CSTEIN - compute the eigenvectors of a real symmetric
tridiagonal matrix T corresponding to specified eigenval
ues, using inverse iteration
SYNOPSIS
SUBROUTINE CSTEIN( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ,
WORK, IWORK, IFAIL, INFO )
INTEGER INFO, LDZ, M, N
INTEGER IBLOCK( * ), IFAIL( * ), ISPLIT( * ),
IWORK( * )
REAL D( * ), E( * ), W( * ), WORK( * )
COMPLEX Z( LDZ, * )
PURPOSE
CSTEIN computes the eigenvectors of a real symmetric
tridiagonal matrix T corresponding to specified eigenval
ues, using inverse iteration. The maximum number of iter
ations 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.
ARGUMENTS
N (input) INTEGER
The order of the matrix. N >= 0.
D (input) REAL array, dimension (N)
The n diagonal elements of the tridiagonal matrix
T.
E (input) REAL 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) REAL 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
block. ( The output array W from SSTEBZ with
ORDER = 'B' is expected here. )
IBLOCK (input) INTEGER array, dimension (N)
The submatrix indices associated with the corre
sponding eigenvalues in W; IBLOCK(i)=1 if eigen
value 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) 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 SSTEBZ is
expected here. )
Z (output) COMPLEX array, dimension (LDZ, M)
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) INTEGER
The leading dimension of the array Z. LDZ >=
max(1,N).
WORK (workspace) REAL 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 ille
gal value
> 0: if INFO = i, then i eigenvectors failed to
converge in MAXITS iterations. Their indices are
stored in array IFAIL.
PARAMETERS
MAXITS INTEGER, default = 5
The maximum number of iterations performed.
The number of iterations performed after norm
growth criterion is satisfied, should be at least
1.
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