zstein
zstein - compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration
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(*)
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
#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);
zstein 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
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.
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* D (input)
-
The n diagonal elements of the tridiagonal matrix T.
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* 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. )
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* 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 eigenvectors are set to zero.
-
* LDZ (input)
-
The leading dimension of the array Z. LDZ >= max(1,N).
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* WORK (workspace)
-
dimension(5*N)
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* IWORK (workspace)
-
dimension(N)
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* 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)
-