CSTEIN(l) ) CSTEIN(l)NAME
CSTEIN - compute the eigenvectors of a real symmetric tridiagonal
matrix T corresponding to specified eigenvalues, using inverse itera‐
tion
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 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.
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 and ordered from smallest to largest
within the 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 corresponding eigen‐
values 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) 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 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) 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 illegal 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.
EXTRA INTEGER, default = 2
The number of iterations performed after norm growth criterion
is satisfied, should be at least 1.
LAPACK version 3.0 15 June 2000 CSTEIN(l)
