ZSTEIN(3F) ZSTEIN(3F)
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 )
INTEGER INFO, LDZ, M, N
INTEGER IBLOCK( * ), IFAIL( * ), ISPLIT( * ), IWORK( * )
DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * )
COMPLEX*16 Z( LDZ, * )
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 ZUNMTR or ZUPMTR for back
transformation to the eigenvectors of a complex Hermitian matrix which
was reduced to tridiagonal form.
N (input) INTEGER
The order of the matrix. N >= 0.
D (input) DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the tridiagonal matrix T.
E (input) DOUBLE PRECISION array, dimension (N)
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) INTEGER
The number of eigenvectors to be found. 0 <= M <= N.
W (input) DOUBLE PRECISION array, dimension (N)
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 DSTEBZ with ORDER =
'B' is expected here. )
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ZSTEIN(3F) ZSTEIN(3F)
IBLOCK (input) INTEGER array, dimension (N)
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 DSTEBZ is
expected here. )
ISPLIT (input) INTEGER array, dimension (N)
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 DSTEBZ is expected here. )
Z (output) COMPLEX*16 array, dimension (LDZ, M)
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) INTEGER
The leading dimension of the array Z. LDZ >= max(1,N).
WORK (workspace) DOUBLE PRECISION array, dimension (5*N)
IWORK (workspace) INTEGER array, 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) INTEGER
= 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.
MAXITS INTEGER, default = 5
The maximum number of iterations performed.
EXTRA INTEGER, default = 2
The number of iterations performed after norm growth criterion is
satisfied, should be at least 1.
ZSTEIN(3F) ZSTEIN(3F)
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 )
INTEGER INFO, LDZ, M, N
INTEGER IBLOCK( * ), IFAIL( * ), ISPLIT( * ), IWORK( * )
DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * )
COMPLEX*16 Z( LDZ, * )
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 ZUNMTR or ZUPMTR for back
transformation to the eigenvectors of a complex Hermitian matrix which
was reduced to tridiagonal form.
N (input) INTEGER
The order of the matrix. N >= 0.
D (input) DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the tridiagonal matrix T.
E (input) DOUBLE PRECISION array, dimension (N)
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) INTEGER
The number of eigenvectors to be found. 0 <= M <= N.
W (input) DOUBLE PRECISION array, dimension (N)
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 DSTEBZ with ORDER =
'B' is expected here. )
Page 1
ZSTEIN(3F) ZSTEIN(3F)
IBLOCK (input) INTEGER array, dimension (N)
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 DSTEBZ is
expected here. )
ISPLIT (input) INTEGER array, dimension (N)
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 DSTEBZ is expected here. )
Z (output) COMPLEX*16 array, dimension (LDZ, M)
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) INTEGER
The leading dimension of the array Z. LDZ >= max(1,N).
WORK (workspace) DOUBLE PRECISION array, dimension (5*N)
IWORK (workspace) INTEGER array, 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) INTEGER
= 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.
MAXITS INTEGER, default = 5
The maximum number of iterations performed.
EXTRA INTEGER, default = 2
The number of iterations performed after norm growth criterion is
satisfied, should be at least 1.
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