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/* cheevd.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"
#include "blaswrap.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 cheevd_(char *jobz, char *uplo, integer *n, complex *a,
integer *lda, real *w, complex *work, integer *lwork, real *rwork,
integer *lrwork, integer *iwork, integer *liwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
real r__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
real eps;
integer inde;
real anrm;
integer imax;
real rmin, rmax;
integer lopt;
real sigma;
extern logical lsame_(char *, char *);
integer iinfo;
extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
integer lwmin, liopt;
logical lower;
integer llrwk, lropt;
logical wantz;
integer indwk2, llwrk2;
extern doublereal clanhe_(char *, char *, integer *, complex *, integer *,
real *);
integer iscale;
extern /* Subroutine */ int clascl_(char *, integer *, integer *, real *,
real *, integer *, integer *, complex *, integer *, integer *), cstedc_(char *, integer *, real *, real *, complex *,
integer *, complex *, integer *, real *, integer *, integer *,
integer *, integer *);
extern doublereal slamch_(char *);
extern /* Subroutine */ int chetrd_(char *, integer *, complex *, integer
*, real *, real *, complex *, complex *, integer *, integer *), clacpy_(char *, integer *, integer *, complex *, integer
*, complex *, integer *);
real safmin;
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int xerbla_(char *, integer *);
real bignum;
integer indtau, indrwk, indwrk, liwmin;
extern /* Subroutine */ int ssterf_(integer *, real *, real *, integer *);
integer lrwmin;
extern /* Subroutine */ int cunmtr_(char *, char *, char *, integer *,
integer *, complex *, integer *, complex *, complex *, integer *,
complex *, integer *, integer *);
integer llwork;
real smlnum;
logical lquery;
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CHEEVD computes all eigenvalues and, optionally, eigenvectors of a */
/* complex Hermitian matrix A. If eigenvectors are desired, it uses a */
/* divide and conquer algorithm. */
/* The divide and conquer algorithm makes very mild assumptions about */
/* floating point arithmetic. It will work on machines with a guard */
/* digit in add/subtract, or on those binary machines without guard */
/* digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */
/* Cray-2. It could conceivably fail on hexadecimal or decimal machines */
/* without guard digits, but we know of none. */
/* 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 (MAX(1,LWORK)) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The length of the array WORK. */
/* If N <= 1, LWORK must be at least 1. */
/* If JOBZ = 'N' and N > 1, LWORK must be at least N + 1. */
/* If JOBZ = 'V' and N > 1, LWORK must be at least 2*N + N**2. */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates the optimal sizes of the WORK, RWORK and */
/* IWORK arrays, returns these values as the first entries of */
/* the WORK, RWORK and IWORK arrays, and no error message */
/* related to LWORK or LRWORK or LIWORK is issued by XERBLA. */
/* RWORK (workspace/output) REAL array, */
/* dimension (LRWORK) */
/* On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. */
/* LRWORK (input) INTEGER */
/* The dimension of the array RWORK. */
/* If N <= 1, LRWORK must be at least 1. */
/* If JOBZ = 'N' and N > 1, LRWORK must be at least N. */
/* If JOBZ = 'V' and N > 1, LRWORK must be at least */
/* 1 + 5*N + 2*N**2. */
/* If LRWORK = -1, then a workspace query is assumed; the */
/* routine only calculates the optimal sizes of the WORK, RWORK */
/* and IWORK arrays, returns these values as the first entries */
/* of the WORK, RWORK and IWORK arrays, and no error message */
/* related to LWORK or LRWORK or LIWORK is issued by XERBLA. */
/* IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) */
/* On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */
/* LIWORK (input) INTEGER */
/* The dimension of the array IWORK. */
/* If N <= 1, LIWORK must be at least 1. */
/* If JOBZ = 'N' and N > 1, LIWORK must be at least 1. */
/* If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N. */
/* If LIWORK = -1, then a workspace query is assumed; the */
/* routine only calculates the optimal sizes of the WORK, RWORK */
/* and IWORK arrays, returns these values as the first entries */
/* of the WORK, RWORK and IWORK arrays, and no error message */
/* related to LWORK or LRWORK or LIWORK is issued by XERBLA. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: if INFO = i and JOBZ = 'N', then the algorithm failed */
/* to converge; i off-diagonal elements of an intermediate */
/* tridiagonal form did not converge to zero; */
/* if INFO = i and JOBZ = 'V', then the algorithm failed */
/* to compute an eigenvalue while working on the submatrix */
/* lying in rows and columns INFO/(N+1) through */
/* mod(INFO,N+1). */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* Jeff Rutter, Computer Science Division, University of California */
/* at Berkeley, USA */
/* Modified description of INFO. Sven, 16 Feb 05. */
/* ===================================================================== */
/* .. 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;
--iwork;
/* Function Body */
wantz = lsame_(jobz, "V");
lower = lsame_(uplo, "L");
lquery = *lwork == -1 || *lrwork == -1 || *liwork == -1;
*info = 0;
if (! (wantz || lsame_(jobz, "N"))) {
*info = -1;
} else if (! (lower || lsame_(uplo, "U"))) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*lda < max(1,*n)) {
*info = -5;
}
if (*info == 0) {
if (*n <= 1) {
lwmin = 1;
lrwmin = 1;
liwmin = 1;
lopt = lwmin;
lropt = lrwmin;
liopt = liwmin;
} else {
if (wantz) {
lwmin = (*n << 1) + *n * *n;
/* Computing 2nd power */
i__1 = *n;
lrwmin = *n * 5 + 1 + (i__1 * i__1 << 1);
liwmin = *n * 5 + 3;
} else {
lwmin = *n + 1;
lrwmin = *n;
liwmin = 1;
}
/* Computing MAX */
i__1 = lwmin, i__2 = *n + ilaenv_(&c__1, "CHETRD", uplo, n, &c_n1,
&c_n1, &c_n1);
lopt = max(i__1,i__2);
lropt = lrwmin;
liopt = liwmin;
}
work[1].r = (real) lopt, work[1].i = 0.f;
rwork[1] = (real) lropt;
iwork[1] = liopt;
if (*lwork < lwmin && ! lquery) {
*info = -8;
} else if (*lrwork < lrwmin && ! lquery) {
*info = -10;
} else if (*liwork < liwmin && ! lquery) {
*info = -12;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CHEEVD", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
if (*n == 1) {
i__1 = a_dim1 + 1;
w[1] = a[i__1].r;
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");
eps = slamch_("Precision");
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]);
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);
}
/* Call CHETRD to reduce Hermitian matrix to tridiagonal form. */
inde = 1;
indtau = 1;
indwrk = indtau + *n;
indrwk = inde + *n;
indwk2 = indwrk + *n * *n;
llwork = *lwork - indwrk + 1;
llwrk2 = *lwork - indwk2 + 1;
llrwk = *lrwork - indrwk + 1;
chetrd_(uplo, n, &a[a_offset], lda, &w[1], &rwork[inde], &work[indtau], &
work[indwrk], &llwork, &iinfo);
/* For eigenvalues only, call SSTERF. For eigenvectors, first call */
/* CSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the */
/* tridiagonal matrix, then call CUNMTR to multiply it to the */
/* Householder transformations represented as Householder vectors in */
/* A. */
if (! wantz) {
ssterf_(n, &w[1], &rwork[inde], info);
} else {
cstedc_("I", n, &w[1], &rwork[inde], &work[indwrk], n, &work[indwk2],
&llwrk2, &rwork[indrwk], &llrwk, &iwork[1], liwork, info);
cunmtr_("L", uplo, "N", n, n, &a[a_offset], lda, &work[indtau], &work[
indwrk], n, &work[indwk2], &llwrk2, &iinfo);
clacpy_("A", n, n, &work[indwrk], n, &a[a_offset], lda);
}
/* 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);
}
work[1].r = (real) lopt, work[1].i = 0.f;
rwork[1] = (real) lropt;
iwork[1] = liopt;
return 0;
/* End of CHEEVD */
} /* cheevd_ */
|
