Contents
sstevx - compute selected eigenvalues and, optionally,
eigenvectors of a real symmetric tridiagonal matrix A
SUBROUTINE SSTEVX(JOBZ, RANGE, N, DIAG, OFFD, 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 DIAG(*), OFFD(*), W(*), Z(LDZ,*), WORK(*)
SUBROUTINE SSTEVX_64(JOBZ, RANGE, N, DIAG, OFFD, 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 DIAG(*), OFFD(*), W(*), Z(LDZ,*), WORK(*)
F95 INTERFACE
SUBROUTINE STEVX(JOBZ, RANGE, N, DIAG, OFFD, 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(:) :: DIAG, OFFD, W, WORK
REAL, DIMENSION(:,:) :: Z
SUBROUTINE STEVX_64(JOBZ, RANGE, N, DIAG, OFFD, 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(:) :: DIAG, OFFD, W, WORK
REAL, DIMENSION(:,:) :: Z
C INTERFACE
#include <sunperf.h>
void sstevx(char jobz, char range, int n, float *diag, float
*offd, 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 *diag,
float *offd, float vl, float vu, long il, long iu,
float abtol, long *nfound, float *w, float *z,
long ldz, long *ifail, long *info);
sstevx computes selected eigenvalues and, optionally, eigen-
vectors of a real symmetric tridiagonal matrix A. Eigen-
values and eigenvectors can be selected by specifying either
a range of values or a range of indices for the desired
eigenvalues.
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.
DIAG (input/output)
On entry, the n diagonal elements of the tridiago-
nal matrix A. On exit, DIAG may be multiplied by
a constant factor chosen to avoid over/underflow
in computing the eigenvalues.
OFFD (input/output)
On entry, the (n-1) subdiagonal elements of the
tridiagonal matrix A in elements 1 to N-1 of OFFD;
OFFD(N) need not be set. On exit, OFFD 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 smallest 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 approximate eigenvalue is accepted as converged
when it is determined 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 (input) If JOBZ = 'V', then if INFO = 0, the first NFOUND
columns of Z contain the orthonormal eigenvectors
of the matrix A corresponding to the selected
eigenvalues, with the i-th column of Z holding the
eigenvector associated with W(i). If an eigenvec-
tor 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)
IFAIL (output)
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 ille-
gal value
> 0: if INFO = i, then i eigenvectors failed to
converge. Their indices are stored in array
IFAIL.