zstein(3F)

NAME
     ZSTEIN - compute the eigenvectors of a real symmetric tridiagonal matrix
     T corresponding to specified eigenvalues, using 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, 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.



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 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.

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.