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/* ../../../dependencies/lapack/src/cheev.f -- translated by f2c (version 20061008).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
/* Table of constant values */
static integer c__1 = 1;
static integer c_n1 = -1;
static integer c__0 = 0;
static real c_b18 = 1.f;
/* Subroutine */ int cheev_(char *jobz, char *uplo, integer *n, complex *a,
integer *lda, real *w, complex *work, integer *lwork, real *rwork,
integer *info, ftnlen jobz_len, ftnlen uplo_len)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
real r__1;
complex q__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
static integer nb;
static real eps;
static integer inde;
static real anrm;
static integer imax;
static real rmin, rmax;
static integer lopt;
static real sigma;
extern logical lsame_(char *, char *, ftnlen, ftnlen);
static integer iinfo;
extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
static logical lower, wantz;
extern doublereal clanhe_(char *, char *, integer *, complex *, integer *,
real *, ftnlen, ftnlen);
static integer iscale;
extern /* Subroutine */ int clascl_(char *, integer *, integer *, real *,
real *, integer *, integer *, complex *, integer *, integer *,
ftnlen);
extern doublereal slamch_(char *, ftnlen);
extern /* Subroutine */ int chetrd_(char *, integer *, complex *, integer
*, real *, real *, complex *, complex *, integer *, integer *,
ftnlen);
static real safmin;
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
static real bignum;
static integer indtau, indwrk;
extern /* Subroutine */ int csteqr_(char *, integer *, real *, real *,
complex *, integer *, real *, integer *, ftnlen), cungtr_(char *,
integer *, complex *, integer *, complex *, complex *, integer *,
integer *, ftnlen), ssterf_(integer *, real *, real *, integer *);
static integer llwork;
static real smlnum;
static integer lwkopt;
static logical lquery;
/* -- LAPACK driver routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* June 30, 1999 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CHEEV computes all eigenvalues and, optionally, eigenvectors of a */
/* complex Hermitian matrix A. */
/* Arguments */
/* ========= */
/* JOBZ (input) CHARACTER*1 */
/* = 'N': Compute eigenvalues only; */
/* = 'V': Compute eigenvalues and eigenvectors. */
/* UPLO (input) CHARACTER*1 */
/* = 'U': Upper triangle of A is stored; */
/* = 'L': Lower triangle of A is stored. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* A (input/output) COMPLEX array, dimension (LDA, N) */
/* On entry, the Hermitian matrix A. If UPLO = 'U', the */
/* leading N-by-N upper triangular part of A contains the */
/* upper triangular part of the matrix A. If UPLO = 'L', */
/* the leading N-by-N lower triangular part of A contains */
/* the lower triangular part of the matrix A. */
/* On exit, if JOBZ = 'V', then if INFO = 0, A contains the */
/* orthonormal eigenvectors of the matrix A. */
/* If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') */
/* or the upper triangle (if UPLO='U') of A, including the */
/* diagonal, is destroyed. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* W (output) REAL array, dimension (N) */
/* If INFO = 0, the eigenvalues in ascending order. */
/* WORK (workspace/output) COMPLEX array, dimension (LWORK) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The length of the array WORK. LWORK >= max(1,2*N-1). */
/* For optimal efficiency, LWORK >= (NB+1)*N, */
/* where NB is the blocksize for CHETRD returned by ILAENV. */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates the optimal size of the WORK array, returns */
/* this value as the first entry of the WORK array, and no error */
/* message related to LWORK is issued by XERBLA. */
/* RWORK (workspace) REAL array, dimension (max(1, 3*N-2)) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: if INFO = i, the algorithm failed to converge; i */
/* off-diagonal elements of an intermediate tridiagonal */
/* form did not converge to zero. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--w;
--work;
--rwork;
/* Function Body */
wantz = lsame_(jobz, "V", (ftnlen)1, (ftnlen)1);
lower = lsame_(uplo, "L", (ftnlen)1, (ftnlen)1);
lquery = *lwork == -1;
*info = 0;
if (! (wantz || lsame_(jobz, "N", (ftnlen)1, (ftnlen)1))) {
*info = -1;
} else if (! (lower || lsame_(uplo, "U", (ftnlen)1, (ftnlen)1))) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*lda < max(1,*n)) {
*info = -5;
} else /* if(complicated condition) */ {
/* Computing MAX */
i__1 = 1, i__2 = (*n << 1) - 1;
if (*lwork < max(i__1,i__2) && ! lquery) {
*info = -8;
}
}
if (*info == 0) {
nb = ilaenv_(&c__1, "CHETRD", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6,
(ftnlen)1);
/* Computing MAX */
i__1 = 1, i__2 = (nb + 1) * *n;
lwkopt = max(i__1,i__2);
work[1].r = (real) lwkopt, work[1].i = 0.f;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CHEEV ", &i__1, (ftnlen)6);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
work[1].r = 1.f, work[1].i = 0.f;
return 0;
}
if (*n == 1) {
i__1 = a_dim1 + 1;
w[1] = a[i__1].r;
work[1].r = 3.f, work[1].i = 0.f;
if (wantz) {
i__1 = a_dim1 + 1;
a[i__1].r = 1.f, a[i__1].i = 0.f;
}
return 0;
}
/* Get machine constants. */
safmin = slamch_("Safe minimum", (ftnlen)12);
eps = slamch_("Precision", (ftnlen)9);
smlnum = safmin / eps;
bignum = 1.f / smlnum;
rmin = sqrt(smlnum);
rmax = sqrt(bignum);
/* Scale matrix to allowable range, if necessary. */
anrm = clanhe_("M", uplo, n, &a[a_offset], lda, &rwork[1], (ftnlen)1, (
ftnlen)1);
iscale = 0;
if (anrm > 0.f && anrm < rmin) {
iscale = 1;
sigma = rmin / anrm;
} else if (anrm > rmax) {
iscale = 1;
sigma = rmax / anrm;
}
if (iscale == 1) {
clascl_(uplo, &c__0, &c__0, &c_b18, &sigma, n, n, &a[a_offset], lda,
info, (ftnlen)1);
}
/* Call CHETRD to reduce Hermitian matrix to tridiagonal form. */
inde = 1;
indtau = 1;
indwrk = indtau + *n;
llwork = *lwork - indwrk + 1;
chetrd_(uplo, n, &a[a_offset], lda, &w[1], &rwork[inde], &work[indtau], &
work[indwrk], &llwork, &iinfo, (ftnlen)1);
i__1 = indwrk;
q__1.r = *n + work[i__1].r, q__1.i = work[i__1].i;
lopt = q__1.r;
/* For eigenvalues only, call SSTERF. For eigenvectors, first call */
/* CUNGTR to generate the unitary matrix, then call CSTEQR. */
if (! wantz) {
ssterf_(n, &w[1], &rwork[inde], info);
} else {
cungtr_(uplo, n, &a[a_offset], lda, &work[indtau], &work[indwrk], &
llwork, &iinfo, (ftnlen)1);
indwrk = inde + *n;
csteqr_(jobz, n, &w[1], &rwork[inde], &a[a_offset], lda, &rwork[
indwrk], info, (ftnlen)1);
}
/* If matrix was scaled, then rescale eigenvalues appropriately. */
if (iscale == 1) {
if (*info == 0) {
imax = *n;
} else {
imax = *info - 1;
}
r__1 = 1.f / sigma;
sscal_(&imax, &r__1, &w[1], &c__1);
}
/* Set WORK(1) to optimal complex workspace size. */
work[1].r = (real) lwkopt, work[1].i = 0.f;
return 0;
/* End of CHEEV */
} /* cheev_ */
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