zstein(3)

NAME

ZSTEIN - compute the eigenvectors of a real symmetric

tridiagonal matrix T corresponding to specified eigenvalues, us

ing inverse iteration

SYNOPSIS

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, * )

PURPOSE

ZSTEIN computes the eigenvectors of a real symmetric

tridiagonal matrix T corresponding to specified eigenvalues, us

ing 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.

ARGUMENTS

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. )

IBLOCK (input) INTEGER array, dimension (N)

The submatrix indices associated with the corre

sponding 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 IS

PLIT( 2 ), etc. ( The output array ISPLIT from DSTEBZ is expect

ed here. )

Z (output) COMPLEX*16 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 converge is set to its current it

erate after MAXITS iterations. The imaginary parts of the eigen

vectors 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 itera

tions, 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.

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

ZSTEIN(3)