Merge pull request #2347 from jewettaij/math_eigen
Replace eigensolver code in LAMMPS with math_eigen.h and updated docs
This commit is contained in:
Axel Kohlmeyer
@ -431,6 +431,7 @@ INPUT = @LAMMPS_SOURCE_DIR@/utils.cpp \
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@LAMMPS_SOURCE_DIR@/my_page.h \
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@LAMMPS_SOURCE_DIR@/my_pool_chunk.cpp \
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@LAMMPS_SOURCE_DIR@/my_pool_chunk.h \
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@LAMMPS_SOURCE_DIR@/math_eigen.h \
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# The EXCLUDE_SYMLINKS tag can be used to select whether or not files or
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# directories that are symbolic links (a Unix file system feature) are excluded
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@ -10,7 +10,7 @@ strings into specific types of numbers with checking for validity. This
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reduces redundant implementations and encourages consistent behavior.
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I/O with status check
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^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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^^^^^^^^^^^^^^^^^^^^^
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These are wrappers around the corresponding C library calls like
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``fgets()`` or ``fread()``. They will check if there were errors
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@ -26,6 +26,8 @@ indicating the name of the problematic file, if possible.
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.. doxygenfunction:: sfread
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:project: progguide
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----------
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String to number conversions with validity check
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^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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@ -281,6 +283,8 @@ This code example should produce the following output:
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:project: progguide
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:members: what
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----------
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File reader classes
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====================
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@ -333,6 +337,8 @@ convert numbers, so that LAMMPS will be aborted.
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A file that would be parsed by the reader code fragment looks like this:
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.. parsed-literal::
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# DATE: 2015-02-19 UNITS: metal CONTRIBUTOR: Ray Shan CITATION: Streitz and Mintmire, Phys Rev B, 50, 11996-12003 (1994)
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#
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# X (eV) J (eV) gamma (1/\AA) zeta (1/\AA) Z (e)
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@ -351,7 +357,6 @@ A file that would be parsed by the reader code fragment looks like this:
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:project: progguide
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:members:
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----------
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Memory pool classes
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@ -415,3 +420,43 @@ its size is registered later with :cpp:func:`vgot()
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.. doxygenclass:: LAMMPS_NS::MyPoolChunk
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:project: progguide
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:members:
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----------
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Eigensolver functions
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=====================
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The ``MathEigen`` sub-namespace of the ``LAMMPS_NS`` namespace contains
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functions and classes for eigensolvers. Currently only the
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:cpp:func:`jacobi3 function <MathEigen::jacobi3>` is used in various
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places in LAMMPS. That function is built on top of a group of more
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generic eigensolvers that are maintained in the ``math_eigen_impl.h``
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header file. This header contains the implementation of three template
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classes:
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#. "Jacobi" calculates all of the eigenvalues and eigenvectors
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of a dense, symmetric, real matrix.
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#. The "PEigenDense" class only calculates the principal eigenvalue
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(ie. the largest or smallest eigenvalue), and its corresponding
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eigenvector. However it is much more efficient than "Jacobi" when
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applied to large matrices (larger than 13x13). PEigenDense also can
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understand complex-valued Hermitian matrices.
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#. The "LambdaLanczos" class is a generalization of "PEigenDense" which can be
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applied to arbitrary sparse matrices.
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The "math_eigen_impl.h" code is an amalgamation of `jacobi_pd
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<https://github.com/jewettaij/jacobi_pd>`_ by Andrew Jewett at Scripps
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Research (under CC0-1.0 license) and `Lambda Lanczos
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<https://github.com/mrcdr/lambda-lanczos>`_ by Yuya Kurebayashi at
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Tohoku University (under MIT license)
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----------
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.. doxygenfunction:: MathEigen::jacobi3(double const *const *mat, double *eval, double **evec)
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:project: progguide
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.. doxygenfunction:: MathEigen::jacobi3(double const mat[3][3], double *eval, double evec[3][3])
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:project: progguide
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@ -325,6 +325,7 @@ Buyl
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Bybee
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bz
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cadetblue
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calc
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calibre
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caltech
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Caltech
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@ -397,6 +398,7 @@ ChiralIDs
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chiralIDs
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chirality
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Cho
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ChooseOffset
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chris
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Christoph
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Chu
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@ -469,6 +471,7 @@ config
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configfile
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configurational
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conformational
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ConstMatrix
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Contrib
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cooperativity
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coord
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@ -639,7 +642,10 @@ dhex
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dia
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diag
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diagonalization
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diagonalize
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diagonalized
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diagonalizers
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diagonalizing
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Diallo
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diel
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differentiable
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@ -778,8 +784,15 @@ Eggebrecht
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ehex
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eHEX
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Ei
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Eigen
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Eigensolve
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eigen
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eigensolve
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eigensolver
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eigensolvers
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eigendecomposition
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eigenvalue
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eigenvalues
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eigenvector
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eigenvectors
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eij
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Eij
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Eijnden
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@ -893,6 +906,11 @@ eV
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evalue
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Evanseck
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evdwl
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evector
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evec
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evecs
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eval
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evals
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Everaers
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Evgeny
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evirials
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@ -1069,6 +1087,7 @@ Germann
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Germano
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gerolf
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Gerolf
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Gershgorin
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gettimeofday
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gewald
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Gezelter
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@ -1184,6 +1203,7 @@ Henkelman
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Henkes
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henrich
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Henrich
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Hermitian
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Herrmann
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Hertizian
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hertzian
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@ -1257,6 +1277,7 @@ icosahedral
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idealgas
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IDR
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idx
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ie
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ielement
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ieni
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ifdefs
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@ -1279,6 +1300,7 @@ Imageint
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Imagemagick
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imd
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Impey
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impl
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impropers
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Impropers
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includelink
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@ -1348,6 +1370,8 @@ isothermal
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isotropically
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isovolume
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Isralewitz
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iter
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iters
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iteratively
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Ith
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Itsets
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@ -1524,6 +1548,7 @@ Kub
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Kubo
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Kumagai
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Kumar
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Kurebayashi
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Kuronen
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Kusters
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Kutta
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@ -1534,12 +1559,14 @@ Ladd
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lagrangian
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lambdai
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lamda
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LambdaLanczos
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lammps
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Lammps
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LAMMPS
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lammpsplot
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Lampis
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Lamoureux
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Lanczos
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Lande
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Landron
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langevin
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@ -1847,6 +1874,7 @@ Microscale
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midnightblue
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mie
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Mie
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Mij
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Mikami
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Militzer
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Minary
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@ -1945,6 +1973,7 @@ Muccioli
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mui
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Mukherjee
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Mulders
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mult
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multi
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multibody
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Multibody
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@ -2331,6 +2360,7 @@ peachpuff
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Pearlman
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Pedersen
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peID
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PEigenDense
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Peng
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peptide
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peratom
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@ -2559,6 +2589,8 @@ rdf
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RDideal
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rdx
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reacter
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realTypeMap
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real_t
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README
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realtime
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reamin
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@ -2741,6 +2773,7 @@ Schuring
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Schwen
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screenshot
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screenshots
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Scripps
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Scripta
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sdk
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sdpd
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@ -3069,6 +3102,7 @@ Tmin
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tmp
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tN
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Tobias
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Tohoku
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tokenizer
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tokyo
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tol
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@ -3132,6 +3166,8 @@ tu
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Tuckerman
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tue
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tunable
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tuple
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tuples
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Turkand
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Tutein
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tweakable
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@ -3425,6 +3461,7 @@ Yuh
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yukawa
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Yukawa
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Yusof
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Yuya
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yx
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yy
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yz
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1
src/.gitignore
vendored
1
src/.gitignore
vendored
@ -33,7 +33,6 @@
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/pair_kim.h
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/superpose3d.h
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/math_eigen.h
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/kokkos.cpp
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/kokkos.h
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@ -17,6 +17,7 @@
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#include "atom_vec_body.h"
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#include "error.h"
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#include "math_extra.h"
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#include "math_eigen.h"
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#include "memory.h"
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#include "my_pool_chunk.h"
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@ -136,7 +137,7 @@ void BodyNparticle::data_body(int ibonus, int ninteger, int ndouble,
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double *inertia = bonus->inertia;
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double evectors[3][3];
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int ierror = MathExtra::jacobi(tensor,inertia,evectors);
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int ierror = MathEigen::jacobi3(tensor,inertia,evectors);
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if (ierror) error->one(FLERR,
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"Insufficient Jacobi rotations for body nparticle");
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@ -22,6 +22,7 @@
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#include "domain.h"
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#include "error.h"
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#include "math_extra.h"
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#include "math_eigen.h"
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#include "memory.h"
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#include "my_pool_chunk.h"
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@ -198,7 +199,7 @@ void BodyRoundedPolygon::data_body(int ibonus, int ninteger, int ndouble,
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double *inertia = bonus->inertia;
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double evectors[3][3];
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int ierror = MathExtra::jacobi(tensor,inertia,evectors);
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int ierror = MathEigen::jacobi3(tensor,inertia,evectors);
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if (ierror) error->one(FLERR,
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"Insufficient Jacobi rotations for body nparticle");
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@ -21,6 +21,7 @@
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#include "atom_vec_body.h"
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#include "error.h"
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#include "math_extra.h"
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#include "math_eigen.h"
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#include "memory.h"
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#include "my_pool_chunk.h"
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@ -242,7 +243,7 @@ void BodyRoundedPolyhedron::data_body(int ibonus, int ninteger, int ndouble,
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double *inertia = bonus->inertia;
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double evectors[3][3];
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int ierror = MathExtra::jacobi(tensor,inertia,evectors);
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int ierror = MathEigen::jacobi3(tensor,inertia,evectors);
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if (ierror) error->one(FLERR,
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"Insufficient Jacobi rotations for body nparticle");
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|
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@ -34,8 +34,7 @@
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#include "citeme.h"
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#include "memory.h"
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#include "error.h"
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|
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|
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#include "math_eigen.h"
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using namespace LAMMPS_NS;
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using namespace FixConst;
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@ -44,7 +43,6 @@ using namespace FixConst;
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#define DELTA 128
|
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#define TOLERANCE 1.0e-6
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#define EPSILON 1.0e-7
|
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#define MAXJACOBI 50
|
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|
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static const char cite_fix_poems[] =
|
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"fix poems command:\n\n"
|
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@ -492,7 +490,7 @@ void FixPOEMS::init()
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tensor[1][2] = tensor[2][1] = all[ibody][4];
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tensor[0][2] = tensor[2][0] = all[ibody][5];
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ierror = jacobi(tensor,inertia[ibody],evectors);
|
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ierror = MathEigen::jacobi3(tensor,inertia[ibody],evectors);
|
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if (ierror) error->all(FLERR,"Insufficient Jacobi rotations for POEMS body");
|
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|
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ex_space[ibody][0] = evectors[0][0];
|
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@ -1283,88 +1281,6 @@ int FixPOEMS::loopcheck(int nvert, int nedge, tagint **elist)
|
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return 0;
|
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}
|
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|
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/* ----------------------------------------------------------------------
|
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compute evalues and evectors of 3x3 real symmetric matrix
|
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based on Jacobi rotations
|
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adapted from Numerical Recipes jacobi() function
|
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------------------------------------------------------------------------- */
|
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|
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int FixPOEMS::jacobi(double **matrix, double *evalues, double **evectors)
|
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{
|
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int i,j,k;
|
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double tresh,theta,tau,t,sm,s,h,g,c,b[3],z[3];
|
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|
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for (i = 0; i < 3; i++) {
|
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for (j = 0; j < 3; j++) evectors[i][j] = 0.0;
|
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evectors[i][i] = 1.0;
|
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}
|
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for (i = 0; i < 3; i++) {
|
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b[i] = evalues[i] = matrix[i][i];
|
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z[i] = 0.0;
|
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}
|
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|
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for (int iter = 1; iter <= MAXJACOBI; iter++) {
|
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sm = 0.0;
|
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for (i = 0; i < 2; i++)
|
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for (j = i+1; j < 3; j++)
|
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sm += fabs(matrix[i][j]);
|
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if (sm == 0.0) return 0;
|
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|
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if (iter < 4) tresh = 0.2*sm/(3*3);
|
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else tresh = 0.0;
|
||||
|
||||
for (i = 0; i < 2; i++) {
|
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for (j = i+1; j < 3; j++) {
|
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g = 100.0*fabs(matrix[i][j]);
|
||||
if (iter > 4 && fabs(evalues[i])+g == fabs(evalues[i])
|
||||
&& fabs(evalues[j])+g == fabs(evalues[j]))
|
||||
matrix[i][j] = 0.0;
|
||||
else if (fabs(matrix[i][j]) > tresh) {
|
||||
h = evalues[j]-evalues[i];
|
||||
if (fabs(h)+g == fabs(h)) t = (matrix[i][j])/h;
|
||||
else {
|
||||
theta = 0.5*h/(matrix[i][j]);
|
||||
t = 1.0/(fabs(theta)+sqrt(1.0+theta*theta));
|
||||
if (theta < 0.0) t = -t;
|
||||
}
|
||||
c = 1.0/sqrt(1.0+t*t);
|
||||
s = t*c;
|
||||
tau = s/(1.0+c);
|
||||
h = t*matrix[i][j];
|
||||
z[i] -= h;
|
||||
z[j] += h;
|
||||
evalues[i] -= h;
|
||||
evalues[j] += h;
|
||||
matrix[i][j] = 0.0;
|
||||
for (k = 0; k < i; k++) rotate(matrix,k,i,k,j,s,tau);
|
||||
for (k = i+1; k < j; k++) rotate(matrix,i,k,k,j,s,tau);
|
||||
for (k = j+1; k < 3; k++) rotate(matrix,i,k,j,k,s,tau);
|
||||
for (k = 0; k < 3; k++) rotate(evectors,k,i,k,j,s,tau);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
for (i = 0; i < 3; i++) {
|
||||
evalues[i] = b[i] += z[i];
|
||||
z[i] = 0.0;
|
||||
}
|
||||
}
|
||||
return 1;
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
perform a single Jacobi rotation
|
||||
------------------------------------------------------------------------- */
|
||||
|
||||
void FixPOEMS::rotate(double **matrix, int i, int j, int k, int l,
|
||||
double s, double tau)
|
||||
{
|
||||
double g = matrix[i][j];
|
||||
double h = matrix[k][l];
|
||||
matrix[i][j] = g-s*(h+g*tau);
|
||||
matrix[k][l] = h+s*(g-h*tau);
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
compute omega from angular momentum
|
||||
w = omega = angular velocity in space frame
|
||||
|
||||
@ -106,8 +106,6 @@ class FixPOEMS : public Fix {
|
||||
void jointbuild();
|
||||
void sortlist(int, tagint **);
|
||||
int loopcheck(int, int, tagint **);
|
||||
int jacobi(double **, double *, double **);
|
||||
void rotate(double **, int, int, int, int, double, double);
|
||||
void omega_from_mq(double *, double *, double *, double *,
|
||||
double *, double *);
|
||||
void set_v();
|
||||
|
||||
@ -17,6 +17,7 @@
|
||||
|
||||
#include <cstring>
|
||||
#include "math_extra.h"
|
||||
#include "math_eigen.h"
|
||||
#include "atom.h"
|
||||
#include "atom_vec_ellipsoid.h"
|
||||
#include "atom_vec_line.h"
|
||||
@ -1959,7 +1960,7 @@ void FixRigid::setup_bodies_static()
|
||||
tensor[0][2] = tensor[2][0] = all[ibody][4];
|
||||
tensor[0][1] = tensor[1][0] = all[ibody][5];
|
||||
|
||||
ierror = MathExtra::jacobi(tensor,inertia[ibody],evectors);
|
||||
ierror = MathEigen::jacobi3(tensor,inertia[ibody],evectors);
|
||||
if (ierror) error->all(FLERR,
|
||||
"Insufficient Jacobi rotations for rigid body");
|
||||
|
||||
|
||||
@ -18,6 +18,7 @@
|
||||
#include <cstring>
|
||||
#include <utility>
|
||||
#include "math_extra.h"
|
||||
#include "math_eigen.h"
|
||||
#include "atom.h"
|
||||
#include "atom_vec_ellipsoid.h"
|
||||
#include "atom_vec_line.h"
|
||||
@ -2100,7 +2101,7 @@ void FixRigidSmall::setup_bodies_static()
|
||||
tensor[0][1] = tensor[1][0] = itensor[ibody][5];
|
||||
|
||||
inertia = body[ibody].inertia;
|
||||
ierror = MathExtra::jacobi(tensor,inertia,evectors);
|
||||
ierror = MathEigen::jacobi3(tensor,inertia,evectors);
|
||||
if (ierror) error->all(FLERR,
|
||||
"Insufficient Jacobi rotations for rigid body");
|
||||
|
||||
|
||||
@ -21,6 +21,7 @@
|
||||
#include <cstring>
|
||||
#include "error.h"
|
||||
#include "math_extra.h"
|
||||
#include "math_eigen.h"
|
||||
#include "math_special.h"
|
||||
#include "modify.h"
|
||||
#include "update.h"
|
||||
@ -95,7 +96,7 @@ void ComputeGyrationShape::compute_vector()
|
||||
ione[1][2] = ione[2][1] = gyration_tensor[4];
|
||||
ione[0][2] = ione[2][0] = gyration_tensor[5];
|
||||
|
||||
int ierror = MathExtra::jacobi(ione,evalues,evectors);
|
||||
int ierror = MathEigen::jacobi3(ione,evalues,evectors);
|
||||
if (ierror) error->all(FLERR, "Insufficient Jacobi rotations "
|
||||
"for gyration/shape");
|
||||
|
||||
|
||||
@ -21,6 +21,7 @@
|
||||
#include <cstring>
|
||||
#include "error.h"
|
||||
#include "math_extra.h"
|
||||
#include "math_eigen.h"
|
||||
#include "math_special.h"
|
||||
#include "modify.h"
|
||||
#include "memory.h"
|
||||
@ -125,7 +126,7 @@ void ComputeGyrationShapeChunk::compute_array()
|
||||
ione[0][2] = ione[2][0] = gyration_tensor[ichunk][4];
|
||||
ione[1][2] = ione[2][1] = gyration_tensor[ichunk][5];
|
||||
|
||||
int ierror = MathExtra::jacobi(ione,evalues,evectors);
|
||||
int ierror = MathEigen::jacobi3(ione,evalues,evectors);
|
||||
if (ierror) error->all(FLERR, "Insufficient Jacobi rotations "
|
||||
"for gyration/shape");
|
||||
|
||||
|
||||
@ -22,10 +22,10 @@
|
||||
/// @author Andrew Jewett
|
||||
/// @license MIT
|
||||
|
||||
#ifndef _SUPERPOSE3D_H
|
||||
#define _SUPERPOSE3D_H
|
||||
#ifndef LMP_SUPERPOSE3D_H
|
||||
#define LMP_SUPERPOSE3D_H
|
||||
|
||||
#include "math_eigen.h" //functions to calculate eigenvalues and eigenvectors
|
||||
#include "math_eigen_impl.h" //functions to calculate eigenvalues and eigenvectors
|
||||
|
||||
// -----------------------------------------------------------
|
||||
// ------------------------ INTERFACE ------------------------
|
||||
@ -144,11 +144,6 @@ Superpose(ConstArrayOfCoords aaXf, // coords for the "frozen" object
|
||||
ConstArrayOfCoords aaXm, // coords for the "mobile" object
|
||||
bool allow_rescale) // rescale mobile object? (c!=1?)
|
||||
{
|
||||
assert(aaXf && aaXm);
|
||||
assert(aaXf_shifted && aaXm_shifted);
|
||||
assert(aWeights);
|
||||
assert(R && T);
|
||||
|
||||
// Find the center of mass of each object:
|
||||
Scalar aCenter_f[3] = {0.0, 0.0, 0.0};
|
||||
Scalar aCenter_m[3] = {0.0, 0.0, 0.0};
|
||||
@ -161,7 +156,9 @@ Superpose(ConstArrayOfCoords aaXf, // coords for the "frozen" object
|
||||
}
|
||||
sum_weights += weight;
|
||||
}
|
||||
assert(sum_weights != 0.0);
|
||||
|
||||
//assert(sum_weights != 0.0);
|
||||
|
||||
for (int d=0; d < 3; d++) {
|
||||
aCenter_f[d] /= sum_weights;
|
||||
aCenter_m[d] /= sum_weights;
|
||||
@ -425,7 +422,9 @@ Superpose3D(const Superpose3D<Scalar, ConstArrayOfCoords, ConstArray>& source)
|
||||
{
|
||||
Init();
|
||||
Alloc(source.N);
|
||||
assert(N == source.N);
|
||||
|
||||
//assert(N == source.N);
|
||||
|
||||
for (int i = 0; i < N; i++) {
|
||||
std::copy(source.aaXf_shifted[i],
|
||||
source.aaXf_shifted[i] + 3,
|
||||
@ -463,4 +462,4 @@ operator = (Superpose3D<Scalar, ConstArrayOfCoords, ConstArray> source) {
|
||||
}
|
||||
|
||||
|
||||
#endif //#ifndef _SUPERPOSE3D_H
|
||||
#endif //#ifndef LMP_SUPERPOSE3D_H
|
||||
|
||||
@ -19,6 +19,7 @@
|
||||
#include "fix.h"
|
||||
#include "math_const.h"
|
||||
#include "math_extra.h"
|
||||
#include "math_eigen.h"
|
||||
#include "memory.h"
|
||||
#include "modify.h"
|
||||
|
||||
@ -555,7 +556,7 @@ void AtomVecTri::data_atom_bonus(int m, char **values)
|
||||
tensor[0][2] = tensor[2][0] = inertia[4];
|
||||
tensor[0][1] = tensor[1][0] = inertia[5];
|
||||
|
||||
int ierror = MathExtra::jacobi(tensor,bonus[nlocal_bonus].inertia,evectors);
|
||||
int ierror = MathEigen::jacobi3(tensor,bonus[nlocal_bonus].inertia,evectors);
|
||||
if (ierror) error->one(FLERR,"Insufficient Jacobi rotations for triangle");
|
||||
|
||||
double ex_space[3],ey_space[3],ez_space[3];
|
||||
|
||||
@ -20,6 +20,7 @@
|
||||
#include "compute_chunk_atom.h"
|
||||
#include "domain.h"
|
||||
#include "math_extra.h"
|
||||
#include "math_eigen.h"
|
||||
#include "memory.h"
|
||||
#include "error.h"
|
||||
|
||||
@ -250,10 +251,10 @@ void ComputeOmegaChunk::compute_array()
|
||||
|
||||
// handle each (nearly) singular I matrix
|
||||
// due to 2-atom chunk or linear molecule
|
||||
// use jacobi() and angmom_to_omega() to calculate valid omega
|
||||
// use jacobi3() and angmom_to_omega() to calculate valid omega
|
||||
|
||||
} else {
|
||||
int ierror = MathExtra::jacobi(ione,idiag,evectors);
|
||||
int ierror = MathEigen::jacobi3(ione,idiag,evectors);
|
||||
if (ierror) error->all(FLERR,
|
||||
"Insufficient Jacobi rotations for omega/chunk");
|
||||
|
||||
|
||||
@ -23,6 +23,7 @@
|
||||
#include "force.h"
|
||||
#include "input.h"
|
||||
#include "math_extra.h"
|
||||
#include "math_eigen.h"
|
||||
#include "memory.h"
|
||||
#include "modify.h"
|
||||
#include "output.h"
|
||||
@ -1727,11 +1728,11 @@ void Group::omega(double *angmom, double inertia[3][3], double *w)
|
||||
|
||||
// handle (nearly) singular I matrix
|
||||
// typically due to 2-atom group or linear molecule
|
||||
// use jacobi() and angmom_to_omega() to calculate valid omega
|
||||
// use jacobi3() and angmom_to_omega() to calculate valid omega
|
||||
// less exact answer than matrix inversion, due to iterative Jacobi method
|
||||
|
||||
} else {
|
||||
int ierror = MathExtra::jacobi(inertia,idiag,evectors);
|
||||
int ierror = MathEigen::jacobi3(inertia, idiag, evectors);
|
||||
if (ierror) error->all(FLERR,
|
||||
"Insufficient Jacobi rotations for group::omega");
|
||||
|
||||
|
||||
78
src/math_eigen.cpp
Normal file
78
src/math_eigen.cpp
Normal file
@ -0,0 +1,78 @@
|
||||
/* ----------------------------------------------------------------------
|
||||
LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
|
||||
http://lammps.sandia.gov, Sandia National Laboratories
|
||||
Steve Plimpton, sjplimp@sandia.gov
|
||||
|
||||
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 author: Andrew Jewett (Scripps Research)
|
||||
------------------------------------------------------------------------- */
|
||||
|
||||
#include "math_eigen.h"
|
||||
#include "math_eigen_impl.h"
|
||||
|
||||
#include<array>
|
||||
|
||||
using std::vector;
|
||||
using std::array;
|
||||
using namespace MathEigen;
|
||||
|
||||
// Special case: 3x3 matrices
|
||||
|
||||
typedef Jacobi<double,double*,double(*)[3],double const(*)[3]> Jacobi_v1;
|
||||
typedef Jacobi<double,double*,double**,double const*const*> Jacobi_v2;
|
||||
|
||||
int MathEigen::jacobi3(double const mat[3][3], double *eval, double evec[3][3])
|
||||
{
|
||||
// make copy of const matrix
|
||||
|
||||
double mat_cpy[3][3] = { {mat[0][0], mat[0][1], mat[0][2]},
|
||||
{mat[1][0], mat[1][1], mat[1][2]},
|
||||
{mat[2][0], mat[2][1], mat[2][2]} };
|
||||
double *M[3] = { &(mat_cpy[0][0]), &(mat_cpy[1][0]), &(mat_cpy[2][0]) };
|
||||
int midx[3];
|
||||
|
||||
// create instance of generic Jacobi class and get eigenvalues and -vectors
|
||||
|
||||
Jacobi_v1 ecalc3(3, M, midx);
|
||||
int ierror = ecalc3.Diagonalize(mat, eval, evec, Jacobi_v1::SORT_DECREASING_EVALS);
|
||||
|
||||
// transpose the evec matrix
|
||||
|
||||
for (int i=0; i<3; i++)
|
||||
for (int j=i+1; j<3; j++)
|
||||
std::swap(evec[i][j], evec[j][i]);
|
||||
|
||||
return ierror;
|
||||
}
|
||||
|
||||
int MathEigen::jacobi3(double const* const* mat, double *eval, double **evec)
|
||||
{
|
||||
// make copy of const matrix
|
||||
|
||||
double mat_cpy[3][3] = { {mat[0][0], mat[0][1], mat[0][2]},
|
||||
{mat[1][0], mat[1][1], mat[1][2]},
|
||||
{mat[2][0], mat[2][1], mat[2][2]} };
|
||||
double *M[3] = { &(mat_cpy[0][0]), &(mat_cpy[1][0]), &(mat_cpy[2][0]) };
|
||||
int midx[3];
|
||||
|
||||
// create instance of generic Jacobi class and get eigenvalues and -vectors
|
||||
|
||||
Jacobi_v2 ecalc3(3, M, midx);
|
||||
int ierror = ecalc3.Diagonalize(mat, eval, evec, Jacobi_v2::SORT_DECREASING_EVALS);
|
||||
|
||||
// transpose the evec matrix
|
||||
|
||||
for (int i=0; i<3; i++)
|
||||
for (int j=i+1; j<3; j++)
|
||||
std::swap(evec[i][j], evec[j][i]);
|
||||
|
||||
return ierror;
|
||||
}
|
||||
36
src/math_eigen.h
Normal file
36
src/math_eigen.h
Normal file
@ -0,0 +1,36 @@
|
||||
/* -*- c++ -*- ----------------------------------------------------------
|
||||
LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
|
||||
http://lammps.sandia.gov, Sandia National Laboratories
|
||||
Steve Plimpton, sjplimp@sandia.gov
|
||||
|
||||
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.
|
||||
------------------------------------------------------------------------- */
|
||||
|
||||
|
||||
#ifndef LMP_MATH_EIGEN_H
|
||||
#define LMP_MATH_EIGEN_H
|
||||
|
||||
namespace MathEigen {
|
||||
|
||||
/** A specialized function which finds the eigenvalues and eigenvectors
|
||||
* of a 3x3 matrix (in double ** format).
|
||||
*
|
||||
* \param mat the 3x3 matrix you wish to diagonalize
|
||||
* \param eval store the eigenvalues here
|
||||
* \param evec store the eigenvectors here...
|
||||
* \return 0 if eigenvalue calculation converged, 1 if it failed */
|
||||
|
||||
int jacobi3(double const* const* mat, double *eval, double **evec);
|
||||
|
||||
/** \overload */
|
||||
|
||||
int jacobi3(double const mat[3][3], double *eval, double evec[3][3]);
|
||||
|
||||
}
|
||||
|
||||
#endif //#ifndef LMP_MATH_EIGEN_H
|
||||
@ -16,31 +16,31 @@
|
||||
Andrew Jewett (Scripps Research, Jacobi algorithm)
|
||||
------------------------------------------------------------------------- */
|
||||
|
||||
#ifndef _MATH_EIGEN_H
|
||||
#define _MATH_EIGEN_H
|
||||
#ifndef LMP_MATH_EIGEN_IMPL_H
|
||||
#define LMP_MATH_EIGEN_IMPL_H
|
||||
|
||||
/// @file This file contains a library of functions and classes which can
|
||||
/// efficiently perform eigendecomposition for an extremely broad
|
||||
/// range of matrix types: both real and complex, dense and sparse.
|
||||
/// Matrices need not be of type "double **", for example.
|
||||
/// In principle, almost any type of C++ container can be used.
|
||||
/// Some general C++11 compatible functions for allocating matrices and
|
||||
/// calculating norms of real and complex vectors are also provided.
|
||||
/// @note
|
||||
/// The "Jacobi" and "PEigenDense" classes are used for calculating
|
||||
/// eigenvalues and eigenvectors of conventional dense square matrices.
|
||||
/// @note
|
||||
/// The "LambdaLanczos" class can calculate eigenalues and eigenvectors
|
||||
/// of more general types of matrices, especially large, sparse matrices.
|
||||
/// It uses C++ lambda expressions to simplify and generalize the way
|
||||
/// matrices can be represented. This allows it to be applied to
|
||||
/// nearly any kind of sparse (or dense) matrix representation.
|
||||
/// @note
|
||||
/// The source code for Jacobi and LambdaLanczos is also available at:
|
||||
/// https://github.com/jewettaij/jacobi_pd (CC0-1.0 license)
|
||||
/// https://github.com/mrcdr/lambda-lanczos (MIT license)
|
||||
// This file contains a library of functions and classes which can
|
||||
// efficiently perform eigendecomposition for an extremely broad
|
||||
// range of matrix types: both real and complex, dense and sparse.
|
||||
// Matrices need not be of type "double **", for example.
|
||||
// In principle, almost any type of C++ container can be used.
|
||||
// Some general C++11 compatible functions for allocating matrices and
|
||||
// calculating norms of real and complex vectors are also provided.
|
||||
// note
|
||||
// The "Jacobi" and "PEigenDense" classes are used for calculating
|
||||
// eigenvalues and eigenvectors of conventional dense square matrices.
|
||||
// note
|
||||
// The "LambdaLanczos" class can calculate eigenalues and eigenvectors
|
||||
// of more general types of matrices, especially large, sparse matrices.
|
||||
// It uses C++ lambda expressions to simplify and generalize the way
|
||||
// matrices can be represented. This allows it to be applied to
|
||||
// nearly any kind of sparse (or dense) matrix representation.
|
||||
// note
|
||||
// The source code for Jacobi and LambdaLanczos is also available at:
|
||||
// https://github.com/jewettaij/jacobi_pd (CC0-1.0 license)
|
||||
// https://github.com/mrcdr/lambda-lanczos (MIT license)
|
||||
|
||||
#include <cassert>
|
||||
//#include <cassert>
|
||||
#include <numeric>
|
||||
#include <complex>
|
||||
#include <limits>
|
||||
@ -53,34 +53,37 @@ namespace MathEigen {
|
||||
|
||||
// --- Memory allocation for matrices ---
|
||||
|
||||
/// @brief Allocate an arbitrary 2-dimensional array. (Uses row-major order.)
|
||||
/// @note This function was intended for relatively small matrices (eg 4x4).
|
||||
/// For large arrays, please use the 2d create() function from "memory.h"
|
||||
// Allocate an arbitrary 2-dimensional array. (Uses row-major order.)
|
||||
// note This function was intended for relatively small matrices (eg 4x4).
|
||||
// For large arrays, please use the 2d create() function from "memory.h"
|
||||
template<typename Entry>
|
||||
void Alloc2D(size_t nrows, //!< size of the array (number of rows)
|
||||
size_t ncols, //!< size of the array (number of columns)
|
||||
Entry ***paaX); //!< pointer to a 2D C-style array
|
||||
void Alloc2D(size_t nrows, // size of the array (number of rows)
|
||||
size_t ncols, // size of the array (number of columns)
|
||||
Entry ***paaX); // pointer to a 2D C-style array
|
||||
|
||||
/// @brief Deallocate arrays that were created using Alloc2D().
|
||||
// Deallocate arrays that were created using Alloc2D().
|
||||
template<typename Entry>
|
||||
void Dealloc2D(Entry ***paaX); //!< pointer to 2D multidimensional array
|
||||
void Dealloc2D(Entry ***paaX); // pointer to 2D multidimensional array
|
||||
|
||||
// --- Complex numbers ---
|
||||
|
||||
/// @brief "realTypeMap" struct is used to the define "real_t<T>" type mapper
|
||||
/// which returns the C++ type corresponding to the real component of T.
|
||||
/// @details Consider a function ("l2_norm()") that calculates the
|
||||
/// (Euclidian) length of a vector of numbers (either real or complex):
|
||||
/// @code
|
||||
/// template <typename T> real_t<T> l2_norm(const std::vector<T>& vec);
|
||||
/// @endcode
|
||||
/// The l2_norm is always real by definition.
|
||||
/// (See https://en.wikipedia.org/wiki/Norm_(mathematics)#Euclidean_norm)
|
||||
/// The return type of this function ("real_t<T>") indicates that
|
||||
/// it returns a real number, even if the entries (of type T)
|
||||
/// are complex numbers. In other words, by default, real_t<T> returns T.
|
||||
/// However real_t<std::complex<T>> returns T (not std::complex<T>).
|
||||
/// We define "real_t<T>" below using C++ template specializations:
|
||||
/// @brief
|
||||
/// "realTypeMap" struct is used to the define "real_t<T>" type mapper.
|
||||
/// The "real_t" type mapper is used by the "LambdaLanczos" and "PEigenDense"
|
||||
/// classes, so it is documented here to help users understand those classes.
|
||||
/// "real_t<T>" returns the C++ type corresponding to the real component of T.
|
||||
///
|
||||
/// @details
|
||||
/// For example, suppose you have a matrix of type std::complex<double>**.
|
||||
/// The eigenvalues calculated by "LambdaLanczos" and "PEigenDense" should be
|
||||
/// of type "double" (which is the same as "real_T<std::complex<double>>"),
|
||||
/// not "std::complex<double>". (This is because the algorithm assumes the
|
||||
/// matrix is Hermitian, and the eigenvalues of a Hermitian matrix are always
|
||||
/// real. So if you attempt to pass a reference to a complex number as the
|
||||
/// first argument to LambdaLanczos::run(), the compiler will complain.)
|
||||
///
|
||||
/// Implementation details: "real_t<T>" is defined using C++ template
|
||||
/// specializations.
|
||||
|
||||
template <typename T>
|
||||
struct realTypeMap {
|
||||
@ -96,65 +99,38 @@ using real_t = typename realTypeMap<T>::type;
|
||||
|
||||
// --- Operations on vectors (of real and complex numbers) ---
|
||||
|
||||
/// @brief Calculate the inner product of two vectors.
|
||||
/// (For vectors of complex numbers, std::conj() is used.)
|
||||
// Calculate the inner product of two vectors.
|
||||
// (For vectors of complex numbers, std::conj() is used.)
|
||||
template <typename T>
|
||||
T inner_prod(const std::vector<T>& v1, const std::vector<T>& v2);
|
||||
|
||||
/// @brief Compute the sum of the absolute values of the entries in v
|
||||
/// @returns a real number (of type real_t<T>).
|
||||
// Compute the sum of the absolute values of the entries in v
|
||||
// returns a real number (of type real_t<T>).
|
||||
template <typename T>
|
||||
real_t<T> l1_norm(const std::vector<T>& v);
|
||||
|
||||
/// @brief Calculate the l2_norm (Euclidian length) of vector v.
|
||||
/// @returns a real number (of type real_t<T>).
|
||||
// Calculate the l2_norm (Euclidian length) of vector v.
|
||||
// returns a real number (of type real_t<T>).
|
||||
template <typename T>
|
||||
real_t<T> l2_norm(const std::vector<T>& v);
|
||||
|
||||
/// @brief Multiply a vector (v) by a scalar (c).
|
||||
/// Multiply a vector (v) by a scalar (c).
|
||||
template <typename T1, typename T2>
|
||||
void scalar_mul(T1 c, std::vector<T2>& v);
|
||||
|
||||
/// @brief Divide vector "v" in-place by it's length (l2_norm(v)).
|
||||
/// Divide vector "v" in-place by it's length (l2_norm(v)).
|
||||
template <typename T>
|
||||
void normalize(std::vector<T>& v);
|
||||
|
||||
|
||||
// ---- Eigendecomposition of small dense symmetric matrices ----
|
||||
|
||||
/// @class Jacobi
|
||||
/// @brief Calculate the eigenvalues and eigevectors of a symmetric matrix
|
||||
/// using the Jacobi eigenvalue algorithm. Code for the Jacobi class
|
||||
/// (along with tests and benchmarks) is available free of copyright at
|
||||
/// @brief Calculate the eigenvalues and eigenvectors of a symmetric matrix
|
||||
/// using the Jacobi eigenvalue algorithm. This code (along with tests
|
||||
/// and benchmarks) is available free of license restrictions at:
|
||||
/// https://github.com/jewettaij/jacobi_pd
|
||||
/// @note The "Vector" and "Matrix" type arguments can be any
|
||||
/// C or C++ object that support indexing, including pointers or vectors.
|
||||
/// @details
|
||||
/// -- Example: --
|
||||
///
|
||||
/// int n = 5; // Matrix size
|
||||
/// double **M; // A symmetric n x n matrix you want to diagonalize
|
||||
/// double *evals; // Store the eigenvalues here.
|
||||
/// double **evects; // Store the eigenvectors here.
|
||||
/// // Allocate space for M, evals, and evects, and load contents of M (omitted)
|
||||
///
|
||||
/// // Now create an instance of Jacobi ("eigen_calc"). This will allocate space
|
||||
/// // for storing intermediate calculations. Once created, it can be reused
|
||||
/// // multiple times without paying the cost of allocating memory on the heap.
|
||||
///
|
||||
/// Jacobi<double, double*, double**> eigen_calc(n);
|
||||
///
|
||||
/// // Note:
|
||||
/// // If the matrix you plan to diagonalize (M) is read-only, use this instead:
|
||||
/// // Jacobi<double, double*, double**, double const*const*> eigen_calc(n);
|
||||
/// // If you prefer using vectors over C-style pointers, this works also:
|
||||
/// // Jacobi<double, vector<double>&, vector<vector<double>>&> eigen_calc(n);
|
||||
///
|
||||
/// // Now, calculate the eigenvalues and eigenvectors of M
|
||||
///
|
||||
/// eigen_calc.Diagonalize(M, evals, evects);
|
||||
///
|
||||
/// --- end of example ---
|
||||
/// @note The "Vector", "Matrix", and "ConstMatrix" type arguments can be any
|
||||
/// C or C++ object that supports indexing, including pointers or vectors.
|
||||
|
||||
template<typename Scalar,
|
||||
typename Vector,
|
||||
@ -172,15 +148,16 @@ class Jacobi
|
||||
int *max_idx_row; //!< = keep track of the the maximum element in row i (>i)
|
||||
|
||||
public:
|
||||
|
||||
/// @brief Specify the size of the matrices you want to diagonalize later.
|
||||
/// @param n the size (ie. number of rows) of the (square) matrix.
|
||||
Jacobi(int n);
|
||||
|
||||
~Jacobi();
|
||||
|
||||
/// @brief Change the size of the matrices you want to diagonalize.
|
||||
/// @param n the size (ie. number of rows) of the (square) matrix.
|
||||
void SetSize(int n);
|
||||
|
||||
Jacobi(int n = 0) { Init(); SetSize(n); }
|
||||
|
||||
~Jacobi() { Dealloc(); }
|
||||
|
||||
// @typedef choose the criteria for sorting eigenvalues and eigenvectors
|
||||
typedef enum eSortCriteria {
|
||||
DO_NOT_SORT,
|
||||
@ -190,10 +167,12 @@ public:
|
||||
SORT_INCREASING_ABS_EVALS
|
||||
} SortCriteria;
|
||||
|
||||
/// @brief Calculate the eigenvalues and eigevectors of a symmetric matrix
|
||||
/// @brief Calculate the eigenvalues and eigenvectors of a symmetric matrix
|
||||
/// using the Jacobi eigenvalue algorithm.
|
||||
/// @returns The number_of_sweeps (= number_of_iterations / (n*(n-1)/2)).
|
||||
/// If this equals max_num_sweeps, the algorithm failed to converge.
|
||||
/// @returns 0 if the algorithm converged,
|
||||
/// 1 if the algorithm failed to converge. (IE, if the number of
|
||||
/// pivot iterations exceeded max_num_sweeps * iters_per_sweep,
|
||||
/// where iters_per_sweep = (n*(n-1)/2))
|
||||
/// @note To reduce the computation time further, set calc_evecs=false.
|
||||
int
|
||||
Diagonalize(ConstMatrix mat, //!< the matrix you wish to diagonalize (size n)
|
||||
@ -201,10 +180,28 @@ public:
|
||||
Matrix evec, //!< store the eigenvectors here (in rows)
|
||||
SortCriteria sort_criteria=SORT_DECREASING_EVALS,//!<sort results?
|
||||
bool calc_evecs=true, //!< calculate the eigenvectors?
|
||||
int max_num_sweeps = 50); //!< limit the number of iterations
|
||||
int max_num_sweeps=50 //!< limit the number of iterations
|
||||
);
|
||||
|
||||
// An alternative constructor is provided, if, for some reason,
|
||||
// you want to avoid allocating memory on the heap during
|
||||
// initialization. In that case, you can allocate space for the "M"
|
||||
// and "max_idx_row" arrays on the stack in advance, and pass them
|
||||
// to the constructor. (The vast majority of users probably
|
||||
// do not need this feature. Unless you do, I encourage you
|
||||
// to use the regular constructor instead.)
|
||||
// n the size (ie. number of rows) of the (square) matrix.
|
||||
// M optional preallocated n x n array
|
||||
// max_idx_row optional preallocated array of size n
|
||||
// note If either the "M" or "max_idx_row" arguments are specified,
|
||||
// they both must be specified.
|
||||
Jacobi(int n, Scalar **M, int *max_idx_row);
|
||||
|
||||
private:
|
||||
bool is_preallocated;
|
||||
|
||||
// (Descriptions of private functions can be found in their implementation.)
|
||||
void _Jacobi(int n, Scalar **M, int *max_idx_row);
|
||||
void CalcRot(Scalar const *const *M, int i, int j);
|
||||
void ApplyRot(Scalar **M, int i, int j);
|
||||
void ApplyRotLeft(Matrix E, int i, int j);
|
||||
@ -223,19 +220,15 @@ public:
|
||||
|
||||
}; // class Jacobi
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
// ---- Eigendecomposition of large sparse (and dense) matrices ----
|
||||
// ---- Eigendecomposition of large sparse (or dense) matrices ----
|
||||
|
||||
// The "LambdaLanczos" is a class useful for calculating eigenvalues
|
||||
// and eigenvectors of large sparse matrices. Unfortunately, before the
|
||||
// LambdaLanczos class can be declared, several additional expressions,
|
||||
// classes and functions that it depends on must be declared first.
|
||||
|
||||
// @brief Create random vectors used at the beginning of the Lanczos algorithm.
|
||||
// @note "Partially specialization of function" is not allowed, so
|
||||
// Create random vectors used at the beginning of the Lanczos algorithm.
|
||||
// note "Partially specialization of function" is not allowed, so
|
||||
// it is mimicked by wrapping the "init" function with a class template.
|
||||
template <typename T>
|
||||
struct VectorRandomInitializer {
|
||||
@ -249,64 +242,28 @@ public:
|
||||
static void init(std::vector<std::complex<T>>&);
|
||||
};
|
||||
|
||||
/// @brief Return the number of significant decimal digits of type T.
|
||||
// Return the number of significant decimal digits of type T.
|
||||
template <typename T>
|
||||
inline constexpr int sig_decimal_digit() {
|
||||
return (int)(std::numeric_limits<T>::digits *
|
||||
std::log10(std::numeric_limits<T>::radix));
|
||||
}
|
||||
|
||||
/// @brief Return 10^-n where n=number of significant decimal digits of type T.
|
||||
// Return 10^-n where n=number of significant decimal digits of type T.
|
||||
template <typename T>
|
||||
inline constexpr T minimum_effective_decimal() {
|
||||
return std::pow(10, -sig_decimal_digit<T>());
|
||||
}
|
||||
|
||||
|
||||
/// @class LambdaLanczos
|
||||
/// @brief The LambdaLanczos class provides a general way to calculate
|
||||
/// the smallest or largest eigenvalue and the corresponding eigenvector
|
||||
/// of a symmetric (Hermitian) matrix using the Lanczos algorithm.
|
||||
/// of a Hermitian matrix using the Lanczos algorithm.
|
||||
/// The characteristic feature of LambdaLanczos is that the matrix-vector
|
||||
/// multiplication routine used in the Lanczos algorithm is adaptable.
|
||||
/// @details
|
||||
/// @code
|
||||
///
|
||||
/// //Example:
|
||||
/// const int n = 3;
|
||||
/// double M[n][n] = { {-1.0, -1.0, 1.0},
|
||||
/// {-1.0, 1.0, 1.0},
|
||||
/// { 1.0, 1.0, 1.0} };
|
||||
/// // (Its eigenvalues are {-2, 1, 2})
|
||||
///
|
||||
/// // Specify the matrix-vector multiplication function
|
||||
/// auto mv_mul = [&](const vector<double>& in, vector<double>& out) {
|
||||
/// for(int i = 0;i < n;i++) {
|
||||
/// for(int j = 0;j < n;j++) {
|
||||
/// out[i] += M[i][j]*in[j];
|
||||
/// }
|
||||
/// }
|
||||
/// };
|
||||
///
|
||||
/// LambdaLanczos<double> engine(mv_mul, n, true);
|
||||
/// // ("true" means to calculate the largest eigenvalue.)
|
||||
/// engine.eigenvalue_offset = 3.0 # = max_i{Σ_j|Mij|} (see below)
|
||||
/// double eigenvalue;
|
||||
/// vector<double> eigenvector(n);
|
||||
/// int itern = engine.run(eigenvalue, eigenvector);
|
||||
///
|
||||
/// cout << "Iteration count: " << itern << endl;
|
||||
/// cout << "Eigen value: " << setprecision(16) << eigenvalue << endl;
|
||||
/// cout << "Eigen vector:";
|
||||
/// for(int i = 0; i < n; i++) {
|
||||
/// cout << eigenvector[i] << " ";
|
||||
/// }
|
||||
/// cout << endl;
|
||||
///
|
||||
/// @endcode
|
||||
/// This feature allows you to use a matrix whose elements are partially given,
|
||||
/// e.g. a sparse matrix whose non-zero elements are stored as a list of
|
||||
/// {row-index, column-index, value} tuples. You can also easily combine
|
||||
/// LambdaLanczos with existing matrix libraries (e.g. Eigen)
|
||||
/// This code (along with automatic unit tests) is also distributed
|
||||
/// under the MIT license at https://github.com/mrcdr/lambda-lanczos
|
||||
///
|
||||
/// @note
|
||||
/// If the matrices you want to analyze are ordinary square matrices, (as in
|
||||
@ -315,29 +272,8 @@ inline constexpr T minimum_effective_decimal() {
|
||||
///
|
||||
/// @note
|
||||
/// IMPORTANT:
|
||||
/// The Lanczos algorithm finds the largest magnitude eigenvalue, so you
|
||||
/// MUST ensure that the eigenvalue you are seeking has the largest magnitude
|
||||
/// (regardless of whether it is the maximum or minimum eigenvalue).
|
||||
/// To insure that this is so, you can add or subtract a number to all
|
||||
/// of the eigenvalues of the matrix by specifying the "eigenvalue_offset".
|
||||
/// This number should exceed the largest magnitude eigenvalue of the matrix.
|
||||
/// According to the Gershgorin theorem, you can estimate this number using
|
||||
/// r = max_i{Σ_j|Mij|} = max_j{Σ_i|Mij|}
|
||||
/// (where Mij are the elements of the matrix and Σ_j denotes the sum over j).
|
||||
/// If find_maximum == true (if you are seeking the maximum eigenvalue), then
|
||||
/// eigenvalue_offset = +r
|
||||
/// If find_maximum == false, then
|
||||
/// eigenvalue_offset = -r
|
||||
/// The eigenvalue_offset MUST be specified by the user. LambdaLanczos does
|
||||
/// not have an efficient and general way to access the elements of the matrix.
|
||||
///
|
||||
/// (You can omit this step if you are seeking the maximum eigenvalue,
|
||||
/// and the matrix is positive definite, or if you are seeking the minimum
|
||||
/// eigenvalue and the matrix is negative definite.)
|
||||
///
|
||||
/// @note
|
||||
/// LambdaLanczos is available under the MIT license and downloadable at:
|
||||
/// https://github.com/mrcdr/lambda-lanczos
|
||||
/// Unless the matrix you are solving is positive or negative definite, you
|
||||
/// MUST set the "eigenvalue_offset" parameter. See the "pg_developer" docs.
|
||||
|
||||
template <typename T>
|
||||
class LambdaLanczos {
|
||||
@ -370,11 +306,10 @@ public:
|
||||
/// iteration (ie. during LambdaLanczos::run()). The goal is to insure
|
||||
/// that the correct eigenvalue is selected (the one with the maximum
|
||||
/// magnitude).
|
||||
/// @note The eigevalue returned by LambdaLanczos::run() is not effected
|
||||
/// because after the iteration is finished, it will subtract this
|
||||
/// @note Unless your matrix is positive definite or negative definite, you
|
||||
/// MUST specify eigenvalue_offset. See comment above for details.
|
||||
/// @note After LambdaLanczos::run() has finished, it will subtract this
|
||||
/// number from the eigenvalue before it is returned to the caller.
|
||||
/// @note Unless your matrix is positive definite or negative definite,
|
||||
/// you MUST specify eigenvalue_offset. See comment above for details.
|
||||
real_t<T> eigenvalue_offset = 0.0;
|
||||
|
||||
/// @brief This function sets "eigenvalue_offset" automatically.
|
||||
@ -390,7 +325,7 @@ public:
|
||||
std::function<void(std::vector<T>&)> init_vector =
|
||||
VectorRandomInitializer<T>::init;
|
||||
|
||||
// (for those who prefer "Set" functions...)
|
||||
// (for those who prefer using "Set" functions...)
|
||||
int SetSize(int matrix_size);
|
||||
void SetMul(std::function<void(const std::vector<T>&,
|
||||
std::vector<T>&)> mv_mul);
|
||||
@ -416,17 +351,17 @@ private:
|
||||
|
||||
|
||||
|
||||
/// @class PEigenDense
|
||||
/// @brief
|
||||
/// PEigenDense is a class containing only one useful member function:
|
||||
/// PrincipalEigen(). This function calculates the principal (largest
|
||||
/// or smallest) eigenvalue and corresponding eigenvector of a square
|
||||
/// n x n matrix. This can be faster than diagionalizing the entire matrix.
|
||||
/// (For example by using the Lanczos algorithm or something similar.)
|
||||
/// n x n matrix. This can be faster than diagonalizing the entire matrix.
|
||||
/// @note
|
||||
/// This code is a wrapper. Internally, it uses the "LambdaLanczos" class.
|
||||
/// @note
|
||||
/// For matrices larger than 13x13, PEigenDense::PrincipleEigen()
|
||||
/// is usually faster than Jacobi::Diagonalize().)
|
||||
/// For dense matrices smaller than 13x13, Jacobi::Diagonalize(),
|
||||
/// is usually faster than PEigenDense::PrincipleEigen().
|
||||
|
||||
template<typename Scalar, typename Vector, typename ConstMatrix>
|
||||
class PEigenDense
|
||||
@ -435,23 +370,18 @@ class PEigenDense
|
||||
std::vector<Scalar> evec; // preallocated vector
|
||||
|
||||
public:
|
||||
void SetSize(int matrix_size) {
|
||||
n = matrix_size;
|
||||
evec.resize(n);
|
||||
}
|
||||
|
||||
PEigenDense(int matrix_size=0):evec(matrix_size) {
|
||||
SetSize(matrix_size);
|
||||
}
|
||||
PEigenDense(int matrix_size=0);
|
||||
|
||||
/// @brief Calculate the principal eigenvalue and eigenvector of a matrix.
|
||||
/// @return Return the principal eigenvalue of the matrix.
|
||||
/// If you want the eigenvector, pass a non-null "evector" argument.
|
||||
Scalar
|
||||
PrincipalEigen(ConstMatrix matrix, //!< the input patrix
|
||||
real_t<Scalar>
|
||||
PrincipalEigen(ConstMatrix matrix, //!< the input matrix
|
||||
Vector evector, //!< the eigenvector is stored here
|
||||
bool find_max=false); //!< want the max or min eigenvalue?
|
||||
|
||||
void SetSize(int matrix_size); //change matrix size after instantiation
|
||||
|
||||
}; // class PEigenDense
|
||||
|
||||
|
||||
@ -460,16 +390,13 @@ public:
|
||||
// ----------- IMPLEMENTATION -----------
|
||||
// --------------------------------------
|
||||
|
||||
|
||||
|
||||
|
||||
// --- Implementation: Memory allocation for matrices ---
|
||||
template<typename Entry>
|
||||
void Alloc2D(size_t nrows, // size of the array (number of rows)
|
||||
size_t ncols, // size of the array (number of columns)
|
||||
Entry ***paaX) // pointer to a 2D C-style array
|
||||
{
|
||||
assert(paaX);
|
||||
//assert(paaX);
|
||||
*paaX = new Entry* [nrows]; //conventional 2D C array (pointer-to-pointer)
|
||||
(*paaX)[0] = new Entry [nrows * ncols]; // 1D C array (contiguous memor)
|
||||
for(size_t iy=0; iy<nrows; iy++)
|
||||
@ -535,7 +462,6 @@ inline void normalize(std::vector<T>& vec) {
|
||||
scalar_mul(1.0/l2_norm(vec), vec);
|
||||
}
|
||||
|
||||
|
||||
template <typename T>
|
||||
inline real_t<T> l1_norm(const std::vector<T>& vec) {
|
||||
real_t<T> norm = real_t<T>(); // Zero initialization
|
||||
@ -549,6 +475,52 @@ inline real_t<T> l1_norm(const std::vector<T>& vec) {
|
||||
|
||||
// --- Implementation: Eigendecomposition of small dense matrices ---
|
||||
|
||||
|
||||
template<typename Scalar,typename Vector,typename Matrix,typename ConstMatrix>
|
||||
Jacobi<Scalar, Vector, Matrix, ConstMatrix>::
|
||||
Jacobi(int n) {
|
||||
_Jacobi(n, nullptr, nullptr);
|
||||
}
|
||||
|
||||
|
||||
template<typename Scalar,typename Vector,typename Matrix,typename ConstMatrix>
|
||||
Jacobi<Scalar, Vector, Matrix, ConstMatrix>::
|
||||
Jacobi(int n, Scalar **M, int *max_idx_row) {
|
||||
_Jacobi(n, M, max_idx_row);
|
||||
}
|
||||
|
||||
|
||||
// _Jacobi() is a function which is invoked by the two constructors and it
|
||||
// does all of the work. (Splitting the constructor into multiple functions
|
||||
// was technically unnecessary, but it makes documenting the code easier.)
|
||||
|
||||
template<typename Scalar,typename Vector,typename Matrix,typename ConstMatrix>
|
||||
void
|
||||
Jacobi<Scalar, Vector, Matrix, ConstMatrix>::
|
||||
_Jacobi(int n, Scalar **M, int *max_idx_row) {
|
||||
Init();
|
||||
if (M) { // if caller supplies their own "M" array, don't allocate M
|
||||
is_preallocated = true;
|
||||
this->n = n;
|
||||
this->M = M;
|
||||
this->max_idx_row = max_idx_row;
|
||||
//assert(this->max_idx_row);
|
||||
}
|
||||
else {
|
||||
is_preallocated = false;
|
||||
SetSize(n); // allocate the "M" and "max_int_row" arrays
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
template<typename Scalar,typename Vector,typename Matrix,typename ConstMatrix>
|
||||
Jacobi<Scalar, Vector, Matrix, ConstMatrix>::
|
||||
~Jacobi() {
|
||||
if (! is_preallocated)
|
||||
Dealloc();
|
||||
}
|
||||
|
||||
|
||||
template<typename Scalar,typename Vector,typename Matrix,typename ConstMatrix>
|
||||
int Jacobi<Scalar, Vector, Matrix, ConstMatrix>::
|
||||
Diagonalize(ConstMatrix mat, // the matrix you wish to diagonalize (size n)
|
||||
@ -602,7 +574,7 @@ Diagonalize(ConstMatrix mat, // the matrix you wish to diagonalize (size n)
|
||||
// Optional: Sort results by eigenvalue.
|
||||
SortRows(eval, evec, n, sort_criteria);
|
||||
|
||||
return n_iters / (n*(n-1)/2); //returns the number of "sweeps" (converged?)
|
||||
return (n_iters == max_num_iters);
|
||||
}
|
||||
|
||||
|
||||
@ -634,7 +606,7 @@ CalcRot(Scalar const *const *M, //!< matrix
|
||||
t = -t;
|
||||
}
|
||||
}
|
||||
assert(std::abs(t) <= 1.0);
|
||||
//assert(std::abs(t) <= 1.0);
|
||||
c = 1.0 / std::sqrt(1 + t*t);
|
||||
s = c*t;
|
||||
}
|
||||
@ -699,7 +671,7 @@ ApplyRot(Scalar **M, // matrix
|
||||
M[j][j] += t * M[i][j];
|
||||
|
||||
//Update the off-diagonal elements of M which will change (above the diagonal)
|
||||
assert(i < j);
|
||||
//assert(i < j);
|
||||
M[i][j] = 0.0;
|
||||
|
||||
//compute M[w][i] and M[i][w] for all w!=i,considering above-diagonal elements
|
||||
@ -849,6 +821,7 @@ Init() {
|
||||
n = 0;
|
||||
M = nullptr;
|
||||
max_idx_row = nullptr;
|
||||
is_preallocated = false;
|
||||
}
|
||||
|
||||
template<typename Scalar,typename Vector,typename Matrix,typename ConstMatrix>
|
||||
@ -863,6 +836,7 @@ SetSize(int n) {
|
||||
template<typename Scalar,typename Vector,typename Matrix,typename ConstMatrix>
|
||||
void Jacobi<Scalar, Vector, Matrix, ConstMatrix>::
|
||||
Alloc(int n) {
|
||||
//assert(! is_preallocated);
|
||||
this->n = n;
|
||||
if (n > 0) {
|
||||
max_idx_row = new int[n];
|
||||
@ -873,8 +847,7 @@ Alloc(int n) {
|
||||
template<typename Scalar,typename Vector,typename Matrix,typename ConstMatrix>
|
||||
void Jacobi<Scalar, Vector, Matrix, ConstMatrix>::
|
||||
Dealloc() {
|
||||
if (max_idx_row)
|
||||
delete [] max_idx_row;
|
||||
//assert(! is_preallocated);
|
||||
Dealloc2D(&M);
|
||||
Init();
|
||||
}
|
||||
@ -887,7 +860,8 @@ Jacobi(const Jacobi<Scalar, Vector, Matrix, ConstMatrix>& source)
|
||||
{
|
||||
Init();
|
||||
SetSize(source.n);
|
||||
assert(n == source.n);
|
||||
|
||||
//assert(n == source.n);
|
||||
// The following lines aren't really necessary, because the contents
|
||||
// of source.M and source.max_idx_row are not needed (since they are
|
||||
// overwritten every time Jacobi::Diagonalize() is invoked).
|
||||
@ -904,6 +878,7 @@ template<typename Scalar,typename Vector,typename Matrix,typename ConstMatrix>
|
||||
void Jacobi<Scalar, Vector, Matrix, ConstMatrix>::
|
||||
swap(Jacobi<Scalar, Vector, Matrix, ConstMatrix> &other) {
|
||||
std::swap(n, other.n);
|
||||
std::swap(is_preallocated, other.is_preallocated);
|
||||
std::swap(max_idx_row, other.max_idx_row);
|
||||
std::swap(M, other.M);
|
||||
}
|
||||
@ -913,7 +888,7 @@ template<typename Scalar,typename Vector,typename Matrix,typename ConstMatrix>
|
||||
Jacobi<Scalar, Vector, Matrix, ConstMatrix>::
|
||||
Jacobi(Jacobi<Scalar, Vector, Matrix, ConstMatrix>&& other) {
|
||||
Init();
|
||||
swap(*this, other);
|
||||
this->swap(other);
|
||||
}
|
||||
|
||||
// Using the "copy-swap" idiom for the assignment operator
|
||||
@ -933,7 +908,7 @@ template <typename T>
|
||||
inline LambdaLanczos<T>::LambdaLanczos() {
|
||||
this->matrix_size = 0;
|
||||
this->max_iteration = 0;
|
||||
this->find_maximum = 0;
|
||||
this->find_maximum = false;
|
||||
}
|
||||
|
||||
|
||||
@ -955,8 +930,8 @@ template <typename T>
|
||||
inline int LambdaLanczos<T>::
|
||||
run(real_t<T>& eigvalue, std::vector<T>& eigvec) const
|
||||
{
|
||||
assert(matrix_size > 0);
|
||||
assert(0 < this->tridiag_eps_ratio && this->tridiag_eps_ratio < 1);
|
||||
//assert(matrix_size > 0);
|
||||
//assert(0 < this->tridiag_eps_ratio && this->tridiag_eps_ratio < 1);
|
||||
|
||||
std::vector<std::vector<T>> u; // Lanczos vectors
|
||||
std::vector<real_t<T>> alpha; // Diagonal elements of an approximated tridiagonal matrix
|
||||
@ -1322,12 +1297,25 @@ init(std::vector<std::complex<T>>& v)
|
||||
// --- Implementation of PEigenDense
|
||||
|
||||
template<typename Scalar, typename Vector, typename ConstMatrix>
|
||||
Scalar PEigenDense<Scalar, Vector, ConstMatrix>::
|
||||
void PEigenDense<Scalar, Vector, ConstMatrix>::
|
||||
SetSize(int matrix_size) {
|
||||
n = matrix_size;
|
||||
evec.resize(n);
|
||||
}
|
||||
|
||||
template<typename Scalar, typename Vector, typename ConstMatrix>
|
||||
PEigenDense<Scalar, Vector, ConstMatrix>::
|
||||
PEigenDense(int matrix_size):evec(matrix_size) {
|
||||
SetSize(matrix_size);
|
||||
}
|
||||
|
||||
template<typename Scalar, typename Vector, typename ConstMatrix>
|
||||
real_t<Scalar> PEigenDense<Scalar, Vector, ConstMatrix>::
|
||||
PrincipalEigen(ConstMatrix matrix,
|
||||
Vector eigenvector,
|
||||
bool find_max)
|
||||
{
|
||||
assert(n > 0);
|
||||
//assert(n > 0);
|
||||
auto matmul = [&](const std::vector<Scalar>& in, std::vector<Scalar>& out) {
|
||||
for(int i = 0; i < n; i++) {
|
||||
for(int j = 0; j < n; j++) {
|
||||
@ -1373,8 +1361,12 @@ PrincipalEigen(ConstMatrix matrix,
|
||||
return eval;
|
||||
}
|
||||
|
||||
|
||||
} //namespace MathEigen
|
||||
|
||||
|
||||
#endif //#ifndef _MATH_EIGEN_H
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
#endif //#ifndef LMP_MATH_EIGEN_IMPL_H
|
||||
@ -19,8 +19,6 @@
|
||||
#include <cstdio>
|
||||
#include <cstring>
|
||||
|
||||
#define MAXJACOBI 50
|
||||
|
||||
namespace MathExtra {
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
@ -92,88 +90,6 @@ int mldivide3(const double m[3][3], const double *v, double *ans)
|
||||
return 0;
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
compute evalues and evectors of 3x3 real symmetric matrix
|
||||
based on Jacobi rotations
|
||||
adapted from Numerical Recipes jacobi() function
|
||||
------------------------------------------------------------------------- */
|
||||
|
||||
int jacobi(double matrix[3][3], double *evalues, double evectors[3][3])
|
||||
{
|
||||
int i,j,k;
|
||||
double tresh,theta,tau,t,sm,s,h,g,c,b[3],z[3];
|
||||
|
||||
for (i = 0; i < 3; i++) {
|
||||
for (j = 0; j < 3; j++) evectors[i][j] = 0.0;
|
||||
evectors[i][i] = 1.0;
|
||||
}
|
||||
for (i = 0; i < 3; i++) {
|
||||
b[i] = evalues[i] = matrix[i][i];
|
||||
z[i] = 0.0;
|
||||
}
|
||||
|
||||
for (int iter = 1; iter <= MAXJACOBI; iter++) {
|
||||
sm = 0.0;
|
||||
for (i = 0; i < 2; i++)
|
||||
for (j = i+1; j < 3; j++)
|
||||
sm += fabs(matrix[i][j]);
|
||||
if (sm == 0.0) return 0;
|
||||
|
||||
if (iter < 4) tresh = 0.2*sm/(3*3);
|
||||
else tresh = 0.0;
|
||||
|
||||
for (i = 0; i < 2; i++) {
|
||||
for (j = i+1; j < 3; j++) {
|
||||
g = 100.0*fabs(matrix[i][j]);
|
||||
if (iter > 4 && fabs(evalues[i])+g == fabs(evalues[i])
|
||||
&& fabs(evalues[j])+g == fabs(evalues[j]))
|
||||
matrix[i][j] = 0.0;
|
||||
else if (fabs(matrix[i][j]) > tresh) {
|
||||
h = evalues[j]-evalues[i];
|
||||
if (fabs(h)+g == fabs(h)) t = (matrix[i][j])/h;
|
||||
else {
|
||||
theta = 0.5*h/(matrix[i][j]);
|
||||
t = 1.0/(fabs(theta)+sqrt(1.0+theta*theta));
|
||||
if (theta < 0.0) t = -t;
|
||||
}
|
||||
c = 1.0/sqrt(1.0+t*t);
|
||||
s = t*c;
|
||||
tau = s/(1.0+c);
|
||||
h = t*matrix[i][j];
|
||||
z[i] -= h;
|
||||
z[j] += h;
|
||||
evalues[i] -= h;
|
||||
evalues[j] += h;
|
||||
matrix[i][j] = 0.0;
|
||||
for (k = 0; k < i; k++) rotate(matrix,k,i,k,j,s,tau);
|
||||
for (k = i+1; k < j; k++) rotate(matrix,i,k,k,j,s,tau);
|
||||
for (k = j+1; k < 3; k++) rotate(matrix,i,k,j,k,s,tau);
|
||||
for (k = 0; k < 3; k++) rotate(evectors,k,i,k,j,s,tau);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
for (i = 0; i < 3; i++) {
|
||||
evalues[i] = b[i] += z[i];
|
||||
z[i] = 0.0;
|
||||
}
|
||||
}
|
||||
return 1;
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
perform a single Jacobi rotation
|
||||
------------------------------------------------------------------------- */
|
||||
|
||||
void rotate(double matrix[3][3], int i, int j, int k, int l,
|
||||
double s, double tau)
|
||||
{
|
||||
double g = matrix[i][j];
|
||||
double h = matrix[k][l];
|
||||
matrix[i][j] = g-s*(h+g*tau);
|
||||
matrix[k][l] = h+s*(g-h*tau);
|
||||
}
|
||||
|
||||
/* ----------------------------------------------------------------------
|
||||
Richardson iteration to update quaternion from angular momentum
|
||||
return new normalized quaternion q
|
||||
|
||||
@ -85,7 +85,6 @@ namespace MathExtra {
|
||||
|
||||
void write3(const double mat[3][3]);
|
||||
int mldivide3(const double mat[3][3], const double *vec, double *ans);
|
||||
int jacobi(double matrix[3][3], double *evalues, double evectors[3][3]);
|
||||
void rotate(double matrix[3][3], int i, int j, int k, int l,
|
||||
double s, double tau);
|
||||
void richardson(double *q, double *m, double *w, double *moments, double dtq);
|
||||
|
||||
@ -21,6 +21,7 @@
|
||||
#include "error.h"
|
||||
#include "force.h"
|
||||
#include "math_extra.h"
|
||||
#include "math_eigen.h"
|
||||
#include "memory.h"
|
||||
#include "tokenizer.h"
|
||||
|
||||
@ -349,7 +350,7 @@ void Molecule::compute_inertia()
|
||||
tensor[0][2] = tensor[2][0] = itensor[4];
|
||||
tensor[0][1] = tensor[1][0] = itensor[5];
|
||||
|
||||
if (MathExtra::jacobi(tensor,inertia,evectors))
|
||||
if (MathEigen::jacobi3(tensor,inertia,evectors))
|
||||
error->all(FLERR,"Insufficient Jacobi rotations for rigid molecule");
|
||||
|
||||
ex[0] = evectors[0][0];
|
||||
|
||||
@ -1,7 +1,7 @@
|
||||
---
|
||||
lammps_version: 24 Aug 2020
|
||||
date_generated: Tue Sep 15 09:44:41 202
|
||||
epsilon: 2.5e-13
|
||||
date_generated: Tue Sep 15 22:36:53 202
|
||||
epsilon: 5e-13
|
||||
prerequisites: ! |
|
||||
atom full
|
||||
fix rigid
|
||||
@ -13,65 +13,65 @@ post_commands: ! |
|
||||
input_file: in.fourmol
|
||||
natoms: 29
|
||||
run_stress: ! |-
|
||||
-1.4245356937318927e+03 -1.4496493315649675e+03 -3.6144360984224963e+03 8.4840626828643849e+02 2.0318336761611764e+02 -6.0622397707969685e+02
|
||||
-1.4245356937318884e+03 -1.4496493315649705e+03 -3.6144360984225009e+03 8.4840626828644258e+02 2.0318336761611707e+02 -6.0622397707970117e+02
|
||||
global_scalar: 15.7115214231781
|
||||
run_pos: ! |2
|
||||
1 -2.7899546863891622e-01 2.4731857340328216e+00 -1.7290667740241872e-01
|
||||
2 3.0296221610264007e-01 2.9517129916957545e+00 -8.5798904387772823e-01
|
||||
3 -6.9368802364134852e-01 1.2445115421754183e+00 -6.2281111198650230e-01
|
||||
4 -1.5764879647103172e+00 1.4919714415841274e+00 -1.2492069414674600e+00
|
||||
5 -8.9434512967430013e-01 9.3651699743510730e-01 4.0191726558261431e-01
|
||||
6 2.9454439634451690e-01 2.2724545792544065e-01 -1.2845195053960263e+00
|
||||
7 3.4049112903270062e-01 -9.4655678322440595e-03 -2.4634480020857059e+00
|
||||
8 1.1644354555804877e+00 -4.8367776650961369e-01 -6.7663643940735896e-01
|
||||
9 1.3781717822696469e+00 -2.5332509530010827e-01 2.6864954436590061e-01
|
||||
10 2.0186368606041905e+00 -1.4285861423625792e+00 -9.6712491252780297e-01
|
||||
11 1.7929137227577470e+00 -1.9875455388407410e+00 -1.8836565352266557e+00
|
||||
12 3.0032775230399604e+00 -4.8983022415173838e-01 -1.6190248017343647e+00
|
||||
13 4.0448964162125947e+00 -9.0213155122390720e-01 -1.6385398399479572e+00
|
||||
14 2.6035151245015831e+00 -4.0874995493218902e-01 -2.6555999074786611e+00
|
||||
15 2.9761196776172314e+00 5.6287237454108840e-01 -1.2442626196083382e+00
|
||||
16 2.6517373021566191e+00 -2.3957035508393720e+00 3.3389262100689376e-02
|
||||
17 2.2311114924744988e+00 -2.1018393228798540e+00 1.1496088522377521e+00
|
||||
18 2.1390642573201788e+00 3.0164773560693772e+00 -3.5143984803853874e+00
|
||||
19 1.5353246655146275e+00 2.6305911186316124e+00 -4.2455871034737074e+00
|
||||
20 2.7649421538938386e+00 3.6818603528430827e+00 -3.9364115785985558e+00
|
||||
21 4.9043112657298868e+00 -4.0774268210397873e+00 -3.6200836396129810e+00
|
||||
22 4.3665322424283302e+00 -4.2075138112953594e+00 -4.4636587264885854e+00
|
||||
23 5.7355405581985170e+00 -3.5789558641908905e+00 -3.8805763324089964e+00
|
||||
24 2.0692780332810123e+00 3.1504920436416004e+00 3.1571131300668775e+00
|
||||
25 1.3007297593169085e+00 3.2745259354179486e+00 2.5110163874103657e+00
|
||||
26 2.5819416446099748e+00 4.0104903120756585e+00 3.2150249624526013e+00
|
||||
1 -2.7899546863891489e-01 2.4731857340328216e+00 -1.7290667740242327e-01
|
||||
2 3.0296221610264151e-01 2.9517129916957532e+00 -8.5798904387773267e-01
|
||||
3 -6.9368802364134807e-01 1.2445115421754180e+00 -6.2281111198650496e-01
|
||||
4 -1.5764879647103154e+00 1.4919714415841261e+00 -1.2492069414674631e+00
|
||||
5 -8.9434512967430058e-01 9.3651699743510919e-01 4.0191726558261187e-01
|
||||
6 2.9454439634451712e-01 2.2724545792543988e-01 -1.2845195053960272e+00
|
||||
7 3.4049112903270107e-01 -9.4655678322462800e-03 -2.4634480020857055e+00
|
||||
8 1.1644354555804874e+00 -4.8367776650961330e-01 -6.7663643940735863e-01
|
||||
9 1.3781717822696467e+00 -2.5332509530010694e-01 2.6864954436590061e-01
|
||||
10 2.0186368606041896e+00 -1.4285861423625787e+00 -9.6712491252780097e-01
|
||||
11 1.7929137227577463e+00 -1.9875455388407417e+00 -1.8836565352266530e+00
|
||||
12 3.0032775230399609e+00 -4.8983022415173938e-01 -1.6190248017343634e+00
|
||||
13 4.0448964162125947e+00 -9.0213155122390887e-01 -1.6385398399479545e+00
|
||||
14 2.6035151245015831e+00 -4.0874995493219152e-01 -2.6555999074786603e+00
|
||||
15 2.9761196776172318e+00 5.6287237454108718e-01 -1.2442626196083382e+00
|
||||
16 2.6517373021566177e+00 -2.3957035508393694e+00 3.3389262100692485e-02
|
||||
17 2.2311114924744970e+00 -2.1018393228798504e+00 1.1496088522377548e+00
|
||||
18 2.1390642573201784e+00 3.0164773560693781e+00 -3.5143984803853878e+00
|
||||
19 1.5353246655146278e+00 2.6305911186316133e+00 -4.2455871034737074e+00
|
||||
20 2.7649421538938390e+00 3.6818603528430849e+00 -3.9364115785985550e+00
|
||||
21 4.9043112657298877e+00 -4.0774268210397882e+00 -3.6200836396129836e+00
|
||||
22 4.3665322424283310e+00 -4.2075138112953594e+00 -4.4636587264885881e+00
|
||||
23 5.7355405581985188e+00 -3.5789558641908918e+00 -3.8805763324089981e+00
|
||||
24 2.0692780332810115e+00 3.1504920436416004e+00 3.1571131300668789e+00
|
||||
25 1.3007297593169076e+00 3.2745259354179481e+00 2.5110163874103675e+00
|
||||
26 2.5819416446099739e+00 4.0104903120756576e+00 3.2150249624526035e+00
|
||||
27 -1.9613581876744359e+00 -4.3556300596085160e+00 2.1101467673534788e+00
|
||||
28 -2.7406520384725965e+00 -4.0207251278130975e+00 1.5828689861678511e+00
|
||||
29 -1.3108232656499081e+00 -3.5992986322410760e+00 2.2680459788743503e+00
|
||||
run_vel: ! |2
|
||||
1 4.7093289825842518e-04 2.6351122778447999e-04 -4.4905093064114991e-04
|
||||
2 4.9594625316470484e-04 9.4561370489631939e-05 -5.4581359894047949e-04
|
||||
3 3.3306085115756087e-04 2.3224943880673381e-04 -2.3659455671746045e-04
|
||||
4 3.3692327392261114e-04 2.1926810694051279e-04 -2.4716631558862527e-04
|
||||
5 3.3642542694186013e-04 4.1797578013265895e-04 -1.8011341766657651e-04
|
||||
6 2.0926869754934733e-04 2.6449308951578761e-05 -1.0508938983871863e-04
|
||||
7 1.4629043007907862e-04 -1.6873376665350138e-04 -6.8354048774351599e-05
|
||||
8 1.5844101624224864e-04 3.7728761274000492e-05 -1.9162715667091517e-05
|
||||
9 2.1299362072601976e-04 1.6917140529157604e-04 -6.3528165037846039e-05
|
||||
10 5.4261629412254251e-05 -9.4655528376811197e-05 1.0511362869146629e-04
|
||||
11 -3.2194160796503320e-05 -2.2025095264758748e-04 2.0300202946212385e-04
|
||||
12 1.2640586304750342e-04 -2.9851080445665075e-04 -7.9476371818247547e-05
|
||||
13 8.4523575162142323e-05 -4.0583135407330540e-04 -4.7551111331702706e-05
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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||||
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|
||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
|
||||
@ -1,7 +1,7 @@
|
||||
---
|
||||
lammps_version: 24 Aug 2020
|
||||
date_generated: Tue Sep 15 09:44:41 202
|
||||
epsilon: 2.5e-13
|
||||
date_generated: Tue Sep 15 22:36:54 202
|
||||
epsilon: 5e-13
|
||||
prerequisites: ! |
|
||||
atom full
|
||||
fix rigid
|
||||
@ -13,7 +13,7 @@ post_commands: ! |
|
||||
input_file: in.fourmol
|
||||
natoms: 29
|
||||
run_stress: ! |-
|
||||
-4.9200116134790363e+01 -2.6907707565987732e+01 -6.0080860422282560e+00 -2.5620423972101747e+01 -1.3450224059984075e+01 -1.4947288487004844e+00
|
||||
-4.9200116134789894e+01 -2.6907707565987600e+01 -6.0080860422279923e+00 -2.5620423972101459e+01 -1.3450224059984031e+01 -1.4947288487004347e+00
|
||||
global_scalar: 18.3405601674144
|
||||
run_pos: ! |2
|
||||
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|
||||
@ -33,15 +33,15 @@ run_pos: ! |2
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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||||
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|
||||
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|
||||
@ -63,15 +63,15 @@ run_vel: ! |2
|
||||
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|
||||
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||||
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||||
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||||
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|
||||
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||||
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||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
|
||||
@ -1,6 +1,6 @@
|
||||
---
|
||||
lammps_version: 24 Aug 2020
|
||||
date_generated: Tue Sep 15 09:44:41 202
|
||||
date_generated: Tue Sep 15 22:36:54 202
|
||||
epsilon: 5e-12
|
||||
prerequisites: ! |
|
||||
atom full
|
||||
@ -14,7 +14,7 @@ post_commands: ! |
|
||||
input_file: in.fourmol
|
||||
natoms: 29
|
||||
run_stress: ! |-
|
||||
-4.9200116134791799e+01 -2.6907707565986644e+01 -6.0080860422294684e+00 -2.5620423972101577e+01 -1.3450224059984462e+01 -1.4947288487000847e+00
|
||||
-4.9200116134789241e+01 -2.6907707565985238e+01 -6.0080860422273377e+00 -2.5620423972099417e+01 -1.3450224059984127e+01 -1.4947288486998911e+00
|
||||
global_scalar: 18.3405601674143
|
||||
run_pos: ! |2
|
||||
1 -2.7993683669226854e-01 2.4726588069312836e+00 -1.7200860244148508e-01
|
||||
@ -35,14 +35,14 @@ run_pos: ! |2
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
@ -64,15 +64,15 @@ run_vel: ! |2
|
||||
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|
||||
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|
||||
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|
||||
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||||
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||||
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||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
|
||||
@ -1,7 +1,7 @@
|
||||
---
|
||||
lammps_version: 24 Aug 2020
|
||||
date_generated: Tue Sep 15 09:44:41 202
|
||||
epsilon: 2.5e-13
|
||||
date_generated: Tue Sep 15 22:36:55 202
|
||||
epsilon: 5e-13
|
||||
prerequisites: ! |
|
||||
atom full
|
||||
fix rigid/nph
|
||||
@ -13,38 +13,38 @@ post_commands: ! |
|
||||
input_file: in.fourmol
|
||||
natoms: 29
|
||||
run_stress: ! |2-
|
||||
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|
||||
global_scalar: 29.0236364415722
|
||||
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|
||||
global_scalar: 29.023636440848
|
||||
run_pos: ! |2
|
||||
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|
||||
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|
||||
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|
||||
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||||
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||||
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|
||||
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||||
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||||
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|
||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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||||
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||||
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|
||||
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|
||||
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||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
run_vel: ! |2
|
||||
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|
||||
2 2.7129529964126462e-03 4.6286427111164284e-03 3.5805549693846352e-03
|
||||
@ -63,15 +63,15 @@ run_vel: ! |2
|
||||
15 -4.3301707382721859e-03 -3.1802661664634938e-03 3.2037919043360571e-03
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
|
||||
@ -1,7 +1,7 @@
|
||||
---
|
||||
lammps_version: 24 Aug 2020
|
||||
date_generated: Tue Sep 15 09:44:41 202
|
||||
epsilon: 2.5e-13
|
||||
date_generated: Tue Sep 15 22:36:55 202
|
||||
epsilon: 5e-13
|
||||
prerequisites: ! |
|
||||
atom full
|
||||
fix rigid/nph/small
|
||||
@ -13,38 +13,38 @@ post_commands: ! |
|
||||
input_file: in.fourmol
|
||||
natoms: 29
|
||||
run_stress: ! |2-
|
||||
2.7340318969496678e+01 4.7963870140135469e+00 6.8884396850629400e+01 2.9853310008504316e+01 -1.0857139901179401e+01 -5.1889756547613537e+00
|
||||
global_scalar: 9.77678786322453
|
||||
2.7340318973870428e+01 4.7963870091858531e+00 6.8884396847592484e+01 2.9853310007358978e+01 -1.0857139901347637e+01 -5.1889756561453346e+00
|
||||
global_scalar: 9.77678786310451
|
||||
run_pos: ! |2
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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||||
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||||
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|
||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
29 -1.6779316575994301e+00 -4.0348635219024889e+00 3.1144975929056571e+00
|
||||
run_vel: ! |2
|
||||
1 7.7867804888392077e-04 5.8970331623292821e-04 -2.2179517633030531e-04
|
||||
2 2.7129529964126462e-03 4.6286427111164284e-03 3.5805549693846352e-03
|
||||
@ -63,15 +63,15 @@ run_vel: ! |2
|
||||
15 -4.3301707382721859e-03 -3.1802661664634938e-03 3.2037919043360571e-03
|
||||
16 -9.6715751018414326e-05 -5.0016572678960377e-04 1.4945658875149626e-03
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
22 -1.4151473871025083e-03 -1.3502255396192354e-03 1.1972773108803675e-03
|
||||
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|
||||
24 7.5594375538132891e-04 -8.1321044009404451e-04 3.9340911288127442e-04
|
||||
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|
||||
26 -1.4806168648241629e-03 3.7766934332214119e-04 2.1280924227254782e-03
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
24 7.5594375541558048e-04 -8.1321043994394464e-04 3.9340911295780760e-04
|
||||
25 1.4373446731689036e-03 -1.9778020567486213e-03 -6.1842201918304457e-04
|
||||
26 -1.4806168650325995e-03 3.7766934274110835e-04 2.1280924225288347e-03
|
||||
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|
||||
28 -2.3068708109787484e-04 -8.5663070212203200e-04 2.1302563179109169e-03
|
||||
29 -2.5054744388303732e-03 -1.6773997805290820e-04 2.8436699761004796e-03
|
||||
|
||||
@ -1,7 +1,7 @@
|
||||
---
|
||||
lammps_version: 24 Aug 2020
|
||||
date_generated: Tue Sep 15 09:44:41 202
|
||||
epsilon: 2.5e-13
|
||||
date_generated: Tue Sep 15 22:36:56 202
|
||||
epsilon: 5e-13
|
||||
prerequisites: ! |
|
||||
atom full
|
||||
fix rigid/npt
|
||||
@ -12,65 +12,65 @@ post_commands: ! |
|
||||
input_file: in.fourmol
|
||||
natoms: 29
|
||||
run_stress: ! |-
|
||||
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@ -1,7 +1,7 @@
|
||||
---
|
||||
lammps_version: 24 Aug 2020
|
||||
date_generated: Tue Sep 15 09:44:41 202
|
||||
epsilon: 2.5e-13
|
||||
date_generated: Tue Sep 15 22:36:56 202
|
||||
epsilon: 5e-13
|
||||
prerequisites: ! |
|
||||
atom full
|
||||
fix rigid/npt/small
|
||||
@ -12,38 +12,38 @@ post_commands: ! |
|
||||
input_file: in.fourmol
|
||||
natoms: 29
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
run_vel: ! |2
|
||||
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|
||||
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|
||||
@ -62,15 +62,15 @@ run_vel: ! |2
|
||||
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|
||||
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|
||||
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|
||||
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||||
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||||
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||||
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||||
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|
||||
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|
||||
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|
||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
|
||||
@ -1,7 +1,7 @@
|
||||
---
|
||||
lammps_version: 24 Aug 2020
|
||||
date_generated: Tue Sep 15 09:44:42 202
|
||||
epsilon: 2.5e-13
|
||||
date_generated: Tue Sep 15 22:36:57 202
|
||||
epsilon: 5e-13
|
||||
prerequisites: ! |
|
||||
atom full
|
||||
fix rigid/nve
|
||||
@ -13,65 +13,65 @@ post_commands: ! |
|
||||
input_file: in.fourmol
|
||||
natoms: 29
|
||||
run_stress: ! |-
|
||||
-1.4245356938010630e+03 -1.4496493316651863e+03 -3.6144360982531375e+03 8.4840626794791422e+02 2.0318336802435149e+02 -6.0622397695991776e+02
|
||||
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|
||||
global_scalar: 15.7115214231781
|
||||
run_pos: ! |2
|
||||
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|
||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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|
||||
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||||
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||||
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||||
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||||
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|
||||
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|
||||
run_vel: ! |2
|
||||
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|
||||
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||||
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|
||||
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|
||||
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||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
16 -9.0958138549712697e-06 3.7774817121341365e-06 2.4035199548835218e-04
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
5 3.3642542694184180e-04 4.1797578013266394e-04 -1.8011341766654835e-04
|
||||
6 2.0926869754934465e-04 2.6449308951570318e-05 -1.0508938983871884e-04
|
||||
7 1.4629043007908249e-04 -1.6873376665352393e-04 -6.8354048774366371e-05
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
23 -9.7629260480938673e-04 -1.3100872491594617e-03 7.2687284219704544e-04
|
||||
24 4.3308126651259079e-04 -6.6527658087322801e-04 8.4451298670663660e-04
|
||||
25 4.4565811905441442e-04 -5.1298436273583461e-04 8.5878867884521515e-04
|
||||
26 5.9865972692023438e-04 -7.6385263287079188e-04 8.4259943226842502e-04
|
||||
27 -2.6510179146429716e-04 3.6306203629019116e-04 -5.6235585400647747e-04
|
||||
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|
||||
29 -2.5054744388303732e-03 -1.6773997805290820e-04 2.8436699761004796e-03
|
||||
|
||||
@ -1,7 +1,7 @@
|
||||
---
|
||||
lammps_version: 24 Aug 2020
|
||||
date_generated: Tue Sep 15 09:44:42 202
|
||||
epsilon: 2.5e-13
|
||||
date_generated: Tue Sep 15 22:36:57 202
|
||||
epsilon: 5e-13
|
||||
prerequisites: ! |
|
||||
atom full
|
||||
fix rigid/nve
|
||||
@ -13,8 +13,8 @@ post_commands: ! |
|
||||
input_file: in.fourmol
|
||||
natoms: 29
|
||||
run_stress: ! |-
|
||||
-4.9200114783104425e+01 -2.6907707681632978e+01 -6.0080872466970643e+00 -2.5620425754068116e+01 -1.3450222537284642e+01 -1.4947348675137455e+00
|
||||
global_scalar: 18.3405601681427
|
||||
-4.9200114774917928e+01 -2.6907707694141234e+01 -6.0080872444876876e+00 -2.5620425756344922e+01 -1.3450222538011758e+01 -1.4947348732783965e+00
|
||||
global_scalar: 18.3405601673644
|
||||
run_pos: ! |2
|
||||
1 -2.7993683669226832e-01 2.4726588069312840e+00 -1.7200860244148433e-01
|
||||
2 3.0197083955402204e-01 2.9515239068888608e+00 -8.5689735572907566e-01
|
||||
@ -33,15 +33,15 @@ run_pos: ! |2
|
||||
15 2.9756315249791303e+00 5.6334269722969288e-01 -1.2437650754599008e+00
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
29 -1.3108232656499081e+00 -3.5992986322410760e+00 2.2680459788743503e+00
|
||||
@ -63,15 +63,15 @@ run_vel: ! |2
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
|
||||
@ -1,7 +1,7 @@
|
||||
---
|
||||
lammps_version: 24 Aug 2020
|
||||
date_generated: Tue Sep 15 09:44:42 202
|
||||
epsilon: 2.5e-13
|
||||
date_generated: Tue Sep 15 22:36:58 202
|
||||
epsilon: 5e-13
|
||||
prerequisites: ! |
|
||||
atom full
|
||||
fix rigid/nve
|
||||
@ -13,26 +13,26 @@ post_commands: ! |
|
||||
input_file: in.fourmol
|
||||
natoms: 29
|
||||
run_stress: ! |-
|
||||
-1.3754817467882001e+03 -1.4228425246443051e+03 -3.6087196200592211e+03 8.7407043142561224e+02 2.1665316510417915e+02 -6.0480791467760923e+02
|
||||
global_scalar: 4.53142303857025
|
||||
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|
||||
global_scalar: 4.53142303857033
|
||||
run_pos: ! |2
|
||||
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|
||||
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|
||||
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|
||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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|
||||
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||||
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||||
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|
||||
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|
||||
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||||
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|
||||
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|
||||
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||||
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||||
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|
||||
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||||
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||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
@ -46,23 +46,23 @@ run_pos: ! |2
|
||||
28 -2.7406520384725965e+00 -4.0207251278130975e+00 1.5828689861678511e+00
|
||||
29 -1.3108232656499081e+00 -3.5992986322410760e+00 2.2680459788743503e+00
|
||||
run_vel: ! |2
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
1 4.7093296226164512e-04 2.6351124312060207e-04 -4.4905063547613525e-04
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
16 -9.0959360838789561e-06 3.7773746063112143e-06 2.4035204669043016e-04
|
||||
17 5.7507084250803752e-05 2.2629200960629542e-04 2.0686926033796743e-04
|
||||
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|
||||
19 -6.9919768291957119e-04 -3.6060777270430031e-03 4.2833405289822791e-03
|
||||
20 4.7777805013736515e-03 5.1003745845520452e-03 1.8002873923729241e-03
|
||||
|
||||
@ -1,7 +1,7 @@
|
||||
---
|
||||
lammps_version: 24 Aug 2020
|
||||
date_generated: Tue Sep 15 09:44:42 202
|
||||
epsilon: 2.5e-13
|
||||
date_generated: Tue Sep 15 22:36:58 202
|
||||
epsilon: 5e-13
|
||||
prerequisites: ! |
|
||||
atom full
|
||||
fix rigid/nve/small
|
||||
@ -13,8 +13,8 @@ post_commands: ! |
|
||||
input_file: in.fourmol
|
||||
natoms: 29
|
||||
run_stress: ! |-
|
||||
-4.9200114783104425e+01 -2.6907707681632978e+01 -6.0080872466970643e+00 -2.5620425754068116e+01 -1.3450222537284642e+01 -1.4947348675137455e+00
|
||||
global_scalar: 0.500731871980239
|
||||
-4.9200114774917928e+01 -2.6907707694141234e+01 -6.0080872444876876e+00 -2.5620425756344922e+01 -1.3450222538011758e+01 -1.4947348732783965e+00
|
||||
global_scalar: 0.50073187196632
|
||||
run_pos: ! |2
|
||||
1 -2.7993683669226832e-01 2.4726588069312840e+00 -1.7200860244148433e-01
|
||||
2 3.0197083955402204e-01 2.9515239068888608e+00 -8.5689735572907566e-01
|
||||
@ -33,15 +33,15 @@ run_pos: ! |2
|
||||
15 2.9756315249791303e+00 5.6334269722969288e-01 -1.2437650754599008e+00
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
25 1.3030170721038390e+00 3.2711173927738786e+00 2.5081940917867680e+00
|
||||
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|
||||
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|
||||
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|
||||
29 -1.3108232656499081e+00 -3.5992986322410760e+00 2.2680459788743503e+00
|
||||
@ -63,15 +63,15 @@ run_vel: ! |2
|
||||
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|
||||
16 -9.6715751018414326e-05 -5.0016572678960377e-04 1.4945658875149626e-03
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
|
||||
@ -1,6 +1,6 @@
|
||||
---
|
||||
lammps_version: 24 Aug 2020
|
||||
date_generated: Tue Sep 15 09:44:42 202
|
||||
date_generated: Tue Sep 15 22:36:59 202
|
||||
epsilon: 5e-13
|
||||
prerequisites: ! |
|
||||
atom full
|
||||
@ -12,26 +12,26 @@ post_commands: ! |
|
||||
input_file: in.fourmol
|
||||
natoms: 29
|
||||
run_stress: ! |-
|
||||
-1.3123962047751329e+03 -1.3675423591737690e+03 -3.5468492999580276e+03 7.8271738572462300e+02 2.6480486115425720e+02 -7.6950536863901277e+02
|
||||
global_scalar: 68.0865964742217
|
||||
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|
||||
global_scalar: 68.0865964742317
|
||||
run_pos: ! |2
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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||||
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||||
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|
||||
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|
||||
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|
||||
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||||
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||||
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|
||||
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|
||||
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||||
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|
||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
@ -45,23 +45,23 @@ run_pos: ! |2
|
||||
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|
||||
29 -1.3108232656499081e+00 -3.5992986322410760e+00 2.2680459788743503e+00
|
||||
run_vel: ! |2
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
17 2.5969943716026037e-04 8.7075266710270329e-04 7.7887058799645153e-04
|
||||
18 -6.0936815808025862e-04 -9.3774557532468582e-04 -3.3558072507805731e-04
|
||||
19 -6.9919768291957119e-04 -3.6060777270430031e-03 4.2833405289822791e-03
|
||||
20 4.7777805013736515e-03 5.1003745845520452e-03 1.8002873923729241e-03
|
||||
|
||||
@ -1,7 +1,7 @@
|
||||
---
|
||||
lammps_version: 24 Aug 2020
|
||||
date_generated: Tue Sep 15 09:44:42 202
|
||||
epsilon: 2.5e-13
|
||||
date_generated: Tue Sep 15 22:36:59 202
|
||||
epsilon: 5e-13
|
||||
prerequisites: ! |
|
||||
atom full
|
||||
fix rigid/nvt/small
|
||||
@ -12,8 +12,8 @@ post_commands: ! |
|
||||
input_file: in.fourmol
|
||||
natoms: 29
|
||||
run_stress: ! |-
|
||||
-1.4827261120559041e+02 -1.8411194247813761e+01 -1.0752762861073667e+02 -2.1814511473385389e+02 1.7027764309482512e+02 2.1058942295369583e+01
|
||||
global_scalar: 0.953260955609303
|
||||
-1.4827261116680450e+02 -1.8411194349753366e+01 -1.0752762859308652e+02 -2.1814511477016262e+02 1.7027764307147635e+02 2.1058942244057143e+01
|
||||
global_scalar: 0.953260955473961
|
||||
run_pos: ! |2
|
||||
1 -2.7993683669226832e-01 2.4726588069312840e+00 -1.7200860244148433e-01
|
||||
2 3.0197083955402204e-01 2.9515239068888608e+00 -8.5689735572907566e-01
|
||||
@ -32,15 +32,15 @@ run_pos: ! |2
|
||||
15 2.9756315249791303e+00 5.6334269722969288e-01 -1.2437650754599008e+00
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
29 -1.3108232656499081e+00 -3.5992986322410760e+00 2.2680459788743503e+00
|
||||
@ -62,15 +62,15 @@ run_vel: ! |2
|
||||
15 -4.3301707382721859e-03 -3.1802661664634938e-03 3.2037919043360571e-03
|
||||
16 -9.6715751018414326e-05 -5.0016572678960377e-04 1.4945658875149626e-03
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
24 1.8727912311097637e-03 -2.0349136820274911e-03 1.1951471753018509e-03
|
||||
25 3.4887365958745937e-03 -4.8232966889391275e-03 -1.2263764490291341e-03
|
||||
26 -3.4770258010749858e-03 7.8662050223200905e-04 5.3381090661352281e-03
|
||||
27 -2.6510179146429716e-04 3.6306203629019116e-04 -5.6235585400647747e-04
|
||||
28 -2.3068708109787484e-04 -8.5663070212203200e-04 2.1302563179109169e-03
|
||||
29 -2.5054744388303732e-03 -1.6773997805290820e-04 2.8436699761004796e-03
|
||||
|
||||
@ -1,7 +1,7 @@
|
||||
---
|
||||
lammps_version: 24 Aug 2020
|
||||
date_generated: Tue Sep 15 09:44:42 202
|
||||
epsilon: 2.5e-13
|
||||
date_generated: Tue Sep 15 22:37:00 202
|
||||
epsilon: 5e-13
|
||||
prerequisites: ! |
|
||||
atom full
|
||||
fix rigid
|
||||
@ -13,26 +13,26 @@ post_commands: ! |
|
||||
input_file: in.fourmol
|
||||
natoms: 29
|
||||
run_stress: ! |-
|
||||
-1.3754817466835852e+03 -1.4228425246165939e+03 -3.6087196201913630e+03 8.7407043149698166e+02 2.1665316519768876e+02 -6.0480791462031175e+02
|
||||
global_scalar: 4.53142303857031
|
||||
-1.3754817466835989e+03 -1.4228425246166139e+03 -3.6087196201914344e+03 8.7407043149698939e+02 2.1665316519769868e+02 -6.0480791462033017e+02
|
||||
global_scalar: 4.53142303857029
|
||||
run_pos: ! |2
|
||||
1 -2.7899546859693181e-01 2.4731857340428789e+00 -1.7290667720876129e-01
|
||||
2 3.0296221616793595e-01 2.9517129917211555e+00 -8.5798904365355089e-01
|
||||
3 -6.9368802362166315e-01 1.2445115422149753e+00 -6.2281111185285432e-01
|
||||
4 -1.5764879646739509e+00 1.4919714416722003e+00 -1.2492069413381559e+00
|
||||
5 -8.9434512967954460e-01 9.3651699743538708e-01 4.0191726569957620e-01
|
||||
6 2.9454439635065854e-01 2.2724545796943085e-01 -1.2845195052894232e+00
|
||||
7 3.4049112905311674e-01 -9.4655677385591108e-03 -2.4634480019885245e+00
|
||||
8 1.1644354555589662e+00 -4.8367776651302741e-01 -6.7663643931660777e-01
|
||||
9 1.3781717822376685e+00 -2.5332509534947545e-01 2.6864954447021527e-01
|
||||
10 2.0186368605645773e+00 -1.4285861423742925e+00 -9.6712491246325638e-01
|
||||
11 1.7929137227200924e+00 -1.9875455388074488e+00 -1.8836565351900403e+00
|
||||
12 3.0032775230343129e+00 -4.8983022415935262e-01 -1.6190248016126150e+00
|
||||
13 4.0448964161972292e+00 -9.0213155125606903e-01 -1.6385398398262687e+00
|
||||
14 2.6035151245155346e+00 -4.0874995488538102e-01 -2.6555999073602141e+00
|
||||
15 2.9761196776308703e+00 5.6287237451798355e-01 -1.2442626194416762e+00
|
||||
16 2.6517373020764223e+00 -2.3957035509096416e+00 3.3389262134315478e-02
|
||||
17 2.2311114923824862e+00 -2.1018393229879826e+00 1.1496088522768946e+00
|
||||
1 -2.7899546859693136e-01 2.4731857340428784e+00 -1.7290667720876285e-01
|
||||
2 3.0296221616793728e-01 2.9517129917211546e+00 -8.5798904365355155e-01
|
||||
3 -6.9368802362166204e-01 1.2445115422149751e+00 -6.2281111185285498e-01
|
||||
4 -1.5764879646739487e+00 1.4919714416722010e+00 -1.2492069413381564e+00
|
||||
5 -8.9434512967954416e-01 9.3651699743538730e-01 4.0191726569957442e-01
|
||||
6 2.9454439635065910e-01 2.2724545796943096e-01 -1.2845195052894232e+00
|
||||
7 3.4049112905311751e-01 -9.4655677385591108e-03 -2.4634480019885228e+00
|
||||
8 1.1644354555589662e+00 -4.8367776651302724e-01 -6.7663643931660777e-01
|
||||
9 1.3781717822376680e+00 -2.5332509534947545e-01 2.6864954447021416e-01
|
||||
10 2.0186368605645764e+00 -1.4285861423742918e+00 -9.6712491246325605e-01
|
||||
11 1.7929137227200918e+00 -1.9875455388074483e+00 -1.8836565351900385e+00
|
||||
12 3.0032775230343125e+00 -4.8983022415935312e-01 -1.6190248016126132e+00
|
||||
13 4.0448964161972283e+00 -9.0213155125606947e-01 -1.6385398398262669e+00
|
||||
14 2.6035151245155355e+00 -4.0874995488538129e-01 -2.6555999073602123e+00
|
||||
15 2.9761196776308694e+00 5.6287237451798222e-01 -1.2442626194416753e+00
|
||||
16 2.6517373020764219e+00 -2.3957035509096407e+00 3.3389262134315700e-02
|
||||
17 2.2311114923824857e+00 -2.1018393229879817e+00 1.1496088522768926e+00
|
||||
18 2.1384791188033843e+00 3.0177261773770208e+00 -3.5160827596876225e+00
|
||||
19 1.5349125211132961e+00 2.6315969880333707e+00 -4.2472859440220647e+00
|
||||
20 2.7641167828863153e+00 3.6833419064000221e+00 -3.9380850623312638e+00
|
||||
@ -46,23 +46,23 @@ run_pos: ! |2
|
||||
28 -2.7406520384725965e+00 -4.0207251278130975e+00 1.5828689861678511e+00
|
||||
29 -1.3108232656499081e+00 -3.5992986322410760e+00 2.2680459788743503e+00
|
||||
run_vel: ! |2
|
||||
1 4.7093296226165759e-04 2.6351124312057328e-04 -4.4905063547614815e-04
|
||||
2 4.9594635271877263e-04 9.4561409237138648e-05 -5.4581325723053584e-04
|
||||
3 3.3306088119083106e-04 2.3224949911015489e-04 -2.3659435306900921e-04
|
||||
4 3.3692332940286711e-04 2.1926824120529708e-04 -2.4716611858556546e-04
|
||||
5 3.3642541894624088e-04 4.1797578053943778e-04 -1.8011323945929135e-04
|
||||
6 2.0926870695908297e-04 2.6449376032441632e-05 -1.0508922741401441e-04
|
||||
7 1.4629046128362895e-04 -1.6873362379723160e-04 -6.8353900724071678e-05
|
||||
8 1.5844098346817962e-04 3.7728756087619151e-05 -1.9162577392849499e-05
|
||||
9 2.1299357198253027e-04 1.6917133003966806e-04 -6.3528006071200595e-05
|
||||
10 5.4261569071246100e-05 -9.4655546204698788e-05 1.0511372702289762e-04
|
||||
11 -3.2194218121523160e-05 -2.2025090185602363e-04 2.0300208519292848e-04
|
||||
12 1.2640585449263567e-04 -2.9851081600946788e-04 -7.9476186245575856e-05
|
||||
13 8.4523551795102534e-05 -4.0583140303608248e-04 -4.7550925831931509e-05
|
||||
14 9.9954071734163638e-05 -4.2610809338913916e-04 -7.9255453072662124e-05
|
||||
15 2.4417483202630001e-04 -2.3521005781669064e-04 -2.4875292755152092e-04
|
||||
16 -9.0959360838833471e-06 3.7773746063198897e-06 2.4035204669042528e-04
|
||||
17 5.7507084250808007e-05 2.2629200960629450e-04 2.0686926033794596e-04
|
||||
1 4.7093296226165726e-04 2.6351124312057247e-04 -4.4905063547614652e-04
|
||||
2 4.9594635271877252e-04 9.4561409237138173e-05 -5.4581325723053399e-04
|
||||
3 3.3306088119083085e-04 2.3224949911015443e-04 -2.3659435306900835e-04
|
||||
4 3.3692332940286711e-04 2.1926824120529689e-04 -2.4716611858556487e-04
|
||||
5 3.3642541894624033e-04 4.1797578053943675e-04 -1.8011323945929070e-04
|
||||
6 2.0926870695908275e-04 2.6449376032441517e-05 -1.0508922741401380e-04
|
||||
7 1.4629046128362901e-04 -1.6873362379723092e-04 -6.8353900724071163e-05
|
||||
8 1.5844098346817922e-04 3.7728756087618725e-05 -1.9162577392849018e-05
|
||||
9 2.1299357198252964e-04 1.6917133003966706e-04 -6.3528006071199931e-05
|
||||
10 5.4261569071245721e-05 -9.4655546204699004e-05 1.0511372702289778e-04
|
||||
11 -3.2194218121523377e-05 -2.2025090185602322e-04 2.0300208519292837e-04
|
||||
12 1.2640585449263546e-04 -2.9851081600946783e-04 -7.9476186245574907e-05
|
||||
13 8.4523551795102276e-05 -4.0583140303608237e-04 -4.7550925831930506e-05
|
||||
14 9.9954071734163652e-05 -4.2610809338913862e-04 -7.9255453072661283e-05
|
||||
15 2.4417483202629974e-04 -2.3521005781669077e-04 -2.4875292755151935e-04
|
||||
16 -9.0959360838839976e-06 3.7773746063190714e-06 2.4035204669042517e-04
|
||||
17 5.7507084250807059e-05 2.2629200960629290e-04 2.0686926033794590e-04
|
||||
18 -6.0936815808025862e-04 -9.3774557532468582e-04 -3.3558072507805731e-04
|
||||
19 -6.9919768291957119e-04 -3.6060777270430031e-03 4.2833405289822791e-03
|
||||
20 4.7777805013736515e-03 5.1003745845520452e-03 1.8002873923729241e-03
|
||||
|
||||
@ -1,7 +1,7 @@
|
||||
---
|
||||
lammps_version: 24 Aug 2020
|
||||
date_generated: Tue Sep 15 09:44:42 202
|
||||
epsilon: 2.5e-13
|
||||
date_generated: Tue Sep 15 22:37:00 202
|
||||
epsilon: 5e-13
|
||||
prerequisites: ! |
|
||||
atom full
|
||||
fix rigid/small
|
||||
@ -13,7 +13,7 @@ post_commands: ! |
|
||||
input_file: in.fourmol
|
||||
natoms: 29
|
||||
run_stress: ! |-
|
||||
-4.9200116134790363e+01 -2.6907707565987732e+01 -6.0080860422282560e+00 -2.5620423972101747e+01 -1.3450224059984075e+01 -1.4947288487004844e+00
|
||||
-4.9200116134789894e+01 -2.6907707565987600e+01 -6.0080860422279923e+00 -2.5620423972101459e+01 -1.3450224059984031e+01 -1.4947288487004347e+00
|
||||
global_scalar: 18.3405601674144
|
||||
run_pos: ! |2
|
||||
1 -2.7993683669226832e-01 2.4726588069312840e+00 -1.7200860244148433e-01
|
||||
@ -33,15 +33,15 @@ run_pos: ! |2
|
||||
15 2.9756315249791303e+00 5.6334269722969288e-01 -1.2437650754599008e+00
|
||||
16 2.6517554244980306e+00 -2.3957110424978438e+00 3.2908335999178327e-02
|
||||
17 2.2309964792710639e+00 -2.1022918943319384e+00 1.1491948328949437e+00
|
||||
18 2.1392027588271301e+00 3.0171068018412783e+00 -3.5144628518856349e+00
|
||||
19 1.5366124997074573e+00 2.6286809834111744e+00 -4.2452547844370221e+00
|
||||
20 2.7628161763455852e+00 3.6842251687634779e+00 -3.9370881219352558e+00
|
||||
21 4.9036621347791245e+00 -4.0757648442838548e+00 -3.6192617654515908e+00
|
||||
18 2.1392027588271301e+00 3.0171068018412779e+00 -3.5144628518856349e+00
|
||||
19 1.5366124997074571e+00 2.6286809834111748e+00 -4.2452547844370221e+00
|
||||
20 2.7628161763455852e+00 3.6842251687634775e+00 -3.9370881219352554e+00
|
||||
21 4.9036621347791245e+00 -4.0757648442838548e+00 -3.6192617654515904e+00
|
||||
22 4.3655322291888483e+00 -4.2084949965552561e+00 -4.4622011117402334e+00
|
||||
23 5.7380414793463101e+00 -3.5841969195032672e+00 -3.8827839830470219e+00
|
||||
24 2.0701314765323930e+00 3.1499370533342330e+00 3.1565324852522938e+00
|
||||
25 1.3030170721374783e+00 3.2711173927682244e+00 2.5081940917429759e+00
|
||||
26 2.5776230782480041e+00 4.0127347068243884e+00 3.2182355138709284e+00
|
||||
25 1.3030170721374779e+00 3.2711173927682249e+00 2.5081940917429768e+00
|
||||
26 2.5776230782480045e+00 4.0127347068243875e+00 3.2182355138709275e+00
|
||||
27 -1.9613581876744359e+00 -4.3556300596085160e+00 2.1101467673534788e+00
|
||||
28 -2.7406520384725965e+00 -4.0207251278130975e+00 1.5828689861678511e+00
|
||||
29 -1.3108232656499081e+00 -3.5992986322410760e+00 2.2680459788743503e+00
|
||||
@ -63,15 +63,15 @@ run_vel: ! |2
|
||||
15 -4.3301707382721859e-03 -3.1802661664634938e-03 3.2037919043360571e-03
|
||||
16 -9.6715751018414326e-05 -5.0016572678960377e-04 1.4945658875149626e-03
|
||||
17 6.5692180538157174e-04 3.6635779995305095e-04 8.3495414466050911e-04
|
||||
18 3.6149625095704870e-04 -3.1032459262908302e-04 8.1043030117346052e-04
|
||||
19 8.5103884665345441e-04 -1.4572280596788099e-03 1.0163621287634116e-03
|
||||
20 -6.5204659278590758e-04 4.3989037444289831e-04 4.9909839028507966e-04
|
||||
21 -1.3888125881903919e-03 -3.1978049143082570e-04 1.1455681499836646e-03
|
||||
22 -1.6084223477729497e-03 -1.5355394240821158e-03 1.4772010826232373e-03
|
||||
23 2.6392672378804886e-04 -3.9375414431174760e-03 -3.6991583139728127e-04
|
||||
24 8.6062827067890290e-04 -9.4179873474469259e-04 5.5396395550012367e-04
|
||||
25 1.5933645477487557e-03 -2.2139156625681682e-03 -5.5078029695647412e-04
|
||||
26 -1.5679561743998888e-03 3.5146224354725948e-04 2.4446924193334482e-03
|
||||
18 3.6149625095704908e-04 -3.1032459262908286e-04 8.1043030117346042e-04
|
||||
19 8.5103884665345452e-04 -1.4572280596788108e-03 1.0163621287634116e-03
|
||||
20 -6.5204659278590683e-04 4.3989037444289853e-04 4.9909839028507890e-04
|
||||
21 -1.3888125881903923e-03 -3.1978049143082407e-04 1.1455681499836646e-03
|
||||
22 -1.6084223477729508e-03 -1.5355394240821113e-03 1.4772010826232373e-03
|
||||
23 2.6392672378805081e-04 -3.9375414431174812e-03 -3.6991583139728051e-04
|
||||
24 8.6062827067890236e-04 -9.4179873474469237e-04 5.5396395550012442e-04
|
||||
25 1.5933645477487542e-03 -2.2139156625681699e-03 -5.5078029695647488e-04
|
||||
26 -1.5679561743998840e-03 3.5146224354726122e-04 2.4446924193334474e-03
|
||||
27 -2.6510179146429716e-04 3.6306203629019116e-04 -5.6235585400647747e-04
|
||||
28 -2.3068708109787484e-04 -8.5663070212203200e-04 2.1302563179109169e-03
|
||||
29 -2.5054744388303732e-03 -1.6773997805290820e-04 2.8436699761004796e-03
|
||||
|
||||
@ -62,6 +62,7 @@ if (PKG_COMPRESS)
|
||||
set_tests_properties(DumpLocalGZ PROPERTIES ENVIRONMENT "LAMMPS_POTENTIALS=${LAMMPS_POTENTIALS_DIR}")
|
||||
set_tests_properties(DumpLocalGZ PROPERTIES ENVIRONMENT "GZIP_BINARY=${GZIP_BINARY}")
|
||||
|
||||
if(Zstd_FOUND)
|
||||
find_program(ZSTD_BINARY NAMES zstd)
|
||||
|
||||
if (ZSTD_BINARY)
|
||||
@ -96,6 +97,7 @@ if (PKG_COMPRESS)
|
||||
set_tests_properties(DumpLocalZstd PROPERTIES ENVIRONMENT "ZSTD_BINARY=${ZSTD_BINARY}")
|
||||
endif()
|
||||
endif()
|
||||
endif()
|
||||
|
||||
add_executable(test_dump_custom test_dump_custom.cpp)
|
||||
target_link_libraries(test_dump_custom PRIVATE lammps GTest::GMock GTest::GTest)
|
||||
|
||||
File diff suppressed because it is too large
Load Diff
@ -14,3 +14,7 @@ set_tests_properties(Utils PROPERTIES ENVIRONMENT "LAMMPS_POTENTIALS=${LAMMPS_PO
|
||||
add_executable(test_fmtlib test_fmtlib.cpp)
|
||||
target_link_libraries(test_fmtlib PRIVATE lammps GTest::GMockMain GTest::GMock GTest::GTest)
|
||||
add_test(FmtLib test_fmtlib)
|
||||
|
||||
add_executable(test_math_eigen_impl test_math_eigen_impl.cpp)
|
||||
target_include_directories(test_math_eigen_impl PRIVATE ${LAMMPS_SOURCE_DIR})
|
||||
add_test(MathEigen test_math_eigen_impl 10 5)
|
||||
|
||||
766
unittest/utils/test_math_eigen_impl.cpp
Normal file
766
unittest/utils/test_math_eigen_impl.cpp
Normal file
@ -0,0 +1,766 @@
|
||||
// THIS FILE USED TO BE EASY TO READ until I added "#if defined" statements.
|
||||
// (They were added to test for many different kinds of array formats.)
|
||||
|
||||
#include <iostream>
|
||||
#include <cassert>
|
||||
#include <cmath>
|
||||
#include <iomanip>
|
||||
#include <cstdlib>
|
||||
#include <chrono>
|
||||
#include <random>
|
||||
#include <algorithm>
|
||||
#include <vector>
|
||||
#include <array>
|
||||
#include "math_eigen_impl.h"
|
||||
|
||||
using std::cout;
|
||||
using std::cerr;
|
||||
using std::endl;
|
||||
using std::setprecision;
|
||||
using std::vector;
|
||||
using std::array;
|
||||
using namespace MathEigen;
|
||||
|
||||
|
||||
// This code works with various types of C++ matrices (for example,
|
||||
// double **, vector<vector<double>> array<array<double,5>,5>).
|
||||
// I use "#if defined" statements to test different matrix types.
|
||||
// For some of these (eg. array<array<double,5>,5>), the size of the matrix
|
||||
// must be known at compile time. I specify that size now.
|
||||
#if defined USE_ARRAY_OF_ARRAYS
|
||||
const int NF=5; //(the array size must be known at compile time)
|
||||
#elif defined USE_C_FIXED_SIZE_ARRAYS
|
||||
const int NF=5; //(the array size must be known at compile time)
|
||||
#endif
|
||||
|
||||
|
||||
// @brief Are two numbers "similar"?
|
||||
template<typename Scalar>
|
||||
inline static bool Similar(Scalar a, Scalar b,
|
||||
Scalar eps=1.0e-06,
|
||||
Scalar ratio=1.0e-06,
|
||||
Scalar ratio_denom=1.0)
|
||||
{
|
||||
return ((std::abs(a-b)<=std::abs(eps))
|
||||
||
|
||||
(std::abs(ratio_denom)*std::abs(a-b)
|
||||
<=
|
||||
std::abs(ratio)*0.5*(std::abs(a)+std::abs(b))));
|
||||
}
|
||||
|
||||
/// @brief Are two vectors (containing n numbers) similar?
|
||||
template<typename Scalar, typename Vector>
|
||||
inline static bool SimilarVec(Vector a, Vector b, int n,
|
||||
Scalar eps=1.0e-06,
|
||||
Scalar ratio=1.0e-06,
|
||||
Scalar ratio_denom=1.0)
|
||||
{
|
||||
for (int i = 0; i < n; i++)
|
||||
if (not Similar(a[i], b[i], eps, ratio, ratio_denom))
|
||||
return false;
|
||||
return true;
|
||||
}
|
||||
|
||||
/// @brief Are two vectors (or their reflections) similar?
|
||||
template<typename Scalar, typename Vector>
|
||||
inline static bool SimilarVecUnsigned(Vector a, Vector b, int n,
|
||||
Scalar eps=1.0e-06,
|
||||
Scalar ratio=1.0e-06,
|
||||
Scalar ratio_denom=1.0)
|
||||
{
|
||||
if (SimilarVec(a, b, n, eps))
|
||||
return true;
|
||||
else {
|
||||
for (int i = 0; i < n; i++)
|
||||
if (not Similar(a[i], -b[i], eps, ratio, ratio_denom))
|
||||
return false;
|
||||
return true;
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
/// @brief Multiply two matrices A and B, store the result in C. (C = AB).
|
||||
|
||||
template<typename Matrix, typename ConstMatrix>
|
||||
void mmult(ConstMatrix A, //<! input array
|
||||
ConstMatrix B, //<! input array
|
||||
Matrix C, //<! store result here
|
||||
int m, //<! number of rows of A
|
||||
int n=0, //<! optional: number of columns of B (=m by default)
|
||||
int K=0 //<! optional: number of columns of A = num rows of B (=m by default)
|
||||
)
|
||||
{
|
||||
if (n == 0) n = m; // if not specified, then assume the matrices are square
|
||||
if (K == 0) K = m; // if not specified, then assume the matrices are square
|
||||
|
||||
for (int i = 0; i < m; i++)
|
||||
for (int j = 0; j < n; j++)
|
||||
C[i][j] = 0.0;
|
||||
|
||||
// perform matrix multiplication
|
||||
for (int i = 0; i < m; i++)
|
||||
for (int j = 0; j < n; j++)
|
||||
for (int k = 0; k < K; k++)
|
||||
C[i][j] += A[i][k] * B[k][j];
|
||||
}
|
||||
|
||||
|
||||
|
||||
/// @brief
|
||||
///Sort the rows of a matrix "evec" by the numbers contained in "eval"
|
||||
///(This is a simple O(n^2) sorting method, but O(n^2) is a lower bound anyway.)
|
||||
///This is the same as the Jacobi::SortRows(), but that function is private.
|
||||
template<typename Scalar, typename Vector, typename Matrix>
|
||||
void
|
||||
SortRows(Vector eval,
|
||||
Matrix evec,
|
||||
int n,
|
||||
bool sort_decreasing=true,
|
||||
bool sort_abs=false)
|
||||
{
|
||||
for (int i = 0; i < n-1; i++) {
|
||||
int i_max = i;
|
||||
for (int j = i+1; j < n; j++) {
|
||||
if (sort_decreasing) {
|
||||
if (sort_abs) { //sort by absolute value?
|
||||
if (std::abs(eval[j]) > std::abs(eval[i_max]))
|
||||
i_max = j;
|
||||
}
|
||||
else if (eval[j] > eval[i_max])
|
||||
i_max = j;
|
||||
}
|
||||
else {
|
||||
if (sort_abs) { //sort by absolute value?
|
||||
if (std::abs(eval[j]) < std::abs(eval[i_max]))
|
||||
i_max = j;
|
||||
}
|
||||
else if (eval[j] < eval[i_max])
|
||||
i_max = j;
|
||||
}
|
||||
}
|
||||
std::swap(eval[i], eval[i_max]); // sort "eval"
|
||||
for (int k = 0; k < n; k++)
|
||||
std::swap(evec[i][k], evec[i_max][k]); // sort "evec"
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
|
||||
/// @brief Generate a random orthonormal n x n matrix
|
||||
|
||||
template<typename Scalar, typename Matrix>
|
||||
void GenRandOrth(Matrix R,
|
||||
int n,
|
||||
std::default_random_engine &rand_generator)
|
||||
{
|
||||
std::normal_distribution<Scalar> gaussian_distribution(0,1);
|
||||
std::vector<Scalar> v(n);
|
||||
|
||||
for (int i = 0; i < n; i++) {
|
||||
// Generate a vector, "v", in a random direction subject to the constraint
|
||||
// that it is orthogonal to the first i-1 rows-vectors of the R matrix.
|
||||
Scalar rsq = 0.0;
|
||||
while (rsq == 0.0) {
|
||||
// Generate a vector in a random direction
|
||||
// (This works because we are using a normal (Gaussian) distribution)
|
||||
for (int j = 0; j < n; j++)
|
||||
v[j] = gaussian_distribution(rand_generator);
|
||||
|
||||
//Now subtract from v, the projection of v onto the first i-1 rows of R.
|
||||
//This will produce a vector which is orthogonal to these i-1 row-vectors.
|
||||
//(They are already normalized and orthogonal to each other.)
|
||||
for (int k = 0; k < i; k++) {
|
||||
Scalar v_dot_Rk = 0.0;
|
||||
for (int j = 0; j < n; j++)
|
||||
v_dot_Rk += v[j] * R[k][j];
|
||||
for (int j = 0; j < n; j++)
|
||||
v[j] -= v_dot_Rk * R[k][j];
|
||||
}
|
||||
// check if it is linearly independent of the other vectors and non-zero
|
||||
rsq = 0.0;
|
||||
for (int j = 0; j < n; j++)
|
||||
rsq += v[j]*v[j];
|
||||
}
|
||||
// Now normalize the vector
|
||||
Scalar r_inv = 1.0 / std::sqrt(rsq);
|
||||
for (int j = 0; j < n; j++)
|
||||
v[j] *= r_inv;
|
||||
// Now copy this vector to the i'th row of R
|
||||
for (int j = 0; j < n; j++)
|
||||
R[i][j] = v[j];
|
||||
} //for (int i = 0; i < n; i++)
|
||||
} //void GenRandOrth()
|
||||
|
||||
|
||||
|
||||
/// @brief Generate a random symmetric n x n matrix, M.
|
||||
/// This function generates random numbers for the eigenvalues ("evals_known")
|
||||
/// as well as the eigenvectors ("evecs_known"), and uses them to generate M.
|
||||
/// The "eval_magnitude_range" argument specifies the the base-10 logarithm
|
||||
/// of the range of eigenvalues desired. The "n_degeneracy" argument specifies
|
||||
/// the number of repeated eigenvalues desired (if any).
|
||||
/// @returns This function does not return a value. However after it is
|
||||
/// invoked, the M matrix will be filled with random numbers.
|
||||
/// Additionally, the "evals" and "evecs" arguments will contain
|
||||
/// the eigenvalues and eigenvectors (one eigenvector per row)
|
||||
/// of the matrix. Later, they can be compared with the eigenvalues
|
||||
/// and eigenvectors calculated by Jacobi::Diagonalize()
|
||||
|
||||
template <typename Scalar, typename Vector, typename Matrix>
|
||||
void GenRandSymm(Matrix M, //<! store the matrix here
|
||||
int n, //<! matrix size
|
||||
Vector evals, //<! store the eigenvalues of here
|
||||
Matrix evecs, //<! store the eigenvectors here
|
||||
std::default_random_engine &rand_generator,//<! makes random numbers
|
||||
Scalar min_eval_size=0.1, //<! minimum possible eigenvalue size
|
||||
Scalar max_eval_size=10.0,//<! maximum possible eigenvalue size
|
||||
int n_degeneracy=1//<!number of repeated eigevalues(1disables)
|
||||
)
|
||||
{
|
||||
assert(n_degeneracy <= n);
|
||||
std::uniform_real_distribution<Scalar> random_real01;
|
||||
std::normal_distribution<Scalar> gaussian_distribution(0, max_eval_size);
|
||||
bool use_log_uniform_distribution = false;
|
||||
if (min_eval_size > 0.0)
|
||||
use_log_uniform_distribution = true;
|
||||
#if defined USE_VECTOR_OF_VECTORS
|
||||
vector<vector<Scalar> > D(n, vector<Scalar>(n));
|
||||
vector<vector<Scalar> > tmp(n, vector<Scalar>(n));
|
||||
#elif defined USE_ARRAY_OF_ARRAYS
|
||||
array<array<Scalar, NF>, NF> D;
|
||||
array<array<Scalar, NF>, NF> tmp;
|
||||
#elif defined USE_C_FIXED_SIZE_ARRAYS
|
||||
Scalar D[NF][NF], tmp[NF][NF];
|
||||
#else
|
||||
#define USE_C_POINTER_TO_POINTERS
|
||||
Scalar **D, **tmp;
|
||||
Alloc2D(n, n, &D);
|
||||
Alloc2D(n, n, &tmp);
|
||||
#endif
|
||||
|
||||
// Randomly generate the eigenvalues
|
||||
for (int i = 0; i < n; i++) {
|
||||
if (use_log_uniform_distribution) {
|
||||
// Use a "log-uniform distribution" (a.k.a. "reciprocal distribution")
|
||||
// (This is a way to specify numbers with a precise range of magnitudes.)
|
||||
assert((min_eval_size > 0.0) && (max_eval_size > 0.0));
|
||||
Scalar log_min = std::log(std::abs(min_eval_size));
|
||||
Scalar log_max = std::log(std::abs(max_eval_size));
|
||||
Scalar log_eval = (log_min + random_real01(rand_generator)*(log_max-log_min));
|
||||
evals[i] = std::exp(log_eval);
|
||||
// also consider both positive and negative eigenvalues:
|
||||
if (random_real01(rand_generator) < 0.5)
|
||||
evals[i] = -evals[i];
|
||||
}
|
||||
else {
|
||||
evals[i] = gaussian_distribution(rand_generator);
|
||||
}
|
||||
}
|
||||
|
||||
// Does the user want us to force some of the eigenvalues to be the same?
|
||||
if (n_degeneracy > 1) {
|
||||
int *permutation = new int[n]; //a random permutation from 0...n-1
|
||||
for (int i = 0; i < n; i++)
|
||||
permutation[i] = i;
|
||||
std::shuffle(permutation, permutation+n, rand_generator);
|
||||
for (int i = 1; i < n_degeneracy; i++) //set the first n_degeneracy to same
|
||||
evals[permutation[i]] = evals[permutation[0]];
|
||||
delete [] permutation;
|
||||
}
|
||||
|
||||
// D is a diagonal matrix whose diagonal elements are the eigenvalues
|
||||
for (int i = 0; i < n; i++)
|
||||
for (int j = 0; j < n; j++)
|
||||
D[i][j] = ((i == j) ? evals[i] : 0.0);
|
||||
|
||||
// Now randomly generate the (transpose of) the "evecs" matrix
|
||||
GenRandOrth<Scalar, Matrix>(evecs, n, rand_generator); //(will transpose it later)
|
||||
|
||||
// Construct the test matrix, M, where M = Rt * D * R
|
||||
|
||||
// Original code:
|
||||
//mmult(evecs, D, tmp, n); // <--> tmp = Rt * D
|
||||
// Unfortunately, C++ guesses the types incorrectly. Must manually specify:
|
||||
// #ifdefs making the code ugly again:
|
||||
#if defined USE_VECTOR_OF_VECTORS
|
||||
mmult<vector<vector<Scalar> >&, const vector<vector<Scalar> >&>
|
||||
#elif defined USE_ARRAY_OF_ARRAYS
|
||||
mmult<array<array<Scalar,NF>,NF>&, const array<array<Scalar,NF>,NF>&>
|
||||
#elif defined USE_C_FIXED_SIZE_ARRAYS
|
||||
mmult<Scalar (*)[NF], Scalar (*)[NF]>
|
||||
#else
|
||||
mmult<Scalar**, Scalar const *const *>
|
||||
#endif
|
||||
(evecs, D, tmp, n);
|
||||
|
||||
for (int i = 0; i < n-1; i++)
|
||||
for (int j = i+1; j < n; j++)
|
||||
std::swap(evecs[i][j], evecs[j][i]); //transpose "evecs"
|
||||
|
||||
// Original code:
|
||||
//mmult(tmp, evecs, M, n);
|
||||
// Unfortunately, C++ guesses the types incorrectly. Must manually specify:
|
||||
// #ifdefs making the code ugly again:
|
||||
#if defined USE_VECTOR_OF_VECTORS
|
||||
mmult<vector<vector<Scalar> >&, const vector<vector<Scalar> >&>
|
||||
#elif defined USE_ARRAY_OF_ARRAYS
|
||||
mmult<array<array<Scalar,NF>,NF>&, const array<array<Scalar,NF>,NF>&>
|
||||
#elif defined USE_C_FIXED_SIZE_ARRAYS
|
||||
mmult<Scalar (*)[NF], Scalar (*)[NF]>
|
||||
#else
|
||||
mmult<Scalar**, Scalar const *const *>
|
||||
#endif
|
||||
(tmp, evecs, M, n);
|
||||
//at this point M = Rt*D*R (where "R"="evecs")
|
||||
|
||||
#if defined USE_C_POINTER_TO_POINTERS
|
||||
Dealloc2D(&D);
|
||||
Dealloc2D(&tmp);
|
||||
#endif
|
||||
} // GenRandSymm()
|
||||
|
||||
|
||||
|
||||
template <typename Scalar>
|
||||
void TestJacobi(int n, //<! matrix size
|
||||
int n_matrices=100, //<! number of matrices to test
|
||||
Scalar min_eval_size=0.1, //<! minimum possible eigenvalue sizw
|
||||
Scalar max_eval_size=10.0, //<! maximum possible eigenvalue size
|
||||
int n_tests_per_matrix=1, //<! repeat test for benchmarking?
|
||||
|
||||
int n_degeneracy=1, //<! repeated eigenvalues?
|
||||
unsigned seed=0, //<! random seed (if 0 then use the clock)
|
||||
Scalar eps=1.0e-06
|
||||
)
|
||||
{
|
||||
bool test_code_coverage = false;
|
||||
if (n_tests_per_matrix < 1) {
|
||||
cout << "-- Testing code-coverage --" << endl;
|
||||
test_code_coverage = true;
|
||||
n_tests_per_matrix = 1;
|
||||
}
|
||||
cout << endl << "-- Diagonalization test (real symmetric) --" << endl;
|
||||
|
||||
// construct a random generator engine using a time-based seed:
|
||||
|
||||
if (seed == 0) // if the caller did not specify a seed, use the system clock
|
||||
seed = std::chrono::system_clock::now().time_since_epoch().count();
|
||||
std::default_random_engine rand_generator(seed);
|
||||
|
||||
|
||||
|
||||
// Create an instance of the Jacobi diagonalizer, and allocate the matrix
|
||||
// we will test it on, as well as the arrays that will store the resulting
|
||||
// eigenvalues and eigenvectors.
|
||||
// The way we do this depends on what version of the code we are using.
|
||||
// This is controlled by "#if defined" statements.
|
||||
|
||||
#if defined USE_VECTOR_OF_VECTORS
|
||||
|
||||
Jacobi<Scalar,
|
||||
vector<Scalar>&,
|
||||
vector<vector<Scalar> >&,
|
||||
const vector<vector<Scalar> >& > ecalc(n);
|
||||
|
||||
// allocate the matrix, eigenvalues, eigenvectors
|
||||
vector<vector<Scalar> > M(n, vector<Scalar>(n));
|
||||
vector<vector<Scalar> > evecs(n, vector<Scalar>(n));
|
||||
vector<vector<Scalar> > evecs_known(n, vector<Scalar>(n));
|
||||
vector<Scalar> evals(n);
|
||||
vector<Scalar> evals_known(n);
|
||||
vector<Scalar> test_evec(n);
|
||||
|
||||
#elif defined USE_ARRAY_OF_ARRAYS
|
||||
|
||||
n = NF;
|
||||
cout << "Testing std::array (fixed size).\n"
|
||||
"(Ignoring first argument, and setting matrix size to " << n << ")" << endl;
|
||||
|
||||
Jacobi<Scalar,
|
||||
array<Scalar, NF>&,
|
||||
array<array<Scalar, NF>, NF>&,
|
||||
const array<array<Scalar, NF>, NF>&> ecalc(n);
|
||||
|
||||
// allocate the matrix, eigenvalues, eigenvectors
|
||||
array<array<Scalar, NF>, NF> M;
|
||||
array<array<Scalar, NF>, NF> evecs;
|
||||
array<array<Scalar, NF>, NF> evecs_known;
|
||||
array<Scalar, NF> evals;
|
||||
array<Scalar, NF> evals_known;
|
||||
array<Scalar, NF> test_evec;
|
||||
|
||||
#elif defined USE_C_FIXED_SIZE_ARRAYS
|
||||
|
||||
n = NF;
|
||||
cout << "Testing C fixed size arrays.\n"
|
||||
"(Ignoring first argument, and setting matrix size to " << n << ")" << endl;
|
||||
Jacobi<Scalar,
|
||||
Scalar*,
|
||||
Scalar (*)[NF],
|
||||
Scalar const (*)[NF]> ecalc(n);
|
||||
|
||||
// allocate the matrix, eigenvalues, eigenvectors
|
||||
Scalar M[NF][NF];
|
||||
Scalar evecs[NF][NF];
|
||||
Scalar evecs_known[NF][NF];
|
||||
Scalar evals[NF];
|
||||
Scalar evals_known[NF];
|
||||
Scalar test_evec[NF];
|
||||
|
||||
#else
|
||||
|
||||
#define USE_C_POINTER_TO_POINTERS
|
||||
|
||||
// Note: Normally, you would just use this to instantiate Jacobi:
|
||||
// Jacobi<Scalar, Scalar*, Scalar**, Scalar const*const*> ecalc(n);
|
||||
// -------------------------
|
||||
// ..but since Jacobi manages its own memory using new and delete, I also want
|
||||
// to test that the copy constructors, copy operators, and destructors work.
|
||||
// The following lines do this:
|
||||
Jacobi<Scalar, Scalar*, Scalar**, Scalar const*const*> ecalc_test_mem1(n);
|
||||
Jacobi<Scalar, Scalar*, Scalar**, Scalar const*const*> ecalc_test_mem2(2);
|
||||
// test the = operator
|
||||
ecalc_test_mem2 = ecalc_test_mem1;
|
||||
// test the copy constructor
|
||||
Jacobi<Scalar, Scalar*, Scalar**, Scalar const*const*> ecalc(ecalc_test_mem2);
|
||||
// allocate the matrix, eigenvalues, eigenvectors
|
||||
Scalar **M, **evecs, **evecs_known;
|
||||
Alloc2D(n, n, &M);
|
||||
Alloc2D(n, n, &evecs);
|
||||
Alloc2D(n, n, &evecs_known);
|
||||
Scalar *evals = new Scalar[n];
|
||||
Scalar *evals_known = new Scalar[n];
|
||||
Scalar *test_evec = new Scalar[n];
|
||||
|
||||
#endif
|
||||
|
||||
|
||||
// --------------------------------------------------------------------
|
||||
// Now, generate random matrices and test Jacobi::Diagonalize() on them.
|
||||
// --------------------------------------------------------------------
|
||||
|
||||
for(int imat = 0; imat < n_matrices; imat++) {
|
||||
|
||||
// Create a randomly generated symmetric matrix.
|
||||
//This function generates random numbers for the eigenvalues ("evals_known")
|
||||
//as well as the eigenvectors ("evecs_known"), and uses them to generate M.
|
||||
|
||||
#if defined USE_VECTOR_OF_VECTORS
|
||||
GenRandSymm<Scalar, vector<Scalar>&, vector<vector<Scalar> >&>
|
||||
#elif defined USE_ARRAY_OF_ARRAYS
|
||||
GenRandSymm<Scalar, array<Scalar,NF>&, array<array<Scalar,NF>,NF>&>
|
||||
#elif defined USE_C_FIXED_SIZE_ARRAYS
|
||||
GenRandSymm<Scalar, Scalar*, Scalar (*)[NF]>
|
||||
#else
|
||||
GenRandSymm<Scalar, Scalar*, Scalar**>
|
||||
#endif
|
||||
(M,
|
||||
n,
|
||||
evals_known,
|
||||
evecs_known,
|
||||
rand_generator,
|
||||
min_eval_size,
|
||||
max_eval_size,
|
||||
n_degeneracy);
|
||||
|
||||
// Sort the matrix evals and eigenvector rows:
|
||||
// Original code:
|
||||
//SortRows<Scalar>(evals_known, evecs_known, n);
|
||||
// Unfortunately, C++ guesses the types incorrectly. Must use #ifdefs again:
|
||||
#if defined USE_VECTOR_OF_VECTORS
|
||||
SortRows<Scalar, vector<Scalar>&, vector<vector<Scalar> >&>
|
||||
#elif defined USE_ARRAY_OF_ARRAYS
|
||||
SortRows<Scalar, array<Scalar,NF>&, array<array<Scalar,NF>,NF>&>
|
||||
#elif defined USE_C_FIXED_SIZE_ARRAYS
|
||||
SortRows<Scalar, Scalar*, Scalar (*)[NF]>
|
||||
#else
|
||||
SortRows<Scalar, Scalar*, Scalar**>
|
||||
#endif
|
||||
(evals_known, evecs_known, n);
|
||||
|
||||
|
||||
if (n_matrices == 1) {
|
||||
cout << "Eigenvalues (after sorting):\n";
|
||||
for (int i = 0; i < n; i++)
|
||||
cout << evals_known[i] << " ";
|
||||
cout << "\n";
|
||||
cout << "Eigenvectors (rows) which are known in advance:\n";
|
||||
for (int i = 0; i < n; i++) {
|
||||
for (int j = 0; j < n; j++)
|
||||
cout << evecs_known[i][j] << " ";
|
||||
cout << "\n";
|
||||
}
|
||||
cout << " (The eigenvectors calculated by Jacobi::Diagonalize() should match these.)\n";
|
||||
}
|
||||
|
||||
for (int i_test = 0; i_test < n_tests_per_matrix; i_test++) {
|
||||
|
||||
if (test_code_coverage) {
|
||||
|
||||
// test SORT_INCREASING_ABS_EVALS:
|
||||
#if defined USE_VECTOR_OF_VECTORS
|
||||
ecalc.Diagonalize(M,
|
||||
evals,
|
||||
evecs,
|
||||
Jacobi<Scalar,
|
||||
vector<Scalar>&,
|
||||
vector<vector<Scalar> >&,
|
||||
const vector<vector<Scalar> >& >::SORT_INCREASING_ABS_EVALS);
|
||||
#elif defined USE_ARRAY_OF_ARRAYS
|
||||
ecalc.Diagonalize(M,
|
||||
evals,
|
||||
evecs,
|
||||
Jacobi<Scalar,
|
||||
array<Scalar,NF>&,
|
||||
array<array<Scalar,NF>,NF>&,
|
||||
const array<array<Scalar,NF>,NF>&>::SORT_INCREASING_ABS_EVALS);
|
||||
#elif defined USE_C_FIXED_SIZE_ARRAYS
|
||||
ecalc.Diagonalize(M,
|
||||
evals,
|
||||
evecs,
|
||||
Jacobi<Scalar,
|
||||
Scalar*,
|
||||
Scalar (*)[NF],
|
||||
Scalar const (*)[NF]>::SORT_INCREASING_ABS_EVALS);
|
||||
#else
|
||||
ecalc.Diagonalize(M,
|
||||
evals,
|
||||
evecs,
|
||||
Jacobi<Scalar,
|
||||
Scalar*,
|
||||
Scalar**,
|
||||
Scalar const*const*>::SORT_INCREASING_ABS_EVALS);
|
||||
#endif
|
||||
|
||||
for (int i = 1; i < n; i++)
|
||||
assert(std::abs(evals[i-1])<=std::abs(evals[i]));
|
||||
|
||||
// test SORT_DECREASING_ABS_EVALS:
|
||||
#if defined USE_VECTOR_OF_VECTORS
|
||||
ecalc.Diagonalize(M,
|
||||
evals,
|
||||
evecs,
|
||||
Jacobi<Scalar,
|
||||
vector<Scalar>&,
|
||||
vector<vector<Scalar> >&,
|
||||
const vector<vector<Scalar> >& >::SORT_DECREASING_ABS_EVALS);
|
||||
#elif defined USE_ARRAY_OF_ARRAYS
|
||||
ecalc.Diagonalize(M,
|
||||
evals,
|
||||
evecs,
|
||||
Jacobi<Scalar,
|
||||
array<Scalar,NF>&,
|
||||
array<array<Scalar,NF>,NF>&,
|
||||
const array<array<Scalar,NF>,NF>&>::SORT_DECREASING_ABS_EVALS);
|
||||
#elif defined USE_C_FIXED_SIZE_ARRAYS
|
||||
ecalc.Diagonalize(M,
|
||||
evals,
|
||||
evecs,
|
||||
Jacobi<Scalar,
|
||||
Scalar*,
|
||||
Scalar (*)[NF],
|
||||
Scalar const (*)[NF]>::SORT_DECREASING_ABS_EVALS);
|
||||
#else
|
||||
ecalc.Diagonalize(M,
|
||||
evals,
|
||||
evecs,
|
||||
Jacobi<Scalar,
|
||||
Scalar*,
|
||||
Scalar**,
|
||||
Scalar const*const*>::SORT_DECREASING_ABS_EVALS);
|
||||
#endif
|
||||
|
||||
for (int i = 1; i < n; i++)
|
||||
assert(std::abs(evals[i-1])>=std::abs(evals[i]));
|
||||
|
||||
// test SORT_INCREASING_EVALS:
|
||||
#if defined USE_VECTOR_OF_VECTORS
|
||||
ecalc.Diagonalize(M,
|
||||
evals,
|
||||
evecs,
|
||||
Jacobi<Scalar,
|
||||
vector<Scalar>&,
|
||||
vector<vector<Scalar> >&,
|
||||
const vector<vector<Scalar> >& >::SORT_INCREASING_EVALS);
|
||||
#elif defined USE_ARRAY_OF_ARRAYS
|
||||
ecalc.Diagonalize(M,
|
||||
evals,
|
||||
evecs,
|
||||
Jacobi<Scalar,
|
||||
array<Scalar,NF>&,
|
||||
array<array<Scalar,NF>,NF>&,
|
||||
const array<array<Scalar,NF>,NF>&>::SORT_INCREASING_EVALS);
|
||||
#elif defined USE_C_FIXED_SIZE_ARRAYS
|
||||
ecalc.Diagonalize(M,
|
||||
evals,
|
||||
evecs,
|
||||
Jacobi<Scalar,
|
||||
Scalar*,
|
||||
Scalar (*)[NF],
|
||||
Scalar const (*)[NF]>::SORT_INCREASING_EVALS);
|
||||
#else
|
||||
ecalc.Diagonalize(M,
|
||||
evals,
|
||||
evecs,
|
||||
Jacobi<Scalar,
|
||||
Scalar*,
|
||||
Scalar**,
|
||||
Scalar const*const*>::SORT_INCREASING_EVALS);
|
||||
#endif
|
||||
for (int i = 1; i < n; i++)
|
||||
assert(evals[i-1] <= evals[i]);
|
||||
|
||||
// test DO_NOT_SORT
|
||||
#if defined USE_VECTOR_OF_VECTORS
|
||||
ecalc.Diagonalize(M,
|
||||
evals,
|
||||
evecs,
|
||||
Jacobi<Scalar,
|
||||
vector<Scalar>&,
|
||||
vector<vector<Scalar> >&,
|
||||
const vector<vector<Scalar> >& >::DO_NOT_SORT);
|
||||
#elif defined USE_ARRAY_OF_ARRAYS
|
||||
ecalc.Diagonalize(M,
|
||||
evals,
|
||||
evecs,
|
||||
Jacobi<Scalar,
|
||||
array<Scalar,NF>&,
|
||||
array<array<Scalar,NF>,NF>&,
|
||||
const array<array<Scalar,NF>,NF>&>::DO_NOT_SORT);
|
||||
#elif defined USE_C_FIXED_SIZE_ARRAYS
|
||||
ecalc.Diagonalize(M,
|
||||
evals,
|
||||
evecs,
|
||||
Jacobi<Scalar,
|
||||
Scalar*,
|
||||
Scalar (*)[NF],
|
||||
Scalar const (*)[NF]>::DO_NOT_SORT);
|
||||
#else
|
||||
ecalc.Diagonalize(M,
|
||||
evals,
|
||||
evecs,
|
||||
Jacobi<Scalar,
|
||||
Scalar*,
|
||||
Scalar**,
|
||||
Scalar const*const*>::DO_NOT_SORT);
|
||||
#endif
|
||||
|
||||
} //if (test_code_coverage)
|
||||
|
||||
|
||||
// Now (finally) calculate the eigenvalues and eigenvectors
|
||||
int n_sweeps = ecalc.Diagonalize(M, evals, evecs);
|
||||
|
||||
if ((n_matrices == 1) && (i_test == 0)) {
|
||||
cout <<"Jacobi::Diagonalize() ran for "<<n_sweeps<<" iters (sweeps).\n";
|
||||
cout << "Eigenvalues calculated by Jacobi::Diagonalize()\n";
|
||||
for (int i = 0; i < n; i++)
|
||||
cout << evals[i] << " ";
|
||||
cout << "\n";
|
||||
cout << "Eigenvectors (rows) calculated by Jacobi::Diagonalize()\n";
|
||||
for (int i = 0; i < n; i++) {
|
||||
for (int j = 0; j < n; j++)
|
||||
cout << evecs[i][j] << " ";
|
||||
cout << "\n";
|
||||
}
|
||||
}
|
||||
|
||||
assert(SimilarVec(evals, evals_known, n, eps*max_eval_size, eps));
|
||||
//Check that each eigenvector satisfies Mv = λv
|
||||
// <--> Σ_b M[a][b]*evecs[i][b] = evals[i]*evecs[i][b] (for all a)
|
||||
for (int i = 0; i < n; i++) {
|
||||
for (int a = 0; a < n; a++) {
|
||||
test_evec[a] = 0.0;
|
||||
for (int b = 0; b < n; b++)
|
||||
test_evec[a] += M[a][b] * evecs[i][b];
|
||||
assert(Similar(test_evec[a],
|
||||
evals[i] * evecs[i][a],
|
||||
eps, // tolerance (absolute difference)
|
||||
eps*max_eval_size, // tolerance ratio (numerator)
|
||||
evals_known[i] // tolerance ration (denominator)
|
||||
));
|
||||
}
|
||||
}
|
||||
|
||||
} //for (int i_test = 0; i_test < n_tests_per_matrix; i++)
|
||||
|
||||
} //for(int imat = 0; imat < n_matrices; imat++) {
|
||||
|
||||
#if defined USE_C_POINTER_TO_POINTERS
|
||||
Dealloc2D(&M);
|
||||
Dealloc2D(&evecs);
|
||||
Dealloc2D(&evecs_known);
|
||||
delete [] evals;
|
||||
delete [] evals_known;
|
||||
delete [] test_evec;
|
||||
#endif
|
||||
|
||||
} //TestJacobi()
|
||||
|
||||
|
||||
int main(int argc, char **argv) {
|
||||
int n_size = 2;
|
||||
int n_matr = 1;
|
||||
double emin = 0.0;
|
||||
double emax = 1.0;
|
||||
int n_tests = 1;
|
||||
int n_degeneracy = 1;
|
||||
unsigned seed = 0;
|
||||
|
||||
if (argc <= 1) {
|
||||
cerr <<
|
||||
"Error: This program requires at least 1 argument.\n"
|
||||
"\n"
|
||||
"Description: Run Jacobi::Diagonalize() on randomly generated matrices.\n"
|
||||
"\n"
|
||||
"Arguments: n_size [n_matr emin emax n_degeneracy n_tests seed eps]\n"
|
||||
" n_size = the size of the matrices\n"
|
||||
" (NOTE: The remaining arguments are optional.)\n"
|
||||
" n_matr = the number of randomly generated matrices to test\n"
|
||||
" emin = the smallest possible eigenvalue magnitude (eg. 1e-05)\n"
|
||||
" emax = the largest possible eigenvalue magnitude (>0 eg. 1e+05)\n"
|
||||
" (NOTE: If emin=0, a normal distribution is used centered at 0.\n"
|
||||
" Otherwise a log-uniform distribution is used from emin to emax.)\n"
|
||||
" n_degeneracy = the number of repeated eigenvalues (1 disables, default)\n"
|
||||
" n_tests = the number of times the eigenvalues and eigenvectors\n"
|
||||
" are calculated for EACH matrix. By default this is 1.\n"
|
||||
" (Increase this to at least 20 if you plan to use this\n"
|
||||
" program for benchmarking (speed testing), because the time\n"
|
||||
" needed for generating a random matrix is not negligible.)\n"
|
||||
" (IF THIS NUMBER IS 0, it will test CODE-COVERAGE instead.)\n"
|
||||
" seed = the seed used by the random number \"rand_generator\".\n"
|
||||
" (If this number is 0, which is the default, the system\n"
|
||||
" clock is used to choose a random seed.)\n"
|
||||
" eps = the tolerance. The difference between eigenvalues and their\n"
|
||||
" true value, cannot exceed this (multiplied by the eigenvalue\n"
|
||||
" of maximum magnitude). Similarly, the difference between\n"
|
||||
" the eigenvectors after multiplication by the matrix and by\n"
|
||||
" and after multiplication by the eigenvalue, cannot exceed\n"
|
||||
" eps*maximum_eigenvalue/eigenvalue. The default value is\n"
|
||||
" 1.0e-06 (which works well for double precision numbers).\n"
|
||||
<< endl;
|
||||
return 1;
|
||||
}
|
||||
|
||||
n_size = std::stoi(argv[1]);
|
||||
if (argc > 2)
|
||||
n_matr = std::stoi(argv[2]);
|
||||
if (argc > 3)
|
||||
emin = std::stof(argv[3]);
|
||||
if (argc > 4)
|
||||
emax = std::stof(argv[4]);
|
||||
if (argc > 5)
|
||||
n_degeneracy = std::stoi(argv[5]);
|
||||
if (argc > 6)
|
||||
n_tests = std::stoi(argv[6]);
|
||||
if (argc > 7)
|
||||
seed = std::stoi(argv[7]);
|
||||
double eps = 1.0e-06;
|
||||
if (argc > 8)
|
||||
eps = std::stof(argv[8]);
|
||||
|
||||
TestJacobi(n_size, n_matr, emin, emax, n_tests, n_degeneracy, seed, eps);
|
||||
|
||||
cout << "test passed\n" << endl;
|
||||
return EXIT_SUCCESS;
|
||||
}
|
||||
Reference in New Issue
Block a user