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/* chbev.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 real c_b11 = 1.f;
static integer c__1 = 1;
/* Subroutine */ int chbev_(char *jobz, char *uplo, integer *n, integer *kd,
complex *ab, integer *ldab, real *w, complex *z__, integer *ldz,
complex *work, real *rwork, integer *info)
{
/* System generated locals */
integer ab_dim1, ab_offset, z_dim1, z_offset, i__1;
real r__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
real eps;
integer inde;
real anrm;
integer imax;
real rmin, rmax, sigma;
extern logical lsame_(char *, char *);
integer iinfo;
extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
logical lower, wantz;
extern doublereal clanhb_(char *, char *, integer *, integer *, complex *,
integer *, real *);
integer iscale;
extern /* Subroutine */ int clascl_(char *, integer *, integer *, real *,
real *, integer *, integer *, complex *, integer *, integer *), chbtrd_(char *, char *, integer *, integer *, complex *,
integer *, real *, real *, complex *, integer *, complex *,
integer *);
extern doublereal slamch_(char *);
real safmin;
extern /* Subroutine */ int xerbla_(char *, integer *);
real bignum;
integer indrwk;
extern /* Subroutine */ int csteqr_(char *, integer *, real *, real *,
complex *, integer *, real *, integer *), ssterf_(integer
*, real *, real *, integer *);
real smlnum;
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CHBEV computes all the eigenvalues and, optionally, eigenvectors of */
/* a complex Hermitian band 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. */
/* KD (input) INTEGER */
/* The number of superdiagonals of the matrix A if UPLO = 'U', */
/* or the number of subdiagonals if UPLO = 'L'. KD >= 0. */
/* AB (input/output) COMPLEX array, dimension (LDAB, N) */
/* On entry, the upper or lower triangle of the Hermitian band */
/* matrix A, stored in the first KD+1 rows of the array. The */
/* j-th column of A is stored in the j-th column of the array AB */
/* as follows: */
/* if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; */
/* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). */
/* On exit, AB is overwritten by values generated during the */
/* reduction to tridiagonal form. If UPLO = 'U', the first */
/* superdiagonal and the diagonal of the tridiagonal matrix T */
/* are returned in rows KD and KD+1 of AB, and if UPLO = 'L', */
/* the diagonal and first subdiagonal of T are returned in the */
/* first two rows of AB. */
/* LDAB (input) INTEGER */
/* The leading dimension of the array AB. LDAB >= KD + 1. */
/* W (output) REAL array, dimension (N) */
/* If INFO = 0, the eigenvalues in ascending order. */
/* Z (output) COMPLEX array, dimension (LDZ, N) */
/* If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal */
/* eigenvectors of the matrix A, with the i-th column of Z */
/* holding the eigenvector associated with W(i). */
/* If JOBZ = 'N', then Z is not referenced. */
/* LDZ (input) INTEGER */
/* The leading dimension of the array Z. LDZ >= 1, and if */
/* JOBZ = 'V', LDZ >= max(1,N). */
/* WORK (workspace) COMPLEX array, dimension (N) */
/* 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 */
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
--w;
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
--work;
--rwork;
/* Function Body */
wantz = lsame_(jobz, "V");
lower = lsame_(uplo, "L");
*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 (*kd < 0) {
*info = -4;
} else if (*ldab < *kd + 1) {
*info = -6;
} else if (*ldz < 1 || wantz && *ldz < *n) {
*info = -9;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CHBEV ", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
if (*n == 1) {
if (lower) {
i__1 = ab_dim1 + 1;
w[1] = ab[i__1].r;
} else {
i__1 = *kd + 1 + ab_dim1;
w[1] = ab[i__1].r;
}
if (wantz) {
i__1 = z_dim1 + 1;
z__[i__1].r = 1.f, z__[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 = clanhb_("M", uplo, n, kd, &ab[ab_offset], ldab, &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) {
if (lower) {
clascl_("B", kd, kd, &c_b11, &sigma, n, n, &ab[ab_offset], ldab,
info);
} else {
clascl_("Q", kd, kd, &c_b11, &sigma, n, n, &ab[ab_offset], ldab,
info);
}
}
/* Call CHBTRD to reduce Hermitian band matrix to tridiagonal form. */
inde = 1;
chbtrd_(jobz, uplo, n, kd, &ab[ab_offset], ldab, &w[1], &rwork[inde], &
z__[z_offset], ldz, &work[1], &iinfo);
/* For eigenvalues only, call SSTERF. For eigenvectors, call CSTEQR. */
if (! wantz) {
ssterf_(n, &w[1], &rwork[inde], info);
} else {
indrwk = inde + *n;
csteqr_(jobz, n, &w[1], &rwork[inde], &z__[z_offset], ldz, &rwork[
indrwk], info);
}
/* 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);
}
return 0;
/* End of CHBEV */
} /* chbev_ */
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