#include "blaswrap.h"
#include "f2c.h"
/* Subroutine */ int sspevd_(char *jobz, char *uplo, integer *n, real *ap,
real *w, real *z__, integer *ldz, real *work, integer *lwork, integer
*iwork, integer *liwork, integer *info )
{
/* -- LAPACK driver routine (version 3.1) --
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
Purpose
=======
SSPEVD computes all the eigenvalues and, optionally, eigenvectors
of a real symmetric matrix A in packed storage. 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.
AP (input/output) REAL array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the symmetric matrix
A, packed columnwise in a linear array. The j-th column of A
is stored in the array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
On exit, AP is overwritten by values generated during the
reduction to tridiagonal form. If UPLO = 'U', the diagonal
and first superdiagonal of the tridiagonal matrix T overwrite
the corresponding elements of A, and if UPLO = 'L', the
diagonal and first subdiagonal of T overwrite the
corresponding elements of A.
W (output) REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
Z (output) REAL 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/output) REAL array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the required LWORK.
LWORK (input) INTEGER
The dimension of the array WORK.
If N <= 1, LWORK must be at least 1.
If JOBZ = 'N' and N > 1, LWORK must be at least 2*N.
If JOBZ = 'V' and N > 1, LWORK must be at least
1 + 6*N + N**2.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the required sizes of the WORK and IWORK
arrays, returns these values as the first entries of the WORK
and IWORK arrays, and no error message related to LWORK or
LIWORK is issued by XERBLA.
IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
LIWORK (input) INTEGER
The dimension of the array IWORK.
If JOBZ = 'N' or 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 required sizes of the WORK and
IWORK arrays, returns these values as the first entries of
the WORK and IWORK arrays, and no error message related to
LWORK 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, the algorithm failed to converge; i
off-diagonal elements of an intermediate tridiagonal
form did not converge to zero.
=====================================================================
Test the input parameters.
Parameter adjustments */
/* Table of constant values */
static integer c__1 = 1;
/* System generated locals */
integer z_dim1, z_offset, i__1;
real r__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
static real eps;
static integer inde;
static real anrm, rmin, rmax, sigma;
extern logical lsame_(char *, char *);
static integer iinfo;
extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
static integer lwmin;
static logical wantz;
static integer iscale;
extern doublereal slamch_(char *);
static real safmin;
extern /* Subroutine */ int xerbla_(char *, integer *);
static real bignum;
static integer indtau;
extern /* Subroutine */ int sstedc_(char *, integer *, real *, real *,
real *, integer *, real *, integer *, integer *, integer *,
integer *);
static integer indwrk, liwmin;
extern doublereal slansp_(char *, char *, integer *, real *, real *);
extern /* Subroutine */ int ssterf_(integer *, real *, real *, integer *);
static integer llwork;
static real smlnum;
extern /* Subroutine */ int ssptrd_(char *, integer *, real *, real *,
real *, real *, integer *);
static logical lquery;
extern /* Subroutine */ int sopmtr_(char *, char *, char *, integer *,
integer *, real *, real *, real *, integer *, real *, integer *);
--ap;
--w;
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
--work;
--iwork;
/* Function Body */
wantz = lsame_(jobz, "V");
lquery = *lwork == -1 || *liwork == -1;
*info = 0;
if (! (wantz || lsame_(jobz, "N"))) {
*info = -1;
} else if (! (lsame_(uplo, "U") || lsame_(uplo,
"L"))) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*ldz < 1 || wantz && *ldz < *n) {
*info = -7;
}
if (*info == 0) {
if (*n <= 1) {
liwmin = 1;
lwmin = 1;
} else {
if (wantz) {
liwmin = *n * 5 + 3;
/* Computing 2nd power */
i__1 = *n;
lwmin = *n * 6 + 1 + i__1 * i__1;
} else {
liwmin = 1;
lwmin = *n << 1;
}
}
iwork[1] = liwmin;
work[1] = (real) lwmin;
if (*lwork < lwmin && ! lquery) {
*info = -9;
} else if (*liwork < liwmin && ! lquery) {
*info = -11;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SSPEVD", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
if (*n == 1) {
w[1] = ap[1];
if (wantz) {
z__[z_dim1 + 1] = 1.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 = slansp_("M", uplo, n, &ap[1], &work[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) {
i__1 = *n * (*n + 1) / 2;
sscal_(&i__1, &sigma, &ap[1], &c__1);
}
/* Call SSPTRD to reduce symmetric packed matrix to tridiagonal form. */
inde = 1;
indtau = inde + *n;
ssptrd_(uplo, n, &ap[1], &w[1], &work[inde], &work[indtau], &iinfo);
/* For eigenvalues only, call SSTERF. For eigenvectors, first call
SSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
tridiagonal matrix, then call SOPMTR to multiply it by the
Householder transformations represented in AP. */
if (! wantz) {
ssterf_(n, &w[1], &work[inde], info);
} else {
indwrk = indtau + *n;
llwork = *lwork - indwrk + 1;
sstedc_("I", n, &w[1], &work[inde], &z__[z_offset], ldz, &work[indwrk]
, &llwork, &iwork[1], liwork, info);
sopmtr_("L", uplo, "N", n, n, &ap[1], &work[indtau], &z__[z_offset],
ldz, &work[indwrk], &iinfo);
}
/* If matrix was scaled, then rescale eigenvalues appropriately. */
if (iscale == 1) {
r__1 = 1.f / sigma;
sscal_(n, &r__1, &w[1], &c__1);
}
work[1] = (real) lwmin;
iwork[1] = liwmin;
return 0;
/* End of SSPEVD */
} /* sspevd_ */