sstevx - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A
SUBROUTINE SSTEVX(JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, IWORK2, IFAIL, INFO) CHARACTER*1 JOBZ, RANGE INTEGER N, IL, IU, NFOUND, LDZ, INFO INTEGER IWORK2(*), IFAIL(*) REAL VL, VU, ABTOL REAL D(*), E(*), W(*), Z(LDZ,*), WORK(*) SUBROUTINE SSTEVX_64(JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, IWORK2, IFAIL, INFO) CHARACTER*1 JOBZ, RANGE INTEGER*8 N, IL, IU, NFOUND, LDZ, INFO INTEGER*8 IWORK2(*), IFAIL(*) REAL VL, VU, ABTOL REAL D(*), E(*), W(*), Z(LDZ,*), WORK(*) F95 INTERFACE SUBROUTINE STEVX(JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, IWORK2, IFAIL, INFO) CHARACTER(LEN=1) :: JOBZ, RANGE INTEGER :: N, IL, IU, NFOUND, LDZ, INFO INTEGER, DIMENSION(:) :: IWORK2, IFAIL REAL :: VL, VU, ABTOL REAL, DIMENSION(:) :: D, E, W, WORK REAL, DIMENSION(:,:) :: Z SUBROUTINE STEVX_64(JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, IWORK2, IFAIL, INFO) CHARACTER(LEN=1) :: JOBZ, RANGE INTEGER(8) :: N, IL, IU, NFOUND, LDZ, INFO INTEGER(8), DIMENSION(:) :: IWORK2, IFAIL REAL :: VL, VU, ABTOL REAL, DIMENSION(:) :: D, E, W, WORK REAL, DIMENSION(:,:) :: Z C INTERFACE #include <sunperf.h> void sstevx(char jobz, char range, int n, float *d, float *e, float vl, float vu, int il, int iu, float abtol, int *nfound, float *w, float *z, int ldz, int *ifail, int *info); void sstevx_64(char jobz, char range, long n, float *d, float *e, float vl, float vu, long il, long iu, float abtol, long *nfound, float *w, float *z, long ldz, long *ifail, long *info);
Oracle Solaris Studio Performance Library sstevx(3P)
NAME
sstevx - compute selected eigenvalues and, optionally, eigenvectors of
a real symmetric tridiagonal matrix A
SYNOPSIS
SUBROUTINE SSTEVX(JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABTOL,
NFOUND, W, Z, LDZ, WORK, IWORK2, IFAIL, INFO)
CHARACTER*1 JOBZ, RANGE
INTEGER N, IL, IU, NFOUND, LDZ, INFO
INTEGER IWORK2(*), IFAIL(*)
REAL VL, VU, ABTOL
REAL D(*), E(*), W(*), Z(LDZ,*), WORK(*)
SUBROUTINE SSTEVX_64(JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
ABTOL, NFOUND, W, Z, LDZ, WORK, IWORK2, IFAIL, INFO)
CHARACTER*1 JOBZ, RANGE
INTEGER*8 N, IL, IU, NFOUND, LDZ, INFO
INTEGER*8 IWORK2(*), IFAIL(*)
REAL VL, VU, ABTOL
REAL D(*), E(*), W(*), Z(LDZ,*), WORK(*)
F95 INTERFACE
SUBROUTINE STEVX(JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABTOL,
NFOUND, W, Z, LDZ, WORK, IWORK2, IFAIL, INFO)
CHARACTER(LEN=1) :: JOBZ, RANGE
INTEGER :: N, IL, IU, NFOUND, LDZ, INFO
INTEGER, DIMENSION(:) :: IWORK2, IFAIL
REAL :: VL, VU, ABTOL
REAL, DIMENSION(:) :: D, E, W, WORK
REAL, DIMENSION(:,:) :: Z
SUBROUTINE STEVX_64(JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
ABTOL, NFOUND, W, Z, LDZ, WORK, IWORK2, IFAIL, INFO)
CHARACTER(LEN=1) :: JOBZ, RANGE
INTEGER(8) :: N, IL, IU, NFOUND, LDZ, INFO
INTEGER(8), DIMENSION(:) :: IWORK2, IFAIL
REAL :: VL, VU, ABTOL
REAL, DIMENSION(:) :: D, E, W, WORK
REAL, DIMENSION(:,:) :: Z
C INTERFACE
#include <sunperf.h>
void sstevx(char jobz, char range, int n, float *d, float *e, float vl,
float vu, int il, int iu, float abtol, int *nfound, float *w,
float *z, int ldz, int *ifail, int *info);
void sstevx_64(char jobz, char range, long n, float *d, float *e, float
vl, float vu, long il, long iu, float abtol, long *nfound,
float *w, float *z, long ldz, long *ifail, long *info);
PURPOSE
sstevx computes selected eigenvalues and, optionally, eigenvectors of a
real symmetric tridiagonal matrix A. Eigenvalues and eigenvectors can
be selected by specifying either a range of values or a range of
indices for the desired eigenvalues.
ARGUMENTS
JOBZ (input)
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
RANGE (input)
= 'A': all eigenvalues will be found.
= 'V': all eigenvalues in the half-open interval (VL,VU] will
be found. = 'I': the IL-th through IU-th eigenvalues will be
found.
N (input) The order of the matrix. N >= 0.
D (input/output)
On entry, the n diagonal elements of the tridiagonal matrix
A. On exit, D may be multiplied by a constant factor chosen
to avoid over/underflow in computing the eigenvalues.
E (input/output)
On entry, the (n-1) subdiagonal elements of the tridiagonal
matrix A in elements 1 to N-1 of E; E(N) need not be set. On
exit, E may be multiplied by a constant factor chosen to
avoid over/underflow in computing the eigenvalues.
VL (input)
If RANGE='V', the lower and upper bounds of the interval to
be searched for eigenvalues. VL < VU. Not referenced if
RANGE = 'A' or 'I'.
VU (input)
See the description of VL.
IL (input)
If RANGE='I', the indices (in ascending order) of the small-
est and largest eigenvalues to be returned. 1 <= IL <= IU <=
N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if
RANGE = 'A' or 'V'.
IU (input)
See the description of IL.
ABTOL (input)
The absolute error tolerance for the eigenvalues. An approx-
imate eigenvalue is accepted as converged when it is deter-
mined to lie in an interval [a,b] of width less than or equal
to
ABTOL + EPS * max( |a|,|b| ) ,
where EPS is the machine precision. If ABTOL is less than or
equal to zero, then EPS*|T| will be used in its place,
where |T| is the 1-norm of the tridiagonal matrix.
Eigenvalues will be computed most accurately when ABTOL is
set to twice the underflow threshold 2*SLAMCH('S'), not zero.
If this routine returns with INFO>0, indicating that some
eigenvectors did not converge, try setting ABTOL to
2*SLAMCH('S').
See "Computing Small Singular Values of Bidiagonal Matrices
with Guaranteed High Relative Accuracy," by Demmel and Kahan,
LAPACK Working Note #3.
NFOUND (output)
The total number of eigenvalues found. 0 <= NFOUND <= N. If
RANGE = 'A', NFOUND = N, and if RANGE = 'I', NFOUND = IU-
IL+1.
W (output)
The first NFOUND elements contain the selected eigenvalues in
ascending order.
Z (output)
If JOBZ = 'V', then if INFO = 0, the first NFOUND columns of
Z contain the orthonormal eigenvectors of the matrix A corre-
sponding to the selected eigenvalues, with the i-th column of
Z holding the eigenvector associated with W(i). If an eigen-
vector fails to converge (INFO > 0), then that column of Z
contains the latest approximation to the eigenvector, and the
index of the eigenvector is returned in IFAIL. If JOBZ =
'N', then Z is not referenced. Note: the user must ensure
that at least max(1,NFOUND) columns are supplied in the array
Z; if RANGE = 'V', the exact value of NFOUND is not known in
advance and an upper bound must be used.
LDZ (input)
The leading dimension of the array Z. LDZ >= 1, and if JOBZ
= 'V', LDZ >= max(1,N).
WORK (workspace)
dimension(5*N)
IWORK2 (workspace) INTEGER array, dimension (5*N)
IFAIL (output) INTEGER array, dimension (N)
If JOBZ = 'V', then if INFO = 0, the first NFOUND elements of
IFAIL are zero. If INFO > 0, then IFAIL contains the indices
of the eigenvectors that failed to converge. If JOBZ = 'N',
then IFAIL is not referenced.
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, then i eigenvectors failed to converge.
Their indices are stored in array IFAIL.
7 Nov 2015 sstevx(3P)