387 lines
12 KiB
C++
387 lines
12 KiB
C++
/* fortran/dlaeda.f -- translated by f2c (version 20200916).
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You must link the resulting object file with libf2c:
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on Microsoft Windows system, link with libf2c.lib;
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm
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or, if you install libf2c.a in a standard place, with -lf2c -lm
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-- in that order, at the end of the command line, as in
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cc *.o -lf2c -lm
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
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http://www.netlib.org/f2c/libf2c.zip
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*/
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#ifdef __cplusplus
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extern "C" {
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#endif
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#include "lmp_f2c.h"
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/* Table of constant values */
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static integer c__2 = 2;
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static integer c__1 = 1;
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static doublereal c_b24 = 1.;
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static doublereal c_b26 = 0.;
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/* > \brief \b DLAEDA used by DSTEDC. Computes the Z vector determining the rank-one modification of the diago
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nal matrix. Used when the original matrix is dense. */
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/* =========== DOCUMENTATION =========== */
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/* Online html documentation available at */
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/* http://www.netlib.org/lapack/explore-html/ */
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/* > \htmlonly */
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/* > Download DLAEDA + dependencies */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaeda.
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f"> */
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/* > [TGZ]</a> */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaeda.
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f"> */
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/* > [ZIP]</a> */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaeda.
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f"> */
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/* > [TXT]</a> */
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/* > \endhtmlonly */
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/* Definition: */
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/* =========== */
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/* SUBROUTINE DLAEDA( N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR, */
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/* GIVCOL, GIVNUM, Q, QPTR, Z, ZTEMP, INFO ) */
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/* .. Scalar Arguments .. */
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/* INTEGER CURLVL, CURPBM, INFO, N, TLVLS */
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/* .. */
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/* .. Array Arguments .. */
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/* INTEGER GIVCOL( 2, * ), GIVPTR( * ), PERM( * ), */
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/* $ PRMPTR( * ), QPTR( * ) */
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/* DOUBLE PRECISION GIVNUM( 2, * ), Q( * ), Z( * ), ZTEMP( * ) */
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/* .. */
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/* > \par Purpose: */
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/* ============= */
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/* > */
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/* > \verbatim */
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/* > */
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/* > DLAEDA computes the Z vector corresponding to the merge step in the */
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/* > CURLVLth step of the merge process with TLVLS steps for the CURPBMth */
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/* > problem. */
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/* > \endverbatim */
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/* Arguments: */
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/* ========== */
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/* > \param[in] N */
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/* > \verbatim */
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/* > N is INTEGER */
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/* > The dimension of the symmetric tridiagonal matrix. N >= 0. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] TLVLS */
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/* > \verbatim */
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/* > TLVLS is INTEGER */
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/* > The total number of merging levels in the overall divide and */
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/* > conquer tree. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] CURLVL */
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/* > \verbatim */
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/* > CURLVL is INTEGER */
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/* > The current level in the overall merge routine, */
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/* > 0 <= curlvl <= tlvls. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] CURPBM */
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/* > \verbatim */
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/* > CURPBM is INTEGER */
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/* > The current problem in the current level in the overall */
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/* > merge routine (counting from upper left to lower right). */
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/* > \endverbatim */
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/* > */
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/* > \param[in] PRMPTR */
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/* > \verbatim */
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/* > PRMPTR is INTEGER array, dimension (N lg N) */
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/* > Contains a list of pointers which indicate where in PERM a */
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/* > level's permutation is stored. PRMPTR(i+1) - PRMPTR(i) */
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/* > indicates the size of the permutation and incidentally the */
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/* > size of the full, non-deflated problem. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] PERM */
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/* > \verbatim */
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/* > PERM is INTEGER array, dimension (N lg N) */
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/* > Contains the permutations (from deflation and sorting) to be */
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/* > applied to each eigenblock. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] GIVPTR */
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/* > \verbatim */
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/* > GIVPTR is INTEGER array, dimension (N lg N) */
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/* > Contains a list of pointers which indicate where in GIVCOL a */
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/* > level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i) */
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/* > indicates the number of Givens rotations. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] GIVCOL */
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/* > \verbatim */
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/* > GIVCOL is INTEGER array, dimension (2, N lg N) */
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/* > Each pair of numbers indicates a pair of columns to take place */
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/* > in a Givens rotation. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] GIVNUM */
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/* > \verbatim */
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/* > GIVNUM is DOUBLE PRECISION array, dimension (2, N lg N) */
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/* > Each number indicates the S value to be used in the */
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/* > corresponding Givens rotation. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] Q */
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/* > \verbatim */
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/* > Q is DOUBLE PRECISION array, dimension (N**2) */
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/* > Contains the square eigenblocks from previous levels, the */
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/* > starting positions for blocks are given by QPTR. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] QPTR */
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/* > \verbatim */
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/* > QPTR is INTEGER array, dimension (N+2) */
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/* > Contains a list of pointers which indicate where in Q an */
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/* > eigenblock is stored. SQRT( QPTR(i+1) - QPTR(i) ) indicates */
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/* > the size of the block. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] Z */
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/* > \verbatim */
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/* > Z is DOUBLE PRECISION array, dimension (N) */
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/* > On output this vector contains the updating vector (the last */
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/* > row of the first sub-eigenvector matrix and the first row of */
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/* > the second sub-eigenvector matrix). */
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/* > \endverbatim */
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/* > */
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/* > \param[out] ZTEMP */
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/* > \verbatim */
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/* > ZTEMP is DOUBLE PRECISION array, dimension (N) */
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/* > \endverbatim */
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/* > */
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/* > \param[out] INFO */
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/* > \verbatim */
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/* > INFO is INTEGER */
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/* > = 0: successful exit. */
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/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
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/* > \endverbatim */
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/* Authors: */
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/* ======== */
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/* > \author Univ. of Tennessee */
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/* > \author Univ. of California Berkeley */
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/* > \author Univ. of Colorado Denver */
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/* > \author NAG Ltd. */
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/* > \ingroup auxOTHERcomputational */
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/* > \par Contributors: */
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/* ================== */
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/* > */
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/* > Jeff Rutter, Computer Science Division, University of California */
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/* > at Berkeley, USA */
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/* ===================================================================== */
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/* Subroutine */ int dlaeda_(integer *n, integer *tlvls, integer *curlvl,
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integer *curpbm, integer *prmptr, integer *perm, integer *givptr,
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integer *givcol, doublereal *givnum, doublereal *q, integer *qptr,
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doublereal *z__, doublereal *ztemp, integer *info)
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{
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/* System generated locals */
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integer i__1, i__2, i__3;
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/* Builtin functions */
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integer pow_ii(integer *, integer *);
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double sqrt(doublereal);
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/* Local variables */
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integer i__, k, mid, ptr;
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extern /* Subroutine */ int drot_(integer *, doublereal *, integer *,
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doublereal *, integer *, doublereal *, doublereal *);
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integer curr, bsiz1, bsiz2, psiz1, psiz2, zptr1;
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extern /* Subroutine */ int dgemv_(char *, integer *, integer *,
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doublereal *, doublereal *, integer *, doublereal *, integer *,
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doublereal *, doublereal *, integer *, ftnlen), dcopy_(integer *,
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doublereal *, integer *, doublereal *, integer *), xerbla_(char *,
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integer *, ftnlen);
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/* -- LAPACK computational routine -- */
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/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
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/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
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/* .. Scalar Arguments .. */
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/* .. */
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/* .. Array Arguments .. */
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/* .. */
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/* ===================================================================== */
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/* .. Parameters .. */
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/* .. */
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/* .. Local Scalars .. */
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/* .. */
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/* .. External Subroutines .. */
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/* .. */
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/* .. Intrinsic Functions .. */
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/* .. */
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/* .. Executable Statements .. */
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/* Test the input parameters. */
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/* Parameter adjustments */
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--ztemp;
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--z__;
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--qptr;
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--q;
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givnum -= 3;
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givcol -= 3;
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--givptr;
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--perm;
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--prmptr;
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/* Function Body */
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*info = 0;
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if (*n < 0) {
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*info = -1;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_((char *)"DLAEDA", &i__1, (ftnlen)6);
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return 0;
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}
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/* Quick return if possible */
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if (*n == 0) {
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return 0;
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}
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/* Determine location of first number in second half. */
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mid = *n / 2 + 1;
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/* Gather last/first rows of appropriate eigenblocks into center of Z */
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ptr = 1;
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/* Determine location of lowest level subproblem in the full storage */
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/* scheme */
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i__1 = *curlvl - 1;
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curr = ptr + *curpbm * pow_ii(&c__2, curlvl) + pow_ii(&c__2, &i__1) - 1;
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/* Determine size of these matrices. We add HALF to the value of */
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/* the SQRT in case the machine underestimates one of these square */
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/* roots. */
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bsiz1 = (integer) (sqrt((doublereal) (qptr[curr + 1] - qptr[curr])) + .5);
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bsiz2 = (integer) (sqrt((doublereal) (qptr[curr + 2] - qptr[curr + 1])) +
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.5);
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i__1 = mid - bsiz1 - 1;
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for (k = 1; k <= i__1; ++k) {
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z__[k] = 0.;
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/* L10: */
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}
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dcopy_(&bsiz1, &q[qptr[curr] + bsiz1 - 1], &bsiz1, &z__[mid - bsiz1], &
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c__1);
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dcopy_(&bsiz2, &q[qptr[curr + 1]], &bsiz2, &z__[mid], &c__1);
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i__1 = *n;
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for (k = mid + bsiz2; k <= i__1; ++k) {
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z__[k] = 0.;
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/* L20: */
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}
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/* Loop through remaining levels 1 -> CURLVL applying the Givens */
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/* rotations and permutation and then multiplying the center matrices */
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/* against the current Z. */
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ptr = pow_ii(&c__2, tlvls) + 1;
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i__1 = *curlvl - 1;
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for (k = 1; k <= i__1; ++k) {
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i__2 = *curlvl - k;
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i__3 = *curlvl - k - 1;
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curr = ptr + *curpbm * pow_ii(&c__2, &i__2) + pow_ii(&c__2, &i__3) -
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1;
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psiz1 = prmptr[curr + 1] - prmptr[curr];
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psiz2 = prmptr[curr + 2] - prmptr[curr + 1];
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zptr1 = mid - psiz1;
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/* Apply Givens at CURR and CURR+1 */
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i__2 = givptr[curr + 1] - 1;
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for (i__ = givptr[curr]; i__ <= i__2; ++i__) {
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drot_(&c__1, &z__[zptr1 + givcol[(i__ << 1) + 1] - 1], &c__1, &
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z__[zptr1 + givcol[(i__ << 1) + 2] - 1], &c__1, &givnum[(
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i__ << 1) + 1], &givnum[(i__ << 1) + 2]);
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/* L30: */
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}
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i__2 = givptr[curr + 2] - 1;
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for (i__ = givptr[curr + 1]; i__ <= i__2; ++i__) {
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drot_(&c__1, &z__[mid - 1 + givcol[(i__ << 1) + 1]], &c__1, &z__[
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mid - 1 + givcol[(i__ << 1) + 2]], &c__1, &givnum[(i__ <<
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1) + 1], &givnum[(i__ << 1) + 2]);
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/* L40: */
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}
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psiz1 = prmptr[curr + 1] - prmptr[curr];
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psiz2 = prmptr[curr + 2] - prmptr[curr + 1];
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i__2 = psiz1 - 1;
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for (i__ = 0; i__ <= i__2; ++i__) {
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ztemp[i__ + 1] = z__[zptr1 + perm[prmptr[curr] + i__] - 1];
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/* L50: */
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}
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i__2 = psiz2 - 1;
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for (i__ = 0; i__ <= i__2; ++i__) {
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ztemp[psiz1 + i__ + 1] = z__[mid + perm[prmptr[curr + 1] + i__] -
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1];
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/* L60: */
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}
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/* Multiply Blocks at CURR and CURR+1 */
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/* Determine size of these matrices. We add HALF to the value of */
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/* the SQRT in case the machine underestimates one of these */
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/* square roots. */
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bsiz1 = (integer) (sqrt((doublereal) (qptr[curr + 1] - qptr[curr])) +
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.5);
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bsiz2 = (integer) (sqrt((doublereal) (qptr[curr + 2] - qptr[curr + 1])
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) + .5);
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if (bsiz1 > 0) {
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dgemv_((char *)"T", &bsiz1, &bsiz1, &c_b24, &q[qptr[curr]], &bsiz1, &
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ztemp[1], &c__1, &c_b26, &z__[zptr1], &c__1, (ftnlen)1);
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}
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i__2 = psiz1 - bsiz1;
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dcopy_(&i__2, &ztemp[bsiz1 + 1], &c__1, &z__[zptr1 + bsiz1], &c__1);
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if (bsiz2 > 0) {
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dgemv_((char *)"T", &bsiz2, &bsiz2, &c_b24, &q[qptr[curr + 1]], &bsiz2, &
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ztemp[psiz1 + 1], &c__1, &c_b26, &z__[mid], &c__1, (
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ftnlen)1);
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}
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i__2 = psiz2 - bsiz2;
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dcopy_(&i__2, &ztemp[psiz1 + bsiz2 + 1], &c__1, &z__[mid + bsiz2], &
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c__1);
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i__2 = *tlvls - k;
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ptr += pow_ii(&c__2, &i__2);
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/* L70: */
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}
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return 0;
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/* End of DLAEDA */
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} /* dlaeda_ */
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#ifdef __cplusplus
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}
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#endif
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