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.