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DSTEIN2(l)                             )                            DSTEIN2(l)


NAME

       DSTEIN2 - compute the eigenvectors of a real symmetric tridiagonal
       matrix T corresponding to specified eigenvalues, using inverse
       iteration


SYNOPSIS

       SUBROUTINE DSTEIN2( N, D, E, M, W, IBLOCK, ISPLIT, ORFAC, Z, LDZ, WORK,
                           IWORK, IFAIL, INFO )
           INTEGER INFO, LDZ, M, N
           DOUBLE PRECISION ORFAC
           INTEGER IBLOCK( * ), IFAIL( * ), ISPLIT( * ), IWORK( * )
           DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * )


PURPOSE

       DSTEIN2 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).


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, 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. )

       ORFAC   (input) DOUBLE PRECISION
               ORFAC specifies which eigenvectors should be orthogonalized.
               Eigenvectors that correspond to eigenvalues which are within
               ORFAC*||T|| of each other are to be orthogonalized.

       Z       (output) DOUBLE PRECISION 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.

       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.

ScaLAPACK version 1.7           13 August 2001                      DSTEIN2(l)

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