446 lines
15 KiB
C++
446 lines
15 KiB
C++
/* fortran/dsygvd.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 doublereal c_b11 = 1.;
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/* > \brief \b DSYGVD */
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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 DSYGVD + dependencies */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsygvd.
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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/dsygvd.
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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/dsygvd.
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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 DSYGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, */
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/* LWORK, IWORK, LIWORK, INFO ) */
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/* .. Scalar Arguments .. */
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/* CHARACTER JOBZ, UPLO */
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/* INTEGER INFO, ITYPE, LDA, LDB, LIWORK, LWORK, N */
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/* .. */
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/* .. Array Arguments .. */
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/* INTEGER IWORK( * ) */
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/* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * ) */
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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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/* > DSYGVD computes all the eigenvalues, and optionally, the eigenvectors */
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/* > of a real generalized symmetric-definite eigenproblem, of the form */
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/* > A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and */
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/* > B are assumed to be symmetric and B is also positive definite. */
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/* > If eigenvectors are desired, it uses a divide and conquer algorithm. */
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/* > */
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/* > The divide and conquer algorithm makes very mild assumptions about */
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/* > floating point arithmetic. It will work on machines with a guard */
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/* > digit in add/subtract, or on those binary machines without guard */
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/* > digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */
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/* > Cray-2. It could conceivably fail on hexadecimal or decimal machines */
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/* > without guard digits, but we know of none. */
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/* > \endverbatim */
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/* Arguments: */
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/* ========== */
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/* > \param[in] ITYPE */
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/* > \verbatim */
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/* > ITYPE is INTEGER */
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/* > Specifies the problem type to be solved: */
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/* > = 1: A*x = (lambda)*B*x */
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/* > = 2: A*B*x = (lambda)*x */
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/* > = 3: B*A*x = (lambda)*x */
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/* > \endverbatim */
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/* > */
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/* > \param[in] JOBZ */
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/* > \verbatim */
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/* > JOBZ is CHARACTER*1 */
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/* > = 'N': Compute eigenvalues only; */
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/* > = 'V': Compute eigenvalues and eigenvectors. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] UPLO */
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/* > \verbatim */
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/* > UPLO is CHARACTER*1 */
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/* > = 'U': Upper triangles of A and B are stored; */
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/* > = 'L': Lower triangles of A and B are stored. */
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/* > \endverbatim */
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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 order of the matrices A and B. N >= 0. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] A */
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/* > \verbatim */
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/* > A is DOUBLE PRECISION array, dimension (LDA, N) */
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/* > On entry, the symmetric matrix A. If UPLO = 'U', the */
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/* > leading N-by-N upper triangular part of A contains the */
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/* > upper triangular part of the matrix A. If UPLO = 'L', */
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/* > the leading N-by-N lower triangular part of A contains */
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/* > the lower triangular part of the matrix A. */
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/* > */
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/* > On exit, if JOBZ = 'V', then if INFO = 0, A contains the */
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/* > matrix Z of eigenvectors. The eigenvectors are normalized */
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/* > as follows: */
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/* > if ITYPE = 1 or 2, Z**T*B*Z = I; */
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/* > if ITYPE = 3, Z**T*inv(B)*Z = I. */
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/* > If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') */
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/* > or the lower triangle (if UPLO='L') of A, including the */
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/* > diagonal, is destroyed. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDA */
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/* > \verbatim */
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/* > LDA is INTEGER */
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/* > The leading dimension of the array A. LDA >= max(1,N). */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] B */
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/* > \verbatim */
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/* > B is DOUBLE PRECISION array, dimension (LDB, N) */
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/* > On entry, the symmetric matrix B. If UPLO = 'U', the */
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/* > leading N-by-N upper triangular part of B contains the */
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/* > upper triangular part of the matrix B. If UPLO = 'L', */
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/* > the leading N-by-N lower triangular part of B contains */
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/* > the lower triangular part of the matrix B. */
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/* > */
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/* > On exit, if INFO <= N, the part of B containing the matrix is */
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/* > overwritten by the triangular factor U or L from the Cholesky */
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/* > factorization B = U**T*U or B = L*L**T. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDB */
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/* > \verbatim */
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/* > LDB is INTEGER */
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/* > The leading dimension of the array B. LDB >= max(1,N). */
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/* > \endverbatim */
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/* > */
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/* > \param[out] W */
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/* > \verbatim */
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/* > W is DOUBLE PRECISION array, dimension (N) */
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/* > If INFO = 0, the eigenvalues in ascending order. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] WORK */
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/* > \verbatim */
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/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
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/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LWORK */
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/* > \verbatim */
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/* > LWORK is INTEGER */
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/* > The dimension of the array WORK. */
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/* > If N <= 1, LWORK >= 1. */
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/* > If JOBZ = 'N' and N > 1, LWORK >= 2*N+1. */
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/* > If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2. */
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/* > */
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/* > If LWORK = -1, then a workspace query is assumed; the routine */
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/* > only calculates the optimal sizes of the WORK and IWORK */
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/* > arrays, returns these values as the first entries of the WORK */
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/* > and IWORK arrays, and no error message related to LWORK or */
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/* > LIWORK is issued by XERBLA. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] IWORK */
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/* > \verbatim */
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/* > IWORK is INTEGER array, dimension (MAX(1,LIWORK)) */
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/* > On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LIWORK */
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/* > \verbatim */
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/* > LIWORK is INTEGER */
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/* > The dimension of the array IWORK. */
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/* > If N <= 1, LIWORK >= 1. */
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/* > If JOBZ = 'N' and N > 1, LIWORK >= 1. */
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/* > If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. */
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/* > */
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/* > If LIWORK = -1, then a workspace query is assumed; the */
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/* > routine only calculates the optimal sizes of the WORK and */
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/* > IWORK arrays, returns these values as the first entries of */
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/* > the WORK and IWORK arrays, and no error message related to */
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/* > LWORK or LIWORK is issued by XERBLA. */
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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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/* > > 0: DPOTRF or DSYEVD returned an error code: */
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/* > <= N: if INFO = i and JOBZ = 'N', then the algorithm */
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/* > failed to converge; i off-diagonal elements of an */
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/* > intermediate tridiagonal form did not converge to */
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/* > zero; */
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/* > if INFO = i and JOBZ = 'V', then the algorithm */
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/* > failed to compute an eigenvalue while working on */
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/* > the submatrix lying in rows and columns INFO/(N+1) */
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/* > through mod(INFO,N+1); */
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/* > > N: if INFO = N + i, for 1 <= i <= N, then the leading */
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/* > minor of order i of B is not positive definite. */
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/* > The factorization of B could not be completed and */
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/* > no eigenvalues or eigenvectors were computed. */
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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 doubleSYeigen */
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/* > \par Further Details: */
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/* ===================== */
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/* > */
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/* > \verbatim */
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/* > */
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/* > Modified so that no backsubstitution is performed if DSYEVD fails to */
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/* > converge (NEIG in old code could be greater than N causing out of */
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/* > bounds reference to A - reported by Ralf Meyer). Also corrected the */
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/* > description of INFO and the test on ITYPE. Sven, 16 Feb 05. */
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/* > \endverbatim */
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/* > \par Contributors: */
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/* ================== */
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/* > */
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/* > Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA */
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/* > */
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/* ===================================================================== */
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/* Subroutine */ int dsygvd_(integer *itype, char *jobz, char *uplo, integer *
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n, doublereal *a, integer *lda, doublereal *b, integer *ldb,
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doublereal *w, doublereal *work, integer *lwork, integer *iwork,
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integer *liwork, integer *info, ftnlen jobz_len, ftnlen uplo_len)
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{
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/* System generated locals */
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integer a_dim1, a_offset, b_dim1, b_offset, i__1;
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doublereal d__1, d__2;
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/* Local variables */
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integer lopt;
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extern logical lsame_(char *, char *, ftnlen, ftnlen);
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extern /* Subroutine */ int dtrmm_(char *, char *, char *, char *,
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integer *, integer *, doublereal *, doublereal *, integer *,
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doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen);
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integer lwmin;
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char trans[1];
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integer liopt;
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extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *,
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integer *, integer *, doublereal *, doublereal *, integer *,
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doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen);
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logical upper, wantz;
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extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), dpotrf_(
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char *, integer *, doublereal *, integer *, integer *, ftnlen);
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integer liwmin;
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extern /* Subroutine */ int dsyevd_(char *, char *, integer *, doublereal
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*, integer *, doublereal *, doublereal *, integer *, integer *,
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integer *, integer *, ftnlen, ftnlen), dsygst_(integer *, char *,
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integer *, doublereal *, integer *, doublereal *, integer *,
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integer *, ftnlen);
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logical lquery;
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/* -- LAPACK driver 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 Functions .. */
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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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a_dim1 = *lda;
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a_offset = 1 + a_dim1;
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a -= a_offset;
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b_dim1 = *ldb;
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b_offset = 1 + b_dim1;
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b -= b_offset;
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--w;
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--work;
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--iwork;
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/* Function Body */
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wantz = lsame_(jobz, (char *)"V", (ftnlen)1, (ftnlen)1);
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upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1);
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lquery = *lwork == -1 || *liwork == -1;
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*info = 0;
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if (*n <= 1) {
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liwmin = 1;
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lwmin = 1;
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} else if (wantz) {
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liwmin = *n * 5 + 3;
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/* Computing 2nd power */
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i__1 = *n;
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lwmin = *n * 6 + 1 + (i__1 * i__1 << 1);
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} else {
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liwmin = 1;
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lwmin = (*n << 1) + 1;
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}
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lopt = lwmin;
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liopt = liwmin;
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if (*itype < 1 || *itype > 3) {
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*info = -1;
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} else if (! (wantz || lsame_(jobz, (char *)"N", (ftnlen)1, (ftnlen)1))) {
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*info = -2;
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} else if (! (upper || lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1))) {
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*info = -3;
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} else if (*n < 0) {
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*info = -4;
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} else if (*lda < max(1,*n)) {
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*info = -6;
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} else if (*ldb < max(1,*n)) {
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*info = -8;
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}
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if (*info == 0) {
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work[1] = (doublereal) lopt;
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iwork[1] = liopt;
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if (*lwork < lwmin && ! lquery) {
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*info = -11;
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} else if (*liwork < liwmin && ! lquery) {
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*info = -13;
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}
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_((char *)"DSYGVD", &i__1, (ftnlen)6);
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return 0;
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} else if (lquery) {
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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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/* Form a Cholesky factorization of B. */
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dpotrf_(uplo, n, &b[b_offset], ldb, info, (ftnlen)1);
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if (*info != 0) {
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*info = *n + *info;
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return 0;
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}
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/* Transform problem to standard eigenvalue problem and solve. */
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dsygst_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info, (
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ftnlen)1);
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dsyevd_(jobz, uplo, n, &a[a_offset], lda, &w[1], &work[1], lwork, &iwork[
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1], liwork, info, (ftnlen)1, (ftnlen)1);
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/* Computing MAX */
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d__1 = (doublereal) lopt;
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lopt = (integer) max(d__1,work[1]);
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/* Computing MAX */
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d__1 = (doublereal) liopt, d__2 = (doublereal) iwork[1];
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liopt = (integer) max(d__1,d__2);
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if (wantz && *info == 0) {
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/* Backtransform eigenvectors to the original problem. */
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if (*itype == 1 || *itype == 2) {
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/* For A*x=(lambda)*B*x and A*B*x=(lambda)*x; */
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/* backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y */
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if (upper) {
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*(unsigned char *)trans = 'N';
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} else {
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*(unsigned char *)trans = 'T';
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}
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dtrsm_((char *)"Left", uplo, trans, (char *)"Non-unit", n, n, &c_b11, &b[b_offset]
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, ldb, &a[a_offset], lda, (ftnlen)4, (ftnlen)1, (ftnlen)1,
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(ftnlen)8);
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} else if (*itype == 3) {
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/* For B*A*x=(lambda)*x; */
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/* backtransform eigenvectors: x = L*y or U**T*y */
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if (upper) {
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*(unsigned char *)trans = 'T';
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} else {
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*(unsigned char *)trans = 'N';
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}
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dtrmm_((char *)"Left", uplo, trans, (char *)"Non-unit", n, n, &c_b11, &b[b_offset]
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, ldb, &a[a_offset], lda, (ftnlen)4, (ftnlen)1, (ftnlen)1,
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(ftnlen)8);
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}
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}
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work[1] = (doublereal) lopt;
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iwork[1] = liopt;
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return 0;
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/* End of DSYGVD */
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} /* dsygvd_ */
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#ifdef __cplusplus
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}
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#endif
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