zstein(3P) Sun Performance Library zstein(3P)NAMEzstein - compute the eigenvectors of a real symmetric tridiagonal
matrix T corresponding to specified eigenvalues, using inverse itera‐
tion
SYNOPSIS
SUBROUTINE ZSTEIN(N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, IWORK,
IFAIL, INFO)
DOUBLE COMPLEX Z(LDZ,*)
INTEGER N, M, LDZ, INFO
INTEGER IBLOCK(*), ISPLIT(*), IWORK(*), IFAIL(*)
DOUBLE PRECISION D(*), E(*), W(*), WORK(*)
SUBROUTINE ZSTEIN_64(N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK,
IWORK, IFAIL, INFO)
DOUBLE COMPLEX Z(LDZ,*)
INTEGER*8 N, M, LDZ, INFO
INTEGER*8 IBLOCK(*), ISPLIT(*), IWORK(*), IFAIL(*)
DOUBLE PRECISION D(*), E(*), W(*), WORK(*)
F95 INTERFACE
SUBROUTINE STEIN([N], D, E, [M], W, IBLOCK, ISPLIT, Z, [LDZ], [WORK],
[IWORK], IFAIL, [INFO])
COMPLEX(8), DIMENSION(:,:) :: Z
INTEGER :: N, M, LDZ, INFO
INTEGER, DIMENSION(:) :: IBLOCK, ISPLIT, IWORK, IFAIL
REAL(8), DIMENSION(:) :: D, E, W, WORK
SUBROUTINE STEIN_64([N], D, E, [M], W, IBLOCK, ISPLIT, Z, [LDZ],
[WORK], [IWORK], IFAIL, [INFO])
COMPLEX(8), DIMENSION(:,:) :: Z
INTEGER(8) :: N, M, LDZ, INFO
INTEGER(8), DIMENSION(:) :: IBLOCK, ISPLIT, IWORK, IFAIL
REAL(8), DIMENSION(:) :: D, E, W, WORK
C INTERFACE
#include <sunperf.h>
void zstein(int n, double *d, double *e, int m, double *w, int *iblock,
int *isplit, doublecomplex *z, int ldz, int *ifail, int
*info);
void zstein_64(long n, double *d, double *e, long m, double *w, long
*iblock, long *isplit, doublecomplex *z, long ldz, long
*ifail, long *info);
PURPOSEzstein computes the eigenvectors of a real symmetric tridiagonal matrix
T corresponding to specified eigenvalues, using inverse iteration.
The maximum number of iterations allowed for each eigenvector is speci‐
fied 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 ZUNMTR or ZUPMTR for back
transformation to the eigenvectors of a complex Hermitian matrix which
was reduced to tridiagonal form.
ARGUMENTS
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 ei‐
genvalues in W; IBLOCK(i)=1 if eigenvalue W(i) belongs to the
first submatrix from the top, =2 if W(i) belongs to the sec‐
ond 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 associated with
the eigenvalue W(i) is stored in the i-th column of Z. Any
vector which fails to converge is set to its current iterate
after MAXITS iterations. The imaginary parts of the eigen‐
vectors 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) INTEGER array, dimension (M)
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 illegal value
> 0: if INFO = i, then i eigenvectors failed to converge in
MAXITS iterations. Their indices are stored in array IFAIL.
6 Mar 2009 zstein(3P)
