convert linalg library from Fortran to C++
This commit is contained in:
Axel Kohlmeyer
379
lib/linalg/zheev.cpp
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379
lib/linalg/zheev.cpp
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/* fortran/zheev.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__1 = 1;
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static integer c_n1 = -1;
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static integer c__0 = 0;
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static doublereal c_b18 = 1.;
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/* > \brief <b> ZHEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matr
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ices</b> */
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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 ZHEEV + dependencies */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zheev.f
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"> */
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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/zheev.f
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"> */
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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/zheev.f
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"> */
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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 ZHEEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, */
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/* INFO ) */
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/* .. Scalar Arguments .. */
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/* CHARACTER JOBZ, UPLO */
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/* INTEGER INFO, LDA, LWORK, N */
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/* .. */
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/* .. Array Arguments .. */
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/* DOUBLE PRECISION RWORK( * ), W( * ) */
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/* COMPLEX*16 A( LDA, * ), 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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/* > ZHEEV computes all eigenvalues and, optionally, eigenvectors of a */
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/* > complex Hermitian matrix A. */
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/* > \endverbatim */
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/* Arguments: */
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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 triangle of A is stored; */
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/* > = 'L': Lower triangle of A is 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 matrix A. 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 COMPLEX*16 array, dimension (LDA, N) */
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/* > On entry, the Hermitian 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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/* > On exit, if JOBZ = 'V', then if INFO = 0, A contains the */
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/* > orthonormal eigenvectors of the matrix A. */
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/* > If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') */
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/* > or the upper triangle (if UPLO='U') 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[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 COMPLEX*16 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 length of the array WORK. LWORK >= max(1,2*N-1). */
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/* > For optimal efficiency, LWORK >= (NB+1)*N, */
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/* > where NB is the blocksize for ZHETRD returned by ILAENV. */
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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 size of the WORK array, returns */
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/* > this value as the first entry of the WORK array, and no error */
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/* > message related to LWORK is issued by XERBLA. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] RWORK */
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/* > \verbatim */
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/* > RWORK is DOUBLE PRECISION array, dimension (max(1, 3*N-2)) */
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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: if INFO = i, the algorithm failed to converge; i */
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/* > off-diagonal elements of an intermediate tridiagonal */
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/* > form did not converge to zero. */
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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 complex16HEeigen */
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/* ===================================================================== */
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/* Subroutine */ int zheev_(char *jobz, char *uplo, integer *n, doublecomplex
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*a, integer *lda, doublereal *w, doublecomplex *work, integer *lwork,
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doublereal *rwork, 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, i__1, i__2;
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doublereal d__1;
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/* Builtin functions */
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double sqrt(doublereal);
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/* Local variables */
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integer nb;
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doublereal eps;
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integer inde;
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doublereal anrm;
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integer imax;
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doublereal rmin, rmax;
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extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
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integer *);
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doublereal sigma;
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extern logical lsame_(char *, char *, ftnlen, ftnlen);
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integer iinfo;
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logical lower, wantz;
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extern doublereal dlamch_(char *, ftnlen);
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integer iscale;
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doublereal safmin;
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extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
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integer *, integer *, ftnlen, ftnlen);
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extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
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doublereal bignum;
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extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *,
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integer *, doublereal *, ftnlen, ftnlen);
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integer indtau;
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extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *,
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integer *), zlascl_(char *, integer *, integer *, doublereal *,
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doublereal *, integer *, integer *, doublecomplex *, integer *,
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integer *, ftnlen);
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integer indwrk;
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extern /* Subroutine */ int zhetrd_(char *, integer *, doublecomplex *,
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integer *, doublereal *, doublereal *, doublecomplex *,
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doublecomplex *, integer *, integer *, ftnlen);
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integer llwork;
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doublereal smlnum;
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integer lwkopt;
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logical lquery;
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extern /* Subroutine */ int zsteqr_(char *, integer *, doublereal *,
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doublereal *, doublecomplex *, integer *, doublereal *, integer *,
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ftnlen), zungtr_(char *, integer *, doublecomplex *, integer *,
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doublecomplex *, doublecomplex *, integer *, integer *, ftnlen);
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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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--w;
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--work;
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--rwork;
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/* Function Body */
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wantz = lsame_(jobz, (char *)"V", (ftnlen)1, (ftnlen)1);
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lower = lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1);
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lquery = *lwork == -1;
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*info = 0;
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if (! (wantz || lsame_(jobz, (char *)"N", (ftnlen)1, (ftnlen)1))) {
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*info = -1;
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} else if (! (lower || lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1))) {
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*info = -2;
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} else if (*n < 0) {
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*info = -3;
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} else if (*lda < max(1,*n)) {
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*info = -5;
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}
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if (*info == 0) {
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nb = ilaenv_(&c__1, (char *)"ZHETRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6,
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(ftnlen)1);
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/* Computing MAX */
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i__1 = 1, i__2 = (nb + 1) * *n;
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lwkopt = max(i__1,i__2);
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work[1].r = (doublereal) lwkopt, work[1].i = 0.;
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/* Computing MAX */
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i__1 = 1, i__2 = (*n << 1) - 1;
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if (*lwork < max(i__1,i__2) && ! lquery) {
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*info = -8;
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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 *)"ZHEEV ", &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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if (*n == 1) {
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i__1 = a_dim1 + 1;
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w[1] = a[i__1].r;
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work[1].r = 1., work[1].i = 0.;
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if (wantz) {
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i__1 = a_dim1 + 1;
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a[i__1].r = 1., a[i__1].i = 0.;
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}
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return 0;
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}
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/* Get machine constants. */
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safmin = dlamch_((char *)"Safe minimum", (ftnlen)12);
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eps = dlamch_((char *)"Precision", (ftnlen)9);
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smlnum = safmin / eps;
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bignum = 1. / smlnum;
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rmin = sqrt(smlnum);
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rmax = sqrt(bignum);
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/* Scale matrix to allowable range, if necessary. */
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anrm = zlanhe_((char *)"M", uplo, n, &a[a_offset], lda, &rwork[1], (ftnlen)1, (
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ftnlen)1);
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iscale = 0;
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if (anrm > 0. && anrm < rmin) {
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iscale = 1;
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sigma = rmin / anrm;
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} else if (anrm > rmax) {
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iscale = 1;
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sigma = rmax / anrm;
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}
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if (iscale == 1) {
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zlascl_(uplo, &c__0, &c__0, &c_b18, &sigma, n, n, &a[a_offset], lda,
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info, (ftnlen)1);
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}
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/* Call ZHETRD to reduce Hermitian matrix to tridiagonal form. */
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inde = 1;
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indtau = 1;
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indwrk = indtau + *n;
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llwork = *lwork - indwrk + 1;
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zhetrd_(uplo, n, &a[a_offset], lda, &w[1], &rwork[inde], &work[indtau], &
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work[indwrk], &llwork, &iinfo, (ftnlen)1);
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/* For eigenvalues only, call DSTERF. For eigenvectors, first call */
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/* ZUNGTR to generate the unitary matrix, then call ZSTEQR. */
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if (! wantz) {
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dsterf_(n, &w[1], &rwork[inde], info);
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} else {
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zungtr_(uplo, n, &a[a_offset], lda, &work[indtau], &work[indwrk], &
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llwork, &iinfo, (ftnlen)1);
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indwrk = inde + *n;
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zsteqr_(jobz, n, &w[1], &rwork[inde], &a[a_offset], lda, &rwork[
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indwrk], info, (ftnlen)1);
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}
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/* If matrix was scaled, then rescale eigenvalues appropriately. */
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if (iscale == 1) {
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if (*info == 0) {
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imax = *n;
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} else {
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imax = *info - 1;
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}
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d__1 = 1. / sigma;
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dscal_(&imax, &d__1, &w[1], &c__1);
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}
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/* Set WORK(1) to optimal complex workspace size. */
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work[1].r = (doublereal) lwkopt, work[1].i = 0.;
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return 0;
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/* End of ZHEEV */
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} /* zheev_ */
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#ifdef __cplusplus
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}
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#endif
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