dstevx(3P) Sun Performance Library dstevx(3P)NAMEdstevx - compute selected eigenvalues and, optionally, eigenvectors of
a real symmetric tridiagonal matrix A
SYNOPSIS
SUBROUTINE DSTEVX(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(*)
DOUBLE PRECISION VL, VU, ABTOL
DOUBLE PRECISION D(*), E(*), W(*), Z(LDZ,*), WORK(*)
SUBROUTINE DSTEVX_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(*)
DOUBLE PRECISION VL, VU, ABTOL
DOUBLE PRECISION 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(8) :: VL, VU, ABTOL
REAL(8), DIMENSION(:) :: D, E, W, WORK
REAL(8), 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(8) :: VL, VU, ABTOL
REAL(8), DIMENSION(:) :: D, E, W, WORK
REAL(8), DIMENSION(:,:) :: Z
C INTERFACE
#include <sunperf.h>
void dstevx(char jobz, char range, int n, double *d, double *e, double
vl, double vu, int il, int iu, double abtol, int *nfound,
double *w, double *z, int ldz, int *ifail, int *info);
void dstevx_64(char jobz, char range, long n, double *d, double *e,
double vl, double vu, long il, long iu, double abtol, long
*nfound, double *w, double *z, long ldz, long *ifail, long
*info);
PURPOSEdstevx 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*DLAMCH('S'), not zero.
If this routine returns with INFO>0, indicating that some
eigenvectors did not converge, try setting ABTOL to
2*DLAMCH('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.
6 Mar 2009 dstevx(3P)
