/* zheev.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 doublereal c_b18 = 1.;
/* Subroutine */ int zheev_(char *jobz, char *uplo, integer *n, doublecomplex
*a, integer *lda, doublereal *w, doublecomplex *work, integer *lwork,
doublereal *rwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
doublereal d__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer nb;
doublereal eps;
integer inde;
doublereal anrm;
integer imax;
doublereal rmin, rmax;
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *);
doublereal sigma;
extern logical lsame_(char *, char *);
integer iinfo;
logical lower, wantz;
extern doublereal dlamch_(char *);
integer iscale;
doublereal safmin;
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int xerbla_(char *, integer *);
doublereal bignum;
extern doublereal zlanhe_(char *, char *, integer *, doublecomplex *,
integer *, doublereal *);
integer indtau;
extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *,
integer *), zlascl_(char *, integer *, integer *, doublereal *,
doublereal *, integer *, integer *, doublecomplex *, integer *,
integer *);
integer indwrk;
extern /* Subroutine */ int zhetrd_(char *, integer *, doublecomplex *,
integer *, doublereal *, doublereal *, doublecomplex *,
doublecomplex *, integer *, integer *);
integer llwork;
doublereal smlnum;
integer lwkopt;
logical lquery;
extern /* Subroutine */ int zsteqr_(char *, integer *, doublereal *,
doublereal *, doublecomplex *, integer *, doublereal *, integer *), zungtr_(char *, integer *, doublecomplex *, integer *,
doublecomplex *, doublecomplex *, integer *, integer *);
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZHEEV 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*16 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) DOUBLE PRECISION array, dimension (N) */
/* If INFO = 0, the eigenvalues in ascending order. */
/* WORK (workspace/output) COMPLEX*16 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. LWORK >= max(1,2*N-1). */
/* For optimal efficiency, LWORK >= (NB+1)*N, */
/* where NB is the blocksize for ZHETRD 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) DOUBLE PRECISION 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");
lower = lsame_(uplo, "L");
lquery = *lwork == -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) {
nb = ilaenv_(&c__1, "ZHETRD", uplo, n, &c_n1, &c_n1, &c_n1);
/* Computing MAX */
i__1 = 1, i__2 = (nb + 1) * *n;
lwkopt = max(i__1,i__2);
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
/* Computing MAX */
i__1 = 1, i__2 = (*n << 1) - 1;
if (*lwork < max(i__1,i__2) && ! lquery) {
*info = -8;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZHEEV ", &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;
work[1].r = 1., work[1].i = 0.;
if (wantz) {
i__1 = a_dim1 + 1;
a[i__1].r = 1., a[i__1].i = 0.;
}
return 0;
}
/* Get machine constants. */
safmin = dlamch_("Safe minimum");
eps = dlamch_("Precision");
smlnum = safmin / eps;
bignum = 1. / smlnum;
rmin = sqrt(smlnum);
rmax = sqrt(bignum);
/* Scale matrix to allowable range, if necessary. */
anrm = zlanhe_("M", uplo, n, &a[a_offset], lda, &rwork[1]);
iscale = 0;
if (anrm > 0. && anrm < rmin) {
iscale = 1;
sigma = rmin / anrm;
} else if (anrm > rmax) {
iscale = 1;
sigma = rmax / anrm;
}
if (iscale == 1) {
zlascl_(uplo, &c__0, &c__0, &c_b18, &sigma, n, n, &a[a_offset], lda,
info);
}
/* Call ZHETRD to reduce Hermitian matrix to tridiagonal form. */
inde = 1;
indtau = 1;
indwrk = indtau + *n;
llwork = *lwork - indwrk + 1;
zhetrd_(uplo, n, &a[a_offset], lda, &w[1], &rwork[inde], &work[indtau], &
work[indwrk], &llwork, &iinfo);
/* For eigenvalues only, call DSTERF. For eigenvectors, first call */
/* ZUNGTR to generate the unitary matrix, then call ZSTEQR. */
if (! wantz) {
dsterf_(n, &w[1], &rwork[inde], info);
} else {
zungtr_(uplo, n, &a[a_offset], lda, &work[indtau], &work[indwrk], &
llwork, &iinfo);
indwrk = inde + *n;
zsteqr_(jobz, n, &w[1], &rwork[inde], &a[a_offset], lda, &rwork[
indwrk], info);
}
/* If matrix was scaled, then rescale eigenvalues appropriately. */
if (iscale == 1) {
if (*info == 0) {
imax = *n;
} else {
imax = *info - 1;
}
d__1 = 1. / sigma;
dscal_(&imax, &d__1, &w[1], &c__1);
}
/* Set WORK(1) to optimal complex workspace size. */
work[1].r = (doublereal) lwkopt, work[1].i = 0.;
return 0;
/* End of ZHEEV */
} /* zheev_ */
