Contents
cstein - compute the eigenvectors of a real symmetric tridi-
agonal matrix T corresponding to specified eigenvalues,
using inverse iteration
SUBROUTINE CSTEIN(N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, IWORK,
IFAIL, INFO)
COMPLEX Z(LDZ,*)
INTEGER N, M, LDZ, INFO
INTEGER IBLOCK(*), ISPLIT(*), IWORK(*), IFAIL(*)
REAL D(*), E(*), W(*), WORK(*)
SUBROUTINE CSTEIN_64(N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK,
IWORK, IFAIL, INFO)
COMPLEX Z(LDZ,*)
INTEGER*8 N, M, LDZ, INFO
INTEGER*8 IBLOCK(*), ISPLIT(*), IWORK(*), IFAIL(*)
REAL D(*), E(*), W(*), WORK(*)
F95 INTERFACE
SUBROUTINE STEIN([N], D, E, [M], W, IBLOCK, ISPLIT, Z, [LDZ], [WORK],
[IWORK], IFAIL, [INFO])
COMPLEX, DIMENSION(:,:) :: Z
INTEGER :: N, M, LDZ, INFO
INTEGER, DIMENSION(:) :: IBLOCK, ISPLIT, IWORK, IFAIL
REAL, DIMENSION(:) :: D, E, W, WORK
SUBROUTINE STEIN_64([N], D, E, [M], W, IBLOCK, ISPLIT, Z, [LDZ],
[WORK], [IWORK], IFAIL, [INFO])
COMPLEX, DIMENSION(:,:) :: Z
INTEGER(8) :: N, M, LDZ, INFO
INTEGER(8), DIMENSION(:) :: IBLOCK, ISPLIT, IWORK, IFAIL
REAL, DIMENSION(:) :: D, E, W, WORK
C INTERFACE
#include <sunperf.h>
void cstein(int n, float *d, float *e, int m, float *w, int
*iblock, int *isplit, complex *z, int ldz, int
*ifail, int *info);
void cstein_64(long n, float *d, float *e, long m, float *w,
long *iblock, long *isplit, complex *z, long ldz,
long *ifail, long *info);
cstein computes the eigenvectors of a real symmetric tridi-
agonal matrix T corresponding to specified eigenvalues,
using inverse iteration.
The maximum number of iterations allowed for each eigenvec-
tor is specified by an internal parameter MAXITS (currently
set to 5).
Although the eigenvectors are real, they are stored in a
complex array, which may be passed to CUNMTR or CUPMTR for
back
transformation to the eigenvectors of a complex Hermitian
matrix which was reduced to tridiagonal form.
N (input) The order of the matrix. N >= 0.
D (input) The n diagonal elements of the tridiagonal matrix
T.
E (input) The (n-1) subdiagonal elements of the tridiagonal
matrix T, stored in elements 1 to N-1; E(N) need
not be set.
M (input) The number of eigenvectors to be found. 0 <= M <=
N.
W (input) The first M elements of W contain the eigenvalues
for which eigenvectors are to be computed. The
eigenvalues should be grouped by split-off block
and ordered from smallest to largest within the
block. ( The output array W from SSTEBZ with
ORDER = 'B' is expected here. )
IBLOCK (input)
The submatrix indices associated with the
corresponding eigenvalues in W; IBLOCK(i)=1 if
eigenvalue W(i) belongs to the first submatrix
from the top, =2 if W(i) belongs to the second
submatrix, etc. ( The output array IBLOCK from
SSTEBZ is expected here. )
ISPLIT (input)
The splitting points, at which T breaks up into
submatrices. The first submatrix consists of
rows/columns 1 to ISPLIT( 1 ), the second of
rows/columns ISPLIT( 1 )+1 through ISPLIT( 2 ),
etc. ( The output array ISPLIT from SSTEBZ is
expected here. )
Z (output)
The computed eigenvectors. The eigenvector asso-
ciated with the eigenvalue W(i) is stored in the
i-th column of Z. Any vector which fails to con-
verge is set to its current iterate after MAXITS
iterations. The imaginary parts of the eigenvec-
tors are set to zero.
LDZ (input)
The leading dimension of the array Z. LDZ >=
max(1,N).
WORK (workspace)
dimension(5*N)
IWORK (workspace)
dimension(N)
IFAIL (output)
On normal exit, all elements of IFAIL are zero.
If one or more eigenvectors fail to converge after
MAXITS iterations, then their indices are stored
in array IFAIL.
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 in MAXITS iterations. Their indices are
stored in array IFAIL.