal matrix. */ -/* > If COMPZ = 'N', then Z is not referenced. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDZ */ -/* > \verbatim */ -/* > LDZ is INTEGER */ -/* > The leading dimension of the array Z. LDZ >= 1. */ -/* > If eigenvectors are desired, then LDZ >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ -/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LWORK */ -/* > \verbatim */ -/* > LWORK is INTEGER */ -/* > The dimension of the array WORK. */ -/* > If COMPZ = 'N' or N <= 1 then LWORK must be at least 1. */ -/* > If COMPZ = 'V' and N > 1 then LWORK must be at least */ -/* > ( 1 + 3*N + 2*N*lg N + 4*N**2 ), */ -/* > where lg( N ) = smallest integer k such */ -/* > that 2**k >= N. */ -/* > If COMPZ = 'I' and N > 1 then LWORK must be at least */ -/* > ( 1 + 4*N + N**2 ). */ -/* > Note that for COMPZ = 'I' or 'V', then if N is less than or */ -/* > equal to the minimum divide size, usually 25, then LWORK need */ -/* > only be max(1,2*(N-1)). */ -/* > */ -/* > If LWORK = -1, then a workspace query is assumed; the routine */ -/* > only calculates the optimal size of the WORK array, returns */ -/* > this value as the first entry of the WORK array, and no error */ -/* > message related to LWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] IWORK */ -/* > \verbatim */ -/* > IWORK is INTEGER array, dimension (MAX(1,LIWORK)) */ -/* > On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LIWORK */ -/* > \verbatim */ -/* > LIWORK is INTEGER */ -/* > The dimension of the array IWORK. */ -/* > If COMPZ = 'N' or N <= 1 then LIWORK must be at least 1. */ -/* > If COMPZ = 'V' and N > 1 then LIWORK must be at least */ -/* > ( 6 + 6*N + 5*N*lg N ). */ -/* > If COMPZ = 'I' and N > 1 then LIWORK must be at least */ -/* > ( 3 + 5*N ). */ -/* > Note that for COMPZ = 'I' or 'V', then if N is less than or */ -/* > equal to the minimum divide size, usually 25, then LIWORK */ -/* > need only be 1. */ -/* > */ -/* > If LIWORK = -1, then a workspace query is assumed; the */ -/* > routine only calculates the optimal size of the IWORK array, */ -/* > returns this value as the first entry of the IWORK array, and */ -/* > no error message related to LIWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit. */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ -/* > > 0: The algorithm failed to compute an eigenvalue while */ -/* > working on the submatrix lying in rows and columns */ -/* > INFO/(N+1) through mod(INFO,N+1). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup auxOTHERcomputational */ - -/* > \par Contributors: */ -/* ================== */ -/* > */ -/* > Jeff Rutter, Computer Science Division, University of California */ -/* > at Berkeley, USA \n */ -/* > Modified by Francoise Tisseur, University of Tennessee */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dstedc_(char *compz, integer *n, doublereal *d__, - doublereal *e, doublereal *z__, integer *ldz, doublereal *work, - integer *lwork, integer *iwork, integer *liwork, integer *info, - ftnlen compz_len) +int dstedc_(char *compz, integer *n, doublereal *d__, doublereal *e, doublereal *z__, integer *ldz, + doublereal *work, integer *lwork, integer *iwork, integer *liwork, integer *info, + ftnlen compz_len) { - /* System generated locals */ integer z_dim1, z_offset, i__1, i__2; doublereal d__1, d__2; - - /* Builtin functions */ double log(doublereal); integer pow_lmp_ii(integer *, integer *); double sqrt(doublereal); - - /* Local variables */ integer i__, j, k, m; doublereal p; integer ii, lgn; doublereal eps, tiny; - extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); + extern int dgemm_(char *, char *, integer *, integer *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, + ftnlen, ftnlen); extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, - doublereal *, integer *); + extern int dswap_(integer *, doublereal *, integer *, doublereal *, integer *); integer lwmin; - extern /* Subroutine */ int dlaed0_(integer *, integer *, integer *, - doublereal *, doublereal *, doublereal *, integer *, doublereal *, - integer *, doublereal *, integer *, integer *); + extern int dlaed0_(integer *, integer *, integer *, doublereal *, doublereal *, doublereal *, + integer *, doublereal *, integer *, doublereal *, integer *, integer *); integer start; extern doublereal dlamch_(char *, ftnlen); - extern /* Subroutine */ int dlascl_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, integer *, doublereal *, - integer *, integer *, ftnlen), dlacpy_(char *, integer *, integer - *, doublereal *, integer *, doublereal *, integer *, ftnlen), - dlaset_(char *, integer *, integer *, doublereal *, doublereal *, - doublereal *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern int dlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, + integer *, doublereal *, integer *, integer *, ftnlen), + dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, + ftnlen), + dlaset_(char *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, + ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); + extern int xerbla_(char *, integer *, ftnlen); integer finish; - extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *, - ftnlen); - extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *, - integer *), dlasrt_(char *, integer *, doublereal *, integer *, - ftnlen); + extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *, ftnlen); + extern int dsterf_(integer *, doublereal *, doublereal *, integer *), + dlasrt_(char *, integer *, doublereal *, integer *, ftnlen); integer liwmin, icompz; - extern /* Subroutine */ int dsteqr_(char *, integer *, doublereal *, - doublereal *, doublereal *, integer *, doublereal *, integer *, - ftnlen); + extern int dsteqr_(char *, integer *, doublereal *, doublereal *, doublereal *, integer *, + doublereal *, integer *, ftnlen); doublereal orgnrm; logical lquery; integer smlsiz, storez, strtrw; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ --d__; --e; z_dim1 = *ldz; @@ -300,11 +57,8 @@ f"> */ z__ -= z_offset; --work; --iwork; - - /* Function Body */ *info = 0; lquery = *lwork == -1 || *liwork == -1; - if (lsame_(compz, (char *)"N", (ftnlen)1, (ftnlen)1)) { icompz = 0; } else if (lsame_(compz, (char *)"V", (ftnlen)1, (ftnlen)1)) { @@ -318,16 +72,11 @@ f"> */ *info = -1; } else if (*n < 0) { *info = -2; - } else if (*ldz < 1 || icompz > 0 && *ldz < max(1,*n)) { + } else if (*ldz < 1 || icompz > 0 && *ldz < max(1, *n)) { *info = -6; } - if (*info == 0) { - -/* Compute the workspace requirements */ - - smlsiz = ilaenv_(&c__9, (char *)"DSTEDC", (char *)" ", &c__0, &c__0, &c__0, &c__0, ( - ftnlen)6, (ftnlen)1); + smlsiz = ilaenv_(&c__9, (char *)"DSTEDC", (char *)" ", &c__0, &c__0, &c__0, &c__0, (ftnlen)6, (ftnlen)1); if (*n <= 1 || icompz == 0) { liwmin = 1; lwmin = 1; @@ -335,7 +84,7 @@ f"> */ liwmin = 1; lwmin = *n - 1 << 1; } else { - lgn = (integer) (log((doublereal) (*n)) / log(2.)); + lgn = (integer)(log((doublereal)(*n)) / log(2.)); if (pow_lmp_ii(&c__2, &lgn) < *n) { ++lgn; } @@ -343,27 +92,23 @@ f"> */ ++lgn; } if (icompz == 1) { -/* Computing 2nd power */ i__1 = *n; lwmin = *n * 3 + 1 + (*n << 1) * lgn + (i__1 * i__1 << 2); liwmin = *n * 6 + 6 + *n * 5 * lgn; } else if (icompz == 2) { -/* Computing 2nd power */ i__1 = *n; lwmin = (*n << 2) + 1 + i__1 * i__1; liwmin = *n * 5 + 3; } } - work[1] = (doublereal) lwmin; + work[1] = (doublereal)lwmin; iwork[1] = liwmin; - - if (*lwork < lwmin && ! lquery) { + if (*lwork < lwmin && !lquery) { *info = -8; - } else if (*liwork < liwmin && ! lquery) { + } else if (*liwork < liwmin && !lquery) { *info = -10; } } - if (*info != 0) { i__1 = -(*info); xerbla_((char *)"DSTEDC", &i__1, (ftnlen)6); @@ -371,9 +116,6 @@ f"> */ } else if (lquery) { return 0; } - -/* Quick return if possible */ - if (*n == 0) { return 0; } @@ -383,135 +125,75 @@ f"> */ } return 0; } - -/* If the following conditional clause is removed, then the routine */ -/* will use the Divide and Conquer routine to compute only the */ -/* eigenvalues, which requires (3N + 3N**2) real workspace and */ -/* (2 + 5N + 2N lg(N)) integer workspace. */ -/* Since on many architectures DSTERF is much faster than any other */ -/* algorithm for finding eigenvalues only, it is used here */ -/* as the default. If the conditional clause is removed, then */ -/* information on the size of workspace needs to be changed. */ - -/* If COMPZ = 'N', use DSTERF to compute the eigenvalues. */ - if (icompz == 0) { dsterf_(n, &d__[1], &e[1], info); goto L50; } - -/* If N is smaller than the minimum divide size (SMLSIZ+1), then */ -/* solve the problem with another solver. */ - if (*n <= smlsiz) { - - dsteqr_(compz, n, &d__[1], &e[1], &z__[z_offset], ldz, &work[1], info, - (ftnlen)1); - + dsteqr_(compz, n, &d__[1], &e[1], &z__[z_offset], ldz, &work[1], info, (ftnlen)1); } else { - -/* If COMPZ = 'V', the Z matrix must be stored elsewhere for later */ -/* use. */ - if (icompz == 1) { storez = *n * *n + 1; } else { storez = 1; } - if (icompz == 2) { - dlaset_((char *)"Full", n, n, &c_b17, &c_b18, &z__[z_offset], ldz, ( - ftnlen)4); + dlaset_((char *)"Full", n, n, &c_b17, &c_b18, &z__[z_offset], ldz, (ftnlen)4); } - -/* Scale. */ - orgnrm = dlanst_((char *)"M", n, &d__[1], &e[1], (ftnlen)1); if (orgnrm == 0.) { goto L50; } - eps = dlamch_((char *)"Epsilon", (ftnlen)7); - start = 1; - -/* while ( START <= N ) */ - -L10: + L10: if (start <= *n) { - -/* Let FINISH be the position of the next subdiagonal entry */ -/* such that E( FINISH ) <= TINY or FINISH = N if no such */ -/* subdiagonal exists. The matrix identified by the elements */ -/* between START and FINISH constitutes an independent */ -/* sub-problem. */ - finish = start; -L20: + L20: if (finish < *n) { - tiny = eps * sqrt((d__1 = d__[finish], abs(d__1))) * sqrt(( - d__2 = d__[finish + 1], abs(d__2))); + tiny = eps * sqrt((d__1 = d__[finish], abs(d__1))) * + sqrt((d__2 = d__[finish + 1], abs(d__2))); if ((d__1 = e[finish], abs(d__1)) > tiny) { ++finish; goto L20; } } - -/* (Sub) Problem determined. Compute its size and solve it. */ - m = finish - start + 1; if (m == 1) { start = finish + 1; goto L10; } if (m > smlsiz) { - -/* Scale. */ - orgnrm = dlanst_((char *)"M", &m, &d__[start], &e[start], (ftnlen)1); - dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b18, &m, &c__1, &d__[ - start], &m, info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b18, &m, &c__1, &d__[start], &m, info, + (ftnlen)1); i__1 = m - 1; i__2 = m - 1; - dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b18, &i__1, &c__1, &e[ - start], &i__2, info, (ftnlen)1); - + dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b18, &i__1, &c__1, &e[start], &i__2, info, + (ftnlen)1); if (icompz == 1) { strtrw = 1; } else { strtrw = start; } - dlaed0_(&icompz, n, &m, &d__[start], &e[start], &z__[strtrw + - start * z_dim1], ldz, &work[1], n, &work[storez], & - iwork[1], info); + dlaed0_(&icompz, n, &m, &d__[start], &e[start], &z__[strtrw + start * z_dim1], ldz, + &work[1], n, &work[storez], &iwork[1], info); if (*info != 0) { - *info = (*info / (m + 1) + start - 1) * (*n + 1) + *info % - (m + 1) + start - 1; + *info = (*info / (m + 1) + start - 1) * (*n + 1) + *info % (m + 1) + start - 1; goto L50; } - -/* Scale back. */ - - dlascl_((char *)"G", &c__0, &c__0, &c_b18, &orgnrm, &m, &c__1, &d__[ - start], &m, info, (ftnlen)1); - + dlascl_((char *)"G", &c__0, &c__0, &c_b18, &orgnrm, &m, &c__1, &d__[start], &m, info, + (ftnlen)1); } else { if (icompz == 1) { - -/* Since QR won't update a Z matrix which is larger than */ -/* the length of D, we must solve the sub-problem in a */ -/* workspace and then multiply back into Z. */ - - dsteqr_((char *)"I", &m, &d__[start], &e[start], &work[1], &m, & - work[m * m + 1], info, (ftnlen)1); - dlacpy_((char *)"A", n, &m, &z__[start * z_dim1 + 1], ldz, &work[ - storez], n, (ftnlen)1); - dgemm_((char *)"N", (char *)"N", n, &m, &m, &c_b18, &work[storez], n, & - work[1], &m, &c_b17, &z__[start * z_dim1 + 1], - ldz, (ftnlen)1, (ftnlen)1); + dsteqr_((char *)"I", &m, &d__[start], &e[start], &work[1], &m, &work[m * m + 1], info, + (ftnlen)1); + dlacpy_((char *)"A", n, &m, &z__[start * z_dim1 + 1], ldz, &work[storez], n, (ftnlen)1); + dgemm_((char *)"N", (char *)"N", n, &m, &m, &c_b18, &work[storez], n, &work[1], &m, &c_b17, + &z__[start * z_dim1 + 1], ldz, (ftnlen)1, (ftnlen)1); } else if (icompz == 2) { - dsteqr_((char *)"I", &m, &d__[start], &e[start], &z__[start + - start * z_dim1], ldz, &work[1], info, (ftnlen)1); + dsteqr_((char *)"I", &m, &d__[start], &e[start], &z__[start + start * z_dim1], ldz, + &work[1], info, (ftnlen)1); } else { dsterf_(&m, &d__[start], &e[start], info); } @@ -520,23 +202,12 @@ L20: goto L50; } } - start = finish + 1; goto L10; } - -/* endwhile */ - if (icompz == 0) { - -/* Use Quick Sort */ - dlasrt_((char *)"I", n, &d__[1], info, (ftnlen)1); - } else { - -/* Use Selection Sort to minimize swaps of eigenvectors */ - i__1 = *n; for (ii = 2; ii <= i__1; ++ii) { i__ = ii - 1; @@ -548,29 +219,20 @@ L20: k = j; p = d__[j]; } -/* L30: */ } if (k != i__) { d__[k] = d__[i__]; d__[i__] = p; - dswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1 - + 1], &c__1); + dswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1 + 1], &c__1); } -/* L40: */ } } } - L50: - work[1] = (doublereal) lwmin; + work[1] = (doublereal)lwmin; iwork[1] = liwmin; - return 0; - -/* End of DSTEDC */ - -} /* dstedc_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dsteqr.cpp b/lib/linalg/dsteqr.cpp index 2f590595e7..4a611d4102 100644 --- a/lib/linalg/dsteqr.cpp +++ b/lib/linalg/dsteqr.cpp @@ -1,172 +1,18 @@ -/* fortran/dsteqr.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static doublereal c_b9 = 0.; static doublereal c_b10 = 1.; static integer c__0 = 0; static integer c__1 = 1; static integer c__2 = 2; - -/* > \brief \b DSTEQR */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DSTEQR + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER COMPZ */ -/* INTEGER INFO, LDZ, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DSTEQR computes all eigenvalues and, optionally, eigenvectors of a */ -/* > symmetric tridiagonal matrix using the implicit QL or QR method. */ -/* > The eigenvectors of a full or band symmetric matrix can also be found */ -/* > if DSYTRD or DSPTRD or DSBTRD has been used to reduce this matrix to */ -/* > tridiagonal form. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] COMPZ */ -/* > \verbatim */ -/* > COMPZ is CHARACTER*1 */ -/* > = 'N': Compute eigenvalues only. */ -/* > = 'V': Compute eigenvalues and eigenvectors of the original */ -/* > symmetric matrix. On entry, Z must contain the */ -/* > orthogonal matrix used to reduce the original matrix */ -/* > to tridiagonal form. */ -/* > = 'I': Compute eigenvalues and eigenvectors of the */ -/* > tridiagonal matrix. Z is initialized to the identity */ -/* > matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrix. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension (N) */ -/* > On entry, the diagonal elements of the tridiagonal matrix. */ -/* > On exit, if INFO = 0, the eigenvalues in ascending order. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] E */ -/* > \verbatim */ -/* > E is DOUBLE PRECISION array, dimension (N-1) */ -/* > On entry, the (n-1) subdiagonal elements of the tridiagonal */ -/* > matrix. */ -/* > On exit, E has been destroyed. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] Z */ -/* > \verbatim */ -/* > Z is DOUBLE PRECISION array, dimension (LDZ, N) */ -/* > On entry, if COMPZ = 'V', then Z contains the orthogonal */ -/* > matrix used in the reduction to tridiagonal form. */ -/* > On exit, if INFO = 0, then if COMPZ = 'V', Z contains the */ -/* > orthonormal eigenvectors of the original symmetric matrix, */ -/* > and if COMPZ = 'I', Z contains the orthonormal eigenvectors */ -/* > of the symmetric tridiagonal matrix. */ -/* > If COMPZ = 'N', then Z is not referenced. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDZ */ -/* > \verbatim */ -/* > LDZ is INTEGER */ -/* > The leading dimension of the array Z. LDZ >= 1, and if */ -/* > eigenvectors are desired, then LDZ >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (max(1,2*N-2)) */ -/* > If COMPZ = 'N', then WORK is not referenced. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > > 0: the algorithm has failed to find all the eigenvalues in */ -/* > a total of 30*N iterations; if INFO = i, then i */ -/* > elements of E have not converged to zero; on exit, D */ -/* > and E contain the elements of a symmetric tridiagonal */ -/* > matrix which is orthogonally similar to the original */ -/* > matrix. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup auxOTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dsteqr_(char *compz, integer *n, doublereal *d__, - doublereal *e, doublereal *z__, integer *ldz, doublereal *work, - integer *info, ftnlen compz_len) +int dsteqr_(char *compz, integer *n, doublereal *d__, doublereal *e, doublereal *z__, integer *ldz, + doublereal *work, integer *info, ftnlen compz_len) { - /* System generated locals */ integer z_dim1, z_offset, i__1, i__2; doublereal d__1, d__2; - - /* Builtin functions */ double sqrt(doublereal), d_lmp_sign(doublereal *, doublereal *); - - /* Local variables */ doublereal b, c__, f, g; integer i__, j, k, l, m; doublereal p, r__, s; @@ -175,76 +21,38 @@ f"> */ integer lsv; doublereal tst, eps2; integer lend, jtot; - extern /* Subroutine */ int dlae2_(doublereal *, doublereal *, doublereal - *, doublereal *, doublereal *); + extern int dlae2_(doublereal *, doublereal *, doublereal *, doublereal *, doublereal *); extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int dlasr_(char *, char *, char *, integer *, - integer *, doublereal *, doublereal *, doublereal *, integer *, - ftnlen, ftnlen, ftnlen); + extern int dlasr_(char *, char *, char *, integer *, integer *, doublereal *, doublereal *, + doublereal *, integer *, ftnlen, ftnlen, ftnlen); doublereal anorm; - extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, - doublereal *, integer *), dlaev2_(doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *, doublereal *, - doublereal *); + extern int dswap_(integer *, doublereal *, integer *, doublereal *, integer *), + dlaev2_(doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *); integer lendm1, lendp1; - extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, - ftnlen); + extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, ftnlen); integer iscale; - extern /* Subroutine */ int dlascl_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, integer *, doublereal *, - integer *, integer *, ftnlen), dlaset_(char *, integer *, integer - *, doublereal *, doublereal *, doublereal *, integer *, ftnlen); + extern int dlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, + integer *, doublereal *, integer *, integer *, ftnlen), + dlaset_(char *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, + ftnlen); doublereal safmin; - extern /* Subroutine */ int dlartg_(doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *); + extern int dlartg_(doublereal *, doublereal *, doublereal *, doublereal *, doublereal *); doublereal safmax; - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *, - ftnlen); - extern /* Subroutine */ int dlasrt_(char *, integer *, doublereal *, - integer *, ftnlen); + extern int xerbla_(char *, integer *, ftnlen); + extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *, ftnlen); + extern int dlasrt_(char *, integer *, doublereal *, integer *, ftnlen); integer lendsv; doublereal ssfmin; integer nmaxit, icompz; doublereal ssfmax; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ --d__; --e; z_dim1 = *ldz; z_offset = 1 + z_dim1; z__ -= z_offset; --work; - - /* Function Body */ *info = 0; - if (lsame_(compz, (char *)"N", (ftnlen)1, (ftnlen)1)) { icompz = 0; } else if (lsame_(compz, (char *)"V", (ftnlen)1, (ftnlen)1)) { @@ -258,7 +66,7 @@ f"> */ *info = -1; } else if (*n < 0) { *info = -2; - } else if (*ldz < 1 || icompz > 0 && *ldz < max(1,*n)) { + } else if (*ldz < 1 || icompz > 0 && *ldz < max(1, *n)) { *info = -6; } if (*info != 0) { @@ -266,48 +74,29 @@ f"> */ xerbla_((char *)"DSTEQR", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*n == 0) { return 0; } - if (*n == 1) { if (icompz == 2) { z__[z_dim1 + 1] = 1.; } return 0; } - -/* Determine the unit roundoff and over/underflow thresholds. */ - eps = dlamch_((char *)"E", (ftnlen)1); -/* Computing 2nd power */ d__1 = eps; eps2 = d__1 * d__1; safmin = dlamch_((char *)"S", (ftnlen)1); safmax = 1. / safmin; ssfmax = sqrt(safmax) / 3.; ssfmin = sqrt(safmin) / eps2; - -/* Compute the eigenvalues and eigenvectors of the tridiagonal */ -/* matrix. */ - if (icompz == 2) { dlaset_((char *)"Full", n, n, &c_b9, &c_b10, &z__[z_offset], ldz, (ftnlen)4); } - nmaxit = *n * 30; jtot = 0; - -/* Determine where the matrix splits and choose QL or QR iteration */ -/* for each block, according to whether top or bottom diagonal */ -/* element is smaller. */ - l1 = 1; nm1 = *n - 1; - L10: if (l1 > *n) { goto L160; @@ -322,16 +111,14 @@ L10: if (tst == 0.) { goto L30; } - if (tst <= sqrt((d__1 = d__[m], abs(d__1))) * sqrt((d__2 = d__[m - + 1], abs(d__2))) * eps) { + if (tst <= + sqrt((d__1 = d__[m], abs(d__1))) * sqrt((d__2 = d__[m + 1], abs(d__2))) * eps) { e[m] = 0.; goto L30; } -/* L20: */ } } m = *n; - L30: l = l1; lsv = l; @@ -341,9 +128,6 @@ L30: if (lend == l) { goto L10; } - -/* Scale submatrix in rows and columns L to LEND */ - i__1 = lend - l + 1; anorm = dlanst_((char *)"M", &i__1, &d__[l], &e[l], (ftnlen)1); iscale = 0; @@ -353,53 +137,36 @@ L30: if (anorm > ssfmax) { iscale = 1; i__1 = lend - l + 1; - dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n, - info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n, info, (ftnlen)1); i__1 = lend - l; - dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &e[l], n, - info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &e[l], n, info, (ftnlen)1); } else if (anorm < ssfmin) { iscale = 2; i__1 = lend - l + 1; - dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n, - info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n, info, (ftnlen)1); i__1 = lend - l; - dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n, - info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n, info, (ftnlen)1); } - -/* Choose between QL and QR iteration */ - if ((d__1 = d__[lend], abs(d__1)) < (d__2 = d__[l], abs(d__2))) { lend = lsv; l = lendsv; } - if (lend > l) { - -/* QL Iteration */ - -/* Look for small subdiagonal element. */ - -L40: + L40: if (l != lend) { lendm1 = lend - 1; i__1 = lendm1; for (m = l; m <= i__1; ++m) { -/* Computing 2nd power */ d__2 = (d__1 = e[m], abs(d__1)); tst = d__2 * d__2; - if (tst <= eps2 * (d__1 = d__[m], abs(d__1)) * (d__2 = d__[m - + 1], abs(d__2)) + safmin) { + if (tst <= + eps2 * (d__1 = d__[m], abs(d__1)) * (d__2 = d__[m + 1], abs(d__2)) + safmin) { goto L60; } -/* L50: */ } } - m = lend; - -L60: + L60: if (m < lend) { e[m] = 0.; } @@ -407,18 +174,13 @@ L60: if (m == l) { goto L80; } - -/* If remaining matrix is 2-by-2, use DLAE2 or SLAEV2 */ -/* to compute its eigensystem. */ - if (m == l + 1) { if (icompz > 0) { dlaev2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2, &c__, &s); work[l] = c__; work[*n - 1 + l] = s; - dlasr_((char *)"R", (char *)"V", (char *)"B", n, &c__2, &work[l], &work[*n - 1 + l], & - z__[l * z_dim1 + 1], ldz, (ftnlen)1, (ftnlen)1, ( - ftnlen)1); + dlasr_((char *)"R", (char *)"V", (char *)"B", n, &c__2, &work[l], &work[*n - 1 + l], &z__[l * z_dim1 + 1], + ldz, (ftnlen)1, (ftnlen)1, (ftnlen)1); } else { dlae2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2); } @@ -431,24 +193,16 @@ L60: } goto L140; } - if (jtot == nmaxit) { goto L140; } ++jtot; - -/* Form shift. */ - g = (d__[l + 1] - p) / (e[l] * 2.); r__ = dlapy2_(&g, &c_b10); g = d__[m] - p + e[l] / (g + d_lmp_sign(&r__, &g)); - s = 1.; c__ = 1.; p = 0.; - -/* Inner loop */ - mm1 = m - 1; i__1 = l; for (i__ = mm1; i__ >= i__1; --i__) { @@ -463,65 +217,42 @@ L60: p = s * r__; d__[i__ + 1] = g + p; g = c__ * r__ - b; - -/* If eigenvectors are desired, then save rotations. */ - if (icompz > 0) { work[i__] = c__; work[*n - 1 + i__] = -s; } - -/* L70: */ } - -/* If eigenvectors are desired, then apply saved rotations. */ - if (icompz > 0) { mm = m - l + 1; - dlasr_((char *)"R", (char *)"V", (char *)"B", n, &mm, &work[l], &work[*n - 1 + l], &z__[l - * z_dim1 + 1], ldz, (ftnlen)1, (ftnlen)1, (ftnlen)1); + dlasr_((char *)"R", (char *)"V", (char *)"B", n, &mm, &work[l], &work[*n - 1 + l], &z__[l * z_dim1 + 1], ldz, + (ftnlen)1, (ftnlen)1, (ftnlen)1); } - d__[l] -= p; e[l] = g; goto L40; - -/* Eigenvalue found. */ - -L80: + L80: d__[l] = p; - ++l; if (l <= lend) { goto L40; } goto L140; - } else { - -/* QR Iteration */ - -/* Look for small superdiagonal element. */ - -L90: + L90: if (l != lend) { lendp1 = lend + 1; i__1 = lendp1; for (m = l; m >= i__1; --m) { -/* Computing 2nd power */ d__2 = (d__1 = e[m - 1], abs(d__1)); tst = d__2 * d__2; - if (tst <= eps2 * (d__1 = d__[m], abs(d__1)) * (d__2 = d__[m - - 1], abs(d__2)) + safmin) { + if (tst <= + eps2 * (d__1 = d__[m], abs(d__1)) * (d__2 = d__[m - 1], abs(d__2)) + safmin) { goto L110; } -/* L100: */ } } - m = lend; - -L110: + L110: if (m > lend) { e[m - 1] = 0.; } @@ -529,19 +260,13 @@ L110: if (m == l) { goto L130; } - -/* If remaining matrix is 2-by-2, use DLAE2 or SLAEV2 */ -/* to compute its eigensystem. */ - if (m == l - 1) { if (icompz > 0) { - dlaev2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2, &c__, &s) - ; + dlaev2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2, &c__, &s); work[m] = c__; work[*n - 1 + m] = s; - dlasr_((char *)"R", (char *)"V", (char *)"F", n, &c__2, &work[m], &work[*n - 1 + m], & - z__[(l - 1) * z_dim1 + 1], ldz, (ftnlen)1, (ftnlen)1, - (ftnlen)1); + dlasr_((char *)"R", (char *)"V", (char *)"F", n, &c__2, &work[m], &work[*n - 1 + m], + &z__[(l - 1) * z_dim1 + 1], ldz, (ftnlen)1, (ftnlen)1, (ftnlen)1); } else { dlae2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2); } @@ -554,24 +279,16 @@ L110: } goto L140; } - if (jtot == nmaxit) { goto L140; } ++jtot; - -/* Form shift. */ - g = (d__[l - 1] - p) / (e[l - 1] * 2.); r__ = dlapy2_(&g, &c_b10); g = d__[m] - p + e[l - 1] / (g + d_lmp_sign(&r__, &g)); - s = 1.; c__ = 1.; p = 0.; - -/* Inner loop */ - lm1 = l - 1; i__1 = lm1; for (i__ = m; i__ <= i__1; ++i__) { @@ -586,64 +303,39 @@ L110: p = s * r__; d__[i__] = g + p; g = c__ * r__ - b; - -/* If eigenvectors are desired, then save rotations. */ - if (icompz > 0) { work[i__] = c__; work[*n - 1 + i__] = s; } - -/* L120: */ } - -/* If eigenvectors are desired, then apply saved rotations. */ - if (icompz > 0) { mm = l - m + 1; - dlasr_((char *)"R", (char *)"V", (char *)"F", n, &mm, &work[m], &work[*n - 1 + m], &z__[m - * z_dim1 + 1], ldz, (ftnlen)1, (ftnlen)1, (ftnlen)1); + dlasr_((char *)"R", (char *)"V", (char *)"F", n, &mm, &work[m], &work[*n - 1 + m], &z__[m * z_dim1 + 1], ldz, + (ftnlen)1, (ftnlen)1, (ftnlen)1); } - d__[l] -= p; e[lm1] = g; goto L90; - -/* Eigenvalue found. */ - -L130: + L130: d__[l] = p; - --l; if (l >= lend) { goto L90; } goto L140; - } - -/* Undo scaling if necessary */ - L140: if (iscale == 1) { i__1 = lendsv - lsv + 1; - dlascl_((char *)"G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv], - n, info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv], n, info, (ftnlen)1); i__1 = lendsv - lsv; - dlascl_((char *)"G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &e[lsv], n, - info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &e[lsv], n, info, (ftnlen)1); } else if (iscale == 2) { i__1 = lendsv - lsv + 1; - dlascl_((char *)"G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[lsv], - n, info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[lsv], n, info, (ftnlen)1); i__1 = lendsv - lsv; - dlascl_((char *)"G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &e[lsv], n, - info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &e[lsv], n, info, (ftnlen)1); } - -/* Check for no convergence to an eigenvalue after a total */ -/* of N*MAXIT iterations. */ - if (jtot < nmaxit) { goto L10; } @@ -652,23 +344,12 @@ L140: if (e[i__] != 0.) { ++(*info); } -/* L150: */ } goto L190; - -/* Order eigenvalues and eigenvectors. */ - L160: if (icompz == 0) { - -/* Use Quick Sort */ - dlasrt_((char *)"I", n, &d__[1], info, (ftnlen)1); - } else { - -/* Use Selection Sort to minimize swaps of eigenvectors */ - i__1 = *n; for (ii = 2; ii <= i__1; ++ii) { i__ = ii - 1; @@ -680,25 +361,17 @@ L160: k = j; p = d__[j]; } -/* L170: */ } if (k != i__) { d__[k] = d__[i__]; d__[i__] = p; - dswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1 + 1], - &c__1); + dswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1 + 1], &c__1); } -/* L180: */ } } - L190: return 0; - -/* End of DSTEQR */ - -} /* dsteqr_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dsterf.cpp b/lib/linalg/dsterf.cpp index 687cbf943b..438cc47dc3 100644 --- a/lib/linalg/dsterf.cpp +++ b/lib/linalg/dsterf.cpp @@ -1,124 +1,15 @@ -/* fortran/dsterf.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__0 = 0; static integer c__1 = 1; static doublereal c_b33 = 1.; - -/* > \brief \b DSTERF */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DSTERF + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DSTERF( N, D, E, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INFO, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION D( * ), E( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DSTERF computes all eigenvalues of a symmetric tridiagonal matrix */ -/* > using the Pal-Walker-Kahan variant of the QL or QR algorithm. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrix. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension (N) */ -/* > On entry, the n diagonal elements of the tridiagonal matrix. */ -/* > On exit, if INFO = 0, the eigenvalues in ascending order. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] E */ -/* > \verbatim */ -/* > E is DOUBLE PRECISION array, dimension (N-1) */ -/* > On entry, the (n-1) subdiagonal elements of the tridiagonal */ -/* > matrix. */ -/* > On exit, E has been destroyed. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > > 0: the algorithm failed to find all of the eigenvalues in */ -/* > a total of 30*N iterations; if INFO = i, then i */ -/* > elements of E have not converged to zero. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup auxOTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dsterf_(integer *n, doublereal *d__, doublereal *e, - integer *info) +int dsterf_(integer *n, doublereal *d__, doublereal *e, integer *info) { - /* System generated locals */ integer i__1; doublereal d__1, d__2, d__3; - - /* Builtin functions */ double sqrt(doublereal), d_lmp_sign(doublereal *, doublereal *); - - /* Local variables */ doublereal c__; integer i__, l, m; doublereal p, r__, s; @@ -129,62 +20,24 @@ f"> */ integer lend; doublereal rmax; integer jtot; - extern /* Subroutine */ int dlae2_(doublereal *, doublereal *, doublereal - *, doublereal *, doublereal *); + extern int dlae2_(doublereal *, doublereal *, doublereal *, doublereal *, doublereal *); doublereal gamma, alpha, sigma, anorm; - extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, - ftnlen); + extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, ftnlen); integer iscale; - extern /* Subroutine */ int dlascl_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, integer *, doublereal *, - integer *, integer *, ftnlen); + extern int dlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, + integer *, doublereal *, integer *, integer *, ftnlen); doublereal oldgam, safmin; - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern int xerbla_(char *, integer *, ftnlen); doublereal safmax; - extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *, - ftnlen); - extern /* Subroutine */ int dlasrt_(char *, integer *, doublereal *, - integer *, ftnlen); + extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *, ftnlen); + extern int dlasrt_(char *, integer *, doublereal *, integer *, ftnlen); integer lendsv; doublereal ssfmin; integer nmaxit; doublereal ssfmax; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ --e; --d__; - - /* Function Body */ *info = 0; - -/* Quick return if possible */ - if (*n < 0) { *info = -1; i__1 = -(*info); @@ -194,11 +47,7 @@ f"> */ if (*n <= 1) { return 0; } - -/* Determine the unit roundoff for this environment. */ - eps = dlamch_((char *)"E", (ftnlen)1); -/* Computing 2nd power */ d__1 = eps; eps2 = d__1 * d__1; safmin = dlamch_((char *)"S", (ftnlen)1); @@ -206,19 +55,10 @@ f"> */ ssfmax = sqrt(safmax) / 3.; ssfmin = sqrt(safmin) / eps2; rmax = dlamch_((char *)"O", (ftnlen)1); - -/* Compute the eigenvalues of the tridiagonal matrix. */ - nmaxit = *n * 30; sigma = 0.; jtot = 0; - -/* Determine where the matrix splits and choose QL or QR iteration */ -/* for each block, according to whether top or bottom diagonal */ -/* element is smaller. */ - l1 = 1; - L10: if (l1 > *n) { goto L170; @@ -228,15 +68,13 @@ L10: } i__1 = *n - 1; for (m = l1; m <= i__1; ++m) { - if ((d__3 = e[m], abs(d__3)) <= sqrt((d__1 = d__[m], abs(d__1))) * - sqrt((d__2 = d__[m + 1], abs(d__2))) * eps) { + if ((d__3 = e[m], abs(d__3)) <= + sqrt((d__1 = d__[m], abs(d__1))) * sqrt((d__2 = d__[m + 1], abs(d__2))) * eps) { e[m] = 0.; goto L30; } -/* L20: */ } m = *n; - L30: l = l1; lsv = l; @@ -246,9 +84,6 @@ L30: if (lend == l) { goto L10; } - -/* Scale submatrix in rows and columns L to LEND */ - i__1 = lend - l + 1; anorm = dlanst_((char *)"M", &i__1, &d__[l], &e[l], (ftnlen)1); iscale = 0; @@ -258,56 +93,37 @@ L30: if (anorm > ssfmax) { iscale = 1; i__1 = lend - l + 1; - dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n, - info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n, info, (ftnlen)1); i__1 = lend - l; - dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &e[l], n, - info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &e[l], n, info, (ftnlen)1); } else if (anorm < ssfmin) { iscale = 2; i__1 = lend - l + 1; - dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n, - info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n, info, (ftnlen)1); i__1 = lend - l; - dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n, - info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n, info, (ftnlen)1); } - i__1 = lend - 1; for (i__ = l; i__ <= i__1; ++i__) { -/* Computing 2nd power */ d__1 = e[i__]; e[i__] = d__1 * d__1; -/* L40: */ } - -/* Choose between QL and QR iteration */ - if ((d__1 = d__[lend], abs(d__1)) < (d__2 = d__[l], abs(d__2))) { lend = lsv; l = lendsv; } - if (lend >= l) { - -/* QL Iteration */ - -/* Look for small subdiagonal element. */ - -L50: + L50: if (l != lend) { i__1 = lend - 1; for (m = l; m <= i__1; ++m) { - if ((d__2 = e[m], abs(d__2)) <= eps2 * (d__1 = d__[m] * d__[m - + 1], abs(d__1))) { + if ((d__2 = e[m], abs(d__2)) <= eps2 * (d__1 = d__[m] * d__[m + 1], abs(d__1))) { goto L70; } -/* L60: */ } } m = lend; - -L70: + L70: if (m < lend) { e[m] = 0.; } @@ -315,10 +131,6 @@ L70: if (m == l) { goto L90; } - -/* If remaining matrix is 2 by 2, use DLAE2 to compute its */ -/* eigenvalues. */ - if (m == l + 1) { rte = sqrt(e[l]); dlae2_(&d__[l], &rte, &d__[l + 1], &rt1, &rt2); @@ -331,26 +143,18 @@ L70: } goto L150; } - if (jtot == nmaxit) { goto L150; } ++jtot; - -/* Form shift. */ - rte = sqrt(e[l]); sigma = (d__[l + 1] - p) / (rte * 2.); r__ = dlapy2_(&sigma, &c_b33); sigma = p - rte / (sigma + d_lmp_sign(&r__, &sigma)); - c__ = 1.; s = 0.; gamma = d__[m] - sigma; p = gamma * gamma; - -/* Inner loop */ - i__1 = l; for (i__ = m - 1; i__ >= i__1; --i__) { bb = e[i__]; @@ -370,42 +174,27 @@ L70: } else { p = oldc * bb; } -/* L80: */ } - e[l] = s * p; d__[l] = sigma + gamma; goto L50; - -/* Eigenvalue found. */ - -L90: + L90: d__[l] = p; - ++l; if (l <= lend) { goto L50; } goto L150; - } else { - -/* QR Iteration */ - -/* Look for small superdiagonal element. */ - -L100: + L100: i__1 = lend + 1; for (m = l; m >= i__1; --m) { - if ((d__2 = e[m - 1], abs(d__2)) <= eps2 * (d__1 = d__[m] * d__[m - - 1], abs(d__1))) { + if ((d__2 = e[m - 1], abs(d__2)) <= eps2 * (d__1 = d__[m] * d__[m - 1], abs(d__1))) { goto L120; } -/* L110: */ } m = lend; - -L120: + L120: if (m > lend) { e[m - 1] = 0.; } @@ -413,10 +202,6 @@ L120: if (m == l) { goto L140; } - -/* If remaining matrix is 2 by 2, use DLAE2 to compute its */ -/* eigenvalues. */ - if (m == l - 1) { rte = sqrt(e[l - 1]); dlae2_(&d__[l], &rte, &d__[l - 1], &rt1, &rt2); @@ -429,26 +214,18 @@ L120: } goto L150; } - if (jtot == nmaxit) { goto L150; } ++jtot; - -/* Form shift. */ - rte = sqrt(e[l - 1]); sigma = (d__[l - 1] - p) / (rte * 2.); r__ = dlapy2_(&sigma, &c_b33); sigma = p - rte / (sigma + d_lmp_sign(&r__, &sigma)); - c__ = 1.; s = 0.; gamma = d__[m] - sigma; p = gamma * gamma; - -/* Inner loop */ - i__1 = l - 1; for (i__ = m; i__ <= i__1; ++i__) { bb = e[i__]; @@ -468,43 +245,27 @@ L120: } else { p = oldc * bb; } -/* L130: */ } - e[l - 1] = s * p; d__[l] = sigma + gamma; goto L100; - -/* Eigenvalue found. */ - -L140: + L140: d__[l] = p; - --l; if (l >= lend) { goto L100; } goto L150; - } - -/* Undo scaling if necessary */ - L150: if (iscale == 1) { i__1 = lendsv - lsv + 1; - dlascl_((char *)"G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv], - n, info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv], n, info, (ftnlen)1); } if (iscale == 2) { i__1 = lendsv - lsv + 1; - dlascl_((char *)"G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[lsv], - n, info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[lsv], n, info, (ftnlen)1); } - -/* Check for no convergence to an eigenvalue after a total */ -/* of N*MAXIT iterations. */ - if (jtot < nmaxit) { goto L10; } @@ -513,22 +274,13 @@ L150: if (e[i__] != 0.) { ++(*info); } -/* L160: */ } goto L180; - -/* Sort eigenvalues in increasing order. */ - L170: dlasrt_((char *)"I", n, &d__[1], info, (ftnlen)1); - L180: return 0; - -/* End of DSTERF */ - -} /* dsterf_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dswap.cpp b/lib/linalg/dswap.cpp index 4cb6a77f67..e3b98c9151 100644 --- a/lib/linalg/dswap.cpp +++ b/lib/linalg/dswap.cpp @@ -1,141 +1,18 @@ -/* fortran/dswap.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DSWAP */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DSWAP(N,DX,INCX,DY,INCY) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INCX,INCY,N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION DX(*),DY(*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DSWAP interchanges two vectors. */ -/* > uses unrolled loops for increments equal to 1. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > number of elements in input vector(s) */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] DX */ -/* > \verbatim */ -/* > DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > storage spacing between elements of DX */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] DY */ -/* > \verbatim */ -/* > DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCY */ -/* > \verbatim */ -/* > INCY is INTEGER */ -/* > storage spacing between elements of DY */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup double_blas_level1 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > jack dongarra, linpack, 3/11/78. */ -/* > modified 12/3/93, array(1) declarations changed to array(*) */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dswap_(integer *n, doublereal *dx, integer *incx, - doublereal *dy, integer *incy) +int dswap_(integer *n, doublereal *dx, integer *incx, doublereal *dy, integer *incy) { - /* System generated locals */ integer i__1; - - /* Local variables */ integer i__, m, ix, iy, mp1; doublereal dtemp; - - -/* -- Reference BLAS level1 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Local Scalars .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ - /* Parameter adjustments */ --dy; --dx; - - /* Function Body */ if (*n <= 0) { return 0; } if (*incx == 1 && *incy == 1) { - -/* code for both increments equal to 1 */ - - -/* clean-up loop */ - m = *n % 3; if (m != 0) { i__1 = m; @@ -162,10 +39,6 @@ extern "C" { dy[i__ + 2] = dtemp; } } else { - -/* code for unequal increments or equal increments not equal */ -/* to 1 */ - ix = 1; iy = 1; if (*incx < 0) { @@ -184,11 +57,7 @@ extern "C" { } } return 0; - -/* End of DSWAP */ - -} /* dswap_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dsyev.cpp b/lib/linalg/dsyev.cpp index a222fc4b09..ccbdd9e998 100644 --- a/lib/linalg/dsyev.cpp +++ b/lib/linalg/dsyev.cpp @@ -1,277 +1,80 @@ -/* fortran/dsyev.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static integer c_n1 = -1; static integer c__0 = 0; static doublereal c_b17 = 1.; - -/* > \brief DSYEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matr -ices */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DSYEV + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DSYEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER JOBZ, UPLO */ -/* INTEGER INFO, LDA, LWORK, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DSYEV computes all eigenvalues and, optionally, eigenvectors of a */ -/* > real symmetric matrix A. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] JOBZ */ -/* > \verbatim */ -/* > JOBZ is CHARACTER*1 */ -/* > = 'N': Compute eigenvalues only; */ -/* > = 'V': Compute eigenvalues and eigenvectors. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > = 'U': Upper triangle of A is stored; */ -/* > = 'L': Lower triangle of A is stored. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA, N) */ -/* > On entry, the symmetric matrix A. If UPLO = 'U', the */ -/* > leading N-by-N upper triangular part of A contains the */ -/* > upper triangular part of the matrix A. If UPLO = 'L', */ -/* > the leading N-by-N lower triangular part of A contains */ -/* > the lower triangular part of the matrix A. */ -/* > On exit, if JOBZ = 'V', then if INFO = 0, A contains the */ -/* > orthonormal eigenvectors of the matrix A. */ -/* > If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') */ -/* > or the upper triangle (if UPLO='U') of A, including the */ -/* > diagonal, is destroyed. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] W */ -/* > \verbatim */ -/* > W is DOUBLE PRECISION array, dimension (N) */ -/* > If INFO = 0, the eigenvalues in ascending order. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ -/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LWORK */ -/* > \verbatim */ -/* > LWORK is INTEGER */ -/* > The length of the array WORK. LWORK >= max(1,3*N-1). */ -/* > For optimal efficiency, LWORK >= (NB+2)*N, */ -/* > where NB is the blocksize for DSYTRD returned by ILAENV. */ -/* > */ -/* > If LWORK = -1, then a workspace query is assumed; the routine */ -/* > only calculates the optimal size of the WORK array, returns */ -/* > this value as the first entry of the WORK array, and no error */ -/* > message related to LWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > > 0: if INFO = i, the algorithm failed to converge; i */ -/* > off-diagonal elements of an intermediate tridiagonal */ -/* > form did not converge to zero. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleSYeigen */ - -/* ===================================================================== */ -/* Subroutine */ int dsyev_(char *jobz, char *uplo, integer *n, doublereal *a, - integer *lda, doublereal *w, doublereal *work, integer *lwork, - integer *info, ftnlen jobz_len, ftnlen uplo_len) +int dsyev_(char *jobz, char *uplo, integer *n, doublereal *a, integer *lda, doublereal *w, + doublereal *work, integer *lwork, integer *info, ftnlen jobz_len, ftnlen uplo_len) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; doublereal d__1; - - /* Builtin functions */ double sqrt(doublereal); - - /* Local variables */ integer nb; doublereal eps; integer inde; doublereal anrm; integer imax; doublereal rmin, rmax; - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *); + extern int dscal_(integer *, doublereal *, doublereal *, integer *); doublereal sigma; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer iinfo; logical lower, wantz; extern doublereal dlamch_(char *, ftnlen); integer iscale; - extern /* Subroutine */ int dlascl_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, integer *, doublereal *, - integer *, integer *, ftnlen); + extern int dlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, + integer *, doublereal *, integer *, integer *, ftnlen); doublereal safmin; - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); + extern int xerbla_(char *, integer *, ftnlen); doublereal bignum; integer indtau; - extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *, - integer *); - extern doublereal dlansy_(char *, char *, integer *, doublereal *, - integer *, doublereal *, ftnlen, ftnlen); + extern int dsterf_(integer *, doublereal *, doublereal *, integer *); + extern doublereal dlansy_(char *, char *, integer *, doublereal *, integer *, doublereal *, + ftnlen, ftnlen); integer indwrk; - extern /* Subroutine */ int dorgtr_(char *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, integer *, - ftnlen), dsteqr_(char *, integer *, doublereal *, doublereal *, - doublereal *, integer *, doublereal *, integer *, ftnlen), - dsytrd_(char *, integer *, doublereal *, integer *, doublereal *, - doublereal *, doublereal *, doublereal *, integer *, integer *, - ftnlen); + extern int dorgtr_(char *, integer *, doublereal *, integer *, doublereal *, doublereal *, + integer *, integer *, ftnlen), + dsteqr_(char *, integer *, doublereal *, doublereal *, doublereal *, integer *, + doublereal *, integer *, ftnlen), + dsytrd_(char *, integer *, doublereal *, integer *, doublereal *, doublereal *, + doublereal *, doublereal *, integer *, integer *, ftnlen); integer llwork; doublereal smlnum; integer lwkopt; logical lquery; - - -/* -- LAPACK driver routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --w; --work; - - /* Function Body */ wantz = lsame_(jobz, (char *)"V", (ftnlen)1, (ftnlen)1); lower = lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1); lquery = *lwork == -1; - *info = 0; - if (! (wantz || lsame_(jobz, (char *)"N", (ftnlen)1, (ftnlen)1))) { + if (!(wantz || lsame_(jobz, (char *)"N", (ftnlen)1, (ftnlen)1))) { *info = -1; - } else if (! (lower || lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1))) { + } else if (!(lower || lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1))) { *info = -2; } else if (*n < 0) { *info = -3; - } else if (*lda < max(1,*n)) { + } else if (*lda < max(1, *n)) { *info = -5; } - if (*info == 0) { - nb = ilaenv_(&c__1, (char *)"DSYTRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, - (ftnlen)1); -/* Computing MAX */ + nb = ilaenv_(&c__1, (char *)"DSYTRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); i__1 = 1, i__2 = (nb + 2) * *n; - lwkopt = max(i__1,i__2); - work[1] = (doublereal) lwkopt; - -/* Computing MAX */ + lwkopt = max(i__1, i__2); + work[1] = (doublereal)lwkopt; i__1 = 1, i__2 = *n * 3 - 1; - if (*lwork < max(i__1,i__2) && ! lquery) { + if (*lwork < max(i__1, i__2) && !lquery) { *info = -8; } } - if (*info != 0) { i__1 = -(*info); xerbla_((char *)"DSYEV ", &i__1, (ftnlen)6); @@ -279,13 +82,9 @@ ices */ } else if (lquery) { return 0; } - -/* Quick return if possible */ - if (*n == 0) { return 0; } - if (*n == 1) { w[1] = a[a_dim1 + 1]; work[1] = 2.; @@ -294,20 +93,13 @@ ices */ } return 0; } - -/* Get machine constants. */ - safmin = dlamch_((char *)"Safe minimum", (ftnlen)12); eps = dlamch_((char *)"Precision", (ftnlen)9); smlnum = safmin / eps; bignum = 1. / smlnum; rmin = sqrt(smlnum); rmax = sqrt(bignum); - -/* Scale matrix to allowable range, if necessary. */ - - anrm = dlansy_((char *)"M", uplo, n, &a[a_offset], lda, &work[1], (ftnlen)1, ( - ftnlen)1); + anrm = dlansy_((char *)"M", uplo, n, &a[a_offset], lda, &work[1], (ftnlen)1, (ftnlen)1); iscale = 0; if (anrm > 0. && anrm < rmin) { iscale = 1; @@ -317,33 +109,21 @@ ices */ sigma = rmax / anrm; } if (iscale == 1) { - dlascl_(uplo, &c__0, &c__0, &c_b17, &sigma, n, n, &a[a_offset], lda, - info, (ftnlen)1); + dlascl_(uplo, &c__0, &c__0, &c_b17, &sigma, n, n, &a[a_offset], lda, info, (ftnlen)1); } - -/* Call DSYTRD to reduce symmetric matrix to tridiagonal form. */ - inde = 1; indtau = inde + *n; indwrk = indtau + *n; llwork = *lwork - indwrk + 1; - dsytrd_(uplo, n, &a[a_offset], lda, &w[1], &work[inde], &work[indtau], & - work[indwrk], &llwork, &iinfo, (ftnlen)1); - -/* For eigenvalues only, call DSTERF. For eigenvectors, first call */ -/* DORGTR to generate the orthogonal matrix, then call DSTEQR. */ - - if (! wantz) { + dsytrd_(uplo, n, &a[a_offset], lda, &w[1], &work[inde], &work[indtau], &work[indwrk], &llwork, + &iinfo, (ftnlen)1); + if (!wantz) { dsterf_(n, &w[1], &work[inde], info); } else { - dorgtr_(uplo, n, &a[a_offset], lda, &work[indtau], &work[indwrk], & - llwork, &iinfo, (ftnlen)1); - dsteqr_(jobz, n, &w[1], &work[inde], &a[a_offset], lda, &work[indtau], - info, (ftnlen)1); + dorgtr_(uplo, n, &a[a_offset], lda, &work[indtau], &work[indwrk], &llwork, &iinfo, + (ftnlen)1); + dsteqr_(jobz, n, &w[1], &work[inde], &a[a_offset], lda, &work[indtau], info, (ftnlen)1); } - -/* If matrix was scaled, then rescale eigenvalues appropriately. */ - if (iscale == 1) { if (*info == 0) { imax = *n; @@ -353,17 +133,9 @@ ices */ d__1 = 1. / sigma; dscal_(&imax, &d__1, &w[1], &c__1); } - -/* Set WORK(1) to optimal workspace size. */ - - work[1] = (doublereal) lwkopt; - + work[1] = (doublereal)lwkopt; return 0; - -/* End of DSYEV */ - -} /* dsyev_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dsyevd.cpp b/lib/linalg/dsyevd.cpp index 2f8d5a145b..5c02bc14da 100644 --- a/lib/linalg/dsyevd.cpp +++ b/lib/linalg/dsyevd.cpp @@ -1,230 +1,23 @@ -/* fortran/dsyevd.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static integer c_n1 = -1; static integer c__0 = 0; static doublereal c_b17 = 1.; - -/* > \brief DSYEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY mat -rices */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DSYEVD + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK, */ -/* LIWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER JOBZ, UPLO */ -/* INTEGER INFO, LDA, LIWORK, LWORK, N */ -/* .. */ -/* .. Array Arguments .. */ -/* INTEGER IWORK( * ) */ -/* DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DSYEVD computes all eigenvalues and, optionally, eigenvectors of a */ -/* > real symmetric matrix A. If eigenvectors are desired, it uses a */ -/* > divide and conquer algorithm. */ -/* > */ -/* > The divide and conquer algorithm makes very mild assumptions about */ -/* > floating point arithmetic. It will work on machines with a guard */ -/* > digit in add/subtract, or on those binary machines without guard */ -/* > digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */ -/* > Cray-2. It could conceivably fail on hexadecimal or decimal machines */ -/* > without guard digits, but we know of none. */ -/* > */ -/* > Because of large use of BLAS of level 3, DSYEVD needs N**2 more */ -/* > workspace than DSYEVX. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] JOBZ */ -/* > \verbatim */ -/* > JOBZ is CHARACTER*1 */ -/* > = 'N': Compute eigenvalues only; */ -/* > = 'V': Compute eigenvalues and eigenvectors. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > = 'U': Upper triangle of A is stored; */ -/* > = 'L': Lower triangle of A is stored. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA, N) */ -/* > On entry, the symmetric matrix A. If UPLO = 'U', the */ -/* > leading N-by-N upper triangular part of A contains the */ -/* > upper triangular part of the matrix A. If UPLO = 'L', */ -/* > the leading N-by-N lower triangular part of A contains */ -/* > the lower triangular part of the matrix A. */ -/* > On exit, if JOBZ = 'V', then if INFO = 0, A contains the */ -/* > orthonormal eigenvectors of the matrix A. */ -/* > If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') */ -/* > or the upper triangle (if UPLO='U') of A, including the */ -/* > diagonal, is destroyed. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] W */ -/* > \verbatim */ -/* > W is DOUBLE PRECISION array, dimension (N) */ -/* > If INFO = 0, the eigenvalues in ascending order. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, */ -/* > dimension (LWORK) */ -/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LWORK */ -/* > \verbatim */ -/* > LWORK is INTEGER */ -/* > The dimension of the array WORK. */ -/* > If N <= 1, LWORK must be at least 1. */ -/* > If JOBZ = 'N' and N > 1, LWORK must be at least 2*N+1. */ -/* > If JOBZ = 'V' and N > 1, LWORK must be at least */ -/* > 1 + 6*N + 2*N**2. */ -/* > */ -/* > If LWORK = -1, then a workspace query is assumed; the routine */ -/* > only calculates the optimal sizes of the WORK and IWORK */ -/* > arrays, returns these values as the first entries of the WORK */ -/* > and IWORK arrays, and no error message related to LWORK or */ -/* > LIWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] IWORK */ -/* > \verbatim */ -/* > IWORK is INTEGER array, dimension (MAX(1,LIWORK)) */ -/* > On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LIWORK */ -/* > \verbatim */ -/* > LIWORK is INTEGER */ -/* > The dimension of the array IWORK. */ -/* > If N <= 1, LIWORK must be at least 1. */ -/* > If JOBZ = 'N' and N > 1, LIWORK must be at least 1. */ -/* > If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N. */ -/* > */ -/* > If LIWORK = -1, then a workspace query is assumed; the */ -/* > routine only calculates the optimal sizes of the WORK and */ -/* > IWORK arrays, returns these values as the first entries of */ -/* > the WORK and IWORK arrays, and no error message related to */ -/* > LWORK or LIWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > > 0: if INFO = i and JOBZ = 'N', then the algorithm failed */ -/* > to converge; i off-diagonal elements of an intermediate */ -/* > tridiagonal form did not converge to zero; */ -/* > if INFO = i and JOBZ = 'V', then the algorithm failed */ -/* > to compute an eigenvalue while working on the submatrix */ -/* > lying in rows and columns INFO/(N+1) through */ -/* > mod(INFO,N+1). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleSYeigen */ - -/* > \par Contributors: */ -/* ================== */ -/* > */ -/* > Jeff Rutter, Computer Science Division, University of California */ -/* > at Berkeley, USA \n */ -/* > Modified by Francoise Tisseur, University of Tennessee \n */ -/* > Modified description of INFO. Sven, 16 Feb 05. \n */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dsyevd_(char *jobz, char *uplo, integer *n, doublereal * - a, integer *lda, doublereal *w, doublereal *work, integer *lwork, - integer *iwork, integer *liwork, integer *info, ftnlen jobz_len, - ftnlen uplo_len) +int dsyevd_(char *jobz, char *uplo, integer *n, doublereal *a, integer *lda, doublereal *w, + doublereal *work, integer *lwork, integer *iwork, integer *liwork, integer *info, + ftnlen jobz_len, ftnlen uplo_len) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; doublereal d__1; - - /* Builtin functions */ double sqrt(doublereal); - - /* Local variables */ doublereal eps; integer inde; doublereal anrm, rmin, rmax; integer lopt; - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *); + extern int dscal_(integer *, doublereal *, doublereal *, integer *); doublereal sigma; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer iinfo, lwmin, liopt; @@ -232,85 +25,49 @@ f"> */ integer indwk2, llwrk2; extern doublereal dlamch_(char *, ftnlen); integer iscale; - extern /* Subroutine */ int dlascl_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, integer *, doublereal *, - integer *, integer *, ftnlen), dstedc_(char *, integer *, - doublereal *, doublereal *, doublereal *, integer *, doublereal *, - integer *, integer *, integer *, integer *, ftnlen), dlacpy_( - char *, integer *, integer *, doublereal *, integer *, doublereal - *, integer *, ftnlen); + extern int dlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, + integer *, doublereal *, integer *, integer *, ftnlen), + dstedc_(char *, integer *, doublereal *, doublereal *, doublereal *, integer *, + doublereal *, integer *, integer *, integer *, integer *, ftnlen), + dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, + ftnlen); doublereal safmin; - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); + extern int xerbla_(char *, integer *, ftnlen); doublereal bignum; integer indtau; - extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *, - integer *); - extern doublereal dlansy_(char *, char *, integer *, doublereal *, - integer *, doublereal *, ftnlen, ftnlen); + extern int dsterf_(integer *, doublereal *, doublereal *, integer *); + extern doublereal dlansy_(char *, char *, integer *, doublereal *, integer *, doublereal *, + ftnlen, ftnlen); integer indwrk, liwmin; - extern /* Subroutine */ int dormtr_(char *, char *, char *, integer *, - integer *, doublereal *, integer *, doublereal *, doublereal *, - integer *, doublereal *, integer *, integer *, ftnlen, ftnlen, - ftnlen), dsytrd_(char *, integer *, doublereal *, integer *, - doublereal *, doublereal *, doublereal *, doublereal *, integer *, - integer *, ftnlen); + extern int dormtr_(char *, char *, char *, integer *, integer *, doublereal *, integer *, + doublereal *, doublereal *, integer *, doublereal *, integer *, integer *, + ftnlen, ftnlen, ftnlen), + dsytrd_(char *, integer *, doublereal *, integer *, doublereal *, doublereal *, + doublereal *, doublereal *, integer *, integer *, ftnlen); integer llwork; doublereal smlnum; logical lquery; - - -/* -- LAPACK driver routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ - -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --w; --work; --iwork; - - /* Function Body */ wantz = lsame_(jobz, (char *)"V", (ftnlen)1, (ftnlen)1); lower = lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1); lquery = *lwork == -1 || *liwork == -1; - *info = 0; - if (! (wantz || lsame_(jobz, (char *)"N", (ftnlen)1, (ftnlen)1))) { + if (!(wantz || lsame_(jobz, (char *)"N", (ftnlen)1, (ftnlen)1))) { *info = -1; - } else if (! (lower || lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1))) { + } else if (!(lower || lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1))) { *info = -2; } else if (*n < 0) { *info = -3; - } else if (*lda < max(1,*n)) { + } else if (*lda < max(1, *n)) { *info = -5; } - if (*info == 0) { if (*n <= 1) { liwmin = 1; @@ -320,29 +77,25 @@ f"> */ } else { if (wantz) { liwmin = *n * 5 + 3; -/* Computing 2nd power */ i__1 = *n; lwmin = *n * 6 + 1 + (i__1 * i__1 << 1); } else { liwmin = 1; lwmin = (*n << 1) + 1; } -/* Computing MAX */ - i__1 = lwmin, i__2 = (*n << 1) + *n * ilaenv_(&c__1, (char *)"DSYTRD", - uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); - lopt = max(i__1,i__2); + i__1 = lwmin, i__2 = (*n << 1) + *n * ilaenv_(&c__1, (char *)"DSYTRD", uplo, n, &c_n1, &c_n1, + &c_n1, (ftnlen)6, (ftnlen)1); + lopt = max(i__1, i__2); liopt = liwmin; } - work[1] = (doublereal) lopt; + work[1] = (doublereal)lopt; iwork[1] = liopt; - - if (*lwork < lwmin && ! lquery) { + if (*lwork < lwmin && !lquery) { *info = -8; - } else if (*liwork < liwmin && ! lquery) { + } else if (*liwork < liwmin && !lquery) { *info = -10; } } - if (*info != 0) { i__1 = -(*info); xerbla_((char *)"DSYEVD", &i__1, (ftnlen)6); @@ -350,13 +103,9 @@ f"> */ } else if (lquery) { return 0; } - -/* Quick return if possible */ - if (*n == 0) { return 0; } - if (*n == 1) { w[1] = a[a_dim1 + 1]; if (wantz) { @@ -364,20 +113,13 @@ f"> */ } return 0; } - -/* Get machine constants. */ - safmin = dlamch_((char *)"Safe minimum", (ftnlen)12); eps = dlamch_((char *)"Precision", (ftnlen)9); smlnum = safmin / eps; bignum = 1. / smlnum; rmin = sqrt(smlnum); rmax = sqrt(bignum); - -/* Scale matrix to allowable range, if necessary. */ - - anrm = dlansy_((char *)"M", uplo, n, &a[a_offset], lda, &work[1], (ftnlen)1, ( - ftnlen)1); + anrm = dlansy_((char *)"M", uplo, n, &a[a_offset], lda, &work[1], (ftnlen)1, (ftnlen)1); iscale = 0; if (anrm > 0. && anrm < rmin) { iscale = 1; @@ -387,54 +129,33 @@ f"> */ sigma = rmax / anrm; } if (iscale == 1) { - dlascl_(uplo, &c__0, &c__0, &c_b17, &sigma, n, n, &a[a_offset], lda, - info, (ftnlen)1); + dlascl_(uplo, &c__0, &c__0, &c_b17, &sigma, n, n, &a[a_offset], lda, info, (ftnlen)1); } - -/* Call DSYTRD to reduce symmetric matrix to tridiagonal form. */ - inde = 1; indtau = inde + *n; indwrk = indtau + *n; llwork = *lwork - indwrk + 1; indwk2 = indwrk + *n * *n; llwrk2 = *lwork - indwk2 + 1; - - dsytrd_(uplo, n, &a[a_offset], lda, &w[1], &work[inde], &work[indtau], & - work[indwrk], &llwork, &iinfo, (ftnlen)1); - -/* For eigenvalues only, call DSTERF. For eigenvectors, first call */ -/* DSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the */ -/* tridiagonal matrix, then call DORMTR to multiply it by the */ -/* Householder transformations stored in A. */ - - if (! wantz) { + dsytrd_(uplo, n, &a[a_offset], lda, &w[1], &work[inde], &work[indtau], &work[indwrk], &llwork, + &iinfo, (ftnlen)1); + if (!wantz) { dsterf_(n, &w[1], &work[inde], info); } else { - dstedc_((char *)"I", n, &w[1], &work[inde], &work[indwrk], n, &work[indwk2], & - llwrk2, &iwork[1], liwork, info, (ftnlen)1); - dormtr_((char *)"L", uplo, (char *)"N", n, n, &a[a_offset], lda, &work[indtau], &work[ - indwrk], n, &work[indwk2], &llwrk2, &iinfo, (ftnlen)1, ( - ftnlen)1, (ftnlen)1); + dstedc_((char *)"I", n, &w[1], &work[inde], &work[indwrk], n, &work[indwk2], &llwrk2, &iwork[1], + liwork, info, (ftnlen)1); + dormtr_((char *)"L", uplo, (char *)"N", n, n, &a[a_offset], lda, &work[indtau], &work[indwrk], n, + &work[indwk2], &llwrk2, &iinfo, (ftnlen)1, (ftnlen)1, (ftnlen)1); dlacpy_((char *)"A", n, n, &work[indwrk], n, &a[a_offset], lda, (ftnlen)1); } - -/* If matrix was scaled, then rescale eigenvalues appropriately. */ - if (iscale == 1) { d__1 = 1. / sigma; dscal_(n, &d__1, &w[1], &c__1); } - - work[1] = (doublereal) lopt; + work[1] = (doublereal)lopt; iwork[1] = liopt; - return 0; - -/* End of DSYEVD */ - -} /* dsyevd_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dsygs2.cpp b/lib/linalg/dsygs2.cpp index 785aeb4f27..c0b2972537 100644 --- a/lib/linalg/dsygs2.cpp +++ b/lib/linalg/dsygs2.cpp @@ -1,226 +1,45 @@ -/* fortran/dsygs2.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static doublereal c_b6 = -1.; static integer c__1 = 1; static doublereal c_b27 = 1.; - -/* > \brief \b DSYGS2 reduces a symmetric definite generalized eigenproblem to standard form, using the factor -ization results obtained from spotrf (unblocked algorithm). */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DSYGS2 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DSYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER UPLO */ -/* INTEGER INFO, ITYPE, LDA, LDB, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), B( LDB, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DSYGS2 reduces a real symmetric-definite generalized eigenproblem */ -/* > to standard form. */ -/* > */ -/* > If ITYPE = 1, the problem is A*x = lambda*B*x, */ -/* > and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T) */ -/* > */ -/* > If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or */ -/* > B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T *A*L. */ -/* > */ -/* > B must have been previously factorized as U**T *U or L*L**T by DPOTRF. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] ITYPE */ -/* > \verbatim */ -/* > ITYPE is INTEGER */ -/* > = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T); */ -/* > = 2 or 3: compute U*A*U**T or L**T *A*L. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > Specifies whether the upper or lower triangular part of the */ -/* > symmetric matrix A is stored, and how B has been factorized. */ -/* > = 'U': Upper triangular */ -/* > = 'L': Lower triangular */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrices A and B. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On entry, the symmetric matrix A. If UPLO = 'U', the leading */ -/* > n by n upper triangular part of A contains the upper */ -/* > triangular part of the matrix A, and the strictly lower */ -/* > triangular part of A is not referenced. If UPLO = 'L', the */ -/* > leading n by n lower triangular part of A contains the lower */ -/* > triangular part of the matrix A, and the strictly upper */ -/* > triangular part of A is not referenced. */ -/* > */ -/* > On exit, if INFO = 0, the transformed matrix, stored in the */ -/* > same format as A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] B */ -/* > \verbatim */ -/* > B is DOUBLE PRECISION array, dimension (LDB,N) */ -/* > The triangular factor from the Cholesky factorization of B, */ -/* > as returned by DPOTRF. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDB */ -/* > \verbatim */ -/* > LDB is INTEGER */ -/* > The leading dimension of the array B. LDB >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit. */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleSYcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dsygs2_(integer *itype, char *uplo, integer *n, - doublereal *a, integer *lda, doublereal *b, integer *ldb, integer * - info, ftnlen uplo_len) +int dsygs2_(integer *itype, char *uplo, integer *n, doublereal *a, integer *lda, doublereal *b, + integer *ldb, integer *info, ftnlen uplo_len) { - /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2; doublereal d__1; - - /* Local variables */ integer k; doublereal ct, akk, bkk; - extern /* Subroutine */ int dsyr2_(char *, integer *, doublereal *, - doublereal *, integer *, doublereal *, integer *, doublereal *, - integer *, ftnlen), dscal_(integer *, doublereal *, doublereal *, - integer *); + extern int dsyr2_(char *, integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, integer *, ftnlen), + dscal_(integer *, doublereal *, doublereal *, integer *); extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *, - integer *, doublereal *, integer *); + extern int daxpy_(integer *, doublereal *, doublereal *, integer *, doublereal *, integer *); logical upper; - extern /* Subroutine */ int dtrmv_(char *, char *, char *, integer *, - doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, - ftnlen), dtrsv_(char *, char *, char *, integer *, doublereal *, - integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen), - xerbla_(char *, integer *, ftnlen); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ + extern int dtrmv_(char *, char *, char *, integer *, doublereal *, integer *, doublereal *, + integer *, ftnlen, ftnlen, ftnlen), + dtrsv_(char *, char *, char *, integer *, doublereal *, integer *, doublereal *, integer *, + ftnlen, ftnlen, ftnlen), + xerbla_(char *, integer *, ftnlen); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; - - /* Function Body */ *info = 0; upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); if (*itype < 1 || *itype > 3) { *info = -1; - } else if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + } else if (!upper && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { *info = -2; } else if (*n < 0) { *info = -3; - } else if (*lda < max(1,*n)) { + } else if (*lda < max(1, *n)) { *info = -5; - } else if (*ldb < max(1,*n)) { + } else if (*ldb < max(1, *n)) { *info = -7; } if (*info != 0) { @@ -228,20 +47,12 @@ f"> */ xerbla_((char *)"DSYGS2", &i__1, (ftnlen)6); return 0; } - if (*itype == 1) { if (upper) { - -/* Compute inv(U**T)*A*inv(U) */ - i__1 = *n; for (k = 1; k <= i__1; ++k) { - -/* Update the upper triangle of A(k:n,k:n) */ - akk = a[k + k * a_dim1]; bkk = b[k + k * b_dim1]; -/* Computing 2nd power */ d__1 = bkk; akk /= d__1 * d__1; a[k + k * a_dim1] = akk; @@ -251,34 +62,25 @@ f"> */ dscal_(&i__2, &d__1, &a[k + (k + 1) * a_dim1], lda); ct = akk * -.5; i__2 = *n - k; - daxpy_(&i__2, &ct, &b[k + (k + 1) * b_dim1], ldb, &a[k + ( - k + 1) * a_dim1], lda); + daxpy_(&i__2, &ct, &b[k + (k + 1) * b_dim1], ldb, &a[k + (k + 1) * a_dim1], + lda); i__2 = *n - k; dsyr2_(uplo, &i__2, &c_b6, &a[k + (k + 1) * a_dim1], lda, - &b[k + (k + 1) * b_dim1], ldb, &a[k + 1 + (k + 1) - * a_dim1], lda, (ftnlen)1); + &b[k + (k + 1) * b_dim1], ldb, &a[k + 1 + (k + 1) * a_dim1], lda, + (ftnlen)1); i__2 = *n - k; - daxpy_(&i__2, &ct, &b[k + (k + 1) * b_dim1], ldb, &a[k + ( - k + 1) * a_dim1], lda); + daxpy_(&i__2, &ct, &b[k + (k + 1) * b_dim1], ldb, &a[k + (k + 1) * a_dim1], + lda); i__2 = *n - k; - dtrsv_(uplo, (char *)"Transpose", (char *)"Non-unit", &i__2, &b[k + 1 + ( - k + 1) * b_dim1], ldb, &a[k + (k + 1) * a_dim1], - lda, (ftnlen)1, (ftnlen)9, (ftnlen)8); + dtrsv_(uplo, (char *)"Transpose", (char *)"Non-unit", &i__2, &b[k + 1 + (k + 1) * b_dim1], ldb, + &a[k + (k + 1) * a_dim1], lda, (ftnlen)1, (ftnlen)9, (ftnlen)8); } -/* L10: */ } } else { - -/* Compute inv(L)*A*inv(L**T) */ - i__1 = *n; for (k = 1; k <= i__1; ++k) { - -/* Update the lower triangle of A(k:n,k:n) */ - akk = a[k + k * a_dim1]; bkk = b[k + k * b_dim1]; -/* Computing 2nd power */ d__1 = bkk; akk /= d__1 * d__1; a[k + k * a_dim1] = akk; @@ -288,94 +90,68 @@ f"> */ dscal_(&i__2, &d__1, &a[k + 1 + k * a_dim1], &c__1); ct = akk * -.5; i__2 = *n - k; - daxpy_(&i__2, &ct, &b[k + 1 + k * b_dim1], &c__1, &a[k + - 1 + k * a_dim1], &c__1); + daxpy_(&i__2, &ct, &b[k + 1 + k * b_dim1], &c__1, &a[k + 1 + k * a_dim1], + &c__1); i__2 = *n - k; dsyr2_(uplo, &i__2, &c_b6, &a[k + 1 + k * a_dim1], &c__1, - &b[k + 1 + k * b_dim1], &c__1, &a[k + 1 + (k + 1) - * a_dim1], lda, (ftnlen)1); + &b[k + 1 + k * b_dim1], &c__1, &a[k + 1 + (k + 1) * a_dim1], lda, + (ftnlen)1); i__2 = *n - k; - daxpy_(&i__2, &ct, &b[k + 1 + k * b_dim1], &c__1, &a[k + - 1 + k * a_dim1], &c__1); + daxpy_(&i__2, &ct, &b[k + 1 + k * b_dim1], &c__1, &a[k + 1 + k * a_dim1], + &c__1); i__2 = *n - k; - dtrsv_(uplo, (char *)"No transpose", (char *)"Non-unit", &i__2, &b[k + 1 - + (k + 1) * b_dim1], ldb, &a[k + 1 + k * a_dim1], - &c__1, (ftnlen)1, (ftnlen)12, (ftnlen)8); + dtrsv_(uplo, (char *)"No transpose", (char *)"Non-unit", &i__2, &b[k + 1 + (k + 1) * b_dim1], + ldb, &a[k + 1 + k * a_dim1], &c__1, (ftnlen)1, (ftnlen)12, (ftnlen)8); } -/* L20: */ } } } else { if (upper) { - -/* Compute U*A*U**T */ - i__1 = *n; for (k = 1; k <= i__1; ++k) { - -/* Update the upper triangle of A(1:k,1:k) */ - akk = a[k + k * a_dim1]; bkk = b[k + k * b_dim1]; i__2 = k - 1; - dtrmv_(uplo, (char *)"No transpose", (char *)"Non-unit", &i__2, &b[b_offset], - ldb, &a[k * a_dim1 + 1], &c__1, (ftnlen)1, (ftnlen)12, - (ftnlen)8); + dtrmv_(uplo, (char *)"No transpose", (char *)"Non-unit", &i__2, &b[b_offset], ldb, + &a[k * a_dim1 + 1], &c__1, (ftnlen)1, (ftnlen)12, (ftnlen)8); ct = akk * .5; i__2 = k - 1; - daxpy_(&i__2, &ct, &b[k * b_dim1 + 1], &c__1, &a[k * a_dim1 + - 1], &c__1); + daxpy_(&i__2, &ct, &b[k * b_dim1 + 1], &c__1, &a[k * a_dim1 + 1], &c__1); i__2 = k - 1; - dsyr2_(uplo, &i__2, &c_b27, &a[k * a_dim1 + 1], &c__1, &b[k * - b_dim1 + 1], &c__1, &a[a_offset], lda, (ftnlen)1); + dsyr2_(uplo, &i__2, &c_b27, &a[k * a_dim1 + 1], &c__1, &b[k * b_dim1 + 1], &c__1, + &a[a_offset], lda, (ftnlen)1); i__2 = k - 1; - daxpy_(&i__2, &ct, &b[k * b_dim1 + 1], &c__1, &a[k * a_dim1 + - 1], &c__1); + daxpy_(&i__2, &ct, &b[k * b_dim1 + 1], &c__1, &a[k * a_dim1 + 1], &c__1); i__2 = k - 1; dscal_(&i__2, &bkk, &a[k * a_dim1 + 1], &c__1); -/* Computing 2nd power */ d__1 = bkk; a[k + k * a_dim1] = akk * (d__1 * d__1); -/* L30: */ } } else { - -/* Compute L**T *A*L */ - i__1 = *n; for (k = 1; k <= i__1; ++k) { - -/* Update the lower triangle of A(1:k,1:k) */ - akk = a[k + k * a_dim1]; bkk = b[k + k * b_dim1]; i__2 = k - 1; - dtrmv_(uplo, (char *)"Transpose", (char *)"Non-unit", &i__2, &b[b_offset], - ldb, &a[k + a_dim1], lda, (ftnlen)1, (ftnlen)9, ( - ftnlen)8); + dtrmv_(uplo, (char *)"Transpose", (char *)"Non-unit", &i__2, &b[b_offset], ldb, &a[k + a_dim1], lda, + (ftnlen)1, (ftnlen)9, (ftnlen)8); ct = akk * .5; i__2 = k - 1; daxpy_(&i__2, &ct, &b[k + b_dim1], ldb, &a[k + a_dim1], lda); i__2 = k - 1; - dsyr2_(uplo, &i__2, &c_b27, &a[k + a_dim1], lda, &b[k + - b_dim1], ldb, &a[a_offset], lda, (ftnlen)1); + dsyr2_(uplo, &i__2, &c_b27, &a[k + a_dim1], lda, &b[k + b_dim1], ldb, &a[a_offset], + lda, (ftnlen)1); i__2 = k - 1; daxpy_(&i__2, &ct, &b[k + b_dim1], ldb, &a[k + a_dim1], lda); i__2 = k - 1; dscal_(&i__2, &bkk, &a[k + a_dim1], lda); -/* Computing 2nd power */ d__1 = bkk; a[k + k * a_dim1] = akk * (d__1 * d__1); -/* L40: */ } } } return 0; - -/* End of DSYGS2 */ - -} /* dsygs2_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dsygst.cpp b/lib/linalg/dsygst.cpp index 0ad89918d3..dcf546a181 100644 --- a/lib/linalg/dsygst.cpp +++ b/lib/linalg/dsygst.cpp @@ -1,231 +1,52 @@ -/* fortran/dsygst.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static integer c_n1 = -1; static doublereal c_b14 = 1.; static doublereal c_b16 = -.5; static doublereal c_b19 = -1.; static doublereal c_b52 = .5; - -/* > \brief \b DSYGST */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DSYGST + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER UPLO */ -/* INTEGER INFO, ITYPE, LDA, LDB, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), B( LDB, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DSYGST reduces a real symmetric-definite generalized eigenproblem */ -/* > to standard form. */ -/* > */ -/* > If ITYPE = 1, the problem is A*x = lambda*B*x, */ -/* > and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T) */ -/* > */ -/* > If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or */ -/* > B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T*A*L. */ -/* > */ -/* > B must have been previously factorized as U**T*U or L*L**T by DPOTRF. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] ITYPE */ -/* > \verbatim */ -/* > ITYPE is INTEGER */ -/* > = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T); */ -/* > = 2 or 3: compute U*A*U**T or L**T*A*L. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > = 'U': Upper triangle of A is stored and B is factored as */ -/* > U**T*U; */ -/* > = 'L': Lower triangle of A is stored and B is factored as */ -/* > L*L**T. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrices A and B. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On entry, the symmetric matrix A. If UPLO = 'U', the leading */ -/* > N-by-N upper triangular part of A contains the upper */ -/* > triangular part of the matrix A, and the strictly lower */ -/* > triangular part of A is not referenced. If UPLO = 'L', the */ -/* > leading N-by-N lower triangular part of A contains the lower */ -/* > triangular part of the matrix A, and the strictly upper */ -/* > triangular part of A is not referenced. */ -/* > */ -/* > On exit, if INFO = 0, the transformed matrix, stored in the */ -/* > same format as A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] B */ -/* > \verbatim */ -/* > B is DOUBLE PRECISION array, dimension (LDB,N) */ -/* > The triangular factor from the Cholesky factorization of B, */ -/* > as returned by DPOTRF. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDB */ -/* > \verbatim */ -/* > LDB is INTEGER */ -/* > The leading dimension of the array B. LDB >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleSYcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dsygst_(integer *itype, char *uplo, integer *n, - doublereal *a, integer *lda, doublereal *b, integer *ldb, integer * - info, ftnlen uplo_len) +int dsygst_(integer *itype, char *uplo, integer *n, doublereal *a, integer *lda, doublereal *b, + integer *ldb, integer *info, ftnlen uplo_len) { - /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3; - - /* Local variables */ integer k, kb, nb; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int dtrmm_(char *, char *, char *, char *, - integer *, integer *, doublereal *, doublereal *, integer *, - doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen), dsymm_( - char *, char *, integer *, integer *, doublereal *, doublereal *, - integer *, doublereal *, integer *, doublereal *, doublereal *, - integer *, ftnlen, ftnlen); + extern int dtrmm_(char *, char *, char *, char *, integer *, integer *, doublereal *, + doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, + ftnlen), + dsymm_(char *, char *, integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); logical upper; - extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, - integer *, integer *, doublereal *, doublereal *, integer *, - doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen), dsygs2_( - integer *, char *, integer *, doublereal *, integer *, doublereal - *, integer *, integer *, ftnlen), dsyr2k_(char *, char *, integer - *, integer *, doublereal *, doublereal *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen) - , xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ + extern int dtrsm_(char *, char *, char *, char *, integer *, integer *, doublereal *, + doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, + ftnlen), + dsygs2_(integer *, char *, integer *, doublereal *, integer *, doublereal *, integer *, + integer *, ftnlen), + dsyr2k_(char *, char *, integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen), + xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; - - /* Function Body */ *info = 0; upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); if (*itype < 1 || *itype > 3) { *info = -1; - } else if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + } else if (!upper && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { *info = -2; } else if (*n < 0) { *info = -3; - } else if (*lda < max(1,*n)) { + } else if (*lda < max(1, *n)) { *info = -5; - } else if (*ldb < max(1,*n)) { + } else if (*ldb < max(1, *n)) { *info = -7; } if (*info != 0) { @@ -233,204 +54,138 @@ f"> */ xerbla_((char *)"DSYGST", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*n == 0) { return 0; } - -/* Determine the block size for this environment. */ - - nb = ilaenv_(&c__1, (char *)"DSYGST", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, ( - ftnlen)1); - + nb = ilaenv_(&c__1, (char *)"DSYGST", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); if (nb <= 1 || nb >= *n) { - -/* Use unblocked code */ - - dsygs2_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info, ( - ftnlen)1); + dsygs2_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info, (ftnlen)1); } else { - -/* Use blocked code */ - if (*itype == 1) { if (upper) { - -/* Compute inv(U**T)*A*inv(U) */ - i__1 = *n; i__2 = nb; for (k = 1; i__2 < 0 ? k >= i__1 : k <= i__1; k += i__2) { -/* Computing MIN */ i__3 = *n - k + 1; - kb = min(i__3,nb); - -/* Update the upper triangle of A(k:n,k:n) */ - - dsygs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k + - k * b_dim1], ldb, info, (ftnlen)1); + kb = min(i__3, nb); + dsygs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k + k * b_dim1], ldb, + info, (ftnlen)1); if (k + kb <= *n) { i__3 = *n - k - kb + 1; - dtrsm_((char *)"Left", uplo, (char *)"Transpose", (char *)"Non-unit", &kb, & - i__3, &c_b14, &b[k + k * b_dim1], ldb, &a[k + - (k + kb) * a_dim1], lda, (ftnlen)4, (ftnlen)1, - (ftnlen)9, (ftnlen)8); + dtrsm_((char *)"Left", uplo, (char *)"Transpose", (char *)"Non-unit", &kb, &i__3, &c_b14, + &b[k + k * b_dim1], ldb, &a[k + (k + kb) * a_dim1], lda, (ftnlen)4, + (ftnlen)1, (ftnlen)9, (ftnlen)8); i__3 = *n - k - kb + 1; - dsymm_((char *)"Left", uplo, &kb, &i__3, &c_b16, &a[k + k * - a_dim1], lda, &b[k + (k + kb) * b_dim1], ldb, - &c_b14, &a[k + (k + kb) * a_dim1], lda, ( - ftnlen)4, (ftnlen)1); + dsymm_((char *)"Left", uplo, &kb, &i__3, &c_b16, &a[k + k * a_dim1], lda, + &b[k + (k + kb) * b_dim1], ldb, &c_b14, &a[k + (k + kb) * a_dim1], + lda, (ftnlen)4, (ftnlen)1); i__3 = *n - k - kb + 1; - dsyr2k_(uplo, (char *)"Transpose", &i__3, &kb, &c_b19, &a[k + - (k + kb) * a_dim1], lda, &b[k + (k + kb) * - b_dim1], ldb, &c_b14, &a[k + kb + (k + kb) * - a_dim1], lda, (ftnlen)1, (ftnlen)9); + dsyr2k_(uplo, (char *)"Transpose", &i__3, &kb, &c_b19, &a[k + (k + kb) * a_dim1], + lda, &b[k + (k + kb) * b_dim1], ldb, &c_b14, + &a[k + kb + (k + kb) * a_dim1], lda, (ftnlen)1, (ftnlen)9); i__3 = *n - k - kb + 1; - dsymm_((char *)"Left", uplo, &kb, &i__3, &c_b16, &a[k + k * - a_dim1], lda, &b[k + (k + kb) * b_dim1], ldb, - &c_b14, &a[k + (k + kb) * a_dim1], lda, ( - ftnlen)4, (ftnlen)1); + dsymm_((char *)"Left", uplo, &kb, &i__3, &c_b16, &a[k + k * a_dim1], lda, + &b[k + (k + kb) * b_dim1], ldb, &c_b14, &a[k + (k + kb) * a_dim1], + lda, (ftnlen)4, (ftnlen)1); i__3 = *n - k - kb + 1; - dtrsm_((char *)"Right", uplo, (char *)"No transpose", (char *)"Non-unit", &kb, - &i__3, &c_b14, &b[k + kb + (k + kb) * b_dim1] - , ldb, &a[k + (k + kb) * a_dim1], lda, ( - ftnlen)5, (ftnlen)1, (ftnlen)12, (ftnlen)8); + dtrsm_((char *)"Right", uplo, (char *)"No transpose", (char *)"Non-unit", &kb, &i__3, &c_b14, + &b[k + kb + (k + kb) * b_dim1], ldb, &a[k + (k + kb) * a_dim1], lda, + (ftnlen)5, (ftnlen)1, (ftnlen)12, (ftnlen)8); } -/* L10: */ } } else { - -/* Compute inv(L)*A*inv(L**T) */ - i__2 = *n; i__1 = nb; for (k = 1; i__1 < 0 ? k >= i__2 : k <= i__2; k += i__1) { -/* Computing MIN */ i__3 = *n - k + 1; - kb = min(i__3,nb); - -/* Update the lower triangle of A(k:n,k:n) */ - - dsygs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k + - k * b_dim1], ldb, info, (ftnlen)1); + kb = min(i__3, nb); + dsygs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k + k * b_dim1], ldb, + info, (ftnlen)1); if (k + kb <= *n) { i__3 = *n - k - kb + 1; - dtrsm_((char *)"Right", uplo, (char *)"Transpose", (char *)"Non-unit", &i__3, - &kb, &c_b14, &b[k + k * b_dim1], ldb, &a[k + - kb + k * a_dim1], lda, (ftnlen)5, (ftnlen)1, ( - ftnlen)9, (ftnlen)8); + dtrsm_((char *)"Right", uplo, (char *)"Transpose", (char *)"Non-unit", &i__3, &kb, &c_b14, + &b[k + k * b_dim1], ldb, &a[k + kb + k * a_dim1], lda, (ftnlen)5, + (ftnlen)1, (ftnlen)9, (ftnlen)8); i__3 = *n - k - kb + 1; - dsymm_((char *)"Right", uplo, &i__3, &kb, &c_b16, &a[k + k * - a_dim1], lda, &b[k + kb + k * b_dim1], ldb, & - c_b14, &a[k + kb + k * a_dim1], lda, (ftnlen) - 5, (ftnlen)1); + dsymm_((char *)"Right", uplo, &i__3, &kb, &c_b16, &a[k + k * a_dim1], lda, + &b[k + kb + k * b_dim1], ldb, &c_b14, &a[k + kb + k * a_dim1], lda, + (ftnlen)5, (ftnlen)1); i__3 = *n - k - kb + 1; - dsyr2k_(uplo, (char *)"No transpose", &i__3, &kb, &c_b19, &a[ - k + kb + k * a_dim1], lda, &b[k + kb + k * - b_dim1], ldb, &c_b14, &a[k + kb + (k + kb) * - a_dim1], lda, (ftnlen)1, (ftnlen)12); + dsyr2k_(uplo, (char *)"No transpose", &i__3, &kb, &c_b19, &a[k + kb + k * a_dim1], + lda, &b[k + kb + k * b_dim1], ldb, &c_b14, + &a[k + kb + (k + kb) * a_dim1], lda, (ftnlen)1, (ftnlen)12); i__3 = *n - k - kb + 1; - dsymm_((char *)"Right", uplo, &i__3, &kb, &c_b16, &a[k + k * - a_dim1], lda, &b[k + kb + k * b_dim1], ldb, & - c_b14, &a[k + kb + k * a_dim1], lda, (ftnlen) - 5, (ftnlen)1); + dsymm_((char *)"Right", uplo, &i__3, &kb, &c_b16, &a[k + k * a_dim1], lda, + &b[k + kb + k * b_dim1], ldb, &c_b14, &a[k + kb + k * a_dim1], lda, + (ftnlen)5, (ftnlen)1); i__3 = *n - k - kb + 1; - dtrsm_((char *)"Left", uplo, (char *)"No transpose", (char *)"Non-unit", & - i__3, &kb, &c_b14, &b[k + kb + (k + kb) * - b_dim1], ldb, &a[k + kb + k * a_dim1], lda, ( - ftnlen)4, (ftnlen)1, (ftnlen)12, (ftnlen)8); + dtrsm_((char *)"Left", uplo, (char *)"No transpose", (char *)"Non-unit", &i__3, &kb, &c_b14, + &b[k + kb + (k + kb) * b_dim1], ldb, &a[k + kb + k * a_dim1], lda, + (ftnlen)4, (ftnlen)1, (ftnlen)12, (ftnlen)8); } -/* L20: */ } } } else { if (upper) { - -/* Compute U*A*U**T */ - i__1 = *n; i__2 = nb; for (k = 1; i__2 < 0 ? k >= i__1 : k <= i__1; k += i__2) { -/* Computing MIN */ i__3 = *n - k + 1; - kb = min(i__3,nb); - -/* Update the upper triangle of A(1:k+kb-1,1:k+kb-1) */ - + kb = min(i__3, nb); i__3 = k - 1; - dtrmm_((char *)"Left", uplo, (char *)"No transpose", (char *)"Non-unit", &i__3, & - kb, &c_b14, &b[b_offset], ldb, &a[k * a_dim1 + 1], - lda, (ftnlen)4, (ftnlen)1, (ftnlen)12, (ftnlen)8) - ; + dtrmm_((char *)"Left", uplo, (char *)"No transpose", (char *)"Non-unit", &i__3, &kb, &c_b14, + &b[b_offset], ldb, &a[k * a_dim1 + 1], lda, (ftnlen)4, (ftnlen)1, + (ftnlen)12, (ftnlen)8); i__3 = k - 1; - dsymm_((char *)"Right", uplo, &i__3, &kb, &c_b52, &a[k + k * - a_dim1], lda, &b[k * b_dim1 + 1], ldb, &c_b14, &a[ - k * a_dim1 + 1], lda, (ftnlen)5, (ftnlen)1); + dsymm_((char *)"Right", uplo, &i__3, &kb, &c_b52, &a[k + k * a_dim1], lda, + &b[k * b_dim1 + 1], ldb, &c_b14, &a[k * a_dim1 + 1], lda, (ftnlen)5, + (ftnlen)1); i__3 = k - 1; - dsyr2k_(uplo, (char *)"No transpose", &i__3, &kb, &c_b14, &a[k * - a_dim1 + 1], lda, &b[k * b_dim1 + 1], ldb, &c_b14, - &a[a_offset], lda, (ftnlen)1, (ftnlen)12); + dsyr2k_(uplo, (char *)"No transpose", &i__3, &kb, &c_b14, &a[k * a_dim1 + 1], lda, + &b[k * b_dim1 + 1], ldb, &c_b14, &a[a_offset], lda, (ftnlen)1, + (ftnlen)12); i__3 = k - 1; - dsymm_((char *)"Right", uplo, &i__3, &kb, &c_b52, &a[k + k * - a_dim1], lda, &b[k * b_dim1 + 1], ldb, &c_b14, &a[ - k * a_dim1 + 1], lda, (ftnlen)5, (ftnlen)1); + dsymm_((char *)"Right", uplo, &i__3, &kb, &c_b52, &a[k + k * a_dim1], lda, + &b[k * b_dim1 + 1], ldb, &c_b14, &a[k * a_dim1 + 1], lda, (ftnlen)5, + (ftnlen)1); i__3 = k - 1; - dtrmm_((char *)"Right", uplo, (char *)"Transpose", (char *)"Non-unit", &i__3, &kb, - &c_b14, &b[k + k * b_dim1], ldb, &a[k * a_dim1 + - 1], lda, (ftnlen)5, (ftnlen)1, (ftnlen)9, (ftnlen) - 8); - dsygs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k + - k * b_dim1], ldb, info, (ftnlen)1); -/* L30: */ + dtrmm_((char *)"Right", uplo, (char *)"Transpose", (char *)"Non-unit", &i__3, &kb, &c_b14, + &b[k + k * b_dim1], ldb, &a[k * a_dim1 + 1], lda, (ftnlen)5, (ftnlen)1, + (ftnlen)9, (ftnlen)8); + dsygs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k + k * b_dim1], ldb, + info, (ftnlen)1); } } else { - -/* Compute L**T*A*L */ - i__2 = *n; i__1 = nb; for (k = 1; i__1 < 0 ? k >= i__2 : k <= i__2; k += i__1) { -/* Computing MIN */ i__3 = *n - k + 1; - kb = min(i__3,nb); - -/* Update the lower triangle of A(1:k+kb-1,1:k+kb-1) */ - + kb = min(i__3, nb); i__3 = k - 1; - dtrmm_((char *)"Right", uplo, (char *)"No transpose", (char *)"Non-unit", &kb, & - i__3, &c_b14, &b[b_offset], ldb, &a[k + a_dim1], - lda, (ftnlen)5, (ftnlen)1, (ftnlen)12, (ftnlen)8); + dtrmm_((char *)"Right", uplo, (char *)"No transpose", (char *)"Non-unit", &kb, &i__3, &c_b14, + &b[b_offset], ldb, &a[k + a_dim1], lda, (ftnlen)5, (ftnlen)1, (ftnlen)12, + (ftnlen)8); i__3 = k - 1; - dsymm_((char *)"Left", uplo, &kb, &i__3, &c_b52, &a[k + k * - a_dim1], lda, &b[k + b_dim1], ldb, &c_b14, &a[k + - a_dim1], lda, (ftnlen)4, (ftnlen)1); + dsymm_((char *)"Left", uplo, &kb, &i__3, &c_b52, &a[k + k * a_dim1], lda, + &b[k + b_dim1], ldb, &c_b14, &a[k + a_dim1], lda, (ftnlen)4, (ftnlen)1); i__3 = k - 1; - dsyr2k_(uplo, (char *)"Transpose", &i__3, &kb, &c_b14, &a[k + - a_dim1], lda, &b[k + b_dim1], ldb, &c_b14, &a[ - a_offset], lda, (ftnlen)1, (ftnlen)9); + dsyr2k_(uplo, (char *)"Transpose", &i__3, &kb, &c_b14, &a[k + a_dim1], lda, + &b[k + b_dim1], ldb, &c_b14, &a[a_offset], lda, (ftnlen)1, (ftnlen)9); i__3 = k - 1; - dsymm_((char *)"Left", uplo, &kb, &i__3, &c_b52, &a[k + k * - a_dim1], lda, &b[k + b_dim1], ldb, &c_b14, &a[k + - a_dim1], lda, (ftnlen)4, (ftnlen)1); + dsymm_((char *)"Left", uplo, &kb, &i__3, &c_b52, &a[k + k * a_dim1], lda, + &b[k + b_dim1], ldb, &c_b14, &a[k + a_dim1], lda, (ftnlen)4, (ftnlen)1); i__3 = k - 1; - dtrmm_((char *)"Left", uplo, (char *)"Transpose", (char *)"Non-unit", &kb, &i__3, - &c_b14, &b[k + k * b_dim1], ldb, &a[k + a_dim1], - lda, (ftnlen)4, (ftnlen)1, (ftnlen)9, (ftnlen)8); - dsygs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k + - k * b_dim1], ldb, info, (ftnlen)1); -/* L40: */ + dtrmm_((char *)"Left", uplo, (char *)"Transpose", (char *)"Non-unit", &kb, &i__3, &c_b14, + &b[k + k * b_dim1], ldb, &a[k + a_dim1], lda, (ftnlen)4, (ftnlen)1, + (ftnlen)9, (ftnlen)8); + dsygs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k + k * b_dim1], ldb, + info, (ftnlen)1); } } } } return 0; - -/* End of DSYGST */ - -} /* dsygst_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dsygv.cpp b/lib/linalg/dsygv.cpp index bc7ed2cc76..62194ee354 100644 --- a/lib/linalg/dsygv.cpp +++ b/lib/linalg/dsygv.cpp @@ -1,263 +1,37 @@ -/* fortran/dsygv.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static integer c_n1 = -1; static doublereal c_b16 = 1.; - -/* > \brief \b DSYGV */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DSYGV + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DSYGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, */ -/* LWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER JOBZ, UPLO */ -/* INTEGER INFO, ITYPE, LDA, LDB, LWORK, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DSYGV computes all the eigenvalues, and optionally, the eigenvectors */ -/* > of a real generalized symmetric-definite eigenproblem, of the form */ -/* > A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. */ -/* > Here A and B are assumed to be symmetric and B is also */ -/* > positive definite. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] ITYPE */ -/* > \verbatim */ -/* > ITYPE is INTEGER */ -/* > Specifies the problem type to be solved: */ -/* > = 1: A*x = (lambda)*B*x */ -/* > = 2: A*B*x = (lambda)*x */ -/* > = 3: B*A*x = (lambda)*x */ -/* > \endverbatim */ -/* > */ -/* > \param[in] JOBZ */ -/* > \verbatim */ -/* > JOBZ is CHARACTER*1 */ -/* > = 'N': Compute eigenvalues only; */ -/* > = 'V': Compute eigenvalues and eigenvectors. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > = 'U': Upper triangles of A and B are stored; */ -/* > = 'L': Lower triangles of A and B are stored. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrices A and B. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA, N) */ -/* > On entry, the symmetric matrix A. If UPLO = 'U', the */ -/* > leading N-by-N upper triangular part of A contains the */ -/* > upper triangular part of the matrix A. If UPLO = 'L', */ -/* > the leading N-by-N lower triangular part of A contains */ -/* > the lower triangular part of the matrix A. */ -/* > */ -/* > On exit, if JOBZ = 'V', then if INFO = 0, A contains the */ -/* > matrix Z of eigenvectors. The eigenvectors are normalized */ -/* > as follows: */ -/* > if ITYPE = 1 or 2, Z**T*B*Z = I; */ -/* > if ITYPE = 3, Z**T*inv(B)*Z = I. */ -/* > If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') */ -/* > or the lower triangle (if UPLO='L') of A, including the */ -/* > diagonal, is destroyed. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] B */ -/* > \verbatim */ -/* > B is DOUBLE PRECISION array, dimension (LDB, N) */ -/* > On entry, the symmetric positive definite matrix B. */ -/* > If UPLO = 'U', the leading N-by-N upper triangular part of B */ -/* > contains the upper triangular part of the matrix B. */ -/* > If UPLO = 'L', the leading N-by-N lower triangular part of B */ -/* > contains the lower triangular part of the matrix B. */ -/* > */ -/* > On exit, if INFO <= N, the part of B containing the matrix is */ -/* > overwritten by the triangular factor U or L from the Cholesky */ -/* > factorization B = U**T*U or B = L*L**T. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDB */ -/* > \verbatim */ -/* > LDB is INTEGER */ -/* > The leading dimension of the array B. LDB >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] W */ -/* > \verbatim */ -/* > W is DOUBLE PRECISION array, dimension (N) */ -/* > If INFO = 0, the eigenvalues in ascending order. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ -/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LWORK */ -/* > \verbatim */ -/* > LWORK is INTEGER */ -/* > The length of the array WORK. LWORK >= max(1,3*N-1). */ -/* > For optimal efficiency, LWORK >= (NB+2)*N, */ -/* > where NB is the blocksize for DSYTRD returned by ILAENV. */ -/* > */ -/* > If LWORK = -1, then a workspace query is assumed; the routine */ -/* > only calculates the optimal size of the WORK array, returns */ -/* > this value as the first entry of the WORK array, and no error */ -/* > message related to LWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > > 0: DPOTRF or DSYEV returned an error code: */ -/* > <= N: if INFO = i, DSYEV failed to converge; */ -/* > i off-diagonal elements of an intermediate */ -/* > tridiagonal form did not converge to zero; */ -/* > > N: if INFO = N + i, for 1 <= i <= N, then the leading */ -/* > minor of order i of B is not positive definite. */ -/* > The factorization of B could not be completed and */ -/* > no eigenvalues or eigenvectors were computed. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleSYeigen */ - -/* ===================================================================== */ -/* Subroutine */ int dsygv_(integer *itype, char *jobz, char *uplo, integer * - n, doublereal *a, integer *lda, doublereal *b, integer *ldb, - doublereal *w, doublereal *work, integer *lwork, integer *info, - ftnlen jobz_len, ftnlen uplo_len) +int dsygv_(integer *itype, char *jobz, char *uplo, integer *n, doublereal *a, integer *lda, + doublereal *b, integer *ldb, doublereal *w, doublereal *work, integer *lwork, + integer *info, ftnlen jobz_len, ftnlen uplo_len) { - /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2; - - /* Local variables */ integer nb, neig; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int dtrmm_(char *, char *, char *, char *, - integer *, integer *, doublereal *, doublereal *, integer *, - doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + extern int dtrmm_(char *, char *, char *, char *, integer *, integer *, doublereal *, + doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, + ftnlen); char trans[1]; - extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, - integer *, integer *, doublereal *, doublereal *, integer *, - doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + extern int dtrsm_(char *, char *, char *, char *, integer *, integer *, doublereal *, + doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, + ftnlen); logical upper; - extern /* Subroutine */ int dsyev_(char *, char *, integer *, doublereal * - , integer *, doublereal *, doublereal *, integer *, integer *, - ftnlen, ftnlen); + extern int dsyev_(char *, char *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, integer *, ftnlen, ftnlen); logical wantz; - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - extern /* Subroutine */ int dpotrf_(char *, integer *, doublereal *, - integer *, integer *, ftnlen); + extern int xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); + extern int dpotrf_(char *, integer *, doublereal *, integer *, integer *, ftnlen); integer lwkmin; - extern /* Subroutine */ int dsygst_(integer *, char *, integer *, - doublereal *, integer *, doublereal *, integer *, integer *, - ftnlen); + extern int dsygst_(integer *, char *, integer *, doublereal *, integer *, doublereal *, + integer *, integer *, ftnlen); integer lwkopt; logical lquery; - - -/* -- LAPACK driver routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; @@ -266,43 +40,34 @@ static doublereal c_b16 = 1.; b -= b_offset; --w; --work; - - /* Function Body */ wantz = lsame_(jobz, (char *)"V", (ftnlen)1, (ftnlen)1); upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); lquery = *lwork == -1; - *info = 0; if (*itype < 1 || *itype > 3) { *info = -1; - } else if (! (wantz || lsame_(jobz, (char *)"N", (ftnlen)1, (ftnlen)1))) { + } else if (!(wantz || lsame_(jobz, (char *)"N", (ftnlen)1, (ftnlen)1))) { *info = -2; - } else if (! (upper || lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1))) { + } else if (!(upper || lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1))) { *info = -3; } else if (*n < 0) { *info = -4; - } else if (*lda < max(1,*n)) { + } else if (*lda < max(1, *n)) { *info = -6; - } else if (*ldb < max(1,*n)) { + } else if (*ldb < max(1, *n)) { *info = -8; } - if (*info == 0) { -/* Computing MAX */ i__1 = 1, i__2 = *n * 3 - 1; - lwkmin = max(i__1,i__2); - nb = ilaenv_(&c__1, (char *)"DSYTRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, - (ftnlen)1); -/* Computing MAX */ + lwkmin = max(i__1, i__2); + nb = ilaenv_(&c__1, (char *)"DSYTRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); i__1 = lwkmin, i__2 = (nb + 2) * *n; - lwkopt = max(i__1,i__2); - work[1] = (doublereal) lwkopt; - - if (*lwork < lwkmin && ! lquery) { + lwkopt = max(i__1, i__2); + work[1] = (doublereal)lwkopt; + if (*lwork < lwkmin && !lquery) { *info = -11; } } - if (*info != 0) { i__1 = -(*info); xerbla_((char *)"DSYGV ", &i__1, (ftnlen)6); @@ -310,75 +75,42 @@ static doublereal c_b16 = 1.; } else if (lquery) { return 0; } - -/* Quick return if possible */ - if (*n == 0) { return 0; } - -/* Form a Cholesky factorization of B. */ - dpotrf_(uplo, n, &b[b_offset], ldb, info, (ftnlen)1); if (*info != 0) { *info = *n + *info; return 0; } - -/* Transform problem to standard eigenvalue problem and solve. */ - - dsygst_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info, ( - ftnlen)1); - dsyev_(jobz, uplo, n, &a[a_offset], lda, &w[1], &work[1], lwork, info, ( - ftnlen)1, (ftnlen)1); - + dsygst_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info, (ftnlen)1); + dsyev_(jobz, uplo, n, &a[a_offset], lda, &w[1], &work[1], lwork, info, (ftnlen)1, (ftnlen)1); if (wantz) { - -/* Backtransform eigenvectors to the original problem. */ - neig = *n; if (*info > 0) { neig = *info - 1; } if (*itype == 1 || *itype == 2) { - -/* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; */ -/* backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y */ - if (upper) { *(unsigned char *)trans = 'N'; } else { *(unsigned char *)trans = 'T'; } - - dtrsm_((char *)"Left", uplo, trans, (char *)"Non-unit", n, &neig, &c_b16, &b[ - b_offset], ldb, &a[a_offset], lda, (ftnlen)4, (ftnlen)1, ( - ftnlen)1, (ftnlen)8); - + dtrsm_((char *)"Left", uplo, trans, (char *)"Non-unit", n, &neig, &c_b16, &b[b_offset], ldb, + &a[a_offset], lda, (ftnlen)4, (ftnlen)1, (ftnlen)1, (ftnlen)8); } else if (*itype == 3) { - -/* For B*A*x=(lambda)*x; */ -/* backtransform eigenvectors: x = L*y or U**T*y */ - if (upper) { *(unsigned char *)trans = 'T'; } else { *(unsigned char *)trans = 'N'; } - - dtrmm_((char *)"Left", uplo, trans, (char *)"Non-unit", n, &neig, &c_b16, &b[ - b_offset], ldb, &a[a_offset], lda, (ftnlen)4, (ftnlen)1, ( - ftnlen)1, (ftnlen)8); + dtrmm_((char *)"Left", uplo, trans, (char *)"Non-unit", n, &neig, &c_b16, &b[b_offset], ldb, + &a[a_offset], lda, (ftnlen)4, (ftnlen)1, (ftnlen)1, (ftnlen)8); } } - - work[1] = (doublereal) lwkopt; + work[1] = (doublereal)lwkopt; return 0; - -/* End of DSYGV */ - -} /* dsygv_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dsygvd.cpp b/lib/linalg/dsygvd.cpp index c44f6239f6..59c69d21d1 100644 --- a/lib/linalg/dsygvd.cpp +++ b/lib/linalg/dsygvd.cpp @@ -1,310 +1,34 @@ -/* fortran/dsygvd.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static doublereal c_b11 = 1.; - -/* > \brief \b DSYGVD */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DSYGVD + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DSYGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, */ -/* LWORK, IWORK, LIWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER JOBZ, UPLO */ -/* INTEGER INFO, ITYPE, LDA, LDB, LIWORK, LWORK, N */ -/* .. */ -/* .. Array Arguments .. */ -/* INTEGER IWORK( * ) */ -/* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DSYGVD computes all the eigenvalues, and optionally, the eigenvectors */ -/* > of a real generalized symmetric-definite eigenproblem, of the form */ -/* > A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and */ -/* > B are assumed to be symmetric and B is also positive definite. */ -/* > If eigenvectors are desired, it uses a divide and conquer algorithm. */ -/* > */ -/* > The divide and conquer algorithm makes very mild assumptions about */ -/* > floating point arithmetic. It will work on machines with a guard */ -/* > digit in add/subtract, or on those binary machines without guard */ -/* > digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */ -/* > Cray-2. It could conceivably fail on hexadecimal or decimal machines */ -/* > without guard digits, but we know of none. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] ITYPE */ -/* > \verbatim */ -/* > ITYPE is INTEGER */ -/* > Specifies the problem type to be solved: */ -/* > = 1: A*x = (lambda)*B*x */ -/* > = 2: A*B*x = (lambda)*x */ -/* > = 3: B*A*x = (lambda)*x */ -/* > \endverbatim */ -/* > */ -/* > \param[in] JOBZ */ -/* > \verbatim */ -/* > JOBZ is CHARACTER*1 */ -/* > = 'N': Compute eigenvalues only; */ -/* > = 'V': Compute eigenvalues and eigenvectors. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > = 'U': Upper triangles of A and B are stored; */ -/* > = 'L': Lower triangles of A and B are stored. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrices A and B. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA, N) */ -/* > On entry, the symmetric matrix A. If UPLO = 'U', the */ -/* > leading N-by-N upper triangular part of A contains the */ -/* > upper triangular part of the matrix A. If UPLO = 'L', */ -/* > the leading N-by-N lower triangular part of A contains */ -/* > the lower triangular part of the matrix A. */ -/* > */ -/* > On exit, if JOBZ = 'V', then if INFO = 0, A contains the */ -/* > matrix Z of eigenvectors. The eigenvectors are normalized */ -/* > as follows: */ -/* > if ITYPE = 1 or 2, Z**T*B*Z = I; */ -/* > if ITYPE = 3, Z**T*inv(B)*Z = I. */ -/* > If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') */ -/* > or the lower triangle (if UPLO='L') of A, including the */ -/* > diagonal, is destroyed. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] B */ -/* > \verbatim */ -/* > B is DOUBLE PRECISION array, dimension (LDB, N) */ -/* > On entry, the symmetric matrix B. If UPLO = 'U', the */ -/* > leading N-by-N upper triangular part of B contains the */ -/* > upper triangular part of the matrix B. If UPLO = 'L', */ -/* > the leading N-by-N lower triangular part of B contains */ -/* > the lower triangular part of the matrix B. */ -/* > */ -/* > On exit, if INFO <= N, the part of B containing the matrix is */ -/* > overwritten by the triangular factor U or L from the Cholesky */ -/* > factorization B = U**T*U or B = L*L**T. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDB */ -/* > \verbatim */ -/* > LDB is INTEGER */ -/* > The leading dimension of the array B. LDB >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] W */ -/* > \verbatim */ -/* > W is DOUBLE PRECISION array, dimension (N) */ -/* > If INFO = 0, the eigenvalues in ascending order. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ -/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LWORK */ -/* > \verbatim */ -/* > LWORK is INTEGER */ -/* > The dimension of the array WORK. */ -/* > If N <= 1, LWORK >= 1. */ -/* > If JOBZ = 'N' and N > 1, LWORK >= 2*N+1. */ -/* > If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2. */ -/* > */ -/* > If LWORK = -1, then a workspace query is assumed; the routine */ -/* > only calculates the optimal sizes of the WORK and IWORK */ -/* > arrays, returns these values as the first entries of the WORK */ -/* > and IWORK arrays, and no error message related to LWORK or */ -/* > LIWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] IWORK */ -/* > \verbatim */ -/* > IWORK is INTEGER array, dimension (MAX(1,LIWORK)) */ -/* > On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LIWORK */ -/* > \verbatim */ -/* > LIWORK is INTEGER */ -/* > The dimension of the array IWORK. */ -/* > If N <= 1, LIWORK >= 1. */ -/* > If JOBZ = 'N' and N > 1, LIWORK >= 1. */ -/* > If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. */ -/* > */ -/* > If LIWORK = -1, then a workspace query is assumed; the */ -/* > routine only calculates the optimal sizes of the WORK and */ -/* > IWORK arrays, returns these values as the first entries of */ -/* > the WORK and IWORK arrays, and no error message related to */ -/* > LWORK or LIWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > > 0: DPOTRF or DSYEVD returned an error code: */ -/* > <= N: if INFO = i and JOBZ = 'N', then the algorithm */ -/* > failed to converge; i off-diagonal elements of an */ -/* > intermediate tridiagonal form did not converge to */ -/* > zero; */ -/* > if INFO = i and JOBZ = 'V', then the algorithm */ -/* > failed to compute an eigenvalue while working on */ -/* > the submatrix lying in rows and columns INFO/(N+1) */ -/* > through mod(INFO,N+1); */ -/* > > N: if INFO = N + i, for 1 <= i <= N, then the leading */ -/* > minor of order i of B is not positive definite. */ -/* > The factorization of B could not be completed and */ -/* > no eigenvalues or eigenvectors were computed. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleSYeigen */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > Modified so that no backsubstitution is performed if DSYEVD fails to */ -/* > converge (NEIG in old code could be greater than N causing out of */ -/* > bounds reference to A - reported by Ralf Meyer). Also corrected the */ -/* > description of INFO and the test on ITYPE. Sven, 16 Feb 05. */ -/* > \endverbatim */ - -/* > \par Contributors: */ -/* ================== */ -/* > */ -/* > Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dsygvd_(integer *itype, char *jobz, char *uplo, integer * - n, doublereal *a, integer *lda, doublereal *b, integer *ldb, - doublereal *w, doublereal *work, integer *lwork, integer *iwork, - integer *liwork, integer *info, ftnlen jobz_len, ftnlen uplo_len) +int dsygvd_(integer *itype, char *jobz, char *uplo, integer *n, doublereal *a, integer *lda, + doublereal *b, integer *ldb, doublereal *w, doublereal *work, integer *lwork, + integer *iwork, integer *liwork, integer *info, ftnlen jobz_len, ftnlen uplo_len) { - /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1; doublereal d__1, d__2; - - /* Local variables */ integer lopt; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int dtrmm_(char *, char *, char *, char *, - integer *, integer *, doublereal *, doublereal *, integer *, - doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + extern int dtrmm_(char *, char *, char *, char *, integer *, integer *, doublereal *, + doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, + ftnlen); integer lwmin; char trans[1]; integer liopt; - extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, - integer *, integer *, doublereal *, doublereal *, integer *, - doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + extern int dtrsm_(char *, char *, char *, char *, integer *, integer *, doublereal *, + doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, + ftnlen); logical upper, wantz; - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), dpotrf_( - char *, integer *, doublereal *, integer *, integer *, ftnlen); + extern int xerbla_(char *, integer *, ftnlen), + dpotrf_(char *, integer *, doublereal *, integer *, integer *, ftnlen); integer liwmin; - extern /* Subroutine */ int dsyevd_(char *, char *, integer *, doublereal - *, integer *, doublereal *, doublereal *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen), dsygst_(integer *, char *, - integer *, doublereal *, integer *, doublereal *, integer *, - integer *, ftnlen); + extern int dsyevd_(char *, char *, integer *, doublereal *, integer *, doublereal *, + doublereal *, integer *, integer *, integer *, integer *, ftnlen, ftnlen), + dsygst_(integer *, char *, integer *, doublereal *, integer *, doublereal *, integer *, + integer *, ftnlen); logical lquery; - - -/* -- LAPACK driver routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; @@ -314,19 +38,15 @@ f"> */ --w; --work; --iwork; - - /* Function Body */ wantz = lsame_(jobz, (char *)"V", (ftnlen)1, (ftnlen)1); upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); lquery = *lwork == -1 || *liwork == -1; - *info = 0; if (*n <= 1) { liwmin = 1; lwmin = 1; } else if (wantz) { liwmin = *n * 5 + 3; -/* Computing 2nd power */ i__1 = *n; lwmin = *n * 6 + 1 + (i__1 * i__1 << 1); } else { @@ -337,29 +57,26 @@ f"> */ liopt = liwmin; if (*itype < 1 || *itype > 3) { *info = -1; - } else if (! (wantz || lsame_(jobz, (char *)"N", (ftnlen)1, (ftnlen)1))) { + } else if (!(wantz || lsame_(jobz, (char *)"N", (ftnlen)1, (ftnlen)1))) { *info = -2; - } else if (! (upper || lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1))) { + } else if (!(upper || lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1))) { *info = -3; } else if (*n < 0) { *info = -4; - } else if (*lda < max(1,*n)) { + } else if (*lda < max(1, *n)) { *info = -6; - } else if (*ldb < max(1,*n)) { + } else if (*ldb < max(1, *n)) { *info = -8; } - if (*info == 0) { - work[1] = (doublereal) lopt; + work[1] = (doublereal)lopt; iwork[1] = liopt; - - if (*lwork < lwmin && ! lquery) { + if (*lwork < lwmin && !lquery) { *info = -11; - } else if (*liwork < liwmin && ! lquery) { + } else if (*liwork < liwmin && !lquery) { *info = -13; } } - if (*info != 0) { i__1 = -(*info); xerbla_((char *)"DSYGVD", &i__1, (ftnlen)6); @@ -367,79 +84,44 @@ f"> */ } else if (lquery) { return 0; } - -/* Quick return if possible */ - if (*n == 0) { return 0; } - -/* Form a Cholesky factorization of B. */ - dpotrf_(uplo, n, &b[b_offset], ldb, info, (ftnlen)1); if (*info != 0) { *info = *n + *info; return 0; } - -/* Transform problem to standard eigenvalue problem and solve. */ - - dsygst_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info, ( - ftnlen)1); - dsyevd_(jobz, uplo, n, &a[a_offset], lda, &w[1], &work[1], lwork, &iwork[ - 1], liwork, info, (ftnlen)1, (ftnlen)1); -/* Computing MAX */ - d__1 = (doublereal) lopt; - lopt = (integer) max(d__1,work[1]); -/* Computing MAX */ - d__1 = (doublereal) liopt, d__2 = (doublereal) iwork[1]; - liopt = (integer) max(d__1,d__2); - + dsygst_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info, (ftnlen)1); + dsyevd_(jobz, uplo, n, &a[a_offset], lda, &w[1], &work[1], lwork, &iwork[1], liwork, info, + (ftnlen)1, (ftnlen)1); + d__1 = (doublereal)lopt; + lopt = (integer)max(d__1, work[1]); + d__1 = (doublereal)liopt, d__2 = (doublereal)iwork[1]; + liopt = (integer)max(d__1, d__2); if (wantz && *info == 0) { - -/* Backtransform eigenvectors to the original problem. */ - if (*itype == 1 || *itype == 2) { - -/* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; */ -/* backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y */ - if (upper) { *(unsigned char *)trans = 'N'; } else { *(unsigned char *)trans = 'T'; } - - dtrsm_((char *)"Left", uplo, trans, (char *)"Non-unit", n, n, &c_b11, &b[b_offset] - , ldb, &a[a_offset], lda, (ftnlen)4, (ftnlen)1, (ftnlen)1, - (ftnlen)8); - + dtrsm_((char *)"Left", uplo, trans, (char *)"Non-unit", n, n, &c_b11, &b[b_offset], ldb, &a[a_offset], + lda, (ftnlen)4, (ftnlen)1, (ftnlen)1, (ftnlen)8); } else if (*itype == 3) { - -/* For B*A*x=(lambda)*x; */ -/* backtransform eigenvectors: x = L*y or U**T*y */ - if (upper) { *(unsigned char *)trans = 'T'; } else { *(unsigned char *)trans = 'N'; } - - dtrmm_((char *)"Left", uplo, trans, (char *)"Non-unit", n, n, &c_b11, &b[b_offset] - , ldb, &a[a_offset], lda, (ftnlen)4, (ftnlen)1, (ftnlen)1, - (ftnlen)8); + dtrmm_((char *)"Left", uplo, trans, (char *)"Non-unit", n, n, &c_b11, &b[b_offset], ldb, &a[a_offset], + lda, (ftnlen)4, (ftnlen)1, (ftnlen)1, (ftnlen)8); } } - - work[1] = (doublereal) lopt; + work[1] = (doublereal)lopt; iwork[1] = liopt; - return 0; - -/* End of DSYGVD */ - -} /* dsygvd_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dsymm.cpp b/lib/linalg/dsymm.cpp index 83538c9c27..f50e24cf3c 100644 --- a/lib/linalg/dsymm.cpp +++ b/lib/linalg/dsymm.cpp @@ -1,250 +1,18 @@ -/* fortran/dsymm.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DSYMM */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC) */ - -/* .. Scalar Arguments .. */ -/* DOUBLE PRECISION ALPHA,BETA */ -/* INTEGER LDA,LDB,LDC,M,N */ -/* CHARACTER SIDE,UPLO */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DSYMM performs one of the matrix-matrix operations */ -/* > */ -/* > C := alpha*A*B + beta*C, */ -/* > */ -/* > or */ -/* > */ -/* > C := alpha*B*A + beta*C, */ -/* > */ -/* > where alpha and beta are scalars, A is a symmetric matrix and B and */ -/* > C are m by n matrices. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] SIDE */ -/* > \verbatim */ -/* > SIDE is CHARACTER*1 */ -/* > On entry, SIDE specifies whether the symmetric matrix A */ -/* > appears on the left or right in the operation as follows: */ -/* > */ -/* > SIDE = 'L' or 'l' C := alpha*A*B + beta*C, */ -/* > */ -/* > SIDE = 'R' or 'r' C := alpha*B*A + beta*C, */ -/* > \endverbatim */ -/* > */ -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > On entry, UPLO specifies whether the upper or lower */ -/* > triangular part of the symmetric matrix A is to be */ -/* > referenced as follows: */ -/* > */ -/* > UPLO = 'U' or 'u' Only the upper triangular part of the */ -/* > symmetric matrix is to be referenced. */ -/* > */ -/* > UPLO = 'L' or 'l' Only the lower triangular part of the */ -/* > symmetric matrix is to be referenced. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > On entry, M specifies the number of rows of the matrix C. */ -/* > M must be at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > On entry, N specifies the number of columns of the matrix C. */ -/* > N must be at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] ALPHA */ -/* > \verbatim */ -/* > ALPHA is DOUBLE PRECISION. */ -/* > On entry, ALPHA specifies the scalar alpha. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is */ -/* > m when SIDE = 'L' or 'l' and is n otherwise. */ -/* > Before entry with SIDE = 'L' or 'l', the m by m part of */ -/* > the array A must contain the symmetric matrix, such that */ -/* > when UPLO = 'U' or 'u', the leading m by m upper triangular */ -/* > part of the array A must contain the upper triangular part */ -/* > of the symmetric matrix and the strictly lower triangular */ -/* > part of A is not referenced, and when UPLO = 'L' or 'l', */ -/* > the leading m by m lower triangular part of the array A */ -/* > must contain the lower triangular part of the symmetric */ -/* > matrix and the strictly upper triangular part of A is not */ -/* > referenced. */ -/* > Before entry with SIDE = 'R' or 'r', the n by n part of */ -/* > the array A must contain the symmetric matrix, such that */ -/* > when UPLO = 'U' or 'u', the leading n by n upper triangular */ -/* > part of the array A must contain the upper triangular part */ -/* > of the symmetric matrix and the strictly lower triangular */ -/* > part of A is not referenced, and when UPLO = 'L' or 'l', */ -/* > the leading n by n lower triangular part of the array A */ -/* > must contain the lower triangular part of the symmetric */ -/* > matrix and the strictly upper triangular part of A is not */ -/* > referenced. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > On entry, LDA specifies the first dimension of A as declared */ -/* > in the calling (sub) program. When SIDE = 'L' or 'l' then */ -/* > LDA must be at least max( 1, m ), otherwise LDA must be at */ -/* > least max( 1, n ). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] B */ -/* > \verbatim */ -/* > B is DOUBLE PRECISION array, dimension ( LDB, N ) */ -/* > Before entry, the leading m by n part of the array B must */ -/* > contain the matrix B. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDB */ -/* > \verbatim */ -/* > LDB is INTEGER */ -/* > On entry, LDB specifies the first dimension of B as declared */ -/* > in the calling (sub) program. LDB must be at least */ -/* > max( 1, m ). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] BETA */ -/* > \verbatim */ -/* > BETA is DOUBLE PRECISION. */ -/* > On entry, BETA specifies the scalar beta. When BETA is */ -/* > supplied as zero then C need not be set on input. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] C */ -/* > \verbatim */ -/* > C is DOUBLE PRECISION array, dimension ( LDC, N ) */ -/* > Before entry, the leading m by n part of the array C must */ -/* > contain the matrix C, except when beta is zero, in which */ -/* > case C need not be set on entry. */ -/* > On exit, the array C is overwritten by the m by n updated */ -/* > matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDC */ -/* > \verbatim */ -/* > LDC is INTEGER */ -/* > On entry, LDC specifies the first dimension of C as declared */ -/* > in the calling (sub) program. LDC must be at least */ -/* > max( 1, m ). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup double_blas_level3 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > Level 3 Blas routine. */ -/* > */ -/* > -- Written on 8-February-1989. */ -/* > Jack Dongarra, Argonne National Laboratory. */ -/* > Iain Duff, AERE Harwell. */ -/* > Jeremy Du Croz, Numerical Algorithms Group Ltd. */ -/* > Sven Hammarling, Numerical Algorithms Group Ltd. */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dsymm_(char *side, char *uplo, integer *m, integer *n, - doublereal *alpha, doublereal *a, integer *lda, doublereal *b, - integer *ldb, doublereal *beta, doublereal *c__, integer *ldc, ftnlen - side_len, ftnlen uplo_len) +int dsymm_(char *side, char *uplo, integer *m, integer *n, doublereal *alpha, doublereal *a, + integer *lda, doublereal *b, integer *ldb, doublereal *beta, doublereal *c__, + integer *ldc, ftnlen side_len, ftnlen uplo_len) { - /* System generated locals */ - integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, - i__3; - - /* Local variables */ + integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, i__3; integer i__, j, k, info; doublereal temp1, temp2; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer nrowa; logical upper; - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - - -/* -- Reference BLAS level3 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. Parameters .. */ -/* .. */ - -/* Set NROWA as the number of rows of A. */ - - /* Parameter adjustments */ + extern int xerbla_(char *, integer *, ftnlen); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; @@ -254,47 +22,35 @@ extern "C" { c_dim1 = *ldc; c_offset = 1 + c_dim1; c__ -= c_offset; - - /* Function Body */ if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { nrowa = *m; } else { nrowa = *n; } upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); - -/* Test the input parameters. */ - info = 0; - if (! lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1) && ! lsame_(side, (char *)"R", ( - ftnlen)1, (ftnlen)1)) { + if (!lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1) && !lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { info = 1; - } else if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + } else if (!upper && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { info = 2; } else if (*m < 0) { info = 3; } else if (*n < 0) { info = 4; - } else if (*lda < max(1,nrowa)) { + } else if (*lda < max(1, nrowa)) { info = 7; - } else if (*ldb < max(1,*m)) { + } else if (*ldb < max(1, *m)) { info = 9; - } else if (*ldc < max(1,*m)) { + } else if (*ldc < max(1, *m)) { info = 12; } if (info != 0) { xerbla_((char *)"DSYMM ", &info, (ftnlen)6); return 0; } - -/* Quick return if possible. */ - if (*m == 0 || *n == 0 || *alpha == 0. && *beta == 1.) { return 0; } - -/* And when alpha.eq.zero. */ - if (*alpha == 0.) { if (*beta == 0.) { i__1 = *n; @@ -302,9 +58,7 @@ extern "C" { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { c__[i__ + j * c_dim1] = 0.; -/* L10: */ } -/* L20: */ } } else { i__1 = *n; @@ -312,20 +66,12 @@ extern "C" { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; -/* L30: */ } -/* L40: */ } } return 0; } - -/* Start the operations. */ - if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { - -/* Form C := alpha*A*B + beta*C. */ - if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { @@ -337,19 +83,14 @@ extern "C" { for (k = 1; k <= i__3; ++k) { c__[k + j * c_dim1] += temp1 * a[k + i__ * a_dim1]; temp2 += b[k + j * b_dim1] * a[k + i__ * a_dim1]; -/* L50: */ } if (*beta == 0.) { - c__[i__ + j * c_dim1] = temp1 * a[i__ + i__ * a_dim1] - + *alpha * temp2; + c__[i__ + j * c_dim1] = temp1 * a[i__ + i__ * a_dim1] + *alpha * temp2; } else { - c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1] - + temp1 * a[i__ + i__ * a_dim1] + *alpha * - temp2; + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1] + + temp1 * a[i__ + i__ * a_dim1] + *alpha * temp2; } -/* L60: */ } -/* L70: */ } } else { i__1 = *n; @@ -361,25 +102,17 @@ extern "C" { for (k = i__ + 1; k <= i__2; ++k) { c__[k + j * c_dim1] += temp1 * a[k + i__ * a_dim1]; temp2 += b[k + j * b_dim1] * a[k + i__ * a_dim1]; -/* L80: */ } if (*beta == 0.) { - c__[i__ + j * c_dim1] = temp1 * a[i__ + i__ * a_dim1] - + *alpha * temp2; + c__[i__ + j * c_dim1] = temp1 * a[i__ + i__ * a_dim1] + *alpha * temp2; } else { - c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1] - + temp1 * a[i__ + i__ * a_dim1] + *alpha * - temp2; + c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1] + + temp1 * a[i__ + i__ * a_dim1] + *alpha * temp2; } -/* L90: */ } -/* L100: */ } } } else { - -/* Form C := alpha*B*A + beta*C. */ - i__1 = *n; for (j = 1; j <= i__1; ++j) { temp1 = *alpha * a[j + j * a_dim1]; @@ -387,14 +120,12 @@ extern "C" { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { c__[i__ + j * c_dim1] = temp1 * b[i__ + j * b_dim1]; -/* L110: */ } } else { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { - c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1] + - temp1 * b[i__ + j * b_dim1]; -/* L120: */ + c__[i__ + j * c_dim1] = + *beta * c__[i__ + j * c_dim1] + temp1 * b[i__ + j * b_dim1]; } } i__2 = j - 1; @@ -407,9 +138,7 @@ extern "C" { i__3 = *m; for (i__ = 1; i__ <= i__3; ++i__) { c__[i__ + j * c_dim1] += temp1 * b[i__ + k * b_dim1]; -/* L130: */ } -/* L140: */ } i__2 = *n; for (k = j + 1; k <= i__2; ++k) { @@ -421,20 +150,12 @@ extern "C" { i__3 = *m; for (i__ = 1; i__ <= i__3; ++i__) { c__[i__ + j * c_dim1] += temp1 * b[i__ + k * b_dim1]; -/* L150: */ } -/* L160: */ } -/* L170: */ } } - return 0; - -/* End of DSYMM */ - -} /* dsymm_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dsymv.cpp b/lib/linalg/dsymv.cpp index 542c12c97c..07fea66571 100644 --- a/lib/linalg/dsymv.cpp +++ b/lib/linalg/dsymv.cpp @@ -1,223 +1,26 @@ -/* fortran/dsymv.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DSYMV */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DSYMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) */ - -/* .. Scalar Arguments .. */ -/* DOUBLE PRECISION ALPHA,BETA */ -/* INTEGER INCX,INCY,LDA,N */ -/* CHARACTER UPLO */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A(LDA,*),X(*),Y(*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DSYMV performs the matrix-vector operation */ -/* > */ -/* > y := alpha*A*x + beta*y, */ -/* > */ -/* > where alpha and beta are scalars, x and y are n element vectors and */ -/* > A is an n by n symmetric matrix. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > On entry, UPLO specifies whether the upper or lower */ -/* > triangular part of the array A is to be referenced as */ -/* > follows: */ -/* > */ -/* > UPLO = 'U' or 'u' Only the upper triangular part of A */ -/* > is to be referenced. */ -/* > */ -/* > UPLO = 'L' or 'l' Only the lower triangular part of A */ -/* > is to be referenced. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > On entry, N specifies the order of the matrix A. */ -/* > N must be at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] ALPHA */ -/* > \verbatim */ -/* > ALPHA is DOUBLE PRECISION. */ -/* > On entry, ALPHA specifies the scalar alpha. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension ( LDA, N ) */ -/* > Before entry with UPLO = 'U' or 'u', the leading n by n */ -/* > upper triangular part of the array A must contain the upper */ -/* > triangular part of the symmetric matrix and the strictly */ -/* > lower triangular part of A is not referenced. */ -/* > Before entry with UPLO = 'L' or 'l', the leading n by n */ -/* > lower triangular part of the array A must contain the lower */ -/* > triangular part of the symmetric matrix and the strictly */ -/* > upper triangular part of A is not referenced. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > On entry, LDA specifies the first dimension of A as declared */ -/* > in the calling (sub) program. LDA must be at least */ -/* > max( 1, n ). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] X */ -/* > \verbatim */ -/* > X is DOUBLE PRECISION array, dimension at least */ -/* > ( 1 + ( n - 1 )*abs( INCX ) ). */ -/* > Before entry, the incremented array X must contain the n */ -/* > element vector x. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > On entry, INCX specifies the increment for the elements of */ -/* > X. INCX must not be zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] BETA */ -/* > \verbatim */ -/* > BETA is DOUBLE PRECISION. */ -/* > On entry, BETA specifies the scalar beta. When BETA is */ -/* > supplied as zero then Y need not be set on input. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] Y */ -/* > \verbatim */ -/* > Y is DOUBLE PRECISION array, dimension at least */ -/* > ( 1 + ( n - 1 )*abs( INCY ) ). */ -/* > Before entry, the incremented array Y must contain the n */ -/* > element vector y. On exit, Y is overwritten by the updated */ -/* > vector y. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCY */ -/* > \verbatim */ -/* > INCY is INTEGER */ -/* > On entry, INCY specifies the increment for the elements of */ -/* > Y. INCY must not be zero. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup double_blas_level2 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > Level 2 Blas routine. */ -/* > The vector and matrix arguments are not referenced when N = 0, or M = 0 */ -/* > */ -/* > -- Written on 22-October-1986. */ -/* > Jack Dongarra, Argonne National Lab. */ -/* > Jeremy Du Croz, Nag Central Office. */ -/* > Sven Hammarling, Nag Central Office. */ -/* > Richard Hanson, Sandia National Labs. */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dsymv_(char *uplo, integer *n, doublereal *alpha, - doublereal *a, integer *lda, doublereal *x, integer *incx, doublereal - *beta, doublereal *y, integer *incy, ftnlen uplo_len) +int dsymv_(char *uplo, integer *n, doublereal *alpha, doublereal *a, integer *lda, doublereal *x, + integer *incx, doublereal *beta, doublereal *y, integer *incy, ftnlen uplo_len) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; - - /* Local variables */ integer i__, j, ix, iy, jx, jy, kx, ky, info; doublereal temp1, temp2; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - - -/* -- Reference BLAS level2 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ + extern int xerbla_(char *, integer *, ftnlen); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --x; --y; - - /* Function Body */ info = 0; - if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", ( - ftnlen)1, (ftnlen)1)) { + if (!lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { info = 1; } else if (*n < 0) { info = 2; - } else if (*lda < max(1,*n)) { + } else if (*lda < max(1, *n)) { info = 5; } else if (*incx == 0) { info = 7; @@ -228,15 +31,9 @@ extern "C" { xerbla_((char *)"DSYMV ", &info, (ftnlen)6); return 0; } - -/* Quick return if possible. */ - if (*n == 0 || *alpha == 0. && *beta == 1.) { return 0; } - -/* Set up the start points in X and Y. */ - if (*incx > 0) { kx = 1; } else { @@ -247,26 +44,17 @@ extern "C" { } else { ky = 1 - (*n - 1) * *incy; } - -/* Start the operations. In this version the elements of A are */ -/* accessed sequentially with one pass through the triangular part */ -/* of A. */ - -/* First form y := beta*y. */ - if (*beta != 1.) { if (*incy == 1) { if (*beta == 0.) { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { y[i__] = 0.; -/* L10: */ } } else { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { y[i__] = *beta * y[i__]; -/* L20: */ } } } else { @@ -276,14 +64,12 @@ extern "C" { for (i__ = 1; i__ <= i__1; ++i__) { y[iy] = 0.; iy += *incy; -/* L30: */ } } else { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { y[iy] = *beta * y[iy]; iy += *incy; -/* L40: */ } } } @@ -292,9 +78,6 @@ extern "C" { return 0; } if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { - -/* Form y when A is stored in upper triangle. */ - if (*incx == 1 && *incy == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { @@ -304,10 +87,8 @@ extern "C" { for (i__ = 1; i__ <= i__2; ++i__) { y[i__] += temp1 * a[i__ + j * a_dim1]; temp2 += a[i__ + j * a_dim1] * x[i__]; -/* L50: */ } y[j] = y[j] + temp1 * a[j + j * a_dim1] + *alpha * temp2; -/* L60: */ } } else { jx = kx; @@ -324,18 +105,13 @@ extern "C" { temp2 += a[i__ + j * a_dim1] * x[ix]; ix += *incx; iy += *incy; -/* L70: */ } y[jy] = y[jy] + temp1 * a[j + j * a_dim1] + *alpha * temp2; jx += *incx; jy += *incy; -/* L80: */ } } } else { - -/* Form y when A is stored in lower triangle. */ - if (*incx == 1 && *incy == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { @@ -346,10 +122,8 @@ extern "C" { for (i__ = j + 1; i__ <= i__2; ++i__) { y[i__] += temp1 * a[i__ + j * a_dim1]; temp2 += a[i__ + j * a_dim1] * x[i__]; -/* L90: */ } y[j] += *alpha * temp2; -/* L100: */ } } else { jx = kx; @@ -367,22 +141,15 @@ extern "C" { iy += *incy; y[iy] += temp1 * a[i__ + j * a_dim1]; temp2 += a[i__ + j * a_dim1] * x[ix]; -/* L110: */ } y[jy] += *alpha * temp2; jx += *incx; jy += *incy; -/* L120: */ } } } - return 0; - -/* End of DSYMV */ - -} /* dsymv_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dsyr2.cpp b/lib/linalg/dsyr2.cpp index d4395ee996..b3e43c9b9b 100644 --- a/lib/linalg/dsyr2.cpp +++ b/lib/linalg/dsyr2.cpp @@ -1,214 +1,22 @@ -/* fortran/dsyr2.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DSYR2 */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DSYR2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA) */ - -/* .. Scalar Arguments .. */ -/* DOUBLE PRECISION ALPHA */ -/* INTEGER INCX,INCY,LDA,N */ -/* CHARACTER UPLO */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A(LDA,*),X(*),Y(*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DSYR2 performs the symmetric rank 2 operation */ -/* > */ -/* > A := alpha*x*y**T + alpha*y*x**T + A, */ -/* > */ -/* > where alpha is a scalar, x and y are n element vectors and A is an n */ -/* > by n symmetric matrix. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > On entry, UPLO specifies whether the upper or lower */ -/* > triangular part of the array A is to be referenced as */ -/* > follows: */ -/* > */ -/* > UPLO = 'U' or 'u' Only the upper triangular part of A */ -/* > is to be referenced. */ -/* > */ -/* > UPLO = 'L' or 'l' Only the lower triangular part of A */ -/* > is to be referenced. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > On entry, N specifies the order of the matrix A. */ -/* > N must be at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] ALPHA */ -/* > \verbatim */ -/* > ALPHA is DOUBLE PRECISION. */ -/* > On entry, ALPHA specifies the scalar alpha. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] X */ -/* > \verbatim */ -/* > X is DOUBLE PRECISION array, dimension at least */ -/* > ( 1 + ( n - 1 )*abs( INCX ) ). */ -/* > Before entry, the incremented array X must contain the n */ -/* > element vector x. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > On entry, INCX specifies the increment for the elements of */ -/* > X. INCX must not be zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] Y */ -/* > \verbatim */ -/* > Y is DOUBLE PRECISION array, dimension at least */ -/* > ( 1 + ( n - 1 )*abs( INCY ) ). */ -/* > Before entry, the incremented array Y must contain the n */ -/* > element vector y. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCY */ -/* > \verbatim */ -/* > INCY is INTEGER */ -/* > On entry, INCY specifies the increment for the elements of */ -/* > Y. INCY must not be zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension ( LDA, N ) */ -/* > Before entry with UPLO = 'U' or 'u', the leading n by n */ -/* > upper triangular part of the array A must contain the upper */ -/* > triangular part of the symmetric matrix and the strictly */ -/* > lower triangular part of A is not referenced. On exit, the */ -/* > upper triangular part of the array A is overwritten by the */ -/* > upper triangular part of the updated matrix. */ -/* > Before entry with UPLO = 'L' or 'l', the leading n by n */ -/* > lower triangular part of the array A must contain the lower */ -/* > triangular part of the symmetric matrix and the strictly */ -/* > upper triangular part of A is not referenced. On exit, the */ -/* > lower triangular part of the array A is overwritten by the */ -/* > lower triangular part of the updated matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > On entry, LDA specifies the first dimension of A as declared */ -/* > in the calling (sub) program. LDA must be at least */ -/* > max( 1, n ). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup double_blas_level2 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > Level 2 Blas routine. */ -/* > */ -/* > -- Written on 22-October-1986. */ -/* > Jack Dongarra, Argonne National Lab. */ -/* > Jeremy Du Croz, Nag Central Office. */ -/* > Sven Hammarling, Nag Central Office. */ -/* > Richard Hanson, Sandia National Labs. */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dsyr2_(char *uplo, integer *n, doublereal *alpha, - doublereal *x, integer *incx, doublereal *y, integer *incy, - doublereal *a, integer *lda, ftnlen uplo_len) +int dsyr2_(char *uplo, integer *n, doublereal *alpha, doublereal *x, integer *incx, doublereal *y, + integer *incy, doublereal *a, integer *lda, ftnlen uplo_len) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; - - /* Local variables */ integer i__, j, ix, iy, jx, jy, kx, ky, info; doublereal temp1, temp2; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - - -/* -- Reference BLAS level2 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ + extern int xerbla_(char *, integer *, ftnlen); --x; --y; a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; - - /* Function Body */ info = 0; - if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", ( - ftnlen)1, (ftnlen)1)) { + if (!lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { info = 1; } else if (*n < 0) { info = 2; @@ -216,23 +24,16 @@ extern "C" { info = 5; } else if (*incy == 0) { info = 7; - } else if (*lda < max(1,*n)) { + } else if (*lda < max(1, *n)) { info = 9; } if (info != 0) { xerbla_((char *)"DSYR2 ", &info, (ftnlen)6); return 0; } - -/* Quick return if possible. */ - if (*n == 0 || *alpha == 0.) { return 0; } - -/* Set up the start points in X and Y if the increments are not both */ -/* unity. */ - if (*incx != 1 || *incy != 1) { if (*incx > 0) { kx = 1; @@ -247,15 +48,7 @@ extern "C" { jx = kx; jy = ky; } - -/* Start the operations. In this version the elements of A are */ -/* accessed sequentially with one pass through the triangular part */ -/* of A. */ - if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { - -/* Form A when A is stored in the upper triangle. */ - if (*incx == 1 && *incy == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { @@ -264,12 +57,9 @@ extern "C" { temp2 = *alpha * x[j]; i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { - a[i__ + j * a_dim1] = a[i__ + j * a_dim1] + x[i__] * - temp1 + y[i__] * temp2; -/* L10: */ + a[i__ + j * a_dim1] = a[i__ + j * a_dim1] + x[i__] * temp1 + y[i__] * temp2; } } -/* L20: */ } } else { i__1 = *n; @@ -281,22 +71,16 @@ extern "C" { iy = ky; i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { - a[i__ + j * a_dim1] = a[i__ + j * a_dim1] + x[ix] * - temp1 + y[iy] * temp2; + a[i__ + j * a_dim1] = a[i__ + j * a_dim1] + x[ix] * temp1 + y[iy] * temp2; ix += *incx; iy += *incy; -/* L30: */ } } jx += *incx; jy += *incy; -/* L40: */ } } } else { - -/* Form A when A is stored in the lower triangle. */ - if (*incx == 1 && *incy == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { @@ -305,12 +89,9 @@ extern "C" { temp2 = *alpha * x[j]; i__2 = *n; for (i__ = j; i__ <= i__2; ++i__) { - a[i__ + j * a_dim1] = a[i__ + j * a_dim1] + x[i__] * - temp1 + y[i__] * temp2; -/* L50: */ + a[i__ + j * a_dim1] = a[i__ + j * a_dim1] + x[i__] * temp1 + y[i__] * temp2; } } -/* L60: */ } } else { i__1 = *n; @@ -322,26 +103,18 @@ extern "C" { iy = jy; i__2 = *n; for (i__ = j; i__ <= i__2; ++i__) { - a[i__ + j * a_dim1] = a[i__ + j * a_dim1] + x[ix] * - temp1 + y[iy] * temp2; + a[i__ + j * a_dim1] = a[i__ + j * a_dim1] + x[ix] * temp1 + y[iy] * temp2; ix += *incx; iy += *incy; -/* L70: */ } } jx += *incx; jy += *incy; -/* L80: */ } } } - return 0; - -/* End of DSYR2 */ - -} /* dsyr2_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dsyr2k.cpp b/lib/linalg/dsyr2k.cpp index 29f16539b2..9928b2e618 100644 --- a/lib/linalg/dsyr2k.cpp +++ b/lib/linalg/dsyr2k.cpp @@ -1,253 +1,18 @@ -/* fortran/dsyr2k.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DSYR2K */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) */ - -/* .. Scalar Arguments .. */ -/* DOUBLE PRECISION ALPHA,BETA */ -/* INTEGER K,LDA,LDB,LDC,N */ -/* CHARACTER TRANS,UPLO */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DSYR2K performs one of the symmetric rank 2k operations */ -/* > */ -/* > C := alpha*A*B**T + alpha*B*A**T + beta*C, */ -/* > */ -/* > or */ -/* > */ -/* > C := alpha*A**T*B + alpha*B**T*A + beta*C, */ -/* > */ -/* > where alpha and beta are scalars, C is an n by n symmetric matrix */ -/* > and A and B are n by k matrices in the first case and k by n */ -/* > matrices in the second case. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > On entry, UPLO specifies whether the upper or lower */ -/* > triangular part of the array C is to be referenced as */ -/* > follows: */ -/* > */ -/* > UPLO = 'U' or 'u' Only the upper triangular part of C */ -/* > is to be referenced. */ -/* > */ -/* > UPLO = 'L' or 'l' Only the lower triangular part of C */ -/* > is to be referenced. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TRANS */ -/* > \verbatim */ -/* > TRANS is CHARACTER*1 */ -/* > On entry, TRANS specifies the operation to be performed as */ -/* > follows: */ -/* > */ -/* > TRANS = 'N' or 'n' C := alpha*A*B**T + alpha*B*A**T + */ -/* > beta*C. */ -/* > */ -/* > TRANS = 'T' or 't' C := alpha*A**T*B + alpha*B**T*A + */ -/* > beta*C. */ -/* > */ -/* > TRANS = 'C' or 'c' C := alpha*A**T*B + alpha*B**T*A + */ -/* > beta*C. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > On entry, N specifies the order of the matrix C. N must be */ -/* > at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > On entry with TRANS = 'N' or 'n', K specifies the number */ -/* > of columns of the matrices A and B, and on entry with */ -/* > TRANS = 'T' or 't' or 'C' or 'c', K specifies the number */ -/* > of rows of the matrices A and B. K must be at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] ALPHA */ -/* > \verbatim */ -/* > ALPHA is DOUBLE PRECISION. */ -/* > On entry, ALPHA specifies the scalar alpha. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is */ -/* > k when TRANS = 'N' or 'n', and is n otherwise. */ -/* > Before entry with TRANS = 'N' or 'n', the leading n by k */ -/* > part of the array A must contain the matrix A, otherwise */ -/* > the leading k by n part of the array A must contain the */ -/* > matrix A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > On entry, LDA specifies the first dimension of A as declared */ -/* > in the calling (sub) program. When TRANS = 'N' or 'n' */ -/* > then LDA must be at least max( 1, n ), otherwise LDA must */ -/* > be at least max( 1, k ). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] B */ -/* > \verbatim */ -/* > B is DOUBLE PRECISION array, dimension ( LDB, kb ), where kb is */ -/* > k when TRANS = 'N' or 'n', and is n otherwise. */ -/* > Before entry with TRANS = 'N' or 'n', the leading n by k */ -/* > part of the array B must contain the matrix B, otherwise */ -/* > the leading k by n part of the array B must contain the */ -/* > matrix B. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDB */ -/* > \verbatim */ -/* > LDB is INTEGER */ -/* > On entry, LDB specifies the first dimension of B as declared */ -/* > in the calling (sub) program. When TRANS = 'N' or 'n' */ -/* > then LDB must be at least max( 1, n ), otherwise LDB must */ -/* > be at least max( 1, k ). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] BETA */ -/* > \verbatim */ -/* > BETA is DOUBLE PRECISION. */ -/* > On entry, BETA specifies the scalar beta. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] C */ -/* > \verbatim */ -/* > C is DOUBLE PRECISION array, dimension ( LDC, N ) */ -/* > Before entry with UPLO = 'U' or 'u', the leading n by n */ -/* > upper triangular part of the array C must contain the upper */ -/* > triangular part of the symmetric matrix and the strictly */ -/* > lower triangular part of C is not referenced. On exit, the */ -/* > upper triangular part of the array C is overwritten by the */ -/* > upper triangular part of the updated matrix. */ -/* > Before entry with UPLO = 'L' or 'l', the leading n by n */ -/* > lower triangular part of the array C must contain the lower */ -/* > triangular part of the symmetric matrix and the strictly */ -/* > upper triangular part of C is not referenced. On exit, the */ -/* > lower triangular part of the array C is overwritten by the */ -/* > lower triangular part of the updated matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDC */ -/* > \verbatim */ -/* > LDC is INTEGER */ -/* > On entry, LDC specifies the first dimension of C as declared */ -/* > in the calling (sub) program. LDC must be at least */ -/* > max( 1, n ). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup double_blas_level3 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > Level 3 Blas routine. */ -/* > */ -/* > */ -/* > -- Written on 8-February-1989. */ -/* > Jack Dongarra, Argonne National Laboratory. */ -/* > Iain Duff, AERE Harwell. */ -/* > Jeremy Du Croz, Numerical Algorithms Group Ltd. */ -/* > Sven Hammarling, Numerical Algorithms Group Ltd. */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dsyr2k_(char *uplo, char *trans, integer *n, integer *k, - doublereal *alpha, doublereal *a, integer *lda, doublereal *b, - integer *ldb, doublereal *beta, doublereal *c__, integer *ldc, ftnlen - uplo_len, ftnlen trans_len) +int dsyr2k_(char *uplo, char *trans, integer *n, integer *k, doublereal *alpha, doublereal *a, + integer *lda, doublereal *b, integer *ldb, doublereal *beta, doublereal *c__, + integer *ldc, ftnlen uplo_len, ftnlen trans_len) { - /* System generated locals */ - integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, - i__3; - - /* Local variables */ + integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, i__3; integer i__, j, l, info; doublereal temp1, temp2; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer nrowa; logical upper; - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - - -/* -- Reference BLAS level3 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. Parameters .. */ -/* .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ + extern int xerbla_(char *, integer *, ftnlen); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; @@ -257,46 +22,37 @@ extern "C" { c_dim1 = *ldc; c_offset = 1 + c_dim1; c__ -= c_offset; - - /* Function Body */ if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { nrowa = *n; } else { nrowa = *k; } upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); - info = 0; - if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + if (!upper && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { info = 1; - } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, - (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, ( - ftnlen)1)) { + } else if (!lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && + !lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1) && + !lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { info = 2; } else if (*n < 0) { info = 3; } else if (*k < 0) { info = 4; - } else if (*lda < max(1,nrowa)) { + } else if (*lda < max(1, nrowa)) { info = 7; - } else if (*ldb < max(1,nrowa)) { + } else if (*ldb < max(1, nrowa)) { info = 9; - } else if (*ldc < max(1,*n)) { + } else if (*ldc < max(1, *n)) { info = 12; } if (info != 0) { xerbla_((char *)"DSYR2K", &info, (ftnlen)6); return 0; } - -/* Quick return if possible. */ - if (*n == 0 || (*alpha == 0. || *k == 0) && *beta == 1.) { return 0; } - -/* And when alpha.eq.zero. */ - if (*alpha == 0.) { if (upper) { if (*beta == 0.) { @@ -305,9 +61,7 @@ extern "C" { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { c__[i__ + j * c_dim1] = 0.; -/* L10: */ } -/* L20: */ } } else { i__1 = *n; @@ -315,9 +69,7 @@ extern "C" { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; -/* L30: */ } -/* L40: */ } } } else { @@ -327,9 +79,7 @@ extern "C" { i__2 = *n; for (i__ = j; i__ <= i__2; ++i__) { c__[i__ + j * c_dim1] = 0.; -/* L50: */ } -/* L60: */ } } else { i__1 = *n; @@ -337,21 +87,13 @@ extern "C" { i__2 = *n; for (i__ = j; i__ <= i__2; ++i__) { c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; -/* L70: */ } -/* L80: */ } } } return 0; } - -/* Start the operations. */ - if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { - -/* Form C := alpha*A*B**T + alpha*B*A**T + C. */ - if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { @@ -359,13 +101,11 @@ extern "C" { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { c__[i__ + j * c_dim1] = 0.; -/* L90: */ } } else if (*beta != 1.) { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; -/* L100: */ } } i__2 = *k; @@ -375,15 +115,12 @@ extern "C" { temp2 = *alpha * a[j + l * a_dim1]; i__3 = j; for (i__ = 1; i__ <= i__3; ++i__) { - c__[i__ + j * c_dim1] = c__[i__ + j * c_dim1] + a[ - i__ + l * a_dim1] * temp1 + b[i__ + l * - b_dim1] * temp2; -/* L110: */ + c__[i__ + j * c_dim1] = c__[i__ + j * c_dim1] + + a[i__ + l * a_dim1] * temp1 + + b[i__ + l * b_dim1] * temp2; } } -/* L120: */ } -/* L130: */ } } else { i__1 = *n; @@ -392,13 +129,11 @@ extern "C" { i__2 = *n; for (i__ = j; i__ <= i__2; ++i__) { c__[i__ + j * c_dim1] = 0.; -/* L140: */ } } else if (*beta != 1.) { i__2 = *n; for (i__ = j; i__ <= i__2; ++i__) { c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; -/* L150: */ } } i__2 = *k; @@ -408,21 +143,15 @@ extern "C" { temp2 = *alpha * a[j + l * a_dim1]; i__3 = *n; for (i__ = j; i__ <= i__3; ++i__) { - c__[i__ + j * c_dim1] = c__[i__ + j * c_dim1] + a[ - i__ + l * a_dim1] * temp1 + b[i__ + l * - b_dim1] * temp2; -/* L160: */ + c__[i__ + j * c_dim1] = c__[i__ + j * c_dim1] + + a[i__ + l * a_dim1] * temp1 + + b[i__ + l * b_dim1] * temp2; } } -/* L170: */ } -/* L180: */ } } } else { - -/* Form C := alpha*A**T*B + alpha*B**T*A + C. */ - if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { @@ -434,18 +163,14 @@ extern "C" { for (l = 1; l <= i__3; ++l) { temp1 += a[l + i__ * a_dim1] * b[l + j * b_dim1]; temp2 += b[l + i__ * b_dim1] * a[l + j * a_dim1]; -/* L190: */ } if (*beta == 0.) { - c__[i__ + j * c_dim1] = *alpha * temp1 + *alpha * - temp2; + c__[i__ + j * c_dim1] = *alpha * temp1 + *alpha * temp2; } else { - c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1] - + *alpha * temp1 + *alpha * temp2; + c__[i__ + j * c_dim1] = + *beta * c__[i__ + j * c_dim1] + *alpha * temp1 + *alpha * temp2; } -/* L200: */ } -/* L210: */ } } else { i__1 = *n; @@ -458,28 +183,19 @@ extern "C" { for (l = 1; l <= i__3; ++l) { temp1 += a[l + i__ * a_dim1] * b[l + j * b_dim1]; temp2 += b[l + i__ * b_dim1] * a[l + j * a_dim1]; -/* L220: */ } if (*beta == 0.) { - c__[i__ + j * c_dim1] = *alpha * temp1 + *alpha * - temp2; + c__[i__ + j * c_dim1] = *alpha * temp1 + *alpha * temp2; } else { - c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1] - + *alpha * temp1 + *alpha * temp2; + c__[i__ + j * c_dim1] = + *beta * c__[i__ + j * c_dim1] + *alpha * temp1 + *alpha * temp2; } -/* L230: */ } -/* L240: */ } } } - return 0; - -/* End of DSYR2K */ - -} /* dsyr2k_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dsyrk.cpp b/lib/linalg/dsyrk.cpp index 4fb3e554f9..1c383f311f 100644 --- a/lib/linalg/dsyrk.cpp +++ b/lib/linalg/dsyrk.cpp @@ -1,272 +1,53 @@ -/* fortran/dsyrk.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DSYRK */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC) */ - -/* .. Scalar Arguments .. */ -/* DOUBLE PRECISION ALPHA,BETA */ -/* INTEGER K,LDA,LDC,N */ -/* CHARACTER TRANS,UPLO */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A(LDA,*),C(LDC,*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DSYRK performs one of the symmetric rank k operations */ -/* > */ -/* > C := alpha*A*A**T + beta*C, */ -/* > */ -/* > or */ -/* > */ -/* > C := alpha*A**T*A + beta*C, */ -/* > */ -/* > where alpha and beta are scalars, C is an n by n symmetric matrix */ -/* > and A is an n by k matrix in the first case and a k by n matrix */ -/* > in the second case. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > On entry, UPLO specifies whether the upper or lower */ -/* > triangular part of the array C is to be referenced as */ -/* > follows: */ -/* > */ -/* > UPLO = 'U' or 'u' Only the upper triangular part of C */ -/* > is to be referenced. */ -/* > */ -/* > UPLO = 'L' or 'l' Only the lower triangular part of C */ -/* > is to be referenced. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TRANS */ -/* > \verbatim */ -/* > TRANS is CHARACTER*1 */ -/* > On entry, TRANS specifies the operation to be performed as */ -/* > follows: */ -/* > */ -/* > TRANS = 'N' or 'n' C := alpha*A*A**T + beta*C. */ -/* > */ -/* > TRANS = 'T' or 't' C := alpha*A**T*A + beta*C. */ -/* > */ -/* > TRANS = 'C' or 'c' C := alpha*A**T*A + beta*C. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > On entry, N specifies the order of the matrix C. N must be */ -/* > at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > On entry with TRANS = 'N' or 'n', K specifies the number */ -/* > of columns of the matrix A, and on entry with */ -/* > TRANS = 'T' or 't' or 'C' or 'c', K specifies the number */ -/* > of rows of the matrix A. K must be at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] ALPHA */ -/* > \verbatim */ -/* > ALPHA is DOUBLE PRECISION. */ -/* > On entry, ALPHA specifies the scalar alpha. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is */ -/* > k when TRANS = 'N' or 'n', and is n otherwise. */ -/* > Before entry with TRANS = 'N' or 'n', the leading n by k */ -/* > part of the array A must contain the matrix A, otherwise */ -/* > the leading k by n part of the array A must contain the */ -/* > matrix A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > On entry, LDA specifies the first dimension of A as declared */ -/* > in the calling (sub) program. When TRANS = 'N' or 'n' */ -/* > then LDA must be at least max( 1, n ), otherwise LDA must */ -/* > be at least max( 1, k ). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] BETA */ -/* > \verbatim */ -/* > BETA is DOUBLE PRECISION. */ -/* > On entry, BETA specifies the scalar beta. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] C */ -/* > \verbatim */ -/* > C is DOUBLE PRECISION array, dimension ( LDC, N ) */ -/* > Before entry with UPLO = 'U' or 'u', the leading n by n */ -/* > upper triangular part of the array C must contain the upper */ -/* > triangular part of the symmetric matrix and the strictly */ -/* > lower triangular part of C is not referenced. On exit, the */ -/* > upper triangular part of the array C is overwritten by the */ -/* > upper triangular part of the updated matrix. */ -/* > Before entry with UPLO = 'L' or 'l', the leading n by n */ -/* > lower triangular part of the array C must contain the lower */ -/* > triangular part of the symmetric matrix and the strictly */ -/* > upper triangular part of C is not referenced. On exit, the */ -/* > lower triangular part of the array C is overwritten by the */ -/* > lower triangular part of the updated matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDC */ -/* > \verbatim */ -/* > LDC is INTEGER */ -/* > On entry, LDC specifies the first dimension of C as declared */ -/* > in the calling (sub) program. LDC must be at least */ -/* > max( 1, n ). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup double_blas_level3 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > Level 3 Blas routine. */ -/* > */ -/* > -- Written on 8-February-1989. */ -/* > Jack Dongarra, Argonne National Laboratory. */ -/* > Iain Duff, AERE Harwell. */ -/* > Jeremy Du Croz, Numerical Algorithms Group Ltd. */ -/* > Sven Hammarling, Numerical Algorithms Group Ltd. */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dsyrk_(char *uplo, char *trans, integer *n, integer *k, - doublereal *alpha, doublereal *a, integer *lda, doublereal *beta, - doublereal *c__, integer *ldc, ftnlen uplo_len, ftnlen trans_len) +int dsyrk_(char *uplo, char *trans, integer *n, integer *k, doublereal *alpha, doublereal *a, + integer *lda, doublereal *beta, doublereal *c__, integer *ldc, ftnlen uplo_len, + ftnlen trans_len) { - /* System generated locals */ integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3; - - /* Local variables */ integer i__, j, l, info; doublereal temp; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer nrowa; logical upper; - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - - -/* -- Reference BLAS level3 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. Parameters .. */ -/* .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ + extern int xerbla_(char *, integer *, ftnlen); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; c_dim1 = *ldc; c_offset = 1 + c_dim1; c__ -= c_offset; - - /* Function Body */ if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { nrowa = *n; } else { nrowa = *k; } upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); - info = 0; - if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + if (!upper && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { info = 1; - } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, - (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, ( - ftnlen)1)) { + } else if (!lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && + !lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1) && + !lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { info = 2; } else if (*n < 0) { info = 3; } else if (*k < 0) { info = 4; - } else if (*lda < max(1,nrowa)) { + } else if (*lda < max(1, nrowa)) { info = 7; - } else if (*ldc < max(1,*n)) { + } else if (*ldc < max(1, *n)) { info = 10; } if (info != 0) { xerbla_((char *)"DSYRK ", &info, (ftnlen)6); return 0; } - -/* Quick return if possible. */ - if (*n == 0 || (*alpha == 0. || *k == 0) && *beta == 1.) { return 0; } - -/* And when alpha.eq.zero. */ - if (*alpha == 0.) { if (upper) { if (*beta == 0.) { @@ -275,9 +56,7 @@ extern "C" { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { c__[i__ + j * c_dim1] = 0.; -/* L10: */ } -/* L20: */ } } else { i__1 = *n; @@ -285,9 +64,7 @@ extern "C" { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; -/* L30: */ } -/* L40: */ } } } else { @@ -297,9 +74,7 @@ extern "C" { i__2 = *n; for (i__ = j; i__ <= i__2; ++i__) { c__[i__ + j * c_dim1] = 0.; -/* L50: */ } -/* L60: */ } } else { i__1 = *n; @@ -307,21 +82,13 @@ extern "C" { i__2 = *n; for (i__ = j; i__ <= i__2; ++i__) { c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; -/* L70: */ } -/* L80: */ } } } return 0; } - -/* Start the operations. */ - if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { - -/* Form C := alpha*A*A**T + beta*C. */ - if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { @@ -329,13 +96,11 @@ extern "C" { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { c__[i__ + j * c_dim1] = 0.; -/* L90: */ } } else if (*beta != 1.) { i__2 = j; for (i__ = 1; i__ <= i__2; ++i__) { c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; -/* L100: */ } } i__2 = *k; @@ -344,14 +109,10 @@ extern "C" { temp = *alpha * a[j + l * a_dim1]; i__3 = j; for (i__ = 1; i__ <= i__3; ++i__) { - c__[i__ + j * c_dim1] += temp * a[i__ + l * - a_dim1]; -/* L110: */ + c__[i__ + j * c_dim1] += temp * a[i__ + l * a_dim1]; } } -/* L120: */ } -/* L130: */ } } else { i__1 = *n; @@ -360,13 +121,11 @@ extern "C" { i__2 = *n; for (i__ = j; i__ <= i__2; ++i__) { c__[i__ + j * c_dim1] = 0.; -/* L140: */ } } else if (*beta != 1.) { i__2 = *n; for (i__ = j; i__ <= i__2; ++i__) { c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]; -/* L150: */ } } i__2 = *k; @@ -375,20 +134,13 @@ extern "C" { temp = *alpha * a[j + l * a_dim1]; i__3 = *n; for (i__ = j; i__ <= i__3; ++i__) { - c__[i__ + j * c_dim1] += temp * a[i__ + l * - a_dim1]; -/* L160: */ + c__[i__ + j * c_dim1] += temp * a[i__ + l * a_dim1]; } } -/* L170: */ } -/* L180: */ } } } else { - -/* Form C := alpha*A**T*A + beta*C. */ - if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { @@ -398,17 +150,13 @@ extern "C" { i__3 = *k; for (l = 1; l <= i__3; ++l) { temp += a[l + i__ * a_dim1] * a[l + j * a_dim1]; -/* L190: */ } if (*beta == 0.) { c__[i__ + j * c_dim1] = *alpha * temp; } else { - c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[ - i__ + j * c_dim1]; + c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[i__ + j * c_dim1]; } -/* L200: */ } -/* L210: */ } } else { i__1 = *n; @@ -419,27 +167,18 @@ extern "C" { i__3 = *k; for (l = 1; l <= i__3; ++l) { temp += a[l + i__ * a_dim1] * a[l + j * a_dim1]; -/* L220: */ } if (*beta == 0.) { c__[i__ + j * c_dim1] = *alpha * temp; } else { - c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[ - i__ + j * c_dim1]; + c__[i__ + j * c_dim1] = *alpha * temp + *beta * c__[i__ + j * c_dim1]; } -/* L230: */ } -/* L240: */ } } } - return 0; - -/* End of DSYRK */ - -} /* dsyrk_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dsytd2.cpp b/lib/linalg/dsytd2.cpp index acf22710af..57362588af 100644 --- a/lib/linalg/dsytd2.cpp +++ b/lib/linalg/dsytd2.cpp @@ -1,269 +1,40 @@ -/* fortran/dsytd2.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static doublereal c_b8 = 0.; static doublereal c_b14 = -1.; - -/* > \brief \b DSYTD2 reduces a symmetric matrix to real symmetric tridiagonal form by an orthogonal similarit -y transformation (unblocked algorithm). */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DSYTD2 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DSYTD2( UPLO, N, A, LDA, D, E, TAU, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER UPLO */ -/* INTEGER INFO, LDA, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), TAU( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DSYTD2 reduces a real symmetric matrix A to symmetric tridiagonal */ -/* > form T by an orthogonal similarity transformation: Q**T * A * Q = T. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > Specifies whether the upper or lower triangular part of the */ -/* > symmetric matrix A is stored: */ -/* > = 'U': Upper triangular */ -/* > = 'L': Lower triangular */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On entry, the symmetric matrix A. If UPLO = 'U', the leading */ -/* > n-by-n upper triangular part of A contains the upper */ -/* > triangular part of the matrix A, and the strictly lower */ -/* > triangular part of A is not referenced. If UPLO = 'L', the */ -/* > leading n-by-n lower triangular part of A contains the lower */ -/* > triangular part of the matrix A, and the strictly upper */ -/* > triangular part of A is not referenced. */ -/* > On exit, if UPLO = 'U', the diagonal and first superdiagonal */ -/* > of A are overwritten by the corresponding elements of the */ -/* > tridiagonal matrix T, and the elements above the first */ -/* > superdiagonal, with the array TAU, represent the orthogonal */ -/* > matrix Q as a product of elementary reflectors; if UPLO */ -/* > = 'L', the diagonal and first subdiagonal of A are over- */ -/* > written by the corresponding elements of the tridiagonal */ -/* > matrix T, and the elements below the first subdiagonal, with */ -/* > the array TAU, represent the orthogonal matrix Q as a product */ -/* > of elementary reflectors. See Further Details. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension (N) */ -/* > The diagonal elements of the tridiagonal matrix T: */ -/* > D(i) = A(i,i). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] E */ -/* > \verbatim */ -/* > E is DOUBLE PRECISION array, dimension (N-1) */ -/* > The off-diagonal elements of the tridiagonal matrix T: */ -/* > E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] TAU */ -/* > \verbatim */ -/* > TAU is DOUBLE PRECISION array, dimension (N-1) */ -/* > The scalar factors of the elementary reflectors (see Further */ -/* > Details). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleSYcomputational */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > If UPLO = 'U', the matrix Q is represented as a product of elementary */ -/* > reflectors */ -/* > */ -/* > Q = H(n-1) . . . H(2) H(1). */ -/* > */ -/* > Each H(i) has the form */ -/* > */ -/* > H(i) = I - tau * v * v**T */ -/* > */ -/* > where tau is a real scalar, and v is a real vector with */ -/* > v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in */ -/* > A(1:i-1,i+1), and tau in TAU(i). */ -/* > */ -/* > If UPLO = 'L', the matrix Q is represented as a product of elementary */ -/* > reflectors */ -/* > */ -/* > Q = H(1) H(2) . . . H(n-1). */ -/* > */ -/* > Each H(i) has the form */ -/* > */ -/* > H(i) = I - tau * v * v**T */ -/* > */ -/* > where tau is a real scalar, and v is a real vector with */ -/* > v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), */ -/* > and tau in TAU(i). */ -/* > */ -/* > The contents of A on exit are illustrated by the following examples */ -/* > with n = 5: */ -/* > */ -/* > if UPLO = 'U': if UPLO = 'L': */ -/* > */ -/* > ( d e v2 v3 v4 ) ( d ) */ -/* > ( d e v3 v4 ) ( e d ) */ -/* > ( d e v4 ) ( v1 e d ) */ -/* > ( d e ) ( v1 v2 e d ) */ -/* > ( d ) ( v1 v2 v3 e d ) */ -/* > */ -/* > where d and e denote diagonal and off-diagonal elements of T, and vi */ -/* > denotes an element of the vector defining H(i). */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dsytd2_(char *uplo, integer *n, doublereal *a, integer * - lda, doublereal *d__, doublereal *e, doublereal *tau, integer *info, - ftnlen uplo_len) +int dsytd2_(char *uplo, integer *n, doublereal *a, integer *lda, doublereal *d__, doublereal *e, + doublereal *tau, integer *info, ftnlen uplo_len) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; - - /* Local variables */ integer i__; - extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, - integer *); + extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, integer *); doublereal taui; - extern /* Subroutine */ int dsyr2_(char *, integer *, doublereal *, - doublereal *, integer *, doublereal *, integer *, doublereal *, - integer *, ftnlen); + extern int dsyr2_(char *, integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, integer *, ftnlen); doublereal alpha; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *, - integer *, doublereal *, integer *); + extern int daxpy_(integer *, doublereal *, doublereal *, integer *, doublereal *, integer *); logical upper; - extern /* Subroutine */ int dsymv_(char *, integer *, doublereal *, - doublereal *, integer *, doublereal *, integer *, doublereal *, - doublereal *, integer *, ftnlen), dlarfg_(integer *, doublereal *, - doublereal *, integer *, doublereal *), xerbla_(char *, integer * - , ftnlen); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters */ - - /* Parameter adjustments */ + extern int dsymv_(char *, integer *, doublereal *, doublereal *, integer *, doublereal *, + integer *, doublereal *, doublereal *, integer *, ftnlen), + dlarfg_(integer *, doublereal *, doublereal *, integer *, doublereal *), + xerbla_(char *, integer *, ftnlen); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --d__; --e; --tau; - - /* Function Body */ *info = 0; upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); - if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + if (!upper && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { *info = -1; } else if (*n < 0) { *info = -2; - } else if (*lda < max(1,*n)) { + } else if (*lda < max(1, *n)) { *info = -4; } if (*info != 0) { @@ -271,119 +42,57 @@ f"> */ xerbla_((char *)"DSYTD2", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*n <= 0) { return 0; } - if (upper) { - -/* Reduce the upper triangle of A */ - for (i__ = *n - 1; i__ >= 1; --i__) { - -/* Generate elementary reflector H(i) = I - tau * v * v**T */ -/* to annihilate A(1:i-1,i+1) */ - - dlarfg_(&i__, &a[i__ + (i__ + 1) * a_dim1], &a[(i__ + 1) * a_dim1 - + 1], &c__1, &taui); + dlarfg_(&i__, &a[i__ + (i__ + 1) * a_dim1], &a[(i__ + 1) * a_dim1 + 1], &c__1, &taui); e[i__] = a[i__ + (i__ + 1) * a_dim1]; - if (taui != 0.) { - -/* Apply H(i) from both sides to A(1:i,1:i) */ - a[i__ + (i__ + 1) * a_dim1] = 1.; - -/* Compute x := tau * A * v storing x in TAU(1:i) */ - - dsymv_(uplo, &i__, &taui, &a[a_offset], lda, &a[(i__ + 1) * - a_dim1 + 1], &c__1, &c_b8, &tau[1], &c__1, (ftnlen)1); - -/* Compute w := x - 1/2 * tau * (x**T * v) * v */ - - alpha = taui * -.5 * ddot_(&i__, &tau[1], &c__1, &a[(i__ + 1) - * a_dim1 + 1], &c__1); - daxpy_(&i__, &alpha, &a[(i__ + 1) * a_dim1 + 1], &c__1, &tau[ - 1], &c__1); - -/* Apply the transformation as a rank-2 update: */ -/* A := A - v * w**T - w * v**T */ - - dsyr2_(uplo, &i__, &c_b14, &a[(i__ + 1) * a_dim1 + 1], &c__1, - &tau[1], &c__1, &a[a_offset], lda, (ftnlen)1); - + dsymv_(uplo, &i__, &taui, &a[a_offset], lda, &a[(i__ + 1) * a_dim1 + 1], &c__1, + &c_b8, &tau[1], &c__1, (ftnlen)1); + alpha = taui * -.5 * ddot_(&i__, &tau[1], &c__1, &a[(i__ + 1) * a_dim1 + 1], &c__1); + daxpy_(&i__, &alpha, &a[(i__ + 1) * a_dim1 + 1], &c__1, &tau[1], &c__1); + dsyr2_(uplo, &i__, &c_b14, &a[(i__ + 1) * a_dim1 + 1], &c__1, &tau[1], &c__1, + &a[a_offset], lda, (ftnlen)1); a[i__ + (i__ + 1) * a_dim1] = e[i__]; } d__[i__ + 1] = a[i__ + 1 + (i__ + 1) * a_dim1]; tau[i__] = taui; -/* L10: */ } d__[1] = a[a_dim1 + 1]; } else { - -/* Reduce the lower triangle of A */ - i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { - -/* Generate elementary reflector H(i) = I - tau * v * v**T */ -/* to annihilate A(i+2:n,i) */ - i__2 = *n - i__; -/* Computing MIN */ i__3 = i__ + 2; - dlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3,*n) + i__ * - a_dim1], &c__1, &taui); + dlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3, *n) + i__ * a_dim1], &c__1, + &taui); e[i__] = a[i__ + 1 + i__ * a_dim1]; - if (taui != 0.) { - -/* Apply H(i) from both sides to A(i+1:n,i+1:n) */ - a[i__ + 1 + i__ * a_dim1] = 1.; - -/* Compute x := tau * A * v storing y in TAU(i:n-1) */ - i__2 = *n - i__; - dsymv_(uplo, &i__2, &taui, &a[i__ + 1 + (i__ + 1) * a_dim1], - lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b8, &tau[ - i__], &c__1, (ftnlen)1); - -/* Compute w := x - 1/2 * tau * (x**T * v) * v */ - + dsymv_(uplo, &i__2, &taui, &a[i__ + 1 + (i__ + 1) * a_dim1], lda, + &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b8, &tau[i__], &c__1, (ftnlen)1); i__2 = *n - i__; - alpha = taui * -.5 * ddot_(&i__2, &tau[i__], &c__1, &a[i__ + - 1 + i__ * a_dim1], &c__1); + alpha = + taui * -.5 * ddot_(&i__2, &tau[i__], &c__1, &a[i__ + 1 + i__ * a_dim1], &c__1); i__2 = *n - i__; - daxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &tau[ - i__], &c__1); - -/* Apply the transformation as a rank-2 update: */ -/* A := A - v * w**T - w * v**T */ - + daxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &tau[i__], &c__1); i__2 = *n - i__; - dsyr2_(uplo, &i__2, &c_b14, &a[i__ + 1 + i__ * a_dim1], &c__1, - &tau[i__], &c__1, &a[i__ + 1 + (i__ + 1) * a_dim1], - lda, (ftnlen)1); - + dsyr2_(uplo, &i__2, &c_b14, &a[i__ + 1 + i__ * a_dim1], &c__1, &tau[i__], &c__1, + &a[i__ + 1 + (i__ + 1) * a_dim1], lda, (ftnlen)1); a[i__ + 1 + i__ * a_dim1] = e[i__]; } d__[i__] = a[i__ + i__ * a_dim1]; tau[i__] = taui; -/* L20: */ } d__[*n] = a[*n + *n * a_dim1]; } - return 0; - -/* End of DSYTD2 */ - -} /* dsytd2_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dsytrd.cpp b/lib/linalg/dsytrd.cpp index b29df9fb10..a414b9a530 100644 --- a/lib/linalg/dsytrd.cpp +++ b/lib/linalg/dsytrd.cpp @@ -1,274 +1,32 @@ -/* fortran/dsytrd.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static integer c_n1 = -1; static integer c__3 = 3; static integer c__2 = 2; static doublereal c_b22 = -1.; static doublereal c_b23 = 1.; - -/* > \brief \b DSYTRD */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DSYTRD + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DSYTRD( UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER UPLO */ -/* INTEGER INFO, LDA, LWORK, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), TAU( * ), */ -/* $ WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DSYTRD reduces a real symmetric matrix A to real symmetric */ -/* > tridiagonal form T by an orthogonal similarity transformation: */ -/* > Q**T * A * Q = T. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > = 'U': Upper triangle of A is stored; */ -/* > = 'L': Lower triangle of A is stored. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On entry, the symmetric matrix A. If UPLO = 'U', the leading */ -/* > N-by-N upper triangular part of A contains the upper */ -/* > triangular part of the matrix A, and the strictly lower */ -/* > triangular part of A is not referenced. If UPLO = 'L', the */ -/* > leading N-by-N lower triangular part of A contains the lower */ -/* > triangular part of the matrix A, and the strictly upper */ -/* > triangular part of A is not referenced. */ -/* > On exit, if UPLO = 'U', the diagonal and first superdiagonal */ -/* > of A are overwritten by the corresponding elements of the */ -/* > tridiagonal matrix T, and the elements above the first */ -/* > superdiagonal, with the array TAU, represent the orthogonal */ -/* > matrix Q as a product of elementary reflectors; if UPLO */ -/* > = 'L', the diagonal and first subdiagonal of A are over- */ -/* > written by the corresponding elements of the tridiagonal */ -/* > matrix T, and the elements below the first subdiagonal, with */ -/* > the array TAU, represent the orthogonal matrix Q as a product */ -/* > of elementary reflectors. See Further Details. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension (N) */ -/* > The diagonal elements of the tridiagonal matrix T: */ -/* > D(i) = A(i,i). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] E */ -/* > \verbatim */ -/* > E is DOUBLE PRECISION array, dimension (N-1) */ -/* > The off-diagonal elements of the tridiagonal matrix T: */ -/* > E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] TAU */ -/* > \verbatim */ -/* > TAU is DOUBLE PRECISION array, dimension (N-1) */ -/* > The scalar factors of the elementary reflectors (see Further */ -/* > Details). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */ -/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LWORK */ -/* > \verbatim */ -/* > LWORK is INTEGER */ -/* > The dimension of the array WORK. LWORK >= 1. */ -/* > For optimum performance LWORK >= N*NB, where NB is the */ -/* > optimal blocksize. */ -/* > */ -/* > If LWORK = -1, then a workspace query is assumed; the routine */ -/* > only calculates the optimal size of the WORK array, returns */ -/* > this value as the first entry of the WORK array, and no error */ -/* > message related to LWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleSYcomputational */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > If UPLO = 'U', the matrix Q is represented as a product of elementary */ -/* > reflectors */ -/* > */ -/* > Q = H(n-1) . . . H(2) H(1). */ -/* > */ -/* > Each H(i) has the form */ -/* > */ -/* > H(i) = I - tau * v * v**T */ -/* > */ -/* > where tau is a real scalar, and v is a real vector with */ -/* > v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in */ -/* > A(1:i-1,i+1), and tau in TAU(i). */ -/* > */ -/* > If UPLO = 'L', the matrix Q is represented as a product of elementary */ -/* > reflectors */ -/* > */ -/* > Q = H(1) H(2) . . . H(n-1). */ -/* > */ -/* > Each H(i) has the form */ -/* > */ -/* > H(i) = I - tau * v * v**T */ -/* > */ -/* > where tau is a real scalar, and v is a real vector with */ -/* > v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), */ -/* > and tau in TAU(i). */ -/* > */ -/* > The contents of A on exit are illustrated by the following examples */ -/* > with n = 5: */ -/* > */ -/* > if UPLO = 'U': if UPLO = 'L': */ -/* > */ -/* > ( d e v2 v3 v4 ) ( d ) */ -/* > ( d e v3 v4 ) ( e d ) */ -/* > ( d e v4 ) ( v1 e d ) */ -/* > ( d e ) ( v1 v2 e d ) */ -/* > ( d ) ( v1 v2 v3 e d ) */ -/* > */ -/* > where d and e denote diagonal and off-diagonal elements of T, and vi */ -/* > denotes an element of the vector defining H(i). */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dsytrd_(char *uplo, integer *n, doublereal *a, integer * - lda, doublereal *d__, doublereal *e, doublereal *tau, doublereal * - work, integer *lwork, integer *info, ftnlen uplo_len) +int dsytrd_(char *uplo, integer *n, doublereal *a, integer *lda, doublereal *d__, doublereal *e, + doublereal *tau, doublereal *work, integer *lwork, integer *info, ftnlen uplo_len) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; - - /* Local variables */ integer i__, j, nb, kk, nx, iws; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer nbmin, iinfo; logical upper; - extern /* Subroutine */ int dsytd2_(char *, integer *, doublereal *, - integer *, doublereal *, doublereal *, doublereal *, integer *, - ftnlen), dsyr2k_(char *, char *, integer *, integer *, doublereal - *, doublereal *, integer *, doublereal *, integer *, doublereal *, - doublereal *, integer *, ftnlen, ftnlen), dlatrd_(char *, - integer *, integer *, doublereal *, integer *, doublereal *, - doublereal *, doublereal *, integer *, ftnlen), xerbla_(char *, - integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern int dsytd2_(char *, integer *, doublereal *, integer *, doublereal *, doublereal *, + doublereal *, integer *, ftnlen), + dsyr2k_(char *, char *, integer *, integer *, doublereal *, doublereal *, integer *, + doublereal *, integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen), + dlatrd_(char *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, + doublereal *, integer *, ftnlen), + xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); integer ldwork, lwkopt; logical lquery; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; @@ -276,31 +34,23 @@ f"> */ --e; --tau; --work; - - /* Function Body */ *info = 0; upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); lquery = *lwork == -1; - if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + if (!upper && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { *info = -1; } else if (*n < 0) { *info = -2; - } else if (*lda < max(1,*n)) { + } else if (*lda < max(1, *n)) { *info = -4; - } else if (*lwork < 1 && ! lquery) { + } else if (*lwork < 1 && !lquery) { *info = -9; } - if (*info == 0) { - -/* Determine the block size. */ - - nb = ilaenv_(&c__1, (char *)"DSYTRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, - (ftnlen)1); + nb = ilaenv_(&c__1, (char *)"DSYTRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); lwkopt = *n * nb; - work[1] = (doublereal) lwkopt; + work[1] = (doublereal)lwkopt; } - if (*info != 0) { i__1 = -(*info); xerbla_((char *)"DSYTRD", &i__1, (ftnlen)6); @@ -308,42 +58,24 @@ f"> */ } else if (lquery) { return 0; } - -/* Quick return if possible */ - if (*n == 0) { work[1] = 1.; return 0; } - nx = *n; iws = 1; if (nb > 1 && nb < *n) { - -/* Determine when to cross over from blocked to unblocked code */ -/* (last block is always handled by unblocked code). */ - -/* Computing MAX */ - i__1 = nb, i__2 = ilaenv_(&c__3, (char *)"DSYTRD", uplo, n, &c_n1, &c_n1, & - c_n1, (ftnlen)6, (ftnlen)1); - nx = max(i__1,i__2); + i__1 = nb, + i__2 = ilaenv_(&c__3, (char *)"DSYTRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); + nx = max(i__1, i__2); if (nx < *n) { - -/* Determine if workspace is large enough for blocked code. */ - ldwork = *n; iws = ldwork * nb; if (*lwork < iws) { - -/* Not enough workspace to use optimal NB: determine the */ -/* minimum value of NB, and reduce NB or force use of */ -/* unblocked code by setting NX = N. */ - -/* Computing MAX */ i__1 = *lwork / ldwork; - nb = max(i__1,1); - nbmin = ilaenv_(&c__2, (char *)"DSYTRD", uplo, n, &c_n1, &c_n1, &c_n1, - (ftnlen)6, (ftnlen)1); + nb = max(i__1, 1); + nbmin = + ilaenv_(&c__2, (char *)"DSYTRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); if (nb < nbmin) { nx = *n; } @@ -354,101 +86,48 @@ f"> */ } else { nb = 1; } - if (upper) { - -/* Reduce the upper triangle of A. */ -/* Columns 1:kk are handled by the unblocked method. */ - kk = *n - (*n - nx + nb - 1) / nb * nb; i__1 = kk + 1; i__2 = -nb; - for (i__ = *n - nb + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += - i__2) { - -/* Reduce columns i:i+nb-1 to tridiagonal form and form the */ -/* matrix W which is needed to update the unreduced part of */ -/* the matrix */ - + for (i__ = *n - nb + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { i__3 = i__ + nb - 1; - dlatrd_(uplo, &i__3, &nb, &a[a_offset], lda, &e[1], &tau[1], & - work[1], &ldwork, (ftnlen)1); - -/* Update the unreduced submatrix A(1:i-1,1:i-1), using an */ -/* update of the form: A := A - V*W**T - W*V**T */ - + dlatrd_(uplo, &i__3, &nb, &a[a_offset], lda, &e[1], &tau[1], &work[1], &ldwork, + (ftnlen)1); i__3 = i__ - 1; - dsyr2k_(uplo, (char *)"No transpose", &i__3, &nb, &c_b22, &a[i__ * a_dim1 - + 1], lda, &work[1], &ldwork, &c_b23, &a[a_offset], lda, ( - ftnlen)1, (ftnlen)12); - -/* Copy superdiagonal elements back into A, and diagonal */ -/* elements into D */ - + dsyr2k_(uplo, (char *)"No transpose", &i__3, &nb, &c_b22, &a[i__ * a_dim1 + 1], lda, &work[1], + &ldwork, &c_b23, &a[a_offset], lda, (ftnlen)1, (ftnlen)12); i__3 = i__ + nb - 1; for (j = i__; j <= i__3; ++j) { a[j - 1 + j * a_dim1] = e[j - 1]; d__[j] = a[j + j * a_dim1]; -/* L10: */ } -/* L20: */ } - -/* Use unblocked code to reduce the last or only block */ - - dsytd2_(uplo, &kk, &a[a_offset], lda, &d__[1], &e[1], &tau[1], &iinfo, - (ftnlen)1); + dsytd2_(uplo, &kk, &a[a_offset], lda, &d__[1], &e[1], &tau[1], &iinfo, (ftnlen)1); } else { - -/* Reduce the lower triangle of A */ - i__2 = *n - nx; i__1 = nb; for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) { - -/* Reduce columns i:i+nb-1 to tridiagonal form and form the */ -/* matrix W which is needed to update the unreduced part of */ -/* the matrix */ - i__3 = *n - i__ + 1; - dlatrd_(uplo, &i__3, &nb, &a[i__ + i__ * a_dim1], lda, &e[i__], & - tau[i__], &work[1], &ldwork, (ftnlen)1); - -/* Update the unreduced submatrix A(i+ib:n,i+ib:n), using */ -/* an update of the form: A := A - V*W**T - W*V**T */ - + dlatrd_(uplo, &i__3, &nb, &a[i__ + i__ * a_dim1], lda, &e[i__], &tau[i__], &work[1], + &ldwork, (ftnlen)1); i__3 = *n - i__ - nb + 1; - dsyr2k_(uplo, (char *)"No transpose", &i__3, &nb, &c_b22, &a[i__ + nb + - i__ * a_dim1], lda, &work[nb + 1], &ldwork, &c_b23, &a[ - i__ + nb + (i__ + nb) * a_dim1], lda, (ftnlen)1, (ftnlen) - 12); - -/* Copy subdiagonal elements back into A, and diagonal */ -/* elements into D */ - + dsyr2k_(uplo, (char *)"No transpose", &i__3, &nb, &c_b22, &a[i__ + nb + i__ * a_dim1], lda, + &work[nb + 1], &ldwork, &c_b23, &a[i__ + nb + (i__ + nb) * a_dim1], lda, + (ftnlen)1, (ftnlen)12); i__3 = i__ + nb - 1; for (j = i__; j <= i__3; ++j) { a[j + 1 + j * a_dim1] = e[j]; d__[j] = a[j + j * a_dim1]; -/* L30: */ } -/* L40: */ } - -/* Use unblocked code to reduce the last or only block */ - i__1 = *n - i__ + 1; - dsytd2_(uplo, &i__1, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[i__], - &tau[i__], &iinfo, (ftnlen)1); + dsytd2_(uplo, &i__1, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[i__], &tau[i__], &iinfo, + (ftnlen)1); } - - work[1] = (doublereal) lwkopt; + work[1] = (doublereal)lwkopt; return 0; - -/* End of DSYTRD */ - -} /* dsytrd_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dtrmm.cpp b/lib/linalg/dtrmm.cpp index 1a61cf72b1..1ef32afb54 100644 --- a/lib/linalg/dtrmm.cpp +++ b/lib/linalg/dtrmm.cpp @@ -1,247 +1,26 @@ -/* fortran/dtrmm.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DTRMM */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) */ - -/* .. Scalar Arguments .. */ -/* DOUBLE PRECISION ALPHA */ -/* INTEGER LDA,LDB,M,N */ -/* CHARACTER DIAG,SIDE,TRANSA,UPLO */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A(LDA,*),B(LDB,*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DTRMM performs one of the matrix-matrix operations */ -/* > */ -/* > B := alpha*op( A )*B, or B := alpha*B*op( A ), */ -/* > */ -/* > where alpha is a scalar, B is an m by n matrix, A is a unit, or */ -/* > non-unit, upper or lower triangular matrix and op( A ) is one of */ -/* > */ -/* > op( A ) = A or op( A ) = A**T. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] SIDE */ -/* > \verbatim */ -/* > SIDE is CHARACTER*1 */ -/* > On entry, SIDE specifies whether op( A ) multiplies B from */ -/* > the left or right as follows: */ -/* > */ -/* > SIDE = 'L' or 'l' B := alpha*op( A )*B. */ -/* > */ -/* > SIDE = 'R' or 'r' B := alpha*B*op( A ). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > On entry, UPLO specifies whether the matrix A is an upper or */ -/* > lower triangular matrix as follows: */ -/* > */ -/* > UPLO = 'U' or 'u' A is an upper triangular matrix. */ -/* > */ -/* > UPLO = 'L' or 'l' A is a lower triangular matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TRANSA */ -/* > \verbatim */ -/* > TRANSA is CHARACTER*1 */ -/* > On entry, TRANSA specifies the form of op( A ) to be used in */ -/* > the matrix multiplication as follows: */ -/* > */ -/* > TRANSA = 'N' or 'n' op( A ) = A. */ -/* > */ -/* > TRANSA = 'T' or 't' op( A ) = A**T. */ -/* > */ -/* > TRANSA = 'C' or 'c' op( A ) = A**T. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DIAG */ -/* > \verbatim */ -/* > DIAG is CHARACTER*1 */ -/* > On entry, DIAG specifies whether or not A is unit triangular */ -/* > as follows: */ -/* > */ -/* > DIAG = 'U' or 'u' A is assumed to be unit triangular. */ -/* > */ -/* > DIAG = 'N' or 'n' A is not assumed to be unit */ -/* > triangular. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > On entry, M specifies the number of rows of B. M must be at */ -/* > least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > On entry, N specifies the number of columns of B. N must be */ -/* > at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] ALPHA */ -/* > \verbatim */ -/* > ALPHA is DOUBLE PRECISION. */ -/* > On entry, ALPHA specifies the scalar alpha. When alpha is */ -/* > zero then A is not referenced and B need not be set before */ -/* > entry. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension ( LDA, k ), where k is m */ -/* > when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. */ -/* > Before entry with UPLO = 'U' or 'u', the leading k by k */ -/* > upper triangular part of the array A must contain the upper */ -/* > triangular matrix and the strictly lower triangular part of */ -/* > A is not referenced. */ -/* > Before entry with UPLO = 'L' or 'l', the leading k by k */ -/* > lower triangular part of the array A must contain the lower */ -/* > triangular matrix and the strictly upper triangular part of */ -/* > A is not referenced. */ -/* > Note that when DIAG = 'U' or 'u', the diagonal elements of */ -/* > A are not referenced either, but are assumed to be unity. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > On entry, LDA specifies the first dimension of A as declared */ -/* > in the calling (sub) program. When SIDE = 'L' or 'l' then */ -/* > LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' */ -/* > then LDA must be at least max( 1, n ). */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] B */ -/* > \verbatim */ -/* > B is DOUBLE PRECISION array, dimension ( LDB, N ) */ -/* > Before entry, the leading m by n part of the array B must */ -/* > contain the matrix B, and on exit is overwritten by the */ -/* > transformed matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDB */ -/* > \verbatim */ -/* > LDB is INTEGER */ -/* > On entry, LDB specifies the first dimension of B as declared */ -/* > in the calling (sub) program. LDB must be at least */ -/* > max( 1, m ). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup double_blas_level3 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > Level 3 Blas routine. */ -/* > */ -/* > -- Written on 8-February-1989. */ -/* > Jack Dongarra, Argonne National Laboratory. */ -/* > Iain Duff, AERE Harwell. */ -/* > Jeremy Du Croz, Numerical Algorithms Group Ltd. */ -/* > Sven Hammarling, Numerical Algorithms Group Ltd. */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dtrmm_(char *side, char *uplo, char *transa, char *diag, - integer *m, integer *n, doublereal *alpha, doublereal *a, integer * - lda, doublereal *b, integer *ldb, ftnlen side_len, ftnlen uplo_len, - ftnlen transa_len, ftnlen diag_len) +int dtrmm_(char *side, char *uplo, char *transa, char *diag, integer *m, integer *n, + doublereal *alpha, doublereal *a, integer *lda, doublereal *b, integer *ldb, + ftnlen side_len, ftnlen uplo_len, ftnlen transa_len, ftnlen diag_len) { - /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3; - - /* Local variables */ integer i__, j, k, info; doublereal temp; logical lside; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer nrowa; logical upper; - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern int xerbla_(char *, integer *, ftnlen); logical nounit; - - -/* -- Reference BLAS level3 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. Parameters .. */ -/* .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; - - /* Function Body */ lside = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); if (lside) { nrowa = *m; @@ -250,61 +29,46 @@ extern "C" { } nounit = lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1); upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); - info = 0; - if (! lside && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + if (!lside && !lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { info = 1; - } else if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + } else if (!upper && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { info = 2; - } else if (! lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(transa, - (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(transa, (char *)"C", (ftnlen)1, ( - ftnlen)1)) { + } else if (!lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1) && + !lsame_(transa, (char *)"T", (ftnlen)1, (ftnlen)1) && + !lsame_(transa, (char *)"C", (ftnlen)1, (ftnlen)1)) { info = 3; - } else if (! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, - (char *)"N", (ftnlen)1, (ftnlen)1)) { + } else if (!lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && + !lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1)) { info = 4; } else if (*m < 0) { info = 5; } else if (*n < 0) { info = 6; - } else if (*lda < max(1,nrowa)) { + } else if (*lda < max(1, nrowa)) { info = 9; - } else if (*ldb < max(1,*m)) { + } else if (*ldb < max(1, *m)) { info = 11; } if (info != 0) { xerbla_((char *)"DTRMM ", &info, (ftnlen)6); return 0; } - -/* Quick return if possible. */ - if (*m == 0 || *n == 0) { return 0; } - -/* And when alpha.eq.zero. */ - if (*alpha == 0.) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { b[i__ + j * b_dim1] = 0.; -/* L10: */ } -/* L20: */ } return 0; } - -/* Start the operations. */ - if (lside) { if (lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1)) { - -/* Form B := alpha*A*B. */ - if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { @@ -314,18 +78,14 @@ extern "C" { temp = *alpha * b[k + j * b_dim1]; i__3 = k - 1; for (i__ = 1; i__ <= i__3; ++i__) { - b[i__ + j * b_dim1] += temp * a[i__ + k * - a_dim1]; -/* L30: */ + b[i__ + j * b_dim1] += temp * a[i__ + k * a_dim1]; } if (nounit) { temp *= a[k + k * a_dim1]; } b[k + j * b_dim1] = temp; } -/* L40: */ } -/* L50: */ } } else { i__1 = *n; @@ -339,20 +99,13 @@ extern "C" { } i__2 = *m; for (i__ = k + 1; i__ <= i__2; ++i__) { - b[i__ + j * b_dim1] += temp * a[i__ + k * - a_dim1]; -/* L60: */ + b[i__ + j * b_dim1] += temp * a[i__ + k * a_dim1]; } } -/* L70: */ } -/* L80: */ } } } else { - -/* Form B := alpha*A**T*B. */ - if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { @@ -364,12 +117,9 @@ extern "C" { i__2 = i__ - 1; for (k = 1; k <= i__2; ++k) { temp += a[k + i__ * a_dim1] * b[k + j * b_dim1]; -/* L90: */ } b[i__ + j * b_dim1] = *alpha * temp; -/* L100: */ } -/* L110: */ } } else { i__1 = *n; @@ -383,20 +133,14 @@ extern "C" { i__3 = *m; for (k = i__ + 1; k <= i__3; ++k) { temp += a[k + i__ * a_dim1] * b[k + j * b_dim1]; -/* L120: */ } b[i__ + j * b_dim1] = *alpha * temp; -/* L130: */ } -/* L140: */ } } } } else { if (lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1)) { - -/* Form B := alpha*B*A. */ - if (upper) { for (j = *n; j >= 1; --j) { temp = *alpha; @@ -406,7 +150,6 @@ extern "C" { i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1]; -/* L150: */ } i__1 = j - 1; for (k = 1; k <= i__1; ++k) { @@ -414,14 +157,10 @@ extern "C" { temp = *alpha * a[k + j * a_dim1]; i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { - b[i__ + j * b_dim1] += temp * b[i__ + k * - b_dim1]; -/* L160: */ + b[i__ + j * b_dim1] += temp * b[i__ + k * b_dim1]; } } -/* L170: */ } -/* L180: */ } } else { i__1 = *n; @@ -433,7 +172,6 @@ extern "C" { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1]; -/* L190: */ } i__2 = *n; for (k = j + 1; k <= i__2; ++k) { @@ -441,20 +179,13 @@ extern "C" { temp = *alpha * a[k + j * a_dim1]; i__3 = *m; for (i__ = 1; i__ <= i__3; ++i__) { - b[i__ + j * b_dim1] += temp * b[i__ + k * - b_dim1]; -/* L200: */ + b[i__ + j * b_dim1] += temp * b[i__ + k * b_dim1]; } } -/* L210: */ } -/* L220: */ } } } else { - -/* Form B := alpha*B*A**T. */ - if (upper) { i__1 = *n; for (k = 1; k <= i__1; ++k) { @@ -464,12 +195,9 @@ extern "C" { temp = *alpha * a[j + k * a_dim1]; i__3 = *m; for (i__ = 1; i__ <= i__3; ++i__) { - b[i__ + j * b_dim1] += temp * b[i__ + k * - b_dim1]; -/* L230: */ + b[i__ + j * b_dim1] += temp * b[i__ + k * b_dim1]; } } -/* L240: */ } temp = *alpha; if (nounit) { @@ -479,10 +207,8 @@ extern "C" { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1]; -/* L250: */ } } -/* L260: */ } } else { for (k = *n; k >= 1; --k) { @@ -492,12 +218,9 @@ extern "C" { temp = *alpha * a[j + k * a_dim1]; i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { - b[i__ + j * b_dim1] += temp * b[i__ + k * - b_dim1]; -/* L270: */ + b[i__ + j * b_dim1] += temp * b[i__ + k * b_dim1]; } } -/* L280: */ } temp = *alpha; if (nounit) { @@ -507,21 +230,14 @@ extern "C" { i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1]; -/* L290: */ } } -/* L300: */ } } } } - return 0; - -/* End of DTRMM */ - -} /* dtrmm_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dtrmv.cpp b/lib/linalg/dtrmv.cpp index 597fcae137..3631f6fb24 100644 --- a/lib/linalg/dtrmv.cpp +++ b/lib/linalg/dtrmv.cpp @@ -1,225 +1,33 @@ -/* fortran/dtrmv.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DTRMV */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INCX,LDA,N */ -/* CHARACTER DIAG,TRANS,UPLO */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A(LDA,*),X(*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DTRMV performs one of the matrix-vector operations */ -/* > */ -/* > x := A*x, or x := A**T*x, */ -/* > */ -/* > where x is an n element vector and A is an n by n unit, or non-unit, */ -/* > upper or lower triangular matrix. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > On entry, UPLO specifies whether the matrix is an upper or */ -/* > lower triangular matrix as follows: */ -/* > */ -/* > UPLO = 'U' or 'u' A is an upper triangular matrix. */ -/* > */ -/* > UPLO = 'L' or 'l' A is a lower triangular matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TRANS */ -/* > \verbatim */ -/* > TRANS is CHARACTER*1 */ -/* > On entry, TRANS specifies the operation to be performed as */ -/* > follows: */ -/* > */ -/* > TRANS = 'N' or 'n' x := A*x. */ -/* > */ -/* > TRANS = 'T' or 't' x := A**T*x. */ -/* > */ -/* > TRANS = 'C' or 'c' x := A**T*x. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DIAG */ -/* > \verbatim */ -/* > DIAG is CHARACTER*1 */ -/* > On entry, DIAG specifies whether or not A is unit */ -/* > triangular as follows: */ -/* > */ -/* > DIAG = 'U' or 'u' A is assumed to be unit triangular. */ -/* > */ -/* > DIAG = 'N' or 'n' A is not assumed to be unit */ -/* > triangular. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > On entry, N specifies the order of the matrix A. */ -/* > N must be at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension ( LDA, N ) */ -/* > Before entry with UPLO = 'U' or 'u', the leading n by n */ -/* > upper triangular part of the array A must contain the upper */ -/* > triangular matrix and the strictly lower triangular part of */ -/* > A is not referenced. */ -/* > Before entry with UPLO = 'L' or 'l', the leading n by n */ -/* > lower triangular part of the array A must contain the lower */ -/* > triangular matrix and the strictly upper triangular part of */ -/* > A is not referenced. */ -/* > Note that when DIAG = 'U' or 'u', the diagonal elements of */ -/* > A are not referenced either, but are assumed to be unity. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > On entry, LDA specifies the first dimension of A as declared */ -/* > in the calling (sub) program. LDA must be at least */ -/* > max( 1, n ). */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] X */ -/* > \verbatim */ -/* > X is DOUBLE PRECISION array, dimension at least */ -/* > ( 1 + ( n - 1 )*abs( INCX ) ). */ -/* > Before entry, the incremented array X must contain the n */ -/* > element vector x. On exit, X is overwritten with the */ -/* > transformed vector x. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > On entry, INCX specifies the increment for the elements of */ -/* > X. INCX must not be zero. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup double_blas_level2 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > Level 2 Blas routine. */ -/* > The vector and matrix arguments are not referenced when N = 0, or M = 0 */ -/* > */ -/* > -- Written on 22-October-1986. */ -/* > Jack Dongarra, Argonne National Lab. */ -/* > Jeremy Du Croz, Nag Central Office. */ -/* > Sven Hammarling, Nag Central Office. */ -/* > Richard Hanson, Sandia National Labs. */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dtrmv_(char *uplo, char *trans, char *diag, integer *n, - doublereal *a, integer *lda, doublereal *x, integer *incx, ftnlen - uplo_len, ftnlen trans_len, ftnlen diag_len) +int dtrmv_(char *uplo, char *trans, char *diag, integer *n, doublereal *a, integer *lda, + doublereal *x, integer *incx, ftnlen uplo_len, ftnlen trans_len, ftnlen diag_len) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; - - /* Local variables */ integer i__, j, ix, jx, kx, info; doublereal temp; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern int xerbla_(char *, integer *, ftnlen); logical nounit; - - -/* -- Reference BLAS level2 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --x; - - /* Function Body */ info = 0; - if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", ( - ftnlen)1, (ftnlen)1)) { + if (!lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { info = 1; - } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, - (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, ( - ftnlen)1)) { + } else if (!lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && + !lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1) && + !lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { info = 2; - } else if (! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, - (char *)"N", (ftnlen)1, (ftnlen)1)) { + } else if (!lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && + !lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1)) { info = 3; } else if (*n < 0) { info = 4; - } else if (*lda < max(1,*n)) { + } else if (*lda < max(1, *n)) { info = 6; } else if (*incx == 0) { info = 8; @@ -228,31 +36,16 @@ extern "C" { xerbla_((char *)"DTRMV ", &info, (ftnlen)6); return 0; } - -/* Quick return if possible. */ - if (*n == 0) { return 0; } - nounit = lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1); - -/* Set up the start point in X if the increment is not unity. This */ -/* will be ( N - 1 )*INCX too small for descending loops. */ - if (*incx <= 0) { kx = 1 - (*n - 1) * *incx; } else if (*incx != 1) { kx = 1; } - -/* Start the operations. In this version the elements of A are */ -/* accessed sequentially with one pass through A. */ - if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { - -/* Form x := A*x. */ - if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { if (*incx == 1) { i__1 = *n; @@ -262,13 +55,11 @@ extern "C" { i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { x[i__] += temp * a[i__ + j * a_dim1]; -/* L10: */ } if (nounit) { x[j] *= a[j + j * a_dim1]; } } -/* L20: */ } } else { jx = kx; @@ -281,14 +72,12 @@ extern "C" { for (i__ = 1; i__ <= i__2; ++i__) { x[ix] += temp * a[i__ + j * a_dim1]; ix += *incx; -/* L30: */ } if (nounit) { x[jx] *= a[j + j * a_dim1]; } } jx += *incx; -/* L40: */ } } } else { @@ -299,13 +88,11 @@ extern "C" { i__1 = j + 1; for (i__ = *n; i__ >= i__1; --i__) { x[i__] += temp * a[i__ + j * a_dim1]; -/* L50: */ } if (nounit) { x[j] *= a[j + j * a_dim1]; } } -/* L60: */ } } else { kx += (*n - 1) * *incx; @@ -318,21 +105,16 @@ extern "C" { for (i__ = *n; i__ >= i__1; --i__) { x[ix] += temp * a[i__ + j * a_dim1]; ix -= *incx; -/* L70: */ } if (nounit) { x[jx] *= a[j + j * a_dim1]; } } jx -= *incx; -/* L80: */ } } } } else { - -/* Form x := A**T*x. */ - if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { if (*incx == 1) { for (j = *n; j >= 1; --j) { @@ -342,10 +124,8 @@ extern "C" { } for (i__ = j - 1; i__ >= 1; --i__) { temp += a[i__ + j * a_dim1] * x[i__]; -/* L90: */ } x[j] = temp; -/* L100: */ } } else { jx = kx + (*n - 1) * *incx; @@ -358,11 +138,9 @@ extern "C" { for (i__ = j - 1; i__ >= 1; --i__) { ix -= *incx; temp += a[i__ + j * a_dim1] * x[ix]; -/* L110: */ } x[jx] = temp; jx -= *incx; -/* L120: */ } } } else { @@ -376,10 +154,8 @@ extern "C" { i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { temp += a[i__ + j * a_dim1] * x[i__]; -/* L130: */ } x[j] = temp; -/* L140: */ } } else { jx = kx; @@ -394,22 +170,15 @@ extern "C" { for (i__ = j + 1; i__ <= i__2; ++i__) { ix += *incx; temp += a[i__ + j * a_dim1] * x[ix]; -/* L150: */ } x[jx] = temp; jx += *incx; -/* L160: */ } } } } - return 0; - -/* End of DTRMV */ - -} /* dtrmv_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dtrsm.cpp b/lib/linalg/dtrsm.cpp index 8b815c5300..9c0873f8dc 100644 --- a/lib/linalg/dtrsm.cpp +++ b/lib/linalg/dtrsm.cpp @@ -1,251 +1,26 @@ -/* fortran/dtrsm.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DTRSM */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) */ - -/* .. Scalar Arguments .. */ -/* DOUBLE PRECISION ALPHA */ -/* INTEGER LDA,LDB,M,N */ -/* CHARACTER DIAG,SIDE,TRANSA,UPLO */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A(LDA,*),B(LDB,*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DTRSM solves one of the matrix equations */ -/* > */ -/* > op( A )*X = alpha*B, or X*op( A ) = alpha*B, */ -/* > */ -/* > where alpha is a scalar, X and B are m by n matrices, A is a unit, or */ -/* > non-unit, upper or lower triangular matrix and op( A ) is one of */ -/* > */ -/* > op( A ) = A or op( A ) = A**T. */ -/* > */ -/* > The matrix X is overwritten on B. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] SIDE */ -/* > \verbatim */ -/* > SIDE is CHARACTER*1 */ -/* > On entry, SIDE specifies whether op( A ) appears on the left */ -/* > or right of X as follows: */ -/* > */ -/* > SIDE = 'L' or 'l' op( A )*X = alpha*B. */ -/* > */ -/* > SIDE = 'R' or 'r' X*op( A ) = alpha*B. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > On entry, UPLO specifies whether the matrix A is an upper or */ -/* > lower triangular matrix as follows: */ -/* > */ -/* > UPLO = 'U' or 'u' A is an upper triangular matrix. */ -/* > */ -/* > UPLO = 'L' or 'l' A is a lower triangular matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TRANSA */ -/* > \verbatim */ -/* > TRANSA is CHARACTER*1 */ -/* > On entry, TRANSA specifies the form of op( A ) to be used in */ -/* > the matrix multiplication as follows: */ -/* > */ -/* > TRANSA = 'N' or 'n' op( A ) = A. */ -/* > */ -/* > TRANSA = 'T' or 't' op( A ) = A**T. */ -/* > */ -/* > TRANSA = 'C' or 'c' op( A ) = A**T. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DIAG */ -/* > \verbatim */ -/* > DIAG is CHARACTER*1 */ -/* > On entry, DIAG specifies whether or not A is unit triangular */ -/* > as follows: */ -/* > */ -/* > DIAG = 'U' or 'u' A is assumed to be unit triangular. */ -/* > */ -/* > DIAG = 'N' or 'n' A is not assumed to be unit */ -/* > triangular. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > On entry, M specifies the number of rows of B. M must be at */ -/* > least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > On entry, N specifies the number of columns of B. N must be */ -/* > at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] ALPHA */ -/* > \verbatim */ -/* > ALPHA is DOUBLE PRECISION. */ -/* > On entry, ALPHA specifies the scalar alpha. When alpha is */ -/* > zero then A is not referenced and B need not be set before */ -/* > entry. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension ( LDA, k ), */ -/* > where k is m when SIDE = 'L' or 'l' */ -/* > and k is n when SIDE = 'R' or 'r'. */ -/* > Before entry with UPLO = 'U' or 'u', the leading k by k */ -/* > upper triangular part of the array A must contain the upper */ -/* > triangular matrix and the strictly lower triangular part of */ -/* > A is not referenced. */ -/* > Before entry with UPLO = 'L' or 'l', the leading k by k */ -/* > lower triangular part of the array A must contain the lower */ -/* > triangular matrix and the strictly upper triangular part of */ -/* > A is not referenced. */ -/* > Note that when DIAG = 'U' or 'u', the diagonal elements of */ -/* > A are not referenced either, but are assumed to be unity. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > On entry, LDA specifies the first dimension of A as declared */ -/* > in the calling (sub) program. When SIDE = 'L' or 'l' then */ -/* > LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' */ -/* > then LDA must be at least max( 1, n ). */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] B */ -/* > \verbatim */ -/* > B is DOUBLE PRECISION array, dimension ( LDB, N ) */ -/* > Before entry, the leading m by n part of the array B must */ -/* > contain the right-hand side matrix B, and on exit is */ -/* > overwritten by the solution matrix X. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDB */ -/* > \verbatim */ -/* > LDB is INTEGER */ -/* > On entry, LDB specifies the first dimension of B as declared */ -/* > in the calling (sub) program. LDB must be at least */ -/* > max( 1, m ). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup double_blas_level3 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > Level 3 Blas routine. */ -/* > */ -/* > */ -/* > -- Written on 8-February-1989. */ -/* > Jack Dongarra, Argonne National Laboratory. */ -/* > Iain Duff, AERE Harwell. */ -/* > Jeremy Du Croz, Numerical Algorithms Group Ltd. */ -/* > Sven Hammarling, Numerical Algorithms Group Ltd. */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int dtrsm_(char *side, char *uplo, char *transa, char *diag, - integer *m, integer *n, doublereal *alpha, doublereal *a, integer * - lda, doublereal *b, integer *ldb, ftnlen side_len, ftnlen uplo_len, - ftnlen transa_len, ftnlen diag_len) +int dtrsm_(char *side, char *uplo, char *transa, char *diag, integer *m, integer *n, + doublereal *alpha, doublereal *a, integer *lda, doublereal *b, integer *ldb, + ftnlen side_len, ftnlen uplo_len, ftnlen transa_len, ftnlen diag_len) { - /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3; - - /* Local variables */ integer i__, j, k, info; doublereal temp; logical lside; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer nrowa; logical upper; - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern int xerbla_(char *, integer *, ftnlen); logical nounit; - - -/* -- Reference BLAS level3 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. Parameters .. */ -/* .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; - - /* Function Body */ lside = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); if (lside) { nrowa = *m; @@ -254,70 +29,53 @@ extern "C" { } nounit = lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1); upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); - info = 0; - if (! lside && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + if (!lside && !lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { info = 1; - } else if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + } else if (!upper && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { info = 2; - } else if (! lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(transa, - (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(transa, (char *)"C", (ftnlen)1, ( - ftnlen)1)) { + } else if (!lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1) && + !lsame_(transa, (char *)"T", (ftnlen)1, (ftnlen)1) && + !lsame_(transa, (char *)"C", (ftnlen)1, (ftnlen)1)) { info = 3; - } else if (! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, - (char *)"N", (ftnlen)1, (ftnlen)1)) { + } else if (!lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && + !lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1)) { info = 4; } else if (*m < 0) { info = 5; } else if (*n < 0) { info = 6; - } else if (*lda < max(1,nrowa)) { + } else if (*lda < max(1, nrowa)) { info = 9; - } else if (*ldb < max(1,*m)) { + } else if (*ldb < max(1, *m)) { info = 11; } if (info != 0) { xerbla_((char *)"DTRSM ", &info, (ftnlen)6); return 0; } - -/* Quick return if possible. */ - if (*m == 0 || *n == 0) { return 0; } - -/* And when alpha.eq.zero. */ - if (*alpha == 0.) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { b[i__ + j * b_dim1] = 0.; -/* L10: */ } -/* L20: */ } return 0; } - -/* Start the operations. */ - if (lside) { if (lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1)) { - -/* Form B := alpha*inv( A )*B. */ - if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (*alpha != 1.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { - b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1] - ; -/* L30: */ + b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1]; } } for (k = *m; k >= 1; --k) { @@ -327,14 +85,10 @@ extern "C" { } i__2 = k - 1; for (i__ = 1; i__ <= i__2; ++i__) { - b[i__ + j * b_dim1] -= b[k + j * b_dim1] * a[ - i__ + k * a_dim1]; -/* L40: */ + b[i__ + j * b_dim1] -= b[k + j * b_dim1] * a[i__ + k * a_dim1]; } } -/* L50: */ } -/* L60: */ } } else { i__1 = *n; @@ -342,9 +96,7 @@ extern "C" { if (*alpha != 1.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { - b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1] - ; -/* L70: */ + b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1]; } } i__2 = *m; @@ -355,20 +107,13 @@ extern "C" { } i__3 = *m; for (i__ = k + 1; i__ <= i__3; ++i__) { - b[i__ + j * b_dim1] -= b[k + j * b_dim1] * a[ - i__ + k * a_dim1]; -/* L80: */ + b[i__ + j * b_dim1] -= b[k + j * b_dim1] * a[i__ + k * a_dim1]; } } -/* L90: */ } -/* L100: */ } } } else { - -/* Form B := alpha*inv( A**T )*B. */ - if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { @@ -378,15 +123,12 @@ extern "C" { i__3 = i__ - 1; for (k = 1; k <= i__3; ++k) { temp -= a[k + i__ * a_dim1] * b[k + j * b_dim1]; -/* L110: */ } if (nounit) { temp /= a[i__ + i__ * a_dim1]; } b[i__ + j * b_dim1] = temp; -/* L120: */ } -/* L130: */ } } else { i__1 = *n; @@ -396,32 +138,24 @@ extern "C" { i__2 = *m; for (k = i__ + 1; k <= i__2; ++k) { temp -= a[k + i__ * a_dim1] * b[k + j * b_dim1]; -/* L140: */ } if (nounit) { temp /= a[i__ + i__ * a_dim1]; } b[i__ + j * b_dim1] = temp; -/* L150: */ } -/* L160: */ } } } } else { if (lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1)) { - -/* Form B := alpha*B*inv( A ). */ - if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (*alpha != 1.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { - b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1] - ; -/* L170: */ + b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1]; } } i__2 = j - 1; @@ -429,31 +163,24 @@ extern "C" { if (a[k + j * a_dim1] != 0.) { i__3 = *m; for (i__ = 1; i__ <= i__3; ++i__) { - b[i__ + j * b_dim1] -= a[k + j * a_dim1] * b[ - i__ + k * b_dim1]; -/* L180: */ + b[i__ + j * b_dim1] -= a[k + j * a_dim1] * b[i__ + k * b_dim1]; } } -/* L190: */ } if (nounit) { temp = 1. / a[j + j * a_dim1]; i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1]; -/* L200: */ } } -/* L210: */ } } else { for (j = *n; j >= 1; --j) { if (*alpha != 1.) { i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { - b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1] - ; -/* L220: */ + b[i__ + j * b_dim1] = *alpha * b[i__ + j * b_dim1]; } } i__1 = *n; @@ -461,28 +188,20 @@ extern "C" { if (a[k + j * a_dim1] != 0.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { - b[i__ + j * b_dim1] -= a[k + j * a_dim1] * b[ - i__ + k * b_dim1]; -/* L230: */ + b[i__ + j * b_dim1] -= a[k + j * a_dim1] * b[i__ + k * b_dim1]; } } -/* L240: */ } if (nounit) { temp = 1. / a[j + j * a_dim1]; i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1]; -/* L250: */ } } -/* L260: */ } } } else { - -/* Form B := alpha*B*inv( A**T ). */ - if (upper) { for (k = *n; k >= 1; --k) { if (nounit) { @@ -490,7 +209,6 @@ extern "C" { i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1]; -/* L270: */ } } i__1 = k - 1; @@ -499,22 +217,16 @@ extern "C" { temp = a[j + k * a_dim1]; i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { - b[i__ + j * b_dim1] -= temp * b[i__ + k * - b_dim1]; -/* L280: */ + b[i__ + j * b_dim1] -= temp * b[i__ + k * b_dim1]; } } -/* L290: */ } if (*alpha != 1.) { i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { - b[i__ + k * b_dim1] = *alpha * b[i__ + k * b_dim1] - ; -/* L300: */ + b[i__ + k * b_dim1] = *alpha * b[i__ + k * b_dim1]; } } -/* L310: */ } } else { i__1 = *n; @@ -524,7 +236,6 @@ extern "C" { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1]; -/* L320: */ } } i__2 = *n; @@ -533,33 +244,22 @@ extern "C" { temp = a[j + k * a_dim1]; i__3 = *m; for (i__ = 1; i__ <= i__3; ++i__) { - b[i__ + j * b_dim1] -= temp * b[i__ + k * - b_dim1]; -/* L330: */ + b[i__ + j * b_dim1] -= temp * b[i__ + k * b_dim1]; } } -/* L340: */ } if (*alpha != 1.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { - b[i__ + k * b_dim1] = *alpha * b[i__ + k * b_dim1] - ; -/* L350: */ + b[i__ + k * b_dim1] = *alpha * b[i__ + k * b_dim1]; } } -/* L360: */ } } } } - return 0; - -/* End of DTRSM */ - -} /* dtrsm_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dtrsv.cpp b/lib/linalg/dtrsv.cpp index 4044c819f6..51d3436ebf 100644 --- a/lib/linalg/dtrsv.cpp +++ b/lib/linalg/dtrsv.cpp @@ -1,221 +1,33 @@ -/* fortran/dtrsv.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DTRSV */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INCX,LDA,N */ -/* CHARACTER DIAG,TRANS,UPLO */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A(LDA,*),X(*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DTRSV solves one of the systems of equations */ -/* > */ -/* > A*x = b, or A**T*x = b, */ -/* > */ -/* > where b and x are n element vectors and A is an n by n unit, or */ -/* > non-unit, upper or lower triangular matrix. */ -/* > */ -/* > No test for singularity or near-singularity is included in this */ -/* > routine. Such tests must be performed before calling this routine. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > On entry, UPLO specifies whether the matrix is an upper or */ -/* > lower triangular matrix as follows: */ -/* > */ -/* > UPLO = 'U' or 'u' A is an upper triangular matrix. */ -/* > */ -/* > UPLO = 'L' or 'l' A is a lower triangular matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TRANS */ -/* > \verbatim */ -/* > TRANS is CHARACTER*1 */ -/* > On entry, TRANS specifies the equations to be solved as */ -/* > follows: */ -/* > */ -/* > TRANS = 'N' or 'n' A*x = b. */ -/* > */ -/* > TRANS = 'T' or 't' A**T*x = b. */ -/* > */ -/* > TRANS = 'C' or 'c' A**T*x = b. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DIAG */ -/* > \verbatim */ -/* > DIAG is CHARACTER*1 */ -/* > On entry, DIAG specifies whether or not A is unit */ -/* > triangular as follows: */ -/* > */ -/* > DIAG = 'U' or 'u' A is assumed to be unit triangular. */ -/* > */ -/* > DIAG = 'N' or 'n' A is not assumed to be unit */ -/* > triangular. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > On entry, N specifies the order of the matrix A. */ -/* > N must be at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension ( LDA, N ) */ -/* > Before entry with UPLO = 'U' or 'u', the leading n by n */ -/* > upper triangular part of the array A must contain the upper */ -/* > triangular matrix and the strictly lower triangular part of */ -/* > A is not referenced. */ -/* > Before entry with UPLO = 'L' or 'l', the leading n by n */ -/* > lower triangular part of the array A must contain the lower */ -/* > triangular matrix and the strictly upper triangular part of */ -/* > A is not referenced. */ -/* > Note that when DIAG = 'U' or 'u', the diagonal elements of */ -/* > A are not referenced either, but are assumed to be unity. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > On entry, LDA specifies the first dimension of A as declared */ -/* > in the calling (sub) program. LDA must be at least */ -/* > max( 1, n ). */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] X */ -/* > \verbatim */ -/* > X is DOUBLE PRECISION array, dimension at least */ -/* > ( 1 + ( n - 1 )*abs( INCX ) ). */ -/* > Before entry, the incremented array X must contain the n */ -/* > element right-hand side vector b. On exit, X is overwritten */ -/* > with the solution vector x. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > On entry, INCX specifies the increment for the elements of */ -/* > X. INCX must not be zero. */ -/* > */ -/* > Level 2 Blas routine. */ -/* > */ -/* > -- Written on 22-October-1986. */ -/* > Jack Dongarra, Argonne National Lab. */ -/* > Jeremy Du Croz, Nag Central Office. */ -/* > Sven Hammarling, Nag Central Office. */ -/* > Richard Hanson, Sandia National Labs. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup double_blas_level1 */ - -/* ===================================================================== */ -/* Subroutine */ int dtrsv_(char *uplo, char *trans, char *diag, integer *n, - doublereal *a, integer *lda, doublereal *x, integer *incx, ftnlen - uplo_len, ftnlen trans_len, ftnlen diag_len) +int dtrsv_(char *uplo, char *trans, char *diag, integer *n, doublereal *a, integer *lda, + doublereal *x, integer *incx, ftnlen uplo_len, ftnlen trans_len, ftnlen diag_len) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; - - /* Local variables */ integer i__, j, ix, jx, kx, info; doublereal temp; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern int xerbla_(char *, integer *, ftnlen); logical nounit; - - -/* -- Reference BLAS level1 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --x; - - /* Function Body */ info = 0; - if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", ( - ftnlen)1, (ftnlen)1)) { + if (!lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { info = 1; - } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, - (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, ( - ftnlen)1)) { + } else if (!lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && + !lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1) && + !lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { info = 2; - } else if (! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, - (char *)"N", (ftnlen)1, (ftnlen)1)) { + } else if (!lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && + !lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1)) { info = 3; } else if (*n < 0) { info = 4; - } else if (*lda < max(1,*n)) { + } else if (*lda < max(1, *n)) { info = 6; } else if (*incx == 0) { info = 8; @@ -224,31 +36,16 @@ extern "C" { xerbla_((char *)"DTRSV ", &info, (ftnlen)6); return 0; } - -/* Quick return if possible. */ - if (*n == 0) { return 0; } - nounit = lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1); - -/* Set up the start point in X if the increment is not unity. This */ -/* will be ( N - 1 )*INCX too small for descending loops. */ - if (*incx <= 0) { kx = 1 - (*n - 1) * *incx; } else if (*incx != 1) { kx = 1; } - -/* Start the operations. In this version the elements of A are */ -/* accessed sequentially with one pass through A. */ - if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { - -/* Form x := inv( A )*x. */ - if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { if (*incx == 1) { for (j = *n; j >= 1; --j) { @@ -259,10 +56,8 @@ extern "C" { temp = x[j]; for (i__ = j - 1; i__ >= 1; --i__) { x[i__] -= temp * a[i__ + j * a_dim1]; -/* L10: */ } } -/* L20: */ } } else { jx = kx + (*n - 1) * *incx; @@ -276,11 +71,9 @@ extern "C" { for (i__ = j - 1; i__ >= 1; --i__) { ix -= *incx; x[ix] -= temp * a[i__ + j * a_dim1]; -/* L30: */ } } jx -= *incx; -/* L40: */ } } } else { @@ -295,10 +88,8 @@ extern "C" { i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { x[i__] -= temp * a[i__ + j * a_dim1]; -/* L50: */ } } -/* L60: */ } } else { jx = kx; @@ -314,18 +105,13 @@ extern "C" { for (i__ = j + 1; i__ <= i__2; ++i__) { ix += *incx; x[ix] -= temp * a[i__ + j * a_dim1]; -/* L70: */ } } jx += *incx; -/* L80: */ } } } } else { - -/* Form x := inv( A**T )*x. */ - if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { if (*incx == 1) { i__1 = *n; @@ -334,13 +120,11 @@ extern "C" { i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { temp -= a[i__ + j * a_dim1] * x[i__]; -/* L90: */ } if (nounit) { temp /= a[j + j * a_dim1]; } x[j] = temp; -/* L100: */ } } else { jx = kx; @@ -352,14 +136,12 @@ extern "C" { for (i__ = 1; i__ <= i__2; ++i__) { temp -= a[i__ + j * a_dim1] * x[ix]; ix += *incx; -/* L110: */ } if (nounit) { temp /= a[j + j * a_dim1]; } x[jx] = temp; jx += *incx; -/* L120: */ } } } else { @@ -369,13 +151,11 @@ extern "C" { i__1 = j + 1; for (i__ = *n; i__ >= i__1; --i__) { temp -= a[i__ + j * a_dim1] * x[i__]; -/* L130: */ } if (nounit) { temp /= a[j + j * a_dim1]; } x[j] = temp; -/* L140: */ } } else { kx += (*n - 1) * *incx; @@ -387,25 +167,18 @@ extern "C" { for (i__ = *n; i__ >= i__1; --i__) { temp -= a[i__ + j * a_dim1] * x[ix]; ix -= *incx; -/* L150: */ } if (nounit) { temp /= a[j + j * a_dim1]; } x[jx] = temp; jx -= *incx; -/* L160: */ } } } } - return 0; - -/* End of DTRSV */ - -} /* dtrsv_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dtrti2.cpp b/lib/linalg/dtrti2.cpp index 79cc64b359..a0e26f9268 100644 --- a/lib/linalg/dtrti2.cpp +++ b/lib/linalg/dtrti2.cpp @@ -1,195 +1,34 @@ -/* fortran/dtrti2.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; - -/* > \brief \b DTRTI2 computes the inverse of a triangular matrix (unblocked algorithm). */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DTRTI2 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DTRTI2( UPLO, DIAG, N, A, LDA, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER DIAG, UPLO */ -/* INTEGER INFO, LDA, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DTRTI2 computes the inverse of a real upper or lower triangular */ -/* > matrix. */ -/* > */ -/* > This is the Level 2 BLAS version of the algorithm. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > Specifies whether the matrix A is upper or lower triangular. */ -/* > = 'U': Upper triangular */ -/* > = 'L': Lower triangular */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DIAG */ -/* > \verbatim */ -/* > DIAG is CHARACTER*1 */ -/* > Specifies whether or not the matrix A is unit triangular. */ -/* > = 'N': Non-unit triangular */ -/* > = 'U': Unit triangular */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On entry, the triangular matrix A. If UPLO = 'U', the */ -/* > leading n by n upper triangular part of the array A contains */ -/* > the upper triangular matrix, and the strictly lower */ -/* > triangular part of A is not referenced. If UPLO = 'L', the */ -/* > leading n by n lower triangular part of the array A contains */ -/* > the lower triangular matrix, and the strictly upper */ -/* > triangular part of A is not referenced. If DIAG = 'U', the */ -/* > diagonal elements of A are also not referenced and are */ -/* > assumed to be 1. */ -/* > */ -/* > On exit, the (triangular) inverse of the original matrix, in */ -/* > the same storage format. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -k, the k-th argument had an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleOTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dtrti2_(char *uplo, char *diag, integer *n, doublereal * - a, integer *lda, integer *info, ftnlen uplo_len, ftnlen diag_len) +int dtrti2_(char *uplo, char *diag, integer *n, doublereal *a, integer *lda, integer *info, + ftnlen uplo_len, ftnlen diag_len) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; - - /* Local variables */ integer j; doublereal ajj; - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *); + extern int dscal_(integer *, doublereal *, doublereal *, integer *); extern logical lsame_(char *, char *, ftnlen, ftnlen); logical upper; - extern /* Subroutine */ int dtrmv_(char *, char *, char *, integer *, - doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, - ftnlen), xerbla_(char *, integer *, ftnlen); + extern int dtrmv_(char *, char *, char *, integer *, doublereal *, integer *, doublereal *, + integer *, ftnlen, ftnlen, ftnlen), + xerbla_(char *, integer *, ftnlen); logical nounit; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; - - /* Function Body */ *info = 0; upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); nounit = lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1); - if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + if (!upper && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { *info = -1; - } else if (! nounit && ! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1)) { + } else if (!nounit && !lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1)) { *info = -2; } else if (*n < 0) { *info = -3; - } else if (*lda < max(1,*n)) { + } else if (*lda < max(1, *n)) { *info = -5; } if (*info != 0) { @@ -197,11 +36,7 @@ f"> */ xerbla_((char *)"DTRTI2", &i__1, (ftnlen)6); return 0; } - if (upper) { - -/* Compute inverse of upper triangular matrix. */ - i__1 = *n; for (j = 1; j <= i__1; ++j) { if (nounit) { @@ -210,21 +45,13 @@ f"> */ } else { ajj = -1.; } - -/* Compute elements 1:j-1 of j-th column. */ - i__2 = j - 1; - dtrmv_((char *)"Upper", (char *)"No transpose", diag, &i__2, &a[a_offset], lda, & - a[j * a_dim1 + 1], &c__1, (ftnlen)5, (ftnlen)12, (ftnlen) - 1); + dtrmv_((char *)"Upper", (char *)"No transpose", diag, &i__2, &a[a_offset], lda, &a[j * a_dim1 + 1], + &c__1, (ftnlen)5, (ftnlen)12, (ftnlen)1); i__2 = j - 1; dscal_(&i__2, &ajj, &a[j * a_dim1 + 1], &c__1); -/* L10: */ } } else { - -/* Compute inverse of lower triangular matrix. */ - for (j = *n; j >= 1; --j) { if (nounit) { a[j + j * a_dim1] = 1. / a[j + j * a_dim1]; @@ -233,26 +60,16 @@ f"> */ ajj = -1.; } if (j < *n) { - -/* Compute elements j+1:n of j-th column. */ - i__1 = *n - j; - dtrmv_((char *)"Lower", (char *)"No transpose", diag, &i__1, &a[j + 1 + (j + - 1) * a_dim1], lda, &a[j + 1 + j * a_dim1], &c__1, ( - ftnlen)5, (ftnlen)12, (ftnlen)1); + dtrmv_((char *)"Lower", (char *)"No transpose", diag, &i__1, &a[j + 1 + (j + 1) * a_dim1], lda, + &a[j + 1 + j * a_dim1], &c__1, (ftnlen)5, (ftnlen)12, (ftnlen)1); i__1 = *n - j; dscal_(&i__1, &ajj, &a[j + 1 + j * a_dim1], &c__1); } -/* L20: */ } } - return 0; - -/* End of DTRTI2 */ - -} /* dtrti2_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dtrtri.cpp b/lib/linalg/dtrtri.cpp index 91742619b0..55c6b1b01f 100644 --- a/lib/linalg/dtrtri.cpp +++ b/lib/linalg/dtrtri.cpp @@ -1,208 +1,46 @@ -/* fortran/dtrtri.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static integer c_n1 = -1; static integer c__2 = 2; static doublereal c_b18 = 1.; static doublereal c_b22 = -1.; - -/* > \brief \b DTRTRI */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download DTRTRI + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE DTRTRI( UPLO, DIAG, N, A, LDA, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER DIAG, UPLO */ -/* INTEGER INFO, LDA, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DTRTRI computes the inverse of a real upper or lower triangular */ -/* > matrix A. */ -/* > */ -/* > This is the Level 3 BLAS version of the algorithm. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > = 'U': A is upper triangular; */ -/* > = 'L': A is lower triangular. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DIAG */ -/* > \verbatim */ -/* > DIAG is CHARACTER*1 */ -/* > = 'N': A is non-unit triangular; */ -/* > = 'U': A is unit triangular. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > On entry, the triangular matrix A. If UPLO = 'U', the */ -/* > leading N-by-N upper triangular part of the array A contains */ -/* > the upper triangular matrix, and the strictly lower */ -/* > triangular part of A is not referenced. If UPLO = 'L', the */ -/* > leading N-by-N lower triangular part of the array A contains */ -/* > the lower triangular matrix, and the strictly upper */ -/* > triangular part of A is not referenced. If DIAG = 'U', the */ -/* > diagonal elements of A are also not referenced and are */ -/* > assumed to be 1. */ -/* > On exit, the (triangular) inverse of the original matrix, in */ -/* > the same storage format. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > > 0: if INFO = i, A(i,i) is exactly zero. The triangular */ -/* > matrix is singular and its inverse can not be computed. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup doubleOTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int dtrtri_(char *uplo, char *diag, integer *n, doublereal * - a, integer *lda, integer *info, ftnlen uplo_len, ftnlen diag_len) +int dtrtri_(char *uplo, char *diag, integer *n, doublereal *a, integer *lda, integer *info, + ftnlen uplo_len, ftnlen diag_len) { - /* System generated locals */ address a__1[2]; integer a_dim1, a_offset, i__1, i__2[2], i__3, i__4, i__5; char ch__1[2]; - - /* Builtin functions */ - /* Subroutine */ int s_lmp_cat(char *, char **, integer *, integer *, ftnlen); - - /* Local variables */ + int s_lmp_cat(char *, char **, integer *, integer *, ftnlen); integer j, jb, nb, nn; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int dtrmm_(char *, char *, char *, char *, - integer *, integer *, doublereal *, doublereal *, integer *, - doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen), dtrsm_( - char *, char *, char *, char *, integer *, integer *, doublereal * - , doublereal *, integer *, doublereal *, integer *, ftnlen, - ftnlen, ftnlen, ftnlen); + extern int dtrmm_(char *, char *, char *, char *, integer *, integer *, doublereal *, + doublereal *, integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, + ftnlen), + dtrsm_(char *, char *, char *, char *, integer *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); logical upper; - extern /* Subroutine */ int dtrti2_(char *, char *, integer *, doublereal - *, integer *, integer *, ftnlen, ftnlen), xerbla_(char *, integer - *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern int dtrti2_(char *, char *, integer *, doublereal *, integer *, integer *, ftnlen, + ftnlen), + xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); logical nounit; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; - - /* Function Body */ *info = 0; upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); nounit = lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1); - if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + if (!upper && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { *info = -1; - } else if (! nounit && ! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1)) { + } else if (!nounit && !lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1)) { *info = -2; } else if (*n < 0) { *info = -3; - } else if (*lda < max(1,*n)) { + } else if (*lda < max(1, *n)) { *info = -5; } if (*info != 0) { @@ -210,112 +48,62 @@ f"> */ xerbla_((char *)"DTRTRI", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*n == 0) { return 0; } - -/* Check for singularity if non-unit. */ - if (nounit) { i__1 = *n; for (*info = 1; *info <= i__1; ++(*info)) { if (a[*info + *info * a_dim1] == 0.) { return 0; } -/* L10: */ } *info = 0; } - -/* Determine the block size for this environment. */ - -/* Writing concatenation */ i__2[0] = 1, a__1[0] = uplo; i__2[1] = 1, a__1[1] = diag; s_lmp_cat(ch__1, a__1, i__2, &c__2, (ftnlen)2); - nb = ilaenv_(&c__1, (char *)"DTRTRI", ch__1, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, ( - ftnlen)2); + nb = ilaenv_(&c__1, (char *)"DTRTRI", ch__1, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (ftnlen)2); if (nb <= 1 || nb >= *n) { - -/* Use unblocked code */ - dtrti2_(uplo, diag, n, &a[a_offset], lda, info, (ftnlen)1, (ftnlen)1); } else { - -/* Use blocked code */ - if (upper) { - -/* Compute inverse of upper triangular matrix */ - i__1 = *n; i__3 = nb; for (j = 1; i__3 < 0 ? j >= i__1 : j <= i__1; j += i__3) { -/* Computing MIN */ i__4 = nb, i__5 = *n - j + 1; - jb = min(i__4,i__5); - -/* Compute rows 1:j-1 of current block column */ - + jb = min(i__4, i__5); i__4 = j - 1; - dtrmm_((char *)"Left", (char *)"Upper", (char *)"No transpose", diag, &i__4, &jb, & - c_b18, &a[a_offset], lda, &a[j * a_dim1 + 1], lda, ( - ftnlen)4, (ftnlen)5, (ftnlen)12, (ftnlen)1); + dtrmm_((char *)"Left", (char *)"Upper", (char *)"No transpose", diag, &i__4, &jb, &c_b18, &a[a_offset], lda, + &a[j * a_dim1 + 1], lda, (ftnlen)4, (ftnlen)5, (ftnlen)12, (ftnlen)1); i__4 = j - 1; - dtrsm_((char *)"Right", (char *)"Upper", (char *)"No transpose", diag, &i__4, &jb, & - c_b22, &a[j + j * a_dim1], lda, &a[j * a_dim1 + 1], - lda, (ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)1); - -/* Compute inverse of current diagonal block */ - - dtrti2_((char *)"Upper", diag, &jb, &a[j + j * a_dim1], lda, info, ( - ftnlen)5, (ftnlen)1); -/* L20: */ + dtrsm_((char *)"Right", (char *)"Upper", (char *)"No transpose", diag, &i__4, &jb, &c_b22, + &a[j + j * a_dim1], lda, &a[j * a_dim1 + 1], lda, (ftnlen)5, (ftnlen)5, + (ftnlen)12, (ftnlen)1); + dtrti2_((char *)"Upper", diag, &jb, &a[j + j * a_dim1], lda, info, (ftnlen)5, (ftnlen)1); } } else { - -/* Compute inverse of lower triangular matrix */ - nn = (*n - 1) / nb * nb + 1; i__3 = -nb; for (j = nn; i__3 < 0 ? j >= 1 : j <= 1; j += i__3) { -/* Computing MIN */ i__1 = nb, i__4 = *n - j + 1; - jb = min(i__1,i__4); + jb = min(i__1, i__4); if (j + jb <= *n) { - -/* Compute rows j+jb:n of current block column */ - i__1 = *n - j - jb + 1; - dtrmm_((char *)"Left", (char *)"Lower", (char *)"No transpose", diag, &i__1, &jb, - &c_b18, &a[j + jb + (j + jb) * a_dim1], lda, &a[j - + jb + j * a_dim1], lda, (ftnlen)4, (ftnlen)5, ( - ftnlen)12, (ftnlen)1); + dtrmm_((char *)"Left", (char *)"Lower", (char *)"No transpose", diag, &i__1, &jb, &c_b18, + &a[j + jb + (j + jb) * a_dim1], lda, &a[j + jb + j * a_dim1], lda, + (ftnlen)4, (ftnlen)5, (ftnlen)12, (ftnlen)1); i__1 = *n - j - jb + 1; - dtrsm_((char *)"Right", (char *)"Lower", (char *)"No transpose", diag, &i__1, &jb, - &c_b22, &a[j + j * a_dim1], lda, &a[j + jb + j * - a_dim1], lda, (ftnlen)5, (ftnlen)5, (ftnlen)12, ( - ftnlen)1); + dtrsm_((char *)"Right", (char *)"Lower", (char *)"No transpose", diag, &i__1, &jb, &c_b22, + &a[j + j * a_dim1], lda, &a[j + jb + j * a_dim1], lda, (ftnlen)5, + (ftnlen)5, (ftnlen)12, (ftnlen)1); } - -/* Compute inverse of current diagonal block */ - - dtrti2_((char *)"Lower", diag, &jb, &a[j + j * a_dim1], lda, info, ( - ftnlen)5, (ftnlen)1); -/* L30: */ + dtrti2_((char *)"Lower", diag, &jb, &a[j + j * a_dim1], lda, info, (ftnlen)5, (ftnlen)1); } } } - return 0; - -/* End of DTRTRI */ - -} /* dtrtri_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/dznrm2.cpp b/lib/linalg/dznrm2.cpp index 5041b7280e..f636330367 100644 --- a/lib/linalg/dznrm2.cpp +++ b/lib/linalg/dznrm2.cpp @@ -1,140 +1,20 @@ -/* fortran/dznrm2.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b DZNRM2 */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* DOUBLE PRECISION FUNCTION DZNRM2(N,X,INCX) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INCX,N */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 X(*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > DZNRM2 returns the euclidean norm of a vector via the function */ -/* > name, so that */ -/* > */ -/* > DZNRM2 := sqrt( x**H*x ) */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > number of elements in input vector(s) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] X */ -/* > \verbatim */ -/* > X is COMPLEX*16 array, dimension (N) */ -/* > complex vector with N elements */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > storage spacing between elements of X */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \date December 2016 */ - -/* > \ingroup double_blas_level1 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > -- This version written on 25-October-1982. */ -/* > Modified on 14-October-1993 to inline the call to ZLASSQ. */ -/* > Sven Hammarling, Nag Ltd. */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ doublereal dznrm2_(integer *n, doublecomplex *x, integer *incx) { - /* System generated locals */ integer i__1, i__2, i__3; doublereal ret_val, d__1; - - /* Builtin functions */ double d_lmp_imag(doublecomplex *), sqrt(doublereal); - - /* Local variables */ integer ix; doublereal ssq, temp, norm, scale; - - -/* -- Reference BLAS level1 routine (version 3.7.0) -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ -/* December 2016 */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ - /* Parameter adjustments */ --x; - - /* Function Body */ if (*n < 1 || *incx < 1) { norm = 0.; } else { scale = 0.; ssq = 1.; -/* The following loop is equivalent to this call to the LAPACK */ -/* auxiliary routine: */ -/* CALL ZLASSQ( N, X, INCX, SCALE, SSQ ) */ - i__1 = (*n - 1) * *incx + 1; i__2 = *incx; for (ix = 1; i__2 < 0 ? ix >= i__1 : ix <= i__1; ix += i__2) { @@ -143,12 +23,10 @@ doublereal dznrm2_(integer *n, doublecomplex *x, integer *incx) i__3 = ix; temp = (d__1 = x[i__3].r, abs(d__1)); if (scale < temp) { -/* Computing 2nd power */ d__1 = scale / temp; ssq = ssq * (d__1 * d__1) + 1.; scale = temp; } else { -/* Computing 2nd power */ d__1 = temp / scale; ssq += d__1 * d__1; } @@ -156,28 +34,20 @@ doublereal dznrm2_(integer *n, doublecomplex *x, integer *incx) if (d_lmp_imag(&x[ix]) != 0.) { temp = (d__1 = d_lmp_imag(&x[ix]), abs(d__1)); if (scale < temp) { -/* Computing 2nd power */ d__1 = scale / temp; ssq = ssq * (d__1 * d__1) + 1.; scale = temp; } else { -/* Computing 2nd power */ d__1 = temp / scale; ssq += d__1 * d__1; } } -/* L10: */ } norm = scale * sqrt(ssq); } - ret_val = norm; return ret_val; - -/* End of DZNRM2. */ - -} /* dznrm2_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/idamax.cpp b/lib/linalg/idamax.cpp index e50c15bd38..ab2c24dc15 100644 --- a/lib/linalg/idamax.cpp +++ b/lib/linalg/idamax.cpp @@ -1,119 +1,14 @@ -/* fortran/idamax.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b IDAMAX */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* INTEGER FUNCTION IDAMAX(N,DX,INCX) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INCX,N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION DX(*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > IDAMAX finds the index of the first element having maximum absolute value. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > number of elements in input vector(s) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DX */ -/* > \verbatim */ -/* > DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > storage spacing between elements of DX */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup aux_blas */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > jack dongarra, linpack, 3/11/78. */ -/* > modified 3/93 to return if incx .le. 0. */ -/* > modified 12/3/93, array(1) declarations changed to array(*) */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ integer idamax_(integer *n, doublereal *dx, integer *incx) { - /* System generated locals */ integer ret_val, i__1; doublereal d__1; - - /* Local variables */ integer i__, ix; doublereal dmax__; - - -/* -- Reference BLAS level1 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Local Scalars .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ - /* Parameter adjustments */ --dx; - - /* Function Body */ ret_val = 0; if (*n < 1 || *incx <= 0) { return ret_val; @@ -123,9 +18,6 @@ integer idamax_(integer *n, doublereal *dx, integer *incx) return ret_val; } if (*incx == 1) { - -/* code for increment equal to 1 */ - dmax__ = abs(dx[1]); i__1 = *n; for (i__ = 2; i__ <= i__1; ++i__) { @@ -135,9 +27,6 @@ integer idamax_(integer *n, doublereal *dx, integer *incx) } } } else { - -/* code for increment not equal to 1 */ - ix = 1; dmax__ = abs(dx[1]); ix += *incx; @@ -151,11 +40,7 @@ integer idamax_(integer *n, doublereal *dx, integer *incx) } } return ret_val; - -/* End of IDAMAX */ - -} /* idamax_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/ieeeck.cpp b/lib/linalg/ieeeck.cpp index 783a87df9d..c8cf58ba81 100644 --- a/lib/linalg/ieeeck.cpp +++ b/lib/linalg/ieeeck.cpp @@ -1,228 +1,87 @@ -/* fortran/ieeeck.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b IEEECK */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download IEEECK + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* INTEGER FUNCTION IEEECK( ISPEC, ZERO, ONE ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER ISPEC */ -/* REAL ONE, ZERO */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > IEEECK is called from the ILAENV to verify that Infinity and */ -/* > possibly NaN arithmetic is safe (i.e. will not trap). */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] ISPEC */ -/* > \verbatim */ -/* > ISPEC is INTEGER */ -/* > Specifies whether to test just for infinity arithmetic */ -/* > or whether to test for infinity and NaN arithmetic. */ -/* > = 0: Verify infinity arithmetic only. */ -/* > = 1: Verify infinity and NaN arithmetic. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] ZERO */ -/* > \verbatim */ -/* > ZERO is REAL */ -/* > Must contain the value 0.0 */ -/* > This is passed to prevent the compiler from optimizing */ -/* > away this code. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] ONE */ -/* > \verbatim */ -/* > ONE is REAL */ -/* > Must contain the value 1.0 */ -/* > This is passed to prevent the compiler from optimizing */ -/* > away this code. */ -/* > */ -/* > RETURN VALUE: INTEGER */ -/* > = 0: Arithmetic failed to produce the correct answers */ -/* > = 1: Arithmetic produced the correct answers */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup OTHERauxiliary */ - -/* ===================================================================== */ integer ieeeck_(integer *ispec, real *zero, real *one) { - /* System generated locals */ integer ret_val; - - /* Local variables */ real nan1, nan2, nan3, nan4, nan5, nan6, neginf, posinf, negzro, newzro; - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Local Scalars .. */ -/* .. */ -/* .. Executable Statements .. */ ret_val = 1; - posinf = *one / *zero; if (posinf <= *one) { ret_val = 0; return ret_val; } - neginf = -(*one) / *zero; if (neginf >= *zero) { ret_val = 0; return ret_val; } - negzro = *one / (neginf + *one); if (negzro != *zero) { ret_val = 0; return ret_val; } - neginf = *one / negzro; if (neginf >= *zero) { ret_val = 0; return ret_val; } - newzro = negzro + *zero; if (newzro != *zero) { ret_val = 0; return ret_val; } - posinf = *one / newzro; if (posinf <= *one) { ret_val = 0; return ret_val; } - neginf *= posinf; if (neginf >= *zero) { ret_val = 0; return ret_val; } - posinf *= posinf; if (posinf <= *one) { ret_val = 0; return ret_val; } - - - - -/* Return if we were only asked to check infinity arithmetic */ - if (*ispec == 0) { return ret_val; } - nan1 = posinf + neginf; - nan2 = posinf / neginf; - nan3 = posinf / posinf; - nan4 = posinf * *zero; - nan5 = neginf * negzro; - nan6 = nan5 * *zero; - if (nan1 == nan1) { ret_val = 0; return ret_val; } - if (nan2 == nan2) { ret_val = 0; return ret_val; } - if (nan3 == nan3) { ret_val = 0; return ret_val; } - if (nan4 == nan4) { ret_val = 0; return ret_val; } - if (nan5 == nan5) { ret_val = 0; return ret_val; } - if (nan6 == nan6) { ret_val = 0; return ret_val; } - return ret_val; -} /* ieeeck_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/iladlc.cpp b/lib/linalg/iladlc.cpp index 20355f1a94..019cf7f056 100644 --- a/lib/linalg/iladlc.cpp +++ b/lib/linalg/iladlc.cpp @@ -1,138 +1,19 @@ -/* fortran/iladlc.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b ILADLC scans a matrix for its last non-zero column. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ILADLC + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* INTEGER FUNCTION ILADLC( M, N, A, LDA ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER M, N, LDA */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ILADLC scans A for its last non-zero column. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > The m by n matrix A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,M). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup OTHERauxiliary */ - -/* ===================================================================== */ integer iladlc_(integer *m, integer *n, doublereal *a, integer *lda) { - /* System generated locals */ integer a_dim1, a_offset, ret_val, i__1; - - /* Local variables */ integer i__; - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Quick test for the common case where one corner is non-zero. */ - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; - - /* Function Body */ if (*n == 0) { ret_val = *n; } else if (a[*n * a_dim1 + 1] != 0. || a[*m + *n * a_dim1] != 0.) { ret_val = *n; } else { -/* Now scan each column from the end, returning with the first non-zero. */ for (ret_val = *n; ret_val >= 1; --ret_val) { i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { @@ -143,8 +24,7 @@ integer iladlc_(integer *m, integer *n, doublereal *a, integer *lda) } } return ret_val; -} /* iladlc_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/iladlr.cpp b/lib/linalg/iladlr.cpp index a68f2a665e..9718267951 100644 --- a/lib/linalg/iladlr.cpp +++ b/lib/linalg/iladlr.cpp @@ -1,151 +1,31 @@ -/* fortran/iladlr.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b ILADLR scans a matrix for its last non-zero row. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ILADLR + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* INTEGER FUNCTION ILADLR( M, N, A, LDA ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER M, N, LDA */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION A( LDA, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ILADLR scans A for its last non-zero row. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is DOUBLE PRECISION array, dimension (LDA,N) */ -/* > The m by n matrix A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,M). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup OTHERauxiliary */ - -/* ===================================================================== */ integer iladlr_(integer *m, integer *n, doublereal *a, integer *lda) { - /* System generated locals */ integer a_dim1, a_offset, ret_val, i__1; - - /* Local variables */ integer i__, j; - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Quick test for the common case where one corner is non-zero. */ - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; - - /* Function Body */ if (*m == 0) { ret_val = *m; } else if (a[*m + a_dim1] != 0. || a[*m + *n * a_dim1] != 0.) { ret_val = *m; } else { -/* Scan up each column tracking the last zero row seen. */ ret_val = 0; i__1 = *n; for (j = 1; j <= i__1; ++j) { i__ = *m; - while(a[max(i__,1) + j * a_dim1] == 0. && i__ >= 1) { + while (a[max(i__, 1) + j * a_dim1] == 0. && i__ >= 1) { --i__; } - ret_val = max(ret_val,i__); + ret_val = max(ret_val, i__); } } return ret_val; -} /* iladlr_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/ilaenv.cpp b/lib/linalg/ilaenv.cpp index 355b2a9429..1cc1c571f1 100644 --- a/lib/linalg/ilaenv.cpp +++ b/lib/linalg/ilaenv.cpp @@ -1,202 +1,17 @@ -/* fortran/ilaenv.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static real c_b176 = (float)0.; static real c_b177 = (float)1.; static integer c__0 = 0; - -/* > \brief \b ILAENV */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ILAENV + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* INTEGER FUNCTION ILAENV( ISPEC, NAME, OPTS, N1, N2, N3, N4 ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER*( * ) NAME, OPTS */ -/* INTEGER ISPEC, N1, N2, N3, N4 */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ILAENV is called from the LAPACK routines to choose problem-dependent */ -/* > parameters for the local environment. See ISPEC for a description of */ -/* > the parameters. */ -/* > */ -/* > ILAENV returns an INTEGER */ -/* > if ILAENV >= 0: ILAENV returns the value of the parameter specified by ISPEC */ -/* > if ILAENV < 0: if ILAENV = -k, the k-th argument had an illegal value. */ -/* > */ -/* > This version provides a set of parameters which should give good, */ -/* > but not optimal, performance on many of the currently available */ -/* > computers. Users are encouraged to modify this subroutine to set */ -/* > the tuning parameters for their particular machine using the option */ -/* > and problem size information in the arguments. */ -/* > */ -/* > This routine will not function correctly if it is converted to all */ -/* > lower case. Converting it to all upper case is allowed. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] ISPEC */ -/* > \verbatim */ -/* > ISPEC is INTEGER */ -/* > Specifies the parameter to be returned as the value of */ -/* > ILAENV. */ -/* > = 1: the optimal blocksize; if this value is 1, an unblocked */ -/* > algorithm will give the best performance. */ -/* > = 2: the minimum block size for which the block routine */ -/* > should be used; if the usable block size is less than */ -/* > this value, an unblocked routine should be used. */ -/* > = 3: the crossover point (in a block routine, for N less */ -/* > than this value, an unblocked routine should be used) */ -/* > = 4: the number of shifts, used in the nonsymmetric */ -/* > eigenvalue routines (DEPRECATED) */ -/* > = 5: the minimum column dimension for blocking to be used; */ -/* > rectangular blocks must have dimension at least k by m, */ -/* > where k is given by ILAENV(2,...) and m by ILAENV(5,...) */ -/* > = 6: the crossover point for the SVD (when reducing an m by n */ -/* > matrix to bidiagonal form, if max(m,n)/min(m,n) exceeds */ -/* > this value, a QR factorization is used first to reduce */ -/* > the matrix to a triangular form.) */ -/* > = 7: the number of processors */ -/* > = 8: the crossover point for the multishift QR method */ -/* > for nonsymmetric eigenvalue problems (DEPRECATED) */ -/* > = 9: maximum size of the subproblems at the bottom of the */ -/* > computation tree in the divide-and-conquer algorithm */ -/* > (used by xGELSD and xGESDD) */ -/* > =10: ieee infinity and NaN arithmetic can be trusted not to trap */ -/* > =11: infinity arithmetic can be trusted not to trap */ -/* > 12 <= ISPEC <= 17: */ -/* > xHSEQR or related subroutines, */ -/* > see IPARMQ for detailed explanation */ -/* > \endverbatim */ -/* > */ -/* > \param[in] NAME */ -/* > \verbatim */ -/* > NAME is CHARACTER*(*) */ -/* > The name of the calling subroutine, in either upper case or */ -/* > lower case. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] OPTS */ -/* > \verbatim */ -/* > OPTS is CHARACTER*(*) */ -/* > The character options to the subroutine NAME, concatenated */ -/* > into a single character string. For example, UPLO = 'U', */ -/* > TRANS = 'T', and DIAG = 'N' for a triangular routine would */ -/* > be specified as OPTS = 'UTN'. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N1 */ -/* > \verbatim */ -/* > N1 is INTEGER */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N2 */ -/* > \verbatim */ -/* > N2 is INTEGER */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N3 */ -/* > \verbatim */ -/* > N3 is INTEGER */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N4 */ -/* > \verbatim */ -/* > N4 is INTEGER */ -/* > Problem dimensions for the subroutine NAME; these may not all */ -/* > be required. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup OTHERauxiliary */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > The following conventions have been used when calling ILAENV from the */ -/* > LAPACK routines: */ -/* > 1) OPTS is a concatenation of all of the character options to */ -/* > subroutine NAME, in the same order that they appear in the */ -/* > argument list for NAME, even if they are not used in determining */ -/* > the value of the parameter specified by ISPEC. */ -/* > 2) The problem dimensions N1, N2, N3, N4 are specified in the order */ -/* > that they appear in the argument list for NAME. N1 is used */ -/* > first, N2 second, and so on, and unused problem dimensions are */ -/* > passed a value of -1. */ -/* > 3) The parameter value returned by ILAENV is checked for validity in */ -/* > the calling subroutine. For example, ILAENV is used to retrieve */ -/* > the optimal blocksize for STRTRI as follows: */ -/* > */ -/* > NB = ILAENV( 1, 'STRTRI', UPLO // DIAG, N, -1, -1, -1 ) */ -/* > IF( NB.LE.1 ) NB = MAX( 1, N ) */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -integer ilaenv_(integer *ispec, char *name__, char *opts, integer *n1, - integer *n2, integer *n3, integer *n4, ftnlen name_len, ftnlen - opts_len) +integer ilaenv_(integer *ispec, char *name__, char *opts, integer *n1, integer *n2, integer *n3, + integer *n4, ftnlen name_len, ftnlen opts_len) { - /* System generated locals */ integer ret_val, i__1, i__2, i__3; - - /* Builtin functions */ - /* Subroutine */ int s_lmp_copy(char *, char *, ftnlen, ftnlen); + int s_lmp_copy(char *, char *, ftnlen, ftnlen); integer i_lmp_len(char *, ftnlen), s_lmp_cmp(char *, char *, ftnlen, ftnlen); - - /* Local variables */ logical twostage; integer i__; char c1[1], c2[2], c3[3], c4[2]; @@ -206,140 +21,103 @@ integer ilaenv_(integer *ispec, char *name__, char *opts, integer *n1, logical sname; extern integer ieeeck_(integer *, real *, real *); char subnam[16]; - extern integer iparmq_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Local Scalars .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - + extern integer iparmq_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); switch (*ispec) { - case 1: goto L10; - case 2: goto L10; - case 3: goto L10; - case 4: goto L80; - case 5: goto L90; - case 6: goto L100; - case 7: goto L110; - case 8: goto L120; - case 9: goto L130; - case 10: goto L140; - case 11: goto L150; - case 12: goto L160; - case 13: goto L160; - case 14: goto L160; - case 15: goto L160; - case 16: goto L160; - case 17: goto L160; + case 1: + goto L10; + case 2: + goto L10; + case 3: + goto L10; + case 4: + goto L80; + case 5: + goto L90; + case 6: + goto L100; + case 7: + goto L110; + case 8: + goto L120; + case 9: + goto L130; + case 10: + goto L140; + case 11: + goto L150; + case 12: + goto L160; + case 13: + goto L160; + case 14: + goto L160; + case 15: + goto L160; + case 16: + goto L160; + case 17: + goto L160; } - -/* Invalid value for ISPEC */ - ret_val = -1; return ret_val; - L10: - -/* Convert NAME to upper case if the first character is lower case. */ - ret_val = 1; s_lmp_copy(subnam, name__, (ftnlen)16, name_len); ic = *(unsigned char *)subnam; iz = 'Z'; if (iz == 90 || iz == 122) { - -/* ASCII character set */ - if (ic >= 97 && ic <= 122) { - *(unsigned char *)subnam = (char) (ic - 32); + *(unsigned char *)subnam = (char)(ic - 32); for (i__ = 2; i__ <= 6; ++i__) { ic = *(unsigned char *)&subnam[i__ - 1]; if (ic >= 97 && ic <= 122) { - *(unsigned char *)&subnam[i__ - 1] = (char) (ic - 32); + *(unsigned char *)&subnam[i__ - 1] = (char)(ic - 32); } -/* L20: */ } } - } else if (iz == 233 || iz == 169) { - -/* EBCDIC character set */ - - if (ic >= 129 && ic <= 137 || ic >= 145 && ic <= 153 || ic >= 162 && - ic <= 169) { - *(unsigned char *)subnam = (char) (ic + 64); + if (ic >= 129 && ic <= 137 || ic >= 145 && ic <= 153 || ic >= 162 && ic <= 169) { + *(unsigned char *)subnam = (char)(ic + 64); for (i__ = 2; i__ <= 6; ++i__) { ic = *(unsigned char *)&subnam[i__ - 1]; - if (ic >= 129 && ic <= 137 || ic >= 145 && ic <= 153 || ic >= - 162 && ic <= 169) { - *(unsigned char *)&subnam[i__ - 1] = (char) (ic + 64); + if (ic >= 129 && ic <= 137 || ic >= 145 && ic <= 153 || ic >= 162 && ic <= 169) { + *(unsigned char *)&subnam[i__ - 1] = (char)(ic + 64); } -/* L30: */ } } - } else if (iz == 218 || iz == 250) { - -/* Prime machines: ASCII+128 */ - if (ic >= 225 && ic <= 250) { - *(unsigned char *)subnam = (char) (ic - 32); + *(unsigned char *)subnam = (char)(ic - 32); for (i__ = 2; i__ <= 6; ++i__) { ic = *(unsigned char *)&subnam[i__ - 1]; if (ic >= 225 && ic <= 250) { - *(unsigned char *)&subnam[i__ - 1] = (char) (ic - 32); + *(unsigned char *)&subnam[i__ - 1] = (char)(ic - 32); } -/* L40: */ } } } - *(unsigned char *)c1 = *(unsigned char *)subnam; sname = *(unsigned char *)c1 == 'S' || *(unsigned char *)c1 == 'D'; cname = *(unsigned char *)c1 == 'C' || *(unsigned char *)c1 == 'Z'; - if (! (cname || sname)) { + if (!(cname || sname)) { return ret_val; } s_lmp_copy(c2, subnam + 1, (ftnlen)2, (ftnlen)2); s_lmp_copy(c3, subnam + 3, (ftnlen)3, (ftnlen)3); s_lmp_copy(c4, c3 + 1, (ftnlen)2, (ftnlen)2); - twostage = i_lmp_len(subnam, (ftnlen)16) >= 11 && *(unsigned char *)&subnam[ - 10] == '2'; - + twostage = i_lmp_len(subnam, (ftnlen)16) >= 11 && *(unsigned char *)&subnam[10] == '2'; switch (*ispec) { - case 1: goto L50; - case 2: goto L60; - case 3: goto L70; + case 1: + goto L50; + case 2: + goto L60; + case 3: + goto L70; } - L50: - -/* ISPEC = 1: block size */ - -/* In these examples, separate code is provided for setting NB for */ -/* real and complex. We assume that NB will take the same value in */ -/* single or double precision. */ - nb = 1; - if (s_lmp_cmp(subnam + 1, (char *)"LAORH", (ftnlen)5, (ftnlen)5) == 0) { - -/* This is for *LAORHR_GETRFNP routine */ - if (sname) { nb = 32; } else { @@ -352,10 +130,10 @@ L50: } else { nb = 64; } - } else if (s_lmp_cmp(c3, (char *)"QRF", (ftnlen)3, (ftnlen)3) == 0 || s_lmp_cmp(c3, - (char *)"RQF", (ftnlen)3, (ftnlen)3) == 0 || s_lmp_cmp(c3, (char *)"LQF", (ftnlen) - 3, (ftnlen)3) == 0 || s_lmp_cmp(c3, (char *)"QLF", (ftnlen)3, (ftnlen)3) - == 0) { + } else if (s_lmp_cmp(c3, (char *)"QRF", (ftnlen)3, (ftnlen)3) == 0 || + s_lmp_cmp(c3, (char *)"RQF", (ftnlen)3, (ftnlen)3) == 0 || + s_lmp_cmp(c3, (char *)"LQF", (ftnlen)3, (ftnlen)3) == 0 || + s_lmp_cmp(c3, (char *)"QLF", (ftnlen)3, (ftnlen)3) == 0) { if (sname) { nb = 32; } else { @@ -364,7 +142,6 @@ L50: } else if (s_lmp_cmp(c3, (char *)"QR ", (ftnlen)3, (ftnlen)3) == 0) { if (*n3 == 1) { if (sname) { -/* M*N */ if (*n1 * *n2 <= 131072 || *n1 <= 8192) { nb = *n1; } else { @@ -387,7 +164,6 @@ L50: } else if (s_lmp_cmp(c3, (char *)"LQ ", (ftnlen)3, (ftnlen)3) == 0) { if (*n3 == 2) { if (sname) { -/* M*N */ if (*n1 * *n2 <= 131072 || *n1 <= 8192) { nb = *n1; } else { @@ -468,41 +244,45 @@ L50: } } else if (sname && s_lmp_cmp(c2, (char *)"OR", (ftnlen)2, (ftnlen)2) == 0) { if (*(unsigned char *)c3 == 'G') { - if (s_lmp_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"RQ", - (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"LQ", (ftnlen)2, ( - ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == - 0 || s_lmp_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp( - c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"BR", ( - ftnlen)2, (ftnlen)2) == 0) { + if (s_lmp_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"RQ", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"LQ", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"BR", (ftnlen)2, (ftnlen)2) == 0) { nb = 32; } } else if (*(unsigned char *)c3 == 'M') { - if (s_lmp_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"RQ", - (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"LQ", (ftnlen)2, ( - ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == - 0 || s_lmp_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp( - c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"BR", ( - ftnlen)2, (ftnlen)2) == 0) { + if (s_lmp_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"RQ", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"LQ", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"BR", (ftnlen)2, (ftnlen)2) == 0) { nb = 32; } } } else if (cname && s_lmp_cmp(c2, (char *)"UN", (ftnlen)2, (ftnlen)2) == 0) { if (*(unsigned char *)c3 == 'G') { - if (s_lmp_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"RQ", - (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"LQ", (ftnlen)2, ( - ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == - 0 || s_lmp_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp( - c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"BR", ( - ftnlen)2, (ftnlen)2) == 0) { + if (s_lmp_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"RQ", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"LQ", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"BR", (ftnlen)2, (ftnlen)2) == 0) { nb = 32; } } else if (*(unsigned char *)c3 == 'M') { - if (s_lmp_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"RQ", - (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"LQ", (ftnlen)2, ( - ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == - 0 || s_lmp_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp( - c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"BR", ( - ftnlen)2, (ftnlen)2) == 0) { + if (s_lmp_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"RQ", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"LQ", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"BR", (ftnlen)2, (ftnlen)2) == 0) { nb = 32; } } @@ -552,19 +332,14 @@ L50: nb = 64; } } else if (s_lmp_cmp(c3, (char *)"SYL", (ftnlen)3, (ftnlen)3) == 0) { -/* The upper bound is to prevent overly aggressive scaling. */ if (sname) { -/* Computing MIN */ -/* Computing MAX */ - i__2 = 48, i__3 = (min(*n1,*n2) << 4) / 100; - i__1 = max(i__2,i__3); - nb = min(i__1,240); + i__2 = 48, i__3 = (min(*n1, *n2) << 4) / 100; + i__1 = max(i__2, i__3); + nb = min(i__1, 240); } else { -/* Computing MIN */ -/* Computing MAX */ - i__2 = 24, i__3 = (min(*n1,*n2) << 3) / 100; - i__1 = max(i__2,i__3); - nb = min(i__1,80); + i__2 = 24, i__3 = (min(*n1, *n2) << 3) / 100; + i__1 = max(i__2, i__3); + nb = min(i__1, 80); } } } else if (s_lmp_cmp(c2, (char *)"LA", (ftnlen)2, (ftnlen)2) == 0) { @@ -597,17 +372,13 @@ L50: } ret_val = nb; return ret_val; - L60: - -/* ISPEC = 2: minimum block size */ - nbmin = 2; if (s_lmp_cmp(c2, (char *)"GE", (ftnlen)2, (ftnlen)2) == 0) { - if (s_lmp_cmp(c3, (char *)"QRF", (ftnlen)3, (ftnlen)3) == 0 || s_lmp_cmp(c3, (char *)"RQF", ( - ftnlen)3, (ftnlen)3) == 0 || s_lmp_cmp(c3, (char *)"LQF", (ftnlen)3, ( - ftnlen)3) == 0 || s_lmp_cmp(c3, (char *)"QLF", (ftnlen)3, (ftnlen)3) == 0) - { + if (s_lmp_cmp(c3, (char *)"QRF", (ftnlen)3, (ftnlen)3) == 0 || + s_lmp_cmp(c3, (char *)"RQF", (ftnlen)3, (ftnlen)3) == 0 || + s_lmp_cmp(c3, (char *)"LQF", (ftnlen)3, (ftnlen)3) == 0 || + s_lmp_cmp(c3, (char *)"QLF", (ftnlen)3, (ftnlen)3) == 0) { if (sname) { nbmin = 2; } else { @@ -648,41 +419,45 @@ L60: } } else if (sname && s_lmp_cmp(c2, (char *)"OR", (ftnlen)2, (ftnlen)2) == 0) { if (*(unsigned char *)c3 == 'G') { - if (s_lmp_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"RQ", - (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"LQ", (ftnlen)2, ( - ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == - 0 || s_lmp_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp( - c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"BR", ( - ftnlen)2, (ftnlen)2) == 0) { + if (s_lmp_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"RQ", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"LQ", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"BR", (ftnlen)2, (ftnlen)2) == 0) { nbmin = 2; } } else if (*(unsigned char *)c3 == 'M') { - if (s_lmp_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"RQ", - (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"LQ", (ftnlen)2, ( - ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == - 0 || s_lmp_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp( - c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"BR", ( - ftnlen)2, (ftnlen)2) == 0) { + if (s_lmp_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"RQ", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"LQ", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"BR", (ftnlen)2, (ftnlen)2) == 0) { nbmin = 2; } } } else if (cname && s_lmp_cmp(c2, (char *)"UN", (ftnlen)2, (ftnlen)2) == 0) { if (*(unsigned char *)c3 == 'G') { - if (s_lmp_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"RQ", - (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"LQ", (ftnlen)2, ( - ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == - 0 || s_lmp_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp( - c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"BR", ( - ftnlen)2, (ftnlen)2) == 0) { + if (s_lmp_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"RQ", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"LQ", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"BR", (ftnlen)2, (ftnlen)2) == 0) { nbmin = 2; } } else if (*(unsigned char *)c3 == 'M') { - if (s_lmp_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"RQ", - (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"LQ", (ftnlen)2, ( - ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == - 0 || s_lmp_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp( - c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"BR", ( - ftnlen)2, (ftnlen)2) == 0) { + if (s_lmp_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"RQ", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"LQ", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"BR", (ftnlen)2, (ftnlen)2) == 0) { nbmin = 2; } } @@ -694,17 +469,13 @@ L60: } ret_val = nbmin; return ret_val; - L70: - -/* ISPEC = 3: crossover point */ - nx = 0; if (s_lmp_cmp(c2, (char *)"GE", (ftnlen)2, (ftnlen)2) == 0) { - if (s_lmp_cmp(c3, (char *)"QRF", (ftnlen)3, (ftnlen)3) == 0 || s_lmp_cmp(c3, (char *)"RQF", ( - ftnlen)3, (ftnlen)3) == 0 || s_lmp_cmp(c3, (char *)"LQF", (ftnlen)3, ( - ftnlen)3) == 0 || s_lmp_cmp(c3, (char *)"QLF", (ftnlen)3, (ftnlen)3) == 0) - { + if (s_lmp_cmp(c3, (char *)"QRF", (ftnlen)3, (ftnlen)3) == 0 || + s_lmp_cmp(c3, (char *)"RQF", (ftnlen)3, (ftnlen)3) == 0 || + s_lmp_cmp(c3, (char *)"LQF", (ftnlen)3, (ftnlen)3) == 0 || + s_lmp_cmp(c3, (char *)"QLF", (ftnlen)3, (ftnlen)3) == 0) { if (sname) { nx = 128; } else { @@ -733,23 +504,25 @@ L70: } } else if (sname && s_lmp_cmp(c2, (char *)"OR", (ftnlen)2, (ftnlen)2) == 0) { if (*(unsigned char *)c3 == 'G') { - if (s_lmp_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"RQ", - (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"LQ", (ftnlen)2, ( - ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == - 0 || s_lmp_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp( - c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"BR", ( - ftnlen)2, (ftnlen)2) == 0) { + if (s_lmp_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"RQ", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"LQ", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"BR", (ftnlen)2, (ftnlen)2) == 0) { nx = 128; } } } else if (cname && s_lmp_cmp(c2, (char *)"UN", (ftnlen)2, (ftnlen)2) == 0) { if (*(unsigned char *)c3 == 'G') { - if (s_lmp_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"RQ", - (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"LQ", (ftnlen)2, ( - ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == - 0 || s_lmp_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp( - c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || s_lmp_cmp(c4, (char *)"BR", ( - ftnlen)2, (ftnlen)2) == 0) { + if (s_lmp_cmp(c4, (char *)"QR", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"RQ", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"LQ", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"QL", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"HR", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"TR", (ftnlen)2, (ftnlen)2) == 0 || + s_lmp_cmp(c4, (char *)"BR", (ftnlen)2, (ftnlen)2) == 0) { nx = 128; } } @@ -761,85 +534,40 @@ L70: } ret_val = nx; return ret_val; - L80: - -/* ISPEC = 4: number of shifts (used by xHSEQR) */ - ret_val = 6; return ret_val; - L90: - -/* ISPEC = 5: minimum column dimension (not used) */ - ret_val = 2; return ret_val; - L100: - -/* ISPEC = 6: crossover point for SVD (used by xGELSS and xGESVD) */ - - ret_val = (integer) ((real) min(*n1,*n2) * (float)1.6); + ret_val = (integer)((real)min(*n1, *n2) * (float)1.6); return ret_val; - L110: - -/* ISPEC = 7: number of processors (not used) */ - ret_val = 1; return ret_val; - L120: - -/* ISPEC = 8: crossover point for multishift (used by xHSEQR) */ - ret_val = 50; return ret_val; - L130: - -/* ISPEC = 9: maximum size of the subproblems at the bottom of the */ -/* computation tree in the divide-and-conquer algorithm */ -/* (used by xGELSD and xGESDD) */ - ret_val = 25; return ret_val; - L140: - -/* ISPEC = 10: ieee and infinity NaN arithmetic can be trusted not to trap */ - -/* ILAENV = 0 */ ret_val = 1; if (ret_val == 1) { ret_val = ieeeck_(&c__1, &c_b176, &c_b177); } return ret_val; - L150: - -/* ISPEC = 11: ieee infinity arithmetic can be trusted not to trap */ - -/* ILAENV = 0 */ ret_val = 1; if (ret_val == 1) { ret_val = ieeeck_(&c__0, &c_b176, &c_b177); } return ret_val; - L160: - -/* 12 <= ISPEC <= 17: xHSEQR or related subroutines. */ - - ret_val = iparmq_(ispec, name__, opts, n1, n2, n3, n4, name_len, opts_len) - ; + ret_val = iparmq_(ispec, name__, opts, n1, n2, n3, n4, name_len, opts_len); return ret_val; - -/* End of ILAENV */ - -} /* ilaenv_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/ilazlc.cpp b/lib/linalg/ilazlc.cpp index eb3f9ed604..6832710dac 100644 --- a/lib/linalg/ilazlc.cpp +++ b/lib/linalg/ilazlc.cpp @@ -1,142 +1,22 @@ -/* fortran/ilazlc.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b ILAZLC scans a matrix for its last non-zero column. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ILAZLC + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* INTEGER FUNCTION ILAZLC( M, N, A, LDA ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER M, N, LDA */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 A( LDA, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ILAZLC scans A for its last non-zero column. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is COMPLEX*16 array, dimension (LDA,N) */ -/* > The m by n matrix A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,M). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16OTHERauxiliary */ - -/* ===================================================================== */ integer ilazlc_(integer *m, integer *n, doublecomplex *a, integer *lda) { - /* System generated locals */ integer a_dim1, a_offset, ret_val, i__1, i__2; - - /* Local variables */ integer i__; - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Quick test for the common case where one corner is non-zero. */ - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; - - /* Function Body */ if (*n == 0) { ret_val = *n; - } else /* if(complicated condition) */ { + } else { i__1 = *n * a_dim1 + 1; i__2 = *m + *n * a_dim1; - if (a[i__1].r != 0. || a[i__1].i != 0. || (a[i__2].r != 0. || a[i__2] - .i != 0.)) { + if (a[i__1].r != 0. || a[i__1].i != 0. || (a[i__2].r != 0. || a[i__2].i != 0.)) { ret_val = *n; } else { -/* Now scan each column from the end, returning with the first non-zero. */ for (ret_val = *n; ret_val >= 1; --ret_val) { i__1 = *m; for (i__ = 1; i__ <= i__1; ++i__) { @@ -149,8 +29,7 @@ integer ilazlc_(integer *m, integer *n, doublecomplex *a, integer *lda) } } return ret_val; -} /* ilazlc_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/ilazlr.cpp b/lib/linalg/ilazlr.cpp index ebef3fa0e1..dd741985be 100644 --- a/lib/linalg/ilazlr.cpp +++ b/lib/linalg/ilazlr.cpp @@ -1,159 +1,37 @@ -/* fortran/ilazlr.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b ILAZLR scans a matrix for its last non-zero row. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ILAZLR + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* INTEGER FUNCTION ILAZLR( M, N, A, LDA ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER M, N, LDA */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 A( LDA, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ILAZLR scans A for its last non-zero row. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is COMPLEX*16 array, dimension (LDA,N) */ -/* > The m by n matrix A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,M). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16OTHERauxiliary */ - -/* ===================================================================== */ integer ilazlr_(integer *m, integer *n, doublecomplex *a, integer *lda) { - /* System generated locals */ integer a_dim1, a_offset, ret_val, i__1, i__2; - - /* Local variables */ integer i__, j; - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Quick test for the common case where one corner is non-zero. */ - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; - - /* Function Body */ if (*m == 0) { ret_val = *m; - } else /* if(complicated condition) */ { + } else { i__1 = *m + a_dim1; i__2 = *m + *n * a_dim1; - if (a[i__1].r != 0. || a[i__1].i != 0. || (a[i__2].r != 0. || a[i__2] - .i != 0.)) { + if (a[i__1].r != 0. || a[i__1].i != 0. || (a[i__2].r != 0. || a[i__2].i != 0.)) { ret_val = *m; } else { -/* Scan up each column tracking the last zero row seen. */ ret_val = 0; i__1 = *n; for (j = 1; j <= i__1; ++j) { i__ = *m; - for(;;) { /* while(complicated condition) */ - i__2 = max(i__,1) + j * a_dim1; - if (!(a[i__2].r == 0. && a[i__2].i == 0. && i__ >= 1)) - break; + for (;;) { + i__2 = max(i__, 1) + j * a_dim1; + if (!(a[i__2].r == 0. && a[i__2].i == 0. && i__ >= 1)) break; --i__; } - ret_val = max(ret_val,i__); + ret_val = max(ret_val, i__); } } } return ret_val; -} /* ilazlr_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/iparmq.cpp b/lib/linalg/iparmq.cpp index 0b8e981525..3ed8cd778a 100644 --- a/lib/linalg/iparmq.cpp +++ b/lib/linalg/iparmq.cpp @@ -1,287 +1,19 @@ -/* fortran/iparmq.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b IPARMQ */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download IPARMQ + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* INTEGER FUNCTION IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER IHI, ILO, ISPEC, LWORK, N */ -/* CHARACTER NAME*( * ), OPTS*( * ) */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > This program sets problem and machine dependent parameters */ -/* > useful for xHSEQR and related subroutines for eigenvalue */ -/* > problems. It is called whenever */ -/* > IPARMQ is called with 12 <= ISPEC <= 16 */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] ISPEC */ -/* > \verbatim */ -/* > ISPEC is INTEGER */ -/* > ISPEC specifies which tunable parameter IPARMQ should */ -/* > return. */ -/* > */ -/* > ISPEC=12: (INMIN) Matrices of order nmin or less */ -/* > are sent directly to xLAHQR, the implicit */ -/* > double shift QR algorithm. NMIN must be */ -/* > at least 11. */ -/* > */ -/* > ISPEC=13: (INWIN) Size of the deflation window. */ -/* > This is best set greater than or equal to */ -/* > the number of simultaneous shifts NS. */ -/* > Larger matrices benefit from larger deflation */ -/* > windows. */ -/* > */ -/* > ISPEC=14: (INIBL) Determines when to stop nibbling and */ -/* > invest in an (expensive) multi-shift QR sweep. */ -/* > If the aggressive early deflation subroutine */ -/* > finds LD converged eigenvalues from an order */ -/* > NW deflation window and LD > (NW*NIBBLE)/100, */ -/* > then the next QR sweep is skipped and early */ -/* > deflation is applied immediately to the */ -/* > remaining active diagonal block. Setting */ -/* > IPARMQ(ISPEC=14) = 0 causes TTQRE to skip a */ -/* > multi-shift QR sweep whenever early deflation */ -/* > finds a converged eigenvalue. Setting */ -/* > IPARMQ(ISPEC=14) greater than or equal to 100 */ -/* > prevents TTQRE from skipping a multi-shift */ -/* > QR sweep. */ -/* > */ -/* > ISPEC=15: (NSHFTS) The number of simultaneous shifts in */ -/* > a multi-shift QR iteration. */ -/* > */ -/* > ISPEC=16: (IACC22) IPARMQ is set to 0, 1 or 2 with the */ -/* > following meanings. */ -/* > 0: During the multi-shift QR/QZ sweep, */ -/* > blocked eigenvalue reordering, blocked */ -/* > Hessenberg-triangular reduction, */ -/* > reflections and/or rotations are not */ -/* > accumulated when updating the */ -/* > far-from-diagonal matrix entries. */ -/* > 1: During the multi-shift QR/QZ sweep, */ -/* > blocked eigenvalue reordering, blocked */ -/* > Hessenberg-triangular reduction, */ -/* > reflections and/or rotations are */ -/* > accumulated, and matrix-matrix */ -/* > multiplication is used to update the */ -/* > far-from-diagonal matrix entries. */ -/* > 2: During the multi-shift QR/QZ sweep, */ -/* > blocked eigenvalue reordering, blocked */ -/* > Hessenberg-triangular reduction, */ -/* > reflections and/or rotations are */ -/* > accumulated, and 2-by-2 block structure */ -/* > is exploited during matrix-matrix */ -/* > multiplies. */ -/* > (If xTRMM is slower than xGEMM, then */ -/* > IPARMQ(ISPEC=16)=1 may be more efficient than */ -/* > IPARMQ(ISPEC=16)=2 despite the greater level of */ -/* > arithmetic work implied by the latter choice.) */ -/* > */ -/* > ISPEC=17: (ICOST) An estimate of the relative cost of flops */ -/* > within the near-the-diagonal shift chase compared */ -/* > to flops within the BLAS calls of a QZ sweep. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] NAME */ -/* > \verbatim */ -/* > NAME is CHARACTER string */ -/* > Name of the calling subroutine */ -/* > \endverbatim */ -/* > */ -/* > \param[in] OPTS */ -/* > \verbatim */ -/* > OPTS is CHARACTER string */ -/* > This is a concatenation of the string arguments to */ -/* > TTQRE. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > N is the order of the Hessenberg matrix H. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] ILO */ -/* > \verbatim */ -/* > ILO is INTEGER */ -/* > \endverbatim */ -/* > */ -/* > \param[in] IHI */ -/* > \verbatim */ -/* > IHI is INTEGER */ -/* > It is assumed that H is already upper triangular */ -/* > in rows and columns 1:ILO-1 and IHI+1:N. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LWORK */ -/* > \verbatim */ -/* > LWORK is INTEGER */ -/* > The amount of workspace available. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup OTHERauxiliary */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > Little is known about how best to choose these parameters. */ -/* > It is possible to use different values of the parameters */ -/* > for each of CHSEQR, DHSEQR, SHSEQR and ZHSEQR. */ -/* > */ -/* > It is probably best to choose different parameters for */ -/* > different matrices and different parameters at different */ -/* > times during the iteration, but this has not been */ -/* > implemented --- yet. */ -/* > */ -/* > */ -/* > The best choices of most of the parameters depend */ -/* > in an ill-understood way on the relative execution */ -/* > rate of xLAQR3 and xLAQR5 and on the nature of each */ -/* > particular eigenvalue problem. Experiment may be the */ -/* > only practical way to determine which choices are most */ -/* > effective. */ -/* > */ -/* > Following is a list of default values supplied by IPARMQ. */ -/* > These defaults may be adjusted in order to attain better */ -/* > performance in any particular computational environment. */ -/* > */ -/* > IPARMQ(ISPEC=12) The xLAHQR vs xLAQR0 crossover point. */ -/* > Default: 75. (Must be at least 11.) */ -/* > */ -/* > IPARMQ(ISPEC=13) Recommended deflation window size. */ -/* > This depends on ILO, IHI and NS, the */ -/* > number of simultaneous shifts returned */ -/* > by IPARMQ(ISPEC=15). The default for */ -/* > (IHI-ILO+1) <= 500 is NS. The default */ -/* > for (IHI-ILO+1) > 500 is 3*NS/2. */ -/* > */ -/* > IPARMQ(ISPEC=14) Nibble crossover point. Default: 14. */ -/* > */ -/* > IPARMQ(ISPEC=15) Number of simultaneous shifts, NS. */ -/* > a multi-shift QR iteration. */ -/* > */ -/* > If IHI-ILO+1 is ... */ -/* > */ -/* > greater than ...but less ... the */ -/* > or equal to ... than default is */ -/* > */ -/* > 0 30 NS = 2+ */ -/* > 30 60 NS = 4+ */ -/* > 60 150 NS = 10 */ -/* > 150 590 NS = ** */ -/* > 590 3000 NS = 64 */ -/* > 3000 6000 NS = 128 */ -/* > 6000 infinity NS = 256 */ -/* > */ -/* > (+) By default matrices of this order are */ -/* > passed to the implicit double shift routine */ -/* > xLAHQR. See IPARMQ(ISPEC=12) above. These */ -/* > values of NS are used only in case of a rare */ -/* > xLAHQR failure. */ -/* > */ -/* > (**) The asterisks (**) indicate an ad-hoc */ -/* > function increasing from 10 to 64. */ -/* > */ -/* > IPARMQ(ISPEC=16) Select structured matrix multiply. */ -/* > (See ISPEC=16 above for details.) */ -/* > Default: 3. */ -/* > */ -/* > IPARMQ(ISPEC=17) Relative cost heuristic for blocksize selection. */ -/* > Expressed as a percentage. */ -/* > Default: 10. */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -integer iparmq_(integer *ispec, char *name__, char *opts, integer *n, integer - *ilo, integer *ihi, integer *lwork, ftnlen name_len, ftnlen opts_len) +integer iparmq_(integer *ispec, char *name__, char *opts, integer *n, integer *ilo, integer *ihi, + integer *lwork, ftnlen name_len, ftnlen opts_len) { - /* System generated locals */ integer ret_val, i__1, i__2; real r__1; - - /* Builtin functions */ double log(doublereal); integer i_lmp_nint(real *); - /* Subroutine */ int s_lmp_copy(char *, char *, ftnlen, ftnlen); + int s_lmp_copy(char *, char *, ftnlen, ftnlen); integer s_lmp_cmp(char *, char *, ftnlen, ftnlen); - - /* Local variables */ integer i__, ic, nh, ns, iz; char subnam[6]; - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ - -/* ================================================================ */ -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ if (*ispec == 15 || *ispec == 13 || *ispec == 16) { - -/* ==== Set the number simultaneous shifts ==== */ - nh = *ihi - *ilo + 1; ns = 2; if (nh >= 30) { @@ -291,10 +23,9 @@ integer iparmq_(integer *ispec, char *name__, char *opts, integer *n, integer ns = 10; } if (nh >= 150) { -/* Computing MAX */ - r__1 = log((real) nh) / log((float)2.); + r__1 = log((real)nh) / log((float)2.); i__1 = 10, i__2 = nh / i_lmp_nint(&r__1); - ns = max(i__1,i__2); + ns = max(i__1, i__2); } if (nh >= 590) { ns = 64; @@ -305,107 +36,60 @@ integer iparmq_(integer *ispec, char *name__, char *opts, integer *n, integer if (nh >= 6000) { ns = 256; } -/* Computing MAX */ i__1 = 2, i__2 = ns - ns % 2; - ns = max(i__1,i__2); + ns = max(i__1, i__2); } - if (*ispec == 12) { - - -/* ===== Matrices of order smaller than NMIN get sent */ -/* . to xLAHQR, the classic double shift algorithm. */ -/* . This must be at least 11. ==== */ - ret_val = 75; - } else if (*ispec == 14) { - -/* ==== INIBL: skip a multi-shift qr iteration and */ -/* . whenever aggressive early deflation finds */ -/* . at least (NIBBLE*(window size)/100) deflations. ==== */ - ret_val = 14; - } else if (*ispec == 15) { - -/* ==== NSHFTS: The number of simultaneous shifts ===== */ - ret_val = ns; - } else if (*ispec == 13) { - -/* ==== NW: deflation window size. ==== */ - if (nh <= 500) { ret_val = ns; } else { ret_val = ns * 3 / 2; } - } else if (*ispec == 16) { - -/* ==== IACC22: Whether to accumulate reflections */ -/* . before updating the far-from-diagonal elements */ -/* . and whether to use 2-by-2 block structure while */ -/* . doing it. A small amount of work could be saved */ -/* . by making this choice dependent also upon the */ -/* . NH=IHI-ILO+1. */ - - -/* Convert NAME to upper case if the first character is lower case. */ - ret_val = 0; s_lmp_copy(subnam, name__, (ftnlen)6, name_len); ic = *(unsigned char *)subnam; iz = 'Z'; if (iz == 90 || iz == 122) { - -/* ASCII character set */ - if (ic >= 97 && ic <= 122) { - *(unsigned char *)subnam = (char) (ic - 32); + *(unsigned char *)subnam = (char)(ic - 32); for (i__ = 2; i__ <= 6; ++i__) { ic = *(unsigned char *)&subnam[i__ - 1]; if (ic >= 97 && ic <= 122) { - *(unsigned char *)&subnam[i__ - 1] = (char) (ic - 32); + *(unsigned char *)&subnam[i__ - 1] = (char)(ic - 32); } } } - } else if (iz == 233 || iz == 169) { - -/* EBCDIC character set */ - - if (ic >= 129 && ic <= 137 || ic >= 145 && ic <= 153 || ic >= 162 - && ic <= 169) { - *(unsigned char *)subnam = (char) (ic + 64); + if (ic >= 129 && ic <= 137 || ic >= 145 && ic <= 153 || ic >= 162 && ic <= 169) { + *(unsigned char *)subnam = (char)(ic + 64); for (i__ = 2; i__ <= 6; ++i__) { ic = *(unsigned char *)&subnam[i__ - 1]; if (ic >= 129 && ic <= 137 || ic >= 145 && ic <= 153 || - ic >= 162 && ic <= 169) { - *(unsigned char *)&subnam[i__ - 1] = (char) (ic + 64); + ic >= 162 && ic <= 169) { + *(unsigned char *)&subnam[i__ - 1] = (char)(ic + 64); } } } - } else if (iz == 218 || iz == 250) { - -/* Prime machines: ASCII+128 */ - if (ic >= 225 && ic <= 250) { - *(unsigned char *)subnam = (char) (ic - 32); + *(unsigned char *)subnam = (char)(ic - 32); for (i__ = 2; i__ <= 6; ++i__) { ic = *(unsigned char *)&subnam[i__ - 1]; if (ic >= 225 && ic <= 250) { - *(unsigned char *)&subnam[i__ - 1] = (char) (ic - 32); + *(unsigned char *)&subnam[i__ - 1] = (char)(ic - 32); } } } } - - if (s_lmp_cmp(subnam + 1, (char *)"GGHRD", (ftnlen)5, (ftnlen)5) == 0 || s_lmp_cmp( - subnam + 1, (char *)"GGHD3", (ftnlen)5, (ftnlen)5) == 0) { + if (s_lmp_cmp(subnam + 1, (char *)"GGHRD", (ftnlen)5, (ftnlen)5) == 0 || + s_lmp_cmp(subnam + 1, (char *)"GGHD3", (ftnlen)5, (ftnlen)5) == 0) { ret_val = 1; if (nh >= 14) { ret_val = 2; @@ -418,7 +102,7 @@ integer iparmq_(integer *ispec, char *name__, char *opts, integer *n, integer ret_val = 2; } } else if (s_lmp_cmp(subnam + 1, (char *)"HSEQR", (ftnlen)5, (ftnlen)5) == 0 || - s_lmp_cmp(subnam + 1, (char *)"LAQR", (ftnlen)4, (ftnlen)4) == 0) { + s_lmp_cmp(subnam + 1, (char *)"LAQR", (ftnlen)4, (ftnlen)4) == 0) { if (ns >= 14) { ret_val = 1; } @@ -426,24 +110,13 @@ integer iparmq_(integer *ispec, char *name__, char *opts, integer *n, integer ret_val = 2; } } - } else if (*ispec == 17) { - -/* === Relative cost of near-the-diagonal chase vs */ -/* BLAS updates === */ - ret_val = 10; } else { -/* ===== invalid value of ispec ===== */ ret_val = -1; - } - -/* ==== End of IPARMQ ==== */ - return ret_val; -} /* iparmq_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/lsame.cpp b/lib/linalg/lsame.cpp index dcb89e3d00..480ae93bc9 100644 --- a/lib/linalg/lsame.cpp +++ b/lib/linalg/lsame.cpp @@ -7,11 +7,11 @@ extern "C" { logical lsame_(const char *a, const char *b) { - char ua, ub; - if (!a || !b) return FALSE_; + char ua, ub; + if (!a || !b) return FALSE_; - ua = toupper(*a); - ub = toupper(*b); - return (ua == ub) ? TRUE_ : FALSE_; + ua = toupper(*a); + ub = toupper(*b); + return (ua == ub) ? TRUE_ : FALSE_; } } diff --git a/lib/linalg/pow_lmp_di.cpp b/lib/linalg/pow_lmp_di.cpp index 9c3d89d536..83a0da1a87 100644 --- a/lib/linalg/pow_lmp_di.cpp +++ b/lib/linalg/pow_lmp_di.cpp @@ -10,8 +10,8 @@ double pow_lmp_di(doublereal *ap, integer *bp) unsigned long u; pow = 1; - x = *ap; - n = *bp; + x = *ap; + n = *bp; if (n != 0) { if (n < 0) { diff --git a/lib/linalg/s_lmp_cmp.cpp b/lib/linalg/s_lmp_cmp.cpp index b51817defa..73b011a799 100644 --- a/lib/linalg/s_lmp_cmp.cpp +++ b/lib/linalg/s_lmp_cmp.cpp @@ -8,8 +8,8 @@ extern "C" { integer s_lmp_cmp(char *a0, char *b0, ftnlen la, ftnlen lb) { register unsigned char *a, *aend, *b, *bend; - a = (unsigned char *)a0; - b = (unsigned char *)b0; + a = (unsigned char *)a0; + b = (unsigned char *)b0; aend = a + la; bend = b + lb; diff --git a/lib/linalg/static/.clang-format b/lib/linalg/static/.clang-format index cb352b37f5..8856e00947 100644 --- a/lib/linalg/static/.clang-format +++ b/lib/linalg/static/.clang-format @@ -2,7 +2,7 @@ Language: Cpp BasedOnStyle: LLVM AccessModifierOffset: -4 -AlignConsecutiveAssignments: true +AlignConsecutiveAssignments: false AlignEscapedNewlines: Left AllowShortFunctionsOnASingleLine: Inline AllowShortLambdasOnASingleLine: None diff --git a/lib/linalg/static/disnan.cpp b/lib/linalg/static/disnan.cpp index 9e5bc1094e..dcdaad77e1 100644 --- a/lib/linalg/static/disnan.cpp +++ b/lib/linalg/static/disnan.cpp @@ -7,8 +7,8 @@ extern "C" { logical disnan_(const doublereal *din) { - if (!din) return TRUE_; + if (!din) return TRUE_; - return std::isnan(*din) ? TRUE_ : FALSE_; + return std::isnan(*din) ? TRUE_ : FALSE_; } } diff --git a/lib/linalg/static/dlamch.cpp b/lib/linalg/static/dlamch.cpp index 3d616d95d2..277096e6f3 100644 --- a/lib/linalg/static/dlamch.cpp +++ b/lib/linalg/static/dlamch.cpp @@ -12,34 +12,34 @@ extern "C" { doublereal dlamch_(const char *cmach) { - if (!cmach) return 0.0; - char select = toupper(*cmach); + if (!cmach) return 0.0; + char select = toupper(*cmach); - // BLAS assumes rounding not truncation => epsilon is half - const double eps = 0.5 * std::numeric_limits::epsilon(); - if (select == 'E') return eps; + // BLAS assumes rounding not truncation => epsilon is half + const double eps = 0.5 * std::numeric_limits::epsilon(); + if (select == 'E') return eps; - double min = std::numeric_limits::min(); - const double max = std::numeric_limits::max(); - double small = 1.0 / max; - if (small >= min) min = small * (1.0 + eps); - if (select == 'S') return min; + double min = std::numeric_limits::min(); + const double max = std::numeric_limits::max(); + double small = 1.0 / max; + if (small >= min) min = small * (1.0 + eps); + if (select == 'S') return min; - const double radix = std::numeric_limits::radix; - if (select == 'B') return radix; + const double radix = std::numeric_limits::radix; + if (select == 'B') return radix; - if (select == 'P') return eps * radix; + if (select == 'P') return eps * radix; - if (select == 'N') return std::numeric_limits::digits; + if (select == 'N') return std::numeric_limits::digits; - if (select == 'M') return std::numeric_limits::min_exponent; + if (select == 'M') return std::numeric_limits::min_exponent; - if (select == 'U') return min; + if (select == 'U') return min; - if (select == 'L') return std::numeric_limits::max_exponent; + if (select == 'L') return std::numeric_limits::max_exponent; - if (select == 'O') return max; + if (select == 'O') return max; - return 0.0; + return 0.0; } } diff --git a/lib/linalg/static/lsame.cpp b/lib/linalg/static/lsame.cpp index dcb89e3d00..480ae93bc9 100644 --- a/lib/linalg/static/lsame.cpp +++ b/lib/linalg/static/lsame.cpp @@ -7,11 +7,11 @@ extern "C" { logical lsame_(const char *a, const char *b) { - char ua, ub; - if (!a || !b) return FALSE_; + char ua, ub; + if (!a || !b) return FALSE_; - ua = toupper(*a); - ub = toupper(*b); - return (ua == ub) ? TRUE_ : FALSE_; + ua = toupper(*a); + ub = toupper(*b); + return (ua == ub) ? TRUE_ : FALSE_; } } diff --git a/lib/linalg/static/pow_lmp_di.cpp b/lib/linalg/static/pow_lmp_di.cpp index 9c3d89d536..83a0da1a87 100644 --- a/lib/linalg/static/pow_lmp_di.cpp +++ b/lib/linalg/static/pow_lmp_di.cpp @@ -10,8 +10,8 @@ double pow_lmp_di(doublereal *ap, integer *bp) unsigned long u; pow = 1; - x = *ap; - n = *bp; + x = *ap; + n = *bp; if (n != 0) { if (n < 0) { diff --git a/lib/linalg/static/s_lmp_cmp.cpp b/lib/linalg/static/s_lmp_cmp.cpp index b51817defa..73b011a799 100644 --- a/lib/linalg/static/s_lmp_cmp.cpp +++ b/lib/linalg/static/s_lmp_cmp.cpp @@ -8,8 +8,8 @@ extern "C" { integer s_lmp_cmp(char *a0, char *b0, ftnlen la, ftnlen lb) { register unsigned char *a, *aend, *b, *bend; - a = (unsigned char *)a0; - b = (unsigned char *)b0; + a = (unsigned char *)a0; + b = (unsigned char *)b0; aend = a + la; bend = b + lb; diff --git a/lib/linalg/static/xerbla.cpp b/lib/linalg/static/xerbla.cpp index 325bd7030d..6346126c67 100644 --- a/lib/linalg/static/xerbla.cpp +++ b/lib/linalg/static/xerbla.cpp @@ -24,7 +24,7 @@ integer xerbla_(const char *srname, integer *info) buf[i + 16] = srname[i]; } int len = strlen(buf); - snprintf(buf+len, BUFSZ-len, " parameter number %d had an illegal value\n", *info); + snprintf(buf + len, BUFSZ - len, " parameter number %d had an illegal value\n", *info); exit(1); return 0; } diff --git a/lib/linalg/static/z_lmp_div.cpp b/lib/linalg/static/z_lmp_div.cpp index 5f742506da..66218f8fc8 100644 --- a/lib/linalg/static/z_lmp_div.cpp +++ b/lib/linalg/static/z_lmp_div.cpp @@ -17,14 +17,14 @@ void z_lmp_div(doublecomplex *c, doublecomplex *a, doublecomplex *b) return; } ratio = b->r / b->i; - den = b->i * (1 + ratio * ratio); - cr = (a->r * ratio + a->i) / den; - c->i = (a->i * ratio - a->r) / den; + den = b->i * (1 + ratio * ratio); + cr = (a->r * ratio + a->i) / den; + c->i = (a->i * ratio - a->r) / den; } else { ratio = b->i / b->r; - den = b->r * (1 + ratio * ratio); - cr = (a->r + a->i * ratio) / den; - c->i = (a->i - a->r * ratio) / den; + den = b->r * (1 + ratio * ratio); + cr = (a->r + a->i * ratio) / den; + c->i = (a->i - a->r * ratio) / den; } c->r = cr; } diff --git a/lib/linalg/whitespace.conf b/lib/linalg/whitespace.conf deleted file mode 100644 index 7988edc506..0000000000 --- a/lib/linalg/whitespace.conf +++ /dev/null @@ -1,13 +0,0 @@ ---- -recursive: false -include: - - "." - - "static/**" -exclude: - - "Makefile.*" - - "*.py" -patterns: - - "*.cpp" - - "*.h" - - "README" -... diff --git a/lib/linalg/xerbla.cpp b/lib/linalg/xerbla.cpp index 325bd7030d..6346126c67 100644 --- a/lib/linalg/xerbla.cpp +++ b/lib/linalg/xerbla.cpp @@ -24,7 +24,7 @@ integer xerbla_(const char *srname, integer *info) buf[i + 16] = srname[i]; } int len = strlen(buf); - snprintf(buf+len, BUFSZ-len, " parameter number %d had an illegal value\n", *info); + snprintf(buf + len, BUFSZ - len, " parameter number %d had an illegal value\n", *info); exit(1); return 0; } diff --git a/lib/linalg/z_lmp_div.cpp b/lib/linalg/z_lmp_div.cpp index 5f742506da..66218f8fc8 100644 --- a/lib/linalg/z_lmp_div.cpp +++ b/lib/linalg/z_lmp_div.cpp @@ -17,14 +17,14 @@ void z_lmp_div(doublecomplex *c, doublecomplex *a, doublecomplex *b) return; } ratio = b->r / b->i; - den = b->i * (1 + ratio * ratio); - cr = (a->r * ratio + a->i) / den; - c->i = (a->i * ratio - a->r) / den; + den = b->i * (1 + ratio * ratio); + cr = (a->r * ratio + a->i) / den; + c->i = (a->i * ratio - a->r) / den; } else { ratio = b->i / b->r; - den = b->r * (1 + ratio * ratio); - cr = (a->r + a->i * ratio) / den; - c->i = (a->i - a->r * ratio) / den; + den = b->r * (1 + ratio * ratio); + cr = (a->r + a->i * ratio) / den; + c->i = (a->i - a->r * ratio) / den; } c->r = cr; } diff --git a/lib/linalg/zaxpy.cpp b/lib/linalg/zaxpy.cpp index 6939872757..13c4e819db 100644 --- a/lib/linalg/zaxpy.cpp +++ b/lib/linalg/zaxpy.cpp @@ -1,138 +1,16 @@ -/* fortran/zaxpy.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b ZAXPY */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZAXPY(N,ZA,ZX,INCX,ZY,INCY) */ - -/* .. Scalar Arguments .. */ -/* COMPLEX*16 ZA */ -/* INTEGER INCX,INCY,N */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 ZX(*),ZY(*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZAXPY constant times a vector plus a vector. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > number of elements in input vector(s) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] ZA */ -/* > \verbatim */ -/* > ZA is COMPLEX*16 */ -/* > On entry, ZA specifies the scalar alpha. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] ZX */ -/* > \verbatim */ -/* > ZX is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > storage spacing between elements of ZX */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] ZY */ -/* > \verbatim */ -/* > ZY is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCY */ -/* > \verbatim */ -/* > INCY is INTEGER */ -/* > storage spacing between elements of ZY */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16_blas_level1 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > jack dongarra, 3/11/78. */ -/* > modified 12/3/93, array(1) declarations changed to array(*) */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int zaxpy_(integer *n, doublecomplex *za, doublecomplex *zx, - integer *incx, doublecomplex *zy, integer *incy) +int zaxpy_(integer *n, doublecomplex *za, doublecomplex *zx, integer *incx, doublecomplex *zy, + integer *incy) { - /* System generated locals */ integer i__1, i__2, i__3, i__4; doublecomplex z__1, z__2; - - /* Local variables */ integer i__, ix, iy; extern doublereal dcabs1_(doublecomplex *); - - -/* -- Reference BLAS level1 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ - /* Parameter adjustments */ --zy; --zx; - - /* Function Body */ if (*n <= 0) { return 0; } @@ -140,24 +18,17 @@ extern "C" { return 0; } if (*incx == 1 && *incy == 1) { - -/* code for both increments equal to 1 */ - i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; i__3 = i__; i__4 = i__; - z__2.r = za->r * zx[i__4].r - za->i * zx[i__4].i, z__2.i = za->r * - zx[i__4].i + za->i * zx[i__4].r; + z__2.r = za->r * zx[i__4].r - za->i * zx[i__4].i, + z__2.i = za->r * zx[i__4].i + za->i * zx[i__4].r; z__1.r = zy[i__3].r + z__2.r, z__1.i = zy[i__3].i + z__2.i; zy[i__2].r = z__1.r, zy[i__2].i = z__1.i; } } else { - -/* code for unequal increments or equal increments */ -/* not equal to 1 */ - ix = 1; iy = 1; if (*incx < 0) { @@ -171,21 +42,16 @@ extern "C" { i__2 = iy; i__3 = iy; i__4 = ix; - z__2.r = za->r * zx[i__4].r - za->i * zx[i__4].i, z__2.i = za->r * - zx[i__4].i + za->i * zx[i__4].r; + z__2.r = za->r * zx[i__4].r - za->i * zx[i__4].i, + z__2.i = za->r * zx[i__4].i + za->i * zx[i__4].r; z__1.r = zy[i__3].r + z__2.r, z__1.i = zy[i__3].i + z__2.i; zy[i__2].r = z__1.r, zy[i__2].i = z__1.i; ix += *incx; iy += *incy; } } - return 0; - -/* End of ZAXPY */ - -} /* zaxpy_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zcopy.cpp b/lib/linalg/zcopy.cpp index 97d1250228..4ec6ae0b78 100644 --- a/lib/linalg/zcopy.cpp +++ b/lib/linalg/zcopy.cpp @@ -1,134 +1,17 @@ -/* fortran/zcopy.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b ZCOPY */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZCOPY(N,ZX,INCX,ZY,INCY) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INCX,INCY,N */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 ZX(*),ZY(*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZCOPY copies a vector, x, to a vector, y. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > number of elements in input vector(s) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] ZX */ -/* > \verbatim */ -/* > ZX is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > storage spacing between elements of ZX */ -/* > \endverbatim */ -/* > */ -/* > \param[out] ZY */ -/* > \verbatim */ -/* > ZY is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCY */ -/* > \verbatim */ -/* > INCY is INTEGER */ -/* > storage spacing between elements of ZY */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16_blas_level1 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > jack dongarra, linpack, 4/11/78. */ -/* > modified 12/3/93, array(1) declarations changed to array(*) */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int zcopy_(integer *n, doublecomplex *zx, integer *incx, - doublecomplex *zy, integer *incy) +int zcopy_(integer *n, doublecomplex *zx, integer *incx, doublecomplex *zy, integer *incy) { - /* System generated locals */ integer i__1, i__2, i__3; - - /* Local variables */ integer i__, ix, iy; - - -/* -- Reference BLAS level1 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Local Scalars .. */ -/* .. */ - /* Parameter adjustments */ --zy; --zx; - - /* Function Body */ if (*n <= 0) { return 0; } if (*incx == 1 && *incy == 1) { - -/* code for both increments equal to 1 */ - i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; @@ -136,10 +19,6 @@ extern "C" { zy[i__2].r = zx[i__3].r, zy[i__2].i = zx[i__3].i; } } else { - -/* code for unequal increments or equal increments */ -/* not equal to 1 */ - ix = 1; iy = 1; if (*incx < 0) { @@ -158,11 +37,7 @@ extern "C" { } } return 0; - -/* End of ZCOPY */ - -} /* zcopy_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zdotc.cpp b/lib/linalg/zdotc.cpp index 2697cc1c2c..0bf457ed45 100644 --- a/lib/linalg/zdotc.cpp +++ b/lib/linalg/zdotc.cpp @@ -1,159 +1,33 @@ -/* fortran/zdotc.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b ZDOTC */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* COMPLEX*16 FUNCTION ZDOTC(N,ZX,INCX,ZY,INCY) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INCX,INCY,N */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 ZX(*),ZY(*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZDOTC forms the dot product of two complex vectors */ -/* > ZDOTC = X^H * Y */ -/* > */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > number of elements in input vector(s) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] ZX */ -/* > \verbatim */ -/* > ZX is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > storage spacing between elements of ZX */ -/* > \endverbatim */ -/* > */ -/* > \param[in] ZY */ -/* > \verbatim */ -/* > ZY is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCY */ -/* > \verbatim */ -/* > INCY is INTEGER */ -/* > storage spacing between elements of ZY */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16_blas_level1 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > jack dongarra, 3/11/78. */ -/* > modified 12/3/93, array(1) declarations changed to array(*) */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Double Complex */ VOID zdotc_(doublecomplex * ret_val, integer *n, - doublecomplex *zx, integer *incx, doublecomplex *zy, integer *incy) +VOID zdotc_(doublecomplex *ret_val, integer *n, doublecomplex *zx, integer *incx, doublecomplex *zy, + integer *incy) { - /* System generated locals */ integer i__1, i__2; doublecomplex z__1, z__2, z__3; - - /* Builtin functions */ void d_lmp_cnjg(doublecomplex *, doublecomplex *); - - /* Local variables */ integer i__, ix, iy; doublecomplex ztemp; - - -/* -- Reference BLAS level1 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Local Scalars .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ - /* Parameter adjustments */ --zy; --zx; - - /* Function Body */ ztemp.r = 0., ztemp.i = 0.; - ret_val->r = 0., ret_val->i = 0.; + ret_val->r = 0., ret_val->i = 0.; if (*n <= 0) { - return ; + return; } if (*incx == 1 && *incy == 1) { - -/* code for both increments equal to 1 */ - i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { d_lmp_cnjg(&z__3, &zx[i__]); i__2 = i__; - z__2.r = z__3.r * zy[i__2].r - z__3.i * zy[i__2].i, z__2.i = - z__3.r * zy[i__2].i + z__3.i * zy[i__2].r; + z__2.r = z__3.r * zy[i__2].r - z__3.i * zy[i__2].i, + z__2.i = z__3.r * zy[i__2].i + z__3.i * zy[i__2].r; z__1.r = ztemp.r + z__2.r, z__1.i = ztemp.i + z__2.i; ztemp.r = z__1.r, ztemp.i = z__1.i; } } else { - -/* code for unequal increments or equal increments */ -/* not equal to 1 */ - ix = 1; iy = 1; if (*incx < 0) { @@ -166,21 +40,17 @@ extern "C" { for (i__ = 1; i__ <= i__1; ++i__) { d_lmp_cnjg(&z__3, &zx[ix]); i__2 = iy; - z__2.r = z__3.r * zy[i__2].r - z__3.i * zy[i__2].i, z__2.i = - z__3.r * zy[i__2].i + z__3.i * zy[i__2].r; + z__2.r = z__3.r * zy[i__2].r - z__3.i * zy[i__2].i, + z__2.i = z__3.r * zy[i__2].i + z__3.i * zy[i__2].r; z__1.r = ztemp.r + z__2.r, z__1.i = ztemp.i + z__2.i; ztemp.r = z__1.r, ztemp.i = z__1.i; ix += *incx; iy += *incy; } } - ret_val->r = ztemp.r, ret_val->i = ztemp.i; - return ; - -/* End of ZDOTC */ - -} /* zdotc_ */ - + ret_val->r = ztemp.r, ret_val->i = ztemp.i; + return; +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zdrot.cpp b/lib/linalg/zdrot.cpp index e4c66f5480..fb9cc8995f 100644 --- a/lib/linalg/zdrot.cpp +++ b/lib/linalg/zdrot.cpp @@ -1,155 +1,20 @@ -/* fortran/zdrot.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b ZDROT */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZDROT( N, ZX, INCX, ZY, INCY, C, S ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INCX, INCY, N */ -/* DOUBLE PRECISION C, S */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 ZX( * ), ZY( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > Applies a plane rotation, where the cos and sin (c and s) are real */ -/* > and the vectors cx and cy are complex. */ -/* > jack dongarra, linpack, 3/11/78. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > On entry, N specifies the order of the vectors cx and cy. */ -/* > N must be at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] ZX */ -/* > \verbatim */ -/* > ZX is COMPLEX*16 array, dimension at least */ -/* > ( 1 + ( N - 1 )*abs( INCX ) ). */ -/* > Before entry, the incremented array ZX must contain the n */ -/* > element vector cx. On exit, ZX is overwritten by the updated */ -/* > vector cx. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > On entry, INCX specifies the increment for the elements of */ -/* > ZX. INCX must not be zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] ZY */ -/* > \verbatim */ -/* > ZY is COMPLEX*16 array, dimension at least */ -/* > ( 1 + ( N - 1 )*abs( INCY ) ). */ -/* > Before entry, the incremented array ZY must contain the n */ -/* > element vector cy. On exit, ZY is overwritten by the updated */ -/* > vector cy. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCY */ -/* > \verbatim */ -/* > INCY is INTEGER */ -/* > On entry, INCY specifies the increment for the elements of */ -/* > ZY. INCY must not be zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] C */ -/* > \verbatim */ -/* > C is DOUBLE PRECISION */ -/* > On entry, C specifies the cosine, cos. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] S */ -/* > \verbatim */ -/* > S is DOUBLE PRECISION */ -/* > On entry, S specifies the sine, sin. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16_blas_level1 */ - -/* ===================================================================== */ -/* Subroutine */ int zdrot_(integer *n, doublecomplex *zx, integer *incx, - doublecomplex *zy, integer *incy, doublereal *c__, doublereal *s) +int zdrot_(integer *n, doublecomplex *zx, integer *incx, doublecomplex *zy, integer *incy, + doublereal *c__, doublereal *s) { - /* System generated locals */ integer i__1, i__2, i__3, i__4; doublecomplex z__1, z__2, z__3; - - /* Local variables */ integer i__, ix, iy; doublecomplex ctemp; - - -/* -- Reference BLAS level1 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Local Scalars .. */ -/* .. */ -/* .. Executable Statements .. */ - - /* Parameter adjustments */ --zy; --zx; - - /* Function Body */ if (*n <= 0) { return 0; } if (*incx == 1 && *incy == 1) { - -/* code for both increments equal to 1 */ - i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; @@ -169,10 +34,6 @@ extern "C" { zx[i__2].r = ctemp.r, zx[i__2].i = ctemp.i; } } else { - -/* code for unequal increments or equal increments not equal */ -/* to 1 */ - ix = 1; iy = 1; if (*incx < 0) { @@ -203,11 +64,7 @@ extern "C" { } } return 0; - -/* End of ZDROT */ - -} /* zdrot_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zdscal.cpp b/lib/linalg/zdscal.cpp index ebe50c247d..d9b2773739 100644 --- a/lib/linalg/zdscal.cpp +++ b/lib/linalg/zdscal.cpp @@ -1,138 +1,19 @@ -/* fortran/zdscal.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b ZDSCAL */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZDSCAL(N,DA,ZX,INCX) */ - -/* .. Scalar Arguments .. */ -/* DOUBLE PRECISION DA */ -/* INTEGER INCX,N */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 ZX(*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZDSCAL scales a vector by a constant. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > number of elements in input vector(s) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DA */ -/* > \verbatim */ -/* > DA is DOUBLE PRECISION */ -/* > On entry, DA specifies the scalar alpha. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] ZX */ -/* > \verbatim */ -/* > ZX is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > storage spacing between elements of ZX */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16_blas_level1 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > jack dongarra, 3/11/78. */ -/* > modified 3/93 to return if incx .le. 0. */ -/* > modified 12/3/93, array(1) declarations changed to array(*) */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int zdscal_(integer *n, doublereal *da, doublecomplex *zx, - integer *incx) +int zdscal_(integer *n, doublereal *da, doublecomplex *zx, integer *incx) { - /* System generated locals */ integer i__1, i__2, i__3, i__4; doublereal d__1, d__2; doublecomplex z__1; - - /* Builtin functions */ double d_lmp_imag(doublecomplex *); - - /* Local variables */ integer i__, nincx; - - -/* -- Reference BLAS level1 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Local Scalars .. */ -/* .. Parameters .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ - /* Parameter adjustments */ --zx; - - /* Function Body */ if (*n <= 0 || *incx <= 0 || *da == 1.) { return 0; } if (*incx == 1) { - -/* code for increment equal to 1 */ - i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; @@ -143,9 +24,6 @@ extern "C" { zx[i__2].r = z__1.r, zx[i__2].i = z__1.i; } } else { - -/* code for increment not equal to 1 */ - nincx = *n * *incx; i__1 = nincx; i__2 = *incx; @@ -159,11 +37,7 @@ extern "C" { } } return 0; - -/* End of ZDSCAL */ - -} /* zdscal_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zgemm.cpp b/lib/linalg/zgemm.cpp index c49b0a4e57..75c72106ef 100644 --- a/lib/linalg/zgemm.cpp +++ b/lib/linalg/zgemm.cpp @@ -1,256 +1,22 @@ -/* fortran/zgemm.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b ZGEMM */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) */ - -/* .. Scalar Arguments .. */ -/* COMPLEX*16 ALPHA,BETA */ -/* INTEGER K,LDA,LDB,LDC,M,N */ -/* CHARACTER TRANSA,TRANSB */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZGEMM performs one of the matrix-matrix operations */ -/* > */ -/* > C := alpha*op( A )*op( B ) + beta*C, */ -/* > */ -/* > where op( X ) is one of */ -/* > */ -/* > op( X ) = X or op( X ) = X**T or op( X ) = X**H, */ -/* > */ -/* > alpha and beta are scalars, and A, B and C are matrices, with op( A ) */ -/* > an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] TRANSA */ -/* > \verbatim */ -/* > TRANSA is CHARACTER*1 */ -/* > On entry, TRANSA specifies the form of op( A ) to be used in */ -/* > the matrix multiplication as follows: */ -/* > */ -/* > TRANSA = 'N' or 'n', op( A ) = A. */ -/* > */ -/* > TRANSA = 'T' or 't', op( A ) = A**T. */ -/* > */ -/* > TRANSA = 'C' or 'c', op( A ) = A**H. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TRANSB */ -/* > \verbatim */ -/* > TRANSB is CHARACTER*1 */ -/* > On entry, TRANSB specifies the form of op( B ) to be used in */ -/* > the matrix multiplication as follows: */ -/* > */ -/* > TRANSB = 'N' or 'n', op( B ) = B. */ -/* > */ -/* > TRANSB = 'T' or 't', op( B ) = B**T. */ -/* > */ -/* > TRANSB = 'C' or 'c', op( B ) = B**H. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > On entry, M specifies the number of rows of the matrix */ -/* > op( A ) and of the matrix C. M must be at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > On entry, N specifies the number of columns of the matrix */ -/* > op( B ) and the number of columns of the matrix C. N must be */ -/* > at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > On entry, K specifies the number of columns of the matrix */ -/* > op( A ) and the number of rows of the matrix op( B ). K must */ -/* > be at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] ALPHA */ -/* > \verbatim */ -/* > ALPHA is COMPLEX*16 */ -/* > On entry, ALPHA specifies the scalar alpha. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is COMPLEX*16 array, dimension ( LDA, ka ), where ka is */ -/* > k when TRANSA = 'N' or 'n', and is m otherwise. */ -/* > Before entry with TRANSA = 'N' or 'n', the leading m by k */ -/* > part of the array A must contain the matrix A, otherwise */ -/* > the leading k by m part of the array A must contain the */ -/* > matrix A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > On entry, LDA specifies the first dimension of A as declared */ -/* > in the calling (sub) program. When TRANSA = 'N' or 'n' then */ -/* > LDA must be at least max( 1, m ), otherwise LDA must be at */ -/* > least max( 1, k ). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] B */ -/* > \verbatim */ -/* > B is COMPLEX*16 array, dimension ( LDB, kb ), where kb is */ -/* > n when TRANSB = 'N' or 'n', and is k otherwise. */ -/* > Before entry with TRANSB = 'N' or 'n', the leading k by n */ -/* > part of the array B must contain the matrix B, otherwise */ -/* > the leading n by k part of the array B must contain the */ -/* > matrix B. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDB */ -/* > \verbatim */ -/* > LDB is INTEGER */ -/* > On entry, LDB specifies the first dimension of B as declared */ -/* > in the calling (sub) program. When TRANSB = 'N' or 'n' then */ -/* > LDB must be at least max( 1, k ), otherwise LDB must be at */ -/* > least max( 1, n ). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] BETA */ -/* > \verbatim */ -/* > BETA is COMPLEX*16 */ -/* > On entry, BETA specifies the scalar beta. When BETA is */ -/* > supplied as zero then C need not be set on input. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] C */ -/* > \verbatim */ -/* > C is COMPLEX*16 array, dimension ( LDC, N ) */ -/* > Before entry, the leading m by n part of the array C must */ -/* > contain the matrix C, except when beta is zero, in which */ -/* > case C need not be set on entry. */ -/* > On exit, the array C is overwritten by the m by n matrix */ -/* > ( alpha*op( A )*op( B ) + beta*C ). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDC */ -/* > \verbatim */ -/* > LDC is INTEGER */ -/* > On entry, LDC specifies the first dimension of C as declared */ -/* > in the calling (sub) program. LDC must be at least */ -/* > max( 1, m ). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16_blas_level3 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > Level 3 Blas routine. */ -/* > */ -/* > -- Written on 8-February-1989. */ -/* > Jack Dongarra, Argonne National Laboratory. */ -/* > Iain Duff, AERE Harwell. */ -/* > Jeremy Du Croz, Numerical Algorithms Group Ltd. */ -/* > Sven Hammarling, Numerical Algorithms Group Ltd. */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int zgemm_(char *transa, char *transb, integer *m, integer * - n, integer *k, doublecomplex *alpha, doublecomplex *a, integer *lda, - doublecomplex *b, integer *ldb, doublecomplex *beta, doublecomplex * - c__, integer *ldc, ftnlen transa_len, ftnlen transb_len) +int zgemm_(char *transa, char *transb, integer *m, integer *n, integer *k, doublecomplex *alpha, + doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, doublecomplex *beta, + doublecomplex *c__, integer *ldc, ftnlen transa_len, ftnlen transb_len) { - /* System generated locals */ - integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, - i__3, i__4, i__5, i__6; + integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, i__3, i__4, i__5, + i__6; doublecomplex z__1, z__2, z__3, z__4; - - /* Builtin functions */ void d_lmp_cnjg(doublecomplex *, doublecomplex *); - - /* Local variables */ integer i__, j, l, info; logical nota, notb; doublecomplex temp; logical conja, conjb; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer nrowa, nrowb; - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - - -/* -- Reference BLAS level3 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. Parameters .. */ -/* .. */ - -/* Set NOTA and NOTB as true if A and B respectively are not */ -/* conjugated or transposed, set CONJA and CONJB as true if A and */ -/* B respectively are to be transposed but not conjugated and set */ -/* NROWA and NROWB as the number of rows of A and B respectively. */ - - /* Parameter adjustments */ + extern int xerbla_(char *, integer *, ftnlen); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; @@ -260,8 +26,6 @@ extern "C" { c_dim1 = *ldc; c_offset = 1 + c_dim1; c__ -= c_offset; - - /* Function Body */ nota = lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1); notb = lsame_(transb, (char *)"N", (ftnlen)1, (ftnlen)1); conja = lsame_(transa, (char *)"C", (ftnlen)1, (ftnlen)1); @@ -276,14 +40,10 @@ extern "C" { } else { nrowb = *n; } - -/* Test the input parameters. */ - info = 0; - if (! nota && ! conja && ! lsame_(transa, (char *)"T", (ftnlen)1, (ftnlen)1)) { + if (!nota && !conja && !lsame_(transa, (char *)"T", (ftnlen)1, (ftnlen)1)) { info = 1; - } else if (! notb && ! conjb && ! lsame_(transb, (char *)"T", (ftnlen)1, (ftnlen) - 1)) { + } else if (!notb && !conjb && !lsame_(transb, (char *)"T", (ftnlen)1, (ftnlen)1)) { info = 2; } else if (*m < 0) { info = 3; @@ -291,27 +51,21 @@ extern "C" { info = 4; } else if (*k < 0) { info = 5; - } else if (*lda < max(1,nrowa)) { + } else if (*lda < max(1, nrowa)) { info = 8; - } else if (*ldb < max(1,nrowb)) { + } else if (*ldb < max(1, nrowb)) { info = 10; - } else if (*ldc < max(1,*m)) { + } else if (*ldc < max(1, *m)) { info = 13; } if (info != 0) { xerbla_((char *)"ZGEMM ", &info, (ftnlen)6); return 0; } - -/* Quick return if possible. */ - - if (*m == 0 || *n == 0 || (alpha->r == 0. && alpha->i == 0. || *k == 0) && - (beta->r == 1. && beta->i == 0.)) { + if (*m == 0 || *n == 0 || + (alpha->r == 0. && alpha->i == 0. || *k == 0) && (beta->r == 1. && beta->i == 0.)) { return 0; } - -/* And when alpha.eq.zero. */ - if (alpha->r == 0. && alpha->i == 0.) { if (beta->r == 0. && beta->i == 0.) { i__1 = *n; @@ -320,9 +74,7 @@ extern "C" { for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * c_dim1; c__[i__3].r = 0., c__[i__3].i = 0.; -/* L10: */ } -/* L20: */ } } else { i__1 = *n; @@ -332,24 +84,15 @@ extern "C" { i__3 = i__ + j * c_dim1; i__4 = i__ + j * c_dim1; z__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4].i, - z__1.i = beta->r * c__[i__4].i + beta->i * c__[ - i__4].r; + z__1.i = beta->r * c__[i__4].i + beta->i * c__[i__4].r; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; -/* L30: */ } -/* L40: */ } } return 0; } - -/* Start the operations. */ - if (notb) { if (nota) { - -/* Form C := alpha*A*B + beta*C. */ - i__1 = *n; for (j = 1; j <= i__1; ++j) { if (beta->r == 0. && beta->i == 0.) { @@ -357,26 +100,22 @@ extern "C" { for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * c_dim1; c__[i__3].r = 0., c__[i__3].i = 0.; -/* L50: */ } } else if (beta->r != 1. || beta->i != 0.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * c_dim1; i__4 = i__ + j * c_dim1; - z__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4] - .i, z__1.i = beta->r * c__[i__4].i + beta->i * - c__[i__4].r; + z__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4].i, + z__1.i = beta->r * c__[i__4].i + beta->i * c__[i__4].r; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; -/* L60: */ } } i__2 = *k; for (l = 1; l <= i__2; ++l) { i__3 = l + j * b_dim1; z__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3].i, - z__1.i = alpha->r * b[i__3].i + alpha->i * b[i__3] - .r; + z__1.i = alpha->r * b[i__3].i + alpha->i * b[i__3].r; temp.r = z__1.r, temp.i = z__1.i; i__3 = *m; for (i__ = 1; i__ <= i__3; ++i__) { @@ -384,21 +123,13 @@ extern "C" { i__5 = i__ + j * c_dim1; i__6 = i__ + l * a_dim1; z__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i, - z__2.i = temp.r * a[i__6].i + temp.i * a[i__6] - .r; - z__1.r = c__[i__5].r + z__2.r, z__1.i = c__[i__5].i + - z__2.i; + z__2.i = temp.r * a[i__6].i + temp.i * a[i__6].r; + z__1.r = c__[i__5].r + z__2.r, z__1.i = c__[i__5].i + z__2.i; c__[i__4].r = z__1.r, c__[i__4].i = z__1.i; -/* L70: */ } -/* L80: */ } -/* L90: */ } } else if (conja) { - -/* Form C := alpha*A**H*B + beta*C. */ - i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; @@ -409,38 +140,28 @@ extern "C" { d_lmp_cnjg(&z__3, &a[l + i__ * a_dim1]); i__4 = l + j * b_dim1; z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4].i, - z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4] - .r; + z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4].r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; -/* L100: */ } if (beta->r == 0. && beta->i == 0.) { i__3 = i__ + j * c_dim1; z__1.r = alpha->r * temp.r - alpha->i * temp.i, - z__1.i = alpha->r * temp.i + alpha->i * - temp.r; + z__1.i = alpha->r * temp.i + alpha->i * temp.r; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } else { i__3 = i__ + j * c_dim1; z__2.r = alpha->r * temp.r - alpha->i * temp.i, - z__2.i = alpha->r * temp.i + alpha->i * - temp.r; + z__2.i = alpha->r * temp.i + alpha->i * temp.r; i__4 = i__ + j * c_dim1; - z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4] - .i, z__3.i = beta->r * c__[i__4].i + beta->i * - c__[i__4].r; + z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4].i, + z__3.i = beta->r * c__[i__4].i + beta->i * c__[i__4].r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } -/* L110: */ } -/* L120: */ } } else { - -/* Form C := alpha*A**T*B + beta*C */ - i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; @@ -450,41 +171,31 @@ extern "C" { for (l = 1; l <= i__3; ++l) { i__4 = l + i__ * a_dim1; i__5 = l + j * b_dim1; - z__2.r = a[i__4].r * b[i__5].r - a[i__4].i * b[i__5] - .i, z__2.i = a[i__4].r * b[i__5].i + a[i__4] - .i * b[i__5].r; + z__2.r = a[i__4].r * b[i__5].r - a[i__4].i * b[i__5].i, + z__2.i = a[i__4].r * b[i__5].i + a[i__4].i * b[i__5].r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; -/* L130: */ } if (beta->r == 0. && beta->i == 0.) { i__3 = i__ + j * c_dim1; z__1.r = alpha->r * temp.r - alpha->i * temp.i, - z__1.i = alpha->r * temp.i + alpha->i * - temp.r; + z__1.i = alpha->r * temp.i + alpha->i * temp.r; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } else { i__3 = i__ + j * c_dim1; z__2.r = alpha->r * temp.r - alpha->i * temp.i, - z__2.i = alpha->r * temp.i + alpha->i * - temp.r; + z__2.i = alpha->r * temp.i + alpha->i * temp.r; i__4 = i__ + j * c_dim1; - z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4] - .i, z__3.i = beta->r * c__[i__4].i + beta->i * - c__[i__4].r; + z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4].i, + z__3.i = beta->r * c__[i__4].i + beta->i * c__[i__4].r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } -/* L140: */ } -/* L150: */ } } } else if (nota) { if (conjb) { - -/* Form C := alpha*A*B**H + beta*C. */ - i__1 = *n; for (j = 1; j <= i__1; ++j) { if (beta->r == 0. && beta->i == 0.) { @@ -492,25 +203,22 @@ extern "C" { for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * c_dim1; c__[i__3].r = 0., c__[i__3].i = 0.; -/* L160: */ } } else if (beta->r != 1. || beta->i != 0.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * c_dim1; i__4 = i__ + j * c_dim1; - z__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4] - .i, z__1.i = beta->r * c__[i__4].i + beta->i * - c__[i__4].r; + z__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4].i, + z__1.i = beta->r * c__[i__4].i + beta->i * c__[i__4].r; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; -/* L170: */ } } i__2 = *k; for (l = 1; l <= i__2; ++l) { d_lmp_cnjg(&z__2, &b[j + l * b_dim1]); - z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = - alpha->r * z__2.i + alpha->i * z__2.r; + z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, + z__1.i = alpha->r * z__2.i + alpha->i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; i__3 = *m; for (i__ = 1; i__ <= i__3; ++i__) { @@ -518,21 +226,13 @@ extern "C" { i__5 = i__ + j * c_dim1; i__6 = i__ + l * a_dim1; z__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i, - z__2.i = temp.r * a[i__6].i + temp.i * a[i__6] - .r; - z__1.r = c__[i__5].r + z__2.r, z__1.i = c__[i__5].i + - z__2.i; + z__2.i = temp.r * a[i__6].i + temp.i * a[i__6].r; + z__1.r = c__[i__5].r + z__2.r, z__1.i = c__[i__5].i + z__2.i; c__[i__4].r = z__1.r, c__[i__4].i = z__1.i; -/* L180: */ } -/* L190: */ } -/* L200: */ } } else { - -/* Form C := alpha*A*B**T + beta*C */ - i__1 = *n; for (j = 1; j <= i__1; ++j) { if (beta->r == 0. && beta->i == 0.) { @@ -540,26 +240,22 @@ extern "C" { for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * c_dim1; c__[i__3].r = 0., c__[i__3].i = 0.; -/* L210: */ } } else if (beta->r != 1. || beta->i != 0.) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * c_dim1; i__4 = i__ + j * c_dim1; - z__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4] - .i, z__1.i = beta->r * c__[i__4].i + beta->i * - c__[i__4].r; + z__1.r = beta->r * c__[i__4].r - beta->i * c__[i__4].i, + z__1.i = beta->r * c__[i__4].i + beta->i * c__[i__4].r; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; -/* L220: */ } } i__2 = *k; for (l = 1; l <= i__2; ++l) { i__3 = j + l * b_dim1; z__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3].i, - z__1.i = alpha->r * b[i__3].i + alpha->i * b[i__3] - .r; + z__1.i = alpha->r * b[i__3].i + alpha->i * b[i__3].r; temp.r = z__1.r, temp.i = z__1.i; i__3 = *m; for (i__ = 1; i__ <= i__3; ++i__) { @@ -567,23 +263,15 @@ extern "C" { i__5 = i__ + j * c_dim1; i__6 = i__ + l * a_dim1; z__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i, - z__2.i = temp.r * a[i__6].i + temp.i * a[i__6] - .r; - z__1.r = c__[i__5].r + z__2.r, z__1.i = c__[i__5].i + - z__2.i; + z__2.i = temp.r * a[i__6].i + temp.i * a[i__6].r; + z__1.r = c__[i__5].r + z__2.r, z__1.i = c__[i__5].i + z__2.i; c__[i__4].r = z__1.r, c__[i__4].i = z__1.i; -/* L230: */ } -/* L240: */ } -/* L250: */ } } } else if (conja) { if (conjb) { - -/* Form C := alpha*A**H*B**H + beta*C. */ - i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; @@ -593,38 +281,29 @@ extern "C" { for (l = 1; l <= i__3; ++l) { d_lmp_cnjg(&z__3, &a[l + i__ * a_dim1]); d_lmp_cnjg(&z__4, &b[j + l * b_dim1]); - z__2.r = z__3.r * z__4.r - z__3.i * z__4.i, z__2.i = - z__3.r * z__4.i + z__3.i * z__4.r; + z__2.r = z__3.r * z__4.r - z__3.i * z__4.i, + z__2.i = z__3.r * z__4.i + z__3.i * z__4.r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; -/* L260: */ } if (beta->r == 0. && beta->i == 0.) { i__3 = i__ + j * c_dim1; z__1.r = alpha->r * temp.r - alpha->i * temp.i, - z__1.i = alpha->r * temp.i + alpha->i * - temp.r; + z__1.i = alpha->r * temp.i + alpha->i * temp.r; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } else { i__3 = i__ + j * c_dim1; z__2.r = alpha->r * temp.r - alpha->i * temp.i, - z__2.i = alpha->r * temp.i + alpha->i * - temp.r; + z__2.i = alpha->r * temp.i + alpha->i * temp.r; i__4 = i__ + j * c_dim1; - z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4] - .i, z__3.i = beta->r * c__[i__4].i + beta->i * - c__[i__4].r; + z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4].i, + z__3.i = beta->r * c__[i__4].i + beta->i * c__[i__4].r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } -/* L270: */ } -/* L280: */ } } else { - -/* Form C := alpha*A**H*B**T + beta*C */ - i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; @@ -635,40 +314,30 @@ extern "C" { d_lmp_cnjg(&z__3, &a[l + i__ * a_dim1]); i__4 = j + l * b_dim1; z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4].i, - z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4] - .r; + z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4].r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; -/* L290: */ } if (beta->r == 0. && beta->i == 0.) { i__3 = i__ + j * c_dim1; z__1.r = alpha->r * temp.r - alpha->i * temp.i, - z__1.i = alpha->r * temp.i + alpha->i * - temp.r; + z__1.i = alpha->r * temp.i + alpha->i * temp.r; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } else { i__3 = i__ + j * c_dim1; z__2.r = alpha->r * temp.r - alpha->i * temp.i, - z__2.i = alpha->r * temp.i + alpha->i * - temp.r; + z__2.i = alpha->r * temp.i + alpha->i * temp.r; i__4 = i__ + j * c_dim1; - z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4] - .i, z__3.i = beta->r * c__[i__4].i + beta->i * - c__[i__4].r; + z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4].i, + z__3.i = beta->r * c__[i__4].i + beta->i * c__[i__4].r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } -/* L300: */ } -/* L310: */ } } } else { if (conjb) { - -/* Form C := alpha*A**T*B**H + beta*C */ - i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; @@ -679,38 +348,28 @@ extern "C" { i__4 = l + i__ * a_dim1; d_lmp_cnjg(&z__3, &b[j + l * b_dim1]); z__2.r = a[i__4].r * z__3.r - a[i__4].i * z__3.i, - z__2.i = a[i__4].r * z__3.i + a[i__4].i * - z__3.r; + z__2.i = a[i__4].r * z__3.i + a[i__4].i * z__3.r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; -/* L320: */ } if (beta->r == 0. && beta->i == 0.) { i__3 = i__ + j * c_dim1; z__1.r = alpha->r * temp.r - alpha->i * temp.i, - z__1.i = alpha->r * temp.i + alpha->i * - temp.r; + z__1.i = alpha->r * temp.i + alpha->i * temp.r; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } else { i__3 = i__ + j * c_dim1; z__2.r = alpha->r * temp.r - alpha->i * temp.i, - z__2.i = alpha->r * temp.i + alpha->i * - temp.r; + z__2.i = alpha->r * temp.i + alpha->i * temp.r; i__4 = i__ + j * c_dim1; - z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4] - .i, z__3.i = beta->r * c__[i__4].i + beta->i * - c__[i__4].r; + z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4].i, + z__3.i = beta->r * c__[i__4].i + beta->i * c__[i__4].r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } -/* L330: */ } -/* L340: */ } } else { - -/* Form C := alpha*A**T*B**T + beta*C */ - i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; @@ -720,44 +379,32 @@ extern "C" { for (l = 1; l <= i__3; ++l) { i__4 = l + i__ * a_dim1; i__5 = j + l * b_dim1; - z__2.r = a[i__4].r * b[i__5].r - a[i__4].i * b[i__5] - .i, z__2.i = a[i__4].r * b[i__5].i + a[i__4] - .i * b[i__5].r; + z__2.r = a[i__4].r * b[i__5].r - a[i__4].i * b[i__5].i, + z__2.i = a[i__4].r * b[i__5].i + a[i__4].i * b[i__5].r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; -/* L350: */ } if (beta->r == 0. && beta->i == 0.) { i__3 = i__ + j * c_dim1; z__1.r = alpha->r * temp.r - alpha->i * temp.i, - z__1.i = alpha->r * temp.i + alpha->i * - temp.r; + z__1.i = alpha->r * temp.i + alpha->i * temp.r; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } else { i__3 = i__ + j * c_dim1; z__2.r = alpha->r * temp.r - alpha->i * temp.i, - z__2.i = alpha->r * temp.i + alpha->i * - temp.r; + z__2.i = alpha->r * temp.i + alpha->i * temp.r; i__4 = i__ + j * c_dim1; - z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4] - .i, z__3.i = beta->r * c__[i__4].i + beta->i * - c__[i__4].r; + z__3.r = beta->r * c__[i__4].r - beta->i * c__[i__4].i, + z__3.i = beta->r * c__[i__4].i + beta->i * c__[i__4].r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } -/* L360: */ } -/* L370: */ } } } - return 0; - -/* End of ZGEMM */ - -} /* zgemm_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zgemv.cpp b/lib/linalg/zgemv.cpp index 68736014b7..ddf5377740 100644 --- a/lib/linalg/zgemv.cpp +++ b/lib/linalg/zgemv.cpp @@ -1,239 +1,34 @@ -/* fortran/zgemv.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b ZGEMV */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) */ - -/* .. Scalar Arguments .. */ -/* COMPLEX*16 ALPHA,BETA */ -/* INTEGER INCX,INCY,LDA,M,N */ -/* CHARACTER TRANS */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 A(LDA,*),X(*),Y(*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZGEMV performs one of the matrix-vector operations */ -/* > */ -/* > y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, or */ -/* > */ -/* > y := alpha*A**H*x + beta*y, */ -/* > */ -/* > where alpha and beta are scalars, x and y are vectors and A is an */ -/* > m by n matrix. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] TRANS */ -/* > \verbatim */ -/* > TRANS is CHARACTER*1 */ -/* > On entry, TRANS specifies the operation to be performed as */ -/* > follows: */ -/* > */ -/* > TRANS = 'N' or 'n' y := alpha*A*x + beta*y. */ -/* > */ -/* > TRANS = 'T' or 't' y := alpha*A**T*x + beta*y. */ -/* > */ -/* > TRANS = 'C' or 'c' y := alpha*A**H*x + beta*y. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > On entry, M specifies the number of rows of the matrix A. */ -/* > M must be at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > On entry, N specifies the number of columns of the matrix A. */ -/* > N must be at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] ALPHA */ -/* > \verbatim */ -/* > ALPHA is COMPLEX*16 */ -/* > On entry, ALPHA specifies the scalar alpha. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is COMPLEX*16 array, dimension ( LDA, N ) */ -/* > Before entry, the leading m by n part of the array A must */ -/* > contain the matrix of coefficients. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > On entry, LDA specifies the first dimension of A as declared */ -/* > in the calling (sub) program. LDA must be at least */ -/* > max( 1, m ). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] X */ -/* > \verbatim */ -/* > X is COMPLEX*16 array, dimension at least */ -/* > ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' */ -/* > and at least */ -/* > ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. */ -/* > Before entry, the incremented array X must contain the */ -/* > vector x. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > On entry, INCX specifies the increment for the elements of */ -/* > X. INCX must not be zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] BETA */ -/* > \verbatim */ -/* > BETA is COMPLEX*16 */ -/* > On entry, BETA specifies the scalar beta. When BETA is */ -/* > supplied as zero then Y need not be set on input. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] Y */ -/* > \verbatim */ -/* > Y is COMPLEX*16 array, dimension at least */ -/* > ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' */ -/* > and at least */ -/* > ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. */ -/* > Before entry with BETA non-zero, the incremented array Y */ -/* > must contain the vector y. On exit, Y is overwritten by the */ -/* > updated vector y. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCY */ -/* > \verbatim */ -/* > INCY is INTEGER */ -/* > On entry, INCY specifies the increment for the elements of */ -/* > Y. INCY must not be zero. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16_blas_level2 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > Level 2 Blas routine. */ -/* > The vector and matrix arguments are not referenced when N = 0, or M = 0 */ -/* > */ -/* > -- Written on 22-October-1986. */ -/* > Jack Dongarra, Argonne National Lab. */ -/* > Jeremy Du Croz, Nag Central Office. */ -/* > Sven Hammarling, Nag Central Office. */ -/* > Richard Hanson, Sandia National Labs. */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int zgemv_(char *trans, integer *m, integer *n, - doublecomplex *alpha, doublecomplex *a, integer *lda, doublecomplex * - x, integer *incx, doublecomplex *beta, doublecomplex *y, integer * - incy, ftnlen trans_len) +int zgemv_(char *trans, integer *m, integer *n, doublecomplex *alpha, doublecomplex *a, + integer *lda, doublecomplex *x, integer *incx, doublecomplex *beta, doublecomplex *y, + integer *incy, ftnlen trans_len) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; doublecomplex z__1, z__2, z__3; - - /* Builtin functions */ void d_lmp_cnjg(doublecomplex *, doublecomplex *); - - /* Local variables */ integer i__, j, ix, iy, jx, jy, kx, ky, info; doublecomplex temp; integer lenx, leny; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern int xerbla_(char *, integer *, ftnlen); logical noconj; - - -/* -- Reference BLAS level2 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --x; --y; - - /* Function Body */ info = 0; - if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"T", ( - ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1) - ) { + if (!lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && !lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1) && + !lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { info = 1; } else if (*m < 0) { info = 2; } else if (*n < 0) { info = 3; - } else if (*lda < max(1,*m)) { + } else if (*lda < max(1, *m)) { info = 6; } else if (*incx == 0) { info = 8; @@ -244,19 +39,11 @@ extern "C" { xerbla_((char *)"ZGEMV ", &info, (ftnlen)6); return 0; } - -/* Quick return if possible. */ - - if (*m == 0 || *n == 0 || alpha->r == 0. && alpha->i == 0. && (beta->r == - 1. && beta->i == 0.)) { + if (*m == 0 || *n == 0 || + alpha->r == 0. && alpha->i == 0. && (beta->r == 1. && beta->i == 0.)) { return 0; } - noconj = lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1); - -/* Set LENX and LENY, the lengths of the vectors x and y, and set */ -/* up the start points in X and Y. */ - if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { lenx = *n; leny = *m; @@ -274,12 +61,6 @@ extern "C" { } else { ky = 1 - (leny - 1) * *incy; } - -/* Start the operations. In this version the elements of A are */ -/* accessed sequentially with one pass through A. */ - -/* First form y := beta*y. */ - if (beta->r != 1. || beta->i != 0.) { if (*incy == 1) { if (beta->r == 0. && beta->i == 0.) { @@ -287,7 +68,6 @@ extern "C" { for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; y[i__2].r = 0., y[i__2].i = 0.; -/* L10: */ } } else { i__1 = leny; @@ -295,10 +75,8 @@ extern "C" { i__2 = i__; i__3 = i__; z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i, - z__1.i = beta->r * y[i__3].i + beta->i * y[i__3] - .r; + z__1.i = beta->r * y[i__3].i + beta->i * y[i__3].r; y[i__2].r = z__1.r, y[i__2].i = z__1.i; -/* L20: */ } } } else { @@ -309,7 +87,6 @@ extern "C" { i__2 = iy; y[i__2].r = 0., y[i__2].i = 0.; iy += *incy; -/* L30: */ } } else { i__1 = leny; @@ -317,11 +94,9 @@ extern "C" { i__2 = iy; i__3 = iy; z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i, - z__1.i = beta->r * y[i__3].i + beta->i * y[i__3] - .r; + z__1.i = beta->r * y[i__3].i + beta->i * y[i__3].r; y[i__2].r = z__1.r, y[i__2].i = z__1.i; iy += *incy; -/* L40: */ } } } @@ -330,37 +105,32 @@ extern "C" { return 0; } if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { - -/* Form y := alpha*A*x + y. */ - jx = kx; if (*incy == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = jx; - z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i = - alpha->r * x[i__2].i + alpha->i * x[i__2].r; + z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, + z__1.i = alpha->r * x[i__2].i + alpha->i * x[i__2].r; temp.r = z__1.r, temp.i = z__1.i; i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__; i__4 = i__; i__5 = i__ + j * a_dim1; - z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, z__2.i = - temp.r * a[i__5].i + temp.i * a[i__5].r; + z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, + z__2.i = temp.r * a[i__5].i + temp.i * a[i__5].r; z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; y[i__3].r = z__1.r, y[i__3].i = z__1.i; -/* L50: */ } jx += *incx; -/* L60: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = jx; - z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i = - alpha->r * x[i__2].i + alpha->i * x[i__2].r; + z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, + z__1.i = alpha->r * x[i__2].i + alpha->i * x[i__2].r; temp.r = z__1.r, temp.i = z__1.i; iy = ky; i__2 = *m; @@ -368,21 +138,16 @@ extern "C" { i__3 = iy; i__4 = iy; i__5 = i__ + j * a_dim1; - z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, z__2.i = - temp.r * a[i__5].i + temp.i * a[i__5].r; + z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, + z__2.i = temp.r * a[i__5].i + temp.i * a[i__5].r; z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; y[i__3].r = z__1.r, y[i__3].i = z__1.i; iy += *incy; -/* L70: */ } jx += *incx; -/* L80: */ } } } else { - -/* Form y := alpha*A**T*x + y or y := alpha*A**H*x + y. */ - jy = ky; if (*incx == 1) { i__1 = *n; @@ -393,12 +158,10 @@ extern "C" { for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * a_dim1; i__4 = i__; - z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[i__4] - .i, z__2.i = a[i__3].r * x[i__4].i + a[i__3] - .i * x[i__4].r; + z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[i__4].i, + z__2.i = a[i__3].r * x[i__4].i + a[i__3].i * x[i__4].r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; -/* L90: */ } } else { i__2 = *m; @@ -406,21 +169,18 @@ extern "C" { d_lmp_cnjg(&z__3, &a[i__ + j * a_dim1]); i__3 = i__; z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, - z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3] - .r; + z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3].r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; -/* L100: */ } } i__2 = jy; i__3 = jy; - z__2.r = alpha->r * temp.r - alpha->i * temp.i, z__2.i = - alpha->r * temp.i + alpha->i * temp.r; + z__2.r = alpha->r * temp.r - alpha->i * temp.i, + z__2.i = alpha->r * temp.i + alpha->i * temp.r; z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i; y[i__2].r = z__1.r, y[i__2].i = z__1.i; jy += *incy; -/* L110: */ } } else { i__1 = *n; @@ -432,13 +192,11 @@ extern "C" { for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * a_dim1; i__4 = ix; - z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[i__4] - .i, z__2.i = a[i__3].r * x[i__4].i + a[i__3] - .i * x[i__4].r; + z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[i__4].i, + z__2.i = a[i__3].r * x[i__4].i + a[i__3].i * x[i__4].r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; ix += *incx; -/* L120: */ } } else { i__2 = *m; @@ -446,32 +204,24 @@ extern "C" { d_lmp_cnjg(&z__3, &a[i__ + j * a_dim1]); i__3 = ix; z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, - z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3] - .r; + z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3].r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; ix += *incx; -/* L130: */ } } i__2 = jy; i__3 = jy; - z__2.r = alpha->r * temp.r - alpha->i * temp.i, z__2.i = - alpha->r * temp.i + alpha->i * temp.r; + z__2.r = alpha->r * temp.r - alpha->i * temp.i, + z__2.i = alpha->r * temp.i + alpha->i * temp.r; z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i; y[i__2].r = z__1.r, y[i__2].i = z__1.i; jy += *incy; -/* L140: */ } } } - return 0; - -/* End of ZGEMV */ - -} /* zgemv_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zgerc.cpp b/lib/linalg/zgerc.cpp index 04dde8606a..b22e3f3e6d 100644 --- a/lib/linalg/zgerc.cpp +++ b/lib/linalg/zgerc.cpp @@ -1,195 +1,21 @@ -/* fortran/zgerc.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b ZGERC */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZGERC(M,N,ALPHA,X,INCX,Y,INCY,A,LDA) */ - -/* .. Scalar Arguments .. */ -/* COMPLEX*16 ALPHA */ -/* INTEGER INCX,INCY,LDA,M,N */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 A(LDA,*),X(*),Y(*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZGERC performs the rank 1 operation */ -/* > */ -/* > A := alpha*x*y**H + A, */ -/* > */ -/* > where alpha is a scalar, x is an m element vector, y is an n element */ -/* > vector and A is an m by n matrix. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > On entry, M specifies the number of rows of the matrix A. */ -/* > M must be at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > On entry, N specifies the number of columns of the matrix A. */ -/* > N must be at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] ALPHA */ -/* > \verbatim */ -/* > ALPHA is COMPLEX*16 */ -/* > On entry, ALPHA specifies the scalar alpha. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] X */ -/* > \verbatim */ -/* > X is COMPLEX*16 array, dimension at least */ -/* > ( 1 + ( m - 1 )*abs( INCX ) ). */ -/* > Before entry, the incremented array X must contain the m */ -/* > element vector x. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > On entry, INCX specifies the increment for the elements of */ -/* > X. INCX must not be zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] Y */ -/* > \verbatim */ -/* > Y is COMPLEX*16 array, dimension at least */ -/* > ( 1 + ( n - 1 )*abs( INCY ) ). */ -/* > Before entry, the incremented array Y must contain the n */ -/* > element vector y. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCY */ -/* > \verbatim */ -/* > INCY is INTEGER */ -/* > On entry, INCY specifies the increment for the elements of */ -/* > Y. INCY must not be zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is COMPLEX*16 array, dimension ( LDA, N ) */ -/* > Before entry, the leading m by n part of the array A must */ -/* > contain the matrix of coefficients. On exit, A is */ -/* > overwritten by the updated matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > On entry, LDA specifies the first dimension of A as declared */ -/* > in the calling (sub) program. LDA must be at least */ -/* > max( 1, m ). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16_blas_level2 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > Level 2 Blas routine. */ -/* > */ -/* > -- Written on 22-October-1986. */ -/* > Jack Dongarra, Argonne National Lab. */ -/* > Jeremy Du Croz, Nag Central Office. */ -/* > Sven Hammarling, Nag Central Office. */ -/* > Richard Hanson, Sandia National Labs. */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int zgerc_(integer *m, integer *n, doublecomplex *alpha, - doublecomplex *x, integer *incx, doublecomplex *y, integer *incy, - doublecomplex *a, integer *lda) +int zgerc_(integer *m, integer *n, doublecomplex *alpha, doublecomplex *x, integer *incx, + doublecomplex *y, integer *incy, doublecomplex *a, integer *lda) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; doublecomplex z__1, z__2; - - /* Builtin functions */ void d_lmp_cnjg(doublecomplex *, doublecomplex *); - - /* Local variables */ integer i__, j, ix, jy, kx, info; doublecomplex temp; - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - - -/* -- Reference BLAS level2 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ + extern int xerbla_(char *, integer *, ftnlen); --x; --y; a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; - - /* Function Body */ info = 0; if (*m < 0) { info = 1; @@ -199,23 +25,16 @@ extern "C" { info = 5; } else if (*incy == 0) { info = 7; - } else if (*lda < max(1,*m)) { + } else if (*lda < max(1, *m)) { info = 9; } if (info != 0) { xerbla_((char *)"ZGERC ", &info, (ftnlen)6); return 0; } - -/* Quick return if possible. */ - if (*m == 0 || *n == 0 || alpha->r == 0. && alpha->i == 0.) { return 0; } - -/* Start the operations. In this version the elements of A are */ -/* accessed sequentially with one pass through A. */ - if (*incy > 0) { jy = 1; } else { @@ -227,23 +46,21 @@ extern "C" { i__2 = jy; if (y[i__2].r != 0. || y[i__2].i != 0.) { d_lmp_cnjg(&z__2, &y[jy]); - z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = - alpha->r * z__2.i + alpha->i * z__2.r; + z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, + z__1.i = alpha->r * z__2.i + alpha->i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * a_dim1; i__4 = i__ + j * a_dim1; i__5 = i__; - z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, z__2.i = - x[i__5].r * temp.i + x[i__5].i * temp.r; + z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, + z__2.i = x[i__5].r * temp.i + x[i__5].i * temp.r; z__1.r = a[i__4].r + z__2.r, z__1.i = a[i__4].i + z__2.i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; -/* L10: */ } } jy += *incy; -/* L20: */ } } else { if (*incx > 0) { @@ -256,8 +73,8 @@ extern "C" { i__2 = jy; if (y[i__2].r != 0. || y[i__2].i != 0.) { d_lmp_cnjg(&z__2, &y[jy]); - z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = - alpha->r * z__2.i + alpha->i * z__2.r; + z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, + z__1.i = alpha->r * z__2.i + alpha->i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; ix = kx; i__2 = *m; @@ -265,25 +82,18 @@ extern "C" { i__3 = i__ + j * a_dim1; i__4 = i__ + j * a_dim1; i__5 = ix; - z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, z__2.i = - x[i__5].r * temp.i + x[i__5].i * temp.r; + z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, + z__2.i = x[i__5].r * temp.i + x[i__5].i * temp.r; z__1.r = a[i__4].r + z__2.r, z__1.i = a[i__4].i + z__2.i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; ix += *incx; -/* L30: */ } } jy += *incy; -/* L40: */ } } - return 0; - -/* End of ZGERC */ - -} /* zgerc_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zheev.cpp b/lib/linalg/zheev.cpp index 52661d9511..1238239431 100644 --- a/lib/linalg/zheev.cpp +++ b/lib/linalg/zheev.cpp @@ -1,188 +1,25 @@ -/* fortran/zheev.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static integer c_n1 = -1; static integer c__0 = 0; static doublereal c_b18 = 1.; - -/* > \brief ZHEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matr -ices */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZHEEV + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZHEEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, */ -/* INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER JOBZ, UPLO */ -/* INTEGER INFO, LDA, LWORK, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION RWORK( * ), W( * ) */ -/* COMPLEX*16 A( LDA, * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZHEEV computes all eigenvalues and, optionally, eigenvectors of a */ -/* > complex Hermitian matrix A. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] JOBZ */ -/* > \verbatim */ -/* > JOBZ is CHARACTER*1 */ -/* > = 'N': Compute eigenvalues only; */ -/* > = 'V': Compute eigenvalues and eigenvectors. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > = 'U': Upper triangle of A is stored; */ -/* > = 'L': Lower triangle of A is stored. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is COMPLEX*16 array, dimension (LDA, N) */ -/* > On entry, the Hermitian matrix A. If UPLO = 'U', the */ -/* > leading N-by-N upper triangular part of A contains the */ -/* > upper triangular part of the matrix A. If UPLO = 'L', */ -/* > the leading N-by-N lower triangular part of A contains */ -/* > the lower triangular part of the matrix A. */ -/* > On exit, if JOBZ = 'V', then if INFO = 0, A contains the */ -/* > orthonormal eigenvectors of the matrix A. */ -/* > If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') */ -/* > or the upper triangle (if UPLO='U') of A, including the */ -/* > diagonal, is destroyed. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] W */ -/* > \verbatim */ -/* > W is DOUBLE PRECISION array, dimension (N) */ -/* > If INFO = 0, the eigenvalues in ascending order. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) */ -/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LWORK */ -/* > \verbatim */ -/* > LWORK is INTEGER */ -/* > The length of the array WORK. LWORK >= max(1,2*N-1). */ -/* > For optimal efficiency, LWORK >= (NB+1)*N, */ -/* > where NB is the blocksize for ZHETRD returned by ILAENV. */ -/* > */ -/* > If LWORK = -1, then a workspace query is assumed; the routine */ -/* > only calculates the optimal size of the WORK array, returns */ -/* > this value as the first entry of the WORK array, and no error */ -/* > message related to LWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] RWORK */ -/* > \verbatim */ -/* > RWORK is DOUBLE PRECISION array, dimension (max(1, 3*N-2)) */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > > 0: if INFO = i, the algorithm failed to converge; i */ -/* > off-diagonal elements of an intermediate tridiagonal */ -/* > form did not converge to zero. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16HEeigen */ - -/* ===================================================================== */ -/* Subroutine */ int zheev_(char *jobz, char *uplo, integer *n, doublecomplex - *a, integer *lda, doublereal *w, doublecomplex *work, integer *lwork, - doublereal *rwork, integer *info, ftnlen jobz_len, ftnlen uplo_len) +int zheev_(char *jobz, char *uplo, integer *n, doublecomplex *a, integer *lda, doublereal *w, + doublecomplex *work, integer *lwork, doublereal *rwork, integer *info, ftnlen jobz_len, + ftnlen uplo_len) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; doublereal d__1; - - /* Builtin functions */ double sqrt(doublereal); - - /* Local variables */ integer nb; doublereal eps; integer inde; doublereal anrm; integer imax; doublereal rmin, rmax; - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *); + extern int dscal_(integer *, doublereal *, doublereal *, integer *); doublereal sigma; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer iinfo; @@ -190,95 +27,56 @@ ices */ extern doublereal dlamch_(char *, ftnlen); integer iscale; doublereal safmin; - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); + extern int xerbla_(char *, integer *, ftnlen); doublereal bignum; - extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *, - integer *, doublereal *, ftnlen, ftnlen); + extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *, integer *, doublereal *, + ftnlen, ftnlen); integer indtau; - extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *, - integer *), zlascl_(char *, integer *, integer *, doublereal *, - doublereal *, integer *, integer *, doublecomplex *, integer *, - integer *, ftnlen); + extern int dsterf_(integer *, doublereal *, doublereal *, integer *), + zlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, integer *, + doublecomplex *, integer *, integer *, ftnlen); integer indwrk; - extern /* Subroutine */ int zhetrd_(char *, integer *, doublecomplex *, - integer *, doublereal *, doublereal *, doublecomplex *, - doublecomplex *, integer *, integer *, ftnlen); + extern int zhetrd_(char *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, + doublecomplex *, doublecomplex *, integer *, integer *, ftnlen); integer llwork; doublereal smlnum; integer lwkopt; logical lquery; - extern /* Subroutine */ int zsteqr_(char *, integer *, doublereal *, - doublereal *, doublecomplex *, integer *, doublereal *, integer *, - ftnlen), zungtr_(char *, integer *, doublecomplex *, integer *, - doublecomplex *, doublecomplex *, integer *, integer *, ftnlen); - - -/* -- LAPACK driver routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ + extern int zsteqr_(char *, integer *, doublereal *, doublereal *, doublecomplex *, integer *, + doublereal *, integer *, ftnlen), + zungtr_(char *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, + integer *, integer *, ftnlen); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --w; --work; --rwork; - - /* Function Body */ wantz = lsame_(jobz, (char *)"V", (ftnlen)1, (ftnlen)1); lower = lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1); lquery = *lwork == -1; - *info = 0; - if (! (wantz || lsame_(jobz, (char *)"N", (ftnlen)1, (ftnlen)1))) { + if (!(wantz || lsame_(jobz, (char *)"N", (ftnlen)1, (ftnlen)1))) { *info = -1; - } else if (! (lower || lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1))) { + } else if (!(lower || lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1))) { *info = -2; } else if (*n < 0) { *info = -3; - } else if (*lda < max(1,*n)) { + } else if (*lda < max(1, *n)) { *info = -5; } - if (*info == 0) { - nb = ilaenv_(&c__1, (char *)"ZHETRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, - (ftnlen)1); -/* Computing MAX */ + nb = ilaenv_(&c__1, (char *)"ZHETRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); i__1 = 1, i__2 = (nb + 1) * *n; - lwkopt = max(i__1,i__2); - work[1].r = (doublereal) lwkopt, work[1].i = 0.; - -/* Computing MAX */ + lwkopt = max(i__1, i__2); + work[1].r = (doublereal)lwkopt, work[1].i = 0.; i__1 = 1, i__2 = (*n << 1) - 1; - if (*lwork < max(i__1,i__2) && ! lquery) { + if (*lwork < max(i__1, i__2) && !lquery) { *info = -8; } } - if (*info != 0) { i__1 = -(*info); xerbla_((char *)"ZHEEV ", &i__1, (ftnlen)6); @@ -286,13 +84,9 @@ ices */ } else if (lquery) { return 0; } - -/* Quick return if possible */ - if (*n == 0) { return 0; } - if (*n == 1) { i__1 = a_dim1 + 1; w[1] = a[i__1].r; @@ -303,20 +97,13 @@ ices */ } return 0; } - -/* Get machine constants. */ - safmin = dlamch_((char *)"Safe minimum", (ftnlen)12); eps = dlamch_((char *)"Precision", (ftnlen)9); smlnum = safmin / eps; bignum = 1. / smlnum; rmin = sqrt(smlnum); rmax = sqrt(bignum); - -/* Scale matrix to allowable range, if necessary. */ - - anrm = zlanhe_((char *)"M", uplo, n, &a[a_offset], lda, &rwork[1], (ftnlen)1, ( - ftnlen)1); + anrm = zlanhe_((char *)"M", uplo, n, &a[a_offset], lda, &rwork[1], (ftnlen)1, (ftnlen)1); iscale = 0; if (anrm > 0. && anrm < rmin) { iscale = 1; @@ -326,34 +113,22 @@ ices */ sigma = rmax / anrm; } if (iscale == 1) { - zlascl_(uplo, &c__0, &c__0, &c_b18, &sigma, n, n, &a[a_offset], lda, - info, (ftnlen)1); + zlascl_(uplo, &c__0, &c__0, &c_b18, &sigma, n, n, &a[a_offset], lda, info, (ftnlen)1); } - -/* Call ZHETRD to reduce Hermitian matrix to tridiagonal form. */ - inde = 1; indtau = 1; indwrk = indtau + *n; llwork = *lwork - indwrk + 1; - zhetrd_(uplo, n, &a[a_offset], lda, &w[1], &rwork[inde], &work[indtau], & - work[indwrk], &llwork, &iinfo, (ftnlen)1); - -/* For eigenvalues only, call DSTERF. For eigenvectors, first call */ -/* ZUNGTR to generate the unitary matrix, then call ZSTEQR. */ - - if (! wantz) { + zhetrd_(uplo, n, &a[a_offset], lda, &w[1], &rwork[inde], &work[indtau], &work[indwrk], &llwork, + &iinfo, (ftnlen)1); + if (!wantz) { dsterf_(n, &w[1], &rwork[inde], info); } else { - zungtr_(uplo, n, &a[a_offset], lda, &work[indtau], &work[indwrk], & - llwork, &iinfo, (ftnlen)1); + zungtr_(uplo, n, &a[a_offset], lda, &work[indtau], &work[indwrk], &llwork, &iinfo, + (ftnlen)1); indwrk = inde + *n; - zsteqr_(jobz, n, &w[1], &rwork[inde], &a[a_offset], lda, &rwork[ - indwrk], info, (ftnlen)1); + zsteqr_(jobz, n, &w[1], &rwork[inde], &a[a_offset], lda, &rwork[indwrk], info, (ftnlen)1); } - -/* If matrix was scaled, then rescale eigenvalues appropriately. */ - if (iscale == 1) { if (*info == 0) { imax = *n; @@ -363,17 +138,9 @@ ices */ d__1 = 1. / sigma; dscal_(&imax, &d__1, &w[1], &c__1); } - -/* Set WORK(1) to optimal complex workspace size. */ - - work[1].r = (doublereal) lwkopt, work[1].i = 0.; - + work[1].r = (doublereal)lwkopt, work[1].i = 0.; return 0; - -/* End of ZHEEV */ - -} /* zheev_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zheevd.cpp b/lib/linalg/zheevd.cpp index 83747a7962..094bf2216d 100644 --- a/lib/linalg/zheevd.cpp +++ b/lib/linalg/zheevd.cpp @@ -1,254 +1,25 @@ -/* fortran/zheevd.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static integer c_n1 = -1; static integer c__0 = 0; static doublereal c_b18 = 1.; - -/* > \brief ZHEEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE mat -rices */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZHEEVD + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, */ -/* LRWORK, IWORK, LIWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER JOBZ, UPLO */ -/* INTEGER INFO, LDA, LIWORK, LRWORK, LWORK, N */ -/* .. */ -/* .. Array Arguments .. */ -/* INTEGER IWORK( * ) */ -/* DOUBLE PRECISION RWORK( * ), W( * ) */ -/* COMPLEX*16 A( LDA, * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZHEEVD computes all eigenvalues and, optionally, eigenvectors of a */ -/* > complex Hermitian matrix A. If eigenvectors are desired, it uses a */ -/* > divide and conquer algorithm. */ -/* > */ -/* > The divide and conquer algorithm makes very mild assumptions about */ -/* > floating point arithmetic. It will work on machines with a guard */ -/* > digit in add/subtract, or on those binary machines without guard */ -/* > digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */ -/* > Cray-2. It could conceivably fail on hexadecimal or decimal machines */ -/* > without guard digits, but we know of none. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] JOBZ */ -/* > \verbatim */ -/* > JOBZ is CHARACTER*1 */ -/* > = 'N': Compute eigenvalues only; */ -/* > = 'V': Compute eigenvalues and eigenvectors. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > = 'U': Upper triangle of A is stored; */ -/* > = 'L': Lower triangle of A is stored. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is COMPLEX*16 array, dimension (LDA, N) */ -/* > On entry, the Hermitian matrix A. If UPLO = 'U', the */ -/* > leading N-by-N upper triangular part of A contains the */ -/* > upper triangular part of the matrix A. If UPLO = 'L', */ -/* > the leading N-by-N lower triangular part of A contains */ -/* > the lower triangular part of the matrix A. */ -/* > On exit, if JOBZ = 'V', then if INFO = 0, A contains the */ -/* > orthonormal eigenvectors of the matrix A. */ -/* > If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') */ -/* > or the upper triangle (if UPLO='U') of A, including the */ -/* > diagonal, is destroyed. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] W */ -/* > \verbatim */ -/* > W is DOUBLE PRECISION array, dimension (N) */ -/* > If INFO = 0, the eigenvalues in ascending order. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) */ -/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LWORK */ -/* > \verbatim */ -/* > LWORK is INTEGER */ -/* > The length of the array WORK. */ -/* > If N <= 1, LWORK must be at least 1. */ -/* > If JOBZ = 'N' and N > 1, LWORK must be at least N + 1. */ -/* > If JOBZ = 'V' and N > 1, LWORK must be at least 2*N + N**2. */ -/* > */ -/* > If LWORK = -1, then a workspace query is assumed; the routine */ -/* > only calculates the optimal sizes of the WORK, RWORK and */ -/* > IWORK arrays, returns these values as the first entries of */ -/* > the WORK, RWORK and IWORK arrays, and no error message */ -/* > related to LWORK or LRWORK or LIWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] RWORK */ -/* > \verbatim */ -/* > RWORK is DOUBLE PRECISION array, */ -/* > dimension (LRWORK) */ -/* > On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LRWORK */ -/* > \verbatim */ -/* > LRWORK is INTEGER */ -/* > The dimension of the array RWORK. */ -/* > If N <= 1, LRWORK must be at least 1. */ -/* > If JOBZ = 'N' and N > 1, LRWORK must be at least N. */ -/* > If JOBZ = 'V' and N > 1, LRWORK must be at least */ -/* > 1 + 5*N + 2*N**2. */ -/* > */ -/* > If LRWORK = -1, then a workspace query is assumed; the */ -/* > routine only calculates the optimal sizes of the WORK, RWORK */ -/* > and IWORK arrays, returns these values as the first entries */ -/* > of the WORK, RWORK and IWORK arrays, and no error message */ -/* > related to LWORK or LRWORK or LIWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] IWORK */ -/* > \verbatim */ -/* > IWORK is INTEGER array, dimension (MAX(1,LIWORK)) */ -/* > On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LIWORK */ -/* > \verbatim */ -/* > LIWORK is INTEGER */ -/* > The dimension of the array IWORK. */ -/* > If N <= 1, LIWORK must be at least 1. */ -/* > If JOBZ = 'N' and N > 1, LIWORK must be at least 1. */ -/* > If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N. */ -/* > */ -/* > If LIWORK = -1, then a workspace query is assumed; the */ -/* > routine only calculates the optimal sizes of the WORK, RWORK */ -/* > and IWORK arrays, returns these values as the first entries */ -/* > of the WORK, RWORK and IWORK arrays, and no error message */ -/* > related to LWORK or LRWORK or LIWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > > 0: if INFO = i and JOBZ = 'N', then the algorithm failed */ -/* > to converge; i off-diagonal elements of an intermediate */ -/* > tridiagonal form did not converge to zero; */ -/* > if INFO = i and JOBZ = 'V', then the algorithm failed */ -/* > to compute an eigenvalue while working on the submatrix */ -/* > lying in rows and columns INFO/(N+1) through */ -/* > mod(INFO,N+1). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16HEeigen */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > Modified description of INFO. Sven, 16 Feb 05. */ - -/* > \par Contributors: */ -/* ================== */ -/* > */ -/* > Jeff Rutter, Computer Science Division, University of California */ -/* > at Berkeley, USA */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int zheevd_(char *jobz, char *uplo, integer *n, - doublecomplex *a, integer *lda, doublereal *w, doublecomplex *work, - integer *lwork, doublereal *rwork, integer *lrwork, integer *iwork, - integer *liwork, integer *info, ftnlen jobz_len, ftnlen uplo_len) +int zheevd_(char *jobz, char *uplo, integer *n, doublecomplex *a, integer *lda, doublereal *w, + doublecomplex *work, integer *lwork, doublereal *rwork, integer *lrwork, integer *iwork, + integer *liwork, integer *info, ftnlen jobz_len, ftnlen uplo_len) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; doublereal d__1; - - /* Builtin functions */ double sqrt(doublereal); - - /* Local variables */ doublereal eps; integer inde; doublereal anrm; integer imax; doublereal rmin, rmax; integer lopt; - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *); + extern int dscal_(integer *, doublereal *, doublereal *, integer *); doublereal sigma; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer iinfo, lwmin, liopt; @@ -259,61 +30,30 @@ f"> */ extern doublereal dlamch_(char *, ftnlen); integer iscale; doublereal safmin; - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); + extern int xerbla_(char *, integer *, ftnlen); doublereal bignum; - extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *, - integer *, doublereal *, ftnlen, ftnlen); + extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *, integer *, doublereal *, + ftnlen, ftnlen); integer indtau; - extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *, - integer *), zlascl_(char *, integer *, integer *, doublereal *, - doublereal *, integer *, integer *, doublecomplex *, integer *, - integer *, ftnlen), zstedc_(char *, integer *, doublereal *, - doublereal *, doublecomplex *, integer *, doublecomplex *, - integer *, doublereal *, integer *, integer *, integer *, integer - *, ftnlen); + extern int dsterf_(integer *, doublereal *, doublereal *, integer *), + zlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, integer *, + doublecomplex *, integer *, integer *, ftnlen), + zstedc_(char *, integer *, doublereal *, doublereal *, doublecomplex *, integer *, + doublecomplex *, integer *, doublereal *, integer *, integer *, integer *, + integer *, ftnlen); integer indrwk, indwrk, liwmin; - extern /* Subroutine */ int zhetrd_(char *, integer *, doublecomplex *, - integer *, doublereal *, doublereal *, doublecomplex *, - doublecomplex *, integer *, integer *, ftnlen), zlacpy_(char *, - integer *, integer *, doublecomplex *, integer *, doublecomplex *, - integer *, ftnlen); + extern int zhetrd_(char *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, + doublecomplex *, doublecomplex *, integer *, integer *, ftnlen), + zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, + integer *, ftnlen); integer lrwmin, llwork; doublereal smlnum; logical lquery; - extern /* Subroutine */ int zunmtr_(char *, char *, char *, integer *, - integer *, doublecomplex *, integer *, doublecomplex *, - doublecomplex *, integer *, doublecomplex *, integer *, integer *, - ftnlen, ftnlen, ftnlen); - - -/* -- LAPACK driver routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ + extern int zunmtr_(char *, char *, char *, integer *, integer *, doublecomplex *, integer *, + doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, + integer *, ftnlen, ftnlen, ftnlen); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; @@ -321,23 +61,19 @@ f"> */ --work; --rwork; --iwork; - - /* Function Body */ wantz = lsame_(jobz, (char *)"V", (ftnlen)1, (ftnlen)1); lower = lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1); lquery = *lwork == -1 || *lrwork == -1 || *liwork == -1; - *info = 0; - if (! (wantz || lsame_(jobz, (char *)"N", (ftnlen)1, (ftnlen)1))) { + if (!(wantz || lsame_(jobz, (char *)"N", (ftnlen)1, (ftnlen)1))) { *info = -1; - } else if (! (lower || lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1))) { + } else if (!(lower || lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1))) { *info = -2; } else if (*n < 0) { *info = -3; - } else if (*lda < max(1,*n)) { + } else if (*lda < max(1, *n)) { *info = -5; } - if (*info == 0) { if (*n <= 1) { lwmin = 1; @@ -349,7 +85,6 @@ f"> */ } else { if (wantz) { lwmin = (*n << 1) + *n * *n; -/* Computing 2nd power */ i__1 = *n; lrwmin = *n * 5 + 1 + (i__1 * i__1 << 1); liwmin = *n * 5 + 3; @@ -358,26 +93,23 @@ f"> */ lrwmin = *n; liwmin = 1; } -/* Computing MAX */ - i__1 = lwmin, i__2 = *n + *n * ilaenv_(&c__1, (char *)"ZHETRD", uplo, n, & - c_n1, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); - lopt = max(i__1,i__2); + i__1 = lwmin, i__2 = *n + *n * ilaenv_(&c__1, (char *)"ZHETRD", uplo, n, &c_n1, &c_n1, &c_n1, + (ftnlen)6, (ftnlen)1); + lopt = max(i__1, i__2); lropt = lrwmin; liopt = liwmin; } - work[1].r = (doublereal) lopt, work[1].i = 0.; - rwork[1] = (doublereal) lropt; + work[1].r = (doublereal)lopt, work[1].i = 0.; + rwork[1] = (doublereal)lropt; iwork[1] = liopt; - - if (*lwork < lwmin && ! lquery) { + if (*lwork < lwmin && !lquery) { *info = -8; - } else if (*lrwork < lrwmin && ! lquery) { + } else if (*lrwork < lrwmin && !lquery) { *info = -10; - } else if (*liwork < liwmin && ! lquery) { + } else if (*liwork < liwmin && !lquery) { *info = -12; } } - if (*info != 0) { i__1 = -(*info); xerbla_((char *)"ZHEEVD", &i__1, (ftnlen)6); @@ -385,13 +117,9 @@ f"> */ } else if (lquery) { return 0; } - -/* Quick return if possible */ - if (*n == 0) { return 0; } - if (*n == 1) { i__1 = a_dim1 + 1; w[1] = a[i__1].r; @@ -401,20 +129,13 @@ f"> */ } return 0; } - -/* Get machine constants. */ - safmin = dlamch_((char *)"Safe minimum", (ftnlen)12); eps = dlamch_((char *)"Precision", (ftnlen)9); smlnum = safmin / eps; bignum = 1. / smlnum; rmin = sqrt(smlnum); rmax = sqrt(bignum); - -/* Scale matrix to allowable range, if necessary. */ - - anrm = zlanhe_((char *)"M", uplo, n, &a[a_offset], lda, &rwork[1], (ftnlen)1, ( - ftnlen)1); + anrm = zlanhe_((char *)"M", uplo, n, &a[a_offset], lda, &rwork[1], (ftnlen)1, (ftnlen)1); iscale = 0; if (anrm > 0. && anrm < rmin) { iscale = 1; @@ -424,12 +145,8 @@ f"> */ sigma = rmax / anrm; } if (iscale == 1) { - zlascl_(uplo, &c__0, &c__0, &c_b18, &sigma, n, n, &a[a_offset], lda, - info, (ftnlen)1); + zlascl_(uplo, &c__0, &c__0, &c_b18, &sigma, n, n, &a[a_offset], lda, info, (ftnlen)1); } - -/* Call ZHETRD to reduce Hermitian matrix to tridiagonal form. */ - inde = 1; indtau = 1; indwrk = indtau + *n; @@ -438,29 +155,17 @@ f"> */ llwork = *lwork - indwrk + 1; llwrk2 = *lwork - indwk2 + 1; llrwk = *lrwork - indrwk + 1; - zhetrd_(uplo, n, &a[a_offset], lda, &w[1], &rwork[inde], &work[indtau], & - work[indwrk], &llwork, &iinfo, (ftnlen)1); - -/* For eigenvalues only, call DSTERF. For eigenvectors, first call */ -/* ZSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the */ -/* tridiagonal matrix, then call ZUNMTR to multiply it to the */ -/* Householder transformations represented as Householder vectors in */ -/* A. */ - - if (! wantz) { + zhetrd_(uplo, n, &a[a_offset], lda, &w[1], &rwork[inde], &work[indtau], &work[indwrk], &llwork, + &iinfo, (ftnlen)1); + if (!wantz) { dsterf_(n, &w[1], &rwork[inde], info); } else { - zstedc_((char *)"I", n, &w[1], &rwork[inde], &work[indwrk], n, &work[indwk2], - &llwrk2, &rwork[indrwk], &llrwk, &iwork[1], liwork, info, ( - ftnlen)1); - zunmtr_((char *)"L", uplo, (char *)"N", n, n, &a[a_offset], lda, &work[indtau], &work[ - indwrk], n, &work[indwk2], &llwrk2, &iinfo, (ftnlen)1, ( - ftnlen)1, (ftnlen)1); + zstedc_((char *)"I", n, &w[1], &rwork[inde], &work[indwrk], n, &work[indwk2], &llwrk2, + &rwork[indrwk], &llrwk, &iwork[1], liwork, info, (ftnlen)1); + zunmtr_((char *)"L", uplo, (char *)"N", n, n, &a[a_offset], lda, &work[indtau], &work[indwrk], n, + &work[indwk2], &llwrk2, &iinfo, (ftnlen)1, (ftnlen)1, (ftnlen)1); zlacpy_((char *)"A", n, n, &work[indwrk], n, &a[a_offset], lda, (ftnlen)1); } - -/* If matrix was scaled, then rescale eigenvalues appropriately. */ - if (iscale == 1) { if (*info == 0) { imax = *n; @@ -470,17 +175,11 @@ f"> */ d__1 = 1. / sigma; dscal_(&imax, &d__1, &w[1], &c__1); } - - work[1].r = (doublereal) lopt, work[1].i = 0.; - rwork[1] = (doublereal) lropt; + work[1].r = (doublereal)lopt, work[1].i = 0.; + rwork[1] = (doublereal)lropt; iwork[1] = liopt; - return 0; - -/* End of ZHEEVD */ - -} /* zheevd_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zhemv.cpp b/lib/linalg/zhemv.cpp index f26dbadf2b..566e74fab6 100644 --- a/lib/linalg/zhemv.cpp +++ b/lib/linalg/zhemv.cpp @@ -1,230 +1,30 @@ -/* fortran/zhemv.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b ZHEMV */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZHEMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) */ - -/* .. Scalar Arguments .. */ -/* COMPLEX*16 ALPHA,BETA */ -/* INTEGER INCX,INCY,LDA,N */ -/* CHARACTER UPLO */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 A(LDA,*),X(*),Y(*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZHEMV performs the matrix-vector operation */ -/* > */ -/* > y := alpha*A*x + beta*y, */ -/* > */ -/* > where alpha and beta are scalars, x and y are n element vectors and */ -/* > A is an n by n hermitian matrix. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > On entry, UPLO specifies whether the upper or lower */ -/* > triangular part of the array A is to be referenced as */ -/* > follows: */ -/* > */ -/* > UPLO = 'U' or 'u' Only the upper triangular part of A */ -/* > is to be referenced. */ -/* > */ -/* > UPLO = 'L' or 'l' Only the lower triangular part of A */ -/* > is to be referenced. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > On entry, N specifies the order of the matrix A. */ -/* > N must be at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] ALPHA */ -/* > \verbatim */ -/* > ALPHA is COMPLEX*16 */ -/* > On entry, ALPHA specifies the scalar alpha. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is COMPLEX*16 array, dimension ( LDA, N ) */ -/* > Before entry with UPLO = 'U' or 'u', the leading n by n */ -/* > upper triangular part of the array A must contain the upper */ -/* > triangular part of the hermitian matrix and the strictly */ -/* > lower triangular part of A is not referenced. */ -/* > Before entry with UPLO = 'L' or 'l', the leading n by n */ -/* > lower triangular part of the array A must contain the lower */ -/* > triangular part of the hermitian matrix and the strictly */ -/* > upper triangular part of A is not referenced. */ -/* > Note that the imaginary parts of the diagonal elements need */ -/* > not be set and are assumed to be zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > On entry, LDA specifies the first dimension of A as declared */ -/* > in the calling (sub) program. LDA must be at least */ -/* > max( 1, n ). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] X */ -/* > \verbatim */ -/* > X is COMPLEX*16 array, dimension at least */ -/* > ( 1 + ( n - 1 )*abs( INCX ) ). */ -/* > Before entry, the incremented array X must contain the n */ -/* > element vector x. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > On entry, INCX specifies the increment for the elements of */ -/* > X. INCX must not be zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] BETA */ -/* > \verbatim */ -/* > BETA is COMPLEX*16 */ -/* > On entry, BETA specifies the scalar beta. When BETA is */ -/* > supplied as zero then Y need not be set on input. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] Y */ -/* > \verbatim */ -/* > Y is COMPLEX*16 array, dimension at least */ -/* > ( 1 + ( n - 1 )*abs( INCY ) ). */ -/* > Before entry, the incremented array Y must contain the n */ -/* > element vector y. On exit, Y is overwritten by the updated */ -/* > vector y. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCY */ -/* > \verbatim */ -/* > INCY is INTEGER */ -/* > On entry, INCY specifies the increment for the elements of */ -/* > Y. INCY must not be zero. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16_blas_level2 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > Level 2 Blas routine. */ -/* > The vector and matrix arguments are not referenced when N = 0, or M = 0 */ -/* > */ -/* > -- Written on 22-October-1986. */ -/* > Jack Dongarra, Argonne National Lab. */ -/* > Jeremy Du Croz, Nag Central Office. */ -/* > Sven Hammarling, Nag Central Office. */ -/* > Richard Hanson, Sandia National Labs. */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int zhemv_(char *uplo, integer *n, doublecomplex *alpha, - doublecomplex *a, integer *lda, doublecomplex *x, integer *incx, - doublecomplex *beta, doublecomplex *y, integer *incy, ftnlen uplo_len) +int zhemv_(char *uplo, integer *n, doublecomplex *alpha, doublecomplex *a, integer *lda, + doublecomplex *x, integer *incx, doublecomplex *beta, doublecomplex *y, integer *incy, + ftnlen uplo_len) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; doublereal d__1; doublecomplex z__1, z__2, z__3, z__4; - - /* Builtin functions */ void d_lmp_cnjg(doublecomplex *, doublecomplex *); - - /* Local variables */ integer i__, j, ix, iy, jx, jy, kx, ky, info; doublecomplex temp1, temp2; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - - -/* -- Reference BLAS level2 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ + extern int xerbla_(char *, integer *, ftnlen); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --x; --y; - - /* Function Body */ info = 0; - if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", ( - ftnlen)1, (ftnlen)1)) { + if (!lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { info = 1; } else if (*n < 0) { info = 2; - } else if (*lda < max(1,*n)) { + } else if (*lda < max(1, *n)) { info = 5; } else if (*incx == 0) { info = 7; @@ -235,16 +35,9 @@ extern "C" { xerbla_((char *)"ZHEMV ", &info, (ftnlen)6); return 0; } - -/* Quick return if possible. */ - - if (*n == 0 || alpha->r == 0. && alpha->i == 0. && (beta->r == 1. && - beta->i == 0.)) { + if (*n == 0 || alpha->r == 0. && alpha->i == 0. && (beta->r == 1. && beta->i == 0.)) { return 0; } - -/* Set up the start points in X and Y. */ - if (*incx > 0) { kx = 1; } else { @@ -255,13 +48,6 @@ extern "C" { } else { ky = 1 - (*n - 1) * *incy; } - -/* Start the operations. In this version the elements of A are */ -/* accessed sequentially with one pass through the triangular part */ -/* of A. */ - -/* First form y := beta*y. */ - if (beta->r != 1. || beta->i != 0.) { if (*incy == 1) { if (beta->r == 0. && beta->i == 0.) { @@ -269,7 +55,6 @@ extern "C" { for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; y[i__2].r = 0., y[i__2].i = 0.; -/* L10: */ } } else { i__1 = *n; @@ -277,10 +62,8 @@ extern "C" { i__2 = i__; i__3 = i__; z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i, - z__1.i = beta->r * y[i__3].i + beta->i * y[i__3] - .r; + z__1.i = beta->r * y[i__3].i + beta->i * y[i__3].r; y[i__2].r = z__1.r, y[i__2].i = z__1.i; -/* L20: */ } } } else { @@ -291,7 +74,6 @@ extern "C" { i__2 = iy; y[i__2].r = 0., y[i__2].i = 0.; iy += *incy; -/* L30: */ } } else { i__1 = *n; @@ -299,11 +81,9 @@ extern "C" { i__2 = iy; i__3 = iy; z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i, - z__1.i = beta->r * y[i__3].i + beta->i * y[i__3] - .r; + z__1.i = beta->r * y[i__3].i + beta->i * y[i__3].r; y[i__2].r = z__1.r, y[i__2].i = z__1.i; iy += *incy; -/* L40: */ } } } @@ -312,15 +92,12 @@ extern "C" { return 0; } if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { - -/* Form y when A is stored in upper triangle. */ - if (*incx == 1 && *incy == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; - z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i = - alpha->r * x[i__2].i + alpha->i * x[i__2].r; + z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, + z__1.i = alpha->r * x[i__2].i + alpha->i * x[i__2].r; temp1.r = z__1.r, temp1.i = z__1.i; temp2.r = 0., temp2.i = 0.; i__2 = j - 1; @@ -329,17 +106,15 @@ extern "C" { i__4 = i__; i__5 = i__ + j * a_dim1; z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, - z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5] - .r; + z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5].r; z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; y[i__3].r = z__1.r, y[i__3].i = z__1.i; d_lmp_cnjg(&z__3, &a[i__ + j * a_dim1]); i__3 = i__; - z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = - z__3.r * x[i__3].i + z__3.i * x[i__3].r; + z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, + z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3].r; z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; temp2.r = z__1.r, temp2.i = z__1.i; -/* L50: */ } i__2 = j; i__3 = j; @@ -347,11 +122,10 @@ extern "C" { d__1 = a[i__4].r; z__3.r = d__1 * temp1.r, z__3.i = d__1 * temp1.i; z__2.r = y[i__3].r + z__3.r, z__2.i = y[i__3].i + z__3.i; - z__4.r = alpha->r * temp2.r - alpha->i * temp2.i, z__4.i = - alpha->r * temp2.i + alpha->i * temp2.r; + z__4.r = alpha->r * temp2.r - alpha->i * temp2.i, + z__4.i = alpha->r * temp2.i + alpha->i * temp2.r; z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; y[i__2].r = z__1.r, y[i__2].i = z__1.i; -/* L60: */ } } else { jx = kx; @@ -359,8 +133,8 @@ extern "C" { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = jx; - z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i = - alpha->r * x[i__2].i + alpha->i * x[i__2].r; + z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, + z__1.i = alpha->r * x[i__2].i + alpha->i * x[i__2].r; temp1.r = z__1.r, temp1.i = z__1.i; temp2.r = 0., temp2.i = 0.; ix = kx; @@ -371,19 +145,17 @@ extern "C" { i__4 = iy; i__5 = i__ + j * a_dim1; z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, - z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5] - .r; + z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5].r; z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; y[i__3].r = z__1.r, y[i__3].i = z__1.i; d_lmp_cnjg(&z__3, &a[i__ + j * a_dim1]); i__3 = ix; - z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = - z__3.r * x[i__3].i + z__3.i * x[i__3].r; + z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, + z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3].r; z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; temp2.r = z__1.r, temp2.i = z__1.i; ix += *incx; iy += *incy; -/* L70: */ } i__2 = jy; i__3 = jy; @@ -391,25 +163,21 @@ extern "C" { d__1 = a[i__4].r; z__3.r = d__1 * temp1.r, z__3.i = d__1 * temp1.i; z__2.r = y[i__3].r + z__3.r, z__2.i = y[i__3].i + z__3.i; - z__4.r = alpha->r * temp2.r - alpha->i * temp2.i, z__4.i = - alpha->r * temp2.i + alpha->i * temp2.r; + z__4.r = alpha->r * temp2.r - alpha->i * temp2.i, + z__4.i = alpha->r * temp2.i + alpha->i * temp2.r; z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; y[i__2].r = z__1.r, y[i__2].i = z__1.i; jx += *incx; jy += *incy; -/* L80: */ } } } else { - -/* Form y when A is stored in lower triangle. */ - if (*incx == 1 && *incy == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; - z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i = - alpha->r * x[i__2].i + alpha->i * x[i__2].r; + z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, + z__1.i = alpha->r * x[i__2].i + alpha->i * x[i__2].r; temp1.r = z__1.r, temp1.i = z__1.i; temp2.r = 0., temp2.i = 0.; i__2 = j; @@ -425,25 +193,22 @@ extern "C" { i__4 = i__; i__5 = i__ + j * a_dim1; z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, - z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5] - .r; + z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5].r; z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; y[i__3].r = z__1.r, y[i__3].i = z__1.i; d_lmp_cnjg(&z__3, &a[i__ + j * a_dim1]); i__3 = i__; - z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = - z__3.r * x[i__3].i + z__3.i * x[i__3].r; + z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, + z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3].r; z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; temp2.r = z__1.r, temp2.i = z__1.i; -/* L90: */ } i__2 = j; i__3 = j; - z__2.r = alpha->r * temp2.r - alpha->i * temp2.i, z__2.i = - alpha->r * temp2.i + alpha->i * temp2.r; + z__2.r = alpha->r * temp2.r - alpha->i * temp2.i, + z__2.i = alpha->r * temp2.i + alpha->i * temp2.r; z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i; y[i__2].r = z__1.r, y[i__2].i = z__1.i; -/* L100: */ } } else { jx = kx; @@ -451,8 +216,8 @@ extern "C" { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = jx; - z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i = - alpha->r * x[i__2].i + alpha->i * x[i__2].r; + z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, + z__1.i = alpha->r * x[i__2].i + alpha->i * x[i__2].r; temp1.r = z__1.r, temp1.i = z__1.i; temp2.r = 0., temp2.i = 0.; i__2 = jy; @@ -472,37 +237,29 @@ extern "C" { i__4 = iy; i__5 = i__ + j * a_dim1; z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i, - z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5] - .r; + z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5].r; z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i; y[i__3].r = z__1.r, y[i__3].i = z__1.i; d_lmp_cnjg(&z__3, &a[i__ + j * a_dim1]); i__3 = ix; - z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, z__2.i = - z__3.r * x[i__3].i + z__3.i * x[i__3].r; + z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, + z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3].r; z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; temp2.r = z__1.r, temp2.i = z__1.i; -/* L110: */ } i__2 = jy; i__3 = jy; - z__2.r = alpha->r * temp2.r - alpha->i * temp2.i, z__2.i = - alpha->r * temp2.i + alpha->i * temp2.r; + z__2.r = alpha->r * temp2.r - alpha->i * temp2.i, + z__2.i = alpha->r * temp2.i + alpha->i * temp2.r; z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i; y[i__2].r = z__1.r, y[i__2].i = z__1.i; jx += *incx; jy += *incy; -/* L120: */ } } } - return 0; - -/* End of ZHEMV */ - -} /* zhemv_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zher2.cpp b/lib/linalg/zher2.cpp index 6f66534dd4..d70b5f04e2 100644 --- a/lib/linalg/zher2.cpp +++ b/lib/linalg/zher2.cpp @@ -1,222 +1,25 @@ -/* fortran/zher2.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b ZHER2 */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZHER2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA) */ - -/* .. Scalar Arguments .. */ -/* COMPLEX*16 ALPHA */ -/* INTEGER INCX,INCY,LDA,N */ -/* CHARACTER UPLO */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 A(LDA,*),X(*),Y(*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZHER2 performs the hermitian rank 2 operation */ -/* > */ -/* > A := alpha*x*y**H + conjg( alpha )*y*x**H + A, */ -/* > */ -/* > where alpha is a scalar, x and y are n element vectors and A is an n */ -/* > by n hermitian matrix. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > On entry, UPLO specifies whether the upper or lower */ -/* > triangular part of the array A is to be referenced as */ -/* > follows: */ -/* > */ -/* > UPLO = 'U' or 'u' Only the upper triangular part of A */ -/* > is to be referenced. */ -/* > */ -/* > UPLO = 'L' or 'l' Only the lower triangular part of A */ -/* > is to be referenced. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > On entry, N specifies the order of the matrix A. */ -/* > N must be at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] ALPHA */ -/* > \verbatim */ -/* > ALPHA is COMPLEX*16 */ -/* > On entry, ALPHA specifies the scalar alpha. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] X */ -/* > \verbatim */ -/* > X is COMPLEX*16 array, dimension at least */ -/* > ( 1 + ( n - 1 )*abs( INCX ) ). */ -/* > Before entry, the incremented array X must contain the n */ -/* > element vector x. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > On entry, INCX specifies the increment for the elements of */ -/* > X. INCX must not be zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] Y */ -/* > \verbatim */ -/* > Y is COMPLEX*16 array, dimension at least */ -/* > ( 1 + ( n - 1 )*abs( INCY ) ). */ -/* > Before entry, the incremented array Y must contain the n */ -/* > element vector y. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCY */ -/* > \verbatim */ -/* > INCY is INTEGER */ -/* > On entry, INCY specifies the increment for the elements of */ -/* > Y. INCY must not be zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is COMPLEX*16 array, dimension ( LDA, N ) */ -/* > Before entry with UPLO = 'U' or 'u', the leading n by n */ -/* > upper triangular part of the array A must contain the upper */ -/* > triangular part of the hermitian matrix and the strictly */ -/* > lower triangular part of A is not referenced. On exit, the */ -/* > upper triangular part of the array A is overwritten by the */ -/* > upper triangular part of the updated matrix. */ -/* > Before entry with UPLO = 'L' or 'l', the leading n by n */ -/* > lower triangular part of the array A must contain the lower */ -/* > triangular part of the hermitian matrix and the strictly */ -/* > upper triangular part of A is not referenced. On exit, the */ -/* > lower triangular part of the array A is overwritten by the */ -/* > lower triangular part of the updated matrix. */ -/* > Note that the imaginary parts of the diagonal elements need */ -/* > not be set, they are assumed to be zero, and on exit they */ -/* > are set to zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > On entry, LDA specifies the first dimension of A as declared */ -/* > in the calling (sub) program. LDA must be at least */ -/* > max( 1, n ). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16_blas_level2 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > Level 2 Blas routine. */ -/* > */ -/* > -- Written on 22-October-1986. */ -/* > Jack Dongarra, Argonne National Lab. */ -/* > Jeremy Du Croz, Nag Central Office. */ -/* > Sven Hammarling, Nag Central Office. */ -/* > Richard Hanson, Sandia National Labs. */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int zher2_(char *uplo, integer *n, doublecomplex *alpha, - doublecomplex *x, integer *incx, doublecomplex *y, integer *incy, - doublecomplex *a, integer *lda, ftnlen uplo_len) +int zher2_(char *uplo, integer *n, doublecomplex *alpha, doublecomplex *x, integer *incx, + doublecomplex *y, integer *incy, doublecomplex *a, integer *lda, ftnlen uplo_len) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6; doublereal d__1; doublecomplex z__1, z__2, z__3, z__4; - - /* Builtin functions */ void d_lmp_cnjg(doublecomplex *, doublecomplex *); - - /* Local variables */ integer i__, j, ix, iy, jx, jy, kx, ky, info; doublecomplex temp1, temp2; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - - -/* -- Reference BLAS level2 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ + extern int xerbla_(char *, integer *, ftnlen); --x; --y; a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; - - /* Function Body */ info = 0; - if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", ( - ftnlen)1, (ftnlen)1)) { + if (!lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { info = 1; } else if (*n < 0) { info = 2; @@ -224,23 +27,16 @@ extern "C" { info = 5; } else if (*incy == 0) { info = 7; - } else if (*lda < max(1,*n)) { + } else if (*lda < max(1, *n)) { info = 9; } if (info != 0) { xerbla_((char *)"ZHER2 ", &info, (ftnlen)6); return 0; } - -/* Quick return if possible. */ - if (*n == 0 || alpha->r == 0. && alpha->i == 0.) { return 0; } - -/* Set up the start points in X and Y if the increments are not both */ -/* unity. */ - if (*incx != 1 || *incy != 1) { if (*incx > 0) { kx = 1; @@ -255,30 +51,20 @@ extern "C" { jx = kx; jy = ky; } - -/* Start the operations. In this version the elements of A are */ -/* accessed sequentially with one pass through the triangular part */ -/* of A. */ - if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { - -/* Form A when A is stored in the upper triangle. */ - if (*incx == 1 && *incy == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; i__3 = j; - if (x[i__2].r != 0. || x[i__2].i != 0. || (y[i__3].r != 0. || - y[i__3].i != 0.)) { + if (x[i__2].r != 0. || x[i__2].i != 0. || (y[i__3].r != 0. || y[i__3].i != 0.)) { d_lmp_cnjg(&z__2, &y[j]); - z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = - alpha->r * z__2.i + alpha->i * z__2.r; + z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, + z__1.i = alpha->r * z__2.i + alpha->i * z__2.r; temp1.r = z__1.r, temp1.i = z__1.i; i__2 = j; z__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, - z__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2] - .r; + z__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2].r; d_lmp_cnjg(&z__1, &z__2); temp2.r = z__1.r, temp2.i = z__1.i; i__2 = j - 1; @@ -287,28 +73,22 @@ extern "C" { i__4 = i__ + j * a_dim1; i__5 = i__; z__3.r = x[i__5].r * temp1.r - x[i__5].i * temp1.i, - z__3.i = x[i__5].r * temp1.i + x[i__5].i * - temp1.r; - z__2.r = a[i__4].r + z__3.r, z__2.i = a[i__4].i + - z__3.i; + z__3.i = x[i__5].r * temp1.i + x[i__5].i * temp1.r; + z__2.r = a[i__4].r + z__3.r, z__2.i = a[i__4].i + z__3.i; i__6 = i__; z__4.r = y[i__6].r * temp2.r - y[i__6].i * temp2.i, - z__4.i = y[i__6].r * temp2.i + y[i__6].i * - temp2.r; + z__4.i = y[i__6].r * temp2.i + y[i__6].i * temp2.r; z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; -/* L10: */ } i__2 = j + j * a_dim1; i__3 = j + j * a_dim1; i__4 = j; z__2.r = x[i__4].r * temp1.r - x[i__4].i * temp1.i, - z__2.i = x[i__4].r * temp1.i + x[i__4].i * - temp1.r; + z__2.i = x[i__4].r * temp1.i + x[i__4].i * temp1.r; i__5 = j; z__3.r = y[i__5].r * temp2.r - y[i__5].i * temp2.i, - z__3.i = y[i__5].r * temp2.i + y[i__5].i * - temp2.r; + z__3.i = y[i__5].r * temp2.i + y[i__5].i * temp2.r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; d__1 = a[i__3].r + z__1.r; a[i__2].r = d__1, a[i__2].i = 0.; @@ -318,23 +98,20 @@ extern "C" { d__1 = a[i__3].r; a[i__2].r = d__1, a[i__2].i = 0.; } -/* L20: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = jx; i__3 = jy; - if (x[i__2].r != 0. || x[i__2].i != 0. || (y[i__3].r != 0. || - y[i__3].i != 0.)) { + if (x[i__2].r != 0. || x[i__2].i != 0. || (y[i__3].r != 0. || y[i__3].i != 0.)) { d_lmp_cnjg(&z__2, &y[jy]); - z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = - alpha->r * z__2.i + alpha->i * z__2.r; + z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, + z__1.i = alpha->r * z__2.i + alpha->i * z__2.r; temp1.r = z__1.r, temp1.i = z__1.i; i__2 = jx; z__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, - z__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2] - .r; + z__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2].r; d_lmp_cnjg(&z__1, &z__2); temp2.r = z__1.r, temp2.i = z__1.i; ix = kx; @@ -345,30 +122,24 @@ extern "C" { i__4 = i__ + j * a_dim1; i__5 = ix; z__3.r = x[i__5].r * temp1.r - x[i__5].i * temp1.i, - z__3.i = x[i__5].r * temp1.i + x[i__5].i * - temp1.r; - z__2.r = a[i__4].r + z__3.r, z__2.i = a[i__4].i + - z__3.i; + z__3.i = x[i__5].r * temp1.i + x[i__5].i * temp1.r; + z__2.r = a[i__4].r + z__3.r, z__2.i = a[i__4].i + z__3.i; i__6 = iy; z__4.r = y[i__6].r * temp2.r - y[i__6].i * temp2.i, - z__4.i = y[i__6].r * temp2.i + y[i__6].i * - temp2.r; + z__4.i = y[i__6].r * temp2.i + y[i__6].i * temp2.r; z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; ix += *incx; iy += *incy; -/* L30: */ } i__2 = j + j * a_dim1; i__3 = j + j * a_dim1; i__4 = jx; z__2.r = x[i__4].r * temp1.r - x[i__4].i * temp1.i, - z__2.i = x[i__4].r * temp1.i + x[i__4].i * - temp1.r; + z__2.i = x[i__4].r * temp1.i + x[i__4].i * temp1.r; i__5 = jy; z__3.r = y[i__5].r * temp2.r - y[i__5].i * temp2.i, - z__3.i = y[i__5].r * temp2.i + y[i__5].i * - temp2.r; + z__3.i = y[i__5].r * temp2.i + y[i__5].i * temp2.r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; d__1 = a[i__3].r + z__1.r; a[i__2].r = d__1, a[i__2].i = 0.; @@ -380,40 +151,32 @@ extern "C" { } jx += *incx; jy += *incy; -/* L40: */ } } } else { - -/* Form A when A is stored in the lower triangle. */ - if (*incx == 1 && *incy == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = j; i__3 = j; - if (x[i__2].r != 0. || x[i__2].i != 0. || (y[i__3].r != 0. || - y[i__3].i != 0.)) { + if (x[i__2].r != 0. || x[i__2].i != 0. || (y[i__3].r != 0. || y[i__3].i != 0.)) { d_lmp_cnjg(&z__2, &y[j]); - z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = - alpha->r * z__2.i + alpha->i * z__2.r; + z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, + z__1.i = alpha->r * z__2.i + alpha->i * z__2.r; temp1.r = z__1.r, temp1.i = z__1.i; i__2 = j; z__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, - z__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2] - .r; + z__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2].r; d_lmp_cnjg(&z__1, &z__2); temp2.r = z__1.r, temp2.i = z__1.i; i__2 = j + j * a_dim1; i__3 = j + j * a_dim1; i__4 = j; z__2.r = x[i__4].r * temp1.r - x[i__4].i * temp1.i, - z__2.i = x[i__4].r * temp1.i + x[i__4].i * - temp1.r; + z__2.i = x[i__4].r * temp1.i + x[i__4].i * temp1.r; i__5 = j; z__3.r = y[i__5].r * temp2.r - y[i__5].i * temp2.i, - z__3.i = y[i__5].r * temp2.i + y[i__5].i * - temp2.r; + z__3.i = y[i__5].r * temp2.i + y[i__5].i * temp2.r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; d__1 = a[i__3].r + z__1.r; a[i__2].r = d__1, a[i__2].i = 0.; @@ -423,17 +186,13 @@ extern "C" { i__4 = i__ + j * a_dim1; i__5 = i__; z__3.r = x[i__5].r * temp1.r - x[i__5].i * temp1.i, - z__3.i = x[i__5].r * temp1.i + x[i__5].i * - temp1.r; - z__2.r = a[i__4].r + z__3.r, z__2.i = a[i__4].i + - z__3.i; + z__3.i = x[i__5].r * temp1.i + x[i__5].i * temp1.r; + z__2.r = a[i__4].r + z__3.r, z__2.i = a[i__4].i + z__3.i; i__6 = i__; z__4.r = y[i__6].r * temp2.r - y[i__6].i * temp2.i, - z__4.i = y[i__6].r * temp2.i + y[i__6].i * - temp2.r; + z__4.i = y[i__6].r * temp2.i + y[i__6].i * temp2.r; z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; -/* L50: */ } } else { i__2 = j + j * a_dim1; @@ -441,35 +200,30 @@ extern "C" { d__1 = a[i__3].r; a[i__2].r = d__1, a[i__2].i = 0.; } -/* L60: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = jx; i__3 = jy; - if (x[i__2].r != 0. || x[i__2].i != 0. || (y[i__3].r != 0. || - y[i__3].i != 0.)) { + if (x[i__2].r != 0. || x[i__2].i != 0. || (y[i__3].r != 0. || y[i__3].i != 0.)) { d_lmp_cnjg(&z__2, &y[jy]); - z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = - alpha->r * z__2.i + alpha->i * z__2.r; + z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, + z__1.i = alpha->r * z__2.i + alpha->i * z__2.r; temp1.r = z__1.r, temp1.i = z__1.i; i__2 = jx; z__2.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, - z__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2] - .r; + z__2.i = alpha->r * x[i__2].i + alpha->i * x[i__2].r; d_lmp_cnjg(&z__1, &z__2); temp2.r = z__1.r, temp2.i = z__1.i; i__2 = j + j * a_dim1; i__3 = j + j * a_dim1; i__4 = jx; z__2.r = x[i__4].r * temp1.r - x[i__4].i * temp1.i, - z__2.i = x[i__4].r * temp1.i + x[i__4].i * - temp1.r; + z__2.i = x[i__4].r * temp1.i + x[i__4].i * temp1.r; i__5 = jy; z__3.r = y[i__5].r * temp2.r - y[i__5].i * temp2.i, - z__3.i = y[i__5].r * temp2.i + y[i__5].i * - temp2.r; + z__3.i = y[i__5].r * temp2.i + y[i__5].i * temp2.r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; d__1 = a[i__3].r + z__1.r; a[i__2].r = d__1, a[i__2].i = 0.; @@ -483,17 +237,13 @@ extern "C" { i__4 = i__ + j * a_dim1; i__5 = ix; z__3.r = x[i__5].r * temp1.r - x[i__5].i * temp1.i, - z__3.i = x[i__5].r * temp1.i + x[i__5].i * - temp1.r; - z__2.r = a[i__4].r + z__3.r, z__2.i = a[i__4].i + - z__3.i; + z__3.i = x[i__5].r * temp1.i + x[i__5].i * temp1.r; + z__2.r = a[i__4].r + z__3.r, z__2.i = a[i__4].i + z__3.i; i__6 = iy; z__4.r = y[i__6].r * temp2.r - y[i__6].i * temp2.i, - z__4.i = y[i__6].r * temp2.i + y[i__6].i * - temp2.r; + z__4.i = y[i__6].r * temp2.i + y[i__6].i * temp2.r; z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; -/* L70: */ } } else { i__2 = j + j * a_dim1; @@ -503,17 +253,11 @@ extern "C" { } jx += *incx; jy += *incy; -/* L80: */ } } } - return 0; - -/* End of ZHER2 */ - -} /* zher2_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zher2k.cpp b/lib/linalg/zher2k.cpp index 01ce32deb9..c98e401dd3 100644 --- a/lib/linalg/zher2k.cpp +++ b/lib/linalg/zher2k.cpp @@ -1,264 +1,22 @@ -/* fortran/zher2k.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b ZHER2K */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZHER2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) */ - -/* .. Scalar Arguments .. */ -/* COMPLEX*16 ALPHA */ -/* DOUBLE PRECISION BETA */ -/* INTEGER K,LDA,LDB,LDC,N */ -/* CHARACTER TRANS,UPLO */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZHER2K performs one of the hermitian rank 2k operations */ -/* > */ -/* > C := alpha*A*B**H + conjg( alpha )*B*A**H + beta*C, */ -/* > */ -/* > or */ -/* > */ -/* > C := alpha*A**H*B + conjg( alpha )*B**H*A + beta*C, */ -/* > */ -/* > where alpha and beta are scalars with beta real, C is an n by n */ -/* > hermitian matrix and A and B are n by k matrices in the first case */ -/* > and k by n matrices in the second case. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > On entry, UPLO specifies whether the upper or lower */ -/* > triangular part of the array C is to be referenced as */ -/* > follows: */ -/* > */ -/* > UPLO = 'U' or 'u' Only the upper triangular part of C */ -/* > is to be referenced. */ -/* > */ -/* > UPLO = 'L' or 'l' Only the lower triangular part of C */ -/* > is to be referenced. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TRANS */ -/* > \verbatim */ -/* > TRANS is CHARACTER*1 */ -/* > On entry, TRANS specifies the operation to be performed as */ -/* > follows: */ -/* > */ -/* > TRANS = 'N' or 'n' C := alpha*A*B**H + */ -/* > conjg( alpha )*B*A**H + */ -/* > beta*C. */ -/* > */ -/* > TRANS = 'C' or 'c' C := alpha*A**H*B + */ -/* > conjg( alpha )*B**H*A + */ -/* > beta*C. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > On entry, N specifies the order of the matrix C. N must be */ -/* > at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > On entry with TRANS = 'N' or 'n', K specifies the number */ -/* > of columns of the matrices A and B, and on entry with */ -/* > TRANS = 'C' or 'c', K specifies the number of rows of the */ -/* > matrices A and B. K must be at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] ALPHA */ -/* > \verbatim */ -/* > ALPHA is COMPLEX*16 . */ -/* > On entry, ALPHA specifies the scalar alpha. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is COMPLEX*16 array, dimension ( LDA, ka ), where ka is */ -/* > k when TRANS = 'N' or 'n', and is n otherwise. */ -/* > Before entry with TRANS = 'N' or 'n', the leading n by k */ -/* > part of the array A must contain the matrix A, otherwise */ -/* > the leading k by n part of the array A must contain the */ -/* > matrix A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > On entry, LDA specifies the first dimension of A as declared */ -/* > in the calling (sub) program. When TRANS = 'N' or 'n' */ -/* > then LDA must be at least max( 1, n ), otherwise LDA must */ -/* > be at least max( 1, k ). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] B */ -/* > \verbatim */ -/* > B is COMPLEX*16 array, dimension ( LDB, kb ), where kb is */ -/* > k when TRANS = 'N' or 'n', and is n otherwise. */ -/* > Before entry with TRANS = 'N' or 'n', the leading n by k */ -/* > part of the array B must contain the matrix B, otherwise */ -/* > the leading k by n part of the array B must contain the */ -/* > matrix B. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDB */ -/* > \verbatim */ -/* > LDB is INTEGER */ -/* > On entry, LDB specifies the first dimension of B as declared */ -/* > in the calling (sub) program. When TRANS = 'N' or 'n' */ -/* > then LDB must be at least max( 1, n ), otherwise LDB must */ -/* > be at least max( 1, k ). */ -/* > Unchanged on exit. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] BETA */ -/* > \verbatim */ -/* > BETA is DOUBLE PRECISION . */ -/* > On entry, BETA specifies the scalar beta. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] C */ -/* > \verbatim */ -/* > C is COMPLEX*16 array, dimension ( LDC, N ) */ -/* > Before entry with UPLO = 'U' or 'u', the leading n by n */ -/* > upper triangular part of the array C must contain the upper */ -/* > triangular part of the hermitian matrix and the strictly */ -/* > lower triangular part of C is not referenced. On exit, the */ -/* > upper triangular part of the array C is overwritten by the */ -/* > upper triangular part of the updated matrix. */ -/* > Before entry with UPLO = 'L' or 'l', the leading n by n */ -/* > lower triangular part of the array C must contain the lower */ -/* > triangular part of the hermitian matrix and the strictly */ -/* > upper triangular part of C is not referenced. On exit, the */ -/* > lower triangular part of the array C is overwritten by the */ -/* > lower triangular part of the updated matrix. */ -/* > Note that the imaginary parts of the diagonal elements need */ -/* > not be set, they are assumed to be zero, and on exit they */ -/* > are set to zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDC */ -/* > \verbatim */ -/* > LDC is INTEGER */ -/* > On entry, LDC specifies the first dimension of C as declared */ -/* > in the calling (sub) program. LDC must be at least */ -/* > max( 1, n ). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16_blas_level3 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > Level 3 Blas routine. */ -/* > */ -/* > -- Written on 8-February-1989. */ -/* > Jack Dongarra, Argonne National Laboratory. */ -/* > Iain Duff, AERE Harwell. */ -/* > Jeremy Du Croz, Numerical Algorithms Group Ltd. */ -/* > Sven Hammarling, Numerical Algorithms Group Ltd. */ -/* > */ -/* > -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1. */ -/* > Ed Anderson, Cray Research Inc. */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int zher2k_(char *uplo, char *trans, integer *n, integer *k, - doublecomplex *alpha, doublecomplex *a, integer *lda, doublecomplex * - b, integer *ldb, doublereal *beta, doublecomplex *c__, integer *ldc, - ftnlen uplo_len, ftnlen trans_len) +int zher2k_(char *uplo, char *trans, integer *n, integer *k, doublecomplex *alpha, doublecomplex *a, + integer *lda, doublecomplex *b, integer *ldb, doublereal *beta, doublecomplex *c__, + integer *ldc, ftnlen uplo_len, ftnlen trans_len) { - /* System generated locals */ - integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, - i__3, i__4, i__5, i__6, i__7; + integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, i__3, i__4, i__5, + i__6, i__7; doublereal d__1; doublecomplex z__1, z__2, z__3, z__4, z__5, z__6; - - /* Builtin functions */ void d_lmp_cnjg(doublecomplex *, doublecomplex *); - - /* Local variables */ integer i__, j, l, info; doublecomplex temp1, temp2; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer nrowa; logical upper; - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - - -/* -- Reference BLAS level3 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. Parameters .. */ -/* .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ + extern int xerbla_(char *, integer *, ftnlen); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; @@ -268,46 +26,36 @@ extern "C" { c_dim1 = *ldc; c_offset = 1 + c_dim1; c__ -= c_offset; - - /* Function Body */ if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { nrowa = *n; } else { nrowa = *k; } upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); - info = 0; - if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + if (!upper && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { info = 1; - } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, - (char *)"C", (ftnlen)1, (ftnlen)1)) { + } else if (!lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && + !lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { info = 2; } else if (*n < 0) { info = 3; } else if (*k < 0) { info = 4; - } else if (*lda < max(1,nrowa)) { + } else if (*lda < max(1, nrowa)) { info = 7; - } else if (*ldb < max(1,nrowa)) { + } else if (*ldb < max(1, nrowa)) { info = 9; - } else if (*ldc < max(1,*n)) { + } else if (*ldc < max(1, *n)) { info = 12; } if (info != 0) { xerbla_((char *)"ZHER2K", &info, (ftnlen)6); return 0; } - -/* Quick return if possible. */ - - if (*n == 0 || (alpha->r == 0. && alpha->i == 0. || *k == 0) && *beta == - 1.) { + if (*n == 0 || (alpha->r == 0. && alpha->i == 0. || *k == 0) && *beta == 1.) { return 0; } - -/* And when alpha.eq.zero. */ - if (alpha->r == 0. && alpha->i == 0.) { if (upper) { if (*beta == 0.) { @@ -317,9 +65,7 @@ extern "C" { for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * c_dim1; c__[i__3].r = 0., c__[i__3].i = 0.; -/* L10: */ } -/* L20: */ } } else { i__1 = *n; @@ -328,16 +74,13 @@ extern "C" { for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * c_dim1; i__4 = i__ + j * c_dim1; - z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[ - i__4].i; + z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[i__4].i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; -/* L30: */ } i__2 = j + j * c_dim1; i__3 = j + j * c_dim1; d__1 = *beta * c__[i__3].r; c__[i__2].r = d__1, c__[i__2].i = 0.; -/* L40: */ } } } else { @@ -348,9 +91,7 @@ extern "C" { for (i__ = j; i__ <= i__2; ++i__) { i__3 = i__ + j * c_dim1; c__[i__3].r = 0., c__[i__3].i = 0.; -/* L50: */ } -/* L60: */ } } else { i__1 = *n; @@ -363,25 +104,15 @@ extern "C" { for (i__ = j + 1; i__ <= i__2; ++i__) { i__3 = i__ + j * c_dim1; i__4 = i__ + j * c_dim1; - z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[ - i__4].i; + z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[i__4].i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; -/* L70: */ } -/* L80: */ } } } return 0; } - -/* Start the operations. */ - if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { - -/* Form C := alpha*A*B**H + conjg( alpha )*B*A**H + */ -/* C. */ - if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { @@ -390,17 +121,14 @@ extern "C" { for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * c_dim1; c__[i__3].r = 0., c__[i__3].i = 0.; -/* L90: */ } } else if (*beta != 1.) { i__2 = j - 1; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * c_dim1; i__4 = i__ + j * c_dim1; - z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[ - i__4].i; + z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[i__4].i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; -/* L100: */ } i__2 = j + j * c_dim1; i__3 = j + j * c_dim1; @@ -416,17 +144,15 @@ extern "C" { for (l = 1; l <= i__2; ++l) { i__3 = j + l * a_dim1; i__4 = j + l * b_dim1; - if (a[i__3].r != 0. || a[i__3].i != 0. || (b[i__4].r != - 0. || b[i__4].i != 0.)) { + if (a[i__3].r != 0. || a[i__3].i != 0. || + (b[i__4].r != 0. || b[i__4].i != 0.)) { d_lmp_cnjg(&z__2, &b[j + l * b_dim1]); z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, - z__1.i = alpha->r * z__2.i + alpha->i * - z__2.r; + z__1.i = alpha->r * z__2.i + alpha->i * z__2.r; temp1.r = z__1.r, temp1.i = z__1.i; i__3 = j + l * a_dim1; z__2.r = alpha->r * a[i__3].r - alpha->i * a[i__3].i, - z__2.i = alpha->r * a[i__3].i + alpha->i * a[ - i__3].r; + z__2.i = alpha->r * a[i__3].i + alpha->i * a[i__3].r; d_lmp_cnjg(&z__1, &z__2); temp2.r = z__1.r, temp2.i = z__1.i; i__3 = j - 1; @@ -434,37 +160,28 @@ extern "C" { i__4 = i__ + j * c_dim1; i__5 = i__ + j * c_dim1; i__6 = i__ + l * a_dim1; - z__3.r = a[i__6].r * temp1.r - a[i__6].i * - temp1.i, z__3.i = a[i__6].r * temp1.i + a[ - i__6].i * temp1.r; - z__2.r = c__[i__5].r + z__3.r, z__2.i = c__[i__5] - .i + z__3.i; + z__3.r = a[i__6].r * temp1.r - a[i__6].i * temp1.i, + z__3.i = a[i__6].r * temp1.i + a[i__6].i * temp1.r; + z__2.r = c__[i__5].r + z__3.r, z__2.i = c__[i__5].i + z__3.i; i__7 = i__ + l * b_dim1; - z__4.r = b[i__7].r * temp2.r - b[i__7].i * - temp2.i, z__4.i = b[i__7].r * temp2.i + b[ - i__7].i * temp2.r; - z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + - z__4.i; + z__4.r = b[i__7].r * temp2.r - b[i__7].i * temp2.i, + z__4.i = b[i__7].r * temp2.i + b[i__7].i * temp2.r; + z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; c__[i__4].r = z__1.r, c__[i__4].i = z__1.i; -/* L110: */ } i__3 = j + j * c_dim1; i__4 = j + j * c_dim1; i__5 = j + l * a_dim1; z__2.r = a[i__5].r * temp1.r - a[i__5].i * temp1.i, - z__2.i = a[i__5].r * temp1.i + a[i__5].i * - temp1.r; + z__2.i = a[i__5].r * temp1.i + a[i__5].i * temp1.r; i__6 = j + l * b_dim1; z__3.r = b[i__6].r * temp2.r - b[i__6].i * temp2.i, - z__3.i = b[i__6].r * temp2.i + b[i__6].i * - temp2.r; + z__3.i = b[i__6].r * temp2.i + b[i__6].i * temp2.r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; d__1 = c__[i__4].r + z__1.r; c__[i__3].r = d__1, c__[i__3].i = 0.; } -/* L120: */ } -/* L130: */ } } else { i__1 = *n; @@ -474,17 +191,14 @@ extern "C" { for (i__ = j; i__ <= i__2; ++i__) { i__3 = i__ + j * c_dim1; c__[i__3].r = 0., c__[i__3].i = 0.; -/* L140: */ } } else if (*beta != 1.) { i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { i__3 = i__ + j * c_dim1; i__4 = i__ + j * c_dim1; - z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[ - i__4].i; + z__1.r = *beta * c__[i__4].r, z__1.i = *beta * c__[i__4].i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; -/* L150: */ } i__2 = j + j * c_dim1; i__3 = j + j * c_dim1; @@ -500,17 +214,15 @@ extern "C" { for (l = 1; l <= i__2; ++l) { i__3 = j + l * a_dim1; i__4 = j + l * b_dim1; - if (a[i__3].r != 0. || a[i__3].i != 0. || (b[i__4].r != - 0. || b[i__4].i != 0.)) { + if (a[i__3].r != 0. || a[i__3].i != 0. || + (b[i__4].r != 0. || b[i__4].i != 0.)) { d_lmp_cnjg(&z__2, &b[j + l * b_dim1]); z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, - z__1.i = alpha->r * z__2.i + alpha->i * - z__2.r; + z__1.i = alpha->r * z__2.i + alpha->i * z__2.r; temp1.r = z__1.r, temp1.i = z__1.i; i__3 = j + l * a_dim1; z__2.r = alpha->r * a[i__3].r - alpha->i * a[i__3].i, - z__2.i = alpha->r * a[i__3].i + alpha->i * a[ - i__3].r; + z__2.i = alpha->r * a[i__3].i + alpha->i * a[i__3].r; d_lmp_cnjg(&z__1, &z__2); temp2.r = z__1.r, temp2.i = z__1.i; i__3 = *n; @@ -518,44 +230,31 @@ extern "C" { i__4 = i__ + j * c_dim1; i__5 = i__ + j * c_dim1; i__6 = i__ + l * a_dim1; - z__3.r = a[i__6].r * temp1.r - a[i__6].i * - temp1.i, z__3.i = a[i__6].r * temp1.i + a[ - i__6].i * temp1.r; - z__2.r = c__[i__5].r + z__3.r, z__2.i = c__[i__5] - .i + z__3.i; + z__3.r = a[i__6].r * temp1.r - a[i__6].i * temp1.i, + z__3.i = a[i__6].r * temp1.i + a[i__6].i * temp1.r; + z__2.r = c__[i__5].r + z__3.r, z__2.i = c__[i__5].i + z__3.i; i__7 = i__ + l * b_dim1; - z__4.r = b[i__7].r * temp2.r - b[i__7].i * - temp2.i, z__4.i = b[i__7].r * temp2.i + b[ - i__7].i * temp2.r; - z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + - z__4.i; + z__4.r = b[i__7].r * temp2.r - b[i__7].i * temp2.i, + z__4.i = b[i__7].r * temp2.i + b[i__7].i * temp2.r; + z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i; c__[i__4].r = z__1.r, c__[i__4].i = z__1.i; -/* L160: */ } i__3 = j + j * c_dim1; i__4 = j + j * c_dim1; i__5 = j + l * a_dim1; z__2.r = a[i__5].r * temp1.r - a[i__5].i * temp1.i, - z__2.i = a[i__5].r * temp1.i + a[i__5].i * - temp1.r; + z__2.i = a[i__5].r * temp1.i + a[i__5].i * temp1.r; i__6 = j + l * b_dim1; z__3.r = b[i__6].r * temp2.r - b[i__6].i * temp2.i, - z__3.i = b[i__6].r * temp2.i + b[i__6].i * - temp2.r; + z__3.i = b[i__6].r * temp2.i + b[i__6].i * temp2.r; z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; d__1 = c__[i__4].r + z__1.r; c__[i__3].r = d__1, c__[i__3].i = 0.; } -/* L170: */ } -/* L180: */ } } } else { - -/* Form C := alpha*A**H*B + conjg( alpha )*B**H*A + */ -/* C. */ - if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { @@ -568,45 +267,36 @@ extern "C" { d_lmp_cnjg(&z__3, &a[l + i__ * a_dim1]); i__4 = l + j * b_dim1; z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4].i, - z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4] - .r; + z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4].r; z__1.r = temp1.r + z__2.r, z__1.i = temp1.i + z__2.i; temp1.r = z__1.r, temp1.i = z__1.i; d_lmp_cnjg(&z__3, &b[l + i__ * b_dim1]); i__4 = l + j * a_dim1; z__2.r = z__3.r * a[i__4].r - z__3.i * a[i__4].i, - z__2.i = z__3.r * a[i__4].i + z__3.i * a[i__4] - .r; + z__2.i = z__3.r * a[i__4].i + z__3.i * a[i__4].r; z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; temp2.r = z__1.r, temp2.i = z__1.i; -/* L190: */ } if (i__ == j) { if (*beta == 0.) { i__3 = j + j * c_dim1; z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, - z__2.i = alpha->r * temp1.i + alpha->i * - temp1.r; + z__2.i = alpha->r * temp1.i + alpha->i * temp1.r; d_lmp_cnjg(&z__4, alpha); z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, - z__3.i = z__4.r * temp2.i + z__4.i * - temp2.r; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; + z__3.i = z__4.r * temp2.i + z__4.i * temp2.r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; d__1 = z__1.r; c__[i__3].r = d__1, c__[i__3].i = 0.; } else { i__3 = j + j * c_dim1; i__4 = j + j * c_dim1; z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, - z__2.i = alpha->r * temp1.i + alpha->i * - temp1.r; + z__2.i = alpha->r * temp1.i + alpha->i * temp1.r; d_lmp_cnjg(&z__4, alpha); z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, - z__3.i = z__4.r * temp2.i + z__4.i * - temp2.r; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; + z__3.i = z__4.r * temp2.i + z__4.i * temp2.r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; d__1 = *beta * c__[i__4].r + z__1.r; c__[i__3].r = d__1, c__[i__3].i = 0.; } @@ -614,37 +304,27 @@ extern "C" { if (*beta == 0.) { i__3 = i__ + j * c_dim1; z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, - z__2.i = alpha->r * temp1.i + alpha->i * - temp1.r; + z__2.i = alpha->r * temp1.i + alpha->i * temp1.r; d_lmp_cnjg(&z__4, alpha); z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, - z__3.i = z__4.r * temp2.i + z__4.i * - temp2.r; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; + z__3.i = z__4.r * temp2.i + z__4.i * temp2.r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } else { i__3 = i__ + j * c_dim1; i__4 = i__ + j * c_dim1; - z__3.r = *beta * c__[i__4].r, z__3.i = *beta * - c__[i__4].i; + z__3.r = *beta * c__[i__4].r, z__3.i = *beta * c__[i__4].i; z__4.r = alpha->r * temp1.r - alpha->i * temp1.i, - z__4.i = alpha->r * temp1.i + alpha->i * - temp1.r; - z__2.r = z__3.r + z__4.r, z__2.i = z__3.i + - z__4.i; + z__4.i = alpha->r * temp1.i + alpha->i * temp1.r; + z__2.r = z__3.r + z__4.r, z__2.i = z__3.i + z__4.i; d_lmp_cnjg(&z__6, alpha); z__5.r = z__6.r * temp2.r - z__6.i * temp2.i, - z__5.i = z__6.r * temp2.i + z__6.i * - temp2.r; - z__1.r = z__2.r + z__5.r, z__1.i = z__2.i + - z__5.i; + z__5.i = z__6.r * temp2.i + z__6.i * temp2.r; + z__1.r = z__2.r + z__5.r, z__1.i = z__2.i + z__5.i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } } -/* L200: */ } -/* L210: */ } } else { i__1 = *n; @@ -658,45 +338,36 @@ extern "C" { d_lmp_cnjg(&z__3, &a[l + i__ * a_dim1]); i__4 = l + j * b_dim1; z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4].i, - z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4] - .r; + z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4].r; z__1.r = temp1.r + z__2.r, z__1.i = temp1.i + z__2.i; temp1.r = z__1.r, temp1.i = z__1.i; d_lmp_cnjg(&z__3, &b[l + i__ * b_dim1]); i__4 = l + j * a_dim1; z__2.r = z__3.r * a[i__4].r - z__3.i * a[i__4].i, - z__2.i = z__3.r * a[i__4].i + z__3.i * a[i__4] - .r; + z__2.i = z__3.r * a[i__4].i + z__3.i * a[i__4].r; z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i; temp2.r = z__1.r, temp2.i = z__1.i; -/* L220: */ } if (i__ == j) { if (*beta == 0.) { i__3 = j + j * c_dim1; z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, - z__2.i = alpha->r * temp1.i + alpha->i * - temp1.r; + z__2.i = alpha->r * temp1.i + alpha->i * temp1.r; d_lmp_cnjg(&z__4, alpha); z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, - z__3.i = z__4.r * temp2.i + z__4.i * - temp2.r; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; + z__3.i = z__4.r * temp2.i + z__4.i * temp2.r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; d__1 = z__1.r; c__[i__3].r = d__1, c__[i__3].i = 0.; } else { i__3 = j + j * c_dim1; i__4 = j + j * c_dim1; z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, - z__2.i = alpha->r * temp1.i + alpha->i * - temp1.r; + z__2.i = alpha->r * temp1.i + alpha->i * temp1.r; d_lmp_cnjg(&z__4, alpha); z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, - z__3.i = z__4.r * temp2.i + z__4.i * - temp2.r; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; + z__3.i = z__4.r * temp2.i + z__4.i * temp2.r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; d__1 = *beta * c__[i__4].r + z__1.r; c__[i__3].r = d__1, c__[i__3].i = 0.; } @@ -704,47 +375,32 @@ extern "C" { if (*beta == 0.) { i__3 = i__ + j * c_dim1; z__2.r = alpha->r * temp1.r - alpha->i * temp1.i, - z__2.i = alpha->r * temp1.i + alpha->i * - temp1.r; + z__2.i = alpha->r * temp1.i + alpha->i * temp1.r; d_lmp_cnjg(&z__4, alpha); z__3.r = z__4.r * temp2.r - z__4.i * temp2.i, - z__3.i = z__4.r * temp2.i + z__4.i * - temp2.r; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; + z__3.i = z__4.r * temp2.i + z__4.i * temp2.r; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } else { i__3 = i__ + j * c_dim1; i__4 = i__ + j * c_dim1; - z__3.r = *beta * c__[i__4].r, z__3.i = *beta * - c__[i__4].i; + z__3.r = *beta * c__[i__4].r, z__3.i = *beta * c__[i__4].i; z__4.r = alpha->r * temp1.r - alpha->i * temp1.i, - z__4.i = alpha->r * temp1.i + alpha->i * - temp1.r; - z__2.r = z__3.r + z__4.r, z__2.i = z__3.i + - z__4.i; + z__4.i = alpha->r * temp1.i + alpha->i * temp1.r; + z__2.r = z__3.r + z__4.r, z__2.i = z__3.i + z__4.i; d_lmp_cnjg(&z__6, alpha); z__5.r = z__6.r * temp2.r - z__6.i * temp2.i, - z__5.i = z__6.r * temp2.i + z__6.i * - temp2.r; - z__1.r = z__2.r + z__5.r, z__1.i = z__2.i + - z__5.i; + z__5.i = z__6.r * temp2.i + z__6.i * temp2.r; + z__1.r = z__2.r + z__5.r, z__1.i = z__2.i + z__5.i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; } } -/* L230: */ } -/* L240: */ } } } - return 0; - -/* End of ZHER2K */ - -} /* zher2k_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zhetd2.cpp b/lib/linalg/zhetd2.cpp index 71ad2aeab4..46ec1316e0 100644 --- a/lib/linalg/zhetd2.cpp +++ b/lib/linalg/zhetd2.cpp @@ -1,272 +1,44 @@ -/* fortran/zhetd2.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - -static doublecomplex c_b2 = {0.,0.}; +static doublecomplex c_b2 = {0., 0.}; static integer c__1 = 1; - -/* > \brief \b ZHETD2 reduces a Hermitian matrix to real symmetric tridiagonal form by an unitary similarity t -ransformation (unblocked algorithm). */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZHETD2 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZHETD2( UPLO, N, A, LDA, D, E, TAU, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER UPLO */ -/* INTEGER INFO, LDA, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION D( * ), E( * ) */ -/* COMPLEX*16 A( LDA, * ), TAU( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZHETD2 reduces a complex Hermitian matrix A to real symmetric */ -/* > tridiagonal form T by a unitary similarity transformation: */ -/* > Q**H * A * Q = T. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > Specifies whether the upper or lower triangular part of the */ -/* > Hermitian matrix A is stored: */ -/* > = 'U': Upper triangular */ -/* > = 'L': Lower triangular */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is COMPLEX*16 array, dimension (LDA,N) */ -/* > On entry, the Hermitian matrix A. If UPLO = 'U', the leading */ -/* > n-by-n upper triangular part of A contains the upper */ -/* > triangular part of the matrix A, and the strictly lower */ -/* > triangular part of A is not referenced. If UPLO = 'L', the */ -/* > leading n-by-n lower triangular part of A contains the lower */ -/* > triangular part of the matrix A, and the strictly upper */ -/* > triangular part of A is not referenced. */ -/* > On exit, if UPLO = 'U', the diagonal and first superdiagonal */ -/* > of A are overwritten by the corresponding elements of the */ -/* > tridiagonal matrix T, and the elements above the first */ -/* > superdiagonal, with the array TAU, represent the unitary */ -/* > matrix Q as a product of elementary reflectors; if UPLO */ -/* > = 'L', the diagonal and first subdiagonal of A are over- */ -/* > written by the corresponding elements of the tridiagonal */ -/* > matrix T, and the elements below the first subdiagonal, with */ -/* > the array TAU, represent the unitary matrix Q as a product */ -/* > of elementary reflectors. See Further Details. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension (N) */ -/* > The diagonal elements of the tridiagonal matrix T: */ -/* > D(i) = A(i,i). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] E */ -/* > \verbatim */ -/* > E is DOUBLE PRECISION array, dimension (N-1) */ -/* > The off-diagonal elements of the tridiagonal matrix T: */ -/* > E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] TAU */ -/* > \verbatim */ -/* > TAU is COMPLEX*16 array, dimension (N-1) */ -/* > The scalar factors of the elementary reflectors (see Further */ -/* > Details). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16HEcomputational */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > If UPLO = 'U', the matrix Q is represented as a product of elementary */ -/* > reflectors */ -/* > */ -/* > Q = H(n-1) . . . H(2) H(1). */ -/* > */ -/* > Each H(i) has the form */ -/* > */ -/* > H(i) = I - tau * v * v**H */ -/* > */ -/* > where tau is a complex scalar, and v is a complex vector with */ -/* > v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in */ -/* > A(1:i-1,i+1), and tau in TAU(i). */ -/* > */ -/* > If UPLO = 'L', the matrix Q is represented as a product of elementary */ -/* > reflectors */ -/* > */ -/* > Q = H(1) H(2) . . . H(n-1). */ -/* > */ -/* > Each H(i) has the form */ -/* > */ -/* > H(i) = I - tau * v * v**H */ -/* > */ -/* > where tau is a complex scalar, and v is a complex vector with */ -/* > v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), */ -/* > and tau in TAU(i). */ -/* > */ -/* > The contents of A on exit are illustrated by the following examples */ -/* > with n = 5: */ -/* > */ -/* > if UPLO = 'U': if UPLO = 'L': */ -/* > */ -/* > ( d e v2 v3 v4 ) ( d ) */ -/* > ( d e v3 v4 ) ( e d ) */ -/* > ( d e v4 ) ( v1 e d ) */ -/* > ( d e ) ( v1 v2 e d ) */ -/* > ( d ) ( v1 v2 v3 e d ) */ -/* > */ -/* > where d and e denote diagonal and off-diagonal elements of T, and vi */ -/* > denotes an element of the vector defining H(i). */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int zhetd2_(char *uplo, integer *n, doublecomplex *a, - integer *lda, doublereal *d__, doublereal *e, doublecomplex *tau, - integer *info, ftnlen uplo_len) +int zhetd2_(char *uplo, integer *n, doublecomplex *a, integer *lda, doublereal *d__, doublereal *e, + doublecomplex *tau, integer *info, ftnlen uplo_len) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; doublereal d__1; doublecomplex z__1, z__2, z__3, z__4; - - /* Local variables */ integer i__; doublecomplex taui; - extern /* Subroutine */ int zher2_(char *, integer *, doublecomplex *, - doublecomplex *, integer *, doublecomplex *, integer *, - doublecomplex *, integer *, ftnlen); + extern int zher2_(char *, integer *, doublecomplex *, doublecomplex *, integer *, + doublecomplex *, integer *, doublecomplex *, integer *, ftnlen); doublecomplex alpha; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *, - doublecomplex *, integer *, doublecomplex *, integer *); - extern /* Subroutine */ int zhemv_(char *, integer *, doublecomplex *, - doublecomplex *, integer *, doublecomplex *, integer *, - doublecomplex *, doublecomplex *, integer *, ftnlen); + extern VOID zdotc_(doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, + integer *); + extern int zhemv_(char *, integer *, doublecomplex *, doublecomplex *, integer *, + doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, + ftnlen); logical upper; - extern /* Subroutine */ int zaxpy_(integer *, doublecomplex *, - doublecomplex *, integer *, doublecomplex *, integer *), xerbla_( - char *, integer *, ftnlen), zlarfg_(integer *, doublecomplex *, - doublecomplex *, integer *, doublecomplex *); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters */ - - /* Parameter adjustments */ + extern int zaxpy_(integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, + integer *), + xerbla_(char *, integer *, ftnlen), + zlarfg_(integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --d__; --e; --tau; - - /* Function Body */ *info = 0; upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); - if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + if (!upper && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { *info = -1; } else if (*n < 0) { *info = -2; - } else if (*lda < max(1,*n)) { + } else if (*lda < max(1, *n)) { *info = -4; } if (*info != 0) { @@ -274,63 +46,35 @@ f"> */ xerbla_((char *)"ZHETD2", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*n <= 0) { return 0; } - if (upper) { - -/* Reduce the upper triangle of A */ - i__1 = *n + *n * a_dim1; i__2 = *n + *n * a_dim1; d__1 = a[i__2].r; a[i__1].r = d__1, a[i__1].i = 0.; for (i__ = *n - 1; i__ >= 1; --i__) { - -/* Generate elementary reflector H(i) = I - tau * v * v**H */ -/* to annihilate A(1:i-1,i+1) */ - i__1 = i__ + (i__ + 1) * a_dim1; alpha.r = a[i__1].r, alpha.i = a[i__1].i; zlarfg_(&i__, &alpha, &a[(i__ + 1) * a_dim1 + 1], &c__1, &taui); e[i__] = alpha.r; - if (taui.r != 0. || taui.i != 0.) { - -/* Apply H(i) from both sides to A(1:i,1:i) */ - i__1 = i__ + (i__ + 1) * a_dim1; a[i__1].r = 1., a[i__1].i = 0.; - -/* Compute x := tau * A * v storing x in TAU(1:i) */ - - zhemv_(uplo, &i__, &taui, &a[a_offset], lda, &a[(i__ + 1) * - a_dim1 + 1], &c__1, &c_b2, &tau[1], &c__1, (ftnlen)1); - -/* Compute w := x - 1/2 * tau * (x**H * v) * v */ - + zhemv_(uplo, &i__, &taui, &a[a_offset], lda, &a[(i__ + 1) * a_dim1 + 1], &c__1, + &c_b2, &tau[1], &c__1, (ftnlen)1); z__3.r = -.5, z__3.i = -0.; - z__2.r = z__3.r * taui.r - z__3.i * taui.i, z__2.i = z__3.r * - taui.i + z__3.i * taui.r; - zdotc_(&z__4, &i__, &tau[1], &c__1, &a[(i__ + 1) * a_dim1 + 1] - , &c__1); - z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, z__1.i = z__2.r * - z__4.i + z__2.i * z__4.r; + z__2.r = z__3.r * taui.r - z__3.i * taui.i, + z__2.i = z__3.r * taui.i + z__3.i * taui.r; + zdotc_(&z__4, &i__, &tau[1], &c__1, &a[(i__ + 1) * a_dim1 + 1], &c__1); + z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, + z__1.i = z__2.r * z__4.i + z__2.i * z__4.r; alpha.r = z__1.r, alpha.i = z__1.i; - zaxpy_(&i__, &alpha, &a[(i__ + 1) * a_dim1 + 1], &c__1, &tau[ - 1], &c__1); - -/* Apply the transformation as a rank-2 update: */ -/* A := A - v * w**H - w * v**H */ - + zaxpy_(&i__, &alpha, &a[(i__ + 1) * a_dim1 + 1], &c__1, &tau[1], &c__1); z__1.r = -1., z__1.i = -0.; - zher2_(uplo, &i__, &z__1, &a[(i__ + 1) * a_dim1 + 1], &c__1, & - tau[1], &c__1, &a[a_offset], lda, (ftnlen)1); - + zher2_(uplo, &i__, &z__1, &a[(i__ + 1) * a_dim1 + 1], &c__1, &tau[1], &c__1, + &a[a_offset], lda, (ftnlen)1); } else { i__1 = i__ + i__ * a_dim1; i__2 = i__ + i__ * a_dim1; @@ -344,71 +88,42 @@ f"> */ d__[i__ + 1] = a[i__1].r; i__1 = i__; tau[i__1].r = taui.r, tau[i__1].i = taui.i; -/* L10: */ } i__1 = a_dim1 + 1; d__[1] = a[i__1].r; } else { - -/* Reduce the lower triangle of A */ - i__1 = a_dim1 + 1; i__2 = a_dim1 + 1; d__1 = a[i__2].r; a[i__1].r = d__1, a[i__1].i = 0.; i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { - -/* Generate elementary reflector H(i) = I - tau * v * v**H */ -/* to annihilate A(i+2:n,i) */ - i__2 = i__ + 1 + i__ * a_dim1; alpha.r = a[i__2].r, alpha.i = a[i__2].i; i__2 = *n - i__; -/* Computing MIN */ i__3 = i__ + 2; - zlarfg_(&i__2, &alpha, &a[min(i__3,*n) + i__ * a_dim1], &c__1, & - taui); + zlarfg_(&i__2, &alpha, &a[min(i__3, *n) + i__ * a_dim1], &c__1, &taui); e[i__] = alpha.r; - if (taui.r != 0. || taui.i != 0.) { - -/* Apply H(i) from both sides to A(i+1:n,i+1:n) */ - i__2 = i__ + 1 + i__ * a_dim1; a[i__2].r = 1., a[i__2].i = 0.; - -/* Compute x := tau * A * v storing y in TAU(i:n-1) */ - i__2 = *n - i__; - zhemv_(uplo, &i__2, &taui, &a[i__ + 1 + (i__ + 1) * a_dim1], - lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b2, &tau[ - i__], &c__1, (ftnlen)1); - -/* Compute w := x - 1/2 * tau * (x**H * v) * v */ - + zhemv_(uplo, &i__2, &taui, &a[i__ + 1 + (i__ + 1) * a_dim1], lda, + &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b2, &tau[i__], &c__1, (ftnlen)1); z__3.r = -.5, z__3.i = -0.; - z__2.r = z__3.r * taui.r - z__3.i * taui.i, z__2.i = z__3.r * - taui.i + z__3.i * taui.r; + z__2.r = z__3.r * taui.r - z__3.i * taui.i, + z__2.i = z__3.r * taui.i + z__3.i * taui.r; i__2 = *n - i__; - zdotc_(&z__4, &i__2, &tau[i__], &c__1, &a[i__ + 1 + i__ * - a_dim1], &c__1); - z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, z__1.i = z__2.r * - z__4.i + z__2.i * z__4.r; + zdotc_(&z__4, &i__2, &tau[i__], &c__1, &a[i__ + 1 + i__ * a_dim1], &c__1); + z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, + z__1.i = z__2.r * z__4.i + z__2.i * z__4.r; alpha.r = z__1.r, alpha.i = z__1.i; i__2 = *n - i__; - zaxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &tau[ - i__], &c__1); - -/* Apply the transformation as a rank-2 update: */ -/* A := A - v * w**H - w * v**H */ - + zaxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &tau[i__], &c__1); i__2 = *n - i__; z__1.r = -1., z__1.i = -0.; - zher2_(uplo, &i__2, &z__1, &a[i__ + 1 + i__ * a_dim1], &c__1, - &tau[i__], &c__1, &a[i__ + 1 + (i__ + 1) * a_dim1], - lda, (ftnlen)1); - + zher2_(uplo, &i__2, &z__1, &a[i__ + 1 + i__ * a_dim1], &c__1, &tau[i__], &c__1, + &a[i__ + 1 + (i__ + 1) * a_dim1], lda, (ftnlen)1); } else { i__2 = i__ + 1 + (i__ + 1) * a_dim1; i__3 = i__ + 1 + (i__ + 1) * a_dim1; @@ -422,18 +137,12 @@ f"> */ d__[i__] = a[i__2].r; i__2 = i__; tau[i__2].r = taui.r, tau[i__2].i = taui.i; -/* L20: */ } i__1 = *n + *n * a_dim1; d__[*n] = a[i__1].r; } - return 0; - -/* End of ZHETD2 */ - -} /* zhetd2_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zhetrd.cpp b/lib/linalg/zhetrd.cpp index ed3de347ef..94df1e8159 100644 --- a/lib/linalg/zhetrd.cpp +++ b/lib/linalg/zhetrd.cpp @@ -1,275 +1,33 @@ -/* fortran/zhetrd.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static integer c_n1 = -1; static integer c__3 = 3; static integer c__2 = 2; static doublereal c_b23 = 1.; - -/* > \brief \b ZHETRD */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZHETRD + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZHETRD( UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER UPLO */ -/* INTEGER INFO, LDA, LWORK, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION D( * ), E( * ) */ -/* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZHETRD reduces a complex Hermitian matrix A to real symmetric */ -/* > tridiagonal form T by a unitary similarity transformation: */ -/* > Q**H * A * Q = T. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > = 'U': Upper triangle of A is stored; */ -/* > = 'L': Lower triangle of A is stored. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is COMPLEX*16 array, dimension (LDA,N) */ -/* > On entry, the Hermitian matrix A. If UPLO = 'U', the leading */ -/* > N-by-N upper triangular part of A contains the upper */ -/* > triangular part of the matrix A, and the strictly lower */ -/* > triangular part of A is not referenced. If UPLO = 'L', the */ -/* > leading N-by-N lower triangular part of A contains the lower */ -/* > triangular part of the matrix A, and the strictly upper */ -/* > triangular part of A is not referenced. */ -/* > On exit, if UPLO = 'U', the diagonal and first superdiagonal */ -/* > of A are overwritten by the corresponding elements of the */ -/* > tridiagonal matrix T, and the elements above the first */ -/* > superdiagonal, with the array TAU, represent the unitary */ -/* > matrix Q as a product of elementary reflectors; if UPLO */ -/* > = 'L', the diagonal and first subdiagonal of A are over- */ -/* > written by the corresponding elements of the tridiagonal */ -/* > matrix T, and the elements below the first subdiagonal, with */ -/* > the array TAU, represent the unitary matrix Q as a product */ -/* > of elementary reflectors. See Further Details. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension (N) */ -/* > The diagonal elements of the tridiagonal matrix T: */ -/* > D(i) = A(i,i). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] E */ -/* > \verbatim */ -/* > E is DOUBLE PRECISION array, dimension (N-1) */ -/* > The off-diagonal elements of the tridiagonal matrix T: */ -/* > E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] TAU */ -/* > \verbatim */ -/* > TAU is COMPLEX*16 array, dimension (N-1) */ -/* > The scalar factors of the elementary reflectors (see Further */ -/* > Details). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) */ -/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LWORK */ -/* > \verbatim */ -/* > LWORK is INTEGER */ -/* > The dimension of the array WORK. LWORK >= 1. */ -/* > For optimum performance LWORK >= N*NB, where NB is the */ -/* > optimal blocksize. */ -/* > */ -/* > If LWORK = -1, then a workspace query is assumed; the routine */ -/* > only calculates the optimal size of the WORK array, returns */ -/* > this value as the first entry of the WORK array, and no error */ -/* > message related to LWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16HEcomputational */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > If UPLO = 'U', the matrix Q is represented as a product of elementary */ -/* > reflectors */ -/* > */ -/* > Q = H(n-1) . . . H(2) H(1). */ -/* > */ -/* > Each H(i) has the form */ -/* > */ -/* > H(i) = I - tau * v * v**H */ -/* > */ -/* > where tau is a complex scalar, and v is a complex vector with */ -/* > v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in */ -/* > A(1:i-1,i+1), and tau in TAU(i). */ -/* > */ -/* > If UPLO = 'L', the matrix Q is represented as a product of elementary */ -/* > reflectors */ -/* > */ -/* > Q = H(1) H(2) . . . H(n-1). */ -/* > */ -/* > Each H(i) has the form */ -/* > */ -/* > H(i) = I - tau * v * v**H */ -/* > */ -/* > where tau is a complex scalar, and v is a complex vector with */ -/* > v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), */ -/* > and tau in TAU(i). */ -/* > */ -/* > The contents of A on exit are illustrated by the following examples */ -/* > with n = 5: */ -/* > */ -/* > if UPLO = 'U': if UPLO = 'L': */ -/* > */ -/* > ( d e v2 v3 v4 ) ( d ) */ -/* > ( d e v3 v4 ) ( e d ) */ -/* > ( d e v4 ) ( v1 e d ) */ -/* > ( d e ) ( v1 v2 e d ) */ -/* > ( d ) ( v1 v2 v3 e d ) */ -/* > */ -/* > where d and e denote diagonal and off-diagonal elements of T, and vi */ -/* > denotes an element of the vector defining H(i). */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int zhetrd_(char *uplo, integer *n, doublecomplex *a, - integer *lda, doublereal *d__, doublereal *e, doublecomplex *tau, - doublecomplex *work, integer *lwork, integer *info, ftnlen uplo_len) +int zhetrd_(char *uplo, integer *n, doublecomplex *a, integer *lda, doublereal *d__, doublereal *e, + doublecomplex *tau, doublecomplex *work, integer *lwork, integer *info, ftnlen uplo_len) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; doublecomplex z__1; - - /* Local variables */ integer i__, j, nb, kk, nx, iws; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer nbmin, iinfo; logical upper; - extern /* Subroutine */ int zhetd2_(char *, integer *, doublecomplex *, - integer *, doublereal *, doublereal *, doublecomplex *, integer *, - ftnlen), zher2k_(char *, char *, integer *, integer *, - doublecomplex *, doublecomplex *, integer *, doublecomplex *, - integer *, doublereal *, doublecomplex *, integer *, ftnlen, - ftnlen), xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - extern /* Subroutine */ int zlatrd_(char *, integer *, integer *, - doublecomplex *, integer *, doublereal *, doublecomplex *, - doublecomplex *, integer *, ftnlen); + extern int zhetd2_(char *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, + doublecomplex *, integer *, ftnlen), + zher2k_(char *, char *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, + doublecomplex *, integer *, doublereal *, doublecomplex *, integer *, ftnlen, + ftnlen), + xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); + extern int zlatrd_(char *, integer *, integer *, doublecomplex *, integer *, doublereal *, + doublecomplex *, doublecomplex *, integer *, ftnlen); integer ldwork, lwkopt; logical lquery; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; @@ -277,31 +35,23 @@ f"> */ --e; --tau; --work; - - /* Function Body */ *info = 0; upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); lquery = *lwork == -1; - if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + if (!upper && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { *info = -1; } else if (*n < 0) { *info = -2; - } else if (*lda < max(1,*n)) { + } else if (*lda < max(1, *n)) { *info = -4; - } else if (*lwork < 1 && ! lquery) { + } else if (*lwork < 1 && !lquery) { *info = -9; } - if (*info == 0) { - -/* Determine the block size. */ - - nb = ilaenv_(&c__1, (char *)"ZHETRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, - (ftnlen)1); + nb = ilaenv_(&c__1, (char *)"ZHETRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); lwkopt = *n * nb; - work[1].r = (doublereal) lwkopt, work[1].i = 0.; + work[1].r = (doublereal)lwkopt, work[1].i = 0.; } - if (*info != 0) { i__1 = -(*info); xerbla_((char *)"ZHETRD", &i__1, (ftnlen)6); @@ -309,42 +59,24 @@ f"> */ } else if (lquery) { return 0; } - -/* Quick return if possible */ - if (*n == 0) { work[1].r = 1., work[1].i = 0.; return 0; } - nx = *n; iws = 1; if (nb > 1 && nb < *n) { - -/* Determine when to cross over from blocked to unblocked code */ -/* (last block is always handled by unblocked code). */ - -/* Computing MAX */ - i__1 = nb, i__2 = ilaenv_(&c__3, (char *)"ZHETRD", uplo, n, &c_n1, &c_n1, & - c_n1, (ftnlen)6, (ftnlen)1); - nx = max(i__1,i__2); + i__1 = nb, + i__2 = ilaenv_(&c__3, (char *)"ZHETRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); + nx = max(i__1, i__2); if (nx < *n) { - -/* Determine if workspace is large enough for blocked code. */ - ldwork = *n; iws = ldwork * nb; if (*lwork < iws) { - -/* Not enough workspace to use optimal NB: determine the */ -/* minimum value of NB, and reduce NB or force use of */ -/* unblocked code by setting NX = N. */ - -/* Computing MAX */ i__1 = *lwork / ldwork; - nb = max(i__1,1); - nbmin = ilaenv_(&c__2, (char *)"ZHETRD", uplo, n, &c_n1, &c_n1, &c_n1, - (ftnlen)6, (ftnlen)1); + nb = max(i__1, 1); + nbmin = + ilaenv_(&c__2, (char *)"ZHETRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); if (nb < nbmin) { nx = *n; } @@ -355,38 +87,18 @@ f"> */ } else { nb = 1; } - if (upper) { - -/* Reduce the upper triangle of A. */ -/* Columns 1:kk are handled by the unblocked method. */ - kk = *n - (*n - nx + nb - 1) / nb * nb; i__1 = kk + 1; i__2 = -nb; - for (i__ = *n - nb + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += - i__2) { - -/* Reduce columns i:i+nb-1 to tridiagonal form and form the */ -/* matrix W which is needed to update the unreduced part of */ -/* the matrix */ - + for (i__ = *n - nb + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { i__3 = i__ + nb - 1; - zlatrd_(uplo, &i__3, &nb, &a[a_offset], lda, &e[1], &tau[1], & - work[1], &ldwork, (ftnlen)1); - -/* Update the unreduced submatrix A(1:i-1,1:i-1), using an */ -/* update of the form: A := A - V*W**H - W*V**H */ - + zlatrd_(uplo, &i__3, &nb, &a[a_offset], lda, &e[1], &tau[1], &work[1], &ldwork, + (ftnlen)1); i__3 = i__ - 1; z__1.r = -1., z__1.i = -0.; - zher2k_(uplo, (char *)"No transpose", &i__3, &nb, &z__1, &a[i__ * a_dim1 - + 1], lda, &work[1], &ldwork, &c_b23, &a[a_offset], lda, ( - ftnlen)1, (ftnlen)12); - -/* Copy superdiagonal elements back into A, and diagonal */ -/* elements into D */ - + zher2k_(uplo, (char *)"No transpose", &i__3, &nb, &z__1, &a[i__ * a_dim1 + 1], lda, &work[1], + &ldwork, &c_b23, &a[a_offset], lda, (ftnlen)1, (ftnlen)12); i__3 = i__ + nb - 1; for (j = i__; j <= i__3; ++j) { i__4 = j - 1 + j * a_dim1; @@ -394,44 +106,21 @@ f"> */ a[i__4].r = e[i__5], a[i__4].i = 0.; i__4 = j + j * a_dim1; d__[j] = a[i__4].r; -/* L10: */ } -/* L20: */ } - -/* Use unblocked code to reduce the last or only block */ - - zhetd2_(uplo, &kk, &a[a_offset], lda, &d__[1], &e[1], &tau[1], &iinfo, - (ftnlen)1); + zhetd2_(uplo, &kk, &a[a_offset], lda, &d__[1], &e[1], &tau[1], &iinfo, (ftnlen)1); } else { - -/* Reduce the lower triangle of A */ - i__2 = *n - nx; i__1 = nb; for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) { - -/* Reduce columns i:i+nb-1 to tridiagonal form and form the */ -/* matrix W which is needed to update the unreduced part of */ -/* the matrix */ - i__3 = *n - i__ + 1; - zlatrd_(uplo, &i__3, &nb, &a[i__ + i__ * a_dim1], lda, &e[i__], & - tau[i__], &work[1], &ldwork, (ftnlen)1); - -/* Update the unreduced submatrix A(i+nb:n,i+nb:n), using */ -/* an update of the form: A := A - V*W**H - W*V**H */ - + zlatrd_(uplo, &i__3, &nb, &a[i__ + i__ * a_dim1], lda, &e[i__], &tau[i__], &work[1], + &ldwork, (ftnlen)1); i__3 = *n - i__ - nb + 1; z__1.r = -1., z__1.i = -0.; - zher2k_(uplo, (char *)"No transpose", &i__3, &nb, &z__1, &a[i__ + nb + - i__ * a_dim1], lda, &work[nb + 1], &ldwork, &c_b23, &a[ - i__ + nb + (i__ + nb) * a_dim1], lda, (ftnlen)1, (ftnlen) - 12); - -/* Copy subdiagonal elements back into A, and diagonal */ -/* elements into D */ - + zher2k_(uplo, (char *)"No transpose", &i__3, &nb, &z__1, &a[i__ + nb + i__ * a_dim1], lda, + &work[nb + 1], &ldwork, &c_b23, &a[i__ + nb + (i__ + nb) * a_dim1], lda, + (ftnlen)1, (ftnlen)12); i__3 = i__ + nb - 1; for (j = i__; j <= i__3; ++j) { i__4 = j + 1 + j * a_dim1; @@ -439,25 +128,15 @@ f"> */ a[i__4].r = e[i__5], a[i__4].i = 0.; i__4 = j + j * a_dim1; d__[j] = a[i__4].r; -/* L30: */ } -/* L40: */ } - -/* Use unblocked code to reduce the last or only block */ - i__1 = *n - i__ + 1; - zhetd2_(uplo, &i__1, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[i__], - &tau[i__], &iinfo, (ftnlen)1); + zhetd2_(uplo, &i__1, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[i__], &tau[i__], &iinfo, + (ftnlen)1); } - - work[1].r = (doublereal) lwkopt, work[1].i = 0.; + work[1].r = (doublereal)lwkopt, work[1].i = 0.; return 0; - -/* End of ZHETRD */ - -} /* zhetrd_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zhpr.cpp b/lib/linalg/zhpr.cpp index 29ed826c46..9e1e441830 100644 --- a/lib/linalg/zhpr.cpp +++ b/lib/linalg/zhpr.cpp @@ -1,198 +1,22 @@ -/* fortran/zhpr.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b ZHPR */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZHPR(UPLO,N,ALPHA,X,INCX,AP) */ - -/* .. Scalar Arguments .. */ -/* DOUBLE PRECISION ALPHA */ -/* INTEGER INCX,N */ -/* CHARACTER UPLO */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 AP(*),X(*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZHPR performs the hermitian rank 1 operation */ -/* > */ -/* > A := alpha*x*x**H + A, */ -/* > */ -/* > where alpha is a real scalar, x is an n element vector and A is an */ -/* > n by n hermitian matrix, supplied in packed form. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > On entry, UPLO specifies whether the upper or lower */ -/* > triangular part of the matrix A is supplied in the packed */ -/* > array AP as follows: */ -/* > */ -/* > UPLO = 'U' or 'u' The upper triangular part of A is */ -/* > supplied in AP. */ -/* > */ -/* > UPLO = 'L' or 'l' The lower triangular part of A is */ -/* > supplied in AP. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > On entry, N specifies the order of the matrix A. */ -/* > N must be at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] ALPHA */ -/* > \verbatim */ -/* > ALPHA is DOUBLE PRECISION. */ -/* > On entry, ALPHA specifies the scalar alpha. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] X */ -/* > \verbatim */ -/* > X is COMPLEX*16 array, dimension at least */ -/* > ( 1 + ( n - 1 )*abs( INCX ) ). */ -/* > Before entry, the incremented array X must contain the n */ -/* > element vector x. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > On entry, INCX specifies the increment for the elements of */ -/* > X. INCX must not be zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] AP */ -/* > \verbatim */ -/* > AP is COMPLEX*16 array, dimension at least */ -/* > ( ( n*( n + 1 ) )/2 ). */ -/* > Before entry with UPLO = 'U' or 'u', the array AP must */ -/* > contain the upper triangular part of the hermitian matrix */ -/* > packed sequentially, column by column, so that AP( 1 ) */ -/* > contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) */ -/* > and a( 2, 2 ) respectively, and so on. On exit, the array */ -/* > AP is overwritten by the upper triangular part of the */ -/* > updated matrix. */ -/* > Before entry with UPLO = 'L' or 'l', the array AP must */ -/* > contain the lower triangular part of the hermitian matrix */ -/* > packed sequentially, column by column, so that AP( 1 ) */ -/* > contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) */ -/* > and a( 3, 1 ) respectively, and so on. On exit, the array */ -/* > AP is overwritten by the lower triangular part of the */ -/* > updated matrix. */ -/* > Note that the imaginary parts of the diagonal elements need */ -/* > not be set, they are assumed to be zero, and on exit they */ -/* > are set to zero. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16_blas_level2 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > Level 2 Blas routine. */ -/* > */ -/* > -- Written on 22-October-1986. */ -/* > Jack Dongarra, Argonne National Lab. */ -/* > Jeremy Du Croz, Nag Central Office. */ -/* > Sven Hammarling, Nag Central Office. */ -/* > Richard Hanson, Sandia National Labs. */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int zhpr_(char *uplo, integer *n, doublereal *alpha, - doublecomplex *x, integer *incx, doublecomplex *ap, ftnlen uplo_len) +int zhpr_(char *uplo, integer *n, doublereal *alpha, doublecomplex *x, integer *incx, + doublecomplex *ap, ftnlen uplo_len) { - /* System generated locals */ integer i__1, i__2, i__3, i__4, i__5; doublereal d__1; doublecomplex z__1, z__2; - - /* Builtin functions */ void d_lmp_cnjg(doublecomplex *, doublecomplex *); - - /* Local variables */ integer i__, j, k, kk, ix, jx, kx, info; doublecomplex temp; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - - -/* -- Reference BLAS level2 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ + extern int xerbla_(char *, integer *, ftnlen); --ap; --x; - - /* Function Body */ info = 0; - if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", ( - ftnlen)1, (ftnlen)1)) { + if (!lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { info = 1; } else if (*n < 0) { info = 2; @@ -203,29 +27,16 @@ extern "C" { xerbla_((char *)"ZHPR ", &info, (ftnlen)6); return 0; } - -/* Quick return if possible. */ - if (*n == 0 || *alpha == 0.) { return 0; } - -/* Set the start point in X if the increment is not unity. */ - if (*incx <= 0) { kx = 1 - (*n - 1) * *incx; } else if (*incx != 1) { kx = 1; } - -/* Start the operations. In this version the elements of the array AP */ -/* are accessed sequentially with one pass through AP. */ - kk = 1; if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { - -/* Form A when upper triangle is stored in AP. */ - if (*incx == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { @@ -241,19 +52,16 @@ extern "C" { i__4 = k; i__5 = i__; z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, - z__2.i = x[i__5].r * temp.i + x[i__5].i * - temp.r; - z__1.r = ap[i__4].r + z__2.r, z__1.i = ap[i__4].i + - z__2.i; + z__2.i = x[i__5].r * temp.i + x[i__5].i * temp.r; + z__1.r = ap[i__4].r + z__2.r, z__1.i = ap[i__4].i + z__2.i; ap[i__3].r = z__1.r, ap[i__3].i = z__1.i; ++k; -/* L10: */ } i__2 = kk + j - 1; i__3 = kk + j - 1; i__4 = j; - z__1.r = x[i__4].r * temp.r - x[i__4].i * temp.i, z__1.i = - x[i__4].r * temp.i + x[i__4].i * temp.r; + z__1.r = x[i__4].r * temp.r - x[i__4].i * temp.i, + z__1.i = x[i__4].r * temp.i + x[i__4].i * temp.r; d__1 = ap[i__3].r + z__1.r; ap[i__2].r = d__1, ap[i__2].i = 0.; } else { @@ -263,7 +71,6 @@ extern "C" { ap[i__2].r = d__1, ap[i__2].i = 0.; } kk += j; -/* L20: */ } } else { jx = kx; @@ -281,19 +88,16 @@ extern "C" { i__4 = k; i__5 = ix; z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, - z__2.i = x[i__5].r * temp.i + x[i__5].i * - temp.r; - z__1.r = ap[i__4].r + z__2.r, z__1.i = ap[i__4].i + - z__2.i; + z__2.i = x[i__5].r * temp.i + x[i__5].i * temp.r; + z__1.r = ap[i__4].r + z__2.r, z__1.i = ap[i__4].i + z__2.i; ap[i__3].r = z__1.r, ap[i__3].i = z__1.i; ix += *incx; -/* L30: */ } i__2 = kk + j - 1; i__3 = kk + j - 1; i__4 = jx; - z__1.r = x[i__4].r * temp.r - x[i__4].i * temp.i, z__1.i = - x[i__4].r * temp.i + x[i__4].i * temp.r; + z__1.r = x[i__4].r * temp.r - x[i__4].i * temp.i, + z__1.i = x[i__4].r * temp.i + x[i__4].i * temp.r; d__1 = ap[i__3].r + z__1.r; ap[i__2].r = d__1, ap[i__2].i = 0.; } else { @@ -304,13 +108,9 @@ extern "C" { } jx += *incx; kk += j; -/* L40: */ } } } else { - -/* Form A when lower triangle is stored in AP. */ - if (*incx == 1) { i__1 = *n; for (j = 1; j <= i__1; ++j) { @@ -322,8 +122,8 @@ extern "C" { i__2 = kk; i__3 = kk; i__4 = j; - z__1.r = temp.r * x[i__4].r - temp.i * x[i__4].i, z__1.i = - temp.r * x[i__4].i + temp.i * x[i__4].r; + z__1.r = temp.r * x[i__4].r - temp.i * x[i__4].i, + z__1.i = temp.r * x[i__4].i + temp.i * x[i__4].r; d__1 = ap[i__3].r + z__1.r; ap[i__2].r = d__1, ap[i__2].i = 0.; k = kk + 1; @@ -333,13 +133,10 @@ extern "C" { i__4 = k; i__5 = i__; z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, - z__2.i = x[i__5].r * temp.i + x[i__5].i * - temp.r; - z__1.r = ap[i__4].r + z__2.r, z__1.i = ap[i__4].i + - z__2.i; + z__2.i = x[i__5].r * temp.i + x[i__5].i * temp.r; + z__1.r = ap[i__4].r + z__2.r, z__1.i = ap[i__4].i + z__2.i; ap[i__3].r = z__1.r, ap[i__3].i = z__1.i; ++k; -/* L50: */ } } else { i__2 = kk; @@ -348,7 +145,6 @@ extern "C" { ap[i__2].r = d__1, ap[i__2].i = 0.; } kk = kk + *n - j + 1; -/* L60: */ } } else { jx = kx; @@ -362,8 +158,8 @@ extern "C" { i__2 = kk; i__3 = kk; i__4 = jx; - z__1.r = temp.r * x[i__4].r - temp.i * x[i__4].i, z__1.i = - temp.r * x[i__4].i + temp.i * x[i__4].r; + z__1.r = temp.r * x[i__4].r - temp.i * x[i__4].i, + z__1.i = temp.r * x[i__4].i + temp.i * x[i__4].r; d__1 = ap[i__3].r + z__1.r; ap[i__2].r = d__1, ap[i__2].i = 0.; ix = jx; @@ -374,12 +170,9 @@ extern "C" { i__4 = k; i__5 = ix; z__2.r = x[i__5].r * temp.r - x[i__5].i * temp.i, - z__2.i = x[i__5].r * temp.i + x[i__5].i * - temp.r; - z__1.r = ap[i__4].r + z__2.r, z__1.i = ap[i__4].i + - z__2.i; + z__2.i = x[i__5].r * temp.i + x[i__5].i * temp.r; + z__1.r = ap[i__4].r + z__2.r, z__1.i = ap[i__4].i + z__2.i; ap[i__3].r = z__1.r, ap[i__3].i = z__1.i; -/* L70: */ } } else { i__2 = kk; @@ -389,17 +182,11 @@ extern "C" { } jx += *incx; kk = kk + *n - j + 1; -/* L80: */ } } } - return 0; - -/* End of ZHPR */ - -} /* zhpr_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zlacgv.cpp b/lib/linalg/zlacgv.cpp index d73cd7b759..bf6a1e8a42 100644 --- a/lib/linalg/zlacgv.cpp +++ b/lib/linalg/zlacgv.cpp @@ -1,136 +1,20 @@ -/* fortran/zlacgv.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b ZLACGV conjugates a complex vector. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZLACGV + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZLACGV( N, X, INCX ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INCX, N */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 X( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZLACGV conjugates a complex vector of length N. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The length of the vector X. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] X */ -/* > \verbatim */ -/* > X is COMPLEX*16 array, dimension */ -/* > (1+(N-1)*abs(INCX)) */ -/* > On entry, the vector of length N to be conjugated. */ -/* > On exit, X is overwritten with conjg(X). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > The spacing between successive elements of X. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16OTHERauxiliary */ - -/* ===================================================================== */ -/* Subroutine */ int zlacgv_(integer *n, doublecomplex *x, integer *incx) +int zlacgv_(integer *n, doublecomplex *x, integer *incx) { - /* System generated locals */ integer i__1, i__2; doublecomplex z__1; - - /* Builtin functions */ void d_lmp_cnjg(doublecomplex *, doublecomplex *); - - /* Local variables */ integer i__, ioff; - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Local Scalars .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - - /* Parameter adjustments */ --x; - - /* Function Body */ if (*incx == 1) { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; d_lmp_cnjg(&z__1, &x[i__]); x[i__2].r = z__1.r, x[i__2].i = z__1.i; -/* L10: */ } } else { ioff = 1; @@ -143,15 +27,10 @@ f"> */ d_lmp_cnjg(&z__1, &x[ioff]); x[i__2].r = z__1.r, x[i__2].i = z__1.i; ioff += *incx; -/* L20: */ } } return 0; - -/* End of ZLACGV */ - -} /* zlacgv_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zlacpy.cpp b/lib/linalg/zlacpy.cpp index 4a68cd9e07..18db0fac60 100644 --- a/lib/linalg/zlacpy.cpp +++ b/lib/linalg/zlacpy.cpp @@ -1,177 +1,29 @@ -/* fortran/zlacpy.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b ZLACPY copies all or part of one two-dimensional array to another. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZLACPY + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZLACPY( UPLO, M, N, A, LDA, B, LDB ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER UPLO */ -/* INTEGER LDA, LDB, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 A( LDA, * ), B( LDB, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZLACPY copies all or part of a two-dimensional matrix A to another */ -/* > matrix B. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > Specifies the part of the matrix A to be copied to B. */ -/* > = 'U': Upper triangular part */ -/* > = 'L': Lower triangular part */ -/* > Otherwise: All of the matrix A */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix A. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is COMPLEX*16 array, dimension (LDA,N) */ -/* > The m by n matrix A. If UPLO = 'U', only the upper trapezium */ -/* > is accessed; if UPLO = 'L', only the lower trapezium is */ -/* > accessed. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] B */ -/* > \verbatim */ -/* > B is COMPLEX*16 array, dimension (LDB,N) */ -/* > On exit, B = A in the locations specified by UPLO. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDB */ -/* > \verbatim */ -/* > LDB is INTEGER */ -/* > The leading dimension of the array B. LDB >= max(1,M). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16OTHERauxiliary */ - -/* ===================================================================== */ -/* Subroutine */ int zlacpy_(char *uplo, integer *m, integer *n, - doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, - ftnlen uplo_len) +int zlacpy_(char *uplo, integer *m, integer *n, doublecomplex *a, integer *lda, doublecomplex *b, + integer *ldb, ftnlen uplo_len) { - /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4; - - /* Local variables */ integer i__, j; extern logical lsame_(char *, char *, ftnlen, ftnlen); - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; - - /* Function Body */ if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { i__1 = *n; for (j = 1; j <= i__1; ++j) { - i__2 = min(j,*m); + i__2 = min(j, *m); for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * b_dim1; i__4 = i__ + j * a_dim1; b[i__3].r = a[i__4].r, b[i__3].i = a[i__4].i; -/* L10: */ } -/* L20: */ } - } else if (lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { i__1 = *n; for (j = 1; j <= i__1; ++j) { @@ -180,11 +32,8 @@ f"> */ i__3 = i__ + j * b_dim1; i__4 = i__ + j * a_dim1; b[i__3].r = a[i__4].r, b[i__3].i = a[i__4].i; -/* L30: */ } -/* L40: */ } - } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { @@ -193,18 +42,11 @@ f"> */ i__3 = i__ + j * b_dim1; i__4 = i__ + j * a_dim1; b[i__3].r = a[i__4].r, b[i__3].i = a[i__4].i; -/* L50: */ } -/* L60: */ } } - return 0; - -/* End of ZLACPY */ - -} /* zlacpy_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zlacrm.cpp b/lib/linalg/zlacrm.cpp index c3415cb29b..4d736ac15f 100644 --- a/lib/linalg/zlacrm.cpp +++ b/lib/linalg/zlacrm.cpp @@ -1,184 +1,20 @@ -/* fortran/zlacrm.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static doublereal c_b6 = 1.; static doublereal c_b7 = 0.; - -/* > \brief \b ZLACRM multiplies a complex matrix by a square real matrix. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZLACRM + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZLACRM( M, N, A, LDA, B, LDB, C, LDC, RWORK ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER LDA, LDB, LDC, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION B( LDB, * ), RWORK( * ) */ -/* COMPLEX*16 A( LDA, * ), C( LDC, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZLACRM performs a very simple matrix-matrix multiplication: */ -/* > C := A * B, */ -/* > where A is M by N and complex; B is N by N and real; */ -/* > C is M by N and complex. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix A and of the matrix C. */ -/* > M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns and rows of the matrix B and */ -/* > the number of columns of the matrix C. */ -/* > N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is COMPLEX*16 array, dimension (LDA, N) */ -/* > On entry, A contains the M by N matrix A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >=max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] B */ -/* > \verbatim */ -/* > B is DOUBLE PRECISION array, dimension (LDB, N) */ -/* > On entry, B contains the N by N matrix B. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDB */ -/* > \verbatim */ -/* > LDB is INTEGER */ -/* > The leading dimension of the array B. LDB >=max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] C */ -/* > \verbatim */ -/* > C is COMPLEX*16 array, dimension (LDC, N) */ -/* > On exit, C contains the M by N matrix C. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDC */ -/* > \verbatim */ -/* > LDC is INTEGER */ -/* > The leading dimension of the array C. LDC >=max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] RWORK */ -/* > \verbatim */ -/* > RWORK is DOUBLE PRECISION array, dimension (2*M*N) */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16OTHERauxiliary */ - -/* ===================================================================== */ -/* Subroutine */ int zlacrm_(integer *m, integer *n, doublecomplex *a, - integer *lda, doublereal *b, integer *ldb, doublecomplex *c__, - integer *ldc, doublereal *rwork) +int zlacrm_(integer *m, integer *n, doublecomplex *a, integer *lda, doublereal *b, integer *ldb, + doublecomplex *c__, integer *ldc, doublereal *rwork) { - /* System generated locals */ - integer b_dim1, b_offset, a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, - i__3, i__4, i__5; + integer b_dim1, b_offset, a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3, i__4, i__5; doublereal d__1; doublecomplex z__1; - - /* Builtin functions */ double d_lmp_imag(doublecomplex *); - - /* Local variables */ integer i__, j, l; - extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen); - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Quick return if possible. */ - - /* Parameter adjustments */ + extern int dgemm_(char *, char *, integer *, integer *, integer *, doublereal *, doublereal *, + integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, + ftnlen, ftnlen); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; @@ -189,26 +25,20 @@ f"> */ c_offset = 1 + c_dim1; c__ -= c_offset; --rwork; - - /* Function Body */ if (*m == 0 || *n == 0) { return 0; } - i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * a_dim1; rwork[(j - 1) * *m + i__] = a[i__3].r; -/* L10: */ } -/* L20: */ } - l = *m * *n + 1; - dgemm_((char *)"N", (char *)"N", m, n, n, &c_b6, &rwork[1], m, &b[b_offset], ldb, &c_b7, & - rwork[l], m, (ftnlen)1, (ftnlen)1); + dgemm_((char *)"N", (char *)"N", m, n, n, &c_b6, &rwork[1], m, &b[b_offset], ldb, &c_b7, &rwork[l], m, + (ftnlen)1, (ftnlen)1); i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; @@ -216,22 +46,17 @@ f"> */ i__3 = i__ + j * c_dim1; i__4 = l + (j - 1) * *m + i__ - 1; c__[i__3].r = rwork[i__4], c__[i__3].i = 0.; -/* L30: */ } -/* L40: */ } - i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { rwork[(j - 1) * *m + i__] = d_lmp_imag(&a[i__ + j * a_dim1]); -/* L50: */ } -/* L60: */ } - dgemm_((char *)"N", (char *)"N", m, n, n, &c_b6, &rwork[1], m, &b[b_offset], ldb, &c_b7, & - rwork[l], m, (ftnlen)1, (ftnlen)1); + dgemm_((char *)"N", (char *)"N", m, n, n, &c_b6, &rwork[1], m, &b[b_offset], ldb, &c_b7, &rwork[l], m, + (ftnlen)1, (ftnlen)1); i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; @@ -242,17 +67,10 @@ f"> */ i__5 = l + (j - 1) * *m + i__ - 1; z__1.r = d__1, z__1.i = rwork[i__5]; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; -/* L70: */ } -/* L80: */ } - return 0; - -/* End of ZLACRM */ - -} /* zlacrm_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zladiv.cpp b/lib/linalg/zladiv.cpp index 105560e1a5..ec130d40d9 100644 --- a/lib/linalg/zladiv.cpp +++ b/lib/linalg/zladiv.cpp @@ -1,132 +1,24 @@ -/* fortran/zladiv.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b ZLADIV performs complex division in real arithmetic, avoiding unnecessary overflow. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZLADIV + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* COMPLEX*16 FUNCTION ZLADIV( X, Y ) */ - -/* .. Scalar Arguments .. */ -/* COMPLEX*16 X, Y */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZLADIV := X / Y, where X and Y are complex. The computation of X / Y */ -/* > will not overflow on an intermediary step unless the results */ -/* > overflows. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] X */ -/* > \verbatim */ -/* > X is COMPLEX*16 */ -/* > \endverbatim */ -/* > */ -/* > \param[in] Y */ -/* > \verbatim */ -/* > Y is COMPLEX*16 */ -/* > The complex scalars X and Y. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16OTHERauxiliary */ - -/* ===================================================================== */ -/* Double Complex */ VOID zladiv_(doublecomplex * ret_val, doublecomplex *x, - doublecomplex *y) +VOID zladiv_(doublecomplex *ret_val, doublecomplex *x, doublecomplex *y) { - /* System generated locals */ doublereal d__1, d__2, d__3, d__4; doublecomplex z__1; - - /* Builtin functions */ double d_lmp_imag(doublecomplex *); - - /* Local variables */ doublereal zi, zr; - extern /* Subroutine */ int dladiv_(doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *, doublereal *); - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - + extern int dladiv_(doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *); d__1 = x->r; d__2 = d_lmp_imag(x); d__3 = y->r; d__4 = d_lmp_imag(y); dladiv_(&d__1, &d__2, &d__3, &d__4, &zr, &zi); z__1.r = zr, z__1.i = zi; - ret_val->r = z__1.r, ret_val->i = z__1.i; - - return ; - -/* End of ZLADIV */ - -} /* zladiv_ */ - + ret_val->r = z__1.r, ret_val->i = z__1.i; + return; +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zlaed0.cpp b/lib/linalg/zlaed0.cpp index 5895127d75..6729b532c9 100644 --- a/lib/linalg/zlaed0.cpp +++ b/lib/linalg/zlaed0.cpp @@ -1,241 +1,39 @@ -/* fortran/zlaed0.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__9 = 9; static integer c__0 = 0; static integer c__2 = 2; static integer c__1 = 1; - -/* > \brief \b ZLAED0 used by ZSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced -symmetric tridiagonal matrix using the divide and conquer method. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZLAED0 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZLAED0( QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, RWORK, */ -/* IWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INFO, LDQ, LDQS, N, QSIZ */ -/* .. */ -/* .. Array Arguments .. */ -/* INTEGER IWORK( * ) */ -/* DOUBLE PRECISION D( * ), E( * ), RWORK( * ) */ -/* COMPLEX*16 Q( LDQ, * ), QSTORE( LDQS, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > Using the divide and conquer method, ZLAED0 computes all eigenvalues */ -/* > of a symmetric tridiagonal matrix which is one diagonal block of */ -/* > those from reducing a dense or band Hermitian matrix and */ -/* > corresponding eigenvectors of the dense or band matrix. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] QSIZ */ -/* > \verbatim */ -/* > QSIZ is INTEGER */ -/* > The dimension of the unitary matrix used to reduce */ -/* > the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The dimension of the symmetric tridiagonal matrix. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension (N) */ -/* > On entry, the diagonal elements of the tridiagonal matrix. */ -/* > On exit, the eigenvalues in ascending order. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] E */ -/* > \verbatim */ -/* > E is DOUBLE PRECISION array, dimension (N-1) */ -/* > On entry, the off-diagonal elements of the tridiagonal matrix. */ -/* > On exit, E has been destroyed. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] Q */ -/* > \verbatim */ -/* > Q is COMPLEX*16 array, dimension (LDQ,N) */ -/* > On entry, Q must contain an QSIZ x N matrix whose columns */ -/* > unitarily orthonormal. It is a part of the unitary matrix */ -/* > that reduces the full dense Hermitian matrix to a */ -/* > (reducible) symmetric tridiagonal matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDQ */ -/* > \verbatim */ -/* > LDQ is INTEGER */ -/* > The leading dimension of the array Q. LDQ >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] IWORK */ -/* > \verbatim */ -/* > IWORK is INTEGER array, */ -/* > the dimension of IWORK must be at least */ -/* > 6 + 6*N + 5*N*lg N */ -/* > ( lg( N ) = smallest integer k */ -/* > such that 2^k >= N ) */ -/* > \endverbatim */ -/* > */ -/* > \param[out] RWORK */ -/* > \verbatim */ -/* > RWORK is DOUBLE PRECISION array, */ -/* > dimension (1 + 3*N + 2*N*lg N + 3*N**2) */ -/* > ( lg( N ) = smallest integer k */ -/* > such that 2^k >= N ) */ -/* > \endverbatim */ -/* > */ -/* > \param[out] QSTORE */ -/* > \verbatim */ -/* > QSTORE is COMPLEX*16 array, dimension (LDQS, N) */ -/* > Used to store parts of */ -/* > the eigenvector matrix when the updating matrix multiplies */ -/* > take place. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDQS */ -/* > \verbatim */ -/* > LDQS is INTEGER */ -/* > The leading dimension of the array QSTORE. */ -/* > LDQS >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit. */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ -/* > > 0: The algorithm failed to compute an eigenvalue while */ -/* > working on the submatrix lying in rows and columns */ -/* > INFO/(N+1) through mod(INFO,N+1). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16OTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int zlaed0_(integer *qsiz, integer *n, doublereal *d__, - doublereal *e, doublecomplex *q, integer *ldq, doublecomplex *qstore, - integer *ldqs, doublereal *rwork, integer *iwork, integer *info) +int zlaed0_(integer *qsiz, integer *n, doublereal *d__, doublereal *e, doublecomplex *q, + integer *ldq, doublecomplex *qstore, integer *ldqs, doublereal *rwork, integer *iwork, + integer *info) { - /* System generated locals */ integer q_dim1, q_offset, qstore_dim1, qstore_offset, i__1, i__2; doublereal d__1; - - /* Builtin functions */ double log(doublereal); integer pow_lmp_ii(integer *, integer *); - - /* Local variables */ integer i__, j, k, ll, iq, lgn, msd2, smm1, spm1, spm2; doublereal temp; integer curr, iperm; - extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, - doublereal *, integer *); + extern int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *); integer indxq, iwrem, iqptr, tlvls; - extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, - doublecomplex *, integer *), zlaed7_(integer *, integer *, - integer *, integer *, integer *, integer *, doublereal *, - doublecomplex *, integer *, doublereal *, integer *, doublereal *, - integer *, integer *, integer *, integer *, integer *, - doublereal *, doublecomplex *, doublereal *, integer *, integer *) - ; + extern int zcopy_(integer *, doublecomplex *, integer *, doublecomplex *, integer *), + zlaed7_(integer *, integer *, integer *, integer *, integer *, integer *, doublereal *, + doublecomplex *, integer *, doublereal *, integer *, doublereal *, integer *, + integer *, integer *, integer *, integer *, doublereal *, doublecomplex *, + doublereal *, integer *, integer *); integer igivcl; - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - extern /* Subroutine */ int zlacrm_(integer *, integer *, doublecomplex *, - integer *, doublereal *, integer *, doublecomplex *, integer *, - doublereal *); + extern int xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); + extern int zlacrm_(integer *, integer *, doublecomplex *, integer *, doublereal *, integer *, + doublecomplex *, integer *, doublereal *); integer igivnm, submat, curprb, subpbs, igivpt; - extern /* Subroutine */ int dsteqr_(char *, integer *, doublereal *, - doublereal *, doublereal *, integer *, doublereal *, integer *, - ftnlen); + extern int dsteqr_(char *, integer *, doublereal *, doublereal *, doublereal *, integer *, + doublereal *, integer *, ftnlen); integer curlvl, matsiz, iprmpt, smlsiz; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* Warning: N could be as big as QSIZ! */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ --d__; --e; q_dim1 = *ldq; @@ -246,21 +44,14 @@ f"> */ qstore -= qstore_offset; --rwork; --iwork; - - /* Function Body */ *info = 0; - -/* IF( ICOMPQ .LT. 0 .OR. ICOMPQ .GT. 2 ) THEN */ -/* INFO = -1 */ -/* ELSE IF( ( ICOMPQ .EQ. 1 ) .AND. ( QSIZ .LT. MAX( 0, N ) ) ) */ -/* $ THEN */ - if (*qsiz < max(0,*n)) { + if (*qsiz < max(0, *n)) { *info = -1; } else if (*n < 0) { *info = -2; - } else if (*ldq < max(1,*n)) { + } else if (*ldq < max(1, *n)) { *info = -6; - } else if (*ldqs < max(1,*n)) { + } else if (*ldqs < max(1, *n)) { *info = -8; } if (*info != 0) { @@ -268,19 +59,10 @@ f"> */ xerbla_((char *)"ZLAED0", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*n == 0) { return 0; } - - smlsiz = ilaenv_(&c__9, (char *)"ZLAED0", (char *)" ", &c__0, &c__0, &c__0, &c__0, ( - ftnlen)6, (ftnlen)1); - -/* Determine the size and placement of the submatrices, and save in */ -/* the leading elements of IWORK. */ - + smlsiz = ilaenv_(&c__9, (char *)"ZLAED0", (char *)" ", &c__0, &c__0, &c__0, &c__0, (ftnlen)6, (ftnlen)1); iwork[1] = *n; subpbs = 1; tlvls = 0; @@ -289,7 +71,6 @@ L10: for (j = subpbs; j >= 1; --j) { iwork[j * 2] = (iwork[j] + 1) / 2; iwork[(j << 1) - 1] = iwork[j] / 2; -/* L20: */ } ++tlvls; subpbs <<= 1; @@ -298,12 +79,7 @@ L10: i__1 = subpbs; for (j = 2; j <= i__1; ++j) { iwork[j] += iwork[j - 1]; -/* L30: */ } - -/* Divide the matrix into SUBPBS submatrices of size at most SMLSIZ+1 */ -/* using rank-1 modifications (cuts). */ - spm1 = subpbs - 1; i__1 = spm1; for (i__ = 1; i__ <= i__1; ++i__) { @@ -311,16 +87,10 @@ L10: smm1 = submat - 1; d__[smm1] -= (d__1 = e[smm1], abs(d__1)); d__[submat] -= (d__1 = e[smm1], abs(d__1)); -/* L40: */ } - indxq = (*n << 2) + 3; - -/* Set up workspaces for eigenvalues only/accumulate new vectors */ -/* routine */ - - temp = log((doublereal) (*n)) / log(2.); - lgn = (integer) temp; + temp = log((doublereal)(*n)) / log(2.); + lgn = (integer)temp; if (pow_lmp_ii(&c__2, &lgn) < *n) { ++lgn; } @@ -332,24 +102,16 @@ L10: iqptr = iperm + *n * lgn; igivpt = iqptr + *n + 2; igivcl = igivpt + *n * lgn; - igivnm = 1; iq = igivnm + (*n << 1) * lgn; -/* Computing 2nd power */ i__1 = *n; iwrem = iq + i__1 * i__1 + 1; -/* Initialize pointers */ i__1 = subpbs; for (i__ = 0; i__ <= i__1; ++i__) { iwork[iprmpt + i__] = 1; iwork[igivpt + i__] = 1; -/* L50: */ } iwork[iqptr] = 1; - -/* Solve each submatrix eigenproblem at the bottom of the divide and */ -/* conquer tree. */ - curr = 0; i__1 = spm1; for (i__ = 0; i__ <= i__1; ++i__) { @@ -361,12 +123,10 @@ L10: matsiz = iwork[i__ + 1] - iwork[i__]; } ll = iq - 1 + iwork[iqptr + curr]; - dsteqr_((char *)"I", &matsiz, &d__[submat], &e[submat], &rwork[ll], &matsiz, & - rwork[1], info, (ftnlen)1); - zlacrm_(qsiz, &matsiz, &q[submat * q_dim1 + 1], ldq, &rwork[ll], & - matsiz, &qstore[submat * qstore_dim1 + 1], ldqs, &rwork[iwrem] - ); -/* Computing 2nd power */ + dsteqr_((char *)"I", &matsiz, &d__[submat], &e[submat], &rwork[ll], &matsiz, &rwork[1], info, + (ftnlen)1); + zlacrm_(qsiz, &matsiz, &q[submat * q_dim1 + 1], ldq, &rwork[ll], &matsiz, + &qstore[submat * qstore_dim1 + 1], ldqs, &rwork[iwrem]); i__2 = matsiz; iwork[iqptr + curr + 1] = iwork[iqptr + curr] + i__2 * i__2; ++curr; @@ -379,16 +139,8 @@ L10: for (j = submat; j <= i__2; ++j) { iwork[indxq + j] = k; ++k; -/* L60: */ } -/* L70: */ } - -/* Successively merge eigensystems of adjacent submatrices */ -/* into eigensystem for the corresponding larger matrix. */ - -/* while ( SUBPBS > 1 ) */ - curlvl = 1; L80: if (subpbs > 1) { @@ -406,53 +158,30 @@ L80: msd2 = matsiz / 2; ++curprb; } - -/* Merge lower order eigensystems (of size MSD2 and MATSIZ - MSD2) */ -/* into an eigensystem of size MATSIZ. ZLAED7 handles the case */ -/* when the eigenvectors of a full or band Hermitian matrix (which */ -/* was reduced to tridiagonal form) are desired. */ - -/* I am free to use Q as a valuable working space until Loop 150. */ - - zlaed7_(&matsiz, &msd2, qsiz, &tlvls, &curlvl, &curprb, &d__[ - submat], &qstore[submat * qstore_dim1 + 1], ldqs, &e[ - submat + msd2 - 1], &iwork[indxq + submat], &rwork[iq], & - iwork[iqptr], &iwork[iprmpt], &iwork[iperm], &iwork[ - igivpt], &iwork[igivcl], &rwork[igivnm], &q[submat * - q_dim1 + 1], &rwork[iwrem], &iwork[subpbs + 1], info); + zlaed7_(&matsiz, &msd2, qsiz, &tlvls, &curlvl, &curprb, &d__[submat], + &qstore[submat * qstore_dim1 + 1], ldqs, &e[submat + msd2 - 1], + &iwork[indxq + submat], &rwork[iq], &iwork[iqptr], &iwork[iprmpt], + &iwork[iperm], &iwork[igivpt], &iwork[igivcl], &rwork[igivnm], + &q[submat * q_dim1 + 1], &rwork[iwrem], &iwork[subpbs + 1], info); if (*info > 0) { *info = submat * (*n + 1) + submat + matsiz - 1; return 0; } iwork[i__ / 2 + 1] = iwork[i__ + 2]; -/* L90: */ } subpbs /= 2; ++curlvl; goto L80; } - -/* end while */ - -/* Re-merge the eigenvalues/vectors which were deflated at the final */ -/* merge step. */ - i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { j = iwork[indxq + i__]; rwork[i__] = d__[j]; - zcopy_(qsiz, &qstore[j * qstore_dim1 + 1], &c__1, &q[i__ * q_dim1 + 1] - , &c__1); -/* L100: */ + zcopy_(qsiz, &qstore[j * qstore_dim1 + 1], &c__1, &q[i__ * q_dim1 + 1], &c__1); } dcopy_(n, &rwork[1], &c__1, &d__[1], &c__1); - return 0; - -/* End of ZLAED0 */ - -} /* zlaed0_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zlaed7.cpp b/lib/linalg/zlaed7.cpp index 11b29341bb..1a045d7edd 100644 --- a/lib/linalg/zlaed7.cpp +++ b/lib/linalg/zlaed7.cpp @@ -1,331 +1,35 @@ -/* fortran/zlaed7.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__2 = 2; static integer c__1 = 1; static integer c_n1 = -1; - -/* > \brief \b ZLAED7 used by ZSTEDC. Computes the updated eigensystem of a diagonal matrix after modification - by a rank-one symmetric matrix. Used when the original matrix is dense. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZLAED7 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZLAED7( N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, */ -/* LDQ, RHO, INDXQ, QSTORE, QPTR, PRMPTR, PERM, */ -/* GIVPTR, GIVCOL, GIVNUM, WORK, RWORK, IWORK, */ -/* INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER CURLVL, CURPBM, CUTPNT, INFO, LDQ, N, QSIZ, */ -/* $ TLVLS */ -/* DOUBLE PRECISION RHO */ -/* .. */ -/* .. Array Arguments .. */ -/* INTEGER GIVCOL( 2, * ), GIVPTR( * ), INDXQ( * ), */ -/* $ IWORK( * ), PERM( * ), PRMPTR( * ), QPTR( * ) */ -/* DOUBLE PRECISION D( * ), GIVNUM( 2, * ), QSTORE( * ), RWORK( * ) */ -/* COMPLEX*16 Q( LDQ, * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZLAED7 computes the updated eigensystem of a diagonal */ -/* > matrix after modification by a rank-one symmetric matrix. This */ -/* > routine is used only for the eigenproblem which requires all */ -/* > eigenvalues and optionally eigenvectors of a dense or banded */ -/* > Hermitian matrix that has been reduced to tridiagonal form. */ -/* > */ -/* > T = Q(in) ( D(in) + RHO * Z*Z**H ) Q**H(in) = Q(out) * D(out) * Q**H(out) */ -/* > */ -/* > where Z = Q**Hu, u is a vector of length N with ones in the */ -/* > CUTPNT and CUTPNT + 1 th elements and zeros elsewhere. */ -/* > */ -/* > The eigenvectors of the original matrix are stored in Q, and the */ -/* > eigenvalues are in D. The algorithm consists of three stages: */ -/* > */ -/* > The first stage consists of deflating the size of the problem */ -/* > when there are multiple eigenvalues or if there is a zero in */ -/* > the Z vector. For each such occurrence the dimension of the */ -/* > secular equation problem is reduced by one. This stage is */ -/* > performed by the routine DLAED2. */ -/* > */ -/* > The second stage consists of calculating the updated */ -/* > eigenvalues. This is done by finding the roots of the secular */ -/* > equation via the routine DLAED4 (as called by SLAED3). */ -/* > This routine also calculates the eigenvectors of the current */ -/* > problem. */ -/* > */ -/* > The final stage consists of computing the updated eigenvectors */ -/* > directly using the updated eigenvalues. The eigenvectors for */ -/* > the current problem are multiplied with the eigenvectors from */ -/* > the overall problem. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The dimension of the symmetric tridiagonal matrix. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] CUTPNT */ -/* > \verbatim */ -/* > CUTPNT is INTEGER */ -/* > Contains the location of the last eigenvalue in the leading */ -/* > sub-matrix. min(1,N) <= CUTPNT <= N. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] QSIZ */ -/* > \verbatim */ -/* > QSIZ is INTEGER */ -/* > The dimension of the unitary matrix used to reduce */ -/* > the full matrix to tridiagonal form. QSIZ >= N. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TLVLS */ -/* > \verbatim */ -/* > TLVLS is INTEGER */ -/* > The total number of merging levels in the overall divide and */ -/* > conquer tree. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] CURLVL */ -/* > \verbatim */ -/* > CURLVL is INTEGER */ -/* > The current level in the overall merge routine, */ -/* > 0 <= curlvl <= tlvls. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] CURPBM */ -/* > \verbatim */ -/* > CURPBM is INTEGER */ -/* > The current problem in the current level in the overall */ -/* > merge routine (counting from upper left to lower right). */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension (N) */ -/* > On entry, the eigenvalues of the rank-1-perturbed matrix. */ -/* > On exit, the eigenvalues of the repaired matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] Q */ -/* > \verbatim */ -/* > Q is COMPLEX*16 array, dimension (LDQ,N) */ -/* > On entry, the eigenvectors of the rank-1-perturbed matrix. */ -/* > On exit, the eigenvectors of the repaired tridiagonal matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDQ */ -/* > \verbatim */ -/* > LDQ is INTEGER */ -/* > The leading dimension of the array Q. LDQ >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] RHO */ -/* > \verbatim */ -/* > RHO is DOUBLE PRECISION */ -/* > Contains the subdiagonal element used to create the rank-1 */ -/* > modification. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INDXQ */ -/* > \verbatim */ -/* > INDXQ is INTEGER array, dimension (N) */ -/* > This contains the permutation which will reintegrate the */ -/* > subproblem just solved back into sorted order, */ -/* > ie. D( INDXQ( I = 1, N ) ) will be in ascending order. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] IWORK */ -/* > \verbatim */ -/* > IWORK is INTEGER array, dimension (4*N) */ -/* > \endverbatim */ -/* > */ -/* > \param[out] RWORK */ -/* > \verbatim */ -/* > RWORK is DOUBLE PRECISION array, */ -/* > dimension (3*N+2*QSIZ*N) */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is COMPLEX*16 array, dimension (QSIZ*N) */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] QSTORE */ -/* > \verbatim */ -/* > QSTORE is DOUBLE PRECISION array, dimension (N**2+1) */ -/* > Stores eigenvectors of submatrices encountered during */ -/* > divide and conquer, packed together. QPTR points to */ -/* > beginning of the submatrices. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] QPTR */ -/* > \verbatim */ -/* > QPTR is INTEGER array, dimension (N+2) */ -/* > List of indices pointing to beginning of submatrices stored */ -/* > in QSTORE. The submatrices are numbered starting at the */ -/* > bottom left of the divide and conquer tree, from left to */ -/* > right and bottom to top. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] PRMPTR */ -/* > \verbatim */ -/* > PRMPTR is INTEGER array, dimension (N lg N) */ -/* > Contains a list of pointers which indicate where in PERM a */ -/* > level's permutation is stored. PRMPTR(i+1) - PRMPTR(i) */ -/* > indicates the size of the permutation and also the size of */ -/* > the full, non-deflated problem. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] PERM */ -/* > \verbatim */ -/* > PERM is INTEGER array, dimension (N lg N) */ -/* > Contains the permutations (from deflation and sorting) to be */ -/* > applied to each eigenblock. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] GIVPTR */ -/* > \verbatim */ -/* > GIVPTR is INTEGER array, dimension (N lg N) */ -/* > Contains a list of pointers which indicate where in GIVCOL a */ -/* > level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i) */ -/* > indicates the number of Givens rotations. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] GIVCOL */ -/* > \verbatim */ -/* > GIVCOL is INTEGER array, dimension (2, N lg N) */ -/* > Each pair of numbers indicates a pair of columns to take place */ -/* > in a Givens rotation. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] GIVNUM */ -/* > \verbatim */ -/* > GIVNUM is DOUBLE PRECISION array, dimension (2, N lg N) */ -/* > Each number indicates the S value to be used in the */ -/* > corresponding Givens rotation. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit. */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ -/* > > 0: if INFO = 1, an eigenvalue did not converge */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16OTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int zlaed7_(integer *n, integer *cutpnt, integer *qsiz, - integer *tlvls, integer *curlvl, integer *curpbm, doublereal *d__, - doublecomplex *q, integer *ldq, doublereal *rho, integer *indxq, - doublereal *qstore, integer *qptr, integer *prmptr, integer *perm, - integer *givptr, integer *givcol, doublereal *givnum, doublecomplex * - work, doublereal *rwork, integer *iwork, integer *info) +int zlaed7_(integer *n, integer *cutpnt, integer *qsiz, integer *tlvls, integer *curlvl, + integer *curpbm, doublereal *d__, doublecomplex *q, integer *ldq, doublereal *rho, + integer *indxq, doublereal *qstore, integer *qptr, integer *prmptr, integer *perm, + integer *givptr, integer *givcol, doublereal *givnum, doublecomplex *work, + doublereal *rwork, integer *iwork, integer *info) { - /* System generated locals */ integer q_dim1, q_offset, i__1, i__2; - - /* Builtin functions */ integer pow_lmp_ii(integer *, integer *); - - /* Local variables */ integer i__, k, n1, n2, iq, iw, iz, ptr, indx, curr, indxc, indxp; - extern /* Subroutine */ int dlaed9_(integer *, integer *, integer *, - integer *, doublereal *, doublereal *, integer *, doublereal *, - doublereal *, doublereal *, doublereal *, integer *, integer *), - zlaed8_(integer *, integer *, integer *, doublecomplex *, integer - *, doublereal *, doublereal *, integer *, doublereal *, - doublereal *, doublecomplex *, integer *, doublereal *, integer *, - integer *, integer *, integer *, integer *, integer *, - doublereal *, integer *), dlaeda_(integer *, integer *, integer *, - integer *, integer *, integer *, integer *, integer *, - doublereal *, doublereal *, integer *, doublereal *, doublereal *, - integer *); + extern int dlaed9_(integer *, integer *, integer *, integer *, doublereal *, doublereal *, + integer *, doublereal *, doublereal *, doublereal *, doublereal *, integer *, + integer *), + zlaed8_(integer *, integer *, integer *, doublecomplex *, integer *, doublereal *, + doublereal *, integer *, doublereal *, doublereal *, doublecomplex *, integer *, + doublereal *, integer *, integer *, integer *, integer *, integer *, integer *, + doublereal *, integer *), + dlaeda_(integer *, integer *, integer *, integer *, integer *, integer *, integer *, + integer *, doublereal *, doublereal *, integer *, doublereal *, doublereal *, + integer *); integer idlmda; - extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *, - integer *, integer *, integer *), xerbla_(char *, integer *, - ftnlen), zlacrm_(integer *, integer *, doublecomplex *, integer *, - doublereal *, integer *, doublecomplex *, integer *, doublereal * - ); + extern int dlamrg_(integer *, integer *, doublereal *, integer *, integer *, integer *), + xerbla_(char *, integer *, ftnlen), + zlacrm_(integer *, integer *, doublecomplex *, integer *, doublereal *, integer *, + doublecomplex *, integer *, doublereal *); integer coltyp; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ --d__; q_dim1 = *ldq; q_offset = 1 + q_dim1; @@ -341,20 +45,14 @@ f"> */ --work; --rwork; --iwork; - - /* Function Body */ *info = 0; - -/* IF( ICOMPQ.LT.0 .OR. ICOMPQ.GT.1 ) THEN */ -/* INFO = -1 */ -/* ELSE IF( N.LT.0 ) THEN */ if (*n < 0) { *info = -1; - } else if (min(1,*n) > *cutpnt || *n < *cutpnt) { + } else if (min(1, *n) > *cutpnt || *n < *cutpnt) { *info = -2; } else if (*qsiz < *n) { *info = -3; - } else if (*ldq < max(1,*n)) { + } else if (*ldq < max(1, *n)) { *info = -9; } if (*info != 0) { @@ -362,77 +60,46 @@ f"> */ xerbla_((char *)"ZLAED7", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*n == 0) { return 0; } - -/* The following values are for bookkeeping purposes only. They are */ -/* integer pointers which indicate the portion of the workspace */ -/* used by a particular array in DLAED2 and SLAED3. */ - iz = 1; idlmda = iz + *n; iw = idlmda + *n; iq = iw + *n; - indx = 1; indxc = indx + *n; coltyp = indxc + *n; indxp = coltyp + *n; - -/* Form the z-vector which consists of the last row of Q_1 and the */ -/* first row of Q_2. */ - ptr = pow_lmp_ii(&c__2, tlvls) + 1; i__1 = *curlvl - 1; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = *tlvls - i__; ptr += pow_lmp_ii(&c__2, &i__2); -/* L10: */ } curr = ptr + *curpbm; - dlaeda_(n, tlvls, curlvl, curpbm, &prmptr[1], &perm[1], &givptr[1], & - givcol[3], &givnum[3], &qstore[1], &qptr[1], &rwork[iz], &rwork[ - iz + *n], info); - -/* When solving the final problem, we no longer need the stored data, */ -/* so we will overwrite the data from this level onto the previously */ -/* used storage space. */ - + dlaeda_(n, tlvls, curlvl, curpbm, &prmptr[1], &perm[1], &givptr[1], &givcol[3], &givnum[3], + &qstore[1], &qptr[1], &rwork[iz], &rwork[iz + *n], info); if (*curlvl == *tlvls) { qptr[curr] = 1; prmptr[curr] = 1; givptr[curr] = 1; } - -/* Sort and Deflate eigenvalues. */ - - zlaed8_(&k, n, qsiz, &q[q_offset], ldq, &d__[1], rho, cutpnt, &rwork[iz], - &rwork[idlmda], &work[1], qsiz, &rwork[iw], &iwork[indxp], &iwork[ - indx], &indxq[1], &perm[prmptr[curr]], &givptr[curr + 1], &givcol[ - (givptr[curr] << 1) + 1], &givnum[(givptr[curr] << 1) + 1], info); + zlaed8_(&k, n, qsiz, &q[q_offset], ldq, &d__[1], rho, cutpnt, &rwork[iz], &rwork[idlmda], + &work[1], qsiz, &rwork[iw], &iwork[indxp], &iwork[indx], &indxq[1], &perm[prmptr[curr]], + &givptr[curr + 1], &givcol[(givptr[curr] << 1) + 1], &givnum[(givptr[curr] << 1) + 1], + info); prmptr[curr + 1] = prmptr[curr] + *n; givptr[curr + 1] += givptr[curr]; - -/* Solve Secular Equation. */ - if (k != 0) { - dlaed9_(&k, &c__1, &k, n, &d__[1], &rwork[iq], &k, rho, &rwork[idlmda] - , &rwork[iw], &qstore[qptr[curr]], &k, info); - zlacrm_(qsiz, &k, &work[1], qsiz, &qstore[qptr[curr]], &k, &q[ - q_offset], ldq, &rwork[iq]); -/* Computing 2nd power */ + dlaed9_(&k, &c__1, &k, n, &d__[1], &rwork[iq], &k, rho, &rwork[idlmda], &rwork[iw], + &qstore[qptr[curr]], &k, info); + zlacrm_(qsiz, &k, &work[1], qsiz, &qstore[qptr[curr]], &k, &q[q_offset], ldq, &rwork[iq]); i__1 = k; qptr[curr + 1] = qptr[curr] + i__1 * i__1; if (*info != 0) { return 0; } - -/* Prepare the INDXQ sorting premutation. */ - n1 = k; n2 = *n - k; dlamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &indxq[1]); @@ -441,16 +108,10 @@ f"> */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { indxq[i__] = i__; -/* L20: */ } } - return 0; - -/* End of ZLAED7 */ - -} /* zlaed7_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zlaed8.cpp b/lib/linalg/zlaed8.cpp index 77c07f385e..d29b380587 100644 --- a/lib/linalg/zlaed8.cpp +++ b/lib/linalg/zlaed8.cpp @@ -1,315 +1,35 @@ -/* fortran/zlaed8.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static doublereal c_b3 = -1.; static integer c__1 = 1; - -/* > \brief \b ZLAED8 used by ZSTEDC. Merges eigenvalues and deflates secular equation. Used when the original - matrix is dense. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZLAED8 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZLAED8( K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA, */ -/* Q2, LDQ2, W, INDXP, INDX, INDXQ, PERM, GIVPTR, */ -/* GIVCOL, GIVNUM, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER CUTPNT, GIVPTR, INFO, K, LDQ, LDQ2, N, QSIZ */ -/* DOUBLE PRECISION RHO */ -/* .. */ -/* .. Array Arguments .. */ -/* INTEGER GIVCOL( 2, * ), INDX( * ), INDXP( * ), */ -/* $ INDXQ( * ), PERM( * ) */ -/* DOUBLE PRECISION D( * ), DLAMDA( * ), GIVNUM( 2, * ), W( * ), */ -/* $ Z( * ) */ -/* COMPLEX*16 Q( LDQ, * ), Q2( LDQ2, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZLAED8 merges the two sets of eigenvalues together into a single */ -/* > sorted set. Then it tries to deflate the size of the problem. */ -/* > There are two ways in which deflation can occur: when two or more */ -/* > eigenvalues are close together or if there is a tiny element in the */ -/* > Z vector. For each such occurrence the order of the related secular */ -/* > equation problem is reduced by one. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[out] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > Contains the number of non-deflated eigenvalues. */ -/* > This is the order of the related secular equation. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The dimension of the symmetric tridiagonal matrix. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] QSIZ */ -/* > \verbatim */ -/* > QSIZ is INTEGER */ -/* > The dimension of the unitary matrix used to reduce */ -/* > the dense or band matrix to tridiagonal form. */ -/* > QSIZ >= N if ICOMPQ = 1. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] Q */ -/* > \verbatim */ -/* > Q is COMPLEX*16 array, dimension (LDQ,N) */ -/* > On entry, Q contains the eigenvectors of the partially solved */ -/* > system which has been previously updated in matrix */ -/* > multiplies with other partially solved eigensystems. */ -/* > On exit, Q contains the trailing (N-K) updated eigenvectors */ -/* > (those which were deflated) in its last N-K columns. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDQ */ -/* > \verbatim */ -/* > LDQ is INTEGER */ -/* > The leading dimension of the array Q. LDQ >= max( 1, N ). */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension (N) */ -/* > On entry, D contains the eigenvalues of the two submatrices to */ -/* > be combined. On exit, D contains the trailing (N-K) updated */ -/* > eigenvalues (those which were deflated) sorted into increasing */ -/* > order. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] RHO */ -/* > \verbatim */ -/* > RHO is DOUBLE PRECISION */ -/* > Contains the off diagonal element associated with the rank-1 */ -/* > cut which originally split the two submatrices which are now */ -/* > being recombined. RHO is modified during the computation to */ -/* > the value required by DLAED3. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] CUTPNT */ -/* > \verbatim */ -/* > CUTPNT is INTEGER */ -/* > Contains the location of the last eigenvalue in the leading */ -/* > sub-matrix. MIN(1,N) <= CUTPNT <= N. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] Z */ -/* > \verbatim */ -/* > Z is DOUBLE PRECISION array, dimension (N) */ -/* > On input this vector contains the updating vector (the last */ -/* > row of the first sub-eigenvector matrix and the first row of */ -/* > the second sub-eigenvector matrix). The contents of Z are */ -/* > destroyed during the updating process. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] DLAMDA */ -/* > \verbatim */ -/* > DLAMDA is DOUBLE PRECISION array, dimension (N) */ -/* > Contains a copy of the first K eigenvalues which will be used */ -/* > by DLAED3 to form the secular equation. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] Q2 */ -/* > \verbatim */ -/* > Q2 is COMPLEX*16 array, dimension (LDQ2,N) */ -/* > If ICOMPQ = 0, Q2 is not referenced. Otherwise, */ -/* > Contains a copy of the first K eigenvectors which will be used */ -/* > by DLAED7 in a matrix multiply (DGEMM) to update the new */ -/* > eigenvectors. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDQ2 */ -/* > \verbatim */ -/* > LDQ2 is INTEGER */ -/* > The leading dimension of the array Q2. LDQ2 >= max( 1, N ). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] W */ -/* > \verbatim */ -/* > W is DOUBLE PRECISION array, dimension (N) */ -/* > This will hold the first k values of the final */ -/* > deflation-altered z-vector and will be passed to DLAED3. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INDXP */ -/* > \verbatim */ -/* > INDXP is INTEGER array, dimension (N) */ -/* > This will contain the permutation used to place deflated */ -/* > values of D at the end of the array. On output INDXP(1:K) */ -/* > points to the nondeflated D-values and INDXP(K+1:N) */ -/* > points to the deflated eigenvalues. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INDX */ -/* > \verbatim */ -/* > INDX is INTEGER array, dimension (N) */ -/* > This will contain the permutation used to sort the contents of */ -/* > D into ascending order. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INDXQ */ -/* > \verbatim */ -/* > INDXQ is INTEGER array, dimension (N) */ -/* > This contains the permutation which separately sorts the two */ -/* > sub-problems in D into ascending order. Note that elements in */ -/* > the second half of this permutation must first have CUTPNT */ -/* > added to their values in order to be accurate. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] PERM */ -/* > \verbatim */ -/* > PERM is INTEGER array, dimension (N) */ -/* > Contains the permutations (from deflation and sorting) to be */ -/* > applied to each eigenblock. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] GIVPTR */ -/* > \verbatim */ -/* > GIVPTR is INTEGER */ -/* > Contains the number of Givens rotations which took place in */ -/* > this subproblem. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] GIVCOL */ -/* > \verbatim */ -/* > GIVCOL is INTEGER array, dimension (2, N) */ -/* > Each pair of numbers indicates a pair of columns to take place */ -/* > in a Givens rotation. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] GIVNUM */ -/* > \verbatim */ -/* > GIVNUM is DOUBLE PRECISION array, dimension (2, N) */ -/* > Each number indicates the S value to be used in the */ -/* > corresponding Givens rotation. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit. */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16OTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int zlaed8_(integer *k, integer *n, integer *qsiz, - doublecomplex *q, integer *ldq, doublereal *d__, doublereal *rho, - integer *cutpnt, doublereal *z__, doublereal *dlamda, doublecomplex * - q2, integer *ldq2, doublereal *w, integer *indxp, integer *indx, - integer *indxq, integer *perm, integer *givptr, integer *givcol, - doublereal *givnum, integer *info) +int zlaed8_(integer *k, integer *n, integer *qsiz, doublecomplex *q, integer *ldq, doublereal *d__, + doublereal *rho, integer *cutpnt, doublereal *z__, doublereal *dlamda, + doublecomplex *q2, integer *ldq2, doublereal *w, integer *indxp, integer *indx, + integer *indxq, integer *perm, integer *givptr, integer *givcol, doublereal *givnum, + integer *info) { - /* System generated locals */ integer q_dim1, q_offset, q2_dim1, q2_offset, i__1; doublereal d__1; - - /* Builtin functions */ double sqrt(doublereal); - - /* Local variables */ doublereal c__; integer i__, j; doublereal s, t; integer k2, n1, n2, jp, n1p1; doublereal eps, tau, tol; integer jlam, imax, jmax; - extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, - integer *), dcopy_(integer *, doublereal *, integer *, doublereal - *, integer *), zdrot_(integer *, doublecomplex *, integer *, - doublecomplex *, integer *, doublereal *, doublereal *), zcopy_( - integer *, doublecomplex *, integer *, doublecomplex *, integer *) - ; - extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, - ftnlen); + extern int dscal_(integer *, doublereal *, doublereal *, integer *), + dcopy_(integer *, doublereal *, integer *, doublereal *, integer *), + zdrot_(integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, + doublereal *), + zcopy_(integer *, doublecomplex *, integer *, doublecomplex *, integer *); + extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, ftnlen); extern integer idamax_(integer *, doublereal *, integer *); - extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *, - integer *, integer *, integer *), xerbla_(char *, integer *, - ftnlen), zlacpy_(char *, integer *, integer *, doublecomplex *, - integer *, doublecomplex *, integer *, ftnlen); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ + extern int dlamrg_(integer *, integer *, doublereal *, integer *, integer *, integer *), + xerbla_(char *, integer *, ftnlen), + zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, + integer *, ftnlen); q_dim1 = *ldq; q_offset = 1 + q_dim1; q -= q_offset; @@ -326,19 +46,16 @@ f"> */ --perm; givcol -= 3; givnum -= 3; - - /* Function Body */ *info = 0; - if (*n < 0) { *info = -2; } else if (*qsiz < *n) { *info = -3; - } else if (*ldq < max(1,*n)) { + } else if (*ldq < max(1, *n)) { *info = -5; - } else if (*cutpnt < min(1,*n) || *cutpnt > *n) { + } else if (*cutpnt < min(1, *n) || *cutpnt > *n) { *info = -8; - } else if (*ldq2 < max(1,*n)) { + } else if (*ldq2 < max(1, *n)) { *info = -12; } if (*info != 0) { @@ -346,51 +63,31 @@ f"> */ xerbla_((char *)"ZLAED8", &i__1, (ftnlen)6); return 0; } - -/* Need to initialize GIVPTR to O here in case of quick exit */ -/* to prevent an unspecified code behavior (usually sigfault) */ -/* when IWORK array on entry to *stedc is not zeroed */ -/* (or at least some IWORK entries which used in *laed7 for GIVPTR). */ - *givptr = 0; - -/* Quick return if possible */ - if (*n == 0) { return 0; } - n1 = *cutpnt; n2 = *n - n1; n1p1 = n1 + 1; - if (*rho < 0.) { dscal_(&n2, &c_b3, &z__[n1p1], &c__1); } - -/* Normalize z so that norm(z) = 1 */ - t = 1. / sqrt(2.); i__1 = *n; for (j = 1; j <= i__1; ++j) { indx[j] = j; -/* L10: */ } dscal_(n, &t, &z__[1], &c__1); *rho = (d__1 = *rho * 2., abs(d__1)); - -/* Sort the eigenvalues into increasing order */ - i__1 = *n; for (i__ = *cutpnt + 1; i__ <= i__1; ++i__) { indxq[i__] += *cutpnt; -/* L20: */ } i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { dlamda[i__] = d__[indxq[i__]]; w[i__] = z__[indxq[i__]]; -/* L30: */ } i__ = 1; j = *cutpnt + 1; @@ -399,48 +96,26 @@ f"> */ for (i__ = 1; i__ <= i__1; ++i__) { d__[i__] = dlamda[indx[i__]]; z__[i__] = w[indx[i__]]; -/* L40: */ } - -/* Calculate the allowable deflation tolerance */ - imax = idamax_(n, &z__[1], &c__1); jmax = idamax_(n, &d__[1], &c__1); eps = dlamch_((char *)"Epsilon", (ftnlen)7); tol = eps * 8. * (d__1 = d__[jmax], abs(d__1)); - -/* If the rank-1 modifier is small enough, no more needs to be done */ -/* -- except to reorganize Q so that its columns correspond with the */ -/* elements in D. */ - if (*rho * (d__1 = z__[imax], abs(d__1)) <= tol) { *k = 0; i__1 = *n; for (j = 1; j <= i__1; ++j) { perm[j] = indxq[indx[j]]; - zcopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 + 1] - , &c__1); -/* L50: */ + zcopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 + 1], &c__1); } - zlacpy_((char *)"A", qsiz, n, &q2[q2_dim1 + 1], ldq2, &q[q_dim1 + 1], ldq, ( - ftnlen)1); + zlacpy_((char *)"A", qsiz, n, &q2[q2_dim1 + 1], ldq2, &q[q_dim1 + 1], ldq, (ftnlen)1); return 0; } - -/* If there are multiple eigenvalues then the problem deflates. Here */ -/* the number of equal eigenvalues are found. As each equal */ -/* eigenvalue is found, an elementary reflector is computed to rotate */ -/* the corresponding eigensubspace so that the corresponding */ -/* components of Z are zero in this new basis. */ - *k = 0; k2 = *n + 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { if (*rho * (d__1 = z__[j], abs(d__1)) <= tol) { - -/* Deflate due to small z component. */ - --k2; indxp[k2] = j; if (j == *n) { @@ -450,7 +125,6 @@ f"> */ jlam = j; goto L70; } -/* L60: */ } L70: ++j; @@ -458,47 +132,31 @@ L70: goto L90; } if (*rho * (d__1 = z__[j], abs(d__1)) <= tol) { - -/* Deflate due to small z component. */ - --k2; indxp[k2] = j; } else { - -/* Check if eigenvalues are close enough to allow deflation. */ - s = z__[jlam]; c__ = z__[j]; - -/* Find sqrt(a**2+b**2) without overflow or */ -/* destructive underflow. */ - tau = dlapy2_(&c__, &s); t = d__[j] - d__[jlam]; c__ /= tau; s = -s / tau; if ((d__1 = t * c__ * s, abs(d__1)) <= tol) { - -/* Deflation is possible. */ - z__[j] = tau; z__[jlam] = 0.; - -/* Record the appropriate Givens rotation */ - ++(*givptr); givcol[(*givptr << 1) + 1] = indxq[indx[jlam]]; givcol[(*givptr << 1) + 2] = indxq[indx[j]]; givnum[(*givptr << 1) + 1] = c__; givnum[(*givptr << 1) + 2] = s; - zdrot_(qsiz, &q[indxq[indx[jlam]] * q_dim1 + 1], &c__1, &q[indxq[ - indx[j]] * q_dim1 + 1], &c__1, &c__, &s); + zdrot_(qsiz, &q[indxq[indx[jlam]] * q_dim1 + 1], &c__1, &q[indxq[indx[j]] * q_dim1 + 1], + &c__1, &c__, &s); t = d__[jlam] * c__ * c__ + d__[j] * s * s; d__[j] = d__[jlam] * s * s + d__[j] * c__ * c__; d__[jlam] = t; --k2; i__ = 1; -L80: + L80: if (k2 + i__ <= *n) { if (d__[jlam] < d__[indxp[k2 + i__]]) { indxp[k2 + i__ - 1] = indxp[k2 + i__]; @@ -522,48 +180,27 @@ L80: } goto L70; L90: - -/* Record the last eigenvalue. */ - ++(*k); w[*k] = z__[jlam]; dlamda[*k] = d__[jlam]; indxp[*k] = jlam; - L100: - -/* Sort the eigenvalues and corresponding eigenvectors into DLAMDA */ -/* and Q2 respectively. The eigenvalues/vectors which were not */ -/* deflated go into the first K slots of DLAMDA and Q2 respectively, */ -/* while those which were deflated go into the last N - K slots. */ - i__1 = *n; for (j = 1; j <= i__1; ++j) { jp = indxp[j]; dlamda[j] = d__[jp]; perm[j] = indxq[indx[jp]]; - zcopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 + 1], & - c__1); -/* L110: */ + zcopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 + 1], &c__1); } - -/* The deflated eigenvalues and their corresponding vectors go back */ -/* into the last N - K slots of D and Q respectively. */ - if (*k < *n) { i__1 = *n - *k; dcopy_(&i__1, &dlamda[*k + 1], &c__1, &d__[*k + 1], &c__1); i__1 = *n - *k; - zlacpy_((char *)"A", qsiz, &i__1, &q2[(*k + 1) * q2_dim1 + 1], ldq2, &q[(*k + - 1) * q_dim1 + 1], ldq, (ftnlen)1); + zlacpy_((char *)"A", qsiz, &i__1, &q2[(*k + 1) * q2_dim1 + 1], ldq2, &q[(*k + 1) * q_dim1 + 1], ldq, + (ftnlen)1); } - return 0; - -/* End of ZLAED8 */ - -} /* zlaed8_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zlanhe.cpp b/lib/linalg/zlanhe.cpp index 6db6cc5cef..e0538d3084 100644 --- a/lib/linalg/zlanhe.cpp +++ b/lib/linalg/zlanhe.cpp @@ -1,206 +1,27 @@ -/* fortran/zlanhe.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; - -/* > \brief \b ZLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the ele -ment of largest absolute value of a complex Hermitian matrix. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZLANHE + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* DOUBLE PRECISION FUNCTION ZLANHE( NORM, UPLO, N, A, LDA, WORK ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER NORM, UPLO */ -/* INTEGER LDA, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION WORK( * ) */ -/* COMPLEX*16 A( LDA, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZLANHE returns the value of the one norm, or the Frobenius norm, or */ -/* > the infinity norm, or the element of largest absolute value of a */ -/* > complex hermitian matrix A. */ -/* > \endverbatim */ -/* > */ -/* > \return ZLANHE */ -/* > \verbatim */ -/* > */ -/* > ZLANHE = ( max(abs(A(i,j))), NORM = 'M' or 'm' */ -/* > ( */ -/* > ( norm1(A), NORM = '1', 'O' or 'o' */ -/* > ( */ -/* > ( normI(A), NORM = 'I' or 'i' */ -/* > ( */ -/* > ( normF(A), NORM = 'F', 'f', 'E' or 'e' */ -/* > */ -/* > where norm1 denotes the one norm of a matrix (maximum column sum), */ -/* > normI denotes the infinity norm of a matrix (maximum row sum) and */ -/* > normF denotes the Frobenius norm of a matrix (square root of sum of */ -/* > squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] NORM */ -/* > \verbatim */ -/* > NORM is CHARACTER*1 */ -/* > Specifies the value to be returned in ZLANHE as described */ -/* > above. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > Specifies whether the upper or lower triangular part of the */ -/* > hermitian matrix A is to be referenced. */ -/* > = 'U': Upper triangular part of A is referenced */ -/* > = 'L': Lower triangular part of A is referenced */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrix A. N >= 0. When N = 0, ZLANHE is */ -/* > set to zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is COMPLEX*16 array, dimension (LDA,N) */ -/* > The hermitian matrix A. If UPLO = 'U', the leading n by n */ -/* > upper triangular part of A contains the upper triangular part */ -/* > of the matrix A, and the strictly lower triangular part of A */ -/* > is not referenced. If UPLO = 'L', the leading n by n lower */ -/* > triangular part of A contains the lower triangular part of */ -/* > the matrix A, and the strictly upper triangular part of A is */ -/* > not referenced. Note that the imaginary parts of the diagonal */ -/* > elements need not be set and are assumed to be zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(N,1). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), */ -/* > where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, */ -/* > WORK is not referenced. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16HEauxiliary */ - -/* ===================================================================== */ -doublereal zlanhe_(char *norm, char *uplo, integer *n, doublecomplex *a, - integer *lda, doublereal *work, ftnlen norm_len, ftnlen uplo_len) +doublereal zlanhe_(char *norm, char *uplo, integer *n, doublecomplex *a, integer *lda, + doublereal *work, ftnlen norm_len, ftnlen uplo_len) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; doublereal ret_val, d__1; - - /* Builtin functions */ double z_lmp_abs(doublecomplex *), sqrt(doublereal); - - /* Local variables */ integer i__, j; doublereal sum, absa, scale; extern logical lsame_(char *, char *, ftnlen, ftnlen); doublereal value; extern logical disnan_(doublereal *); - extern /* Subroutine */ int zlassq_(integer *, doublecomplex *, integer *, - doublereal *, doublereal *); - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - - /* Parameter adjustments */ + extern int zlassq_(integer *, doublecomplex *, integer *, doublereal *, doublereal *); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --work; - - /* Function Body */ if (*n == 0) { value = 0.; } else if (lsame_(norm, (char *)"M", (ftnlen)1, (ftnlen)1)) { - -/* Find max(abs(A(i,j))). */ - value = 0.; if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { i__1 = *n; @@ -211,14 +32,12 @@ doublereal zlanhe_(char *norm, char *uplo, integer *n, doublecomplex *a, if (value < sum || disnan_(&sum)) { value = sum; } -/* L10: */ } i__2 = j + j * a_dim1; sum = (d__1 = a[i__2].r, abs(d__1)); if (value < sum || disnan_(&sum)) { value = sum; } -/* L20: */ } } else { i__1 = *n; @@ -234,16 +53,11 @@ doublereal zlanhe_(char *norm, char *uplo, integer *n, doublecomplex *a, if (value < sum || disnan_(&sum)) { value = sum; } -/* L30: */ } -/* L40: */ } } - } else if (lsame_(norm, (char *)"I", (ftnlen)1, (ftnlen)1) || lsame_(norm, (char *)"O", ( - ftnlen)1, (ftnlen)1) || *(unsigned char *)norm == '1') { - -/* Find normI(A) ( = norm1(A), since A is hermitian). */ - + } else if (lsame_(norm, (char *)"I", (ftnlen)1, (ftnlen)1) || lsame_(norm, (char *)"O", (ftnlen)1, (ftnlen)1) || + *(unsigned char *)norm == '1') { value = 0.; if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { i__1 = *n; @@ -254,11 +68,9 @@ doublereal zlanhe_(char *norm, char *uplo, integer *n, doublecomplex *a, absa = z_lmp_abs(&a[i__ + j * a_dim1]); sum += absa; work[i__] += absa; -/* L50: */ } i__2 = j + j * a_dim1; work[j] = sum + (d__1 = a[i__2].r, abs(d__1)); -/* L60: */ } i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { @@ -266,13 +78,11 @@ doublereal zlanhe_(char *norm, char *uplo, integer *n, doublecomplex *a, if (value < sum || disnan_(&sum)) { value = sum; } -/* L70: */ } } else { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { work[i__] = 0.; -/* L80: */ } i__1 = *n; for (j = 1; j <= i__1; ++j) { @@ -283,19 +93,13 @@ doublereal zlanhe_(char *norm, char *uplo, integer *n, doublecomplex *a, absa = z_lmp_abs(&a[i__ + j * a_dim1]); sum += absa; work[i__] += absa; -/* L90: */ } if (value < sum || disnan_(&sum)) { value = sum; } -/* L100: */ } } - } else if (lsame_(norm, (char *)"F", (ftnlen)1, (ftnlen)1) || lsame_(norm, (char *)"E", ( - ftnlen)1, (ftnlen)1)) { - -/* Find normF(A). */ - + } else if (lsame_(norm, (char *)"F", (ftnlen)1, (ftnlen)1) || lsame_(norm, (char *)"E", (ftnlen)1, (ftnlen)1)) { scale = 0.; sum = 1.; if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { @@ -303,14 +107,12 @@ doublereal zlanhe_(char *norm, char *uplo, integer *n, doublecomplex *a, for (j = 2; j <= i__1; ++j) { i__2 = j - 1; zlassq_(&i__2, &a[j * a_dim1 + 1], &c__1, &scale, &sum); -/* L110: */ } } else { i__1 = *n - 1; for (j = 1; j <= i__1; ++j) { i__2 = *n - j; zlassq_(&i__2, &a[j + 1 + j * a_dim1], &c__1, &scale, &sum); -/* L120: */ } } sum *= 2; @@ -321,28 +123,20 @@ doublereal zlanhe_(char *norm, char *uplo, integer *n, doublecomplex *a, i__2 = i__ + i__ * a_dim1; absa = (d__1 = a[i__2].r, abs(d__1)); if (scale < absa) { -/* Computing 2nd power */ d__1 = scale / absa; sum = sum * (d__1 * d__1) + 1.; scale = absa; } else { -/* Computing 2nd power */ d__1 = absa / scale; sum += d__1 * d__1; } } -/* L130: */ } value = scale * sqrt(sum); } - ret_val = value; return ret_val; - -/* End of ZLANHE */ - -} /* zlanhe_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zlarf.cpp b/lib/linalg/zlarf.cpp index 7bee520eae..7f7468bcf9 100644 --- a/lib/linalg/zlarf.cpp +++ b/lib/linalg/zlarf.cpp @@ -1,213 +1,35 @@ -/* fortran/zlarf.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - -static doublecomplex c_b1 = {1.,0.}; -static doublecomplex c_b2 = {0.,0.}; +static doublecomplex c_b1 = {1., 0.}; +static doublecomplex c_b2 = {0., 0.}; static integer c__1 = 1; - -/* > \brief \b ZLARF applies an elementary reflector to a general rectangular matrix. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZLARF + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER SIDE */ -/* INTEGER INCV, LDC, M, N */ -/* COMPLEX*16 TAU */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 C( LDC, * ), V( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZLARF applies a complex elementary reflector H to a complex M-by-N */ -/* > matrix C, from either the left or the right. H is represented in the */ -/* > form */ -/* > */ -/* > H = I - tau * v * v**H */ -/* > */ -/* > where tau is a complex scalar and v is a complex vector. */ -/* > */ -/* > If tau = 0, then H is taken to be the unit matrix. */ -/* > */ -/* > To apply H**H, supply conjg(tau) instead */ -/* > tau. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] SIDE */ -/* > \verbatim */ -/* > SIDE is CHARACTER*1 */ -/* > = 'L': form H * C */ -/* > = 'R': form C * H */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix C. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix C. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] V */ -/* > \verbatim */ -/* > V is COMPLEX*16 array, dimension */ -/* > (1 + (M-1)*abs(INCV)) if SIDE = 'L' */ -/* > or (1 + (N-1)*abs(INCV)) if SIDE = 'R' */ -/* > The vector v in the representation of H. V is not used if */ -/* > TAU = 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCV */ -/* > \verbatim */ -/* > INCV is INTEGER */ -/* > The increment between elements of v. INCV <> 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TAU */ -/* > \verbatim */ -/* > TAU is COMPLEX*16 */ -/* > The value tau in the representation of H. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] C */ -/* > \verbatim */ -/* > C is COMPLEX*16 array, dimension (LDC,N) */ -/* > On entry, the M-by-N matrix C. */ -/* > On exit, C is overwritten by the matrix H * C if SIDE = 'L', */ -/* > or C * H if SIDE = 'R'. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDC */ -/* > \verbatim */ -/* > LDC is INTEGER */ -/* > The leading dimension of the array C. LDC >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is COMPLEX*16 array, dimension */ -/* > (N) if SIDE = 'L' */ -/* > or (M) if SIDE = 'R' */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16OTHERauxiliary */ - -/* ===================================================================== */ -/* Subroutine */ int zlarf_(char *side, integer *m, integer *n, doublecomplex - *v, integer *incv, doublecomplex *tau, doublecomplex *c__, integer * - ldc, doublecomplex *work, ftnlen side_len) +int zlarf_(char *side, integer *m, integer *n, doublecomplex *v, integer *incv, doublecomplex *tau, + doublecomplex *c__, integer *ldc, doublecomplex *work, ftnlen side_len) { - /* System generated locals */ integer c_dim1, c_offset, i__1; doublecomplex z__1; - - /* Local variables */ integer i__; logical applyleft; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer lastc; - extern /* Subroutine */ int zgerc_(integer *, integer *, doublecomplex *, - doublecomplex *, integer *, doublecomplex *, integer *, - doublecomplex *, integer *), zgemv_(char *, integer *, integer *, - doublecomplex *, doublecomplex *, integer *, doublecomplex *, - integer *, doublecomplex *, doublecomplex *, integer *, ftnlen); + extern int zgerc_(integer *, integer *, doublecomplex *, doublecomplex *, integer *, + doublecomplex *, integer *, doublecomplex *, integer *), + zgemv_(char *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, + doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, ftnlen); integer lastv; extern integer ilazlc_(integer *, integer *, doublecomplex *, integer *), - ilazlr_(integer *, integer *, doublecomplex *, integer *); - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - - /* Parameter adjustments */ + ilazlr_(integer *, integer *, doublecomplex *, integer *); --v; c_dim1 = *ldc; c_offset = 1 + c_dim1; c__ -= c_offset; --work; - - /* Function Body */ applyleft = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); lastv = 0; lastc = 0; if (tau->r != 0. || tau->i != 0.) { -/* Set up variables for scanning V. LASTV begins pointing to the end */ -/* of V. */ if (applyleft) { lastv = *m; } else { @@ -218,66 +40,35 @@ static integer c__1 = 1; } else { i__ = 1; } -/* Look for the last non-zero row in V. */ - for(;;) { /* while(complicated condition) */ + for (;;) { i__1 = i__; - if (!(lastv > 0 && (v[i__1].r == 0. && v[i__1].i == 0.))) - break; + if (!(lastv > 0 && (v[i__1].r == 0. && v[i__1].i == 0.))) break; --lastv; i__ -= *incv; } if (applyleft) { -/* Scan for the last non-zero column in C(1:lastv,:). */ lastc = ilazlc_(&lastv, n, &c__[c_offset], ldc); } else { -/* Scan for the last non-zero row in C(:,1:lastv). */ lastc = ilazlr_(m, &lastv, &c__[c_offset], ldc); } } -/* Note that lastc.eq.0 renders the BLAS operations null; no special */ -/* case is needed at this level. */ if (applyleft) { - -/* Form H * C */ - if (lastv > 0) { - -/* w(1:lastc,1) := C(1:lastv,1:lastc)**H * v(1:lastv,1) */ - - zgemv_((char *)"Conjugate transpose", &lastv, &lastc, &c_b1, &c__[ - c_offset], ldc, &v[1], incv, &c_b2, &work[1], &c__1, ( - ftnlen)19); - -/* C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**H */ - + zgemv_((char *)"Conjugate transpose", &lastv, &lastc, &c_b1, &c__[c_offset], ldc, &v[1], incv, + &c_b2, &work[1], &c__1, (ftnlen)19); z__1.r = -tau->r, z__1.i = -tau->i; - zgerc_(&lastv, &lastc, &z__1, &v[1], incv, &work[1], &c__1, &c__[ - c_offset], ldc); + zgerc_(&lastv, &lastc, &z__1, &v[1], incv, &work[1], &c__1, &c__[c_offset], ldc); } } else { - -/* Form C * H */ - if (lastv > 0) { - -/* w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1) */ - - zgemv_((char *)"No transpose", &lastc, &lastv, &c_b1, &c__[c_offset], ldc, - &v[1], incv, &c_b2, &work[1], &c__1, (ftnlen)12); - -/* C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**H */ - + zgemv_((char *)"No transpose", &lastc, &lastv, &c_b1, &c__[c_offset], ldc, &v[1], incv, &c_b2, + &work[1], &c__1, (ftnlen)12); z__1.r = -tau->r, z__1.i = -tau->i; - zgerc_(&lastc, &lastv, &z__1, &work[1], &c__1, &v[1], incv, &c__[ - c_offset], ldc); + zgerc_(&lastc, &lastv, &z__1, &work[1], &c__1, &v[1], incv, &c__[c_offset], ldc); } } return 0; - -/* End of ZLARF */ - -} /* zlarf_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zlarfb.cpp b/lib/linalg/zlarfb.cpp index e9015669ca..6b0d62e99f 100644 --- a/lib/linalg/zlarfb.cpp +++ b/lib/linalg/zlarfb.cpp @@ -1,277 +1,29 @@ -/* fortran/zlarfb.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - -static doublecomplex c_b1 = {1.,0.}; +static doublecomplex c_b1 = {1., 0.}; static integer c__1 = 1; - -/* > \brief \b ZLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZLARFB + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, */ -/* T, LDT, C, LDC, WORK, LDWORK ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER DIRECT, SIDE, STOREV, TRANS */ -/* INTEGER K, LDC, LDT, LDV, LDWORK, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 C( LDC, * ), T( LDT, * ), V( LDV, * ), */ -/* $ WORK( LDWORK, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZLARFB applies a complex block reflector H or its transpose H**H to a */ -/* > complex M-by-N matrix C, from either the left or the right. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] SIDE */ -/* > \verbatim */ -/* > SIDE is CHARACTER*1 */ -/* > = 'L': apply H or H**H from the Left */ -/* > = 'R': apply H or H**H from the Right */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TRANS */ -/* > \verbatim */ -/* > TRANS is CHARACTER*1 */ -/* > = 'N': apply H (No transpose) */ -/* > = 'C': apply H**H (Conjugate transpose) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DIRECT */ -/* > \verbatim */ -/* > DIRECT is CHARACTER*1 */ -/* > Indicates how H is formed from a product of elementary */ -/* > reflectors */ -/* > = 'F': H = H(1) H(2) . . . H(k) (Forward) */ -/* > = 'B': H = H(k) . . . H(2) H(1) (Backward) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] STOREV */ -/* > \verbatim */ -/* > STOREV is CHARACTER*1 */ -/* > Indicates how the vectors which define the elementary */ -/* > reflectors are stored: */ -/* > = 'C': Columnwise */ -/* > = 'R': Rowwise */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix C. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix C. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > The order of the matrix T (= the number of elementary */ -/* > reflectors whose product defines the block reflector). */ -/* > If SIDE = 'L', M >= K >= 0; */ -/* > if SIDE = 'R', N >= K >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] V */ -/* > \verbatim */ -/* > V is COMPLEX*16 array, dimension */ -/* > (LDV,K) if STOREV = 'C' */ -/* > (LDV,M) if STOREV = 'R' and SIDE = 'L' */ -/* > (LDV,N) if STOREV = 'R' and SIDE = 'R' */ -/* > See Further Details. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDV */ -/* > \verbatim */ -/* > LDV is INTEGER */ -/* > The leading dimension of the array V. */ -/* > If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M); */ -/* > if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N); */ -/* > if STOREV = 'R', LDV >= K. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] T */ -/* > \verbatim */ -/* > T is COMPLEX*16 array, dimension (LDT,K) */ -/* > The triangular K-by-K matrix T in the representation of the */ -/* > block reflector. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDT */ -/* > \verbatim */ -/* > LDT is INTEGER */ -/* > The leading dimension of the array T. LDT >= K. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] C */ -/* > \verbatim */ -/* > C is COMPLEX*16 array, dimension (LDC,N) */ -/* > On entry, the M-by-N matrix C. */ -/* > On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDC */ -/* > \verbatim */ -/* > LDC is INTEGER */ -/* > The leading dimension of the array C. LDC >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is COMPLEX*16 array, dimension (LDWORK,K) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDWORK */ -/* > \verbatim */ -/* > LDWORK is INTEGER */ -/* > The leading dimension of the array WORK. */ -/* > If SIDE = 'L', LDWORK >= max(1,N); */ -/* > if SIDE = 'R', LDWORK >= max(1,M). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16OTHERauxiliary */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > The shape of the matrix V and the storage of the vectors which define */ -/* > the H(i) is best illustrated by the following example with n = 5 and */ -/* > k = 3. The elements equal to 1 are not stored; the corresponding */ -/* > array elements are modified but restored on exit. The rest of the */ -/* > array is not used. */ -/* > */ -/* > DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': */ -/* > */ -/* > V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) */ -/* > ( v1 1 ) ( 1 v2 v2 v2 ) */ -/* > ( v1 v2 1 ) ( 1 v3 v3 ) */ -/* > ( v1 v2 v3 ) */ -/* > ( v1 v2 v3 ) */ -/* > */ -/* > DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': */ -/* > */ -/* > V = ( v1 v2 v3 ) V = ( v1 v1 1 ) */ -/* > ( v1 v2 v3 ) ( v2 v2 v2 1 ) */ -/* > ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) */ -/* > ( 1 v3 ) */ -/* > ( 1 ) */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int zlarfb_(char *side, char *trans, char *direct, char * - storev, integer *m, integer *n, integer *k, doublecomplex *v, integer - *ldv, doublecomplex *t, integer *ldt, doublecomplex *c__, integer * - ldc, doublecomplex *work, integer *ldwork, ftnlen side_len, ftnlen - trans_len, ftnlen direct_len, ftnlen storev_len) +int zlarfb_(char *side, char *trans, char *direct, char *storev, integer *m, integer *n, integer *k, + doublecomplex *v, integer *ldv, doublecomplex *t, integer *ldt, doublecomplex *c__, + integer *ldc, doublecomplex *work, integer *ldwork, ftnlen side_len, ftnlen trans_len, + ftnlen direct_len, ftnlen storev_len) { - /* System generated locals */ - integer c_dim1, c_offset, t_dim1, t_offset, v_dim1, v_offset, work_dim1, - work_offset, i__1, i__2, i__3, i__4, i__5; + integer c_dim1, c_offset, t_dim1, t_offset, v_dim1, v_offset, work_dim1, work_offset, i__1, + i__2, i__3, i__4, i__5; doublecomplex z__1, z__2; - - /* Builtin functions */ void d_lmp_cnjg(doublecomplex *, doublecomplex *); - - /* Local variables */ integer i__, j; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *, - integer *, doublecomplex *, doublecomplex *, integer *, - doublecomplex *, integer *, doublecomplex *, doublecomplex *, - integer *, ftnlen, ftnlen), zcopy_(integer *, doublecomplex *, - integer *, doublecomplex *, integer *), ztrmm_(char *, char *, - char *, char *, integer *, integer *, doublecomplex *, - doublecomplex *, integer *, doublecomplex *, integer *, ftnlen, - ftnlen, ftnlen, ftnlen), zlacgv_(integer *, doublecomplex *, - integer *); + extern int zgemm_(char *, char *, integer *, integer *, integer *, doublecomplex *, + doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, + doublecomplex *, integer *, ftnlen, ftnlen), + zcopy_(integer *, doublecomplex *, integer *, doublecomplex *, integer *), + ztrmm_(char *, char *, char *, char *, integer *, integer *, doublecomplex *, + doublecomplex *, integer *, doublecomplex *, integer *, ftnlen, ftnlen, ftnlen, + ftnlen), + zlacgv_(integer *, doublecomplex *, integer *); char transt[1]; - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Quick return if possible */ - - /* Parameter adjustments */ v_dim1 = *ldv; v_offset = 1 + v_dim1; v -= v_offset; @@ -284,87 +36,42 @@ f"> */ work_dim1 = *ldwork; work_offset = 1 + work_dim1; work -= work_offset; - - /* Function Body */ if (*m <= 0 || *n <= 0) { return 0; } - if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { *(unsigned char *)transt = 'C'; } else { *(unsigned char *)transt = 'N'; } - if (lsame_(storev, (char *)"C", (ftnlen)1, (ftnlen)1)) { - if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { - -/* Let V = ( V1 ) (first K rows) */ -/* ( V2 ) */ -/* where V1 is unit lower triangular. */ - if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { - -/* Form H * C or H**H * C where C = ( C1 ) */ -/* ( C2 ) */ - -/* W := C**H * V = (C1**H * V1 + C2**H * V2) (stored in WORK) */ - -/* W := C1**H */ - i__1 = *k; for (j = 1; j <= i__1; ++j) { - zcopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1], - &c__1); + zcopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1], &c__1); zlacgv_(n, &work[j * work_dim1 + 1], &c__1); -/* L10: */ } - -/* W := W * V1 */ - - ztrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", n, k, &c_b1, - &v[v_offset], ldv, &work[work_offset], ldwork, ( - ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); + ztrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", n, k, &c_b1, &v[v_offset], ldv, + &work[work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); if (*m > *k) { - -/* W := W + C2**H * V2 */ - i__1 = *m - *k; - zgemm_((char *)"Conjugate transpose", (char *)"No transpose", n, k, &i__1, - &c_b1, &c__[*k + 1 + c_dim1], ldc, &v[*k + 1 + - v_dim1], ldv, &c_b1, &work[work_offset], ldwork, ( - ftnlen)19, (ftnlen)12); + zgemm_((char *)"Conjugate transpose", (char *)"No transpose", n, k, &i__1, &c_b1, + &c__[*k + 1 + c_dim1], ldc, &v[*k + 1 + v_dim1], ldv, &c_b1, + &work[work_offset], ldwork, (ftnlen)19, (ftnlen)12); } - -/* W := W * T**H or W * T */ - - ztrmm_((char *)"Right", (char *)"Upper", transt, (char *)"Non-unit", n, k, &c_b1, &t[ - t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, - (ftnlen)5, (ftnlen)1, (ftnlen)8); - -/* C := C - V * W**H */ - + ztrmm_((char *)"Right", (char *)"Upper", transt, (char *)"Non-unit", n, k, &c_b1, &t[t_offset], ldt, + &work[work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)1, (ftnlen)8); if (*m > *k) { - -/* C2 := C2 - V2 * W**H */ - i__1 = *m - *k; z__1.r = -1., z__1.i = -0.; - zgemm_((char *)"No transpose", (char *)"Conjugate transpose", &i__1, n, k, - &z__1, &v[*k + 1 + v_dim1], ldv, &work[ - work_offset], ldwork, &c_b1, &c__[*k + 1 + c_dim1] - , ldc, (ftnlen)12, (ftnlen)19); + zgemm_((char *)"No transpose", (char *)"Conjugate transpose", &i__1, n, k, &z__1, + &v[*k + 1 + v_dim1], ldv, &work[work_offset], ldwork, &c_b1, + &c__[*k + 1 + c_dim1], ldc, (ftnlen)12, (ftnlen)19); } - -/* W := W * V1**H */ - - ztrmm_((char *)"Right", (char *)"Lower", (char *)"Conjugate transpose", (char *)"Unit", n, k, - &c_b1, &v[v_offset], ldv, &work[work_offset], ldwork, - (ftnlen)5, (ftnlen)5, (ftnlen)19, (ftnlen)4); - -/* C1 := C1 - W**H */ - + ztrmm_((char *)"Right", (char *)"Lower", (char *)"Conjugate transpose", (char *)"Unit", n, k, &c_b1, &v[v_offset], + ldv, &work[work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)19, + (ftnlen)4); i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *n; @@ -372,73 +79,35 @@ f"> */ i__3 = j + i__ * c_dim1; i__4 = j + i__ * c_dim1; d_lmp_cnjg(&z__2, &work[i__ + j * work_dim1]); - z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i - - z__2.i; + z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i - z__2.i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; -/* L20: */ } -/* L30: */ } - } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { - -/* Form C * H or C * H**H where C = ( C1 C2 ) */ - -/* W := C * V = (C1*V1 + C2*V2) (stored in WORK) */ - -/* W := C1 */ - i__1 = *k; for (j = 1; j <= i__1; ++j) { - zcopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j * - work_dim1 + 1], &c__1); -/* L40: */ + zcopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j * work_dim1 + 1], &c__1); } - -/* W := W * V1 */ - - ztrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", m, k, &c_b1, - &v[v_offset], ldv, &work[work_offset], ldwork, ( - ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); + ztrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", m, k, &c_b1, &v[v_offset], ldv, + &work[work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); if (*n > *k) { - -/* W := W + C2 * V2 */ - i__1 = *n - *k; zgemm_((char *)"No transpose", (char *)"No transpose", m, k, &i__1, &c_b1, - &c__[(*k + 1) * c_dim1 + 1], ldc, &v[*k + 1 + - v_dim1], ldv, &c_b1, &work[work_offset], ldwork, ( - ftnlen)12, (ftnlen)12); + &c__[(*k + 1) * c_dim1 + 1], ldc, &v[*k + 1 + v_dim1], ldv, &c_b1, + &work[work_offset], ldwork, (ftnlen)12, (ftnlen)12); } - -/* W := W * T or W * T**H */ - - ztrmm_((char *)"Right", (char *)"Upper", trans, (char *)"Non-unit", m, k, &c_b1, &t[ - t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, - (ftnlen)5, (ftnlen)1, (ftnlen)8); - -/* C := C - W * V**H */ - + ztrmm_((char *)"Right", (char *)"Upper", trans, (char *)"Non-unit", m, k, &c_b1, &t[t_offset], ldt, + &work[work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)1, (ftnlen)8); if (*n > *k) { - -/* C2 := C2 - W * V2**H */ - i__1 = *n - *k; z__1.r = -1., z__1.i = -0.; - zgemm_((char *)"No transpose", (char *)"Conjugate transpose", m, &i__1, k, - &z__1, &work[work_offset], ldwork, &v[*k + 1 + - v_dim1], ldv, &c_b1, &c__[(*k + 1) * c_dim1 + 1], - ldc, (ftnlen)12, (ftnlen)19); + zgemm_((char *)"No transpose", (char *)"Conjugate transpose", m, &i__1, k, &z__1, + &work[work_offset], ldwork, &v[*k + 1 + v_dim1], ldv, &c_b1, + &c__[(*k + 1) * c_dim1 + 1], ldc, (ftnlen)12, (ftnlen)19); } - -/* W := W * V1**H */ - - ztrmm_((char *)"Right", (char *)"Lower", (char *)"Conjugate transpose", (char *)"Unit", m, k, - &c_b1, &v[v_offset], ldv, &work[work_offset], ldwork, - (ftnlen)5, (ftnlen)5, (ftnlen)19, (ftnlen)4); - -/* C1 := C1 - W */ - + ztrmm_((char *)"Right", (char *)"Lower", (char *)"Conjugate transpose", (char *)"Unit", m, k, &c_b1, &v[v_offset], + ldv, &work[work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)19, + (ftnlen)4); i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *m; @@ -446,83 +115,39 @@ f"> */ i__3 = i__ + j * c_dim1; i__4 = i__ + j * c_dim1; i__5 = i__ + j * work_dim1; - z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[ - i__4].i - work[i__5].i; + z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[i__4].i - work[i__5].i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; -/* L50: */ } -/* L60: */ } } - } else { - -/* Let V = ( V1 ) */ -/* ( V2 ) (last K rows) */ -/* where V2 is unit upper triangular. */ - if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { - -/* Form H * C or H**H * C where C = ( C1 ) */ -/* ( C2 ) */ - -/* W := C**H * V = (C1**H * V1 + C2**H * V2) (stored in WORK) */ - -/* W := C2**H */ - i__1 = *k; for (j = 1; j <= i__1; ++j) { - zcopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j * - work_dim1 + 1], &c__1); + zcopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j * work_dim1 + 1], &c__1); zlacgv_(n, &work[j * work_dim1 + 1], &c__1); -/* L70: */ } - -/* W := W * V2 */ - ztrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", n, k, &c_b1, - &v[*m - *k + 1 + v_dim1], ldv, &work[work_offset], - ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); + &v[*m - *k + 1 + v_dim1], ldv, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)12, (ftnlen)4); if (*m > *k) { - -/* W := W + C1**H * V1 */ - i__1 = *m - *k; - zgemm_((char *)"Conjugate transpose", (char *)"No transpose", n, k, &i__1, - &c_b1, &c__[c_offset], ldc, &v[v_offset], ldv, & - c_b1, &work[work_offset], ldwork, (ftnlen)19, ( - ftnlen)12); + zgemm_((char *)"Conjugate transpose", (char *)"No transpose", n, k, &i__1, &c_b1, + &c__[c_offset], ldc, &v[v_offset], ldv, &c_b1, &work[work_offset], + ldwork, (ftnlen)19, (ftnlen)12); } - -/* W := W * T**H or W * T */ - - ztrmm_((char *)"Right", (char *)"Lower", transt, (char *)"Non-unit", n, k, &c_b1, &t[ - t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, - (ftnlen)5, (ftnlen)1, (ftnlen)8); - -/* C := C - V * W**H */ - + ztrmm_((char *)"Right", (char *)"Lower", transt, (char *)"Non-unit", n, k, &c_b1, &t[t_offset], ldt, + &work[work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)1, (ftnlen)8); if (*m > *k) { - -/* C1 := C1 - V1 * W**H */ - i__1 = *m - *k; z__1.r = -1., z__1.i = -0.; - zgemm_((char *)"No transpose", (char *)"Conjugate transpose", &i__1, n, k, - &z__1, &v[v_offset], ldv, &work[work_offset], - ldwork, &c_b1, &c__[c_offset], ldc, (ftnlen)12, ( - ftnlen)19); + zgemm_((char *)"No transpose", (char *)"Conjugate transpose", &i__1, n, k, &z__1, &v[v_offset], + ldv, &work[work_offset], ldwork, &c_b1, &c__[c_offset], ldc, (ftnlen)12, + (ftnlen)19); } - -/* W := W * V2**H */ - - ztrmm_((char *)"Right", (char *)"Upper", (char *)"Conjugate transpose", (char *)"Unit", n, k, - &c_b1, &v[*m - *k + 1 + v_dim1], ldv, &work[ - work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen) - 19, (ftnlen)4); - -/* C2 := C2 - W**H */ - + ztrmm_((char *)"Right", (char *)"Upper", (char *)"Conjugate transpose", (char *)"Unit", n, k, &c_b1, + &v[*m - *k + 1 + v_dim1], ldv, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)19, (ftnlen)4); i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *n; @@ -530,74 +155,37 @@ f"> */ i__3 = *m - *k + j + i__ * c_dim1; i__4 = *m - *k + j + i__ * c_dim1; d_lmp_cnjg(&z__2, &work[i__ + j * work_dim1]); - z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i - - z__2.i; + z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i - z__2.i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; -/* L80: */ } -/* L90: */ } - } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { - -/* Form C * H or C * H**H where C = ( C1 C2 ) */ - -/* W := C * V = (C1*V1 + C2*V2) (stored in WORK) */ - -/* W := C2 */ - i__1 = *k; for (j = 1; j <= i__1; ++j) { - zcopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[ - j * work_dim1 + 1], &c__1); -/* L100: */ + zcopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[j * work_dim1 + 1], + &c__1); } - -/* W := W * V2 */ - ztrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", m, k, &c_b1, - &v[*n - *k + 1 + v_dim1], ldv, &work[work_offset], - ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); + &v[*n - *k + 1 + v_dim1], ldv, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)12, (ftnlen)4); if (*n > *k) { - -/* W := W + C1 * V1 */ - i__1 = *n - *k; - zgemm_((char *)"No transpose", (char *)"No transpose", m, k, &i__1, &c_b1, - &c__[c_offset], ldc, &v[v_offset], ldv, &c_b1, & - work[work_offset], ldwork, (ftnlen)12, (ftnlen)12) - ; + zgemm_((char *)"No transpose", (char *)"No transpose", m, k, &i__1, &c_b1, &c__[c_offset], ldc, + &v[v_offset], ldv, &c_b1, &work[work_offset], ldwork, (ftnlen)12, + (ftnlen)12); } - -/* W := W * T or W * T**H */ - - ztrmm_((char *)"Right", (char *)"Lower", trans, (char *)"Non-unit", m, k, &c_b1, &t[ - t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, - (ftnlen)5, (ftnlen)1, (ftnlen)8); - -/* C := C - W * V**H */ - + ztrmm_((char *)"Right", (char *)"Lower", trans, (char *)"Non-unit", m, k, &c_b1, &t[t_offset], ldt, + &work[work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)1, (ftnlen)8); if (*n > *k) { - -/* C1 := C1 - W * V1**H */ - i__1 = *n - *k; z__1.r = -1., z__1.i = -0.; - zgemm_((char *)"No transpose", (char *)"Conjugate transpose", m, &i__1, k, - &z__1, &work[work_offset], ldwork, &v[v_offset], - ldv, &c_b1, &c__[c_offset], ldc, (ftnlen)12, ( - ftnlen)19); + zgemm_((char *)"No transpose", (char *)"Conjugate transpose", m, &i__1, k, &z__1, + &work[work_offset], ldwork, &v[v_offset], ldv, &c_b1, &c__[c_offset], + ldc, (ftnlen)12, (ftnlen)19); } - -/* W := W * V2**H */ - - ztrmm_((char *)"Right", (char *)"Upper", (char *)"Conjugate transpose", (char *)"Unit", m, k, - &c_b1, &v[*n - *k + 1 + v_dim1], ldv, &work[ - work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen) - 19, (ftnlen)4); - -/* C2 := C2 - W */ - + ztrmm_((char *)"Right", (char *)"Upper", (char *)"Conjugate transpose", (char *)"Unit", m, k, &c_b1, + &v[*n - *k + 1 + v_dim1], ldv, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)19, (ftnlen)4); i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *m; @@ -605,84 +193,40 @@ f"> */ i__3 = i__ + (*n - *k + j) * c_dim1; i__4 = i__ + (*n - *k + j) * c_dim1; i__5 = i__ + j * work_dim1; - z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[ - i__4].i - work[i__5].i; + z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[i__4].i - work[i__5].i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; -/* L110: */ } -/* L120: */ } } } - } else if (lsame_(storev, (char *)"R", (ftnlen)1, (ftnlen)1)) { - if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { - -/* Let V = ( V1 V2 ) (V1: first K columns) */ -/* where V1 is unit upper triangular. */ - if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { - -/* Form H * C or H**H * C where C = ( C1 ) */ -/* ( C2 ) */ - -/* W := C**H * V**H = (C1**H * V1**H + C2**H * V2**H) (stored in WORK) */ - -/* W := C1**H */ - i__1 = *k; for (j = 1; j <= i__1; ++j) { - zcopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1], - &c__1); + zcopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1], &c__1); zlacgv_(n, &work[j * work_dim1 + 1], &c__1); -/* L130: */ } - -/* W := W * V1**H */ - - ztrmm_((char *)"Right", (char *)"Upper", (char *)"Conjugate transpose", (char *)"Unit", n, k, - &c_b1, &v[v_offset], ldv, &work[work_offset], ldwork, - (ftnlen)5, (ftnlen)5, (ftnlen)19, (ftnlen)4); + ztrmm_((char *)"Right", (char *)"Upper", (char *)"Conjugate transpose", (char *)"Unit", n, k, &c_b1, &v[v_offset], + ldv, &work[work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)19, + (ftnlen)4); if (*m > *k) { - -/* W := W + C2**H * V2**H */ - i__1 = *m - *k; - zgemm_((char *)"Conjugate transpose", (char *)"Conjugate transpose", n, k, - &i__1, &c_b1, &c__[*k + 1 + c_dim1], ldc, &v[(*k - + 1) * v_dim1 + 1], ldv, &c_b1, &work[work_offset] - , ldwork, (ftnlen)19, (ftnlen)19); + zgemm_((char *)"Conjugate transpose", (char *)"Conjugate transpose", n, k, &i__1, &c_b1, + &c__[*k + 1 + c_dim1], ldc, &v[(*k + 1) * v_dim1 + 1], ldv, &c_b1, + &work[work_offset], ldwork, (ftnlen)19, (ftnlen)19); } - -/* W := W * T**H or W * T */ - - ztrmm_((char *)"Right", (char *)"Upper", transt, (char *)"Non-unit", n, k, &c_b1, &t[ - t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, - (ftnlen)5, (ftnlen)1, (ftnlen)8); - -/* C := C - V**H * W**H */ - + ztrmm_((char *)"Right", (char *)"Upper", transt, (char *)"Non-unit", n, k, &c_b1, &t[t_offset], ldt, + &work[work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)1, (ftnlen)8); if (*m > *k) { - -/* C2 := C2 - V2**H * W**H */ - i__1 = *m - *k; z__1.r = -1., z__1.i = -0.; - zgemm_((char *)"Conjugate transpose", (char *)"Conjugate transpose", & - i__1, n, k, &z__1, &v[(*k + 1) * v_dim1 + 1], ldv, - &work[work_offset], ldwork, &c_b1, &c__[*k + 1 + - c_dim1], ldc, (ftnlen)19, (ftnlen)19); + zgemm_((char *)"Conjugate transpose", (char *)"Conjugate transpose", &i__1, n, k, &z__1, + &v[(*k + 1) * v_dim1 + 1], ldv, &work[work_offset], ldwork, &c_b1, + &c__[*k + 1 + c_dim1], ldc, (ftnlen)19, (ftnlen)19); } - -/* W := W * V1 */ - - ztrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", n, k, &c_b1, - &v[v_offset], ldv, &work[work_offset], ldwork, ( - ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); - -/* C1 := C1 - W**H */ - + ztrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", n, k, &c_b1, &v[v_offset], ldv, + &work[work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *n; @@ -690,73 +234,35 @@ f"> */ i__3 = j + i__ * c_dim1; i__4 = j + i__ * c_dim1; d_lmp_cnjg(&z__2, &work[i__ + j * work_dim1]); - z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i - - z__2.i; + z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i - z__2.i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; -/* L140: */ } -/* L150: */ } - } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { - -/* Form C * H or C * H**H where C = ( C1 C2 ) */ - -/* W := C * V**H = (C1*V1**H + C2*V2**H) (stored in WORK) */ - -/* W := C1 */ - i__1 = *k; for (j = 1; j <= i__1; ++j) { - zcopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j * - work_dim1 + 1], &c__1); -/* L160: */ + zcopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j * work_dim1 + 1], &c__1); } - -/* W := W * V1**H */ - - ztrmm_((char *)"Right", (char *)"Upper", (char *)"Conjugate transpose", (char *)"Unit", m, k, - &c_b1, &v[v_offset], ldv, &work[work_offset], ldwork, - (ftnlen)5, (ftnlen)5, (ftnlen)19, (ftnlen)4); + ztrmm_((char *)"Right", (char *)"Upper", (char *)"Conjugate transpose", (char *)"Unit", m, k, &c_b1, &v[v_offset], + ldv, &work[work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)19, + (ftnlen)4); if (*n > *k) { - -/* W := W + C2 * V2**H */ - i__1 = *n - *k; - zgemm_((char *)"No transpose", (char *)"Conjugate transpose", m, k, &i__1, - &c_b1, &c__[(*k + 1) * c_dim1 + 1], ldc, &v[(*k - + 1) * v_dim1 + 1], ldv, &c_b1, &work[work_offset] - , ldwork, (ftnlen)12, (ftnlen)19); + zgemm_((char *)"No transpose", (char *)"Conjugate transpose", m, k, &i__1, &c_b1, + &c__[(*k + 1) * c_dim1 + 1], ldc, &v[(*k + 1) * v_dim1 + 1], ldv, &c_b1, + &work[work_offset], ldwork, (ftnlen)12, (ftnlen)19); } - -/* W := W * T or W * T**H */ - - ztrmm_((char *)"Right", (char *)"Upper", trans, (char *)"Non-unit", m, k, &c_b1, &t[ - t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, - (ftnlen)5, (ftnlen)1, (ftnlen)8); - -/* C := C - W * V */ - + ztrmm_((char *)"Right", (char *)"Upper", trans, (char *)"Non-unit", m, k, &c_b1, &t[t_offset], ldt, + &work[work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)1, (ftnlen)8); if (*n > *k) { - -/* C2 := C2 - W * V2 */ - i__1 = *n - *k; z__1.r = -1., z__1.i = -0.; - zgemm_((char *)"No transpose", (char *)"No transpose", m, &i__1, k, &z__1, - &work[work_offset], ldwork, &v[(*k + 1) * v_dim1 - + 1], ldv, &c_b1, &c__[(*k + 1) * c_dim1 + 1], - ldc, (ftnlen)12, (ftnlen)12); + zgemm_((char *)"No transpose", (char *)"No transpose", m, &i__1, k, &z__1, &work[work_offset], + ldwork, &v[(*k + 1) * v_dim1 + 1], ldv, &c_b1, + &c__[(*k + 1) * c_dim1 + 1], ldc, (ftnlen)12, (ftnlen)12); } - -/* W := W * V1 */ - - ztrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", m, k, &c_b1, - &v[v_offset], ldv, &work[work_offset], ldwork, ( - ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); - -/* C1 := C1 - W */ - + ztrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", m, k, &c_b1, &v[v_offset], ldv, + &work[work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4); i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *m; @@ -764,84 +270,39 @@ f"> */ i__3 = i__ + j * c_dim1; i__4 = i__ + j * c_dim1; i__5 = i__ + j * work_dim1; - z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[ - i__4].i - work[i__5].i; + z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[i__4].i - work[i__5].i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; -/* L170: */ } -/* L180: */ } - } - } else { - -/* Let V = ( V1 V2 ) (V2: last K columns) */ -/* where V2 is unit lower triangular. */ - if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { - -/* Form H * C or H**H * C where C = ( C1 ) */ -/* ( C2 ) */ - -/* W := C**H * V**H = (C1**H * V1**H + C2**H * V2**H) (stored in WORK) */ - -/* W := C2**H */ - i__1 = *k; for (j = 1; j <= i__1; ++j) { - zcopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j * - work_dim1 + 1], &c__1); + zcopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j * work_dim1 + 1], &c__1); zlacgv_(n, &work[j * work_dim1 + 1], &c__1); -/* L190: */ } - -/* W := W * V2**H */ - - ztrmm_((char *)"Right", (char *)"Lower", (char *)"Conjugate transpose", (char *)"Unit", n, k, - &c_b1, &v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[ - work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen) - 19, (ftnlen)4); + ztrmm_((char *)"Right", (char *)"Lower", (char *)"Conjugate transpose", (char *)"Unit", n, k, &c_b1, + &v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)19, (ftnlen)4); if (*m > *k) { - -/* W := W + C1**H * V1**H */ - i__1 = *m - *k; - zgemm_((char *)"Conjugate transpose", (char *)"Conjugate transpose", n, k, - &i__1, &c_b1, &c__[c_offset], ldc, &v[v_offset], - ldv, &c_b1, &work[work_offset], ldwork, (ftnlen) - 19, (ftnlen)19); + zgemm_((char *)"Conjugate transpose", (char *)"Conjugate transpose", n, k, &i__1, &c_b1, + &c__[c_offset], ldc, &v[v_offset], ldv, &c_b1, &work[work_offset], + ldwork, (ftnlen)19, (ftnlen)19); } - -/* W := W * T**H or W * T */ - - ztrmm_((char *)"Right", (char *)"Lower", transt, (char *)"Non-unit", n, k, &c_b1, &t[ - t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, - (ftnlen)5, (ftnlen)1, (ftnlen)8); - -/* C := C - V**H * W**H */ - + ztrmm_((char *)"Right", (char *)"Lower", transt, (char *)"Non-unit", n, k, &c_b1, &t[t_offset], ldt, + &work[work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)1, (ftnlen)8); if (*m > *k) { - -/* C1 := C1 - V1**H * W**H */ - i__1 = *m - *k; z__1.r = -1., z__1.i = -0.; - zgemm_((char *)"Conjugate transpose", (char *)"Conjugate transpose", & - i__1, n, k, &z__1, &v[v_offset], ldv, &work[ - work_offset], ldwork, &c_b1, &c__[c_offset], ldc, - (ftnlen)19, (ftnlen)19); + zgemm_((char *)"Conjugate transpose", (char *)"Conjugate transpose", &i__1, n, k, &z__1, + &v[v_offset], ldv, &work[work_offset], ldwork, &c_b1, &c__[c_offset], + ldc, (ftnlen)19, (ftnlen)19); } - -/* W := W * V2 */ - ztrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", n, k, &c_b1, - &v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[ - work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen) - 12, (ftnlen)4); - -/* C2 := C2 - W**H */ - + &v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)12, (ftnlen)4); i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *n; @@ -849,75 +310,37 @@ f"> */ i__3 = *m - *k + j + i__ * c_dim1; i__4 = *m - *k + j + i__ * c_dim1; d_lmp_cnjg(&z__2, &work[i__ + j * work_dim1]); - z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i - - z__2.i; + z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i - z__2.i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; -/* L200: */ } -/* L210: */ } - } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { - -/* Form C * H or C * H**H where C = ( C1 C2 ) */ - -/* W := C * V**H = (C1*V1**H + C2*V2**H) (stored in WORK) */ - -/* W := C2 */ - i__1 = *k; for (j = 1; j <= i__1; ++j) { - zcopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[ - j * work_dim1 + 1], &c__1); -/* L220: */ + zcopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[j * work_dim1 + 1], + &c__1); } - -/* W := W * V2**H */ - - ztrmm_((char *)"Right", (char *)"Lower", (char *)"Conjugate transpose", (char *)"Unit", m, k, - &c_b1, &v[(*n - *k + 1) * v_dim1 + 1], ldv, &work[ - work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen) - 19, (ftnlen)4); + ztrmm_((char *)"Right", (char *)"Lower", (char *)"Conjugate transpose", (char *)"Unit", m, k, &c_b1, + &v[(*n - *k + 1) * v_dim1 + 1], ldv, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)19, (ftnlen)4); if (*n > *k) { - -/* W := W + C1 * V1**H */ - i__1 = *n - *k; - zgemm_((char *)"No transpose", (char *)"Conjugate transpose", m, k, &i__1, - &c_b1, &c__[c_offset], ldc, &v[v_offset], ldv, & - c_b1, &work[work_offset], ldwork, (ftnlen)12, ( - ftnlen)19); + zgemm_((char *)"No transpose", (char *)"Conjugate transpose", m, k, &i__1, &c_b1, + &c__[c_offset], ldc, &v[v_offset], ldv, &c_b1, &work[work_offset], + ldwork, (ftnlen)12, (ftnlen)19); } - -/* W := W * T or W * T**H */ - - ztrmm_((char *)"Right", (char *)"Lower", trans, (char *)"Non-unit", m, k, &c_b1, &t[ - t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5, - (ftnlen)5, (ftnlen)1, (ftnlen)8); - -/* C := C - W * V */ - + ztrmm_((char *)"Right", (char *)"Lower", trans, (char *)"Non-unit", m, k, &c_b1, &t[t_offset], ldt, + &work[work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)1, (ftnlen)8); if (*n > *k) { - -/* C1 := C1 - W * V1 */ - i__1 = *n - *k; z__1.r = -1., z__1.i = -0.; - zgemm_((char *)"No transpose", (char *)"No transpose", m, &i__1, k, &z__1, - &work[work_offset], ldwork, &v[v_offset], ldv, & - c_b1, &c__[c_offset], ldc, (ftnlen)12, (ftnlen)12) - ; + zgemm_((char *)"No transpose", (char *)"No transpose", m, &i__1, k, &z__1, &work[work_offset], + ldwork, &v[v_offset], ldv, &c_b1, &c__[c_offset], ldc, (ftnlen)12, + (ftnlen)12); } - -/* W := W * V2 */ - ztrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", m, k, &c_b1, - &v[(*n - *k + 1) * v_dim1 + 1], ldv, &work[ - work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen) - 12, (ftnlen)4); - -/* C1 := C1 - W */ - + &v[(*n - *k + 1) * v_dim1 + 1], ldv, &work[work_offset], ldwork, (ftnlen)5, + (ftnlen)5, (ftnlen)12, (ftnlen)4); i__1 = *k; for (j = 1; j <= i__1; ++j) { i__2 = *m; @@ -925,25 +348,15 @@ f"> */ i__3 = i__ + (*n - *k + j) * c_dim1; i__4 = i__ + (*n - *k + j) * c_dim1; i__5 = i__ + j * work_dim1; - z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[ - i__4].i - work[i__5].i; + z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[i__4].i - work[i__5].i; c__[i__3].r = z__1.r, c__[i__3].i = z__1.i; -/* L230: */ } -/* L240: */ } - } - } } - return 0; - -/* End of ZLARFB */ - -} /* zlarfb_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zlarfg.cpp b/lib/linalg/zlarfg.cpp index 518ba9bcbb..84f5efad01 100644 --- a/lib/linalg/zlarfg.cpp +++ b/lib/linalg/zlarfg.cpp @@ -1,216 +1,43 @@ -/* fortran/zlarfg.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - -static doublecomplex c_b5 = {1.,0.}; - -/* > \brief \b ZLARFG generates an elementary reflector (Householder matrix). */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZLARFG + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZLARFG( N, ALPHA, X, INCX, TAU ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INCX, N */ -/* COMPLEX*16 ALPHA, TAU */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 X( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZLARFG generates a complex elementary reflector H of order n, such */ -/* > that */ -/* > */ -/* > H**H * ( alpha ) = ( beta ), H**H * H = I. */ -/* > ( x ) ( 0 ) */ -/* > */ -/* > where alpha and beta are scalars, with beta real, and x is an */ -/* > (n-1)-element complex vector. H is represented in the form */ -/* > */ -/* > H = I - tau * ( 1 ) * ( 1 v**H ) , */ -/* > ( v ) */ -/* > */ -/* > where tau is a complex scalar and v is a complex (n-1)-element */ -/* > vector. Note that H is not hermitian. */ -/* > */ -/* > If the elements of x are all zero and alpha is real, then tau = 0 */ -/* > and H is taken to be the unit matrix. */ -/* > */ -/* > Otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1 . */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the elementary reflector. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] ALPHA */ -/* > \verbatim */ -/* > ALPHA is COMPLEX*16 */ -/* > On entry, the value alpha. */ -/* > On exit, it is overwritten with the value beta. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] X */ -/* > \verbatim */ -/* > X is COMPLEX*16 array, dimension */ -/* > (1+(N-2)*abs(INCX)) */ -/* > On entry, the vector x. */ -/* > On exit, it is overwritten with the vector v. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > The increment between elements of X. INCX > 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] TAU */ -/* > \verbatim */ -/* > TAU is COMPLEX*16 */ -/* > The value tau. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16OTHERauxiliary */ - -/* ===================================================================== */ -/* Subroutine */ int zlarfg_(integer *n, doublecomplex *alpha, doublecomplex * - x, integer *incx, doublecomplex *tau) +static doublecomplex c_b5 = {1., 0.}; +int zlarfg_(integer *n, doublecomplex *alpha, doublecomplex *x, integer *incx, doublecomplex *tau) { - /* System generated locals */ integer i__1; doublereal d__1, d__2; doublecomplex z__1, z__2; - - /* Builtin functions */ double d_lmp_imag(doublecomplex *), d_lmp_sign(doublereal *, doublereal *); - - /* Local variables */ integer j, knt; doublereal beta, alphi, alphr; - extern /* Subroutine */ int zscal_(integer *, doublecomplex *, - doublecomplex *, integer *); + extern int zscal_(integer *, doublecomplex *, doublecomplex *, integer *); doublereal xnorm; extern doublereal dlapy3_(doublereal *, doublereal *, doublereal *), - dznrm2_(integer *, doublecomplex *, integer *), dlamch_(char *, - ftnlen); + dznrm2_(integer *, doublecomplex *, integer *), dlamch_(char *, ftnlen); doublereal safmin; - extern /* Subroutine */ int zdscal_(integer *, doublereal *, - doublecomplex *, integer *); + extern int zdscal_(integer *, doublereal *, doublecomplex *, integer *); doublereal rsafmn; - extern /* Double Complex */ VOID zladiv_(doublecomplex *, doublecomplex *, - doublecomplex *); - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Executable Statements .. */ - - /* Parameter adjustments */ + extern VOID zladiv_(doublecomplex *, doublecomplex *, doublecomplex *); --x; - - /* Function Body */ if (*n <= 0) { tau->r = 0., tau->i = 0.; return 0; } - i__1 = *n - 1; xnorm = dznrm2_(&i__1, &x[1], incx); alphr = alpha->r; alphi = d_lmp_imag(alpha); - if (xnorm == 0. && alphi == 0.) { - -/* H = I */ - tau->r = 0., tau->i = 0.; } else { - -/* general case */ - d__1 = dlapy3_(&alphr, &alphi, &xnorm); beta = -d_lmp_sign(&d__1, &alphr); safmin = dlamch_((char *)"S", (ftnlen)1) / dlamch_((char *)"E", (ftnlen)1); rsafmn = 1. / safmin; - knt = 0; if (abs(beta) < safmin) { - -/* XNORM, BETA may be inaccurate; scale X and recompute them */ - -L10: + L10: ++knt; i__1 = *n - 1; zdscal_(&i__1, &rsafmn, &x[1], incx); @@ -220,9 +47,6 @@ L10: if (abs(beta) < safmin && knt < 20) { goto L10; } - -/* New BETA is at most 1, at least SAFMIN */ - i__1 = *n - 1; xnorm = dznrm2_(&i__1, &x[1], incx); z__1.r = alphr, z__1.i = alphi; @@ -239,23 +63,14 @@ L10: alpha->r = z__1.r, alpha->i = z__1.i; i__1 = *n - 1; zscal_(&i__1, alpha, &x[1], incx); - -/* If ALPHA is subnormal, it may lose relative accuracy */ - i__1 = knt; for (j = 1; j <= i__1; ++j) { beta *= safmin; -/* L20: */ } alpha->r = beta, alpha->i = 0.; } - return 0; - -/* End of ZLARFG */ - -} /* zlarfg_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zlarft.cpp b/lib/linalg/zlarft.cpp index 391de106cf..f778f646d2 100644 --- a/lib/linalg/zlarft.cpp +++ b/lib/linalg/zlarft.cpp @@ -1,239 +1,26 @@ -/* static/zlarft.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - -static doublecomplex c_b1 = {1.,0.}; +static doublecomplex c_b1 = {1., 0.}; static integer c__1 = 1; - -/* > \brief \b ZLARFT forms the triangular factor T of a block reflector H = I - vtvH */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZLARFT + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER DIRECT, STOREV */ -/* INTEGER K, LDT, LDV, N */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 T( LDT, * ), TAU( * ), V( LDV, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZLARFT forms the triangular factor T of a complex block reflector H */ -/* > of order n, which is defined as a product of k elementary reflectors. */ -/* > */ -/* > If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; */ -/* > */ -/* > If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. */ -/* > */ -/* > If STOREV = 'C', the vector which defines the elementary reflector */ -/* > H(i) is stored in the i-th column of the array V, and */ -/* > */ -/* > H = I - V * T * V**H */ -/* > */ -/* > If STOREV = 'R', the vector which defines the elementary reflector */ -/* > H(i) is stored in the i-th row of the array V, and */ -/* > */ -/* > H = I - V**H * T * V */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] DIRECT */ -/* > \verbatim */ -/* > DIRECT is CHARACTER*1 */ -/* > Specifies the order in which the elementary reflectors are */ -/* > multiplied to form the block reflector: */ -/* > = 'F': H = H(1) H(2) . . . H(k) (Forward) */ -/* > = 'B': H = H(k) . . . H(2) H(1) (Backward) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] STOREV */ -/* > \verbatim */ -/* > STOREV is CHARACTER*1 */ -/* > Specifies how the vectors which define the elementary */ -/* > reflectors are stored (see also Further Details): */ -/* > = 'C': columnwise */ -/* > = 'R': rowwise */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the block reflector H. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > The order of the triangular factor T (= the number of */ -/* > elementary reflectors). K >= 1. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] V */ -/* > \verbatim */ -/* > V is COMPLEX*16 array, dimension */ -/* > (LDV,K) if STOREV = 'C' */ -/* > (LDV,N) if STOREV = 'R' */ -/* > The matrix V. See further details. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDV */ -/* > \verbatim */ -/* > LDV is INTEGER */ -/* > The leading dimension of the array V. */ -/* > If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TAU */ -/* > \verbatim */ -/* > TAU is COMPLEX*16 array, dimension (K) */ -/* > TAU(i) must contain the scalar factor of the elementary */ -/* > reflector H(i). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] T */ -/* > \verbatim */ -/* > T is COMPLEX*16 array, dimension (LDT,K) */ -/* > The k by k triangular factor T of the block reflector. */ -/* > If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is */ -/* > lower triangular. The rest of the array is not used. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDT */ -/* > \verbatim */ -/* > LDT is INTEGER */ -/* > The leading dimension of the array T. LDT >= K. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16OTHERauxiliary */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > The shape of the matrix V and the storage of the vectors which define */ -/* > the H(i) is best illustrated by the following example with n = 5 and */ -/* > k = 3. The elements equal to 1 are not stored. */ -/* > */ -/* > DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': */ -/* > */ -/* > V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) */ -/* > ( v1 1 ) ( 1 v2 v2 v2 ) */ -/* > ( v1 v2 1 ) ( 1 v3 v3 ) */ -/* > ( v1 v2 v3 ) */ -/* > ( v1 v2 v3 ) */ -/* > */ -/* > DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': */ -/* > */ -/* > V = ( v1 v2 v3 ) V = ( v1 v1 1 ) */ -/* > ( v1 v2 v3 ) ( v2 v2 v2 1 ) */ -/* > ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) */ -/* > ( 1 v3 ) */ -/* > ( 1 ) */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int zlarft_(char *direct, char *storev, integer *n, integer * - k, doublecomplex *v, integer *ldv, doublecomplex *tau, doublecomplex * - t, integer *ldt, ftnlen direct_len, ftnlen storev_len) +int zlarft_(char *direct, char *storev, integer *n, integer *k, doublecomplex *v, integer *ldv, + doublecomplex *tau, doublecomplex *t, integer *ldt, ftnlen direct_len, + ftnlen storev_len) { - /* System generated locals */ integer t_dim1, t_offset, v_dim1, v_offset, i__1, i__2, i__3, i__4, i__5; doublecomplex z__1, z__2, z__3; - - /* Builtin functions */ void d_lmp_cnjg(doublecomplex *, doublecomplex *); - - /* Local variables */ integer i__, j, prevlastv; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *, - integer *, doublecomplex *, doublecomplex *, integer *, - doublecomplex *, integer *, doublecomplex *, doublecomplex *, - integer *, ftnlen, ftnlen), zgemv_(char *, integer *, integer *, - doublecomplex *, doublecomplex *, integer *, doublecomplex *, - integer *, doublecomplex *, doublecomplex *, integer *, ftnlen); + extern int zgemm_(char *, char *, integer *, integer *, integer *, doublecomplex *, + doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, + doublecomplex *, integer *, ftnlen, ftnlen), + zgemv_(char *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, + doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, ftnlen); integer lastv; - extern /* Subroutine */ int ztrmv_(char *, char *, char *, integer *, - doublecomplex *, integer *, doublecomplex *, integer *, ftnlen, - ftnlen, ftnlen); - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Quick return if possible */ - - /* Parameter adjustments */ + extern int ztrmv_(char *, char *, char *, integer *, doublecomplex *, integer *, + doublecomplex *, integer *, ftnlen, ftnlen, ftnlen); v_dim1 = *ldv; v_offset = 1 + v_dim1; v -= v_offset; @@ -241,33 +28,23 @@ f"> */ t_dim1 = *ldt; t_offset = 1 + t_dim1; t -= t_offset; - - /* Function Body */ if (*n == 0) { return 0; } - if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { prevlastv = *n; i__1 = *k; for (i__ = 1; i__ <= i__1; ++i__) { - prevlastv = max(prevlastv,i__); + prevlastv = max(prevlastv, i__); i__2 = i__; if (tau[i__2].r == 0. && tau[i__2].i == 0.) { - -/* H(i) = I */ - i__2 = i__; for (j = 1; j <= i__2; ++j) { i__3 = j + i__ * t_dim1; t[i__3].r = 0., t[i__3].i = 0.; } } else { - -/* general case */ - if (lsame_(storev, (char *)"C", (ftnlen)1, (ftnlen)1)) { -/* Skip any trailing zeros. */ i__2 = i__ + 1; for (lastv = *n; lastv >= i__2; --lastv) { i__3 = lastv + i__ * v_dim1; @@ -275,31 +52,26 @@ f"> */ goto L220; } } -L220: + L220: i__2 = i__ - 1; for (j = 1; j <= i__2; ++j) { i__3 = j + i__ * t_dim1; i__4 = i__; z__2.r = -tau[i__4].r, z__2.i = -tau[i__4].i; d_lmp_cnjg(&z__3, &v[i__ + j * v_dim1]); - z__1.r = z__2.r * z__3.r - z__2.i * z__3.i, z__1.i = - z__2.r * z__3.i + z__2.i * z__3.r; + z__1.r = z__2.r * z__3.r - z__2.i * z__3.i, + z__1.i = z__2.r * z__3.i + z__2.i * z__3.r; t[i__3].r = z__1.r, t[i__3].i = z__1.i; } - j = min(lastv,prevlastv); - -/* T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**H * V(i:j,i) */ - + j = min(lastv, prevlastv); i__2 = j - i__; i__3 = i__ - 1; i__4 = i__; z__1.r = -tau[i__4].r, z__1.i = -tau[i__4].i; - zgemv_((char *)"Conjugate transpose", &i__2, &i__3, &z__1, &v[i__ - + 1 + v_dim1], ldv, &v[i__ + 1 + i__ * v_dim1], & - c__1, &c_b1, &t[i__ * t_dim1 + 1], &c__1, (ftnlen) - 19); + zgemv_((char *)"Conjugate transpose", &i__2, &i__3, &z__1, &v[i__ + 1 + v_dim1], ldv, + &v[i__ + 1 + i__ * v_dim1], &c__1, &c_b1, &t[i__ * t_dim1 + 1], &c__1, + (ftnlen)19); } else { -/* Skip any trailing zeros. */ i__2 = i__ + 1; for (lastv = *n; lastv >= i__2; --lastv) { i__3 = i__ + lastv * v_dim1; @@ -307,7 +79,7 @@ L220: goto L236; } } -L236: + L236: i__2 = i__ - 1; for (j = 1; j <= i__2; ++j) { i__3 = j + i__ * t_dim1; @@ -315,35 +87,26 @@ L236: z__2.r = -tau[i__4].r, z__2.i = -tau[i__4].i; i__5 = j + i__ * v_dim1; z__1.r = z__2.r * v[i__5].r - z__2.i * v[i__5].i, - z__1.i = z__2.r * v[i__5].i + z__2.i * v[i__5] - .r; + z__1.i = z__2.r * v[i__5].i + z__2.i * v[i__5].r; t[i__3].r = z__1.r, t[i__3].i = z__1.i; } - j = min(lastv,prevlastv); - -/* T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**H */ - + j = min(lastv, prevlastv); i__2 = i__ - 1; i__3 = j - i__; i__4 = i__; z__1.r = -tau[i__4].r, z__1.i = -tau[i__4].i; - zgemm_((char *)"N", (char *)"C", &i__2, &c__1, &i__3, &z__1, &v[(i__ + 1) - * v_dim1 + 1], ldv, &v[i__ + (i__ + 1) * v_dim1], - ldv, &c_b1, &t[i__ * t_dim1 + 1], ldt, (ftnlen)1, - (ftnlen)1); + zgemm_((char *)"N", (char *)"C", &i__2, &c__1, &i__3, &z__1, &v[(i__ + 1) * v_dim1 + 1], ldv, + &v[i__ + (i__ + 1) * v_dim1], ldv, &c_b1, &t[i__ * t_dim1 + 1], ldt, + (ftnlen)1, (ftnlen)1); } - -/* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) */ - i__2 = i__ - 1; - ztrmv_((char *)"Upper", (char *)"No transpose", (char *)"Non-unit", &i__2, &t[ - t_offset], ldt, &t[i__ * t_dim1 + 1], &c__1, (ftnlen) - 5, (ftnlen)12, (ftnlen)8); + ztrmv_((char *)"Upper", (char *)"No transpose", (char *)"Non-unit", &i__2, &t[t_offset], ldt, + &t[i__ * t_dim1 + 1], &c__1, (ftnlen)5, (ftnlen)12, (ftnlen)8); i__2 = i__ + i__ * t_dim1; i__3 = i__; t[i__2].r = tau[i__3].r, t[i__2].i = tau[i__3].i; if (i__ > 1) { - prevlastv = max(prevlastv,lastv); + prevlastv = max(prevlastv, lastv); } else { prevlastv = lastv; } @@ -354,21 +117,14 @@ L236: for (i__ = *k; i__ >= 1; --i__) { i__1 = i__; if (tau[i__1].r == 0. && tau[i__1].i == 0.) { - -/* H(i) = I */ - i__1 = *k; for (j = i__; j <= i__1; ++j) { i__2 = j + i__ * t_dim1; t[i__2].r = 0., t[i__2].i = 0.; } } else { - -/* general case */ - if (i__ < *k) { if (lsame_(storev, (char *)"C", (ftnlen)1, (ftnlen)1)) { -/* Skip any leading zeros. */ i__1 = i__ - 1; for (lastv = 1; lastv <= i__1; ++lastv) { i__2 = lastv + i__ * v_dim1; @@ -376,7 +132,7 @@ L236: goto L281; } } -L281: + L281: i__1 = *k; for (j = i__ + 1; j <= i__1; ++j) { i__2 = j + i__ * t_dim1; @@ -384,24 +140,18 @@ L281: z__2.r = -tau[i__3].r, z__2.i = -tau[i__3].i; d_lmp_cnjg(&z__3, &v[*n - *k + i__ + j * v_dim1]); z__1.r = z__2.r * z__3.r - z__2.i * z__3.i, - z__1.i = z__2.r * z__3.i + z__2.i * - z__3.r; + z__1.i = z__2.r * z__3.i + z__2.i * z__3.r; t[i__2].r = z__1.r, t[i__2].i = z__1.i; } - j = max(lastv,prevlastv); - -/* T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**H * V(j:n-k+i,i) */ - + j = max(lastv, prevlastv); i__1 = *n - *k + i__ - j; i__2 = *k - i__; i__3 = i__; z__1.r = -tau[i__3].r, z__1.i = -tau[i__3].i; - zgemv_((char *)"Conjugate transpose", &i__1, &i__2, &z__1, &v[ - j + (i__ + 1) * v_dim1], ldv, &v[j + i__ * - v_dim1], &c__1, &c_b1, &t[i__ + 1 + i__ * - t_dim1], &c__1, (ftnlen)19); + zgemv_((char *)"Conjugate transpose", &i__1, &i__2, &z__1, + &v[j + (i__ + 1) * v_dim1], ldv, &v[j + i__ * v_dim1], &c__1, &c_b1, + &t[i__ + 1 + i__ * t_dim1], &c__1, (ftnlen)19); } else { -/* Skip any leading zeros. */ i__1 = i__ - 1; for (lastv = 1; lastv <= i__1; ++lastv) { i__2 = i__ + lastv * v_dim1; @@ -409,7 +159,7 @@ L281: goto L297; } } -L297: + L297: i__1 = *k; for (j = i__ + 1; j <= i__1; ++j) { i__2 = j + i__ * t_dim1; @@ -417,33 +167,24 @@ L297: z__2.r = -tau[i__3].r, z__2.i = -tau[i__3].i; i__4 = j + (*n - *k + i__) * v_dim1; z__1.r = z__2.r * v[i__4].r - z__2.i * v[i__4].i, - z__1.i = z__2.r * v[i__4].i + z__2.i * v[ - i__4].r; + z__1.i = z__2.r * v[i__4].i + z__2.i * v[i__4].r; t[i__2].r = z__1.r, t[i__2].i = z__1.i; } - j = max(lastv,prevlastv); - -/* T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**H */ - + j = max(lastv, prevlastv); i__1 = *k - i__; i__2 = *n - *k + i__ - j; i__3 = i__; z__1.r = -tau[i__3].r, z__1.i = -tau[i__3].i; - zgemm_((char *)"N", (char *)"C", &i__1, &c__1, &i__2, &z__1, &v[i__ + - 1 + j * v_dim1], ldv, &v[i__ + j * v_dim1], - ldv, &c_b1, &t[i__ + 1 + i__ * t_dim1], ldt, ( - ftnlen)1, (ftnlen)1); + zgemm_((char *)"N", (char *)"C", &i__1, &c__1, &i__2, &z__1, &v[i__ + 1 + j * v_dim1], ldv, + &v[i__ + j * v_dim1], ldv, &c_b1, &t[i__ + 1 + i__ * t_dim1], ldt, + (ftnlen)1, (ftnlen)1); } - -/* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) */ - i__1 = *k - i__; - ztrmv_((char *)"Lower", (char *)"No transpose", (char *)"Non-unit", &i__1, &t[i__ - + 1 + (i__ + 1) * t_dim1], ldt, &t[i__ + 1 + i__ * - t_dim1], &c__1, (ftnlen)5, (ftnlen)12, (ftnlen)8) - ; + ztrmv_((char *)"Lower", (char *)"No transpose", (char *)"Non-unit", &i__1, + &t[i__ + 1 + (i__ + 1) * t_dim1], ldt, &t[i__ + 1 + i__ * t_dim1], &c__1, + (ftnlen)5, (ftnlen)12, (ftnlen)8); if (i__ > 1) { - prevlastv = min(prevlastv,lastv); + prevlastv = min(prevlastv, lastv); } else { prevlastv = lastv; } @@ -455,11 +196,7 @@ L297: } } return 0; - -/* End of ZLARFT */ - -} /* zlarft_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zlascl.cpp b/lib/linalg/zlascl.cpp index 8cea99ddb0..293da0739e 100644 --- a/lib/linalg/zlascl.cpp +++ b/lib/linalg/zlascl.cpp @@ -1,173 +1,12 @@ -/* fortran/zlascl.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b ZLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZLASCL + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZLASCL( TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER TYPE */ -/* INTEGER INFO, KL, KU, LDA, M, N */ -/* DOUBLE PRECISION CFROM, CTO */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 A( LDA, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZLASCL multiplies the M by N complex matrix A by the real scalar */ -/* > CTO/CFROM. This is done without over/underflow as long as the final */ -/* > result CTO*A(I,J)/CFROM does not over/underflow. TYPE specifies that */ -/* > A may be full, upper triangular, lower triangular, upper Hessenberg, */ -/* > or banded. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] TYPE */ -/* > \verbatim */ -/* > TYPE is CHARACTER*1 */ -/* > TYPE indices the storage type of the input matrix. */ -/* > = 'G': A is a full matrix. */ -/* > = 'L': A is a lower triangular matrix. */ -/* > = 'U': A is an upper triangular matrix. */ -/* > = 'H': A is an upper Hessenberg matrix. */ -/* > = 'B': A is a symmetric band matrix with lower bandwidth KL */ -/* > and upper bandwidth KU and with the only the lower */ -/* > half stored. */ -/* > = 'Q': A is a symmetric band matrix with lower bandwidth KL */ -/* > and upper bandwidth KU and with the only the upper */ -/* > half stored. */ -/* > = 'Z': A is a band matrix with lower bandwidth KL and upper */ -/* > bandwidth KU. See ZGBTRF for storage details. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] KL */ -/* > \verbatim */ -/* > KL is INTEGER */ -/* > The lower bandwidth of A. Referenced only if TYPE = 'B', */ -/* > 'Q' or 'Z'. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] KU */ -/* > \verbatim */ -/* > KU is INTEGER */ -/* > The upper bandwidth of A. Referenced only if TYPE = 'B', */ -/* > 'Q' or 'Z'. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] CFROM */ -/* > \verbatim */ -/* > CFROM is DOUBLE PRECISION */ -/* > \endverbatim */ -/* > */ -/* > \param[in] CTO */ -/* > \verbatim */ -/* > CTO is DOUBLE PRECISION */ -/* > */ -/* > The matrix A is multiplied by CTO/CFROM. A(I,J) is computed */ -/* > without over/underflow if the final result CTO*A(I,J)/CFROM */ -/* > can be represented without over/underflow. CFROM must be */ -/* > nonzero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix A. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is COMPLEX*16 array, dimension (LDA,N) */ -/* > The matrix to be multiplied by CTO/CFROM. See TYPE for the */ -/* > storage type. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. */ -/* > If TYPE = 'G', 'L', 'U', 'H', LDA >= max(1,M); */ -/* > TYPE = 'B', LDA >= KL+1; */ -/* > TYPE = 'Q', LDA >= KU+1; */ -/* > TYPE = 'Z', LDA >= 2*KL+KU+1. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > 0 - successful exit */ -/* > <0 - if INFO = -i, the i-th argument had an illegal value. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16OTHERauxiliary */ - -/* ===================================================================== */ -/* Subroutine */ int zlascl_(char *type__, integer *kl, integer *ku, - doublereal *cfrom, doublereal *cto, integer *m, integer *n, - doublecomplex *a, integer *lda, integer *info, ftnlen type_len) +int zlascl_(char *type__, integer *kl, integer *ku, doublereal *cfrom, doublereal *cto, integer *m, + integer *n, doublecomplex *a, integer *lda, integer *info, ftnlen type_len) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; doublecomplex z__1; - - /* Local variables */ integer i__, j, k1, k2, k3, k4; doublereal mul, cto1; logical done; @@ -178,43 +17,12 @@ f"> */ extern doublereal dlamch_(char *, ftnlen); doublereal cfromc; extern logical disnan_(doublereal *); - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern int xerbla_(char *, integer *, ftnlen); doublereal bignum, smlnum; - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; - - /* Function Body */ *info = 0; - if (lsame_(type__, (char *)"G", (ftnlen)1, (ftnlen)1)) { itype = 0; } else if (lsame_(type__, (char *)"L", (ftnlen)1, (ftnlen)1)) { @@ -232,7 +40,6 @@ f"> */ } else { itype = -1; } - if (itype == -1) { *info = -1; } else if (*cfrom == 0. || disnan_(cfrom)) { @@ -243,59 +50,43 @@ f"> */ *info = -6; } else if (*n < 0 || itype == 4 && *n != *m || itype == 5 && *n != *m) { *info = -7; - } else if (itype <= 3 && *lda < max(1,*m)) { + } else if (itype <= 3 && *lda < max(1, *m)) { *info = -9; } else if (itype >= 4) { -/* Computing MAX */ i__1 = *m - 1; - if (*kl < 0 || *kl > max(i__1,0)) { + if (*kl < 0 || *kl > max(i__1, 0)) { *info = -2; - } else /* if(complicated condition) */ { -/* Computing MAX */ + } else { i__1 = *n - 1; - if (*ku < 0 || *ku > max(i__1,0) || (itype == 4 || itype == 5) && - *kl != *ku) { + if (*ku < 0 || *ku > max(i__1, 0) || (itype == 4 || itype == 5) && *kl != *ku) { *info = -3; - } else if (itype == 4 && *lda < *kl + 1 || itype == 5 && *lda < * - ku + 1 || itype == 6 && *lda < (*kl << 1) + *ku + 1) { + } else if (itype == 4 && *lda < *kl + 1 || itype == 5 && *lda < *ku + 1 || + itype == 6 && *lda < (*kl << 1) + *ku + 1) { *info = -9; } } } - if (*info != 0) { i__1 = -(*info); xerbla_((char *)"ZLASCL", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*n == 0 || *m == 0) { return 0; } - -/* Get machine parameters */ - smlnum = dlamch_((char *)"S", (ftnlen)1); bignum = 1. / smlnum; - cfromc = *cfrom; ctoc = *cto; - L10: cfrom1 = cfromc * smlnum; if (cfrom1 == cfromc) { -/* CFROMC is an inf. Multiply by a correctly signed zero for */ -/* finite CTOC, or a NaN if CTOC is infinite. */ mul = ctoc / cfromc; done = TRUE_; cto1 = ctoc; } else { cto1 = ctoc / bignum; if (cto1 == ctoc) { -/* CTOC is either 0 or an inf. In both cases, CTOC itself */ -/* serves as the correct multiplication factor. */ mul = ctoc; done = TRUE_; cfromc = 1.; @@ -315,11 +106,7 @@ L10: } } } - if (itype == 0) { - -/* Full matrix */ - i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; @@ -328,15 +115,9 @@ L10: i__4 = i__ + j * a_dim1; z__1.r = mul * a[i__4].r, z__1.i = mul * a[i__4].i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; -/* L20: */ } -/* L30: */ } - } else if (itype == 1) { - -/* Lower triangular matrix */ - i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; @@ -345,126 +126,82 @@ L10: i__4 = i__ + j * a_dim1; z__1.r = mul * a[i__4].r, z__1.i = mul * a[i__4].i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; -/* L40: */ } -/* L50: */ } - } else if (itype == 2) { - -/* Upper triangular matrix */ - i__1 = *n; for (j = 1; j <= i__1; ++j) { - i__2 = min(j,*m); + i__2 = min(j, *m); for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * a_dim1; i__4 = i__ + j * a_dim1; z__1.r = mul * a[i__4].r, z__1.i = mul * a[i__4].i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; -/* L60: */ } -/* L70: */ } - } else if (itype == 3) { - -/* Upper Hessenberg matrix */ - i__1 = *n; for (j = 1; j <= i__1; ++j) { -/* Computing MIN */ i__3 = j + 1; - i__2 = min(i__3,*m); + i__2 = min(i__3, *m); for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * a_dim1; i__4 = i__ + j * a_dim1; z__1.r = mul * a[i__4].r, z__1.i = mul * a[i__4].i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; -/* L80: */ } -/* L90: */ } - } else if (itype == 4) { - -/* Lower half of a symmetric band matrix */ - k3 = *kl + 1; k4 = *n + 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { -/* Computing MIN */ i__3 = k3, i__4 = k4 - j; - i__2 = min(i__3,i__4); + i__2 = min(i__3, i__4); for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * a_dim1; i__4 = i__ + j * a_dim1; z__1.r = mul * a[i__4].r, z__1.i = mul * a[i__4].i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; -/* L100: */ } -/* L110: */ } - } else if (itype == 5) { - -/* Upper half of a symmetric band matrix */ - k1 = *ku + 2; k3 = *ku + 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { -/* Computing MAX */ i__2 = k1 - j; i__3 = k3; - for (i__ = max(i__2,1); i__ <= i__3; ++i__) { + for (i__ = max(i__2, 1); i__ <= i__3; ++i__) { i__2 = i__ + j * a_dim1; i__4 = i__ + j * a_dim1; z__1.r = mul * a[i__4].r, z__1.i = mul * a[i__4].i; a[i__2].r = z__1.r, a[i__2].i = z__1.i; -/* L120: */ } -/* L130: */ } - } else if (itype == 6) { - -/* Band matrix */ - k1 = *kl + *ku + 2; k2 = *kl + 1; k3 = (*kl << 1) + *ku + 1; k4 = *kl + *ku + 1 + *m; i__1 = *n; for (j = 1; j <= i__1; ++j) { -/* Computing MAX */ i__3 = k1 - j; -/* Computing MIN */ i__4 = k3, i__5 = k4 - j; - i__2 = min(i__4,i__5); - for (i__ = max(i__3,k2); i__ <= i__2; ++i__) { + i__2 = min(i__4, i__5); + for (i__ = max(i__3, k2); i__ <= i__2; ++i__) { i__3 = i__ + j * a_dim1; i__4 = i__ + j * a_dim1; z__1.r = mul * a[i__4].r, z__1.i = mul * a[i__4].i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; -/* L140: */ } -/* L150: */ } - } - - if (! done) { + if (!done) { goto L10; } - return 0; - -/* End of ZLASCL */ - -} /* zlascl_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zlaset.cpp b/lib/linalg/zlaset.cpp index 782cc99055..dc5dd4740c 100644 --- a/lib/linalg/zlaset.cpp +++ b/lib/linalg/zlaset.cpp @@ -1,240 +1,62 @@ -/* fortran/zlaset.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given val -ues. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZLASET + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZLASET( UPLO, M, N, ALPHA, BETA, A, LDA ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER UPLO */ -/* INTEGER LDA, M, N */ -/* COMPLEX*16 ALPHA, BETA */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 A( LDA, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZLASET initializes a 2-D array A to BETA on the diagonal and */ -/* > ALPHA on the offdiagonals. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > Specifies the part of the matrix A to be set. */ -/* > = 'U': Upper triangular part is set. The lower triangle */ -/* > is unchanged. */ -/* > = 'L': Lower triangular part is set. The upper triangle */ -/* > is unchanged. */ -/* > Otherwise: All of the matrix A is set. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > On entry, M specifies the number of rows of A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > On entry, N specifies the number of columns of A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] ALPHA */ -/* > \verbatim */ -/* > ALPHA is COMPLEX*16 */ -/* > All the offdiagonal array elements are set to ALPHA. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] BETA */ -/* > \verbatim */ -/* > BETA is COMPLEX*16 */ -/* > All the diagonal array elements are set to BETA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] A */ -/* > \verbatim */ -/* > A is COMPLEX*16 array, dimension (LDA,N) */ -/* > On entry, the m by n matrix A. */ -/* > On exit, A(i,j) = ALPHA, 1 <= i <= m, 1 <= j <= n, i.ne.j; */ -/* > A(i,i) = BETA , 1 <= i <= min(m,n) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,M). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16OTHERauxiliary */ - -/* ===================================================================== */ -/* Subroutine */ int zlaset_(char *uplo, integer *m, integer *n, - doublecomplex *alpha, doublecomplex *beta, doublecomplex *a, integer * - lda, ftnlen uplo_len) +int zlaset_(char *uplo, integer *m, integer *n, doublecomplex *alpha, doublecomplex *beta, + doublecomplex *a, integer *lda, ftnlen uplo_len) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; - - /* Local variables */ integer i__, j; extern logical lsame_(char *, char *, ftnlen, ftnlen); - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; - - /* Function Body */ if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { - -/* Set the diagonal to BETA and the strictly upper triangular */ -/* part of the array to ALPHA. */ - i__1 = *n; for (j = 2; j <= i__1; ++j) { -/* Computing MIN */ i__3 = j - 1; - i__2 = min(i__3,*m); + i__2 = min(i__3, *m); for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * a_dim1; a[i__3].r = alpha->r, a[i__3].i = alpha->i; -/* L10: */ } -/* L20: */ } - i__1 = min(*n,*m); + i__1 = min(*n, *m); for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__ + i__ * a_dim1; a[i__2].r = beta->r, a[i__2].i = beta->i; -/* L30: */ } - } else if (lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { - -/* Set the diagonal to BETA and the strictly lower triangular */ -/* part of the array to ALPHA. */ - - i__1 = min(*m,*n); + i__1 = min(*m, *n); for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = j + 1; i__ <= i__2; ++i__) { i__3 = i__ + j * a_dim1; a[i__3].r = alpha->r, a[i__3].i = alpha->i; -/* L40: */ } -/* L50: */ } - i__1 = min(*n,*m); + i__1 = min(*n, *m); for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__ + i__ * a_dim1; a[i__2].r = beta->r, a[i__2].i = beta->i; -/* L60: */ } - } else { - -/* Set the array to BETA on the diagonal and ALPHA on the */ -/* offdiagonal. */ - i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * a_dim1; a[i__3].r = alpha->r, a[i__3].i = alpha->i; -/* L70: */ } -/* L80: */ } - i__1 = min(*m,*n); + i__1 = min(*m, *n); for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__ + i__ * a_dim1; a[i__2].r = beta->r, a[i__2].i = beta->i; -/* L90: */ } } - return 0; - -/* End of ZLASET */ - -} /* zlaset_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zlasr.cpp b/lib/linalg/zlasr.cpp index 51c9797679..06dc5606d2 100644 --- a/lib/linalg/zlasr.cpp +++ b/lib/linalg/zlasr.cpp @@ -1,302 +1,48 @@ -/* fortran/zlasr.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b ZLASR applies a sequence of plane rotations to a general rectangular matrix. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZLASR + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER DIRECT, PIVOT, SIDE */ -/* INTEGER LDA, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION C( * ), S( * ) */ -/* COMPLEX*16 A( LDA, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZLASR applies a sequence of real plane rotations to a complex matrix */ -/* > A, from either the left or the right. */ -/* > */ -/* > When SIDE = 'L', the transformation takes the form */ -/* > */ -/* > A := P*A */ -/* > */ -/* > and when SIDE = 'R', the transformation takes the form */ -/* > */ -/* > A := A*P**T */ -/* > */ -/* > where P is an orthogonal matrix consisting of a sequence of z plane */ -/* > rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R', */ -/* > and P**T is the transpose of P. */ -/* > */ -/* > When DIRECT = 'F' (Forward sequence), then */ -/* > */ -/* > P = P(z-1) * ... * P(2) * P(1) */ -/* > */ -/* > and when DIRECT = 'B' (Backward sequence), then */ -/* > */ -/* > P = P(1) * P(2) * ... * P(z-1) */ -/* > */ -/* > where P(k) is a plane rotation matrix defined by the 2-by-2 rotation */ -/* > */ -/* > R(k) = ( c(k) s(k) ) */ -/* > = ( -s(k) c(k) ). */ -/* > */ -/* > When PIVOT = 'V' (Variable pivot), the rotation is performed */ -/* > for the plane (k,k+1), i.e., P(k) has the form */ -/* > */ -/* > P(k) = ( 1 ) */ -/* > ( ... ) */ -/* > ( 1 ) */ -/* > ( c(k) s(k) ) */ -/* > ( -s(k) c(k) ) */ -/* > ( 1 ) */ -/* > ( ... ) */ -/* > ( 1 ) */ -/* > */ -/* > where R(k) appears as a rank-2 modification to the identity matrix in */ -/* > rows and columns k and k+1. */ -/* > */ -/* > When PIVOT = 'T' (Top pivot), the rotation is performed for the */ -/* > plane (1,k+1), so P(k) has the form */ -/* > */ -/* > P(k) = ( c(k) s(k) ) */ -/* > ( 1 ) */ -/* > ( ... ) */ -/* > ( 1 ) */ -/* > ( -s(k) c(k) ) */ -/* > ( 1 ) */ -/* > ( ... ) */ -/* > ( 1 ) */ -/* > */ -/* > where R(k) appears in rows and columns 1 and k+1. */ -/* > */ -/* > Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is */ -/* > performed for the plane (k,z), giving P(k) the form */ -/* > */ -/* > P(k) = ( 1 ) */ -/* > ( ... ) */ -/* > ( 1 ) */ -/* > ( c(k) s(k) ) */ -/* > ( 1 ) */ -/* > ( ... ) */ -/* > ( 1 ) */ -/* > ( -s(k) c(k) ) */ -/* > */ -/* > where R(k) appears in rows and columns k and z. The rotations are */ -/* > performed without ever forming P(k) explicitly. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] SIDE */ -/* > \verbatim */ -/* > SIDE is CHARACTER*1 */ -/* > Specifies whether the plane rotation matrix P is applied to */ -/* > A on the left or the right. */ -/* > = 'L': Left, compute A := P*A */ -/* > = 'R': Right, compute A:= A*P**T */ -/* > \endverbatim */ -/* > */ -/* > \param[in] PIVOT */ -/* > \verbatim */ -/* > PIVOT is CHARACTER*1 */ -/* > Specifies the plane for which P(k) is a plane rotation */ -/* > matrix. */ -/* > = 'V': Variable pivot, the plane (k,k+1) */ -/* > = 'T': Top pivot, the plane (1,k+1) */ -/* > = 'B': Bottom pivot, the plane (k,z) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DIRECT */ -/* > \verbatim */ -/* > DIRECT is CHARACTER*1 */ -/* > Specifies whether P is a forward or backward sequence of */ -/* > plane rotations. */ -/* > = 'F': Forward, P = P(z-1)*...*P(2)*P(1) */ -/* > = 'B': Backward, P = P(1)*P(2)*...*P(z-1) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix A. If m <= 1, an immediate */ -/* > return is effected. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix A. If n <= 1, an */ -/* > immediate return is effected. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] C */ -/* > \verbatim */ -/* > C is DOUBLE PRECISION array, dimension */ -/* > (M-1) if SIDE = 'L' */ -/* > (N-1) if SIDE = 'R' */ -/* > The cosines c(k) of the plane rotations. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] S */ -/* > \verbatim */ -/* > S is DOUBLE PRECISION array, dimension */ -/* > (M-1) if SIDE = 'L' */ -/* > (N-1) if SIDE = 'R' */ -/* > The sines s(k) of the plane rotations. The 2-by-2 plane */ -/* > rotation part of the matrix P(k), R(k), has the form */ -/* > R(k) = ( c(k) s(k) ) */ -/* > ( -s(k) c(k) ). */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is COMPLEX*16 array, dimension (LDA,N) */ -/* > The M-by-N matrix A. On exit, A is overwritten by P*A if */ -/* > SIDE = 'R' or by A*P**T if SIDE = 'L'. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,M). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16OTHERauxiliary */ - -/* ===================================================================== */ -/* Subroutine */ int zlasr_(char *side, char *pivot, char *direct, integer *m, - integer *n, doublereal *c__, doublereal *s, doublecomplex *a, - integer *lda, ftnlen side_len, ftnlen pivot_len, ftnlen direct_len) +int zlasr_(char *side, char *pivot, char *direct, integer *m, integer *n, doublereal *c__, + doublereal *s, doublecomplex *a, integer *lda, ftnlen side_len, ftnlen pivot_len, + ftnlen direct_len) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4; doublecomplex z__1, z__2, z__3; - - /* Local variables */ integer i__, j, info; doublecomplex temp; extern logical lsame_(char *, char *, ftnlen, ftnlen); doublereal ctemp, stemp; - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters */ - - /* Parameter adjustments */ + extern int xerbla_(char *, integer *, ftnlen); --c__; --s; a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; - - /* Function Body */ info = 0; - if (! (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1) || lsame_(side, (char *)"R", ( - ftnlen)1, (ftnlen)1))) { + if (!(lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1) || lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1))) { info = 1; - } else if (! (lsame_(pivot, (char *)"V", (ftnlen)1, (ftnlen)1) || lsame_(pivot, - (char *)"T", (ftnlen)1, (ftnlen)1) || lsame_(pivot, (char *)"B", (ftnlen)1, ( - ftnlen)1))) { + } else if (!(lsame_(pivot, (char *)"V", (ftnlen)1, (ftnlen)1) || + lsame_(pivot, (char *)"T", (ftnlen)1, (ftnlen)1) || + lsame_(pivot, (char *)"B", (ftnlen)1, (ftnlen)1))) { info = 2; - } else if (! (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1) || lsame_(direct, - (char *)"B", (ftnlen)1, (ftnlen)1))) { + } else if (!(lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1) || + lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1))) { info = 3; } else if (*m < 0) { info = 4; } else if (*n < 0) { info = 5; - } else if (*lda < max(1,*m)) { + } else if (*lda < max(1, *m)) { info = 9; } if (info != 0) { xerbla_((char *)"ZLASR ", &info, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*m == 0 || *n == 0) { return 0; } if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) { - -/* Form P * A */ - if (lsame_(pivot, (char *)"V", (ftnlen)1, (ftnlen)1)) { if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { i__1 = *m - 1; @@ -311,23 +57,17 @@ extern "C" { i__3 = j + 1 + i__ * a_dim1; z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i; i__4 = j + i__ * a_dim1; - z__3.r = stemp * a[i__4].r, z__3.i = stemp * a[ - i__4].i; - z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - - z__3.i; + z__3.r = stemp * a[i__4].r, z__3.i = stemp * a[i__4].i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; i__3 = j + i__ * a_dim1; z__2.r = stemp * temp.r, z__2.i = stemp * temp.i; i__4 = j + i__ * a_dim1; - z__3.r = ctemp * a[i__4].r, z__3.i = ctemp * a[ - i__4].i; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; + z__3.r = ctemp * a[i__4].r, z__3.i = ctemp * a[i__4].i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; -/* L10: */ } } -/* L20: */ } } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { for (j = *m - 1; j >= 1; --j) { @@ -341,23 +81,17 @@ extern "C" { i__2 = j + 1 + i__ * a_dim1; z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i; i__3 = j + i__ * a_dim1; - z__3.r = stemp * a[i__3].r, z__3.i = stemp * a[ - i__3].i; - z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - - z__3.i; + z__3.r = stemp * a[i__3].r, z__3.i = stemp * a[i__3].i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i; a[i__2].r = z__1.r, a[i__2].i = z__1.i; i__2 = j + i__ * a_dim1; z__2.r = stemp * temp.r, z__2.i = stemp * temp.i; i__3 = j + i__ * a_dim1; - z__3.r = ctemp * a[i__3].r, z__3.i = ctemp * a[ - i__3].i; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; + z__3.r = ctemp * a[i__3].r, z__3.i = ctemp * a[i__3].i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; a[i__2].r = z__1.r, a[i__2].i = z__1.i; -/* L30: */ } } -/* L40: */ } } } else if (lsame_(pivot, (char *)"T", (ftnlen)1, (ftnlen)1)) { @@ -374,23 +108,17 @@ extern "C" { i__3 = j + i__ * a_dim1; z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i; i__4 = i__ * a_dim1 + 1; - z__3.r = stemp * a[i__4].r, z__3.i = stemp * a[ - i__4].i; - z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - - z__3.i; + z__3.r = stemp * a[i__4].r, z__3.i = stemp * a[i__4].i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; i__3 = i__ * a_dim1 + 1; z__2.r = stemp * temp.r, z__2.i = stemp * temp.i; i__4 = i__ * a_dim1 + 1; - z__3.r = ctemp * a[i__4].r, z__3.i = ctemp * a[ - i__4].i; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; + z__3.r = ctemp * a[i__4].r, z__3.i = ctemp * a[i__4].i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; -/* L50: */ } } -/* L60: */ } } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { for (j = *m; j >= 2; --j) { @@ -404,23 +132,17 @@ extern "C" { i__2 = j + i__ * a_dim1; z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i; i__3 = i__ * a_dim1 + 1; - z__3.r = stemp * a[i__3].r, z__3.i = stemp * a[ - i__3].i; - z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - - z__3.i; + z__3.r = stemp * a[i__3].r, z__3.i = stemp * a[i__3].i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i; a[i__2].r = z__1.r, a[i__2].i = z__1.i; i__2 = i__ * a_dim1 + 1; z__2.r = stemp * temp.r, z__2.i = stemp * temp.i; i__3 = i__ * a_dim1 + 1; - z__3.r = ctemp * a[i__3].r, z__3.i = ctemp * a[ - i__3].i; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; + z__3.r = ctemp * a[i__3].r, z__3.i = ctemp * a[i__3].i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; a[i__2].r = z__1.r, a[i__2].i = z__1.i; -/* L70: */ } } -/* L80: */ } } } else if (lsame_(pivot, (char *)"B", (ftnlen)1, (ftnlen)1)) { @@ -436,24 +158,18 @@ extern "C" { temp.r = a[i__3].r, temp.i = a[i__3].i; i__3 = j + i__ * a_dim1; i__4 = *m + i__ * a_dim1; - z__2.r = stemp * a[i__4].r, z__2.i = stemp * a[ - i__4].i; + z__2.r = stemp * a[i__4].r, z__2.i = stemp * a[i__4].i; z__3.r = ctemp * temp.r, z__3.i = ctemp * temp.i; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; i__3 = *m + i__ * a_dim1; i__4 = *m + i__ * a_dim1; - z__2.r = ctemp * a[i__4].r, z__2.i = ctemp * a[ - i__4].i; + z__2.r = ctemp * a[i__4].r, z__2.i = ctemp * a[i__4].i; z__3.r = stemp * temp.r, z__3.i = stemp * temp.i; - z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - - z__3.i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; -/* L90: */ } } -/* L100: */ } } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { for (j = *m - 1; j >= 1; --j) { @@ -466,31 +182,22 @@ extern "C" { temp.r = a[i__2].r, temp.i = a[i__2].i; i__2 = j + i__ * a_dim1; i__3 = *m + i__ * a_dim1; - z__2.r = stemp * a[i__3].r, z__2.i = stemp * a[ - i__3].i; + z__2.r = stemp * a[i__3].r, z__2.i = stemp * a[i__3].i; z__3.r = ctemp * temp.r, z__3.i = ctemp * temp.i; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; a[i__2].r = z__1.r, a[i__2].i = z__1.i; i__2 = *m + i__ * a_dim1; i__3 = *m + i__ * a_dim1; - z__2.r = ctemp * a[i__3].r, z__2.i = ctemp * a[ - i__3].i; + z__2.r = ctemp * a[i__3].r, z__2.i = ctemp * a[i__3].i; z__3.r = stemp * temp.r, z__3.i = stemp * temp.i; - z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - - z__3.i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i; a[i__2].r = z__1.r, a[i__2].i = z__1.i; -/* L110: */ } } -/* L120: */ } } } } else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { - -/* Form A * P**T */ - if (lsame_(pivot, (char *)"V", (ftnlen)1, (ftnlen)1)) { if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) { i__1 = *n - 1; @@ -505,23 +212,17 @@ extern "C" { i__3 = i__ + (j + 1) * a_dim1; z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i; i__4 = i__ + j * a_dim1; - z__3.r = stemp * a[i__4].r, z__3.i = stemp * a[ - i__4].i; - z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - - z__3.i; + z__3.r = stemp * a[i__4].r, z__3.i = stemp * a[i__4].i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; i__3 = i__ + j * a_dim1; z__2.r = stemp * temp.r, z__2.i = stemp * temp.i; i__4 = i__ + j * a_dim1; - z__3.r = ctemp * a[i__4].r, z__3.i = ctemp * a[ - i__4].i; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; + z__3.r = ctemp * a[i__4].r, z__3.i = ctemp * a[i__4].i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; -/* L130: */ } } -/* L140: */ } } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { for (j = *n - 1; j >= 1; --j) { @@ -535,23 +236,17 @@ extern "C" { i__2 = i__ + (j + 1) * a_dim1; z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i; i__3 = i__ + j * a_dim1; - z__3.r = stemp * a[i__3].r, z__3.i = stemp * a[ - i__3].i; - z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - - z__3.i; + z__3.r = stemp * a[i__3].r, z__3.i = stemp * a[i__3].i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i; a[i__2].r = z__1.r, a[i__2].i = z__1.i; i__2 = i__ + j * a_dim1; z__2.r = stemp * temp.r, z__2.i = stemp * temp.i; i__3 = i__ + j * a_dim1; - z__3.r = ctemp * a[i__3].r, z__3.i = ctemp * a[ - i__3].i; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; + z__3.r = ctemp * a[i__3].r, z__3.i = ctemp * a[i__3].i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; a[i__2].r = z__1.r, a[i__2].i = z__1.i; -/* L150: */ } } -/* L160: */ } } } else if (lsame_(pivot, (char *)"T", (ftnlen)1, (ftnlen)1)) { @@ -568,23 +263,17 @@ extern "C" { i__3 = i__ + j * a_dim1; z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i; i__4 = i__ + a_dim1; - z__3.r = stemp * a[i__4].r, z__3.i = stemp * a[ - i__4].i; - z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - - z__3.i; + z__3.r = stemp * a[i__4].r, z__3.i = stemp * a[i__4].i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; i__3 = i__ + a_dim1; z__2.r = stemp * temp.r, z__2.i = stemp * temp.i; i__4 = i__ + a_dim1; - z__3.r = ctemp * a[i__4].r, z__3.i = ctemp * a[ - i__4].i; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; + z__3.r = ctemp * a[i__4].r, z__3.i = ctemp * a[i__4].i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; -/* L170: */ } } -/* L180: */ } } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { for (j = *n; j >= 2; --j) { @@ -598,23 +287,17 @@ extern "C" { i__2 = i__ + j * a_dim1; z__2.r = ctemp * temp.r, z__2.i = ctemp * temp.i; i__3 = i__ + a_dim1; - z__3.r = stemp * a[i__3].r, z__3.i = stemp * a[ - i__3].i; - z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - - z__3.i; + z__3.r = stemp * a[i__3].r, z__3.i = stemp * a[i__3].i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i; a[i__2].r = z__1.r, a[i__2].i = z__1.i; i__2 = i__ + a_dim1; z__2.r = stemp * temp.r, z__2.i = stemp * temp.i; i__3 = i__ + a_dim1; - z__3.r = ctemp * a[i__3].r, z__3.i = ctemp * a[ - i__3].i; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; + z__3.r = ctemp * a[i__3].r, z__3.i = ctemp * a[i__3].i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; a[i__2].r = z__1.r, a[i__2].i = z__1.i; -/* L190: */ } } -/* L200: */ } } } else if (lsame_(pivot, (char *)"B", (ftnlen)1, (ftnlen)1)) { @@ -630,24 +313,18 @@ extern "C" { temp.r = a[i__3].r, temp.i = a[i__3].i; i__3 = i__ + j * a_dim1; i__4 = i__ + *n * a_dim1; - z__2.r = stemp * a[i__4].r, z__2.i = stemp * a[ - i__4].i; + z__2.r = stemp * a[i__4].r, z__2.i = stemp * a[i__4].i; z__3.r = ctemp * temp.r, z__3.i = ctemp * temp.i; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; i__3 = i__ + *n * a_dim1; i__4 = i__ + *n * a_dim1; - z__2.r = ctemp * a[i__4].r, z__2.i = ctemp * a[ - i__4].i; + z__2.r = ctemp * a[i__4].r, z__2.i = ctemp * a[i__4].i; z__3.r = stemp * temp.r, z__3.i = stemp * temp.i; - z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - - z__3.i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; -/* L210: */ } } -/* L220: */ } } else if (lsame_(direct, (char *)"B", (ftnlen)1, (ftnlen)1)) { for (j = *n - 1; j >= 1; --j) { @@ -660,35 +337,24 @@ extern "C" { temp.r = a[i__2].r, temp.i = a[i__2].i; i__2 = i__ + j * a_dim1; i__3 = i__ + *n * a_dim1; - z__2.r = stemp * a[i__3].r, z__2.i = stemp * a[ - i__3].i; + z__2.r = stemp * a[i__3].r, z__2.i = stemp * a[i__3].i; z__3.r = ctemp * temp.r, z__3.i = ctemp * temp.i; - z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + - z__3.i; + z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i; a[i__2].r = z__1.r, a[i__2].i = z__1.i; i__2 = i__ + *n * a_dim1; i__3 = i__ + *n * a_dim1; - z__2.r = ctemp * a[i__3].r, z__2.i = ctemp * a[ - i__3].i; + z__2.r = ctemp * a[i__3].r, z__2.i = ctemp * a[i__3].i; z__3.r = stemp * temp.r, z__3.i = stemp * temp.i; - z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - - z__3.i; + z__1.r = z__2.r - z__3.r, z__1.i = z__2.i - z__3.i; a[i__2].r = z__1.r, a[i__2].i = z__1.i; -/* L230: */ } } -/* L240: */ } } } } - return 0; - -/* End of ZLASR */ - -} /* zlasr_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zlassq.cpp b/lib/linalg/zlassq.cpp index 31c0f15f4c..b60831044f 100644 --- a/lib/linalg/zlassq.cpp +++ b/lib/linalg/zlassq.cpp @@ -1,171 +1,16 @@ -/* fortran/zlassq.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b ZLASSQ updates a sum of squares represented in scaled form. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZLASSQ + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZLASSQ( N, X, INCX, SCALE, SUMSQ ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INCX, N */ -/* DOUBLE PRECISION SCALE, SUMSQ */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 X( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZLASSQ returns the values scl and ssq such that */ -/* > */ -/* > ( scl**2 )*ssq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq, */ -/* > */ -/* > where x( i ) = abs( X( 1 + ( i - 1 )*INCX ) ). The value of sumsq is */ -/* > assumed to be at least unity and the value of ssq will then satisfy */ -/* > */ -/* > 1.0 .le. ssq .le. ( sumsq + 2*n ). */ -/* > */ -/* > scale is assumed to be non-negative and scl returns the value */ -/* > */ -/* > scl = max( scale, abs( real( x( i ) ) ), abs( aimag( x( i ) ) ) ), */ -/* > i */ -/* > */ -/* > scale and sumsq must be supplied in SCALE and SUMSQ respectively. */ -/* > SCALE and SUMSQ are overwritten by scl and ssq respectively. */ -/* > */ -/* > The routine makes only one pass through the vector X. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of elements to be used from the vector X. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] X */ -/* > \verbatim */ -/* > X is COMPLEX*16 array, dimension (N) */ -/* > The vector x as described above. */ -/* > x( i ) = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > The increment between successive values of the vector X. */ -/* > INCX > 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] SCALE */ -/* > \verbatim */ -/* > SCALE is DOUBLE PRECISION */ -/* > On entry, the value scale in the equation above. */ -/* > On exit, SCALE is overwritten with the value scl . */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] SUMSQ */ -/* > \verbatim */ -/* > SUMSQ is DOUBLE PRECISION */ -/* > On entry, the value sumsq in the equation above. */ -/* > On exit, SUMSQ is overwritten with the value ssq . */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \date December 2016 */ - -/* > \ingroup complex16OTHERauxiliary */ - -/* ===================================================================== */ -/* Subroutine */ int zlassq_(integer *n, doublecomplex *x, integer *incx, - doublereal *scale, doublereal *sumsq) +int zlassq_(integer *n, doublecomplex *x, integer *incx, doublereal *scale, doublereal *sumsq) { - /* System generated locals */ integer i__1, i__2, i__3; doublereal d__1; - - /* Builtin functions */ double d_lmp_imag(doublecomplex *); - - /* Local variables */ integer ix; doublereal temp1; extern logical disnan_(doublereal *); - - -/* -- LAPACK auxiliary routine (version 3.7.0) -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ -/* December 2016 */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - - /* Parameter adjustments */ --x; - - /* Function Body */ if (*n > 0) { i__1 = (*n - 1) * *incx + 1; i__2 = *incx; @@ -174,12 +19,10 @@ f"> */ temp1 = (d__1 = x[i__3].r, abs(d__1)); if (temp1 > 0. || disnan_(&temp1)) { if (*scale < temp1) { -/* Computing 2nd power */ d__1 = *scale / temp1; *sumsq = *sumsq * (d__1 * d__1) + 1; *scale = temp1; } else { -/* Computing 2nd power */ d__1 = temp1 / *scale; *sumsq += d__1 * d__1; } @@ -187,26 +30,18 @@ f"> */ temp1 = (d__1 = d_lmp_imag(&x[ix]), abs(d__1)); if (temp1 > 0. || disnan_(&temp1)) { if (*scale < temp1) { -/* Computing 2nd power */ d__1 = *scale / temp1; *sumsq = *sumsq * (d__1 * d__1) + 1; *scale = temp1; } else { -/* Computing 2nd power */ d__1 = temp1 / *scale; *sumsq += d__1 * d__1; } } -/* L10: */ } } - return 0; - -/* End of ZLASSQ */ - -} /* zlassq_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zlatrd.cpp b/lib/linalg/zlatrd.cpp index d471ea96eb..4f2a1750df 100644 --- a/lib/linalg/zlatrd.cpp +++ b/lib/linalg/zlatrd.cpp @@ -1,282 +1,30 @@ -/* fortran/zlatrd.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - -static doublecomplex c_b1 = {0.,0.}; -static doublecomplex c_b2 = {1.,0.}; +static doublecomplex c_b1 = {0., 0.}; +static doublecomplex c_b2 = {1., 0.}; static integer c__1 = 1; - -/* > \brief \b ZLATRD reduces the first nb rows and columns of a symmetric/Hermitian matrix A to real tridiago -nal form by an unitary similarity transformation. */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZLATRD + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZLATRD( UPLO, N, NB, A, LDA, E, TAU, W, LDW ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER UPLO */ -/* INTEGER LDA, LDW, N, NB */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION E( * ) */ -/* COMPLEX*16 A( LDA, * ), TAU( * ), W( LDW, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZLATRD reduces NB rows and columns of a complex Hermitian matrix A to */ -/* > Hermitian tridiagonal form by a unitary similarity */ -/* > transformation Q**H * A * Q, and returns the matrices V and W which are */ -/* > needed to apply the transformation to the unreduced part of A. */ -/* > */ -/* > If UPLO = 'U', ZLATRD reduces the last NB rows and columns of a */ -/* > matrix, of which the upper triangle is supplied; */ -/* > if UPLO = 'L', ZLATRD reduces the first NB rows and columns of a */ -/* > matrix, of which the lower triangle is supplied. */ -/* > */ -/* > This is an auxiliary routine called by ZHETRD. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > Specifies whether the upper or lower triangular part of the */ -/* > Hermitian matrix A is stored: */ -/* > = 'U': Upper triangular */ -/* > = 'L': Lower triangular */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrix A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] NB */ -/* > \verbatim */ -/* > NB is INTEGER */ -/* > The number of rows and columns to be reduced. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is COMPLEX*16 array, dimension (LDA,N) */ -/* > On entry, the Hermitian matrix A. If UPLO = 'U', the leading */ -/* > n-by-n upper triangular part of A contains the upper */ -/* > triangular part of the matrix A, and the strictly lower */ -/* > triangular part of A is not referenced. If UPLO = 'L', the */ -/* > leading n-by-n lower triangular part of A contains the lower */ -/* > triangular part of the matrix A, and the strictly upper */ -/* > triangular part of A is not referenced. */ -/* > On exit: */ -/* > if UPLO = 'U', the last NB columns have been reduced to */ -/* > tridiagonal form, with the diagonal elements overwriting */ -/* > the diagonal elements of A; the elements above the diagonal */ -/* > with the array TAU, represent the unitary matrix Q as a */ -/* > product of elementary reflectors; */ -/* > if UPLO = 'L', the first NB columns have been reduced to */ -/* > tridiagonal form, with the diagonal elements overwriting */ -/* > the diagonal elements of A; the elements below the diagonal */ -/* > with the array TAU, represent the unitary matrix Q as a */ -/* > product of elementary reflectors. */ -/* > See Further Details. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] E */ -/* > \verbatim */ -/* > E is DOUBLE PRECISION array, dimension (N-1) */ -/* > If UPLO = 'U', E(n-nb:n-1) contains the superdiagonal */ -/* > elements of the last NB columns of the reduced matrix; */ -/* > if UPLO = 'L', E(1:nb) contains the subdiagonal elements of */ -/* > the first NB columns of the reduced matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] TAU */ -/* > \verbatim */ -/* > TAU is COMPLEX*16 array, dimension (N-1) */ -/* > The scalar factors of the elementary reflectors, stored in */ -/* > TAU(n-nb:n-1) if UPLO = 'U', and in TAU(1:nb) if UPLO = 'L'. */ -/* > See Further Details. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] W */ -/* > \verbatim */ -/* > W is COMPLEX*16 array, dimension (LDW,NB) */ -/* > The n-by-nb matrix W required to update the unreduced part */ -/* > of A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDW */ -/* > \verbatim */ -/* > LDW is INTEGER */ -/* > The leading dimension of the array W. LDW >= max(1,N). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16OTHERauxiliary */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > If UPLO = 'U', the matrix Q is represented as a product of elementary */ -/* > reflectors */ -/* > */ -/* > Q = H(n) H(n-1) . . . H(n-nb+1). */ -/* > */ -/* > Each H(i) has the form */ -/* > */ -/* > H(i) = I - tau * v * v**H */ -/* > */ -/* > where tau is a complex scalar, and v is a complex vector with */ -/* > v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i), */ -/* > and tau in TAU(i-1). */ -/* > */ -/* > If UPLO = 'L', the matrix Q is represented as a product of elementary */ -/* > reflectors */ -/* > */ -/* > Q = H(1) H(2) . . . H(nb). */ -/* > */ -/* > Each H(i) has the form */ -/* > */ -/* > H(i) = I - tau * v * v**H */ -/* > */ -/* > where tau is a complex scalar, and v is a complex vector with */ -/* > v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i), */ -/* > and tau in TAU(i). */ -/* > */ -/* > The elements of the vectors v together form the n-by-nb matrix V */ -/* > which is needed, with W, to apply the transformation to the unreduced */ -/* > part of the matrix, using a Hermitian rank-2k update of the form: */ -/* > A := A - V*W**H - W*V**H. */ -/* > */ -/* > The contents of A on exit are illustrated by the following examples */ -/* > with n = 5 and nb = 2: */ -/* > */ -/* > if UPLO = 'U': if UPLO = 'L': */ -/* > */ -/* > ( a a a v4 v5 ) ( d ) */ -/* > ( a a v4 v5 ) ( 1 d ) */ -/* > ( a 1 v5 ) ( v1 1 a ) */ -/* > ( d 1 ) ( v1 v2 a a ) */ -/* > ( d ) ( v1 v2 a a a ) */ -/* > */ -/* > where d denotes a diagonal element of the reduced matrix, a denotes */ -/* > an element of the original matrix that is unchanged, and vi denotes */ -/* > an element of the vector defining H(i). */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int zlatrd_(char *uplo, integer *n, integer *nb, - doublecomplex *a, integer *lda, doublereal *e, doublecomplex *tau, - doublecomplex *w, integer *ldw, ftnlen uplo_len) +int zlatrd_(char *uplo, integer *n, integer *nb, doublecomplex *a, integer *lda, doublereal *e, + doublecomplex *tau, doublecomplex *w, integer *ldw, ftnlen uplo_len) { - /* System generated locals */ integer a_dim1, a_offset, w_dim1, w_offset, i__1, i__2, i__3; doublereal d__1; doublecomplex z__1, z__2, z__3, z__4; - - /* Local variables */ integer i__, iw; doublecomplex alpha; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int zscal_(integer *, doublecomplex *, - doublecomplex *, integer *); - extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *, - doublecomplex *, integer *, doublecomplex *, integer *); - extern /* Subroutine */ int zgemv_(char *, integer *, integer *, - doublecomplex *, doublecomplex *, integer *, doublecomplex *, - integer *, doublecomplex *, doublecomplex *, integer *, ftnlen), - zhemv_(char *, integer *, doublecomplex *, doublecomplex *, - integer *, doublecomplex *, integer *, doublecomplex *, - doublecomplex *, integer *, ftnlen), zaxpy_(integer *, - doublecomplex *, doublecomplex *, integer *, doublecomplex *, - integer *), zlarfg_(integer *, doublecomplex *, doublecomplex *, - integer *, doublecomplex *), zlacgv_(integer *, doublecomplex *, - integer *); - - -/* -- LAPACK auxiliary routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Quick return if possible */ - - /* Parameter adjustments */ + extern int zscal_(integer *, doublecomplex *, doublecomplex *, integer *); + extern VOID zdotc_(doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, + integer *); + extern int zgemv_(char *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, + doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, + ftnlen), + zhemv_(char *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, + integer *, doublecomplex *, doublecomplex *, integer *, ftnlen), + zaxpy_(integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *), + zlarfg_(integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *), + zlacgv_(integer *, doublecomplex *, integer *); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; @@ -285,23 +33,14 @@ f"> */ w_dim1 = *ldw; w_offset = 1 + w_dim1; w -= w_offset; - - /* Function Body */ if (*n <= 0) { return 0; } - if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { - -/* Reduce last NB columns of upper triangle */ - i__1 = *n - *nb + 1; for (i__ = *n; i__ >= i__1; --i__) { iw = i__ - *n + *nb; if (i__ < *n) { - -/* Update A(1:i,i) */ - i__2 = i__ + i__ * a_dim1; i__3 = i__ + i__ * a_dim1; d__1 = a[i__3].r; @@ -310,18 +49,18 @@ f"> */ zlacgv_(&i__2, &w[i__ + (iw + 1) * w_dim1], ldw); i__2 = *n - i__; z__1.r = -1., z__1.i = -0.; - zgemv_((char *)"No transpose", &i__, &i__2, &z__1, &a[(i__ + 1) * - a_dim1 + 1], lda, &w[i__ + (iw + 1) * w_dim1], ldw, & - c_b2, &a[i__ * a_dim1 + 1], &c__1, (ftnlen)12); + zgemv_((char *)"No transpose", &i__, &i__2, &z__1, &a[(i__ + 1) * a_dim1 + 1], lda, + &w[i__ + (iw + 1) * w_dim1], ldw, &c_b2, &a[i__ * a_dim1 + 1], &c__1, + (ftnlen)12); i__2 = *n - i__; zlacgv_(&i__2, &w[i__ + (iw + 1) * w_dim1], ldw); i__2 = *n - i__; zlacgv_(&i__2, &a[i__ + (i__ + 1) * a_dim1], lda); i__2 = *n - i__; z__1.r = -1., z__1.i = -0.; - zgemv_((char *)"No transpose", &i__, &i__2, &z__1, &w[(iw + 1) * - w_dim1 + 1], ldw, &a[i__ + (i__ + 1) * a_dim1], lda, & - c_b2, &a[i__ * a_dim1 + 1], &c__1, (ftnlen)12); + zgemv_((char *)"No transpose", &i__, &i__2, &z__1, &w[(iw + 1) * w_dim1 + 1], ldw, + &a[i__ + (i__ + 1) * a_dim1], lda, &c_b2, &a[i__ * a_dim1 + 1], &c__1, + (ftnlen)12); i__2 = *n - i__; zlacgv_(&i__2, &a[i__ + (i__ + 1) * a_dim1], lda); i__2 = i__ + i__ * a_dim1; @@ -330,81 +69,58 @@ f"> */ a[i__2].r = d__1, a[i__2].i = 0.; } if (i__ > 1) { - -/* Generate elementary reflector H(i) to annihilate */ -/* A(1:i-2,i) */ - i__2 = i__ - 1 + i__ * a_dim1; alpha.r = a[i__2].r, alpha.i = a[i__2].i; i__2 = i__ - 1; - zlarfg_(&i__2, &alpha, &a[i__ * a_dim1 + 1], &c__1, &tau[i__ - - 1]); + zlarfg_(&i__2, &alpha, &a[i__ * a_dim1 + 1], &c__1, &tau[i__ - 1]); e[i__ - 1] = alpha.r; i__2 = i__ - 1 + i__ * a_dim1; a[i__2].r = 1., a[i__2].i = 0.; - -/* Compute W(1:i-1,i) */ - i__2 = i__ - 1; - zhemv_((char *)"Upper", &i__2, &c_b2, &a[a_offset], lda, &a[i__ * - a_dim1 + 1], &c__1, &c_b1, &w[iw * w_dim1 + 1], &c__1, - (ftnlen)5); + zhemv_((char *)"Upper", &i__2, &c_b2, &a[a_offset], lda, &a[i__ * a_dim1 + 1], &c__1, &c_b1, + &w[iw * w_dim1 + 1], &c__1, (ftnlen)5); if (i__ < *n) { i__2 = i__ - 1; i__3 = *n - i__; - zgemv_((char *)"Conjugate transpose", &i__2, &i__3, &c_b2, &w[(iw - + 1) * w_dim1 + 1], ldw, &a[i__ * a_dim1 + 1], & - c__1, &c_b1, &w[i__ + 1 + iw * w_dim1], &c__1, ( - ftnlen)19); + zgemv_((char *)"Conjugate transpose", &i__2, &i__3, &c_b2, &w[(iw + 1) * w_dim1 + 1], + ldw, &a[i__ * a_dim1 + 1], &c__1, &c_b1, &w[i__ + 1 + iw * w_dim1], + &c__1, (ftnlen)19); i__2 = i__ - 1; i__3 = *n - i__; z__1.r = -1., z__1.i = -0.; - zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &a[(i__ + 1) * - a_dim1 + 1], lda, &w[i__ + 1 + iw * w_dim1], & - c__1, &c_b2, &w[iw * w_dim1 + 1], &c__1, (ftnlen) - 12); + zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &a[(i__ + 1) * a_dim1 + 1], lda, + &w[i__ + 1 + iw * w_dim1], &c__1, &c_b2, &w[iw * w_dim1 + 1], &c__1, + (ftnlen)12); i__2 = i__ - 1; i__3 = *n - i__; - zgemv_((char *)"Conjugate transpose", &i__2, &i__3, &c_b2, &a[( - i__ + 1) * a_dim1 + 1], lda, &a[i__ * a_dim1 + 1], - &c__1, &c_b1, &w[i__ + 1 + iw * w_dim1], &c__1, ( - ftnlen)19); + zgemv_((char *)"Conjugate transpose", &i__2, &i__3, &c_b2, &a[(i__ + 1) * a_dim1 + 1], + lda, &a[i__ * a_dim1 + 1], &c__1, &c_b1, &w[i__ + 1 + iw * w_dim1], + &c__1, (ftnlen)19); i__2 = i__ - 1; i__3 = *n - i__; z__1.r = -1., z__1.i = -0.; - zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &w[(iw + 1) * - w_dim1 + 1], ldw, &w[i__ + 1 + iw * w_dim1], & - c__1, &c_b2, &w[iw * w_dim1 + 1], &c__1, (ftnlen) - 12); + zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &w[(iw + 1) * w_dim1 + 1], ldw, + &w[i__ + 1 + iw * w_dim1], &c__1, &c_b2, &w[iw * w_dim1 + 1], &c__1, + (ftnlen)12); } i__2 = i__ - 1; zscal_(&i__2, &tau[i__ - 1], &w[iw * w_dim1 + 1], &c__1); z__3.r = -.5, z__3.i = -0.; i__2 = i__ - 1; - z__2.r = z__3.r * tau[i__2].r - z__3.i * tau[i__2].i, z__2.i = - z__3.r * tau[i__2].i + z__3.i * tau[i__2].r; + z__2.r = z__3.r * tau[i__2].r - z__3.i * tau[i__2].i, + z__2.i = z__3.r * tau[i__2].i + z__3.i * tau[i__2].r; i__3 = i__ - 1; - zdotc_(&z__4, &i__3, &w[iw * w_dim1 + 1], &c__1, &a[i__ * - a_dim1 + 1], &c__1); - z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, z__1.i = z__2.r * - z__4.i + z__2.i * z__4.r; + zdotc_(&z__4, &i__3, &w[iw * w_dim1 + 1], &c__1, &a[i__ * a_dim1 + 1], &c__1); + z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, + z__1.i = z__2.r * z__4.i + z__2.i * z__4.r; alpha.r = z__1.r, alpha.i = z__1.i; i__2 = i__ - 1; - zaxpy_(&i__2, &alpha, &a[i__ * a_dim1 + 1], &c__1, &w[iw * - w_dim1 + 1], &c__1); + zaxpy_(&i__2, &alpha, &a[i__ * a_dim1 + 1], &c__1, &w[iw * w_dim1 + 1], &c__1); } - -/* L10: */ } } else { - -/* Reduce first NB columns of lower triangle */ - i__1 = *nb; for (i__ = 1; i__ <= i__1; ++i__) { - -/* Update A(i:n,i) */ - i__2 = i__ + i__ * a_dim1; i__3 = i__ + i__ * a_dim1; d__1 = a[i__3].r; @@ -414,9 +130,8 @@ f"> */ i__2 = *n - i__ + 1; i__3 = i__ - 1; z__1.r = -1., z__1.i = -0.; - zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &a[i__ + a_dim1], lda, - &w[i__ + w_dim1], ldw, &c_b2, &a[i__ + i__ * a_dim1], & - c__1, (ftnlen)12); + zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &a[i__ + a_dim1], lda, &w[i__ + w_dim1], + ldw, &c_b2, &a[i__ + i__ * a_dim1], &c__1, (ftnlen)12); i__2 = i__ - 1; zlacgv_(&i__2, &w[i__ + w_dim1], ldw); i__2 = i__ - 1; @@ -424,9 +139,8 @@ f"> */ i__2 = *n - i__ + 1; i__3 = i__ - 1; z__1.r = -1., z__1.i = -0.; - zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &w[i__ + w_dim1], ldw, - &a[i__ + a_dim1], lda, &c_b2, &a[i__ + i__ * a_dim1], & - c__1, (ftnlen)12); + zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &w[i__ + w_dim1], ldw, &a[i__ + a_dim1], + lda, &c_b2, &a[i__ + i__ * a_dim1], &c__1, (ftnlen)12); i__2 = i__ - 1; zlacgv_(&i__2, &a[i__ + a_dim1], lda); i__2 = i__ + i__ * a_dim1; @@ -434,76 +148,60 @@ f"> */ d__1 = a[i__3].r; a[i__2].r = d__1, a[i__2].i = 0.; if (i__ < *n) { - -/* Generate elementary reflector H(i) to annihilate */ -/* A(i+2:n,i) */ - i__2 = i__ + 1 + i__ * a_dim1; alpha.r = a[i__2].r, alpha.i = a[i__2].i; i__2 = *n - i__; -/* Computing MIN */ i__3 = i__ + 2; - zlarfg_(&i__2, &alpha, &a[min(i__3,*n) + i__ * a_dim1], &c__1, - &tau[i__]); + zlarfg_(&i__2, &alpha, &a[min(i__3, *n) + i__ * a_dim1], &c__1, &tau[i__]); e[i__] = alpha.r; i__2 = i__ + 1 + i__ * a_dim1; a[i__2].r = 1., a[i__2].i = 0.; - -/* Compute W(i+1:n,i) */ - i__2 = *n - i__; - zhemv_((char *)"Lower", &i__2, &c_b2, &a[i__ + 1 + (i__ + 1) * a_dim1] - , lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b1, &w[ - i__ + 1 + i__ * w_dim1], &c__1, (ftnlen)5); + zhemv_((char *)"Lower", &i__2, &c_b2, &a[i__ + 1 + (i__ + 1) * a_dim1], lda, + &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b1, &w[i__ + 1 + i__ * w_dim1], &c__1, + (ftnlen)5); i__2 = *n - i__; i__3 = i__ - 1; - zgemv_((char *)"Conjugate transpose", &i__2, &i__3, &c_b2, &w[i__ + 1 - + w_dim1], ldw, &a[i__ + 1 + i__ * a_dim1], &c__1, & - c_b1, &w[i__ * w_dim1 + 1], &c__1, (ftnlen)19); + zgemv_((char *)"Conjugate transpose", &i__2, &i__3, &c_b2, &w[i__ + 1 + w_dim1], ldw, + &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b1, &w[i__ * w_dim1 + 1], &c__1, + (ftnlen)19); i__2 = *n - i__; i__3 = i__ - 1; z__1.r = -1., z__1.i = -0.; - zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &a[i__ + 1 + - a_dim1], lda, &w[i__ * w_dim1 + 1], &c__1, &c_b2, &w[ - i__ + 1 + i__ * w_dim1], &c__1, (ftnlen)12); + zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &a[i__ + 1 + a_dim1], lda, + &w[i__ * w_dim1 + 1], &c__1, &c_b2, &w[i__ + 1 + i__ * w_dim1], &c__1, + (ftnlen)12); i__2 = *n - i__; i__3 = i__ - 1; - zgemv_((char *)"Conjugate transpose", &i__2, &i__3, &c_b2, &a[i__ + 1 - + a_dim1], lda, &a[i__ + 1 + i__ * a_dim1], &c__1, & - c_b1, &w[i__ * w_dim1 + 1], &c__1, (ftnlen)19); + zgemv_((char *)"Conjugate transpose", &i__2, &i__3, &c_b2, &a[i__ + 1 + a_dim1], lda, + &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b1, &w[i__ * w_dim1 + 1], &c__1, + (ftnlen)19); i__2 = *n - i__; i__3 = i__ - 1; z__1.r = -1., z__1.i = -0.; - zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &w[i__ + 1 + - w_dim1], ldw, &w[i__ * w_dim1 + 1], &c__1, &c_b2, &w[ - i__ + 1 + i__ * w_dim1], &c__1, (ftnlen)12); + zgemv_((char *)"No transpose", &i__2, &i__3, &z__1, &w[i__ + 1 + w_dim1], ldw, + &w[i__ * w_dim1 + 1], &c__1, &c_b2, &w[i__ + 1 + i__ * w_dim1], &c__1, + (ftnlen)12); i__2 = *n - i__; zscal_(&i__2, &tau[i__], &w[i__ + 1 + i__ * w_dim1], &c__1); z__3.r = -.5, z__3.i = -0.; i__2 = i__; - z__2.r = z__3.r * tau[i__2].r - z__3.i * tau[i__2].i, z__2.i = - z__3.r * tau[i__2].i + z__3.i * tau[i__2].r; + z__2.r = z__3.r * tau[i__2].r - z__3.i * tau[i__2].i, + z__2.i = z__3.r * tau[i__2].i + z__3.i * tau[i__2].r; i__3 = *n - i__; - zdotc_(&z__4, &i__3, &w[i__ + 1 + i__ * w_dim1], &c__1, &a[ - i__ + 1 + i__ * a_dim1], &c__1); - z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, z__1.i = z__2.r * - z__4.i + z__2.i * z__4.r; + zdotc_(&z__4, &i__3, &w[i__ + 1 + i__ * w_dim1], &c__1, &a[i__ + 1 + i__ * a_dim1], + &c__1); + z__1.r = z__2.r * z__4.r - z__2.i * z__4.i, + z__1.i = z__2.r * z__4.i + z__2.i * z__4.r; alpha.r = z__1.r, alpha.i = z__1.i; i__2 = *n - i__; - zaxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &w[ - i__ + 1 + i__ * w_dim1], &c__1); + zaxpy_(&i__2, &alpha, &a[i__ + 1 + i__ * a_dim1], &c__1, &w[i__ + 1 + i__ * w_dim1], + &c__1); } - -/* L20: */ } } - return 0; - -/* End of ZLATRD */ - -} /* zlatrd_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zpptrf.cpp b/lib/linalg/zpptrf.cpp index d14e3678be..7c7049c6a1 100644 --- a/lib/linalg/zpptrf.cpp +++ b/lib/linalg/zpptrf.cpp @@ -1,203 +1,31 @@ -/* fortran/zpptrf.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static doublereal c_b16 = -1.; - -/* > \brief \b ZPPTRF */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZPPTRF + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZPPTRF( UPLO, N, AP, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER UPLO */ -/* INTEGER INFO, N */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 AP( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZPPTRF computes the Cholesky factorization of a complex Hermitian */ -/* > positive definite matrix A stored in packed format. */ -/* > */ -/* > The factorization has the form */ -/* > A = U**H * U, if UPLO = 'U', or */ -/* > A = L * L**H, if UPLO = 'L', */ -/* > where U is an upper triangular matrix and L is lower triangular. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > = 'U': Upper triangle of A is stored; */ -/* > = 'L': Lower triangle of A is stored. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] AP */ -/* > \verbatim */ -/* > AP is COMPLEX*16 array, dimension (N*(N+1)/2) */ -/* > On entry, the upper or lower triangle of the Hermitian matrix */ -/* > A, packed columnwise in a linear array. The j-th column of A */ -/* > is stored in the array AP as follows: */ -/* > if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */ -/* > if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. */ -/* > See below for further details. */ -/* > */ -/* > On exit, if INFO = 0, the triangular factor U or L from the */ -/* > Cholesky factorization A = U**H*U or A = L*L**H, in the same */ -/* > storage format as A. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > > 0: if INFO = i, the leading minor of order i is not */ -/* > positive definite, and the factorization could not be */ -/* > completed. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16OTHERcomputational */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > The packed storage scheme is illustrated by the following example */ -/* > when N = 4, UPLO = 'U': */ -/* > */ -/* > Two-dimensional storage of the Hermitian matrix A: */ -/* > */ -/* > a11 a12 a13 a14 */ -/* > a22 a23 a24 */ -/* > a33 a34 (aij = conjg(aji)) */ -/* > a44 */ -/* > */ -/* > Packed storage of the upper triangle of A: */ -/* > */ -/* > AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ] */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int zpptrf_(char *uplo, integer *n, doublecomplex *ap, - integer *info, ftnlen uplo_len) +int zpptrf_(char *uplo, integer *n, doublecomplex *ap, integer *info, ftnlen uplo_len) { - /* System generated locals */ integer i__1, i__2, i__3; doublereal d__1; doublecomplex z__1; - - /* Builtin functions */ double sqrt(doublereal); - - /* Local variables */ integer j, jc, jj; doublereal ajj; - extern /* Subroutine */ int zhpr_(char *, integer *, doublereal *, - doublecomplex *, integer *, doublecomplex *, ftnlen); + extern int zhpr_(char *, integer *, doublereal *, doublecomplex *, integer *, doublecomplex *, + ftnlen); extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *, - doublecomplex *, integer *, doublecomplex *, integer *); + extern VOID zdotc_(doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, + integer *); logical upper; - extern /* Subroutine */ int ztpsv_(char *, char *, char *, integer *, - doublecomplex *, doublecomplex *, integer *, ftnlen, ftnlen, - ftnlen), xerbla_(char *, integer *, ftnlen), zdscal_(integer *, - doublereal *, doublecomplex *, integer *); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ + extern int ztpsv_(char *, char *, char *, integer *, doublecomplex *, doublecomplex *, + integer *, ftnlen, ftnlen, ftnlen), + xerbla_(char *, integer *, ftnlen), + zdscal_(integer *, doublereal *, doublecomplex *, integer *); --ap; - - /* Function Body */ *info = 0; upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); - if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + if (!upper && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { *info = -1; } else if (*n < 0) { *info = -2; @@ -207,33 +35,20 @@ f"> */ xerbla_((char *)"ZPPTRF", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*n == 0) { return 0; } - if (upper) { - -/* Compute the Cholesky factorization A = U**H * U. */ - jj = 0; i__1 = *n; for (j = 1; j <= i__1; ++j) { jc = jj + 1; jj += j; - -/* Compute elements 1:J-1 of column J. */ - if (j > 1) { i__2 = j - 1; - ztpsv_((char *)"Upper", (char *)"Conjugate transpose", (char *)"Non-unit", &i__2, &ap[ - 1], &ap[jc], &c__1, (ftnlen)5, (ftnlen)19, (ftnlen)8); + ztpsv_((char *)"Upper", (char *)"Conjugate transpose", (char *)"Non-unit", &i__2, &ap[1], &ap[jc], &c__1, + (ftnlen)5, (ftnlen)19, (ftnlen)8); } - -/* Compute U(J,J) and test for non-positive-definiteness. */ - i__2 = jj; i__3 = j - 1; zdotc_(&z__1, &i__3, &ap[jc], &c__1, &ap[jc], &c__1); @@ -246,18 +61,11 @@ f"> */ i__2 = jj; d__1 = sqrt(ajj); ap[i__2].r = d__1, ap[i__2].i = 0.; -/* L10: */ } } else { - -/* Compute the Cholesky factorization A = L * L**H. */ - jj = 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { - -/* Compute L(J,J) and test for non-positive-definiteness. */ - i__2 = jj; ajj = ap[i__2].r; if (ajj <= 0.) { @@ -268,34 +76,22 @@ f"> */ ajj = sqrt(ajj); i__2 = jj; ap[i__2].r = ajj, ap[i__2].i = 0.; - -/* Compute elements J+1:N of column J and update the trailing */ -/* submatrix. */ - if (j < *n) { i__2 = *n - j; d__1 = 1. / ajj; zdscal_(&i__2, &d__1, &ap[jj + 1], &c__1); i__2 = *n - j; - zhpr_((char *)"Lower", &i__2, &c_b16, &ap[jj + 1], &c__1, &ap[jj + *n - - j + 1], (ftnlen)5); + zhpr_((char *)"Lower", &i__2, &c_b16, &ap[jj + 1], &c__1, &ap[jj + *n - j + 1], (ftnlen)5); jj = jj + *n - j + 1; } -/* L20: */ } } goto L40; - L30: *info = j; - L40: return 0; - -/* End of ZPPTRF */ - -} /* zpptrf_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zpptri.cpp b/lib/linalg/zpptri.cpp index e804683c79..947af9b38d 100644 --- a/lib/linalg/zpptri.cpp +++ b/lib/linalg/zpptri.cpp @@ -1,176 +1,32 @@ -/* fortran/zpptri.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static doublereal c_b8 = 1.; static integer c__1 = 1; - -/* > \brief \b ZPPTRI */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZPPTRI + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZPPTRI( UPLO, N, AP, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER UPLO */ -/* INTEGER INFO, N */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 AP( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZPPTRI computes the inverse of a complex Hermitian positive definite */ -/* > matrix A using the Cholesky factorization A = U**H*U or A = L*L**H */ -/* > computed by ZPPTRF. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > = 'U': Upper triangular factor is stored in AP; */ -/* > = 'L': Lower triangular factor is stored in AP. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] AP */ -/* > \verbatim */ -/* > AP is COMPLEX*16 array, dimension (N*(N+1)/2) */ -/* > On entry, the triangular factor U or L from the Cholesky */ -/* > factorization A = U**H*U or A = L*L**H, packed columnwise as */ -/* > a linear array. The j-th column of U or L is stored in the */ -/* > array AP as follows: */ -/* > if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j; */ -/* > if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n. */ -/* > */ -/* > On exit, the upper or lower triangle of the (Hermitian) */ -/* > inverse of A, overwriting the input factor U or L. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > > 0: if INFO = i, the (i,i) element of the factor U or L is */ -/* > zero, and the inverse could not be computed. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16OTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int zpptri_(char *uplo, integer *n, doublecomplex *ap, - integer *info, ftnlen uplo_len) +int zpptri_(char *uplo, integer *n, doublecomplex *ap, integer *info, ftnlen uplo_len) { - /* System generated locals */ integer i__1, i__2, i__3; doublereal d__1; doublecomplex z__1; - - /* Local variables */ integer j, jc, jj; doublereal ajj; integer jjn; - extern /* Subroutine */ int zhpr_(char *, integer *, doublereal *, - doublecomplex *, integer *, doublecomplex *, ftnlen); + extern int zhpr_(char *, integer *, doublereal *, doublecomplex *, integer *, doublecomplex *, + ftnlen); extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *, - doublecomplex *, integer *, doublecomplex *, integer *); + extern VOID zdotc_(doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, + integer *); logical upper; - extern /* Subroutine */ int ztpmv_(char *, char *, char *, integer *, - doublecomplex *, doublecomplex *, integer *, ftnlen, ftnlen, - ftnlen), xerbla_(char *, integer *, ftnlen), zdscal_(integer *, - doublereal *, doublecomplex *, integer *), ztptri_(char *, char *, - integer *, doublecomplex *, integer *, ftnlen, ftnlen); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ + extern int ztpmv_(char *, char *, char *, integer *, doublecomplex *, doublecomplex *, + integer *, ftnlen, ftnlen, ftnlen), + xerbla_(char *, integer *, ftnlen), + zdscal_(integer *, doublereal *, doublecomplex *, integer *), + ztptri_(char *, char *, integer *, doublecomplex *, integer *, ftnlen, ftnlen); --ap; - - /* Function Body */ *info = 0; upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); - if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + if (!upper && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { *info = -1; } else if (*n < 0) { *info = -2; @@ -180,23 +36,14 @@ f"> */ xerbla_((char *)"ZPPTRI", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*n == 0) { return 0; } - -/* Invert the triangular Cholesky factor U or L. */ - ztptri_(uplo, (char *)"Non-unit", n, &ap[1], info, (ftnlen)1, (ftnlen)8); if (*info > 0) { return 0; } if (upper) { - -/* Compute the product inv(U) * inv(U)**H. */ - jj = 0; i__1 = *n; for (j = 1; j <= i__1; ++j) { @@ -204,19 +51,13 @@ f"> */ jj += j; if (j > 1) { i__2 = j - 1; - zhpr_((char *)"Upper", &i__2, &c_b8, &ap[jc], &c__1, &ap[1], (ftnlen) - 5); + zhpr_((char *)"Upper", &i__2, &c_b8, &ap[jc], &c__1, &ap[1], (ftnlen)5); } i__2 = jj; ajj = ap[i__2].r; zdscal_(&j, &ajj, &ap[jc], &c__1); -/* L10: */ } - } else { - -/* Compute the product inv(L)**H * inv(L). */ - jj = 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { @@ -228,21 +69,14 @@ f"> */ ap[i__2].r = d__1, ap[i__2].i = 0.; if (j < *n) { i__2 = *n - j; - ztpmv_((char *)"Lower", (char *)"Conjugate transpose", (char *)"Non-unit", &i__2, &ap[ - jjn], &ap[jj + 1], &c__1, (ftnlen)5, (ftnlen)19, ( - ftnlen)8); + ztpmv_((char *)"Lower", (char *)"Conjugate transpose", (char *)"Non-unit", &i__2, &ap[jjn], &ap[jj + 1], + &c__1, (ftnlen)5, (ftnlen)19, (ftnlen)8); } jj = jjn; -/* L20: */ } } - return 0; - -/* End of ZPPTRI */ - -} /* zpptri_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zscal.cpp b/lib/linalg/zscal.cpp index 6efc02ee5e..ee91d39b21 100644 --- a/lib/linalg/zscal.cpp +++ b/lib/linalg/zscal.cpp @@ -1,162 +1,39 @@ -/* fortran/zscal.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b ZSCAL */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZSCAL(N,ZA,ZX,INCX) */ - -/* .. Scalar Arguments .. */ -/* COMPLEX*16 ZA */ -/* INTEGER INCX,N */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 ZX(*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZSCAL scales a vector by a constant. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > number of elements in input vector(s) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] ZA */ -/* > \verbatim */ -/* > ZA is COMPLEX*16 */ -/* > On entry, ZA specifies the scalar alpha. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] ZX */ -/* > \verbatim */ -/* > ZX is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > storage spacing between elements of ZX */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16_blas_level1 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > jack dongarra, 3/11/78. */ -/* > modified 3/93 to return if incx .le. 0. */ -/* > modified 12/3/93, array(1) declarations changed to array(*) */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int zscal_(integer *n, doublecomplex *za, doublecomplex *zx, - integer *incx) +int zscal_(integer *n, doublecomplex *za, doublecomplex *zx, integer *incx) { - /* System generated locals */ integer i__1, i__2, i__3, i__4; doublecomplex z__1; - - /* Local variables */ integer i__, nincx; - - -/* -- Reference BLAS level1 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Local Scalars .. */ -/* .. */ -/* .. Parameters .. */ -/* .. */ - /* Parameter adjustments */ --zx; - - /* Function Body */ if (*n <= 0 || *incx <= 0 || za->r == 1. && za->i == 0.) { return 0; } if (*incx == 1) { - -/* code for increment equal to 1 */ - i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; i__3 = i__; - z__1.r = za->r * zx[i__3].r - za->i * zx[i__3].i, z__1.i = za->r * - zx[i__3].i + za->i * zx[i__3].r; + z__1.r = za->r * zx[i__3].r - za->i * zx[i__3].i, + z__1.i = za->r * zx[i__3].i + za->i * zx[i__3].r; zx[i__2].r = z__1.r, zx[i__2].i = z__1.i; } } else { - -/* code for increment not equal to 1 */ - nincx = *n * *incx; i__1 = nincx; i__2 = *incx; for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { i__3 = i__; i__4 = i__; - z__1.r = za->r * zx[i__4].r - za->i * zx[i__4].i, z__1.i = za->r * - zx[i__4].i + za->i * zx[i__4].r; + z__1.r = za->r * zx[i__4].r - za->i * zx[i__4].i, + z__1.i = za->r * zx[i__4].i + za->i * zx[i__4].r; zx[i__3].r = z__1.r, zx[i__3].i = z__1.i; } } return 0; - -/* End of ZSCAL */ - -} /* zscal_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zstedc.cpp b/lib/linalg/zstedc.cpp index fc6d9a782b..99804fef30 100644 --- a/lib/linalg/zstedc.cpp +++ b/lib/linalg/zstedc.cpp @@ -1,324 +1,57 @@ -/* fortran/zstedc.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__9 = 9; static integer c__0 = 0; static integer c__2 = 2; static doublereal c_b17 = 0.; static doublereal c_b18 = 1.; static integer c__1 = 1; - -/* > \brief \b ZSTEDC */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZSTEDC + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, RWORK, */ -/* LRWORK, IWORK, LIWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER COMPZ */ -/* INTEGER INFO, LDZ, LIWORK, LRWORK, LWORK, N */ -/* .. */ -/* .. Array Arguments .. */ -/* INTEGER IWORK( * ) */ -/* DOUBLE PRECISION D( * ), E( * ), RWORK( * ) */ -/* COMPLEX*16 WORK( * ), Z( LDZ, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZSTEDC computes all eigenvalues and, optionally, eigenvectors of a */ -/* > symmetric tridiagonal matrix using the divide and conquer method. */ -/* > The eigenvectors of a full or band complex Hermitian matrix can also */ -/* > be found if ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this */ -/* > matrix to tridiagonal form. */ -/* > */ -/* > This code makes very mild assumptions about floating point */ -/* > arithmetic. It will work on machines with a guard digit in */ -/* > add/subtract, or on those binary machines without guard digits */ -/* > which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. */ -/* > It could conceivably fail on hexadecimal or decimal machines */ -/* > without guard digits, but we know of none. See DLAED3 for details. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] COMPZ */ -/* > \verbatim */ -/* > COMPZ is CHARACTER*1 */ -/* > = 'N': Compute eigenvalues only. */ -/* > = 'I': Compute eigenvectors of tridiagonal matrix also. */ -/* > = 'V': Compute eigenvectors of original Hermitian matrix */ -/* > also. On entry, Z contains the unitary matrix used */ -/* > to reduce the original matrix to tridiagonal form. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The dimension of the symmetric tridiagonal matrix. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension (N) */ -/* > On entry, the diagonal elements of the tridiagonal matrix. */ -/* > On exit, if INFO = 0, the eigenvalues in ascending order. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] E */ -/* > \verbatim */ -/* > E is DOUBLE PRECISION array, dimension (N-1) */ -/* > On entry, the subdiagonal elements of the tridiagonal matrix. */ -/* > On exit, E has been destroyed. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] Z */ -/* > \verbatim */ -/* > Z is COMPLEX*16 array, dimension (LDZ,N) */ -/* > On entry, if COMPZ = 'V', then Z contains the unitary */ -/* > matrix used in the reduction to tridiagonal form. */ -/* > On exit, if INFO = 0, then if COMPZ = 'V', Z contains the */ -/* > orthonormal eigenvectors of the original Hermitian matrix, */ -/* > and if COMPZ = 'I', Z contains the orthonormal eigenvectors */ -/* > of the symmetric tridiagonal matrix. */ -/* > If COMPZ = 'N', then Z is not referenced. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDZ */ -/* > \verbatim */ -/* > LDZ is INTEGER */ -/* > The leading dimension of the array Z. LDZ >= 1. */ -/* > If eigenvectors are desired, then LDZ >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) */ -/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LWORK */ -/* > \verbatim */ -/* > LWORK is INTEGER */ -/* > The dimension of the array WORK. */ -/* > If COMPZ = 'N' or 'I', or N <= 1, LWORK must be at least 1. */ -/* > If COMPZ = 'V' and N > 1, LWORK must be at least N*N. */ -/* > Note that for COMPZ = 'V', then if N is less than or */ -/* > equal to the minimum divide size, usually 25, then LWORK need */ -/* > only be 1. */ -/* > */ -/* > If LWORK = -1, then a workspace query is assumed; the routine */ -/* > only calculates the optimal sizes of the WORK, RWORK and */ -/* > IWORK arrays, returns these values as the first entries of */ -/* > the WORK, RWORK and IWORK arrays, and no error message */ -/* > related to LWORK or LRWORK or LIWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] RWORK */ -/* > \verbatim */ -/* > RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) */ -/* > On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LRWORK */ -/* > \verbatim */ -/* > LRWORK is INTEGER */ -/* > The dimension of the array RWORK. */ -/* > If COMPZ = 'N' or N <= 1, LRWORK must be at least 1. */ -/* > If COMPZ = 'V' and N > 1, LRWORK must be at least */ -/* > 1 + 3*N + 2*N*lg N + 4*N**2 , */ -/* > where lg( N ) = smallest integer k such */ -/* > that 2**k >= N. */ -/* > If COMPZ = 'I' and N > 1, LRWORK must be at least */ -/* > 1 + 4*N + 2*N**2 . */ -/* > Note that for COMPZ = 'I' or 'V', then if N is less than or */ -/* > equal to the minimum divide size, usually 25, then LRWORK */ -/* > need only be max(1,2*(N-1)). */ -/* > */ -/* > If LRWORK = -1, then a workspace query is assumed; the */ -/* > routine only calculates the optimal sizes of the WORK, RWORK */ -/* > and IWORK arrays, returns these values as the first entries */ -/* > of the WORK, RWORK and IWORK arrays, and no error message */ -/* > related to LWORK or LRWORK or LIWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] IWORK */ -/* > \verbatim */ -/* > IWORK is INTEGER array, dimension (MAX(1,LIWORK)) */ -/* > On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LIWORK */ -/* > \verbatim */ -/* > LIWORK is INTEGER */ -/* > The dimension of the array IWORK. */ -/* > If COMPZ = 'N' or N <= 1, LIWORK must be at least 1. */ -/* > If COMPZ = 'V' or N > 1, LIWORK must be at least */ -/* > 6 + 6*N + 5*N*lg N. */ -/* > If COMPZ = 'I' or N > 1, LIWORK must be at least */ -/* > 3 + 5*N . */ -/* > Note that for COMPZ = 'I' or 'V', then if N is less than or */ -/* > equal to the minimum divide size, usually 25, then LIWORK */ -/* > need only be 1. */ -/* > */ -/* > If LIWORK = -1, then a workspace query is assumed; the */ -/* > routine only calculates the optimal sizes of the WORK, RWORK */ -/* > and IWORK arrays, returns these values as the first entries */ -/* > of the WORK, RWORK and IWORK arrays, and no error message */ -/* > related to LWORK or LRWORK or LIWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit. */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value. */ -/* > > 0: The algorithm failed to compute an eigenvalue while */ -/* > working on the submatrix lying in rows and columns */ -/* > INFO/(N+1) through mod(INFO,N+1). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16OTHERcomputational */ - -/* > \par Contributors: */ -/* ================== */ -/* > */ -/* > Jeff Rutter, Computer Science Division, University of California */ -/* > at Berkeley, USA */ - -/* ===================================================================== */ -/* Subroutine */ int zstedc_(char *compz, integer *n, doublereal *d__, - doublereal *e, doublecomplex *z__, integer *ldz, doublecomplex *work, - integer *lwork, doublereal *rwork, integer *lrwork, integer *iwork, - integer *liwork, integer *info, ftnlen compz_len) +int zstedc_(char *compz, integer *n, doublereal *d__, doublereal *e, doublecomplex *z__, + integer *ldz, doublecomplex *work, integer *lwork, doublereal *rwork, integer *lrwork, + integer *iwork, integer *liwork, integer *info, ftnlen compz_len) { - /* System generated locals */ integer z_dim1, z_offset, i__1, i__2, i__3, i__4; doublereal d__1, d__2; - - /* Builtin functions */ double log(doublereal); integer pow_lmp_ii(integer *, integer *); double sqrt(doublereal); - - /* Local variables */ integer i__, j, k, m; doublereal p; integer ii, ll, lgn; doublereal eps, tiny; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer lwmin, start; - extern /* Subroutine */ int zswap_(integer *, doublecomplex *, integer *, - doublecomplex *, integer *), zlaed0_(integer *, integer *, - doublereal *, doublereal *, doublecomplex *, integer *, - doublecomplex *, integer *, doublereal *, integer *, integer *); + extern int zswap_(integer *, doublecomplex *, integer *, doublecomplex *, integer *), + zlaed0_(integer *, integer *, doublereal *, doublereal *, doublecomplex *, integer *, + doublecomplex *, integer *, doublereal *, integer *, integer *); extern doublereal dlamch_(char *, ftnlen); - extern /* Subroutine */ int dlascl_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, integer *, doublereal *, - integer *, integer *, ftnlen), dstedc_(char *, integer *, - doublereal *, doublereal *, doublereal *, integer *, doublereal *, - integer *, integer *, integer *, integer *, ftnlen), dlaset_( - char *, integer *, integer *, doublereal *, doublereal *, - doublereal *, integer *, ftnlen), xerbla_(char *, integer *, - ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern int dlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, + integer *, doublereal *, integer *, integer *, ftnlen), + dstedc_(char *, integer *, doublereal *, doublereal *, doublereal *, integer *, + doublereal *, integer *, integer *, integer *, integer *, ftnlen), + dlaset_(char *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, + ftnlen), + xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); integer finish; - extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *, - ftnlen); - extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *, - integer *), zlacrm_(integer *, integer *, doublecomplex *, - integer *, doublereal *, integer *, doublecomplex *, integer *, - doublereal *); + extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *, ftnlen); + extern int dsterf_(integer *, doublereal *, doublereal *, integer *), + zlacrm_(integer *, integer *, doublecomplex *, integer *, doublereal *, integer *, + doublecomplex *, integer *, doublereal *); integer liwmin, icompz; - extern /* Subroutine */ int dsteqr_(char *, integer *, doublereal *, - doublereal *, doublereal *, integer *, doublereal *, integer *, - ftnlen), zlacpy_(char *, integer *, integer *, doublecomplex *, - integer *, doublecomplex *, integer *, ftnlen); + extern int dsteqr_(char *, integer *, doublereal *, doublereal *, doublereal *, integer *, + doublereal *, integer *, ftnlen), + zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, + integer *, ftnlen); doublereal orgnrm; integer lrwmin; logical lquery; integer smlsiz; - extern /* Subroutine */ int zsteqr_(char *, integer *, doublereal *, - doublereal *, doublecomplex *, integer *, doublereal *, integer *, - ftnlen); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ + extern int zsteqr_(char *, integer *, doublereal *, doublereal *, doublecomplex *, integer *, + doublereal *, integer *, ftnlen); --d__; --e; z_dim1 = *ldz; @@ -327,11 +60,8 @@ f"> */ --work; --rwork; --iwork; - - /* Function Body */ *info = 0; lquery = *lwork == -1 || *lrwork == -1 || *liwork == -1; - if (lsame_(compz, (char *)"N", (ftnlen)1, (ftnlen)1)) { icompz = 0; } else if (lsame_(compz, (char *)"V", (ftnlen)1, (ftnlen)1)) { @@ -345,16 +75,11 @@ f"> */ *info = -1; } else if (*n < 0) { *info = -2; - } else if (*ldz < 1 || icompz > 0 && *ldz < max(1,*n)) { + } else if (*ldz < 1 || icompz > 0 && *ldz < max(1, *n)) { *info = -6; } - if (*info == 0) { - -/* Compute the workspace requirements */ - - smlsiz = ilaenv_(&c__9, (char *)"ZSTEDC", (char *)" ", &c__0, &c__0, &c__0, &c__0, ( - ftnlen)6, (ftnlen)1); + smlsiz = ilaenv_(&c__9, (char *)"ZSTEDC", (char *)" ", &c__0, &c__0, &c__0, &c__0, (ftnlen)6, (ftnlen)1); if (*n <= 1 || icompz == 0) { lwmin = 1; liwmin = 1; @@ -364,7 +89,7 @@ f"> */ liwmin = 1; lrwmin = *n - 1 << 1; } else if (icompz == 1) { - lgn = (integer) (log((doublereal) (*n)) / log(2.)); + lgn = (integer)(log((doublereal)(*n)) / log(2.)); if (pow_lmp_ii(&c__2, &lgn) < *n) { ++lgn; } @@ -372,30 +97,26 @@ f"> */ ++lgn; } lwmin = *n * *n; -/* Computing 2nd power */ i__1 = *n; lrwmin = *n * 3 + 1 + (*n << 1) * lgn + (i__1 * i__1 << 2); liwmin = *n * 6 + 6 + *n * 5 * lgn; } else if (icompz == 2) { lwmin = 1; -/* Computing 2nd power */ i__1 = *n; lrwmin = (*n << 2) + 1 + (i__1 * i__1 << 1); liwmin = *n * 5 + 3; } - work[1].r = (doublereal) lwmin, work[1].i = 0.; - rwork[1] = (doublereal) lrwmin; + work[1].r = (doublereal)lwmin, work[1].i = 0.; + rwork[1] = (doublereal)lrwmin; iwork[1] = liwmin; - - if (*lwork < lwmin && ! lquery) { + if (*lwork < lwmin && !lquery) { *info = -8; - } else if (*lrwork < lrwmin && ! lquery) { + } else if (*lrwork < lrwmin && !lquery) { *info = -10; - } else if (*liwork < liwmin && ! lquery) { + } else if (*liwork < liwmin && !lquery) { *info = -12; } } - if (*info != 0) { i__1 = -(*info); xerbla_((char *)"ZSTEDC", &i__1, (ftnlen)6); @@ -403,9 +124,6 @@ f"> */ } else if (lquery) { return 0; } - -/* Quick return if possible */ - if (*n == 0) { return 0; } @@ -416,41 +134,19 @@ f"> */ } return 0; } - -/* If the following conditional clause is removed, then the routine */ -/* will use the Divide and Conquer routine to compute only the */ -/* eigenvalues, which requires (3N + 3N**2) real workspace and */ -/* (2 + 5N + 2N lg(N)) integer workspace. */ -/* Since on many architectures DSTERF is much faster than any other */ -/* algorithm for finding eigenvalues only, it is used here */ -/* as the default. If the conditional clause is removed, then */ -/* information on the size of workspace needs to be changed. */ - -/* If COMPZ = 'N', use DSTERF to compute the eigenvalues. */ - if (icompz == 0) { dsterf_(n, &d__[1], &e[1], info); goto L70; } - -/* If N is smaller than the minimum divide size (SMLSIZ+1), then */ -/* solve the problem with another solver. */ - if (*n <= smlsiz) { - - zsteqr_(compz, n, &d__[1], &e[1], &z__[z_offset], ldz, &rwork[1], - info, (ftnlen)1); - + zsteqr_(compz, n, &d__[1], &e[1], &z__[z_offset], ldz, &rwork[1], info, (ftnlen)1); } else { - -/* If COMPZ = 'I', we simply call DSTEDC instead. */ - if (icompz == 2) { dlaset_((char *)"Full", n, n, &c_b17, &c_b18, &rwork[1], n, (ftnlen)4); ll = *n * *n + 1; i__1 = *lrwork - ll + 1; - dstedc_((char *)"I", n, &d__[1], &e[1], &rwork[1], n, &rwork[ll], &i__1, & - iwork[1], liwork, info, (ftnlen)1); + dstedc_((char *)"I", n, &d__[1], &e[1], &rwork[1], n, &rwork[ll], &i__1, &iwork[1], liwork, + info, (ftnlen)1); i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *n; @@ -458,99 +154,59 @@ f"> */ i__3 = i__ + j * z_dim1; i__4 = (j - 1) * *n + i__; z__[i__3].r = rwork[i__4], z__[i__3].i = 0.; -/* L10: */ } -/* L20: */ } goto L70; } - -/* From now on, only option left to be handled is COMPZ = 'V', */ -/* i.e. ICOMPZ = 1. */ - -/* Scale. */ - orgnrm = dlanst_((char *)"M", n, &d__[1], &e[1], (ftnlen)1); if (orgnrm == 0.) { goto L70; } - eps = dlamch_((char *)"Epsilon", (ftnlen)7); - start = 1; - -/* while ( START <= N ) */ - -L30: + L30: if (start <= *n) { - -/* Let FINISH be the position of the next subdiagonal entry */ -/* such that E( FINISH ) <= TINY or FINISH = N if no such */ -/* subdiagonal exists. The matrix identified by the elements */ -/* between START and FINISH constitutes an independent */ -/* sub-problem. */ - finish = start; -L40: + L40: if (finish < *n) { - tiny = eps * sqrt((d__1 = d__[finish], abs(d__1))) * sqrt(( - d__2 = d__[finish + 1], abs(d__2))); + tiny = eps * sqrt((d__1 = d__[finish], abs(d__1))) * + sqrt((d__2 = d__[finish + 1], abs(d__2))); if ((d__1 = e[finish], abs(d__1)) > tiny) { ++finish; goto L40; } } - -/* (Sub) Problem determined. Compute its size and solve it. */ - m = finish - start + 1; if (m > smlsiz) { - -/* Scale. */ - orgnrm = dlanst_((char *)"M", &m, &d__[start], &e[start], (ftnlen)1); - dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b18, &m, &c__1, &d__[ - start], &m, info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b18, &m, &c__1, &d__[start], &m, info, + (ftnlen)1); i__1 = m - 1; i__2 = m - 1; - dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b18, &i__1, &c__1, &e[ - start], &i__2, info, (ftnlen)1); - - zlaed0_(n, &m, &d__[start], &e[start], &z__[start * z_dim1 + - 1], ldz, &work[1], n, &rwork[1], &iwork[1], info); + dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b18, &i__1, &c__1, &e[start], &i__2, info, + (ftnlen)1); + zlaed0_(n, &m, &d__[start], &e[start], &z__[start * z_dim1 + 1], ldz, &work[1], n, + &rwork[1], &iwork[1], info); if (*info > 0) { - *info = (*info / (m + 1) + start - 1) * (*n + 1) + *info % - (m + 1) + start - 1; + *info = (*info / (m + 1) + start - 1) * (*n + 1) + *info % (m + 1) + start - 1; goto L70; } - -/* Scale back. */ - - dlascl_((char *)"G", &c__0, &c__0, &c_b18, &orgnrm, &m, &c__1, &d__[ - start], &m, info, (ftnlen)1); - + dlascl_((char *)"G", &c__0, &c__0, &c_b18, &orgnrm, &m, &c__1, &d__[start], &m, info, + (ftnlen)1); } else { - dsteqr_((char *)"I", &m, &d__[start], &e[start], &rwork[1], &m, & - rwork[m * m + 1], info, (ftnlen)1); - zlacrm_(n, &m, &z__[start * z_dim1 + 1], ldz, &rwork[1], &m, & - work[1], n, &rwork[m * m + 1]); - zlacpy_((char *)"A", n, &m, &work[1], n, &z__[start * z_dim1 + 1], - ldz, (ftnlen)1); + dsteqr_((char *)"I", &m, &d__[start], &e[start], &rwork[1], &m, &rwork[m * m + 1], info, + (ftnlen)1); + zlacrm_(n, &m, &z__[start * z_dim1 + 1], ldz, &rwork[1], &m, &work[1], n, + &rwork[m * m + 1]); + zlacpy_((char *)"A", n, &m, &work[1], n, &z__[start * z_dim1 + 1], ldz, (ftnlen)1); if (*info > 0) { *info = start * (*n + 1) + finish; goto L70; } } - start = finish + 1; goto L30; } - -/* endwhile */ - - -/* Use Selection Sort to minimize swaps of eigenvectors */ - i__1 = *n; for (ii = 2; ii <= i__1; ++ii) { i__ = ii - 1; @@ -562,29 +218,20 @@ L40: k = j; p = d__[j]; } -/* L50: */ } if (k != i__) { d__[k] = d__[i__]; d__[i__] = p; - zswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1 + 1], - &c__1); + zswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1 + 1], &c__1); } -/* L60: */ } } - L70: - work[1].r = (doublereal) lwmin, work[1].i = 0.; - rwork[1] = (doublereal) lrwmin; + work[1].r = (doublereal)lwmin, work[1].i = 0.; + rwork[1] = (doublereal)lrwmin; iwork[1] = liwmin; - return 0; - -/* End of ZSTEDC */ - -} /* zstedc_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zsteqr.cpp b/lib/linalg/zsteqr.cpp index 2085ccbaae..acf4f9168b 100644 --- a/lib/linalg/zsteqr.cpp +++ b/lib/linalg/zsteqr.cpp @@ -1,174 +1,19 @@ -/* fortran/zsteqr.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - -static doublecomplex c_b1 = {0.,0.}; -static doublecomplex c_b2 = {1.,0.}; +static doublecomplex c_b1 = {0., 0.}; +static doublecomplex c_b2 = {1., 0.}; static integer c__0 = 0; static integer c__1 = 1; static integer c__2 = 2; static doublereal c_b41 = 1.; - -/* > \brief \b ZSTEQR */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZSTEQR + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER COMPZ */ -/* INTEGER INFO, LDZ, N */ -/* .. */ -/* .. Array Arguments .. */ -/* DOUBLE PRECISION D( * ), E( * ), WORK( * ) */ -/* COMPLEX*16 Z( LDZ, * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZSTEQR computes all eigenvalues and, optionally, eigenvectors of a */ -/* > symmetric tridiagonal matrix using the implicit QL or QR method. */ -/* > The eigenvectors of a full or band complex Hermitian matrix can also */ -/* > be found if ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this */ -/* > matrix to tridiagonal form. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] COMPZ */ -/* > \verbatim */ -/* > COMPZ is CHARACTER*1 */ -/* > = 'N': Compute eigenvalues only. */ -/* > = 'V': Compute eigenvalues and eigenvectors of the original */ -/* > Hermitian matrix. On entry, Z must contain the */ -/* > unitary matrix used to reduce the original matrix */ -/* > to tridiagonal form. */ -/* > = 'I': Compute eigenvalues and eigenvectors of the */ -/* > tridiagonal matrix. Z is initialized to the identity */ -/* > matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrix. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] D */ -/* > \verbatim */ -/* > D is DOUBLE PRECISION array, dimension (N) */ -/* > On entry, the diagonal elements of the tridiagonal matrix. */ -/* > On exit, if INFO = 0, the eigenvalues in ascending order. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] E */ -/* > \verbatim */ -/* > E is DOUBLE PRECISION array, dimension (N-1) */ -/* > On entry, the (n-1) subdiagonal elements of the tridiagonal */ -/* > matrix. */ -/* > On exit, E has been destroyed. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] Z */ -/* > \verbatim */ -/* > Z is COMPLEX*16 array, dimension (LDZ, N) */ -/* > On entry, if COMPZ = 'V', then Z contains the unitary */ -/* > matrix used in the reduction to tridiagonal form. */ -/* > On exit, if INFO = 0, then if COMPZ = 'V', Z contains the */ -/* > orthonormal eigenvectors of the original Hermitian matrix, */ -/* > and if COMPZ = 'I', Z contains the orthonormal eigenvectors */ -/* > of the symmetric tridiagonal matrix. */ -/* > If COMPZ = 'N', then Z is not referenced. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDZ */ -/* > \verbatim */ -/* > LDZ is INTEGER */ -/* > The leading dimension of the array Z. LDZ >= 1, and if */ -/* > eigenvectors are desired, then LDZ >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is DOUBLE PRECISION array, dimension (max(1,2*N-2)) */ -/* > If COMPZ = 'N', then WORK is not referenced. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > > 0: the algorithm has failed to find all the eigenvalues in */ -/* > a total of 30*N iterations; if INFO = i, then i */ -/* > elements of E have not converged to zero; on exit, D */ -/* > and E contain the elements of a symmetric tridiagonal */ -/* > matrix which is unitarily similar to the original */ -/* > matrix. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16OTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int zsteqr_(char *compz, integer *n, doublereal *d__, - doublereal *e, doublecomplex *z__, integer *ldz, doublereal *work, - integer *info, ftnlen compz_len) +int zsteqr_(char *compz, integer *n, doublereal *d__, doublereal *e, doublecomplex *z__, + integer *ldz, doublereal *work, integer *info, ftnlen compz_len) { - /* System generated locals */ integer z_dim1, z_offset, i__1, i__2; doublereal d__1, d__2; - - /* Builtin functions */ double sqrt(doublereal), d_lmp_sign(doublereal *, doublereal *); - - /* Local variables */ doublereal b, c__, f, g; integer i__, j, k, l, m; doublereal p, r__, s; @@ -177,77 +22,38 @@ f"> */ integer lsv; doublereal tst, eps2; integer lend, jtot; - extern /* Subroutine */ int dlae2_(doublereal *, doublereal *, doublereal - *, doublereal *, doublereal *); + extern int dlae2_(doublereal *, doublereal *, doublereal *, doublereal *, doublereal *); extern logical lsame_(char *, char *, ftnlen, ftnlen); doublereal anorm; - extern /* Subroutine */ int zlasr_(char *, char *, char *, integer *, - integer *, doublereal *, doublereal *, doublecomplex *, integer *, - ftnlen, ftnlen, ftnlen), zswap_(integer *, doublecomplex *, - integer *, doublecomplex *, integer *), dlaev2_(doublereal *, - doublereal *, doublereal *, doublereal *, doublereal *, - doublereal *, doublereal *); + extern int zlasr_(char *, char *, char *, integer *, integer *, doublereal *, doublereal *, + doublecomplex *, integer *, ftnlen, ftnlen, ftnlen), + zswap_(integer *, doublecomplex *, integer *, doublecomplex *, integer *), + dlaev2_(doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, + doublereal *); integer lendm1, lendp1; - extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, - ftnlen); + extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *, ftnlen); integer iscale; - extern /* Subroutine */ int dlascl_(char *, integer *, integer *, - doublereal *, doublereal *, integer *, integer *, doublereal *, - integer *, integer *, ftnlen); + extern int dlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, + integer *, doublereal *, integer *, integer *, ftnlen); doublereal safmin; - extern /* Subroutine */ int dlartg_(doublereal *, doublereal *, - doublereal *, doublereal *, doublereal *); + extern int dlartg_(doublereal *, doublereal *, doublereal *, doublereal *, doublereal *); doublereal safmax; - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *, - ftnlen); - extern /* Subroutine */ int dlasrt_(char *, integer *, doublereal *, - integer *, ftnlen); + extern int xerbla_(char *, integer *, ftnlen); + extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *, ftnlen); + extern int dlasrt_(char *, integer *, doublereal *, integer *, ftnlen); integer lendsv; doublereal ssfmin; integer nmaxit, icompz; doublereal ssfmax; - extern /* Subroutine */ int zlaset_(char *, integer *, integer *, - doublecomplex *, doublecomplex *, doublecomplex *, integer *, - ftnlen); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ + extern int zlaset_(char *, integer *, integer *, doublecomplex *, doublecomplex *, + doublecomplex *, integer *, ftnlen); --d__; --e; z_dim1 = *ldz; z_offset = 1 + z_dim1; z__ -= z_offset; --work; - - /* Function Body */ *info = 0; - if (lsame_(compz, (char *)"N", (ftnlen)1, (ftnlen)1)) { icompz = 0; } else if (lsame_(compz, (char *)"V", (ftnlen)1, (ftnlen)1)) { @@ -261,7 +67,7 @@ f"> */ *info = -1; } else if (*n < 0) { *info = -2; - } else if (*ldz < 1 || icompz > 0 && *ldz < max(1,*n)) { + } else if (*ldz < 1 || icompz > 0 && *ldz < max(1, *n)) { *info = -6; } if (*info != 0) { @@ -269,13 +75,9 @@ f"> */ xerbla_((char *)"ZSTEQR", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*n == 0) { return 0; } - if (*n == 1) { if (icompz == 2) { i__1 = z_dim1 + 1; @@ -283,35 +85,20 @@ f"> */ } return 0; } - -/* Determine the unit roundoff and over/underflow thresholds. */ - eps = dlamch_((char *)"E", (ftnlen)1); -/* Computing 2nd power */ d__1 = eps; eps2 = d__1 * d__1; safmin = dlamch_((char *)"S", (ftnlen)1); safmax = 1. / safmin; ssfmax = sqrt(safmax) / 3.; ssfmin = sqrt(safmin) / eps2; - -/* Compute the eigenvalues and eigenvectors of the tridiagonal */ -/* matrix. */ - if (icompz == 2) { zlaset_((char *)"Full", n, n, &c_b1, &c_b2, &z__[z_offset], ldz, (ftnlen)4); } - nmaxit = *n * 30; jtot = 0; - -/* Determine where the matrix splits and choose QL or QR iteration */ -/* for each block, according to whether top or bottom diagonal */ -/* element is smaller. */ - l1 = 1; nm1 = *n - 1; - L10: if (l1 > *n) { goto L160; @@ -326,16 +113,14 @@ L10: if (tst == 0.) { goto L30; } - if (tst <= sqrt((d__1 = d__[m], abs(d__1))) * sqrt((d__2 = d__[m - + 1], abs(d__2))) * eps) { + if (tst <= + sqrt((d__1 = d__[m], abs(d__1))) * sqrt((d__2 = d__[m + 1], abs(d__2))) * eps) { e[m] = 0.; goto L30; } -/* L20: */ } } m = *n; - L30: l = l1; lsv = l; @@ -345,9 +130,6 @@ L30: if (lend == l) { goto L10; } - -/* Scale submatrix in rows and columns L to LEND */ - i__1 = lend - l + 1; anorm = dlanst_((char *)"I", &i__1, &d__[l], &e[l], (ftnlen)1); iscale = 0; @@ -357,53 +139,36 @@ L30: if (anorm > ssfmax) { iscale = 1; i__1 = lend - l + 1; - dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n, - info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &d__[l], n, info, (ftnlen)1); i__1 = lend - l; - dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &e[l], n, - info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmax, &i__1, &c__1, &e[l], n, info, (ftnlen)1); } else if (anorm < ssfmin) { iscale = 2; i__1 = lend - l + 1; - dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n, - info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &d__[l], n, info, (ftnlen)1); i__1 = lend - l; - dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n, - info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &anorm, &ssfmin, &i__1, &c__1, &e[l], n, info, (ftnlen)1); } - -/* Choose between QL and QR iteration */ - if ((d__1 = d__[lend], abs(d__1)) < (d__2 = d__[l], abs(d__2))) { lend = lsv; l = lendsv; } - if (lend > l) { - -/* QL Iteration */ - -/* Look for small subdiagonal element. */ - -L40: + L40: if (l != lend) { lendm1 = lend - 1; i__1 = lendm1; for (m = l; m <= i__1; ++m) { -/* Computing 2nd power */ d__2 = (d__1 = e[m], abs(d__1)); tst = d__2 * d__2; - if (tst <= eps2 * (d__1 = d__[m], abs(d__1)) * (d__2 = d__[m - + 1], abs(d__2)) + safmin) { + if (tst <= + eps2 * (d__1 = d__[m], abs(d__1)) * (d__2 = d__[m + 1], abs(d__2)) + safmin) { goto L60; } -/* L50: */ } } - m = lend; - -L60: + L60: if (m < lend) { e[m] = 0.; } @@ -411,18 +176,13 @@ L60: if (m == l) { goto L80; } - -/* If remaining matrix is 2-by-2, use DLAE2 or SLAEV2 */ -/* to compute its eigensystem. */ - if (m == l + 1) { if (icompz > 0) { dlaev2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2, &c__, &s); work[l] = c__; work[*n - 1 + l] = s; - zlasr_((char *)"R", (char *)"V", (char *)"B", n, &c__2, &work[l], &work[*n - 1 + l], & - z__[l * z_dim1 + 1], ldz, (ftnlen)1, (ftnlen)1, ( - ftnlen)1); + zlasr_((char *)"R", (char *)"V", (char *)"B", n, &c__2, &work[l], &work[*n - 1 + l], &z__[l * z_dim1 + 1], + ldz, (ftnlen)1, (ftnlen)1, (ftnlen)1); } else { dlae2_(&d__[l], &e[l], &d__[l + 1], &rt1, &rt2); } @@ -435,24 +195,16 @@ L60: } goto L140; } - if (jtot == nmaxit) { goto L140; } ++jtot; - -/* Form shift. */ - g = (d__[l + 1] - p) / (e[l] * 2.); r__ = dlapy2_(&g, &c_b41); g = d__[m] - p + e[l] / (g + d_lmp_sign(&r__, &g)); - s = 1.; c__ = 1.; p = 0.; - -/* Inner loop */ - mm1 = m - 1; i__1 = l; for (i__ = mm1; i__ >= i__1; --i__) { @@ -467,65 +219,42 @@ L60: p = s * r__; d__[i__ + 1] = g + p; g = c__ * r__ - b; - -/* If eigenvectors are desired, then save rotations. */ - if (icompz > 0) { work[i__] = c__; work[*n - 1 + i__] = -s; } - -/* L70: */ } - -/* If eigenvectors are desired, then apply saved rotations. */ - if (icompz > 0) { mm = m - l + 1; - zlasr_((char *)"R", (char *)"V", (char *)"B", n, &mm, &work[l], &work[*n - 1 + l], &z__[l - * z_dim1 + 1], ldz, (ftnlen)1, (ftnlen)1, (ftnlen)1); + zlasr_((char *)"R", (char *)"V", (char *)"B", n, &mm, &work[l], &work[*n - 1 + l], &z__[l * z_dim1 + 1], ldz, + (ftnlen)1, (ftnlen)1, (ftnlen)1); } - d__[l] -= p; e[l] = g; goto L40; - -/* Eigenvalue found. */ - -L80: + L80: d__[l] = p; - ++l; if (l <= lend) { goto L40; } goto L140; - } else { - -/* QR Iteration */ - -/* Look for small superdiagonal element. */ - -L90: + L90: if (l != lend) { lendp1 = lend + 1; i__1 = lendp1; for (m = l; m >= i__1; --m) { -/* Computing 2nd power */ d__2 = (d__1 = e[m - 1], abs(d__1)); tst = d__2 * d__2; - if (tst <= eps2 * (d__1 = d__[m], abs(d__1)) * (d__2 = d__[m - - 1], abs(d__2)) + safmin) { + if (tst <= + eps2 * (d__1 = d__[m], abs(d__1)) * (d__2 = d__[m - 1], abs(d__2)) + safmin) { goto L110; } -/* L100: */ } } - m = lend; - -L110: + L110: if (m > lend) { e[m - 1] = 0.; } @@ -533,19 +262,13 @@ L110: if (m == l) { goto L130; } - -/* If remaining matrix is 2-by-2, use DLAE2 or SLAEV2 */ -/* to compute its eigensystem. */ - if (m == l - 1) { if (icompz > 0) { - dlaev2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2, &c__, &s) - ; + dlaev2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2, &c__, &s); work[m] = c__; work[*n - 1 + m] = s; - zlasr_((char *)"R", (char *)"V", (char *)"F", n, &c__2, &work[m], &work[*n - 1 + m], & - z__[(l - 1) * z_dim1 + 1], ldz, (ftnlen)1, (ftnlen)1, - (ftnlen)1); + zlasr_((char *)"R", (char *)"V", (char *)"F", n, &c__2, &work[m], &work[*n - 1 + m], + &z__[(l - 1) * z_dim1 + 1], ldz, (ftnlen)1, (ftnlen)1, (ftnlen)1); } else { dlae2_(&d__[l - 1], &e[l - 1], &d__[l], &rt1, &rt2); } @@ -558,24 +281,16 @@ L110: } goto L140; } - if (jtot == nmaxit) { goto L140; } ++jtot; - -/* Form shift. */ - g = (d__[l - 1] - p) / (e[l - 1] * 2.); r__ = dlapy2_(&g, &c_b41); g = d__[m] - p + e[l - 1] / (g + d_lmp_sign(&r__, &g)); - s = 1.; c__ = 1.; p = 0.; - -/* Inner loop */ - lm1 = l - 1; i__1 = lm1; for (i__ = m; i__ <= i__1; ++i__) { @@ -590,89 +305,53 @@ L110: p = s * r__; d__[i__] = g + p; g = c__ * r__ - b; - -/* If eigenvectors are desired, then save rotations. */ - if (icompz > 0) { work[i__] = c__; work[*n - 1 + i__] = s; } - -/* L120: */ } - -/* If eigenvectors are desired, then apply saved rotations. */ - if (icompz > 0) { mm = l - m + 1; - zlasr_((char *)"R", (char *)"V", (char *)"F", n, &mm, &work[m], &work[*n - 1 + m], &z__[m - * z_dim1 + 1], ldz, (ftnlen)1, (ftnlen)1, (ftnlen)1); + zlasr_((char *)"R", (char *)"V", (char *)"F", n, &mm, &work[m], &work[*n - 1 + m], &z__[m * z_dim1 + 1], ldz, + (ftnlen)1, (ftnlen)1, (ftnlen)1); } - d__[l] -= p; e[lm1] = g; goto L90; - -/* Eigenvalue found. */ - -L130: + L130: d__[l] = p; - --l; if (l >= lend) { goto L90; } goto L140; - } - -/* Undo scaling if necessary */ - L140: if (iscale == 1) { i__1 = lendsv - lsv + 1; - dlascl_((char *)"G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv], - n, info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &d__[lsv], n, info, (ftnlen)1); i__1 = lendsv - lsv; - dlascl_((char *)"G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &e[lsv], n, - info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &ssfmax, &anorm, &i__1, &c__1, &e[lsv], n, info, (ftnlen)1); } else if (iscale == 2) { i__1 = lendsv - lsv + 1; - dlascl_((char *)"G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[lsv], - n, info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &d__[lsv], n, info, (ftnlen)1); i__1 = lendsv - lsv; - dlascl_((char *)"G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &e[lsv], n, - info, (ftnlen)1); + dlascl_((char *)"G", &c__0, &c__0, &ssfmin, &anorm, &i__1, &c__1, &e[lsv], n, info, (ftnlen)1); } - -/* Check for no convergence to an eigenvalue after a total */ -/* of N*MAXIT iterations. */ - if (jtot == nmaxit) { i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { if (e[i__] != 0.) { ++(*info); } -/* L150: */ } return 0; } goto L10; - -/* Order eigenvalues and eigenvectors. */ - L160: if (icompz == 0) { - -/* Use Quick Sort */ - dlasrt_((char *)"I", n, &d__[1], info, (ftnlen)1); - } else { - -/* Use Selection Sort to minimize swaps of eigenvectors */ - i__1 = *n; for (ii = 2; ii <= i__1; ++ii) { i__ = ii - 1; @@ -684,23 +363,16 @@ L160: k = j; p = d__[j]; } -/* L170: */ } if (k != i__) { d__[k] = d__[i__]; d__[i__] = p; - zswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1 + 1], - &c__1); + zswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1 + 1], &c__1); } -/* L180: */ } } return 0; - -/* End of ZSTEQR */ - -} /* zsteqr_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zswap.cpp b/lib/linalg/zswap.cpp index ff04833b04..1ead5a7262 100644 --- a/lib/linalg/zswap.cpp +++ b/lib/linalg/zswap.cpp @@ -1,134 +1,18 @@ -/* fortran/zswap.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b ZSWAP */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZSWAP(N,ZX,INCX,ZY,INCY) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INCX,INCY,N */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 ZX(*),ZY(*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZSWAP interchanges two vectors. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > number of elements in input vector(s) */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] ZX */ -/* > \verbatim */ -/* > ZX is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > storage spacing between elements of ZX */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] ZY */ -/* > \verbatim */ -/* > ZY is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCY */ -/* > \verbatim */ -/* > INCY is INTEGER */ -/* > storage spacing between elements of ZY */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16_blas_level1 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > jack dongarra, 3/11/78. */ -/* > modified 12/3/93, array(1) declarations changed to array(*) */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int zswap_(integer *n, doublecomplex *zx, integer *incx, - doublecomplex *zy, integer *incy) +int zswap_(integer *n, doublecomplex *zx, integer *incx, doublecomplex *zy, integer *incy) { - /* System generated locals */ integer i__1, i__2, i__3; - - /* Local variables */ integer i__, ix, iy; doublecomplex ztemp; - - -/* -- Reference BLAS level1 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Local Scalars .. */ -/* .. */ - /* Parameter adjustments */ --zy; --zx; - - /* Function Body */ if (*n <= 0) { return 0; } if (*incx == 1 && *incy == 1) { - -/* code for both increments equal to 1 */ i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__; @@ -140,10 +24,6 @@ extern "C" { zy[i__2].r = ztemp.r, zy[i__2].i = ztemp.i; } } else { - -/* code for unequal increments or equal increments not equal */ -/* to 1 */ - ix = 1; iy = 1; if (*incx < 0) { @@ -166,11 +46,7 @@ extern "C" { } } return 0; - -/* End of ZSWAP */ - -} /* zswap_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/ztpmv.cpp b/lib/linalg/ztpmv.cpp index 9e4a16df42..41c8602cea 100644 --- a/lib/linalg/ztpmv.cpp +++ b/lib/linalg/ztpmv.cpp @@ -1,218 +1,29 @@ -/* fortran/ztpmv.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b ZTPMV */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INCX,N */ -/* CHARACTER DIAG,TRANS,UPLO */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 AP(*),X(*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZTPMV performs one of the matrix-vector operations */ -/* > */ -/* > x := A*x, or x := A**T*x, or x := A**H*x, */ -/* > */ -/* > where x is an n element vector and A is an n by n unit, or non-unit, */ -/* > upper or lower triangular matrix, supplied in packed form. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > On entry, UPLO specifies whether the matrix is an upper or */ -/* > lower triangular matrix as follows: */ -/* > */ -/* > UPLO = 'U' or 'u' A is an upper triangular matrix. */ -/* > */ -/* > UPLO = 'L' or 'l' A is a lower triangular matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TRANS */ -/* > \verbatim */ -/* > TRANS is CHARACTER*1 */ -/* > On entry, TRANS specifies the operation to be performed as */ -/* > follows: */ -/* > */ -/* > TRANS = 'N' or 'n' x := A*x. */ -/* > */ -/* > TRANS = 'T' or 't' x := A**T*x. */ -/* > */ -/* > TRANS = 'C' or 'c' x := A**H*x. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DIAG */ -/* > \verbatim */ -/* > DIAG is CHARACTER*1 */ -/* > On entry, DIAG specifies whether or not A is unit */ -/* > triangular as follows: */ -/* > */ -/* > DIAG = 'U' or 'u' A is assumed to be unit triangular. */ -/* > */ -/* > DIAG = 'N' or 'n' A is not assumed to be unit */ -/* > triangular. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > On entry, N specifies the order of the matrix A. */ -/* > N must be at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] AP */ -/* > \verbatim */ -/* > AP is COMPLEX*16 array, dimension at least */ -/* > ( ( n*( n + 1 ) )/2 ). */ -/* > Before entry with UPLO = 'U' or 'u', the array AP must */ -/* > contain the upper triangular matrix packed sequentially, */ -/* > column by column, so that AP( 1 ) contains a( 1, 1 ), */ -/* > AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) */ -/* > respectively, and so on. */ -/* > Before entry with UPLO = 'L' or 'l', the array AP must */ -/* > contain the lower triangular matrix packed sequentially, */ -/* > column by column, so that AP( 1 ) contains a( 1, 1 ), */ -/* > AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) */ -/* > respectively, and so on. */ -/* > Note that when DIAG = 'U' or 'u', the diagonal elements of */ -/* > A are not referenced, but are assumed to be unity. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] X */ -/* > \verbatim */ -/* > X is COMPLEX*16 array, dimension at least */ -/* > ( 1 + ( n - 1 )*abs( INCX ) ). */ -/* > Before entry, the incremented array X must contain the n */ -/* > element vector x. On exit, X is overwritten with the */ -/* > transformed vector x. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > On entry, INCX specifies the increment for the elements of */ -/* > X. INCX must not be zero. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16_blas_level2 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > Level 2 Blas routine. */ -/* > The vector and matrix arguments are not referenced when N = 0, or M = 0 */ -/* > */ -/* > -- Written on 22-October-1986. */ -/* > Jack Dongarra, Argonne National Lab. */ -/* > Jeremy Du Croz, Nag Central Office. */ -/* > Sven Hammarling, Nag Central Office. */ -/* > Richard Hanson, Sandia National Labs. */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int ztpmv_(char *uplo, char *trans, char *diag, integer *n, - doublecomplex *ap, doublecomplex *x, integer *incx, ftnlen uplo_len, - ftnlen trans_len, ftnlen diag_len) +int ztpmv_(char *uplo, char *trans, char *diag, integer *n, doublecomplex *ap, doublecomplex *x, + integer *incx, ftnlen uplo_len, ftnlen trans_len, ftnlen diag_len) { - /* System generated locals */ integer i__1, i__2, i__3, i__4, i__5; doublecomplex z__1, z__2, z__3; - - /* Builtin functions */ void d_lmp_cnjg(doublecomplex *, doublecomplex *); - - /* Local variables */ integer i__, j, k, kk, ix, jx, kx, info; doublecomplex temp; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern int xerbla_(char *, integer *, ftnlen); logical noconj, nounit; - - -/* -- Reference BLAS level2 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ --x; --ap; - - /* Function Body */ info = 0; - if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", ( - ftnlen)1, (ftnlen)1)) { + if (!lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { info = 1; - } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, - (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, ( - ftnlen)1)) { + } else if (!lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && + !lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1) && + !lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { info = 2; - } else if (! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, - (char *)"N", (ftnlen)1, (ftnlen)1)) { + } else if (!lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && + !lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1)) { info = 3; } else if (*n < 0) { info = 4; @@ -223,32 +34,17 @@ extern "C" { xerbla_((char *)"ZTPMV ", &info, (ftnlen)6); return 0; } - -/* Quick return if possible. */ - if (*n == 0) { return 0; } - noconj = lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1); nounit = lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1); - -/* Set up the start point in X if the increment is not unity. This */ -/* will be ( N - 1 )*INCX too small for descending loops. */ - if (*incx <= 0) { kx = 1 - (*n - 1) * *incx; } else if (*incx != 1) { kx = 1; } - -/* Start the operations. In this version the elements of AP are */ -/* accessed sequentially with one pass through AP. */ - if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { - -/* Form x:= A*x. */ - if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { kk = 1; if (*incx == 1) { @@ -264,27 +60,22 @@ extern "C" { i__3 = i__; i__4 = i__; i__5 = k; - z__2.r = temp.r * ap[i__5].r - temp.i * ap[i__5] - .i, z__2.i = temp.r * ap[i__5].i + temp.i - * ap[i__5].r; - z__1.r = x[i__4].r + z__2.r, z__1.i = x[i__4].i + - z__2.i; + z__2.r = temp.r * ap[i__5].r - temp.i * ap[i__5].i, + z__2.i = temp.r * ap[i__5].i + temp.i * ap[i__5].r; + z__1.r = x[i__4].r + z__2.r, z__1.i = x[i__4].i + z__2.i; x[i__3].r = z__1.r, x[i__3].i = z__1.i; ++k; -/* L10: */ } if (nounit) { i__2 = j; i__3 = j; i__4 = kk + j - 1; - z__1.r = x[i__3].r * ap[i__4].r - x[i__3].i * ap[ - i__4].i, z__1.i = x[i__3].r * ap[i__4].i - + x[i__3].i * ap[i__4].r; + z__1.r = x[i__3].r * ap[i__4].r - x[i__3].i * ap[i__4].i, + z__1.i = x[i__3].r * ap[i__4].i + x[i__3].i * ap[i__4].r; x[i__2].r = z__1.r, x[i__2].i = z__1.i; } } kk += j; -/* L20: */ } } else { jx = kx; @@ -300,28 +91,23 @@ extern "C" { i__3 = ix; i__4 = ix; i__5 = k; - z__2.r = temp.r * ap[i__5].r - temp.i * ap[i__5] - .i, z__2.i = temp.r * ap[i__5].i + temp.i - * ap[i__5].r; - z__1.r = x[i__4].r + z__2.r, z__1.i = x[i__4].i + - z__2.i; + z__2.r = temp.r * ap[i__5].r - temp.i * ap[i__5].i, + z__2.i = temp.r * ap[i__5].i + temp.i * ap[i__5].r; + z__1.r = x[i__4].r + z__2.r, z__1.i = x[i__4].i + z__2.i; x[i__3].r = z__1.r, x[i__3].i = z__1.i; ix += *incx; -/* L30: */ } if (nounit) { i__2 = jx; i__3 = jx; i__4 = kk + j - 1; - z__1.r = x[i__3].r * ap[i__4].r - x[i__3].i * ap[ - i__4].i, z__1.i = x[i__3].r * ap[i__4].i - + x[i__3].i * ap[i__4].r; + z__1.r = x[i__3].r * ap[i__4].r - x[i__3].i * ap[i__4].i, + z__1.i = x[i__3].r * ap[i__4].i + x[i__3].i * ap[i__4].r; x[i__2].r = z__1.r, x[i__2].i = z__1.i; } } jx += *incx; kk += j; -/* L40: */ } } } else { @@ -338,27 +124,22 @@ extern "C" { i__2 = i__; i__3 = i__; i__4 = k; - z__2.r = temp.r * ap[i__4].r - temp.i * ap[i__4] - .i, z__2.i = temp.r * ap[i__4].i + temp.i - * ap[i__4].r; - z__1.r = x[i__3].r + z__2.r, z__1.i = x[i__3].i + - z__2.i; + z__2.r = temp.r * ap[i__4].r - temp.i * ap[i__4].i, + z__2.i = temp.r * ap[i__4].i + temp.i * ap[i__4].r; + z__1.r = x[i__3].r + z__2.r, z__1.i = x[i__3].i + z__2.i; x[i__2].r = z__1.r, x[i__2].i = z__1.i; --k; -/* L50: */ } if (nounit) { i__1 = j; i__2 = j; i__3 = kk - *n + j; - z__1.r = x[i__2].r * ap[i__3].r - x[i__2].i * ap[ - i__3].i, z__1.i = x[i__2].r * ap[i__3].i - + x[i__2].i * ap[i__3].r; + z__1.r = x[i__2].r * ap[i__3].r - x[i__2].i * ap[i__3].i, + z__1.i = x[i__2].r * ap[i__3].i + x[i__2].i * ap[i__3].r; x[i__1].r = z__1.r, x[i__1].i = z__1.i; } } kk -= *n - j + 1; -/* L60: */ } } else { kx += (*n - 1) * *incx; @@ -374,35 +155,27 @@ extern "C" { i__2 = ix; i__3 = ix; i__4 = k; - z__2.r = temp.r * ap[i__4].r - temp.i * ap[i__4] - .i, z__2.i = temp.r * ap[i__4].i + temp.i - * ap[i__4].r; - z__1.r = x[i__3].r + z__2.r, z__1.i = x[i__3].i + - z__2.i; + z__2.r = temp.r * ap[i__4].r - temp.i * ap[i__4].i, + z__2.i = temp.r * ap[i__4].i + temp.i * ap[i__4].r; + z__1.r = x[i__3].r + z__2.r, z__1.i = x[i__3].i + z__2.i; x[i__2].r = z__1.r, x[i__2].i = z__1.i; ix -= *incx; -/* L70: */ } if (nounit) { i__1 = jx; i__2 = jx; i__3 = kk - *n + j; - z__1.r = x[i__2].r * ap[i__3].r - x[i__2].i * ap[ - i__3].i, z__1.i = x[i__2].r * ap[i__3].i - + x[i__2].i * ap[i__3].r; + z__1.r = x[i__2].r * ap[i__3].r - x[i__2].i * ap[i__3].i, + z__1.i = x[i__2].r * ap[i__3].i + x[i__2].i * ap[i__3].r; x[i__1].r = z__1.r, x[i__1].i = z__1.i; } } jx -= *incx; kk -= *n - j + 1; -/* L80: */ } } } } else { - -/* Form x := A**T*x or x := A**H*x. */ - if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { kk = *n * (*n + 1) / 2; if (*incx == 1) { @@ -413,48 +186,39 @@ extern "C" { if (noconj) { if (nounit) { i__1 = kk; - z__1.r = temp.r * ap[i__1].r - temp.i * ap[i__1] - .i, z__1.i = temp.r * ap[i__1].i + temp.i - * ap[i__1].r; + z__1.r = temp.r * ap[i__1].r - temp.i * ap[i__1].i, + z__1.i = temp.r * ap[i__1].i + temp.i * ap[i__1].r; temp.r = z__1.r, temp.i = z__1.i; } for (i__ = j - 1; i__ >= 1; --i__) { i__1 = k; i__2 = i__; - z__2.r = ap[i__1].r * x[i__2].r - ap[i__1].i * x[ - i__2].i, z__2.i = ap[i__1].r * x[i__2].i - + ap[i__1].i * x[i__2].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; + z__2.r = ap[i__1].r * x[i__2].r - ap[i__1].i * x[i__2].i, + z__2.i = ap[i__1].r * x[i__2].i + ap[i__1].i * x[i__2].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; --k; -/* L90: */ } } else { if (nounit) { d_lmp_cnjg(&z__2, &ap[kk]); z__1.r = temp.r * z__2.r - temp.i * z__2.i, - z__1.i = temp.r * z__2.i + temp.i * - z__2.r; + z__1.i = temp.r * z__2.i + temp.i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } for (i__ = j - 1; i__ >= 1; --i__) { d_lmp_cnjg(&z__3, &ap[k]); i__1 = i__; z__2.r = z__3.r * x[i__1].r - z__3.i * x[i__1].i, - z__2.i = z__3.r * x[i__1].i + z__3.i * x[ - i__1].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; + z__2.i = z__3.r * x[i__1].i + z__3.i * x[i__1].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; --k; -/* L100: */ } } i__1 = j; x[i__1].r = temp.r, x[i__1].i = temp.i; kk -= j; -/* L110: */ } } else { jx = kx + (*n - 1) * *incx; @@ -465,9 +229,8 @@ extern "C" { if (noconj) { if (nounit) { i__1 = kk; - z__1.r = temp.r * ap[i__1].r - temp.i * ap[i__1] - .i, z__1.i = temp.r * ap[i__1].i + temp.i - * ap[i__1].r; + z__1.r = temp.r * ap[i__1].r - temp.i * ap[i__1].i, + z__1.i = temp.r * ap[i__1].i + temp.i * ap[i__1].r; temp.r = z__1.r, temp.i = z__1.i; } i__1 = kk - j + 1; @@ -475,20 +238,16 @@ extern "C" { ix -= *incx; i__2 = k; i__3 = ix; - z__2.r = ap[i__2].r * x[i__3].r - ap[i__2].i * x[ - i__3].i, z__2.i = ap[i__2].r * x[i__3].i - + ap[i__2].i * x[i__3].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; + z__2.r = ap[i__2].r * x[i__3].r - ap[i__2].i * x[i__3].i, + z__2.i = ap[i__2].r * x[i__3].i + ap[i__2].i * x[i__3].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; -/* L120: */ } } else { if (nounit) { d_lmp_cnjg(&z__2, &ap[kk]); z__1.r = temp.r * z__2.r - temp.i * z__2.i, - z__1.i = temp.r * z__2.i + temp.i * - z__2.r; + z__1.i = temp.r * z__2.i + temp.i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } i__1 = kk - j + 1; @@ -497,19 +256,15 @@ extern "C" { d_lmp_cnjg(&z__3, &ap[k]); i__2 = ix; z__2.r = z__3.r * x[i__2].r - z__3.i * x[i__2].i, - z__2.i = z__3.r * x[i__2].i + z__3.i * x[ - i__2].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; + z__2.i = z__3.r * x[i__2].i + z__3.i * x[i__2].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; -/* L130: */ } } i__1 = jx; x[i__1].r = temp.r, x[i__1].i = temp.i; jx -= *incx; kk -= j; -/* L140: */ } } } else { @@ -523,30 +278,25 @@ extern "C" { if (noconj) { if (nounit) { i__2 = kk; - z__1.r = temp.r * ap[i__2].r - temp.i * ap[i__2] - .i, z__1.i = temp.r * ap[i__2].i + temp.i - * ap[i__2].r; + z__1.r = temp.r * ap[i__2].r - temp.i * ap[i__2].i, + z__1.i = temp.r * ap[i__2].i + temp.i * ap[i__2].r; temp.r = z__1.r, temp.i = z__1.i; } i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { i__3 = k; i__4 = i__; - z__2.r = ap[i__3].r * x[i__4].r - ap[i__3].i * x[ - i__4].i, z__2.i = ap[i__3].r * x[i__4].i - + ap[i__3].i * x[i__4].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; + z__2.r = ap[i__3].r * x[i__4].r - ap[i__3].i * x[i__4].i, + z__2.i = ap[i__3].r * x[i__4].i + ap[i__3].i * x[i__4].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; ++k; -/* L150: */ } } else { if (nounit) { d_lmp_cnjg(&z__2, &ap[kk]); z__1.r = temp.r * z__2.r - temp.i * z__2.i, - z__1.i = temp.r * z__2.i + temp.i * - z__2.r; + z__1.i = temp.r * z__2.i + temp.i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } i__2 = *n; @@ -554,19 +304,15 @@ extern "C" { d_lmp_cnjg(&z__3, &ap[k]); i__3 = i__; z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, - z__2.i = z__3.r * x[i__3].i + z__3.i * x[ - i__3].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; + z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; ++k; -/* L160: */ } } i__2 = j; x[i__2].r = temp.r, x[i__2].i = temp.i; kk += *n - j + 1; -/* L170: */ } } else { jx = kx; @@ -578,9 +324,8 @@ extern "C" { if (noconj) { if (nounit) { i__2 = kk; - z__1.r = temp.r * ap[i__2].r - temp.i * ap[i__2] - .i, z__1.i = temp.r * ap[i__2].i + temp.i - * ap[i__2].r; + z__1.r = temp.r * ap[i__2].r - temp.i * ap[i__2].i, + z__1.i = temp.r * ap[i__2].i + temp.i * ap[i__2].r; temp.r = z__1.r, temp.i = z__1.i; } i__2 = kk + *n - j; @@ -588,20 +333,16 @@ extern "C" { ix += *incx; i__3 = k; i__4 = ix; - z__2.r = ap[i__3].r * x[i__4].r - ap[i__3].i * x[ - i__4].i, z__2.i = ap[i__3].r * x[i__4].i - + ap[i__3].i * x[i__4].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; + z__2.r = ap[i__3].r * x[i__4].r - ap[i__3].i * x[i__4].i, + z__2.i = ap[i__3].r * x[i__4].i + ap[i__3].i * x[i__4].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; -/* L180: */ } } else { if (nounit) { d_lmp_cnjg(&z__2, &ap[kk]); z__1.r = temp.r * z__2.r - temp.i * z__2.i, - z__1.i = temp.r * z__2.i + temp.i * - z__2.r; + z__1.i = temp.r * z__2.i + temp.i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } i__2 = kk + *n - j; @@ -610,30 +351,21 @@ extern "C" { d_lmp_cnjg(&z__3, &ap[k]); i__3 = ix; z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, - z__2.i = z__3.r * x[i__3].i + z__3.i * x[ - i__3].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; + z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; -/* L190: */ } } i__2 = jx; x[i__2].r = temp.r, x[i__2].i = temp.i; jx += *incx; kk += *n - j + 1; -/* L200: */ } } } } - return 0; - -/* End of ZTPMV */ - -} /* ztpmv_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/ztpsv.cpp b/lib/linalg/ztpsv.cpp index a1bddbbeb9..483dcc4513 100644 --- a/lib/linalg/ztpsv.cpp +++ b/lib/linalg/ztpsv.cpp @@ -1,221 +1,30 @@ -/* fortran/ztpsv.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b ZTPSV */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INCX,N */ -/* CHARACTER DIAG,TRANS,UPLO */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 AP(*),X(*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZTPSV solves one of the systems of equations */ -/* > */ -/* > A*x = b, or A**T*x = b, or A**H*x = b, */ -/* > */ -/* > where b and x are n element vectors and A is an n by n unit, or */ -/* > non-unit, upper or lower triangular matrix, supplied in packed form. */ -/* > */ -/* > No test for singularity or near-singularity is included in this */ -/* > routine. Such tests must be performed before calling this routine. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > On entry, UPLO specifies whether the matrix is an upper or */ -/* > lower triangular matrix as follows: */ -/* > */ -/* > UPLO = 'U' or 'u' A is an upper triangular matrix. */ -/* > */ -/* > UPLO = 'L' or 'l' A is a lower triangular matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TRANS */ -/* > \verbatim */ -/* > TRANS is CHARACTER*1 */ -/* > On entry, TRANS specifies the equations to be solved as */ -/* > follows: */ -/* > */ -/* > TRANS = 'N' or 'n' A*x = b. */ -/* > */ -/* > TRANS = 'T' or 't' A**T*x = b. */ -/* > */ -/* > TRANS = 'C' or 'c' A**H*x = b. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DIAG */ -/* > \verbatim */ -/* > DIAG is CHARACTER*1 */ -/* > On entry, DIAG specifies whether or not A is unit */ -/* > triangular as follows: */ -/* > */ -/* > DIAG = 'U' or 'u' A is assumed to be unit triangular. */ -/* > */ -/* > DIAG = 'N' or 'n' A is not assumed to be unit */ -/* > triangular. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > On entry, N specifies the order of the matrix A. */ -/* > N must be at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] AP */ -/* > \verbatim */ -/* > AP is COMPLEX*16 array, dimension at least */ -/* > ( ( n*( n + 1 ) )/2 ). */ -/* > Before entry with UPLO = 'U' or 'u', the array AP must */ -/* > contain the upper triangular matrix packed sequentially, */ -/* > column by column, so that AP( 1 ) contains a( 1, 1 ), */ -/* > AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) */ -/* > respectively, and so on. */ -/* > Before entry with UPLO = 'L' or 'l', the array AP must */ -/* > contain the lower triangular matrix packed sequentially, */ -/* > column by column, so that AP( 1 ) contains a( 1, 1 ), */ -/* > AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) */ -/* > respectively, and so on. */ -/* > Note that when DIAG = 'U' or 'u', the diagonal elements of */ -/* > A are not referenced, but are assumed to be unity. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] X */ -/* > \verbatim */ -/* > X is COMPLEX*16 array, dimension at least */ -/* > ( 1 + ( n - 1 )*abs( INCX ) ). */ -/* > Before entry, the incremented array X must contain the n */ -/* > element right-hand side vector b. On exit, X is overwritten */ -/* > with the solution vector x. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > On entry, INCX specifies the increment for the elements of */ -/* > X. INCX must not be zero. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16_blas_level2 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > Level 2 Blas routine. */ -/* > */ -/* > -- Written on 22-October-1986. */ -/* > Jack Dongarra, Argonne National Lab. */ -/* > Jeremy Du Croz, Nag Central Office. */ -/* > Sven Hammarling, Nag Central Office. */ -/* > Richard Hanson, Sandia National Labs. */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int ztpsv_(char *uplo, char *trans, char *diag, integer *n, - doublecomplex *ap, doublecomplex *x, integer *incx, ftnlen uplo_len, - ftnlen trans_len, ftnlen diag_len) +int ztpsv_(char *uplo, char *trans, char *diag, integer *n, doublecomplex *ap, doublecomplex *x, + integer *incx, ftnlen uplo_len, ftnlen trans_len, ftnlen diag_len) { - /* System generated locals */ integer i__1, i__2, i__3, i__4, i__5; doublecomplex z__1, z__2, z__3; - - /* Builtin functions */ - void z_lmp_div(doublecomplex *, doublecomplex *, doublecomplex *), d_lmp_cnjg( - doublecomplex *, doublecomplex *); - - /* Local variables */ + void z_lmp_div(doublecomplex *, doublecomplex *, doublecomplex *), + d_lmp_cnjg(doublecomplex *, doublecomplex *); integer i__, j, k, kk, ix, jx, kx, info; doublecomplex temp; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern int xerbla_(char *, integer *, ftnlen); logical noconj, nounit; - - -/* -- Reference BLAS level2 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ --x; --ap; - - /* Function Body */ info = 0; - if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", ( - ftnlen)1, (ftnlen)1)) { + if (!lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { info = 1; - } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, - (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, ( - ftnlen)1)) { + } else if (!lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && + !lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1) && + !lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { info = 2; - } else if (! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, - (char *)"N", (ftnlen)1, (ftnlen)1)) { + } else if (!lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && + !lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1)) { info = 3; } else if (*n < 0) { info = 4; @@ -226,32 +35,17 @@ extern "C" { xerbla_((char *)"ZTPSV ", &info, (ftnlen)6); return 0; } - -/* Quick return if possible. */ - if (*n == 0) { return 0; } - noconj = lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1); nounit = lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1); - -/* Set up the start point in X if the increment is not unity. This */ -/* will be ( N - 1 )*INCX too small for descending loops. */ - if (*incx <= 0) { kx = 1 - (*n - 1) * *incx; } else if (*incx != 1) { kx = 1; } - -/* Start the operations. In this version the elements of AP are */ -/* accessed sequentially with one pass through AP. */ - if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { - -/* Form x := inv( A )*x. */ - if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { kk = *n * (*n + 1) / 2; if (*incx == 1) { @@ -270,18 +64,14 @@ extern "C" { i__1 = i__; i__2 = i__; i__3 = k; - z__2.r = temp.r * ap[i__3].r - temp.i * ap[i__3] - .i, z__2.i = temp.r * ap[i__3].i + temp.i - * ap[i__3].r; - z__1.r = x[i__2].r - z__2.r, z__1.i = x[i__2].i - - z__2.i; + z__2.r = temp.r * ap[i__3].r - temp.i * ap[i__3].i, + z__2.i = temp.r * ap[i__3].i + temp.i * ap[i__3].r; + z__1.r = x[i__2].r - z__2.r, z__1.i = x[i__2].i - z__2.i; x[i__1].r = z__1.r, x[i__1].i = z__1.i; --k; -/* L10: */ } } kk -= j; -/* L20: */ } } else { jx = kx + (*n - 1) * *incx; @@ -302,18 +92,14 @@ extern "C" { i__2 = ix; i__3 = ix; i__4 = k; - z__2.r = temp.r * ap[i__4].r - temp.i * ap[i__4] - .i, z__2.i = temp.r * ap[i__4].i + temp.i - * ap[i__4].r; - z__1.r = x[i__3].r - z__2.r, z__1.i = x[i__3].i - - z__2.i; + z__2.r = temp.r * ap[i__4].r - temp.i * ap[i__4].i, + z__2.i = temp.r * ap[i__4].i + temp.i * ap[i__4].r; + z__1.r = x[i__3].r - z__2.r, z__1.i = x[i__3].i - z__2.i; x[i__2].r = z__1.r, x[i__2].i = z__1.i; -/* L30: */ } } jx -= *incx; kk -= j; -/* L40: */ } } } else { @@ -336,18 +122,14 @@ extern "C" { i__3 = i__; i__4 = i__; i__5 = k; - z__2.r = temp.r * ap[i__5].r - temp.i * ap[i__5] - .i, z__2.i = temp.r * ap[i__5].i + temp.i - * ap[i__5].r; - z__1.r = x[i__4].r - z__2.r, z__1.i = x[i__4].i - - z__2.i; + z__2.r = temp.r * ap[i__5].r - temp.i * ap[i__5].i, + z__2.i = temp.r * ap[i__5].i + temp.i * ap[i__5].r; + z__1.r = x[i__4].r - z__2.r, z__1.i = x[i__4].i - z__2.i; x[i__3].r = z__1.r, x[i__3].i = z__1.i; ++k; -/* L50: */ } } kk += *n - j + 1; -/* L60: */ } } else { jx = kx; @@ -369,25 +151,18 @@ extern "C" { i__3 = ix; i__4 = ix; i__5 = k; - z__2.r = temp.r * ap[i__5].r - temp.i * ap[i__5] - .i, z__2.i = temp.r * ap[i__5].i + temp.i - * ap[i__5].r; - z__1.r = x[i__4].r - z__2.r, z__1.i = x[i__4].i - - z__2.i; + z__2.r = temp.r * ap[i__5].r - temp.i * ap[i__5].i, + z__2.i = temp.r * ap[i__5].i + temp.i * ap[i__5].r; + z__1.r = x[i__4].r - z__2.r, z__1.i = x[i__4].i - z__2.i; x[i__3].r = z__1.r, x[i__3].i = z__1.i; -/* L70: */ } } jx += *incx; kk += *n - j + 1; -/* L80: */ } } } } else { - -/* Form x := inv( A**T )*x or x := inv( A**H )*x. */ - if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { kk = 1; if (*incx == 1) { @@ -401,14 +176,11 @@ extern "C" { for (i__ = 1; i__ <= i__2; ++i__) { i__3 = k; i__4 = i__; - z__2.r = ap[i__3].r * x[i__4].r - ap[i__3].i * x[ - i__4].i, z__2.i = ap[i__3].r * x[i__4].i - + ap[i__3].i * x[i__4].r; - z__1.r = temp.r - z__2.r, z__1.i = temp.i - - z__2.i; + z__2.r = ap[i__3].r * x[i__4].r - ap[i__3].i * x[i__4].i, + z__2.i = ap[i__3].r * x[i__4].i + ap[i__3].i * x[i__4].r; + z__1.r = temp.r - z__2.r, z__1.i = temp.i - z__2.i; temp.r = z__1.r, temp.i = z__1.i; ++k; -/* L90: */ } if (nounit) { z_lmp_div(&z__1, &temp, &ap[kk + j - 1]); @@ -420,13 +192,10 @@ extern "C" { d_lmp_cnjg(&z__3, &ap[k]); i__3 = i__; z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, - z__2.i = z__3.r * x[i__3].i + z__3.i * x[ - i__3].r; - z__1.r = temp.r - z__2.r, z__1.i = temp.i - - z__2.i; + z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3].r; + z__1.r = temp.r - z__2.r, z__1.i = temp.i - z__2.i; temp.r = z__1.r, temp.i = z__1.i; ++k; -/* L100: */ } if (nounit) { d_lmp_cnjg(&z__2, &ap[kk + j - 1]); @@ -437,7 +206,6 @@ extern "C" { i__2 = j; x[i__2].r = temp.r, x[i__2].i = temp.i; kk += j; -/* L110: */ } } else { jx = kx; @@ -451,14 +219,11 @@ extern "C" { for (k = kk; k <= i__2; ++k) { i__3 = k; i__4 = ix; - z__2.r = ap[i__3].r * x[i__4].r - ap[i__3].i * x[ - i__4].i, z__2.i = ap[i__3].r * x[i__4].i - + ap[i__3].i * x[i__4].r; - z__1.r = temp.r - z__2.r, z__1.i = temp.i - - z__2.i; + z__2.r = ap[i__3].r * x[i__4].r - ap[i__3].i * x[i__4].i, + z__2.i = ap[i__3].r * x[i__4].i + ap[i__3].i * x[i__4].r; + z__1.r = temp.r - z__2.r, z__1.i = temp.i - z__2.i; temp.r = z__1.r, temp.i = z__1.i; ix += *incx; -/* L120: */ } if (nounit) { z_lmp_div(&z__1, &temp, &ap[kk + j - 1]); @@ -470,13 +235,10 @@ extern "C" { d_lmp_cnjg(&z__3, &ap[k]); i__3 = ix; z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, - z__2.i = z__3.r * x[i__3].i + z__3.i * x[ - i__3].r; - z__1.r = temp.r - z__2.r, z__1.i = temp.i - - z__2.i; + z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3].r; + z__1.r = temp.r - z__2.r, z__1.i = temp.i - z__2.i; temp.r = z__1.r, temp.i = z__1.i; ix += *incx; -/* L130: */ } if (nounit) { d_lmp_cnjg(&z__2, &ap[kk + j - 1]); @@ -488,7 +250,6 @@ extern "C" { x[i__2].r = temp.r, x[i__2].i = temp.i; jx += *incx; kk += j; -/* L140: */ } } } else { @@ -503,14 +264,11 @@ extern "C" { for (i__ = *n; i__ >= i__1; --i__) { i__2 = k; i__3 = i__; - z__2.r = ap[i__2].r * x[i__3].r - ap[i__2].i * x[ - i__3].i, z__2.i = ap[i__2].r * x[i__3].i - + ap[i__2].i * x[i__3].r; - z__1.r = temp.r - z__2.r, z__1.i = temp.i - - z__2.i; + z__2.r = ap[i__2].r * x[i__3].r - ap[i__2].i * x[i__3].i, + z__2.i = ap[i__2].r * x[i__3].i + ap[i__2].i * x[i__3].r; + z__1.r = temp.r - z__2.r, z__1.i = temp.i - z__2.i; temp.r = z__1.r, temp.i = z__1.i; --k; -/* L150: */ } if (nounit) { z_lmp_div(&z__1, &temp, &ap[kk - *n + j]); @@ -522,13 +280,10 @@ extern "C" { d_lmp_cnjg(&z__3, &ap[k]); i__2 = i__; z__2.r = z__3.r * x[i__2].r - z__3.i * x[i__2].i, - z__2.i = z__3.r * x[i__2].i + z__3.i * x[ - i__2].r; - z__1.r = temp.r - z__2.r, z__1.i = temp.i - - z__2.i; + z__2.i = z__3.r * x[i__2].i + z__3.i * x[i__2].r; + z__1.r = temp.r - z__2.r, z__1.i = temp.i - z__2.i; temp.r = z__1.r, temp.i = z__1.i; --k; -/* L160: */ } if (nounit) { d_lmp_cnjg(&z__2, &ap[kk - *n + j]); @@ -539,7 +294,6 @@ extern "C" { i__1 = j; x[i__1].r = temp.r, x[i__1].i = temp.i; kk -= *n - j + 1; -/* L170: */ } } else { kx += (*n - 1) * *incx; @@ -553,14 +307,11 @@ extern "C" { for (k = kk; k >= i__1; --k) { i__2 = k; i__3 = ix; - z__2.r = ap[i__2].r * x[i__3].r - ap[i__2].i * x[ - i__3].i, z__2.i = ap[i__2].r * x[i__3].i - + ap[i__2].i * x[i__3].r; - z__1.r = temp.r - z__2.r, z__1.i = temp.i - - z__2.i; + z__2.r = ap[i__2].r * x[i__3].r - ap[i__2].i * x[i__3].i, + z__2.i = ap[i__2].r * x[i__3].i + ap[i__2].i * x[i__3].r; + z__1.r = temp.r - z__2.r, z__1.i = temp.i - z__2.i; temp.r = z__1.r, temp.i = z__1.i; ix -= *incx; -/* L180: */ } if (nounit) { z_lmp_div(&z__1, &temp, &ap[kk - *n + j]); @@ -572,13 +323,10 @@ extern "C" { d_lmp_cnjg(&z__3, &ap[k]); i__2 = ix; z__2.r = z__3.r * x[i__2].r - z__3.i * x[i__2].i, - z__2.i = z__3.r * x[i__2].i + z__3.i * x[ - i__2].r; - z__1.r = temp.r - z__2.r, z__1.i = temp.i - - z__2.i; + z__2.i = z__3.r * x[i__2].i + z__3.i * x[i__2].r; + z__1.r = temp.r - z__2.r, z__1.i = temp.i - z__2.i; temp.r = z__1.r, temp.i = z__1.i; ix -= *incx; -/* L190: */ } if (nounit) { d_lmp_cnjg(&z__2, &ap[kk - *n + j]); @@ -590,18 +338,12 @@ extern "C" { x[i__1].r = temp.r, x[i__1].i = temp.i; jx -= *incx; kk -= *n - j + 1; -/* L200: */ } } } } - return 0; - -/* End of ZTPSV */ - -} /* ztpsv_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/ztptri.cpp b/lib/linalg/ztptri.cpp index 29377adc03..86129d42d3 100644 --- a/lib/linalg/ztptri.cpp +++ b/lib/linalg/ztptri.cpp @@ -1,200 +1,32 @@ -/* fortran/ztptri.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - -static doublecomplex c_b1 = {1.,0.}; +static doublecomplex c_b1 = {1., 0.}; static integer c__1 = 1; - -/* > \brief \b ZTPTRI */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZTPTRI + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZTPTRI( UPLO, DIAG, N, AP, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER DIAG, UPLO */ -/* INTEGER INFO, N */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 AP( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZTPTRI computes the inverse of a complex upper or lower triangular */ -/* > matrix A stored in packed format. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > = 'U': A is upper triangular; */ -/* > = 'L': A is lower triangular. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DIAG */ -/* > \verbatim */ -/* > DIAG is CHARACTER*1 */ -/* > = 'N': A is non-unit triangular; */ -/* > = 'U': A is unit triangular. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrix A. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] AP */ -/* > \verbatim */ -/* > AP is COMPLEX*16 array, dimension (N*(N+1)/2) */ -/* > On entry, the upper or lower triangular matrix A, stored */ -/* > columnwise in a linear array. The j-th column of A is stored */ -/* > in the array AP as follows: */ -/* > if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */ -/* > if UPLO = 'L', AP(i + (j-1)*((2*n-j)/2) = A(i,j) for j<=i<=n. */ -/* > See below for further details. */ -/* > On exit, the (triangular) inverse of the original matrix, in */ -/* > the same packed storage format. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > > 0: if INFO = i, A(i,i) is exactly zero. The triangular */ -/* > matrix is singular and its inverse can not be computed. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16OTHERcomputational */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > A triangular matrix A can be transferred to packed storage using one */ -/* > of the following program segments: */ -/* > */ -/* > UPLO = 'U': UPLO = 'L': */ -/* > */ -/* > JC = 1 JC = 1 */ -/* > DO 2 J = 1, N DO 2 J = 1, N */ -/* > DO 1 I = 1, J DO 1 I = J, N */ -/* > AP(JC+I-1) = A(I,J) AP(JC+I-J) = A(I,J) */ -/* > 1 CONTINUE 1 CONTINUE */ -/* > JC = JC + J JC = JC + N - J + 1 */ -/* > 2 CONTINUE 2 CONTINUE */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int ztptri_(char *uplo, char *diag, integer *n, - doublecomplex *ap, integer *info, ftnlen uplo_len, ftnlen diag_len) +int ztptri_(char *uplo, char *diag, integer *n, doublecomplex *ap, integer *info, ftnlen uplo_len, + ftnlen diag_len) { - /* System generated locals */ integer i__1, i__2; doublecomplex z__1; - - /* Builtin functions */ void z_lmp_div(doublecomplex *, doublecomplex *, doublecomplex *); - - /* Local variables */ integer j, jc, jj; doublecomplex ajj; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int zscal_(integer *, doublecomplex *, - doublecomplex *, integer *); + extern int zscal_(integer *, doublecomplex *, doublecomplex *, integer *); logical upper; - extern /* Subroutine */ int ztpmv_(char *, char *, char *, integer *, - doublecomplex *, doublecomplex *, integer *, ftnlen, ftnlen, - ftnlen), xerbla_(char *, integer *, ftnlen); + extern int ztpmv_(char *, char *, char *, integer *, doublecomplex *, doublecomplex *, + integer *, ftnlen, ftnlen, ftnlen), + xerbla_(char *, integer *, ftnlen); integer jclast; logical nounit; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ --ap; - - /* Function Body */ *info = 0; upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); nounit = lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1); - if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + if (!upper && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { *info = -1; - } else if (! nounit && ! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1)) { + } else if (!nounit && !lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1)) { *info = -2; } else if (*n < 0) { *info = -3; @@ -204,9 +36,6 @@ f"> */ xerbla_((char *)"ZTPTRI", &i__1, (ftnlen)6); return 0; } - -/* Check for singularity if non-unit. */ - if (nounit) { if (upper) { jj = 0; @@ -217,7 +46,6 @@ f"> */ if (ap[i__2].r == 0. && ap[i__2].i == 0.) { return 0; } -/* L10: */ } } else { jj = 1; @@ -228,16 +56,11 @@ f"> */ return 0; } jj = jj + *n - *info + 1; -/* L20: */ } } *info = 0; } - if (upper) { - -/* Compute inverse of upper triangular matrix. */ - jc = 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { @@ -252,22 +75,14 @@ f"> */ z__1.r = -1., z__1.i = -0.; ajj.r = z__1.r, ajj.i = z__1.i; } - -/* Compute elements 1:j-1 of j-th column. */ - i__2 = j - 1; - ztpmv_((char *)"Upper", (char *)"No transpose", diag, &i__2, &ap[1], &ap[jc], & - c__1, (ftnlen)5, (ftnlen)12, (ftnlen)1); + ztpmv_((char *)"Upper", (char *)"No transpose", diag, &i__2, &ap[1], &ap[jc], &c__1, (ftnlen)5, + (ftnlen)12, (ftnlen)1); i__2 = j - 1; zscal_(&i__2, &ajj, &ap[jc], &c__1); jc += j; -/* L30: */ } - } else { - -/* Compute inverse of lower triangular matrix. */ - jc = *n * (*n + 1) / 2; for (j = *n; j >= 1; --j) { if (nounit) { @@ -282,27 +97,18 @@ f"> */ ajj.r = z__1.r, ajj.i = z__1.i; } if (j < *n) { - -/* Compute elements j+1:n of j-th column. */ - i__1 = *n - j; - ztpmv_((char *)"Lower", (char *)"No transpose", diag, &i__1, &ap[jclast], &ap[ - jc + 1], &c__1, (ftnlen)5, (ftnlen)12, (ftnlen)1); + ztpmv_((char *)"Lower", (char *)"No transpose", diag, &i__1, &ap[jclast], &ap[jc + 1], &c__1, + (ftnlen)5, (ftnlen)12, (ftnlen)1); i__1 = *n - j; zscal_(&i__1, &ajj, &ap[jc + 1], &c__1); } jclast = jc; jc = jc - *n + j - 2; -/* L40: */ } } - return 0; - -/* End of ZTPTRI */ - -} /* ztptri_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/ztrmm.cpp b/lib/linalg/ztrmm.cpp index a44eec9bb1..579080dce5 100644 --- a/lib/linalg/ztrmm.cpp +++ b/lib/linalg/ztrmm.cpp @@ -1,252 +1,28 @@ -/* fortran/ztrmm.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b ZTRMM */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) */ - -/* .. Scalar Arguments .. */ -/* COMPLEX*16 ALPHA */ -/* INTEGER LDA,LDB,M,N */ -/* CHARACTER DIAG,SIDE,TRANSA,UPLO */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 A(LDA,*),B(LDB,*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZTRMM performs one of the matrix-matrix operations */ -/* > */ -/* > B := alpha*op( A )*B, or B := alpha*B*op( A ) */ -/* > */ -/* > where alpha is a scalar, B is an m by n matrix, A is a unit, or */ -/* > non-unit, upper or lower triangular matrix and op( A ) is one of */ -/* > */ -/* > op( A ) = A or op( A ) = A**T or op( A ) = A**H. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] SIDE */ -/* > \verbatim */ -/* > SIDE is CHARACTER*1 */ -/* > On entry, SIDE specifies whether op( A ) multiplies B from */ -/* > the left or right as follows: */ -/* > */ -/* > SIDE = 'L' or 'l' B := alpha*op( A )*B. */ -/* > */ -/* > SIDE = 'R' or 'r' B := alpha*B*op( A ). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > On entry, UPLO specifies whether the matrix A is an upper or */ -/* > lower triangular matrix as follows: */ -/* > */ -/* > UPLO = 'U' or 'u' A is an upper triangular matrix. */ -/* > */ -/* > UPLO = 'L' or 'l' A is a lower triangular matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TRANSA */ -/* > \verbatim */ -/* > TRANSA is CHARACTER*1 */ -/* > On entry, TRANSA specifies the form of op( A ) to be used in */ -/* > the matrix multiplication as follows: */ -/* > */ -/* > TRANSA = 'N' or 'n' op( A ) = A. */ -/* > */ -/* > TRANSA = 'T' or 't' op( A ) = A**T. */ -/* > */ -/* > TRANSA = 'C' or 'c' op( A ) = A**H. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DIAG */ -/* > \verbatim */ -/* > DIAG is CHARACTER*1 */ -/* > On entry, DIAG specifies whether or not A is unit triangular */ -/* > as follows: */ -/* > */ -/* > DIAG = 'U' or 'u' A is assumed to be unit triangular. */ -/* > */ -/* > DIAG = 'N' or 'n' A is not assumed to be unit */ -/* > triangular. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > On entry, M specifies the number of rows of B. M must be at */ -/* > least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > On entry, N specifies the number of columns of B. N must be */ -/* > at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] ALPHA */ -/* > \verbatim */ -/* > ALPHA is COMPLEX*16 */ -/* > On entry, ALPHA specifies the scalar alpha. When alpha is */ -/* > zero then A is not referenced and B need not be set before */ -/* > entry. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is COMPLEX*16 array, dimension ( LDA, k ), where k is m */ -/* > when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. */ -/* > Before entry with UPLO = 'U' or 'u', the leading k by k */ -/* > upper triangular part of the array A must contain the upper */ -/* > triangular matrix and the strictly lower triangular part of */ -/* > A is not referenced. */ -/* > Before entry with UPLO = 'L' or 'l', the leading k by k */ -/* > lower triangular part of the array A must contain the lower */ -/* > triangular matrix and the strictly upper triangular part of */ -/* > A is not referenced. */ -/* > Note that when DIAG = 'U' or 'u', the diagonal elements of */ -/* > A are not referenced either, but are assumed to be unity. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > On entry, LDA specifies the first dimension of A as declared */ -/* > in the calling (sub) program. When SIDE = 'L' or 'l' then */ -/* > LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' */ -/* > then LDA must be at least max( 1, n ). */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] B */ -/* > \verbatim */ -/* > B is COMPLEX*16 array, dimension ( LDB, N ). */ -/* > Before entry, the leading m by n part of the array B must */ -/* > contain the matrix B, and on exit is overwritten by the */ -/* > transformed matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDB */ -/* > \verbatim */ -/* > LDB is INTEGER */ -/* > On entry, LDB specifies the first dimension of B as declared */ -/* > in the calling (sub) program. LDB must be at least */ -/* > max( 1, m ). */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16_blas_level3 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > Level 3 Blas routine. */ -/* > */ -/* > -- Written on 8-February-1989. */ -/* > Jack Dongarra, Argonne National Laboratory. */ -/* > Iain Duff, AERE Harwell. */ -/* > Jeremy Du Croz, Numerical Algorithms Group Ltd. */ -/* > Sven Hammarling, Numerical Algorithms Group Ltd. */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int ztrmm_(char *side, char *uplo, char *transa, char *diag, - integer *m, integer *n, doublecomplex *alpha, doublecomplex *a, - integer *lda, doublecomplex *b, integer *ldb, ftnlen side_len, ftnlen - uplo_len, ftnlen transa_len, ftnlen diag_len) +int ztrmm_(char *side, char *uplo, char *transa, char *diag, integer *m, integer *n, + doublecomplex *alpha, doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, + ftnlen side_len, ftnlen uplo_len, ftnlen transa_len, ftnlen diag_len) { - /* System generated locals */ - integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4, i__5, - i__6; + integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4, i__5, i__6; doublecomplex z__1, z__2, z__3; - - /* Builtin functions */ void d_lmp_cnjg(doublecomplex *, doublecomplex *); - - /* Local variables */ integer i__, j, k, info; doublecomplex temp; logical lside; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer nrowa; logical upper; - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern int xerbla_(char *, integer *, ftnlen); logical noconj, nounit; - - -/* -- Reference BLAS level3 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. Parameters .. */ -/* .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; - - /* Function Body */ lside = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); if (lside) { nrowa = *m; @@ -256,41 +32,34 @@ extern "C" { noconj = lsame_(transa, (char *)"T", (ftnlen)1, (ftnlen)1); nounit = lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1); upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); - info = 0; - if (! lside && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + if (!lside && !lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { info = 1; - } else if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + } else if (!upper && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { info = 2; - } else if (! lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(transa, - (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(transa, (char *)"C", (ftnlen)1, ( - ftnlen)1)) { + } else if (!lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1) && + !lsame_(transa, (char *)"T", (ftnlen)1, (ftnlen)1) && + !lsame_(transa, (char *)"C", (ftnlen)1, (ftnlen)1)) { info = 3; - } else if (! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, - (char *)"N", (ftnlen)1, (ftnlen)1)) { + } else if (!lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && + !lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1)) { info = 4; } else if (*m < 0) { info = 5; } else if (*n < 0) { info = 6; - } else if (*lda < max(1,nrowa)) { + } else if (*lda < max(1, nrowa)) { info = 9; - } else if (*ldb < max(1,*m)) { + } else if (*ldb < max(1, *m)) { info = 11; } if (info != 0) { xerbla_((char *)"ZTRMM ", &info, (ftnlen)6); return 0; } - -/* Quick return if possible. */ - if (*m == 0 || *n == 0) { return 0; } - -/* And when alpha.eq.zero. */ - if (alpha->r == 0. && alpha->i == 0.) { i__1 = *n; for (j = 1; j <= i__1; ++j) { @@ -298,20 +67,12 @@ extern "C" { for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * b_dim1; b[i__3].r = 0., b[i__3].i = 0.; -/* L10: */ } -/* L20: */ } return 0; } - -/* Start the operations. */ - if (lside) { if (lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1)) { - -/* Form B := alpha*A*B. */ - if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { @@ -320,36 +81,29 @@ extern "C" { i__3 = k + j * b_dim1; if (b[i__3].r != 0. || b[i__3].i != 0.) { i__3 = k + j * b_dim1; - z__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3] - .i, z__1.i = alpha->r * b[i__3].i + - alpha->i * b[i__3].r; + z__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3].i, + z__1.i = alpha->r * b[i__3].i + alpha->i * b[i__3].r; temp.r = z__1.r, temp.i = z__1.i; i__3 = k - 1; for (i__ = 1; i__ <= i__3; ++i__) { i__4 = i__ + j * b_dim1; i__5 = i__ + j * b_dim1; i__6 = i__ + k * a_dim1; - z__2.r = temp.r * a[i__6].r - temp.i * a[i__6] - .i, z__2.i = temp.r * a[i__6].i + - temp.i * a[i__6].r; - z__1.r = b[i__5].r + z__2.r, z__1.i = b[i__5] - .i + z__2.i; + z__2.r = temp.r * a[i__6].r - temp.i * a[i__6].i, + z__2.i = temp.r * a[i__6].i + temp.i * a[i__6].r; + z__1.r = b[i__5].r + z__2.r, z__1.i = b[i__5].i + z__2.i; b[i__4].r = z__1.r, b[i__4].i = z__1.i; -/* L30: */ } if (nounit) { i__3 = k + k * a_dim1; - z__1.r = temp.r * a[i__3].r - temp.i * a[i__3] - .i, z__1.i = temp.r * a[i__3].i + - temp.i * a[i__3].r; + z__1.r = temp.r * a[i__3].r - temp.i * a[i__3].i, + z__1.i = temp.r * a[i__3].i + temp.i * a[i__3].r; temp.r = z__1.r, temp.i = z__1.i; } i__3 = k + j * b_dim1; b[i__3].r = temp.r, b[i__3].i = temp.i; } -/* L40: */ } -/* L50: */ } } else { i__1 = *n; @@ -358,9 +112,8 @@ extern "C" { i__2 = k + j * b_dim1; if (b[i__2].r != 0. || b[i__2].i != 0.) { i__2 = k + j * b_dim1; - z__1.r = alpha->r * b[i__2].r - alpha->i * b[i__2] - .i, z__1.i = alpha->r * b[i__2].i + - alpha->i * b[i__2].r; + z__1.r = alpha->r * b[i__2].r - alpha->i * b[i__2].i, + z__1.i = alpha->r * b[i__2].i + alpha->i * b[i__2].r; temp.r = z__1.r, temp.i = z__1.i; i__2 = k + j * b_dim1; b[i__2].r = temp.r, b[i__2].i = temp.i; @@ -368,9 +121,8 @@ extern "C" { i__2 = k + j * b_dim1; i__3 = k + j * b_dim1; i__4 = k + k * a_dim1; - z__1.r = b[i__3].r * a[i__4].r - b[i__3].i * - a[i__4].i, z__1.i = b[i__3].r * a[ - i__4].i + b[i__3].i * a[i__4].r; + z__1.r = b[i__3].r * a[i__4].r - b[i__3].i * a[i__4].i, + z__1.i = b[i__3].r * a[i__4].i + b[i__3].i * a[i__4].r; b[i__2].r = z__1.r, b[i__2].i = z__1.i; } i__2 = *m; @@ -378,24 +130,16 @@ extern "C" { i__3 = i__ + j * b_dim1; i__4 = i__ + j * b_dim1; i__5 = i__ + k * a_dim1; - z__2.r = temp.r * a[i__5].r - temp.i * a[i__5] - .i, z__2.i = temp.r * a[i__5].i + - temp.i * a[i__5].r; - z__1.r = b[i__4].r + z__2.r, z__1.i = b[i__4] - .i + z__2.i; + z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, + z__2.i = temp.r * a[i__5].i + temp.i * a[i__5].r; + z__1.r = b[i__4].r + z__2.r, z__1.i = b[i__4].i + z__2.i; b[i__3].r = z__1.r, b[i__3].i = z__1.i; -/* L60: */ } } -/* L70: */ } -/* L80: */ } } } else { - -/* Form B := alpha*A**T*B or B := alpha*A**H*B. */ - if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { @@ -405,52 +149,41 @@ extern "C" { if (noconj) { if (nounit) { i__2 = i__ + i__ * a_dim1; - z__1.r = temp.r * a[i__2].r - temp.i * a[i__2] - .i, z__1.i = temp.r * a[i__2].i + - temp.i * a[i__2].r; + z__1.r = temp.r * a[i__2].r - temp.i * a[i__2].i, + z__1.i = temp.r * a[i__2].i + temp.i * a[i__2].r; temp.r = z__1.r, temp.i = z__1.i; } i__2 = i__ - 1; for (k = 1; k <= i__2; ++k) { i__3 = k + i__ * a_dim1; i__4 = k + j * b_dim1; - z__2.r = a[i__3].r * b[i__4].r - a[i__3].i * - b[i__4].i, z__2.i = a[i__3].r * b[ - i__4].i + a[i__3].i * b[i__4].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; + z__2.r = a[i__3].r * b[i__4].r - a[i__3].i * b[i__4].i, + z__2.i = a[i__3].r * b[i__4].i + a[i__3].i * b[i__4].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; -/* L90: */ } } else { if (nounit) { d_lmp_cnjg(&z__2, &a[i__ + i__ * a_dim1]); z__1.r = temp.r * z__2.r - temp.i * z__2.i, - z__1.i = temp.r * z__2.i + temp.i * - z__2.r; + z__1.i = temp.r * z__2.i + temp.i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } i__2 = i__ - 1; for (k = 1; k <= i__2; ++k) { d_lmp_cnjg(&z__3, &a[k + i__ * a_dim1]); i__3 = k + j * b_dim1; - z__2.r = z__3.r * b[i__3].r - z__3.i * b[i__3] - .i, z__2.i = z__3.r * b[i__3].i + - z__3.i * b[i__3].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; + z__2.r = z__3.r * b[i__3].r - z__3.i * b[i__3].i, + z__2.i = z__3.r * b[i__3].i + z__3.i * b[i__3].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; -/* L100: */ } } i__2 = i__ + j * b_dim1; z__1.r = alpha->r * temp.r - alpha->i * temp.i, - z__1.i = alpha->r * temp.i + alpha->i * - temp.r; + z__1.i = alpha->r * temp.i + alpha->i * temp.r; b[i__2].r = z__1.r, b[i__2].i = z__1.i; -/* L110: */ } -/* L120: */ } } else { i__1 = *n; @@ -462,68 +195,53 @@ extern "C" { if (noconj) { if (nounit) { i__3 = i__ + i__ * a_dim1; - z__1.r = temp.r * a[i__3].r - temp.i * a[i__3] - .i, z__1.i = temp.r * a[i__3].i + - temp.i * a[i__3].r; + z__1.r = temp.r * a[i__3].r - temp.i * a[i__3].i, + z__1.i = temp.r * a[i__3].i + temp.i * a[i__3].r; temp.r = z__1.r, temp.i = z__1.i; } i__3 = *m; for (k = i__ + 1; k <= i__3; ++k) { i__4 = k + i__ * a_dim1; i__5 = k + j * b_dim1; - z__2.r = a[i__4].r * b[i__5].r - a[i__4].i * - b[i__5].i, z__2.i = a[i__4].r * b[ - i__5].i + a[i__4].i * b[i__5].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; + z__2.r = a[i__4].r * b[i__5].r - a[i__4].i * b[i__5].i, + z__2.i = a[i__4].r * b[i__5].i + a[i__4].i * b[i__5].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; -/* L130: */ } } else { if (nounit) { d_lmp_cnjg(&z__2, &a[i__ + i__ * a_dim1]); z__1.r = temp.r * z__2.r - temp.i * z__2.i, - z__1.i = temp.r * z__2.i + temp.i * - z__2.r; + z__1.i = temp.r * z__2.i + temp.i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } i__3 = *m; for (k = i__ + 1; k <= i__3; ++k) { d_lmp_cnjg(&z__3, &a[k + i__ * a_dim1]); i__4 = k + j * b_dim1; - z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4] - .i, z__2.i = z__3.r * b[i__4].i + - z__3.i * b[i__4].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; + z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4].i, + z__2.i = z__3.r * b[i__4].i + z__3.i * b[i__4].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; -/* L140: */ } } i__3 = i__ + j * b_dim1; z__1.r = alpha->r * temp.r - alpha->i * temp.i, - z__1.i = alpha->r * temp.i + alpha->i * - temp.r; + z__1.i = alpha->r * temp.i + alpha->i * temp.r; b[i__3].r = z__1.r, b[i__3].i = z__1.i; -/* L150: */ } -/* L160: */ } } } } else { if (lsame_(transa, (char *)"N", (ftnlen)1, (ftnlen)1)) { - -/* Form B := alpha*B*A. */ - if (upper) { for (j = *n; j >= 1; --j) { temp.r = alpha->r, temp.i = alpha->i; if (nounit) { i__1 = j + j * a_dim1; z__1.r = temp.r * a[i__1].r - temp.i * a[i__1].i, - z__1.i = temp.r * a[i__1].i + temp.i * a[i__1] - .r; + z__1.i = temp.r * a[i__1].i + temp.i * a[i__1].r; temp.r = z__1.r, temp.i = z__1.i; } i__1 = *m; @@ -531,37 +249,29 @@ extern "C" { i__2 = i__ + j * b_dim1; i__3 = i__ + j * b_dim1; z__1.r = temp.r * b[i__3].r - temp.i * b[i__3].i, - z__1.i = temp.r * b[i__3].i + temp.i * b[i__3] - .r; + z__1.i = temp.r * b[i__3].i + temp.i * b[i__3].r; b[i__2].r = z__1.r, b[i__2].i = z__1.i; -/* L170: */ } i__1 = j - 1; for (k = 1; k <= i__1; ++k) { i__2 = k + j * a_dim1; if (a[i__2].r != 0. || a[i__2].i != 0.) { i__2 = k + j * a_dim1; - z__1.r = alpha->r * a[i__2].r - alpha->i * a[i__2] - .i, z__1.i = alpha->r * a[i__2].i + - alpha->i * a[i__2].r; + z__1.r = alpha->r * a[i__2].r - alpha->i * a[i__2].i, + z__1.i = alpha->r * a[i__2].i + alpha->i * a[i__2].r; temp.r = z__1.r, temp.i = z__1.i; i__2 = *m; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * b_dim1; i__4 = i__ + j * b_dim1; i__5 = i__ + k * b_dim1; - z__2.r = temp.r * b[i__5].r - temp.i * b[i__5] - .i, z__2.i = temp.r * b[i__5].i + - temp.i * b[i__5].r; - z__1.r = b[i__4].r + z__2.r, z__1.i = b[i__4] - .i + z__2.i; + z__2.r = temp.r * b[i__5].r - temp.i * b[i__5].i, + z__2.i = temp.r * b[i__5].i + temp.i * b[i__5].r; + z__1.r = b[i__4].r + z__2.r, z__1.i = b[i__4].i + z__2.i; b[i__3].r = z__1.r, b[i__3].i = z__1.i; -/* L180: */ } } -/* L190: */ } -/* L200: */ } } else { i__1 = *n; @@ -570,8 +280,7 @@ extern "C" { if (nounit) { i__2 = j + j * a_dim1; z__1.r = temp.r * a[i__2].r - temp.i * a[i__2].i, - z__1.i = temp.r * a[i__2].i + temp.i * a[i__2] - .r; + z__1.i = temp.r * a[i__2].i + temp.i * a[i__2].r; temp.r = z__1.r, temp.i = z__1.i; } i__2 = *m; @@ -579,43 +288,32 @@ extern "C" { i__3 = i__ + j * b_dim1; i__4 = i__ + j * b_dim1; z__1.r = temp.r * b[i__4].r - temp.i * b[i__4].i, - z__1.i = temp.r * b[i__4].i + temp.i * b[i__4] - .r; + z__1.i = temp.r * b[i__4].i + temp.i * b[i__4].r; b[i__3].r = z__1.r, b[i__3].i = z__1.i; -/* L210: */ } i__2 = *n; for (k = j + 1; k <= i__2; ++k) { i__3 = k + j * a_dim1; if (a[i__3].r != 0. || a[i__3].i != 0.) { i__3 = k + j * a_dim1; - z__1.r = alpha->r * a[i__3].r - alpha->i * a[i__3] - .i, z__1.i = alpha->r * a[i__3].i + - alpha->i * a[i__3].r; + z__1.r = alpha->r * a[i__3].r - alpha->i * a[i__3].i, + z__1.i = alpha->r * a[i__3].i + alpha->i * a[i__3].r; temp.r = z__1.r, temp.i = z__1.i; i__3 = *m; for (i__ = 1; i__ <= i__3; ++i__) { i__4 = i__ + j * b_dim1; i__5 = i__ + j * b_dim1; i__6 = i__ + k * b_dim1; - z__2.r = temp.r * b[i__6].r - temp.i * b[i__6] - .i, z__2.i = temp.r * b[i__6].i + - temp.i * b[i__6].r; - z__1.r = b[i__5].r + z__2.r, z__1.i = b[i__5] - .i + z__2.i; + z__2.r = temp.r * b[i__6].r - temp.i * b[i__6].i, + z__2.i = temp.r * b[i__6].i + temp.i * b[i__6].r; + z__1.r = b[i__5].r + z__2.r, z__1.i = b[i__5].i + z__2.i; b[i__4].r = z__1.r, b[i__4].i = z__1.i; -/* L220: */ } } -/* L230: */ } -/* L240: */ } } } else { - -/* Form B := alpha*B*A**T or B := alpha*B*A**H. */ - if (upper) { i__1 = *n; for (k = 1; k <= i__1; ++k) { @@ -625,15 +323,13 @@ extern "C" { if (a[i__3].r != 0. || a[i__3].i != 0.) { if (noconj) { i__3 = j + k * a_dim1; - z__1.r = alpha->r * a[i__3].r - alpha->i * a[ - i__3].i, z__1.i = alpha->r * a[i__3] - .i + alpha->i * a[i__3].r; + z__1.r = alpha->r * a[i__3].r - alpha->i * a[i__3].i, + z__1.i = alpha->r * a[i__3].i + alpha->i * a[i__3].r; temp.r = z__1.r, temp.i = z__1.i; } else { d_lmp_cnjg(&z__2, &a[j + k * a_dim1]); - z__1.r = alpha->r * z__2.r - alpha->i * - z__2.i, z__1.i = alpha->r * z__2.i + - alpha->i * z__2.r; + z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, + z__1.i = alpha->r * z__2.i + alpha->i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } i__3 = *m; @@ -641,30 +337,24 @@ extern "C" { i__4 = i__ + j * b_dim1; i__5 = i__ + j * b_dim1; i__6 = i__ + k * b_dim1; - z__2.r = temp.r * b[i__6].r - temp.i * b[i__6] - .i, z__2.i = temp.r * b[i__6].i + - temp.i * b[i__6].r; - z__1.r = b[i__5].r + z__2.r, z__1.i = b[i__5] - .i + z__2.i; + z__2.r = temp.r * b[i__6].r - temp.i * b[i__6].i, + z__2.i = temp.r * b[i__6].i + temp.i * b[i__6].r; + z__1.r = b[i__5].r + z__2.r, z__1.i = b[i__5].i + z__2.i; b[i__4].r = z__1.r, b[i__4].i = z__1.i; -/* L250: */ } } -/* L260: */ } temp.r = alpha->r, temp.i = alpha->i; if (nounit) { if (noconj) { i__2 = k + k * a_dim1; z__1.r = temp.r * a[i__2].r - temp.i * a[i__2].i, - z__1.i = temp.r * a[i__2].i + temp.i * a[ - i__2].r; + z__1.i = temp.r * a[i__2].i + temp.i * a[i__2].r; temp.r = z__1.r, temp.i = z__1.i; } else { d_lmp_cnjg(&z__2, &a[k + k * a_dim1]); z__1.r = temp.r * z__2.r - temp.i * z__2.i, - z__1.i = temp.r * z__2.i + temp.i * - z__2.r; + z__1.i = temp.r * z__2.i + temp.i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } } @@ -674,13 +364,10 @@ extern "C" { i__3 = i__ + k * b_dim1; i__4 = i__ + k * b_dim1; z__1.r = temp.r * b[i__4].r - temp.i * b[i__4].i, - z__1.i = temp.r * b[i__4].i + temp.i * b[ - i__4].r; + z__1.i = temp.r * b[i__4].i + temp.i * b[i__4].r; b[i__3].r = z__1.r, b[i__3].i = z__1.i; -/* L270: */ } } -/* L280: */ } } else { for (k = *n; k >= 1; --k) { @@ -690,15 +377,13 @@ extern "C" { if (a[i__2].r != 0. || a[i__2].i != 0.) { if (noconj) { i__2 = j + k * a_dim1; - z__1.r = alpha->r * a[i__2].r - alpha->i * a[ - i__2].i, z__1.i = alpha->r * a[i__2] - .i + alpha->i * a[i__2].r; + z__1.r = alpha->r * a[i__2].r - alpha->i * a[i__2].i, + z__1.i = alpha->r * a[i__2].i + alpha->i * a[i__2].r; temp.r = z__1.r, temp.i = z__1.i; } else { d_lmp_cnjg(&z__2, &a[j + k * a_dim1]); - z__1.r = alpha->r * z__2.r - alpha->i * - z__2.i, z__1.i = alpha->r * z__2.i + - alpha->i * z__2.r; + z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, + z__1.i = alpha->r * z__2.i + alpha->i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } i__2 = *m; @@ -706,30 +391,24 @@ extern "C" { i__3 = i__ + j * b_dim1; i__4 = i__ + j * b_dim1; i__5 = i__ + k * b_dim1; - z__2.r = temp.r * b[i__5].r - temp.i * b[i__5] - .i, z__2.i = temp.r * b[i__5].i + - temp.i * b[i__5].r; - z__1.r = b[i__4].r + z__2.r, z__1.i = b[i__4] - .i + z__2.i; + z__2.r = temp.r * b[i__5].r - temp.i * b[i__5].i, + z__2.i = temp.r * b[i__5].i + temp.i * b[i__5].r; + z__1.r = b[i__4].r + z__2.r, z__1.i = b[i__4].i + z__2.i; b[i__3].r = z__1.r, b[i__3].i = z__1.i; -/* L290: */ } } -/* L300: */ } temp.r = alpha->r, temp.i = alpha->i; if (nounit) { if (noconj) { i__1 = k + k * a_dim1; z__1.r = temp.r * a[i__1].r - temp.i * a[i__1].i, - z__1.i = temp.r * a[i__1].i + temp.i * a[ - i__1].r; + z__1.i = temp.r * a[i__1].i + temp.i * a[i__1].r; temp.r = z__1.r, temp.i = z__1.i; } else { d_lmp_cnjg(&z__2, &a[k + k * a_dim1]); z__1.r = temp.r * z__2.r - temp.i * z__2.i, - z__1.i = temp.r * z__2.i + temp.i * - z__2.r; + z__1.i = temp.r * z__2.i + temp.i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } } @@ -739,24 +418,16 @@ extern "C" { i__2 = i__ + k * b_dim1; i__3 = i__ + k * b_dim1; z__1.r = temp.r * b[i__3].r - temp.i * b[i__3].i, - z__1.i = temp.r * b[i__3].i + temp.i * b[ - i__3].r; + z__1.i = temp.r * b[i__3].i + temp.i * b[i__3].r; b[i__2].r = z__1.r, b[i__2].i = z__1.i; -/* L310: */ } } -/* L320: */ } } } } - return 0; - -/* End of ZTRMM */ - -} /* ztrmm_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/ztrmv.cpp b/lib/linalg/ztrmv.cpp index 9d9877638f..dff4c36ef6 100644 --- a/lib/linalg/ztrmv.cpp +++ b/lib/linalg/ztrmv.cpp @@ -1,229 +1,35 @@ -/* fortran/ztrmv.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b ZTRMV */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INCX,LDA,N */ -/* CHARACTER DIAG,TRANS,UPLO */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 A(LDA,*),X(*) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZTRMV performs one of the matrix-vector operations */ -/* > */ -/* > x := A*x, or x := A**T*x, or x := A**H*x, */ -/* > */ -/* > where x is an n element vector and A is an n by n unit, or non-unit, */ -/* > upper or lower triangular matrix. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > On entry, UPLO specifies whether the matrix is an upper or */ -/* > lower triangular matrix as follows: */ -/* > */ -/* > UPLO = 'U' or 'u' A is an upper triangular matrix. */ -/* > */ -/* > UPLO = 'L' or 'l' A is a lower triangular matrix. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TRANS */ -/* > \verbatim */ -/* > TRANS is CHARACTER*1 */ -/* > On entry, TRANS specifies the operation to be performed as */ -/* > follows: */ -/* > */ -/* > TRANS = 'N' or 'n' x := A*x. */ -/* > */ -/* > TRANS = 'T' or 't' x := A**T*x. */ -/* > */ -/* > TRANS = 'C' or 'c' x := A**H*x. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] DIAG */ -/* > \verbatim */ -/* > DIAG is CHARACTER*1 */ -/* > On entry, DIAG specifies whether or not A is unit */ -/* > triangular as follows: */ -/* > */ -/* > DIAG = 'U' or 'u' A is assumed to be unit triangular. */ -/* > */ -/* > DIAG = 'N' or 'n' A is not assumed to be unit */ -/* > triangular. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > On entry, N specifies the order of the matrix A. */ -/* > N must be at least zero. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is COMPLEX*16 array, dimension ( LDA, N ). */ -/* > Before entry with UPLO = 'U' or 'u', the leading n by n */ -/* > upper triangular part of the array A must contain the upper */ -/* > triangular matrix and the strictly lower triangular part of */ -/* > A is not referenced. */ -/* > Before entry with UPLO = 'L' or 'l', the leading n by n */ -/* > lower triangular part of the array A must contain the lower */ -/* > triangular matrix and the strictly upper triangular part of */ -/* > A is not referenced. */ -/* > Note that when DIAG = 'U' or 'u', the diagonal elements of */ -/* > A are not referenced either, but are assumed to be unity. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > On entry, LDA specifies the first dimension of A as declared */ -/* > in the calling (sub) program. LDA must be at least */ -/* > max( 1, n ). */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] X */ -/* > \verbatim */ -/* > X is COMPLEX*16 array, dimension at least */ -/* > ( 1 + ( n - 1 )*abs( INCX ) ). */ -/* > Before entry, the incremented array X must contain the n */ -/* > element vector x. On exit, X is overwritten with the */ -/* > transformed vector x. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] INCX */ -/* > \verbatim */ -/* > INCX is INTEGER */ -/* > On entry, INCX specifies the increment for the elements of */ -/* > X. INCX must not be zero. */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16_blas_level2 */ - -/* > \par Further Details: */ -/* ===================== */ -/* > */ -/* > \verbatim */ -/* > */ -/* > Level 2 Blas routine. */ -/* > The vector and matrix arguments are not referenced when N = 0, or M = 0 */ -/* > */ -/* > -- Written on 22-October-1986. */ -/* > Jack Dongarra, Argonne National Lab. */ -/* > Jeremy Du Croz, Nag Central Office. */ -/* > Sven Hammarling, Nag Central Office. */ -/* > Richard Hanson, Sandia National Labs. */ -/* > \endverbatim */ -/* > */ -/* ===================================================================== */ -/* Subroutine */ int ztrmv_(char *uplo, char *trans, char *diag, integer *n, - doublecomplex *a, integer *lda, doublecomplex *x, integer *incx, - ftnlen uplo_len, ftnlen trans_len, ftnlen diag_len) +int ztrmv_(char *uplo, char *trans, char *diag, integer *n, doublecomplex *a, integer *lda, + doublecomplex *x, integer *incx, ftnlen uplo_len, ftnlen trans_len, ftnlen diag_len) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; doublecomplex z__1, z__2, z__3; - - /* Builtin functions */ void d_lmp_cnjg(doublecomplex *, doublecomplex *); - - /* Local variables */ integer i__, j, ix, jx, kx, info; doublecomplex temp; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); + extern int xerbla_(char *, integer *, ftnlen); logical noconj, nounit; - - -/* -- Reference BLAS level2 routine -- */ -/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ - -/* Test the input parameters. */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --x; - - /* Function Body */ info = 0; - if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", ( - ftnlen)1, (ftnlen)1)) { + if (!lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { info = 1; - } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, - (char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, ( - ftnlen)1)) { + } else if (!lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && + !lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1) && + !lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { info = 2; - } else if (! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag, - (char *)"N", (ftnlen)1, (ftnlen)1)) { + } else if (!lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && + !lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1)) { info = 3; } else if (*n < 0) { info = 4; - } else if (*lda < max(1,*n)) { + } else if (*lda < max(1, *n)) { info = 6; } else if (*incx == 0) { info = 8; @@ -232,32 +38,17 @@ extern "C" { xerbla_((char *)"ZTRMV ", &info, (ftnlen)6); return 0; } - -/* Quick return if possible. */ - if (*n == 0) { return 0; } - noconj = lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1); nounit = lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1); - -/* Set up the start point in X if the increment is not unity. This */ -/* will be ( N - 1 )*INCX too small for descending loops. */ - if (*incx <= 0) { kx = 1 - (*n - 1) * *incx; } else if (*incx != 1) { kx = 1; } - -/* Start the operations. In this version the elements of A are */ -/* accessed sequentially with one pass through A. */ - if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) { - -/* Form x := A*x. */ - if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { if (*incx == 1) { i__1 = *n; @@ -272,24 +63,19 @@ extern "C" { i__4 = i__; i__5 = i__ + j * a_dim1; z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, - z__2.i = temp.r * a[i__5].i + temp.i * a[ - i__5].r; - z__1.r = x[i__4].r + z__2.r, z__1.i = x[i__4].i + - z__2.i; + z__2.i = temp.r * a[i__5].i + temp.i * a[i__5].r; + z__1.r = x[i__4].r + z__2.r, z__1.i = x[i__4].i + z__2.i; x[i__3].r = z__1.r, x[i__3].i = z__1.i; -/* L10: */ } if (nounit) { i__2 = j; i__3 = j; i__4 = j + j * a_dim1; - z__1.r = x[i__3].r * a[i__4].r - x[i__3].i * a[ - i__4].i, z__1.i = x[i__3].r * a[i__4].i + - x[i__3].i * a[i__4].r; + z__1.r = x[i__3].r * a[i__4].r - x[i__3].i * a[i__4].i, + z__1.i = x[i__3].r * a[i__4].i + x[i__3].i * a[i__4].r; x[i__2].r = z__1.r, x[i__2].i = z__1.i; } } -/* L20: */ } } else { jx = kx; @@ -306,26 +92,21 @@ extern "C" { i__4 = ix; i__5 = i__ + j * a_dim1; z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i, - z__2.i = temp.r * a[i__5].i + temp.i * a[ - i__5].r; - z__1.r = x[i__4].r + z__2.r, z__1.i = x[i__4].i + - z__2.i; + z__2.i = temp.r * a[i__5].i + temp.i * a[i__5].r; + z__1.r = x[i__4].r + z__2.r, z__1.i = x[i__4].i + z__2.i; x[i__3].r = z__1.r, x[i__3].i = z__1.i; ix += *incx; -/* L30: */ } if (nounit) { i__2 = jx; i__3 = jx; i__4 = j + j * a_dim1; - z__1.r = x[i__3].r * a[i__4].r - x[i__3].i * a[ - i__4].i, z__1.i = x[i__3].r * a[i__4].i + - x[i__3].i * a[i__4].r; + z__1.r = x[i__3].r * a[i__4].r - x[i__3].i * a[i__4].i, + z__1.i = x[i__3].r * a[i__4].i + x[i__3].i * a[i__4].r; x[i__2].r = z__1.r, x[i__2].i = z__1.i; } } jx += *incx; -/* L40: */ } } } else { @@ -341,24 +122,19 @@ extern "C" { i__3 = i__; i__4 = i__ + j * a_dim1; z__2.r = temp.r * a[i__4].r - temp.i * a[i__4].i, - z__2.i = temp.r * a[i__4].i + temp.i * a[ - i__4].r; - z__1.r = x[i__3].r + z__2.r, z__1.i = x[i__3].i + - z__2.i; + z__2.i = temp.r * a[i__4].i + temp.i * a[i__4].r; + z__1.r = x[i__3].r + z__2.r, z__1.i = x[i__3].i + z__2.i; x[i__2].r = z__1.r, x[i__2].i = z__1.i; -/* L50: */ } if (nounit) { i__1 = j; i__2 = j; i__3 = j + j * a_dim1; - z__1.r = x[i__2].r * a[i__3].r - x[i__2].i * a[ - i__3].i, z__1.i = x[i__2].r * a[i__3].i + - x[i__2].i * a[i__3].r; + z__1.r = x[i__2].r * a[i__3].r - x[i__2].i * a[i__3].i, + z__1.i = x[i__2].r * a[i__3].i + x[i__2].i * a[i__3].r; x[i__1].r = z__1.r, x[i__1].i = z__1.i; } } -/* L60: */ } } else { kx += (*n - 1) * *incx; @@ -375,33 +151,25 @@ extern "C" { i__3 = ix; i__4 = i__ + j * a_dim1; z__2.r = temp.r * a[i__4].r - temp.i * a[i__4].i, - z__2.i = temp.r * a[i__4].i + temp.i * a[ - i__4].r; - z__1.r = x[i__3].r + z__2.r, z__1.i = x[i__3].i + - z__2.i; + z__2.i = temp.r * a[i__4].i + temp.i * a[i__4].r; + z__1.r = x[i__3].r + z__2.r, z__1.i = x[i__3].i + z__2.i; x[i__2].r = z__1.r, x[i__2].i = z__1.i; ix -= *incx; -/* L70: */ } if (nounit) { i__1 = jx; i__2 = jx; i__3 = j + j * a_dim1; - z__1.r = x[i__2].r * a[i__3].r - x[i__2].i * a[ - i__3].i, z__1.i = x[i__2].r * a[i__3].i + - x[i__2].i * a[i__3].r; + z__1.r = x[i__2].r * a[i__3].r - x[i__2].i * a[i__3].i, + z__1.i = x[i__2].r * a[i__3].i + x[i__2].i * a[i__3].r; x[i__1].r = z__1.r, x[i__1].i = z__1.i; } } jx -= *incx; -/* L80: */ } } } } else { - -/* Form x := A**T*x or x := A**H*x. */ - if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { if (*incx == 1) { for (j = *n; j >= 1; --j) { @@ -411,44 +179,35 @@ extern "C" { if (nounit) { i__1 = j + j * a_dim1; z__1.r = temp.r * a[i__1].r - temp.i * a[i__1].i, - z__1.i = temp.r * a[i__1].i + temp.i * a[ - i__1].r; + z__1.i = temp.r * a[i__1].i + temp.i * a[i__1].r; temp.r = z__1.r, temp.i = z__1.i; } for (i__ = j - 1; i__ >= 1; --i__) { i__1 = i__ + j * a_dim1; i__2 = i__; - z__2.r = a[i__1].r * x[i__2].r - a[i__1].i * x[ - i__2].i, z__2.i = a[i__1].r * x[i__2].i + - a[i__1].i * x[i__2].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; + z__2.r = a[i__1].r * x[i__2].r - a[i__1].i * x[i__2].i, + z__2.i = a[i__1].r * x[i__2].i + a[i__1].i * x[i__2].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; -/* L90: */ } } else { if (nounit) { d_lmp_cnjg(&z__2, &a[j + j * a_dim1]); z__1.r = temp.r * z__2.r - temp.i * z__2.i, - z__1.i = temp.r * z__2.i + temp.i * - z__2.r; + z__1.i = temp.r * z__2.i + temp.i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } for (i__ = j - 1; i__ >= 1; --i__) { d_lmp_cnjg(&z__3, &a[i__ + j * a_dim1]); i__1 = i__; z__2.r = z__3.r * x[i__1].r - z__3.i * x[i__1].i, - z__2.i = z__3.r * x[i__1].i + z__3.i * x[ - i__1].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; + z__2.i = z__3.r * x[i__1].i + z__3.i * x[i__1].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; -/* L100: */ } } i__1 = j; x[i__1].r = temp.r, x[i__1].i = temp.i; -/* L110: */ } } else { jx = kx + (*n - 1) * *incx; @@ -460,28 +219,23 @@ extern "C" { if (nounit) { i__1 = j + j * a_dim1; z__1.r = temp.r * a[i__1].r - temp.i * a[i__1].i, - z__1.i = temp.r * a[i__1].i + temp.i * a[ - i__1].r; + z__1.i = temp.r * a[i__1].i + temp.i * a[i__1].r; temp.r = z__1.r, temp.i = z__1.i; } for (i__ = j - 1; i__ >= 1; --i__) { ix -= *incx; i__1 = i__ + j * a_dim1; i__2 = ix; - z__2.r = a[i__1].r * x[i__2].r - a[i__1].i * x[ - i__2].i, z__2.i = a[i__1].r * x[i__2].i + - a[i__1].i * x[i__2].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; + z__2.r = a[i__1].r * x[i__2].r - a[i__1].i * x[i__2].i, + z__2.i = a[i__1].r * x[i__2].i + a[i__1].i * x[i__2].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; -/* L120: */ } } else { if (nounit) { d_lmp_cnjg(&z__2, &a[j + j * a_dim1]); z__1.r = temp.r * z__2.r - temp.i * z__2.i, - z__1.i = temp.r * z__2.i + temp.i * - z__2.r; + z__1.i = temp.r * z__2.i + temp.i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } for (i__ = j - 1; i__ >= 1; --i__) { @@ -489,18 +243,14 @@ extern "C" { d_lmp_cnjg(&z__3, &a[i__ + j * a_dim1]); i__1 = ix; z__2.r = z__3.r * x[i__1].r - z__3.i * x[i__1].i, - z__2.i = z__3.r * x[i__1].i + z__3.i * x[ - i__1].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; + z__2.i = z__3.r * x[i__1].i + z__3.i * x[i__1].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; -/* L130: */ } } i__1 = jx; x[i__1].r = temp.r, x[i__1].i = temp.i; jx -= *incx; -/* L140: */ } } } else { @@ -513,28 +263,23 @@ extern "C" { if (nounit) { i__2 = j + j * a_dim1; z__1.r = temp.r * a[i__2].r - temp.i * a[i__2].i, - z__1.i = temp.r * a[i__2].i + temp.i * a[ - i__2].r; + z__1.i = temp.r * a[i__2].i + temp.i * a[i__2].r; temp.r = z__1.r, temp.i = z__1.i; } i__2 = *n; for (i__ = j + 1; i__ <= i__2; ++i__) { i__3 = i__ + j * a_dim1; i__4 = i__; - z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[ - i__4].i, z__2.i = a[i__3].r * x[i__4].i + - a[i__3].i * x[i__4].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; + z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[i__4].i, + z__2.i = a[i__3].r * x[i__4].i + a[i__3].i * x[i__4].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; -/* L150: */ } } else { if (nounit) { d_lmp_cnjg(&z__2, &a[j + j * a_dim1]); z__1.r = temp.r * z__2.r - temp.i * z__2.i, - z__1.i = temp.r * z__2.i + temp.i * - z__2.r; + z__1.i = temp.r * z__2.i + temp.i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } i__2 = *n; @@ -542,17 +287,13 @@ extern "C" { d_lmp_cnjg(&z__3, &a[i__ + j * a_dim1]); i__3 = i__; z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, - z__2.i = z__3.r * x[i__3].i + z__3.i * x[ - i__3].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; + z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; -/* L160: */ } } i__2 = j; x[i__2].r = temp.r, x[i__2].i = temp.i; -/* L170: */ } } else { jx = kx; @@ -565,8 +306,7 @@ extern "C" { if (nounit) { i__2 = j + j * a_dim1; z__1.r = temp.r * a[i__2].r - temp.i * a[i__2].i, - z__1.i = temp.r * a[i__2].i + temp.i * a[ - i__2].r; + z__1.i = temp.r * a[i__2].i + temp.i * a[i__2].r; temp.r = z__1.r, temp.i = z__1.i; } i__2 = *n; @@ -574,20 +314,16 @@ extern "C" { ix += *incx; i__3 = i__ + j * a_dim1; i__4 = ix; - z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[ - i__4].i, z__2.i = a[i__3].r * x[i__4].i + - a[i__3].i * x[i__4].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; + z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[i__4].i, + z__2.i = a[i__3].r * x[i__4].i + a[i__3].i * x[i__4].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; -/* L180: */ } } else { if (nounit) { d_lmp_cnjg(&z__2, &a[j + j * a_dim1]); z__1.r = temp.r * z__2.r - temp.i * z__2.i, - z__1.i = temp.r * z__2.i + temp.i * - z__2.r; + z__1.i = temp.r * z__2.i + temp.i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } i__2 = *n; @@ -596,29 +332,20 @@ extern "C" { d_lmp_cnjg(&z__3, &a[i__ + j * a_dim1]); i__3 = ix; z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i, - z__2.i = z__3.r * x[i__3].i + z__3.i * x[ - i__3].r; - z__1.r = temp.r + z__2.r, z__1.i = temp.i + - z__2.i; + z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3].r; + z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; -/* L190: */ } } i__2 = jx; x[i__2].r = temp.r, x[i__2].i = temp.i; jx += *incx; -/* L200: */ } } } } - return 0; - -/* End of ZTRMV */ - -} /* ztrmv_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zung2l.cpp b/lib/linalg/zung2l.cpp index 4c4f96c5b0..ab3da15caa 100644 --- a/lib/linalg/zung2l.cpp +++ b/lib/linalg/zung2l.cpp @@ -1,188 +1,23 @@ -/* fortran/zung2l.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; - -/* > \brief \b ZUNG2L generates all or part of the unitary matrix Q from a QL factorization determined by cgeq -lf (unblocked algorithm). */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZUNG2L + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZUNG2L( M, N, K, A, LDA, TAU, WORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INFO, K, LDA, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZUNG2L generates an m by n complex matrix Q with orthonormal columns, */ -/* > which is defined as the last n columns of a product of k elementary */ -/* > reflectors of order m */ -/* > */ -/* > Q = H(k) . . . H(2) H(1) */ -/* > */ -/* > as returned by ZGEQLF. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix Q. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix Q. M >= N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > The number of elementary reflectors whose product defines the */ -/* > matrix Q. N >= K >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is COMPLEX*16 array, dimension (LDA,N) */ -/* > On entry, the (n-k+i)-th column must contain the vector which */ -/* > defines the elementary reflector H(i), for i = 1,2,...,k, as */ -/* > returned by ZGEQLF in the last k columns of its array */ -/* > argument A. */ -/* > On exit, the m-by-n matrix Q. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The first dimension of the array A. LDA >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TAU */ -/* > \verbatim */ -/* > TAU is COMPLEX*16 array, dimension (K) */ -/* > TAU(i) must contain the scalar factor of the elementary */ -/* > reflector H(i), as returned by ZGEQLF. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is COMPLEX*16 array, dimension (N) */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument has an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16OTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int zung2l_(integer *m, integer *n, integer *k, - doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex * - work, integer *info) +int zung2l_(integer *m, integer *n, integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, + doublecomplex *work, integer *info) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; doublecomplex z__1; - - /* Local variables */ integer i__, j, l, ii; - extern /* Subroutine */ int zscal_(integer *, doublecomplex *, - doublecomplex *, integer *), zlarf_(char *, integer *, integer *, - doublecomplex *, integer *, doublecomplex *, doublecomplex *, - integer *, doublecomplex *, ftnlen), xerbla_(char *, integer *, - ftnlen); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments */ - - /* Parameter adjustments */ + extern int zscal_(integer *, doublecomplex *, doublecomplex *, integer *), + zlarf_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, + doublecomplex *, integer *, doublecomplex *, ftnlen), + xerbla_(char *, integer *, ftnlen); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --tau; --work; - - /* Function Body */ *info = 0; if (*m < 0) { *info = -1; @@ -190,7 +25,7 @@ f"> */ *info = -2; } else if (*k < 0 || *k > *n) { *info = -3; - } else if (*lda < max(1,*m)) { + } else if (*lda < max(1, *m)) { *info = -5; } if (*info != 0) { @@ -198,40 +33,28 @@ f"> */ xerbla_((char *)"ZUNG2L", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*n <= 0) { return 0; } - -/* Initialise columns 1:n-k to columns of the unit matrix */ - i__1 = *n - *k; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (l = 1; l <= i__2; ++l) { i__3 = l + j * a_dim1; a[i__3].r = 0., a[i__3].i = 0.; -/* L10: */ } i__2 = *m - *n + j + j * a_dim1; a[i__2].r = 1., a[i__2].i = 0.; -/* L20: */ } - i__1 = *k; for (i__ = 1; i__ <= i__1; ++i__) { ii = *n - *k + i__; - -/* Apply H(i) to A(1:m-k+i,1:n-k+i) from the left */ - i__2 = *m - *n + ii + ii * a_dim1; a[i__2].r = 1., a[i__2].i = 0.; i__2 = *m - *n + ii; i__3 = ii - 1; - zlarf_((char *)"Left", &i__2, &i__3, &a[ii * a_dim1 + 1], &c__1, &tau[i__], & - a[a_offset], lda, &work[1], (ftnlen)4); + zlarf_((char *)"Left", &i__2, &i__3, &a[ii * a_dim1 + 1], &c__1, &tau[i__], &a[a_offset], lda, + &work[1], (ftnlen)4); i__2 = *m - *n + ii - 1; i__3 = i__; z__1.r = -tau[i__3].r, z__1.i = -tau[i__3].i; @@ -240,23 +63,14 @@ f"> */ i__3 = i__; z__1.r = 1. - tau[i__3].r, z__1.i = 0. - tau[i__3].i; a[i__2].r = z__1.r, a[i__2].i = z__1.i; - -/* Set A(m-k+i+1:m,n-k+i) to zero */ - i__2 = *m; for (l = *m - *n + ii + 1; l <= i__2; ++l) { i__3 = l + ii * a_dim1; a[i__3].r = 0., a[i__3].i = 0.; -/* L30: */ } -/* L40: */ } return 0; - -/* End of ZUNG2L */ - -} /* zung2l_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zung2r.cpp b/lib/linalg/zung2r.cpp index 044df4d2b0..20b7b0957e 100644 --- a/lib/linalg/zung2r.cpp +++ b/lib/linalg/zung2r.cpp @@ -1,187 +1,23 @@ -/* fortran/zung2r.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; - -/* > \brief \b ZUNG2R */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZUNG2R + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZUNG2R( M, N, K, A, LDA, TAU, WORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INFO, K, LDA, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZUNG2R generates an m by n complex matrix Q with orthonormal columns, */ -/* > which is defined as the first n columns of a product of k elementary */ -/* > reflectors of order m */ -/* > */ -/* > Q = H(1) H(2) . . . H(k) */ -/* > */ -/* > as returned by ZGEQRF. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix Q. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix Q. M >= N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > The number of elementary reflectors whose product defines the */ -/* > matrix Q. N >= K >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is COMPLEX*16 array, dimension (LDA,N) */ -/* > On entry, the i-th column must contain the vector which */ -/* > defines the elementary reflector H(i), for i = 1,2,...,k, as */ -/* > returned by ZGEQRF in the first k columns of its array */ -/* > argument A. */ -/* > On exit, the m by n matrix Q. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The first dimension of the array A. LDA >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TAU */ -/* > \verbatim */ -/* > TAU is COMPLEX*16 array, dimension (K) */ -/* > TAU(i) must contain the scalar factor of the elementary */ -/* > reflector H(i), as returned by ZGEQRF. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is COMPLEX*16 array, dimension (N) */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument has an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16OTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int zung2r_(integer *m, integer *n, integer *k, - doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex * - work, integer *info) +int zung2r_(integer *m, integer *n, integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, + doublecomplex *work, integer *info) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; doublecomplex z__1; - - /* Local variables */ integer i__, j, l; - extern /* Subroutine */ int zscal_(integer *, doublecomplex *, - doublecomplex *, integer *), zlarf_(char *, integer *, integer *, - doublecomplex *, integer *, doublecomplex *, doublecomplex *, - integer *, doublecomplex *, ftnlen), xerbla_(char *, integer *, - ftnlen); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments */ - - /* Parameter adjustments */ + extern int zscal_(integer *, doublecomplex *, doublecomplex *, integer *), + zlarf_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, + doublecomplex *, integer *, doublecomplex *, ftnlen), + xerbla_(char *, integer *, ftnlen); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --tau; --work; - - /* Function Body */ *info = 0; if (*m < 0) { *info = -1; @@ -189,7 +25,7 @@ f"> */ *info = -2; } else if (*k < 0 || *k > *n) { *info = -3; - } else if (*lda < max(1,*m)) { + } else if (*lda < max(1, *m)) { *info = -5; } if (*info != 0) { @@ -197,40 +33,27 @@ f"> */ xerbla_((char *)"ZUNG2R", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*n <= 0) { return 0; } - -/* Initialise columns k+1:n to columns of the unit matrix */ - i__1 = *n; for (j = *k + 1; j <= i__1; ++j) { i__2 = *m; for (l = 1; l <= i__2; ++l) { i__3 = l + j * a_dim1; a[i__3].r = 0., a[i__3].i = 0.; -/* L10: */ } i__2 = j + j * a_dim1; a[i__2].r = 1., a[i__2].i = 0.; -/* L20: */ } - for (i__ = *k; i__ >= 1; --i__) { - -/* Apply H(i) to A(i:m,i:n) from the left */ - if (i__ < *n) { i__1 = i__ + i__ * a_dim1; a[i__1].r = 1., a[i__1].i = 0.; i__1 = *m - i__ + 1; i__2 = *n - i__; - zlarf_((char *)"Left", &i__1, &i__2, &a[i__ + i__ * a_dim1], &c__1, &tau[ - i__], &a[i__ + (i__ + 1) * a_dim1], lda, &work[1], ( - ftnlen)4); + zlarf_((char *)"Left", &i__1, &i__2, &a[i__ + i__ * a_dim1], &c__1, &tau[i__], + &a[i__ + (i__ + 1) * a_dim1], lda, &work[1], (ftnlen)4); } if (i__ < *m) { i__1 = *m - i__; @@ -242,23 +65,14 @@ f"> */ i__2 = i__; z__1.r = 1. - tau[i__2].r, z__1.i = 0. - tau[i__2].i; a[i__1].r = z__1.r, a[i__1].i = z__1.i; - -/* Set A(1:i-1,i) to zero */ - i__1 = i__ - 1; for (l = 1; l <= i__1; ++l) { i__2 = l + i__ * a_dim1; a[i__2].r = 0., a[i__2].i = 0.; -/* L30: */ } -/* L40: */ } return 0; - -/* End of ZUNG2R */ - -} /* zung2r_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zungl2.cpp b/lib/linalg/zungl2.cpp index 44213e5927..7ac8d65292 100644 --- a/lib/linalg/zungl2.cpp +++ b/lib/linalg/zungl2.cpp @@ -1,186 +1,23 @@ -/* fortran/zungl2.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* > \brief \b ZUNGL2 generates all or part of the unitary matrix Q from an LQ factorization determined by cge -lqf (unblocked algorithm). */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZUNGL2 + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZUNGL2( M, N, K, A, LDA, TAU, WORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INFO, K, LDA, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZUNGL2 generates an m-by-n complex matrix Q with orthonormal rows, */ -/* > which is defined as the first m rows of a product of k elementary */ -/* > reflectors of order n */ -/* > */ -/* > Q = H(k)**H . . . H(2)**H H(1)**H */ -/* > */ -/* > as returned by ZGELQF. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix Q. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix Q. N >= M. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > The number of elementary reflectors whose product defines the */ -/* > matrix Q. M >= K >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is COMPLEX*16 array, dimension (LDA,N) */ -/* > On entry, the i-th row must contain the vector which defines */ -/* > the elementary reflector H(i), for i = 1,2,...,k, as returned */ -/* > by ZGELQF in the first k rows of its array argument A. */ -/* > On exit, the m by n matrix Q. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The first dimension of the array A. LDA >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TAU */ -/* > \verbatim */ -/* > TAU is COMPLEX*16 array, dimension (K) */ -/* > TAU(i) must contain the scalar factor of the elementary */ -/* > reflector H(i), as returned by ZGELQF. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is COMPLEX*16 array, dimension (M) */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument has an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16OTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int zungl2_(integer *m, integer *n, integer *k, - doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex * - work, integer *info) +int zungl2_(integer *m, integer *n, integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, + doublecomplex *work, integer *info) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; doublecomplex z__1, z__2; - - /* Builtin functions */ void d_lmp_cnjg(doublecomplex *, doublecomplex *); - - /* Local variables */ integer i__, j, l; - extern /* Subroutine */ int zscal_(integer *, doublecomplex *, - doublecomplex *, integer *), zlarf_(char *, integer *, integer *, - doublecomplex *, integer *, doublecomplex *, doublecomplex *, - integer *, doublecomplex *, ftnlen), xerbla_(char *, integer *, - ftnlen), zlacgv_(integer *, doublecomplex *, integer *); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments */ - - /* Parameter adjustments */ + extern int zscal_(integer *, doublecomplex *, doublecomplex *, integer *), + zlarf_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, + doublecomplex *, integer *, doublecomplex *, ftnlen), + xerbla_(char *, integer *, ftnlen), zlacgv_(integer *, doublecomplex *, integer *); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --tau; --work; - - /* Function Body */ *info = 0; if (*m < 0) { *info = -1; @@ -188,7 +25,7 @@ f"> */ *info = -2; } else if (*k < 0 || *k > *m) { *info = -3; - } else if (*lda < max(1,*m)) { + } else if (*lda < max(1, *m)) { *info = -5; } if (*info != 0) { @@ -196,37 +33,24 @@ f"> */ xerbla_((char *)"ZUNGL2", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*m <= 0) { return 0; } - if (*k < *m) { - -/* Initialise rows k+1:m to rows of the unit matrix */ - i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (l = *k + 1; l <= i__2; ++l) { i__3 = l + j * a_dim1; a[i__3].r = 0., a[i__3].i = 0.; -/* L10: */ } if (j > *k && j <= *m) { i__2 = j + j * a_dim1; a[i__2].r = 1., a[i__2].i = 0.; } -/* L20: */ } } - for (i__ = *k; i__ >= 1; --i__) { - -/* Apply H(i)**H to A(i:m,i:n) from the right */ - if (i__ < *n) { i__1 = *n - i__; zlacgv_(&i__1, &a[i__ + (i__ + 1) * a_dim1], lda); @@ -236,9 +60,8 @@ f"> */ i__1 = *m - i__; i__2 = *n - i__ + 1; d_lmp_cnjg(&z__1, &tau[i__]); - zlarf_((char *)"Right", &i__1, &i__2, &a[i__ + i__ * a_dim1], lda, & - z__1, &a[i__ + 1 + i__ * a_dim1], lda, &work[1], ( - ftnlen)5); + zlarf_((char *)"Right", &i__1, &i__2, &a[i__ + i__ * a_dim1], lda, &z__1, + &a[i__ + 1 + i__ * a_dim1], lda, &work[1], (ftnlen)5); } i__1 = *n - i__; i__2 = i__; @@ -251,23 +74,14 @@ f"> */ d_lmp_cnjg(&z__2, &tau[i__]); z__1.r = 1. - z__2.r, z__1.i = 0. - z__2.i; a[i__1].r = z__1.r, a[i__1].i = z__1.i; - -/* Set A(i,1:i-1) to zero */ - i__1 = i__ - 1; for (l = 1; l <= i__1; ++l) { i__2 = i__ + l * a_dim1; a[i__2].r = 0., a[i__2].i = 0.; -/* L30: */ } -/* L40: */ } return 0; - -/* End of ZUNGL2 */ - -} /* zungl2_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zungql.cpp b/lib/linalg/zungql.cpp index 8ee03838d4..4250c31d03 100644 --- a/lib/linalg/zungql.cpp +++ b/lib/linalg/zungql.cpp @@ -1,215 +1,34 @@ -/* fortran/zungql.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static integer c_n1 = -1; static integer c__3 = 3; static integer c__2 = 2; - -/* > \brief \b ZUNGQL */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZUNGQL + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZUNGQL( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INFO, K, LDA, LWORK, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZUNGQL generates an M-by-N complex matrix Q with orthonormal columns, */ -/* > which is defined as the last N columns of a product of K elementary */ -/* > reflectors of order M */ -/* > */ -/* > Q = H(k) . . . H(2) H(1) */ -/* > */ -/* > as returned by ZGEQLF. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix Q. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix Q. M >= N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > The number of elementary reflectors whose product defines the */ -/* > matrix Q. N >= K >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is COMPLEX*16 array, dimension (LDA,N) */ -/* > On entry, the (n-k+i)-th column must contain the vector which */ -/* > defines the elementary reflector H(i), for i = 1,2,...,k, as */ -/* > returned by ZGEQLF in the last k columns of its array */ -/* > argument A. */ -/* > On exit, the M-by-N matrix Q. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The first dimension of the array A. LDA >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TAU */ -/* > \verbatim */ -/* > TAU is COMPLEX*16 array, dimension (K) */ -/* > TAU(i) must contain the scalar factor of the elementary */ -/* > reflector H(i), as returned by ZGEQLF. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) */ -/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LWORK */ -/* > \verbatim */ -/* > LWORK is INTEGER */ -/* > The dimension of the array WORK. LWORK >= max(1,N). */ -/* > For optimum performance LWORK >= N*NB, where NB is the */ -/* > optimal blocksize. */ -/* > */ -/* > If LWORK = -1, then a workspace query is assumed; the routine */ -/* > only calculates the optimal size of the WORK array, returns */ -/* > this value as the first entry of the WORK array, and no error */ -/* > message related to LWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument has an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16OTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int zungql_(integer *m, integer *n, integer *k, - doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex * - work, integer *lwork, integer *info) +int zungql_(integer *m, integer *n, integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, + doublecomplex *work, integer *lwork, integer *info) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5; - - /* Local variables */ integer i__, j, l, ib, nb, kk, nx, iws, nbmin, iinfo; - extern /* Subroutine */ int zung2l_(integer *, integer *, integer *, - doublecomplex *, integer *, doublecomplex *, doublecomplex *, - integer *), xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *, - integer *, integer *, integer *, doublecomplex *, integer *, - doublecomplex *, integer *, doublecomplex *, integer *, - doublecomplex *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + extern int zung2l_(integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, + doublecomplex *, integer *), + xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); + extern int zlarfb_(char *, char *, char *, char *, integer *, integer *, integer *, + doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, + integer *, doublecomplex *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); integer ldwork; - extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *, - doublecomplex *, integer *, doublecomplex *, doublecomplex *, - integer *, ftnlen, ftnlen); + extern int zlarft_(char *, char *, integer *, integer *, doublecomplex *, integer *, + doublecomplex *, doublecomplex *, integer *, ftnlen, ftnlen); logical lquery; integer lwkopt; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --tau; --work; - - /* Function Body */ *info = 0; lquery = *lwork == -1; if (*m < 0) { @@ -218,25 +37,21 @@ f"> */ *info = -2; } else if (*k < 0 || *k > *n) { *info = -3; - } else if (*lda < max(1,*m)) { + } else if (*lda < max(1, *m)) { *info = -5; } - if (*info == 0) { if (*n == 0) { lwkopt = 1; } else { - nb = ilaenv_(&c__1, (char *)"ZUNGQL", (char *)" ", m, n, k, &c_n1, (ftnlen)6, ( - ftnlen)1); + nb = ilaenv_(&c__1, (char *)"ZUNGQL", (char *)" ", m, n, k, &c_n1, (ftnlen)6, (ftnlen)1); lwkopt = *n * nb; } - work[1].r = (doublereal) lwkopt, work[1].i = 0.; - - if (*lwork < max(1,*n) && ! lquery) { + work[1].r = (doublereal)lwkopt, work[1].i = 0.; + if (*lwork < max(1, *n) && !lquery) { *info = -8; } } - if (*info != 0) { i__1 = -(*info); xerbla_((char *)"ZUNGQL", &i__1, (ftnlen)6); @@ -244,138 +59,76 @@ f"> */ } else if (lquery) { return 0; } - -/* Quick return if possible */ - if (*n <= 0) { return 0; } - nbmin = 2; nx = 0; iws = *n; if (nb > 1 && nb < *k) { - -/* Determine when to cross over from blocked to unblocked code. */ - -/* Computing MAX */ - i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"ZUNGQL", (char *)" ", m, n, k, &c_n1, ( - ftnlen)6, (ftnlen)1); - nx = max(i__1,i__2); + i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"ZUNGQL", (char *)" ", m, n, k, &c_n1, (ftnlen)6, (ftnlen)1); + nx = max(i__1, i__2); if (nx < *k) { - -/* Determine if workspace is large enough for blocked code. */ - ldwork = *n; iws = ldwork * nb; if (*lwork < iws) { - -/* Not enough workspace to use optimal NB: reduce NB and */ -/* determine the minimum value of NB. */ - nb = *lwork / ldwork; -/* Computing MAX */ - i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"ZUNGQL", (char *)" ", m, n, k, &c_n1, - (ftnlen)6, (ftnlen)1); - nbmin = max(i__1,i__2); + i__1 = 2, + i__2 = ilaenv_(&c__2, (char *)"ZUNGQL", (char *)" ", m, n, k, &c_n1, (ftnlen)6, (ftnlen)1); + nbmin = max(i__1, i__2); } } } - if (nb >= nbmin && nb < *k && nx < *k) { - -/* Use blocked code after the first block. */ -/* The last kk columns are handled by the block method. */ - -/* Computing MIN */ i__1 = *k, i__2 = (*k - nx + nb - 1) / nb * nb; - kk = min(i__1,i__2); - -/* Set A(m-kk+1:m,1:n-kk) to zero. */ - + kk = min(i__1, i__2); i__1 = *n - kk; for (j = 1; j <= i__1; ++j) { i__2 = *m; for (i__ = *m - kk + 1; i__ <= i__2; ++i__) { i__3 = i__ + j * a_dim1; a[i__3].r = 0., a[i__3].i = 0.; -/* L10: */ } -/* L20: */ } } else { kk = 0; } - -/* Use unblocked code for the first or only block. */ - i__1 = *m - kk; i__2 = *n - kk; i__3 = *k - kk; - zung2l_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], &work[1], &iinfo) - ; - + zung2l_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], &work[1], &iinfo); if (kk > 0) { - -/* Use blocked code */ - i__1 = *k; i__2 = nb; - for (i__ = *k - kk + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += - i__2) { -/* Computing MIN */ + for (i__ = *k - kk + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { i__3 = nb, i__4 = *k - i__ + 1; - ib = min(i__3,i__4); + ib = min(i__3, i__4); if (*n - *k + i__ > 1) { - -/* Form the triangular factor of the block reflector */ -/* H = H(i+ib-1) . . . H(i+1) H(i) */ - i__3 = *m - *k + i__ + ib - 1; - zlarft_((char *)"Backward", (char *)"Columnwise", &i__3, &ib, &a[(*n - *k + - i__) * a_dim1 + 1], lda, &tau[i__], &work[1], &ldwork, - (ftnlen)8, (ftnlen)10); - -/* Apply H to A(1:m-k+i+ib-1,1:n-k+i-1) from the left */ - + zlarft_((char *)"Backward", (char *)"Columnwise", &i__3, &ib, &a[(*n - *k + i__) * a_dim1 + 1], lda, + &tau[i__], &work[1], &ldwork, (ftnlen)8, (ftnlen)10); i__3 = *m - *k + i__ + ib - 1; i__4 = *n - *k + i__ - 1; - zlarfb_((char *)"Left", (char *)"No transpose", (char *)"Backward", (char *)"Columnwise", & - i__3, &i__4, &ib, &a[(*n - *k + i__) * a_dim1 + 1], - lda, &work[1], &ldwork, &a[a_offset], lda, &work[ib + - 1], &ldwork, (ftnlen)4, (ftnlen)12, (ftnlen)8, ( - ftnlen)10); + zlarfb_((char *)"Left", (char *)"No transpose", (char *)"Backward", (char *)"Columnwise", &i__3, &i__4, &ib, + &a[(*n - *k + i__) * a_dim1 + 1], lda, &work[1], &ldwork, &a[a_offset], lda, + &work[ib + 1], &ldwork, (ftnlen)4, (ftnlen)12, (ftnlen)8, (ftnlen)10); } - -/* Apply H to rows 1:m-k+i+ib-1 of current block */ - i__3 = *m - *k + i__ + ib - 1; - zung2l_(&i__3, &ib, &ib, &a[(*n - *k + i__) * a_dim1 + 1], lda, & - tau[i__], &work[1], &iinfo); - -/* Set rows m-k+i+ib:m of current block to zero */ - + zung2l_(&i__3, &ib, &ib, &a[(*n - *k + i__) * a_dim1 + 1], lda, &tau[i__], &work[1], + &iinfo); i__3 = *n - *k + i__ + ib - 1; for (j = *n - *k + i__; j <= i__3; ++j) { i__4 = *m; for (l = *m - *k + i__ + ib; l <= i__4; ++l) { i__5 = l + j * a_dim1; a[i__5].r = 0., a[i__5].i = 0.; -/* L30: */ } -/* L40: */ } -/* L50: */ } } - - work[1].r = (doublereal) iws, work[1].i = 0.; + work[1].r = (doublereal)iws, work[1].i = 0.; return 0; - -/* End of ZUNGQL */ - -} /* zungql_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zungqr.cpp b/lib/linalg/zungqr.cpp index a79c87eedd..5368d9130d 100644 --- a/lib/linalg/zungqr.cpp +++ b/lib/linalg/zungqr.cpp @@ -1,219 +1,38 @@ -/* fortran/zungqr.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static integer c_n1 = -1; static integer c__3 = 3; static integer c__2 = 2; - -/* > \brief \b ZUNGQR */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZUNGQR + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZUNGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* INTEGER INFO, K, LDA, LWORK, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZUNGQR generates an M-by-N complex matrix Q with orthonormal columns, */ -/* > which is defined as the first N columns of a product of K elementary */ -/* > reflectors of order M */ -/* > */ -/* > Q = H(1) H(2) . . . H(k) */ -/* > */ -/* > as returned by ZGEQRF. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix Q. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix Q. M >= N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > The number of elementary reflectors whose product defines the */ -/* > matrix Q. N >= K >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is COMPLEX*16 array, dimension (LDA,N) */ -/* > On entry, the i-th column must contain the vector which */ -/* > defines the elementary reflector H(i), for i = 1,2,...,k, as */ -/* > returned by ZGEQRF in the first k columns of its array */ -/* > argument A. */ -/* > On exit, the M-by-N matrix Q. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The first dimension of the array A. LDA >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TAU */ -/* > \verbatim */ -/* > TAU is COMPLEX*16 array, dimension (K) */ -/* > TAU(i) must contain the scalar factor of the elementary */ -/* > reflector H(i), as returned by ZGEQRF. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) */ -/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LWORK */ -/* > \verbatim */ -/* > LWORK is INTEGER */ -/* > The dimension of the array WORK. LWORK >= max(1,N). */ -/* > For optimum performance LWORK >= N*NB, where NB is the */ -/* > optimal blocksize. */ -/* > */ -/* > If LWORK = -1, then a workspace query is assumed; the routine */ -/* > only calculates the optimal size of the WORK array, returns */ -/* > this value as the first entry of the WORK array, and no error */ -/* > message related to LWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument has an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16OTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int zungqr_(integer *m, integer *n, integer *k, - doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex * - work, integer *lwork, integer *info) +int zungqr_(integer *m, integer *n, integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, + doublecomplex *work, integer *lwork, integer *info) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4; - - /* Local variables */ integer i__, j, l, ib, nb, ki, kk, nx, iws, nbmin, iinfo; - extern /* Subroutine */ int zung2r_(integer *, integer *, integer *, - doublecomplex *, integer *, doublecomplex *, doublecomplex *, - integer *), xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *, - integer *, integer *, integer *, doublecomplex *, integer *, - doublecomplex *, integer *, doublecomplex *, integer *, - doublecomplex *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + extern int zung2r_(integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, + doublecomplex *, integer *), + xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); + extern int zlarfb_(char *, char *, char *, char *, integer *, integer *, integer *, + doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, + integer *, doublecomplex *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); integer ldwork; - extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *, - doublecomplex *, integer *, doublecomplex *, doublecomplex *, - integer *, ftnlen, ftnlen); + extern int zlarft_(char *, char *, integer *, integer *, doublecomplex *, integer *, + doublecomplex *, doublecomplex *, integer *, ftnlen, ftnlen); integer lwkopt; logical lquery; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --tau; --work; - - /* Function Body */ *info = 0; nb = ilaenv_(&c__1, (char *)"ZUNGQR", (char *)" ", m, n, k, &c_n1, (ftnlen)6, (ftnlen)1); - lwkopt = max(1,*n) * nb; - work[1].r = (doublereal) lwkopt, work[1].i = 0.; + lwkopt = max(1, *n) * nb; + work[1].r = (doublereal)lwkopt, work[1].i = 0.; lquery = *lwork == -1; if (*m < 0) { *info = -1; @@ -221,9 +40,9 @@ f"> */ *info = -2; } else if (*k < 0 || *k > *n) { *info = -3; - } else if (*lda < max(1,*m)) { + } else if (*lda < max(1, *m)) { *info = -5; - } else if (*lwork < max(1,*n) && ! lquery) { + } else if (*lwork < max(1, *n) && !lquery) { *info = -8; } if (*info != 0) { @@ -233,140 +52,80 @@ f"> */ } else if (lquery) { return 0; } - -/* Quick return if possible */ - if (*n <= 0) { work[1].r = 1., work[1].i = 0.; return 0; } - nbmin = 2; nx = 0; iws = *n; if (nb > 1 && nb < *k) { - -/* Determine when to cross over from blocked to unblocked code. */ - -/* Computing MAX */ - i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"ZUNGQR", (char *)" ", m, n, k, &c_n1, ( - ftnlen)6, (ftnlen)1); - nx = max(i__1,i__2); + i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"ZUNGQR", (char *)" ", m, n, k, &c_n1, (ftnlen)6, (ftnlen)1); + nx = max(i__1, i__2); if (nx < *k) { - -/* Determine if workspace is large enough for blocked code. */ - ldwork = *n; iws = ldwork * nb; if (*lwork < iws) { - -/* Not enough workspace to use optimal NB: reduce NB and */ -/* determine the minimum value of NB. */ - nb = *lwork / ldwork; -/* Computing MAX */ - i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"ZUNGQR", (char *)" ", m, n, k, &c_n1, - (ftnlen)6, (ftnlen)1); - nbmin = max(i__1,i__2); + i__1 = 2, + i__2 = ilaenv_(&c__2, (char *)"ZUNGQR", (char *)" ", m, n, k, &c_n1, (ftnlen)6, (ftnlen)1); + nbmin = max(i__1, i__2); } } } - if (nb >= nbmin && nb < *k && nx < *k) { - -/* Use blocked code after the last block. */ -/* The first kk columns are handled by the block method. */ - ki = (*k - nx - 1) / nb * nb; -/* Computing MIN */ i__1 = *k, i__2 = ki + nb; - kk = min(i__1,i__2); - -/* Set A(1:kk,kk+1:n) to zero. */ - + kk = min(i__1, i__2); i__1 = *n; for (j = kk + 1; j <= i__1; ++j) { i__2 = kk; for (i__ = 1; i__ <= i__2; ++i__) { i__3 = i__ + j * a_dim1; a[i__3].r = 0., a[i__3].i = 0.; -/* L10: */ } -/* L20: */ } } else { kk = 0; } - -/* Use unblocked code for the last or only block. */ - if (kk < *n) { i__1 = *m - kk; i__2 = *n - kk; i__3 = *k - kk; - zung2r_(&i__1, &i__2, &i__3, &a[kk + 1 + (kk + 1) * a_dim1], lda, & - tau[kk + 1], &work[1], &iinfo); + zung2r_(&i__1, &i__2, &i__3, &a[kk + 1 + (kk + 1) * a_dim1], lda, &tau[kk + 1], &work[1], + &iinfo); } - if (kk > 0) { - -/* Use blocked code */ - i__1 = -nb; for (i__ = ki + 1; i__1 < 0 ? i__ >= 1 : i__ <= 1; i__ += i__1) { -/* Computing MIN */ i__2 = nb, i__3 = *k - i__ + 1; - ib = min(i__2,i__3); + ib = min(i__2, i__3); if (i__ + ib <= *n) { - -/* Form the triangular factor of the block reflector */ -/* H = H(i) H(i+1) . . . H(i+ib-1) */ - i__2 = *m - i__ + 1; - zlarft_((char *)"Forward", (char *)"Columnwise", &i__2, &ib, &a[i__ + i__ * - a_dim1], lda, &tau[i__], &work[1], &ldwork, (ftnlen)7, - (ftnlen)10); - -/* Apply H to A(i:m,i+ib:n) from the left */ - + zlarft_((char *)"Forward", (char *)"Columnwise", &i__2, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], + &work[1], &ldwork, (ftnlen)7, (ftnlen)10); i__2 = *m - i__ + 1; i__3 = *n - i__ - ib + 1; - zlarfb_((char *)"Left", (char *)"No transpose", (char *)"Forward", (char *)"Columnwise", & - i__2, &i__3, &ib, &a[i__ + i__ * a_dim1], lda, &work[ - 1], &ldwork, &a[i__ + (i__ + ib) * a_dim1], lda, & - work[ib + 1], &ldwork, (ftnlen)4, (ftnlen)12, (ftnlen) - 7, (ftnlen)10); + zlarfb_((char *)"Left", (char *)"No transpose", (char *)"Forward", (char *)"Columnwise", &i__2, &i__3, &ib, + &a[i__ + i__ * a_dim1], lda, &work[1], &ldwork, + &a[i__ + (i__ + ib) * a_dim1], lda, &work[ib + 1], &ldwork, (ftnlen)4, + (ftnlen)12, (ftnlen)7, (ftnlen)10); } - -/* Apply H to rows i:m of current block */ - i__2 = *m - i__ + 1; - zung2r_(&i__2, &ib, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], & - work[1], &iinfo); - -/* Set rows 1:i-1 of current block to zero */ - + zung2r_(&i__2, &ib, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[1], &iinfo); i__2 = i__ + ib - 1; for (j = i__; j <= i__2; ++j) { i__3 = i__ - 1; for (l = 1; l <= i__3; ++l) { i__4 = l + j * a_dim1; a[i__4].r = 0., a[i__4].i = 0.; -/* L30: */ } -/* L40: */ } -/* L50: */ } } - - work[1].r = (doublereal) iws, work[1].i = 0.; + work[1].r = (doublereal)iws, work[1].i = 0.; return 0; - -/* End of ZUNGQR */ - -} /* zungqr_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zungtr.cpp b/lib/linalg/zungtr.cpp index 86c03cb474..9a2ba97b64 100644 --- a/lib/linalg/zungtr.cpp +++ b/lib/linalg/zungtr.cpp @@ -1,243 +1,62 @@ -/* fortran/zungtr.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static integer c_n1 = -1; - -/* > \brief \b ZUNGTR */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZUNGTR + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZUNGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER UPLO */ -/* INTEGER INFO, LDA, LWORK, N */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZUNGTR generates a complex unitary matrix Q which is defined as the */ -/* > product of n-1 elementary reflectors of order N, as returned by */ -/* > ZHETRD: */ -/* > */ -/* > if UPLO = 'U', Q = H(n-1) . . . H(2) H(1), */ -/* > */ -/* > if UPLO = 'L', Q = H(1) H(2) . . . H(n-1). */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > = 'U': Upper triangle of A contains elementary reflectors */ -/* > from ZHETRD; */ -/* > = 'L': Lower triangle of A contains elementary reflectors */ -/* > from ZHETRD. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The order of the matrix Q. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] A */ -/* > \verbatim */ -/* > A is COMPLEX*16 array, dimension (LDA,N) */ -/* > On entry, the vectors which define the elementary reflectors, */ -/* > as returned by ZHETRD. */ -/* > On exit, the N-by-N unitary matrix Q. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. LDA >= N. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TAU */ -/* > \verbatim */ -/* > TAU is COMPLEX*16 array, dimension (N-1) */ -/* > TAU(i) must contain the scalar factor of the elementary */ -/* > reflector H(i), as returned by ZHETRD. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) */ -/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LWORK */ -/* > \verbatim */ -/* > LWORK is INTEGER */ -/* > The dimension of the array WORK. LWORK >= N-1. */ -/* > For optimum performance LWORK >= (N-1)*NB, where NB is */ -/* > the optimal blocksize. */ -/* > */ -/* > If LWORK = -1, then a workspace query is assumed; the routine */ -/* > only calculates the optimal size of the WORK array, returns */ -/* > this value as the first entry of the WORK array, and no error */ -/* > message related to LWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16OTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int zungtr_(char *uplo, integer *n, doublecomplex *a, - integer *lda, doublecomplex *tau, doublecomplex *work, integer *lwork, - integer *info, ftnlen uplo_len) +int zungtr_(char *uplo, integer *n, doublecomplex *a, integer *lda, doublecomplex *tau, + doublecomplex *work, integer *lwork, integer *info, ftnlen uplo_len) { - /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4; - - /* Local variables */ integer i__, j, nb; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer iinfo; logical upper; - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern int xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); integer lwkopt; logical lquery; - extern /* Subroutine */ int zungql_(integer *, integer *, integer *, - doublecomplex *, integer *, doublecomplex *, doublecomplex *, - integer *, integer *), zungqr_(integer *, integer *, integer *, - doublecomplex *, integer *, doublecomplex *, doublecomplex *, - integer *, integer *); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments */ - - /* Parameter adjustments */ + extern int zungql_(integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, + doublecomplex *, integer *, integer *), + zungqr_(integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, + doublecomplex *, integer *, integer *); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --tau; --work; - - /* Function Body */ *info = 0; lquery = *lwork == -1; upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); - if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + if (!upper && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { *info = -1; } else if (*n < 0) { *info = -2; - } else if (*lda < max(1,*n)) { + } else if (*lda < max(1, *n)) { *info = -4; - } else /* if(complicated condition) */ { -/* Computing MAX */ + } else { i__1 = 1, i__2 = *n - 1; - if (*lwork < max(i__1,i__2) && ! lquery) { + if (*lwork < max(i__1, i__2) && !lquery) { *info = -7; } } - if (*info == 0) { if (upper) { i__1 = *n - 1; i__2 = *n - 1; i__3 = *n - 1; - nb = ilaenv_(&c__1, (char *)"ZUNGQL", (char *)" ", &i__1, &i__2, &i__3, &c_n1, ( - ftnlen)6, (ftnlen)1); + nb = ilaenv_(&c__1, (char *)"ZUNGQL", (char *)" ", &i__1, &i__2, &i__3, &c_n1, (ftnlen)6, (ftnlen)1); } else { i__1 = *n - 1; i__2 = *n - 1; i__3 = *n - 1; - nb = ilaenv_(&c__1, (char *)"ZUNGQR", (char *)" ", &i__1, &i__2, &i__3, &c_n1, ( - ftnlen)6, (ftnlen)1); + nb = ilaenv_(&c__1, (char *)"ZUNGQR", (char *)" ", &i__1, &i__2, &i__3, &c_n1, (ftnlen)6, (ftnlen)1); } -/* Computing MAX */ i__1 = 1, i__2 = *n - 1; - lwkopt = max(i__1,i__2) * nb; - work[1].r = (doublereal) lwkopt, work[1].i = 0.; + lwkopt = max(i__1, i__2) * nb; + work[1].r = (doublereal)lwkopt, work[1].i = 0.; } - if (*info != 0) { i__1 = -(*info); xerbla_((char *)"ZUNGTR", &i__1, (ftnlen)6); @@ -245,22 +64,11 @@ f"> */ } else if (lquery) { return 0; } - -/* Quick return if possible */ - if (*n == 0) { work[1].r = 1., work[1].i = 0.; return 0; } - if (upper) { - -/* Q was determined by a call to ZHETRD with UPLO = 'U' */ - -/* Shift the vectors which define the elementary reflectors one */ -/* column to the left, and set the last row and column of Q to */ -/* those of the unit matrix */ - i__1 = *n - 1; for (j = 1; j <= i__1; ++j) { i__2 = j - 1; @@ -268,37 +76,22 @@ f"> */ i__3 = i__ + j * a_dim1; i__4 = i__ + (j + 1) * a_dim1; a[i__3].r = a[i__4].r, a[i__3].i = a[i__4].i; -/* L10: */ } i__2 = *n + j * a_dim1; a[i__2].r = 0., a[i__2].i = 0.; -/* L20: */ } i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = i__ + *n * a_dim1; a[i__2].r = 0., a[i__2].i = 0.; -/* L30: */ } i__1 = *n + *n * a_dim1; a[i__1].r = 1., a[i__1].i = 0.; - -/* Generate Q(1:n-1,1:n-1) */ - i__1 = *n - 1; i__2 = *n - 1; i__3 = *n - 1; - zungql_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], &work[1], - lwork, &iinfo); - + zungql_(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], &work[1], lwork, &iinfo); } else { - -/* Q was determined by a call to ZHETRD with UPLO = 'L'. */ - -/* Shift the vectors which define the elementary reflectors one */ -/* column to the right, and set the first row and column of Q to */ -/* those of the unit matrix */ - for (j = *n; j >= 2; --j) { i__1 = j * a_dim1 + 1; a[i__1].r = 0., a[i__1].i = 0.; @@ -307,9 +100,7 @@ f"> */ i__2 = i__ + j * a_dim1; i__3 = i__ + (j - 1) * a_dim1; a[i__2].r = a[i__3].r, a[i__2].i = a[i__3].i; -/* L40: */ } -/* L50: */ } i__1 = a_dim1 + 1; a[i__1].r = 1., a[i__1].i = 0.; @@ -317,26 +108,18 @@ f"> */ for (i__ = 2; i__ <= i__1; ++i__) { i__2 = i__ + a_dim1; a[i__2].r = 0., a[i__2].i = 0.; -/* L60: */ } if (*n > 1) { - -/* Generate Q(2:n,2:n) */ - i__1 = *n - 1; i__2 = *n - 1; i__3 = *n - 1; - zungqr_(&i__1, &i__2, &i__3, &a[(a_dim1 << 1) + 2], lda, &tau[1], - &work[1], lwork, &iinfo); + zungqr_(&i__1, &i__2, &i__3, &a[(a_dim1 << 1) + 2], lda, &tau[1], &work[1], lwork, + &iinfo); } } - work[1].r = (doublereal) lwkopt, work[1].i = 0.; + work[1].r = (doublereal)lwkopt, work[1].i = 0.; return 0; - -/* End of ZUNGTR */ - -} /* zungtr_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zunm2l.cpp b/lib/linalg/zunm2l.cpp index 3e5b63f574..6358ee33a3 100644 --- a/lib/linalg/zunm2l.cpp +++ b/lib/linalg/zunm2l.cpp @@ -1,235 +1,24 @@ -/* fortran/zunm2l.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; - -/* > \brief \b ZUNM2L multiplies a general matrix by the unitary matrix from a QL factorization determined by -cgeqlf (unblocked algorithm). */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZUNM2L + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZUNM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, */ -/* WORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER SIDE, TRANS */ -/* INTEGER INFO, K, LDA, LDC, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZUNM2L overwrites the general complex m-by-n matrix C with */ -/* > */ -/* > Q * C if SIDE = 'L' and TRANS = 'N', or */ -/* > */ -/* > Q**H* C if SIDE = 'L' and TRANS = 'C', or */ -/* > */ -/* > C * Q if SIDE = 'R' and TRANS = 'N', or */ -/* > */ -/* > C * Q**H if SIDE = 'R' and TRANS = 'C', */ -/* > */ -/* > where Q is a complex unitary matrix defined as the product of k */ -/* > elementary reflectors */ -/* > */ -/* > Q = H(k) . . . H(2) H(1) */ -/* > */ -/* > as returned by ZGEQLF. Q is of order m if SIDE = 'L' and of order n */ -/* > if SIDE = 'R'. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] SIDE */ -/* > \verbatim */ -/* > SIDE is CHARACTER*1 */ -/* > = 'L': apply Q or Q**H from the Left */ -/* > = 'R': apply Q or Q**H from the Right */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TRANS */ -/* > \verbatim */ -/* > TRANS is CHARACTER*1 */ -/* > = 'N': apply Q (No transpose) */ -/* > = 'C': apply Q**H (Conjugate transpose) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix C. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix C. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > The number of elementary reflectors whose product defines */ -/* > the matrix Q. */ -/* > If SIDE = 'L', M >= K >= 0; */ -/* > if SIDE = 'R', N >= K >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is COMPLEX*16 array, dimension (LDA,K) */ -/* > The i-th column must contain the vector which defines the */ -/* > elementary reflector H(i), for i = 1,2,...,k, as returned by */ -/* > ZGEQLF in the last k columns of its array argument A. */ -/* > A is modified by the routine but restored on exit. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. */ -/* > If SIDE = 'L', LDA >= max(1,M); */ -/* > if SIDE = 'R', LDA >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TAU */ -/* > \verbatim */ -/* > TAU is COMPLEX*16 array, dimension (K) */ -/* > TAU(i) must contain the scalar factor of the elementary */ -/* > reflector H(i), as returned by ZGEQLF. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] C */ -/* > \verbatim */ -/* > C is COMPLEX*16 array, dimension (LDC,N) */ -/* > On entry, the m-by-n matrix C. */ -/* > On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDC */ -/* > \verbatim */ -/* > LDC is INTEGER */ -/* > The leading dimension of the array C. LDC >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is COMPLEX*16 array, dimension */ -/* > (N) if SIDE = 'L', */ -/* > (M) if SIDE = 'R' */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16OTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int zunm2l_(char *side, char *trans, integer *m, integer *n, - integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, - doublecomplex *c__, integer *ldc, doublecomplex *work, integer *info, - ftnlen side_len, ftnlen trans_len) +int zunm2l_(char *side, char *trans, integer *m, integer *n, integer *k, doublecomplex *a, + integer *lda, doublecomplex *tau, doublecomplex *c__, integer *ldc, doublecomplex *work, + integer *info, ftnlen side_len, ftnlen trans_len) { - /* System generated locals */ integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3; doublecomplex z__1; - - /* Builtin functions */ void d_lmp_cnjg(doublecomplex *, doublecomplex *); - - /* Local variables */ integer i__, i1, i2, i3, mi, ni, nq; doublecomplex aii; logical left; doublecomplex taui; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int zlarf_(char *, integer *, integer *, - doublecomplex *, integer *, doublecomplex *, doublecomplex *, - integer *, doublecomplex *, ftnlen), xerbla_(char *, integer *, - ftnlen); + extern int zlarf_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, + doublecomplex *, integer *, doublecomplex *, ftnlen), + xerbla_(char *, integer *, ftnlen); logical notran; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; @@ -238,22 +27,17 @@ f"> */ c_offset = 1 + c_dim1; c__ -= c_offset; --work; - - /* Function Body */ *info = 0; left = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); notran = lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1); - -/* NQ is the order of Q */ - if (left) { nq = *m; } else { nq = *n; } - if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + if (!left && !lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { *info = -1; - } else if (! notran && ! lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { + } else if (!notran && !lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { *info = -2; } else if (*m < 0) { *info = -3; @@ -261,9 +45,9 @@ f"> */ *info = -4; } else if (*k < 0 || *k > nq) { *info = -5; - } else if (*lda < max(1,nq)) { + } else if (*lda < max(1, nq)) { *info = -7; - } else if (*ldc < max(1,*m)) { + } else if (*ldc < max(1, *m)) { *info = -10; } if (*info != 0) { @@ -271,14 +55,10 @@ f"> */ xerbla_((char *)"ZUNM2L", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*m == 0 || *n == 0 || *k == 0) { return 0; } - - if (left && notran || ! left && ! notran) { + if (left && notran || !left && !notran) { i1 = 1; i2 = *k; i3 = 1; @@ -287,30 +67,19 @@ f"> */ i2 = 1; i3 = -1; } - if (left) { ni = *n; } else { mi = *m; } - i__1 = i2; i__2 = i3; for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { if (left) { - -/* H(i) or H(i)**H is applied to C(1:m-k+i,1:n) */ - mi = *m - *k + i__; } else { - -/* H(i) or H(i)**H is applied to C(1:m,1:n-k+i) */ - ni = *n - *k + i__; } - -/* Apply H(i) or H(i)**H */ - if (notran) { i__3 = i__; taui.r = tau[i__3].r, taui.i = tau[i__3].i; @@ -322,18 +91,13 @@ f"> */ aii.r = a[i__3].r, aii.i = a[i__3].i; i__3 = nq - *k + i__ + i__ * a_dim1; a[i__3].r = 1., a[i__3].i = 0.; - zlarf_(side, &mi, &ni, &a[i__ * a_dim1 + 1], &c__1, &taui, &c__[ - c_offset], ldc, &work[1], (ftnlen)1); + zlarf_(side, &mi, &ni, &a[i__ * a_dim1 + 1], &c__1, &taui, &c__[c_offset], ldc, &work[1], + (ftnlen)1); i__3 = nq - *k + i__ + i__ * a_dim1; a[i__3].r = aii.r, a[i__3].i = aii.i; -/* L10: */ } return 0; - -/* End of ZUNM2L */ - -} /* zunm2l_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zunm2r.cpp b/lib/linalg/zunm2r.cpp index cbfdfb2f42..e1c04b13f5 100644 --- a/lib/linalg/zunm2r.cpp +++ b/lib/linalg/zunm2r.cpp @@ -1,235 +1,24 @@ -/* fortran/zunm2r.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; - -/* > \brief \b ZUNM2R multiplies a general matrix by the unitary matrix from a QR factorization determined by -cgeqrf (unblocked algorithm). */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZUNM2R + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZUNM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, */ -/* WORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER SIDE, TRANS */ -/* INTEGER INFO, K, LDA, LDC, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZUNM2R overwrites the general complex m-by-n matrix C with */ -/* > */ -/* > Q * C if SIDE = 'L' and TRANS = 'N', or */ -/* > */ -/* > Q**H* C if SIDE = 'L' and TRANS = 'C', or */ -/* > */ -/* > C * Q if SIDE = 'R' and TRANS = 'N', or */ -/* > */ -/* > C * Q**H if SIDE = 'R' and TRANS = 'C', */ -/* > */ -/* > where Q is a complex unitary matrix defined as the product of k */ -/* > elementary reflectors */ -/* > */ -/* > Q = H(1) H(2) . . . H(k) */ -/* > */ -/* > as returned by ZGEQRF. Q is of order m if SIDE = 'L' and of order n */ -/* > if SIDE = 'R'. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] SIDE */ -/* > \verbatim */ -/* > SIDE is CHARACTER*1 */ -/* > = 'L': apply Q or Q**H from the Left */ -/* > = 'R': apply Q or Q**H from the Right */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TRANS */ -/* > \verbatim */ -/* > TRANS is CHARACTER*1 */ -/* > = 'N': apply Q (No transpose) */ -/* > = 'C': apply Q**H (Conjugate transpose) */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix C. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix C. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > The number of elementary reflectors whose product defines */ -/* > the matrix Q. */ -/* > If SIDE = 'L', M >= K >= 0; */ -/* > if SIDE = 'R', N >= K >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is COMPLEX*16 array, dimension (LDA,K) */ -/* > The i-th column must contain the vector which defines the */ -/* > elementary reflector H(i), for i = 1,2,...,k, as returned by */ -/* > ZGEQRF in the first k columns of its array argument A. */ -/* > A is modified by the routine but restored on exit. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. */ -/* > If SIDE = 'L', LDA >= max(1,M); */ -/* > if SIDE = 'R', LDA >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TAU */ -/* > \verbatim */ -/* > TAU is COMPLEX*16 array, dimension (K) */ -/* > TAU(i) must contain the scalar factor of the elementary */ -/* > reflector H(i), as returned by ZGEQRF. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] C */ -/* > \verbatim */ -/* > C is COMPLEX*16 array, dimension (LDC,N) */ -/* > On entry, the m-by-n matrix C. */ -/* > On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDC */ -/* > \verbatim */ -/* > LDC is INTEGER */ -/* > The leading dimension of the array C. LDC >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is COMPLEX*16 array, dimension */ -/* > (N) if SIDE = 'L', */ -/* > (M) if SIDE = 'R' */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16OTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int zunm2r_(char *side, char *trans, integer *m, integer *n, - integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, - doublecomplex *c__, integer *ldc, doublecomplex *work, integer *info, - ftnlen side_len, ftnlen trans_len) +int zunm2r_(char *side, char *trans, integer *m, integer *n, integer *k, doublecomplex *a, + integer *lda, doublecomplex *tau, doublecomplex *c__, integer *ldc, doublecomplex *work, + integer *info, ftnlen side_len, ftnlen trans_len) { - /* System generated locals */ integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3; doublecomplex z__1; - - /* Builtin functions */ void d_lmp_cnjg(doublecomplex *, doublecomplex *); - - /* Local variables */ integer i__, i1, i2, i3, ic, jc, mi, ni, nq; doublecomplex aii; logical left; doublecomplex taui; extern logical lsame_(char *, char *, ftnlen, ftnlen); - extern /* Subroutine */ int zlarf_(char *, integer *, integer *, - doublecomplex *, integer *, doublecomplex *, doublecomplex *, - integer *, doublecomplex *, ftnlen), xerbla_(char *, integer *, - ftnlen); + extern int zlarf_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, + doublecomplex *, integer *, doublecomplex *, ftnlen), + xerbla_(char *, integer *, ftnlen); logical notran; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; @@ -238,22 +27,17 @@ f"> */ c_offset = 1 + c_dim1; c__ -= c_offset; --work; - - /* Function Body */ *info = 0; left = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); notran = lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1); - -/* NQ is the order of Q */ - if (left) { nq = *m; } else { nq = *n; } - if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + if (!left && !lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { *info = -1; - } else if (! notran && ! lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { + } else if (!notran && !lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { *info = -2; } else if (*m < 0) { *info = -3; @@ -261,9 +45,9 @@ f"> */ *info = -4; } else if (*k < 0 || *k > nq) { *info = -5; - } else if (*lda < max(1,nq)) { + } else if (*lda < max(1, nq)) { *info = -7; - } else if (*ldc < max(1,*m)) { + } else if (*ldc < max(1, *m)) { *info = -10; } if (*info != 0) { @@ -271,14 +55,10 @@ f"> */ xerbla_((char *)"ZUNM2R", &i__1, (ftnlen)6); return 0; } - -/* Quick return if possible */ - if (*m == 0 || *n == 0 || *k == 0) { return 0; } - - if (left && ! notran || ! left && notran) { + if (left && !notran || !left && notran) { i1 = 1; i2 = *k; i3 = 1; @@ -287,7 +67,6 @@ f"> */ i2 = 1; i3 = -1; } - if (left) { ni = *n; jc = 1; @@ -295,26 +74,16 @@ f"> */ mi = *m; ic = 1; } - i__1 = i2; i__2 = i3; for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { if (left) { - -/* H(i) or H(i)**H is applied to C(i:m,1:n) */ - mi = *m - i__ + 1; ic = i__; } else { - -/* H(i) or H(i)**H is applied to C(1:m,i:n) */ - ni = *n - i__ + 1; jc = i__; } - -/* Apply H(i) or H(i)**H */ - if (notran) { i__3 = i__; taui.r = tau[i__3].r, taui.i = tau[i__3].i; @@ -326,18 +95,13 @@ f"> */ aii.r = a[i__3].r, aii.i = a[i__3].i; i__3 = i__ + i__ * a_dim1; a[i__3].r = 1., a[i__3].i = 0.; - zlarf_(side, &mi, &ni, &a[i__ + i__ * a_dim1], &c__1, &taui, &c__[ic - + jc * c_dim1], ldc, &work[1], (ftnlen)1); + zlarf_(side, &mi, &ni, &a[i__ + i__ * a_dim1], &c__1, &taui, &c__[ic + jc * c_dim1], ldc, + &work[1], (ftnlen)1); i__3 = i__ + i__ * a_dim1; a[i__3].r = aii.r, a[i__3].i = aii.i; -/* L10: */ } return 0; - -/* End of ZUNM2R */ - -} /* zunm2r_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zunmql.cpp b/lib/linalg/zunmql.cpp index 694c8f776c..11eca14656 100644 --- a/lib/linalg/zunmql.cpp +++ b/lib/linalg/zunmql.cpp @@ -1,258 +1,38 @@ -/* fortran/zunmql.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static integer c_n1 = -1; static integer c__2 = 2; static integer c__65 = 65; - -/* > \brief \b ZUNMQL */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZUNMQL + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZUNMQL( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, */ -/* WORK, LWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER SIDE, TRANS */ -/* INTEGER INFO, K, LDA, LDC, LWORK, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZUNMQL overwrites the general complex M-by-N matrix C with */ -/* > */ -/* > SIDE = 'L' SIDE = 'R' */ -/* > TRANS = 'N': Q * C C * Q */ -/* > TRANS = 'C': Q**H * C C * Q**H */ -/* > */ -/* > where Q is a complex unitary matrix defined as the product of k */ -/* > elementary reflectors */ -/* > */ -/* > Q = H(k) . . . H(2) H(1) */ -/* > */ -/* > as returned by ZGEQLF. Q is of order M if SIDE = 'L' and of order N */ -/* > if SIDE = 'R'. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] SIDE */ -/* > \verbatim */ -/* > SIDE is CHARACTER*1 */ -/* > = 'L': apply Q or Q**H from the Left; */ -/* > = 'R': apply Q or Q**H from the Right. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TRANS */ -/* > \verbatim */ -/* > TRANS is CHARACTER*1 */ -/* > = 'N': No transpose, apply Q; */ -/* > = 'C': Conjugate transpose, apply Q**H. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix C. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix C. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > The number of elementary reflectors whose product defines */ -/* > the matrix Q. */ -/* > If SIDE = 'L', M >= K >= 0; */ -/* > if SIDE = 'R', N >= K >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is COMPLEX*16 array, dimension (LDA,K) */ -/* > The i-th column must contain the vector which defines the */ -/* > elementary reflector H(i), for i = 1,2,...,k, as returned by */ -/* > ZGEQLF in the last k columns of its array argument A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. */ -/* > If SIDE = 'L', LDA >= max(1,M); */ -/* > if SIDE = 'R', LDA >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TAU */ -/* > \verbatim */ -/* > TAU is COMPLEX*16 array, dimension (K) */ -/* > TAU(i) must contain the scalar factor of the elementary */ -/* > reflector H(i), as returned by ZGEQLF. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] C */ -/* > \verbatim */ -/* > C is COMPLEX*16 array, dimension (LDC,N) */ -/* > On entry, the M-by-N matrix C. */ -/* > On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDC */ -/* > \verbatim */ -/* > LDC is INTEGER */ -/* > The leading dimension of the array C. LDC >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) */ -/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LWORK */ -/* > \verbatim */ -/* > LWORK is INTEGER */ -/* > The dimension of the array WORK. */ -/* > If SIDE = 'L', LWORK >= max(1,N); */ -/* > if SIDE = 'R', LWORK >= max(1,M). */ -/* > For good performance, LWORK should generally be larger. */ -/* > */ -/* > If LWORK = -1, then a workspace query is assumed; the routine */ -/* > only calculates the optimal size of the WORK array, returns */ -/* > this value as the first entry of the WORK array, and no error */ -/* > message related to LWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16OTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int zunmql_(char *side, char *trans, integer *m, integer *n, - integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, - doublecomplex *c__, integer *ldc, doublecomplex *work, integer *lwork, - integer *info, ftnlen side_len, ftnlen trans_len) +int zunmql_(char *side, char *trans, integer *m, integer *n, integer *k, doublecomplex *a, + integer *lda, doublecomplex *tau, doublecomplex *c__, integer *ldc, doublecomplex *work, + integer *lwork, integer *info, ftnlen side_len, ftnlen trans_len) { - /* System generated locals */ address a__1[2]; - integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4, - i__5; + integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4, i__5; char ch__1[2]; - - /* Builtin functions */ - /* Subroutine */ int s_lmp_cat(char *, char **, integer *, integer *, ftnlen); - - /* Local variables */ + int s_lmp_cat(char *, char **, integer *, integer *, ftnlen); integer i__, i1, i2, i3, ib, nb, mi, ni, nq, nw, iwt; logical left; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer nbmin, iinfo; - extern /* Subroutine */ int zunm2l_(char *, char *, integer *, integer *, - integer *, doublecomplex *, integer *, doublecomplex *, - doublecomplex *, integer *, doublecomplex *, integer *, ftnlen, - ftnlen), xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *, - integer *, integer *, integer *, doublecomplex *, integer *, - doublecomplex *, integer *, doublecomplex *, integer *, - doublecomplex *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + extern int zunm2l_(char *, char *, integer *, integer *, integer *, doublecomplex *, integer *, + doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, + ftnlen, ftnlen), + xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); + extern int zlarfb_(char *, char *, char *, char *, integer *, integer *, integer *, + doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, + integer *, doublecomplex *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); logical notran; integer ldwork; - extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *, - doublecomplex *, integer *, doublecomplex *, doublecomplex *, - integer *, ftnlen, ftnlen); + extern int zlarft_(char *, char *, integer *, integer *, doublecomplex *, integer *, + doublecomplex *, doublecomplex *, integer *, ftnlen, ftnlen); integer lwkopt; logical lquery; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; @@ -261,25 +41,20 @@ f"> */ c_offset = 1 + c_dim1; c__ -= c_offset; --work; - - /* Function Body */ *info = 0; left = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); notran = lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1); lquery = *lwork == -1; - -/* NQ is the order of Q and NW is the minimum dimension of WORK */ - if (left) { nq = *m; - nw = max(1,*n); + nw = max(1, *n); } else { nq = *n; - nw = max(1,*m); + nw = max(1, *m); } - if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + if (!left && !lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { *info = -1; - } else if (! notran && ! lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { + } else if (!notran && !lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { *info = -2; } else if (*m < 0) { *info = -3; @@ -287,34 +62,26 @@ f"> */ *info = -4; } else if (*k < 0 || *k > nq) { *info = -5; - } else if (*lda < max(1,nq)) { + } else if (*lda < max(1, nq)) { *info = -7; - } else if (*ldc < max(1,*m)) { + } else if (*ldc < max(1, *m)) { *info = -10; - } else if (*lwork < nw && ! lquery) { + } else if (*lwork < nw && !lquery) { *info = -12; } - if (*info == 0) { - -/* Compute the workspace requirements */ - if (*m == 0 || *n == 0) { lwkopt = 1; } else { -/* Computing MIN */ -/* Writing concatenation */ i__3[0] = 1, a__1[0] = side; i__3[1] = 1, a__1[1] = trans; s_lmp_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); - i__1 = 64, i__2 = ilaenv_(&c__1, (char *)"ZUNMQL", ch__1, m, n, k, &c_n1, - (ftnlen)6, (ftnlen)2); - nb = min(i__1,i__2); + i__1 = 64, i__2 = ilaenv_(&c__1, (char *)"ZUNMQL", ch__1, m, n, k, &c_n1, (ftnlen)6, (ftnlen)2); + nb = min(i__1, i__2); lwkopt = nw * nb + 4160; } - work[1].r = (doublereal) lwkopt, work[1].i = 0.; + work[1].r = (doublereal)lwkopt, work[1].i = 0.; } - if (*info != 0) { i__1 = -(*info); xerbla_((char *)"ZUNMQL", &i__1, (ftnlen)6); @@ -322,41 +89,27 @@ f"> */ } else if (lquery) { return 0; } - -/* Quick return if possible */ - if (*m == 0 || *n == 0) { return 0; } - nbmin = 2; ldwork = nw; if (nb > 1 && nb < *k) { if (*lwork < lwkopt) { nb = (*lwork - 4160) / ldwork; -/* Computing MAX */ -/* Writing concatenation */ i__3[0] = 1, a__1[0] = side; i__3[1] = 1, a__1[1] = trans; s_lmp_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); - i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"ZUNMQL", ch__1, m, n, k, &c_n1, ( - ftnlen)6, (ftnlen)2); - nbmin = max(i__1,i__2); + i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"ZUNMQL", ch__1, m, n, k, &c_n1, (ftnlen)6, (ftnlen)2); + nbmin = max(i__1, i__2); } } - if (nb < nbmin || nb >= *k) { - -/* Use unblocked code */ - - zunm2l_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[ - c_offset], ldc, &work[1], &iinfo, (ftnlen)1, (ftnlen)1); + zunm2l_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[c_offset], ldc, &work[1], + &iinfo, (ftnlen)1, (ftnlen)1); } else { - -/* Use blocked code */ - iwt = nw * nb + 1; - if (left && notran || ! left && ! notran) { + if (left && notran || !left && !notran) { i1 = 1; i2 = *k; i3 = nb; @@ -365,55 +118,32 @@ f"> */ i2 = 1; i3 = -nb; } - if (left) { ni = *n; } else { mi = *m; } - i__1 = i2; i__2 = i3; for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { -/* Computing MIN */ i__4 = nb, i__5 = *k - i__ + 1; - ib = min(i__4,i__5); - -/* Form the triangular factor of the block reflector */ -/* H = H(i+ib-1) . . . H(i+1) H(i) */ - + ib = min(i__4, i__5); i__4 = nq - *k + i__ + ib - 1; - zlarft_((char *)"Backward", (char *)"Columnwise", &i__4, &ib, &a[i__ * a_dim1 + 1] - , lda, &tau[i__], &work[iwt], &c__65, (ftnlen)8, (ftnlen) - 10); + zlarft_((char *)"Backward", (char *)"Columnwise", &i__4, &ib, &a[i__ * a_dim1 + 1], lda, &tau[i__], + &work[iwt], &c__65, (ftnlen)8, (ftnlen)10); if (left) { - -/* H or H**H is applied to C(1:m-k+i+ib-1,1:n) */ - mi = *m - *k + i__ + ib - 1; } else { - -/* H or H**H is applied to C(1:m,1:n-k+i+ib-1) */ - ni = *n - *k + i__ + ib - 1; } - -/* Apply H or H**H */ - - zlarfb_(side, trans, (char *)"Backward", (char *)"Columnwise", &mi, &ni, &ib, &a[ - i__ * a_dim1 + 1], lda, &work[iwt], &c__65, &c__[c_offset] - , ldc, &work[1], &ldwork, (ftnlen)1, (ftnlen)1, (ftnlen)8, - (ftnlen)10); -/* L10: */ + zlarfb_(side, trans, (char *)"Backward", (char *)"Columnwise", &mi, &ni, &ib, &a[i__ * a_dim1 + 1], lda, + &work[iwt], &c__65, &c__[c_offset], ldc, &work[1], &ldwork, (ftnlen)1, + (ftnlen)1, (ftnlen)8, (ftnlen)10); } } - work[1].r = (doublereal) lwkopt, work[1].i = 0.; + work[1].r = (doublereal)lwkopt, work[1].i = 0.; return 0; - -/* End of ZUNMQL */ - -} /* zunmql_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zunmqr.cpp b/lib/linalg/zunmqr.cpp index 6718cdc001..7a82cd0681 100644 --- a/lib/linalg/zunmqr.cpp +++ b/lib/linalg/zunmqr.cpp @@ -1,258 +1,38 @@ -/* fortran/zunmqr.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static integer c_n1 = -1; static integer c__2 = 2; static integer c__65 = 65; - -/* > \brief \b ZUNMQR */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZUNMQR + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZUNMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, */ -/* WORK, LWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER SIDE, TRANS */ -/* INTEGER INFO, K, LDA, LDC, LWORK, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZUNMQR overwrites the general complex M-by-N matrix C with */ -/* > */ -/* > SIDE = 'L' SIDE = 'R' */ -/* > TRANS = 'N': Q * C C * Q */ -/* > TRANS = 'C': Q**H * C C * Q**H */ -/* > */ -/* > where Q is a complex unitary matrix defined as the product of k */ -/* > elementary reflectors */ -/* > */ -/* > Q = H(1) H(2) . . . H(k) */ -/* > */ -/* > as returned by ZGEQRF. Q is of order M if SIDE = 'L' and of order N */ -/* > if SIDE = 'R'. */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] SIDE */ -/* > \verbatim */ -/* > SIDE is CHARACTER*1 */ -/* > = 'L': apply Q or Q**H from the Left; */ -/* > = 'R': apply Q or Q**H from the Right. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TRANS */ -/* > \verbatim */ -/* > TRANS is CHARACTER*1 */ -/* > = 'N': No transpose, apply Q; */ -/* > = 'C': Conjugate transpose, apply Q**H. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix C. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix C. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] K */ -/* > \verbatim */ -/* > K is INTEGER */ -/* > The number of elementary reflectors whose product defines */ -/* > the matrix Q. */ -/* > If SIDE = 'L', M >= K >= 0; */ -/* > if SIDE = 'R', N >= K >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is COMPLEX*16 array, dimension (LDA,K) */ -/* > The i-th column must contain the vector which defines the */ -/* > elementary reflector H(i), for i = 1,2,...,k, as returned by */ -/* > ZGEQRF in the first k columns of its array argument A. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. */ -/* > If SIDE = 'L', LDA >= max(1,M); */ -/* > if SIDE = 'R', LDA >= max(1,N). */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TAU */ -/* > \verbatim */ -/* > TAU is COMPLEX*16 array, dimension (K) */ -/* > TAU(i) must contain the scalar factor of the elementary */ -/* > reflector H(i), as returned by ZGEQRF. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] C */ -/* > \verbatim */ -/* > C is COMPLEX*16 array, dimension (LDC,N) */ -/* > On entry, the M-by-N matrix C. */ -/* > On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDC */ -/* > \verbatim */ -/* > LDC is INTEGER */ -/* > The leading dimension of the array C. LDC >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) */ -/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LWORK */ -/* > \verbatim */ -/* > LWORK is INTEGER */ -/* > The dimension of the array WORK. */ -/* > If SIDE = 'L', LWORK >= max(1,N); */ -/* > if SIDE = 'R', LWORK >= max(1,M). */ -/* > For good performance, LWORK should generally be larger. */ -/* > */ -/* > If LWORK = -1, then a workspace query is assumed; the routine */ -/* > only calculates the optimal size of the WORK array, returns */ -/* > this value as the first entry of the WORK array, and no error */ -/* > message related to LWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16OTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int zunmqr_(char *side, char *trans, integer *m, integer *n, - integer *k, doublecomplex *a, integer *lda, doublecomplex *tau, - doublecomplex *c__, integer *ldc, doublecomplex *work, integer *lwork, - integer *info, ftnlen side_len, ftnlen trans_len) +int zunmqr_(char *side, char *trans, integer *m, integer *n, integer *k, doublecomplex *a, + integer *lda, doublecomplex *tau, doublecomplex *c__, integer *ldc, doublecomplex *work, + integer *lwork, integer *info, ftnlen side_len, ftnlen trans_len) { - /* System generated locals */ address a__1[2]; - integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4, - i__5; + integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4, i__5; char ch__1[2]; - - /* Builtin functions */ - /* Subroutine */ int s_lmp_cat(char *, char **, integer *, integer *, ftnlen); - - /* Local variables */ + int s_lmp_cat(char *, char **, integer *, integer *, ftnlen); integer i__, i1, i2, i3, ib, ic, jc, nb, mi, ni, nq, nw, iwt; logical left; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer nbmin, iinfo; - extern /* Subroutine */ int zunm2r_(char *, char *, integer *, integer *, - integer *, doublecomplex *, integer *, doublecomplex *, - doublecomplex *, integer *, doublecomplex *, integer *, ftnlen, - ftnlen), xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); - extern /* Subroutine */ int zlarfb_(char *, char *, char *, char *, - integer *, integer *, integer *, doublecomplex *, integer *, - doublecomplex *, integer *, doublecomplex *, integer *, - doublecomplex *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); + extern int zunm2r_(char *, char *, integer *, integer *, integer *, doublecomplex *, integer *, + doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, + ftnlen, ftnlen), + xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); + extern int zlarfb_(char *, char *, char *, char *, integer *, integer *, integer *, + doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, + integer *, doublecomplex *, integer *, ftnlen, ftnlen, ftnlen, ftnlen); logical notran; integer ldwork; - extern /* Subroutine */ int zlarft_(char *, char *, integer *, integer *, - doublecomplex *, integer *, doublecomplex *, doublecomplex *, - integer *, ftnlen, ftnlen); + extern int zlarft_(char *, char *, integer *, integer *, doublecomplex *, integer *, + doublecomplex *, doublecomplex *, integer *, ftnlen, ftnlen); integer lwkopt; logical lquery; - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Parameters .. */ -/* .. */ -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments */ - - /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; @@ -261,25 +41,20 @@ f"> */ c_offset = 1 + c_dim1; c__ -= c_offset; --work; - - /* Function Body */ *info = 0; left = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); notran = lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1); lquery = *lwork == -1; - -/* NQ is the order of Q and NW is the minimum dimension of WORK */ - if (left) { nq = *m; - nw = max(1,*n); + nw = max(1, *n); } else { nq = *n; - nw = max(1,*m); + nw = max(1, *m); } - if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + if (!left && !lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { *info = -1; - } else if (! notran && ! lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { + } else if (!notran && !lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { *info = -2; } else if (*m < 0) { *info = -3; @@ -287,30 +62,22 @@ f"> */ *info = -4; } else if (*k < 0 || *k > nq) { *info = -5; - } else if (*lda < max(1,nq)) { + } else if (*lda < max(1, nq)) { *info = -7; - } else if (*ldc < max(1,*m)) { + } else if (*ldc < max(1, *m)) { *info = -10; - } else if (*lwork < nw && ! lquery) { + } else if (*lwork < nw && !lquery) { *info = -12; } - if (*info == 0) { - -/* Compute the workspace requirements */ - -/* Computing MIN */ -/* Writing concatenation */ i__3[0] = 1, a__1[0] = side; i__3[1] = 1, a__1[1] = trans; s_lmp_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); - i__1 = 64, i__2 = ilaenv_(&c__1, (char *)"ZUNMQR", ch__1, m, n, k, &c_n1, ( - ftnlen)6, (ftnlen)2); - nb = min(i__1,i__2); + i__1 = 64, i__2 = ilaenv_(&c__1, (char *)"ZUNMQR", ch__1, m, n, k, &c_n1, (ftnlen)6, (ftnlen)2); + nb = min(i__1, i__2); lwkopt = nw * nb + 4160; - work[1].r = (doublereal) lwkopt, work[1].i = 0.; + work[1].r = (doublereal)lwkopt, work[1].i = 0.; } - if (*info != 0) { i__1 = -(*info); xerbla_((char *)"ZUNMQR", &i__1, (ftnlen)6); @@ -318,42 +85,28 @@ f"> */ } else if (lquery) { return 0; } - -/* Quick return if possible */ - if (*m == 0 || *n == 0 || *k == 0) { work[1].r = 1., work[1].i = 0.; return 0; } - nbmin = 2; ldwork = nw; if (nb > 1 && nb < *k) { if (*lwork < lwkopt) { nb = (*lwork - 4160) / ldwork; -/* Computing MAX */ -/* Writing concatenation */ i__3[0] = 1, a__1[0] = side; i__3[1] = 1, a__1[1] = trans; s_lmp_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2); - i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"ZUNMQR", ch__1, m, n, k, &c_n1, ( - ftnlen)6, (ftnlen)2); - nbmin = max(i__1,i__2); + i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"ZUNMQR", ch__1, m, n, k, &c_n1, (ftnlen)6, (ftnlen)2); + nbmin = max(i__1, i__2); } } - if (nb < nbmin || nb >= *k) { - -/* Use unblocked code */ - - zunm2r_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[ - c_offset], ldc, &work[1], &iinfo, (ftnlen)1, (ftnlen)1); + zunm2r_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[c_offset], ldc, &work[1], + &iinfo, (ftnlen)1, (ftnlen)1); } else { - -/* Use blocked code */ - iwt = nw * nb + 1; - if (left && ! notran || ! left && notran) { + if (left && !notran || !left && notran) { i1 = 1; i2 = *k; i3 = nb; @@ -362,7 +115,6 @@ f"> */ i2 = 1; i3 = -nb; } - if (left) { ni = *n; jc = 1; @@ -370,51 +122,29 @@ f"> */ mi = *m; ic = 1; } - i__1 = i2; i__2 = i3; for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { -/* Computing MIN */ i__4 = nb, i__5 = *k - i__ + 1; - ib = min(i__4,i__5); - -/* Form the triangular factor of the block reflector */ -/* H = H(i) H(i+1) . . . H(i+ib-1) */ - + ib = min(i__4, i__5); i__4 = nq - i__ + 1; - zlarft_((char *)"Forward", (char *)"Columnwise", &i__4, &ib, &a[i__ + i__ * - a_dim1], lda, &tau[i__], &work[iwt], &c__65, (ftnlen)7, ( - ftnlen)10); + zlarft_((char *)"Forward", (char *)"Columnwise", &i__4, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], + &work[iwt], &c__65, (ftnlen)7, (ftnlen)10); if (left) { - -/* H or H**H is applied to C(i:m,1:n) */ - mi = *m - i__ + 1; ic = i__; } else { - -/* H or H**H is applied to C(1:m,i:n) */ - ni = *n - i__ + 1; jc = i__; } - -/* Apply H or H**H */ - - zlarfb_(side, trans, (char *)"Forward", (char *)"Columnwise", &mi, &ni, &ib, &a[ - i__ + i__ * a_dim1], lda, &work[iwt], &c__65, &c__[ic + - jc * c_dim1], ldc, &work[1], &ldwork, (ftnlen)1, (ftnlen) - 1, (ftnlen)7, (ftnlen)10); -/* L10: */ + zlarfb_(side, trans, (char *)"Forward", (char *)"Columnwise", &mi, &ni, &ib, &a[i__ + i__ * a_dim1], + lda, &work[iwt], &c__65, &c__[ic + jc * c_dim1], ldc, &work[1], &ldwork, + (ftnlen)1, (ftnlen)1, (ftnlen)7, (ftnlen)10); } } - work[1].r = (doublereal) lwkopt, work[1].i = 0.; + work[1].r = (doublereal)lwkopt, work[1].i = 0.; return 0; - -/* End of ZUNMQR */ - -} /* zunmqr_ */ - +} #ifdef __cplusplus - } +} #endif diff --git a/lib/linalg/zunmtr.cpp b/lib/linalg/zunmtr.cpp index f4f4f55761..86530bb9c6 100644 --- a/lib/linalg/zunmtr.cpp +++ b/lib/linalg/zunmtr.cpp @@ -1,254 +1,34 @@ -/* fortran/zunmtr.f -- translated by f2c (version 20200916). - You must link the resulting object file with libf2c: - on Microsoft Windows system, link with libf2c.lib; - on Linux or Unix systems, link with .../path/to/libf2c.a -lm - or, if you install libf2c.a in a standard place, with -lf2c -lm - -- in that order, at the end of the command line, as in - cc *.o -lf2c -lm - Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., - - http://www.netlib.org/f2c/libf2c.zip -*/ - #ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" - -/* Table of constant values */ - static integer c__1 = 1; static integer c_n1 = -1; static integer c__2 = 2; - -/* > \brief \b ZUNMTR */ - -/* =========== DOCUMENTATION =========== */ - -/* Online html documentation available at */ -/* http://www.netlib.org/lapack/explore-html/ */ - -/* > \htmlonly */ -/* > Download ZUNMTR + dependencies */ -/* > */ -/* > [TGZ] */ -/* > */ -/* > [ZIP] */ -/* > */ -/* > [TXT] */ -/* > \endhtmlonly */ - -/* Definition: */ -/* =========== */ - -/* SUBROUTINE ZUNMTR( SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC, */ -/* WORK, LWORK, INFO ) */ - -/* .. Scalar Arguments .. */ -/* CHARACTER SIDE, TRANS, UPLO */ -/* INTEGER INFO, LDA, LDC, LWORK, M, N */ -/* .. */ -/* .. Array Arguments .. */ -/* COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) */ -/* .. */ - - -/* > \par Purpose: */ -/* ============= */ -/* > */ -/* > \verbatim */ -/* > */ -/* > ZUNMTR overwrites the general complex M-by-N matrix C with */ -/* > */ -/* > SIDE = 'L' SIDE = 'R' */ -/* > TRANS = 'N': Q * C C * Q */ -/* > TRANS = 'C': Q**H * C C * Q**H */ -/* > */ -/* > where Q is a complex unitary matrix of order nq, with nq = m if */ -/* > SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of */ -/* > nq-1 elementary reflectors, as returned by ZHETRD: */ -/* > */ -/* > if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1); */ -/* > */ -/* > if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1). */ -/* > \endverbatim */ - -/* Arguments: */ -/* ========== */ - -/* > \param[in] SIDE */ -/* > \verbatim */ -/* > SIDE is CHARACTER*1 */ -/* > = 'L': apply Q or Q**H from the Left; */ -/* > = 'R': apply Q or Q**H from the Right. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] UPLO */ -/* > \verbatim */ -/* > UPLO is CHARACTER*1 */ -/* > = 'U': Upper triangle of A contains elementary reflectors */ -/* > from ZHETRD; */ -/* > = 'L': Lower triangle of A contains elementary reflectors */ -/* > from ZHETRD. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TRANS */ -/* > \verbatim */ -/* > TRANS is CHARACTER*1 */ -/* > = 'N': No transpose, apply Q; */ -/* > = 'C': Conjugate transpose, apply Q**H. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] M */ -/* > \verbatim */ -/* > M is INTEGER */ -/* > The number of rows of the matrix C. M >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] N */ -/* > \verbatim */ -/* > N is INTEGER */ -/* > The number of columns of the matrix C. N >= 0. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] A */ -/* > \verbatim */ -/* > A is COMPLEX*16 array, dimension */ -/* > (LDA,M) if SIDE = 'L' */ -/* > (LDA,N) if SIDE = 'R' */ -/* > The vectors which define the elementary reflectors, as */ -/* > returned by ZHETRD. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDA */ -/* > \verbatim */ -/* > LDA is INTEGER */ -/* > The leading dimension of the array A. */ -/* > LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] TAU */ -/* > \verbatim */ -/* > TAU is COMPLEX*16 array, dimension */ -/* > (M-1) if SIDE = 'L' */ -/* > (N-1) if SIDE = 'R' */ -/* > TAU(i) must contain the scalar factor of the elementary */ -/* > reflector H(i), as returned by ZHETRD. */ -/* > \endverbatim */ -/* > */ -/* > \param[in,out] C */ -/* > \verbatim */ -/* > C is COMPLEX*16 array, dimension (LDC,N) */ -/* > On entry, the M-by-N matrix C. */ -/* > On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LDC */ -/* > \verbatim */ -/* > LDC is INTEGER */ -/* > The leading dimension of the array C. LDC >= max(1,M). */ -/* > \endverbatim */ -/* > */ -/* > \param[out] WORK */ -/* > \verbatim */ -/* > WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) */ -/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ -/* > \endverbatim */ -/* > */ -/* > \param[in] LWORK */ -/* > \verbatim */ -/* > LWORK is INTEGER */ -/* > The dimension of the array WORK. */ -/* > If SIDE = 'L', LWORK >= max(1,N); */ -/* > if SIDE = 'R', LWORK >= max(1,M). */ -/* > For optimum performance LWORK >= N*NB if SIDE = 'L', and */ -/* > LWORK >=M*NB if SIDE = 'R', where NB is the optimal */ -/* > blocksize. */ -/* > */ -/* > If LWORK = -1, then a workspace query is assumed; the routine */ -/* > only calculates the optimal size of the WORK array, returns */ -/* > this value as the first entry of the WORK array, and no error */ -/* > message related to LWORK is issued by XERBLA. */ -/* > \endverbatim */ -/* > */ -/* > \param[out] INFO */ -/* > \verbatim */ -/* > INFO is INTEGER */ -/* > = 0: successful exit */ -/* > < 0: if INFO = -i, the i-th argument had an illegal value */ -/* > \endverbatim */ - -/* Authors: */ -/* ======== */ - -/* > \author Univ. of Tennessee */ -/* > \author Univ. of California Berkeley */ -/* > \author Univ. of Colorado Denver */ -/* > \author NAG Ltd. */ - -/* > \ingroup complex16OTHERcomputational */ - -/* ===================================================================== */ -/* Subroutine */ int zunmtr_(char *side, char *uplo, char *trans, integer *m, - integer *n, doublecomplex *a, integer *lda, doublecomplex *tau, - doublecomplex *c__, integer *ldc, doublecomplex *work, integer *lwork, - integer *info, ftnlen side_len, ftnlen uplo_len, ftnlen trans_len) +int zunmtr_(char *side, char *uplo, char *trans, integer *m, integer *n, doublecomplex *a, + integer *lda, doublecomplex *tau, doublecomplex *c__, integer *ldc, doublecomplex *work, + integer *lwork, integer *info, ftnlen side_len, ftnlen uplo_len, ftnlen trans_len) { - /* System generated locals */ address a__1[2]; integer a_dim1, a_offset, c_dim1, c_offset, i__1[2], i__2, i__3; char ch__1[2]; - - /* Builtin functions */ - /* Subroutine */ int s_lmp_cat(char *, char **, integer *, integer *, ftnlen); - - /* Local variables */ + int s_lmp_cat(char *, char **, integer *, integer *, ftnlen); integer i1, i2, nb, mi, ni, nq, nw; logical left; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer iinfo; logical upper; - extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); - extern integer ilaenv_(integer *, char *, char *, integer *, integer *, - integer *, integer *, ftnlen, ftnlen); + extern int xerbla_(char *, integer *, ftnlen); + extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, + ftnlen, ftnlen); integer lwkopt; logical lquery; - extern /* Subroutine */ int zunmql_(char *, char *, integer *, integer *, - integer *, doublecomplex *, integer *, doublecomplex *, - doublecomplex *, integer *, doublecomplex *, integer *, integer *, - ftnlen, ftnlen), zunmqr_(char *, char *, integer *, integer *, - integer *, doublecomplex *, integer *, doublecomplex *, - doublecomplex *, integer *, doublecomplex *, integer *, integer *, - ftnlen, ftnlen); - - -/* -- LAPACK computational routine -- */ -/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ -/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ - -/* .. Scalar Arguments .. */ -/* .. */ -/* .. Array Arguments .. */ -/* .. */ - -/* ===================================================================== */ - -/* .. Local Scalars .. */ -/* .. */ -/* .. External Functions .. */ -/* .. */ -/* .. External Subroutines .. */ -/* .. */ -/* .. Intrinsic Functions .. */ -/* .. */ -/* .. Executable Statements .. */ - -/* Test the input arguments */ - - /* Parameter adjustments */ + extern int zunmql_(char *, char *, integer *, integer *, integer *, doublecomplex *, integer *, + doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, + integer *, ftnlen, ftnlen), + zunmqr_(char *, char *, integer *, integer *, integer *, doublecomplex *, integer *, + doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, + ftnlen, ftnlen); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; @@ -257,87 +37,72 @@ f"> */ c_offset = 1 + c_dim1; c__ -= c_offset; --work; - - /* Function Body */ *info = 0; left = lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1); upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); lquery = *lwork == -1; - -/* NQ is the order of Q and NW is the minimum dimension of WORK */ - if (left) { nq = *m; - nw = max(1,*n); + nw = max(1, *n); } else { nq = *n; - nw = max(1,*m); + nw = max(1, *m); } - if (! left && ! lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { + if (!left && !lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) { *info = -1; - } else if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { + } else if (!upper && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { *info = -2; - } else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, - (char *)"C", (ftnlen)1, (ftnlen)1)) { + } else if (!lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && + !lsame_(trans, (char *)"C", (ftnlen)1, (ftnlen)1)) { *info = -3; } else if (*m < 0) { *info = -4; } else if (*n < 0) { *info = -5; - } else if (*lda < max(1,nq)) { + } else if (*lda < max(1, nq)) { *info = -7; - } else if (*ldc < max(1,*m)) { + } else if (*ldc < max(1, *m)) { *info = -10; - } else if (*lwork < nw && ! lquery) { + } else if (*lwork < nw && !lquery) { *info = -12; } - if (*info == 0) { if (upper) { if (left) { -/* Writing concatenation */ i__1[0] = 1, a__1[0] = side; i__1[1] = 1, a__1[1] = trans; s_lmp_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); i__2 = *m - 1; i__3 = *m - 1; - nb = ilaenv_(&c__1, (char *)"ZUNMQL", ch__1, &i__2, n, &i__3, &c_n1, ( - ftnlen)6, (ftnlen)2); + nb = ilaenv_(&c__1, (char *)"ZUNMQL", ch__1, &i__2, n, &i__3, &c_n1, (ftnlen)6, (ftnlen)2); } else { -/* Writing concatenation */ i__1[0] = 1, a__1[0] = side; i__1[1] = 1, a__1[1] = trans; s_lmp_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); i__2 = *n - 1; i__3 = *n - 1; - nb = ilaenv_(&c__1, (char *)"ZUNMQL", ch__1, m, &i__2, &i__3, &c_n1, ( - ftnlen)6, (ftnlen)2); + nb = ilaenv_(&c__1, (char *)"ZUNMQL", ch__1, m, &i__2, &i__3, &c_n1, (ftnlen)6, (ftnlen)2); } } else { if (left) { -/* Writing concatenation */ i__1[0] = 1, a__1[0] = side; i__1[1] = 1, a__1[1] = trans; s_lmp_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); i__2 = *m - 1; i__3 = *m - 1; - nb = ilaenv_(&c__1, (char *)"ZUNMQR", ch__1, &i__2, n, &i__3, &c_n1, ( - ftnlen)6, (ftnlen)2); + nb = ilaenv_(&c__1, (char *)"ZUNMQR", ch__1, &i__2, n, &i__3, &c_n1, (ftnlen)6, (ftnlen)2); } else { -/* Writing concatenation */ i__1[0] = 1, a__1[0] = side; i__1[1] = 1, a__1[1] = trans; s_lmp_cat(ch__1, a__1, i__1, &c__2, (ftnlen)2); i__2 = *n - 1; i__3 = *n - 1; - nb = ilaenv_(&c__1, (char *)"ZUNMQR", ch__1, m, &i__2, &i__3, &c_n1, ( - ftnlen)6, (ftnlen)2); + nb = ilaenv_(&c__1, (char *)"ZUNMQR", ch__1, m, &i__2, &i__3, &c_n1, (ftnlen)6, (ftnlen)2); } } lwkopt = nw * nb; - work[1].r = (doublereal) lwkopt, work[1].i = 0.; + work[1].r = (doublereal)lwkopt, work[1].i = 0.; } - if (*info != 0) { i__2 = -(*info); xerbla_((char *)"ZUNMTR", &i__2, (ftnlen)6); @@ -345,14 +110,10 @@ f"> */ } else if (lquery) { return 0; } - -/* Quick return if possible */ - if (*m == 0 || *n == 0 || nq == 1) { work[1].r = 1., work[1].i = 0.; return 0; } - if (left) { mi = *m - 1; ni = *n; @@ -360,19 +121,11 @@ f"> */ mi = *m; ni = *n - 1; } - if (upper) { - -/* Q was determined by a call to ZHETRD with UPLO = 'U' */ - i__2 = nq - 1; - zunmql_(side, trans, &mi, &ni, &i__2, &a[(a_dim1 << 1) + 1], lda, & - tau[1], &c__[c_offset], ldc, &work[1], lwork, &iinfo, (ftnlen) - 1, (ftnlen)1); + zunmql_(side, trans, &mi, &ni, &i__2, &a[(a_dim1 << 1) + 1], lda, &tau[1], &c__[c_offset], + ldc, &work[1], lwork, &iinfo, (ftnlen)1, (ftnlen)1); } else { - -/* Q was determined by a call to ZHETRD with UPLO = 'L' */ - if (left) { i1 = 2; i2 = 1; @@ -381,17 +134,12 @@ f"> */ i2 = 2; } i__2 = nq - 1; - zunmqr_(side, trans, &mi, &ni, &i__2, &a[a_dim1 + 2], lda, &tau[1], & - c__[i1 + i2 * c_dim1], ldc, &work[1], lwork, &iinfo, (ftnlen) - 1, (ftnlen)1); + zunmqr_(side, trans, &mi, &ni, &i__2, &a[a_dim1 + 2], lda, &tau[1], &c__[i1 + i2 * c_dim1], + ldc, &work[1], lwork, &iinfo, (ftnlen)1, (ftnlen)1); } - work[1].r = (doublereal) lwkopt, work[1].i = 0.; + work[1].r = (doublereal)lwkopt, work[1].i = 0.; return 0; - -/* End of ZUNMTR */ - -} /* zunmtr_ */ - +} #ifdef __cplusplus - } +} #endif From 9d06a3b9a101ece5f508fda9ecc629031f34e060 Mon Sep 17 00:00:00 2001 From: Axel Kohlmeyer Date: Wed, 28 Dec 2022 17:18:33 -0500 Subject: [PATCH 31/47] with linalg now being C++, a few more packages can be built natively on Windows --- cmake/presets/windows.cmake | 3 +++ 1 file changed, 3 insertions(+) diff --git a/cmake/presets/windows.cmake b/cmake/presets/windows.cmake index 21be0efefb..e93cd35daa 100644 --- a/cmake/presets/windows.cmake +++ b/cmake/presets/windows.cmake @@ -1,6 +1,7 @@ set(WIN_PACKAGES AMOEBA ASPHERE + AWPMD BOCS BODY BPM @@ -20,6 +21,7 @@ set(WIN_PACKAGES DPD-SMOOTH DRUDE EFF + ELECTRODE EXTRA-COMPUTE EXTRA-DUMP EXTRA-FIX @@ -35,6 +37,7 @@ set(WIN_PACKAGES MEAM MISC ML-IAP + ML-POD ML-SNAP MOFFF MOLECULE From dba3eb0cf7d27a6bf384da03b0cdb29005fa2b7f Mon Sep 17 00:00:00 2001 From: Axel Kohlmeyer Date: Wed, 28 Dec 2022 17:39:38 -0500 Subject: [PATCH 32/47] make AWPMD compatible with MSVC and c++-linalg on Windows --- lib/awpmd/ivutils/include/erf.h | 19 ------ lib/awpmd/ivutils/include/lapack_inter.h | 67 +++++++------------ lib/awpmd/systems/interact/TCP/wpmd.h | 2 - lib/awpmd/systems/interact/TCP/wpmd_split.cpp | 2 - 4 files changed, 25 insertions(+), 65 deletions(-) delete mode 100644 lib/awpmd/ivutils/include/erf.h diff --git a/lib/awpmd/ivutils/include/erf.h b/lib/awpmd/ivutils/include/erf.h deleted file mode 100644 index b1cdbcb9dc..0000000000 --- a/lib/awpmd/ivutils/include/erf.h +++ /dev/null @@ -1,19 +0,0 @@ -# ifndef ERF_H -# define ERF_H - -# ifdef _WIN32 - -# ifdef __cplusplus -extern "C" { -# endif - -double erf(double x); -double erfc(double x); - -# ifdef __cplusplus -} -# endif - -# endif - -# endif diff --git a/lib/awpmd/ivutils/include/lapack_inter.h b/lib/awpmd/ivutils/include/lapack_inter.h index ac3e062b5b..a48ea5d821 100644 --- a/lib/awpmd/ivutils/include/lapack_inter.h +++ b/lib/awpmd/ivutils/include/lapack_inter.h @@ -1,53 +1,36 @@ // Interface for LAPACK function -# ifndef LAPACK_INTER_H -# define LAPACK_INTER_H +#ifndef LAPACK_INTER_H +#define LAPACK_INTER_H #include typedef int lapack_int; typedef complex lapack_complex_float; typedef complex lapack_complex_double; -#if defined(_WIN32) && !defined(__MINGW32__) +#define DGETRF dgetrf_ +#define DGETRS dgetrs_ +#define DGETRI dgetri_ +#define ZPPTRF zpptrf_ +#define ZPPTRI zpptri_ - //#define MKL_Complex8 lapack_complex_float - //#define MKL_Complex16 lapack_complex_double - #include "mkl.h" - - inline void ZPPTRF( char* uplo, const lapack_int* n, lapack_complex_double* ap, lapack_int* info ) { - ZPPTRF(uplo, (int*)n, (MKL_Complex16*)ap, (int*)info); - } - inline void ZPPTRI( char* uplo, const lapack_int* n, lapack_complex_double* ap, lapack_int* info ){ - ZPPTRI(uplo, (int*)n, (MKL_Complex16*)ap, (int*)info); - } - -#else - - #define DGETRF dgetrf_ - #define DGETRS dgetrs_ - #define DGETRI dgetri_ - #define ZPPTRF zpptrf_ - #define ZPPTRI zpptri_ - - #ifdef __cplusplus - extern "C" { - #endif /* __cplusplus */ - void dgetrf_( const lapack_int* m, const lapack_int* n, double* a, const lapack_int* lda, - lapack_int* ipiv, lapack_int* info ); - void dgetrs_( const char* trans, const lapack_int* n, const lapack_int* nrhs, - const double* a, const lapack_int* lda, const lapack_int* ipiv, - double* b, const lapack_int* ldb, lapack_int* info ); - void dgetri_( const lapack_int* n, double* a, const lapack_int* lda, - const lapack_int* ipiv, double* work, const lapack_int* lwork, - lapack_int* info ); - void zpptrf_( const char* uplo, const lapack_int* n, lapack_complex_double* ap, - lapack_int* info ); - void zpptri_( const char* uplo, const lapack_int* n, lapack_complex_double* ap, - lapack_int* info ); - #ifdef __cplusplus - } - #endif /* __cplusplus */ - -#endif +#ifdef __cplusplus +extern "C" { +#endif /* __cplusplus */ +void dgetrf_(const lapack_int *m, const lapack_int *n, double *a, + const lapack_int *lda, lapack_int *ipiv, lapack_int *info); +void dgetrs_(const char *trans, const lapack_int *n, const lapack_int *nrhs, + const double *a, const lapack_int *lda, const lapack_int *ipiv, + double *b, const lapack_int *ldb, lapack_int *info); +void dgetri_(const lapack_int *n, double *a, const lapack_int *lda, + const lapack_int *ipiv, double *work, const lapack_int *lwork, + lapack_int *info); +void zpptrf_(const char *uplo, const lapack_int *n, lapack_complex_double *ap, + lapack_int *info); +void zpptri_(const char *uplo, const lapack_int *n, lapack_complex_double *ap, + lapack_int *info); +#ifdef __cplusplus +} +#endif /* __cplusplus */ #endif /* lapack_intER_H */ diff --git a/lib/awpmd/systems/interact/TCP/wpmd.h b/lib/awpmd/systems/interact/TCP/wpmd.h index 4c65440014..06ac5886c3 100644 --- a/lib/awpmd/systems/interact/TCP/wpmd.h +++ b/lib/awpmd/systems/interact/TCP/wpmd.h @@ -149,10 +149,8 @@ # include "pairhash.h" # include "TCP/tcpdefs.h" # include "wavepacket.h" -# include "erf.h" # include "cerf.h" - using namespace std; # include "lapack_inter.h" diff --git a/lib/awpmd/systems/interact/TCP/wpmd_split.cpp b/lib/awpmd/systems/interact/TCP/wpmd_split.cpp index f85b1ebf59..46a5776fef 100644 --- a/lib/awpmd/systems/interact/TCP/wpmd_split.cpp +++ b/lib/awpmd/systems/interact/TCP/wpmd_split.cpp @@ -1,6 +1,4 @@ # include "wpmd_split.h" -//# include "erf.h" - void AWPMD_split::resize(int flag){ for(int s=0;s<2;s++){ From 6e60131f1449f737ad59ed61f8410444207c15be Mon Sep 17 00:00:00 2001 From: Axel Kohlmeyer Date: Wed, 28 Dec 2022 20:53:53 -0500 Subject: [PATCH 33/47] Windows portability changes --- cmake/CMakeSettings.json | 6 +++--- lib/colvars/colvarbias_meta.cpp | 2 +- lib/colvars/colvarproxy.cpp | 10 +++++----- 3 files changed, 9 insertions(+), 9 deletions(-) diff --git a/cmake/CMakeSettings.json b/cmake/CMakeSettings.json index c139114c0b..205b443bf1 100644 --- a/cmake/CMakeSettings.json +++ b/cmake/CMakeSettings.json @@ -72,7 +72,7 @@ "configurationType": "Debug", "buildRoot": "${workspaceRoot}\\build\\${name}", "installRoot": "${workspaceRoot}\\install\\${name}", - "cmakeCommandArgs": "-C ${workspaceRoot}\\cmake\\presets\\windows.cmake -DCMAKE_C_COMPILER=clang-cl.exe -DCMAKE_CXX_COMPILER=clang-cl.exe", + "cmakeCommandArgs": "-C ${workspaceRoot}\\cmake\\presets\\windows.cmake -DCMAKE_C_COMPILER=clang-cl.exe -DCMAKE_CXX_COMPILER=clang-cl.exe -DBUILD_MPI=off", "buildCommandArgs": "", "ctestCommandArgs": "", "inheritEnvironments": [ "clang_cl_x64" ], @@ -105,7 +105,7 @@ "configurationType": "Release", "buildRoot": "${workspaceRoot}\\build\\${name}", "installRoot": "${workspaceRoot}\\install\\${name}", - "cmakeCommandArgs": "-C ${workspaceRoot}\\cmake\\presets\\windows.cmake -DCMAKE_C_COMPILER=clang-cl.exe -DCMAKE_CXX_COMPILER=clang-cl.exe", + "cmakeCommandArgs": "-C ${workspaceRoot}\\cmake\\presets\\windows.cmake -DCMAKE_C_COMPILER=clang-cl.exe -DCMAKE_CXX_COMPILER=clang-cl.exe -DBUILD_MPI=off", "buildCommandArgs": "", "ctestCommandArgs": "-V", "inheritEnvironments": [ "clang_cl_x64" ], @@ -305,4 +305,4 @@ ] } ] -} +} \ No newline at end of file diff --git a/lib/colvars/colvarbias_meta.cpp b/lib/colvars/colvarbias_meta.cpp index 911a1d89c1..0b31479276 100644 --- a/lib/colvars/colvarbias_meta.cpp +++ b/lib/colvars/colvarbias_meta.cpp @@ -14,7 +14,7 @@ #include // used to set the absolute path of a replica file -#if defined(WIN32) && !defined(__CYGWIN__) +#if defined(_WIN32) && !defined(__CYGWIN__) #include #define CHDIR ::_chdir #define GETCWD ::_getcwd diff --git a/lib/colvars/colvarproxy.cpp b/lib/colvars/colvarproxy.cpp index c091df828c..3d4c9c439b 100644 --- a/lib/colvars/colvarproxy.cpp +++ b/lib/colvars/colvarproxy.cpp @@ -8,10 +8,10 @@ // Colvars repository at GitHub. // Using access() to check if a file exists (until we can assume C++14/17) -#if !defined(WIN32) || defined(__CYGWIN__) +#if !defined(_WIN32) || defined(__CYGWIN__) #include #endif -#if defined(WIN32) +#if defined(_WIN32) #include #endif @@ -678,7 +678,7 @@ int colvarproxy_io::backup_file(char const *filename) // Simplified version of NAMD_file_exists() int exit_code; do { -#if defined(WIN32) && !defined(__CYGWIN__) +#if defined(_WIN32) && !defined(__CYGWIN__) // We could use _access_s here, but it is probably too new exit_code = _access(filename, 00); #else @@ -708,7 +708,7 @@ int colvarproxy_io::backup_file(char const *filename) int colvarproxy_io::remove_file(char const *filename) { int error_code = COLVARS_OK; -#if defined(WIN32) && !defined(__CYGWIN__) +#if defined(_WIN32) && !defined(__CYGWIN__) // Because the file may be open by other processes, rename it to filename.old std::string const renamed_file(std::string(filename)+".old"); // It may still be there from an interrupted run, so remove it to be safe @@ -741,7 +741,7 @@ int colvarproxy_io::remove_file(char const *filename) int colvarproxy_io::rename_file(char const *filename, char const *newfilename) { int error_code = COLVARS_OK; -#if defined(WIN32) && !defined(__CYGWIN__) +#if defined(_WIN32) && !defined(__CYGWIN__) // On straight Windows, must remove the destination before renaming it error_code |= remove_file(newfilename); #endif From 4552a2791d8ad9bf8392907b042e7e1d47c173f3 Mon Sep 17 00:00:00 2001 From: Axel Kohlmeyer Date: Wed, 28 Dec 2022 21:41:31 -0500 Subject: [PATCH 34/47] add explicit dependency and link on linalg when used --- cmake/CMakeLists.txt | 1 + 1 file changed, 1 insertion(+) diff --git a/cmake/CMakeLists.txt b/cmake/CMakeLists.txt index 4351c40d75..21157afc7a 100644 --- a/cmake/CMakeLists.txt +++ b/cmake/CMakeLists.txt @@ -445,6 +445,7 @@ if(PKG_MSCG OR PKG_ATC OR PKG_AWPMD OR PKG_ML-QUIP OR PKG_ML-POD OR PKG_LATTE OR set_target_properties(linalg PROPERTIES OUTPUT_NAME lammps_linalg${LAMMPS_MACHINE}) set(BLAS_LIBRARIES "$") set(LAPACK_LIBRARIES "$") + target_link_libraries(lammps PRIVATE linalg) else() list(APPEND LAPACK_LIBRARIES ${BLAS_LIBRARIES}) endif() From 57790ef35ffd576d3600ad339f0d0d9b4a22cf29 Mon Sep 17 00:00:00 2001 From: Axel Kohlmeyer Date: Sat, 31 Dec 2022 16:59:25 -0500 Subject: [PATCH 35/47] remove fortran sources and update README with pointer to the conversion package --- lib/linalg/README | 11 +- lib/linalg/convert.sh | 65 - lib/linalg/fortran/dasum.f | 131 -- lib/linalg/fortran/daxpy.f | 152 -- lib/linalg/fortran/dbdsqr.f | 864 -------- lib/linalg/fortran/dcabs1.f | 66 - lib/linalg/fortran/dcopy.f | 146 -- lib/linalg/fortran/ddot.f | 148 -- lib/linalg/fortran/dgebd2.f | 317 --- lib/linalg/fortran/dgebrd.f | 349 --- lib/linalg/fortran/dgecon.f | 258 --- lib/linalg/fortran/dgelq2.f | 197 -- lib/linalg/fortran/dgelqf.f | 274 --- lib/linalg/fortran/dgelsd.f | 626 ------ lib/linalg/fortran/dgelss.f | 744 ------- lib/linalg/fortran/dgemm.f | 379 ---- lib/linalg/fortran/dgemv.f | 327 --- lib/linalg/fortran/dgeqr2.f | 198 -- lib/linalg/fortran/dgeqrf.f | 282 --- lib/linalg/fortran/dger.f | 224 -- lib/linalg/fortran/dgesv.f | 176 -- lib/linalg/fortran/dgesvd.f | 3501 ------------------------------ lib/linalg/fortran/dgetf2.f | 210 -- lib/linalg/fortran/dgetrf.f | 222 -- lib/linalg/fortran/dgetrf2.f | 269 --- lib/linalg/fortran/dgetri.f | 258 --- lib/linalg/fortran/dgetrs.f | 222 -- lib/linalg/fortran/disnan.f | 77 - lib/linalg/fortran/dlabad.f | 102 - lib/linalg/fortran/dlabrd.f | 378 ---- lib/linalg/fortran/dlacn2.f | 304 --- lib/linalg/fortran/dlacpy.f | 153 -- lib/linalg/fortran/dladiv.f | 251 --- lib/linalg/fortran/dlae2.f | 182 -- lib/linalg/fortran/dlaed0.f | 431 ---- lib/linalg/fortran/dlaed1.f | 271 --- lib/linalg/fortran/dlaed2.f | 536 ----- lib/linalg/fortran/dlaed3.f | 350 --- lib/linalg/fortran/dlaed4.f | 917 -------- lib/linalg/fortran/dlaed5.f | 186 -- lib/linalg/fortran/dlaed6.f | 407 ---- lib/linalg/fortran/dlaed7.f | 404 ---- lib/linalg/fortran/dlaed8.f | 521 ----- lib/linalg/fortran/dlaed9.f | 291 --- lib/linalg/fortran/dlaeda.f | 305 --- lib/linalg/fortran/dlaev2.f | 235 -- lib/linalg/fortran/dlaisnan.f | 88 - lib/linalg/fortran/dlals0.f | 496 ----- lib/linalg/fortran/dlalsa.f | 490 ----- lib/linalg/fortran/dlalsd.f | 520 ----- lib/linalg/fortran/dlamch.f | 189 -- lib/linalg/fortran/dlamrg.f | 168 -- lib/linalg/fortran/dlange.f | 208 -- lib/linalg/fortran/dlanst.f | 183 -- lib/linalg/fortran/dlansy.f | 238 -- lib/linalg/fortran/dlapy2.f | 117 - lib/linalg/fortran/dlapy3.f | 112 - lib/linalg/fortran/dlarf.f | 224 -- lib/linalg/fortran/dlarfb.f | 709 ------ lib/linalg/fortran/dlarfg.f | 193 -- lib/linalg/fortran/dlarft.f | 323 --- lib/linalg/fortran/dlartg.f | 204 -- lib/linalg/fortran/dlas2.f | 180 -- lib/linalg/fortran/dlascl.f | 367 ---- lib/linalg/fortran/dlasd4.f | 1058 --------- lib/linalg/fortran/dlasd5.f | 228 -- lib/linalg/fortran/dlasd6.f | 440 ---- lib/linalg/fortran/dlasd7.f | 577 ----- lib/linalg/fortran/dlasd8.f | 339 --- lib/linalg/fortran/dlasda.f | 511 ----- lib/linalg/fortran/dlasdq.f | 410 ---- lib/linalg/fortran/dlasdt.f | 169 -- lib/linalg/fortran/dlaset.f | 181 -- lib/linalg/fortran/dlasq1.f | 221 -- lib/linalg/fortran/dlasq2.f | 586 ----- lib/linalg/fortran/dlasq3.f | 418 ---- lib/linalg/fortran/dlasq4.f | 421 ---- lib/linalg/fortran/dlasq5.f | 407 ---- lib/linalg/fortran/dlasq6.f | 251 --- lib/linalg/fortran/dlasr.f | 433 ---- lib/linalg/fortran/dlasrt.f | 300 --- lib/linalg/fortran/dlassq.f | 155 -- lib/linalg/fortran/dlasv2.f | 322 --- lib/linalg/fortran/dlaswp.f | 190 -- lib/linalg/fortran/dlatrd.f | 333 --- lib/linalg/fortran/dlatrs.f | 843 ------- lib/linalg/fortran/dnrm2.f | 132 -- lib/linalg/fortran/dorg2l.f | 195 -- lib/linalg/fortran/dorg2r.f | 197 -- lib/linalg/fortran/dorgbr.f | 334 --- lib/linalg/fortran/dorgl2.f | 201 -- lib/linalg/fortran/dorglq.f | 286 --- lib/linalg/fortran/dorgql.f | 293 --- lib/linalg/fortran/dorgqr.f | 287 --- lib/linalg/fortran/dorgtr.f | 252 --- lib/linalg/fortran/dorm2l.f | 275 --- lib/linalg/fortran/dorm2r.f | 279 --- lib/linalg/fortran/dormbr.f | 369 ---- lib/linalg/fortran/dorml2.f | 279 --- lib/linalg/fortran/dormlq.f | 344 --- lib/linalg/fortran/dormql.f | 336 --- lib/linalg/fortran/dormqr.f | 337 --- lib/linalg/fortran/dormtr.f | 307 --- lib/linalg/fortran/dposv.f | 190 -- lib/linalg/fortran/dpotf2.f | 227 -- lib/linalg/fortran/dpotrf.f | 243 --- lib/linalg/fortran/dpotrf2.f | 234 -- lib/linalg/fortran/dpotrs.f | 201 -- lib/linalg/fortran/drot.f | 142 -- lib/linalg/fortran/drscl.f | 171 -- lib/linalg/fortran/dscal.f | 139 -- lib/linalg/fortran/dstedc.f | 479 ---- lib/linalg/fortran/dsteqr.f | 569 ----- lib/linalg/fortran/dsterf.f | 423 ---- lib/linalg/fortran/dswap.f | 153 -- lib/linalg/fortran/dsyev.f | 283 --- lib/linalg/fortran/dsyevd.f | 354 --- lib/linalg/fortran/dsygs2.f | 280 --- lib/linalg/fortran/dsygst.f | 318 --- lib/linalg/fortran/dsygv.f | 311 --- lib/linalg/fortran/dsygvd.f | 377 ---- lib/linalg/fortran/dsymm.f | 364 ---- lib/linalg/fortran/dsymv.f | 330 --- lib/linalg/fortran/dsyr2.f | 295 --- lib/linalg/fortran/dsyr2k.f | 396 ---- lib/linalg/fortran/dsyrk.f | 361 --- lib/linalg/fortran/dsytd2.f | 320 --- lib/linalg/fortran/dsytrd.f | 373 ---- lib/linalg/fortran/dtrmm.f | 412 ---- 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lib/linalg/static/i_lmp_nint.cpp delete mode 100644 lib/linalg/static/lsame.cpp delete mode 100644 lib/linalg/static/pow_lmp_dd.cpp delete mode 100644 lib/linalg/static/pow_lmp_di.cpp delete mode 100644 lib/linalg/static/pow_lmp_ii.cpp delete mode 100644 lib/linalg/static/s_lmp_cat.cpp delete mode 100644 lib/linalg/static/s_lmp_cmp.cpp delete mode 100644 lib/linalg/static/s_lmp_copy.cpp delete mode 100644 lib/linalg/static/xerbla.cpp delete mode 100644 lib/linalg/static/z_lmp_abs.cpp delete mode 100644 lib/linalg/static/z_lmp_div.cpp delete mode 100644 lib/linalg/static/zlarft.f diff --git a/lib/linalg/README b/lib/linalg/README index 68f17d9986..6c04225d17 100644 --- a/lib/linalg/README +++ b/lib/linalg/README @@ -1,10 +1,13 @@ This directory has generic BLAS and LAPACK source files needed by the ATC, AWPMD, ELECTRODE, LATTE, and ML-POD packages (and possibly by other packages) in the future that can be used instead of platform or vendor -optimized BLAS/LAPACK library. For increased portability, the -BLAS/LAPACK source files have been translated to C++ with f2c. A few -subroutines using Fortran runtime functions have been re-implemented -in C++. Please see the convert.sh script for how the conversion was done. +optimized BLAS/LAPACK library. To simplify installation, these files +have been translated from the Fortran versions of the BLAS and LAPACK +references source files at https://netlib.org/lapack/ to C++ with f2c. +The package with the tools to do the translation and the matching +original Fortran sources are at https://github.com/lammps/linalg. +Please note that even through the files are C++ source code the +resulting library will follow the Fortran binary conventions. Note that this is an *incomplete* subset of full BLAS/LAPACK. diff --git a/lib/linalg/convert.sh b/lib/linalg/convert.sh deleted file mode 100755 index 0dba27c9e3..0000000000 --- a/lib/linalg/convert.sh +++ /dev/null @@ -1,65 +0,0 @@ -#!/bin/bash - -has_f2c=$(type f2c > /dev/null 2>&1 && echo 1 || echo 0) -if test ${has_f2c} -eq 0 -then - echo "Must have f2c installed to run this script" - exit 1 -fi - -# cleanup -rm -f *.c *.cpp *.P *~ *.orig *.bak *.rej - -# translate original files directly -for f in fortran/*.f -do \ - b=$(basename $f .f) - # skip files for which we have replacements - if test $b == dgetrf2 || test $b == disnan || test $b == dlaisnan || \ - test $b == dlamch || test $b == dlarft || test $b == dpotrf2 || \ - test $b == lsame || test $b == xerbla || test $b == zlarft - then - echo Skipping $b - else - # convert to C++ with f2c, make local variables dynamic, - # strip comments, and reindent with clang-format. - f2c -C++ -a -f < $f \ - | g++ -fpreprocessed -dD -P -E - \ - | clang-format -style=file:static/.clang-format > $b.cpp || exit 2 - # silence c++ compiler warnings about string constants, use custom f2c header - sed -i -e 's/\("[^"]\+"\)/(char *)\1/g' -e 's/^extern.*"C"/extern "C"/' \ - -e 's/^#include.*"f2c.h"/#include "lmp_f2c.h"/' $b.cpp - # replace libf2c functions with local versions under different names - sed -i -e 's/s_\(cat\|cmp\|copy\)(/s_lmp_\1(/g' \ - -e 's/d_\(sign\|cnjg\|imag\|lg10\)(/d_lmp_\1(/g' \ - -e 's/z_\(abs\|div\)(/z_lmp_\1(/g' \ - -e 's/i_\(len\|nint\|dnnt\)(/i_lmp_\1(/g' \ - -e 's/pow_\(dd\|di\|ii\)(/pow_lmp_\1(/g' $b.cpp - fi -done - -# translate modified versions -for f in static/*.f -do \ - b=$(basename $f .f) - # convert to C++ with f2c, make local variables dynamic, - # strip comments, and reindent with clang-format. - f2c -C++ -a -f < $f \ - | g++ -fpreprocessed -dD -P -E - \ - | clang-format -style=file:static/.clang-format > $b.cpp || exit 2 - # silence c++ compiler warnings about string constants, use custom f2c header - sed -i -e 's/\("[^"]\+"\)/(char *)\1/g' -e 's/^extern.*"C"/extern "C"/' \ - -e 's/^#include.*"f2c.h"/#include "lmp_f2c.h"/' $b.cpp - # replace libf2c functions with local versions under different names - sed -i -e 's/s_\(cat\|cmp\|copy\)(/s_lmp_\1(/g' \ - -e 's/d_\(sign\|cnjg\|imag\|lg10\)(/d_lmp_\1(/g' \ - -e 's/z_\(abs\|div\)(/z_lmp_\1(/g' \ - -e 's/i_\(len\|nint\|dnnt\)(/i_lmp_\1(/g' \ - -e 's/pow_\(dd\|di\|ii\)(/pow_lmp_\1(/g' $b.cpp -done - -# copy direct C++ alternatives -for c in static/*.cpp -do \ - cp -v $c . -done diff --git a/lib/linalg/fortran/dasum.f b/lib/linalg/fortran/dasum.f deleted file mode 100644 index 9a360b5acd..0000000000 --- a/lib/linalg/fortran/dasum.f +++ /dev/null @@ -1,131 +0,0 @@ -*> \brief \b DASUM -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* DOUBLE PRECISION FUNCTION DASUM(N,DX,INCX) -* -* .. Scalar Arguments .. -* INTEGER INCX,N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION DX(*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DASUM takes the sum of the absolute values. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> number of elements in input vector(s) -*> \endverbatim -*> -*> \param[in] DX -*> \verbatim -*> DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> storage spacing between elements of DX -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup double_blas_level1 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> jack dongarra, linpack, 3/11/78. -*> modified 3/93 to return if incx .le. 0. -*> modified 12/3/93, array(1) declarations changed to array(*) -*> \endverbatim -*> -* ===================================================================== - DOUBLE PRECISION FUNCTION DASUM(N,DX,INCX) -* -* -- Reference BLAS level1 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INCX,N -* .. -* .. Array Arguments .. - DOUBLE PRECISION DX(*) -* .. -* -* ===================================================================== -* -* .. Local Scalars .. - DOUBLE PRECISION DTEMP - INTEGER I,M,MP1,NINCX -* .. -* .. Intrinsic Functions .. - INTRINSIC DABS,MOD -* .. - DASUM = 0.0d0 - DTEMP = 0.0d0 - IF (N.LE.0 .OR. INCX.LE.0) RETURN - IF (INCX.EQ.1) THEN -* code for increment equal to 1 -* -* -* clean-up loop -* - M = MOD(N,6) - IF (M.NE.0) THEN - DO I = 1,M - DTEMP = DTEMP + DABS(DX(I)) - END DO - IF (N.LT.6) THEN - DASUM = DTEMP - RETURN - END IF - END IF - MP1 = M + 1 - DO I = MP1,N,6 - DTEMP = DTEMP + DABS(DX(I)) + DABS(DX(I+1)) + - $ DABS(DX(I+2)) + DABS(DX(I+3)) + - $ DABS(DX(I+4)) + DABS(DX(I+5)) - END DO - ELSE -* -* code for increment not equal to 1 -* - NINCX = N*INCX - DO I = 1,NINCX,INCX - DTEMP = DTEMP + DABS(DX(I)) - END DO - END IF - DASUM = DTEMP - RETURN -* -* End of DASUM -* - END diff --git a/lib/linalg/fortran/daxpy.f b/lib/linalg/fortran/daxpy.f deleted file mode 100644 index 421f7c630b..0000000000 --- a/lib/linalg/fortran/daxpy.f +++ /dev/null @@ -1,152 +0,0 @@ -*> \brief \b DAXPY -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE DAXPY(N,DA,DX,INCX,DY,INCY) -* -* .. Scalar Arguments .. -* DOUBLE PRECISION DA -* INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION DX(*),DY(*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DAXPY constant times a vector plus a vector. -*> uses unrolled loops for increments equal to one. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> number of elements in input vector(s) -*> \endverbatim -*> -*> \param[in] DA -*> \verbatim -*> DA is DOUBLE PRECISION -*> On entry, DA specifies the scalar alpha. -*> \endverbatim -*> -*> \param[in] DX -*> \verbatim -*> DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> storage spacing between elements of DX -*> \endverbatim -*> -*> \param[in,out] DY -*> \verbatim -*> DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) -*> \endverbatim -*> -*> \param[in] INCY -*> \verbatim -*> INCY is INTEGER -*> storage spacing between elements of DY -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup double_blas_level1 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> jack dongarra, linpack, 3/11/78. -*> modified 12/3/93, array(1) declarations changed to array(*) -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DAXPY(N,DA,DX,INCX,DY,INCY) -* -* -- Reference BLAS level1 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - DOUBLE PRECISION DA - INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. - DOUBLE PRECISION DX(*),DY(*) -* .. -* -* ===================================================================== -* -* .. Local Scalars .. - INTEGER I,IX,IY,M,MP1 -* .. -* .. Intrinsic Functions .. - INTRINSIC MOD -* .. - IF (N.LE.0) RETURN - IF (DA.EQ.0.0d0) RETURN - IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN -* -* code for both increments equal to 1 -* -* -* clean-up loop -* - M = MOD(N,4) - IF (M.NE.0) THEN - DO I = 1,M - DY(I) = DY(I) + DA*DX(I) - END DO - END IF - IF (N.LT.4) RETURN - MP1 = M + 1 - DO I = MP1,N,4 - DY(I) = DY(I) + DA*DX(I) - DY(I+1) = DY(I+1) + DA*DX(I+1) - DY(I+2) = DY(I+2) + DA*DX(I+2) - DY(I+3) = DY(I+3) + DA*DX(I+3) - END DO - ELSE -* -* code for unequal increments or equal increments -* not equal to 1 -* - IX = 1 - IY = 1 - IF (INCX.LT.0) IX = (-N+1)*INCX + 1 - IF (INCY.LT.0) IY = (-N+1)*INCY + 1 - DO I = 1,N - DY(IY) = DY(IY) + DA*DX(IX) - IX = IX + INCX - IY = IY + INCY - END DO - END IF - RETURN -* -* End of DAXPY -* - END diff --git a/lib/linalg/fortran/dbdsqr.f b/lib/linalg/fortran/dbdsqr.f deleted file mode 100644 index c220a5875d..0000000000 --- a/lib/linalg/fortran/dbdsqr.f +++ /dev/null @@ -1,864 +0,0 @@ -*> \brief \b DBDSQR -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DBDSQR + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DBDSQR( UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, -* LDU, C, LDC, WORK, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER UPLO -* INTEGER INFO, LDC, LDU, LDVT, N, NCC, NCVT, NRU -* .. -* .. Array Arguments .. -* DOUBLE PRECISION C( LDC, * ), D( * ), E( * ), U( LDU, * ), -* $ VT( LDVT, * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DBDSQR computes the singular values and, optionally, the right and/or -*> left singular vectors from the singular value decomposition (SVD) of -*> a real N-by-N (upper or lower) bidiagonal matrix B using the implicit -*> zero-shift QR algorithm. The SVD of B has the form -*> -*> B = Q * S * P**T -*> -*> where S is the diagonal matrix of singular values, Q is an orthogonal -*> matrix of left singular vectors, and P is an orthogonal matrix of -*> right singular vectors. If left singular vectors are requested, this -*> subroutine actually returns U*Q instead of Q, and, if right singular -*> vectors are requested, this subroutine returns P**T*VT instead of -*> P**T, for given real input matrices U and VT. When U and VT are the -*> orthogonal matrices that reduce a general matrix A to bidiagonal -*> form: A = U*B*VT, as computed by DGEBRD, then -*> -*> A = (U*Q) * S * (P**T*VT) -*> -*> is the SVD of A. Optionally, the subroutine may also compute Q**T*C -*> for a given real input matrix C. -*> -*> See "Computing Small Singular Values of Bidiagonal Matrices With -*> Guaranteed High Relative Accuracy," by J. Demmel and W. Kahan, -*> LAPACK Working Note #3 (or SIAM J. Sci. Statist. Comput. vol. 11, -*> no. 5, pp. 873-912, Sept 1990) and -*> "Accurate singular values and differential qd algorithms," by -*> B. Parlett and V. Fernando, Technical Report CPAM-554, Mathematics -*> Department, University of California at Berkeley, July 1992 -*> for a detailed description of the algorithm. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> = 'U': B is upper bidiagonal; -*> = 'L': B is lower bidiagonal. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrix B. N >= 0. -*> \endverbatim -*> -*> \param[in] NCVT -*> \verbatim -*> NCVT is INTEGER -*> The number of columns of the matrix VT. NCVT >= 0. -*> \endverbatim -*> -*> \param[in] NRU -*> \verbatim -*> NRU is INTEGER -*> The number of rows of the matrix U. NRU >= 0. -*> \endverbatim -*> -*> \param[in] NCC -*> \verbatim -*> NCC is INTEGER -*> The number of columns of the matrix C. NCC >= 0. -*> \endverbatim -*> -*> \param[in,out] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension (N) -*> On entry, the n diagonal elements of the bidiagonal matrix B. -*> On exit, if INFO=0, the singular values of B in decreasing -*> order. -*> \endverbatim -*> -*> \param[in,out] E -*> \verbatim -*> E is DOUBLE PRECISION array, dimension (N-1) -*> On entry, the N-1 offdiagonal elements of the bidiagonal -*> matrix B. -*> On exit, if INFO = 0, E is destroyed; if INFO > 0, D and E -*> will contain the diagonal and superdiagonal elements of a -*> bidiagonal matrix orthogonally equivalent to the one given -*> as input. -*> \endverbatim -*> -*> \param[in,out] VT -*> \verbatim -*> VT is DOUBLE PRECISION array, dimension (LDVT, NCVT) -*> On entry, an N-by-NCVT matrix VT. -*> On exit, VT is overwritten by P**T * VT. -*> Not referenced if NCVT = 0. -*> \endverbatim -*> -*> \param[in] LDVT -*> \verbatim -*> LDVT is INTEGER -*> The leading dimension of the array VT. -*> LDVT >= max(1,N) if NCVT > 0; LDVT >= 1 if NCVT = 0. -*> \endverbatim -*> -*> \param[in,out] U -*> \verbatim -*> U is DOUBLE PRECISION array, dimension (LDU, N) -*> On entry, an NRU-by-N matrix U. -*> On exit, U is overwritten by U * Q. -*> Not referenced if NRU = 0. -*> \endverbatim -*> -*> \param[in] LDU -*> \verbatim -*> LDU is INTEGER -*> The leading dimension of the array U. LDU >= max(1,NRU). -*> \endverbatim -*> -*> \param[in,out] C -*> \verbatim -*> C is DOUBLE PRECISION array, dimension (LDC, NCC) -*> On entry, an N-by-NCC matrix C. -*> On exit, C is overwritten by Q**T * C. -*> Not referenced if NCC = 0. -*> \endverbatim -*> -*> \param[in] LDC -*> \verbatim -*> LDC is INTEGER -*> The leading dimension of the array C. -*> LDC >= max(1,N) if NCC > 0; LDC >=1 if NCC = 0. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (4*(N-1)) -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: If INFO = -i, the i-th argument had an illegal value -*> > 0: -*> if NCVT = NRU = NCC = 0, -*> = 1, a split was marked by a positive value in E -*> = 2, current block of Z not diagonalized after 30*N -*> iterations (in inner while loop) -*> = 3, termination criterion of outer while loop not met -*> (program created more than N unreduced blocks) -*> else NCVT = NRU = NCC = 0, -*> the algorithm did not converge; D and E contain the -*> elements of a bidiagonal matrix which is orthogonally -*> similar to the input matrix B; if INFO = i, i -*> elements of E have not converged to zero. -*> \endverbatim -* -*> \par Internal Parameters: -* ========================= -*> -*> \verbatim -*> TOLMUL DOUBLE PRECISION, default = max(10,min(100,EPS**(-1/8))) -*> TOLMUL controls the convergence criterion of the QR loop. -*> If it is positive, TOLMUL*EPS is the desired relative -*> precision in the computed singular values. -*> If it is negative, abs(TOLMUL*EPS*sigma_max) is the -*> desired absolute accuracy in the computed singular -*> values (corresponds to relative accuracy -*> abs(TOLMUL*EPS) in the largest singular value. -*> abs(TOLMUL) should be between 1 and 1/EPS, and preferably -*> between 10 (for fast convergence) and .1/EPS -*> (for there to be some accuracy in the results). -*> Default is to lose at either one eighth or 2 of the -*> available decimal digits in each computed singular value -*> (whichever is smaller). -*> -*> MAXITR INTEGER, default = 6 -*> MAXITR controls the maximum number of passes of the -*> algorithm through its inner loop. The algorithms stops -*> (and so fails to converge) if the number of passes -*> through the inner loop exceeds MAXITR*N**2. -*> -*> \endverbatim -* -*> \par Note: -* =========== -*> -*> \verbatim -*> Bug report from Cezary Dendek. -*> On March 23rd 2017, the INTEGER variable MAXIT = MAXITR*N**2 is -*> removed since it can overflow pretty easily (for N larger or equal -*> than 18,919). We instead use MAXITDIVN = MAXITR*N. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup auxOTHERcomputational -* -* ===================================================================== - SUBROUTINE DBDSQR( UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, - $ LDU, C, LDC, WORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER UPLO - INTEGER INFO, LDC, LDU, LDVT, N, NCC, NCVT, NRU -* .. -* .. Array Arguments .. - DOUBLE PRECISION C( LDC, * ), D( * ), E( * ), U( LDU, * ), - $ VT( LDVT, * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO - PARAMETER ( ZERO = 0.0D0 ) - DOUBLE PRECISION ONE - PARAMETER ( ONE = 1.0D0 ) - DOUBLE PRECISION NEGONE - PARAMETER ( NEGONE = -1.0D0 ) - DOUBLE PRECISION HNDRTH - PARAMETER ( HNDRTH = 0.01D0 ) - DOUBLE PRECISION TEN - PARAMETER ( TEN = 10.0D0 ) - DOUBLE PRECISION HNDRD - PARAMETER ( HNDRD = 100.0D0 ) - DOUBLE PRECISION MEIGTH - PARAMETER ( MEIGTH = -0.125D0 ) - INTEGER MAXITR - PARAMETER ( MAXITR = 6 ) -* .. -* .. Local Scalars .. - LOGICAL LOWER, ROTATE - INTEGER I, IDIR, ISUB, ITER, ITERDIVN, J, LL, LLL, M, - $ MAXITDIVN, NM1, NM12, NM13, OLDLL, OLDM - DOUBLE PRECISION ABSE, ABSS, COSL, COSR, CS, EPS, F, G, H, MU, - $ OLDCS, OLDSN, R, SHIFT, SIGMN, SIGMX, SINL, - $ SINR, SLL, SMAX, SMIN, SMINL, SMINOA, - $ SN, THRESH, TOL, TOLMUL, UNFL -* .. -* .. External Functions .. - LOGICAL LSAME - DOUBLE PRECISION DLAMCH - EXTERNAL LSAME, DLAMCH -* .. -* .. External Subroutines .. - EXTERNAL DLARTG, DLAS2, DLASQ1, DLASR, DLASV2, DROT, - $ DSCAL, DSWAP, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, DBLE, MAX, MIN, SIGN, SQRT -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 - LOWER = LSAME( UPLO, 'L' ) - IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LOWER ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( NCVT.LT.0 ) THEN - INFO = -3 - ELSE IF( NRU.LT.0 ) THEN - INFO = -4 - ELSE IF( NCC.LT.0 ) THEN - INFO = -5 - ELSE IF( ( NCVT.EQ.0 .AND. LDVT.LT.1 ) .OR. - $ ( NCVT.GT.0 .AND. LDVT.LT.MAX( 1, N ) ) ) THEN - INFO = -9 - ELSE IF( LDU.LT.MAX( 1, NRU ) ) THEN - INFO = -11 - ELSE IF( ( NCC.EQ.0 .AND. LDC.LT.1 ) .OR. - $ ( NCC.GT.0 .AND. LDC.LT.MAX( 1, N ) ) ) THEN - INFO = -13 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DBDSQR', -INFO ) - RETURN - END IF - IF( N.EQ.0 ) - $ RETURN - IF( N.EQ.1 ) - $ GO TO 160 -* -* ROTATE is true if any singular vectors desired, false otherwise -* - ROTATE = ( NCVT.GT.0 ) .OR. ( NRU.GT.0 ) .OR. ( NCC.GT.0 ) -* -* If no singular vectors desired, use qd algorithm -* - IF( .NOT.ROTATE ) THEN - CALL DLASQ1( N, D, E, WORK, INFO ) -* -* If INFO equals 2, dqds didn't finish, try to finish -* - IF( INFO .NE. 2 ) RETURN - INFO = 0 - END IF -* - NM1 = N - 1 - NM12 = NM1 + NM1 - NM13 = NM12 + NM1 - IDIR = 0 -* -* Get machine constants -* - EPS = DLAMCH( 'Epsilon' ) - UNFL = DLAMCH( 'Safe minimum' ) -* -* If matrix lower bidiagonal, rotate to be upper bidiagonal -* by applying Givens rotations on the left -* - IF( LOWER ) THEN - DO 10 I = 1, N - 1 - CALL DLARTG( D( I ), E( I ), CS, SN, R ) - D( I ) = R - E( I ) = SN*D( I+1 ) - D( I+1 ) = CS*D( I+1 ) - WORK( I ) = CS - WORK( NM1+I ) = SN - 10 CONTINUE -* -* Update singular vectors if desired -* - IF( NRU.GT.0 ) - $ CALL DLASR( 'R', 'V', 'F', NRU, N, WORK( 1 ), WORK( N ), U, - $ LDU ) - IF( NCC.GT.0 ) - $ CALL DLASR( 'L', 'V', 'F', N, NCC, WORK( 1 ), WORK( N ), C, - $ LDC ) - END IF -* -* Compute singular values to relative accuracy TOL -* (By setting TOL to be negative, algorithm will compute -* singular values to absolute accuracy ABS(TOL)*norm(input matrix)) -* - TOLMUL = MAX( TEN, MIN( HNDRD, EPS**MEIGTH ) ) - TOL = TOLMUL*EPS -* -* Compute approximate maximum, minimum singular values -* - SMAX = ZERO - DO 20 I = 1, N - SMAX = MAX( SMAX, ABS( D( I ) ) ) - 20 CONTINUE - DO 30 I = 1, N - 1 - SMAX = MAX( SMAX, ABS( E( I ) ) ) - 30 CONTINUE - SMINL = ZERO - IF( TOL.GE.ZERO ) THEN -* -* Relative accuracy desired -* - SMINOA = ABS( D( 1 ) ) - IF( SMINOA.EQ.ZERO ) - $ GO TO 50 - MU = SMINOA - DO 40 I = 2, N - MU = ABS( D( I ) )*( MU / ( MU+ABS( E( I-1 ) ) ) ) - SMINOA = MIN( SMINOA, MU ) - IF( SMINOA.EQ.ZERO ) - $ GO TO 50 - 40 CONTINUE - 50 CONTINUE - SMINOA = SMINOA / SQRT( DBLE( N ) ) - THRESH = MAX( TOL*SMINOA, MAXITR*(N*(N*UNFL)) ) - ELSE -* -* Absolute accuracy desired -* - THRESH = MAX( ABS( TOL )*SMAX, MAXITR*(N*(N*UNFL)) ) - END IF -* -* Prepare for main iteration loop for the singular values -* (MAXIT is the maximum number of passes through the inner -* loop permitted before nonconvergence signalled.) -* - MAXITDIVN = MAXITR*N - ITERDIVN = 0 - ITER = -1 - OLDLL = -1 - OLDM = -1 -* -* M points to last element of unconverged part of matrix -* - M = N -* -* Begin main iteration loop -* - 60 CONTINUE -* -* Check for convergence or exceeding iteration count -* - IF( M.LE.1 ) - $ GO TO 160 -* - IF( ITER.GE.N ) THEN - ITER = ITER - N - ITERDIVN = ITERDIVN + 1 - IF( ITERDIVN.GE.MAXITDIVN ) - $ GO TO 200 - END IF -* -* Find diagonal block of matrix to work on -* - IF( TOL.LT.ZERO .AND. ABS( D( M ) ).LE.THRESH ) - $ D( M ) = ZERO - SMAX = ABS( D( M ) ) - SMIN = SMAX - DO 70 LLL = 1, M - 1 - LL = M - LLL - ABSS = ABS( D( LL ) ) - ABSE = ABS( E( LL ) ) - IF( TOL.LT.ZERO .AND. ABSS.LE.THRESH ) - $ D( LL ) = ZERO - IF( ABSE.LE.THRESH ) - $ GO TO 80 - SMIN = MIN( SMIN, ABSS ) - SMAX = MAX( SMAX, ABSS, ABSE ) - 70 CONTINUE - LL = 0 - GO TO 90 - 80 CONTINUE - E( LL ) = ZERO -* -* Matrix splits since E(LL) = 0 -* - IF( LL.EQ.M-1 ) THEN -* -* Convergence of bottom singular value, return to top of loop -* - M = M - 1 - GO TO 60 - END IF - 90 CONTINUE - LL = LL + 1 -* -* E(LL) through E(M-1) are nonzero, E(LL-1) is zero -* - IF( LL.EQ.M-1 ) THEN -* -* 2 by 2 block, handle separately -* - CALL DLASV2( D( M-1 ), E( M-1 ), D( M ), SIGMN, SIGMX, SINR, - $ COSR, SINL, COSL ) - D( M-1 ) = SIGMX - E( M-1 ) = ZERO - D( M ) = SIGMN -* -* Compute singular vectors, if desired -* - IF( NCVT.GT.0 ) - $ CALL DROT( NCVT, VT( M-1, 1 ), LDVT, VT( M, 1 ), LDVT, COSR, - $ SINR ) - IF( NRU.GT.0 ) - $ CALL DROT( NRU, U( 1, M-1 ), 1, U( 1, M ), 1, COSL, SINL ) - IF( NCC.GT.0 ) - $ CALL DROT( NCC, C( M-1, 1 ), LDC, C( M, 1 ), LDC, COSL, - $ SINL ) - M = M - 2 - GO TO 60 - END IF -* -* If working on new submatrix, choose shift direction -* (from larger end diagonal element towards smaller) -* - IF( LL.GT.OLDM .OR. M.LT.OLDLL ) THEN - IF( ABS( D( LL ) ).GE.ABS( D( M ) ) ) THEN -* -* Chase bulge from top (big end) to bottom (small end) -* - IDIR = 1 - ELSE -* -* Chase bulge from bottom (big end) to top (small end) -* - IDIR = 2 - END IF - END IF -* -* Apply convergence tests -* - IF( IDIR.EQ.1 ) THEN -* -* Run convergence test in forward direction -* First apply standard test to bottom of matrix -* - IF( ABS( E( M-1 ) ).LE.ABS( TOL )*ABS( D( M ) ) .OR. - $ ( TOL.LT.ZERO .AND. ABS( E( M-1 ) ).LE.THRESH ) ) THEN - E( M-1 ) = ZERO - GO TO 60 - END IF -* - IF( TOL.GE.ZERO ) THEN -* -* If relative accuracy desired, -* apply convergence criterion forward -* - MU = ABS( D( LL ) ) - SMINL = MU - DO 100 LLL = LL, M - 1 - IF( ABS( E( LLL ) ).LE.TOL*MU ) THEN - E( LLL ) = ZERO - GO TO 60 - END IF - MU = ABS( D( LLL+1 ) )*( MU / ( MU+ABS( E( LLL ) ) ) ) - SMINL = MIN( SMINL, MU ) - 100 CONTINUE - END IF -* - ELSE -* -* Run convergence test in backward direction -* First apply standard test to top of matrix -* - IF( ABS( E( LL ) ).LE.ABS( TOL )*ABS( D( LL ) ) .OR. - $ ( TOL.LT.ZERO .AND. ABS( E( LL ) ).LE.THRESH ) ) THEN - E( LL ) = ZERO - GO TO 60 - END IF -* - IF( TOL.GE.ZERO ) THEN -* -* If relative accuracy desired, -* apply convergence criterion backward -* - MU = ABS( D( M ) ) - SMINL = MU - DO 110 LLL = M - 1, LL, -1 - IF( ABS( E( LLL ) ).LE.TOL*MU ) THEN - E( LLL ) = ZERO - GO TO 60 - END IF - MU = ABS( D( LLL ) )*( MU / ( MU+ABS( E( LLL ) ) ) ) - SMINL = MIN( SMINL, MU ) - 110 CONTINUE - END IF - END IF - OLDLL = LL - OLDM = M -* -* Compute shift. First, test if shifting would ruin relative -* accuracy, and if so set the shift to zero. -* - IF( TOL.GE.ZERO .AND. N*TOL*( SMINL / SMAX ).LE. - $ MAX( EPS, HNDRTH*TOL ) ) THEN -* -* Use a zero shift to avoid loss of relative accuracy -* - SHIFT = ZERO - ELSE -* -* Compute the shift from 2-by-2 block at end of matrix -* - IF( IDIR.EQ.1 ) THEN - SLL = ABS( D( LL ) ) - CALL DLAS2( D( M-1 ), E( M-1 ), D( M ), SHIFT, R ) - ELSE - SLL = ABS( D( M ) ) - CALL DLAS2( D( LL ), E( LL ), D( LL+1 ), SHIFT, R ) - END IF -* -* Test if shift negligible, and if so set to zero -* - IF( SLL.GT.ZERO ) THEN - IF( ( SHIFT / SLL )**2.LT.EPS ) - $ SHIFT = ZERO - END IF - END IF -* -* Increment iteration count -* - ITER = ITER + M - LL -* -* If SHIFT = 0, do simplified QR iteration -* - IF( SHIFT.EQ.ZERO ) THEN - IF( IDIR.EQ.1 ) THEN -* -* Chase bulge from top to bottom -* Save cosines and sines for later singular vector updates -* - CS = ONE - OLDCS = ONE - DO 120 I = LL, M - 1 - CALL DLARTG( D( I )*CS, E( I ), CS, SN, R ) - IF( I.GT.LL ) - $ E( I-1 ) = OLDSN*R - CALL DLARTG( OLDCS*R, D( I+1 )*SN, OLDCS, OLDSN, D( I ) ) - WORK( I-LL+1 ) = CS - WORK( I-LL+1+NM1 ) = SN - WORK( I-LL+1+NM12 ) = OLDCS - WORK( I-LL+1+NM13 ) = OLDSN - 120 CONTINUE - H = D( M )*CS - D( M ) = H*OLDCS - E( M-1 ) = H*OLDSN -* -* Update singular vectors -* - IF( NCVT.GT.0 ) - $ CALL DLASR( 'L', 'V', 'F', M-LL+1, NCVT, WORK( 1 ), - $ WORK( N ), VT( LL, 1 ), LDVT ) - IF( NRU.GT.0 ) - $ CALL DLASR( 'R', 'V', 'F', NRU, M-LL+1, WORK( NM12+1 ), - $ WORK( NM13+1 ), U( 1, LL ), LDU ) - IF( NCC.GT.0 ) - $ CALL DLASR( 'L', 'V', 'F', M-LL+1, NCC, WORK( NM12+1 ), - $ WORK( NM13+1 ), C( LL, 1 ), LDC ) -* -* Test convergence -* - IF( ABS( E( M-1 ) ).LE.THRESH ) - $ E( M-1 ) = ZERO -* - ELSE -* -* Chase bulge from bottom to top -* Save cosines and sines for later singular vector updates -* - CS = ONE - OLDCS = ONE - DO 130 I = M, LL + 1, -1 - CALL DLARTG( D( I )*CS, E( I-1 ), CS, SN, R ) - IF( I.LT.M ) - $ E( I ) = OLDSN*R - CALL DLARTG( OLDCS*R, D( I-1 )*SN, OLDCS, OLDSN, D( I ) ) - WORK( I-LL ) = CS - WORK( I-LL+NM1 ) = -SN - WORK( I-LL+NM12 ) = OLDCS - WORK( I-LL+NM13 ) = -OLDSN - 130 CONTINUE - H = D( LL )*CS - D( LL ) = H*OLDCS - E( LL ) = H*OLDSN -* -* Update singular vectors -* - IF( NCVT.GT.0 ) - $ CALL DLASR( 'L', 'V', 'B', M-LL+1, NCVT, WORK( NM12+1 ), - $ WORK( NM13+1 ), VT( LL, 1 ), LDVT ) - IF( NRU.GT.0 ) - $ CALL DLASR( 'R', 'V', 'B', NRU, M-LL+1, WORK( 1 ), - $ WORK( N ), U( 1, LL ), LDU ) - IF( NCC.GT.0 ) - $ CALL DLASR( 'L', 'V', 'B', M-LL+1, NCC, WORK( 1 ), - $ WORK( N ), C( LL, 1 ), LDC ) -* -* Test convergence -* - IF( ABS( E( LL ) ).LE.THRESH ) - $ E( LL ) = ZERO - END IF - ELSE -* -* Use nonzero shift -* - IF( IDIR.EQ.1 ) THEN -* -* Chase bulge from top to bottom -* Save cosines and sines for later singular vector updates -* - F = ( ABS( D( LL ) )-SHIFT )* - $ ( SIGN( ONE, D( LL ) )+SHIFT / D( LL ) ) - G = E( LL ) - DO 140 I = LL, M - 1 - CALL DLARTG( F, G, COSR, SINR, R ) - IF( I.GT.LL ) - $ E( I-1 ) = R - F = COSR*D( I ) + SINR*E( I ) - E( I ) = COSR*E( I ) - SINR*D( I ) - G = SINR*D( I+1 ) - D( I+1 ) = COSR*D( I+1 ) - CALL DLARTG( F, G, COSL, SINL, R ) - D( I ) = R - F = COSL*E( I ) + SINL*D( I+1 ) - D( I+1 ) = COSL*D( I+1 ) - SINL*E( I ) - IF( I.LT.M-1 ) THEN - G = SINL*E( I+1 ) - E( I+1 ) = COSL*E( I+1 ) - END IF - WORK( I-LL+1 ) = COSR - WORK( I-LL+1+NM1 ) = SINR - WORK( I-LL+1+NM12 ) = COSL - WORK( I-LL+1+NM13 ) = SINL - 140 CONTINUE - E( M-1 ) = F -* -* Update singular vectors -* - IF( NCVT.GT.0 ) - $ CALL DLASR( 'L', 'V', 'F', M-LL+1, NCVT, WORK( 1 ), - $ WORK( N ), VT( LL, 1 ), LDVT ) - IF( NRU.GT.0 ) - $ CALL DLASR( 'R', 'V', 'F', NRU, M-LL+1, WORK( NM12+1 ), - $ WORK( NM13+1 ), U( 1, LL ), LDU ) - IF( NCC.GT.0 ) - $ CALL DLASR( 'L', 'V', 'F', M-LL+1, NCC, WORK( NM12+1 ), - $ WORK( NM13+1 ), C( LL, 1 ), LDC ) -* -* Test convergence -* - IF( ABS( E( M-1 ) ).LE.THRESH ) - $ E( M-1 ) = ZERO -* - ELSE -* -* Chase bulge from bottom to top -* Save cosines and sines for later singular vector updates -* - F = ( ABS( D( M ) )-SHIFT )*( SIGN( ONE, D( M ) )+SHIFT / - $ D( M ) ) - G = E( M-1 ) - DO 150 I = M, LL + 1, -1 - CALL DLARTG( F, G, COSR, SINR, R ) - IF( I.LT.M ) - $ E( I ) = R - F = COSR*D( I ) + SINR*E( I-1 ) - E( I-1 ) = COSR*E( I-1 ) - SINR*D( I ) - G = SINR*D( I-1 ) - D( I-1 ) = COSR*D( I-1 ) - CALL DLARTG( F, G, COSL, SINL, R ) - D( I ) = R - F = COSL*E( I-1 ) + SINL*D( I-1 ) - D( I-1 ) = COSL*D( I-1 ) - SINL*E( I-1 ) - IF( I.GT.LL+1 ) THEN - G = SINL*E( I-2 ) - E( I-2 ) = COSL*E( I-2 ) - END IF - WORK( I-LL ) = COSR - WORK( I-LL+NM1 ) = -SINR - WORK( I-LL+NM12 ) = COSL - WORK( I-LL+NM13 ) = -SINL - 150 CONTINUE - E( LL ) = F -* -* Test convergence -* - IF( ABS( E( LL ) ).LE.THRESH ) - $ E( LL ) = ZERO -* -* Update singular vectors if desired -* - IF( NCVT.GT.0 ) - $ CALL DLASR( 'L', 'V', 'B', M-LL+1, NCVT, WORK( NM12+1 ), - $ WORK( NM13+1 ), VT( LL, 1 ), LDVT ) - IF( NRU.GT.0 ) - $ CALL DLASR( 'R', 'V', 'B', NRU, M-LL+1, WORK( 1 ), - $ WORK( N ), U( 1, LL ), LDU ) - IF( NCC.GT.0 ) - $ CALL DLASR( 'L', 'V', 'B', M-LL+1, NCC, WORK( 1 ), - $ WORK( N ), C( LL, 1 ), LDC ) - END IF - END IF -* -* QR iteration finished, go back and check convergence -* - GO TO 60 -* -* All singular values converged, so make them positive -* - 160 CONTINUE - DO 170 I = 1, N - IF( D( I ).LT.ZERO ) THEN - D( I ) = -D( I ) -* -* Change sign of singular vectors, if desired -* - IF( NCVT.GT.0 ) - $ CALL DSCAL( NCVT, NEGONE, VT( I, 1 ), LDVT ) - END IF - 170 CONTINUE -* -* Sort the singular values into decreasing order (insertion sort on -* singular values, but only one transposition per singular vector) -* - DO 190 I = 1, N - 1 -* -* Scan for smallest D(I) -* - ISUB = 1 - SMIN = D( 1 ) - DO 180 J = 2, N + 1 - I - IF( D( J ).LE.SMIN ) THEN - ISUB = J - SMIN = D( J ) - END IF - 180 CONTINUE - IF( ISUB.NE.N+1-I ) THEN -* -* Swap singular values and vectors -* - D( ISUB ) = D( N+1-I ) - D( N+1-I ) = SMIN - IF( NCVT.GT.0 ) - $ CALL DSWAP( NCVT, VT( ISUB, 1 ), LDVT, VT( N+1-I, 1 ), - $ LDVT ) - IF( NRU.GT.0 ) - $ CALL DSWAP( NRU, U( 1, ISUB ), 1, U( 1, N+1-I ), 1 ) - IF( NCC.GT.0 ) - $ CALL DSWAP( NCC, C( ISUB, 1 ), LDC, C( N+1-I, 1 ), LDC ) - END IF - 190 CONTINUE - GO TO 220 -* -* Maximum number of iterations exceeded, failure to converge -* - 200 CONTINUE - INFO = 0 - DO 210 I = 1, N - 1 - IF( E( I ).NE.ZERO ) - $ INFO = INFO + 1 - 210 CONTINUE - 220 CONTINUE - RETURN -* -* End of DBDSQR -* - END diff --git a/lib/linalg/fortran/dcabs1.f b/lib/linalg/fortran/dcabs1.f deleted file mode 100644 index f6212a8595..0000000000 --- a/lib/linalg/fortran/dcabs1.f +++ /dev/null @@ -1,66 +0,0 @@ -*> \brief \b DCABS1 -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* DOUBLE PRECISION FUNCTION DCABS1(Z) -* -* .. Scalar Arguments .. -* COMPLEX*16 Z -* .. -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DCABS1 computes |Re(.)| + |Im(.)| of a double complex number -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] Z -*> \verbatim -*> Z is COMPLEX*16 -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup double_blas_level1 -* -* ===================================================================== - DOUBLE PRECISION FUNCTION DCABS1(Z) -* -* -- Reference BLAS level1 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - COMPLEX*16 Z -* .. -* .. -* ===================================================================== -* -* .. Intrinsic Functions .. - INTRINSIC ABS,DBLE,DIMAG -* - DCABS1 = ABS(DBLE(Z)) + ABS(DIMAG(Z)) - RETURN -* -* End of DCABS1 -* - END diff --git a/lib/linalg/fortran/dcopy.f b/lib/linalg/fortran/dcopy.f deleted file mode 100644 index ded46c5ecf..0000000000 --- a/lib/linalg/fortran/dcopy.f +++ /dev/null @@ -1,146 +0,0 @@ -*> \brief \b DCOPY -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE DCOPY(N,DX,INCX,DY,INCY) -* -* .. Scalar Arguments .. -* INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION DX(*),DY(*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DCOPY copies a vector, x, to a vector, y. -*> uses unrolled loops for increments equal to 1. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> number of elements in input vector(s) -*> \endverbatim -*> -*> \param[in] DX -*> \verbatim -*> DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> storage spacing between elements of DX -*> \endverbatim -*> -*> \param[out] DY -*> \verbatim -*> DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) -*> \endverbatim -*> -*> \param[in] INCY -*> \verbatim -*> INCY is INTEGER -*> storage spacing between elements of DY -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup double_blas_level1 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> jack dongarra, linpack, 3/11/78. -*> modified 12/3/93, array(1) declarations changed to array(*) -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DCOPY(N,DX,INCX,DY,INCY) -* -* -- Reference BLAS level1 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. - DOUBLE PRECISION DX(*),DY(*) -* .. -* -* ===================================================================== -* -* .. Local Scalars .. - INTEGER I,IX,IY,M,MP1 -* .. -* .. Intrinsic Functions .. - INTRINSIC MOD -* .. - IF (N.LE.0) RETURN - IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN -* -* code for both increments equal to 1 -* -* -* clean-up loop -* - M = MOD(N,7) - IF (M.NE.0) THEN - DO I = 1,M - DY(I) = DX(I) - END DO - IF (N.LT.7) RETURN - END IF - MP1 = M + 1 - DO I = MP1,N,7 - DY(I) = DX(I) - DY(I+1) = DX(I+1) - DY(I+2) = DX(I+2) - DY(I+3) = DX(I+3) - DY(I+4) = DX(I+4) - DY(I+5) = DX(I+5) - DY(I+6) = DX(I+6) - END DO - ELSE -* -* code for unequal increments or equal increments -* not equal to 1 -* - IX = 1 - IY = 1 - IF (INCX.LT.0) IX = (-N+1)*INCX + 1 - IF (INCY.LT.0) IY = (-N+1)*INCY + 1 - DO I = 1,N - DY(IY) = DX(IX) - IX = IX + INCX - IY = IY + INCY - END DO - END IF - RETURN -* -* End of DCOPY -* - END diff --git a/lib/linalg/fortran/ddot.f b/lib/linalg/fortran/ddot.f deleted file mode 100644 index 683a04bd46..0000000000 --- a/lib/linalg/fortran/ddot.f +++ /dev/null @@ -1,148 +0,0 @@ -*> \brief \b DDOT -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* DOUBLE PRECISION FUNCTION DDOT(N,DX,INCX,DY,INCY) -* -* .. Scalar Arguments .. -* INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION DX(*),DY(*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DDOT forms the dot product of two vectors. -*> uses unrolled loops for increments equal to one. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> number of elements in input vector(s) -*> \endverbatim -*> -*> \param[in] DX -*> \verbatim -*> DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> storage spacing between elements of DX -*> \endverbatim -*> -*> \param[in] DY -*> \verbatim -*> DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) -*> \endverbatim -*> -*> \param[in] INCY -*> \verbatim -*> INCY is INTEGER -*> storage spacing between elements of DY -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup double_blas_level1 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> jack dongarra, linpack, 3/11/78. -*> modified 12/3/93, array(1) declarations changed to array(*) -*> \endverbatim -*> -* ===================================================================== - DOUBLE PRECISION FUNCTION DDOT(N,DX,INCX,DY,INCY) -* -* -- Reference BLAS level1 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. - DOUBLE PRECISION DX(*),DY(*) -* .. -* -* ===================================================================== -* -* .. Local Scalars .. - DOUBLE PRECISION DTEMP - INTEGER I,IX,IY,M,MP1 -* .. -* .. Intrinsic Functions .. - INTRINSIC MOD -* .. - DDOT = 0.0d0 - DTEMP = 0.0d0 - IF (N.LE.0) RETURN - IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN -* -* code for both increments equal to 1 -* -* -* clean-up loop -* - M = MOD(N,5) - IF (M.NE.0) THEN - DO I = 1,M - DTEMP = DTEMP + DX(I)*DY(I) - END DO - IF (N.LT.5) THEN - DDOT=DTEMP - RETURN - END IF - END IF - MP1 = M + 1 - DO I = MP1,N,5 - DTEMP = DTEMP + DX(I)*DY(I) + DX(I+1)*DY(I+1) + - $ DX(I+2)*DY(I+2) + DX(I+3)*DY(I+3) + DX(I+4)*DY(I+4) - END DO - ELSE -* -* code for unequal increments or equal increments -* not equal to 1 -* - IX = 1 - IY = 1 - IF (INCX.LT.0) IX = (-N+1)*INCX + 1 - IF (INCY.LT.0) IY = (-N+1)*INCY + 1 - DO I = 1,N - DTEMP = DTEMP + DX(IX)*DY(IY) - IX = IX + INCX - IY = IY + INCY - END DO - END IF - DDOT = DTEMP - RETURN -* -* End of DDOT -* - END diff --git a/lib/linalg/fortran/dgebd2.f b/lib/linalg/fortran/dgebd2.f deleted file mode 100644 index daaa187aff..0000000000 --- a/lib/linalg/fortran/dgebd2.f +++ /dev/null @@ -1,317 +0,0 @@ -*> \brief \b DGEBD2 reduces a general matrix to bidiagonal form using an unblocked algorithm. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DGEBD2 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DGEBD2( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, INFO ) -* -* .. Scalar Arguments .. -* INTEGER INFO, LDA, M, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), TAUP( * ), -* $ TAUQ( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DGEBD2 reduces a real general m by n matrix A to upper or lower -*> bidiagonal form B by an orthogonal transformation: Q**T * A * P = B. -*> -*> If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows in the matrix A. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns in the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the m by n general matrix to be reduced. -*> On exit, -*> if m >= n, the diagonal and the first superdiagonal are -*> overwritten with the upper bidiagonal matrix B; the -*> elements below the diagonal, with the array TAUQ, represent -*> the orthogonal matrix Q as a product of elementary -*> reflectors, and the elements above the first superdiagonal, -*> with the array TAUP, represent the orthogonal matrix P as -*> a product of elementary reflectors; -*> if m < n, the diagonal and the first subdiagonal are -*> overwritten with the lower bidiagonal matrix B; the -*> elements below the first subdiagonal, with the array TAUQ, -*> represent the orthogonal matrix Q as a product of -*> elementary reflectors, and the elements above the diagonal, -*> with the array TAUP, represent the orthogonal matrix P as -*> a product of elementary reflectors. -*> See Further Details. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,M). -*> \endverbatim -*> -*> \param[out] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension (min(M,N)) -*> The diagonal elements of the bidiagonal matrix B: -*> D(i) = A(i,i). -*> \endverbatim -*> -*> \param[out] E -*> \verbatim -*> E is DOUBLE PRECISION array, dimension (min(M,N)-1) -*> The off-diagonal elements of the bidiagonal matrix B: -*> if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1; -*> if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1. -*> \endverbatim -*> -*> \param[out] TAUQ -*> \verbatim -*> TAUQ is DOUBLE PRECISION array, dimension (min(M,N)) -*> The scalar factors of the elementary reflectors which -*> represent the orthogonal matrix Q. See Further Details. -*> \endverbatim -*> -*> \param[out] TAUP -*> \verbatim -*> TAUP is DOUBLE PRECISION array, dimension (min(M,N)) -*> The scalar factors of the elementary reflectors which -*> represent the orthogonal matrix P. See Further Details. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (max(M,N)) -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit. -*> < 0: if INFO = -i, the i-th argument had an illegal value. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleGEcomputational -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> The matrices Q and P are represented as products of elementary -*> reflectors: -*> -*> If m >= n, -*> -*> Q = H(1) H(2) . . . H(n) and P = G(1) G(2) . . . G(n-1) -*> -*> Each H(i) and G(i) has the form: -*> -*> H(i) = I - tauq * v * v**T and G(i) = I - taup * u * u**T -*> -*> where tauq and taup are real scalars, and v and u are real vectors; -*> v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in A(i+1:m,i); -*> u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in A(i,i+2:n); -*> tauq is stored in TAUQ(i) and taup in TAUP(i). -*> -*> If m < n, -*> -*> Q = H(1) H(2) . . . H(m-1) and P = G(1) G(2) . . . G(m) -*> -*> Each H(i) and G(i) has the form: -*> -*> H(i) = I - tauq * v * v**T and G(i) = I - taup * u * u**T -*> -*> where tauq and taup are real scalars, and v and u are real vectors; -*> v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i); -*> u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n); -*> tauq is stored in TAUQ(i) and taup in TAUP(i). -*> -*> The contents of A on exit are illustrated by the following examples: -*> -*> m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n): -*> -*> ( d e u1 u1 u1 ) ( d u1 u1 u1 u1 u1 ) -*> ( v1 d e u2 u2 ) ( e d u2 u2 u2 u2 ) -*> ( v1 v2 d e u3 ) ( v1 e d u3 u3 u3 ) -*> ( v1 v2 v3 d e ) ( v1 v2 e d u4 u4 ) -*> ( v1 v2 v3 v4 d ) ( v1 v2 v3 e d u5 ) -*> ( v1 v2 v3 v4 v5 ) -*> -*> where d and e denote diagonal and off-diagonal elements of B, vi -*> denotes an element of the vector defining H(i), and ui an element of -*> the vector defining G(i). -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DGEBD2( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INFO, LDA, M, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), TAUP( * ), - $ TAUQ( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) -* .. -* .. Local Scalars .. - INTEGER I -* .. -* .. External Subroutines .. - EXTERNAL DLARF, DLARFG, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, MIN -* .. -* .. Executable Statements .. -* -* Test the input parameters -* - INFO = 0 - IF( M.LT.0 ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( LDA.LT.MAX( 1, M ) ) THEN - INFO = -4 - END IF - IF( INFO.LT.0 ) THEN - CALL XERBLA( 'DGEBD2', -INFO ) - RETURN - END IF -* - IF( M.GE.N ) THEN -* -* Reduce to upper bidiagonal form -* - DO 10 I = 1, N -* -* Generate elementary reflector H(i) to annihilate A(i+1:m,i) -* - CALL DLARFG( M-I+1, A( I, I ), A( MIN( I+1, M ), I ), 1, - $ TAUQ( I ) ) - D( I ) = A( I, I ) - A( I, I ) = ONE -* -* Apply H(i) to A(i:m,i+1:n) from the left -* - IF( I.LT.N ) - $ CALL DLARF( 'Left', M-I+1, N-I, A( I, I ), 1, TAUQ( I ), - $ A( I, I+1 ), LDA, WORK ) - A( I, I ) = D( I ) -* - IF( I.LT.N ) THEN -* -* Generate elementary reflector G(i) to annihilate -* A(i,i+2:n) -* - CALL DLARFG( N-I, A( I, I+1 ), A( I, MIN( I+2, N ) ), - $ LDA, TAUP( I ) ) - E( I ) = A( I, I+1 ) - A( I, I+1 ) = ONE -* -* Apply G(i) to A(i+1:m,i+1:n) from the right -* - CALL DLARF( 'Right', M-I, N-I, A( I, I+1 ), LDA, - $ TAUP( I ), A( I+1, I+1 ), LDA, WORK ) - A( I, I+1 ) = E( I ) - ELSE - TAUP( I ) = ZERO - END IF - 10 CONTINUE - ELSE -* -* Reduce to lower bidiagonal form -* - DO 20 I = 1, M -* -* Generate elementary reflector G(i) to annihilate A(i,i+1:n) -* - CALL DLARFG( N-I+1, A( I, I ), A( I, MIN( I+1, N ) ), LDA, - $ TAUP( I ) ) - D( I ) = A( I, I ) - A( I, I ) = ONE -* -* Apply G(i) to A(i+1:m,i:n) from the right -* - IF( I.LT.M ) - $ CALL DLARF( 'Right', M-I, N-I+1, A( I, I ), LDA, - $ TAUP( I ), A( I+1, I ), LDA, WORK ) - A( I, I ) = D( I ) -* - IF( I.LT.M ) THEN -* -* Generate elementary reflector H(i) to annihilate -* A(i+2:m,i) -* - CALL DLARFG( M-I, A( I+1, I ), A( MIN( I+2, M ), I ), 1, - $ TAUQ( I ) ) - E( I ) = A( I+1, I ) - A( I+1, I ) = ONE -* -* Apply H(i) to A(i+1:m,i+1:n) from the left -* - CALL DLARF( 'Left', M-I, N-I, A( I+1, I ), 1, TAUQ( I ), - $ A( I+1, I+1 ), LDA, WORK ) - A( I+1, I ) = E( I ) - ELSE - TAUQ( I ) = ZERO - END IF - 20 CONTINUE - END IF - RETURN -* -* End of DGEBD2 -* - END diff --git a/lib/linalg/fortran/dgebrd.f b/lib/linalg/fortran/dgebrd.f deleted file mode 100644 index 0f0d1651a7..0000000000 --- a/lib/linalg/fortran/dgebrd.f +++ /dev/null @@ -1,349 +0,0 @@ -*> \brief \b DGEBRD -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DGEBRD + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DGEBRD( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK, -* INFO ) -* -* .. Scalar Arguments .. -* INTEGER INFO, LDA, LWORK, M, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), TAUP( * ), -* $ TAUQ( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DGEBRD reduces a general real M-by-N matrix A to upper or lower -*> bidiagonal form B by an orthogonal transformation: Q**T * A * P = B. -*> -*> If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows in the matrix A. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns in the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the M-by-N general matrix to be reduced. -*> On exit, -*> if m >= n, the diagonal and the first superdiagonal are -*> overwritten with the upper bidiagonal matrix B; the -*> elements below the diagonal, with the array TAUQ, represent -*> the orthogonal matrix Q as a product of elementary -*> reflectors, and the elements above the first superdiagonal, -*> with the array TAUP, represent the orthogonal matrix P as -*> a product of elementary reflectors; -*> if m < n, the diagonal and the first subdiagonal are -*> overwritten with the lower bidiagonal matrix B; the -*> elements below the first subdiagonal, with the array TAUQ, -*> represent the orthogonal matrix Q as a product of -*> elementary reflectors, and the elements above the diagonal, -*> with the array TAUP, represent the orthogonal matrix P as -*> a product of elementary reflectors. -*> See Further Details. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,M). -*> \endverbatim -*> -*> \param[out] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension (min(M,N)) -*> The diagonal elements of the bidiagonal matrix B: -*> D(i) = A(i,i). -*> \endverbatim -*> -*> \param[out] E -*> \verbatim -*> E is DOUBLE PRECISION array, dimension (min(M,N)-1) -*> The off-diagonal elements of the bidiagonal matrix B: -*> if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1; -*> if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1. -*> \endverbatim -*> -*> \param[out] TAUQ -*> \verbatim -*> TAUQ is DOUBLE PRECISION array, dimension (min(M,N)) -*> The scalar factors of the elementary reflectors which -*> represent the orthogonal matrix Q. See Further Details. -*> \endverbatim -*> -*> \param[out] TAUP -*> \verbatim -*> TAUP is DOUBLE PRECISION array, dimension (min(M,N)) -*> The scalar factors of the elementary reflectors which -*> represent the orthogonal matrix P. See Further Details. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) -*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -*> \endverbatim -*> -*> \param[in] LWORK -*> \verbatim -*> LWORK is INTEGER -*> The length of the array WORK. LWORK >= max(1,M,N). -*> For optimum performance LWORK >= (M+N)*NB, where NB -*> is the optimal blocksize. -*> -*> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal size of the WORK array, returns -*> this value as the first entry of the WORK array, and no error -*> message related to LWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleGEcomputational -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> The matrices Q and P are represented as products of elementary -*> reflectors: -*> -*> If m >= n, -*> -*> Q = H(1) H(2) . . . H(n) and P = G(1) G(2) . . . G(n-1) -*> -*> Each H(i) and G(i) has the form: -*> -*> H(i) = I - tauq * v * v**T and G(i) = I - taup * u * u**T -*> -*> where tauq and taup are real scalars, and v and u are real vectors; -*> v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in A(i+1:m,i); -*> u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in A(i,i+2:n); -*> tauq is stored in TAUQ(i) and taup in TAUP(i). -*> -*> If m < n, -*> -*> Q = H(1) H(2) . . . H(m-1) and P = G(1) G(2) . . . G(m) -*> -*> Each H(i) and G(i) has the form: -*> -*> H(i) = I - tauq * v * v**T and G(i) = I - taup * u * u**T -*> -*> where tauq and taup are real scalars, and v and u are real vectors; -*> v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i); -*> u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n); -*> tauq is stored in TAUQ(i) and taup in TAUP(i). -*> -*> The contents of A on exit are illustrated by the following examples: -*> -*> m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n): -*> -*> ( d e u1 u1 u1 ) ( d u1 u1 u1 u1 u1 ) -*> ( v1 d e u2 u2 ) ( e d u2 u2 u2 u2 ) -*> ( v1 v2 d e u3 ) ( v1 e d u3 u3 u3 ) -*> ( v1 v2 v3 d e ) ( v1 v2 e d u4 u4 ) -*> ( v1 v2 v3 v4 d ) ( v1 v2 v3 e d u5 ) -*> ( v1 v2 v3 v4 v5 ) -*> -*> where d and e denote diagonal and off-diagonal elements of B, vi -*> denotes an element of the vector defining H(i), and ui an element of -*> the vector defining G(i). -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DGEBRD( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK, - $ INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INFO, LDA, LWORK, M, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), TAUP( * ), - $ TAUQ( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE - PARAMETER ( ONE = 1.0D+0 ) -* .. -* .. Local Scalars .. - LOGICAL LQUERY - INTEGER I, IINFO, J, LDWRKX, LDWRKY, LWKOPT, MINMN, NB, - $ NBMIN, NX, WS -* .. -* .. External Subroutines .. - EXTERNAL DGEBD2, DGEMM, DLABRD, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC DBLE, MAX, MIN -* .. -* .. External Functions .. - INTEGER ILAENV - EXTERNAL ILAENV -* .. -* .. Executable Statements .. -* -* Test the input parameters -* - INFO = 0 - NB = MAX( 1, ILAENV( 1, 'DGEBRD', ' ', M, N, -1, -1 ) ) - LWKOPT = ( M+N )*NB - WORK( 1 ) = DBLE( LWKOPT ) - LQUERY = ( LWORK.EQ.-1 ) - IF( M.LT.0 ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( LDA.LT.MAX( 1, M ) ) THEN - INFO = -4 - ELSE IF( LWORK.LT.MAX( 1, M, N ) .AND. .NOT.LQUERY ) THEN - INFO = -10 - END IF - IF( INFO.LT.0 ) THEN - CALL XERBLA( 'DGEBRD', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - RETURN - END IF -* -* Quick return if possible -* - MINMN = MIN( M, N ) - IF( MINMN.EQ.0 ) THEN - WORK( 1 ) = 1 - RETURN - END IF -* - WS = MAX( M, N ) - LDWRKX = M - LDWRKY = N -* - IF( NB.GT.1 .AND. NB.LT.MINMN ) THEN -* -* Set the crossover point NX. -* - NX = MAX( NB, ILAENV( 3, 'DGEBRD', ' ', M, N, -1, -1 ) ) -* -* Determine when to switch from blocked to unblocked code. -* - IF( NX.LT.MINMN ) THEN - WS = ( M+N )*NB - IF( LWORK.LT.WS ) THEN -* -* Not enough work space for the optimal NB, consider using -* a smaller block size. -* - NBMIN = ILAENV( 2, 'DGEBRD', ' ', M, N, -1, -1 ) - IF( LWORK.GE.( M+N )*NBMIN ) THEN - NB = LWORK / ( M+N ) - ELSE - NB = 1 - NX = MINMN - END IF - END IF - END IF - ELSE - NX = MINMN - END IF -* - DO 30 I = 1, MINMN - NX, NB -* -* Reduce rows and columns i:i+nb-1 to bidiagonal form and return -* the matrices X and Y which are needed to update the unreduced -* part of the matrix -* - CALL DLABRD( M-I+1, N-I+1, NB, A( I, I ), LDA, D( I ), E( I ), - $ TAUQ( I ), TAUP( I ), WORK, LDWRKX, - $ WORK( LDWRKX*NB+1 ), LDWRKY ) -* -* Update the trailing submatrix A(i+nb:m,i+nb:n), using an update -* of the form A := A - V*Y**T - X*U**T -* - CALL DGEMM( 'No transpose', 'Transpose', M-I-NB+1, N-I-NB+1, - $ NB, -ONE, A( I+NB, I ), LDA, - $ WORK( LDWRKX*NB+NB+1 ), LDWRKY, ONE, - $ A( I+NB, I+NB ), LDA ) - CALL DGEMM( 'No transpose', 'No transpose', M-I-NB+1, N-I-NB+1, - $ NB, -ONE, WORK( NB+1 ), LDWRKX, A( I, I+NB ), LDA, - $ ONE, A( I+NB, I+NB ), LDA ) -* -* Copy diagonal and off-diagonal elements of B back into A -* - IF( M.GE.N ) THEN - DO 10 J = I, I + NB - 1 - A( J, J ) = D( J ) - A( J, J+1 ) = E( J ) - 10 CONTINUE - ELSE - DO 20 J = I, I + NB - 1 - A( J, J ) = D( J ) - A( J+1, J ) = E( J ) - 20 CONTINUE - END IF - 30 CONTINUE -* -* Use unblocked code to reduce the remainder of the matrix -* - CALL DGEBD2( M-I+1, N-I+1, A( I, I ), LDA, D( I ), E( I ), - $ TAUQ( I ), TAUP( I ), WORK, IINFO ) - WORK( 1 ) = WS - RETURN -* -* End of DGEBRD -* - END diff --git a/lib/linalg/fortran/dgecon.f b/lib/linalg/fortran/dgecon.f deleted file mode 100644 index aa10dee9a2..0000000000 --- a/lib/linalg/fortran/dgecon.f +++ /dev/null @@ -1,258 +0,0 @@ -*> \brief \b DGECON -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DGECON + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DGECON( NORM, N, A, LDA, ANORM, RCOND, WORK, IWORK, -* INFO ) -* -* .. Scalar Arguments .. -* CHARACTER NORM -* INTEGER INFO, LDA, N -* DOUBLE PRECISION ANORM, RCOND -* .. -* .. Array Arguments .. -* INTEGER IWORK( * ) -* DOUBLE PRECISION A( LDA, * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DGECON estimates the reciprocal of the condition number of a general -*> real matrix A, in either the 1-norm or the infinity-norm, using -*> the LU factorization computed by DGETRF. -*> -*> An estimate is obtained for norm(inv(A)), and the reciprocal of the -*> condition number is computed as -*> RCOND = 1 / ( norm(A) * norm(inv(A)) ). -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] NORM -*> \verbatim -*> NORM is CHARACTER*1 -*> Specifies whether the 1-norm condition number or the -*> infinity-norm condition number is required: -*> = '1' or 'O': 1-norm; -*> = 'I': Infinity-norm. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> The factors L and U from the factorization A = P*L*U -*> as computed by DGETRF. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,N). -*> \endverbatim -*> -*> \param[in] ANORM -*> \verbatim -*> ANORM is DOUBLE PRECISION -*> If NORM = '1' or 'O', the 1-norm of the original matrix A. -*> If NORM = 'I', the infinity-norm of the original matrix A. -*> \endverbatim -*> -*> \param[out] RCOND -*> \verbatim -*> RCOND is DOUBLE PRECISION -*> The reciprocal of the condition number of the matrix A, -*> computed as RCOND = 1/(norm(A) * norm(inv(A))). -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (4*N) -*> \endverbatim -*> -*> \param[out] IWORK -*> \verbatim -*> IWORK is INTEGER array, dimension (N) -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleGEcomputational -* -* ===================================================================== - SUBROUTINE DGECON( NORM, N, A, LDA, ANORM, RCOND, WORK, IWORK, - $ INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER NORM - INTEGER INFO, LDA, N - DOUBLE PRECISION ANORM, RCOND -* .. -* .. Array Arguments .. - INTEGER IWORK( * ) - DOUBLE PRECISION A( LDA, * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE, ZERO - PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) -* .. -* .. Local Scalars .. - LOGICAL ONENRM - CHARACTER NORMIN - INTEGER IX, KASE, KASE1 - DOUBLE PRECISION AINVNM, SCALE, SL, SMLNUM, SU -* .. -* .. Local Arrays .. - INTEGER ISAVE( 3 ) -* .. -* .. External Functions .. - LOGICAL LSAME - INTEGER IDAMAX - DOUBLE PRECISION DLAMCH - EXTERNAL LSAME, IDAMAX, DLAMCH -* .. -* .. External Subroutines .. - EXTERNAL DLACN2, DLATRS, DRSCL, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, MAX -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 - ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' ) - IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -4 - ELSE IF( ANORM.LT.ZERO ) THEN - INFO = -5 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DGECON', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - RCOND = ZERO - IF( N.EQ.0 ) THEN - RCOND = ONE - RETURN - ELSE IF( ANORM.EQ.ZERO ) THEN - RETURN - END IF -* - SMLNUM = DLAMCH( 'Safe minimum' ) -* -* Estimate the norm of inv(A). -* - AINVNM = ZERO - NORMIN = 'N' - IF( ONENRM ) THEN - KASE1 = 1 - ELSE - KASE1 = 2 - END IF - KASE = 0 - 10 CONTINUE - CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE ) - IF( KASE.NE.0 ) THEN - IF( KASE.EQ.KASE1 ) THEN -* -* Multiply by inv(L). -* - CALL DLATRS( 'Lower', 'No transpose', 'Unit', NORMIN, N, A, - $ LDA, WORK, SL, WORK( 2*N+1 ), INFO ) -* -* Multiply by inv(U). -* - CALL DLATRS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N, - $ A, LDA, WORK, SU, WORK( 3*N+1 ), INFO ) - ELSE -* -* Multiply by inv(U**T). -* - CALL DLATRS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N, A, - $ LDA, WORK, SU, WORK( 3*N+1 ), INFO ) -* -* Multiply by inv(L**T). -* - CALL DLATRS( 'Lower', 'Transpose', 'Unit', NORMIN, N, A, - $ LDA, WORK, SL, WORK( 2*N+1 ), INFO ) - END IF -* -* Divide X by 1/(SL*SU) if doing so will not cause overflow. -* - SCALE = SL*SU - NORMIN = 'Y' - IF( SCALE.NE.ONE ) THEN - IX = IDAMAX( N, WORK, 1 ) - IF( SCALE.LT.ABS( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO ) - $ GO TO 20 - CALL DRSCL( N, SCALE, WORK, 1 ) - END IF - GO TO 10 - END IF -* -* Compute the estimate of the reciprocal condition number. -* - IF( AINVNM.NE.ZERO ) - $ RCOND = ( ONE / AINVNM ) / ANORM -* - 20 CONTINUE - RETURN -* -* End of DGECON -* - END diff --git a/lib/linalg/fortran/dgelq2.f b/lib/linalg/fortran/dgelq2.f deleted file mode 100644 index 9915c57d47..0000000000 --- a/lib/linalg/fortran/dgelq2.f +++ /dev/null @@ -1,197 +0,0 @@ -*> \brief \b DGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DGELQ2 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DGELQ2( M, N, A, LDA, TAU, WORK, INFO ) -* -* .. Scalar Arguments .. -* INTEGER INFO, LDA, M, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DGELQ2 computes an LQ factorization of a real m-by-n matrix A: -*> -*> A = ( L 0 ) * Q -*> -*> where: -*> -*> Q is a n-by-n orthogonal matrix; -*> L is a lower-triangular m-by-m matrix; -*> 0 is a m-by-(n-m) zero matrix, if m < n. -*> -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix A. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the m by n matrix A. -*> On exit, the elements on and below the diagonal of the array -*> contain the m by min(m,n) lower trapezoidal matrix L (L is -*> lower triangular if m <= n); the elements above the diagonal, -*> with the array TAU, represent the orthogonal matrix Q as a -*> product of elementary reflectors (see Further Details). -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,M). -*> \endverbatim -*> -*> \param[out] TAU -*> \verbatim -*> TAU is DOUBLE PRECISION array, dimension (min(M,N)) -*> The scalar factors of the elementary reflectors (see Further -*> Details). -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (M) -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleGEcomputational -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> The matrix Q is represented as a product of elementary reflectors -*> -*> Q = H(k) . . . H(2) H(1), where k = min(m,n). -*> -*> Each H(i) has the form -*> -*> H(i) = I - tau * v * v**T -*> -*> where tau is a real scalar, and v is a real vector with -*> v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n), -*> and tau in TAU(i). -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DGELQ2( M, N, A, LDA, TAU, WORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INFO, LDA, M, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE - PARAMETER ( ONE = 1.0D+0 ) -* .. -* .. Local Scalars .. - INTEGER I, K - DOUBLE PRECISION AII -* .. -* .. External Subroutines .. - EXTERNAL DLARF, DLARFG, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, MIN -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - INFO = 0 - IF( M.LT.0 ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( LDA.LT.MAX( 1, M ) ) THEN - INFO = -4 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DGELQ2', -INFO ) - RETURN - END IF -* - K = MIN( M, N ) -* - DO 10 I = 1, K -* -* Generate elementary reflector H(i) to annihilate A(i,i+1:n) -* - CALL DLARFG( N-I+1, A( I, I ), A( I, MIN( I+1, N ) ), LDA, - $ TAU( I ) ) - IF( I.LT.M ) THEN -* -* Apply H(i) to A(i+1:m,i:n) from the right -* - AII = A( I, I ) - A( I, I ) = ONE - CALL DLARF( 'Right', M-I, N-I+1, A( I, I ), LDA, TAU( I ), - $ A( I+1, I ), LDA, WORK ) - A( I, I ) = AII - END IF - 10 CONTINUE - RETURN -* -* End of DGELQ2 -* - END diff --git a/lib/linalg/fortran/dgelqf.f b/lib/linalg/fortran/dgelqf.f deleted file mode 100644 index ed3372f965..0000000000 --- a/lib/linalg/fortran/dgelqf.f +++ /dev/null @@ -1,274 +0,0 @@ -*> \brief \b DGELQF -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DGELQF + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) -* -* .. Scalar Arguments .. -* INTEGER INFO, LDA, LWORK, M, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DGELQF computes an LQ factorization of a real M-by-N matrix A: -*> -*> A = ( L 0 ) * Q -*> -*> where: -*> -*> Q is a N-by-N orthogonal matrix; -*> L is a lower-triangular M-by-M matrix; -*> 0 is a M-by-(N-M) zero matrix, if M < N. -*> -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix A. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the M-by-N matrix A. -*> On exit, the elements on and below the diagonal of the array -*> contain the m-by-min(m,n) lower trapezoidal matrix L (L is -*> lower triangular if m <= n); the elements above the diagonal, -*> with the array TAU, represent the orthogonal matrix Q as a -*> product of elementary reflectors (see Further Details). -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,M). -*> \endverbatim -*> -*> \param[out] TAU -*> \verbatim -*> TAU is DOUBLE PRECISION array, dimension (min(M,N)) -*> The scalar factors of the elementary reflectors (see Further -*> Details). -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) -*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -*> \endverbatim -*> -*> \param[in] LWORK -*> \verbatim -*> LWORK is INTEGER -*> The dimension of the array WORK. LWORK >= max(1,M). -*> For optimum performance LWORK >= M*NB, where NB is the -*> optimal blocksize. -*> -*> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal size of the WORK array, returns -*> this value as the first entry of the WORK array, and no error -*> message related to LWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleGEcomputational -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> The matrix Q is represented as a product of elementary reflectors -*> -*> Q = H(k) . . . H(2) H(1), where k = min(m,n). -*> -*> Each H(i) has the form -*> -*> H(i) = I - tau * v * v**T -*> -*> where tau is a real scalar, and v is a real vector with -*> v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n), -*> and tau in TAU(i). -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INFO, LDA, LWORK, M, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Local Scalars .. - LOGICAL LQUERY - INTEGER I, IB, IINFO, IWS, K, LDWORK, LWKOPT, NB, - $ NBMIN, NX -* .. -* .. External Subroutines .. - EXTERNAL DGELQ2, DLARFB, DLARFT, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, MIN -* .. -* .. External Functions .. - INTEGER ILAENV - EXTERNAL ILAENV -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - INFO = 0 - NB = ILAENV( 1, 'DGELQF', ' ', M, N, -1, -1 ) - LWKOPT = M*NB - WORK( 1 ) = LWKOPT - LQUERY = ( LWORK.EQ.-1 ) - IF( M.LT.0 ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( LDA.LT.MAX( 1, M ) ) THEN - INFO = -4 - ELSE IF( LWORK.LT.MAX( 1, M ) .AND. .NOT.LQUERY ) THEN - INFO = -7 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DGELQF', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - RETURN - END IF -* -* Quick return if possible -* - K = MIN( M, N ) - IF( K.EQ.0 ) THEN - WORK( 1 ) = 1 - RETURN - END IF -* - NBMIN = 2 - NX = 0 - IWS = M - IF( NB.GT.1 .AND. NB.LT.K ) THEN -* -* Determine when to cross over from blocked to unblocked code. -* - NX = MAX( 0, ILAENV( 3, 'DGELQF', ' ', M, N, -1, -1 ) ) - IF( NX.LT.K ) THEN -* -* Determine if workspace is large enough for blocked code. -* - LDWORK = M - IWS = LDWORK*NB - IF( LWORK.LT.IWS ) THEN -* -* Not enough workspace to use optimal NB: reduce NB and -* determine the minimum value of NB. -* - NB = LWORK / LDWORK - NBMIN = MAX( 2, ILAENV( 2, 'DGELQF', ' ', M, N, -1, - $ -1 ) ) - END IF - END IF - END IF -* - IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN -* -* Use blocked code initially -* - DO 10 I = 1, K - NX, NB - IB = MIN( K-I+1, NB ) -* -* Compute the LQ factorization of the current block -* A(i:i+ib-1,i:n) -* - CALL DGELQ2( IB, N-I+1, A( I, I ), LDA, TAU( I ), WORK, - $ IINFO ) - IF( I+IB.LE.M ) THEN -* -* Form the triangular factor of the block reflector -* H = H(i) H(i+1) . . . H(i+ib-1) -* - CALL DLARFT( 'Forward', 'Rowwise', N-I+1, IB, A( I, I ), - $ LDA, TAU( I ), WORK, LDWORK ) -* -* Apply H to A(i+ib:m,i:n) from the right -* - CALL DLARFB( 'Right', 'No transpose', 'Forward', - $ 'Rowwise', M-I-IB+1, N-I+1, IB, A( I, I ), - $ LDA, WORK, LDWORK, A( I+IB, I ), LDA, - $ WORK( IB+1 ), LDWORK ) - END IF - 10 CONTINUE - ELSE - I = 1 - END IF -* -* Use unblocked code to factor the last or only block. -* - IF( I.LE.K ) - $ CALL DGELQ2( M-I+1, N-I+1, A( I, I ), LDA, TAU( I ), WORK, - $ IINFO ) -* - WORK( 1 ) = IWS - RETURN -* -* End of DGELQF -* - END diff --git a/lib/linalg/fortran/dgelsd.f b/lib/linalg/fortran/dgelsd.f deleted file mode 100644 index b3b3d8b2d3..0000000000 --- a/lib/linalg/fortran/dgelsd.f +++ /dev/null @@ -1,626 +0,0 @@ -*> \brief DGELSD computes the minimum-norm solution to a linear least squares problem for GE matrices -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DGELSD + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DGELSD( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, -* WORK, LWORK, IWORK, INFO ) -* -* .. Scalar Arguments .. -* INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS, RANK -* DOUBLE PRECISION RCOND -* .. -* .. Array Arguments .. -* INTEGER IWORK( * ) -* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), S( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DGELSD computes the minimum-norm solution to a real linear least -*> squares problem: -*> minimize 2-norm(| b - A*x |) -*> using the singular value decomposition (SVD) of A. A is an M-by-N -*> matrix which may be rank-deficient. -*> -*> Several right hand side vectors b and solution vectors x can be -*> handled in a single call; they are stored as the columns of the -*> M-by-NRHS right hand side matrix B and the N-by-NRHS solution -*> matrix X. -*> -*> The problem is solved in three steps: -*> (1) Reduce the coefficient matrix A to bidiagonal form with -*> Householder transformations, reducing the original problem -*> into a "bidiagonal least squares problem" (BLS) -*> (2) Solve the BLS using a divide and conquer approach. -*> (3) Apply back all the Householder transformations to solve -*> the original least squares problem. -*> -*> The effective rank of A is determined by treating as zero those -*> singular values which are less than RCOND times the largest singular -*> value. -*> -*> The divide and conquer algorithm makes very mild assumptions about -*> floating point arithmetic. It will work on machines with a guard -*> digit in add/subtract, or on those binary machines without guard -*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or -*> Cray-2. It could conceivably fail on hexadecimal or decimal machines -*> without guard digits, but we know of none. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of A. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of A. N >= 0. -*> \endverbatim -*> -*> \param[in] NRHS -*> \verbatim -*> NRHS is INTEGER -*> The number of right hand sides, i.e., the number of columns -*> of the matrices B and X. NRHS >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the M-by-N matrix A. -*> On exit, A has been destroyed. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,M). -*> \endverbatim -*> -*> \param[in,out] B -*> \verbatim -*> B is DOUBLE PRECISION array, dimension (LDB,NRHS) -*> On entry, the M-by-NRHS right hand side matrix B. -*> On exit, B is overwritten by the N-by-NRHS solution -*> matrix X. If m >= n and RANK = n, the residual -*> sum-of-squares for the solution in the i-th column is given -*> by the sum of squares of elements n+1:m in that column. -*> \endverbatim -*> -*> \param[in] LDB -*> \verbatim -*> LDB is INTEGER -*> The leading dimension of the array B. LDB >= max(1,max(M,N)). -*> \endverbatim -*> -*> \param[out] S -*> \verbatim -*> S is DOUBLE PRECISION array, dimension (min(M,N)) -*> The singular values of A in decreasing order. -*> The condition number of A in the 2-norm = S(1)/S(min(m,n)). -*> \endverbatim -*> -*> \param[in] RCOND -*> \verbatim -*> RCOND is DOUBLE PRECISION -*> RCOND is used to determine the effective rank of A. -*> Singular values S(i) <= RCOND*S(1) are treated as zero. -*> If RCOND < 0, machine precision is used instead. -*> \endverbatim -*> -*> \param[out] RANK -*> \verbatim -*> RANK is INTEGER -*> The effective rank of A, i.e., the number of singular values -*> which are greater than RCOND*S(1). -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) -*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -*> \endverbatim -*> -*> \param[in] LWORK -*> \verbatim -*> LWORK is INTEGER -*> The dimension of the array WORK. LWORK must be at least 1. -*> The exact minimum amount of workspace needed depends on M, -*> N and NRHS. As long as LWORK is at least -*> 12*N + 2*N*SMLSIZ + 8*N*NLVL + N*NRHS + (SMLSIZ+1)**2, -*> if M is greater than or equal to N or -*> 12*M + 2*M*SMLSIZ + 8*M*NLVL + M*NRHS + (SMLSIZ+1)**2, -*> if M is less than N, the code will execute correctly. -*> SMLSIZ is returned by ILAENV and is equal to the maximum -*> size of the subproblems at the bottom of the computation -*> tree (usually about 25), and -*> NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 ) -*> For good performance, LWORK should generally be larger. -*> -*> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal size of the WORK array, returns -*> this value as the first entry of the WORK array, and no error -*> message related to LWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] IWORK -*> \verbatim -*> IWORK is INTEGER array, dimension (MAX(1,LIWORK)) -*> LIWORK >= max(1, 3 * MINMN * NLVL + 11 * MINMN), -*> where MINMN = MIN( M,N ). -*> On exit, if INFO = 0, IWORK(1) returns the minimum LIWORK. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value. -*> > 0: the algorithm for computing the SVD failed to converge; -*> if INFO = i, i off-diagonal elements of an intermediate -*> bidiagonal form did not converge to zero. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleGEsolve -* -*> \par Contributors: -* ================== -*> -*> Ming Gu and Ren-Cang Li, Computer Science Division, University of -*> California at Berkeley, USA \n -*> Osni Marques, LBNL/NERSC, USA \n -* -* ===================================================================== - SUBROUTINE DGELSD( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, - $ WORK, LWORK, IWORK, INFO ) -* -* -- LAPACK driver routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS, RANK - DOUBLE PRECISION RCOND -* .. -* .. Array Arguments .. - INTEGER IWORK( * ) - DOUBLE PRECISION A( LDA, * ), B( LDB, * ), S( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, ONE, TWO - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0 ) -* .. -* .. Local Scalars .. - LOGICAL LQUERY - INTEGER IASCL, IBSCL, IE, IL, ITAU, ITAUP, ITAUQ, - $ LDWORK, LIWORK, MAXMN, MAXWRK, MINMN, MINWRK, - $ MM, MNTHR, NLVL, NWORK, SMLSIZ, WLALSD - DOUBLE PRECISION ANRM, BIGNUM, BNRM, EPS, SFMIN, SMLNUM -* .. -* .. External Subroutines .. - EXTERNAL DGEBRD, DGELQF, DGEQRF, DLABAD, DLACPY, DLALSD, - $ DLASCL, DLASET, DORMBR, DORMLQ, DORMQR, XERBLA -* .. -* .. External Functions .. - INTEGER ILAENV - DOUBLE PRECISION DLAMCH, DLANGE - EXTERNAL ILAENV, DLAMCH, DLANGE -* .. -* .. Intrinsic Functions .. - INTRINSIC DBLE, INT, LOG, MAX, MIN -* .. -* .. Executable Statements .. -* -* Test the input arguments. -* - INFO = 0 - MINMN = MIN( M, N ) - MAXMN = MAX( M, N ) - MNTHR = ILAENV( 6, 'DGELSD', ' ', M, N, NRHS, -1 ) - LQUERY = ( LWORK.EQ.-1 ) - IF( M.LT.0 ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( NRHS.LT.0 ) THEN - INFO = -3 - ELSE IF( LDA.LT.MAX( 1, M ) ) THEN - INFO = -5 - ELSE IF( LDB.LT.MAX( 1, MAXMN ) ) THEN - INFO = -7 - END IF -* - SMLSIZ = ILAENV( 9, 'DGELSD', ' ', 0, 0, 0, 0 ) -* -* Compute workspace. -* (Note: Comments in the code beginning "Workspace:" describe the -* minimal amount of workspace needed at that point in the code, -* as well as the preferred amount for good performance. -* NB refers to the optimal block size for the immediately -* following subroutine, as returned by ILAENV.) -* - MINWRK = 1 - LIWORK = 1 - MINMN = MAX( 1, MINMN ) - NLVL = MAX( INT( LOG( DBLE( MINMN ) / DBLE( SMLSIZ+1 ) ) / - $ LOG( TWO ) ) + 1, 0 ) -* - IF( INFO.EQ.0 ) THEN - MAXWRK = 0 - LIWORK = 3*MINMN*NLVL + 11*MINMN - MM = M - IF( M.GE.N .AND. M.GE.MNTHR ) THEN -* -* Path 1a - overdetermined, with many more rows than columns. -* - MM = N - MAXWRK = MAX( MAXWRK, N+N*ILAENV( 1, 'DGEQRF', ' ', M, N, - $ -1, -1 ) ) - MAXWRK = MAX( MAXWRK, N+NRHS* - $ ILAENV( 1, 'DORMQR', 'LT', M, NRHS, N, -1 ) ) - END IF - IF( M.GE.N ) THEN -* -* Path 1 - overdetermined or exactly determined. -* - MAXWRK = MAX( MAXWRK, 3*N+( MM+N )* - $ ILAENV( 1, 'DGEBRD', ' ', MM, N, -1, -1 ) ) - MAXWRK = MAX( MAXWRK, 3*N+NRHS* - $ ILAENV( 1, 'DORMBR', 'QLT', MM, NRHS, N, -1 ) ) - MAXWRK = MAX( MAXWRK, 3*N+( N-1 )* - $ ILAENV( 1, 'DORMBR', 'PLN', N, NRHS, N, -1 ) ) - WLALSD = 9*N+2*N*SMLSIZ+8*N*NLVL+N*NRHS+(SMLSIZ+1)**2 - MAXWRK = MAX( MAXWRK, 3*N+WLALSD ) - MINWRK = MAX( 3*N+MM, 3*N+NRHS, 3*N+WLALSD ) - END IF - IF( N.GT.M ) THEN - WLALSD = 9*M+2*M*SMLSIZ+8*M*NLVL+M*NRHS+(SMLSIZ+1)**2 - IF( N.GE.MNTHR ) THEN -* -* Path 2a - underdetermined, with many more columns -* than rows. -* - MAXWRK = M + M*ILAENV( 1, 'DGELQF', ' ', M, N, -1, -1 ) - MAXWRK = MAX( MAXWRK, M*M+4*M+2*M* - $ ILAENV( 1, 'DGEBRD', ' ', M, M, -1, -1 ) ) - MAXWRK = MAX( MAXWRK, M*M+4*M+NRHS* - $ ILAENV( 1, 'DORMBR', 'QLT', M, NRHS, M, -1 ) ) - MAXWRK = MAX( MAXWRK, M*M+4*M+( M-1 )* - $ ILAENV( 1, 'DORMBR', 'PLN', M, NRHS, M, -1 ) ) - IF( NRHS.GT.1 ) THEN - MAXWRK = MAX( MAXWRK, M*M+M+M*NRHS ) - ELSE - MAXWRK = MAX( MAXWRK, M*M+2*M ) - END IF - MAXWRK = MAX( MAXWRK, M+NRHS* - $ ILAENV( 1, 'DORMLQ', 'LT', N, NRHS, M, -1 ) ) - MAXWRK = MAX( MAXWRK, M*M+4*M+WLALSD ) -! XXX: Ensure the Path 2a case below is triggered. The workspace -! calculation should use queries for all routines eventually. - MAXWRK = MAX( MAXWRK, - $ 4*M+M*M+MAX( M, 2*M-4, NRHS, N-3*M ) ) - ELSE -* -* Path 2 - remaining underdetermined cases. -* - MAXWRK = 3*M + ( N+M )*ILAENV( 1, 'DGEBRD', ' ', M, N, - $ -1, -1 ) - MAXWRK = MAX( MAXWRK, 3*M+NRHS* - $ ILAENV( 1, 'DORMBR', 'QLT', M, NRHS, N, -1 ) ) - MAXWRK = MAX( MAXWRK, 3*M+M* - $ ILAENV( 1, 'DORMBR', 'PLN', N, NRHS, M, -1 ) ) - MAXWRK = MAX( MAXWRK, 3*M+WLALSD ) - END IF - MINWRK = MAX( 3*M+NRHS, 3*M+M, 3*M+WLALSD ) - END IF - MINWRK = MIN( MINWRK, MAXWRK ) - WORK( 1 ) = MAXWRK - IWORK( 1 ) = LIWORK - - IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN - INFO = -12 - END IF - END IF -* - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DGELSD', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - GO TO 10 - END IF -* -* Quick return if possible. -* - IF( M.EQ.0 .OR. N.EQ.0 ) THEN - RANK = 0 - RETURN - END IF -* -* Get machine parameters. -* - EPS = DLAMCH( 'P' ) - SFMIN = DLAMCH( 'S' ) - SMLNUM = SFMIN / EPS - BIGNUM = ONE / SMLNUM - CALL DLABAD( SMLNUM, BIGNUM ) -* -* Scale A if max entry outside range [SMLNUM,BIGNUM]. -* - ANRM = DLANGE( 'M', M, N, A, LDA, WORK ) - IASCL = 0 - IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN -* -* Scale matrix norm up to SMLNUM. -* - CALL DLASCL( 'G', 0, 0, ANRM, SMLNUM, M, N, A, LDA, INFO ) - IASCL = 1 - ELSE IF( ANRM.GT.BIGNUM ) THEN -* -* Scale matrix norm down to BIGNUM. -* - CALL DLASCL( 'G', 0, 0, ANRM, BIGNUM, M, N, A, LDA, INFO ) - IASCL = 2 - ELSE IF( ANRM.EQ.ZERO ) THEN -* -* Matrix all zero. Return zero solution. -* - CALL DLASET( 'F', MAX( M, N ), NRHS, ZERO, ZERO, B, LDB ) - CALL DLASET( 'F', MINMN, 1, ZERO, ZERO, S, 1 ) - RANK = 0 - GO TO 10 - END IF -* -* Scale B if max entry outside range [SMLNUM,BIGNUM]. -* - BNRM = DLANGE( 'M', M, NRHS, B, LDB, WORK ) - IBSCL = 0 - IF( BNRM.GT.ZERO .AND. BNRM.LT.SMLNUM ) THEN -* -* Scale matrix norm up to SMLNUM. -* - CALL DLASCL( 'G', 0, 0, BNRM, SMLNUM, M, NRHS, B, LDB, INFO ) - IBSCL = 1 - ELSE IF( BNRM.GT.BIGNUM ) THEN -* -* Scale matrix norm down to BIGNUM. -* - CALL DLASCL( 'G', 0, 0, BNRM, BIGNUM, M, NRHS, B, LDB, INFO ) - IBSCL = 2 - END IF -* -* If M < N make sure certain entries of B are zero. -* - IF( M.LT.N ) - $ CALL DLASET( 'F', N-M, NRHS, ZERO, ZERO, B( M+1, 1 ), LDB ) -* -* Overdetermined case. -* - IF( M.GE.N ) THEN -* -* Path 1 - overdetermined or exactly determined. -* - MM = M - IF( M.GE.MNTHR ) THEN -* -* Path 1a - overdetermined, with many more rows than columns. -* - MM = N - ITAU = 1 - NWORK = ITAU + N -* -* Compute A=Q*R. -* (Workspace: need 2*N, prefer N+N*NB) -* - CALL DGEQRF( M, N, A, LDA, WORK( ITAU ), WORK( NWORK ), - $ LWORK-NWORK+1, INFO ) -* -* Multiply B by transpose(Q). -* (Workspace: need N+NRHS, prefer N+NRHS*NB) -* - CALL DORMQR( 'L', 'T', M, NRHS, N, A, LDA, WORK( ITAU ), B, - $ LDB, WORK( NWORK ), LWORK-NWORK+1, INFO ) -* -* Zero out below R. -* - IF( N.GT.1 ) THEN - CALL DLASET( 'L', N-1, N-1, ZERO, ZERO, A( 2, 1 ), LDA ) - END IF - END IF -* - IE = 1 - ITAUQ = IE + N - ITAUP = ITAUQ + N - NWORK = ITAUP + N -* -* Bidiagonalize R in A. -* (Workspace: need 3*N+MM, prefer 3*N+(MM+N)*NB) -* - CALL DGEBRD( MM, N, A, LDA, S, WORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( NWORK ), LWORK-NWORK+1, - $ INFO ) -* -* Multiply B by transpose of left bidiagonalizing vectors of R. -* (Workspace: need 3*N+NRHS, prefer 3*N+NRHS*NB) -* - CALL DORMBR( 'Q', 'L', 'T', MM, NRHS, N, A, LDA, WORK( ITAUQ ), - $ B, LDB, WORK( NWORK ), LWORK-NWORK+1, INFO ) -* -* Solve the bidiagonal least squares problem. -* - CALL DLALSD( 'U', SMLSIZ, N, NRHS, S, WORK( IE ), B, LDB, - $ RCOND, RANK, WORK( NWORK ), IWORK, INFO ) - IF( INFO.NE.0 ) THEN - GO TO 10 - END IF -* -* Multiply B by right bidiagonalizing vectors of R. -* - CALL DORMBR( 'P', 'L', 'N', N, NRHS, N, A, LDA, WORK( ITAUP ), - $ B, LDB, WORK( NWORK ), LWORK-NWORK+1, INFO ) -* - ELSE IF( N.GE.MNTHR .AND. LWORK.GE.4*M+M*M+ - $ MAX( M, 2*M-4, NRHS, N-3*M, WLALSD ) ) THEN -* -* Path 2a - underdetermined, with many more columns than rows -* and sufficient workspace for an efficient algorithm. -* - LDWORK = M - IF( LWORK.GE.MAX( 4*M+M*LDA+MAX( M, 2*M-4, NRHS, N-3*M ), - $ M*LDA+M+M*NRHS, 4*M+M*LDA+WLALSD ) )LDWORK = LDA - ITAU = 1 - NWORK = M + 1 -* -* Compute A=L*Q. -* (Workspace: need 2*M, prefer M+M*NB) -* - CALL DGELQF( M, N, A, LDA, WORK( ITAU ), WORK( NWORK ), - $ LWORK-NWORK+1, INFO ) - IL = NWORK -* -* Copy L to WORK(IL), zeroing out above its diagonal. -* - CALL DLACPY( 'L', M, M, A, LDA, WORK( IL ), LDWORK ) - CALL DLASET( 'U', M-1, M-1, ZERO, ZERO, WORK( IL+LDWORK ), - $ LDWORK ) - IE = IL + LDWORK*M - ITAUQ = IE + M - ITAUP = ITAUQ + M - NWORK = ITAUP + M -* -* Bidiagonalize L in WORK(IL). -* (Workspace: need M*M+5*M, prefer M*M+4*M+2*M*NB) -* - CALL DGEBRD( M, M, WORK( IL ), LDWORK, S, WORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), WORK( NWORK ), - $ LWORK-NWORK+1, INFO ) -* -* Multiply B by transpose of left bidiagonalizing vectors of L. -* (Workspace: need M*M+4*M+NRHS, prefer M*M+4*M+NRHS*NB) -* - CALL DORMBR( 'Q', 'L', 'T', M, NRHS, M, WORK( IL ), LDWORK, - $ WORK( ITAUQ ), B, LDB, WORK( NWORK ), - $ LWORK-NWORK+1, INFO ) -* -* Solve the bidiagonal least squares problem. -* - CALL DLALSD( 'U', SMLSIZ, M, NRHS, S, WORK( IE ), B, LDB, - $ RCOND, RANK, WORK( NWORK ), IWORK, INFO ) - IF( INFO.NE.0 ) THEN - GO TO 10 - END IF -* -* Multiply B by right bidiagonalizing vectors of L. -* - CALL DORMBR( 'P', 'L', 'N', M, NRHS, M, WORK( IL ), LDWORK, - $ WORK( ITAUP ), B, LDB, WORK( NWORK ), - $ LWORK-NWORK+1, INFO ) -* -* Zero out below first M rows of B. -* - CALL DLASET( 'F', N-M, NRHS, ZERO, ZERO, B( M+1, 1 ), LDB ) - NWORK = ITAU + M -* -* Multiply transpose(Q) by B. -* (Workspace: need M+NRHS, prefer M+NRHS*NB) -* - CALL DORMLQ( 'L', 'T', N, NRHS, M, A, LDA, WORK( ITAU ), B, - $ LDB, WORK( NWORK ), LWORK-NWORK+1, INFO ) -* - ELSE -* -* Path 2 - remaining underdetermined cases. -* - IE = 1 - ITAUQ = IE + M - ITAUP = ITAUQ + M - NWORK = ITAUP + M -* -* Bidiagonalize A. -* (Workspace: need 3*M+N, prefer 3*M+(M+N)*NB) -* - CALL DGEBRD( M, N, A, LDA, S, WORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( NWORK ), LWORK-NWORK+1, - $ INFO ) -* -* Multiply B by transpose of left bidiagonalizing vectors. -* (Workspace: need 3*M+NRHS, prefer 3*M+NRHS*NB) -* - CALL DORMBR( 'Q', 'L', 'T', M, NRHS, N, A, LDA, WORK( ITAUQ ), - $ B, LDB, WORK( NWORK ), LWORK-NWORK+1, INFO ) -* -* Solve the bidiagonal least squares problem. -* - CALL DLALSD( 'L', SMLSIZ, M, NRHS, S, WORK( IE ), B, LDB, - $ RCOND, RANK, WORK( NWORK ), IWORK, INFO ) - IF( INFO.NE.0 ) THEN - GO TO 10 - END IF -* -* Multiply B by right bidiagonalizing vectors of A. -* - CALL DORMBR( 'P', 'L', 'N', N, NRHS, M, A, LDA, WORK( ITAUP ), - $ B, LDB, WORK( NWORK ), LWORK-NWORK+1, INFO ) -* - END IF -* -* Undo scaling. -* - IF( IASCL.EQ.1 ) THEN - CALL DLASCL( 'G', 0, 0, ANRM, SMLNUM, N, NRHS, B, LDB, INFO ) - CALL DLASCL( 'G', 0, 0, SMLNUM, ANRM, MINMN, 1, S, MINMN, - $ INFO ) - ELSE IF( IASCL.EQ.2 ) THEN - CALL DLASCL( 'G', 0, 0, ANRM, BIGNUM, N, NRHS, B, LDB, INFO ) - CALL DLASCL( 'G', 0, 0, BIGNUM, ANRM, MINMN, 1, S, MINMN, - $ INFO ) - END IF - IF( IBSCL.EQ.1 ) THEN - CALL DLASCL( 'G', 0, 0, SMLNUM, BNRM, N, NRHS, B, LDB, INFO ) - ELSE IF( IBSCL.EQ.2 ) THEN - CALL DLASCL( 'G', 0, 0, BIGNUM, BNRM, N, NRHS, B, LDB, INFO ) - END IF -* - 10 CONTINUE - WORK( 1 ) = MAXWRK - IWORK( 1 ) = LIWORK - RETURN -* -* End of DGELSD -* - END diff --git a/lib/linalg/fortran/dgelss.f b/lib/linalg/fortran/dgelss.f deleted file mode 100644 index c4190f2e09..0000000000 --- a/lib/linalg/fortran/dgelss.f +++ /dev/null @@ -1,744 +0,0 @@ -*> \brief DGELSS solves overdetermined or underdetermined systems for GE matrices -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DGELSS + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DGELSS( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, -* WORK, LWORK, INFO ) -* -* .. Scalar Arguments .. -* INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS, RANK -* DOUBLE PRECISION RCOND -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), S( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DGELSS computes the minimum norm solution to a real linear least -*> squares problem: -*> -*> Minimize 2-norm(| b - A*x |). -*> -*> using the singular value decomposition (SVD) of A. A is an M-by-N -*> matrix which may be rank-deficient. -*> -*> Several right hand side vectors b and solution vectors x can be -*> handled in a single call; they are stored as the columns of the -*> M-by-NRHS right hand side matrix B and the N-by-NRHS solution matrix -*> X. -*> -*> The effective rank of A is determined by treating as zero those -*> singular values which are less than RCOND times the largest singular -*> value. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix A. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in] NRHS -*> \verbatim -*> NRHS is INTEGER -*> The number of right hand sides, i.e., the number of columns -*> of the matrices B and X. NRHS >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the M-by-N matrix A. -*> On exit, the first min(m,n) rows of A are overwritten with -*> its right singular vectors, stored rowwise. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,M). -*> \endverbatim -*> -*> \param[in,out] B -*> \verbatim -*> B is DOUBLE PRECISION array, dimension (LDB,NRHS) -*> On entry, the M-by-NRHS right hand side matrix B. -*> On exit, B is overwritten by the N-by-NRHS solution -*> matrix X. If m >= n and RANK = n, the residual -*> sum-of-squares for the solution in the i-th column is given -*> by the sum of squares of elements n+1:m in that column. -*> \endverbatim -*> -*> \param[in] LDB -*> \verbatim -*> LDB is INTEGER -*> The leading dimension of the array B. LDB >= max(1,max(M,N)). -*> \endverbatim -*> -*> \param[out] S -*> \verbatim -*> S is DOUBLE PRECISION array, dimension (min(M,N)) -*> The singular values of A in decreasing order. -*> The condition number of A in the 2-norm = S(1)/S(min(m,n)). -*> \endverbatim -*> -*> \param[in] RCOND -*> \verbatim -*> RCOND is DOUBLE PRECISION -*> RCOND is used to determine the effective rank of A. -*> Singular values S(i) <= RCOND*S(1) are treated as zero. -*> If RCOND < 0, machine precision is used instead. -*> \endverbatim -*> -*> \param[out] RANK -*> \verbatim -*> RANK is INTEGER -*> The effective rank of A, i.e., the number of singular values -*> which are greater than RCOND*S(1). -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) -*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -*> \endverbatim -*> -*> \param[in] LWORK -*> \verbatim -*> LWORK is INTEGER -*> The dimension of the array WORK. LWORK >= 1, and also: -*> LWORK >= 3*min(M,N) + max( 2*min(M,N), max(M,N), NRHS ) -*> For good performance, LWORK should generally be larger. -*> -*> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal size of the WORK array, returns -*> this value as the first entry of the WORK array, and no error -*> message related to LWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value. -*> > 0: the algorithm for computing the SVD failed to converge; -*> if INFO = i, i off-diagonal elements of an intermediate -*> bidiagonal form did not converge to zero. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleGEsolve -* -* ===================================================================== - SUBROUTINE DGELSS( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, - $ WORK, LWORK, INFO ) -* -* -- LAPACK driver routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS, RANK - DOUBLE PRECISION RCOND -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), B( LDB, * ), S( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) -* .. -* .. Local Scalars .. - LOGICAL LQUERY - INTEGER BDSPAC, BL, CHUNK, I, IASCL, IBSCL, IE, IL, - $ ITAU, ITAUP, ITAUQ, IWORK, LDWORK, MAXMN, - $ MAXWRK, MINMN, MINWRK, MM, MNTHR - INTEGER LWORK_DGEQRF, LWORK_DORMQR, LWORK_DGEBRD, - $ LWORK_DORMBR, LWORK_DORGBR, LWORK_DORMLQ, - $ LWORK_DGELQF - DOUBLE PRECISION ANRM, BIGNUM, BNRM, EPS, SFMIN, SMLNUM, THR -* .. -* .. Local Arrays .. - DOUBLE PRECISION DUM( 1 ) -* .. -* .. External Subroutines .. - EXTERNAL DBDSQR, DCOPY, DGEBRD, DGELQF, DGEMM, DGEMV, - $ DGEQRF, DLABAD, DLACPY, DLASCL, DLASET, DORGBR, - $ DORMBR, DORMLQ, DORMQR, DRSCL, XERBLA -* .. -* .. External Functions .. - INTEGER ILAENV - DOUBLE PRECISION DLAMCH, DLANGE - EXTERNAL ILAENV, DLAMCH, DLANGE -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, MIN -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - INFO = 0 - MINMN = MIN( M, N ) - MAXMN = MAX( M, N ) - LQUERY = ( LWORK.EQ.-1 ) - IF( M.LT.0 ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( NRHS.LT.0 ) THEN - INFO = -3 - ELSE IF( LDA.LT.MAX( 1, M ) ) THEN - INFO = -5 - ELSE IF( LDB.LT.MAX( 1, MAXMN ) ) THEN - INFO = -7 - END IF -* -* Compute workspace -* (Note: Comments in the code beginning "Workspace:" describe the -* minimal amount of workspace needed at that point in the code, -* as well as the preferred amount for good performance. -* NB refers to the optimal block size for the immediately -* following subroutine, as returned by ILAENV.) -* - IF( INFO.EQ.0 ) THEN - MINWRK = 1 - MAXWRK = 1 - IF( MINMN.GT.0 ) THEN - MM = M - MNTHR = ILAENV( 6, 'DGELSS', ' ', M, N, NRHS, -1 ) - IF( M.GE.N .AND. M.GE.MNTHR ) THEN -* -* Path 1a - overdetermined, with many more rows than -* columns -* -* Compute space needed for DGEQRF - CALL DGEQRF( M, N, A, LDA, DUM(1), DUM(1), -1, INFO ) - LWORK_DGEQRF = INT( DUM(1) ) -* Compute space needed for DORMQR - CALL DORMQR( 'L', 'T', M, NRHS, N, A, LDA, DUM(1), B, - $ LDB, DUM(1), -1, INFO ) - LWORK_DORMQR = INT( DUM(1) ) - MM = N - MAXWRK = MAX( MAXWRK, N + LWORK_DGEQRF ) - MAXWRK = MAX( MAXWRK, N + LWORK_DORMQR ) - END IF - IF( M.GE.N ) THEN -* -* Path 1 - overdetermined or exactly determined -* -* Compute workspace needed for DBDSQR -* - BDSPAC = MAX( 1, 5*N ) -* Compute space needed for DGEBRD - CALL DGEBRD( MM, N, A, LDA, S, DUM(1), DUM(1), - $ DUM(1), DUM(1), -1, INFO ) - LWORK_DGEBRD = INT( DUM(1) ) -* Compute space needed for DORMBR - CALL DORMBR( 'Q', 'L', 'T', MM, NRHS, N, A, LDA, DUM(1), - $ B, LDB, DUM(1), -1, INFO ) - LWORK_DORMBR = INT( DUM(1) ) -* Compute space needed for DORGBR - CALL DORGBR( 'P', N, N, N, A, LDA, DUM(1), - $ DUM(1), -1, INFO ) - LWORK_DORGBR = INT( DUM(1) ) -* Compute total workspace needed - MAXWRK = MAX( MAXWRK, 3*N + LWORK_DGEBRD ) - MAXWRK = MAX( MAXWRK, 3*N + LWORK_DORMBR ) - MAXWRK = MAX( MAXWRK, 3*N + LWORK_DORGBR ) - MAXWRK = MAX( MAXWRK, BDSPAC ) - MAXWRK = MAX( MAXWRK, N*NRHS ) - MINWRK = MAX( 3*N + MM, 3*N + NRHS, BDSPAC ) - MAXWRK = MAX( MINWRK, MAXWRK ) - END IF - IF( N.GT.M ) THEN -* -* Compute workspace needed for DBDSQR -* - BDSPAC = MAX( 1, 5*M ) - MINWRK = MAX( 3*M+NRHS, 3*M+N, BDSPAC ) - IF( N.GE.MNTHR ) THEN -* -* Path 2a - underdetermined, with many more columns -* than rows -* -* Compute space needed for DGELQF - CALL DGELQF( M, N, A, LDA, DUM(1), DUM(1), - $ -1, INFO ) - LWORK_DGELQF = INT( DUM(1) ) -* Compute space needed for DGEBRD - CALL DGEBRD( M, M, A, LDA, S, DUM(1), DUM(1), - $ DUM(1), DUM(1), -1, INFO ) - LWORK_DGEBRD = INT( DUM(1) ) -* Compute space needed for DORMBR - CALL DORMBR( 'Q', 'L', 'T', M, NRHS, N, A, LDA, - $ DUM(1), B, LDB, DUM(1), -1, INFO ) - LWORK_DORMBR = INT( DUM(1) ) -* Compute space needed for DORGBR - CALL DORGBR( 'P', M, M, M, A, LDA, DUM(1), - $ DUM(1), -1, INFO ) - LWORK_DORGBR = INT( DUM(1) ) -* Compute space needed for DORMLQ - CALL DORMLQ( 'L', 'T', N, NRHS, M, A, LDA, DUM(1), - $ B, LDB, DUM(1), -1, INFO ) - LWORK_DORMLQ = INT( DUM(1) ) -* Compute total workspace needed - MAXWRK = M + LWORK_DGELQF - MAXWRK = MAX( MAXWRK, M*M + 4*M + LWORK_DGEBRD ) - MAXWRK = MAX( MAXWRK, M*M + 4*M + LWORK_DORMBR ) - MAXWRK = MAX( MAXWRK, M*M + 4*M + LWORK_DORGBR ) - MAXWRK = MAX( MAXWRK, M*M + M + BDSPAC ) - IF( NRHS.GT.1 ) THEN - MAXWRK = MAX( MAXWRK, M*M + M + M*NRHS ) - ELSE - MAXWRK = MAX( MAXWRK, M*M + 2*M ) - END IF - MAXWRK = MAX( MAXWRK, M + LWORK_DORMLQ ) - ELSE -* -* Path 2 - underdetermined -* -* Compute space needed for DGEBRD - CALL DGEBRD( M, N, A, LDA, S, DUM(1), DUM(1), - $ DUM(1), DUM(1), -1, INFO ) - LWORK_DGEBRD = INT( DUM(1) ) -* Compute space needed for DORMBR - CALL DORMBR( 'Q', 'L', 'T', M, NRHS, M, A, LDA, - $ DUM(1), B, LDB, DUM(1), -1, INFO ) - LWORK_DORMBR = INT( DUM(1) ) -* Compute space needed for DORGBR - CALL DORGBR( 'P', M, N, M, A, LDA, DUM(1), - $ DUM(1), -1, INFO ) - LWORK_DORGBR = INT( DUM(1) ) - MAXWRK = 3*M + LWORK_DGEBRD - MAXWRK = MAX( MAXWRK, 3*M + LWORK_DORMBR ) - MAXWRK = MAX( MAXWRK, 3*M + LWORK_DORGBR ) - MAXWRK = MAX( MAXWRK, BDSPAC ) - MAXWRK = MAX( MAXWRK, N*NRHS ) - END IF - END IF - MAXWRK = MAX( MINWRK, MAXWRK ) - END IF - WORK( 1 ) = MAXWRK -* - IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) - $ INFO = -12 - END IF -* - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DGELSS', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - RETURN - END IF -* -* Quick return if possible -* - IF( M.EQ.0 .OR. N.EQ.0 ) THEN - RANK = 0 - RETURN - END IF -* -* Get machine parameters -* - EPS = DLAMCH( 'P' ) - SFMIN = DLAMCH( 'S' ) - SMLNUM = SFMIN / EPS - BIGNUM = ONE / SMLNUM - CALL DLABAD( SMLNUM, BIGNUM ) -* -* Scale A if max element outside range [SMLNUM,BIGNUM] -* - ANRM = DLANGE( 'M', M, N, A, LDA, WORK ) - IASCL = 0 - IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN -* -* Scale matrix norm up to SMLNUM -* - CALL DLASCL( 'G', 0, 0, ANRM, SMLNUM, M, N, A, LDA, INFO ) - IASCL = 1 - ELSE IF( ANRM.GT.BIGNUM ) THEN -* -* Scale matrix norm down to BIGNUM -* - CALL DLASCL( 'G', 0, 0, ANRM, BIGNUM, M, N, A, LDA, INFO ) - IASCL = 2 - ELSE IF( ANRM.EQ.ZERO ) THEN -* -* Matrix all zero. Return zero solution. -* - CALL DLASET( 'F', MAX( M, N ), NRHS, ZERO, ZERO, B, LDB ) - CALL DLASET( 'F', MINMN, 1, ZERO, ZERO, S, MINMN ) - RANK = 0 - GO TO 70 - END IF -* -* Scale B if max element outside range [SMLNUM,BIGNUM] -* - BNRM = DLANGE( 'M', M, NRHS, B, LDB, WORK ) - IBSCL = 0 - IF( BNRM.GT.ZERO .AND. BNRM.LT.SMLNUM ) THEN -* -* Scale matrix norm up to SMLNUM -* - CALL DLASCL( 'G', 0, 0, BNRM, SMLNUM, M, NRHS, B, LDB, INFO ) - IBSCL = 1 - ELSE IF( BNRM.GT.BIGNUM ) THEN -* -* Scale matrix norm down to BIGNUM -* - CALL DLASCL( 'G', 0, 0, BNRM, BIGNUM, M, NRHS, B, LDB, INFO ) - IBSCL = 2 - END IF -* -* Overdetermined case -* - IF( M.GE.N ) THEN -* -* Path 1 - overdetermined or exactly determined -* - MM = M - IF( M.GE.MNTHR ) THEN -* -* Path 1a - overdetermined, with many more rows than columns -* - MM = N - ITAU = 1 - IWORK = ITAU + N -* -* Compute A=Q*R -* (Workspace: need 2*N, prefer N+N*NB) -* - CALL DGEQRF( M, N, A, LDA, WORK( ITAU ), WORK( IWORK ), - $ LWORK-IWORK+1, INFO ) -* -* Multiply B by transpose(Q) -* (Workspace: need N+NRHS, prefer N+NRHS*NB) -* - CALL DORMQR( 'L', 'T', M, NRHS, N, A, LDA, WORK( ITAU ), B, - $ LDB, WORK( IWORK ), LWORK-IWORK+1, INFO ) -* -* Zero out below R -* - IF( N.GT.1 ) - $ CALL DLASET( 'L', N-1, N-1, ZERO, ZERO, A( 2, 1 ), LDA ) - END IF -* - IE = 1 - ITAUQ = IE + N - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Bidiagonalize R in A -* (Workspace: need 3*N+MM, prefer 3*N+(MM+N)*NB) -* - CALL DGEBRD( MM, N, A, LDA, S, WORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( IWORK ), LWORK-IWORK+1, - $ INFO ) -* -* Multiply B by transpose of left bidiagonalizing vectors of R -* (Workspace: need 3*N+NRHS, prefer 3*N+NRHS*NB) -* - CALL DORMBR( 'Q', 'L', 'T', MM, NRHS, N, A, LDA, WORK( ITAUQ ), - $ B, LDB, WORK( IWORK ), LWORK-IWORK+1, INFO ) -* -* Generate right bidiagonalizing vectors of R in A -* (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB) -* - CALL DORGBR( 'P', N, N, N, A, LDA, WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, INFO ) - IWORK = IE + N -* -* Perform bidiagonal QR iteration -* multiply B by transpose of left singular vectors -* compute right singular vectors in A -* (Workspace: need BDSPAC) -* - CALL DBDSQR( 'U', N, N, 0, NRHS, S, WORK( IE ), A, LDA, DUM, - $ 1, B, LDB, WORK( IWORK ), INFO ) - IF( INFO.NE.0 ) - $ GO TO 70 -* -* Multiply B by reciprocals of singular values -* - THR = MAX( RCOND*S( 1 ), SFMIN ) - IF( RCOND.LT.ZERO ) - $ THR = MAX( EPS*S( 1 ), SFMIN ) - RANK = 0 - DO 10 I = 1, N - IF( S( I ).GT.THR ) THEN - CALL DRSCL( NRHS, S( I ), B( I, 1 ), LDB ) - RANK = RANK + 1 - ELSE - CALL DLASET( 'F', 1, NRHS, ZERO, ZERO, B( I, 1 ), LDB ) - END IF - 10 CONTINUE -* -* Multiply B by right singular vectors -* (Workspace: need N, prefer N*NRHS) -* - IF( LWORK.GE.LDB*NRHS .AND. NRHS.GT.1 ) THEN - CALL DGEMM( 'T', 'N', N, NRHS, N, ONE, A, LDA, B, LDB, ZERO, - $ WORK, LDB ) - CALL DLACPY( 'G', N, NRHS, WORK, LDB, B, LDB ) - ELSE IF( NRHS.GT.1 ) THEN - CHUNK = LWORK / N - DO 20 I = 1, NRHS, CHUNK - BL = MIN( NRHS-I+1, CHUNK ) - CALL DGEMM( 'T', 'N', N, BL, N, ONE, A, LDA, B( 1, I ), - $ LDB, ZERO, WORK, N ) - CALL DLACPY( 'G', N, BL, WORK, N, B( 1, I ), LDB ) - 20 CONTINUE - ELSE - CALL DGEMV( 'T', N, N, ONE, A, LDA, B, 1, ZERO, WORK, 1 ) - CALL DCOPY( N, WORK, 1, B, 1 ) - END IF -* - ELSE IF( N.GE.MNTHR .AND. LWORK.GE.4*M+M*M+ - $ MAX( M, 2*M-4, NRHS, N-3*M ) ) THEN -* -* Path 2a - underdetermined, with many more columns than rows -* and sufficient workspace for an efficient algorithm -* - LDWORK = M - IF( LWORK.GE.MAX( 4*M+M*LDA+MAX( M, 2*M-4, NRHS, N-3*M ), - $ M*LDA+M+M*NRHS ) )LDWORK = LDA - ITAU = 1 - IWORK = M + 1 -* -* Compute A=L*Q -* (Workspace: need 2*M, prefer M+M*NB) -* - CALL DGELQF( M, N, A, LDA, WORK( ITAU ), WORK( IWORK ), - $ LWORK-IWORK+1, INFO ) - IL = IWORK -* -* Copy L to WORK(IL), zeroing out above it -* - CALL DLACPY( 'L', M, M, A, LDA, WORK( IL ), LDWORK ) - CALL DLASET( 'U', M-1, M-1, ZERO, ZERO, WORK( IL+LDWORK ), - $ LDWORK ) - IE = IL + LDWORK*M - ITAUQ = IE + M - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Bidiagonalize L in WORK(IL) -* (Workspace: need M*M+5*M, prefer M*M+4*M+2*M*NB) -* - CALL DGEBRD( M, M, WORK( IL ), LDWORK, S, WORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, INFO ) -* -* Multiply B by transpose of left bidiagonalizing vectors of L -* (Workspace: need M*M+4*M+NRHS, prefer M*M+4*M+NRHS*NB) -* - CALL DORMBR( 'Q', 'L', 'T', M, NRHS, M, WORK( IL ), LDWORK, - $ WORK( ITAUQ ), B, LDB, WORK( IWORK ), - $ LWORK-IWORK+1, INFO ) -* -* Generate right bidiagonalizing vectors of R in WORK(IL) -* (Workspace: need M*M+5*M-1, prefer M*M+4*M+(M-1)*NB) -* - CALL DORGBR( 'P', M, M, M, WORK( IL ), LDWORK, WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, INFO ) - IWORK = IE + M -* -* Perform bidiagonal QR iteration, -* computing right singular vectors of L in WORK(IL) and -* multiplying B by transpose of left singular vectors -* (Workspace: need M*M+M+BDSPAC) -* - CALL DBDSQR( 'U', M, M, 0, NRHS, S, WORK( IE ), WORK( IL ), - $ LDWORK, A, LDA, B, LDB, WORK( IWORK ), INFO ) - IF( INFO.NE.0 ) - $ GO TO 70 -* -* Multiply B by reciprocals of singular values -* - THR = MAX( RCOND*S( 1 ), SFMIN ) - IF( RCOND.LT.ZERO ) - $ THR = MAX( EPS*S( 1 ), SFMIN ) - RANK = 0 - DO 30 I = 1, M - IF( S( I ).GT.THR ) THEN - CALL DRSCL( NRHS, S( I ), B( I, 1 ), LDB ) - RANK = RANK + 1 - ELSE - CALL DLASET( 'F', 1, NRHS, ZERO, ZERO, B( I, 1 ), LDB ) - END IF - 30 CONTINUE - IWORK = IE -* -* Multiply B by right singular vectors of L in WORK(IL) -* (Workspace: need M*M+2*M, prefer M*M+M+M*NRHS) -* - IF( LWORK.GE.LDB*NRHS+IWORK-1 .AND. NRHS.GT.1 ) THEN - CALL DGEMM( 'T', 'N', M, NRHS, M, ONE, WORK( IL ), LDWORK, - $ B, LDB, ZERO, WORK( IWORK ), LDB ) - CALL DLACPY( 'G', M, NRHS, WORK( IWORK ), LDB, B, LDB ) - ELSE IF( NRHS.GT.1 ) THEN - CHUNK = ( LWORK-IWORK+1 ) / M - DO 40 I = 1, NRHS, CHUNK - BL = MIN( NRHS-I+1, CHUNK ) - CALL DGEMM( 'T', 'N', M, BL, M, ONE, WORK( IL ), LDWORK, - $ B( 1, I ), LDB, ZERO, WORK( IWORK ), M ) - CALL DLACPY( 'G', M, BL, WORK( IWORK ), M, B( 1, I ), - $ LDB ) - 40 CONTINUE - ELSE - CALL DGEMV( 'T', M, M, ONE, WORK( IL ), LDWORK, B( 1, 1 ), - $ 1, ZERO, WORK( IWORK ), 1 ) - CALL DCOPY( M, WORK( IWORK ), 1, B( 1, 1 ), 1 ) - END IF -* -* Zero out below first M rows of B -* - CALL DLASET( 'F', N-M, NRHS, ZERO, ZERO, B( M+1, 1 ), LDB ) - IWORK = ITAU + M -* -* Multiply transpose(Q) by B -* (Workspace: need M+NRHS, prefer M+NRHS*NB) -* - CALL DORMLQ( 'L', 'T', N, NRHS, M, A, LDA, WORK( ITAU ), B, - $ LDB, WORK( IWORK ), LWORK-IWORK+1, INFO ) -* - ELSE -* -* Path 2 - remaining underdetermined cases -* - IE = 1 - ITAUQ = IE + M - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Bidiagonalize A -* (Workspace: need 3*M+N, prefer 3*M+(M+N)*NB) -* - CALL DGEBRD( M, N, A, LDA, S, WORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( IWORK ), LWORK-IWORK+1, - $ INFO ) -* -* Multiply B by transpose of left bidiagonalizing vectors -* (Workspace: need 3*M+NRHS, prefer 3*M+NRHS*NB) -* - CALL DORMBR( 'Q', 'L', 'T', M, NRHS, N, A, LDA, WORK( ITAUQ ), - $ B, LDB, WORK( IWORK ), LWORK-IWORK+1, INFO ) -* -* Generate right bidiagonalizing vectors in A -* (Workspace: need 4*M, prefer 3*M+M*NB) -* - CALL DORGBR( 'P', M, N, M, A, LDA, WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, INFO ) - IWORK = IE + M -* -* Perform bidiagonal QR iteration, -* computing right singular vectors of A in A and -* multiplying B by transpose of left singular vectors -* (Workspace: need BDSPAC) -* - CALL DBDSQR( 'L', M, N, 0, NRHS, S, WORK( IE ), A, LDA, DUM, - $ 1, B, LDB, WORK( IWORK ), INFO ) - IF( INFO.NE.0 ) - $ GO TO 70 -* -* Multiply B by reciprocals of singular values -* - THR = MAX( RCOND*S( 1 ), SFMIN ) - IF( RCOND.LT.ZERO ) - $ THR = MAX( EPS*S( 1 ), SFMIN ) - RANK = 0 - DO 50 I = 1, M - IF( S( I ).GT.THR ) THEN - CALL DRSCL( NRHS, S( I ), B( I, 1 ), LDB ) - RANK = RANK + 1 - ELSE - CALL DLASET( 'F', 1, NRHS, ZERO, ZERO, B( I, 1 ), LDB ) - END IF - 50 CONTINUE -* -* Multiply B by right singular vectors of A -* (Workspace: need N, prefer N*NRHS) -* - IF( LWORK.GE.LDB*NRHS .AND. NRHS.GT.1 ) THEN - CALL DGEMM( 'T', 'N', N, NRHS, M, ONE, A, LDA, B, LDB, ZERO, - $ WORK, LDB ) - CALL DLACPY( 'F', N, NRHS, WORK, LDB, B, LDB ) - ELSE IF( NRHS.GT.1 ) THEN - CHUNK = LWORK / N - DO 60 I = 1, NRHS, CHUNK - BL = MIN( NRHS-I+1, CHUNK ) - CALL DGEMM( 'T', 'N', N, BL, M, ONE, A, LDA, B( 1, I ), - $ LDB, ZERO, WORK, N ) - CALL DLACPY( 'F', N, BL, WORK, N, B( 1, I ), LDB ) - 60 CONTINUE - ELSE - CALL DGEMV( 'T', M, N, ONE, A, LDA, B, 1, ZERO, WORK, 1 ) - CALL DCOPY( N, WORK, 1, B, 1 ) - END IF - END IF -* -* Undo scaling -* - IF( IASCL.EQ.1 ) THEN - CALL DLASCL( 'G', 0, 0, ANRM, SMLNUM, N, NRHS, B, LDB, INFO ) - CALL DLASCL( 'G', 0, 0, SMLNUM, ANRM, MINMN, 1, S, MINMN, - $ INFO ) - ELSE IF( IASCL.EQ.2 ) THEN - CALL DLASCL( 'G', 0, 0, ANRM, BIGNUM, N, NRHS, B, LDB, INFO ) - CALL DLASCL( 'G', 0, 0, BIGNUM, ANRM, MINMN, 1, S, MINMN, - $ INFO ) - END IF - IF( IBSCL.EQ.1 ) THEN - CALL DLASCL( 'G', 0, 0, SMLNUM, BNRM, N, NRHS, B, LDB, INFO ) - ELSE IF( IBSCL.EQ.2 ) THEN - CALL DLASCL( 'G', 0, 0, BIGNUM, BNRM, N, NRHS, B, LDB, INFO ) - END IF -* - 70 CONTINUE - WORK( 1 ) = MAXWRK - RETURN -* -* End of DGELSS -* - END diff --git a/lib/linalg/fortran/dgemm.f b/lib/linalg/fortran/dgemm.f deleted file mode 100644 index 8c1b4f2066..0000000000 --- a/lib/linalg/fortran/dgemm.f +++ /dev/null @@ -1,379 +0,0 @@ -*> \brief \b DGEMM -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE DGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) -* -* .. Scalar Arguments .. -* DOUBLE PRECISION ALPHA,BETA -* INTEGER K,LDA,LDB,LDC,M,N -* CHARACTER TRANSA,TRANSB -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DGEMM performs one of the matrix-matrix operations -*> -*> C := alpha*op( A )*op( B ) + beta*C, -*> -*> where op( X ) is one of -*> -*> op( X ) = X or op( X ) = X**T, -*> -*> alpha and beta are scalars, and A, B and C are matrices, with op( A ) -*> an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] TRANSA -*> \verbatim -*> TRANSA is CHARACTER*1 -*> On entry, TRANSA specifies the form of op( A ) to be used in -*> the matrix multiplication as follows: -*> -*> TRANSA = 'N' or 'n', op( A ) = A. -*> -*> TRANSA = 'T' or 't', op( A ) = A**T. -*> -*> TRANSA = 'C' or 'c', op( A ) = A**T. -*> \endverbatim -*> -*> \param[in] TRANSB -*> \verbatim -*> TRANSB is CHARACTER*1 -*> On entry, TRANSB specifies the form of op( B ) to be used in -*> the matrix multiplication as follows: -*> -*> TRANSB = 'N' or 'n', op( B ) = B. -*> -*> TRANSB = 'T' or 't', op( B ) = B**T. -*> -*> TRANSB = 'C' or 'c', op( B ) = B**T. -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> On entry, M specifies the number of rows of the matrix -*> op( A ) and of the matrix C. M must be at least zero. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> On entry, N specifies the number of columns of the matrix -*> op( B ) and the number of columns of the matrix C. N must be -*> at least zero. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> On entry, K specifies the number of columns of the matrix -*> op( A ) and the number of rows of the matrix op( B ). K must -*> be at least zero. -*> \endverbatim -*> -*> \param[in] ALPHA -*> \verbatim -*> ALPHA is DOUBLE PRECISION. -*> On entry, ALPHA specifies the scalar alpha. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is -*> k when TRANSA = 'N' or 'n', and is m otherwise. -*> Before entry with TRANSA = 'N' or 'n', the leading m by k -*> part of the array A must contain the matrix A, otherwise -*> the leading k by m part of the array A must contain the -*> matrix A. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> On entry, LDA specifies the first dimension of A as declared -*> in the calling (sub) program. When TRANSA = 'N' or 'n' then -*> LDA must be at least max( 1, m ), otherwise LDA must be at -*> least max( 1, k ). -*> \endverbatim -*> -*> \param[in] B -*> \verbatim -*> B is DOUBLE PRECISION array, dimension ( LDB, kb ), where kb is -*> n when TRANSB = 'N' or 'n', and is k otherwise. -*> Before entry with TRANSB = 'N' or 'n', the leading k by n -*> part of the array B must contain the matrix B, otherwise -*> the leading n by k part of the array B must contain the -*> matrix B. -*> \endverbatim -*> -*> \param[in] LDB -*> \verbatim -*> LDB is INTEGER -*> On entry, LDB specifies the first dimension of B as declared -*> in the calling (sub) program. When TRANSB = 'N' or 'n' then -*> LDB must be at least max( 1, k ), otherwise LDB must be at -*> least max( 1, n ). -*> \endverbatim -*> -*> \param[in] BETA -*> \verbatim -*> BETA is DOUBLE PRECISION. -*> On entry, BETA specifies the scalar beta. When BETA is -*> supplied as zero then C need not be set on input. -*> \endverbatim -*> -*> \param[in,out] C -*> \verbatim -*> C is DOUBLE PRECISION array, dimension ( LDC, N ) -*> Before entry, the leading m by n part of the array C must -*> contain the matrix C, except when beta is zero, in which -*> case C need not be set on entry. -*> On exit, the array C is overwritten by the m by n matrix -*> ( alpha*op( A )*op( B ) + beta*C ). -*> \endverbatim -*> -*> \param[in] LDC -*> \verbatim -*> LDC is INTEGER -*> On entry, LDC specifies the first dimension of C as declared -*> in the calling (sub) program. LDC must be at least -*> max( 1, m ). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup double_blas_level3 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> Level 3 Blas routine. -*> -*> -- Written on 8-February-1989. -*> Jack Dongarra, Argonne National Laboratory. -*> Iain Duff, AERE Harwell. -*> Jeremy Du Croz, Numerical Algorithms Group Ltd. -*> Sven Hammarling, Numerical Algorithms Group Ltd. -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) -* -* -- Reference BLAS level3 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - DOUBLE PRECISION ALPHA,BETA - INTEGER K,LDA,LDB,LDC,M,N - CHARACTER TRANSA,TRANSB -* .. -* .. Array Arguments .. - DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*) -* .. -* -* ===================================================================== -* -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* .. Local Scalars .. - DOUBLE PRECISION TEMP - INTEGER I,INFO,J,L,NROWA,NROWB - LOGICAL NOTA,NOTB -* .. -* .. Parameters .. - DOUBLE PRECISION ONE,ZERO - PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) -* .. -* -* Set NOTA and NOTB as true if A and B respectively are not -* transposed and set NROWA and NROWB as the number of rows of A -* and B respectively. -* - NOTA = LSAME(TRANSA,'N') - NOTB = LSAME(TRANSB,'N') - IF (NOTA) THEN - NROWA = M - ELSE - NROWA = K - END IF - IF (NOTB) THEN - NROWB = K - ELSE - NROWB = N - END IF -* -* Test the input parameters. -* - INFO = 0 - IF ((.NOT.NOTA) .AND. (.NOT.LSAME(TRANSA,'C')) .AND. - + (.NOT.LSAME(TRANSA,'T'))) THEN - INFO = 1 - ELSE IF ((.NOT.NOTB) .AND. (.NOT.LSAME(TRANSB,'C')) .AND. - + (.NOT.LSAME(TRANSB,'T'))) THEN - INFO = 2 - ELSE IF (M.LT.0) THEN - INFO = 3 - ELSE IF (N.LT.0) THEN - INFO = 4 - ELSE IF (K.LT.0) THEN - INFO = 5 - ELSE IF (LDA.LT.MAX(1,NROWA)) THEN - INFO = 8 - ELSE IF (LDB.LT.MAX(1,NROWB)) THEN - INFO = 10 - ELSE IF (LDC.LT.MAX(1,M)) THEN - INFO = 13 - END IF - IF (INFO.NE.0) THEN - CALL XERBLA('DGEMM ',INFO) - RETURN - END IF -* -* Quick return if possible. -* - IF ((M.EQ.0) .OR. (N.EQ.0) .OR. - + (((ALPHA.EQ.ZERO).OR. (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN -* -* And if alpha.eq.zero. -* - IF (ALPHA.EQ.ZERO) THEN - IF (BETA.EQ.ZERO) THEN - DO 20 J = 1,N - DO 10 I = 1,M - C(I,J) = ZERO - 10 CONTINUE - 20 CONTINUE - ELSE - DO 40 J = 1,N - DO 30 I = 1,M - C(I,J) = BETA*C(I,J) - 30 CONTINUE - 40 CONTINUE - END IF - RETURN - END IF -* -* Start the operations. -* - IF (NOTB) THEN - IF (NOTA) THEN -* -* Form C := alpha*A*B + beta*C. -* - DO 90 J = 1,N - IF (BETA.EQ.ZERO) THEN - DO 50 I = 1,M - C(I,J) = ZERO - 50 CONTINUE - ELSE IF (BETA.NE.ONE) THEN - DO 60 I = 1,M - C(I,J) = BETA*C(I,J) - 60 CONTINUE - END IF - DO 80 L = 1,K - TEMP = ALPHA*B(L,J) - DO 70 I = 1,M - C(I,J) = C(I,J) + TEMP*A(I,L) - 70 CONTINUE - 80 CONTINUE - 90 CONTINUE - ELSE -* -* Form C := alpha*A**T*B + beta*C -* - DO 120 J = 1,N - DO 110 I = 1,M - TEMP = ZERO - DO 100 L = 1,K - TEMP = TEMP + A(L,I)*B(L,J) - 100 CONTINUE - IF (BETA.EQ.ZERO) THEN - C(I,J) = ALPHA*TEMP - ELSE - C(I,J) = ALPHA*TEMP + BETA*C(I,J) - END IF - 110 CONTINUE - 120 CONTINUE - END IF - ELSE - IF (NOTA) THEN -* -* Form C := alpha*A*B**T + beta*C -* - DO 170 J = 1,N - IF (BETA.EQ.ZERO) THEN - DO 130 I = 1,M - C(I,J) = ZERO - 130 CONTINUE - ELSE IF (BETA.NE.ONE) THEN - DO 140 I = 1,M - C(I,J) = BETA*C(I,J) - 140 CONTINUE - END IF - DO 160 L = 1,K - TEMP = ALPHA*B(J,L) - DO 150 I = 1,M - C(I,J) = C(I,J) + TEMP*A(I,L) - 150 CONTINUE - 160 CONTINUE - 170 CONTINUE - ELSE -* -* Form C := alpha*A**T*B**T + beta*C -* - DO 200 J = 1,N - DO 190 I = 1,M - TEMP = ZERO - DO 180 L = 1,K - TEMP = TEMP + A(L,I)*B(J,L) - 180 CONTINUE - IF (BETA.EQ.ZERO) THEN - C(I,J) = ALPHA*TEMP - ELSE - C(I,J) = ALPHA*TEMP + BETA*C(I,J) - END IF - 190 CONTINUE - 200 CONTINUE - END IF - END IF -* - RETURN -* -* End of DGEMM -* - END diff --git a/lib/linalg/fortran/dgemv.f b/lib/linalg/fortran/dgemv.f deleted file mode 100644 index 6625509b3a..0000000000 --- a/lib/linalg/fortran/dgemv.f +++ /dev/null @@ -1,327 +0,0 @@ -*> \brief \b DGEMV -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE DGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) -* -* .. Scalar Arguments .. -* DOUBLE PRECISION ALPHA,BETA -* INTEGER INCX,INCY,LDA,M,N -* CHARACTER TRANS -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A(LDA,*),X(*),Y(*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DGEMV performs one of the matrix-vector operations -*> -*> y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, -*> -*> where alpha and beta are scalars, x and y are vectors and A is an -*> m by n matrix. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] TRANS -*> \verbatim -*> TRANS is CHARACTER*1 -*> On entry, TRANS specifies the operation to be performed as -*> follows: -*> -*> TRANS = 'N' or 'n' y := alpha*A*x + beta*y. -*> -*> TRANS = 'T' or 't' y := alpha*A**T*x + beta*y. -*> -*> TRANS = 'C' or 'c' y := alpha*A**T*x + beta*y. -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> On entry, M specifies the number of rows of the matrix A. -*> M must be at least zero. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> On entry, N specifies the number of columns of the matrix A. -*> N must be at least zero. -*> \endverbatim -*> -*> \param[in] ALPHA -*> \verbatim -*> ALPHA is DOUBLE PRECISION. -*> On entry, ALPHA specifies the scalar alpha. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension ( LDA, N ) -*> Before entry, the leading m by n part of the array A must -*> contain the matrix of coefficients. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> On entry, LDA specifies the first dimension of A as declared -*> in the calling (sub) program. LDA must be at least -*> max( 1, m ). -*> \endverbatim -*> -*> \param[in] X -*> \verbatim -*> X is DOUBLE PRECISION array, dimension at least -*> ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' -*> and at least -*> ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. -*> Before entry, the incremented array X must contain the -*> vector x. -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> On entry, INCX specifies the increment for the elements of -*> X. INCX must not be zero. -*> \endverbatim -*> -*> \param[in] BETA -*> \verbatim -*> BETA is DOUBLE PRECISION. -*> On entry, BETA specifies the scalar beta. When BETA is -*> supplied as zero then Y need not be set on input. -*> \endverbatim -*> -*> \param[in,out] Y -*> \verbatim -*> Y is DOUBLE PRECISION array, dimension at least -*> ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' -*> and at least -*> ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. -*> Before entry with BETA non-zero, the incremented array Y -*> must contain the vector y. On exit, Y is overwritten by the -*> updated vector y. -*> \endverbatim -*> -*> \param[in] INCY -*> \verbatim -*> INCY is INTEGER -*> On entry, INCY specifies the increment for the elements of -*> Y. INCY must not be zero. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup double_blas_level2 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> Level 2 Blas routine. -*> The vector and matrix arguments are not referenced when N = 0, or M = 0 -*> -*> -- Written on 22-October-1986. -*> Jack Dongarra, Argonne National Lab. -*> Jeremy Du Croz, Nag Central Office. -*> Sven Hammarling, Nag Central Office. -*> Richard Hanson, Sandia National Labs. -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) -* -* -- Reference BLAS level2 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - DOUBLE PRECISION ALPHA,BETA - INTEGER INCX,INCY,LDA,M,N - CHARACTER TRANS -* .. -* .. Array Arguments .. - DOUBLE PRECISION A(LDA,*),X(*),Y(*) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE,ZERO - PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) -* .. -* .. Local Scalars .. - DOUBLE PRECISION TEMP - INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY,LENX,LENY -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* -* Test the input parameters. -* - INFO = 0 - IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. - + .NOT.LSAME(TRANS,'C')) THEN - INFO = 1 - ELSE IF (M.LT.0) THEN - INFO = 2 - ELSE IF (N.LT.0) THEN - INFO = 3 - ELSE IF (LDA.LT.MAX(1,M)) THEN - INFO = 6 - ELSE IF (INCX.EQ.0) THEN - INFO = 8 - ELSE IF (INCY.EQ.0) THEN - INFO = 11 - END IF - IF (INFO.NE.0) THEN - CALL XERBLA('DGEMV ',INFO) - RETURN - END IF -* -* Quick return if possible. -* - IF ((M.EQ.0) .OR. (N.EQ.0) .OR. - + ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN -* -* Set LENX and LENY, the lengths of the vectors x and y, and set -* up the start points in X and Y. -* - IF (LSAME(TRANS,'N')) THEN - LENX = N - LENY = M - ELSE - LENX = M - LENY = N - END IF - IF (INCX.GT.0) THEN - KX = 1 - ELSE - KX = 1 - (LENX-1)*INCX - END IF - IF (INCY.GT.0) THEN - KY = 1 - ELSE - KY = 1 - (LENY-1)*INCY - END IF -* -* Start the operations. In this version the elements of A are -* accessed sequentially with one pass through A. -* -* First form y := beta*y. -* - IF (BETA.NE.ONE) THEN - IF (INCY.EQ.1) THEN - IF (BETA.EQ.ZERO) THEN - DO 10 I = 1,LENY - Y(I) = ZERO - 10 CONTINUE - ELSE - DO 20 I = 1,LENY - Y(I) = BETA*Y(I) - 20 CONTINUE - END IF - ELSE - IY = KY - IF (BETA.EQ.ZERO) THEN - DO 30 I = 1,LENY - Y(IY) = ZERO - IY = IY + INCY - 30 CONTINUE - ELSE - DO 40 I = 1,LENY - Y(IY) = BETA*Y(IY) - IY = IY + INCY - 40 CONTINUE - END IF - END IF - END IF - IF (ALPHA.EQ.ZERO) RETURN - IF (LSAME(TRANS,'N')) THEN -* -* Form y := alpha*A*x + y. -* - JX = KX - IF (INCY.EQ.1) THEN - DO 60 J = 1,N - TEMP = ALPHA*X(JX) - DO 50 I = 1,M - Y(I) = Y(I) + TEMP*A(I,J) - 50 CONTINUE - JX = JX + INCX - 60 CONTINUE - ELSE - DO 80 J = 1,N - TEMP = ALPHA*X(JX) - IY = KY - DO 70 I = 1,M - Y(IY) = Y(IY) + TEMP*A(I,J) - IY = IY + INCY - 70 CONTINUE - JX = JX + INCX - 80 CONTINUE - END IF - ELSE -* -* Form y := alpha*A**T*x + y. -* - JY = KY - IF (INCX.EQ.1) THEN - DO 100 J = 1,N - TEMP = ZERO - DO 90 I = 1,M - TEMP = TEMP + A(I,J)*X(I) - 90 CONTINUE - Y(JY) = Y(JY) + ALPHA*TEMP - JY = JY + INCY - 100 CONTINUE - ELSE - DO 120 J = 1,N - TEMP = ZERO - IX = KX - DO 110 I = 1,M - TEMP = TEMP + A(I,J)*X(IX) - IX = IX + INCX - 110 CONTINUE - Y(JY) = Y(JY) + ALPHA*TEMP - JY = JY + INCY - 120 CONTINUE - END IF - END IF -* - RETURN -* -* End of DGEMV -* - END diff --git a/lib/linalg/fortran/dgeqr2.f b/lib/linalg/fortran/dgeqr2.f deleted file mode 100644 index 5791b3a915..0000000000 --- a/lib/linalg/fortran/dgeqr2.f +++ /dev/null @@ -1,198 +0,0 @@ -*> \brief \b DGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DGEQR2 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DGEQR2( M, N, A, LDA, TAU, WORK, INFO ) -* -* .. Scalar Arguments .. -* INTEGER INFO, LDA, M, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DGEQR2 computes a QR factorization of a real m-by-n matrix A: -*> -*> A = Q * ( R ), -*> ( 0 ) -*> -*> where: -*> -*> Q is a m-by-m orthogonal matrix; -*> R is an upper-triangular n-by-n matrix; -*> 0 is a (m-n)-by-n zero matrix, if m > n. -*> -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix A. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the m by n matrix A. -*> On exit, the elements on and above the diagonal of the array -*> contain the min(m,n) by n upper trapezoidal matrix R (R is -*> upper triangular if m >= n); the elements below the diagonal, -*> with the array TAU, represent the orthogonal matrix Q as a -*> product of elementary reflectors (see Further Details). -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,M). -*> \endverbatim -*> -*> \param[out] TAU -*> \verbatim -*> TAU is DOUBLE PRECISION array, dimension (min(M,N)) -*> The scalar factors of the elementary reflectors (see Further -*> Details). -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (N) -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleGEcomputational -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> The matrix Q is represented as a product of elementary reflectors -*> -*> Q = H(1) H(2) . . . H(k), where k = min(m,n). -*> -*> Each H(i) has the form -*> -*> H(i) = I - tau * v * v**T -*> -*> where tau is a real scalar, and v is a real vector with -*> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), -*> and tau in TAU(i). -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DGEQR2( M, N, A, LDA, TAU, WORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INFO, LDA, M, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE - PARAMETER ( ONE = 1.0D+0 ) -* .. -* .. Local Scalars .. - INTEGER I, K - DOUBLE PRECISION AII -* .. -* .. External Subroutines .. - EXTERNAL DLARF, DLARFG, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, MIN -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - INFO = 0 - IF( M.LT.0 ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( LDA.LT.MAX( 1, M ) ) THEN - INFO = -4 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DGEQR2', -INFO ) - RETURN - END IF -* - K = MIN( M, N ) -* - DO 10 I = 1, K -* -* Generate elementary reflector H(i) to annihilate A(i+1:m,i) -* - CALL DLARFG( M-I+1, A( I, I ), A( MIN( I+1, M ), I ), 1, - $ TAU( I ) ) - IF( I.LT.N ) THEN -* -* Apply H(i) to A(i:m,i+1:n) from the left -* - AII = A( I, I ) - A( I, I ) = ONE - CALL DLARF( 'Left', M-I+1, N-I, A( I, I ), 1, TAU( I ), - $ A( I, I+1 ), LDA, WORK ) - A( I, I ) = AII - END IF - 10 CONTINUE - RETURN -* -* End of DGEQR2 -* - END diff --git a/lib/linalg/fortran/dgeqrf.f b/lib/linalg/fortran/dgeqrf.f deleted file mode 100644 index 705e939286..0000000000 --- a/lib/linalg/fortran/dgeqrf.f +++ /dev/null @@ -1,282 +0,0 @@ -*> \brief \b DGEQRF -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DGEQRF + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DGEQRF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) -* -* .. Scalar Arguments .. -* INTEGER INFO, LDA, LWORK, M, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DGEQRF computes a QR factorization of a real M-by-N matrix A: -*> -*> A = Q * ( R ), -*> ( 0 ) -*> -*> where: -*> -*> Q is a M-by-M orthogonal matrix; -*> R is an upper-triangular N-by-N matrix; -*> 0 is a (M-N)-by-N zero matrix, if M > N. -*> -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix A. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the M-by-N matrix A. -*> On exit, the elements on and above the diagonal of the array -*> contain the min(M,N)-by-N upper trapezoidal matrix R (R is -*> upper triangular if m >= n); the elements below the diagonal, -*> with the array TAU, represent the orthogonal matrix Q as a -*> product of min(m,n) elementary reflectors (see Further -*> Details). -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,M). -*> \endverbatim -*> -*> \param[out] TAU -*> \verbatim -*> TAU is DOUBLE PRECISION array, dimension (min(M,N)) -*> The scalar factors of the elementary reflectors (see Further -*> Details). -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) -*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -*> \endverbatim -*> -*> \param[in] LWORK -*> \verbatim -*> LWORK is INTEGER -*> The dimension of the array WORK. -*> LWORK >= 1, if MIN(M,N) = 0, and LWORK >= N, otherwise. -*> For optimum performance LWORK >= N*NB, where NB is -*> the optimal blocksize. -*> -*> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal size of the WORK array, returns -*> this value as the first entry of the WORK array, and no error -*> message related to LWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleGEcomputational -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> The matrix Q is represented as a product of elementary reflectors -*> -*> Q = H(1) H(2) . . . H(k), where k = min(m,n). -*> -*> Each H(i) has the form -*> -*> H(i) = I - tau * v * v**T -*> -*> where tau is a real scalar, and v is a real vector with -*> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), -*> and tau in TAU(i). -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DGEQRF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INFO, LDA, LWORK, M, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Local Scalars .. - LOGICAL LQUERY - INTEGER I, IB, IINFO, IWS, K, LDWORK, LWKOPT, NB, - $ NBMIN, NX -* .. -* .. External Subroutines .. - EXTERNAL DGEQR2, DLARFB, DLARFT, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, MIN -* .. -* .. External Functions .. - INTEGER ILAENV - EXTERNAL ILAENV -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - K = MIN( M, N ) - INFO = 0 - NB = ILAENV( 1, 'DGEQRF', ' ', M, N, -1, -1 ) - LQUERY = ( LWORK.EQ.-1 ) - IF( M.LT.0 ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( LDA.LT.MAX( 1, M ) ) THEN - INFO = -4 - ELSE IF( .NOT.LQUERY ) THEN - IF( LWORK.LE.0 .OR. ( M.GT.0 .AND. LWORK.LT.MAX( 1, N ) ) ) - $ INFO = -7 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DGEQRF', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - IF( K.EQ.0 ) THEN - LWKOPT = 1 - ELSE - LWKOPT = N*NB - END IF - WORK( 1 ) = LWKOPT - RETURN - END IF -* -* Quick return if possible -* - IF( K.EQ.0 ) THEN - WORK( 1 ) = 1 - RETURN - END IF -* - NBMIN = 2 - NX = 0 - IWS = N - IF( NB.GT.1 .AND. NB.LT.K ) THEN -* -* Determine when to cross over from blocked to unblocked code. -* - NX = MAX( 0, ILAENV( 3, 'DGEQRF', ' ', M, N, -1, -1 ) ) - IF( NX.LT.K ) THEN -* -* Determine if workspace is large enough for blocked code. -* - LDWORK = N - IWS = LDWORK*NB - IF( LWORK.LT.IWS ) THEN -* -* Not enough workspace to use optimal NB: reduce NB and -* determine the minimum value of NB. -* - NB = LWORK / LDWORK - NBMIN = MAX( 2, ILAENV( 2, 'DGEQRF', ' ', M, N, -1, - $ -1 ) ) - END IF - END IF - END IF -* - IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN -* -* Use blocked code initially -* - DO 10 I = 1, K - NX, NB - IB = MIN( K-I+1, NB ) -* -* Compute the QR factorization of the current block -* A(i:m,i:i+ib-1) -* - CALL DGEQR2( M-I+1, IB, A( I, I ), LDA, TAU( I ), WORK, - $ IINFO ) - IF( I+IB.LE.N ) THEN -* -* Form the triangular factor of the block reflector -* H = H(i) H(i+1) . . . H(i+ib-1) -* - CALL DLARFT( 'Forward', 'Columnwise', M-I+1, IB, - $ A( I, I ), LDA, TAU( I ), WORK, LDWORK ) -* -* Apply H**T to A(i:m,i+ib:n) from the left -* - CALL DLARFB( 'Left', 'Transpose', 'Forward', - $ 'Columnwise', M-I+1, N-I-IB+1, IB, - $ A( I, I ), LDA, WORK, LDWORK, A( I, I+IB ), - $ LDA, WORK( IB+1 ), LDWORK ) - END IF - 10 CONTINUE - ELSE - I = 1 - END IF -* -* Use unblocked code to factor the last or only block. -* - IF( I.LE.K ) - $ CALL DGEQR2( M-I+1, N-I+1, A( I, I ), LDA, TAU( I ), WORK, - $ IINFO ) -* - WORK( 1 ) = IWS - RETURN -* -* End of DGEQRF -* - END diff --git a/lib/linalg/fortran/dger.f b/lib/linalg/fortran/dger.f deleted file mode 100644 index 8c19cb4e41..0000000000 --- a/lib/linalg/fortran/dger.f +++ /dev/null @@ -1,224 +0,0 @@ -*> \brief \b DGER -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE DGER(M,N,ALPHA,X,INCX,Y,INCY,A,LDA) -* -* .. Scalar Arguments .. -* DOUBLE PRECISION ALPHA -* INTEGER INCX,INCY,LDA,M,N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A(LDA,*),X(*),Y(*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DGER performs the rank 1 operation -*> -*> A := alpha*x*y**T + A, -*> -*> where alpha is a scalar, x is an m element vector, y is an n element -*> vector and A is an m by n matrix. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> On entry, M specifies the number of rows of the matrix A. -*> M must be at least zero. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> On entry, N specifies the number of columns of the matrix A. -*> N must be at least zero. -*> \endverbatim -*> -*> \param[in] ALPHA -*> \verbatim -*> ALPHA is DOUBLE PRECISION. -*> On entry, ALPHA specifies the scalar alpha. -*> \endverbatim -*> -*> \param[in] X -*> \verbatim -*> X is DOUBLE PRECISION array, dimension at least -*> ( 1 + ( m - 1 )*abs( INCX ) ). -*> Before entry, the incremented array X must contain the m -*> element vector x. -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> On entry, INCX specifies the increment for the elements of -*> X. INCX must not be zero. -*> \endverbatim -*> -*> \param[in] Y -*> \verbatim -*> Y is DOUBLE PRECISION array, dimension at least -*> ( 1 + ( n - 1 )*abs( INCY ) ). -*> Before entry, the incremented array Y must contain the n -*> element vector y. -*> \endverbatim -*> -*> \param[in] INCY -*> \verbatim -*> INCY is INTEGER -*> On entry, INCY specifies the increment for the elements of -*> Y. INCY must not be zero. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension ( LDA, N ) -*> Before entry, the leading m by n part of the array A must -*> contain the matrix of coefficients. On exit, A is -*> overwritten by the updated matrix. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> On entry, LDA specifies the first dimension of A as declared -*> in the calling (sub) program. LDA must be at least -*> max( 1, m ). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup double_blas_level2 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> Level 2 Blas routine. -*> -*> -- Written on 22-October-1986. -*> Jack Dongarra, Argonne National Lab. -*> Jeremy Du Croz, Nag Central Office. -*> Sven Hammarling, Nag Central Office. -*> Richard Hanson, Sandia National Labs. -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DGER(M,N,ALPHA,X,INCX,Y,INCY,A,LDA) -* -* -- Reference BLAS level2 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - DOUBLE PRECISION ALPHA - INTEGER INCX,INCY,LDA,M,N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A(LDA,*),X(*),Y(*) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO - PARAMETER (ZERO=0.0D+0) -* .. -* .. Local Scalars .. - DOUBLE PRECISION TEMP - INTEGER I,INFO,IX,J,JY,KX -* .. -* .. External Subroutines .. - EXTERNAL XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* -* Test the input parameters. -* - INFO = 0 - IF (M.LT.0) THEN - INFO = 1 - ELSE IF (N.LT.0) THEN - INFO = 2 - ELSE IF (INCX.EQ.0) THEN - INFO = 5 - ELSE IF (INCY.EQ.0) THEN - INFO = 7 - ELSE IF (LDA.LT.MAX(1,M)) THEN - INFO = 9 - END IF - IF (INFO.NE.0) THEN - CALL XERBLA('DGER ',INFO) - RETURN - END IF -* -* Quick return if possible. -* - IF ((M.EQ.0) .OR. (N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN -* -* Start the operations. In this version the elements of A are -* accessed sequentially with one pass through A. -* - IF (INCY.GT.0) THEN - JY = 1 - ELSE - JY = 1 - (N-1)*INCY - END IF - IF (INCX.EQ.1) THEN - DO 20 J = 1,N - IF (Y(JY).NE.ZERO) THEN - TEMP = ALPHA*Y(JY) - DO 10 I = 1,M - A(I,J) = A(I,J) + X(I)*TEMP - 10 CONTINUE - END IF - JY = JY + INCY - 20 CONTINUE - ELSE - IF (INCX.GT.0) THEN - KX = 1 - ELSE - KX = 1 - (M-1)*INCX - END IF - DO 40 J = 1,N - IF (Y(JY).NE.ZERO) THEN - TEMP = ALPHA*Y(JY) - IX = KX - DO 30 I = 1,M - A(I,J) = A(I,J) + X(IX)*TEMP - IX = IX + INCX - 30 CONTINUE - END IF - JY = JY + INCY - 40 CONTINUE - END IF -* - RETURN -* -* End of DGER -* - END diff --git a/lib/linalg/fortran/dgesv.f b/lib/linalg/fortran/dgesv.f deleted file mode 100644 index 3609c52f47..0000000000 --- a/lib/linalg/fortran/dgesv.f +++ /dev/null @@ -1,176 +0,0 @@ -*> \brief DGESV computes the solution to system of linear equations A * X = B for GE matrices -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DGESV + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DGESV( N, NRHS, A, LDA, IPIV, B, LDB, INFO ) -* -* .. Scalar Arguments .. -* INTEGER INFO, LDA, LDB, N, NRHS -* .. -* .. Array Arguments .. -* INTEGER IPIV( * ) -* DOUBLE PRECISION A( LDA, * ), B( LDB, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DGESV computes the solution to a real system of linear equations -*> A * X = B, -*> where A is an N-by-N matrix and X and B are N-by-NRHS matrices. -*> -*> The LU decomposition with partial pivoting and row interchanges is -*> used to factor A as -*> A = P * L * U, -*> where P is a permutation matrix, L is unit lower triangular, and U is -*> upper triangular. The factored form of A is then used to solve the -*> system of equations A * X = B. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of linear equations, i.e., the order of the -*> matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in] NRHS -*> \verbatim -*> NRHS is INTEGER -*> The number of right hand sides, i.e., the number of columns -*> of the matrix B. NRHS >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the N-by-N coefficient matrix A. -*> On exit, the factors L and U from the factorization -*> A = P*L*U; the unit diagonal elements of L are not stored. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,N). -*> \endverbatim -*> -*> \param[out] IPIV -*> \verbatim -*> IPIV is INTEGER array, dimension (N) -*> The pivot indices that define the permutation matrix P; -*> row i of the matrix was interchanged with row IPIV(i). -*> \endverbatim -*> -*> \param[in,out] B -*> \verbatim -*> B is DOUBLE PRECISION array, dimension (LDB,NRHS) -*> On entry, the N-by-NRHS matrix of right hand side matrix B. -*> On exit, if INFO = 0, the N-by-NRHS solution matrix X. -*> \endverbatim -*> -*> \param[in] LDB -*> \verbatim -*> LDB is INTEGER -*> The leading dimension of the array B. LDB >= max(1,N). -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, U(i,i) is exactly zero. The factorization -*> has been completed, but the factor U is exactly -*> singular, so the solution could not be computed. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleGEsolve -* -* ===================================================================== - SUBROUTINE DGESV( N, NRHS, A, LDA, IPIV, B, LDB, INFO ) -* -* -- LAPACK driver routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INFO, LDA, LDB, N, NRHS -* .. -* .. Array Arguments .. - INTEGER IPIV( * ) - DOUBLE PRECISION A( LDA, * ), B( LDB, * ) -* .. -* -* ===================================================================== -* -* .. External Subroutines .. - EXTERNAL DGETRF, DGETRS, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 - IF( N.LT.0 ) THEN - INFO = -1 - ELSE IF( NRHS.LT.0 ) THEN - INFO = -2 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -4 - ELSE IF( LDB.LT.MAX( 1, N ) ) THEN - INFO = -7 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DGESV ', -INFO ) - RETURN - END IF -* -* Compute the LU factorization of A. -* - CALL DGETRF( N, N, A, LDA, IPIV, INFO ) - IF( INFO.EQ.0 ) THEN -* -* Solve the system A*X = B, overwriting B with X. -* - CALL DGETRS( 'No transpose', N, NRHS, A, LDA, IPIV, B, LDB, - $ INFO ) - END IF - RETURN -* -* End of DGESV -* - END diff --git a/lib/linalg/fortran/dgesvd.f b/lib/linalg/fortran/dgesvd.f deleted file mode 100644 index 7cc8b35129..0000000000 --- a/lib/linalg/fortran/dgesvd.f +++ /dev/null @@ -1,3501 +0,0 @@ -*> \brief DGESVD computes the singular value decomposition (SVD) for GE matrices -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DGESVD + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, -* WORK, LWORK, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER JOBU, JOBVT -* INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), S( * ), U( LDU, * ), -* $ VT( LDVT, * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DGESVD computes the singular value decomposition (SVD) of a real -*> M-by-N matrix A, optionally computing the left and/or right singular -*> vectors. The SVD is written -*> -*> A = U * SIGMA * transpose(V) -*> -*> where SIGMA is an M-by-N matrix which is zero except for its -*> min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and -*> V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA -*> are the singular values of A; they are real and non-negative, and -*> are returned in descending order. The first min(m,n) columns of -*> U and V are the left and right singular vectors of A. -*> -*> Note that the routine returns V**T, not V. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] JOBU -*> \verbatim -*> JOBU is CHARACTER*1 -*> Specifies options for computing all or part of the matrix U: -*> = 'A': all M columns of U are returned in array U: -*> = 'S': the first min(m,n) columns of U (the left singular -*> vectors) are returned in the array U; -*> = 'O': the first min(m,n) columns of U (the left singular -*> vectors) are overwritten on the array A; -*> = 'N': no columns of U (no left singular vectors) are -*> computed. -*> \endverbatim -*> -*> \param[in] JOBVT -*> \verbatim -*> JOBVT is CHARACTER*1 -*> Specifies options for computing all or part of the matrix -*> V**T: -*> = 'A': all N rows of V**T are returned in the array VT; -*> = 'S': the first min(m,n) rows of V**T (the right singular -*> vectors) are returned in the array VT; -*> = 'O': the first min(m,n) rows of V**T (the right singular -*> vectors) are overwritten on the array A; -*> = 'N': no rows of V**T (no right singular vectors) are -*> computed. -*> -*> JOBVT and JOBU cannot both be 'O'. -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the input matrix A. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the input matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the M-by-N matrix A. -*> On exit, -*> if JOBU = 'O', A is overwritten with the first min(m,n) -*> columns of U (the left singular vectors, -*> stored columnwise); -*> if JOBVT = 'O', A is overwritten with the first min(m,n) -*> rows of V**T (the right singular vectors, -*> stored rowwise); -*> if JOBU .ne. 'O' and JOBVT .ne. 'O', the contents of A -*> are destroyed. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,M). -*> \endverbatim -*> -*> \param[out] S -*> \verbatim -*> S is DOUBLE PRECISION array, dimension (min(M,N)) -*> The singular values of A, sorted so that S(i) >= S(i+1). -*> \endverbatim -*> -*> \param[out] U -*> \verbatim -*> U is DOUBLE PRECISION array, dimension (LDU,UCOL) -*> (LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'S'. -*> If JOBU = 'A', U contains the M-by-M orthogonal matrix U; -*> if JOBU = 'S', U contains the first min(m,n) columns of U -*> (the left singular vectors, stored columnwise); -*> if JOBU = 'N' or 'O', U is not referenced. -*> \endverbatim -*> -*> \param[in] LDU -*> \verbatim -*> LDU is INTEGER -*> The leading dimension of the array U. LDU >= 1; if -*> JOBU = 'S' or 'A', LDU >= M. -*> \endverbatim -*> -*> \param[out] VT -*> \verbatim -*> VT is DOUBLE PRECISION array, dimension (LDVT,N) -*> If JOBVT = 'A', VT contains the N-by-N orthogonal matrix -*> V**T; -*> if JOBVT = 'S', VT contains the first min(m,n) rows of -*> V**T (the right singular vectors, stored rowwise); -*> if JOBVT = 'N' or 'O', VT is not referenced. -*> \endverbatim -*> -*> \param[in] LDVT -*> \verbatim -*> LDVT is INTEGER -*> The leading dimension of the array VT. LDVT >= 1; if -*> JOBVT = 'A', LDVT >= N; if JOBVT = 'S', LDVT >= min(M,N). -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) -*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK; -*> if INFO > 0, WORK(2:MIN(M,N)) contains the unconverged -*> superdiagonal elements of an upper bidiagonal matrix B -*> whose diagonal is in S (not necessarily sorted). B -*> satisfies A = U * B * VT, so it has the same singular values -*> as A, and singular vectors related by U and VT. -*> \endverbatim -*> -*> \param[in] LWORK -*> \verbatim -*> LWORK is INTEGER -*> The dimension of the array WORK. -*> LWORK >= MAX(1,5*MIN(M,N)) for the paths (see comments inside code): -*> - PATH 1 (M much larger than N, JOBU='N') -*> - PATH 1t (N much larger than M, JOBVT='N') -*> LWORK >= MAX(1,3*MIN(M,N) + MAX(M,N),5*MIN(M,N)) for the other paths -*> For good performance, LWORK should generally be larger. -*> -*> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal size of the WORK array, returns -*> this value as the first entry of the WORK array, and no error -*> message related to LWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit. -*> < 0: if INFO = -i, the i-th argument had an illegal value. -*> > 0: if DBDSQR did not converge, INFO specifies how many -*> superdiagonals of an intermediate bidiagonal form B -*> did not converge to zero. See the description of WORK -*> above for details. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleGEsing -* -* ===================================================================== - SUBROUTINE DGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, - $ VT, LDVT, WORK, LWORK, INFO ) -* -* -- LAPACK driver routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER JOBU, JOBVT - INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), S( * ), U( LDU, * ), - $ VT( LDVT, * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) -* .. -* .. Local Scalars .. - LOGICAL LQUERY, WNTUA, WNTUAS, WNTUN, WNTUO, WNTUS, - $ WNTVA, WNTVAS, WNTVN, WNTVO, WNTVS - INTEGER BDSPAC, BLK, CHUNK, I, IE, IERR, IR, ISCL, - $ ITAU, ITAUP, ITAUQ, IU, IWORK, LDWRKR, LDWRKU, - $ MAXWRK, MINMN, MINWRK, MNTHR, NCU, NCVT, NRU, - $ NRVT, WRKBL - INTEGER LWORK_DGEQRF, LWORK_DORGQR_N, LWORK_DORGQR_M, - $ LWORK_DGEBRD, LWORK_DORGBR_P, LWORK_DORGBR_Q, - $ LWORK_DGELQF, LWORK_DORGLQ_N, LWORK_DORGLQ_M - DOUBLE PRECISION ANRM, BIGNUM, EPS, SMLNUM -* .. -* .. Local Arrays .. - DOUBLE PRECISION DUM( 1 ) -* .. -* .. External Subroutines .. - EXTERNAL DBDSQR, DGEBRD, DGELQF, DGEMM, DGEQRF, DLACPY, - $ DLASCL, DLASET, DORGBR, DORGLQ, DORGQR, DORMBR, - $ XERBLA -* .. -* .. External Functions .. - LOGICAL LSAME - INTEGER ILAENV - DOUBLE PRECISION DLAMCH, DLANGE - EXTERNAL LSAME, ILAENV, DLAMCH, DLANGE -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, MIN, SQRT -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - INFO = 0 - MINMN = MIN( M, N ) - WNTUA = LSAME( JOBU, 'A' ) - WNTUS = LSAME( JOBU, 'S' ) - WNTUAS = WNTUA .OR. WNTUS - WNTUO = LSAME( JOBU, 'O' ) - WNTUN = LSAME( JOBU, 'N' ) - WNTVA = LSAME( JOBVT, 'A' ) - WNTVS = LSAME( JOBVT, 'S' ) - WNTVAS = WNTVA .OR. WNTVS - WNTVO = LSAME( JOBVT, 'O' ) - WNTVN = LSAME( JOBVT, 'N' ) - LQUERY = ( LWORK.EQ.-1 ) -* - IF( .NOT.( WNTUA .OR. WNTUS .OR. WNTUO .OR. WNTUN ) ) THEN - INFO = -1 - ELSE IF( .NOT.( WNTVA .OR. WNTVS .OR. WNTVO .OR. WNTVN ) .OR. - $ ( WNTVO .AND. WNTUO ) ) THEN - INFO = -2 - ELSE IF( M.LT.0 ) THEN - INFO = -3 - ELSE IF( N.LT.0 ) THEN - INFO = -4 - ELSE IF( LDA.LT.MAX( 1, M ) ) THEN - INFO = -6 - ELSE IF( LDU.LT.1 .OR. ( WNTUAS .AND. LDU.LT.M ) ) THEN - INFO = -9 - ELSE IF( LDVT.LT.1 .OR. ( WNTVA .AND. LDVT.LT.N ) .OR. - $ ( WNTVS .AND. LDVT.LT.MINMN ) ) THEN - INFO = -11 - END IF -* -* Compute workspace -* (Note: Comments in the code beginning "Workspace:" describe the -* minimal amount of workspace needed at that point in the code, -* as well as the preferred amount for good performance. -* NB refers to the optimal block size for the immediately -* following subroutine, as returned by ILAENV.) -* - IF( INFO.EQ.0 ) THEN - MINWRK = 1 - MAXWRK = 1 - IF( M.GE.N .AND. MINMN.GT.0 ) THEN -* -* Compute space needed for DBDSQR -* - MNTHR = ILAENV( 6, 'DGESVD', JOBU // JOBVT, M, N, 0, 0 ) - BDSPAC = 5*N -* Compute space needed for DGEQRF - CALL DGEQRF( M, N, A, LDA, DUM(1), DUM(1), -1, IERR ) - LWORK_DGEQRF = INT( DUM(1) ) -* Compute space needed for DORGQR - CALL DORGQR( M, N, N, A, LDA, DUM(1), DUM(1), -1, IERR ) - LWORK_DORGQR_N = INT( DUM(1) ) - CALL DORGQR( M, M, N, A, LDA, DUM(1), DUM(1), -1, IERR ) - LWORK_DORGQR_M = INT( DUM(1) ) -* Compute space needed for DGEBRD - CALL DGEBRD( N, N, A, LDA, S, DUM(1), DUM(1), - $ DUM(1), DUM(1), -1, IERR ) - LWORK_DGEBRD = INT( DUM(1) ) -* Compute space needed for DORGBR P - CALL DORGBR( 'P', N, N, N, A, LDA, DUM(1), - $ DUM(1), -1, IERR ) - LWORK_DORGBR_P = INT( DUM(1) ) -* Compute space needed for DORGBR Q - CALL DORGBR( 'Q', N, N, N, A, LDA, DUM(1), - $ DUM(1), -1, IERR ) - LWORK_DORGBR_Q = INT( DUM(1) ) -* - IF( M.GE.MNTHR ) THEN - IF( WNTUN ) THEN -* -* Path 1 (M much larger than N, JOBU='N') -* - MAXWRK = N + LWORK_DGEQRF - MAXWRK = MAX( MAXWRK, 3*N + LWORK_DGEBRD ) - IF( WNTVO .OR. WNTVAS ) - $ MAXWRK = MAX( MAXWRK, 3*N + LWORK_DORGBR_P ) - MAXWRK = MAX( MAXWRK, BDSPAC ) - MINWRK = MAX( 4*N, BDSPAC ) - ELSE IF( WNTUO .AND. WNTVN ) THEN -* -* Path 2 (M much larger than N, JOBU='O', JOBVT='N') -* - WRKBL = N + LWORK_DGEQRF - WRKBL = MAX( WRKBL, N + LWORK_DORGQR_N ) - WRKBL = MAX( WRKBL, 3*N + LWORK_DGEBRD ) - WRKBL = MAX( WRKBL, 3*N + LWORK_DORGBR_Q ) - WRKBL = MAX( WRKBL, BDSPAC ) - MAXWRK = MAX( N*N + WRKBL, N*N + M*N + N ) - MINWRK = MAX( 3*N + M, BDSPAC ) - ELSE IF( WNTUO .AND. WNTVAS ) THEN -* -* Path 3 (M much larger than N, JOBU='O', JOBVT='S' or -* 'A') -* - WRKBL = N + LWORK_DGEQRF - WRKBL = MAX( WRKBL, N + LWORK_DORGQR_N ) - WRKBL = MAX( WRKBL, 3*N + LWORK_DGEBRD ) - WRKBL = MAX( WRKBL, 3*N + LWORK_DORGBR_Q ) - WRKBL = MAX( WRKBL, 3*N + LWORK_DORGBR_P ) - WRKBL = MAX( WRKBL, BDSPAC ) - MAXWRK = MAX( N*N + WRKBL, N*N + M*N + N ) - MINWRK = MAX( 3*N + M, BDSPAC ) - ELSE IF( WNTUS .AND. WNTVN ) THEN -* -* Path 4 (M much larger than N, JOBU='S', JOBVT='N') -* - WRKBL = N + LWORK_DGEQRF - WRKBL = MAX( WRKBL, N + LWORK_DORGQR_N ) - WRKBL = MAX( WRKBL, 3*N + LWORK_DGEBRD ) - WRKBL = MAX( WRKBL, 3*N + LWORK_DORGBR_Q ) - WRKBL = MAX( WRKBL, BDSPAC ) - MAXWRK = N*N + WRKBL - MINWRK = MAX( 3*N + M, BDSPAC ) - ELSE IF( WNTUS .AND. WNTVO ) THEN -* -* Path 5 (M much larger than N, JOBU='S', JOBVT='O') -* - WRKBL = N + LWORK_DGEQRF - WRKBL = MAX( WRKBL, N + LWORK_DORGQR_N ) - WRKBL = MAX( WRKBL, 3*N + LWORK_DGEBRD ) - WRKBL = MAX( WRKBL, 3*N + LWORK_DORGBR_Q ) - WRKBL = MAX( WRKBL, 3*N + LWORK_DORGBR_P ) - WRKBL = MAX( WRKBL, BDSPAC ) - MAXWRK = 2*N*N + WRKBL - MINWRK = MAX( 3*N + M, BDSPAC ) - ELSE IF( WNTUS .AND. WNTVAS ) THEN -* -* Path 6 (M much larger than N, JOBU='S', JOBVT='S' or -* 'A') -* - WRKBL = N + LWORK_DGEQRF - WRKBL = MAX( WRKBL, N + LWORK_DORGQR_N ) - WRKBL = MAX( WRKBL, 3*N + LWORK_DGEBRD ) - WRKBL = MAX( WRKBL, 3*N + LWORK_DORGBR_Q ) - WRKBL = MAX( WRKBL, 3*N + LWORK_DORGBR_P ) - WRKBL = MAX( WRKBL, BDSPAC ) - MAXWRK = N*N + WRKBL - MINWRK = MAX( 3*N + M, BDSPAC ) - ELSE IF( WNTUA .AND. WNTVN ) THEN -* -* Path 7 (M much larger than N, JOBU='A', JOBVT='N') -* - WRKBL = N + LWORK_DGEQRF - WRKBL = MAX( WRKBL, N + LWORK_DORGQR_M ) - WRKBL = MAX( WRKBL, 3*N + LWORK_DGEBRD ) - WRKBL = MAX( WRKBL, 3*N + LWORK_DORGBR_Q ) - WRKBL = MAX( WRKBL, BDSPAC ) - MAXWRK = N*N + WRKBL - MINWRK = MAX( 3*N + M, BDSPAC ) - ELSE IF( WNTUA .AND. WNTVO ) THEN -* -* Path 8 (M much larger than N, JOBU='A', JOBVT='O') -* - WRKBL = N + LWORK_DGEQRF - WRKBL = MAX( WRKBL, N + LWORK_DORGQR_M ) - WRKBL = MAX( WRKBL, 3*N + LWORK_DGEBRD ) - WRKBL = MAX( WRKBL, 3*N + LWORK_DORGBR_Q ) - WRKBL = MAX( WRKBL, 3*N + LWORK_DORGBR_P ) - WRKBL = MAX( WRKBL, BDSPAC ) - MAXWRK = 2*N*N + WRKBL - MINWRK = MAX( 3*N + M, BDSPAC ) - ELSE IF( WNTUA .AND. WNTVAS ) THEN -* -* Path 9 (M much larger than N, JOBU='A', JOBVT='S' or -* 'A') -* - WRKBL = N + LWORK_DGEQRF - WRKBL = MAX( WRKBL, N + LWORK_DORGQR_M ) - WRKBL = MAX( WRKBL, 3*N + LWORK_DGEBRD ) - WRKBL = MAX( WRKBL, 3*N + LWORK_DORGBR_Q ) - WRKBL = MAX( WRKBL, 3*N + LWORK_DORGBR_P ) - WRKBL = MAX( WRKBL, BDSPAC ) - MAXWRK = N*N + WRKBL - MINWRK = MAX( 3*N + M, BDSPAC ) - END IF - ELSE -* -* Path 10 (M at least N, but not much larger) -* - CALL DGEBRD( M, N, A, LDA, S, DUM(1), DUM(1), - $ DUM(1), DUM(1), -1, IERR ) - LWORK_DGEBRD = INT( DUM(1) ) - MAXWRK = 3*N + LWORK_DGEBRD - IF( WNTUS .OR. WNTUO ) THEN - CALL DORGBR( 'Q', M, N, N, A, LDA, DUM(1), - $ DUM(1), -1, IERR ) - LWORK_DORGBR_Q = INT( DUM(1) ) - MAXWRK = MAX( MAXWRK, 3*N + LWORK_DORGBR_Q ) - END IF - IF( WNTUA ) THEN - CALL DORGBR( 'Q', M, M, N, A, LDA, DUM(1), - $ DUM(1), -1, IERR ) - LWORK_DORGBR_Q = INT( DUM(1) ) - MAXWRK = MAX( MAXWRK, 3*N + LWORK_DORGBR_Q ) - END IF - IF( .NOT.WNTVN ) THEN - MAXWRK = MAX( MAXWRK, 3*N + LWORK_DORGBR_P ) - END IF - MAXWRK = MAX( MAXWRK, BDSPAC ) - MINWRK = MAX( 3*N + M, BDSPAC ) - END IF - ELSE IF( MINMN.GT.0 ) THEN -* -* Compute space needed for DBDSQR -* - MNTHR = ILAENV( 6, 'DGESVD', JOBU // JOBVT, M, N, 0, 0 ) - BDSPAC = 5*M -* Compute space needed for DGELQF - CALL DGELQF( M, N, A, LDA, DUM(1), DUM(1), -1, IERR ) - LWORK_DGELQF = INT( DUM(1) ) -* Compute space needed for DORGLQ - CALL DORGLQ( N, N, M, DUM(1), N, DUM(1), DUM(1), -1, IERR ) - LWORK_DORGLQ_N = INT( DUM(1) ) - CALL DORGLQ( M, N, M, A, LDA, DUM(1), DUM(1), -1, IERR ) - LWORK_DORGLQ_M = INT( DUM(1) ) -* Compute space needed for DGEBRD - CALL DGEBRD( M, M, A, LDA, S, DUM(1), DUM(1), - $ DUM(1), DUM(1), -1, IERR ) - LWORK_DGEBRD = INT( DUM(1) ) -* Compute space needed for DORGBR P - CALL DORGBR( 'P', M, M, M, A, N, DUM(1), - $ DUM(1), -1, IERR ) - LWORK_DORGBR_P = INT( DUM(1) ) -* Compute space needed for DORGBR Q - CALL DORGBR( 'Q', M, M, M, A, N, DUM(1), - $ DUM(1), -1, IERR ) - LWORK_DORGBR_Q = INT( DUM(1) ) - IF( N.GE.MNTHR ) THEN - IF( WNTVN ) THEN -* -* Path 1t(N much larger than M, JOBVT='N') -* - MAXWRK = M + LWORK_DGELQF - MAXWRK = MAX( MAXWRK, 3*M + LWORK_DGEBRD ) - IF( WNTUO .OR. WNTUAS ) - $ MAXWRK = MAX( MAXWRK, 3*M + LWORK_DORGBR_Q ) - MAXWRK = MAX( MAXWRK, BDSPAC ) - MINWRK = MAX( 4*M, BDSPAC ) - ELSE IF( WNTVO .AND. WNTUN ) THEN -* -* Path 2t(N much larger than M, JOBU='N', JOBVT='O') -* - WRKBL = M + LWORK_DGELQF - WRKBL = MAX( WRKBL, M + LWORK_DORGLQ_M ) - WRKBL = MAX( WRKBL, 3*M + LWORK_DGEBRD ) - WRKBL = MAX( WRKBL, 3*M + LWORK_DORGBR_P ) - WRKBL = MAX( WRKBL, BDSPAC ) - MAXWRK = MAX( M*M + WRKBL, M*M + M*N + M ) - MINWRK = MAX( 3*M + N, BDSPAC ) - ELSE IF( WNTVO .AND. WNTUAS ) THEN -* -* Path 3t(N much larger than M, JOBU='S' or 'A', -* JOBVT='O') -* - WRKBL = M + LWORK_DGELQF - WRKBL = MAX( WRKBL, M + LWORK_DORGLQ_M ) - WRKBL = MAX( WRKBL, 3*M + LWORK_DGEBRD ) - WRKBL = MAX( WRKBL, 3*M + LWORK_DORGBR_P ) - WRKBL = MAX( WRKBL, 3*M + LWORK_DORGBR_Q ) - WRKBL = MAX( WRKBL, BDSPAC ) - MAXWRK = MAX( M*M + WRKBL, M*M + M*N + M ) - MINWRK = MAX( 3*M + N, BDSPAC ) - ELSE IF( WNTVS .AND. WNTUN ) THEN -* -* Path 4t(N much larger than M, JOBU='N', JOBVT='S') -* - WRKBL = M + LWORK_DGELQF - WRKBL = MAX( WRKBL, M + LWORK_DORGLQ_M ) - WRKBL = MAX( WRKBL, 3*M + LWORK_DGEBRD ) - WRKBL = MAX( WRKBL, 3*M + LWORK_DORGBR_P ) - WRKBL = MAX( WRKBL, BDSPAC ) - MAXWRK = M*M + WRKBL - MINWRK = MAX( 3*M + N, BDSPAC ) - ELSE IF( WNTVS .AND. WNTUO ) THEN -* -* Path 5t(N much larger than M, JOBU='O', JOBVT='S') -* - WRKBL = M + LWORK_DGELQF - WRKBL = MAX( WRKBL, M + LWORK_DORGLQ_M ) - WRKBL = MAX( WRKBL, 3*M + LWORK_DGEBRD ) - WRKBL = MAX( WRKBL, 3*M + LWORK_DORGBR_P ) - WRKBL = MAX( WRKBL, 3*M + LWORK_DORGBR_Q ) - WRKBL = MAX( WRKBL, BDSPAC ) - MAXWRK = 2*M*M + WRKBL - MINWRK = MAX( 3*M + N, BDSPAC ) - ELSE IF( WNTVS .AND. WNTUAS ) THEN -* -* Path 6t(N much larger than M, JOBU='S' or 'A', -* JOBVT='S') -* - WRKBL = M + LWORK_DGELQF - WRKBL = MAX( WRKBL, M + LWORK_DORGLQ_M ) - WRKBL = MAX( WRKBL, 3*M + LWORK_DGEBRD ) - WRKBL = MAX( WRKBL, 3*M + LWORK_DORGBR_P ) - WRKBL = MAX( WRKBL, 3*M + LWORK_DORGBR_Q ) - WRKBL = MAX( WRKBL, BDSPAC ) - MAXWRK = M*M + WRKBL - MINWRK = MAX( 3*M + N, BDSPAC ) - ELSE IF( WNTVA .AND. WNTUN ) THEN -* -* Path 7t(N much larger than M, JOBU='N', JOBVT='A') -* - WRKBL = M + LWORK_DGELQF - WRKBL = MAX( WRKBL, M + LWORK_DORGLQ_N ) - WRKBL = MAX( WRKBL, 3*M + LWORK_DGEBRD ) - WRKBL = MAX( WRKBL, 3*M + LWORK_DORGBR_P ) - WRKBL = MAX( WRKBL, BDSPAC ) - MAXWRK = M*M + WRKBL - MINWRK = MAX( 3*M + N, BDSPAC ) - ELSE IF( WNTVA .AND. WNTUO ) THEN -* -* Path 8t(N much larger than M, JOBU='O', JOBVT='A') -* - WRKBL = M + LWORK_DGELQF - WRKBL = MAX( WRKBL, M + LWORK_DORGLQ_N ) - WRKBL = MAX( WRKBL, 3*M + LWORK_DGEBRD ) - WRKBL = MAX( WRKBL, 3*M + LWORK_DORGBR_P ) - WRKBL = MAX( WRKBL, 3*M + LWORK_DORGBR_Q ) - WRKBL = MAX( WRKBL, BDSPAC ) - MAXWRK = 2*M*M + WRKBL - MINWRK = MAX( 3*M + N, BDSPAC ) - ELSE IF( WNTVA .AND. WNTUAS ) THEN -* -* Path 9t(N much larger than M, JOBU='S' or 'A', -* JOBVT='A') -* - WRKBL = M + LWORK_DGELQF - WRKBL = MAX( WRKBL, M + LWORK_DORGLQ_N ) - WRKBL = MAX( WRKBL, 3*M + LWORK_DGEBRD ) - WRKBL = MAX( WRKBL, 3*M + LWORK_DORGBR_P ) - WRKBL = MAX( WRKBL, 3*M + LWORK_DORGBR_Q ) - WRKBL = MAX( WRKBL, BDSPAC ) - MAXWRK = M*M + WRKBL - MINWRK = MAX( 3*M + N, BDSPAC ) - END IF - ELSE -* -* Path 10t(N greater than M, but not much larger) -* - CALL DGEBRD( M, N, A, LDA, S, DUM(1), DUM(1), - $ DUM(1), DUM(1), -1, IERR ) - LWORK_DGEBRD = INT( DUM(1) ) - MAXWRK = 3*M + LWORK_DGEBRD - IF( WNTVS .OR. WNTVO ) THEN -* Compute space needed for DORGBR P - CALL DORGBR( 'P', M, N, M, A, N, DUM(1), - $ DUM(1), -1, IERR ) - LWORK_DORGBR_P = INT( DUM(1) ) - MAXWRK = MAX( MAXWRK, 3*M + LWORK_DORGBR_P ) - END IF - IF( WNTVA ) THEN - CALL DORGBR( 'P', N, N, M, A, N, DUM(1), - $ DUM(1), -1, IERR ) - LWORK_DORGBR_P = INT( DUM(1) ) - MAXWRK = MAX( MAXWRK, 3*M + LWORK_DORGBR_P ) - END IF - IF( .NOT.WNTUN ) THEN - MAXWRK = MAX( MAXWRK, 3*M + LWORK_DORGBR_Q ) - END IF - MAXWRK = MAX( MAXWRK, BDSPAC ) - MINWRK = MAX( 3*M + N, BDSPAC ) - END IF - END IF - MAXWRK = MAX( MAXWRK, MINWRK ) - WORK( 1 ) = MAXWRK -* - IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN - INFO = -13 - END IF - END IF -* - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DGESVD', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - RETURN - END IF -* -* Quick return if possible -* - IF( M.EQ.0 .OR. N.EQ.0 ) THEN - RETURN - END IF -* -* Get machine constants -* - EPS = DLAMCH( 'P' ) - SMLNUM = SQRT( DLAMCH( 'S' ) ) / EPS - BIGNUM = ONE / SMLNUM -* -* Scale A if max element outside range [SMLNUM,BIGNUM] -* - ANRM = DLANGE( 'M', M, N, A, LDA, DUM ) - ISCL = 0 - IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN - ISCL = 1 - CALL DLASCL( 'G', 0, 0, ANRM, SMLNUM, M, N, A, LDA, IERR ) - ELSE IF( ANRM.GT.BIGNUM ) THEN - ISCL = 1 - CALL DLASCL( 'G', 0, 0, ANRM, BIGNUM, M, N, A, LDA, IERR ) - END IF -* - IF( M.GE.N ) THEN -* -* A has at least as many rows as columns. If A has sufficiently -* more rows than columns, first reduce using the QR -* decomposition (if sufficient workspace available) -* - IF( M.GE.MNTHR ) THEN -* - IF( WNTUN ) THEN -* -* Path 1 (M much larger than N, JOBU='N') -* No left singular vectors to be computed -* - ITAU = 1 - IWORK = ITAU + N -* -* Compute A=Q*R -* (Workspace: need 2*N, prefer N + N*NB) -* - CALL DGEQRF( M, N, A, LDA, WORK( ITAU ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Zero out below R -* - IF( N .GT. 1 ) THEN - CALL DLASET( 'L', N-1, N-1, ZERO, ZERO, A( 2, 1 ), - $ LDA ) - END IF - IE = 1 - ITAUQ = IE + N - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Bidiagonalize R in A -* (Workspace: need 4*N, prefer 3*N + 2*N*NB) -* - CALL DGEBRD( N, N, A, LDA, S, WORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( IWORK ), LWORK-IWORK+1, - $ IERR ) - NCVT = 0 - IF( WNTVO .OR. WNTVAS ) THEN -* -* If right singular vectors desired, generate P'. -* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) -* - CALL DORGBR( 'P', N, N, N, A, LDA, WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - NCVT = N - END IF - IWORK = IE + N -* -* Perform bidiagonal QR iteration, computing right -* singular vectors of A in A if desired -* (Workspace: need BDSPAC) -* - CALL DBDSQR( 'U', N, NCVT, 0, 0, S, WORK( IE ), A, LDA, - $ DUM, 1, DUM, 1, WORK( IWORK ), INFO ) -* -* If right singular vectors desired in VT, copy them there -* - IF( WNTVAS ) - $ CALL DLACPY( 'F', N, N, A, LDA, VT, LDVT ) -* - ELSE IF( WNTUO .AND. WNTVN ) THEN -* -* Path 2 (M much larger than N, JOBU='O', JOBVT='N') -* N left singular vectors to be overwritten on A and -* no right singular vectors to be computed -* - IF( LWORK.GE.N*N+MAX( 4*N, BDSPAC ) ) THEN -* -* Sufficient workspace for a fast algorithm -* - IR = 1 - IF( LWORK.GE.MAX( WRKBL, LDA*N + N ) + LDA*N ) THEN -* -* WORK(IU) is LDA by N, WORK(IR) is LDA by N -* - LDWRKU = LDA - LDWRKR = LDA - ELSE IF( LWORK.GE.MAX( WRKBL, LDA*N + N ) + N*N ) THEN -* -* WORK(IU) is LDA by N, WORK(IR) is N by N -* - LDWRKU = LDA - LDWRKR = N - ELSE -* -* WORK(IU) is LDWRKU by N, WORK(IR) is N by N -* - LDWRKU = ( LWORK-N*N-N ) / N - LDWRKR = N - END IF - ITAU = IR + LDWRKR*N - IWORK = ITAU + N -* -* Compute A=Q*R -* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) -* - CALL DGEQRF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy R to WORK(IR) and zero out below it -* - CALL DLACPY( 'U', N, N, A, LDA, WORK( IR ), LDWRKR ) - CALL DLASET( 'L', N-1, N-1, ZERO, ZERO, WORK( IR+1 ), - $ LDWRKR ) -* -* Generate Q in A -* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) -* - CALL DORGQR( M, N, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = ITAU - ITAUQ = IE + N - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Bidiagonalize R in WORK(IR) -* (Workspace: need N*N + 4*N, prefer N*N + 3*N + 2*N*NB) -* - CALL DGEBRD( N, N, WORK( IR ), LDWRKR, S, WORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Generate left vectors bidiagonalizing R -* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB) -* - CALL DORGBR( 'Q', N, N, N, WORK( IR ), LDWRKR, - $ WORK( ITAUQ ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - IWORK = IE + N -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of R in WORK(IR) -* (Workspace: need N*N + BDSPAC) -* - CALL DBDSQR( 'U', N, 0, N, 0, S, WORK( IE ), DUM, 1, - $ WORK( IR ), LDWRKR, DUM, 1, - $ WORK( IWORK ), INFO ) - IU = IE + N -* -* Multiply Q in A by left singular vectors of R in -* WORK(IR), storing result in WORK(IU) and copying to A -* (Workspace: need N*N + 2*N, prefer N*N + M*N + N) -* - DO 10 I = 1, M, LDWRKU - CHUNK = MIN( M-I+1, LDWRKU ) - CALL DGEMM( 'N', 'N', CHUNK, N, N, ONE, A( I, 1 ), - $ LDA, WORK( IR ), LDWRKR, ZERO, - $ WORK( IU ), LDWRKU ) - CALL DLACPY( 'F', CHUNK, N, WORK( IU ), LDWRKU, - $ A( I, 1 ), LDA ) - 10 CONTINUE -* - ELSE -* -* Insufficient workspace for a fast algorithm -* - IE = 1 - ITAUQ = IE + N - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Bidiagonalize A -* (Workspace: need 3*N + M, prefer 3*N + (M + N)*NB) -* - CALL DGEBRD( M, N, A, LDA, S, WORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Generate left vectors bidiagonalizing A -* (Workspace: need 4*N, prefer 3*N + N*NB) -* - CALL DORGBR( 'Q', M, N, N, A, LDA, WORK( ITAUQ ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IWORK = IE + N -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of A in A -* (Workspace: need BDSPAC) -* - CALL DBDSQR( 'U', N, 0, M, 0, S, WORK( IE ), DUM, 1, - $ A, LDA, DUM, 1, WORK( IWORK ), INFO ) -* - END IF -* - ELSE IF( WNTUO .AND. WNTVAS ) THEN -* -* Path 3 (M much larger than N, JOBU='O', JOBVT='S' or 'A') -* N left singular vectors to be overwritten on A and -* N right singular vectors to be computed in VT -* - IF( LWORK.GE.N*N+MAX( 4*N, BDSPAC ) ) THEN -* -* Sufficient workspace for a fast algorithm -* - IR = 1 - IF( LWORK.GE.MAX( WRKBL, LDA*N + N ) + LDA*N ) THEN -* -* WORK(IU) is LDA by N and WORK(IR) is LDA by N -* - LDWRKU = LDA - LDWRKR = LDA - ELSE IF( LWORK.GE.MAX( WRKBL, LDA*N + N ) + N*N ) THEN -* -* WORK(IU) is LDA by N and WORK(IR) is N by N -* - LDWRKU = LDA - LDWRKR = N - ELSE -* -* WORK(IU) is LDWRKU by N and WORK(IR) is N by N -* - LDWRKU = ( LWORK-N*N-N ) / N - LDWRKR = N - END IF - ITAU = IR + LDWRKR*N - IWORK = ITAU + N -* -* Compute A=Q*R -* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) -* - CALL DGEQRF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy R to VT, zeroing out below it -* - CALL DLACPY( 'U', N, N, A, LDA, VT, LDVT ) - IF( N.GT.1 ) - $ CALL DLASET( 'L', N-1, N-1, ZERO, ZERO, - $ VT( 2, 1 ), LDVT ) -* -* Generate Q in A -* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) -* - CALL DORGQR( M, N, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = ITAU - ITAUQ = IE + N - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Bidiagonalize R in VT, copying result to WORK(IR) -* (Workspace: need N*N + 4*N, prefer N*N + 3*N + 2*N*NB) -* - CALL DGEBRD( N, N, VT, LDVT, S, WORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL DLACPY( 'L', N, N, VT, LDVT, WORK( IR ), LDWRKR ) -* -* Generate left vectors bidiagonalizing R in WORK(IR) -* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB) -* - CALL DORGBR( 'Q', N, N, N, WORK( IR ), LDWRKR, - $ WORK( ITAUQ ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate right vectors bidiagonalizing R in VT -* (Workspace: need N*N + 4*N-1, prefer N*N + 3*N + (N-1)*NB) -* - CALL DORGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IWORK = IE + N -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of R in WORK(IR) and computing right -* singular vectors of R in VT -* (Workspace: need N*N + BDSPAC) -* - CALL DBDSQR( 'U', N, N, N, 0, S, WORK( IE ), VT, LDVT, - $ WORK( IR ), LDWRKR, DUM, 1, - $ WORK( IWORK ), INFO ) - IU = IE + N -* -* Multiply Q in A by left singular vectors of R in -* WORK(IR), storing result in WORK(IU) and copying to A -* (Workspace: need N*N + 2*N, prefer N*N + M*N + N) -* - DO 20 I = 1, M, LDWRKU - CHUNK = MIN( M-I+1, LDWRKU ) - CALL DGEMM( 'N', 'N', CHUNK, N, N, ONE, A( I, 1 ), - $ LDA, WORK( IR ), LDWRKR, ZERO, - $ WORK( IU ), LDWRKU ) - CALL DLACPY( 'F', CHUNK, N, WORK( IU ), LDWRKU, - $ A( I, 1 ), LDA ) - 20 CONTINUE -* - ELSE -* -* Insufficient workspace for a fast algorithm -* - ITAU = 1 - IWORK = ITAU + N -* -* Compute A=Q*R -* (Workspace: need 2*N, prefer N + N*NB) -* - CALL DGEQRF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy R to VT, zeroing out below it -* - CALL DLACPY( 'U', N, N, A, LDA, VT, LDVT ) - IF( N.GT.1 ) - $ CALL DLASET( 'L', N-1, N-1, ZERO, ZERO, - $ VT( 2, 1 ), LDVT ) -* -* Generate Q in A -* (Workspace: need 2*N, prefer N + N*NB) -* - CALL DORGQR( M, N, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = ITAU - ITAUQ = IE + N - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Bidiagonalize R in VT -* (Workspace: need 4*N, prefer 3*N + 2*N*NB) -* - CALL DGEBRD( N, N, VT, LDVT, S, WORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Multiply Q in A by left vectors bidiagonalizing R -* (Workspace: need 3*N + M, prefer 3*N + M*NB) -* - CALL DORMBR( 'Q', 'R', 'N', M, N, N, VT, LDVT, - $ WORK( ITAUQ ), A, LDA, WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate right vectors bidiagonalizing R in VT -* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) -* - CALL DORGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IWORK = IE + N -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of A in A and computing right -* singular vectors of A in VT -* (Workspace: need BDSPAC) -* - CALL DBDSQR( 'U', N, N, M, 0, S, WORK( IE ), VT, LDVT, - $ A, LDA, DUM, 1, WORK( IWORK ), INFO ) -* - END IF -* - ELSE IF( WNTUS ) THEN -* - IF( WNTVN ) THEN -* -* Path 4 (M much larger than N, JOBU='S', JOBVT='N') -* N left singular vectors to be computed in U and -* no right singular vectors to be computed -* - IF( LWORK.GE.N*N+MAX( 4*N, BDSPAC ) ) THEN -* -* Sufficient workspace for a fast algorithm -* - IR = 1 - IF( LWORK.GE.WRKBL+LDA*N ) THEN -* -* WORK(IR) is LDA by N -* - LDWRKR = LDA - ELSE -* -* WORK(IR) is N by N -* - LDWRKR = N - END IF - ITAU = IR + LDWRKR*N - IWORK = ITAU + N -* -* Compute A=Q*R -* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) -* - CALL DGEQRF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy R to WORK(IR), zeroing out below it -* - CALL DLACPY( 'U', N, N, A, LDA, WORK( IR ), - $ LDWRKR ) - CALL DLASET( 'L', N-1, N-1, ZERO, ZERO, - $ WORK( IR+1 ), LDWRKR ) -* -* Generate Q in A -* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) -* - CALL DORGQR( M, N, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = ITAU - ITAUQ = IE + N - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Bidiagonalize R in WORK(IR) -* (Workspace: need N*N + 4*N, prefer N*N + 3*N + 2*N*NB) -* - CALL DGEBRD( N, N, WORK( IR ), LDWRKR, S, - $ WORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate left vectors bidiagonalizing R in WORK(IR) -* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB) -* - CALL DORGBR( 'Q', N, N, N, WORK( IR ), LDWRKR, - $ WORK( ITAUQ ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - IWORK = IE + N -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of R in WORK(IR) -* (Workspace: need N*N + BDSPAC) -* - CALL DBDSQR( 'U', N, 0, N, 0, S, WORK( IE ), DUM, - $ 1, WORK( IR ), LDWRKR, DUM, 1, - $ WORK( IWORK ), INFO ) -* -* Multiply Q in A by left singular vectors of R in -* WORK(IR), storing result in U -* (Workspace: need N*N) -* - CALL DGEMM( 'N', 'N', M, N, N, ONE, A, LDA, - $ WORK( IR ), LDWRKR, ZERO, U, LDU ) -* - ELSE -* -* Insufficient workspace for a fast algorithm -* - ITAU = 1 - IWORK = ITAU + N -* -* Compute A=Q*R, copying result to U -* (Workspace: need 2*N, prefer N + N*NB) -* - CALL DGEQRF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL DLACPY( 'L', M, N, A, LDA, U, LDU ) -* -* Generate Q in U -* (Workspace: need 2*N, prefer N + N*NB) -* - CALL DORGQR( M, N, N, U, LDU, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = ITAU - ITAUQ = IE + N - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Zero out below R in A -* - IF( N .GT. 1 ) THEN - CALL DLASET( 'L', N-1, N-1, ZERO, ZERO, - $ A( 2, 1 ), LDA ) - END IF -* -* Bidiagonalize R in A -* (Workspace: need 4*N, prefer 3*N + 2*N*NB) -* - CALL DGEBRD( N, N, A, LDA, S, WORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Multiply Q in U by left vectors bidiagonalizing R -* (Workspace: need 3*N + M, prefer 3*N + M*NB) -* - CALL DORMBR( 'Q', 'R', 'N', M, N, N, A, LDA, - $ WORK( ITAUQ ), U, LDU, WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - IWORK = IE + N -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of A in U -* (Workspace: need BDSPAC) -* - CALL DBDSQR( 'U', N, 0, M, 0, S, WORK( IE ), DUM, - $ 1, U, LDU, DUM, 1, WORK( IWORK ), - $ INFO ) -* - END IF -* - ELSE IF( WNTVO ) THEN -* -* Path 5 (M much larger than N, JOBU='S', JOBVT='O') -* N left singular vectors to be computed in U and -* N right singular vectors to be overwritten on A -* - IF( LWORK.GE.2*N*N+MAX( 4*N, BDSPAC ) ) THEN -* -* Sufficient workspace for a fast algorithm -* - IU = 1 - IF( LWORK.GE.WRKBL+2*LDA*N ) THEN -* -* WORK(IU) is LDA by N and WORK(IR) is LDA by N -* - LDWRKU = LDA - IR = IU + LDWRKU*N - LDWRKR = LDA - ELSE IF( LWORK.GE.WRKBL+( LDA + N )*N ) THEN -* -* WORK(IU) is LDA by N and WORK(IR) is N by N -* - LDWRKU = LDA - IR = IU + LDWRKU*N - LDWRKR = N - ELSE -* -* WORK(IU) is N by N and WORK(IR) is N by N -* - LDWRKU = N - IR = IU + LDWRKU*N - LDWRKR = N - END IF - ITAU = IR + LDWRKR*N - IWORK = ITAU + N -* -* Compute A=Q*R -* (Workspace: need 2*N*N + 2*N, prefer 2*N*N + N + N*NB) -* - CALL DGEQRF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy R to WORK(IU), zeroing out below it -* - CALL DLACPY( 'U', N, N, A, LDA, WORK( IU ), - $ LDWRKU ) - CALL DLASET( 'L', N-1, N-1, ZERO, ZERO, - $ WORK( IU+1 ), LDWRKU ) -* -* Generate Q in A -* (Workspace: need 2*N*N + 2*N, prefer 2*N*N + N + N*NB) -* - CALL DORGQR( M, N, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = ITAU - ITAUQ = IE + N - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Bidiagonalize R in WORK(IU), copying result to -* WORK(IR) -* (Workspace: need 2*N*N + 4*N, -* prefer 2*N*N+3*N+2*N*NB) -* - CALL DGEBRD( N, N, WORK( IU ), LDWRKU, S, - $ WORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - CALL DLACPY( 'U', N, N, WORK( IU ), LDWRKU, - $ WORK( IR ), LDWRKR ) -* -* Generate left bidiagonalizing vectors in WORK(IU) -* (Workspace: need 2*N*N + 4*N, prefer 2*N*N + 3*N + N*NB) -* - CALL DORGBR( 'Q', N, N, N, WORK( IU ), LDWRKU, - $ WORK( ITAUQ ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate right bidiagonalizing vectors in WORK(IR) -* (Workspace: need 2*N*N + 4*N-1, -* prefer 2*N*N+3*N+(N-1)*NB) -* - CALL DORGBR( 'P', N, N, N, WORK( IR ), LDWRKR, - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - IWORK = IE + N -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of R in WORK(IU) and computing -* right singular vectors of R in WORK(IR) -* (Workspace: need 2*N*N + BDSPAC) -* - CALL DBDSQR( 'U', N, N, N, 0, S, WORK( IE ), - $ WORK( IR ), LDWRKR, WORK( IU ), - $ LDWRKU, DUM, 1, WORK( IWORK ), INFO ) -* -* Multiply Q in A by left singular vectors of R in -* WORK(IU), storing result in U -* (Workspace: need N*N) -* - CALL DGEMM( 'N', 'N', M, N, N, ONE, A, LDA, - $ WORK( IU ), LDWRKU, ZERO, U, LDU ) -* -* Copy right singular vectors of R to A -* (Workspace: need N*N) -* - CALL DLACPY( 'F', N, N, WORK( IR ), LDWRKR, A, - $ LDA ) -* - ELSE -* -* Insufficient workspace for a fast algorithm -* - ITAU = 1 - IWORK = ITAU + N -* -* Compute A=Q*R, copying result to U -* (Workspace: need 2*N, prefer N + N*NB) -* - CALL DGEQRF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL DLACPY( 'L', M, N, A, LDA, U, LDU ) -* -* Generate Q in U -* (Workspace: need 2*N, prefer N + N*NB) -* - CALL DORGQR( M, N, N, U, LDU, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = ITAU - ITAUQ = IE + N - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Zero out below R in A -* - IF( N .GT. 1 ) THEN - CALL DLASET( 'L', N-1, N-1, ZERO, ZERO, - $ A( 2, 1 ), LDA ) - END IF -* -* Bidiagonalize R in A -* (Workspace: need 4*N, prefer 3*N + 2*N*NB) -* - CALL DGEBRD( N, N, A, LDA, S, WORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Multiply Q in U by left vectors bidiagonalizing R -* (Workspace: need 3*N + M, prefer 3*N + M*NB) -* - CALL DORMBR( 'Q', 'R', 'N', M, N, N, A, LDA, - $ WORK( ITAUQ ), U, LDU, WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate right vectors bidiagonalizing R in A -* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) -* - CALL DORGBR( 'P', N, N, N, A, LDA, WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IWORK = IE + N -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of A in U and computing right -* singular vectors of A in A -* (Workspace: need BDSPAC) -* - CALL DBDSQR( 'U', N, N, M, 0, S, WORK( IE ), A, - $ LDA, U, LDU, DUM, 1, WORK( IWORK ), - $ INFO ) -* - END IF -* - ELSE IF( WNTVAS ) THEN -* -* Path 6 (M much larger than N, JOBU='S', JOBVT='S' -* or 'A') -* N left singular vectors to be computed in U and -* N right singular vectors to be computed in VT -* - IF( LWORK.GE.N*N+MAX( 4*N, BDSPAC ) ) THEN -* -* Sufficient workspace for a fast algorithm -* - IU = 1 - IF( LWORK.GE.WRKBL+LDA*N ) THEN -* -* WORK(IU) is LDA by N -* - LDWRKU = LDA - ELSE -* -* WORK(IU) is N by N -* - LDWRKU = N - END IF - ITAU = IU + LDWRKU*N - IWORK = ITAU + N -* -* Compute A=Q*R -* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) -* - CALL DGEQRF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy R to WORK(IU), zeroing out below it -* - CALL DLACPY( 'U', N, N, A, LDA, WORK( IU ), - $ LDWRKU ) - CALL DLASET( 'L', N-1, N-1, ZERO, ZERO, - $ WORK( IU+1 ), LDWRKU ) -* -* Generate Q in A -* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) -* - CALL DORGQR( M, N, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = ITAU - ITAUQ = IE + N - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Bidiagonalize R in WORK(IU), copying result to VT -* (Workspace: need N*N + 4*N, prefer N*N + 3*N + 2*N*NB) -* - CALL DGEBRD( N, N, WORK( IU ), LDWRKU, S, - $ WORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - CALL DLACPY( 'U', N, N, WORK( IU ), LDWRKU, VT, - $ LDVT ) -* -* Generate left bidiagonalizing vectors in WORK(IU) -* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB) -* - CALL DORGBR( 'Q', N, N, N, WORK( IU ), LDWRKU, - $ WORK( ITAUQ ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate right bidiagonalizing vectors in VT -* (Workspace: need N*N + 4*N-1, -* prefer N*N+3*N+(N-1)*NB) -* - CALL DORGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IWORK = IE + N -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of R in WORK(IU) and computing -* right singular vectors of R in VT -* (Workspace: need N*N + BDSPAC) -* - CALL DBDSQR( 'U', N, N, N, 0, S, WORK( IE ), VT, - $ LDVT, WORK( IU ), LDWRKU, DUM, 1, - $ WORK( IWORK ), INFO ) -* -* Multiply Q in A by left singular vectors of R in -* WORK(IU), storing result in U -* (Workspace: need N*N) -* - CALL DGEMM( 'N', 'N', M, N, N, ONE, A, LDA, - $ WORK( IU ), LDWRKU, ZERO, U, LDU ) -* - ELSE -* -* Insufficient workspace for a fast algorithm -* - ITAU = 1 - IWORK = ITAU + N -* -* Compute A=Q*R, copying result to U -* (Workspace: need 2*N, prefer N + N*NB) -* - CALL DGEQRF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL DLACPY( 'L', M, N, A, LDA, U, LDU ) -* -* Generate Q in U -* (Workspace: need 2*N, prefer N + N*NB) -* - CALL DORGQR( M, N, N, U, LDU, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy R to VT, zeroing out below it -* - CALL DLACPY( 'U', N, N, A, LDA, VT, LDVT ) - IF( N.GT.1 ) - $ CALL DLASET( 'L', N-1, N-1, ZERO, ZERO, - $ VT( 2, 1 ), LDVT ) - IE = ITAU - ITAUQ = IE + N - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Bidiagonalize R in VT -* (Workspace: need 4*N, prefer 3*N + 2*N*NB) -* - CALL DGEBRD( N, N, VT, LDVT, S, WORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Multiply Q in U by left bidiagonalizing vectors -* in VT -* (Workspace: need 3*N + M, prefer 3*N + M*NB) -* - CALL DORMBR( 'Q', 'R', 'N', M, N, N, VT, LDVT, - $ WORK( ITAUQ ), U, LDU, WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate right bidiagonalizing vectors in VT -* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) -* - CALL DORGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IWORK = IE + N -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of A in U and computing right -* singular vectors of A in VT -* (Workspace: need BDSPAC) -* - CALL DBDSQR( 'U', N, N, M, 0, S, WORK( IE ), VT, - $ LDVT, U, LDU, DUM, 1, WORK( IWORK ), - $ INFO ) -* - END IF -* - END IF -* - ELSE IF( WNTUA ) THEN -* - IF( WNTVN ) THEN -* -* Path 7 (M much larger than N, JOBU='A', JOBVT='N') -* M left singular vectors to be computed in U and -* no right singular vectors to be computed -* - IF( LWORK.GE.N*N+MAX( N+M, 4*N, BDSPAC ) ) THEN -* -* Sufficient workspace for a fast algorithm -* - IR = 1 - IF( LWORK.GE.WRKBL+LDA*N ) THEN -* -* WORK(IR) is LDA by N -* - LDWRKR = LDA - ELSE -* -* WORK(IR) is N by N -* - LDWRKR = N - END IF - ITAU = IR + LDWRKR*N - IWORK = ITAU + N -* -* Compute A=Q*R, copying result to U -* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) -* - CALL DGEQRF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL DLACPY( 'L', M, N, A, LDA, U, LDU ) -* -* Copy R to WORK(IR), zeroing out below it -* - CALL DLACPY( 'U', N, N, A, LDA, WORK( IR ), - $ LDWRKR ) - CALL DLASET( 'L', N-1, N-1, ZERO, ZERO, - $ WORK( IR+1 ), LDWRKR ) -* -* Generate Q in U -* (Workspace: need N*N + N + M, prefer N*N + N + M*NB) -* - CALL DORGQR( M, M, N, U, LDU, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = ITAU - ITAUQ = IE + N - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Bidiagonalize R in WORK(IR) -* (Workspace: need N*N + 4*N, prefer N*N + 3*N + 2*N*NB) -* - CALL DGEBRD( N, N, WORK( IR ), LDWRKR, S, - $ WORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate left bidiagonalizing vectors in WORK(IR) -* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB) -* - CALL DORGBR( 'Q', N, N, N, WORK( IR ), LDWRKR, - $ WORK( ITAUQ ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - IWORK = IE + N -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of R in WORK(IR) -* (Workspace: need N*N + BDSPAC) -* - CALL DBDSQR( 'U', N, 0, N, 0, S, WORK( IE ), DUM, - $ 1, WORK( IR ), LDWRKR, DUM, 1, - $ WORK( IWORK ), INFO ) -* -* Multiply Q in U by left singular vectors of R in -* WORK(IR), storing result in A -* (Workspace: need N*N) -* - CALL DGEMM( 'N', 'N', M, N, N, ONE, U, LDU, - $ WORK( IR ), LDWRKR, ZERO, A, LDA ) -* -* Copy left singular vectors of A from A to U -* - CALL DLACPY( 'F', M, N, A, LDA, U, LDU ) -* - ELSE -* -* Insufficient workspace for a fast algorithm -* - ITAU = 1 - IWORK = ITAU + N -* -* Compute A=Q*R, copying result to U -* (Workspace: need 2*N, prefer N + N*NB) -* - CALL DGEQRF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL DLACPY( 'L', M, N, A, LDA, U, LDU ) -* -* Generate Q in U -* (Workspace: need N + M, prefer N + M*NB) -* - CALL DORGQR( M, M, N, U, LDU, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = ITAU - ITAUQ = IE + N - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Zero out below R in A -* - IF( N .GT. 1 ) THEN - CALL DLASET( 'L', N-1, N-1, ZERO, ZERO, - $ A( 2, 1 ), LDA ) - END IF -* -* Bidiagonalize R in A -* (Workspace: need 4*N, prefer 3*N + 2*N*NB) -* - CALL DGEBRD( N, N, A, LDA, S, WORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Multiply Q in U by left bidiagonalizing vectors -* in A -* (Workspace: need 3*N + M, prefer 3*N + M*NB) -* - CALL DORMBR( 'Q', 'R', 'N', M, N, N, A, LDA, - $ WORK( ITAUQ ), U, LDU, WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - IWORK = IE + N -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of A in U -* (Workspace: need BDSPAC) -* - CALL DBDSQR( 'U', N, 0, M, 0, S, WORK( IE ), DUM, - $ 1, U, LDU, DUM, 1, WORK( IWORK ), - $ INFO ) -* - END IF -* - ELSE IF( WNTVO ) THEN -* -* Path 8 (M much larger than N, JOBU='A', JOBVT='O') -* M left singular vectors to be computed in U and -* N right singular vectors to be overwritten on A -* - IF( LWORK.GE.2*N*N+MAX( N+M, 4*N, BDSPAC ) ) THEN -* -* Sufficient workspace for a fast algorithm -* - IU = 1 - IF( LWORK.GE.WRKBL+2*LDA*N ) THEN -* -* WORK(IU) is LDA by N and WORK(IR) is LDA by N -* - LDWRKU = LDA - IR = IU + LDWRKU*N - LDWRKR = LDA - ELSE IF( LWORK.GE.WRKBL+( LDA + N )*N ) THEN -* -* WORK(IU) is LDA by N and WORK(IR) is N by N -* - LDWRKU = LDA - IR = IU + LDWRKU*N - LDWRKR = N - ELSE -* -* WORK(IU) is N by N and WORK(IR) is N by N -* - LDWRKU = N - IR = IU + LDWRKU*N - LDWRKR = N - END IF - ITAU = IR + LDWRKR*N - IWORK = ITAU + N -* -* Compute A=Q*R, copying result to U -* (Workspace: need 2*N*N + 2*N, prefer 2*N*N + N + N*NB) -* - CALL DGEQRF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL DLACPY( 'L', M, N, A, LDA, U, LDU ) -* -* Generate Q in U -* (Workspace: need 2*N*N + N + M, prefer 2*N*N + N + M*NB) -* - CALL DORGQR( M, M, N, U, LDU, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy R to WORK(IU), zeroing out below it -* - CALL DLACPY( 'U', N, N, A, LDA, WORK( IU ), - $ LDWRKU ) - CALL DLASET( 'L', N-1, N-1, ZERO, ZERO, - $ WORK( IU+1 ), LDWRKU ) - IE = ITAU - ITAUQ = IE + N - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Bidiagonalize R in WORK(IU), copying result to -* WORK(IR) -* (Workspace: need 2*N*N + 4*N, -* prefer 2*N*N+3*N+2*N*NB) -* - CALL DGEBRD( N, N, WORK( IU ), LDWRKU, S, - $ WORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - CALL DLACPY( 'U', N, N, WORK( IU ), LDWRKU, - $ WORK( IR ), LDWRKR ) -* -* Generate left bidiagonalizing vectors in WORK(IU) -* (Workspace: need 2*N*N + 4*N, prefer 2*N*N + 3*N + N*NB) -* - CALL DORGBR( 'Q', N, N, N, WORK( IU ), LDWRKU, - $ WORK( ITAUQ ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate right bidiagonalizing vectors in WORK(IR) -* (Workspace: need 2*N*N + 4*N-1, -* prefer 2*N*N+3*N+(N-1)*NB) -* - CALL DORGBR( 'P', N, N, N, WORK( IR ), LDWRKR, - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - IWORK = IE + N -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of R in WORK(IU) and computing -* right singular vectors of R in WORK(IR) -* (Workspace: need 2*N*N + BDSPAC) -* - CALL DBDSQR( 'U', N, N, N, 0, S, WORK( IE ), - $ WORK( IR ), LDWRKR, WORK( IU ), - $ LDWRKU, DUM, 1, WORK( IWORK ), INFO ) -* -* Multiply Q in U by left singular vectors of R in -* WORK(IU), storing result in A -* (Workspace: need N*N) -* - CALL DGEMM( 'N', 'N', M, N, N, ONE, U, LDU, - $ WORK( IU ), LDWRKU, ZERO, A, LDA ) -* -* Copy left singular vectors of A from A to U -* - CALL DLACPY( 'F', M, N, A, LDA, U, LDU ) -* -* Copy right singular vectors of R from WORK(IR) to A -* - CALL DLACPY( 'F', N, N, WORK( IR ), LDWRKR, A, - $ LDA ) -* - ELSE -* -* Insufficient workspace for a fast algorithm -* - ITAU = 1 - IWORK = ITAU + N -* -* Compute A=Q*R, copying result to U -* (Workspace: need 2*N, prefer N + N*NB) -* - CALL DGEQRF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL DLACPY( 'L', M, N, A, LDA, U, LDU ) -* -* Generate Q in U -* (Workspace: need N + M, prefer N + M*NB) -* - CALL DORGQR( M, M, N, U, LDU, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = ITAU - ITAUQ = IE + N - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Zero out below R in A -* - IF( N .GT. 1 ) THEN - CALL DLASET( 'L', N-1, N-1, ZERO, ZERO, - $ A( 2, 1 ), LDA ) - END IF -* -* Bidiagonalize R in A -* (Workspace: need 4*N, prefer 3*N + 2*N*NB) -* - CALL DGEBRD( N, N, A, LDA, S, WORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Multiply Q in U by left bidiagonalizing vectors -* in A -* (Workspace: need 3*N + M, prefer 3*N + M*NB) -* - CALL DORMBR( 'Q', 'R', 'N', M, N, N, A, LDA, - $ WORK( ITAUQ ), U, LDU, WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate right bidiagonalizing vectors in A -* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) -* - CALL DORGBR( 'P', N, N, N, A, LDA, WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IWORK = IE + N -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of A in U and computing right -* singular vectors of A in A -* (Workspace: need BDSPAC) -* - CALL DBDSQR( 'U', N, N, M, 0, S, WORK( IE ), A, - $ LDA, U, LDU, DUM, 1, WORK( IWORK ), - $ INFO ) -* - END IF -* - ELSE IF( WNTVAS ) THEN -* -* Path 9 (M much larger than N, JOBU='A', JOBVT='S' -* or 'A') -* M left singular vectors to be computed in U and -* N right singular vectors to be computed in VT -* - IF( LWORK.GE.N*N+MAX( N+M, 4*N, BDSPAC ) ) THEN -* -* Sufficient workspace for a fast algorithm -* - IU = 1 - IF( LWORK.GE.WRKBL+LDA*N ) THEN -* -* WORK(IU) is LDA by N -* - LDWRKU = LDA - ELSE -* -* WORK(IU) is N by N -* - LDWRKU = N - END IF - ITAU = IU + LDWRKU*N - IWORK = ITAU + N -* -* Compute A=Q*R, copying result to U -* (Workspace: need N*N + 2*N, prefer N*N + N + N*NB) -* - CALL DGEQRF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL DLACPY( 'L', M, N, A, LDA, U, LDU ) -* -* Generate Q in U -* (Workspace: need N*N + N + M, prefer N*N + N + M*NB) -* - CALL DORGQR( M, M, N, U, LDU, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy R to WORK(IU), zeroing out below it -* - CALL DLACPY( 'U', N, N, A, LDA, WORK( IU ), - $ LDWRKU ) - CALL DLASET( 'L', N-1, N-1, ZERO, ZERO, - $ WORK( IU+1 ), LDWRKU ) - IE = ITAU - ITAUQ = IE + N - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Bidiagonalize R in WORK(IU), copying result to VT -* (Workspace: need N*N + 4*N, prefer N*N + 3*N + 2*N*NB) -* - CALL DGEBRD( N, N, WORK( IU ), LDWRKU, S, - $ WORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - CALL DLACPY( 'U', N, N, WORK( IU ), LDWRKU, VT, - $ LDVT ) -* -* Generate left bidiagonalizing vectors in WORK(IU) -* (Workspace: need N*N + 4*N, prefer N*N + 3*N + N*NB) -* - CALL DORGBR( 'Q', N, N, N, WORK( IU ), LDWRKU, - $ WORK( ITAUQ ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate right bidiagonalizing vectors in VT -* (Workspace: need N*N + 4*N-1, -* prefer N*N+3*N+(N-1)*NB) -* - CALL DORGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IWORK = IE + N -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of R in WORK(IU) and computing -* right singular vectors of R in VT -* (Workspace: need N*N + BDSPAC) -* - CALL DBDSQR( 'U', N, N, N, 0, S, WORK( IE ), VT, - $ LDVT, WORK( IU ), LDWRKU, DUM, 1, - $ WORK( IWORK ), INFO ) -* -* Multiply Q in U by left singular vectors of R in -* WORK(IU), storing result in A -* (Workspace: need N*N) -* - CALL DGEMM( 'N', 'N', M, N, N, ONE, U, LDU, - $ WORK( IU ), LDWRKU, ZERO, A, LDA ) -* -* Copy left singular vectors of A from A to U -* - CALL DLACPY( 'F', M, N, A, LDA, U, LDU ) -* - ELSE -* -* Insufficient workspace for a fast algorithm -* - ITAU = 1 - IWORK = ITAU + N -* -* Compute A=Q*R, copying result to U -* (Workspace: need 2*N, prefer N + N*NB) -* - CALL DGEQRF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL DLACPY( 'L', M, N, A, LDA, U, LDU ) -* -* Generate Q in U -* (Workspace: need N + M, prefer N + M*NB) -* - CALL DORGQR( M, M, N, U, LDU, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy R from A to VT, zeroing out below it -* - CALL DLACPY( 'U', N, N, A, LDA, VT, LDVT ) - IF( N.GT.1 ) - $ CALL DLASET( 'L', N-1, N-1, ZERO, ZERO, - $ VT( 2, 1 ), LDVT ) - IE = ITAU - ITAUQ = IE + N - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Bidiagonalize R in VT -* (Workspace: need 4*N, prefer 3*N + 2*N*NB) -* - CALL DGEBRD( N, N, VT, LDVT, S, WORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Multiply Q in U by left bidiagonalizing vectors -* in VT -* (Workspace: need 3*N + M, prefer 3*N + M*NB) -* - CALL DORMBR( 'Q', 'R', 'N', M, N, N, VT, LDVT, - $ WORK( ITAUQ ), U, LDU, WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate right bidiagonalizing vectors in VT -* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) -* - CALL DORGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IWORK = IE + N -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of A in U and computing right -* singular vectors of A in VT -* (Workspace: need BDSPAC) -* - CALL DBDSQR( 'U', N, N, M, 0, S, WORK( IE ), VT, - $ LDVT, U, LDU, DUM, 1, WORK( IWORK ), - $ INFO ) -* - END IF -* - END IF -* - END IF -* - ELSE -* -* M .LT. MNTHR -* -* Path 10 (M at least N, but not much larger) -* Reduce to bidiagonal form without QR decomposition -* - IE = 1 - ITAUQ = IE + N - ITAUP = ITAUQ + N - IWORK = ITAUP + N -* -* Bidiagonalize A -* (Workspace: need 3*N + M, prefer 3*N + (M + N)*NB) -* - CALL DGEBRD( M, N, A, LDA, S, WORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( IWORK ), LWORK-IWORK+1, - $ IERR ) - IF( WNTUAS ) THEN -* -* If left singular vectors desired in U, copy result to U -* and generate left bidiagonalizing vectors in U -* (Workspace: need 3*N + NCU, prefer 3*N + NCU*NB) -* - CALL DLACPY( 'L', M, N, A, LDA, U, LDU ) - IF( WNTUS ) - $ NCU = N - IF( WNTUA ) - $ NCU = M - CALL DORGBR( 'Q', M, NCU, N, U, LDU, WORK( ITAUQ ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - END IF - IF( WNTVAS ) THEN -* -* If right singular vectors desired in VT, copy result to -* VT and generate right bidiagonalizing vectors in VT -* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) -* - CALL DLACPY( 'U', N, N, A, LDA, VT, LDVT ) - CALL DORGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - END IF - IF( WNTUO ) THEN -* -* If left singular vectors desired in A, generate left -* bidiagonalizing vectors in A -* (Workspace: need 4*N, prefer 3*N + N*NB) -* - CALL DORGBR( 'Q', M, N, N, A, LDA, WORK( ITAUQ ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - END IF - IF( WNTVO ) THEN -* -* If right singular vectors desired in A, generate right -* bidiagonalizing vectors in A -* (Workspace: need 4*N-1, prefer 3*N + (N-1)*NB) -* - CALL DORGBR( 'P', N, N, N, A, LDA, WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - END IF - IWORK = IE + N - IF( WNTUAS .OR. WNTUO ) - $ NRU = M - IF( WNTUN ) - $ NRU = 0 - IF( WNTVAS .OR. WNTVO ) - $ NCVT = N - IF( WNTVN ) - $ NCVT = 0 - IF( ( .NOT.WNTUO ) .AND. ( .NOT.WNTVO ) ) THEN -* -* Perform bidiagonal QR iteration, if desired, computing -* left singular vectors in U and computing right singular -* vectors in VT -* (Workspace: need BDSPAC) -* - CALL DBDSQR( 'U', N, NCVT, NRU, 0, S, WORK( IE ), VT, - $ LDVT, U, LDU, DUM, 1, WORK( IWORK ), INFO ) - ELSE IF( ( .NOT.WNTUO ) .AND. WNTVO ) THEN -* -* Perform bidiagonal QR iteration, if desired, computing -* left singular vectors in U and computing right singular -* vectors in A -* (Workspace: need BDSPAC) -* - CALL DBDSQR( 'U', N, NCVT, NRU, 0, S, WORK( IE ), A, LDA, - $ U, LDU, DUM, 1, WORK( IWORK ), INFO ) - ELSE -* -* Perform bidiagonal QR iteration, if desired, computing -* left singular vectors in A and computing right singular -* vectors in VT -* (Workspace: need BDSPAC) -* - CALL DBDSQR( 'U', N, NCVT, NRU, 0, S, WORK( IE ), VT, - $ LDVT, A, LDA, DUM, 1, WORK( IWORK ), INFO ) - END IF -* - END IF -* - ELSE -* -* A has more columns than rows. If A has sufficiently more -* columns than rows, first reduce using the LQ decomposition (if -* sufficient workspace available) -* - IF( N.GE.MNTHR ) THEN -* - IF( WNTVN ) THEN -* -* Path 1t(N much larger than M, JOBVT='N') -* No right singular vectors to be computed -* - ITAU = 1 - IWORK = ITAU + M -* -* Compute A=L*Q -* (Workspace: need 2*M, prefer M + M*NB) -* - CALL DGELQF( M, N, A, LDA, WORK( ITAU ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Zero out above L -* - CALL DLASET( 'U', M-1, M-1, ZERO, ZERO, A( 1, 2 ), LDA ) - IE = 1 - ITAUQ = IE + M - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Bidiagonalize L in A -* (Workspace: need 4*M, prefer 3*M + 2*M*NB) -* - CALL DGEBRD( M, M, A, LDA, S, WORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( IWORK ), LWORK-IWORK+1, - $ IERR ) - IF( WNTUO .OR. WNTUAS ) THEN -* -* If left singular vectors desired, generate Q -* (Workspace: need 4*M, prefer 3*M + M*NB) -* - CALL DORGBR( 'Q', M, M, M, A, LDA, WORK( ITAUQ ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - END IF - IWORK = IE + M - NRU = 0 - IF( WNTUO .OR. WNTUAS ) - $ NRU = M -* -* Perform bidiagonal QR iteration, computing left singular -* vectors of A in A if desired -* (Workspace: need BDSPAC) -* - CALL DBDSQR( 'U', M, 0, NRU, 0, S, WORK( IE ), DUM, 1, A, - $ LDA, DUM, 1, WORK( IWORK ), INFO ) -* -* If left singular vectors desired in U, copy them there -* - IF( WNTUAS ) - $ CALL DLACPY( 'F', M, M, A, LDA, U, LDU ) -* - ELSE IF( WNTVO .AND. WNTUN ) THEN -* -* Path 2t(N much larger than M, JOBU='N', JOBVT='O') -* M right singular vectors to be overwritten on A and -* no left singular vectors to be computed -* - IF( LWORK.GE.M*M+MAX( 4*M, BDSPAC ) ) THEN -* -* Sufficient workspace for a fast algorithm -* - IR = 1 - IF( LWORK.GE.MAX( WRKBL, LDA*N + M ) + LDA*M ) THEN -* -* WORK(IU) is LDA by N and WORK(IR) is LDA by M -* - LDWRKU = LDA - CHUNK = N - LDWRKR = LDA - ELSE IF( LWORK.GE.MAX( WRKBL, LDA*N + M ) + M*M ) THEN -* -* WORK(IU) is LDA by N and WORK(IR) is M by M -* - LDWRKU = LDA - CHUNK = N - LDWRKR = M - ELSE -* -* WORK(IU) is M by CHUNK and WORK(IR) is M by M -* - LDWRKU = M - CHUNK = ( LWORK-M*M-M ) / M - LDWRKR = M - END IF - ITAU = IR + LDWRKR*M - IWORK = ITAU + M -* -* Compute A=L*Q -* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) -* - CALL DGELQF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy L to WORK(IR) and zero out above it -* - CALL DLACPY( 'L', M, M, A, LDA, WORK( IR ), LDWRKR ) - CALL DLASET( 'U', M-1, M-1, ZERO, ZERO, - $ WORK( IR+LDWRKR ), LDWRKR ) -* -* Generate Q in A -* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) -* - CALL DORGLQ( M, N, M, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = ITAU - ITAUQ = IE + M - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Bidiagonalize L in WORK(IR) -* (Workspace: need M*M + 4*M, prefer M*M + 3*M + 2*M*NB) -* - CALL DGEBRD( M, M, WORK( IR ), LDWRKR, S, WORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Generate right vectors bidiagonalizing L -* (Workspace: need M*M + 4*M-1, prefer M*M + 3*M + (M-1)*NB) -* - CALL DORGBR( 'P', M, M, M, WORK( IR ), LDWRKR, - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - IWORK = IE + M -* -* Perform bidiagonal QR iteration, computing right -* singular vectors of L in WORK(IR) -* (Workspace: need M*M + BDSPAC) -* - CALL DBDSQR( 'U', M, M, 0, 0, S, WORK( IE ), - $ WORK( IR ), LDWRKR, DUM, 1, DUM, 1, - $ WORK( IWORK ), INFO ) - IU = IE + M -* -* Multiply right singular vectors of L in WORK(IR) by Q -* in A, storing result in WORK(IU) and copying to A -* (Workspace: need M*M + 2*M, prefer M*M + M*N + M) -* - DO 30 I = 1, N, CHUNK - BLK = MIN( N-I+1, CHUNK ) - CALL DGEMM( 'N', 'N', M, BLK, M, ONE, WORK( IR ), - $ LDWRKR, A( 1, I ), LDA, ZERO, - $ WORK( IU ), LDWRKU ) - CALL DLACPY( 'F', M, BLK, WORK( IU ), LDWRKU, - $ A( 1, I ), LDA ) - 30 CONTINUE -* - ELSE -* -* Insufficient workspace for a fast algorithm -* - IE = 1 - ITAUQ = IE + M - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Bidiagonalize A -* (Workspace: need 3*M + N, prefer 3*M + (M + N)*NB) -* - CALL DGEBRD( M, N, A, LDA, S, WORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Generate right vectors bidiagonalizing A -* (Workspace: need 4*M, prefer 3*M + M*NB) -* - CALL DORGBR( 'P', M, N, M, A, LDA, WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IWORK = IE + M -* -* Perform bidiagonal QR iteration, computing right -* singular vectors of A in A -* (Workspace: need BDSPAC) -* - CALL DBDSQR( 'L', M, N, 0, 0, S, WORK( IE ), A, LDA, - $ DUM, 1, DUM, 1, WORK( IWORK ), INFO ) -* - END IF -* - ELSE IF( WNTVO .AND. WNTUAS ) THEN -* -* Path 3t(N much larger than M, JOBU='S' or 'A', JOBVT='O') -* M right singular vectors to be overwritten on A and -* M left singular vectors to be computed in U -* - IF( LWORK.GE.M*M+MAX( 4*M, BDSPAC ) ) THEN -* -* Sufficient workspace for a fast algorithm -* - IR = 1 - IF( LWORK.GE.MAX( WRKBL, LDA*N + M ) + LDA*M ) THEN -* -* WORK(IU) is LDA by N and WORK(IR) is LDA by M -* - LDWRKU = LDA - CHUNK = N - LDWRKR = LDA - ELSE IF( LWORK.GE.MAX( WRKBL, LDA*N + M ) + M*M ) THEN -* -* WORK(IU) is LDA by N and WORK(IR) is M by M -* - LDWRKU = LDA - CHUNK = N - LDWRKR = M - ELSE -* -* WORK(IU) is M by CHUNK and WORK(IR) is M by M -* - LDWRKU = M - CHUNK = ( LWORK-M*M-M ) / M - LDWRKR = M - END IF - ITAU = IR + LDWRKR*M - IWORK = ITAU + M -* -* Compute A=L*Q -* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) -* - CALL DGELQF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy L to U, zeroing about above it -* - CALL DLACPY( 'L', M, M, A, LDA, U, LDU ) - CALL DLASET( 'U', M-1, M-1, ZERO, ZERO, U( 1, 2 ), - $ LDU ) -* -* Generate Q in A -* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) -* - CALL DORGLQ( M, N, M, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = ITAU - ITAUQ = IE + M - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Bidiagonalize L in U, copying result to WORK(IR) -* (Workspace: need M*M + 4*M, prefer M*M + 3*M + 2*M*NB) -* - CALL DGEBRD( M, M, U, LDU, S, WORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL DLACPY( 'U', M, M, U, LDU, WORK( IR ), LDWRKR ) -* -* Generate right vectors bidiagonalizing L in WORK(IR) -* (Workspace: need M*M + 4*M-1, prefer M*M + 3*M + (M-1)*NB) -* - CALL DORGBR( 'P', M, M, M, WORK( IR ), LDWRKR, - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate left vectors bidiagonalizing L in U -* (Workspace: need M*M + 4*M, prefer M*M + 3*M + M*NB) -* - CALL DORGBR( 'Q', M, M, M, U, LDU, WORK( ITAUQ ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IWORK = IE + M -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of L in U, and computing right -* singular vectors of L in WORK(IR) -* (Workspace: need M*M + BDSPAC) -* - CALL DBDSQR( 'U', M, M, M, 0, S, WORK( IE ), - $ WORK( IR ), LDWRKR, U, LDU, DUM, 1, - $ WORK( IWORK ), INFO ) - IU = IE + M -* -* Multiply right singular vectors of L in WORK(IR) by Q -* in A, storing result in WORK(IU) and copying to A -* (Workspace: need M*M + 2*M, prefer M*M + M*N + M)) -* - DO 40 I = 1, N, CHUNK - BLK = MIN( N-I+1, CHUNK ) - CALL DGEMM( 'N', 'N', M, BLK, M, ONE, WORK( IR ), - $ LDWRKR, A( 1, I ), LDA, ZERO, - $ WORK( IU ), LDWRKU ) - CALL DLACPY( 'F', M, BLK, WORK( IU ), LDWRKU, - $ A( 1, I ), LDA ) - 40 CONTINUE -* - ELSE -* -* Insufficient workspace for a fast algorithm -* - ITAU = 1 - IWORK = ITAU + M -* -* Compute A=L*Q -* (Workspace: need 2*M, prefer M + M*NB) -* - CALL DGELQF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy L to U, zeroing out above it -* - CALL DLACPY( 'L', M, M, A, LDA, U, LDU ) - CALL DLASET( 'U', M-1, M-1, ZERO, ZERO, U( 1, 2 ), - $ LDU ) -* -* Generate Q in A -* (Workspace: need 2*M, prefer M + M*NB) -* - CALL DORGLQ( M, N, M, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = ITAU - ITAUQ = IE + M - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Bidiagonalize L in U -* (Workspace: need 4*M, prefer 3*M + 2*M*NB) -* - CALL DGEBRD( M, M, U, LDU, S, WORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Multiply right vectors bidiagonalizing L by Q in A -* (Workspace: need 3*M + N, prefer 3*M + N*NB) -* - CALL DORMBR( 'P', 'L', 'T', M, N, M, U, LDU, - $ WORK( ITAUP ), A, LDA, WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate left vectors bidiagonalizing L in U -* (Workspace: need 4*M, prefer 3*M + M*NB) -* - CALL DORGBR( 'Q', M, M, M, U, LDU, WORK( ITAUQ ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IWORK = IE + M -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of A in U and computing right -* singular vectors of A in A -* (Workspace: need BDSPAC) -* - CALL DBDSQR( 'U', M, N, M, 0, S, WORK( IE ), A, LDA, - $ U, LDU, DUM, 1, WORK( IWORK ), INFO ) -* - END IF -* - ELSE IF( WNTVS ) THEN -* - IF( WNTUN ) THEN -* -* Path 4t(N much larger than M, JOBU='N', JOBVT='S') -* M right singular vectors to be computed in VT and -* no left singular vectors to be computed -* - IF( LWORK.GE.M*M+MAX( 4*M, BDSPAC ) ) THEN -* -* Sufficient workspace for a fast algorithm -* - IR = 1 - IF( LWORK.GE.WRKBL+LDA*M ) THEN -* -* WORK(IR) is LDA by M -* - LDWRKR = LDA - ELSE -* -* WORK(IR) is M by M -* - LDWRKR = M - END IF - ITAU = IR + LDWRKR*M - IWORK = ITAU + M -* -* Compute A=L*Q -* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) -* - CALL DGELQF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy L to WORK(IR), zeroing out above it -* - CALL DLACPY( 'L', M, M, A, LDA, WORK( IR ), - $ LDWRKR ) - CALL DLASET( 'U', M-1, M-1, ZERO, ZERO, - $ WORK( IR+LDWRKR ), LDWRKR ) -* -* Generate Q in A -* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) -* - CALL DORGLQ( M, N, M, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = ITAU - ITAUQ = IE + M - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Bidiagonalize L in WORK(IR) -* (Workspace: need M*M + 4*M, prefer M*M + 3*M + 2*M*NB) -* - CALL DGEBRD( M, M, WORK( IR ), LDWRKR, S, - $ WORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate right vectors bidiagonalizing L in -* WORK(IR) -* (Workspace: need M*M + 4*M, prefer M*M + 3*M + (M-1)*NB) -* - CALL DORGBR( 'P', M, M, M, WORK( IR ), LDWRKR, - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - IWORK = IE + M -* -* Perform bidiagonal QR iteration, computing right -* singular vectors of L in WORK(IR) -* (Workspace: need M*M + BDSPAC) -* - CALL DBDSQR( 'U', M, M, 0, 0, S, WORK( IE ), - $ WORK( IR ), LDWRKR, DUM, 1, DUM, 1, - $ WORK( IWORK ), INFO ) -* -* Multiply right singular vectors of L in WORK(IR) by -* Q in A, storing result in VT -* (Workspace: need M*M) -* - CALL DGEMM( 'N', 'N', M, N, M, ONE, WORK( IR ), - $ LDWRKR, A, LDA, ZERO, VT, LDVT ) -* - ELSE -* -* Insufficient workspace for a fast algorithm -* - ITAU = 1 - IWORK = ITAU + M -* -* Compute A=L*Q -* (Workspace: need 2*M, prefer M + M*NB) -* - CALL DGELQF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy result to VT -* - CALL DLACPY( 'U', M, N, A, LDA, VT, LDVT ) -* -* Generate Q in VT -* (Workspace: need 2*M, prefer M + M*NB) -* - CALL DORGLQ( M, N, M, VT, LDVT, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = ITAU - ITAUQ = IE + M - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Zero out above L in A -* - CALL DLASET( 'U', M-1, M-1, ZERO, ZERO, A( 1, 2 ), - $ LDA ) -* -* Bidiagonalize L in A -* (Workspace: need 4*M, prefer 3*M + 2*M*NB) -* - CALL DGEBRD( M, M, A, LDA, S, WORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Multiply right vectors bidiagonalizing L by Q in VT -* (Workspace: need 3*M + N, prefer 3*M + N*NB) -* - CALL DORMBR( 'P', 'L', 'T', M, N, M, A, LDA, - $ WORK( ITAUP ), VT, LDVT, - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IWORK = IE + M -* -* Perform bidiagonal QR iteration, computing right -* singular vectors of A in VT -* (Workspace: need BDSPAC) -* - CALL DBDSQR( 'U', M, N, 0, 0, S, WORK( IE ), VT, - $ LDVT, DUM, 1, DUM, 1, WORK( IWORK ), - $ INFO ) -* - END IF -* - ELSE IF( WNTUO ) THEN -* -* Path 5t(N much larger than M, JOBU='O', JOBVT='S') -* M right singular vectors to be computed in VT and -* M left singular vectors to be overwritten on A -* - IF( LWORK.GE.2*M*M+MAX( 4*M, BDSPAC ) ) THEN -* -* Sufficient workspace for a fast algorithm -* - IU = 1 - IF( LWORK.GE.WRKBL+2*LDA*M ) THEN -* -* WORK(IU) is LDA by M and WORK(IR) is LDA by M -* - LDWRKU = LDA - IR = IU + LDWRKU*M - LDWRKR = LDA - ELSE IF( LWORK.GE.WRKBL+( LDA + M )*M ) THEN -* -* WORK(IU) is LDA by M and WORK(IR) is M by M -* - LDWRKU = LDA - IR = IU + LDWRKU*M - LDWRKR = M - ELSE -* -* WORK(IU) is M by M and WORK(IR) is M by M -* - LDWRKU = M - IR = IU + LDWRKU*M - LDWRKR = M - END IF - ITAU = IR + LDWRKR*M - IWORK = ITAU + M -* -* Compute A=L*Q -* (Workspace: need 2*M*M + 2*M, prefer 2*M*M + M + M*NB) -* - CALL DGELQF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy L to WORK(IU), zeroing out below it -* - CALL DLACPY( 'L', M, M, A, LDA, WORK( IU ), - $ LDWRKU ) - CALL DLASET( 'U', M-1, M-1, ZERO, ZERO, - $ WORK( IU+LDWRKU ), LDWRKU ) -* -* Generate Q in A -* (Workspace: need 2*M*M + 2*M, prefer 2*M*M + M + M*NB) -* - CALL DORGLQ( M, N, M, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = ITAU - ITAUQ = IE + M - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Bidiagonalize L in WORK(IU), copying result to -* WORK(IR) -* (Workspace: need 2*M*M + 4*M, -* prefer 2*M*M+3*M+2*M*NB) -* - CALL DGEBRD( M, M, WORK( IU ), LDWRKU, S, - $ WORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - CALL DLACPY( 'L', M, M, WORK( IU ), LDWRKU, - $ WORK( IR ), LDWRKR ) -* -* Generate right bidiagonalizing vectors in WORK(IU) -* (Workspace: need 2*M*M + 4*M-1, -* prefer 2*M*M+3*M+(M-1)*NB) -* - CALL DORGBR( 'P', M, M, M, WORK( IU ), LDWRKU, - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate left bidiagonalizing vectors in WORK(IR) -* (Workspace: need 2*M*M + 4*M, prefer 2*M*M + 3*M + M*NB) -* - CALL DORGBR( 'Q', M, M, M, WORK( IR ), LDWRKR, - $ WORK( ITAUQ ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - IWORK = IE + M -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of L in WORK(IR) and computing -* right singular vectors of L in WORK(IU) -* (Workspace: need 2*M*M + BDSPAC) -* - CALL DBDSQR( 'U', M, M, M, 0, S, WORK( IE ), - $ WORK( IU ), LDWRKU, WORK( IR ), - $ LDWRKR, DUM, 1, WORK( IWORK ), INFO ) -* -* Multiply right singular vectors of L in WORK(IU) by -* Q in A, storing result in VT -* (Workspace: need M*M) -* - CALL DGEMM( 'N', 'N', M, N, M, ONE, WORK( IU ), - $ LDWRKU, A, LDA, ZERO, VT, LDVT ) -* -* Copy left singular vectors of L to A -* (Workspace: need M*M) -* - CALL DLACPY( 'F', M, M, WORK( IR ), LDWRKR, A, - $ LDA ) -* - ELSE -* -* Insufficient workspace for a fast algorithm -* - ITAU = 1 - IWORK = ITAU + M -* -* Compute A=L*Q, copying result to VT -* (Workspace: need 2*M, prefer M + M*NB) -* - CALL DGELQF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL DLACPY( 'U', M, N, A, LDA, VT, LDVT ) -* -* Generate Q in VT -* (Workspace: need 2*M, prefer M + M*NB) -* - CALL DORGLQ( M, N, M, VT, LDVT, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = ITAU - ITAUQ = IE + M - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Zero out above L in A -* - CALL DLASET( 'U', M-1, M-1, ZERO, ZERO, A( 1, 2 ), - $ LDA ) -* -* Bidiagonalize L in A -* (Workspace: need 4*M, prefer 3*M + 2*M*NB) -* - CALL DGEBRD( M, M, A, LDA, S, WORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Multiply right vectors bidiagonalizing L by Q in VT -* (Workspace: need 3*M + N, prefer 3*M + N*NB) -* - CALL DORMBR( 'P', 'L', 'T', M, N, M, A, LDA, - $ WORK( ITAUP ), VT, LDVT, - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Generate left bidiagonalizing vectors of L in A -* (Workspace: need 4*M, prefer 3*M + M*NB) -* - CALL DORGBR( 'Q', M, M, M, A, LDA, WORK( ITAUQ ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IWORK = IE + M -* -* Perform bidiagonal QR iteration, compute left -* singular vectors of A in A and compute right -* singular vectors of A in VT -* (Workspace: need BDSPAC) -* - CALL DBDSQR( 'U', M, N, M, 0, S, WORK( IE ), VT, - $ LDVT, A, LDA, DUM, 1, WORK( IWORK ), - $ INFO ) -* - END IF -* - ELSE IF( WNTUAS ) THEN -* -* Path 6t(N much larger than M, JOBU='S' or 'A', -* JOBVT='S') -* M right singular vectors to be computed in VT and -* M left singular vectors to be computed in U -* - IF( LWORK.GE.M*M+MAX( 4*M, BDSPAC ) ) THEN -* -* Sufficient workspace for a fast algorithm -* - IU = 1 - IF( LWORK.GE.WRKBL+LDA*M ) THEN -* -* WORK(IU) is LDA by N -* - LDWRKU = LDA - ELSE -* -* WORK(IU) is LDA by M -* - LDWRKU = M - END IF - ITAU = IU + LDWRKU*M - IWORK = ITAU + M -* -* Compute A=L*Q -* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) -* - CALL DGELQF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy L to WORK(IU), zeroing out above it -* - CALL DLACPY( 'L', M, M, A, LDA, WORK( IU ), - $ LDWRKU ) - CALL DLASET( 'U', M-1, M-1, ZERO, ZERO, - $ WORK( IU+LDWRKU ), LDWRKU ) -* -* Generate Q in A -* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) -* - CALL DORGLQ( M, N, M, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = ITAU - ITAUQ = IE + M - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Bidiagonalize L in WORK(IU), copying result to U -* (Workspace: need M*M + 4*M, prefer M*M + 3*M + 2*M*NB) -* - CALL DGEBRD( M, M, WORK( IU ), LDWRKU, S, - $ WORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - CALL DLACPY( 'L', M, M, WORK( IU ), LDWRKU, U, - $ LDU ) -* -* Generate right bidiagonalizing vectors in WORK(IU) -* (Workspace: need M*M + 4*M-1, -* prefer M*M+3*M+(M-1)*NB) -* - CALL DORGBR( 'P', M, M, M, WORK( IU ), LDWRKU, - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate left bidiagonalizing vectors in U -* (Workspace: need M*M + 4*M, prefer M*M + 3*M + M*NB) -* - CALL DORGBR( 'Q', M, M, M, U, LDU, WORK( ITAUQ ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IWORK = IE + M -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of L in U and computing right -* singular vectors of L in WORK(IU) -* (Workspace: need M*M + BDSPAC) -* - CALL DBDSQR( 'U', M, M, M, 0, S, WORK( IE ), - $ WORK( IU ), LDWRKU, U, LDU, DUM, 1, - $ WORK( IWORK ), INFO ) -* -* Multiply right singular vectors of L in WORK(IU) by -* Q in A, storing result in VT -* (Workspace: need M*M) -* - CALL DGEMM( 'N', 'N', M, N, M, ONE, WORK( IU ), - $ LDWRKU, A, LDA, ZERO, VT, LDVT ) -* - ELSE -* -* Insufficient workspace for a fast algorithm -* - ITAU = 1 - IWORK = ITAU + M -* -* Compute A=L*Q, copying result to VT -* (Workspace: need 2*M, prefer M + M*NB) -* - CALL DGELQF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL DLACPY( 'U', M, N, A, LDA, VT, LDVT ) -* -* Generate Q in VT -* (Workspace: need 2*M, prefer M + M*NB) -* - CALL DORGLQ( M, N, M, VT, LDVT, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy L to U, zeroing out above it -* - CALL DLACPY( 'L', M, M, A, LDA, U, LDU ) - CALL DLASET( 'U', M-1, M-1, ZERO, ZERO, U( 1, 2 ), - $ LDU ) - IE = ITAU - ITAUQ = IE + M - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Bidiagonalize L in U -* (Workspace: need 4*M, prefer 3*M + 2*M*NB) -* - CALL DGEBRD( M, M, U, LDU, S, WORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Multiply right bidiagonalizing vectors in U by Q -* in VT -* (Workspace: need 3*M + N, prefer 3*M + N*NB) -* - CALL DORMBR( 'P', 'L', 'T', M, N, M, U, LDU, - $ WORK( ITAUP ), VT, LDVT, - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Generate left bidiagonalizing vectors in U -* (Workspace: need 4*M, prefer 3*M + M*NB) -* - CALL DORGBR( 'Q', M, M, M, U, LDU, WORK( ITAUQ ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IWORK = IE + M -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of A in U and computing right -* singular vectors of A in VT -* (Workspace: need BDSPAC) -* - CALL DBDSQR( 'U', M, N, M, 0, S, WORK( IE ), VT, - $ LDVT, U, LDU, DUM, 1, WORK( IWORK ), - $ INFO ) -* - END IF -* - END IF -* - ELSE IF( WNTVA ) THEN -* - IF( WNTUN ) THEN -* -* Path 7t(N much larger than M, JOBU='N', JOBVT='A') -* N right singular vectors to be computed in VT and -* no left singular vectors to be computed -* - IF( LWORK.GE.M*M+MAX( N + M, 4*M, BDSPAC ) ) THEN -* -* Sufficient workspace for a fast algorithm -* - IR = 1 - IF( LWORK.GE.WRKBL+LDA*M ) THEN -* -* WORK(IR) is LDA by M -* - LDWRKR = LDA - ELSE -* -* WORK(IR) is M by M -* - LDWRKR = M - END IF - ITAU = IR + LDWRKR*M - IWORK = ITAU + M -* -* Compute A=L*Q, copying result to VT -* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) -* - CALL DGELQF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL DLACPY( 'U', M, N, A, LDA, VT, LDVT ) -* -* Copy L to WORK(IR), zeroing out above it -* - CALL DLACPY( 'L', M, M, A, LDA, WORK( IR ), - $ LDWRKR ) - CALL DLASET( 'U', M-1, M-1, ZERO, ZERO, - $ WORK( IR+LDWRKR ), LDWRKR ) -* -* Generate Q in VT -* (Workspace: need M*M + M + N, prefer M*M + M + N*NB) -* - CALL DORGLQ( N, N, M, VT, LDVT, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = ITAU - ITAUQ = IE + M - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Bidiagonalize L in WORK(IR) -* (Workspace: need M*M + 4*M, prefer M*M + 3*M + 2*M*NB) -* - CALL DGEBRD( M, M, WORK( IR ), LDWRKR, S, - $ WORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate right bidiagonalizing vectors in WORK(IR) -* (Workspace: need M*M + 4*M-1, -* prefer M*M+3*M+(M-1)*NB) -* - CALL DORGBR( 'P', M, M, M, WORK( IR ), LDWRKR, - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - IWORK = IE + M -* -* Perform bidiagonal QR iteration, computing right -* singular vectors of L in WORK(IR) -* (Workspace: need M*M + BDSPAC) -* - CALL DBDSQR( 'U', M, M, 0, 0, S, WORK( IE ), - $ WORK( IR ), LDWRKR, DUM, 1, DUM, 1, - $ WORK( IWORK ), INFO ) -* -* Multiply right singular vectors of L in WORK(IR) by -* Q in VT, storing result in A -* (Workspace: need M*M) -* - CALL DGEMM( 'N', 'N', M, N, M, ONE, WORK( IR ), - $ LDWRKR, VT, LDVT, ZERO, A, LDA ) -* -* Copy right singular vectors of A from A to VT -* - CALL DLACPY( 'F', M, N, A, LDA, VT, LDVT ) -* - ELSE -* -* Insufficient workspace for a fast algorithm -* - ITAU = 1 - IWORK = ITAU + M -* -* Compute A=L*Q, copying result to VT -* (Workspace: need 2*M, prefer M + M*NB) -* - CALL DGELQF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL DLACPY( 'U', M, N, A, LDA, VT, LDVT ) -* -* Generate Q in VT -* (Workspace: need M + N, prefer M + N*NB) -* - CALL DORGLQ( N, N, M, VT, LDVT, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = ITAU - ITAUQ = IE + M - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Zero out above L in A -* - CALL DLASET( 'U', M-1, M-1, ZERO, ZERO, A( 1, 2 ), - $ LDA ) -* -* Bidiagonalize L in A -* (Workspace: need 4*M, prefer 3*M + 2*M*NB) -* - CALL DGEBRD( M, M, A, LDA, S, WORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Multiply right bidiagonalizing vectors in A by Q -* in VT -* (Workspace: need 3*M + N, prefer 3*M + N*NB) -* - CALL DORMBR( 'P', 'L', 'T', M, N, M, A, LDA, - $ WORK( ITAUP ), VT, LDVT, - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IWORK = IE + M -* -* Perform bidiagonal QR iteration, computing right -* singular vectors of A in VT -* (Workspace: need BDSPAC) -* - CALL DBDSQR( 'U', M, N, 0, 0, S, WORK( IE ), VT, - $ LDVT, DUM, 1, DUM, 1, WORK( IWORK ), - $ INFO ) -* - END IF -* - ELSE IF( WNTUO ) THEN -* -* Path 8t(N much larger than M, JOBU='O', JOBVT='A') -* N right singular vectors to be computed in VT and -* M left singular vectors to be overwritten on A -* - IF( LWORK.GE.2*M*M+MAX( N + M, 4*M, BDSPAC ) ) THEN -* -* Sufficient workspace for a fast algorithm -* - IU = 1 - IF( LWORK.GE.WRKBL+2*LDA*M ) THEN -* -* WORK(IU) is LDA by M and WORK(IR) is LDA by M -* - LDWRKU = LDA - IR = IU + LDWRKU*M - LDWRKR = LDA - ELSE IF( LWORK.GE.WRKBL+( LDA + M )*M ) THEN -* -* WORK(IU) is LDA by M and WORK(IR) is M by M -* - LDWRKU = LDA - IR = IU + LDWRKU*M - LDWRKR = M - ELSE -* -* WORK(IU) is M by M and WORK(IR) is M by M -* - LDWRKU = M - IR = IU + LDWRKU*M - LDWRKR = M - END IF - ITAU = IR + LDWRKR*M - IWORK = ITAU + M -* -* Compute A=L*Q, copying result to VT -* (Workspace: need 2*M*M + 2*M, prefer 2*M*M + M + M*NB) -* - CALL DGELQF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL DLACPY( 'U', M, N, A, LDA, VT, LDVT ) -* -* Generate Q in VT -* (Workspace: need 2*M*M + M + N, prefer 2*M*M + M + N*NB) -* - CALL DORGLQ( N, N, M, VT, LDVT, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy L to WORK(IU), zeroing out above it -* - CALL DLACPY( 'L', M, M, A, LDA, WORK( IU ), - $ LDWRKU ) - CALL DLASET( 'U', M-1, M-1, ZERO, ZERO, - $ WORK( IU+LDWRKU ), LDWRKU ) - IE = ITAU - ITAUQ = IE + M - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Bidiagonalize L in WORK(IU), copying result to -* WORK(IR) -* (Workspace: need 2*M*M + 4*M, -* prefer 2*M*M+3*M+2*M*NB) -* - CALL DGEBRD( M, M, WORK( IU ), LDWRKU, S, - $ WORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - CALL DLACPY( 'L', M, M, WORK( IU ), LDWRKU, - $ WORK( IR ), LDWRKR ) -* -* Generate right bidiagonalizing vectors in WORK(IU) -* (Workspace: need 2*M*M + 4*M-1, -* prefer 2*M*M+3*M+(M-1)*NB) -* - CALL DORGBR( 'P', M, M, M, WORK( IU ), LDWRKU, - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate left bidiagonalizing vectors in WORK(IR) -* (Workspace: need 2*M*M + 4*M, prefer 2*M*M + 3*M + M*NB) -* - CALL DORGBR( 'Q', M, M, M, WORK( IR ), LDWRKR, - $ WORK( ITAUQ ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - IWORK = IE + M -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of L in WORK(IR) and computing -* right singular vectors of L in WORK(IU) -* (Workspace: need 2*M*M + BDSPAC) -* - CALL DBDSQR( 'U', M, M, M, 0, S, WORK( IE ), - $ WORK( IU ), LDWRKU, WORK( IR ), - $ LDWRKR, DUM, 1, WORK( IWORK ), INFO ) -* -* Multiply right singular vectors of L in WORK(IU) by -* Q in VT, storing result in A -* (Workspace: need M*M) -* - CALL DGEMM( 'N', 'N', M, N, M, ONE, WORK( IU ), - $ LDWRKU, VT, LDVT, ZERO, A, LDA ) -* -* Copy right singular vectors of A from A to VT -* - CALL DLACPY( 'F', M, N, A, LDA, VT, LDVT ) -* -* Copy left singular vectors of A from WORK(IR) to A -* - CALL DLACPY( 'F', M, M, WORK( IR ), LDWRKR, A, - $ LDA ) -* - ELSE -* -* Insufficient workspace for a fast algorithm -* - ITAU = 1 - IWORK = ITAU + M -* -* Compute A=L*Q, copying result to VT -* (Workspace: need 2*M, prefer M + M*NB) -* - CALL DGELQF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL DLACPY( 'U', M, N, A, LDA, VT, LDVT ) -* -* Generate Q in VT -* (Workspace: need M + N, prefer M + N*NB) -* - CALL DORGLQ( N, N, M, VT, LDVT, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IE = ITAU - ITAUQ = IE + M - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Zero out above L in A -* - CALL DLASET( 'U', M-1, M-1, ZERO, ZERO, A( 1, 2 ), - $ LDA ) -* -* Bidiagonalize L in A -* (Workspace: need 4*M, prefer 3*M + 2*M*NB) -* - CALL DGEBRD( M, M, A, LDA, S, WORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Multiply right bidiagonalizing vectors in A by Q -* in VT -* (Workspace: need 3*M + N, prefer 3*M + N*NB) -* - CALL DORMBR( 'P', 'L', 'T', M, N, M, A, LDA, - $ WORK( ITAUP ), VT, LDVT, - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Generate left bidiagonalizing vectors in A -* (Workspace: need 4*M, prefer 3*M + M*NB) -* - CALL DORGBR( 'Q', M, M, M, A, LDA, WORK( ITAUQ ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IWORK = IE + M -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of A in A and computing right -* singular vectors of A in VT -* (Workspace: need BDSPAC) -* - CALL DBDSQR( 'U', M, N, M, 0, S, WORK( IE ), VT, - $ LDVT, A, LDA, DUM, 1, WORK( IWORK ), - $ INFO ) -* - END IF -* - ELSE IF( WNTUAS ) THEN -* -* Path 9t(N much larger than M, JOBU='S' or 'A', -* JOBVT='A') -* N right singular vectors to be computed in VT and -* M left singular vectors to be computed in U -* - IF( LWORK.GE.M*M+MAX( N + M, 4*M, BDSPAC ) ) THEN -* -* Sufficient workspace for a fast algorithm -* - IU = 1 - IF( LWORK.GE.WRKBL+LDA*M ) THEN -* -* WORK(IU) is LDA by M -* - LDWRKU = LDA - ELSE -* -* WORK(IU) is M by M -* - LDWRKU = M - END IF - ITAU = IU + LDWRKU*M - IWORK = ITAU + M -* -* Compute A=L*Q, copying result to VT -* (Workspace: need M*M + 2*M, prefer M*M + M + M*NB) -* - CALL DGELQF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL DLACPY( 'U', M, N, A, LDA, VT, LDVT ) -* -* Generate Q in VT -* (Workspace: need M*M + M + N, prefer M*M + M + N*NB) -* - CALL DORGLQ( N, N, M, VT, LDVT, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy L to WORK(IU), zeroing out above it -* - CALL DLACPY( 'L', M, M, A, LDA, WORK( IU ), - $ LDWRKU ) - CALL DLASET( 'U', M-1, M-1, ZERO, ZERO, - $ WORK( IU+LDWRKU ), LDWRKU ) - IE = ITAU - ITAUQ = IE + M - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Bidiagonalize L in WORK(IU), copying result to U -* (Workspace: need M*M + 4*M, prefer M*M + 3*M + 2*M*NB) -* - CALL DGEBRD( M, M, WORK( IU ), LDWRKU, S, - $ WORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) - CALL DLACPY( 'L', M, M, WORK( IU ), LDWRKU, U, - $ LDU ) -* -* Generate right bidiagonalizing vectors in WORK(IU) -* (Workspace: need M*M + 4*M, prefer M*M + 3*M + (M-1)*NB) -* - CALL DORGBR( 'P', M, M, M, WORK( IU ), LDWRKU, - $ WORK( ITAUP ), WORK( IWORK ), - $ LWORK-IWORK+1, IERR ) -* -* Generate left bidiagonalizing vectors in U -* (Workspace: need M*M + 4*M, prefer M*M + 3*M + M*NB) -* - CALL DORGBR( 'Q', M, M, M, U, LDU, WORK( ITAUQ ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IWORK = IE + M -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of L in U and computing right -* singular vectors of L in WORK(IU) -* (Workspace: need M*M + BDSPAC) -* - CALL DBDSQR( 'U', M, M, M, 0, S, WORK( IE ), - $ WORK( IU ), LDWRKU, U, LDU, DUM, 1, - $ WORK( IWORK ), INFO ) -* -* Multiply right singular vectors of L in WORK(IU) by -* Q in VT, storing result in A -* (Workspace: need M*M) -* - CALL DGEMM( 'N', 'N', M, N, M, ONE, WORK( IU ), - $ LDWRKU, VT, LDVT, ZERO, A, LDA ) -* -* Copy right singular vectors of A from A to VT -* - CALL DLACPY( 'F', M, N, A, LDA, VT, LDVT ) -* - ELSE -* -* Insufficient workspace for a fast algorithm -* - ITAU = 1 - IWORK = ITAU + M -* -* Compute A=L*Q, copying result to VT -* (Workspace: need 2*M, prefer M + M*NB) -* - CALL DGELQF( M, N, A, LDA, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - CALL DLACPY( 'U', M, N, A, LDA, VT, LDVT ) -* -* Generate Q in VT -* (Workspace: need M + N, prefer M + N*NB) -* - CALL DORGLQ( N, N, M, VT, LDVT, WORK( ITAU ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Copy L to U, zeroing out above it -* - CALL DLACPY( 'L', M, M, A, LDA, U, LDU ) - CALL DLASET( 'U', M-1, M-1, ZERO, ZERO, U( 1, 2 ), - $ LDU ) - IE = ITAU - ITAUQ = IE + M - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Bidiagonalize L in U -* (Workspace: need 4*M, prefer 3*M + 2*M*NB) -* - CALL DGEBRD( M, M, U, LDU, S, WORK( IE ), - $ WORK( ITAUQ ), WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Multiply right bidiagonalizing vectors in U by Q -* in VT -* (Workspace: need 3*M + N, prefer 3*M + N*NB) -* - CALL DORMBR( 'P', 'L', 'T', M, N, M, U, LDU, - $ WORK( ITAUP ), VT, LDVT, - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) -* -* Generate left bidiagonalizing vectors in U -* (Workspace: need 4*M, prefer 3*M + M*NB) -* - CALL DORGBR( 'Q', M, M, M, U, LDU, WORK( ITAUQ ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - IWORK = IE + M -* -* Perform bidiagonal QR iteration, computing left -* singular vectors of A in U and computing right -* singular vectors of A in VT -* (Workspace: need BDSPAC) -* - CALL DBDSQR( 'U', M, N, M, 0, S, WORK( IE ), VT, - $ LDVT, U, LDU, DUM, 1, WORK( IWORK ), - $ INFO ) -* - END IF -* - END IF -* - END IF -* - ELSE -* -* N .LT. MNTHR -* -* Path 10t(N greater than M, but not much larger) -* Reduce to bidiagonal form without LQ decomposition -* - IE = 1 - ITAUQ = IE + M - ITAUP = ITAUQ + M - IWORK = ITAUP + M -* -* Bidiagonalize A -* (Workspace: need 3*M + N, prefer 3*M + (M + N)*NB) -* - CALL DGEBRD( M, N, A, LDA, S, WORK( IE ), WORK( ITAUQ ), - $ WORK( ITAUP ), WORK( IWORK ), LWORK-IWORK+1, - $ IERR ) - IF( WNTUAS ) THEN -* -* If left singular vectors desired in U, copy result to U -* and generate left bidiagonalizing vectors in U -* (Workspace: need 4*M-1, prefer 3*M + (M-1)*NB) -* - CALL DLACPY( 'L', M, M, A, LDA, U, LDU ) - CALL DORGBR( 'Q', M, M, N, U, LDU, WORK( ITAUQ ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - END IF - IF( WNTVAS ) THEN -* -* If right singular vectors desired in VT, copy result to -* VT and generate right bidiagonalizing vectors in VT -* (Workspace: need 3*M + NRVT, prefer 3*M + NRVT*NB) -* - CALL DLACPY( 'U', M, N, A, LDA, VT, LDVT ) - IF( WNTVA ) - $ NRVT = N - IF( WNTVS ) - $ NRVT = M - CALL DORGBR( 'P', NRVT, N, M, VT, LDVT, WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - END IF - IF( WNTUO ) THEN -* -* If left singular vectors desired in A, generate left -* bidiagonalizing vectors in A -* (Workspace: need 4*M-1, prefer 3*M + (M-1)*NB) -* - CALL DORGBR( 'Q', M, M, N, A, LDA, WORK( ITAUQ ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - END IF - IF( WNTVO ) THEN -* -* If right singular vectors desired in A, generate right -* bidiagonalizing vectors in A -* (Workspace: need 4*M, prefer 3*M + M*NB) -* - CALL DORGBR( 'P', M, N, M, A, LDA, WORK( ITAUP ), - $ WORK( IWORK ), LWORK-IWORK+1, IERR ) - END IF - IWORK = IE + M - IF( WNTUAS .OR. WNTUO ) - $ NRU = M - IF( WNTUN ) - $ NRU = 0 - IF( WNTVAS .OR. WNTVO ) - $ NCVT = N - IF( WNTVN ) - $ NCVT = 0 - IF( ( .NOT.WNTUO ) .AND. ( .NOT.WNTVO ) ) THEN -* -* Perform bidiagonal QR iteration, if desired, computing -* left singular vectors in U and computing right singular -* vectors in VT -* (Workspace: need BDSPAC) -* - CALL DBDSQR( 'L', M, NCVT, NRU, 0, S, WORK( IE ), VT, - $ LDVT, U, LDU, DUM, 1, WORK( IWORK ), INFO ) - ELSE IF( ( .NOT.WNTUO ) .AND. WNTVO ) THEN -* -* Perform bidiagonal QR iteration, if desired, computing -* left singular vectors in U and computing right singular -* vectors in A -* (Workspace: need BDSPAC) -* - CALL DBDSQR( 'L', M, NCVT, NRU, 0, S, WORK( IE ), A, LDA, - $ U, LDU, DUM, 1, WORK( IWORK ), INFO ) - ELSE -* -* Perform bidiagonal QR iteration, if desired, computing -* left singular vectors in A and computing right singular -* vectors in VT -* (Workspace: need BDSPAC) -* - CALL DBDSQR( 'L', M, NCVT, NRU, 0, S, WORK( IE ), VT, - $ LDVT, A, LDA, DUM, 1, WORK( IWORK ), INFO ) - END IF -* - END IF -* - END IF -* -* If DBDSQR failed to converge, copy unconverged superdiagonals -* to WORK( 2:MINMN ) -* - IF( INFO.NE.0 ) THEN - IF( IE.GT.2 ) THEN - DO 50 I = 1, MINMN - 1 - WORK( I+1 ) = WORK( I+IE-1 ) - 50 CONTINUE - END IF - IF( IE.LT.2 ) THEN - DO 60 I = MINMN - 1, 1, -1 - WORK( I+1 ) = WORK( I+IE-1 ) - 60 CONTINUE - END IF - END IF -* -* Undo scaling if necessary -* - IF( ISCL.EQ.1 ) THEN - IF( ANRM.GT.BIGNUM ) - $ CALL DLASCL( 'G', 0, 0, BIGNUM, ANRM, MINMN, 1, S, MINMN, - $ IERR ) - IF( INFO.NE.0 .AND. ANRM.GT.BIGNUM ) - $ CALL DLASCL( 'G', 0, 0, BIGNUM, ANRM, MINMN-1, 1, WORK( 2 ), - $ MINMN, IERR ) - IF( ANRM.LT.SMLNUM ) - $ CALL DLASCL( 'G', 0, 0, SMLNUM, ANRM, MINMN, 1, S, MINMN, - $ IERR ) - IF( INFO.NE.0 .AND. ANRM.LT.SMLNUM ) - $ CALL DLASCL( 'G', 0, 0, SMLNUM, ANRM, MINMN-1, 1, WORK( 2 ), - $ MINMN, IERR ) - END IF -* -* Return optimal workspace in WORK(1) -* - WORK( 1 ) = MAXWRK -* - RETURN -* -* End of DGESVD -* - END diff --git a/lib/linalg/fortran/dgetf2.f b/lib/linalg/fortran/dgetf2.f deleted file mode 100644 index fc1587842e..0000000000 --- a/lib/linalg/fortran/dgetf2.f +++ /dev/null @@ -1,210 +0,0 @@ -*> \brief \b DGETF2 computes the LU factorization of a general m-by-n matrix using partial pivoting with row interchanges (unblocked algorithm). -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DGETF2 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DGETF2( M, N, A, LDA, IPIV, INFO ) -* -* .. Scalar Arguments .. -* INTEGER INFO, LDA, M, N -* .. -* .. Array Arguments .. -* INTEGER IPIV( * ) -* DOUBLE PRECISION A( LDA, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DGETF2 computes an LU factorization of a general m-by-n matrix A -*> using partial pivoting with row interchanges. -*> -*> The factorization has the form -*> A = P * L * U -*> where P is a permutation matrix, L is lower triangular with unit -*> diagonal elements (lower trapezoidal if m > n), and U is upper -*> triangular (upper trapezoidal if m < n). -*> -*> This is the right-looking Level 2 BLAS version of the algorithm. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix A. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the m by n matrix to be factored. -*> On exit, the factors L and U from the factorization -*> A = P*L*U; the unit diagonal elements of L are not stored. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,M). -*> \endverbatim -*> -*> \param[out] IPIV -*> \verbatim -*> IPIV is INTEGER array, dimension (min(M,N)) -*> The pivot indices; for 1 <= i <= min(M,N), row i of the -*> matrix was interchanged with row IPIV(i). -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -k, the k-th argument had an illegal value -*> > 0: if INFO = k, U(k,k) is exactly zero. The factorization -*> has been completed, but the factor U is exactly -*> singular, and division by zero will occur if it is used -*> to solve a system of equations. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleGEcomputational -* -* ===================================================================== - SUBROUTINE DGETF2( M, N, A, LDA, IPIV, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INFO, LDA, M, N -* .. -* .. Array Arguments .. - INTEGER IPIV( * ) - DOUBLE PRECISION A( LDA, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE, ZERO - PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) -* .. -* .. Local Scalars .. - DOUBLE PRECISION SFMIN - INTEGER I, J, JP -* .. -* .. External Functions .. - DOUBLE PRECISION DLAMCH - INTEGER IDAMAX - EXTERNAL DLAMCH, IDAMAX -* .. -* .. External Subroutines .. - EXTERNAL DGER, DSCAL, DSWAP, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, MIN -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 - IF( M.LT.0 ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( LDA.LT.MAX( 1, M ) ) THEN - INFO = -4 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DGETF2', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( M.EQ.0 .OR. N.EQ.0 ) - $ RETURN -* -* Compute machine safe minimum -* - SFMIN = DLAMCH('S') -* - DO 10 J = 1, MIN( M, N ) -* -* Find pivot and test for singularity. -* - JP = J - 1 + IDAMAX( M-J+1, A( J, J ), 1 ) - IPIV( J ) = JP - IF( A( JP, J ).NE.ZERO ) THEN -* -* Apply the interchange to columns 1:N. -* - IF( JP.NE.J ) - $ CALL DSWAP( N, A( J, 1 ), LDA, A( JP, 1 ), LDA ) -* -* Compute elements J+1:M of J-th column. -* - IF( J.LT.M ) THEN - IF( ABS(A( J, J )) .GE. SFMIN ) THEN - CALL DSCAL( M-J, ONE / A( J, J ), A( J+1, J ), 1 ) - ELSE - DO 20 I = 1, M-J - A( J+I, J ) = A( J+I, J ) / A( J, J ) - 20 CONTINUE - END IF - END IF -* - ELSE IF( INFO.EQ.0 ) THEN -* - INFO = J - END IF -* - IF( J.LT.MIN( M, N ) ) THEN -* -* Update trailing submatrix. -* - CALL DGER( M-J, N-J, -ONE, A( J+1, J ), 1, A( J, J+1 ), LDA, - $ A( J+1, J+1 ), LDA ) - END IF - 10 CONTINUE - RETURN -* -* End of DGETF2 -* - END diff --git a/lib/linalg/fortran/dgetrf.f b/lib/linalg/fortran/dgetrf.f deleted file mode 100644 index 73d0f3601a..0000000000 --- a/lib/linalg/fortran/dgetrf.f +++ /dev/null @@ -1,222 +0,0 @@ -*> \brief \b DGETRF -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DGETRF + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DGETRF( M, N, A, LDA, IPIV, INFO ) -* -* .. Scalar Arguments .. -* INTEGER INFO, LDA, M, N -* .. -* .. Array Arguments .. -* INTEGER IPIV( * ) -* DOUBLE PRECISION A( LDA, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DGETRF computes an LU factorization of a general M-by-N matrix A -*> using partial pivoting with row interchanges. -*> -*> The factorization has the form -*> A = P * L * U -*> where P is a permutation matrix, L is lower triangular with unit -*> diagonal elements (lower trapezoidal if m > n), and U is upper -*> triangular (upper trapezoidal if m < n). -*> -*> This is the right-looking Level 3 BLAS version of the algorithm. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix A. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the M-by-N matrix to be factored. -*> On exit, the factors L and U from the factorization -*> A = P*L*U; the unit diagonal elements of L are not stored. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,M). -*> \endverbatim -*> -*> \param[out] IPIV -*> \verbatim -*> IPIV is INTEGER array, dimension (min(M,N)) -*> The pivot indices; for 1 <= i <= min(M,N), row i of the -*> matrix was interchanged with row IPIV(i). -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, U(i,i) is exactly zero. The factorization -*> has been completed, but the factor U is exactly -*> singular, and division by zero will occur if it is used -*> to solve a system of equations. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleGEcomputational -* -* ===================================================================== - SUBROUTINE DGETRF( M, N, A, LDA, IPIV, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INFO, LDA, M, N -* .. -* .. Array Arguments .. - INTEGER IPIV( * ) - DOUBLE PRECISION A( LDA, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE - PARAMETER ( ONE = 1.0D+0 ) -* .. -* .. Local Scalars .. - INTEGER I, IINFO, J, JB, NB -* .. -* .. External Subroutines .. - EXTERNAL DGEMM, DGETRF2, DLASWP, DTRSM, XERBLA -* .. -* .. External Functions .. - INTEGER ILAENV - EXTERNAL ILAENV -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, MIN -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 - IF( M.LT.0 ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( LDA.LT.MAX( 1, M ) ) THEN - INFO = -4 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DGETRF', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( M.EQ.0 .OR. N.EQ.0 ) - $ RETURN -* -* Determine the block size for this environment. -* - NB = ILAENV( 1, 'DGETRF', ' ', M, N, -1, -1 ) - IF( NB.LE.1 .OR. NB.GE.MIN( M, N ) ) THEN -* -* Use unblocked code. -* - CALL DGETRF2( M, N, A, LDA, IPIV, INFO ) - ELSE -* -* Use blocked code. -* - DO 20 J = 1, MIN( M, N ), NB - JB = MIN( MIN( M, N )-J+1, NB ) -* -* Factor diagonal and subdiagonal blocks and test for exact -* singularity. -* - CALL DGETRF2( M-J+1, JB, A( J, J ), LDA, IPIV( J ), IINFO ) -* -* Adjust INFO and the pivot indices. -* - IF( INFO.EQ.0 .AND. IINFO.GT.0 ) - $ INFO = IINFO + J - 1 - DO 10 I = J, MIN( M, J+JB-1 ) - IPIV( I ) = J - 1 + IPIV( I ) - 10 CONTINUE -* -* Apply interchanges to columns 1:J-1. -* - CALL DLASWP( J-1, A, LDA, J, J+JB-1, IPIV, 1 ) -* - IF( J+JB.LE.N ) THEN -* -* Apply interchanges to columns J+JB:N. -* - CALL DLASWP( N-J-JB+1, A( 1, J+JB ), LDA, J, J+JB-1, - $ IPIV, 1 ) -* -* Compute block row of U. -* - CALL DTRSM( 'Left', 'Lower', 'No transpose', 'Unit', JB, - $ N-J-JB+1, ONE, A( J, J ), LDA, A( J, J+JB ), - $ LDA ) - IF( J+JB.LE.M ) THEN -* -* Update trailing submatrix. -* - CALL DGEMM( 'No transpose', 'No transpose', M-J-JB+1, - $ N-J-JB+1, JB, -ONE, A( J+JB, J ), LDA, - $ A( J, J+JB ), LDA, ONE, A( J+JB, J+JB ), - $ LDA ) - END IF - END IF - 20 CONTINUE - END IF - RETURN -* -* End of DGETRF -* - END diff --git a/lib/linalg/fortran/dgetrf2.f b/lib/linalg/fortran/dgetrf2.f deleted file mode 100644 index 40af0793dd..0000000000 --- a/lib/linalg/fortran/dgetrf2.f +++ /dev/null @@ -1,269 +0,0 @@ -*> \brief \b DGETRF2 -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* RECURSIVE SUBROUTINE DGETRF2( M, N, A, LDA, IPIV, INFO ) -* -* .. Scalar Arguments .. -* INTEGER INFO, LDA, M, N -* .. -* .. Array Arguments .. -* INTEGER IPIV( * ) -* DOUBLE PRECISION A( LDA, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DGETRF2 computes an LU factorization of a general M-by-N matrix A -*> using partial pivoting with row interchanges. -*> -*> The factorization has the form -*> A = P * L * U -*> where P is a permutation matrix, L is lower triangular with unit -*> diagonal elements (lower trapezoidal if m > n), and U is upper -*> triangular (upper trapezoidal if m < n). -*> -*> This is the recursive version of the algorithm. It divides -*> the matrix into four submatrices: -*> -*> [ A11 | A12 ] where A11 is n1 by n1 and A22 is n2 by n2 -*> A = [ -----|----- ] with n1 = min(m,n)/2 -*> [ A21 | A22 ] n2 = n-n1 -*> -*> [ A11 ] -*> The subroutine calls itself to factor [ --- ], -*> [ A12 ] -*> [ A12 ] -*> do the swaps on [ --- ], solve A12, update A22, -*> [ A22 ] -*> -*> then calls itself to factor A22 and do the swaps on A21. -*> -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix A. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the M-by-N matrix to be factored. -*> On exit, the factors L and U from the factorization -*> A = P*L*U; the unit diagonal elements of L are not stored. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,M). -*> \endverbatim -*> -*> \param[out] IPIV -*> \verbatim -*> IPIV is INTEGER array, dimension (min(M,N)) -*> The pivot indices; for 1 <= i <= min(M,N), row i of the -*> matrix was interchanged with row IPIV(i). -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, U(i,i) is exactly zero. The factorization -*> has been completed, but the factor U is exactly -*> singular, and division by zero will occur if it is used -*> to solve a system of equations. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleGEcomputational -* -* ===================================================================== - RECURSIVE SUBROUTINE DGETRF2( M, N, A, LDA, IPIV, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INFO, LDA, M, N -* .. -* .. Array Arguments .. - INTEGER IPIV( * ) - DOUBLE PRECISION A( LDA, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE, ZERO - PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) -* .. -* .. Local Scalars .. - DOUBLE PRECISION SFMIN, TEMP - INTEGER I, IINFO, N1, N2 -* .. -* .. External Functions .. - DOUBLE PRECISION DLAMCH - INTEGER IDAMAX - EXTERNAL DLAMCH, IDAMAX -* .. -* .. External Subroutines .. - EXTERNAL DGEMM, DSCAL, DLASWP, DTRSM, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, MIN -* .. -* .. Executable Statements .. -* -* Test the input parameters -* - INFO = 0 - IF( M.LT.0 ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( LDA.LT.MAX( 1, M ) ) THEN - INFO = -4 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DGETRF2', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( M.EQ.0 .OR. N.EQ.0 ) - $ RETURN - - IF ( M.EQ.1 ) THEN -* -* Use unblocked code for one row case -* Just need to handle IPIV and INFO -* - IPIV( 1 ) = 1 - IF ( A(1,1).EQ.ZERO ) - $ INFO = 1 -* - ELSE IF( N.EQ.1 ) THEN -* -* Use unblocked code for one column case -* -* -* Compute machine safe minimum -* - SFMIN = DLAMCH('S') -* -* Find pivot and test for singularity -* - I = IDAMAX( M, A( 1, 1 ), 1 ) - IPIV( 1 ) = I - IF( A( I, 1 ).NE.ZERO ) THEN -* -* Apply the interchange -* - IF( I.NE.1 ) THEN - TEMP = A( 1, 1 ) - A( 1, 1 ) = A( I, 1 ) - A( I, 1 ) = TEMP - END IF -* -* Compute elements 2:M of the column -* - IF( ABS(A( 1, 1 )) .GE. SFMIN ) THEN - CALL DSCAL( M-1, ONE / A( 1, 1 ), A( 2, 1 ), 1 ) - ELSE - DO 10 I = 1, M-1 - A( 1+I, 1 ) = A( 1+I, 1 ) / A( 1, 1 ) - 10 CONTINUE - END IF -* - ELSE - INFO = 1 - END IF -* - ELSE -* -* Use recursive code -* - N1 = MIN( M, N ) / 2 - N2 = N-N1 -* -* [ A11 ] -* Factor [ --- ] -* [ A21 ] -* - CALL DGETRF2( M, N1, A, LDA, IPIV, IINFO ) - - IF ( INFO.EQ.0 .AND. IINFO.GT.0 ) - $ INFO = IINFO -* -* [ A12 ] -* Apply interchanges to [ --- ] -* [ A22 ] -* - CALL DLASWP( N2, A( 1, N1+1 ), LDA, 1, N1, IPIV, 1 ) -* -* Solve A12 -* - CALL DTRSM( 'L', 'L', 'N', 'U', N1, N2, ONE, A, LDA, - $ A( 1, N1+1 ), LDA ) -* -* Update A22 -* - CALL DGEMM( 'N', 'N', M-N1, N2, N1, -ONE, A( N1+1, 1 ), LDA, - $ A( 1, N1+1 ), LDA, ONE, A( N1+1, N1+1 ), LDA ) -* -* Factor A22 -* - CALL DGETRF2( M-N1, N2, A( N1+1, N1+1 ), LDA, IPIV( N1+1 ), - $ IINFO ) -* -* Adjust INFO and the pivot indices -* - IF ( INFO.EQ.0 .AND. IINFO.GT.0 ) - $ INFO = IINFO + N1 - DO 20 I = N1+1, MIN( M, N ) - IPIV( I ) = IPIV( I ) + N1 - 20 CONTINUE -* -* Apply interchanges to A21 -* - CALL DLASWP( N1, A( 1, 1 ), LDA, N1+1, MIN( M, N), IPIV, 1 ) -* - END IF - RETURN -* -* End of DGETRF2 -* - END diff --git a/lib/linalg/fortran/dgetri.f b/lib/linalg/fortran/dgetri.f deleted file mode 100644 index 92ef90c186..0000000000 --- a/lib/linalg/fortran/dgetri.f +++ /dev/null @@ -1,258 +0,0 @@ -*> \brief \b DGETRI -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DGETRI + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO ) -* -* .. Scalar Arguments .. -* INTEGER INFO, LDA, LWORK, N -* .. -* .. Array Arguments .. -* INTEGER IPIV( * ) -* DOUBLE PRECISION A( LDA, * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DGETRI computes the inverse of a matrix using the LU factorization -*> computed by DGETRF. -*> -*> This method inverts U and then computes inv(A) by solving the system -*> inv(A)*L = inv(U) for inv(A). -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the factors L and U from the factorization -*> A = P*L*U as computed by DGETRF. -*> On exit, if INFO = 0, the inverse of the original matrix A. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,N). -*> \endverbatim -*> -*> \param[in] IPIV -*> \verbatim -*> IPIV is INTEGER array, dimension (N) -*> The pivot indices from DGETRF; for 1<=i<=N, row i of the -*> matrix was interchanged with row IPIV(i). -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) -*> On exit, if INFO=0, then WORK(1) returns the optimal LWORK. -*> \endverbatim -*> -*> \param[in] LWORK -*> \verbatim -*> LWORK is INTEGER -*> The dimension of the array WORK. LWORK >= max(1,N). -*> For optimal performance LWORK >= N*NB, where NB is -*> the optimal blocksize returned by ILAENV. -*> -*> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal size of the WORK array, returns -*> this value as the first entry of the WORK array, and no error -*> message related to LWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, U(i,i) is exactly zero; the matrix is -*> singular and its inverse could not be computed. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleGEcomputational -* -* ===================================================================== - SUBROUTINE DGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INFO, LDA, LWORK, N -* .. -* .. Array Arguments .. - INTEGER IPIV( * ) - DOUBLE PRECISION A( LDA, * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) -* .. -* .. Local Scalars .. - LOGICAL LQUERY - INTEGER I, IWS, J, JB, JJ, JP, LDWORK, LWKOPT, NB, - $ NBMIN, NN -* .. -* .. External Functions .. - INTEGER ILAENV - EXTERNAL ILAENV -* .. -* .. External Subroutines .. - EXTERNAL DGEMM, DGEMV, DSWAP, DTRSM, DTRTRI, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, MIN -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 - NB = ILAENV( 1, 'DGETRI', ' ', N, -1, -1, -1 ) - LWKOPT = N*NB - WORK( 1 ) = LWKOPT - LQUERY = ( LWORK.EQ.-1 ) - IF( N.LT.0 ) THEN - INFO = -1 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -3 - ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN - INFO = -6 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DGETRI', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - RETURN - END IF -* -* Quick return if possible -* - IF( N.EQ.0 ) - $ RETURN -* -* Form inv(U). If INFO > 0 from DTRTRI, then U is singular, -* and the inverse is not computed. -* - CALL DTRTRI( 'Upper', 'Non-unit', N, A, LDA, INFO ) - IF( INFO.GT.0 ) - $ RETURN -* - NBMIN = 2 - LDWORK = N - IF( NB.GT.1 .AND. NB.LT.N ) THEN - IWS = MAX( LDWORK*NB, 1 ) - IF( LWORK.LT.IWS ) THEN - NB = LWORK / LDWORK - NBMIN = MAX( 2, ILAENV( 2, 'DGETRI', ' ', N, -1, -1, -1 ) ) - END IF - ELSE - IWS = N - END IF -* -* Solve the equation inv(A)*L = inv(U) for inv(A). -* - IF( NB.LT.NBMIN .OR. NB.GE.N ) THEN -* -* Use unblocked code. -* - DO 20 J = N, 1, -1 -* -* Copy current column of L to WORK and replace with zeros. -* - DO 10 I = J + 1, N - WORK( I ) = A( I, J ) - A( I, J ) = ZERO - 10 CONTINUE -* -* Compute current column of inv(A). -* - IF( J.LT.N ) - $ CALL DGEMV( 'No transpose', N, N-J, -ONE, A( 1, J+1 ), - $ LDA, WORK( J+1 ), 1, ONE, A( 1, J ), 1 ) - 20 CONTINUE - ELSE -* -* Use blocked code. -* - NN = ( ( N-1 ) / NB )*NB + 1 - DO 50 J = NN, 1, -NB - JB = MIN( NB, N-J+1 ) -* -* Copy current block column of L to WORK and replace with -* zeros. -* - DO 40 JJ = J, J + JB - 1 - DO 30 I = JJ + 1, N - WORK( I+( JJ-J )*LDWORK ) = A( I, JJ ) - A( I, JJ ) = ZERO - 30 CONTINUE - 40 CONTINUE -* -* Compute current block column of inv(A). -* - IF( J+JB.LE.N ) - $ CALL DGEMM( 'No transpose', 'No transpose', N, JB, - $ N-J-JB+1, -ONE, A( 1, J+JB ), LDA, - $ WORK( J+JB ), LDWORK, ONE, A( 1, J ), LDA ) - CALL DTRSM( 'Right', 'Lower', 'No transpose', 'Unit', N, JB, - $ ONE, WORK( J ), LDWORK, A( 1, J ), LDA ) - 50 CONTINUE - END IF -* -* Apply column interchanges. -* - DO 60 J = N - 1, 1, -1 - JP = IPIV( J ) - IF( JP.NE.J ) - $ CALL DSWAP( N, A( 1, J ), 1, A( 1, JP ), 1 ) - 60 CONTINUE -* - WORK( 1 ) = IWS - RETURN -* -* End of DGETRI -* - END diff --git a/lib/linalg/fortran/dgetrs.f b/lib/linalg/fortran/dgetrs.f deleted file mode 100644 index d3464f685a..0000000000 --- a/lib/linalg/fortran/dgetrs.f +++ /dev/null @@ -1,222 +0,0 @@ -*> \brief \b DGETRS -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DGETRS + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DGETRS( TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER TRANS -* INTEGER INFO, LDA, LDB, N, NRHS -* .. -* .. Array Arguments .. -* INTEGER IPIV( * ) -* DOUBLE PRECISION A( LDA, * ), B( LDB, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DGETRS solves a system of linear equations -*> A * X = B or A**T * X = B -*> with a general N-by-N matrix A using the LU factorization computed -*> by DGETRF. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] TRANS -*> \verbatim -*> TRANS is CHARACTER*1 -*> Specifies the form of the system of equations: -*> = 'N': A * X = B (No transpose) -*> = 'T': A**T* X = B (Transpose) -*> = 'C': A**T* X = B (Conjugate transpose = Transpose) -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in] NRHS -*> \verbatim -*> NRHS is INTEGER -*> The number of right hand sides, i.e., the number of columns -*> of the matrix B. NRHS >= 0. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> The factors L and U from the factorization A = P*L*U -*> as computed by DGETRF. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,N). -*> \endverbatim -*> -*> \param[in] IPIV -*> \verbatim -*> IPIV is INTEGER array, dimension (N) -*> The pivot indices from DGETRF; for 1<=i<=N, row i of the -*> matrix was interchanged with row IPIV(i). -*> \endverbatim -*> -*> \param[in,out] B -*> \verbatim -*> B is DOUBLE PRECISION array, dimension (LDB,NRHS) -*> On entry, the right hand side matrix B. -*> On exit, the solution matrix X. -*> \endverbatim -*> -*> \param[in] LDB -*> \verbatim -*> LDB is INTEGER -*> The leading dimension of the array B. LDB >= max(1,N). -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleGEcomputational -* -* ===================================================================== - SUBROUTINE DGETRS( TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER TRANS - INTEGER INFO, LDA, LDB, N, NRHS -* .. -* .. Array Arguments .. - INTEGER IPIV( * ) - DOUBLE PRECISION A( LDA, * ), B( LDB, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE - PARAMETER ( ONE = 1.0D+0 ) -* .. -* .. Local Scalars .. - LOGICAL NOTRAN -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL DLASWP, DTRSM, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 - NOTRAN = LSAME( TRANS, 'N' ) - IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) .AND. .NOT. - $ LSAME( TRANS, 'C' ) ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( NRHS.LT.0 ) THEN - INFO = -3 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -5 - ELSE IF( LDB.LT.MAX( 1, N ) ) THEN - INFO = -8 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DGETRS', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( N.EQ.0 .OR. NRHS.EQ.0 ) - $ RETURN -* - IF( NOTRAN ) THEN -* -* Solve A * X = B. -* -* Apply row interchanges to the right hand sides. -* - CALL DLASWP( NRHS, B, LDB, 1, N, IPIV, 1 ) -* -* Solve L*X = B, overwriting B with X. -* - CALL DTRSM( 'Left', 'Lower', 'No transpose', 'Unit', N, NRHS, - $ ONE, A, LDA, B, LDB ) -* -* Solve U*X = B, overwriting B with X. -* - CALL DTRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', N, - $ NRHS, ONE, A, LDA, B, LDB ) - ELSE -* -* Solve A**T * X = B. -* -* Solve U**T *X = B, overwriting B with X. -* - CALL DTRSM( 'Left', 'Upper', 'Transpose', 'Non-unit', N, NRHS, - $ ONE, A, LDA, B, LDB ) -* -* Solve L**T *X = B, overwriting B with X. -* - CALL DTRSM( 'Left', 'Lower', 'Transpose', 'Unit', N, NRHS, ONE, - $ A, LDA, B, LDB ) -* -* Apply row interchanges to the solution vectors. -* - CALL DLASWP( NRHS, B, LDB, 1, N, IPIV, -1 ) - END IF -* - RETURN -* -* End of DGETRS -* - END diff --git a/lib/linalg/fortran/disnan.f b/lib/linalg/fortran/disnan.f deleted file mode 100644 index e621b2589c..0000000000 --- a/lib/linalg/fortran/disnan.f +++ /dev/null @@ -1,77 +0,0 @@ -*> \brief \b DISNAN tests input for NaN. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DISNAN + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* LOGICAL FUNCTION DISNAN( DIN ) -* -* .. Scalar Arguments .. -* DOUBLE PRECISION, INTENT(IN) :: DIN -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DISNAN returns .TRUE. if its argument is NaN, and .FALSE. -*> otherwise. To be replaced by the Fortran 2003 intrinsic in the -*> future. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] DIN -*> \verbatim -*> DIN is DOUBLE PRECISION -*> Input to test for NaN. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup OTHERauxiliary -* -* ===================================================================== - LOGICAL FUNCTION DISNAN( DIN ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - DOUBLE PRECISION, INTENT(IN) :: DIN -* .. -* -* ===================================================================== -* -* .. External Functions .. - LOGICAL DLAISNAN - EXTERNAL DLAISNAN -* .. -* .. Executable Statements .. - DISNAN = DLAISNAN(DIN,DIN) - RETURN - END diff --git a/lib/linalg/fortran/dlabad.f b/lib/linalg/fortran/dlabad.f deleted file mode 100644 index 95b35e53b8..0000000000 --- a/lib/linalg/fortran/dlabad.f +++ /dev/null @@ -1,102 +0,0 @@ -*> \brief \b DLABAD -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLABAD + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLABAD( SMALL, LARGE ) -* -* .. Scalar Arguments .. -* DOUBLE PRECISION LARGE, SMALL -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLABAD takes as input the values computed by DLAMCH for underflow and -*> overflow, and returns the square root of each of these values if the -*> log of LARGE is sufficiently large. This subroutine is intended to -*> identify machines with a large exponent range, such as the Crays, and -*> redefine the underflow and overflow limits to be the square roots of -*> the values computed by DLAMCH. This subroutine is needed because -*> DLAMCH does not compensate for poor arithmetic in the upper half of -*> the exponent range, as is found on a Cray. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in,out] SMALL -*> \verbatim -*> SMALL is DOUBLE PRECISION -*> On entry, the underflow threshold as computed by DLAMCH. -*> On exit, if LOG10(LARGE) is sufficiently large, the square -*> root of SMALL, otherwise unchanged. -*> \endverbatim -*> -*> \param[in,out] LARGE -*> \verbatim -*> LARGE is DOUBLE PRECISION -*> On entry, the overflow threshold as computed by DLAMCH. -*> On exit, if LOG10(LARGE) is sufficiently large, the square -*> root of LARGE, otherwise unchanged. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup OTHERauxiliary -* -* ===================================================================== - SUBROUTINE DLABAD( SMALL, LARGE ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - DOUBLE PRECISION LARGE, SMALL -* .. -* -* ===================================================================== -* -* .. Intrinsic Functions .. - INTRINSIC LOG10, SQRT -* .. -* .. Executable Statements .. -* -* If it looks like we're on a Cray, take the square root of -* SMALL and LARGE to avoid overflow and underflow problems. -* - IF( LOG10( LARGE ).GT.2000.D0 ) THEN - SMALL = SQRT( SMALL ) - LARGE = SQRT( LARGE ) - END IF -* - RETURN -* -* End of DLABAD -* - END diff --git a/lib/linalg/fortran/dlabrd.f b/lib/linalg/fortran/dlabrd.f deleted file mode 100644 index 86dfc10c7c..0000000000 --- a/lib/linalg/fortran/dlabrd.f +++ /dev/null @@ -1,378 +0,0 @@ -*> \brief \b DLABRD reduces the first nb rows and columns of a general matrix to a bidiagonal form. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLABRD + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLABRD( M, N, NB, A, LDA, D, E, TAUQ, TAUP, X, LDX, Y, -* LDY ) -* -* .. Scalar Arguments .. -* INTEGER LDA, LDX, LDY, M, N, NB -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), TAUP( * ), -* $ TAUQ( * ), X( LDX, * ), Y( LDY, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLABRD reduces the first NB rows and columns of a real general -*> m by n matrix A to upper or lower bidiagonal form by an orthogonal -*> transformation Q**T * A * P, and returns the matrices X and Y which -*> are needed to apply the transformation to the unreduced part of A. -*> -*> If m >= n, A is reduced to upper bidiagonal form; if m < n, to lower -*> bidiagonal form. -*> -*> This is an auxiliary routine called by DGEBRD -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows in the matrix A. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns in the matrix A. -*> \endverbatim -*> -*> \param[in] NB -*> \verbatim -*> NB is INTEGER -*> The number of leading rows and columns of A to be reduced. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the m by n general matrix to be reduced. -*> On exit, the first NB rows and columns of the matrix are -*> overwritten; the rest of the array is unchanged. -*> If m >= n, elements on and below the diagonal in the first NB -*> columns, with the array TAUQ, represent the orthogonal -*> matrix Q as a product of elementary reflectors; and -*> elements above the diagonal in the first NB rows, with the -*> array TAUP, represent the orthogonal matrix P as a product -*> of elementary reflectors. -*> If m < n, elements below the diagonal in the first NB -*> columns, with the array TAUQ, represent the orthogonal -*> matrix Q as a product of elementary reflectors, and -*> elements on and above the diagonal in the first NB rows, -*> with the array TAUP, represent the orthogonal matrix P as -*> a product of elementary reflectors. -*> See Further Details. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,M). -*> \endverbatim -*> -*> \param[out] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension (NB) -*> The diagonal elements of the first NB rows and columns of -*> the reduced matrix. D(i) = A(i,i). -*> \endverbatim -*> -*> \param[out] E -*> \verbatim -*> E is DOUBLE PRECISION array, dimension (NB) -*> The off-diagonal elements of the first NB rows and columns of -*> the reduced matrix. -*> \endverbatim -*> -*> \param[out] TAUQ -*> \verbatim -*> TAUQ is DOUBLE PRECISION array, dimension (NB) -*> The scalar factors of the elementary reflectors which -*> represent the orthogonal matrix Q. See Further Details. -*> \endverbatim -*> -*> \param[out] TAUP -*> \verbatim -*> TAUP is DOUBLE PRECISION array, dimension (NB) -*> The scalar factors of the elementary reflectors which -*> represent the orthogonal matrix P. See Further Details. -*> \endverbatim -*> -*> \param[out] X -*> \verbatim -*> X is DOUBLE PRECISION array, dimension (LDX,NB) -*> The m-by-nb matrix X required to update the unreduced part -*> of A. -*> \endverbatim -*> -*> \param[in] LDX -*> \verbatim -*> LDX is INTEGER -*> The leading dimension of the array X. LDX >= max(1,M). -*> \endverbatim -*> -*> \param[out] Y -*> \verbatim -*> Y is DOUBLE PRECISION array, dimension (LDY,NB) -*> The n-by-nb matrix Y required to update the unreduced part -*> of A. -*> \endverbatim -*> -*> \param[in] LDY -*> \verbatim -*> LDY is INTEGER -*> The leading dimension of the array Y. LDY >= max(1,N). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleOTHERauxiliary -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> The matrices Q and P are represented as products of elementary -*> reflectors: -*> -*> Q = H(1) H(2) . . . H(nb) and P = G(1) G(2) . . . G(nb) -*> -*> Each H(i) and G(i) has the form: -*> -*> H(i) = I - tauq * v * v**T and G(i) = I - taup * u * u**T -*> -*> where tauq and taup are real scalars, and v and u are real vectors. -*> -*> If m >= n, v(1:i-1) = 0, v(i) = 1, and v(i:m) is stored on exit in -*> A(i:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+1:n) is stored on exit in -*> A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i). -*> -*> If m < n, v(1:i) = 0, v(i+1) = 1, and v(i+1:m) is stored on exit in -*> A(i+2:m,i); u(1:i-1) = 0, u(i) = 1, and u(i:n) is stored on exit in -*> A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i). -*> -*> The elements of the vectors v and u together form the m-by-nb matrix -*> V and the nb-by-n matrix U**T which are needed, with X and Y, to apply -*> the transformation to the unreduced part of the matrix, using a block -*> update of the form: A := A - V*Y**T - X*U**T. -*> -*> The contents of A on exit are illustrated by the following examples -*> with nb = 2: -*> -*> m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n): -*> -*> ( 1 1 u1 u1 u1 ) ( 1 u1 u1 u1 u1 u1 ) -*> ( v1 1 1 u2 u2 ) ( 1 1 u2 u2 u2 u2 ) -*> ( v1 v2 a a a ) ( v1 1 a a a a ) -*> ( v1 v2 a a a ) ( v1 v2 a a a a ) -*> ( v1 v2 a a a ) ( v1 v2 a a a a ) -*> ( v1 v2 a a a ) -*> -*> where a denotes an element of the original matrix which is unchanged, -*> vi denotes an element of the vector defining H(i), and ui an element -*> of the vector defining G(i). -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DLABRD( M, N, NB, A, LDA, D, E, TAUQ, TAUP, X, LDX, Y, - $ LDY ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER LDA, LDX, LDY, M, N, NB -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), TAUP( * ), - $ TAUQ( * ), X( LDX, * ), Y( LDY, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) -* .. -* .. Local Scalars .. - INTEGER I -* .. -* .. External Subroutines .. - EXTERNAL DGEMV, DLARFG, DSCAL -* .. -* .. Intrinsic Functions .. - INTRINSIC MIN -* .. -* .. Executable Statements .. -* -* Quick return if possible -* - IF( M.LE.0 .OR. N.LE.0 ) - $ RETURN -* - IF( M.GE.N ) THEN -* -* Reduce to upper bidiagonal form -* - DO 10 I = 1, NB -* -* Update A(i:m,i) -* - CALL DGEMV( 'No transpose', M-I+1, I-1, -ONE, A( I, 1 ), - $ LDA, Y( I, 1 ), LDY, ONE, A( I, I ), 1 ) - CALL DGEMV( 'No transpose', M-I+1, I-1, -ONE, X( I, 1 ), - $ LDX, A( 1, I ), 1, ONE, A( I, I ), 1 ) -* -* Generate reflection Q(i) to annihilate A(i+1:m,i) -* - CALL DLARFG( M-I+1, A( I, I ), A( MIN( I+1, M ), I ), 1, - $ TAUQ( I ) ) - D( I ) = A( I, I ) - IF( I.LT.N ) THEN - A( I, I ) = ONE -* -* Compute Y(i+1:n,i) -* - CALL DGEMV( 'Transpose', M-I+1, N-I, ONE, A( I, I+1 ), - $ LDA, A( I, I ), 1, ZERO, Y( I+1, I ), 1 ) - CALL DGEMV( 'Transpose', M-I+1, I-1, ONE, A( I, 1 ), LDA, - $ A( I, I ), 1, ZERO, Y( 1, I ), 1 ) - CALL DGEMV( 'No transpose', N-I, I-1, -ONE, Y( I+1, 1 ), - $ LDY, Y( 1, I ), 1, ONE, Y( I+1, I ), 1 ) - CALL DGEMV( 'Transpose', M-I+1, I-1, ONE, X( I, 1 ), LDX, - $ A( I, I ), 1, ZERO, Y( 1, I ), 1 ) - CALL DGEMV( 'Transpose', I-1, N-I, -ONE, A( 1, I+1 ), - $ LDA, Y( 1, I ), 1, ONE, Y( I+1, I ), 1 ) - CALL DSCAL( N-I, TAUQ( I ), Y( I+1, I ), 1 ) -* -* Update A(i,i+1:n) -* - CALL DGEMV( 'No transpose', N-I, I, -ONE, Y( I+1, 1 ), - $ LDY, A( I, 1 ), LDA, ONE, A( I, I+1 ), LDA ) - CALL DGEMV( 'Transpose', I-1, N-I, -ONE, A( 1, I+1 ), - $ LDA, X( I, 1 ), LDX, ONE, A( I, I+1 ), LDA ) -* -* Generate reflection P(i) to annihilate A(i,i+2:n) -* - CALL DLARFG( N-I, A( I, I+1 ), A( I, MIN( I+2, N ) ), - $ LDA, TAUP( I ) ) - E( I ) = A( I, I+1 ) - A( I, I+1 ) = ONE -* -* Compute X(i+1:m,i) -* - CALL DGEMV( 'No transpose', M-I, N-I, ONE, A( I+1, I+1 ), - $ LDA, A( I, I+1 ), LDA, ZERO, X( I+1, I ), 1 ) - CALL DGEMV( 'Transpose', N-I, I, ONE, Y( I+1, 1 ), LDY, - $ A( I, I+1 ), LDA, ZERO, X( 1, I ), 1 ) - CALL DGEMV( 'No transpose', M-I, I, -ONE, A( I+1, 1 ), - $ LDA, X( 1, I ), 1, ONE, X( I+1, I ), 1 ) - CALL DGEMV( 'No transpose', I-1, N-I, ONE, A( 1, I+1 ), - $ LDA, A( I, I+1 ), LDA, ZERO, X( 1, I ), 1 ) - CALL DGEMV( 'No transpose', M-I, I-1, -ONE, X( I+1, 1 ), - $ LDX, X( 1, I ), 1, ONE, X( I+1, I ), 1 ) - CALL DSCAL( M-I, TAUP( I ), X( I+1, I ), 1 ) - END IF - 10 CONTINUE - ELSE -* -* Reduce to lower bidiagonal form -* - DO 20 I = 1, NB -* -* Update A(i,i:n) -* - CALL DGEMV( 'No transpose', N-I+1, I-1, -ONE, Y( I, 1 ), - $ LDY, A( I, 1 ), LDA, ONE, A( I, I ), LDA ) - CALL DGEMV( 'Transpose', I-1, N-I+1, -ONE, A( 1, I ), LDA, - $ X( I, 1 ), LDX, ONE, A( I, I ), LDA ) -* -* Generate reflection P(i) to annihilate A(i,i+1:n) -* - CALL DLARFG( N-I+1, A( I, I ), A( I, MIN( I+1, N ) ), LDA, - $ TAUP( I ) ) - D( I ) = A( I, I ) - IF( I.LT.M ) THEN - A( I, I ) = ONE -* -* Compute X(i+1:m,i) -* - CALL DGEMV( 'No transpose', M-I, N-I+1, ONE, A( I+1, I ), - $ LDA, A( I, I ), LDA, ZERO, X( I+1, I ), 1 ) - CALL DGEMV( 'Transpose', N-I+1, I-1, ONE, Y( I, 1 ), LDY, - $ A( I, I ), LDA, ZERO, X( 1, I ), 1 ) - CALL DGEMV( 'No transpose', M-I, I-1, -ONE, A( I+1, 1 ), - $ LDA, X( 1, I ), 1, ONE, X( I+1, I ), 1 ) - CALL DGEMV( 'No transpose', I-1, N-I+1, ONE, A( 1, I ), - $ LDA, A( I, I ), LDA, ZERO, X( 1, I ), 1 ) - CALL DGEMV( 'No transpose', M-I, I-1, -ONE, X( I+1, 1 ), - $ LDX, X( 1, I ), 1, ONE, X( I+1, I ), 1 ) - CALL DSCAL( M-I, TAUP( I ), X( I+1, I ), 1 ) -* -* Update A(i+1:m,i) -* - CALL DGEMV( 'No transpose', M-I, I-1, -ONE, A( I+1, 1 ), - $ LDA, Y( I, 1 ), LDY, ONE, A( I+1, I ), 1 ) - CALL DGEMV( 'No transpose', M-I, I, -ONE, X( I+1, 1 ), - $ LDX, A( 1, I ), 1, ONE, A( I+1, I ), 1 ) -* -* Generate reflection Q(i) to annihilate A(i+2:m,i) -* - CALL DLARFG( M-I, A( I+1, I ), A( MIN( I+2, M ), I ), 1, - $ TAUQ( I ) ) - E( I ) = A( I+1, I ) - A( I+1, I ) = ONE -* -* Compute Y(i+1:n,i) -* - CALL DGEMV( 'Transpose', M-I, N-I, ONE, A( I+1, I+1 ), - $ LDA, A( I+1, I ), 1, ZERO, Y( I+1, I ), 1 ) - CALL DGEMV( 'Transpose', M-I, I-1, ONE, A( I+1, 1 ), LDA, - $ A( I+1, I ), 1, ZERO, Y( 1, I ), 1 ) - CALL DGEMV( 'No transpose', N-I, I-1, -ONE, Y( I+1, 1 ), - $ LDY, Y( 1, I ), 1, ONE, Y( I+1, I ), 1 ) - CALL DGEMV( 'Transpose', M-I, I, ONE, X( I+1, 1 ), LDX, - $ A( I+1, I ), 1, ZERO, Y( 1, I ), 1 ) - CALL DGEMV( 'Transpose', I, N-I, -ONE, A( 1, I+1 ), LDA, - $ Y( 1, I ), 1, ONE, Y( I+1, I ), 1 ) - CALL DSCAL( N-I, TAUQ( I ), Y( I+1, I ), 1 ) - END IF - 20 CONTINUE - END IF - RETURN -* -* End of DLABRD -* - END diff --git a/lib/linalg/fortran/dlacn2.f b/lib/linalg/fortran/dlacn2.f deleted file mode 100644 index ee2e7ca266..0000000000 --- a/lib/linalg/fortran/dlacn2.f +++ /dev/null @@ -1,304 +0,0 @@ -*> \brief \b DLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLACN2 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLACN2( N, V, X, ISGN, EST, KASE, ISAVE ) -* -* .. Scalar Arguments .. -* INTEGER KASE, N -* DOUBLE PRECISION EST -* .. -* .. Array Arguments .. -* INTEGER ISGN( * ), ISAVE( 3 ) -* DOUBLE PRECISION V( * ), X( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLACN2 estimates the 1-norm of a square, real matrix A. -*> Reverse communication is used for evaluating matrix-vector products. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrix. N >= 1. -*> \endverbatim -*> -*> \param[out] V -*> \verbatim -*> V is DOUBLE PRECISION array, dimension (N) -*> On the final return, V = A*W, where EST = norm(V)/norm(W) -*> (W is not returned). -*> \endverbatim -*> -*> \param[in,out] X -*> \verbatim -*> X is DOUBLE PRECISION array, dimension (N) -*> On an intermediate return, X should be overwritten by -*> A * X, if KASE=1, -*> A**T * X, if KASE=2, -*> and DLACN2 must be re-called with all the other parameters -*> unchanged. -*> \endverbatim -*> -*> \param[out] ISGN -*> \verbatim -*> ISGN is INTEGER array, dimension (N) -*> \endverbatim -*> -*> \param[in,out] EST -*> \verbatim -*> EST is DOUBLE PRECISION -*> On entry with KASE = 1 or 2 and ISAVE(1) = 3, EST should be -*> unchanged from the previous call to DLACN2. -*> On exit, EST is an estimate (a lower bound) for norm(A). -*> \endverbatim -*> -*> \param[in,out] KASE -*> \verbatim -*> KASE is INTEGER -*> On the initial call to DLACN2, KASE should be 0. -*> On an intermediate return, KASE will be 1 or 2, indicating -*> whether X should be overwritten by A * X or A**T * X. -*> On the final return from DLACN2, KASE will again be 0. -*> \endverbatim -*> -*> \param[in,out] ISAVE -*> \verbatim -*> ISAVE is INTEGER array, dimension (3) -*> ISAVE is used to save variables between calls to DLACN2 -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleOTHERauxiliary -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> Originally named SONEST, dated March 16, 1988. -*> -*> This is a thread safe version of DLACON, which uses the array ISAVE -*> in place of a SAVE statement, as follows: -*> -*> DLACON DLACN2 -*> JUMP ISAVE(1) -*> J ISAVE(2) -*> ITER ISAVE(3) -*> \endverbatim -* -*> \par Contributors: -* ================== -*> -*> Nick Higham, University of Manchester -* -*> \par References: -* ================ -*> -*> N.J. Higham, "FORTRAN codes for estimating the one-norm of -*> a real or complex matrix, with applications to condition estimation", -*> ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988. -*> -* ===================================================================== - SUBROUTINE DLACN2( N, V, X, ISGN, EST, KASE, ISAVE ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER KASE, N - DOUBLE PRECISION EST -* .. -* .. Array Arguments .. - INTEGER ISGN( * ), ISAVE( 3 ) - DOUBLE PRECISION V( * ), X( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - INTEGER ITMAX - PARAMETER ( ITMAX = 5 ) - DOUBLE PRECISION ZERO, ONE, TWO - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0 ) -* .. -* .. Local Scalars .. - INTEGER I, JLAST - DOUBLE PRECISION ALTSGN, ESTOLD, TEMP, XS -* .. -* .. External Functions .. - INTEGER IDAMAX - DOUBLE PRECISION DASUM - EXTERNAL IDAMAX, DASUM -* .. -* .. External Subroutines .. - EXTERNAL DCOPY -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, DBLE, NINT -* .. -* .. Executable Statements .. -* - IF( KASE.EQ.0 ) THEN - DO 10 I = 1, N - X( I ) = ONE / DBLE( N ) - 10 CONTINUE - KASE = 1 - ISAVE( 1 ) = 1 - RETURN - END IF -* - GO TO ( 20, 40, 70, 110, 140 )ISAVE( 1 ) -* -* ................ ENTRY (ISAVE( 1 ) = 1) -* FIRST ITERATION. X HAS BEEN OVERWRITTEN BY A*X. -* - 20 CONTINUE - IF( N.EQ.1 ) THEN - V( 1 ) = X( 1 ) - EST = ABS( V( 1 ) ) -* ... QUIT - GO TO 150 - END IF - EST = DASUM( N, X, 1 ) -* - DO 30 I = 1, N - IF( X(I).GE.ZERO ) THEN - X(I) = ONE - ELSE - X(I) = -ONE - END IF - ISGN( I ) = NINT( X( I ) ) - 30 CONTINUE - KASE = 2 - ISAVE( 1 ) = 2 - RETURN -* -* ................ ENTRY (ISAVE( 1 ) = 2) -* FIRST ITERATION. X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X. -* - 40 CONTINUE - ISAVE( 2 ) = IDAMAX( N, X, 1 ) - ISAVE( 3 ) = 2 -* -* MAIN LOOP - ITERATIONS 2,3,...,ITMAX. -* - 50 CONTINUE - DO 60 I = 1, N - X( I ) = ZERO - 60 CONTINUE - X( ISAVE( 2 ) ) = ONE - KASE = 1 - ISAVE( 1 ) = 3 - RETURN -* -* ................ ENTRY (ISAVE( 1 ) = 3) -* X HAS BEEN OVERWRITTEN BY A*X. -* - 70 CONTINUE - CALL DCOPY( N, X, 1, V, 1 ) - ESTOLD = EST - EST = DASUM( N, V, 1 ) - DO 80 I = 1, N - IF( X(I).GE.ZERO ) THEN - XS = ONE - ELSE - XS = -ONE - END IF - IF( NINT( XS ).NE.ISGN( I ) ) - $ GO TO 90 - 80 CONTINUE -* REPEATED SIGN VECTOR DETECTED, HENCE ALGORITHM HAS CONVERGED. - GO TO 120 -* - 90 CONTINUE -* TEST FOR CYCLING. - IF( EST.LE.ESTOLD ) - $ GO TO 120 -* - DO 100 I = 1, N - IF( X(I).GE.ZERO ) THEN - X(I) = ONE - ELSE - X(I) = -ONE - END IF - ISGN( I ) = NINT( X( I ) ) - 100 CONTINUE - KASE = 2 - ISAVE( 1 ) = 4 - RETURN -* -* ................ ENTRY (ISAVE( 1 ) = 4) -* X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X. -* - 110 CONTINUE - JLAST = ISAVE( 2 ) - ISAVE( 2 ) = IDAMAX( N, X, 1 ) - IF( ( X( JLAST ).NE.ABS( X( ISAVE( 2 ) ) ) ) .AND. - $ ( ISAVE( 3 ).LT.ITMAX ) ) THEN - ISAVE( 3 ) = ISAVE( 3 ) + 1 - GO TO 50 - END IF -* -* ITERATION COMPLETE. FINAL STAGE. -* - 120 CONTINUE - ALTSGN = ONE - DO 130 I = 1, N - X( I ) = ALTSGN*( ONE+DBLE( I-1 ) / DBLE( N-1 ) ) - ALTSGN = -ALTSGN - 130 CONTINUE - KASE = 1 - ISAVE( 1 ) = 5 - RETURN -* -* ................ ENTRY (ISAVE( 1 ) = 5) -* X HAS BEEN OVERWRITTEN BY A*X. -* - 140 CONTINUE - TEMP = TWO*( DASUM( N, X, 1 ) / DBLE( 3*N ) ) - IF( TEMP.GT.EST ) THEN - CALL DCOPY( N, X, 1, V, 1 ) - EST = TEMP - END IF -* - 150 CONTINUE - KASE = 0 - RETURN -* -* End of DLACN2 -* - END diff --git a/lib/linalg/fortran/dlacpy.f b/lib/linalg/fortran/dlacpy.f deleted file mode 100644 index 917aa1e2a2..0000000000 --- a/lib/linalg/fortran/dlacpy.f +++ /dev/null @@ -1,153 +0,0 @@ -*> \brief \b DLACPY copies all or part of one two-dimensional array to another. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLACPY + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLACPY( UPLO, M, N, A, LDA, B, LDB ) -* -* .. Scalar Arguments .. -* CHARACTER UPLO -* INTEGER LDA, LDB, M, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), B( LDB, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLACPY copies all or part of a two-dimensional matrix A to another -*> matrix B. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> Specifies the part of the matrix A to be copied to B. -*> = 'U': Upper triangular part -*> = 'L': Lower triangular part -*> Otherwise: All of the matrix A -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix A. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> The m by n matrix A. If UPLO = 'U', only the upper triangle -*> or trapezoid is accessed; if UPLO = 'L', only the lower -*> triangle or trapezoid is accessed. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,M). -*> \endverbatim -*> -*> \param[out] B -*> \verbatim -*> B is DOUBLE PRECISION array, dimension (LDB,N) -*> On exit, B = A in the locations specified by UPLO. -*> \endverbatim -*> -*> \param[in] LDB -*> \verbatim -*> LDB is INTEGER -*> The leading dimension of the array B. LDB >= max(1,M). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup OTHERauxiliary -* -* ===================================================================== - SUBROUTINE DLACPY( UPLO, M, N, A, LDA, B, LDB ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER UPLO - INTEGER LDA, LDB, M, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), B( LDB, * ) -* .. -* -* ===================================================================== -* -* .. Local Scalars .. - INTEGER I, J -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. Intrinsic Functions .. - INTRINSIC MIN -* .. -* .. Executable Statements .. -* - IF( LSAME( UPLO, 'U' ) ) THEN - DO 20 J = 1, N - DO 10 I = 1, MIN( J, M ) - B( I, J ) = A( I, J ) - 10 CONTINUE - 20 CONTINUE - ELSE IF( LSAME( UPLO, 'L' ) ) THEN - DO 40 J = 1, N - DO 30 I = J, M - B( I, J ) = A( I, J ) - 30 CONTINUE - 40 CONTINUE - ELSE - DO 60 J = 1, N - DO 50 I = 1, M - B( I, J ) = A( I, J ) - 50 CONTINUE - 60 CONTINUE - END IF - RETURN -* -* End of DLACPY -* - END diff --git a/lib/linalg/fortran/dladiv.f b/lib/linalg/fortran/dladiv.f deleted file mode 100644 index 4265618fed..0000000000 --- a/lib/linalg/fortran/dladiv.f +++ /dev/null @@ -1,251 +0,0 @@ -*> \brief \b DLADIV performs complex division in real arithmetic, avoiding unnecessary overflow. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLADIV + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLADIV( A, B, C, D, P, Q ) -* -* .. Scalar Arguments .. -* DOUBLE PRECISION A, B, C, D, P, Q -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLADIV performs complex division in real arithmetic -*> -*> a + i*b -*> p + i*q = --------- -*> c + i*d -*> -*> The algorithm is due to Michael Baudin and Robert L. Smith -*> and can be found in the paper -*> "A Robust Complex Division in Scilab" -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] A -*> \verbatim -*> A is DOUBLE PRECISION -*> \endverbatim -*> -*> \param[in] B -*> \verbatim -*> B is DOUBLE PRECISION -*> \endverbatim -*> -*> \param[in] C -*> \verbatim -*> C is DOUBLE PRECISION -*> \endverbatim -*> -*> \param[in] D -*> \verbatim -*> D is DOUBLE PRECISION -*> The scalars a, b, c, and d in the above expression. -*> \endverbatim -*> -*> \param[out] P -*> \verbatim -*> P is DOUBLE PRECISION -*> \endverbatim -*> -*> \param[out] Q -*> \verbatim -*> Q is DOUBLE PRECISION -*> The scalars p and q in the above expression. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleOTHERauxiliary -* -* ===================================================================== - SUBROUTINE DLADIV( A, B, C, D, P, Q ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - DOUBLE PRECISION A, B, C, D, P, Q -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION BS - PARAMETER ( BS = 2.0D0 ) - DOUBLE PRECISION HALF - PARAMETER ( HALF = 0.5D0 ) - DOUBLE PRECISION TWO - PARAMETER ( TWO = 2.0D0 ) -* -* .. Local Scalars .. - DOUBLE PRECISION AA, BB, CC, DD, AB, CD, S, OV, UN, BE, EPS -* .. -* .. External Functions .. - DOUBLE PRECISION DLAMCH - EXTERNAL DLAMCH -* .. -* .. External Subroutines .. - EXTERNAL DLADIV1 -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, MAX -* .. -* .. Executable Statements .. -* - AA = A - BB = B - CC = C - DD = D - AB = MAX( ABS(A), ABS(B) ) - CD = MAX( ABS(C), ABS(D) ) - S = 1.0D0 - - OV = DLAMCH( 'Overflow threshold' ) - UN = DLAMCH( 'Safe minimum' ) - EPS = DLAMCH( 'Epsilon' ) - BE = BS / (EPS*EPS) - - IF( AB >= HALF*OV ) THEN - AA = HALF * AA - BB = HALF * BB - S = TWO * S - END IF - IF( CD >= HALF*OV ) THEN - CC = HALF * CC - DD = HALF * DD - S = HALF * S - END IF - IF( AB <= UN*BS/EPS ) THEN - AA = AA * BE - BB = BB * BE - S = S / BE - END IF - IF( CD <= UN*BS/EPS ) THEN - CC = CC * BE - DD = DD * BE - S = S * BE - END IF - IF( ABS( D ).LE.ABS( C ) ) THEN - CALL DLADIV1(AA, BB, CC, DD, P, Q) - ELSE - CALL DLADIV1(BB, AA, DD, CC, P, Q) - Q = -Q - END IF - P = P * S - Q = Q * S -* - RETURN -* -* End of DLADIV -* - END - -*> \ingroup doubleOTHERauxiliary - - - SUBROUTINE DLADIV1( A, B, C, D, P, Q ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - DOUBLE PRECISION A, B, C, D, P, Q -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE - PARAMETER ( ONE = 1.0D0 ) -* -* .. Local Scalars .. - DOUBLE PRECISION R, T -* .. -* .. External Functions .. - DOUBLE PRECISION DLADIV2 - EXTERNAL DLADIV2 -* .. -* .. Executable Statements .. -* - R = D / C - T = ONE / (C + D * R) - P = DLADIV2(A, B, C, D, R, T) - A = -A - Q = DLADIV2(B, A, C, D, R, T) -* - RETURN -* -* End of DLADIV1 -* - END - -*> \ingroup doubleOTHERauxiliary - - DOUBLE PRECISION FUNCTION DLADIV2( A, B, C, D, R, T ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - DOUBLE PRECISION A, B, C, D, R, T -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO - PARAMETER ( ZERO = 0.0D0 ) -* -* .. Local Scalars .. - DOUBLE PRECISION BR -* .. -* .. Executable Statements .. -* - IF( R.NE.ZERO ) THEN - BR = B * R - IF( BR.NE.ZERO ) THEN - DLADIV2 = (A + BR) * T - ELSE - DLADIV2 = A * T + (B * T) * R - END IF - ELSE - DLADIV2 = (A + D * (B / C)) * T - END IF -* - RETURN -* -* End of DLADIV2 -* - END diff --git a/lib/linalg/fortran/dlae2.f b/lib/linalg/fortran/dlae2.f deleted file mode 100644 index a0e3971b41..0000000000 --- a/lib/linalg/fortran/dlae2.f +++ /dev/null @@ -1,182 +0,0 @@ -*> \brief \b DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLAE2 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLAE2( A, B, C, RT1, RT2 ) -* -* .. Scalar Arguments .. -* DOUBLE PRECISION A, B, C, RT1, RT2 -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix -*> [ A B ] -*> [ B C ]. -*> On return, RT1 is the eigenvalue of larger absolute value, and RT2 -*> is the eigenvalue of smaller absolute value. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] A -*> \verbatim -*> A is DOUBLE PRECISION -*> The (1,1) element of the 2-by-2 matrix. -*> \endverbatim -*> -*> \param[in] B -*> \verbatim -*> B is DOUBLE PRECISION -*> The (1,2) and (2,1) elements of the 2-by-2 matrix. -*> \endverbatim -*> -*> \param[in] C -*> \verbatim -*> C is DOUBLE PRECISION -*> The (2,2) element of the 2-by-2 matrix. -*> \endverbatim -*> -*> \param[out] RT1 -*> \verbatim -*> RT1 is DOUBLE PRECISION -*> The eigenvalue of larger absolute value. -*> \endverbatim -*> -*> \param[out] RT2 -*> \verbatim -*> RT2 is DOUBLE PRECISION -*> The eigenvalue of smaller absolute value. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup OTHERauxiliary -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> RT1 is accurate to a few ulps barring over/underflow. -*> -*> RT2 may be inaccurate if there is massive cancellation in the -*> determinant A*C-B*B; higher precision or correctly rounded or -*> correctly truncated arithmetic would be needed to compute RT2 -*> accurately in all cases. -*> -*> Overflow is possible only if RT1 is within a factor of 5 of overflow. -*> Underflow is harmless if the input data is 0 or exceeds -*> underflow_threshold / macheps. -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DLAE2( A, B, C, RT1, RT2 ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - DOUBLE PRECISION A, B, C, RT1, RT2 -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE - PARAMETER ( ONE = 1.0D0 ) - DOUBLE PRECISION TWO - PARAMETER ( TWO = 2.0D0 ) - DOUBLE PRECISION ZERO - PARAMETER ( ZERO = 0.0D0 ) - DOUBLE PRECISION HALF - PARAMETER ( HALF = 0.5D0 ) -* .. -* .. Local Scalars .. - DOUBLE PRECISION AB, ACMN, ACMX, ADF, DF, RT, SM, TB -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, SQRT -* .. -* .. Executable Statements .. -* -* Compute the eigenvalues -* - SM = A + C - DF = A - C - ADF = ABS( DF ) - TB = B + B - AB = ABS( TB ) - IF( ABS( A ).GT.ABS( C ) ) THEN - ACMX = A - ACMN = C - ELSE - ACMX = C - ACMN = A - END IF - IF( ADF.GT.AB ) THEN - RT = ADF*SQRT( ONE+( AB / ADF )**2 ) - ELSE IF( ADF.LT.AB ) THEN - RT = AB*SQRT( ONE+( ADF / AB )**2 ) - ELSE -* -* Includes case AB=ADF=0 -* - RT = AB*SQRT( TWO ) - END IF - IF( SM.LT.ZERO ) THEN - RT1 = HALF*( SM-RT ) -* -* Order of execution important. -* To get fully accurate smaller eigenvalue, -* next line needs to be executed in higher precision. -* - RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B - ELSE IF( SM.GT.ZERO ) THEN - RT1 = HALF*( SM+RT ) -* -* Order of execution important. -* To get fully accurate smaller eigenvalue, -* next line needs to be executed in higher precision. -* - RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B - ELSE -* -* Includes case RT1 = RT2 = 0 -* - RT1 = HALF*RT - RT2 = -HALF*RT - END IF - RETURN -* -* End of DLAE2 -* - END diff --git a/lib/linalg/fortran/dlaed0.f b/lib/linalg/fortran/dlaed0.f deleted file mode 100644 index fe3b6249e9..0000000000 --- a/lib/linalg/fortran/dlaed0.f +++ /dev/null @@ -1,431 +0,0 @@ -*> \brief \b DLAED0 used by DSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLAED0 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, -* WORK, IWORK, INFO ) -* -* .. Scalar Arguments .. -* INTEGER ICOMPQ, INFO, LDQ, LDQS, N, QSIZ -* .. -* .. Array Arguments .. -* INTEGER IWORK( * ) -* DOUBLE PRECISION D( * ), E( * ), Q( LDQ, * ), QSTORE( LDQS, * ), -* $ WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLAED0 computes all eigenvalues and corresponding eigenvectors of a -*> symmetric tridiagonal matrix using the divide and conquer method. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] ICOMPQ -*> \verbatim -*> ICOMPQ is INTEGER -*> = 0: Compute eigenvalues only. -*> = 1: Compute eigenvectors of original dense symmetric matrix -*> also. On entry, Q contains the orthogonal matrix used -*> to reduce the original matrix to tridiagonal form. -*> = 2: Compute eigenvalues and eigenvectors of tridiagonal -*> matrix. -*> \endverbatim -*> -*> \param[in] QSIZ -*> \verbatim -*> QSIZ is INTEGER -*> The dimension of the orthogonal matrix used to reduce -*> the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The dimension of the symmetric tridiagonal matrix. N >= 0. -*> \endverbatim -*> -*> \param[in,out] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension (N) -*> On entry, the main diagonal of the tridiagonal matrix. -*> On exit, its eigenvalues. -*> \endverbatim -*> -*> \param[in] E -*> \verbatim -*> E is DOUBLE PRECISION array, dimension (N-1) -*> The off-diagonal elements of the tridiagonal matrix. -*> On exit, E has been destroyed. -*> \endverbatim -*> -*> \param[in,out] Q -*> \verbatim -*> Q is DOUBLE PRECISION array, dimension (LDQ, N) -*> On entry, Q must contain an N-by-N orthogonal matrix. -*> If ICOMPQ = 0 Q is not referenced. -*> If ICOMPQ = 1 On entry, Q is a subset of the columns of the -*> orthogonal matrix used to reduce the full -*> matrix to tridiagonal form corresponding to -*> the subset of the full matrix which is being -*> decomposed at this time. -*> If ICOMPQ = 2 On entry, Q will be the identity matrix. -*> On exit, Q contains the eigenvectors of the -*> tridiagonal matrix. -*> \endverbatim -*> -*> \param[in] LDQ -*> \verbatim -*> LDQ is INTEGER -*> The leading dimension of the array Q. If eigenvectors are -*> desired, then LDQ >= max(1,N). In any case, LDQ >= 1. -*> \endverbatim -*> -*> \param[out] QSTORE -*> \verbatim -*> QSTORE is DOUBLE PRECISION array, dimension (LDQS, N) -*> Referenced only when ICOMPQ = 1. Used to store parts of -*> the eigenvector matrix when the updating matrix multiplies -*> take place. -*> \endverbatim -*> -*> \param[in] LDQS -*> \verbatim -*> LDQS is INTEGER -*> The leading dimension of the array QSTORE. If ICOMPQ = 1, -*> then LDQS >= max(1,N). In any case, LDQS >= 1. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, -*> If ICOMPQ = 0 or 1, the dimension of WORK must be at least -*> 1 + 3*N + 2*N*lg N + 3*N**2 -*> ( lg( N ) = smallest integer k -*> such that 2^k >= N ) -*> If ICOMPQ = 2, the dimension of WORK must be at least -*> 4*N + N**2. -*> \endverbatim -*> -*> \param[out] IWORK -*> \verbatim -*> IWORK is INTEGER array, -*> If ICOMPQ = 0 or 1, the dimension of IWORK must be at least -*> 6 + 6*N + 5*N*lg N. -*> ( lg( N ) = smallest integer k -*> such that 2^k >= N ) -*> If ICOMPQ = 2, the dimension of IWORK must be at least -*> 3 + 5*N. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit. -*> < 0: if INFO = -i, the i-th argument had an illegal value. -*> > 0: The algorithm failed to compute an eigenvalue while -*> working on the submatrix lying in rows and columns -*> INFO/(N+1) through mod(INFO,N+1). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup auxOTHERcomputational -* -*> \par Contributors: -* ================== -*> -*> Jeff Rutter, Computer Science Division, University of California -*> at Berkeley, USA -* -* ===================================================================== - SUBROUTINE DLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, - $ WORK, IWORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER ICOMPQ, INFO, LDQ, LDQS, N, QSIZ -* .. -* .. Array Arguments .. - INTEGER IWORK( * ) - DOUBLE PRECISION D( * ), E( * ), Q( LDQ, * ), QSTORE( LDQS, * ), - $ WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, ONE, TWO - PARAMETER ( ZERO = 0.D0, ONE = 1.D0, TWO = 2.D0 ) -* .. -* .. Local Scalars .. - INTEGER CURLVL, CURPRB, CURR, I, IGIVCL, IGIVNM, - $ IGIVPT, INDXQ, IPERM, IPRMPT, IQ, IQPTR, IWREM, - $ J, K, LGN, MATSIZ, MSD2, SMLSIZ, SMM1, SPM1, - $ SPM2, SUBMAT, SUBPBS, TLVLS - DOUBLE PRECISION TEMP -* .. -* .. External Subroutines .. - EXTERNAL DCOPY, DGEMM, DLACPY, DLAED1, DLAED7, DSTEQR, - $ XERBLA -* .. -* .. External Functions .. - INTEGER ILAENV - EXTERNAL ILAENV -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, DBLE, INT, LOG, MAX -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 -* - IF( ICOMPQ.LT.0 .OR. ICOMPQ.GT.2 ) THEN - INFO = -1 - ELSE IF( ( ICOMPQ.EQ.1 ) .AND. ( QSIZ.LT.MAX( 0, N ) ) ) THEN - INFO = -2 - ELSE IF( N.LT.0 ) THEN - INFO = -3 - ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN - INFO = -7 - ELSE IF( LDQS.LT.MAX( 1, N ) ) THEN - INFO = -9 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DLAED0', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( N.EQ.0 ) - $ RETURN -* - SMLSIZ = ILAENV( 9, 'DLAED0', ' ', 0, 0, 0, 0 ) -* -* Determine the size and placement of the submatrices, and save in -* the leading elements of IWORK. -* - IWORK( 1 ) = N - SUBPBS = 1 - TLVLS = 0 - 10 CONTINUE - IF( IWORK( SUBPBS ).GT.SMLSIZ ) THEN - DO 20 J = SUBPBS, 1, -1 - IWORK( 2*J ) = ( IWORK( J )+1 ) / 2 - IWORK( 2*J-1 ) = IWORK( J ) / 2 - 20 CONTINUE - TLVLS = TLVLS + 1 - SUBPBS = 2*SUBPBS - GO TO 10 - END IF - DO 30 J = 2, SUBPBS - IWORK( J ) = IWORK( J ) + IWORK( J-1 ) - 30 CONTINUE -* -* Divide the matrix into SUBPBS submatrices of size at most SMLSIZ+1 -* using rank-1 modifications (cuts). -* - SPM1 = SUBPBS - 1 - DO 40 I = 1, SPM1 - SUBMAT = IWORK( I ) + 1 - SMM1 = SUBMAT - 1 - D( SMM1 ) = D( SMM1 ) - ABS( E( SMM1 ) ) - D( SUBMAT ) = D( SUBMAT ) - ABS( E( SMM1 ) ) - 40 CONTINUE -* - INDXQ = 4*N + 3 - IF( ICOMPQ.NE.2 ) THEN -* -* Set up workspaces for eigenvalues only/accumulate new vectors -* routine -* - TEMP = LOG( DBLE( N ) ) / LOG( TWO ) - LGN = INT( TEMP ) - IF( 2**LGN.LT.N ) - $ LGN = LGN + 1 - IF( 2**LGN.LT.N ) - $ LGN = LGN + 1 - IPRMPT = INDXQ + N + 1 - IPERM = IPRMPT + N*LGN - IQPTR = IPERM + N*LGN - IGIVPT = IQPTR + N + 2 - IGIVCL = IGIVPT + N*LGN -* - IGIVNM = 1 - IQ = IGIVNM + 2*N*LGN - IWREM = IQ + N**2 + 1 -* -* Initialize pointers -* - DO 50 I = 0, SUBPBS - IWORK( IPRMPT+I ) = 1 - IWORK( IGIVPT+I ) = 1 - 50 CONTINUE - IWORK( IQPTR ) = 1 - END IF -* -* Solve each submatrix eigenproblem at the bottom of the divide and -* conquer tree. -* - CURR = 0 - DO 70 I = 0, SPM1 - IF( I.EQ.0 ) THEN - SUBMAT = 1 - MATSIZ = IWORK( 1 ) - ELSE - SUBMAT = IWORK( I ) + 1 - MATSIZ = IWORK( I+1 ) - IWORK( I ) - END IF - IF( ICOMPQ.EQ.2 ) THEN - CALL DSTEQR( 'I', MATSIZ, D( SUBMAT ), E( SUBMAT ), - $ Q( SUBMAT, SUBMAT ), LDQ, WORK, INFO ) - IF( INFO.NE.0 ) - $ GO TO 130 - ELSE - CALL DSTEQR( 'I', MATSIZ, D( SUBMAT ), E( SUBMAT ), - $ WORK( IQ-1+IWORK( IQPTR+CURR ) ), MATSIZ, WORK, - $ INFO ) - IF( INFO.NE.0 ) - $ GO TO 130 - IF( ICOMPQ.EQ.1 ) THEN - CALL DGEMM( 'N', 'N', QSIZ, MATSIZ, MATSIZ, ONE, - $ Q( 1, SUBMAT ), LDQ, WORK( IQ-1+IWORK( IQPTR+ - $ CURR ) ), MATSIZ, ZERO, QSTORE( 1, SUBMAT ), - $ LDQS ) - END IF - IWORK( IQPTR+CURR+1 ) = IWORK( IQPTR+CURR ) + MATSIZ**2 - CURR = CURR + 1 - END IF - K = 1 - DO 60 J = SUBMAT, IWORK( I+1 ) - IWORK( INDXQ+J ) = K - K = K + 1 - 60 CONTINUE - 70 CONTINUE -* -* Successively merge eigensystems of adjacent submatrices -* into eigensystem for the corresponding larger matrix. -* -* while ( SUBPBS > 1 ) -* - CURLVL = 1 - 80 CONTINUE - IF( SUBPBS.GT.1 ) THEN - SPM2 = SUBPBS - 2 - DO 90 I = 0, SPM2, 2 - IF( I.EQ.0 ) THEN - SUBMAT = 1 - MATSIZ = IWORK( 2 ) - MSD2 = IWORK( 1 ) - CURPRB = 0 - ELSE - SUBMAT = IWORK( I ) + 1 - MATSIZ = IWORK( I+2 ) - IWORK( I ) - MSD2 = MATSIZ / 2 - CURPRB = CURPRB + 1 - END IF -* -* Merge lower order eigensystems (of size MSD2 and MATSIZ - MSD2) -* into an eigensystem of size MATSIZ. -* DLAED1 is used only for the full eigensystem of a tridiagonal -* matrix. -* DLAED7 handles the cases in which eigenvalues only or eigenvalues -* and eigenvectors of a full symmetric matrix (which was reduced to -* tridiagonal form) are desired. -* - IF( ICOMPQ.EQ.2 ) THEN - CALL DLAED1( MATSIZ, D( SUBMAT ), Q( SUBMAT, SUBMAT ), - $ LDQ, IWORK( INDXQ+SUBMAT ), - $ E( SUBMAT+MSD2-1 ), MSD2, WORK, - $ IWORK( SUBPBS+1 ), INFO ) - ELSE - CALL DLAED7( ICOMPQ, MATSIZ, QSIZ, TLVLS, CURLVL, CURPRB, - $ D( SUBMAT ), QSTORE( 1, SUBMAT ), LDQS, - $ IWORK( INDXQ+SUBMAT ), E( SUBMAT+MSD2-1 ), - $ MSD2, WORK( IQ ), IWORK( IQPTR ), - $ IWORK( IPRMPT ), IWORK( IPERM ), - $ IWORK( IGIVPT ), IWORK( IGIVCL ), - $ WORK( IGIVNM ), WORK( IWREM ), - $ IWORK( SUBPBS+1 ), INFO ) - END IF - IF( INFO.NE.0 ) - $ GO TO 130 - IWORK( I / 2+1 ) = IWORK( I+2 ) - 90 CONTINUE - SUBPBS = SUBPBS / 2 - CURLVL = CURLVL + 1 - GO TO 80 - END IF -* -* end while -* -* Re-merge the eigenvalues/vectors which were deflated at the final -* merge step. -* - IF( ICOMPQ.EQ.1 ) THEN - DO 100 I = 1, N - J = IWORK( INDXQ+I ) - WORK( I ) = D( J ) - CALL DCOPY( QSIZ, QSTORE( 1, J ), 1, Q( 1, I ), 1 ) - 100 CONTINUE - CALL DCOPY( N, WORK, 1, D, 1 ) - ELSE IF( ICOMPQ.EQ.2 ) THEN - DO 110 I = 1, N - J = IWORK( INDXQ+I ) - WORK( I ) = D( J ) - CALL DCOPY( N, Q( 1, J ), 1, WORK( N*I+1 ), 1 ) - 110 CONTINUE - CALL DCOPY( N, WORK, 1, D, 1 ) - CALL DLACPY( 'A', N, N, WORK( N+1 ), N, Q, LDQ ) - ELSE - DO 120 I = 1, N - J = IWORK( INDXQ+I ) - WORK( I ) = D( J ) - 120 CONTINUE - CALL DCOPY( N, WORK, 1, D, 1 ) - END IF - GO TO 140 -* - 130 CONTINUE - INFO = SUBMAT*( N+1 ) + SUBMAT + MATSIZ - 1 -* - 140 CONTINUE - RETURN -* -* End of DLAED0 -* - END diff --git a/lib/linalg/fortran/dlaed1.f b/lib/linalg/fortran/dlaed1.f deleted file mode 100644 index 3718139c14..0000000000 --- a/lib/linalg/fortran/dlaed1.f +++ /dev/null @@ -1,271 +0,0 @@ -*> \brief \b DLAED1 used by DSTEDC. Computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. Used when the original matrix is tridiagonal. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLAED1 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLAED1( N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK, -* INFO ) -* -* .. Scalar Arguments .. -* INTEGER CUTPNT, INFO, LDQ, N -* DOUBLE PRECISION RHO -* .. -* .. Array Arguments .. -* INTEGER INDXQ( * ), IWORK( * ) -* DOUBLE PRECISION D( * ), Q( LDQ, * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLAED1 computes the updated eigensystem of a diagonal -*> matrix after modification by a rank-one symmetric matrix. This -*> routine is used only for the eigenproblem which requires all -*> eigenvalues and eigenvectors of a tridiagonal matrix. DLAED7 handles -*> the case in which eigenvalues only or eigenvalues and eigenvectors -*> of a full symmetric matrix (which was reduced to tridiagonal form) -*> are desired. -*> -*> T = Q(in) ( D(in) + RHO * Z*Z**T ) Q**T(in) = Q(out) * D(out) * Q**T(out) -*> -*> where Z = Q**T*u, u is a vector of length N with ones in the -*> CUTPNT and CUTPNT + 1 th elements and zeros elsewhere. -*> -*> The eigenvectors of the original matrix are stored in Q, and the -*> eigenvalues are in D. The algorithm consists of three stages: -*> -*> The first stage consists of deflating the size of the problem -*> when there are multiple eigenvalues or if there is a zero in -*> the Z vector. For each such occurrence the dimension of the -*> secular equation problem is reduced by one. This stage is -*> performed by the routine DLAED2. -*> -*> The second stage consists of calculating the updated -*> eigenvalues. This is done by finding the roots of the secular -*> equation via the routine DLAED4 (as called by DLAED3). -*> This routine also calculates the eigenvectors of the current -*> problem. -*> -*> The final stage consists of computing the updated eigenvectors -*> directly using the updated eigenvalues. The eigenvectors for -*> the current problem are multiplied with the eigenvectors from -*> the overall problem. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The dimension of the symmetric tridiagonal matrix. N >= 0. -*> \endverbatim -*> -*> \param[in,out] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension (N) -*> On entry, the eigenvalues of the rank-1-perturbed matrix. -*> On exit, the eigenvalues of the repaired matrix. -*> \endverbatim -*> -*> \param[in,out] Q -*> \verbatim -*> Q is DOUBLE PRECISION array, dimension (LDQ,N) -*> On entry, the eigenvectors of the rank-1-perturbed matrix. -*> On exit, the eigenvectors of the repaired tridiagonal matrix. -*> \endverbatim -*> -*> \param[in] LDQ -*> \verbatim -*> LDQ is INTEGER -*> The leading dimension of the array Q. LDQ >= max(1,N). -*> \endverbatim -*> -*> \param[in,out] INDXQ -*> \verbatim -*> INDXQ is INTEGER array, dimension (N) -*> On entry, the permutation which separately sorts the two -*> subproblems in D into ascending order. -*> On exit, the permutation which will reintegrate the -*> subproblems back into sorted order, -*> i.e. D( INDXQ( I = 1, N ) ) will be in ascending order. -*> \endverbatim -*> -*> \param[in] RHO -*> \verbatim -*> RHO is DOUBLE PRECISION -*> The subdiagonal entry used to create the rank-1 modification. -*> \endverbatim -*> -*> \param[in] CUTPNT -*> \verbatim -*> CUTPNT is INTEGER -*> The location of the last eigenvalue in the leading sub-matrix. -*> min(1,N) <= CUTPNT <= N/2. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (4*N + N**2) -*> \endverbatim -*> -*> \param[out] IWORK -*> \verbatim -*> IWORK is INTEGER array, dimension (4*N) -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit. -*> < 0: if INFO = -i, the i-th argument had an illegal value. -*> > 0: if INFO = 1, an eigenvalue did not converge -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup auxOTHERcomputational -* -*> \par Contributors: -* ================== -*> -*> Jeff Rutter, Computer Science Division, University of California -*> at Berkeley, USA \n -*> Modified by Francoise Tisseur, University of Tennessee -*> -* ===================================================================== - SUBROUTINE DLAED1( N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK, - $ INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER CUTPNT, INFO, LDQ, N - DOUBLE PRECISION RHO -* .. -* .. Array Arguments .. - INTEGER INDXQ( * ), IWORK( * ) - DOUBLE PRECISION D( * ), Q( LDQ, * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Local Scalars .. - INTEGER COLTYP, I, IDLMDA, INDX, INDXC, INDXP, IQ2, IS, - $ IW, IZ, K, N1, N2, ZPP1 -* .. -* .. External Subroutines .. - EXTERNAL DCOPY, DLAED2, DLAED3, DLAMRG, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, MIN -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 -* - IF( N.LT.0 ) THEN - INFO = -1 - ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN - INFO = -4 - ELSE IF( MIN( 1, N / 2 ).GT.CUTPNT .OR. ( N / 2 ).LT.CUTPNT ) THEN - INFO = -7 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DLAED1', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( N.EQ.0 ) - $ RETURN -* -* The following values are integer pointers which indicate -* the portion of the workspace -* used by a particular array in DLAED2 and DLAED3. -* - IZ = 1 - IDLMDA = IZ + N - IW = IDLMDA + N - IQ2 = IW + N -* - INDX = 1 - INDXC = INDX + N - COLTYP = INDXC + N - INDXP = COLTYP + N -* -* -* Form the z-vector which consists of the last row of Q_1 and the -* first row of Q_2. -* - CALL DCOPY( CUTPNT, Q( CUTPNT, 1 ), LDQ, WORK( IZ ), 1 ) - ZPP1 = CUTPNT + 1 - CALL DCOPY( N-CUTPNT, Q( ZPP1, ZPP1 ), LDQ, WORK( IZ+CUTPNT ), 1 ) -* -* Deflate eigenvalues. -* - CALL DLAED2( K, N, CUTPNT, D, Q, LDQ, INDXQ, RHO, WORK( IZ ), - $ WORK( IDLMDA ), WORK( IW ), WORK( IQ2 ), - $ IWORK( INDX ), IWORK( INDXC ), IWORK( INDXP ), - $ IWORK( COLTYP ), INFO ) -* - IF( INFO.NE.0 ) - $ GO TO 20 -* -* Solve Secular Equation. -* - IF( K.NE.0 ) THEN - IS = ( IWORK( COLTYP )+IWORK( COLTYP+1 ) )*CUTPNT + - $ ( IWORK( COLTYP+1 )+IWORK( COLTYP+2 ) )*( N-CUTPNT ) + IQ2 - CALL DLAED3( K, N, CUTPNT, D, Q, LDQ, RHO, WORK( IDLMDA ), - $ WORK( IQ2 ), IWORK( INDXC ), IWORK( COLTYP ), - $ WORK( IW ), WORK( IS ), INFO ) - IF( INFO.NE.0 ) - $ GO TO 20 -* -* Prepare the INDXQ sorting permutation. -* - N1 = K - N2 = N - K - CALL DLAMRG( N1, N2, D, 1, -1, INDXQ ) - ELSE - DO 10 I = 1, N - INDXQ( I ) = I - 10 CONTINUE - END IF -* - 20 CONTINUE - RETURN -* -* End of DLAED1 -* - END diff --git a/lib/linalg/fortran/dlaed2.f b/lib/linalg/fortran/dlaed2.f deleted file mode 100644 index 9b1f1e0930..0000000000 --- a/lib/linalg/fortran/dlaed2.f +++ /dev/null @@ -1,536 +0,0 @@ -*> \brief \b DLAED2 used by DSTEDC. Merges eigenvalues and deflates secular equation. Used when the original matrix is tridiagonal. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLAED2 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLAED2( K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W, -* Q2, INDX, INDXC, INDXP, COLTYP, INFO ) -* -* .. Scalar Arguments .. -* INTEGER INFO, K, LDQ, N, N1 -* DOUBLE PRECISION RHO -* .. -* .. Array Arguments .. -* INTEGER COLTYP( * ), INDX( * ), INDXC( * ), INDXP( * ), -* $ INDXQ( * ) -* DOUBLE PRECISION D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( * ), -* $ W( * ), Z( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLAED2 merges the two sets of eigenvalues together into a single -*> sorted set. Then it tries to deflate the size of the problem. -*> There are two ways in which deflation can occur: when two or more -*> eigenvalues are close together or if there is a tiny entry in the -*> Z vector. For each such occurrence the order of the related secular -*> equation problem is reduced by one. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[out] K -*> \verbatim -*> K is INTEGER -*> The number of non-deflated eigenvalues, and the order of the -*> related secular equation. 0 <= K <=N. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The dimension of the symmetric tridiagonal matrix. N >= 0. -*> \endverbatim -*> -*> \param[in] N1 -*> \verbatim -*> N1 is INTEGER -*> The location of the last eigenvalue in the leading sub-matrix. -*> min(1,N) <= N1 <= N/2. -*> \endverbatim -*> -*> \param[in,out] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension (N) -*> On entry, D contains the eigenvalues of the two submatrices to -*> be combined. -*> On exit, D contains the trailing (N-K) updated eigenvalues -*> (those which were deflated) sorted into increasing order. -*> \endverbatim -*> -*> \param[in,out] Q -*> \verbatim -*> Q is DOUBLE PRECISION array, dimension (LDQ, N) -*> On entry, Q contains the eigenvectors of two submatrices in -*> the two square blocks with corners at (1,1), (N1,N1) -*> and (N1+1, N1+1), (N,N). -*> On exit, Q contains the trailing (N-K) updated eigenvectors -*> (those which were deflated) in its last N-K columns. -*> \endverbatim -*> -*> \param[in] LDQ -*> \verbatim -*> LDQ is INTEGER -*> The leading dimension of the array Q. LDQ >= max(1,N). -*> \endverbatim -*> -*> \param[in,out] INDXQ -*> \verbatim -*> INDXQ is INTEGER array, dimension (N) -*> The permutation which separately sorts the two sub-problems -*> in D into ascending order. Note that elements in the second -*> half of this permutation must first have N1 added to their -*> values. Destroyed on exit. -*> \endverbatim -*> -*> \param[in,out] RHO -*> \verbatim -*> RHO is DOUBLE PRECISION -*> On entry, the off-diagonal element associated with the rank-1 -*> cut which originally split the two submatrices which are now -*> being recombined. -*> On exit, RHO has been modified to the value required by -*> DLAED3. -*> \endverbatim -*> -*> \param[in] Z -*> \verbatim -*> Z is DOUBLE PRECISION array, dimension (N) -*> On entry, Z contains the updating vector (the last -*> row of the first sub-eigenvector matrix and the first row of -*> the second sub-eigenvector matrix). -*> On exit, the contents of Z have been destroyed by the updating -*> process. -*> \endverbatim -*> -*> \param[out] DLAMDA -*> \verbatim -*> DLAMDA is DOUBLE PRECISION array, dimension (N) -*> A copy of the first K eigenvalues which will be used by -*> DLAED3 to form the secular equation. -*> \endverbatim -*> -*> \param[out] W -*> \verbatim -*> W is DOUBLE PRECISION array, dimension (N) -*> The first k values of the final deflation-altered z-vector -*> which will be passed to DLAED3. -*> \endverbatim -*> -*> \param[out] Q2 -*> \verbatim -*> Q2 is DOUBLE PRECISION array, dimension (N1**2+(N-N1)**2) -*> A copy of the first K eigenvectors which will be used by -*> DLAED3 in a matrix multiply (DGEMM) to solve for the new -*> eigenvectors. -*> \endverbatim -*> -*> \param[out] INDX -*> \verbatim -*> INDX is INTEGER array, dimension (N) -*> The permutation used to sort the contents of DLAMDA into -*> ascending order. -*> \endverbatim -*> -*> \param[out] INDXC -*> \verbatim -*> INDXC is INTEGER array, dimension (N) -*> The permutation used to arrange the columns of the deflated -*> Q matrix into three groups: the first group contains non-zero -*> elements only at and above N1, the second contains -*> non-zero elements only below N1, and the third is dense. -*> \endverbatim -*> -*> \param[out] INDXP -*> \verbatim -*> INDXP is INTEGER array, dimension (N) -*> The permutation used to place deflated values of D at the end -*> of the array. INDXP(1:K) points to the nondeflated D-values -*> and INDXP(K+1:N) points to the deflated eigenvalues. -*> \endverbatim -*> -*> \param[out] COLTYP -*> \verbatim -*> COLTYP is INTEGER array, dimension (N) -*> During execution, a label which will indicate which of the -*> following types a column in the Q2 matrix is: -*> 1 : non-zero in the upper half only; -*> 2 : dense; -*> 3 : non-zero in the lower half only; -*> 4 : deflated. -*> On exit, COLTYP(i) is the number of columns of type i, -*> for i=1 to 4 only. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit. -*> < 0: if INFO = -i, the i-th argument had an illegal value. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup auxOTHERcomputational -* -*> \par Contributors: -* ================== -*> -*> Jeff Rutter, Computer Science Division, University of California -*> at Berkeley, USA \n -*> Modified by Francoise Tisseur, University of Tennessee -*> -* ===================================================================== - SUBROUTINE DLAED2( K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W, - $ Q2, INDX, INDXC, INDXP, COLTYP, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INFO, K, LDQ, N, N1 - DOUBLE PRECISION RHO -* .. -* .. Array Arguments .. - INTEGER COLTYP( * ), INDX( * ), INDXC( * ), INDXP( * ), - $ INDXQ( * ) - DOUBLE PRECISION D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( * ), - $ W( * ), Z( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION MONE, ZERO, ONE, TWO, EIGHT - PARAMETER ( MONE = -1.0D0, ZERO = 0.0D0, ONE = 1.0D0, - $ TWO = 2.0D0, EIGHT = 8.0D0 ) -* .. -* .. Local Arrays .. - INTEGER CTOT( 4 ), PSM( 4 ) -* .. -* .. Local Scalars .. - INTEGER CT, I, IMAX, IQ1, IQ2, J, JMAX, JS, K2, N1P1, - $ N2, NJ, PJ - DOUBLE PRECISION C, EPS, S, T, TAU, TOL -* .. -* .. External Functions .. - INTEGER IDAMAX - DOUBLE PRECISION DLAMCH, DLAPY2 - EXTERNAL IDAMAX, DLAMCH, DLAPY2 -* .. -* .. External Subroutines .. - EXTERNAL DCOPY, DLACPY, DLAMRG, DROT, DSCAL, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, MAX, MIN, SQRT -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 -* - IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN - INFO = -6 - ELSE IF( MIN( 1, ( N / 2 ) ).GT.N1 .OR. ( N / 2 ).LT.N1 ) THEN - INFO = -3 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DLAED2', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( N.EQ.0 ) - $ RETURN -* - N2 = N - N1 - N1P1 = N1 + 1 -* - IF( RHO.LT.ZERO ) THEN - CALL DSCAL( N2, MONE, Z( N1P1 ), 1 ) - END IF -* -* Normalize z so that norm(z) = 1. Since z is the concatenation of -* two normalized vectors, norm2(z) = sqrt(2). -* - T = ONE / SQRT( TWO ) - CALL DSCAL( N, T, Z, 1 ) -* -* RHO = ABS( norm(z)**2 * RHO ) -* - RHO = ABS( TWO*RHO ) -* -* Sort the eigenvalues into increasing order -* - DO 10 I = N1P1, N - INDXQ( I ) = INDXQ( I ) + N1 - 10 CONTINUE -* -* re-integrate the deflated parts from the last pass -* - DO 20 I = 1, N - DLAMDA( I ) = D( INDXQ( I ) ) - 20 CONTINUE - CALL DLAMRG( N1, N2, DLAMDA, 1, 1, INDXC ) - DO 30 I = 1, N - INDX( I ) = INDXQ( INDXC( I ) ) - 30 CONTINUE -* -* Calculate the allowable deflation tolerance -* - IMAX = IDAMAX( N, Z, 1 ) - JMAX = IDAMAX( N, D, 1 ) - EPS = DLAMCH( 'Epsilon' ) - TOL = EIGHT*EPS*MAX( ABS( D( JMAX ) ), ABS( Z( IMAX ) ) ) -* -* If the rank-1 modifier is small enough, no more needs to be done -* except to reorganize Q so that its columns correspond with the -* elements in D. -* - IF( RHO*ABS( Z( IMAX ) ).LE.TOL ) THEN - K = 0 - IQ2 = 1 - DO 40 J = 1, N - I = INDX( J ) - CALL DCOPY( N, Q( 1, I ), 1, Q2( IQ2 ), 1 ) - DLAMDA( J ) = D( I ) - IQ2 = IQ2 + N - 40 CONTINUE - CALL DLACPY( 'A', N, N, Q2, N, Q, LDQ ) - CALL DCOPY( N, DLAMDA, 1, D, 1 ) - GO TO 190 - END IF -* -* If there are multiple eigenvalues then the problem deflates. Here -* the number of equal eigenvalues are found. As each equal -* eigenvalue is found, an elementary reflector is computed to rotate -* the corresponding eigensubspace so that the corresponding -* components of Z are zero in this new basis. -* - DO 50 I = 1, N1 - COLTYP( I ) = 1 - 50 CONTINUE - DO 60 I = N1P1, N - COLTYP( I ) = 3 - 60 CONTINUE -* -* - K = 0 - K2 = N + 1 - DO 70 J = 1, N - NJ = INDX( J ) - IF( RHO*ABS( Z( NJ ) ).LE.TOL ) THEN -* -* Deflate due to small z component. -* - K2 = K2 - 1 - COLTYP( NJ ) = 4 - INDXP( K2 ) = NJ - IF( J.EQ.N ) - $ GO TO 100 - ELSE - PJ = NJ - GO TO 80 - END IF - 70 CONTINUE - 80 CONTINUE - J = J + 1 - NJ = INDX( J ) - IF( J.GT.N ) - $ GO TO 100 - IF( RHO*ABS( Z( NJ ) ).LE.TOL ) THEN -* -* Deflate due to small z component. -* - K2 = K2 - 1 - COLTYP( NJ ) = 4 - INDXP( K2 ) = NJ - ELSE -* -* Check if eigenvalues are close enough to allow deflation. -* - S = Z( PJ ) - C = Z( NJ ) -* -* Find sqrt(a**2+b**2) without overflow or -* destructive underflow. -* - TAU = DLAPY2( C, S ) - T = D( NJ ) - D( PJ ) - C = C / TAU - S = -S / TAU - IF( ABS( T*C*S ).LE.TOL ) THEN -* -* Deflation is possible. -* - Z( NJ ) = TAU - Z( PJ ) = ZERO - IF( COLTYP( NJ ).NE.COLTYP( PJ ) ) - $ COLTYP( NJ ) = 2 - COLTYP( PJ ) = 4 - CALL DROT( N, Q( 1, PJ ), 1, Q( 1, NJ ), 1, C, S ) - T = D( PJ )*C**2 + D( NJ )*S**2 - D( NJ ) = D( PJ )*S**2 + D( NJ )*C**2 - D( PJ ) = T - K2 = K2 - 1 - I = 1 - 90 CONTINUE - IF( K2+I.LE.N ) THEN - IF( D( PJ ).LT.D( INDXP( K2+I ) ) ) THEN - INDXP( K2+I-1 ) = INDXP( K2+I ) - INDXP( K2+I ) = PJ - I = I + 1 - GO TO 90 - ELSE - INDXP( K2+I-1 ) = PJ - END IF - ELSE - INDXP( K2+I-1 ) = PJ - END IF - PJ = NJ - ELSE - K = K + 1 - DLAMDA( K ) = D( PJ ) - W( K ) = Z( PJ ) - INDXP( K ) = PJ - PJ = NJ - END IF - END IF - GO TO 80 - 100 CONTINUE -* -* Record the last eigenvalue. -* - K = K + 1 - DLAMDA( K ) = D( PJ ) - W( K ) = Z( PJ ) - INDXP( K ) = PJ -* -* Count up the total number of the various types of columns, then -* form a permutation which positions the four column types into -* four uniform groups (although one or more of these groups may be -* empty). -* - DO 110 J = 1, 4 - CTOT( J ) = 0 - 110 CONTINUE - DO 120 J = 1, N - CT = COLTYP( J ) - CTOT( CT ) = CTOT( CT ) + 1 - 120 CONTINUE -* -* PSM(*) = Position in SubMatrix (of types 1 through 4) -* - PSM( 1 ) = 1 - PSM( 2 ) = 1 + CTOT( 1 ) - PSM( 3 ) = PSM( 2 ) + CTOT( 2 ) - PSM( 4 ) = PSM( 3 ) + CTOT( 3 ) - K = N - CTOT( 4 ) -* -* Fill out the INDXC array so that the permutation which it induces -* will place all type-1 columns first, all type-2 columns next, -* then all type-3's, and finally all type-4's. -* - DO 130 J = 1, N - JS = INDXP( J ) - CT = COLTYP( JS ) - INDX( PSM( CT ) ) = JS - INDXC( PSM( CT ) ) = J - PSM( CT ) = PSM( CT ) + 1 - 130 CONTINUE -* -* Sort the eigenvalues and corresponding eigenvectors into DLAMDA -* and Q2 respectively. The eigenvalues/vectors which were not -* deflated go into the first K slots of DLAMDA and Q2 respectively, -* while those which were deflated go into the last N - K slots. -* - I = 1 - IQ1 = 1 - IQ2 = 1 + ( CTOT( 1 )+CTOT( 2 ) )*N1 - DO 140 J = 1, CTOT( 1 ) - JS = INDX( I ) - CALL DCOPY( N1, Q( 1, JS ), 1, Q2( IQ1 ), 1 ) - Z( I ) = D( JS ) - I = I + 1 - IQ1 = IQ1 + N1 - 140 CONTINUE -* - DO 150 J = 1, CTOT( 2 ) - JS = INDX( I ) - CALL DCOPY( N1, Q( 1, JS ), 1, Q2( IQ1 ), 1 ) - CALL DCOPY( N2, Q( N1+1, JS ), 1, Q2( IQ2 ), 1 ) - Z( I ) = D( JS ) - I = I + 1 - IQ1 = IQ1 + N1 - IQ2 = IQ2 + N2 - 150 CONTINUE -* - DO 160 J = 1, CTOT( 3 ) - JS = INDX( I ) - CALL DCOPY( N2, Q( N1+1, JS ), 1, Q2( IQ2 ), 1 ) - Z( I ) = D( JS ) - I = I + 1 - IQ2 = IQ2 + N2 - 160 CONTINUE -* - IQ1 = IQ2 - DO 170 J = 1, CTOT( 4 ) - JS = INDX( I ) - CALL DCOPY( N, Q( 1, JS ), 1, Q2( IQ2 ), 1 ) - IQ2 = IQ2 + N - Z( I ) = D( JS ) - I = I + 1 - 170 CONTINUE -* -* The deflated eigenvalues and their corresponding vectors go back -* into the last N - K slots of D and Q respectively. -* - IF( K.LT.N ) THEN - CALL DLACPY( 'A', N, CTOT( 4 ), Q2( IQ1 ), N, - $ Q( 1, K+1 ), LDQ ) - CALL DCOPY( N-K, Z( K+1 ), 1, D( K+1 ), 1 ) - END IF -* -* Copy CTOT into COLTYP for referencing in DLAED3. -* - DO 180 J = 1, 4 - COLTYP( J ) = CTOT( J ) - 180 CONTINUE -* - 190 CONTINUE - RETURN -* -* End of DLAED2 -* - END diff --git a/lib/linalg/fortran/dlaed3.f b/lib/linalg/fortran/dlaed3.f deleted file mode 100644 index c58944e604..0000000000 --- a/lib/linalg/fortran/dlaed3.f +++ /dev/null @@ -1,350 +0,0 @@ -*> \brief \b DLAED3 used by DSTEDC. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is tridiagonal. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLAED3 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLAED3( K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX, -* CTOT, W, S, INFO ) -* -* .. Scalar Arguments .. -* INTEGER INFO, K, LDQ, N, N1 -* DOUBLE PRECISION RHO -* .. -* .. Array Arguments .. -* INTEGER CTOT( * ), INDX( * ) -* DOUBLE PRECISION D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( * ), -* $ S( * ), W( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLAED3 finds the roots of the secular equation, as defined by the -*> values in D, W, and RHO, between 1 and K. It makes the -*> appropriate calls to DLAED4 and then updates the eigenvectors by -*> multiplying the matrix of eigenvectors of the pair of eigensystems -*> being combined by the matrix of eigenvectors of the K-by-K system -*> which is solved here. -*> -*> This code makes very mild assumptions about floating point -*> arithmetic. It will work on machines with a guard digit in -*> add/subtract, or on those binary machines without guard digits -*> which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. -*> It could conceivably fail on hexadecimal or decimal machines -*> without guard digits, but we know of none. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> The number of terms in the rational function to be solved by -*> DLAED4. K >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of rows and columns in the Q matrix. -*> N >= K (deflation may result in N>K). -*> \endverbatim -*> -*> \param[in] N1 -*> \verbatim -*> N1 is INTEGER -*> The location of the last eigenvalue in the leading submatrix. -*> min(1,N) <= N1 <= N/2. -*> \endverbatim -*> -*> \param[out] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension (N) -*> D(I) contains the updated eigenvalues for -*> 1 <= I <= K. -*> \endverbatim -*> -*> \param[out] Q -*> \verbatim -*> Q is DOUBLE PRECISION array, dimension (LDQ,N) -*> Initially the first K columns are used as workspace. -*> On output the columns 1 to K contain -*> the updated eigenvectors. -*> \endverbatim -*> -*> \param[in] LDQ -*> \verbatim -*> LDQ is INTEGER -*> The leading dimension of the array Q. LDQ >= max(1,N). -*> \endverbatim -*> -*> \param[in] RHO -*> \verbatim -*> RHO is DOUBLE PRECISION -*> The value of the parameter in the rank one update equation. -*> RHO >= 0 required. -*> \endverbatim -*> -*> \param[in,out] DLAMDA -*> \verbatim -*> DLAMDA is DOUBLE PRECISION array, dimension (K) -*> The first K elements of this array contain the old roots -*> of the deflated updating problem. These are the poles -*> of the secular equation. May be changed on output by -*> having lowest order bit set to zero on Cray X-MP, Cray Y-MP, -*> Cray-2, or Cray C-90, as described above. -*> \endverbatim -*> -*> \param[in] Q2 -*> \verbatim -*> Q2 is DOUBLE PRECISION array, dimension (LDQ2*N) -*> The first K columns of this matrix contain the non-deflated -*> eigenvectors for the split problem. -*> \endverbatim -*> -*> \param[in] INDX -*> \verbatim -*> INDX is INTEGER array, dimension (N) -*> The permutation used to arrange the columns of the deflated -*> Q matrix into three groups (see DLAED2). -*> The rows of the eigenvectors found by DLAED4 must be likewise -*> permuted before the matrix multiply can take place. -*> \endverbatim -*> -*> \param[in] CTOT -*> \verbatim -*> CTOT is INTEGER array, dimension (4) -*> A count of the total number of the various types of columns -*> in Q, as described in INDX. The fourth column type is any -*> column which has been deflated. -*> \endverbatim -*> -*> \param[in,out] W -*> \verbatim -*> W is DOUBLE PRECISION array, dimension (K) -*> The first K elements of this array contain the components -*> of the deflation-adjusted updating vector. Destroyed on -*> output. -*> \endverbatim -*> -*> \param[out] S -*> \verbatim -*> S is DOUBLE PRECISION array, dimension (N1 + 1)*K -*> Will contain the eigenvectors of the repaired matrix which -*> will be multiplied by the previously accumulated eigenvectors -*> to update the system. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit. -*> < 0: if INFO = -i, the i-th argument had an illegal value. -*> > 0: if INFO = 1, an eigenvalue did not converge -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup auxOTHERcomputational -* -*> \par Contributors: -* ================== -*> -*> Jeff Rutter, Computer Science Division, University of California -*> at Berkeley, USA \n -*> Modified by Francoise Tisseur, University of Tennessee -*> -* ===================================================================== - SUBROUTINE DLAED3( K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX, - $ CTOT, W, S, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INFO, K, LDQ, N, N1 - DOUBLE PRECISION RHO -* .. -* .. Array Arguments .. - INTEGER CTOT( * ), INDX( * ) - DOUBLE PRECISION D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( * ), - $ S( * ), W( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE, ZERO - PARAMETER ( ONE = 1.0D0, ZERO = 0.0D0 ) -* .. -* .. Local Scalars .. - INTEGER I, II, IQ2, J, N12, N2, N23 - DOUBLE PRECISION TEMP -* .. -* .. External Functions .. - DOUBLE PRECISION DLAMC3, DNRM2 - EXTERNAL DLAMC3, DNRM2 -* .. -* .. External Subroutines .. - EXTERNAL DCOPY, DGEMM, DLACPY, DLAED4, DLASET, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, SIGN, SQRT -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 -* - IF( K.LT.0 ) THEN - INFO = -1 - ELSE IF( N.LT.K ) THEN - INFO = -2 - ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN - INFO = -6 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DLAED3', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( K.EQ.0 ) - $ RETURN -* -* Modify values DLAMDA(i) to make sure all DLAMDA(i)-DLAMDA(j) can -* be computed with high relative accuracy (barring over/underflow). -* This is a problem on machines without a guard digit in -* add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2). -* The following code replaces DLAMDA(I) by 2*DLAMDA(I)-DLAMDA(I), -* which on any of these machines zeros out the bottommost -* bit of DLAMDA(I) if it is 1; this makes the subsequent -* subtractions DLAMDA(I)-DLAMDA(J) unproblematic when cancellation -* occurs. On binary machines with a guard digit (almost all -* machines) it does not change DLAMDA(I) at all. On hexadecimal -* and decimal machines with a guard digit, it slightly -* changes the bottommost bits of DLAMDA(I). It does not account -* for hexadecimal or decimal machines without guard digits -* (we know of none). We use a subroutine call to compute -* 2*DLAMBDA(I) to prevent optimizing compilers from eliminating -* this code. -* - DO 10 I = 1, K - DLAMDA( I ) = DLAMC3( DLAMDA( I ), DLAMDA( I ) ) - DLAMDA( I ) - 10 CONTINUE -* - DO 20 J = 1, K - CALL DLAED4( K, J, DLAMDA, W, Q( 1, J ), RHO, D( J ), INFO ) -* -* If the zero finder fails, the computation is terminated. -* - IF( INFO.NE.0 ) - $ GO TO 120 - 20 CONTINUE -* - IF( K.EQ.1 ) - $ GO TO 110 - IF( K.EQ.2 ) THEN - DO 30 J = 1, K - W( 1 ) = Q( 1, J ) - W( 2 ) = Q( 2, J ) - II = INDX( 1 ) - Q( 1, J ) = W( II ) - II = INDX( 2 ) - Q( 2, J ) = W( II ) - 30 CONTINUE - GO TO 110 - END IF -* -* Compute updated W. -* - CALL DCOPY( K, W, 1, S, 1 ) -* -* Initialize W(I) = Q(I,I) -* - CALL DCOPY( K, Q, LDQ+1, W, 1 ) - DO 60 J = 1, K - DO 40 I = 1, J - 1 - W( I ) = W( I )*( Q( I, J ) / ( DLAMDA( I )-DLAMDA( J ) ) ) - 40 CONTINUE - DO 50 I = J + 1, K - W( I ) = W( I )*( Q( I, J ) / ( DLAMDA( I )-DLAMDA( J ) ) ) - 50 CONTINUE - 60 CONTINUE - DO 70 I = 1, K - W( I ) = SIGN( SQRT( -W( I ) ), S( I ) ) - 70 CONTINUE -* -* Compute eigenvectors of the modified rank-1 modification. -* - DO 100 J = 1, K - DO 80 I = 1, K - S( I ) = W( I ) / Q( I, J ) - 80 CONTINUE - TEMP = DNRM2( K, S, 1 ) - DO 90 I = 1, K - II = INDX( I ) - Q( I, J ) = S( II ) / TEMP - 90 CONTINUE - 100 CONTINUE -* -* Compute the updated eigenvectors. -* - 110 CONTINUE -* - N2 = N - N1 - N12 = CTOT( 1 ) + CTOT( 2 ) - N23 = CTOT( 2 ) + CTOT( 3 ) -* - CALL DLACPY( 'A', N23, K, Q( CTOT( 1 )+1, 1 ), LDQ, S, N23 ) - IQ2 = N1*N12 + 1 - IF( N23.NE.0 ) THEN - CALL DGEMM( 'N', 'N', N2, K, N23, ONE, Q2( IQ2 ), N2, S, N23, - $ ZERO, Q( N1+1, 1 ), LDQ ) - ELSE - CALL DLASET( 'A', N2, K, ZERO, ZERO, Q( N1+1, 1 ), LDQ ) - END IF -* - CALL DLACPY( 'A', N12, K, Q, LDQ, S, N12 ) - IF( N12.NE.0 ) THEN - CALL DGEMM( 'N', 'N', N1, K, N12, ONE, Q2, N1, S, N12, ZERO, Q, - $ LDQ ) - ELSE - CALL DLASET( 'A', N1, K, ZERO, ZERO, Q( 1, 1 ), LDQ ) - END IF -* -* - 120 CONTINUE - RETURN -* -* End of DLAED3 -* - END diff --git a/lib/linalg/fortran/dlaed4.f b/lib/linalg/fortran/dlaed4.f deleted file mode 100644 index b51e23d850..0000000000 --- a/lib/linalg/fortran/dlaed4.f +++ /dev/null @@ -1,917 +0,0 @@ -*> \brief \b DLAED4 used by DSTEDC. Finds a single root of the secular equation. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLAED4 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLAED4( N, I, D, Z, DELTA, RHO, DLAM, INFO ) -* -* .. Scalar Arguments .. -* INTEGER I, INFO, N -* DOUBLE PRECISION DLAM, RHO -* .. -* .. Array Arguments .. -* DOUBLE PRECISION D( * ), DELTA( * ), Z( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> This subroutine computes the I-th updated eigenvalue of a symmetric -*> rank-one modification to a diagonal matrix whose elements are -*> given in the array d, and that -*> -*> D(i) < D(j) for i < j -*> -*> and that RHO > 0. This is arranged by the calling routine, and is -*> no loss in generality. The rank-one modified system is thus -*> -*> diag( D ) + RHO * Z * Z_transpose. -*> -*> where we assume the Euclidean norm of Z is 1. -*> -*> The method consists of approximating the rational functions in the -*> secular equation by simpler interpolating rational functions. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The length of all arrays. -*> \endverbatim -*> -*> \param[in] I -*> \verbatim -*> I is INTEGER -*> The index of the eigenvalue to be computed. 1 <= I <= N. -*> \endverbatim -*> -*> \param[in] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension (N) -*> The original eigenvalues. It is assumed that they are in -*> order, D(I) < D(J) for I < J. -*> \endverbatim -*> -*> \param[in] Z -*> \verbatim -*> Z is DOUBLE PRECISION array, dimension (N) -*> The components of the updating vector. -*> \endverbatim -*> -*> \param[out] DELTA -*> \verbatim -*> DELTA is DOUBLE PRECISION array, dimension (N) -*> If N > 2, DELTA contains (D(j) - lambda_I) in its j-th -*> component. If N = 1, then DELTA(1) = 1. If N = 2, see DLAED5 -*> for detail. The vector DELTA contains the information necessary -*> to construct the eigenvectors by DLAED3 and DLAED9. -*> \endverbatim -*> -*> \param[in] RHO -*> \verbatim -*> RHO is DOUBLE PRECISION -*> The scalar in the symmetric updating formula. -*> \endverbatim -*> -*> \param[out] DLAM -*> \verbatim -*> DLAM is DOUBLE PRECISION -*> The computed lambda_I, the I-th updated eigenvalue. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> > 0: if INFO = 1, the updating process failed. -*> \endverbatim -* -*> \par Internal Parameters: -* ========================= -*> -*> \verbatim -*> Logical variable ORGATI (origin-at-i?) is used for distinguishing -*> whether D(i) or D(i+1) is treated as the origin. -*> -*> ORGATI = .true. origin at i -*> ORGATI = .false. origin at i+1 -*> -*> Logical variable SWTCH3 (switch-for-3-poles?) is for noting -*> if we are working with THREE poles! -*> -*> MAXIT is the maximum number of iterations allowed for each -*> eigenvalue. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup auxOTHERcomputational -* -*> \par Contributors: -* ================== -*> -*> Ren-Cang Li, Computer Science Division, University of California -*> at Berkeley, USA -*> -* ===================================================================== - SUBROUTINE DLAED4( N, I, D, Z, DELTA, RHO, DLAM, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER I, INFO, N - DOUBLE PRECISION DLAM, RHO -* .. -* .. Array Arguments .. - DOUBLE PRECISION D( * ), DELTA( * ), Z( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - INTEGER MAXIT - PARAMETER ( MAXIT = 30 ) - DOUBLE PRECISION ZERO, ONE, TWO, THREE, FOUR, EIGHT, TEN - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0, - $ THREE = 3.0D0, FOUR = 4.0D0, EIGHT = 8.0D0, - $ TEN = 10.0D0 ) -* .. -* .. Local Scalars .. - LOGICAL ORGATI, SWTCH, SWTCH3 - INTEGER II, IIM1, IIP1, IP1, ITER, J, NITER - DOUBLE PRECISION A, B, C, DEL, DLTLB, DLTUB, DPHI, DPSI, DW, - $ EPS, ERRETM, ETA, MIDPT, PHI, PREW, PSI, - $ RHOINV, TAU, TEMP, TEMP1, W -* .. -* .. Local Arrays .. - DOUBLE PRECISION ZZ( 3 ) -* .. -* .. External Functions .. - DOUBLE PRECISION DLAMCH - EXTERNAL DLAMCH -* .. -* .. External Subroutines .. - EXTERNAL DLAED5, DLAED6 -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, MAX, MIN, SQRT -* .. -* .. Executable Statements .. -* -* Since this routine is called in an inner loop, we do no argument -* checking. -* -* Quick return for N=1 and 2. -* - INFO = 0 - IF( N.EQ.1 ) THEN -* -* Presumably, I=1 upon entry -* - DLAM = D( 1 ) + RHO*Z( 1 )*Z( 1 ) - DELTA( 1 ) = ONE - RETURN - END IF - IF( N.EQ.2 ) THEN - CALL DLAED5( I, D, Z, DELTA, RHO, DLAM ) - RETURN - END IF -* -* Compute machine epsilon -* - EPS = DLAMCH( 'Epsilon' ) - RHOINV = ONE / RHO -* -* The case I = N -* - IF( I.EQ.N ) THEN -* -* Initialize some basic variables -* - II = N - 1 - NITER = 1 -* -* Calculate initial guess -* - MIDPT = RHO / TWO -* -* If ||Z||_2 is not one, then TEMP should be set to -* RHO * ||Z||_2^2 / TWO -* - DO 10 J = 1, N - DELTA( J ) = ( D( J )-D( I ) ) - MIDPT - 10 CONTINUE -* - PSI = ZERO - DO 20 J = 1, N - 2 - PSI = PSI + Z( J )*Z( J ) / DELTA( J ) - 20 CONTINUE -* - C = RHOINV + PSI - W = C + Z( II )*Z( II ) / DELTA( II ) + - $ Z( N )*Z( N ) / DELTA( N ) -* - IF( W.LE.ZERO ) THEN - TEMP = Z( N-1 )*Z( N-1 ) / ( D( N )-D( N-1 )+RHO ) + - $ Z( N )*Z( N ) / RHO - IF( C.LE.TEMP ) THEN - TAU = RHO - ELSE - DEL = D( N ) - D( N-1 ) - A = -C*DEL + Z( N-1 )*Z( N-1 ) + Z( N )*Z( N ) - B = Z( N )*Z( N )*DEL - IF( A.LT.ZERO ) THEN - TAU = TWO*B / ( SQRT( A*A+FOUR*B*C )-A ) - ELSE - TAU = ( A+SQRT( A*A+FOUR*B*C ) ) / ( TWO*C ) - END IF - END IF -* -* It can be proved that -* D(N)+RHO/2 <= LAMBDA(N) < D(N)+TAU <= D(N)+RHO -* - DLTLB = MIDPT - DLTUB = RHO - ELSE - DEL = D( N ) - D( N-1 ) - A = -C*DEL + Z( N-1 )*Z( N-1 ) + Z( N )*Z( N ) - B = Z( N )*Z( N )*DEL - IF( A.LT.ZERO ) THEN - TAU = TWO*B / ( SQRT( A*A+FOUR*B*C )-A ) - ELSE - TAU = ( A+SQRT( A*A+FOUR*B*C ) ) / ( TWO*C ) - END IF -* -* It can be proved that -* D(N) < D(N)+TAU < LAMBDA(N) < D(N)+RHO/2 -* - DLTLB = ZERO - DLTUB = MIDPT - END IF -* - DO 30 J = 1, N - DELTA( J ) = ( D( J )-D( I ) ) - TAU - 30 CONTINUE -* -* Evaluate PSI and the derivative DPSI -* - DPSI = ZERO - PSI = ZERO - ERRETM = ZERO - DO 40 J = 1, II - TEMP = Z( J ) / DELTA( J ) - PSI = PSI + Z( J )*TEMP - DPSI = DPSI + TEMP*TEMP - ERRETM = ERRETM + PSI - 40 CONTINUE - ERRETM = ABS( ERRETM ) -* -* Evaluate PHI and the derivative DPHI -* - TEMP = Z( N ) / DELTA( N ) - PHI = Z( N )*TEMP - DPHI = TEMP*TEMP - ERRETM = EIGHT*( -PHI-PSI ) + ERRETM - PHI + RHOINV + - $ ABS( TAU )*( DPSI+DPHI ) -* - W = RHOINV + PHI + PSI -* -* Test for convergence -* - IF( ABS( W ).LE.EPS*ERRETM ) THEN - DLAM = D( I ) + TAU - GO TO 250 - END IF -* - IF( W.LE.ZERO ) THEN - DLTLB = MAX( DLTLB, TAU ) - ELSE - DLTUB = MIN( DLTUB, TAU ) - END IF -* -* Calculate the new step -* - NITER = NITER + 1 - C = W - DELTA( N-1 )*DPSI - DELTA( N )*DPHI - A = ( DELTA( N-1 )+DELTA( N ) )*W - - $ DELTA( N-1 )*DELTA( N )*( DPSI+DPHI ) - B = DELTA( N-1 )*DELTA( N )*W - IF( C.LT.ZERO ) - $ C = ABS( C ) - IF( C.EQ.ZERO ) THEN -* ETA = B/A -* ETA = RHO - TAU -* ETA = DLTUB - TAU -* -* Update proposed by Li, Ren-Cang: - ETA = -W / ( DPSI+DPHI ) - ELSE IF( A.GE.ZERO ) THEN - ETA = ( A+SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C ) - ELSE - ETA = TWO*B / ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) - END IF -* -* Note, eta should be positive if w is negative, and -* eta should be negative otherwise. However, -* if for some reason caused by roundoff, eta*w > 0, -* we simply use one Newton step instead. This way -* will guarantee eta*w < 0. -* - IF( W*ETA.GT.ZERO ) - $ ETA = -W / ( DPSI+DPHI ) - TEMP = TAU + ETA - IF( TEMP.GT.DLTUB .OR. TEMP.LT.DLTLB ) THEN - IF( W.LT.ZERO ) THEN - ETA = ( DLTUB-TAU ) / TWO - ELSE - ETA = ( DLTLB-TAU ) / TWO - END IF - END IF - DO 50 J = 1, N - DELTA( J ) = DELTA( J ) - ETA - 50 CONTINUE -* - TAU = TAU + ETA -* -* Evaluate PSI and the derivative DPSI -* - DPSI = ZERO - PSI = ZERO - ERRETM = ZERO - DO 60 J = 1, II - TEMP = Z( J ) / DELTA( J ) - PSI = PSI + Z( J )*TEMP - DPSI = DPSI + TEMP*TEMP - ERRETM = ERRETM + PSI - 60 CONTINUE - ERRETM = ABS( ERRETM ) -* -* Evaluate PHI and the derivative DPHI -* - TEMP = Z( N ) / DELTA( N ) - PHI = Z( N )*TEMP - DPHI = TEMP*TEMP - ERRETM = EIGHT*( -PHI-PSI ) + ERRETM - PHI + RHOINV + - $ ABS( TAU )*( DPSI+DPHI ) -* - W = RHOINV + PHI + PSI -* -* Main loop to update the values of the array DELTA -* - ITER = NITER + 1 -* - DO 90 NITER = ITER, MAXIT -* -* Test for convergence -* - IF( ABS( W ).LE.EPS*ERRETM ) THEN - DLAM = D( I ) + TAU - GO TO 250 - END IF -* - IF( W.LE.ZERO ) THEN - DLTLB = MAX( DLTLB, TAU ) - ELSE - DLTUB = MIN( DLTUB, TAU ) - END IF -* -* Calculate the new step -* - C = W - DELTA( N-1 )*DPSI - DELTA( N )*DPHI - A = ( DELTA( N-1 )+DELTA( N ) )*W - - $ DELTA( N-1 )*DELTA( N )*( DPSI+DPHI ) - B = DELTA( N-1 )*DELTA( N )*W - IF( A.GE.ZERO ) THEN - ETA = ( A+SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C ) - ELSE - ETA = TWO*B / ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) - END IF -* -* Note, eta should be positive if w is negative, and -* eta should be negative otherwise. However, -* if for some reason caused by roundoff, eta*w > 0, -* we simply use one Newton step instead. This way -* will guarantee eta*w < 0. -* - IF( W*ETA.GT.ZERO ) - $ ETA = -W / ( DPSI+DPHI ) - TEMP = TAU + ETA - IF( TEMP.GT.DLTUB .OR. TEMP.LT.DLTLB ) THEN - IF( W.LT.ZERO ) THEN - ETA = ( DLTUB-TAU ) / TWO - ELSE - ETA = ( DLTLB-TAU ) / TWO - END IF - END IF - DO 70 J = 1, N - DELTA( J ) = DELTA( J ) - ETA - 70 CONTINUE -* - TAU = TAU + ETA -* -* Evaluate PSI and the derivative DPSI -* - DPSI = ZERO - PSI = ZERO - ERRETM = ZERO - DO 80 J = 1, II - TEMP = Z( J ) / DELTA( J ) - PSI = PSI + Z( J )*TEMP - DPSI = DPSI + TEMP*TEMP - ERRETM = ERRETM + PSI - 80 CONTINUE - ERRETM = ABS( ERRETM ) -* -* Evaluate PHI and the derivative DPHI -* - TEMP = Z( N ) / DELTA( N ) - PHI = Z( N )*TEMP - DPHI = TEMP*TEMP - ERRETM = EIGHT*( -PHI-PSI ) + ERRETM - PHI + RHOINV + - $ ABS( TAU )*( DPSI+DPHI ) -* - W = RHOINV + PHI + PSI - 90 CONTINUE -* -* Return with INFO = 1, NITER = MAXIT and not converged -* - INFO = 1 - DLAM = D( I ) + TAU - GO TO 250 -* -* End for the case I = N -* - ELSE -* -* The case for I < N -* - NITER = 1 - IP1 = I + 1 -* -* Calculate initial guess -* - DEL = D( IP1 ) - D( I ) - MIDPT = DEL / TWO - DO 100 J = 1, N - DELTA( J ) = ( D( J )-D( I ) ) - MIDPT - 100 CONTINUE -* - PSI = ZERO - DO 110 J = 1, I - 1 - PSI = PSI + Z( J )*Z( J ) / DELTA( J ) - 110 CONTINUE -* - PHI = ZERO - DO 120 J = N, I + 2, -1 - PHI = PHI + Z( J )*Z( J ) / DELTA( J ) - 120 CONTINUE - C = RHOINV + PSI + PHI - W = C + Z( I )*Z( I ) / DELTA( I ) + - $ Z( IP1 )*Z( IP1 ) / DELTA( IP1 ) -* - IF( W.GT.ZERO ) THEN -* -* d(i)< the ith eigenvalue < (d(i)+d(i+1))/2 -* -* We choose d(i) as origin. -* - ORGATI = .TRUE. - A = C*DEL + Z( I )*Z( I ) + Z( IP1 )*Z( IP1 ) - B = Z( I )*Z( I )*DEL - IF( A.GT.ZERO ) THEN - TAU = TWO*B / ( A+SQRT( ABS( A*A-FOUR*B*C ) ) ) - ELSE - TAU = ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C ) - END IF - DLTLB = ZERO - DLTUB = MIDPT - ELSE -* -* (d(i)+d(i+1))/2 <= the ith eigenvalue < d(i+1) -* -* We choose d(i+1) as origin. -* - ORGATI = .FALSE. - A = C*DEL - Z( I )*Z( I ) - Z( IP1 )*Z( IP1 ) - B = Z( IP1 )*Z( IP1 )*DEL - IF( A.LT.ZERO ) THEN - TAU = TWO*B / ( A-SQRT( ABS( A*A+FOUR*B*C ) ) ) - ELSE - TAU = -( A+SQRT( ABS( A*A+FOUR*B*C ) ) ) / ( TWO*C ) - END IF - DLTLB = -MIDPT - DLTUB = ZERO - END IF -* - IF( ORGATI ) THEN - DO 130 J = 1, N - DELTA( J ) = ( D( J )-D( I ) ) - TAU - 130 CONTINUE - ELSE - DO 140 J = 1, N - DELTA( J ) = ( D( J )-D( IP1 ) ) - TAU - 140 CONTINUE - END IF - IF( ORGATI ) THEN - II = I - ELSE - II = I + 1 - END IF - IIM1 = II - 1 - IIP1 = II + 1 -* -* Evaluate PSI and the derivative DPSI -* - DPSI = ZERO - PSI = ZERO - ERRETM = ZERO - DO 150 J = 1, IIM1 - TEMP = Z( J ) / DELTA( J ) - PSI = PSI + Z( J )*TEMP - DPSI = DPSI + TEMP*TEMP - ERRETM = ERRETM + PSI - 150 CONTINUE - ERRETM = ABS( ERRETM ) -* -* Evaluate PHI and the derivative DPHI -* - DPHI = ZERO - PHI = ZERO - DO 160 J = N, IIP1, -1 - TEMP = Z( J ) / DELTA( J ) - PHI = PHI + Z( J )*TEMP - DPHI = DPHI + TEMP*TEMP - ERRETM = ERRETM + PHI - 160 CONTINUE -* - W = RHOINV + PHI + PSI -* -* W is the value of the secular function with -* its ii-th element removed. -* - SWTCH3 = .FALSE. - IF( ORGATI ) THEN - IF( W.LT.ZERO ) - $ SWTCH3 = .TRUE. - ELSE - IF( W.GT.ZERO ) - $ SWTCH3 = .TRUE. - END IF - IF( II.EQ.1 .OR. II.EQ.N ) - $ SWTCH3 = .FALSE. -* - TEMP = Z( II ) / DELTA( II ) - DW = DPSI + DPHI + TEMP*TEMP - TEMP = Z( II )*TEMP - W = W + TEMP - ERRETM = EIGHT*( PHI-PSI ) + ERRETM + TWO*RHOINV + - $ THREE*ABS( TEMP ) + ABS( TAU )*DW -* -* Test for convergence -* - IF( ABS( W ).LE.EPS*ERRETM ) THEN - IF( ORGATI ) THEN - DLAM = D( I ) + TAU - ELSE - DLAM = D( IP1 ) + TAU - END IF - GO TO 250 - END IF -* - IF( W.LE.ZERO ) THEN - DLTLB = MAX( DLTLB, TAU ) - ELSE - DLTUB = MIN( DLTUB, TAU ) - END IF -* -* Calculate the new step -* - NITER = NITER + 1 - IF( .NOT.SWTCH3 ) THEN - IF( ORGATI ) THEN - C = W - DELTA( IP1 )*DW - ( D( I )-D( IP1 ) )* - $ ( Z( I ) / DELTA( I ) )**2 - ELSE - C = W - DELTA( I )*DW - ( D( IP1 )-D( I ) )* - $ ( Z( IP1 ) / DELTA( IP1 ) )**2 - END IF - A = ( DELTA( I )+DELTA( IP1 ) )*W - - $ DELTA( I )*DELTA( IP1 )*DW - B = DELTA( I )*DELTA( IP1 )*W - IF( C.EQ.ZERO ) THEN - IF( A.EQ.ZERO ) THEN - IF( ORGATI ) THEN - A = Z( I )*Z( I ) + DELTA( IP1 )*DELTA( IP1 )* - $ ( DPSI+DPHI ) - ELSE - A = Z( IP1 )*Z( IP1 ) + DELTA( I )*DELTA( I )* - $ ( DPSI+DPHI ) - END IF - END IF - ETA = B / A - ELSE IF( A.LE.ZERO ) THEN - ETA = ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C ) - ELSE - ETA = TWO*B / ( A+SQRT( ABS( A*A-FOUR*B*C ) ) ) - END IF - ELSE -* -* Interpolation using THREE most relevant poles -* - TEMP = RHOINV + PSI + PHI - IF( ORGATI ) THEN - TEMP1 = Z( IIM1 ) / DELTA( IIM1 ) - TEMP1 = TEMP1*TEMP1 - C = TEMP - DELTA( IIP1 )*( DPSI+DPHI ) - - $ ( D( IIM1 )-D( IIP1 ) )*TEMP1 - ZZ( 1 ) = Z( IIM1 )*Z( IIM1 ) - ZZ( 3 ) = DELTA( IIP1 )*DELTA( IIP1 )* - $ ( ( DPSI-TEMP1 )+DPHI ) - ELSE - TEMP1 = Z( IIP1 ) / DELTA( IIP1 ) - TEMP1 = TEMP1*TEMP1 - C = TEMP - DELTA( IIM1 )*( DPSI+DPHI ) - - $ ( D( IIP1 )-D( IIM1 ) )*TEMP1 - ZZ( 1 ) = DELTA( IIM1 )*DELTA( IIM1 )* - $ ( DPSI+( DPHI-TEMP1 ) ) - ZZ( 3 ) = Z( IIP1 )*Z( IIP1 ) - END IF - ZZ( 2 ) = Z( II )*Z( II ) - CALL DLAED6( NITER, ORGATI, C, DELTA( IIM1 ), ZZ, W, ETA, - $ INFO ) - IF( INFO.NE.0 ) - $ GO TO 250 - END IF -* -* Note, eta should be positive if w is negative, and -* eta should be negative otherwise. However, -* if for some reason caused by roundoff, eta*w > 0, -* we simply use one Newton step instead. This way -* will guarantee eta*w < 0. -* - IF( W*ETA.GE.ZERO ) - $ ETA = -W / DW - TEMP = TAU + ETA - IF( TEMP.GT.DLTUB .OR. TEMP.LT.DLTLB ) THEN - IF( W.LT.ZERO ) THEN - ETA = ( DLTUB-TAU ) / TWO - ELSE - ETA = ( DLTLB-TAU ) / TWO - END IF - END IF -* - PREW = W -* - DO 180 J = 1, N - DELTA( J ) = DELTA( J ) - ETA - 180 CONTINUE -* -* Evaluate PSI and the derivative DPSI -* - DPSI = ZERO - PSI = ZERO - ERRETM = ZERO - DO 190 J = 1, IIM1 - TEMP = Z( J ) / DELTA( J ) - PSI = PSI + Z( J )*TEMP - DPSI = DPSI + TEMP*TEMP - ERRETM = ERRETM + PSI - 190 CONTINUE - ERRETM = ABS( ERRETM ) -* -* Evaluate PHI and the derivative DPHI -* - DPHI = ZERO - PHI = ZERO - DO 200 J = N, IIP1, -1 - TEMP = Z( J ) / DELTA( J ) - PHI = PHI + Z( J )*TEMP - DPHI = DPHI + TEMP*TEMP - ERRETM = ERRETM + PHI - 200 CONTINUE -* - TEMP = Z( II ) / DELTA( II ) - DW = DPSI + DPHI + TEMP*TEMP - TEMP = Z( II )*TEMP - W = RHOINV + PHI + PSI + TEMP - ERRETM = EIGHT*( PHI-PSI ) + ERRETM + TWO*RHOINV + - $ THREE*ABS( TEMP ) + ABS( TAU+ETA )*DW -* - SWTCH = .FALSE. - IF( ORGATI ) THEN - IF( -W.GT.ABS( PREW ) / TEN ) - $ SWTCH = .TRUE. - ELSE - IF( W.GT.ABS( PREW ) / TEN ) - $ SWTCH = .TRUE. - END IF -* - TAU = TAU + ETA -* -* Main loop to update the values of the array DELTA -* - ITER = NITER + 1 -* - DO 240 NITER = ITER, MAXIT -* -* Test for convergence -* - IF( ABS( W ).LE.EPS*ERRETM ) THEN - IF( ORGATI ) THEN - DLAM = D( I ) + TAU - ELSE - DLAM = D( IP1 ) + TAU - END IF - GO TO 250 - END IF -* - IF( W.LE.ZERO ) THEN - DLTLB = MAX( DLTLB, TAU ) - ELSE - DLTUB = MIN( DLTUB, TAU ) - END IF -* -* Calculate the new step -* - IF( .NOT.SWTCH3 ) THEN - IF( .NOT.SWTCH ) THEN - IF( ORGATI ) THEN - C = W - DELTA( IP1 )*DW - - $ ( D( I )-D( IP1 ) )*( Z( I ) / DELTA( I ) )**2 - ELSE - C = W - DELTA( I )*DW - ( D( IP1 )-D( I ) )* - $ ( Z( IP1 ) / DELTA( IP1 ) )**2 - END IF - ELSE - TEMP = Z( II ) / DELTA( II ) - IF( ORGATI ) THEN - DPSI = DPSI + TEMP*TEMP - ELSE - DPHI = DPHI + TEMP*TEMP - END IF - C = W - DELTA( I )*DPSI - DELTA( IP1 )*DPHI - END IF - A = ( DELTA( I )+DELTA( IP1 ) )*W - - $ DELTA( I )*DELTA( IP1 )*DW - B = DELTA( I )*DELTA( IP1 )*W - IF( C.EQ.ZERO ) THEN - IF( A.EQ.ZERO ) THEN - IF( .NOT.SWTCH ) THEN - IF( ORGATI ) THEN - A = Z( I )*Z( I ) + DELTA( IP1 )* - $ DELTA( IP1 )*( DPSI+DPHI ) - ELSE - A = Z( IP1 )*Z( IP1 ) + - $ DELTA( I )*DELTA( I )*( DPSI+DPHI ) - END IF - ELSE - A = DELTA( I )*DELTA( I )*DPSI + - $ DELTA( IP1 )*DELTA( IP1 )*DPHI - END IF - END IF - ETA = B / A - ELSE IF( A.LE.ZERO ) THEN - ETA = ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C ) - ELSE - ETA = TWO*B / ( A+SQRT( ABS( A*A-FOUR*B*C ) ) ) - END IF - ELSE -* -* Interpolation using THREE most relevant poles -* - TEMP = RHOINV + PSI + PHI - IF( SWTCH ) THEN - C = TEMP - DELTA( IIM1 )*DPSI - DELTA( IIP1 )*DPHI - ZZ( 1 ) = DELTA( IIM1 )*DELTA( IIM1 )*DPSI - ZZ( 3 ) = DELTA( IIP1 )*DELTA( IIP1 )*DPHI - ELSE - IF( ORGATI ) THEN - TEMP1 = Z( IIM1 ) / DELTA( IIM1 ) - TEMP1 = TEMP1*TEMP1 - C = TEMP - DELTA( IIP1 )*( DPSI+DPHI ) - - $ ( D( IIM1 )-D( IIP1 ) )*TEMP1 - ZZ( 1 ) = Z( IIM1 )*Z( IIM1 ) - ZZ( 3 ) = DELTA( IIP1 )*DELTA( IIP1 )* - $ ( ( DPSI-TEMP1 )+DPHI ) - ELSE - TEMP1 = Z( IIP1 ) / DELTA( IIP1 ) - TEMP1 = TEMP1*TEMP1 - C = TEMP - DELTA( IIM1 )*( DPSI+DPHI ) - - $ ( D( IIP1 )-D( IIM1 ) )*TEMP1 - ZZ( 1 ) = DELTA( IIM1 )*DELTA( IIM1 )* - $ ( DPSI+( DPHI-TEMP1 ) ) - ZZ( 3 ) = Z( IIP1 )*Z( IIP1 ) - END IF - END IF - CALL DLAED6( NITER, ORGATI, C, DELTA( IIM1 ), ZZ, W, ETA, - $ INFO ) - IF( INFO.NE.0 ) - $ GO TO 250 - END IF -* -* Note, eta should be positive if w is negative, and -* eta should be negative otherwise. However, -* if for some reason caused by roundoff, eta*w > 0, -* we simply use one Newton step instead. This way -* will guarantee eta*w < 0. -* - IF( W*ETA.GE.ZERO ) - $ ETA = -W / DW - TEMP = TAU + ETA - IF( TEMP.GT.DLTUB .OR. TEMP.LT.DLTLB ) THEN - IF( W.LT.ZERO ) THEN - ETA = ( DLTUB-TAU ) / TWO - ELSE - ETA = ( DLTLB-TAU ) / TWO - END IF - END IF -* - DO 210 J = 1, N - DELTA( J ) = DELTA( J ) - ETA - 210 CONTINUE -* - TAU = TAU + ETA - PREW = W -* -* Evaluate PSI and the derivative DPSI -* - DPSI = ZERO - PSI = ZERO - ERRETM = ZERO - DO 220 J = 1, IIM1 - TEMP = Z( J ) / DELTA( J ) - PSI = PSI + Z( J )*TEMP - DPSI = DPSI + TEMP*TEMP - ERRETM = ERRETM + PSI - 220 CONTINUE - ERRETM = ABS( ERRETM ) -* -* Evaluate PHI and the derivative DPHI -* - DPHI = ZERO - PHI = ZERO - DO 230 J = N, IIP1, -1 - TEMP = Z( J ) / DELTA( J ) - PHI = PHI + Z( J )*TEMP - DPHI = DPHI + TEMP*TEMP - ERRETM = ERRETM + PHI - 230 CONTINUE -* - TEMP = Z( II ) / DELTA( II ) - DW = DPSI + DPHI + TEMP*TEMP - TEMP = Z( II )*TEMP - W = RHOINV + PHI + PSI + TEMP - ERRETM = EIGHT*( PHI-PSI ) + ERRETM + TWO*RHOINV + - $ THREE*ABS( TEMP ) + ABS( TAU )*DW - IF( W*PREW.GT.ZERO .AND. ABS( W ).GT.ABS( PREW ) / TEN ) - $ SWTCH = .NOT.SWTCH -* - 240 CONTINUE -* -* Return with INFO = 1, NITER = MAXIT and not converged -* - INFO = 1 - IF( ORGATI ) THEN - DLAM = D( I ) + TAU - ELSE - DLAM = D( IP1 ) + TAU - END IF -* - END IF -* - 250 CONTINUE -* - RETURN -* -* End of DLAED4 -* - END diff --git a/lib/linalg/fortran/dlaed5.f b/lib/linalg/fortran/dlaed5.f deleted file mode 100644 index d9e977e6b7..0000000000 --- a/lib/linalg/fortran/dlaed5.f +++ /dev/null @@ -1,186 +0,0 @@ -*> \brief \b DLAED5 used by DSTEDC. Solves the 2-by-2 secular equation. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLAED5 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLAED5( I, D, Z, DELTA, RHO, DLAM ) -* -* .. Scalar Arguments .. -* INTEGER I -* DOUBLE PRECISION DLAM, RHO -* .. -* .. Array Arguments .. -* DOUBLE PRECISION D( 2 ), DELTA( 2 ), Z( 2 ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> This subroutine computes the I-th eigenvalue of a symmetric rank-one -*> modification of a 2-by-2 diagonal matrix -*> -*> diag( D ) + RHO * Z * transpose(Z) . -*> -*> The diagonal elements in the array D are assumed to satisfy -*> -*> D(i) < D(j) for i < j . -*> -*> We also assume RHO > 0 and that the Euclidean norm of the vector -*> Z is one. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] I -*> \verbatim -*> I is INTEGER -*> The index of the eigenvalue to be computed. I = 1 or I = 2. -*> \endverbatim -*> -*> \param[in] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension (2) -*> The original eigenvalues. We assume D(1) < D(2). -*> \endverbatim -*> -*> \param[in] Z -*> \verbatim -*> Z is DOUBLE PRECISION array, dimension (2) -*> The components of the updating vector. -*> \endverbatim -*> -*> \param[out] DELTA -*> \verbatim -*> DELTA is DOUBLE PRECISION array, dimension (2) -*> The vector DELTA contains the information necessary -*> to construct the eigenvectors. -*> \endverbatim -*> -*> \param[in] RHO -*> \verbatim -*> RHO is DOUBLE PRECISION -*> The scalar in the symmetric updating formula. -*> \endverbatim -*> -*> \param[out] DLAM -*> \verbatim -*> DLAM is DOUBLE PRECISION -*> The computed lambda_I, the I-th updated eigenvalue. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup auxOTHERcomputational -* -*> \par Contributors: -* ================== -*> -*> Ren-Cang Li, Computer Science Division, University of California -*> at Berkeley, USA -*> -* ===================================================================== - SUBROUTINE DLAED5( I, D, Z, DELTA, RHO, DLAM ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER I - DOUBLE PRECISION DLAM, RHO -* .. -* .. Array Arguments .. - DOUBLE PRECISION D( 2 ), DELTA( 2 ), Z( 2 ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, ONE, TWO, FOUR - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0, - $ FOUR = 4.0D0 ) -* .. -* .. Local Scalars .. - DOUBLE PRECISION B, C, DEL, TAU, TEMP, W -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, SQRT -* .. -* .. Executable Statements .. -* - DEL = D( 2 ) - D( 1 ) - IF( I.EQ.1 ) THEN - W = ONE + TWO*RHO*( Z( 2 )*Z( 2 )-Z( 1 )*Z( 1 ) ) / DEL - IF( W.GT.ZERO ) THEN - B = DEL + RHO*( Z( 1 )*Z( 1 )+Z( 2 )*Z( 2 ) ) - C = RHO*Z( 1 )*Z( 1 )*DEL -* -* B > ZERO, always -* - TAU = TWO*C / ( B+SQRT( ABS( B*B-FOUR*C ) ) ) - DLAM = D( 1 ) + TAU - DELTA( 1 ) = -Z( 1 ) / TAU - DELTA( 2 ) = Z( 2 ) / ( DEL-TAU ) - ELSE - B = -DEL + RHO*( Z( 1 )*Z( 1 )+Z( 2 )*Z( 2 ) ) - C = RHO*Z( 2 )*Z( 2 )*DEL - IF( B.GT.ZERO ) THEN - TAU = -TWO*C / ( B+SQRT( B*B+FOUR*C ) ) - ELSE - TAU = ( B-SQRT( B*B+FOUR*C ) ) / TWO - END IF - DLAM = D( 2 ) + TAU - DELTA( 1 ) = -Z( 1 ) / ( DEL+TAU ) - DELTA( 2 ) = -Z( 2 ) / TAU - END IF - TEMP = SQRT( DELTA( 1 )*DELTA( 1 )+DELTA( 2 )*DELTA( 2 ) ) - DELTA( 1 ) = DELTA( 1 ) / TEMP - DELTA( 2 ) = DELTA( 2 ) / TEMP - ELSE -* -* Now I=2 -* - B = -DEL + RHO*( Z( 1 )*Z( 1 )+Z( 2 )*Z( 2 ) ) - C = RHO*Z( 2 )*Z( 2 )*DEL - IF( B.GT.ZERO ) THEN - TAU = ( B+SQRT( B*B+FOUR*C ) ) / TWO - ELSE - TAU = TWO*C / ( -B+SQRT( B*B+FOUR*C ) ) - END IF - DLAM = D( 2 ) + TAU - DELTA( 1 ) = -Z( 1 ) / ( DEL+TAU ) - DELTA( 2 ) = -Z( 2 ) / TAU - TEMP = SQRT( DELTA( 1 )*DELTA( 1 )+DELTA( 2 )*DELTA( 2 ) ) - DELTA( 1 ) = DELTA( 1 ) / TEMP - DELTA( 2 ) = DELTA( 2 ) / TEMP - END IF - RETURN -* -* End of DLAED5 -* - END diff --git a/lib/linalg/fortran/dlaed6.f b/lib/linalg/fortran/dlaed6.f deleted file mode 100644 index a0c0364e56..0000000000 --- a/lib/linalg/fortran/dlaed6.f +++ /dev/null @@ -1,407 +0,0 @@ -*> \brief \b DLAED6 used by DSTEDC. Computes one Newton step in solution of the secular equation. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLAED6 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLAED6( KNITER, ORGATI, RHO, D, Z, FINIT, TAU, INFO ) -* -* .. Scalar Arguments .. -* LOGICAL ORGATI -* INTEGER INFO, KNITER -* DOUBLE PRECISION FINIT, RHO, TAU -* .. -* .. Array Arguments .. -* DOUBLE PRECISION D( 3 ), Z( 3 ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLAED6 computes the positive or negative root (closest to the origin) -*> of -*> z(1) z(2) z(3) -*> f(x) = rho + --------- + ---------- + --------- -*> d(1)-x d(2)-x d(3)-x -*> -*> It is assumed that -*> -*> if ORGATI = .true. the root is between d(2) and d(3); -*> otherwise it is between d(1) and d(2) -*> -*> This routine will be called by DLAED4 when necessary. In most cases, -*> the root sought is the smallest in magnitude, though it might not be -*> in some extremely rare situations. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] KNITER -*> \verbatim -*> KNITER is INTEGER -*> Refer to DLAED4 for its significance. -*> \endverbatim -*> -*> \param[in] ORGATI -*> \verbatim -*> ORGATI is LOGICAL -*> If ORGATI is true, the needed root is between d(2) and -*> d(3); otherwise it is between d(1) and d(2). See -*> DLAED4 for further details. -*> \endverbatim -*> -*> \param[in] RHO -*> \verbatim -*> RHO is DOUBLE PRECISION -*> Refer to the equation f(x) above. -*> \endverbatim -*> -*> \param[in] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension (3) -*> D satisfies d(1) < d(2) < d(3). -*> \endverbatim -*> -*> \param[in] Z -*> \verbatim -*> Z is DOUBLE PRECISION array, dimension (3) -*> Each of the elements in z must be positive. -*> \endverbatim -*> -*> \param[in] FINIT -*> \verbatim -*> FINIT is DOUBLE PRECISION -*> The value of f at 0. It is more accurate than the one -*> evaluated inside this routine (if someone wants to do -*> so). -*> \endverbatim -*> -*> \param[out] TAU -*> \verbatim -*> TAU is DOUBLE PRECISION -*> The root of the equation f(x). -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> > 0: if INFO = 1, failure to converge -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup auxOTHERcomputational -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> 10/02/03: This version has a few statements commented out for thread -*> safety (machine parameters are computed on each entry). SJH. -*> -*> 05/10/06: Modified from a new version of Ren-Cang Li, use -*> Gragg-Thornton-Warner cubic convergent scheme for better stability. -*> \endverbatim -* -*> \par Contributors: -* ================== -*> -*> Ren-Cang Li, Computer Science Division, University of California -*> at Berkeley, USA -*> -* ===================================================================== - SUBROUTINE DLAED6( KNITER, ORGATI, RHO, D, Z, FINIT, TAU, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - LOGICAL ORGATI - INTEGER INFO, KNITER - DOUBLE PRECISION FINIT, RHO, TAU -* .. -* .. Array Arguments .. - DOUBLE PRECISION D( 3 ), Z( 3 ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - INTEGER MAXIT - PARAMETER ( MAXIT = 40 ) - DOUBLE PRECISION ZERO, ONE, TWO, THREE, FOUR, EIGHT - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0, - $ THREE = 3.0D0, FOUR = 4.0D0, EIGHT = 8.0D0 ) -* .. -* .. External Functions .. - DOUBLE PRECISION DLAMCH - EXTERNAL DLAMCH -* .. -* .. Local Arrays .. - DOUBLE PRECISION DSCALE( 3 ), ZSCALE( 3 ) -* .. -* .. Local Scalars .. - LOGICAL SCALE - INTEGER I, ITER, NITER - DOUBLE PRECISION A, B, BASE, C, DDF, DF, EPS, ERRETM, ETA, F, - $ FC, SCLFAC, SCLINV, SMALL1, SMALL2, SMINV1, - $ SMINV2, TEMP, TEMP1, TEMP2, TEMP3, TEMP4, - $ LBD, UBD -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, INT, LOG, MAX, MIN, SQRT -* .. -* .. Executable Statements .. -* - INFO = 0 -* - IF( ORGATI ) THEN - LBD = D(2) - UBD = D(3) - ELSE - LBD = D(1) - UBD = D(2) - END IF - IF( FINIT .LT. ZERO )THEN - LBD = ZERO - ELSE - UBD = ZERO - END IF -* - NITER = 1 - TAU = ZERO - IF( KNITER.EQ.2 ) THEN - IF( ORGATI ) THEN - TEMP = ( D( 3 )-D( 2 ) ) / TWO - C = RHO + Z( 1 ) / ( ( D( 1 )-D( 2 ) )-TEMP ) - A = C*( D( 2 )+D( 3 ) ) + Z( 2 ) + Z( 3 ) - B = C*D( 2 )*D( 3 ) + Z( 2 )*D( 3 ) + Z( 3 )*D( 2 ) - ELSE - TEMP = ( D( 1 )-D( 2 ) ) / TWO - C = RHO + Z( 3 ) / ( ( D( 3 )-D( 2 ) )-TEMP ) - A = C*( D( 1 )+D( 2 ) ) + Z( 1 ) + Z( 2 ) - B = C*D( 1 )*D( 2 ) + Z( 1 )*D( 2 ) + Z( 2 )*D( 1 ) - END IF - TEMP = MAX( ABS( A ), ABS( B ), ABS( C ) ) - A = A / TEMP - B = B / TEMP - C = C / TEMP - IF( C.EQ.ZERO ) THEN - TAU = B / A - ELSE IF( A.LE.ZERO ) THEN - TAU = ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C ) - ELSE - TAU = TWO*B / ( A+SQRT( ABS( A*A-FOUR*B*C ) ) ) - END IF - IF( TAU .LT. LBD .OR. TAU .GT. UBD ) - $ TAU = ( LBD+UBD )/TWO - IF( D(1).EQ.TAU .OR. D(2).EQ.TAU .OR. D(3).EQ.TAU ) THEN - TAU = ZERO - ELSE - TEMP = FINIT + TAU*Z(1)/( D(1)*( D( 1 )-TAU ) ) + - $ TAU*Z(2)/( D(2)*( D( 2 )-TAU ) ) + - $ TAU*Z(3)/( D(3)*( D( 3 )-TAU ) ) - IF( TEMP .LE. ZERO )THEN - LBD = TAU - ELSE - UBD = TAU - END IF - IF( ABS( FINIT ).LE.ABS( TEMP ) ) - $ TAU = ZERO - END IF - END IF -* -* get machine parameters for possible scaling to avoid overflow -* -* modified by Sven: parameters SMALL1, SMINV1, SMALL2, -* SMINV2, EPS are not SAVEd anymore between one call to the -* others but recomputed at each call -* - EPS = DLAMCH( 'Epsilon' ) - BASE = DLAMCH( 'Base' ) - SMALL1 = BASE**( INT( LOG( DLAMCH( 'SafMin' ) ) / LOG( BASE ) / - $ THREE ) ) - SMINV1 = ONE / SMALL1 - SMALL2 = SMALL1*SMALL1 - SMINV2 = SMINV1*SMINV1 -* -* Determine if scaling of inputs necessary to avoid overflow -* when computing 1/TEMP**3 -* - IF( ORGATI ) THEN - TEMP = MIN( ABS( D( 2 )-TAU ), ABS( D( 3 )-TAU ) ) - ELSE - TEMP = MIN( ABS( D( 1 )-TAU ), ABS( D( 2 )-TAU ) ) - END IF - SCALE = .FALSE. - IF( TEMP.LE.SMALL1 ) THEN - SCALE = .TRUE. - IF( TEMP.LE.SMALL2 ) THEN -* -* Scale up by power of radix nearest 1/SAFMIN**(2/3) -* - SCLFAC = SMINV2 - SCLINV = SMALL2 - ELSE -* -* Scale up by power of radix nearest 1/SAFMIN**(1/3) -* - SCLFAC = SMINV1 - SCLINV = SMALL1 - END IF -* -* Scaling up safe because D, Z, TAU scaled elsewhere to be O(1) -* - DO 10 I = 1, 3 - DSCALE( I ) = D( I )*SCLFAC - ZSCALE( I ) = Z( I )*SCLFAC - 10 CONTINUE - TAU = TAU*SCLFAC - LBD = LBD*SCLFAC - UBD = UBD*SCLFAC - ELSE -* -* Copy D and Z to DSCALE and ZSCALE -* - DO 20 I = 1, 3 - DSCALE( I ) = D( I ) - ZSCALE( I ) = Z( I ) - 20 CONTINUE - END IF -* - FC = ZERO - DF = ZERO - DDF = ZERO - DO 30 I = 1, 3 - TEMP = ONE / ( DSCALE( I )-TAU ) - TEMP1 = ZSCALE( I )*TEMP - TEMP2 = TEMP1*TEMP - TEMP3 = TEMP2*TEMP - FC = FC + TEMP1 / DSCALE( I ) - DF = DF + TEMP2 - DDF = DDF + TEMP3 - 30 CONTINUE - F = FINIT + TAU*FC -* - IF( ABS( F ).LE.ZERO ) - $ GO TO 60 - IF( F .LE. ZERO )THEN - LBD = TAU - ELSE - UBD = TAU - END IF -* -* Iteration begins -- Use Gragg-Thornton-Warner cubic convergent -* scheme -* -* It is not hard to see that -* -* 1) Iterations will go up monotonically -* if FINIT < 0; -* -* 2) Iterations will go down monotonically -* if FINIT > 0. -* - ITER = NITER + 1 -* - DO 50 NITER = ITER, MAXIT -* - IF( ORGATI ) THEN - TEMP1 = DSCALE( 2 ) - TAU - TEMP2 = DSCALE( 3 ) - TAU - ELSE - TEMP1 = DSCALE( 1 ) - TAU - TEMP2 = DSCALE( 2 ) - TAU - END IF - A = ( TEMP1+TEMP2 )*F - TEMP1*TEMP2*DF - B = TEMP1*TEMP2*F - C = F - ( TEMP1+TEMP2 )*DF + TEMP1*TEMP2*DDF - TEMP = MAX( ABS( A ), ABS( B ), ABS( C ) ) - A = A / TEMP - B = B / TEMP - C = C / TEMP - IF( C.EQ.ZERO ) THEN - ETA = B / A - ELSE IF( A.LE.ZERO ) THEN - ETA = ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C ) - ELSE - ETA = TWO*B / ( A+SQRT( ABS( A*A-FOUR*B*C ) ) ) - END IF - IF( F*ETA.GE.ZERO ) THEN - ETA = -F / DF - END IF -* - TAU = TAU + ETA - IF( TAU .LT. LBD .OR. TAU .GT. UBD ) - $ TAU = ( LBD + UBD )/TWO -* - FC = ZERO - ERRETM = ZERO - DF = ZERO - DDF = ZERO - DO 40 I = 1, 3 - IF ( ( DSCALE( I )-TAU ).NE.ZERO ) THEN - TEMP = ONE / ( DSCALE( I )-TAU ) - TEMP1 = ZSCALE( I )*TEMP - TEMP2 = TEMP1*TEMP - TEMP3 = TEMP2*TEMP - TEMP4 = TEMP1 / DSCALE( I ) - FC = FC + TEMP4 - ERRETM = ERRETM + ABS( TEMP4 ) - DF = DF + TEMP2 - DDF = DDF + TEMP3 - ELSE - GO TO 60 - END IF - 40 CONTINUE - F = FINIT + TAU*FC - ERRETM = EIGHT*( ABS( FINIT )+ABS( TAU )*ERRETM ) + - $ ABS( TAU )*DF - IF( ( ABS( F ).LE.FOUR*EPS*ERRETM ) .OR. - $ ( (UBD-LBD).LE.FOUR*EPS*ABS(TAU) ) ) - $ GO TO 60 - IF( F .LE. ZERO )THEN - LBD = TAU - ELSE - UBD = TAU - END IF - 50 CONTINUE - INFO = 1 - 60 CONTINUE -* -* Undo scaling -* - IF( SCALE ) - $ TAU = TAU*SCLINV - RETURN -* -* End of DLAED6 -* - END diff --git a/lib/linalg/fortran/dlaed7.f b/lib/linalg/fortran/dlaed7.f deleted file mode 100644 index d968c56752..0000000000 --- a/lib/linalg/fortran/dlaed7.f +++ /dev/null @@ -1,404 +0,0 @@ -*> \brief \b DLAED7 used by DSTEDC. Computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. Used when the original matrix is dense. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLAED7 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLAED7( ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, -* LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR, -* PERM, GIVPTR, GIVCOL, GIVNUM, WORK, IWORK, -* INFO ) -* -* .. Scalar Arguments .. -* INTEGER CURLVL, CURPBM, CUTPNT, ICOMPQ, INFO, LDQ, N, -* $ QSIZ, TLVLS -* DOUBLE PRECISION RHO -* .. -* .. Array Arguments .. -* INTEGER GIVCOL( 2, * ), GIVPTR( * ), INDXQ( * ), -* $ IWORK( * ), PERM( * ), PRMPTR( * ), QPTR( * ) -* DOUBLE PRECISION D( * ), GIVNUM( 2, * ), Q( LDQ, * ), -* $ QSTORE( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLAED7 computes the updated eigensystem of a diagonal -*> matrix after modification by a rank-one symmetric matrix. This -*> routine is used only for the eigenproblem which requires all -*> eigenvalues and optionally eigenvectors of a dense symmetric matrix -*> that has been reduced to tridiagonal form. DLAED1 handles -*> the case in which all eigenvalues and eigenvectors of a symmetric -*> tridiagonal matrix are desired. -*> -*> T = Q(in) ( D(in) + RHO * Z*Z**T ) Q**T(in) = Q(out) * D(out) * Q**T(out) -*> -*> where Z = Q**Tu, u is a vector of length N with ones in the -*> CUTPNT and CUTPNT + 1 th elements and zeros elsewhere. -*> -*> The eigenvectors of the original matrix are stored in Q, and the -*> eigenvalues are in D. The algorithm consists of three stages: -*> -*> The first stage consists of deflating the size of the problem -*> when there are multiple eigenvalues or if there is a zero in -*> the Z vector. For each such occurrence the dimension of the -*> secular equation problem is reduced by one. This stage is -*> performed by the routine DLAED8. -*> -*> The second stage consists of calculating the updated -*> eigenvalues. This is done by finding the roots of the secular -*> equation via the routine DLAED4 (as called by DLAED9). -*> This routine also calculates the eigenvectors of the current -*> problem. -*> -*> The final stage consists of computing the updated eigenvectors -*> directly using the updated eigenvalues. The eigenvectors for -*> the current problem are multiplied with the eigenvectors from -*> the overall problem. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] ICOMPQ -*> \verbatim -*> ICOMPQ is INTEGER -*> = 0: Compute eigenvalues only. -*> = 1: Compute eigenvectors of original dense symmetric matrix -*> also. On entry, Q contains the orthogonal matrix used -*> to reduce the original matrix to tridiagonal form. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The dimension of the symmetric tridiagonal matrix. N >= 0. -*> \endverbatim -*> -*> \param[in] QSIZ -*> \verbatim -*> QSIZ is INTEGER -*> The dimension of the orthogonal matrix used to reduce -*> the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. -*> \endverbatim -*> -*> \param[in] TLVLS -*> \verbatim -*> TLVLS is INTEGER -*> The total number of merging levels in the overall divide and -*> conquer tree. -*> \endverbatim -*> -*> \param[in] CURLVL -*> \verbatim -*> CURLVL is INTEGER -*> The current level in the overall merge routine, -*> 0 <= CURLVL <= TLVLS. -*> \endverbatim -*> -*> \param[in] CURPBM -*> \verbatim -*> CURPBM is INTEGER -*> The current problem in the current level in the overall -*> merge routine (counting from upper left to lower right). -*> \endverbatim -*> -*> \param[in,out] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension (N) -*> On entry, the eigenvalues of the rank-1-perturbed matrix. -*> On exit, the eigenvalues of the repaired matrix. -*> \endverbatim -*> -*> \param[in,out] Q -*> \verbatim -*> Q is DOUBLE PRECISION array, dimension (LDQ, N) -*> On entry, the eigenvectors of the rank-1-perturbed matrix. -*> On exit, the eigenvectors of the repaired tridiagonal matrix. -*> \endverbatim -*> -*> \param[in] LDQ -*> \verbatim -*> LDQ is INTEGER -*> The leading dimension of the array Q. LDQ >= max(1,N). -*> \endverbatim -*> -*> \param[out] INDXQ -*> \verbatim -*> INDXQ is INTEGER array, dimension (N) -*> The permutation which will reintegrate the subproblem just -*> solved back into sorted order, i.e., D( INDXQ( I = 1, N ) ) -*> will be in ascending order. -*> \endverbatim -*> -*> \param[in] RHO -*> \verbatim -*> RHO is DOUBLE PRECISION -*> The subdiagonal element used to create the rank-1 -*> modification. -*> \endverbatim -*> -*> \param[in] CUTPNT -*> \verbatim -*> CUTPNT is INTEGER -*> Contains the location of the last eigenvalue in the leading -*> sub-matrix. min(1,N) <= CUTPNT <= N. -*> \endverbatim -*> -*> \param[in,out] QSTORE -*> \verbatim -*> QSTORE is DOUBLE PRECISION array, dimension (N**2+1) -*> Stores eigenvectors of submatrices encountered during -*> divide and conquer, packed together. QPTR points to -*> beginning of the submatrices. -*> \endverbatim -*> -*> \param[in,out] QPTR -*> \verbatim -*> QPTR is INTEGER array, dimension (N+2) -*> List of indices pointing to beginning of submatrices stored -*> in QSTORE. The submatrices are numbered starting at the -*> bottom left of the divide and conquer tree, from left to -*> right and bottom to top. -*> \endverbatim -*> -*> \param[in] PRMPTR -*> \verbatim -*> PRMPTR is INTEGER array, dimension (N lg N) -*> Contains a list of pointers which indicate where in PERM a -*> level's permutation is stored. PRMPTR(i+1) - PRMPTR(i) -*> indicates the size of the permutation and also the size of -*> the full, non-deflated problem. -*> \endverbatim -*> -*> \param[in] PERM -*> \verbatim -*> PERM is INTEGER array, dimension (N lg N) -*> Contains the permutations (from deflation and sorting) to be -*> applied to each eigenblock. -*> \endverbatim -*> -*> \param[in] GIVPTR -*> \verbatim -*> GIVPTR is INTEGER array, dimension (N lg N) -*> Contains a list of pointers which indicate where in GIVCOL a -*> level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i) -*> indicates the number of Givens rotations. -*> \endverbatim -*> -*> \param[in] GIVCOL -*> \verbatim -*> GIVCOL is INTEGER array, dimension (2, N lg N) -*> Each pair of numbers indicates a pair of columns to take place -*> in a Givens rotation. -*> \endverbatim -*> -*> \param[in] GIVNUM -*> \verbatim -*> GIVNUM is DOUBLE PRECISION array, dimension (2, N lg N) -*> Each number indicates the S value to be used in the -*> corresponding Givens rotation. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (3*N+2*QSIZ*N) -*> \endverbatim -*> -*> \param[out] IWORK -*> \verbatim -*> IWORK is INTEGER array, dimension (4*N) -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit. -*> < 0: if INFO = -i, the i-th argument had an illegal value. -*> > 0: if INFO = 1, an eigenvalue did not converge -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup auxOTHERcomputational -* -*> \par Contributors: -* ================== -*> -*> Jeff Rutter, Computer Science Division, University of California -*> at Berkeley, USA -* -* ===================================================================== - SUBROUTINE DLAED7( ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, - $ LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR, - $ PERM, GIVPTR, GIVCOL, GIVNUM, WORK, IWORK, - $ INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER CURLVL, CURPBM, CUTPNT, ICOMPQ, INFO, LDQ, N, - $ QSIZ, TLVLS - DOUBLE PRECISION RHO -* .. -* .. Array Arguments .. - INTEGER GIVCOL( 2, * ), GIVPTR( * ), INDXQ( * ), - $ IWORK( * ), PERM( * ), PRMPTR( * ), QPTR( * ) - DOUBLE PRECISION D( * ), GIVNUM( 2, * ), Q( LDQ, * ), - $ QSTORE( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE, ZERO - PARAMETER ( ONE = 1.0D0, ZERO = 0.0D0 ) -* .. -* .. Local Scalars .. - INTEGER COLTYP, CURR, I, IDLMDA, INDX, INDXC, INDXP, - $ IQ2, IS, IW, IZ, K, LDQ2, N1, N2, PTR -* .. -* .. External Subroutines .. - EXTERNAL DGEMM, DLAED8, DLAED9, DLAEDA, DLAMRG, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, MIN -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 -* - IF( ICOMPQ.LT.0 .OR. ICOMPQ.GT.1 ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( ICOMPQ.EQ.1 .AND. QSIZ.LT.N ) THEN - INFO = -3 - ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN - INFO = -9 - ELSE IF( MIN( 1, N ).GT.CUTPNT .OR. N.LT.CUTPNT ) THEN - INFO = -12 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DLAED7', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( N.EQ.0 ) - $ RETURN -* -* The following values are for bookkeeping purposes only. They are -* integer pointers which indicate the portion of the workspace -* used by a particular array in DLAED8 and DLAED9. -* - IF( ICOMPQ.EQ.1 ) THEN - LDQ2 = QSIZ - ELSE - LDQ2 = N - END IF -* - IZ = 1 - IDLMDA = IZ + N - IW = IDLMDA + N - IQ2 = IW + N - IS = IQ2 + N*LDQ2 -* - INDX = 1 - INDXC = INDX + N - COLTYP = INDXC + N - INDXP = COLTYP + N -* -* Form the z-vector which consists of the last row of Q_1 and the -* first row of Q_2. -* - PTR = 1 + 2**TLVLS - DO 10 I = 1, CURLVL - 1 - PTR = PTR + 2**( TLVLS-I ) - 10 CONTINUE - CURR = PTR + CURPBM - CALL DLAEDA( N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR, - $ GIVCOL, GIVNUM, QSTORE, QPTR, WORK( IZ ), - $ WORK( IZ+N ), INFO ) -* -* When solving the final problem, we no longer need the stored data, -* so we will overwrite the data from this level onto the previously -* used storage space. -* - IF( CURLVL.EQ.TLVLS ) THEN - QPTR( CURR ) = 1 - PRMPTR( CURR ) = 1 - GIVPTR( CURR ) = 1 - END IF -* -* Sort and Deflate eigenvalues. -* - CALL DLAED8( ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, CUTPNT, - $ WORK( IZ ), WORK( IDLMDA ), WORK( IQ2 ), LDQ2, - $ WORK( IW ), PERM( PRMPTR( CURR ) ), GIVPTR( CURR+1 ), - $ GIVCOL( 1, GIVPTR( CURR ) ), - $ GIVNUM( 1, GIVPTR( CURR ) ), IWORK( INDXP ), - $ IWORK( INDX ), INFO ) - PRMPTR( CURR+1 ) = PRMPTR( CURR ) + N - GIVPTR( CURR+1 ) = GIVPTR( CURR+1 ) + GIVPTR( CURR ) -* -* Solve Secular Equation. -* - IF( K.NE.0 ) THEN - CALL DLAED9( K, 1, K, N, D, WORK( IS ), K, RHO, WORK( IDLMDA ), - $ WORK( IW ), QSTORE( QPTR( CURR ) ), K, INFO ) - IF( INFO.NE.0 ) - $ GO TO 30 - IF( ICOMPQ.EQ.1 ) THEN - CALL DGEMM( 'N', 'N', QSIZ, K, K, ONE, WORK( IQ2 ), LDQ2, - $ QSTORE( QPTR( CURR ) ), K, ZERO, Q, LDQ ) - END IF - QPTR( CURR+1 ) = QPTR( CURR ) + K**2 -* -* Prepare the INDXQ sorting permutation. -* - N1 = K - N2 = N - K - CALL DLAMRG( N1, N2, D, 1, -1, INDXQ ) - ELSE - QPTR( CURR+1 ) = QPTR( CURR ) - DO 20 I = 1, N - INDXQ( I ) = I - 20 CONTINUE - END IF -* - 30 CONTINUE - RETURN -* -* End of DLAED7 -* - END diff --git a/lib/linalg/fortran/dlaed8.f b/lib/linalg/fortran/dlaed8.f deleted file mode 100644 index 3631fb4566..0000000000 --- a/lib/linalg/fortran/dlaed8.f +++ /dev/null @@ -1,521 +0,0 @@ -*> \brief \b DLAED8 used by DSTEDC. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLAED8 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLAED8( ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, -* CUTPNT, Z, DLAMDA, Q2, LDQ2, W, PERM, GIVPTR, -* GIVCOL, GIVNUM, INDXP, INDX, INFO ) -* -* .. Scalar Arguments .. -* INTEGER CUTPNT, GIVPTR, ICOMPQ, INFO, K, LDQ, LDQ2, N, -* $ QSIZ -* DOUBLE PRECISION RHO -* .. -* .. Array Arguments .. -* INTEGER GIVCOL( 2, * ), INDX( * ), INDXP( * ), -* $ INDXQ( * ), PERM( * ) -* DOUBLE PRECISION D( * ), DLAMDA( * ), GIVNUM( 2, * ), -* $ Q( LDQ, * ), Q2( LDQ2, * ), W( * ), Z( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLAED8 merges the two sets of eigenvalues together into a single -*> sorted set. Then it tries to deflate the size of the problem. -*> There are two ways in which deflation can occur: when two or more -*> eigenvalues are close together or if there is a tiny element in the -*> Z vector. For each such occurrence the order of the related secular -*> equation problem is reduced by one. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] ICOMPQ -*> \verbatim -*> ICOMPQ is INTEGER -*> = 0: Compute eigenvalues only. -*> = 1: Compute eigenvectors of original dense symmetric matrix -*> also. On entry, Q contains the orthogonal matrix used -*> to reduce the original matrix to tridiagonal form. -*> \endverbatim -*> -*> \param[out] K -*> \verbatim -*> K is INTEGER -*> The number of non-deflated eigenvalues, and the order of the -*> related secular equation. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The dimension of the symmetric tridiagonal matrix. N >= 0. -*> \endverbatim -*> -*> \param[in] QSIZ -*> \verbatim -*> QSIZ is INTEGER -*> The dimension of the orthogonal matrix used to reduce -*> the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. -*> \endverbatim -*> -*> \param[in,out] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension (N) -*> On entry, the eigenvalues of the two submatrices to be -*> combined. On exit, the trailing (N-K) updated eigenvalues -*> (those which were deflated) sorted into increasing order. -*> \endverbatim -*> -*> \param[in,out] Q -*> \verbatim -*> Q is DOUBLE PRECISION array, dimension (LDQ,N) -*> If ICOMPQ = 0, Q is not referenced. Otherwise, -*> on entry, Q contains the eigenvectors of the partially solved -*> system which has been previously updated in matrix -*> multiplies with other partially solved eigensystems. -*> On exit, Q contains the trailing (N-K) updated eigenvectors -*> (those which were deflated) in its last N-K columns. -*> \endverbatim -*> -*> \param[in] LDQ -*> \verbatim -*> LDQ is INTEGER -*> The leading dimension of the array Q. LDQ >= max(1,N). -*> \endverbatim -*> -*> \param[in] INDXQ -*> \verbatim -*> INDXQ is INTEGER array, dimension (N) -*> The permutation which separately sorts the two sub-problems -*> in D into ascending order. Note that elements in the second -*> half of this permutation must first have CUTPNT added to -*> their values in order to be accurate. -*> \endverbatim -*> -*> \param[in,out] RHO -*> \verbatim -*> RHO is DOUBLE PRECISION -*> On entry, the off-diagonal element associated with the rank-1 -*> cut which originally split the two submatrices which are now -*> being recombined. -*> On exit, RHO has been modified to the value required by -*> DLAED3. -*> \endverbatim -*> -*> \param[in] CUTPNT -*> \verbatim -*> CUTPNT is INTEGER -*> The location of the last eigenvalue in the leading -*> sub-matrix. min(1,N) <= CUTPNT <= N. -*> \endverbatim -*> -*> \param[in] Z -*> \verbatim -*> Z is DOUBLE PRECISION array, dimension (N) -*> On entry, Z contains the updating vector (the last row of -*> the first sub-eigenvector matrix and the first row of the -*> second sub-eigenvector matrix). -*> On exit, the contents of Z are destroyed by the updating -*> process. -*> \endverbatim -*> -*> \param[out] DLAMDA -*> \verbatim -*> DLAMDA is DOUBLE PRECISION array, dimension (N) -*> A copy of the first K eigenvalues which will be used by -*> DLAED3 to form the secular equation. -*> \endverbatim -*> -*> \param[out] Q2 -*> \verbatim -*> Q2 is DOUBLE PRECISION array, dimension (LDQ2,N) -*> If ICOMPQ = 0, Q2 is not referenced. Otherwise, -*> a copy of the first K eigenvectors which will be used by -*> DLAED7 in a matrix multiply (DGEMM) to update the new -*> eigenvectors. -*> \endverbatim -*> -*> \param[in] LDQ2 -*> \verbatim -*> LDQ2 is INTEGER -*> The leading dimension of the array Q2. LDQ2 >= max(1,N). -*> \endverbatim -*> -*> \param[out] W -*> \verbatim -*> W is DOUBLE PRECISION array, dimension (N) -*> The first k values of the final deflation-altered z-vector and -*> will be passed to DLAED3. -*> \endverbatim -*> -*> \param[out] PERM -*> \verbatim -*> PERM is INTEGER array, dimension (N) -*> The permutations (from deflation and sorting) to be applied -*> to each eigenblock. -*> \endverbatim -*> -*> \param[out] GIVPTR -*> \verbatim -*> GIVPTR is INTEGER -*> The number of Givens rotations which took place in this -*> subproblem. -*> \endverbatim -*> -*> \param[out] GIVCOL -*> \verbatim -*> GIVCOL is INTEGER array, dimension (2, N) -*> Each pair of numbers indicates a pair of columns to take place -*> in a Givens rotation. -*> \endverbatim -*> -*> \param[out] GIVNUM -*> \verbatim -*> GIVNUM is DOUBLE PRECISION array, dimension (2, N) -*> Each number indicates the S value to be used in the -*> corresponding Givens rotation. -*> \endverbatim -*> -*> \param[out] INDXP -*> \verbatim -*> INDXP is INTEGER array, dimension (N) -*> The permutation used to place deflated values of D at the end -*> of the array. INDXP(1:K) points to the nondeflated D-values -*> and INDXP(K+1:N) points to the deflated eigenvalues. -*> \endverbatim -*> -*> \param[out] INDX -*> \verbatim -*> INDX is INTEGER array, dimension (N) -*> The permutation used to sort the contents of D into ascending -*> order. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit. -*> < 0: if INFO = -i, the i-th argument had an illegal value. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup auxOTHERcomputational -* -*> \par Contributors: -* ================== -*> -*> Jeff Rutter, Computer Science Division, University of California -*> at Berkeley, USA -* -* ===================================================================== - SUBROUTINE DLAED8( ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, - $ CUTPNT, Z, DLAMDA, Q2, LDQ2, W, PERM, GIVPTR, - $ GIVCOL, GIVNUM, INDXP, INDX, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER CUTPNT, GIVPTR, ICOMPQ, INFO, K, LDQ, LDQ2, N, - $ QSIZ - DOUBLE PRECISION RHO -* .. -* .. Array Arguments .. - INTEGER GIVCOL( 2, * ), INDX( * ), INDXP( * ), - $ INDXQ( * ), PERM( * ) - DOUBLE PRECISION D( * ), DLAMDA( * ), GIVNUM( 2, * ), - $ Q( LDQ, * ), Q2( LDQ2, * ), W( * ), Z( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION MONE, ZERO, ONE, TWO, EIGHT - PARAMETER ( MONE = -1.0D0, ZERO = 0.0D0, ONE = 1.0D0, - $ TWO = 2.0D0, EIGHT = 8.0D0 ) -* .. -* .. Local Scalars .. -* - INTEGER I, IMAX, J, JLAM, JMAX, JP, K2, N1, N1P1, N2 - DOUBLE PRECISION C, EPS, S, T, TAU, TOL -* .. -* .. External Functions .. - INTEGER IDAMAX - DOUBLE PRECISION DLAMCH, DLAPY2 - EXTERNAL IDAMAX, DLAMCH, DLAPY2 -* .. -* .. External Subroutines .. - EXTERNAL DCOPY, DLACPY, DLAMRG, DROT, DSCAL, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, MAX, MIN, SQRT -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 -* - IF( ICOMPQ.LT.0 .OR. ICOMPQ.GT.1 ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -3 - ELSE IF( ICOMPQ.EQ.1 .AND. QSIZ.LT.N ) THEN - INFO = -4 - ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN - INFO = -7 - ELSE IF( CUTPNT.LT.MIN( 1, N ) .OR. CUTPNT.GT.N ) THEN - INFO = -10 - ELSE IF( LDQ2.LT.MAX( 1, N ) ) THEN - INFO = -14 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DLAED8', -INFO ) - RETURN - END IF -* -* Need to initialize GIVPTR to O here in case of quick exit -* to prevent an unspecified code behavior (usually sigfault) -* when IWORK array on entry to *stedc is not zeroed -* (or at least some IWORK entries which used in *laed7 for GIVPTR). -* - GIVPTR = 0 -* -* Quick return if possible -* - IF( N.EQ.0 ) - $ RETURN -* - N1 = CUTPNT - N2 = N - N1 - N1P1 = N1 + 1 -* - IF( RHO.LT.ZERO ) THEN - CALL DSCAL( N2, MONE, Z( N1P1 ), 1 ) - END IF -* -* Normalize z so that norm(z) = 1 -* - T = ONE / SQRT( TWO ) - DO 10 J = 1, N - INDX( J ) = J - 10 CONTINUE - CALL DSCAL( N, T, Z, 1 ) - RHO = ABS( TWO*RHO ) -* -* Sort the eigenvalues into increasing order -* - DO 20 I = CUTPNT + 1, N - INDXQ( I ) = INDXQ( I ) + CUTPNT - 20 CONTINUE - DO 30 I = 1, N - DLAMDA( I ) = D( INDXQ( I ) ) - W( I ) = Z( INDXQ( I ) ) - 30 CONTINUE - I = 1 - J = CUTPNT + 1 - CALL DLAMRG( N1, N2, DLAMDA, 1, 1, INDX ) - DO 40 I = 1, N - D( I ) = DLAMDA( INDX( I ) ) - Z( I ) = W( INDX( I ) ) - 40 CONTINUE -* -* Calculate the allowable deflation tolerance -* - IMAX = IDAMAX( N, Z, 1 ) - JMAX = IDAMAX( N, D, 1 ) - EPS = DLAMCH( 'Epsilon' ) - TOL = EIGHT*EPS*ABS( D( JMAX ) ) -* -* If the rank-1 modifier is small enough, no more needs to be done -* except to reorganize Q so that its columns correspond with the -* elements in D. -* - IF( RHO*ABS( Z( IMAX ) ).LE.TOL ) THEN - K = 0 - IF( ICOMPQ.EQ.0 ) THEN - DO 50 J = 1, N - PERM( J ) = INDXQ( INDX( J ) ) - 50 CONTINUE - ELSE - DO 60 J = 1, N - PERM( J ) = INDXQ( INDX( J ) ) - CALL DCOPY( QSIZ, Q( 1, PERM( J ) ), 1, Q2( 1, J ), 1 ) - 60 CONTINUE - CALL DLACPY( 'A', QSIZ, N, Q2( 1, 1 ), LDQ2, Q( 1, 1 ), - $ LDQ ) - END IF - RETURN - END IF -* -* If there are multiple eigenvalues then the problem deflates. Here -* the number of equal eigenvalues are found. As each equal -* eigenvalue is found, an elementary reflector is computed to rotate -* the corresponding eigensubspace so that the corresponding -* components of Z are zero in this new basis. -* - K = 0 - K2 = N + 1 - DO 70 J = 1, N - IF( RHO*ABS( Z( J ) ).LE.TOL ) THEN -* -* Deflate due to small z component. -* - K2 = K2 - 1 - INDXP( K2 ) = J - IF( J.EQ.N ) - $ GO TO 110 - ELSE - JLAM = J - GO TO 80 - END IF - 70 CONTINUE - 80 CONTINUE - J = J + 1 - IF( J.GT.N ) - $ GO TO 100 - IF( RHO*ABS( Z( J ) ).LE.TOL ) THEN -* -* Deflate due to small z component. -* - K2 = K2 - 1 - INDXP( K2 ) = J - ELSE -* -* Check if eigenvalues are close enough to allow deflation. -* - S = Z( JLAM ) - C = Z( J ) -* -* Find sqrt(a**2+b**2) without overflow or -* destructive underflow. -* - TAU = DLAPY2( C, S ) - T = D( J ) - D( JLAM ) - C = C / TAU - S = -S / TAU - IF( ABS( T*C*S ).LE.TOL ) THEN -* -* Deflation is possible. -* - Z( J ) = TAU - Z( JLAM ) = ZERO -* -* Record the appropriate Givens rotation -* - GIVPTR = GIVPTR + 1 - GIVCOL( 1, GIVPTR ) = INDXQ( INDX( JLAM ) ) - GIVCOL( 2, GIVPTR ) = INDXQ( INDX( J ) ) - GIVNUM( 1, GIVPTR ) = C - GIVNUM( 2, GIVPTR ) = S - IF( ICOMPQ.EQ.1 ) THEN - CALL DROT( QSIZ, Q( 1, INDXQ( INDX( JLAM ) ) ), 1, - $ Q( 1, INDXQ( INDX( J ) ) ), 1, C, S ) - END IF - T = D( JLAM )*C*C + D( J )*S*S - D( J ) = D( JLAM )*S*S + D( J )*C*C - D( JLAM ) = T - K2 = K2 - 1 - I = 1 - 90 CONTINUE - IF( K2+I.LE.N ) THEN - IF( D( JLAM ).LT.D( INDXP( K2+I ) ) ) THEN - INDXP( K2+I-1 ) = INDXP( K2+I ) - INDXP( K2+I ) = JLAM - I = I + 1 - GO TO 90 - ELSE - INDXP( K2+I-1 ) = JLAM - END IF - ELSE - INDXP( K2+I-1 ) = JLAM - END IF - JLAM = J - ELSE - K = K + 1 - W( K ) = Z( JLAM ) - DLAMDA( K ) = D( JLAM ) - INDXP( K ) = JLAM - JLAM = J - END IF - END IF - GO TO 80 - 100 CONTINUE -* -* Record the last eigenvalue. -* - K = K + 1 - W( K ) = Z( JLAM ) - DLAMDA( K ) = D( JLAM ) - INDXP( K ) = JLAM -* - 110 CONTINUE -* -* Sort the eigenvalues and corresponding eigenvectors into DLAMDA -* and Q2 respectively. The eigenvalues/vectors which were not -* deflated go into the first K slots of DLAMDA and Q2 respectively, -* while those which were deflated go into the last N - K slots. -* - IF( ICOMPQ.EQ.0 ) THEN - DO 120 J = 1, N - JP = INDXP( J ) - DLAMDA( J ) = D( JP ) - PERM( J ) = INDXQ( INDX( JP ) ) - 120 CONTINUE - ELSE - DO 130 J = 1, N - JP = INDXP( J ) - DLAMDA( J ) = D( JP ) - PERM( J ) = INDXQ( INDX( JP ) ) - CALL DCOPY( QSIZ, Q( 1, PERM( J ) ), 1, Q2( 1, J ), 1 ) - 130 CONTINUE - END IF -* -* The deflated eigenvalues and their corresponding vectors go back -* into the last N - K slots of D and Q respectively. -* - IF( K.LT.N ) THEN - IF( ICOMPQ.EQ.0 ) THEN - CALL DCOPY( N-K, DLAMDA( K+1 ), 1, D( K+1 ), 1 ) - ELSE - CALL DCOPY( N-K, DLAMDA( K+1 ), 1, D( K+1 ), 1 ) - CALL DLACPY( 'A', QSIZ, N-K, Q2( 1, K+1 ), LDQ2, - $ Q( 1, K+1 ), LDQ ) - END IF - END IF -* - RETURN -* -* End of DLAED8 -* - END diff --git a/lib/linalg/fortran/dlaed9.f b/lib/linalg/fortran/dlaed9.f deleted file mode 100644 index b88cdd9077..0000000000 --- a/lib/linalg/fortran/dlaed9.f +++ /dev/null @@ -1,291 +0,0 @@ -*> \brief \b DLAED9 used by DSTEDC. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is dense. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLAED9 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLAED9( K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA, W, -* S, LDS, INFO ) -* -* .. Scalar Arguments .. -* INTEGER INFO, K, KSTART, KSTOP, LDQ, LDS, N -* DOUBLE PRECISION RHO -* .. -* .. Array Arguments .. -* DOUBLE PRECISION D( * ), DLAMDA( * ), Q( LDQ, * ), S( LDS, * ), -* $ W( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLAED9 finds the roots of the secular equation, as defined by the -*> values in D, Z, and RHO, between KSTART and KSTOP. It makes the -*> appropriate calls to DLAED4 and then stores the new matrix of -*> eigenvectors for use in calculating the next level of Z vectors. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> The number of terms in the rational function to be solved by -*> DLAED4. K >= 0. -*> \endverbatim -*> -*> \param[in] KSTART -*> \verbatim -*> KSTART is INTEGER -*> \endverbatim -*> -*> \param[in] KSTOP -*> \verbatim -*> KSTOP is INTEGER -*> The updated eigenvalues Lambda(I), KSTART <= I <= KSTOP -*> are to be computed. 1 <= KSTART <= KSTOP <= K. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of rows and columns in the Q matrix. -*> N >= K (delation may result in N > K). -*> \endverbatim -*> -*> \param[out] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension (N) -*> D(I) contains the updated eigenvalues -*> for KSTART <= I <= KSTOP. -*> \endverbatim -*> -*> \param[out] Q -*> \verbatim -*> Q is DOUBLE PRECISION array, dimension (LDQ,N) -*> \endverbatim -*> -*> \param[in] LDQ -*> \verbatim -*> LDQ is INTEGER -*> The leading dimension of the array Q. LDQ >= max( 1, N ). -*> \endverbatim -*> -*> \param[in] RHO -*> \verbatim -*> RHO is DOUBLE PRECISION -*> The value of the parameter in the rank one update equation. -*> RHO >= 0 required. -*> \endverbatim -*> -*> \param[in] DLAMDA -*> \verbatim -*> DLAMDA is DOUBLE PRECISION array, dimension (K) -*> The first K elements of this array contain the old roots -*> of the deflated updating problem. These are the poles -*> of the secular equation. -*> \endverbatim -*> -*> \param[in] W -*> \verbatim -*> W is DOUBLE PRECISION array, dimension (K) -*> The first K elements of this array contain the components -*> of the deflation-adjusted updating vector. -*> \endverbatim -*> -*> \param[out] S -*> \verbatim -*> S is DOUBLE PRECISION array, dimension (LDS, K) -*> Will contain the eigenvectors of the repaired matrix which -*> will be stored for subsequent Z vector calculation and -*> multiplied by the previously accumulated eigenvectors -*> to update the system. -*> \endverbatim -*> -*> \param[in] LDS -*> \verbatim -*> LDS is INTEGER -*> The leading dimension of S. LDS >= max( 1, K ). -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit. -*> < 0: if INFO = -i, the i-th argument had an illegal value. -*> > 0: if INFO = 1, an eigenvalue did not converge -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup auxOTHERcomputational -* -*> \par Contributors: -* ================== -*> -*> Jeff Rutter, Computer Science Division, University of California -*> at Berkeley, USA -* -* ===================================================================== - SUBROUTINE DLAED9( K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA, W, - $ S, LDS, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INFO, K, KSTART, KSTOP, LDQ, LDS, N - DOUBLE PRECISION RHO -* .. -* .. Array Arguments .. - DOUBLE PRECISION D( * ), DLAMDA( * ), Q( LDQ, * ), S( LDS, * ), - $ W( * ) -* .. -* -* ===================================================================== -* -* .. Local Scalars .. - INTEGER I, J - DOUBLE PRECISION TEMP -* .. -* .. External Functions .. - DOUBLE PRECISION DLAMC3, DNRM2 - EXTERNAL DLAMC3, DNRM2 -* .. -* .. External Subroutines .. - EXTERNAL DCOPY, DLAED4, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, SIGN, SQRT -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 -* - IF( K.LT.0 ) THEN - INFO = -1 - ELSE IF( KSTART.LT.1 .OR. KSTART.GT.MAX( 1, K ) ) THEN - INFO = -2 - ELSE IF( MAX( 1, KSTOP ).LT.KSTART .OR. KSTOP.GT.MAX( 1, K ) ) - $ THEN - INFO = -3 - ELSE IF( N.LT.K ) THEN - INFO = -4 - ELSE IF( LDQ.LT.MAX( 1, K ) ) THEN - INFO = -7 - ELSE IF( LDS.LT.MAX( 1, K ) ) THEN - INFO = -12 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DLAED9', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( K.EQ.0 ) - $ RETURN -* -* Modify values DLAMDA(i) to make sure all DLAMDA(i)-DLAMDA(j) can -* be computed with high relative accuracy (barring over/underflow). -* This is a problem on machines without a guard digit in -* add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2). -* The following code replaces DLAMDA(I) by 2*DLAMDA(I)-DLAMDA(I), -* which on any of these machines zeros out the bottommost -* bit of DLAMDA(I) if it is 1; this makes the subsequent -* subtractions DLAMDA(I)-DLAMDA(J) unproblematic when cancellation -* occurs. On binary machines with a guard digit (almost all -* machines) it does not change DLAMDA(I) at all. On hexadecimal -* and decimal machines with a guard digit, it slightly -* changes the bottommost bits of DLAMDA(I). It does not account -* for hexadecimal or decimal machines without guard digits -* (we know of none). We use a subroutine call to compute -* 2*DLAMBDA(I) to prevent optimizing compilers from eliminating -* this code. -* - DO 10 I = 1, N - DLAMDA( I ) = DLAMC3( DLAMDA( I ), DLAMDA( I ) ) - DLAMDA( I ) - 10 CONTINUE -* - DO 20 J = KSTART, KSTOP - CALL DLAED4( K, J, DLAMDA, W, Q( 1, J ), RHO, D( J ), INFO ) -* -* If the zero finder fails, the computation is terminated. -* - IF( INFO.NE.0 ) - $ GO TO 120 - 20 CONTINUE -* - IF( K.EQ.1 .OR. K.EQ.2 ) THEN - DO 40 I = 1, K - DO 30 J = 1, K - S( J, I ) = Q( J, I ) - 30 CONTINUE - 40 CONTINUE - GO TO 120 - END IF -* -* Compute updated W. -* - CALL DCOPY( K, W, 1, S, 1 ) -* -* Initialize W(I) = Q(I,I) -* - CALL DCOPY( K, Q, LDQ+1, W, 1 ) - DO 70 J = 1, K - DO 50 I = 1, J - 1 - W( I ) = W( I )*( Q( I, J ) / ( DLAMDA( I )-DLAMDA( J ) ) ) - 50 CONTINUE - DO 60 I = J + 1, K - W( I ) = W( I )*( Q( I, J ) / ( DLAMDA( I )-DLAMDA( J ) ) ) - 60 CONTINUE - 70 CONTINUE - DO 80 I = 1, K - W( I ) = SIGN( SQRT( -W( I ) ), S( I, 1 ) ) - 80 CONTINUE -* -* Compute eigenvectors of the modified rank-1 modification. -* - DO 110 J = 1, K - DO 90 I = 1, K - Q( I, J ) = W( I ) / Q( I, J ) - 90 CONTINUE - TEMP = DNRM2( K, Q( 1, J ), 1 ) - DO 100 I = 1, K - S( I, J ) = Q( I, J ) / TEMP - 100 CONTINUE - 110 CONTINUE -* - 120 CONTINUE - RETURN -* -* End of DLAED9 -* - END diff --git a/lib/linalg/fortran/dlaeda.f b/lib/linalg/fortran/dlaeda.f deleted file mode 100644 index 8864fd7f2a..0000000000 --- a/lib/linalg/fortran/dlaeda.f +++ /dev/null @@ -1,305 +0,0 @@ -*> \brief \b DLAEDA used by DSTEDC. Computes the Z vector determining the rank-one modification of the diagonal matrix. Used when the original matrix is dense. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLAEDA + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLAEDA( N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR, -* GIVCOL, GIVNUM, Q, QPTR, Z, ZTEMP, INFO ) -* -* .. Scalar Arguments .. -* INTEGER CURLVL, CURPBM, INFO, N, TLVLS -* .. -* .. Array Arguments .. -* INTEGER GIVCOL( 2, * ), GIVPTR( * ), PERM( * ), -* $ PRMPTR( * ), QPTR( * ) -* DOUBLE PRECISION GIVNUM( 2, * ), Q( * ), Z( * ), ZTEMP( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLAEDA computes the Z vector corresponding to the merge step in the -*> CURLVLth step of the merge process with TLVLS steps for the CURPBMth -*> problem. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The dimension of the symmetric tridiagonal matrix. N >= 0. -*> \endverbatim -*> -*> \param[in] TLVLS -*> \verbatim -*> TLVLS is INTEGER -*> The total number of merging levels in the overall divide and -*> conquer tree. -*> \endverbatim -*> -*> \param[in] CURLVL -*> \verbatim -*> CURLVL is INTEGER -*> The current level in the overall merge routine, -*> 0 <= curlvl <= tlvls. -*> \endverbatim -*> -*> \param[in] CURPBM -*> \verbatim -*> CURPBM is INTEGER -*> The current problem in the current level in the overall -*> merge routine (counting from upper left to lower right). -*> \endverbatim -*> -*> \param[in] PRMPTR -*> \verbatim -*> PRMPTR is INTEGER array, dimension (N lg N) -*> Contains a list of pointers which indicate where in PERM a -*> level's permutation is stored. PRMPTR(i+1) - PRMPTR(i) -*> indicates the size of the permutation and incidentally the -*> size of the full, non-deflated problem. -*> \endverbatim -*> -*> \param[in] PERM -*> \verbatim -*> PERM is INTEGER array, dimension (N lg N) -*> Contains the permutations (from deflation and sorting) to be -*> applied to each eigenblock. -*> \endverbatim -*> -*> \param[in] GIVPTR -*> \verbatim -*> GIVPTR is INTEGER array, dimension (N lg N) -*> Contains a list of pointers which indicate where in GIVCOL a -*> level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i) -*> indicates the number of Givens rotations. -*> \endverbatim -*> -*> \param[in] GIVCOL -*> \verbatim -*> GIVCOL is INTEGER array, dimension (2, N lg N) -*> Each pair of numbers indicates a pair of columns to take place -*> in a Givens rotation. -*> \endverbatim -*> -*> \param[in] GIVNUM -*> \verbatim -*> GIVNUM is DOUBLE PRECISION array, dimension (2, N lg N) -*> Each number indicates the S value to be used in the -*> corresponding Givens rotation. -*> \endverbatim -*> -*> \param[in] Q -*> \verbatim -*> Q is DOUBLE PRECISION array, dimension (N**2) -*> Contains the square eigenblocks from previous levels, the -*> starting positions for blocks are given by QPTR. -*> \endverbatim -*> -*> \param[in] QPTR -*> \verbatim -*> QPTR is INTEGER array, dimension (N+2) -*> Contains a list of pointers which indicate where in Q an -*> eigenblock is stored. SQRT( QPTR(i+1) - QPTR(i) ) indicates -*> the size of the block. -*> \endverbatim -*> -*> \param[out] Z -*> \verbatim -*> Z is DOUBLE PRECISION array, dimension (N) -*> On output this vector contains the updating vector (the last -*> row of the first sub-eigenvector matrix and the first row of -*> the second sub-eigenvector matrix). -*> \endverbatim -*> -*> \param[out] ZTEMP -*> \verbatim -*> ZTEMP is DOUBLE PRECISION array, dimension (N) -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit. -*> < 0: if INFO = -i, the i-th argument had an illegal value. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup auxOTHERcomputational -* -*> \par Contributors: -* ================== -*> -*> Jeff Rutter, Computer Science Division, University of California -*> at Berkeley, USA -* -* ===================================================================== - SUBROUTINE DLAEDA( N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR, - $ GIVCOL, GIVNUM, Q, QPTR, Z, ZTEMP, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER CURLVL, CURPBM, INFO, N, TLVLS -* .. -* .. Array Arguments .. - INTEGER GIVCOL( 2, * ), GIVPTR( * ), PERM( * ), - $ PRMPTR( * ), QPTR( * ) - DOUBLE PRECISION GIVNUM( 2, * ), Q( * ), Z( * ), ZTEMP( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, HALF, ONE - PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0 ) -* .. -* .. Local Scalars .. - INTEGER BSIZ1, BSIZ2, CURR, I, K, MID, PSIZ1, PSIZ2, - $ PTR, ZPTR1 -* .. -* .. External Subroutines .. - EXTERNAL DCOPY, DGEMV, DROT, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC DBLE, INT, SQRT -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 -* - IF( N.LT.0 ) THEN - INFO = -1 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DLAEDA', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( N.EQ.0 ) - $ RETURN -* -* Determine location of first number in second half. -* - MID = N / 2 + 1 -* -* Gather last/first rows of appropriate eigenblocks into center of Z -* - PTR = 1 -* -* Determine location of lowest level subproblem in the full storage -* scheme -* - CURR = PTR + CURPBM*2**CURLVL + 2**( CURLVL-1 ) - 1 -* -* Determine size of these matrices. We add HALF to the value of -* the SQRT in case the machine underestimates one of these square -* roots. -* - BSIZ1 = INT( HALF+SQRT( DBLE( QPTR( CURR+1 )-QPTR( CURR ) ) ) ) - BSIZ2 = INT( HALF+SQRT( DBLE( QPTR( CURR+2 )-QPTR( CURR+1 ) ) ) ) - DO 10 K = 1, MID - BSIZ1 - 1 - Z( K ) = ZERO - 10 CONTINUE - CALL DCOPY( BSIZ1, Q( QPTR( CURR )+BSIZ1-1 ), BSIZ1, - $ Z( MID-BSIZ1 ), 1 ) - CALL DCOPY( BSIZ2, Q( QPTR( CURR+1 ) ), BSIZ2, Z( MID ), 1 ) - DO 20 K = MID + BSIZ2, N - Z( K ) = ZERO - 20 CONTINUE -* -* Loop through remaining levels 1 -> CURLVL applying the Givens -* rotations and permutation and then multiplying the center matrices -* against the current Z. -* - PTR = 2**TLVLS + 1 - DO 70 K = 1, CURLVL - 1 - CURR = PTR + CURPBM*2**( CURLVL-K ) + 2**( CURLVL-K-1 ) - 1 - PSIZ1 = PRMPTR( CURR+1 ) - PRMPTR( CURR ) - PSIZ2 = PRMPTR( CURR+2 ) - PRMPTR( CURR+1 ) - ZPTR1 = MID - PSIZ1 -* -* Apply Givens at CURR and CURR+1 -* - DO 30 I = GIVPTR( CURR ), GIVPTR( CURR+1 ) - 1 - CALL DROT( 1, Z( ZPTR1+GIVCOL( 1, I )-1 ), 1, - $ Z( ZPTR1+GIVCOL( 2, I )-1 ), 1, GIVNUM( 1, I ), - $ GIVNUM( 2, I ) ) - 30 CONTINUE - DO 40 I = GIVPTR( CURR+1 ), GIVPTR( CURR+2 ) - 1 - CALL DROT( 1, Z( MID-1+GIVCOL( 1, I ) ), 1, - $ Z( MID-1+GIVCOL( 2, I ) ), 1, GIVNUM( 1, I ), - $ GIVNUM( 2, I ) ) - 40 CONTINUE - PSIZ1 = PRMPTR( CURR+1 ) - PRMPTR( CURR ) - PSIZ2 = PRMPTR( CURR+2 ) - PRMPTR( CURR+1 ) - DO 50 I = 0, PSIZ1 - 1 - ZTEMP( I+1 ) = Z( ZPTR1+PERM( PRMPTR( CURR )+I )-1 ) - 50 CONTINUE - DO 60 I = 0, PSIZ2 - 1 - ZTEMP( PSIZ1+I+1 ) = Z( MID+PERM( PRMPTR( CURR+1 )+I )-1 ) - 60 CONTINUE -* -* Multiply Blocks at CURR and CURR+1 -* -* Determine size of these matrices. We add HALF to the value of -* the SQRT in case the machine underestimates one of these -* square roots. -* - BSIZ1 = INT( HALF+SQRT( DBLE( QPTR( CURR+1 )-QPTR( CURR ) ) ) ) - BSIZ2 = INT( HALF+SQRT( DBLE( QPTR( CURR+2 )-QPTR( CURR+ - $ 1 ) ) ) ) - IF( BSIZ1.GT.0 ) THEN - CALL DGEMV( 'T', BSIZ1, BSIZ1, ONE, Q( QPTR( CURR ) ), - $ BSIZ1, ZTEMP( 1 ), 1, ZERO, Z( ZPTR1 ), 1 ) - END IF - CALL DCOPY( PSIZ1-BSIZ1, ZTEMP( BSIZ1+1 ), 1, Z( ZPTR1+BSIZ1 ), - $ 1 ) - IF( BSIZ2.GT.0 ) THEN - CALL DGEMV( 'T', BSIZ2, BSIZ2, ONE, Q( QPTR( CURR+1 ) ), - $ BSIZ2, ZTEMP( PSIZ1+1 ), 1, ZERO, Z( MID ), 1 ) - END IF - CALL DCOPY( PSIZ2-BSIZ2, ZTEMP( PSIZ1+BSIZ2+1 ), 1, - $ Z( MID+BSIZ2 ), 1 ) -* - PTR = PTR + 2**( TLVLS-K ) - 70 CONTINUE -* - RETURN -* -* End of DLAEDA -* - END diff --git a/lib/linalg/fortran/dlaev2.f b/lib/linalg/fortran/dlaev2.f deleted file mode 100644 index 9e29991a6d..0000000000 --- a/lib/linalg/fortran/dlaev2.f +++ /dev/null @@ -1,235 +0,0 @@ -*> \brief \b DLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLAEV2 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLAEV2( A, B, C, RT1, RT2, CS1, SN1 ) -* -* .. Scalar Arguments .. -* DOUBLE PRECISION A, B, C, CS1, RT1, RT2, SN1 -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix -*> [ A B ] -*> [ B C ]. -*> On return, RT1 is the eigenvalue of larger absolute value, RT2 is the -*> eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right -*> eigenvector for RT1, giving the decomposition -*> -*> [ CS1 SN1 ] [ A B ] [ CS1 -SN1 ] = [ RT1 0 ] -*> [-SN1 CS1 ] [ B C ] [ SN1 CS1 ] [ 0 RT2 ]. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] A -*> \verbatim -*> A is DOUBLE PRECISION -*> The (1,1) element of the 2-by-2 matrix. -*> \endverbatim -*> -*> \param[in] B -*> \verbatim -*> B is DOUBLE PRECISION -*> The (1,2) element and the conjugate of the (2,1) element of -*> the 2-by-2 matrix. -*> \endverbatim -*> -*> \param[in] C -*> \verbatim -*> C is DOUBLE PRECISION -*> The (2,2) element of the 2-by-2 matrix. -*> \endverbatim -*> -*> \param[out] RT1 -*> \verbatim -*> RT1 is DOUBLE PRECISION -*> The eigenvalue of larger absolute value. -*> \endverbatim -*> -*> \param[out] RT2 -*> \verbatim -*> RT2 is DOUBLE PRECISION -*> The eigenvalue of smaller absolute value. -*> \endverbatim -*> -*> \param[out] CS1 -*> \verbatim -*> CS1 is DOUBLE PRECISION -*> \endverbatim -*> -*> \param[out] SN1 -*> \verbatim -*> SN1 is DOUBLE PRECISION -*> The vector (CS1, SN1) is a unit right eigenvector for RT1. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup OTHERauxiliary -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> RT1 is accurate to a few ulps barring over/underflow. -*> -*> RT2 may be inaccurate if there is massive cancellation in the -*> determinant A*C-B*B; higher precision or correctly rounded or -*> correctly truncated arithmetic would be needed to compute RT2 -*> accurately in all cases. -*> -*> CS1 and SN1 are accurate to a few ulps barring over/underflow. -*> -*> Overflow is possible only if RT1 is within a factor of 5 of overflow. -*> Underflow is harmless if the input data is 0 or exceeds -*> underflow_threshold / macheps. -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DLAEV2( A, B, C, RT1, RT2, CS1, SN1 ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - DOUBLE PRECISION A, B, C, CS1, RT1, RT2, SN1 -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE - PARAMETER ( ONE = 1.0D0 ) - DOUBLE PRECISION TWO - PARAMETER ( TWO = 2.0D0 ) - DOUBLE PRECISION ZERO - PARAMETER ( ZERO = 0.0D0 ) - DOUBLE PRECISION HALF - PARAMETER ( HALF = 0.5D0 ) -* .. -* .. Local Scalars .. - INTEGER SGN1, SGN2 - DOUBLE PRECISION AB, ACMN, ACMX, ACS, ADF, CS, CT, DF, RT, SM, - $ TB, TN -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, SQRT -* .. -* .. Executable Statements .. -* -* Compute the eigenvalues -* - SM = A + C - DF = A - C - ADF = ABS( DF ) - TB = B + B - AB = ABS( TB ) - IF( ABS( A ).GT.ABS( C ) ) THEN - ACMX = A - ACMN = C - ELSE - ACMX = C - ACMN = A - END IF - IF( ADF.GT.AB ) THEN - RT = ADF*SQRT( ONE+( AB / ADF )**2 ) - ELSE IF( ADF.LT.AB ) THEN - RT = AB*SQRT( ONE+( ADF / AB )**2 ) - ELSE -* -* Includes case AB=ADF=0 -* - RT = AB*SQRT( TWO ) - END IF - IF( SM.LT.ZERO ) THEN - RT1 = HALF*( SM-RT ) - SGN1 = -1 -* -* Order of execution important. -* To get fully accurate smaller eigenvalue, -* next line needs to be executed in higher precision. -* - RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B - ELSE IF( SM.GT.ZERO ) THEN - RT1 = HALF*( SM+RT ) - SGN1 = 1 -* -* Order of execution important. -* To get fully accurate smaller eigenvalue, -* next line needs to be executed in higher precision. -* - RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B - ELSE -* -* Includes case RT1 = RT2 = 0 -* - RT1 = HALF*RT - RT2 = -HALF*RT - SGN1 = 1 - END IF -* -* Compute the eigenvector -* - IF( DF.GE.ZERO ) THEN - CS = DF + RT - SGN2 = 1 - ELSE - CS = DF - RT - SGN2 = -1 - END IF - ACS = ABS( CS ) - IF( ACS.GT.AB ) THEN - CT = -TB / CS - SN1 = ONE / SQRT( ONE+CT*CT ) - CS1 = CT*SN1 - ELSE - IF( AB.EQ.ZERO ) THEN - CS1 = ONE - SN1 = ZERO - ELSE - TN = -CS / TB - CS1 = ONE / SQRT( ONE+TN*TN ) - SN1 = TN*CS1 - END IF - END IF - IF( SGN1.EQ.SGN2 ) THEN - TN = CS1 - CS1 = -SN1 - SN1 = TN - END IF - RETURN -* -* End of DLAEV2 -* - END diff --git a/lib/linalg/fortran/dlaisnan.f b/lib/linalg/fortran/dlaisnan.f deleted file mode 100644 index 2caf5fb1d0..0000000000 --- a/lib/linalg/fortran/dlaisnan.f +++ /dev/null @@ -1,88 +0,0 @@ -*> \brief \b DLAISNAN tests input for NaN by comparing two arguments for inequality. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLAISNAN + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* LOGICAL FUNCTION DLAISNAN( DIN1, DIN2 ) -* -* .. Scalar Arguments .. -* DOUBLE PRECISION, INTENT(IN) :: DIN1, DIN2 -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> This routine is not for general use. It exists solely to avoid -*> over-optimization in DISNAN. -*> -*> DLAISNAN checks for NaNs by comparing its two arguments for -*> inequality. NaN is the only floating-point value where NaN != NaN -*> returns .TRUE. To check for NaNs, pass the same variable as both -*> arguments. -*> -*> A compiler must assume that the two arguments are -*> not the same variable, and the test will not be optimized away. -*> Interprocedural or whole-program optimization may delete this -*> test. The ISNAN functions will be replaced by the correct -*> Fortran 03 intrinsic once the intrinsic is widely available. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] DIN1 -*> \verbatim -*> DIN1 is DOUBLE PRECISION -*> \endverbatim -*> -*> \param[in] DIN2 -*> \verbatim -*> DIN2 is DOUBLE PRECISION -*> Two numbers to compare for inequality. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup OTHERauxiliary -* -* ===================================================================== - LOGICAL FUNCTION DLAISNAN( DIN1, DIN2 ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - DOUBLE PRECISION, INTENT(IN) :: DIN1, DIN2 -* .. -* -* ===================================================================== -* -* .. Executable Statements .. - DLAISNAN = (DIN1.NE.DIN2) - RETURN - END diff --git a/lib/linalg/fortran/dlals0.f b/lib/linalg/fortran/dlals0.f deleted file mode 100644 index cfca222806..0000000000 --- a/lib/linalg/fortran/dlals0.f +++ /dev/null @@ -1,496 +0,0 @@ -*> \brief \b DLALS0 applies back multiplying factors in solving the least squares problem using divide and conquer SVD approach. Used by sgelsd. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLALS0 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLALS0( ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX, -* PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, -* POLES, DIFL, DIFR, Z, K, C, S, WORK, INFO ) -* -* .. Scalar Arguments .. -* INTEGER GIVPTR, ICOMPQ, INFO, K, LDB, LDBX, LDGCOL, -* $ LDGNUM, NL, NR, NRHS, SQRE -* DOUBLE PRECISION C, S -* .. -* .. Array Arguments .. -* INTEGER GIVCOL( LDGCOL, * ), PERM( * ) -* DOUBLE PRECISION B( LDB, * ), BX( LDBX, * ), DIFL( * ), -* $ DIFR( LDGNUM, * ), GIVNUM( LDGNUM, * ), -* $ POLES( LDGNUM, * ), WORK( * ), Z( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLALS0 applies back the multiplying factors of either the left or the -*> right singular vector matrix of a diagonal matrix appended by a row -*> to the right hand side matrix B in solving the least squares problem -*> using the divide-and-conquer SVD approach. -*> -*> For the left singular vector matrix, three types of orthogonal -*> matrices are involved: -*> -*> (1L) Givens rotations: the number of such rotations is GIVPTR; the -*> pairs of columns/rows they were applied to are stored in GIVCOL; -*> and the C- and S-values of these rotations are stored in GIVNUM. -*> -*> (2L) Permutation. The (NL+1)-st row of B is to be moved to the first -*> row, and for J=2:N, PERM(J)-th row of B is to be moved to the -*> J-th row. -*> -*> (3L) The left singular vector matrix of the remaining matrix. -*> -*> For the right singular vector matrix, four types of orthogonal -*> matrices are involved: -*> -*> (1R) The right singular vector matrix of the remaining matrix. -*> -*> (2R) If SQRE = 1, one extra Givens rotation to generate the right -*> null space. -*> -*> (3R) The inverse transformation of (2L). -*> -*> (4R) The inverse transformation of (1L). -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] ICOMPQ -*> \verbatim -*> ICOMPQ is INTEGER -*> Specifies whether singular vectors are to be computed in -*> factored form: -*> = 0: Left singular vector matrix. -*> = 1: Right singular vector matrix. -*> \endverbatim -*> -*> \param[in] NL -*> \verbatim -*> NL is INTEGER -*> The row dimension of the upper block. NL >= 1. -*> \endverbatim -*> -*> \param[in] NR -*> \verbatim -*> NR is INTEGER -*> The row dimension of the lower block. NR >= 1. -*> \endverbatim -*> -*> \param[in] SQRE -*> \verbatim -*> SQRE is INTEGER -*> = 0: the lower block is an NR-by-NR square matrix. -*> = 1: the lower block is an NR-by-(NR+1) rectangular matrix. -*> -*> The bidiagonal matrix has row dimension N = NL + NR + 1, -*> and column dimension M = N + SQRE. -*> \endverbatim -*> -*> \param[in] NRHS -*> \verbatim -*> NRHS is INTEGER -*> The number of columns of B and BX. NRHS must be at least 1. -*> \endverbatim -*> -*> \param[in,out] B -*> \verbatim -*> B is DOUBLE PRECISION array, dimension ( LDB, NRHS ) -*> On input, B contains the right hand sides of the least -*> squares problem in rows 1 through M. On output, B contains -*> the solution X in rows 1 through N. -*> \endverbatim -*> -*> \param[in] LDB -*> \verbatim -*> LDB is INTEGER -*> The leading dimension of B. LDB must be at least -*> max(1,MAX( M, N ) ). -*> \endverbatim -*> -*> \param[out] BX -*> \verbatim -*> BX is DOUBLE PRECISION array, dimension ( LDBX, NRHS ) -*> \endverbatim -*> -*> \param[in] LDBX -*> \verbatim -*> LDBX is INTEGER -*> The leading dimension of BX. -*> \endverbatim -*> -*> \param[in] PERM -*> \verbatim -*> PERM is INTEGER array, dimension ( N ) -*> The permutations (from deflation and sorting) applied -*> to the two blocks. -*> \endverbatim -*> -*> \param[in] GIVPTR -*> \verbatim -*> GIVPTR is INTEGER -*> The number of Givens rotations which took place in this -*> subproblem. -*> \endverbatim -*> -*> \param[in] GIVCOL -*> \verbatim -*> GIVCOL is INTEGER array, dimension ( LDGCOL, 2 ) -*> Each pair of numbers indicates a pair of rows/columns -*> involved in a Givens rotation. -*> \endverbatim -*> -*> \param[in] LDGCOL -*> \verbatim -*> LDGCOL is INTEGER -*> The leading dimension of GIVCOL, must be at least N. -*> \endverbatim -*> -*> \param[in] GIVNUM -*> \verbatim -*> GIVNUM is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) -*> Each number indicates the C or S value used in the -*> corresponding Givens rotation. -*> \endverbatim -*> -*> \param[in] LDGNUM -*> \verbatim -*> LDGNUM is INTEGER -*> The leading dimension of arrays DIFR, POLES and -*> GIVNUM, must be at least K. -*> \endverbatim -*> -*> \param[in] POLES -*> \verbatim -*> POLES is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) -*> On entry, POLES(1:K, 1) contains the new singular -*> values obtained from solving the secular equation, and -*> POLES(1:K, 2) is an array containing the poles in the secular -*> equation. -*> \endverbatim -*> -*> \param[in] DIFL -*> \verbatim -*> DIFL is DOUBLE PRECISION array, dimension ( K ). -*> On entry, DIFL(I) is the distance between I-th updated -*> (undeflated) singular value and the I-th (undeflated) old -*> singular value. -*> \endverbatim -*> -*> \param[in] DIFR -*> \verbatim -*> DIFR is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ). -*> On entry, DIFR(I, 1) contains the distances between I-th -*> updated (undeflated) singular value and the I+1-th -*> (undeflated) old singular value. And DIFR(I, 2) is the -*> normalizing factor for the I-th right singular vector. -*> \endverbatim -*> -*> \param[in] Z -*> \verbatim -*> Z is DOUBLE PRECISION array, dimension ( K ) -*> Contain the components of the deflation-adjusted updating row -*> vector. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> Contains the dimension of the non-deflated matrix, -*> This is the order of the related secular equation. 1 <= K <=N. -*> \endverbatim -*> -*> \param[in] C -*> \verbatim -*> C is DOUBLE PRECISION -*> C contains garbage if SQRE =0 and the C-value of a Givens -*> rotation related to the right null space if SQRE = 1. -*> \endverbatim -*> -*> \param[in] S -*> \verbatim -*> S is DOUBLE PRECISION -*> S contains garbage if SQRE =0 and the S-value of a Givens -*> rotation related to the right null space if SQRE = 1. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension ( K ) -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit. -*> < 0: if INFO = -i, the i-th argument had an illegal value. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleOTHERcomputational -* -*> \par Contributors: -* ================== -*> -*> Ming Gu and Ren-Cang Li, Computer Science Division, University of -*> California at Berkeley, USA \n -*> Osni Marques, LBNL/NERSC, USA \n -* -* ===================================================================== - SUBROUTINE DLALS0( ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX, - $ PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, - $ POLES, DIFL, DIFR, Z, K, C, S, WORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER GIVPTR, ICOMPQ, INFO, K, LDB, LDBX, LDGCOL, - $ LDGNUM, NL, NR, NRHS, SQRE - DOUBLE PRECISION C, S -* .. -* .. Array Arguments .. - INTEGER GIVCOL( LDGCOL, * ), PERM( * ) - DOUBLE PRECISION B( LDB, * ), BX( LDBX, * ), DIFL( * ), - $ DIFR( LDGNUM, * ), GIVNUM( LDGNUM, * ), - $ POLES( LDGNUM, * ), WORK( * ), Z( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE, ZERO, NEGONE - PARAMETER ( ONE = 1.0D0, ZERO = 0.0D0, NEGONE = -1.0D0 ) -* .. -* .. Local Scalars .. - INTEGER I, J, M, N, NLP1 - DOUBLE PRECISION DIFLJ, DIFRJ, DJ, DSIGJ, DSIGJP, TEMP -* .. -* .. External Subroutines .. - EXTERNAL DCOPY, DGEMV, DLACPY, DLASCL, DROT, DSCAL, - $ XERBLA -* .. -* .. External Functions .. - DOUBLE PRECISION DLAMC3, DNRM2 - EXTERNAL DLAMC3, DNRM2 -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 - N = NL + NR + 1 -* - IF( ( ICOMPQ.LT.0 ) .OR. ( ICOMPQ.GT.1 ) ) THEN - INFO = -1 - ELSE IF( NL.LT.1 ) THEN - INFO = -2 - ELSE IF( NR.LT.1 ) THEN - INFO = -3 - ELSE IF( ( SQRE.LT.0 ) .OR. ( SQRE.GT.1 ) ) THEN - INFO = -4 - ELSE IF( NRHS.LT.1 ) THEN - INFO = -5 - ELSE IF( LDB.LT.N ) THEN - INFO = -7 - ELSE IF( LDBX.LT.N ) THEN - INFO = -9 - ELSE IF( GIVPTR.LT.0 ) THEN - INFO = -11 - ELSE IF( LDGCOL.LT.N ) THEN - INFO = -13 - ELSE IF( LDGNUM.LT.N ) THEN - INFO = -15 - ELSE IF( K.LT.1 ) THEN - INFO = -20 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DLALS0', -INFO ) - RETURN - END IF -* - M = N + SQRE - NLP1 = NL + 1 -* - IF( ICOMPQ.EQ.0 ) THEN -* -* Apply back orthogonal transformations from the left. -* -* Step (1L): apply back the Givens rotations performed. -* - DO 10 I = 1, GIVPTR - CALL DROT( NRHS, B( GIVCOL( I, 2 ), 1 ), LDB, - $ B( GIVCOL( I, 1 ), 1 ), LDB, GIVNUM( I, 2 ), - $ GIVNUM( I, 1 ) ) - 10 CONTINUE -* -* Step (2L): permute rows of B. -* - CALL DCOPY( NRHS, B( NLP1, 1 ), LDB, BX( 1, 1 ), LDBX ) - DO 20 I = 2, N - CALL DCOPY( NRHS, B( PERM( I ), 1 ), LDB, BX( I, 1 ), LDBX ) - 20 CONTINUE -* -* Step (3L): apply the inverse of the left singular vector -* matrix to BX. -* - IF( K.EQ.1 ) THEN - CALL DCOPY( NRHS, BX, LDBX, B, LDB ) - IF( Z( 1 ).LT.ZERO ) THEN - CALL DSCAL( NRHS, NEGONE, B, LDB ) - END IF - ELSE - DO 50 J = 1, K - DIFLJ = DIFL( J ) - DJ = POLES( J, 1 ) - DSIGJ = -POLES( J, 2 ) - IF( J.LT.K ) THEN - DIFRJ = -DIFR( J, 1 ) - DSIGJP = -POLES( J+1, 2 ) - END IF - IF( ( Z( J ).EQ.ZERO ) .OR. ( POLES( J, 2 ).EQ.ZERO ) ) - $ THEN - WORK( J ) = ZERO - ELSE - WORK( J ) = -POLES( J, 2 )*Z( J ) / DIFLJ / - $ ( POLES( J, 2 )+DJ ) - END IF - DO 30 I = 1, J - 1 - IF( ( Z( I ).EQ.ZERO ) .OR. - $ ( POLES( I, 2 ).EQ.ZERO ) ) THEN - WORK( I ) = ZERO - ELSE - WORK( I ) = POLES( I, 2 )*Z( I ) / - $ ( DLAMC3( POLES( I, 2 ), DSIGJ )- - $ DIFLJ ) / ( POLES( I, 2 )+DJ ) - END IF - 30 CONTINUE - DO 40 I = J + 1, K - IF( ( Z( I ).EQ.ZERO ) .OR. - $ ( POLES( I, 2 ).EQ.ZERO ) ) THEN - WORK( I ) = ZERO - ELSE - WORK( I ) = POLES( I, 2 )*Z( I ) / - $ ( DLAMC3( POLES( I, 2 ), DSIGJP )+ - $ DIFRJ ) / ( POLES( I, 2 )+DJ ) - END IF - 40 CONTINUE - WORK( 1 ) = NEGONE - TEMP = DNRM2( K, WORK, 1 ) - CALL DGEMV( 'T', K, NRHS, ONE, BX, LDBX, WORK, 1, ZERO, - $ B( J, 1 ), LDB ) - CALL DLASCL( 'G', 0, 0, TEMP, ONE, 1, NRHS, B( J, 1 ), - $ LDB, INFO ) - 50 CONTINUE - END IF -* -* Move the deflated rows of BX to B also. -* - IF( K.LT.MAX( M, N ) ) - $ CALL DLACPY( 'A', N-K, NRHS, BX( K+1, 1 ), LDBX, - $ B( K+1, 1 ), LDB ) - ELSE -* -* Apply back the right orthogonal transformations. -* -* Step (1R): apply back the new right singular vector matrix -* to B. -* - IF( K.EQ.1 ) THEN - CALL DCOPY( NRHS, B, LDB, BX, LDBX ) - ELSE - DO 80 J = 1, K - DSIGJ = POLES( J, 2 ) - IF( Z( J ).EQ.ZERO ) THEN - WORK( J ) = ZERO - ELSE - WORK( J ) = -Z( J ) / DIFL( J ) / - $ ( DSIGJ+POLES( J, 1 ) ) / DIFR( J, 2 ) - END IF - DO 60 I = 1, J - 1 - IF( Z( J ).EQ.ZERO ) THEN - WORK( I ) = ZERO - ELSE - WORK( I ) = Z( J ) / ( DLAMC3( DSIGJ, -POLES( I+1, - $ 2 ) )-DIFR( I, 1 ) ) / - $ ( DSIGJ+POLES( I, 1 ) ) / DIFR( I, 2 ) - END IF - 60 CONTINUE - DO 70 I = J + 1, K - IF( Z( J ).EQ.ZERO ) THEN - WORK( I ) = ZERO - ELSE - WORK( I ) = Z( J ) / ( DLAMC3( DSIGJ, -POLES( I, - $ 2 ) )-DIFL( I ) ) / - $ ( DSIGJ+POLES( I, 1 ) ) / DIFR( I, 2 ) - END IF - 70 CONTINUE - CALL DGEMV( 'T', K, NRHS, ONE, B, LDB, WORK, 1, ZERO, - $ BX( J, 1 ), LDBX ) - 80 CONTINUE - END IF -* -* Step (2R): if SQRE = 1, apply back the rotation that is -* related to the right null space of the subproblem. -* - IF( SQRE.EQ.1 ) THEN - CALL DCOPY( NRHS, B( M, 1 ), LDB, BX( M, 1 ), LDBX ) - CALL DROT( NRHS, BX( 1, 1 ), LDBX, BX( M, 1 ), LDBX, C, S ) - END IF - IF( K.LT.MAX( M, N ) ) - $ CALL DLACPY( 'A', N-K, NRHS, B( K+1, 1 ), LDB, BX( K+1, 1 ), - $ LDBX ) -* -* Step (3R): permute rows of B. -* - CALL DCOPY( NRHS, BX( 1, 1 ), LDBX, B( NLP1, 1 ), LDB ) - IF( SQRE.EQ.1 ) THEN - CALL DCOPY( NRHS, BX( M, 1 ), LDBX, B( M, 1 ), LDB ) - END IF - DO 90 I = 2, N - CALL DCOPY( NRHS, BX( I, 1 ), LDBX, B( PERM( I ), 1 ), LDB ) - 90 CONTINUE -* -* Step (4R): apply back the Givens rotations performed. -* - DO 100 I = GIVPTR, 1, -1 - CALL DROT( NRHS, B( GIVCOL( I, 2 ), 1 ), LDB, - $ B( GIVCOL( I, 1 ), 1 ), LDB, GIVNUM( I, 2 ), - $ -GIVNUM( I, 1 ) ) - 100 CONTINUE - END IF -* - RETURN -* -* End of DLALS0 -* - END diff --git a/lib/linalg/fortran/dlalsa.f b/lib/linalg/fortran/dlalsa.f deleted file mode 100644 index da8e0fa175..0000000000 --- a/lib/linalg/fortran/dlalsa.f +++ /dev/null @@ -1,490 +0,0 @@ -*> \brief \b DLALSA computes the SVD of the coefficient matrix in compact form. Used by sgelsd. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLALSA + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLALSA( ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U, -* LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR, -* GIVCOL, LDGCOL, PERM, GIVNUM, C, S, WORK, -* IWORK, INFO ) -* -* .. Scalar Arguments .. -* INTEGER ICOMPQ, INFO, LDB, LDBX, LDGCOL, LDU, N, NRHS, -* $ SMLSIZ -* .. -* .. Array Arguments .. -* INTEGER GIVCOL( LDGCOL, * ), GIVPTR( * ), IWORK( * ), -* $ K( * ), PERM( LDGCOL, * ) -* DOUBLE PRECISION B( LDB, * ), BX( LDBX, * ), C( * ), -* $ DIFL( LDU, * ), DIFR( LDU, * ), -* $ GIVNUM( LDU, * ), POLES( LDU, * ), S( * ), -* $ U( LDU, * ), VT( LDU, * ), WORK( * ), -* $ Z( LDU, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLALSA is an itermediate step in solving the least squares problem -*> by computing the SVD of the coefficient matrix in compact form (The -*> singular vectors are computed as products of simple orthorgonal -*> matrices.). -*> -*> If ICOMPQ = 0, DLALSA applies the inverse of the left singular vector -*> matrix of an upper bidiagonal matrix to the right hand side; and if -*> ICOMPQ = 1, DLALSA applies the right singular vector matrix to the -*> right hand side. The singular vector matrices were generated in -*> compact form by DLALSA. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] ICOMPQ -*> \verbatim -*> ICOMPQ is INTEGER -*> Specifies whether the left or the right singular vector -*> matrix is involved. -*> = 0: Left singular vector matrix -*> = 1: Right singular vector matrix -*> \endverbatim -*> -*> \param[in] SMLSIZ -*> \verbatim -*> SMLSIZ is INTEGER -*> The maximum size of the subproblems at the bottom of the -*> computation tree. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The row and column dimensions of the upper bidiagonal matrix. -*> \endverbatim -*> -*> \param[in] NRHS -*> \verbatim -*> NRHS is INTEGER -*> The number of columns of B and BX. NRHS must be at least 1. -*> \endverbatim -*> -*> \param[in,out] B -*> \verbatim -*> B is DOUBLE PRECISION array, dimension ( LDB, NRHS ) -*> On input, B contains the right hand sides of the least -*> squares problem in rows 1 through M. -*> On output, B contains the solution X in rows 1 through N. -*> \endverbatim -*> -*> \param[in] LDB -*> \verbatim -*> LDB is INTEGER -*> The leading dimension of B in the calling subprogram. -*> LDB must be at least max(1,MAX( M, N ) ). -*> \endverbatim -*> -*> \param[out] BX -*> \verbatim -*> BX is DOUBLE PRECISION array, dimension ( LDBX, NRHS ) -*> On exit, the result of applying the left or right singular -*> vector matrix to B. -*> \endverbatim -*> -*> \param[in] LDBX -*> \verbatim -*> LDBX is INTEGER -*> The leading dimension of BX. -*> \endverbatim -*> -*> \param[in] U -*> \verbatim -*> U is DOUBLE PRECISION array, dimension ( LDU, SMLSIZ ). -*> On entry, U contains the left singular vector matrices of all -*> subproblems at the bottom level. -*> \endverbatim -*> -*> \param[in] LDU -*> \verbatim -*> LDU is INTEGER, LDU = > N. -*> The leading dimension of arrays U, VT, DIFL, DIFR, -*> POLES, GIVNUM, and Z. -*> \endverbatim -*> -*> \param[in] VT -*> \verbatim -*> VT is DOUBLE PRECISION array, dimension ( LDU, SMLSIZ+1 ). -*> On entry, VT**T contains the right singular vector matrices of -*> all subproblems at the bottom level. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER array, dimension ( N ). -*> \endverbatim -*> -*> \param[in] DIFL -*> \verbatim -*> DIFL is DOUBLE PRECISION array, dimension ( LDU, NLVL ). -*> where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1. -*> \endverbatim -*> -*> \param[in] DIFR -*> \verbatim -*> DIFR is DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ). -*> On entry, DIFL(*, I) and DIFR(*, 2 * I -1) record -*> distances between singular values on the I-th level and -*> singular values on the (I -1)-th level, and DIFR(*, 2 * I) -*> record the normalizing factors of the right singular vectors -*> matrices of subproblems on I-th level. -*> \endverbatim -*> -*> \param[in] Z -*> \verbatim -*> Z is DOUBLE PRECISION array, dimension ( LDU, NLVL ). -*> On entry, Z(1, I) contains the components of the deflation- -*> adjusted updating row vector for subproblems on the I-th -*> level. -*> \endverbatim -*> -*> \param[in] POLES -*> \verbatim -*> POLES is DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ). -*> On entry, POLES(*, 2 * I -1: 2 * I) contains the new and old -*> singular values involved in the secular equations on the I-th -*> level. -*> \endverbatim -*> -*> \param[in] GIVPTR -*> \verbatim -*> GIVPTR is INTEGER array, dimension ( N ). -*> On entry, GIVPTR( I ) records the number of Givens -*> rotations performed on the I-th problem on the computation -*> tree. -*> \endverbatim -*> -*> \param[in] GIVCOL -*> \verbatim -*> GIVCOL is INTEGER array, dimension ( LDGCOL, 2 * NLVL ). -*> On entry, for each I, GIVCOL(*, 2 * I - 1: 2 * I) records the -*> locations of Givens rotations performed on the I-th level on -*> the computation tree. -*> \endverbatim -*> -*> \param[in] LDGCOL -*> \verbatim -*> LDGCOL is INTEGER, LDGCOL = > N. -*> The leading dimension of arrays GIVCOL and PERM. -*> \endverbatim -*> -*> \param[in] PERM -*> \verbatim -*> PERM is INTEGER array, dimension ( LDGCOL, NLVL ). -*> On entry, PERM(*, I) records permutations done on the I-th -*> level of the computation tree. -*> \endverbatim -*> -*> \param[in] GIVNUM -*> \verbatim -*> GIVNUM is DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ). -*> On entry, GIVNUM(*, 2 *I -1 : 2 * I) records the C- and S- -*> values of Givens rotations performed on the I-th level on the -*> computation tree. -*> \endverbatim -*> -*> \param[in] C -*> \verbatim -*> C is DOUBLE PRECISION array, dimension ( N ). -*> On entry, if the I-th subproblem is not square, -*> C( I ) contains the C-value of a Givens rotation related to -*> the right null space of the I-th subproblem. -*> \endverbatim -*> -*> \param[in] S -*> \verbatim -*> S is DOUBLE PRECISION array, dimension ( N ). -*> On entry, if the I-th subproblem is not square, -*> S( I ) contains the S-value of a Givens rotation related to -*> the right null space of the I-th subproblem. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (N) -*> \endverbatim -*> -*> \param[out] IWORK -*> \verbatim -*> IWORK is INTEGER array, dimension (3*N) -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit. -*> < 0: if INFO = -i, the i-th argument had an illegal value. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleOTHERcomputational -* -*> \par Contributors: -* ================== -*> -*> Ming Gu and Ren-Cang Li, Computer Science Division, University of -*> California at Berkeley, USA \n -*> Osni Marques, LBNL/NERSC, USA \n -* -* ===================================================================== - SUBROUTINE DLALSA( ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U, - $ LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR, - $ GIVCOL, LDGCOL, PERM, GIVNUM, C, S, WORK, - $ IWORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER ICOMPQ, INFO, LDB, LDBX, LDGCOL, LDU, N, NRHS, - $ SMLSIZ -* .. -* .. Array Arguments .. - INTEGER GIVCOL( LDGCOL, * ), GIVPTR( * ), IWORK( * ), - $ K( * ), PERM( LDGCOL, * ) - DOUBLE PRECISION B( LDB, * ), BX( LDBX, * ), C( * ), - $ DIFL( LDU, * ), DIFR( LDU, * ), - $ GIVNUM( LDU, * ), POLES( LDU, * ), S( * ), - $ U( LDU, * ), VT( LDU, * ), WORK( * ), - $ Z( LDU, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) -* .. -* .. Local Scalars .. - INTEGER I, I1, IC, IM1, INODE, J, LF, LL, LVL, LVL2, - $ ND, NDB1, NDIML, NDIMR, NL, NLF, NLP1, NLVL, - $ NR, NRF, NRP1, SQRE -* .. -* .. External Subroutines .. - EXTERNAL DCOPY, DGEMM, DLALS0, DLASDT, XERBLA -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 -* - IF( ( ICOMPQ.LT.0 ) .OR. ( ICOMPQ.GT.1 ) ) THEN - INFO = -1 - ELSE IF( SMLSIZ.LT.3 ) THEN - INFO = -2 - ELSE IF( N.LT.SMLSIZ ) THEN - INFO = -3 - ELSE IF( NRHS.LT.1 ) THEN - INFO = -4 - ELSE IF( LDB.LT.N ) THEN - INFO = -6 - ELSE IF( LDBX.LT.N ) THEN - INFO = -8 - ELSE IF( LDU.LT.N ) THEN - INFO = -10 - ELSE IF( LDGCOL.LT.N ) THEN - INFO = -19 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DLALSA', -INFO ) - RETURN - END IF -* -* Book-keeping and setting up the computation tree. -* - INODE = 1 - NDIML = INODE + N - NDIMR = NDIML + N -* - CALL DLASDT( N, NLVL, ND, IWORK( INODE ), IWORK( NDIML ), - $ IWORK( NDIMR ), SMLSIZ ) -* -* The following code applies back the left singular vector factors. -* For applying back the right singular vector factors, go to 50. -* - IF( ICOMPQ.EQ.1 ) THEN - GO TO 50 - END IF -* -* The nodes on the bottom level of the tree were solved -* by DLASDQ. The corresponding left and right singular vector -* matrices are in explicit form. First apply back the left -* singular vector matrices. -* - NDB1 = ( ND+1 ) / 2 - DO 10 I = NDB1, ND -* -* IC : center row of each node -* NL : number of rows of left subproblem -* NR : number of rows of right subproblem -* NLF: starting row of the left subproblem -* NRF: starting row of the right subproblem -* - I1 = I - 1 - IC = IWORK( INODE+I1 ) - NL = IWORK( NDIML+I1 ) - NR = IWORK( NDIMR+I1 ) - NLF = IC - NL - NRF = IC + 1 - CALL DGEMM( 'T', 'N', NL, NRHS, NL, ONE, U( NLF, 1 ), LDU, - $ B( NLF, 1 ), LDB, ZERO, BX( NLF, 1 ), LDBX ) - CALL DGEMM( 'T', 'N', NR, NRHS, NR, ONE, U( NRF, 1 ), LDU, - $ B( NRF, 1 ), LDB, ZERO, BX( NRF, 1 ), LDBX ) - 10 CONTINUE -* -* Next copy the rows of B that correspond to unchanged rows -* in the bidiagonal matrix to BX. -* - DO 20 I = 1, ND - IC = IWORK( INODE+I-1 ) - CALL DCOPY( NRHS, B( IC, 1 ), LDB, BX( IC, 1 ), LDBX ) - 20 CONTINUE -* -* Finally go through the left singular vector matrices of all -* the other subproblems bottom-up on the tree. -* - J = 2**NLVL - SQRE = 0 -* - DO 40 LVL = NLVL, 1, -1 - LVL2 = 2*LVL - 1 -* -* find the first node LF and last node LL on -* the current level LVL -* - IF( LVL.EQ.1 ) THEN - LF = 1 - LL = 1 - ELSE - LF = 2**( LVL-1 ) - LL = 2*LF - 1 - END IF - DO 30 I = LF, LL - IM1 = I - 1 - IC = IWORK( INODE+IM1 ) - NL = IWORK( NDIML+IM1 ) - NR = IWORK( NDIMR+IM1 ) - NLF = IC - NL - NRF = IC + 1 - J = J - 1 - CALL DLALS0( ICOMPQ, NL, NR, SQRE, NRHS, BX( NLF, 1 ), LDBX, - $ B( NLF, 1 ), LDB, PERM( NLF, LVL ), - $ GIVPTR( J ), GIVCOL( NLF, LVL2 ), LDGCOL, - $ GIVNUM( NLF, LVL2 ), LDU, POLES( NLF, LVL2 ), - $ DIFL( NLF, LVL ), DIFR( NLF, LVL2 ), - $ Z( NLF, LVL ), K( J ), C( J ), S( J ), WORK, - $ INFO ) - 30 CONTINUE - 40 CONTINUE - GO TO 90 -* -* ICOMPQ = 1: applying back the right singular vector factors. -* - 50 CONTINUE -* -* First now go through the right singular vector matrices of all -* the tree nodes top-down. -* - J = 0 - DO 70 LVL = 1, NLVL - LVL2 = 2*LVL - 1 -* -* Find the first node LF and last node LL on -* the current level LVL. -* - IF( LVL.EQ.1 ) THEN - LF = 1 - LL = 1 - ELSE - LF = 2**( LVL-1 ) - LL = 2*LF - 1 - END IF - DO 60 I = LL, LF, -1 - IM1 = I - 1 - IC = IWORK( INODE+IM1 ) - NL = IWORK( NDIML+IM1 ) - NR = IWORK( NDIMR+IM1 ) - NLF = IC - NL - NRF = IC + 1 - IF( I.EQ.LL ) THEN - SQRE = 0 - ELSE - SQRE = 1 - END IF - J = J + 1 - CALL DLALS0( ICOMPQ, NL, NR, SQRE, NRHS, B( NLF, 1 ), LDB, - $ BX( NLF, 1 ), LDBX, PERM( NLF, LVL ), - $ GIVPTR( J ), GIVCOL( NLF, LVL2 ), LDGCOL, - $ GIVNUM( NLF, LVL2 ), LDU, POLES( NLF, LVL2 ), - $ DIFL( NLF, LVL ), DIFR( NLF, LVL2 ), - $ Z( NLF, LVL ), K( J ), C( J ), S( J ), WORK, - $ INFO ) - 60 CONTINUE - 70 CONTINUE -* -* The nodes on the bottom level of the tree were solved -* by DLASDQ. The corresponding right singular vector -* matrices are in explicit form. Apply them back. -* - NDB1 = ( ND+1 ) / 2 - DO 80 I = NDB1, ND - I1 = I - 1 - IC = IWORK( INODE+I1 ) - NL = IWORK( NDIML+I1 ) - NR = IWORK( NDIMR+I1 ) - NLP1 = NL + 1 - IF( I.EQ.ND ) THEN - NRP1 = NR - ELSE - NRP1 = NR + 1 - END IF - NLF = IC - NL - NRF = IC + 1 - CALL DGEMM( 'T', 'N', NLP1, NRHS, NLP1, ONE, VT( NLF, 1 ), LDU, - $ B( NLF, 1 ), LDB, ZERO, BX( NLF, 1 ), LDBX ) - CALL DGEMM( 'T', 'N', NRP1, NRHS, NRP1, ONE, VT( NRF, 1 ), LDU, - $ B( NRF, 1 ), LDB, ZERO, BX( NRF, 1 ), LDBX ) - 80 CONTINUE -* - 90 CONTINUE -* - RETURN -* -* End of DLALSA -* - END diff --git a/lib/linalg/fortran/dlalsd.f b/lib/linalg/fortran/dlalsd.f deleted file mode 100644 index d22c45dc6e..0000000000 --- a/lib/linalg/fortran/dlalsd.f +++ /dev/null @@ -1,520 +0,0 @@ -*> \brief \b DLALSD uses the singular value decomposition of A to solve the least squares problem. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLALSD + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND, -* RANK, WORK, IWORK, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER UPLO -* INTEGER INFO, LDB, N, NRHS, RANK, SMLSIZ -* DOUBLE PRECISION RCOND -* .. -* .. Array Arguments .. -* INTEGER IWORK( * ) -* DOUBLE PRECISION B( LDB, * ), D( * ), E( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLALSD uses the singular value decomposition of A to solve the least -*> squares problem of finding X to minimize the Euclidean norm of each -*> column of A*X-B, where A is N-by-N upper bidiagonal, and X and B -*> are N-by-NRHS. The solution X overwrites B. -*> -*> The singular values of A smaller than RCOND times the largest -*> singular value are treated as zero in solving the least squares -*> problem; in this case a minimum norm solution is returned. -*> The actual singular values are returned in D in ascending order. -*> -*> This code makes very mild assumptions about floating point -*> arithmetic. It will work on machines with a guard digit in -*> add/subtract, or on those binary machines without guard digits -*> which subtract like the Cray XMP, Cray YMP, Cray C 90, or Cray 2. -*> It could conceivably fail on hexadecimal or decimal machines -*> without guard digits, but we know of none. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> = 'U': D and E define an upper bidiagonal matrix. -*> = 'L': D and E define a lower bidiagonal matrix. -*> \endverbatim -*> -*> \param[in] SMLSIZ -*> \verbatim -*> SMLSIZ is INTEGER -*> The maximum size of the subproblems at the bottom of the -*> computation tree. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The dimension of the bidiagonal matrix. N >= 0. -*> \endverbatim -*> -*> \param[in] NRHS -*> \verbatim -*> NRHS is INTEGER -*> The number of columns of B. NRHS must be at least 1. -*> \endverbatim -*> -*> \param[in,out] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension (N) -*> On entry D contains the main diagonal of the bidiagonal -*> matrix. On exit, if INFO = 0, D contains its singular values. -*> \endverbatim -*> -*> \param[in,out] E -*> \verbatim -*> E is DOUBLE PRECISION array, dimension (N-1) -*> Contains the super-diagonal entries of the bidiagonal matrix. -*> On exit, E has been destroyed. -*> \endverbatim -*> -*> \param[in,out] B -*> \verbatim -*> B is DOUBLE PRECISION array, dimension (LDB,NRHS) -*> On input, B contains the right hand sides of the least -*> squares problem. On output, B contains the solution X. -*> \endverbatim -*> -*> \param[in] LDB -*> \verbatim -*> LDB is INTEGER -*> The leading dimension of B in the calling subprogram. -*> LDB must be at least max(1,N). -*> \endverbatim -*> -*> \param[in] RCOND -*> \verbatim -*> RCOND is DOUBLE PRECISION -*> The singular values of A less than or equal to RCOND times -*> the largest singular value are treated as zero in solving -*> the least squares problem. If RCOND is negative, -*> machine precision is used instead. -*> For example, if diag(S)*X=B were the least squares problem, -*> where diag(S) is a diagonal matrix of singular values, the -*> solution would be X(i) = B(i) / S(i) if S(i) is greater than -*> RCOND*max(S), and X(i) = 0 if S(i) is less than or equal to -*> RCOND*max(S). -*> \endverbatim -*> -*> \param[out] RANK -*> \verbatim -*> RANK is INTEGER -*> The number of singular values of A greater than RCOND times -*> the largest singular value. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension at least -*> (9*N + 2*N*SMLSIZ + 8*N*NLVL + N*NRHS + (SMLSIZ+1)**2), -*> where NLVL = max(0, INT(log_2 (N/(SMLSIZ+1))) + 1). -*> \endverbatim -*> -*> \param[out] IWORK -*> \verbatim -*> IWORK is INTEGER array, dimension at least -*> (3*N*NLVL + 11*N) -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit. -*> < 0: if INFO = -i, the i-th argument had an illegal value. -*> > 0: The algorithm failed to compute a singular value while -*> working on the submatrix lying in rows and columns -*> INFO/(N+1) through MOD(INFO,N+1). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleOTHERcomputational -* -*> \par Contributors: -* ================== -*> -*> Ming Gu and Ren-Cang Li, Computer Science Division, University of -*> California at Berkeley, USA \n -*> Osni Marques, LBNL/NERSC, USA \n -* -* ===================================================================== - SUBROUTINE DLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND, - $ RANK, WORK, IWORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER UPLO - INTEGER INFO, LDB, N, NRHS, RANK, SMLSIZ - DOUBLE PRECISION RCOND -* .. -* .. Array Arguments .. - INTEGER IWORK( * ) - DOUBLE PRECISION B( LDB, * ), D( * ), E( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, ONE, TWO - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0 ) -* .. -* .. Local Scalars .. - INTEGER BX, BXST, C, DIFL, DIFR, GIVCOL, GIVNUM, - $ GIVPTR, I, ICMPQ1, ICMPQ2, IWK, J, K, NLVL, - $ NM1, NSIZE, NSUB, NWORK, PERM, POLES, S, SIZEI, - $ SMLSZP, SQRE, ST, ST1, U, VT, Z - DOUBLE PRECISION CS, EPS, ORGNRM, R, RCND, SN, TOL -* .. -* .. External Functions .. - INTEGER IDAMAX - DOUBLE PRECISION DLAMCH, DLANST - EXTERNAL IDAMAX, DLAMCH, DLANST -* .. -* .. External Subroutines .. - EXTERNAL DCOPY, DGEMM, DLACPY, DLALSA, DLARTG, DLASCL, - $ DLASDA, DLASDQ, DLASET, DLASRT, DROT, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, DBLE, INT, LOG, SIGN -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 -* - IF( N.LT.0 ) THEN - INFO = -3 - ELSE IF( NRHS.LT.1 ) THEN - INFO = -4 - ELSE IF( ( LDB.LT.1 ) .OR. ( LDB.LT.N ) ) THEN - INFO = -8 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DLALSD', -INFO ) - RETURN - END IF -* - EPS = DLAMCH( 'Epsilon' ) -* -* Set up the tolerance. -* - IF( ( RCOND.LE.ZERO ) .OR. ( RCOND.GE.ONE ) ) THEN - RCND = EPS - ELSE - RCND = RCOND - END IF -* - RANK = 0 -* -* Quick return if possible. -* - IF( N.EQ.0 ) THEN - RETURN - ELSE IF( N.EQ.1 ) THEN - IF( D( 1 ).EQ.ZERO ) THEN - CALL DLASET( 'A', 1, NRHS, ZERO, ZERO, B, LDB ) - ELSE - RANK = 1 - CALL DLASCL( 'G', 0, 0, D( 1 ), ONE, 1, NRHS, B, LDB, INFO ) - D( 1 ) = ABS( D( 1 ) ) - END IF - RETURN - END IF -* -* Rotate the matrix if it is lower bidiagonal. -* - IF( UPLO.EQ.'L' ) THEN - DO 10 I = 1, N - 1 - CALL DLARTG( D( I ), E( I ), CS, SN, R ) - D( I ) = R - E( I ) = SN*D( I+1 ) - D( I+1 ) = CS*D( I+1 ) - IF( NRHS.EQ.1 ) THEN - CALL DROT( 1, B( I, 1 ), 1, B( I+1, 1 ), 1, CS, SN ) - ELSE - WORK( I*2-1 ) = CS - WORK( I*2 ) = SN - END IF - 10 CONTINUE - IF( NRHS.GT.1 ) THEN - DO 30 I = 1, NRHS - DO 20 J = 1, N - 1 - CS = WORK( J*2-1 ) - SN = WORK( J*2 ) - CALL DROT( 1, B( J, I ), 1, B( J+1, I ), 1, CS, SN ) - 20 CONTINUE - 30 CONTINUE - END IF - END IF -* -* Scale. -* - NM1 = N - 1 - ORGNRM = DLANST( 'M', N, D, E ) - IF( ORGNRM.EQ.ZERO ) THEN - CALL DLASET( 'A', N, NRHS, ZERO, ZERO, B, LDB ) - RETURN - END IF -* - CALL DLASCL( 'G', 0, 0, ORGNRM, ONE, N, 1, D, N, INFO ) - CALL DLASCL( 'G', 0, 0, ORGNRM, ONE, NM1, 1, E, NM1, INFO ) -* -* If N is smaller than the minimum divide size SMLSIZ, then solve -* the problem with another solver. -* - IF( N.LE.SMLSIZ ) THEN - NWORK = 1 + N*N - CALL DLASET( 'A', N, N, ZERO, ONE, WORK, N ) - CALL DLASDQ( 'U', 0, N, N, 0, NRHS, D, E, WORK, N, WORK, N, B, - $ LDB, WORK( NWORK ), INFO ) - IF( INFO.NE.0 ) THEN - RETURN - END IF - TOL = RCND*ABS( D( IDAMAX( N, D, 1 ) ) ) - DO 40 I = 1, N - IF( D( I ).LE.TOL ) THEN - CALL DLASET( 'A', 1, NRHS, ZERO, ZERO, B( I, 1 ), LDB ) - ELSE - CALL DLASCL( 'G', 0, 0, D( I ), ONE, 1, NRHS, B( I, 1 ), - $ LDB, INFO ) - RANK = RANK + 1 - END IF - 40 CONTINUE - CALL DGEMM( 'T', 'N', N, NRHS, N, ONE, WORK, N, B, LDB, ZERO, - $ WORK( NWORK ), N ) - CALL DLACPY( 'A', N, NRHS, WORK( NWORK ), N, B, LDB ) -* -* Unscale. -* - CALL DLASCL( 'G', 0, 0, ONE, ORGNRM, N, 1, D, N, INFO ) - CALL DLASRT( 'D', N, D, INFO ) - CALL DLASCL( 'G', 0, 0, ORGNRM, ONE, N, NRHS, B, LDB, INFO ) -* - RETURN - END IF -* -* Book-keeping and setting up some constants. -* - NLVL = INT( LOG( DBLE( N ) / DBLE( SMLSIZ+1 ) ) / LOG( TWO ) ) + 1 -* - SMLSZP = SMLSIZ + 1 -* - U = 1 - VT = 1 + SMLSIZ*N - DIFL = VT + SMLSZP*N - DIFR = DIFL + NLVL*N - Z = DIFR + NLVL*N*2 - C = Z + NLVL*N - S = C + N - POLES = S + N - GIVNUM = POLES + 2*NLVL*N - BX = GIVNUM + 2*NLVL*N - NWORK = BX + N*NRHS -* - SIZEI = 1 + N - K = SIZEI + N - GIVPTR = K + N - PERM = GIVPTR + N - GIVCOL = PERM + NLVL*N - IWK = GIVCOL + NLVL*N*2 -* - ST = 1 - SQRE = 0 - ICMPQ1 = 1 - ICMPQ2 = 0 - NSUB = 0 -* - DO 50 I = 1, N - IF( ABS( D( I ) ).LT.EPS ) THEN - D( I ) = SIGN( EPS, D( I ) ) - END IF - 50 CONTINUE -* - DO 60 I = 1, NM1 - IF( ( ABS( E( I ) ).LT.EPS ) .OR. ( I.EQ.NM1 ) ) THEN - NSUB = NSUB + 1 - IWORK( NSUB ) = ST -* -* Subproblem found. First determine its size and then -* apply divide and conquer on it. -* - IF( I.LT.NM1 ) THEN -* -* A subproblem with E(I) small for I < NM1. -* - NSIZE = I - ST + 1 - IWORK( SIZEI+NSUB-1 ) = NSIZE - ELSE IF( ABS( E( I ) ).GE.EPS ) THEN -* -* A subproblem with E(NM1) not too small but I = NM1. -* - NSIZE = N - ST + 1 - IWORK( SIZEI+NSUB-1 ) = NSIZE - ELSE -* -* A subproblem with E(NM1) small. This implies an -* 1-by-1 subproblem at D(N), which is not solved -* explicitly. -* - NSIZE = I - ST + 1 - IWORK( SIZEI+NSUB-1 ) = NSIZE - NSUB = NSUB + 1 - IWORK( NSUB ) = N - IWORK( SIZEI+NSUB-1 ) = 1 - CALL DCOPY( NRHS, B( N, 1 ), LDB, WORK( BX+NM1 ), N ) - END IF - ST1 = ST - 1 - IF( NSIZE.EQ.1 ) THEN -* -* This is a 1-by-1 subproblem and is not solved -* explicitly. -* - CALL DCOPY( NRHS, B( ST, 1 ), LDB, WORK( BX+ST1 ), N ) - ELSE IF( NSIZE.LE.SMLSIZ ) THEN -* -* This is a small subproblem and is solved by DLASDQ. -* - CALL DLASET( 'A', NSIZE, NSIZE, ZERO, ONE, - $ WORK( VT+ST1 ), N ) - CALL DLASDQ( 'U', 0, NSIZE, NSIZE, 0, NRHS, D( ST ), - $ E( ST ), WORK( VT+ST1 ), N, WORK( NWORK ), - $ N, B( ST, 1 ), LDB, WORK( NWORK ), INFO ) - IF( INFO.NE.0 ) THEN - RETURN - END IF - CALL DLACPY( 'A', NSIZE, NRHS, B( ST, 1 ), LDB, - $ WORK( BX+ST1 ), N ) - ELSE -* -* A large problem. Solve it using divide and conquer. -* - CALL DLASDA( ICMPQ1, SMLSIZ, NSIZE, SQRE, D( ST ), - $ E( ST ), WORK( U+ST1 ), N, WORK( VT+ST1 ), - $ IWORK( K+ST1 ), WORK( DIFL+ST1 ), - $ WORK( DIFR+ST1 ), WORK( Z+ST1 ), - $ WORK( POLES+ST1 ), IWORK( GIVPTR+ST1 ), - $ IWORK( GIVCOL+ST1 ), N, IWORK( PERM+ST1 ), - $ WORK( GIVNUM+ST1 ), WORK( C+ST1 ), - $ WORK( S+ST1 ), WORK( NWORK ), IWORK( IWK ), - $ INFO ) - IF( INFO.NE.0 ) THEN - RETURN - END IF - BXST = BX + ST1 - CALL DLALSA( ICMPQ2, SMLSIZ, NSIZE, NRHS, B( ST, 1 ), - $ LDB, WORK( BXST ), N, WORK( U+ST1 ), N, - $ WORK( VT+ST1 ), IWORK( K+ST1 ), - $ WORK( DIFL+ST1 ), WORK( DIFR+ST1 ), - $ WORK( Z+ST1 ), WORK( POLES+ST1 ), - $ IWORK( GIVPTR+ST1 ), IWORK( GIVCOL+ST1 ), N, - $ IWORK( PERM+ST1 ), WORK( GIVNUM+ST1 ), - $ WORK( C+ST1 ), WORK( S+ST1 ), WORK( NWORK ), - $ IWORK( IWK ), INFO ) - IF( INFO.NE.0 ) THEN - RETURN - END IF - END IF - ST = I + 1 - END IF - 60 CONTINUE -* -* Apply the singular values and treat the tiny ones as zero. -* - TOL = RCND*ABS( D( IDAMAX( N, D, 1 ) ) ) -* - DO 70 I = 1, N -* -* Some of the elements in D can be negative because 1-by-1 -* subproblems were not solved explicitly. -* - IF( ABS( D( I ) ).LE.TOL ) THEN - CALL DLASET( 'A', 1, NRHS, ZERO, ZERO, WORK( BX+I-1 ), N ) - ELSE - RANK = RANK + 1 - CALL DLASCL( 'G', 0, 0, D( I ), ONE, 1, NRHS, - $ WORK( BX+I-1 ), N, INFO ) - END IF - D( I ) = ABS( D( I ) ) - 70 CONTINUE -* -* Now apply back the right singular vectors. -* - ICMPQ2 = 1 - DO 80 I = 1, NSUB - ST = IWORK( I ) - ST1 = ST - 1 - NSIZE = IWORK( SIZEI+I-1 ) - BXST = BX + ST1 - IF( NSIZE.EQ.1 ) THEN - CALL DCOPY( NRHS, WORK( BXST ), N, B( ST, 1 ), LDB ) - ELSE IF( NSIZE.LE.SMLSIZ ) THEN - CALL DGEMM( 'T', 'N', NSIZE, NRHS, NSIZE, ONE, - $ WORK( VT+ST1 ), N, WORK( BXST ), N, ZERO, - $ B( ST, 1 ), LDB ) - ELSE - CALL DLALSA( ICMPQ2, SMLSIZ, NSIZE, NRHS, WORK( BXST ), N, - $ B( ST, 1 ), LDB, WORK( U+ST1 ), N, - $ WORK( VT+ST1 ), IWORK( K+ST1 ), - $ WORK( DIFL+ST1 ), WORK( DIFR+ST1 ), - $ WORK( Z+ST1 ), WORK( POLES+ST1 ), - $ IWORK( GIVPTR+ST1 ), IWORK( GIVCOL+ST1 ), N, - $ IWORK( PERM+ST1 ), WORK( GIVNUM+ST1 ), - $ WORK( C+ST1 ), WORK( S+ST1 ), WORK( NWORK ), - $ IWORK( IWK ), INFO ) - IF( INFO.NE.0 ) THEN - RETURN - END IF - END IF - 80 CONTINUE -* -* Unscale and sort the singular values. -* - CALL DLASCL( 'G', 0, 0, ONE, ORGNRM, N, 1, D, N, INFO ) - CALL DLASRT( 'D', N, D, INFO ) - CALL DLASCL( 'G', 0, 0, ORGNRM, ONE, N, NRHS, B, LDB, INFO ) -* - RETURN -* -* End of DLALSD -* - END diff --git a/lib/linalg/fortran/dlamch.f b/lib/linalg/fortran/dlamch.f deleted file mode 100644 index 76f875cef6..0000000000 --- a/lib/linalg/fortran/dlamch.f +++ /dev/null @@ -1,189 +0,0 @@ -*> \brief \b DLAMCH -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* DOUBLE PRECISION FUNCTION DLAMCH( CMACH ) -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLAMCH determines double precision machine parameters. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] CMACH -*> \verbatim -*> Specifies the value to be returned by DLAMCH: -*> = 'E' or 'e', DLAMCH := eps -*> = 'S' or 's , DLAMCH := sfmin -*> = 'B' or 'b', DLAMCH := base -*> = 'P' or 'p', DLAMCH := eps*base -*> = 'N' or 'n', DLAMCH := t -*> = 'R' or 'r', DLAMCH := rnd -*> = 'M' or 'm', DLAMCH := emin -*> = 'U' or 'u', DLAMCH := rmin -*> = 'L' or 'l', DLAMCH := emax -*> = 'O' or 'o', DLAMCH := rmax -*> where -*> eps = relative machine precision -*> sfmin = safe minimum, such that 1/sfmin does not overflow -*> base = base of the machine -*> prec = eps*base -*> t = number of (base) digits in the mantissa -*> rnd = 1.0 when rounding occurs in addition, 0.0 otherwise -*> emin = minimum exponent before (gradual) underflow -*> rmin = underflow threshold - base**(emin-1) -*> emax = largest exponent before overflow -*> rmax = overflow threshold - (base**emax)*(1-eps) -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \date December 2016 -* -*> \ingroup auxOTHERauxiliary -* -* ===================================================================== - DOUBLE PRECISION FUNCTION DLAMCH( CMACH ) -* -* -- LAPACK auxiliary routine (version 3.7.0) -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* December 2016 -* -* .. Scalar Arguments .. - CHARACTER CMACH -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE, ZERO - PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) -* .. -* .. Local Scalars .. - DOUBLE PRECISION RND, EPS, SFMIN, SMALL, RMACH -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. Intrinsic Functions .. - INTRINSIC DIGITS, EPSILON, HUGE, MAXEXPONENT, - $ MINEXPONENT, RADIX, TINY -* .. -* .. Executable Statements .. -* -* -* Assume rounding, not chopping. Always. -* - RND = ONE -* - IF( ONE.EQ.RND ) THEN - EPS = EPSILON(ZERO) * 0.5 - ELSE - EPS = EPSILON(ZERO) - END IF -* - IF( LSAME( CMACH, 'E' ) ) THEN - RMACH = EPS - ELSE IF( LSAME( CMACH, 'S' ) ) THEN - SFMIN = TINY(ZERO) - SMALL = ONE / HUGE(ZERO) - IF( SMALL.GE.SFMIN ) THEN -* -* Use SMALL plus a bit, to avoid the possibility of rounding -* causing overflow when computing 1/sfmin. -* - SFMIN = SMALL*( ONE+EPS ) - END IF - RMACH = SFMIN - ELSE IF( LSAME( CMACH, 'B' ) ) THEN - RMACH = RADIX(ZERO) - ELSE IF( LSAME( CMACH, 'P' ) ) THEN - RMACH = EPS * RADIX(ZERO) - ELSE IF( LSAME( CMACH, 'N' ) ) THEN - RMACH = DIGITS(ZERO) - ELSE IF( LSAME( CMACH, 'R' ) ) THEN - RMACH = RND - ELSE IF( LSAME( CMACH, 'M' ) ) THEN - RMACH = MINEXPONENT(ZERO) - ELSE IF( LSAME( CMACH, 'U' ) ) THEN - RMACH = tiny(zero) - ELSE IF( LSAME( CMACH, 'L' ) ) THEN - RMACH = MAXEXPONENT(ZERO) - ELSE IF( LSAME( CMACH, 'O' ) ) THEN - RMACH = HUGE(ZERO) - ELSE - RMACH = ZERO - END IF -* - DLAMCH = RMACH - RETURN -* -* End of DLAMCH -* - END -************************************************************************ -*> \brief \b DLAMC3 -*> \details -*> \b Purpose: -*> \verbatim -*> DLAMC3 is intended to force A and B to be stored prior to doing -*> the addition of A and B , for use in situations where optimizers -*> might hold one of these in a register. -*> \endverbatim -*> \author LAPACK is a software package provided by Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd.. -*> \date December 2016 -*> \ingroup auxOTHERauxiliary -*> -*> \param[in] A -*> \verbatim -*> A is a DOUBLE PRECISION -*> \endverbatim -*> -*> \param[in] B -*> \verbatim -*> B is a DOUBLE PRECISION -*> The values A and B. -*> \endverbatim -*> - DOUBLE PRECISION FUNCTION DLAMC3( A, B ) -* -* -- LAPACK auxiliary routine (version 3.7.0) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2010 -* -* .. Scalar Arguments .. - DOUBLE PRECISION A, B -* .. -* ===================================================================== -* -* .. Executable Statements .. -* - DLAMC3 = A + B -* - RETURN -* -* End of DLAMC3 -* - END -* -************************************************************************ diff --git a/lib/linalg/fortran/dlamrg.f b/lib/linalg/fortran/dlamrg.f deleted file mode 100644 index 80bd354b97..0000000000 --- a/lib/linalg/fortran/dlamrg.f +++ /dev/null @@ -1,168 +0,0 @@ -*> \brief \b DLAMRG creates a permutation list to merge the entries of two independently sorted sets into a single set sorted in ascending order. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLAMRG + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLAMRG( N1, N2, A, DTRD1, DTRD2, INDEX ) -* -* .. Scalar Arguments .. -* INTEGER DTRD1, DTRD2, N1, N2 -* .. -* .. Array Arguments .. -* INTEGER INDEX( * ) -* DOUBLE PRECISION A( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLAMRG will create a permutation list which will merge the elements -*> of A (which is composed of two independently sorted sets) into a -*> single set which is sorted in ascending order. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N1 -*> \verbatim -*> N1 is INTEGER -*> \endverbatim -*> -*> \param[in] N2 -*> \verbatim -*> N2 is INTEGER -*> These arguments contain the respective lengths of the two -*> sorted lists to be merged. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (N1+N2) -*> The first N1 elements of A contain a list of numbers which -*> are sorted in either ascending or descending order. Likewise -*> for the final N2 elements. -*> \endverbatim -*> -*> \param[in] DTRD1 -*> \verbatim -*> DTRD1 is INTEGER -*> \endverbatim -*> -*> \param[in] DTRD2 -*> \verbatim -*> DTRD2 is INTEGER -*> These are the strides to be taken through the array A. -*> Allowable strides are 1 and -1. They indicate whether a -*> subset of A is sorted in ascending (DTRDx = 1) or descending -*> (DTRDx = -1) order. -*> \endverbatim -*> -*> \param[out] INDEX -*> \verbatim -*> INDEX is INTEGER array, dimension (N1+N2) -*> On exit this array will contain a permutation such that -*> if B( I ) = A( INDEX( I ) ) for I=1,N1+N2, then B will be -*> sorted in ascending order. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup auxOTHERcomputational -* -* ===================================================================== - SUBROUTINE DLAMRG( N1, N2, A, DTRD1, DTRD2, INDEX ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER DTRD1, DTRD2, N1, N2 -* .. -* .. Array Arguments .. - INTEGER INDEX( * ) - DOUBLE PRECISION A( * ) -* .. -* -* ===================================================================== -* -* .. Local Scalars .. - INTEGER I, IND1, IND2, N1SV, N2SV -* .. -* .. Executable Statements .. -* - N1SV = N1 - N2SV = N2 - IF( DTRD1.GT.0 ) THEN - IND1 = 1 - ELSE - IND1 = N1 - END IF - IF( DTRD2.GT.0 ) THEN - IND2 = 1 + N1 - ELSE - IND2 = N1 + N2 - END IF - I = 1 -* while ( (N1SV > 0) & (N2SV > 0) ) - 10 CONTINUE - IF( N1SV.GT.0 .AND. N2SV.GT.0 ) THEN - IF( A( IND1 ).LE.A( IND2 ) ) THEN - INDEX( I ) = IND1 - I = I + 1 - IND1 = IND1 + DTRD1 - N1SV = N1SV - 1 - ELSE - INDEX( I ) = IND2 - I = I + 1 - IND2 = IND2 + DTRD2 - N2SV = N2SV - 1 - END IF - GO TO 10 - END IF -* end while - IF( N1SV.EQ.0 ) THEN - DO 20 N1SV = 1, N2SV - INDEX( I ) = IND2 - I = I + 1 - IND2 = IND2 + DTRD2 - 20 CONTINUE - ELSE -* N2SV .EQ. 0 - DO 30 N2SV = 1, N1SV - INDEX( I ) = IND1 - I = I + 1 - IND1 = IND1 + DTRD1 - 30 CONTINUE - END IF -* - RETURN -* -* End of DLAMRG -* - END diff --git a/lib/linalg/fortran/dlange.f b/lib/linalg/fortran/dlange.f deleted file mode 100644 index 9d214cb542..0000000000 --- a/lib/linalg/fortran/dlange.f +++ /dev/null @@ -1,208 +0,0 @@ -*> \brief \b DLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general rectangular matrix. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLANGE + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* DOUBLE PRECISION FUNCTION DLANGE( NORM, M, N, A, LDA, WORK ) -* -* .. Scalar Arguments .. -* CHARACTER NORM -* INTEGER LDA, M, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLANGE returns the value of the one norm, or the Frobenius norm, or -*> the infinity norm, or the element of largest absolute value of a -*> real matrix A. -*> \endverbatim -*> -*> \return DLANGE -*> \verbatim -*> -*> DLANGE = ( max(abs(A(i,j))), NORM = 'M' or 'm' -*> ( -*> ( norm1(A), NORM = '1', 'O' or 'o' -*> ( -*> ( normI(A), NORM = 'I' or 'i' -*> ( -*> ( normF(A), NORM = 'F', 'f', 'E' or 'e' -*> -*> where norm1 denotes the one norm of a matrix (maximum column sum), -*> normI denotes the infinity norm of a matrix (maximum row sum) and -*> normF denotes the Frobenius norm of a matrix (square root of sum of -*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] NORM -*> \verbatim -*> NORM is CHARACTER*1 -*> Specifies the value to be returned in DLANGE as described -*> above. -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix A. M >= 0. When M = 0, -*> DLANGE is set to zero. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix A. N >= 0. When N = 0, -*> DLANGE is set to zero. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> The m by n matrix A. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(M,1). -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), -*> where LWORK >= M when NORM = 'I'; otherwise, WORK is not -*> referenced. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleGEauxiliary -* -* ===================================================================== - DOUBLE PRECISION FUNCTION DLANGE( NORM, M, N, A, LDA, WORK ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER NORM - INTEGER LDA, M, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE, ZERO - PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) -* .. -* .. Local Scalars .. - INTEGER I, J - DOUBLE PRECISION SCALE, SUM, VALUE, TEMP -* .. -* .. External Subroutines .. - EXTERNAL DLASSQ -* .. -* .. External Functions .. - LOGICAL LSAME, DISNAN - EXTERNAL LSAME, DISNAN -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, MIN, SQRT -* .. -* .. Executable Statements .. -* - IF( MIN( M, N ).EQ.0 ) THEN - VALUE = ZERO - ELSE IF( LSAME( NORM, 'M' ) ) THEN -* -* Find max(abs(A(i,j))). -* - VALUE = ZERO - DO 20 J = 1, N - DO 10 I = 1, M - TEMP = ABS( A( I, J ) ) - IF( VALUE.LT.TEMP .OR. DISNAN( TEMP ) ) VALUE = TEMP - 10 CONTINUE - 20 CONTINUE - ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN -* -* Find norm1(A). -* - VALUE = ZERO - DO 40 J = 1, N - SUM = ZERO - DO 30 I = 1, M - SUM = SUM + ABS( A( I, J ) ) - 30 CONTINUE - IF( VALUE.LT.SUM .OR. DISNAN( SUM ) ) VALUE = SUM - 40 CONTINUE - ELSE IF( LSAME( NORM, 'I' ) ) THEN -* -* Find normI(A). -* - DO 50 I = 1, M - WORK( I ) = ZERO - 50 CONTINUE - DO 70 J = 1, N - DO 60 I = 1, M - WORK( I ) = WORK( I ) + ABS( A( I, J ) ) - 60 CONTINUE - 70 CONTINUE - VALUE = ZERO - DO 80 I = 1, M - TEMP = WORK( I ) - IF( VALUE.LT.TEMP .OR. DISNAN( TEMP ) ) VALUE = TEMP - 80 CONTINUE - ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN -* -* Find normF(A). -* - SCALE = ZERO - SUM = ONE - DO 90 J = 1, N - CALL DLASSQ( M, A( 1, J ), 1, SCALE, SUM ) - 90 CONTINUE - VALUE = SCALE*SQRT( SUM ) - END IF -* - DLANGE = VALUE - RETURN -* -* End of DLANGE -* - END diff --git a/lib/linalg/fortran/dlanst.f b/lib/linalg/fortran/dlanst.f deleted file mode 100644 index c5bc7ea038..0000000000 --- a/lib/linalg/fortran/dlanst.f +++ /dev/null @@ -1,183 +0,0 @@ -*> \brief \b DLANST returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLANST + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* DOUBLE PRECISION FUNCTION DLANST( NORM, N, D, E ) -* -* .. Scalar Arguments .. -* CHARACTER NORM -* INTEGER N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION D( * ), E( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLANST returns the value of the one norm, or the Frobenius norm, or -*> the infinity norm, or the element of largest absolute value of a -*> real symmetric tridiagonal matrix A. -*> \endverbatim -*> -*> \return DLANST -*> \verbatim -*> -*> DLANST = ( max(abs(A(i,j))), NORM = 'M' or 'm' -*> ( -*> ( norm1(A), NORM = '1', 'O' or 'o' -*> ( -*> ( normI(A), NORM = 'I' or 'i' -*> ( -*> ( normF(A), NORM = 'F', 'f', 'E' or 'e' -*> -*> where norm1 denotes the one norm of a matrix (maximum column sum), -*> normI denotes the infinity norm of a matrix (maximum row sum) and -*> normF denotes the Frobenius norm of a matrix (square root of sum of -*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] NORM -*> \verbatim -*> NORM is CHARACTER*1 -*> Specifies the value to be returned in DLANST as described -*> above. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrix A. N >= 0. When N = 0, DLANST is -*> set to zero. -*> \endverbatim -*> -*> \param[in] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension (N) -*> The diagonal elements of A. -*> \endverbatim -*> -*> \param[in] E -*> \verbatim -*> E is DOUBLE PRECISION array, dimension (N-1) -*> The (n-1) sub-diagonal or super-diagonal elements of A. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup OTHERauxiliary -* -* ===================================================================== - DOUBLE PRECISION FUNCTION DLANST( NORM, N, D, E ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER NORM - INTEGER N -* .. -* .. Array Arguments .. - DOUBLE PRECISION D( * ), E( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE, ZERO - PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) -* .. -* .. Local Scalars .. - INTEGER I - DOUBLE PRECISION ANORM, SCALE, SUM -* .. -* .. External Functions .. - LOGICAL LSAME, DISNAN - EXTERNAL LSAME, DISNAN -* .. -* .. External Subroutines .. - EXTERNAL DLASSQ -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, SQRT -* .. -* .. Executable Statements .. -* - IF( N.LE.0 ) THEN - ANORM = ZERO - ELSE IF( LSAME( NORM, 'M' ) ) THEN -* -* Find max(abs(A(i,j))). -* - ANORM = ABS( D( N ) ) - DO 10 I = 1, N - 1 - SUM = ABS( D( I ) ) - IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM - SUM = ABS( E( I ) ) - IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM - 10 CONTINUE - ELSE IF( LSAME( NORM, 'O' ) .OR. NORM.EQ.'1' .OR. - $ LSAME( NORM, 'I' ) ) THEN -* -* Find norm1(A). -* - IF( N.EQ.1 ) THEN - ANORM = ABS( D( 1 ) ) - ELSE - ANORM = ABS( D( 1 ) )+ABS( E( 1 ) ) - SUM = ABS( E( N-1 ) )+ABS( D( N ) ) - IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM - DO 20 I = 2, N - 1 - SUM = ABS( D( I ) )+ABS( E( I ) )+ABS( E( I-1 ) ) - IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM - 20 CONTINUE - END IF - ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN -* -* Find normF(A). -* - SCALE = ZERO - SUM = ONE - IF( N.GT.1 ) THEN - CALL DLASSQ( N-1, E, 1, SCALE, SUM ) - SUM = 2*SUM - END IF - CALL DLASSQ( N, D, 1, SCALE, SUM ) - ANORM = SCALE*SQRT( SUM ) - END IF -* - DLANST = ANORM - RETURN -* -* End of DLANST -* - END diff --git a/lib/linalg/fortran/dlansy.f b/lib/linalg/fortran/dlansy.f deleted file mode 100644 index 949c5535a2..0000000000 --- a/lib/linalg/fortran/dlansy.f +++ /dev/null @@ -1,238 +0,0 @@ -*> \brief \b DLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLANSY + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* DOUBLE PRECISION FUNCTION DLANSY( NORM, UPLO, N, A, LDA, WORK ) -* -* .. Scalar Arguments .. -* CHARACTER NORM, UPLO -* INTEGER LDA, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLANSY returns the value of the one norm, or the Frobenius norm, or -*> the infinity norm, or the element of largest absolute value of a -*> real symmetric matrix A. -*> \endverbatim -*> -*> \return DLANSY -*> \verbatim -*> -*> DLANSY = ( max(abs(A(i,j))), NORM = 'M' or 'm' -*> ( -*> ( norm1(A), NORM = '1', 'O' or 'o' -*> ( -*> ( normI(A), NORM = 'I' or 'i' -*> ( -*> ( normF(A), NORM = 'F', 'f', 'E' or 'e' -*> -*> where norm1 denotes the one norm of a matrix (maximum column sum), -*> normI denotes the infinity norm of a matrix (maximum row sum) and -*> normF denotes the Frobenius norm of a matrix (square root of sum of -*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] NORM -*> \verbatim -*> NORM is CHARACTER*1 -*> Specifies the value to be returned in DLANSY as described -*> above. -*> \endverbatim -*> -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> Specifies whether the upper or lower triangular part of the -*> symmetric matrix A is to be referenced. -*> = 'U': Upper triangular part of A is referenced -*> = 'L': Lower triangular part of A is referenced -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrix A. N >= 0. When N = 0, DLANSY is -*> set to zero. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> The symmetric matrix A. If UPLO = 'U', the leading n by n -*> upper triangular part of A contains the upper triangular part -*> of the matrix A, and the strictly lower triangular part of A -*> is not referenced. If UPLO = 'L', the leading n by n lower -*> triangular part of A contains the lower triangular part of -*> the matrix A, and the strictly upper triangular part of A is -*> not referenced. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(N,1). -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), -*> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, -*> WORK is not referenced. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleSYauxiliary -* -* ===================================================================== - DOUBLE PRECISION FUNCTION DLANSY( NORM, UPLO, N, A, LDA, WORK ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER NORM, UPLO - INTEGER LDA, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE, ZERO - PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) -* .. -* .. Local Scalars .. - INTEGER I, J - DOUBLE PRECISION ABSA, SCALE, SUM, VALUE -* .. -* .. External Subroutines .. - EXTERNAL DLASSQ -* .. -* .. External Functions .. - LOGICAL LSAME, DISNAN - EXTERNAL LSAME, DISNAN -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, SQRT -* .. -* .. Executable Statements .. -* - IF( N.EQ.0 ) THEN - VALUE = ZERO - ELSE IF( LSAME( NORM, 'M' ) ) THEN -* -* Find max(abs(A(i,j))). -* - VALUE = ZERO - IF( LSAME( UPLO, 'U' ) ) THEN - DO 20 J = 1, N - DO 10 I = 1, J - SUM = ABS( A( I, J ) ) - IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM - 10 CONTINUE - 20 CONTINUE - ELSE - DO 40 J = 1, N - DO 30 I = J, N - SUM = ABS( A( I, J ) ) - IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM - 30 CONTINUE - 40 CONTINUE - END IF - ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR. - $ ( NORM.EQ.'1' ) ) THEN -* -* Find normI(A) ( = norm1(A), since A is symmetric). -* - VALUE = ZERO - IF( LSAME( UPLO, 'U' ) ) THEN - DO 60 J = 1, N - SUM = ZERO - DO 50 I = 1, J - 1 - ABSA = ABS( A( I, J ) ) - SUM = SUM + ABSA - WORK( I ) = WORK( I ) + ABSA - 50 CONTINUE - WORK( J ) = SUM + ABS( A( J, J ) ) - 60 CONTINUE - DO 70 I = 1, N - SUM = WORK( I ) - IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM - 70 CONTINUE - ELSE - DO 80 I = 1, N - WORK( I ) = ZERO - 80 CONTINUE - DO 100 J = 1, N - SUM = WORK( J ) + ABS( A( J, J ) ) - DO 90 I = J + 1, N - ABSA = ABS( A( I, J ) ) - SUM = SUM + ABSA - WORK( I ) = WORK( I ) + ABSA - 90 CONTINUE - IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM - 100 CONTINUE - END IF - ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN -* -* Find normF(A). -* - SCALE = ZERO - SUM = ONE - IF( LSAME( UPLO, 'U' ) ) THEN - DO 110 J = 2, N - CALL DLASSQ( J-1, A( 1, J ), 1, SCALE, SUM ) - 110 CONTINUE - ELSE - DO 120 J = 1, N - 1 - CALL DLASSQ( N-J, A( J+1, J ), 1, SCALE, SUM ) - 120 CONTINUE - END IF - SUM = 2*SUM - CALL DLASSQ( N, A, LDA+1, SCALE, SUM ) - VALUE = SCALE*SQRT( SUM ) - END IF -* - DLANSY = VALUE - RETURN -* -* End of DLANSY -* - END diff --git a/lib/linalg/fortran/dlapy2.f b/lib/linalg/fortran/dlapy2.f deleted file mode 100644 index 1f63193bb7..0000000000 --- a/lib/linalg/fortran/dlapy2.f +++ /dev/null @@ -1,117 +0,0 @@ -*> \brief \b DLAPY2 returns sqrt(x2+y2). -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLAPY2 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* DOUBLE PRECISION FUNCTION DLAPY2( X, Y ) -* -* .. Scalar Arguments .. -* DOUBLE PRECISION X, Y -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLAPY2 returns sqrt(x**2+y**2), taking care not to cause unnecessary -*> overflow and unnecessary underflow. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] X -*> \verbatim -*> X is DOUBLE PRECISION -*> \endverbatim -*> -*> \param[in] Y -*> \verbatim -*> Y is DOUBLE PRECISION -*> X and Y specify the values x and y. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup OTHERauxiliary -* -* ===================================================================== - DOUBLE PRECISION FUNCTION DLAPY2( X, Y ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - DOUBLE PRECISION X, Y -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO - PARAMETER ( ZERO = 0.0D0 ) - DOUBLE PRECISION ONE - PARAMETER ( ONE = 1.0D0 ) -* .. -* .. Local Scalars .. - DOUBLE PRECISION W, XABS, YABS, Z, HUGEVAL - LOGICAL X_IS_NAN, Y_IS_NAN -* .. -* .. External Functions .. - LOGICAL DISNAN - EXTERNAL DISNAN -* .. -* .. External Subroutines .. - DOUBLE PRECISION DLAMCH -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, MAX, MIN, SQRT -* .. -* .. Executable Statements .. -* - X_IS_NAN = DISNAN( X ) - Y_IS_NAN = DISNAN( Y ) - IF ( X_IS_NAN ) DLAPY2 = X - IF ( Y_IS_NAN ) DLAPY2 = Y - HUGEVAL = DLAMCH( 'Overflow' ) -* - IF ( .NOT.( X_IS_NAN.OR.Y_IS_NAN ) ) THEN - XABS = ABS( X ) - YABS = ABS( Y ) - W = MAX( XABS, YABS ) - Z = MIN( XABS, YABS ) - IF( Z.EQ.ZERO .OR. W.GT.HUGEVAL ) THEN - DLAPY2 = W - ELSE - DLAPY2 = W*SQRT( ONE+( Z / W )**2 ) - END IF - END IF - RETURN -* -* End of DLAPY2 -* - END diff --git a/lib/linalg/fortran/dlapy3.f b/lib/linalg/fortran/dlapy3.f deleted file mode 100644 index 230a65cdb2..0000000000 --- a/lib/linalg/fortran/dlapy3.f +++ /dev/null @@ -1,112 +0,0 @@ -*> \brief \b DLAPY3 returns sqrt(x2+y2+z2). -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLAPY3 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* DOUBLE PRECISION FUNCTION DLAPY3( X, Y, Z ) -* -* .. Scalar Arguments .. -* DOUBLE PRECISION X, Y, Z -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLAPY3 returns sqrt(x**2+y**2+z**2), taking care not to cause -*> unnecessary overflow and unnecessary underflow. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] X -*> \verbatim -*> X is DOUBLE PRECISION -*> \endverbatim -*> -*> \param[in] Y -*> \verbatim -*> Y is DOUBLE PRECISION -*> \endverbatim -*> -*> \param[in] Z -*> \verbatim -*> Z is DOUBLE PRECISION -*> X, Y and Z specify the values x, y and z. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup OTHERauxiliary -* -* ===================================================================== - DOUBLE PRECISION FUNCTION DLAPY3( X, Y, Z ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - DOUBLE PRECISION X, Y, Z -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO - PARAMETER ( ZERO = 0.0D0 ) -* .. -* .. Local Scalars .. - DOUBLE PRECISION W, XABS, YABS, ZABS, HUGEVAL -* .. -* .. External Subroutines .. - DOUBLE PRECISION DLAMCH -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, MAX, SQRT -* .. -* .. Executable Statements .. -* - HUGEVAL = DLAMCH( 'Overflow' ) - XABS = ABS( X ) - YABS = ABS( Y ) - ZABS = ABS( Z ) - W = MAX( XABS, YABS, ZABS ) - IF( W.EQ.ZERO .OR. W.GT.HUGEVAL ) THEN -* W can be zero for max(0,nan,0) -* adding all three entries together will make sure -* NaN will not disappear. - DLAPY3 = XABS + YABS + ZABS - ELSE - DLAPY3 = W*SQRT( ( XABS / W )**2+( YABS / W )**2+ - $ ( ZABS / W )**2 ) - END IF - RETURN -* -* End of DLAPY3 -* - END diff --git a/lib/linalg/fortran/dlarf.f b/lib/linalg/fortran/dlarf.f deleted file mode 100644 index ed21638645..0000000000 --- a/lib/linalg/fortran/dlarf.f +++ /dev/null @@ -1,224 +0,0 @@ -*> \brief \b DLARF applies an elementary reflector to a general rectangular matrix. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLARF + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK ) -* -* .. Scalar Arguments .. -* CHARACTER SIDE -* INTEGER INCV, LDC, M, N -* DOUBLE PRECISION TAU -* .. -* .. Array Arguments .. -* DOUBLE PRECISION C( LDC, * ), V( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLARF applies a real elementary reflector H to a real m by n matrix -*> C, from either the left or the right. H is represented in the form -*> -*> H = I - tau * v * v**T -*> -*> where tau is a real scalar and v is a real vector. -*> -*> If tau = 0, then H is taken to be the unit matrix. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] SIDE -*> \verbatim -*> SIDE is CHARACTER*1 -*> = 'L': form H * C -*> = 'R': form C * H -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix C. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix C. -*> \endverbatim -*> -*> \param[in] V -*> \verbatim -*> V is DOUBLE PRECISION array, dimension -*> (1 + (M-1)*abs(INCV)) if SIDE = 'L' -*> or (1 + (N-1)*abs(INCV)) if SIDE = 'R' -*> The vector v in the representation of H. V is not used if -*> TAU = 0. -*> \endverbatim -*> -*> \param[in] INCV -*> \verbatim -*> INCV is INTEGER -*> The increment between elements of v. INCV <> 0. -*> \endverbatim -*> -*> \param[in] TAU -*> \verbatim -*> TAU is DOUBLE PRECISION -*> The value tau in the representation of H. -*> \endverbatim -*> -*> \param[in,out] C -*> \verbatim -*> C is DOUBLE PRECISION array, dimension (LDC,N) -*> On entry, the m by n matrix C. -*> On exit, C is overwritten by the matrix H * C if SIDE = 'L', -*> or C * H if SIDE = 'R'. -*> \endverbatim -*> -*> \param[in] LDC -*> \verbatim -*> LDC is INTEGER -*> The leading dimension of the array C. LDC >= max(1,M). -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension -*> (N) if SIDE = 'L' -*> or (M) if SIDE = 'R' -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleOTHERauxiliary -* -* ===================================================================== - SUBROUTINE DLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER SIDE - INTEGER INCV, LDC, M, N - DOUBLE PRECISION TAU -* .. -* .. Array Arguments .. - DOUBLE PRECISION C( LDC, * ), V( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE, ZERO - PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) -* .. -* .. Local Scalars .. - LOGICAL APPLYLEFT - INTEGER I, LASTV, LASTC -* .. -* .. External Subroutines .. - EXTERNAL DGEMV, DGER -* .. -* .. External Functions .. - LOGICAL LSAME - INTEGER ILADLR, ILADLC - EXTERNAL LSAME, ILADLR, ILADLC -* .. -* .. Executable Statements .. -* - APPLYLEFT = LSAME( SIDE, 'L' ) - LASTV = 0 - LASTC = 0 - IF( TAU.NE.ZERO ) THEN -! Set up variables for scanning V. LASTV begins pointing to the end -! of V. - IF( APPLYLEFT ) THEN - LASTV = M - ELSE - LASTV = N - END IF - IF( INCV.GT.0 ) THEN - I = 1 + (LASTV-1) * INCV - ELSE - I = 1 - END IF -! Look for the last non-zero row in V. - DO WHILE( LASTV.GT.0 .AND. V( I ).EQ.ZERO ) - LASTV = LASTV - 1 - I = I - INCV - END DO - IF( APPLYLEFT ) THEN -! Scan for the last non-zero column in C(1:lastv,:). - LASTC = ILADLC(LASTV, N, C, LDC) - ELSE -! Scan for the last non-zero row in C(:,1:lastv). - LASTC = ILADLR(M, LASTV, C, LDC) - END IF - END IF -! Note that lastc.eq.0 renders the BLAS operations null; no special -! case is needed at this level. - IF( APPLYLEFT ) THEN -* -* Form H * C -* - IF( LASTV.GT.0 ) THEN -* -* w(1:lastc,1) := C(1:lastv,1:lastc)**T * v(1:lastv,1) -* - CALL DGEMV( 'Transpose', LASTV, LASTC, ONE, C, LDC, V, INCV, - $ ZERO, WORK, 1 ) -* -* C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**T -* - CALL DGER( LASTV, LASTC, -TAU, V, INCV, WORK, 1, C, LDC ) - END IF - ELSE -* -* Form C * H -* - IF( LASTV.GT.0 ) THEN -* -* w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1) -* - CALL DGEMV( 'No transpose', LASTC, LASTV, ONE, C, LDC, - $ V, INCV, ZERO, WORK, 1 ) -* -* C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**T -* - CALL DGER( LASTC, LASTV, -TAU, WORK, 1, V, INCV, C, LDC ) - END IF - END IF - RETURN -* -* End of DLARF -* - END diff --git a/lib/linalg/fortran/dlarfb.f b/lib/linalg/fortran/dlarfb.f deleted file mode 100644 index a3fa083b43..0000000000 --- a/lib/linalg/fortran/dlarfb.f +++ /dev/null @@ -1,709 +0,0 @@ -*> \brief \b DLARFB applies a block reflector or its transpose to a general rectangular matrix. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLARFB + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, -* T, LDT, C, LDC, WORK, LDWORK ) -* -* .. Scalar Arguments .. -* CHARACTER DIRECT, SIDE, STOREV, TRANS -* INTEGER K, LDC, LDT, LDV, LDWORK, M, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION C( LDC, * ), T( LDT, * ), V( LDV, * ), -* $ WORK( LDWORK, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLARFB applies a real block reflector H or its transpose H**T to a -*> real m by n matrix C, from either the left or the right. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] SIDE -*> \verbatim -*> SIDE is CHARACTER*1 -*> = 'L': apply H or H**T from the Left -*> = 'R': apply H or H**T from the Right -*> \endverbatim -*> -*> \param[in] TRANS -*> \verbatim -*> TRANS is CHARACTER*1 -*> = 'N': apply H (No transpose) -*> = 'T': apply H**T (Transpose) -*> \endverbatim -*> -*> \param[in] DIRECT -*> \verbatim -*> DIRECT is CHARACTER*1 -*> Indicates how H is formed from a product of elementary -*> reflectors -*> = 'F': H = H(1) H(2) . . . H(k) (Forward) -*> = 'B': H = H(k) . . . H(2) H(1) (Backward) -*> \endverbatim -*> -*> \param[in] STOREV -*> \verbatim -*> STOREV is CHARACTER*1 -*> Indicates how the vectors which define the elementary -*> reflectors are stored: -*> = 'C': Columnwise -*> = 'R': Rowwise -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix C. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix C. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> The order of the matrix T (= the number of elementary -*> reflectors whose product defines the block reflector). -*> If SIDE = 'L', M >= K >= 0; -*> if SIDE = 'R', N >= K >= 0. -*> \endverbatim -*> -*> \param[in] V -*> \verbatim -*> V is DOUBLE PRECISION array, dimension -*> (LDV,K) if STOREV = 'C' -*> (LDV,M) if STOREV = 'R' and SIDE = 'L' -*> (LDV,N) if STOREV = 'R' and SIDE = 'R' -*> The matrix V. See Further Details. -*> \endverbatim -*> -*> \param[in] LDV -*> \verbatim -*> LDV is INTEGER -*> The leading dimension of the array V. -*> If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M); -*> if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N); -*> if STOREV = 'R', LDV >= K. -*> \endverbatim -*> -*> \param[in] T -*> \verbatim -*> T is DOUBLE PRECISION array, dimension (LDT,K) -*> The triangular k by k matrix T in the representation of the -*> block reflector. -*> \endverbatim -*> -*> \param[in] LDT -*> \verbatim -*> LDT is INTEGER -*> The leading dimension of the array T. LDT >= K. -*> \endverbatim -*> -*> \param[in,out] C -*> \verbatim -*> C is DOUBLE PRECISION array, dimension (LDC,N) -*> On entry, the m by n matrix C. -*> On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T. -*> \endverbatim -*> -*> \param[in] LDC -*> \verbatim -*> LDC is INTEGER -*> The leading dimension of the array C. LDC >= max(1,M). -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (LDWORK,K) -*> \endverbatim -*> -*> \param[in] LDWORK -*> \verbatim -*> LDWORK is INTEGER -*> The leading dimension of the array WORK. -*> If SIDE = 'L', LDWORK >= max(1,N); -*> if SIDE = 'R', LDWORK >= max(1,M). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleOTHERauxiliary -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> The shape of the matrix V and the storage of the vectors which define -*> the H(i) is best illustrated by the following example with n = 5 and -*> k = 3. The elements equal to 1 are not stored; the corresponding -*> array elements are modified but restored on exit. The rest of the -*> array is not used. -*> -*> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': -*> -*> V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) -*> ( v1 1 ) ( 1 v2 v2 v2 ) -*> ( v1 v2 1 ) ( 1 v3 v3 ) -*> ( v1 v2 v3 ) -*> ( v1 v2 v3 ) -*> -*> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': -*> -*> V = ( v1 v2 v3 ) V = ( v1 v1 1 ) -*> ( v1 v2 v3 ) ( v2 v2 v2 1 ) -*> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) -*> ( 1 v3 ) -*> ( 1 ) -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, - $ T, LDT, C, LDC, WORK, LDWORK ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER DIRECT, SIDE, STOREV, TRANS - INTEGER K, LDC, LDT, LDV, LDWORK, M, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION C( LDC, * ), T( LDT, * ), V( LDV, * ), - $ WORK( LDWORK, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE - PARAMETER ( ONE = 1.0D+0 ) -* .. -* .. Local Scalars .. - CHARACTER TRANST - INTEGER I, J -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL DCOPY, DGEMM, DTRMM -* .. -* .. Executable Statements .. -* -* Quick return if possible -* - IF( M.LE.0 .OR. N.LE.0 ) - $ RETURN -* - IF( LSAME( TRANS, 'N' ) ) THEN - TRANST = 'T' - ELSE - TRANST = 'N' - END IF -* - IF( LSAME( STOREV, 'C' ) ) THEN -* - IF( LSAME( DIRECT, 'F' ) ) THEN -* -* Let V = ( V1 ) (first K rows) -* ( V2 ) -* where V1 is unit lower triangular. -* - IF( LSAME( SIDE, 'L' ) ) THEN -* -* Form H * C or H**T * C where C = ( C1 ) -* ( C2 ) -* -* W := C**T * V = (C1**T * V1 + C2**T * V2) (stored in WORK) -* -* W := C1**T -* - DO 10 J = 1, K - CALL DCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 ) - 10 CONTINUE -* -* W := W * V1 -* - CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit', N, - $ K, ONE, V, LDV, WORK, LDWORK ) - IF( M.GT.K ) THEN -* -* W := W + C2**T * V2 -* - CALL DGEMM( 'Transpose', 'No transpose', N, K, M-K, - $ ONE, C( K+1, 1 ), LDC, V( K+1, 1 ), LDV, - $ ONE, WORK, LDWORK ) - END IF -* -* W := W * T**T or W * T -* - CALL DTRMM( 'Right', 'Upper', TRANST, 'Non-unit', N, K, - $ ONE, T, LDT, WORK, LDWORK ) -* -* C := C - V * W**T -* - IF( M.GT.K ) THEN -* -* C2 := C2 - V2 * W**T -* - CALL DGEMM( 'No transpose', 'Transpose', M-K, N, K, - $ -ONE, V( K+1, 1 ), LDV, WORK, LDWORK, ONE, - $ C( K+1, 1 ), LDC ) - END IF -* -* W := W * V1**T -* - CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit', N, K, - $ ONE, V, LDV, WORK, LDWORK ) -* -* C1 := C1 - W**T -* - DO 30 J = 1, K - DO 20 I = 1, N - C( J, I ) = C( J, I ) - WORK( I, J ) - 20 CONTINUE - 30 CONTINUE -* - ELSE IF( LSAME( SIDE, 'R' ) ) THEN -* -* Form C * H or C * H**T where C = ( C1 C2 ) -* -* W := C * V = (C1*V1 + C2*V2) (stored in WORK) -* -* W := C1 -* - DO 40 J = 1, K - CALL DCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 ) - 40 CONTINUE -* -* W := W * V1 -* - CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit', M, - $ K, ONE, V, LDV, WORK, LDWORK ) - IF( N.GT.K ) THEN -* -* W := W + C2 * V2 -* - CALL DGEMM( 'No transpose', 'No transpose', M, K, N-K, - $ ONE, C( 1, K+1 ), LDC, V( K+1, 1 ), LDV, - $ ONE, WORK, LDWORK ) - END IF -* -* W := W * T or W * T**T -* - CALL DTRMM( 'Right', 'Upper', TRANS, 'Non-unit', M, K, - $ ONE, T, LDT, WORK, LDWORK ) -* -* C := C - W * V**T -* - IF( N.GT.K ) THEN -* -* C2 := C2 - W * V2**T -* - CALL DGEMM( 'No transpose', 'Transpose', M, N-K, K, - $ -ONE, WORK, LDWORK, V( K+1, 1 ), LDV, ONE, - $ C( 1, K+1 ), LDC ) - END IF -* -* W := W * V1**T -* - CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit', M, K, - $ ONE, V, LDV, WORK, LDWORK ) -* -* C1 := C1 - W -* - DO 60 J = 1, K - DO 50 I = 1, M - C( I, J ) = C( I, J ) - WORK( I, J ) - 50 CONTINUE - 60 CONTINUE - END IF -* - ELSE -* -* Let V = ( V1 ) -* ( V2 ) (last K rows) -* where V2 is unit upper triangular. -* - IF( LSAME( SIDE, 'L' ) ) THEN -* -* Form H * C or H**T * C where C = ( C1 ) -* ( C2 ) -* -* W := C**T * V = (C1**T * V1 + C2**T * V2) (stored in WORK) -* -* W := C2**T -* - DO 70 J = 1, K - CALL DCOPY( N, C( M-K+J, 1 ), LDC, WORK( 1, J ), 1 ) - 70 CONTINUE -* -* W := W * V2 -* - CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit', N, - $ K, ONE, V( M-K+1, 1 ), LDV, WORK, LDWORK ) - IF( M.GT.K ) THEN -* -* W := W + C1**T * V1 -* - CALL DGEMM( 'Transpose', 'No transpose', N, K, M-K, - $ ONE, C, LDC, V, LDV, ONE, WORK, LDWORK ) - END IF -* -* W := W * T**T or W * T -* - CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, - $ ONE, T, LDT, WORK, LDWORK ) -* -* C := C - V * W**T -* - IF( M.GT.K ) THEN -* -* C1 := C1 - V1 * W**T -* - CALL DGEMM( 'No transpose', 'Transpose', M-K, N, K, - $ -ONE, V, LDV, WORK, LDWORK, ONE, C, LDC ) - END IF -* -* W := W * V2**T -* - CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit', N, K, - $ ONE, V( M-K+1, 1 ), LDV, WORK, LDWORK ) -* -* C2 := C2 - W**T -* - DO 90 J = 1, K - DO 80 I = 1, N - C( M-K+J, I ) = C( M-K+J, I ) - WORK( I, J ) - 80 CONTINUE - 90 CONTINUE -* - ELSE IF( LSAME( SIDE, 'R' ) ) THEN -* -* Form C * H or C * H**T where C = ( C1 C2 ) -* -* W := C * V = (C1*V1 + C2*V2) (stored in WORK) -* -* W := C2 -* - DO 100 J = 1, K - CALL DCOPY( M, C( 1, N-K+J ), 1, WORK( 1, J ), 1 ) - 100 CONTINUE -* -* W := W * V2 -* - CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit', M, - $ K, ONE, V( N-K+1, 1 ), LDV, WORK, LDWORK ) - IF( N.GT.K ) THEN -* -* W := W + C1 * V1 -* - CALL DGEMM( 'No transpose', 'No transpose', M, K, N-K, - $ ONE, C, LDC, V, LDV, ONE, WORK, LDWORK ) - END IF -* -* W := W * T or W * T**T -* - CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, - $ ONE, T, LDT, WORK, LDWORK ) -* -* C := C - W * V**T -* - IF( N.GT.K ) THEN -* -* C1 := C1 - W * V1**T -* - CALL DGEMM( 'No transpose', 'Transpose', M, N-K, K, - $ -ONE, WORK, LDWORK, V, LDV, ONE, C, LDC ) - END IF -* -* W := W * V2**T -* - CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit', M, K, - $ ONE, V( N-K+1, 1 ), LDV, WORK, LDWORK ) -* -* C2 := C2 - W -* - DO 120 J = 1, K - DO 110 I = 1, M - C( I, N-K+J ) = C( I, N-K+J ) - WORK( I, J ) - 110 CONTINUE - 120 CONTINUE - END IF - END IF -* - ELSE IF( LSAME( STOREV, 'R' ) ) THEN -* - IF( LSAME( DIRECT, 'F' ) ) THEN -* -* Let V = ( V1 V2 ) (V1: first K columns) -* where V1 is unit upper triangular. -* - IF( LSAME( SIDE, 'L' ) ) THEN -* -* Form H * C or H**T * C where C = ( C1 ) -* ( C2 ) -* -* W := C**T * V**T = (C1**T * V1**T + C2**T * V2**T) (stored in WORK) -* -* W := C1**T -* - DO 130 J = 1, K - CALL DCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 ) - 130 CONTINUE -* -* W := W * V1**T -* - CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit', N, K, - $ ONE, V, LDV, WORK, LDWORK ) - IF( M.GT.K ) THEN -* -* W := W + C2**T * V2**T -* - CALL DGEMM( 'Transpose', 'Transpose', N, K, M-K, ONE, - $ C( K+1, 1 ), LDC, V( 1, K+1 ), LDV, ONE, - $ WORK, LDWORK ) - END IF -* -* W := W * T**T or W * T -* - CALL DTRMM( 'Right', 'Upper', TRANST, 'Non-unit', N, K, - $ ONE, T, LDT, WORK, LDWORK ) -* -* C := C - V**T * W**T -* - IF( M.GT.K ) THEN -* -* C2 := C2 - V2**T * W**T -* - CALL DGEMM( 'Transpose', 'Transpose', M-K, N, K, -ONE, - $ V( 1, K+1 ), LDV, WORK, LDWORK, ONE, - $ C( K+1, 1 ), LDC ) - END IF -* -* W := W * V1 -* - CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit', N, - $ K, ONE, V, LDV, WORK, LDWORK ) -* -* C1 := C1 - W**T -* - DO 150 J = 1, K - DO 140 I = 1, N - C( J, I ) = C( J, I ) - WORK( I, J ) - 140 CONTINUE - 150 CONTINUE -* - ELSE IF( LSAME( SIDE, 'R' ) ) THEN -* -* Form C * H or C * H**T where C = ( C1 C2 ) -* -* W := C * V**T = (C1*V1**T + C2*V2**T) (stored in WORK) -* -* W := C1 -* - DO 160 J = 1, K - CALL DCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 ) - 160 CONTINUE -* -* W := W * V1**T -* - CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit', M, K, - $ ONE, V, LDV, WORK, LDWORK ) - IF( N.GT.K ) THEN -* -* W := W + C2 * V2**T -* - CALL DGEMM( 'No transpose', 'Transpose', M, K, N-K, - $ ONE, C( 1, K+1 ), LDC, V( 1, K+1 ), LDV, - $ ONE, WORK, LDWORK ) - END IF -* -* W := W * T or W * T**T -* - CALL DTRMM( 'Right', 'Upper', TRANS, 'Non-unit', M, K, - $ ONE, T, LDT, WORK, LDWORK ) -* -* C := C - W * V -* - IF( N.GT.K ) THEN -* -* C2 := C2 - W * V2 -* - CALL DGEMM( 'No transpose', 'No transpose', M, N-K, K, - $ -ONE, WORK, LDWORK, V( 1, K+1 ), LDV, ONE, - $ C( 1, K+1 ), LDC ) - END IF -* -* W := W * V1 -* - CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit', M, - $ K, ONE, V, LDV, WORK, LDWORK ) -* -* C1 := C1 - W -* - DO 180 J = 1, K - DO 170 I = 1, M - C( I, J ) = C( I, J ) - WORK( I, J ) - 170 CONTINUE - 180 CONTINUE -* - END IF -* - ELSE -* -* Let V = ( V1 V2 ) (V2: last K columns) -* where V2 is unit lower triangular. -* - IF( LSAME( SIDE, 'L' ) ) THEN -* -* Form H * C or H**T * C where C = ( C1 ) -* ( C2 ) -* -* W := C**T * V**T = (C1**T * V1**T + C2**T * V2**T) (stored in WORK) -* -* W := C2**T -* - DO 190 J = 1, K - CALL DCOPY( N, C( M-K+J, 1 ), LDC, WORK( 1, J ), 1 ) - 190 CONTINUE -* -* W := W * V2**T -* - CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit', N, K, - $ ONE, V( 1, M-K+1 ), LDV, WORK, LDWORK ) - IF( M.GT.K ) THEN -* -* W := W + C1**T * V1**T -* - CALL DGEMM( 'Transpose', 'Transpose', N, K, M-K, ONE, - $ C, LDC, V, LDV, ONE, WORK, LDWORK ) - END IF -* -* W := W * T**T or W * T -* - CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, - $ ONE, T, LDT, WORK, LDWORK ) -* -* C := C - V**T * W**T -* - IF( M.GT.K ) THEN -* -* C1 := C1 - V1**T * W**T -* - CALL DGEMM( 'Transpose', 'Transpose', M-K, N, K, -ONE, - $ V, LDV, WORK, LDWORK, ONE, C, LDC ) - END IF -* -* W := W * V2 -* - CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit', N, - $ K, ONE, V( 1, M-K+1 ), LDV, WORK, LDWORK ) -* -* C2 := C2 - W**T -* - DO 210 J = 1, K - DO 200 I = 1, N - C( M-K+J, I ) = C( M-K+J, I ) - WORK( I, J ) - 200 CONTINUE - 210 CONTINUE -* - ELSE IF( LSAME( SIDE, 'R' ) ) THEN -* -* Form C * H or C * H' where C = ( C1 C2 ) -* -* W := C * V**T = (C1*V1**T + C2*V2**T) (stored in WORK) -* -* W := C2 -* - DO 220 J = 1, K - CALL DCOPY( M, C( 1, N-K+J ), 1, WORK( 1, J ), 1 ) - 220 CONTINUE -* -* W := W * V2**T -* - CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit', M, K, - $ ONE, V( 1, N-K+1 ), LDV, WORK, LDWORK ) - IF( N.GT.K ) THEN -* -* W := W + C1 * V1**T -* - CALL DGEMM( 'No transpose', 'Transpose', M, K, N-K, - $ ONE, C, LDC, V, LDV, ONE, WORK, LDWORK ) - END IF -* -* W := W * T or W * T**T -* - CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, - $ ONE, T, LDT, WORK, LDWORK ) -* -* C := C - W * V -* - IF( N.GT.K ) THEN -* -* C1 := C1 - W * V1 -* - CALL DGEMM( 'No transpose', 'No transpose', M, N-K, K, - $ -ONE, WORK, LDWORK, V, LDV, ONE, C, LDC ) - END IF -* -* W := W * V2 -* - CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit', M, - $ K, ONE, V( 1, N-K+1 ), LDV, WORK, LDWORK ) -* -* C1 := C1 - W -* - DO 240 J = 1, K - DO 230 I = 1, M - C( I, N-K+J ) = C( I, N-K+J ) - WORK( I, J ) - 230 CONTINUE - 240 CONTINUE -* - END IF -* - END IF - END IF -* - RETURN -* -* End of DLARFB -* - END diff --git a/lib/linalg/fortran/dlarfg.f b/lib/linalg/fortran/dlarfg.f deleted file mode 100644 index 9bfb45a6b0..0000000000 --- a/lib/linalg/fortran/dlarfg.f +++ /dev/null @@ -1,193 +0,0 @@ -*> \brief \b DLARFG generates an elementary reflector (Householder matrix). -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLARFG + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU ) -* -* .. Scalar Arguments .. -* INTEGER INCX, N -* DOUBLE PRECISION ALPHA, TAU -* .. -* .. Array Arguments .. -* DOUBLE PRECISION X( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLARFG generates a real elementary reflector H of order n, such -*> that -*> -*> H * ( alpha ) = ( beta ), H**T * H = I. -*> ( x ) ( 0 ) -*> -*> where alpha and beta are scalars, and x is an (n-1)-element real -*> vector. H is represented in the form -*> -*> H = I - tau * ( 1 ) * ( 1 v**T ) , -*> ( v ) -*> -*> where tau is a real scalar and v is a real (n-1)-element -*> vector. -*> -*> If the elements of x are all zero, then tau = 0 and H is taken to be -*> the unit matrix. -*> -*> Otherwise 1 <= tau <= 2. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the elementary reflector. -*> \endverbatim -*> -*> \param[in,out] ALPHA -*> \verbatim -*> ALPHA is DOUBLE PRECISION -*> On entry, the value alpha. -*> On exit, it is overwritten with the value beta. -*> \endverbatim -*> -*> \param[in,out] X -*> \verbatim -*> X is DOUBLE PRECISION array, dimension -*> (1+(N-2)*abs(INCX)) -*> On entry, the vector x. -*> On exit, it is overwritten with the vector v. -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> The increment between elements of X. INCX > 0. -*> \endverbatim -*> -*> \param[out] TAU -*> \verbatim -*> TAU is DOUBLE PRECISION -*> The value tau. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleOTHERauxiliary -* -* ===================================================================== - SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INCX, N - DOUBLE PRECISION ALPHA, TAU -* .. -* .. Array Arguments .. - DOUBLE PRECISION X( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE, ZERO - PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) -* .. -* .. Local Scalars .. - INTEGER J, KNT - DOUBLE PRECISION BETA, RSAFMN, SAFMIN, XNORM -* .. -* .. External Functions .. - DOUBLE PRECISION DLAMCH, DLAPY2, DNRM2 - EXTERNAL DLAMCH, DLAPY2, DNRM2 -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, SIGN -* .. -* .. External Subroutines .. - EXTERNAL DSCAL -* .. -* .. Executable Statements .. -* - IF( N.LE.1 ) THEN - TAU = ZERO - RETURN - END IF -* - XNORM = DNRM2( N-1, X, INCX ) -* - IF( XNORM.EQ.ZERO ) THEN -* -* H = I -* - TAU = ZERO - ELSE -* -* general case -* - BETA = -SIGN( DLAPY2( ALPHA, XNORM ), ALPHA ) - SAFMIN = DLAMCH( 'S' ) / DLAMCH( 'E' ) - KNT = 0 - IF( ABS( BETA ).LT.SAFMIN ) THEN -* -* XNORM, BETA may be inaccurate; scale X and recompute them -* - RSAFMN = ONE / SAFMIN - 10 CONTINUE - KNT = KNT + 1 - CALL DSCAL( N-1, RSAFMN, X, INCX ) - BETA = BETA*RSAFMN - ALPHA = ALPHA*RSAFMN - IF( (ABS( BETA ).LT.SAFMIN) .AND. (KNT .LT. 20) ) - $ GO TO 10 -* -* New BETA is at most 1, at least SAFMIN -* - XNORM = DNRM2( N-1, X, INCX ) - BETA = -SIGN( DLAPY2( ALPHA, XNORM ), ALPHA ) - END IF - TAU = ( BETA-ALPHA ) / BETA - CALL DSCAL( N-1, ONE / ( ALPHA-BETA ), X, INCX ) -* -* If ALPHA is subnormal, it may lose relative accuracy -* - DO 20 J = 1, KNT - BETA = BETA*SAFMIN - 20 CONTINUE - ALPHA = BETA - END IF -* - RETURN -* -* End of DLARFG -* - END diff --git a/lib/linalg/fortran/dlarft.f b/lib/linalg/fortran/dlarft.f deleted file mode 100644 index a8d9de61f1..0000000000 --- a/lib/linalg/fortran/dlarft.f +++ /dev/null @@ -1,323 +0,0 @@ -*> \brief \b DLARFT forms the triangular factor T of a block reflector H = I - vtvH -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLARFT + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) -* -* .. Scalar Arguments .. -* CHARACTER DIRECT, STOREV -* INTEGER K, LDT, LDV, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLARFT forms the triangular factor T of a real block reflector H -*> of order n, which is defined as a product of k elementary reflectors. -*> -*> If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; -*> -*> If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. -*> -*> If STOREV = 'C', the vector which defines the elementary reflector -*> H(i) is stored in the i-th column of the array V, and -*> -*> H = I - V * T * V**T -*> -*> If STOREV = 'R', the vector which defines the elementary reflector -*> H(i) is stored in the i-th row of the array V, and -*> -*> H = I - V**T * T * V -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] DIRECT -*> \verbatim -*> DIRECT is CHARACTER*1 -*> Specifies the order in which the elementary reflectors are -*> multiplied to form the block reflector: -*> = 'F': H = H(1) H(2) . . . H(k) (Forward) -*> = 'B': H = H(k) . . . H(2) H(1) (Backward) -*> \endverbatim -*> -*> \param[in] STOREV -*> \verbatim -*> STOREV is CHARACTER*1 -*> Specifies how the vectors which define the elementary -*> reflectors are stored (see also Further Details): -*> = 'C': columnwise -*> = 'R': rowwise -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the block reflector H. N >= 0. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> The order of the triangular factor T (= the number of -*> elementary reflectors). K >= 1. -*> \endverbatim -*> -*> \param[in] V -*> \verbatim -*> V is DOUBLE PRECISION array, dimension -*> (LDV,K) if STOREV = 'C' -*> (LDV,N) if STOREV = 'R' -*> The matrix V. See further details. -*> \endverbatim -*> -*> \param[in] LDV -*> \verbatim -*> LDV is INTEGER -*> The leading dimension of the array V. -*> If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. -*> \endverbatim -*> -*> \param[in] TAU -*> \verbatim -*> TAU is DOUBLE PRECISION array, dimension (K) -*> TAU(i) must contain the scalar factor of the elementary -*> reflector H(i). -*> \endverbatim -*> -*> \param[out] T -*> \verbatim -*> T is DOUBLE PRECISION array, dimension (LDT,K) -*> The k by k triangular factor T of the block reflector. -*> If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is -*> lower triangular. The rest of the array is not used. -*> \endverbatim -*> -*> \param[in] LDT -*> \verbatim -*> LDT is INTEGER -*> The leading dimension of the array T. LDT >= K. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleOTHERauxiliary -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> The shape of the matrix V and the storage of the vectors which define -*> the H(i) is best illustrated by the following example with n = 5 and -*> k = 3. The elements equal to 1 are not stored. -*> -*> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': -*> -*> V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) -*> ( v1 1 ) ( 1 v2 v2 v2 ) -*> ( v1 v2 1 ) ( 1 v3 v3 ) -*> ( v1 v2 v3 ) -*> ( v1 v2 v3 ) -*> -*> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': -*> -*> V = ( v1 v2 v3 ) V = ( v1 v1 1 ) -*> ( v1 v2 v3 ) ( v2 v2 v2 1 ) -*> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) -*> ( 1 v3 ) -*> ( 1 ) -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER DIRECT, STOREV - INTEGER K, LDT, LDV, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE, ZERO - PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) -* .. -* .. Local Scalars .. - INTEGER I, J, PREVLASTV, LASTV -* .. -* .. External Subroutines .. - EXTERNAL DGEMV, DTRMV -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. Executable Statements .. -* -* Quick return if possible -* - IF( N.EQ.0 ) - $ RETURN -* - IF( LSAME( DIRECT, 'F' ) ) THEN - PREVLASTV = N - DO I = 1, K - PREVLASTV = MAX( I, PREVLASTV ) - IF( TAU( I ).EQ.ZERO ) THEN -* -* H(i) = I -* - DO J = 1, I - T( J, I ) = ZERO - END DO - ELSE -* -* general case -* - IF( LSAME( STOREV, 'C' ) ) THEN -* Skip any trailing zeros. - DO LASTV = N, I+1, -1 - IF( V( LASTV, I ).NE.ZERO ) EXIT - END DO - DO J = 1, I-1 - T( J, I ) = -TAU( I ) * V( I , J ) - END DO - J = MIN( LASTV, PREVLASTV ) -* -* T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**T * V(i:j,i) -* - CALL DGEMV( 'Transpose', J-I, I-1, -TAU( I ), - $ V( I+1, 1 ), LDV, V( I+1, I ), 1, ONE, - $ T( 1, I ), 1 ) - ELSE -* Skip any trailing zeros. - DO LASTV = N, I+1, -1 - IF( V( I, LASTV ).NE.ZERO ) EXIT - END DO - DO J = 1, I-1 - T( J, I ) = -TAU( I ) * V( J , I ) - END DO - J = MIN( LASTV, PREVLASTV ) -* -* T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**T -* - CALL DGEMV( 'No transpose', I-1, J-I, -TAU( I ), - $ V( 1, I+1 ), LDV, V( I, I+1 ), LDV, ONE, - $ T( 1, I ), 1 ) - END IF -* -* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) -* - CALL DTRMV( 'Upper', 'No transpose', 'Non-unit', I-1, T, - $ LDT, T( 1, I ), 1 ) - T( I, I ) = TAU( I ) - IF( I.GT.1 ) THEN - PREVLASTV = MAX( PREVLASTV, LASTV ) - ELSE - PREVLASTV = LASTV - END IF - END IF - END DO - ELSE - PREVLASTV = 1 - DO I = K, 1, -1 - IF( TAU( I ).EQ.ZERO ) THEN -* -* H(i) = I -* - DO J = I, K - T( J, I ) = ZERO - END DO - ELSE -* -* general case -* - IF( I.LT.K ) THEN - IF( LSAME( STOREV, 'C' ) ) THEN -* Skip any leading zeros. - DO LASTV = 1, I-1 - IF( V( LASTV, I ).NE.ZERO ) EXIT - END DO - DO J = I+1, K - T( J, I ) = -TAU( I ) * V( N-K+I , J ) - END DO - J = MAX( LASTV, PREVLASTV ) -* -* T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**T * V(j:n-k+i,i) -* - CALL DGEMV( 'Transpose', N-K+I-J, K-I, -TAU( I ), - $ V( J, I+1 ), LDV, V( J, I ), 1, ONE, - $ T( I+1, I ), 1 ) - ELSE -* Skip any leading zeros. - DO LASTV = 1, I-1 - IF( V( I, LASTV ).NE.ZERO ) EXIT - END DO - DO J = I+1, K - T( J, I ) = -TAU( I ) * V( J, N-K+I ) - END DO - J = MAX( LASTV, PREVLASTV ) -* -* T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**T -* - CALL DGEMV( 'No transpose', K-I, N-K+I-J, - $ -TAU( I ), V( I+1, J ), LDV, V( I, J ), LDV, - $ ONE, T( I+1, I ), 1 ) - END IF -* -* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) -* - CALL DTRMV( 'Lower', 'No transpose', 'Non-unit', K-I, - $ T( I+1, I+1 ), LDT, T( I+1, I ), 1 ) - IF( I.GT.1 ) THEN - PREVLASTV = MIN( PREVLASTV, LASTV ) - ELSE - PREVLASTV = LASTV - END IF - END IF - T( I, I ) = TAU( I ) - END IF - END DO - END IF - RETURN -* -* End of DLARFT -* - END diff --git a/lib/linalg/fortran/dlartg.f b/lib/linalg/fortran/dlartg.f deleted file mode 100644 index 1c7c46f638..0000000000 --- a/lib/linalg/fortran/dlartg.f +++ /dev/null @@ -1,204 +0,0 @@ -*> \brief \b DLARTG generates a plane rotation with real cosine and real sine. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLARTG + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLARTG( F, G, CS, SN, R ) -* -* .. Scalar Arguments .. -* DOUBLE PRECISION CS, F, G, R, SN -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLARTG generate a plane rotation so that -*> -*> [ CS SN ] . [ F ] = [ R ] where CS**2 + SN**2 = 1. -*> [ -SN CS ] [ G ] [ 0 ] -*> -*> This is a slower, more accurate version of the BLAS1 routine DROTG, -*> with the following other differences: -*> F and G are unchanged on return. -*> If G=0, then CS=1 and SN=0. -*> If F=0 and (G .ne. 0), then CS=0 and SN=1 without doing any -*> floating point operations (saves work in DBDSQR when -*> there are zeros on the diagonal). -*> -*> If F exceeds G in magnitude, CS will be positive. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] F -*> \verbatim -*> F is DOUBLE PRECISION -*> The first component of vector to be rotated. -*> \endverbatim -*> -*> \param[in] G -*> \verbatim -*> G is DOUBLE PRECISION -*> The second component of vector to be rotated. -*> \endverbatim -*> -*> \param[out] CS -*> \verbatim -*> CS is DOUBLE PRECISION -*> The cosine of the rotation. -*> \endverbatim -*> -*> \param[out] SN -*> \verbatim -*> SN is DOUBLE PRECISION -*> The sine of the rotation. -*> \endverbatim -*> -*> \param[out] R -*> \verbatim -*> R is DOUBLE PRECISION -*> The nonzero component of the rotated vector. -*> -*> This version has a few statements commented out for thread safety -*> (machine parameters are computed on each entry). 10 feb 03, SJH. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \date December 2016 -* -*> \ingroup OTHERauxiliary -* -* ===================================================================== - SUBROUTINE DLARTG( F, G, CS, SN, R ) -* -* -- LAPACK auxiliary routine (version 3.7.0) -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* December 2016 -* -* .. Scalar Arguments .. - DOUBLE PRECISION CS, F, G, R, SN -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO - PARAMETER ( ZERO = 0.0D0 ) - DOUBLE PRECISION ONE - PARAMETER ( ONE = 1.0D0 ) - DOUBLE PRECISION TWO - PARAMETER ( TWO = 2.0D0 ) -* .. -* .. Local Scalars .. -* LOGICAL FIRST - INTEGER COUNT, I - DOUBLE PRECISION EPS, F1, G1, SAFMIN, SAFMN2, SAFMX2, SCALE -* .. -* .. External Functions .. - DOUBLE PRECISION DLAMCH - EXTERNAL DLAMCH -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, INT, LOG, MAX, SQRT -* .. -* .. Save statement .. -* SAVE FIRST, SAFMX2, SAFMIN, SAFMN2 -* .. -* .. Data statements .. -* DATA FIRST / .TRUE. / -* .. -* .. Executable Statements .. -* -* IF( FIRST ) THEN - SAFMIN = DLAMCH( 'S' ) - EPS = DLAMCH( 'E' ) - SAFMN2 = DLAMCH( 'B' )**INT( LOG( SAFMIN / EPS ) / - $ LOG( DLAMCH( 'B' ) ) / TWO ) - SAFMX2 = ONE / SAFMN2 -* FIRST = .FALSE. -* END IF - IF( G.EQ.ZERO ) THEN - CS = ONE - SN = ZERO - R = F - ELSE IF( F.EQ.ZERO ) THEN - CS = ZERO - SN = ONE - R = G - ELSE - F1 = F - G1 = G - SCALE = MAX( ABS( F1 ), ABS( G1 ) ) - IF( SCALE.GE.SAFMX2 ) THEN - COUNT = 0 - 10 CONTINUE - COUNT = COUNT + 1 - F1 = F1*SAFMN2 - G1 = G1*SAFMN2 - SCALE = MAX( ABS( F1 ), ABS( G1 ) ) - IF( SCALE.GE.SAFMX2 ) - $ GO TO 10 - R = SQRT( F1**2+G1**2 ) - CS = F1 / R - SN = G1 / R - DO 20 I = 1, COUNT - R = R*SAFMX2 - 20 CONTINUE - ELSE IF( SCALE.LE.SAFMN2 ) THEN - COUNT = 0 - 30 CONTINUE - COUNT = COUNT + 1 - F1 = F1*SAFMX2 - G1 = G1*SAFMX2 - SCALE = MAX( ABS( F1 ), ABS( G1 ) ) - IF( SCALE.LE.SAFMN2 ) - $ GO TO 30 - R = SQRT( F1**2+G1**2 ) - CS = F1 / R - SN = G1 / R - DO 40 I = 1, COUNT - R = R*SAFMN2 - 40 CONTINUE - ELSE - R = SQRT( F1**2+G1**2 ) - CS = F1 / R - SN = G1 / R - END IF - IF( ABS( F ).GT.ABS( G ) .AND. CS.LT.ZERO ) THEN - CS = -CS - SN = -SN - R = -R - END IF - END IF - RETURN -* -* End of DLARTG -* - END diff --git a/lib/linalg/fortran/dlas2.f b/lib/linalg/fortran/dlas2.f deleted file mode 100644 index ea929e86f7..0000000000 --- a/lib/linalg/fortran/dlas2.f +++ /dev/null @@ -1,180 +0,0 @@ -*> \brief \b DLAS2 computes singular values of a 2-by-2 triangular matrix. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLAS2 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLAS2( F, G, H, SSMIN, SSMAX ) -* -* .. Scalar Arguments .. -* DOUBLE PRECISION F, G, H, SSMAX, SSMIN -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLAS2 computes the singular values of the 2-by-2 matrix -*> [ F G ] -*> [ 0 H ]. -*> On return, SSMIN is the smaller singular value and SSMAX is the -*> larger singular value. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] F -*> \verbatim -*> F is DOUBLE PRECISION -*> The (1,1) element of the 2-by-2 matrix. -*> \endverbatim -*> -*> \param[in] G -*> \verbatim -*> G is DOUBLE PRECISION -*> The (1,2) element of the 2-by-2 matrix. -*> \endverbatim -*> -*> \param[in] H -*> \verbatim -*> H is DOUBLE PRECISION -*> The (2,2) element of the 2-by-2 matrix. -*> \endverbatim -*> -*> \param[out] SSMIN -*> \verbatim -*> SSMIN is DOUBLE PRECISION -*> The smaller singular value. -*> \endverbatim -*> -*> \param[out] SSMAX -*> \verbatim -*> SSMAX is DOUBLE PRECISION -*> The larger singular value. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup OTHERauxiliary -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> Barring over/underflow, all output quantities are correct to within -*> a few units in the last place (ulps), even in the absence of a guard -*> digit in addition/subtraction. -*> -*> In IEEE arithmetic, the code works correctly if one matrix element is -*> infinite. -*> -*> Overflow will not occur unless the largest singular value itself -*> overflows, or is within a few ulps of overflow. (On machines with -*> partial overflow, like the Cray, overflow may occur if the largest -*> singular value is within a factor of 2 of overflow.) -*> -*> Underflow is harmless if underflow is gradual. Otherwise, results -*> may correspond to a matrix modified by perturbations of size near -*> the underflow threshold. -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DLAS2( F, G, H, SSMIN, SSMAX ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - DOUBLE PRECISION F, G, H, SSMAX, SSMIN -* .. -* -* ==================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO - PARAMETER ( ZERO = 0.0D0 ) - DOUBLE PRECISION ONE - PARAMETER ( ONE = 1.0D0 ) - DOUBLE PRECISION TWO - PARAMETER ( TWO = 2.0D0 ) -* .. -* .. Local Scalars .. - DOUBLE PRECISION AS, AT, AU, C, FA, FHMN, FHMX, GA, HA -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, MAX, MIN, SQRT -* .. -* .. Executable Statements .. -* - FA = ABS( F ) - GA = ABS( G ) - HA = ABS( H ) - FHMN = MIN( FA, HA ) - FHMX = MAX( FA, HA ) - IF( FHMN.EQ.ZERO ) THEN - SSMIN = ZERO - IF( FHMX.EQ.ZERO ) THEN - SSMAX = GA - ELSE - SSMAX = MAX( FHMX, GA )*SQRT( ONE+ - $ ( MIN( FHMX, GA ) / MAX( FHMX, GA ) )**2 ) - END IF - ELSE - IF( GA.LT.FHMX ) THEN - AS = ONE + FHMN / FHMX - AT = ( FHMX-FHMN ) / FHMX - AU = ( GA / FHMX )**2 - C = TWO / ( SQRT( AS*AS+AU )+SQRT( AT*AT+AU ) ) - SSMIN = FHMN*C - SSMAX = FHMX / C - ELSE - AU = FHMX / GA - IF( AU.EQ.ZERO ) THEN -* -* Avoid possible harmful underflow if exponent range -* asymmetric (true SSMIN may not underflow even if -* AU underflows) -* - SSMIN = ( FHMN*FHMX ) / GA - SSMAX = GA - ELSE - AS = ONE + FHMN / FHMX - AT = ( FHMX-FHMN ) / FHMX - C = ONE / ( SQRT( ONE+( AS*AU )**2 )+ - $ SQRT( ONE+( AT*AU )**2 ) ) - SSMIN = ( FHMN*C )*AU - SSMIN = SSMIN + SSMIN - SSMAX = GA / ( C+C ) - END IF - END IF - END IF - RETURN -* -* End of DLAS2 -* - END diff --git a/lib/linalg/fortran/dlascl.f b/lib/linalg/fortran/dlascl.f deleted file mode 100644 index 0a4bf21ce1..0000000000 --- a/lib/linalg/fortran/dlascl.f +++ /dev/null @@ -1,367 +0,0 @@ -*> \brief \b DLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLASCL + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLASCL( TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER TYPE -* INTEGER INFO, KL, KU, LDA, M, N -* DOUBLE PRECISION CFROM, CTO -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLASCL multiplies the M by N real matrix A by the real scalar -*> CTO/CFROM. This is done without over/underflow as long as the final -*> result CTO*A(I,J)/CFROM does not over/underflow. TYPE specifies that -*> A may be full, upper triangular, lower triangular, upper Hessenberg, -*> or banded. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] TYPE -*> \verbatim -*> TYPE is CHARACTER*1 -*> TYPE indices the storage type of the input matrix. -*> = 'G': A is a full matrix. -*> = 'L': A is a lower triangular matrix. -*> = 'U': A is an upper triangular matrix. -*> = 'H': A is an upper Hessenberg matrix. -*> = 'B': A is a symmetric band matrix with lower bandwidth KL -*> and upper bandwidth KU and with the only the lower -*> half stored. -*> = 'Q': A is a symmetric band matrix with lower bandwidth KL -*> and upper bandwidth KU and with the only the upper -*> half stored. -*> = 'Z': A is a band matrix with lower bandwidth KL and upper -*> bandwidth KU. See DGBTRF for storage details. -*> \endverbatim -*> -*> \param[in] KL -*> \verbatim -*> KL is INTEGER -*> The lower bandwidth of A. Referenced only if TYPE = 'B', -*> 'Q' or 'Z'. -*> \endverbatim -*> -*> \param[in] KU -*> \verbatim -*> KU is INTEGER -*> The upper bandwidth of A. Referenced only if TYPE = 'B', -*> 'Q' or 'Z'. -*> \endverbatim -*> -*> \param[in] CFROM -*> \verbatim -*> CFROM is DOUBLE PRECISION -*> \endverbatim -*> -*> \param[in] CTO -*> \verbatim -*> CTO is DOUBLE PRECISION -*> -*> The matrix A is multiplied by CTO/CFROM. A(I,J) is computed -*> without over/underflow if the final result CTO*A(I,J)/CFROM -*> can be represented without over/underflow. CFROM must be -*> nonzero. -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix A. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> The matrix to be multiplied by CTO/CFROM. See TYPE for the -*> storage type. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. -*> If TYPE = 'G', 'L', 'U', 'H', LDA >= max(1,M); -*> TYPE = 'B', LDA >= KL+1; -*> TYPE = 'Q', LDA >= KU+1; -*> TYPE = 'Z', LDA >= 2*KL+KU+1. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> 0 - successful exit -*> <0 - if INFO = -i, the i-th argument had an illegal value. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup OTHERauxiliary -* -* ===================================================================== - SUBROUTINE DLASCL( TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER TYPE - INTEGER INFO, KL, KU, LDA, M, N - DOUBLE PRECISION CFROM, CTO -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) -* .. -* .. Local Scalars .. - LOGICAL DONE - INTEGER I, ITYPE, J, K1, K2, K3, K4 - DOUBLE PRECISION BIGNUM, CFROM1, CFROMC, CTO1, CTOC, MUL, SMLNUM -* .. -* .. External Functions .. - LOGICAL LSAME, DISNAN - DOUBLE PRECISION DLAMCH - EXTERNAL LSAME, DLAMCH, DISNAN -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, MAX, MIN -* .. -* .. External Subroutines .. - EXTERNAL XERBLA -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - INFO = 0 -* - IF( LSAME( TYPE, 'G' ) ) THEN - ITYPE = 0 - ELSE IF( LSAME( TYPE, 'L' ) ) THEN - ITYPE = 1 - ELSE IF( LSAME( TYPE, 'U' ) ) THEN - ITYPE = 2 - ELSE IF( LSAME( TYPE, 'H' ) ) THEN - ITYPE = 3 - ELSE IF( LSAME( TYPE, 'B' ) ) THEN - ITYPE = 4 - ELSE IF( LSAME( TYPE, 'Q' ) ) THEN - ITYPE = 5 - ELSE IF( LSAME( TYPE, 'Z' ) ) THEN - ITYPE = 6 - ELSE - ITYPE = -1 - END IF -* - IF( ITYPE.EQ.-1 ) THEN - INFO = -1 - ELSE IF( CFROM.EQ.ZERO .OR. DISNAN(CFROM) ) THEN - INFO = -4 - ELSE IF( DISNAN(CTO) ) THEN - INFO = -5 - ELSE IF( M.LT.0 ) THEN - INFO = -6 - ELSE IF( N.LT.0 .OR. ( ITYPE.EQ.4 .AND. N.NE.M ) .OR. - $ ( ITYPE.EQ.5 .AND. N.NE.M ) ) THEN - INFO = -7 - ELSE IF( ITYPE.LE.3 .AND. LDA.LT.MAX( 1, M ) ) THEN - INFO = -9 - ELSE IF( ITYPE.GE.4 ) THEN - IF( KL.LT.0 .OR. KL.GT.MAX( M-1, 0 ) ) THEN - INFO = -2 - ELSE IF( KU.LT.0 .OR. KU.GT.MAX( N-1, 0 ) .OR. - $ ( ( ITYPE.EQ.4 .OR. ITYPE.EQ.5 ) .AND. KL.NE.KU ) ) - $ THEN - INFO = -3 - ELSE IF( ( ITYPE.EQ.4 .AND. LDA.LT.KL+1 ) .OR. - $ ( ITYPE.EQ.5 .AND. LDA.LT.KU+1 ) .OR. - $ ( ITYPE.EQ.6 .AND. LDA.LT.2*KL+KU+1 ) ) THEN - INFO = -9 - END IF - END IF -* - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DLASCL', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( N.EQ.0 .OR. M.EQ.0 ) - $ RETURN -* -* Get machine parameters -* - SMLNUM = DLAMCH( 'S' ) - BIGNUM = ONE / SMLNUM -* - CFROMC = CFROM - CTOC = CTO -* - 10 CONTINUE - CFROM1 = CFROMC*SMLNUM - IF( CFROM1.EQ.CFROMC ) THEN -! CFROMC is an inf. Multiply by a correctly signed zero for -! finite CTOC, or a NaN if CTOC is infinite. - MUL = CTOC / CFROMC - DONE = .TRUE. - CTO1 = CTOC - ELSE - CTO1 = CTOC / BIGNUM - IF( CTO1.EQ.CTOC ) THEN -! CTOC is either 0 or an inf. In both cases, CTOC itself -! serves as the correct multiplication factor. - MUL = CTOC - DONE = .TRUE. - CFROMC = ONE - ELSE IF( ABS( CFROM1 ).GT.ABS( CTOC ) .AND. CTOC.NE.ZERO ) THEN - MUL = SMLNUM - DONE = .FALSE. - CFROMC = CFROM1 - ELSE IF( ABS( CTO1 ).GT.ABS( CFROMC ) ) THEN - MUL = BIGNUM - DONE = .FALSE. - CTOC = CTO1 - ELSE - MUL = CTOC / CFROMC - DONE = .TRUE. - IF (MUL .EQ. ONE) - $ RETURN - END IF - END IF -* - IF( ITYPE.EQ.0 ) THEN -* -* Full matrix -* - DO 30 J = 1, N - DO 20 I = 1, M - A( I, J ) = A( I, J )*MUL - 20 CONTINUE - 30 CONTINUE -* - ELSE IF( ITYPE.EQ.1 ) THEN -* -* Lower triangular matrix -* - DO 50 J = 1, N - DO 40 I = J, M - A( I, J ) = A( I, J )*MUL - 40 CONTINUE - 50 CONTINUE -* - ELSE IF( ITYPE.EQ.2 ) THEN -* -* Upper triangular matrix -* - DO 70 J = 1, N - DO 60 I = 1, MIN( J, M ) - A( I, J ) = A( I, J )*MUL - 60 CONTINUE - 70 CONTINUE -* - ELSE IF( ITYPE.EQ.3 ) THEN -* -* Upper Hessenberg matrix -* - DO 90 J = 1, N - DO 80 I = 1, MIN( J+1, M ) - A( I, J ) = A( I, J )*MUL - 80 CONTINUE - 90 CONTINUE -* - ELSE IF( ITYPE.EQ.4 ) THEN -* -* Lower half of a symmetric band matrix -* - K3 = KL + 1 - K4 = N + 1 - DO 110 J = 1, N - DO 100 I = 1, MIN( K3, K4-J ) - A( I, J ) = A( I, J )*MUL - 100 CONTINUE - 110 CONTINUE -* - ELSE IF( ITYPE.EQ.5 ) THEN -* -* Upper half of a symmetric band matrix -* - K1 = KU + 2 - K3 = KU + 1 - DO 130 J = 1, N - DO 120 I = MAX( K1-J, 1 ), K3 - A( I, J ) = A( I, J )*MUL - 120 CONTINUE - 130 CONTINUE -* - ELSE IF( ITYPE.EQ.6 ) THEN -* -* Band matrix -* - K1 = KL + KU + 2 - K2 = KL + 1 - K3 = 2*KL + KU + 1 - K4 = KL + KU + 1 + M - DO 150 J = 1, N - DO 140 I = MAX( K1-J, K2 ), MIN( K3, K4-J ) - A( I, J ) = A( I, J )*MUL - 140 CONTINUE - 150 CONTINUE -* - END IF -* - IF( .NOT.DONE ) - $ GO TO 10 -* - RETURN -* -* End of DLASCL -* - END diff --git a/lib/linalg/fortran/dlasd4.f b/lib/linalg/fortran/dlasd4.f deleted file mode 100644 index acfd896b3b..0000000000 --- a/lib/linalg/fortran/dlasd4.f +++ /dev/null @@ -1,1058 +0,0 @@ -*> \brief \b DLASD4 computes the square root of the i-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix. Used by dbdsdc. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLASD4 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLASD4( N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO ) -* -* .. Scalar Arguments .. -* INTEGER I, INFO, N -* DOUBLE PRECISION RHO, SIGMA -* .. -* .. Array Arguments .. -* DOUBLE PRECISION D( * ), DELTA( * ), WORK( * ), Z( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> This subroutine computes the square root of the I-th updated -*> eigenvalue of a positive symmetric rank-one modification to -*> a positive diagonal matrix whose entries are given as the squares -*> of the corresponding entries in the array d, and that -*> -*> 0 <= D(i) < D(j) for i < j -*> -*> and that RHO > 0. This is arranged by the calling routine, and is -*> no loss in generality. The rank-one modified system is thus -*> -*> diag( D ) * diag( D ) + RHO * Z * Z_transpose. -*> -*> where we assume the Euclidean norm of Z is 1. -*> -*> The method consists of approximating the rational functions in the -*> secular equation by simpler interpolating rational functions. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The length of all arrays. -*> \endverbatim -*> -*> \param[in] I -*> \verbatim -*> I is INTEGER -*> The index of the eigenvalue to be computed. 1 <= I <= N. -*> \endverbatim -*> -*> \param[in] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension ( N ) -*> The original eigenvalues. It is assumed that they are in -*> order, 0 <= D(I) < D(J) for I < J. -*> \endverbatim -*> -*> \param[in] Z -*> \verbatim -*> Z is DOUBLE PRECISION array, dimension ( N ) -*> The components of the updating vector. -*> \endverbatim -*> -*> \param[out] DELTA -*> \verbatim -*> DELTA is DOUBLE PRECISION array, dimension ( N ) -*> If N .ne. 1, DELTA contains (D(j) - sigma_I) in its j-th -*> component. If N = 1, then DELTA(1) = 1. The vector DELTA -*> contains the information necessary to construct the -*> (singular) eigenvectors. -*> \endverbatim -*> -*> \param[in] RHO -*> \verbatim -*> RHO is DOUBLE PRECISION -*> The scalar in the symmetric updating formula. -*> \endverbatim -*> -*> \param[out] SIGMA -*> \verbatim -*> SIGMA is DOUBLE PRECISION -*> The computed sigma_I, the I-th updated eigenvalue. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension ( N ) -*> If N .ne. 1, WORK contains (D(j) + sigma_I) in its j-th -*> component. If N = 1, then WORK( 1 ) = 1. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> > 0: if INFO = 1, the updating process failed. -*> \endverbatim -* -*> \par Internal Parameters: -* ========================= -*> -*> \verbatim -*> Logical variable ORGATI (origin-at-i?) is used for distinguishing -*> whether D(i) or D(i+1) is treated as the origin. -*> -*> ORGATI = .true. origin at i -*> ORGATI = .false. origin at i+1 -*> -*> Logical variable SWTCH3 (switch-for-3-poles?) is for noting -*> if we are working with THREE poles! -*> -*> MAXIT is the maximum number of iterations allowed for each -*> eigenvalue. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup OTHERauxiliary -* -*> \par Contributors: -* ================== -*> -*> Ren-Cang Li, Computer Science Division, University of California -*> at Berkeley, USA -*> -* ===================================================================== - SUBROUTINE DLASD4( N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER I, INFO, N - DOUBLE PRECISION RHO, SIGMA -* .. -* .. Array Arguments .. - DOUBLE PRECISION D( * ), DELTA( * ), WORK( * ), Z( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - INTEGER MAXIT - PARAMETER ( MAXIT = 400 ) - DOUBLE PRECISION ZERO, ONE, TWO, THREE, FOUR, EIGHT, TEN - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0, - $ THREE = 3.0D+0, FOUR = 4.0D+0, EIGHT = 8.0D+0, - $ TEN = 10.0D+0 ) -* .. -* .. Local Scalars .. - LOGICAL ORGATI, SWTCH, SWTCH3, GEOMAVG - INTEGER II, IIM1, IIP1, IP1, ITER, J, NITER - DOUBLE PRECISION A, B, C, DELSQ, DELSQ2, SQ2, DPHI, DPSI, DTIIM, - $ DTIIP, DTIPSQ, DTISQ, DTNSQ, DTNSQ1, DW, EPS, - $ ERRETM, ETA, PHI, PREW, PSI, RHOINV, SGLB, - $ SGUB, TAU, TAU2, TEMP, TEMP1, TEMP2, W -* .. -* .. Local Arrays .. - DOUBLE PRECISION DD( 3 ), ZZ( 3 ) -* .. -* .. External Subroutines .. - EXTERNAL DLAED6, DLASD5 -* .. -* .. External Functions .. - DOUBLE PRECISION DLAMCH - EXTERNAL DLAMCH -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, MAX, MIN, SQRT -* .. -* .. Executable Statements .. -* -* Since this routine is called in an inner loop, we do no argument -* checking. -* -* Quick return for N=1 and 2. -* - INFO = 0 - IF( N.EQ.1 ) THEN -* -* Presumably, I=1 upon entry -* - SIGMA = SQRT( D( 1 )*D( 1 )+RHO*Z( 1 )*Z( 1 ) ) - DELTA( 1 ) = ONE - WORK( 1 ) = ONE - RETURN - END IF - IF( N.EQ.2 ) THEN - CALL DLASD5( I, D, Z, DELTA, RHO, SIGMA, WORK ) - RETURN - END IF -* -* Compute machine epsilon -* - EPS = DLAMCH( 'Epsilon' ) - RHOINV = ONE / RHO - TAU2= ZERO -* -* The case I = N -* - IF( I.EQ.N ) THEN -* -* Initialize some basic variables -* - II = N - 1 - NITER = 1 -* -* Calculate initial guess -* - TEMP = RHO / TWO -* -* If ||Z||_2 is not one, then TEMP should be set to -* RHO * ||Z||_2^2 / TWO -* - TEMP1 = TEMP / ( D( N )+SQRT( D( N )*D( N )+TEMP ) ) - DO 10 J = 1, N - WORK( J ) = D( J ) + D( N ) + TEMP1 - DELTA( J ) = ( D( J )-D( N ) ) - TEMP1 - 10 CONTINUE -* - PSI = ZERO - DO 20 J = 1, N - 2 - PSI = PSI + Z( J )*Z( J ) / ( DELTA( J )*WORK( J ) ) - 20 CONTINUE -* - C = RHOINV + PSI - W = C + Z( II )*Z( II ) / ( DELTA( II )*WORK( II ) ) + - $ Z( N )*Z( N ) / ( DELTA( N )*WORK( N ) ) -* - IF( W.LE.ZERO ) THEN - TEMP1 = SQRT( D( N )*D( N )+RHO ) - TEMP = Z( N-1 )*Z( N-1 ) / ( ( D( N-1 )+TEMP1 )* - $ ( D( N )-D( N-1 )+RHO / ( D( N )+TEMP1 ) ) ) + - $ Z( N )*Z( N ) / RHO -* -* The following TAU2 is to approximate -* SIGMA_n^2 - D( N )*D( N ) -* - IF( C.LE.TEMP ) THEN - TAU = RHO - ELSE - DELSQ = ( D( N )-D( N-1 ) )*( D( N )+D( N-1 ) ) - A = -C*DELSQ + Z( N-1 )*Z( N-1 ) + Z( N )*Z( N ) - B = Z( N )*Z( N )*DELSQ - IF( A.LT.ZERO ) THEN - TAU2 = TWO*B / ( SQRT( A*A+FOUR*B*C )-A ) - ELSE - TAU2 = ( A+SQRT( A*A+FOUR*B*C ) ) / ( TWO*C ) - END IF - TAU = TAU2 / ( D( N )+SQRT( D( N )*D( N )+TAU2 ) ) - END IF -* -* It can be proved that -* D(N)^2+RHO/2 <= SIGMA_n^2 < D(N)^2+TAU2 <= D(N)^2+RHO -* - ELSE - DELSQ = ( D( N )-D( N-1 ) )*( D( N )+D( N-1 ) ) - A = -C*DELSQ + Z( N-1 )*Z( N-1 ) + Z( N )*Z( N ) - B = Z( N )*Z( N )*DELSQ -* -* The following TAU2 is to approximate -* SIGMA_n^2 - D( N )*D( N ) -* - IF( A.LT.ZERO ) THEN - TAU2 = TWO*B / ( SQRT( A*A+FOUR*B*C )-A ) - ELSE - TAU2 = ( A+SQRT( A*A+FOUR*B*C ) ) / ( TWO*C ) - END IF - TAU = TAU2 / ( D( N )+SQRT( D( N )*D( N )+TAU2 ) ) - -* -* It can be proved that -* D(N)^2 < D(N)^2+TAU2 < SIGMA(N)^2 < D(N)^2+RHO/2 -* - END IF -* -* The following TAU is to approximate SIGMA_n - D( N ) -* -* TAU = TAU2 / ( D( N )+SQRT( D( N )*D( N )+TAU2 ) ) -* - SIGMA = D( N ) + TAU - DO 30 J = 1, N - DELTA( J ) = ( D( J )-D( N ) ) - TAU - WORK( J ) = D( J ) + D( N ) + TAU - 30 CONTINUE -* -* Evaluate PSI and the derivative DPSI -* - DPSI = ZERO - PSI = ZERO - ERRETM = ZERO - DO 40 J = 1, II - TEMP = Z( J ) / ( DELTA( J )*WORK( J ) ) - PSI = PSI + Z( J )*TEMP - DPSI = DPSI + TEMP*TEMP - ERRETM = ERRETM + PSI - 40 CONTINUE - ERRETM = ABS( ERRETM ) -* -* Evaluate PHI and the derivative DPHI -* - TEMP = Z( N ) / ( DELTA( N )*WORK( N ) ) - PHI = Z( N )*TEMP - DPHI = TEMP*TEMP - ERRETM = EIGHT*( -PHI-PSI ) + ERRETM - PHI + RHOINV -* $ + ABS( TAU2 )*( DPSI+DPHI ) -* - W = RHOINV + PHI + PSI -* -* Test for convergence -* - IF( ABS( W ).LE.EPS*ERRETM ) THEN - GO TO 240 - END IF -* -* Calculate the new step -* - NITER = NITER + 1 - DTNSQ1 = WORK( N-1 )*DELTA( N-1 ) - DTNSQ = WORK( N )*DELTA( N ) - C = W - DTNSQ1*DPSI - DTNSQ*DPHI - A = ( DTNSQ+DTNSQ1 )*W - DTNSQ*DTNSQ1*( DPSI+DPHI ) - B = DTNSQ*DTNSQ1*W - IF( C.LT.ZERO ) - $ C = ABS( C ) - IF( C.EQ.ZERO ) THEN - ETA = RHO - SIGMA*SIGMA - ELSE IF( A.GE.ZERO ) THEN - ETA = ( A+SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C ) - ELSE - ETA = TWO*B / ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) - END IF -* -* Note, eta should be positive if w is negative, and -* eta should be negative otherwise. However, -* if for some reason caused by roundoff, eta*w > 0, -* we simply use one Newton step instead. This way -* will guarantee eta*w < 0. -* - IF( W*ETA.GT.ZERO ) - $ ETA = -W / ( DPSI+DPHI ) - TEMP = ETA - DTNSQ - IF( TEMP.GT.RHO ) - $ ETA = RHO + DTNSQ -* - ETA = ETA / ( SIGMA+SQRT( ETA+SIGMA*SIGMA ) ) - TAU = TAU + ETA - SIGMA = SIGMA + ETA -* - DO 50 J = 1, N - DELTA( J ) = DELTA( J ) - ETA - WORK( J ) = WORK( J ) + ETA - 50 CONTINUE -* -* Evaluate PSI and the derivative DPSI -* - DPSI = ZERO - PSI = ZERO - ERRETM = ZERO - DO 60 J = 1, II - TEMP = Z( J ) / ( WORK( J )*DELTA( J ) ) - PSI = PSI + Z( J )*TEMP - DPSI = DPSI + TEMP*TEMP - ERRETM = ERRETM + PSI - 60 CONTINUE - ERRETM = ABS( ERRETM ) -* -* Evaluate PHI and the derivative DPHI -* - TAU2 = WORK( N )*DELTA( N ) - TEMP = Z( N ) / TAU2 - PHI = Z( N )*TEMP - DPHI = TEMP*TEMP - ERRETM = EIGHT*( -PHI-PSI ) + ERRETM - PHI + RHOINV -* $ + ABS( TAU2 )*( DPSI+DPHI ) -* - W = RHOINV + PHI + PSI -* -* Main loop to update the values of the array DELTA -* - ITER = NITER + 1 -* - DO 90 NITER = ITER, MAXIT -* -* Test for convergence -* - IF( ABS( W ).LE.EPS*ERRETM ) THEN - GO TO 240 - END IF -* -* Calculate the new step -* - DTNSQ1 = WORK( N-1 )*DELTA( N-1 ) - DTNSQ = WORK( N )*DELTA( N ) - C = W - DTNSQ1*DPSI - DTNSQ*DPHI - A = ( DTNSQ+DTNSQ1 )*W - DTNSQ1*DTNSQ*( DPSI+DPHI ) - B = DTNSQ1*DTNSQ*W - IF( A.GE.ZERO ) THEN - ETA = ( A+SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C ) - ELSE - ETA = TWO*B / ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) - END IF -* -* Note, eta should be positive if w is negative, and -* eta should be negative otherwise. However, -* if for some reason caused by roundoff, eta*w > 0, -* we simply use one Newton step instead. This way -* will guarantee eta*w < 0. -* - IF( W*ETA.GT.ZERO ) - $ ETA = -W / ( DPSI+DPHI ) - TEMP = ETA - DTNSQ - IF( TEMP.LE.ZERO ) - $ ETA = ETA / TWO -* - ETA = ETA / ( SIGMA+SQRT( ETA+SIGMA*SIGMA ) ) - TAU = TAU + ETA - SIGMA = SIGMA + ETA -* - DO 70 J = 1, N - DELTA( J ) = DELTA( J ) - ETA - WORK( J ) = WORK( J ) + ETA - 70 CONTINUE -* -* Evaluate PSI and the derivative DPSI -* - DPSI = ZERO - PSI = ZERO - ERRETM = ZERO - DO 80 J = 1, II - TEMP = Z( J ) / ( WORK( J )*DELTA( J ) ) - PSI = PSI + Z( J )*TEMP - DPSI = DPSI + TEMP*TEMP - ERRETM = ERRETM + PSI - 80 CONTINUE - ERRETM = ABS( ERRETM ) -* -* Evaluate PHI and the derivative DPHI -* - TAU2 = WORK( N )*DELTA( N ) - TEMP = Z( N ) / TAU2 - PHI = Z( N )*TEMP - DPHI = TEMP*TEMP - ERRETM = EIGHT*( -PHI-PSI ) + ERRETM - PHI + RHOINV -* $ + ABS( TAU2 )*( DPSI+DPHI ) -* - W = RHOINV + PHI + PSI - 90 CONTINUE -* -* Return with INFO = 1, NITER = MAXIT and not converged -* - INFO = 1 - GO TO 240 -* -* End for the case I = N -* - ELSE -* -* The case for I < N -* - NITER = 1 - IP1 = I + 1 -* -* Calculate initial guess -* - DELSQ = ( D( IP1 )-D( I ) )*( D( IP1 )+D( I ) ) - DELSQ2 = DELSQ / TWO - SQ2=SQRT( ( D( I )*D( I )+D( IP1 )*D( IP1 ) ) / TWO ) - TEMP = DELSQ2 / ( D( I )+SQ2 ) - DO 100 J = 1, N - WORK( J ) = D( J ) + D( I ) + TEMP - DELTA( J ) = ( D( J )-D( I ) ) - TEMP - 100 CONTINUE -* - PSI = ZERO - DO 110 J = 1, I - 1 - PSI = PSI + Z( J )*Z( J ) / ( WORK( J )*DELTA( J ) ) - 110 CONTINUE -* - PHI = ZERO - DO 120 J = N, I + 2, -1 - PHI = PHI + Z( J )*Z( J ) / ( WORK( J )*DELTA( J ) ) - 120 CONTINUE - C = RHOINV + PSI + PHI - W = C + Z( I )*Z( I ) / ( WORK( I )*DELTA( I ) ) + - $ Z( IP1 )*Z( IP1 ) / ( WORK( IP1 )*DELTA( IP1 ) ) -* - GEOMAVG = .FALSE. - IF( W.GT.ZERO ) THEN -* -* d(i)^2 < the ith sigma^2 < (d(i)^2+d(i+1)^2)/2 -* -* We choose d(i) as origin. -* - ORGATI = .TRUE. - II = I - SGLB = ZERO - SGUB = DELSQ2 / ( D( I )+SQ2 ) - A = C*DELSQ + Z( I )*Z( I ) + Z( IP1 )*Z( IP1 ) - B = Z( I )*Z( I )*DELSQ - IF( A.GT.ZERO ) THEN - TAU2 = TWO*B / ( A+SQRT( ABS( A*A-FOUR*B*C ) ) ) - ELSE - TAU2 = ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C ) - END IF -* -* TAU2 now is an estimation of SIGMA^2 - D( I )^2. The -* following, however, is the corresponding estimation of -* SIGMA - D( I ). -* - TAU = TAU2 / ( D( I )+SQRT( D( I )*D( I )+TAU2 ) ) - TEMP = SQRT(EPS) - IF( (D(I).LE.TEMP*D(IP1)).AND.(ABS(Z(I)).LE.TEMP) - $ .AND.(D(I).GT.ZERO) ) THEN - TAU = MIN( TEN*D(I), SGUB ) - GEOMAVG = .TRUE. - END IF - ELSE -* -* (d(i)^2+d(i+1)^2)/2 <= the ith sigma^2 < d(i+1)^2/2 -* -* We choose d(i+1) as origin. -* - ORGATI = .FALSE. - II = IP1 - SGLB = -DELSQ2 / ( D( II )+SQ2 ) - SGUB = ZERO - A = C*DELSQ - Z( I )*Z( I ) - Z( IP1 )*Z( IP1 ) - B = Z( IP1 )*Z( IP1 )*DELSQ - IF( A.LT.ZERO ) THEN - TAU2 = TWO*B / ( A-SQRT( ABS( A*A+FOUR*B*C ) ) ) - ELSE - TAU2 = -( A+SQRT( ABS( A*A+FOUR*B*C ) ) ) / ( TWO*C ) - END IF -* -* TAU2 now is an estimation of SIGMA^2 - D( IP1 )^2. The -* following, however, is the corresponding estimation of -* SIGMA - D( IP1 ). -* - TAU = TAU2 / ( D( IP1 )+SQRT( ABS( D( IP1 )*D( IP1 )+ - $ TAU2 ) ) ) - END IF -* - SIGMA = D( II ) + TAU - DO 130 J = 1, N - WORK( J ) = D( J ) + D( II ) + TAU - DELTA( J ) = ( D( J )-D( II ) ) - TAU - 130 CONTINUE - IIM1 = II - 1 - IIP1 = II + 1 -* -* Evaluate PSI and the derivative DPSI -* - DPSI = ZERO - PSI = ZERO - ERRETM = ZERO - DO 150 J = 1, IIM1 - TEMP = Z( J ) / ( WORK( J )*DELTA( J ) ) - PSI = PSI + Z( J )*TEMP - DPSI = DPSI + TEMP*TEMP - ERRETM = ERRETM + PSI - 150 CONTINUE - ERRETM = ABS( ERRETM ) -* -* Evaluate PHI and the derivative DPHI -* - DPHI = ZERO - PHI = ZERO - DO 160 J = N, IIP1, -1 - TEMP = Z( J ) / ( WORK( J )*DELTA( J ) ) - PHI = PHI + Z( J )*TEMP - DPHI = DPHI + TEMP*TEMP - ERRETM = ERRETM + PHI - 160 CONTINUE -* - W = RHOINV + PHI + PSI -* -* W is the value of the secular function with -* its ii-th element removed. -* - SWTCH3 = .FALSE. - IF( ORGATI ) THEN - IF( W.LT.ZERO ) - $ SWTCH3 = .TRUE. - ELSE - IF( W.GT.ZERO ) - $ SWTCH3 = .TRUE. - END IF - IF( II.EQ.1 .OR. II.EQ.N ) - $ SWTCH3 = .FALSE. -* - TEMP = Z( II ) / ( WORK( II )*DELTA( II ) ) - DW = DPSI + DPHI + TEMP*TEMP - TEMP = Z( II )*TEMP - W = W + TEMP - ERRETM = EIGHT*( PHI-PSI ) + ERRETM + TWO*RHOINV - $ + THREE*ABS( TEMP ) -* $ + ABS( TAU2 )*DW -* -* Test for convergence -* - IF( ABS( W ).LE.EPS*ERRETM ) THEN - GO TO 240 - END IF -* - IF( W.LE.ZERO ) THEN - SGLB = MAX( SGLB, TAU ) - ELSE - SGUB = MIN( SGUB, TAU ) - END IF -* -* Calculate the new step -* - NITER = NITER + 1 - IF( .NOT.SWTCH3 ) THEN - DTIPSQ = WORK( IP1 )*DELTA( IP1 ) - DTISQ = WORK( I )*DELTA( I ) - IF( ORGATI ) THEN - C = W - DTIPSQ*DW + DELSQ*( Z( I ) / DTISQ )**2 - ELSE - C = W - DTISQ*DW - DELSQ*( Z( IP1 ) / DTIPSQ )**2 - END IF - A = ( DTIPSQ+DTISQ )*W - DTIPSQ*DTISQ*DW - B = DTIPSQ*DTISQ*W - IF( C.EQ.ZERO ) THEN - IF( A.EQ.ZERO ) THEN - IF( ORGATI ) THEN - A = Z( I )*Z( I ) + DTIPSQ*DTIPSQ*( DPSI+DPHI ) - ELSE - A = Z( IP1 )*Z( IP1 ) + DTISQ*DTISQ*( DPSI+DPHI ) - END IF - END IF - ETA = B / A - ELSE IF( A.LE.ZERO ) THEN - ETA = ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C ) - ELSE - ETA = TWO*B / ( A+SQRT( ABS( A*A-FOUR*B*C ) ) ) - END IF - ELSE -* -* Interpolation using THREE most relevant poles -* - DTIIM = WORK( IIM1 )*DELTA( IIM1 ) - DTIIP = WORK( IIP1 )*DELTA( IIP1 ) - TEMP = RHOINV + PSI + PHI - IF( ORGATI ) THEN - TEMP1 = Z( IIM1 ) / DTIIM - TEMP1 = TEMP1*TEMP1 - C = ( TEMP - DTIIP*( DPSI+DPHI ) ) - - $ ( D( IIM1 )-D( IIP1 ) )*( D( IIM1 )+D( IIP1 ) )*TEMP1 - ZZ( 1 ) = Z( IIM1 )*Z( IIM1 ) - IF( DPSI.LT.TEMP1 ) THEN - ZZ( 3 ) = DTIIP*DTIIP*DPHI - ELSE - ZZ( 3 ) = DTIIP*DTIIP*( ( DPSI-TEMP1 )+DPHI ) - END IF - ELSE - TEMP1 = Z( IIP1 ) / DTIIP - TEMP1 = TEMP1*TEMP1 - C = ( TEMP - DTIIM*( DPSI+DPHI ) ) - - $ ( D( IIP1 )-D( IIM1 ) )*( D( IIM1 )+D( IIP1 ) )*TEMP1 - IF( DPHI.LT.TEMP1 ) THEN - ZZ( 1 ) = DTIIM*DTIIM*DPSI - ELSE - ZZ( 1 ) = DTIIM*DTIIM*( DPSI+( DPHI-TEMP1 ) ) - END IF - ZZ( 3 ) = Z( IIP1 )*Z( IIP1 ) - END IF - ZZ( 2 ) = Z( II )*Z( II ) - DD( 1 ) = DTIIM - DD( 2 ) = DELTA( II )*WORK( II ) - DD( 3 ) = DTIIP - CALL DLAED6( NITER, ORGATI, C, DD, ZZ, W, ETA, INFO ) -* - IF( INFO.NE.0 ) THEN -* -* If INFO is not 0, i.e., DLAED6 failed, switch back -* to 2 pole interpolation. -* - SWTCH3 = .FALSE. - INFO = 0 - DTIPSQ = WORK( IP1 )*DELTA( IP1 ) - DTISQ = WORK( I )*DELTA( I ) - IF( ORGATI ) THEN - C = W - DTIPSQ*DW + DELSQ*( Z( I ) / DTISQ )**2 - ELSE - C = W - DTISQ*DW - DELSQ*( Z( IP1 ) / DTIPSQ )**2 - END IF - A = ( DTIPSQ+DTISQ )*W - DTIPSQ*DTISQ*DW - B = DTIPSQ*DTISQ*W - IF( C.EQ.ZERO ) THEN - IF( A.EQ.ZERO ) THEN - IF( ORGATI ) THEN - A = Z( I )*Z( I ) + DTIPSQ*DTIPSQ*( DPSI+DPHI ) - ELSE - A = Z( IP1 )*Z( IP1 ) + DTISQ*DTISQ*( DPSI+DPHI) - END IF - END IF - ETA = B / A - ELSE IF( A.LE.ZERO ) THEN - ETA = ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C ) - ELSE - ETA = TWO*B / ( A+SQRT( ABS( A*A-FOUR*B*C ) ) ) - END IF - END IF - END IF -* -* Note, eta should be positive if w is negative, and -* eta should be negative otherwise. However, -* if for some reason caused by roundoff, eta*w > 0, -* we simply use one Newton step instead. This way -* will guarantee eta*w < 0. -* - IF( W*ETA.GE.ZERO ) - $ ETA = -W / DW -* - ETA = ETA / ( SIGMA+SQRT( SIGMA*SIGMA+ETA ) ) - TEMP = TAU + ETA - IF( TEMP.GT.SGUB .OR. TEMP.LT.SGLB ) THEN - IF( W.LT.ZERO ) THEN - ETA = ( SGUB-TAU ) / TWO - ELSE - ETA = ( SGLB-TAU ) / TWO - END IF - IF( GEOMAVG ) THEN - IF( W .LT. ZERO ) THEN - IF( TAU .GT. ZERO ) THEN - ETA = SQRT(SGUB*TAU)-TAU - END IF - ELSE - IF( SGLB .GT. ZERO ) THEN - ETA = SQRT(SGLB*TAU)-TAU - END IF - END IF - END IF - END IF -* - PREW = W -* - TAU = TAU + ETA - SIGMA = SIGMA + ETA -* - DO 170 J = 1, N - WORK( J ) = WORK( J ) + ETA - DELTA( J ) = DELTA( J ) - ETA - 170 CONTINUE -* -* Evaluate PSI and the derivative DPSI -* - DPSI = ZERO - PSI = ZERO - ERRETM = ZERO - DO 180 J = 1, IIM1 - TEMP = Z( J ) / ( WORK( J )*DELTA( J ) ) - PSI = PSI + Z( J )*TEMP - DPSI = DPSI + TEMP*TEMP - ERRETM = ERRETM + PSI - 180 CONTINUE - ERRETM = ABS( ERRETM ) -* -* Evaluate PHI and the derivative DPHI -* - DPHI = ZERO - PHI = ZERO - DO 190 J = N, IIP1, -1 - TEMP = Z( J ) / ( WORK( J )*DELTA( J ) ) - PHI = PHI + Z( J )*TEMP - DPHI = DPHI + TEMP*TEMP - ERRETM = ERRETM + PHI - 190 CONTINUE -* - TAU2 = WORK( II )*DELTA( II ) - TEMP = Z( II ) / TAU2 - DW = DPSI + DPHI + TEMP*TEMP - TEMP = Z( II )*TEMP - W = RHOINV + PHI + PSI + TEMP - ERRETM = EIGHT*( PHI-PSI ) + ERRETM + TWO*RHOINV - $ + THREE*ABS( TEMP ) -* $ + ABS( TAU2 )*DW -* - SWTCH = .FALSE. - IF( ORGATI ) THEN - IF( -W.GT.ABS( PREW ) / TEN ) - $ SWTCH = .TRUE. - ELSE - IF( W.GT.ABS( PREW ) / TEN ) - $ SWTCH = .TRUE. - END IF -* -* Main loop to update the values of the array DELTA and WORK -* - ITER = NITER + 1 -* - DO 230 NITER = ITER, MAXIT -* -* Test for convergence -* - IF( ABS( W ).LE.EPS*ERRETM ) THEN -* $ .OR. (SGUB-SGLB).LE.EIGHT*ABS(SGUB+SGLB) ) THEN - GO TO 240 - END IF -* - IF( W.LE.ZERO ) THEN - SGLB = MAX( SGLB, TAU ) - ELSE - SGUB = MIN( SGUB, TAU ) - END IF -* -* Calculate the new step -* - IF( .NOT.SWTCH3 ) THEN - DTIPSQ = WORK( IP1 )*DELTA( IP1 ) - DTISQ = WORK( I )*DELTA( I ) - IF( .NOT.SWTCH ) THEN - IF( ORGATI ) THEN - C = W - DTIPSQ*DW + DELSQ*( Z( I ) / DTISQ )**2 - ELSE - C = W - DTISQ*DW - DELSQ*( Z( IP1 ) / DTIPSQ )**2 - END IF - ELSE - TEMP = Z( II ) / ( WORK( II )*DELTA( II ) ) - IF( ORGATI ) THEN - DPSI = DPSI + TEMP*TEMP - ELSE - DPHI = DPHI + TEMP*TEMP - END IF - C = W - DTISQ*DPSI - DTIPSQ*DPHI - END IF - A = ( DTIPSQ+DTISQ )*W - DTIPSQ*DTISQ*DW - B = DTIPSQ*DTISQ*W - IF( C.EQ.ZERO ) THEN - IF( A.EQ.ZERO ) THEN - IF( .NOT.SWTCH ) THEN - IF( ORGATI ) THEN - A = Z( I )*Z( I ) + DTIPSQ*DTIPSQ* - $ ( DPSI+DPHI ) - ELSE - A = Z( IP1 )*Z( IP1 ) + - $ DTISQ*DTISQ*( DPSI+DPHI ) - END IF - ELSE - A = DTISQ*DTISQ*DPSI + DTIPSQ*DTIPSQ*DPHI - END IF - END IF - ETA = B / A - ELSE IF( A.LE.ZERO ) THEN - ETA = ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C ) - ELSE - ETA = TWO*B / ( A+SQRT( ABS( A*A-FOUR*B*C ) ) ) - END IF - ELSE -* -* Interpolation using THREE most relevant poles -* - DTIIM = WORK( IIM1 )*DELTA( IIM1 ) - DTIIP = WORK( IIP1 )*DELTA( IIP1 ) - TEMP = RHOINV + PSI + PHI - IF( SWTCH ) THEN - C = TEMP - DTIIM*DPSI - DTIIP*DPHI - ZZ( 1 ) = DTIIM*DTIIM*DPSI - ZZ( 3 ) = DTIIP*DTIIP*DPHI - ELSE - IF( ORGATI ) THEN - TEMP1 = Z( IIM1 ) / DTIIM - TEMP1 = TEMP1*TEMP1 - TEMP2 = ( D( IIM1 )-D( IIP1 ) )* - $ ( D( IIM1 )+D( IIP1 ) )*TEMP1 - C = TEMP - DTIIP*( DPSI+DPHI ) - TEMP2 - ZZ( 1 ) = Z( IIM1 )*Z( IIM1 ) - IF( DPSI.LT.TEMP1 ) THEN - ZZ( 3 ) = DTIIP*DTIIP*DPHI - ELSE - ZZ( 3 ) = DTIIP*DTIIP*( ( DPSI-TEMP1 )+DPHI ) - END IF - ELSE - TEMP1 = Z( IIP1 ) / DTIIP - TEMP1 = TEMP1*TEMP1 - TEMP2 = ( D( IIP1 )-D( IIM1 ) )* - $ ( D( IIM1 )+D( IIP1 ) )*TEMP1 - C = TEMP - DTIIM*( DPSI+DPHI ) - TEMP2 - IF( DPHI.LT.TEMP1 ) THEN - ZZ( 1 ) = DTIIM*DTIIM*DPSI - ELSE - ZZ( 1 ) = DTIIM*DTIIM*( DPSI+( DPHI-TEMP1 ) ) - END IF - ZZ( 3 ) = Z( IIP1 )*Z( IIP1 ) - END IF - END IF - DD( 1 ) = DTIIM - DD( 2 ) = DELTA( II )*WORK( II ) - DD( 3 ) = DTIIP - CALL DLAED6( NITER, ORGATI, C, DD, ZZ, W, ETA, INFO ) -* - IF( INFO.NE.0 ) THEN -* -* If INFO is not 0, i.e., DLAED6 failed, switch -* back to two pole interpolation -* - SWTCH3 = .FALSE. - INFO = 0 - DTIPSQ = WORK( IP1 )*DELTA( IP1 ) - DTISQ = WORK( I )*DELTA( I ) - IF( .NOT.SWTCH ) THEN - IF( ORGATI ) THEN - C = W - DTIPSQ*DW + DELSQ*( Z( I )/DTISQ )**2 - ELSE - C = W - DTISQ*DW - DELSQ*( Z( IP1 )/DTIPSQ )**2 - END IF - ELSE - TEMP = Z( II ) / ( WORK( II )*DELTA( II ) ) - IF( ORGATI ) THEN - DPSI = DPSI + TEMP*TEMP - ELSE - DPHI = DPHI + TEMP*TEMP - END IF - C = W - DTISQ*DPSI - DTIPSQ*DPHI - END IF - A = ( DTIPSQ+DTISQ )*W - DTIPSQ*DTISQ*DW - B = DTIPSQ*DTISQ*W - IF( C.EQ.ZERO ) THEN - IF( A.EQ.ZERO ) THEN - IF( .NOT.SWTCH ) THEN - IF( ORGATI ) THEN - A = Z( I )*Z( I ) + DTIPSQ*DTIPSQ* - $ ( DPSI+DPHI ) - ELSE - A = Z( IP1 )*Z( IP1 ) + - $ DTISQ*DTISQ*( DPSI+DPHI ) - END IF - ELSE - A = DTISQ*DTISQ*DPSI + DTIPSQ*DTIPSQ*DPHI - END IF - END IF - ETA = B / A - ELSE IF( A.LE.ZERO ) THEN - ETA = ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C ) - ELSE - ETA = TWO*B / ( A+SQRT( ABS( A*A-FOUR*B*C ) ) ) - END IF - END IF - END IF -* -* Note, eta should be positive if w is negative, and -* eta should be negative otherwise. However, -* if for some reason caused by roundoff, eta*w > 0, -* we simply use one Newton step instead. This way -* will guarantee eta*w < 0. -* - IF( W*ETA.GE.ZERO ) - $ ETA = -W / DW -* - ETA = ETA / ( SIGMA+SQRT( SIGMA*SIGMA+ETA ) ) - TEMP=TAU+ETA - IF( TEMP.GT.SGUB .OR. TEMP.LT.SGLB ) THEN - IF( W.LT.ZERO ) THEN - ETA = ( SGUB-TAU ) / TWO - ELSE - ETA = ( SGLB-TAU ) / TWO - END IF - IF( GEOMAVG ) THEN - IF( W .LT. ZERO ) THEN - IF( TAU .GT. ZERO ) THEN - ETA = SQRT(SGUB*TAU)-TAU - END IF - ELSE - IF( SGLB .GT. ZERO ) THEN - ETA = SQRT(SGLB*TAU)-TAU - END IF - END IF - END IF - END IF -* - PREW = W -* - TAU = TAU + ETA - SIGMA = SIGMA + ETA -* - DO 200 J = 1, N - WORK( J ) = WORK( J ) + ETA - DELTA( J ) = DELTA( J ) - ETA - 200 CONTINUE -* -* Evaluate PSI and the derivative DPSI -* - DPSI = ZERO - PSI = ZERO - ERRETM = ZERO - DO 210 J = 1, IIM1 - TEMP = Z( J ) / ( WORK( J )*DELTA( J ) ) - PSI = PSI + Z( J )*TEMP - DPSI = DPSI + TEMP*TEMP - ERRETM = ERRETM + PSI - 210 CONTINUE - ERRETM = ABS( ERRETM ) -* -* Evaluate PHI and the derivative DPHI -* - DPHI = ZERO - PHI = ZERO - DO 220 J = N, IIP1, -1 - TEMP = Z( J ) / ( WORK( J )*DELTA( J ) ) - PHI = PHI + Z( J )*TEMP - DPHI = DPHI + TEMP*TEMP - ERRETM = ERRETM + PHI - 220 CONTINUE -* - TAU2 = WORK( II )*DELTA( II ) - TEMP = Z( II ) / TAU2 - DW = DPSI + DPHI + TEMP*TEMP - TEMP = Z( II )*TEMP - W = RHOINV + PHI + PSI + TEMP - ERRETM = EIGHT*( PHI-PSI ) + ERRETM + TWO*RHOINV - $ + THREE*ABS( TEMP ) -* $ + ABS( TAU2 )*DW -* - IF( W*PREW.GT.ZERO .AND. ABS( W ).GT.ABS( PREW ) / TEN ) - $ SWTCH = .NOT.SWTCH -* - 230 CONTINUE -* -* Return with INFO = 1, NITER = MAXIT and not converged -* - INFO = 1 -* - END IF -* - 240 CONTINUE - RETURN -* -* End of DLASD4 -* - END diff --git a/lib/linalg/fortran/dlasd5.f b/lib/linalg/fortran/dlasd5.f deleted file mode 100644 index 645c2fdc3e..0000000000 --- a/lib/linalg/fortran/dlasd5.f +++ /dev/null @@ -1,228 +0,0 @@ -*> \brief \b DLASD5 computes the square root of the i-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix. Used by sbdsdc. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLASD5 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLASD5( I, D, Z, DELTA, RHO, DSIGMA, WORK ) -* -* .. Scalar Arguments .. -* INTEGER I -* DOUBLE PRECISION DSIGMA, RHO -* .. -* .. Array Arguments .. -* DOUBLE PRECISION D( 2 ), DELTA( 2 ), WORK( 2 ), Z( 2 ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> This subroutine computes the square root of the I-th eigenvalue -*> of a positive symmetric rank-one modification of a 2-by-2 diagonal -*> matrix -*> -*> diag( D ) * diag( D ) + RHO * Z * transpose(Z) . -*> -*> The diagonal entries in the array D are assumed to satisfy -*> -*> 0 <= D(i) < D(j) for i < j . -*> -*> We also assume RHO > 0 and that the Euclidean norm of the vector -*> Z is one. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] I -*> \verbatim -*> I is INTEGER -*> The index of the eigenvalue to be computed. I = 1 or I = 2. -*> \endverbatim -*> -*> \param[in] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension ( 2 ) -*> The original eigenvalues. We assume 0 <= D(1) < D(2). -*> \endverbatim -*> -*> \param[in] Z -*> \verbatim -*> Z is DOUBLE PRECISION array, dimension ( 2 ) -*> The components of the updating vector. -*> \endverbatim -*> -*> \param[out] DELTA -*> \verbatim -*> DELTA is DOUBLE PRECISION array, dimension ( 2 ) -*> Contains (D(j) - sigma_I) in its j-th component. -*> The vector DELTA contains the information necessary -*> to construct the eigenvectors. -*> \endverbatim -*> -*> \param[in] RHO -*> \verbatim -*> RHO is DOUBLE PRECISION -*> The scalar in the symmetric updating formula. -*> \endverbatim -*> -*> \param[out] DSIGMA -*> \verbatim -*> DSIGMA is DOUBLE PRECISION -*> The computed sigma_I, the I-th updated eigenvalue. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension ( 2 ) -*> WORK contains (D(j) + sigma_I) in its j-th component. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup OTHERauxiliary -* -*> \par Contributors: -* ================== -*> -*> Ren-Cang Li, Computer Science Division, University of California -*> at Berkeley, USA -*> -* ===================================================================== - SUBROUTINE DLASD5( I, D, Z, DELTA, RHO, DSIGMA, WORK ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER I - DOUBLE PRECISION DSIGMA, RHO -* .. -* .. Array Arguments .. - DOUBLE PRECISION D( 2 ), DELTA( 2 ), WORK( 2 ), Z( 2 ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, ONE, TWO, THREE, FOUR - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0, - $ THREE = 3.0D+0, FOUR = 4.0D+0 ) -* .. -* .. Local Scalars .. - DOUBLE PRECISION B, C, DEL, DELSQ, TAU, W -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, SQRT -* .. -* .. Executable Statements .. -* - DEL = D( 2 ) - D( 1 ) - DELSQ = DEL*( D( 2 )+D( 1 ) ) - IF( I.EQ.1 ) THEN - W = ONE + FOUR*RHO*( Z( 2 )*Z( 2 ) / ( D( 1 )+THREE*D( 2 ) )- - $ Z( 1 )*Z( 1 ) / ( THREE*D( 1 )+D( 2 ) ) ) / DEL - IF( W.GT.ZERO ) THEN - B = DELSQ + RHO*( Z( 1 )*Z( 1 )+Z( 2 )*Z( 2 ) ) - C = RHO*Z( 1 )*Z( 1 )*DELSQ -* -* B > ZERO, always -* -* The following TAU is DSIGMA * DSIGMA - D( 1 ) * D( 1 ) -* - TAU = TWO*C / ( B+SQRT( ABS( B*B-FOUR*C ) ) ) -* -* The following TAU is DSIGMA - D( 1 ) -* - TAU = TAU / ( D( 1 )+SQRT( D( 1 )*D( 1 )+TAU ) ) - DSIGMA = D( 1 ) + TAU - DELTA( 1 ) = -TAU - DELTA( 2 ) = DEL - TAU - WORK( 1 ) = TWO*D( 1 ) + TAU - WORK( 2 ) = ( D( 1 )+TAU ) + D( 2 ) -* DELTA( 1 ) = -Z( 1 ) / TAU -* DELTA( 2 ) = Z( 2 ) / ( DEL-TAU ) - ELSE - B = -DELSQ + RHO*( Z( 1 )*Z( 1 )+Z( 2 )*Z( 2 ) ) - C = RHO*Z( 2 )*Z( 2 )*DELSQ -* -* The following TAU is DSIGMA * DSIGMA - D( 2 ) * D( 2 ) -* - IF( B.GT.ZERO ) THEN - TAU = -TWO*C / ( B+SQRT( B*B+FOUR*C ) ) - ELSE - TAU = ( B-SQRT( B*B+FOUR*C ) ) / TWO - END IF -* -* The following TAU is DSIGMA - D( 2 ) -* - TAU = TAU / ( D( 2 )+SQRT( ABS( D( 2 )*D( 2 )+TAU ) ) ) - DSIGMA = D( 2 ) + TAU - DELTA( 1 ) = -( DEL+TAU ) - DELTA( 2 ) = -TAU - WORK( 1 ) = D( 1 ) + TAU + D( 2 ) - WORK( 2 ) = TWO*D( 2 ) + TAU -* DELTA( 1 ) = -Z( 1 ) / ( DEL+TAU ) -* DELTA( 2 ) = -Z( 2 ) / TAU - END IF -* TEMP = SQRT( DELTA( 1 )*DELTA( 1 )+DELTA( 2 )*DELTA( 2 ) ) -* DELTA( 1 ) = DELTA( 1 ) / TEMP -* DELTA( 2 ) = DELTA( 2 ) / TEMP - ELSE -* -* Now I=2 -* - B = -DELSQ + RHO*( Z( 1 )*Z( 1 )+Z( 2 )*Z( 2 ) ) - C = RHO*Z( 2 )*Z( 2 )*DELSQ -* -* The following TAU is DSIGMA * DSIGMA - D( 2 ) * D( 2 ) -* - IF( B.GT.ZERO ) THEN - TAU = ( B+SQRT( B*B+FOUR*C ) ) / TWO - ELSE - TAU = TWO*C / ( -B+SQRT( B*B+FOUR*C ) ) - END IF -* -* The following TAU is DSIGMA - D( 2 ) -* - TAU = TAU / ( D( 2 )+SQRT( D( 2 )*D( 2 )+TAU ) ) - DSIGMA = D( 2 ) + TAU - DELTA( 1 ) = -( DEL+TAU ) - DELTA( 2 ) = -TAU - WORK( 1 ) = D( 1 ) + TAU + D( 2 ) - WORK( 2 ) = TWO*D( 2 ) + TAU -* DELTA( 1 ) = -Z( 1 ) / ( DEL+TAU ) -* DELTA( 2 ) = -Z( 2 ) / TAU -* TEMP = SQRT( DELTA( 1 )*DELTA( 1 )+DELTA( 2 )*DELTA( 2 ) ) -* DELTA( 1 ) = DELTA( 1 ) / TEMP -* DELTA( 2 ) = DELTA( 2 ) / TEMP - END IF - RETURN -* -* End of DLASD5 -* - END diff --git a/lib/linalg/fortran/dlasd6.f b/lib/linalg/fortran/dlasd6.f deleted file mode 100644 index 51e67588dd..0000000000 --- a/lib/linalg/fortran/dlasd6.f +++ /dev/null @@ -1,440 +0,0 @@ -*> \brief \b DLASD6 computes the SVD of an updated upper bidiagonal matrix obtained by merging two smaller ones by appending a row. Used by sbdsdc. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLASD6 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLASD6( ICOMPQ, NL, NR, SQRE, D, VF, VL, ALPHA, BETA, -* IDXQ, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, -* LDGNUM, POLES, DIFL, DIFR, Z, K, C, S, WORK, -* IWORK, INFO ) -* -* .. Scalar Arguments .. -* INTEGER GIVPTR, ICOMPQ, INFO, K, LDGCOL, LDGNUM, NL, -* $ NR, SQRE -* DOUBLE PRECISION ALPHA, BETA, C, S -* .. -* .. Array Arguments .. -* INTEGER GIVCOL( LDGCOL, * ), IDXQ( * ), IWORK( * ), -* $ PERM( * ) -* DOUBLE PRECISION D( * ), DIFL( * ), DIFR( * ), -* $ GIVNUM( LDGNUM, * ), POLES( LDGNUM, * ), -* $ VF( * ), VL( * ), WORK( * ), Z( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLASD6 computes the SVD of an updated upper bidiagonal matrix B -*> obtained by merging two smaller ones by appending a row. This -*> routine is used only for the problem which requires all singular -*> values and optionally singular vector matrices in factored form. -*> B is an N-by-M matrix with N = NL + NR + 1 and M = N + SQRE. -*> A related subroutine, DLASD1, handles the case in which all singular -*> values and singular vectors of the bidiagonal matrix are desired. -*> -*> DLASD6 computes the SVD as follows: -*> -*> ( D1(in) 0 0 0 ) -*> B = U(in) * ( Z1**T a Z2**T b ) * VT(in) -*> ( 0 0 D2(in) 0 ) -*> -*> = U(out) * ( D(out) 0) * VT(out) -*> -*> where Z**T = (Z1**T a Z2**T b) = u**T VT**T, and u is a vector of dimension M -*> with ALPHA and BETA in the NL+1 and NL+2 th entries and zeros -*> elsewhere; and the entry b is empty if SQRE = 0. -*> -*> The singular values of B can be computed using D1, D2, the first -*> components of all the right singular vectors of the lower block, and -*> the last components of all the right singular vectors of the upper -*> block. These components are stored and updated in VF and VL, -*> respectively, in DLASD6. Hence U and VT are not explicitly -*> referenced. -*> -*> The singular values are stored in D. The algorithm consists of two -*> stages: -*> -*> The first stage consists of deflating the size of the problem -*> when there are multiple singular values or if there is a zero -*> in the Z vector. For each such occurrence the dimension of the -*> secular equation problem is reduced by one. This stage is -*> performed by the routine DLASD7. -*> -*> The second stage consists of calculating the updated -*> singular values. This is done by finding the roots of the -*> secular equation via the routine DLASD4 (as called by DLASD8). -*> This routine also updates VF and VL and computes the distances -*> between the updated singular values and the old singular -*> values. -*> -*> DLASD6 is called from DLASDA. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] ICOMPQ -*> \verbatim -*> ICOMPQ is INTEGER -*> Specifies whether singular vectors are to be computed in -*> factored form: -*> = 0: Compute singular values only. -*> = 1: Compute singular vectors in factored form as well. -*> \endverbatim -*> -*> \param[in] NL -*> \verbatim -*> NL is INTEGER -*> The row dimension of the upper block. NL >= 1. -*> \endverbatim -*> -*> \param[in] NR -*> \verbatim -*> NR is INTEGER -*> The row dimension of the lower block. NR >= 1. -*> \endverbatim -*> -*> \param[in] SQRE -*> \verbatim -*> SQRE is INTEGER -*> = 0: the lower block is an NR-by-NR square matrix. -*> = 1: the lower block is an NR-by-(NR+1) rectangular matrix. -*> -*> The bidiagonal matrix has row dimension N = NL + NR + 1, -*> and column dimension M = N + SQRE. -*> \endverbatim -*> -*> \param[in,out] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension ( NL+NR+1 ). -*> On entry D(1:NL,1:NL) contains the singular values of the -*> upper block, and D(NL+2:N) contains the singular values -*> of the lower block. On exit D(1:N) contains the singular -*> values of the modified matrix. -*> \endverbatim -*> -*> \param[in,out] VF -*> \verbatim -*> VF is DOUBLE PRECISION array, dimension ( M ) -*> On entry, VF(1:NL+1) contains the first components of all -*> right singular vectors of the upper block; and VF(NL+2:M) -*> contains the first components of all right singular vectors -*> of the lower block. On exit, VF contains the first components -*> of all right singular vectors of the bidiagonal matrix. -*> \endverbatim -*> -*> \param[in,out] VL -*> \verbatim -*> VL is DOUBLE PRECISION array, dimension ( M ) -*> On entry, VL(1:NL+1) contains the last components of all -*> right singular vectors of the upper block; and VL(NL+2:M) -*> contains the last components of all right singular vectors of -*> the lower block. On exit, VL contains the last components of -*> all right singular vectors of the bidiagonal matrix. -*> \endverbatim -*> -*> \param[in,out] ALPHA -*> \verbatim -*> ALPHA is DOUBLE PRECISION -*> Contains the diagonal element associated with the added row. -*> \endverbatim -*> -*> \param[in,out] BETA -*> \verbatim -*> BETA is DOUBLE PRECISION -*> Contains the off-diagonal element associated with the added -*> row. -*> \endverbatim -*> -*> \param[in,out] IDXQ -*> \verbatim -*> IDXQ is INTEGER array, dimension ( N ) -*> This contains the permutation which will reintegrate the -*> subproblem just solved back into sorted order, i.e. -*> D( IDXQ( I = 1, N ) ) will be in ascending order. -*> \endverbatim -*> -*> \param[out] PERM -*> \verbatim -*> PERM is INTEGER array, dimension ( N ) -*> The permutations (from deflation and sorting) to be applied -*> to each block. Not referenced if ICOMPQ = 0. -*> \endverbatim -*> -*> \param[out] GIVPTR -*> \verbatim -*> GIVPTR is INTEGER -*> The number of Givens rotations which took place in this -*> subproblem. Not referenced if ICOMPQ = 0. -*> \endverbatim -*> -*> \param[out] GIVCOL -*> \verbatim -*> GIVCOL is INTEGER array, dimension ( LDGCOL, 2 ) -*> Each pair of numbers indicates a pair of columns to take place -*> in a Givens rotation. Not referenced if ICOMPQ = 0. -*> \endverbatim -*> -*> \param[in] LDGCOL -*> \verbatim -*> LDGCOL is INTEGER -*> leading dimension of GIVCOL, must be at least N. -*> \endverbatim -*> -*> \param[out] GIVNUM -*> \verbatim -*> GIVNUM is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) -*> Each number indicates the C or S value to be used in the -*> corresponding Givens rotation. Not referenced if ICOMPQ = 0. -*> \endverbatim -*> -*> \param[in] LDGNUM -*> \verbatim -*> LDGNUM is INTEGER -*> The leading dimension of GIVNUM and POLES, must be at least N. -*> \endverbatim -*> -*> \param[out] POLES -*> \verbatim -*> POLES is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) -*> On exit, POLES(1,*) is an array containing the new singular -*> values obtained from solving the secular equation, and -*> POLES(2,*) is an array containing the poles in the secular -*> equation. Not referenced if ICOMPQ = 0. -*> \endverbatim -*> -*> \param[out] DIFL -*> \verbatim -*> DIFL is DOUBLE PRECISION array, dimension ( N ) -*> On exit, DIFL(I) is the distance between I-th updated -*> (undeflated) singular value and the I-th (undeflated) old -*> singular value. -*> \endverbatim -*> -*> \param[out] DIFR -*> \verbatim -*> DIFR is DOUBLE PRECISION array, -*> dimension ( LDDIFR, 2 ) if ICOMPQ = 1 and -*> dimension ( K ) if ICOMPQ = 0. -*> On exit, DIFR(I,1) = D(I) - DSIGMA(I+1), DIFR(K,1) is not -*> defined and will not be referenced. -*> -*> If ICOMPQ = 1, DIFR(1:K,2) is an array containing the -*> normalizing factors for the right singular vector matrix. -*> -*> See DLASD8 for details on DIFL and DIFR. -*> \endverbatim -*> -*> \param[out] Z -*> \verbatim -*> Z is DOUBLE PRECISION array, dimension ( M ) -*> The first elements of this array contain the components -*> of the deflation-adjusted updating row vector. -*> \endverbatim -*> -*> \param[out] K -*> \verbatim -*> K is INTEGER -*> Contains the dimension of the non-deflated matrix, -*> This is the order of the related secular equation. 1 <= K <=N. -*> \endverbatim -*> -*> \param[out] C -*> \verbatim -*> C is DOUBLE PRECISION -*> C contains garbage if SQRE =0 and the C-value of a Givens -*> rotation related to the right null space if SQRE = 1. -*> \endverbatim -*> -*> \param[out] S -*> \verbatim -*> S is DOUBLE PRECISION -*> S contains garbage if SQRE =0 and the S-value of a Givens -*> rotation related to the right null space if SQRE = 1. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension ( 4 * M ) -*> \endverbatim -*> -*> \param[out] IWORK -*> \verbatim -*> IWORK is INTEGER array, dimension ( 3 * N ) -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit. -*> < 0: if INFO = -i, the i-th argument had an illegal value. -*> > 0: if INFO = 1, a singular value did not converge -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup OTHERauxiliary -* -*> \par Contributors: -* ================== -*> -*> Ming Gu and Huan Ren, Computer Science Division, University of -*> California at Berkeley, USA -*> -* ===================================================================== - SUBROUTINE DLASD6( ICOMPQ, NL, NR, SQRE, D, VF, VL, ALPHA, BETA, - $ IDXQ, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, - $ LDGNUM, POLES, DIFL, DIFR, Z, K, C, S, WORK, - $ IWORK, INFO ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER GIVPTR, ICOMPQ, INFO, K, LDGCOL, LDGNUM, NL, - $ NR, SQRE - DOUBLE PRECISION ALPHA, BETA, C, S -* .. -* .. Array Arguments .. - INTEGER GIVCOL( LDGCOL, * ), IDXQ( * ), IWORK( * ), - $ PERM( * ) - DOUBLE PRECISION D( * ), DIFL( * ), DIFR( * ), - $ GIVNUM( LDGNUM, * ), POLES( LDGNUM, * ), - $ VF( * ), VL( * ), WORK( * ), Z( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE, ZERO - PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) -* .. -* .. Local Scalars .. - INTEGER I, IDX, IDXC, IDXP, ISIGMA, IVFW, IVLW, IW, M, - $ N, N1, N2 - DOUBLE PRECISION ORGNRM -* .. -* .. External Subroutines .. - EXTERNAL DCOPY, DLAMRG, DLASCL, DLASD7, DLASD8, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, MAX -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 - N = NL + NR + 1 - M = N + SQRE -* - IF( ( ICOMPQ.LT.0 ) .OR. ( ICOMPQ.GT.1 ) ) THEN - INFO = -1 - ELSE IF( NL.LT.1 ) THEN - INFO = -2 - ELSE IF( NR.LT.1 ) THEN - INFO = -3 - ELSE IF( ( SQRE.LT.0 ) .OR. ( SQRE.GT.1 ) ) THEN - INFO = -4 - ELSE IF( LDGCOL.LT.N ) THEN - INFO = -14 - ELSE IF( LDGNUM.LT.N ) THEN - INFO = -16 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DLASD6', -INFO ) - RETURN - END IF -* -* The following values are for bookkeeping purposes only. They are -* integer pointers which indicate the portion of the workspace -* used by a particular array in DLASD7 and DLASD8. -* - ISIGMA = 1 - IW = ISIGMA + N - IVFW = IW + M - IVLW = IVFW + M -* - IDX = 1 - IDXC = IDX + N - IDXP = IDXC + N -* -* Scale. -* - ORGNRM = MAX( ABS( ALPHA ), ABS( BETA ) ) - D( NL+1 ) = ZERO - DO 10 I = 1, N - IF( ABS( D( I ) ).GT.ORGNRM ) THEN - ORGNRM = ABS( D( I ) ) - END IF - 10 CONTINUE - CALL DLASCL( 'G', 0, 0, ORGNRM, ONE, N, 1, D, N, INFO ) - ALPHA = ALPHA / ORGNRM - BETA = BETA / ORGNRM -* -* Sort and Deflate singular values. -* - CALL DLASD7( ICOMPQ, NL, NR, SQRE, K, D, Z, WORK( IW ), VF, - $ WORK( IVFW ), VL, WORK( IVLW ), ALPHA, BETA, - $ WORK( ISIGMA ), IWORK( IDX ), IWORK( IDXP ), IDXQ, - $ PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, C, S, - $ INFO ) -* -* Solve Secular Equation, compute DIFL, DIFR, and update VF, VL. -* - CALL DLASD8( ICOMPQ, K, D, Z, VF, VL, DIFL, DIFR, LDGNUM, - $ WORK( ISIGMA ), WORK( IW ), INFO ) -* -* Report the possible convergence failure. -* - IF( INFO.NE.0 ) THEN - RETURN - END IF -* -* Save the poles if ICOMPQ = 1. -* - IF( ICOMPQ.EQ.1 ) THEN - CALL DCOPY( K, D, 1, POLES( 1, 1 ), 1 ) - CALL DCOPY( K, WORK( ISIGMA ), 1, POLES( 1, 2 ), 1 ) - END IF -* -* Unscale. -* - CALL DLASCL( 'G', 0, 0, ONE, ORGNRM, N, 1, D, N, INFO ) -* -* Prepare the IDXQ sorting permutation. -* - N1 = K - N2 = N - K - CALL DLAMRG( N1, N2, D, 1, -1, IDXQ ) -* - RETURN -* -* End of DLASD6 -* - END diff --git a/lib/linalg/fortran/dlasd7.f b/lib/linalg/fortran/dlasd7.f deleted file mode 100644 index ff9ba4c36a..0000000000 --- a/lib/linalg/fortran/dlasd7.f +++ /dev/null @@ -1,577 +0,0 @@ -*> \brief \b DLASD7 merges the two sets of singular values together into a single sorted set. Then it tries to deflate the size of the problem. Used by sbdsdc. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLASD7 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLASD7( ICOMPQ, NL, NR, SQRE, K, D, Z, ZW, VF, VFW, VL, -* VLW, ALPHA, BETA, DSIGMA, IDX, IDXP, IDXQ, -* PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, -* C, S, INFO ) -* -* .. Scalar Arguments .. -* INTEGER GIVPTR, ICOMPQ, INFO, K, LDGCOL, LDGNUM, NL, -* $ NR, SQRE -* DOUBLE PRECISION ALPHA, BETA, C, S -* .. -* .. Array Arguments .. -* INTEGER GIVCOL( LDGCOL, * ), IDX( * ), IDXP( * ), -* $ IDXQ( * ), PERM( * ) -* DOUBLE PRECISION D( * ), DSIGMA( * ), GIVNUM( LDGNUM, * ), -* $ VF( * ), VFW( * ), VL( * ), VLW( * ), Z( * ), -* $ ZW( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLASD7 merges the two sets of singular values together into a single -*> sorted set. Then it tries to deflate the size of the problem. There -*> are two ways in which deflation can occur: when two or more singular -*> values are close together or if there is a tiny entry in the Z -*> vector. For each such occurrence the order of the related -*> secular equation problem is reduced by one. -*> -*> DLASD7 is called from DLASD6. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] ICOMPQ -*> \verbatim -*> ICOMPQ is INTEGER -*> Specifies whether singular vectors are to be computed -*> in compact form, as follows: -*> = 0: Compute singular values only. -*> = 1: Compute singular vectors of upper -*> bidiagonal matrix in compact form. -*> \endverbatim -*> -*> \param[in] NL -*> \verbatim -*> NL is INTEGER -*> The row dimension of the upper block. NL >= 1. -*> \endverbatim -*> -*> \param[in] NR -*> \verbatim -*> NR is INTEGER -*> The row dimension of the lower block. NR >= 1. -*> \endverbatim -*> -*> \param[in] SQRE -*> \verbatim -*> SQRE is INTEGER -*> = 0: the lower block is an NR-by-NR square matrix. -*> = 1: the lower block is an NR-by-(NR+1) rectangular matrix. -*> -*> The bidiagonal matrix has -*> N = NL + NR + 1 rows and -*> M = N + SQRE >= N columns. -*> \endverbatim -*> -*> \param[out] K -*> \verbatim -*> K is INTEGER -*> Contains the dimension of the non-deflated matrix, this is -*> the order of the related secular equation. 1 <= K <=N. -*> \endverbatim -*> -*> \param[in,out] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension ( N ) -*> On entry D contains the singular values of the two submatrices -*> to be combined. On exit D contains the trailing (N-K) updated -*> singular values (those which were deflated) sorted into -*> increasing order. -*> \endverbatim -*> -*> \param[out] Z -*> \verbatim -*> Z is DOUBLE PRECISION array, dimension ( M ) -*> On exit Z contains the updating row vector in the secular -*> equation. -*> \endverbatim -*> -*> \param[out] ZW -*> \verbatim -*> ZW is DOUBLE PRECISION array, dimension ( M ) -*> Workspace for Z. -*> \endverbatim -*> -*> \param[in,out] VF -*> \verbatim -*> VF is DOUBLE PRECISION array, dimension ( M ) -*> On entry, VF(1:NL+1) contains the first components of all -*> right singular vectors of the upper block; and VF(NL+2:M) -*> contains the first components of all right singular vectors -*> of the lower block. On exit, VF contains the first components -*> of all right singular vectors of the bidiagonal matrix. -*> \endverbatim -*> -*> \param[out] VFW -*> \verbatim -*> VFW is DOUBLE PRECISION array, dimension ( M ) -*> Workspace for VF. -*> \endverbatim -*> -*> \param[in,out] VL -*> \verbatim -*> VL is DOUBLE PRECISION array, dimension ( M ) -*> On entry, VL(1:NL+1) contains the last components of all -*> right singular vectors of the upper block; and VL(NL+2:M) -*> contains the last components of all right singular vectors -*> of the lower block. On exit, VL contains the last components -*> of all right singular vectors of the bidiagonal matrix. -*> \endverbatim -*> -*> \param[out] VLW -*> \verbatim -*> VLW is DOUBLE PRECISION array, dimension ( M ) -*> Workspace for VL. -*> \endverbatim -*> -*> \param[in] ALPHA -*> \verbatim -*> ALPHA is DOUBLE PRECISION -*> Contains the diagonal element associated with the added row. -*> \endverbatim -*> -*> \param[in] BETA -*> \verbatim -*> BETA is DOUBLE PRECISION -*> Contains the off-diagonal element associated with the added -*> row. -*> \endverbatim -*> -*> \param[out] DSIGMA -*> \verbatim -*> DSIGMA is DOUBLE PRECISION array, dimension ( N ) -*> Contains a copy of the diagonal elements (K-1 singular values -*> and one zero) in the secular equation. -*> \endverbatim -*> -*> \param[out] IDX -*> \verbatim -*> IDX is INTEGER array, dimension ( N ) -*> This will contain the permutation used to sort the contents of -*> D into ascending order. -*> \endverbatim -*> -*> \param[out] IDXP -*> \verbatim -*> IDXP is INTEGER array, dimension ( N ) -*> This will contain the permutation used to place deflated -*> values of D at the end of the array. On output IDXP(2:K) -*> points to the nondeflated D-values and IDXP(K+1:N) -*> points to the deflated singular values. -*> \endverbatim -*> -*> \param[in] IDXQ -*> \verbatim -*> IDXQ is INTEGER array, dimension ( N ) -*> This contains the permutation which separately sorts the two -*> sub-problems in D into ascending order. Note that entries in -*> the first half of this permutation must first be moved one -*> position backward; and entries in the second half -*> must first have NL+1 added to their values. -*> \endverbatim -*> -*> \param[out] PERM -*> \verbatim -*> PERM is INTEGER array, dimension ( N ) -*> The permutations (from deflation and sorting) to be applied -*> to each singular block. Not referenced if ICOMPQ = 0. -*> \endverbatim -*> -*> \param[out] GIVPTR -*> \verbatim -*> GIVPTR is INTEGER -*> The number of Givens rotations which took place in this -*> subproblem. Not referenced if ICOMPQ = 0. -*> \endverbatim -*> -*> \param[out] GIVCOL -*> \verbatim -*> GIVCOL is INTEGER array, dimension ( LDGCOL, 2 ) -*> Each pair of numbers indicates a pair of columns to take place -*> in a Givens rotation. Not referenced if ICOMPQ = 0. -*> \endverbatim -*> -*> \param[in] LDGCOL -*> \verbatim -*> LDGCOL is INTEGER -*> The leading dimension of GIVCOL, must be at least N. -*> \endverbatim -*> -*> \param[out] GIVNUM -*> \verbatim -*> GIVNUM is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) -*> Each number indicates the C or S value to be used in the -*> corresponding Givens rotation. Not referenced if ICOMPQ = 0. -*> \endverbatim -*> -*> \param[in] LDGNUM -*> \verbatim -*> LDGNUM is INTEGER -*> The leading dimension of GIVNUM, must be at least N. -*> \endverbatim -*> -*> \param[out] C -*> \verbatim -*> C is DOUBLE PRECISION -*> C contains garbage if SQRE =0 and the C-value of a Givens -*> rotation related to the right null space if SQRE = 1. -*> \endverbatim -*> -*> \param[out] S -*> \verbatim -*> S is DOUBLE PRECISION -*> S contains garbage if SQRE =0 and the S-value of a Givens -*> rotation related to the right null space if SQRE = 1. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit. -*> < 0: if INFO = -i, the i-th argument had an illegal value. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup OTHERauxiliary -* -*> \par Contributors: -* ================== -*> -*> Ming Gu and Huan Ren, Computer Science Division, University of -*> California at Berkeley, USA -*> -* ===================================================================== - SUBROUTINE DLASD7( ICOMPQ, NL, NR, SQRE, K, D, Z, ZW, VF, VFW, VL, - $ VLW, ALPHA, BETA, DSIGMA, IDX, IDXP, IDXQ, - $ PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, - $ C, S, INFO ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER GIVPTR, ICOMPQ, INFO, K, LDGCOL, LDGNUM, NL, - $ NR, SQRE - DOUBLE PRECISION ALPHA, BETA, C, S -* .. -* .. Array Arguments .. - INTEGER GIVCOL( LDGCOL, * ), IDX( * ), IDXP( * ), - $ IDXQ( * ), PERM( * ) - DOUBLE PRECISION D( * ), DSIGMA( * ), GIVNUM( LDGNUM, * ), - $ VF( * ), VFW( * ), VL( * ), VLW( * ), Z( * ), - $ ZW( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, ONE, TWO, EIGHT - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0, - $ EIGHT = 8.0D+0 ) -* .. -* .. Local Scalars .. -* - INTEGER I, IDXI, IDXJ, IDXJP, J, JP, JPREV, K2, M, N, - $ NLP1, NLP2 - DOUBLE PRECISION EPS, HLFTOL, TAU, TOL, Z1 -* .. -* .. External Subroutines .. - EXTERNAL DCOPY, DLAMRG, DROT, XERBLA -* .. -* .. External Functions .. - DOUBLE PRECISION DLAMCH, DLAPY2 - EXTERNAL DLAMCH, DLAPY2 -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, MAX -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 - N = NL + NR + 1 - M = N + SQRE -* - IF( ( ICOMPQ.LT.0 ) .OR. ( ICOMPQ.GT.1 ) ) THEN - INFO = -1 - ELSE IF( NL.LT.1 ) THEN - INFO = -2 - ELSE IF( NR.LT.1 ) THEN - INFO = -3 - ELSE IF( ( SQRE.LT.0 ) .OR. ( SQRE.GT.1 ) ) THEN - INFO = -4 - ELSE IF( LDGCOL.LT.N ) THEN - INFO = -22 - ELSE IF( LDGNUM.LT.N ) THEN - INFO = -24 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DLASD7', -INFO ) - RETURN - END IF -* - NLP1 = NL + 1 - NLP2 = NL + 2 - IF( ICOMPQ.EQ.1 ) THEN - GIVPTR = 0 - END IF -* -* Generate the first part of the vector Z and move the singular -* values in the first part of D one position backward. -* - Z1 = ALPHA*VL( NLP1 ) - VL( NLP1 ) = ZERO - TAU = VF( NLP1 ) - DO 10 I = NL, 1, -1 - Z( I+1 ) = ALPHA*VL( I ) - VL( I ) = ZERO - VF( I+1 ) = VF( I ) - D( I+1 ) = D( I ) - IDXQ( I+1 ) = IDXQ( I ) + 1 - 10 CONTINUE - VF( 1 ) = TAU -* -* Generate the second part of the vector Z. -* - DO 20 I = NLP2, M - Z( I ) = BETA*VF( I ) - VF( I ) = ZERO - 20 CONTINUE -* -* Sort the singular values into increasing order -* - DO 30 I = NLP2, N - IDXQ( I ) = IDXQ( I ) + NLP1 - 30 CONTINUE -* -* DSIGMA, IDXC, IDXC, and ZW are used as storage space. -* - DO 40 I = 2, N - DSIGMA( I ) = D( IDXQ( I ) ) - ZW( I ) = Z( IDXQ( I ) ) - VFW( I ) = VF( IDXQ( I ) ) - VLW( I ) = VL( IDXQ( I ) ) - 40 CONTINUE -* - CALL DLAMRG( NL, NR, DSIGMA( 2 ), 1, 1, IDX( 2 ) ) -* - DO 50 I = 2, N - IDXI = 1 + IDX( I ) - D( I ) = DSIGMA( IDXI ) - Z( I ) = ZW( IDXI ) - VF( I ) = VFW( IDXI ) - VL( I ) = VLW( IDXI ) - 50 CONTINUE -* -* Calculate the allowable deflation tolerance -* - EPS = DLAMCH( 'Epsilon' ) - TOL = MAX( ABS( ALPHA ), ABS( BETA ) ) - TOL = EIGHT*EIGHT*EPS*MAX( ABS( D( N ) ), TOL ) -* -* There are 2 kinds of deflation -- first a value in the z-vector -* is small, second two (or more) singular values are very close -* together (their difference is small). -* -* If the value in the z-vector is small, we simply permute the -* array so that the corresponding singular value is moved to the -* end. -* -* If two values in the D-vector are close, we perform a two-sided -* rotation designed to make one of the corresponding z-vector -* entries zero, and then permute the array so that the deflated -* singular value is moved to the end. -* -* If there are multiple singular values then the problem deflates. -* Here the number of equal singular values are found. As each equal -* singular value is found, an elementary reflector is computed to -* rotate the corresponding singular subspace so that the -* corresponding components of Z are zero in this new basis. -* - K = 1 - K2 = N + 1 - DO 60 J = 2, N - IF( ABS( Z( J ) ).LE.TOL ) THEN -* -* Deflate due to small z component. -* - K2 = K2 - 1 - IDXP( K2 ) = J - IF( J.EQ.N ) - $ GO TO 100 - ELSE - JPREV = J - GO TO 70 - END IF - 60 CONTINUE - 70 CONTINUE - J = JPREV - 80 CONTINUE - J = J + 1 - IF( J.GT.N ) - $ GO TO 90 - IF( ABS( Z( J ) ).LE.TOL ) THEN -* -* Deflate due to small z component. -* - K2 = K2 - 1 - IDXP( K2 ) = J - ELSE -* -* Check if singular values are close enough to allow deflation. -* - IF( ABS( D( J )-D( JPREV ) ).LE.TOL ) THEN -* -* Deflation is possible. -* - S = Z( JPREV ) - C = Z( J ) -* -* Find sqrt(a**2+b**2) without overflow or -* destructive underflow. -* - TAU = DLAPY2( C, S ) - Z( J ) = TAU - Z( JPREV ) = ZERO - C = C / TAU - S = -S / TAU -* -* Record the appropriate Givens rotation -* - IF( ICOMPQ.EQ.1 ) THEN - GIVPTR = GIVPTR + 1 - IDXJP = IDXQ( IDX( JPREV )+1 ) - IDXJ = IDXQ( IDX( J )+1 ) - IF( IDXJP.LE.NLP1 ) THEN - IDXJP = IDXJP - 1 - END IF - IF( IDXJ.LE.NLP1 ) THEN - IDXJ = IDXJ - 1 - END IF - GIVCOL( GIVPTR, 2 ) = IDXJP - GIVCOL( GIVPTR, 1 ) = IDXJ - GIVNUM( GIVPTR, 2 ) = C - GIVNUM( GIVPTR, 1 ) = S - END IF - CALL DROT( 1, VF( JPREV ), 1, VF( J ), 1, C, S ) - CALL DROT( 1, VL( JPREV ), 1, VL( J ), 1, C, S ) - K2 = K2 - 1 - IDXP( K2 ) = JPREV - JPREV = J - ELSE - K = K + 1 - ZW( K ) = Z( JPREV ) - DSIGMA( K ) = D( JPREV ) - IDXP( K ) = JPREV - JPREV = J - END IF - END IF - GO TO 80 - 90 CONTINUE -* -* Record the last singular value. -* - K = K + 1 - ZW( K ) = Z( JPREV ) - DSIGMA( K ) = D( JPREV ) - IDXP( K ) = JPREV -* - 100 CONTINUE -* -* Sort the singular values into DSIGMA. The singular values which -* were not deflated go into the first K slots of DSIGMA, except -* that DSIGMA(1) is treated separately. -* - DO 110 J = 2, N - JP = IDXP( J ) - DSIGMA( J ) = D( JP ) - VFW( J ) = VF( JP ) - VLW( J ) = VL( JP ) - 110 CONTINUE - IF( ICOMPQ.EQ.1 ) THEN - DO 120 J = 2, N - JP = IDXP( J ) - PERM( J ) = IDXQ( IDX( JP )+1 ) - IF( PERM( J ).LE.NLP1 ) THEN - PERM( J ) = PERM( J ) - 1 - END IF - 120 CONTINUE - END IF -* -* The deflated singular values go back into the last N - K slots of -* D. -* - CALL DCOPY( N-K, DSIGMA( K+1 ), 1, D( K+1 ), 1 ) -* -* Determine DSIGMA(1), DSIGMA(2), Z(1), VF(1), VL(1), VF(M), and -* VL(M). -* - DSIGMA( 1 ) = ZERO - HLFTOL = TOL / TWO - IF( ABS( DSIGMA( 2 ) ).LE.HLFTOL ) - $ DSIGMA( 2 ) = HLFTOL - IF( M.GT.N ) THEN - Z( 1 ) = DLAPY2( Z1, Z( M ) ) - IF( Z( 1 ).LE.TOL ) THEN - C = ONE - S = ZERO - Z( 1 ) = TOL - ELSE - C = Z1 / Z( 1 ) - S = -Z( M ) / Z( 1 ) - END IF - CALL DROT( 1, VF( M ), 1, VF( 1 ), 1, C, S ) - CALL DROT( 1, VL( M ), 1, VL( 1 ), 1, C, S ) - ELSE - IF( ABS( Z1 ).LE.TOL ) THEN - Z( 1 ) = TOL - ELSE - Z( 1 ) = Z1 - END IF - END IF -* -* Restore Z, VF, and VL. -* - CALL DCOPY( K-1, ZW( 2 ), 1, Z( 2 ), 1 ) - CALL DCOPY( N-1, VFW( 2 ), 1, VF( 2 ), 1 ) - CALL DCOPY( N-1, VLW( 2 ), 1, VL( 2 ), 1 ) -* - RETURN -* -* End of DLASD7 -* - END diff --git a/lib/linalg/fortran/dlasd8.f b/lib/linalg/fortran/dlasd8.f deleted file mode 100644 index a769bdb22e..0000000000 --- a/lib/linalg/fortran/dlasd8.f +++ /dev/null @@ -1,339 +0,0 @@ -*> \brief \b DLASD8 finds the square roots of the roots of the secular equation, and stores, for each element in D, the distance to its two nearest poles. Used by sbdsdc. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLASD8 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLASD8( ICOMPQ, K, D, Z, VF, VL, DIFL, DIFR, LDDIFR, -* DSIGMA, WORK, INFO ) -* -* .. Scalar Arguments .. -* INTEGER ICOMPQ, INFO, K, LDDIFR -* .. -* .. Array Arguments .. -* DOUBLE PRECISION D( * ), DIFL( * ), DIFR( LDDIFR, * ), -* $ DSIGMA( * ), VF( * ), VL( * ), WORK( * ), -* $ Z( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLASD8 finds the square roots of the roots of the secular equation, -*> as defined by the values in DSIGMA and Z. It makes the appropriate -*> calls to DLASD4, and stores, for each element in D, the distance -*> to its two nearest poles (elements in DSIGMA). It also updates -*> the arrays VF and VL, the first and last components of all the -*> right singular vectors of the original bidiagonal matrix. -*> -*> DLASD8 is called from DLASD6. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] ICOMPQ -*> \verbatim -*> ICOMPQ is INTEGER -*> Specifies whether singular vectors are to be computed in -*> factored form in the calling routine: -*> = 0: Compute singular values only. -*> = 1: Compute singular vectors in factored form as well. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> The number of terms in the rational function to be solved -*> by DLASD4. K >= 1. -*> \endverbatim -*> -*> \param[out] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension ( K ) -*> On output, D contains the updated singular values. -*> \endverbatim -*> -*> \param[in,out] Z -*> \verbatim -*> Z is DOUBLE PRECISION array, dimension ( K ) -*> On entry, the first K elements of this array contain the -*> components of the deflation-adjusted updating row vector. -*> On exit, Z is updated. -*> \endverbatim -*> -*> \param[in,out] VF -*> \verbatim -*> VF is DOUBLE PRECISION array, dimension ( K ) -*> On entry, VF contains information passed through DBEDE8. -*> On exit, VF contains the first K components of the first -*> components of all right singular vectors of the bidiagonal -*> matrix. -*> \endverbatim -*> -*> \param[in,out] VL -*> \verbatim -*> VL is DOUBLE PRECISION array, dimension ( K ) -*> On entry, VL contains information passed through DBEDE8. -*> On exit, VL contains the first K components of the last -*> components of all right singular vectors of the bidiagonal -*> matrix. -*> \endverbatim -*> -*> \param[out] DIFL -*> \verbatim -*> DIFL is DOUBLE PRECISION array, dimension ( K ) -*> On exit, DIFL(I) = D(I) - DSIGMA(I). -*> \endverbatim -*> -*> \param[out] DIFR -*> \verbatim -*> DIFR is DOUBLE PRECISION array, -*> dimension ( LDDIFR, 2 ) if ICOMPQ = 1 and -*> dimension ( K ) if ICOMPQ = 0. -*> On exit, DIFR(I,1) = D(I) - DSIGMA(I+1), DIFR(K,1) is not -*> defined and will not be referenced. -*> -*> If ICOMPQ = 1, DIFR(1:K,2) is an array containing the -*> normalizing factors for the right singular vector matrix. -*> \endverbatim -*> -*> \param[in] LDDIFR -*> \verbatim -*> LDDIFR is INTEGER -*> The leading dimension of DIFR, must be at least K. -*> \endverbatim -*> -*> \param[in,out] DSIGMA -*> \verbatim -*> DSIGMA is DOUBLE PRECISION array, dimension ( K ) -*> On entry, the first K elements of this array contain the old -*> roots of the deflated updating problem. These are the poles -*> of the secular equation. -*> On exit, the elements of DSIGMA may be very slightly altered -*> in value. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (3*K) -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit. -*> < 0: if INFO = -i, the i-th argument had an illegal value. -*> > 0: if INFO = 1, a singular value did not converge -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup OTHERauxiliary -* -*> \par Contributors: -* ================== -*> -*> Ming Gu and Huan Ren, Computer Science Division, University of -*> California at Berkeley, USA -*> -* ===================================================================== - SUBROUTINE DLASD8( ICOMPQ, K, D, Z, VF, VL, DIFL, DIFR, LDDIFR, - $ DSIGMA, WORK, INFO ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER ICOMPQ, INFO, K, LDDIFR -* .. -* .. Array Arguments .. - DOUBLE PRECISION D( * ), DIFL( * ), DIFR( LDDIFR, * ), - $ DSIGMA( * ), VF( * ), VL( * ), WORK( * ), - $ Z( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE - PARAMETER ( ONE = 1.0D+0 ) -* .. -* .. Local Scalars .. - INTEGER I, IWK1, IWK2, IWK2I, IWK3, IWK3I, J - DOUBLE PRECISION DIFLJ, DIFRJ, DJ, DSIGJ, DSIGJP, RHO, TEMP -* .. -* .. External Subroutines .. - EXTERNAL DCOPY, DLASCL, DLASD4, DLASET, XERBLA -* .. -* .. External Functions .. - DOUBLE PRECISION DDOT, DLAMC3, DNRM2 - EXTERNAL DDOT, DLAMC3, DNRM2 -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, SIGN, SQRT -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 -* - IF( ( ICOMPQ.LT.0 ) .OR. ( ICOMPQ.GT.1 ) ) THEN - INFO = -1 - ELSE IF( K.LT.1 ) THEN - INFO = -2 - ELSE IF( LDDIFR.LT.K ) THEN - INFO = -9 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DLASD8', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( K.EQ.1 ) THEN - D( 1 ) = ABS( Z( 1 ) ) - DIFL( 1 ) = D( 1 ) - IF( ICOMPQ.EQ.1 ) THEN - DIFL( 2 ) = ONE - DIFR( 1, 2 ) = ONE - END IF - RETURN - END IF -* -* Modify values DSIGMA(i) to make sure all DSIGMA(i)-DSIGMA(j) can -* be computed with high relative accuracy (barring over/underflow). -* This is a problem on machines without a guard digit in -* add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2). -* The following code replaces DSIGMA(I) by 2*DSIGMA(I)-DSIGMA(I), -* which on any of these machines zeros out the bottommost -* bit of DSIGMA(I) if it is 1; this makes the subsequent -* subtractions DSIGMA(I)-DSIGMA(J) unproblematic when cancellation -* occurs. On binary machines with a guard digit (almost all -* machines) it does not change DSIGMA(I) at all. On hexadecimal -* and decimal machines with a guard digit, it slightly -* changes the bottommost bits of DSIGMA(I). It does not account -* for hexadecimal or decimal machines without guard digits -* (we know of none). We use a subroutine call to compute -* 2*DLAMBDA(I) to prevent optimizing compilers from eliminating -* this code. -* - DO 10 I = 1, K - DSIGMA( I ) = DLAMC3( DSIGMA( I ), DSIGMA( I ) ) - DSIGMA( I ) - 10 CONTINUE -* -* Book keeping. -* - IWK1 = 1 - IWK2 = IWK1 + K - IWK3 = IWK2 + K - IWK2I = IWK2 - 1 - IWK3I = IWK3 - 1 -* -* Normalize Z. -* - RHO = DNRM2( K, Z, 1 ) - CALL DLASCL( 'G', 0, 0, RHO, ONE, K, 1, Z, K, INFO ) - RHO = RHO*RHO -* -* Initialize WORK(IWK3). -* - CALL DLASET( 'A', K, 1, ONE, ONE, WORK( IWK3 ), K ) -* -* Compute the updated singular values, the arrays DIFL, DIFR, -* and the updated Z. -* - DO 40 J = 1, K - CALL DLASD4( K, J, DSIGMA, Z, WORK( IWK1 ), RHO, D( J ), - $ WORK( IWK2 ), INFO ) -* -* If the root finder fails, report the convergence failure. -* - IF( INFO.NE.0 ) THEN - RETURN - END IF - WORK( IWK3I+J ) = WORK( IWK3I+J )*WORK( J )*WORK( IWK2I+J ) - DIFL( J ) = -WORK( J ) - DIFR( J, 1 ) = -WORK( J+1 ) - DO 20 I = 1, J - 1 - WORK( IWK3I+I ) = WORK( IWK3I+I )*WORK( I )* - $ WORK( IWK2I+I ) / ( DSIGMA( I )- - $ DSIGMA( J ) ) / ( DSIGMA( I )+ - $ DSIGMA( J ) ) - 20 CONTINUE - DO 30 I = J + 1, K - WORK( IWK3I+I ) = WORK( IWK3I+I )*WORK( I )* - $ WORK( IWK2I+I ) / ( DSIGMA( I )- - $ DSIGMA( J ) ) / ( DSIGMA( I )+ - $ DSIGMA( J ) ) - 30 CONTINUE - 40 CONTINUE -* -* Compute updated Z. -* - DO 50 I = 1, K - Z( I ) = SIGN( SQRT( ABS( WORK( IWK3I+I ) ) ), Z( I ) ) - 50 CONTINUE -* -* Update VF and VL. -* - DO 80 J = 1, K - DIFLJ = DIFL( J ) - DJ = D( J ) - DSIGJ = -DSIGMA( J ) - IF( J.LT.K ) THEN - DIFRJ = -DIFR( J, 1 ) - DSIGJP = -DSIGMA( J+1 ) - END IF - WORK( J ) = -Z( J ) / DIFLJ / ( DSIGMA( J )+DJ ) - DO 60 I = 1, J - 1 - WORK( I ) = Z( I ) / ( DLAMC3( DSIGMA( I ), DSIGJ )-DIFLJ ) - $ / ( DSIGMA( I )+DJ ) - 60 CONTINUE - DO 70 I = J + 1, K - WORK( I ) = Z( I ) / ( DLAMC3( DSIGMA( I ), DSIGJP )+DIFRJ ) - $ / ( DSIGMA( I )+DJ ) - 70 CONTINUE - TEMP = DNRM2( K, WORK, 1 ) - WORK( IWK2I+J ) = DDOT( K, WORK, 1, VF, 1 ) / TEMP - WORK( IWK3I+J ) = DDOT( K, WORK, 1, VL, 1 ) / TEMP - IF( ICOMPQ.EQ.1 ) THEN - DIFR( J, 2 ) = TEMP - END IF - 80 CONTINUE -* - CALL DCOPY( K, WORK( IWK2 ), 1, VF, 1 ) - CALL DCOPY( K, WORK( IWK3 ), 1, VL, 1 ) -* - RETURN -* -* End of DLASD8 -* - END - diff --git a/lib/linalg/fortran/dlasda.f b/lib/linalg/fortran/dlasda.f deleted file mode 100644 index 3e169a4edb..0000000000 --- a/lib/linalg/fortran/dlasda.f +++ /dev/null @@ -1,511 +0,0 @@ -*> \brief \b DLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLASDA + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLASDA( ICOMPQ, SMLSIZ, N, SQRE, D, E, U, LDU, VT, K, -* DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, -* PERM, GIVNUM, C, S, WORK, IWORK, INFO ) -* -* .. Scalar Arguments .. -* INTEGER ICOMPQ, INFO, LDGCOL, LDU, N, SMLSIZ, SQRE -* .. -* .. Array Arguments .. -* INTEGER GIVCOL( LDGCOL, * ), GIVPTR( * ), IWORK( * ), -* $ K( * ), PERM( LDGCOL, * ) -* DOUBLE PRECISION C( * ), D( * ), DIFL( LDU, * ), DIFR( LDU, * ), -* $ E( * ), GIVNUM( LDU, * ), POLES( LDU, * ), -* $ S( * ), U( LDU, * ), VT( LDU, * ), WORK( * ), -* $ Z( LDU, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> Using a divide and conquer approach, DLASDA computes the singular -*> value decomposition (SVD) of a real upper bidiagonal N-by-M matrix -*> B with diagonal D and offdiagonal E, where M = N + SQRE. The -*> algorithm computes the singular values in the SVD B = U * S * VT. -*> The orthogonal matrices U and VT are optionally computed in -*> compact form. -*> -*> A related subroutine, DLASD0, computes the singular values and -*> the singular vectors in explicit form. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] ICOMPQ -*> \verbatim -*> ICOMPQ is INTEGER -*> Specifies whether singular vectors are to be computed -*> in compact form, as follows -*> = 0: Compute singular values only. -*> = 1: Compute singular vectors of upper bidiagonal -*> matrix in compact form. -*> \endverbatim -*> -*> \param[in] SMLSIZ -*> \verbatim -*> SMLSIZ is INTEGER -*> The maximum size of the subproblems at the bottom of the -*> computation tree. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The row dimension of the upper bidiagonal matrix. This is -*> also the dimension of the main diagonal array D. -*> \endverbatim -*> -*> \param[in] SQRE -*> \verbatim -*> SQRE is INTEGER -*> Specifies the column dimension of the bidiagonal matrix. -*> = 0: The bidiagonal matrix has column dimension M = N; -*> = 1: The bidiagonal matrix has column dimension M = N + 1. -*> \endverbatim -*> -*> \param[in,out] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension ( N ) -*> On entry D contains the main diagonal of the bidiagonal -*> matrix. On exit D, if INFO = 0, contains its singular values. -*> \endverbatim -*> -*> \param[in] E -*> \verbatim -*> E is DOUBLE PRECISION array, dimension ( M-1 ) -*> Contains the subdiagonal entries of the bidiagonal matrix. -*> On exit, E has been destroyed. -*> \endverbatim -*> -*> \param[out] U -*> \verbatim -*> U is DOUBLE PRECISION array, -*> dimension ( LDU, SMLSIZ ) if ICOMPQ = 1, and not referenced -*> if ICOMPQ = 0. If ICOMPQ = 1, on exit, U contains the left -*> singular vector matrices of all subproblems at the bottom -*> level. -*> \endverbatim -*> -*> \param[in] LDU -*> \verbatim -*> LDU is INTEGER, LDU = > N. -*> The leading dimension of arrays U, VT, DIFL, DIFR, POLES, -*> GIVNUM, and Z. -*> \endverbatim -*> -*> \param[out] VT -*> \verbatim -*> VT is DOUBLE PRECISION array, -*> dimension ( LDU, SMLSIZ+1 ) if ICOMPQ = 1, and not referenced -*> if ICOMPQ = 0. If ICOMPQ = 1, on exit, VT**T contains the right -*> singular vector matrices of all subproblems at the bottom -*> level. -*> \endverbatim -*> -*> \param[out] K -*> \verbatim -*> K is INTEGER array, -*> dimension ( N ) if ICOMPQ = 1 and dimension 1 if ICOMPQ = 0. -*> If ICOMPQ = 1, on exit, K(I) is the dimension of the I-th -*> secular equation on the computation tree. -*> \endverbatim -*> -*> \param[out] DIFL -*> \verbatim -*> DIFL is DOUBLE PRECISION array, dimension ( LDU, NLVL ), -*> where NLVL = floor(log_2 (N/SMLSIZ))). -*> \endverbatim -*> -*> \param[out] DIFR -*> \verbatim -*> DIFR is DOUBLE PRECISION array, -*> dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1 and -*> dimension ( N ) if ICOMPQ = 0. -*> If ICOMPQ = 1, on exit, DIFL(1:N, I) and DIFR(1:N, 2 * I - 1) -*> record distances between singular values on the I-th -*> level and singular values on the (I -1)-th level, and -*> DIFR(1:N, 2 * I ) contains the normalizing factors for -*> the right singular vector matrix. See DLASD8 for details. -*> \endverbatim -*> -*> \param[out] Z -*> \verbatim -*> Z is DOUBLE PRECISION array, -*> dimension ( LDU, NLVL ) if ICOMPQ = 1 and -*> dimension ( N ) if ICOMPQ = 0. -*> The first K elements of Z(1, I) contain the components of -*> the deflation-adjusted updating row vector for subproblems -*> on the I-th level. -*> \endverbatim -*> -*> \param[out] POLES -*> \verbatim -*> POLES is DOUBLE PRECISION array, -*> dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not referenced -*> if ICOMPQ = 0. If ICOMPQ = 1, on exit, POLES(1, 2*I - 1) and -*> POLES(1, 2*I) contain the new and old singular values -*> involved in the secular equations on the I-th level. -*> \endverbatim -*> -*> \param[out] GIVPTR -*> \verbatim -*> GIVPTR is INTEGER array, -*> dimension ( N ) if ICOMPQ = 1, and not referenced if -*> ICOMPQ = 0. If ICOMPQ = 1, on exit, GIVPTR( I ) records -*> the number of Givens rotations performed on the I-th -*> problem on the computation tree. -*> \endverbatim -*> -*> \param[out] GIVCOL -*> \verbatim -*> GIVCOL is INTEGER array, -*> dimension ( LDGCOL, 2 * NLVL ) if ICOMPQ = 1, and not -*> referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, -*> GIVCOL(1, 2 *I - 1) and GIVCOL(1, 2 *I) record the locations -*> of Givens rotations performed on the I-th level on the -*> computation tree. -*> \endverbatim -*> -*> \param[in] LDGCOL -*> \verbatim -*> LDGCOL is INTEGER, LDGCOL = > N. -*> The leading dimension of arrays GIVCOL and PERM. -*> \endverbatim -*> -*> \param[out] PERM -*> \verbatim -*> PERM is INTEGER array, -*> dimension ( LDGCOL, NLVL ) if ICOMPQ = 1, and not referenced -*> if ICOMPQ = 0. If ICOMPQ = 1, on exit, PERM(1, I) records -*> permutations done on the I-th level of the computation tree. -*> \endverbatim -*> -*> \param[out] GIVNUM -*> \verbatim -*> GIVNUM is DOUBLE PRECISION array, -*> dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not -*> referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, -*> GIVNUM(1, 2 *I - 1) and GIVNUM(1, 2 *I) record the C- and S- -*> values of Givens rotations performed on the I-th level on -*> the computation tree. -*> \endverbatim -*> -*> \param[out] C -*> \verbatim -*> C is DOUBLE PRECISION array, -*> dimension ( N ) if ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. -*> If ICOMPQ = 1 and the I-th subproblem is not square, on exit, -*> C( I ) contains the C-value of a Givens rotation related to -*> the right null space of the I-th subproblem. -*> \endverbatim -*> -*> \param[out] S -*> \verbatim -*> S is DOUBLE PRECISION array, dimension ( N ) if -*> ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1 -*> and the I-th subproblem is not square, on exit, S( I ) -*> contains the S-value of a Givens rotation related to -*> the right null space of the I-th subproblem. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension -*> (6 * N + (SMLSIZ + 1)*(SMLSIZ + 1)). -*> \endverbatim -*> -*> \param[out] IWORK -*> \verbatim -*> IWORK is INTEGER array, dimension (7*N) -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit. -*> < 0: if INFO = -i, the i-th argument had an illegal value. -*> > 0: if INFO = 1, a singular value did not converge -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup OTHERauxiliary -* -*> \par Contributors: -* ================== -*> -*> Ming Gu and Huan Ren, Computer Science Division, University of -*> California at Berkeley, USA -*> -* ===================================================================== - SUBROUTINE DLASDA( ICOMPQ, SMLSIZ, N, SQRE, D, E, U, LDU, VT, K, - $ DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, - $ PERM, GIVNUM, C, S, WORK, IWORK, INFO ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER ICOMPQ, INFO, LDGCOL, LDU, N, SMLSIZ, SQRE -* .. -* .. Array Arguments .. - INTEGER GIVCOL( LDGCOL, * ), GIVPTR( * ), IWORK( * ), - $ K( * ), PERM( LDGCOL, * ) - DOUBLE PRECISION C( * ), D( * ), DIFL( LDU, * ), DIFR( LDU, * ), - $ E( * ), GIVNUM( LDU, * ), POLES( LDU, * ), - $ S( * ), U( LDU, * ), VT( LDU, * ), WORK( * ), - $ Z( LDU, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) -* .. -* .. Local Scalars .. - INTEGER I, I1, IC, IDXQ, IDXQI, IM1, INODE, ITEMP, IWK, - $ J, LF, LL, LVL, LVL2, M, NCC, ND, NDB1, NDIML, - $ NDIMR, NL, NLF, NLP1, NLVL, NR, NRF, NRP1, NRU, - $ NWORK1, NWORK2, SMLSZP, SQREI, VF, VFI, VL, VLI - DOUBLE PRECISION ALPHA, BETA -* .. -* .. External Subroutines .. - EXTERNAL DCOPY, DLASD6, DLASDQ, DLASDT, DLASET, XERBLA -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 -* - IF( ( ICOMPQ.LT.0 ) .OR. ( ICOMPQ.GT.1 ) ) THEN - INFO = -1 - ELSE IF( SMLSIZ.LT.3 ) THEN - INFO = -2 - ELSE IF( N.LT.0 ) THEN - INFO = -3 - ELSE IF( ( SQRE.LT.0 ) .OR. ( SQRE.GT.1 ) ) THEN - INFO = -4 - ELSE IF( LDU.LT.( N+SQRE ) ) THEN - INFO = -8 - ELSE IF( LDGCOL.LT.N ) THEN - INFO = -17 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DLASDA', -INFO ) - RETURN - END IF -* - M = N + SQRE -* -* If the input matrix is too small, call DLASDQ to find the SVD. -* - IF( N.LE.SMLSIZ ) THEN - IF( ICOMPQ.EQ.0 ) THEN - CALL DLASDQ( 'U', SQRE, N, 0, 0, 0, D, E, VT, LDU, U, LDU, - $ U, LDU, WORK, INFO ) - ELSE - CALL DLASDQ( 'U', SQRE, N, M, N, 0, D, E, VT, LDU, U, LDU, - $ U, LDU, WORK, INFO ) - END IF - RETURN - END IF -* -* Book-keeping and set up the computation tree. -* - INODE = 1 - NDIML = INODE + N - NDIMR = NDIML + N - IDXQ = NDIMR + N - IWK = IDXQ + N -* - NCC = 0 - NRU = 0 -* - SMLSZP = SMLSIZ + 1 - VF = 1 - VL = VF + M - NWORK1 = VL + M - NWORK2 = NWORK1 + SMLSZP*SMLSZP -* - CALL DLASDT( N, NLVL, ND, IWORK( INODE ), IWORK( NDIML ), - $ IWORK( NDIMR ), SMLSIZ ) -* -* for the nodes on bottom level of the tree, solve -* their subproblems by DLASDQ. -* - NDB1 = ( ND+1 ) / 2 - DO 30 I = NDB1, ND -* -* IC : center row of each node -* NL : number of rows of left subproblem -* NR : number of rows of right subproblem -* NLF: starting row of the left subproblem -* NRF: starting row of the right subproblem -* - I1 = I - 1 - IC = IWORK( INODE+I1 ) - NL = IWORK( NDIML+I1 ) - NLP1 = NL + 1 - NR = IWORK( NDIMR+I1 ) - NLF = IC - NL - NRF = IC + 1 - IDXQI = IDXQ + NLF - 2 - VFI = VF + NLF - 1 - VLI = VL + NLF - 1 - SQREI = 1 - IF( ICOMPQ.EQ.0 ) THEN - CALL DLASET( 'A', NLP1, NLP1, ZERO, ONE, WORK( NWORK1 ), - $ SMLSZP ) - CALL DLASDQ( 'U', SQREI, NL, NLP1, NRU, NCC, D( NLF ), - $ E( NLF ), WORK( NWORK1 ), SMLSZP, - $ WORK( NWORK2 ), NL, WORK( NWORK2 ), NL, - $ WORK( NWORK2 ), INFO ) - ITEMP = NWORK1 + NL*SMLSZP - CALL DCOPY( NLP1, WORK( NWORK1 ), 1, WORK( VFI ), 1 ) - CALL DCOPY( NLP1, WORK( ITEMP ), 1, WORK( VLI ), 1 ) - ELSE - CALL DLASET( 'A', NL, NL, ZERO, ONE, U( NLF, 1 ), LDU ) - CALL DLASET( 'A', NLP1, NLP1, ZERO, ONE, VT( NLF, 1 ), LDU ) - CALL DLASDQ( 'U', SQREI, NL, NLP1, NL, NCC, D( NLF ), - $ E( NLF ), VT( NLF, 1 ), LDU, U( NLF, 1 ), LDU, - $ U( NLF, 1 ), LDU, WORK( NWORK1 ), INFO ) - CALL DCOPY( NLP1, VT( NLF, 1 ), 1, WORK( VFI ), 1 ) - CALL DCOPY( NLP1, VT( NLF, NLP1 ), 1, WORK( VLI ), 1 ) - END IF - IF( INFO.NE.0 ) THEN - RETURN - END IF - DO 10 J = 1, NL - IWORK( IDXQI+J ) = J - 10 CONTINUE - IF( ( I.EQ.ND ) .AND. ( SQRE.EQ.0 ) ) THEN - SQREI = 0 - ELSE - SQREI = 1 - END IF - IDXQI = IDXQI + NLP1 - VFI = VFI + NLP1 - VLI = VLI + NLP1 - NRP1 = NR + SQREI - IF( ICOMPQ.EQ.0 ) THEN - CALL DLASET( 'A', NRP1, NRP1, ZERO, ONE, WORK( NWORK1 ), - $ SMLSZP ) - CALL DLASDQ( 'U', SQREI, NR, NRP1, NRU, NCC, D( NRF ), - $ E( NRF ), WORK( NWORK1 ), SMLSZP, - $ WORK( NWORK2 ), NR, WORK( NWORK2 ), NR, - $ WORK( NWORK2 ), INFO ) - ITEMP = NWORK1 + ( NRP1-1 )*SMLSZP - CALL DCOPY( NRP1, WORK( NWORK1 ), 1, WORK( VFI ), 1 ) - CALL DCOPY( NRP1, WORK( ITEMP ), 1, WORK( VLI ), 1 ) - ELSE - CALL DLASET( 'A', NR, NR, ZERO, ONE, U( NRF, 1 ), LDU ) - CALL DLASET( 'A', NRP1, NRP1, ZERO, ONE, VT( NRF, 1 ), LDU ) - CALL DLASDQ( 'U', SQREI, NR, NRP1, NR, NCC, D( NRF ), - $ E( NRF ), VT( NRF, 1 ), LDU, U( NRF, 1 ), LDU, - $ U( NRF, 1 ), LDU, WORK( NWORK1 ), INFO ) - CALL DCOPY( NRP1, VT( NRF, 1 ), 1, WORK( VFI ), 1 ) - CALL DCOPY( NRP1, VT( NRF, NRP1 ), 1, WORK( VLI ), 1 ) - END IF - IF( INFO.NE.0 ) THEN - RETURN - END IF - DO 20 J = 1, NR - IWORK( IDXQI+J ) = J - 20 CONTINUE - 30 CONTINUE -* -* Now conquer each subproblem bottom-up. -* - J = 2**NLVL - DO 50 LVL = NLVL, 1, -1 - LVL2 = LVL*2 - 1 -* -* Find the first node LF and last node LL on -* the current level LVL. -* - IF( LVL.EQ.1 ) THEN - LF = 1 - LL = 1 - ELSE - LF = 2**( LVL-1 ) - LL = 2*LF - 1 - END IF - DO 40 I = LF, LL - IM1 = I - 1 - IC = IWORK( INODE+IM1 ) - NL = IWORK( NDIML+IM1 ) - NR = IWORK( NDIMR+IM1 ) - NLF = IC - NL - NRF = IC + 1 - IF( I.EQ.LL ) THEN - SQREI = SQRE - ELSE - SQREI = 1 - END IF - VFI = VF + NLF - 1 - VLI = VL + NLF - 1 - IDXQI = IDXQ + NLF - 1 - ALPHA = D( IC ) - BETA = E( IC ) - IF( ICOMPQ.EQ.0 ) THEN - CALL DLASD6( ICOMPQ, NL, NR, SQREI, D( NLF ), - $ WORK( VFI ), WORK( VLI ), ALPHA, BETA, - $ IWORK( IDXQI ), PERM, GIVPTR( 1 ), GIVCOL, - $ LDGCOL, GIVNUM, LDU, POLES, DIFL, DIFR, Z, - $ K( 1 ), C( 1 ), S( 1 ), WORK( NWORK1 ), - $ IWORK( IWK ), INFO ) - ELSE - J = J - 1 - CALL DLASD6( ICOMPQ, NL, NR, SQREI, D( NLF ), - $ WORK( VFI ), WORK( VLI ), ALPHA, BETA, - $ IWORK( IDXQI ), PERM( NLF, LVL ), - $ GIVPTR( J ), GIVCOL( NLF, LVL2 ), LDGCOL, - $ GIVNUM( NLF, LVL2 ), LDU, - $ POLES( NLF, LVL2 ), DIFL( NLF, LVL ), - $ DIFR( NLF, LVL2 ), Z( NLF, LVL ), K( J ), - $ C( J ), S( J ), WORK( NWORK1 ), - $ IWORK( IWK ), INFO ) - END IF - IF( INFO.NE.0 ) THEN - RETURN - END IF - 40 CONTINUE - 50 CONTINUE -* - RETURN -* -* End of DLASDA -* - END diff --git a/lib/linalg/fortran/dlasdq.f b/lib/linalg/fortran/dlasdq.f deleted file mode 100644 index 0c39b24f0d..0000000000 --- a/lib/linalg/fortran/dlasdq.f +++ /dev/null @@ -1,410 +0,0 @@ -*> \brief \b DLASDQ computes the SVD of a real bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLASDQ + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLASDQ( UPLO, SQRE, N, NCVT, NRU, NCC, D, E, VT, LDVT, -* U, LDU, C, LDC, WORK, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER UPLO -* INTEGER INFO, LDC, LDU, LDVT, N, NCC, NCVT, NRU, SQRE -* .. -* .. Array Arguments .. -* DOUBLE PRECISION C( LDC, * ), D( * ), E( * ), U( LDU, * ), -* $ VT( LDVT, * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLASDQ computes the singular value decomposition (SVD) of a real -*> (upper or lower) bidiagonal matrix with diagonal D and offdiagonal -*> E, accumulating the transformations if desired. Letting B denote -*> the input bidiagonal matrix, the algorithm computes orthogonal -*> matrices Q and P such that B = Q * S * P**T (P**T denotes the transpose -*> of P). The singular values S are overwritten on D. -*> -*> The input matrix U is changed to U * Q if desired. -*> The input matrix VT is changed to P**T * VT if desired. -*> The input matrix C is changed to Q**T * C if desired. -*> -*> See "Computing Small Singular Values of Bidiagonal Matrices With -*> Guaranteed High Relative Accuracy," by J. Demmel and W. Kahan, -*> LAPACK Working Note #3, for a detailed description of the algorithm. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> On entry, UPLO specifies whether the input bidiagonal matrix -*> is upper or lower bidiagonal, and whether it is square are -*> not. -*> UPLO = 'U' or 'u' B is upper bidiagonal. -*> UPLO = 'L' or 'l' B is lower bidiagonal. -*> \endverbatim -*> -*> \param[in] SQRE -*> \verbatim -*> SQRE is INTEGER -*> = 0: then the input matrix is N-by-N. -*> = 1: then the input matrix is N-by-(N+1) if UPLU = 'U' and -*> (N+1)-by-N if UPLU = 'L'. -*> -*> The bidiagonal matrix has -*> N = NL + NR + 1 rows and -*> M = N + SQRE >= N columns. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> On entry, N specifies the number of rows and columns -*> in the matrix. N must be at least 0. -*> \endverbatim -*> -*> \param[in] NCVT -*> \verbatim -*> NCVT is INTEGER -*> On entry, NCVT specifies the number of columns of -*> the matrix VT. NCVT must be at least 0. -*> \endverbatim -*> -*> \param[in] NRU -*> \verbatim -*> NRU is INTEGER -*> On entry, NRU specifies the number of rows of -*> the matrix U. NRU must be at least 0. -*> \endverbatim -*> -*> \param[in] NCC -*> \verbatim -*> NCC is INTEGER -*> On entry, NCC specifies the number of columns of -*> the matrix C. NCC must be at least 0. -*> \endverbatim -*> -*> \param[in,out] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension (N) -*> On entry, D contains the diagonal entries of the -*> bidiagonal matrix whose SVD is desired. On normal exit, -*> D contains the singular values in ascending order. -*> \endverbatim -*> -*> \param[in,out] E -*> \verbatim -*> E is DOUBLE PRECISION array. -*> dimension is (N-1) if SQRE = 0 and N if SQRE = 1. -*> On entry, the entries of E contain the offdiagonal entries -*> of the bidiagonal matrix whose SVD is desired. On normal -*> exit, E will contain 0. If the algorithm does not converge, -*> D and E will contain the diagonal and superdiagonal entries -*> of a bidiagonal matrix orthogonally equivalent to the one -*> given as input. -*> \endverbatim -*> -*> \param[in,out] VT -*> \verbatim -*> VT is DOUBLE PRECISION array, dimension (LDVT, NCVT) -*> On entry, contains a matrix which on exit has been -*> premultiplied by P**T, dimension N-by-NCVT if SQRE = 0 -*> and (N+1)-by-NCVT if SQRE = 1 (not referenced if NCVT=0). -*> \endverbatim -*> -*> \param[in] LDVT -*> \verbatim -*> LDVT is INTEGER -*> On entry, LDVT specifies the leading dimension of VT as -*> declared in the calling (sub) program. LDVT must be at -*> least 1. If NCVT is nonzero LDVT must also be at least N. -*> \endverbatim -*> -*> \param[in,out] U -*> \verbatim -*> U is DOUBLE PRECISION array, dimension (LDU, N) -*> On entry, contains a matrix which on exit has been -*> postmultiplied by Q, dimension NRU-by-N if SQRE = 0 -*> and NRU-by-(N+1) if SQRE = 1 (not referenced if NRU=0). -*> \endverbatim -*> -*> \param[in] LDU -*> \verbatim -*> LDU is INTEGER -*> On entry, LDU specifies the leading dimension of U as -*> declared in the calling (sub) program. LDU must be at -*> least max( 1, NRU ) . -*> \endverbatim -*> -*> \param[in,out] C -*> \verbatim -*> C is DOUBLE PRECISION array, dimension (LDC, NCC) -*> On entry, contains an N-by-NCC matrix which on exit -*> has been premultiplied by Q**T dimension N-by-NCC if SQRE = 0 -*> and (N+1)-by-NCC if SQRE = 1 (not referenced if NCC=0). -*> \endverbatim -*> -*> \param[in] LDC -*> \verbatim -*> LDC is INTEGER -*> On entry, LDC specifies the leading dimension of C as -*> declared in the calling (sub) program. LDC must be at -*> least 1. If NCC is nonzero, LDC must also be at least N. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (4*N) -*> Workspace. Only referenced if one of NCVT, NRU, or NCC is -*> nonzero, and if N is at least 2. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> On exit, a value of 0 indicates a successful exit. -*> If INFO < 0, argument number -INFO is illegal. -*> If INFO > 0, the algorithm did not converge, and INFO -*> specifies how many superdiagonals did not converge. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup OTHERauxiliary -* -*> \par Contributors: -* ================== -*> -*> Ming Gu and Huan Ren, Computer Science Division, University of -*> California at Berkeley, USA -*> -* ===================================================================== - SUBROUTINE DLASDQ( UPLO, SQRE, N, NCVT, NRU, NCC, D, E, VT, LDVT, - $ U, LDU, C, LDC, WORK, INFO ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER UPLO - INTEGER INFO, LDC, LDU, LDVT, N, NCC, NCVT, NRU, SQRE -* .. -* .. Array Arguments .. - DOUBLE PRECISION C( LDC, * ), D( * ), E( * ), U( LDU, * ), - $ VT( LDVT, * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO - PARAMETER ( ZERO = 0.0D+0 ) -* .. -* .. Local Scalars .. - LOGICAL ROTATE - INTEGER I, ISUB, IUPLO, J, NP1, SQRE1 - DOUBLE PRECISION CS, R, SMIN, SN -* .. -* .. External Subroutines .. - EXTERNAL DBDSQR, DLARTG, DLASR, DSWAP, XERBLA -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 - IUPLO = 0 - IF( LSAME( UPLO, 'U' ) ) - $ IUPLO = 1 - IF( LSAME( UPLO, 'L' ) ) - $ IUPLO = 2 - IF( IUPLO.EQ.0 ) THEN - INFO = -1 - ELSE IF( ( SQRE.LT.0 ) .OR. ( SQRE.GT.1 ) ) THEN - INFO = -2 - ELSE IF( N.LT.0 ) THEN - INFO = -3 - ELSE IF( NCVT.LT.0 ) THEN - INFO = -4 - ELSE IF( NRU.LT.0 ) THEN - INFO = -5 - ELSE IF( NCC.LT.0 ) THEN - INFO = -6 - ELSE IF( ( NCVT.EQ.0 .AND. LDVT.LT.1 ) .OR. - $ ( NCVT.GT.0 .AND. LDVT.LT.MAX( 1, N ) ) ) THEN - INFO = -10 - ELSE IF( LDU.LT.MAX( 1, NRU ) ) THEN - INFO = -12 - ELSE IF( ( NCC.EQ.0 .AND. LDC.LT.1 ) .OR. - $ ( NCC.GT.0 .AND. LDC.LT.MAX( 1, N ) ) ) THEN - INFO = -14 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DLASDQ', -INFO ) - RETURN - END IF - IF( N.EQ.0 ) - $ RETURN -* -* ROTATE is true if any singular vectors desired, false otherwise -* - ROTATE = ( NCVT.GT.0 ) .OR. ( NRU.GT.0 ) .OR. ( NCC.GT.0 ) - NP1 = N + 1 - SQRE1 = SQRE -* -* If matrix non-square upper bidiagonal, rotate to be lower -* bidiagonal. The rotations are on the right. -* - IF( ( IUPLO.EQ.1 ) .AND. ( SQRE1.EQ.1 ) ) THEN - DO 10 I = 1, N - 1 - CALL DLARTG( D( I ), E( I ), CS, SN, R ) - D( I ) = R - E( I ) = SN*D( I+1 ) - D( I+1 ) = CS*D( I+1 ) - IF( ROTATE ) THEN - WORK( I ) = CS - WORK( N+I ) = SN - END IF - 10 CONTINUE - CALL DLARTG( D( N ), E( N ), CS, SN, R ) - D( N ) = R - E( N ) = ZERO - IF( ROTATE ) THEN - WORK( N ) = CS - WORK( N+N ) = SN - END IF - IUPLO = 2 - SQRE1 = 0 -* -* Update singular vectors if desired. -* - IF( NCVT.GT.0 ) - $ CALL DLASR( 'L', 'V', 'F', NP1, NCVT, WORK( 1 ), - $ WORK( NP1 ), VT, LDVT ) - END IF -* -* If matrix lower bidiagonal, rotate to be upper bidiagonal -* by applying Givens rotations on the left. -* - IF( IUPLO.EQ.2 ) THEN - DO 20 I = 1, N - 1 - CALL DLARTG( D( I ), E( I ), CS, SN, R ) - D( I ) = R - E( I ) = SN*D( I+1 ) - D( I+1 ) = CS*D( I+1 ) - IF( ROTATE ) THEN - WORK( I ) = CS - WORK( N+I ) = SN - END IF - 20 CONTINUE -* -* If matrix (N+1)-by-N lower bidiagonal, one additional -* rotation is needed. -* - IF( SQRE1.EQ.1 ) THEN - CALL DLARTG( D( N ), E( N ), CS, SN, R ) - D( N ) = R - IF( ROTATE ) THEN - WORK( N ) = CS - WORK( N+N ) = SN - END IF - END IF -* -* Update singular vectors if desired. -* - IF( NRU.GT.0 ) THEN - IF( SQRE1.EQ.0 ) THEN - CALL DLASR( 'R', 'V', 'F', NRU, N, WORK( 1 ), - $ WORK( NP1 ), U, LDU ) - ELSE - CALL DLASR( 'R', 'V', 'F', NRU, NP1, WORK( 1 ), - $ WORK( NP1 ), U, LDU ) - END IF - END IF - IF( NCC.GT.0 ) THEN - IF( SQRE1.EQ.0 ) THEN - CALL DLASR( 'L', 'V', 'F', N, NCC, WORK( 1 ), - $ WORK( NP1 ), C, LDC ) - ELSE - CALL DLASR( 'L', 'V', 'F', NP1, NCC, WORK( 1 ), - $ WORK( NP1 ), C, LDC ) - END IF - END IF - END IF -* -* Call DBDSQR to compute the SVD of the reduced real -* N-by-N upper bidiagonal matrix. -* - CALL DBDSQR( 'U', N, NCVT, NRU, NCC, D, E, VT, LDVT, U, LDU, C, - $ LDC, WORK, INFO ) -* -* Sort the singular values into ascending order (insertion sort on -* singular values, but only one transposition per singular vector) -* - DO 40 I = 1, N -* -* Scan for smallest D(I). -* - ISUB = I - SMIN = D( I ) - DO 30 J = I + 1, N - IF( D( J ).LT.SMIN ) THEN - ISUB = J - SMIN = D( J ) - END IF - 30 CONTINUE - IF( ISUB.NE.I ) THEN -* -* Swap singular values and vectors. -* - D( ISUB ) = D( I ) - D( I ) = SMIN - IF( NCVT.GT.0 ) - $ CALL DSWAP( NCVT, VT( ISUB, 1 ), LDVT, VT( I, 1 ), LDVT ) - IF( NRU.GT.0 ) - $ CALL DSWAP( NRU, U( 1, ISUB ), 1, U( 1, I ), 1 ) - IF( NCC.GT.0 ) - $ CALL DSWAP( NCC, C( ISUB, 1 ), LDC, C( I, 1 ), LDC ) - END IF - 40 CONTINUE -* - RETURN -* -* End of DLASDQ -* - END diff --git a/lib/linalg/fortran/dlasdt.f b/lib/linalg/fortran/dlasdt.f deleted file mode 100644 index 0d9999ea62..0000000000 --- a/lib/linalg/fortran/dlasdt.f +++ /dev/null @@ -1,169 +0,0 @@ -*> \brief \b DLASDT creates a tree of subproblems for bidiagonal divide and conquer. Used by sbdsdc. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLASDT + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLASDT( N, LVL, ND, INODE, NDIML, NDIMR, MSUB ) -* -* .. Scalar Arguments .. -* INTEGER LVL, MSUB, N, ND -* .. -* .. Array Arguments .. -* INTEGER INODE( * ), NDIML( * ), NDIMR( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLASDT creates a tree of subproblems for bidiagonal divide and -*> conquer. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> On entry, the number of diagonal elements of the -*> bidiagonal matrix. -*> \endverbatim -*> -*> \param[out] LVL -*> \verbatim -*> LVL is INTEGER -*> On exit, the number of levels on the computation tree. -*> \endverbatim -*> -*> \param[out] ND -*> \verbatim -*> ND is INTEGER -*> On exit, the number of nodes on the tree. -*> \endverbatim -*> -*> \param[out] INODE -*> \verbatim -*> INODE is INTEGER array, dimension ( N ) -*> On exit, centers of subproblems. -*> \endverbatim -*> -*> \param[out] NDIML -*> \verbatim -*> NDIML is INTEGER array, dimension ( N ) -*> On exit, row dimensions of left children. -*> \endverbatim -*> -*> \param[out] NDIMR -*> \verbatim -*> NDIMR is INTEGER array, dimension ( N ) -*> On exit, row dimensions of right children. -*> \endverbatim -*> -*> \param[in] MSUB -*> \verbatim -*> MSUB is INTEGER -*> On entry, the maximum row dimension each subproblem at the -*> bottom of the tree can be of. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup OTHERauxiliary -* -*> \par Contributors: -* ================== -*> -*> Ming Gu and Huan Ren, Computer Science Division, University of -*> California at Berkeley, USA -*> -* ===================================================================== - SUBROUTINE DLASDT( N, LVL, ND, INODE, NDIML, NDIMR, MSUB ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER LVL, MSUB, N, ND -* .. -* .. Array Arguments .. - INTEGER INODE( * ), NDIML( * ), NDIMR( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION TWO - PARAMETER ( TWO = 2.0D+0 ) -* .. -* .. Local Scalars .. - INTEGER I, IL, IR, LLST, MAXN, NCRNT, NLVL - DOUBLE PRECISION TEMP -* .. -* .. Intrinsic Functions .. - INTRINSIC DBLE, INT, LOG, MAX -* .. -* .. Executable Statements .. -* -* Find the number of levels on the tree. -* - MAXN = MAX( 1, N ) - TEMP = LOG( DBLE( MAXN ) / DBLE( MSUB+1 ) ) / LOG( TWO ) - LVL = INT( TEMP ) + 1 -* - I = N / 2 - INODE( 1 ) = I + 1 - NDIML( 1 ) = I - NDIMR( 1 ) = N - I - 1 - IL = 0 - IR = 1 - LLST = 1 - DO 20 NLVL = 1, LVL - 1 -* -* Constructing the tree at (NLVL+1)-st level. The number of -* nodes created on this level is LLST * 2. -* - DO 10 I = 0, LLST - 1 - IL = IL + 2 - IR = IR + 2 - NCRNT = LLST + I - NDIML( IL ) = NDIML( NCRNT ) / 2 - NDIMR( IL ) = NDIML( NCRNT ) - NDIML( IL ) - 1 - INODE( IL ) = INODE( NCRNT ) - NDIMR( IL ) - 1 - NDIML( IR ) = NDIMR( NCRNT ) / 2 - NDIMR( IR ) = NDIMR( NCRNT ) - NDIML( IR ) - 1 - INODE( IR ) = INODE( NCRNT ) + NDIML( IR ) + 1 - 10 CONTINUE - LLST = LLST*2 - 20 CONTINUE - ND = LLST*2 - 1 -* - RETURN -* -* End of DLASDT -* - END diff --git a/lib/linalg/fortran/dlaset.f b/lib/linalg/fortran/dlaset.f deleted file mode 100644 index 625c757b6b..0000000000 --- a/lib/linalg/fortran/dlaset.f +++ /dev/null @@ -1,181 +0,0 @@ -*> \brief \b DLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLASET + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLASET( UPLO, M, N, ALPHA, BETA, A, LDA ) -* -* .. Scalar Arguments .. -* CHARACTER UPLO -* INTEGER LDA, M, N -* DOUBLE PRECISION ALPHA, BETA -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLASET initializes an m-by-n matrix A to BETA on the diagonal and -*> ALPHA on the offdiagonals. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> Specifies the part of the matrix A to be set. -*> = 'U': Upper triangular part is set; the strictly lower -*> triangular part of A is not changed. -*> = 'L': Lower triangular part is set; the strictly upper -*> triangular part of A is not changed. -*> Otherwise: All of the matrix A is set. -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix A. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in] ALPHA -*> \verbatim -*> ALPHA is DOUBLE PRECISION -*> The constant to which the offdiagonal elements are to be set. -*> \endverbatim -*> -*> \param[in] BETA -*> \verbatim -*> BETA is DOUBLE PRECISION -*> The constant to which the diagonal elements are to be set. -*> \endverbatim -*> -*> \param[out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On exit, the leading m-by-n submatrix of A is set as follows: -*> -*> if UPLO = 'U', A(i,j) = ALPHA, 1<=i<=j-1, 1<=j<=n, -*> if UPLO = 'L', A(i,j) = ALPHA, j+1<=i<=m, 1<=j<=n, -*> otherwise, A(i,j) = ALPHA, 1<=i<=m, 1<=j<=n, i.ne.j, -*> -*> and, for all UPLO, A(i,i) = BETA, 1<=i<=min(m,n). -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,M). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup OTHERauxiliary -* -* ===================================================================== - SUBROUTINE DLASET( UPLO, M, N, ALPHA, BETA, A, LDA ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER UPLO - INTEGER LDA, M, N - DOUBLE PRECISION ALPHA, BETA -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ) -* .. -* -* ===================================================================== -* -* .. Local Scalars .. - INTEGER I, J -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. Intrinsic Functions .. - INTRINSIC MIN -* .. -* .. Executable Statements .. -* - IF( LSAME( UPLO, 'U' ) ) THEN -* -* Set the strictly upper triangular or trapezoidal part of the -* array to ALPHA. -* - DO 20 J = 2, N - DO 10 I = 1, MIN( J-1, M ) - A( I, J ) = ALPHA - 10 CONTINUE - 20 CONTINUE -* - ELSE IF( LSAME( UPLO, 'L' ) ) THEN -* -* Set the strictly lower triangular or trapezoidal part of the -* array to ALPHA. -* - DO 40 J = 1, MIN( M, N ) - DO 30 I = J + 1, M - A( I, J ) = ALPHA - 30 CONTINUE - 40 CONTINUE -* - ELSE -* -* Set the leading m-by-n submatrix to ALPHA. -* - DO 60 J = 1, N - DO 50 I = 1, M - A( I, J ) = ALPHA - 50 CONTINUE - 60 CONTINUE - END IF -* -* Set the first min(M,N) diagonal elements to BETA. -* - DO 70 I = 1, MIN( M, N ) - A( I, I ) = BETA - 70 CONTINUE -* - RETURN -* -* End of DLASET -* - END diff --git a/lib/linalg/fortran/dlasq1.f b/lib/linalg/fortran/dlasq1.f deleted file mode 100644 index 27fa30736e..0000000000 --- a/lib/linalg/fortran/dlasq1.f +++ /dev/null @@ -1,221 +0,0 @@ -*> \brief \b DLASQ1 computes the singular values of a real square bidiagonal matrix. Used by sbdsqr. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLASQ1 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLASQ1( N, D, E, WORK, INFO ) -* -* .. Scalar Arguments .. -* INTEGER INFO, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION D( * ), E( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLASQ1 computes the singular values of a real N-by-N bidiagonal -*> matrix with diagonal D and off-diagonal E. The singular values -*> are computed to high relative accuracy, in the absence of -*> denormalization, underflow and overflow. The algorithm was first -*> presented in -*> -*> "Accurate singular values and differential qd algorithms" by K. V. -*> Fernando and B. N. Parlett, Numer. Math., Vol-67, No. 2, pp. 191-230, -*> 1994, -*> -*> and the present implementation is described in "An implementation of -*> the dqds Algorithm (Positive Case)", LAPACK Working Note. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of rows and columns in the matrix. N >= 0. -*> \endverbatim -*> -*> \param[in,out] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension (N) -*> On entry, D contains the diagonal elements of the -*> bidiagonal matrix whose SVD is desired. On normal exit, -*> D contains the singular values in decreasing order. -*> \endverbatim -*> -*> \param[in,out] E -*> \verbatim -*> E is DOUBLE PRECISION array, dimension (N) -*> On entry, elements E(1:N-1) contain the off-diagonal elements -*> of the bidiagonal matrix whose SVD is desired. -*> On exit, E is overwritten. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (4*N) -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: the algorithm failed -*> = 1, a split was marked by a positive value in E -*> = 2, current block of Z not diagonalized after 100*N -*> iterations (in inner while loop) On exit D and E -*> represent a matrix with the same singular values -*> which the calling subroutine could use to finish the -*> computation, or even feed back into DLASQ1 -*> = 3, termination criterion of outer while loop not met -*> (program created more than N unreduced blocks) -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup auxOTHERcomputational -* -* ===================================================================== - SUBROUTINE DLASQ1( N, D, E, WORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INFO, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION D( * ), E( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO - PARAMETER ( ZERO = 0.0D0 ) -* .. -* .. Local Scalars .. - INTEGER I, IINFO - DOUBLE PRECISION EPS, SCALE, SAFMIN, SIGMN, SIGMX -* .. -* .. External Subroutines .. - EXTERNAL DCOPY, DLAS2, DLASCL, DLASQ2, DLASRT, XERBLA -* .. -* .. External Functions .. - DOUBLE PRECISION DLAMCH - EXTERNAL DLAMCH -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, MAX, SQRT -* .. -* .. Executable Statements .. -* - INFO = 0 - IF( N.LT.0 ) THEN - INFO = -1 - CALL XERBLA( 'DLASQ1', -INFO ) - RETURN - ELSE IF( N.EQ.0 ) THEN - RETURN - ELSE IF( N.EQ.1 ) THEN - D( 1 ) = ABS( D( 1 ) ) - RETURN - ELSE IF( N.EQ.2 ) THEN - CALL DLAS2( D( 1 ), E( 1 ), D( 2 ), SIGMN, SIGMX ) - D( 1 ) = SIGMX - D( 2 ) = SIGMN - RETURN - END IF -* -* Estimate the largest singular value. -* - SIGMX = ZERO - DO 10 I = 1, N - 1 - D( I ) = ABS( D( I ) ) - SIGMX = MAX( SIGMX, ABS( E( I ) ) ) - 10 CONTINUE - D( N ) = ABS( D( N ) ) -* -* Early return if SIGMX is zero (matrix is already diagonal). -* - IF( SIGMX.EQ.ZERO ) THEN - CALL DLASRT( 'D', N, D, IINFO ) - RETURN - END IF -* - DO 20 I = 1, N - SIGMX = MAX( SIGMX, D( I ) ) - 20 CONTINUE -* -* Copy D and E into WORK (in the Z format) and scale (squaring the -* input data makes scaling by a power of the radix pointless). -* - EPS = DLAMCH( 'Precision' ) - SAFMIN = DLAMCH( 'Safe minimum' ) - SCALE = SQRT( EPS / SAFMIN ) - CALL DCOPY( N, D, 1, WORK( 1 ), 2 ) - CALL DCOPY( N-1, E, 1, WORK( 2 ), 2 ) - CALL DLASCL( 'G', 0, 0, SIGMX, SCALE, 2*N-1, 1, WORK, 2*N-1, - $ IINFO ) -* -* Compute the q's and e's. -* - DO 30 I = 1, 2*N - 1 - WORK( I ) = WORK( I )**2 - 30 CONTINUE - WORK( 2*N ) = ZERO -* - CALL DLASQ2( N, WORK, INFO ) -* - IF( INFO.EQ.0 ) THEN - DO 40 I = 1, N - D( I ) = SQRT( WORK( I ) ) - 40 CONTINUE - CALL DLASCL( 'G', 0, 0, SCALE, SIGMX, N, 1, D, N, IINFO ) - ELSE IF( INFO.EQ.2 ) THEN -* -* Maximum number of iterations exceeded. Move data from WORK -* into D and E so the calling subroutine can try to finish -* - DO I = 1, N - D( I ) = SQRT( WORK( 2*I-1 ) ) - E( I ) = SQRT( WORK( 2*I ) ) - END DO - CALL DLASCL( 'G', 0, 0, SCALE, SIGMX, N, 1, D, N, IINFO ) - CALL DLASCL( 'G', 0, 0, SCALE, SIGMX, N, 1, E, N, IINFO ) - END IF -* - RETURN -* -* End of DLASQ1 -* - END diff --git a/lib/linalg/fortran/dlasq2.f b/lib/linalg/fortran/dlasq2.f deleted file mode 100644 index 608ca7a619..0000000000 --- a/lib/linalg/fortran/dlasq2.f +++ /dev/null @@ -1,586 +0,0 @@ -*> \brief \b DLASQ2 computes all the eigenvalues of the symmetric positive definite tridiagonal matrix associated with the qd Array Z to high relative accuracy. Used by sbdsqr and sstegr. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLASQ2 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLASQ2( N, Z, INFO ) -* -* .. Scalar Arguments .. -* INTEGER INFO, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION Z( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLASQ2 computes all the eigenvalues of the symmetric positive -*> definite tridiagonal matrix associated with the qd array Z to high -*> relative accuracy are computed to high relative accuracy, in the -*> absence of denormalization, underflow and overflow. -*> -*> To see the relation of Z to the tridiagonal matrix, let L be a -*> unit lower bidiagonal matrix with subdiagonals Z(2,4,6,,..) and -*> let U be an upper bidiagonal matrix with 1's above and diagonal -*> Z(1,3,5,,..). The tridiagonal is L*U or, if you prefer, the -*> symmetric tridiagonal to which it is similar. -*> -*> Note : DLASQ2 defines a logical variable, IEEE, which is true -*> on machines which follow ieee-754 floating-point standard in their -*> handling of infinities and NaNs, and false otherwise. This variable -*> is passed to DLASQ3. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of rows and columns in the matrix. N >= 0. -*> \endverbatim -*> -*> \param[in,out] Z -*> \verbatim -*> Z is DOUBLE PRECISION array, dimension ( 4*N ) -*> On entry Z holds the qd array. On exit, entries 1 to N hold -*> the eigenvalues in decreasing order, Z( 2*N+1 ) holds the -*> trace, and Z( 2*N+2 ) holds the sum of the eigenvalues. If -*> N > 2, then Z( 2*N+3 ) holds the iteration count, Z( 2*N+4 ) -*> holds NDIVS/NIN^2, and Z( 2*N+5 ) holds the percentage of -*> shifts that failed. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if the i-th argument is a scalar and had an illegal -*> value, then INFO = -i, if the i-th argument is an -*> array and the j-entry had an illegal value, then -*> INFO = -(i*100+j) -*> > 0: the algorithm failed -*> = 1, a split was marked by a positive value in E -*> = 2, current block of Z not diagonalized after 100*N -*> iterations (in inner while loop). On exit Z holds -*> a qd array with the same eigenvalues as the given Z. -*> = 3, termination criterion of outer while loop not met -*> (program created more than N unreduced blocks) -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup auxOTHERcomputational -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> Local Variables: I0:N0 defines a current unreduced segment of Z. -*> The shifts are accumulated in SIGMA. Iteration count is in ITER. -*> Ping-pong is controlled by PP (alternates between 0 and 1). -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DLASQ2( N, Z, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INFO, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION Z( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION CBIAS - PARAMETER ( CBIAS = 1.50D0 ) - DOUBLE PRECISION ZERO, HALF, ONE, TWO, FOUR, HUNDRD - PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0, - $ TWO = 2.0D0, FOUR = 4.0D0, HUNDRD = 100.0D0 ) -* .. -* .. Local Scalars .. - LOGICAL IEEE - INTEGER I0, I1, I4, IINFO, IPN4, ITER, IWHILA, IWHILB, - $ K, KMIN, N0, N1, NBIG, NDIV, NFAIL, PP, SPLT, - $ TTYPE - DOUBLE PRECISION D, DEE, DEEMIN, DESIG, DMIN, DMIN1, DMIN2, DN, - $ DN1, DN2, E, EMAX, EMIN, EPS, G, OLDEMN, QMAX, - $ QMIN, S, SAFMIN, SIGMA, T, TAU, TEMP, TOL, - $ TOL2, TRACE, ZMAX, TEMPE, TEMPQ -* .. -* .. External Subroutines .. - EXTERNAL DLASQ3, DLASRT, XERBLA -* .. -* .. External Functions .. - INTEGER ILAENV - DOUBLE PRECISION DLAMCH - EXTERNAL DLAMCH, ILAENV -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, DBLE, MAX, MIN, SQRT -* .. -* .. Executable Statements .. -* -* Test the input arguments. -* (in case DLASQ2 is not called by DLASQ1) -* - INFO = 0 - EPS = DLAMCH( 'Precision' ) - SAFMIN = DLAMCH( 'Safe minimum' ) - TOL = EPS*HUNDRD - TOL2 = TOL**2 -* - IF( N.LT.0 ) THEN - INFO = -1 - CALL XERBLA( 'DLASQ2', 1 ) - RETURN - ELSE IF( N.EQ.0 ) THEN - RETURN - ELSE IF( N.EQ.1 ) THEN -* -* 1-by-1 case. -* - IF( Z( 1 ).LT.ZERO ) THEN - INFO = -201 - CALL XERBLA( 'DLASQ2', 2 ) - END IF - RETURN - ELSE IF( N.EQ.2 ) THEN -* -* 2-by-2 case. -* - IF( Z( 1 ).LT.ZERO ) THEN - INFO = -201 - CALL XERBLA( 'DLASQ2', 2 ) - RETURN - ELSE IF( Z( 2 ).LT.ZERO ) THEN - INFO = -202 - CALL XERBLA( 'DLASQ2', 2 ) - RETURN - ELSE IF( Z( 3 ).LT.ZERO ) THEN - INFO = -203 - CALL XERBLA( 'DLASQ2', 2 ) - RETURN - ELSE IF( Z( 3 ).GT.Z( 1 ) ) THEN - D = Z( 3 ) - Z( 3 ) = Z( 1 ) - Z( 1 ) = D - END IF - Z( 5 ) = Z( 1 ) + Z( 2 ) + Z( 3 ) - IF( Z( 2 ).GT.Z( 3 )*TOL2 ) THEN - T = HALF*( ( Z( 1 )-Z( 3 ) )+Z( 2 ) ) - S = Z( 3 )*( Z( 2 ) / T ) - IF( S.LE.T ) THEN - S = Z( 3 )*( Z( 2 ) / ( T*( ONE+SQRT( ONE+S / T ) ) ) ) - ELSE - S = Z( 3 )*( Z( 2 ) / ( T+SQRT( T )*SQRT( T+S ) ) ) - END IF - T = Z( 1 ) + ( S+Z( 2 ) ) - Z( 3 ) = Z( 3 )*( Z( 1 ) / T ) - Z( 1 ) = T - END IF - Z( 2 ) = Z( 3 ) - Z( 6 ) = Z( 2 ) + Z( 1 ) - RETURN - END IF -* -* Check for negative data and compute sums of q's and e's. -* - Z( 2*N ) = ZERO - EMIN = Z( 2 ) - QMAX = ZERO - ZMAX = ZERO - D = ZERO - E = ZERO -* - DO 10 K = 1, 2*( N-1 ), 2 - IF( Z( K ).LT.ZERO ) THEN - INFO = -( 200+K ) - CALL XERBLA( 'DLASQ2', 2 ) - RETURN - ELSE IF( Z( K+1 ).LT.ZERO ) THEN - INFO = -( 200+K+1 ) - CALL XERBLA( 'DLASQ2', 2 ) - RETURN - END IF - D = D + Z( K ) - E = E + Z( K+1 ) - QMAX = MAX( QMAX, Z( K ) ) - EMIN = MIN( EMIN, Z( K+1 ) ) - ZMAX = MAX( QMAX, ZMAX, Z( K+1 ) ) - 10 CONTINUE - IF( Z( 2*N-1 ).LT.ZERO ) THEN - INFO = -( 200+2*N-1 ) - CALL XERBLA( 'DLASQ2', 2 ) - RETURN - END IF - D = D + Z( 2*N-1 ) - QMAX = MAX( QMAX, Z( 2*N-1 ) ) - ZMAX = MAX( QMAX, ZMAX ) -* -* Check for diagonality. -* - IF( E.EQ.ZERO ) THEN - DO 20 K = 2, N - Z( K ) = Z( 2*K-1 ) - 20 CONTINUE - CALL DLASRT( 'D', N, Z, IINFO ) - Z( 2*N-1 ) = D - RETURN - END IF -* - TRACE = D + E -* -* Check for zero data. -* - IF( TRACE.EQ.ZERO ) THEN - Z( 2*N-1 ) = ZERO - RETURN - END IF -* -* Check whether the machine is IEEE conformable. -* - IEEE = ( ILAENV( 10, 'DLASQ2', 'N', 1, 2, 3, 4 ).EQ.1 ) -* -* Rearrange data for locality: Z=(q1,qq1,e1,ee1,q2,qq2,e2,ee2,...). -* - DO 30 K = 2*N, 2, -2 - Z( 2*K ) = ZERO - Z( 2*K-1 ) = Z( K ) - Z( 2*K-2 ) = ZERO - Z( 2*K-3 ) = Z( K-1 ) - 30 CONTINUE -* - I0 = 1 - N0 = N -* -* Reverse the qd-array, if warranted. -* - IF( CBIAS*Z( 4*I0-3 ).LT.Z( 4*N0-3 ) ) THEN - IPN4 = 4*( I0+N0 ) - DO 40 I4 = 4*I0, 2*( I0+N0-1 ), 4 - TEMP = Z( I4-3 ) - Z( I4-3 ) = Z( IPN4-I4-3 ) - Z( IPN4-I4-3 ) = TEMP - TEMP = Z( I4-1 ) - Z( I4-1 ) = Z( IPN4-I4-5 ) - Z( IPN4-I4-5 ) = TEMP - 40 CONTINUE - END IF -* -* Initial split checking via dqd and Li's test. -* - PP = 0 -* - DO 80 K = 1, 2 -* - D = Z( 4*N0+PP-3 ) - DO 50 I4 = 4*( N0-1 ) + PP, 4*I0 + PP, -4 - IF( Z( I4-1 ).LE.TOL2*D ) THEN - Z( I4-1 ) = -ZERO - D = Z( I4-3 ) - ELSE - D = Z( I4-3 )*( D / ( D+Z( I4-1 ) ) ) - END IF - 50 CONTINUE -* -* dqd maps Z to ZZ plus Li's test. -* - EMIN = Z( 4*I0+PP+1 ) - D = Z( 4*I0+PP-3 ) - DO 60 I4 = 4*I0 + PP, 4*( N0-1 ) + PP, 4 - Z( I4-2*PP-2 ) = D + Z( I4-1 ) - IF( Z( I4-1 ).LE.TOL2*D ) THEN - Z( I4-1 ) = -ZERO - Z( I4-2*PP-2 ) = D - Z( I4-2*PP ) = ZERO - D = Z( I4+1 ) - ELSE IF( SAFMIN*Z( I4+1 ).LT.Z( I4-2*PP-2 ) .AND. - $ SAFMIN*Z( I4-2*PP-2 ).LT.Z( I4+1 ) ) THEN - TEMP = Z( I4+1 ) / Z( I4-2*PP-2 ) - Z( I4-2*PP ) = Z( I4-1 )*TEMP - D = D*TEMP - ELSE - Z( I4-2*PP ) = Z( I4+1 )*( Z( I4-1 ) / Z( I4-2*PP-2 ) ) - D = Z( I4+1 )*( D / Z( I4-2*PP-2 ) ) - END IF - EMIN = MIN( EMIN, Z( I4-2*PP ) ) - 60 CONTINUE - Z( 4*N0-PP-2 ) = D -* -* Now find qmax. -* - QMAX = Z( 4*I0-PP-2 ) - DO 70 I4 = 4*I0 - PP + 2, 4*N0 - PP - 2, 4 - QMAX = MAX( QMAX, Z( I4 ) ) - 70 CONTINUE -* -* Prepare for the next iteration on K. -* - PP = 1 - PP - 80 CONTINUE -* -* Initialise variables to pass to DLASQ3. -* - TTYPE = 0 - DMIN1 = ZERO - DMIN2 = ZERO - DN = ZERO - DN1 = ZERO - DN2 = ZERO - G = ZERO - TAU = ZERO -* - ITER = 2 - NFAIL = 0 - NDIV = 2*( N0-I0 ) -* - DO 160 IWHILA = 1, N + 1 - IF( N0.LT.1 ) - $ GO TO 170 -* -* While array unfinished do -* -* E(N0) holds the value of SIGMA when submatrix in I0:N0 -* splits from the rest of the array, but is negated. -* - DESIG = ZERO - IF( N0.EQ.N ) THEN - SIGMA = ZERO - ELSE - SIGMA = -Z( 4*N0-1 ) - END IF - IF( SIGMA.LT.ZERO ) THEN - INFO = 1 - RETURN - END IF -* -* Find last unreduced submatrix's top index I0, find QMAX and -* EMIN. Find Gershgorin-type bound if Q's much greater than E's. -* - EMAX = ZERO - IF( N0.GT.I0 ) THEN - EMIN = ABS( Z( 4*N0-5 ) ) - ELSE - EMIN = ZERO - END IF - QMIN = Z( 4*N0-3 ) - QMAX = QMIN - DO 90 I4 = 4*N0, 8, -4 - IF( Z( I4-5 ).LE.ZERO ) - $ GO TO 100 - IF( QMIN.GE.FOUR*EMAX ) THEN - QMIN = MIN( QMIN, Z( I4-3 ) ) - EMAX = MAX( EMAX, Z( I4-5 ) ) - END IF - QMAX = MAX( QMAX, Z( I4-7 )+Z( I4-5 ) ) - EMIN = MIN( EMIN, Z( I4-5 ) ) - 90 CONTINUE - I4 = 4 -* - 100 CONTINUE - I0 = I4 / 4 - PP = 0 -* - IF( N0-I0.GT.1 ) THEN - DEE = Z( 4*I0-3 ) - DEEMIN = DEE - KMIN = I0 - DO 110 I4 = 4*I0+1, 4*N0-3, 4 - DEE = Z( I4 )*( DEE /( DEE+Z( I4-2 ) ) ) - IF( DEE.LE.DEEMIN ) THEN - DEEMIN = DEE - KMIN = ( I4+3 )/4 - END IF - 110 CONTINUE - IF( (KMIN-I0)*2.LT.N0-KMIN .AND. - $ DEEMIN.LE.HALF*Z(4*N0-3) ) THEN - IPN4 = 4*( I0+N0 ) - PP = 2 - DO 120 I4 = 4*I0, 2*( I0+N0-1 ), 4 - TEMP = Z( I4-3 ) - Z( I4-3 ) = Z( IPN4-I4-3 ) - Z( IPN4-I4-3 ) = TEMP - TEMP = Z( I4-2 ) - Z( I4-2 ) = Z( IPN4-I4-2 ) - Z( IPN4-I4-2 ) = TEMP - TEMP = Z( I4-1 ) - Z( I4-1 ) = Z( IPN4-I4-5 ) - Z( IPN4-I4-5 ) = TEMP - TEMP = Z( I4 ) - Z( I4 ) = Z( IPN4-I4-4 ) - Z( IPN4-I4-4 ) = TEMP - 120 CONTINUE - END IF - END IF -* -* Put -(initial shift) into DMIN. -* - DMIN = -MAX( ZERO, QMIN-TWO*SQRT( QMIN )*SQRT( EMAX ) ) -* -* Now I0:N0 is unreduced. -* PP = 0 for ping, PP = 1 for pong. -* PP = 2 indicates that flipping was applied to the Z array and -* and that the tests for deflation upon entry in DLASQ3 -* should not be performed. -* - NBIG = 100*( N0-I0+1 ) - DO 140 IWHILB = 1, NBIG - IF( I0.GT.N0 ) - $ GO TO 150 -* -* While submatrix unfinished take a good dqds step. -* - CALL DLASQ3( I0, N0, Z, PP, DMIN, SIGMA, DESIG, QMAX, NFAIL, - $ ITER, NDIV, IEEE, TTYPE, DMIN1, DMIN2, DN, DN1, - $ DN2, G, TAU ) -* - PP = 1 - PP -* -* When EMIN is very small check for splits. -* - IF( PP.EQ.0 .AND. N0-I0.GE.3 ) THEN - IF( Z( 4*N0 ).LE.TOL2*QMAX .OR. - $ Z( 4*N0-1 ).LE.TOL2*SIGMA ) THEN - SPLT = I0 - 1 - QMAX = Z( 4*I0-3 ) - EMIN = Z( 4*I0-1 ) - OLDEMN = Z( 4*I0 ) - DO 130 I4 = 4*I0, 4*( N0-3 ), 4 - IF( Z( I4 ).LE.TOL2*Z( I4-3 ) .OR. - $ Z( I4-1 ).LE.TOL2*SIGMA ) THEN - Z( I4-1 ) = -SIGMA - SPLT = I4 / 4 - QMAX = ZERO - EMIN = Z( I4+3 ) - OLDEMN = Z( I4+4 ) - ELSE - QMAX = MAX( QMAX, Z( I4+1 ) ) - EMIN = MIN( EMIN, Z( I4-1 ) ) - OLDEMN = MIN( OLDEMN, Z( I4 ) ) - END IF - 130 CONTINUE - Z( 4*N0-1 ) = EMIN - Z( 4*N0 ) = OLDEMN - I0 = SPLT + 1 - END IF - END IF -* - 140 CONTINUE -* - INFO = 2 -* -* Maximum number of iterations exceeded, restore the shift -* SIGMA and place the new d's and e's in a qd array. -* This might need to be done for several blocks -* - I1 = I0 - N1 = N0 - 145 CONTINUE - TEMPQ = Z( 4*I0-3 ) - Z( 4*I0-3 ) = Z( 4*I0-3 ) + SIGMA - DO K = I0+1, N0 - TEMPE = Z( 4*K-5 ) - Z( 4*K-5 ) = Z( 4*K-5 ) * (TEMPQ / Z( 4*K-7 )) - TEMPQ = Z( 4*K-3 ) - Z( 4*K-3 ) = Z( 4*K-3 ) + SIGMA + TEMPE - Z( 4*K-5 ) - END DO -* -* Prepare to do this on the previous block if there is one -* - IF( I1.GT.1 ) THEN - N1 = I1-1 - DO WHILE( ( I1.GE.2 ) .AND. ( Z(4*I1-5).GE.ZERO ) ) - I1 = I1 - 1 - END DO - SIGMA = -Z(4*N1-1) - GO TO 145 - END IF - - DO K = 1, N - Z( 2*K-1 ) = Z( 4*K-3 ) -* -* Only the block 1..N0 is unfinished. The rest of the e's -* must be essentially zero, although sometimes other data -* has been stored in them. -* - IF( K.LT.N0 ) THEN - Z( 2*K ) = Z( 4*K-1 ) - ELSE - Z( 2*K ) = 0 - END IF - END DO - RETURN -* -* end IWHILB -* - 150 CONTINUE -* - 160 CONTINUE -* - INFO = 3 - RETURN -* -* end IWHILA -* - 170 CONTINUE -* -* Move q's to the front. -* - DO 180 K = 2, N - Z( K ) = Z( 4*K-3 ) - 180 CONTINUE -* -* Sort and compute sum of eigenvalues. -* - CALL DLASRT( 'D', N, Z, IINFO ) -* - E = ZERO - DO 190 K = N, 1, -1 - E = E + Z( K ) - 190 CONTINUE -* -* Store trace, sum(eigenvalues) and information on performance. -* - Z( 2*N+1 ) = TRACE - Z( 2*N+2 ) = E - Z( 2*N+3 ) = DBLE( ITER ) - Z( 2*N+4 ) = DBLE( NDIV ) / DBLE( N**2 ) - Z( 2*N+5 ) = HUNDRD*NFAIL / DBLE( ITER ) - RETURN -* -* End of DLASQ2 -* - END diff --git a/lib/linalg/fortran/dlasq3.f b/lib/linalg/fortran/dlasq3.f deleted file mode 100644 index e4bdafe06e..0000000000 --- a/lib/linalg/fortran/dlasq3.f +++ /dev/null @@ -1,418 +0,0 @@ -*> \brief \b DLASQ3 checks for deflation, computes a shift and calls dqds. Used by sbdsqr. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLASQ3 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLASQ3( I0, N0, Z, PP, DMIN, SIGMA, DESIG, QMAX, NFAIL, -* ITER, NDIV, IEEE, TTYPE, DMIN1, DMIN2, DN, DN1, -* DN2, G, TAU ) -* -* .. Scalar Arguments .. -* LOGICAL IEEE -* INTEGER I0, ITER, N0, NDIV, NFAIL, PP -* DOUBLE PRECISION DESIG, DMIN, DMIN1, DMIN2, DN, DN1, DN2, G, -* $ QMAX, SIGMA, TAU -* .. -* .. Array Arguments .. -* DOUBLE PRECISION Z( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLASQ3 checks for deflation, computes a shift (TAU) and calls dqds. -*> In case of failure it changes shifts, and tries again until output -*> is positive. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] I0 -*> \verbatim -*> I0 is INTEGER -*> First index. -*> \endverbatim -*> -*> \param[in,out] N0 -*> \verbatim -*> N0 is INTEGER -*> Last index. -*> \endverbatim -*> -*> \param[in,out] Z -*> \verbatim -*> Z is DOUBLE PRECISION array, dimension ( 4*N0 ) -*> Z holds the qd array. -*> \endverbatim -*> -*> \param[in,out] PP -*> \verbatim -*> PP is INTEGER -*> PP=0 for ping, PP=1 for pong. -*> PP=2 indicates that flipping was applied to the Z array -*> and that the initial tests for deflation should not be -*> performed. -*> \endverbatim -*> -*> \param[out] DMIN -*> \verbatim -*> DMIN is DOUBLE PRECISION -*> Minimum value of d. -*> \endverbatim -*> -*> \param[out] SIGMA -*> \verbatim -*> SIGMA is DOUBLE PRECISION -*> Sum of shifts used in current segment. -*> \endverbatim -*> -*> \param[in,out] DESIG -*> \verbatim -*> DESIG is DOUBLE PRECISION -*> Lower order part of SIGMA -*> \endverbatim -*> -*> \param[in] QMAX -*> \verbatim -*> QMAX is DOUBLE PRECISION -*> Maximum value of q. -*> \endverbatim -*> -*> \param[in,out] NFAIL -*> \verbatim -*> NFAIL is INTEGER -*> Increment NFAIL by 1 each time the shift was too big. -*> \endverbatim -*> -*> \param[in,out] ITER -*> \verbatim -*> ITER is INTEGER -*> Increment ITER by 1 for each iteration. -*> \endverbatim -*> -*> \param[in,out] NDIV -*> \verbatim -*> NDIV is INTEGER -*> Increment NDIV by 1 for each division. -*> \endverbatim -*> -*> \param[in] IEEE -*> \verbatim -*> IEEE is LOGICAL -*> Flag for IEEE or non IEEE arithmetic (passed to DLASQ5). -*> \endverbatim -*> -*> \param[in,out] TTYPE -*> \verbatim -*> TTYPE is INTEGER -*> Shift type. -*> \endverbatim -*> -*> \param[in,out] DMIN1 -*> \verbatim -*> DMIN1 is DOUBLE PRECISION -*> \endverbatim -*> -*> \param[in,out] DMIN2 -*> \verbatim -*> DMIN2 is DOUBLE PRECISION -*> \endverbatim -*> -*> \param[in,out] DN -*> \verbatim -*> DN is DOUBLE PRECISION -*> \endverbatim -*> -*> \param[in,out] DN1 -*> \verbatim -*> DN1 is DOUBLE PRECISION -*> \endverbatim -*> -*> \param[in,out] DN2 -*> \verbatim -*> DN2 is DOUBLE PRECISION -*> \endverbatim -*> -*> \param[in,out] G -*> \verbatim -*> G is DOUBLE PRECISION -*> \endverbatim -*> -*> \param[in,out] TAU -*> \verbatim -*> TAU is DOUBLE PRECISION -*> -*> These are passed as arguments in order to save their values -*> between calls to DLASQ3. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup auxOTHERcomputational -* -* ===================================================================== - SUBROUTINE DLASQ3( I0, N0, Z, PP, DMIN, SIGMA, DESIG, QMAX, NFAIL, - $ ITER, NDIV, IEEE, TTYPE, DMIN1, DMIN2, DN, DN1, - $ DN2, G, TAU ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - LOGICAL IEEE - INTEGER I0, ITER, N0, NDIV, NFAIL, PP - DOUBLE PRECISION DESIG, DMIN, DMIN1, DMIN2, DN, DN1, DN2, G, - $ QMAX, SIGMA, TAU -* .. -* .. Array Arguments .. - DOUBLE PRECISION Z( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION CBIAS - PARAMETER ( CBIAS = 1.50D0 ) - DOUBLE PRECISION ZERO, QURTR, HALF, ONE, TWO, HUNDRD - PARAMETER ( ZERO = 0.0D0, QURTR = 0.250D0, HALF = 0.5D0, - $ ONE = 1.0D0, TWO = 2.0D0, HUNDRD = 100.0D0 ) -* .. -* .. Local Scalars .. - INTEGER IPN4, J4, N0IN, NN, TTYPE - DOUBLE PRECISION EPS, S, T, TEMP, TOL, TOL2 -* .. -* .. External Subroutines .. - EXTERNAL DLASQ4, DLASQ5, DLASQ6 -* .. -* .. External Function .. - DOUBLE PRECISION DLAMCH - LOGICAL DISNAN - EXTERNAL DISNAN, DLAMCH -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, MAX, MIN, SQRT -* .. -* .. Executable Statements .. -* - N0IN = N0 - EPS = DLAMCH( 'Precision' ) - TOL = EPS*HUNDRD - TOL2 = TOL**2 -* -* Check for deflation. -* - 10 CONTINUE -* - IF( N0.LT.I0 ) - $ RETURN - IF( N0.EQ.I0 ) - $ GO TO 20 - NN = 4*N0 + PP - IF( N0.EQ.( I0+1 ) ) - $ GO TO 40 -* -* Check whether E(N0-1) is negligible, 1 eigenvalue. -* - IF( Z( NN-5 ).GT.TOL2*( SIGMA+Z( NN-3 ) ) .AND. - $ Z( NN-2*PP-4 ).GT.TOL2*Z( NN-7 ) ) - $ GO TO 30 -* - 20 CONTINUE -* - Z( 4*N0-3 ) = Z( 4*N0+PP-3 ) + SIGMA - N0 = N0 - 1 - GO TO 10 -* -* Check whether E(N0-2) is negligible, 2 eigenvalues. -* - 30 CONTINUE -* - IF( Z( NN-9 ).GT.TOL2*SIGMA .AND. - $ Z( NN-2*PP-8 ).GT.TOL2*Z( NN-11 ) ) - $ GO TO 50 -* - 40 CONTINUE -* - IF( Z( NN-3 ).GT.Z( NN-7 ) ) THEN - S = Z( NN-3 ) - Z( NN-3 ) = Z( NN-7 ) - Z( NN-7 ) = S - END IF - T = HALF*( ( Z( NN-7 )-Z( NN-3 ) )+Z( NN-5 ) ) - IF( Z( NN-5 ).GT.Z( NN-3 )*TOL2.AND.T.NE.ZERO ) THEN - S = Z( NN-3 )*( Z( NN-5 ) / T ) - IF( S.LE.T ) THEN - S = Z( NN-3 )*( Z( NN-5 ) / - $ ( T*( ONE+SQRT( ONE+S / T ) ) ) ) - ELSE - S = Z( NN-3 )*( Z( NN-5 ) / ( T+SQRT( T )*SQRT( T+S ) ) ) - END IF - T = Z( NN-7 ) + ( S+Z( NN-5 ) ) - Z( NN-3 ) = Z( NN-3 )*( Z( NN-7 ) / T ) - Z( NN-7 ) = T - END IF - Z( 4*N0-7 ) = Z( NN-7 ) + SIGMA - Z( 4*N0-3 ) = Z( NN-3 ) + SIGMA - N0 = N0 - 2 - GO TO 10 -* - 50 CONTINUE - IF( PP.EQ.2 ) - $ PP = 0 -* -* Reverse the qd-array, if warranted. -* - IF( DMIN.LE.ZERO .OR. N0.LT.N0IN ) THEN - IF( CBIAS*Z( 4*I0+PP-3 ).LT.Z( 4*N0+PP-3 ) ) THEN - IPN4 = 4*( I0+N0 ) - DO 60 J4 = 4*I0, 2*( I0+N0-1 ), 4 - TEMP = Z( J4-3 ) - Z( J4-3 ) = Z( IPN4-J4-3 ) - Z( IPN4-J4-3 ) = TEMP - TEMP = Z( J4-2 ) - Z( J4-2 ) = Z( IPN4-J4-2 ) - Z( IPN4-J4-2 ) = TEMP - TEMP = Z( J4-1 ) - Z( J4-1 ) = Z( IPN4-J4-5 ) - Z( IPN4-J4-5 ) = TEMP - TEMP = Z( J4 ) - Z( J4 ) = Z( IPN4-J4-4 ) - Z( IPN4-J4-4 ) = TEMP - 60 CONTINUE - IF( N0-I0.LE.4 ) THEN - Z( 4*N0+PP-1 ) = Z( 4*I0+PP-1 ) - Z( 4*N0-PP ) = Z( 4*I0-PP ) - END IF - DMIN2 = MIN( DMIN2, Z( 4*N0+PP-1 ) ) - Z( 4*N0+PP-1 ) = MIN( Z( 4*N0+PP-1 ), Z( 4*I0+PP-1 ), - $ Z( 4*I0+PP+3 ) ) - Z( 4*N0-PP ) = MIN( Z( 4*N0-PP ), Z( 4*I0-PP ), - $ Z( 4*I0-PP+4 ) ) - QMAX = MAX( QMAX, Z( 4*I0+PP-3 ), Z( 4*I0+PP+1 ) ) - DMIN = -ZERO - END IF - END IF -* -* Choose a shift. -* - CALL DLASQ4( I0, N0, Z, PP, N0IN, DMIN, DMIN1, DMIN2, DN, DN1, - $ DN2, TAU, TTYPE, G ) -* -* Call dqds until DMIN > 0. -* - 70 CONTINUE -* - CALL DLASQ5( I0, N0, Z, PP, TAU, SIGMA, DMIN, DMIN1, DMIN2, DN, - $ DN1, DN2, IEEE, EPS ) -* - NDIV = NDIV + ( N0-I0+2 ) - ITER = ITER + 1 -* -* Check status. -* - IF( DMIN.GE.ZERO .AND. DMIN1.GE.ZERO ) THEN -* -* Success. -* - GO TO 90 -* - ELSE IF( DMIN.LT.ZERO .AND. DMIN1.GT.ZERO .AND. - $ Z( 4*( N0-1 )-PP ).LT.TOL*( SIGMA+DN1 ) .AND. - $ ABS( DN ).LT.TOL*SIGMA ) THEN -* -* Convergence hidden by negative DN. -* - Z( 4*( N0-1 )-PP+2 ) = ZERO - DMIN = ZERO - GO TO 90 - ELSE IF( DMIN.LT.ZERO ) THEN -* -* TAU too big. Select new TAU and try again. -* - NFAIL = NFAIL + 1 - IF( TTYPE.LT.-22 ) THEN -* -* Failed twice. Play it safe. -* - TAU = ZERO - ELSE IF( DMIN1.GT.ZERO ) THEN -* -* Late failure. Gives excellent shift. -* - TAU = ( TAU+DMIN )*( ONE-TWO*EPS ) - TTYPE = TTYPE - 11 - ELSE -* -* Early failure. Divide by 4. -* - TAU = QURTR*TAU - TTYPE = TTYPE - 12 - END IF - GO TO 70 - ELSE IF( DISNAN( DMIN ) ) THEN -* -* NaN. -* - IF( TAU.EQ.ZERO ) THEN - GO TO 80 - ELSE - TAU = ZERO - GO TO 70 - END IF - ELSE -* -* Possible underflow. Play it safe. -* - GO TO 80 - END IF -* -* Risk of underflow. -* - 80 CONTINUE - CALL DLASQ6( I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN, DN1, DN2 ) - NDIV = NDIV + ( N0-I0+2 ) - ITER = ITER + 1 - TAU = ZERO -* - 90 CONTINUE - IF( TAU.LT.SIGMA ) THEN - DESIG = DESIG + TAU - T = SIGMA + DESIG - DESIG = DESIG - ( T-SIGMA ) - ELSE - T = SIGMA + TAU - DESIG = SIGMA - ( T-TAU ) + DESIG - END IF - SIGMA = T -* - RETURN -* -* End of DLASQ3 -* - END diff --git a/lib/linalg/fortran/dlasq4.f b/lib/linalg/fortran/dlasq4.f deleted file mode 100644 index 2652ddb2ba..0000000000 --- a/lib/linalg/fortran/dlasq4.f +++ /dev/null @@ -1,421 +0,0 @@ -*> \brief \b DLASQ4 computes an approximation to the smallest eigenvalue using values of d from the previous transform. Used by sbdsqr. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLASQ4 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLASQ4( I0, N0, Z, PP, N0IN, DMIN, DMIN1, DMIN2, DN, -* DN1, DN2, TAU, TTYPE, G ) -* -* .. Scalar Arguments .. -* INTEGER I0, N0, N0IN, PP, TTYPE -* DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DN1, DN2, G, TAU -* .. -* .. Array Arguments .. -* DOUBLE PRECISION Z( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLASQ4 computes an approximation TAU to the smallest eigenvalue -*> using values of d from the previous transform. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] I0 -*> \verbatim -*> I0 is INTEGER -*> First index. -*> \endverbatim -*> -*> \param[in] N0 -*> \verbatim -*> N0 is INTEGER -*> Last index. -*> \endverbatim -*> -*> \param[in] Z -*> \verbatim -*> Z is DOUBLE PRECISION array, dimension ( 4*N0 ) -*> Z holds the qd array. -*> \endverbatim -*> -*> \param[in] PP -*> \verbatim -*> PP is INTEGER -*> PP=0 for ping, PP=1 for pong. -*> \endverbatim -*> -*> \param[in] N0IN -*> \verbatim -*> N0IN is INTEGER -*> The value of N0 at start of EIGTEST. -*> \endverbatim -*> -*> \param[in] DMIN -*> \verbatim -*> DMIN is DOUBLE PRECISION -*> Minimum value of d. -*> \endverbatim -*> -*> \param[in] DMIN1 -*> \verbatim -*> DMIN1 is DOUBLE PRECISION -*> Minimum value of d, excluding D( N0 ). -*> \endverbatim -*> -*> \param[in] DMIN2 -*> \verbatim -*> DMIN2 is DOUBLE PRECISION -*> Minimum value of d, excluding D( N0 ) and D( N0-1 ). -*> \endverbatim -*> -*> \param[in] DN -*> \verbatim -*> DN is DOUBLE PRECISION -*> d(N) -*> \endverbatim -*> -*> \param[in] DN1 -*> \verbatim -*> DN1 is DOUBLE PRECISION -*> d(N-1) -*> \endverbatim -*> -*> \param[in] DN2 -*> \verbatim -*> DN2 is DOUBLE PRECISION -*> d(N-2) -*> \endverbatim -*> -*> \param[out] TAU -*> \verbatim -*> TAU is DOUBLE PRECISION -*> This is the shift. -*> \endverbatim -*> -*> \param[out] TTYPE -*> \verbatim -*> TTYPE is INTEGER -*> Shift type. -*> \endverbatim -*> -*> \param[in,out] G -*> \verbatim -*> G is DOUBLE PRECISION -*> G is passed as an argument in order to save its value between -*> calls to DLASQ4. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup auxOTHERcomputational -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> CNST1 = 9/16 -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DLASQ4( I0, N0, Z, PP, N0IN, DMIN, DMIN1, DMIN2, DN, - $ DN1, DN2, TAU, TTYPE, G ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER I0, N0, N0IN, PP, TTYPE - DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DN1, DN2, G, TAU -* .. -* .. Array Arguments .. - DOUBLE PRECISION Z( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION CNST1, CNST2, CNST3 - PARAMETER ( CNST1 = 0.5630D0, CNST2 = 1.010D0, - $ CNST3 = 1.050D0 ) - DOUBLE PRECISION QURTR, THIRD, HALF, ZERO, ONE, TWO, HUNDRD - PARAMETER ( QURTR = 0.250D0, THIRD = 0.3330D0, - $ HALF = 0.50D0, ZERO = 0.0D0, ONE = 1.0D0, - $ TWO = 2.0D0, HUNDRD = 100.0D0 ) -* .. -* .. Local Scalars .. - INTEGER I4, NN, NP - DOUBLE PRECISION A2, B1, B2, GAM, GAP1, GAP2, S -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, MIN, SQRT -* .. -* .. Executable Statements .. -* -* A negative DMIN forces the shift to take that absolute value -* TTYPE records the type of shift. -* - IF( DMIN.LE.ZERO ) THEN - TAU = -DMIN - TTYPE = -1 - RETURN - END IF -* - NN = 4*N0 + PP - IF( N0IN.EQ.N0 ) THEN -* -* No eigenvalues deflated. -* - IF( DMIN.EQ.DN .OR. DMIN.EQ.DN1 ) THEN -* - B1 = SQRT( Z( NN-3 ) )*SQRT( Z( NN-5 ) ) - B2 = SQRT( Z( NN-7 ) )*SQRT( Z( NN-9 ) ) - A2 = Z( NN-7 ) + Z( NN-5 ) -* -* Cases 2 and 3. -* - IF( DMIN.EQ.DN .AND. DMIN1.EQ.DN1 ) THEN - GAP2 = DMIN2 - A2 - DMIN2*QURTR - IF( GAP2.GT.ZERO .AND. GAP2.GT.B2 ) THEN - GAP1 = A2 - DN - ( B2 / GAP2 )*B2 - ELSE - GAP1 = A2 - DN - ( B1+B2 ) - END IF - IF( GAP1.GT.ZERO .AND. GAP1.GT.B1 ) THEN - S = MAX( DN-( B1 / GAP1 )*B1, HALF*DMIN ) - TTYPE = -2 - ELSE - S = ZERO - IF( DN.GT.B1 ) - $ S = DN - B1 - IF( A2.GT.( B1+B2 ) ) - $ S = MIN( S, A2-( B1+B2 ) ) - S = MAX( S, THIRD*DMIN ) - TTYPE = -3 - END IF - ELSE -* -* Case 4. -* - TTYPE = -4 - S = QURTR*DMIN - IF( DMIN.EQ.DN ) THEN - GAM = DN - A2 = ZERO - IF( Z( NN-5 ) .GT. Z( NN-7 ) ) - $ RETURN - B2 = Z( NN-5 ) / Z( NN-7 ) - NP = NN - 9 - ELSE - NP = NN - 2*PP - GAM = DN1 - IF( Z( NP-4 ) .GT. Z( NP-2 ) ) - $ RETURN - A2 = Z( NP-4 ) / Z( NP-2 ) - IF( Z( NN-9 ) .GT. Z( NN-11 ) ) - $ RETURN - B2 = Z( NN-9 ) / Z( NN-11 ) - NP = NN - 13 - END IF -* -* Approximate contribution to norm squared from I < NN-1. -* - A2 = A2 + B2 - DO 10 I4 = NP, 4*I0 - 1 + PP, -4 - IF( B2.EQ.ZERO ) - $ GO TO 20 - B1 = B2 - IF( Z( I4 ) .GT. Z( I4-2 ) ) - $ RETURN - B2 = B2*( Z( I4 ) / Z( I4-2 ) ) - A2 = A2 + B2 - IF( HUNDRD*MAX( B2, B1 ).LT.A2 .OR. CNST1.LT.A2 ) - $ GO TO 20 - 10 CONTINUE - 20 CONTINUE - A2 = CNST3*A2 -* -* Rayleigh quotient residual bound. -* - IF( A2.LT.CNST1 ) - $ S = GAM*( ONE-SQRT( A2 ) ) / ( ONE+A2 ) - END IF - ELSE IF( DMIN.EQ.DN2 ) THEN -* -* Case 5. -* - TTYPE = -5 - S = QURTR*DMIN -* -* Compute contribution to norm squared from I > NN-2. -* - NP = NN - 2*PP - B1 = Z( NP-2 ) - B2 = Z( NP-6 ) - GAM = DN2 - IF( Z( NP-8 ).GT.B2 .OR. Z( NP-4 ).GT.B1 ) - $ RETURN - A2 = ( Z( NP-8 ) / B2 )*( ONE+Z( NP-4 ) / B1 ) -* -* Approximate contribution to norm squared from I < NN-2. -* - IF( N0-I0.GT.2 ) THEN - B2 = Z( NN-13 ) / Z( NN-15 ) - A2 = A2 + B2 - DO 30 I4 = NN - 17, 4*I0 - 1 + PP, -4 - IF( B2.EQ.ZERO ) - $ GO TO 40 - B1 = B2 - IF( Z( I4 ) .GT. Z( I4-2 ) ) - $ RETURN - B2 = B2*( Z( I4 ) / Z( I4-2 ) ) - A2 = A2 + B2 - IF( HUNDRD*MAX( B2, B1 ).LT.A2 .OR. CNST1.LT.A2 ) - $ GO TO 40 - 30 CONTINUE - 40 CONTINUE - A2 = CNST3*A2 - END IF -* - IF( A2.LT.CNST1 ) - $ S = GAM*( ONE-SQRT( A2 ) ) / ( ONE+A2 ) - ELSE -* -* Case 6, no information to guide us. -* - IF( TTYPE.EQ.-6 ) THEN - G = G + THIRD*( ONE-G ) - ELSE IF( TTYPE.EQ.-18 ) THEN - G = QURTR*THIRD - ELSE - G = QURTR - END IF - S = G*DMIN - TTYPE = -6 - END IF -* - ELSE IF( N0IN.EQ.( N0+1 ) ) THEN -* -* One eigenvalue just deflated. Use DMIN1, DN1 for DMIN and DN. -* - IF( DMIN1.EQ.DN1 .AND. DMIN2.EQ.DN2 ) THEN -* -* Cases 7 and 8. -* - TTYPE = -7 - S = THIRD*DMIN1 - IF( Z( NN-5 ).GT.Z( NN-7 ) ) - $ RETURN - B1 = Z( NN-5 ) / Z( NN-7 ) - B2 = B1 - IF( B2.EQ.ZERO ) - $ GO TO 60 - DO 50 I4 = 4*N0 - 9 + PP, 4*I0 - 1 + PP, -4 - A2 = B1 - IF( Z( I4 ).GT.Z( I4-2 ) ) - $ RETURN - B1 = B1*( Z( I4 ) / Z( I4-2 ) ) - B2 = B2 + B1 - IF( HUNDRD*MAX( B1, A2 ).LT.B2 ) - $ GO TO 60 - 50 CONTINUE - 60 CONTINUE - B2 = SQRT( CNST3*B2 ) - A2 = DMIN1 / ( ONE+B2**2 ) - GAP2 = HALF*DMIN2 - A2 - IF( GAP2.GT.ZERO .AND. GAP2.GT.B2*A2 ) THEN - S = MAX( S, A2*( ONE-CNST2*A2*( B2 / GAP2 )*B2 ) ) - ELSE - S = MAX( S, A2*( ONE-CNST2*B2 ) ) - TTYPE = -8 - END IF - ELSE -* -* Case 9. -* - S = QURTR*DMIN1 - IF( DMIN1.EQ.DN1 ) - $ S = HALF*DMIN1 - TTYPE = -9 - END IF -* - ELSE IF( N0IN.EQ.( N0+2 ) ) THEN -* -* Two eigenvalues deflated. Use DMIN2, DN2 for DMIN and DN. -* -* Cases 10 and 11. -* - IF( DMIN2.EQ.DN2 .AND. TWO*Z( NN-5 ).LT.Z( NN-7 ) ) THEN - TTYPE = -10 - S = THIRD*DMIN2 - IF( Z( NN-5 ).GT.Z( NN-7 ) ) - $ RETURN - B1 = Z( NN-5 ) / Z( NN-7 ) - B2 = B1 - IF( B2.EQ.ZERO ) - $ GO TO 80 - DO 70 I4 = 4*N0 - 9 + PP, 4*I0 - 1 + PP, -4 - IF( Z( I4 ).GT.Z( I4-2 ) ) - $ RETURN - B1 = B1*( Z( I4 ) / Z( I4-2 ) ) - B2 = B2 + B1 - IF( HUNDRD*B1.LT.B2 ) - $ GO TO 80 - 70 CONTINUE - 80 CONTINUE - B2 = SQRT( CNST3*B2 ) - A2 = DMIN2 / ( ONE+B2**2 ) - GAP2 = Z( NN-7 ) + Z( NN-9 ) - - $ SQRT( Z( NN-11 ) )*SQRT( Z( NN-9 ) ) - A2 - IF( GAP2.GT.ZERO .AND. GAP2.GT.B2*A2 ) THEN - S = MAX( S, A2*( ONE-CNST2*A2*( B2 / GAP2 )*B2 ) ) - ELSE - S = MAX( S, A2*( ONE-CNST2*B2 ) ) - END IF - ELSE - S = QURTR*DMIN2 - TTYPE = -11 - END IF - ELSE IF( N0IN.GT.( N0+2 ) ) THEN -* -* Case 12, more than two eigenvalues deflated. No information. -* - S = ZERO - TTYPE = -12 - END IF -* - TAU = S - RETURN -* -* End of DLASQ4 -* - END diff --git a/lib/linalg/fortran/dlasq5.f b/lib/linalg/fortran/dlasq5.f deleted file mode 100644 index 5679ab60a5..0000000000 --- a/lib/linalg/fortran/dlasq5.f +++ /dev/null @@ -1,407 +0,0 @@ -*> \brief \b DLASQ5 computes one dqds transform in ping-pong form. Used by sbdsqr and sstegr. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLASQ5 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLASQ5( I0, N0, Z, PP, TAU, SIGMA, DMIN, DMIN1, DMIN2, DN, -* DNM1, DNM2, IEEE, EPS ) -* -* .. Scalar Arguments .. -* LOGICAL IEEE -* INTEGER I0, N0, PP -* DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DNM1, DNM2, TAU, SIGMA, EPS -* .. -* .. Array Arguments .. -* DOUBLE PRECISION Z( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLASQ5 computes one dqds transform in ping-pong form, one -*> version for IEEE machines another for non IEEE machines. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] I0 -*> \verbatim -*> I0 is INTEGER -*> First index. -*> \endverbatim -*> -*> \param[in] N0 -*> \verbatim -*> N0 is INTEGER -*> Last index. -*> \endverbatim -*> -*> \param[in] Z -*> \verbatim -*> Z is DOUBLE PRECISION array, dimension ( 4*N ) -*> Z holds the qd array. EMIN is stored in Z(4*N0) to avoid -*> an extra argument. -*> \endverbatim -*> -*> \param[in] PP -*> \verbatim -*> PP is INTEGER -*> PP=0 for ping, PP=1 for pong. -*> \endverbatim -*> -*> \param[in] TAU -*> \verbatim -*> TAU is DOUBLE PRECISION -*> This is the shift. -*> \endverbatim -*> -*> \param[in] SIGMA -*> \verbatim -*> SIGMA is DOUBLE PRECISION -*> This is the accumulated shift up to this step. -*> \endverbatim -*> -*> \param[out] DMIN -*> \verbatim -*> DMIN is DOUBLE PRECISION -*> Minimum value of d. -*> \endverbatim -*> -*> \param[out] DMIN1 -*> \verbatim -*> DMIN1 is DOUBLE PRECISION -*> Minimum value of d, excluding D( N0 ). -*> \endverbatim -*> -*> \param[out] DMIN2 -*> \verbatim -*> DMIN2 is DOUBLE PRECISION -*> Minimum value of d, excluding D( N0 ) and D( N0-1 ). -*> \endverbatim -*> -*> \param[out] DN -*> \verbatim -*> DN is DOUBLE PRECISION -*> d(N0), the last value of d. -*> \endverbatim -*> -*> \param[out] DNM1 -*> \verbatim -*> DNM1 is DOUBLE PRECISION -*> d(N0-1). -*> \endverbatim -*> -*> \param[out] DNM2 -*> \verbatim -*> DNM2 is DOUBLE PRECISION -*> d(N0-2). -*> \endverbatim -*> -*> \param[in] IEEE -*> \verbatim -*> IEEE is LOGICAL -*> Flag for IEEE or non IEEE arithmetic. -*> \endverbatim -*> -*> \param[in] EPS -*> \verbatim -*> EPS is DOUBLE PRECISION -*> This is the value of epsilon used. -*> \endverbatim -*> -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup auxOTHERcomputational -* -* ===================================================================== - SUBROUTINE DLASQ5( I0, N0, Z, PP, TAU, SIGMA, DMIN, DMIN1, DMIN2, - $ DN, DNM1, DNM2, IEEE, EPS ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - LOGICAL IEEE - INTEGER I0, N0, PP - DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DNM1, DNM2, TAU, - $ SIGMA, EPS -* .. -* .. Array Arguments .. - DOUBLE PRECISION Z( * ) -* .. -* -* ===================================================================== -* -* .. Parameter .. - DOUBLE PRECISION ZERO, HALF - PARAMETER ( ZERO = 0.0D0, HALF = 0.5 ) -* .. -* .. Local Scalars .. - INTEGER J4, J4P2 - DOUBLE PRECISION D, EMIN, TEMP, DTHRESH -* .. -* .. Intrinsic Functions .. - INTRINSIC MIN -* .. -* .. Executable Statements .. -* - IF( ( N0-I0-1 ).LE.0 ) - $ RETURN -* - DTHRESH = EPS*(SIGMA+TAU) - IF( TAU.LT.DTHRESH*HALF ) TAU = ZERO - IF( TAU.NE.ZERO ) THEN - J4 = 4*I0 + PP - 3 - EMIN = Z( J4+4 ) - D = Z( J4 ) - TAU - DMIN = D - DMIN1 = -Z( J4 ) -* - IF( IEEE ) THEN -* -* Code for IEEE arithmetic. -* - IF( PP.EQ.0 ) THEN - DO 10 J4 = 4*I0, 4*( N0-3 ), 4 - Z( J4-2 ) = D + Z( J4-1 ) - TEMP = Z( J4+1 ) / Z( J4-2 ) - D = D*TEMP - TAU - DMIN = MIN( DMIN, D ) - Z( J4 ) = Z( J4-1 )*TEMP - EMIN = MIN( Z( J4 ), EMIN ) - 10 CONTINUE - ELSE - DO 20 J4 = 4*I0, 4*( N0-3 ), 4 - Z( J4-3 ) = D + Z( J4 ) - TEMP = Z( J4+2 ) / Z( J4-3 ) - D = D*TEMP - TAU - DMIN = MIN( DMIN, D ) - Z( J4-1 ) = Z( J4 )*TEMP - EMIN = MIN( Z( J4-1 ), EMIN ) - 20 CONTINUE - END IF -* -* Unroll last two steps. -* - DNM2 = D - DMIN2 = DMIN - J4 = 4*( N0-2 ) - PP - J4P2 = J4 + 2*PP - 1 - Z( J4-2 ) = DNM2 + Z( J4P2 ) - Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) ) - DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) ) - TAU - DMIN = MIN( DMIN, DNM1 ) -* - DMIN1 = DMIN - J4 = J4 + 4 - J4P2 = J4 + 2*PP - 1 - Z( J4-2 ) = DNM1 + Z( J4P2 ) - Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) ) - DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) ) - TAU - DMIN = MIN( DMIN, DN ) -* - ELSE -* -* Code for non IEEE arithmetic. -* - IF( PP.EQ.0 ) THEN - DO 30 J4 = 4*I0, 4*( N0-3 ), 4 - Z( J4-2 ) = D + Z( J4-1 ) - IF( D.LT.ZERO ) THEN - RETURN - ELSE - Z( J4 ) = Z( J4+1 )*( Z( J4-1 ) / Z( J4-2 ) ) - D = Z( J4+1 )*( D / Z( J4-2 ) ) - TAU - END IF - DMIN = MIN( DMIN, D ) - EMIN = MIN( EMIN, Z( J4 ) ) - 30 CONTINUE - ELSE - DO 40 J4 = 4*I0, 4*( N0-3 ), 4 - Z( J4-3 ) = D + Z( J4 ) - IF( D.LT.ZERO ) THEN - RETURN - ELSE - Z( J4-1 ) = Z( J4+2 )*( Z( J4 ) / Z( J4-3 ) ) - D = Z( J4+2 )*( D / Z( J4-3 ) ) - TAU - END IF - DMIN = MIN( DMIN, D ) - EMIN = MIN( EMIN, Z( J4-1 ) ) - 40 CONTINUE - END IF -* -* Unroll last two steps. -* - DNM2 = D - DMIN2 = DMIN - J4 = 4*( N0-2 ) - PP - J4P2 = J4 + 2*PP - 1 - Z( J4-2 ) = DNM2 + Z( J4P2 ) - IF( DNM2.LT.ZERO ) THEN - RETURN - ELSE - Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) ) - DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) ) - TAU - END IF - DMIN = MIN( DMIN, DNM1 ) -* - DMIN1 = DMIN - J4 = J4 + 4 - J4P2 = J4 + 2*PP - 1 - Z( J4-2 ) = DNM1 + Z( J4P2 ) - IF( DNM1.LT.ZERO ) THEN - RETURN - ELSE - Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) ) - DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) ) - TAU - END IF - DMIN = MIN( DMIN, DN ) -* - END IF - ELSE -* This is the version that sets d's to zero if they are small enough - J4 = 4*I0 + PP - 3 - EMIN = Z( J4+4 ) - D = Z( J4 ) - TAU - DMIN = D - DMIN1 = -Z( J4 ) - IF( IEEE ) THEN -* -* Code for IEEE arithmetic. -* - IF( PP.EQ.0 ) THEN - DO 50 J4 = 4*I0, 4*( N0-3 ), 4 - Z( J4-2 ) = D + Z( J4-1 ) - TEMP = Z( J4+1 ) / Z( J4-2 ) - D = D*TEMP - TAU - IF( D.LT.DTHRESH ) D = ZERO - DMIN = MIN( DMIN, D ) - Z( J4 ) = Z( J4-1 )*TEMP - EMIN = MIN( Z( J4 ), EMIN ) - 50 CONTINUE - ELSE - DO 60 J4 = 4*I0, 4*( N0-3 ), 4 - Z( J4-3 ) = D + Z( J4 ) - TEMP = Z( J4+2 ) / Z( J4-3 ) - D = D*TEMP - TAU - IF( D.LT.DTHRESH ) D = ZERO - DMIN = MIN( DMIN, D ) - Z( J4-1 ) = Z( J4 )*TEMP - EMIN = MIN( Z( J4-1 ), EMIN ) - 60 CONTINUE - END IF -* -* Unroll last two steps. -* - DNM2 = D - DMIN2 = DMIN - J4 = 4*( N0-2 ) - PP - J4P2 = J4 + 2*PP - 1 - Z( J4-2 ) = DNM2 + Z( J4P2 ) - Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) ) - DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) ) - TAU - DMIN = MIN( DMIN, DNM1 ) -* - DMIN1 = DMIN - J4 = J4 + 4 - J4P2 = J4 + 2*PP - 1 - Z( J4-2 ) = DNM1 + Z( J4P2 ) - Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) ) - DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) ) - TAU - DMIN = MIN( DMIN, DN ) -* - ELSE -* -* Code for non IEEE arithmetic. -* - IF( PP.EQ.0 ) THEN - DO 70 J4 = 4*I0, 4*( N0-3 ), 4 - Z( J4-2 ) = D + Z( J4-1 ) - IF( D.LT.ZERO ) THEN - RETURN - ELSE - Z( J4 ) = Z( J4+1 )*( Z( J4-1 ) / Z( J4-2 ) ) - D = Z( J4+1 )*( D / Z( J4-2 ) ) - TAU - END IF - IF( D.LT.DTHRESH) D = ZERO - DMIN = MIN( DMIN, D ) - EMIN = MIN( EMIN, Z( J4 ) ) - 70 CONTINUE - ELSE - DO 80 J4 = 4*I0, 4*( N0-3 ), 4 - Z( J4-3 ) = D + Z( J4 ) - IF( D.LT.ZERO ) THEN - RETURN - ELSE - Z( J4-1 ) = Z( J4+2 )*( Z( J4 ) / Z( J4-3 ) ) - D = Z( J4+2 )*( D / Z( J4-3 ) ) - TAU - END IF - IF( D.LT.DTHRESH) D = ZERO - DMIN = MIN( DMIN, D ) - EMIN = MIN( EMIN, Z( J4-1 ) ) - 80 CONTINUE - END IF -* -* Unroll last two steps. -* - DNM2 = D - DMIN2 = DMIN - J4 = 4*( N0-2 ) - PP - J4P2 = J4 + 2*PP - 1 - Z( J4-2 ) = DNM2 + Z( J4P2 ) - IF( DNM2.LT.ZERO ) THEN - RETURN - ELSE - Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) ) - DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) ) - TAU - END IF - DMIN = MIN( DMIN, DNM1 ) -* - DMIN1 = DMIN - J4 = J4 + 4 - J4P2 = J4 + 2*PP - 1 - Z( J4-2 ) = DNM1 + Z( J4P2 ) - IF( DNM1.LT.ZERO ) THEN - RETURN - ELSE - Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) ) - DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) ) - TAU - END IF - DMIN = MIN( DMIN, DN ) -* - END IF - END IF -* - Z( J4+2 ) = DN - Z( 4*N0-PP ) = EMIN - RETURN -* -* End of DLASQ5 -* - END diff --git a/lib/linalg/fortran/dlasq6.f b/lib/linalg/fortran/dlasq6.f deleted file mode 100644 index 9218b5060e..0000000000 --- a/lib/linalg/fortran/dlasq6.f +++ /dev/null @@ -1,251 +0,0 @@ -*> \brief \b DLASQ6 computes one dqd transform in ping-pong form. Used by sbdsqr and sstegr. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLASQ6 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLASQ6( I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN, -* DNM1, DNM2 ) -* -* .. Scalar Arguments .. -* INTEGER I0, N0, PP -* DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DNM1, DNM2 -* .. -* .. Array Arguments .. -* DOUBLE PRECISION Z( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLASQ6 computes one dqd (shift equal to zero) transform in -*> ping-pong form, with protection against underflow and overflow. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] I0 -*> \verbatim -*> I0 is INTEGER -*> First index. -*> \endverbatim -*> -*> \param[in] N0 -*> \verbatim -*> N0 is INTEGER -*> Last index. -*> \endverbatim -*> -*> \param[in] Z -*> \verbatim -*> Z is DOUBLE PRECISION array, dimension ( 4*N ) -*> Z holds the qd array. EMIN is stored in Z(4*N0) to avoid -*> an extra argument. -*> \endverbatim -*> -*> \param[in] PP -*> \verbatim -*> PP is INTEGER -*> PP=0 for ping, PP=1 for pong. -*> \endverbatim -*> -*> \param[out] DMIN -*> \verbatim -*> DMIN is DOUBLE PRECISION -*> Minimum value of d. -*> \endverbatim -*> -*> \param[out] DMIN1 -*> \verbatim -*> DMIN1 is DOUBLE PRECISION -*> Minimum value of d, excluding D( N0 ). -*> \endverbatim -*> -*> \param[out] DMIN2 -*> \verbatim -*> DMIN2 is DOUBLE PRECISION -*> Minimum value of d, excluding D( N0 ) and D( N0-1 ). -*> \endverbatim -*> -*> \param[out] DN -*> \verbatim -*> DN is DOUBLE PRECISION -*> d(N0), the last value of d. -*> \endverbatim -*> -*> \param[out] DNM1 -*> \verbatim -*> DNM1 is DOUBLE PRECISION -*> d(N0-1). -*> \endverbatim -*> -*> \param[out] DNM2 -*> \verbatim -*> DNM2 is DOUBLE PRECISION -*> d(N0-2). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup auxOTHERcomputational -* -* ===================================================================== - SUBROUTINE DLASQ6( I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN, - $ DNM1, DNM2 ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER I0, N0, PP - DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DNM1, DNM2 -* .. -* .. Array Arguments .. - DOUBLE PRECISION Z( * ) -* .. -* -* ===================================================================== -* -* .. Parameter .. - DOUBLE PRECISION ZERO - PARAMETER ( ZERO = 0.0D0 ) -* .. -* .. Local Scalars .. - INTEGER J4, J4P2 - DOUBLE PRECISION D, EMIN, SAFMIN, TEMP -* .. -* .. External Function .. - DOUBLE PRECISION DLAMCH - EXTERNAL DLAMCH -* .. -* .. Intrinsic Functions .. - INTRINSIC MIN -* .. -* .. Executable Statements .. -* - IF( ( N0-I0-1 ).LE.0 ) - $ RETURN -* - SAFMIN = DLAMCH( 'Safe minimum' ) - J4 = 4*I0 + PP - 3 - EMIN = Z( J4+4 ) - D = Z( J4 ) - DMIN = D -* - IF( PP.EQ.0 ) THEN - DO 10 J4 = 4*I0, 4*( N0-3 ), 4 - Z( J4-2 ) = D + Z( J4-1 ) - IF( Z( J4-2 ).EQ.ZERO ) THEN - Z( J4 ) = ZERO - D = Z( J4+1 ) - DMIN = D - EMIN = ZERO - ELSE IF( SAFMIN*Z( J4+1 ).LT.Z( J4-2 ) .AND. - $ SAFMIN*Z( J4-2 ).LT.Z( J4+1 ) ) THEN - TEMP = Z( J4+1 ) / Z( J4-2 ) - Z( J4 ) = Z( J4-1 )*TEMP - D = D*TEMP - ELSE - Z( J4 ) = Z( J4+1 )*( Z( J4-1 ) / Z( J4-2 ) ) - D = Z( J4+1 )*( D / Z( J4-2 ) ) - END IF - DMIN = MIN( DMIN, D ) - EMIN = MIN( EMIN, Z( J4 ) ) - 10 CONTINUE - ELSE - DO 20 J4 = 4*I0, 4*( N0-3 ), 4 - Z( J4-3 ) = D + Z( J4 ) - IF( Z( J4-3 ).EQ.ZERO ) THEN - Z( J4-1 ) = ZERO - D = Z( J4+2 ) - DMIN = D - EMIN = ZERO - ELSE IF( SAFMIN*Z( J4+2 ).LT.Z( J4-3 ) .AND. - $ SAFMIN*Z( J4-3 ).LT.Z( J4+2 ) ) THEN - TEMP = Z( J4+2 ) / Z( J4-3 ) - Z( J4-1 ) = Z( J4 )*TEMP - D = D*TEMP - ELSE - Z( J4-1 ) = Z( J4+2 )*( Z( J4 ) / Z( J4-3 ) ) - D = Z( J4+2 )*( D / Z( J4-3 ) ) - END IF - DMIN = MIN( DMIN, D ) - EMIN = MIN( EMIN, Z( J4-1 ) ) - 20 CONTINUE - END IF -* -* Unroll last two steps. -* - DNM2 = D - DMIN2 = DMIN - J4 = 4*( N0-2 ) - PP - J4P2 = J4 + 2*PP - 1 - Z( J4-2 ) = DNM2 + Z( J4P2 ) - IF( Z( J4-2 ).EQ.ZERO ) THEN - Z( J4 ) = ZERO - DNM1 = Z( J4P2+2 ) - DMIN = DNM1 - EMIN = ZERO - ELSE IF( SAFMIN*Z( J4P2+2 ).LT.Z( J4-2 ) .AND. - $ SAFMIN*Z( J4-2 ).LT.Z( J4P2+2 ) ) THEN - TEMP = Z( J4P2+2 ) / Z( J4-2 ) - Z( J4 ) = Z( J4P2 )*TEMP - DNM1 = DNM2*TEMP - ELSE - Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) ) - DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) ) - END IF - DMIN = MIN( DMIN, DNM1 ) -* - DMIN1 = DMIN - J4 = J4 + 4 - J4P2 = J4 + 2*PP - 1 - Z( J4-2 ) = DNM1 + Z( J4P2 ) - IF( Z( J4-2 ).EQ.ZERO ) THEN - Z( J4 ) = ZERO - DN = Z( J4P2+2 ) - DMIN = DN - EMIN = ZERO - ELSE IF( SAFMIN*Z( J4P2+2 ).LT.Z( J4-2 ) .AND. - $ SAFMIN*Z( J4-2 ).LT.Z( J4P2+2 ) ) THEN - TEMP = Z( J4P2+2 ) / Z( J4-2 ) - Z( J4 ) = Z( J4P2 )*TEMP - DN = DNM1*TEMP - ELSE - Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) ) - DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) ) - END IF - DMIN = MIN( DMIN, DN ) -* - Z( J4+2 ) = DN - Z( 4*N0-PP ) = EMIN - RETURN -* -* End of DLASQ6 -* - END diff --git a/lib/linalg/fortran/dlasr.f b/lib/linalg/fortran/dlasr.f deleted file mode 100644 index dd0cedd85e..0000000000 --- a/lib/linalg/fortran/dlasr.f +++ /dev/null @@ -1,433 +0,0 @@ -*> \brief \b DLASR applies a sequence of plane rotations to a general rectangular matrix. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLASR + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA ) -* -* .. Scalar Arguments .. -* CHARACTER DIRECT, PIVOT, SIDE -* INTEGER LDA, M, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), C( * ), S( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLASR applies a sequence of plane rotations to a real matrix A, -*> from either the left or the right. -*> -*> When SIDE = 'L', the transformation takes the form -*> -*> A := P*A -*> -*> and when SIDE = 'R', the transformation takes the form -*> -*> A := A*P**T -*> -*> where P is an orthogonal matrix consisting of a sequence of z plane -*> rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R', -*> and P**T is the transpose of P. -*> -*> When DIRECT = 'F' (Forward sequence), then -*> -*> P = P(z-1) * ... * P(2) * P(1) -*> -*> and when DIRECT = 'B' (Backward sequence), then -*> -*> P = P(1) * P(2) * ... * P(z-1) -*> -*> where P(k) is a plane rotation matrix defined by the 2-by-2 rotation -*> -*> R(k) = ( c(k) s(k) ) -*> = ( -s(k) c(k) ). -*> -*> When PIVOT = 'V' (Variable pivot), the rotation is performed -*> for the plane (k,k+1), i.e., P(k) has the form -*> -*> P(k) = ( 1 ) -*> ( ... ) -*> ( 1 ) -*> ( c(k) s(k) ) -*> ( -s(k) c(k) ) -*> ( 1 ) -*> ( ... ) -*> ( 1 ) -*> -*> where R(k) appears as a rank-2 modification to the identity matrix in -*> rows and columns k and k+1. -*> -*> When PIVOT = 'T' (Top pivot), the rotation is performed for the -*> plane (1,k+1), so P(k) has the form -*> -*> P(k) = ( c(k) s(k) ) -*> ( 1 ) -*> ( ... ) -*> ( 1 ) -*> ( -s(k) c(k) ) -*> ( 1 ) -*> ( ... ) -*> ( 1 ) -*> -*> where R(k) appears in rows and columns 1 and k+1. -*> -*> Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is -*> performed for the plane (k,z), giving P(k) the form -*> -*> P(k) = ( 1 ) -*> ( ... ) -*> ( 1 ) -*> ( c(k) s(k) ) -*> ( 1 ) -*> ( ... ) -*> ( 1 ) -*> ( -s(k) c(k) ) -*> -*> where R(k) appears in rows and columns k and z. The rotations are -*> performed without ever forming P(k) explicitly. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] SIDE -*> \verbatim -*> SIDE is CHARACTER*1 -*> Specifies whether the plane rotation matrix P is applied to -*> A on the left or the right. -*> = 'L': Left, compute A := P*A -*> = 'R': Right, compute A:= A*P**T -*> \endverbatim -*> -*> \param[in] PIVOT -*> \verbatim -*> PIVOT is CHARACTER*1 -*> Specifies the plane for which P(k) is a plane rotation -*> matrix. -*> = 'V': Variable pivot, the plane (k,k+1) -*> = 'T': Top pivot, the plane (1,k+1) -*> = 'B': Bottom pivot, the plane (k,z) -*> \endverbatim -*> -*> \param[in] DIRECT -*> \verbatim -*> DIRECT is CHARACTER*1 -*> Specifies whether P is a forward or backward sequence of -*> plane rotations. -*> = 'F': Forward, P = P(z-1)*...*P(2)*P(1) -*> = 'B': Backward, P = P(1)*P(2)*...*P(z-1) -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix A. If m <= 1, an immediate -*> return is effected. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix A. If n <= 1, an -*> immediate return is effected. -*> \endverbatim -*> -*> \param[in] C -*> \verbatim -*> C is DOUBLE PRECISION array, dimension -*> (M-1) if SIDE = 'L' -*> (N-1) if SIDE = 'R' -*> The cosines c(k) of the plane rotations. -*> \endverbatim -*> -*> \param[in] S -*> \verbatim -*> S is DOUBLE PRECISION array, dimension -*> (M-1) if SIDE = 'L' -*> (N-1) if SIDE = 'R' -*> The sines s(k) of the plane rotations. The 2-by-2 plane -*> rotation part of the matrix P(k), R(k), has the form -*> R(k) = ( c(k) s(k) ) -*> ( -s(k) c(k) ). -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> The M-by-N matrix A. On exit, A is overwritten by P*A if -*> SIDE = 'L' or by A*P**T if SIDE = 'R'. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,M). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup OTHERauxiliary -* -* ===================================================================== - SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER DIRECT, PIVOT, SIDE - INTEGER LDA, M, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), C( * ), S( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE, ZERO - PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) -* .. -* .. Local Scalars .. - INTEGER I, INFO, J - DOUBLE PRECISION CTEMP, STEMP, TEMP -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* .. Executable Statements .. -* -* Test the input parameters -* - INFO = 0 - IF( .NOT.( LSAME( SIDE, 'L' ) .OR. LSAME( SIDE, 'R' ) ) ) THEN - INFO = 1 - ELSE IF( .NOT.( LSAME( PIVOT, 'V' ) .OR. LSAME( PIVOT, - $ 'T' ) .OR. LSAME( PIVOT, 'B' ) ) ) THEN - INFO = 2 - ELSE IF( .NOT.( LSAME( DIRECT, 'F' ) .OR. LSAME( DIRECT, 'B' ) ) ) - $ THEN - INFO = 3 - ELSE IF( M.LT.0 ) THEN - INFO = 4 - ELSE IF( N.LT.0 ) THEN - INFO = 5 - ELSE IF( LDA.LT.MAX( 1, M ) ) THEN - INFO = 9 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DLASR ', INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( ( M.EQ.0 ) .OR. ( N.EQ.0 ) ) - $ RETURN - IF( LSAME( SIDE, 'L' ) ) THEN -* -* Form P * A -* - IF( LSAME( PIVOT, 'V' ) ) THEN - IF( LSAME( DIRECT, 'F' ) ) THEN - DO 20 J = 1, M - 1 - CTEMP = C( J ) - STEMP = S( J ) - IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN - DO 10 I = 1, N - TEMP = A( J+1, I ) - A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I ) - A( J, I ) = STEMP*TEMP + CTEMP*A( J, I ) - 10 CONTINUE - END IF - 20 CONTINUE - ELSE IF( LSAME( DIRECT, 'B' ) ) THEN - DO 40 J = M - 1, 1, -1 - CTEMP = C( J ) - STEMP = S( J ) - IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN - DO 30 I = 1, N - TEMP = A( J+1, I ) - A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I ) - A( J, I ) = STEMP*TEMP + CTEMP*A( J, I ) - 30 CONTINUE - END IF - 40 CONTINUE - END IF - ELSE IF( LSAME( PIVOT, 'T' ) ) THEN - IF( LSAME( DIRECT, 'F' ) ) THEN - DO 60 J = 2, M - CTEMP = C( J-1 ) - STEMP = S( J-1 ) - IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN - DO 50 I = 1, N - TEMP = A( J, I ) - A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I ) - A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I ) - 50 CONTINUE - END IF - 60 CONTINUE - ELSE IF( LSAME( DIRECT, 'B' ) ) THEN - DO 80 J = M, 2, -1 - CTEMP = C( J-1 ) - STEMP = S( J-1 ) - IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN - DO 70 I = 1, N - TEMP = A( J, I ) - A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I ) - A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I ) - 70 CONTINUE - END IF - 80 CONTINUE - END IF - ELSE IF( LSAME( PIVOT, 'B' ) ) THEN - IF( LSAME( DIRECT, 'F' ) ) THEN - DO 100 J = 1, M - 1 - CTEMP = C( J ) - STEMP = S( J ) - IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN - DO 90 I = 1, N - TEMP = A( J, I ) - A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP - A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP - 90 CONTINUE - END IF - 100 CONTINUE - ELSE IF( LSAME( DIRECT, 'B' ) ) THEN - DO 120 J = M - 1, 1, -1 - CTEMP = C( J ) - STEMP = S( J ) - IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN - DO 110 I = 1, N - TEMP = A( J, I ) - A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP - A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP - 110 CONTINUE - END IF - 120 CONTINUE - END IF - END IF - ELSE IF( LSAME( SIDE, 'R' ) ) THEN -* -* Form A * P**T -* - IF( LSAME( PIVOT, 'V' ) ) THEN - IF( LSAME( DIRECT, 'F' ) ) THEN - DO 140 J = 1, N - 1 - CTEMP = C( J ) - STEMP = S( J ) - IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN - DO 130 I = 1, M - TEMP = A( I, J+1 ) - A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J ) - A( I, J ) = STEMP*TEMP + CTEMP*A( I, J ) - 130 CONTINUE - END IF - 140 CONTINUE - ELSE IF( LSAME( DIRECT, 'B' ) ) THEN - DO 160 J = N - 1, 1, -1 - CTEMP = C( J ) - STEMP = S( J ) - IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN - DO 150 I = 1, M - TEMP = A( I, J+1 ) - A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J ) - A( I, J ) = STEMP*TEMP + CTEMP*A( I, J ) - 150 CONTINUE - END IF - 160 CONTINUE - END IF - ELSE IF( LSAME( PIVOT, 'T' ) ) THEN - IF( LSAME( DIRECT, 'F' ) ) THEN - DO 180 J = 2, N - CTEMP = C( J-1 ) - STEMP = S( J-1 ) - IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN - DO 170 I = 1, M - TEMP = A( I, J ) - A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 ) - A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 ) - 170 CONTINUE - END IF - 180 CONTINUE - ELSE IF( LSAME( DIRECT, 'B' ) ) THEN - DO 200 J = N, 2, -1 - CTEMP = C( J-1 ) - STEMP = S( J-1 ) - IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN - DO 190 I = 1, M - TEMP = A( I, J ) - A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 ) - A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 ) - 190 CONTINUE - END IF - 200 CONTINUE - END IF - ELSE IF( LSAME( PIVOT, 'B' ) ) THEN - IF( LSAME( DIRECT, 'F' ) ) THEN - DO 220 J = 1, N - 1 - CTEMP = C( J ) - STEMP = S( J ) - IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN - DO 210 I = 1, M - TEMP = A( I, J ) - A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP - A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP - 210 CONTINUE - END IF - 220 CONTINUE - ELSE IF( LSAME( DIRECT, 'B' ) ) THEN - DO 240 J = N - 1, 1, -1 - CTEMP = C( J ) - STEMP = S( J ) - IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN - DO 230 I = 1, M - TEMP = A( I, J ) - A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP - A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP - 230 CONTINUE - END IF - 240 CONTINUE - END IF - END IF - END IF -* - RETURN -* -* End of DLASR -* - END diff --git a/lib/linalg/fortran/dlasrt.f b/lib/linalg/fortran/dlasrt.f deleted file mode 100644 index d789239e3d..0000000000 --- a/lib/linalg/fortran/dlasrt.f +++ /dev/null @@ -1,300 +0,0 @@ -*> \brief \b DLASRT sorts numbers in increasing or decreasing order. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLASRT + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLASRT( ID, N, D, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER ID -* INTEGER INFO, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION D( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> Sort the numbers in D in increasing order (if ID = 'I') or -*> in decreasing order (if ID = 'D' ). -*> -*> Use Quick Sort, reverting to Insertion sort on arrays of -*> size <= 20. Dimension of STACK limits N to about 2**32. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] ID -*> \verbatim -*> ID is CHARACTER*1 -*> = 'I': sort D in increasing order; -*> = 'D': sort D in decreasing order. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The length of the array D. -*> \endverbatim -*> -*> \param[in,out] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension (N) -*> On entry, the array to be sorted. -*> On exit, D has been sorted into increasing order -*> (D(1) <= ... <= D(N) ) or into decreasing order -*> (D(1) >= ... >= D(N) ), depending on ID. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup auxOTHERcomputational -* -* ===================================================================== - SUBROUTINE DLASRT( ID, N, D, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER ID - INTEGER INFO, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION D( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - INTEGER SELECT - PARAMETER ( SELECT = 20 ) -* .. -* .. Local Scalars .. - INTEGER DIR, ENDD, I, J, START, STKPNT - DOUBLE PRECISION D1, D2, D3, DMNMX, TMP -* .. -* .. Local Arrays .. - INTEGER STACK( 2, 32 ) -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL XERBLA -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 - DIR = -1 - IF( LSAME( ID, 'D' ) ) THEN - DIR = 0 - ELSE IF( LSAME( ID, 'I' ) ) THEN - DIR = 1 - END IF - IF( DIR.EQ.-1 ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DLASRT', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( N.LE.1 ) - $ RETURN -* - STKPNT = 1 - STACK( 1, 1 ) = 1 - STACK( 2, 1 ) = N - 10 CONTINUE - START = STACK( 1, STKPNT ) - ENDD = STACK( 2, STKPNT ) - STKPNT = STKPNT - 1 - IF( ENDD-START.LE.SELECT .AND. ENDD-START.GT.0 ) THEN -* -* Do Insertion sort on D( START:ENDD ) -* - IF( DIR.EQ.0 ) THEN -* -* Sort into decreasing order -* - DO 30 I = START + 1, ENDD - DO 20 J = I, START + 1, -1 - IF( D( J ).GT.D( J-1 ) ) THEN - DMNMX = D( J ) - D( J ) = D( J-1 ) - D( J-1 ) = DMNMX - ELSE - GO TO 30 - END IF - 20 CONTINUE - 30 CONTINUE -* - ELSE -* -* Sort into increasing order -* - DO 50 I = START + 1, ENDD - DO 40 J = I, START + 1, -1 - IF( D( J ).LT.D( J-1 ) ) THEN - DMNMX = D( J ) - D( J ) = D( J-1 ) - D( J-1 ) = DMNMX - ELSE - GO TO 50 - END IF - 40 CONTINUE - 50 CONTINUE -* - END IF -* - ELSE IF( ENDD-START.GT.SELECT ) THEN -* -* Partition D( START:ENDD ) and stack parts, largest one first -* -* Choose partition entry as median of 3 -* - D1 = D( START ) - D2 = D( ENDD ) - I = ( START+ENDD ) / 2 - D3 = D( I ) - IF( D1.LT.D2 ) THEN - IF( D3.LT.D1 ) THEN - DMNMX = D1 - ELSE IF( D3.LT.D2 ) THEN - DMNMX = D3 - ELSE - DMNMX = D2 - END IF - ELSE - IF( D3.LT.D2 ) THEN - DMNMX = D2 - ELSE IF( D3.LT.D1 ) THEN - DMNMX = D3 - ELSE - DMNMX = D1 - END IF - END IF -* - IF( DIR.EQ.0 ) THEN -* -* Sort into decreasing order -* - I = START - 1 - J = ENDD + 1 - 60 CONTINUE - 70 CONTINUE - J = J - 1 - IF( D( J ).LT.DMNMX ) - $ GO TO 70 - 80 CONTINUE - I = I + 1 - IF( D( I ).GT.DMNMX ) - $ GO TO 80 - IF( I.LT.J ) THEN - TMP = D( I ) - D( I ) = D( J ) - D( J ) = TMP - GO TO 60 - END IF - IF( J-START.GT.ENDD-J-1 ) THEN - STKPNT = STKPNT + 1 - STACK( 1, STKPNT ) = START - STACK( 2, STKPNT ) = J - STKPNT = STKPNT + 1 - STACK( 1, STKPNT ) = J + 1 - STACK( 2, STKPNT ) = ENDD - ELSE - STKPNT = STKPNT + 1 - STACK( 1, STKPNT ) = J + 1 - STACK( 2, STKPNT ) = ENDD - STKPNT = STKPNT + 1 - STACK( 1, STKPNT ) = START - STACK( 2, STKPNT ) = J - END IF - ELSE -* -* Sort into increasing order -* - I = START - 1 - J = ENDD + 1 - 90 CONTINUE - 100 CONTINUE - J = J - 1 - IF( D( J ).GT.DMNMX ) - $ GO TO 100 - 110 CONTINUE - I = I + 1 - IF( D( I ).LT.DMNMX ) - $ GO TO 110 - IF( I.LT.J ) THEN - TMP = D( I ) - D( I ) = D( J ) - D( J ) = TMP - GO TO 90 - END IF - IF( J-START.GT.ENDD-J-1 ) THEN - STKPNT = STKPNT + 1 - STACK( 1, STKPNT ) = START - STACK( 2, STKPNT ) = J - STKPNT = STKPNT + 1 - STACK( 1, STKPNT ) = J + 1 - STACK( 2, STKPNT ) = ENDD - ELSE - STKPNT = STKPNT + 1 - STACK( 1, STKPNT ) = J + 1 - STACK( 2, STKPNT ) = ENDD - STKPNT = STKPNT + 1 - STACK( 1, STKPNT ) = START - STACK( 2, STKPNT ) = J - END IF - END IF - END IF - IF( STKPNT.GT.0 ) - $ GO TO 10 - RETURN -* -* End of DLASRT -* - END diff --git a/lib/linalg/fortran/dlassq.f b/lib/linalg/fortran/dlassq.f deleted file mode 100644 index 885395e3c9..0000000000 --- a/lib/linalg/fortran/dlassq.f +++ /dev/null @@ -1,155 +0,0 @@ -*> \brief \b DLASSQ updates a sum of squares represented in scaled form. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLASSQ + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLASSQ( N, X, INCX, SCALE, SUMSQ ) -* -* .. Scalar Arguments .. -* INTEGER INCX, N -* DOUBLE PRECISION SCALE, SUMSQ -* .. -* .. Array Arguments .. -* DOUBLE PRECISION X( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLASSQ returns the values scl and smsq such that -*> -*> ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq, -*> -*> where x( i ) = X( 1 + ( i - 1 )*INCX ). The value of sumsq is -*> assumed to be non-negative and scl returns the value -*> -*> scl = max( scale, abs( x( i ) ) ). -*> -*> scale and sumsq must be supplied in SCALE and SUMSQ and -*> scl and smsq are overwritten on SCALE and SUMSQ respectively. -*> -*> The routine makes only one pass through the vector x. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of elements to be used from the vector X. -*> \endverbatim -*> -*> \param[in] X -*> \verbatim -*> X is DOUBLE PRECISION array, dimension (N) -*> The vector for which a scaled sum of squares is computed. -*> x( i ) = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n. -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> The increment between successive values of the vector X. -*> INCX > 0. -*> \endverbatim -*> -*> \param[in,out] SCALE -*> \verbatim -*> SCALE is DOUBLE PRECISION -*> On entry, the value scale in the equation above. -*> On exit, SCALE is overwritten with scl , the scaling factor -*> for the sum of squares. -*> \endverbatim -*> -*> \param[in,out] SUMSQ -*> \verbatim -*> SUMSQ is DOUBLE PRECISION -*> On entry, the value sumsq in the equation above. -*> On exit, SUMSQ is overwritten with smsq , the basic sum of -*> squares from which scl has been factored out. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \date December 2016 -* -*> \ingroup OTHERauxiliary -* -* ===================================================================== - SUBROUTINE DLASSQ( N, X, INCX, SCALE, SUMSQ ) -* -* -- LAPACK auxiliary routine (version 3.7.0) -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* December 2016 -* -* .. Scalar Arguments .. - INTEGER INCX, N - DOUBLE PRECISION SCALE, SUMSQ -* .. -* .. Array Arguments .. - DOUBLE PRECISION X( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO - PARAMETER ( ZERO = 0.0D+0 ) -* .. -* .. Local Scalars .. - INTEGER IX - DOUBLE PRECISION ABSXI -* .. -* .. External Functions .. - LOGICAL DISNAN - EXTERNAL DISNAN -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS -* .. -* .. Executable Statements .. -* - IF( N.GT.0 ) THEN - DO 10 IX = 1, 1 + ( N-1 )*INCX, INCX - ABSXI = ABS( X( IX ) ) - IF( ABSXI.GT.ZERO.OR.DISNAN( ABSXI ) ) THEN - IF( SCALE.LT.ABSXI ) THEN - SUMSQ = 1 + SUMSQ*( SCALE / ABSXI )**2 - SCALE = ABSXI - ELSE - SUMSQ = SUMSQ + ( ABSXI / SCALE )**2 - END IF - END IF - 10 CONTINUE - END IF - RETURN -* -* End of DLASSQ -* - END diff --git a/lib/linalg/fortran/dlasv2.f b/lib/linalg/fortran/dlasv2.f deleted file mode 100644 index 64a06dee1a..0000000000 --- a/lib/linalg/fortran/dlasv2.f +++ /dev/null @@ -1,322 +0,0 @@ -*> \brief \b DLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLASV2 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLASV2( F, G, H, SSMIN, SSMAX, SNR, CSR, SNL, CSL ) -* -* .. Scalar Arguments .. -* DOUBLE PRECISION CSL, CSR, F, G, H, SNL, SNR, SSMAX, SSMIN -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLASV2 computes the singular value decomposition of a 2-by-2 -*> triangular matrix -*> [ F G ] -*> [ 0 H ]. -*> On return, abs(SSMAX) is the larger singular value, abs(SSMIN) is the -*> smaller singular value, and (CSL,SNL) and (CSR,SNR) are the left and -*> right singular vectors for abs(SSMAX), giving the decomposition -*> -*> [ CSL SNL ] [ F G ] [ CSR -SNR ] = [ SSMAX 0 ] -*> [-SNL CSL ] [ 0 H ] [ SNR CSR ] [ 0 SSMIN ]. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] F -*> \verbatim -*> F is DOUBLE PRECISION -*> The (1,1) element of the 2-by-2 matrix. -*> \endverbatim -*> -*> \param[in] G -*> \verbatim -*> G is DOUBLE PRECISION -*> The (1,2) element of the 2-by-2 matrix. -*> \endverbatim -*> -*> \param[in] H -*> \verbatim -*> H is DOUBLE PRECISION -*> The (2,2) element of the 2-by-2 matrix. -*> \endverbatim -*> -*> \param[out] SSMIN -*> \verbatim -*> SSMIN is DOUBLE PRECISION -*> abs(SSMIN) is the smaller singular value. -*> \endverbatim -*> -*> \param[out] SSMAX -*> \verbatim -*> SSMAX is DOUBLE PRECISION -*> abs(SSMAX) is the larger singular value. -*> \endverbatim -*> -*> \param[out] SNL -*> \verbatim -*> SNL is DOUBLE PRECISION -*> \endverbatim -*> -*> \param[out] CSL -*> \verbatim -*> CSL is DOUBLE PRECISION -*> The vector (CSL, SNL) is a unit left singular vector for the -*> singular value abs(SSMAX). -*> \endverbatim -*> -*> \param[out] SNR -*> \verbatim -*> SNR is DOUBLE PRECISION -*> \endverbatim -*> -*> \param[out] CSR -*> \verbatim -*> CSR is DOUBLE PRECISION -*> The vector (CSR, SNR) is a unit right singular vector for the -*> singular value abs(SSMAX). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup OTHERauxiliary -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> Any input parameter may be aliased with any output parameter. -*> -*> Barring over/underflow and assuming a guard digit in subtraction, all -*> output quantities are correct to within a few units in the last -*> place (ulps). -*> -*> In IEEE arithmetic, the code works correctly if one matrix element is -*> infinite. -*> -*> Overflow will not occur unless the largest singular value itself -*> overflows or is within a few ulps of overflow. (On machines with -*> partial overflow, like the Cray, overflow may occur if the largest -*> singular value is within a factor of 2 of overflow.) -*> -*> Underflow is harmless if underflow is gradual. Otherwise, results -*> may correspond to a matrix modified by perturbations of size near -*> the underflow threshold. -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DLASV2( F, G, H, SSMIN, SSMAX, SNR, CSR, SNL, CSL ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - DOUBLE PRECISION CSL, CSR, F, G, H, SNL, SNR, SSMAX, SSMIN -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO - PARAMETER ( ZERO = 0.0D0 ) - DOUBLE PRECISION HALF - PARAMETER ( HALF = 0.5D0 ) - DOUBLE PRECISION ONE - PARAMETER ( ONE = 1.0D0 ) - DOUBLE PRECISION TWO - PARAMETER ( TWO = 2.0D0 ) - DOUBLE PRECISION FOUR - PARAMETER ( FOUR = 4.0D0 ) -* .. -* .. Local Scalars .. - LOGICAL GASMAL, SWAP - INTEGER PMAX - DOUBLE PRECISION A, CLT, CRT, D, FA, FT, GA, GT, HA, HT, L, M, - $ MM, R, S, SLT, SRT, T, TEMP, TSIGN, TT -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, SIGN, SQRT -* .. -* .. External Functions .. - DOUBLE PRECISION DLAMCH - EXTERNAL DLAMCH -* .. -* .. Executable Statements .. -* - FT = F - FA = ABS( FT ) - HT = H - HA = ABS( H ) -* -* PMAX points to the maximum absolute element of matrix -* PMAX = 1 if F largest in absolute values -* PMAX = 2 if G largest in absolute values -* PMAX = 3 if H largest in absolute values -* - PMAX = 1 - SWAP = ( HA.GT.FA ) - IF( SWAP ) THEN - PMAX = 3 - TEMP = FT - FT = HT - HT = TEMP - TEMP = FA - FA = HA - HA = TEMP -* -* Now FA .ge. HA -* - END IF - GT = G - GA = ABS( GT ) - IF( GA.EQ.ZERO ) THEN -* -* Diagonal matrix -* - SSMIN = HA - SSMAX = FA - CLT = ONE - CRT = ONE - SLT = ZERO - SRT = ZERO - ELSE - GASMAL = .TRUE. - IF( GA.GT.FA ) THEN - PMAX = 2 - IF( ( FA / GA ).LT.DLAMCH( 'EPS' ) ) THEN -* -* Case of very large GA -* - GASMAL = .FALSE. - SSMAX = GA - IF( HA.GT.ONE ) THEN - SSMIN = FA / ( GA / HA ) - ELSE - SSMIN = ( FA / GA )*HA - END IF - CLT = ONE - SLT = HT / GT - SRT = ONE - CRT = FT / GT - END IF - END IF - IF( GASMAL ) THEN -* -* Normal case -* - D = FA - HA - IF( D.EQ.FA ) THEN -* -* Copes with infinite F or H -* - L = ONE - ELSE - L = D / FA - END IF -* -* Note that 0 .le. L .le. 1 -* - M = GT / FT -* -* Note that abs(M) .le. 1/macheps -* - T = TWO - L -* -* Note that T .ge. 1 -* - MM = M*M - TT = T*T - S = SQRT( TT+MM ) -* -* Note that 1 .le. S .le. 1 + 1/macheps -* - IF( L.EQ.ZERO ) THEN - R = ABS( M ) - ELSE - R = SQRT( L*L+MM ) - END IF -* -* Note that 0 .le. R .le. 1 + 1/macheps -* - A = HALF*( S+R ) -* -* Note that 1 .le. A .le. 1 + abs(M) -* - SSMIN = HA / A - SSMAX = FA*A - IF( MM.EQ.ZERO ) THEN -* -* Note that M is very tiny -* - IF( L.EQ.ZERO ) THEN - T = SIGN( TWO, FT )*SIGN( ONE, GT ) - ELSE - T = GT / SIGN( D, FT ) + M / T - END IF - ELSE - T = ( M / ( S+T )+M / ( R+L ) )*( ONE+A ) - END IF - L = SQRT( T*T+FOUR ) - CRT = TWO / L - SRT = T / L - CLT = ( CRT+SRT*M ) / A - SLT = ( HT / FT )*SRT / A - END IF - END IF - IF( SWAP ) THEN - CSL = SRT - SNL = CRT - CSR = SLT - SNR = CLT - ELSE - CSL = CLT - SNL = SLT - CSR = CRT - SNR = SRT - END IF -* -* Correct signs of SSMAX and SSMIN -* - IF( PMAX.EQ.1 ) - $ TSIGN = SIGN( ONE, CSR )*SIGN( ONE, CSL )*SIGN( ONE, F ) - IF( PMAX.EQ.2 ) - $ TSIGN = SIGN( ONE, SNR )*SIGN( ONE, CSL )*SIGN( ONE, G ) - IF( PMAX.EQ.3 ) - $ TSIGN = SIGN( ONE, SNR )*SIGN( ONE, SNL )*SIGN( ONE, H ) - SSMAX = SIGN( SSMAX, TSIGN ) - SSMIN = SIGN( SSMIN, TSIGN*SIGN( ONE, F )*SIGN( ONE, H ) ) - RETURN -* -* End of DLASV2 -* - END diff --git a/lib/linalg/fortran/dlaswp.f b/lib/linalg/fortran/dlaswp.f deleted file mode 100644 index b35729a205..0000000000 --- a/lib/linalg/fortran/dlaswp.f +++ /dev/null @@ -1,190 +0,0 @@ -*> \brief \b DLASWP performs a series of row interchanges on a general rectangular matrix. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLASWP + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLASWP( N, A, LDA, K1, K2, IPIV, INCX ) -* -* .. Scalar Arguments .. -* INTEGER INCX, K1, K2, LDA, N -* .. -* .. Array Arguments .. -* INTEGER IPIV( * ) -* DOUBLE PRECISION A( LDA, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLASWP performs a series of row interchanges on the matrix A. -*> One row interchange is initiated for each of rows K1 through K2 of A. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix A. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the matrix of column dimension N to which the row -*> interchanges will be applied. -*> On exit, the permuted matrix. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. -*> \endverbatim -*> -*> \param[in] K1 -*> \verbatim -*> K1 is INTEGER -*> The first element of IPIV for which a row interchange will -*> be done. -*> \endverbatim -*> -*> \param[in] K2 -*> \verbatim -*> K2 is INTEGER -*> (K2-K1+1) is the number of elements of IPIV for which a row -*> interchange will be done. -*> \endverbatim -*> -*> \param[in] IPIV -*> \verbatim -*> IPIV is INTEGER array, dimension (K1+(K2-K1)*abs(INCX)) -*> The vector of pivot indices. Only the elements in positions -*> K1 through K1+(K2-K1)*abs(INCX) of IPIV are accessed. -*> IPIV(K1+(K-K1)*abs(INCX)) = L implies rows K and L are to be -*> interchanged. -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> The increment between successive values of IPIV. If INCX -*> is negative, the pivots are applied in reverse order. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleOTHERauxiliary -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> Modified by -*> R. C. Whaley, Computer Science Dept., Univ. of Tenn., Knoxville, USA -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DLASWP( N, A, LDA, K1, K2, IPIV, INCX ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INCX, K1, K2, LDA, N -* .. -* .. Array Arguments .. - INTEGER IPIV( * ) - DOUBLE PRECISION A( LDA, * ) -* .. -* -* ===================================================================== -* -* .. Local Scalars .. - INTEGER I, I1, I2, INC, IP, IX, IX0, J, K, N32 - DOUBLE PRECISION TEMP -* .. -* .. Executable Statements .. -* -* Interchange row I with row IPIV(K1+(I-K1)*abs(INCX)) for each of rows -* K1 through K2. -* - IF( INCX.GT.0 ) THEN - IX0 = K1 - I1 = K1 - I2 = K2 - INC = 1 - ELSE IF( INCX.LT.0 ) THEN - IX0 = K1 + ( K1-K2 )*INCX - I1 = K2 - I2 = K1 - INC = -1 - ELSE - RETURN - END IF -* - N32 = ( N / 32 )*32 - IF( N32.NE.0 ) THEN - DO 30 J = 1, N32, 32 - IX = IX0 - DO 20 I = I1, I2, INC - IP = IPIV( IX ) - IF( IP.NE.I ) THEN - DO 10 K = J, J + 31 - TEMP = A( I, K ) - A( I, K ) = A( IP, K ) - A( IP, K ) = TEMP - 10 CONTINUE - END IF - IX = IX + INCX - 20 CONTINUE - 30 CONTINUE - END IF - IF( N32.NE.N ) THEN - N32 = N32 + 1 - IX = IX0 - DO 50 I = I1, I2, INC - IP = IPIV( IX ) - IF( IP.NE.I ) THEN - DO 40 K = N32, N - TEMP = A( I, K ) - A( I, K ) = A( IP, K ) - A( IP, K ) = TEMP - 40 CONTINUE - END IF - IX = IX + INCX - 50 CONTINUE - END IF -* - RETURN -* -* End of DLASWP -* - END diff --git a/lib/linalg/fortran/dlatrd.f b/lib/linalg/fortran/dlatrd.f deleted file mode 100644 index 010a85a212..0000000000 --- a/lib/linalg/fortran/dlatrd.f +++ /dev/null @@ -1,333 +0,0 @@ -*> \brief \b DLATRD reduces the first nb rows and columns of a symmetric/Hermitian matrix A to real tridiagonal form by an orthogonal similarity transformation. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLATRD + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLATRD( UPLO, N, NB, A, LDA, E, TAU, W, LDW ) -* -* .. Scalar Arguments .. -* CHARACTER UPLO -* INTEGER LDA, LDW, N, NB -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), E( * ), TAU( * ), W( LDW, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLATRD reduces NB rows and columns of a real symmetric matrix A to -*> symmetric tridiagonal form by an orthogonal similarity -*> transformation Q**T * A * Q, and returns the matrices V and W which are -*> needed to apply the transformation to the unreduced part of A. -*> -*> If UPLO = 'U', DLATRD reduces the last NB rows and columns of a -*> matrix, of which the upper triangle is supplied; -*> if UPLO = 'L', DLATRD reduces the first NB rows and columns of a -*> matrix, of which the lower triangle is supplied. -*> -*> This is an auxiliary routine called by DSYTRD. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> Specifies whether the upper or lower triangular part of the -*> symmetric matrix A is stored: -*> = 'U': Upper triangular -*> = 'L': Lower triangular -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrix A. -*> \endverbatim -*> -*> \param[in] NB -*> \verbatim -*> NB is INTEGER -*> The number of rows and columns to be reduced. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the symmetric matrix A. If UPLO = 'U', the leading -*> n-by-n upper triangular part of A contains the upper -*> triangular part of the matrix A, and the strictly lower -*> triangular part of A is not referenced. If UPLO = 'L', the -*> leading n-by-n lower triangular part of A contains the lower -*> triangular part of the matrix A, and the strictly upper -*> triangular part of A is not referenced. -*> On exit: -*> if UPLO = 'U', the last NB columns have been reduced to -*> tridiagonal form, with the diagonal elements overwriting -*> the diagonal elements of A; the elements above the diagonal -*> with the array TAU, represent the orthogonal matrix Q as a -*> product of elementary reflectors; -*> if UPLO = 'L', the first NB columns have been reduced to -*> tridiagonal form, with the diagonal elements overwriting -*> the diagonal elements of A; the elements below the diagonal -*> with the array TAU, represent the orthogonal matrix Q as a -*> product of elementary reflectors. -*> See Further Details. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= (1,N). -*> \endverbatim -*> -*> \param[out] E -*> \verbatim -*> E is DOUBLE PRECISION array, dimension (N-1) -*> If UPLO = 'U', E(n-nb:n-1) contains the superdiagonal -*> elements of the last NB columns of the reduced matrix; -*> if UPLO = 'L', E(1:nb) contains the subdiagonal elements of -*> the first NB columns of the reduced matrix. -*> \endverbatim -*> -*> \param[out] TAU -*> \verbatim -*> TAU is DOUBLE PRECISION array, dimension (N-1) -*> The scalar factors of the elementary reflectors, stored in -*> TAU(n-nb:n-1) if UPLO = 'U', and in TAU(1:nb) if UPLO = 'L'. -*> See Further Details. -*> \endverbatim -*> -*> \param[out] W -*> \verbatim -*> W is DOUBLE PRECISION array, dimension (LDW,NB) -*> The n-by-nb matrix W required to update the unreduced part -*> of A. -*> \endverbatim -*> -*> \param[in] LDW -*> \verbatim -*> LDW is INTEGER -*> The leading dimension of the array W. LDW >= max(1,N). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleOTHERauxiliary -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> If UPLO = 'U', the matrix Q is represented as a product of elementary -*> reflectors -*> -*> Q = H(n) H(n-1) . . . H(n-nb+1). -*> -*> Each H(i) has the form -*> -*> H(i) = I - tau * v * v**T -*> -*> where tau is a real scalar, and v is a real vector with -*> v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i), -*> and tau in TAU(i-1). -*> -*> If UPLO = 'L', the matrix Q is represented as a product of elementary -*> reflectors -*> -*> Q = H(1) H(2) . . . H(nb). -*> -*> Each H(i) has the form -*> -*> H(i) = I - tau * v * v**T -*> -*> where tau is a real scalar, and v is a real vector with -*> v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i), -*> and tau in TAU(i). -*> -*> The elements of the vectors v together form the n-by-nb matrix V -*> which is needed, with W, to apply the transformation to the unreduced -*> part of the matrix, using a symmetric rank-2k update of the form: -*> A := A - V*W**T - W*V**T. -*> -*> The contents of A on exit are illustrated by the following examples -*> with n = 5 and nb = 2: -*> -*> if UPLO = 'U': if UPLO = 'L': -*> -*> ( a a a v4 v5 ) ( d ) -*> ( a a v4 v5 ) ( 1 d ) -*> ( a 1 v5 ) ( v1 1 a ) -*> ( d 1 ) ( v1 v2 a a ) -*> ( d ) ( v1 v2 a a a ) -*> -*> where d denotes a diagonal element of the reduced matrix, a denotes -*> an element of the original matrix that is unchanged, and vi denotes -*> an element of the vector defining H(i). -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DLATRD( UPLO, N, NB, A, LDA, E, TAU, W, LDW ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER UPLO - INTEGER LDA, LDW, N, NB -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), E( * ), TAU( * ), W( LDW, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, ONE, HALF - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, HALF = 0.5D+0 ) -* .. -* .. Local Scalars .. - INTEGER I, IW - DOUBLE PRECISION ALPHA -* .. -* .. External Subroutines .. - EXTERNAL DAXPY, DGEMV, DLARFG, DSCAL, DSYMV -* .. -* .. External Functions .. - LOGICAL LSAME - DOUBLE PRECISION DDOT - EXTERNAL LSAME, DDOT -* .. -* .. Intrinsic Functions .. - INTRINSIC MIN -* .. -* .. Executable Statements .. -* -* Quick return if possible -* - IF( N.LE.0 ) - $ RETURN -* - IF( LSAME( UPLO, 'U' ) ) THEN -* -* Reduce last NB columns of upper triangle -* - DO 10 I = N, N - NB + 1, -1 - IW = I - N + NB - IF( I.LT.N ) THEN -* -* Update A(1:i,i) -* - CALL DGEMV( 'No transpose', I, N-I, -ONE, A( 1, I+1 ), - $ LDA, W( I, IW+1 ), LDW, ONE, A( 1, I ), 1 ) - CALL DGEMV( 'No transpose', I, N-I, -ONE, W( 1, IW+1 ), - $ LDW, A( I, I+1 ), LDA, ONE, A( 1, I ), 1 ) - END IF - IF( I.GT.1 ) THEN -* -* Generate elementary reflector H(i) to annihilate -* A(1:i-2,i) -* - CALL DLARFG( I-1, A( I-1, I ), A( 1, I ), 1, TAU( I-1 ) ) - E( I-1 ) = A( I-1, I ) - A( I-1, I ) = ONE -* -* Compute W(1:i-1,i) -* - CALL DSYMV( 'Upper', I-1, ONE, A, LDA, A( 1, I ), 1, - $ ZERO, W( 1, IW ), 1 ) - IF( I.LT.N ) THEN - CALL DGEMV( 'Transpose', I-1, N-I, ONE, W( 1, IW+1 ), - $ LDW, A( 1, I ), 1, ZERO, W( I+1, IW ), 1 ) - CALL DGEMV( 'No transpose', I-1, N-I, -ONE, - $ A( 1, I+1 ), LDA, W( I+1, IW ), 1, ONE, - $ W( 1, IW ), 1 ) - CALL DGEMV( 'Transpose', I-1, N-I, ONE, A( 1, I+1 ), - $ LDA, A( 1, I ), 1, ZERO, W( I+1, IW ), 1 ) - CALL DGEMV( 'No transpose', I-1, N-I, -ONE, - $ W( 1, IW+1 ), LDW, W( I+1, IW ), 1, ONE, - $ W( 1, IW ), 1 ) - END IF - CALL DSCAL( I-1, TAU( I-1 ), W( 1, IW ), 1 ) - ALPHA = -HALF*TAU( I-1 )*DDOT( I-1, W( 1, IW ), 1, - $ A( 1, I ), 1 ) - CALL DAXPY( I-1, ALPHA, A( 1, I ), 1, W( 1, IW ), 1 ) - END IF -* - 10 CONTINUE - ELSE -* -* Reduce first NB columns of lower triangle -* - DO 20 I = 1, NB -* -* Update A(i:n,i) -* - CALL DGEMV( 'No transpose', N-I+1, I-1, -ONE, A( I, 1 ), - $ LDA, W( I, 1 ), LDW, ONE, A( I, I ), 1 ) - CALL DGEMV( 'No transpose', N-I+1, I-1, -ONE, W( I, 1 ), - $ LDW, A( I, 1 ), LDA, ONE, A( I, I ), 1 ) - IF( I.LT.N ) THEN -* -* Generate elementary reflector H(i) to annihilate -* A(i+2:n,i) -* - CALL DLARFG( N-I, A( I+1, I ), A( MIN( I+2, N ), I ), 1, - $ TAU( I ) ) - E( I ) = A( I+1, I ) - A( I+1, I ) = ONE -* -* Compute W(i+1:n,i) -* - CALL DSYMV( 'Lower', N-I, ONE, A( I+1, I+1 ), LDA, - $ A( I+1, I ), 1, ZERO, W( I+1, I ), 1 ) - CALL DGEMV( 'Transpose', N-I, I-1, ONE, W( I+1, 1 ), LDW, - $ A( I+1, I ), 1, ZERO, W( 1, I ), 1 ) - CALL DGEMV( 'No transpose', N-I, I-1, -ONE, A( I+1, 1 ), - $ LDA, W( 1, I ), 1, ONE, W( I+1, I ), 1 ) - CALL DGEMV( 'Transpose', N-I, I-1, ONE, A( I+1, 1 ), LDA, - $ A( I+1, I ), 1, ZERO, W( 1, I ), 1 ) - CALL DGEMV( 'No transpose', N-I, I-1, -ONE, W( I+1, 1 ), - $ LDW, W( 1, I ), 1, ONE, W( I+1, I ), 1 ) - CALL DSCAL( N-I, TAU( I ), W( I+1, I ), 1 ) - ALPHA = -HALF*TAU( I )*DDOT( N-I, W( I+1, I ), 1, - $ A( I+1, I ), 1 ) - CALL DAXPY( N-I, ALPHA, A( I+1, I ), 1, W( I+1, I ), 1 ) - END IF -* - 20 CONTINUE - END IF -* - RETURN -* -* End of DLATRD -* - END diff --git a/lib/linalg/fortran/dlatrs.f b/lib/linalg/fortran/dlatrs.f deleted file mode 100644 index be156bee20..0000000000 --- a/lib/linalg/fortran/dlatrs.f +++ /dev/null @@ -1,843 +0,0 @@ -*> \brief \b DLATRS solves a triangular system of equations with the scale factor set to prevent overflow. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLATRS + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLATRS( UPLO, TRANS, DIAG, NORMIN, N, A, LDA, X, SCALE, -* CNORM, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER DIAG, NORMIN, TRANS, UPLO -* INTEGER INFO, LDA, N -* DOUBLE PRECISION SCALE -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), CNORM( * ), X( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLATRS solves one of the triangular systems -*> -*> A *x = s*b or A**T *x = s*b -*> -*> with scaling to prevent overflow. Here A is an upper or lower -*> triangular matrix, A**T denotes the transpose of A, x and b are -*> n-element vectors, and s is a scaling factor, usually less than -*> or equal to 1, chosen so that the components of x will be less than -*> the overflow threshold. If the unscaled problem will not cause -*> overflow, the Level 2 BLAS routine DTRSV is called. If the matrix A -*> is singular (A(j,j) = 0 for some j), then s is set to 0 and a -*> non-trivial solution to A*x = 0 is returned. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> Specifies whether the matrix A is upper or lower triangular. -*> = 'U': Upper triangular -*> = 'L': Lower triangular -*> \endverbatim -*> -*> \param[in] TRANS -*> \verbatim -*> TRANS is CHARACTER*1 -*> Specifies the operation applied to A. -*> = 'N': Solve A * x = s*b (No transpose) -*> = 'T': Solve A**T* x = s*b (Transpose) -*> = 'C': Solve A**T* x = s*b (Conjugate transpose = Transpose) -*> \endverbatim -*> -*> \param[in] DIAG -*> \verbatim -*> DIAG is CHARACTER*1 -*> Specifies whether or not the matrix A is unit triangular. -*> = 'N': Non-unit triangular -*> = 'U': Unit triangular -*> \endverbatim -*> -*> \param[in] NORMIN -*> \verbatim -*> NORMIN is CHARACTER*1 -*> Specifies whether CNORM has been set or not. -*> = 'Y': CNORM contains the column norms on entry -*> = 'N': CNORM is not set on entry. On exit, the norms will -*> be computed and stored in CNORM. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> The triangular matrix A. If UPLO = 'U', the leading n by n -*> upper triangular part of the array A contains the upper -*> triangular matrix, and the strictly lower triangular part of -*> A is not referenced. If UPLO = 'L', the leading n by n lower -*> triangular part of the array A contains the lower triangular -*> matrix, and the strictly upper triangular part of A is not -*> referenced. If DIAG = 'U', the diagonal elements of A are -*> also not referenced and are assumed to be 1. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max (1,N). -*> \endverbatim -*> -*> \param[in,out] X -*> \verbatim -*> X is DOUBLE PRECISION array, dimension (N) -*> On entry, the right hand side b of the triangular system. -*> On exit, X is overwritten by the solution vector x. -*> \endverbatim -*> -*> \param[out] SCALE -*> \verbatim -*> SCALE is DOUBLE PRECISION -*> The scaling factor s for the triangular system -*> A * x = s*b or A**T* x = s*b. -*> If SCALE = 0, the matrix A is singular or badly scaled, and -*> the vector x is an exact or approximate solution to A*x = 0. -*> \endverbatim -*> -*> \param[in,out] CNORM -*> \verbatim -*> CNORM is DOUBLE PRECISION array, dimension (N) -*> -*> If NORMIN = 'Y', CNORM is an input argument and CNORM(j) -*> contains the norm of the off-diagonal part of the j-th column -*> of A. If TRANS = 'N', CNORM(j) must be greater than or equal -*> to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j) -*> must be greater than or equal to the 1-norm. -*> -*> If NORMIN = 'N', CNORM is an output argument and CNORM(j) -*> returns the 1-norm of the offdiagonal part of the j-th column -*> of A. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -k, the k-th argument had an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleOTHERauxiliary -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> A rough bound on x is computed; if that is less than overflow, DTRSV -*> is called, otherwise, specific code is used which checks for possible -*> overflow or divide-by-zero at every operation. -*> -*> A columnwise scheme is used for solving A*x = b. The basic algorithm -*> if A is lower triangular is -*> -*> x[1:n] := b[1:n] -*> for j = 1, ..., n -*> x(j) := x(j) / A(j,j) -*> x[j+1:n] := x[j+1:n] - x(j) * A[j+1:n,j] -*> end -*> -*> Define bounds on the components of x after j iterations of the loop: -*> M(j) = bound on x[1:j] -*> G(j) = bound on x[j+1:n] -*> Initially, let M(0) = 0 and G(0) = max{x(i), i=1,...,n}. -*> -*> Then for iteration j+1 we have -*> M(j+1) <= G(j) / | A(j+1,j+1) | -*> G(j+1) <= G(j) + M(j+1) * | A[j+2:n,j+1] | -*> <= G(j) ( 1 + CNORM(j+1) / | A(j+1,j+1) | ) -*> -*> where CNORM(j+1) is greater than or equal to the infinity-norm of -*> column j+1 of A, not counting the diagonal. Hence -*> -*> G(j) <= G(0) product ( 1 + CNORM(i) / | A(i,i) | ) -*> 1<=i<=j -*> and -*> -*> |x(j)| <= ( G(0) / |A(j,j)| ) product ( 1 + CNORM(i) / |A(i,i)| ) -*> 1<=i< j -*> -*> Since |x(j)| <= M(j), we use the Level 2 BLAS routine DTRSV if the -*> reciprocal of the largest M(j), j=1,..,n, is larger than -*> max(underflow, 1/overflow). -*> -*> The bound on x(j) is also used to determine when a step in the -*> columnwise method can be performed without fear of overflow. If -*> the computed bound is greater than a large constant, x is scaled to -*> prevent overflow, but if the bound overflows, x is set to 0, x(j) to -*> 1, and scale to 0, and a non-trivial solution to A*x = 0 is found. -*> -*> Similarly, a row-wise scheme is used to solve A**T*x = b. The basic -*> algorithm for A upper triangular is -*> -*> for j = 1, ..., n -*> x(j) := ( b(j) - A[1:j-1,j]**T * x[1:j-1] ) / A(j,j) -*> end -*> -*> We simultaneously compute two bounds -*> G(j) = bound on ( b(i) - A[1:i-1,i]**T * x[1:i-1] ), 1<=i<=j -*> M(j) = bound on x(i), 1<=i<=j -*> -*> The initial values are G(0) = 0, M(0) = max{b(i), i=1,..,n}, and we -*> add the constraint G(j) >= G(j-1) and M(j) >= M(j-1) for j >= 1. -*> Then the bound on x(j) is -*> -*> M(j) <= M(j-1) * ( 1 + CNORM(j) ) / | A(j,j) | -*> -*> <= M(0) * product ( ( 1 + CNORM(i) ) / |A(i,i)| ) -*> 1<=i<=j -*> -*> and we can safely call DTRSV if 1/M(n) and 1/G(n) are both greater -*> than max(underflow, 1/overflow). -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DLATRS( UPLO, TRANS, DIAG, NORMIN, N, A, LDA, X, SCALE, - $ CNORM, INFO ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER DIAG, NORMIN, TRANS, UPLO - INTEGER INFO, LDA, N - DOUBLE PRECISION SCALE -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), CNORM( * ), X( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, HALF, ONE - PARAMETER ( ZERO = 0.0D+0, HALF = 0.5D+0, ONE = 1.0D+0 ) -* .. -* .. Local Scalars .. - LOGICAL NOTRAN, NOUNIT, UPPER - INTEGER I, IMAX, J, JFIRST, JINC, JLAST - DOUBLE PRECISION BIGNUM, GROW, REC, SMLNUM, SUMJ, TJJ, TJJS, - $ TMAX, TSCAL, USCAL, XBND, XJ, XMAX -* .. -* .. External Functions .. - LOGICAL LSAME - INTEGER IDAMAX - DOUBLE PRECISION DASUM, DDOT, DLAMCH, DLANGE - EXTERNAL LSAME, IDAMAX, DASUM, DDOT, DLAMCH, DLANGE -* .. -* .. External Subroutines .. - EXTERNAL DAXPY, DSCAL, DTRSV, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, MAX, MIN -* .. -* .. Executable Statements .. -* - INFO = 0 - UPPER = LSAME( UPLO, 'U' ) - NOTRAN = LSAME( TRANS, 'N' ) - NOUNIT = LSAME( DIAG, 'N' ) -* -* Test the input parameters. -* - IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN - INFO = -1 - ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) .AND. .NOT. - $ LSAME( TRANS, 'C' ) ) THEN - INFO = -2 - ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN - INFO = -3 - ELSE IF( .NOT.LSAME( NORMIN, 'Y' ) .AND. .NOT. - $ LSAME( NORMIN, 'N' ) ) THEN - INFO = -4 - ELSE IF( N.LT.0 ) THEN - INFO = -5 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -7 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DLATRS', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - SCALE = ONE - IF( N.EQ.0 ) - $ RETURN -* -* Determine machine dependent parameters to control overflow. -* - SMLNUM = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' ) - BIGNUM = ONE / SMLNUM -* - IF( LSAME( NORMIN, 'N' ) ) THEN -* -* Compute the 1-norm of each column, not including the diagonal. -* - IF( UPPER ) THEN -* -* A is upper triangular. -* - DO 10 J = 1, N - CNORM( J ) = DASUM( J-1, A( 1, J ), 1 ) - 10 CONTINUE - ELSE -* -* A is lower triangular. -* - DO 20 J = 1, N - 1 - CNORM( J ) = DASUM( N-J, A( J+1, J ), 1 ) - 20 CONTINUE - CNORM( N ) = ZERO - END IF - END IF -* -* Scale the column norms by TSCAL if the maximum element in CNORM is -* greater than BIGNUM. -* - IMAX = IDAMAX( N, CNORM, 1 ) - TMAX = CNORM( IMAX ) - IF( TMAX.LE.BIGNUM ) THEN - TSCAL = ONE - ELSE -* -* Avoid NaN generation if entries in CNORM exceed the -* overflow threshold -* - IF( TMAX.LE.DLAMCH('Overflow') ) THEN -* Case 1: All entries in CNORM are valid floating-point numbers - TSCAL = ONE / ( SMLNUM*TMAX ) - CALL DSCAL( N, TSCAL, CNORM, 1 ) - ELSE -* Case 2: At least one column norm of A cannot be represented -* as floating-point number. Find the offdiagonal entry A( I, J ) -* with the largest absolute value. If this entry is not +/- Infinity, -* use this value as TSCAL. - TMAX = ZERO - IF( UPPER ) THEN -* -* A is upper triangular. -* - DO J = 2, N - TMAX = MAX( DLANGE( 'M', J-1, 1, A( 1, J ), 1, SUMJ ), - $ TMAX ) - END DO - ELSE -* -* A is lower triangular. -* - DO J = 1, N - 1 - TMAX = MAX( DLANGE( 'M', N-J, 1, A( J+1, J ), 1, - $ SUMJ ), TMAX ) - END DO - END IF -* - IF( TMAX.LE.DLAMCH('Overflow') ) THEN - TSCAL = ONE / ( SMLNUM*TMAX ) - DO J = 1, N - IF( CNORM( J ).LE.DLAMCH('Overflow') ) THEN - CNORM( J ) = CNORM( J )*TSCAL - ELSE -* Recompute the 1-norm without introducing Infinity -* in the summation - CNORM( J ) = ZERO - IF( UPPER ) THEN - DO I = 1, J - 1 - CNORM( J ) = CNORM( J ) + - $ TSCAL * ABS( A( I, J ) ) - END DO - ELSE - DO I = J + 1, N - CNORM( J ) = CNORM( J ) + - $ TSCAL * ABS( A( I, J ) ) - END DO - END IF - END IF - END DO - ELSE -* At least one entry of A is not a valid floating-point entry. -* Rely on TRSV to propagate Inf and NaN. - CALL DTRSV( UPLO, TRANS, DIAG, N, A, LDA, X, 1 ) - RETURN - END IF - END IF - END IF -* -* Compute a bound on the computed solution vector to see if the -* Level 2 BLAS routine DTRSV can be used. -* - J = IDAMAX( N, X, 1 ) - XMAX = ABS( X( J ) ) - XBND = XMAX - IF( NOTRAN ) THEN -* -* Compute the growth in A * x = b. -* - IF( UPPER ) THEN - JFIRST = N - JLAST = 1 - JINC = -1 - ELSE - JFIRST = 1 - JLAST = N - JINC = 1 - END IF -* - IF( TSCAL.NE.ONE ) THEN - GROW = ZERO - GO TO 50 - END IF -* - IF( NOUNIT ) THEN -* -* A is non-unit triangular. -* -* Compute GROW = 1/G(j) and XBND = 1/M(j). -* Initially, G(0) = max{x(i), i=1,...,n}. -* - GROW = ONE / MAX( XBND, SMLNUM ) - XBND = GROW - DO 30 J = JFIRST, JLAST, JINC -* -* Exit the loop if the growth factor is too small. -* - IF( GROW.LE.SMLNUM ) - $ GO TO 50 -* -* M(j) = G(j-1) / abs(A(j,j)) -* - TJJ = ABS( A( J, J ) ) - XBND = MIN( XBND, MIN( ONE, TJJ )*GROW ) - IF( TJJ+CNORM( J ).GE.SMLNUM ) THEN -* -* G(j) = G(j-1)*( 1 + CNORM(j) / abs(A(j,j)) ) -* - GROW = GROW*( TJJ / ( TJJ+CNORM( J ) ) ) - ELSE -* -* G(j) could overflow, set GROW to 0. -* - GROW = ZERO - END IF - 30 CONTINUE - GROW = XBND - ELSE -* -* A is unit triangular. -* -* Compute GROW = 1/G(j), where G(0) = max{x(i), i=1,...,n}. -* - GROW = MIN( ONE, ONE / MAX( XBND, SMLNUM ) ) - DO 40 J = JFIRST, JLAST, JINC -* -* Exit the loop if the growth factor is too small. -* - IF( GROW.LE.SMLNUM ) - $ GO TO 50 -* -* G(j) = G(j-1)*( 1 + CNORM(j) ) -* - GROW = GROW*( ONE / ( ONE+CNORM( J ) ) ) - 40 CONTINUE - END IF - 50 CONTINUE -* - ELSE -* -* Compute the growth in A**T * x = b. -* - IF( UPPER ) THEN - JFIRST = 1 - JLAST = N - JINC = 1 - ELSE - JFIRST = N - JLAST = 1 - JINC = -1 - END IF -* - IF( TSCAL.NE.ONE ) THEN - GROW = ZERO - GO TO 80 - END IF -* - IF( NOUNIT ) THEN -* -* A is non-unit triangular. -* -* Compute GROW = 1/G(j) and XBND = 1/M(j). -* Initially, M(0) = max{x(i), i=1,...,n}. -* - GROW = ONE / MAX( XBND, SMLNUM ) - XBND = GROW - DO 60 J = JFIRST, JLAST, JINC -* -* Exit the loop if the growth factor is too small. -* - IF( GROW.LE.SMLNUM ) - $ GO TO 80 -* -* G(j) = max( G(j-1), M(j-1)*( 1 + CNORM(j) ) ) -* - XJ = ONE + CNORM( J ) - GROW = MIN( GROW, XBND / XJ ) -* -* M(j) = M(j-1)*( 1 + CNORM(j) ) / abs(A(j,j)) -* - TJJ = ABS( A( J, J ) ) - IF( XJ.GT.TJJ ) - $ XBND = XBND*( TJJ / XJ ) - 60 CONTINUE - GROW = MIN( GROW, XBND ) - ELSE -* -* A is unit triangular. -* -* Compute GROW = 1/G(j), where G(0) = max{x(i), i=1,...,n}. -* - GROW = MIN( ONE, ONE / MAX( XBND, SMLNUM ) ) - DO 70 J = JFIRST, JLAST, JINC -* -* Exit the loop if the growth factor is too small. -* - IF( GROW.LE.SMLNUM ) - $ GO TO 80 -* -* G(j) = ( 1 + CNORM(j) )*G(j-1) -* - XJ = ONE + CNORM( J ) - GROW = GROW / XJ - 70 CONTINUE - END IF - 80 CONTINUE - END IF -* - IF( ( GROW*TSCAL ).GT.SMLNUM ) THEN -* -* Use the Level 2 BLAS solve if the reciprocal of the bound on -* elements of X is not too small. -* - CALL DTRSV( UPLO, TRANS, DIAG, N, A, LDA, X, 1 ) - ELSE -* -* Use a Level 1 BLAS solve, scaling intermediate results. -* - IF( XMAX.GT.BIGNUM ) THEN -* -* Scale X so that its components are less than or equal to -* BIGNUM in absolute value. -* - SCALE = BIGNUM / XMAX - CALL DSCAL( N, SCALE, X, 1 ) - XMAX = BIGNUM - END IF -* - IF( NOTRAN ) THEN -* -* Solve A * x = b -* - DO 110 J = JFIRST, JLAST, JINC -* -* Compute x(j) = b(j) / A(j,j), scaling x if necessary. -* - XJ = ABS( X( J ) ) - IF( NOUNIT ) THEN - TJJS = A( J, J )*TSCAL - ELSE - TJJS = TSCAL - IF( TSCAL.EQ.ONE ) - $ GO TO 100 - END IF - TJJ = ABS( TJJS ) - IF( TJJ.GT.SMLNUM ) THEN -* -* abs(A(j,j)) > SMLNUM: -* - IF( TJJ.LT.ONE ) THEN - IF( XJ.GT.TJJ*BIGNUM ) THEN -* -* Scale x by 1/b(j). -* - REC = ONE / XJ - CALL DSCAL( N, REC, X, 1 ) - SCALE = SCALE*REC - XMAX = XMAX*REC - END IF - END IF - X( J ) = X( J ) / TJJS - XJ = ABS( X( J ) ) - ELSE IF( TJJ.GT.ZERO ) THEN -* -* 0 < abs(A(j,j)) <= SMLNUM: -* - IF( XJ.GT.TJJ*BIGNUM ) THEN -* -* Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM -* to avoid overflow when dividing by A(j,j). -* - REC = ( TJJ*BIGNUM ) / XJ - IF( CNORM( J ).GT.ONE ) THEN -* -* Scale by 1/CNORM(j) to avoid overflow when -* multiplying x(j) times column j. -* - REC = REC / CNORM( J ) - END IF - CALL DSCAL( N, REC, X, 1 ) - SCALE = SCALE*REC - XMAX = XMAX*REC - END IF - X( J ) = X( J ) / TJJS - XJ = ABS( X( J ) ) - ELSE -* -* A(j,j) = 0: Set x(1:n) = 0, x(j) = 1, and -* scale = 0, and compute a solution to A*x = 0. -* - DO 90 I = 1, N - X( I ) = ZERO - 90 CONTINUE - X( J ) = ONE - XJ = ONE - SCALE = ZERO - XMAX = ZERO - END IF - 100 CONTINUE -* -* Scale x if necessary to avoid overflow when adding a -* multiple of column j of A. -* - IF( XJ.GT.ONE ) THEN - REC = ONE / XJ - IF( CNORM( J ).GT.( BIGNUM-XMAX )*REC ) THEN -* -* Scale x by 1/(2*abs(x(j))). -* - REC = REC*HALF - CALL DSCAL( N, REC, X, 1 ) - SCALE = SCALE*REC - END IF - ELSE IF( XJ*CNORM( J ).GT.( BIGNUM-XMAX ) ) THEN -* -* Scale x by 1/2. -* - CALL DSCAL( N, HALF, X, 1 ) - SCALE = SCALE*HALF - END IF -* - IF( UPPER ) THEN - IF( J.GT.1 ) THEN -* -* Compute the update -* x(1:j-1) := x(1:j-1) - x(j) * A(1:j-1,j) -* - CALL DAXPY( J-1, -X( J )*TSCAL, A( 1, J ), 1, X, - $ 1 ) - I = IDAMAX( J-1, X, 1 ) - XMAX = ABS( X( I ) ) - END IF - ELSE - IF( J.LT.N ) THEN -* -* Compute the update -* x(j+1:n) := x(j+1:n) - x(j) * A(j+1:n,j) -* - CALL DAXPY( N-J, -X( J )*TSCAL, A( J+1, J ), 1, - $ X( J+1 ), 1 ) - I = J + IDAMAX( N-J, X( J+1 ), 1 ) - XMAX = ABS( X( I ) ) - END IF - END IF - 110 CONTINUE -* - ELSE -* -* Solve A**T * x = b -* - DO 160 J = JFIRST, JLAST, JINC -* -* Compute x(j) = b(j) - sum A(k,j)*x(k). -* k<>j -* - XJ = ABS( X( J ) ) - USCAL = TSCAL - REC = ONE / MAX( XMAX, ONE ) - IF( CNORM( J ).GT.( BIGNUM-XJ )*REC ) THEN -* -* If x(j) could overflow, scale x by 1/(2*XMAX). -* - REC = REC*HALF - IF( NOUNIT ) THEN - TJJS = A( J, J )*TSCAL - ELSE - TJJS = TSCAL - END IF - TJJ = ABS( TJJS ) - IF( TJJ.GT.ONE ) THEN -* -* Divide by A(j,j) when scaling x if A(j,j) > 1. -* - REC = MIN( ONE, REC*TJJ ) - USCAL = USCAL / TJJS - END IF - IF( REC.LT.ONE ) THEN - CALL DSCAL( N, REC, X, 1 ) - SCALE = SCALE*REC - XMAX = XMAX*REC - END IF - END IF -* - SUMJ = ZERO - IF( USCAL.EQ.ONE ) THEN -* -* If the scaling needed for A in the dot product is 1, -* call DDOT to perform the dot product. -* - IF( UPPER ) THEN - SUMJ = DDOT( J-1, A( 1, J ), 1, X, 1 ) - ELSE IF( J.LT.N ) THEN - SUMJ = DDOT( N-J, A( J+1, J ), 1, X( J+1 ), 1 ) - END IF - ELSE -* -* Otherwise, use in-line code for the dot product. -* - IF( UPPER ) THEN - DO 120 I = 1, J - 1 - SUMJ = SUMJ + ( A( I, J )*USCAL )*X( I ) - 120 CONTINUE - ELSE IF( J.LT.N ) THEN - DO 130 I = J + 1, N - SUMJ = SUMJ + ( A( I, J )*USCAL )*X( I ) - 130 CONTINUE - END IF - END IF -* - IF( USCAL.EQ.TSCAL ) THEN -* -* Compute x(j) := ( x(j) - sumj ) / A(j,j) if 1/A(j,j) -* was not used to scale the dotproduct. -* - X( J ) = X( J ) - SUMJ - XJ = ABS( X( J ) ) - IF( NOUNIT ) THEN - TJJS = A( J, J )*TSCAL - ELSE - TJJS = TSCAL - IF( TSCAL.EQ.ONE ) - $ GO TO 150 - END IF -* -* Compute x(j) = x(j) / A(j,j), scaling if necessary. -* - TJJ = ABS( TJJS ) - IF( TJJ.GT.SMLNUM ) THEN -* -* abs(A(j,j)) > SMLNUM: -* - IF( TJJ.LT.ONE ) THEN - IF( XJ.GT.TJJ*BIGNUM ) THEN -* -* Scale X by 1/abs(x(j)). -* - REC = ONE / XJ - CALL DSCAL( N, REC, X, 1 ) - SCALE = SCALE*REC - XMAX = XMAX*REC - END IF - END IF - X( J ) = X( J ) / TJJS - ELSE IF( TJJ.GT.ZERO ) THEN -* -* 0 < abs(A(j,j)) <= SMLNUM: -* - IF( XJ.GT.TJJ*BIGNUM ) THEN -* -* Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM. -* - REC = ( TJJ*BIGNUM ) / XJ - CALL DSCAL( N, REC, X, 1 ) - SCALE = SCALE*REC - XMAX = XMAX*REC - END IF - X( J ) = X( J ) / TJJS - ELSE -* -* A(j,j) = 0: Set x(1:n) = 0, x(j) = 1, and -* scale = 0, and compute a solution to A**T*x = 0. -* - DO 140 I = 1, N - X( I ) = ZERO - 140 CONTINUE - X( J ) = ONE - SCALE = ZERO - XMAX = ZERO - END IF - 150 CONTINUE - ELSE -* -* Compute x(j) := x(j) / A(j,j) - sumj if the dot -* product has already been divided by 1/A(j,j). -* - X( J ) = X( J ) / TJJS - SUMJ - END IF - XMAX = MAX( XMAX, ABS( X( J ) ) ) - 160 CONTINUE - END IF - SCALE = SCALE / TSCAL - END IF -* -* Scale the column norms by 1/TSCAL for return. -* - IF( TSCAL.NE.ONE ) THEN - CALL DSCAL( N, ONE / TSCAL, CNORM, 1 ) - END IF -* - RETURN -* -* End of DLATRS -* - END diff --git a/lib/linalg/fortran/dnrm2.f b/lib/linalg/fortran/dnrm2.f deleted file mode 100644 index 30552e1d1d..0000000000 --- a/lib/linalg/fortran/dnrm2.f +++ /dev/null @@ -1,132 +0,0 @@ -*> \brief \b DNRM2 -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* DOUBLE PRECISION FUNCTION DNRM2(N,X,INCX) -* -* .. Scalar Arguments .. -* INTEGER INCX,N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION X(*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DNRM2 returns the euclidean norm of a vector via the function -*> name, so that -*> -*> DNRM2 := sqrt( x'*x ) -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> number of elements in input vector(s) -*> \endverbatim -*> -*> \param[in] X -*> \verbatim -*> X is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> storage spacing between elements of DX -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \date December 2016 -* -*> \ingroup double_blas_level1 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> -- This version written on 25-October-1982. -*> Modified on 14-October-1993 to inline the call to DLASSQ. -*> Sven Hammarling, Nag Ltd. -*> \endverbatim -*> -* ===================================================================== - DOUBLE PRECISION FUNCTION DNRM2(N,X,INCX) -* -* -- Reference BLAS level1 routine (version 3.7.0) -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* December 2016 -* -* .. Scalar Arguments .. - INTEGER INCX,N -* .. -* .. Array Arguments .. - DOUBLE PRECISION X(*) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE,ZERO - PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) -* .. -* .. Local Scalars .. - DOUBLE PRECISION ABSXI,NORM,SCALE,SSQ - INTEGER IX -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS,SQRT -* .. - IF (N.LT.1 .OR. INCX.LT.1) THEN - NORM = ZERO - ELSE IF (N.EQ.1) THEN - NORM = ABS(X(1)) - ELSE - SCALE = ZERO - SSQ = ONE -* The following loop is equivalent to this call to the LAPACK -* auxiliary routine: -* CALL DLASSQ( N, X, INCX, SCALE, SSQ ) -* - DO 10 IX = 1,1 + (N-1)*INCX,INCX - IF (X(IX).NE.ZERO) THEN - ABSXI = ABS(X(IX)) - IF (SCALE.LT.ABSXI) THEN - SSQ = ONE + SSQ* (SCALE/ABSXI)**2 - SCALE = ABSXI - ELSE - SSQ = SSQ + (ABSXI/SCALE)**2 - END IF - END IF - 10 CONTINUE - NORM = SCALE*SQRT(SSQ) - END IF -* - DNRM2 = NORM - RETURN -* -* End of DNRM2. -* - END diff --git a/lib/linalg/fortran/dorg2l.f b/lib/linalg/fortran/dorg2l.f deleted file mode 100644 index 0a42d4cf5a..0000000000 --- a/lib/linalg/fortran/dorg2l.f +++ /dev/null @@ -1,195 +0,0 @@ -*> \brief \b DORG2L generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm). -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DORG2L + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DORG2L( M, N, K, A, LDA, TAU, WORK, INFO ) -* -* .. Scalar Arguments .. -* INTEGER INFO, K, LDA, M, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DORG2L generates an m by n real matrix Q with orthonormal columns, -*> which is defined as the last n columns of a product of k elementary -*> reflectors of order m -*> -*> Q = H(k) . . . H(2) H(1) -*> -*> as returned by DGEQLF. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix Q. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix Q. M >= N >= 0. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> The number of elementary reflectors whose product defines the -*> matrix Q. N >= K >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the (n-k+i)-th column must contain the vector which -*> defines the elementary reflector H(i), for i = 1,2,...,k, as -*> returned by DGEQLF in the last k columns of its array -*> argument A. -*> On exit, the m by n matrix Q. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The first dimension of the array A. LDA >= max(1,M). -*> \endverbatim -*> -*> \param[in] TAU -*> \verbatim -*> TAU is DOUBLE PRECISION array, dimension (K) -*> TAU(i) must contain the scalar factor of the elementary -*> reflector H(i), as returned by DGEQLF. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (N) -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument has an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleOTHERcomputational -* -* ===================================================================== - SUBROUTINE DORG2L( M, N, K, A, LDA, TAU, WORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INFO, K, LDA, M, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE, ZERO - PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) -* .. -* .. Local Scalars .. - INTEGER I, II, J, L -* .. -* .. External Subroutines .. - EXTERNAL DLARF, DSCAL, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - INFO = 0 - IF( M.LT.0 ) THEN - INFO = -1 - ELSE IF( N.LT.0 .OR. N.GT.M ) THEN - INFO = -2 - ELSE IF( K.LT.0 .OR. K.GT.N ) THEN - INFO = -3 - ELSE IF( LDA.LT.MAX( 1, M ) ) THEN - INFO = -5 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DORG2L', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( N.LE.0 ) - $ RETURN -* -* Initialise columns 1:n-k to columns of the unit matrix -* - DO 20 J = 1, N - K - DO 10 L = 1, M - A( L, J ) = ZERO - 10 CONTINUE - A( M-N+J, J ) = ONE - 20 CONTINUE -* - DO 40 I = 1, K - II = N - K + I -* -* Apply H(i) to A(1:m-k+i,1:n-k+i) from the left -* - A( M-N+II, II ) = ONE - CALL DLARF( 'Left', M-N+II, II-1, A( 1, II ), 1, TAU( I ), A, - $ LDA, WORK ) - CALL DSCAL( M-N+II-1, -TAU( I ), A( 1, II ), 1 ) - A( M-N+II, II ) = ONE - TAU( I ) -* -* Set A(m-k+i+1:m,n-k+i) to zero -* - DO 30 L = M - N + II + 1, M - A( L, II ) = ZERO - 30 CONTINUE - 40 CONTINUE - RETURN -* -* End of DORG2L -* - END diff --git a/lib/linalg/fortran/dorg2r.f b/lib/linalg/fortran/dorg2r.f deleted file mode 100644 index c64ad4b0ac..0000000000 --- a/lib/linalg/fortran/dorg2r.f +++ /dev/null @@ -1,197 +0,0 @@ -*> \brief \b DORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf (unblocked algorithm). -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DORG2R + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DORG2R( M, N, K, A, LDA, TAU, WORK, INFO ) -* -* .. Scalar Arguments .. -* INTEGER INFO, K, LDA, M, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DORG2R generates an m by n real matrix Q with orthonormal columns, -*> which is defined as the first n columns of a product of k elementary -*> reflectors of order m -*> -*> Q = H(1) H(2) . . . H(k) -*> -*> as returned by DGEQRF. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix Q. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix Q. M >= N >= 0. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> The number of elementary reflectors whose product defines the -*> matrix Q. N >= K >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the i-th column must contain the vector which -*> defines the elementary reflector H(i), for i = 1,2,...,k, as -*> returned by DGEQRF in the first k columns of its array -*> argument A. -*> On exit, the m-by-n matrix Q. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The first dimension of the array A. LDA >= max(1,M). -*> \endverbatim -*> -*> \param[in] TAU -*> \verbatim -*> TAU is DOUBLE PRECISION array, dimension (K) -*> TAU(i) must contain the scalar factor of the elementary -*> reflector H(i), as returned by DGEQRF. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (N) -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument has an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleOTHERcomputational -* -* ===================================================================== - SUBROUTINE DORG2R( M, N, K, A, LDA, TAU, WORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INFO, K, LDA, M, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE, ZERO - PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) -* .. -* .. Local Scalars .. - INTEGER I, J, L -* .. -* .. External Subroutines .. - EXTERNAL DLARF, DSCAL, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - INFO = 0 - IF( M.LT.0 ) THEN - INFO = -1 - ELSE IF( N.LT.0 .OR. N.GT.M ) THEN - INFO = -2 - ELSE IF( K.LT.0 .OR. K.GT.N ) THEN - INFO = -3 - ELSE IF( LDA.LT.MAX( 1, M ) ) THEN - INFO = -5 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DORG2R', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( N.LE.0 ) - $ RETURN -* -* Initialise columns k+1:n to columns of the unit matrix -* - DO 20 J = K + 1, N - DO 10 L = 1, M - A( L, J ) = ZERO - 10 CONTINUE - A( J, J ) = ONE - 20 CONTINUE -* - DO 40 I = K, 1, -1 -* -* Apply H(i) to A(i:m,i:n) from the left -* - IF( I.LT.N ) THEN - A( I, I ) = ONE - CALL DLARF( 'Left', M-I+1, N-I, A( I, I ), 1, TAU( I ), - $ A( I, I+1 ), LDA, WORK ) - END IF - IF( I.LT.M ) - $ CALL DSCAL( M-I, -TAU( I ), A( I+1, I ), 1 ) - A( I, I ) = ONE - TAU( I ) -* -* Set A(1:i-1,i) to zero -* - DO 30 L = 1, I - 1 - A( L, I ) = ZERO - 30 CONTINUE - 40 CONTINUE - RETURN -* -* End of DORG2R -* - END diff --git a/lib/linalg/fortran/dorgbr.f b/lib/linalg/fortran/dorgbr.f deleted file mode 100644 index 7dfd03961e..0000000000 --- a/lib/linalg/fortran/dorgbr.f +++ /dev/null @@ -1,334 +0,0 @@ -*> \brief \b DORGBR -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DORGBR + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER VECT -* INTEGER INFO, K, LDA, LWORK, M, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DORGBR generates one of the real orthogonal matrices Q or P**T -*> determined by DGEBRD when reducing a real matrix A to bidiagonal -*> form: A = Q * B * P**T. Q and P**T are defined as products of -*> elementary reflectors H(i) or G(i) respectively. -*> -*> If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q -*> is of order M: -*> if m >= k, Q = H(1) H(2) . . . H(k) and DORGBR returns the first n -*> columns of Q, where m >= n >= k; -*> if m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR returns Q as an -*> M-by-M matrix. -*> -*> If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T -*> is of order N: -*> if k < n, P**T = G(k) . . . G(2) G(1) and DORGBR returns the first m -*> rows of P**T, where n >= m >= k; -*> if k >= n, P**T = G(n-1) . . . G(2) G(1) and DORGBR returns P**T as -*> an N-by-N matrix. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] VECT -*> \verbatim -*> VECT is CHARACTER*1 -*> Specifies whether the matrix Q or the matrix P**T is -*> required, as defined in the transformation applied by DGEBRD: -*> = 'Q': generate Q; -*> = 'P': generate P**T. -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix Q or P**T to be returned. -*> M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix Q or P**T to be returned. -*> N >= 0. -*> If VECT = 'Q', M >= N >= min(M,K); -*> if VECT = 'P', N >= M >= min(N,K). -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> If VECT = 'Q', the number of columns in the original M-by-K -*> matrix reduced by DGEBRD. -*> If VECT = 'P', the number of rows in the original K-by-N -*> matrix reduced by DGEBRD. -*> K >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the vectors which define the elementary reflectors, -*> as returned by DGEBRD. -*> On exit, the M-by-N matrix Q or P**T. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,M). -*> \endverbatim -*> -*> \param[in] TAU -*> \verbatim -*> TAU is DOUBLE PRECISION array, dimension -*> (min(M,K)) if VECT = 'Q' -*> (min(N,K)) if VECT = 'P' -*> TAU(i) must contain the scalar factor of the elementary -*> reflector H(i) or G(i), which determines Q or P**T, as -*> returned by DGEBRD in its array argument TAUQ or TAUP. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) -*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -*> \endverbatim -*> -*> \param[in] LWORK -*> \verbatim -*> LWORK is INTEGER -*> The dimension of the array WORK. LWORK >= max(1,min(M,N)). -*> For optimum performance LWORK >= min(M,N)*NB, where NB -*> is the optimal blocksize. -*> -*> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal size of the WORK array, returns -*> this value as the first entry of the WORK array, and no error -*> message related to LWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleGBcomputational -* -* ===================================================================== - SUBROUTINE DORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER VECT - INTEGER INFO, K, LDA, LWORK, M, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) -* .. -* .. Local Scalars .. - LOGICAL LQUERY, WANTQ - INTEGER I, IINFO, J, LWKOPT, MN -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL DORGLQ, DORGQR, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, MIN -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - INFO = 0 - WANTQ = LSAME( VECT, 'Q' ) - MN = MIN( M, N ) - LQUERY = ( LWORK.EQ.-1 ) - IF( .NOT.WANTQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN - INFO = -1 - ELSE IF( M.LT.0 ) THEN - INFO = -2 - ELSE IF( N.LT.0 .OR. ( WANTQ .AND. ( N.GT.M .OR. N.LT.MIN( M, - $ K ) ) ) .OR. ( .NOT.WANTQ .AND. ( M.GT.N .OR. M.LT. - $ MIN( N, K ) ) ) ) THEN - INFO = -3 - ELSE IF( K.LT.0 ) THEN - INFO = -4 - ELSE IF( LDA.LT.MAX( 1, M ) ) THEN - INFO = -6 - ELSE IF( LWORK.LT.MAX( 1, MN ) .AND. .NOT.LQUERY ) THEN - INFO = -9 - END IF -* - IF( INFO.EQ.0 ) THEN - WORK( 1 ) = 1 - IF( WANTQ ) THEN - IF( M.GE.K ) THEN - CALL DORGQR( M, N, K, A, LDA, TAU, WORK, -1, IINFO ) - ELSE - IF( M.GT.1 ) THEN - CALL DORGQR( M-1, M-1, M-1, A, LDA, TAU, WORK, -1, - $ IINFO ) - END IF - END IF - ELSE - IF( K.LT.N ) THEN - CALL DORGLQ( M, N, K, A, LDA, TAU, WORK, -1, IINFO ) - ELSE - IF( N.GT.1 ) THEN - CALL DORGLQ( N-1, N-1, N-1, A, LDA, TAU, WORK, -1, - $ IINFO ) - END IF - END IF - END IF - LWKOPT = INT( WORK( 1 ) ) - LWKOPT = MAX (LWKOPT, MN) - END IF -* - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DORGBR', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - WORK( 1 ) = LWKOPT - RETURN - END IF -* -* Quick return if possible -* - IF( M.EQ.0 .OR. N.EQ.0 ) THEN - WORK( 1 ) = 1 - RETURN - END IF -* - IF( WANTQ ) THEN -* -* Form Q, determined by a call to DGEBRD to reduce an m-by-k -* matrix -* - IF( M.GE.K ) THEN -* -* If m >= k, assume m >= n >= k -* - CALL DORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO ) -* - ELSE -* -* If m < k, assume m = n -* -* Shift the vectors which define the elementary reflectors one -* column to the right, and set the first row and column of Q -* to those of the unit matrix -* - DO 20 J = M, 2, -1 - A( 1, J ) = ZERO - DO 10 I = J + 1, M - A( I, J ) = A( I, J-1 ) - 10 CONTINUE - 20 CONTINUE - A( 1, 1 ) = ONE - DO 30 I = 2, M - A( I, 1 ) = ZERO - 30 CONTINUE - IF( M.GT.1 ) THEN -* -* Form Q(2:m,2:m) -* - CALL DORGQR( M-1, M-1, M-1, A( 2, 2 ), LDA, TAU, WORK, - $ LWORK, IINFO ) - END IF - END IF - ELSE -* -* Form P**T, determined by a call to DGEBRD to reduce a k-by-n -* matrix -* - IF( K.LT.N ) THEN -* -* If k < n, assume k <= m <= n -* - CALL DORGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO ) -* - ELSE -* -* If k >= n, assume m = n -* -* Shift the vectors which define the elementary reflectors one -* row downward, and set the first row and column of P**T to -* those of the unit matrix -* - A( 1, 1 ) = ONE - DO 40 I = 2, N - A( I, 1 ) = ZERO - 40 CONTINUE - DO 60 J = 2, N - DO 50 I = J - 1, 2, -1 - A( I, J ) = A( I-1, J ) - 50 CONTINUE - A( 1, J ) = ZERO - 60 CONTINUE - IF( N.GT.1 ) THEN -* -* Form P**T(2:n,2:n) -* - CALL DORGLQ( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK, - $ LWORK, IINFO ) - END IF - END IF - END IF - WORK( 1 ) = LWKOPT - RETURN -* -* End of DORGBR -* - END diff --git a/lib/linalg/fortran/dorgl2.f b/lib/linalg/fortran/dorgl2.f deleted file mode 100644 index ce1d2c6750..0000000000 --- a/lib/linalg/fortran/dorgl2.f +++ /dev/null @@ -1,201 +0,0 @@ -*> \brief \b DORGL2 -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DORGL2 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DORGL2( M, N, K, A, LDA, TAU, WORK, INFO ) -* -* .. Scalar Arguments .. -* INTEGER INFO, K, LDA, M, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DORGL2 generates an m by n real matrix Q with orthonormal rows, -*> which is defined as the first m rows of a product of k elementary -*> reflectors of order n -*> -*> Q = H(k) . . . H(2) H(1) -*> -*> as returned by DGELQF. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix Q. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix Q. N >= M. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> The number of elementary reflectors whose product defines the -*> matrix Q. M >= K >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the i-th row must contain the vector which defines -*> the elementary reflector H(i), for i = 1,2,...,k, as returned -*> by DGELQF in the first k rows of its array argument A. -*> On exit, the m-by-n matrix Q. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The first dimension of the array A. LDA >= max(1,M). -*> \endverbatim -*> -*> \param[in] TAU -*> \verbatim -*> TAU is DOUBLE PRECISION array, dimension (K) -*> TAU(i) must contain the scalar factor of the elementary -*> reflector H(i), as returned by DGELQF. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (M) -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument has an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleOTHERcomputational -* -* ===================================================================== - SUBROUTINE DORGL2( M, N, K, A, LDA, TAU, WORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INFO, K, LDA, M, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE, ZERO - PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) -* .. -* .. Local Scalars .. - INTEGER I, J, L -* .. -* .. External Subroutines .. - EXTERNAL DLARF, DSCAL, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - INFO = 0 - IF( M.LT.0 ) THEN - INFO = -1 - ELSE IF( N.LT.M ) THEN - INFO = -2 - ELSE IF( K.LT.0 .OR. K.GT.M ) THEN - INFO = -3 - ELSE IF( LDA.LT.MAX( 1, M ) ) THEN - INFO = -5 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DORGL2', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( M.LE.0 ) - $ RETURN -* - IF( K.LT.M ) THEN -* -* Initialise rows k+1:m to rows of the unit matrix -* - DO 20 J = 1, N - DO 10 L = K + 1, M - A( L, J ) = ZERO - 10 CONTINUE - IF( J.GT.K .AND. J.LE.M ) - $ A( J, J ) = ONE - 20 CONTINUE - END IF -* - DO 40 I = K, 1, -1 -* -* Apply H(i) to A(i:m,i:n) from the right -* - IF( I.LT.N ) THEN - IF( I.LT.M ) THEN - A( I, I ) = ONE - CALL DLARF( 'Right', M-I, N-I+1, A( I, I ), LDA, - $ TAU( I ), A( I+1, I ), LDA, WORK ) - END IF - CALL DSCAL( N-I, -TAU( I ), A( I, I+1 ), LDA ) - END IF - A( I, I ) = ONE - TAU( I ) -* -* Set A(i,1:i-1) to zero -* - DO 30 L = 1, I - 1 - A( I, L ) = ZERO - 30 CONTINUE - 40 CONTINUE - RETURN -* -* End of DORGL2 -* - END diff --git a/lib/linalg/fortran/dorglq.f b/lib/linalg/fortran/dorglq.f deleted file mode 100644 index 8c37c18b75..0000000000 --- a/lib/linalg/fortran/dorglq.f +++ /dev/null @@ -1,286 +0,0 @@ -*> \brief \b DORGLQ -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DORGLQ + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DORGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) -* -* .. Scalar Arguments .. -* INTEGER INFO, K, LDA, LWORK, M, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DORGLQ generates an M-by-N real matrix Q with orthonormal rows, -*> which is defined as the first M rows of a product of K elementary -*> reflectors of order N -*> -*> Q = H(k) . . . H(2) H(1) -*> -*> as returned by DGELQF. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix Q. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix Q. N >= M. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> The number of elementary reflectors whose product defines the -*> matrix Q. M >= K >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the i-th row must contain the vector which defines -*> the elementary reflector H(i), for i = 1,2,...,k, as returned -*> by DGELQF in the first k rows of its array argument A. -*> On exit, the M-by-N matrix Q. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The first dimension of the array A. LDA >= max(1,M). -*> \endverbatim -*> -*> \param[in] TAU -*> \verbatim -*> TAU is DOUBLE PRECISION array, dimension (K) -*> TAU(i) must contain the scalar factor of the elementary -*> reflector H(i), as returned by DGELQF. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) -*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -*> \endverbatim -*> -*> \param[in] LWORK -*> \verbatim -*> LWORK is INTEGER -*> The dimension of the array WORK. LWORK >= max(1,M). -*> For optimum performance LWORK >= M*NB, where NB is -*> the optimal blocksize. -*> -*> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal size of the WORK array, returns -*> this value as the first entry of the WORK array, and no error -*> message related to LWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument has an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleOTHERcomputational -* -* ===================================================================== - SUBROUTINE DORGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INFO, K, LDA, LWORK, M, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO - PARAMETER ( ZERO = 0.0D+0 ) -* .. -* .. Local Scalars .. - LOGICAL LQUERY - INTEGER I, IB, IINFO, IWS, J, KI, KK, L, LDWORK, - $ LWKOPT, NB, NBMIN, NX -* .. -* .. External Subroutines .. - EXTERNAL DLARFB, DLARFT, DORGL2, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, MIN -* .. -* .. External Functions .. - INTEGER ILAENV - EXTERNAL ILAENV -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - INFO = 0 - NB = ILAENV( 1, 'DORGLQ', ' ', M, N, K, -1 ) - LWKOPT = MAX( 1, M )*NB - WORK( 1 ) = LWKOPT - LQUERY = ( LWORK.EQ.-1 ) - IF( M.LT.0 ) THEN - INFO = -1 - ELSE IF( N.LT.M ) THEN - INFO = -2 - ELSE IF( K.LT.0 .OR. K.GT.M ) THEN - INFO = -3 - ELSE IF( LDA.LT.MAX( 1, M ) ) THEN - INFO = -5 - ELSE IF( LWORK.LT.MAX( 1, M ) .AND. .NOT.LQUERY ) THEN - INFO = -8 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DORGLQ', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - RETURN - END IF -* -* Quick return if possible -* - IF( M.LE.0 ) THEN - WORK( 1 ) = 1 - RETURN - END IF -* - NBMIN = 2 - NX = 0 - IWS = M - IF( NB.GT.1 .AND. NB.LT.K ) THEN -* -* Determine when to cross over from blocked to unblocked code. -* - NX = MAX( 0, ILAENV( 3, 'DORGLQ', ' ', M, N, K, -1 ) ) - IF( NX.LT.K ) THEN -* -* Determine if workspace is large enough for blocked code. -* - LDWORK = M - IWS = LDWORK*NB - IF( LWORK.LT.IWS ) THEN -* -* Not enough workspace to use optimal NB: reduce NB and -* determine the minimum value of NB. -* - NB = LWORK / LDWORK - NBMIN = MAX( 2, ILAENV( 2, 'DORGLQ', ' ', M, N, K, -1 ) ) - END IF - END IF - END IF -* - IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN -* -* Use blocked code after the last block. -* The first kk rows are handled by the block method. -* - KI = ( ( K-NX-1 ) / NB )*NB - KK = MIN( K, KI+NB ) -* -* Set A(kk+1:m,1:kk) to zero. -* - DO 20 J = 1, KK - DO 10 I = KK + 1, M - A( I, J ) = ZERO - 10 CONTINUE - 20 CONTINUE - ELSE - KK = 0 - END IF -* -* Use unblocked code for the last or only block. -* - IF( KK.LT.M ) - $ CALL DORGL2( M-KK, N-KK, K-KK, A( KK+1, KK+1 ), LDA, - $ TAU( KK+1 ), WORK, IINFO ) -* - IF( KK.GT.0 ) THEN -* -* Use blocked code -* - DO 50 I = KI + 1, 1, -NB - IB = MIN( NB, K-I+1 ) - IF( I+IB.LE.M ) THEN -* -* Form the triangular factor of the block reflector -* H = H(i) H(i+1) . . . H(i+ib-1) -* - CALL DLARFT( 'Forward', 'Rowwise', N-I+1, IB, A( I, I ), - $ LDA, TAU( I ), WORK, LDWORK ) -* -* Apply H**T to A(i+ib:m,i:n) from the right -* - CALL DLARFB( 'Right', 'Transpose', 'Forward', 'Rowwise', - $ M-I-IB+1, N-I+1, IB, A( I, I ), LDA, WORK, - $ LDWORK, A( I+IB, I ), LDA, WORK( IB+1 ), - $ LDWORK ) - END IF -* -* Apply H**T to columns i:n of current block -* - CALL DORGL2( IB, N-I+1, IB, A( I, I ), LDA, TAU( I ), WORK, - $ IINFO ) -* -* Set columns 1:i-1 of current block to zero -* - DO 40 J = 1, I - 1 - DO 30 L = I, I + IB - 1 - A( L, J ) = ZERO - 30 CONTINUE - 40 CONTINUE - 50 CONTINUE - END IF -* - WORK( 1 ) = IWS - RETURN -* -* End of DORGLQ -* - END diff --git a/lib/linalg/fortran/dorgql.f b/lib/linalg/fortran/dorgql.f deleted file mode 100644 index 45e5bf19f1..0000000000 --- a/lib/linalg/fortran/dorgql.f +++ /dev/null @@ -1,293 +0,0 @@ -*> \brief \b DORGQL -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DORGQL + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DORGQL( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) -* -* .. Scalar Arguments .. -* INTEGER INFO, K, LDA, LWORK, M, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DORGQL generates an M-by-N real matrix Q with orthonormal columns, -*> which is defined as the last N columns of a product of K elementary -*> reflectors of order M -*> -*> Q = H(k) . . . H(2) H(1) -*> -*> as returned by DGEQLF. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix Q. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix Q. M >= N >= 0. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> The number of elementary reflectors whose product defines the -*> matrix Q. N >= K >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the (n-k+i)-th column must contain the vector which -*> defines the elementary reflector H(i), for i = 1,2,...,k, as -*> returned by DGEQLF in the last k columns of its array -*> argument A. -*> On exit, the M-by-N matrix Q. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The first dimension of the array A. LDA >= max(1,M). -*> \endverbatim -*> -*> \param[in] TAU -*> \verbatim -*> TAU is DOUBLE PRECISION array, dimension (K) -*> TAU(i) must contain the scalar factor of the elementary -*> reflector H(i), as returned by DGEQLF. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) -*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -*> \endverbatim -*> -*> \param[in] LWORK -*> \verbatim -*> LWORK is INTEGER -*> The dimension of the array WORK. LWORK >= max(1,N). -*> For optimum performance LWORK >= N*NB, where NB is the -*> optimal blocksize. -*> -*> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal size of the WORK array, returns -*> this value as the first entry of the WORK array, and no error -*> message related to LWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument has an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleOTHERcomputational -* -* ===================================================================== - SUBROUTINE DORGQL( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INFO, K, LDA, LWORK, M, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO - PARAMETER ( ZERO = 0.0D+0 ) -* .. -* .. Local Scalars .. - LOGICAL LQUERY - INTEGER I, IB, IINFO, IWS, J, KK, L, LDWORK, LWKOPT, - $ NB, NBMIN, NX -* .. -* .. External Subroutines .. - EXTERNAL DLARFB, DLARFT, DORG2L, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, MIN -* .. -* .. External Functions .. - INTEGER ILAENV - EXTERNAL ILAENV -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - INFO = 0 - LQUERY = ( LWORK.EQ.-1 ) - IF( M.LT.0 ) THEN - INFO = -1 - ELSE IF( N.LT.0 .OR. N.GT.M ) THEN - INFO = -2 - ELSE IF( K.LT.0 .OR. K.GT.N ) THEN - INFO = -3 - ELSE IF( LDA.LT.MAX( 1, M ) ) THEN - INFO = -5 - END IF -* - IF( INFO.EQ.0 ) THEN - IF( N.EQ.0 ) THEN - LWKOPT = 1 - ELSE - NB = ILAENV( 1, 'DORGQL', ' ', M, N, K, -1 ) - LWKOPT = N*NB - END IF - WORK( 1 ) = LWKOPT -* - IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN - INFO = -8 - END IF - END IF -* - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DORGQL', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - RETURN - END IF -* -* Quick return if possible -* - IF( N.LE.0 ) THEN - RETURN - END IF -* - NBMIN = 2 - NX = 0 - IWS = N - IF( NB.GT.1 .AND. NB.LT.K ) THEN -* -* Determine when to cross over from blocked to unblocked code. -* - NX = MAX( 0, ILAENV( 3, 'DORGQL', ' ', M, N, K, -1 ) ) - IF( NX.LT.K ) THEN -* -* Determine if workspace is large enough for blocked code. -* - LDWORK = N - IWS = LDWORK*NB - IF( LWORK.LT.IWS ) THEN -* -* Not enough workspace to use optimal NB: reduce NB and -* determine the minimum value of NB. -* - NB = LWORK / LDWORK - NBMIN = MAX( 2, ILAENV( 2, 'DORGQL', ' ', M, N, K, -1 ) ) - END IF - END IF - END IF -* - IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN -* -* Use blocked code after the first block. -* The last kk columns are handled by the block method. -* - KK = MIN( K, ( ( K-NX+NB-1 ) / NB )*NB ) -* -* Set A(m-kk+1:m,1:n-kk) to zero. -* - DO 20 J = 1, N - KK - DO 10 I = M - KK + 1, M - A( I, J ) = ZERO - 10 CONTINUE - 20 CONTINUE - ELSE - KK = 0 - END IF -* -* Use unblocked code for the first or only block. -* - CALL DORG2L( M-KK, N-KK, K-KK, A, LDA, TAU, WORK, IINFO ) -* - IF( KK.GT.0 ) THEN -* -* Use blocked code -* - DO 50 I = K - KK + 1, K, NB - IB = MIN( NB, K-I+1 ) - IF( N-K+I.GT.1 ) THEN -* -* Form the triangular factor of the block reflector -* H = H(i+ib-1) . . . H(i+1) H(i) -* - CALL DLARFT( 'Backward', 'Columnwise', M-K+I+IB-1, IB, - $ A( 1, N-K+I ), LDA, TAU( I ), WORK, LDWORK ) -* -* Apply H to A(1:m-k+i+ib-1,1:n-k+i-1) from the left -* - CALL DLARFB( 'Left', 'No transpose', 'Backward', - $ 'Columnwise', M-K+I+IB-1, N-K+I-1, IB, - $ A( 1, N-K+I ), LDA, WORK, LDWORK, A, LDA, - $ WORK( IB+1 ), LDWORK ) - END IF -* -* Apply H to rows 1:m-k+i+ib-1 of current block -* - CALL DORG2L( M-K+I+IB-1, IB, IB, A( 1, N-K+I ), LDA, - $ TAU( I ), WORK, IINFO ) -* -* Set rows m-k+i+ib:m of current block to zero -* - DO 40 J = N - K + I, N - K + I + IB - 1 - DO 30 L = M - K + I + IB, M - A( L, J ) = ZERO - 30 CONTINUE - 40 CONTINUE - 50 CONTINUE - END IF -* - WORK( 1 ) = IWS - RETURN -* -* End of DORGQL -* - END diff --git a/lib/linalg/fortran/dorgqr.f b/lib/linalg/fortran/dorgqr.f deleted file mode 100644 index a41ce7ed56..0000000000 --- a/lib/linalg/fortran/dorgqr.f +++ /dev/null @@ -1,287 +0,0 @@ -*> \brief \b DORGQR -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DORGQR + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) -* -* .. Scalar Arguments .. -* INTEGER INFO, K, LDA, LWORK, M, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DORGQR generates an M-by-N real matrix Q with orthonormal columns, -*> which is defined as the first N columns of a product of K elementary -*> reflectors of order M -*> -*> Q = H(1) H(2) . . . H(k) -*> -*> as returned by DGEQRF. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix Q. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix Q. M >= N >= 0. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> The number of elementary reflectors whose product defines the -*> matrix Q. N >= K >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the i-th column must contain the vector which -*> defines the elementary reflector H(i), for i = 1,2,...,k, as -*> returned by DGEQRF in the first k columns of its array -*> argument A. -*> On exit, the M-by-N matrix Q. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The first dimension of the array A. LDA >= max(1,M). -*> \endverbatim -*> -*> \param[in] TAU -*> \verbatim -*> TAU is DOUBLE PRECISION array, dimension (K) -*> TAU(i) must contain the scalar factor of the elementary -*> reflector H(i), as returned by DGEQRF. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) -*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -*> \endverbatim -*> -*> \param[in] LWORK -*> \verbatim -*> LWORK is INTEGER -*> The dimension of the array WORK. LWORK >= max(1,N). -*> For optimum performance LWORK >= N*NB, where NB is the -*> optimal blocksize. -*> -*> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal size of the WORK array, returns -*> this value as the first entry of the WORK array, and no error -*> message related to LWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument has an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleOTHERcomputational -* -* ===================================================================== - SUBROUTINE DORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INFO, K, LDA, LWORK, M, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO - PARAMETER ( ZERO = 0.0D+0 ) -* .. -* .. Local Scalars .. - LOGICAL LQUERY - INTEGER I, IB, IINFO, IWS, J, KI, KK, L, LDWORK, - $ LWKOPT, NB, NBMIN, NX -* .. -* .. External Subroutines .. - EXTERNAL DLARFB, DLARFT, DORG2R, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, MIN -* .. -* .. External Functions .. - INTEGER ILAENV - EXTERNAL ILAENV -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - INFO = 0 - NB = ILAENV( 1, 'DORGQR', ' ', M, N, K, -1 ) - LWKOPT = MAX( 1, N )*NB - WORK( 1 ) = LWKOPT - LQUERY = ( LWORK.EQ.-1 ) - IF( M.LT.0 ) THEN - INFO = -1 - ELSE IF( N.LT.0 .OR. N.GT.M ) THEN - INFO = -2 - ELSE IF( K.LT.0 .OR. K.GT.N ) THEN - INFO = -3 - ELSE IF( LDA.LT.MAX( 1, M ) ) THEN - INFO = -5 - ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN - INFO = -8 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DORGQR', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - RETURN - END IF -* -* Quick return if possible -* - IF( N.LE.0 ) THEN - WORK( 1 ) = 1 - RETURN - END IF -* - NBMIN = 2 - NX = 0 - IWS = N - IF( NB.GT.1 .AND. NB.LT.K ) THEN -* -* Determine when to cross over from blocked to unblocked code. -* - NX = MAX( 0, ILAENV( 3, 'DORGQR', ' ', M, N, K, -1 ) ) - IF( NX.LT.K ) THEN -* -* Determine if workspace is large enough for blocked code. -* - LDWORK = N - IWS = LDWORK*NB - IF( LWORK.LT.IWS ) THEN -* -* Not enough workspace to use optimal NB: reduce NB and -* determine the minimum value of NB. -* - NB = LWORK / LDWORK - NBMIN = MAX( 2, ILAENV( 2, 'DORGQR', ' ', M, N, K, -1 ) ) - END IF - END IF - END IF -* - IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN -* -* Use blocked code after the last block. -* The first kk columns are handled by the block method. -* - KI = ( ( K-NX-1 ) / NB )*NB - KK = MIN( K, KI+NB ) -* -* Set A(1:kk,kk+1:n) to zero. -* - DO 20 J = KK + 1, N - DO 10 I = 1, KK - A( I, J ) = ZERO - 10 CONTINUE - 20 CONTINUE - ELSE - KK = 0 - END IF -* -* Use unblocked code for the last or only block. -* - IF( KK.LT.N ) - $ CALL DORG2R( M-KK, N-KK, K-KK, A( KK+1, KK+1 ), LDA, - $ TAU( KK+1 ), WORK, IINFO ) -* - IF( KK.GT.0 ) THEN -* -* Use blocked code -* - DO 50 I = KI + 1, 1, -NB - IB = MIN( NB, K-I+1 ) - IF( I+IB.LE.N ) THEN -* -* Form the triangular factor of the block reflector -* H = H(i) H(i+1) . . . H(i+ib-1) -* - CALL DLARFT( 'Forward', 'Columnwise', M-I+1, IB, - $ A( I, I ), LDA, TAU( I ), WORK, LDWORK ) -* -* Apply H to A(i:m,i+ib:n) from the left -* - CALL DLARFB( 'Left', 'No transpose', 'Forward', - $ 'Columnwise', M-I+1, N-I-IB+1, IB, - $ A( I, I ), LDA, WORK, LDWORK, A( I, I+IB ), - $ LDA, WORK( IB+1 ), LDWORK ) - END IF -* -* Apply H to rows i:m of current block -* - CALL DORG2R( M-I+1, IB, IB, A( I, I ), LDA, TAU( I ), WORK, - $ IINFO ) -* -* Set rows 1:i-1 of current block to zero -* - DO 40 J = I, I + IB - 1 - DO 30 L = 1, I - 1 - A( L, J ) = ZERO - 30 CONTINUE - 40 CONTINUE - 50 CONTINUE - END IF -* - WORK( 1 ) = IWS - RETURN -* -* End of DORGQR -* - END diff --git a/lib/linalg/fortran/dorgtr.f b/lib/linalg/fortran/dorgtr.f deleted file mode 100644 index 0a0ab15a78..0000000000 --- a/lib/linalg/fortran/dorgtr.f +++ /dev/null @@ -1,252 +0,0 @@ -*> \brief \b DORGTR -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DORGTR + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DORGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER UPLO -* INTEGER INFO, LDA, LWORK, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DORGTR generates a real orthogonal matrix Q which is defined as the -*> product of n-1 elementary reflectors of order N, as returned by -*> DSYTRD: -*> -*> if UPLO = 'U', Q = H(n-1) . . . H(2) H(1), -*> -*> if UPLO = 'L', Q = H(1) H(2) . . . H(n-1). -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> = 'U': Upper triangle of A contains elementary reflectors -*> from DSYTRD; -*> = 'L': Lower triangle of A contains elementary reflectors -*> from DSYTRD. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrix Q. N >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the vectors which define the elementary reflectors, -*> as returned by DSYTRD. -*> On exit, the N-by-N orthogonal matrix Q. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,N). -*> \endverbatim -*> -*> \param[in] TAU -*> \verbatim -*> TAU is DOUBLE PRECISION array, dimension (N-1) -*> TAU(i) must contain the scalar factor of the elementary -*> reflector H(i), as returned by DSYTRD. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) -*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -*> \endverbatim -*> -*> \param[in] LWORK -*> \verbatim -*> LWORK is INTEGER -*> The dimension of the array WORK. LWORK >= max(1,N-1). -*> For optimum performance LWORK >= (N-1)*NB, where NB is -*> the optimal blocksize. -*> -*> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal size of the WORK array, returns -*> this value as the first entry of the WORK array, and no error -*> message related to LWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleOTHERcomputational -* -* ===================================================================== - SUBROUTINE DORGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER UPLO - INTEGER INFO, LDA, LWORK, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) -* .. -* .. Local Scalars .. - LOGICAL LQUERY, UPPER - INTEGER I, IINFO, J, LWKOPT, NB -* .. -* .. External Functions .. - LOGICAL LSAME - INTEGER ILAENV - EXTERNAL LSAME, ILAENV -* .. -* .. External Subroutines .. - EXTERNAL DORGQL, DORGQR, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - INFO = 0 - LQUERY = ( LWORK.EQ.-1 ) - UPPER = LSAME( UPLO, 'U' ) - IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -4 - ELSE IF( LWORK.LT.MAX( 1, N-1 ) .AND. .NOT.LQUERY ) THEN - INFO = -7 - END IF -* - IF( INFO.EQ.0 ) THEN - IF( UPPER ) THEN - NB = ILAENV( 1, 'DORGQL', ' ', N-1, N-1, N-1, -1 ) - ELSE - NB = ILAENV( 1, 'DORGQR', ' ', N-1, N-1, N-1, -1 ) - END IF - LWKOPT = MAX( 1, N-1 )*NB - WORK( 1 ) = LWKOPT - END IF -* - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DORGTR', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - RETURN - END IF -* -* Quick return if possible -* - IF( N.EQ.0 ) THEN - WORK( 1 ) = 1 - RETURN - END IF -* - IF( UPPER ) THEN -* -* Q was determined by a call to DSYTRD with UPLO = 'U' -* -* Shift the vectors which define the elementary reflectors one -* column to the left, and set the last row and column of Q to -* those of the unit matrix -* - DO 20 J = 1, N - 1 - DO 10 I = 1, J - 1 - A( I, J ) = A( I, J+1 ) - 10 CONTINUE - A( N, J ) = ZERO - 20 CONTINUE - DO 30 I = 1, N - 1 - A( I, N ) = ZERO - 30 CONTINUE - A( N, N ) = ONE -* -* Generate Q(1:n-1,1:n-1) -* - CALL DORGQL( N-1, N-1, N-1, A, LDA, TAU, WORK, LWORK, IINFO ) -* - ELSE -* -* Q was determined by a call to DSYTRD with UPLO = 'L'. -* -* Shift the vectors which define the elementary reflectors one -* column to the right, and set the first row and column of Q to -* those of the unit matrix -* - DO 50 J = N, 2, -1 - A( 1, J ) = ZERO - DO 40 I = J + 1, N - A( I, J ) = A( I, J-1 ) - 40 CONTINUE - 50 CONTINUE - A( 1, 1 ) = ONE - DO 60 I = 2, N - A( I, 1 ) = ZERO - 60 CONTINUE - IF( N.GT.1 ) THEN -* -* Generate Q(2:n,2:n) -* - CALL DORGQR( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK, - $ LWORK, IINFO ) - END IF - END IF - WORK( 1 ) = LWKOPT - RETURN -* -* End of DORGTR -* - END diff --git a/lib/linalg/fortran/dorm2l.f b/lib/linalg/fortran/dorm2l.f deleted file mode 100644 index c99039c541..0000000000 --- a/lib/linalg/fortran/dorm2l.f +++ /dev/null @@ -1,275 +0,0 @@ -*> \brief \b DORM2L multiplies a general matrix by the orthogonal matrix from a QL factorization determined by sgeqlf (unblocked algorithm). -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DORM2L + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DORM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, -* WORK, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER SIDE, TRANS -* INTEGER INFO, K, LDA, LDC, M, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DORM2L overwrites the general real m by n matrix C with -*> -*> Q * C if SIDE = 'L' and TRANS = 'N', or -*> -*> Q**T * C if SIDE = 'L' and TRANS = 'T', or -*> -*> C * Q if SIDE = 'R' and TRANS = 'N', or -*> -*> C * Q**T if SIDE = 'R' and TRANS = 'T', -*> -*> where Q is a real orthogonal matrix defined as the product of k -*> elementary reflectors -*> -*> Q = H(k) . . . H(2) H(1) -*> -*> as returned by DGEQLF. Q is of order m if SIDE = 'L' and of order n -*> if SIDE = 'R'. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] SIDE -*> \verbatim -*> SIDE is CHARACTER*1 -*> = 'L': apply Q or Q**T from the Left -*> = 'R': apply Q or Q**T from the Right -*> \endverbatim -*> -*> \param[in] TRANS -*> \verbatim -*> TRANS is CHARACTER*1 -*> = 'N': apply Q (No transpose) -*> = 'T': apply Q**T (Transpose) -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix C. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix C. N >= 0. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> The number of elementary reflectors whose product defines -*> the matrix Q. -*> If SIDE = 'L', M >= K >= 0; -*> if SIDE = 'R', N >= K >= 0. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,K) -*> The i-th column must contain the vector which defines the -*> elementary reflector H(i), for i = 1,2,...,k, as returned by -*> DGEQLF in the last k columns of its array argument A. -*> A is modified by the routine but restored on exit. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. -*> If SIDE = 'L', LDA >= max(1,M); -*> if SIDE = 'R', LDA >= max(1,N). -*> \endverbatim -*> -*> \param[in] TAU -*> \verbatim -*> TAU is DOUBLE PRECISION array, dimension (K) -*> TAU(i) must contain the scalar factor of the elementary -*> reflector H(i), as returned by DGEQLF. -*> \endverbatim -*> -*> \param[in,out] C -*> \verbatim -*> C is DOUBLE PRECISION array, dimension (LDC,N) -*> On entry, the m by n matrix C. -*> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. -*> \endverbatim -*> -*> \param[in] LDC -*> \verbatim -*> LDC is INTEGER -*> The leading dimension of the array C. LDC >= max(1,M). -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension -*> (N) if SIDE = 'L', -*> (M) if SIDE = 'R' -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleOTHERcomputational -* -* ===================================================================== - SUBROUTINE DORM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, - $ WORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER SIDE, TRANS - INTEGER INFO, K, LDA, LDC, M, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE - PARAMETER ( ONE = 1.0D+0 ) -* .. -* .. Local Scalars .. - LOGICAL LEFT, NOTRAN - INTEGER I, I1, I2, I3, MI, NI, NQ - DOUBLE PRECISION AII -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL DLARF, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - INFO = 0 - LEFT = LSAME( SIDE, 'L' ) - NOTRAN = LSAME( TRANS, 'N' ) -* -* NQ is the order of Q -* - IF( LEFT ) THEN - NQ = M - ELSE - NQ = N - END IF - IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN - INFO = -1 - ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN - INFO = -2 - ELSE IF( M.LT.0 ) THEN - INFO = -3 - ELSE IF( N.LT.0 ) THEN - INFO = -4 - ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN - INFO = -5 - ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN - INFO = -7 - ELSE IF( LDC.LT.MAX( 1, M ) ) THEN - INFO = -10 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DORM2L', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) - $ RETURN -* - IF( ( LEFT .AND. NOTRAN ) .OR. ( .NOT.LEFT .AND. .NOT.NOTRAN ) ) - $ THEN - I1 = 1 - I2 = K - I3 = 1 - ELSE - I1 = K - I2 = 1 - I3 = -1 - END IF -* - IF( LEFT ) THEN - NI = N - ELSE - MI = M - END IF -* - DO 10 I = I1, I2, I3 - IF( LEFT ) THEN -* -* H(i) is applied to C(1:m-k+i,1:n) -* - MI = M - K + I - ELSE -* -* H(i) is applied to C(1:m,1:n-k+i) -* - NI = N - K + I - END IF -* -* Apply H(i) -* - AII = A( NQ-K+I, I ) - A( NQ-K+I, I ) = ONE - CALL DLARF( SIDE, MI, NI, A( 1, I ), 1, TAU( I ), C, LDC, - $ WORK ) - A( NQ-K+I, I ) = AII - 10 CONTINUE - RETURN -* -* End of DORM2L -* - END diff --git a/lib/linalg/fortran/dorm2r.f b/lib/linalg/fortran/dorm2r.f deleted file mode 100644 index ac88eec8dc..0000000000 --- a/lib/linalg/fortran/dorm2r.f +++ /dev/null @@ -1,279 +0,0 @@ -*> \brief \b DORM2R multiplies a general matrix by the orthogonal matrix from a QR factorization determined by sgeqrf (unblocked algorithm). -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DORM2R + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DORM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, -* WORK, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER SIDE, TRANS -* INTEGER INFO, K, LDA, LDC, M, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DORM2R overwrites the general real m by n matrix C with -*> -*> Q * C if SIDE = 'L' and TRANS = 'N', or -*> -*> Q**T* C if SIDE = 'L' and TRANS = 'T', or -*> -*> C * Q if SIDE = 'R' and TRANS = 'N', or -*> -*> C * Q**T if SIDE = 'R' and TRANS = 'T', -*> -*> where Q is a real orthogonal matrix defined as the product of k -*> elementary reflectors -*> -*> Q = H(1) H(2) . . . H(k) -*> -*> as returned by DGEQRF. Q is of order m if SIDE = 'L' and of order n -*> if SIDE = 'R'. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] SIDE -*> \verbatim -*> SIDE is CHARACTER*1 -*> = 'L': apply Q or Q**T from the Left -*> = 'R': apply Q or Q**T from the Right -*> \endverbatim -*> -*> \param[in] TRANS -*> \verbatim -*> TRANS is CHARACTER*1 -*> = 'N': apply Q (No transpose) -*> = 'T': apply Q**T (Transpose) -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix C. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix C. N >= 0. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> The number of elementary reflectors whose product defines -*> the matrix Q. -*> If SIDE = 'L', M >= K >= 0; -*> if SIDE = 'R', N >= K >= 0. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,K) -*> The i-th column must contain the vector which defines the -*> elementary reflector H(i), for i = 1,2,...,k, as returned by -*> DGEQRF in the first k columns of its array argument A. -*> A is modified by the routine but restored on exit. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. -*> If SIDE = 'L', LDA >= max(1,M); -*> if SIDE = 'R', LDA >= max(1,N). -*> \endverbatim -*> -*> \param[in] TAU -*> \verbatim -*> TAU is DOUBLE PRECISION array, dimension (K) -*> TAU(i) must contain the scalar factor of the elementary -*> reflector H(i), as returned by DGEQRF. -*> \endverbatim -*> -*> \param[in,out] C -*> \verbatim -*> C is DOUBLE PRECISION array, dimension (LDC,N) -*> On entry, the m by n matrix C. -*> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. -*> \endverbatim -*> -*> \param[in] LDC -*> \verbatim -*> LDC is INTEGER -*> The leading dimension of the array C. LDC >= max(1,M). -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension -*> (N) if SIDE = 'L', -*> (M) if SIDE = 'R' -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleOTHERcomputational -* -* ===================================================================== - SUBROUTINE DORM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, - $ WORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER SIDE, TRANS - INTEGER INFO, K, LDA, LDC, M, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE - PARAMETER ( ONE = 1.0D+0 ) -* .. -* .. Local Scalars .. - LOGICAL LEFT, NOTRAN - INTEGER I, I1, I2, I3, IC, JC, MI, NI, NQ - DOUBLE PRECISION AII -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL DLARF, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - INFO = 0 - LEFT = LSAME( SIDE, 'L' ) - NOTRAN = LSAME( TRANS, 'N' ) -* -* NQ is the order of Q -* - IF( LEFT ) THEN - NQ = M - ELSE - NQ = N - END IF - IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN - INFO = -1 - ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN - INFO = -2 - ELSE IF( M.LT.0 ) THEN - INFO = -3 - ELSE IF( N.LT.0 ) THEN - INFO = -4 - ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN - INFO = -5 - ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN - INFO = -7 - ELSE IF( LDC.LT.MAX( 1, M ) ) THEN - INFO = -10 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DORM2R', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) - $ RETURN -* - IF( ( LEFT .AND. .NOT.NOTRAN ) .OR. ( .NOT.LEFT .AND. NOTRAN ) ) - $ THEN - I1 = 1 - I2 = K - I3 = 1 - ELSE - I1 = K - I2 = 1 - I3 = -1 - END IF -* - IF( LEFT ) THEN - NI = N - JC = 1 - ELSE - MI = M - IC = 1 - END IF -* - DO 10 I = I1, I2, I3 - IF( LEFT ) THEN -* -* H(i) is applied to C(i:m,1:n) -* - MI = M - I + 1 - IC = I - ELSE -* -* H(i) is applied to C(1:m,i:n) -* - NI = N - I + 1 - JC = I - END IF -* -* Apply H(i) -* - AII = A( I, I ) - A( I, I ) = ONE - CALL DLARF( SIDE, MI, NI, A( I, I ), 1, TAU( I ), C( IC, JC ), - $ LDC, WORK ) - A( I, I ) = AII - 10 CONTINUE - RETURN -* -* End of DORM2R -* - END diff --git a/lib/linalg/fortran/dormbr.f b/lib/linalg/fortran/dormbr.f deleted file mode 100644 index 86abb10072..0000000000 --- a/lib/linalg/fortran/dormbr.f +++ /dev/null @@ -1,369 +0,0 @@ -*> \brief \b DORMBR -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DORMBR + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, -* LDC, WORK, LWORK, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER SIDE, TRANS, VECT -* INTEGER INFO, K, LDA, LDC, LWORK, M, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> If VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C -*> with -*> SIDE = 'L' SIDE = 'R' -*> TRANS = 'N': Q * C C * Q -*> TRANS = 'T': Q**T * C C * Q**T -*> -*> If VECT = 'P', DORMBR overwrites the general real M-by-N matrix C -*> with -*> SIDE = 'L' SIDE = 'R' -*> TRANS = 'N': P * C C * P -*> TRANS = 'T': P**T * C C * P**T -*> -*> Here Q and P**T are the orthogonal matrices determined by DGEBRD when -*> reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and -*> P**T are defined as products of elementary reflectors H(i) and G(i) -*> respectively. -*> -*> Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the -*> order of the orthogonal matrix Q or P**T that is applied. -*> -*> If VECT = 'Q', A is assumed to have been an NQ-by-K matrix: -*> if nq >= k, Q = H(1) H(2) . . . H(k); -*> if nq < k, Q = H(1) H(2) . . . H(nq-1). -*> -*> If VECT = 'P', A is assumed to have been a K-by-NQ matrix: -*> if k < nq, P = G(1) G(2) . . . G(k); -*> if k >= nq, P = G(1) G(2) . . . G(nq-1). -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] VECT -*> \verbatim -*> VECT is CHARACTER*1 -*> = 'Q': apply Q or Q**T; -*> = 'P': apply P or P**T. -*> \endverbatim -*> -*> \param[in] SIDE -*> \verbatim -*> SIDE is CHARACTER*1 -*> = 'L': apply Q, Q**T, P or P**T from the Left; -*> = 'R': apply Q, Q**T, P or P**T from the Right. -*> \endverbatim -*> -*> \param[in] TRANS -*> \verbatim -*> TRANS is CHARACTER*1 -*> = 'N': No transpose, apply Q or P; -*> = 'T': Transpose, apply Q**T or P**T. -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix C. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix C. N >= 0. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> If VECT = 'Q', the number of columns in the original -*> matrix reduced by DGEBRD. -*> If VECT = 'P', the number of rows in the original -*> matrix reduced by DGEBRD. -*> K >= 0. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension -*> (LDA,min(nq,K)) if VECT = 'Q' -*> (LDA,nq) if VECT = 'P' -*> The vectors which define the elementary reflectors H(i) and -*> G(i), whose products determine the matrices Q and P, as -*> returned by DGEBRD. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. -*> If VECT = 'Q', LDA >= max(1,nq); -*> if VECT = 'P', LDA >= max(1,min(nq,K)). -*> \endverbatim -*> -*> \param[in] TAU -*> \verbatim -*> TAU is DOUBLE PRECISION array, dimension (min(nq,K)) -*> TAU(i) must contain the scalar factor of the elementary -*> reflector H(i) or G(i) which determines Q or P, as returned -*> by DGEBRD in the array argument TAUQ or TAUP. -*> \endverbatim -*> -*> \param[in,out] C -*> \verbatim -*> C is DOUBLE PRECISION array, dimension (LDC,N) -*> On entry, the M-by-N matrix C. -*> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q -*> or P*C or P**T*C or C*P or C*P**T. -*> \endverbatim -*> -*> \param[in] LDC -*> \verbatim -*> LDC is INTEGER -*> The leading dimension of the array C. LDC >= max(1,M). -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) -*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -*> \endverbatim -*> -*> \param[in] LWORK -*> \verbatim -*> LWORK is INTEGER -*> The dimension of the array WORK. -*> If SIDE = 'L', LWORK >= max(1,N); -*> if SIDE = 'R', LWORK >= max(1,M). -*> For optimum performance LWORK >= N*NB if SIDE = 'L', and -*> LWORK >= M*NB if SIDE = 'R', where NB is the optimal -*> blocksize. -*> -*> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal size of the WORK array, returns -*> this value as the first entry of the WORK array, and no error -*> message related to LWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleOTHERcomputational -* -* ===================================================================== - SUBROUTINE DORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, - $ LDC, WORK, LWORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER SIDE, TRANS, VECT - INTEGER INFO, K, LDA, LDC, LWORK, M, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Local Scalars .. - LOGICAL APPLYQ, LEFT, LQUERY, NOTRAN - CHARACTER TRANST - INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW -* .. -* .. External Functions .. - LOGICAL LSAME - INTEGER ILAENV - EXTERNAL LSAME, ILAENV -* .. -* .. External Subroutines .. - EXTERNAL DORMLQ, DORMQR, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, MIN -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - INFO = 0 - APPLYQ = LSAME( VECT, 'Q' ) - LEFT = LSAME( SIDE, 'L' ) - NOTRAN = LSAME( TRANS, 'N' ) - LQUERY = ( LWORK.EQ.-1 ) -* -* NQ is the order of Q or P and NW is the minimum dimension of WORK -* - IF( LEFT ) THEN - NQ = M - NW = MAX( 1, N ) - ELSE - NQ = N - NW = MAX( 1, M ) - END IF - IF( .NOT.APPLYQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN - INFO = -1 - ELSE IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN - INFO = -2 - ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN - INFO = -3 - ELSE IF( M.LT.0 ) THEN - INFO = -4 - ELSE IF( N.LT.0 ) THEN - INFO = -5 - ELSE IF( K.LT.0 ) THEN - INFO = -6 - ELSE IF( ( APPLYQ .AND. LDA.LT.MAX( 1, NQ ) ) .OR. - $ ( .NOT.APPLYQ .AND. LDA.LT.MAX( 1, MIN( NQ, K ) ) ) ) - $ THEN - INFO = -8 - ELSE IF( LDC.LT.MAX( 1, M ) ) THEN - INFO = -11 - ELSE IF( LWORK.LT.NW .AND. .NOT.LQUERY ) THEN - INFO = -13 - END IF -* - IF( INFO.EQ.0 ) THEN - IF( APPLYQ ) THEN - IF( LEFT ) THEN - NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, M-1, N, M-1, - $ -1 ) - ELSE - NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, M, N-1, N-1, - $ -1 ) - END IF - ELSE - IF( LEFT ) THEN - NB = ILAENV( 1, 'DORMLQ', SIDE // TRANS, M-1, N, M-1, - $ -1 ) - ELSE - NB = ILAENV( 1, 'DORMLQ', SIDE // TRANS, M, N-1, N-1, - $ -1 ) - END IF - END IF - LWKOPT = NW*NB - WORK( 1 ) = LWKOPT - END IF -* - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DORMBR', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - RETURN - END IF -* -* Quick return if possible -* - WORK( 1 ) = 1 - IF( M.EQ.0 .OR. N.EQ.0 ) - $ RETURN -* - IF( APPLYQ ) THEN -* -* Apply Q -* - IF( NQ.GE.K ) THEN -* -* Q was determined by a call to DGEBRD with nq >= k -* - CALL DORMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, - $ WORK, LWORK, IINFO ) - ELSE IF( NQ.GT.1 ) THEN -* -* Q was determined by a call to DGEBRD with nq < k -* - IF( LEFT ) THEN - MI = M - 1 - NI = N - I1 = 2 - I2 = 1 - ELSE - MI = M - NI = N - 1 - I1 = 1 - I2 = 2 - END IF - CALL DORMQR( SIDE, TRANS, MI, NI, NQ-1, A( 2, 1 ), LDA, TAU, - $ C( I1, I2 ), LDC, WORK, LWORK, IINFO ) - END IF - ELSE -* -* Apply P -* - IF( NOTRAN ) THEN - TRANST = 'T' - ELSE - TRANST = 'N' - END IF - IF( NQ.GT.K ) THEN -* -* P was determined by a call to DGEBRD with nq > k -* - CALL DORMLQ( SIDE, TRANST, M, N, K, A, LDA, TAU, C, LDC, - $ WORK, LWORK, IINFO ) - ELSE IF( NQ.GT.1 ) THEN -* -* P was determined by a call to DGEBRD with nq <= k -* - IF( LEFT ) THEN - MI = M - 1 - NI = N - I1 = 2 - I2 = 1 - ELSE - MI = M - NI = N - 1 - I1 = 1 - I2 = 2 - END IF - CALL DORMLQ( SIDE, TRANST, MI, NI, NQ-1, A( 1, 2 ), LDA, - $ TAU, C( I1, I2 ), LDC, WORK, LWORK, IINFO ) - END IF - END IF - WORK( 1 ) = LWKOPT - RETURN -* -* End of DORMBR -* - END diff --git a/lib/linalg/fortran/dorml2.f b/lib/linalg/fortran/dorml2.f deleted file mode 100644 index a9ddd460d8..0000000000 --- a/lib/linalg/fortran/dorml2.f +++ /dev/null @@ -1,279 +0,0 @@ -*> \brief \b DORML2 multiplies a general matrix by the orthogonal matrix from a LQ factorization determined by sgelqf (unblocked algorithm). -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DORML2 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DORML2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, -* WORK, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER SIDE, TRANS -* INTEGER INFO, K, LDA, LDC, M, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DORML2 overwrites the general real m by n matrix C with -*> -*> Q * C if SIDE = 'L' and TRANS = 'N', or -*> -*> Q**T* C if SIDE = 'L' and TRANS = 'T', or -*> -*> C * Q if SIDE = 'R' and TRANS = 'N', or -*> -*> C * Q**T if SIDE = 'R' and TRANS = 'T', -*> -*> where Q is a real orthogonal matrix defined as the product of k -*> elementary reflectors -*> -*> Q = H(k) . . . H(2) H(1) -*> -*> as returned by DGELQF. Q is of order m if SIDE = 'L' and of order n -*> if SIDE = 'R'. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] SIDE -*> \verbatim -*> SIDE is CHARACTER*1 -*> = 'L': apply Q or Q**T from the Left -*> = 'R': apply Q or Q**T from the Right -*> \endverbatim -*> -*> \param[in] TRANS -*> \verbatim -*> TRANS is CHARACTER*1 -*> = 'N': apply Q (No transpose) -*> = 'T': apply Q**T (Transpose) -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix C. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix C. N >= 0. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> The number of elementary reflectors whose product defines -*> the matrix Q. -*> If SIDE = 'L', M >= K >= 0; -*> if SIDE = 'R', N >= K >= 0. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension -*> (LDA,M) if SIDE = 'L', -*> (LDA,N) if SIDE = 'R' -*> The i-th row must contain the vector which defines the -*> elementary reflector H(i), for i = 1,2,...,k, as returned by -*> DGELQF in the first k rows of its array argument A. -*> A is modified by the routine but restored on exit. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,K). -*> \endverbatim -*> -*> \param[in] TAU -*> \verbatim -*> TAU is DOUBLE PRECISION array, dimension (K) -*> TAU(i) must contain the scalar factor of the elementary -*> reflector H(i), as returned by DGELQF. -*> \endverbatim -*> -*> \param[in,out] C -*> \verbatim -*> C is DOUBLE PRECISION array, dimension (LDC,N) -*> On entry, the m by n matrix C. -*> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. -*> \endverbatim -*> -*> \param[in] LDC -*> \verbatim -*> LDC is INTEGER -*> The leading dimension of the array C. LDC >= max(1,M). -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension -*> (N) if SIDE = 'L', -*> (M) if SIDE = 'R' -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleOTHERcomputational -* -* ===================================================================== - SUBROUTINE DORML2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, - $ WORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER SIDE, TRANS - INTEGER INFO, K, LDA, LDC, M, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE - PARAMETER ( ONE = 1.0D+0 ) -* .. -* .. Local Scalars .. - LOGICAL LEFT, NOTRAN - INTEGER I, I1, I2, I3, IC, JC, MI, NI, NQ - DOUBLE PRECISION AII -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL DLARF, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - INFO = 0 - LEFT = LSAME( SIDE, 'L' ) - NOTRAN = LSAME( TRANS, 'N' ) -* -* NQ is the order of Q -* - IF( LEFT ) THEN - NQ = M - ELSE - NQ = N - END IF - IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN - INFO = -1 - ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN - INFO = -2 - ELSE IF( M.LT.0 ) THEN - INFO = -3 - ELSE IF( N.LT.0 ) THEN - INFO = -4 - ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN - INFO = -5 - ELSE IF( LDA.LT.MAX( 1, K ) ) THEN - INFO = -7 - ELSE IF( LDC.LT.MAX( 1, M ) ) THEN - INFO = -10 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DORML2', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) - $ RETURN -* - IF( ( LEFT .AND. NOTRAN ) .OR. ( .NOT.LEFT .AND. .NOT.NOTRAN ) ) - $ THEN - I1 = 1 - I2 = K - I3 = 1 - ELSE - I1 = K - I2 = 1 - I3 = -1 - END IF -* - IF( LEFT ) THEN - NI = N - JC = 1 - ELSE - MI = M - IC = 1 - END IF -* - DO 10 I = I1, I2, I3 - IF( LEFT ) THEN -* -* H(i) is applied to C(i:m,1:n) -* - MI = M - I + 1 - IC = I - ELSE -* -* H(i) is applied to C(1:m,i:n) -* - NI = N - I + 1 - JC = I - END IF -* -* Apply H(i) -* - AII = A( I, I ) - A( I, I ) = ONE - CALL DLARF( SIDE, MI, NI, A( I, I ), LDA, TAU( I ), - $ C( IC, JC ), LDC, WORK ) - A( I, I ) = AII - 10 CONTINUE - RETURN -* -* End of DORML2 -* - END diff --git a/lib/linalg/fortran/dormlq.f b/lib/linalg/fortran/dormlq.f deleted file mode 100644 index ef039285ab..0000000000 --- a/lib/linalg/fortran/dormlq.f +++ /dev/null @@ -1,344 +0,0 @@ -*> \brief \b DORMLQ -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DORMLQ + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DORMLQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, -* WORK, LWORK, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER SIDE, TRANS -* INTEGER INFO, K, LDA, LDC, LWORK, M, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DORMLQ overwrites the general real M-by-N matrix C with -*> -*> SIDE = 'L' SIDE = 'R' -*> TRANS = 'N': Q * C C * Q -*> TRANS = 'T': Q**T * C C * Q**T -*> -*> where Q is a real orthogonal matrix defined as the product of k -*> elementary reflectors -*> -*> Q = H(k) . . . H(2) H(1) -*> -*> as returned by DGELQF. Q is of order M if SIDE = 'L' and of order N -*> if SIDE = 'R'. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] SIDE -*> \verbatim -*> SIDE is CHARACTER*1 -*> = 'L': apply Q or Q**T from the Left; -*> = 'R': apply Q or Q**T from the Right. -*> \endverbatim -*> -*> \param[in] TRANS -*> \verbatim -*> TRANS is CHARACTER*1 -*> = 'N': No transpose, apply Q; -*> = 'T': Transpose, apply Q**T. -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix C. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix C. N >= 0. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> The number of elementary reflectors whose product defines -*> the matrix Q. -*> If SIDE = 'L', M >= K >= 0; -*> if SIDE = 'R', N >= K >= 0. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension -*> (LDA,M) if SIDE = 'L', -*> (LDA,N) if SIDE = 'R' -*> The i-th row must contain the vector which defines the -*> elementary reflector H(i), for i = 1,2,...,k, as returned by -*> DGELQF in the first k rows of its array argument A. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,K). -*> \endverbatim -*> -*> \param[in] TAU -*> \verbatim -*> TAU is DOUBLE PRECISION array, dimension (K) -*> TAU(i) must contain the scalar factor of the elementary -*> reflector H(i), as returned by DGELQF. -*> \endverbatim -*> -*> \param[in,out] C -*> \verbatim -*> C is DOUBLE PRECISION array, dimension (LDC,N) -*> On entry, the M-by-N matrix C. -*> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. -*> \endverbatim -*> -*> \param[in] LDC -*> \verbatim -*> LDC is INTEGER -*> The leading dimension of the array C. LDC >= max(1,M). -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) -*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -*> \endverbatim -*> -*> \param[in] LWORK -*> \verbatim -*> LWORK is INTEGER -*> The dimension of the array WORK. -*> If SIDE = 'L', LWORK >= max(1,N); -*> if SIDE = 'R', LWORK >= max(1,M). -*> For good performance, LWORK should generally be larger. -*> -*> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal size of the WORK array, returns -*> this value as the first entry of the WORK array, and no error -*> message related to LWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleOTHERcomputational -* -* ===================================================================== - SUBROUTINE DORMLQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, - $ WORK, LWORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER SIDE, TRANS - INTEGER INFO, K, LDA, LDC, LWORK, M, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - INTEGER NBMAX, LDT, TSIZE - PARAMETER ( NBMAX = 64, LDT = NBMAX+1, - $ TSIZE = LDT*NBMAX ) -* .. -* .. Local Scalars .. - LOGICAL LEFT, LQUERY, NOTRAN - CHARACTER TRANST - INTEGER I, I1, I2, I3, IB, IC, IINFO, IWT, JC, LDWORK, - $ LWKOPT, MI, NB, NBMIN, NI, NQ, NW -* .. -* .. External Functions .. - LOGICAL LSAME - INTEGER ILAENV - EXTERNAL LSAME, ILAENV -* .. -* .. External Subroutines .. - EXTERNAL DLARFB, DLARFT, DORML2, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, MIN -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - INFO = 0 - LEFT = LSAME( SIDE, 'L' ) - NOTRAN = LSAME( TRANS, 'N' ) - LQUERY = ( LWORK.EQ.-1 ) -* -* NQ is the order of Q and NW is the minimum dimension of WORK -* - IF( LEFT ) THEN - NQ = M - NW = MAX( 1, N ) - ELSE - NQ = N - NW = MAX( 1, M ) - END IF - IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN - INFO = -1 - ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN - INFO = -2 - ELSE IF( M.LT.0 ) THEN - INFO = -3 - ELSE IF( N.LT.0 ) THEN - INFO = -4 - ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN - INFO = -5 - ELSE IF( LDA.LT.MAX( 1, K ) ) THEN - INFO = -7 - ELSE IF( LDC.LT.MAX( 1, M ) ) THEN - INFO = -10 - ELSE IF( LWORK.LT.NW .AND. .NOT.LQUERY ) THEN - INFO = -12 - END IF -* - IF( INFO.EQ.0 ) THEN -* -* Compute the workspace requirements -* - NB = MIN( NBMAX, ILAENV( 1, 'DORMLQ', SIDE // TRANS, M, N, K, - $ -1 ) ) - LWKOPT = NW*NB + TSIZE - WORK( 1 ) = LWKOPT - END IF -* - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DORMLQ', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - RETURN - END IF -* -* Quick return if possible -* - IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) THEN - WORK( 1 ) = 1 - RETURN - END IF -* - NBMIN = 2 - LDWORK = NW - IF( NB.GT.1 .AND. NB.LT.K ) THEN - IF( LWORK.LT.LWKOPT ) THEN - NB = (LWORK-TSIZE) / LDWORK - NBMIN = MAX( 2, ILAENV( 2, 'DORMLQ', SIDE // TRANS, M, N, K, - $ -1 ) ) - END IF - END IF -* - IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN -* -* Use unblocked code -* - CALL DORML2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, - $ IINFO ) - ELSE -* -* Use blocked code -* - IWT = 1 + NW*NB - IF( ( LEFT .AND. NOTRAN ) .OR. - $ ( .NOT.LEFT .AND. .NOT.NOTRAN ) ) THEN - I1 = 1 - I2 = K - I3 = NB - ELSE - I1 = ( ( K-1 ) / NB )*NB + 1 - I2 = 1 - I3 = -NB - END IF -* - IF( LEFT ) THEN - NI = N - JC = 1 - ELSE - MI = M - IC = 1 - END IF -* - IF( NOTRAN ) THEN - TRANST = 'T' - ELSE - TRANST = 'N' - END IF -* - DO 10 I = I1, I2, I3 - IB = MIN( NB, K-I+1 ) -* -* Form the triangular factor of the block reflector -* H = H(i) H(i+1) . . . H(i+ib-1) -* - CALL DLARFT( 'Forward', 'Rowwise', NQ-I+1, IB, A( I, I ), - $ LDA, TAU( I ), WORK( IWT ), LDT ) - IF( LEFT ) THEN -* -* H or H**T is applied to C(i:m,1:n) -* - MI = M - I + 1 - IC = I - ELSE -* -* H or H**T is applied to C(1:m,i:n) -* - NI = N - I + 1 - JC = I - END IF -* -* Apply H or H**T -* - CALL DLARFB( SIDE, TRANST, 'Forward', 'Rowwise', MI, NI, IB, - $ A( I, I ), LDA, WORK( IWT ), LDT, - $ C( IC, JC ), LDC, WORK, LDWORK ) - 10 CONTINUE - END IF - WORK( 1 ) = LWKOPT - RETURN -* -* End of DORMLQ -* - END diff --git a/lib/linalg/fortran/dormql.f b/lib/linalg/fortran/dormql.f deleted file mode 100644 index 7c9f189e0d..0000000000 --- a/lib/linalg/fortran/dormql.f +++ /dev/null @@ -1,336 +0,0 @@ -*> \brief \b DORMQL -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DORMQL + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DORMQL( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, -* WORK, LWORK, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER SIDE, TRANS -* INTEGER INFO, K, LDA, LDC, LWORK, M, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DORMQL overwrites the general real M-by-N matrix C with -*> -*> SIDE = 'L' SIDE = 'R' -*> TRANS = 'N': Q * C C * Q -*> TRANS = 'T': Q**T * C C * Q**T -*> -*> where Q is a real orthogonal matrix defined as the product of k -*> elementary reflectors -*> -*> Q = H(k) . . . H(2) H(1) -*> -*> as returned by DGEQLF. Q is of order M if SIDE = 'L' and of order N -*> if SIDE = 'R'. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] SIDE -*> \verbatim -*> SIDE is CHARACTER*1 -*> = 'L': apply Q or Q**T from the Left; -*> = 'R': apply Q or Q**T from the Right. -*> \endverbatim -*> -*> \param[in] TRANS -*> \verbatim -*> TRANS is CHARACTER*1 -*> = 'N': No transpose, apply Q; -*> = 'T': Transpose, apply Q**T. -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix C. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix C. N >= 0. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> The number of elementary reflectors whose product defines -*> the matrix Q. -*> If SIDE = 'L', M >= K >= 0; -*> if SIDE = 'R', N >= K >= 0. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,K) -*> The i-th column must contain the vector which defines the -*> elementary reflector H(i), for i = 1,2,...,k, as returned by -*> DGEQLF in the last k columns of its array argument A. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. -*> If SIDE = 'L', LDA >= max(1,M); -*> if SIDE = 'R', LDA >= max(1,N). -*> \endverbatim -*> -*> \param[in] TAU -*> \verbatim -*> TAU is DOUBLE PRECISION array, dimension (K) -*> TAU(i) must contain the scalar factor of the elementary -*> reflector H(i), as returned by DGEQLF. -*> \endverbatim -*> -*> \param[in,out] C -*> \verbatim -*> C is DOUBLE PRECISION array, dimension (LDC,N) -*> On entry, the M-by-N matrix C. -*> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. -*> \endverbatim -*> -*> \param[in] LDC -*> \verbatim -*> LDC is INTEGER -*> The leading dimension of the array C. LDC >= max(1,M). -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) -*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -*> \endverbatim -*> -*> \param[in] LWORK -*> \verbatim -*> LWORK is INTEGER -*> The dimension of the array WORK. -*> If SIDE = 'L', LWORK >= max(1,N); -*> if SIDE = 'R', LWORK >= max(1,M). -*> For good performance, LWORK should generally be larger. -*> -*> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal size of the WORK array, returns -*> this value as the first entry of the WORK array, and no error -*> message related to LWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleOTHERcomputational -* -* ===================================================================== - SUBROUTINE DORMQL( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, - $ WORK, LWORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER SIDE, TRANS - INTEGER INFO, K, LDA, LDC, LWORK, M, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - INTEGER NBMAX, LDT, TSIZE - PARAMETER ( NBMAX = 64, LDT = NBMAX+1, - $ TSIZE = LDT*NBMAX ) -* .. -* .. Local Scalars .. - LOGICAL LEFT, LQUERY, NOTRAN - INTEGER I, I1, I2, I3, IB, IINFO, IWT, LDWORK, LWKOPT, - $ MI, NB, NBMIN, NI, NQ, NW -* .. -* .. External Functions .. - LOGICAL LSAME - INTEGER ILAENV - EXTERNAL LSAME, ILAENV -* .. -* .. External Subroutines .. - EXTERNAL DLARFB, DLARFT, DORM2L, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, MIN -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - INFO = 0 - LEFT = LSAME( SIDE, 'L' ) - NOTRAN = LSAME( TRANS, 'N' ) - LQUERY = ( LWORK.EQ.-1 ) -* -* NQ is the order of Q and NW is the minimum dimension of WORK -* - IF( LEFT ) THEN - NQ = M - NW = MAX( 1, N ) - ELSE - NQ = N - NW = MAX( 1, M ) - END IF - IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN - INFO = -1 - ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN - INFO = -2 - ELSE IF( M.LT.0 ) THEN - INFO = -3 - ELSE IF( N.LT.0 ) THEN - INFO = -4 - ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN - INFO = -5 - ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN - INFO = -7 - ELSE IF( LDC.LT.MAX( 1, M ) ) THEN - INFO = -10 - ELSE IF( LWORK.LT.NW .AND. .NOT.LQUERY ) THEN - INFO = -12 - END IF -* - IF( INFO.EQ.0 ) THEN -* -* Compute the workspace requirements -* - IF( M.EQ.0 .OR. N.EQ.0 ) THEN - LWKOPT = 1 - ELSE - NB = MIN( NBMAX, ILAENV( 1, 'DORMQL', SIDE // TRANS, M, N, - $ K, -1 ) ) - LWKOPT = NW*NB + TSIZE - END IF - WORK( 1 ) = LWKOPT - END IF -* - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DORMQL', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - RETURN - END IF -* -* Quick return if possible -* - IF( M.EQ.0 .OR. N.EQ.0 ) THEN - RETURN - END IF -* - NBMIN = 2 - LDWORK = NW - IF( NB.GT.1 .AND. NB.LT.K ) THEN - IF( LWORK.LT.LWKOPT ) THEN - NB = (LWORK-TSIZE) / LDWORK - NBMIN = MAX( 2, ILAENV( 2, 'DORMQL', SIDE // TRANS, M, N, K, - $ -1 ) ) - END IF - END IF -* - IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN -* -* Use unblocked code -* - CALL DORM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, - $ IINFO ) - ELSE -* -* Use blocked code -* - IWT = 1 + NW*NB - IF( ( LEFT .AND. NOTRAN ) .OR. - $ ( .NOT.LEFT .AND. .NOT.NOTRAN ) ) THEN - I1 = 1 - I2 = K - I3 = NB - ELSE - I1 = ( ( K-1 ) / NB )*NB + 1 - I2 = 1 - I3 = -NB - END IF -* - IF( LEFT ) THEN - NI = N - ELSE - MI = M - END IF -* - DO 10 I = I1, I2, I3 - IB = MIN( NB, K-I+1 ) -* -* Form the triangular factor of the block reflector -* H = H(i+ib-1) . . . H(i+1) H(i) -* - CALL DLARFT( 'Backward', 'Columnwise', NQ-K+I+IB-1, IB, - $ A( 1, I ), LDA, TAU( I ), WORK( IWT ), LDT ) - IF( LEFT ) THEN -* -* H or H**T is applied to C(1:m-k+i+ib-1,1:n) -* - MI = M - K + I + IB - 1 - ELSE -* -* H or H**T is applied to C(1:m,1:n-k+i+ib-1) -* - NI = N - K + I + IB - 1 - END IF -* -* Apply H or H**T -* - CALL DLARFB( SIDE, TRANS, 'Backward', 'Columnwise', MI, NI, - $ IB, A( 1, I ), LDA, WORK( IWT ), LDT, C, LDC, - $ WORK, LDWORK ) - 10 CONTINUE - END IF - WORK( 1 ) = LWKOPT - RETURN -* -* End of DORMQL -* - END diff --git a/lib/linalg/fortran/dormqr.f b/lib/linalg/fortran/dormqr.f deleted file mode 100644 index 4d0bae3a5f..0000000000 --- a/lib/linalg/fortran/dormqr.f +++ /dev/null @@ -1,337 +0,0 @@ -*> \brief \b DORMQR -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DORMQR + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DORMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, -* WORK, LWORK, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER SIDE, TRANS -* INTEGER INFO, K, LDA, LDC, LWORK, M, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DORMQR overwrites the general real M-by-N matrix C with -*> -*> SIDE = 'L' SIDE = 'R' -*> TRANS = 'N': Q * C C * Q -*> TRANS = 'T': Q**T * C C * Q**T -*> -*> where Q is a real orthogonal matrix defined as the product of k -*> elementary reflectors -*> -*> Q = H(1) H(2) . . . H(k) -*> -*> as returned by DGEQRF. Q is of order M if SIDE = 'L' and of order N -*> if SIDE = 'R'. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] SIDE -*> \verbatim -*> SIDE is CHARACTER*1 -*> = 'L': apply Q or Q**T from the Left; -*> = 'R': apply Q or Q**T from the Right. -*> \endverbatim -*> -*> \param[in] TRANS -*> \verbatim -*> TRANS is CHARACTER*1 -*> = 'N': No transpose, apply Q; -*> = 'T': Transpose, apply Q**T. -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix C. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix C. N >= 0. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> The number of elementary reflectors whose product defines -*> the matrix Q. -*> If SIDE = 'L', M >= K >= 0; -*> if SIDE = 'R', N >= K >= 0. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,K) -*> The i-th column must contain the vector which defines the -*> elementary reflector H(i), for i = 1,2,...,k, as returned by -*> DGEQRF in the first k columns of its array argument A. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. -*> If SIDE = 'L', LDA >= max(1,M); -*> if SIDE = 'R', LDA >= max(1,N). -*> \endverbatim -*> -*> \param[in] TAU -*> \verbatim -*> TAU is DOUBLE PRECISION array, dimension (K) -*> TAU(i) must contain the scalar factor of the elementary -*> reflector H(i), as returned by DGEQRF. -*> \endverbatim -*> -*> \param[in,out] C -*> \verbatim -*> C is DOUBLE PRECISION array, dimension (LDC,N) -*> On entry, the M-by-N matrix C. -*> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. -*> \endverbatim -*> -*> \param[in] LDC -*> \verbatim -*> LDC is INTEGER -*> The leading dimension of the array C. LDC >= max(1,M). -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) -*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -*> \endverbatim -*> -*> \param[in] LWORK -*> \verbatim -*> LWORK is INTEGER -*> The dimension of the array WORK. -*> If SIDE = 'L', LWORK >= max(1,N); -*> if SIDE = 'R', LWORK >= max(1,M). -*> For good performance, LWORK should generally be larger. -*> -*> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal size of the WORK array, returns -*> this value as the first entry of the WORK array, and no error -*> message related to LWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleOTHERcomputational -* -* ===================================================================== - SUBROUTINE DORMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, - $ WORK, LWORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER SIDE, TRANS - INTEGER INFO, K, LDA, LDC, LWORK, M, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - INTEGER NBMAX, LDT, TSIZE - PARAMETER ( NBMAX = 64, LDT = NBMAX+1, - $ TSIZE = LDT*NBMAX ) -* .. -* .. Local Scalars .. - LOGICAL LEFT, LQUERY, NOTRAN - INTEGER I, I1, I2, I3, IB, IC, IINFO, IWT, JC, LDWORK, - $ LWKOPT, MI, NB, NBMIN, NI, NQ, NW -* .. -* .. External Functions .. - LOGICAL LSAME - INTEGER ILAENV - EXTERNAL LSAME, ILAENV -* .. -* .. External Subroutines .. - EXTERNAL DLARFB, DLARFT, DORM2R, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, MIN -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - INFO = 0 - LEFT = LSAME( SIDE, 'L' ) - NOTRAN = LSAME( TRANS, 'N' ) - LQUERY = ( LWORK.EQ.-1 ) -* -* NQ is the order of Q and NW is the minimum dimension of WORK -* - IF( LEFT ) THEN - NQ = M - NW = MAX( 1, N ) - ELSE - NQ = N - NW = MAX( 1, M ) - END IF - IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN - INFO = -1 - ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN - INFO = -2 - ELSE IF( M.LT.0 ) THEN - INFO = -3 - ELSE IF( N.LT.0 ) THEN - INFO = -4 - ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN - INFO = -5 - ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN - INFO = -7 - ELSE IF( LDC.LT.MAX( 1, M ) ) THEN - INFO = -10 - ELSE IF( LWORK.LT.NW .AND. .NOT.LQUERY ) THEN - INFO = -12 - END IF -* - IF( INFO.EQ.0 ) THEN -* -* Compute the workspace requirements -* - NB = MIN( NBMAX, ILAENV( 1, 'DORMQR', SIDE // TRANS, M, N, K, - $ -1 ) ) - LWKOPT = NW*NB + TSIZE - WORK( 1 ) = LWKOPT - END IF -* - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DORMQR', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - RETURN - END IF -* -* Quick return if possible -* - IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) THEN - WORK( 1 ) = 1 - RETURN - END IF -* - NBMIN = 2 - LDWORK = NW - IF( NB.GT.1 .AND. NB.LT.K ) THEN - IF( LWORK.LT.LWKOPT ) THEN - NB = (LWORK-TSIZE) / LDWORK - NBMIN = MAX( 2, ILAENV( 2, 'DORMQR', SIDE // TRANS, M, N, K, - $ -1 ) ) - END IF - END IF -* - IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN -* -* Use unblocked code -* - CALL DORM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, - $ IINFO ) - ELSE -* -* Use blocked code -* - IWT = 1 + NW*NB - IF( ( LEFT .AND. .NOT.NOTRAN ) .OR. - $ ( .NOT.LEFT .AND. NOTRAN ) ) THEN - I1 = 1 - I2 = K - I3 = NB - ELSE - I1 = ( ( K-1 ) / NB )*NB + 1 - I2 = 1 - I3 = -NB - END IF -* - IF( LEFT ) THEN - NI = N - JC = 1 - ELSE - MI = M - IC = 1 - END IF -* - DO 10 I = I1, I2, I3 - IB = MIN( NB, K-I+1 ) -* -* Form the triangular factor of the block reflector -* H = H(i) H(i+1) . . . H(i+ib-1) -* - CALL DLARFT( 'Forward', 'Columnwise', NQ-I+1, IB, A( I, I ), - $ LDA, TAU( I ), WORK( IWT ), LDT ) - IF( LEFT ) THEN -* -* H or H**T is applied to C(i:m,1:n) -* - MI = M - I + 1 - IC = I - ELSE -* -* H or H**T is applied to C(1:m,i:n) -* - NI = N - I + 1 - JC = I - END IF -* -* Apply H or H**T -* - CALL DLARFB( SIDE, TRANS, 'Forward', 'Columnwise', MI, NI, - $ IB, A( I, I ), LDA, WORK( IWT ), LDT, - $ C( IC, JC ), LDC, WORK, LDWORK ) - 10 CONTINUE - END IF - WORK( 1 ) = LWKOPT - RETURN -* -* End of DORMQR -* - END diff --git a/lib/linalg/fortran/dormtr.f b/lib/linalg/fortran/dormtr.f deleted file mode 100644 index 1f664d63cc..0000000000 --- a/lib/linalg/fortran/dormtr.f +++ /dev/null @@ -1,307 +0,0 @@ -*> \brief \b DORMTR -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DORMTR + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DORMTR( SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC, -* WORK, LWORK, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER SIDE, TRANS, UPLO -* INTEGER INFO, LDA, LDC, LWORK, M, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DORMTR overwrites the general real M-by-N matrix C with -*> -*> SIDE = 'L' SIDE = 'R' -*> TRANS = 'N': Q * C C * Q -*> TRANS = 'T': Q**T * C C * Q**T -*> -*> where Q is a real orthogonal matrix of order nq, with nq = m if -*> SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of -*> nq-1 elementary reflectors, as returned by DSYTRD: -*> -*> if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1); -*> -*> if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1). -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] SIDE -*> \verbatim -*> SIDE is CHARACTER*1 -*> = 'L': apply Q or Q**T from the Left; -*> = 'R': apply Q or Q**T from the Right. -*> \endverbatim -*> -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> = 'U': Upper triangle of A contains elementary reflectors -*> from DSYTRD; -*> = 'L': Lower triangle of A contains elementary reflectors -*> from DSYTRD. -*> \endverbatim -*> -*> \param[in] TRANS -*> \verbatim -*> TRANS is CHARACTER*1 -*> = 'N': No transpose, apply Q; -*> = 'T': Transpose, apply Q**T. -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix C. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix C. N >= 0. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension -*> (LDA,M) if SIDE = 'L' -*> (LDA,N) if SIDE = 'R' -*> The vectors which define the elementary reflectors, as -*> returned by DSYTRD. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. -*> LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'. -*> \endverbatim -*> -*> \param[in] TAU -*> \verbatim -*> TAU is DOUBLE PRECISION array, dimension -*> (M-1) if SIDE = 'L' -*> (N-1) if SIDE = 'R' -*> TAU(i) must contain the scalar factor of the elementary -*> reflector H(i), as returned by DSYTRD. -*> \endverbatim -*> -*> \param[in,out] C -*> \verbatim -*> C is DOUBLE PRECISION array, dimension (LDC,N) -*> On entry, the M-by-N matrix C. -*> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. -*> \endverbatim -*> -*> \param[in] LDC -*> \verbatim -*> LDC is INTEGER -*> The leading dimension of the array C. LDC >= max(1,M). -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) -*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -*> \endverbatim -*> -*> \param[in] LWORK -*> \verbatim -*> LWORK is INTEGER -*> The dimension of the array WORK. -*> If SIDE = 'L', LWORK >= max(1,N); -*> if SIDE = 'R', LWORK >= max(1,M). -*> For optimum performance LWORK >= N*NB if SIDE = 'L', and -*> LWORK >= M*NB if SIDE = 'R', where NB is the optimal -*> blocksize. -*> -*> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal size of the WORK array, returns -*> this value as the first entry of the WORK array, and no error -*> message related to LWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleOTHERcomputational -* -* ===================================================================== - SUBROUTINE DORMTR( SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC, - $ WORK, LWORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER SIDE, TRANS, UPLO - INTEGER INFO, LDA, LDC, LWORK, M, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Local Scalars .. - LOGICAL LEFT, LQUERY, UPPER - INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW -* .. -* .. External Functions .. - LOGICAL LSAME - INTEGER ILAENV - EXTERNAL LSAME, ILAENV -* .. -* .. External Subroutines .. - EXTERNAL DORMQL, DORMQR, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - INFO = 0 - LEFT = LSAME( SIDE, 'L' ) - UPPER = LSAME( UPLO, 'U' ) - LQUERY = ( LWORK.EQ.-1 ) -* -* NQ is the order of Q and NW is the minimum dimension of WORK -* - IF( LEFT ) THEN - NQ = M - NW = MAX( 1, N ) - ELSE - NQ = N - NW = MAX( 1, M ) - END IF - IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN - INFO = -1 - ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN - INFO = -2 - ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT.LSAME( TRANS, 'T' ) ) - $ THEN - INFO = -3 - ELSE IF( M.LT.0 ) THEN - INFO = -4 - ELSE IF( N.LT.0 ) THEN - INFO = -5 - ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN - INFO = -7 - ELSE IF( LDC.LT.MAX( 1, M ) ) THEN - INFO = -10 - ELSE IF( LWORK.LT.NW .AND. .NOT.LQUERY ) THEN - INFO = -12 - END IF -* - IF( INFO.EQ.0 ) THEN - IF( UPPER ) THEN - IF( LEFT ) THEN - NB = ILAENV( 1, 'DORMQL', SIDE // TRANS, M-1, N, M-1, - $ -1 ) - ELSE - NB = ILAENV( 1, 'DORMQL', SIDE // TRANS, M, N-1, N-1, - $ -1 ) - END IF - ELSE - IF( LEFT ) THEN - NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, M-1, N, M-1, - $ -1 ) - ELSE - NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, M, N-1, N-1, - $ -1 ) - END IF - END IF - LWKOPT = NW*NB - WORK( 1 ) = LWKOPT - END IF -* - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DORMTR', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - RETURN - END IF -* -* Quick return if possible -* - IF( M.EQ.0 .OR. N.EQ.0 .OR. NQ.EQ.1 ) THEN - WORK( 1 ) = 1 - RETURN - END IF -* - IF( LEFT ) THEN - MI = M - 1 - NI = N - ELSE - MI = M - NI = N - 1 - END IF -* - IF( UPPER ) THEN -* -* Q was determined by a call to DSYTRD with UPLO = 'U' -* - CALL DORMQL( SIDE, TRANS, MI, NI, NQ-1, A( 1, 2 ), LDA, TAU, C, - $ LDC, WORK, LWORK, IINFO ) - ELSE -* -* Q was determined by a call to DSYTRD with UPLO = 'L' -* - IF( LEFT ) THEN - I1 = 2 - I2 = 1 - ELSE - I1 = 1 - I2 = 2 - END IF - CALL DORMQR( SIDE, TRANS, MI, NI, NQ-1, A( 2, 1 ), LDA, TAU, - $ C( I1, I2 ), LDC, WORK, LWORK, IINFO ) - END IF - WORK( 1 ) = LWKOPT - RETURN -* -* End of DORMTR -* - END diff --git a/lib/linalg/fortran/dposv.f b/lib/linalg/fortran/dposv.f deleted file mode 100644 index ee2988e6fd..0000000000 --- a/lib/linalg/fortran/dposv.f +++ /dev/null @@ -1,190 +0,0 @@ -*> \brief DPOSV computes the solution to system of linear equations A * X = B for PO matrices -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DPOSV + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DPOSV( UPLO, N, NRHS, A, LDA, B, LDB, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER UPLO -* INTEGER INFO, LDA, LDB, N, NRHS -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), B( LDB, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DPOSV computes the solution to a real system of linear equations -*> A * X = B, -*> where A is an N-by-N symmetric positive definite matrix and X and B -*> are N-by-NRHS matrices. -*> -*> The Cholesky decomposition is used to factor A as -*> A = U**T* U, if UPLO = 'U', or -*> A = L * L**T, if UPLO = 'L', -*> where U is an upper triangular matrix and L is a lower triangular -*> matrix. The factored form of A is then used to solve the system of -*> equations A * X = B. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> = 'U': Upper triangle of A is stored; -*> = 'L': Lower triangle of A is stored. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of linear equations, i.e., the order of the -*> matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in] NRHS -*> \verbatim -*> NRHS is INTEGER -*> The number of right hand sides, i.e., the number of columns -*> of the matrix B. NRHS >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the symmetric matrix A. If UPLO = 'U', the leading -*> N-by-N upper triangular part of A contains the upper -*> triangular part of the matrix A, and the strictly lower -*> triangular part of A is not referenced. If UPLO = 'L', the -*> leading N-by-N lower triangular part of A contains the lower -*> triangular part of the matrix A, and the strictly upper -*> triangular part of A is not referenced. -*> -*> On exit, if INFO = 0, the factor U or L from the Cholesky -*> factorization A = U**T*U or A = L*L**T. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,N). -*> \endverbatim -*> -*> \param[in,out] B -*> \verbatim -*> B is DOUBLE PRECISION array, dimension (LDB,NRHS) -*> On entry, the N-by-NRHS right hand side matrix B. -*> On exit, if INFO = 0, the N-by-NRHS solution matrix X. -*> \endverbatim -*> -*> \param[in] LDB -*> \verbatim -*> LDB is INTEGER -*> The leading dimension of the array B. LDB >= max(1,N). -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i of A is not -*> positive definite, so the factorization could not be -*> completed, and the solution has not been computed. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doublePOsolve -* -* ===================================================================== - SUBROUTINE DPOSV( UPLO, N, NRHS, A, LDA, B, LDB, INFO ) -* -* -- LAPACK driver routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER UPLO - INTEGER INFO, LDA, LDB, N, NRHS -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), B( LDB, * ) -* .. -* -* ===================================================================== -* -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL DPOTRF, DPOTRS, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 - IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( NRHS.LT.0 ) THEN - INFO = -3 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -5 - ELSE IF( LDB.LT.MAX( 1, N ) ) THEN - INFO = -7 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DPOSV ', -INFO ) - RETURN - END IF -* -* Compute the Cholesky factorization A = U**T*U or A = L*L**T. -* - CALL DPOTRF( UPLO, N, A, LDA, INFO ) - IF( INFO.EQ.0 ) THEN -* -* Solve the system A*X = B, overwriting B with X. -* - CALL DPOTRS( UPLO, N, NRHS, A, LDA, B, LDB, INFO ) -* - END IF - RETURN -* -* End of DPOSV -* - END diff --git a/lib/linalg/fortran/dpotf2.f b/lib/linalg/fortran/dpotf2.f deleted file mode 100644 index 08fa4957fd..0000000000 --- a/lib/linalg/fortran/dpotf2.f +++ /dev/null @@ -1,227 +0,0 @@ -*> \brief \b DPOTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix (unblocked algorithm). -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DPOTF2 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DPOTF2( UPLO, N, A, LDA, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER UPLO -* INTEGER INFO, LDA, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DPOTF2 computes the Cholesky factorization of a real symmetric -*> positive definite matrix A. -*> -*> The factorization has the form -*> A = U**T * U , if UPLO = 'U', or -*> A = L * L**T, if UPLO = 'L', -*> where U is an upper triangular matrix and L is lower triangular. -*> -*> This is the unblocked version of the algorithm, calling Level 2 BLAS. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> Specifies whether the upper or lower triangular part of the -*> symmetric matrix A is stored. -*> = 'U': Upper triangular -*> = 'L': Lower triangular -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the symmetric matrix A. If UPLO = 'U', the leading -*> n by n upper triangular part of A contains the upper -*> triangular part of the matrix A, and the strictly lower -*> triangular part of A is not referenced. If UPLO = 'L', the -*> leading n by n lower triangular part of A contains the lower -*> triangular part of the matrix A, and the strictly upper -*> triangular part of A is not referenced. -*> -*> On exit, if INFO = 0, the factor U or L from the Cholesky -*> factorization A = U**T *U or A = L*L**T. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,N). -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -k, the k-th argument had an illegal value -*> > 0: if INFO = k, the leading minor of order k is not -*> positive definite, and the factorization could not be -*> completed. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doublePOcomputational -* -* ===================================================================== - SUBROUTINE DPOTF2( UPLO, N, A, LDA, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER UPLO - INTEGER INFO, LDA, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE, ZERO - PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) -* .. -* .. Local Scalars .. - LOGICAL UPPER - INTEGER J - DOUBLE PRECISION AJJ -* .. -* .. External Functions .. - LOGICAL LSAME, DISNAN - DOUBLE PRECISION DDOT - EXTERNAL LSAME, DDOT, DISNAN -* .. -* .. External Subroutines .. - EXTERNAL DGEMV, DSCAL, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, SQRT -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 - UPPER = LSAME( UPLO, 'U' ) - IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -4 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DPOTF2', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( N.EQ.0 ) - $ RETURN -* - IF( UPPER ) THEN -* -* Compute the Cholesky factorization A = U**T *U. -* - DO 10 J = 1, N -* -* Compute U(J,J) and test for non-positive-definiteness. -* - AJJ = A( J, J ) - DDOT( J-1, A( 1, J ), 1, A( 1, J ), 1 ) - IF( AJJ.LE.ZERO.OR.DISNAN( AJJ ) ) THEN - A( J, J ) = AJJ - GO TO 30 - END IF - AJJ = SQRT( AJJ ) - A( J, J ) = AJJ -* -* Compute elements J+1:N of row J. -* - IF( J.LT.N ) THEN - CALL DGEMV( 'Transpose', J-1, N-J, -ONE, A( 1, J+1 ), - $ LDA, A( 1, J ), 1, ONE, A( J, J+1 ), LDA ) - CALL DSCAL( N-J, ONE / AJJ, A( J, J+1 ), LDA ) - END IF - 10 CONTINUE - ELSE -* -* Compute the Cholesky factorization A = L*L**T. -* - DO 20 J = 1, N -* -* Compute L(J,J) and test for non-positive-definiteness. -* - AJJ = A( J, J ) - DDOT( J-1, A( J, 1 ), LDA, A( J, 1 ), - $ LDA ) - IF( AJJ.LE.ZERO.OR.DISNAN( AJJ ) ) THEN - A( J, J ) = AJJ - GO TO 30 - END IF - AJJ = SQRT( AJJ ) - A( J, J ) = AJJ -* -* Compute elements J+1:N of column J. -* - IF( J.LT.N ) THEN - CALL DGEMV( 'No transpose', N-J, J-1, -ONE, A( J+1, 1 ), - $ LDA, A( J, 1 ), LDA, ONE, A( J+1, J ), 1 ) - CALL DSCAL( N-J, ONE / AJJ, A( J+1, J ), 1 ) - END IF - 20 CONTINUE - END IF - GO TO 40 -* - 30 CONTINUE - INFO = J -* - 40 CONTINUE - RETURN -* -* End of DPOTF2 -* - END diff --git a/lib/linalg/fortran/dpotrf.f b/lib/linalg/fortran/dpotrf.f deleted file mode 100644 index 1679fc3cd8..0000000000 --- a/lib/linalg/fortran/dpotrf.f +++ /dev/null @@ -1,243 +0,0 @@ -*> \brief \b DPOTRF -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DPOTRF + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DPOTRF( UPLO, N, A, LDA, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER UPLO -* INTEGER INFO, LDA, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DPOTRF computes the Cholesky factorization of a real symmetric -*> positive definite matrix A. -*> -*> The factorization has the form -*> A = U**T * U, if UPLO = 'U', or -*> A = L * L**T, if UPLO = 'L', -*> where U is an upper triangular matrix and L is lower triangular. -*> -*> This is the block version of the algorithm, calling Level 3 BLAS. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> = 'U': Upper triangle of A is stored; -*> = 'L': Lower triangle of A is stored. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the symmetric matrix A. If UPLO = 'U', the leading -*> N-by-N upper triangular part of A contains the upper -*> triangular part of the matrix A, and the strictly lower -*> triangular part of A is not referenced. If UPLO = 'L', the -*> leading N-by-N lower triangular part of A contains the lower -*> triangular part of the matrix A, and the strictly upper -*> triangular part of A is not referenced. -*> -*> On exit, if INFO = 0, the factor U or L from the Cholesky -*> factorization A = U**T*U or A = L*L**T. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,N). -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i is not -*> positive definite, and the factorization could not be -*> completed. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doublePOcomputational -* -* ===================================================================== - SUBROUTINE DPOTRF( UPLO, N, A, LDA, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER UPLO - INTEGER INFO, LDA, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE - PARAMETER ( ONE = 1.0D+0 ) -* .. -* .. Local Scalars .. - LOGICAL UPPER - INTEGER J, JB, NB -* .. -* .. External Functions .. - LOGICAL LSAME - INTEGER ILAENV - EXTERNAL LSAME, ILAENV -* .. -* .. External Subroutines .. - EXTERNAL DGEMM, DPOTRF2, DSYRK, DTRSM, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, MIN -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 - UPPER = LSAME( UPLO, 'U' ) - IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -4 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DPOTRF', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( N.EQ.0 ) - $ RETURN -* -* Determine the block size for this environment. -* - NB = ILAENV( 1, 'DPOTRF', UPLO, N, -1, -1, -1 ) - IF( NB.LE.1 .OR. NB.GE.N ) THEN -* -* Use unblocked code. -* - CALL DPOTRF2( UPLO, N, A, LDA, INFO ) - ELSE -* -* Use blocked code. -* - IF( UPPER ) THEN -* -* Compute the Cholesky factorization A = U**T*U. -* - DO 10 J = 1, N, NB -* -* Update and factorize the current diagonal block and test -* for non-positive-definiteness. -* - JB = MIN( NB, N-J+1 ) - CALL DSYRK( 'Upper', 'Transpose', JB, J-1, -ONE, - $ A( 1, J ), LDA, ONE, A( J, J ), LDA ) - CALL DPOTRF2( 'Upper', JB, A( J, J ), LDA, INFO ) - IF( INFO.NE.0 ) - $ GO TO 30 - IF( J+JB.LE.N ) THEN -* -* Compute the current block row. -* - CALL DGEMM( 'Transpose', 'No transpose', JB, N-J-JB+1, - $ J-1, -ONE, A( 1, J ), LDA, A( 1, J+JB ), - $ LDA, ONE, A( J, J+JB ), LDA ) - CALL DTRSM( 'Left', 'Upper', 'Transpose', 'Non-unit', - $ JB, N-J-JB+1, ONE, A( J, J ), LDA, - $ A( J, J+JB ), LDA ) - END IF - 10 CONTINUE -* - ELSE -* -* Compute the Cholesky factorization A = L*L**T. -* - DO 20 J = 1, N, NB -* -* Update and factorize the current diagonal block and test -* for non-positive-definiteness. -* - JB = MIN( NB, N-J+1 ) - CALL DSYRK( 'Lower', 'No transpose', JB, J-1, -ONE, - $ A( J, 1 ), LDA, ONE, A( J, J ), LDA ) - CALL DPOTRF2( 'Lower', JB, A( J, J ), LDA, INFO ) - IF( INFO.NE.0 ) - $ GO TO 30 - IF( J+JB.LE.N ) THEN -* -* Compute the current block column. -* - CALL DGEMM( 'No transpose', 'Transpose', N-J-JB+1, JB, - $ J-1, -ONE, A( J+JB, 1 ), LDA, A( J, 1 ), - $ LDA, ONE, A( J+JB, J ), LDA ) - CALL DTRSM( 'Right', 'Lower', 'Transpose', 'Non-unit', - $ N-J-JB+1, JB, ONE, A( J, J ), LDA, - $ A( J+JB, J ), LDA ) - END IF - 20 CONTINUE - END IF - END IF - GO TO 40 -* - 30 CONTINUE - INFO = INFO + J - 1 -* - 40 CONTINUE - RETURN -* -* End of DPOTRF -* - END diff --git a/lib/linalg/fortran/dpotrf2.f b/lib/linalg/fortran/dpotrf2.f deleted file mode 100644 index 6c28ce6d67..0000000000 --- a/lib/linalg/fortran/dpotrf2.f +++ /dev/null @@ -1,234 +0,0 @@ -*> \brief \b DPOTRF2 -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* RECURSIVE SUBROUTINE DPOTRF2( UPLO, N, A, LDA, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER UPLO -* INTEGER INFO, LDA, N -* .. -* .. Array Arguments .. -* REAL A( LDA, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DPOTRF2 computes the Cholesky factorization of a real symmetric -*> positive definite matrix A using the recursive algorithm. -*> -*> The factorization has the form -*> A = U**T * U, if UPLO = 'U', or -*> A = L * L**T, if UPLO = 'L', -*> where U is an upper triangular matrix and L is lower triangular. -*> -*> This is the recursive version of the algorithm. It divides -*> the matrix into four submatrices: -*> -*> [ A11 | A12 ] where A11 is n1 by n1 and A22 is n2 by n2 -*> A = [ -----|----- ] with n1 = n/2 -*> [ A21 | A22 ] n2 = n-n1 -*> -*> The subroutine calls itself to factor A11. Update and scale A21 -*> or A12, update A22 then calls itself to factor A22. -*> -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> = 'U': Upper triangle of A is stored; -*> = 'L': Lower triangle of A is stored. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the symmetric matrix A. If UPLO = 'U', the leading -*> N-by-N upper triangular part of A contains the upper -*> triangular part of the matrix A, and the strictly lower -*> triangular part of A is not referenced. If UPLO = 'L', the -*> leading N-by-N lower triangular part of A contains the lower -*> triangular part of the matrix A, and the strictly upper -*> triangular part of A is not referenced. -*> -*> On exit, if INFO = 0, the factor U or L from the Cholesky -*> factorization A = U**T*U or A = L*L**T. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,N). -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i is not -*> positive definite, and the factorization could not be -*> completed. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doublePOcomputational -* -* ===================================================================== - RECURSIVE SUBROUTINE DPOTRF2( UPLO, N, A, LDA, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER UPLO - INTEGER INFO, LDA, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE, ZERO - PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) -* .. -* .. Local Scalars .. - LOGICAL UPPER - INTEGER N1, N2, IINFO -* .. -* .. External Functions .. - LOGICAL LSAME, DISNAN - EXTERNAL LSAME, DISNAN -* .. -* .. External Subroutines .. - EXTERNAL DSYRK, DTRSM, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, SQRT -* .. -* .. Executable Statements .. -* -* Test the input parameters -* - INFO = 0 - UPPER = LSAME( UPLO, 'U' ) - IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -4 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DPOTRF2', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( N.EQ.0 ) - $ RETURN -* -* N=1 case -* - IF( N.EQ.1 ) THEN -* -* Test for non-positive-definiteness -* - IF( A( 1, 1 ).LE.ZERO.OR.DISNAN( A( 1, 1 ) ) ) THEN - INFO = 1 - RETURN - END IF -* -* Factor -* - A( 1, 1 ) = SQRT( A( 1, 1 ) ) -* -* Use recursive code -* - ELSE - N1 = N/2 - N2 = N-N1 -* -* Factor A11 -* - CALL DPOTRF2( UPLO, N1, A( 1, 1 ), LDA, IINFO ) - IF ( IINFO.NE.0 ) THEN - INFO = IINFO - RETURN - END IF -* -* Compute the Cholesky factorization A = U**T*U -* - IF( UPPER ) THEN -* -* Update and scale A12 -* - CALL DTRSM( 'L', 'U', 'T', 'N', N1, N2, ONE, - $ A( 1, 1 ), LDA, A( 1, N1+1 ), LDA ) -* -* Update and factor A22 -* - CALL DSYRK( UPLO, 'T', N2, N1, -ONE, A( 1, N1+1 ), LDA, - $ ONE, A( N1+1, N1+1 ), LDA ) - CALL DPOTRF2( UPLO, N2, A( N1+1, N1+1 ), LDA, IINFO ) - IF ( IINFO.NE.0 ) THEN - INFO = IINFO + N1 - RETURN - END IF -* -* Compute the Cholesky factorization A = L*L**T -* - ELSE -* -* Update and scale A21 -* - CALL DTRSM( 'R', 'L', 'T', 'N', N2, N1, ONE, - $ A( 1, 1 ), LDA, A( N1+1, 1 ), LDA ) -* -* Update and factor A22 -* - CALL DSYRK( UPLO, 'N', N2, N1, -ONE, A( N1+1, 1 ), LDA, - $ ONE, A( N1+1, N1+1 ), LDA ) - CALL DPOTRF2( UPLO, N2, A( N1+1, N1+1 ), LDA, IINFO ) - IF ( IINFO.NE.0 ) THEN - INFO = IINFO + N1 - RETURN - END IF - END IF - END IF - RETURN -* -* End of DPOTRF2 -* - END diff --git a/lib/linalg/fortran/dpotrs.f b/lib/linalg/fortran/dpotrs.f deleted file mode 100644 index 862ee078fd..0000000000 --- a/lib/linalg/fortran/dpotrs.f +++ /dev/null @@ -1,201 +0,0 @@ -*> \brief \b DPOTRS -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DPOTRS + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DPOTRS( UPLO, N, NRHS, A, LDA, B, LDB, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER UPLO -* INTEGER INFO, LDA, LDB, N, NRHS -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), B( LDB, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DPOTRS solves a system of linear equations A*X = B with a symmetric -*> positive definite matrix A using the Cholesky factorization -*> A = U**T*U or A = L*L**T computed by DPOTRF. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> = 'U': Upper triangle of A is stored; -*> = 'L': Lower triangle of A is stored. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in] NRHS -*> \verbatim -*> NRHS is INTEGER -*> The number of right hand sides, i.e., the number of columns -*> of the matrix B. NRHS >= 0. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> The triangular factor U or L from the Cholesky factorization -*> A = U**T*U or A = L*L**T, as computed by DPOTRF. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,N). -*> \endverbatim -*> -*> \param[in,out] B -*> \verbatim -*> B is DOUBLE PRECISION array, dimension (LDB,NRHS) -*> On entry, the right hand side matrix B. -*> On exit, the solution matrix X. -*> \endverbatim -*> -*> \param[in] LDB -*> \verbatim -*> LDB is INTEGER -*> The leading dimension of the array B. LDB >= max(1,N). -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doublePOcomputational -* -* ===================================================================== - SUBROUTINE DPOTRS( UPLO, N, NRHS, A, LDA, B, LDB, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER UPLO - INTEGER INFO, LDA, LDB, N, NRHS -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), B( LDB, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE - PARAMETER ( ONE = 1.0D+0 ) -* .. -* .. Local Scalars .. - LOGICAL UPPER -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL DTRSM, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 - UPPER = LSAME( UPLO, 'U' ) - IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( NRHS.LT.0 ) THEN - INFO = -3 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -5 - ELSE IF( LDB.LT.MAX( 1, N ) ) THEN - INFO = -7 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DPOTRS', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( N.EQ.0 .OR. NRHS.EQ.0 ) - $ RETURN -* - IF( UPPER ) THEN -* -* Solve A*X = B where A = U**T *U. -* -* Solve U**T *X = B, overwriting B with X. -* - CALL DTRSM( 'Left', 'Upper', 'Transpose', 'Non-unit', N, NRHS, - $ ONE, A, LDA, B, LDB ) -* -* Solve U*X = B, overwriting B with X. -* - CALL DTRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', N, - $ NRHS, ONE, A, LDA, B, LDB ) - ELSE -* -* Solve A*X = B where A = L*L**T. -* -* Solve L*X = B, overwriting B with X. -* - CALL DTRSM( 'Left', 'Lower', 'No transpose', 'Non-unit', N, - $ NRHS, ONE, A, LDA, B, LDB ) -* -* Solve L**T *X = B, overwriting B with X. -* - CALL DTRSM( 'Left', 'Lower', 'Transpose', 'Non-unit', N, NRHS, - $ ONE, A, LDA, B, LDB ) - END IF -* - RETURN -* -* End of DPOTRS -* - END diff --git a/lib/linalg/fortran/drot.f b/lib/linalg/fortran/drot.f deleted file mode 100644 index 0386626c8f..0000000000 --- a/lib/linalg/fortran/drot.f +++ /dev/null @@ -1,142 +0,0 @@ -*> \brief \b DROT -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE DROT(N,DX,INCX,DY,INCY,C,S) -* -* .. Scalar Arguments .. -* DOUBLE PRECISION C,S -* INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION DX(*),DY(*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DROT applies a plane rotation. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> number of elements in input vector(s) -*> \endverbatim -*> -*> \param[in,out] DX -*> \verbatim -*> DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> storage spacing between elements of DX -*> \endverbatim -*> -*> \param[in,out] DY -*> \verbatim -*> DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) -*> \endverbatim -*> -*> \param[in] INCY -*> \verbatim -*> INCY is INTEGER -*> storage spacing between elements of DY -*> \endverbatim -*> -*> \param[in] C -*> \verbatim -*> C is DOUBLE PRECISION -*> \endverbatim -*> -*> \param[in] S -*> \verbatim -*> S is DOUBLE PRECISION -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup double_blas_level1 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> jack dongarra, linpack, 3/11/78. -*> modified 12/3/93, array(1) declarations changed to array(*) -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DROT(N,DX,INCX,DY,INCY,C,S) -* -* -- Reference BLAS level1 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - DOUBLE PRECISION C,S - INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. - DOUBLE PRECISION DX(*),DY(*) -* .. -* -* ===================================================================== -* -* .. Local Scalars .. - DOUBLE PRECISION DTEMP - INTEGER I,IX,IY -* .. - IF (N.LE.0) RETURN - IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN -* -* code for both increments equal to 1 -* - DO I = 1,N - DTEMP = C*DX(I) + S*DY(I) - DY(I) = C*DY(I) - S*DX(I) - DX(I) = DTEMP - END DO - ELSE -* -* code for unequal increments or equal increments not equal -* to 1 -* - IX = 1 - IY = 1 - IF (INCX.LT.0) IX = (-N+1)*INCX + 1 - IF (INCY.LT.0) IY = (-N+1)*INCY + 1 - DO I = 1,N - DTEMP = C*DX(IX) + S*DY(IY) - DY(IY) = C*DY(IY) - S*DX(IX) - DX(IX) = DTEMP - IX = IX + INCX - IY = IY + INCY - END DO - END IF - RETURN -* -* End of DROT -* - END diff --git a/lib/linalg/fortran/drscl.f b/lib/linalg/fortran/drscl.f deleted file mode 100644 index fcd8569650..0000000000 --- a/lib/linalg/fortran/drscl.f +++ /dev/null @@ -1,171 +0,0 @@ -*> \brief \b DRSCL multiplies a vector by the reciprocal of a real scalar. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DRSCL + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DRSCL( N, SA, SX, INCX ) -* -* .. Scalar Arguments .. -* INTEGER INCX, N -* DOUBLE PRECISION SA -* .. -* .. Array Arguments .. -* DOUBLE PRECISION SX( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DRSCL multiplies an n-element real vector x by the real scalar 1/a. -*> This is done without overflow or underflow as long as -*> the final result x/a does not overflow or underflow. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of components of the vector x. -*> \endverbatim -*> -*> \param[in] SA -*> \verbatim -*> SA is DOUBLE PRECISION -*> The scalar a which is used to divide each component of x. -*> SA must be >= 0, or the subroutine will divide by zero. -*> \endverbatim -*> -*> \param[in,out] SX -*> \verbatim -*> SX is DOUBLE PRECISION array, dimension -*> (1+(N-1)*abs(INCX)) -*> The n-element vector x. -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> The increment between successive values of the vector SX. -*> > 0: SX(1) = X(1) and SX(1+(i-1)*INCX) = x(i), 1< i<= n -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleOTHERauxiliary -* -* ===================================================================== - SUBROUTINE DRSCL( N, SA, SX, INCX ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INCX, N - DOUBLE PRECISION SA -* .. -* .. Array Arguments .. - DOUBLE PRECISION SX( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE, ZERO - PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) -* .. -* .. Local Scalars .. - LOGICAL DONE - DOUBLE PRECISION BIGNUM, CDEN, CDEN1, CNUM, CNUM1, MUL, SMLNUM -* .. -* .. External Functions .. - DOUBLE PRECISION DLAMCH - EXTERNAL DLAMCH -* .. -* .. External Subroutines .. - EXTERNAL DSCAL, DLABAD -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS -* .. -* .. Executable Statements .. -* -* Quick return if possible -* - IF( N.LE.0 ) - $ RETURN -* -* Get machine parameters -* - SMLNUM = DLAMCH( 'S' ) - BIGNUM = ONE / SMLNUM - CALL DLABAD( SMLNUM, BIGNUM ) -* -* Initialize the denominator to SA and the numerator to 1. -* - CDEN = SA - CNUM = ONE -* - 10 CONTINUE - CDEN1 = CDEN*SMLNUM - CNUM1 = CNUM / BIGNUM - IF( ABS( CDEN1 ).GT.ABS( CNUM ) .AND. CNUM.NE.ZERO ) THEN -* -* Pre-multiply X by SMLNUM if CDEN is large compared to CNUM. -* - MUL = SMLNUM - DONE = .FALSE. - CDEN = CDEN1 - ELSE IF( ABS( CNUM1 ).GT.ABS( CDEN ) ) THEN -* -* Pre-multiply X by BIGNUM if CDEN is small compared to CNUM. -* - MUL = BIGNUM - DONE = .FALSE. - CNUM = CNUM1 - ELSE -* -* Multiply X by CNUM / CDEN and return. -* - MUL = CNUM / CDEN - DONE = .TRUE. - END IF -* -* Scale the vector X by MUL -* - CALL DSCAL( N, MUL, SX, INCX ) -* - IF( .NOT.DONE ) - $ GO TO 10 -* - RETURN -* -* End of DRSCL -* - END diff --git a/lib/linalg/fortran/dscal.f b/lib/linalg/fortran/dscal.f deleted file mode 100644 index e055d198af..0000000000 --- a/lib/linalg/fortran/dscal.f +++ /dev/null @@ -1,139 +0,0 @@ -*> \brief \b DSCAL -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE DSCAL(N,DA,DX,INCX) -* -* .. Scalar Arguments .. -* DOUBLE PRECISION DA -* INTEGER INCX,N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION DX(*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DSCAL scales a vector by a constant. -*> uses unrolled loops for increment equal to 1. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> number of elements in input vector(s) -*> \endverbatim -*> -*> \param[in] DA -*> \verbatim -*> DA is DOUBLE PRECISION -*> On entry, DA specifies the scalar alpha. -*> \endverbatim -*> -*> \param[in,out] DX -*> \verbatim -*> DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> storage spacing between elements of DX -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup double_blas_level1 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> jack dongarra, linpack, 3/11/78. -*> modified 3/93 to return if incx .le. 0. -*> modified 12/3/93, array(1) declarations changed to array(*) -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DSCAL(N,DA,DX,INCX) -* -* -- Reference BLAS level1 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - DOUBLE PRECISION DA - INTEGER INCX,N -* .. -* .. Array Arguments .. - DOUBLE PRECISION DX(*) -* .. -* -* ===================================================================== -* -* .. Local Scalars .. - INTEGER I,M,MP1,NINCX -* .. Parameters .. - DOUBLE PRECISION ONE - PARAMETER (ONE=1.0D+0) -* .. -* .. Intrinsic Functions .. - INTRINSIC MOD -* .. - IF (N.LE.0 .OR. INCX.LE.0 .OR. DA.EQ.ONE) RETURN - IF (INCX.EQ.1) THEN -* -* code for increment equal to 1 -* -* -* clean-up loop -* - M = MOD(N,5) - IF (M.NE.0) THEN - DO I = 1,M - DX(I) = DA*DX(I) - END DO - IF (N.LT.5) RETURN - END IF - MP1 = M + 1 - DO I = MP1,N,5 - DX(I) = DA*DX(I) - DX(I+1) = DA*DX(I+1) - DX(I+2) = DA*DX(I+2) - DX(I+3) = DA*DX(I+3) - DX(I+4) = DA*DX(I+4) - END DO - ELSE -* -* code for increment not equal to 1 -* - NINCX = N*INCX - DO I = 1,NINCX,INCX - DX(I) = DA*DX(I) - END DO - END IF - RETURN -* -* End of DSCAL -* - END diff --git a/lib/linalg/fortran/dstedc.f b/lib/linalg/fortran/dstedc.f deleted file mode 100644 index 2ed84afaac..0000000000 --- a/lib/linalg/fortran/dstedc.f +++ /dev/null @@ -1,479 +0,0 @@ -*> \brief \b DSTEDC -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DSTEDC + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, -* LIWORK, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER COMPZ -* INTEGER INFO, LDZ, LIWORK, LWORK, N -* .. -* .. Array Arguments .. -* INTEGER IWORK( * ) -* DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DSTEDC computes all eigenvalues and, optionally, eigenvectors of a -*> symmetric tridiagonal matrix using the divide and conquer method. -*> The eigenvectors of a full or band real symmetric matrix can also be -*> found if DSYTRD or DSPTRD or DSBTRD has been used to reduce this -*> matrix to tridiagonal form. -*> -*> This code makes very mild assumptions about floating point -*> arithmetic. It will work on machines with a guard digit in -*> add/subtract, or on those binary machines without guard digits -*> which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. -*> It could conceivably fail on hexadecimal or decimal machines -*> without guard digits, but we know of none. See DLAED3 for details. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] COMPZ -*> \verbatim -*> COMPZ is CHARACTER*1 -*> = 'N': Compute eigenvalues only. -*> = 'I': Compute eigenvectors of tridiagonal matrix also. -*> = 'V': Compute eigenvectors of original dense symmetric -*> matrix also. On entry, Z contains the orthogonal -*> matrix used to reduce the original matrix to -*> tridiagonal form. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The dimension of the symmetric tridiagonal matrix. N >= 0. -*> \endverbatim -*> -*> \param[in,out] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension (N) -*> On entry, the diagonal elements of the tridiagonal matrix. -*> On exit, if INFO = 0, the eigenvalues in ascending order. -*> \endverbatim -*> -*> \param[in,out] E -*> \verbatim -*> E is DOUBLE PRECISION array, dimension (N-1) -*> On entry, the subdiagonal elements of the tridiagonal matrix. -*> On exit, E has been destroyed. -*> \endverbatim -*> -*> \param[in,out] Z -*> \verbatim -*> Z is DOUBLE PRECISION array, dimension (LDZ,N) -*> On entry, if COMPZ = 'V', then Z contains the orthogonal -*> matrix used in the reduction to tridiagonal form. -*> On exit, if INFO = 0, then if COMPZ = 'V', Z contains the -*> orthonormal eigenvectors of the original symmetric matrix, -*> and if COMPZ = 'I', Z contains the orthonormal eigenvectors -*> of the symmetric tridiagonal matrix. -*> If COMPZ = 'N', then Z is not referenced. -*> \endverbatim -*> -*> \param[in] LDZ -*> \verbatim -*> LDZ is INTEGER -*> The leading dimension of the array Z. LDZ >= 1. -*> If eigenvectors are desired, then LDZ >= max(1,N). -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) -*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -*> \endverbatim -*> -*> \param[in] LWORK -*> \verbatim -*> LWORK is INTEGER -*> The dimension of the array WORK. -*> If COMPZ = 'N' or N <= 1 then LWORK must be at least 1. -*> If COMPZ = 'V' and N > 1 then LWORK must be at least -*> ( 1 + 3*N + 2*N*lg N + 4*N**2 ), -*> where lg( N ) = smallest integer k such -*> that 2**k >= N. -*> If COMPZ = 'I' and N > 1 then LWORK must be at least -*> ( 1 + 4*N + N**2 ). -*> Note that for COMPZ = 'I' or 'V', then if N is less than or -*> equal to the minimum divide size, usually 25, then LWORK need -*> only be max(1,2*(N-1)). -*> -*> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal size of the WORK array, returns -*> this value as the first entry of the WORK array, and no error -*> message related to LWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] IWORK -*> \verbatim -*> IWORK is INTEGER array, dimension (MAX(1,LIWORK)) -*> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. -*> \endverbatim -*> -*> \param[in] LIWORK -*> \verbatim -*> LIWORK is INTEGER -*> The dimension of the array IWORK. -*> If COMPZ = 'N' or N <= 1 then LIWORK must be at least 1. -*> If COMPZ = 'V' and N > 1 then LIWORK must be at least -*> ( 6 + 6*N + 5*N*lg N ). -*> If COMPZ = 'I' and N > 1 then LIWORK must be at least -*> ( 3 + 5*N ). -*> Note that for COMPZ = 'I' or 'V', then if N is less than or -*> equal to the minimum divide size, usually 25, then LIWORK -*> need only be 1. -*> -*> If LIWORK = -1, then a workspace query is assumed; the -*> routine only calculates the optimal size of the IWORK array, -*> returns this value as the first entry of the IWORK array, and -*> no error message related to LIWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit. -*> < 0: if INFO = -i, the i-th argument had an illegal value. -*> > 0: The algorithm failed to compute an eigenvalue while -*> working on the submatrix lying in rows and columns -*> INFO/(N+1) through mod(INFO,N+1). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup auxOTHERcomputational -* -*> \par Contributors: -* ================== -*> -*> Jeff Rutter, Computer Science Division, University of California -*> at Berkeley, USA \n -*> Modified by Francoise Tisseur, University of Tennessee -*> -* ===================================================================== - SUBROUTINE DSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, - $ LIWORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER COMPZ - INTEGER INFO, LDZ, LIWORK, LWORK, N -* .. -* .. Array Arguments .. - INTEGER IWORK( * ) - DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, ONE, TWO - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0 ) -* .. -* .. Local Scalars .. - LOGICAL LQUERY - INTEGER FINISH, I, ICOMPZ, II, J, K, LGN, LIWMIN, - $ LWMIN, M, SMLSIZ, START, STOREZ, STRTRW - DOUBLE PRECISION EPS, ORGNRM, P, TINY -* .. -* .. External Functions .. - LOGICAL LSAME - INTEGER ILAENV - DOUBLE PRECISION DLAMCH, DLANST - EXTERNAL LSAME, ILAENV, DLAMCH, DLANST -* .. -* .. External Subroutines .. - EXTERNAL DGEMM, DLACPY, DLAED0, DLASCL, DLASET, DLASRT, - $ DSTEQR, DSTERF, DSWAP, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, DBLE, INT, LOG, MAX, MOD, SQRT -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 - LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 ) -* - IF( LSAME( COMPZ, 'N' ) ) THEN - ICOMPZ = 0 - ELSE IF( LSAME( COMPZ, 'V' ) ) THEN - ICOMPZ = 1 - ELSE IF( LSAME( COMPZ, 'I' ) ) THEN - ICOMPZ = 2 - ELSE - ICOMPZ = -1 - END IF - IF( ICOMPZ.LT.0 ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( ( LDZ.LT.1 ) .OR. - $ ( ICOMPZ.GT.0 .AND. LDZ.LT.MAX( 1, N ) ) ) THEN - INFO = -6 - END IF -* - IF( INFO.EQ.0 ) THEN -* -* Compute the workspace requirements -* - SMLSIZ = ILAENV( 9, 'DSTEDC', ' ', 0, 0, 0, 0 ) - IF( N.LE.1 .OR. ICOMPZ.EQ.0 ) THEN - LIWMIN = 1 - LWMIN = 1 - ELSE IF( N.LE.SMLSIZ ) THEN - LIWMIN = 1 - LWMIN = 2*( N - 1 ) - ELSE - LGN = INT( LOG( DBLE( N ) )/LOG( TWO ) ) - IF( 2**LGN.LT.N ) - $ LGN = LGN + 1 - IF( 2**LGN.LT.N ) - $ LGN = LGN + 1 - IF( ICOMPZ.EQ.1 ) THEN - LWMIN = 1 + 3*N + 2*N*LGN + 4*N**2 - LIWMIN = 6 + 6*N + 5*N*LGN - ELSE IF( ICOMPZ.EQ.2 ) THEN - LWMIN = 1 + 4*N + N**2 - LIWMIN = 3 + 5*N - END IF - END IF - WORK( 1 ) = LWMIN - IWORK( 1 ) = LIWMIN -* - IF( LWORK.LT.LWMIN .AND. .NOT. LQUERY ) THEN - INFO = -8 - ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT. LQUERY ) THEN - INFO = -10 - END IF - END IF -* - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DSTEDC', -INFO ) - RETURN - ELSE IF (LQUERY) THEN - RETURN - END IF -* -* Quick return if possible -* - IF( N.EQ.0 ) - $ RETURN - IF( N.EQ.1 ) THEN - IF( ICOMPZ.NE.0 ) - $ Z( 1, 1 ) = ONE - RETURN - END IF -* -* If the following conditional clause is removed, then the routine -* will use the Divide and Conquer routine to compute only the -* eigenvalues, which requires (3N + 3N**2) real workspace and -* (2 + 5N + 2N lg(N)) integer workspace. -* Since on many architectures DSTERF is much faster than any other -* algorithm for finding eigenvalues only, it is used here -* as the default. If the conditional clause is removed, then -* information on the size of workspace needs to be changed. -* -* If COMPZ = 'N', use DSTERF to compute the eigenvalues. -* - IF( ICOMPZ.EQ.0 ) THEN - CALL DSTERF( N, D, E, INFO ) - GO TO 50 - END IF -* -* If N is smaller than the minimum divide size (SMLSIZ+1), then -* solve the problem with another solver. -* - IF( N.LE.SMLSIZ ) THEN -* - CALL DSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO ) -* - ELSE -* -* If COMPZ = 'V', the Z matrix must be stored elsewhere for later -* use. -* - IF( ICOMPZ.EQ.1 ) THEN - STOREZ = 1 + N*N - ELSE - STOREZ = 1 - END IF -* - IF( ICOMPZ.EQ.2 ) THEN - CALL DLASET( 'Full', N, N, ZERO, ONE, Z, LDZ ) - END IF -* -* Scale. -* - ORGNRM = DLANST( 'M', N, D, E ) - IF( ORGNRM.EQ.ZERO ) - $ GO TO 50 -* - EPS = DLAMCH( 'Epsilon' ) -* - START = 1 -* -* while ( START <= N ) -* - 10 CONTINUE - IF( START.LE.N ) THEN -* -* Let FINISH be the position of the next subdiagonal entry -* such that E( FINISH ) <= TINY or FINISH = N if no such -* subdiagonal exists. The matrix identified by the elements -* between START and FINISH constitutes an independent -* sub-problem. -* - FINISH = START - 20 CONTINUE - IF( FINISH.LT.N ) THEN - TINY = EPS*SQRT( ABS( D( FINISH ) ) )* - $ SQRT( ABS( D( FINISH+1 ) ) ) - IF( ABS( E( FINISH ) ).GT.TINY ) THEN - FINISH = FINISH + 1 - GO TO 20 - END IF - END IF -* -* (Sub) Problem determined. Compute its size and solve it. -* - M = FINISH - START + 1 - IF( M.EQ.1 ) THEN - START = FINISH + 1 - GO TO 10 - END IF - IF( M.GT.SMLSIZ ) THEN -* -* Scale. -* - ORGNRM = DLANST( 'M', M, D( START ), E( START ) ) - CALL DLASCL( 'G', 0, 0, ORGNRM, ONE, M, 1, D( START ), M, - $ INFO ) - CALL DLASCL( 'G', 0, 0, ORGNRM, ONE, M-1, 1, E( START ), - $ M-1, INFO ) -* - IF( ICOMPZ.EQ.1 ) THEN - STRTRW = 1 - ELSE - STRTRW = START - END IF - CALL DLAED0( ICOMPZ, N, M, D( START ), E( START ), - $ Z( STRTRW, START ), LDZ, WORK( 1 ), N, - $ WORK( STOREZ ), IWORK, INFO ) - IF( INFO.NE.0 ) THEN - INFO = ( INFO / ( M+1 )+START-1 )*( N+1 ) + - $ MOD( INFO, ( M+1 ) ) + START - 1 - GO TO 50 - END IF -* -* Scale back. -* - CALL DLASCL( 'G', 0, 0, ONE, ORGNRM, M, 1, D( START ), M, - $ INFO ) -* - ELSE - IF( ICOMPZ.EQ.1 ) THEN -* -* Since QR won't update a Z matrix which is larger than -* the length of D, we must solve the sub-problem in a -* workspace and then multiply back into Z. -* - CALL DSTEQR( 'I', M, D( START ), E( START ), WORK, M, - $ WORK( M*M+1 ), INFO ) - CALL DLACPY( 'A', N, M, Z( 1, START ), LDZ, - $ WORK( STOREZ ), N ) - CALL DGEMM( 'N', 'N', N, M, M, ONE, - $ WORK( STOREZ ), N, WORK, M, ZERO, - $ Z( 1, START ), LDZ ) - ELSE IF( ICOMPZ.EQ.2 ) THEN - CALL DSTEQR( 'I', M, D( START ), E( START ), - $ Z( START, START ), LDZ, WORK, INFO ) - ELSE - CALL DSTERF( M, D( START ), E( START ), INFO ) - END IF - IF( INFO.NE.0 ) THEN - INFO = START*( N+1 ) + FINISH - GO TO 50 - END IF - END IF -* - START = FINISH + 1 - GO TO 10 - END IF -* -* endwhile -* - IF( ICOMPZ.EQ.0 ) THEN -* -* Use Quick Sort -* - CALL DLASRT( 'I', N, D, INFO ) -* - ELSE -* -* Use Selection Sort to minimize swaps of eigenvectors -* - DO 40 II = 2, N - I = II - 1 - K = I - P = D( I ) - DO 30 J = II, N - IF( D( J ).LT.P ) THEN - K = J - P = D( J ) - END IF - 30 CONTINUE - IF( K.NE.I ) THEN - D( K ) = D( I ) - D( I ) = P - CALL DSWAP( N, Z( 1, I ), 1, Z( 1, K ), 1 ) - END IF - 40 CONTINUE - END IF - END IF -* - 50 CONTINUE - WORK( 1 ) = LWMIN - IWORK( 1 ) = LIWMIN -* - RETURN -* -* End of DSTEDC -* - END diff --git a/lib/linalg/fortran/dsteqr.f b/lib/linalg/fortran/dsteqr.f deleted file mode 100644 index 50a9188c7c..0000000000 --- a/lib/linalg/fortran/dsteqr.f +++ /dev/null @@ -1,569 +0,0 @@ -*> \brief \b DSTEQR -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DSTEQR + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER COMPZ -* INTEGER INFO, LDZ, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DSTEQR computes all eigenvalues and, optionally, eigenvectors of a -*> symmetric tridiagonal matrix using the implicit QL or QR method. -*> The eigenvectors of a full or band symmetric matrix can also be found -*> if DSYTRD or DSPTRD or DSBTRD has been used to reduce this matrix to -*> tridiagonal form. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] COMPZ -*> \verbatim -*> COMPZ is CHARACTER*1 -*> = 'N': Compute eigenvalues only. -*> = 'V': Compute eigenvalues and eigenvectors of the original -*> symmetric matrix. On entry, Z must contain the -*> orthogonal matrix used to reduce the original matrix -*> to tridiagonal form. -*> = 'I': Compute eigenvalues and eigenvectors of the -*> tridiagonal matrix. Z is initialized to the identity -*> matrix. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrix. N >= 0. -*> \endverbatim -*> -*> \param[in,out] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension (N) -*> On entry, the diagonal elements of the tridiagonal matrix. -*> On exit, if INFO = 0, the eigenvalues in ascending order. -*> \endverbatim -*> -*> \param[in,out] E -*> \verbatim -*> E is DOUBLE PRECISION array, dimension (N-1) -*> On entry, the (n-1) subdiagonal elements of the tridiagonal -*> matrix. -*> On exit, E has been destroyed. -*> \endverbatim -*> -*> \param[in,out] Z -*> \verbatim -*> Z is DOUBLE PRECISION array, dimension (LDZ, N) -*> On entry, if COMPZ = 'V', then Z contains the orthogonal -*> matrix used in the reduction to tridiagonal form. -*> On exit, if INFO = 0, then if COMPZ = 'V', Z contains the -*> orthonormal eigenvectors of the original symmetric matrix, -*> and if COMPZ = 'I', Z contains the orthonormal eigenvectors -*> of the symmetric tridiagonal matrix. -*> If COMPZ = 'N', then Z is not referenced. -*> \endverbatim -*> -*> \param[in] LDZ -*> \verbatim -*> LDZ is INTEGER -*> The leading dimension of the array Z. LDZ >= 1, and if -*> eigenvectors are desired, then LDZ >= max(1,N). -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (max(1,2*N-2)) -*> If COMPZ = 'N', then WORK is not referenced. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: the algorithm has failed to find all the eigenvalues in -*> a total of 30*N iterations; if INFO = i, then i -*> elements of E have not converged to zero; on exit, D -*> and E contain the elements of a symmetric tridiagonal -*> matrix which is orthogonally similar to the original -*> matrix. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup auxOTHERcomputational -* -* ===================================================================== - SUBROUTINE DSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER COMPZ - INTEGER INFO, LDZ, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, ONE, TWO, THREE - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0, - $ THREE = 3.0D0 ) - INTEGER MAXIT - PARAMETER ( MAXIT = 30 ) -* .. -* .. Local Scalars .. - INTEGER I, ICOMPZ, II, ISCALE, J, JTOT, K, L, L1, LEND, - $ LENDM1, LENDP1, LENDSV, LM1, LSV, M, MM, MM1, - $ NM1, NMAXIT - DOUBLE PRECISION ANORM, B, C, EPS, EPS2, F, G, P, R, RT1, RT2, - $ S, SAFMAX, SAFMIN, SSFMAX, SSFMIN, TST -* .. -* .. External Functions .. - LOGICAL LSAME - DOUBLE PRECISION DLAMCH, DLANST, DLAPY2 - EXTERNAL LSAME, DLAMCH, DLANST, DLAPY2 -* .. -* .. External Subroutines .. - EXTERNAL DLAE2, DLAEV2, DLARTG, DLASCL, DLASET, DLASR, - $ DLASRT, DSWAP, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, MAX, SIGN, SQRT -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 -* - IF( LSAME( COMPZ, 'N' ) ) THEN - ICOMPZ = 0 - ELSE IF( LSAME( COMPZ, 'V' ) ) THEN - ICOMPZ = 1 - ELSE IF( LSAME( COMPZ, 'I' ) ) THEN - ICOMPZ = 2 - ELSE - ICOMPZ = -1 - END IF - IF( ICOMPZ.LT.0 ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( ( LDZ.LT.1 ) .OR. ( ICOMPZ.GT.0 .AND. LDZ.LT.MAX( 1, - $ N ) ) ) THEN - INFO = -6 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DSTEQR', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( N.EQ.0 ) - $ RETURN -* - IF( N.EQ.1 ) THEN - IF( ICOMPZ.EQ.2 ) - $ Z( 1, 1 ) = ONE - RETURN - END IF -* -* Determine the unit roundoff and over/underflow thresholds. -* - EPS = DLAMCH( 'E' ) - EPS2 = EPS**2 - SAFMIN = DLAMCH( 'S' ) - SAFMAX = ONE / SAFMIN - SSFMAX = SQRT( SAFMAX ) / THREE - SSFMIN = SQRT( SAFMIN ) / EPS2 -* -* Compute the eigenvalues and eigenvectors of the tridiagonal -* matrix. -* - IF( ICOMPZ.EQ.2 ) - $ CALL DLASET( 'Full', N, N, ZERO, ONE, Z, LDZ ) -* - NMAXIT = N*MAXIT - JTOT = 0 -* -* Determine where the matrix splits and choose QL or QR iteration -* for each block, according to whether top or bottom diagonal -* element is smaller. -* - L1 = 1 - NM1 = N - 1 -* - 10 CONTINUE - IF( L1.GT.N ) - $ GO TO 160 - IF( L1.GT.1 ) - $ E( L1-1 ) = ZERO - IF( L1.LE.NM1 ) THEN - DO 20 M = L1, NM1 - TST = ABS( E( M ) ) - IF( TST.EQ.ZERO ) - $ GO TO 30 - IF( TST.LE.( SQRT( ABS( D( M ) ) )*SQRT( ABS( D( M+ - $ 1 ) ) ) )*EPS ) THEN - E( M ) = ZERO - GO TO 30 - END IF - 20 CONTINUE - END IF - M = N -* - 30 CONTINUE - L = L1 - LSV = L - LEND = M - LENDSV = LEND - L1 = M + 1 - IF( LEND.EQ.L ) - $ GO TO 10 -* -* Scale submatrix in rows and columns L to LEND -* - ANORM = DLANST( 'M', LEND-L+1, D( L ), E( L ) ) - ISCALE = 0 - IF( ANORM.EQ.ZERO ) - $ GO TO 10 - IF( ANORM.GT.SSFMAX ) THEN - ISCALE = 1 - CALL DLASCL( 'G', 0, 0, ANORM, SSFMAX, LEND-L+1, 1, D( L ), N, - $ INFO ) - CALL DLASCL( 'G', 0, 0, ANORM, SSFMAX, LEND-L, 1, E( L ), N, - $ INFO ) - ELSE IF( ANORM.LT.SSFMIN ) THEN - ISCALE = 2 - CALL DLASCL( 'G', 0, 0, ANORM, SSFMIN, LEND-L+1, 1, D( L ), N, - $ INFO ) - CALL DLASCL( 'G', 0, 0, ANORM, SSFMIN, LEND-L, 1, E( L ), N, - $ INFO ) - END IF -* -* Choose between QL and QR iteration -* - IF( ABS( D( LEND ) ).LT.ABS( D( L ) ) ) THEN - LEND = LSV - L = LENDSV - END IF -* - IF( LEND.GT.L ) THEN -* -* QL Iteration -* -* Look for small subdiagonal element. -* - 40 CONTINUE - IF( L.NE.LEND ) THEN - LENDM1 = LEND - 1 - DO 50 M = L, LENDM1 - TST = ABS( E( M ) )**2 - IF( TST.LE.( EPS2*ABS( D( M ) ) )*ABS( D( M+1 ) )+ - $ SAFMIN )GO TO 60 - 50 CONTINUE - END IF -* - M = LEND -* - 60 CONTINUE - IF( M.LT.LEND ) - $ E( M ) = ZERO - P = D( L ) - IF( M.EQ.L ) - $ GO TO 80 -* -* If remaining matrix is 2-by-2, use DLAE2 or SLAEV2 -* to compute its eigensystem. -* - IF( M.EQ.L+1 ) THEN - IF( ICOMPZ.GT.0 ) THEN - CALL DLAEV2( D( L ), E( L ), D( L+1 ), RT1, RT2, C, S ) - WORK( L ) = C - WORK( N-1+L ) = S - CALL DLASR( 'R', 'V', 'B', N, 2, WORK( L ), - $ WORK( N-1+L ), Z( 1, L ), LDZ ) - ELSE - CALL DLAE2( D( L ), E( L ), D( L+1 ), RT1, RT2 ) - END IF - D( L ) = RT1 - D( L+1 ) = RT2 - E( L ) = ZERO - L = L + 2 - IF( L.LE.LEND ) - $ GO TO 40 - GO TO 140 - END IF -* - IF( JTOT.EQ.NMAXIT ) - $ GO TO 140 - JTOT = JTOT + 1 -* -* Form shift. -* - G = ( D( L+1 )-P ) / ( TWO*E( L ) ) - R = DLAPY2( G, ONE ) - G = D( M ) - P + ( E( L ) / ( G+SIGN( R, G ) ) ) -* - S = ONE - C = ONE - P = ZERO -* -* Inner loop -* - MM1 = M - 1 - DO 70 I = MM1, L, -1 - F = S*E( I ) - B = C*E( I ) - CALL DLARTG( G, F, C, S, R ) - IF( I.NE.M-1 ) - $ E( I+1 ) = R - G = D( I+1 ) - P - R = ( D( I )-G )*S + TWO*C*B - P = S*R - D( I+1 ) = G + P - G = C*R - B -* -* If eigenvectors are desired, then save rotations. -* - IF( ICOMPZ.GT.0 ) THEN - WORK( I ) = C - WORK( N-1+I ) = -S - END IF -* - 70 CONTINUE -* -* If eigenvectors are desired, then apply saved rotations. -* - IF( ICOMPZ.GT.0 ) THEN - MM = M - L + 1 - CALL DLASR( 'R', 'V', 'B', N, MM, WORK( L ), WORK( N-1+L ), - $ Z( 1, L ), LDZ ) - END IF -* - D( L ) = D( L ) - P - E( L ) = G - GO TO 40 -* -* Eigenvalue found. -* - 80 CONTINUE - D( L ) = P -* - L = L + 1 - IF( L.LE.LEND ) - $ GO TO 40 - GO TO 140 -* - ELSE -* -* QR Iteration -* -* Look for small superdiagonal element. -* - 90 CONTINUE - IF( L.NE.LEND ) THEN - LENDP1 = LEND + 1 - DO 100 M = L, LENDP1, -1 - TST = ABS( E( M-1 ) )**2 - IF( TST.LE.( EPS2*ABS( D( M ) ) )*ABS( D( M-1 ) )+ - $ SAFMIN )GO TO 110 - 100 CONTINUE - END IF -* - M = LEND -* - 110 CONTINUE - IF( M.GT.LEND ) - $ E( M-1 ) = ZERO - P = D( L ) - IF( M.EQ.L ) - $ GO TO 130 -* -* If remaining matrix is 2-by-2, use DLAE2 or SLAEV2 -* to compute its eigensystem. -* - IF( M.EQ.L-1 ) THEN - IF( ICOMPZ.GT.0 ) THEN - CALL DLAEV2( D( L-1 ), E( L-1 ), D( L ), RT1, RT2, C, S ) - WORK( M ) = C - WORK( N-1+M ) = S - CALL DLASR( 'R', 'V', 'F', N, 2, WORK( M ), - $ WORK( N-1+M ), Z( 1, L-1 ), LDZ ) - ELSE - CALL DLAE2( D( L-1 ), E( L-1 ), D( L ), RT1, RT2 ) - END IF - D( L-1 ) = RT1 - D( L ) = RT2 - E( L-1 ) = ZERO - L = L - 2 - IF( L.GE.LEND ) - $ GO TO 90 - GO TO 140 - END IF -* - IF( JTOT.EQ.NMAXIT ) - $ GO TO 140 - JTOT = JTOT + 1 -* -* Form shift. -* - G = ( D( L-1 )-P ) / ( TWO*E( L-1 ) ) - R = DLAPY2( G, ONE ) - G = D( M ) - P + ( E( L-1 ) / ( G+SIGN( R, G ) ) ) -* - S = ONE - C = ONE - P = ZERO -* -* Inner loop -* - LM1 = L - 1 - DO 120 I = M, LM1 - F = S*E( I ) - B = C*E( I ) - CALL DLARTG( G, F, C, S, R ) - IF( I.NE.M ) - $ E( I-1 ) = R - G = D( I ) - P - R = ( D( I+1 )-G )*S + TWO*C*B - P = S*R - D( I ) = G + P - G = C*R - B -* -* If eigenvectors are desired, then save rotations. -* - IF( ICOMPZ.GT.0 ) THEN - WORK( I ) = C - WORK( N-1+I ) = S - END IF -* - 120 CONTINUE -* -* If eigenvectors are desired, then apply saved rotations. -* - IF( ICOMPZ.GT.0 ) THEN - MM = L - M + 1 - CALL DLASR( 'R', 'V', 'F', N, MM, WORK( M ), WORK( N-1+M ), - $ Z( 1, M ), LDZ ) - END IF -* - D( L ) = D( L ) - P - E( LM1 ) = G - GO TO 90 -* -* Eigenvalue found. -* - 130 CONTINUE - D( L ) = P -* - L = L - 1 - IF( L.GE.LEND ) - $ GO TO 90 - GO TO 140 -* - END IF -* -* Undo scaling if necessary -* - 140 CONTINUE - IF( ISCALE.EQ.1 ) THEN - CALL DLASCL( 'G', 0, 0, SSFMAX, ANORM, LENDSV-LSV+1, 1, - $ D( LSV ), N, INFO ) - CALL DLASCL( 'G', 0, 0, SSFMAX, ANORM, LENDSV-LSV, 1, E( LSV ), - $ N, INFO ) - ELSE IF( ISCALE.EQ.2 ) THEN - CALL DLASCL( 'G', 0, 0, SSFMIN, ANORM, LENDSV-LSV+1, 1, - $ D( LSV ), N, INFO ) - CALL DLASCL( 'G', 0, 0, SSFMIN, ANORM, LENDSV-LSV, 1, E( LSV ), - $ N, INFO ) - END IF -* -* Check for no convergence to an eigenvalue after a total -* of N*MAXIT iterations. -* - IF( JTOT.LT.NMAXIT ) - $ GO TO 10 - DO 150 I = 1, N - 1 - IF( E( I ).NE.ZERO ) - $ INFO = INFO + 1 - 150 CONTINUE - GO TO 190 -* -* Order eigenvalues and eigenvectors. -* - 160 CONTINUE - IF( ICOMPZ.EQ.0 ) THEN -* -* Use Quick Sort -* - CALL DLASRT( 'I', N, D, INFO ) -* - ELSE -* -* Use Selection Sort to minimize swaps of eigenvectors -* - DO 180 II = 2, N - I = II - 1 - K = I - P = D( I ) - DO 170 J = II, N - IF( D( J ).LT.P ) THEN - K = J - P = D( J ) - END IF - 170 CONTINUE - IF( K.NE.I ) THEN - D( K ) = D( I ) - D( I ) = P - CALL DSWAP( N, Z( 1, I ), 1, Z( 1, K ), 1 ) - END IF - 180 CONTINUE - END IF -* - 190 CONTINUE - RETURN -* -* End of DSTEQR -* - END diff --git a/lib/linalg/fortran/dsterf.f b/lib/linalg/fortran/dsterf.f deleted file mode 100644 index b0f8d36084..0000000000 --- a/lib/linalg/fortran/dsterf.f +++ /dev/null @@ -1,423 +0,0 @@ -*> \brief \b DSTERF -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DSTERF + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DSTERF( N, D, E, INFO ) -* -* .. Scalar Arguments .. -* INTEGER INFO, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION D( * ), E( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DSTERF computes all eigenvalues of a symmetric tridiagonal matrix -*> using the Pal-Walker-Kahan variant of the QL or QR algorithm. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrix. N >= 0. -*> \endverbatim -*> -*> \param[in,out] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension (N) -*> On entry, the n diagonal elements of the tridiagonal matrix. -*> On exit, if INFO = 0, the eigenvalues in ascending order. -*> \endverbatim -*> -*> \param[in,out] E -*> \verbatim -*> E is DOUBLE PRECISION array, dimension (N-1) -*> On entry, the (n-1) subdiagonal elements of the tridiagonal -*> matrix. -*> On exit, E has been destroyed. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: the algorithm failed to find all of the eigenvalues in -*> a total of 30*N iterations; if INFO = i, then i -*> elements of E have not converged to zero. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup auxOTHERcomputational -* -* ===================================================================== - SUBROUTINE DSTERF( N, D, E, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INFO, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION D( * ), E( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, ONE, TWO, THREE - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0, - $ THREE = 3.0D0 ) - INTEGER MAXIT - PARAMETER ( MAXIT = 30 ) -* .. -* .. Local Scalars .. - INTEGER I, ISCALE, JTOT, L, L1, LEND, LENDSV, LSV, M, - $ NMAXIT - DOUBLE PRECISION ALPHA, ANORM, BB, C, EPS, EPS2, GAMMA, OLDC, - $ OLDGAM, P, R, RT1, RT2, RTE, S, SAFMAX, SAFMIN, - $ SIGMA, SSFMAX, SSFMIN, RMAX -* .. -* .. External Functions .. - DOUBLE PRECISION DLAMCH, DLANST, DLAPY2 - EXTERNAL DLAMCH, DLANST, DLAPY2 -* .. -* .. External Subroutines .. - EXTERNAL DLAE2, DLASCL, DLASRT, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, SIGN, SQRT -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 -* -* Quick return if possible -* - IF( N.LT.0 ) THEN - INFO = -1 - CALL XERBLA( 'DSTERF', -INFO ) - RETURN - END IF - IF( N.LE.1 ) - $ RETURN -* -* Determine the unit roundoff for this environment. -* - EPS = DLAMCH( 'E' ) - EPS2 = EPS**2 - SAFMIN = DLAMCH( 'S' ) - SAFMAX = ONE / SAFMIN - SSFMAX = SQRT( SAFMAX ) / THREE - SSFMIN = SQRT( SAFMIN ) / EPS2 - RMAX = DLAMCH( 'O' ) -* -* Compute the eigenvalues of the tridiagonal matrix. -* - NMAXIT = N*MAXIT - SIGMA = ZERO - JTOT = 0 -* -* Determine where the matrix splits and choose QL or QR iteration -* for each block, according to whether top or bottom diagonal -* element is smaller. -* - L1 = 1 -* - 10 CONTINUE - IF( L1.GT.N ) - $ GO TO 170 - IF( L1.GT.1 ) - $ E( L1-1 ) = ZERO - DO 20 M = L1, N - 1 - IF( ABS( E( M ) ).LE.( SQRT( ABS( D( M ) ) )*SQRT( ABS( D( M+ - $ 1 ) ) ) )*EPS ) THEN - E( M ) = ZERO - GO TO 30 - END IF - 20 CONTINUE - M = N -* - 30 CONTINUE - L = L1 - LSV = L - LEND = M - LENDSV = LEND - L1 = M + 1 - IF( LEND.EQ.L ) - $ GO TO 10 -* -* Scale submatrix in rows and columns L to LEND -* - ANORM = DLANST( 'M', LEND-L+1, D( L ), E( L ) ) - ISCALE = 0 - IF( ANORM.EQ.ZERO ) - $ GO TO 10 - IF( (ANORM.GT.SSFMAX) ) THEN - ISCALE = 1 - CALL DLASCL( 'G', 0, 0, ANORM, SSFMAX, LEND-L+1, 1, D( L ), N, - $ INFO ) - CALL DLASCL( 'G', 0, 0, ANORM, SSFMAX, LEND-L, 1, E( L ), N, - $ INFO ) - ELSE IF( ANORM.LT.SSFMIN ) THEN - ISCALE = 2 - CALL DLASCL( 'G', 0, 0, ANORM, SSFMIN, LEND-L+1, 1, D( L ), N, - $ INFO ) - CALL DLASCL( 'G', 0, 0, ANORM, SSFMIN, LEND-L, 1, E( L ), N, - $ INFO ) - END IF -* - DO 40 I = L, LEND - 1 - E( I ) = E( I )**2 - 40 CONTINUE -* -* Choose between QL and QR iteration -* - IF( ABS( D( LEND ) ).LT.ABS( D( L ) ) ) THEN - LEND = LSV - L = LENDSV - END IF -* - IF( LEND.GE.L ) THEN -* -* QL Iteration -* -* Look for small subdiagonal element. -* - 50 CONTINUE - IF( L.NE.LEND ) THEN - DO 60 M = L, LEND - 1 - IF( ABS( E( M ) ).LE.EPS2*ABS( D( M )*D( M+1 ) ) ) - $ GO TO 70 - 60 CONTINUE - END IF - M = LEND -* - 70 CONTINUE - IF( M.LT.LEND ) - $ E( M ) = ZERO - P = D( L ) - IF( M.EQ.L ) - $ GO TO 90 -* -* If remaining matrix is 2 by 2, use DLAE2 to compute its -* eigenvalues. -* - IF( M.EQ.L+1 ) THEN - RTE = SQRT( E( L ) ) - CALL DLAE2( D( L ), RTE, D( L+1 ), RT1, RT2 ) - D( L ) = RT1 - D( L+1 ) = RT2 - E( L ) = ZERO - L = L + 2 - IF( L.LE.LEND ) - $ GO TO 50 - GO TO 150 - END IF -* - IF( JTOT.EQ.NMAXIT ) - $ GO TO 150 - JTOT = JTOT + 1 -* -* Form shift. -* - RTE = SQRT( E( L ) ) - SIGMA = ( D( L+1 )-P ) / ( TWO*RTE ) - R = DLAPY2( SIGMA, ONE ) - SIGMA = P - ( RTE / ( SIGMA+SIGN( R, SIGMA ) ) ) -* - C = ONE - S = ZERO - GAMMA = D( M ) - SIGMA - P = GAMMA*GAMMA -* -* Inner loop -* - DO 80 I = M - 1, L, -1 - BB = E( I ) - R = P + BB - IF( I.NE.M-1 ) - $ E( I+1 ) = S*R - OLDC = C - C = P / R - S = BB / R - OLDGAM = GAMMA - ALPHA = D( I ) - GAMMA = C*( ALPHA-SIGMA ) - S*OLDGAM - D( I+1 ) = OLDGAM + ( ALPHA-GAMMA ) - IF( C.NE.ZERO ) THEN - P = ( GAMMA*GAMMA ) / C - ELSE - P = OLDC*BB - END IF - 80 CONTINUE -* - E( L ) = S*P - D( L ) = SIGMA + GAMMA - GO TO 50 -* -* Eigenvalue found. -* - 90 CONTINUE - D( L ) = P -* - L = L + 1 - IF( L.LE.LEND ) - $ GO TO 50 - GO TO 150 -* - ELSE -* -* QR Iteration -* -* Look for small superdiagonal element. -* - 100 CONTINUE - DO 110 M = L, LEND + 1, -1 - IF( ABS( E( M-1 ) ).LE.EPS2*ABS( D( M )*D( M-1 ) ) ) - $ GO TO 120 - 110 CONTINUE - M = LEND -* - 120 CONTINUE - IF( M.GT.LEND ) - $ E( M-1 ) = ZERO - P = D( L ) - IF( M.EQ.L ) - $ GO TO 140 -* -* If remaining matrix is 2 by 2, use DLAE2 to compute its -* eigenvalues. -* - IF( M.EQ.L-1 ) THEN - RTE = SQRT( E( L-1 ) ) - CALL DLAE2( D( L ), RTE, D( L-1 ), RT1, RT2 ) - D( L ) = RT1 - D( L-1 ) = RT2 - E( L-1 ) = ZERO - L = L - 2 - IF( L.GE.LEND ) - $ GO TO 100 - GO TO 150 - END IF -* - IF( JTOT.EQ.NMAXIT ) - $ GO TO 150 - JTOT = JTOT + 1 -* -* Form shift. -* - RTE = SQRT( E( L-1 ) ) - SIGMA = ( D( L-1 )-P ) / ( TWO*RTE ) - R = DLAPY2( SIGMA, ONE ) - SIGMA = P - ( RTE / ( SIGMA+SIGN( R, SIGMA ) ) ) -* - C = ONE - S = ZERO - GAMMA = D( M ) - SIGMA - P = GAMMA*GAMMA -* -* Inner loop -* - DO 130 I = M, L - 1 - BB = E( I ) - R = P + BB - IF( I.NE.M ) - $ E( I-1 ) = S*R - OLDC = C - C = P / R - S = BB / R - OLDGAM = GAMMA - ALPHA = D( I+1 ) - GAMMA = C*( ALPHA-SIGMA ) - S*OLDGAM - D( I ) = OLDGAM + ( ALPHA-GAMMA ) - IF( C.NE.ZERO ) THEN - P = ( GAMMA*GAMMA ) / C - ELSE - P = OLDC*BB - END IF - 130 CONTINUE -* - E( L-1 ) = S*P - D( L ) = SIGMA + GAMMA - GO TO 100 -* -* Eigenvalue found. -* - 140 CONTINUE - D( L ) = P -* - L = L - 1 - IF( L.GE.LEND ) - $ GO TO 100 - GO TO 150 -* - END IF -* -* Undo scaling if necessary -* - 150 CONTINUE - IF( ISCALE.EQ.1 ) - $ CALL DLASCL( 'G', 0, 0, SSFMAX, ANORM, LENDSV-LSV+1, 1, - $ D( LSV ), N, INFO ) - IF( ISCALE.EQ.2 ) - $ CALL DLASCL( 'G', 0, 0, SSFMIN, ANORM, LENDSV-LSV+1, 1, - $ D( LSV ), N, INFO ) -* -* Check for no convergence to an eigenvalue after a total -* of N*MAXIT iterations. -* - IF( JTOT.LT.NMAXIT ) - $ GO TO 10 - DO 160 I = 1, N - 1 - IF( E( I ).NE.ZERO ) - $ INFO = INFO + 1 - 160 CONTINUE - GO TO 180 -* -* Sort eigenvalues in increasing order. -* - 170 CONTINUE - CALL DLASRT( 'I', N, D, INFO ) -* - 180 CONTINUE - RETURN -* -* End of DSTERF -* - END diff --git a/lib/linalg/fortran/dswap.f b/lib/linalg/fortran/dswap.f deleted file mode 100644 index b7600aa2d4..0000000000 --- a/lib/linalg/fortran/dswap.f +++ /dev/null @@ -1,153 +0,0 @@ -*> \brief \b DSWAP -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE DSWAP(N,DX,INCX,DY,INCY) -* -* .. Scalar Arguments .. -* INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION DX(*),DY(*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DSWAP interchanges two vectors. -*> uses unrolled loops for increments equal to 1. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> number of elements in input vector(s) -*> \endverbatim -*> -*> \param[in,out] DX -*> \verbatim -*> DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> storage spacing between elements of DX -*> \endverbatim -*> -*> \param[in,out] DY -*> \verbatim -*> DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) -*> \endverbatim -*> -*> \param[in] INCY -*> \verbatim -*> INCY is INTEGER -*> storage spacing between elements of DY -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup double_blas_level1 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> jack dongarra, linpack, 3/11/78. -*> modified 12/3/93, array(1) declarations changed to array(*) -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DSWAP(N,DX,INCX,DY,INCY) -* -* -- Reference BLAS level1 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. - DOUBLE PRECISION DX(*),DY(*) -* .. -* -* ===================================================================== -* -* .. Local Scalars .. - DOUBLE PRECISION DTEMP - INTEGER I,IX,IY,M,MP1 -* .. -* .. Intrinsic Functions .. - INTRINSIC MOD -* .. - IF (N.LE.0) RETURN - IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN -* -* code for both increments equal to 1 -* -* -* clean-up loop -* - M = MOD(N,3) - IF (M.NE.0) THEN - DO I = 1,M - DTEMP = DX(I) - DX(I) = DY(I) - DY(I) = DTEMP - END DO - IF (N.LT.3) RETURN - END IF - MP1 = M + 1 - DO I = MP1,N,3 - DTEMP = DX(I) - DX(I) = DY(I) - DY(I) = DTEMP - DTEMP = DX(I+1) - DX(I+1) = DY(I+1) - DY(I+1) = DTEMP - DTEMP = DX(I+2) - DX(I+2) = DY(I+2) - DY(I+2) = DTEMP - END DO - ELSE -* -* code for unequal increments or equal increments not equal -* to 1 -* - IX = 1 - IY = 1 - IF (INCX.LT.0) IX = (-N+1)*INCX + 1 - IF (INCY.LT.0) IY = (-N+1)*INCY + 1 - DO I = 1,N - DTEMP = DX(IX) - DX(IX) = DY(IY) - DY(IY) = DTEMP - IX = IX + INCX - IY = IY + INCY - END DO - END IF - RETURN -* -* End of DSWAP -* - END diff --git a/lib/linalg/fortran/dsyev.f b/lib/linalg/fortran/dsyev.f deleted file mode 100644 index da7557ee02..0000000000 --- a/lib/linalg/fortran/dsyev.f +++ /dev/null @@ -1,283 +0,0 @@ -*> \brief DSYEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DSYEV + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DSYEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER JOBZ, UPLO -* INTEGER INFO, LDA, LWORK, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DSYEV computes all eigenvalues and, optionally, eigenvectors of a -*> real symmetric matrix A. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] JOBZ -*> \verbatim -*> JOBZ is CHARACTER*1 -*> = 'N': Compute eigenvalues only; -*> = 'V': Compute eigenvalues and eigenvectors. -*> \endverbatim -*> -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> = 'U': Upper triangle of A is stored; -*> = 'L': Lower triangle of A is stored. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA, N) -*> On entry, the symmetric matrix A. If UPLO = 'U', the -*> leading N-by-N upper triangular part of A contains the -*> upper triangular part of the matrix A. If UPLO = 'L', -*> the leading N-by-N lower triangular part of A contains -*> the lower triangular part of the matrix A. -*> On exit, if JOBZ = 'V', then if INFO = 0, A contains the -*> orthonormal eigenvectors of the matrix A. -*> If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') -*> or the upper triangle (if UPLO='U') of A, including the -*> diagonal, is destroyed. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,N). -*> \endverbatim -*> -*> \param[out] W -*> \verbatim -*> W is DOUBLE PRECISION array, dimension (N) -*> If INFO = 0, the eigenvalues in ascending order. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) -*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -*> \endverbatim -*> -*> \param[in] LWORK -*> \verbatim -*> LWORK is INTEGER -*> The length of the array WORK. LWORK >= max(1,3*N-1). -*> For optimal efficiency, LWORK >= (NB+2)*N, -*> where NB is the blocksize for DSYTRD returned by ILAENV. -*> -*> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal size of the WORK array, returns -*> this value as the first entry of the WORK array, and no error -*> message related to LWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the algorithm failed to converge; i -*> off-diagonal elements of an intermediate tridiagonal -*> form did not converge to zero. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleSYeigen -* -* ===================================================================== - SUBROUTINE DSYEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, INFO ) -* -* -- LAPACK driver routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER JOBZ, UPLO - INTEGER INFO, LDA, LWORK, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) -* .. -* .. Local Scalars .. - LOGICAL LOWER, LQUERY, WANTZ - INTEGER IINFO, IMAX, INDE, INDTAU, INDWRK, ISCALE, - $ LLWORK, LWKOPT, NB - DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, - $ SMLNUM -* .. -* .. External Functions .. - LOGICAL LSAME - INTEGER ILAENV - DOUBLE PRECISION DLAMCH, DLANSY - EXTERNAL LSAME, ILAENV, DLAMCH, DLANSY -* .. -* .. External Subroutines .. - EXTERNAL DLASCL, DORGTR, DSCAL, DSTEQR, DSTERF, DSYTRD, - $ XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, SQRT -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - WANTZ = LSAME( JOBZ, 'V' ) - LOWER = LSAME( UPLO, 'L' ) - LQUERY = ( LWORK.EQ.-1 ) -* - INFO = 0 - IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN - INFO = -1 - ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN - INFO = -2 - ELSE IF( N.LT.0 ) THEN - INFO = -3 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -5 - END IF -* - IF( INFO.EQ.0 ) THEN - NB = ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 ) - LWKOPT = MAX( 1, ( NB+2 )*N ) - WORK( 1 ) = LWKOPT -* - IF( LWORK.LT.MAX( 1, 3*N-1 ) .AND. .NOT.LQUERY ) - $ INFO = -8 - END IF -* - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DSYEV ', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - RETURN - END IF -* -* Quick return if possible -* - IF( N.EQ.0 ) THEN - RETURN - END IF -* - IF( N.EQ.1 ) THEN - W( 1 ) = A( 1, 1 ) - WORK( 1 ) = 2 - IF( WANTZ ) - $ A( 1, 1 ) = ONE - RETURN - END IF -* -* Get machine constants. -* - SAFMIN = DLAMCH( 'Safe minimum' ) - EPS = DLAMCH( 'Precision' ) - SMLNUM = SAFMIN / EPS - BIGNUM = ONE / SMLNUM - RMIN = SQRT( SMLNUM ) - RMAX = SQRT( BIGNUM ) -* -* Scale matrix to allowable range, if necessary. -* - ANRM = DLANSY( 'M', UPLO, N, A, LDA, WORK ) - ISCALE = 0 - IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN - ISCALE = 1 - SIGMA = RMIN / ANRM - ELSE IF( ANRM.GT.RMAX ) THEN - ISCALE = 1 - SIGMA = RMAX / ANRM - END IF - IF( ISCALE.EQ.1 ) - $ CALL DLASCL( UPLO, 0, 0, ONE, SIGMA, N, N, A, LDA, INFO ) -* -* Call DSYTRD to reduce symmetric matrix to tridiagonal form. -* - INDE = 1 - INDTAU = INDE + N - INDWRK = INDTAU + N - LLWORK = LWORK - INDWRK + 1 - CALL DSYTRD( UPLO, N, A, LDA, W, WORK( INDE ), WORK( INDTAU ), - $ WORK( INDWRK ), LLWORK, IINFO ) -* -* For eigenvalues only, call DSTERF. For eigenvectors, first call -* DORGTR to generate the orthogonal matrix, then call DSTEQR. -* - IF( .NOT.WANTZ ) THEN - CALL DSTERF( N, W, WORK( INDE ), INFO ) - ELSE - CALL DORGTR( UPLO, N, A, LDA, WORK( INDTAU ), WORK( INDWRK ), - $ LLWORK, IINFO ) - CALL DSTEQR( JOBZ, N, W, WORK( INDE ), A, LDA, WORK( INDTAU ), - $ INFO ) - END IF -* -* If matrix was scaled, then rescale eigenvalues appropriately. -* - IF( ISCALE.EQ.1 ) THEN - IF( INFO.EQ.0 ) THEN - IMAX = N - ELSE - IMAX = INFO - 1 - END IF - CALL DSCAL( IMAX, ONE / SIGMA, W, 1 ) - END IF -* -* Set WORK(1) to optimal workspace size. -* - WORK( 1 ) = LWKOPT -* - RETURN -* -* End of DSYEV -* - END diff --git a/lib/linalg/fortran/dsyevd.f b/lib/linalg/fortran/dsyevd.f deleted file mode 100644 index eaaecd8d98..0000000000 --- a/lib/linalg/fortran/dsyevd.f +++ /dev/null @@ -1,354 +0,0 @@ -*> \brief DSYEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DSYEVD + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK, -* LIWORK, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER JOBZ, UPLO -* INTEGER INFO, LDA, LIWORK, LWORK, N -* .. -* .. Array Arguments .. -* INTEGER IWORK( * ) -* DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DSYEVD computes all eigenvalues and, optionally, eigenvectors of a -*> real symmetric matrix A. If eigenvectors are desired, it uses a -*> divide and conquer algorithm. -*> -*> The divide and conquer algorithm makes very mild assumptions about -*> floating point arithmetic. It will work on machines with a guard -*> digit in add/subtract, or on those binary machines without guard -*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or -*> Cray-2. It could conceivably fail on hexadecimal or decimal machines -*> without guard digits, but we know of none. -*> -*> Because of large use of BLAS of level 3, DSYEVD needs N**2 more -*> workspace than DSYEVX. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] JOBZ -*> \verbatim -*> JOBZ is CHARACTER*1 -*> = 'N': Compute eigenvalues only; -*> = 'V': Compute eigenvalues and eigenvectors. -*> \endverbatim -*> -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> = 'U': Upper triangle of A is stored; -*> = 'L': Lower triangle of A is stored. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA, N) -*> On entry, the symmetric matrix A. If UPLO = 'U', the -*> leading N-by-N upper triangular part of A contains the -*> upper triangular part of the matrix A. If UPLO = 'L', -*> the leading N-by-N lower triangular part of A contains -*> the lower triangular part of the matrix A. -*> On exit, if JOBZ = 'V', then if INFO = 0, A contains the -*> orthonormal eigenvectors of the matrix A. -*> If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') -*> or the upper triangle (if UPLO='U') of A, including the -*> diagonal, is destroyed. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,N). -*> \endverbatim -*> -*> \param[out] W -*> \verbatim -*> W is DOUBLE PRECISION array, dimension (N) -*> If INFO = 0, the eigenvalues in ascending order. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, -*> dimension (LWORK) -*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -*> \endverbatim -*> -*> \param[in] LWORK -*> \verbatim -*> LWORK is INTEGER -*> The dimension of the array WORK. -*> If N <= 1, LWORK must be at least 1. -*> If JOBZ = 'N' and N > 1, LWORK must be at least 2*N+1. -*> If JOBZ = 'V' and N > 1, LWORK must be at least -*> 1 + 6*N + 2*N**2. -*> -*> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal sizes of the WORK and IWORK -*> arrays, returns these values as the first entries of the WORK -*> and IWORK arrays, and no error message related to LWORK or -*> LIWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] IWORK -*> \verbatim -*> IWORK is INTEGER array, dimension (MAX(1,LIWORK)) -*> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. -*> \endverbatim -*> -*> \param[in] LIWORK -*> \verbatim -*> LIWORK is INTEGER -*> The dimension of the array IWORK. -*> If N <= 1, LIWORK must be at least 1. -*> If JOBZ = 'N' and N > 1, LIWORK must be at least 1. -*> If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N. -*> -*> If LIWORK = -1, then a workspace query is assumed; the -*> routine only calculates the optimal sizes of the WORK and -*> IWORK arrays, returns these values as the first entries of -*> the WORK and IWORK arrays, and no error message related to -*> LWORK or LIWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i and JOBZ = 'N', then the algorithm failed -*> to converge; i off-diagonal elements of an intermediate -*> tridiagonal form did not converge to zero; -*> if INFO = i and JOBZ = 'V', then the algorithm failed -*> to compute an eigenvalue while working on the submatrix -*> lying in rows and columns INFO/(N+1) through -*> mod(INFO,N+1). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleSYeigen -* -*> \par Contributors: -* ================== -*> -*> Jeff Rutter, Computer Science Division, University of California -*> at Berkeley, USA \n -*> Modified by Francoise Tisseur, University of Tennessee \n -*> Modified description of INFO. Sven, 16 Feb 05. \n - - -*> -* ===================================================================== - SUBROUTINE DSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK, - $ LIWORK, INFO ) -* -* -- LAPACK driver routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER JOBZ, UPLO - INTEGER INFO, LDA, LIWORK, LWORK, N -* .. -* .. Array Arguments .. - INTEGER IWORK( * ) - DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) -* .. -* .. Local Scalars .. -* - LOGICAL LOWER, LQUERY, WANTZ - INTEGER IINFO, INDE, INDTAU, INDWK2, INDWRK, ISCALE, - $ LIOPT, LIWMIN, LLWORK, LLWRK2, LOPT, LWMIN - DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, - $ SMLNUM -* .. -* .. External Functions .. - LOGICAL LSAME - INTEGER ILAENV - DOUBLE PRECISION DLAMCH, DLANSY - EXTERNAL LSAME, DLAMCH, DLANSY, ILAENV -* .. -* .. External Subroutines .. - EXTERNAL DLACPY, DLASCL, DORMTR, DSCAL, DSTEDC, DSTERF, - $ DSYTRD, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, SQRT -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - WANTZ = LSAME( JOBZ, 'V' ) - LOWER = LSAME( UPLO, 'L' ) - LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 ) -* - INFO = 0 - IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN - INFO = -1 - ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN - INFO = -2 - ELSE IF( N.LT.0 ) THEN - INFO = -3 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -5 - END IF -* - IF( INFO.EQ.0 ) THEN - IF( N.LE.1 ) THEN - LIWMIN = 1 - LWMIN = 1 - LOPT = LWMIN - LIOPT = LIWMIN - ELSE - IF( WANTZ ) THEN - LIWMIN = 3 + 5*N - LWMIN = 1 + 6*N + 2*N**2 - ELSE - LIWMIN = 1 - LWMIN = 2*N + 1 - END IF - LOPT = MAX( LWMIN, 2*N + - $ N*ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 ) ) - LIOPT = LIWMIN - END IF - WORK( 1 ) = LOPT - IWORK( 1 ) = LIOPT -* - IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN - INFO = -8 - ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN - INFO = -10 - END IF - END IF -* - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DSYEVD', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - RETURN - END IF -* -* Quick return if possible -* - IF( N.EQ.0 ) - $ RETURN -* - IF( N.EQ.1 ) THEN - W( 1 ) = A( 1, 1 ) - IF( WANTZ ) - $ A( 1, 1 ) = ONE - RETURN - END IF -* -* Get machine constants. -* - SAFMIN = DLAMCH( 'Safe minimum' ) - EPS = DLAMCH( 'Precision' ) - SMLNUM = SAFMIN / EPS - BIGNUM = ONE / SMLNUM - RMIN = SQRT( SMLNUM ) - RMAX = SQRT( BIGNUM ) -* -* Scale matrix to allowable range, if necessary. -* - ANRM = DLANSY( 'M', UPLO, N, A, LDA, WORK ) - ISCALE = 0 - IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN - ISCALE = 1 - SIGMA = RMIN / ANRM - ELSE IF( ANRM.GT.RMAX ) THEN - ISCALE = 1 - SIGMA = RMAX / ANRM - END IF - IF( ISCALE.EQ.1 ) - $ CALL DLASCL( UPLO, 0, 0, ONE, SIGMA, N, N, A, LDA, INFO ) -* -* Call DSYTRD to reduce symmetric matrix to tridiagonal form. -* - INDE = 1 - INDTAU = INDE + N - INDWRK = INDTAU + N - LLWORK = LWORK - INDWRK + 1 - INDWK2 = INDWRK + N*N - LLWRK2 = LWORK - INDWK2 + 1 -* - CALL DSYTRD( UPLO, N, A, LDA, W, WORK( INDE ), WORK( INDTAU ), - $ WORK( INDWRK ), LLWORK, IINFO ) -* -* For eigenvalues only, call DSTERF. For eigenvectors, first call -* DSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the -* tridiagonal matrix, then call DORMTR to multiply it by the -* Householder transformations stored in A. -* - IF( .NOT.WANTZ ) THEN - CALL DSTERF( N, W, WORK( INDE ), INFO ) - ELSE - CALL DSTEDC( 'I', N, W, WORK( INDE ), WORK( INDWRK ), N, - $ WORK( INDWK2 ), LLWRK2, IWORK, LIWORK, INFO ) - CALL DORMTR( 'L', UPLO, 'N', N, N, A, LDA, WORK( INDTAU ), - $ WORK( INDWRK ), N, WORK( INDWK2 ), LLWRK2, IINFO ) - CALL DLACPY( 'A', N, N, WORK( INDWRK ), N, A, LDA ) - END IF -* -* If matrix was scaled, then rescale eigenvalues appropriately. -* - IF( ISCALE.EQ.1 ) - $ CALL DSCAL( N, ONE / SIGMA, W, 1 ) -* - WORK( 1 ) = LOPT - IWORK( 1 ) = LIOPT -* - RETURN -* -* End of DSYEVD -* - END diff --git a/lib/linalg/fortran/dsygs2.f b/lib/linalg/fortran/dsygs2.f deleted file mode 100644 index 8a39bea77e..0000000000 --- a/lib/linalg/fortran/dsygs2.f +++ /dev/null @@ -1,280 +0,0 @@ -*> \brief \b DSYGS2 reduces a symmetric definite generalized eigenproblem to standard form, using the factorization results obtained from spotrf (unblocked algorithm). -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DSYGS2 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DSYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER UPLO -* INTEGER INFO, ITYPE, LDA, LDB, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), B( LDB, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DSYGS2 reduces a real symmetric-definite generalized eigenproblem -*> to standard form. -*> -*> If ITYPE = 1, the problem is A*x = lambda*B*x, -*> and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T) -*> -*> If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or -*> B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T *A*L. -*> -*> B must have been previously factorized as U**T *U or L*L**T by DPOTRF. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] ITYPE -*> \verbatim -*> ITYPE is INTEGER -*> = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T); -*> = 2 or 3: compute U*A*U**T or L**T *A*L. -*> \endverbatim -*> -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> Specifies whether the upper or lower triangular part of the -*> symmetric matrix A is stored, and how B has been factorized. -*> = 'U': Upper triangular -*> = 'L': Lower triangular -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrices A and B. N >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the symmetric matrix A. If UPLO = 'U', the leading -*> n by n upper triangular part of A contains the upper -*> triangular part of the matrix A, and the strictly lower -*> triangular part of A is not referenced. If UPLO = 'L', the -*> leading n by n lower triangular part of A contains the lower -*> triangular part of the matrix A, and the strictly upper -*> triangular part of A is not referenced. -*> -*> On exit, if INFO = 0, the transformed matrix, stored in the -*> same format as A. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,N). -*> \endverbatim -*> -*> \param[in] B -*> \verbatim -*> B is DOUBLE PRECISION array, dimension (LDB,N) -*> The triangular factor from the Cholesky factorization of B, -*> as returned by DPOTRF. -*> \endverbatim -*> -*> \param[in] LDB -*> \verbatim -*> LDB is INTEGER -*> The leading dimension of the array B. LDB >= max(1,N). -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit. -*> < 0: if INFO = -i, the i-th argument had an illegal value. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleSYcomputational -* -* ===================================================================== - SUBROUTINE DSYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER UPLO - INTEGER INFO, ITYPE, LDA, LDB, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), B( LDB, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE, HALF - PARAMETER ( ONE = 1.0D0, HALF = 0.5D0 ) -* .. -* .. Local Scalars .. - LOGICAL UPPER - INTEGER K - DOUBLE PRECISION AKK, BKK, CT -* .. -* .. External Subroutines .. - EXTERNAL DAXPY, DSCAL, DSYR2, DTRMV, DTRSV, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 - UPPER = LSAME( UPLO, 'U' ) - IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN - INFO = -1 - ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN - INFO = -2 - ELSE IF( N.LT.0 ) THEN - INFO = -3 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -5 - ELSE IF( LDB.LT.MAX( 1, N ) ) THEN - INFO = -7 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DSYGS2', -INFO ) - RETURN - END IF -* - IF( ITYPE.EQ.1 ) THEN - IF( UPPER ) THEN -* -* Compute inv(U**T)*A*inv(U) -* - DO 10 K = 1, N -* -* Update the upper triangle of A(k:n,k:n) -* - AKK = A( K, K ) - BKK = B( K, K ) - AKK = AKK / BKK**2 - A( K, K ) = AKK - IF( K.LT.N ) THEN - CALL DSCAL( N-K, ONE / BKK, A( K, K+1 ), LDA ) - CT = -HALF*AKK - CALL DAXPY( N-K, CT, B( K, K+1 ), LDB, A( K, K+1 ), - $ LDA ) - CALL DSYR2( UPLO, N-K, -ONE, A( K, K+1 ), LDA, - $ B( K, K+1 ), LDB, A( K+1, K+1 ), LDA ) - CALL DAXPY( N-K, CT, B( K, K+1 ), LDB, A( K, K+1 ), - $ LDA ) - CALL DTRSV( UPLO, 'Transpose', 'Non-unit', N-K, - $ B( K+1, K+1 ), LDB, A( K, K+1 ), LDA ) - END IF - 10 CONTINUE - ELSE -* -* Compute inv(L)*A*inv(L**T) -* - DO 20 K = 1, N -* -* Update the lower triangle of A(k:n,k:n) -* - AKK = A( K, K ) - BKK = B( K, K ) - AKK = AKK / BKK**2 - A( K, K ) = AKK - IF( K.LT.N ) THEN - CALL DSCAL( N-K, ONE / BKK, A( K+1, K ), 1 ) - CT = -HALF*AKK - CALL DAXPY( N-K, CT, B( K+1, K ), 1, A( K+1, K ), 1 ) - CALL DSYR2( UPLO, N-K, -ONE, A( K+1, K ), 1, - $ B( K+1, K ), 1, A( K+1, K+1 ), LDA ) - CALL DAXPY( N-K, CT, B( K+1, K ), 1, A( K+1, K ), 1 ) - CALL DTRSV( UPLO, 'No transpose', 'Non-unit', N-K, - $ B( K+1, K+1 ), LDB, A( K+1, K ), 1 ) - END IF - 20 CONTINUE - END IF - ELSE - IF( UPPER ) THEN -* -* Compute U*A*U**T -* - DO 30 K = 1, N -* -* Update the upper triangle of A(1:k,1:k) -* - AKK = A( K, K ) - BKK = B( K, K ) - CALL DTRMV( UPLO, 'No transpose', 'Non-unit', K-1, B, - $ LDB, A( 1, K ), 1 ) - CT = HALF*AKK - CALL DAXPY( K-1, CT, B( 1, K ), 1, A( 1, K ), 1 ) - CALL DSYR2( UPLO, K-1, ONE, A( 1, K ), 1, B( 1, K ), 1, - $ A, LDA ) - CALL DAXPY( K-1, CT, B( 1, K ), 1, A( 1, K ), 1 ) - CALL DSCAL( K-1, BKK, A( 1, K ), 1 ) - A( K, K ) = AKK*BKK**2 - 30 CONTINUE - ELSE -* -* Compute L**T *A*L -* - DO 40 K = 1, N -* -* Update the lower triangle of A(1:k,1:k) -* - AKK = A( K, K ) - BKK = B( K, K ) - CALL DTRMV( UPLO, 'Transpose', 'Non-unit', K-1, B, LDB, - $ A( K, 1 ), LDA ) - CT = HALF*AKK - CALL DAXPY( K-1, CT, B( K, 1 ), LDB, A( K, 1 ), LDA ) - CALL DSYR2( UPLO, K-1, ONE, A( K, 1 ), LDA, B( K, 1 ), - $ LDB, A, LDA ) - CALL DAXPY( K-1, CT, B( K, 1 ), LDB, A( K, 1 ), LDA ) - CALL DSCAL( K-1, BKK, A( K, 1 ), LDA ) - A( K, K ) = AKK*BKK**2 - 40 CONTINUE - END IF - END IF - RETURN -* -* End of DSYGS2 -* - END diff --git a/lib/linalg/fortran/dsygst.f b/lib/linalg/fortran/dsygst.f deleted file mode 100644 index 05b90372ab..0000000000 --- a/lib/linalg/fortran/dsygst.f +++ /dev/null @@ -1,318 +0,0 @@ -*> \brief \b DSYGST -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DSYGST + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER UPLO -* INTEGER INFO, ITYPE, LDA, LDB, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), B( LDB, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DSYGST reduces a real symmetric-definite generalized eigenproblem -*> to standard form. -*> -*> If ITYPE = 1, the problem is A*x = lambda*B*x, -*> and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T) -*> -*> If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or -*> B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T*A*L. -*> -*> B must have been previously factorized as U**T*U or L*L**T by DPOTRF. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] ITYPE -*> \verbatim -*> ITYPE is INTEGER -*> = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T); -*> = 2 or 3: compute U*A*U**T or L**T*A*L. -*> \endverbatim -*> -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> = 'U': Upper triangle of A is stored and B is factored as -*> U**T*U; -*> = 'L': Lower triangle of A is stored and B is factored as -*> L*L**T. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrices A and B. N >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the symmetric matrix A. If UPLO = 'U', the leading -*> N-by-N upper triangular part of A contains the upper -*> triangular part of the matrix A, and the strictly lower -*> triangular part of A is not referenced. If UPLO = 'L', the -*> leading N-by-N lower triangular part of A contains the lower -*> triangular part of the matrix A, and the strictly upper -*> triangular part of A is not referenced. -*> -*> On exit, if INFO = 0, the transformed matrix, stored in the -*> same format as A. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,N). -*> \endverbatim -*> -*> \param[in] B -*> \verbatim -*> B is DOUBLE PRECISION array, dimension (LDB,N) -*> The triangular factor from the Cholesky factorization of B, -*> as returned by DPOTRF. -*> \endverbatim -*> -*> \param[in] LDB -*> \verbatim -*> LDB is INTEGER -*> The leading dimension of the array B. LDB >= max(1,N). -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleSYcomputational -* -* ===================================================================== - SUBROUTINE DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER UPLO - INTEGER INFO, ITYPE, LDA, LDB, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), B( LDB, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE, HALF - PARAMETER ( ONE = 1.0D0, HALF = 0.5D0 ) -* .. -* .. Local Scalars .. - LOGICAL UPPER - INTEGER K, KB, NB -* .. -* .. External Subroutines .. - EXTERNAL DSYGS2, DSYMM, DSYR2K, DTRMM, DTRSM, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, MIN -* .. -* .. External Functions .. - LOGICAL LSAME - INTEGER ILAENV - EXTERNAL LSAME, ILAENV -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 - UPPER = LSAME( UPLO, 'U' ) - IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN - INFO = -1 - ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN - INFO = -2 - ELSE IF( N.LT.0 ) THEN - INFO = -3 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -5 - ELSE IF( LDB.LT.MAX( 1, N ) ) THEN - INFO = -7 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DSYGST', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( N.EQ.0 ) - $ RETURN -* -* Determine the block size for this environment. -* - NB = ILAENV( 1, 'DSYGST', UPLO, N, -1, -1, -1 ) -* - IF( NB.LE.1 .OR. NB.GE.N ) THEN -* -* Use unblocked code -* - CALL DSYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) - ELSE -* -* Use blocked code -* - IF( ITYPE.EQ.1 ) THEN - IF( UPPER ) THEN -* -* Compute inv(U**T)*A*inv(U) -* - DO 10 K = 1, N, NB - KB = MIN( N-K+1, NB ) -* -* Update the upper triangle of A(k:n,k:n) -* - CALL DSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA, - $ B( K, K ), LDB, INFO ) - IF( K+KB.LE.N ) THEN - CALL DTRSM( 'Left', UPLO, 'Transpose', 'Non-unit', - $ KB, N-K-KB+1, ONE, B( K, K ), LDB, - $ A( K, K+KB ), LDA ) - CALL DSYMM( 'Left', UPLO, KB, N-K-KB+1, -HALF, - $ A( K, K ), LDA, B( K, K+KB ), LDB, ONE, - $ A( K, K+KB ), LDA ) - CALL DSYR2K( UPLO, 'Transpose', N-K-KB+1, KB, -ONE, - $ A( K, K+KB ), LDA, B( K, K+KB ), LDB, - $ ONE, A( K+KB, K+KB ), LDA ) - CALL DSYMM( 'Left', UPLO, KB, N-K-KB+1, -HALF, - $ A( K, K ), LDA, B( K, K+KB ), LDB, ONE, - $ A( K, K+KB ), LDA ) - CALL DTRSM( 'Right', UPLO, 'No transpose', - $ 'Non-unit', KB, N-K-KB+1, ONE, - $ B( K+KB, K+KB ), LDB, A( K, K+KB ), - $ LDA ) - END IF - 10 CONTINUE - ELSE -* -* Compute inv(L)*A*inv(L**T) -* - DO 20 K = 1, N, NB - KB = MIN( N-K+1, NB ) -* -* Update the lower triangle of A(k:n,k:n) -* - CALL DSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA, - $ B( K, K ), LDB, INFO ) - IF( K+KB.LE.N ) THEN - CALL DTRSM( 'Right', UPLO, 'Transpose', 'Non-unit', - $ N-K-KB+1, KB, ONE, B( K, K ), LDB, - $ A( K+KB, K ), LDA ) - CALL DSYMM( 'Right', UPLO, N-K-KB+1, KB, -HALF, - $ A( K, K ), LDA, B( K+KB, K ), LDB, ONE, - $ A( K+KB, K ), LDA ) - CALL DSYR2K( UPLO, 'No transpose', N-K-KB+1, KB, - $ -ONE, A( K+KB, K ), LDA, B( K+KB, K ), - $ LDB, ONE, A( K+KB, K+KB ), LDA ) - CALL DSYMM( 'Right', UPLO, N-K-KB+1, KB, -HALF, - $ A( K, K ), LDA, B( K+KB, K ), LDB, ONE, - $ A( K+KB, K ), LDA ) - CALL DTRSM( 'Left', UPLO, 'No transpose', - $ 'Non-unit', N-K-KB+1, KB, ONE, - $ B( K+KB, K+KB ), LDB, A( K+KB, K ), - $ LDA ) - END IF - 20 CONTINUE - END IF - ELSE - IF( UPPER ) THEN -* -* Compute U*A*U**T -* - DO 30 K = 1, N, NB - KB = MIN( N-K+1, NB ) -* -* Update the upper triangle of A(1:k+kb-1,1:k+kb-1) -* - CALL DTRMM( 'Left', UPLO, 'No transpose', 'Non-unit', - $ K-1, KB, ONE, B, LDB, A( 1, K ), LDA ) - CALL DSYMM( 'Right', UPLO, K-1, KB, HALF, A( K, K ), - $ LDA, B( 1, K ), LDB, ONE, A( 1, K ), LDA ) - CALL DSYR2K( UPLO, 'No transpose', K-1, KB, ONE, - $ A( 1, K ), LDA, B( 1, K ), LDB, ONE, A, - $ LDA ) - CALL DSYMM( 'Right', UPLO, K-1, KB, HALF, A( K, K ), - $ LDA, B( 1, K ), LDB, ONE, A( 1, K ), LDA ) - CALL DTRMM( 'Right', UPLO, 'Transpose', 'Non-unit', - $ K-1, KB, ONE, B( K, K ), LDB, A( 1, K ), - $ LDA ) - CALL DSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA, - $ B( K, K ), LDB, INFO ) - 30 CONTINUE - ELSE -* -* Compute L**T*A*L -* - DO 40 K = 1, N, NB - KB = MIN( N-K+1, NB ) -* -* Update the lower triangle of A(1:k+kb-1,1:k+kb-1) -* - CALL DTRMM( 'Right', UPLO, 'No transpose', 'Non-unit', - $ KB, K-1, ONE, B, LDB, A( K, 1 ), LDA ) - CALL DSYMM( 'Left', UPLO, KB, K-1, HALF, A( K, K ), - $ LDA, B( K, 1 ), LDB, ONE, A( K, 1 ), LDA ) - CALL DSYR2K( UPLO, 'Transpose', K-1, KB, ONE, - $ A( K, 1 ), LDA, B( K, 1 ), LDB, ONE, A, - $ LDA ) - CALL DSYMM( 'Left', UPLO, KB, K-1, HALF, A( K, K ), - $ LDA, B( K, 1 ), LDB, ONE, A( K, 1 ), LDA ) - CALL DTRMM( 'Left', UPLO, 'Transpose', 'Non-unit', KB, - $ K-1, ONE, B( K, K ), LDB, A( K, 1 ), LDA ) - CALL DSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA, - $ B( K, K ), LDB, INFO ) - 40 CONTINUE - END IF - END IF - END IF - RETURN -* -* End of DSYGST -* - END diff --git a/lib/linalg/fortran/dsygv.f b/lib/linalg/fortran/dsygv.f deleted file mode 100644 index 5208dbb1f1..0000000000 --- a/lib/linalg/fortran/dsygv.f +++ /dev/null @@ -1,311 +0,0 @@ -*> \brief \b DSYGV -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DSYGV + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DSYGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, -* LWORK, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER JOBZ, UPLO -* INTEGER INFO, ITYPE, LDA, LDB, LWORK, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DSYGV computes all the eigenvalues, and optionally, the eigenvectors -*> of a real generalized symmetric-definite eigenproblem, of the form -*> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. -*> Here A and B are assumed to be symmetric and B is also -*> positive definite. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] ITYPE -*> \verbatim -*> ITYPE is INTEGER -*> Specifies the problem type to be solved: -*> = 1: A*x = (lambda)*B*x -*> = 2: A*B*x = (lambda)*x -*> = 3: B*A*x = (lambda)*x -*> \endverbatim -*> -*> \param[in] JOBZ -*> \verbatim -*> JOBZ is CHARACTER*1 -*> = 'N': Compute eigenvalues only; -*> = 'V': Compute eigenvalues and eigenvectors. -*> \endverbatim -*> -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> = 'U': Upper triangles of A and B are stored; -*> = 'L': Lower triangles of A and B are stored. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrices A and B. N >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA, N) -*> On entry, the symmetric matrix A. If UPLO = 'U', the -*> leading N-by-N upper triangular part of A contains the -*> upper triangular part of the matrix A. If UPLO = 'L', -*> the leading N-by-N lower triangular part of A contains -*> the lower triangular part of the matrix A. -*> -*> On exit, if JOBZ = 'V', then if INFO = 0, A contains the -*> matrix Z of eigenvectors. The eigenvectors are normalized -*> as follows: -*> if ITYPE = 1 or 2, Z**T*B*Z = I; -*> if ITYPE = 3, Z**T*inv(B)*Z = I. -*> If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') -*> or the lower triangle (if UPLO='L') of A, including the -*> diagonal, is destroyed. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,N). -*> \endverbatim -*> -*> \param[in,out] B -*> \verbatim -*> B is DOUBLE PRECISION array, dimension (LDB, N) -*> On entry, the symmetric positive definite matrix B. -*> If UPLO = 'U', the leading N-by-N upper triangular part of B -*> contains the upper triangular part of the matrix B. -*> If UPLO = 'L', the leading N-by-N lower triangular part of B -*> contains the lower triangular part of the matrix B. -*> -*> On exit, if INFO <= N, the part of B containing the matrix is -*> overwritten by the triangular factor U or L from the Cholesky -*> factorization B = U**T*U or B = L*L**T. -*> \endverbatim -*> -*> \param[in] LDB -*> \verbatim -*> LDB is INTEGER -*> The leading dimension of the array B. LDB >= max(1,N). -*> \endverbatim -*> -*> \param[out] W -*> \verbatim -*> W is DOUBLE PRECISION array, dimension (N) -*> If INFO = 0, the eigenvalues in ascending order. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) -*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -*> \endverbatim -*> -*> \param[in] LWORK -*> \verbatim -*> LWORK is INTEGER -*> The length of the array WORK. LWORK >= max(1,3*N-1). -*> For optimal efficiency, LWORK >= (NB+2)*N, -*> where NB is the blocksize for DSYTRD returned by ILAENV. -*> -*> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal size of the WORK array, returns -*> this value as the first entry of the WORK array, and no error -*> message related to LWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: DPOTRF or DSYEV returned an error code: -*> <= N: if INFO = i, DSYEV failed to converge; -*> i off-diagonal elements of an intermediate -*> tridiagonal form did not converge to zero; -*> > N: if INFO = N + i, for 1 <= i <= N, then the leading -*> minor of order i of B is not positive definite. -*> The factorization of B could not be completed and -*> no eigenvalues or eigenvectors were computed. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleSYeigen -* -* ===================================================================== - SUBROUTINE DSYGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, - $ LWORK, INFO ) -* -* -- LAPACK driver routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER JOBZ, UPLO - INTEGER INFO, ITYPE, LDA, LDB, LWORK, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE - PARAMETER ( ONE = 1.0D+0 ) -* .. -* .. Local Scalars .. - LOGICAL LQUERY, UPPER, WANTZ - CHARACTER TRANS - INTEGER LWKMIN, LWKOPT, NB, NEIG -* .. -* .. External Functions .. - LOGICAL LSAME - INTEGER ILAENV - EXTERNAL LSAME, ILAENV -* .. -* .. External Subroutines .. - EXTERNAL DPOTRF, DSYEV, DSYGST, DTRMM, DTRSM, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - WANTZ = LSAME( JOBZ, 'V' ) - UPPER = LSAME( UPLO, 'U' ) - LQUERY = ( LWORK.EQ.-1 ) -* - INFO = 0 - IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN - INFO = -1 - ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN - INFO = -2 - ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN - INFO = -3 - ELSE IF( N.LT.0 ) THEN - INFO = -4 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -6 - ELSE IF( LDB.LT.MAX( 1, N ) ) THEN - INFO = -8 - END IF -* - IF( INFO.EQ.0 ) THEN - LWKMIN = MAX( 1, 3*N - 1 ) - NB = ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 ) - LWKOPT = MAX( LWKMIN, ( NB + 2 )*N ) - WORK( 1 ) = LWKOPT -* - IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN - INFO = -11 - END IF - END IF -* - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DSYGV ', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - RETURN - END IF -* -* Quick return if possible -* - IF( N.EQ.0 ) - $ RETURN -* -* Form a Cholesky factorization of B. -* - CALL DPOTRF( UPLO, N, B, LDB, INFO ) - IF( INFO.NE.0 ) THEN - INFO = N + INFO - RETURN - END IF -* -* Transform problem to standard eigenvalue problem and solve. -* - CALL DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) - CALL DSYEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, INFO ) -* - IF( WANTZ ) THEN -* -* Backtransform eigenvectors to the original problem. -* - NEIG = N - IF( INFO.GT.0 ) - $ NEIG = INFO - 1 - IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN -* -* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; -* backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y -* - IF( UPPER ) THEN - TRANS = 'N' - ELSE - TRANS = 'T' - END IF -* - CALL DTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE, - $ B, LDB, A, LDA ) -* - ELSE IF( ITYPE.EQ.3 ) THEN -* -* For B*A*x=(lambda)*x; -* backtransform eigenvectors: x = L*y or U**T*y -* - IF( UPPER ) THEN - TRANS = 'T' - ELSE - TRANS = 'N' - END IF -* - CALL DTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE, - $ B, LDB, A, LDA ) - END IF - END IF -* - WORK( 1 ) = LWKOPT - RETURN -* -* End of DSYGV -* - END diff --git a/lib/linalg/fortran/dsygvd.f b/lib/linalg/fortran/dsygvd.f deleted file mode 100644 index 3b38665a75..0000000000 --- a/lib/linalg/fortran/dsygvd.f +++ /dev/null @@ -1,377 +0,0 @@ -*> \brief \b DSYGVD -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DSYGVD + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DSYGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, -* LWORK, IWORK, LIWORK, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER JOBZ, UPLO -* INTEGER INFO, ITYPE, LDA, LDB, LIWORK, LWORK, N -* .. -* .. Array Arguments .. -* INTEGER IWORK( * ) -* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DSYGVD computes all the eigenvalues, and optionally, the eigenvectors -*> of a real generalized symmetric-definite eigenproblem, of the form -*> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and -*> B are assumed to be symmetric and B is also positive definite. -*> If eigenvectors are desired, it uses a divide and conquer algorithm. -*> -*> The divide and conquer algorithm makes very mild assumptions about -*> floating point arithmetic. It will work on machines with a guard -*> digit in add/subtract, or on those binary machines without guard -*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or -*> Cray-2. It could conceivably fail on hexadecimal or decimal machines -*> without guard digits, but we know of none. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] ITYPE -*> \verbatim -*> ITYPE is INTEGER -*> Specifies the problem type to be solved: -*> = 1: A*x = (lambda)*B*x -*> = 2: A*B*x = (lambda)*x -*> = 3: B*A*x = (lambda)*x -*> \endverbatim -*> -*> \param[in] JOBZ -*> \verbatim -*> JOBZ is CHARACTER*1 -*> = 'N': Compute eigenvalues only; -*> = 'V': Compute eigenvalues and eigenvectors. -*> \endverbatim -*> -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> = 'U': Upper triangles of A and B are stored; -*> = 'L': Lower triangles of A and B are stored. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrices A and B. N >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA, N) -*> On entry, the symmetric matrix A. If UPLO = 'U', the -*> leading N-by-N upper triangular part of A contains the -*> upper triangular part of the matrix A. If UPLO = 'L', -*> the leading N-by-N lower triangular part of A contains -*> the lower triangular part of the matrix A. -*> -*> On exit, if JOBZ = 'V', then if INFO = 0, A contains the -*> matrix Z of eigenvectors. The eigenvectors are normalized -*> as follows: -*> if ITYPE = 1 or 2, Z**T*B*Z = I; -*> if ITYPE = 3, Z**T*inv(B)*Z = I. -*> If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') -*> or the lower triangle (if UPLO='L') of A, including the -*> diagonal, is destroyed. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,N). -*> \endverbatim -*> -*> \param[in,out] B -*> \verbatim -*> B is DOUBLE PRECISION array, dimension (LDB, N) -*> On entry, the symmetric matrix B. If UPLO = 'U', the -*> leading N-by-N upper triangular part of B contains the -*> upper triangular part of the matrix B. If UPLO = 'L', -*> the leading N-by-N lower triangular part of B contains -*> the lower triangular part of the matrix B. -*> -*> On exit, if INFO <= N, the part of B containing the matrix is -*> overwritten by the triangular factor U or L from the Cholesky -*> factorization B = U**T*U or B = L*L**T. -*> \endverbatim -*> -*> \param[in] LDB -*> \verbatim -*> LDB is INTEGER -*> The leading dimension of the array B. LDB >= max(1,N). -*> \endverbatim -*> -*> \param[out] W -*> \verbatim -*> W is DOUBLE PRECISION array, dimension (N) -*> If INFO = 0, the eigenvalues in ascending order. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) -*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -*> \endverbatim -*> -*> \param[in] LWORK -*> \verbatim -*> LWORK is INTEGER -*> The dimension of the array WORK. -*> If N <= 1, LWORK >= 1. -*> If JOBZ = 'N' and N > 1, LWORK >= 2*N+1. -*> If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2. -*> -*> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal sizes of the WORK and IWORK -*> arrays, returns these values as the first entries of the WORK -*> and IWORK arrays, and no error message related to LWORK or -*> LIWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] IWORK -*> \verbatim -*> IWORK is INTEGER array, dimension (MAX(1,LIWORK)) -*> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. -*> \endverbatim -*> -*> \param[in] LIWORK -*> \verbatim -*> LIWORK is INTEGER -*> The dimension of the array IWORK. -*> If N <= 1, LIWORK >= 1. -*> If JOBZ = 'N' and N > 1, LIWORK >= 1. -*> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. -*> -*> If LIWORK = -1, then a workspace query is assumed; the -*> routine only calculates the optimal sizes of the WORK and -*> IWORK arrays, returns these values as the first entries of -*> the WORK and IWORK arrays, and no error message related to -*> LWORK or LIWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: DPOTRF or DSYEVD returned an error code: -*> <= N: if INFO = i and JOBZ = 'N', then the algorithm -*> failed to converge; i off-diagonal elements of an -*> intermediate tridiagonal form did not converge to -*> zero; -*> if INFO = i and JOBZ = 'V', then the algorithm -*> failed to compute an eigenvalue while working on -*> the submatrix lying in rows and columns INFO/(N+1) -*> through mod(INFO,N+1); -*> > N: if INFO = N + i, for 1 <= i <= N, then the leading -*> minor of order i of B is not positive definite. -*> The factorization of B could not be completed and -*> no eigenvalues or eigenvectors were computed. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleSYeigen -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> Modified so that no backsubstitution is performed if DSYEVD fails to -*> converge (NEIG in old code could be greater than N causing out of -*> bounds reference to A - reported by Ralf Meyer). Also corrected the -*> description of INFO and the test on ITYPE. Sven, 16 Feb 05. -*> \endverbatim -* -*> \par Contributors: -* ================== -*> -*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA -*> -* ===================================================================== - SUBROUTINE DSYGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, - $ LWORK, IWORK, LIWORK, INFO ) -* -* -- LAPACK driver routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER JOBZ, UPLO - INTEGER INFO, ITYPE, LDA, LDB, LIWORK, LWORK, N -* .. -* .. Array Arguments .. - INTEGER IWORK( * ) - DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE - PARAMETER ( ONE = 1.0D+0 ) -* .. -* .. Local Scalars .. - LOGICAL LQUERY, UPPER, WANTZ - CHARACTER TRANS - INTEGER LIOPT, LIWMIN, LOPT, LWMIN -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL DPOTRF, DSYEVD, DSYGST, DTRMM, DTRSM, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC DBLE, MAX -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - WANTZ = LSAME( JOBZ, 'V' ) - UPPER = LSAME( UPLO, 'U' ) - LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 ) -* - INFO = 0 - IF( N.LE.1 ) THEN - LIWMIN = 1 - LWMIN = 1 - ELSE IF( WANTZ ) THEN - LIWMIN = 3 + 5*N - LWMIN = 1 + 6*N + 2*N**2 - ELSE - LIWMIN = 1 - LWMIN = 2*N + 1 - END IF - LOPT = LWMIN - LIOPT = LIWMIN - IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN - INFO = -1 - ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN - INFO = -2 - ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN - INFO = -3 - ELSE IF( N.LT.0 ) THEN - INFO = -4 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -6 - ELSE IF( LDB.LT.MAX( 1, N ) ) THEN - INFO = -8 - END IF -* - IF( INFO.EQ.0 ) THEN - WORK( 1 ) = LOPT - IWORK( 1 ) = LIOPT -* - IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN - INFO = -11 - ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN - INFO = -13 - END IF - END IF -* - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DSYGVD', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - RETURN - END IF -* -* Quick return if possible -* - IF( N.EQ.0 ) - $ RETURN -* -* Form a Cholesky factorization of B. -* - CALL DPOTRF( UPLO, N, B, LDB, INFO ) - IF( INFO.NE.0 ) THEN - INFO = N + INFO - RETURN - END IF -* -* Transform problem to standard eigenvalue problem and solve. -* - CALL DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) - CALL DSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK, LIWORK, - $ INFO ) - LOPT = INT( MAX( DBLE( LOPT ), DBLE( WORK( 1 ) ) ) ) - LIOPT = INT( MAX( DBLE( LIOPT ), DBLE( IWORK( 1 ) ) ) ) -* - IF( WANTZ .AND. INFO.EQ.0 ) THEN -* -* Backtransform eigenvectors to the original problem. -* - IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN -* -* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; -* backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y -* - IF( UPPER ) THEN - TRANS = 'N' - ELSE - TRANS = 'T' - END IF -* - CALL DTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, N, ONE, - $ B, LDB, A, LDA ) -* - ELSE IF( ITYPE.EQ.3 ) THEN -* -* For B*A*x=(lambda)*x; -* backtransform eigenvectors: x = L*y or U**T*y -* - IF( UPPER ) THEN - TRANS = 'T' - ELSE - TRANS = 'N' - END IF -* - CALL DTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, N, ONE, - $ B, LDB, A, LDA ) - END IF - END IF -* - WORK( 1 ) = LOPT - IWORK( 1 ) = LIOPT -* - RETURN -* -* End of DSYGVD -* - END diff --git a/lib/linalg/fortran/dsymm.f b/lib/linalg/fortran/dsymm.f deleted file mode 100644 index 683e79f6ad..0000000000 --- a/lib/linalg/fortran/dsymm.f +++ /dev/null @@ -1,364 +0,0 @@ -*> \brief \b DSYMM -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE DSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC) -* -* .. Scalar Arguments .. -* DOUBLE PRECISION ALPHA,BETA -* INTEGER LDA,LDB,LDC,M,N -* CHARACTER SIDE,UPLO -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DSYMM performs one of the matrix-matrix operations -*> -*> C := alpha*A*B + beta*C, -*> -*> or -*> -*> C := alpha*B*A + beta*C, -*> -*> where alpha and beta are scalars, A is a symmetric matrix and B and -*> C are m by n matrices. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] SIDE -*> \verbatim -*> SIDE is CHARACTER*1 -*> On entry, SIDE specifies whether the symmetric matrix A -*> appears on the left or right in the operation as follows: -*> -*> SIDE = 'L' or 'l' C := alpha*A*B + beta*C, -*> -*> SIDE = 'R' or 'r' C := alpha*B*A + beta*C, -*> \endverbatim -*> -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> On entry, UPLO specifies whether the upper or lower -*> triangular part of the symmetric matrix A is to be -*> referenced as follows: -*> -*> UPLO = 'U' or 'u' Only the upper triangular part of the -*> symmetric matrix is to be referenced. -*> -*> UPLO = 'L' or 'l' Only the lower triangular part of the -*> symmetric matrix is to be referenced. -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> On entry, M specifies the number of rows of the matrix C. -*> M must be at least zero. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> On entry, N specifies the number of columns of the matrix C. -*> N must be at least zero. -*> \endverbatim -*> -*> \param[in] ALPHA -*> \verbatim -*> ALPHA is DOUBLE PRECISION. -*> On entry, ALPHA specifies the scalar alpha. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is -*> m when SIDE = 'L' or 'l' and is n otherwise. -*> Before entry with SIDE = 'L' or 'l', the m by m part of -*> the array A must contain the symmetric matrix, such that -*> when UPLO = 'U' or 'u', the leading m by m upper triangular -*> part of the array A must contain the upper triangular part -*> of the symmetric matrix and the strictly lower triangular -*> part of A is not referenced, and when UPLO = 'L' or 'l', -*> the leading m by m lower triangular part of the array A -*> must contain the lower triangular part of the symmetric -*> matrix and the strictly upper triangular part of A is not -*> referenced. -*> Before entry with SIDE = 'R' or 'r', the n by n part of -*> the array A must contain the symmetric matrix, such that -*> when UPLO = 'U' or 'u', the leading n by n upper triangular -*> part of the array A must contain the upper triangular part -*> of the symmetric matrix and the strictly lower triangular -*> part of A is not referenced, and when UPLO = 'L' or 'l', -*> the leading n by n lower triangular part of the array A -*> must contain the lower triangular part of the symmetric -*> matrix and the strictly upper triangular part of A is not -*> referenced. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> On entry, LDA specifies the first dimension of A as declared -*> in the calling (sub) program. When SIDE = 'L' or 'l' then -*> LDA must be at least max( 1, m ), otherwise LDA must be at -*> least max( 1, n ). -*> \endverbatim -*> -*> \param[in] B -*> \verbatim -*> B is DOUBLE PRECISION array, dimension ( LDB, N ) -*> Before entry, the leading m by n part of the array B must -*> contain the matrix B. -*> \endverbatim -*> -*> \param[in] LDB -*> \verbatim -*> LDB is INTEGER -*> On entry, LDB specifies the first dimension of B as declared -*> in the calling (sub) program. LDB must be at least -*> max( 1, m ). -*> \endverbatim -*> -*> \param[in] BETA -*> \verbatim -*> BETA is DOUBLE PRECISION. -*> On entry, BETA specifies the scalar beta. When BETA is -*> supplied as zero then C need not be set on input. -*> \endverbatim -*> -*> \param[in,out] C -*> \verbatim -*> C is DOUBLE PRECISION array, dimension ( LDC, N ) -*> Before entry, the leading m by n part of the array C must -*> contain the matrix C, except when beta is zero, in which -*> case C need not be set on entry. -*> On exit, the array C is overwritten by the m by n updated -*> matrix. -*> \endverbatim -*> -*> \param[in] LDC -*> \verbatim -*> LDC is INTEGER -*> On entry, LDC specifies the first dimension of C as declared -*> in the calling (sub) program. LDC must be at least -*> max( 1, m ). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup double_blas_level3 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> Level 3 Blas routine. -*> -*> -- Written on 8-February-1989. -*> Jack Dongarra, Argonne National Laboratory. -*> Iain Duff, AERE Harwell. -*> Jeremy Du Croz, Numerical Algorithms Group Ltd. -*> Sven Hammarling, Numerical Algorithms Group Ltd. -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC) -* -* -- Reference BLAS level3 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - DOUBLE PRECISION ALPHA,BETA - INTEGER LDA,LDB,LDC,M,N - CHARACTER SIDE,UPLO -* .. -* .. Array Arguments .. - DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*) -* .. -* -* ===================================================================== -* -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* .. Local Scalars .. - DOUBLE PRECISION TEMP1,TEMP2 - INTEGER I,INFO,J,K,NROWA - LOGICAL UPPER -* .. -* .. Parameters .. - DOUBLE PRECISION ONE,ZERO - PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) -* .. -* -* Set NROWA as the number of rows of A. -* - IF (LSAME(SIDE,'L')) THEN - NROWA = M - ELSE - NROWA = N - END IF - UPPER = LSAME(UPLO,'U') -* -* Test the input parameters. -* - INFO = 0 - IF ((.NOT.LSAME(SIDE,'L')) .AND. (.NOT.LSAME(SIDE,'R'))) THEN - INFO = 1 - ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN - INFO = 2 - ELSE IF (M.LT.0) THEN - INFO = 3 - ELSE IF (N.LT.0) THEN - INFO = 4 - ELSE IF (LDA.LT.MAX(1,NROWA)) THEN - INFO = 7 - ELSE IF (LDB.LT.MAX(1,M)) THEN - INFO = 9 - ELSE IF (LDC.LT.MAX(1,M)) THEN - INFO = 12 - END IF - IF (INFO.NE.0) THEN - CALL XERBLA('DSYMM ',INFO) - RETURN - END IF -* -* Quick return if possible. -* - IF ((M.EQ.0) .OR. (N.EQ.0) .OR. - + ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN -* -* And when alpha.eq.zero. -* - IF (ALPHA.EQ.ZERO) THEN - IF (BETA.EQ.ZERO) THEN - DO 20 J = 1,N - DO 10 I = 1,M - C(I,J) = ZERO - 10 CONTINUE - 20 CONTINUE - ELSE - DO 40 J = 1,N - DO 30 I = 1,M - C(I,J) = BETA*C(I,J) - 30 CONTINUE - 40 CONTINUE - END IF - RETURN - END IF -* -* Start the operations. -* - IF (LSAME(SIDE,'L')) THEN -* -* Form C := alpha*A*B + beta*C. -* - IF (UPPER) THEN - DO 70 J = 1,N - DO 60 I = 1,M - TEMP1 = ALPHA*B(I,J) - TEMP2 = ZERO - DO 50 K = 1,I - 1 - C(K,J) = C(K,J) + TEMP1*A(K,I) - TEMP2 = TEMP2 + B(K,J)*A(K,I) - 50 CONTINUE - IF (BETA.EQ.ZERO) THEN - C(I,J) = TEMP1*A(I,I) + ALPHA*TEMP2 - ELSE - C(I,J) = BETA*C(I,J) + TEMP1*A(I,I) + - + ALPHA*TEMP2 - END IF - 60 CONTINUE - 70 CONTINUE - ELSE - DO 100 J = 1,N - DO 90 I = M,1,-1 - TEMP1 = ALPHA*B(I,J) - TEMP2 = ZERO - DO 80 K = I + 1,M - C(K,J) = C(K,J) + TEMP1*A(K,I) - TEMP2 = TEMP2 + B(K,J)*A(K,I) - 80 CONTINUE - IF (BETA.EQ.ZERO) THEN - C(I,J) = TEMP1*A(I,I) + ALPHA*TEMP2 - ELSE - C(I,J) = BETA*C(I,J) + TEMP1*A(I,I) + - + ALPHA*TEMP2 - END IF - 90 CONTINUE - 100 CONTINUE - END IF - ELSE -* -* Form C := alpha*B*A + beta*C. -* - DO 170 J = 1,N - TEMP1 = ALPHA*A(J,J) - IF (BETA.EQ.ZERO) THEN - DO 110 I = 1,M - C(I,J) = TEMP1*B(I,J) - 110 CONTINUE - ELSE - DO 120 I = 1,M - C(I,J) = BETA*C(I,J) + TEMP1*B(I,J) - 120 CONTINUE - END IF - DO 140 K = 1,J - 1 - IF (UPPER) THEN - TEMP1 = ALPHA*A(K,J) - ELSE - TEMP1 = ALPHA*A(J,K) - END IF - DO 130 I = 1,M - C(I,J) = C(I,J) + TEMP1*B(I,K) - 130 CONTINUE - 140 CONTINUE - DO 160 K = J + 1,N - IF (UPPER) THEN - TEMP1 = ALPHA*A(J,K) - ELSE - TEMP1 = ALPHA*A(K,J) - END IF - DO 150 I = 1,M - C(I,J) = C(I,J) + TEMP1*B(I,K) - 150 CONTINUE - 160 CONTINUE - 170 CONTINUE - END IF -* - RETURN -* -* End of DSYMM -* - END diff --git a/lib/linalg/fortran/dsymv.f b/lib/linalg/fortran/dsymv.f deleted file mode 100644 index 17310d7c62..0000000000 --- a/lib/linalg/fortran/dsymv.f +++ /dev/null @@ -1,330 +0,0 @@ -*> \brief \b DSYMV -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE DSYMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) -* -* .. Scalar Arguments .. -* DOUBLE PRECISION ALPHA,BETA -* INTEGER INCX,INCY,LDA,N -* CHARACTER UPLO -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A(LDA,*),X(*),Y(*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DSYMV performs the matrix-vector operation -*> -*> y := alpha*A*x + beta*y, -*> -*> where alpha and beta are scalars, x and y are n element vectors and -*> A is an n by n symmetric matrix. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> On entry, UPLO specifies whether the upper or lower -*> triangular part of the array A is to be referenced as -*> follows: -*> -*> UPLO = 'U' or 'u' Only the upper triangular part of A -*> is to be referenced. -*> -*> UPLO = 'L' or 'l' Only the lower triangular part of A -*> is to be referenced. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> On entry, N specifies the order of the matrix A. -*> N must be at least zero. -*> \endverbatim -*> -*> \param[in] ALPHA -*> \verbatim -*> ALPHA is DOUBLE PRECISION. -*> On entry, ALPHA specifies the scalar alpha. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension ( LDA, N ) -*> Before entry with UPLO = 'U' or 'u', the leading n by n -*> upper triangular part of the array A must contain the upper -*> triangular part of the symmetric matrix and the strictly -*> lower triangular part of A is not referenced. -*> Before entry with UPLO = 'L' or 'l', the leading n by n -*> lower triangular part of the array A must contain the lower -*> triangular part of the symmetric matrix and the strictly -*> upper triangular part of A is not referenced. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> On entry, LDA specifies the first dimension of A as declared -*> in the calling (sub) program. LDA must be at least -*> max( 1, n ). -*> \endverbatim -*> -*> \param[in] X -*> \verbatim -*> X is DOUBLE PRECISION array, dimension at least -*> ( 1 + ( n - 1 )*abs( INCX ) ). -*> Before entry, the incremented array X must contain the n -*> element vector x. -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> On entry, INCX specifies the increment for the elements of -*> X. INCX must not be zero. -*> \endverbatim -*> -*> \param[in] BETA -*> \verbatim -*> BETA is DOUBLE PRECISION. -*> On entry, BETA specifies the scalar beta. When BETA is -*> supplied as zero then Y need not be set on input. -*> \endverbatim -*> -*> \param[in,out] Y -*> \verbatim -*> Y is DOUBLE PRECISION array, dimension at least -*> ( 1 + ( n - 1 )*abs( INCY ) ). -*> Before entry, the incremented array Y must contain the n -*> element vector y. On exit, Y is overwritten by the updated -*> vector y. -*> \endverbatim -*> -*> \param[in] INCY -*> \verbatim -*> INCY is INTEGER -*> On entry, INCY specifies the increment for the elements of -*> Y. INCY must not be zero. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup double_blas_level2 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> Level 2 Blas routine. -*> The vector and matrix arguments are not referenced when N = 0, or M = 0 -*> -*> -- Written on 22-October-1986. -*> Jack Dongarra, Argonne National Lab. -*> Jeremy Du Croz, Nag Central Office. -*> Sven Hammarling, Nag Central Office. -*> Richard Hanson, Sandia National Labs. -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DSYMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) -* -* -- Reference BLAS level2 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - DOUBLE PRECISION ALPHA,BETA - INTEGER INCX,INCY,LDA,N - CHARACTER UPLO -* .. -* .. Array Arguments .. - DOUBLE PRECISION A(LDA,*),X(*),Y(*) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE,ZERO - PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) -* .. -* .. Local Scalars .. - DOUBLE PRECISION TEMP1,TEMP2 - INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* -* Test the input parameters. -* - INFO = 0 - IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN - INFO = 1 - ELSE IF (N.LT.0) THEN - INFO = 2 - ELSE IF (LDA.LT.MAX(1,N)) THEN - INFO = 5 - ELSE IF (INCX.EQ.0) THEN - INFO = 7 - ELSE IF (INCY.EQ.0) THEN - INFO = 10 - END IF - IF (INFO.NE.0) THEN - CALL XERBLA('DSYMV ',INFO) - RETURN - END IF -* -* Quick return if possible. -* - IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN -* -* Set up the start points in X and Y. -* - IF (INCX.GT.0) THEN - KX = 1 - ELSE - KX = 1 - (N-1)*INCX - END IF - IF (INCY.GT.0) THEN - KY = 1 - ELSE - KY = 1 - (N-1)*INCY - END IF -* -* Start the operations. In this version the elements of A are -* accessed sequentially with one pass through the triangular part -* of A. -* -* First form y := beta*y. -* - IF (BETA.NE.ONE) THEN - IF (INCY.EQ.1) THEN - IF (BETA.EQ.ZERO) THEN - DO 10 I = 1,N - Y(I) = ZERO - 10 CONTINUE - ELSE - DO 20 I = 1,N - Y(I) = BETA*Y(I) - 20 CONTINUE - END IF - ELSE - IY = KY - IF (BETA.EQ.ZERO) THEN - DO 30 I = 1,N - Y(IY) = ZERO - IY = IY + INCY - 30 CONTINUE - ELSE - DO 40 I = 1,N - Y(IY) = BETA*Y(IY) - IY = IY + INCY - 40 CONTINUE - END IF - END IF - END IF - IF (ALPHA.EQ.ZERO) RETURN - IF (LSAME(UPLO,'U')) THEN -* -* Form y when A is stored in upper triangle. -* - IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN - DO 60 J = 1,N - TEMP1 = ALPHA*X(J) - TEMP2 = ZERO - DO 50 I = 1,J - 1 - Y(I) = Y(I) + TEMP1*A(I,J) - TEMP2 = TEMP2 + A(I,J)*X(I) - 50 CONTINUE - Y(J) = Y(J) + TEMP1*A(J,J) + ALPHA*TEMP2 - 60 CONTINUE - ELSE - JX = KX - JY = KY - DO 80 J = 1,N - TEMP1 = ALPHA*X(JX) - TEMP2 = ZERO - IX = KX - IY = KY - DO 70 I = 1,J - 1 - Y(IY) = Y(IY) + TEMP1*A(I,J) - TEMP2 = TEMP2 + A(I,J)*X(IX) - IX = IX + INCX - IY = IY + INCY - 70 CONTINUE - Y(JY) = Y(JY) + TEMP1*A(J,J) + ALPHA*TEMP2 - JX = JX + INCX - JY = JY + INCY - 80 CONTINUE - END IF - ELSE -* -* Form y when A is stored in lower triangle. -* - IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN - DO 100 J = 1,N - TEMP1 = ALPHA*X(J) - TEMP2 = ZERO - Y(J) = Y(J) + TEMP1*A(J,J) - DO 90 I = J + 1,N - Y(I) = Y(I) + TEMP1*A(I,J) - TEMP2 = TEMP2 + A(I,J)*X(I) - 90 CONTINUE - Y(J) = Y(J) + ALPHA*TEMP2 - 100 CONTINUE - ELSE - JX = KX - JY = KY - DO 120 J = 1,N - TEMP1 = ALPHA*X(JX) - TEMP2 = ZERO - Y(JY) = Y(JY) + TEMP1*A(J,J) - IX = JX - IY = JY - DO 110 I = J + 1,N - IX = IX + INCX - IY = IY + INCY - Y(IY) = Y(IY) + TEMP1*A(I,J) - TEMP2 = TEMP2 + A(I,J)*X(IX) - 110 CONTINUE - Y(JY) = Y(JY) + ALPHA*TEMP2 - JX = JX + INCX - JY = JY + INCY - 120 CONTINUE - END IF - END IF -* - RETURN -* -* End of DSYMV -* - END diff --git a/lib/linalg/fortran/dsyr2.f b/lib/linalg/fortran/dsyr2.f deleted file mode 100644 index 4bad19b96b..0000000000 --- a/lib/linalg/fortran/dsyr2.f +++ /dev/null @@ -1,295 +0,0 @@ -*> \brief \b DSYR2 -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE DSYR2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA) -* -* .. Scalar Arguments .. -* DOUBLE PRECISION ALPHA -* INTEGER INCX,INCY,LDA,N -* CHARACTER UPLO -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A(LDA,*),X(*),Y(*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DSYR2 performs the symmetric rank 2 operation -*> -*> A := alpha*x*y**T + alpha*y*x**T + A, -*> -*> where alpha is a scalar, x and y are n element vectors and A is an n -*> by n symmetric matrix. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> On entry, UPLO specifies whether the upper or lower -*> triangular part of the array A is to be referenced as -*> follows: -*> -*> UPLO = 'U' or 'u' Only the upper triangular part of A -*> is to be referenced. -*> -*> UPLO = 'L' or 'l' Only the lower triangular part of A -*> is to be referenced. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> On entry, N specifies the order of the matrix A. -*> N must be at least zero. -*> \endverbatim -*> -*> \param[in] ALPHA -*> \verbatim -*> ALPHA is DOUBLE PRECISION. -*> On entry, ALPHA specifies the scalar alpha. -*> \endverbatim -*> -*> \param[in] X -*> \verbatim -*> X is DOUBLE PRECISION array, dimension at least -*> ( 1 + ( n - 1 )*abs( INCX ) ). -*> Before entry, the incremented array X must contain the n -*> element vector x. -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> On entry, INCX specifies the increment for the elements of -*> X. INCX must not be zero. -*> \endverbatim -*> -*> \param[in] Y -*> \verbatim -*> Y is DOUBLE PRECISION array, dimension at least -*> ( 1 + ( n - 1 )*abs( INCY ) ). -*> Before entry, the incremented array Y must contain the n -*> element vector y. -*> \endverbatim -*> -*> \param[in] INCY -*> \verbatim -*> INCY is INTEGER -*> On entry, INCY specifies the increment for the elements of -*> Y. INCY must not be zero. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension ( LDA, N ) -*> Before entry with UPLO = 'U' or 'u', the leading n by n -*> upper triangular part of the array A must contain the upper -*> triangular part of the symmetric matrix and the strictly -*> lower triangular part of A is not referenced. On exit, the -*> upper triangular part of the array A is overwritten by the -*> upper triangular part of the updated matrix. -*> Before entry with UPLO = 'L' or 'l', the leading n by n -*> lower triangular part of the array A must contain the lower -*> triangular part of the symmetric matrix and the strictly -*> upper triangular part of A is not referenced. On exit, the -*> lower triangular part of the array A is overwritten by the -*> lower triangular part of the updated matrix. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> On entry, LDA specifies the first dimension of A as declared -*> in the calling (sub) program. LDA must be at least -*> max( 1, n ). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup double_blas_level2 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> Level 2 Blas routine. -*> -*> -- Written on 22-October-1986. -*> Jack Dongarra, Argonne National Lab. -*> Jeremy Du Croz, Nag Central Office. -*> Sven Hammarling, Nag Central Office. -*> Richard Hanson, Sandia National Labs. -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DSYR2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA) -* -* -- Reference BLAS level2 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - DOUBLE PRECISION ALPHA - INTEGER INCX,INCY,LDA,N - CHARACTER UPLO -* .. -* .. Array Arguments .. - DOUBLE PRECISION A(LDA,*),X(*),Y(*) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO - PARAMETER (ZERO=0.0D+0) -* .. -* .. Local Scalars .. - DOUBLE PRECISION TEMP1,TEMP2 - INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* -* Test the input parameters. -* - INFO = 0 - IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN - INFO = 1 - ELSE IF (N.LT.0) THEN - INFO = 2 - ELSE IF (INCX.EQ.0) THEN - INFO = 5 - ELSE IF (INCY.EQ.0) THEN - INFO = 7 - ELSE IF (LDA.LT.MAX(1,N)) THEN - INFO = 9 - END IF - IF (INFO.NE.0) THEN - CALL XERBLA('DSYR2 ',INFO) - RETURN - END IF -* -* Quick return if possible. -* - IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN -* -* Set up the start points in X and Y if the increments are not both -* unity. -* - IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN - IF (INCX.GT.0) THEN - KX = 1 - ELSE - KX = 1 - (N-1)*INCX - END IF - IF (INCY.GT.0) THEN - KY = 1 - ELSE - KY = 1 - (N-1)*INCY - END IF - JX = KX - JY = KY - END IF -* -* Start the operations. In this version the elements of A are -* accessed sequentially with one pass through the triangular part -* of A. -* - IF (LSAME(UPLO,'U')) THEN -* -* Form A when A is stored in the upper triangle. -* - IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN - DO 20 J = 1,N - IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN - TEMP1 = ALPHA*Y(J) - TEMP2 = ALPHA*X(J) - DO 10 I = 1,J - A(I,J) = A(I,J) + X(I)*TEMP1 + Y(I)*TEMP2 - 10 CONTINUE - END IF - 20 CONTINUE - ELSE - DO 40 J = 1,N - IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN - TEMP1 = ALPHA*Y(JY) - TEMP2 = ALPHA*X(JX) - IX = KX - IY = KY - DO 30 I = 1,J - A(I,J) = A(I,J) + X(IX)*TEMP1 + Y(IY)*TEMP2 - IX = IX + INCX - IY = IY + INCY - 30 CONTINUE - END IF - JX = JX + INCX - JY = JY + INCY - 40 CONTINUE - END IF - ELSE -* -* Form A when A is stored in the lower triangle. -* - IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN - DO 60 J = 1,N - IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN - TEMP1 = ALPHA*Y(J) - TEMP2 = ALPHA*X(J) - DO 50 I = J,N - A(I,J) = A(I,J) + X(I)*TEMP1 + Y(I)*TEMP2 - 50 CONTINUE - END IF - 60 CONTINUE - ELSE - DO 80 J = 1,N - IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN - TEMP1 = ALPHA*Y(JY) - TEMP2 = ALPHA*X(JX) - IX = JX - IY = JY - DO 70 I = J,N - A(I,J) = A(I,J) + X(IX)*TEMP1 + Y(IY)*TEMP2 - IX = IX + INCX - IY = IY + INCY - 70 CONTINUE - END IF - JX = JX + INCX - JY = JY + INCY - 80 CONTINUE - END IF - END IF -* - RETURN -* -* End of DSYR2 -* - END diff --git a/lib/linalg/fortran/dsyr2k.f b/lib/linalg/fortran/dsyr2k.f deleted file mode 100644 index f5d16e0854..0000000000 --- a/lib/linalg/fortran/dsyr2k.f +++ /dev/null @@ -1,396 +0,0 @@ -*> \brief \b DSYR2K -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE DSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) -* -* .. Scalar Arguments .. -* DOUBLE PRECISION ALPHA,BETA -* INTEGER K,LDA,LDB,LDC,N -* CHARACTER TRANS,UPLO -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DSYR2K performs one of the symmetric rank 2k operations -*> -*> C := alpha*A*B**T + alpha*B*A**T + beta*C, -*> -*> or -*> -*> C := alpha*A**T*B + alpha*B**T*A + beta*C, -*> -*> where alpha and beta are scalars, C is an n by n symmetric matrix -*> and A and B are n by k matrices in the first case and k by n -*> matrices in the second case. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> On entry, UPLO specifies whether the upper or lower -*> triangular part of the array C is to be referenced as -*> follows: -*> -*> UPLO = 'U' or 'u' Only the upper triangular part of C -*> is to be referenced. -*> -*> UPLO = 'L' or 'l' Only the lower triangular part of C -*> is to be referenced. -*> \endverbatim -*> -*> \param[in] TRANS -*> \verbatim -*> TRANS is CHARACTER*1 -*> On entry, TRANS specifies the operation to be performed as -*> follows: -*> -*> TRANS = 'N' or 'n' C := alpha*A*B**T + alpha*B*A**T + -*> beta*C. -*> -*> TRANS = 'T' or 't' C := alpha*A**T*B + alpha*B**T*A + -*> beta*C. -*> -*> TRANS = 'C' or 'c' C := alpha*A**T*B + alpha*B**T*A + -*> beta*C. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> On entry, N specifies the order of the matrix C. N must be -*> at least zero. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> On entry with TRANS = 'N' or 'n', K specifies the number -*> of columns of the matrices A and B, and on entry with -*> TRANS = 'T' or 't' or 'C' or 'c', K specifies the number -*> of rows of the matrices A and B. K must be at least zero. -*> \endverbatim -*> -*> \param[in] ALPHA -*> \verbatim -*> ALPHA is DOUBLE PRECISION. -*> On entry, ALPHA specifies the scalar alpha. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is -*> k when TRANS = 'N' or 'n', and is n otherwise. -*> Before entry with TRANS = 'N' or 'n', the leading n by k -*> part of the array A must contain the matrix A, otherwise -*> the leading k by n part of the array A must contain the -*> matrix A. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> On entry, LDA specifies the first dimension of A as declared -*> in the calling (sub) program. When TRANS = 'N' or 'n' -*> then LDA must be at least max( 1, n ), otherwise LDA must -*> be at least max( 1, k ). -*> \endverbatim -*> -*> \param[in] B -*> \verbatim -*> B is DOUBLE PRECISION array, dimension ( LDB, kb ), where kb is -*> k when TRANS = 'N' or 'n', and is n otherwise. -*> Before entry with TRANS = 'N' or 'n', the leading n by k -*> part of the array B must contain the matrix B, otherwise -*> the leading k by n part of the array B must contain the -*> matrix B. -*> \endverbatim -*> -*> \param[in] LDB -*> \verbatim -*> LDB is INTEGER -*> On entry, LDB specifies the first dimension of B as declared -*> in the calling (sub) program. When TRANS = 'N' or 'n' -*> then LDB must be at least max( 1, n ), otherwise LDB must -*> be at least max( 1, k ). -*> \endverbatim -*> -*> \param[in] BETA -*> \verbatim -*> BETA is DOUBLE PRECISION. -*> On entry, BETA specifies the scalar beta. -*> \endverbatim -*> -*> \param[in,out] C -*> \verbatim -*> C is DOUBLE PRECISION array, dimension ( LDC, N ) -*> Before entry with UPLO = 'U' or 'u', the leading n by n -*> upper triangular part of the array C must contain the upper -*> triangular part of the symmetric matrix and the strictly -*> lower triangular part of C is not referenced. On exit, the -*> upper triangular part of the array C is overwritten by the -*> upper triangular part of the updated matrix. -*> Before entry with UPLO = 'L' or 'l', the leading n by n -*> lower triangular part of the array C must contain the lower -*> triangular part of the symmetric matrix and the strictly -*> upper triangular part of C is not referenced. On exit, the -*> lower triangular part of the array C is overwritten by the -*> lower triangular part of the updated matrix. -*> \endverbatim -*> -*> \param[in] LDC -*> \verbatim -*> LDC is INTEGER -*> On entry, LDC specifies the first dimension of C as declared -*> in the calling (sub) program. LDC must be at least -*> max( 1, n ). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup double_blas_level3 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> Level 3 Blas routine. -*> -*> -*> -- Written on 8-February-1989. -*> Jack Dongarra, Argonne National Laboratory. -*> Iain Duff, AERE Harwell. -*> Jeremy Du Croz, Numerical Algorithms Group Ltd. -*> Sven Hammarling, Numerical Algorithms Group Ltd. -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) -* -* -- Reference BLAS level3 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - DOUBLE PRECISION ALPHA,BETA - INTEGER K,LDA,LDB,LDC,N - CHARACTER TRANS,UPLO -* .. -* .. Array Arguments .. - DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*) -* .. -* -* ===================================================================== -* -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* .. Local Scalars .. - DOUBLE PRECISION TEMP1,TEMP2 - INTEGER I,INFO,J,L,NROWA - LOGICAL UPPER -* .. -* .. Parameters .. - DOUBLE PRECISION ONE,ZERO - PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) -* .. -* -* Test the input parameters. -* - IF (LSAME(TRANS,'N')) THEN - NROWA = N - ELSE - NROWA = K - END IF - UPPER = LSAME(UPLO,'U') -* - INFO = 0 - IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN - INFO = 1 - ELSE IF ((.NOT.LSAME(TRANS,'N')) .AND. - + (.NOT.LSAME(TRANS,'T')) .AND. - + (.NOT.LSAME(TRANS,'C'))) THEN - INFO = 2 - ELSE IF (N.LT.0) THEN - INFO = 3 - ELSE IF (K.LT.0) THEN - INFO = 4 - ELSE IF (LDA.LT.MAX(1,NROWA)) THEN - INFO = 7 - ELSE IF (LDB.LT.MAX(1,NROWA)) THEN - INFO = 9 - ELSE IF (LDC.LT.MAX(1,N)) THEN - INFO = 12 - END IF - IF (INFO.NE.0) THEN - CALL XERBLA('DSYR2K',INFO) - RETURN - END IF -* -* Quick return if possible. -* - IF ((N.EQ.0) .OR. (((ALPHA.EQ.ZERO).OR. - + (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN -* -* And when alpha.eq.zero. -* - IF (ALPHA.EQ.ZERO) THEN - IF (UPPER) THEN - IF (BETA.EQ.ZERO) THEN - DO 20 J = 1,N - DO 10 I = 1,J - C(I,J) = ZERO - 10 CONTINUE - 20 CONTINUE - ELSE - DO 40 J = 1,N - DO 30 I = 1,J - C(I,J) = BETA*C(I,J) - 30 CONTINUE - 40 CONTINUE - END IF - ELSE - IF (BETA.EQ.ZERO) THEN - DO 60 J = 1,N - DO 50 I = J,N - C(I,J) = ZERO - 50 CONTINUE - 60 CONTINUE - ELSE - DO 80 J = 1,N - DO 70 I = J,N - C(I,J) = BETA*C(I,J) - 70 CONTINUE - 80 CONTINUE - END IF - END IF - RETURN - END IF -* -* Start the operations. -* - IF (LSAME(TRANS,'N')) THEN -* -* Form C := alpha*A*B**T + alpha*B*A**T + C. -* - IF (UPPER) THEN - DO 130 J = 1,N - IF (BETA.EQ.ZERO) THEN - DO 90 I = 1,J - C(I,J) = ZERO - 90 CONTINUE - ELSE IF (BETA.NE.ONE) THEN - DO 100 I = 1,J - C(I,J) = BETA*C(I,J) - 100 CONTINUE - END IF - DO 120 L = 1,K - IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN - TEMP1 = ALPHA*B(J,L) - TEMP2 = ALPHA*A(J,L) - DO 110 I = 1,J - C(I,J) = C(I,J) + A(I,L)*TEMP1 + - + B(I,L)*TEMP2 - 110 CONTINUE - END IF - 120 CONTINUE - 130 CONTINUE - ELSE - DO 180 J = 1,N - IF (BETA.EQ.ZERO) THEN - DO 140 I = J,N - C(I,J) = ZERO - 140 CONTINUE - ELSE IF (BETA.NE.ONE) THEN - DO 150 I = J,N - C(I,J) = BETA*C(I,J) - 150 CONTINUE - END IF - DO 170 L = 1,K - IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN - TEMP1 = ALPHA*B(J,L) - TEMP2 = ALPHA*A(J,L) - DO 160 I = J,N - C(I,J) = C(I,J) + A(I,L)*TEMP1 + - + B(I,L)*TEMP2 - 160 CONTINUE - END IF - 170 CONTINUE - 180 CONTINUE - END IF - ELSE -* -* Form C := alpha*A**T*B + alpha*B**T*A + C. -* - IF (UPPER) THEN - DO 210 J = 1,N - DO 200 I = 1,J - TEMP1 = ZERO - TEMP2 = ZERO - DO 190 L = 1,K - TEMP1 = TEMP1 + A(L,I)*B(L,J) - TEMP2 = TEMP2 + B(L,I)*A(L,J) - 190 CONTINUE - IF (BETA.EQ.ZERO) THEN - C(I,J) = ALPHA*TEMP1 + ALPHA*TEMP2 - ELSE - C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 + - + ALPHA*TEMP2 - END IF - 200 CONTINUE - 210 CONTINUE - ELSE - DO 240 J = 1,N - DO 230 I = J,N - TEMP1 = ZERO - TEMP2 = ZERO - DO 220 L = 1,K - TEMP1 = TEMP1 + A(L,I)*B(L,J) - TEMP2 = TEMP2 + B(L,I)*A(L,J) - 220 CONTINUE - IF (BETA.EQ.ZERO) THEN - C(I,J) = ALPHA*TEMP1 + ALPHA*TEMP2 - ELSE - C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 + - + ALPHA*TEMP2 - END IF - 230 CONTINUE - 240 CONTINUE - END IF - END IF -* - RETURN -* -* End of DSYR2K -* - END diff --git a/lib/linalg/fortran/dsyrk.f b/lib/linalg/fortran/dsyrk.f deleted file mode 100644 index 0548c0ce2f..0000000000 --- a/lib/linalg/fortran/dsyrk.f +++ /dev/null @@ -1,361 +0,0 @@ -*> \brief \b DSYRK -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE DSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC) -* -* .. Scalar Arguments .. -* DOUBLE PRECISION ALPHA,BETA -* INTEGER K,LDA,LDC,N -* CHARACTER TRANS,UPLO -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A(LDA,*),C(LDC,*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DSYRK performs one of the symmetric rank k operations -*> -*> C := alpha*A*A**T + beta*C, -*> -*> or -*> -*> C := alpha*A**T*A + beta*C, -*> -*> where alpha and beta are scalars, C is an n by n symmetric matrix -*> and A is an n by k matrix in the first case and a k by n matrix -*> in the second case. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> On entry, UPLO specifies whether the upper or lower -*> triangular part of the array C is to be referenced as -*> follows: -*> -*> UPLO = 'U' or 'u' Only the upper triangular part of C -*> is to be referenced. -*> -*> UPLO = 'L' or 'l' Only the lower triangular part of C -*> is to be referenced. -*> \endverbatim -*> -*> \param[in] TRANS -*> \verbatim -*> TRANS is CHARACTER*1 -*> On entry, TRANS specifies the operation to be performed as -*> follows: -*> -*> TRANS = 'N' or 'n' C := alpha*A*A**T + beta*C. -*> -*> TRANS = 'T' or 't' C := alpha*A**T*A + beta*C. -*> -*> TRANS = 'C' or 'c' C := alpha*A**T*A + beta*C. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> On entry, N specifies the order of the matrix C. N must be -*> at least zero. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> On entry with TRANS = 'N' or 'n', K specifies the number -*> of columns of the matrix A, and on entry with -*> TRANS = 'T' or 't' or 'C' or 'c', K specifies the number -*> of rows of the matrix A. K must be at least zero. -*> \endverbatim -*> -*> \param[in] ALPHA -*> \verbatim -*> ALPHA is DOUBLE PRECISION. -*> On entry, ALPHA specifies the scalar alpha. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is -*> k when TRANS = 'N' or 'n', and is n otherwise. -*> Before entry with TRANS = 'N' or 'n', the leading n by k -*> part of the array A must contain the matrix A, otherwise -*> the leading k by n part of the array A must contain the -*> matrix A. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> On entry, LDA specifies the first dimension of A as declared -*> in the calling (sub) program. When TRANS = 'N' or 'n' -*> then LDA must be at least max( 1, n ), otherwise LDA must -*> be at least max( 1, k ). -*> \endverbatim -*> -*> \param[in] BETA -*> \verbatim -*> BETA is DOUBLE PRECISION. -*> On entry, BETA specifies the scalar beta. -*> \endverbatim -*> -*> \param[in,out] C -*> \verbatim -*> C is DOUBLE PRECISION array, dimension ( LDC, N ) -*> Before entry with UPLO = 'U' or 'u', the leading n by n -*> upper triangular part of the array C must contain the upper -*> triangular part of the symmetric matrix and the strictly -*> lower triangular part of C is not referenced. On exit, the -*> upper triangular part of the array C is overwritten by the -*> upper triangular part of the updated matrix. -*> Before entry with UPLO = 'L' or 'l', the leading n by n -*> lower triangular part of the array C must contain the lower -*> triangular part of the symmetric matrix and the strictly -*> upper triangular part of C is not referenced. On exit, the -*> lower triangular part of the array C is overwritten by the -*> lower triangular part of the updated matrix. -*> \endverbatim -*> -*> \param[in] LDC -*> \verbatim -*> LDC is INTEGER -*> On entry, LDC specifies the first dimension of C as declared -*> in the calling (sub) program. LDC must be at least -*> max( 1, n ). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup double_blas_level3 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> Level 3 Blas routine. -*> -*> -- Written on 8-February-1989. -*> Jack Dongarra, Argonne National Laboratory. -*> Iain Duff, AERE Harwell. -*> Jeremy Du Croz, Numerical Algorithms Group Ltd. -*> Sven Hammarling, Numerical Algorithms Group Ltd. -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC) -* -* -- Reference BLAS level3 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - DOUBLE PRECISION ALPHA,BETA - INTEGER K,LDA,LDC,N - CHARACTER TRANS,UPLO -* .. -* .. Array Arguments .. - DOUBLE PRECISION A(LDA,*),C(LDC,*) -* .. -* -* ===================================================================== -* -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* .. Local Scalars .. - DOUBLE PRECISION TEMP - INTEGER I,INFO,J,L,NROWA - LOGICAL UPPER -* .. -* .. Parameters .. - DOUBLE PRECISION ONE,ZERO - PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) -* .. -* -* Test the input parameters. -* - IF (LSAME(TRANS,'N')) THEN - NROWA = N - ELSE - NROWA = K - END IF - UPPER = LSAME(UPLO,'U') -* - INFO = 0 - IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN - INFO = 1 - ELSE IF ((.NOT.LSAME(TRANS,'N')) .AND. - + (.NOT.LSAME(TRANS,'T')) .AND. - + (.NOT.LSAME(TRANS,'C'))) THEN - INFO = 2 - ELSE IF (N.LT.0) THEN - INFO = 3 - ELSE IF (K.LT.0) THEN - INFO = 4 - ELSE IF (LDA.LT.MAX(1,NROWA)) THEN - INFO = 7 - ELSE IF (LDC.LT.MAX(1,N)) THEN - INFO = 10 - END IF - IF (INFO.NE.0) THEN - CALL XERBLA('DSYRK ',INFO) - RETURN - END IF -* -* Quick return if possible. -* - IF ((N.EQ.0) .OR. (((ALPHA.EQ.ZERO).OR. - + (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN -* -* And when alpha.eq.zero. -* - IF (ALPHA.EQ.ZERO) THEN - IF (UPPER) THEN - IF (BETA.EQ.ZERO) THEN - DO 20 J = 1,N - DO 10 I = 1,J - C(I,J) = ZERO - 10 CONTINUE - 20 CONTINUE - ELSE - DO 40 J = 1,N - DO 30 I = 1,J - C(I,J) = BETA*C(I,J) - 30 CONTINUE - 40 CONTINUE - END IF - ELSE - IF (BETA.EQ.ZERO) THEN - DO 60 J = 1,N - DO 50 I = J,N - C(I,J) = ZERO - 50 CONTINUE - 60 CONTINUE - ELSE - DO 80 J = 1,N - DO 70 I = J,N - C(I,J) = BETA*C(I,J) - 70 CONTINUE - 80 CONTINUE - END IF - END IF - RETURN - END IF -* -* Start the operations. -* - IF (LSAME(TRANS,'N')) THEN -* -* Form C := alpha*A*A**T + beta*C. -* - IF (UPPER) THEN - DO 130 J = 1,N - IF (BETA.EQ.ZERO) THEN - DO 90 I = 1,J - C(I,J) = ZERO - 90 CONTINUE - ELSE IF (BETA.NE.ONE) THEN - DO 100 I = 1,J - C(I,J) = BETA*C(I,J) - 100 CONTINUE - END IF - DO 120 L = 1,K - IF (A(J,L).NE.ZERO) THEN - TEMP = ALPHA*A(J,L) - DO 110 I = 1,J - C(I,J) = C(I,J) + TEMP*A(I,L) - 110 CONTINUE - END IF - 120 CONTINUE - 130 CONTINUE - ELSE - DO 180 J = 1,N - IF (BETA.EQ.ZERO) THEN - DO 140 I = J,N - C(I,J) = ZERO - 140 CONTINUE - ELSE IF (BETA.NE.ONE) THEN - DO 150 I = J,N - C(I,J) = BETA*C(I,J) - 150 CONTINUE - END IF - DO 170 L = 1,K - IF (A(J,L).NE.ZERO) THEN - TEMP = ALPHA*A(J,L) - DO 160 I = J,N - C(I,J) = C(I,J) + TEMP*A(I,L) - 160 CONTINUE - END IF - 170 CONTINUE - 180 CONTINUE - END IF - ELSE -* -* Form C := alpha*A**T*A + beta*C. -* - IF (UPPER) THEN - DO 210 J = 1,N - DO 200 I = 1,J - TEMP = ZERO - DO 190 L = 1,K - TEMP = TEMP + A(L,I)*A(L,J) - 190 CONTINUE - IF (BETA.EQ.ZERO) THEN - C(I,J) = ALPHA*TEMP - ELSE - C(I,J) = ALPHA*TEMP + BETA*C(I,J) - END IF - 200 CONTINUE - 210 CONTINUE - ELSE - DO 240 J = 1,N - DO 230 I = J,N - TEMP = ZERO - DO 220 L = 1,K - TEMP = TEMP + A(L,I)*A(L,J) - 220 CONTINUE - IF (BETA.EQ.ZERO) THEN - C(I,J) = ALPHA*TEMP - ELSE - C(I,J) = ALPHA*TEMP + BETA*C(I,J) - END IF - 230 CONTINUE - 240 CONTINUE - END IF - END IF -* - RETURN -* -* End of DSYRK -* - END diff --git a/lib/linalg/fortran/dsytd2.f b/lib/linalg/fortran/dsytd2.f deleted file mode 100644 index 977b6daa41..0000000000 --- a/lib/linalg/fortran/dsytd2.f +++ /dev/null @@ -1,320 +0,0 @@ -*> \brief \b DSYTD2 reduces a symmetric matrix to real symmetric tridiagonal form by an orthogonal similarity transformation (unblocked algorithm). -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DSYTD2 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DSYTD2( UPLO, N, A, LDA, D, E, TAU, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER UPLO -* INTEGER INFO, LDA, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), TAU( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DSYTD2 reduces a real symmetric matrix A to symmetric tridiagonal -*> form T by an orthogonal similarity transformation: Q**T * A * Q = T. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> Specifies whether the upper or lower triangular part of the -*> symmetric matrix A is stored: -*> = 'U': Upper triangular -*> = 'L': Lower triangular -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the symmetric matrix A. If UPLO = 'U', the leading -*> n-by-n upper triangular part of A contains the upper -*> triangular part of the matrix A, and the strictly lower -*> triangular part of A is not referenced. If UPLO = 'L', the -*> leading n-by-n lower triangular part of A contains the lower -*> triangular part of the matrix A, and the strictly upper -*> triangular part of A is not referenced. -*> On exit, if UPLO = 'U', the diagonal and first superdiagonal -*> of A are overwritten by the corresponding elements of the -*> tridiagonal matrix T, and the elements above the first -*> superdiagonal, with the array TAU, represent the orthogonal -*> matrix Q as a product of elementary reflectors; if UPLO -*> = 'L', the diagonal and first subdiagonal of A are over- -*> written by the corresponding elements of the tridiagonal -*> matrix T, and the elements below the first subdiagonal, with -*> the array TAU, represent the orthogonal matrix Q as a product -*> of elementary reflectors. See Further Details. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,N). -*> \endverbatim -*> -*> \param[out] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension (N) -*> The diagonal elements of the tridiagonal matrix T: -*> D(i) = A(i,i). -*> \endverbatim -*> -*> \param[out] E -*> \verbatim -*> E is DOUBLE PRECISION array, dimension (N-1) -*> The off-diagonal elements of the tridiagonal matrix T: -*> E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. -*> \endverbatim -*> -*> \param[out] TAU -*> \verbatim -*> TAU is DOUBLE PRECISION array, dimension (N-1) -*> The scalar factors of the elementary reflectors (see Further -*> Details). -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleSYcomputational -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> If UPLO = 'U', the matrix Q is represented as a product of elementary -*> reflectors -*> -*> Q = H(n-1) . . . H(2) H(1). -*> -*> Each H(i) has the form -*> -*> H(i) = I - tau * v * v**T -*> -*> where tau is a real scalar, and v is a real vector with -*> v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in -*> A(1:i-1,i+1), and tau in TAU(i). -*> -*> If UPLO = 'L', the matrix Q is represented as a product of elementary -*> reflectors -*> -*> Q = H(1) H(2) . . . H(n-1). -*> -*> Each H(i) has the form -*> -*> H(i) = I - tau * v * v**T -*> -*> where tau is a real scalar, and v is a real vector with -*> v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), -*> and tau in TAU(i). -*> -*> The contents of A on exit are illustrated by the following examples -*> with n = 5: -*> -*> if UPLO = 'U': if UPLO = 'L': -*> -*> ( d e v2 v3 v4 ) ( d ) -*> ( d e v3 v4 ) ( e d ) -*> ( d e v4 ) ( v1 e d ) -*> ( d e ) ( v1 v2 e d ) -*> ( d ) ( v1 v2 v3 e d ) -*> -*> where d and e denote diagonal and off-diagonal elements of T, and vi -*> denotes an element of the vector defining H(i). -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DSYTD2( UPLO, N, A, LDA, D, E, TAU, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER UPLO - INTEGER INFO, LDA, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), TAU( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE, ZERO, HALF - PARAMETER ( ONE = 1.0D0, ZERO = 0.0D0, - $ HALF = 1.0D0 / 2.0D0 ) -* .. -* .. Local Scalars .. - LOGICAL UPPER - INTEGER I - DOUBLE PRECISION ALPHA, TAUI -* .. -* .. External Subroutines .. - EXTERNAL DAXPY, DLARFG, DSYMV, DSYR2, XERBLA -* .. -* .. External Functions .. - LOGICAL LSAME - DOUBLE PRECISION DDOT - EXTERNAL LSAME, DDOT -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, MIN -* .. -* .. Executable Statements .. -* -* Test the input parameters -* - INFO = 0 - UPPER = LSAME( UPLO, 'U' ) - IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -4 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DSYTD2', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( N.LE.0 ) - $ RETURN -* - IF( UPPER ) THEN -* -* Reduce the upper triangle of A -* - DO 10 I = N - 1, 1, -1 -* -* Generate elementary reflector H(i) = I - tau * v * v**T -* to annihilate A(1:i-1,i+1) -* - CALL DLARFG( I, A( I, I+1 ), A( 1, I+1 ), 1, TAUI ) - E( I ) = A( I, I+1 ) -* - IF( TAUI.NE.ZERO ) THEN -* -* Apply H(i) from both sides to A(1:i,1:i) -* - A( I, I+1 ) = ONE -* -* Compute x := tau * A * v storing x in TAU(1:i) -* - CALL DSYMV( UPLO, I, TAUI, A, LDA, A( 1, I+1 ), 1, ZERO, - $ TAU, 1 ) -* -* Compute w := x - 1/2 * tau * (x**T * v) * v -* - ALPHA = -HALF*TAUI*DDOT( I, TAU, 1, A( 1, I+1 ), 1 ) - CALL DAXPY( I, ALPHA, A( 1, I+1 ), 1, TAU, 1 ) -* -* Apply the transformation as a rank-2 update: -* A := A - v * w**T - w * v**T -* - CALL DSYR2( UPLO, I, -ONE, A( 1, I+1 ), 1, TAU, 1, A, - $ LDA ) -* - A( I, I+1 ) = E( I ) - END IF - D( I+1 ) = A( I+1, I+1 ) - TAU( I ) = TAUI - 10 CONTINUE - D( 1 ) = A( 1, 1 ) - ELSE -* -* Reduce the lower triangle of A -* - DO 20 I = 1, N - 1 -* -* Generate elementary reflector H(i) = I - tau * v * v**T -* to annihilate A(i+2:n,i) -* - CALL DLARFG( N-I, A( I+1, I ), A( MIN( I+2, N ), I ), 1, - $ TAUI ) - E( I ) = A( I+1, I ) -* - IF( TAUI.NE.ZERO ) THEN -* -* Apply H(i) from both sides to A(i+1:n,i+1:n) -* - A( I+1, I ) = ONE -* -* Compute x := tau * A * v storing y in TAU(i:n-1) -* - CALL DSYMV( UPLO, N-I, TAUI, A( I+1, I+1 ), LDA, - $ A( I+1, I ), 1, ZERO, TAU( I ), 1 ) -* -* Compute w := x - 1/2 * tau * (x**T * v) * v -* - ALPHA = -HALF*TAUI*DDOT( N-I, TAU( I ), 1, A( I+1, I ), - $ 1 ) - CALL DAXPY( N-I, ALPHA, A( I+1, I ), 1, TAU( I ), 1 ) -* -* Apply the transformation as a rank-2 update: -* A := A - v * w**T - w * v**T -* - CALL DSYR2( UPLO, N-I, -ONE, A( I+1, I ), 1, TAU( I ), 1, - $ A( I+1, I+1 ), LDA ) -* - A( I+1, I ) = E( I ) - END IF - D( I ) = A( I, I ) - TAU( I ) = TAUI - 20 CONTINUE - D( N ) = A( N, N ) - END IF -* - RETURN -* -* End of DSYTD2 -* - END diff --git a/lib/linalg/fortran/dsytrd.f b/lib/linalg/fortran/dsytrd.f deleted file mode 100644 index 3dcfc3db2b..0000000000 --- a/lib/linalg/fortran/dsytrd.f +++ /dev/null @@ -1,373 +0,0 @@ -*> \brief \b DSYTRD -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DSYTRD + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DSYTRD( UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER UPLO -* INTEGER INFO, LDA, LWORK, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), TAU( * ), -* $ WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DSYTRD reduces a real symmetric matrix A to real symmetric -*> tridiagonal form T by an orthogonal similarity transformation: -*> Q**T * A * Q = T. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> = 'U': Upper triangle of A is stored; -*> = 'L': Lower triangle of A is stored. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the symmetric matrix A. If UPLO = 'U', the leading -*> N-by-N upper triangular part of A contains the upper -*> triangular part of the matrix A, and the strictly lower -*> triangular part of A is not referenced. If UPLO = 'L', the -*> leading N-by-N lower triangular part of A contains the lower -*> triangular part of the matrix A, and the strictly upper -*> triangular part of A is not referenced. -*> On exit, if UPLO = 'U', the diagonal and first superdiagonal -*> of A are overwritten by the corresponding elements of the -*> tridiagonal matrix T, and the elements above the first -*> superdiagonal, with the array TAU, represent the orthogonal -*> matrix Q as a product of elementary reflectors; if UPLO -*> = 'L', the diagonal and first subdiagonal of A are over- -*> written by the corresponding elements of the tridiagonal -*> matrix T, and the elements below the first subdiagonal, with -*> the array TAU, represent the orthogonal matrix Q as a product -*> of elementary reflectors. See Further Details. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,N). -*> \endverbatim -*> -*> \param[out] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension (N) -*> The diagonal elements of the tridiagonal matrix T: -*> D(i) = A(i,i). -*> \endverbatim -*> -*> \param[out] E -*> \verbatim -*> E is DOUBLE PRECISION array, dimension (N-1) -*> The off-diagonal elements of the tridiagonal matrix T: -*> E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. -*> \endverbatim -*> -*> \param[out] TAU -*> \verbatim -*> TAU is DOUBLE PRECISION array, dimension (N-1) -*> The scalar factors of the elementary reflectors (see Further -*> Details). -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) -*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -*> \endverbatim -*> -*> \param[in] LWORK -*> \verbatim -*> LWORK is INTEGER -*> The dimension of the array WORK. LWORK >= 1. -*> For optimum performance LWORK >= N*NB, where NB is the -*> optimal blocksize. -*> -*> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal size of the WORK array, returns -*> this value as the first entry of the WORK array, and no error -*> message related to LWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleSYcomputational -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> If UPLO = 'U', the matrix Q is represented as a product of elementary -*> reflectors -*> -*> Q = H(n-1) . . . H(2) H(1). -*> -*> Each H(i) has the form -*> -*> H(i) = I - tau * v * v**T -*> -*> where tau is a real scalar, and v is a real vector with -*> v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in -*> A(1:i-1,i+1), and tau in TAU(i). -*> -*> If UPLO = 'L', the matrix Q is represented as a product of elementary -*> reflectors -*> -*> Q = H(1) H(2) . . . H(n-1). -*> -*> Each H(i) has the form -*> -*> H(i) = I - tau * v * v**T -*> -*> where tau is a real scalar, and v is a real vector with -*> v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), -*> and tau in TAU(i). -*> -*> The contents of A on exit are illustrated by the following examples -*> with n = 5: -*> -*> if UPLO = 'U': if UPLO = 'L': -*> -*> ( d e v2 v3 v4 ) ( d ) -*> ( d e v3 v4 ) ( e d ) -*> ( d e v4 ) ( v1 e d ) -*> ( d e ) ( v1 v2 e d ) -*> ( d ) ( v1 v2 v3 e d ) -*> -*> where d and e denote diagonal and off-diagonal elements of T, and vi -*> denotes an element of the vector defining H(i). -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DSYTRD( UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER UPLO - INTEGER INFO, LDA, LWORK, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), TAU( * ), - $ WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE - PARAMETER ( ONE = 1.0D+0 ) -* .. -* .. Local Scalars .. - LOGICAL LQUERY, UPPER - INTEGER I, IINFO, IWS, J, KK, LDWORK, LWKOPT, NB, - $ NBMIN, NX -* .. -* .. External Subroutines .. - EXTERNAL DLATRD, DSYR2K, DSYTD2, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* .. External Functions .. - LOGICAL LSAME - INTEGER ILAENV - EXTERNAL LSAME, ILAENV -* .. -* .. Executable Statements .. -* -* Test the input parameters -* - INFO = 0 - UPPER = LSAME( UPLO, 'U' ) - LQUERY = ( LWORK.EQ.-1 ) - IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -4 - ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN - INFO = -9 - END IF -* - IF( INFO.EQ.0 ) THEN -* -* Determine the block size. -* - NB = ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 ) - LWKOPT = N*NB - WORK( 1 ) = LWKOPT - END IF -* - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DSYTRD', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - RETURN - END IF -* -* Quick return if possible -* - IF( N.EQ.0 ) THEN - WORK( 1 ) = 1 - RETURN - END IF -* - NX = N - IWS = 1 - IF( NB.GT.1 .AND. NB.LT.N ) THEN -* -* Determine when to cross over from blocked to unblocked code -* (last block is always handled by unblocked code). -* - NX = MAX( NB, ILAENV( 3, 'DSYTRD', UPLO, N, -1, -1, -1 ) ) - IF( NX.LT.N ) THEN -* -* Determine if workspace is large enough for blocked code. -* - LDWORK = N - IWS = LDWORK*NB - IF( LWORK.LT.IWS ) THEN -* -* Not enough workspace to use optimal NB: determine the -* minimum value of NB, and reduce NB or force use of -* unblocked code by setting NX = N. -* - NB = MAX( LWORK / LDWORK, 1 ) - NBMIN = ILAENV( 2, 'DSYTRD', UPLO, N, -1, -1, -1 ) - IF( NB.LT.NBMIN ) - $ NX = N - END IF - ELSE - NX = N - END IF - ELSE - NB = 1 - END IF -* - IF( UPPER ) THEN -* -* Reduce the upper triangle of A. -* Columns 1:kk are handled by the unblocked method. -* - KK = N - ( ( N-NX+NB-1 ) / NB )*NB - DO 20 I = N - NB + 1, KK + 1, -NB -* -* Reduce columns i:i+nb-1 to tridiagonal form and form the -* matrix W which is needed to update the unreduced part of -* the matrix -* - CALL DLATRD( UPLO, I+NB-1, NB, A, LDA, E, TAU, WORK, - $ LDWORK ) -* -* Update the unreduced submatrix A(1:i-1,1:i-1), using an -* update of the form: A := A - V*W**T - W*V**T -* - CALL DSYR2K( UPLO, 'No transpose', I-1, NB, -ONE, A( 1, I ), - $ LDA, WORK, LDWORK, ONE, A, LDA ) -* -* Copy superdiagonal elements back into A, and diagonal -* elements into D -* - DO 10 J = I, I + NB - 1 - A( J-1, J ) = E( J-1 ) - D( J ) = A( J, J ) - 10 CONTINUE - 20 CONTINUE -* -* Use unblocked code to reduce the last or only block -* - CALL DSYTD2( UPLO, KK, A, LDA, D, E, TAU, IINFO ) - ELSE -* -* Reduce the lower triangle of A -* - DO 40 I = 1, N - NX, NB -* -* Reduce columns i:i+nb-1 to tridiagonal form and form the -* matrix W which is needed to update the unreduced part of -* the matrix -* - CALL DLATRD( UPLO, N-I+1, NB, A( I, I ), LDA, E( I ), - $ TAU( I ), WORK, LDWORK ) -* -* Update the unreduced submatrix A(i+ib:n,i+ib:n), using -* an update of the form: A := A - V*W**T - W*V**T -* - CALL DSYR2K( UPLO, 'No transpose', N-I-NB+1, NB, -ONE, - $ A( I+NB, I ), LDA, WORK( NB+1 ), LDWORK, ONE, - $ A( I+NB, I+NB ), LDA ) -* -* Copy subdiagonal elements back into A, and diagonal -* elements into D -* - DO 30 J = I, I + NB - 1 - A( J+1, J ) = E( J ) - D( J ) = A( J, J ) - 30 CONTINUE - 40 CONTINUE -* -* Use unblocked code to reduce the last or only block -* - CALL DSYTD2( UPLO, N-I+1, A( I, I ), LDA, D( I ), E( I ), - $ TAU( I ), IINFO ) - END IF -* - WORK( 1 ) = LWKOPT - RETURN -* -* End of DSYTRD -* - END diff --git a/lib/linalg/fortran/dtrmm.f b/lib/linalg/fortran/dtrmm.f deleted file mode 100644 index b2cc0a1fa8..0000000000 --- a/lib/linalg/fortran/dtrmm.f +++ /dev/null @@ -1,412 +0,0 @@ -*> \brief \b DTRMM -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE DTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) -* -* .. Scalar Arguments .. -* DOUBLE PRECISION ALPHA -* INTEGER LDA,LDB,M,N -* CHARACTER DIAG,SIDE,TRANSA,UPLO -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A(LDA,*),B(LDB,*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DTRMM performs one of the matrix-matrix operations -*> -*> B := alpha*op( A )*B, or B := alpha*B*op( A ), -*> -*> where alpha is a scalar, B is an m by n matrix, A is a unit, or -*> non-unit, upper or lower triangular matrix and op( A ) is one of -*> -*> op( A ) = A or op( A ) = A**T. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] SIDE -*> \verbatim -*> SIDE is CHARACTER*1 -*> On entry, SIDE specifies whether op( A ) multiplies B from -*> the left or right as follows: -*> -*> SIDE = 'L' or 'l' B := alpha*op( A )*B. -*> -*> SIDE = 'R' or 'r' B := alpha*B*op( A ). -*> \endverbatim -*> -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> On entry, UPLO specifies whether the matrix A is an upper or -*> lower triangular matrix as follows: -*> -*> UPLO = 'U' or 'u' A is an upper triangular matrix. -*> -*> UPLO = 'L' or 'l' A is a lower triangular matrix. -*> \endverbatim -*> -*> \param[in] TRANSA -*> \verbatim -*> TRANSA is CHARACTER*1 -*> On entry, TRANSA specifies the form of op( A ) to be used in -*> the matrix multiplication as follows: -*> -*> TRANSA = 'N' or 'n' op( A ) = A. -*> -*> TRANSA = 'T' or 't' op( A ) = A**T. -*> -*> TRANSA = 'C' or 'c' op( A ) = A**T. -*> \endverbatim -*> -*> \param[in] DIAG -*> \verbatim -*> DIAG is CHARACTER*1 -*> On entry, DIAG specifies whether or not A is unit triangular -*> as follows: -*> -*> DIAG = 'U' or 'u' A is assumed to be unit triangular. -*> -*> DIAG = 'N' or 'n' A is not assumed to be unit -*> triangular. -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> On entry, M specifies the number of rows of B. M must be at -*> least zero. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> On entry, N specifies the number of columns of B. N must be -*> at least zero. -*> \endverbatim -*> -*> \param[in] ALPHA -*> \verbatim -*> ALPHA is DOUBLE PRECISION. -*> On entry, ALPHA specifies the scalar alpha. When alpha is -*> zero then A is not referenced and B need not be set before -*> entry. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension ( LDA, k ), where k is m -*> when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. -*> Before entry with UPLO = 'U' or 'u', the leading k by k -*> upper triangular part of the array A must contain the upper -*> triangular matrix and the strictly lower triangular part of -*> A is not referenced. -*> Before entry with UPLO = 'L' or 'l', the leading k by k -*> lower triangular part of the array A must contain the lower -*> triangular matrix and the strictly upper triangular part of -*> A is not referenced. -*> Note that when DIAG = 'U' or 'u', the diagonal elements of -*> A are not referenced either, but are assumed to be unity. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> On entry, LDA specifies the first dimension of A as declared -*> in the calling (sub) program. When SIDE = 'L' or 'l' then -*> LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' -*> then LDA must be at least max( 1, n ). -*> \endverbatim -*> -*> \param[in,out] B -*> \verbatim -*> B is DOUBLE PRECISION array, dimension ( LDB, N ) -*> Before entry, the leading m by n part of the array B must -*> contain the matrix B, and on exit is overwritten by the -*> transformed matrix. -*> \endverbatim -*> -*> \param[in] LDB -*> \verbatim -*> LDB is INTEGER -*> On entry, LDB specifies the first dimension of B as declared -*> in the calling (sub) program. LDB must be at least -*> max( 1, m ). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup double_blas_level3 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> Level 3 Blas routine. -*> -*> -- Written on 8-February-1989. -*> Jack Dongarra, Argonne National Laboratory. -*> Iain Duff, AERE Harwell. -*> Jeremy Du Croz, Numerical Algorithms Group Ltd. -*> Sven Hammarling, Numerical Algorithms Group Ltd. -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) -* -* -- Reference BLAS level3 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - DOUBLE PRECISION ALPHA - INTEGER LDA,LDB,M,N - CHARACTER DIAG,SIDE,TRANSA,UPLO -* .. -* .. Array Arguments .. - DOUBLE PRECISION A(LDA,*),B(LDB,*) -* .. -* -* ===================================================================== -* -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* .. Local Scalars .. - DOUBLE PRECISION TEMP - INTEGER I,INFO,J,K,NROWA - LOGICAL LSIDE,NOUNIT,UPPER -* .. -* .. Parameters .. - DOUBLE PRECISION ONE,ZERO - PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) -* .. -* -* Test the input parameters. -* - LSIDE = LSAME(SIDE,'L') - IF (LSIDE) THEN - NROWA = M - ELSE - NROWA = N - END IF - NOUNIT = LSAME(DIAG,'N') - UPPER = LSAME(UPLO,'U') -* - INFO = 0 - IF ((.NOT.LSIDE) .AND. (.NOT.LSAME(SIDE,'R'))) THEN - INFO = 1 - ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN - INFO = 2 - ELSE IF ((.NOT.LSAME(TRANSA,'N')) .AND. - + (.NOT.LSAME(TRANSA,'T')) .AND. - + (.NOT.LSAME(TRANSA,'C'))) THEN - INFO = 3 - ELSE IF ((.NOT.LSAME(DIAG,'U')) .AND. (.NOT.LSAME(DIAG,'N'))) THEN - INFO = 4 - ELSE IF (M.LT.0) THEN - INFO = 5 - ELSE IF (N.LT.0) THEN - INFO = 6 - ELSE IF (LDA.LT.MAX(1,NROWA)) THEN - INFO = 9 - ELSE IF (LDB.LT.MAX(1,M)) THEN - INFO = 11 - END IF - IF (INFO.NE.0) THEN - CALL XERBLA('DTRMM ',INFO) - RETURN - END IF -* -* Quick return if possible. -* - IF (M.EQ.0 .OR. N.EQ.0) RETURN -* -* And when alpha.eq.zero. -* - IF (ALPHA.EQ.ZERO) THEN - DO 20 J = 1,N - DO 10 I = 1,M - B(I,J) = ZERO - 10 CONTINUE - 20 CONTINUE - RETURN - END IF -* -* Start the operations. -* - IF (LSIDE) THEN - IF (LSAME(TRANSA,'N')) THEN -* -* Form B := alpha*A*B. -* - IF (UPPER) THEN - DO 50 J = 1,N - DO 40 K = 1,M - IF (B(K,J).NE.ZERO) THEN - TEMP = ALPHA*B(K,J) - DO 30 I = 1,K - 1 - B(I,J) = B(I,J) + TEMP*A(I,K) - 30 CONTINUE - IF (NOUNIT) TEMP = TEMP*A(K,K) - B(K,J) = TEMP - END IF - 40 CONTINUE - 50 CONTINUE - ELSE - DO 80 J = 1,N - DO 70 K = M,1,-1 - IF (B(K,J).NE.ZERO) THEN - TEMP = ALPHA*B(K,J) - B(K,J) = TEMP - IF (NOUNIT) B(K,J) = B(K,J)*A(K,K) - DO 60 I = K + 1,M - B(I,J) = B(I,J) + TEMP*A(I,K) - 60 CONTINUE - END IF - 70 CONTINUE - 80 CONTINUE - END IF - ELSE -* -* Form B := alpha*A**T*B. -* - IF (UPPER) THEN - DO 110 J = 1,N - DO 100 I = M,1,-1 - TEMP = B(I,J) - IF (NOUNIT) TEMP = TEMP*A(I,I) - DO 90 K = 1,I - 1 - TEMP = TEMP + A(K,I)*B(K,J) - 90 CONTINUE - B(I,J) = ALPHA*TEMP - 100 CONTINUE - 110 CONTINUE - ELSE - DO 140 J = 1,N - DO 130 I = 1,M - TEMP = B(I,J) - IF (NOUNIT) TEMP = TEMP*A(I,I) - DO 120 K = I + 1,M - TEMP = TEMP + A(K,I)*B(K,J) - 120 CONTINUE - B(I,J) = ALPHA*TEMP - 130 CONTINUE - 140 CONTINUE - END IF - END IF - ELSE - IF (LSAME(TRANSA,'N')) THEN -* -* Form B := alpha*B*A. -* - IF (UPPER) THEN - DO 180 J = N,1,-1 - TEMP = ALPHA - IF (NOUNIT) TEMP = TEMP*A(J,J) - DO 150 I = 1,M - B(I,J) = TEMP*B(I,J) - 150 CONTINUE - DO 170 K = 1,J - 1 - IF (A(K,J).NE.ZERO) THEN - TEMP = ALPHA*A(K,J) - DO 160 I = 1,M - B(I,J) = B(I,J) + TEMP*B(I,K) - 160 CONTINUE - END IF - 170 CONTINUE - 180 CONTINUE - ELSE - DO 220 J = 1,N - TEMP = ALPHA - IF (NOUNIT) TEMP = TEMP*A(J,J) - DO 190 I = 1,M - B(I,J) = TEMP*B(I,J) - 190 CONTINUE - DO 210 K = J + 1,N - IF (A(K,J).NE.ZERO) THEN - TEMP = ALPHA*A(K,J) - DO 200 I = 1,M - B(I,J) = B(I,J) + TEMP*B(I,K) - 200 CONTINUE - END IF - 210 CONTINUE - 220 CONTINUE - END IF - ELSE -* -* Form B := alpha*B*A**T. -* - IF (UPPER) THEN - DO 260 K = 1,N - DO 240 J = 1,K - 1 - IF (A(J,K).NE.ZERO) THEN - TEMP = ALPHA*A(J,K) - DO 230 I = 1,M - B(I,J) = B(I,J) + TEMP*B(I,K) - 230 CONTINUE - END IF - 240 CONTINUE - TEMP = ALPHA - IF (NOUNIT) TEMP = TEMP*A(K,K) - IF (TEMP.NE.ONE) THEN - DO 250 I = 1,M - B(I,K) = TEMP*B(I,K) - 250 CONTINUE - END IF - 260 CONTINUE - ELSE - DO 300 K = N,1,-1 - DO 280 J = K + 1,N - IF (A(J,K).NE.ZERO) THEN - TEMP = ALPHA*A(J,K) - DO 270 I = 1,M - B(I,J) = B(I,J) + TEMP*B(I,K) - 270 CONTINUE - END IF - 280 CONTINUE - TEMP = ALPHA - IF (NOUNIT) TEMP = TEMP*A(K,K) - IF (TEMP.NE.ONE) THEN - DO 290 I = 1,M - B(I,K) = TEMP*B(I,K) - 290 CONTINUE - END IF - 300 CONTINUE - END IF - END IF - END IF -* - RETURN -* -* End of DTRMM -* - END diff --git a/lib/linalg/fortran/dtrmv.f b/lib/linalg/fortran/dtrmv.f deleted file mode 100644 index e8af8e6136..0000000000 --- a/lib/linalg/fortran/dtrmv.f +++ /dev/null @@ -1,339 +0,0 @@ -*> \brief \b DTRMV -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE DTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) -* -* .. Scalar Arguments .. -* INTEGER INCX,LDA,N -* CHARACTER DIAG,TRANS,UPLO -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A(LDA,*),X(*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DTRMV performs one of the matrix-vector operations -*> -*> x := A*x, or x := A**T*x, -*> -*> where x is an n element vector and A is an n by n unit, or non-unit, -*> upper or lower triangular matrix. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> On entry, UPLO specifies whether the matrix is an upper or -*> lower triangular matrix as follows: -*> -*> UPLO = 'U' or 'u' A is an upper triangular matrix. -*> -*> UPLO = 'L' or 'l' A is a lower triangular matrix. -*> \endverbatim -*> -*> \param[in] TRANS -*> \verbatim -*> TRANS is CHARACTER*1 -*> On entry, TRANS specifies the operation to be performed as -*> follows: -*> -*> TRANS = 'N' or 'n' x := A*x. -*> -*> TRANS = 'T' or 't' x := A**T*x. -*> -*> TRANS = 'C' or 'c' x := A**T*x. -*> \endverbatim -*> -*> \param[in] DIAG -*> \verbatim -*> DIAG is CHARACTER*1 -*> On entry, DIAG specifies whether or not A is unit -*> triangular as follows: -*> -*> DIAG = 'U' or 'u' A is assumed to be unit triangular. -*> -*> DIAG = 'N' or 'n' A is not assumed to be unit -*> triangular. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> On entry, N specifies the order of the matrix A. -*> N must be at least zero. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension ( LDA, N ) -*> Before entry with UPLO = 'U' or 'u', the leading n by n -*> upper triangular part of the array A must contain the upper -*> triangular matrix and the strictly lower triangular part of -*> A is not referenced. -*> Before entry with UPLO = 'L' or 'l', the leading n by n -*> lower triangular part of the array A must contain the lower -*> triangular matrix and the strictly upper triangular part of -*> A is not referenced. -*> Note that when DIAG = 'U' or 'u', the diagonal elements of -*> A are not referenced either, but are assumed to be unity. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> On entry, LDA specifies the first dimension of A as declared -*> in the calling (sub) program. LDA must be at least -*> max( 1, n ). -*> \endverbatim -*> -*> \param[in,out] X -*> \verbatim -*> X is DOUBLE PRECISION array, dimension at least -*> ( 1 + ( n - 1 )*abs( INCX ) ). -*> Before entry, the incremented array X must contain the n -*> element vector x. On exit, X is overwritten with the -*> transformed vector x. -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> On entry, INCX specifies the increment for the elements of -*> X. INCX must not be zero. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup double_blas_level2 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> Level 2 Blas routine. -*> The vector and matrix arguments are not referenced when N = 0, or M = 0 -*> -*> -- Written on 22-October-1986. -*> Jack Dongarra, Argonne National Lab. -*> Jeremy Du Croz, Nag Central Office. -*> Sven Hammarling, Nag Central Office. -*> Richard Hanson, Sandia National Labs. -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) -* -* -- Reference BLAS level2 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INCX,LDA,N - CHARACTER DIAG,TRANS,UPLO -* .. -* .. Array Arguments .. - DOUBLE PRECISION A(LDA,*),X(*) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO - PARAMETER (ZERO=0.0D+0) -* .. -* .. Local Scalars .. - DOUBLE PRECISION TEMP - INTEGER I,INFO,IX,J,JX,KX - LOGICAL NOUNIT -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* -* Test the input parameters. -* - INFO = 0 - IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN - INFO = 1 - ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. - + .NOT.LSAME(TRANS,'C')) THEN - INFO = 2 - ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN - INFO = 3 - ELSE IF (N.LT.0) THEN - INFO = 4 - ELSE IF (LDA.LT.MAX(1,N)) THEN - INFO = 6 - ELSE IF (INCX.EQ.0) THEN - INFO = 8 - END IF - IF (INFO.NE.0) THEN - CALL XERBLA('DTRMV ',INFO) - RETURN - END IF -* -* Quick return if possible. -* - IF (N.EQ.0) RETURN -* - NOUNIT = LSAME(DIAG,'N') -* -* Set up the start point in X if the increment is not unity. This -* will be ( N - 1 )*INCX too small for descending loops. -* - IF (INCX.LE.0) THEN - KX = 1 - (N-1)*INCX - ELSE IF (INCX.NE.1) THEN - KX = 1 - END IF -* -* Start the operations. In this version the elements of A are -* accessed sequentially with one pass through A. -* - IF (LSAME(TRANS,'N')) THEN -* -* Form x := A*x. -* - IF (LSAME(UPLO,'U')) THEN - IF (INCX.EQ.1) THEN - DO 20 J = 1,N - IF (X(J).NE.ZERO) THEN - TEMP = X(J) - DO 10 I = 1,J - 1 - X(I) = X(I) + TEMP*A(I,J) - 10 CONTINUE - IF (NOUNIT) X(J) = X(J)*A(J,J) - END IF - 20 CONTINUE - ELSE - JX = KX - DO 40 J = 1,N - IF (X(JX).NE.ZERO) THEN - TEMP = X(JX) - IX = KX - DO 30 I = 1,J - 1 - X(IX) = X(IX) + TEMP*A(I,J) - IX = IX + INCX - 30 CONTINUE - IF (NOUNIT) X(JX) = X(JX)*A(J,J) - END IF - JX = JX + INCX - 40 CONTINUE - END IF - ELSE - IF (INCX.EQ.1) THEN - DO 60 J = N,1,-1 - IF (X(J).NE.ZERO) THEN - TEMP = X(J) - DO 50 I = N,J + 1,-1 - X(I) = X(I) + TEMP*A(I,J) - 50 CONTINUE - IF (NOUNIT) X(J) = X(J)*A(J,J) - END IF - 60 CONTINUE - ELSE - KX = KX + (N-1)*INCX - JX = KX - DO 80 J = N,1,-1 - IF (X(JX).NE.ZERO) THEN - TEMP = X(JX) - IX = KX - DO 70 I = N,J + 1,-1 - X(IX) = X(IX) + TEMP*A(I,J) - IX = IX - INCX - 70 CONTINUE - IF (NOUNIT) X(JX) = X(JX)*A(J,J) - END IF - JX = JX - INCX - 80 CONTINUE - END IF - END IF - ELSE -* -* Form x := A**T*x. -* - IF (LSAME(UPLO,'U')) THEN - IF (INCX.EQ.1) THEN - DO 100 J = N,1,-1 - TEMP = X(J) - IF (NOUNIT) TEMP = TEMP*A(J,J) - DO 90 I = J - 1,1,-1 - TEMP = TEMP + A(I,J)*X(I) - 90 CONTINUE - X(J) = TEMP - 100 CONTINUE - ELSE - JX = KX + (N-1)*INCX - DO 120 J = N,1,-1 - TEMP = X(JX) - IX = JX - IF (NOUNIT) TEMP = TEMP*A(J,J) - DO 110 I = J - 1,1,-1 - IX = IX - INCX - TEMP = TEMP + A(I,J)*X(IX) - 110 CONTINUE - X(JX) = TEMP - JX = JX - INCX - 120 CONTINUE - END IF - ELSE - IF (INCX.EQ.1) THEN - DO 140 J = 1,N - TEMP = X(J) - IF (NOUNIT) TEMP = TEMP*A(J,J) - DO 130 I = J + 1,N - TEMP = TEMP + A(I,J)*X(I) - 130 CONTINUE - X(J) = TEMP - 140 CONTINUE - ELSE - JX = KX - DO 160 J = 1,N - TEMP = X(JX) - IX = JX - IF (NOUNIT) TEMP = TEMP*A(J,J) - DO 150 I = J + 1,N - IX = IX + INCX - TEMP = TEMP + A(I,J)*X(IX) - 150 CONTINUE - X(JX) = TEMP - JX = JX + INCX - 160 CONTINUE - END IF - END IF - END IF -* - RETURN -* -* End of DTRMV -* - END diff --git a/lib/linalg/fortran/dtrsm.f b/lib/linalg/fortran/dtrsm.f deleted file mode 100644 index fa8080bc92..0000000000 --- a/lib/linalg/fortran/dtrsm.f +++ /dev/null @@ -1,440 +0,0 @@ -*> \brief \b DTRSM -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE DTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) -* -* .. Scalar Arguments .. -* DOUBLE PRECISION ALPHA -* INTEGER LDA,LDB,M,N -* CHARACTER DIAG,SIDE,TRANSA,UPLO -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A(LDA,*),B(LDB,*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DTRSM solves one of the matrix equations -*> -*> op( A )*X = alpha*B, or X*op( A ) = alpha*B, -*> -*> where alpha is a scalar, X and B are m by n matrices, A is a unit, or -*> non-unit, upper or lower triangular matrix and op( A ) is one of -*> -*> op( A ) = A or op( A ) = A**T. -*> -*> The matrix X is overwritten on B. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] SIDE -*> \verbatim -*> SIDE is CHARACTER*1 -*> On entry, SIDE specifies whether op( A ) appears on the left -*> or right of X as follows: -*> -*> SIDE = 'L' or 'l' op( A )*X = alpha*B. -*> -*> SIDE = 'R' or 'r' X*op( A ) = alpha*B. -*> \endverbatim -*> -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> On entry, UPLO specifies whether the matrix A is an upper or -*> lower triangular matrix as follows: -*> -*> UPLO = 'U' or 'u' A is an upper triangular matrix. -*> -*> UPLO = 'L' or 'l' A is a lower triangular matrix. -*> \endverbatim -*> -*> \param[in] TRANSA -*> \verbatim -*> TRANSA is CHARACTER*1 -*> On entry, TRANSA specifies the form of op( A ) to be used in -*> the matrix multiplication as follows: -*> -*> TRANSA = 'N' or 'n' op( A ) = A. -*> -*> TRANSA = 'T' or 't' op( A ) = A**T. -*> -*> TRANSA = 'C' or 'c' op( A ) = A**T. -*> \endverbatim -*> -*> \param[in] DIAG -*> \verbatim -*> DIAG is CHARACTER*1 -*> On entry, DIAG specifies whether or not A is unit triangular -*> as follows: -*> -*> DIAG = 'U' or 'u' A is assumed to be unit triangular. -*> -*> DIAG = 'N' or 'n' A is not assumed to be unit -*> triangular. -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> On entry, M specifies the number of rows of B. M must be at -*> least zero. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> On entry, N specifies the number of columns of B. N must be -*> at least zero. -*> \endverbatim -*> -*> \param[in] ALPHA -*> \verbatim -*> ALPHA is DOUBLE PRECISION. -*> On entry, ALPHA specifies the scalar alpha. When alpha is -*> zero then A is not referenced and B need not be set before -*> entry. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension ( LDA, k ), -*> where k is m when SIDE = 'L' or 'l' -*> and k is n when SIDE = 'R' or 'r'. -*> Before entry with UPLO = 'U' or 'u', the leading k by k -*> upper triangular part of the array A must contain the upper -*> triangular matrix and the strictly lower triangular part of -*> A is not referenced. -*> Before entry with UPLO = 'L' or 'l', the leading k by k -*> lower triangular part of the array A must contain the lower -*> triangular matrix and the strictly upper triangular part of -*> A is not referenced. -*> Note that when DIAG = 'U' or 'u', the diagonal elements of -*> A are not referenced either, but are assumed to be unity. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> On entry, LDA specifies the first dimension of A as declared -*> in the calling (sub) program. When SIDE = 'L' or 'l' then -*> LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' -*> then LDA must be at least max( 1, n ). -*> \endverbatim -*> -*> \param[in,out] B -*> \verbatim -*> B is DOUBLE PRECISION array, dimension ( LDB, N ) -*> Before entry, the leading m by n part of the array B must -*> contain the right-hand side matrix B, and on exit is -*> overwritten by the solution matrix X. -*> \endverbatim -*> -*> \param[in] LDB -*> \verbatim -*> LDB is INTEGER -*> On entry, LDB specifies the first dimension of B as declared -*> in the calling (sub) program. LDB must be at least -*> max( 1, m ). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup double_blas_level3 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> Level 3 Blas routine. -*> -*> -*> -- Written on 8-February-1989. -*> Jack Dongarra, Argonne National Laboratory. -*> Iain Duff, AERE Harwell. -*> Jeremy Du Croz, Numerical Algorithms Group Ltd. -*> Sven Hammarling, Numerical Algorithms Group Ltd. -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) -* -* -- Reference BLAS level3 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - DOUBLE PRECISION ALPHA - INTEGER LDA,LDB,M,N - CHARACTER DIAG,SIDE,TRANSA,UPLO -* .. -* .. Array Arguments .. - DOUBLE PRECISION A(LDA,*),B(LDB,*) -* .. -* -* ===================================================================== -* -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* .. Local Scalars .. - DOUBLE PRECISION TEMP - INTEGER I,INFO,J,K,NROWA - LOGICAL LSIDE,NOUNIT,UPPER -* .. -* .. Parameters .. - DOUBLE PRECISION ONE,ZERO - PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) -* .. -* -* Test the input parameters. -* - LSIDE = LSAME(SIDE,'L') - IF (LSIDE) THEN - NROWA = M - ELSE - NROWA = N - END IF - NOUNIT = LSAME(DIAG,'N') - UPPER = LSAME(UPLO,'U') -* - INFO = 0 - IF ((.NOT.LSIDE) .AND. (.NOT.LSAME(SIDE,'R'))) THEN - INFO = 1 - ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN - INFO = 2 - ELSE IF ((.NOT.LSAME(TRANSA,'N')) .AND. - + (.NOT.LSAME(TRANSA,'T')) .AND. - + (.NOT.LSAME(TRANSA,'C'))) THEN - INFO = 3 - ELSE IF ((.NOT.LSAME(DIAG,'U')) .AND. (.NOT.LSAME(DIAG,'N'))) THEN - INFO = 4 - ELSE IF (M.LT.0) THEN - INFO = 5 - ELSE IF (N.LT.0) THEN - INFO = 6 - ELSE IF (LDA.LT.MAX(1,NROWA)) THEN - INFO = 9 - ELSE IF (LDB.LT.MAX(1,M)) THEN - INFO = 11 - END IF - IF (INFO.NE.0) THEN - CALL XERBLA('DTRSM ',INFO) - RETURN - END IF -* -* Quick return if possible. -* - IF (M.EQ.0 .OR. N.EQ.0) RETURN -* -* And when alpha.eq.zero. -* - IF (ALPHA.EQ.ZERO) THEN - DO 20 J = 1,N - DO 10 I = 1,M - B(I,J) = ZERO - 10 CONTINUE - 20 CONTINUE - RETURN - END IF -* -* Start the operations. -* - IF (LSIDE) THEN - IF (LSAME(TRANSA,'N')) THEN -* -* Form B := alpha*inv( A )*B. -* - IF (UPPER) THEN - DO 60 J = 1,N - IF (ALPHA.NE.ONE) THEN - DO 30 I = 1,M - B(I,J) = ALPHA*B(I,J) - 30 CONTINUE - END IF - DO 50 K = M,1,-1 - IF (B(K,J).NE.ZERO) THEN - IF (NOUNIT) B(K,J) = B(K,J)/A(K,K) - DO 40 I = 1,K - 1 - B(I,J) = B(I,J) - B(K,J)*A(I,K) - 40 CONTINUE - END IF - 50 CONTINUE - 60 CONTINUE - ELSE - DO 100 J = 1,N - IF (ALPHA.NE.ONE) THEN - DO 70 I = 1,M - B(I,J) = ALPHA*B(I,J) - 70 CONTINUE - END IF - DO 90 K = 1,M - IF (B(K,J).NE.ZERO) THEN - IF (NOUNIT) B(K,J) = B(K,J)/A(K,K) - DO 80 I = K + 1,M - B(I,J) = B(I,J) - B(K,J)*A(I,K) - 80 CONTINUE - END IF - 90 CONTINUE - 100 CONTINUE - END IF - ELSE -* -* Form B := alpha*inv( A**T )*B. -* - IF (UPPER) THEN - DO 130 J = 1,N - DO 120 I = 1,M - TEMP = ALPHA*B(I,J) - DO 110 K = 1,I - 1 - TEMP = TEMP - A(K,I)*B(K,J) - 110 CONTINUE - IF (NOUNIT) TEMP = TEMP/A(I,I) - B(I,J) = TEMP - 120 CONTINUE - 130 CONTINUE - ELSE - DO 160 J = 1,N - DO 150 I = M,1,-1 - TEMP = ALPHA*B(I,J) - DO 140 K = I + 1,M - TEMP = TEMP - A(K,I)*B(K,J) - 140 CONTINUE - IF (NOUNIT) TEMP = TEMP/A(I,I) - B(I,J) = TEMP - 150 CONTINUE - 160 CONTINUE - END IF - END IF - ELSE - IF (LSAME(TRANSA,'N')) THEN -* -* Form B := alpha*B*inv( A ). -* - IF (UPPER) THEN - DO 210 J = 1,N - IF (ALPHA.NE.ONE) THEN - DO 170 I = 1,M - B(I,J) = ALPHA*B(I,J) - 170 CONTINUE - END IF - DO 190 K = 1,J - 1 - IF (A(K,J).NE.ZERO) THEN - DO 180 I = 1,M - B(I,J) = B(I,J) - A(K,J)*B(I,K) - 180 CONTINUE - END IF - 190 CONTINUE - IF (NOUNIT) THEN - TEMP = ONE/A(J,J) - DO 200 I = 1,M - B(I,J) = TEMP*B(I,J) - 200 CONTINUE - END IF - 210 CONTINUE - ELSE - DO 260 J = N,1,-1 - IF (ALPHA.NE.ONE) THEN - DO 220 I = 1,M - B(I,J) = ALPHA*B(I,J) - 220 CONTINUE - END IF - DO 240 K = J + 1,N - IF (A(K,J).NE.ZERO) THEN - DO 230 I = 1,M - B(I,J) = B(I,J) - A(K,J)*B(I,K) - 230 CONTINUE - END IF - 240 CONTINUE - IF (NOUNIT) THEN - TEMP = ONE/A(J,J) - DO 250 I = 1,M - B(I,J) = TEMP*B(I,J) - 250 CONTINUE - END IF - 260 CONTINUE - END IF - ELSE -* -* Form B := alpha*B*inv( A**T ). -* - IF (UPPER) THEN - DO 310 K = N,1,-1 - IF (NOUNIT) THEN - TEMP = ONE/A(K,K) - DO 270 I = 1,M - B(I,K) = TEMP*B(I,K) - 270 CONTINUE - END IF - DO 290 J = 1,K - 1 - IF (A(J,K).NE.ZERO) THEN - TEMP = A(J,K) - DO 280 I = 1,M - B(I,J) = B(I,J) - TEMP*B(I,K) - 280 CONTINUE - END IF - 290 CONTINUE - IF (ALPHA.NE.ONE) THEN - DO 300 I = 1,M - B(I,K) = ALPHA*B(I,K) - 300 CONTINUE - END IF - 310 CONTINUE - ELSE - DO 360 K = 1,N - IF (NOUNIT) THEN - TEMP = ONE/A(K,K) - DO 320 I = 1,M - B(I,K) = TEMP*B(I,K) - 320 CONTINUE - END IF - DO 340 J = K + 1,N - IF (A(J,K).NE.ZERO) THEN - TEMP = A(J,K) - DO 330 I = 1,M - B(I,J) = B(I,J) - TEMP*B(I,K) - 330 CONTINUE - END IF - 340 CONTINUE - IF (ALPHA.NE.ONE) THEN - DO 350 I = 1,M - B(I,K) = ALPHA*B(I,K) - 350 CONTINUE - END IF - 360 CONTINUE - END IF - END IF - END IF -* - RETURN -* -* End of DTRSM -* - END diff --git a/lib/linalg/fortran/dtrsv.f b/lib/linalg/fortran/dtrsv.f deleted file mode 100644 index d8ea9fa898..0000000000 --- a/lib/linalg/fortran/dtrsv.f +++ /dev/null @@ -1,335 +0,0 @@ -*> \brief \b DTRSV -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE DTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) -* -* .. Scalar Arguments .. -* INTEGER INCX,LDA,N -* CHARACTER DIAG,TRANS,UPLO -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A(LDA,*),X(*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DTRSV solves one of the systems of equations -*> -*> A*x = b, or A**T*x = b, -*> -*> where b and x are n element vectors and A is an n by n unit, or -*> non-unit, upper or lower triangular matrix. -*> -*> No test for singularity or near-singularity is included in this -*> routine. Such tests must be performed before calling this routine. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> On entry, UPLO specifies whether the matrix is an upper or -*> lower triangular matrix as follows: -*> -*> UPLO = 'U' or 'u' A is an upper triangular matrix. -*> -*> UPLO = 'L' or 'l' A is a lower triangular matrix. -*> \endverbatim -*> -*> \param[in] TRANS -*> \verbatim -*> TRANS is CHARACTER*1 -*> On entry, TRANS specifies the equations to be solved as -*> follows: -*> -*> TRANS = 'N' or 'n' A*x = b. -*> -*> TRANS = 'T' or 't' A**T*x = b. -*> -*> TRANS = 'C' or 'c' A**T*x = b. -*> \endverbatim -*> -*> \param[in] DIAG -*> \verbatim -*> DIAG is CHARACTER*1 -*> On entry, DIAG specifies whether or not A is unit -*> triangular as follows: -*> -*> DIAG = 'U' or 'u' A is assumed to be unit triangular. -*> -*> DIAG = 'N' or 'n' A is not assumed to be unit -*> triangular. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> On entry, N specifies the order of the matrix A. -*> N must be at least zero. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension ( LDA, N ) -*> Before entry with UPLO = 'U' or 'u', the leading n by n -*> upper triangular part of the array A must contain the upper -*> triangular matrix and the strictly lower triangular part of -*> A is not referenced. -*> Before entry with UPLO = 'L' or 'l', the leading n by n -*> lower triangular part of the array A must contain the lower -*> triangular matrix and the strictly upper triangular part of -*> A is not referenced. -*> Note that when DIAG = 'U' or 'u', the diagonal elements of -*> A are not referenced either, but are assumed to be unity. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> On entry, LDA specifies the first dimension of A as declared -*> in the calling (sub) program. LDA must be at least -*> max( 1, n ). -*> \endverbatim -*> -*> \param[in,out] X -*> \verbatim -*> X is DOUBLE PRECISION array, dimension at least -*> ( 1 + ( n - 1 )*abs( INCX ) ). -*> Before entry, the incremented array X must contain the n -*> element right-hand side vector b. On exit, X is overwritten -*> with the solution vector x. -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> On entry, INCX specifies the increment for the elements of -*> X. INCX must not be zero. -*> -*> Level 2 Blas routine. -*> -*> -- Written on 22-October-1986. -*> Jack Dongarra, Argonne National Lab. -*> Jeremy Du Croz, Nag Central Office. -*> Sven Hammarling, Nag Central Office. -*> Richard Hanson, Sandia National Labs. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup double_blas_level1 -* -* ===================================================================== - SUBROUTINE DTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) -* -* -- Reference BLAS level1 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INCX,LDA,N - CHARACTER DIAG,TRANS,UPLO -* .. -* .. Array Arguments .. - DOUBLE PRECISION A(LDA,*),X(*) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO - PARAMETER (ZERO=0.0D+0) -* .. -* .. Local Scalars .. - DOUBLE PRECISION TEMP - INTEGER I,INFO,IX,J,JX,KX - LOGICAL NOUNIT -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* -* Test the input parameters. -* - INFO = 0 - IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN - INFO = 1 - ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. - + .NOT.LSAME(TRANS,'C')) THEN - INFO = 2 - ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN - INFO = 3 - ELSE IF (N.LT.0) THEN - INFO = 4 - ELSE IF (LDA.LT.MAX(1,N)) THEN - INFO = 6 - ELSE IF (INCX.EQ.0) THEN - INFO = 8 - END IF - IF (INFO.NE.0) THEN - CALL XERBLA('DTRSV ',INFO) - RETURN - END IF -* -* Quick return if possible. -* - IF (N.EQ.0) RETURN -* - NOUNIT = LSAME(DIAG,'N') -* -* Set up the start point in X if the increment is not unity. This -* will be ( N - 1 )*INCX too small for descending loops. -* - IF (INCX.LE.0) THEN - KX = 1 - (N-1)*INCX - ELSE IF (INCX.NE.1) THEN - KX = 1 - END IF -* -* Start the operations. In this version the elements of A are -* accessed sequentially with one pass through A. -* - IF (LSAME(TRANS,'N')) THEN -* -* Form x := inv( A )*x. -* - IF (LSAME(UPLO,'U')) THEN - IF (INCX.EQ.1) THEN - DO 20 J = N,1,-1 - IF (X(J).NE.ZERO) THEN - IF (NOUNIT) X(J) = X(J)/A(J,J) - TEMP = X(J) - DO 10 I = J - 1,1,-1 - X(I) = X(I) - TEMP*A(I,J) - 10 CONTINUE - END IF - 20 CONTINUE - ELSE - JX = KX + (N-1)*INCX - DO 40 J = N,1,-1 - IF (X(JX).NE.ZERO) THEN - IF (NOUNIT) X(JX) = X(JX)/A(J,J) - TEMP = X(JX) - IX = JX - DO 30 I = J - 1,1,-1 - IX = IX - INCX - X(IX) = X(IX) - TEMP*A(I,J) - 30 CONTINUE - END IF - JX = JX - INCX - 40 CONTINUE - END IF - ELSE - IF (INCX.EQ.1) THEN - DO 60 J = 1,N - IF (X(J).NE.ZERO) THEN - IF (NOUNIT) X(J) = X(J)/A(J,J) - TEMP = X(J) - DO 50 I = J + 1,N - X(I) = X(I) - TEMP*A(I,J) - 50 CONTINUE - END IF - 60 CONTINUE - ELSE - JX = KX - DO 80 J = 1,N - IF (X(JX).NE.ZERO) THEN - IF (NOUNIT) X(JX) = X(JX)/A(J,J) - TEMP = X(JX) - IX = JX - DO 70 I = J + 1,N - IX = IX + INCX - X(IX) = X(IX) - TEMP*A(I,J) - 70 CONTINUE - END IF - JX = JX + INCX - 80 CONTINUE - END IF - END IF - ELSE -* -* Form x := inv( A**T )*x. -* - IF (LSAME(UPLO,'U')) THEN - IF (INCX.EQ.1) THEN - DO 100 J = 1,N - TEMP = X(J) - DO 90 I = 1,J - 1 - TEMP = TEMP - A(I,J)*X(I) - 90 CONTINUE - IF (NOUNIT) TEMP = TEMP/A(J,J) - X(J) = TEMP - 100 CONTINUE - ELSE - JX = KX - DO 120 J = 1,N - TEMP = X(JX) - IX = KX - DO 110 I = 1,J - 1 - TEMP = TEMP - A(I,J)*X(IX) - IX = IX + INCX - 110 CONTINUE - IF (NOUNIT) TEMP = TEMP/A(J,J) - X(JX) = TEMP - JX = JX + INCX - 120 CONTINUE - END IF - ELSE - IF (INCX.EQ.1) THEN - DO 140 J = N,1,-1 - TEMP = X(J) - DO 130 I = N,J + 1,-1 - TEMP = TEMP - A(I,J)*X(I) - 130 CONTINUE - IF (NOUNIT) TEMP = TEMP/A(J,J) - X(J) = TEMP - 140 CONTINUE - ELSE - KX = KX + (N-1)*INCX - JX = KX - DO 160 J = N,1,-1 - TEMP = X(JX) - IX = KX - DO 150 I = N,J + 1,-1 - TEMP = TEMP - A(I,J)*X(IX) - IX = IX - INCX - 150 CONTINUE - IF (NOUNIT) TEMP = TEMP/A(J,J) - X(JX) = TEMP - JX = JX - INCX - 160 CONTINUE - END IF - END IF - END IF -* - RETURN -* -* End of DTRSV -* - END diff --git a/lib/linalg/fortran/dtrti2.f b/lib/linalg/fortran/dtrti2.f deleted file mode 100644 index 0d9115554c..0000000000 --- a/lib/linalg/fortran/dtrti2.f +++ /dev/null @@ -1,209 +0,0 @@ -*> \brief \b DTRTI2 computes the inverse of a triangular matrix (unblocked algorithm). -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DTRTI2 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DTRTI2( UPLO, DIAG, N, A, LDA, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER DIAG, UPLO -* INTEGER INFO, LDA, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DTRTI2 computes the inverse of a real upper or lower triangular -*> matrix. -*> -*> This is the Level 2 BLAS version of the algorithm. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> Specifies whether the matrix A is upper or lower triangular. -*> = 'U': Upper triangular -*> = 'L': Lower triangular -*> \endverbatim -*> -*> \param[in] DIAG -*> \verbatim -*> DIAG is CHARACTER*1 -*> Specifies whether or not the matrix A is unit triangular. -*> = 'N': Non-unit triangular -*> = 'U': Unit triangular -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the triangular matrix A. If UPLO = 'U', the -*> leading n by n upper triangular part of the array A contains -*> the upper triangular matrix, and the strictly lower -*> triangular part of A is not referenced. If UPLO = 'L', the -*> leading n by n lower triangular part of the array A contains -*> the lower triangular matrix, and the strictly upper -*> triangular part of A is not referenced. If DIAG = 'U', the -*> diagonal elements of A are also not referenced and are -*> assumed to be 1. -*> -*> On exit, the (triangular) inverse of the original matrix, in -*> the same storage format. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,N). -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -k, the k-th argument had an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleOTHERcomputational -* -* ===================================================================== - SUBROUTINE DTRTI2( UPLO, DIAG, N, A, LDA, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER DIAG, UPLO - INTEGER INFO, LDA, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE - PARAMETER ( ONE = 1.0D+0 ) -* .. -* .. Local Scalars .. - LOGICAL NOUNIT, UPPER - INTEGER J - DOUBLE PRECISION AJJ -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL DSCAL, DTRMV, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 - UPPER = LSAME( UPLO, 'U' ) - NOUNIT = LSAME( DIAG, 'N' ) - IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN - INFO = -1 - ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN - INFO = -2 - ELSE IF( N.LT.0 ) THEN - INFO = -3 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -5 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DTRTI2', -INFO ) - RETURN - END IF -* - IF( UPPER ) THEN -* -* Compute inverse of upper triangular matrix. -* - DO 10 J = 1, N - IF( NOUNIT ) THEN - A( J, J ) = ONE / A( J, J ) - AJJ = -A( J, J ) - ELSE - AJJ = -ONE - END IF -* -* Compute elements 1:j-1 of j-th column. -* - CALL DTRMV( 'Upper', 'No transpose', DIAG, J-1, A, LDA, - $ A( 1, J ), 1 ) - CALL DSCAL( J-1, AJJ, A( 1, J ), 1 ) - 10 CONTINUE - ELSE -* -* Compute inverse of lower triangular matrix. -* - DO 20 J = N, 1, -1 - IF( NOUNIT ) THEN - A( J, J ) = ONE / A( J, J ) - AJJ = -A( J, J ) - ELSE - AJJ = -ONE - END IF - IF( J.LT.N ) THEN -* -* Compute elements j+1:n of j-th column. -* - CALL DTRMV( 'Lower', 'No transpose', DIAG, N-J, - $ A( J+1, J+1 ), LDA, A( J+1, J ), 1 ) - CALL DSCAL( N-J, AJJ, A( J+1, J ), 1 ) - END IF - 20 CONTINUE - END IF -* - RETURN -* -* End of DTRTI2 -* - END diff --git a/lib/linalg/fortran/dtrtri.f b/lib/linalg/fortran/dtrtri.f deleted file mode 100644 index 1cf9a9aafb..0000000000 --- a/lib/linalg/fortran/dtrtri.f +++ /dev/null @@ -1,239 +0,0 @@ -*> \brief \b DTRTRI -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DTRTRI + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DTRTRI( UPLO, DIAG, N, A, LDA, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER DIAG, UPLO -* INTEGER INFO, LDA, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DTRTRI computes the inverse of a real upper or lower triangular -*> matrix A. -*> -*> This is the Level 3 BLAS version of the algorithm. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> = 'U': A is upper triangular; -*> = 'L': A is lower triangular. -*> \endverbatim -*> -*> \param[in] DIAG -*> \verbatim -*> DIAG is CHARACTER*1 -*> = 'N': A is non-unit triangular; -*> = 'U': A is unit triangular. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the triangular matrix A. If UPLO = 'U', the -*> leading N-by-N upper triangular part of the array A contains -*> the upper triangular matrix, and the strictly lower -*> triangular part of A is not referenced. If UPLO = 'L', the -*> leading N-by-N lower triangular part of the array A contains -*> the lower triangular matrix, and the strictly upper -*> triangular part of A is not referenced. If DIAG = 'U', the -*> diagonal elements of A are also not referenced and are -*> assumed to be 1. -*> On exit, the (triangular) inverse of the original matrix, in -*> the same storage format. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,N). -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, A(i,i) is exactly zero. The triangular -*> matrix is singular and its inverse can not be computed. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleOTHERcomputational -* -* ===================================================================== - SUBROUTINE DTRTRI( UPLO, DIAG, N, A, LDA, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER DIAG, UPLO - INTEGER INFO, LDA, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE, ZERO - PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) -* .. -* .. Local Scalars .. - LOGICAL NOUNIT, UPPER - INTEGER J, JB, NB, NN -* .. -* .. External Functions .. - LOGICAL LSAME - INTEGER ILAENV - EXTERNAL LSAME, ILAENV -* .. -* .. External Subroutines .. - EXTERNAL DTRMM, DTRSM, DTRTI2, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, MIN -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 - UPPER = LSAME( UPLO, 'U' ) - NOUNIT = LSAME( DIAG, 'N' ) - IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN - INFO = -1 - ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN - INFO = -2 - ELSE IF( N.LT.0 ) THEN - INFO = -3 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -5 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DTRTRI', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( N.EQ.0 ) - $ RETURN -* -* Check for singularity if non-unit. -* - IF( NOUNIT ) THEN - DO 10 INFO = 1, N - IF( A( INFO, INFO ).EQ.ZERO ) - $ RETURN - 10 CONTINUE - INFO = 0 - END IF -* -* Determine the block size for this environment. -* - NB = ILAENV( 1, 'DTRTRI', UPLO // DIAG, N, -1, -1, -1 ) - IF( NB.LE.1 .OR. NB.GE.N ) THEN -* -* Use unblocked code -* - CALL DTRTI2( UPLO, DIAG, N, A, LDA, INFO ) - ELSE -* -* Use blocked code -* - IF( UPPER ) THEN -* -* Compute inverse of upper triangular matrix -* - DO 20 J = 1, N, NB - JB = MIN( NB, N-J+1 ) -* -* Compute rows 1:j-1 of current block column -* - CALL DTRMM( 'Left', 'Upper', 'No transpose', DIAG, J-1, - $ JB, ONE, A, LDA, A( 1, J ), LDA ) - CALL DTRSM( 'Right', 'Upper', 'No transpose', DIAG, J-1, - $ JB, -ONE, A( J, J ), LDA, A( 1, J ), LDA ) -* -* Compute inverse of current diagonal block -* - CALL DTRTI2( 'Upper', DIAG, JB, A( J, J ), LDA, INFO ) - 20 CONTINUE - ELSE -* -* Compute inverse of lower triangular matrix -* - NN = ( ( N-1 ) / NB )*NB + 1 - DO 30 J = NN, 1, -NB - JB = MIN( NB, N-J+1 ) - IF( J+JB.LE.N ) THEN -* -* Compute rows j+jb:n of current block column -* - CALL DTRMM( 'Left', 'Lower', 'No transpose', DIAG, - $ N-J-JB+1, JB, ONE, A( J+JB, J+JB ), LDA, - $ A( J+JB, J ), LDA ) - CALL DTRSM( 'Right', 'Lower', 'No transpose', DIAG, - $ N-J-JB+1, JB, -ONE, A( J, J ), LDA, - $ A( J+JB, J ), LDA ) - END IF -* -* Compute inverse of current diagonal block -* - CALL DTRTI2( 'Lower', DIAG, JB, A( J, J ), LDA, INFO ) - 30 CONTINUE - END IF - END IF -* - RETURN -* -* End of DTRTRI -* - END diff --git a/lib/linalg/fortran/dznrm2.f b/lib/linalg/fortran/dznrm2.f deleted file mode 100644 index e5a71d98f6..0000000000 --- a/lib/linalg/fortran/dznrm2.f +++ /dev/null @@ -1,140 +0,0 @@ -*> \brief \b DZNRM2 -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* DOUBLE PRECISION FUNCTION DZNRM2(N,X,INCX) -* -* .. Scalar Arguments .. -* INTEGER INCX,N -* .. -* .. Array Arguments .. -* COMPLEX*16 X(*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DZNRM2 returns the euclidean norm of a vector via the function -*> name, so that -*> -*> DZNRM2 := sqrt( x**H*x ) -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> number of elements in input vector(s) -*> \endverbatim -*> -*> \param[in] X -*> \verbatim -*> X is COMPLEX*16 array, dimension (N) -*> complex vector with N elements -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> storage spacing between elements of X -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \date December 2016 -* -*> \ingroup double_blas_level1 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> -- This version written on 25-October-1982. -*> Modified on 14-October-1993 to inline the call to ZLASSQ. -*> Sven Hammarling, Nag Ltd. -*> \endverbatim -*> -* ===================================================================== - DOUBLE PRECISION FUNCTION DZNRM2(N,X,INCX) -* -* -- Reference BLAS level1 routine (version 3.7.0) -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* December 2016 -* -* .. Scalar Arguments .. - INTEGER INCX,N -* .. -* .. Array Arguments .. - COMPLEX*16 X(*) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE,ZERO - PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) -* .. -* .. Local Scalars .. - DOUBLE PRECISION NORM,SCALE,SSQ,TEMP - INTEGER IX -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS,DBLE,DIMAG,SQRT -* .. - IF (N.LT.1 .OR. INCX.LT.1) THEN - NORM = ZERO - ELSE - SCALE = ZERO - SSQ = ONE -* The following loop is equivalent to this call to the LAPACK -* auxiliary routine: -* CALL ZLASSQ( N, X, INCX, SCALE, SSQ ) -* - DO 10 IX = 1,1 + (N-1)*INCX,INCX - IF (DBLE(X(IX)).NE.ZERO) THEN - TEMP = ABS(DBLE(X(IX))) - IF (SCALE.LT.TEMP) THEN - SSQ = ONE + SSQ* (SCALE/TEMP)**2 - SCALE = TEMP - ELSE - SSQ = SSQ + (TEMP/SCALE)**2 - END IF - END IF - IF (DIMAG(X(IX)).NE.ZERO) THEN - TEMP = ABS(DIMAG(X(IX))) - IF (SCALE.LT.TEMP) THEN - SSQ = ONE + SSQ* (SCALE/TEMP)**2 - SCALE = TEMP - ELSE - SSQ = SSQ + (TEMP/SCALE)**2 - END IF - END IF - 10 CONTINUE - NORM = SCALE*SQRT(SSQ) - END IF -* - DZNRM2 = NORM - RETURN -* -* End of DZNRM2. -* - END diff --git a/lib/linalg/fortran/idamax.f b/lib/linalg/fortran/idamax.f deleted file mode 100644 index 1be301ea3e..0000000000 --- a/lib/linalg/fortran/idamax.f +++ /dev/null @@ -1,126 +0,0 @@ -*> \brief \b IDAMAX -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* INTEGER FUNCTION IDAMAX(N,DX,INCX) -* -* .. Scalar Arguments .. -* INTEGER INCX,N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION DX(*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> IDAMAX finds the index of the first element having maximum absolute value. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> number of elements in input vector(s) -*> \endverbatim -*> -*> \param[in] DX -*> \verbatim -*> DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> storage spacing between elements of DX -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup aux_blas -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> jack dongarra, linpack, 3/11/78. -*> modified 3/93 to return if incx .le. 0. -*> modified 12/3/93, array(1) declarations changed to array(*) -*> \endverbatim -*> -* ===================================================================== - INTEGER FUNCTION IDAMAX(N,DX,INCX) -* -* -- Reference BLAS level1 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INCX,N -* .. -* .. Array Arguments .. - DOUBLE PRECISION DX(*) -* .. -* -* ===================================================================== -* -* .. Local Scalars .. - DOUBLE PRECISION DMAX - INTEGER I,IX -* .. -* .. Intrinsic Functions .. - INTRINSIC DABS -* .. - IDAMAX = 0 - IF (N.LT.1 .OR. INCX.LE.0) RETURN - IDAMAX = 1 - IF (N.EQ.1) RETURN - IF (INCX.EQ.1) THEN -* -* code for increment equal to 1 -* - DMAX = DABS(DX(1)) - DO I = 2,N - IF (DABS(DX(I)).GT.DMAX) THEN - IDAMAX = I - DMAX = DABS(DX(I)) - END IF - END DO - ELSE -* -* code for increment not equal to 1 -* - IX = 1 - DMAX = DABS(DX(1)) - IX = IX + INCX - DO I = 2,N - IF (DABS(DX(IX)).GT.DMAX) THEN - IDAMAX = I - DMAX = DABS(DX(IX)) - END IF - IX = IX + INCX - END DO - END IF - RETURN -* -* End of IDAMAX -* - END diff --git a/lib/linalg/fortran/ieeeck.f b/lib/linalg/fortran/ieeeck.f deleted file mode 100644 index f9f6332ecf..0000000000 --- a/lib/linalg/fortran/ieeeck.f +++ /dev/null @@ -1,200 +0,0 @@ -*> \brief \b IEEECK -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download IEEECK + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* INTEGER FUNCTION IEEECK( ISPEC, ZERO, ONE ) -* -* .. Scalar Arguments .. -* INTEGER ISPEC -* REAL ONE, ZERO -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> IEEECK is called from the ILAENV to verify that Infinity and -*> possibly NaN arithmetic is safe (i.e. will not trap). -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] ISPEC -*> \verbatim -*> ISPEC is INTEGER -*> Specifies whether to test just for infinity arithmetic -*> or whether to test for infinity and NaN arithmetic. -*> = 0: Verify infinity arithmetic only. -*> = 1: Verify infinity and NaN arithmetic. -*> \endverbatim -*> -*> \param[in] ZERO -*> \verbatim -*> ZERO is REAL -*> Must contain the value 0.0 -*> This is passed to prevent the compiler from optimizing -*> away this code. -*> \endverbatim -*> -*> \param[in] ONE -*> \verbatim -*> ONE is REAL -*> Must contain the value 1.0 -*> This is passed to prevent the compiler from optimizing -*> away this code. -*> -*> RETURN VALUE: INTEGER -*> = 0: Arithmetic failed to produce the correct answers -*> = 1: Arithmetic produced the correct answers -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup OTHERauxiliary -* -* ===================================================================== - INTEGER FUNCTION IEEECK( ISPEC, ZERO, ONE ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER ISPEC - REAL ONE, ZERO -* .. -* -* ===================================================================== -* -* .. Local Scalars .. - REAL NAN1, NAN2, NAN3, NAN4, NAN5, NAN6, NEGINF, - $ NEGZRO, NEWZRO, POSINF -* .. -* .. Executable Statements .. - IEEECK = 1 -* - POSINF = ONE / ZERO - IF( POSINF.LE.ONE ) THEN - IEEECK = 0 - RETURN - END IF -* - NEGINF = -ONE / ZERO - IF( NEGINF.GE.ZERO ) THEN - IEEECK = 0 - RETURN - END IF -* - NEGZRO = ONE / ( NEGINF+ONE ) - IF( NEGZRO.NE.ZERO ) THEN - IEEECK = 0 - RETURN - END IF -* - NEGINF = ONE / NEGZRO - IF( NEGINF.GE.ZERO ) THEN - IEEECK = 0 - RETURN - END IF -* - NEWZRO = NEGZRO + ZERO - IF( NEWZRO.NE.ZERO ) THEN - IEEECK = 0 - RETURN - END IF -* - POSINF = ONE / NEWZRO - IF( POSINF.LE.ONE ) THEN - IEEECK = 0 - RETURN - END IF -* - NEGINF = NEGINF*POSINF - IF( NEGINF.GE.ZERO ) THEN - IEEECK = 0 - RETURN - END IF -* - POSINF = POSINF*POSINF - IF( POSINF.LE.ONE ) THEN - IEEECK = 0 - RETURN - END IF -* -* -* -* -* Return if we were only asked to check infinity arithmetic -* - IF( ISPEC.EQ.0 ) - $ RETURN -* - NAN1 = POSINF + NEGINF -* - NAN2 = POSINF / NEGINF -* - NAN3 = POSINF / POSINF -* - NAN4 = POSINF*ZERO -* - NAN5 = NEGINF*NEGZRO -* - NAN6 = NAN5*ZERO -* - IF( NAN1.EQ.NAN1 ) THEN - IEEECK = 0 - RETURN - END IF -* - IF( NAN2.EQ.NAN2 ) THEN - IEEECK = 0 - RETURN - END IF -* - IF( NAN3.EQ.NAN3 ) THEN - IEEECK = 0 - RETURN - END IF -* - IF( NAN4.EQ.NAN4 ) THEN - IEEECK = 0 - RETURN - END IF -* - IF( NAN5.EQ.NAN5 ) THEN - IEEECK = 0 - RETURN - END IF -* - IF( NAN6.EQ.NAN6 ) THEN - IEEECK = 0 - RETURN - END IF -* - RETURN - END diff --git a/lib/linalg/fortran/iladlc.f b/lib/linalg/fortran/iladlc.f deleted file mode 100644 index a98e7218bf..0000000000 --- a/lib/linalg/fortran/iladlc.f +++ /dev/null @@ -1,115 +0,0 @@ -*> \brief \b ILADLC scans a matrix for its last non-zero column. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ILADLC + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* INTEGER FUNCTION ILADLC( M, N, A, LDA ) -* -* .. Scalar Arguments .. -* INTEGER M, N, LDA -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ILADLC scans A for its last non-zero column. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix A. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix A. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> The m by n matrix A. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,M). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup OTHERauxiliary -* -* ===================================================================== - INTEGER FUNCTION ILADLC( M, N, A, LDA ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER M, N, LDA -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO - PARAMETER ( ZERO = 0.0D+0 ) -* .. -* .. Local Scalars .. - INTEGER I -* .. -* .. Executable Statements .. -* -* Quick test for the common case where one corner is non-zero. - IF( N.EQ.0 ) THEN - ILADLC = N - ELSE IF( A(1, N).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN - ILADLC = N - ELSE -* Now scan each column from the end, returning with the first non-zero. - DO ILADLC = N, 1, -1 - DO I = 1, M - IF( A(I, ILADLC).NE.ZERO ) RETURN - END DO - END DO - END IF - RETURN - END diff --git a/lib/linalg/fortran/iladlr.f b/lib/linalg/fortran/iladlr.f deleted file mode 100644 index b1abded84b..0000000000 --- a/lib/linalg/fortran/iladlr.f +++ /dev/null @@ -1,118 +0,0 @@ -*> \brief \b ILADLR scans a matrix for its last non-zero row. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ILADLR + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* INTEGER FUNCTION ILADLR( M, N, A, LDA ) -* -* .. Scalar Arguments .. -* INTEGER M, N, LDA -* .. -* .. Array Arguments .. -* DOUBLE PRECISION A( LDA, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ILADLR scans A for its last non-zero row. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix A. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix A. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> The m by n matrix A. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,M). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup OTHERauxiliary -* -* ===================================================================== - INTEGER FUNCTION ILADLR( M, N, A, LDA ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER M, N, LDA -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO - PARAMETER ( ZERO = 0.0D+0 ) -* .. -* .. Local Scalars .. - INTEGER I, J -* .. -* .. Executable Statements .. -* -* Quick test for the common case where one corner is non-zero. - IF( M.EQ.0 ) THEN - ILADLR = M - ELSE IF( A(M, 1).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN - ILADLR = M - ELSE -* Scan up each column tracking the last zero row seen. - ILADLR = 0 - DO J = 1, N - I=M - DO WHILE((A(MAX(I,1),J).EQ.ZERO).AND.(I.GE.1)) - I=I-1 - ENDDO - ILADLR = MAX( ILADLR, I ) - END DO - END IF - RETURN - END diff --git a/lib/linalg/fortran/ilaenv.f b/lib/linalg/fortran/ilaenv.f deleted file mode 100644 index 3f0800b95e..0000000000 --- a/lib/linalg/fortran/ilaenv.f +++ /dev/null @@ -1,730 +0,0 @@ -*> \brief \b ILAENV -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ILAENV + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* INTEGER FUNCTION ILAENV( ISPEC, NAME, OPTS, N1, N2, N3, N4 ) -* -* .. Scalar Arguments .. -* CHARACTER*( * ) NAME, OPTS -* INTEGER ISPEC, N1, N2, N3, N4 -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ILAENV is called from the LAPACK routines to choose problem-dependent -*> parameters for the local environment. See ISPEC for a description of -*> the parameters. -*> -*> ILAENV returns an INTEGER -*> if ILAENV >= 0: ILAENV returns the value of the parameter specified by ISPEC -*> if ILAENV < 0: if ILAENV = -k, the k-th argument had an illegal value. -*> -*> This version provides a set of parameters which should give good, -*> but not optimal, performance on many of the currently available -*> computers. Users are encouraged to modify this subroutine to set -*> the tuning parameters for their particular machine using the option -*> and problem size information in the arguments. -*> -*> This routine will not function correctly if it is converted to all -*> lower case. Converting it to all upper case is allowed. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] ISPEC -*> \verbatim -*> ISPEC is INTEGER -*> Specifies the parameter to be returned as the value of -*> ILAENV. -*> = 1: the optimal blocksize; if this value is 1, an unblocked -*> algorithm will give the best performance. -*> = 2: the minimum block size for which the block routine -*> should be used; if the usable block size is less than -*> this value, an unblocked routine should be used. -*> = 3: the crossover point (in a block routine, for N less -*> than this value, an unblocked routine should be used) -*> = 4: the number of shifts, used in the nonsymmetric -*> eigenvalue routines (DEPRECATED) -*> = 5: the minimum column dimension for blocking to be used; -*> rectangular blocks must have dimension at least k by m, -*> where k is given by ILAENV(2,...) and m by ILAENV(5,...) -*> = 6: the crossover point for the SVD (when reducing an m by n -*> matrix to bidiagonal form, if max(m,n)/min(m,n) exceeds -*> this value, a QR factorization is used first to reduce -*> the matrix to a triangular form.) -*> = 7: the number of processors -*> = 8: the crossover point for the multishift QR method -*> for nonsymmetric eigenvalue problems (DEPRECATED) -*> = 9: maximum size of the subproblems at the bottom of the -*> computation tree in the divide-and-conquer algorithm -*> (used by xGELSD and xGESDD) -*> =10: ieee infinity and NaN arithmetic can be trusted not to trap -*> =11: infinity arithmetic can be trusted not to trap -*> 12 <= ISPEC <= 17: -*> xHSEQR or related subroutines, -*> see IPARMQ for detailed explanation -*> \endverbatim -*> -*> \param[in] NAME -*> \verbatim -*> NAME is CHARACTER*(*) -*> The name of the calling subroutine, in either upper case or -*> lower case. -*> \endverbatim -*> -*> \param[in] OPTS -*> \verbatim -*> OPTS is CHARACTER*(*) -*> The character options to the subroutine NAME, concatenated -*> into a single character string. For example, UPLO = 'U', -*> TRANS = 'T', and DIAG = 'N' for a triangular routine would -*> be specified as OPTS = 'UTN'. -*> \endverbatim -*> -*> \param[in] N1 -*> \verbatim -*> N1 is INTEGER -*> \endverbatim -*> -*> \param[in] N2 -*> \verbatim -*> N2 is INTEGER -*> \endverbatim -*> -*> \param[in] N3 -*> \verbatim -*> N3 is INTEGER -*> \endverbatim -*> -*> \param[in] N4 -*> \verbatim -*> N4 is INTEGER -*> Problem dimensions for the subroutine NAME; these may not all -*> be required. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup OTHERauxiliary -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> The following conventions have been used when calling ILAENV from the -*> LAPACK routines: -*> 1) OPTS is a concatenation of all of the character options to -*> subroutine NAME, in the same order that they appear in the -*> argument list for NAME, even if they are not used in determining -*> the value of the parameter specified by ISPEC. -*> 2) The problem dimensions N1, N2, N3, N4 are specified in the order -*> that they appear in the argument list for NAME. N1 is used -*> first, N2 second, and so on, and unused problem dimensions are -*> passed a value of -1. -*> 3) The parameter value returned by ILAENV is checked for validity in -*> the calling subroutine. For example, ILAENV is used to retrieve -*> the optimal blocksize for STRTRI as follows: -*> -*> NB = ILAENV( 1, 'STRTRI', UPLO // DIAG, N, -1, -1, -1 ) -*> IF( NB.LE.1 ) NB = MAX( 1, N ) -*> \endverbatim -*> -* ===================================================================== - INTEGER FUNCTION ILAENV( ISPEC, NAME, OPTS, N1, N2, N3, N4 ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER*( * ) NAME, OPTS - INTEGER ISPEC, N1, N2, N3, N4 -* .. -* -* ===================================================================== -* -* .. Local Scalars .. - INTEGER I, IC, IZ, NB, NBMIN, NX - LOGICAL CNAME, SNAME, TWOSTAGE - CHARACTER C1*1, C2*2, C4*2, C3*3, SUBNAM*16 -* .. -* .. Intrinsic Functions .. - INTRINSIC CHAR, ICHAR, INT, MIN, REAL -* .. -* .. External Functions .. - INTEGER IEEECK, IPARMQ - EXTERNAL IEEECK, IPARMQ -* .. -* .. Executable Statements .. -* - GO TO ( 10, 10, 10, 80, 90, 100, 110, 120, - $ 130, 140, 150, 160, 160, 160, 160, 160, 160)ISPEC -* -* Invalid value for ISPEC -* - ILAENV = -1 - RETURN -* - 10 CONTINUE -* -* Convert NAME to upper case if the first character is lower case. -* - ILAENV = 1 - SUBNAM = NAME - IC = ICHAR( SUBNAM( 1: 1 ) ) - IZ = ICHAR( 'Z' ) - IF( IZ.EQ.90 .OR. IZ.EQ.122 ) THEN -* -* ASCII character set -* - IF( IC.GE.97 .AND. IC.LE.122 ) THEN - SUBNAM( 1: 1 ) = CHAR( IC-32 ) - DO 20 I = 2, 6 - IC = ICHAR( SUBNAM( I: I ) ) - IF( IC.GE.97 .AND. IC.LE.122 ) - $ SUBNAM( I: I ) = CHAR( IC-32 ) - 20 CONTINUE - END IF -* - ELSE IF( IZ.EQ.233 .OR. IZ.EQ.169 ) THEN -* -* EBCDIC character set -* - IF( ( IC.GE.129 .AND. IC.LE.137 ) .OR. - $ ( IC.GE.145 .AND. IC.LE.153 ) .OR. - $ ( IC.GE.162 .AND. IC.LE.169 ) ) THEN - SUBNAM( 1: 1 ) = CHAR( IC+64 ) - DO 30 I = 2, 6 - IC = ICHAR( SUBNAM( I: I ) ) - IF( ( IC.GE.129 .AND. IC.LE.137 ) .OR. - $ ( IC.GE.145 .AND. IC.LE.153 ) .OR. - $ ( IC.GE.162 .AND. IC.LE.169 ) )SUBNAM( I: - $ I ) = CHAR( IC+64 ) - 30 CONTINUE - END IF -* - ELSE IF( IZ.EQ.218 .OR. IZ.EQ.250 ) THEN -* -* Prime machines: ASCII+128 -* - IF( IC.GE.225 .AND. IC.LE.250 ) THEN - SUBNAM( 1: 1 ) = CHAR( IC-32 ) - DO 40 I = 2, 6 - IC = ICHAR( SUBNAM( I: I ) ) - IF( IC.GE.225 .AND. IC.LE.250 ) - $ SUBNAM( I: I ) = CHAR( IC-32 ) - 40 CONTINUE - END IF - END IF -* - C1 = SUBNAM( 1: 1 ) - SNAME = C1.EQ.'S' .OR. C1.EQ.'D' - CNAME = C1.EQ.'C' .OR. C1.EQ.'Z' - IF( .NOT.( CNAME .OR. SNAME ) ) - $ RETURN - C2 = SUBNAM( 2: 3 ) - C3 = SUBNAM( 4: 6 ) - C4 = C3( 2: 3 ) - TWOSTAGE = LEN( SUBNAM ).GE.11 - $ .AND. SUBNAM( 11: 11 ).EQ.'2' -* - GO TO ( 50, 60, 70 )ISPEC -* - 50 CONTINUE -* -* ISPEC = 1: block size -* -* In these examples, separate code is provided for setting NB for -* real and complex. We assume that NB will take the same value in -* single or double precision. -* - NB = 1 -* - IF( SUBNAM(2:6).EQ.'LAORH' ) THEN -* -* This is for *LAORHR_GETRFNP routine -* - IF( SNAME ) THEN - NB = 32 - ELSE - NB = 32 - END IF - ELSE IF( C2.EQ.'GE' ) THEN - IF( C3.EQ.'TRF' ) THEN - IF( SNAME ) THEN - NB = 64 - ELSE - NB = 64 - END IF - ELSE IF( C3.EQ.'QRF' .OR. C3.EQ.'RQF' .OR. C3.EQ.'LQF' .OR. - $ C3.EQ.'QLF' ) THEN - IF( SNAME ) THEN - NB = 32 - ELSE - NB = 32 - END IF - ELSE IF( C3.EQ.'QR ') THEN - IF( N3 .EQ. 1) THEN - IF( SNAME ) THEN -* M*N - IF ((N1*N2.LE.131072).OR.(N1.LE.8192)) THEN - NB = N1 - ELSE - NB = 32768/N2 - END IF - ELSE - IF ((N1*N2.LE.131072).OR.(N1.LE.8192)) THEN - NB = N1 - ELSE - NB = 32768/N2 - END IF - END IF - ELSE - IF( SNAME ) THEN - NB = 1 - ELSE - NB = 1 - END IF - END IF - ELSE IF( C3.EQ.'LQ ') THEN - IF( N3 .EQ. 2) THEN - IF( SNAME ) THEN -* M*N - IF ((N1*N2.LE.131072).OR.(N1.LE.8192)) THEN - NB = N1 - ELSE - NB = 32768/N2 - END IF - ELSE - IF ((N1*N2.LE.131072).OR.(N1.LE.8192)) THEN - NB = N1 - ELSE - NB = 32768/N2 - END IF - END IF - ELSE - IF( SNAME ) THEN - NB = 1 - ELSE - NB = 1 - END IF - END IF - ELSE IF( C3.EQ.'HRD' ) THEN - IF( SNAME ) THEN - NB = 32 - ELSE - NB = 32 - END IF - ELSE IF( C3.EQ.'BRD' ) THEN - IF( SNAME ) THEN - NB = 32 - ELSE - NB = 32 - END IF - ELSE IF( C3.EQ.'TRI' ) THEN - IF( SNAME ) THEN - NB = 64 - ELSE - NB = 64 - END IF - END IF - ELSE IF( C2.EQ.'PO' ) THEN - IF( C3.EQ.'TRF' ) THEN - IF( SNAME ) THEN - NB = 64 - ELSE - NB = 64 - END IF - END IF - ELSE IF( C2.EQ.'SY' ) THEN - IF( C3.EQ.'TRF' ) THEN - IF( SNAME ) THEN - IF( TWOSTAGE ) THEN - NB = 192 - ELSE - NB = 64 - END IF - ELSE - IF( TWOSTAGE ) THEN - NB = 192 - ELSE - NB = 64 - END IF - END IF - ELSE IF( SNAME .AND. C3.EQ.'TRD' ) THEN - NB = 32 - ELSE IF( SNAME .AND. C3.EQ.'GST' ) THEN - NB = 64 - END IF - ELSE IF( CNAME .AND. C2.EQ.'HE' ) THEN - IF( C3.EQ.'TRF' ) THEN - IF( TWOSTAGE ) THEN - NB = 192 - ELSE - NB = 64 - END IF - ELSE IF( C3.EQ.'TRD' ) THEN - NB = 32 - ELSE IF( C3.EQ.'GST' ) THEN - NB = 64 - END IF - ELSE IF( SNAME .AND. C2.EQ.'OR' ) THEN - IF( C3( 1: 1 ).EQ.'G' ) THEN - IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ. - $ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' ) - $ THEN - NB = 32 - END IF - ELSE IF( C3( 1: 1 ).EQ.'M' ) THEN - IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ. - $ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' ) - $ THEN - NB = 32 - END IF - END IF - ELSE IF( CNAME .AND. C2.EQ.'UN' ) THEN - IF( C3( 1: 1 ).EQ.'G' ) THEN - IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ. - $ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' ) - $ THEN - NB = 32 - END IF - ELSE IF( C3( 1: 1 ).EQ.'M' ) THEN - IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ. - $ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' ) - $ THEN - NB = 32 - END IF - END IF - ELSE IF( C2.EQ.'GB' ) THEN - IF( C3.EQ.'TRF' ) THEN - IF( SNAME ) THEN - IF( N4.LE.64 ) THEN - NB = 1 - ELSE - NB = 32 - END IF - ELSE - IF( N4.LE.64 ) THEN - NB = 1 - ELSE - NB = 32 - END IF - END IF - END IF - ELSE IF( C2.EQ.'PB' ) THEN - IF( C3.EQ.'TRF' ) THEN - IF( SNAME ) THEN - IF( N2.LE.64 ) THEN - NB = 1 - ELSE - NB = 32 - END IF - ELSE - IF( N2.LE.64 ) THEN - NB = 1 - ELSE - NB = 32 - END IF - END IF - END IF - ELSE IF( C2.EQ.'TR' ) THEN - IF( C3.EQ.'TRI' ) THEN - IF( SNAME ) THEN - NB = 64 - ELSE - NB = 64 - END IF - ELSE IF ( C3.EQ.'EVC' ) THEN - IF( SNAME ) THEN - NB = 64 - ELSE - NB = 64 - END IF - ELSE IF( C3.EQ.'SYL' ) THEN -* The upper bound is to prevent overly aggressive scaling. - IF( SNAME ) THEN - NB = MIN( MAX( 48, INT( ( MIN( N1, N2 ) * 16 ) / 100) ), - $ 240 ) - ELSE - NB = MIN( MAX( 24, INT( ( MIN( N1, N2 ) * 8 ) / 100) ), - $ 80 ) - END IF - END IF - ELSE IF( C2.EQ.'LA' ) THEN - IF( C3.EQ.'UUM' ) THEN - IF( SNAME ) THEN - NB = 64 - ELSE - NB = 64 - END IF - ELSE IF( C3.EQ.'TRS' ) THEN - IF( SNAME ) THEN - NB = 32 - ELSE - NB = 32 - END IF - END IF - ELSE IF( SNAME .AND. C2.EQ.'ST' ) THEN - IF( C3.EQ.'EBZ' ) THEN - NB = 1 - END IF - ELSE IF( C2.EQ.'GG' ) THEN - NB = 32 - IF( C3.EQ.'HD3' ) THEN - IF( SNAME ) THEN - NB = 32 - ELSE - NB = 32 - END IF - END IF - END IF - ILAENV = NB - RETURN -* - 60 CONTINUE -* -* ISPEC = 2: minimum block size -* - NBMIN = 2 - IF( C2.EQ.'GE' ) THEN - IF( C3.EQ.'QRF' .OR. C3.EQ.'RQF' .OR. C3.EQ.'LQF' .OR. C3.EQ. - $ 'QLF' ) THEN - IF( SNAME ) THEN - NBMIN = 2 - ELSE - NBMIN = 2 - END IF - ELSE IF( C3.EQ.'HRD' ) THEN - IF( SNAME ) THEN - NBMIN = 2 - ELSE - NBMIN = 2 - END IF - ELSE IF( C3.EQ.'BRD' ) THEN - IF( SNAME ) THEN - NBMIN = 2 - ELSE - NBMIN = 2 - END IF - ELSE IF( C3.EQ.'TRI' ) THEN - IF( SNAME ) THEN - NBMIN = 2 - ELSE - NBMIN = 2 - END IF - END IF - ELSE IF( C2.EQ.'SY' ) THEN - IF( C3.EQ.'TRF' ) THEN - IF( SNAME ) THEN - NBMIN = 8 - ELSE - NBMIN = 8 - END IF - ELSE IF( SNAME .AND. C3.EQ.'TRD' ) THEN - NBMIN = 2 - END IF - ELSE IF( CNAME .AND. C2.EQ.'HE' ) THEN - IF( C3.EQ.'TRD' ) THEN - NBMIN = 2 - END IF - ELSE IF( SNAME .AND. C2.EQ.'OR' ) THEN - IF( C3( 1: 1 ).EQ.'G' ) THEN - IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ. - $ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' ) - $ THEN - NBMIN = 2 - END IF - ELSE IF( C3( 1: 1 ).EQ.'M' ) THEN - IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ. - $ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' ) - $ THEN - NBMIN = 2 - END IF - END IF - ELSE IF( CNAME .AND. C2.EQ.'UN' ) THEN - IF( C3( 1: 1 ).EQ.'G' ) THEN - IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ. - $ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' ) - $ THEN - NBMIN = 2 - END IF - ELSE IF( C3( 1: 1 ).EQ.'M' ) THEN - IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ. - $ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' ) - $ THEN - NBMIN = 2 - END IF - END IF - ELSE IF( C2.EQ.'GG' ) THEN - NBMIN = 2 - IF( C3.EQ.'HD3' ) THEN - NBMIN = 2 - END IF - END IF - ILAENV = NBMIN - RETURN -* - 70 CONTINUE -* -* ISPEC = 3: crossover point -* - NX = 0 - IF( C2.EQ.'GE' ) THEN - IF( C3.EQ.'QRF' .OR. C3.EQ.'RQF' .OR. C3.EQ.'LQF' .OR. C3.EQ. - $ 'QLF' ) THEN - IF( SNAME ) THEN - NX = 128 - ELSE - NX = 128 - END IF - ELSE IF( C3.EQ.'HRD' ) THEN - IF( SNAME ) THEN - NX = 128 - ELSE - NX = 128 - END IF - ELSE IF( C3.EQ.'BRD' ) THEN - IF( SNAME ) THEN - NX = 128 - ELSE - NX = 128 - END IF - END IF - ELSE IF( C2.EQ.'SY' ) THEN - IF( SNAME .AND. C3.EQ.'TRD' ) THEN - NX = 32 - END IF - ELSE IF( CNAME .AND. C2.EQ.'HE' ) THEN - IF( C3.EQ.'TRD' ) THEN - NX = 32 - END IF - ELSE IF( SNAME .AND. C2.EQ.'OR' ) THEN - IF( C3( 1: 1 ).EQ.'G' ) THEN - IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ. - $ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' ) - $ THEN - NX = 128 - END IF - END IF - ELSE IF( CNAME .AND. C2.EQ.'UN' ) THEN - IF( C3( 1: 1 ).EQ.'G' ) THEN - IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ. - $ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' ) - $ THEN - NX = 128 - END IF - END IF - ELSE IF( C2.EQ.'GG' ) THEN - NX = 128 - IF( C3.EQ.'HD3' ) THEN - NX = 128 - END IF - END IF - ILAENV = NX - RETURN -* - 80 CONTINUE -* -* ISPEC = 4: number of shifts (used by xHSEQR) -* - ILAENV = 6 - RETURN -* - 90 CONTINUE -* -* ISPEC = 5: minimum column dimension (not used) -* - ILAENV = 2 - RETURN -* - 100 CONTINUE -* -* ISPEC = 6: crossover point for SVD (used by xGELSS and xGESVD) -* - ILAENV = INT( REAL( MIN( N1, N2 ) )*1.6E0 ) - RETURN -* - 110 CONTINUE -* -* ISPEC = 7: number of processors (not used) -* - ILAENV = 1 - RETURN -* - 120 CONTINUE -* -* ISPEC = 8: crossover point for multishift (used by xHSEQR) -* - ILAENV = 50 - RETURN -* - 130 CONTINUE -* -* ISPEC = 9: maximum size of the subproblems at the bottom of the -* computation tree in the divide-and-conquer algorithm -* (used by xGELSD and xGESDD) -* - ILAENV = 25 - RETURN -* - 140 CONTINUE -* -* ISPEC = 10: ieee and infinity NaN arithmetic can be trusted not to trap -* -* ILAENV = 0 - ILAENV = 1 - IF( ILAENV.EQ.1 ) THEN - ILAENV = IEEECK( 1, 0.0, 1.0 ) - END IF - RETURN -* - 150 CONTINUE -* -* ISPEC = 11: ieee infinity arithmetic can be trusted not to trap -* -* ILAENV = 0 - ILAENV = 1 - IF( ILAENV.EQ.1 ) THEN - ILAENV = IEEECK( 0, 0.0, 1.0 ) - END IF - RETURN -* - 160 CONTINUE -* -* 12 <= ISPEC <= 17: xHSEQR or related subroutines. -* - ILAENV = IPARMQ( ISPEC, NAME, OPTS, N1, N2, N3, N4 ) - RETURN -* -* End of ILAENV -* - END diff --git a/lib/linalg/fortran/ilazlc.f b/lib/linalg/fortran/ilazlc.f deleted file mode 100644 index 8af3430e61..0000000000 --- a/lib/linalg/fortran/ilazlc.f +++ /dev/null @@ -1,115 +0,0 @@ -*> \brief \b ILAZLC scans a matrix for its last non-zero column. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ILAZLC + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* INTEGER FUNCTION ILAZLC( M, N, A, LDA ) -* -* .. Scalar Arguments .. -* INTEGER M, N, LDA -* .. -* .. Array Arguments .. -* COMPLEX*16 A( LDA, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ILAZLC scans A for its last non-zero column. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix A. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix A. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is COMPLEX*16 array, dimension (LDA,N) -*> The m by n matrix A. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,M). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16OTHERauxiliary -* -* ===================================================================== - INTEGER FUNCTION ILAZLC( M, N, A, LDA ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER M, N, LDA -* .. -* .. Array Arguments .. - COMPLEX*16 A( LDA, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - COMPLEX*16 ZERO - PARAMETER ( ZERO = (0.0D+0, 0.0D+0) ) -* .. -* .. Local Scalars .. - INTEGER I -* .. -* .. Executable Statements .. -* -* Quick test for the common case where one corner is non-zero. - IF( N.EQ.0 ) THEN - ILAZLC = N - ELSE IF( A(1, N).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN - ILAZLC = N - ELSE -* Now scan each column from the end, returning with the first non-zero. - DO ILAZLC = N, 1, -1 - DO I = 1, M - IF( A(I, ILAZLC).NE.ZERO ) RETURN - END DO - END DO - END IF - RETURN - END diff --git a/lib/linalg/fortran/ilazlr.f b/lib/linalg/fortran/ilazlr.f deleted file mode 100644 index e0134a6a35..0000000000 --- a/lib/linalg/fortran/ilazlr.f +++ /dev/null @@ -1,118 +0,0 @@ -*> \brief \b ILAZLR scans a matrix for its last non-zero row. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ILAZLR + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* INTEGER FUNCTION ILAZLR( M, N, A, LDA ) -* -* .. Scalar Arguments .. -* INTEGER M, N, LDA -* .. -* .. Array Arguments .. -* COMPLEX*16 A( LDA, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ILAZLR scans A for its last non-zero row. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix A. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix A. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is COMPLEX*16 array, dimension (LDA,N) -*> The m by n matrix A. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,M). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16OTHERauxiliary -* -* ===================================================================== - INTEGER FUNCTION ILAZLR( M, N, A, LDA ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER M, N, LDA -* .. -* .. Array Arguments .. - COMPLEX*16 A( LDA, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - COMPLEX*16 ZERO - PARAMETER ( ZERO = (0.0D+0, 0.0D+0) ) -* .. -* .. Local Scalars .. - INTEGER I, J -* .. -* .. Executable Statements .. -* -* Quick test for the common case where one corner is non-zero. - IF( M.EQ.0 ) THEN - ILAZLR = M - ELSE IF( A(M, 1).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN - ILAZLR = M - ELSE -* Scan up each column tracking the last zero row seen. - ILAZLR = 0 - DO J = 1, N - I=M - DO WHILE((A(MAX(I,1),J).EQ.ZERO).AND.(I.GE.1)) - I=I-1 - ENDDO - ILAZLR = MAX( ILAZLR, I ) - END DO - END IF - RETURN - END diff --git a/lib/linalg/fortran/iparmq.f b/lib/linalg/fortran/iparmq.f deleted file mode 100644 index 54c05471ca..0000000000 --- a/lib/linalg/fortran/iparmq.f +++ /dev/null @@ -1,406 +0,0 @@ -*> \brief \b IPARMQ -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download IPARMQ + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* INTEGER FUNCTION IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK ) -* -* .. Scalar Arguments .. -* INTEGER IHI, ILO, ISPEC, LWORK, N -* CHARACTER NAME*( * ), OPTS*( * ) -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> This program sets problem and machine dependent parameters -*> useful for xHSEQR and related subroutines for eigenvalue -*> problems. It is called whenever -*> IPARMQ is called with 12 <= ISPEC <= 16 -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] ISPEC -*> \verbatim -*> ISPEC is INTEGER -*> ISPEC specifies which tunable parameter IPARMQ should -*> return. -*> -*> ISPEC=12: (INMIN) Matrices of order nmin or less -*> are sent directly to xLAHQR, the implicit -*> double shift QR algorithm. NMIN must be -*> at least 11. -*> -*> ISPEC=13: (INWIN) Size of the deflation window. -*> This is best set greater than or equal to -*> the number of simultaneous shifts NS. -*> Larger matrices benefit from larger deflation -*> windows. -*> -*> ISPEC=14: (INIBL) Determines when to stop nibbling and -*> invest in an (expensive) multi-shift QR sweep. -*> If the aggressive early deflation subroutine -*> finds LD converged eigenvalues from an order -*> NW deflation window and LD > (NW*NIBBLE)/100, -*> then the next QR sweep is skipped and early -*> deflation is applied immediately to the -*> remaining active diagonal block. Setting -*> IPARMQ(ISPEC=14) = 0 causes TTQRE to skip a -*> multi-shift QR sweep whenever early deflation -*> finds a converged eigenvalue. Setting -*> IPARMQ(ISPEC=14) greater than or equal to 100 -*> prevents TTQRE from skipping a multi-shift -*> QR sweep. -*> -*> ISPEC=15: (NSHFTS) The number of simultaneous shifts in -*> a multi-shift QR iteration. -*> -*> ISPEC=16: (IACC22) IPARMQ is set to 0, 1 or 2 with the -*> following meanings. -*> 0: During the multi-shift QR/QZ sweep, -*> blocked eigenvalue reordering, blocked -*> Hessenberg-triangular reduction, -*> reflections and/or rotations are not -*> accumulated when updating the -*> far-from-diagonal matrix entries. -*> 1: During the multi-shift QR/QZ sweep, -*> blocked eigenvalue reordering, blocked -*> Hessenberg-triangular reduction, -*> reflections and/or rotations are -*> accumulated, and matrix-matrix -*> multiplication is used to update the -*> far-from-diagonal matrix entries. -*> 2: During the multi-shift QR/QZ sweep, -*> blocked eigenvalue reordering, blocked -*> Hessenberg-triangular reduction, -*> reflections and/or rotations are -*> accumulated, and 2-by-2 block structure -*> is exploited during matrix-matrix -*> multiplies. -*> (If xTRMM is slower than xGEMM, then -*> IPARMQ(ISPEC=16)=1 may be more efficient than -*> IPARMQ(ISPEC=16)=2 despite the greater level of -*> arithmetic work implied by the latter choice.) -*> -*> ISPEC=17: (ICOST) An estimate of the relative cost of flops -*> within the near-the-diagonal shift chase compared -*> to flops within the BLAS calls of a QZ sweep. -*> \endverbatim -*> -*> \param[in] NAME -*> \verbatim -*> NAME is CHARACTER string -*> Name of the calling subroutine -*> \endverbatim -*> -*> \param[in] OPTS -*> \verbatim -*> OPTS is CHARACTER string -*> This is a concatenation of the string arguments to -*> TTQRE. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> N is the order of the Hessenberg matrix H. -*> \endverbatim -*> -*> \param[in] ILO -*> \verbatim -*> ILO is INTEGER -*> \endverbatim -*> -*> \param[in] IHI -*> \verbatim -*> IHI is INTEGER -*> It is assumed that H is already upper triangular -*> in rows and columns 1:ILO-1 and IHI+1:N. -*> \endverbatim -*> -*> \param[in] LWORK -*> \verbatim -*> LWORK is INTEGER -*> The amount of workspace available. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup OTHERauxiliary -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> Little is known about how best to choose these parameters. -*> It is possible to use different values of the parameters -*> for each of CHSEQR, DHSEQR, SHSEQR and ZHSEQR. -*> -*> It is probably best to choose different parameters for -*> different matrices and different parameters at different -*> times during the iteration, but this has not been -*> implemented --- yet. -*> -*> -*> The best choices of most of the parameters depend -*> in an ill-understood way on the relative execution -*> rate of xLAQR3 and xLAQR5 and on the nature of each -*> particular eigenvalue problem. Experiment may be the -*> only practical way to determine which choices are most -*> effective. -*> -*> Following is a list of default values supplied by IPARMQ. -*> These defaults may be adjusted in order to attain better -*> performance in any particular computational environment. -*> -*> IPARMQ(ISPEC=12) The xLAHQR vs xLAQR0 crossover point. -*> Default: 75. (Must be at least 11.) -*> -*> IPARMQ(ISPEC=13) Recommended deflation window size. -*> This depends on ILO, IHI and NS, the -*> number of simultaneous shifts returned -*> by IPARMQ(ISPEC=15). The default for -*> (IHI-ILO+1) <= 500 is NS. The default -*> for (IHI-ILO+1) > 500 is 3*NS/2. -*> -*> IPARMQ(ISPEC=14) Nibble crossover point. Default: 14. -*> -*> IPARMQ(ISPEC=15) Number of simultaneous shifts, NS. -*> a multi-shift QR iteration. -*> -*> If IHI-ILO+1 is ... -*> -*> greater than ...but less ... the -*> or equal to ... than default is -*> -*> 0 30 NS = 2+ -*> 30 60 NS = 4+ -*> 60 150 NS = 10 -*> 150 590 NS = ** -*> 590 3000 NS = 64 -*> 3000 6000 NS = 128 -*> 6000 infinity NS = 256 -*> -*> (+) By default matrices of this order are -*> passed to the implicit double shift routine -*> xLAHQR. See IPARMQ(ISPEC=12) above. These -*> values of NS are used only in case of a rare -*> xLAHQR failure. -*> -*> (**) The asterisks (**) indicate an ad-hoc -*> function increasing from 10 to 64. -*> -*> IPARMQ(ISPEC=16) Select structured matrix multiply. -*> (See ISPEC=16 above for details.) -*> Default: 3. -*> -*> IPARMQ(ISPEC=17) Relative cost heuristic for blocksize selection. -*> Expressed as a percentage. -*> Default: 10. -*> \endverbatim -*> -* ===================================================================== - INTEGER FUNCTION IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER IHI, ILO, ISPEC, LWORK, N - CHARACTER NAME*( * ), OPTS*( * ) -* -* ================================================================ -* .. Parameters .. - INTEGER INMIN, INWIN, INIBL, ISHFTS, IACC22, ICOST - PARAMETER ( INMIN = 12, INWIN = 13, INIBL = 14, - $ ISHFTS = 15, IACC22 = 16, ICOST = 17 ) - INTEGER NMIN, K22MIN, KACMIN, NIBBLE, KNWSWP, RCOST - PARAMETER ( NMIN = 75, K22MIN = 14, KACMIN = 14, - $ NIBBLE = 14, KNWSWP = 500, RCOST = 10 ) - REAL TWO - PARAMETER ( TWO = 2.0 ) -* .. -* .. Local Scalars .. - INTEGER NH, NS - INTEGER I, IC, IZ - CHARACTER SUBNAM*6 -* .. -* .. Intrinsic Functions .. - INTRINSIC LOG, MAX, MOD, NINT, REAL -* .. -* .. Executable Statements .. - IF( ( ISPEC.EQ.ISHFTS ) .OR. ( ISPEC.EQ.INWIN ) .OR. - $ ( ISPEC.EQ.IACC22 ) ) THEN -* -* ==== Set the number simultaneous shifts ==== -* - NH = IHI - ILO + 1 - NS = 2 - IF( NH.GE.30 ) - $ NS = 4 - IF( NH.GE.60 ) - $ NS = 10 - IF( NH.GE.150 ) - $ NS = MAX( 10, NH / NINT( LOG( REAL( NH ) ) / LOG( TWO ) ) ) - IF( NH.GE.590 ) - $ NS = 64 - IF( NH.GE.3000 ) - $ NS = 128 - IF( NH.GE.6000 ) - $ NS = 256 - NS = MAX( 2, NS-MOD( NS, 2 ) ) - END IF -* - IF( ISPEC.EQ.INMIN ) THEN -* -* -* ===== Matrices of order smaller than NMIN get sent -* . to xLAHQR, the classic double shift algorithm. -* . This must be at least 11. ==== -* - IPARMQ = NMIN -* - ELSE IF( ISPEC.EQ.INIBL ) THEN -* -* ==== INIBL: skip a multi-shift qr iteration and -* . whenever aggressive early deflation finds -* . at least (NIBBLE*(window size)/100) deflations. ==== -* - IPARMQ = NIBBLE -* - ELSE IF( ISPEC.EQ.ISHFTS ) THEN -* -* ==== NSHFTS: The number of simultaneous shifts ===== -* - IPARMQ = NS -* - ELSE IF( ISPEC.EQ.INWIN ) THEN -* -* ==== NW: deflation window size. ==== -* - IF( NH.LE.KNWSWP ) THEN - IPARMQ = NS - ELSE - IPARMQ = 3*NS / 2 - END IF -* - ELSE IF( ISPEC.EQ.IACC22 ) THEN -* -* ==== IACC22: Whether to accumulate reflections -* . before updating the far-from-diagonal elements -* . and whether to use 2-by-2 block structure while -* . doing it. A small amount of work could be saved -* . by making this choice dependent also upon the -* . NH=IHI-ILO+1. -* -* -* Convert NAME to upper case if the first character is lower case. -* - IPARMQ = 0 - SUBNAM = NAME - IC = ICHAR( SUBNAM( 1: 1 ) ) - IZ = ICHAR( 'Z' ) - IF( IZ.EQ.90 .OR. IZ.EQ.122 ) THEN -* -* ASCII character set -* - IF( IC.GE.97 .AND. IC.LE.122 ) THEN - SUBNAM( 1: 1 ) = CHAR( IC-32 ) - DO I = 2, 6 - IC = ICHAR( SUBNAM( I: I ) ) - IF( IC.GE.97 .AND. IC.LE.122 ) - $ SUBNAM( I: I ) = CHAR( IC-32 ) - END DO - END IF -* - ELSE IF( IZ.EQ.233 .OR. IZ.EQ.169 ) THEN -* -* EBCDIC character set -* - IF( ( IC.GE.129 .AND. IC.LE.137 ) .OR. - $ ( IC.GE.145 .AND. IC.LE.153 ) .OR. - $ ( IC.GE.162 .AND. IC.LE.169 ) ) THEN - SUBNAM( 1: 1 ) = CHAR( IC+64 ) - DO I = 2, 6 - IC = ICHAR( SUBNAM( I: I ) ) - IF( ( IC.GE.129 .AND. IC.LE.137 ) .OR. - $ ( IC.GE.145 .AND. IC.LE.153 ) .OR. - $ ( IC.GE.162 .AND. IC.LE.169 ) )SUBNAM( I: - $ I ) = CHAR( IC+64 ) - END DO - END IF -* - ELSE IF( IZ.EQ.218 .OR. IZ.EQ.250 ) THEN -* -* Prime machines: ASCII+128 -* - IF( IC.GE.225 .AND. IC.LE.250 ) THEN - SUBNAM( 1: 1 ) = CHAR( IC-32 ) - DO I = 2, 6 - IC = ICHAR( SUBNAM( I: I ) ) - IF( IC.GE.225 .AND. IC.LE.250 ) - $ SUBNAM( I: I ) = CHAR( IC-32 ) - END DO - END IF - END IF -* - IF( SUBNAM( 2:6 ).EQ.'GGHRD' .OR. - $ SUBNAM( 2:6 ).EQ.'GGHD3' ) THEN - IPARMQ = 1 - IF( NH.GE.K22MIN ) - $ IPARMQ = 2 - ELSE IF ( SUBNAM( 4:6 ).EQ.'EXC' ) THEN - IF( NH.GE.KACMIN ) - $ IPARMQ = 1 - IF( NH.GE.K22MIN ) - $ IPARMQ = 2 - ELSE IF ( SUBNAM( 2:6 ).EQ.'HSEQR' .OR. - $ SUBNAM( 2:5 ).EQ.'LAQR' ) THEN - IF( NS.GE.KACMIN ) - $ IPARMQ = 1 - IF( NS.GE.K22MIN ) - $ IPARMQ = 2 - END IF -* - ELSE IF( ISPEC.EQ.ICOST ) THEN -* -* === Relative cost of near-the-diagonal chase vs -* BLAS updates === -* - IPARMQ = RCOST - ELSE -* ===== invalid value of ispec ===== - IPARMQ = -1 -* - END IF -* -* ==== End of IPARMQ ==== -* - END diff --git a/lib/linalg/fortran/lsame.f b/lib/linalg/fortran/lsame.f deleted file mode 100644 index 6aa4007065..0000000000 --- a/lib/linalg/fortran/lsame.f +++ /dev/null @@ -1,122 +0,0 @@ -*> \brief \b LSAME -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* LOGICAL FUNCTION LSAME(CA,CB) -* -* .. Scalar Arguments .. -* CHARACTER CA,CB -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> LSAME returns .TRUE. if CA is the same letter as CB regardless of -*> case. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] CA -*> \verbatim -*> CA is CHARACTER*1 -*> \endverbatim -*> -*> \param[in] CB -*> \verbatim -*> CB is CHARACTER*1 -*> CA and CB specify the single characters to be compared. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup aux_blas -* -* ===================================================================== - LOGICAL FUNCTION LSAME(CA,CB) -* -* -- Reference BLAS level1 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER CA,CB -* .. -* -* ===================================================================== -* -* .. Intrinsic Functions .. - INTRINSIC ICHAR -* .. -* .. Local Scalars .. - INTEGER INTA,INTB,ZCODE -* .. -* -* Test if the characters are equal -* - LSAME = CA .EQ. CB - IF (LSAME) RETURN -* -* Now test for equivalence if both characters are alphabetic. -* - ZCODE = ICHAR('Z') -* -* Use 'Z' rather than 'A' so that ASCII can be detected on Prime -* machines, on which ICHAR returns a value with bit 8 set. -* ICHAR('A') on Prime machines returns 193 which is the same as -* ICHAR('A') on an EBCDIC machine. -* - INTA = ICHAR(CA) - INTB = ICHAR(CB) -* - IF (ZCODE.EQ.90 .OR. ZCODE.EQ.122) THEN -* -* ASCII is assumed - ZCODE is the ASCII code of either lower or -* upper case 'Z'. -* - IF (INTA.GE.97 .AND. INTA.LE.122) INTA = INTA - 32 - IF (INTB.GE.97 .AND. INTB.LE.122) INTB = INTB - 32 -* - ELSE IF (ZCODE.EQ.233 .OR. ZCODE.EQ.169) THEN -* -* EBCDIC is assumed - ZCODE is the EBCDIC code of either lower or -* upper case 'Z'. -* - IF (INTA.GE.129 .AND. INTA.LE.137 .OR. - + INTA.GE.145 .AND. INTA.LE.153 .OR. - + INTA.GE.162 .AND. INTA.LE.169) INTA = INTA + 64 - IF (INTB.GE.129 .AND. INTB.LE.137 .OR. - + INTB.GE.145 .AND. INTB.LE.153 .OR. - + INTB.GE.162 .AND. INTB.LE.169) INTB = INTB + 64 -* - ELSE IF (ZCODE.EQ.218 .OR. ZCODE.EQ.250) THEN -* -* ASCII is assumed, on Prime machines - ZCODE is the ASCII code -* plus 128 of either lower or upper case 'Z'. -* - IF (INTA.GE.225 .AND. INTA.LE.250) INTA = INTA - 32 - IF (INTB.GE.225 .AND. INTB.LE.250) INTB = INTB - 32 - END IF - LSAME = INTA .EQ. INTB -* -* RETURN -* -* End of LSAME -* - END diff --git a/lib/linalg/fortran/xerbla.f b/lib/linalg/fortran/xerbla.f deleted file mode 100644 index 6b141499ee..0000000000 --- a/lib/linalg/fortran/xerbla.f +++ /dev/null @@ -1,96 +0,0 @@ -*> \brief \b XERBLA -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download XERBLA + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE XERBLA( SRNAME, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER*(*) SRNAME -* INTEGER INFO -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> XERBLA is an error handler for the LAPACK routines. -*> It is called by an LAPACK routine if an input parameter has an -*> invalid value. A message is printed and execution stops. -*> -*> Installers may consider modifying the STOP statement in order to -*> call system-specific exception-handling facilities. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] SRNAME -*> \verbatim -*> SRNAME is CHARACTER*(*) -*> The name of the routine which called XERBLA. -*> \endverbatim -*> -*> \param[in] INFO -*> \verbatim -*> INFO is INTEGER -*> The position of the invalid parameter in the parameter list -*> of the calling routine. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup OTHERauxiliary -* -* ===================================================================== - SUBROUTINE XERBLA( SRNAME, INFO ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER*(*) SRNAME - INTEGER INFO -* .. -* -* ===================================================================== -* -* .. Intrinsic Functions .. - INTRINSIC LEN_TRIM -* .. -* .. Executable Statements .. -* - WRITE( *, FMT = 9999 )SRNAME( 1:LEN_TRIM( SRNAME ) ), INFO -* - STOP -* - 9999 FORMAT( ' ** On entry to ', A, ' parameter number ', I2, ' had ', - $ 'an illegal value' ) -* -* End of XERBLA -* - END diff --git a/lib/linalg/fortran/zaxpy.f b/lib/linalg/fortran/zaxpy.f deleted file mode 100644 index 35c0e4b892..0000000000 --- a/lib/linalg/fortran/zaxpy.f +++ /dev/null @@ -1,139 +0,0 @@ -*> \brief \b ZAXPY -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE ZAXPY(N,ZA,ZX,INCX,ZY,INCY) -* -* .. Scalar Arguments .. -* COMPLEX*16 ZA -* INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. -* COMPLEX*16 ZX(*),ZY(*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZAXPY constant times a vector plus a vector. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> number of elements in input vector(s) -*> \endverbatim -*> -*> \param[in] ZA -*> \verbatim -*> ZA is COMPLEX*16 -*> On entry, ZA specifies the scalar alpha. -*> \endverbatim -*> -*> \param[in] ZX -*> \verbatim -*> ZX is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> storage spacing between elements of ZX -*> \endverbatim -*> -*> \param[in,out] ZY -*> \verbatim -*> ZY is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) -*> \endverbatim -*> -*> \param[in] INCY -*> \verbatim -*> INCY is INTEGER -*> storage spacing between elements of ZY -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16_blas_level1 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> jack dongarra, 3/11/78. -*> modified 12/3/93, array(1) declarations changed to array(*) -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE ZAXPY(N,ZA,ZX,INCX,ZY,INCY) -* -* -- Reference BLAS level1 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - COMPLEX*16 ZA - INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. - COMPLEX*16 ZX(*),ZY(*) -* .. -* -* ===================================================================== -* -* .. Local Scalars .. - INTEGER I,IX,IY -* .. -* .. External Functions .. - DOUBLE PRECISION DCABS1 - EXTERNAL DCABS1 -* .. - IF (N.LE.0) RETURN - IF (DCABS1(ZA).EQ.0.0d0) RETURN - IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN -* -* code for both increments equal to 1 -* - DO I = 1,N - ZY(I) = ZY(I) + ZA*ZX(I) - END DO - ELSE -* -* code for unequal increments or equal increments -* not equal to 1 -* - IX = 1 - IY = 1 - IF (INCX.LT.0) IX = (-N+1)*INCX + 1 - IF (INCY.LT.0) IY = (-N+1)*INCY + 1 - DO I = 1,N - ZY(IY) = ZY(IY) + ZA*ZX(IX) - IX = IX + INCX - IY = IY + INCY - END DO - END IF -* - RETURN -* -* End of ZAXPY -* - END diff --git a/lib/linalg/fortran/zcopy.f b/lib/linalg/fortran/zcopy.f deleted file mode 100644 index 1efcdb6b0f..0000000000 --- a/lib/linalg/fortran/zcopy.f +++ /dev/null @@ -1,125 +0,0 @@ -*> \brief \b ZCOPY -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE ZCOPY(N,ZX,INCX,ZY,INCY) -* -* .. Scalar Arguments .. -* INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. -* COMPLEX*16 ZX(*),ZY(*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZCOPY copies a vector, x, to a vector, y. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> number of elements in input vector(s) -*> \endverbatim -*> -*> \param[in] ZX -*> \verbatim -*> ZX is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> storage spacing between elements of ZX -*> \endverbatim -*> -*> \param[out] ZY -*> \verbatim -*> ZY is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) -*> \endverbatim -*> -*> \param[in] INCY -*> \verbatim -*> INCY is INTEGER -*> storage spacing between elements of ZY -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16_blas_level1 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> jack dongarra, linpack, 4/11/78. -*> modified 12/3/93, array(1) declarations changed to array(*) -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE ZCOPY(N,ZX,INCX,ZY,INCY) -* -* -- Reference BLAS level1 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. - COMPLEX*16 ZX(*),ZY(*) -* .. -* -* ===================================================================== -* -* .. Local Scalars .. - INTEGER I,IX,IY -* .. - IF (N.LE.0) RETURN - IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN -* -* code for both increments equal to 1 -* - DO I = 1,N - ZY(I) = ZX(I) - END DO - ELSE -* -* code for unequal increments or equal increments -* not equal to 1 -* - IX = 1 - IY = 1 - IF (INCX.LT.0) IX = (-N+1)*INCX + 1 - IF (INCY.LT.0) IY = (-N+1)*INCY + 1 - DO I = 1,N - ZY(IY) = ZX(IX) - IX = IX + INCX - IY = IY + INCY - END DO - END IF - RETURN -* -* End of ZCOPY -* - END diff --git a/lib/linalg/fortran/zdotc.f b/lib/linalg/fortran/zdotc.f deleted file mode 100644 index bcc29e2dad..0000000000 --- a/lib/linalg/fortran/zdotc.f +++ /dev/null @@ -1,134 +0,0 @@ -*> \brief \b ZDOTC -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* COMPLEX*16 FUNCTION ZDOTC(N,ZX,INCX,ZY,INCY) -* -* .. Scalar Arguments .. -* INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. -* COMPLEX*16 ZX(*),ZY(*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZDOTC forms the dot product of two complex vectors -*> ZDOTC = X^H * Y -*> -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> number of elements in input vector(s) -*> \endverbatim -*> -*> \param[in] ZX -*> \verbatim -*> ZX is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> storage spacing between elements of ZX -*> \endverbatim -*> -*> \param[in] ZY -*> \verbatim -*> ZY is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) -*> \endverbatim -*> -*> \param[in] INCY -*> \verbatim -*> INCY is INTEGER -*> storage spacing between elements of ZY -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16_blas_level1 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> jack dongarra, 3/11/78. -*> modified 12/3/93, array(1) declarations changed to array(*) -*> \endverbatim -*> -* ===================================================================== - COMPLEX*16 FUNCTION ZDOTC(N,ZX,INCX,ZY,INCY) -* -* -- Reference BLAS level1 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. - COMPLEX*16 ZX(*),ZY(*) -* .. -* -* ===================================================================== -* -* .. Local Scalars .. - COMPLEX*16 ZTEMP - INTEGER I,IX,IY -* .. -* .. Intrinsic Functions .. - INTRINSIC DCONJG -* .. - ZTEMP = (0.0d0,0.0d0) - ZDOTC = (0.0d0,0.0d0) - IF (N.LE.0) RETURN - IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN -* -* code for both increments equal to 1 -* - DO I = 1,N - ZTEMP = ZTEMP + DCONJG(ZX(I))*ZY(I) - END DO - ELSE -* -* code for unequal increments or equal increments -* not equal to 1 -* - IX = 1 - IY = 1 - IF (INCX.LT.0) IX = (-N+1)*INCX + 1 - IF (INCY.LT.0) IY = (-N+1)*INCY + 1 - DO I = 1,N - ZTEMP = ZTEMP + DCONJG(ZX(IX))*ZY(IY) - IX = IX + INCX - IY = IY + INCY - END DO - END IF - ZDOTC = ZTEMP - RETURN -* -* End of ZDOTC -* - END diff --git a/lib/linalg/fortran/zdrot.f b/lib/linalg/fortran/zdrot.f deleted file mode 100644 index 3145561d67..0000000000 --- a/lib/linalg/fortran/zdrot.f +++ /dev/null @@ -1,153 +0,0 @@ -*> \brief \b ZDROT -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE ZDROT( N, ZX, INCX, ZY, INCY, C, S ) -* -* .. Scalar Arguments .. -* INTEGER INCX, INCY, N -* DOUBLE PRECISION C, S -* .. -* .. Array Arguments .. -* COMPLEX*16 ZX( * ), ZY( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> Applies a plane rotation, where the cos and sin (c and s) are real -*> and the vectors cx and cy are complex. -*> jack dongarra, linpack, 3/11/78. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> On entry, N specifies the order of the vectors cx and cy. -*> N must be at least zero. -*> \endverbatim -*> -*> \param[in,out] ZX -*> \verbatim -*> ZX is COMPLEX*16 array, dimension at least -*> ( 1 + ( N - 1 )*abs( INCX ) ). -*> Before entry, the incremented array ZX must contain the n -*> element vector cx. On exit, ZX is overwritten by the updated -*> vector cx. -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> On entry, INCX specifies the increment for the elements of -*> ZX. INCX must not be zero. -*> \endverbatim -*> -*> \param[in,out] ZY -*> \verbatim -*> ZY is COMPLEX*16 array, dimension at least -*> ( 1 + ( N - 1 )*abs( INCY ) ). -*> Before entry, the incremented array ZY must contain the n -*> element vector cy. On exit, ZY is overwritten by the updated -*> vector cy. -*> \endverbatim -*> -*> \param[in] INCY -*> \verbatim -*> INCY is INTEGER -*> On entry, INCY specifies the increment for the elements of -*> ZY. INCY must not be zero. -*> \endverbatim -*> -*> \param[in] C -*> \verbatim -*> C is DOUBLE PRECISION -*> On entry, C specifies the cosine, cos. -*> \endverbatim -*> -*> \param[in] S -*> \verbatim -*> S is DOUBLE PRECISION -*> On entry, S specifies the sine, sin. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16_blas_level1 -* -* ===================================================================== - SUBROUTINE ZDROT( N, ZX, INCX, ZY, INCY, C, S ) -* -* -- Reference BLAS level1 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INCX, INCY, N - DOUBLE PRECISION C, S -* .. -* .. Array Arguments .. - COMPLEX*16 ZX( * ), ZY( * ) -* .. -* -* ===================================================================== -* -* .. Local Scalars .. - INTEGER I, IX, IY - COMPLEX*16 CTEMP -* .. -* .. Executable Statements .. -* - IF( N.LE.0 ) - $ RETURN - IF( INCX.EQ.1 .AND. INCY.EQ.1 ) THEN -* -* code for both increments equal to 1 -* - DO I = 1, N - CTEMP = C*ZX( I ) + S*ZY( I ) - ZY( I ) = C*ZY( I ) - S*ZX( I ) - ZX( I ) = CTEMP - END DO - ELSE -* -* code for unequal increments or equal increments not equal -* to 1 -* - IX = 1 - IY = 1 - IF( INCX.LT.0 ) - $ IX = ( -N+1 )*INCX + 1 - IF( INCY.LT.0 ) - $ IY = ( -N+1 )*INCY + 1 - DO I = 1, N - CTEMP = C*ZX( IX ) + S*ZY( IY ) - ZY( IY ) = C*ZY( IY ) - S*ZX( IX ) - ZX( IX ) = CTEMP - IX = IX + INCX - IY = IY + INCY - END DO - END IF - RETURN -* -* End of ZDROT -* - END diff --git a/lib/linalg/fortran/zdscal.f b/lib/linalg/fortran/zdscal.f deleted file mode 100644 index 5a16048771..0000000000 --- a/lib/linalg/fortran/zdscal.f +++ /dev/null @@ -1,123 +0,0 @@ -*> \brief \b ZDSCAL -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE ZDSCAL(N,DA,ZX,INCX) -* -* .. Scalar Arguments .. -* DOUBLE PRECISION DA -* INTEGER INCX,N -* .. -* .. Array Arguments .. -* COMPLEX*16 ZX(*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZDSCAL scales a vector by a constant. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> number of elements in input vector(s) -*> \endverbatim -*> -*> \param[in] DA -*> \verbatim -*> DA is DOUBLE PRECISION -*> On entry, DA specifies the scalar alpha. -*> \endverbatim -*> -*> \param[in,out] ZX -*> \verbatim -*> ZX is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> storage spacing between elements of ZX -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16_blas_level1 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> jack dongarra, 3/11/78. -*> modified 3/93 to return if incx .le. 0. -*> modified 12/3/93, array(1) declarations changed to array(*) -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE ZDSCAL(N,DA,ZX,INCX) -* -* -- Reference BLAS level1 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - DOUBLE PRECISION DA - INTEGER INCX,N -* .. -* .. Array Arguments .. - COMPLEX*16 ZX(*) -* .. -* -* ===================================================================== -* -* .. Local Scalars .. - INTEGER I,NINCX -* .. Parameters .. - DOUBLE PRECISION ONE - PARAMETER (ONE=1.0D+0) -* .. -* .. Intrinsic Functions .. - INTRINSIC DBLE, DCMPLX, DIMAG -* .. - IF (N.LE.0 .OR. INCX.LE.0 .OR. DA.EQ.ONE) RETURN - IF (INCX.EQ.1) THEN -* -* code for increment equal to 1 -* - DO I = 1,N - ZX(I) = DCMPLX(DA*DBLE(ZX(I)),DA*DIMAG(ZX(I))) - END DO - ELSE -* -* code for increment not equal to 1 -* - NINCX = N*INCX - DO I = 1,NINCX,INCX - ZX(I) = DCMPLX(DA*DBLE(ZX(I)),DA*DIMAG(ZX(I))) - END DO - END IF - RETURN -* -* End of ZDSCAL -* - END diff --git a/lib/linalg/fortran/zgemm.f b/lib/linalg/fortran/zgemm.f deleted file mode 100644 index 0b712f1b73..0000000000 --- a/lib/linalg/fortran/zgemm.f +++ /dev/null @@ -1,477 +0,0 @@ -*> \brief \b ZGEMM -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE ZGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) -* -* .. Scalar Arguments .. -* COMPLEX*16 ALPHA,BETA -* INTEGER K,LDA,LDB,LDC,M,N -* CHARACTER TRANSA,TRANSB -* .. -* .. Array Arguments .. -* COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZGEMM performs one of the matrix-matrix operations -*> -*> C := alpha*op( A )*op( B ) + beta*C, -*> -*> where op( X ) is one of -*> -*> op( X ) = X or op( X ) = X**T or op( X ) = X**H, -*> -*> alpha and beta are scalars, and A, B and C are matrices, with op( A ) -*> an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] TRANSA -*> \verbatim -*> TRANSA is CHARACTER*1 -*> On entry, TRANSA specifies the form of op( A ) to be used in -*> the matrix multiplication as follows: -*> -*> TRANSA = 'N' or 'n', op( A ) = A. -*> -*> TRANSA = 'T' or 't', op( A ) = A**T. -*> -*> TRANSA = 'C' or 'c', op( A ) = A**H. -*> \endverbatim -*> -*> \param[in] TRANSB -*> \verbatim -*> TRANSB is CHARACTER*1 -*> On entry, TRANSB specifies the form of op( B ) to be used in -*> the matrix multiplication as follows: -*> -*> TRANSB = 'N' or 'n', op( B ) = B. -*> -*> TRANSB = 'T' or 't', op( B ) = B**T. -*> -*> TRANSB = 'C' or 'c', op( B ) = B**H. -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> On entry, M specifies the number of rows of the matrix -*> op( A ) and of the matrix C. M must be at least zero. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> On entry, N specifies the number of columns of the matrix -*> op( B ) and the number of columns of the matrix C. N must be -*> at least zero. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> On entry, K specifies the number of columns of the matrix -*> op( A ) and the number of rows of the matrix op( B ). K must -*> be at least zero. -*> \endverbatim -*> -*> \param[in] ALPHA -*> \verbatim -*> ALPHA is COMPLEX*16 -*> On entry, ALPHA specifies the scalar alpha. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is COMPLEX*16 array, dimension ( LDA, ka ), where ka is -*> k when TRANSA = 'N' or 'n', and is m otherwise. -*> Before entry with TRANSA = 'N' or 'n', the leading m by k -*> part of the array A must contain the matrix A, otherwise -*> the leading k by m part of the array A must contain the -*> matrix A. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> On entry, LDA specifies the first dimension of A as declared -*> in the calling (sub) program. When TRANSA = 'N' or 'n' then -*> LDA must be at least max( 1, m ), otherwise LDA must be at -*> least max( 1, k ). -*> \endverbatim -*> -*> \param[in] B -*> \verbatim -*> B is COMPLEX*16 array, dimension ( LDB, kb ), where kb is -*> n when TRANSB = 'N' or 'n', and is k otherwise. -*> Before entry with TRANSB = 'N' or 'n', the leading k by n -*> part of the array B must contain the matrix B, otherwise -*> the leading n by k part of the array B must contain the -*> matrix B. -*> \endverbatim -*> -*> \param[in] LDB -*> \verbatim -*> LDB is INTEGER -*> On entry, LDB specifies the first dimension of B as declared -*> in the calling (sub) program. When TRANSB = 'N' or 'n' then -*> LDB must be at least max( 1, k ), otherwise LDB must be at -*> least max( 1, n ). -*> \endverbatim -*> -*> \param[in] BETA -*> \verbatim -*> BETA is COMPLEX*16 -*> On entry, BETA specifies the scalar beta. When BETA is -*> supplied as zero then C need not be set on input. -*> \endverbatim -*> -*> \param[in,out] C -*> \verbatim -*> C is COMPLEX*16 array, dimension ( LDC, N ) -*> Before entry, the leading m by n part of the array C must -*> contain the matrix C, except when beta is zero, in which -*> case C need not be set on entry. -*> On exit, the array C is overwritten by the m by n matrix -*> ( alpha*op( A )*op( B ) + beta*C ). -*> \endverbatim -*> -*> \param[in] LDC -*> \verbatim -*> LDC is INTEGER -*> On entry, LDC specifies the first dimension of C as declared -*> in the calling (sub) program. LDC must be at least -*> max( 1, m ). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16_blas_level3 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> Level 3 Blas routine. -*> -*> -- Written on 8-February-1989. -*> Jack Dongarra, Argonne National Laboratory. -*> Iain Duff, AERE Harwell. -*> Jeremy Du Croz, Numerical Algorithms Group Ltd. -*> Sven Hammarling, Numerical Algorithms Group Ltd. -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE ZGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) -* -* -- Reference BLAS level3 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - COMPLEX*16 ALPHA,BETA - INTEGER K,LDA,LDB,LDC,M,N - CHARACTER TRANSA,TRANSB -* .. -* .. Array Arguments .. - COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*) -* .. -* -* ===================================================================== -* -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC DCONJG,MAX -* .. -* .. Local Scalars .. - COMPLEX*16 TEMP - INTEGER I,INFO,J,L,NROWA,NROWB - LOGICAL CONJA,CONJB,NOTA,NOTB -* .. -* .. Parameters .. - COMPLEX*16 ONE - PARAMETER (ONE= (1.0D+0,0.0D+0)) - COMPLEX*16 ZERO - PARAMETER (ZERO= (0.0D+0,0.0D+0)) -* .. -* -* Set NOTA and NOTB as true if A and B respectively are not -* conjugated or transposed, set CONJA and CONJB as true if A and -* B respectively are to be transposed but not conjugated and set -* NROWA and NROWB as the number of rows of A and B respectively. -* - NOTA = LSAME(TRANSA,'N') - NOTB = LSAME(TRANSB,'N') - CONJA = LSAME(TRANSA,'C') - CONJB = LSAME(TRANSB,'C') - IF (NOTA) THEN - NROWA = M - ELSE - NROWA = K - END IF - IF (NOTB) THEN - NROWB = K - ELSE - NROWB = N - END IF -* -* Test the input parameters. -* - INFO = 0 - IF ((.NOT.NOTA) .AND. (.NOT.CONJA) .AND. - + (.NOT.LSAME(TRANSA,'T'))) THEN - INFO = 1 - ELSE IF ((.NOT.NOTB) .AND. (.NOT.CONJB) .AND. - + (.NOT.LSAME(TRANSB,'T'))) THEN - INFO = 2 - ELSE IF (M.LT.0) THEN - INFO = 3 - ELSE IF (N.LT.0) THEN - INFO = 4 - ELSE IF (K.LT.0) THEN - INFO = 5 - ELSE IF (LDA.LT.MAX(1,NROWA)) THEN - INFO = 8 - ELSE IF (LDB.LT.MAX(1,NROWB)) THEN - INFO = 10 - ELSE IF (LDC.LT.MAX(1,M)) THEN - INFO = 13 - END IF - IF (INFO.NE.0) THEN - CALL XERBLA('ZGEMM ',INFO) - RETURN - END IF -* -* Quick return if possible. -* - IF ((M.EQ.0) .OR. (N.EQ.0) .OR. - + (((ALPHA.EQ.ZERO).OR. (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN -* -* And when alpha.eq.zero. -* - IF (ALPHA.EQ.ZERO) THEN - IF (BETA.EQ.ZERO) THEN - DO 20 J = 1,N - DO 10 I = 1,M - C(I,J) = ZERO - 10 CONTINUE - 20 CONTINUE - ELSE - DO 40 J = 1,N - DO 30 I = 1,M - C(I,J) = BETA*C(I,J) - 30 CONTINUE - 40 CONTINUE - END IF - RETURN - END IF -* -* Start the operations. -* - IF (NOTB) THEN - IF (NOTA) THEN -* -* Form C := alpha*A*B + beta*C. -* - DO 90 J = 1,N - IF (BETA.EQ.ZERO) THEN - DO 50 I = 1,M - C(I,J) = ZERO - 50 CONTINUE - ELSE IF (BETA.NE.ONE) THEN - DO 60 I = 1,M - C(I,J) = BETA*C(I,J) - 60 CONTINUE - END IF - DO 80 L = 1,K - TEMP = ALPHA*B(L,J) - DO 70 I = 1,M - C(I,J) = C(I,J) + TEMP*A(I,L) - 70 CONTINUE - 80 CONTINUE - 90 CONTINUE - ELSE IF (CONJA) THEN -* -* Form C := alpha*A**H*B + beta*C. -* - DO 120 J = 1,N - DO 110 I = 1,M - TEMP = ZERO - DO 100 L = 1,K - TEMP = TEMP + DCONJG(A(L,I))*B(L,J) - 100 CONTINUE - IF (BETA.EQ.ZERO) THEN - C(I,J) = ALPHA*TEMP - ELSE - C(I,J) = ALPHA*TEMP + BETA*C(I,J) - END IF - 110 CONTINUE - 120 CONTINUE - ELSE -* -* Form C := alpha*A**T*B + beta*C -* - DO 150 J = 1,N - DO 140 I = 1,M - TEMP = ZERO - DO 130 L = 1,K - TEMP = TEMP + A(L,I)*B(L,J) - 130 CONTINUE - IF (BETA.EQ.ZERO) THEN - C(I,J) = ALPHA*TEMP - ELSE - C(I,J) = ALPHA*TEMP + BETA*C(I,J) - END IF - 140 CONTINUE - 150 CONTINUE - END IF - ELSE IF (NOTA) THEN - IF (CONJB) THEN -* -* Form C := alpha*A*B**H + beta*C. -* - DO 200 J = 1,N - IF (BETA.EQ.ZERO) THEN - DO 160 I = 1,M - C(I,J) = ZERO - 160 CONTINUE - ELSE IF (BETA.NE.ONE) THEN - DO 170 I = 1,M - C(I,J) = BETA*C(I,J) - 170 CONTINUE - END IF - DO 190 L = 1,K - TEMP = ALPHA*DCONJG(B(J,L)) - DO 180 I = 1,M - C(I,J) = C(I,J) + TEMP*A(I,L) - 180 CONTINUE - 190 CONTINUE - 200 CONTINUE - ELSE -* -* Form C := alpha*A*B**T + beta*C -* - DO 250 J = 1,N - IF (BETA.EQ.ZERO) THEN - DO 210 I = 1,M - C(I,J) = ZERO - 210 CONTINUE - ELSE IF (BETA.NE.ONE) THEN - DO 220 I = 1,M - C(I,J) = BETA*C(I,J) - 220 CONTINUE - END IF - DO 240 L = 1,K - TEMP = ALPHA*B(J,L) - DO 230 I = 1,M - C(I,J) = C(I,J) + TEMP*A(I,L) - 230 CONTINUE - 240 CONTINUE - 250 CONTINUE - END IF - ELSE IF (CONJA) THEN - IF (CONJB) THEN -* -* Form C := alpha*A**H*B**H + beta*C. -* - DO 280 J = 1,N - DO 270 I = 1,M - TEMP = ZERO - DO 260 L = 1,K - TEMP = TEMP + DCONJG(A(L,I))*DCONJG(B(J,L)) - 260 CONTINUE - IF (BETA.EQ.ZERO) THEN - C(I,J) = ALPHA*TEMP - ELSE - C(I,J) = ALPHA*TEMP + BETA*C(I,J) - END IF - 270 CONTINUE - 280 CONTINUE - ELSE -* -* Form C := alpha*A**H*B**T + beta*C -* - DO 310 J = 1,N - DO 300 I = 1,M - TEMP = ZERO - DO 290 L = 1,K - TEMP = TEMP + DCONJG(A(L,I))*B(J,L) - 290 CONTINUE - IF (BETA.EQ.ZERO) THEN - C(I,J) = ALPHA*TEMP - ELSE - C(I,J) = ALPHA*TEMP + BETA*C(I,J) - END IF - 300 CONTINUE - 310 CONTINUE - END IF - ELSE - IF (CONJB) THEN -* -* Form C := alpha*A**T*B**H + beta*C -* - DO 340 J = 1,N - DO 330 I = 1,M - TEMP = ZERO - DO 320 L = 1,K - TEMP = TEMP + A(L,I)*DCONJG(B(J,L)) - 320 CONTINUE - IF (BETA.EQ.ZERO) THEN - C(I,J) = ALPHA*TEMP - ELSE - C(I,J) = ALPHA*TEMP + BETA*C(I,J) - END IF - 330 CONTINUE - 340 CONTINUE - ELSE -* -* Form C := alpha*A**T*B**T + beta*C -* - DO 370 J = 1,N - DO 360 I = 1,M - TEMP = ZERO - DO 350 L = 1,K - TEMP = TEMP + A(L,I)*B(J,L) - 350 CONTINUE - IF (BETA.EQ.ZERO) THEN - C(I,J) = ALPHA*TEMP - ELSE - C(I,J) = ALPHA*TEMP + BETA*C(I,J) - END IF - 360 CONTINUE - 370 CONTINUE - END IF - END IF -* - RETURN -* -* End of ZGEMM -* - END diff --git a/lib/linalg/fortran/zgemv.f b/lib/linalg/fortran/zgemv.f deleted file mode 100644 index 2664454b94..0000000000 --- a/lib/linalg/fortran/zgemv.f +++ /dev/null @@ -1,347 +0,0 @@ -*> \brief \b ZGEMV -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE ZGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) -* -* .. Scalar Arguments .. -* COMPLEX*16 ALPHA,BETA -* INTEGER INCX,INCY,LDA,M,N -* CHARACTER TRANS -* .. -* .. Array Arguments .. -* COMPLEX*16 A(LDA,*),X(*),Y(*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZGEMV performs one of the matrix-vector operations -*> -*> y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, or -*> -*> y := alpha*A**H*x + beta*y, -*> -*> where alpha and beta are scalars, x and y are vectors and A is an -*> m by n matrix. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] TRANS -*> \verbatim -*> TRANS is CHARACTER*1 -*> On entry, TRANS specifies the operation to be performed as -*> follows: -*> -*> TRANS = 'N' or 'n' y := alpha*A*x + beta*y. -*> -*> TRANS = 'T' or 't' y := alpha*A**T*x + beta*y. -*> -*> TRANS = 'C' or 'c' y := alpha*A**H*x + beta*y. -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> On entry, M specifies the number of rows of the matrix A. -*> M must be at least zero. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> On entry, N specifies the number of columns of the matrix A. -*> N must be at least zero. -*> \endverbatim -*> -*> \param[in] ALPHA -*> \verbatim -*> ALPHA is COMPLEX*16 -*> On entry, ALPHA specifies the scalar alpha. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is COMPLEX*16 array, dimension ( LDA, N ) -*> Before entry, the leading m by n part of the array A must -*> contain the matrix of coefficients. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> On entry, LDA specifies the first dimension of A as declared -*> in the calling (sub) program. LDA must be at least -*> max( 1, m ). -*> \endverbatim -*> -*> \param[in] X -*> \verbatim -*> X is COMPLEX*16 array, dimension at least -*> ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' -*> and at least -*> ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. -*> Before entry, the incremented array X must contain the -*> vector x. -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> On entry, INCX specifies the increment for the elements of -*> X. INCX must not be zero. -*> \endverbatim -*> -*> \param[in] BETA -*> \verbatim -*> BETA is COMPLEX*16 -*> On entry, BETA specifies the scalar beta. When BETA is -*> supplied as zero then Y need not be set on input. -*> \endverbatim -*> -*> \param[in,out] Y -*> \verbatim -*> Y is COMPLEX*16 array, dimension at least -*> ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' -*> and at least -*> ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. -*> Before entry with BETA non-zero, the incremented array Y -*> must contain the vector y. On exit, Y is overwritten by the -*> updated vector y. -*> \endverbatim -*> -*> \param[in] INCY -*> \verbatim -*> INCY is INTEGER -*> On entry, INCY specifies the increment for the elements of -*> Y. INCY must not be zero. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16_blas_level2 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> Level 2 Blas routine. -*> The vector and matrix arguments are not referenced when N = 0, or M = 0 -*> -*> -- Written on 22-October-1986. -*> Jack Dongarra, Argonne National Lab. -*> Jeremy Du Croz, Nag Central Office. -*> Sven Hammarling, Nag Central Office. -*> Richard Hanson, Sandia National Labs. -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE ZGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) -* -* -- Reference BLAS level2 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - COMPLEX*16 ALPHA,BETA - INTEGER INCX,INCY,LDA,M,N - CHARACTER TRANS -* .. -* .. Array Arguments .. - COMPLEX*16 A(LDA,*),X(*),Y(*) -* .. -* -* ===================================================================== -* -* .. Parameters .. - COMPLEX*16 ONE - PARAMETER (ONE= (1.0D+0,0.0D+0)) - COMPLEX*16 ZERO - PARAMETER (ZERO= (0.0D+0,0.0D+0)) -* .. -* .. Local Scalars .. - COMPLEX*16 TEMP - INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY,LENX,LENY - LOGICAL NOCONJ -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC DCONJG,MAX -* .. -* -* Test the input parameters. -* - INFO = 0 - IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. - + .NOT.LSAME(TRANS,'C')) THEN - INFO = 1 - ELSE IF (M.LT.0) THEN - INFO = 2 - ELSE IF (N.LT.0) THEN - INFO = 3 - ELSE IF (LDA.LT.MAX(1,M)) THEN - INFO = 6 - ELSE IF (INCX.EQ.0) THEN - INFO = 8 - ELSE IF (INCY.EQ.0) THEN - INFO = 11 - END IF - IF (INFO.NE.0) THEN - CALL XERBLA('ZGEMV ',INFO) - RETURN - END IF -* -* Quick return if possible. -* - IF ((M.EQ.0) .OR. (N.EQ.0) .OR. - + ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN -* - NOCONJ = LSAME(TRANS,'T') -* -* Set LENX and LENY, the lengths of the vectors x and y, and set -* up the start points in X and Y. -* - IF (LSAME(TRANS,'N')) THEN - LENX = N - LENY = M - ELSE - LENX = M - LENY = N - END IF - IF (INCX.GT.0) THEN - KX = 1 - ELSE - KX = 1 - (LENX-1)*INCX - END IF - IF (INCY.GT.0) THEN - KY = 1 - ELSE - KY = 1 - (LENY-1)*INCY - END IF -* -* Start the operations. In this version the elements of A are -* accessed sequentially with one pass through A. -* -* First form y := beta*y. -* - IF (BETA.NE.ONE) THEN - IF (INCY.EQ.1) THEN - IF (BETA.EQ.ZERO) THEN - DO 10 I = 1,LENY - Y(I) = ZERO - 10 CONTINUE - ELSE - DO 20 I = 1,LENY - Y(I) = BETA*Y(I) - 20 CONTINUE - END IF - ELSE - IY = KY - IF (BETA.EQ.ZERO) THEN - DO 30 I = 1,LENY - Y(IY) = ZERO - IY = IY + INCY - 30 CONTINUE - ELSE - DO 40 I = 1,LENY - Y(IY) = BETA*Y(IY) - IY = IY + INCY - 40 CONTINUE - END IF - END IF - END IF - IF (ALPHA.EQ.ZERO) RETURN - IF (LSAME(TRANS,'N')) THEN -* -* Form y := alpha*A*x + y. -* - JX = KX - IF (INCY.EQ.1) THEN - DO 60 J = 1,N - TEMP = ALPHA*X(JX) - DO 50 I = 1,M - Y(I) = Y(I) + TEMP*A(I,J) - 50 CONTINUE - JX = JX + INCX - 60 CONTINUE - ELSE - DO 80 J = 1,N - TEMP = ALPHA*X(JX) - IY = KY - DO 70 I = 1,M - Y(IY) = Y(IY) + TEMP*A(I,J) - IY = IY + INCY - 70 CONTINUE - JX = JX + INCX - 80 CONTINUE - END IF - ELSE -* -* Form y := alpha*A**T*x + y or y := alpha*A**H*x + y. -* - JY = KY - IF (INCX.EQ.1) THEN - DO 110 J = 1,N - TEMP = ZERO - IF (NOCONJ) THEN - DO 90 I = 1,M - TEMP = TEMP + A(I,J)*X(I) - 90 CONTINUE - ELSE - DO 100 I = 1,M - TEMP = TEMP + DCONJG(A(I,J))*X(I) - 100 CONTINUE - END IF - Y(JY) = Y(JY) + ALPHA*TEMP - JY = JY + INCY - 110 CONTINUE - ELSE - DO 140 J = 1,N - TEMP = ZERO - IX = KX - IF (NOCONJ) THEN - DO 120 I = 1,M - TEMP = TEMP + A(I,J)*X(IX) - IX = IX + INCX - 120 CONTINUE - ELSE - DO 130 I = 1,M - TEMP = TEMP + DCONJG(A(I,J))*X(IX) - IX = IX + INCX - 130 CONTINUE - END IF - Y(JY) = Y(JY) + ALPHA*TEMP - JY = JY + INCY - 140 CONTINUE - END IF - END IF -* - RETURN -* -* End of ZGEMV -* - END diff --git a/lib/linalg/fortran/zgerc.f b/lib/linalg/fortran/zgerc.f deleted file mode 100644 index 2eb4349367..0000000000 --- a/lib/linalg/fortran/zgerc.f +++ /dev/null @@ -1,224 +0,0 @@ -*> \brief \b ZGERC -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE ZGERC(M,N,ALPHA,X,INCX,Y,INCY,A,LDA) -* -* .. Scalar Arguments .. -* COMPLEX*16 ALPHA -* INTEGER INCX,INCY,LDA,M,N -* .. -* .. Array Arguments .. -* COMPLEX*16 A(LDA,*),X(*),Y(*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZGERC performs the rank 1 operation -*> -*> A := alpha*x*y**H + A, -*> -*> where alpha is a scalar, x is an m element vector, y is an n element -*> vector and A is an m by n matrix. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> On entry, M specifies the number of rows of the matrix A. -*> M must be at least zero. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> On entry, N specifies the number of columns of the matrix A. -*> N must be at least zero. -*> \endverbatim -*> -*> \param[in] ALPHA -*> \verbatim -*> ALPHA is COMPLEX*16 -*> On entry, ALPHA specifies the scalar alpha. -*> \endverbatim -*> -*> \param[in] X -*> \verbatim -*> X is COMPLEX*16 array, dimension at least -*> ( 1 + ( m - 1 )*abs( INCX ) ). -*> Before entry, the incremented array X must contain the m -*> element vector x. -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> On entry, INCX specifies the increment for the elements of -*> X. INCX must not be zero. -*> \endverbatim -*> -*> \param[in] Y -*> \verbatim -*> Y is COMPLEX*16 array, dimension at least -*> ( 1 + ( n - 1 )*abs( INCY ) ). -*> Before entry, the incremented array Y must contain the n -*> element vector y. -*> \endverbatim -*> -*> \param[in] INCY -*> \verbatim -*> INCY is INTEGER -*> On entry, INCY specifies the increment for the elements of -*> Y. INCY must not be zero. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is COMPLEX*16 array, dimension ( LDA, N ) -*> Before entry, the leading m by n part of the array A must -*> contain the matrix of coefficients. On exit, A is -*> overwritten by the updated matrix. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> On entry, LDA specifies the first dimension of A as declared -*> in the calling (sub) program. LDA must be at least -*> max( 1, m ). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16_blas_level2 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> Level 2 Blas routine. -*> -*> -- Written on 22-October-1986. -*> Jack Dongarra, Argonne National Lab. -*> Jeremy Du Croz, Nag Central Office. -*> Sven Hammarling, Nag Central Office. -*> Richard Hanson, Sandia National Labs. -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE ZGERC(M,N,ALPHA,X,INCX,Y,INCY,A,LDA) -* -* -- Reference BLAS level2 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - COMPLEX*16 ALPHA - INTEGER INCX,INCY,LDA,M,N -* .. -* .. Array Arguments .. - COMPLEX*16 A(LDA,*),X(*),Y(*) -* .. -* -* ===================================================================== -* -* .. Parameters .. - COMPLEX*16 ZERO - PARAMETER (ZERO= (0.0D+0,0.0D+0)) -* .. -* .. Local Scalars .. - COMPLEX*16 TEMP - INTEGER I,INFO,IX,J,JY,KX -* .. -* .. External Subroutines .. - EXTERNAL XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC DCONJG,MAX -* .. -* -* Test the input parameters. -* - INFO = 0 - IF (M.LT.0) THEN - INFO = 1 - ELSE IF (N.LT.0) THEN - INFO = 2 - ELSE IF (INCX.EQ.0) THEN - INFO = 5 - ELSE IF (INCY.EQ.0) THEN - INFO = 7 - ELSE IF (LDA.LT.MAX(1,M)) THEN - INFO = 9 - END IF - IF (INFO.NE.0) THEN - CALL XERBLA('ZGERC ',INFO) - RETURN - END IF -* -* Quick return if possible. -* - IF ((M.EQ.0) .OR. (N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN -* -* Start the operations. In this version the elements of A are -* accessed sequentially with one pass through A. -* - IF (INCY.GT.0) THEN - JY = 1 - ELSE - JY = 1 - (N-1)*INCY - END IF - IF (INCX.EQ.1) THEN - DO 20 J = 1,N - IF (Y(JY).NE.ZERO) THEN - TEMP = ALPHA*DCONJG(Y(JY)) - DO 10 I = 1,M - A(I,J) = A(I,J) + X(I)*TEMP - 10 CONTINUE - END IF - JY = JY + INCY - 20 CONTINUE - ELSE - IF (INCX.GT.0) THEN - KX = 1 - ELSE - KX = 1 - (M-1)*INCX - END IF - DO 40 J = 1,N - IF (Y(JY).NE.ZERO) THEN - TEMP = ALPHA*DCONJG(Y(JY)) - IX = KX - DO 30 I = 1,M - A(I,J) = A(I,J) + X(IX)*TEMP - IX = IX + INCX - 30 CONTINUE - END IF - JY = JY + INCY - 40 CONTINUE - END IF -* - RETURN -* -* End of ZGERC -* - END diff --git a/lib/linalg/fortran/zheev.f b/lib/linalg/fortran/zheev.f deleted file mode 100644 index 59af34a742..0000000000 --- a/lib/linalg/fortran/zheev.f +++ /dev/null @@ -1,295 +0,0 @@ -*> \brief ZHEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZHEEV + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZHEEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, -* INFO ) -* -* .. Scalar Arguments .. -* CHARACTER JOBZ, UPLO -* INTEGER INFO, LDA, LWORK, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION RWORK( * ), W( * ) -* COMPLEX*16 A( LDA, * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZHEEV computes all eigenvalues and, optionally, eigenvectors of a -*> complex Hermitian matrix A. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] JOBZ -*> \verbatim -*> JOBZ is CHARACTER*1 -*> = 'N': Compute eigenvalues only; -*> = 'V': Compute eigenvalues and eigenvectors. -*> \endverbatim -*> -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> = 'U': Upper triangle of A is stored; -*> = 'L': Lower triangle of A is stored. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is COMPLEX*16 array, dimension (LDA, N) -*> On entry, the Hermitian matrix A. If UPLO = 'U', the -*> leading N-by-N upper triangular part of A contains the -*> upper triangular part of the matrix A. If UPLO = 'L', -*> the leading N-by-N lower triangular part of A contains -*> the lower triangular part of the matrix A. -*> On exit, if JOBZ = 'V', then if INFO = 0, A contains the -*> orthonormal eigenvectors of the matrix A. -*> If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') -*> or the upper triangle (if UPLO='U') of A, including the -*> diagonal, is destroyed. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,N). -*> \endverbatim -*> -*> \param[out] W -*> \verbatim -*> W is DOUBLE PRECISION array, dimension (N) -*> If INFO = 0, the eigenvalues in ascending order. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) -*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -*> \endverbatim -*> -*> \param[in] LWORK -*> \verbatim -*> LWORK is INTEGER -*> The length of the array WORK. LWORK >= max(1,2*N-1). -*> For optimal efficiency, LWORK >= (NB+1)*N, -*> where NB is the blocksize for ZHETRD returned by ILAENV. -*> -*> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal size of the WORK array, returns -*> this value as the first entry of the WORK array, and no error -*> message related to LWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] RWORK -*> \verbatim -*> RWORK is DOUBLE PRECISION array, dimension (max(1, 3*N-2)) -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the algorithm failed to converge; i -*> off-diagonal elements of an intermediate tridiagonal -*> form did not converge to zero. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16HEeigen -* -* ===================================================================== - SUBROUTINE ZHEEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, - $ INFO ) -* -* -- LAPACK driver routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER JOBZ, UPLO - INTEGER INFO, LDA, LWORK, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION RWORK( * ), W( * ) - COMPLEX*16 A( LDA, * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) - COMPLEX*16 CONE - PARAMETER ( CONE = ( 1.0D0, 0.0D0 ) ) -* .. -* .. Local Scalars .. - LOGICAL LOWER, LQUERY, WANTZ - INTEGER IINFO, IMAX, INDE, INDTAU, INDWRK, ISCALE, - $ LLWORK, LWKOPT, NB - DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, - $ SMLNUM -* .. -* .. External Functions .. - LOGICAL LSAME - INTEGER ILAENV - DOUBLE PRECISION DLAMCH, ZLANHE - EXTERNAL LSAME, ILAENV, DLAMCH, ZLANHE -* .. -* .. External Subroutines .. - EXTERNAL DSCAL, DSTERF, XERBLA, ZHETRD, ZLASCL, ZSTEQR, - $ ZUNGTR -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, SQRT -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - WANTZ = LSAME( JOBZ, 'V' ) - LOWER = LSAME( UPLO, 'L' ) - LQUERY = ( LWORK.EQ.-1 ) -* - INFO = 0 - IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN - INFO = -1 - ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN - INFO = -2 - ELSE IF( N.LT.0 ) THEN - INFO = -3 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -5 - END IF -* - IF( INFO.EQ.0 ) THEN - NB = ILAENV( 1, 'ZHETRD', UPLO, N, -1, -1, -1 ) - LWKOPT = MAX( 1, ( NB+1 )*N ) - WORK( 1 ) = LWKOPT -* - IF( LWORK.LT.MAX( 1, 2*N-1 ) .AND. .NOT.LQUERY ) - $ INFO = -8 - END IF -* - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'ZHEEV ', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - RETURN - END IF -* -* Quick return if possible -* - IF( N.EQ.0 ) THEN - RETURN - END IF -* - IF( N.EQ.1 ) THEN - W( 1 ) = DBLE( A( 1, 1 ) ) - WORK( 1 ) = 1 - IF( WANTZ ) - $ A( 1, 1 ) = CONE - RETURN - END IF -* -* Get machine constants. -* - SAFMIN = DLAMCH( 'Safe minimum' ) - EPS = DLAMCH( 'Precision' ) - SMLNUM = SAFMIN / EPS - BIGNUM = ONE / SMLNUM - RMIN = SQRT( SMLNUM ) - RMAX = SQRT( BIGNUM ) -* -* Scale matrix to allowable range, if necessary. -* - ANRM = ZLANHE( 'M', UPLO, N, A, LDA, RWORK ) - ISCALE = 0 - IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN - ISCALE = 1 - SIGMA = RMIN / ANRM - ELSE IF( ANRM.GT.RMAX ) THEN - ISCALE = 1 - SIGMA = RMAX / ANRM - END IF - IF( ISCALE.EQ.1 ) - $ CALL ZLASCL( UPLO, 0, 0, ONE, SIGMA, N, N, A, LDA, INFO ) -* -* Call ZHETRD to reduce Hermitian matrix to tridiagonal form. -* - INDE = 1 - INDTAU = 1 - INDWRK = INDTAU + N - LLWORK = LWORK - INDWRK + 1 - CALL ZHETRD( UPLO, N, A, LDA, W, RWORK( INDE ), WORK( INDTAU ), - $ WORK( INDWRK ), LLWORK, IINFO ) -* -* For eigenvalues only, call DSTERF. For eigenvectors, first call -* ZUNGTR to generate the unitary matrix, then call ZSTEQR. -* - IF( .NOT.WANTZ ) THEN - CALL DSTERF( N, W, RWORK( INDE ), INFO ) - ELSE - CALL ZUNGTR( UPLO, N, A, LDA, WORK( INDTAU ), WORK( INDWRK ), - $ LLWORK, IINFO ) - INDWRK = INDE + N - CALL ZSTEQR( JOBZ, N, W, RWORK( INDE ), A, LDA, - $ RWORK( INDWRK ), INFO ) - END IF -* -* If matrix was scaled, then rescale eigenvalues appropriately. -* - IF( ISCALE.EQ.1 ) THEN - IF( INFO.EQ.0 ) THEN - IMAX = N - ELSE - IMAX = INFO - 1 - END IF - CALL DSCAL( IMAX, ONE / SIGMA, W, 1 ) - END IF -* -* Set WORK(1) to optimal complex workspace size. -* - WORK( 1 ) = LWKOPT -* - RETURN -* -* End of ZHEEV -* - END diff --git a/lib/linalg/fortran/zheevd.f b/lib/linalg/fortran/zheevd.f deleted file mode 100644 index 7f58c7f726..0000000000 --- a/lib/linalg/fortran/zheevd.f +++ /dev/null @@ -1,395 +0,0 @@ -*> \brief ZHEEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZHEEVD + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, -* LRWORK, IWORK, LIWORK, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER JOBZ, UPLO -* INTEGER INFO, LDA, LIWORK, LRWORK, LWORK, N -* .. -* .. Array Arguments .. -* INTEGER IWORK( * ) -* DOUBLE PRECISION RWORK( * ), W( * ) -* COMPLEX*16 A( LDA, * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZHEEVD computes all eigenvalues and, optionally, eigenvectors of a -*> complex Hermitian matrix A. If eigenvectors are desired, it uses a -*> divide and conquer algorithm. -*> -*> The divide and conquer algorithm makes very mild assumptions about -*> floating point arithmetic. It will work on machines with a guard -*> digit in add/subtract, or on those binary machines without guard -*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or -*> Cray-2. It could conceivably fail on hexadecimal or decimal machines -*> without guard digits, but we know of none. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] JOBZ -*> \verbatim -*> JOBZ is CHARACTER*1 -*> = 'N': Compute eigenvalues only; -*> = 'V': Compute eigenvalues and eigenvectors. -*> \endverbatim -*> -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> = 'U': Upper triangle of A is stored; -*> = 'L': Lower triangle of A is stored. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is COMPLEX*16 array, dimension (LDA, N) -*> On entry, the Hermitian matrix A. If UPLO = 'U', the -*> leading N-by-N upper triangular part of A contains the -*> upper triangular part of the matrix A. If UPLO = 'L', -*> the leading N-by-N lower triangular part of A contains -*> the lower triangular part of the matrix A. -*> On exit, if JOBZ = 'V', then if INFO = 0, A contains the -*> orthonormal eigenvectors of the matrix A. -*> If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') -*> or the upper triangle (if UPLO='U') of A, including the -*> diagonal, is destroyed. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,N). -*> \endverbatim -*> -*> \param[out] W -*> \verbatim -*> W is DOUBLE PRECISION array, dimension (N) -*> If INFO = 0, the eigenvalues in ascending order. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) -*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -*> \endverbatim -*> -*> \param[in] LWORK -*> \verbatim -*> LWORK is INTEGER -*> The length of the array WORK. -*> If N <= 1, LWORK must be at least 1. -*> If JOBZ = 'N' and N > 1, LWORK must be at least N + 1. -*> If JOBZ = 'V' and N > 1, LWORK must be at least 2*N + N**2. -*> -*> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal sizes of the WORK, RWORK and -*> IWORK arrays, returns these values as the first entries of -*> the WORK, RWORK and IWORK arrays, and no error message -*> related to LWORK or LRWORK or LIWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] RWORK -*> \verbatim -*> RWORK is DOUBLE PRECISION array, -*> dimension (LRWORK) -*> On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. -*> \endverbatim -*> -*> \param[in] LRWORK -*> \verbatim -*> LRWORK is INTEGER -*> The dimension of the array RWORK. -*> If N <= 1, LRWORK must be at least 1. -*> If JOBZ = 'N' and N > 1, LRWORK must be at least N. -*> If JOBZ = 'V' and N > 1, LRWORK must be at least -*> 1 + 5*N + 2*N**2. -*> -*> If LRWORK = -1, then a workspace query is assumed; the -*> routine only calculates the optimal sizes of the WORK, RWORK -*> and IWORK arrays, returns these values as the first entries -*> of the WORK, RWORK and IWORK arrays, and no error message -*> related to LWORK or LRWORK or LIWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] IWORK -*> \verbatim -*> IWORK is INTEGER array, dimension (MAX(1,LIWORK)) -*> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. -*> \endverbatim -*> -*> \param[in] LIWORK -*> \verbatim -*> LIWORK is INTEGER -*> The dimension of the array IWORK. -*> If N <= 1, LIWORK must be at least 1. -*> If JOBZ = 'N' and N > 1, LIWORK must be at least 1. -*> If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N. -*> -*> If LIWORK = -1, then a workspace query is assumed; the -*> routine only calculates the optimal sizes of the WORK, RWORK -*> and IWORK arrays, returns these values as the first entries -*> of the WORK, RWORK and IWORK arrays, and no error message -*> related to LWORK or LRWORK or LIWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i and JOBZ = 'N', then the algorithm failed -*> to converge; i off-diagonal elements of an intermediate -*> tridiagonal form did not converge to zero; -*> if INFO = i and JOBZ = 'V', then the algorithm failed -*> to compute an eigenvalue while working on the submatrix -*> lying in rows and columns INFO/(N+1) through -*> mod(INFO,N+1). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16HEeigen -* -*> \par Further Details: -* ===================== -*> -*> Modified description of INFO. Sven, 16 Feb 05. -* -*> \par Contributors: -* ================== -*> -*> Jeff Rutter, Computer Science Division, University of California -*> at Berkeley, USA -*> -* ===================================================================== - SUBROUTINE ZHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, - $ LRWORK, IWORK, LIWORK, INFO ) -* -* -- LAPACK driver routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER JOBZ, UPLO - INTEGER INFO, LDA, LIWORK, LRWORK, LWORK, N -* .. -* .. Array Arguments .. - INTEGER IWORK( * ) - DOUBLE PRECISION RWORK( * ), W( * ) - COMPLEX*16 A( LDA, * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) - COMPLEX*16 CONE - PARAMETER ( CONE = ( 1.0D0, 0.0D0 ) ) -* .. -* .. Local Scalars .. - LOGICAL LOWER, LQUERY, WANTZ - INTEGER IINFO, IMAX, INDE, INDRWK, INDTAU, INDWK2, - $ INDWRK, ISCALE, LIOPT, LIWMIN, LLRWK, LLWORK, - $ LLWRK2, LOPT, LROPT, LRWMIN, LWMIN - DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, - $ SMLNUM -* .. -* .. External Functions .. - LOGICAL LSAME - INTEGER ILAENV - DOUBLE PRECISION DLAMCH, ZLANHE - EXTERNAL LSAME, ILAENV, DLAMCH, ZLANHE -* .. -* .. External Subroutines .. - EXTERNAL DSCAL, DSTERF, XERBLA, ZHETRD, ZLACPY, ZLASCL, - $ ZSTEDC, ZUNMTR -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, SQRT -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - WANTZ = LSAME( JOBZ, 'V' ) - LOWER = LSAME( UPLO, 'L' ) - LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 .OR. LIWORK.EQ.-1 ) -* - INFO = 0 - IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN - INFO = -1 - ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN - INFO = -2 - ELSE IF( N.LT.0 ) THEN - INFO = -3 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -5 - END IF -* - IF( INFO.EQ.0 ) THEN - IF( N.LE.1 ) THEN - LWMIN = 1 - LRWMIN = 1 - LIWMIN = 1 - LOPT = LWMIN - LROPT = LRWMIN - LIOPT = LIWMIN - ELSE - IF( WANTZ ) THEN - LWMIN = 2*N + N*N - LRWMIN = 1 + 5*N + 2*N**2 - LIWMIN = 3 + 5*N - ELSE - LWMIN = N + 1 - LRWMIN = N - LIWMIN = 1 - END IF - LOPT = MAX( LWMIN, N + - $ N*ILAENV( 1, 'ZHETRD', UPLO, N, -1, -1, -1 ) ) - LROPT = LRWMIN - LIOPT = LIWMIN - END IF - WORK( 1 ) = LOPT - RWORK( 1 ) = LROPT - IWORK( 1 ) = LIOPT -* - IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN - INFO = -8 - ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN - INFO = -10 - ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN - INFO = -12 - END IF - END IF -* - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'ZHEEVD', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - RETURN - END IF -* -* Quick return if possible -* - IF( N.EQ.0 ) - $ RETURN -* - IF( N.EQ.1 ) THEN - W( 1 ) = DBLE( A( 1, 1 ) ) - IF( WANTZ ) - $ A( 1, 1 ) = CONE - RETURN - END IF -* -* Get machine constants. -* - SAFMIN = DLAMCH( 'Safe minimum' ) - EPS = DLAMCH( 'Precision' ) - SMLNUM = SAFMIN / EPS - BIGNUM = ONE / SMLNUM - RMIN = SQRT( SMLNUM ) - RMAX = SQRT( BIGNUM ) -* -* Scale matrix to allowable range, if necessary. -* - ANRM = ZLANHE( 'M', UPLO, N, A, LDA, RWORK ) - ISCALE = 0 - IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN - ISCALE = 1 - SIGMA = RMIN / ANRM - ELSE IF( ANRM.GT.RMAX ) THEN - ISCALE = 1 - SIGMA = RMAX / ANRM - END IF - IF( ISCALE.EQ.1 ) - $ CALL ZLASCL( UPLO, 0, 0, ONE, SIGMA, N, N, A, LDA, INFO ) -* -* Call ZHETRD to reduce Hermitian matrix to tridiagonal form. -* - INDE = 1 - INDTAU = 1 - INDWRK = INDTAU + N - INDRWK = INDE + N - INDWK2 = INDWRK + N*N - LLWORK = LWORK - INDWRK + 1 - LLWRK2 = LWORK - INDWK2 + 1 - LLRWK = LRWORK - INDRWK + 1 - CALL ZHETRD( UPLO, N, A, LDA, W, RWORK( INDE ), WORK( INDTAU ), - $ WORK( INDWRK ), LLWORK, IINFO ) -* -* For eigenvalues only, call DSTERF. For eigenvectors, first call -* ZSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the -* tridiagonal matrix, then call ZUNMTR to multiply it to the -* Householder transformations represented as Householder vectors in -* A. -* - IF( .NOT.WANTZ ) THEN - CALL DSTERF( N, W, RWORK( INDE ), INFO ) - ELSE - CALL ZSTEDC( 'I', N, W, RWORK( INDE ), WORK( INDWRK ), N, - $ WORK( INDWK2 ), LLWRK2, RWORK( INDRWK ), LLRWK, - $ IWORK, LIWORK, INFO ) - CALL ZUNMTR( 'L', UPLO, 'N', N, N, A, LDA, WORK( INDTAU ), - $ WORK( INDWRK ), N, WORK( INDWK2 ), LLWRK2, IINFO ) - CALL ZLACPY( 'A', N, N, WORK( INDWRK ), N, A, LDA ) - END IF -* -* If matrix was scaled, then rescale eigenvalues appropriately. -* - IF( ISCALE.EQ.1 ) THEN - IF( INFO.EQ.0 ) THEN - IMAX = N - ELSE - IMAX = INFO - 1 - END IF - CALL DSCAL( IMAX, ONE / SIGMA, W, 1 ) - END IF -* - WORK( 1 ) = LOPT - RWORK( 1 ) = LROPT - IWORK( 1 ) = LIOPT -* - RETURN -* -* End of ZHEEVD -* - END diff --git a/lib/linalg/fortran/zhemv.f b/lib/linalg/fortran/zhemv.f deleted file mode 100644 index dad68bf25b..0000000000 --- a/lib/linalg/fortran/zhemv.f +++ /dev/null @@ -1,334 +0,0 @@ -*> \brief \b ZHEMV -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE ZHEMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) -* -* .. Scalar Arguments .. -* COMPLEX*16 ALPHA,BETA -* INTEGER INCX,INCY,LDA,N -* CHARACTER UPLO -* .. -* .. Array Arguments .. -* COMPLEX*16 A(LDA,*),X(*),Y(*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZHEMV performs the matrix-vector operation -*> -*> y := alpha*A*x + beta*y, -*> -*> where alpha and beta are scalars, x and y are n element vectors and -*> A is an n by n hermitian matrix. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> On entry, UPLO specifies whether the upper or lower -*> triangular part of the array A is to be referenced as -*> follows: -*> -*> UPLO = 'U' or 'u' Only the upper triangular part of A -*> is to be referenced. -*> -*> UPLO = 'L' or 'l' Only the lower triangular part of A -*> is to be referenced. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> On entry, N specifies the order of the matrix A. -*> N must be at least zero. -*> \endverbatim -*> -*> \param[in] ALPHA -*> \verbatim -*> ALPHA is COMPLEX*16 -*> On entry, ALPHA specifies the scalar alpha. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is COMPLEX*16 array, dimension ( LDA, N ) -*> Before entry with UPLO = 'U' or 'u', the leading n by n -*> upper triangular part of the array A must contain the upper -*> triangular part of the hermitian matrix and the strictly -*> lower triangular part of A is not referenced. -*> Before entry with UPLO = 'L' or 'l', the leading n by n -*> lower triangular part of the array A must contain the lower -*> triangular part of the hermitian matrix and the strictly -*> upper triangular part of A is not referenced. -*> Note that the imaginary parts of the diagonal elements need -*> not be set and are assumed to be zero. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> On entry, LDA specifies the first dimension of A as declared -*> in the calling (sub) program. LDA must be at least -*> max( 1, n ). -*> \endverbatim -*> -*> \param[in] X -*> \verbatim -*> X is COMPLEX*16 array, dimension at least -*> ( 1 + ( n - 1 )*abs( INCX ) ). -*> Before entry, the incremented array X must contain the n -*> element vector x. -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> On entry, INCX specifies the increment for the elements of -*> X. INCX must not be zero. -*> \endverbatim -*> -*> \param[in] BETA -*> \verbatim -*> BETA is COMPLEX*16 -*> On entry, BETA specifies the scalar beta. When BETA is -*> supplied as zero then Y need not be set on input. -*> \endverbatim -*> -*> \param[in,out] Y -*> \verbatim -*> Y is COMPLEX*16 array, dimension at least -*> ( 1 + ( n - 1 )*abs( INCY ) ). -*> Before entry, the incremented array Y must contain the n -*> element vector y. On exit, Y is overwritten by the updated -*> vector y. -*> \endverbatim -*> -*> \param[in] INCY -*> \verbatim -*> INCY is INTEGER -*> On entry, INCY specifies the increment for the elements of -*> Y. INCY must not be zero. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16_blas_level2 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> Level 2 Blas routine. -*> The vector and matrix arguments are not referenced when N = 0, or M = 0 -*> -*> -- Written on 22-October-1986. -*> Jack Dongarra, Argonne National Lab. -*> Jeremy Du Croz, Nag Central Office. -*> Sven Hammarling, Nag Central Office. -*> Richard Hanson, Sandia National Labs. -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE ZHEMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) -* -* -- Reference BLAS level2 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - COMPLEX*16 ALPHA,BETA - INTEGER INCX,INCY,LDA,N - CHARACTER UPLO -* .. -* .. Array Arguments .. - COMPLEX*16 A(LDA,*),X(*),Y(*) -* .. -* -* ===================================================================== -* -* .. Parameters .. - COMPLEX*16 ONE - PARAMETER (ONE= (1.0D+0,0.0D+0)) - COMPLEX*16 ZERO - PARAMETER (ZERO= (0.0D+0,0.0D+0)) -* .. -* .. Local Scalars .. - COMPLEX*16 TEMP1,TEMP2 - INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC DBLE,DCONJG,MAX -* .. -* -* Test the input parameters. -* - INFO = 0 - IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN - INFO = 1 - ELSE IF (N.LT.0) THEN - INFO = 2 - ELSE IF (LDA.LT.MAX(1,N)) THEN - INFO = 5 - ELSE IF (INCX.EQ.0) THEN - INFO = 7 - ELSE IF (INCY.EQ.0) THEN - INFO = 10 - END IF - IF (INFO.NE.0) THEN - CALL XERBLA('ZHEMV ',INFO) - RETURN - END IF -* -* Quick return if possible. -* - IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN -* -* Set up the start points in X and Y. -* - IF (INCX.GT.0) THEN - KX = 1 - ELSE - KX = 1 - (N-1)*INCX - END IF - IF (INCY.GT.0) THEN - KY = 1 - ELSE - KY = 1 - (N-1)*INCY - END IF -* -* Start the operations. In this version the elements of A are -* accessed sequentially with one pass through the triangular part -* of A. -* -* First form y := beta*y. -* - IF (BETA.NE.ONE) THEN - IF (INCY.EQ.1) THEN - IF (BETA.EQ.ZERO) THEN - DO 10 I = 1,N - Y(I) = ZERO - 10 CONTINUE - ELSE - DO 20 I = 1,N - Y(I) = BETA*Y(I) - 20 CONTINUE - END IF - ELSE - IY = KY - IF (BETA.EQ.ZERO) THEN - DO 30 I = 1,N - Y(IY) = ZERO - IY = IY + INCY - 30 CONTINUE - ELSE - DO 40 I = 1,N - Y(IY) = BETA*Y(IY) - IY = IY + INCY - 40 CONTINUE - END IF - END IF - END IF - IF (ALPHA.EQ.ZERO) RETURN - IF (LSAME(UPLO,'U')) THEN -* -* Form y when A is stored in upper triangle. -* - IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN - DO 60 J = 1,N - TEMP1 = ALPHA*X(J) - TEMP2 = ZERO - DO 50 I = 1,J - 1 - Y(I) = Y(I) + TEMP1*A(I,J) - TEMP2 = TEMP2 + DCONJG(A(I,J))*X(I) - 50 CONTINUE - Y(J) = Y(J) + TEMP1*DBLE(A(J,J)) + ALPHA*TEMP2 - 60 CONTINUE - ELSE - JX = KX - JY = KY - DO 80 J = 1,N - TEMP1 = ALPHA*X(JX) - TEMP2 = ZERO - IX = KX - IY = KY - DO 70 I = 1,J - 1 - Y(IY) = Y(IY) + TEMP1*A(I,J) - TEMP2 = TEMP2 + DCONJG(A(I,J))*X(IX) - IX = IX + INCX - IY = IY + INCY - 70 CONTINUE - Y(JY) = Y(JY) + TEMP1*DBLE(A(J,J)) + ALPHA*TEMP2 - JX = JX + INCX - JY = JY + INCY - 80 CONTINUE - END IF - ELSE -* -* Form y when A is stored in lower triangle. -* - IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN - DO 100 J = 1,N - TEMP1 = ALPHA*X(J) - TEMP2 = ZERO - Y(J) = Y(J) + TEMP1*DBLE(A(J,J)) - DO 90 I = J + 1,N - Y(I) = Y(I) + TEMP1*A(I,J) - TEMP2 = TEMP2 + DCONJG(A(I,J))*X(I) - 90 CONTINUE - Y(J) = Y(J) + ALPHA*TEMP2 - 100 CONTINUE - ELSE - JX = KX - JY = KY - DO 120 J = 1,N - TEMP1 = ALPHA*X(JX) - TEMP2 = ZERO - Y(JY) = Y(JY) + TEMP1*DBLE(A(J,J)) - IX = JX - IY = JY - DO 110 I = J + 1,N - IX = IX + INCX - IY = IY + INCY - Y(IY) = Y(IY) + TEMP1*A(I,J) - TEMP2 = TEMP2 + DCONJG(A(I,J))*X(IX) - 110 CONTINUE - Y(JY) = Y(JY) + ALPHA*TEMP2 - JX = JX + INCX - JY = JY + INCY - 120 CONTINUE - END IF - END IF -* - RETURN -* -* End of ZHEMV -* - END diff --git a/lib/linalg/fortran/zher2.f b/lib/linalg/fortran/zher2.f deleted file mode 100644 index d1f2b57ec4..0000000000 --- a/lib/linalg/fortran/zher2.f +++ /dev/null @@ -1,314 +0,0 @@ -*> \brief \b ZHER2 -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE ZHER2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA) -* -* .. Scalar Arguments .. -* COMPLEX*16 ALPHA -* INTEGER INCX,INCY,LDA,N -* CHARACTER UPLO -* .. -* .. Array Arguments .. -* COMPLEX*16 A(LDA,*),X(*),Y(*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZHER2 performs the hermitian rank 2 operation -*> -*> A := alpha*x*y**H + conjg( alpha )*y*x**H + A, -*> -*> where alpha is a scalar, x and y are n element vectors and A is an n -*> by n hermitian matrix. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> On entry, UPLO specifies whether the upper or lower -*> triangular part of the array A is to be referenced as -*> follows: -*> -*> UPLO = 'U' or 'u' Only the upper triangular part of A -*> is to be referenced. -*> -*> UPLO = 'L' or 'l' Only the lower triangular part of A -*> is to be referenced. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> On entry, N specifies the order of the matrix A. -*> N must be at least zero. -*> \endverbatim -*> -*> \param[in] ALPHA -*> \verbatim -*> ALPHA is COMPLEX*16 -*> On entry, ALPHA specifies the scalar alpha. -*> \endverbatim -*> -*> \param[in] X -*> \verbatim -*> X is COMPLEX*16 array, dimension at least -*> ( 1 + ( n - 1 )*abs( INCX ) ). -*> Before entry, the incremented array X must contain the n -*> element vector x. -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> On entry, INCX specifies the increment for the elements of -*> X. INCX must not be zero. -*> \endverbatim -*> -*> \param[in] Y -*> \verbatim -*> Y is COMPLEX*16 array, dimension at least -*> ( 1 + ( n - 1 )*abs( INCY ) ). -*> Before entry, the incremented array Y must contain the n -*> element vector y. -*> \endverbatim -*> -*> \param[in] INCY -*> \verbatim -*> INCY is INTEGER -*> On entry, INCY specifies the increment for the elements of -*> Y. INCY must not be zero. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is COMPLEX*16 array, dimension ( LDA, N ) -*> Before entry with UPLO = 'U' or 'u', the leading n by n -*> upper triangular part of the array A must contain the upper -*> triangular part of the hermitian matrix and the strictly -*> lower triangular part of A is not referenced. On exit, the -*> upper triangular part of the array A is overwritten by the -*> upper triangular part of the updated matrix. -*> Before entry with UPLO = 'L' or 'l', the leading n by n -*> lower triangular part of the array A must contain the lower -*> triangular part of the hermitian matrix and the strictly -*> upper triangular part of A is not referenced. On exit, the -*> lower triangular part of the array A is overwritten by the -*> lower triangular part of the updated matrix. -*> Note that the imaginary parts of the diagonal elements need -*> not be set, they are assumed to be zero, and on exit they -*> are set to zero. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> On entry, LDA specifies the first dimension of A as declared -*> in the calling (sub) program. LDA must be at least -*> max( 1, n ). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16_blas_level2 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> Level 2 Blas routine. -*> -*> -- Written on 22-October-1986. -*> Jack Dongarra, Argonne National Lab. -*> Jeremy Du Croz, Nag Central Office. -*> Sven Hammarling, Nag Central Office. -*> Richard Hanson, Sandia National Labs. -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE ZHER2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA) -* -* -- Reference BLAS level2 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - COMPLEX*16 ALPHA - INTEGER INCX,INCY,LDA,N - CHARACTER UPLO -* .. -* .. Array Arguments .. - COMPLEX*16 A(LDA,*),X(*),Y(*) -* .. -* -* ===================================================================== -* -* .. Parameters .. - COMPLEX*16 ZERO - PARAMETER (ZERO= (0.0D+0,0.0D+0)) -* .. -* .. Local Scalars .. - COMPLEX*16 TEMP1,TEMP2 - INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC DBLE,DCONJG,MAX -* .. -* -* Test the input parameters. -* - INFO = 0 - IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN - INFO = 1 - ELSE IF (N.LT.0) THEN - INFO = 2 - ELSE IF (INCX.EQ.0) THEN - INFO = 5 - ELSE IF (INCY.EQ.0) THEN - INFO = 7 - ELSE IF (LDA.LT.MAX(1,N)) THEN - INFO = 9 - END IF - IF (INFO.NE.0) THEN - CALL XERBLA('ZHER2 ',INFO) - RETURN - END IF -* -* Quick return if possible. -* - IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN -* -* Set up the start points in X and Y if the increments are not both -* unity. -* - IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN - IF (INCX.GT.0) THEN - KX = 1 - ELSE - KX = 1 - (N-1)*INCX - END IF - IF (INCY.GT.0) THEN - KY = 1 - ELSE - KY = 1 - (N-1)*INCY - END IF - JX = KX - JY = KY - END IF -* -* Start the operations. In this version the elements of A are -* accessed sequentially with one pass through the triangular part -* of A. -* - IF (LSAME(UPLO,'U')) THEN -* -* Form A when A is stored in the upper triangle. -* - IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN - DO 20 J = 1,N - IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN - TEMP1 = ALPHA*DCONJG(Y(J)) - TEMP2 = DCONJG(ALPHA*X(J)) - DO 10 I = 1,J - 1 - A(I,J) = A(I,J) + X(I)*TEMP1 + Y(I)*TEMP2 - 10 CONTINUE - A(J,J) = DBLE(A(J,J)) + - + DBLE(X(J)*TEMP1+Y(J)*TEMP2) - ELSE - A(J,J) = DBLE(A(J,J)) - END IF - 20 CONTINUE - ELSE - DO 40 J = 1,N - IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN - TEMP1 = ALPHA*DCONJG(Y(JY)) - TEMP2 = DCONJG(ALPHA*X(JX)) - IX = KX - IY = KY - DO 30 I = 1,J - 1 - A(I,J) = A(I,J) + X(IX)*TEMP1 + Y(IY)*TEMP2 - IX = IX + INCX - IY = IY + INCY - 30 CONTINUE - A(J,J) = DBLE(A(J,J)) + - + DBLE(X(JX)*TEMP1+Y(JY)*TEMP2) - ELSE - A(J,J) = DBLE(A(J,J)) - END IF - JX = JX + INCX - JY = JY + INCY - 40 CONTINUE - END IF - ELSE -* -* Form A when A is stored in the lower triangle. -* - IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN - DO 60 J = 1,N - IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN - TEMP1 = ALPHA*DCONJG(Y(J)) - TEMP2 = DCONJG(ALPHA*X(J)) - A(J,J) = DBLE(A(J,J)) + - + DBLE(X(J)*TEMP1+Y(J)*TEMP2) - DO 50 I = J + 1,N - A(I,J) = A(I,J) + X(I)*TEMP1 + Y(I)*TEMP2 - 50 CONTINUE - ELSE - A(J,J) = DBLE(A(J,J)) - END IF - 60 CONTINUE - ELSE - DO 80 J = 1,N - IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN - TEMP1 = ALPHA*DCONJG(Y(JY)) - TEMP2 = DCONJG(ALPHA*X(JX)) - A(J,J) = DBLE(A(J,J)) + - + DBLE(X(JX)*TEMP1+Y(JY)*TEMP2) - IX = JX - IY = JY - DO 70 I = J + 1,N - IX = IX + INCX - IY = IY + INCY - A(I,J) = A(I,J) + X(IX)*TEMP1 + Y(IY)*TEMP2 - 70 CONTINUE - ELSE - A(J,J) = DBLE(A(J,J)) - END IF - JX = JX + INCX - JY = JY + INCY - 80 CONTINUE - END IF - END IF -* - RETURN -* -* End of ZHER2 -* - END diff --git a/lib/linalg/fortran/zher2k.f b/lib/linalg/fortran/zher2k.f deleted file mode 100644 index 5c75083cd5..0000000000 --- a/lib/linalg/fortran/zher2k.f +++ /dev/null @@ -1,440 +0,0 @@ -*> \brief \b ZHER2K -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE ZHER2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) -* -* .. Scalar Arguments .. -* COMPLEX*16 ALPHA -* DOUBLE PRECISION BETA -* INTEGER K,LDA,LDB,LDC,N -* CHARACTER TRANS,UPLO -* .. -* .. Array Arguments .. -* COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZHER2K performs one of the hermitian rank 2k operations -*> -*> C := alpha*A*B**H + conjg( alpha )*B*A**H + beta*C, -*> -*> or -*> -*> C := alpha*A**H*B + conjg( alpha )*B**H*A + beta*C, -*> -*> where alpha and beta are scalars with beta real, C is an n by n -*> hermitian matrix and A and B are n by k matrices in the first case -*> and k by n matrices in the second case. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> On entry, UPLO specifies whether the upper or lower -*> triangular part of the array C is to be referenced as -*> follows: -*> -*> UPLO = 'U' or 'u' Only the upper triangular part of C -*> is to be referenced. -*> -*> UPLO = 'L' or 'l' Only the lower triangular part of C -*> is to be referenced. -*> \endverbatim -*> -*> \param[in] TRANS -*> \verbatim -*> TRANS is CHARACTER*1 -*> On entry, TRANS specifies the operation to be performed as -*> follows: -*> -*> TRANS = 'N' or 'n' C := alpha*A*B**H + -*> conjg( alpha )*B*A**H + -*> beta*C. -*> -*> TRANS = 'C' or 'c' C := alpha*A**H*B + -*> conjg( alpha )*B**H*A + -*> beta*C. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> On entry, N specifies the order of the matrix C. N must be -*> at least zero. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> On entry with TRANS = 'N' or 'n', K specifies the number -*> of columns of the matrices A and B, and on entry with -*> TRANS = 'C' or 'c', K specifies the number of rows of the -*> matrices A and B. K must be at least zero. -*> \endverbatim -*> -*> \param[in] ALPHA -*> \verbatim -*> ALPHA is COMPLEX*16 . -*> On entry, ALPHA specifies the scalar alpha. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is COMPLEX*16 array, dimension ( LDA, ka ), where ka is -*> k when TRANS = 'N' or 'n', and is n otherwise. -*> Before entry with TRANS = 'N' or 'n', the leading n by k -*> part of the array A must contain the matrix A, otherwise -*> the leading k by n part of the array A must contain the -*> matrix A. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> On entry, LDA specifies the first dimension of A as declared -*> in the calling (sub) program. When TRANS = 'N' or 'n' -*> then LDA must be at least max( 1, n ), otherwise LDA must -*> be at least max( 1, k ). -*> \endverbatim -*> -*> \param[in] B -*> \verbatim -*> B is COMPLEX*16 array, dimension ( LDB, kb ), where kb is -*> k when TRANS = 'N' or 'n', and is n otherwise. -*> Before entry with TRANS = 'N' or 'n', the leading n by k -*> part of the array B must contain the matrix B, otherwise -*> the leading k by n part of the array B must contain the -*> matrix B. -*> \endverbatim -*> -*> \param[in] LDB -*> \verbatim -*> LDB is INTEGER -*> On entry, LDB specifies the first dimension of B as declared -*> in the calling (sub) program. When TRANS = 'N' or 'n' -*> then LDB must be at least max( 1, n ), otherwise LDB must -*> be at least max( 1, k ). -*> Unchanged on exit. -*> \endverbatim -*> -*> \param[in] BETA -*> \verbatim -*> BETA is DOUBLE PRECISION . -*> On entry, BETA specifies the scalar beta. -*> \endverbatim -*> -*> \param[in,out] C -*> \verbatim -*> C is COMPLEX*16 array, dimension ( LDC, N ) -*> Before entry with UPLO = 'U' or 'u', the leading n by n -*> upper triangular part of the array C must contain the upper -*> triangular part of the hermitian matrix and the strictly -*> lower triangular part of C is not referenced. On exit, the -*> upper triangular part of the array C is overwritten by the -*> upper triangular part of the updated matrix. -*> Before entry with UPLO = 'L' or 'l', the leading n by n -*> lower triangular part of the array C must contain the lower -*> triangular part of the hermitian matrix and the strictly -*> upper triangular part of C is not referenced. On exit, the -*> lower triangular part of the array C is overwritten by the -*> lower triangular part of the updated matrix. -*> Note that the imaginary parts of the diagonal elements need -*> not be set, they are assumed to be zero, and on exit they -*> are set to zero. -*> \endverbatim -*> -*> \param[in] LDC -*> \verbatim -*> LDC is INTEGER -*> On entry, LDC specifies the first dimension of C as declared -*> in the calling (sub) program. LDC must be at least -*> max( 1, n ). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16_blas_level3 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> Level 3 Blas routine. -*> -*> -- Written on 8-February-1989. -*> Jack Dongarra, Argonne National Laboratory. -*> Iain Duff, AERE Harwell. -*> Jeremy Du Croz, Numerical Algorithms Group Ltd. -*> Sven Hammarling, Numerical Algorithms Group Ltd. -*> -*> -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1. -*> Ed Anderson, Cray Research Inc. -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE ZHER2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) -* -* -- Reference BLAS level3 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - COMPLEX*16 ALPHA - DOUBLE PRECISION BETA - INTEGER K,LDA,LDB,LDC,N - CHARACTER TRANS,UPLO -* .. -* .. Array Arguments .. - COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*) -* .. -* -* ===================================================================== -* -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC DBLE,DCONJG,MAX -* .. -* .. Local Scalars .. - COMPLEX*16 TEMP1,TEMP2 - INTEGER I,INFO,J,L,NROWA - LOGICAL UPPER -* .. -* .. Parameters .. - DOUBLE PRECISION ONE - PARAMETER (ONE=1.0D+0) - COMPLEX*16 ZERO - PARAMETER (ZERO= (0.0D+0,0.0D+0)) -* .. -* -* Test the input parameters. -* - IF (LSAME(TRANS,'N')) THEN - NROWA = N - ELSE - NROWA = K - END IF - UPPER = LSAME(UPLO,'U') -* - INFO = 0 - IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN - INFO = 1 - ELSE IF ((.NOT.LSAME(TRANS,'N')) .AND. - + (.NOT.LSAME(TRANS,'C'))) THEN - INFO = 2 - ELSE IF (N.LT.0) THEN - INFO = 3 - ELSE IF (K.LT.0) THEN - INFO = 4 - ELSE IF (LDA.LT.MAX(1,NROWA)) THEN - INFO = 7 - ELSE IF (LDB.LT.MAX(1,NROWA)) THEN - INFO = 9 - ELSE IF (LDC.LT.MAX(1,N)) THEN - INFO = 12 - END IF - IF (INFO.NE.0) THEN - CALL XERBLA('ZHER2K',INFO) - RETURN - END IF -* -* Quick return if possible. -* - IF ((N.EQ.0) .OR. (((ALPHA.EQ.ZERO).OR. - + (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN -* -* And when alpha.eq.zero. -* - IF (ALPHA.EQ.ZERO) THEN - IF (UPPER) THEN - IF (BETA.EQ.DBLE(ZERO)) THEN - DO 20 J = 1,N - DO 10 I = 1,J - C(I,J) = ZERO - 10 CONTINUE - 20 CONTINUE - ELSE - DO 40 J = 1,N - DO 30 I = 1,J - 1 - C(I,J) = BETA*C(I,J) - 30 CONTINUE - C(J,J) = BETA*DBLE(C(J,J)) - 40 CONTINUE - END IF - ELSE - IF (BETA.EQ.DBLE(ZERO)) THEN - DO 60 J = 1,N - DO 50 I = J,N - C(I,J) = ZERO - 50 CONTINUE - 60 CONTINUE - ELSE - DO 80 J = 1,N - C(J,J) = BETA*DBLE(C(J,J)) - DO 70 I = J + 1,N - C(I,J) = BETA*C(I,J) - 70 CONTINUE - 80 CONTINUE - END IF - END IF - RETURN - END IF -* -* Start the operations. -* - IF (LSAME(TRANS,'N')) THEN -* -* Form C := alpha*A*B**H + conjg( alpha )*B*A**H + -* C. -* - IF (UPPER) THEN - DO 130 J = 1,N - IF (BETA.EQ.DBLE(ZERO)) THEN - DO 90 I = 1,J - C(I,J) = ZERO - 90 CONTINUE - ELSE IF (BETA.NE.ONE) THEN - DO 100 I = 1,J - 1 - C(I,J) = BETA*C(I,J) - 100 CONTINUE - C(J,J) = BETA*DBLE(C(J,J)) - ELSE - C(J,J) = DBLE(C(J,J)) - END IF - DO 120 L = 1,K - IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN - TEMP1 = ALPHA*DCONJG(B(J,L)) - TEMP2 = DCONJG(ALPHA*A(J,L)) - DO 110 I = 1,J - 1 - C(I,J) = C(I,J) + A(I,L)*TEMP1 + - + B(I,L)*TEMP2 - 110 CONTINUE - C(J,J) = DBLE(C(J,J)) + - + DBLE(A(J,L)*TEMP1+B(J,L)*TEMP2) - END IF - 120 CONTINUE - 130 CONTINUE - ELSE - DO 180 J = 1,N - IF (BETA.EQ.DBLE(ZERO)) THEN - DO 140 I = J,N - C(I,J) = ZERO - 140 CONTINUE - ELSE IF (BETA.NE.ONE) THEN - DO 150 I = J + 1,N - C(I,J) = BETA*C(I,J) - 150 CONTINUE - C(J,J) = BETA*DBLE(C(J,J)) - ELSE - C(J,J) = DBLE(C(J,J)) - END IF - DO 170 L = 1,K - IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN - TEMP1 = ALPHA*DCONJG(B(J,L)) - TEMP2 = DCONJG(ALPHA*A(J,L)) - DO 160 I = J + 1,N - C(I,J) = C(I,J) + A(I,L)*TEMP1 + - + B(I,L)*TEMP2 - 160 CONTINUE - C(J,J) = DBLE(C(J,J)) + - + DBLE(A(J,L)*TEMP1+B(J,L)*TEMP2) - END IF - 170 CONTINUE - 180 CONTINUE - END IF - ELSE -* -* Form C := alpha*A**H*B + conjg( alpha )*B**H*A + -* C. -* - IF (UPPER) THEN - DO 210 J = 1,N - DO 200 I = 1,J - TEMP1 = ZERO - TEMP2 = ZERO - DO 190 L = 1,K - TEMP1 = TEMP1 + DCONJG(A(L,I))*B(L,J) - TEMP2 = TEMP2 + DCONJG(B(L,I))*A(L,J) - 190 CONTINUE - IF (I.EQ.J) THEN - IF (BETA.EQ.DBLE(ZERO)) THEN - C(J,J) = DBLE(ALPHA*TEMP1+ - + DCONJG(ALPHA)*TEMP2) - ELSE - C(J,J) = BETA*DBLE(C(J,J)) + - + DBLE(ALPHA*TEMP1+ - + DCONJG(ALPHA)*TEMP2) - END IF - ELSE - IF (BETA.EQ.DBLE(ZERO)) THEN - C(I,J) = ALPHA*TEMP1 + DCONJG(ALPHA)*TEMP2 - ELSE - C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 + - + DCONJG(ALPHA)*TEMP2 - END IF - END IF - 200 CONTINUE - 210 CONTINUE - ELSE - DO 240 J = 1,N - DO 230 I = J,N - TEMP1 = ZERO - TEMP2 = ZERO - DO 220 L = 1,K - TEMP1 = TEMP1 + DCONJG(A(L,I))*B(L,J) - TEMP2 = TEMP2 + DCONJG(B(L,I))*A(L,J) - 220 CONTINUE - IF (I.EQ.J) THEN - IF (BETA.EQ.DBLE(ZERO)) THEN - C(J,J) = DBLE(ALPHA*TEMP1+ - + DCONJG(ALPHA)*TEMP2) - ELSE - C(J,J) = BETA*DBLE(C(J,J)) + - + DBLE(ALPHA*TEMP1+ - + DCONJG(ALPHA)*TEMP2) - END IF - ELSE - IF (BETA.EQ.DBLE(ZERO)) THEN - C(I,J) = ALPHA*TEMP1 + DCONJG(ALPHA)*TEMP2 - ELSE - C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 + - + DCONJG(ALPHA)*TEMP2 - END IF - END IF - 230 CONTINUE - 240 CONTINUE - END IF - END IF -* - RETURN -* -* End of ZHER2K -* - END diff --git a/lib/linalg/fortran/zhetd2.f b/lib/linalg/fortran/zhetd2.f deleted file mode 100644 index a6d900b7c7..0000000000 --- a/lib/linalg/fortran/zhetd2.f +++ /dev/null @@ -1,331 +0,0 @@ -*> \brief \b ZHETD2 reduces a Hermitian matrix to real symmetric tridiagonal form by an unitary similarity transformation (unblocked algorithm). -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZHETD2 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZHETD2( UPLO, N, A, LDA, D, E, TAU, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER UPLO -* INTEGER INFO, LDA, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION D( * ), E( * ) -* COMPLEX*16 A( LDA, * ), TAU( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZHETD2 reduces a complex Hermitian matrix A to real symmetric -*> tridiagonal form T by a unitary similarity transformation: -*> Q**H * A * Q = T. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> Specifies whether the upper or lower triangular part of the -*> Hermitian matrix A is stored: -*> = 'U': Upper triangular -*> = 'L': Lower triangular -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is COMPLEX*16 array, dimension (LDA,N) -*> On entry, the Hermitian matrix A. If UPLO = 'U', the leading -*> n-by-n upper triangular part of A contains the upper -*> triangular part of the matrix A, and the strictly lower -*> triangular part of A is not referenced. If UPLO = 'L', the -*> leading n-by-n lower triangular part of A contains the lower -*> triangular part of the matrix A, and the strictly upper -*> triangular part of A is not referenced. -*> On exit, if UPLO = 'U', the diagonal and first superdiagonal -*> of A are overwritten by the corresponding elements of the -*> tridiagonal matrix T, and the elements above the first -*> superdiagonal, with the array TAU, represent the unitary -*> matrix Q as a product of elementary reflectors; if UPLO -*> = 'L', the diagonal and first subdiagonal of A are over- -*> written by the corresponding elements of the tridiagonal -*> matrix T, and the elements below the first subdiagonal, with -*> the array TAU, represent the unitary matrix Q as a product -*> of elementary reflectors. See Further Details. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,N). -*> \endverbatim -*> -*> \param[out] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension (N) -*> The diagonal elements of the tridiagonal matrix T: -*> D(i) = A(i,i). -*> \endverbatim -*> -*> \param[out] E -*> \verbatim -*> E is DOUBLE PRECISION array, dimension (N-1) -*> The off-diagonal elements of the tridiagonal matrix T: -*> E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. -*> \endverbatim -*> -*> \param[out] TAU -*> \verbatim -*> TAU is COMPLEX*16 array, dimension (N-1) -*> The scalar factors of the elementary reflectors (see Further -*> Details). -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16HEcomputational -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> If UPLO = 'U', the matrix Q is represented as a product of elementary -*> reflectors -*> -*> Q = H(n-1) . . . H(2) H(1). -*> -*> Each H(i) has the form -*> -*> H(i) = I - tau * v * v**H -*> -*> where tau is a complex scalar, and v is a complex vector with -*> v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in -*> A(1:i-1,i+1), and tau in TAU(i). -*> -*> If UPLO = 'L', the matrix Q is represented as a product of elementary -*> reflectors -*> -*> Q = H(1) H(2) . . . H(n-1). -*> -*> Each H(i) has the form -*> -*> H(i) = I - tau * v * v**H -*> -*> where tau is a complex scalar, and v is a complex vector with -*> v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), -*> and tau in TAU(i). -*> -*> The contents of A on exit are illustrated by the following examples -*> with n = 5: -*> -*> if UPLO = 'U': if UPLO = 'L': -*> -*> ( d e v2 v3 v4 ) ( d ) -*> ( d e v3 v4 ) ( e d ) -*> ( d e v4 ) ( v1 e d ) -*> ( d e ) ( v1 v2 e d ) -*> ( d ) ( v1 v2 v3 e d ) -*> -*> where d and e denote diagonal and off-diagonal elements of T, and vi -*> denotes an element of the vector defining H(i). -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE ZHETD2( UPLO, N, A, LDA, D, E, TAU, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER UPLO - INTEGER INFO, LDA, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION D( * ), E( * ) - COMPLEX*16 A( LDA, * ), TAU( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - COMPLEX*16 ONE, ZERO, HALF - PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ), - $ ZERO = ( 0.0D+0, 0.0D+0 ), - $ HALF = ( 0.5D+0, 0.0D+0 ) ) -* .. -* .. Local Scalars .. - LOGICAL UPPER - INTEGER I - COMPLEX*16 ALPHA, TAUI -* .. -* .. External Subroutines .. - EXTERNAL XERBLA, ZAXPY, ZHEMV, ZHER2, ZLARFG -* .. -* .. External Functions .. - LOGICAL LSAME - COMPLEX*16 ZDOTC - EXTERNAL LSAME, ZDOTC -* .. -* .. Intrinsic Functions .. - INTRINSIC DBLE, MAX, MIN -* .. -* .. Executable Statements .. -* -* Test the input parameters -* - INFO = 0 - UPPER = LSAME( UPLO, 'U') - IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -4 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'ZHETD2', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( N.LE.0 ) - $ RETURN -* - IF( UPPER ) THEN -* -* Reduce the upper triangle of A -* - A( N, N ) = DBLE( A( N, N ) ) - DO 10 I = N - 1, 1, -1 -* -* Generate elementary reflector H(i) = I - tau * v * v**H -* to annihilate A(1:i-1,i+1) -* - ALPHA = A( I, I+1 ) - CALL ZLARFG( I, ALPHA, A( 1, I+1 ), 1, TAUI ) - E( I ) = DBLE( ALPHA ) -* - IF( TAUI.NE.ZERO ) THEN -* -* Apply H(i) from both sides to A(1:i,1:i) -* - A( I, I+1 ) = ONE -* -* Compute x := tau * A * v storing x in TAU(1:i) -* - CALL ZHEMV( UPLO, I, TAUI, A, LDA, A( 1, I+1 ), 1, ZERO, - $ TAU, 1 ) -* -* Compute w := x - 1/2 * tau * (x**H * v) * v -* - ALPHA = -HALF*TAUI*ZDOTC( I, TAU, 1, A( 1, I+1 ), 1 ) - CALL ZAXPY( I, ALPHA, A( 1, I+1 ), 1, TAU, 1 ) -* -* Apply the transformation as a rank-2 update: -* A := A - v * w**H - w * v**H -* - CALL ZHER2( UPLO, I, -ONE, A( 1, I+1 ), 1, TAU, 1, A, - $ LDA ) -* - ELSE - A( I, I ) = DBLE( A( I, I ) ) - END IF - A( I, I+1 ) = E( I ) - D( I+1 ) = DBLE( A( I+1, I+1 ) ) - TAU( I ) = TAUI - 10 CONTINUE - D( 1 ) = DBLE( A( 1, 1 ) ) - ELSE -* -* Reduce the lower triangle of A -* - A( 1, 1 ) = DBLE( A( 1, 1 ) ) - DO 20 I = 1, N - 1 -* -* Generate elementary reflector H(i) = I - tau * v * v**H -* to annihilate A(i+2:n,i) -* - ALPHA = A( I+1, I ) - CALL ZLARFG( N-I, ALPHA, A( MIN( I+2, N ), I ), 1, TAUI ) - E( I ) = DBLE( ALPHA ) -* - IF( TAUI.NE.ZERO ) THEN -* -* Apply H(i) from both sides to A(i+1:n,i+1:n) -* - A( I+1, I ) = ONE -* -* Compute x := tau * A * v storing y in TAU(i:n-1) -* - CALL ZHEMV( UPLO, N-I, TAUI, A( I+1, I+1 ), LDA, - $ A( I+1, I ), 1, ZERO, TAU( I ), 1 ) -* -* Compute w := x - 1/2 * tau * (x**H * v) * v -* - ALPHA = -HALF*TAUI*ZDOTC( N-I, TAU( I ), 1, A( I+1, I ), - $ 1 ) - CALL ZAXPY( N-I, ALPHA, A( I+1, I ), 1, TAU( I ), 1 ) -* -* Apply the transformation as a rank-2 update: -* A := A - v * w**H - w * v**H -* - CALL ZHER2( UPLO, N-I, -ONE, A( I+1, I ), 1, TAU( I ), 1, - $ A( I+1, I+1 ), LDA ) -* - ELSE - A( I+1, I+1 ) = DBLE( A( I+1, I+1 ) ) - END IF - A( I+1, I ) = E( I ) - D( I ) = DBLE( A( I, I ) ) - TAU( I ) = TAUI - 20 CONTINUE - D( N ) = DBLE( A( N, N ) ) - END IF -* - RETURN -* -* End of ZHETD2 -* - END diff --git a/lib/linalg/fortran/zhetrd.f b/lib/linalg/fortran/zhetrd.f deleted file mode 100644 index 5b7d6546cc..0000000000 --- a/lib/linalg/fortran/zhetrd.f +++ /dev/null @@ -1,375 +0,0 @@ -*> \brief \b ZHETRD -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZHETRD + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZHETRD( UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER UPLO -* INTEGER INFO, LDA, LWORK, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION D( * ), E( * ) -* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZHETRD reduces a complex Hermitian matrix A to real symmetric -*> tridiagonal form T by a unitary similarity transformation: -*> Q**H * A * Q = T. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> = 'U': Upper triangle of A is stored; -*> = 'L': Lower triangle of A is stored. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is COMPLEX*16 array, dimension (LDA,N) -*> On entry, the Hermitian matrix A. If UPLO = 'U', the leading -*> N-by-N upper triangular part of A contains the upper -*> triangular part of the matrix A, and the strictly lower -*> triangular part of A is not referenced. If UPLO = 'L', the -*> leading N-by-N lower triangular part of A contains the lower -*> triangular part of the matrix A, and the strictly upper -*> triangular part of A is not referenced. -*> On exit, if UPLO = 'U', the diagonal and first superdiagonal -*> of A are overwritten by the corresponding elements of the -*> tridiagonal matrix T, and the elements above the first -*> superdiagonal, with the array TAU, represent the unitary -*> matrix Q as a product of elementary reflectors; if UPLO -*> = 'L', the diagonal and first subdiagonal of A are over- -*> written by the corresponding elements of the tridiagonal -*> matrix T, and the elements below the first subdiagonal, with -*> the array TAU, represent the unitary matrix Q as a product -*> of elementary reflectors. See Further Details. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,N). -*> \endverbatim -*> -*> \param[out] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension (N) -*> The diagonal elements of the tridiagonal matrix T: -*> D(i) = A(i,i). -*> \endverbatim -*> -*> \param[out] E -*> \verbatim -*> E is DOUBLE PRECISION array, dimension (N-1) -*> The off-diagonal elements of the tridiagonal matrix T: -*> E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. -*> \endverbatim -*> -*> \param[out] TAU -*> \verbatim -*> TAU is COMPLEX*16 array, dimension (N-1) -*> The scalar factors of the elementary reflectors (see Further -*> Details). -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) -*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -*> \endverbatim -*> -*> \param[in] LWORK -*> \verbatim -*> LWORK is INTEGER -*> The dimension of the array WORK. LWORK >= 1. -*> For optimum performance LWORK >= N*NB, where NB is the -*> optimal blocksize. -*> -*> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal size of the WORK array, returns -*> this value as the first entry of the WORK array, and no error -*> message related to LWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16HEcomputational -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> If UPLO = 'U', the matrix Q is represented as a product of elementary -*> reflectors -*> -*> Q = H(n-1) . . . H(2) H(1). -*> -*> Each H(i) has the form -*> -*> H(i) = I - tau * v * v**H -*> -*> where tau is a complex scalar, and v is a complex vector with -*> v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in -*> A(1:i-1,i+1), and tau in TAU(i). -*> -*> If UPLO = 'L', the matrix Q is represented as a product of elementary -*> reflectors -*> -*> Q = H(1) H(2) . . . H(n-1). -*> -*> Each H(i) has the form -*> -*> H(i) = I - tau * v * v**H -*> -*> where tau is a complex scalar, and v is a complex vector with -*> v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), -*> and tau in TAU(i). -*> -*> The contents of A on exit are illustrated by the following examples -*> with n = 5: -*> -*> if UPLO = 'U': if UPLO = 'L': -*> -*> ( d e v2 v3 v4 ) ( d ) -*> ( d e v3 v4 ) ( e d ) -*> ( d e v4 ) ( v1 e d ) -*> ( d e ) ( v1 v2 e d ) -*> ( d ) ( v1 v2 v3 e d ) -*> -*> where d and e denote diagonal and off-diagonal elements of T, and vi -*> denotes an element of the vector defining H(i). -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE ZHETRD( UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER UPLO - INTEGER INFO, LDA, LWORK, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION D( * ), E( * ) - COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE - PARAMETER ( ONE = 1.0D+0 ) - COMPLEX*16 CONE - PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) ) -* .. -* .. Local Scalars .. - LOGICAL LQUERY, UPPER - INTEGER I, IINFO, IWS, J, KK, LDWORK, LWKOPT, NB, - $ NBMIN, NX -* .. -* .. External Subroutines .. - EXTERNAL XERBLA, ZHER2K, ZHETD2, ZLATRD -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* .. External Functions .. - LOGICAL LSAME - INTEGER ILAENV - EXTERNAL LSAME, ILAENV -* .. -* .. Executable Statements .. -* -* Test the input parameters -* - INFO = 0 - UPPER = LSAME( UPLO, 'U' ) - LQUERY = ( LWORK.EQ.-1 ) - IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -4 - ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN - INFO = -9 - END IF -* - IF( INFO.EQ.0 ) THEN -* -* Determine the block size. -* - NB = ILAENV( 1, 'ZHETRD', UPLO, N, -1, -1, -1 ) - LWKOPT = N*NB - WORK( 1 ) = LWKOPT - END IF -* - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'ZHETRD', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - RETURN - END IF -* -* Quick return if possible -* - IF( N.EQ.0 ) THEN - WORK( 1 ) = 1 - RETURN - END IF -* - NX = N - IWS = 1 - IF( NB.GT.1 .AND. NB.LT.N ) THEN -* -* Determine when to cross over from blocked to unblocked code -* (last block is always handled by unblocked code). -* - NX = MAX( NB, ILAENV( 3, 'ZHETRD', UPLO, N, -1, -1, -1 ) ) - IF( NX.LT.N ) THEN -* -* Determine if workspace is large enough for blocked code. -* - LDWORK = N - IWS = LDWORK*NB - IF( LWORK.LT.IWS ) THEN -* -* Not enough workspace to use optimal NB: determine the -* minimum value of NB, and reduce NB or force use of -* unblocked code by setting NX = N. -* - NB = MAX( LWORK / LDWORK, 1 ) - NBMIN = ILAENV( 2, 'ZHETRD', UPLO, N, -1, -1, -1 ) - IF( NB.LT.NBMIN ) - $ NX = N - END IF - ELSE - NX = N - END IF - ELSE - NB = 1 - END IF -* - IF( UPPER ) THEN -* -* Reduce the upper triangle of A. -* Columns 1:kk are handled by the unblocked method. -* - KK = N - ( ( N-NX+NB-1 ) / NB )*NB - DO 20 I = N - NB + 1, KK + 1, -NB -* -* Reduce columns i:i+nb-1 to tridiagonal form and form the -* matrix W which is needed to update the unreduced part of -* the matrix -* - CALL ZLATRD( UPLO, I+NB-1, NB, A, LDA, E, TAU, WORK, - $ LDWORK ) -* -* Update the unreduced submatrix A(1:i-1,1:i-1), using an -* update of the form: A := A - V*W**H - W*V**H -* - CALL ZHER2K( UPLO, 'No transpose', I-1, NB, -CONE, - $ A( 1, I ), LDA, WORK, LDWORK, ONE, A, LDA ) -* -* Copy superdiagonal elements back into A, and diagonal -* elements into D -* - DO 10 J = I, I + NB - 1 - A( J-1, J ) = E( J-1 ) - D( J ) = DBLE( A( J, J ) ) - 10 CONTINUE - 20 CONTINUE -* -* Use unblocked code to reduce the last or only block -* - CALL ZHETD2( UPLO, KK, A, LDA, D, E, TAU, IINFO ) - ELSE -* -* Reduce the lower triangle of A -* - DO 40 I = 1, N - NX, NB -* -* Reduce columns i:i+nb-1 to tridiagonal form and form the -* matrix W which is needed to update the unreduced part of -* the matrix -* - CALL ZLATRD( UPLO, N-I+1, NB, A( I, I ), LDA, E( I ), - $ TAU( I ), WORK, LDWORK ) -* -* Update the unreduced submatrix A(i+nb:n,i+nb:n), using -* an update of the form: A := A - V*W**H - W*V**H -* - CALL ZHER2K( UPLO, 'No transpose', N-I-NB+1, NB, -CONE, - $ A( I+NB, I ), LDA, WORK( NB+1 ), LDWORK, ONE, - $ A( I+NB, I+NB ), LDA ) -* -* Copy subdiagonal elements back into A, and diagonal -* elements into D -* - DO 30 J = I, I + NB - 1 - A( J+1, J ) = E( J ) - D( J ) = DBLE( A( J, J ) ) - 30 CONTINUE - 40 CONTINUE -* -* Use unblocked code to reduce the last or only block -* - CALL ZHETD2( UPLO, N-I+1, A( I, I ), LDA, D( I ), E( I ), - $ TAU( I ), IINFO ) - END IF -* - WORK( 1 ) = LWKOPT - RETURN -* -* End of ZHETRD -* - END diff --git a/lib/linalg/fortran/zhpr.f b/lib/linalg/fortran/zhpr.f deleted file mode 100644 index 2ba5774a21..0000000000 --- a/lib/linalg/fortran/zhpr.f +++ /dev/null @@ -1,276 +0,0 @@ -*> \brief \b ZHPR -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE ZHPR(UPLO,N,ALPHA,X,INCX,AP) -* -* .. Scalar Arguments .. -* DOUBLE PRECISION ALPHA -* INTEGER INCX,N -* CHARACTER UPLO -* .. -* .. Array Arguments .. -* COMPLEX*16 AP(*),X(*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZHPR performs the hermitian rank 1 operation -*> -*> A := alpha*x*x**H + A, -*> -*> where alpha is a real scalar, x is an n element vector and A is an -*> n by n hermitian matrix, supplied in packed form. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> On entry, UPLO specifies whether the upper or lower -*> triangular part of the matrix A is supplied in the packed -*> array AP as follows: -*> -*> UPLO = 'U' or 'u' The upper triangular part of A is -*> supplied in AP. -*> -*> UPLO = 'L' or 'l' The lower triangular part of A is -*> supplied in AP. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> On entry, N specifies the order of the matrix A. -*> N must be at least zero. -*> \endverbatim -*> -*> \param[in] ALPHA -*> \verbatim -*> ALPHA is DOUBLE PRECISION. -*> On entry, ALPHA specifies the scalar alpha. -*> \endverbatim -*> -*> \param[in] X -*> \verbatim -*> X is COMPLEX*16 array, dimension at least -*> ( 1 + ( n - 1 )*abs( INCX ) ). -*> Before entry, the incremented array X must contain the n -*> element vector x. -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> On entry, INCX specifies the increment for the elements of -*> X. INCX must not be zero. -*> \endverbatim -*> -*> \param[in,out] AP -*> \verbatim -*> AP is COMPLEX*16 array, dimension at least -*> ( ( n*( n + 1 ) )/2 ). -*> Before entry with UPLO = 'U' or 'u', the array AP must -*> contain the upper triangular part of the hermitian matrix -*> packed sequentially, column by column, so that AP( 1 ) -*> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) -*> and a( 2, 2 ) respectively, and so on. On exit, the array -*> AP is overwritten by the upper triangular part of the -*> updated matrix. -*> Before entry with UPLO = 'L' or 'l', the array AP must -*> contain the lower triangular part of the hermitian matrix -*> packed sequentially, column by column, so that AP( 1 ) -*> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) -*> and a( 3, 1 ) respectively, and so on. On exit, the array -*> AP is overwritten by the lower triangular part of the -*> updated matrix. -*> Note that the imaginary parts of the diagonal elements need -*> not be set, they are assumed to be zero, and on exit they -*> are set to zero. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16_blas_level2 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> Level 2 Blas routine. -*> -*> -- Written on 22-October-1986. -*> Jack Dongarra, Argonne National Lab. -*> Jeremy Du Croz, Nag Central Office. -*> Sven Hammarling, Nag Central Office. -*> Richard Hanson, Sandia National Labs. -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE ZHPR(UPLO,N,ALPHA,X,INCX,AP) -* -* -- Reference BLAS level2 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - DOUBLE PRECISION ALPHA - INTEGER INCX,N - CHARACTER UPLO -* .. -* .. Array Arguments .. - COMPLEX*16 AP(*),X(*) -* .. -* -* ===================================================================== -* -* .. Parameters .. - COMPLEX*16 ZERO - PARAMETER (ZERO= (0.0D+0,0.0D+0)) -* .. -* .. Local Scalars .. - COMPLEX*16 TEMP - INTEGER I,INFO,IX,J,JX,K,KK,KX -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC DBLE,DCONJG -* .. -* -* Test the input parameters. -* - INFO = 0 - IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN - INFO = 1 - ELSE IF (N.LT.0) THEN - INFO = 2 - ELSE IF (INCX.EQ.0) THEN - INFO = 5 - END IF - IF (INFO.NE.0) THEN - CALL XERBLA('ZHPR ',INFO) - RETURN - END IF -* -* Quick return if possible. -* - IF ((N.EQ.0) .OR. (ALPHA.EQ.DBLE(ZERO))) RETURN -* -* Set the start point in X if the increment is not unity. -* - IF (INCX.LE.0) THEN - KX = 1 - (N-1)*INCX - ELSE IF (INCX.NE.1) THEN - KX = 1 - END IF -* -* Start the operations. In this version the elements of the array AP -* are accessed sequentially with one pass through AP. -* - KK = 1 - IF (LSAME(UPLO,'U')) THEN -* -* Form A when upper triangle is stored in AP. -* - IF (INCX.EQ.1) THEN - DO 20 J = 1,N - IF (X(J).NE.ZERO) THEN - TEMP = ALPHA*DCONJG(X(J)) - K = KK - DO 10 I = 1,J - 1 - AP(K) = AP(K) + X(I)*TEMP - K = K + 1 - 10 CONTINUE - AP(KK+J-1) = DBLE(AP(KK+J-1)) + DBLE(X(J)*TEMP) - ELSE - AP(KK+J-1) = DBLE(AP(KK+J-1)) - END IF - KK = KK + J - 20 CONTINUE - ELSE - JX = KX - DO 40 J = 1,N - IF (X(JX).NE.ZERO) THEN - TEMP = ALPHA*DCONJG(X(JX)) - IX = KX - DO 30 K = KK,KK + J - 2 - AP(K) = AP(K) + X(IX)*TEMP - IX = IX + INCX - 30 CONTINUE - AP(KK+J-1) = DBLE(AP(KK+J-1)) + DBLE(X(JX)*TEMP) - ELSE - AP(KK+J-1) = DBLE(AP(KK+J-1)) - END IF - JX = JX + INCX - KK = KK + J - 40 CONTINUE - END IF - ELSE -* -* Form A when lower triangle is stored in AP. -* - IF (INCX.EQ.1) THEN - DO 60 J = 1,N - IF (X(J).NE.ZERO) THEN - TEMP = ALPHA*DCONJG(X(J)) - AP(KK) = DBLE(AP(KK)) + DBLE(TEMP*X(J)) - K = KK + 1 - DO 50 I = J + 1,N - AP(K) = AP(K) + X(I)*TEMP - K = K + 1 - 50 CONTINUE - ELSE - AP(KK) = DBLE(AP(KK)) - END IF - KK = KK + N - J + 1 - 60 CONTINUE - ELSE - JX = KX - DO 80 J = 1,N - IF (X(JX).NE.ZERO) THEN - TEMP = ALPHA*DCONJG(X(JX)) - AP(KK) = DBLE(AP(KK)) + DBLE(TEMP*X(JX)) - IX = JX - DO 70 K = KK + 1,KK + N - J - IX = IX + INCX - AP(K) = AP(K) + X(IX)*TEMP - 70 CONTINUE - ELSE - AP(KK) = DBLE(AP(KK)) - END IF - JX = JX + INCX - KK = KK + N - J + 1 - 80 CONTINUE - END IF - END IF -* - RETURN -* -* End of ZHPR -* - END diff --git a/lib/linalg/fortran/zlacgv.f b/lib/linalg/fortran/zlacgv.f deleted file mode 100644 index dc935e08f4..0000000000 --- a/lib/linalg/fortran/zlacgv.f +++ /dev/null @@ -1,113 +0,0 @@ -*> \brief \b ZLACGV conjugates a complex vector. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZLACGV + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZLACGV( N, X, INCX ) -* -* .. Scalar Arguments .. -* INTEGER INCX, N -* .. -* .. Array Arguments .. -* COMPLEX*16 X( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZLACGV conjugates a complex vector of length N. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The length of the vector X. N >= 0. -*> \endverbatim -*> -*> \param[in,out] X -*> \verbatim -*> X is COMPLEX*16 array, dimension -*> (1+(N-1)*abs(INCX)) -*> On entry, the vector of length N to be conjugated. -*> On exit, X is overwritten with conjg(X). -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> The spacing between successive elements of X. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16OTHERauxiliary -* -* ===================================================================== - SUBROUTINE ZLACGV( N, X, INCX ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INCX, N -* .. -* .. Array Arguments .. - COMPLEX*16 X( * ) -* .. -* -* ===================================================================== -* -* .. Local Scalars .. - INTEGER I, IOFF -* .. -* .. Intrinsic Functions .. - INTRINSIC DCONJG -* .. -* .. Executable Statements .. -* - IF( INCX.EQ.1 ) THEN - DO 10 I = 1, N - X( I ) = DCONJG( X( I ) ) - 10 CONTINUE - ELSE - IOFF = 1 - IF( INCX.LT.0 ) - $ IOFF = 1 - ( N-1 )*INCX - DO 20 I = 1, N - X( IOFF ) = DCONJG( X( IOFF ) ) - IOFF = IOFF + INCX - 20 CONTINUE - END IF - RETURN -* -* End of ZLACGV -* - END diff --git a/lib/linalg/fortran/zlacpy.f b/lib/linalg/fortran/zlacpy.f deleted file mode 100644 index 06017509e0..0000000000 --- a/lib/linalg/fortran/zlacpy.f +++ /dev/null @@ -1,156 +0,0 @@ -*> \brief \b ZLACPY copies all or part of one two-dimensional array to another. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZLACPY + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZLACPY( UPLO, M, N, A, LDA, B, LDB ) -* -* .. Scalar Arguments .. -* CHARACTER UPLO -* INTEGER LDA, LDB, M, N -* .. -* .. Array Arguments .. -* COMPLEX*16 A( LDA, * ), B( LDB, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZLACPY copies all or part of a two-dimensional matrix A to another -*> matrix B. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> Specifies the part of the matrix A to be copied to B. -*> = 'U': Upper triangular part -*> = 'L': Lower triangular part -*> Otherwise: All of the matrix A -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix A. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is COMPLEX*16 array, dimension (LDA,N) -*> The m by n matrix A. If UPLO = 'U', only the upper trapezium -*> is accessed; if UPLO = 'L', only the lower trapezium is -*> accessed. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,M). -*> \endverbatim -*> -*> \param[out] B -*> \verbatim -*> B is COMPLEX*16 array, dimension (LDB,N) -*> On exit, B = A in the locations specified by UPLO. -*> \endverbatim -*> -*> \param[in] LDB -*> \verbatim -*> LDB is INTEGER -*> The leading dimension of the array B. LDB >= max(1,M). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16OTHERauxiliary -* -* ===================================================================== - SUBROUTINE ZLACPY( UPLO, M, N, A, LDA, B, LDB ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER UPLO - INTEGER LDA, LDB, M, N -* .. -* .. Array Arguments .. - COMPLEX*16 A( LDA, * ), B( LDB, * ) -* .. -* -* ===================================================================== -* -* .. Local Scalars .. - INTEGER I, J -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. Intrinsic Functions .. - INTRINSIC MIN -* .. -* .. Executable Statements .. -* - IF( LSAME( UPLO, 'U' ) ) THEN - DO 20 J = 1, N - DO 10 I = 1, MIN( J, M ) - B( I, J ) = A( I, J ) - 10 CONTINUE - 20 CONTINUE -* - ELSE IF( LSAME( UPLO, 'L' ) ) THEN - DO 40 J = 1, N - DO 30 I = J, M - B( I, J ) = A( I, J ) - 30 CONTINUE - 40 CONTINUE -* - ELSE - DO 60 J = 1, N - DO 50 I = 1, M - B( I, J ) = A( I, J ) - 50 CONTINUE - 60 CONTINUE - END IF -* - RETURN -* -* End of ZLACPY -* - END diff --git a/lib/linalg/fortran/zlacrm.f b/lib/linalg/fortran/zlacrm.f deleted file mode 100644 index ce8b9b02c5..0000000000 --- a/lib/linalg/fortran/zlacrm.f +++ /dev/null @@ -1,182 +0,0 @@ -*> \brief \b ZLACRM multiplies a complex matrix by a square real matrix. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZLACRM + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZLACRM( M, N, A, LDA, B, LDB, C, LDC, RWORK ) -* -* .. Scalar Arguments .. -* INTEGER LDA, LDB, LDC, M, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION B( LDB, * ), RWORK( * ) -* COMPLEX*16 A( LDA, * ), C( LDC, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZLACRM performs a very simple matrix-matrix multiplication: -*> C := A * B, -*> where A is M by N and complex; B is N by N and real; -*> C is M by N and complex. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix A and of the matrix C. -*> M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns and rows of the matrix B and -*> the number of columns of the matrix C. -*> N >= 0. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is COMPLEX*16 array, dimension (LDA, N) -*> On entry, A contains the M by N matrix A. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >=max(1,M). -*> \endverbatim -*> -*> \param[in] B -*> \verbatim -*> B is DOUBLE PRECISION array, dimension (LDB, N) -*> On entry, B contains the N by N matrix B. -*> \endverbatim -*> -*> \param[in] LDB -*> \verbatim -*> LDB is INTEGER -*> The leading dimension of the array B. LDB >=max(1,N). -*> \endverbatim -*> -*> \param[out] C -*> \verbatim -*> C is COMPLEX*16 array, dimension (LDC, N) -*> On exit, C contains the M by N matrix C. -*> \endverbatim -*> -*> \param[in] LDC -*> \verbatim -*> LDC is INTEGER -*> The leading dimension of the array C. LDC >=max(1,N). -*> \endverbatim -*> -*> \param[out] RWORK -*> \verbatim -*> RWORK is DOUBLE PRECISION array, dimension (2*M*N) -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16OTHERauxiliary -* -* ===================================================================== - SUBROUTINE ZLACRM( M, N, A, LDA, B, LDB, C, LDC, RWORK ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER LDA, LDB, LDC, M, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION B( LDB, * ), RWORK( * ) - COMPLEX*16 A( LDA, * ), C( LDC, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE, ZERO - PARAMETER ( ONE = 1.0D0, ZERO = 0.0D0 ) -* .. -* .. Local Scalars .. - INTEGER I, J, L -* .. -* .. Intrinsic Functions .. - INTRINSIC DBLE, DCMPLX, DIMAG -* .. -* .. External Subroutines .. - EXTERNAL DGEMM -* .. -* .. Executable Statements .. -* -* Quick return if possible. -* - IF( ( M.EQ.0 ) .OR. ( N.EQ.0 ) ) - $ RETURN -* - DO 20 J = 1, N - DO 10 I = 1, M - RWORK( ( J-1 )*M+I ) = DBLE( A( I, J ) ) - 10 CONTINUE - 20 CONTINUE -* - L = M*N + 1 - CALL DGEMM( 'N', 'N', M, N, N, ONE, RWORK, M, B, LDB, ZERO, - $ RWORK( L ), M ) - DO 40 J = 1, N - DO 30 I = 1, M - C( I, J ) = RWORK( L+( J-1 )*M+I-1 ) - 30 CONTINUE - 40 CONTINUE -* - DO 60 J = 1, N - DO 50 I = 1, M - RWORK( ( J-1 )*M+I ) = DIMAG( A( I, J ) ) - 50 CONTINUE - 60 CONTINUE - CALL DGEMM( 'N', 'N', M, N, N, ONE, RWORK, M, B, LDB, ZERO, - $ RWORK( L ), M ) - DO 80 J = 1, N - DO 70 I = 1, M - C( I, J ) = DCMPLX( DBLE( C( I, J ) ), - $ RWORK( L+( J-1 )*M+I-1 ) ) - 70 CONTINUE - 80 CONTINUE -* - RETURN -* -* End of ZLACRM -* - END diff --git a/lib/linalg/fortran/zladiv.f b/lib/linalg/fortran/zladiv.f deleted file mode 100644 index ae111d73d6..0000000000 --- a/lib/linalg/fortran/zladiv.f +++ /dev/null @@ -1,94 +0,0 @@ -*> \brief \b ZLADIV performs complex division in real arithmetic, avoiding unnecessary overflow. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZLADIV + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* COMPLEX*16 FUNCTION ZLADIV( X, Y ) -* -* .. Scalar Arguments .. -* COMPLEX*16 X, Y -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZLADIV := X / Y, where X and Y are complex. The computation of X / Y -*> will not overflow on an intermediary step unless the results -*> overflows. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] X -*> \verbatim -*> X is COMPLEX*16 -*> \endverbatim -*> -*> \param[in] Y -*> \verbatim -*> Y is COMPLEX*16 -*> The complex scalars X and Y. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16OTHERauxiliary -* -* ===================================================================== - COMPLEX*16 FUNCTION ZLADIV( X, Y ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - COMPLEX*16 X, Y -* .. -* -* ===================================================================== -* -* .. Local Scalars .. - DOUBLE PRECISION ZI, ZR -* .. -* .. External Subroutines .. - EXTERNAL DLADIV -* .. -* .. Intrinsic Functions .. - INTRINSIC DBLE, DCMPLX, DIMAG -* .. -* .. Executable Statements .. -* - CALL DLADIV( DBLE( X ), DIMAG( X ), DBLE( Y ), DIMAG( Y ), ZR, - $ ZI ) - ZLADIV = DCMPLX( ZR, ZI ) -* - RETURN -* -* End of ZLADIV -* - END diff --git a/lib/linalg/fortran/zlaed0.f b/lib/linalg/fortran/zlaed0.f deleted file mode 100644 index c4deac037a..0000000000 --- a/lib/linalg/fortran/zlaed0.f +++ /dev/null @@ -1,368 +0,0 @@ -*> \brief \b ZLAED0 used by ZSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZLAED0 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZLAED0( QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, RWORK, -* IWORK, INFO ) -* -* .. Scalar Arguments .. -* INTEGER INFO, LDQ, LDQS, N, QSIZ -* .. -* .. Array Arguments .. -* INTEGER IWORK( * ) -* DOUBLE PRECISION D( * ), E( * ), RWORK( * ) -* COMPLEX*16 Q( LDQ, * ), QSTORE( LDQS, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> Using the divide and conquer method, ZLAED0 computes all eigenvalues -*> of a symmetric tridiagonal matrix which is one diagonal block of -*> those from reducing a dense or band Hermitian matrix and -*> corresponding eigenvectors of the dense or band matrix. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] QSIZ -*> \verbatim -*> QSIZ is INTEGER -*> The dimension of the unitary matrix used to reduce -*> the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The dimension of the symmetric tridiagonal matrix. N >= 0. -*> \endverbatim -*> -*> \param[in,out] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension (N) -*> On entry, the diagonal elements of the tridiagonal matrix. -*> On exit, the eigenvalues in ascending order. -*> \endverbatim -*> -*> \param[in,out] E -*> \verbatim -*> E is DOUBLE PRECISION array, dimension (N-1) -*> On entry, the off-diagonal elements of the tridiagonal matrix. -*> On exit, E has been destroyed. -*> \endverbatim -*> -*> \param[in,out] Q -*> \verbatim -*> Q is COMPLEX*16 array, dimension (LDQ,N) -*> On entry, Q must contain an QSIZ x N matrix whose columns -*> unitarily orthonormal. It is a part of the unitary matrix -*> that reduces the full dense Hermitian matrix to a -*> (reducible) symmetric tridiagonal matrix. -*> \endverbatim -*> -*> \param[in] LDQ -*> \verbatim -*> LDQ is INTEGER -*> The leading dimension of the array Q. LDQ >= max(1,N). -*> \endverbatim -*> -*> \param[out] IWORK -*> \verbatim -*> IWORK is INTEGER array, -*> the dimension of IWORK must be at least -*> 6 + 6*N + 5*N*lg N -*> ( lg( N ) = smallest integer k -*> such that 2^k >= N ) -*> \endverbatim -*> -*> \param[out] RWORK -*> \verbatim -*> RWORK is DOUBLE PRECISION array, -*> dimension (1 + 3*N + 2*N*lg N + 3*N**2) -*> ( lg( N ) = smallest integer k -*> such that 2^k >= N ) -*> \endverbatim -*> -*> \param[out] QSTORE -*> \verbatim -*> QSTORE is COMPLEX*16 array, dimension (LDQS, N) -*> Used to store parts of -*> the eigenvector matrix when the updating matrix multiplies -*> take place. -*> \endverbatim -*> -*> \param[in] LDQS -*> \verbatim -*> LDQS is INTEGER -*> The leading dimension of the array QSTORE. -*> LDQS >= max(1,N). -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit. -*> < 0: if INFO = -i, the i-th argument had an illegal value. -*> > 0: The algorithm failed to compute an eigenvalue while -*> working on the submatrix lying in rows and columns -*> INFO/(N+1) through mod(INFO,N+1). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16OTHERcomputational -* -* ===================================================================== - SUBROUTINE ZLAED0( QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, RWORK, - $ IWORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INFO, LDQ, LDQS, N, QSIZ -* .. -* .. Array Arguments .. - INTEGER IWORK( * ) - DOUBLE PRECISION D( * ), E( * ), RWORK( * ) - COMPLEX*16 Q( LDQ, * ), QSTORE( LDQS, * ) -* .. -* -* ===================================================================== -* -* Warning: N could be as big as QSIZ! -* -* .. Parameters .. - DOUBLE PRECISION TWO - PARAMETER ( TWO = 2.D+0 ) -* .. -* .. Local Scalars .. - INTEGER CURLVL, CURPRB, CURR, I, IGIVCL, IGIVNM, - $ IGIVPT, INDXQ, IPERM, IPRMPT, IQ, IQPTR, IWREM, - $ J, K, LGN, LL, MATSIZ, MSD2, SMLSIZ, SMM1, - $ SPM1, SPM2, SUBMAT, SUBPBS, TLVLS - DOUBLE PRECISION TEMP -* .. -* .. External Subroutines .. - EXTERNAL DCOPY, DSTEQR, XERBLA, ZCOPY, ZLACRM, ZLAED7 -* .. -* .. External Functions .. - INTEGER ILAENV - EXTERNAL ILAENV -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, DBLE, INT, LOG, MAX -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 -* -* IF( ICOMPQ .LT. 0 .OR. ICOMPQ .GT. 2 ) THEN -* INFO = -1 -* ELSE IF( ( ICOMPQ .EQ. 1 ) .AND. ( QSIZ .LT. MAX( 0, N ) ) ) -* $ THEN - IF( QSIZ.LT.MAX( 0, N ) ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN - INFO = -6 - ELSE IF( LDQS.LT.MAX( 1, N ) ) THEN - INFO = -8 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'ZLAED0', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( N.EQ.0 ) - $ RETURN -* - SMLSIZ = ILAENV( 9, 'ZLAED0', ' ', 0, 0, 0, 0 ) -* -* Determine the size and placement of the submatrices, and save in -* the leading elements of IWORK. -* - IWORK( 1 ) = N - SUBPBS = 1 - TLVLS = 0 - 10 CONTINUE - IF( IWORK( SUBPBS ).GT.SMLSIZ ) THEN - DO 20 J = SUBPBS, 1, -1 - IWORK( 2*J ) = ( IWORK( J )+1 ) / 2 - IWORK( 2*J-1 ) = IWORK( J ) / 2 - 20 CONTINUE - TLVLS = TLVLS + 1 - SUBPBS = 2*SUBPBS - GO TO 10 - END IF - DO 30 J = 2, SUBPBS - IWORK( J ) = IWORK( J ) + IWORK( J-1 ) - 30 CONTINUE -* -* Divide the matrix into SUBPBS submatrices of size at most SMLSIZ+1 -* using rank-1 modifications (cuts). -* - SPM1 = SUBPBS - 1 - DO 40 I = 1, SPM1 - SUBMAT = IWORK( I ) + 1 - SMM1 = SUBMAT - 1 - D( SMM1 ) = D( SMM1 ) - ABS( E( SMM1 ) ) - D( SUBMAT ) = D( SUBMAT ) - ABS( E( SMM1 ) ) - 40 CONTINUE -* - INDXQ = 4*N + 3 -* -* Set up workspaces for eigenvalues only/accumulate new vectors -* routine -* - TEMP = LOG( DBLE( N ) ) / LOG( TWO ) - LGN = INT( TEMP ) - IF( 2**LGN.LT.N ) - $ LGN = LGN + 1 - IF( 2**LGN.LT.N ) - $ LGN = LGN + 1 - IPRMPT = INDXQ + N + 1 - IPERM = IPRMPT + N*LGN - IQPTR = IPERM + N*LGN - IGIVPT = IQPTR + N + 2 - IGIVCL = IGIVPT + N*LGN -* - IGIVNM = 1 - IQ = IGIVNM + 2*N*LGN - IWREM = IQ + N**2 + 1 -* Initialize pointers - DO 50 I = 0, SUBPBS - IWORK( IPRMPT+I ) = 1 - IWORK( IGIVPT+I ) = 1 - 50 CONTINUE - IWORK( IQPTR ) = 1 -* -* Solve each submatrix eigenproblem at the bottom of the divide and -* conquer tree. -* - CURR = 0 - DO 70 I = 0, SPM1 - IF( I.EQ.0 ) THEN - SUBMAT = 1 - MATSIZ = IWORK( 1 ) - ELSE - SUBMAT = IWORK( I ) + 1 - MATSIZ = IWORK( I+1 ) - IWORK( I ) - END IF - LL = IQ - 1 + IWORK( IQPTR+CURR ) - CALL DSTEQR( 'I', MATSIZ, D( SUBMAT ), E( SUBMAT ), - $ RWORK( LL ), MATSIZ, RWORK, INFO ) - CALL ZLACRM( QSIZ, MATSIZ, Q( 1, SUBMAT ), LDQ, RWORK( LL ), - $ MATSIZ, QSTORE( 1, SUBMAT ), LDQS, - $ RWORK( IWREM ) ) - IWORK( IQPTR+CURR+1 ) = IWORK( IQPTR+CURR ) + MATSIZ**2 - CURR = CURR + 1 - IF( INFO.GT.0 ) THEN - INFO = SUBMAT*( N+1 ) + SUBMAT + MATSIZ - 1 - RETURN - END IF - K = 1 - DO 60 J = SUBMAT, IWORK( I+1 ) - IWORK( INDXQ+J ) = K - K = K + 1 - 60 CONTINUE - 70 CONTINUE -* -* Successively merge eigensystems of adjacent submatrices -* into eigensystem for the corresponding larger matrix. -* -* while ( SUBPBS > 1 ) -* - CURLVL = 1 - 80 CONTINUE - IF( SUBPBS.GT.1 ) THEN - SPM2 = SUBPBS - 2 - DO 90 I = 0, SPM2, 2 - IF( I.EQ.0 ) THEN - SUBMAT = 1 - MATSIZ = IWORK( 2 ) - MSD2 = IWORK( 1 ) - CURPRB = 0 - ELSE - SUBMAT = IWORK( I ) + 1 - MATSIZ = IWORK( I+2 ) - IWORK( I ) - MSD2 = MATSIZ / 2 - CURPRB = CURPRB + 1 - END IF -* -* Merge lower order eigensystems (of size MSD2 and MATSIZ - MSD2) -* into an eigensystem of size MATSIZ. ZLAED7 handles the case -* when the eigenvectors of a full or band Hermitian matrix (which -* was reduced to tridiagonal form) are desired. -* -* I am free to use Q as a valuable working space until Loop 150. -* - CALL ZLAED7( MATSIZ, MSD2, QSIZ, TLVLS, CURLVL, CURPRB, - $ D( SUBMAT ), QSTORE( 1, SUBMAT ), LDQS, - $ E( SUBMAT+MSD2-1 ), IWORK( INDXQ+SUBMAT ), - $ RWORK( IQ ), IWORK( IQPTR ), IWORK( IPRMPT ), - $ IWORK( IPERM ), IWORK( IGIVPT ), - $ IWORK( IGIVCL ), RWORK( IGIVNM ), - $ Q( 1, SUBMAT ), RWORK( IWREM ), - $ IWORK( SUBPBS+1 ), INFO ) - IF( INFO.GT.0 ) THEN - INFO = SUBMAT*( N+1 ) + SUBMAT + MATSIZ - 1 - RETURN - END IF - IWORK( I / 2+1 ) = IWORK( I+2 ) - 90 CONTINUE - SUBPBS = SUBPBS / 2 - CURLVL = CURLVL + 1 - GO TO 80 - END IF -* -* end while -* -* Re-merge the eigenvalues/vectors which were deflated at the final -* merge step. -* - DO 100 I = 1, N - J = IWORK( INDXQ+I ) - RWORK( I ) = D( J ) - CALL ZCOPY( QSIZ, QSTORE( 1, J ), 1, Q( 1, I ), 1 ) - 100 CONTINUE - CALL DCOPY( N, RWORK, 1, D, 1 ) -* - RETURN -* -* End of ZLAED0 -* - END diff --git a/lib/linalg/fortran/zlaed7.f b/lib/linalg/fortran/zlaed7.f deleted file mode 100644 index 83f32d8b81..0000000000 --- a/lib/linalg/fortran/zlaed7.f +++ /dev/null @@ -1,382 +0,0 @@ -*> \brief \b ZLAED7 used by ZSTEDC. Computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. Used when the original matrix is dense. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZLAED7 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZLAED7( N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, -* LDQ, RHO, INDXQ, QSTORE, QPTR, PRMPTR, PERM, -* GIVPTR, GIVCOL, GIVNUM, WORK, RWORK, IWORK, -* INFO ) -* -* .. Scalar Arguments .. -* INTEGER CURLVL, CURPBM, CUTPNT, INFO, LDQ, N, QSIZ, -* $ TLVLS -* DOUBLE PRECISION RHO -* .. -* .. Array Arguments .. -* INTEGER GIVCOL( 2, * ), GIVPTR( * ), INDXQ( * ), -* $ IWORK( * ), PERM( * ), PRMPTR( * ), QPTR( * ) -* DOUBLE PRECISION D( * ), GIVNUM( 2, * ), QSTORE( * ), RWORK( * ) -* COMPLEX*16 Q( LDQ, * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZLAED7 computes the updated eigensystem of a diagonal -*> matrix after modification by a rank-one symmetric matrix. This -*> routine is used only for the eigenproblem which requires all -*> eigenvalues and optionally eigenvectors of a dense or banded -*> Hermitian matrix that has been reduced to tridiagonal form. -*> -*> T = Q(in) ( D(in) + RHO * Z*Z**H ) Q**H(in) = Q(out) * D(out) * Q**H(out) -*> -*> where Z = Q**Hu, u is a vector of length N with ones in the -*> CUTPNT and CUTPNT + 1 th elements and zeros elsewhere. -*> -*> The eigenvectors of the original matrix are stored in Q, and the -*> eigenvalues are in D. The algorithm consists of three stages: -*> -*> The first stage consists of deflating the size of the problem -*> when there are multiple eigenvalues or if there is a zero in -*> the Z vector. For each such occurrence the dimension of the -*> secular equation problem is reduced by one. This stage is -*> performed by the routine DLAED2. -*> -*> The second stage consists of calculating the updated -*> eigenvalues. This is done by finding the roots of the secular -*> equation via the routine DLAED4 (as called by SLAED3). -*> This routine also calculates the eigenvectors of the current -*> problem. -*> -*> The final stage consists of computing the updated eigenvectors -*> directly using the updated eigenvalues. The eigenvectors for -*> the current problem are multiplied with the eigenvectors from -*> the overall problem. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The dimension of the symmetric tridiagonal matrix. N >= 0. -*> \endverbatim -*> -*> \param[in] CUTPNT -*> \verbatim -*> CUTPNT is INTEGER -*> Contains the location of the last eigenvalue in the leading -*> sub-matrix. min(1,N) <= CUTPNT <= N. -*> \endverbatim -*> -*> \param[in] QSIZ -*> \verbatim -*> QSIZ is INTEGER -*> The dimension of the unitary matrix used to reduce -*> the full matrix to tridiagonal form. QSIZ >= N. -*> \endverbatim -*> -*> \param[in] TLVLS -*> \verbatim -*> TLVLS is INTEGER -*> The total number of merging levels in the overall divide and -*> conquer tree. -*> \endverbatim -*> -*> \param[in] CURLVL -*> \verbatim -*> CURLVL is INTEGER -*> The current level in the overall merge routine, -*> 0 <= curlvl <= tlvls. -*> \endverbatim -*> -*> \param[in] CURPBM -*> \verbatim -*> CURPBM is INTEGER -*> The current problem in the current level in the overall -*> merge routine (counting from upper left to lower right). -*> \endverbatim -*> -*> \param[in,out] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension (N) -*> On entry, the eigenvalues of the rank-1-perturbed matrix. -*> On exit, the eigenvalues of the repaired matrix. -*> \endverbatim -*> -*> \param[in,out] Q -*> \verbatim -*> Q is COMPLEX*16 array, dimension (LDQ,N) -*> On entry, the eigenvectors of the rank-1-perturbed matrix. -*> On exit, the eigenvectors of the repaired tridiagonal matrix. -*> \endverbatim -*> -*> \param[in] LDQ -*> \verbatim -*> LDQ is INTEGER -*> The leading dimension of the array Q. LDQ >= max(1,N). -*> \endverbatim -*> -*> \param[in] RHO -*> \verbatim -*> RHO is DOUBLE PRECISION -*> Contains the subdiagonal element used to create the rank-1 -*> modification. -*> \endverbatim -*> -*> \param[out] INDXQ -*> \verbatim -*> INDXQ is INTEGER array, dimension (N) -*> This contains the permutation which will reintegrate the -*> subproblem just solved back into sorted order, -*> ie. D( INDXQ( I = 1, N ) ) will be in ascending order. -*> \endverbatim -*> -*> \param[out] IWORK -*> \verbatim -*> IWORK is INTEGER array, dimension (4*N) -*> \endverbatim -*> -*> \param[out] RWORK -*> \verbatim -*> RWORK is DOUBLE PRECISION array, -*> dimension (3*N+2*QSIZ*N) -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is COMPLEX*16 array, dimension (QSIZ*N) -*> \endverbatim -*> -*> \param[in,out] QSTORE -*> \verbatim -*> QSTORE is DOUBLE PRECISION array, dimension (N**2+1) -*> Stores eigenvectors of submatrices encountered during -*> divide and conquer, packed together. QPTR points to -*> beginning of the submatrices. -*> \endverbatim -*> -*> \param[in,out] QPTR -*> \verbatim -*> QPTR is INTEGER array, dimension (N+2) -*> List of indices pointing to beginning of submatrices stored -*> in QSTORE. The submatrices are numbered starting at the -*> bottom left of the divide and conquer tree, from left to -*> right and bottom to top. -*> \endverbatim -*> -*> \param[in] PRMPTR -*> \verbatim -*> PRMPTR is INTEGER array, dimension (N lg N) -*> Contains a list of pointers which indicate where in PERM a -*> level's permutation is stored. PRMPTR(i+1) - PRMPTR(i) -*> indicates the size of the permutation and also the size of -*> the full, non-deflated problem. -*> \endverbatim -*> -*> \param[in] PERM -*> \verbatim -*> PERM is INTEGER array, dimension (N lg N) -*> Contains the permutations (from deflation and sorting) to be -*> applied to each eigenblock. -*> \endverbatim -*> -*> \param[in] GIVPTR -*> \verbatim -*> GIVPTR is INTEGER array, dimension (N lg N) -*> Contains a list of pointers which indicate where in GIVCOL a -*> level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i) -*> indicates the number of Givens rotations. -*> \endverbatim -*> -*> \param[in] GIVCOL -*> \verbatim -*> GIVCOL is INTEGER array, dimension (2, N lg N) -*> Each pair of numbers indicates a pair of columns to take place -*> in a Givens rotation. -*> \endverbatim -*> -*> \param[in] GIVNUM -*> \verbatim -*> GIVNUM is DOUBLE PRECISION array, dimension (2, N lg N) -*> Each number indicates the S value to be used in the -*> corresponding Givens rotation. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit. -*> < 0: if INFO = -i, the i-th argument had an illegal value. -*> > 0: if INFO = 1, an eigenvalue did not converge -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16OTHERcomputational -* -* ===================================================================== - SUBROUTINE ZLAED7( N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, - $ LDQ, RHO, INDXQ, QSTORE, QPTR, PRMPTR, PERM, - $ GIVPTR, GIVCOL, GIVNUM, WORK, RWORK, IWORK, - $ INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER CURLVL, CURPBM, CUTPNT, INFO, LDQ, N, QSIZ, - $ TLVLS - DOUBLE PRECISION RHO -* .. -* .. Array Arguments .. - INTEGER GIVCOL( 2, * ), GIVPTR( * ), INDXQ( * ), - $ IWORK( * ), PERM( * ), PRMPTR( * ), QPTR( * ) - DOUBLE PRECISION D( * ), GIVNUM( 2, * ), QSTORE( * ), RWORK( * ) - COMPLEX*16 Q( LDQ, * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Local Scalars .. - INTEGER COLTYP, CURR, I, IDLMDA, INDX, - $ INDXC, INDXP, IQ, IW, IZ, K, N1, N2, PTR -* .. -* .. External Subroutines .. - EXTERNAL DLAED9, DLAEDA, DLAMRG, XERBLA, ZLACRM, ZLAED8 -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, MIN -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 -* -* IF( ICOMPQ.LT.0 .OR. ICOMPQ.GT.1 ) THEN -* INFO = -1 -* ELSE IF( N.LT.0 ) THEN - IF( N.LT.0 ) THEN - INFO = -1 - ELSE IF( MIN( 1, N ).GT.CUTPNT .OR. N.LT.CUTPNT ) THEN - INFO = -2 - ELSE IF( QSIZ.LT.N ) THEN - INFO = -3 - ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN - INFO = -9 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'ZLAED7', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( N.EQ.0 ) - $ RETURN -* -* The following values are for bookkeeping purposes only. They are -* integer pointers which indicate the portion of the workspace -* used by a particular array in DLAED2 and SLAED3. -* - IZ = 1 - IDLMDA = IZ + N - IW = IDLMDA + N - IQ = IW + N -* - INDX = 1 - INDXC = INDX + N - COLTYP = INDXC + N - INDXP = COLTYP + N -* -* Form the z-vector which consists of the last row of Q_1 and the -* first row of Q_2. -* - PTR = 1 + 2**TLVLS - DO 10 I = 1, CURLVL - 1 - PTR = PTR + 2**( TLVLS-I ) - 10 CONTINUE - CURR = PTR + CURPBM - CALL DLAEDA( N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR, - $ GIVCOL, GIVNUM, QSTORE, QPTR, RWORK( IZ ), - $ RWORK( IZ+N ), INFO ) -* -* When solving the final problem, we no longer need the stored data, -* so we will overwrite the data from this level onto the previously -* used storage space. -* - IF( CURLVL.EQ.TLVLS ) THEN - QPTR( CURR ) = 1 - PRMPTR( CURR ) = 1 - GIVPTR( CURR ) = 1 - END IF -* -* Sort and Deflate eigenvalues. -* - CALL ZLAED8( K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, RWORK( IZ ), - $ RWORK( IDLMDA ), WORK, QSIZ, RWORK( IW ), - $ IWORK( INDXP ), IWORK( INDX ), INDXQ, - $ PERM( PRMPTR( CURR ) ), GIVPTR( CURR+1 ), - $ GIVCOL( 1, GIVPTR( CURR ) ), - $ GIVNUM( 1, GIVPTR( CURR ) ), INFO ) - PRMPTR( CURR+1 ) = PRMPTR( CURR ) + N - GIVPTR( CURR+1 ) = GIVPTR( CURR+1 ) + GIVPTR( CURR ) -* -* Solve Secular Equation. -* - IF( K.NE.0 ) THEN - CALL DLAED9( K, 1, K, N, D, RWORK( IQ ), K, RHO, - $ RWORK( IDLMDA ), RWORK( IW ), - $ QSTORE( QPTR( CURR ) ), K, INFO ) - CALL ZLACRM( QSIZ, K, WORK, QSIZ, QSTORE( QPTR( CURR ) ), K, Q, - $ LDQ, RWORK( IQ ) ) - QPTR( CURR+1 ) = QPTR( CURR ) + K**2 - IF( INFO.NE.0 ) THEN - RETURN - END IF -* -* Prepare the INDXQ sorting premutation. -* - N1 = K - N2 = N - K - CALL DLAMRG( N1, N2, D, 1, -1, INDXQ ) - ELSE - QPTR( CURR+1 ) = QPTR( CURR ) - DO 20 I = 1, N - INDXQ( I ) = I - 20 CONTINUE - END IF -* - RETURN -* -* End of ZLAED7 -* - END diff --git a/lib/linalg/fortran/zlaed8.f b/lib/linalg/fortran/zlaed8.f deleted file mode 100644 index 995a673de9..0000000000 --- a/lib/linalg/fortran/zlaed8.f +++ /dev/null @@ -1,483 +0,0 @@ -*> \brief \b ZLAED8 used by ZSTEDC. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZLAED8 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZLAED8( K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA, -* Q2, LDQ2, W, INDXP, INDX, INDXQ, PERM, GIVPTR, -* GIVCOL, GIVNUM, INFO ) -* -* .. Scalar Arguments .. -* INTEGER CUTPNT, GIVPTR, INFO, K, LDQ, LDQ2, N, QSIZ -* DOUBLE PRECISION RHO -* .. -* .. Array Arguments .. -* INTEGER GIVCOL( 2, * ), INDX( * ), INDXP( * ), -* $ INDXQ( * ), PERM( * ) -* DOUBLE PRECISION D( * ), DLAMDA( * ), GIVNUM( 2, * ), W( * ), -* $ Z( * ) -* COMPLEX*16 Q( LDQ, * ), Q2( LDQ2, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZLAED8 merges the two sets of eigenvalues together into a single -*> sorted set. Then it tries to deflate the size of the problem. -*> There are two ways in which deflation can occur: when two or more -*> eigenvalues are close together or if there is a tiny element in the -*> Z vector. For each such occurrence the order of the related secular -*> equation problem is reduced by one. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[out] K -*> \verbatim -*> K is INTEGER -*> Contains the number of non-deflated eigenvalues. -*> This is the order of the related secular equation. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The dimension of the symmetric tridiagonal matrix. N >= 0. -*> \endverbatim -*> -*> \param[in] QSIZ -*> \verbatim -*> QSIZ is INTEGER -*> The dimension of the unitary matrix used to reduce -*> the dense or band matrix to tridiagonal form. -*> QSIZ >= N if ICOMPQ = 1. -*> \endverbatim -*> -*> \param[in,out] Q -*> \verbatim -*> Q is COMPLEX*16 array, dimension (LDQ,N) -*> On entry, Q contains the eigenvectors of the partially solved -*> system which has been previously updated in matrix -*> multiplies with other partially solved eigensystems. -*> On exit, Q contains the trailing (N-K) updated eigenvectors -*> (those which were deflated) in its last N-K columns. -*> \endverbatim -*> -*> \param[in] LDQ -*> \verbatim -*> LDQ is INTEGER -*> The leading dimension of the array Q. LDQ >= max( 1, N ). -*> \endverbatim -*> -*> \param[in,out] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension (N) -*> On entry, D contains the eigenvalues of the two submatrices to -*> be combined. On exit, D contains the trailing (N-K) updated -*> eigenvalues (those which were deflated) sorted into increasing -*> order. -*> \endverbatim -*> -*> \param[in,out] RHO -*> \verbatim -*> RHO is DOUBLE PRECISION -*> Contains the off diagonal element associated with the rank-1 -*> cut which originally split the two submatrices which are now -*> being recombined. RHO is modified during the computation to -*> the value required by DLAED3. -*> \endverbatim -*> -*> \param[in] CUTPNT -*> \verbatim -*> CUTPNT is INTEGER -*> Contains the location of the last eigenvalue in the leading -*> sub-matrix. MIN(1,N) <= CUTPNT <= N. -*> \endverbatim -*> -*> \param[in] Z -*> \verbatim -*> Z is DOUBLE PRECISION array, dimension (N) -*> On input this vector contains the updating vector (the last -*> row of the first sub-eigenvector matrix and the first row of -*> the second sub-eigenvector matrix). The contents of Z are -*> destroyed during the updating process. -*> \endverbatim -*> -*> \param[out] DLAMDA -*> \verbatim -*> DLAMDA is DOUBLE PRECISION array, dimension (N) -*> Contains a copy of the first K eigenvalues which will be used -*> by DLAED3 to form the secular equation. -*> \endverbatim -*> -*> \param[out] Q2 -*> \verbatim -*> Q2 is COMPLEX*16 array, dimension (LDQ2,N) -*> If ICOMPQ = 0, Q2 is not referenced. Otherwise, -*> Contains a copy of the first K eigenvectors which will be used -*> by DLAED7 in a matrix multiply (DGEMM) to update the new -*> eigenvectors. -*> \endverbatim -*> -*> \param[in] LDQ2 -*> \verbatim -*> LDQ2 is INTEGER -*> The leading dimension of the array Q2. LDQ2 >= max( 1, N ). -*> \endverbatim -*> -*> \param[out] W -*> \verbatim -*> W is DOUBLE PRECISION array, dimension (N) -*> This will hold the first k values of the final -*> deflation-altered z-vector and will be passed to DLAED3. -*> \endverbatim -*> -*> \param[out] INDXP -*> \verbatim -*> INDXP is INTEGER array, dimension (N) -*> This will contain the permutation used to place deflated -*> values of D at the end of the array. On output INDXP(1:K) -*> points to the nondeflated D-values and INDXP(K+1:N) -*> points to the deflated eigenvalues. -*> \endverbatim -*> -*> \param[out] INDX -*> \verbatim -*> INDX is INTEGER array, dimension (N) -*> This will contain the permutation used to sort the contents of -*> D into ascending order. -*> \endverbatim -*> -*> \param[in] INDXQ -*> \verbatim -*> INDXQ is INTEGER array, dimension (N) -*> This contains the permutation which separately sorts the two -*> sub-problems in D into ascending order. Note that elements in -*> the second half of this permutation must first have CUTPNT -*> added to their values in order to be accurate. -*> \endverbatim -*> -*> \param[out] PERM -*> \verbatim -*> PERM is INTEGER array, dimension (N) -*> Contains the permutations (from deflation and sorting) to be -*> applied to each eigenblock. -*> \endverbatim -*> -*> \param[out] GIVPTR -*> \verbatim -*> GIVPTR is INTEGER -*> Contains the number of Givens rotations which took place in -*> this subproblem. -*> \endverbatim -*> -*> \param[out] GIVCOL -*> \verbatim -*> GIVCOL is INTEGER array, dimension (2, N) -*> Each pair of numbers indicates a pair of columns to take place -*> in a Givens rotation. -*> \endverbatim -*> -*> \param[out] GIVNUM -*> \verbatim -*> GIVNUM is DOUBLE PRECISION array, dimension (2, N) -*> Each number indicates the S value to be used in the -*> corresponding Givens rotation. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit. -*> < 0: if INFO = -i, the i-th argument had an illegal value. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16OTHERcomputational -* -* ===================================================================== - SUBROUTINE ZLAED8( K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA, - $ Q2, LDQ2, W, INDXP, INDX, INDXQ, PERM, GIVPTR, - $ GIVCOL, GIVNUM, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER CUTPNT, GIVPTR, INFO, K, LDQ, LDQ2, N, QSIZ - DOUBLE PRECISION RHO -* .. -* .. Array Arguments .. - INTEGER GIVCOL( 2, * ), INDX( * ), INDXP( * ), - $ INDXQ( * ), PERM( * ) - DOUBLE PRECISION D( * ), DLAMDA( * ), GIVNUM( 2, * ), W( * ), - $ Z( * ) - COMPLEX*16 Q( LDQ, * ), Q2( LDQ2, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION MONE, ZERO, ONE, TWO, EIGHT - PARAMETER ( MONE = -1.0D0, ZERO = 0.0D0, ONE = 1.0D0, - $ TWO = 2.0D0, EIGHT = 8.0D0 ) -* .. -* .. Local Scalars .. - INTEGER I, IMAX, J, JLAM, JMAX, JP, K2, N1, N1P1, N2 - DOUBLE PRECISION C, EPS, S, T, TAU, TOL -* .. -* .. External Functions .. - INTEGER IDAMAX - DOUBLE PRECISION DLAMCH, DLAPY2 - EXTERNAL IDAMAX, DLAMCH, DLAPY2 -* .. -* .. External Subroutines .. - EXTERNAL DCOPY, DLAMRG, DSCAL, XERBLA, ZCOPY, ZDROT, - $ ZLACPY -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, MAX, MIN, SQRT -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 -* - IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( QSIZ.LT.N ) THEN - INFO = -3 - ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN - INFO = -5 - ELSE IF( CUTPNT.LT.MIN( 1, N ) .OR. CUTPNT.GT.N ) THEN - INFO = -8 - ELSE IF( LDQ2.LT.MAX( 1, N ) ) THEN - INFO = -12 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'ZLAED8', -INFO ) - RETURN - END IF -* -* Need to initialize GIVPTR to O here in case of quick exit -* to prevent an unspecified code behavior (usually sigfault) -* when IWORK array on entry to *stedc is not zeroed -* (or at least some IWORK entries which used in *laed7 for GIVPTR). -* - GIVPTR = 0 -* -* Quick return if possible -* - IF( N.EQ.0 ) - $ RETURN -* - N1 = CUTPNT - N2 = N - N1 - N1P1 = N1 + 1 -* - IF( RHO.LT.ZERO ) THEN - CALL DSCAL( N2, MONE, Z( N1P1 ), 1 ) - END IF -* -* Normalize z so that norm(z) = 1 -* - T = ONE / SQRT( TWO ) - DO 10 J = 1, N - INDX( J ) = J - 10 CONTINUE - CALL DSCAL( N, T, Z, 1 ) - RHO = ABS( TWO*RHO ) -* -* Sort the eigenvalues into increasing order -* - DO 20 I = CUTPNT + 1, N - INDXQ( I ) = INDXQ( I ) + CUTPNT - 20 CONTINUE - DO 30 I = 1, N - DLAMDA( I ) = D( INDXQ( I ) ) - W( I ) = Z( INDXQ( I ) ) - 30 CONTINUE - I = 1 - J = CUTPNT + 1 - CALL DLAMRG( N1, N2, DLAMDA, 1, 1, INDX ) - DO 40 I = 1, N - D( I ) = DLAMDA( INDX( I ) ) - Z( I ) = W( INDX( I ) ) - 40 CONTINUE -* -* Calculate the allowable deflation tolerance -* - IMAX = IDAMAX( N, Z, 1 ) - JMAX = IDAMAX( N, D, 1 ) - EPS = DLAMCH( 'Epsilon' ) - TOL = EIGHT*EPS*ABS( D( JMAX ) ) -* -* If the rank-1 modifier is small enough, no more needs to be done -* -- except to reorganize Q so that its columns correspond with the -* elements in D. -* - IF( RHO*ABS( Z( IMAX ) ).LE.TOL ) THEN - K = 0 - DO 50 J = 1, N - PERM( J ) = INDXQ( INDX( J ) ) - CALL ZCOPY( QSIZ, Q( 1, PERM( J ) ), 1, Q2( 1, J ), 1 ) - 50 CONTINUE - CALL ZLACPY( 'A', QSIZ, N, Q2( 1, 1 ), LDQ2, Q( 1, 1 ), LDQ ) - RETURN - END IF -* -* If there are multiple eigenvalues then the problem deflates. Here -* the number of equal eigenvalues are found. As each equal -* eigenvalue is found, an elementary reflector is computed to rotate -* the corresponding eigensubspace so that the corresponding -* components of Z are zero in this new basis. -* - K = 0 - K2 = N + 1 - DO 60 J = 1, N - IF( RHO*ABS( Z( J ) ).LE.TOL ) THEN -* -* Deflate due to small z component. -* - K2 = K2 - 1 - INDXP( K2 ) = J - IF( J.EQ.N ) - $ GO TO 100 - ELSE - JLAM = J - GO TO 70 - END IF - 60 CONTINUE - 70 CONTINUE - J = J + 1 - IF( J.GT.N ) - $ GO TO 90 - IF( RHO*ABS( Z( J ) ).LE.TOL ) THEN -* -* Deflate due to small z component. -* - K2 = K2 - 1 - INDXP( K2 ) = J - ELSE -* -* Check if eigenvalues are close enough to allow deflation. -* - S = Z( JLAM ) - C = Z( J ) -* -* Find sqrt(a**2+b**2) without overflow or -* destructive underflow. -* - TAU = DLAPY2( C, S ) - T = D( J ) - D( JLAM ) - C = C / TAU - S = -S / TAU - IF( ABS( T*C*S ).LE.TOL ) THEN -* -* Deflation is possible. -* - Z( J ) = TAU - Z( JLAM ) = ZERO -* -* Record the appropriate Givens rotation -* - GIVPTR = GIVPTR + 1 - GIVCOL( 1, GIVPTR ) = INDXQ( INDX( JLAM ) ) - GIVCOL( 2, GIVPTR ) = INDXQ( INDX( J ) ) - GIVNUM( 1, GIVPTR ) = C - GIVNUM( 2, GIVPTR ) = S - CALL ZDROT( QSIZ, Q( 1, INDXQ( INDX( JLAM ) ) ), 1, - $ Q( 1, INDXQ( INDX( J ) ) ), 1, C, S ) - T = D( JLAM )*C*C + D( J )*S*S - D( J ) = D( JLAM )*S*S + D( J )*C*C - D( JLAM ) = T - K2 = K2 - 1 - I = 1 - 80 CONTINUE - IF( K2+I.LE.N ) THEN - IF( D( JLAM ).LT.D( INDXP( K2+I ) ) ) THEN - INDXP( K2+I-1 ) = INDXP( K2+I ) - INDXP( K2+I ) = JLAM - I = I + 1 - GO TO 80 - ELSE - INDXP( K2+I-1 ) = JLAM - END IF - ELSE - INDXP( K2+I-1 ) = JLAM - END IF - JLAM = J - ELSE - K = K + 1 - W( K ) = Z( JLAM ) - DLAMDA( K ) = D( JLAM ) - INDXP( K ) = JLAM - JLAM = J - END IF - END IF - GO TO 70 - 90 CONTINUE -* -* Record the last eigenvalue. -* - K = K + 1 - W( K ) = Z( JLAM ) - DLAMDA( K ) = D( JLAM ) - INDXP( K ) = JLAM -* - 100 CONTINUE -* -* Sort the eigenvalues and corresponding eigenvectors into DLAMDA -* and Q2 respectively. The eigenvalues/vectors which were not -* deflated go into the first K slots of DLAMDA and Q2 respectively, -* while those which were deflated go into the last N - K slots. -* - DO 110 J = 1, N - JP = INDXP( J ) - DLAMDA( J ) = D( JP ) - PERM( J ) = INDXQ( INDX( JP ) ) - CALL ZCOPY( QSIZ, Q( 1, PERM( J ) ), 1, Q2( 1, J ), 1 ) - 110 CONTINUE -* -* The deflated eigenvalues and their corresponding vectors go back -* into the last N - K slots of D and Q respectively. -* - IF( K.LT.N ) THEN - CALL DCOPY( N-K, DLAMDA( K+1 ), 1, D( K+1 ), 1 ) - CALL ZLACPY( 'A', QSIZ, N-K, Q2( 1, K+1 ), LDQ2, Q( 1, K+1 ), - $ LDQ ) - END IF -* - RETURN -* -* End of ZLAED8 -* - END diff --git a/lib/linalg/fortran/zlanhe.f b/lib/linalg/fortran/zlanhe.f deleted file mode 100644 index bbb4843ffd..0000000000 --- a/lib/linalg/fortran/zlanhe.f +++ /dev/null @@ -1,255 +0,0 @@ -*> \brief \b ZLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZLANHE + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* DOUBLE PRECISION FUNCTION ZLANHE( NORM, UPLO, N, A, LDA, WORK ) -* -* .. Scalar Arguments .. -* CHARACTER NORM, UPLO -* INTEGER LDA, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION WORK( * ) -* COMPLEX*16 A( LDA, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZLANHE returns the value of the one norm, or the Frobenius norm, or -*> the infinity norm, or the element of largest absolute value of a -*> complex hermitian matrix A. -*> \endverbatim -*> -*> \return ZLANHE -*> \verbatim -*> -*> ZLANHE = ( max(abs(A(i,j))), NORM = 'M' or 'm' -*> ( -*> ( norm1(A), NORM = '1', 'O' or 'o' -*> ( -*> ( normI(A), NORM = 'I' or 'i' -*> ( -*> ( normF(A), NORM = 'F', 'f', 'E' or 'e' -*> -*> where norm1 denotes the one norm of a matrix (maximum column sum), -*> normI denotes the infinity norm of a matrix (maximum row sum) and -*> normF denotes the Frobenius norm of a matrix (square root of sum of -*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] NORM -*> \verbatim -*> NORM is CHARACTER*1 -*> Specifies the value to be returned in ZLANHE as described -*> above. -*> \endverbatim -*> -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> Specifies whether the upper or lower triangular part of the -*> hermitian matrix A is to be referenced. -*> = 'U': Upper triangular part of A is referenced -*> = 'L': Lower triangular part of A is referenced -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrix A. N >= 0. When N = 0, ZLANHE is -*> set to zero. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is COMPLEX*16 array, dimension (LDA,N) -*> The hermitian matrix A. If UPLO = 'U', the leading n by n -*> upper triangular part of A contains the upper triangular part -*> of the matrix A, and the strictly lower triangular part of A -*> is not referenced. If UPLO = 'L', the leading n by n lower -*> triangular part of A contains the lower triangular part of -*> the matrix A, and the strictly upper triangular part of A is -*> not referenced. Note that the imaginary parts of the diagonal -*> elements need not be set and are assumed to be zero. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(N,1). -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), -*> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, -*> WORK is not referenced. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16HEauxiliary -* -* ===================================================================== - DOUBLE PRECISION FUNCTION ZLANHE( NORM, UPLO, N, A, LDA, WORK ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER NORM, UPLO - INTEGER LDA, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION WORK( * ) - COMPLEX*16 A( LDA, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE, ZERO - PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) -* .. -* .. Local Scalars .. - INTEGER I, J - DOUBLE PRECISION ABSA, SCALE, SUM, VALUE -* .. -* .. External Functions .. - LOGICAL LSAME, DISNAN - EXTERNAL LSAME, DISNAN -* .. -* .. External Subroutines .. - EXTERNAL ZLASSQ -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, DBLE, SQRT -* .. -* .. Executable Statements .. -* - IF( N.EQ.0 ) THEN - VALUE = ZERO - ELSE IF( LSAME( NORM, 'M' ) ) THEN -* -* Find max(abs(A(i,j))). -* - VALUE = ZERO - IF( LSAME( UPLO, 'U' ) ) THEN - DO 20 J = 1, N - DO 10 I = 1, J - 1 - SUM = ABS( A( I, J ) ) - IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM - 10 CONTINUE - SUM = ABS( DBLE( A( J, J ) ) ) - IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM - 20 CONTINUE - ELSE - DO 40 J = 1, N - SUM = ABS( DBLE( A( J, J ) ) ) - IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM - DO 30 I = J + 1, N - SUM = ABS( A( I, J ) ) - IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM - 30 CONTINUE - 40 CONTINUE - END IF - ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR. - $ ( NORM.EQ.'1' ) ) THEN -* -* Find normI(A) ( = norm1(A), since A is hermitian). -* - VALUE = ZERO - IF( LSAME( UPLO, 'U' ) ) THEN - DO 60 J = 1, N - SUM = ZERO - DO 50 I = 1, J - 1 - ABSA = ABS( A( I, J ) ) - SUM = SUM + ABSA - WORK( I ) = WORK( I ) + ABSA - 50 CONTINUE - WORK( J ) = SUM + ABS( DBLE( A( J, J ) ) ) - 60 CONTINUE - DO 70 I = 1, N - SUM = WORK( I ) - IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM - 70 CONTINUE - ELSE - DO 80 I = 1, N - WORK( I ) = ZERO - 80 CONTINUE - DO 100 J = 1, N - SUM = WORK( J ) + ABS( DBLE( A( J, J ) ) ) - DO 90 I = J + 1, N - ABSA = ABS( A( I, J ) ) - SUM = SUM + ABSA - WORK( I ) = WORK( I ) + ABSA - 90 CONTINUE - IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM - 100 CONTINUE - END IF - ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN -* -* Find normF(A). -* - SCALE = ZERO - SUM = ONE - IF( LSAME( UPLO, 'U' ) ) THEN - DO 110 J = 2, N - CALL ZLASSQ( J-1, A( 1, J ), 1, SCALE, SUM ) - 110 CONTINUE - ELSE - DO 120 J = 1, N - 1 - CALL ZLASSQ( N-J, A( J+1, J ), 1, SCALE, SUM ) - 120 CONTINUE - END IF - SUM = 2*SUM - DO 130 I = 1, N - IF( DBLE( A( I, I ) ).NE.ZERO ) THEN - ABSA = ABS( DBLE( A( I, I ) ) ) - IF( SCALE.LT.ABSA ) THEN - SUM = ONE + SUM*( SCALE / ABSA )**2 - SCALE = ABSA - ELSE - SUM = SUM + ( ABSA / SCALE )**2 - END IF - END IF - 130 CONTINUE - VALUE = SCALE*SQRT( SUM ) - END IF -* - ZLANHE = VALUE - RETURN -* -* End of ZLANHE -* - END diff --git a/lib/linalg/fortran/zlarf.f b/lib/linalg/fortran/zlarf.f deleted file mode 100644 index e555d18ecd..0000000000 --- a/lib/linalg/fortran/zlarf.f +++ /dev/null @@ -1,229 +0,0 @@ -*> \brief \b ZLARF applies an elementary reflector to a general rectangular matrix. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZLARF + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK ) -* -* .. Scalar Arguments .. -* CHARACTER SIDE -* INTEGER INCV, LDC, M, N -* COMPLEX*16 TAU -* .. -* .. Array Arguments .. -* COMPLEX*16 C( LDC, * ), V( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZLARF applies a complex elementary reflector H to a complex M-by-N -*> matrix C, from either the left or the right. H is represented in the -*> form -*> -*> H = I - tau * v * v**H -*> -*> where tau is a complex scalar and v is a complex vector. -*> -*> If tau = 0, then H is taken to be the unit matrix. -*> -*> To apply H**H, supply conjg(tau) instead -*> tau. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] SIDE -*> \verbatim -*> SIDE is CHARACTER*1 -*> = 'L': form H * C -*> = 'R': form C * H -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix C. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix C. -*> \endverbatim -*> -*> \param[in] V -*> \verbatim -*> V is COMPLEX*16 array, dimension -*> (1 + (M-1)*abs(INCV)) if SIDE = 'L' -*> or (1 + (N-1)*abs(INCV)) if SIDE = 'R' -*> The vector v in the representation of H. V is not used if -*> TAU = 0. -*> \endverbatim -*> -*> \param[in] INCV -*> \verbatim -*> INCV is INTEGER -*> The increment between elements of v. INCV <> 0. -*> \endverbatim -*> -*> \param[in] TAU -*> \verbatim -*> TAU is COMPLEX*16 -*> The value tau in the representation of H. -*> \endverbatim -*> -*> \param[in,out] C -*> \verbatim -*> C is COMPLEX*16 array, dimension (LDC,N) -*> On entry, the M-by-N matrix C. -*> On exit, C is overwritten by the matrix H * C if SIDE = 'L', -*> or C * H if SIDE = 'R'. -*> \endverbatim -*> -*> \param[in] LDC -*> \verbatim -*> LDC is INTEGER -*> The leading dimension of the array C. LDC >= max(1,M). -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is COMPLEX*16 array, dimension -*> (N) if SIDE = 'L' -*> or (M) if SIDE = 'R' -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16OTHERauxiliary -* -* ===================================================================== - SUBROUTINE ZLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER SIDE - INTEGER INCV, LDC, M, N - COMPLEX*16 TAU -* .. -* .. Array Arguments .. - COMPLEX*16 C( LDC, * ), V( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - COMPLEX*16 ONE, ZERO - PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ), - $ ZERO = ( 0.0D+0, 0.0D+0 ) ) -* .. -* .. Local Scalars .. - LOGICAL APPLYLEFT - INTEGER I, LASTV, LASTC -* .. -* .. External Subroutines .. - EXTERNAL ZGEMV, ZGERC -* .. -* .. External Functions .. - LOGICAL LSAME - INTEGER ILAZLR, ILAZLC - EXTERNAL LSAME, ILAZLR, ILAZLC -* .. -* .. Executable Statements .. -* - APPLYLEFT = LSAME( SIDE, 'L' ) - LASTV = 0 - LASTC = 0 - IF( TAU.NE.ZERO ) THEN -* Set up variables for scanning V. LASTV begins pointing to the end -* of V. - IF( APPLYLEFT ) THEN - LASTV = M - ELSE - LASTV = N - END IF - IF( INCV.GT.0 ) THEN - I = 1 + (LASTV-1) * INCV - ELSE - I = 1 - END IF -* Look for the last non-zero row in V. - DO WHILE( LASTV.GT.0 .AND. V( I ).EQ.ZERO ) - LASTV = LASTV - 1 - I = I - INCV - END DO - IF( APPLYLEFT ) THEN -* Scan for the last non-zero column in C(1:lastv,:). - LASTC = ILAZLC(LASTV, N, C, LDC) - ELSE -* Scan for the last non-zero row in C(:,1:lastv). - LASTC = ILAZLR(M, LASTV, C, LDC) - END IF - END IF -* Note that lastc.eq.0 renders the BLAS operations null; no special -* case is needed at this level. - IF( APPLYLEFT ) THEN -* -* Form H * C -* - IF( LASTV.GT.0 ) THEN -* -* w(1:lastc,1) := C(1:lastv,1:lastc)**H * v(1:lastv,1) -* - CALL ZGEMV( 'Conjugate transpose', LASTV, LASTC, ONE, - $ C, LDC, V, INCV, ZERO, WORK, 1 ) -* -* C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**H -* - CALL ZGERC( LASTV, LASTC, -TAU, V, INCV, WORK, 1, C, LDC ) - END IF - ELSE -* -* Form C * H -* - IF( LASTV.GT.0 ) THEN -* -* w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1) -* - CALL ZGEMV( 'No transpose', LASTC, LASTV, ONE, C, LDC, - $ V, INCV, ZERO, WORK, 1 ) -* -* C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**H -* - CALL ZGERC( LASTC, LASTV, -TAU, WORK, 1, V, INCV, C, LDC ) - END IF - END IF - RETURN -* -* End of ZLARF -* - END diff --git a/lib/linalg/fortran/zlarfb.f b/lib/linalg/fortran/zlarfb.f deleted file mode 100644 index c5f424db31..0000000000 --- a/lib/linalg/fortran/zlarfb.f +++ /dev/null @@ -1,730 +0,0 @@ -*> \brief \b ZLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZLARFB + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, -* T, LDT, C, LDC, WORK, LDWORK ) -* -* .. Scalar Arguments .. -* CHARACTER DIRECT, SIDE, STOREV, TRANS -* INTEGER K, LDC, LDT, LDV, LDWORK, M, N -* .. -* .. Array Arguments .. -* COMPLEX*16 C( LDC, * ), T( LDT, * ), V( LDV, * ), -* $ WORK( LDWORK, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZLARFB applies a complex block reflector H or its transpose H**H to a -*> complex M-by-N matrix C, from either the left or the right. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] SIDE -*> \verbatim -*> SIDE is CHARACTER*1 -*> = 'L': apply H or H**H from the Left -*> = 'R': apply H or H**H from the Right -*> \endverbatim -*> -*> \param[in] TRANS -*> \verbatim -*> TRANS is CHARACTER*1 -*> = 'N': apply H (No transpose) -*> = 'C': apply H**H (Conjugate transpose) -*> \endverbatim -*> -*> \param[in] DIRECT -*> \verbatim -*> DIRECT is CHARACTER*1 -*> Indicates how H is formed from a product of elementary -*> reflectors -*> = 'F': H = H(1) H(2) . . . H(k) (Forward) -*> = 'B': H = H(k) . . . H(2) H(1) (Backward) -*> \endverbatim -*> -*> \param[in] STOREV -*> \verbatim -*> STOREV is CHARACTER*1 -*> Indicates how the vectors which define the elementary -*> reflectors are stored: -*> = 'C': Columnwise -*> = 'R': Rowwise -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix C. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix C. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> The order of the matrix T (= the number of elementary -*> reflectors whose product defines the block reflector). -*> If SIDE = 'L', M >= K >= 0; -*> if SIDE = 'R', N >= K >= 0. -*> \endverbatim -*> -*> \param[in] V -*> \verbatim -*> V is COMPLEX*16 array, dimension -*> (LDV,K) if STOREV = 'C' -*> (LDV,M) if STOREV = 'R' and SIDE = 'L' -*> (LDV,N) if STOREV = 'R' and SIDE = 'R' -*> See Further Details. -*> \endverbatim -*> -*> \param[in] LDV -*> \verbatim -*> LDV is INTEGER -*> The leading dimension of the array V. -*> If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M); -*> if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N); -*> if STOREV = 'R', LDV >= K. -*> \endverbatim -*> -*> \param[in] T -*> \verbatim -*> T is COMPLEX*16 array, dimension (LDT,K) -*> The triangular K-by-K matrix T in the representation of the -*> block reflector. -*> \endverbatim -*> -*> \param[in] LDT -*> \verbatim -*> LDT is INTEGER -*> The leading dimension of the array T. LDT >= K. -*> \endverbatim -*> -*> \param[in,out] C -*> \verbatim -*> C is COMPLEX*16 array, dimension (LDC,N) -*> On entry, the M-by-N matrix C. -*> On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H. -*> \endverbatim -*> -*> \param[in] LDC -*> \verbatim -*> LDC is INTEGER -*> The leading dimension of the array C. LDC >= max(1,M). -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is COMPLEX*16 array, dimension (LDWORK,K) -*> \endverbatim -*> -*> \param[in] LDWORK -*> \verbatim -*> LDWORK is INTEGER -*> The leading dimension of the array WORK. -*> If SIDE = 'L', LDWORK >= max(1,N); -*> if SIDE = 'R', LDWORK >= max(1,M). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16OTHERauxiliary -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> The shape of the matrix V and the storage of the vectors which define -*> the H(i) is best illustrated by the following example with n = 5 and -*> k = 3. The elements equal to 1 are not stored; the corresponding -*> array elements are modified but restored on exit. The rest of the -*> array is not used. -*> -*> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': -*> -*> V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) -*> ( v1 1 ) ( 1 v2 v2 v2 ) -*> ( v1 v2 1 ) ( 1 v3 v3 ) -*> ( v1 v2 v3 ) -*> ( v1 v2 v3 ) -*> -*> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': -*> -*> V = ( v1 v2 v3 ) V = ( v1 v1 1 ) -*> ( v1 v2 v3 ) ( v2 v2 v2 1 ) -*> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) -*> ( 1 v3 ) -*> ( 1 ) -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE ZLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, - $ T, LDT, C, LDC, WORK, LDWORK ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER DIRECT, SIDE, STOREV, TRANS - INTEGER K, LDC, LDT, LDV, LDWORK, M, N -* .. -* .. Array Arguments .. - COMPLEX*16 C( LDC, * ), T( LDT, * ), V( LDV, * ), - $ WORK( LDWORK, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - COMPLEX*16 ONE - PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) -* .. -* .. Local Scalars .. - CHARACTER TRANST - INTEGER I, J -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL ZCOPY, ZGEMM, ZLACGV, ZTRMM -* .. -* .. Intrinsic Functions .. - INTRINSIC DCONJG -* .. -* .. Executable Statements .. -* -* Quick return if possible -* - IF( M.LE.0 .OR. N.LE.0 ) - $ RETURN -* - IF( LSAME( TRANS, 'N' ) ) THEN - TRANST = 'C' - ELSE - TRANST = 'N' - END IF -* - IF( LSAME( STOREV, 'C' ) ) THEN -* - IF( LSAME( DIRECT, 'F' ) ) THEN -* -* Let V = ( V1 ) (first K rows) -* ( V2 ) -* where V1 is unit lower triangular. -* - IF( LSAME( SIDE, 'L' ) ) THEN -* -* Form H * C or H**H * C where C = ( C1 ) -* ( C2 ) -* -* W := C**H * V = (C1**H * V1 + C2**H * V2) (stored in WORK) -* -* W := C1**H -* - DO 10 J = 1, K - CALL ZCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 ) - CALL ZLACGV( N, WORK( 1, J ), 1 ) - 10 CONTINUE -* -* W := W * V1 -* - CALL ZTRMM( 'Right', 'Lower', 'No transpose', 'Unit', N, - $ K, ONE, V, LDV, WORK, LDWORK ) - IF( M.GT.K ) THEN -* -* W := W + C2**H * V2 -* - CALL ZGEMM( 'Conjugate transpose', 'No transpose', N, - $ K, M-K, ONE, C( K+1, 1 ), LDC, - $ V( K+1, 1 ), LDV, ONE, WORK, LDWORK ) - END IF -* -* W := W * T**H or W * T -* - CALL ZTRMM( 'Right', 'Upper', TRANST, 'Non-unit', N, K, - $ ONE, T, LDT, WORK, LDWORK ) -* -* C := C - V * W**H -* - IF( M.GT.K ) THEN -* -* C2 := C2 - V2 * W**H -* - CALL ZGEMM( 'No transpose', 'Conjugate transpose', - $ M-K, N, K, -ONE, V( K+1, 1 ), LDV, WORK, - $ LDWORK, ONE, C( K+1, 1 ), LDC ) - END IF -* -* W := W * V1**H -* - CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose', - $ 'Unit', N, K, ONE, V, LDV, WORK, LDWORK ) -* -* C1 := C1 - W**H -* - DO 30 J = 1, K - DO 20 I = 1, N - C( J, I ) = C( J, I ) - DCONJG( WORK( I, J ) ) - 20 CONTINUE - 30 CONTINUE -* - ELSE IF( LSAME( SIDE, 'R' ) ) THEN -* -* Form C * H or C * H**H where C = ( C1 C2 ) -* -* W := C * V = (C1*V1 + C2*V2) (stored in WORK) -* -* W := C1 -* - DO 40 J = 1, K - CALL ZCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 ) - 40 CONTINUE -* -* W := W * V1 -* - CALL ZTRMM( 'Right', 'Lower', 'No transpose', 'Unit', M, - $ K, ONE, V, LDV, WORK, LDWORK ) - IF( N.GT.K ) THEN -* -* W := W + C2 * V2 -* - CALL ZGEMM( 'No transpose', 'No transpose', M, K, N-K, - $ ONE, C( 1, K+1 ), LDC, V( K+1, 1 ), LDV, - $ ONE, WORK, LDWORK ) - END IF -* -* W := W * T or W * T**H -* - CALL ZTRMM( 'Right', 'Upper', TRANS, 'Non-unit', M, K, - $ ONE, T, LDT, WORK, LDWORK ) -* -* C := C - W * V**H -* - IF( N.GT.K ) THEN -* -* C2 := C2 - W * V2**H -* - CALL ZGEMM( 'No transpose', 'Conjugate transpose', M, - $ N-K, K, -ONE, WORK, LDWORK, V( K+1, 1 ), - $ LDV, ONE, C( 1, K+1 ), LDC ) - END IF -* -* W := W * V1**H -* - CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose', - $ 'Unit', M, K, ONE, V, LDV, WORK, LDWORK ) -* -* C1 := C1 - W -* - DO 60 J = 1, K - DO 50 I = 1, M - C( I, J ) = C( I, J ) - WORK( I, J ) - 50 CONTINUE - 60 CONTINUE - END IF -* - ELSE -* -* Let V = ( V1 ) -* ( V2 ) (last K rows) -* where V2 is unit upper triangular. -* - IF( LSAME( SIDE, 'L' ) ) THEN -* -* Form H * C or H**H * C where C = ( C1 ) -* ( C2 ) -* -* W := C**H * V = (C1**H * V1 + C2**H * V2) (stored in WORK) -* -* W := C2**H -* - DO 70 J = 1, K - CALL ZCOPY( N, C( M-K+J, 1 ), LDC, WORK( 1, J ), 1 ) - CALL ZLACGV( N, WORK( 1, J ), 1 ) - 70 CONTINUE -* -* W := W * V2 -* - CALL ZTRMM( 'Right', 'Upper', 'No transpose', 'Unit', N, - $ K, ONE, V( M-K+1, 1 ), LDV, WORK, LDWORK ) - IF( M.GT.K ) THEN -* -* W := W + C1**H * V1 -* - CALL ZGEMM( 'Conjugate transpose', 'No transpose', N, - $ K, M-K, ONE, C, LDC, V, LDV, ONE, WORK, - $ LDWORK ) - END IF -* -* W := W * T**H or W * T -* - CALL ZTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, - $ ONE, T, LDT, WORK, LDWORK ) -* -* C := C - V * W**H -* - IF( M.GT.K ) THEN -* -* C1 := C1 - V1 * W**H -* - CALL ZGEMM( 'No transpose', 'Conjugate transpose', - $ M-K, N, K, -ONE, V, LDV, WORK, LDWORK, - $ ONE, C, LDC ) - END IF -* -* W := W * V2**H -* - CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose', - $ 'Unit', N, K, ONE, V( M-K+1, 1 ), LDV, WORK, - $ LDWORK ) -* -* C2 := C2 - W**H -* - DO 90 J = 1, K - DO 80 I = 1, N - C( M-K+J, I ) = C( M-K+J, I ) - - $ DCONJG( WORK( I, J ) ) - 80 CONTINUE - 90 CONTINUE -* - ELSE IF( LSAME( SIDE, 'R' ) ) THEN -* -* Form C * H or C * H**H where C = ( C1 C2 ) -* -* W := C * V = (C1*V1 + C2*V2) (stored in WORK) -* -* W := C2 -* - DO 100 J = 1, K - CALL ZCOPY( M, C( 1, N-K+J ), 1, WORK( 1, J ), 1 ) - 100 CONTINUE -* -* W := W * V2 -* - CALL ZTRMM( 'Right', 'Upper', 'No transpose', 'Unit', M, - $ K, ONE, V( N-K+1, 1 ), LDV, WORK, LDWORK ) - IF( N.GT.K ) THEN -* -* W := W + C1 * V1 -* - CALL ZGEMM( 'No transpose', 'No transpose', M, K, N-K, - $ ONE, C, LDC, V, LDV, ONE, WORK, LDWORK ) - END IF -* -* W := W * T or W * T**H -* - CALL ZTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, - $ ONE, T, LDT, WORK, LDWORK ) -* -* C := C - W * V**H -* - IF( N.GT.K ) THEN -* -* C1 := C1 - W * V1**H -* - CALL ZGEMM( 'No transpose', 'Conjugate transpose', M, - $ N-K, K, -ONE, WORK, LDWORK, V, LDV, ONE, - $ C, LDC ) - END IF -* -* W := W * V2**H -* - CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose', - $ 'Unit', M, K, ONE, V( N-K+1, 1 ), LDV, WORK, - $ LDWORK ) -* -* C2 := C2 - W -* - DO 120 J = 1, K - DO 110 I = 1, M - C( I, N-K+J ) = C( I, N-K+J ) - WORK( I, J ) - 110 CONTINUE - 120 CONTINUE - END IF - END IF -* - ELSE IF( LSAME( STOREV, 'R' ) ) THEN -* - IF( LSAME( DIRECT, 'F' ) ) THEN -* -* Let V = ( V1 V2 ) (V1: first K columns) -* where V1 is unit upper triangular. -* - IF( LSAME( SIDE, 'L' ) ) THEN -* -* Form H * C or H**H * C where C = ( C1 ) -* ( C2 ) -* -* W := C**H * V**H = (C1**H * V1**H + C2**H * V2**H) (stored in WORK) -* -* W := C1**H -* - DO 130 J = 1, K - CALL ZCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 ) - CALL ZLACGV( N, WORK( 1, J ), 1 ) - 130 CONTINUE -* -* W := W * V1**H -* - CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose', - $ 'Unit', N, K, ONE, V, LDV, WORK, LDWORK ) - IF( M.GT.K ) THEN -* -* W := W + C2**H * V2**H -* - CALL ZGEMM( 'Conjugate transpose', - $ 'Conjugate transpose', N, K, M-K, ONE, - $ C( K+1, 1 ), LDC, V( 1, K+1 ), LDV, ONE, - $ WORK, LDWORK ) - END IF -* -* W := W * T**H or W * T -* - CALL ZTRMM( 'Right', 'Upper', TRANST, 'Non-unit', N, K, - $ ONE, T, LDT, WORK, LDWORK ) -* -* C := C - V**H * W**H -* - IF( M.GT.K ) THEN -* -* C2 := C2 - V2**H * W**H -* - CALL ZGEMM( 'Conjugate transpose', - $ 'Conjugate transpose', M-K, N, K, -ONE, - $ V( 1, K+1 ), LDV, WORK, LDWORK, ONE, - $ C( K+1, 1 ), LDC ) - END IF -* -* W := W * V1 -* - CALL ZTRMM( 'Right', 'Upper', 'No transpose', 'Unit', N, - $ K, ONE, V, LDV, WORK, LDWORK ) -* -* C1 := C1 - W**H -* - DO 150 J = 1, K - DO 140 I = 1, N - C( J, I ) = C( J, I ) - DCONJG( WORK( I, J ) ) - 140 CONTINUE - 150 CONTINUE -* - ELSE IF( LSAME( SIDE, 'R' ) ) THEN -* -* Form C * H or C * H**H where C = ( C1 C2 ) -* -* W := C * V**H = (C1*V1**H + C2*V2**H) (stored in WORK) -* -* W := C1 -* - DO 160 J = 1, K - CALL ZCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 ) - 160 CONTINUE -* -* W := W * V1**H -* - CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose', - $ 'Unit', M, K, ONE, V, LDV, WORK, LDWORK ) - IF( N.GT.K ) THEN -* -* W := W + C2 * V2**H -* - CALL ZGEMM( 'No transpose', 'Conjugate transpose', M, - $ K, N-K, ONE, C( 1, K+1 ), LDC, - $ V( 1, K+1 ), LDV, ONE, WORK, LDWORK ) - END IF -* -* W := W * T or W * T**H -* - CALL ZTRMM( 'Right', 'Upper', TRANS, 'Non-unit', M, K, - $ ONE, T, LDT, WORK, LDWORK ) -* -* C := C - W * V -* - IF( N.GT.K ) THEN -* -* C2 := C2 - W * V2 -* - CALL ZGEMM( 'No transpose', 'No transpose', M, N-K, K, - $ -ONE, WORK, LDWORK, V( 1, K+1 ), LDV, ONE, - $ C( 1, K+1 ), LDC ) - END IF -* -* W := W * V1 -* - CALL ZTRMM( 'Right', 'Upper', 'No transpose', 'Unit', M, - $ K, ONE, V, LDV, WORK, LDWORK ) -* -* C1 := C1 - W -* - DO 180 J = 1, K - DO 170 I = 1, M - C( I, J ) = C( I, J ) - WORK( I, J ) - 170 CONTINUE - 180 CONTINUE -* - END IF -* - ELSE -* -* Let V = ( V1 V2 ) (V2: last K columns) -* where V2 is unit lower triangular. -* - IF( LSAME( SIDE, 'L' ) ) THEN -* -* Form H * C or H**H * C where C = ( C1 ) -* ( C2 ) -* -* W := C**H * V**H = (C1**H * V1**H + C2**H * V2**H) (stored in WORK) -* -* W := C2**H -* - DO 190 J = 1, K - CALL ZCOPY( N, C( M-K+J, 1 ), LDC, WORK( 1, J ), 1 ) - CALL ZLACGV( N, WORK( 1, J ), 1 ) - 190 CONTINUE -* -* W := W * V2**H -* - CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose', - $ 'Unit', N, K, ONE, V( 1, M-K+1 ), LDV, WORK, - $ LDWORK ) - IF( M.GT.K ) THEN -* -* W := W + C1**H * V1**H -* - CALL ZGEMM( 'Conjugate transpose', - $ 'Conjugate transpose', N, K, M-K, ONE, C, - $ LDC, V, LDV, ONE, WORK, LDWORK ) - END IF -* -* W := W * T**H or W * T -* - CALL ZTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, - $ ONE, T, LDT, WORK, LDWORK ) -* -* C := C - V**H * W**H -* - IF( M.GT.K ) THEN -* -* C1 := C1 - V1**H * W**H -* - CALL ZGEMM( 'Conjugate transpose', - $ 'Conjugate transpose', M-K, N, K, -ONE, V, - $ LDV, WORK, LDWORK, ONE, C, LDC ) - END IF -* -* W := W * V2 -* - CALL ZTRMM( 'Right', 'Lower', 'No transpose', 'Unit', N, - $ K, ONE, V( 1, M-K+1 ), LDV, WORK, LDWORK ) -* -* C2 := C2 - W**H -* - DO 210 J = 1, K - DO 200 I = 1, N - C( M-K+J, I ) = C( M-K+J, I ) - - $ DCONJG( WORK( I, J ) ) - 200 CONTINUE - 210 CONTINUE -* - ELSE IF( LSAME( SIDE, 'R' ) ) THEN -* -* Form C * H or C * H**H where C = ( C1 C2 ) -* -* W := C * V**H = (C1*V1**H + C2*V2**H) (stored in WORK) -* -* W := C2 -* - DO 220 J = 1, K - CALL ZCOPY( M, C( 1, N-K+J ), 1, WORK( 1, J ), 1 ) - 220 CONTINUE -* -* W := W * V2**H -* - CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose', - $ 'Unit', M, K, ONE, V( 1, N-K+1 ), LDV, WORK, - $ LDWORK ) - IF( N.GT.K ) THEN -* -* W := W + C1 * V1**H -* - CALL ZGEMM( 'No transpose', 'Conjugate transpose', M, - $ K, N-K, ONE, C, LDC, V, LDV, ONE, WORK, - $ LDWORK ) - END IF -* -* W := W * T or W * T**H -* - CALL ZTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, - $ ONE, T, LDT, WORK, LDWORK ) -* -* C := C - W * V -* - IF( N.GT.K ) THEN -* -* C1 := C1 - W * V1 -* - CALL ZGEMM( 'No transpose', 'No transpose', M, N-K, K, - $ -ONE, WORK, LDWORK, V, LDV, ONE, C, LDC ) - END IF -* -* W := W * V2 -* - CALL ZTRMM( 'Right', 'Lower', 'No transpose', 'Unit', M, - $ K, ONE, V( 1, N-K+1 ), LDV, WORK, LDWORK ) -* -* C1 := C1 - W -* - DO 240 J = 1, K - DO 230 I = 1, M - C( I, N-K+J ) = C( I, N-K+J ) - WORK( I, J ) - 230 CONTINUE - 240 CONTINUE -* - END IF -* - END IF - END IF -* - RETURN -* -* End of ZLARFB -* - END diff --git a/lib/linalg/fortran/zlarfg.f b/lib/linalg/fortran/zlarfg.f deleted file mode 100644 index d69796cadc..0000000000 --- a/lib/linalg/fortran/zlarfg.f +++ /dev/null @@ -1,200 +0,0 @@ -*> \brief \b ZLARFG generates an elementary reflector (Householder matrix). -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZLARFG + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZLARFG( N, ALPHA, X, INCX, TAU ) -* -* .. Scalar Arguments .. -* INTEGER INCX, N -* COMPLEX*16 ALPHA, TAU -* .. -* .. Array Arguments .. -* COMPLEX*16 X( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZLARFG generates a complex elementary reflector H of order n, such -*> that -*> -*> H**H * ( alpha ) = ( beta ), H**H * H = I. -*> ( x ) ( 0 ) -*> -*> where alpha and beta are scalars, with beta real, and x is an -*> (n-1)-element complex vector. H is represented in the form -*> -*> H = I - tau * ( 1 ) * ( 1 v**H ) , -*> ( v ) -*> -*> where tau is a complex scalar and v is a complex (n-1)-element -*> vector. Note that H is not hermitian. -*> -*> If the elements of x are all zero and alpha is real, then tau = 0 -*> and H is taken to be the unit matrix. -*> -*> Otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1 . -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the elementary reflector. -*> \endverbatim -*> -*> \param[in,out] ALPHA -*> \verbatim -*> ALPHA is COMPLEX*16 -*> On entry, the value alpha. -*> On exit, it is overwritten with the value beta. -*> \endverbatim -*> -*> \param[in,out] X -*> \verbatim -*> X is COMPLEX*16 array, dimension -*> (1+(N-2)*abs(INCX)) -*> On entry, the vector x. -*> On exit, it is overwritten with the vector v. -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> The increment between elements of X. INCX > 0. -*> \endverbatim -*> -*> \param[out] TAU -*> \verbatim -*> TAU is COMPLEX*16 -*> The value tau. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16OTHERauxiliary -* -* ===================================================================== - SUBROUTINE ZLARFG( N, ALPHA, X, INCX, TAU ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INCX, N - COMPLEX*16 ALPHA, TAU -* .. -* .. Array Arguments .. - COMPLEX*16 X( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE, ZERO - PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) -* .. -* .. Local Scalars .. - INTEGER J, KNT - DOUBLE PRECISION ALPHI, ALPHR, BETA, RSAFMN, SAFMIN, XNORM -* .. -* .. External Functions .. - DOUBLE PRECISION DLAMCH, DLAPY3, DZNRM2 - COMPLEX*16 ZLADIV - EXTERNAL DLAMCH, DLAPY3, DZNRM2, ZLADIV -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, DBLE, DCMPLX, DIMAG, SIGN -* .. -* .. External Subroutines .. - EXTERNAL ZDSCAL, ZSCAL -* .. -* .. Executable Statements .. -* - IF( N.LE.0 ) THEN - TAU = ZERO - RETURN - END IF -* - XNORM = DZNRM2( N-1, X, INCX ) - ALPHR = DBLE( ALPHA ) - ALPHI = DIMAG( ALPHA ) -* - IF( XNORM.EQ.ZERO .AND. ALPHI.EQ.ZERO ) THEN -* -* H = I -* - TAU = ZERO - ELSE -* -* general case -* - BETA = -SIGN( DLAPY3( ALPHR, ALPHI, XNORM ), ALPHR ) - SAFMIN = DLAMCH( 'S' ) / DLAMCH( 'E' ) - RSAFMN = ONE / SAFMIN -* - KNT = 0 - IF( ABS( BETA ).LT.SAFMIN ) THEN -* -* XNORM, BETA may be inaccurate; scale X and recompute them -* - 10 CONTINUE - KNT = KNT + 1 - CALL ZDSCAL( N-1, RSAFMN, X, INCX ) - BETA = BETA*RSAFMN - ALPHI = ALPHI*RSAFMN - ALPHR = ALPHR*RSAFMN - IF( (ABS( BETA ).LT.SAFMIN) .AND. (KNT .LT. 20) ) - $ GO TO 10 -* -* New BETA is at most 1, at least SAFMIN -* - XNORM = DZNRM2( N-1, X, INCX ) - ALPHA = DCMPLX( ALPHR, ALPHI ) - BETA = -SIGN( DLAPY3( ALPHR, ALPHI, XNORM ), ALPHR ) - END IF - TAU = DCMPLX( ( BETA-ALPHR ) / BETA, -ALPHI / BETA ) - ALPHA = ZLADIV( DCMPLX( ONE ), ALPHA-BETA ) - CALL ZSCAL( N-1, ALPHA, X, INCX ) -* -* If ALPHA is subnormal, it may lose relative accuracy -* - DO 20 J = 1, KNT - BETA = BETA*SAFMIN - 20 CONTINUE - ALPHA = BETA - END IF -* - RETURN -* -* End of ZLARFG -* - END diff --git a/lib/linalg/fortran/zlarft.f b/lib/linalg/fortran/zlarft.f deleted file mode 100644 index 5ad0996fab..0000000000 --- a/lib/linalg/fortran/zlarft.f +++ /dev/null @@ -1,324 +0,0 @@ -*> \brief \b ZLARFT forms the triangular factor T of a block reflector H = I - vtvH -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZLARFT + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) -* -* .. Scalar Arguments .. -* CHARACTER DIRECT, STOREV -* INTEGER K, LDT, LDV, N -* .. -* .. Array Arguments .. -* COMPLEX*16 T( LDT, * ), TAU( * ), V( LDV, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZLARFT forms the triangular factor T of a complex block reflector H -*> of order n, which is defined as a product of k elementary reflectors. -*> -*> If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; -*> -*> If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. -*> -*> If STOREV = 'C', the vector which defines the elementary reflector -*> H(i) is stored in the i-th column of the array V, and -*> -*> H = I - V * T * V**H -*> -*> If STOREV = 'R', the vector which defines the elementary reflector -*> H(i) is stored in the i-th row of the array V, and -*> -*> H = I - V**H * T * V -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] DIRECT -*> \verbatim -*> DIRECT is CHARACTER*1 -*> Specifies the order in which the elementary reflectors are -*> multiplied to form the block reflector: -*> = 'F': H = H(1) H(2) . . . H(k) (Forward) -*> = 'B': H = H(k) . . . H(2) H(1) (Backward) -*> \endverbatim -*> -*> \param[in] STOREV -*> \verbatim -*> STOREV is CHARACTER*1 -*> Specifies how the vectors which define the elementary -*> reflectors are stored (see also Further Details): -*> = 'C': columnwise -*> = 'R': rowwise -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the block reflector H. N >= 0. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> The order of the triangular factor T (= the number of -*> elementary reflectors). K >= 1. -*> \endverbatim -*> -*> \param[in] V -*> \verbatim -*> V is COMPLEX*16 array, dimension -*> (LDV,K) if STOREV = 'C' -*> (LDV,N) if STOREV = 'R' -*> The matrix V. See further details. -*> \endverbatim -*> -*> \param[in] LDV -*> \verbatim -*> LDV is INTEGER -*> The leading dimension of the array V. -*> If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. -*> \endverbatim -*> -*> \param[in] TAU -*> \verbatim -*> TAU is COMPLEX*16 array, dimension (K) -*> TAU(i) must contain the scalar factor of the elementary -*> reflector H(i). -*> \endverbatim -*> -*> \param[out] T -*> \verbatim -*> T is COMPLEX*16 array, dimension (LDT,K) -*> The k by k triangular factor T of the block reflector. -*> If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is -*> lower triangular. The rest of the array is not used. -*> \endverbatim -*> -*> \param[in] LDT -*> \verbatim -*> LDT is INTEGER -*> The leading dimension of the array T. LDT >= K. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16OTHERauxiliary -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> The shape of the matrix V and the storage of the vectors which define -*> the H(i) is best illustrated by the following example with n = 5 and -*> k = 3. The elements equal to 1 are not stored. -*> -*> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': -*> -*> V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) -*> ( v1 1 ) ( 1 v2 v2 v2 ) -*> ( v1 v2 1 ) ( 1 v3 v3 ) -*> ( v1 v2 v3 ) -*> ( v1 v2 v3 ) -*> -*> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': -*> -*> V = ( v1 v2 v3 ) V = ( v1 v1 1 ) -*> ( v1 v2 v3 ) ( v2 v2 v2 1 ) -*> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) -*> ( 1 v3 ) -*> ( 1 ) -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE ZLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER DIRECT, STOREV - INTEGER K, LDT, LDV, N -* .. -* .. Array Arguments .. - COMPLEX*16 T( LDT, * ), TAU( * ), V( LDV, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - COMPLEX*16 ONE, ZERO - PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ), - $ ZERO = ( 0.0D+0, 0.0D+0 ) ) -* .. -* .. Local Scalars .. - INTEGER I, J, PREVLASTV, LASTV -* .. -* .. External Subroutines .. - EXTERNAL ZGEMV, ZTRMV, ZGEMM -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. Executable Statements .. -* -* Quick return if possible -* - IF( N.EQ.0 ) - $ RETURN -* - IF( LSAME( DIRECT, 'F' ) ) THEN - PREVLASTV = N - DO I = 1, K - PREVLASTV = MAX( PREVLASTV, I ) - IF( TAU( I ).EQ.ZERO ) THEN -* -* H(i) = I -* - DO J = 1, I - T( J, I ) = ZERO - END DO - ELSE -* -* general case -* - IF( LSAME( STOREV, 'C' ) ) THEN -* Skip any trailing zeros. - DO LASTV = N, I+1, -1 - IF( V( LASTV, I ).NE.ZERO ) EXIT - END DO - DO J = 1, I-1 - T( J, I ) = -TAU( I ) * CONJG( V( I , J ) ) - END DO - J = MIN( LASTV, PREVLASTV ) -* -* T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**H * V(i:j,i) -* - CALL ZGEMV( 'Conjugate transpose', J-I, I-1, - $ -TAU( I ), V( I+1, 1 ), LDV, - $ V( I+1, I ), 1, ONE, T( 1, I ), 1 ) - ELSE -* Skip any trailing zeros. - DO LASTV = N, I+1, -1 - IF( V( I, LASTV ).NE.ZERO ) EXIT - END DO - DO J = 1, I-1 - T( J, I ) = -TAU( I ) * V( J , I ) - END DO - J = MIN( LASTV, PREVLASTV ) -* -* T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**H -* - CALL ZGEMM( 'N', 'C', I-1, 1, J-I, -TAU( I ), - $ V( 1, I+1 ), LDV, V( I, I+1 ), LDV, - $ ONE, T( 1, I ), LDT ) - END IF -* -* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) -* - CALL ZTRMV( 'Upper', 'No transpose', 'Non-unit', I-1, T, - $ LDT, T( 1, I ), 1 ) - T( I, I ) = TAU( I ) - IF( I.GT.1 ) THEN - PREVLASTV = MAX( PREVLASTV, LASTV ) - ELSE - PREVLASTV = LASTV - END IF - END IF - END DO - ELSE - PREVLASTV = 1 - DO I = K, 1, -1 - IF( TAU( I ).EQ.ZERO ) THEN -* -* H(i) = I -* - DO J = I, K - T( J, I ) = ZERO - END DO - ELSE -* -* general case -* - IF( I.LT.K ) THEN - IF( LSAME( STOREV, 'C' ) ) THEN -* Skip any leading zeros. - DO LASTV = 1, I-1 - IF( V( LASTV, I ).NE.ZERO ) EXIT - END DO - DO J = I+1, K - T( J, I ) = -TAU( I ) * CONJG( V( N-K+I , J ) ) - END DO - J = MAX( LASTV, PREVLASTV ) -* -* T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**H * V(j:n-k+i,i) -* - CALL ZGEMV( 'Conjugate transpose', N-K+I-J, K-I, - $ -TAU( I ), V( J, I+1 ), LDV, V( J, I ), - $ 1, ONE, T( I+1, I ), 1 ) - ELSE -* Skip any leading zeros. - DO LASTV = 1, I-1 - IF( V( I, LASTV ).NE.ZERO ) EXIT - END DO - DO J = I+1, K - T( J, I ) = -TAU( I ) * V( J, N-K+I ) - END DO - J = MAX( LASTV, PREVLASTV ) -* -* T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**H -* - CALL ZGEMM( 'N', 'C', K-I, 1, N-K+I-J, -TAU( I ), - $ V( I+1, J ), LDV, V( I, J ), LDV, - $ ONE, T( I+1, I ), LDT ) - END IF -* -* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) -* - CALL ZTRMV( 'Lower', 'No transpose', 'Non-unit', K-I, - $ T( I+1, I+1 ), LDT, T( I+1, I ), 1 ) - IF( I.GT.1 ) THEN - PREVLASTV = MIN( PREVLASTV, LASTV ) - ELSE - PREVLASTV = LASTV - END IF - END IF - T( I, I ) = TAU( I ) - END IF - END DO - END IF - RETURN -* -* End of ZLARFT -* - END diff --git a/lib/linalg/fortran/zlascl.f b/lib/linalg/fortran/zlascl.f deleted file mode 100644 index 4cce5ff5e0..0000000000 --- a/lib/linalg/fortran/zlascl.f +++ /dev/null @@ -1,367 +0,0 @@ -*> \brief \b ZLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZLASCL + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZLASCL( TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER TYPE -* INTEGER INFO, KL, KU, LDA, M, N -* DOUBLE PRECISION CFROM, CTO -* .. -* .. Array Arguments .. -* COMPLEX*16 A( LDA, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZLASCL multiplies the M by N complex matrix A by the real scalar -*> CTO/CFROM. This is done without over/underflow as long as the final -*> result CTO*A(I,J)/CFROM does not over/underflow. TYPE specifies that -*> A may be full, upper triangular, lower triangular, upper Hessenberg, -*> or banded. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] TYPE -*> \verbatim -*> TYPE is CHARACTER*1 -*> TYPE indices the storage type of the input matrix. -*> = 'G': A is a full matrix. -*> = 'L': A is a lower triangular matrix. -*> = 'U': A is an upper triangular matrix. -*> = 'H': A is an upper Hessenberg matrix. -*> = 'B': A is a symmetric band matrix with lower bandwidth KL -*> and upper bandwidth KU and with the only the lower -*> half stored. -*> = 'Q': A is a symmetric band matrix with lower bandwidth KL -*> and upper bandwidth KU and with the only the upper -*> half stored. -*> = 'Z': A is a band matrix with lower bandwidth KL and upper -*> bandwidth KU. See ZGBTRF for storage details. -*> \endverbatim -*> -*> \param[in] KL -*> \verbatim -*> KL is INTEGER -*> The lower bandwidth of A. Referenced only if TYPE = 'B', -*> 'Q' or 'Z'. -*> \endverbatim -*> -*> \param[in] KU -*> \verbatim -*> KU is INTEGER -*> The upper bandwidth of A. Referenced only if TYPE = 'B', -*> 'Q' or 'Z'. -*> \endverbatim -*> -*> \param[in] CFROM -*> \verbatim -*> CFROM is DOUBLE PRECISION -*> \endverbatim -*> -*> \param[in] CTO -*> \verbatim -*> CTO is DOUBLE PRECISION -*> -*> The matrix A is multiplied by CTO/CFROM. A(I,J) is computed -*> without over/underflow if the final result CTO*A(I,J)/CFROM -*> can be represented without over/underflow. CFROM must be -*> nonzero. -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix A. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is COMPLEX*16 array, dimension (LDA,N) -*> The matrix to be multiplied by CTO/CFROM. See TYPE for the -*> storage type. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. -*> If TYPE = 'G', 'L', 'U', 'H', LDA >= max(1,M); -*> TYPE = 'B', LDA >= KL+1; -*> TYPE = 'Q', LDA >= KU+1; -*> TYPE = 'Z', LDA >= 2*KL+KU+1. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> 0 - successful exit -*> <0 - if INFO = -i, the i-th argument had an illegal value. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16OTHERauxiliary -* -* ===================================================================== - SUBROUTINE ZLASCL( TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER TYPE - INTEGER INFO, KL, KU, LDA, M, N - DOUBLE PRECISION CFROM, CTO -* .. -* .. Array Arguments .. - COMPLEX*16 A( LDA, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) -* .. -* .. Local Scalars .. - LOGICAL DONE - INTEGER I, ITYPE, J, K1, K2, K3, K4 - DOUBLE PRECISION BIGNUM, CFROM1, CFROMC, CTO1, CTOC, MUL, SMLNUM -* .. -* .. External Functions .. - LOGICAL LSAME, DISNAN - DOUBLE PRECISION DLAMCH - EXTERNAL LSAME, DLAMCH, DISNAN -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, MAX, MIN -* .. -* .. External Subroutines .. - EXTERNAL XERBLA -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - INFO = 0 -* - IF( LSAME( TYPE, 'G' ) ) THEN - ITYPE = 0 - ELSE IF( LSAME( TYPE, 'L' ) ) THEN - ITYPE = 1 - ELSE IF( LSAME( TYPE, 'U' ) ) THEN - ITYPE = 2 - ELSE IF( LSAME( TYPE, 'H' ) ) THEN - ITYPE = 3 - ELSE IF( LSAME( TYPE, 'B' ) ) THEN - ITYPE = 4 - ELSE IF( LSAME( TYPE, 'Q' ) ) THEN - ITYPE = 5 - ELSE IF( LSAME( TYPE, 'Z' ) ) THEN - ITYPE = 6 - ELSE - ITYPE = -1 - END IF -* - IF( ITYPE.EQ.-1 ) THEN - INFO = -1 - ELSE IF( CFROM.EQ.ZERO .OR. DISNAN(CFROM) ) THEN - INFO = -4 - ELSE IF( DISNAN(CTO) ) THEN - INFO = -5 - ELSE IF( M.LT.0 ) THEN - INFO = -6 - ELSE IF( N.LT.0 .OR. ( ITYPE.EQ.4 .AND. N.NE.M ) .OR. - $ ( ITYPE.EQ.5 .AND. N.NE.M ) ) THEN - INFO = -7 - ELSE IF( ITYPE.LE.3 .AND. LDA.LT.MAX( 1, M ) ) THEN - INFO = -9 - ELSE IF( ITYPE.GE.4 ) THEN - IF( KL.LT.0 .OR. KL.GT.MAX( M-1, 0 ) ) THEN - INFO = -2 - ELSE IF( KU.LT.0 .OR. KU.GT.MAX( N-1, 0 ) .OR. - $ ( ( ITYPE.EQ.4 .OR. ITYPE.EQ.5 ) .AND. KL.NE.KU ) ) - $ THEN - INFO = -3 - ELSE IF( ( ITYPE.EQ.4 .AND. LDA.LT.KL+1 ) .OR. - $ ( ITYPE.EQ.5 .AND. LDA.LT.KU+1 ) .OR. - $ ( ITYPE.EQ.6 .AND. LDA.LT.2*KL+KU+1 ) ) THEN - INFO = -9 - END IF - END IF -* - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'ZLASCL', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( N.EQ.0 .OR. M.EQ.0 ) - $ RETURN -* -* Get machine parameters -* - SMLNUM = DLAMCH( 'S' ) - BIGNUM = ONE / SMLNUM -* - CFROMC = CFROM - CTOC = CTO -* - 10 CONTINUE - CFROM1 = CFROMC*SMLNUM - IF( CFROM1.EQ.CFROMC ) THEN -! CFROMC is an inf. Multiply by a correctly signed zero for -! finite CTOC, or a NaN if CTOC is infinite. - MUL = CTOC / CFROMC - DONE = .TRUE. - CTO1 = CTOC - ELSE - CTO1 = CTOC / BIGNUM - IF( CTO1.EQ.CTOC ) THEN -! CTOC is either 0 or an inf. In both cases, CTOC itself -! serves as the correct multiplication factor. - MUL = CTOC - DONE = .TRUE. - CFROMC = ONE - ELSE IF( ABS( CFROM1 ).GT.ABS( CTOC ) .AND. CTOC.NE.ZERO ) THEN - MUL = SMLNUM - DONE = .FALSE. - CFROMC = CFROM1 - ELSE IF( ABS( CTO1 ).GT.ABS( CFROMC ) ) THEN - MUL = BIGNUM - DONE = .FALSE. - CTOC = CTO1 - ELSE - MUL = CTOC / CFROMC - DONE = .TRUE. - IF (MUL .EQ. ONE) - $ RETURN - END IF - END IF -* - IF( ITYPE.EQ.0 ) THEN -* -* Full matrix -* - DO 30 J = 1, N - DO 20 I = 1, M - A( I, J ) = A( I, J )*MUL - 20 CONTINUE - 30 CONTINUE -* - ELSE IF( ITYPE.EQ.1 ) THEN -* -* Lower triangular matrix -* - DO 50 J = 1, N - DO 40 I = J, M - A( I, J ) = A( I, J )*MUL - 40 CONTINUE - 50 CONTINUE -* - ELSE IF( ITYPE.EQ.2 ) THEN -* -* Upper triangular matrix -* - DO 70 J = 1, N - DO 60 I = 1, MIN( J, M ) - A( I, J ) = A( I, J )*MUL - 60 CONTINUE - 70 CONTINUE -* - ELSE IF( ITYPE.EQ.3 ) THEN -* -* Upper Hessenberg matrix -* - DO 90 J = 1, N - DO 80 I = 1, MIN( J+1, M ) - A( I, J ) = A( I, J )*MUL - 80 CONTINUE - 90 CONTINUE -* - ELSE IF( ITYPE.EQ.4 ) THEN -* -* Lower half of a symmetric band matrix -* - K3 = KL + 1 - K4 = N + 1 - DO 110 J = 1, N - DO 100 I = 1, MIN( K3, K4-J ) - A( I, J ) = A( I, J )*MUL - 100 CONTINUE - 110 CONTINUE -* - ELSE IF( ITYPE.EQ.5 ) THEN -* -* Upper half of a symmetric band matrix -* - K1 = KU + 2 - K3 = KU + 1 - DO 130 J = 1, N - DO 120 I = MAX( K1-J, 1 ), K3 - A( I, J ) = A( I, J )*MUL - 120 CONTINUE - 130 CONTINUE -* - ELSE IF( ITYPE.EQ.6 ) THEN -* -* Band matrix -* - K1 = KL + KU + 2 - K2 = KL + 1 - K3 = 2*KL + KU + 1 - K4 = KL + KU + 1 + M - DO 150 J = 1, N - DO 140 I = MAX( K1-J, K2 ), MIN( K3, K4-J ) - A( I, J ) = A( I, J )*MUL - 140 CONTINUE - 150 CONTINUE -* - END IF -* - IF( .NOT.DONE ) - $ GO TO 10 -* - RETURN -* -* End of ZLASCL -* - END diff --git a/lib/linalg/fortran/zlaset.f b/lib/linalg/fortran/zlaset.f deleted file mode 100644 index 00f5f595fc..0000000000 --- a/lib/linalg/fortran/zlaset.f +++ /dev/null @@ -1,181 +0,0 @@ -*> \brief \b ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZLASET + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZLASET( UPLO, M, N, ALPHA, BETA, A, LDA ) -* -* .. Scalar Arguments .. -* CHARACTER UPLO -* INTEGER LDA, M, N -* COMPLEX*16 ALPHA, BETA -* .. -* .. Array Arguments .. -* COMPLEX*16 A( LDA, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZLASET initializes a 2-D array A to BETA on the diagonal and -*> ALPHA on the offdiagonals. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> Specifies the part of the matrix A to be set. -*> = 'U': Upper triangular part is set. The lower triangle -*> is unchanged. -*> = 'L': Lower triangular part is set. The upper triangle -*> is unchanged. -*> Otherwise: All of the matrix A is set. -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> On entry, M specifies the number of rows of A. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> On entry, N specifies the number of columns of A. -*> \endverbatim -*> -*> \param[in] ALPHA -*> \verbatim -*> ALPHA is COMPLEX*16 -*> All the offdiagonal array elements are set to ALPHA. -*> \endverbatim -*> -*> \param[in] BETA -*> \verbatim -*> BETA is COMPLEX*16 -*> All the diagonal array elements are set to BETA. -*> \endverbatim -*> -*> \param[out] A -*> \verbatim -*> A is COMPLEX*16 array, dimension (LDA,N) -*> On entry, the m by n matrix A. -*> On exit, A(i,j) = ALPHA, 1 <= i <= m, 1 <= j <= n, i.ne.j; -*> A(i,i) = BETA , 1 <= i <= min(m,n) -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,M). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16OTHERauxiliary -* -* ===================================================================== - SUBROUTINE ZLASET( UPLO, M, N, ALPHA, BETA, A, LDA ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER UPLO - INTEGER LDA, M, N - COMPLEX*16 ALPHA, BETA -* .. -* .. Array Arguments .. - COMPLEX*16 A( LDA, * ) -* .. -* -* ===================================================================== -* -* .. Local Scalars .. - INTEGER I, J -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. Intrinsic Functions .. - INTRINSIC MIN -* .. -* .. Executable Statements .. -* - IF( LSAME( UPLO, 'U' ) ) THEN -* -* Set the diagonal to BETA and the strictly upper triangular -* part of the array to ALPHA. -* - DO 20 J = 2, N - DO 10 I = 1, MIN( J-1, M ) - A( I, J ) = ALPHA - 10 CONTINUE - 20 CONTINUE - DO 30 I = 1, MIN( N, M ) - A( I, I ) = BETA - 30 CONTINUE -* - ELSE IF( LSAME( UPLO, 'L' ) ) THEN -* -* Set the diagonal to BETA and the strictly lower triangular -* part of the array to ALPHA. -* - DO 50 J = 1, MIN( M, N ) - DO 40 I = J + 1, M - A( I, J ) = ALPHA - 40 CONTINUE - 50 CONTINUE - DO 60 I = 1, MIN( N, M ) - A( I, I ) = BETA - 60 CONTINUE -* - ELSE -* -* Set the array to BETA on the diagonal and ALPHA on the -* offdiagonal. -* - DO 80 J = 1, N - DO 70 I = 1, M - A( I, J ) = ALPHA - 70 CONTINUE - 80 CONTINUE - DO 90 I = 1, MIN( M, N ) - A( I, I ) = BETA - 90 CONTINUE - END IF -* - RETURN -* -* End of ZLASET -* - END diff --git a/lib/linalg/fortran/zlasr.f b/lib/linalg/fortran/zlasr.f deleted file mode 100644 index 07c91329c4..0000000000 --- a/lib/linalg/fortran/zlasr.f +++ /dev/null @@ -1,436 +0,0 @@ -*> \brief \b ZLASR applies a sequence of plane rotations to a general rectangular matrix. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZLASR + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA ) -* -* .. Scalar Arguments .. -* CHARACTER DIRECT, PIVOT, SIDE -* INTEGER LDA, M, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION C( * ), S( * ) -* COMPLEX*16 A( LDA, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZLASR applies a sequence of real plane rotations to a complex matrix -*> A, from either the left or the right. -*> -*> When SIDE = 'L', the transformation takes the form -*> -*> A := P*A -*> -*> and when SIDE = 'R', the transformation takes the form -*> -*> A := A*P**T -*> -*> where P is an orthogonal matrix consisting of a sequence of z plane -*> rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R', -*> and P**T is the transpose of P. -*> -*> When DIRECT = 'F' (Forward sequence), then -*> -*> P = P(z-1) * ... * P(2) * P(1) -*> -*> and when DIRECT = 'B' (Backward sequence), then -*> -*> P = P(1) * P(2) * ... * P(z-1) -*> -*> where P(k) is a plane rotation matrix defined by the 2-by-2 rotation -*> -*> R(k) = ( c(k) s(k) ) -*> = ( -s(k) c(k) ). -*> -*> When PIVOT = 'V' (Variable pivot), the rotation is performed -*> for the plane (k,k+1), i.e., P(k) has the form -*> -*> P(k) = ( 1 ) -*> ( ... ) -*> ( 1 ) -*> ( c(k) s(k) ) -*> ( -s(k) c(k) ) -*> ( 1 ) -*> ( ... ) -*> ( 1 ) -*> -*> where R(k) appears as a rank-2 modification to the identity matrix in -*> rows and columns k and k+1. -*> -*> When PIVOT = 'T' (Top pivot), the rotation is performed for the -*> plane (1,k+1), so P(k) has the form -*> -*> P(k) = ( c(k) s(k) ) -*> ( 1 ) -*> ( ... ) -*> ( 1 ) -*> ( -s(k) c(k) ) -*> ( 1 ) -*> ( ... ) -*> ( 1 ) -*> -*> where R(k) appears in rows and columns 1 and k+1. -*> -*> Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is -*> performed for the plane (k,z), giving P(k) the form -*> -*> P(k) = ( 1 ) -*> ( ... ) -*> ( 1 ) -*> ( c(k) s(k) ) -*> ( 1 ) -*> ( ... ) -*> ( 1 ) -*> ( -s(k) c(k) ) -*> -*> where R(k) appears in rows and columns k and z. The rotations are -*> performed without ever forming P(k) explicitly. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] SIDE -*> \verbatim -*> SIDE is CHARACTER*1 -*> Specifies whether the plane rotation matrix P is applied to -*> A on the left or the right. -*> = 'L': Left, compute A := P*A -*> = 'R': Right, compute A:= A*P**T -*> \endverbatim -*> -*> \param[in] PIVOT -*> \verbatim -*> PIVOT is CHARACTER*1 -*> Specifies the plane for which P(k) is a plane rotation -*> matrix. -*> = 'V': Variable pivot, the plane (k,k+1) -*> = 'T': Top pivot, the plane (1,k+1) -*> = 'B': Bottom pivot, the plane (k,z) -*> \endverbatim -*> -*> \param[in] DIRECT -*> \verbatim -*> DIRECT is CHARACTER*1 -*> Specifies whether P is a forward or backward sequence of -*> plane rotations. -*> = 'F': Forward, P = P(z-1)*...*P(2)*P(1) -*> = 'B': Backward, P = P(1)*P(2)*...*P(z-1) -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix A. If m <= 1, an immediate -*> return is effected. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix A. If n <= 1, an -*> immediate return is effected. -*> \endverbatim -*> -*> \param[in] C -*> \verbatim -*> C is DOUBLE PRECISION array, dimension -*> (M-1) if SIDE = 'L' -*> (N-1) if SIDE = 'R' -*> The cosines c(k) of the plane rotations. -*> \endverbatim -*> -*> \param[in] S -*> \verbatim -*> S is DOUBLE PRECISION array, dimension -*> (M-1) if SIDE = 'L' -*> (N-1) if SIDE = 'R' -*> The sines s(k) of the plane rotations. The 2-by-2 plane -*> rotation part of the matrix P(k), R(k), has the form -*> R(k) = ( c(k) s(k) ) -*> ( -s(k) c(k) ). -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is COMPLEX*16 array, dimension (LDA,N) -*> The M-by-N matrix A. On exit, A is overwritten by P*A if -*> SIDE = 'R' or by A*P**T if SIDE = 'L'. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,M). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16OTHERauxiliary -* -* ===================================================================== - SUBROUTINE ZLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER DIRECT, PIVOT, SIDE - INTEGER LDA, M, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION C( * ), S( * ) - COMPLEX*16 A( LDA, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE, ZERO - PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) -* .. -* .. Local Scalars .. - INTEGER I, INFO, J - DOUBLE PRECISION CTEMP, STEMP - COMPLEX*16 TEMP -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL XERBLA -* .. -* .. Executable Statements .. -* -* Test the input parameters -* - INFO = 0 - IF( .NOT.( LSAME( SIDE, 'L' ) .OR. LSAME( SIDE, 'R' ) ) ) THEN - INFO = 1 - ELSE IF( .NOT.( LSAME( PIVOT, 'V' ) .OR. LSAME( PIVOT, - $ 'T' ) .OR. LSAME( PIVOT, 'B' ) ) ) THEN - INFO = 2 - ELSE IF( .NOT.( LSAME( DIRECT, 'F' ) .OR. LSAME( DIRECT, 'B' ) ) ) - $ THEN - INFO = 3 - ELSE IF( M.LT.0 ) THEN - INFO = 4 - ELSE IF( N.LT.0 ) THEN - INFO = 5 - ELSE IF( LDA.LT.MAX( 1, M ) ) THEN - INFO = 9 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'ZLASR ', INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( ( M.EQ.0 ) .OR. ( N.EQ.0 ) ) - $ RETURN - IF( LSAME( SIDE, 'L' ) ) THEN -* -* Form P * A -* - IF( LSAME( PIVOT, 'V' ) ) THEN - IF( LSAME( DIRECT, 'F' ) ) THEN - DO 20 J = 1, M - 1 - CTEMP = C( J ) - STEMP = S( J ) - IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN - DO 10 I = 1, N - TEMP = A( J+1, I ) - A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I ) - A( J, I ) = STEMP*TEMP + CTEMP*A( J, I ) - 10 CONTINUE - END IF - 20 CONTINUE - ELSE IF( LSAME( DIRECT, 'B' ) ) THEN - DO 40 J = M - 1, 1, -1 - CTEMP = C( J ) - STEMP = S( J ) - IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN - DO 30 I = 1, N - TEMP = A( J+1, I ) - A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I ) - A( J, I ) = STEMP*TEMP + CTEMP*A( J, I ) - 30 CONTINUE - END IF - 40 CONTINUE - END IF - ELSE IF( LSAME( PIVOT, 'T' ) ) THEN - IF( LSAME( DIRECT, 'F' ) ) THEN - DO 60 J = 2, M - CTEMP = C( J-1 ) - STEMP = S( J-1 ) - IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN - DO 50 I = 1, N - TEMP = A( J, I ) - A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I ) - A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I ) - 50 CONTINUE - END IF - 60 CONTINUE - ELSE IF( LSAME( DIRECT, 'B' ) ) THEN - DO 80 J = M, 2, -1 - CTEMP = C( J-1 ) - STEMP = S( J-1 ) - IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN - DO 70 I = 1, N - TEMP = A( J, I ) - A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I ) - A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I ) - 70 CONTINUE - END IF - 80 CONTINUE - END IF - ELSE IF( LSAME( PIVOT, 'B' ) ) THEN - IF( LSAME( DIRECT, 'F' ) ) THEN - DO 100 J = 1, M - 1 - CTEMP = C( J ) - STEMP = S( J ) - IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN - DO 90 I = 1, N - TEMP = A( J, I ) - A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP - A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP - 90 CONTINUE - END IF - 100 CONTINUE - ELSE IF( LSAME( DIRECT, 'B' ) ) THEN - DO 120 J = M - 1, 1, -1 - CTEMP = C( J ) - STEMP = S( J ) - IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN - DO 110 I = 1, N - TEMP = A( J, I ) - A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP - A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP - 110 CONTINUE - END IF - 120 CONTINUE - END IF - END IF - ELSE IF( LSAME( SIDE, 'R' ) ) THEN -* -* Form A * P**T -* - IF( LSAME( PIVOT, 'V' ) ) THEN - IF( LSAME( DIRECT, 'F' ) ) THEN - DO 140 J = 1, N - 1 - CTEMP = C( J ) - STEMP = S( J ) - IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN - DO 130 I = 1, M - TEMP = A( I, J+1 ) - A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J ) - A( I, J ) = STEMP*TEMP + CTEMP*A( I, J ) - 130 CONTINUE - END IF - 140 CONTINUE - ELSE IF( LSAME( DIRECT, 'B' ) ) THEN - DO 160 J = N - 1, 1, -1 - CTEMP = C( J ) - STEMP = S( J ) - IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN - DO 150 I = 1, M - TEMP = A( I, J+1 ) - A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J ) - A( I, J ) = STEMP*TEMP + CTEMP*A( I, J ) - 150 CONTINUE - END IF - 160 CONTINUE - END IF - ELSE IF( LSAME( PIVOT, 'T' ) ) THEN - IF( LSAME( DIRECT, 'F' ) ) THEN - DO 180 J = 2, N - CTEMP = C( J-1 ) - STEMP = S( J-1 ) - IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN - DO 170 I = 1, M - TEMP = A( I, J ) - A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 ) - A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 ) - 170 CONTINUE - END IF - 180 CONTINUE - ELSE IF( LSAME( DIRECT, 'B' ) ) THEN - DO 200 J = N, 2, -1 - CTEMP = C( J-1 ) - STEMP = S( J-1 ) - IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN - DO 190 I = 1, M - TEMP = A( I, J ) - A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 ) - A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 ) - 190 CONTINUE - END IF - 200 CONTINUE - END IF - ELSE IF( LSAME( PIVOT, 'B' ) ) THEN - IF( LSAME( DIRECT, 'F' ) ) THEN - DO 220 J = 1, N - 1 - CTEMP = C( J ) - STEMP = S( J ) - IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN - DO 210 I = 1, M - TEMP = A( I, J ) - A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP - A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP - 210 CONTINUE - END IF - 220 CONTINUE - ELSE IF( LSAME( DIRECT, 'B' ) ) THEN - DO 240 J = N - 1, 1, -1 - CTEMP = C( J ) - STEMP = S( J ) - IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN - DO 230 I = 1, M - TEMP = A( I, J ) - A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP - A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP - 230 CONTINUE - END IF - 240 CONTINUE - END IF - END IF - END IF -* - RETURN -* -* End of ZLASR -* - END diff --git a/lib/linalg/fortran/zlassq.f b/lib/linalg/fortran/zlassq.f deleted file mode 100644 index fd13811bd9..0000000000 --- a/lib/linalg/fortran/zlassq.f +++ /dev/null @@ -1,168 +0,0 @@ -*> \brief \b ZLASSQ updates a sum of squares represented in scaled form. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZLASSQ + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZLASSQ( N, X, INCX, SCALE, SUMSQ ) -* -* .. Scalar Arguments .. -* INTEGER INCX, N -* DOUBLE PRECISION SCALE, SUMSQ -* .. -* .. Array Arguments .. -* COMPLEX*16 X( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZLASSQ returns the values scl and ssq such that -*> -*> ( scl**2 )*ssq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq, -*> -*> where x( i ) = abs( X( 1 + ( i - 1 )*INCX ) ). The value of sumsq is -*> assumed to be at least unity and the value of ssq will then satisfy -*> -*> 1.0 .le. ssq .le. ( sumsq + 2*n ). -*> -*> scale is assumed to be non-negative and scl returns the value -*> -*> scl = max( scale, abs( real( x( i ) ) ), abs( aimag( x( i ) ) ) ), -*> i -*> -*> scale and sumsq must be supplied in SCALE and SUMSQ respectively. -*> SCALE and SUMSQ are overwritten by scl and ssq respectively. -*> -*> The routine makes only one pass through the vector X. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of elements to be used from the vector X. -*> \endverbatim -*> -*> \param[in] X -*> \verbatim -*> X is COMPLEX*16 array, dimension (N) -*> The vector x as described above. -*> x( i ) = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n. -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> The increment between successive values of the vector X. -*> INCX > 0. -*> \endverbatim -*> -*> \param[in,out] SCALE -*> \verbatim -*> SCALE is DOUBLE PRECISION -*> On entry, the value scale in the equation above. -*> On exit, SCALE is overwritten with the value scl . -*> \endverbatim -*> -*> \param[in,out] SUMSQ -*> \verbatim -*> SUMSQ is DOUBLE PRECISION -*> On entry, the value sumsq in the equation above. -*> On exit, SUMSQ is overwritten with the value ssq . -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \date December 2016 -* -*> \ingroup complex16OTHERauxiliary -* -* ===================================================================== - SUBROUTINE ZLASSQ( N, X, INCX, SCALE, SUMSQ ) -* -* -- LAPACK auxiliary routine (version 3.7.0) -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* December 2016 -* -* .. Scalar Arguments .. - INTEGER INCX, N - DOUBLE PRECISION SCALE, SUMSQ -* .. -* .. Array Arguments .. - COMPLEX*16 X( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO - PARAMETER ( ZERO = 0.0D+0 ) -* .. -* .. Local Scalars .. - INTEGER IX - DOUBLE PRECISION TEMP1 -* .. -* .. External Functions .. - LOGICAL DISNAN - EXTERNAL DISNAN -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, DBLE, DIMAG -* .. -* .. Executable Statements .. -* - IF( N.GT.0 ) THEN - DO 10 IX = 1, 1 + ( N-1 )*INCX, INCX - TEMP1 = ABS( DBLE( X( IX ) ) ) - IF( TEMP1.GT.ZERO.OR.DISNAN( TEMP1 ) ) THEN - IF( SCALE.LT.TEMP1 ) THEN - SUMSQ = 1 + SUMSQ*( SCALE / TEMP1 )**2 - SCALE = TEMP1 - ELSE - SUMSQ = SUMSQ + ( TEMP1 / SCALE )**2 - END IF - END IF - TEMP1 = ABS( DIMAG( X( IX ) ) ) - IF( TEMP1.GT.ZERO.OR.DISNAN( TEMP1 ) ) THEN - IF( SCALE.LT.TEMP1 ) THEN - SUMSQ = 1 + SUMSQ*( SCALE / TEMP1 )**2 - SCALE = TEMP1 - ELSE - SUMSQ = SUMSQ + ( TEMP1 / SCALE )**2 - END IF - END IF - 10 CONTINUE - END IF -* - RETURN -* -* End of ZLASSQ -* - END diff --git a/lib/linalg/fortran/zlatrd.f b/lib/linalg/fortran/zlatrd.f deleted file mode 100644 index ee2a484723..0000000000 --- a/lib/linalg/fortran/zlatrd.f +++ /dev/null @@ -1,355 +0,0 @@ -*> \brief \b ZLATRD reduces the first nb rows and columns of a symmetric/Hermitian matrix A to real tridiagonal form by an unitary similarity transformation. -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZLATRD + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZLATRD( UPLO, N, NB, A, LDA, E, TAU, W, LDW ) -* -* .. Scalar Arguments .. -* CHARACTER UPLO -* INTEGER LDA, LDW, N, NB -* .. -* .. Array Arguments .. -* DOUBLE PRECISION E( * ) -* COMPLEX*16 A( LDA, * ), TAU( * ), W( LDW, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZLATRD reduces NB rows and columns of a complex Hermitian matrix A to -*> Hermitian tridiagonal form by a unitary similarity -*> transformation Q**H * A * Q, and returns the matrices V and W which are -*> needed to apply the transformation to the unreduced part of A. -*> -*> If UPLO = 'U', ZLATRD reduces the last NB rows and columns of a -*> matrix, of which the upper triangle is supplied; -*> if UPLO = 'L', ZLATRD reduces the first NB rows and columns of a -*> matrix, of which the lower triangle is supplied. -*> -*> This is an auxiliary routine called by ZHETRD. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> Specifies whether the upper or lower triangular part of the -*> Hermitian matrix A is stored: -*> = 'U': Upper triangular -*> = 'L': Lower triangular -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrix A. -*> \endverbatim -*> -*> \param[in] NB -*> \verbatim -*> NB is INTEGER -*> The number of rows and columns to be reduced. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is COMPLEX*16 array, dimension (LDA,N) -*> On entry, the Hermitian matrix A. If UPLO = 'U', the leading -*> n-by-n upper triangular part of A contains the upper -*> triangular part of the matrix A, and the strictly lower -*> triangular part of A is not referenced. If UPLO = 'L', the -*> leading n-by-n lower triangular part of A contains the lower -*> triangular part of the matrix A, and the strictly upper -*> triangular part of A is not referenced. -*> On exit: -*> if UPLO = 'U', the last NB columns have been reduced to -*> tridiagonal form, with the diagonal elements overwriting -*> the diagonal elements of A; the elements above the diagonal -*> with the array TAU, represent the unitary matrix Q as a -*> product of elementary reflectors; -*> if UPLO = 'L', the first NB columns have been reduced to -*> tridiagonal form, with the diagonal elements overwriting -*> the diagonal elements of A; the elements below the diagonal -*> with the array TAU, represent the unitary matrix Q as a -*> product of elementary reflectors. -*> See Further Details. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,N). -*> \endverbatim -*> -*> \param[out] E -*> \verbatim -*> E is DOUBLE PRECISION array, dimension (N-1) -*> If UPLO = 'U', E(n-nb:n-1) contains the superdiagonal -*> elements of the last NB columns of the reduced matrix; -*> if UPLO = 'L', E(1:nb) contains the subdiagonal elements of -*> the first NB columns of the reduced matrix. -*> \endverbatim -*> -*> \param[out] TAU -*> \verbatim -*> TAU is COMPLEX*16 array, dimension (N-1) -*> The scalar factors of the elementary reflectors, stored in -*> TAU(n-nb:n-1) if UPLO = 'U', and in TAU(1:nb) if UPLO = 'L'. -*> See Further Details. -*> \endverbatim -*> -*> \param[out] W -*> \verbatim -*> W is COMPLEX*16 array, dimension (LDW,NB) -*> The n-by-nb matrix W required to update the unreduced part -*> of A. -*> \endverbatim -*> -*> \param[in] LDW -*> \verbatim -*> LDW is INTEGER -*> The leading dimension of the array W. LDW >= max(1,N). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16OTHERauxiliary -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> If UPLO = 'U', the matrix Q is represented as a product of elementary -*> reflectors -*> -*> Q = H(n) H(n-1) . . . H(n-nb+1). -*> -*> Each H(i) has the form -*> -*> H(i) = I - tau * v * v**H -*> -*> where tau is a complex scalar, and v is a complex vector with -*> v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i), -*> and tau in TAU(i-1). -*> -*> If UPLO = 'L', the matrix Q is represented as a product of elementary -*> reflectors -*> -*> Q = H(1) H(2) . . . H(nb). -*> -*> Each H(i) has the form -*> -*> H(i) = I - tau * v * v**H -*> -*> where tau is a complex scalar, and v is a complex vector with -*> v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i), -*> and tau in TAU(i). -*> -*> The elements of the vectors v together form the n-by-nb matrix V -*> which is needed, with W, to apply the transformation to the unreduced -*> part of the matrix, using a Hermitian rank-2k update of the form: -*> A := A - V*W**H - W*V**H. -*> -*> The contents of A on exit are illustrated by the following examples -*> with n = 5 and nb = 2: -*> -*> if UPLO = 'U': if UPLO = 'L': -*> -*> ( a a a v4 v5 ) ( d ) -*> ( a a v4 v5 ) ( 1 d ) -*> ( a 1 v5 ) ( v1 1 a ) -*> ( d 1 ) ( v1 v2 a a ) -*> ( d ) ( v1 v2 a a a ) -*> -*> where d denotes a diagonal element of the reduced matrix, a denotes -*> an element of the original matrix that is unchanged, and vi denotes -*> an element of the vector defining H(i). -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE ZLATRD( UPLO, N, NB, A, LDA, E, TAU, W, LDW ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER UPLO - INTEGER LDA, LDW, N, NB -* .. -* .. Array Arguments .. - DOUBLE PRECISION E( * ) - COMPLEX*16 A( LDA, * ), TAU( * ), W( LDW, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - COMPLEX*16 ZERO, ONE, HALF - PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ), - $ ONE = ( 1.0D+0, 0.0D+0 ), - $ HALF = ( 0.5D+0, 0.0D+0 ) ) -* .. -* .. Local Scalars .. - INTEGER I, IW - COMPLEX*16 ALPHA -* .. -* .. External Subroutines .. - EXTERNAL ZAXPY, ZGEMV, ZHEMV, ZLACGV, ZLARFG, ZSCAL -* .. -* .. External Functions .. - LOGICAL LSAME - COMPLEX*16 ZDOTC - EXTERNAL LSAME, ZDOTC -* .. -* .. Intrinsic Functions .. - INTRINSIC DBLE, MIN -* .. -* .. Executable Statements .. -* -* Quick return if possible -* - IF( N.LE.0 ) - $ RETURN -* - IF( LSAME( UPLO, 'U' ) ) THEN -* -* Reduce last NB columns of upper triangle -* - DO 10 I = N, N - NB + 1, -1 - IW = I - N + NB - IF( I.LT.N ) THEN -* -* Update A(1:i,i) -* - A( I, I ) = DBLE( A( I, I ) ) - CALL ZLACGV( N-I, W( I, IW+1 ), LDW ) - CALL ZGEMV( 'No transpose', I, N-I, -ONE, A( 1, I+1 ), - $ LDA, W( I, IW+1 ), LDW, ONE, A( 1, I ), 1 ) - CALL ZLACGV( N-I, W( I, IW+1 ), LDW ) - CALL ZLACGV( N-I, A( I, I+1 ), LDA ) - CALL ZGEMV( 'No transpose', I, N-I, -ONE, W( 1, IW+1 ), - $ LDW, A( I, I+1 ), LDA, ONE, A( 1, I ), 1 ) - CALL ZLACGV( N-I, A( I, I+1 ), LDA ) - A( I, I ) = DBLE( A( I, I ) ) - END IF - IF( I.GT.1 ) THEN -* -* Generate elementary reflector H(i) to annihilate -* A(1:i-2,i) -* - ALPHA = A( I-1, I ) - CALL ZLARFG( I-1, ALPHA, A( 1, I ), 1, TAU( I-1 ) ) - E( I-1 ) = DBLE( ALPHA ) - A( I-1, I ) = ONE -* -* Compute W(1:i-1,i) -* - CALL ZHEMV( 'Upper', I-1, ONE, A, LDA, A( 1, I ), 1, - $ ZERO, W( 1, IW ), 1 ) - IF( I.LT.N ) THEN - CALL ZGEMV( 'Conjugate transpose', I-1, N-I, ONE, - $ W( 1, IW+1 ), LDW, A( 1, I ), 1, ZERO, - $ W( I+1, IW ), 1 ) - CALL ZGEMV( 'No transpose', I-1, N-I, -ONE, - $ A( 1, I+1 ), LDA, W( I+1, IW ), 1, ONE, - $ W( 1, IW ), 1 ) - CALL ZGEMV( 'Conjugate transpose', I-1, N-I, ONE, - $ A( 1, I+1 ), LDA, A( 1, I ), 1, ZERO, - $ W( I+1, IW ), 1 ) - CALL ZGEMV( 'No transpose', I-1, N-I, -ONE, - $ W( 1, IW+1 ), LDW, W( I+1, IW ), 1, ONE, - $ W( 1, IW ), 1 ) - END IF - CALL ZSCAL( I-1, TAU( I-1 ), W( 1, IW ), 1 ) - ALPHA = -HALF*TAU( I-1 )*ZDOTC( I-1, W( 1, IW ), 1, - $ A( 1, I ), 1 ) - CALL ZAXPY( I-1, ALPHA, A( 1, I ), 1, W( 1, IW ), 1 ) - END IF -* - 10 CONTINUE - ELSE -* -* Reduce first NB columns of lower triangle -* - DO 20 I = 1, NB -* -* Update A(i:n,i) -* - A( I, I ) = DBLE( A( I, I ) ) - CALL ZLACGV( I-1, W( I, 1 ), LDW ) - CALL ZGEMV( 'No transpose', N-I+1, I-1, -ONE, A( I, 1 ), - $ LDA, W( I, 1 ), LDW, ONE, A( I, I ), 1 ) - CALL ZLACGV( I-1, W( I, 1 ), LDW ) - CALL ZLACGV( I-1, A( I, 1 ), LDA ) - CALL ZGEMV( 'No transpose', N-I+1, I-1, -ONE, W( I, 1 ), - $ LDW, A( I, 1 ), LDA, ONE, A( I, I ), 1 ) - CALL ZLACGV( I-1, A( I, 1 ), LDA ) - A( I, I ) = DBLE( A( I, I ) ) - IF( I.LT.N ) THEN -* -* Generate elementary reflector H(i) to annihilate -* A(i+2:n,i) -* - ALPHA = A( I+1, I ) - CALL ZLARFG( N-I, ALPHA, A( MIN( I+2, N ), I ), 1, - $ TAU( I ) ) - E( I ) = DBLE( ALPHA ) - A( I+1, I ) = ONE -* -* Compute W(i+1:n,i) -* - CALL ZHEMV( 'Lower', N-I, ONE, A( I+1, I+1 ), LDA, - $ A( I+1, I ), 1, ZERO, W( I+1, I ), 1 ) - CALL ZGEMV( 'Conjugate transpose', N-I, I-1, ONE, - $ W( I+1, 1 ), LDW, A( I+1, I ), 1, ZERO, - $ W( 1, I ), 1 ) - CALL ZGEMV( 'No transpose', N-I, I-1, -ONE, A( I+1, 1 ), - $ LDA, W( 1, I ), 1, ONE, W( I+1, I ), 1 ) - CALL ZGEMV( 'Conjugate transpose', N-I, I-1, ONE, - $ A( I+1, 1 ), LDA, A( I+1, I ), 1, ZERO, - $ W( 1, I ), 1 ) - CALL ZGEMV( 'No transpose', N-I, I-1, -ONE, W( I+1, 1 ), - $ LDW, W( 1, I ), 1, ONE, W( I+1, I ), 1 ) - CALL ZSCAL( N-I, TAU( I ), W( I+1, I ), 1 ) - ALPHA = -HALF*TAU( I )*ZDOTC( N-I, W( I+1, I ), 1, - $ A( I+1, I ), 1 ) - CALL ZAXPY( N-I, ALPHA, A( I+1, I ), 1, W( I+1, I ), 1 ) - END IF -* - 20 CONTINUE - END IF -* - RETURN -* -* End of ZLATRD -* - END diff --git a/lib/linalg/fortran/zpptrf.f b/lib/linalg/fortran/zpptrf.f deleted file mode 100644 index a34d639131..0000000000 --- a/lib/linalg/fortran/zpptrf.f +++ /dev/null @@ -1,238 +0,0 @@ -*> \brief \b ZPPTRF -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZPPTRF + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZPPTRF( UPLO, N, AP, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER UPLO -* INTEGER INFO, N -* .. -* .. Array Arguments .. -* COMPLEX*16 AP( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZPPTRF computes the Cholesky factorization of a complex Hermitian -*> positive definite matrix A stored in packed format. -*> -*> The factorization has the form -*> A = U**H * U, if UPLO = 'U', or -*> A = L * L**H, if UPLO = 'L', -*> where U is an upper triangular matrix and L is lower triangular. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> = 'U': Upper triangle of A is stored; -*> = 'L': Lower triangle of A is stored. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in,out] AP -*> \verbatim -*> AP is COMPLEX*16 array, dimension (N*(N+1)/2) -*> On entry, the upper or lower triangle of the Hermitian matrix -*> A, packed columnwise in a linear array. The j-th column of A -*> is stored in the array AP as follows: -*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; -*> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. -*> See below for further details. -*> -*> On exit, if INFO = 0, the triangular factor U or L from the -*> Cholesky factorization A = U**H*U or A = L*L**H, in the same -*> storage format as A. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i is not -*> positive definite, and the factorization could not be -*> completed. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16OTHERcomputational -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> The packed storage scheme is illustrated by the following example -*> when N = 4, UPLO = 'U': -*> -*> Two-dimensional storage of the Hermitian matrix A: -*> -*> a11 a12 a13 a14 -*> a22 a23 a24 -*> a33 a34 (aij = conjg(aji)) -*> a44 -*> -*> Packed storage of the upper triangle of A: -*> -*> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ] -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE ZPPTRF( UPLO, N, AP, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER UPLO - INTEGER INFO, N -* .. -* .. Array Arguments .. - COMPLEX*16 AP( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) -* .. -* .. Local Scalars .. - LOGICAL UPPER - INTEGER J, JC, JJ - DOUBLE PRECISION AJJ -* .. -* .. External Functions .. - LOGICAL LSAME - COMPLEX*16 ZDOTC - EXTERNAL LSAME, ZDOTC -* .. -* .. External Subroutines .. - EXTERNAL XERBLA, ZDSCAL, ZHPR, ZTPSV -* .. -* .. Intrinsic Functions .. - INTRINSIC DBLE, SQRT -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 - UPPER = LSAME( UPLO, 'U' ) - IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'ZPPTRF', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( N.EQ.0 ) - $ RETURN -* - IF( UPPER ) THEN -* -* Compute the Cholesky factorization A = U**H * U. -* - JJ = 0 - DO 10 J = 1, N - JC = JJ + 1 - JJ = JJ + J -* -* Compute elements 1:J-1 of column J. -* - IF( J.GT.1 ) - $ CALL ZTPSV( 'Upper', 'Conjugate transpose', 'Non-unit', - $ J-1, AP, AP( JC ), 1 ) -* -* Compute U(J,J) and test for non-positive-definiteness. -* - AJJ = DBLE( AP( JJ ) ) - DBLE( ZDOTC( J-1, - $ AP( JC ), 1, AP( JC ), 1 ) ) - IF( AJJ.LE.ZERO ) THEN - AP( JJ ) = AJJ - GO TO 30 - END IF - AP( JJ ) = SQRT( AJJ ) - 10 CONTINUE - ELSE -* -* Compute the Cholesky factorization A = L * L**H. -* - JJ = 1 - DO 20 J = 1, N -* -* Compute L(J,J) and test for non-positive-definiteness. -* - AJJ = DBLE( AP( JJ ) ) - IF( AJJ.LE.ZERO ) THEN - AP( JJ ) = AJJ - GO TO 30 - END IF - AJJ = SQRT( AJJ ) - AP( JJ ) = AJJ -* -* Compute elements J+1:N of column J and update the trailing -* submatrix. -* - IF( J.LT.N ) THEN - CALL ZDSCAL( N-J, ONE / AJJ, AP( JJ+1 ), 1 ) - CALL ZHPR( 'Lower', N-J, -ONE, AP( JJ+1 ), 1, - $ AP( JJ+N-J+1 ) ) - JJ = JJ + N - J + 1 - END IF - 20 CONTINUE - END IF - GO TO 40 -* - 30 CONTINUE - INFO = J -* - 40 CONTINUE - RETURN -* -* End of ZPPTRF -* - END diff --git a/lib/linalg/fortran/zpptri.f b/lib/linalg/fortran/zpptri.f deleted file mode 100644 index a74466eb80..0000000000 --- a/lib/linalg/fortran/zpptri.f +++ /dev/null @@ -1,187 +0,0 @@ -*> \brief \b ZPPTRI -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZPPTRI + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZPPTRI( UPLO, N, AP, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER UPLO -* INTEGER INFO, N -* .. -* .. Array Arguments .. -* COMPLEX*16 AP( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZPPTRI computes the inverse of a complex Hermitian positive definite -*> matrix A using the Cholesky factorization A = U**H*U or A = L*L**H -*> computed by ZPPTRF. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> = 'U': Upper triangular factor is stored in AP; -*> = 'L': Lower triangular factor is stored in AP. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in,out] AP -*> \verbatim -*> AP is COMPLEX*16 array, dimension (N*(N+1)/2) -*> On entry, the triangular factor U or L from the Cholesky -*> factorization A = U**H*U or A = L*L**H, packed columnwise as -*> a linear array. The j-th column of U or L is stored in the -*> array AP as follows: -*> if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j; -*> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n. -*> -*> On exit, the upper or lower triangle of the (Hermitian) -*> inverse of A, overwriting the input factor U or L. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the (i,i) element of the factor U or L is -*> zero, and the inverse could not be computed. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16OTHERcomputational -* -* ===================================================================== - SUBROUTINE ZPPTRI( UPLO, N, AP, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER UPLO - INTEGER INFO, N -* .. -* .. Array Arguments .. - COMPLEX*16 AP( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE - PARAMETER ( ONE = 1.0D+0 ) -* .. -* .. Local Scalars .. - LOGICAL UPPER - INTEGER J, JC, JJ, JJN - DOUBLE PRECISION AJJ -* .. -* .. External Functions .. - LOGICAL LSAME - COMPLEX*16 ZDOTC - EXTERNAL LSAME, ZDOTC -* .. -* .. External Subroutines .. - EXTERNAL XERBLA, ZDSCAL, ZHPR, ZTPMV, ZTPTRI -* .. -* .. Intrinsic Functions .. - INTRINSIC DBLE -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 - UPPER = LSAME( UPLO, 'U' ) - IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'ZPPTRI', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( N.EQ.0 ) - $ RETURN -* -* Invert the triangular Cholesky factor U or L. -* - CALL ZTPTRI( UPLO, 'Non-unit', N, AP, INFO ) - IF( INFO.GT.0 ) - $ RETURN - IF( UPPER ) THEN -* -* Compute the product inv(U) * inv(U)**H. -* - JJ = 0 - DO 10 J = 1, N - JC = JJ + 1 - JJ = JJ + J - IF( J.GT.1 ) - $ CALL ZHPR( 'Upper', J-1, ONE, AP( JC ), 1, AP ) - AJJ = DBLE( AP( JJ ) ) - CALL ZDSCAL( J, AJJ, AP( JC ), 1 ) - 10 CONTINUE -* - ELSE -* -* Compute the product inv(L)**H * inv(L). -* - JJ = 1 - DO 20 J = 1, N - JJN = JJ + N - J + 1 - AP( JJ ) = DBLE( ZDOTC( N-J+1, AP( JJ ), 1, AP( JJ ), 1 ) ) - IF( J.LT.N ) - $ CALL ZTPMV( 'Lower', 'Conjugate transpose', 'Non-unit', - $ N-J, AP( JJN ), AP( JJ+1 ), 1 ) - JJ = JJN - 20 CONTINUE - END IF -* - RETURN -* -* End of ZPPTRI -* - END diff --git a/lib/linalg/fortran/zscal.f b/lib/linalg/fortran/zscal.f deleted file mode 100644 index 8b8c2c8ab5..0000000000 --- a/lib/linalg/fortran/zscal.f +++ /dev/null @@ -1,121 +0,0 @@ -*> \brief \b ZSCAL -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE ZSCAL(N,ZA,ZX,INCX) -* -* .. Scalar Arguments .. -* COMPLEX*16 ZA -* INTEGER INCX,N -* .. -* .. Array Arguments .. -* COMPLEX*16 ZX(*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZSCAL scales a vector by a constant. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> number of elements in input vector(s) -*> \endverbatim -*> -*> \param[in] ZA -*> \verbatim -*> ZA is COMPLEX*16 -*> On entry, ZA specifies the scalar alpha. -*> \endverbatim -*> -*> \param[in,out] ZX -*> \verbatim -*> ZX is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> storage spacing between elements of ZX -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16_blas_level1 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> jack dongarra, 3/11/78. -*> modified 3/93 to return if incx .le. 0. -*> modified 12/3/93, array(1) declarations changed to array(*) -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE ZSCAL(N,ZA,ZX,INCX) -* -* -- Reference BLAS level1 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - COMPLEX*16 ZA - INTEGER INCX,N -* .. -* .. Array Arguments .. - COMPLEX*16 ZX(*) -* .. -* -* ===================================================================== -* -* .. Local Scalars .. - INTEGER I,NINCX -* .. -* .. Parameters .. - COMPLEX*16 ONE - PARAMETER (ONE= (1.0D+0,0.0D+0)) -* .. - IF (N.LE.0 .OR. INCX.LE.0 .OR. ZA.EQ.ONE) RETURN - IF (INCX.EQ.1) THEN -* -* code for increment equal to 1 -* - DO I = 1,N - ZX(I) = ZA*ZX(I) - END DO - ELSE -* -* code for increment not equal to 1 -* - NINCX = N*INCX - DO I = 1,NINCX,INCX - ZX(I) = ZA*ZX(I) - END DO - END IF - RETURN -* -* End of ZSCAL -* - END diff --git a/lib/linalg/fortran/zstedc.f b/lib/linalg/fortran/zstedc.f deleted file mode 100644 index 74d390af7e..0000000000 --- a/lib/linalg/fortran/zstedc.f +++ /dev/null @@ -1,483 +0,0 @@ -*> \brief \b ZSTEDC -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZSTEDC + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, RWORK, -* LRWORK, IWORK, LIWORK, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER COMPZ -* INTEGER INFO, LDZ, LIWORK, LRWORK, LWORK, N -* .. -* .. Array Arguments .. -* INTEGER IWORK( * ) -* DOUBLE PRECISION D( * ), E( * ), RWORK( * ) -* COMPLEX*16 WORK( * ), Z( LDZ, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZSTEDC computes all eigenvalues and, optionally, eigenvectors of a -*> symmetric tridiagonal matrix using the divide and conquer method. -*> The eigenvectors of a full or band complex Hermitian matrix can also -*> be found if ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this -*> matrix to tridiagonal form. -*> -*> This code makes very mild assumptions about floating point -*> arithmetic. It will work on machines with a guard digit in -*> add/subtract, or on those binary machines without guard digits -*> which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. -*> It could conceivably fail on hexadecimal or decimal machines -*> without guard digits, but we know of none. See DLAED3 for details. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] COMPZ -*> \verbatim -*> COMPZ is CHARACTER*1 -*> = 'N': Compute eigenvalues only. -*> = 'I': Compute eigenvectors of tridiagonal matrix also. -*> = 'V': Compute eigenvectors of original Hermitian matrix -*> also. On entry, Z contains the unitary matrix used -*> to reduce the original matrix to tridiagonal form. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The dimension of the symmetric tridiagonal matrix. N >= 0. -*> \endverbatim -*> -*> \param[in,out] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension (N) -*> On entry, the diagonal elements of the tridiagonal matrix. -*> On exit, if INFO = 0, the eigenvalues in ascending order. -*> \endverbatim -*> -*> \param[in,out] E -*> \verbatim -*> E is DOUBLE PRECISION array, dimension (N-1) -*> On entry, the subdiagonal elements of the tridiagonal matrix. -*> On exit, E has been destroyed. -*> \endverbatim -*> -*> \param[in,out] Z -*> \verbatim -*> Z is COMPLEX*16 array, dimension (LDZ,N) -*> On entry, if COMPZ = 'V', then Z contains the unitary -*> matrix used in the reduction to tridiagonal form. -*> On exit, if INFO = 0, then if COMPZ = 'V', Z contains the -*> orthonormal eigenvectors of the original Hermitian matrix, -*> and if COMPZ = 'I', Z contains the orthonormal eigenvectors -*> of the symmetric tridiagonal matrix. -*> If COMPZ = 'N', then Z is not referenced. -*> \endverbatim -*> -*> \param[in] LDZ -*> \verbatim -*> LDZ is INTEGER -*> The leading dimension of the array Z. LDZ >= 1. -*> If eigenvectors are desired, then LDZ >= max(1,N). -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) -*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -*> \endverbatim -*> -*> \param[in] LWORK -*> \verbatim -*> LWORK is INTEGER -*> The dimension of the array WORK. -*> If COMPZ = 'N' or 'I', or N <= 1, LWORK must be at least 1. -*> If COMPZ = 'V' and N > 1, LWORK must be at least N*N. -*> Note that for COMPZ = 'V', then if N is less than or -*> equal to the minimum divide size, usually 25, then LWORK need -*> only be 1. -*> -*> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal sizes of the WORK, RWORK and -*> IWORK arrays, returns these values as the first entries of -*> the WORK, RWORK and IWORK arrays, and no error message -*> related to LWORK or LRWORK or LIWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] RWORK -*> \verbatim -*> RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) -*> On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. -*> \endverbatim -*> -*> \param[in] LRWORK -*> \verbatim -*> LRWORK is INTEGER -*> The dimension of the array RWORK. -*> If COMPZ = 'N' or N <= 1, LRWORK must be at least 1. -*> If COMPZ = 'V' and N > 1, LRWORK must be at least -*> 1 + 3*N + 2*N*lg N + 4*N**2 , -*> where lg( N ) = smallest integer k such -*> that 2**k >= N. -*> If COMPZ = 'I' and N > 1, LRWORK must be at least -*> 1 + 4*N + 2*N**2 . -*> Note that for COMPZ = 'I' or 'V', then if N is less than or -*> equal to the minimum divide size, usually 25, then LRWORK -*> need only be max(1,2*(N-1)). -*> -*> If LRWORK = -1, then a workspace query is assumed; the -*> routine only calculates the optimal sizes of the WORK, RWORK -*> and IWORK arrays, returns these values as the first entries -*> of the WORK, RWORK and IWORK arrays, and no error message -*> related to LWORK or LRWORK or LIWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] IWORK -*> \verbatim -*> IWORK is INTEGER array, dimension (MAX(1,LIWORK)) -*> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. -*> \endverbatim -*> -*> \param[in] LIWORK -*> \verbatim -*> LIWORK is INTEGER -*> The dimension of the array IWORK. -*> If COMPZ = 'N' or N <= 1, LIWORK must be at least 1. -*> If COMPZ = 'V' or N > 1, LIWORK must be at least -*> 6 + 6*N + 5*N*lg N. -*> If COMPZ = 'I' or N > 1, LIWORK must be at least -*> 3 + 5*N . -*> Note that for COMPZ = 'I' or 'V', then if N is less than or -*> equal to the minimum divide size, usually 25, then LIWORK -*> need only be 1. -*> -*> If LIWORK = -1, then a workspace query is assumed; the -*> routine only calculates the optimal sizes of the WORK, RWORK -*> and IWORK arrays, returns these values as the first entries -*> of the WORK, RWORK and IWORK arrays, and no error message -*> related to LWORK or LRWORK or LIWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit. -*> < 0: if INFO = -i, the i-th argument had an illegal value. -*> > 0: The algorithm failed to compute an eigenvalue while -*> working on the submatrix lying in rows and columns -*> INFO/(N+1) through mod(INFO,N+1). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16OTHERcomputational -* -*> \par Contributors: -* ================== -*> -*> Jeff Rutter, Computer Science Division, University of California -*> at Berkeley, USA -* -* ===================================================================== - SUBROUTINE ZSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, RWORK, - $ LRWORK, IWORK, LIWORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER COMPZ - INTEGER INFO, LDZ, LIWORK, LRWORK, LWORK, N -* .. -* .. Array Arguments .. - INTEGER IWORK( * ) - DOUBLE PRECISION D( * ), E( * ), RWORK( * ) - COMPLEX*16 WORK( * ), Z( LDZ, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, ONE, TWO - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0 ) -* .. -* .. Local Scalars .. - LOGICAL LQUERY - INTEGER FINISH, I, ICOMPZ, II, J, K, LGN, LIWMIN, LL, - $ LRWMIN, LWMIN, M, SMLSIZ, START - DOUBLE PRECISION EPS, ORGNRM, P, TINY -* .. -* .. External Functions .. - LOGICAL LSAME - INTEGER ILAENV - DOUBLE PRECISION DLAMCH, DLANST - EXTERNAL LSAME, ILAENV, DLAMCH, DLANST -* .. -* .. External Subroutines .. - EXTERNAL DLASCL, DLASET, DSTEDC, DSTEQR, DSTERF, XERBLA, - $ ZLACPY, ZLACRM, ZLAED0, ZSTEQR, ZSWAP -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, DBLE, INT, LOG, MAX, MOD, SQRT -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 - LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 .OR. LIWORK.EQ.-1 ) -* - IF( LSAME( COMPZ, 'N' ) ) THEN - ICOMPZ = 0 - ELSE IF( LSAME( COMPZ, 'V' ) ) THEN - ICOMPZ = 1 - ELSE IF( LSAME( COMPZ, 'I' ) ) THEN - ICOMPZ = 2 - ELSE - ICOMPZ = -1 - END IF - IF( ICOMPZ.LT.0 ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( ( LDZ.LT.1 ) .OR. - $ ( ICOMPZ.GT.0 .AND. LDZ.LT.MAX( 1, N ) ) ) THEN - INFO = -6 - END IF -* - IF( INFO.EQ.0 ) THEN -* -* Compute the workspace requirements -* - SMLSIZ = ILAENV( 9, 'ZSTEDC', ' ', 0, 0, 0, 0 ) - IF( N.LE.1 .OR. ICOMPZ.EQ.0 ) THEN - LWMIN = 1 - LIWMIN = 1 - LRWMIN = 1 - ELSE IF( N.LE.SMLSIZ ) THEN - LWMIN = 1 - LIWMIN = 1 - LRWMIN = 2*( N - 1 ) - ELSE IF( ICOMPZ.EQ.1 ) THEN - LGN = INT( LOG( DBLE( N ) ) / LOG( TWO ) ) - IF( 2**LGN.LT.N ) - $ LGN = LGN + 1 - IF( 2**LGN.LT.N ) - $ LGN = LGN + 1 - LWMIN = N*N - LRWMIN = 1 + 3*N + 2*N*LGN + 4*N**2 - LIWMIN = 6 + 6*N + 5*N*LGN - ELSE IF( ICOMPZ.EQ.2 ) THEN - LWMIN = 1 - LRWMIN = 1 + 4*N + 2*N**2 - LIWMIN = 3 + 5*N - END IF - WORK( 1 ) = LWMIN - RWORK( 1 ) = LRWMIN - IWORK( 1 ) = LIWMIN -* - IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN - INFO = -8 - ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN - INFO = -10 - ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN - INFO = -12 - END IF - END IF -* - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'ZSTEDC', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - RETURN - END IF -* -* Quick return if possible -* - IF( N.EQ.0 ) - $ RETURN - IF( N.EQ.1 ) THEN - IF( ICOMPZ.NE.0 ) - $ Z( 1, 1 ) = ONE - RETURN - END IF -* -* If the following conditional clause is removed, then the routine -* will use the Divide and Conquer routine to compute only the -* eigenvalues, which requires (3N + 3N**2) real workspace and -* (2 + 5N + 2N lg(N)) integer workspace. -* Since on many architectures DSTERF is much faster than any other -* algorithm for finding eigenvalues only, it is used here -* as the default. If the conditional clause is removed, then -* information on the size of workspace needs to be changed. -* -* If COMPZ = 'N', use DSTERF to compute the eigenvalues. -* - IF( ICOMPZ.EQ.0 ) THEN - CALL DSTERF( N, D, E, INFO ) - GO TO 70 - END IF -* -* If N is smaller than the minimum divide size (SMLSIZ+1), then -* solve the problem with another solver. -* - IF( N.LE.SMLSIZ ) THEN -* - CALL ZSTEQR( COMPZ, N, D, E, Z, LDZ, RWORK, INFO ) -* - ELSE -* -* If COMPZ = 'I', we simply call DSTEDC instead. -* - IF( ICOMPZ.EQ.2 ) THEN - CALL DLASET( 'Full', N, N, ZERO, ONE, RWORK, N ) - LL = N*N + 1 - CALL DSTEDC( 'I', N, D, E, RWORK, N, - $ RWORK( LL ), LRWORK-LL+1, IWORK, LIWORK, INFO ) - DO 20 J = 1, N - DO 10 I = 1, N - Z( I, J ) = RWORK( ( J-1 )*N+I ) - 10 CONTINUE - 20 CONTINUE - GO TO 70 - END IF -* -* From now on, only option left to be handled is COMPZ = 'V', -* i.e. ICOMPZ = 1. -* -* Scale. -* - ORGNRM = DLANST( 'M', N, D, E ) - IF( ORGNRM.EQ.ZERO ) - $ GO TO 70 -* - EPS = DLAMCH( 'Epsilon' ) -* - START = 1 -* -* while ( START <= N ) -* - 30 CONTINUE - IF( START.LE.N ) THEN -* -* Let FINISH be the position of the next subdiagonal entry -* such that E( FINISH ) <= TINY or FINISH = N if no such -* subdiagonal exists. The matrix identified by the elements -* between START and FINISH constitutes an independent -* sub-problem. -* - FINISH = START - 40 CONTINUE - IF( FINISH.LT.N ) THEN - TINY = EPS*SQRT( ABS( D( FINISH ) ) )* - $ SQRT( ABS( D( FINISH+1 ) ) ) - IF( ABS( E( FINISH ) ).GT.TINY ) THEN - FINISH = FINISH + 1 - GO TO 40 - END IF - END IF -* -* (Sub) Problem determined. Compute its size and solve it. -* - M = FINISH - START + 1 - IF( M.GT.SMLSIZ ) THEN -* -* Scale. -* - ORGNRM = DLANST( 'M', M, D( START ), E( START ) ) - CALL DLASCL( 'G', 0, 0, ORGNRM, ONE, M, 1, D( START ), M, - $ INFO ) - CALL DLASCL( 'G', 0, 0, ORGNRM, ONE, M-1, 1, E( START ), - $ M-1, INFO ) -* - CALL ZLAED0( N, M, D( START ), E( START ), Z( 1, START ), - $ LDZ, WORK, N, RWORK, IWORK, INFO ) - IF( INFO.GT.0 ) THEN - INFO = ( INFO / ( M+1 )+START-1 )*( N+1 ) + - $ MOD( INFO, ( M+1 ) ) + START - 1 - GO TO 70 - END IF -* -* Scale back. -* - CALL DLASCL( 'G', 0, 0, ONE, ORGNRM, M, 1, D( START ), M, - $ INFO ) -* - ELSE - CALL DSTEQR( 'I', M, D( START ), E( START ), RWORK, M, - $ RWORK( M*M+1 ), INFO ) - CALL ZLACRM( N, M, Z( 1, START ), LDZ, RWORK, M, WORK, N, - $ RWORK( M*M+1 ) ) - CALL ZLACPY( 'A', N, M, WORK, N, Z( 1, START ), LDZ ) - IF( INFO.GT.0 ) THEN - INFO = START*( N+1 ) + FINISH - GO TO 70 - END IF - END IF -* - START = FINISH + 1 - GO TO 30 - END IF -* -* endwhile -* -* -* Use Selection Sort to minimize swaps of eigenvectors -* - DO 60 II = 2, N - I = II - 1 - K = I - P = D( I ) - DO 50 J = II, N - IF( D( J ).LT.P ) THEN - K = J - P = D( J ) - END IF - 50 CONTINUE - IF( K.NE.I ) THEN - D( K ) = D( I ) - D( I ) = P - CALL ZSWAP( N, Z( 1, I ), 1, Z( 1, K ), 1 ) - END IF - 60 CONTINUE - END IF -* - 70 CONTINUE - WORK( 1 ) = LWMIN - RWORK( 1 ) = LRWMIN - IWORK( 1 ) = LIWMIN -* - RETURN -* -* End of ZSTEDC -* - END diff --git a/lib/linalg/fortran/zsteqr.f b/lib/linalg/fortran/zsteqr.f deleted file mode 100644 index 47f4004e8d..0000000000 --- a/lib/linalg/fortran/zsteqr.f +++ /dev/null @@ -1,573 +0,0 @@ -*> \brief \b ZSTEQR -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZSTEQR + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER COMPZ -* INTEGER INFO, LDZ, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION D( * ), E( * ), WORK( * ) -* COMPLEX*16 Z( LDZ, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZSTEQR computes all eigenvalues and, optionally, eigenvectors of a -*> symmetric tridiagonal matrix using the implicit QL or QR method. -*> The eigenvectors of a full or band complex Hermitian matrix can also -*> be found if ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this -*> matrix to tridiagonal form. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] COMPZ -*> \verbatim -*> COMPZ is CHARACTER*1 -*> = 'N': Compute eigenvalues only. -*> = 'V': Compute eigenvalues and eigenvectors of the original -*> Hermitian matrix. On entry, Z must contain the -*> unitary matrix used to reduce the original matrix -*> to tridiagonal form. -*> = 'I': Compute eigenvalues and eigenvectors of the -*> tridiagonal matrix. Z is initialized to the identity -*> matrix. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrix. N >= 0. -*> \endverbatim -*> -*> \param[in,out] D -*> \verbatim -*> D is DOUBLE PRECISION array, dimension (N) -*> On entry, the diagonal elements of the tridiagonal matrix. -*> On exit, if INFO = 0, the eigenvalues in ascending order. -*> \endverbatim -*> -*> \param[in,out] E -*> \verbatim -*> E is DOUBLE PRECISION array, dimension (N-1) -*> On entry, the (n-1) subdiagonal elements of the tridiagonal -*> matrix. -*> On exit, E has been destroyed. -*> \endverbatim -*> -*> \param[in,out] Z -*> \verbatim -*> Z is COMPLEX*16 array, dimension (LDZ, N) -*> On entry, if COMPZ = 'V', then Z contains the unitary -*> matrix used in the reduction to tridiagonal form. -*> On exit, if INFO = 0, then if COMPZ = 'V', Z contains the -*> orthonormal eigenvectors of the original Hermitian matrix, -*> and if COMPZ = 'I', Z contains the orthonormal eigenvectors -*> of the symmetric tridiagonal matrix. -*> If COMPZ = 'N', then Z is not referenced. -*> \endverbatim -*> -*> \param[in] LDZ -*> \verbatim -*> LDZ is INTEGER -*> The leading dimension of the array Z. LDZ >= 1, and if -*> eigenvectors are desired, then LDZ >= max(1,N). -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is DOUBLE PRECISION array, dimension (max(1,2*N-2)) -*> If COMPZ = 'N', then WORK is not referenced. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: the algorithm has failed to find all the eigenvalues in -*> a total of 30*N iterations; if INFO = i, then i -*> elements of E have not converged to zero; on exit, D -*> and E contain the elements of a symmetric tridiagonal -*> matrix which is unitarily similar to the original -*> matrix. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16OTHERcomputational -* -* ===================================================================== - SUBROUTINE ZSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER COMPZ - INTEGER INFO, LDZ, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION D( * ), E( * ), WORK( * ) - COMPLEX*16 Z( LDZ, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ZERO, ONE, TWO, THREE - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0, - $ THREE = 3.0D0 ) - COMPLEX*16 CZERO, CONE - PARAMETER ( CZERO = ( 0.0D0, 0.0D0 ), - $ CONE = ( 1.0D0, 0.0D0 ) ) - INTEGER MAXIT - PARAMETER ( MAXIT = 30 ) -* .. -* .. Local Scalars .. - INTEGER I, ICOMPZ, II, ISCALE, J, JTOT, K, L, L1, LEND, - $ LENDM1, LENDP1, LENDSV, LM1, LSV, M, MM, MM1, - $ NM1, NMAXIT - DOUBLE PRECISION ANORM, B, C, EPS, EPS2, F, G, P, R, RT1, RT2, - $ S, SAFMAX, SAFMIN, SSFMAX, SSFMIN, TST -* .. -* .. External Functions .. - LOGICAL LSAME - DOUBLE PRECISION DLAMCH, DLANST, DLAPY2 - EXTERNAL LSAME, DLAMCH, DLANST, DLAPY2 -* .. -* .. External Subroutines .. - EXTERNAL DLAE2, DLAEV2, DLARTG, DLASCL, DLASRT, XERBLA, - $ ZLASET, ZLASR, ZSWAP -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, MAX, SIGN, SQRT -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 -* - IF( LSAME( COMPZ, 'N' ) ) THEN - ICOMPZ = 0 - ELSE IF( LSAME( COMPZ, 'V' ) ) THEN - ICOMPZ = 1 - ELSE IF( LSAME( COMPZ, 'I' ) ) THEN - ICOMPZ = 2 - ELSE - ICOMPZ = -1 - END IF - IF( ICOMPZ.LT.0 ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( ( LDZ.LT.1 ) .OR. ( ICOMPZ.GT.0 .AND. LDZ.LT.MAX( 1, - $ N ) ) ) THEN - INFO = -6 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'ZSTEQR', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( N.EQ.0 ) - $ RETURN -* - IF( N.EQ.1 ) THEN - IF( ICOMPZ.EQ.2 ) - $ Z( 1, 1 ) = CONE - RETURN - END IF -* -* Determine the unit roundoff and over/underflow thresholds. -* - EPS = DLAMCH( 'E' ) - EPS2 = EPS**2 - SAFMIN = DLAMCH( 'S' ) - SAFMAX = ONE / SAFMIN - SSFMAX = SQRT( SAFMAX ) / THREE - SSFMIN = SQRT( SAFMIN ) / EPS2 -* -* Compute the eigenvalues and eigenvectors of the tridiagonal -* matrix. -* - IF( ICOMPZ.EQ.2 ) - $ CALL ZLASET( 'Full', N, N, CZERO, CONE, Z, LDZ ) -* - NMAXIT = N*MAXIT - JTOT = 0 -* -* Determine where the matrix splits and choose QL or QR iteration -* for each block, according to whether top or bottom diagonal -* element is smaller. -* - L1 = 1 - NM1 = N - 1 -* - 10 CONTINUE - IF( L1.GT.N ) - $ GO TO 160 - IF( L1.GT.1 ) - $ E( L1-1 ) = ZERO - IF( L1.LE.NM1 ) THEN - DO 20 M = L1, NM1 - TST = ABS( E( M ) ) - IF( TST.EQ.ZERO ) - $ GO TO 30 - IF( TST.LE.( SQRT( ABS( D( M ) ) )*SQRT( ABS( D( M+ - $ 1 ) ) ) )*EPS ) THEN - E( M ) = ZERO - GO TO 30 - END IF - 20 CONTINUE - END IF - M = N -* - 30 CONTINUE - L = L1 - LSV = L - LEND = M - LENDSV = LEND - L1 = M + 1 - IF( LEND.EQ.L ) - $ GO TO 10 -* -* Scale submatrix in rows and columns L to LEND -* - ANORM = DLANST( 'I', LEND-L+1, D( L ), E( L ) ) - ISCALE = 0 - IF( ANORM.EQ.ZERO ) - $ GO TO 10 - IF( ANORM.GT.SSFMAX ) THEN - ISCALE = 1 - CALL DLASCL( 'G', 0, 0, ANORM, SSFMAX, LEND-L+1, 1, D( L ), N, - $ INFO ) - CALL DLASCL( 'G', 0, 0, ANORM, SSFMAX, LEND-L, 1, E( L ), N, - $ INFO ) - ELSE IF( ANORM.LT.SSFMIN ) THEN - ISCALE = 2 - CALL DLASCL( 'G', 0, 0, ANORM, SSFMIN, LEND-L+1, 1, D( L ), N, - $ INFO ) - CALL DLASCL( 'G', 0, 0, ANORM, SSFMIN, LEND-L, 1, E( L ), N, - $ INFO ) - END IF -* -* Choose between QL and QR iteration -* - IF( ABS( D( LEND ) ).LT.ABS( D( L ) ) ) THEN - LEND = LSV - L = LENDSV - END IF -* - IF( LEND.GT.L ) THEN -* -* QL Iteration -* -* Look for small subdiagonal element. -* - 40 CONTINUE - IF( L.NE.LEND ) THEN - LENDM1 = LEND - 1 - DO 50 M = L, LENDM1 - TST = ABS( E( M ) )**2 - IF( TST.LE.( EPS2*ABS( D( M ) ) )*ABS( D( M+1 ) )+ - $ SAFMIN )GO TO 60 - 50 CONTINUE - END IF -* - M = LEND -* - 60 CONTINUE - IF( M.LT.LEND ) - $ E( M ) = ZERO - P = D( L ) - IF( M.EQ.L ) - $ GO TO 80 -* -* If remaining matrix is 2-by-2, use DLAE2 or SLAEV2 -* to compute its eigensystem. -* - IF( M.EQ.L+1 ) THEN - IF( ICOMPZ.GT.0 ) THEN - CALL DLAEV2( D( L ), E( L ), D( L+1 ), RT1, RT2, C, S ) - WORK( L ) = C - WORK( N-1+L ) = S - CALL ZLASR( 'R', 'V', 'B', N, 2, WORK( L ), - $ WORK( N-1+L ), Z( 1, L ), LDZ ) - ELSE - CALL DLAE2( D( L ), E( L ), D( L+1 ), RT1, RT2 ) - END IF - D( L ) = RT1 - D( L+1 ) = RT2 - E( L ) = ZERO - L = L + 2 - IF( L.LE.LEND ) - $ GO TO 40 - GO TO 140 - END IF -* - IF( JTOT.EQ.NMAXIT ) - $ GO TO 140 - JTOT = JTOT + 1 -* -* Form shift. -* - G = ( D( L+1 )-P ) / ( TWO*E( L ) ) - R = DLAPY2( G, ONE ) - G = D( M ) - P + ( E( L ) / ( G+SIGN( R, G ) ) ) -* - S = ONE - C = ONE - P = ZERO -* -* Inner loop -* - MM1 = M - 1 - DO 70 I = MM1, L, -1 - F = S*E( I ) - B = C*E( I ) - CALL DLARTG( G, F, C, S, R ) - IF( I.NE.M-1 ) - $ E( I+1 ) = R - G = D( I+1 ) - P - R = ( D( I )-G )*S + TWO*C*B - P = S*R - D( I+1 ) = G + P - G = C*R - B -* -* If eigenvectors are desired, then save rotations. -* - IF( ICOMPZ.GT.0 ) THEN - WORK( I ) = C - WORK( N-1+I ) = -S - END IF -* - 70 CONTINUE -* -* If eigenvectors are desired, then apply saved rotations. -* - IF( ICOMPZ.GT.0 ) THEN - MM = M - L + 1 - CALL ZLASR( 'R', 'V', 'B', N, MM, WORK( L ), WORK( N-1+L ), - $ Z( 1, L ), LDZ ) - END IF -* - D( L ) = D( L ) - P - E( L ) = G - GO TO 40 -* -* Eigenvalue found. -* - 80 CONTINUE - D( L ) = P -* - L = L + 1 - IF( L.LE.LEND ) - $ GO TO 40 - GO TO 140 -* - ELSE -* -* QR Iteration -* -* Look for small superdiagonal element. -* - 90 CONTINUE - IF( L.NE.LEND ) THEN - LENDP1 = LEND + 1 - DO 100 M = L, LENDP1, -1 - TST = ABS( E( M-1 ) )**2 - IF( TST.LE.( EPS2*ABS( D( M ) ) )*ABS( D( M-1 ) )+ - $ SAFMIN )GO TO 110 - 100 CONTINUE - END IF -* - M = LEND -* - 110 CONTINUE - IF( M.GT.LEND ) - $ E( M-1 ) = ZERO - P = D( L ) - IF( M.EQ.L ) - $ GO TO 130 -* -* If remaining matrix is 2-by-2, use DLAE2 or SLAEV2 -* to compute its eigensystem. -* - IF( M.EQ.L-1 ) THEN - IF( ICOMPZ.GT.0 ) THEN - CALL DLAEV2( D( L-1 ), E( L-1 ), D( L ), RT1, RT2, C, S ) - WORK( M ) = C - WORK( N-1+M ) = S - CALL ZLASR( 'R', 'V', 'F', N, 2, WORK( M ), - $ WORK( N-1+M ), Z( 1, L-1 ), LDZ ) - ELSE - CALL DLAE2( D( L-1 ), E( L-1 ), D( L ), RT1, RT2 ) - END IF - D( L-1 ) = RT1 - D( L ) = RT2 - E( L-1 ) = ZERO - L = L - 2 - IF( L.GE.LEND ) - $ GO TO 90 - GO TO 140 - END IF -* - IF( JTOT.EQ.NMAXIT ) - $ GO TO 140 - JTOT = JTOT + 1 -* -* Form shift. -* - G = ( D( L-1 )-P ) / ( TWO*E( L-1 ) ) - R = DLAPY2( G, ONE ) - G = D( M ) - P + ( E( L-1 ) / ( G+SIGN( R, G ) ) ) -* - S = ONE - C = ONE - P = ZERO -* -* Inner loop -* - LM1 = L - 1 - DO 120 I = M, LM1 - F = S*E( I ) - B = C*E( I ) - CALL DLARTG( G, F, C, S, R ) - IF( I.NE.M ) - $ E( I-1 ) = R - G = D( I ) - P - R = ( D( I+1 )-G )*S + TWO*C*B - P = S*R - D( I ) = G + P - G = C*R - B -* -* If eigenvectors are desired, then save rotations. -* - IF( ICOMPZ.GT.0 ) THEN - WORK( I ) = C - WORK( N-1+I ) = S - END IF -* - 120 CONTINUE -* -* If eigenvectors are desired, then apply saved rotations. -* - IF( ICOMPZ.GT.0 ) THEN - MM = L - M + 1 - CALL ZLASR( 'R', 'V', 'F', N, MM, WORK( M ), WORK( N-1+M ), - $ Z( 1, M ), LDZ ) - END IF -* - D( L ) = D( L ) - P - E( LM1 ) = G - GO TO 90 -* -* Eigenvalue found. -* - 130 CONTINUE - D( L ) = P -* - L = L - 1 - IF( L.GE.LEND ) - $ GO TO 90 - GO TO 140 -* - END IF -* -* Undo scaling if necessary -* - 140 CONTINUE - IF( ISCALE.EQ.1 ) THEN - CALL DLASCL( 'G', 0, 0, SSFMAX, ANORM, LENDSV-LSV+1, 1, - $ D( LSV ), N, INFO ) - CALL DLASCL( 'G', 0, 0, SSFMAX, ANORM, LENDSV-LSV, 1, E( LSV ), - $ N, INFO ) - ELSE IF( ISCALE.EQ.2 ) THEN - CALL DLASCL( 'G', 0, 0, SSFMIN, ANORM, LENDSV-LSV+1, 1, - $ D( LSV ), N, INFO ) - CALL DLASCL( 'G', 0, 0, SSFMIN, ANORM, LENDSV-LSV, 1, E( LSV ), - $ N, INFO ) - END IF -* -* Check for no convergence to an eigenvalue after a total -* of N*MAXIT iterations. -* - IF( JTOT.EQ.NMAXIT ) THEN - DO 150 I = 1, N - 1 - IF( E( I ).NE.ZERO ) - $ INFO = INFO + 1 - 150 CONTINUE - RETURN - END IF - GO TO 10 -* -* Order eigenvalues and eigenvectors. -* - 160 CONTINUE - IF( ICOMPZ.EQ.0 ) THEN -* -* Use Quick Sort -* - CALL DLASRT( 'I', N, D, INFO ) -* - ELSE -* -* Use Selection Sort to minimize swaps of eigenvectors -* - DO 180 II = 2, N - I = II - 1 - K = I - P = D( I ) - DO 170 J = II, N - IF( D( J ).LT.P ) THEN - K = J - P = D( J ) - END IF - 170 CONTINUE - IF( K.NE.I ) THEN - D( K ) = D( I ) - D( I ) = P - CALL ZSWAP( N, Z( 1, I ), 1, Z( 1, K ), 1 ) - END IF - 180 CONTINUE - END IF - RETURN -* -* End of ZSTEQR -* - END diff --git a/lib/linalg/fortran/zswap.f b/lib/linalg/fortran/zswap.f deleted file mode 100644 index 93f8fc52d0..0000000000 --- a/lib/linalg/fortran/zswap.f +++ /dev/null @@ -1,129 +0,0 @@ -*> \brief \b ZSWAP -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE ZSWAP(N,ZX,INCX,ZY,INCY) -* -* .. Scalar Arguments .. -* INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. -* COMPLEX*16 ZX(*),ZY(*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZSWAP interchanges two vectors. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> number of elements in input vector(s) -*> \endverbatim -*> -*> \param[in,out] ZX -*> \verbatim -*> ZX is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> storage spacing between elements of ZX -*> \endverbatim -*> -*> \param[in,out] ZY -*> \verbatim -*> ZY is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) -*> \endverbatim -*> -*> \param[in] INCY -*> \verbatim -*> INCY is INTEGER -*> storage spacing between elements of ZY -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16_blas_level1 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> jack dongarra, 3/11/78. -*> modified 12/3/93, array(1) declarations changed to array(*) -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE ZSWAP(N,ZX,INCX,ZY,INCY) -* -* -- Reference BLAS level1 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INCX,INCY,N -* .. -* .. Array Arguments .. - COMPLEX*16 ZX(*),ZY(*) -* .. -* -* ===================================================================== -* -* .. Local Scalars .. - COMPLEX*16 ZTEMP - INTEGER I,IX,IY -* .. - IF (N.LE.0) RETURN - IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN -* -* code for both increments equal to 1 - DO I = 1,N - ZTEMP = ZX(I) - ZX(I) = ZY(I) - ZY(I) = ZTEMP - END DO - ELSE -* -* code for unequal increments or equal increments not equal -* to 1 -* - IX = 1 - IY = 1 - IF (INCX.LT.0) IX = (-N+1)*INCX + 1 - IF (INCY.LT.0) IY = (-N+1)*INCY + 1 - DO I = 1,N - ZTEMP = ZX(IX) - ZX(IX) = ZY(IY) - ZY(IY) = ZTEMP - IX = IX + INCX - IY = IY + INCY - END DO - END IF - RETURN -* -* End of ZSWAP -* - END diff --git a/lib/linalg/fortran/ztpmv.f b/lib/linalg/fortran/ztpmv.f deleted file mode 100644 index 363fd5a2ac..0000000000 --- a/lib/linalg/fortran/ztpmv.f +++ /dev/null @@ -1,385 +0,0 @@ -*> \brief \b ZTPMV -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE ZTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX) -* -* .. Scalar Arguments .. -* INTEGER INCX,N -* CHARACTER DIAG,TRANS,UPLO -* .. -* .. Array Arguments .. -* COMPLEX*16 AP(*),X(*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZTPMV performs one of the matrix-vector operations -*> -*> x := A*x, or x := A**T*x, or x := A**H*x, -*> -*> where x is an n element vector and A is an n by n unit, or non-unit, -*> upper or lower triangular matrix, supplied in packed form. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> On entry, UPLO specifies whether the matrix is an upper or -*> lower triangular matrix as follows: -*> -*> UPLO = 'U' or 'u' A is an upper triangular matrix. -*> -*> UPLO = 'L' or 'l' A is a lower triangular matrix. -*> \endverbatim -*> -*> \param[in] TRANS -*> \verbatim -*> TRANS is CHARACTER*1 -*> On entry, TRANS specifies the operation to be performed as -*> follows: -*> -*> TRANS = 'N' or 'n' x := A*x. -*> -*> TRANS = 'T' or 't' x := A**T*x. -*> -*> TRANS = 'C' or 'c' x := A**H*x. -*> \endverbatim -*> -*> \param[in] DIAG -*> \verbatim -*> DIAG is CHARACTER*1 -*> On entry, DIAG specifies whether or not A is unit -*> triangular as follows: -*> -*> DIAG = 'U' or 'u' A is assumed to be unit triangular. -*> -*> DIAG = 'N' or 'n' A is not assumed to be unit -*> triangular. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> On entry, N specifies the order of the matrix A. -*> N must be at least zero. -*> \endverbatim -*> -*> \param[in] AP -*> \verbatim -*> AP is COMPLEX*16 array, dimension at least -*> ( ( n*( n + 1 ) )/2 ). -*> Before entry with UPLO = 'U' or 'u', the array AP must -*> contain the upper triangular matrix packed sequentially, -*> column by column, so that AP( 1 ) contains a( 1, 1 ), -*> AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) -*> respectively, and so on. -*> Before entry with UPLO = 'L' or 'l', the array AP must -*> contain the lower triangular matrix packed sequentially, -*> column by column, so that AP( 1 ) contains a( 1, 1 ), -*> AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) -*> respectively, and so on. -*> Note that when DIAG = 'U' or 'u', the diagonal elements of -*> A are not referenced, but are assumed to be unity. -*> \endverbatim -*> -*> \param[in,out] X -*> \verbatim -*> X is COMPLEX*16 array, dimension at least -*> ( 1 + ( n - 1 )*abs( INCX ) ). -*> Before entry, the incremented array X must contain the n -*> element vector x. On exit, X is overwritten with the -*> transformed vector x. -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> On entry, INCX specifies the increment for the elements of -*> X. INCX must not be zero. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16_blas_level2 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> Level 2 Blas routine. -*> The vector and matrix arguments are not referenced when N = 0, or M = 0 -*> -*> -- Written on 22-October-1986. -*> Jack Dongarra, Argonne National Lab. -*> Jeremy Du Croz, Nag Central Office. -*> Sven Hammarling, Nag Central Office. -*> Richard Hanson, Sandia National Labs. -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE ZTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX) -* -* -- Reference BLAS level2 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INCX,N - CHARACTER DIAG,TRANS,UPLO -* .. -* .. Array Arguments .. - COMPLEX*16 AP(*),X(*) -* .. -* -* ===================================================================== -* -* .. Parameters .. - COMPLEX*16 ZERO - PARAMETER (ZERO= (0.0D+0,0.0D+0)) -* .. -* .. Local Scalars .. - COMPLEX*16 TEMP - INTEGER I,INFO,IX,J,JX,K,KK,KX - LOGICAL NOCONJ,NOUNIT -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC DCONJG -* .. -* -* Test the input parameters. -* - INFO = 0 - IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN - INFO = 1 - ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. - + .NOT.LSAME(TRANS,'C')) THEN - INFO = 2 - ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN - INFO = 3 - ELSE IF (N.LT.0) THEN - INFO = 4 - ELSE IF (INCX.EQ.0) THEN - INFO = 7 - END IF - IF (INFO.NE.0) THEN - CALL XERBLA('ZTPMV ',INFO) - RETURN - END IF -* -* Quick return if possible. -* - IF (N.EQ.0) RETURN -* - NOCONJ = LSAME(TRANS,'T') - NOUNIT = LSAME(DIAG,'N') -* -* Set up the start point in X if the increment is not unity. This -* will be ( N - 1 )*INCX too small for descending loops. -* - IF (INCX.LE.0) THEN - KX = 1 - (N-1)*INCX - ELSE IF (INCX.NE.1) THEN - KX = 1 - END IF -* -* Start the operations. In this version the elements of AP are -* accessed sequentially with one pass through AP. -* - IF (LSAME(TRANS,'N')) THEN -* -* Form x:= A*x. -* - IF (LSAME(UPLO,'U')) THEN - KK = 1 - IF (INCX.EQ.1) THEN - DO 20 J = 1,N - IF (X(J).NE.ZERO) THEN - TEMP = X(J) - K = KK - DO 10 I = 1,J - 1 - X(I) = X(I) + TEMP*AP(K) - K = K + 1 - 10 CONTINUE - IF (NOUNIT) X(J) = X(J)*AP(KK+J-1) - END IF - KK = KK + J - 20 CONTINUE - ELSE - JX = KX - DO 40 J = 1,N - IF (X(JX).NE.ZERO) THEN - TEMP = X(JX) - IX = KX - DO 30 K = KK,KK + J - 2 - X(IX) = X(IX) + TEMP*AP(K) - IX = IX + INCX - 30 CONTINUE - IF (NOUNIT) X(JX) = X(JX)*AP(KK+J-1) - END IF - JX = JX + INCX - KK = KK + J - 40 CONTINUE - END IF - ELSE - KK = (N* (N+1))/2 - IF (INCX.EQ.1) THEN - DO 60 J = N,1,-1 - IF (X(J).NE.ZERO) THEN - TEMP = X(J) - K = KK - DO 50 I = N,J + 1,-1 - X(I) = X(I) + TEMP*AP(K) - K = K - 1 - 50 CONTINUE - IF (NOUNIT) X(J) = X(J)*AP(KK-N+J) - END IF - KK = KK - (N-J+1) - 60 CONTINUE - ELSE - KX = KX + (N-1)*INCX - JX = KX - DO 80 J = N,1,-1 - IF (X(JX).NE.ZERO) THEN - TEMP = X(JX) - IX = KX - DO 70 K = KK,KK - (N- (J+1)),-1 - X(IX) = X(IX) + TEMP*AP(K) - IX = IX - INCX - 70 CONTINUE - IF (NOUNIT) X(JX) = X(JX)*AP(KK-N+J) - END IF - JX = JX - INCX - KK = KK - (N-J+1) - 80 CONTINUE - END IF - END IF - ELSE -* -* Form x := A**T*x or x := A**H*x. -* - IF (LSAME(UPLO,'U')) THEN - KK = (N* (N+1))/2 - IF (INCX.EQ.1) THEN - DO 110 J = N,1,-1 - TEMP = X(J) - K = KK - 1 - IF (NOCONJ) THEN - IF (NOUNIT) TEMP = TEMP*AP(KK) - DO 90 I = J - 1,1,-1 - TEMP = TEMP + AP(K)*X(I) - K = K - 1 - 90 CONTINUE - ELSE - IF (NOUNIT) TEMP = TEMP*DCONJG(AP(KK)) - DO 100 I = J - 1,1,-1 - TEMP = TEMP + DCONJG(AP(K))*X(I) - K = K - 1 - 100 CONTINUE - END IF - X(J) = TEMP - KK = KK - J - 110 CONTINUE - ELSE - JX = KX + (N-1)*INCX - DO 140 J = N,1,-1 - TEMP = X(JX) - IX = JX - IF (NOCONJ) THEN - IF (NOUNIT) TEMP = TEMP*AP(KK) - DO 120 K = KK - 1,KK - J + 1,-1 - IX = IX - INCX - TEMP = TEMP + AP(K)*X(IX) - 120 CONTINUE - ELSE - IF (NOUNIT) TEMP = TEMP*DCONJG(AP(KK)) - DO 130 K = KK - 1,KK - J + 1,-1 - IX = IX - INCX - TEMP = TEMP + DCONJG(AP(K))*X(IX) - 130 CONTINUE - END IF - X(JX) = TEMP - JX = JX - INCX - KK = KK - J - 140 CONTINUE - END IF - ELSE - KK = 1 - IF (INCX.EQ.1) THEN - DO 170 J = 1,N - TEMP = X(J) - K = KK + 1 - IF (NOCONJ) THEN - IF (NOUNIT) TEMP = TEMP*AP(KK) - DO 150 I = J + 1,N - TEMP = TEMP + AP(K)*X(I) - K = K + 1 - 150 CONTINUE - ELSE - IF (NOUNIT) TEMP = TEMP*DCONJG(AP(KK)) - DO 160 I = J + 1,N - TEMP = TEMP + DCONJG(AP(K))*X(I) - K = K + 1 - 160 CONTINUE - END IF - X(J) = TEMP - KK = KK + (N-J+1) - 170 CONTINUE - ELSE - JX = KX - DO 200 J = 1,N - TEMP = X(JX) - IX = JX - IF (NOCONJ) THEN - IF (NOUNIT) TEMP = TEMP*AP(KK) - DO 180 K = KK + 1,KK + N - J - IX = IX + INCX - TEMP = TEMP + AP(K)*X(IX) - 180 CONTINUE - ELSE - IF (NOUNIT) TEMP = TEMP*DCONJG(AP(KK)) - DO 190 K = KK + 1,KK + N - J - IX = IX + INCX - TEMP = TEMP + DCONJG(AP(K))*X(IX) - 190 CONTINUE - END IF - X(JX) = TEMP - JX = JX + INCX - KK = KK + (N-J+1) - 200 CONTINUE - END IF - END IF - END IF -* - RETURN -* -* End of ZTPMV -* - END diff --git a/lib/linalg/fortran/ztpsv.f b/lib/linalg/fortran/ztpsv.f deleted file mode 100644 index c6f24d0b27..0000000000 --- a/lib/linalg/fortran/ztpsv.f +++ /dev/null @@ -1,387 +0,0 @@ -*> \brief \b ZTPSV -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE ZTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX) -* -* .. Scalar Arguments .. -* INTEGER INCX,N -* CHARACTER DIAG,TRANS,UPLO -* .. -* .. Array Arguments .. -* COMPLEX*16 AP(*),X(*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZTPSV solves one of the systems of equations -*> -*> A*x = b, or A**T*x = b, or A**H*x = b, -*> -*> where b and x are n element vectors and A is an n by n unit, or -*> non-unit, upper or lower triangular matrix, supplied in packed form. -*> -*> No test for singularity or near-singularity is included in this -*> routine. Such tests must be performed before calling this routine. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> On entry, UPLO specifies whether the matrix is an upper or -*> lower triangular matrix as follows: -*> -*> UPLO = 'U' or 'u' A is an upper triangular matrix. -*> -*> UPLO = 'L' or 'l' A is a lower triangular matrix. -*> \endverbatim -*> -*> \param[in] TRANS -*> \verbatim -*> TRANS is CHARACTER*1 -*> On entry, TRANS specifies the equations to be solved as -*> follows: -*> -*> TRANS = 'N' or 'n' A*x = b. -*> -*> TRANS = 'T' or 't' A**T*x = b. -*> -*> TRANS = 'C' or 'c' A**H*x = b. -*> \endverbatim -*> -*> \param[in] DIAG -*> \verbatim -*> DIAG is CHARACTER*1 -*> On entry, DIAG specifies whether or not A is unit -*> triangular as follows: -*> -*> DIAG = 'U' or 'u' A is assumed to be unit triangular. -*> -*> DIAG = 'N' or 'n' A is not assumed to be unit -*> triangular. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> On entry, N specifies the order of the matrix A. -*> N must be at least zero. -*> \endverbatim -*> -*> \param[in] AP -*> \verbatim -*> AP is COMPLEX*16 array, dimension at least -*> ( ( n*( n + 1 ) )/2 ). -*> Before entry with UPLO = 'U' or 'u', the array AP must -*> contain the upper triangular matrix packed sequentially, -*> column by column, so that AP( 1 ) contains a( 1, 1 ), -*> AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) -*> respectively, and so on. -*> Before entry with UPLO = 'L' or 'l', the array AP must -*> contain the lower triangular matrix packed sequentially, -*> column by column, so that AP( 1 ) contains a( 1, 1 ), -*> AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) -*> respectively, and so on. -*> Note that when DIAG = 'U' or 'u', the diagonal elements of -*> A are not referenced, but are assumed to be unity. -*> \endverbatim -*> -*> \param[in,out] X -*> \verbatim -*> X is COMPLEX*16 array, dimension at least -*> ( 1 + ( n - 1 )*abs( INCX ) ). -*> Before entry, the incremented array X must contain the n -*> element right-hand side vector b. On exit, X is overwritten -*> with the solution vector x. -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> On entry, INCX specifies the increment for the elements of -*> X. INCX must not be zero. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16_blas_level2 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> Level 2 Blas routine. -*> -*> -- Written on 22-October-1986. -*> Jack Dongarra, Argonne National Lab. -*> Jeremy Du Croz, Nag Central Office. -*> Sven Hammarling, Nag Central Office. -*> Richard Hanson, Sandia National Labs. -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE ZTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX) -* -* -- Reference BLAS level2 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INCX,N - CHARACTER DIAG,TRANS,UPLO -* .. -* .. Array Arguments .. - COMPLEX*16 AP(*),X(*) -* .. -* -* ===================================================================== -* -* .. Parameters .. - COMPLEX*16 ZERO - PARAMETER (ZERO= (0.0D+0,0.0D+0)) -* .. -* .. Local Scalars .. - COMPLEX*16 TEMP - INTEGER I,INFO,IX,J,JX,K,KK,KX - LOGICAL NOCONJ,NOUNIT -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC DCONJG -* .. -* -* Test the input parameters. -* - INFO = 0 - IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN - INFO = 1 - ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. - + .NOT.LSAME(TRANS,'C')) THEN - INFO = 2 - ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN - INFO = 3 - ELSE IF (N.LT.0) THEN - INFO = 4 - ELSE IF (INCX.EQ.0) THEN - INFO = 7 - END IF - IF (INFO.NE.0) THEN - CALL XERBLA('ZTPSV ',INFO) - RETURN - END IF -* -* Quick return if possible. -* - IF (N.EQ.0) RETURN -* - NOCONJ = LSAME(TRANS,'T') - NOUNIT = LSAME(DIAG,'N') -* -* Set up the start point in X if the increment is not unity. This -* will be ( N - 1 )*INCX too small for descending loops. -* - IF (INCX.LE.0) THEN - KX = 1 - (N-1)*INCX - ELSE IF (INCX.NE.1) THEN - KX = 1 - END IF -* -* Start the operations. In this version the elements of AP are -* accessed sequentially with one pass through AP. -* - IF (LSAME(TRANS,'N')) THEN -* -* Form x := inv( A )*x. -* - IF (LSAME(UPLO,'U')) THEN - KK = (N* (N+1))/2 - IF (INCX.EQ.1) THEN - DO 20 J = N,1,-1 - IF (X(J).NE.ZERO) THEN - IF (NOUNIT) X(J) = X(J)/AP(KK) - TEMP = X(J) - K = KK - 1 - DO 10 I = J - 1,1,-1 - X(I) = X(I) - TEMP*AP(K) - K = K - 1 - 10 CONTINUE - END IF - KK = KK - J - 20 CONTINUE - ELSE - JX = KX + (N-1)*INCX - DO 40 J = N,1,-1 - IF (X(JX).NE.ZERO) THEN - IF (NOUNIT) X(JX) = X(JX)/AP(KK) - TEMP = X(JX) - IX = JX - DO 30 K = KK - 1,KK - J + 1,-1 - IX = IX - INCX - X(IX) = X(IX) - TEMP*AP(K) - 30 CONTINUE - END IF - JX = JX - INCX - KK = KK - J - 40 CONTINUE - END IF - ELSE - KK = 1 - IF (INCX.EQ.1) THEN - DO 60 J = 1,N - IF (X(J).NE.ZERO) THEN - IF (NOUNIT) X(J) = X(J)/AP(KK) - TEMP = X(J) - K = KK + 1 - DO 50 I = J + 1,N - X(I) = X(I) - TEMP*AP(K) - K = K + 1 - 50 CONTINUE - END IF - KK = KK + (N-J+1) - 60 CONTINUE - ELSE - JX = KX - DO 80 J = 1,N - IF (X(JX).NE.ZERO) THEN - IF (NOUNIT) X(JX) = X(JX)/AP(KK) - TEMP = X(JX) - IX = JX - DO 70 K = KK + 1,KK + N - J - IX = IX + INCX - X(IX) = X(IX) - TEMP*AP(K) - 70 CONTINUE - END IF - JX = JX + INCX - KK = KK + (N-J+1) - 80 CONTINUE - END IF - END IF - ELSE -* -* Form x := inv( A**T )*x or x := inv( A**H )*x. -* - IF (LSAME(UPLO,'U')) THEN - KK = 1 - IF (INCX.EQ.1) THEN - DO 110 J = 1,N - TEMP = X(J) - K = KK - IF (NOCONJ) THEN - DO 90 I = 1,J - 1 - TEMP = TEMP - AP(K)*X(I) - K = K + 1 - 90 CONTINUE - IF (NOUNIT) TEMP = TEMP/AP(KK+J-1) - ELSE - DO 100 I = 1,J - 1 - TEMP = TEMP - DCONJG(AP(K))*X(I) - K = K + 1 - 100 CONTINUE - IF (NOUNIT) TEMP = TEMP/DCONJG(AP(KK+J-1)) - END IF - X(J) = TEMP - KK = KK + J - 110 CONTINUE - ELSE - JX = KX - DO 140 J = 1,N - TEMP = X(JX) - IX = KX - IF (NOCONJ) THEN - DO 120 K = KK,KK + J - 2 - TEMP = TEMP - AP(K)*X(IX) - IX = IX + INCX - 120 CONTINUE - IF (NOUNIT) TEMP = TEMP/AP(KK+J-1) - ELSE - DO 130 K = KK,KK + J - 2 - TEMP = TEMP - DCONJG(AP(K))*X(IX) - IX = IX + INCX - 130 CONTINUE - IF (NOUNIT) TEMP = TEMP/DCONJG(AP(KK+J-1)) - END IF - X(JX) = TEMP - JX = JX + INCX - KK = KK + J - 140 CONTINUE - END IF - ELSE - KK = (N* (N+1))/2 - IF (INCX.EQ.1) THEN - DO 170 J = N,1,-1 - TEMP = X(J) - K = KK - IF (NOCONJ) THEN - DO 150 I = N,J + 1,-1 - TEMP = TEMP - AP(K)*X(I) - K = K - 1 - 150 CONTINUE - IF (NOUNIT) TEMP = TEMP/AP(KK-N+J) - ELSE - DO 160 I = N,J + 1,-1 - TEMP = TEMP - DCONJG(AP(K))*X(I) - K = K - 1 - 160 CONTINUE - IF (NOUNIT) TEMP = TEMP/DCONJG(AP(KK-N+J)) - END IF - X(J) = TEMP - KK = KK - (N-J+1) - 170 CONTINUE - ELSE - KX = KX + (N-1)*INCX - JX = KX - DO 200 J = N,1,-1 - TEMP = X(JX) - IX = KX - IF (NOCONJ) THEN - DO 180 K = KK,KK - (N- (J+1)),-1 - TEMP = TEMP - AP(K)*X(IX) - IX = IX - INCX - 180 CONTINUE - IF (NOUNIT) TEMP = TEMP/AP(KK-N+J) - ELSE - DO 190 K = KK,KK - (N- (J+1)),-1 - TEMP = TEMP - DCONJG(AP(K))*X(IX) - IX = IX - INCX - 190 CONTINUE - IF (NOUNIT) TEMP = TEMP/DCONJG(AP(KK-N+J)) - END IF - X(JX) = TEMP - JX = JX - INCX - KK = KK - (N-J+1) - 200 CONTINUE - END IF - END IF - END IF -* - RETURN -* -* End of ZTPSV -* - END diff --git a/lib/linalg/fortran/ztptri.f b/lib/linalg/fortran/ztptri.f deleted file mode 100644 index 31284ad637..0000000000 --- a/lib/linalg/fortran/ztptri.f +++ /dev/null @@ -1,239 +0,0 @@ -*> \brief \b ZTPTRI -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZTPTRI + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZTPTRI( UPLO, DIAG, N, AP, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER DIAG, UPLO -* INTEGER INFO, N -* .. -* .. Array Arguments .. -* COMPLEX*16 AP( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZTPTRI computes the inverse of a complex upper or lower triangular -*> matrix A stored in packed format. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> = 'U': A is upper triangular; -*> = 'L': A is lower triangular. -*> \endverbatim -*> -*> \param[in] DIAG -*> \verbatim -*> DIAG is CHARACTER*1 -*> = 'N': A is non-unit triangular; -*> = 'U': A is unit triangular. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in,out] AP -*> \verbatim -*> AP is COMPLEX*16 array, dimension (N*(N+1)/2) -*> On entry, the upper or lower triangular matrix A, stored -*> columnwise in a linear array. The j-th column of A is stored -*> in the array AP as follows: -*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; -*> if UPLO = 'L', AP(i + (j-1)*((2*n-j)/2) = A(i,j) for j<=i<=n. -*> See below for further details. -*> On exit, the (triangular) inverse of the original matrix, in -*> the same packed storage format. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, A(i,i) is exactly zero. The triangular -*> matrix is singular and its inverse can not be computed. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16OTHERcomputational -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> A triangular matrix A can be transferred to packed storage using one -*> of the following program segments: -*> -*> UPLO = 'U': UPLO = 'L': -*> -*> JC = 1 JC = 1 -*> DO 2 J = 1, N DO 2 J = 1, N -*> DO 1 I = 1, J DO 1 I = J, N -*> AP(JC+I-1) = A(I,J) AP(JC+I-J) = A(I,J) -*> 1 CONTINUE 1 CONTINUE -*> JC = JC + J JC = JC + N - J + 1 -*> 2 CONTINUE 2 CONTINUE -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE ZTPTRI( UPLO, DIAG, N, AP, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER DIAG, UPLO - INTEGER INFO, N -* .. -* .. Array Arguments .. - COMPLEX*16 AP( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - COMPLEX*16 ONE, ZERO - PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ), - $ ZERO = ( 0.0D+0, 0.0D+0 ) ) -* .. -* .. Local Scalars .. - LOGICAL NOUNIT, UPPER - INTEGER J, JC, JCLAST, JJ - COMPLEX*16 AJJ -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL XERBLA, ZSCAL, ZTPMV -* .. -* .. Executable Statements .. -* -* Test the input parameters. -* - INFO = 0 - UPPER = LSAME( UPLO, 'U' ) - NOUNIT = LSAME( DIAG, 'N' ) - IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN - INFO = -1 - ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN - INFO = -2 - ELSE IF( N.LT.0 ) THEN - INFO = -3 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'ZTPTRI', -INFO ) - RETURN - END IF -* -* Check for singularity if non-unit. -* - IF( NOUNIT ) THEN - IF( UPPER ) THEN - JJ = 0 - DO 10 INFO = 1, N - JJ = JJ + INFO - IF( AP( JJ ).EQ.ZERO ) - $ RETURN - 10 CONTINUE - ELSE - JJ = 1 - DO 20 INFO = 1, N - IF( AP( JJ ).EQ.ZERO ) - $ RETURN - JJ = JJ + N - INFO + 1 - 20 CONTINUE - END IF - INFO = 0 - END IF -* - IF( UPPER ) THEN -* -* Compute inverse of upper triangular matrix. -* - JC = 1 - DO 30 J = 1, N - IF( NOUNIT ) THEN - AP( JC+J-1 ) = ONE / AP( JC+J-1 ) - AJJ = -AP( JC+J-1 ) - ELSE - AJJ = -ONE - END IF -* -* Compute elements 1:j-1 of j-th column. -* - CALL ZTPMV( 'Upper', 'No transpose', DIAG, J-1, AP, - $ AP( JC ), 1 ) - CALL ZSCAL( J-1, AJJ, AP( JC ), 1 ) - JC = JC + J - 30 CONTINUE -* - ELSE -* -* Compute inverse of lower triangular matrix. -* - JC = N*( N+1 ) / 2 - DO 40 J = N, 1, -1 - IF( NOUNIT ) THEN - AP( JC ) = ONE / AP( JC ) - AJJ = -AP( JC ) - ELSE - AJJ = -ONE - END IF - IF( J.LT.N ) THEN -* -* Compute elements j+1:n of j-th column. -* - CALL ZTPMV( 'Lower', 'No transpose', DIAG, N-J, - $ AP( JCLAST ), AP( JC+1 ), 1 ) - CALL ZSCAL( N-J, AJJ, AP( JC+1 ), 1 ) - END IF - JCLAST = JC - JC = JC - N + J - 2 - 40 CONTINUE - END IF -* - RETURN -* -* End of ZTPTRI -* - END diff --git a/lib/linalg/fortran/ztrmm.f b/lib/linalg/fortran/ztrmm.f deleted file mode 100644 index c59c367cee..0000000000 --- a/lib/linalg/fortran/ztrmm.f +++ /dev/null @@ -1,449 +0,0 @@ -*> \brief \b ZTRMM -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE ZTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) -* -* .. Scalar Arguments .. -* COMPLEX*16 ALPHA -* INTEGER LDA,LDB,M,N -* CHARACTER DIAG,SIDE,TRANSA,UPLO -* .. -* .. Array Arguments .. -* COMPLEX*16 A(LDA,*),B(LDB,*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZTRMM performs one of the matrix-matrix operations -*> -*> B := alpha*op( A )*B, or B := alpha*B*op( A ) -*> -*> where alpha is a scalar, B is an m by n matrix, A is a unit, or -*> non-unit, upper or lower triangular matrix and op( A ) is one of -*> -*> op( A ) = A or op( A ) = A**T or op( A ) = A**H. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] SIDE -*> \verbatim -*> SIDE is CHARACTER*1 -*> On entry, SIDE specifies whether op( A ) multiplies B from -*> the left or right as follows: -*> -*> SIDE = 'L' or 'l' B := alpha*op( A )*B. -*> -*> SIDE = 'R' or 'r' B := alpha*B*op( A ). -*> \endverbatim -*> -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> On entry, UPLO specifies whether the matrix A is an upper or -*> lower triangular matrix as follows: -*> -*> UPLO = 'U' or 'u' A is an upper triangular matrix. -*> -*> UPLO = 'L' or 'l' A is a lower triangular matrix. -*> \endverbatim -*> -*> \param[in] TRANSA -*> \verbatim -*> TRANSA is CHARACTER*1 -*> On entry, TRANSA specifies the form of op( A ) to be used in -*> the matrix multiplication as follows: -*> -*> TRANSA = 'N' or 'n' op( A ) = A. -*> -*> TRANSA = 'T' or 't' op( A ) = A**T. -*> -*> TRANSA = 'C' or 'c' op( A ) = A**H. -*> \endverbatim -*> -*> \param[in] DIAG -*> \verbatim -*> DIAG is CHARACTER*1 -*> On entry, DIAG specifies whether or not A is unit triangular -*> as follows: -*> -*> DIAG = 'U' or 'u' A is assumed to be unit triangular. -*> -*> DIAG = 'N' or 'n' A is not assumed to be unit -*> triangular. -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> On entry, M specifies the number of rows of B. M must be at -*> least zero. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> On entry, N specifies the number of columns of B. N must be -*> at least zero. -*> \endverbatim -*> -*> \param[in] ALPHA -*> \verbatim -*> ALPHA is COMPLEX*16 -*> On entry, ALPHA specifies the scalar alpha. When alpha is -*> zero then A is not referenced and B need not be set before -*> entry. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is COMPLEX*16 array, dimension ( LDA, k ), where k is m -*> when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. -*> Before entry with UPLO = 'U' or 'u', the leading k by k -*> upper triangular part of the array A must contain the upper -*> triangular matrix and the strictly lower triangular part of -*> A is not referenced. -*> Before entry with UPLO = 'L' or 'l', the leading k by k -*> lower triangular part of the array A must contain the lower -*> triangular matrix and the strictly upper triangular part of -*> A is not referenced. -*> Note that when DIAG = 'U' or 'u', the diagonal elements of -*> A are not referenced either, but are assumed to be unity. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> On entry, LDA specifies the first dimension of A as declared -*> in the calling (sub) program. When SIDE = 'L' or 'l' then -*> LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' -*> then LDA must be at least max( 1, n ). -*> \endverbatim -*> -*> \param[in,out] B -*> \verbatim -*> B is COMPLEX*16 array, dimension ( LDB, N ). -*> Before entry, the leading m by n part of the array B must -*> contain the matrix B, and on exit is overwritten by the -*> transformed matrix. -*> \endverbatim -*> -*> \param[in] LDB -*> \verbatim -*> LDB is INTEGER -*> On entry, LDB specifies the first dimension of B as declared -*> in the calling (sub) program. LDB must be at least -*> max( 1, m ). -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16_blas_level3 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> Level 3 Blas routine. -*> -*> -- Written on 8-February-1989. -*> Jack Dongarra, Argonne National Laboratory. -*> Iain Duff, AERE Harwell. -*> Jeremy Du Croz, Numerical Algorithms Group Ltd. -*> Sven Hammarling, Numerical Algorithms Group Ltd. -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE ZTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) -* -* -- Reference BLAS level3 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - COMPLEX*16 ALPHA - INTEGER LDA,LDB,M,N - CHARACTER DIAG,SIDE,TRANSA,UPLO -* .. -* .. Array Arguments .. - COMPLEX*16 A(LDA,*),B(LDB,*) -* .. -* -* ===================================================================== -* -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC DCONJG,MAX -* .. -* .. Local Scalars .. - COMPLEX*16 TEMP - INTEGER I,INFO,J,K,NROWA - LOGICAL LSIDE,NOCONJ,NOUNIT,UPPER -* .. -* .. Parameters .. - COMPLEX*16 ONE - PARAMETER (ONE= (1.0D+0,0.0D+0)) - COMPLEX*16 ZERO - PARAMETER (ZERO= (0.0D+0,0.0D+0)) -* .. -* -* Test the input parameters. -* - LSIDE = LSAME(SIDE,'L') - IF (LSIDE) THEN - NROWA = M - ELSE - NROWA = N - END IF - NOCONJ = LSAME(TRANSA,'T') - NOUNIT = LSAME(DIAG,'N') - UPPER = LSAME(UPLO,'U') -* - INFO = 0 - IF ((.NOT.LSIDE) .AND. (.NOT.LSAME(SIDE,'R'))) THEN - INFO = 1 - ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN - INFO = 2 - ELSE IF ((.NOT.LSAME(TRANSA,'N')) .AND. - + (.NOT.LSAME(TRANSA,'T')) .AND. - + (.NOT.LSAME(TRANSA,'C'))) THEN - INFO = 3 - ELSE IF ((.NOT.LSAME(DIAG,'U')) .AND. (.NOT.LSAME(DIAG,'N'))) THEN - INFO = 4 - ELSE IF (M.LT.0) THEN - INFO = 5 - ELSE IF (N.LT.0) THEN - INFO = 6 - ELSE IF (LDA.LT.MAX(1,NROWA)) THEN - INFO = 9 - ELSE IF (LDB.LT.MAX(1,M)) THEN - INFO = 11 - END IF - IF (INFO.NE.0) THEN - CALL XERBLA('ZTRMM ',INFO) - RETURN - END IF -* -* Quick return if possible. -* - IF (M.EQ.0 .OR. N.EQ.0) RETURN -* -* And when alpha.eq.zero. -* - IF (ALPHA.EQ.ZERO) THEN - DO 20 J = 1,N - DO 10 I = 1,M - B(I,J) = ZERO - 10 CONTINUE - 20 CONTINUE - RETURN - END IF -* -* Start the operations. -* - IF (LSIDE) THEN - IF (LSAME(TRANSA,'N')) THEN -* -* Form B := alpha*A*B. -* - IF (UPPER) THEN - DO 50 J = 1,N - DO 40 K = 1,M - IF (B(K,J).NE.ZERO) THEN - TEMP = ALPHA*B(K,J) - DO 30 I = 1,K - 1 - B(I,J) = B(I,J) + TEMP*A(I,K) - 30 CONTINUE - IF (NOUNIT) TEMP = TEMP*A(K,K) - B(K,J) = TEMP - END IF - 40 CONTINUE - 50 CONTINUE - ELSE - DO 80 J = 1,N - DO 70 K = M,1,-1 - IF (B(K,J).NE.ZERO) THEN - TEMP = ALPHA*B(K,J) - B(K,J) = TEMP - IF (NOUNIT) B(K,J) = B(K,J)*A(K,K) - DO 60 I = K + 1,M - B(I,J) = B(I,J) + TEMP*A(I,K) - 60 CONTINUE - END IF - 70 CONTINUE - 80 CONTINUE - END IF - ELSE -* -* Form B := alpha*A**T*B or B := alpha*A**H*B. -* - IF (UPPER) THEN - DO 120 J = 1,N - DO 110 I = M,1,-1 - TEMP = B(I,J) - IF (NOCONJ) THEN - IF (NOUNIT) TEMP = TEMP*A(I,I) - DO 90 K = 1,I - 1 - TEMP = TEMP + A(K,I)*B(K,J) - 90 CONTINUE - ELSE - IF (NOUNIT) TEMP = TEMP*DCONJG(A(I,I)) - DO 100 K = 1,I - 1 - TEMP = TEMP + DCONJG(A(K,I))*B(K,J) - 100 CONTINUE - END IF - B(I,J) = ALPHA*TEMP - 110 CONTINUE - 120 CONTINUE - ELSE - DO 160 J = 1,N - DO 150 I = 1,M - TEMP = B(I,J) - IF (NOCONJ) THEN - IF (NOUNIT) TEMP = TEMP*A(I,I) - DO 130 K = I + 1,M - TEMP = TEMP + A(K,I)*B(K,J) - 130 CONTINUE - ELSE - IF (NOUNIT) TEMP = TEMP*DCONJG(A(I,I)) - DO 140 K = I + 1,M - TEMP = TEMP + DCONJG(A(K,I))*B(K,J) - 140 CONTINUE - END IF - B(I,J) = ALPHA*TEMP - 150 CONTINUE - 160 CONTINUE - END IF - END IF - ELSE - IF (LSAME(TRANSA,'N')) THEN -* -* Form B := alpha*B*A. -* - IF (UPPER) THEN - DO 200 J = N,1,-1 - TEMP = ALPHA - IF (NOUNIT) TEMP = TEMP*A(J,J) - DO 170 I = 1,M - B(I,J) = TEMP*B(I,J) - 170 CONTINUE - DO 190 K = 1,J - 1 - IF (A(K,J).NE.ZERO) THEN - TEMP = ALPHA*A(K,J) - DO 180 I = 1,M - B(I,J) = B(I,J) + TEMP*B(I,K) - 180 CONTINUE - END IF - 190 CONTINUE - 200 CONTINUE - ELSE - DO 240 J = 1,N - TEMP = ALPHA - IF (NOUNIT) TEMP = TEMP*A(J,J) - DO 210 I = 1,M - B(I,J) = TEMP*B(I,J) - 210 CONTINUE - DO 230 K = J + 1,N - IF (A(K,J).NE.ZERO) THEN - TEMP = ALPHA*A(K,J) - DO 220 I = 1,M - B(I,J) = B(I,J) + TEMP*B(I,K) - 220 CONTINUE - END IF - 230 CONTINUE - 240 CONTINUE - END IF - ELSE -* -* Form B := alpha*B*A**T or B := alpha*B*A**H. -* - IF (UPPER) THEN - DO 280 K = 1,N - DO 260 J = 1,K - 1 - IF (A(J,K).NE.ZERO) THEN - IF (NOCONJ) THEN - TEMP = ALPHA*A(J,K) - ELSE - TEMP = ALPHA*DCONJG(A(J,K)) - END IF - DO 250 I = 1,M - B(I,J) = B(I,J) + TEMP*B(I,K) - 250 CONTINUE - END IF - 260 CONTINUE - TEMP = ALPHA - IF (NOUNIT) THEN - IF (NOCONJ) THEN - TEMP = TEMP*A(K,K) - ELSE - TEMP = TEMP*DCONJG(A(K,K)) - END IF - END IF - IF (TEMP.NE.ONE) THEN - DO 270 I = 1,M - B(I,K) = TEMP*B(I,K) - 270 CONTINUE - END IF - 280 CONTINUE - ELSE - DO 320 K = N,1,-1 - DO 300 J = K + 1,N - IF (A(J,K).NE.ZERO) THEN - IF (NOCONJ) THEN - TEMP = ALPHA*A(J,K) - ELSE - TEMP = ALPHA*DCONJG(A(J,K)) - END IF - DO 290 I = 1,M - B(I,J) = B(I,J) + TEMP*B(I,K) - 290 CONTINUE - END IF - 300 CONTINUE - TEMP = ALPHA - IF (NOUNIT) THEN - IF (NOCONJ) THEN - TEMP = TEMP*A(K,K) - ELSE - TEMP = TEMP*DCONJG(A(K,K)) - END IF - END IF - IF (TEMP.NE.ONE) THEN - DO 310 I = 1,M - B(I,K) = TEMP*B(I,K) - 310 CONTINUE - END IF - 320 CONTINUE - END IF - END IF - END IF -* - RETURN -* -* End of ZTRMM -* - END diff --git a/lib/linalg/fortran/ztrmv.f b/lib/linalg/fortran/ztrmv.f deleted file mode 100644 index e8314facb7..0000000000 --- a/lib/linalg/fortran/ztrmv.f +++ /dev/null @@ -1,370 +0,0 @@ -*> \brief \b ZTRMV -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* SUBROUTINE ZTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) -* -* .. Scalar Arguments .. -* INTEGER INCX,LDA,N -* CHARACTER DIAG,TRANS,UPLO -* .. -* .. Array Arguments .. -* COMPLEX*16 A(LDA,*),X(*) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZTRMV performs one of the matrix-vector operations -*> -*> x := A*x, or x := A**T*x, or x := A**H*x, -*> -*> where x is an n element vector and A is an n by n unit, or non-unit, -*> upper or lower triangular matrix. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> On entry, UPLO specifies whether the matrix is an upper or -*> lower triangular matrix as follows: -*> -*> UPLO = 'U' or 'u' A is an upper triangular matrix. -*> -*> UPLO = 'L' or 'l' A is a lower triangular matrix. -*> \endverbatim -*> -*> \param[in] TRANS -*> \verbatim -*> TRANS is CHARACTER*1 -*> On entry, TRANS specifies the operation to be performed as -*> follows: -*> -*> TRANS = 'N' or 'n' x := A*x. -*> -*> TRANS = 'T' or 't' x := A**T*x. -*> -*> TRANS = 'C' or 'c' x := A**H*x. -*> \endverbatim -*> -*> \param[in] DIAG -*> \verbatim -*> DIAG is CHARACTER*1 -*> On entry, DIAG specifies whether or not A is unit -*> triangular as follows: -*> -*> DIAG = 'U' or 'u' A is assumed to be unit triangular. -*> -*> DIAG = 'N' or 'n' A is not assumed to be unit -*> triangular. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> On entry, N specifies the order of the matrix A. -*> N must be at least zero. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is COMPLEX*16 array, dimension ( LDA, N ). -*> Before entry with UPLO = 'U' or 'u', the leading n by n -*> upper triangular part of the array A must contain the upper -*> triangular matrix and the strictly lower triangular part of -*> A is not referenced. -*> Before entry with UPLO = 'L' or 'l', the leading n by n -*> lower triangular part of the array A must contain the lower -*> triangular matrix and the strictly upper triangular part of -*> A is not referenced. -*> Note that when DIAG = 'U' or 'u', the diagonal elements of -*> A are not referenced either, but are assumed to be unity. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> On entry, LDA specifies the first dimension of A as declared -*> in the calling (sub) program. LDA must be at least -*> max( 1, n ). -*> \endverbatim -*> -*> \param[in,out] X -*> \verbatim -*> X is COMPLEX*16 array, dimension at least -*> ( 1 + ( n - 1 )*abs( INCX ) ). -*> Before entry, the incremented array X must contain the n -*> element vector x. On exit, X is overwritten with the -*> transformed vector x. -*> \endverbatim -*> -*> \param[in] INCX -*> \verbatim -*> INCX is INTEGER -*> On entry, INCX specifies the increment for the elements of -*> X. INCX must not be zero. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16_blas_level2 -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> Level 2 Blas routine. -*> The vector and matrix arguments are not referenced when N = 0, or M = 0 -*> -*> -- Written on 22-October-1986. -*> Jack Dongarra, Argonne National Lab. -*> Jeremy Du Croz, Nag Central Office. -*> Sven Hammarling, Nag Central Office. -*> Richard Hanson, Sandia National Labs. -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE ZTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) -* -* -- Reference BLAS level2 routine -- -* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INCX,LDA,N - CHARACTER DIAG,TRANS,UPLO -* .. -* .. Array Arguments .. - COMPLEX*16 A(LDA,*),X(*) -* .. -* -* ===================================================================== -* -* .. Parameters .. - COMPLEX*16 ZERO - PARAMETER (ZERO= (0.0D+0,0.0D+0)) -* .. -* .. Local Scalars .. - COMPLEX*16 TEMP - INTEGER I,INFO,IX,J,JX,KX - LOGICAL NOCONJ,NOUNIT -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC DCONJG,MAX -* .. -* -* Test the input parameters. -* - INFO = 0 - IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN - INFO = 1 - ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. - + .NOT.LSAME(TRANS,'C')) THEN - INFO = 2 - ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN - INFO = 3 - ELSE IF (N.LT.0) THEN - INFO = 4 - ELSE IF (LDA.LT.MAX(1,N)) THEN - INFO = 6 - ELSE IF (INCX.EQ.0) THEN - INFO = 8 - END IF - IF (INFO.NE.0) THEN - CALL XERBLA('ZTRMV ',INFO) - RETURN - END IF -* -* Quick return if possible. -* - IF (N.EQ.0) RETURN -* - NOCONJ = LSAME(TRANS,'T') - NOUNIT = LSAME(DIAG,'N') -* -* Set up the start point in X if the increment is not unity. This -* will be ( N - 1 )*INCX too small for descending loops. -* - IF (INCX.LE.0) THEN - KX = 1 - (N-1)*INCX - ELSE IF (INCX.NE.1) THEN - KX = 1 - END IF -* -* Start the operations. In this version the elements of A are -* accessed sequentially with one pass through A. -* - IF (LSAME(TRANS,'N')) THEN -* -* Form x := A*x. -* - IF (LSAME(UPLO,'U')) THEN - IF (INCX.EQ.1) THEN - DO 20 J = 1,N - IF (X(J).NE.ZERO) THEN - TEMP = X(J) - DO 10 I = 1,J - 1 - X(I) = X(I) + TEMP*A(I,J) - 10 CONTINUE - IF (NOUNIT) X(J) = X(J)*A(J,J) - END IF - 20 CONTINUE - ELSE - JX = KX - DO 40 J = 1,N - IF (X(JX).NE.ZERO) THEN - TEMP = X(JX) - IX = KX - DO 30 I = 1,J - 1 - X(IX) = X(IX) + TEMP*A(I,J) - IX = IX + INCX - 30 CONTINUE - IF (NOUNIT) X(JX) = X(JX)*A(J,J) - END IF - JX = JX + INCX - 40 CONTINUE - END IF - ELSE - IF (INCX.EQ.1) THEN - DO 60 J = N,1,-1 - IF (X(J).NE.ZERO) THEN - TEMP = X(J) - DO 50 I = N,J + 1,-1 - X(I) = X(I) + TEMP*A(I,J) - 50 CONTINUE - IF (NOUNIT) X(J) = X(J)*A(J,J) - END IF - 60 CONTINUE - ELSE - KX = KX + (N-1)*INCX - JX = KX - DO 80 J = N,1,-1 - IF (X(JX).NE.ZERO) THEN - TEMP = X(JX) - IX = KX - DO 70 I = N,J + 1,-1 - X(IX) = X(IX) + TEMP*A(I,J) - IX = IX - INCX - 70 CONTINUE - IF (NOUNIT) X(JX) = X(JX)*A(J,J) - END IF - JX = JX - INCX - 80 CONTINUE - END IF - END IF - ELSE -* -* Form x := A**T*x or x := A**H*x. -* - IF (LSAME(UPLO,'U')) THEN - IF (INCX.EQ.1) THEN - DO 110 J = N,1,-1 - TEMP = X(J) - IF (NOCONJ) THEN - IF (NOUNIT) TEMP = TEMP*A(J,J) - DO 90 I = J - 1,1,-1 - TEMP = TEMP + A(I,J)*X(I) - 90 CONTINUE - ELSE - IF (NOUNIT) TEMP = TEMP*DCONJG(A(J,J)) - DO 100 I = J - 1,1,-1 - TEMP = TEMP + DCONJG(A(I,J))*X(I) - 100 CONTINUE - END IF - X(J) = TEMP - 110 CONTINUE - ELSE - JX = KX + (N-1)*INCX - DO 140 J = N,1,-1 - TEMP = X(JX) - IX = JX - IF (NOCONJ) THEN - IF (NOUNIT) TEMP = TEMP*A(J,J) - DO 120 I = J - 1,1,-1 - IX = IX - INCX - TEMP = TEMP + A(I,J)*X(IX) - 120 CONTINUE - ELSE - IF (NOUNIT) TEMP = TEMP*DCONJG(A(J,J)) - DO 130 I = J - 1,1,-1 - IX = IX - INCX - TEMP = TEMP + DCONJG(A(I,J))*X(IX) - 130 CONTINUE - END IF - X(JX) = TEMP - JX = JX - INCX - 140 CONTINUE - END IF - ELSE - IF (INCX.EQ.1) THEN - DO 170 J = 1,N - TEMP = X(J) - IF (NOCONJ) THEN - IF (NOUNIT) TEMP = TEMP*A(J,J) - DO 150 I = J + 1,N - TEMP = TEMP + A(I,J)*X(I) - 150 CONTINUE - ELSE - IF (NOUNIT) TEMP = TEMP*DCONJG(A(J,J)) - DO 160 I = J + 1,N - TEMP = TEMP + DCONJG(A(I,J))*X(I) - 160 CONTINUE - END IF - X(J) = TEMP - 170 CONTINUE - ELSE - JX = KX - DO 200 J = 1,N - TEMP = X(JX) - IX = JX - IF (NOCONJ) THEN - IF (NOUNIT) TEMP = TEMP*A(J,J) - DO 180 I = J + 1,N - IX = IX + INCX - TEMP = TEMP + A(I,J)*X(IX) - 180 CONTINUE - ELSE - IF (NOUNIT) TEMP = TEMP*DCONJG(A(J,J)) - DO 190 I = J + 1,N - IX = IX + INCX - TEMP = TEMP + DCONJG(A(I,J))*X(IX) - 190 CONTINUE - END IF - X(JX) = TEMP - JX = JX + INCX - 200 CONTINUE - END IF - END IF - END IF -* - RETURN -* -* End of ZTRMV -* - END diff --git a/lib/linalg/fortran/zung2l.f b/lib/linalg/fortran/zung2l.f deleted file mode 100644 index add5cb946b..0000000000 --- a/lib/linalg/fortran/zung2l.f +++ /dev/null @@ -1,196 +0,0 @@ -*> \brief \b ZUNG2L generates all or part of the unitary matrix Q from a QL factorization determined by cgeqlf (unblocked algorithm). -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZUNG2L + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZUNG2L( M, N, K, A, LDA, TAU, WORK, INFO ) -* -* .. Scalar Arguments .. -* INTEGER INFO, K, LDA, M, N -* .. -* .. Array Arguments .. -* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZUNG2L generates an m by n complex matrix Q with orthonormal columns, -*> which is defined as the last n columns of a product of k elementary -*> reflectors of order m -*> -*> Q = H(k) . . . H(2) H(1) -*> -*> as returned by ZGEQLF. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix Q. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix Q. M >= N >= 0. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> The number of elementary reflectors whose product defines the -*> matrix Q. N >= K >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is COMPLEX*16 array, dimension (LDA,N) -*> On entry, the (n-k+i)-th column must contain the vector which -*> defines the elementary reflector H(i), for i = 1,2,...,k, as -*> returned by ZGEQLF in the last k columns of its array -*> argument A. -*> On exit, the m-by-n matrix Q. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The first dimension of the array A. LDA >= max(1,M). -*> \endverbatim -*> -*> \param[in] TAU -*> \verbatim -*> TAU is COMPLEX*16 array, dimension (K) -*> TAU(i) must contain the scalar factor of the elementary -*> reflector H(i), as returned by ZGEQLF. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is COMPLEX*16 array, dimension (N) -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument has an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16OTHERcomputational -* -* ===================================================================== - SUBROUTINE ZUNG2L( M, N, K, A, LDA, TAU, WORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INFO, K, LDA, M, N -* .. -* .. Array Arguments .. - COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - COMPLEX*16 ONE, ZERO - PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ), - $ ZERO = ( 0.0D+0, 0.0D+0 ) ) -* .. -* .. Local Scalars .. - INTEGER I, II, J, L -* .. -* .. External Subroutines .. - EXTERNAL XERBLA, ZLARF, ZSCAL -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - INFO = 0 - IF( M.LT.0 ) THEN - INFO = -1 - ELSE IF( N.LT.0 .OR. N.GT.M ) THEN - INFO = -2 - ELSE IF( K.LT.0 .OR. K.GT.N ) THEN - INFO = -3 - ELSE IF( LDA.LT.MAX( 1, M ) ) THEN - INFO = -5 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'ZUNG2L', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( N.LE.0 ) - $ RETURN -* -* Initialise columns 1:n-k to columns of the unit matrix -* - DO 20 J = 1, N - K - DO 10 L = 1, M - A( L, J ) = ZERO - 10 CONTINUE - A( M-N+J, J ) = ONE - 20 CONTINUE -* - DO 40 I = 1, K - II = N - K + I -* -* Apply H(i) to A(1:m-k+i,1:n-k+i) from the left -* - A( M-N+II, II ) = ONE - CALL ZLARF( 'Left', M-N+II, II-1, A( 1, II ), 1, TAU( I ), A, - $ LDA, WORK ) - CALL ZSCAL( M-N+II-1, -TAU( I ), A( 1, II ), 1 ) - A( M-N+II, II ) = ONE - TAU( I ) -* -* Set A(m-k+i+1:m,n-k+i) to zero -* - DO 30 L = M - N + II + 1, M - A( L, II ) = ZERO - 30 CONTINUE - 40 CONTINUE - RETURN -* -* End of ZUNG2L -* - END diff --git a/lib/linalg/fortran/zung2r.f b/lib/linalg/fortran/zung2r.f deleted file mode 100644 index 2823b7ebdd..0000000000 --- a/lib/linalg/fortran/zung2r.f +++ /dev/null @@ -1,198 +0,0 @@ -*> \brief \b ZUNG2R -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZUNG2R + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZUNG2R( M, N, K, A, LDA, TAU, WORK, INFO ) -* -* .. Scalar Arguments .. -* INTEGER INFO, K, LDA, M, N -* .. -* .. Array Arguments .. -* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZUNG2R generates an m by n complex matrix Q with orthonormal columns, -*> which is defined as the first n columns of a product of k elementary -*> reflectors of order m -*> -*> Q = H(1) H(2) . . . H(k) -*> -*> as returned by ZGEQRF. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix Q. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix Q. M >= N >= 0. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> The number of elementary reflectors whose product defines the -*> matrix Q. N >= K >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is COMPLEX*16 array, dimension (LDA,N) -*> On entry, the i-th column must contain the vector which -*> defines the elementary reflector H(i), for i = 1,2,...,k, as -*> returned by ZGEQRF in the first k columns of its array -*> argument A. -*> On exit, the m by n matrix Q. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The first dimension of the array A. LDA >= max(1,M). -*> \endverbatim -*> -*> \param[in] TAU -*> \verbatim -*> TAU is COMPLEX*16 array, dimension (K) -*> TAU(i) must contain the scalar factor of the elementary -*> reflector H(i), as returned by ZGEQRF. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is COMPLEX*16 array, dimension (N) -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument has an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16OTHERcomputational -* -* ===================================================================== - SUBROUTINE ZUNG2R( M, N, K, A, LDA, TAU, WORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INFO, K, LDA, M, N -* .. -* .. Array Arguments .. - COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - COMPLEX*16 ONE, ZERO - PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ), - $ ZERO = ( 0.0D+0, 0.0D+0 ) ) -* .. -* .. Local Scalars .. - INTEGER I, J, L -* .. -* .. External Subroutines .. - EXTERNAL XERBLA, ZLARF, ZSCAL -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - INFO = 0 - IF( M.LT.0 ) THEN - INFO = -1 - ELSE IF( N.LT.0 .OR. N.GT.M ) THEN - INFO = -2 - ELSE IF( K.LT.0 .OR. K.GT.N ) THEN - INFO = -3 - ELSE IF( LDA.LT.MAX( 1, M ) ) THEN - INFO = -5 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'ZUNG2R', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( N.LE.0 ) - $ RETURN -* -* Initialise columns k+1:n to columns of the unit matrix -* - DO 20 J = K + 1, N - DO 10 L = 1, M - A( L, J ) = ZERO - 10 CONTINUE - A( J, J ) = ONE - 20 CONTINUE -* - DO 40 I = K, 1, -1 -* -* Apply H(i) to A(i:m,i:n) from the left -* - IF( I.LT.N ) THEN - A( I, I ) = ONE - CALL ZLARF( 'Left', M-I+1, N-I, A( I, I ), 1, TAU( I ), - $ A( I, I+1 ), LDA, WORK ) - END IF - IF( I.LT.M ) - $ CALL ZSCAL( M-I, -TAU( I ), A( I+1, I ), 1 ) - A( I, I ) = ONE - TAU( I ) -* -* Set A(1:i-1,i) to zero -* - DO 30 L = 1, I - 1 - A( L, I ) = ZERO - 30 CONTINUE - 40 CONTINUE - RETURN -* -* End of ZUNG2R -* - END diff --git a/lib/linalg/fortran/zungl2.f b/lib/linalg/fortran/zungl2.f deleted file mode 100644 index e7a0b59603..0000000000 --- a/lib/linalg/fortran/zungl2.f +++ /dev/null @@ -1,204 +0,0 @@ -*> \brief \b ZUNGL2 generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (unblocked algorithm). -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZUNGL2 + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZUNGL2( M, N, K, A, LDA, TAU, WORK, INFO ) -* -* .. Scalar Arguments .. -* INTEGER INFO, K, LDA, M, N -* .. -* .. Array Arguments .. -* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZUNGL2 generates an m-by-n complex matrix Q with orthonormal rows, -*> which is defined as the first m rows of a product of k elementary -*> reflectors of order n -*> -*> Q = H(k)**H . . . H(2)**H H(1)**H -*> -*> as returned by ZGELQF. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix Q. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix Q. N >= M. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> The number of elementary reflectors whose product defines the -*> matrix Q. M >= K >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is COMPLEX*16 array, dimension (LDA,N) -*> On entry, the i-th row must contain the vector which defines -*> the elementary reflector H(i), for i = 1,2,...,k, as returned -*> by ZGELQF in the first k rows of its array argument A. -*> On exit, the m by n matrix Q. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The first dimension of the array A. LDA >= max(1,M). -*> \endverbatim -*> -*> \param[in] TAU -*> \verbatim -*> TAU is COMPLEX*16 array, dimension (K) -*> TAU(i) must contain the scalar factor of the elementary -*> reflector H(i), as returned by ZGELQF. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is COMPLEX*16 array, dimension (M) -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument has an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16OTHERcomputational -* -* ===================================================================== - SUBROUTINE ZUNGL2( M, N, K, A, LDA, TAU, WORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INFO, K, LDA, M, N -* .. -* .. Array Arguments .. - COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - COMPLEX*16 ONE, ZERO - PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ), - $ ZERO = ( 0.0D+0, 0.0D+0 ) ) -* .. -* .. Local Scalars .. - INTEGER I, J, L -* .. -* .. External Subroutines .. - EXTERNAL XERBLA, ZLACGV, ZLARF, ZSCAL -* .. -* .. Intrinsic Functions .. - INTRINSIC DCONJG, MAX -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - INFO = 0 - IF( M.LT.0 ) THEN - INFO = -1 - ELSE IF( N.LT.M ) THEN - INFO = -2 - ELSE IF( K.LT.0 .OR. K.GT.M ) THEN - INFO = -3 - ELSE IF( LDA.LT.MAX( 1, M ) ) THEN - INFO = -5 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'ZUNGL2', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( M.LE.0 ) - $ RETURN -* - IF( K.LT.M ) THEN -* -* Initialise rows k+1:m to rows of the unit matrix -* - DO 20 J = 1, N - DO 10 L = K + 1, M - A( L, J ) = ZERO - 10 CONTINUE - IF( J.GT.K .AND. J.LE.M ) - $ A( J, J ) = ONE - 20 CONTINUE - END IF -* - DO 40 I = K, 1, -1 -* -* Apply H(i)**H to A(i:m,i:n) from the right -* - IF( I.LT.N ) THEN - CALL ZLACGV( N-I, A( I, I+1 ), LDA ) - IF( I.LT.M ) THEN - A( I, I ) = ONE - CALL ZLARF( 'Right', M-I, N-I+1, A( I, I ), LDA, - $ DCONJG( TAU( I ) ), A( I+1, I ), LDA, WORK ) - END IF - CALL ZSCAL( N-I, -TAU( I ), A( I, I+1 ), LDA ) - CALL ZLACGV( N-I, A( I, I+1 ), LDA ) - END IF - A( I, I ) = ONE - DCONJG( TAU( I ) ) -* -* Set A(i,1:i-1) to zero -* - DO 30 L = 1, I - 1 - A( I, L ) = ZERO - 30 CONTINUE - 40 CONTINUE - RETURN -* -* End of ZUNGL2 -* - END diff --git a/lib/linalg/fortran/zungql.f b/lib/linalg/fortran/zungql.f deleted file mode 100644 index 1804ca65ff..0000000000 --- a/lib/linalg/fortran/zungql.f +++ /dev/null @@ -1,293 +0,0 @@ -*> \brief \b ZUNGQL -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZUNGQL + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZUNGQL( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) -* -* .. Scalar Arguments .. -* INTEGER INFO, K, LDA, LWORK, M, N -* .. -* .. Array Arguments .. -* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZUNGQL generates an M-by-N complex matrix Q with orthonormal columns, -*> which is defined as the last N columns of a product of K elementary -*> reflectors of order M -*> -*> Q = H(k) . . . H(2) H(1) -*> -*> as returned by ZGEQLF. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix Q. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix Q. M >= N >= 0. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> The number of elementary reflectors whose product defines the -*> matrix Q. N >= K >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is COMPLEX*16 array, dimension (LDA,N) -*> On entry, the (n-k+i)-th column must contain the vector which -*> defines the elementary reflector H(i), for i = 1,2,...,k, as -*> returned by ZGEQLF in the last k columns of its array -*> argument A. -*> On exit, the M-by-N matrix Q. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The first dimension of the array A. LDA >= max(1,M). -*> \endverbatim -*> -*> \param[in] TAU -*> \verbatim -*> TAU is COMPLEX*16 array, dimension (K) -*> TAU(i) must contain the scalar factor of the elementary -*> reflector H(i), as returned by ZGEQLF. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) -*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -*> \endverbatim -*> -*> \param[in] LWORK -*> \verbatim -*> LWORK is INTEGER -*> The dimension of the array WORK. LWORK >= max(1,N). -*> For optimum performance LWORK >= N*NB, where NB is the -*> optimal blocksize. -*> -*> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal size of the WORK array, returns -*> this value as the first entry of the WORK array, and no error -*> message related to LWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument has an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16OTHERcomputational -* -* ===================================================================== - SUBROUTINE ZUNGQL( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INFO, K, LDA, LWORK, M, N -* .. -* .. Array Arguments .. - COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - COMPLEX*16 ZERO - PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) -* .. -* .. Local Scalars .. - LOGICAL LQUERY - INTEGER I, IB, IINFO, IWS, J, KK, L, LDWORK, LWKOPT, - $ NB, NBMIN, NX -* .. -* .. External Subroutines .. - EXTERNAL XERBLA, ZLARFB, ZLARFT, ZUNG2L -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, MIN -* .. -* .. External Functions .. - INTEGER ILAENV - EXTERNAL ILAENV -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - INFO = 0 - LQUERY = ( LWORK.EQ.-1 ) - IF( M.LT.0 ) THEN - INFO = -1 - ELSE IF( N.LT.0 .OR. N.GT.M ) THEN - INFO = -2 - ELSE IF( K.LT.0 .OR. K.GT.N ) THEN - INFO = -3 - ELSE IF( LDA.LT.MAX( 1, M ) ) THEN - INFO = -5 - END IF -* - IF( INFO.EQ.0 ) THEN - IF( N.EQ.0 ) THEN - LWKOPT = 1 - ELSE - NB = ILAENV( 1, 'ZUNGQL', ' ', M, N, K, -1 ) - LWKOPT = N*NB - END IF - WORK( 1 ) = LWKOPT -* - IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN - INFO = -8 - END IF - END IF -* - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'ZUNGQL', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - RETURN - END IF -* -* Quick return if possible -* - IF( N.LE.0 ) THEN - RETURN - END IF -* - NBMIN = 2 - NX = 0 - IWS = N - IF( NB.GT.1 .AND. NB.LT.K ) THEN -* -* Determine when to cross over from blocked to unblocked code. -* - NX = MAX( 0, ILAENV( 3, 'ZUNGQL', ' ', M, N, K, -1 ) ) - IF( NX.LT.K ) THEN -* -* Determine if workspace is large enough for blocked code. -* - LDWORK = N - IWS = LDWORK*NB - IF( LWORK.LT.IWS ) THEN -* -* Not enough workspace to use optimal NB: reduce NB and -* determine the minimum value of NB. -* - NB = LWORK / LDWORK - NBMIN = MAX( 2, ILAENV( 2, 'ZUNGQL', ' ', M, N, K, -1 ) ) - END IF - END IF - END IF -* - IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN -* -* Use blocked code after the first block. -* The last kk columns are handled by the block method. -* - KK = MIN( K, ( ( K-NX+NB-1 ) / NB )*NB ) -* -* Set A(m-kk+1:m,1:n-kk) to zero. -* - DO 20 J = 1, N - KK - DO 10 I = M - KK + 1, M - A( I, J ) = ZERO - 10 CONTINUE - 20 CONTINUE - ELSE - KK = 0 - END IF -* -* Use unblocked code for the first or only block. -* - CALL ZUNG2L( M-KK, N-KK, K-KK, A, LDA, TAU, WORK, IINFO ) -* - IF( KK.GT.0 ) THEN -* -* Use blocked code -* - DO 50 I = K - KK + 1, K, NB - IB = MIN( NB, K-I+1 ) - IF( N-K+I.GT.1 ) THEN -* -* Form the triangular factor of the block reflector -* H = H(i+ib-1) . . . H(i+1) H(i) -* - CALL ZLARFT( 'Backward', 'Columnwise', M-K+I+IB-1, IB, - $ A( 1, N-K+I ), LDA, TAU( I ), WORK, LDWORK ) -* -* Apply H to A(1:m-k+i+ib-1,1:n-k+i-1) from the left -* - CALL ZLARFB( 'Left', 'No transpose', 'Backward', - $ 'Columnwise', M-K+I+IB-1, N-K+I-1, IB, - $ A( 1, N-K+I ), LDA, WORK, LDWORK, A, LDA, - $ WORK( IB+1 ), LDWORK ) - END IF -* -* Apply H to rows 1:m-k+i+ib-1 of current block -* - CALL ZUNG2L( M-K+I+IB-1, IB, IB, A( 1, N-K+I ), LDA, - $ TAU( I ), WORK, IINFO ) -* -* Set rows m-k+i+ib:m of current block to zero -* - DO 40 J = N - K + I, N - K + I + IB - 1 - DO 30 L = M - K + I + IB, M - A( L, J ) = ZERO - 30 CONTINUE - 40 CONTINUE - 50 CONTINUE - END IF -* - WORK( 1 ) = IWS - RETURN -* -* End of ZUNGQL -* - END diff --git a/lib/linalg/fortran/zungqr.f b/lib/linalg/fortran/zungqr.f deleted file mode 100644 index b3f2c4507f..0000000000 --- a/lib/linalg/fortran/zungqr.f +++ /dev/null @@ -1,287 +0,0 @@ -*> \brief \b ZUNGQR -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZUNGQR + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZUNGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) -* -* .. Scalar Arguments .. -* INTEGER INFO, K, LDA, LWORK, M, N -* .. -* .. Array Arguments .. -* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZUNGQR generates an M-by-N complex matrix Q with orthonormal columns, -*> which is defined as the first N columns of a product of K elementary -*> reflectors of order M -*> -*> Q = H(1) H(2) . . . H(k) -*> -*> as returned by ZGEQRF. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix Q. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix Q. M >= N >= 0. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> The number of elementary reflectors whose product defines the -*> matrix Q. N >= K >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is COMPLEX*16 array, dimension (LDA,N) -*> On entry, the i-th column must contain the vector which -*> defines the elementary reflector H(i), for i = 1,2,...,k, as -*> returned by ZGEQRF in the first k columns of its array -*> argument A. -*> On exit, the M-by-N matrix Q. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The first dimension of the array A. LDA >= max(1,M). -*> \endverbatim -*> -*> \param[in] TAU -*> \verbatim -*> TAU is COMPLEX*16 array, dimension (K) -*> TAU(i) must contain the scalar factor of the elementary -*> reflector H(i), as returned by ZGEQRF. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) -*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -*> \endverbatim -*> -*> \param[in] LWORK -*> \verbatim -*> LWORK is INTEGER -*> The dimension of the array WORK. LWORK >= max(1,N). -*> For optimum performance LWORK >= N*NB, where NB is the -*> optimal blocksize. -*> -*> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal size of the WORK array, returns -*> this value as the first entry of the WORK array, and no error -*> message related to LWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument has an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16OTHERcomputational -* -* ===================================================================== - SUBROUTINE ZUNGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INFO, K, LDA, LWORK, M, N -* .. -* .. Array Arguments .. - COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - COMPLEX*16 ZERO - PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) -* .. -* .. Local Scalars .. - LOGICAL LQUERY - INTEGER I, IB, IINFO, IWS, J, KI, KK, L, LDWORK, - $ LWKOPT, NB, NBMIN, NX -* .. -* .. External Subroutines .. - EXTERNAL XERBLA, ZLARFB, ZLARFT, ZUNG2R -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, MIN -* .. -* .. External Functions .. - INTEGER ILAENV - EXTERNAL ILAENV -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - INFO = 0 - NB = ILAENV( 1, 'ZUNGQR', ' ', M, N, K, -1 ) - LWKOPT = MAX( 1, N )*NB - WORK( 1 ) = LWKOPT - LQUERY = ( LWORK.EQ.-1 ) - IF( M.LT.0 ) THEN - INFO = -1 - ELSE IF( N.LT.0 .OR. N.GT.M ) THEN - INFO = -2 - ELSE IF( K.LT.0 .OR. K.GT.N ) THEN - INFO = -3 - ELSE IF( LDA.LT.MAX( 1, M ) ) THEN - INFO = -5 - ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN - INFO = -8 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'ZUNGQR', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - RETURN - END IF -* -* Quick return if possible -* - IF( N.LE.0 ) THEN - WORK( 1 ) = 1 - RETURN - END IF -* - NBMIN = 2 - NX = 0 - IWS = N - IF( NB.GT.1 .AND. NB.LT.K ) THEN -* -* Determine when to cross over from blocked to unblocked code. -* - NX = MAX( 0, ILAENV( 3, 'ZUNGQR', ' ', M, N, K, -1 ) ) - IF( NX.LT.K ) THEN -* -* Determine if workspace is large enough for blocked code. -* - LDWORK = N - IWS = LDWORK*NB - IF( LWORK.LT.IWS ) THEN -* -* Not enough workspace to use optimal NB: reduce NB and -* determine the minimum value of NB. -* - NB = LWORK / LDWORK - NBMIN = MAX( 2, ILAENV( 2, 'ZUNGQR', ' ', M, N, K, -1 ) ) - END IF - END IF - END IF -* - IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN -* -* Use blocked code after the last block. -* The first kk columns are handled by the block method. -* - KI = ( ( K-NX-1 ) / NB )*NB - KK = MIN( K, KI+NB ) -* -* Set A(1:kk,kk+1:n) to zero. -* - DO 20 J = KK + 1, N - DO 10 I = 1, KK - A( I, J ) = ZERO - 10 CONTINUE - 20 CONTINUE - ELSE - KK = 0 - END IF -* -* Use unblocked code for the last or only block. -* - IF( KK.LT.N ) - $ CALL ZUNG2R( M-KK, N-KK, K-KK, A( KK+1, KK+1 ), LDA, - $ TAU( KK+1 ), WORK, IINFO ) -* - IF( KK.GT.0 ) THEN -* -* Use blocked code -* - DO 50 I = KI + 1, 1, -NB - IB = MIN( NB, K-I+1 ) - IF( I+IB.LE.N ) THEN -* -* Form the triangular factor of the block reflector -* H = H(i) H(i+1) . . . H(i+ib-1) -* - CALL ZLARFT( 'Forward', 'Columnwise', M-I+1, IB, - $ A( I, I ), LDA, TAU( I ), WORK, LDWORK ) -* -* Apply H to A(i:m,i+ib:n) from the left -* - CALL ZLARFB( 'Left', 'No transpose', 'Forward', - $ 'Columnwise', M-I+1, N-I-IB+1, IB, - $ A( I, I ), LDA, WORK, LDWORK, A( I, I+IB ), - $ LDA, WORK( IB+1 ), LDWORK ) - END IF -* -* Apply H to rows i:m of current block -* - CALL ZUNG2R( M-I+1, IB, IB, A( I, I ), LDA, TAU( I ), WORK, - $ IINFO ) -* -* Set rows 1:i-1 of current block to zero -* - DO 40 J = I, I + IB - 1 - DO 30 L = 1, I - 1 - A( L, J ) = ZERO - 30 CONTINUE - 40 CONTINUE - 50 CONTINUE - END IF -* - WORK( 1 ) = IWS - RETURN -* -* End of ZUNGQR -* - END diff --git a/lib/linalg/fortran/zungtr.f b/lib/linalg/fortran/zungtr.f deleted file mode 100644 index 01e100a8cd..0000000000 --- a/lib/linalg/fortran/zungtr.f +++ /dev/null @@ -1,253 +0,0 @@ -*> \brief \b ZUNGTR -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZUNGTR + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZUNGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER UPLO -* INTEGER INFO, LDA, LWORK, N -* .. -* .. Array Arguments .. -* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZUNGTR generates a complex unitary matrix Q which is defined as the -*> product of n-1 elementary reflectors of order N, as returned by -*> ZHETRD: -*> -*> if UPLO = 'U', Q = H(n-1) . . . H(2) H(1), -*> -*> if UPLO = 'L', Q = H(1) H(2) . . . H(n-1). -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> = 'U': Upper triangle of A contains elementary reflectors -*> from ZHETRD; -*> = 'L': Lower triangle of A contains elementary reflectors -*> from ZHETRD. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrix Q. N >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is COMPLEX*16 array, dimension (LDA,N) -*> On entry, the vectors which define the elementary reflectors, -*> as returned by ZHETRD. -*> On exit, the N-by-N unitary matrix Q. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= N. -*> \endverbatim -*> -*> \param[in] TAU -*> \verbatim -*> TAU is COMPLEX*16 array, dimension (N-1) -*> TAU(i) must contain the scalar factor of the elementary -*> reflector H(i), as returned by ZHETRD. -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) -*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -*> \endverbatim -*> -*> \param[in] LWORK -*> \verbatim -*> LWORK is INTEGER -*> The dimension of the array WORK. LWORK >= N-1. -*> For optimum performance LWORK >= (N-1)*NB, where NB is -*> the optimal blocksize. -*> -*> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal size of the WORK array, returns -*> this value as the first entry of the WORK array, and no error -*> message related to LWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16OTHERcomputational -* -* ===================================================================== - SUBROUTINE ZUNGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER UPLO - INTEGER INFO, LDA, LWORK, N -* .. -* .. Array Arguments .. - COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - COMPLEX*16 ZERO, ONE - PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ), - $ ONE = ( 1.0D+0, 0.0D+0 ) ) -* .. -* .. Local Scalars .. - LOGICAL LQUERY, UPPER - INTEGER I, IINFO, J, LWKOPT, NB -* .. -* .. External Functions .. - LOGICAL LSAME - INTEGER ILAENV - EXTERNAL LSAME, ILAENV -* .. -* .. External Subroutines .. - EXTERNAL XERBLA, ZUNGQL, ZUNGQR -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - INFO = 0 - LQUERY = ( LWORK.EQ.-1 ) - UPPER = LSAME( UPLO, 'U' ) - IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -4 - ELSE IF( LWORK.LT.MAX( 1, N-1 ) .AND. .NOT.LQUERY ) THEN - INFO = -7 - END IF -* - IF( INFO.EQ.0 ) THEN - IF( UPPER ) THEN - NB = ILAENV( 1, 'ZUNGQL', ' ', N-1, N-1, N-1, -1 ) - ELSE - NB = ILAENV( 1, 'ZUNGQR', ' ', N-1, N-1, N-1, -1 ) - END IF - LWKOPT = MAX( 1, N-1 )*NB - WORK( 1 ) = LWKOPT - END IF -* - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'ZUNGTR', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - RETURN - END IF -* -* Quick return if possible -* - IF( N.EQ.0 ) THEN - WORK( 1 ) = 1 - RETURN - END IF -* - IF( UPPER ) THEN -* -* Q was determined by a call to ZHETRD with UPLO = 'U' -* -* Shift the vectors which define the elementary reflectors one -* column to the left, and set the last row and column of Q to -* those of the unit matrix -* - DO 20 J = 1, N - 1 - DO 10 I = 1, J - 1 - A( I, J ) = A( I, J+1 ) - 10 CONTINUE - A( N, J ) = ZERO - 20 CONTINUE - DO 30 I = 1, N - 1 - A( I, N ) = ZERO - 30 CONTINUE - A( N, N ) = ONE -* -* Generate Q(1:n-1,1:n-1) -* - CALL ZUNGQL( N-1, N-1, N-1, A, LDA, TAU, WORK, LWORK, IINFO ) -* - ELSE -* -* Q was determined by a call to ZHETRD with UPLO = 'L'. -* -* Shift the vectors which define the elementary reflectors one -* column to the right, and set the first row and column of Q to -* those of the unit matrix -* - DO 50 J = N, 2, -1 - A( 1, J ) = ZERO - DO 40 I = J + 1, N - A( I, J ) = A( I, J-1 ) - 40 CONTINUE - 50 CONTINUE - A( 1, 1 ) = ONE - DO 60 I = 2, N - A( I, 1 ) = ZERO - 60 CONTINUE - IF( N.GT.1 ) THEN -* -* Generate Q(2:n,2:n) -* - CALL ZUNGQR( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK, - $ LWORK, IINFO ) - END IF - END IF - WORK( 1 ) = LWKOPT - RETURN -* -* End of ZUNGTR -* - END diff --git a/lib/linalg/fortran/zunm2l.f b/lib/linalg/fortran/zunm2l.f deleted file mode 100644 index 48c2dbfc0c..0000000000 --- a/lib/linalg/fortran/zunm2l.f +++ /dev/null @@ -1,278 +0,0 @@ -*> \brief \b ZUNM2L multiplies a general matrix by the unitary matrix from a QL factorization determined by cgeqlf (unblocked algorithm). -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZUNM2L + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZUNM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, -* WORK, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER SIDE, TRANS -* INTEGER INFO, K, LDA, LDC, M, N -* .. -* .. Array Arguments .. -* COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZUNM2L overwrites the general complex m-by-n matrix C with -*> -*> Q * C if SIDE = 'L' and TRANS = 'N', or -*> -*> Q**H* C if SIDE = 'L' and TRANS = 'C', or -*> -*> C * Q if SIDE = 'R' and TRANS = 'N', or -*> -*> C * Q**H if SIDE = 'R' and TRANS = 'C', -*> -*> where Q is a complex unitary matrix defined as the product of k -*> elementary reflectors -*> -*> Q = H(k) . . . H(2) H(1) -*> -*> as returned by ZGEQLF. Q is of order m if SIDE = 'L' and of order n -*> if SIDE = 'R'. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] SIDE -*> \verbatim -*> SIDE is CHARACTER*1 -*> = 'L': apply Q or Q**H from the Left -*> = 'R': apply Q or Q**H from the Right -*> \endverbatim -*> -*> \param[in] TRANS -*> \verbatim -*> TRANS is CHARACTER*1 -*> = 'N': apply Q (No transpose) -*> = 'C': apply Q**H (Conjugate transpose) -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix C. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix C. N >= 0. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> The number of elementary reflectors whose product defines -*> the matrix Q. -*> If SIDE = 'L', M >= K >= 0; -*> if SIDE = 'R', N >= K >= 0. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is COMPLEX*16 array, dimension (LDA,K) -*> The i-th column must contain the vector which defines the -*> elementary reflector H(i), for i = 1,2,...,k, as returned by -*> ZGEQLF in the last k columns of its array argument A. -*> A is modified by the routine but restored on exit. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. -*> If SIDE = 'L', LDA >= max(1,M); -*> if SIDE = 'R', LDA >= max(1,N). -*> \endverbatim -*> -*> \param[in] TAU -*> \verbatim -*> TAU is COMPLEX*16 array, dimension (K) -*> TAU(i) must contain the scalar factor of the elementary -*> reflector H(i), as returned by ZGEQLF. -*> \endverbatim -*> -*> \param[in,out] C -*> \verbatim -*> C is COMPLEX*16 array, dimension (LDC,N) -*> On entry, the m-by-n matrix C. -*> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. -*> \endverbatim -*> -*> \param[in] LDC -*> \verbatim -*> LDC is INTEGER -*> The leading dimension of the array C. LDC >= max(1,M). -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is COMPLEX*16 array, dimension -*> (N) if SIDE = 'L', -*> (M) if SIDE = 'R' -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16OTHERcomputational -* -* ===================================================================== - SUBROUTINE ZUNM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, - $ WORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER SIDE, TRANS - INTEGER INFO, K, LDA, LDC, M, N -* .. -* .. Array Arguments .. - COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - COMPLEX*16 ONE - PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) -* .. -* .. Local Scalars .. - LOGICAL LEFT, NOTRAN - INTEGER I, I1, I2, I3, MI, NI, NQ - COMPLEX*16 AII, TAUI -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL XERBLA, ZLARF -* .. -* .. Intrinsic Functions .. - INTRINSIC DCONJG, MAX -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - INFO = 0 - LEFT = LSAME( SIDE, 'L' ) - NOTRAN = LSAME( TRANS, 'N' ) -* -* NQ is the order of Q -* - IF( LEFT ) THEN - NQ = M - ELSE - NQ = N - END IF - IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN - INFO = -1 - ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN - INFO = -2 - ELSE IF( M.LT.0 ) THEN - INFO = -3 - ELSE IF( N.LT.0 ) THEN - INFO = -4 - ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN - INFO = -5 - ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN - INFO = -7 - ELSE IF( LDC.LT.MAX( 1, M ) ) THEN - INFO = -10 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'ZUNM2L', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) - $ RETURN -* - IF( ( LEFT .AND. NOTRAN .OR. .NOT.LEFT .AND. .NOT.NOTRAN ) ) THEN - I1 = 1 - I2 = K - I3 = 1 - ELSE - I1 = K - I2 = 1 - I3 = -1 - END IF -* - IF( LEFT ) THEN - NI = N - ELSE - MI = M - END IF -* - DO 10 I = I1, I2, I3 - IF( LEFT ) THEN -* -* H(i) or H(i)**H is applied to C(1:m-k+i,1:n) -* - MI = M - K + I - ELSE -* -* H(i) or H(i)**H is applied to C(1:m,1:n-k+i) -* - NI = N - K + I - END IF -* -* Apply H(i) or H(i)**H -* - IF( NOTRAN ) THEN - TAUI = TAU( I ) - ELSE - TAUI = DCONJG( TAU( I ) ) - END IF - AII = A( NQ-K+I, I ) - A( NQ-K+I, I ) = ONE - CALL ZLARF( SIDE, MI, NI, A( 1, I ), 1, TAUI, C, LDC, WORK ) - A( NQ-K+I, I ) = AII - 10 CONTINUE - RETURN -* -* End of ZUNM2L -* - END diff --git a/lib/linalg/fortran/zunm2r.f b/lib/linalg/fortran/zunm2r.f deleted file mode 100644 index aec5a8bcae..0000000000 --- a/lib/linalg/fortran/zunm2r.f +++ /dev/null @@ -1,283 +0,0 @@ -*> \brief \b ZUNM2R multiplies a general matrix by the unitary matrix from a QR factorization determined by cgeqrf (unblocked algorithm). -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZUNM2R + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZUNM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, -* WORK, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER SIDE, TRANS -* INTEGER INFO, K, LDA, LDC, M, N -* .. -* .. Array Arguments .. -* COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZUNM2R overwrites the general complex m-by-n matrix C with -*> -*> Q * C if SIDE = 'L' and TRANS = 'N', or -*> -*> Q**H* C if SIDE = 'L' and TRANS = 'C', or -*> -*> C * Q if SIDE = 'R' and TRANS = 'N', or -*> -*> C * Q**H if SIDE = 'R' and TRANS = 'C', -*> -*> where Q is a complex unitary matrix defined as the product of k -*> elementary reflectors -*> -*> Q = H(1) H(2) . . . H(k) -*> -*> as returned by ZGEQRF. Q is of order m if SIDE = 'L' and of order n -*> if SIDE = 'R'. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] SIDE -*> \verbatim -*> SIDE is CHARACTER*1 -*> = 'L': apply Q or Q**H from the Left -*> = 'R': apply Q or Q**H from the Right -*> \endverbatim -*> -*> \param[in] TRANS -*> \verbatim -*> TRANS is CHARACTER*1 -*> = 'N': apply Q (No transpose) -*> = 'C': apply Q**H (Conjugate transpose) -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix C. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix C. N >= 0. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> The number of elementary reflectors whose product defines -*> the matrix Q. -*> If SIDE = 'L', M >= K >= 0; -*> if SIDE = 'R', N >= K >= 0. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is COMPLEX*16 array, dimension (LDA,K) -*> The i-th column must contain the vector which defines the -*> elementary reflector H(i), for i = 1,2,...,k, as returned by -*> ZGEQRF in the first k columns of its array argument A. -*> A is modified by the routine but restored on exit. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. -*> If SIDE = 'L', LDA >= max(1,M); -*> if SIDE = 'R', LDA >= max(1,N). -*> \endverbatim -*> -*> \param[in] TAU -*> \verbatim -*> TAU is COMPLEX*16 array, dimension (K) -*> TAU(i) must contain the scalar factor of the elementary -*> reflector H(i), as returned by ZGEQRF. -*> \endverbatim -*> -*> \param[in,out] C -*> \verbatim -*> C is COMPLEX*16 array, dimension (LDC,N) -*> On entry, the m-by-n matrix C. -*> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. -*> \endverbatim -*> -*> \param[in] LDC -*> \verbatim -*> LDC is INTEGER -*> The leading dimension of the array C. LDC >= max(1,M). -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is COMPLEX*16 array, dimension -*> (N) if SIDE = 'L', -*> (M) if SIDE = 'R' -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16OTHERcomputational -* -* ===================================================================== - SUBROUTINE ZUNM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, - $ WORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER SIDE, TRANS - INTEGER INFO, K, LDA, LDC, M, N -* .. -* .. Array Arguments .. - COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - COMPLEX*16 ONE - PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) -* .. -* .. Local Scalars .. - LOGICAL LEFT, NOTRAN - INTEGER I, I1, I2, I3, IC, JC, MI, NI, NQ - COMPLEX*16 AII, TAUI -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. External Subroutines .. - EXTERNAL XERBLA, ZLARF -* .. -* .. Intrinsic Functions .. - INTRINSIC DCONJG, MAX -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - INFO = 0 - LEFT = LSAME( SIDE, 'L' ) - NOTRAN = LSAME( TRANS, 'N' ) -* -* NQ is the order of Q -* - IF( LEFT ) THEN - NQ = M - ELSE - NQ = N - END IF - IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN - INFO = -1 - ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN - INFO = -2 - ELSE IF( M.LT.0 ) THEN - INFO = -3 - ELSE IF( N.LT.0 ) THEN - INFO = -4 - ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN - INFO = -5 - ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN - INFO = -7 - ELSE IF( LDC.LT.MAX( 1, M ) ) THEN - INFO = -10 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'ZUNM2R', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) - $ RETURN -* - IF( ( LEFT .AND. .NOT.NOTRAN .OR. .NOT.LEFT .AND. NOTRAN ) ) THEN - I1 = 1 - I2 = K - I3 = 1 - ELSE - I1 = K - I2 = 1 - I3 = -1 - END IF -* - IF( LEFT ) THEN - NI = N - JC = 1 - ELSE - MI = M - IC = 1 - END IF -* - DO 10 I = I1, I2, I3 - IF( LEFT ) THEN -* -* H(i) or H(i)**H is applied to C(i:m,1:n) -* - MI = M - I + 1 - IC = I - ELSE -* -* H(i) or H(i)**H is applied to C(1:m,i:n) -* - NI = N - I + 1 - JC = I - END IF -* -* Apply H(i) or H(i)**H -* - IF( NOTRAN ) THEN - TAUI = TAU( I ) - ELSE - TAUI = DCONJG( TAU( I ) ) - END IF - AII = A( I, I ) - A( I, I ) = ONE - CALL ZLARF( SIDE, MI, NI, A( I, I ), 1, TAUI, C( IC, JC ), LDC, - $ WORK ) - A( I, I ) = AII - 10 CONTINUE - RETURN -* -* End of ZUNM2R -* - END diff --git a/lib/linalg/fortran/zunmql.f b/lib/linalg/fortran/zunmql.f deleted file mode 100644 index 06353a0c75..0000000000 --- a/lib/linalg/fortran/zunmql.f +++ /dev/null @@ -1,336 +0,0 @@ -*> \brief \b ZUNMQL -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZUNMQL + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZUNMQL( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, -* WORK, LWORK, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER SIDE, TRANS -* INTEGER INFO, K, LDA, LDC, LWORK, M, N -* .. -* .. Array Arguments .. -* COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZUNMQL overwrites the general complex M-by-N matrix C with -*> -*> SIDE = 'L' SIDE = 'R' -*> TRANS = 'N': Q * C C * Q -*> TRANS = 'C': Q**H * C C * Q**H -*> -*> where Q is a complex unitary matrix defined as the product of k -*> elementary reflectors -*> -*> Q = H(k) . . . H(2) H(1) -*> -*> as returned by ZGEQLF. Q is of order M if SIDE = 'L' and of order N -*> if SIDE = 'R'. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] SIDE -*> \verbatim -*> SIDE is CHARACTER*1 -*> = 'L': apply Q or Q**H from the Left; -*> = 'R': apply Q or Q**H from the Right. -*> \endverbatim -*> -*> \param[in] TRANS -*> \verbatim -*> TRANS is CHARACTER*1 -*> = 'N': No transpose, apply Q; -*> = 'C': Conjugate transpose, apply Q**H. -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix C. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix C. N >= 0. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> The number of elementary reflectors whose product defines -*> the matrix Q. -*> If SIDE = 'L', M >= K >= 0; -*> if SIDE = 'R', N >= K >= 0. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is COMPLEX*16 array, dimension (LDA,K) -*> The i-th column must contain the vector which defines the -*> elementary reflector H(i), for i = 1,2,...,k, as returned by -*> ZGEQLF in the last k columns of its array argument A. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. -*> If SIDE = 'L', LDA >= max(1,M); -*> if SIDE = 'R', LDA >= max(1,N). -*> \endverbatim -*> -*> \param[in] TAU -*> \verbatim -*> TAU is COMPLEX*16 array, dimension (K) -*> TAU(i) must contain the scalar factor of the elementary -*> reflector H(i), as returned by ZGEQLF. -*> \endverbatim -*> -*> \param[in,out] C -*> \verbatim -*> C is COMPLEX*16 array, dimension (LDC,N) -*> On entry, the M-by-N matrix C. -*> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. -*> \endverbatim -*> -*> \param[in] LDC -*> \verbatim -*> LDC is INTEGER -*> The leading dimension of the array C. LDC >= max(1,M). -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) -*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -*> \endverbatim -*> -*> \param[in] LWORK -*> \verbatim -*> LWORK is INTEGER -*> The dimension of the array WORK. -*> If SIDE = 'L', LWORK >= max(1,N); -*> if SIDE = 'R', LWORK >= max(1,M). -*> For good performance, LWORK should generally be larger. -*> -*> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal size of the WORK array, returns -*> this value as the first entry of the WORK array, and no error -*> message related to LWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16OTHERcomputational -* -* ===================================================================== - SUBROUTINE ZUNMQL( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, - $ WORK, LWORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER SIDE, TRANS - INTEGER INFO, K, LDA, LDC, LWORK, M, N -* .. -* .. Array Arguments .. - COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - INTEGER NBMAX, LDT, TSIZE - PARAMETER ( NBMAX = 64, LDT = NBMAX+1, - $ TSIZE = LDT*NBMAX ) -* .. -* .. Local Scalars .. - LOGICAL LEFT, LQUERY, NOTRAN - INTEGER I, I1, I2, I3, IB, IINFO, IWT, LDWORK, LWKOPT, - $ MI, NB, NBMIN, NI, NQ, NW -* .. -* .. External Functions .. - LOGICAL LSAME - INTEGER ILAENV - EXTERNAL LSAME, ILAENV -* .. -* .. External Subroutines .. - EXTERNAL XERBLA, ZLARFB, ZLARFT, ZUNM2L -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, MIN -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - INFO = 0 - LEFT = LSAME( SIDE, 'L' ) - NOTRAN = LSAME( TRANS, 'N' ) - LQUERY = ( LWORK.EQ.-1 ) -* -* NQ is the order of Q and NW is the minimum dimension of WORK -* - IF( LEFT ) THEN - NQ = M - NW = MAX( 1, N ) - ELSE - NQ = N - NW = MAX( 1, M ) - END IF - IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN - INFO = -1 - ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN - INFO = -2 - ELSE IF( M.LT.0 ) THEN - INFO = -3 - ELSE IF( N.LT.0 ) THEN - INFO = -4 - ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN - INFO = -5 - ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN - INFO = -7 - ELSE IF( LDC.LT.MAX( 1, M ) ) THEN - INFO = -10 - ELSE IF( LWORK.LT.NW .AND. .NOT.LQUERY ) THEN - INFO = -12 - END IF -* - IF( INFO.EQ.0 ) THEN -* -* Compute the workspace requirements -* - IF( M.EQ.0 .OR. N.EQ.0 ) THEN - LWKOPT = 1 - ELSE - NB = MIN( NBMAX, ILAENV( 1, 'ZUNMQL', SIDE // TRANS, M, N, - $ K, -1 ) ) - LWKOPT = NW*NB + TSIZE - END IF - WORK( 1 ) = LWKOPT - END IF -* - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'ZUNMQL', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - RETURN - END IF -* -* Quick return if possible -* - IF( M.EQ.0 .OR. N.EQ.0 ) THEN - RETURN - END IF -* - NBMIN = 2 - LDWORK = NW - IF( NB.GT.1 .AND. NB.LT.K ) THEN - IF( LWORK.LT.LWKOPT ) THEN - NB = (LWORK-TSIZE) / LDWORK - NBMIN = MAX( 2, ILAENV( 2, 'ZUNMQL', SIDE // TRANS, M, N, K, - $ -1 ) ) - END IF - END IF -* - IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN -* -* Use unblocked code -* - CALL ZUNM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, - $ IINFO ) - ELSE -* -* Use blocked code -* - IWT = 1 + NW*NB - IF( ( LEFT .AND. NOTRAN ) .OR. - $ ( .NOT.LEFT .AND. .NOT.NOTRAN ) ) THEN - I1 = 1 - I2 = K - I3 = NB - ELSE - I1 = ( ( K-1 ) / NB )*NB + 1 - I2 = 1 - I3 = -NB - END IF -* - IF( LEFT ) THEN - NI = N - ELSE - MI = M - END IF -* - DO 10 I = I1, I2, I3 - IB = MIN( NB, K-I+1 ) -* -* Form the triangular factor of the block reflector -* H = H(i+ib-1) . . . H(i+1) H(i) -* - CALL ZLARFT( 'Backward', 'Columnwise', NQ-K+I+IB-1, IB, - $ A( 1, I ), LDA, TAU( I ), WORK( IWT ), LDT ) - IF( LEFT ) THEN -* -* H or H**H is applied to C(1:m-k+i+ib-1,1:n) -* - MI = M - K + I + IB - 1 - ELSE -* -* H or H**H is applied to C(1:m,1:n-k+i+ib-1) -* - NI = N - K + I + IB - 1 - END IF -* -* Apply H or H**H -* - CALL ZLARFB( SIDE, TRANS, 'Backward', 'Columnwise', MI, NI, - $ IB, A( 1, I ), LDA, WORK( IWT ), LDT, C, LDC, - $ WORK, LDWORK ) - 10 CONTINUE - END IF - WORK( 1 ) = LWKOPT - RETURN -* -* End of ZUNMQL -* - END diff --git a/lib/linalg/fortran/zunmqr.f b/lib/linalg/fortran/zunmqr.f deleted file mode 100644 index 2ae205f4fd..0000000000 --- a/lib/linalg/fortran/zunmqr.f +++ /dev/null @@ -1,337 +0,0 @@ -*> \brief \b ZUNMQR -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZUNMQR + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZUNMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, -* WORK, LWORK, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER SIDE, TRANS -* INTEGER INFO, K, LDA, LDC, LWORK, M, N -* .. -* .. Array Arguments .. -* COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZUNMQR overwrites the general complex M-by-N matrix C with -*> -*> SIDE = 'L' SIDE = 'R' -*> TRANS = 'N': Q * C C * Q -*> TRANS = 'C': Q**H * C C * Q**H -*> -*> where Q is a complex unitary matrix defined as the product of k -*> elementary reflectors -*> -*> Q = H(1) H(2) . . . H(k) -*> -*> as returned by ZGEQRF. Q is of order M if SIDE = 'L' and of order N -*> if SIDE = 'R'. -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] SIDE -*> \verbatim -*> SIDE is CHARACTER*1 -*> = 'L': apply Q or Q**H from the Left; -*> = 'R': apply Q or Q**H from the Right. -*> \endverbatim -*> -*> \param[in] TRANS -*> \verbatim -*> TRANS is CHARACTER*1 -*> = 'N': No transpose, apply Q; -*> = 'C': Conjugate transpose, apply Q**H. -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix C. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix C. N >= 0. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> The number of elementary reflectors whose product defines -*> the matrix Q. -*> If SIDE = 'L', M >= K >= 0; -*> if SIDE = 'R', N >= K >= 0. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is COMPLEX*16 array, dimension (LDA,K) -*> The i-th column must contain the vector which defines the -*> elementary reflector H(i), for i = 1,2,...,k, as returned by -*> ZGEQRF in the first k columns of its array argument A. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. -*> If SIDE = 'L', LDA >= max(1,M); -*> if SIDE = 'R', LDA >= max(1,N). -*> \endverbatim -*> -*> \param[in] TAU -*> \verbatim -*> TAU is COMPLEX*16 array, dimension (K) -*> TAU(i) must contain the scalar factor of the elementary -*> reflector H(i), as returned by ZGEQRF. -*> \endverbatim -*> -*> \param[in,out] C -*> \verbatim -*> C is COMPLEX*16 array, dimension (LDC,N) -*> On entry, the M-by-N matrix C. -*> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. -*> \endverbatim -*> -*> \param[in] LDC -*> \verbatim -*> LDC is INTEGER -*> The leading dimension of the array C. LDC >= max(1,M). -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) -*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -*> \endverbatim -*> -*> \param[in] LWORK -*> \verbatim -*> LWORK is INTEGER -*> The dimension of the array WORK. -*> If SIDE = 'L', LWORK >= max(1,N); -*> if SIDE = 'R', LWORK >= max(1,M). -*> For good performance, LWORK should generally be larger. -*> -*> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal size of the WORK array, returns -*> this value as the first entry of the WORK array, and no error -*> message related to LWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16OTHERcomputational -* -* ===================================================================== - SUBROUTINE ZUNMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, - $ WORK, LWORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER SIDE, TRANS - INTEGER INFO, K, LDA, LDC, LWORK, M, N -* .. -* .. Array Arguments .. - COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - INTEGER NBMAX, LDT, TSIZE - PARAMETER ( NBMAX = 64, LDT = NBMAX+1, - $ TSIZE = LDT*NBMAX ) -* .. -* .. Local Scalars .. - LOGICAL LEFT, LQUERY, NOTRAN - INTEGER I, I1, I2, I3, IB, IC, IINFO, IWT, JC, LDWORK, - $ LWKOPT, MI, NB, NBMIN, NI, NQ, NW -* .. -* .. External Functions .. - LOGICAL LSAME - INTEGER ILAENV - EXTERNAL LSAME, ILAENV -* .. -* .. External Subroutines .. - EXTERNAL XERBLA, ZLARFB, ZLARFT, ZUNM2R -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, MIN -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - INFO = 0 - LEFT = LSAME( SIDE, 'L' ) - NOTRAN = LSAME( TRANS, 'N' ) - LQUERY = ( LWORK.EQ.-1 ) -* -* NQ is the order of Q and NW is the minimum dimension of WORK -* - IF( LEFT ) THEN - NQ = M - NW = MAX( 1, N ) - ELSE - NQ = N - NW = MAX( 1, M ) - END IF - IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN - INFO = -1 - ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN - INFO = -2 - ELSE IF( M.LT.0 ) THEN - INFO = -3 - ELSE IF( N.LT.0 ) THEN - INFO = -4 - ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN - INFO = -5 - ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN - INFO = -7 - ELSE IF( LDC.LT.MAX( 1, M ) ) THEN - INFO = -10 - ELSE IF( LWORK.LT.NW .AND. .NOT.LQUERY ) THEN - INFO = -12 - END IF -* - IF( INFO.EQ.0 ) THEN -* -* Compute the workspace requirements -* - NB = MIN( NBMAX, ILAENV( 1, 'ZUNMQR', SIDE // TRANS, M, N, K, - $ -1 ) ) - LWKOPT = NW*NB + TSIZE - WORK( 1 ) = LWKOPT - END IF -* - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'ZUNMQR', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - RETURN - END IF -* -* Quick return if possible -* - IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) THEN - WORK( 1 ) = 1 - RETURN - END IF -* - NBMIN = 2 - LDWORK = NW - IF( NB.GT.1 .AND. NB.LT.K ) THEN - IF( LWORK.LT.LWKOPT ) THEN - NB = (LWORK-TSIZE) / LDWORK - NBMIN = MAX( 2, ILAENV( 2, 'ZUNMQR', SIDE // TRANS, M, N, K, - $ -1 ) ) - END IF - END IF -* - IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN -* -* Use unblocked code -* - CALL ZUNM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, - $ IINFO ) - ELSE -* -* Use blocked code -* - IWT = 1 + NW*NB - IF( ( LEFT .AND. .NOT.NOTRAN ) .OR. - $ ( .NOT.LEFT .AND. NOTRAN ) ) THEN - I1 = 1 - I2 = K - I3 = NB - ELSE - I1 = ( ( K-1 ) / NB )*NB + 1 - I2 = 1 - I3 = -NB - END IF -* - IF( LEFT ) THEN - NI = N - JC = 1 - ELSE - MI = M - IC = 1 - END IF -* - DO 10 I = I1, I2, I3 - IB = MIN( NB, K-I+1 ) -* -* Form the triangular factor of the block reflector -* H = H(i) H(i+1) . . . H(i+ib-1) -* - CALL ZLARFT( 'Forward', 'Columnwise', NQ-I+1, IB, A( I, I ), - $ LDA, TAU( I ), WORK( IWT ), LDT ) - IF( LEFT ) THEN -* -* H or H**H is applied to C(i:m,1:n) -* - MI = M - I + 1 - IC = I - ELSE -* -* H or H**H is applied to C(1:m,i:n) -* - NI = N - I + 1 - JC = I - END IF -* -* Apply H or H**H -* - CALL ZLARFB( SIDE, TRANS, 'Forward', 'Columnwise', MI, NI, - $ IB, A( I, I ), LDA, WORK( IWT ), LDT, - $ C( IC, JC ), LDC, WORK, LDWORK ) - 10 CONTINUE - END IF - WORK( 1 ) = LWKOPT - RETURN -* -* End of ZUNMQR -* - END diff --git a/lib/linalg/fortran/zunmtr.f b/lib/linalg/fortran/zunmtr.f deleted file mode 100644 index 441a7c2bcc..0000000000 --- a/lib/linalg/fortran/zunmtr.f +++ /dev/null @@ -1,307 +0,0 @@ -*> \brief \b ZUNMTR -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZUNMTR + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZUNMTR( SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC, -* WORK, LWORK, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER SIDE, TRANS, UPLO -* INTEGER INFO, LDA, LDC, LWORK, M, N -* .. -* .. Array Arguments .. -* COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZUNMTR overwrites the general complex M-by-N matrix C with -*> -*> SIDE = 'L' SIDE = 'R' -*> TRANS = 'N': Q * C C * Q -*> TRANS = 'C': Q**H * C C * Q**H -*> -*> where Q is a complex unitary matrix of order nq, with nq = m if -*> SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of -*> nq-1 elementary reflectors, as returned by ZHETRD: -*> -*> if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1); -*> -*> if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1). -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] SIDE -*> \verbatim -*> SIDE is CHARACTER*1 -*> = 'L': apply Q or Q**H from the Left; -*> = 'R': apply Q or Q**H from the Right. -*> \endverbatim -*> -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> = 'U': Upper triangle of A contains elementary reflectors -*> from ZHETRD; -*> = 'L': Lower triangle of A contains elementary reflectors -*> from ZHETRD. -*> \endverbatim -*> -*> \param[in] TRANS -*> \verbatim -*> TRANS is CHARACTER*1 -*> = 'N': No transpose, apply Q; -*> = 'C': Conjugate transpose, apply Q**H. -*> \endverbatim -*> -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix C. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix C. N >= 0. -*> \endverbatim -*> -*> \param[in] A -*> \verbatim -*> A is COMPLEX*16 array, dimension -*> (LDA,M) if SIDE = 'L' -*> (LDA,N) if SIDE = 'R' -*> The vectors which define the elementary reflectors, as -*> returned by ZHETRD. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. -*> LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'. -*> \endverbatim -*> -*> \param[in] TAU -*> \verbatim -*> TAU is COMPLEX*16 array, dimension -*> (M-1) if SIDE = 'L' -*> (N-1) if SIDE = 'R' -*> TAU(i) must contain the scalar factor of the elementary -*> reflector H(i), as returned by ZHETRD. -*> \endverbatim -*> -*> \param[in,out] C -*> \verbatim -*> C is COMPLEX*16 array, dimension (LDC,N) -*> On entry, the M-by-N matrix C. -*> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. -*> \endverbatim -*> -*> \param[in] LDC -*> \verbatim -*> LDC is INTEGER -*> The leading dimension of the array C. LDC >= max(1,M). -*> \endverbatim -*> -*> \param[out] WORK -*> \verbatim -*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) -*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. -*> \endverbatim -*> -*> \param[in] LWORK -*> \verbatim -*> LWORK is INTEGER -*> The dimension of the array WORK. -*> If SIDE = 'L', LWORK >= max(1,N); -*> if SIDE = 'R', LWORK >= max(1,M). -*> For optimum performance LWORK >= N*NB if SIDE = 'L', and -*> LWORK >=M*NB if SIDE = 'R', where NB is the optimal -*> blocksize. -*> -*> If LWORK = -1, then a workspace query is assumed; the routine -*> only calculates the optimal size of the WORK array, returns -*> this value as the first entry of the WORK array, and no error -*> message related to LWORK is issued by XERBLA. -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16OTHERcomputational -* -* ===================================================================== - SUBROUTINE ZUNMTR( SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC, - $ WORK, LWORK, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER SIDE, TRANS, UPLO - INTEGER INFO, LDA, LDC, LWORK, M, N -* .. -* .. Array Arguments .. - COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) -* .. -* -* ===================================================================== -* -* .. Local Scalars .. - LOGICAL LEFT, LQUERY, UPPER - INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW -* .. -* .. External Functions .. - LOGICAL LSAME - INTEGER ILAENV - EXTERNAL LSAME, ILAENV -* .. -* .. External Subroutines .. - EXTERNAL XERBLA, ZUNMQL, ZUNMQR -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* .. Executable Statements .. -* -* Test the input arguments -* - INFO = 0 - LEFT = LSAME( SIDE, 'L' ) - UPPER = LSAME( UPLO, 'U' ) - LQUERY = ( LWORK.EQ.-1 ) -* -* NQ is the order of Q and NW is the minimum dimension of WORK -* - IF( LEFT ) THEN - NQ = M - NW = MAX( 1, N ) - ELSE - NQ = N - NW = MAX( 1, M ) - END IF - IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN - INFO = -1 - ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN - INFO = -2 - ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT.LSAME( TRANS, 'C' ) ) - $ THEN - INFO = -3 - ELSE IF( M.LT.0 ) THEN - INFO = -4 - ELSE IF( N.LT.0 ) THEN - INFO = -5 - ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN - INFO = -7 - ELSE IF( LDC.LT.MAX( 1, M ) ) THEN - INFO = -10 - ELSE IF( LWORK.LT.NW .AND. .NOT.LQUERY ) THEN - INFO = -12 - END IF -* - IF( INFO.EQ.0 ) THEN - IF( UPPER ) THEN - IF( LEFT ) THEN - NB = ILAENV( 1, 'ZUNMQL', SIDE // TRANS, M-1, N, M-1, - $ -1 ) - ELSE - NB = ILAENV( 1, 'ZUNMQL', SIDE // TRANS, M, N-1, N-1, - $ -1 ) - END IF - ELSE - IF( LEFT ) THEN - NB = ILAENV( 1, 'ZUNMQR', SIDE // TRANS, M-1, N, M-1, - $ -1 ) - ELSE - NB = ILAENV( 1, 'ZUNMQR', SIDE // TRANS, M, N-1, N-1, - $ -1 ) - END IF - END IF - LWKOPT = NW*NB - WORK( 1 ) = LWKOPT - END IF -* - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'ZUNMTR', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - RETURN - END IF -* -* Quick return if possible -* - IF( M.EQ.0 .OR. N.EQ.0 .OR. NQ.EQ.1 ) THEN - WORK( 1 ) = 1 - RETURN - END IF -* - IF( LEFT ) THEN - MI = M - 1 - NI = N - ELSE - MI = M - NI = N - 1 - END IF -* - IF( UPPER ) THEN -* -* Q was determined by a call to ZHETRD with UPLO = 'U' -* - CALL ZUNMQL( SIDE, TRANS, MI, NI, NQ-1, A( 1, 2 ), LDA, TAU, C, - $ LDC, WORK, LWORK, IINFO ) - ELSE -* -* Q was determined by a call to ZHETRD with UPLO = 'L' -* - IF( LEFT ) THEN - I1 = 2 - I2 = 1 - ELSE - I1 = 1 - I2 = 2 - END IF - CALL ZUNMQR( SIDE, TRANS, MI, NI, NQ-1, A( 2, 1 ), LDA, TAU, - $ C( I1, I2 ), LDC, WORK, LWORK, IINFO ) - END IF - WORK( 1 ) = LWKOPT - RETURN -* -* End of ZUNMTR -* - END diff --git a/lib/linalg/s_lmp_cmp.cpp b/lib/linalg/s_lmp_cmp.cpp index 73b011a799..51c47167e4 100644 --- a/lib/linalg/s_lmp_cmp.cpp +++ b/lib/linalg/s_lmp_cmp.cpp @@ -7,7 +7,7 @@ extern "C" { integer s_lmp_cmp(char *a0, char *b0, ftnlen la, ftnlen lb) { - register unsigned char *a, *aend, *b, *bend; + unsigned char *a, *aend, *b, *bend; a = (unsigned char *)a0; b = (unsigned char *)b0; aend = a + la; diff --git a/lib/linalg/s_lmp_copy.cpp b/lib/linalg/s_lmp_copy.cpp index 9b432e08ca..5e09459b1b 100644 --- a/lib/linalg/s_lmp_copy.cpp +++ b/lib/linalg/s_lmp_copy.cpp @@ -5,9 +5,9 @@ extern "C" { /* assign strings: a = b */ -void s_lmp_copy(register char *a, register char *b, ftnlen la, ftnlen lb) +void s_lmp_copy(char *a, char *b, ftnlen la, ftnlen lb) { - register char *aend, *bend; + char *aend, *bend; aend = a + la; diff --git a/lib/linalg/static/.clang-format b/lib/linalg/static/.clang-format deleted file mode 100644 index 8856e00947..0000000000 --- a/lib/linalg/static/.clang-format +++ /dev/null @@ -1,23 +0,0 @@ ---- -Language: Cpp -BasedOnStyle: LLVM -AccessModifierOffset: -4 -AlignConsecutiveAssignments: false -AlignEscapedNewlines: Left -AllowShortFunctionsOnASingleLine: Inline -AllowShortLambdasOnASingleLine: None -AllowShortIfStatementsOnASingleLine: WithoutElse -BraceWrapping: - AfterFunction: true -BreakBeforeBraces: Custom -BreakInheritanceList: AfterColon -BreakConstructorInitializers: AfterColon -ColumnLimit: 100 -IndentCaseLabels: true -IndentWidth: 4 -ObjCBlockIndentWidth: 4 -PenaltyBreakAssignment: 4 -Standard: Cpp11 -TabWidth: 4 -UseTab: Never -... diff --git a/lib/linalg/static/README b/lib/linalg/static/README deleted file mode 100644 index 2d0271db7c..0000000000 --- a/lib/linalg/static/README +++ /dev/null @@ -1,8 +0,0 @@ -The C++ files in this folder are either direct C++ implementations of -their Fortran equivalents using the C++ runtime, or they are adapted -copies of functions from the libf2c runtime. The runtime functions -needed to be renamed to avoid conflics with libgfortran which uses -some of the same function names. - -The Fortran files in this folder are modified from their -original versions, so that f2c can correctly translate them. diff --git a/lib/linalg/static/d_lmp_cnjg.cpp b/lib/linalg/static/d_lmp_cnjg.cpp deleted file mode 100644 index 03ca8f98fd..0000000000 --- a/lib/linalg/static/d_lmp_cnjg.cpp +++ /dev/null @@ -1,13 +0,0 @@ - -#include "lmp_f2c.h" - -extern "C" { - -void d_lmp_cnjg(doublecomplex *r, doublecomplex *z) -{ - doublereal zi = z->i; - - r->r = z->r; - r->i = -zi; -} -} diff --git a/lib/linalg/static/d_lmp_imag.cpp b/lib/linalg/static/d_lmp_imag.cpp deleted file mode 100644 index f0443f7828..0000000000 --- a/lib/linalg/static/d_lmp_imag.cpp +++ /dev/null @@ -1,10 +0,0 @@ - -#include "lmp_f2c.h" - -extern "C" { - -double d_lmp_imag(doublecomplex *z) -{ - return (z->i); -} -} diff --git a/lib/linalg/static/d_lmp_lg10.cpp b/lib/linalg/static/d_lmp_lg10.cpp deleted file mode 100644 index ec48c99839..0000000000 --- a/lib/linalg/static/d_lmp_lg10.cpp +++ /dev/null @@ -1,14 +0,0 @@ - -#include "lmp_f2c.h" -#undef abs - -static constexpr double log10e = 0.43429448190325182765; - -#include - -extern "C" { -double d_lmp_lg10(doublereal *x) -{ - return (log10e * log(*x)); -} -} diff --git a/lib/linalg/static/d_lmp_sign.cpp b/lib/linalg/static/d_lmp_sign.cpp deleted file mode 100644 index fb0a1e79ff..0000000000 --- a/lib/linalg/static/d_lmp_sign.cpp +++ /dev/null @@ -1,12 +0,0 @@ - -#include "lmp_f2c.h" - -extern "C" { - -double d_lmp_sign(doublereal *a, doublereal *b) -{ - double x; - x = (*a >= 0 ? *a : -*a); - return (*b >= 0 ? x : -x); -} -} diff --git a/lib/linalg/static/dgetrf2.f b/lib/linalg/static/dgetrf2.f deleted file mode 100644 index e3d2aac299..0000000000 --- a/lib/linalg/static/dgetrf2.f +++ /dev/null @@ -1,269 +0,0 @@ -*> \brief \b DGETRF2 -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* RECURSIVE SUBROUTINE DGETRF2( M, N, A, LDA, IPIV, INFO ) -* -* .. Scalar Arguments .. -* INTEGER INFO, LDA, M, N -* .. -* .. Array Arguments .. -* INTEGER IPIV( * ) -* DOUBLE PRECISION A( LDA, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DGETRF2 computes an LU factorization of a general M-by-N matrix A -*> using partial pivoting with row interchanges. -*> -*> The factorization has the form -*> A = P * L * U -*> where P is a permutation matrix, L is lower triangular with unit -*> diagonal elements (lower trapezoidal if m > n), and U is upper -*> triangular (upper trapezoidal if m < n). -*> -*> This is the recursive version of the algorithm. It divides -*> the matrix into four submatrices: -*> -*> [ A11 | A12 ] where A11 is n1 by n1 and A22 is n2 by n2 -*> A = [ -----|----- ] with n1 = min(m,n)/2 -*> [ A21 | A22 ] n2 = n-n1 -*> -*> [ A11 ] -*> The subroutine calls itself to factor [ --- ], -*> [ A12 ] -*> [ A12 ] -*> do the swaps on [ --- ], solve A12, update A22, -*> [ A22 ] -*> -*> then calls itself to factor A22 and do the swaps on A21. -*> -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] M -*> \verbatim -*> M is INTEGER -*> The number of rows of the matrix A. M >= 0. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The number of columns of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the M-by-N matrix to be factored. -*> On exit, the factors L and U from the factorization -*> A = P*L*U; the unit diagonal elements of L are not stored. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,M). -*> \endverbatim -*> -*> \param[out] IPIV -*> \verbatim -*> IPIV is INTEGER array, dimension (min(M,N)) -*> The pivot indices; for 1 <= i <= min(M,N), row i of the -*> matrix was interchanged with row IPIV(i). -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, U(i,i) is exactly zero. The factorization -*> has been completed, but the factor U is exactly -*> singular, and division by zero will occur if it is used -*> to solve a system of equations. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleGEcomputational -* -* ===================================================================== - SUBROUTINE DGETRF2( M, N, A, LDA, IPIV, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - INTEGER INFO, LDA, M, N -* .. -* .. Array Arguments .. - INTEGER IPIV( * ) - DOUBLE PRECISION A( LDA, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE, ZERO - PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) -* .. -* .. Local Scalars .. - DOUBLE PRECISION SFMIN, TEMP - INTEGER I, IINFO, N1, N2 -* .. -* .. External Functions .. - DOUBLE PRECISION DLAMCH - INTEGER IDAMAX - EXTERNAL DLAMCH, IDAMAX -* .. -* .. External Subroutines .. - EXTERNAL DGEMM, DSCAL, DLASWP, DTRSM, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, MIN -* .. -* .. Executable Statements .. -* -* Test the input parameters -* - INFO = 0 - IF( M.LT.0 ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( LDA.LT.MAX( 1, M ) ) THEN - INFO = -4 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DGETRF2', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( M.EQ.0 .OR. N.EQ.0 ) - $ RETURN - - IF ( M.EQ.1 ) THEN -* -* Use unblocked code for one row case -* Just need to handle IPIV and INFO -* - IPIV( 1 ) = 1 - IF ( A(1,1).EQ.ZERO ) - $ INFO = 1 -* - ELSE IF( N.EQ.1 ) THEN -* -* Use unblocked code for one column case -* -* -* Compute machine safe minimum -* - SFMIN = DLAMCH('S') -* -* Find pivot and test for singularity -* - I = IDAMAX( M, A( 1, 1 ), 1 ) - IPIV( 1 ) = I - IF( A( I, 1 ).NE.ZERO ) THEN -* -* Apply the interchange -* - IF( I.NE.1 ) THEN - TEMP = A( 1, 1 ) - A( 1, 1 ) = A( I, 1 ) - A( I, 1 ) = TEMP - END IF -* -* Compute elements 2:M of the column -* - IF( ABS(A( 1, 1 )) .GE. SFMIN ) THEN - CALL DSCAL( M-1, ONE / A( 1, 1 ), A( 2, 1 ), 1 ) - ELSE - DO 10 I = 1, M-1 - A( 1+I, 1 ) = A( 1+I, 1 ) / A( 1, 1 ) - 10 CONTINUE - END IF -* - ELSE - INFO = 1 - END IF -* - ELSE -* -* Use recursive code -* - N1 = MIN( M, N ) / 2 - N2 = N-N1 -* -* [ A11 ] -* Factor [ --- ] -* [ A21 ] -* - CALL DGETRF2( M, N1, A, LDA, IPIV, IINFO ) - - IF ( INFO.EQ.0 .AND. IINFO.GT.0 ) - $ INFO = IINFO -* -* [ A12 ] -* Apply interchanges to [ --- ] -* [ A22 ] -* - CALL DLASWP( N2, A( 1, N1+1 ), LDA, 1, N1, IPIV, 1 ) -* -* Solve A12 -* - CALL DTRSM( 'L', 'L', 'N', 'U', N1, N2, ONE, A, LDA, - $ A( 1, N1+1 ), LDA ) -* -* Update A22 -* - CALL DGEMM( 'N', 'N', M-N1, N2, N1, -ONE, A( N1+1, 1 ), LDA, - $ A( 1, N1+1 ), LDA, ONE, A( N1+1, N1+1 ), LDA ) -* -* Factor A22 -* - CALL DGETRF2( M-N1, N2, A( N1+1, N1+1 ), LDA, IPIV( N1+1 ), - $ IINFO ) -* -* Adjust INFO and the pivot indices -* - IF ( INFO.EQ.0 .AND. IINFO.GT.0 ) - $ INFO = IINFO + N1 - DO 20 I = N1+1, MIN( M, N ) - IPIV( I ) = IPIV( I ) + N1 - 20 CONTINUE -* -* Apply interchanges to A21 -* - CALL DLASWP( N1, A( 1, 1 ), LDA, N1+1, MIN( M, N), IPIV, 1 ) -* - END IF - RETURN -* -* End of DGETRF2 -* - END diff --git a/lib/linalg/static/disnan.cpp b/lib/linalg/static/disnan.cpp deleted file mode 100644 index dcdaad77e1..0000000000 --- a/lib/linalg/static/disnan.cpp +++ /dev/null @@ -1,14 +0,0 @@ - -#include - -extern "C" { - -#include "lmp_f2c.h" - -logical disnan_(const doublereal *din) -{ - if (!din) return TRUE_; - - return std::isnan(*din) ? TRUE_ : FALSE_; -} -} diff --git a/lib/linalg/static/dlamc3.f b/lib/linalg/static/dlamc3.f deleted file mode 100644 index 1108297707..0000000000 --- a/lib/linalg/static/dlamc3.f +++ /dev/null @@ -1,45 +0,0 @@ -*> \brief \b DLAMC3 -*> \details -*> \b Purpose: -*> \verbatim -*> DLAMC3 is intended to force A and B to be stored prior to doing -*> the addition of A and B , for use in situations where optimizers -*> might hold one of these in a register. -*> \endverbatim -*> \author LAPACK is a software package provided by Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd.. -*> \date December 2016 -*> \ingroup auxOTHERauxiliary -*> -*> \param[in] A -*> \verbatim -*> A is a DOUBLE PRECISION -*> \endverbatim -*> -*> \param[in] B -*> \verbatim -*> B is a DOUBLE PRECISION -*> The values A and B. -*> \endverbatim -*> - DOUBLE PRECISION FUNCTION DLAMC3( A, B ) -* -* -- LAPACK auxiliary routine (version 3.7.0) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2010 -* -* .. Scalar Arguments .. - DOUBLE PRECISION A, B -* .. -* ===================================================================== -* -* .. Executable Statements .. -* - DLAMC3 = A + B -* - RETURN -* -* End of DLAMC3 -* - END -* -************************************************************************ diff --git a/lib/linalg/static/dlamch.cpp b/lib/linalg/static/dlamch.cpp deleted file mode 100644 index 277096e6f3..0000000000 --- a/lib/linalg/static/dlamch.cpp +++ /dev/null @@ -1,45 +0,0 @@ - -#include -#include - -extern "C" { - -#include "lmp_f2c.h" - -// undefine conflicting f2c macros -#undef min -#undef max - -doublereal dlamch_(const char *cmach) -{ - if (!cmach) return 0.0; - char select = toupper(*cmach); - - // BLAS assumes rounding not truncation => epsilon is half - const double eps = 0.5 * std::numeric_limits::epsilon(); - if (select == 'E') return eps; - - double min = std::numeric_limits::min(); - const double max = std::numeric_limits::max(); - double small = 1.0 / max; - if (small >= min) min = small * (1.0 + eps); - if (select == 'S') return min; - - const double radix = std::numeric_limits::radix; - if (select == 'B') return radix; - - if (select == 'P') return eps * radix; - - if (select == 'N') return std::numeric_limits::digits; - - if (select == 'M') return std::numeric_limits::min_exponent; - - if (select == 'U') return min; - - if (select == 'L') return std::numeric_limits::max_exponent; - - if (select == 'O') return max; - - return 0.0; -} -} diff --git a/lib/linalg/static/dlarft.f b/lib/linalg/static/dlarft.f deleted file mode 100644 index e92c927971..0000000000 --- a/lib/linalg/static/dlarft.f +++ /dev/null @@ -1,327 +0,0 @@ -*> \brief \b DLARFT forms the triangular factor T of a block reflector H = I - vtvH -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download DLARFT + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) -* -* .. Scalar Arguments .. -* CHARACTER DIRECT, STOREV -* INTEGER K, LDT, LDV, N -* .. -* .. Array Arguments .. -* DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DLARFT forms the triangular factor T of a real block reflector H -*> of order n, which is defined as a product of k elementary reflectors. -*> -*> If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; -*> -*> If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. -*> -*> If STOREV = 'C', the vector which defines the elementary reflector -*> H(i) is stored in the i-th column of the array V, and -*> -*> H = I - V * T * V**T -*> -*> If STOREV = 'R', the vector which defines the elementary reflector -*> H(i) is stored in the i-th row of the array V, and -*> -*> H = I - V**T * T * V -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] DIRECT -*> \verbatim -*> DIRECT is CHARACTER*1 -*> Specifies the order in which the elementary reflectors are -*> multiplied to form the block reflector: -*> = 'F': H = H(1) H(2) . . . H(k) (Forward) -*> = 'B': H = H(k) . . . H(2) H(1) (Backward) -*> \endverbatim -*> -*> \param[in] STOREV -*> \verbatim -*> STOREV is CHARACTER*1 -*> Specifies how the vectors which define the elementary -*> reflectors are stored (see also Further Details): -*> = 'C': columnwise -*> = 'R': rowwise -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the block reflector H. N >= 0. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> The order of the triangular factor T (= the number of -*> elementary reflectors). K >= 1. -*> \endverbatim -*> -*> \param[in] V -*> \verbatim -*> V is DOUBLE PRECISION array, dimension -*> (LDV,K) if STOREV = 'C' -*> (LDV,N) if STOREV = 'R' -*> The matrix V. See further details. -*> \endverbatim -*> -*> \param[in] LDV -*> \verbatim -*> LDV is INTEGER -*> The leading dimension of the array V. -*> If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. -*> \endverbatim -*> -*> \param[in] TAU -*> \verbatim -*> TAU is DOUBLE PRECISION array, dimension (K) -*> TAU(i) must contain the scalar factor of the elementary -*> reflector H(i). -*> \endverbatim -*> -*> \param[out] T -*> \verbatim -*> T is DOUBLE PRECISION array, dimension (LDT,K) -*> The k by k triangular factor T of the block reflector. -*> If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is -*> lower triangular. The rest of the array is not used. -*> \endverbatim -*> -*> \param[in] LDT -*> \verbatim -*> LDT is INTEGER -*> The leading dimension of the array T. LDT >= K. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doubleOTHERauxiliary -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> The shape of the matrix V and the storage of the vectors which define -*> the H(i) is best illustrated by the following example with n = 5 and -*> k = 3. The elements equal to 1 are not stored. -*> -*> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': -*> -*> V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) -*> ( v1 1 ) ( 1 v2 v2 v2 ) -*> ( v1 v2 1 ) ( 1 v3 v3 ) -*> ( v1 v2 v3 ) -*> ( v1 v2 v3 ) -*> -*> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': -*> -*> V = ( v1 v2 v3 ) V = ( v1 v1 1 ) -*> ( v1 v2 v3 ) ( v2 v2 v2 1 ) -*> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) -*> ( 1 v3 ) -*> ( 1 ) -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER DIRECT, STOREV - INTEGER K, LDT, LDV, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE, ZERO - PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) -* .. -* .. Local Scalars .. - INTEGER I, J, PREVLASTV, LASTV -* .. -* .. External Subroutines .. - EXTERNAL DGEMV, DTRMV -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. Executable Statements .. -* -* Quick return if possible -* - IF( N.EQ.0 ) - $ RETURN -* - IF( LSAME( DIRECT, 'F' ) ) THEN - PREVLASTV = N - DO I = 1, K - PREVLASTV = MAX( I, PREVLASTV ) - IF( TAU( I ).EQ.ZERO ) THEN -* -* H(i) = I -* - DO J = 1, I - T( J, I ) = ZERO - END DO - ELSE -* -* general case -* - IF( LSAME( STOREV, 'C' ) ) THEN -* Skip any trailing zeros. - DO LASTV = N, I+1, -1 - IF( V( LASTV, I ).NE.ZERO ) GOTO 219 - END DO - 219 CONTINUE - DO J = 1, I-1 - T( J, I ) = -TAU( I ) * V( I , J ) - END DO - J = MIN( LASTV, PREVLASTV ) -* -* T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**T * V(i:j,i) -* - CALL DGEMV( 'Transpose', J-I, I-1, -TAU( I ), - $ V( I+1, 1 ), LDV, V( I+1, I ), 1, ONE, - $ T( 1, I ), 1 ) - ELSE -* Skip any trailing zeros. - DO LASTV = N, I+1, -1 - IF( V( I, LASTV ).NE.ZERO ) GOTO 235 - END DO - 235 CONTINUE - DO J = 1, I-1 - T( J, I ) = -TAU( I ) * V( J , I ) - END DO - J = MIN( LASTV, PREVLASTV ) -* -* T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**T -* - CALL DGEMV( 'No transpose', I-1, J-I, -TAU( I ), - $ V( 1, I+1 ), LDV, V( I, I+1 ), LDV, ONE, - $ T( 1, I ), 1 ) - END IF -* -* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) -* - CALL DTRMV( 'Upper', 'No transpose', 'Non-unit', I-1, T, - $ LDT, T( 1, I ), 1 ) - T( I, I ) = TAU( I ) - IF( I.GT.1 ) THEN - PREVLASTV = MAX( PREVLASTV, LASTV ) - ELSE - PREVLASTV = LASTV - END IF - END IF - END DO - ELSE - PREVLASTV = 1 - DO I = K, 1, -1 - IF( TAU( I ).EQ.ZERO ) THEN -* -* H(i) = I -* - DO J = I, K - T( J, I ) = ZERO - END DO - ELSE -* -* general case -* - IF( I.LT.K ) THEN - IF( LSAME( STOREV, 'C' ) ) THEN -* Skip any leading zeros. - DO LASTV = 1, I-1 - IF( V( LASTV, I ).NE.ZERO ) GOTO 280 - END DO - 280 CONTINUE - DO J = I+1, K - T( J, I ) = -TAU( I ) * V( N-K+I , J ) - END DO - J = MAX( LASTV, PREVLASTV ) -* -* T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**T * V(j:n-k+i,i) -* - CALL DGEMV( 'Transpose', N-K+I-J, K-I, -TAU( I ), - $ V( J, I+1 ), LDV, V( J, I ), 1, ONE, - $ T( I+1, I ), 1 ) - ELSE -* Skip any leading zeros. - DO LASTV = 1, I-1 - IF( V( I, LASTV ).NE.ZERO ) GOTO 296 - END DO - 296 CONTINUE - DO J = I+1, K - T( J, I ) = -TAU( I ) * V( J, N-K+I ) - END DO - J = MAX( LASTV, PREVLASTV ) -* -* T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**T -* - CALL DGEMV( 'No transpose', K-I, N-K+I-J, - $ -TAU( I ), V( I+1, J ), LDV, V( I, J ), LDV, - $ ONE, T( I+1, I ), 1 ) - END IF -* -* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) -* - CALL DTRMV( 'Lower', 'No transpose', 'Non-unit', K-I, - $ T( I+1, I+1 ), LDT, T( I+1, I ), 1 ) - IF( I.GT.1 ) THEN - PREVLASTV = MIN( PREVLASTV, LASTV ) - ELSE - PREVLASTV = LASTV - END IF - END IF - T( I, I ) = TAU( I ) - END IF - END DO - END IF - RETURN -* -* End of DLARFT -* - END diff --git a/lib/linalg/static/dpotrf2.f b/lib/linalg/static/dpotrf2.f deleted file mode 100644 index ba827635a8..0000000000 --- a/lib/linalg/static/dpotrf2.f +++ /dev/null @@ -1,234 +0,0 @@ -*> \brief \b DPOTRF2 -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -* Definition: -* =========== -* -* RECURSIVE SUBROUTINE DPOTRF2( UPLO, N, A, LDA, INFO ) -* -* .. Scalar Arguments .. -* CHARACTER UPLO -* INTEGER INFO, LDA, N -* .. -* .. Array Arguments .. -* REAL A( LDA, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> DPOTRF2 computes the Cholesky factorization of a real symmetric -*> positive definite matrix A using the recursive algorithm. -*> -*> The factorization has the form -*> A = U**T * U, if UPLO = 'U', or -*> A = L * L**T, if UPLO = 'L', -*> where U is an upper triangular matrix and L is lower triangular. -*> -*> This is the recursive version of the algorithm. It divides -*> the matrix into four submatrices: -*> -*> [ A11 | A12 ] where A11 is n1 by n1 and A22 is n2 by n2 -*> A = [ -----|----- ] with n1 = n/2 -*> [ A21 | A22 ] n2 = n-n1 -*> -*> The subroutine calls itself to factor A11. Update and scale A21 -*> or A12, update A22 then calls itself to factor A22. -*> -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] UPLO -*> \verbatim -*> UPLO is CHARACTER*1 -*> = 'U': Upper triangle of A is stored; -*> = 'L': Lower triangle of A is stored. -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the matrix A. N >= 0. -*> \endverbatim -*> -*> \param[in,out] A -*> \verbatim -*> A is DOUBLE PRECISION array, dimension (LDA,N) -*> On entry, the symmetric matrix A. If UPLO = 'U', the leading -*> N-by-N upper triangular part of A contains the upper -*> triangular part of the matrix A, and the strictly lower -*> triangular part of A is not referenced. If UPLO = 'L', the -*> leading N-by-N lower triangular part of A contains the lower -*> triangular part of the matrix A, and the strictly upper -*> triangular part of A is not referenced. -*> -*> On exit, if INFO = 0, the factor U or L from the Cholesky -*> factorization A = U**T*U or A = L*L**T. -*> \endverbatim -*> -*> \param[in] LDA -*> \verbatim -*> LDA is INTEGER -*> The leading dimension of the array A. LDA >= max(1,N). -*> \endverbatim -*> -*> \param[out] INFO -*> \verbatim -*> INFO is INTEGER -*> = 0: successful exit -*> < 0: if INFO = -i, the i-th argument had an illegal value -*> > 0: if INFO = i, the leading minor of order i is not -*> positive definite, and the factorization could not be -*> completed. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup doublePOcomputational -* -* ===================================================================== - SUBROUTINE DPOTRF2( UPLO, N, A, LDA, INFO ) -* -* -- LAPACK computational routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER UPLO - INTEGER INFO, LDA, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE, ZERO - PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) -* .. -* .. Local Scalars .. - LOGICAL UPPER - INTEGER N1, N2, IINFO -* .. -* .. External Functions .. - LOGICAL LSAME, DISNAN - EXTERNAL LSAME, DISNAN -* .. -* .. External Subroutines .. - EXTERNAL DSYRK, DTRSM, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX, SQRT -* .. -* .. Executable Statements .. -* -* Test the input parameters -* - INFO = 0 - UPPER = LSAME( UPLO, 'U' ) - IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -4 - END IF - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DPOTRF2', -INFO ) - RETURN - END IF -* -* Quick return if possible -* - IF( N.EQ.0 ) - $ RETURN -* -* N=1 case -* - IF( N.EQ.1 ) THEN -* -* Test for non-positive-definiteness -* - IF( A( 1, 1 ).LE.ZERO.OR.DISNAN( A( 1, 1 ) ) ) THEN - INFO = 1 - RETURN - END IF -* -* Factor -* - A( 1, 1 ) = SQRT( A( 1, 1 ) ) -* -* Use recursive code -* - ELSE - N1 = N/2 - N2 = N-N1 -* -* Factor A11 -* - CALL DPOTRF2( UPLO, N1, A( 1, 1 ), LDA, IINFO ) - IF ( IINFO.NE.0 ) THEN - INFO = IINFO - RETURN - END IF -* -* Compute the Cholesky factorization A = U**T*U -* - IF( UPPER ) THEN -* -* Update and scale A12 -* - CALL DTRSM( 'L', 'U', 'T', 'N', N1, N2, ONE, - $ A( 1, 1 ), LDA, A( 1, N1+1 ), LDA ) -* -* Update and factor A22 -* - CALL DSYRK( UPLO, 'T', N2, N1, -ONE, A( 1, N1+1 ), LDA, - $ ONE, A( N1+1, N1+1 ), LDA ) - CALL DPOTRF2( UPLO, N2, A( N1+1, N1+1 ), LDA, IINFO ) - IF ( IINFO.NE.0 ) THEN - INFO = IINFO + N1 - RETURN - END IF -* -* Compute the Cholesky factorization A = L*L**T -* - ELSE -* -* Update and scale A21 -* - CALL DTRSM( 'R', 'L', 'T', 'N', N2, N1, ONE, - $ A( 1, 1 ), LDA, A( N1+1, 1 ), LDA ) -* -* Update and factor A22 -* - CALL DSYRK( UPLO, 'N', N2, N1, -ONE, A( N1+1, 1 ), LDA, - $ ONE, A( N1+1, N1+1 ), LDA ) - CALL DPOTRF2( UPLO, N2, A( N1+1, N1+1 ), LDA, IINFO ) - IF ( IINFO.NE.0 ) THEN - INFO = IINFO + N1 - RETURN - END IF - END IF - END IF - RETURN -* -* End of DPOTRF2 -* - END diff --git a/lib/linalg/static/i_lmp_dnnt.cpp b/lib/linalg/static/i_lmp_dnnt.cpp deleted file mode 100644 index 8050697bb9..0000000000 --- a/lib/linalg/static/i_lmp_dnnt.cpp +++ /dev/null @@ -1,12 +0,0 @@ - -#include "lmp_f2c.h" - -#undef abs -#include - -extern "C" { -integer i_lmp_dnnt(doublereal *x) -{ - return (integer)(*x >= 0. ? floor(*x + .5) : -floor(.5 - *x)); -} -} diff --git a/lib/linalg/static/i_lmp_len.cpp b/lib/linalg/static/i_lmp_len.cpp deleted file mode 100644 index b6101b29ad..0000000000 --- a/lib/linalg/static/i_lmp_len.cpp +++ /dev/null @@ -1,10 +0,0 @@ - -#include "lmp_f2c.h" - -extern "C" { - -integer i_lmp_len(char *s, ftnlen n) -{ - return (n); -} -} diff --git a/lib/linalg/static/i_lmp_nint.cpp b/lib/linalg/static/i_lmp_nint.cpp deleted file mode 100644 index f41ca6b3eb..0000000000 --- a/lib/linalg/static/i_lmp_nint.cpp +++ /dev/null @@ -1,13 +0,0 @@ - -#include "lmp_f2c.h" -#undef abs - -#include - -extern "C" { - -integer i_lmp_nint(real *x) -{ - return (integer)(*x >= 0 ? floor(*x + .5) : -floor(.5 - *x)); -} -} diff --git a/lib/linalg/static/lsame.cpp b/lib/linalg/static/lsame.cpp deleted file mode 100644 index 480ae93bc9..0000000000 --- a/lib/linalg/static/lsame.cpp +++ /dev/null @@ -1,17 +0,0 @@ - -#include - -extern "C" { - -#include "lmp_f2c.h" - -logical lsame_(const char *a, const char *b) -{ - char ua, ub; - if (!a || !b) return FALSE_; - - ua = toupper(*a); - ub = toupper(*b); - return (ua == ub) ? TRUE_ : FALSE_; -} -} diff --git a/lib/linalg/static/pow_lmp_dd.cpp b/lib/linalg/static/pow_lmp_dd.cpp deleted file mode 100644 index 4963b04bbc..0000000000 --- a/lib/linalg/static/pow_lmp_dd.cpp +++ /dev/null @@ -1,12 +0,0 @@ - -#include "lmp_f2c.h" -#undef abs - -#include - -extern "C" { -double pow_lmp_dd(doublereal *ap, doublereal *bp) -{ - return (pow(*ap, *bp)); -} -} diff --git a/lib/linalg/static/pow_lmp_di.cpp b/lib/linalg/static/pow_lmp_di.cpp deleted file mode 100644 index 83a0da1a87..0000000000 --- a/lib/linalg/static/pow_lmp_di.cpp +++ /dev/null @@ -1,31 +0,0 @@ - -#include "lmp_f2c.h" - -extern "C" { - -double pow_lmp_di(doublereal *ap, integer *bp) -{ - double pow, x; - integer n; - unsigned long u; - - pow = 1; - x = *ap; - n = *bp; - - if (n != 0) { - if (n < 0) { - n = -n; - x = 1 / x; - } - for (u = n;;) { - if (u & 01) pow *= x; - if (u >>= 1) - x *= x; - else - break; - } - } - return (pow); -} -} diff --git a/lib/linalg/static/pow_lmp_ii.cpp b/lib/linalg/static/pow_lmp_ii.cpp deleted file mode 100644 index ff28c8fd5a..0000000000 --- a/lib/linalg/static/pow_lmp_ii.cpp +++ /dev/null @@ -1,29 +0,0 @@ - -#include "lmp_f2c.h" - -extern "C" { - -integer pow_lmp_ii(integer *ap, integer *bp) -{ - integer pow, x, n; - unsigned long u; - - x = *ap; - n = *bp; - - if (n <= 0) { - if (n == 0 || x == 1) return 1; - if (x != -1) return x == 0 ? 1 / x : 0; - n = -n; - } - u = n; - for (pow = 1;;) { - if (u & 01) pow *= x; - if (u >>= 1) - x *= x; - else - break; - } - return (pow); -} -} diff --git a/lib/linalg/static/s_lmp_cat.cpp b/lib/linalg/static/s_lmp_cat.cpp deleted file mode 100644 index 323b0b671d..0000000000 --- a/lib/linalg/static/s_lmp_cat.cpp +++ /dev/null @@ -1,23 +0,0 @@ - -#include "lmp_f2c.h" - -// concatenate two strings - -extern "C" { -void s_lmp_cat(char *lp, char *rpp[], ftnint rnp[], ftnint *np, ftnlen ll) -{ - ftnlen i, nc; - char *rp; - ftnlen n = *np; - for (i = 0; i < n; ++i) { - nc = ll; - if (rnp[i] < nc) nc = rnp[i]; - ll -= nc; - rp = rpp[i]; - while (--nc >= 0) - *lp++ = *rp++; - } - while (--ll >= 0) - *lp++ = ' '; -} -} diff --git a/lib/linalg/static/s_lmp_cmp.cpp b/lib/linalg/static/s_lmp_cmp.cpp deleted file mode 100644 index 73b011a799..0000000000 --- a/lib/linalg/static/s_lmp_cmp.cpp +++ /dev/null @@ -1,45 +0,0 @@ - -#include "lmp_f2c.h" - -extern "C" { - -// compare two strings - -integer s_lmp_cmp(char *a0, char *b0, ftnlen la, ftnlen lb) -{ - register unsigned char *a, *aend, *b, *bend; - a = (unsigned char *)a0; - b = (unsigned char *)b0; - aend = a + la; - bend = b + lb; - - if (la <= lb) { - while (a < aend) - if (*a != *b) - return (*a - *b); - else { - ++a; - ++b; - } - - while (b < bend) - if (*b != ' ') - return (' ' - *b); - else - ++b; - } else { - while (b < bend) - if (*a == *b) { - ++a; - ++b; - } else - return (*a - *b); - while (a < aend) - if (*a != ' ') - return (*a - ' '); - else - ++a; - } - return (0); -} -} diff --git a/lib/linalg/static/s_lmp_copy.cpp b/lib/linalg/static/s_lmp_copy.cpp deleted file mode 100644 index 9b432e08ca..0000000000 --- a/lib/linalg/static/s_lmp_copy.cpp +++ /dev/null @@ -1,26 +0,0 @@ - -#include "lmp_f2c.h" - -extern "C" { - -/* assign strings: a = b */ - -void s_lmp_copy(register char *a, register char *b, ftnlen la, ftnlen lb) -{ - register char *aend, *bend; - - aend = a + la; - - if (la <= lb) - while (a < aend) - *a++ = *b++; - - else { - bend = b + lb; - while (b < bend) - *a++ = *b++; - while (a < aend) - *a++ = ' '; - } -} -} diff --git a/lib/linalg/static/xerbla.cpp b/lib/linalg/static/xerbla.cpp deleted file mode 100644 index 6346126c67..0000000000 --- a/lib/linalg/static/xerbla.cpp +++ /dev/null @@ -1,31 +0,0 @@ - -#include "lmp_f2c.h" - -#undef abs -#include -#include -#include - -extern "C" { - -static constexpr int BUFSZ = 1024; - -integer xerbla_(const char *srname, integer *info) -{ - char buf[BUFSZ]; - buf[0] = '\0'; - - strcat(buf, " ** On entry to "); - for (int i = 0; i < BUFSZ - 16; ++i) { - if ((srname[i] == '\0') || (srname[i] == ' ')) { - buf[i + 16] = '\0'; - break; - } - buf[i + 16] = srname[i]; - } - int len = strlen(buf); - snprintf(buf + len, BUFSZ - len, " parameter number %d had an illegal value\n", *info); - exit(1); - return 0; -} -} diff --git a/lib/linalg/static/z_lmp_abs.cpp b/lib/linalg/static/z_lmp_abs.cpp deleted file mode 100644 index 2b79d56457..0000000000 --- a/lib/linalg/static/z_lmp_abs.cpp +++ /dev/null @@ -1,31 +0,0 @@ - -#include "lmp_f2c.h" -#undef abs - -#include - -extern "C" { - -static double f__cabs(double real, double imag) -{ - double temp; - - if (real < 0) real = -real; - if (imag < 0) imag = -imag; - if (imag > real) { - temp = real; - real = imag; - imag = temp; - } - if ((real + imag) == real) return (real); - - temp = imag / real; - temp = real * sqrt(1.0 + temp * temp); /*overflow!!*/ - return (temp); -} - -double z_lmp_abs(doublecomplex *z) -{ - return (f__cabs(z->r, z->i)); -} -} diff --git a/lib/linalg/static/z_lmp_div.cpp b/lib/linalg/static/z_lmp_div.cpp deleted file mode 100644 index 66218f8fc8..0000000000 --- a/lib/linalg/static/z_lmp_div.cpp +++ /dev/null @@ -1,31 +0,0 @@ - -#include "lmp_f2c.h" - -extern "C" { - -void z_lmp_div(doublecomplex *c, doublecomplex *a, doublecomplex *b) -{ - double ratio, den; - double abr, abi, cr; - - if ((abr = b->r) < 0.) abr = -abr; - if ((abi = b->i) < 0.) abi = -abi; - if (abr <= abi) { - if (abi == 0) { - if (a->i != 0 || a->r != 0) abi = 1.; - c->i = c->r = abi / abr; - return; - } - ratio = b->r / b->i; - den = b->i * (1 + ratio * ratio); - cr = (a->r * ratio + a->i) / den; - c->i = (a->i * ratio - a->r) / den; - } else { - ratio = b->i / b->r; - den = b->r * (1 + ratio * ratio); - cr = (a->r + a->i * ratio) / den; - c->i = (a->i - a->r * ratio) / den; - } - c->r = cr; -} -} diff --git a/lib/linalg/static/zlarft.f b/lib/linalg/static/zlarft.f deleted file mode 100644 index b59ba93213..0000000000 --- a/lib/linalg/static/zlarft.f +++ /dev/null @@ -1,328 +0,0 @@ -*> \brief \b ZLARFT forms the triangular factor T of a block reflector H = I - vtvH -* -* =========== DOCUMENTATION =========== -* -* Online html documentation available at -* http://www.netlib.org/lapack/explore-html/ -* -*> \htmlonly -*> Download ZLARFT + dependencies -*> -*> [TGZ] -*> -*> [ZIP] -*> -*> [TXT] -*> \endhtmlonly -* -* Definition: -* =========== -* -* SUBROUTINE ZLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) -* -* .. Scalar Arguments .. -* CHARACTER DIRECT, STOREV -* INTEGER K, LDT, LDV, N -* .. -* .. Array Arguments .. -* COMPLEX*16 T( LDT, * ), TAU( * ), V( LDV, * ) -* .. -* -* -*> \par Purpose: -* ============= -*> -*> \verbatim -*> -*> ZLARFT forms the triangular factor T of a complex block reflector H -*> of order n, which is defined as a product of k elementary reflectors. -*> -*> If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; -*> -*> If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. -*> -*> If STOREV = 'C', the vector which defines the elementary reflector -*> H(i) is stored in the i-th column of the array V, and -*> -*> H = I - V * T * V**H -*> -*> If STOREV = 'R', the vector which defines the elementary reflector -*> H(i) is stored in the i-th row of the array V, and -*> -*> H = I - V**H * T * V -*> \endverbatim -* -* Arguments: -* ========== -* -*> \param[in] DIRECT -*> \verbatim -*> DIRECT is CHARACTER*1 -*> Specifies the order in which the elementary reflectors are -*> multiplied to form the block reflector: -*> = 'F': H = H(1) H(2) . . . H(k) (Forward) -*> = 'B': H = H(k) . . . H(2) H(1) (Backward) -*> \endverbatim -*> -*> \param[in] STOREV -*> \verbatim -*> STOREV is CHARACTER*1 -*> Specifies how the vectors which define the elementary -*> reflectors are stored (see also Further Details): -*> = 'C': columnwise -*> = 'R': rowwise -*> \endverbatim -*> -*> \param[in] N -*> \verbatim -*> N is INTEGER -*> The order of the block reflector H. N >= 0. -*> \endverbatim -*> -*> \param[in] K -*> \verbatim -*> K is INTEGER -*> The order of the triangular factor T (= the number of -*> elementary reflectors). K >= 1. -*> \endverbatim -*> -*> \param[in] V -*> \verbatim -*> V is COMPLEX*16 array, dimension -*> (LDV,K) if STOREV = 'C' -*> (LDV,N) if STOREV = 'R' -*> The matrix V. See further details. -*> \endverbatim -*> -*> \param[in] LDV -*> \verbatim -*> LDV is INTEGER -*> The leading dimension of the array V. -*> If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. -*> \endverbatim -*> -*> \param[in] TAU -*> \verbatim -*> TAU is COMPLEX*16 array, dimension (K) -*> TAU(i) must contain the scalar factor of the elementary -*> reflector H(i). -*> \endverbatim -*> -*> \param[out] T -*> \verbatim -*> T is COMPLEX*16 array, dimension (LDT,K) -*> The k by k triangular factor T of the block reflector. -*> If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is -*> lower triangular. The rest of the array is not used. -*> \endverbatim -*> -*> \param[in] LDT -*> \verbatim -*> LDT is INTEGER -*> The leading dimension of the array T. LDT >= K. -*> \endverbatim -* -* Authors: -* ======== -* -*> \author Univ. of Tennessee -*> \author Univ. of California Berkeley -*> \author Univ. of Colorado Denver -*> \author NAG Ltd. -* -*> \ingroup complex16OTHERauxiliary -* -*> \par Further Details: -* ===================== -*> -*> \verbatim -*> -*> The shape of the matrix V and the storage of the vectors which define -*> the H(i) is best illustrated by the following example with n = 5 and -*> k = 3. The elements equal to 1 are not stored. -*> -*> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': -*> -*> V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) -*> ( v1 1 ) ( 1 v2 v2 v2 ) -*> ( v1 v2 1 ) ( 1 v3 v3 ) -*> ( v1 v2 v3 ) -*> ( v1 v2 v3 ) -*> -*> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': -*> -*> V = ( v1 v2 v3 ) V = ( v1 v1 1 ) -*> ( v1 v2 v3 ) ( v2 v2 v2 1 ) -*> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) -*> ( 1 v3 ) -*> ( 1 ) -*> \endverbatim -*> -* ===================================================================== - SUBROUTINE ZLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) -* -* -- LAPACK auxiliary routine -- -* -- LAPACK is a software package provided by Univ. of Tennessee, -- -* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -* .. Scalar Arguments .. - CHARACTER DIRECT, STOREV - INTEGER K, LDT, LDV, N -* .. -* .. Array Arguments .. - COMPLEX*16 T( LDT, * ), TAU( * ), V( LDV, * ) -* .. -* -* ===================================================================== -* -* .. Parameters .. - COMPLEX*16 ONE, ZERO - PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ), - $ ZERO = ( 0.0D+0, 0.0D+0 ) ) -* .. -* .. Local Scalars .. - INTEGER I, J, PREVLASTV, LASTV -* .. -* .. External Subroutines .. - EXTERNAL ZGEMV, ZTRMV, ZGEMM -* .. -* .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME -* .. -* .. Executable Statements .. -* -* Quick return if possible -* - IF( N.EQ.0 ) - $ RETURN -* - IF( LSAME( DIRECT, 'F' ) ) THEN - PREVLASTV = N - DO I = 1, K - PREVLASTV = MAX( PREVLASTV, I ) - IF( TAU( I ).EQ.ZERO ) THEN -* -* H(i) = I -* - DO J = 1, I - T( J, I ) = ZERO - END DO - ELSE -* -* general case -* - IF( LSAME( STOREV, 'C' ) ) THEN -* Skip any trailing zeros. - DO LASTV = N, I+1, -1 - IF( V( LASTV, I ).NE.ZERO ) GOTO 220 - END DO - 220 CONTINUE - DO J = 1, I-1 - T( J, I ) = -TAU( I ) * CONJG( V( I , J ) ) - END DO - J = MIN( LASTV, PREVLASTV ) -* -* T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**H * V(i:j,i) -* - CALL ZGEMV( 'Conjugate transpose', J-I, I-1, - $ -TAU( I ), V( I+1, 1 ), LDV, - $ V( I+1, I ), 1, ONE, T( 1, I ), 1 ) - ELSE -* Skip any trailing zeros. - DO LASTV = N, I+1, -1 - IF( V( I, LASTV ).NE.ZERO ) GOTO 236 - END DO - 236 CONTINUE - DO J = 1, I-1 - T( J, I ) = -TAU( I ) * V( J , I ) - END DO - J = MIN( LASTV, PREVLASTV ) -* -* T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**H -* - CALL ZGEMM( 'N', 'C', I-1, 1, J-I, -TAU( I ), - $ V( 1, I+1 ), LDV, V( I, I+1 ), LDV, - $ ONE, T( 1, I ), LDT ) - END IF -* -* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) -* - CALL ZTRMV( 'Upper', 'No transpose', 'Non-unit', I-1, T, - $ LDT, T( 1, I ), 1 ) - T( I, I ) = TAU( I ) - IF( I.GT.1 ) THEN - PREVLASTV = MAX( PREVLASTV, LASTV ) - ELSE - PREVLASTV = LASTV - END IF - END IF - END DO - ELSE - PREVLASTV = 1 - DO I = K, 1, -1 - IF( TAU( I ).EQ.ZERO ) THEN -* -* H(i) = I -* - DO J = I, K - T( J, I ) = ZERO - END DO - ELSE -* -* general case -* - IF( I.LT.K ) THEN - IF( LSAME( STOREV, 'C' ) ) THEN -* Skip any leading zeros. - DO LASTV = 1, I-1 - IF( V( LASTV, I ).NE.ZERO ) GOTO 281 - END DO - 281 CONTINUE - DO J = I+1, K - T( J, I ) = -TAU( I ) * CONJG( V( N-K+I , J ) ) - END DO - J = MAX( LASTV, PREVLASTV ) -* -* T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**H * V(j:n-k+i,i) -* - CALL ZGEMV( 'Conjugate transpose', N-K+I-J, K-I, - $ -TAU( I ), V( J, I+1 ), LDV, V( J, I ), - $ 1, ONE, T( I+1, I ), 1 ) - ELSE -* Skip any leading zeros. - DO LASTV = 1, I-1 - IF( V( I, LASTV ).NE.ZERO ) GOTO 297 - END DO - 297 CONTINUE - DO J = I+1, K - T( J, I ) = -TAU( I ) * V( J, N-K+I ) - END DO - J = MAX( LASTV, PREVLASTV ) -* -* T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**H -* - CALL ZGEMM( 'N', 'C', K-I, 1, N-K+I-J, -TAU( I ), - $ V( I+1, J ), LDV, V( I, J ), LDV, - $ ONE, T( I+1, I ), LDT ) - END IF -* -* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) -* - CALL ZTRMV( 'Lower', 'No transpose', 'Non-unit', K-I, - $ T( I+1, I+1 ), LDT, T( I+1, I ), 1 ) - IF( I.GT.1 ) THEN - PREVLASTV = MIN( PREVLASTV, LASTV ) - ELSE - PREVLASTV = LASTV - END IF - END IF - T( I, I ) = TAU( I ) - END IF - END DO - END IF - RETURN -* -* End of ZLARFT -* - END From 656505642405168137d531896e106172151791ce Mon Sep 17 00:00:00 2001 From: Yury Lysogorskiy Date: Mon, 2 Jan 2023 12:21:00 +0100 Subject: [PATCH 36/47] WIP: add pair_pace_extrapolation_kokkos.cpp/h --- src/KOKKOS/pair_pace_extrapolation_kokkos.cpp | 1724 +++++++++++++++++ src/KOKKOS/pair_pace_extrapolation_kokkos.h | 334 ++++ 2 files changed, 2058 insertions(+) create mode 100644 src/KOKKOS/pair_pace_extrapolation_kokkos.cpp create mode 100644 src/KOKKOS/pair_pace_extrapolation_kokkos.h diff --git a/src/KOKKOS/pair_pace_extrapolation_kokkos.cpp b/src/KOKKOS/pair_pace_extrapolation_kokkos.cpp new file mode 100644 index 0000000000..b4f4932db4 --- /dev/null +++ b/src/KOKKOS/pair_pace_extrapolation_kokkos.cpp @@ -0,0 +1,1724 @@ +// clang-format off +/* -*- c++ -*- ---------------------------------------------------------- + LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator + https://www.lammps.org/, Sandia National Laboratories + LAMMPS development team: developers@lammps.org + + Copyright (2003) Sandia Corporation. Under the terms of Contract + aE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains + certain rights in this software. This software is distributed under + the GNU General Public License. + + See the README file in the top-level LAMMPS directory. +------------------------------------------------------------------------- */ + +/* ---------------------------------------------------------------------- + Contributing author: Stan Moore (SNL) +------------------------------------------------------------------------- */ + +#include "pair_pace_extrapolation_kokkos.h" + +#include "atom_kokkos.h" +#include "atom_masks.h" +#include "comm.h" +#include "error.h" +#include "force.h" +#include "kokkos.h" +#include "math_const.h" +#include "memory_kokkos.h" +#include "neighbor_kokkos.h" +#include "neigh_request.h" + +#include "ace-evaluator/ace_c_basis.h" +#include "ace-evaluator/ace_evaluator.h" +#include "ace-evaluator/ace_recursive.h" +#include "ace-evaluator/ace_version.h" +#include "ace-evaluator/ace_radial.h" +#include + +namespace LAMMPS_NS { +struct ACEImpl { + ACEImpl() : basis_set(nullptr), ace(nullptr) {} + ~ACEImpl() + { + delete basis_set; + delete ace; + } + ACECTildeBasisSet *basis_set; + ACERecursiveEvaluator *ace; +}; +} // namespace LAMMPS_NS + +using namespace LAMMPS_NS; +using namespace MathConst; + +enum{FS,FS_SHIFTEDSCALED}; + +/* ---------------------------------------------------------------------- */ + +template +PairPACEExtrapolationKokkos::PairPACEExtrapolationKokkos(LAMMPS *lmp) : PairPACE(lmp) +{ + respa_enable = 0; + + kokkosable = 1; + atomKK = (AtomKokkos *) atom; + execution_space = ExecutionSpaceFromDevice::space; + datamask_read = EMPTY_MASK; + datamask_modify = EMPTY_MASK; + + host_flag = (execution_space == Host); +} + +/* ---------------------------------------------------------------------- + check if allocated, since class can be destructed when incomplete +------------------------------------------------------------------------- */ + +template +PairPACEExtrapolationKokkos::~PairPACEExtrapolationKokkos() +{ + if (copymode) return; + + memoryKK->destroy_kokkos(k_eatom,eatom); + memoryKK->destroy_kokkos(k_vatom,vatom); + + // deallocate views of views in serial to prevent issues in Kokkos tools + + if (k_splines_gk.h_view.data()) { + for (int i = 0; i < nelements; i++) { + for (int j = 0; j < nelements; j++) { + k_splines_gk.h_view(i, j).deallocate(); + k_splines_rnl.h_view(i, j).deallocate(); + k_splines_hc.h_view(i, j).deallocate(); + } + } + } +} + +/* ---------------------------------------------------------------------- */ + +template +void PairPACEExtrapolationKokkos::grow(int natom, int maxneigh) +{ + auto basis_set = aceimpl->basis_set; + + if ((int)A.extent(0) < natom) { + + MemKK::realloc_kokkos(A, "pace:A", natom, nelements, nradmax + 1, (lmax + 1) * (lmax + 1)); + MemKK::realloc_kokkos(A_rank1, "pace:A_rank1", natom, nelements, nradbase); + + MemKK::realloc_kokkos(A_list, "pace:A_list", natom, idx_rho_max, basis_set->rankmax); + //size is +1 of max to avoid out-of-boundary array access in double-triangular scheme + MemKK::realloc_kokkos(A_forward_prod, "pace:A_forward_prod", natom, idx_rho_max, basis_set->rankmax + 1); + + MemKK::realloc_kokkos(e_atom, "pace:e_atom", natom); + MemKK::realloc_kokkos(rhos, "pace:rhos", natom, basis_set->ndensitymax + 1); // +1 density for core repulsion + MemKK::realloc_kokkos(dF_drho, "pace:dF_drho", natom, basis_set->ndensitymax + 1); // +1 density for core repulsion + + MemKK::realloc_kokkos(weights, "pace:weights", natom, nelements, nradmax + 1, (lmax + 1) * (lmax + 1)); + MemKK::realloc_kokkos(weights_rank1, "pace:weights_rank1", natom, nelements, nradbase); + + // hard-core repulsion + MemKK::realloc_kokkos(rho_core, "pace:rho_core", natom); + MemKK::realloc_kokkos(dF_drho_core, "pace:dF_drho_core", natom); + MemKK::realloc_kokkos(dB_flatten, "pace:dB_flatten", natom, idx_rho_max, basis_set->rankmax); + } + + if (((int)ylm.extent(0) < natom) || ((int)ylm.extent(1) < maxneigh)) { + + // radial functions + MemKK::realloc_kokkos(fr, "pace:fr", natom, maxneigh, nradmax, lmax + 1); + MemKK::realloc_kokkos(dfr, "pace:dfr", natom, maxneigh, nradmax, lmax + 1); + MemKK::realloc_kokkos(gr, "pace:gr", natom, maxneigh, nradbase); + MemKK::realloc_kokkos(dgr, "pace:dgr", natom, maxneigh, nradbase); + const int max_num_functions = MAX(nradbase, nradmax*(lmax + 1)); + MemKK::realloc_kokkos(d_values, "pace:d_values", natom, maxneigh, max_num_functions); + MemKK::realloc_kokkos(d_derivatives, "pace:d_derivatives", natom, maxneigh, max_num_functions); + + // hard-core repulsion + MemKK::realloc_kokkos(cr, "pace:cr", natom, maxneigh); + MemKK::realloc_kokkos(dcr, "pace:dcr", natom, maxneigh); + + // spherical harmonics + MemKK::realloc_kokkos(plm, "pace:plm", natom, maxneigh, (lmax + 1) * (lmax + 1)); + MemKK::realloc_kokkos(dplm, "pace:dplm", natom, maxneigh, (lmax + 1) * (lmax + 1)); + MemKK::realloc_kokkos(ylm, "pace:ylm", natom, maxneigh, (lmax + 1) * (lmax + 1)); + MemKK::realloc_kokkos(dylm, "pace:dylm", natom, maxneigh, (lmax + 1) * (lmax + 1)); + + // short neigh list + MemKK::realloc_kokkos(d_ncount, "pace:ncount", natom); + MemKK::realloc_kokkos(d_mu, "pace:mu", natom, maxneigh); + MemKK::realloc_kokkos(d_rhats, "pace:rhats", natom, maxneigh); + MemKK::realloc_kokkos(d_rnorms, "pace:rnorms", natom, maxneigh); + MemKK::realloc_kokkos(d_nearest, "pace:nearest", natom, maxneigh); + + MemKK::realloc_kokkos(f_ij, "pace:f_ij", natom, maxneigh); + } +} + +/* ---------------------------------------------------------------------- */ + +template +void PairPACEExtrapolationKokkos::copy_pertype() +{ + auto basis_set = aceimpl->basis_set; + + MemKK::realloc_kokkos(d_rho_core_cutoff, "pace:rho_core_cutoff", nelements); + MemKK::realloc_kokkos(d_drho_core_cutoff, "pace:drho_core_cutoff", nelements); + MemKK::realloc_kokkos(d_E0vals, "pace:E0vals", nelements); + MemKK::realloc_kokkos(d_ndensity, "pace:ndensity", nelements); + MemKK::realloc_kokkos(d_npoti, "pace:npoti", nelements); + + auto h_rho_core_cutoff = Kokkos::create_mirror_view(d_rho_core_cutoff); + auto h_drho_core_cutoff = Kokkos::create_mirror_view(d_drho_core_cutoff); + auto h_E0vals = Kokkos::create_mirror_view(d_E0vals); + auto h_ndensity = Kokkos::create_mirror_view(d_ndensity); + auto h_npoti = Kokkos::create_mirror_view(d_npoti); + + for (int n = 0; n < nelements; n++) { + h_rho_core_cutoff[n] = basis_set->map_embedding_specifications.at(n).rho_core_cutoff; + h_drho_core_cutoff[n] = basis_set->map_embedding_specifications.at(n).drho_core_cutoff; + + h_E0vals(n)= basis_set->E0vals(n); + + h_ndensity(n) = basis_set->map_embedding_specifications.at(n).ndensity; + + string npoti = basis_set->map_embedding_specifications.at(n).npoti; + if (npoti == "FinnisSinclair") + h_npoti(n) = FS; + else if (npoti == "FinnisSinclairShiftedScaled") + h_npoti(n) = FS_SHIFTEDSCALED; + } + + Kokkos::deep_copy(d_rho_core_cutoff, h_rho_core_cutoff); + Kokkos::deep_copy(d_drho_core_cutoff, h_drho_core_cutoff); + Kokkos::deep_copy(d_E0vals, h_E0vals); + Kokkos::deep_copy(d_ndensity, h_ndensity); + Kokkos::deep_copy(d_npoti, h_npoti); + + MemKK::realloc_kokkos(d_wpre, "pace:wpre", nelements, basis_set->ndensitymax); + MemKK::realloc_kokkos(d_mexp, "pace:mexp", nelements, basis_set->ndensitymax); + + auto h_wpre = Kokkos::create_mirror_view(d_wpre); + auto h_mexp = Kokkos::create_mirror_view(d_mexp); + + for (int n = 0; n < nelements; n++) { + const int ndensity = basis_set->map_embedding_specifications.at(n).ndensity; + for (int p = 0; p < ndensity; p++) { + h_wpre(n, p) = basis_set->map_embedding_specifications.at(n).FS_parameters.at(p * 2 + 0); + h_mexp(n, p) = basis_set->map_embedding_specifications.at(n).FS_parameters.at(p * 2 + 1); + } + } + + Kokkos::deep_copy(d_wpre, h_wpre); + Kokkos::deep_copy(d_mexp, h_mexp); +} + +/* ---------------------------------------------------------------------- */ + +template +void PairPACEExtrapolationKokkos::copy_splines() +{ + auto basis_set = aceimpl->basis_set; + + if (k_splines_gk.d_view.data()) { + for (int i = 0; i < nelements; i++) { + for (int j = 0; j < nelements; j++) { + k_splines_gk.h_view(i, j).deallocate(); + k_splines_rnl.h_view(i, j).deallocate(); + k_splines_hc.h_view(i, j).deallocate(); + } + } + } + + k_splines_gk = Kokkos::DualView("pace:splines_gk", nelements, nelements); + k_splines_rnl = Kokkos::DualView("pace:splines_rnl", nelements, nelements); + k_splines_hc = Kokkos::DualView("pace:splines_hc", nelements, nelements); + + ACERadialFunctions* radial_functions = dynamic_cast(basis_set->radial_functions); + + for (int i = 0; i < nelements; i++) { + for (int j = 0; j < nelements; j++) { + k_splines_gk.h_view(i, j) = radial_functions->splines_gk(i, j); + k_splines_rnl.h_view(i, j) = radial_functions->splines_rnl(i, j); + k_splines_hc.h_view(i, j) = radial_functions->splines_hc(i, j); + } + } + + k_splines_gk.modify_host(); + k_splines_rnl.modify_host(); + k_splines_hc.modify_host(); + + k_splines_gk.sync_device(); + k_splines_rnl.sync_device(); + k_splines_hc.sync_device(); +} + +/* ---------------------------------------------------------------------- */ + +template +void PairPACEExtrapolationKokkos::copy_tilde() +{ + auto basis_set = aceimpl->basis_set; + + // flatten loops, get per-element count and max + + idx_rho_max = 0; + int total_basis_size_max = 0; + + MemKK::realloc_kokkos(d_idx_rho_count, "pace:idx_rho_count", nelements); + auto h_idx_rho_count = Kokkos::create_mirror_view(d_idx_rho_count); + + for (int n = 0; n < nelements; n++) { + int idx_rho = 0; + const int total_basis_size_rank1 = basis_set->total_basis_size_rank1[n]; + const int total_basis_size = basis_set->total_basis_size[n]; + + ACECTildeBasisFunction *basis = basis_set->basis[n]; + + // rank=1 + for (int func_rank1_ind = 0; func_rank1_ind < total_basis_size_rank1; ++func_rank1_ind) + idx_rho++; + + // rank > 1 + for (int func_ind = 0; func_ind < total_basis_size; ++func_ind) { + ACECTildeBasisFunction *func = &basis[func_ind]; + + // loop over {ms} combinations in sum + for (int ms_ind = 0; ms_ind < func->num_ms_combs; ++ms_ind) + idx_rho++; + } + h_idx_rho_count(n) = idx_rho; + idx_rho_max = MAX(idx_rho_max, idx_rho); + total_basis_size_max = MAX(total_basis_size_max, total_basis_size_rank1 + total_basis_size); + } + + Kokkos::deep_copy(d_idx_rho_count, h_idx_rho_count); + + MemKK::realloc_kokkos(d_rank, "pace:rank", nelements, total_basis_size_max); + MemKK::realloc_kokkos(d_num_ms_combs, "pace:num_ms_combs", nelements, total_basis_size_max); + MemKK::realloc_kokkos(d_offsets, "pace:offsets", nelements, idx_rho_max); + MemKK::realloc_kokkos(d_mus, "pace:mus", nelements, total_basis_size_max, basis_set->rankmax); + MemKK::realloc_kokkos(d_ns, "pace:ns", nelements, total_basis_size_max, basis_set->rankmax); + MemKK::realloc_kokkos(d_ls, "pace:ls", nelements, total_basis_size_max, basis_set->rankmax); + MemKK::realloc_kokkos(d_ms_combs, "pace:ms_combs", nelements, idx_rho_max, basis_set->rankmax); + MemKK::realloc_kokkos(d_ctildes, "pace:ctildes", nelements, idx_rho_max, basis_set->ndensitymax); + + auto h_rank = Kokkos::create_mirror_view(d_rank); + auto h_num_ms_combs = Kokkos::create_mirror_view(d_num_ms_combs); + auto h_offsets = Kokkos::create_mirror_view(d_offsets); + auto h_mus = Kokkos::create_mirror_view(d_mus); + auto h_ns = Kokkos::create_mirror_view(d_ns); + auto h_ls = Kokkos::create_mirror_view(d_ls); + auto h_ms_combs = Kokkos::create_mirror_view(d_ms_combs); + auto h_ctildes = Kokkos::create_mirror_view(d_ctildes); + + // copy values on host + + for (int n = 0; n < nelements; n++) { + const int total_basis_size_rank1 = basis_set->total_basis_size_rank1[n]; + const int total_basis_size = basis_set->total_basis_size[n]; + + ACECTildeBasisFunction *basis_rank1 = basis_set->basis_rank1[n]; + ACECTildeBasisFunction *basis = basis_set->basis[n]; + + const int ndensity = basis_set->map_embedding_specifications.at(n).ndensity; + + int idx_rho = 0; + + // rank=1 + for (int offset = 0; offset < total_basis_size_rank1; ++offset) { + ACECTildeBasisFunction *func = &basis_rank1[offset]; + h_rank(n, offset) = 1; + h_mus(n, offset, 0) = func->mus[0]; + h_ns(n, offset, 0) = func->ns[0]; + for (int p = 0; p < ndensity; p++) + h_ctildes(n, idx_rho, p) = func->ctildes[p]; + h_offsets(n, idx_rho) = offset; + idx_rho++; + } + + // rank > 1 + for (int func_ind = 0; func_ind < total_basis_size; ++func_ind) { + ACECTildeBasisFunction *func = &basis[func_ind]; + // TODO: check if func->ctildes are zero, then skip + + const int offset = total_basis_size_rank1 + func_ind; + + const int rank = h_rank(n, offset) = func->rank; + h_num_ms_combs(n, offset) = func->num_ms_combs; + for (int t = 0; t < rank; t++) { + h_mus(n, offset, t) = func->mus[t]; + h_ns(n, offset, t) = func->ns[t]; + h_ls(n, offset, t) = func->ls[t]; + } + + // loop over {ms} combinations in sum + for (int ms_ind = 0; ms_ind < func->num_ms_combs; ++ms_ind) { + auto ms = &func->ms_combs[ms_ind * rank]; // current ms-combination (of length = rank) + for (int t = 0; t < rank; t++) + h_ms_combs(n, idx_rho, t) = ms[t]; + + for (int p = 0; p < ndensity; ++p) { + // real-part only multiplication + h_ctildes(n, idx_rho, p) = func->ctildes[ms_ind * ndensity + p]; + } + h_offsets(n, idx_rho) = offset; + idx_rho++; + } + } + } + + Kokkos::deep_copy(d_rank, h_rank); + Kokkos::deep_copy(d_num_ms_combs, h_num_ms_combs); + Kokkos::deep_copy(d_offsets, h_offsets); + Kokkos::deep_copy(d_mus, h_mus); + Kokkos::deep_copy(d_ns, h_ns); + Kokkos::deep_copy(d_ls, h_ls); + Kokkos::deep_copy(d_ms_combs, h_ms_combs); + Kokkos::deep_copy(d_ctildes, h_ctildes); +} + +/* ---------------------------------------------------------------------- + init specific to this pair style +------------------------------------------------------------------------- */ + +template +void PairPACEExtrapolationKokkos::init_style() +{ + if (host_flag) { + if (lmp->kokkos->nthreads > 1) + error->all(FLERR,"Pair style pace/kk can currently only run on a single " + "CPU thread"); + + PairPACE::init_style(); + return; + } + + if (atom->tag_enable == 0) error->all(FLERR, "Pair style PACE requires atom IDs"); + if (force->newton_pair == 0) error->all(FLERR, "Pair style PACE requires newton pair on"); + + // neighbor list request for KOKKOS + + neighflag = lmp->kokkos->neighflag; + + auto request = neighbor->add_request(this, NeighConst::REQ_FULL); + request->set_kokkos_host(std::is_same::value && + !std::is_same::value); + request->set_kokkos_device(std::is_same::value); + if (neighflag == FULL) + error->all(FLERR,"Must use half neighbor list style with pair pace/kk"); + + auto basis_set = aceimpl->basis_set; + + nelements = basis_set->nelements; + lmax = basis_set->lmax; + nradmax = basis_set->nradmax; + nradbase = basis_set->nradbase; + + // spherical harmonics + + MemKK::realloc_kokkos(alm, "pace:alm", (lmax + 1) * (lmax + 1)); + MemKK::realloc_kokkos(blm, "pace:blm", (lmax + 1) * (lmax + 1)); + MemKK::realloc_kokkos(cl, "pace:cl", lmax + 1); + MemKK::realloc_kokkos(dl, "pace:dl", lmax + 1); + + pre_compute_harmonics(lmax); + copy_pertype(); + copy_splines(); + copy_tilde(); +} + +/* ---------------------------------------------------------------------- + init for one type pair i,j and corresponding j,i +------------------------------------------------------------------------- */ + +template +double PairPACEExtrapolationKokkos::init_one(int i, int j) +{ + double cutone = PairPACE::init_one(i,j); + + k_scale.h_view(i,j) = k_scale.h_view(j,i) = scale[i][j]; + k_scale.template modify(); + + k_cutsq.h_view(i,j) = k_cutsq.h_view(j,i) = cutone*cutone; + k_cutsq.template modify(); + + return cutone; +} + +/* ---------------------------------------------------------------------- + set coeffs for one or more type pairs +------------------------------------------------------------------------- */ + +template +void PairPACEExtrapolationKokkos::coeff(int narg, char **arg) +{ + PairPACE::coeff(narg,arg); + + // Set up element lists + + auto h_map = Kokkos::create_mirror_view(d_map); + + for (int i = 1; i <= atom->ntypes; i++) + h_map(i) = map[i]; + + Kokkos::deep_copy(d_map,h_map); +} + +/* ---------------------------------------------------------------------- */ + +template +void PairPACEExtrapolationKokkos::allocate() +{ + PairPACE::allocate(); + + int n = atom->ntypes + 1; + MemKK::realloc_kokkos(d_map, "pace:map", n); + + MemKK::realloc_kokkos(k_cutsq, "pace:cutsq", n, n); + d_cutsq = k_cutsq.template view(); + + MemKK::realloc_kokkos(k_scale, "pace:scale", n, n); + d_scale = k_scale.template view(); +} + +/* ---------------------------------------------------------------------- */ + +template +struct FindMaxNumNeighs { + typedef DeviceType device_type; + NeighListKokkos k_list; + + FindMaxNumNeighs(NeighListKokkos* nl): k_list(*nl) {} + ~FindMaxNumNeighs() {k_list.copymode = 1;} + + KOKKOS_INLINE_FUNCTION + void operator() (const int& ii, int& maxneigh) const { + const int i = k_list.d_ilist[ii]; + const int num_neighs = k_list.d_numneigh[i]; + if (maxneigh < num_neighs) maxneigh = num_neighs; + } +}; + +/* ---------------------------------------------------------------------- */ + +template +void PairPACEExtrapolationKokkos::compute(int eflag_in, int vflag_in) +{ + if (host_flag) { + atomKK->sync(Host,X_MASK|TYPE_MASK); + PairPACE::compute(eflag_in,vflag_in); + atomKK->modified(Host,F_MASK); + return; + } + + eflag = eflag_in; + vflag = vflag_in; + + if (neighflag == FULL) no_virial_fdotr_compute = 1; + + ev_init(eflag,vflag,0); + + // reallocate per-atom arrays if necessary + + if (eflag_atom) { + memoryKK->destroy_kokkos(k_eatom,eatom); + memoryKK->create_kokkos(k_eatom,eatom,maxeatom,"pair:eatom"); + d_eatom = k_eatom.view(); + } + if (vflag_atom) { + memoryKK->destroy_kokkos(k_vatom,vatom); + memoryKK->create_kokkos(k_vatom,vatom,maxvatom,"pair:vatom"); + d_vatom = k_vatom.view(); + } + + copymode = 1; + if (!force->newton_pair) + error->all(FLERR,"PairPACEExtrapolationKokkos requires 'newton on'"); + + if (recursive) + error->all(FLERR,"Must use 'product' algorithm with pair pace/kk on the GPU"); + + atomKK->sync(execution_space,X_MASK|F_MASK|TYPE_MASK); + x = atomKK->k_x.view(); + f = atomKK->k_f.view(); + type = atomKK->k_type.view(); + k_scale.template sync(); + k_cutsq.template sync(); + + NeighListKokkos* k_list = static_cast*>(list); + d_numneigh = k_list->d_numneigh; + d_neighbors = k_list->d_neighbors; + d_ilist = k_list->d_ilist; + inum = list->inum; + + need_dup = lmp->kokkos->need_dup(); + if (need_dup) { + dup_f = Kokkos::Experimental::create_scatter_view(f); + dup_vatom = Kokkos::Experimental::create_scatter_view(d_vatom); + } else { + ndup_f = Kokkos::Experimental::create_scatter_view(f); + ndup_vatom = Kokkos::Experimental::create_scatter_view(d_vatom); + } + + maxneigh = 0; + Kokkos::parallel_reduce("pace::find_maxneigh", inum, FindMaxNumNeighs(k_list), Kokkos::Max(maxneigh)); + + int vector_length_default = 1; + int team_size_default = 1; + if (!host_flag) + team_size_default = 32; + + chunk_size = MIN(chunksize,inum); // "chunksize" variable is set by user + chunk_offset = 0; + + grow(chunk_size, maxneigh); + + EV_FLOAT ev; + + while (chunk_offset < inum) { // chunk up loop to prevent running out of memory + + Kokkos::deep_copy(weights, 0.0); + Kokkos::deep_copy(weights_rank1, 0.0); + Kokkos::deep_copy(A, 0.0); + Kokkos::deep_copy(A_rank1, 0.0); + Kokkos::deep_copy(rhos, 0.0); + + EV_FLOAT ev_tmp; + + if (chunk_size > inum - chunk_offset) + chunk_size = inum - chunk_offset; + + //Neigh + { + int vector_length = vector_length_default; + int team_size = team_size_default; + check_team_size_for(chunk_size,team_size,vector_length); + int scratch_size = scratch_size_helper(team_size * maxneigh); + typename Kokkos::TeamPolicy policy_neigh(chunk_size,team_size,vector_length); + policy_neigh = policy_neigh.set_scratch_size(0, Kokkos::PerTeam(scratch_size)); + Kokkos::parallel_for("ComputeNeigh",policy_neigh,*this); + } + + //ComputeRadial + { + int vector_length = vector_length_default; + int team_size = team_size_default; + check_team_size_for(((chunk_size+team_size-1)/team_size)*maxneigh,team_size,vector_length); + typename Kokkos::TeamPolicy policy_radial(((chunk_size+team_size-1)/team_size)*maxneigh,team_size,vector_length); + Kokkos::parallel_for("ComputeRadial",policy_radial,*this); + } + + //ComputeYlm + { + int vector_length = vector_length_default; + int team_size = 16; + check_team_size_for(((chunk_size+team_size-1)/team_size)*maxneigh,team_size,vector_length); + typename Kokkos::TeamPolicy policy_ylm(((chunk_size+team_size-1)/team_size)*maxneigh,team_size,vector_length); + Kokkos::parallel_for("ComputeYlm",policy_ylm,*this); + } + + //ComputeAi + { + int vector_length = vector_length_default; + int team_size = team_size_default; + check_team_size_for(((chunk_size+team_size-1)/team_size)*maxneigh,team_size,vector_length); + typename Kokkos::TeamPolicy policy_ai(((chunk_size+team_size-1)/team_size)*maxneigh,team_size,vector_length); + Kokkos::parallel_for("ComputeAi",policy_ai,*this); + } + + //ConjugateAi + { + typename Kokkos::RangePolicy policy_conj_ai(0,chunk_size); + Kokkos::parallel_for("ConjugateAi",policy_conj_ai,*this); + } + + //ComputeRho + { + typename Kokkos::RangePolicy policy_rho(0,chunk_size*idx_rho_max); + Kokkos::parallel_for("ComputeRho",policy_rho,*this); + } + + //ComputeFS + { + typename Kokkos::RangePolicy policy_fs(0,chunk_size); + Kokkos::parallel_for("ComputeFS",policy_fs,*this); + } + + //ComputeWeights + { + typename Kokkos::RangePolicy policy_weights(0,chunk_size*idx_rho_max); + Kokkos::parallel_for("ComputeWeights",policy_weights,*this); + } + + //ComputeDerivative + { + int vector_length = vector_length_default; + int team_size = team_size_default; + check_team_size_for(((chunk_size+team_size-1)/team_size)*maxneigh,team_size,vector_length); + typename Kokkos::TeamPolicy policy_derivative(((chunk_size+team_size-1)/team_size)*maxneigh,team_size,vector_length); + Kokkos::parallel_for("ComputeDerivative",policy_derivative,*this); + } + + //ComputeForce + { + if (evflag) { + if (neighflag == HALF) { + typename Kokkos::RangePolicy > policy_force(0,chunk_size); + Kokkos::parallel_reduce(policy_force, *this, ev_tmp); + } else if (neighflag == HALFTHREAD) { + typename Kokkos::RangePolicy > policy_force(0,chunk_size); + Kokkos::parallel_reduce("ComputeForce",policy_force, *this, ev_tmp); + } + } else { + if (neighflag == HALF) { + typename Kokkos::RangePolicy > policy_force(0,chunk_size); + Kokkos::parallel_for(policy_force, *this); + } else if (neighflag == HALFTHREAD) { + typename Kokkos::RangePolicy > policy_force(0,chunk_size); + Kokkos::parallel_for("ComputeForce",policy_force, *this); + } + } + } + ev += ev_tmp; + chunk_offset += chunk_size; + + } // end while + + if (need_dup) + Kokkos::Experimental::contribute(f, dup_f); + + if (eflag_global) eng_vdwl += ev.evdwl; + if (vflag_global) { + virial[0] += ev.v[0]; + virial[1] += ev.v[1]; + virial[2] += ev.v[2]; + virial[3] += ev.v[3]; + virial[4] += ev.v[4]; + virial[5] += ev.v[5]; + } + + if (vflag_fdotr) pair_virial_fdotr_compute(this); + + if (eflag_atom) { + k_eatom.template modify(); + k_eatom.template sync(); + } + + if (vflag_atom) { + if (need_dup) + Kokkos::Experimental::contribute(d_vatom, dup_vatom); + k_vatom.template modify(); + k_vatom.template sync(); + } + + atomKK->modified(execution_space,F_MASK); + + copymode = 0; + + // free duplicated memory + if (need_dup) { + dup_f = decltype(dup_f)(); + dup_vatom = decltype(dup_vatom)(); + } +} + +/* ---------------------------------------------------------------------- */ + +template +KOKKOS_INLINE_FUNCTION +void PairPACEExtrapolationKokkos::operator() (TagPairPACEComputeNeigh,const typename Kokkos::TeamPolicy::member_type& team) const +{ + const int ii = team.league_rank(); + const int i = d_ilist[ii + chunk_offset]; + const int itype = type[i]; + const X_FLOAT xtmp = x(i,0); + const X_FLOAT ytmp = x(i,1); + const X_FLOAT ztmp = x(i,2); + const int jnum = d_numneigh[i]; + + // get a pointer to scratch memory + // This is used to cache whether or not an atom is within the cutoff + // If it is, inside is assigned to 1, otherwise -1 + const int team_rank = team.team_rank(); + const int scratch_shift = team_rank * maxneigh; // offset into pointer for entire team + int* inside = (int*)team.team_shmem().get_shmem(team.team_size() * maxneigh * sizeof(int), 0) + scratch_shift; + + // loop over list of all neighbors within force cutoff + // distsq[] = distance sq to each + // rlist[] = distance vector to each + // nearest[] = atom indices of neighbors + + int ncount = 0; + Kokkos::parallel_reduce(Kokkos::TeamThreadRange(team,jnum), + [&] (const int jj, int& count) { + int j = d_neighbors(i,jj); + j &= NEIGHMASK; + + const int jtype = type(j); + + const F_FLOAT delx = xtmp - x(j,0); + const F_FLOAT dely = ytmp - x(j,1); + const F_FLOAT delz = ztmp - x(j,2); + const F_FLOAT rsq = delx*delx + dely*dely + delz*delz; + + inside[jj] = -1; + if (rsq < d_cutsq(itype,jtype)) { + inside[jj] = 1; + count++; + } + },ncount); + + d_ncount(ii) = ncount; + + Kokkos::parallel_scan(Kokkos::TeamThreadRange(team,jnum), + [&] (const int jj, int& offset, bool final) { + + if (inside[jj] < 0) return; + + if (final) { + int j = d_neighbors(i,jj); + j &= NEIGHMASK; + const F_FLOAT delx = xtmp - x(j,0); + const F_FLOAT dely = ytmp - x(j,1); + const F_FLOAT delz = ztmp - x(j,2); + const F_FLOAT rsq = delx*delx + dely*dely + delz*delz; + const F_FLOAT r = sqrt(rsq); + const F_FLOAT rinv = 1.0/r; + const int mu_j = d_map(type(j)); + d_mu(ii,offset) = mu_j; + d_rnorms(ii,offset) = r; + d_rhats(ii,offset,0) = -delx*rinv; + d_rhats(ii,offset,1) = -dely*rinv; + d_rhats(ii,offset,2) = -delz*rinv; + d_nearest(ii,offset) = j; + } + offset++; + }); +} + +/* ---------------------------------------------------------------------- */ + +template +KOKKOS_INLINE_FUNCTION +void PairPACEExtrapolationKokkos::operator() (TagPairPACEComputeRadial, const typename Kokkos::TeamPolicy::member_type& team) const +{ + // Extract the atom number + int ii = team.team_rank() + team.team_size() * (team.league_rank() % + ((chunk_size+team.team_size()-1)/team.team_size())); + if (ii >= chunk_size) return; + const int i = d_ilist[ii + chunk_offset]; + + // Extract the neighbor number + const int jj = team.league_rank() / ((chunk_size+team.team_size()-1)/team.team_size()); + const int ncount = d_ncount(ii); + if (jj >= ncount) return; + + const double r_norm = d_rnorms(ii, jj); + const int mu_i = d_map(type(i)); + const int mu_j = d_mu(ii, jj); + + evaluate_splines(ii, jj, r_norm, nradbase, nradmax, mu_i, mu_j); +} + +/* ---------------------------------------------------------------------- */ + +template +KOKKOS_INLINE_FUNCTION +void PairPACEExtrapolationKokkos::operator() (TagPairPACEComputeYlm, const typename Kokkos::TeamPolicy::member_type& team) const +{ + // Extract the atom number + int ii = team.team_rank() + team.team_size() * (team.league_rank() % + ((chunk_size+team.team_size()-1)/team.team_size())); + if (ii >= chunk_size) return; + + // Extract the neighbor number + const int jj = team.league_rank() / ((chunk_size+team.team_size()-1)/team.team_size()); + const int ncount = d_ncount(ii); + if (jj >= ncount) return; + + const double xn = d_rhats(ii, jj, 0); + const double yn = d_rhats(ii, jj, 1); + const double zn = d_rhats(ii, jj, 2); + compute_ylm(ii,jj,xn,yn,zn,lmax); +} + +/* ---------------------------------------------------------------------- */ + +template +KOKKOS_INLINE_FUNCTION +void PairPACEExtrapolationKokkos::operator() (TagPairPACEComputeAi, const typename Kokkos::TeamPolicy::member_type& team) const +{ + // Extract the atom number + int ii = team.team_rank() + team.team_size() * (team.league_rank() % + ((chunk_size+team.team_size()-1)/team.team_size())); + if (ii >= chunk_size) return; + + // Extract the neighbor number + const int jj = team.league_rank() / ((chunk_size+team.team_size()-1)/team.team_size()); + const int ncount = d_ncount(ii); + if (jj >= ncount) return; + + const int mu_j = d_mu(ii, jj); + + // rank = 1 + for (int n = 0; n < nradbase; n++) + Kokkos::atomic_add(&A_rank1(ii, mu_j, n), gr(ii, jj, n) * Y00); + + // rank > 1 + for (int n = 0; n < nradmax; n++) { + for (int l = 0; l <= lmax; l++) { + for (int m = 0; m <= l; m++) { + const int idx = l * (l + 1) + m; // (l, m) + Kokkos::atomic_add(&A(ii, mu_j, n, idx).re, fr(ii, jj, n, l) * ylm(ii, jj, idx).re); + Kokkos::atomic_add(&A(ii, mu_j, n, idx).im, fr(ii, jj, n, l) * ylm(ii, jj, idx).im); + } + } + } + + // hard-core repulsion + Kokkos::atomic_add(&rho_core(ii), cr(ii, jj)); +} + +/* ---------------------------------------------------------------------- */ + +template +KOKKOS_INLINE_FUNCTION +void PairPACEExtrapolationKokkos::operator() (TagPairPACEConjugateAi, const int& ii) const +{ + //complex conjugate A's (for NEGATIVE (-m) terms) + // for rank > 1 + for (int mu_j = 0; mu_j < nelements; mu_j++) { + for (int n = 0; n < nradmax; n++) { + for (int l = 0; l <= lmax; l++) { + //fill in -m part in the outer loop using the same m <-> -m symmetry as for Ylm + for (int m = 1; m <= l; m++) { + const int idx = l * (l + 1) + m; // (l, m) + const int idxm = l * (l + 1) - m; // (l, -m) + const int factor = m % 2 == 0 ? 1 : -1; + A(ii, mu_j, n, idxm) = A(ii, mu_j, n, idx).conj() * (double)factor; + } + } + } + } +} + +/* ---------------------------------------------------------------------- */ + +template +KOKKOS_INLINE_FUNCTION +void PairPACEExtrapolationKokkos::operator() (TagPairPACEComputeRho, const int& iter) const +{ + const int idx_rho = iter / chunk_size; + const int ii = iter % chunk_size; + + const int i = d_ilist[ii + chunk_offset]; + const int mu_i = d_map(type(i)); + + if (idx_rho >= d_idx_rho_count(mu_i)) return; + + const int ndensity = d_ndensity(mu_i); + + const int offset = d_offsets(mu_i, idx_rho); + const int rank = d_rank(mu_i, offset); + const int r = rank - 1; + + // Basis functions B with iterative product and density rho(p) calculation + if (rank == 1) { + const int mu = d_mus(mu_i, offset, 0); + const int n = d_ns(mu_i, offset, 0); + double A_cur = A_rank1(ii, mu, n - 1); + for (int p = 0; p < ndensity; ++p) { + //for rank=1 (r=0) only 1 ms-combination exists (ms_ind=0), so index of func.ctildes is 0..ndensity-1 + Kokkos::atomic_add(&rhos(ii, p), d_ctildes(mu_i, idx_rho, p) * A_cur); + } + } else { // rank > 1 + // loop over {ms} combinations in sum + + // loop over m, collect B = product of A with given ms + A_forward_prod(ii, idx_rho, 0) = complex::one(); + + // fill forward A-product triangle + for (int t = 0; t < rank; t++) { + //TODO: optimize ns[t]-1 -> ns[t] during functions construction + const int mu = d_mus(mu_i, offset, t); + const int n = d_ns(mu_i, offset, t); + const int l = d_ls(mu_i, offset, t); + const int m = d_ms_combs(mu_i, idx_rho, t); // current ms-combination (of length = rank) + const int idx = l * (l + 1) + m; // (l, m) + A_list(ii, idx_rho, t) = A(ii, mu, n - 1, idx); + A_forward_prod(ii, idx_rho, t + 1) = A_forward_prod(ii, idx_rho, t) * A_list(ii, idx_rho, t); + } + + complex A_backward_prod = complex::one(); + + // fill backward A-product triangle + for (int t = r; t >= 1; t--) { + const complex dB = A_forward_prod(ii, idx_rho, t) * A_backward_prod; // dB - product of all A's except t-th + dB_flatten(ii, idx_rho, t) = dB; + + A_backward_prod = A_backward_prod * A_list(ii, idx_rho, t); + } + dB_flatten(ii, idx_rho, 0) = A_forward_prod(ii, idx_rho, 0) * A_backward_prod; + + const complex B = A_forward_prod(ii, idx_rho, rank); + + for (int p = 0; p < ndensity; ++p) { + // real-part only multiplication + Kokkos::atomic_add(&rhos(ii, p), B.real_part_product(d_ctildes(mu_i, idx_rho, p))); + } + } +} + +/* ---------------------------------------------------------------------- */ + + +template +KOKKOS_INLINE_FUNCTION +void PairPACEExtrapolationKokkos::operator() (TagPairPACEComputeFS, const int& ii) const +{ + const int i = d_ilist[ii + chunk_offset]; + const int mu_i = d_map(type(i)); + + const double rho_cut = d_rho_core_cutoff(mu_i); + const double drho_cut = d_drho_core_cutoff(mu_i); + const int ndensity = d_ndensity(mu_i); + + double evdwl, fcut, dfcut; + evdwl = fcut = dfcut = 0.0; + + inner_cutoff(rho_core(ii), rho_cut, drho_cut, fcut, dfcut); + FS_values_and_derivatives(ii, evdwl, mu_i); + + dF_drho_core(ii) = evdwl * dfcut + 1; + for (int p = 0; p < ndensity; ++p) + dF_drho(ii, p) *= fcut; + + + // tally energy contribution + if (eflag) { + double evdwl_cut = evdwl * fcut + rho_core(ii); + // E0 shift + evdwl_cut += d_E0vals(mu_i); + e_atom(ii) = evdwl_cut; + } +} + +/* ---------------------------------------------------------------------- */ + +template +KOKKOS_INLINE_FUNCTION +void PairPACEExtrapolationKokkos::operator() (TagPairPACEComputeWeights, const int& iter) const +{ + const int idx_rho = iter / chunk_size; + const int ii = iter % chunk_size; + + const int i = d_ilist[ii + chunk_offset]; + const int mu_i = d_map(type(i)); + + if (idx_rho >= d_idx_rho_count(mu_i)) return; + + const int ndensity = d_ndensity(mu_i); + + const int offset = d_offsets(mu_i, idx_rho); + const int rank = d_rank(mu_i, offset); + + // Weights and theta calculation + + if (rank == 1) { + const int mu = d_mus(mu_i, offset, 0); + const int n = d_ns(mu_i, offset, 0); + double theta = 0.0; + for (int p = 0; p < ndensity; ++p) { + // for rank=1 (r=0) only 1 ms-combination exists (ms_ind=0), so index of func.ctildes is 0..ndensity-1 + theta += dF_drho(ii, p) * d_ctildes(mu_i, idx_rho, p); + } + Kokkos::atomic_add(&weights_rank1(ii, mu, n - 1), theta); + } else { // rank > 1 + double theta = 0.0; + for (int p = 0; p < ndensity; ++p) + theta += dF_drho(ii, p) * d_ctildes(mu_i, idx_rho, p); + + theta *= 0.5; // 0.5 factor due to possible double counting ??? + for (int t = 0; t < rank; ++t) { + const int m_t = d_ms_combs(mu_i, idx_rho, t); + const int factor = (m_t % 2 == 0 ? 1 : -1); + const complex dB = dB_flatten(ii, idx_rho, t); + const int mu_t = d_mus(mu_i, offset, t); + const int n_t = d_ns(mu_i, offset, t); + const int l_t = d_ls(mu_i, offset, t); + const int idx = l_t * (l_t + 1) + m_t; // (l, m) + const complex value = theta * dB; + Kokkos::atomic_add(&(weights(ii, mu_t, n_t - 1, idx).re), value.re); + Kokkos::atomic_add(&(weights(ii, mu_t, n_t - 1, idx).im), value.im); + // update -m_t (that could also be positive), because the basis is half_basis + const int idxm = l_t * (l_t + 1) - m_t; // (l, -m) + const complex valuem = theta * dB.conj() * (double)factor; + Kokkos::atomic_add(&(weights(ii, mu_t, n_t - 1, idxm).re), valuem.re); + Kokkos::atomic_add(&(weights(ii, mu_t, n_t - 1, idxm).im), valuem.im); + } + } +} + +/* ---------------------------------------------------------------------- */ +template +KOKKOS_INLINE_FUNCTION +void PairPACEExtrapolationKokkos::operator() (TagPairPACEComputeDerivative, const typename Kokkos::TeamPolicy::member_type& team) const +{ + // Extract the atom number + int ii = team.team_rank() + team.team_size() * (team.league_rank() % + ((chunk_size+team.team_size()-1)/team.team_size())); + if (ii >= chunk_size) return; + const int i = d_ilist[ii + chunk_offset]; + + // Extract the neighbor number + const int jj = team.league_rank() / ((chunk_size+team.team_size()-1)/team.team_size()); + const int ncount = d_ncount(ii); + if (jj >= ncount) return; + + const int itype = type(i); + const double scale = d_scale(itype,itype); + + const int mu_j = d_mu(ii, jj); + double r_hat[3]; + r_hat[0] = d_rhats(ii, jj, 0); + r_hat[1] = d_rhats(ii, jj, 1); + r_hat[2] = d_rhats(ii, jj, 2); + const double r = d_rnorms(ii, jj); + const double rinv = 1.0/r; + + double f_ji[3]; + f_ji[0] = f_ji[1] = f_ji[2] = 0; + + // for rank = 1 + for (int n = 0; n < nradbase; ++n) { + if (weights_rank1(ii, mu_j, n) == 0) continue; + double &DG = dgr(ii, jj, n); + double DGR = DG * Y00; + DGR *= weights_rank1(ii, mu_j, n); + f_ji[0] += DGR * r_hat[0]; + f_ji[1] += DGR * r_hat[1]; + f_ji[2] += DGR * r_hat[2]; + } + + // for rank > 1 + for (int n = 0; n < nradmax; n++) { + for (int l = 0; l <= lmax; l++) { + const double R_over_r = fr(ii, jj, n, l) * rinv; + const double DR = dfr(ii, jj, n, l); + + // for m >= 0 + for (int m = 0; m <= l; m++) { + const int idx = l * (l + 1) + m; // (l, m) + complex w = weights(ii, mu_j, n, idx); + if (w.re == 0.0 && w.im == 0.0) continue; + // counting for -m cases if m > 0 + if (m > 0) { + w.re *= 2.0; + w.im *= 2.0; + } + + complex DY[3]; + DY[0] = dylm(ii, jj, idx, 0); + DY[1] = dylm(ii, jj, idx, 1); + DY[2] = dylm(ii, jj, idx, 2); + const complex Y_DR = ylm(ii, jj, idx) * DR; + + complex grad_phi_nlm[3]; + grad_phi_nlm[0] = Y_DR * r_hat[0] + DY[0] * R_over_r; + grad_phi_nlm[1] = Y_DR * r_hat[1] + DY[1] * R_over_r; + grad_phi_nlm[2] = Y_DR * r_hat[2] + DY[2] * R_over_r; + // real-part multiplication only + f_ji[0] += w.real_part_product(grad_phi_nlm[0]); + f_ji[1] += w.real_part_product(grad_phi_nlm[1]); + f_ji[2] += w.real_part_product(grad_phi_nlm[2]); + } + } + } + + // hard-core repulsion + const double fpair = dF_drho_core(ii) * dcr(ii,jj); + f_ij(ii, jj, 0) = scale * f_ji[0] + fpair * r_hat[0]; + f_ij(ii, jj, 1) = scale * f_ji[1] + fpair * r_hat[1]; + f_ij(ii, jj, 2) = scale * f_ji[2] + fpair * r_hat[2]; +} + +/* ---------------------------------------------------------------------- */ + +template +template +KOKKOS_INLINE_FUNCTION +void PairPACEExtrapolationKokkos::operator() (TagPairPACEComputeForce, const int& ii, EV_FLOAT& ev) const +{ + // The f array is duplicated for OpenMP, atomic for CUDA, and neither for Serial + const auto v_f = ScatterViewHelper::value,decltype(dup_f),decltype(ndup_f)>::get(dup_f,ndup_f); + const auto a_f = v_f.template access::value>(); + + const int i = d_ilist[ii + chunk_offset]; + const int itype = type(i); + const double scale = d_scale(itype,itype); + + const int ncount = d_ncount(ii); + + F_FLOAT fitmp[3] = {0.0,0.0,0.0}; + for (int jj = 0; jj < ncount; jj++) { + int j = d_nearest(ii,jj); + + double r_hat[3]; + r_hat[0] = d_rhats(ii, jj, 0); + r_hat[1] = d_rhats(ii, jj, 1); + r_hat[2] = d_rhats(ii, jj, 2); + const double r = d_rnorms(ii, jj); + const double delx = -r_hat[0]*r; + const double dely = -r_hat[1]*r; + const double delz = -r_hat[2]*r; + + const double fpairx = f_ij(ii, jj, 0); + const double fpairy = f_ij(ii, jj, 1); + const double fpairz = f_ij(ii, jj, 2); + + fitmp[0] += fpairx; + fitmp[1] += fpairy; + fitmp[2] += fpairz; + a_f(j,0) -= fpairx; + a_f(j,1) -= fpairy; + a_f(j,2) -= fpairz; + + // tally per-atom virial contribution + if (EVFLAG && vflag_either) + v_tally_xyz(ev, i, j, fpairx, fpairy, fpairz, delx, dely, delz); + } + + a_f(i,0) += fitmp[0]; + a_f(i,1) += fitmp[1]; + a_f(i,2) += fitmp[2]; + + // tally energy contribution + if (EVFLAG && eflag_either) { + const double evdwl = scale*e_atom(ii); + //ev_tally_full(i, 2.0 * evdwl, 0.0, 0.0, 0.0, 0.0, 0.0); + if (eflag_global) ev.evdwl += evdwl; + if (eflag_atom) d_eatom[i] += evdwl; + } +} + +template +template +KOKKOS_INLINE_FUNCTION +void PairPACEExtrapolationKokkos::operator() (TagPairPACEComputeForce,const int& ii) const { + EV_FLOAT ev; + this->template operator()(TagPairPACEComputeForce(), ii, ev); +} + +/* ---------------------------------------------------------------------- */ + +template +template +KOKKOS_INLINE_FUNCTION +void PairPACEExtrapolationKokkos::v_tally_xyz(EV_FLOAT &ev, const int &i, const int &j, + const F_FLOAT &fx, const F_FLOAT &fy, const F_FLOAT &fz, + const F_FLOAT &delx, const F_FLOAT &dely, const F_FLOAT &delz) const +{ + // The vatom array is duplicated for OpenMP, atomic for CUDA, and neither for Serial + + auto v_vatom = ScatterViewHelper,decltype(dup_vatom),decltype(ndup_vatom)>::get(dup_vatom,ndup_vatom); + auto a_vatom = v_vatom.template access>(); + + const E_FLOAT v0 = delx*fx; + const E_FLOAT v1 = dely*fy; + const E_FLOAT v2 = delz*fz; + const E_FLOAT v3 = delx*fy; + const E_FLOAT v4 = delx*fz; + const E_FLOAT v5 = dely*fz; + + if (vflag_global) { + ev.v[0] += v0; + ev.v[1] += v1; + ev.v[2] += v2; + ev.v[3] += v3; + ev.v[4] += v4; + ev.v[5] += v5; + } + + if (vflag_atom) { + a_vatom(i,0) += 0.5*v0; + a_vatom(i,1) += 0.5*v1; + a_vatom(i,2) += 0.5*v2; + a_vatom(i,3) += 0.5*v3; + a_vatom(i,4) += 0.5*v4; + a_vatom(i,5) += 0.5*v5; + a_vatom(j,0) += 0.5*v0; + a_vatom(j,1) += 0.5*v1; + a_vatom(j,2) += 0.5*v2; + a_vatom(j,3) += 0.5*v3; + a_vatom(j,4) += 0.5*v4; + a_vatom(j,5) += 0.5*v5; + } +} + +/* ---------------------------------------------------------------------- */ + +template +void PairPACEExtrapolationKokkos::pre_compute_harmonics(int lmax) +{ + auto h_alm = Kokkos::create_mirror_view(alm); + auto h_blm = Kokkos::create_mirror_view(blm); + auto h_cl = Kokkos::create_mirror_view(cl); + auto h_dl = Kokkos::create_mirror_view(dl); + + for (int l = 1; l <= lmax; l++) { + const double lsq = l * l; + const double ld = 2 * l; + const double l1 = (4 * lsq - 1); + const double l2 = lsq - ld + 1; + for (int m = 0; m < l - 1; m++) { + const double msq = m * m; + const double a = sqrt((double(l1)) / (double(lsq - msq))); + const double b = -sqrt((double(l2 - msq)) / (double(4 * l2 - 1))); + const int idx = l * (l + 1) + m; // (l, m) + h_alm(idx) = a; + h_blm(idx) = b; + } + } + + for (int l = 1; l <= lmax; l++) { + h_cl(l) = -sqrt(1.0 + 0.5 / (double(l))); + h_dl(l) = sqrt(double(2 * (l - 1) + 3)); + } + + Kokkos::deep_copy(alm, h_alm); + Kokkos::deep_copy(blm, h_blm); + Kokkos::deep_copy(cl, h_cl); + Kokkos::deep_copy(dl, h_dl); +} + +/* ---------------------------------------------------------------------- */ + +template +KOKKOS_INLINE_FUNCTION +void PairPACEExtrapolationKokkos::compute_barplm(int ii, int jj, double rz, int lmax) const +{ + // requires -1 <= rz <= 1 , NO CHECKING IS PERFORMED !!!!!!!!! + // prefactors include 1/sqrt(2) factor compared to reference + + // l=0, m=0 + // plm(ii, jj, 0, 0) = Y00/sq1o4pi; //= sq1o4pi; + plm(ii, jj, 0) = Y00; //= 1; + dplm(ii, jj, 0) = 0.0; + + if (lmax > 0) { + + // l=1, m=0 + plm(ii, jj, 2) = Y00 * sq3 * rz; + dplm(ii, jj, 2) = Y00 * sq3; + + // l=1, m=1 + plm(ii, jj, 3) = -sq3o2 * Y00; + dplm(ii, jj, 3) = 0.0; + + // loop l = 2, lmax + for (int l = 2; l <= lmax; l++) { + for (int m = 0; m < l - 1; m++) { + const int idx = l * (l + 1) + m; // (l, m) + const int idx1 = (l - 1) * l + m; // (l - 1, m) + const int idx2 = (l - 2) * (l - 1) + m; // (l - 2, m) + plm(ii, jj, idx) = alm(idx) * (rz * plm(ii, jj, idx1) + blm(idx) * plm(ii, jj, idx2)); + dplm(ii, jj, idx) = alm(idx) * (plm(ii, jj, idx1) + rz * dplm(ii, jj, idx1) + blm(idx) * dplm(ii, jj, idx2)); + } + const int idx = l * (l + 1) + l; // (l, l) + const int idx1 = l * (l + 1) + l - 1; // (l, l - 1) + const int idx2 = (l - 1) * l + l - 1; // (l - 1, l - 1) + const double t = dl(l) * plm(ii, jj, idx2); + plm(ii, jj, idx1) = t * rz; + dplm(ii, jj, idx1) = t; + plm(ii, jj, idx) = cl(l) * plm(ii, jj, idx2); + dplm(ii, jj, idx) = 0.0; + } + } +} + +/* ---------------------------------------------------------------------- */ + +template +KOKKOS_INLINE_FUNCTION +void PairPACEExtrapolationKokkos::compute_ylm(int ii, int jj, double rx, double ry, double rz, int lmax) const +{ + // requires rx^2 + ry^2 + rz^2 = 1 , NO CHECKING IS PERFORMED !!!!!!!!! + + complex phase; + complex phasem, mphasem1; + complex dyx, dyy, dyz; + complex rdy; + + phase.re = rx; + phase.im = ry; + + // compute barplm + compute_barplm(ii, jj, rz, lmax); + + // m = 0 + for (int l = 0; l <= lmax; l++) { + const int idx = l * (l + 1); + + ylm(ii, jj, idx).re = plm(ii, jj, idx); + ylm(ii, jj, idx).im = 0.0; + + dyz.re = dplm(ii, jj, idx); + rdy.re = dyz.re * rz; + + dylm(ii, jj, idx, 0).re = -rdy.re * rx; + dylm(ii, jj, idx, 0).im = 0.0; + dylm(ii, jj, idx, 1).re = -rdy.re * ry; + dylm(ii, jj, idx, 1).im = 0.0; + dylm(ii, jj, idx, 2).re = dyz.re - rdy.re * rz; + dylm(ii, jj, idx, 2).im = 0; + } + // m = 1 + for (int l = 1; l <= lmax; l++) { + const int idx = l * (l + 1) + 1; + + ylm(ii, jj, idx) = phase * plm(ii, jj, idx); + + dyx.re = plm(ii, jj, idx); + dyx.im = 0.0; + dyy.re = 0.0; + dyy.im = plm(ii, jj, idx); + dyz.re = phase.re * dplm(ii, jj, idx); + dyz.im = phase.im * dplm(ii, jj, idx); + + rdy.re = rx * dyx.re + +rz * dyz.re; + rdy.im = ry * dyy.im + rz * dyz.im; + + dylm(ii, jj, idx, 0).re = dyx.re - rdy.re * rx; + dylm(ii, jj, idx, 0).im = -rdy.im * rx; + dylm(ii, jj, idx, 1).re = -rdy.re * ry; + dylm(ii, jj, idx, 1).im = dyy.im - rdy.im * ry; + dylm(ii, jj, idx, 2).re = dyz.re - rdy.re * rz; + dylm(ii, jj, idx, 2).im = dyz.im - rdy.im * rz; + } + + // m > 1 + phasem = phase; + for (int m = 2; m <= lmax; m++) { + + mphasem1.re = phasem.re * double(m); + mphasem1.im = phasem.im * double(m); + phasem = phasem * phase; + + for (int l = m; l <= lmax; l++) { + const int idx = l * (l + 1) + m; + + ylm(ii, jj, idx).re = phasem.re * plm(ii, jj, idx); + ylm(ii, jj, idx).im = phasem.im * plm(ii, jj, idx); + + dyx = mphasem1 * plm(ii, jj, idx); + dyy.re = -dyx.im; + dyy.im = dyx.re; + dyz = phasem * dplm(ii, jj, idx); + + rdy.re = rx * dyx.re + ry * dyy.re + rz * dyz.re; + rdy.im = rx * dyx.im + ry * dyy.im + rz * dyz.im; + + dylm(ii, jj, idx, 0).re = dyx.re - rdy.re * rx; + dylm(ii, jj, idx, 0).im = dyx.im - rdy.im * rx; + dylm(ii, jj, idx, 1).re = dyy.re - rdy.re * ry; + dylm(ii, jj, idx, 1).im = dyy.im - rdy.im * ry; + dylm(ii, jj, idx, 2).re = dyz.re - rdy.re * rz; + dylm(ii, jj, idx, 2).im = dyz.im - rdy.im * rz; + } + } +} + +/* ---------------------------------------------------------------------- */ + +template +KOKKOS_INLINE_FUNCTION +void PairPACEExtrapolationKokkos::cutoff_func_poly(const double r, const double r_in, const double delta_in, double &fc, double &dfc) const +{ + if (r <= r_in-delta_in) { + fc = 1; + dfc = 0; + } else if (r >= r_in ) { + fc = 0; + dfc = 0; + } else { + double x = 1 - 2 * (1 + (r - r_in) / delta_in); + fc = 0.5 + 7.5 / 2. * (x / 4. - pow(x, 3) / 6. + pow(x, 5) / 20.); + dfc = -7.5 / delta_in * (0.25 - x * x / 2.0 + pow(x, 4) / 4.); + } +} + +/* ---------------------------------------------------------------------- */ + +template +KOKKOS_INLINE_FUNCTION +void PairPACEExtrapolationKokkos::Fexp(const double x, const double m, double &F, double &DF) const +{ + const double w = 1.e6; + const double eps = 1e-10; + + const double lambda = pow(1.0 / w, m - 1.0); + if (abs(x) > eps) { + double g; + const double a = abs(x); + const double am = pow(a, m); + const double w3x3 = pow(w * a, 3); //// use cube + const double sign_factor = (signbit(x) ? -1 : 1); + if (w3x3 > 30.0) + g = 0.0; + else + g = exp(-w3x3); + + const double omg = 1.0 - g; + F = sign_factor * (omg * am + lambda * g * a); + const double dg = -3.0 * w * w * w * a * a * g; + DF = m * pow(a, m - 1.0) * omg - am * dg + lambda * dg * a + lambda * g; + } else { + F = lambda * x; + DF = lambda; + } +} + +/* ---------------------------------------------------------------------- */ + +template +KOKKOS_INLINE_FUNCTION +void PairPACEExtrapolationKokkos::FexpShiftedScaled(const double rho, const double mexp, double &F, double &DF) const +{ + const double eps = 1e-10; + + if (abs(mexp - 1.0) < eps) { + F = rho; + DF = 1; + } else { + const double a = abs(rho); + const double exprho = exp(-a); + const double nx = 1. / mexp; + const double xoff = pow(nx, (nx / (1.0 - nx))) * exprho; + const double yoff = pow(nx, (1 / (1.0 - nx))) * exprho; + const double sign_factor = (signbit(rho) ? -1 : 1); + F = sign_factor * (pow(xoff + a, mexp) - yoff); + DF = yoff + mexp * (-xoff + 1.0) * pow(xoff + a, mexp - 1.); + } +} + +/* ---------------------------------------------------------------------- */ + +template +KOKKOS_INLINE_FUNCTION +void PairPACEExtrapolationKokkos::inner_cutoff(const double rho_core, const double rho_cut, const double drho_cut, + double &fcut, double &dfcut) const +{ + double rho_low = rho_cut - drho_cut; + if (rho_core >= rho_cut) { + fcut = 0; + dfcut = 0; + } else if (rho_core <= rho_low) { + fcut = 1; + dfcut = 0; + } else { + cutoff_func_poly(rho_core, rho_cut, drho_cut, fcut, dfcut); + } +} + +/* ---------------------------------------------------------------------- */ + +template +KOKKOS_INLINE_FUNCTION +void PairPACEExtrapolationKokkos::FS_values_and_derivatives(const int ii, double &evdwl, const int mu_i) const +{ + double F, DF = 0; + int npoti = d_npoti(mu_i); + int ndensity = d_ndensity(mu_i); + for (int p = 0; p < ndensity; p++) { + const double wpre = d_wpre(mu_i, p); + const double mexp = d_mexp(mu_i, p); + + if (npoti == FS) + Fexp(rhos(ii, p), mexp, F, DF); + else if (npoti == FS_SHIFTEDSCALED) + FexpShiftedScaled(rhos(ii, p), mexp, F, DF); + + evdwl += F * wpre; // * weight (wpre) + dF_drho(ii, p) = DF * wpre; // * weight (wpre) + } +} + +/* ---------------------------------------------------------------------- */ + +template +KOKKOS_INLINE_FUNCTION +void PairPACEExtrapolationKokkos::evaluate_splines(const int ii, const int jj, double r, + int /*nradbase_c*/, int /*nradial_c*/, + int mu_i, int mu_j) const +{ + auto &spline_gk = k_splines_gk.template view()(mu_i, mu_j); + auto &spline_rnl = k_splines_rnl.template view()(mu_i, mu_j); + auto &spline_hc = k_splines_hc.template view()(mu_i, mu_j); + + spline_gk.calcSplines(ii, jj, r, gr, dgr); + + spline_rnl.calcSplines(ii, jj, r, d_values, d_derivatives); + for (int kk = 0; kk < (int)fr.extent(2); kk++) { + for (int ll = 0; ll < (int)fr.extent(3); ll++) { + const int flatten = kk*fr.extent(3) + ll; + fr(ii, jj, kk, ll) = d_values(ii, jj, flatten); + dfr(ii, jj, kk, ll) = d_derivatives(ii, jj, flatten); + } + } + + spline_hc.calcSplines(ii, jj, r, d_values, d_derivatives); + cr(ii, jj) = d_values(ii, jj, 0); + dcr(ii, jj) = d_derivatives(ii, jj, 0); +} + +/* ---------------------------------------------------------------------- */ + +template +KOKKOS_INLINE_FUNCTION +void PairPACEExtrapolationKokkos::SplineInterpolatorKokkos::calcSplines(const int ii, const int jj, const double r, const t_ace_3d &d_values, const t_ace_3d &d_derivatives) const +{ + double wl, wl2, wl3, w2l1, w3l2; + double c[4]; + double x = r * rscalelookup; + int nl = static_cast(floor(x)); + + if (nl <= 0) + Kokkos::abort("Encountered very small distance. Stopping."); + + if (nl < nlut) { + wl = x - double(nl); + wl2 = wl * wl; + wl3 = wl2 * wl; + w2l1 = 2.0 * wl; + w3l2 = 3.0 * wl2; + for (int func_id = 0; func_id < num_of_functions; func_id++) { + for (int idx = 0; idx < 4; idx++) + c[idx] = lookupTable(nl, func_id, idx); + d_values(ii, jj, func_id) = c[0] + c[1] * wl + c[2] * wl2 + c[3] * wl3; + d_derivatives(ii, jj, func_id) = (c[1] + c[2] * w2l1 + c[3] * w3l2) * rscalelookup; + } + } else { // fill with zeroes + for (int func_id = 0; func_id < num_of_functions; func_id++) { + d_values(ii, jj, func_id) = 0.0; + d_derivatives(ii, jj, func_id) = 0.0; + } + } +} + +/* ---------------------------------------------------------------------- */ + +template +template +void PairPACEExtrapolationKokkos::check_team_size_for(int inum, int &team_size, int vector_length) { + int team_size_max; + + team_size_max = Kokkos::TeamPolicy(inum,Kokkos::AUTO).team_size_max(*this,Kokkos::ParallelForTag()); + + if (team_size*vector_length > team_size_max) + team_size = team_size_max/vector_length; +} + +/* ---------------------------------------------------------------------- */ + +template +template +void PairPACEExtrapolationKokkos::check_team_size_reduce(int inum, int &team_size, int vector_length) { + int team_size_max; + + team_size_max = Kokkos::TeamPolicy(inum,Kokkos::AUTO).team_size_max(*this,Kokkos::ParallelReduceTag()); + + if (team_size*vector_length > team_size_max) + team_size = team_size_max/vector_length; +} + +template +template +int PairPACEExtrapolationKokkos::scratch_size_helper(int values_per_team) { + typedef Kokkos::View > ScratchViewType; + + return ScratchViewType::shmem_size(values_per_team); +} + +/* ---------------------------------------------------------------------- + memory usage of arrays +------------------------------------------------------------------------- */ + +template +double PairPACEExtrapolationKokkos::memory_usage() +{ + double bytes = 0; + + bytes += MemKK::memory_usage(A); + bytes += MemKK::memory_usage(A_rank1); + bytes += MemKK::memory_usage(A_list); + bytes += MemKK::memory_usage(A_forward_prod); + bytes += MemKK::memory_usage(e_atom); + bytes += MemKK::memory_usage(rhos); + bytes += MemKK::memory_usage(dF_drho); + bytes += MemKK::memory_usage(weights); + bytes += MemKK::memory_usage(weights_rank1); + bytes += MemKK::memory_usage(rho_core); + bytes += MemKK::memory_usage(dF_drho_core); + bytes += MemKK::memory_usage(dB_flatten); + bytes += MemKK::memory_usage(fr); + bytes += MemKK::memory_usage(dfr); + bytes += MemKK::memory_usage(gr); + bytes += MemKK::memory_usage(dgr); + bytes += MemKK::memory_usage(d_values); + bytes += MemKK::memory_usage(d_derivatives); + bytes += MemKK::memory_usage(cr); + bytes += MemKK::memory_usage(dcr); + bytes += MemKK::memory_usage(plm); + bytes += MemKK::memory_usage(dplm); + bytes += MemKK::memory_usage(ylm); + bytes += MemKK::memory_usage(dylm); + bytes += MemKK::memory_usage(d_ncount); + bytes += MemKK::memory_usage(d_mu); + bytes += MemKK::memory_usage(d_rhats); + bytes += MemKK::memory_usage(d_rnorms); + bytes += MemKK::memory_usage(d_nearest); + bytes += MemKK::memory_usage(f_ij); + bytes += MemKK::memory_usage(d_rho_core_cutoff); + bytes += MemKK::memory_usage(d_drho_core_cutoff); + bytes += MemKK::memory_usage(d_E0vals); + bytes += MemKK::memory_usage(d_ndensity); + bytes += MemKK::memory_usage(d_npoti); + bytes += MemKK::memory_usage(d_wpre); + bytes += MemKK::memory_usage(d_mexp); + bytes += MemKK::memory_usage(d_idx_rho_count); + bytes += MemKK::memory_usage(d_rank); + bytes += MemKK::memory_usage(d_num_ms_combs); + bytes += MemKK::memory_usage(d_offsets); + bytes += MemKK::memory_usage(d_mus); + bytes += MemKK::memory_usage(d_ns); + bytes += MemKK::memory_usage(d_ls); + bytes += MemKK::memory_usage(d_ms_combs); + bytes += MemKK::memory_usage(d_ctildes); + bytes += MemKK::memory_usage(alm); + bytes += MemKK::memory_usage(blm); + bytes += MemKK::memory_usage(cl); + bytes += MemKK::memory_usage(dl); + + if (k_splines_gk.h_view.data()) { + for (int i = 0; i < nelements; i++) { + for (int j = 0; j < nelements; j++) { + bytes += k_splines_gk.h_view(i, j).memory_usage(); + bytes += k_splines_rnl.h_view(i, j).memory_usage(); + bytes += k_splines_hc.h_view(i, j).memory_usage(); + } + } + } + + return bytes; +} + +/* ---------------------------------------------------------------------- */ + +namespace LAMMPS_NS { +template class PairPACEExtrapolationKokkos; +#ifdef LMP_KOKKOS_GPU +template class PairPACEExtrapolationKokkos; +#endif +} diff --git a/src/KOKKOS/pair_pace_extrapolation_kokkos.h b/src/KOKKOS/pair_pace_extrapolation_kokkos.h new file mode 100644 index 0000000000..482d068725 --- /dev/null +++ b/src/KOKKOS/pair_pace_extrapolation_kokkos.h @@ -0,0 +1,334 @@ +/* -*- c++ -*- ---------------------------------------------------------- + LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator + https://www.lammps.org/, Sandia National Laboratories + LAMMPS development team: developers@lammps.org + + Copyright (2003) Sandia Corporation. Under the terms of Contract + DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains + certain rights in this software. This software is distributed under + the GNU General Public License. + + See the README file in the top-level LAMMPS directory. +------------------------------------------------------------------------- */ + +#ifdef PAIR_CLASS +// clang-format off +PairStyle(pace/extrapolation/kk,PairPACEExtrapolationKokkos); +PairStyle(pace/extrapolation/kk/device,PairPACEExtrapolationKokkos); +PairStyle(pace/extrapolation/kk/host,PairPACEExtrapolationKokkos); +// clang-format on +#else + +// clang-format off +#ifndef LMP_PAIR_PACE_EXTRAPOLATION_KOKKOS_H +#define LMP_PAIR_PACE_EXTRAPOLATION_KOKKOS_H + +#include "pair_pace.h" +#include "ace-evaluator/ace_radial.h" +#include "kokkos_type.h" +#include "pair_kokkos.h" + +namespace LAMMPS_NS { + +template +class PairPACEExtrapolationKokkos : public PairPACE { + public: + struct TagPairPACEComputeNeigh{}; + struct TagPairPACEComputeRadial{}; + struct TagPairPACEComputeYlm{}; + struct TagPairPACEComputeAi{}; + struct TagPairPACEConjugateAi{}; + struct TagPairPACEComputeRho{}; + struct TagPairPACEComputeFS{}; + struct TagPairPACEComputeWeights{}; + struct TagPairPACEComputeDerivative{}; + + template + struct TagPairPACEComputeForce{}; + + typedef DeviceType device_type; + typedef ArrayTypes AT; + typedef EV_FLOAT value_type; + using complex = SNAComplex; + + PairPACEExtrapolationKokkos(class LAMMPS *); + ~PairPACEExtrapolationKokkos() override; + + void compute(int, int) override; + void coeff(int, char **) override; + void init_style() override; + double init_one(int, int) override; + + KOKKOS_INLINE_FUNCTION + void operator() (TagPairPACEComputeNeigh,const typename Kokkos::TeamPolicy::member_type& team) const; + + KOKKOS_INLINE_FUNCTION + void operator() (TagPairPACEComputeRadial,const typename Kokkos::TeamPolicy::member_type& team) const; + + KOKKOS_INLINE_FUNCTION + void operator() (TagPairPACEComputeYlm,const typename Kokkos::TeamPolicy::member_type& team) const; + + KOKKOS_INLINE_FUNCTION + void operator() (TagPairPACEComputeAi,const typename Kokkos::TeamPolicy::member_type& team) const; + + KOKKOS_INLINE_FUNCTION + void operator() (TagPairPACEConjugateAi,const int& ii) const; + + KOKKOS_INLINE_FUNCTION + void operator() (TagPairPACEComputeRho,const int& iter) const; + + KOKKOS_INLINE_FUNCTION + void operator() (TagPairPACEComputeFS,const int& ii) const; + + KOKKOS_INLINE_FUNCTION + void operator() (TagPairPACEComputeWeights,const int& iter) const; + + KOKKOS_INLINE_FUNCTION + void operator() (TagPairPACEComputeDerivative,const typename Kokkos::TeamPolicy::member_type& team) const; + + template + KOKKOS_INLINE_FUNCTION + void operator() (TagPairPACEComputeForce,const int& ii) const; + + template + KOKKOS_INLINE_FUNCTION + void operator() (TagPairPACEComputeForce,const int& ii, EV_FLOAT&) const; + + protected: + int inum, maxneigh, chunk_size, chunk_offset, idx_rho_max; + int host_flag; + + int eflag, vflag; + + int neighflag, max_ndensity; + int nelements, lmax, nradmax, nradbase; + + typename AT::t_neighbors_2d d_neighbors; + typename AT::t_int_1d_randomread d_ilist; + typename AT::t_int_1d_randomread d_numneigh; + + DAT::tdual_efloat_1d k_eatom; + DAT::tdual_virial_array k_vatom; + typename AT::t_efloat_1d d_eatom; + typename AT::t_virial_array d_vatom; + + typename AT::t_x_array_randomread x; + typename AT::t_f_array f; + typename AT::t_int_1d_randomread type; + + typedef Kokkos::DualView tdual_fparams; + tdual_fparams k_cutsq, k_scale; + typedef Kokkos::View t_fparams; + t_fparams d_cutsq, d_scale; + + typename AT::t_int_1d d_map; + + int need_dup; + + using KKDeviceType = typename KKDevice::value; + + template + using DupScatterView = KKScatterView; + + template + using NonDupScatterView = KKScatterView; + + DupScatterView dup_f; + DupScatterView dup_vatom; + + NonDupScatterView ndup_f; + NonDupScatterView ndup_vatom; + + friend void pair_virial_fdotr_compute(PairPACEExtrapolationKokkos*); + + void grow(int, int); + void copy_pertype(); + void copy_splines(); + void copy_tilde(); + void allocate() override; + void precompute_harmonics(); + double memory_usage() override; + + template + KOKKOS_INLINE_FUNCTION + void v_tally_xyz(EV_FLOAT &ev, const int &i, const int &j, + const F_FLOAT &fx, const F_FLOAT &fy, const F_FLOAT &fz, + const F_FLOAT &delx, const F_FLOAT &dely, const F_FLOAT &delz) const; + + KOKKOS_INLINE_FUNCTION + void compute_barplm(int, int, double, int) const; + + KOKKOS_INLINE_FUNCTION + void compute_ylm(int, int, double, double, double, int) const; + + KOKKOS_INLINE_FUNCTION + void cutoff_func_poly(const double, const double, const double, double &, double &) const; + + KOKKOS_INLINE_FUNCTION + void Fexp(const double, const double, double &, double &) const; + + KOKKOS_INLINE_FUNCTION + void FexpShiftedScaled(const double, const double, double &, double &) const; + + KOKKOS_INLINE_FUNCTION + void inner_cutoff(const double, const double, const double, double &, double &) const; + + KOKKOS_INLINE_FUNCTION + void FS_values_and_derivatives(const int, double&, const int) const; + + KOKKOS_INLINE_FUNCTION + void evaluate_splines(const int, const int, double, int, int, int, int) const; + + template + void check_team_size_for(int, int&, int); + + template + void check_team_size_reduce(int, int&, int); + + // Utility routine which wraps computing per-team scratch size requirements for + // ComputeNeigh, ComputeUi, and ComputeFusedDeidrj + template + int scratch_size_helper(int values_per_team); + + typedef Kokkos::View t_ace_1i; + typedef Kokkos::View t_ace_2i; + typedef Kokkos::View t_ace_3i; + typedef Kokkos::View t_ace_4i; + typedef Kokkos::View t_ace_1d; + typedef Kokkos::View t_ace_2d; + typedef Kokkos::View t_ace_2d3; + typedef Kokkos::View t_ace_3d; + typedef Kokkos::View t_ace_3d3; + typedef Kokkos::View t_ace_3d4; + typedef Kokkos::View t_ace_4d; + typedef Kokkos::View t_ace_1c; + typedef Kokkos::View t_ace_2c; + typedef Kokkos::View t_ace_3c; + typedef Kokkos::View t_ace_3c3; + typedef Kokkos::View t_ace_4c; + typedef Kokkos::View t_ace_4c3; + + t_ace_3d A_rank1; + t_ace_4c A; + + t_ace_3c A_list; + t_ace_3c A_forward_prod; + + t_ace_3d weights_rank1; + t_ace_4c weights; + + t_ace_1d e_atom; + t_ace_2d rhos; + t_ace_2d dF_drho; + + // hard-core repulsion + t_ace_1d rho_core; + t_ace_3c dB_flatten; + t_ace_2d cr; + t_ace_2d dcr; + t_ace_1d dF_drho_core; + + // radial functions + t_ace_4d fr; + t_ace_4d dfr; + t_ace_3d gr; + t_ace_3d dgr; + t_ace_3d d_values; + t_ace_3d d_derivatives; + + // Spherical Harmonics + + void pre_compute_harmonics(int); + + KOKKOS_INLINE_FUNCTION + void compute_barplm(double rz, int lmaxi); + + KOKKOS_INLINE_FUNCTION + void compute_ylm(double rx, double ry, double rz, int lmaxi); + + t_ace_1d alm; + t_ace_1d blm; + t_ace_1d cl; + t_ace_1d dl; + + t_ace_3d plm; + t_ace_3d dplm; + + t_ace_3c ylm; + t_ace_4c3 dylm; + + // short neigh list + t_ace_1i d_ncount; + t_ace_2d d_mu; + t_ace_2d d_rnorms; + t_ace_3d3 d_rhats; + t_ace_2i d_nearest; + + // per-type + t_ace_1i d_ndensity; + t_ace_1i d_npoti; + t_ace_1d d_rho_core_cutoff; + t_ace_1d d_drho_core_cutoff; + t_ace_1d d_E0vals; + t_ace_2d d_wpre; + t_ace_2d d_mexp; + + // tilde + t_ace_1i d_idx_rho_count; + t_ace_2i d_rank; + t_ace_2i d_num_ms_combs; + t_ace_2i d_offsets; + t_ace_3i d_mus; + t_ace_3i d_ns; + t_ace_3i d_ls; + t_ace_3i d_ms_combs; + t_ace_3d d_ctildes; + + t_ace_3d3 f_ij; + + public: + struct SplineInterpolatorKokkos { + int ntot, nlut, num_of_functions; + double cutoff, deltaSplineBins, invrscalelookup, rscalelookup; + + t_ace_3d4 lookupTable; + + void operator=(const SplineInterpolator &spline) { + cutoff = spline.cutoff; + deltaSplineBins = spline.deltaSplineBins; + ntot = spline.ntot; + nlut = spline.nlut; + invrscalelookup = spline.invrscalelookup; + rscalelookup = spline.rscalelookup; + num_of_functions = spline.num_of_functions; + + lookupTable = t_ace_3d4("lookupTable", ntot+1, num_of_functions); + auto h_lookupTable = Kokkos::create_mirror_view(lookupTable); + for (int i = 0; i < ntot+1; i++) + for (int j = 0; j < num_of_functions; j++) + for (int k = 0; k < 4; k++) + h_lookupTable(i, j, k) = spline.lookupTable(i, j, k); + Kokkos::deep_copy(lookupTable, h_lookupTable); + } + + void deallocate() { + lookupTable = t_ace_3d4(); + } + + double memory_usage() { + return lookupTable.span() * sizeof(typename decltype(lookupTable)::value_type); + } + + KOKKOS_INLINE_FUNCTION + void calcSplines(const int ii, const int jj, const double r, const t_ace_3d &d_values, const t_ace_3d &d_derivatives) const; + }; + + Kokkos::DualView k_splines_gk; + Kokkos::DualView k_splines_rnl; + Kokkos::DualView k_splines_hc; + +}; +} // namespace LAMMPS_NS + +#endif +#endif From 1b92569187093deb1f620d33363e9000d00c4a79 Mon Sep 17 00:00:00 2001 From: Yury Lysogorskiy Date: Mon, 2 Jan 2023 18:29:12 +0100 Subject: [PATCH 37/47] WIP: pair_pace_extrapolation_kokkos.h/cpp: - rename idx_rho_max -> idx_ms_combs_max, d_idx_rho_count ->d_idx_ms_combs_count, d_offsets->d_func_inds - remove d_ctildes, add d_gen_cgs and d_coeffs - use ACEBBasisFunction - update TagPairPACEComputeRho and TagPairPACEComputeWeights - pair_pace_extrapolation.h/cpp: add chunksize option --- src/KOKKOS/pair_pace_extrapolation_kokkos.cpp | 249 ++++++++++-------- src/KOKKOS/pair_pace_extrapolation_kokkos.h | 14 +- src/ML-PACE/pair_pace_extrapolation.cpp | 22 +- src/ML-PACE/pair_pace_extrapolation.h | 4 +- 4 files changed, 164 insertions(+), 125 deletions(-) diff --git a/src/KOKKOS/pair_pace_extrapolation_kokkos.cpp b/src/KOKKOS/pair_pace_extrapolation_kokkos.cpp index b4f4932db4..006cf5e609 100644 --- a/src/KOKKOS/pair_pace_extrapolation_kokkos.cpp +++ b/src/KOKKOS/pair_pace_extrapolation_kokkos.cpp @@ -34,19 +34,30 @@ #include "ace-evaluator/ace_recursive.h" #include "ace-evaluator/ace_version.h" #include "ace-evaluator/ace_radial.h" + +#include "ace/ace_b_basis.h" +#include "ace/ace_b_evaluator.h" + #include namespace LAMMPS_NS { -struct ACEImpl { - ACEImpl() : basis_set(nullptr), ace(nullptr) {} - ~ACEImpl() - { - delete basis_set; - delete ace; - } - ACECTildeBasisSet *basis_set; - ACERecursiveEvaluator *ace; -}; + struct ACEALImpl { + ACEALImpl() : basis_set(nullptr), ace(nullptr), ctilde_basis_set(nullptr), rec_ace(nullptr) {} + + ~ACEALImpl() + { + delete basis_set; + delete ace; + + delete ctilde_basis_set; + delete rec_ace; + } + + ACEBBasisSet *basis_set; + ACEBEvaluator *ace; + ACECTildeBasisSet *ctilde_basis_set; + ACERecursiveEvaluator *rec_ace; + }; } // namespace LAMMPS_NS using namespace LAMMPS_NS; @@ -57,7 +68,7 @@ enum{FS,FS_SHIFTEDSCALED}; /* ---------------------------------------------------------------------- */ template -PairPACEExtrapolationKokkos::PairPACEExtrapolationKokkos(LAMMPS *lmp) : PairPACE(lmp) +PairPACEExtrapolationKokkos::PairPACEExtrapolationKokkos(LAMMPS *lmp) : PairPACEExtrapolation(lmp) { respa_enable = 0; @@ -107,9 +118,9 @@ void PairPACEExtrapolationKokkos::grow(int natom, int maxneigh) MemKK::realloc_kokkos(A, "pace:A", natom, nelements, nradmax + 1, (lmax + 1) * (lmax + 1)); MemKK::realloc_kokkos(A_rank1, "pace:A_rank1", natom, nelements, nradbase); - MemKK::realloc_kokkos(A_list, "pace:A_list", natom, idx_rho_max, basis_set->rankmax); + MemKK::realloc_kokkos(A_list, "pace:A_list", natom, idx_ms_combs_max, basis_set->rankmax); //size is +1 of max to avoid out-of-boundary array access in double-triangular scheme - MemKK::realloc_kokkos(A_forward_prod, "pace:A_forward_prod", natom, idx_rho_max, basis_set->rankmax + 1); + MemKK::realloc_kokkos(A_forward_prod, "pace:A_forward_prod", natom, idx_ms_combs_max, basis_set->rankmax + 1); MemKK::realloc_kokkos(e_atom, "pace:e_atom", natom); MemKK::realloc_kokkos(rhos, "pace:rhos", natom, basis_set->ndensitymax + 1); // +1 density for core repulsion @@ -121,7 +132,7 @@ void PairPACEExtrapolationKokkos::grow(int natom, int maxneigh) // hard-core repulsion MemKK::realloc_kokkos(rho_core, "pace:rho_core", natom); MemKK::realloc_kokkos(dF_drho_core, "pace:dF_drho_core", natom); - MemKK::realloc_kokkos(dB_flatten, "pace:dB_flatten", natom, idx_rho_max, basis_set->rankmax); + MemKK::realloc_kokkos(dB_flatten, "pace:dB_flatten", natom, idx_ms_combs_max, basis_set->rankmax); } if (((int)ylm.extent(0) < natom) || ((int)ylm.extent(1) < maxneigh)) { @@ -263,120 +274,134 @@ void PairPACEExtrapolationKokkos::copy_tilde() // flatten loops, get per-element count and max - idx_rho_max = 0; + idx_ms_combs_max = 0; int total_basis_size_max = 0; - MemKK::realloc_kokkos(d_idx_rho_count, "pace:idx_rho_count", nelements); - auto h_idx_rho_count = Kokkos::create_mirror_view(d_idx_rho_count); + MemKK::realloc_kokkos(d_idx_ms_combs_count, "pace:idx_ms_combs_count", nelements); + auto h_idx_ms_combs_count = Kokkos::create_mirror_view(d_idx_ms_combs_count); - for (int n = 0; n < nelements; n++) { - int idx_rho = 0; - const int total_basis_size_rank1 = basis_set->total_basis_size_rank1[n]; - const int total_basis_size = basis_set->total_basis_size[n]; + for (int mu = 0; mu < nelements; mu++) { + int idx_ms_combs = 0; + const int total_basis_size_rank1 = basis_set->total_basis_size_rank1[mu]; + const int total_basis_size = basis_set->total_basis_size[mu]; - ACECTildeBasisFunction *basis = basis_set->basis[n]; + ACEBBasisFunction *basis = basis_set->basis[mu]; // rank=1 for (int func_rank1_ind = 0; func_rank1_ind < total_basis_size_rank1; ++func_rank1_ind) - idx_rho++; + idx_ms_combs++; // rank > 1 for (int func_ind = 0; func_ind < total_basis_size; ++func_ind) { - ACECTildeBasisFunction *func = &basis[func_ind]; + ACEBBasisFunction *func = &basis[func_ind]; // loop over {ms} combinations in sum for (int ms_ind = 0; ms_ind < func->num_ms_combs; ++ms_ind) - idx_rho++; + idx_ms_combs++; } - h_idx_rho_count(n) = idx_rho; - idx_rho_max = MAX(idx_rho_max, idx_rho); + h_idx_ms_combs_count(mu) = idx_ms_combs; + idx_ms_combs_max = MAX(idx_ms_combs_max, idx_ms_combs); total_basis_size_max = MAX(total_basis_size_max, total_basis_size_rank1 + total_basis_size); } - Kokkos::deep_copy(d_idx_rho_count, h_idx_rho_count); + Kokkos::deep_copy(d_idx_ms_combs_count, h_idx_ms_combs_count); MemKK::realloc_kokkos(d_rank, "pace:rank", nelements, total_basis_size_max); MemKK::realloc_kokkos(d_num_ms_combs, "pace:num_ms_combs", nelements, total_basis_size_max); - MemKK::realloc_kokkos(d_offsets, "pace:offsets", nelements, idx_rho_max); + MemKK::realloc_kokkos(d_func_inds, "pace:func_inds", nelements, idx_ms_combs_max); MemKK::realloc_kokkos(d_mus, "pace:mus", nelements, total_basis_size_max, basis_set->rankmax); MemKK::realloc_kokkos(d_ns, "pace:ns", nelements, total_basis_size_max, basis_set->rankmax); MemKK::realloc_kokkos(d_ls, "pace:ls", nelements, total_basis_size_max, basis_set->rankmax); - MemKK::realloc_kokkos(d_ms_combs, "pace:ms_combs", nelements, idx_rho_max, basis_set->rankmax); - MemKK::realloc_kokkos(d_ctildes, "pace:ctildes", nelements, idx_rho_max, basis_set->ndensitymax); + MemKK::realloc_kokkos(d_ms_combs, "pace:ms_combs", nelements, idx_ms_combs_max, basis_set->rankmax); + //MemKK::realloc_kokkos(d_ctildes, "pace:ctildes", nelements, idx_ms_combs_max, basis_set->ndensitymax); + MemKK::realloc_kokkos(d_gen_cgs, "pace:gen_cgs", nelements, idx_ms_combs_max); + MemKK::realloc_kokkos(d_coeffs, "pace:coeffs", nelements, total_basis_size_max, basis_set->ndensitymax); auto h_rank = Kokkos::create_mirror_view(d_rank); auto h_num_ms_combs = Kokkos::create_mirror_view(d_num_ms_combs); - auto h_offsets = Kokkos::create_mirror_view(d_offsets); + auto h_func_inds = Kokkos::create_mirror_view(d_func_inds); auto h_mus = Kokkos::create_mirror_view(d_mus); auto h_ns = Kokkos::create_mirror_view(d_ns); auto h_ls = Kokkos::create_mirror_view(d_ls); auto h_ms_combs = Kokkos::create_mirror_view(d_ms_combs); - auto h_ctildes = Kokkos::create_mirror_view(d_ctildes); +// auto h_ctildes = Kokkos::create_mirror_view(d_ctildes); + auto h_gen_cgs = Kokkos::create_mirror_view(d_gen_cgs); + auto h_coeffs = Kokkos::create_mirror_view(d_coeffs); // copy values on host - for (int n = 0; n < nelements; n++) { - const int total_basis_size_rank1 = basis_set->total_basis_size_rank1[n]; - const int total_basis_size = basis_set->total_basis_size[n]; + for (int mu = 0; mu < nelements; mu++) { + const int total_basis_size_rank1 = basis_set->total_basis_size_rank1[mu]; + const int total_basis_size = basis_set->total_basis_size[mu]; - ACECTildeBasisFunction *basis_rank1 = basis_set->basis_rank1[n]; - ACECTildeBasisFunction *basis = basis_set->basis[n]; + ACEBBasisFunction *basis_rank1 = basis_set->basis_rank1[mu]; + ACEBBasisFunction *basis = basis_set->basis[mu]; - const int ndensity = basis_set->map_embedding_specifications.at(n).ndensity; + const int ndensity = basis_set->map_embedding_specifications.at(mu).ndensity; - int idx_rho = 0; + int idx_ms_comb = 0; // rank=1 - for (int offset = 0; offset < total_basis_size_rank1; ++offset) { - ACECTildeBasisFunction *func = &basis_rank1[offset]; - h_rank(n, offset) = 1; - h_mus(n, offset, 0) = func->mus[0]; - h_ns(n, offset, 0) = func->ns[0]; - for (int p = 0; p < ndensity; p++) - h_ctildes(n, idx_rho, p) = func->ctildes[p]; - h_offsets(n, idx_rho) = offset; - idx_rho++; + for (int func_ind = 0; func_ind < total_basis_size_rank1; ++func_ind) { + ACEBBasisFunction *func = &basis_rank1[func_ind]; + h_rank(mu, func_ind) = 1; + h_mus(mu, func_ind, 0) = func->mus[0]; + h_ns(mu, func_ind, 0) = func->ns[0]; + + for (int p = 0; p < ndensity; ++p) + h_coeffs(mu, func_ind, p) = func->coeff[p]; + + h_gen_cgs(mu, idx_ms_comb) = func->gen_cgs[0]; + + h_func_inds(mu, idx_ms_comb) = func_ind; + idx_ms_comb++; } // rank > 1 for (int func_ind = 0; func_ind < total_basis_size; ++func_ind) { - ACECTildeBasisFunction *func = &basis[func_ind]; + ACEBBasisFunction *func = &basis[func_ind]; // TODO: check if func->ctildes are zero, then skip - const int offset = total_basis_size_rank1 + func_ind; + const int func_ind_through = total_basis_size_rank1 + func_ind; - const int rank = h_rank(n, offset) = func->rank; - h_num_ms_combs(n, offset) = func->num_ms_combs; + const int rank = h_rank(mu, func_ind_through) = func->rank; + h_num_ms_combs(mu, func_ind_through) = func->num_ms_combs; for (int t = 0; t < rank; t++) { - h_mus(n, offset, t) = func->mus[t]; - h_ns(n, offset, t) = func->ns[t]; - h_ls(n, offset, t) = func->ls[t]; + h_mus(mu, func_ind_through, t) = func->mus[t]; + h_ns(mu, func_ind_through, t) = func->ns[t]; + h_ls(mu, func_ind_through, t) = func->ls[t]; } + for (int p = 0; p < ndensity; ++p) + h_coeffs(mu, func_ind_through, p) = func->coeff[p]; + + // loop over {ms} combinations in sum for (int ms_ind = 0; ms_ind < func->num_ms_combs; ++ms_ind) { auto ms = &func->ms_combs[ms_ind * rank]; // current ms-combination (of length = rank) for (int t = 0; t < rank; t++) - h_ms_combs(n, idx_rho, t) = ms[t]; + h_ms_combs(mu, idx_ms_comb, t) = ms[t]; - for (int p = 0; p < ndensity; ++p) { - // real-part only multiplication - h_ctildes(n, idx_rho, p) = func->ctildes[ms_ind * ndensity + p]; - } - h_offsets(n, idx_rho) = offset; - idx_rho++; + + h_gen_cgs(mu, idx_ms_comb) = func->gen_cgs[ms_ind]; + + + h_func_inds(mu, idx_ms_comb) = func_ind_through; + idx_ms_comb++; } } } Kokkos::deep_copy(d_rank, h_rank); Kokkos::deep_copy(d_num_ms_combs, h_num_ms_combs); - Kokkos::deep_copy(d_offsets, h_offsets); + Kokkos::deep_copy(d_func_inds, h_func_inds); Kokkos::deep_copy(d_mus, h_mus); Kokkos::deep_copy(d_ns, h_ns); Kokkos::deep_copy(d_ls, h_ls); Kokkos::deep_copy(d_ms_combs, h_ms_combs); - Kokkos::deep_copy(d_ctildes, h_ctildes); +// Kokkos::deep_copy(d_ctildes, h_ctildes); + Kokkos::deep_copy(d_gen_cgs, h_gen_cgs); + Kokkos::deep_copy(d_coeffs, h_coeffs); } /* ---------------------------------------------------------------------- @@ -391,7 +416,7 @@ void PairPACEExtrapolationKokkos::init_style() error->all(FLERR,"Pair style pace/kk can currently only run on a single " "CPU thread"); - PairPACE::init_style(); + PairPACEExtrapolation::init_style(); return; } @@ -436,7 +461,7 @@ void PairPACEExtrapolationKokkos::init_style() template double PairPACEExtrapolationKokkos::init_one(int i, int j) { - double cutone = PairPACE::init_one(i,j); + double cutone = PairPACEExtrapolation::init_one(i,j); k_scale.h_view(i,j) = k_scale.h_view(j,i) = scale[i][j]; k_scale.template modify(); @@ -454,7 +479,7 @@ double PairPACEExtrapolationKokkos::init_one(int i, int j) template void PairPACEExtrapolationKokkos::coeff(int narg, char **arg) { - PairPACE::coeff(narg,arg); + PairPACEExtrapolation::coeff(narg,arg); // Set up element lists @@ -471,7 +496,7 @@ void PairPACEExtrapolationKokkos::coeff(int narg, char **arg) template void PairPACEExtrapolationKokkos::allocate() { - PairPACE::allocate(); + PairPACEExtrapolation::allocate(); int n = atom->ntypes + 1; MemKK::realloc_kokkos(d_map, "pace:map", n); @@ -508,11 +533,10 @@ void PairPACEExtrapolationKokkos::compute(int eflag_in, int vflag_in { if (host_flag) { atomKK->sync(Host,X_MASK|TYPE_MASK); - PairPACE::compute(eflag_in,vflag_in); + PairPACEExtrapolation::compute(eflag_in,vflag_in); atomKK->modified(Host,F_MASK); return; } - eflag = eflag_in; vflag = vflag_in; @@ -521,7 +545,6 @@ void PairPACEExtrapolationKokkos::compute(int eflag_in, int vflag_in ev_init(eflag,vflag,0); // reallocate per-atom arrays if necessary - if (eflag_atom) { memoryKK->destroy_kokkos(k_eatom,eatom); memoryKK->create_kokkos(k_eatom,eatom,maxeatom,"pair:eatom"); @@ -532,14 +555,10 @@ void PairPACEExtrapolationKokkos::compute(int eflag_in, int vflag_in memoryKK->create_kokkos(k_vatom,vatom,maxvatom,"pair:vatom"); d_vatom = k_vatom.view(); } - copymode = 1; if (!force->newton_pair) error->all(FLERR,"PairPACEExtrapolationKokkos requires 'newton on'"); - if (recursive) - error->all(FLERR,"Must use 'product' algorithm with pair pace/kk on the GPU"); - atomKK->sync(execution_space,X_MASK|F_MASK|TYPE_MASK); x = atomKK->k_x.view(); f = atomKK->k_f.view(); @@ -636,7 +655,7 @@ void PairPACEExtrapolationKokkos::compute(int eflag_in, int vflag_in //ComputeRho { - typename Kokkos::RangePolicy policy_rho(0,chunk_size*idx_rho_max); + typename Kokkos::RangePolicy policy_rho(0, chunk_size * idx_ms_combs_max); Kokkos::parallel_for("ComputeRho",policy_rho,*this); } @@ -648,7 +667,7 @@ void PairPACEExtrapolationKokkos::compute(int eflag_in, int vflag_in //ComputeWeights { - typename Kokkos::RangePolicy policy_weights(0,chunk_size*idx_rho_max); + typename Kokkos::RangePolicy policy_weights(0, chunk_size * idx_ms_combs_max); Kokkos::parallel_for("ComputeWeights",policy_weights,*this); } @@ -910,63 +929,63 @@ template KOKKOS_INLINE_FUNCTION void PairPACEExtrapolationKokkos::operator() (TagPairPACEComputeRho, const int& iter) const { - const int idx_rho = iter / chunk_size; + const int idx_ms_comb = iter / chunk_size; const int ii = iter % chunk_size; const int i = d_ilist[ii + chunk_offset]; const int mu_i = d_map(type(i)); - if (idx_rho >= d_idx_rho_count(mu_i)) return; + if (idx_ms_comb >= d_idx_ms_combs_count(mu_i)) return; const int ndensity = d_ndensity(mu_i); - const int offset = d_offsets(mu_i, idx_rho); - const int rank = d_rank(mu_i, offset); + const int func_ind = d_func_inds(mu_i, idx_ms_comb); + const int rank = d_rank(mu_i, func_ind); const int r = rank - 1; // Basis functions B with iterative product and density rho(p) calculation if (rank == 1) { - const int mu = d_mus(mu_i, offset, 0); - const int n = d_ns(mu_i, offset, 0); + const int mu = d_mus(mu_i, func_ind, 0); + const int n = d_ns(mu_i, func_ind, 0); double A_cur = A_rank1(ii, mu, n - 1); for (int p = 0; p < ndensity; ++p) { //for rank=1 (r=0) only 1 ms-combination exists (ms_ind=0), so index of func.ctildes is 0..ndensity-1 - Kokkos::atomic_add(&rhos(ii, p), d_ctildes(mu_i, idx_rho, p) * A_cur); + Kokkos::atomic_add(&rhos(ii, p), d_coeffs(mu_i, func_ind, p) * d_gen_cgs(mu_i, idx_ms_comb) * A_cur); } } else { // rank > 1 // loop over {ms} combinations in sum // loop over m, collect B = product of A with given ms - A_forward_prod(ii, idx_rho, 0) = complex::one(); + A_forward_prod(ii, idx_ms_comb, 0) = complex::one(); // fill forward A-product triangle for (int t = 0; t < rank; t++) { //TODO: optimize ns[t]-1 -> ns[t] during functions construction - const int mu = d_mus(mu_i, offset, t); - const int n = d_ns(mu_i, offset, t); - const int l = d_ls(mu_i, offset, t); - const int m = d_ms_combs(mu_i, idx_rho, t); // current ms-combination (of length = rank) + const int mu = d_mus(mu_i, func_ind, t); + const int n = d_ns(mu_i, func_ind, t); + const int l = d_ls(mu_i, func_ind, t); + const int m = d_ms_combs(mu_i, idx_ms_comb, t); // current ms-combination (of length = rank) const int idx = l * (l + 1) + m; // (l, m) - A_list(ii, idx_rho, t) = A(ii, mu, n - 1, idx); - A_forward_prod(ii, idx_rho, t + 1) = A_forward_prod(ii, idx_rho, t) * A_list(ii, idx_rho, t); + A_list(ii, idx_ms_comb, t) = A(ii, mu, n - 1, idx); + A_forward_prod(ii, idx_ms_comb, t + 1) = A_forward_prod(ii, idx_ms_comb, t) * A_list(ii, idx_ms_comb, t); } complex A_backward_prod = complex::one(); // fill backward A-product triangle for (int t = r; t >= 1; t--) { - const complex dB = A_forward_prod(ii, idx_rho, t) * A_backward_prod; // dB - product of all A's except t-th - dB_flatten(ii, idx_rho, t) = dB; + const complex dB = A_forward_prod(ii, idx_ms_comb, t) * A_backward_prod; // dB - product of all A's except t-th + dB_flatten(ii, idx_ms_comb, t) = dB; - A_backward_prod = A_backward_prod * A_list(ii, idx_rho, t); + A_backward_prod = A_backward_prod * A_list(ii, idx_ms_comb, t); } - dB_flatten(ii, idx_rho, 0) = A_forward_prod(ii, idx_rho, 0) * A_backward_prod; + dB_flatten(ii, idx_ms_comb, 0) = A_forward_prod(ii, idx_ms_comb, 0) * A_backward_prod; - const complex B = A_forward_prod(ii, idx_rho, rank); + const complex B = A_forward_prod(ii, idx_ms_comb, rank); for (int p = 0; p < ndensity; ++p) { // real-part only multiplication - Kokkos::atomic_add(&rhos(ii, p), B.real_part_product(d_ctildes(mu_i, idx_rho, p))); + Kokkos::atomic_add(&rhos(ii, p), B.real_part_product(d_coeffs(mu_i, func_ind, p) * d_gen_cgs(mu_i, idx_ms_comb))); } } } @@ -1011,43 +1030,43 @@ template KOKKOS_INLINE_FUNCTION void PairPACEExtrapolationKokkos::operator() (TagPairPACEComputeWeights, const int& iter) const { - const int idx_rho = iter / chunk_size; + const int idx_ms_comb = iter / chunk_size; const int ii = iter % chunk_size; const int i = d_ilist[ii + chunk_offset]; const int mu_i = d_map(type(i)); - if (idx_rho >= d_idx_rho_count(mu_i)) return; + if (idx_ms_comb >= d_idx_ms_combs_count(mu_i)) return; const int ndensity = d_ndensity(mu_i); - const int offset = d_offsets(mu_i, idx_rho); - const int rank = d_rank(mu_i, offset); + const int func_ind = d_func_inds(mu_i, idx_ms_comb); + const int rank = d_rank(mu_i, func_ind); // Weights and theta calculation if (rank == 1) { - const int mu = d_mus(mu_i, offset, 0); - const int n = d_ns(mu_i, offset, 0); + const int mu = d_mus(mu_i, func_ind, 0); + const int n = d_ns(mu_i, func_ind, 0); double theta = 0.0; for (int p = 0; p < ndensity; ++p) { // for rank=1 (r=0) only 1 ms-combination exists (ms_ind=0), so index of func.ctildes is 0..ndensity-1 - theta += dF_drho(ii, p) * d_ctildes(mu_i, idx_rho, p); + theta += dF_drho(ii, p) * d_coeffs(mu_i, func_ind, p) * d_gen_cgs(mu_i, idx_ms_comb); } Kokkos::atomic_add(&weights_rank1(ii, mu, n - 1), theta); } else { // rank > 1 double theta = 0.0; for (int p = 0; p < ndensity; ++p) - theta += dF_drho(ii, p) * d_ctildes(mu_i, idx_rho, p); + theta += dF_drho(ii, p) * d_coeffs(mu_i, func_ind, p) * d_gen_cgs(mu_i, idx_ms_comb); theta *= 0.5; // 0.5 factor due to possible double counting ??? for (int t = 0; t < rank; ++t) { - const int m_t = d_ms_combs(mu_i, idx_rho, t); + const int m_t = d_ms_combs(mu_i, idx_ms_comb, t); const int factor = (m_t % 2 == 0 ? 1 : -1); - const complex dB = dB_flatten(ii, idx_rho, t); - const int mu_t = d_mus(mu_i, offset, t); - const int n_t = d_ns(mu_i, offset, t); - const int l_t = d_ls(mu_i, offset, t); + const complex dB = dB_flatten(ii, idx_ms_comb, t); + const int mu_t = d_mus(mu_i, func_ind, t); + const int n_t = d_ns(mu_i, func_ind, t); + const int l_t = d_ls(mu_i, func_ind, t); const int idx = l_t * (l_t + 1) + m_t; // (l, m) const complex value = theta * dB; Kokkos::atomic_add(&(weights(ii, mu_t, n_t - 1, idx).re), value.re); @@ -1687,15 +1706,17 @@ double PairPACEExtrapolationKokkos::memory_usage() bytes += MemKK::memory_usage(d_npoti); bytes += MemKK::memory_usage(d_wpre); bytes += MemKK::memory_usage(d_mexp); - bytes += MemKK::memory_usage(d_idx_rho_count); + bytes += MemKK::memory_usage(d_idx_ms_combs_count); bytes += MemKK::memory_usage(d_rank); bytes += MemKK::memory_usage(d_num_ms_combs); - bytes += MemKK::memory_usage(d_offsets); + bytes += MemKK::memory_usage(d_func_inds); bytes += MemKK::memory_usage(d_mus); bytes += MemKK::memory_usage(d_ns); bytes += MemKK::memory_usage(d_ls); bytes += MemKK::memory_usage(d_ms_combs); - bytes += MemKK::memory_usage(d_ctildes); +// bytes += MemKK::memory_usage(d_ctildes); + bytes += MemKK::memory_usage(d_gen_cgs); + bytes += MemKK::memory_usage(d_coeffs); bytes += MemKK::memory_usage(alm); bytes += MemKK::memory_usage(blm); bytes += MemKK::memory_usage(cl); diff --git a/src/KOKKOS/pair_pace_extrapolation_kokkos.h b/src/KOKKOS/pair_pace_extrapolation_kokkos.h index 482d068725..568d12b90c 100644 --- a/src/KOKKOS/pair_pace_extrapolation_kokkos.h +++ b/src/KOKKOS/pair_pace_extrapolation_kokkos.h @@ -23,7 +23,7 @@ PairStyle(pace/extrapolation/kk/host,PairPACEExtrapolationKokkos); #ifndef LMP_PAIR_PACE_EXTRAPOLATION_KOKKOS_H #define LMP_PAIR_PACE_EXTRAPOLATION_KOKKOS_H -#include "pair_pace.h" +#include "pair_pace_extrapolation.h" #include "ace-evaluator/ace_radial.h" #include "kokkos_type.h" #include "pair_kokkos.h" @@ -31,7 +31,7 @@ PairStyle(pace/extrapolation/kk/host,PairPACEExtrapolationKokkos); namespace LAMMPS_NS { template -class PairPACEExtrapolationKokkos : public PairPACE { +class PairPACEExtrapolationKokkos : public PairPACEExtrapolation { public: struct TagPairPACEComputeNeigh{}; struct TagPairPACEComputeRadial{}; @@ -95,7 +95,7 @@ class PairPACEExtrapolationKokkos : public PairPACE { void operator() (TagPairPACEComputeForce,const int& ii, EV_FLOAT&) const; protected: - int inum, maxneigh, chunk_size, chunk_offset, idx_rho_max; + int inum, maxneigh, chunk_size, chunk_offset, idx_ms_combs_max; int host_flag; int eflag, vflag; @@ -274,15 +274,17 @@ class PairPACEExtrapolationKokkos : public PairPACE { t_ace_2d d_mexp; // tilde - t_ace_1i d_idx_rho_count; + t_ace_1i d_idx_ms_combs_count; t_ace_2i d_rank; t_ace_2i d_num_ms_combs; - t_ace_2i d_offsets; + t_ace_2i d_func_inds; t_ace_3i d_mus; t_ace_3i d_ns; t_ace_3i d_ls; t_ace_3i d_ms_combs; - t_ace_3d d_ctildes; +// t_ace_3d d_ctildes; + t_ace_2d d_gen_cgs; + t_ace_3d d_coeffs; t_ace_3d3 f_ij; diff --git a/src/ML-PACE/pair_pace_extrapolation.cpp b/src/ML-PACE/pair_pace_extrapolation.cpp index ec185e75df..2c5e5fafe9 100644 --- a/src/ML-PACE/pair_pace_extrapolation.cpp +++ b/src/ML-PACE/pair_pace_extrapolation.cpp @@ -98,6 +98,8 @@ PairPACEExtrapolation::PairPACEExtrapolation(LAMMPS *lmp) : Pair(lmp) scale = nullptr; flag_compute_extrapolation_grade = 0; extrapolation_grade_gamma = nullptr; + + chunksize = 4096; } /* ---------------------------------------------------------------------- @@ -133,7 +135,7 @@ void PairPACEExtrapolation::compute(int eflag, int vflag) double **x = atom->x; double **f = atom->f; - tagint *tag = atom->tag; +// tagint *tag = atom->tag; int *type = atom->type; // number of atoms in cell int nlocal = atom->nlocal; @@ -141,7 +143,7 @@ void PairPACEExtrapolation::compute(int eflag, int vflag) int newton_pair = force->newton_pair; // number of atoms including ghost atoms - int nall = nlocal + atom->nghost; +// int nall = nlocal + atom->nghost; // inum: length of the neighborlists list inum = list->inum; @@ -283,7 +285,20 @@ void PairPACEExtrapolation::allocate() void PairPACEExtrapolation::settings(int narg, char **arg) { - if (narg > 0) error->all(FLERR, "Pair style pace/extrapolation supports no keywords"); +// if (narg > 2) error->all(FLERR, "Pair style pace/extrapolation supports no keywords"); + if (narg > 2) utils::missing_cmd_args(FLERR, "pair_style pace/extrapolation", error); + // ACE potentials are parameterized in metal units + if (strcmp("metal", update->unit_style) != 0) + error->all(FLERR, "ACE potentials require 'metal' units"); + + int iarg = 0; + while (iarg < narg) { + if (strcmp(arg[iarg], "chunksize") == 0) { + chunksize = utils::inumeric(FLERR, arg[iarg + 1], false, lmp); + iarg += 2; + } else + error->all(FLERR, "Unknown pair_style pace keyword: {}", arg[iarg]); + } if (comm->me == 0) utils::logmesg(lmp, "ACE/AL version: {}.{}.{}\n", VERSION_YEAR, VERSION_MONTH, VERSION_DAY); @@ -343,7 +358,6 @@ void PairPACEExtrapolation::coeff(int narg, char **arg) aceimpl->rec_ace->element_type_mapping.init(atom->ntypes + 1); aceimpl->rec_ace->element_type_mapping.fill(-1); //-1 means atom not included into potential - FILE *species_type_file = nullptr; const int n = atom->ntypes; element_names.resize(n); diff --git a/src/ML-PACE/pair_pace_extrapolation.h b/src/ML-PACE/pair_pace_extrapolation.h index c5d9da23db..6f7eeb279e 100644 --- a/src/ML-PACE/pair_pace_extrapolation.h +++ b/src/ML-PACE/pair_pace_extrapolation.h @@ -49,13 +49,15 @@ class PairPACEExtrapolation : public Pair { struct ACEALImpl *aceimpl; int nmax; - void allocate(); + virtual void allocate(); std::vector element_names; // list of elements (used by dump pace/extrapolation) double *extrapolation_grade_gamma; //per-atom gamma value int flag_compute_extrapolation_grade; double **scale; + + int chunksize; }; } // namespace LAMMPS_NS From 014b892e3b13fd3e160d17fe5f7135052a810b49 Mon Sep 17 00:00:00 2001 From: Yury Lysogorskiy Date: Mon, 2 Jan 2023 23:34:24 +0100 Subject: [PATCH 38/47] WIP: - add TagPairPACEComputeGamma kernel - add d_total_basis_size - add gamma_flag, d_ASI, projections and gamma --- src/KOKKOS/pair_pace_extrapolation_kokkos.cpp | 109 ++++++++++++++---- src/KOKKOS/pair_pace_extrapolation_kokkos.h | 12 +- 2 files changed, 100 insertions(+), 21 deletions(-) diff --git a/src/KOKKOS/pair_pace_extrapolation_kokkos.cpp b/src/KOKKOS/pair_pace_extrapolation_kokkos.cpp index 006cf5e609..c5ca97d036 100644 --- a/src/KOKKOS/pair_pace_extrapolation_kokkos.cpp +++ b/src/KOKKOS/pair_pace_extrapolation_kokkos.cpp @@ -13,7 +13,7 @@ ------------------------------------------------------------------------- */ /* ---------------------------------------------------------------------- - Contributing author: Stan Moore (SNL) + Contributing author: Yury Lysogorskiy (ICAMS) ------------------------------------------------------------------------- */ #include "pair_pace_extrapolation_kokkos.h" @@ -29,9 +29,9 @@ #include "neighbor_kokkos.h" #include "neigh_request.h" -#include "ace-evaluator/ace_c_basis.h" -#include "ace-evaluator/ace_evaluator.h" -#include "ace-evaluator/ace_recursive.h" +//#include "ace-evaluator/ace_c_basis.h" +//#include "ace-evaluator/ace_evaluator.h" +//#include "ace-evaluator/ace_recursive.h" #include "ace-evaluator/ace_version.h" #include "ace-evaluator/ace_radial.h" @@ -42,21 +42,16 @@ namespace LAMMPS_NS { struct ACEALImpl { - ACEALImpl() : basis_set(nullptr), ace(nullptr), ctilde_basis_set(nullptr), rec_ace(nullptr) {} + ACEALImpl() : basis_set(nullptr), ace(nullptr) {} ~ACEALImpl() { delete basis_set; delete ace; - - delete ctilde_basis_set; - delete rec_ace; } ACEBBasisSet *basis_set; ACEBEvaluator *ace; - ACECTildeBasisSet *ctilde_basis_set; - ACERecursiveEvaluator *rec_ace; }; } // namespace LAMMPS_NS @@ -132,7 +127,12 @@ void PairPACEExtrapolationKokkos::grow(int natom, int maxneigh) // hard-core repulsion MemKK::realloc_kokkos(rho_core, "pace:rho_core", natom); MemKK::realloc_kokkos(dF_drho_core, "pace:dF_drho_core", natom); + MemKK::realloc_kokkos(dB_flatten, "pace:dB_flatten", natom, idx_ms_combs_max, basis_set->rankmax); + + //B-projections + MemKK::realloc_kokkos(projections, "pace:projections", natom, total_num_functions_max); // per-atom B-projections + MemKK::realloc_kokkos(gamma, "pace:gamma", natom); // per-atom gamma } if (((int)ylm.extent(0) < natom) || ((int)ylm.extent(1) < maxneigh)) { @@ -271,14 +271,17 @@ template void PairPACEExtrapolationKokkos::copy_tilde() { auto basis_set = aceimpl->basis_set; + auto b_evaluator = aceimpl->ace; // flatten loops, get per-element count and max idx_ms_combs_max = 0; - int total_basis_size_max = 0; + total_num_functions_max = 0; MemKK::realloc_kokkos(d_idx_ms_combs_count, "pace:idx_ms_combs_count", nelements); + MemKK::realloc_kokkos(d_total_basis_size, "pace:total_basis_size", nelements); auto h_idx_ms_combs_count = Kokkos::create_mirror_view(d_idx_ms_combs_count); + auto h_total_basis_size = Kokkos::create_mirror_view(d_total_basis_size); for (int mu = 0; mu < nelements; mu++) { int idx_ms_combs = 0; @@ -301,21 +304,25 @@ void PairPACEExtrapolationKokkos::copy_tilde() } h_idx_ms_combs_count(mu) = idx_ms_combs; idx_ms_combs_max = MAX(idx_ms_combs_max, idx_ms_combs); - total_basis_size_max = MAX(total_basis_size_max, total_basis_size_rank1 + total_basis_size); + total_num_functions_max = MAX(total_num_functions_max, total_basis_size_rank1 + total_basis_size); + h_total_basis_size(mu) = total_basis_size_rank1 + total_basis_size; } Kokkos::deep_copy(d_idx_ms_combs_count, h_idx_ms_combs_count); + Kokkos::deep_copy(d_total_basis_size, h_total_basis_size); - MemKK::realloc_kokkos(d_rank, "pace:rank", nelements, total_basis_size_max); - MemKK::realloc_kokkos(d_num_ms_combs, "pace:num_ms_combs", nelements, total_basis_size_max); + MemKK::realloc_kokkos(d_rank, "pace:rank", nelements, total_num_functions_max); + MemKK::realloc_kokkos(d_num_ms_combs, "pace:num_ms_combs", nelements, total_num_functions_max); MemKK::realloc_kokkos(d_func_inds, "pace:func_inds", nelements, idx_ms_combs_max); - MemKK::realloc_kokkos(d_mus, "pace:mus", nelements, total_basis_size_max, basis_set->rankmax); - MemKK::realloc_kokkos(d_ns, "pace:ns", nelements, total_basis_size_max, basis_set->rankmax); - MemKK::realloc_kokkos(d_ls, "pace:ls", nelements, total_basis_size_max, basis_set->rankmax); + MemKK::realloc_kokkos(d_mus, "pace:mus", nelements, total_num_functions_max, basis_set->rankmax); + MemKK::realloc_kokkos(d_ns, "pace:ns", nelements, total_num_functions_max, basis_set->rankmax); + MemKK::realloc_kokkos(d_ls, "pace:ls", nelements, total_num_functions_max, basis_set->rankmax); MemKK::realloc_kokkos(d_ms_combs, "pace:ms_combs", nelements, idx_ms_combs_max, basis_set->rankmax); - //MemKK::realloc_kokkos(d_ctildes, "pace:ctildes", nelements, idx_ms_combs_max, basis_set->ndensitymax); MemKK::realloc_kokkos(d_gen_cgs, "pace:gen_cgs", nelements, idx_ms_combs_max); - MemKK::realloc_kokkos(d_coeffs, "pace:coeffs", nelements, total_basis_size_max, basis_set->ndensitymax); + MemKK::realloc_kokkos(d_coeffs, "pace:coeffs", nelements, total_num_functions_max, basis_set->ndensitymax); + // active set inverted + MemKK::realloc_kokkos(d_ASI, "pace:ASI", nelements, total_num_functions_max, total_num_functions_max); + auto h_rank = Kokkos::create_mirror_view(d_rank); auto h_num_ms_combs = Kokkos::create_mirror_view(d_num_ms_combs); @@ -327,6 +334,8 @@ void PairPACEExtrapolationKokkos::copy_tilde() // auto h_ctildes = Kokkos::create_mirror_view(d_ctildes); auto h_gen_cgs = Kokkos::create_mirror_view(d_gen_cgs); auto h_coeffs = Kokkos::create_mirror_view(d_coeffs); +// asi + auto h_ASI = Kokkos::create_mirror_view(d_ASI); // copy values on host @@ -390,6 +399,14 @@ void PairPACEExtrapolationKokkos::copy_tilde() idx_ms_comb++; } } + + // ASI + const auto &A_as_inv = b_evaluator->A_active_set_inv.at(mu); + for(int i = 0; i < total_basis_size_rank1 + total_basis_size; i++) + for(int j = 0; j < total_basis_size_rank1 + total_basis_size; j++){ + h_ASI(mu,i,j)=A_as_inv(i,j); + } + } Kokkos::deep_copy(d_rank, h_rank); @@ -402,6 +419,7 @@ void PairPACEExtrapolationKokkos::copy_tilde() // Kokkos::deep_copy(d_ctildes, h_ctildes); Kokkos::deep_copy(d_gen_cgs, h_gen_cgs); Kokkos::deep_copy(d_coeffs, h_coeffs); + Kokkos::deep_copy(d_ASI, h_ASI); } /* ---------------------------------------------------------------------- @@ -591,6 +609,7 @@ void PairPACEExtrapolationKokkos::compute(int eflag_in, int vflag_in chunk_size = MIN(chunksize,inum); // "chunksize" variable is set by user chunk_offset = 0; + gamma_flag = 1; grow(chunk_size, maxneigh); @@ -604,6 +623,9 @@ void PairPACEExtrapolationKokkos::compute(int eflag_in, int vflag_in Kokkos::deep_copy(A_rank1, 0.0); Kokkos::deep_copy(rhos, 0.0); + Kokkos::deep_copy(projections, 0.0); + Kokkos::deep_copy(gamma, 0.0); + EV_FLOAT ev_tmp; if (chunk_size > inum - chunk_offset) @@ -665,6 +687,12 @@ void PairPACEExtrapolationKokkos::compute(int eflag_in, int vflag_in Kokkos::parallel_for("ComputeFS",policy_fs,*this); } + //ComputeGamma + if (gamma_flag) { + typename Kokkos::RangePolicy policy_gamma(0,chunk_size); + Kokkos::parallel_for("ComputeGamma",policy_gamma,*this); + } + //ComputeWeights { typename Kokkos::RangePolicy policy_weights(0, chunk_size * idx_ms_combs_max); @@ -952,6 +980,12 @@ void PairPACEExtrapolationKokkos::operator() (TagPairPACEComputeRho, //for rank=1 (r=0) only 1 ms-combination exists (ms_ind=0), so index of func.ctildes is 0..ndensity-1 Kokkos::atomic_add(&rhos(ii, p), d_coeffs(mu_i, func_ind, p) * d_gen_cgs(mu_i, idx_ms_comb) * A_cur); } + + + //gamma_i + if(gamma_flag) + Kokkos::atomic_add(&projections(ii, func_ind), d_gen_cgs(mu_i, idx_ms_comb) * A_cur); + } else { // rank > 1 // loop over {ms} combinations in sum @@ -987,6 +1021,9 @@ void PairPACEExtrapolationKokkos::operator() (TagPairPACEComputeRho, // real-part only multiplication Kokkos::atomic_add(&rhos(ii, p), B.real_part_product(d_coeffs(mu_i, func_ind, p) * d_gen_cgs(mu_i, idx_ms_comb))); } + //gamma_i + if(gamma_flag) + Kokkos::atomic_add(&projections(ii, func_ind), B.real_part_product(d_gen_cgs(mu_i, idx_ms_comb))); } } @@ -1024,6 +1061,35 @@ void PairPACEExtrapolationKokkos::operator() (TagPairPACEComputeFS, } } + +/* ---------------------------------------------------------------------- */ + + +template +KOKKOS_INLINE_FUNCTION +void PairPACEExtrapolationKokkos::operator() (TagPairPACEComputeGamma, const int& ii) const +{ + const int i = d_ilist[ii + chunk_offset]; + const int mu_i = d_map(type(i)); + const int basis_size = d_total_basis_size(mu_i); + + + double gamma_max = 0; + for (int j = 0; j gamma_max) + gamma_max = abs(current_gamma); + } + + // tally energy contribution + gamma(ii) = gamma_max; + +} /* ---------------------------------------------------------------------- */ template @@ -1714,13 +1780,16 @@ double PairPACEExtrapolationKokkos::memory_usage() bytes += MemKK::memory_usage(d_ns); bytes += MemKK::memory_usage(d_ls); bytes += MemKK::memory_usage(d_ms_combs); -// bytes += MemKK::memory_usage(d_ctildes); bytes += MemKK::memory_usage(d_gen_cgs); bytes += MemKK::memory_usage(d_coeffs); bytes += MemKK::memory_usage(alm); bytes += MemKK::memory_usage(blm); bytes += MemKK::memory_usage(cl); bytes += MemKK::memory_usage(dl); + bytes += MemKK::memory_usage(d_total_basis_size); + bytes += MemKK::memory_usage(d_ASI); + bytes += MemKK::memory_usage(projections); + bytes += MemKK::memory_usage(gamma); if (k_splines_gk.h_view.data()) { for (int i = 0; i < nelements; i++) { diff --git a/src/KOKKOS/pair_pace_extrapolation_kokkos.h b/src/KOKKOS/pair_pace_extrapolation_kokkos.h index 568d12b90c..a5b4f8abc7 100644 --- a/src/KOKKOS/pair_pace_extrapolation_kokkos.h +++ b/src/KOKKOS/pair_pace_extrapolation_kokkos.h @@ -40,6 +40,7 @@ class PairPACEExtrapolationKokkos : public PairPACEExtrapolation { struct TagPairPACEConjugateAi{}; struct TagPairPACEComputeRho{}; struct TagPairPACEComputeFS{}; + struct TagPairPACEComputeGamma{}; struct TagPairPACEComputeWeights{}; struct TagPairPACEComputeDerivative{}; @@ -80,6 +81,9 @@ class PairPACEExtrapolationKokkos : public PairPACEExtrapolation { KOKKOS_INLINE_FUNCTION void operator() (TagPairPACEComputeFS,const int& ii) const; + KOKKOS_INLINE_FUNCTION + void operator() (TagPairPACEComputeGamma, const int& ii) const; + KOKKOS_INLINE_FUNCTION void operator() (TagPairPACEComputeWeights,const int& iter) const; @@ -95,8 +99,9 @@ class PairPACEExtrapolationKokkos : public PairPACEExtrapolation { void operator() (TagPairPACEComputeForce,const int& ii, EV_FLOAT&) const; protected: - int inum, maxneigh, chunk_size, chunk_offset, idx_ms_combs_max; + int inum, maxneigh, chunk_size, chunk_offset, idx_ms_combs_max, total_num_functions_max; int host_flag; + int gamma_flag; int eflag, vflag; @@ -236,6 +241,10 @@ class PairPACEExtrapolationKokkos : public PairPACEExtrapolation { t_ace_3d d_values; t_ace_3d d_derivatives; + // inverted active set + t_ace_3d d_ASI; + t_ace_2d projections; + t_ace_1d gamma; // Spherical Harmonics void pre_compute_harmonics(int); @@ -275,6 +284,7 @@ class PairPACEExtrapolationKokkos : public PairPACEExtrapolation { // tilde t_ace_1i d_idx_ms_combs_count; + t_ace_1i d_total_basis_size; t_ace_2i d_rank; t_ace_2i d_num_ms_combs; t_ace_2i d_func_inds; From 1f36bc49ab234151b95525d3e7c502af845782a5 Mon Sep 17 00:00:00 2001 From: Yury Lysogorskiy Date: Tue, 3 Jan 2023 14:08:31 +0100 Subject: [PATCH 39/47] - add extract and extract_peratom methods - rename device gamma array to d_gamma - make host h_gamma array - copy from h_gamma to host extrapolation_grade_gamma array for each chunk - transpose two last dimensions of d_ASI (small improvement of performance) - manage grows of extrapolation_grade_gamma --- src/KOKKOS/pair_pace_extrapolation_kokkos.cpp | 91 +++++++++++++++---- src/KOKKOS/pair_pace_extrapolation_kokkos.h | 14 ++- 2 files changed, 82 insertions(+), 23 deletions(-) diff --git a/src/KOKKOS/pair_pace_extrapolation_kokkos.cpp b/src/KOKKOS/pair_pace_extrapolation_kokkos.cpp index c5ca97d036..cbaf92d800 100644 --- a/src/KOKKOS/pair_pace_extrapolation_kokkos.cpp +++ b/src/KOKKOS/pair_pace_extrapolation_kokkos.cpp @@ -29,9 +29,6 @@ #include "neighbor_kokkos.h" #include "neigh_request.h" -//#include "ace-evaluator/ace_c_basis.h" -//#include "ace-evaluator/ace_evaluator.h" -//#include "ace-evaluator/ace_recursive.h" #include "ace-evaluator/ace_version.h" #include "ace-evaluator/ace_radial.h" @@ -132,7 +129,7 @@ void PairPACEExtrapolationKokkos::grow(int natom, int maxneigh) //B-projections MemKK::realloc_kokkos(projections, "pace:projections", natom, total_num_functions_max); // per-atom B-projections - MemKK::realloc_kokkos(gamma, "pace:gamma", natom); // per-atom gamma + MemKK::realloc_kokkos(d_gamma, "pace:gamma", natom); // per-atom gamma } if (((int)ylm.extent(0) < natom) || ((int)ylm.extent(1) < maxneigh)) { @@ -321,7 +318,9 @@ void PairPACEExtrapolationKokkos::copy_tilde() MemKK::realloc_kokkos(d_gen_cgs, "pace:gen_cgs", nelements, idx_ms_combs_max); MemKK::realloc_kokkos(d_coeffs, "pace:coeffs", nelements, total_num_functions_max, basis_set->ndensitymax); // active set inverted - MemKK::realloc_kokkos(d_ASI, "pace:ASI", nelements, total_num_functions_max, total_num_functions_max); + t_ace_3d d_ASI_temp; + MemKK::realloc_kokkos(d_ASI_temp, "pace:ASI_temp", nelements, total_num_functions_max, total_num_functions_max); + auto h_rank = Kokkos::create_mirror_view(d_rank); @@ -331,11 +330,10 @@ void PairPACEExtrapolationKokkos::copy_tilde() auto h_ns = Kokkos::create_mirror_view(d_ns); auto h_ls = Kokkos::create_mirror_view(d_ls); auto h_ms_combs = Kokkos::create_mirror_view(d_ms_combs); -// auto h_ctildes = Kokkos::create_mirror_view(d_ctildes); auto h_gen_cgs = Kokkos::create_mirror_view(d_gen_cgs); auto h_coeffs = Kokkos::create_mirror_view(d_coeffs); // asi - auto h_ASI = Kokkos::create_mirror_view(d_ASI); + auto h_ASI = Kokkos::create_mirror_view(d_ASI_temp); // copy values on host @@ -404,7 +402,7 @@ void PairPACEExtrapolationKokkos::copy_tilde() const auto &A_as_inv = b_evaluator->A_active_set_inv.at(mu); for(int i = 0; i < total_basis_size_rank1 + total_basis_size; i++) for(int j = 0; j < total_basis_size_rank1 + total_basis_size; j++){ - h_ASI(mu,i,j)=A_as_inv(i,j); + h_ASI(mu,i,j)=A_as_inv(j,i); // transpose back for better performance on GPU } } @@ -416,10 +414,10 @@ void PairPACEExtrapolationKokkos::copy_tilde() Kokkos::deep_copy(d_ns, h_ns); Kokkos::deep_copy(d_ls, h_ls); Kokkos::deep_copy(d_ms_combs, h_ms_combs); -// Kokkos::deep_copy(d_ctildes, h_ctildes); Kokkos::deep_copy(d_gen_cgs, h_gen_cgs); Kokkos::deep_copy(d_coeffs, h_coeffs); - Kokkos::deep_copy(d_ASI, h_ASI); + Kokkos::deep_copy(d_ASI_temp, h_ASI); + d_ASI = d_ASI_temp; // copy from temopary array to const array } /* ---------------------------------------------------------------------- @@ -573,6 +571,15 @@ void PairPACEExtrapolationKokkos::compute(int eflag_in, int vflag_in memoryKK->create_kokkos(k_vatom,vatom,maxvatom,"pair:vatom"); d_vatom = k_vatom.view(); } + + if (gamma_flag && atom->nlocal > nmax) { + memory->destroy(extrapolation_grade_gamma); + nmax = atom->nlocal; + memory->create(extrapolation_grade_gamma, nmax, "pace/atom:gamma"); + //zeroify array + memset(extrapolation_grade_gamma, 0, nmax * sizeof(*extrapolation_grade_gamma)); + } + copymode = 1; if (!force->newton_pair) error->all(FLERR,"PairPACEExtrapolationKokkos requires 'newton on'"); @@ -609,7 +616,7 @@ void PairPACEExtrapolationKokkos::compute(int eflag_in, int vflag_in chunk_size = MIN(chunksize,inum); // "chunksize" variable is set by user chunk_offset = 0; - gamma_flag = 1; + grow(chunk_size, maxneigh); @@ -624,7 +631,7 @@ void PairPACEExtrapolationKokkos::compute(int eflag_in, int vflag_in Kokkos::deep_copy(rhos, 0.0); Kokkos::deep_copy(projections, 0.0); - Kokkos::deep_copy(gamma, 0.0); + Kokkos::deep_copy(d_gamma, 0.0); EV_FLOAT ev_tmp; @@ -729,8 +736,15 @@ void PairPACEExtrapolationKokkos::compute(int eflag_in, int vflag_in } } ev += ev_tmp; - chunk_offset += chunk_size; + //if gamma_flag - copy current d_gamma to extrapolation_grade_gamma + if(gamma_flag){ + h_gamma = Kokkos::create_mirror_view(d_gamma); + Kokkos:deep_copy(h_gamma, d_gamma); + memcpy(extrapolation_grade_gamma+chunk_offset, (void *) h_gamma.data(), sizeof(double)*chunk_size); + } + + chunk_offset += chunk_size; } // end while if (need_dup) @@ -1075,19 +1089,21 @@ void PairPACEExtrapolationKokkos::operator() (TagPairPACEComputeGamm double gamma_max = 0; - for (int j = 0; j gamma_max) - gamma_max = abs(current_gamma); + current_gamma = fabs(current_gamma); + if (current_gamma > gamma_max) + gamma_max = current_gamma; } // tally energy contribution - gamma(ii) = gamma_max; + d_gamma(ii) = gamma_max; } /* ---------------------------------------------------------------------- */ @@ -1789,7 +1805,7 @@ double PairPACEExtrapolationKokkos::memory_usage() bytes += MemKK::memory_usage(d_total_basis_size); bytes += MemKK::memory_usage(d_ASI); bytes += MemKK::memory_usage(projections); - bytes += MemKK::memory_usage(gamma); + bytes += MemKK::memory_usage(d_gamma); if (k_splines_gk.h_view.data()) { for (int i = 0; i < nelements; i++) { @@ -1812,3 +1828,38 @@ template class PairPACEExtrapolationKokkos; template class PairPACEExtrapolationKokkos; #endif } + +/* ---------------------------------------------------------------------- */ +/* ---------------------------------------------------------------------- + extract method for extracting value of scale variable + ---------------------------------------------------------------------- */ +template +void *PairPACEExtrapolationKokkos::extract(const char *str, int &dim) +{ + //check if str=="gamma_flag" then compute extrapolation grades on this iteration + dim = 0; + if (strcmp(str, "gamma_flag") == 0) return (void *) &gamma_flag; + + dim = 2; + if (strcmp(str, "scale") == 0) return (void *) scale; + return nullptr; +} + +/* ---------------------------------------------------------------------- + peratom requests from FixPair + return ptr to requested data + also return ncol = # of quantites per atom + 0 = per-atom vector + 1 or more = # of columns in per-atom array + return NULL if str is not recognized +---------------------------------------------------------------------- */ +template +void *PairPACEExtrapolationKokkos::extract_peratom(const char *str, int &ncol) +{ + if (strcmp(str, "gamma") == 0) { + ncol = 0; + return (void *) extrapolation_grade_gamma; + } + + return nullptr; +} \ No newline at end of file diff --git a/src/KOKKOS/pair_pace_extrapolation_kokkos.h b/src/KOKKOS/pair_pace_extrapolation_kokkos.h index a5b4f8abc7..6983fcc338 100644 --- a/src/KOKKOS/pair_pace_extrapolation_kokkos.h +++ b/src/KOKKOS/pair_pace_extrapolation_kokkos.h @@ -98,6 +98,10 @@ class PairPACEExtrapolationKokkos : public PairPACEExtrapolation { KOKKOS_INLINE_FUNCTION void operator() (TagPairPACEComputeForce,const int& ii, EV_FLOAT&) const; + + void *extract(const char *str, int &dim); + void *extract_peratom(const char *str, int &ncol); + protected: int inum, maxneigh, chunk_size, chunk_offset, idx_ms_combs_max, total_num_functions_max; int host_flag; @@ -203,6 +207,7 @@ class PairPACEExtrapolationKokkos : public PairPACEExtrapolation { typedef Kokkos::View t_ace_2d; typedef Kokkos::View t_ace_2d3; typedef Kokkos::View t_ace_3d; + typedef Kokkos::View tc_ace_3d; typedef Kokkos::View t_ace_3d3; typedef Kokkos::View t_ace_3d4; typedef Kokkos::View t_ace_4d; @@ -213,6 +218,8 @@ class PairPACEExtrapolationKokkos : public PairPACEExtrapolation { typedef Kokkos::View t_ace_4c; typedef Kokkos::View t_ace_4c3; + typedef Kokkos::View::HostMirror th_ace_1d; + t_ace_3d A_rank1; t_ace_4c A; @@ -242,11 +249,12 @@ class PairPACEExtrapolationKokkos : public PairPACEExtrapolation { t_ace_3d d_derivatives; // inverted active set - t_ace_3d d_ASI; + tc_ace_3d d_ASI; t_ace_2d projections; - t_ace_1d gamma; - // Spherical Harmonics + t_ace_1d d_gamma; + th_ace_1d h_gamma; + // Spherical Harmonics void pre_compute_harmonics(int); KOKKOS_INLINE_FUNCTION From e033cebcdd8274299969f1e4e172c232db9ce7b8 Mon Sep 17 00:00:00 2001 From: Yury Lysogorskiy Date: Tue, 3 Jan 2023 14:30:04 +0100 Subject: [PATCH 40/47] update lammps-user-pace version and checksum --- cmake/Modules/Packages/ML-PACE.cmake | 4 ++-- lib/pace/Install.py | 4 ++-- 2 files changed, 4 insertions(+), 4 deletions(-) diff --git a/cmake/Modules/Packages/ML-PACE.cmake b/cmake/Modules/Packages/ML-PACE.cmake index 0159f36c34..b64584e5a7 100644 --- a/cmake/Modules/Packages/ML-PACE.cmake +++ b/cmake/Modules/Packages/ML-PACE.cmake @@ -1,6 +1,6 @@ -set(PACELIB_URL "https://github.com/ICAMS/lammps-user-pace/archive/refs/tags/v.2022.10.15.tar.gz" CACHE STRING "URL for PACE evaluator library sources") +set(PACELIB_URL "https://github.com/ICAMS/lammps-user-pace/archive/refs/tags/v.2023.01.3.tar.gz" CACHE STRING "URL for PACE evaluator library sources") -set(PACELIB_MD5 "848ad6a6cc79fa82745927001fb1c9b5" CACHE STRING "MD5 checksum of PACE evaluator library tarball") +set(PACELIB_MD5 "f418d32b60e531063ac4285bf702b468" CACHE STRING "MD5 checksum of PACE evaluator library tarball") mark_as_advanced(PACELIB_URL) mark_as_advanced(PACELIB_MD5) diff --git a/lib/pace/Install.py b/lib/pace/Install.py index 9f132a9580..f7f50d4f6d 100644 --- a/lib/pace/Install.py +++ b/lib/pace/Install.py @@ -18,11 +18,11 @@ from install_helpers import fullpath, geturl, checkmd5sum # settings thisdir = fullpath('.') -version ='v.2022.10.15' +version ='v.2023.01.3' # known checksums for different PACE versions. used to validate the download. checksums = { \ - 'v.2022.10.15': '848ad6a6cc79fa82745927001fb1c9b5' + 'v.2023.01.3': 'f418d32b60e531063ac4285bf702b468' } parser = ArgumentParser(prog='Install.py', description="LAMMPS library build wrapper script") From 4d50109731a83f8c1a69ba81f0173f72f26a1364 Mon Sep 17 00:00:00 2001 From: Yury Lysogorskiy Date: Tue, 3 Jan 2023 14:43:46 +0100 Subject: [PATCH 41/47] add check that LINEAR ASI must be used --- src/KOKKOS/pair_pace_extrapolation_kokkos.cpp | 6 +++++- 1 file changed, 5 insertions(+), 1 deletion(-) diff --git a/src/KOKKOS/pair_pace_extrapolation_kokkos.cpp b/src/KOKKOS/pair_pace_extrapolation_kokkos.cpp index cbaf92d800..ba5ecafeac 100644 --- a/src/KOKKOS/pair_pace_extrapolation_kokkos.cpp +++ b/src/KOKKOS/pair_pace_extrapolation_kokkos.cpp @@ -429,7 +429,7 @@ void PairPACEExtrapolationKokkos::init_style() { if (host_flag) { if (lmp->kokkos->nthreads > 1) - error->all(FLERR,"Pair style pace/kk can currently only run on a single " + error->all(FLERR,"Pair style pace/extrapolation/kk can currently only run on a single " "CPU thread"); PairPACEExtrapolation::init_style(); @@ -497,6 +497,10 @@ void PairPACEExtrapolationKokkos::coeff(int narg, char **arg) { PairPACEExtrapolation::coeff(narg,arg); + auto b_evaluator = aceimpl->ace; + if (!b_evaluator->get_is_linear_extrapolation_grade()) { + error->all(FLERR,"Must use LINEAR ASI with pair pace/extrapolation/kk"); + } // Set up element lists auto h_map = Kokkos::create_mirror_view(d_map); From cfbc2d88944ffa03852e81f5176d11cde7622088 Mon Sep 17 00:00:00 2001 From: Yury Lysogorskiy Date: Tue, 3 Jan 2023 14:48:25 +0100 Subject: [PATCH 42/47] update pair_pace.rst --- doc/src/pair_pace.rst | 6 +++++- 1 file changed, 5 insertions(+), 1 deletion(-) diff --git a/doc/src/pair_pace.rst b/doc/src/pair_pace.rst index 697a9965b6..01f7df63f6 100644 --- a/doc/src/pair_pace.rst +++ b/doc/src/pair_pace.rst @@ -1,6 +1,7 @@ .. index:: pair_style pace .. index:: pair_style pace/kk .. index:: pair_style pace/extrapolation +.. index:: pair_style pace/extrapolation/kk pair_style pace command ======================= @@ -127,6 +128,9 @@ but not more often than every 20 steps. On all other steps `pair_style pace recursive` will be used. +When using the pair style *pace/extrapolation* with the KOKKOS package on GPUs +product B-basis evaluator is always used and only *linear* ASI is supported. + ---------- See the :doc:`pair_coeff ` page for alternate ways @@ -186,4 +190,4 @@ recursive, chunksize = 4096, .. _Lysogorskiy2022: -**(Lysogorskiy2022)** Lysogorskiy, Bochkarev, Mrovec, Drautz, TBS (2022). +**(Lysogorskiy2022)** Lysogorskiy, Bochkarev, Mrovec, Drautz, arXiv:2212.08716 (2022). From 295d8a69035497ea0b575b6764c349cd82a9af5c Mon Sep 17 00:00:00 2001 From: Yury Lysogorskiy Date: Tue, 3 Jan 2023 15:58:34 +0100 Subject: [PATCH 43/47] fix_pair.cpp: respect lmp->suffix when looking for pair_style name match --- src/fix_pair.cpp | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/src/fix_pair.cpp b/src/fix_pair.cpp index 5e5ccbf810..bd389f6632 100644 --- a/src/fix_pair.cpp +++ b/src/fix_pair.cpp @@ -36,6 +36,10 @@ FixPair::FixPair(LAMMPS *lmp, int narg, char **arg) : if (nevery < 1) error->all(FLERR,"Illegal fix pair every value: {}", nevery); pairname = utils::strdup(arg[4]); + if(lmp->suffix) { + strcat(pairname,"/"); + strcat(pairname,lmp->suffix); + } pstyle = force->pair_match(pairname,1,0); if (pstyle == nullptr) error->all(FLERR,"Pair style {} for fix pair not found", pairname); From a3572b61d84d17c5efec076663c8607aa1325c13 Mon Sep 17 00:00:00 2001 From: Stan Gerald Moore Date: Tue, 3 Jan 2023 10:09:47 -0700 Subject: [PATCH 44/47] Small cleanup --- src/KOKKOS/Install.sh | 2 + src/KOKKOS/pair_pace_extrapolation_kokkos.cpp | 129 +++++++++--------- src/ML-PACE/pair_pace_extrapolation.cpp | 4 - 3 files changed, 64 insertions(+), 71 deletions(-) diff --git a/src/KOKKOS/Install.sh b/src/KOKKOS/Install.sh index a5bf6437fc..77a9932d90 100755 --- a/src/KOKKOS/Install.sh +++ b/src/KOKKOS/Install.sh @@ -320,6 +320,8 @@ action pair_multi_lucy_rx_kokkos.cpp pair_multi_lucy_rx.cpp action pair_multi_lucy_rx_kokkos.h pair_multi_lucy_rx.h action pair_pace_kokkos.cpp pair_pace.cpp action pair_pace_kokkos.h pair_pace.h +action pair_pace_extrapolation_kokkos.cpp pair_pace_extrapolation.cpp +action pair_pace_extrapolation_kokkos.h pair_pace_extrapolation.h action pair_reaxff_kokkos.cpp pair_reaxff.cpp action pair_reaxff_kokkos.h pair_reaxff.h action pair_snap_kokkos.cpp pair_snap.cpp diff --git a/src/KOKKOS/pair_pace_extrapolation_kokkos.cpp b/src/KOKKOS/pair_pace_extrapolation_kokkos.cpp index ba5ecafeac..6369c7fba5 100644 --- a/src/KOKKOS/pair_pace_extrapolation_kokkos.cpp +++ b/src/KOKKOS/pair_pace_extrapolation_kokkos.cpp @@ -38,19 +38,18 @@ #include namespace LAMMPS_NS { - struct ACEALImpl { - ACEALImpl() : basis_set(nullptr), ace(nullptr) {} + struct ACEALImpl { + ACEALImpl() : basis_set(nullptr), ace(nullptr) {} - ~ACEALImpl() - { - delete basis_set; - delete ace; - } + ~ACEALImpl() { + delete basis_set; + delete ace; + } - ACEBBasisSet *basis_set; - ACEBEvaluator *ace; - }; -} // namespace LAMMPS_NS + ACEBBasisSet *basis_set; + ACEBEvaluator *ace; + }; +} // namespace LAMMPS_NS using namespace LAMMPS_NS; using namespace MathConst; @@ -187,7 +186,7 @@ void PairPACEExtrapolationKokkos::copy_pertype() h_rho_core_cutoff[n] = basis_set->map_embedding_specifications.at(n).rho_core_cutoff; h_drho_core_cutoff[n] = basis_set->map_embedding_specifications.at(n).drho_core_cutoff; - h_E0vals(n)= basis_set->E0vals(n); + h_E0vals(n) = basis_set->E0vals(n); h_ndensity(n) = basis_set->map_embedding_specifications.at(n).ndensity; @@ -321,8 +320,6 @@ void PairPACEExtrapolationKokkos::copy_tilde() t_ace_3d d_ASI_temp; MemKK::realloc_kokkos(d_ASI_temp, "pace:ASI_temp", nelements, total_num_functions_max, total_num_functions_max); - - auto h_rank = Kokkos::create_mirror_view(d_rank); auto h_num_ms_combs = Kokkos::create_mirror_view(d_num_ms_combs); auto h_func_inds = Kokkos::create_mirror_view(d_func_inds); @@ -332,7 +329,7 @@ void PairPACEExtrapolationKokkos::copy_tilde() auto h_ms_combs = Kokkos::create_mirror_view(d_ms_combs); auto h_gen_cgs = Kokkos::create_mirror_view(d_gen_cgs); auto h_coeffs = Kokkos::create_mirror_view(d_coeffs); -// asi + // asi auto h_ASI = Kokkos::create_mirror_view(d_ASI_temp); // copy values on host @@ -380,7 +377,7 @@ void PairPACEExtrapolationKokkos::copy_tilde() } for (int p = 0; p < ndensity; ++p) - h_coeffs(mu, func_ind_through, p) = func->coeff[p]; + h_coeffs(mu, func_ind_through, p) = func->coeff[p]; // loop over {ms} combinations in sum @@ -400,11 +397,10 @@ void PairPACEExtrapolationKokkos::copy_tilde() // ASI const auto &A_as_inv = b_evaluator->A_active_set_inv.at(mu); - for(int i = 0; i < total_basis_size_rank1 + total_basis_size; i++) - for(int j = 0; j < total_basis_size_rank1 + total_basis_size; j++){ - h_ASI(mu,i,j)=A_as_inv(j,i); // transpose back for better performance on GPU + for (int i = 0; i < total_basis_size_rank1 + total_basis_size; i++) + for (int j = 0; j < total_basis_size_rank1 + total_basis_size; j++){ + h_ASI(mu,i,j) = A_as_inv(j,i); // transpose back for better performance on GPU } - } Kokkos::deep_copy(d_rank, h_rank); @@ -565,6 +561,7 @@ void PairPACEExtrapolationKokkos::compute(int eflag_in, int vflag_in ev_init(eflag,vflag,0); // reallocate per-atom arrays if necessary + if (eflag_atom) { memoryKK->destroy_kokkos(k_eatom,eatom); memoryKK->create_kokkos(k_eatom,eatom,maxeatom,"pair:eatom"); @@ -742,7 +739,7 @@ void PairPACEExtrapolationKokkos::compute(int eflag_in, int vflag_in ev += ev_tmp; //if gamma_flag - copy current d_gamma to extrapolation_grade_gamma - if(gamma_flag){ + if (gamma_flag){ h_gamma = Kokkos::create_mirror_view(d_gamma); Kokkos:deep_copy(h_gamma, d_gamma); memcpy(extrapolation_grade_gamma+chunk_offset, (void *) h_gamma.data(), sizeof(double)*chunk_size); @@ -1001,7 +998,7 @@ void PairPACEExtrapolationKokkos::operator() (TagPairPACEComputeRho, //gamma_i - if(gamma_flag) + if (gamma_flag) Kokkos::atomic_add(&projections(ii, func_ind), d_gen_cgs(mu_i, idx_ms_comb) * A_cur); } else { // rank > 1 @@ -1040,14 +1037,13 @@ void PairPACEExtrapolationKokkos::operator() (TagPairPACEComputeRho, Kokkos::atomic_add(&rhos(ii, p), B.real_part_product(d_coeffs(mu_i, func_ind, p) * d_gen_cgs(mu_i, idx_ms_comb))); } //gamma_i - if(gamma_flag) - Kokkos::atomic_add(&projections(ii, func_ind), B.real_part_product(d_gen_cgs(mu_i, idx_ms_comb))); + if (gamma_flag) + Kokkos::atomic_add(&projections(ii, func_ind), B.real_part_product(d_gen_cgs(mu_i, idx_ms_comb))); } } /* ---------------------------------------------------------------------- */ - template KOKKOS_INLINE_FUNCTION void PairPACEExtrapolationKokkos::operator() (TagPairPACEComputeFS, const int& ii) const @@ -1079,37 +1075,34 @@ void PairPACEExtrapolationKokkos::operator() (TagPairPACEComputeFS, } } - /* ---------------------------------------------------------------------- */ - template KOKKOS_INLINE_FUNCTION void PairPACEExtrapolationKokkos::operator() (TagPairPACEComputeGamma, const int& ii) const { - const int i = d_ilist[ii + chunk_offset]; - const int mu_i = d_map(type(i)); - const int basis_size = d_total_basis_size(mu_i); + const int i = d_ilist[ii + chunk_offset]; + const int mu_i = d_map(type(i)); + const int basis_size = d_total_basis_size(mu_i); + double gamma_max = 0; + double current_gamma; + for (int j = 0; j gamma_max) - gamma_max = current_gamma; - } - - // tally energy contribution - d_gamma(ii) = gamma_max; + current_gamma = fabs(current_gamma); + if (current_gamma > gamma_max) + gamma_max = current_gamma; + } + // tally energy contribution + d_gamma(ii) = gamma_max; } + /* ---------------------------------------------------------------------- */ template @@ -1824,29 +1817,20 @@ double PairPACEExtrapolationKokkos::memory_usage() return bytes; } -/* ---------------------------------------------------------------------- */ - -namespace LAMMPS_NS { -template class PairPACEExtrapolationKokkos; -#ifdef LMP_KOKKOS_GPU -template class PairPACEExtrapolationKokkos; -#endif -} - -/* ---------------------------------------------------------------------- */ /* ---------------------------------------------------------------------- extract method for extracting value of scale variable ---------------------------------------------------------------------- */ + template void *PairPACEExtrapolationKokkos::extract(const char *str, int &dim) { - //check if str=="gamma_flag" then compute extrapolation grades on this iteration - dim = 0; - if (strcmp(str, "gamma_flag") == 0) return (void *) &gamma_flag; + //check if str=="gamma_flag" then compute extrapolation grades on this iteration + dim = 0; + if (strcmp(str, "gamma_flag") == 0) return (void *) &gamma_flag; - dim = 2; - if (strcmp(str, "scale") == 0) return (void *) scale; - return nullptr; + dim = 2; + if (strcmp(str, "scale") == 0) return (void *) scale; + return nullptr; } /* ---------------------------------------------------------------------- @@ -1857,13 +1841,24 @@ void *PairPACEExtrapolationKokkos::extract(const char *str, int &dim 1 or more = # of columns in per-atom array return NULL if str is not recognized ---------------------------------------------------------------------- */ + template void *PairPACEExtrapolationKokkos::extract_peratom(const char *str, int &ncol) { - if (strcmp(str, "gamma") == 0) { - ncol = 0; - return (void *) extrapolation_grade_gamma; - } + if (strcmp(str, "gamma") == 0) { + ncol = 0; + return (void *) extrapolation_grade_gamma; + } + + return nullptr; +} + +/* ---------------------------------------------------------------------- */ + +namespace LAMMPS_NS { +template class PairPACEExtrapolationKokkos; +#ifdef LMP_KOKKOS_GPU +template class PairPACEExtrapolationKokkos; +#endif +} - return nullptr; -} \ No newline at end of file diff --git a/src/ML-PACE/pair_pace_extrapolation.cpp b/src/ML-PACE/pair_pace_extrapolation.cpp index 2c5e5fafe9..8a0116526a 100644 --- a/src/ML-PACE/pair_pace_extrapolation.cpp +++ b/src/ML-PACE/pair_pace_extrapolation.cpp @@ -135,16 +135,12 @@ void PairPACEExtrapolation::compute(int eflag, int vflag) double **x = atom->x; double **f = atom->f; -// tagint *tag = atom->tag; int *type = atom->type; // number of atoms in cell int nlocal = atom->nlocal; int newton_pair = force->newton_pair; - // number of atoms including ghost atoms -// int nall = nlocal + atom->nghost; - // inum: length of the neighborlists list inum = list->inum; From bcb5285ef9fca4211295d45bd900448b4064ec01 Mon Sep 17 00:00:00 2001 From: Axel Kohlmeyer Date: Tue, 3 Jan 2023 14:15:12 -0500 Subject: [PATCH 45/47] update / correct suffix handling in fix pair --- doc/src/fix_pair.rst | 9 +++++++-- src/fix_pair.cpp | 17 +++++++++++++---- 2 files changed, 20 insertions(+), 6 deletions(-) diff --git a/doc/src/fix_pair.rst b/doc/src/fix_pair.rst index abb44718cd..44c91f18ee 100644 --- a/doc/src/fix_pair.rst +++ b/doc/src/fix_pair.rst @@ -1,7 +1,7 @@ .. index:: fix pair fix pair command -======================= +================ Syntax """""" @@ -47,7 +47,12 @@ These are example use cases: The *N* argument determines how often the fix is invoked. The *pstyle* argument is the name of the pair style. It can be a -sub-style used in a :doc:`pair_style hybrid ` command. +sub-style used in a :doc:`pair_style hybrid ` command. If +there are multiple sub-styles using the same pair style, then *pstyle* +should be specified as "style:N", where *N* is the number of the +instance of the pair style you wish monitor (e.g., the first or second). +For example, *pstyle* could be specified as "pace/extrapolation" or +"amoeba" or "eam:1" or "eam:2". One or more *name/flag* pairs of arguments follow. Each *name* is a per-atom quantity which the pair style must recognize as an extraction diff --git a/src/fix_pair.cpp b/src/fix_pair.cpp index bd389f6632..db7b24dfea 100644 --- a/src/fix_pair.cpp +++ b/src/fix_pair.cpp @@ -36,11 +36,20 @@ FixPair::FixPair(LAMMPS *lmp, int narg, char **arg) : if (nevery < 1) error->all(FLERR,"Illegal fix pair every value: {}", nevery); pairname = utils::strdup(arg[4]); - if(lmp->suffix) { - strcat(pairname,"/"); - strcat(pairname,lmp->suffix); + char *cptr; + int nsub = 0; + if ((cptr = strchr(pairname,':'))) { + *cptr = '\0'; + nsub = utils::inumeric(FLERR,cptr+1,false,lmp); } - pstyle = force->pair_match(pairname,1,0); + + if (lmp->suffix_enable) { + if (lmp->suffix) + pstyle = force->pair_match(fmt::format("{}/{}",pairname,lmp->suffix),1,nsub); + if ((pstyle == nullptr) && lmp->suffix2) + pstyle = force->pair_match(fmt::format("{}/{}",pairname,lmp->suffix2),1,nsub); + } + if (pstyle == nullptr) pstyle = force->pair_match(pairname,1,nsub); if (pstyle == nullptr) error->all(FLERR,"Pair style {} for fix pair not found", pairname); nfield = (narg-5) / 2; From 87a8cfe299f3e194bc6b24d19660a0ed69cb9ca8 Mon Sep 17 00:00:00 2001 From: Yury Lysogorskiy Date: Wed, 4 Jan 2023 12:46:50 +0100 Subject: [PATCH 46/47] - replace #include "ace-evaluator/ace_radial.h" in pair_pace_kokkos.h and pair_pace_extrapolation_kokkos.h with forward declaration "class SplineInterpolator;" - move SplineInterpolatorKokkos::operator=(const SplineInterpolator &spline) to .cpp files --- src/KOKKOS/pair_pace_extrapolation_kokkos.cpp | 18 ++++++++++++++++ src/KOKKOS/pair_pace_extrapolation_kokkos.h | 21 +++---------------- src/KOKKOS/pair_pace_kokkos.cpp | 18 ++++++++++++++++ src/KOKKOS/pair_pace_kokkos.h | 21 +++---------------- 4 files changed, 42 insertions(+), 36 deletions(-) diff --git a/src/KOKKOS/pair_pace_extrapolation_kokkos.cpp b/src/KOKKOS/pair_pace_extrapolation_kokkos.cpp index 6369c7fba5..e6ae694cad 100644 --- a/src/KOKKOS/pair_pace_extrapolation_kokkos.cpp +++ b/src/KOKKOS/pair_pace_extrapolation_kokkos.cpp @@ -1672,7 +1672,25 @@ void PairPACEExtrapolationKokkos::evaluate_splines(const int ii, con } /* ---------------------------------------------------------------------- */ +template +void PairPACEExtrapolationKokkos::SplineInterpolatorKokkos::operator=(const SplineInterpolator &spline) { + cutoff = spline.cutoff; + deltaSplineBins = spline.deltaSplineBins; + ntot = spline.ntot; + nlut = spline.nlut; + invrscalelookup = spline.invrscalelookup; + rscalelookup = spline.rscalelookup; + num_of_functions = spline.num_of_functions; + lookupTable = t_ace_3d4("lookupTable", ntot+1, num_of_functions); + auto h_lookupTable = Kokkos::create_mirror_view(lookupTable); + for (int i = 0; i < ntot+1; i++) + for (int j = 0; j < num_of_functions; j++) + for (int k = 0; k < 4; k++) + h_lookupTable(i, j, k) = spline.lookupTable(i, j, k); + Kokkos::deep_copy(lookupTable, h_lookupTable); +} +/* ---------------------------------------------------------------------- */ template KOKKOS_INLINE_FUNCTION void PairPACEExtrapolationKokkos::SplineInterpolatorKokkos::calcSplines(const int ii, const int jj, const double r, const t_ace_3d &d_values, const t_ace_3d &d_derivatives) const diff --git a/src/KOKKOS/pair_pace_extrapolation_kokkos.h b/src/KOKKOS/pair_pace_extrapolation_kokkos.h index 6983fcc338..a65841f8f6 100644 --- a/src/KOKKOS/pair_pace_extrapolation_kokkos.h +++ b/src/KOKKOS/pair_pace_extrapolation_kokkos.h @@ -24,10 +24,11 @@ PairStyle(pace/extrapolation/kk/host,PairPACEExtrapolationKokkos); #define LMP_PAIR_PACE_EXTRAPOLATION_KOKKOS_H #include "pair_pace_extrapolation.h" -#include "ace-evaluator/ace_radial.h" #include "kokkos_type.h" #include "pair_kokkos.h" +class SplineInterpolator; + namespace LAMMPS_NS { template @@ -313,23 +314,7 @@ class PairPACEExtrapolationKokkos : public PairPACEExtrapolation { t_ace_3d4 lookupTable; - void operator=(const SplineInterpolator &spline) { - cutoff = spline.cutoff; - deltaSplineBins = spline.deltaSplineBins; - ntot = spline.ntot; - nlut = spline.nlut; - invrscalelookup = spline.invrscalelookup; - rscalelookup = spline.rscalelookup; - num_of_functions = spline.num_of_functions; - - lookupTable = t_ace_3d4("lookupTable", ntot+1, num_of_functions); - auto h_lookupTable = Kokkos::create_mirror_view(lookupTable); - for (int i = 0; i < ntot+1; i++) - for (int j = 0; j < num_of_functions; j++) - for (int k = 0; k < 4; k++) - h_lookupTable(i, j, k) = spline.lookupTable(i, j, k); - Kokkos::deep_copy(lookupTable, h_lookupTable); - } + void operator=(const SplineInterpolator &spline); void deallocate() { lookupTable = t_ace_3d4(); diff --git a/src/KOKKOS/pair_pace_kokkos.cpp b/src/KOKKOS/pair_pace_kokkos.cpp index dd5b97fe32..6f1e3feaf8 100644 --- a/src/KOKKOS/pair_pace_kokkos.cpp +++ b/src/KOKKOS/pair_pace_kokkos.cpp @@ -1574,7 +1574,25 @@ void PairPACEKokkos::evaluate_splines(const int ii, const int jj, do } /* ---------------------------------------------------------------------- */ +template +void PairPACEKokkos::SplineInterpolatorKokkos::operator=(const SplineInterpolator &spline) { + cutoff = spline.cutoff; + deltaSplineBins = spline.deltaSplineBins; + ntot = spline.ntot; + nlut = spline.nlut; + invrscalelookup = spline.invrscalelookup; + rscalelookup = spline.rscalelookup; + num_of_functions = spline.num_of_functions; + lookupTable = t_ace_3d4("lookupTable", ntot+1, num_of_functions); + auto h_lookupTable = Kokkos::create_mirror_view(lookupTable); + for (int i = 0; i < ntot+1; i++) + for (int j = 0; j < num_of_functions; j++) + for (int k = 0; k < 4; k++) + h_lookupTable(i, j, k) = spline.lookupTable(i, j, k); + Kokkos::deep_copy(lookupTable, h_lookupTable); +} +/* ---------------------------------------------------------------------- */ template KOKKOS_INLINE_FUNCTION void PairPACEKokkos::SplineInterpolatorKokkos::calcSplines(const int ii, const int jj, const double r, const t_ace_3d &d_values, const t_ace_3d &d_derivatives) const diff --git a/src/KOKKOS/pair_pace_kokkos.h b/src/KOKKOS/pair_pace_kokkos.h index cc2a3cb674..39cfd100f8 100644 --- a/src/KOKKOS/pair_pace_kokkos.h +++ b/src/KOKKOS/pair_pace_kokkos.h @@ -24,10 +24,11 @@ PairStyle(pace/kk/host,PairPACEKokkos); #define LMP_PAIR_PACE_KOKKOS_H #include "pair_pace.h" -#include "ace-evaluator/ace_radial.h" #include "kokkos_type.h" #include "pair_kokkos.h" +class SplineInterpolator; + namespace LAMMPS_NS { template @@ -293,23 +294,7 @@ class PairPACEKokkos : public PairPACE { t_ace_3d4 lookupTable; - void operator=(const SplineInterpolator &spline) { - cutoff = spline.cutoff; - deltaSplineBins = spline.deltaSplineBins; - ntot = spline.ntot; - nlut = spline.nlut; - invrscalelookup = spline.invrscalelookup; - rscalelookup = spline.rscalelookup; - num_of_functions = spline.num_of_functions; - - lookupTable = t_ace_3d4("lookupTable", ntot+1, num_of_functions); - auto h_lookupTable = Kokkos::create_mirror_view(lookupTable); - for (int i = 0; i < ntot+1; i++) - for (int j = 0; j < num_of_functions; j++) - for (int k = 0; k < 4; k++) - h_lookupTable(i, j, k) = spline.lookupTable(i, j, k); - Kokkos::deep_copy(lookupTable, h_lookupTable); - } + void operator=(const SplineInterpolator &spline); void deallocate() { lookupTable = t_ace_3d4(); From 20b6355888d3b005601b62439270cd749dae24e9 Mon Sep 17 00:00:00 2001 From: Yury Lysogorskiy Date: Wed, 4 Jan 2023 15:00:03 +0100 Subject: [PATCH 47/47] refactor fix_pair.h/cpp: extract method "query_pstyle" and call it also in void FixPair::init() --- src/fix_pair.cpp | 40 +++++++++++++++++++++++++--------------- src/fix_pair.h | 2 ++ 2 files changed, 27 insertions(+), 15 deletions(-) diff --git a/src/fix_pair.cpp b/src/fix_pair.cpp index db7b24dfea..59f9dbda4a 100644 --- a/src/fix_pair.cpp +++ b/src/fix_pair.cpp @@ -21,6 +21,7 @@ #include "memory.h" #include "pair.h" #include "update.h" +#include "fmt/format.h" using namespace LAMMPS_NS; using namespace FixConst; @@ -36,20 +37,7 @@ FixPair::FixPair(LAMMPS *lmp, int narg, char **arg) : if (nevery < 1) error->all(FLERR,"Illegal fix pair every value: {}", nevery); pairname = utils::strdup(arg[4]); - char *cptr; - int nsub = 0; - if ((cptr = strchr(pairname,':'))) { - *cptr = '\0'; - nsub = utils::inumeric(FLERR,cptr+1,false,lmp); - } - - if (lmp->suffix_enable) { - if (lmp->suffix) - pstyle = force->pair_match(fmt::format("{}/{}",pairname,lmp->suffix),1,nsub); - if ((pstyle == nullptr) && lmp->suffix2) - pstyle = force->pair_match(fmt::format("{}/{}",pairname,lmp->suffix2),1,nsub); - } - if (pstyle == nullptr) pstyle = force->pair_match(pairname,1,nsub); + query_pstyle(lmp); if (pstyle == nullptr) error->all(FLERR,"Pair style {} for fix pair not found", pairname); nfield = (narg-5) / 2; @@ -143,6 +131,28 @@ FixPair::FixPair(LAMMPS *lmp, int narg, char **arg) : lasttime = -1; } +/* ---------------------------------------------------------------------- */ + +void FixPair::query_pstyle(LAMMPS *lmp) { + char *cptr=nullptr; + int nsub = 0; + if ((cptr = strchr(pairname, ':'))) { + *cptr = '\0'; + nsub = utils::inumeric(FLERR,cptr+1,false,lmp); + } + pstyle = nullptr; + if (lmp->suffix_enable) { + if (lmp->suffix) { + pstyle = force->pair_match(fmt::format("{}/{}", pairname, lmp->suffix), 1, nsub); + if (pstyle == nullptr && (lmp->suffix2)) { + pstyle = force->pair_match(fmt::format("{}/{}", pairname, lmp->suffix2), 1, nsub); + } + } + } + if (pstyle == nullptr) pstyle = force->pair_match(pairname, 1, nsub); +} + + /* ---------------------------------------------------------------------- */ FixPair::~FixPair() @@ -184,7 +194,7 @@ void FixPair::init() { // insure pair style still exists - pstyle = force->pair_match(pairname,1,0); + query_pstyle(lmp); if (pstyle == nullptr) error->all(FLERR,"Pair style {} for fix pair not found", pairname); } diff --git a/src/fix_pair.h b/src/fix_pair.h index 765b261ee5..57fbdf8ecb 100644 --- a/src/fix_pair.h +++ b/src/fix_pair.h @@ -56,6 +56,8 @@ class FixPair : public Fix { class Pair *pstyle; double *vector; double **array; + + void query_pstyle(LAMMPS *lmp); }; } // namespace LAMMPS_NS