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(*)
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
#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, 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.
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
= '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.
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.
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.
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.
dimension(5*N)
= 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.